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+{"text":"\\section{Introduction}\n\\label{intro}\nThe many successes of deep neural networks (DNNs) across domains such as computer vision \\cite{simonyan2014very,he2016deep}, speech recognition \\cite{graves2013speech}, natural language processing \\cite{vaswani2017attention, brown2020language}, biomedicine \\cite{ronneberger2015u, rajpurkar2017chexnet}, and bioinformatics \\cite{jumper2021highly} have made them ubiquitous in both academic and industrial settings.\nHowever, while DNNs boast of being able to achieve state of the art results on a plethora of complex problems, they also have the dubious honour of being untenably large and unsuitable for applications with power, memory, and latency constraints.\nOne way of tackling these issues is to reduce the parameter-counts of DNNs, thereby decreasing their size and energy consumption while improving inference speeds.\nAs a result, the field of \\emph{neural network pruning} which studies techniques for eliminating unnecessary weights in both pre-trained and randomly initialized DNNs without loss of accuracies \\cite{mozer1988skeletonization, hanson1988comparing,lecun1989optimal, hassibi1992second} has seen renewed interest in recent years \\cite{han2015learning,li2016pruning, cheng2017survey, frankle2018lottery, lee2018snip, blalock2020state}.\n\n\\subsection{Related Work}\nIncreased activity on the methodological front has subsequently spurred principled analytical efforts to help explain when or how various pruning methods ostensibly work.\n\nFor instance, by way of deriving generalization bounds for DNNs via compression \\cite{arora2018stronger}, previous work has provided some theoretical justification for pruned sub-networks.\nIterative Magnitude Pruning (IMP) has been explored via the observation that sparse sub-networks that maintain accuracies of the original network are stable to stochastic gradient descent noise and optimize to linearly connected minima in the loss landscape \\cite{frankle2020linear}.\nA related empirical work has also looked into how fundamental phenomena such as  weight evolution and emergence of distinctive connectivity patterns are affected by changes in the iterative pruning procedure \\cite{paganini2020iterative}.\nA gradient-flow based framework \\cite{lubana2020gradient} has been used to show why certain importance measures work for pruning early on in the training cycle.\n\nMore recently, a number of works have also begun studying pruning at initialization, providing insights into gradient-based pruning via conservation laws \\cite{wang2020picking, tanaka2020pruning}, presenting theoretical analyses of pruning schemes that fall under the purview of sensitivity-based pruning \\cite{hayou2020robust}, developing a path-centric framework for studying pruning approaches \\cite{gebhart2021unified}, and looking at magnitude pruning in linear models trained using gradient flow \\cite{elesedy2020lottery}.\n\nUnfortunately, despite the flurry of contemporary work and results in the area, a mathematically rigorous yet intuitive explanation for \\emph{why} IMP works well remains missing.\n\n\\subsection{Contributions}\nGiven its integral place in the present DNN pruning research landscape, there is a strong impetus to establish a precise but flexible framework which uses the same language to speak of not only IMP, but also related problems of theoretical and empirical interest such as the Lottery Ticket Hypothesis (LTH) \\cite{frankle2018lottery}, DNN initialization and generalization \\cite{morcos2019one}, weight rewinding, and fine-tuning \\cite{renda2020comparing}.\n\nTowards this end we utilize the formalism of algebraic topology, which has found increasing application in the characterization of DNN properties such as learning capacity \\cite{guss2018characterizing}, latent and activation space structure \\cite{khrulkov2018geometry, gebhart2019characterizing, carlsson2020topological}, decision boundaries \\cite{ramamurthy2019topological}, and prediction confidence  \\cite{lacombe2021topological}.\nSpecifically, we use \\emph{neural persistence} \\cite{rieck2018neural} -- a measure based on persistent homology for assessing the topological complexity of neural networks -- to ascertain which set of weights in the DNN capture its zeroth-dimensional topological features, and show that IMP with high probability preserves them. \nFollowing this result, the main contributions of our work are:\n\\begin{itemize}\n    \\vspace{-1mm}\n    \\item A formal yet intuitive framework rooted in persistent homology that can reason about magnitude-based pruning at large and other phenomena related to it.\n    \\vspace{-1mm}\n    \\item A mathematically-grounded perspective on IMP that helps explain its empirical success through supporting theoretical lower bounds regarding its ability to preserve topological information in a trained DNN. \n    \\vspace{-1mm}\n    \\item Precise upper bounds on the maximum achievable compression ratios for fully-connected, convolutional, and recurrent layers such that they maintain their zeroth-dimensional topological features, and realizations of the same for some established architecture-dataset pairings in the pruning literature.\n    \\vspace{-1mm}\n    \\item A topologically-driven algorithm for iterative pruning, which would perfectly preserve their zeroth-order topological features throughout the pruning process.\n\\end{itemize}\n\n\\section{Background \\& Notation}\n\\label{background}\n\nIn this section we offer some background on neural network pruning, persistent homology, and neural persistence, while also establishing the relevant notation.\n\n\\subsection{Iterative Magnitude Pruning}\n\\label{sec:imp_bg}\n\nA neural network \\emph{architecture} is a function family $f(x;\\cdot)$, where the architecture consists of the configuration of\nthe network's parameters and the sets of operations it uses to produce outputs from inputs, including the arrangement\nof parameters into convolutions, activation functions, pooling, batch norm, etc.\nA \\emph{model} is a particular instantiation of an architecture, i.e., $f(x; \\mathcal{W})$ with specific parameters $\\mathcal{W}$.\n\nNeural network \\emph{pruning} entails taking as input a model $f(x; \\mathcal{W})$ and producing a new model $f(x; M \\odot \\mathcal{W}^*)$ where $M \\in \\{0,1\\}^{|\\mathcal{W}^*|}$ is a binary mask that fixes certain parameters to 0, $\\odot$ is the elementwise product operator, and $\\mathcal{W}^*$ is a set of parameters that may differ from $\\mathcal{W}$.\nA number of different heuristics called \\emph{scoring functions} may be used to construct the mask $M$, which decide which weights are to be pruned or kept.\nPopular scoring functions include the magnitude of the weights or some form of the gradients of a specified loss with respect to the weights.\nIf the mask $M$ is constructed by scoring the parameters of a model per layer, the pruning scheme is said to be \\emph{local}, whereas if $M$ is constructed by scoring all parameters in the set $\\mathcal{W}$ collectively, the pruning scheme is said to be \\emph{global}. \n\nThe \\emph{sparsity} of the {pruned} model is $\\frac{|f(x;M \\odot \\mathcal{W}^*)|_{\\textrm{nnz}}}{|\\mathcal{W}|}$ where  $|\\cdot|_{\\textrm{nnz}}$ is a function that counts the number of non-zeros of the pruned model and $|\\mathcal{W}|$ is the total number of parameters in the original model. \nThe \\emph{compression ratio} ($\\eta$) is given as $\\frac{|\\mathcal{W}|}{|f(x;M \\odot \\mathcal{W}^*)|_{\\textrm{nnz}}}$ which is simply the inverse of the sparsity.\n\nGiven an initial untrained model $f(x,\\mathcal{W}_0)$, \\emph{iterative magnitude pruning} (IMP) takes the following steps to obtain a sparsified model $f(x;\\mathcal{W}_N)$ with $p\\%$ target sparsity:\n\\begin{enumerate}\n    \\item Train $f(x;\\mathcal{W}_0)$ for $t$ iterations, thereby obtaining the intermediate parameters $\\mathcal{W}_{0,t}$\n    \\item Mask the non-zero $\\frac{p}{N}$\\% parameters of lowest magnitude in $\\mathcal{W}_{0,t}$ to arrive at parameters $\\mathcal{W}_1$.\n    \\item Repeat the aforementioned steps $N$ times.\n    \n\\end{enumerate}\n\n\\subsection{Persistent Homology}\n\nPersistent homology \\cite{edelsbrunner2008persistent} is a tool commonly used in topological data analysis (TDA) to understand high-dimensional manifolds, and has been successfully employed in a range of applications such as analysing natural images \\cite{carlsson2008local}, characterizing graphs \\cite{sizemore2017classification, rieck2017clique}, and finding relevant features in unstructured data \\cite{lum2013extracting}.\n\nFirst, however, the space of interest must be represented as a \\emph{simplicial complex} which is effectively the extension of the idea of a graph to arbitrarily high dimensions.\nThe sequence of \\emph{homology groups} \\cite{edelsbrunner2022computational} of the simplicial complex then formalizes the notion of the topological features which correspond to the arbitrary dimensional ``holes\" in the space.\nFor example, holes of dimension 0, 1, and 2 refer to connected components, tunnels, and voids respectively in the space of interest.\nInformation from the $d^{\\textrm{th}}$\nhomology group is summarized by the $d^{\\textrm{th}}$ \\emph{Betti number} ($\\beta_d$) which\nmerely counts the number of $d$-dimensional holes;\nthus a circle has Betti numbers (1, 1),\ni.e., one connected component and one tunnel, while a disc has Betti numbers (1, 0), i.e., one\nconnected component but no tunnel.\n\nBetti numbers themselves unfortunately are of limited use in practical applications due to their instability and extremely coarse nature, which has prompted the development of {persistent homology}.\nGiven a simplicial complex $K$ with an additional set of\nscales $a_0 \\leq a_1 \\leq ... \\leq a_{m-1} \\leq a_m$, one can put $K$ through a filtration, i.e., a nested sequence of simplicial complices $\\emptyset = K_0 \\subseteq K_1 \\subseteq ... K_{m-1} \\subseteq K_m = K$.\nThe filtration essentially represents the growth of $K$\nas the scale is changed, and during this process topological  features can be created (new\nvertices may be added, for example, which creates a new connected component) or destroyed (two\nconnected components may merge into one).\n\n\\emph{Persistent homology} tracks these changes, and represents\nthe creation and destruction of a feature as a point $(a_i,a_j)\\in \\mathbb{R}^2$ for indices $i \\leq j$ with respect to\nthe filtration.\nThe collection of all points corresponding to $d$-dimensional topological features is called the $d^{\\textrm{th}}$ \\emph{persistence diagram} ($\\mathcal{D}_d$),\nand can be thought of as a collection of Betti numbers at multiple\nscales.\nGiven a point $(x,y) \\in \\mathcal{D}_d$, the quantity $\\operatorname{pers}(x, y) := |y - x|$ is referred to as its \\emph{persistence}, where $|\\cdot|$ is an appropriate metric.\nTypically, high persistence is considered to correspond to features, while low persistence is considered\nto indicate noise \\cite{edelsbrunner2000topological}.\n\n\\subsection{Neural Persistence}\n\n{Neural persistence} is a recently proposed measure of structural complexity for DNNs \\cite{rieck2018neural} that exploits both network architecture and weight information through persistent homology, to capture how well trained a DNN is.\nFor example, one can empirically verify that the ``complexity\" of a simple, fully connected network as measured by neural persistence increases with learning (Fig. \\ref{fig\/NP_plots_dense}).\n\n\\begin{figure}[ht]\n\\vskip 0.1in\n\\begin{center}\n\\centerline{\\includegraphics[width=\\columnwidth]{NP_Plots_dense.png}}\n\\caption{For a fully-connected, 6-layer network trained on the MNIST dataset across 20 epochs of training, (Left) Layer-wise normalized neural persistences and (Right) Trial-wise total neural persistences for the entire network. Means are presented as solid lines, standard deviations are shaded. }\n\\label{fig\/NP_plots_dense}\n\\end{center}\n\\vskip -0.3in\n\\end{figure}\n\nConstruction of the measure itself relies on the idea that one can view a model $f(x;\\mathcal{W})$ as a stratified graph $G$ with vertices $V$, edges $E$, with a mapping function $\\varphi: E \\rightarrow \\mathcal{W}$ that allows for the calculation of the persistent homology of \\emph{every layer} $G_k$ in the model using a filtration induced by sorting the weights.\nMore precisely, given its set of weights $\\mathcal{W}_k$ at any training step, let $w_{\\max }:=\\max _{w \\in \\mathcal{W}_k}|w|$, and $\\mathcal{W}_k^{\\prime}:=\\left\\{|w| \/ w_{\\max } \\mid w \\in \\mathcal{W}\\right\\}$ be the set of transformed weights indexed in non-ascending order, such that $1=w_{0}^{\\prime} \\geq w_{1}^{\\prime} \\geq ... \\geq 0$. This permits one to define a filtration for the $k^{\\textrm{th}}$ layer $G_{k}$ as $G_{k}^{(0)} \\subseteq G_{k}^{(1)} \\subseteq \\ldots$, where $G_{k}^{(i)}:=\\left(V_{k} \\sqcup V_{k+1},\\left\\{(u, v) \\mid(u, v) \\in E_{k} \\wedge \\varphi^{\\prime}(u, v) \\geq w_{i}^{\\prime}\\right\\}\\right)$, and\n$\\varphi_{k}^{\\prime}(u, v) \\in \\mathcal{W}_{k}^{\\prime}$ denotes the transformed weight of an edge.\nThe relative strength of a connection is thus preserved by the filtration, and weaker weights with $|w| \\approx 0$ remain close to 0.\nAdditionally, since $w^{\\prime} \\in[0,1]$ for the transformed weights, the filtration makes the network invariant to scaling of $\\mathcal{W}$, simplifying the comparison of different networks.\nUsing this filtration one can calculate the persistent homology for every layer $G_k$.\nAs the filtration contains at most 1-simplices (edges), the topological information captured is zero-dimensional, i.e. reflects how connected components are created and merged during the filtration, and can be shown graphically with a $0^{\\textrm{th}}$ persistence diagram (Fig. \\ref{fig:persistent}).\n\n\\begin{figure}[ht]\n\\begin{center}\n\\centerline{\\includegraphics[width=\\columnwidth]{persistent_homology_flip.png}}\n\\end{center}\n\\vskip -0.2in\n\\caption{Persistence diagrams show how long a particular model ``persists\" as the network undergoes the defined filtration (i.e, pruning).\nFrom left to right, as the weight threshold, $w^{'}$, decreases, and the number of connections kept in the two layers ($l_{0}$ and $l_{1}$) increases. On the right, the persistence diagram plots the duration of each structure as a coordinate corresponding to the weight threshold at which the structure was created $(w^{'}_{c})$, and the weight threshold at which it was destroyed $(w^{'}_{d})$.\nThe most prominent structure has the greatest \\textit{persistence}, which is measured by its distance from the diagonal.\nIn this example, the point indicated by the yellow arrow would indicate the most persistent feature.}\n\\label{fig:persistent}\n\\vskip -0.1in\n\\end{figure}\n\n\\emph{Neural persistence} of the $k^{\\textrm{th}}$ layer $G_k$ of a DNN is then defined as the $p$-norm of the persistence diagram $\\mathcal{D}_k$ resulting from the previously discussed filtration, i.e.,\n\\begin{equation*}\n\\setlength{\\abovedisplayskip}{2pt}\n\\setlength{\\belowdisplayskip}{2pt}\n\\textrm{NP}(G_k) := ||\\mathcal{D}_k||_p := \\left(\\sum_{(c, d) \\in \\mathcal{D}_{k}} \\operatorname{pers}(c, d)^{p}\\right)^{\\frac{1}{p}}  \n\\end{equation*}\n\nTypically $p = 2$, which captures the Euclidean distance of the points in $\\mathcal{D}_k$ to the diagonal.\n\nWe note that the above definition strictly corresponds to fully-connected layers, but the notion can easily be extended to convolutional and recurrent layers by representing the former using appropriately sized Toeplitz matrices \\cite{goodfellow2016deep} and the latter as multiple ``unrolled\" fully-connected layers, with the same, shared set of weights.\n\nNeural persistence can also be normalized to values in $[0,1]$ in a scale-free manner, thus providing a simple method to compare the structural complexities of differently sized layers\\footnote{For reference see Theorem 1 \\cite{rieck2018neural}.} across various architectures.\nThe total neural persistence of a model with $L$ layers is given by the sum of all the individual layerwise neural persistences, i.e.,\n\n\\vskip -0.1in\n\\begin{equation*}\n\\setlength{\\abovedisplayskip}{2pt}\n\\setlength{\\belowdisplayskip}{2pt}\n    \\operatorname{NP}(G) := \\sum_{k = 1}^{L} \\operatorname{NP}(G_k)  \n\\end{equation*}\n\n\\section{A Topological Perspective on Magnitude-Based Pruning}\n\\label{theory}\n\nThis section details our interpretation of magnitude pruning (MP) via the lens of neural persistence, followed by some insights we glean regarding IMP from this novel perspective.\nConsequently, we provide a lower bound on the relative topological information that is retained by IMP at every iteration, define a quantity that gives an upper bound on how much different types of neural network architectures may be pruned while still conserving its zeroth-dimensional topological features, and present a topologically-motivated version of IMP that guarantees the same.\n\n\\subsection{Neural Persistence \\& Magnitude Pruning}\n\nHere we explicitly mention the key aspects of neural persistence which can be deduced from the background covered in Section \\ref{background} to arrive at a topological understanding of MP:\n\n\\begin{itemize}\n    \\vspace{-1mm}\n    \\item Neural persistence relies on a super-level set filtration \\cite{cohen2009extending, bubenik2015statistical} and sorts only the edges of $G_k$, the DNN layer\\footnote{ Every $G_k$ is a bipartite graph.} it acts on.\n    \\vspace{-1mm}\n    \\item The weights $\\mathcal{W}_k^{\\prime}$ of a layer $G_k$ are normalized to values in $[0,1]$, disregarding the signs of the weights $\\mathcal{W}_k$ while still respecting their relative magnitudes.\n    \\vspace{-1mm}\n    \\item All the vertices of $G_k$ are already present at the beginning of the filtration and result in $m_k + n_k$ connected components at the start of the filtration, where $m_k, n_k$ are the cardinalities of the two vertex sets of $G_k$.\n    \\vspace{-1mm}\n    \\item Entries in the corresponding zeroth-dimensional persistence diagram $\\mathcal{D}_k$ are of the form $(1,x), x \\in \\mathcal{W}_k^{\\prime}$, and are situated below the diagonal.\n    \n    \\item As the filtration progresses, the weights greater than the threshold $a_i$ are introduced in the zeroth-order persistence diagram, so long as it connects two vertices in $G_k$ without creating any cycles \\cite{lacombe2021topological}.\n    \n    \\item As a result, the filtration ends up with the maximum spanning tree\\footnote{For a proof, see Lemmas 1 \\& 2 in \\citeauthor{doraiswamy2020topomap}}$^{,}$\\footnote{For a visual explanation of the filtration, see Appendix \\ref{appx\/superlevel_filtration}.} (MST) of the graph $G_k$.\n\n\\end{itemize}\n\\vskip -0.1in\n\nFrom the \\ul{viewpoint of persistent homology} this implies that all the zeroth-order topological information of $G_k$ as captured by its neural persistence is encapsulated in the weights of $\\mathcal{W}_k^{\\prime}$ which form its MST.\n    \nFrom the \\ul{standpoint of magnitude-based pruning}\\footnote{Since neural persistence by its current definition is applied layer-wise, the insights we gain from using it through the rest of this paper correspond to local pruning.} we have a novel topologically-motivated scoring function, whose goal is to maintain the zeroth-order topological information\\footnote{While it is true that the notion of  persistent homology (and ergo neural persistence) on a set of weights $\\mathcal{W}_k^{\\prime}$ could be extended beyond the zeroth dimension, thus implying higher orders of topological information that are not captured by the current measure, we note that previous work has found that zero-dimensional\ntopological information still captures a significant portion of it \\cite{rieck2016exploring, hofer2017deep}, thereby sufficing for now.} in a set of weights, and the resulting mask $M$ prunes any weights that are not part of the MST of a particular layer.\n\nConsequently, we arrive at the following insight regarding IMP and its practical efficacy:\n\n\\vskip 0.1in\n\\noindent\n\\framebox{\\parbox{\\dimexpr\\linewidth-2\\fboxsep-2\\fboxrule}{\\itshape\n  At every iteration, the weights retained by IMP in a layer are likely to overlap significantly with those present in its MST with relatively high probability.\n  This ensures the pruning step itself does not severely degrade the zeroth-order topological information learnt by the layer in the previous training cycle, and in turn provides the network with a sufficiently informative initialization, allowing it train to high levels of accuracy once again.}}\n \\vskip 0.1in\n\nIn the following subsections, we further formalize this intuition by deriving a definitive lower bound on the expected overlap between the weights in a layer's MST and those retained by IMP, as well as a strict upper bound on how much a layer can be pruned while still maintaining its zeroth-dimensional topological information.\n\n\\subsection{Topologically Critical Compression Ratio}\n\nBuilding off the observation that we only need as many weights as that of the MST of a layer $G_k$ to maintain its zeroth-dimensional topological features, we define the following quantity that allows us to achieve maximal topologically conservative compression.\n\n\\begin{definition}\n\\label{def:topological_compression_ratio}\nThe topologically critical compression ratio ($\\eta_{\\tau}$) for any graph $G$ with edges $E$, vertices $V$, and mapping function $\\varphi: E \\rightarrow \\mathcal{W}$ is defined as the quantity\n$$\\eta_{\\tau} := \\frac{|\\mathcal{W}|}{|\\operatorname{MST}(G)|}$$\n\\end{definition}\nwhere the function $\\operatorname{MST(\\cdot)}$ denotes the MST of the graph in question and $|\\cdot|$ is the cardinality of a set.\n\n$\\eta_{\\tau}$ is the maximal achievable compression for the graph $G$ which would still be able to perfectly preserve the zeroth-order topological complexity of $G$, assuming the right set of weights (i.e., those in the MST of $G$) are retained.   \n\nUsing Def.~\\ref{def:topological_compression_ratio}, in the context of DNN pruning we subsequently arrive at the following result\n\n\\begin{theorem}\n\\label{thm:top_compression_ratios}\nGiven a layer $G_k$ with weights $\\mathcal{W}_k^{\\prime}$ joining $m_k$ input nodes to $n_k$ output nodes, for any compression ratio $\\eta$ that perfectly maintains the zeroth-order topological information of $G_k$, it holds that $\\eta_{\\tau} \\geq \\eta$.\n\nFurthermore,\n\\begin{itemize}\n    \\item When $G_k$ is a fully connected~\\footnote{Also referred to as ``dense\" in some following results.} layer\n    $$\\eta_{\\tau} = \\frac{m_k \\cdot n_k}{m_k + n_k -1 }$$\n    \\item When $G_k$ is a recurrent layer with $\\ell_k$ hidden units\n    $$\\eta_{\\tau} = \\frac{\\ell_k^2}{2\\ell_k-1 }$$\n    \\item When $G_k$ is a convolutional layer\n    $$\\eta_{\\tau} = \\frac{n_k \\cdot f_1 \\cdot f_2}{m_k + n_k - 1}$$\n    with $(f_1,f_2)$ being size of the convolutional kernel.\n    $m_k, n_k$ are the input and output sizes respectively of the spatial activations.\n\\end{itemize}\n\\begin{proof} \nIn Appendix \\ref{appx\/proofs}. \n\\end{proof}\n\\end{theorem}\n\n\\subsection{Bounds on the MST -- MP Fraction of Overlap}\n\nWe now state a lower bound on the expected overlap in the MST of a layer $G_k$ with its top-$\\alpha$ weights, where $\\alpha$ is the number of weights in its MST, to get a sense of how much of the zeroth-order topological information in a layer might be retained if we prune it down to its topologically critical compression ratio simply using the magnitude, thereby formally quantifying IMP's efficacy.\n\n\\begin{theorem}\n\\label{thm:overlap}\nFor a fully connected layer $G_k$ with normalized weights $\\mathcal{W}^{\\prime}_k$ joining $m_k$ nodes at the input to $n_k$ nodes at the output, for a compression ratio of $\\eta_{\\tau}$, the fraction of overlap expected in its top-$\\alpha$ weights by magnitude and those in its MST can be lower bounded as\n$$\n\\mathbb{E}[X] \\geq \\frac{1}{m_k + n_k - 1} \\cdot \\sum^{j}_{i=0}\\left(\\frac{(m_k - i)(n_k - i)}{m_k \\cdot n_k -i}\\right)\n$$\nwhere $j = \\operatorname{min}(m_k,n_k) \\geq 2$ and X is the fraction of overlap between the two quantities of interest.\n\\vskip -0.2in\n$$\\textrm{If }j = 1, \\mathbb{E}[X] = 1$$\n\\end{theorem}\n\n\\begin{proof}\nIn Appendix \\ref{appx\/proofs}.\n\\end{proof}\n\n\\begin{corollary}\nIf the fully connected graph $G_k$ is $p$-sparse, i.e, has a fraction of $p$ non-zero weights $\\geq \\alpha$,\n\n$$\n\\mathbb{E}[X] \\geq \\operatorname{min}\\left\\{1,~ \\frac{1}{m_k + n_k - 1} \\cdot \\sum^{j}_{i=0}\\left(\\frac{(m_k - i)(n_k - i)}{p \\cdot m_k \\cdot n_k -i}\\right)\\right\\}\n$$\nwhere $j = \\operatorname{min}(m_k,n_k) \\geq 2$ and X is the fraction of overlap between the two quantities of interest.\n\\vskip -0.2in\n$$\\textrm{If }j = 1, \\mathbb{E}[X] = 1$$\n\\end{corollary}\n\n\\begin{proof}\nIn Appendix \\ref{appx\/proofs}.\n\\end{proof}\n\nWe note here that these bounds only give us a sense for how much the topological complexity could be maintained;\nThe exact values for the same would rely on the caluculation of the neural persistence and therefore depend on the exact distribution of weights $\\mathcal{W}_k^{\\prime}$.\n\n\\subsection{Topological Iterative Magnitude Pruning}\n\\label{topologicalIMP}\n\nThe aforementioned insights and results thus naturally suggest a simple modification to the IMP algorithm that would ensure preservation of zeroth-order topological information in every layer.\nFollowing a similar structure as the IMP algorithm in Section \\ref{sec:imp_bg}, we now have Topological-IMP (T-IMP) that takes the following steps:\n\n\\begin{enumerate}\n    \\item Find the weights which form the MST and retain them, accounting for $\\alpha$ weights out of $\\frac{p}{N}$\\% that one wishes to keep.\n    \\item From the remaining $\\frac{p}{N}$\\% - $\\alpha$ weights to be retained at that iteration, pick those with the highest magnitudes.\n    \\item Retrain the network.\n    \\item Repreat the process $N$ times until the target sparsity-accuracy is reached.\n\\end{enumerate}\n\n\\section{Empirical Simulations \\& Results}\n\n\\subsection{Topologically Critical Compression}\n\nTo see the practical significance of the topologically critical compression ratio and \nquantify the extent of pruning it can achieve, we experimented with  combinations of popular datasets and architectures (Table \\ref{tab\/eta_c_all}).\nAdditional experiments with MNIST, as well as compression details on a per layer basis are available in the appendix (Appendices \\ref{appx\/mnist_ratios}, \\ref{appx\/layers}).\nOur overall insights from the investigations are as follows:\n\\begin{itemize}\n    \\item Fully connected layers are a lot more redundant and ergo compressible than convolutional layers, and this seems to hold true across dataset-architecture pairings.\n    The compressability of these dense layers is what often seems to present incredibly high numbers for how compressable a particular model is.\n    \\item Amongst the convolutional architectures, inherently more efficient architectures (e.g., ResNet) are slightly less compressable than their more redundant counterparts such as the VGG, even by topological metrics.\n\\end{itemize}\n\n\\begin{table}[t]\n\\caption{Topologically Critical Compression: VGG11 \\& ResNet}\n\\label{tab\/eta_c_all}\n\\vskip 0.15in\n\\begin{center}\n\\begin{small}\n\\begin{sc}\n\\begin{tabular}{lll}\n\\toprule\n\\hfill & VGG11 ($\\eta_{\\tau}$) & ResNet ($\\eta_{\\tau}$) \\\\\n\\midrule\n\\hfill        & Conv: 4.2295  & Conv: 4.1508\\\\\nCIFAR10$^{*}$ & Dense: 9.8273 & Dense: 8.7671\\\\\n\\hfill        & Final: 4.3914 & Final: 4.1679\\\\\n\\abovespace\n\\hfill          & Conv: 4.2295    & Conv: 4.1508\\\\\nCIFAR100$^{*}$  & Dense: 83.7971  & Dense: 39.2638\\\\\n\\hfill          & Final: 6.9239   & Final: 4.4389\\\\\n\\abovespace\n\\hfill                     & Conv: 4.2672     & Conv: 4.3142\\\\\nTiny-ImageNet$^{\\dagger}$  & Dense: 528.3911  & Dense: 144.0225\\\\\n\\hfill                     & Final: 183.3624  & Final: 6.13182\\\\\n \n\\bottomrule\n\\abovespace\n$^{*}$ ResNet-20 \\\\\n$^{\\dagger}$ ResNet-18 \\\\\n\\end{tabular}\n\\end{sc}\n\\end{small}\n\\end{center}\n\\vskip -0.1in\n\\end{table}\n\n\\begin{figure}[ht]\n\\vskip 0.2in\n\\begin{center}\n\\centerline{\\includegraphics[width=\\columnwidth]{MST_Plot_dense_scatter.png}}\n\\caption{Top row: Mean percentage overlap (with standard deviations) that the top-$\\alpha$ weights have with the MST computed over different layers of a fully-connected network trained on the MNIST dataset.\nBlack dots at the bottom represent the derived theoretical lower bound for the overlap for each of the respective layers.}\n\\label{fig:mst_overlap}\n\\end{center}\n\\vskip -0.2in\n\\end{figure}\n\n\\subsection{Bounds on the MST -- MP Fraction of Overlap}\n\nThe bound presented in Thm. \\ref{thm:overlap} was also checked empirically with multiple simulations on different layers of the MNIST fully connected model (Fig.~\\ref{fig:mst_overlap}).\nWhile not the tightest, the bound (and simulations) still provided substantial support that MP does encourage preservation of zeroth-order topological features\\footnote{See Appendix \\ref{appx\/random_probs} for a related discussion.} in the DNN weight space.\nHowever, preservation of zeroth-order topology only forms part of the story concerning which weights ought to be kept when pruning DNNs.\nExtensions to higher order homologies might perhaps help explain these discrepancies better. \n\n\n\n\\section{Discussion \\& Future Work}\n\\label{discussion}\n\nIn this work we presented a novel perspective on IMP leveraging a zeroth-order topological measure, viz., neural persistence.\nThe resulting insights now provide us with the opportunity to pursue some exciting avenues on both, theoretical and empirical fronts.\n\nThese include possible extensions of the stated bounds and subsequent theory to stratified graphs to explain global pruning, as well the extension of NP itself to beyond zeroth-order homology to potentially uncover a fuller picture of the topological complexities of DNNs.\n\nAdditionally, topological perspectives on LTH, weight rewinding, single-shot pruning, and other interesting IMP-adjacent phenomena could lead to not only insights into the interplay between DNN training and inference dynamics, but also topologically-motivated algorithms to achieve data- and compute-efficient deep learning pipelines. \n\n\n\n\n\\section*{Acknowledgements}\nThe authors thank Georgia Tech's Graduate Student Association and College of Engineering for providing financial support to present this work, and the reviewers for their constructive feedback.\nAB would also like to thank Nischita Kaza for helpful comments regarding the paper's exposition.\n\n\\clearpage\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nAmong the most popular models that extend the Standard Model (SM) of particle physics and solve the gauge hierarchy problem are warped extra dimensions \\cite{Randall:1999ee} and composite scenarios \\cite{Kaplan:1983fs,Georgi:1984af} where the Higgs is identified as a pseudo-Nambu-Goldstone boson (PNGB) of a broken shift symmetry \\cite{Agashe:2004rs}.  In the case of warped extra dimensions, the non-factorizable geometry that leads to a slice of $AdS_5$ space is responsible for effectively reducing quadratic contributions to the Higgs mass once the Higgs five-dimensional (5D) scalar  is localized on (brane Higgs) or near (bulk Higgs) the infra-red (IR) brane. Thus, even though there is no implicit symmetry that leads to a light Higgs, once we assume that such a light mass is generated, it remains natural. On the other hand,  explicit calculable realizations of composite PNGB Higgs  were first found in warped scenarios in what are known as Gauge-Higgs Unification (GHU) models.  Here the SM gauge group is \nenlarged to a gauge group G in the bulk of the extra dimension and broken via boundary conditions to the subgroups H (IR-brane) and $SU(2)_L\\times U(1)_Y$ (UV-brane) on the branes. In this way, the fifth component of the gauge field $A_5^{\\hat{a}}$ that belongs to the coset group $G\/H$ has the right quantum numbers to be the Higgs.  Though it is protected by the gauge symmetry at tree-level, it acquires a potential  at loop level that successfully leads to electroweak symmetry breaking (EWSB) and provides a light Higgs mass protected from the UV-physics~\\cite{Agashe:2004rs,Medina:2007hz}. Due to the $AdS\/CFT$ correspondence and through the language of holography, it was realized that these kinds of models are particular realizations of composite Higgs scenarios where the Higgs is a PNGB arising from the spontaneous breaking of a global shift symmetry G, and where SM particles have a degree of compositeness determined by their coupling to operators that reside in the conformal sector. \n\nIn both realizations, the conformal sector is spontaneously broken and a corresponding Goldstone mode is expected in the theory. In the 5D picture, this mode is known as the radion and is associated with the spin-0 fluctuations of the metric. In order to stabilize the extra dimension the radion is coupled to an additional scalar field~\\cite{Goldberger:1999uk}; the gravity-scalar system can provide a stabilizing potential and a mass for the radion, which is expected to be light. From the 4D point of view this can be accomplished if the corresponding Goldstone mode, the dilaton, couples to a nearly marginal operator of dimension  $|\\Delta_{\\mathcal{O}}-4|\\ll 1$~\\cite{Rattazzi:2000hs,Goldberger:2007zk}. Since, besides the other well-known particles of the SM, the LHC has recently discovered what seems to be a light scalar state, it seems reasonable to take the approach that the only new light states accessible at the moment at the LHC are the Higgs and the radion\/dilaton.  Given that these two light scalar \nstates posses the same quantum numbers, mixing between them is expected, which can have important consequences in the phenomenology of this effective two scalar system. \n\nIn this work we begin by studying the less known case of a bulk scalar Higgs in a warped extra dimension that mixes via a term $\\xi R_5 H^{\\dagger}H$ with the radion. We show how in this way one can arrive at an effective Lagrangian that describes the different mixing possibilities encountered in these kinds of models.  We also show that moving the Higgs from the brane into the bulk of the extra dimension can already have important consequences on how the radion couples to SM particles, leading to a different radion phenomenology compared to the brane Higgs case~\\cite{Goldberger:1999un, Giudice:2000av,Csaki:2000zn, Dominici:2002jv, Rizzo:2002pq}. In particular we show that due to the geometry\/conformal symmetry of the radion in the bulk, its couplings to 4D scalar kinetic terms vanish, and therefore the radion coupling to massive gauge bosons is suppressed. The 5D construction is used as a tool to obtain the dependence of the radion and Higgs mixing and couplings on the masses $m_h$, $m_r$ and energy scales \n$v_{ew}\\equiv 246$~GeV, radion decay constant $\\Lambda_r$ which is taken to be of the order of the conformal breaking scale $f$,  $\\Lambda_r\\approx f\\approx 1$~TeV; we allow for freedom in the specific numerical values of dimensionless parameters.\n\nOnce the mixing is taken into account, we perform a numerical scan over the relevant parameters  satisfying the most recent constraints from the LHC on Higgs physics and exotic resonant searches. By matching the lightest mixed state's mass and signal strengths to those measured at the LHC for the 125~GeV resonance, we are able to predict the branching fractions and cross-sections for the most relevant decays of the heaviest mixed state. Interestingly, we find that in some regions the production of two light mixed states via the decay of the heaviest mixed state can contribute as much as 30$\\%$ to the total production cross section. Furthermore we find that in the case of negligible mixing, a light scalar state with mass in the range $m \\sim [150, 250]$~GeV with a sizeable cross-section into diphotons is still allowed by LHC constraints, providing a very interesting motivation to look in the diphoton channel at larger invariant masses than is currently done at the LHC by ATLAS and CMS.\n\nThe paper is organized as follows. In sections~2 and~3 we introduce the radion and a simplified model of a bulk Higgs in warped 5D space and compute the different mixing terms that arise in the presence of the $\\xi R_5H^{\\dagger}H$ bulk term. In sections~4 and~5 we write the effective Lagrangian describing the mixing between the radion\/dilaton and the Higgs and provide the relevant couplings and branching fractions.  Sections~6 and~7 contain the LHC constraints used and the phenomenological study of the heaviest mixed state. Our conclusions are given in section~8.\n\n\n\\section{The Radion}\n\nWe are interested in a 5D background that preserves 4D Lorentz symmetry, which can always be written in the form,\n\\begin{equation}\nds^2=e^{-2A(y)} \\eta_{\\mu\\nu}dx^{\\mu}dx^{\\nu}-dy^2\\label{RS}\\,,\n\\end{equation}\nwhere $y$ is the extra dimensional coordinate and $e^{-A(y)}$ a convex function of $y$. In the Randall-Sundrum solution, $A(y)=k y$ where $k$ is the curvature scale, and the space reduces to a slice of $AdS_5$ with boundaries at $y=0$ (UV-brane) and $y=L$ (IR-brane). By an appropriate gauge choice, one can decouple the spin-0 (radion) from the spin-2 (graviton) fluctuations of the metric Eq.~(\\ref{RS}). The spin-0 fluctuations are given by,\n\\begin{equation}\nds^2=e^{-2A(y)-2F(x,y)} \\eta_{\\mu\\nu}dx^{\\mu}dx^{\\nu}-(1+2F(x,y))^2dy^2 \\,.\\label{RS-spin0}\n\\end{equation}\nIn the absence of a stabilizing mechanism, the radion is massless and it is simple to check that it consists of a single state with a profile in the extra-dimension given by \n\\begin{equation}\\label{radionprofile}\nF(x,y)=e^{2A(y)} \\frac{e^{-kL}}{\\sqrt{3}M_p}r(x)\\equiv e^{2(A(y)-kL)} \\frac{1}{\\Lambda_r}r(x),\n\\end{equation}\nwhere we have used that $M_{P}^2\\approx M_5^3\/k$, with $M_P$ the 4D reduced Planck mass.\n\nIn order to stabilize the extra-dimension, it is customary to introduce an additional scalar in the bulk of the extra dimension with corresponding bulk and brane potentials such that the gravity and scalar sectors mix.  The backreaction of the scalar on the geometry provides a mass for the physical state associated with the radion. This will produce deviations from the pure $AdS_5$ solution for the geometry; however, if the backreaction is not large the deviations tend to be small and the approximate form for the radion profile $F(y)\\sim e^{2ky}$ holds~\\cite{DeWolfe:1999cp}. We will comment in section \\ref{sec:backreaction} on the consequences of the backreaction on the radion-Higgs mixing, which are important once the Higgs is moved to the bulk of the extra dimension.\n\n\n\\section{Radion-Higgs mixing}\n\nLight radion\/dilaton phenomenology and mixing with an IR-brane localized Higgs has been studied extensively in the literature~\\cite{Giudice:2000av,Csaki:2000zn,Dominici:2002jv,Chacko:2012sy,Chacko:2013dra}.  It has been found that current LHC measurements, in particular of the Higgs mass and signal strengths, already put significant constraints on the parameter space of these models~\\cite{Desai:2013pga}.  In this paper we study the consequences of moving the Higgs into the bulk of the extra dimension and mixing it with the gravity sector via a bulk term  $\\xi R_5H^{\\dagger}H$. Such a bulk mixing term was also considered in \\cite{Davoudiasl:2005uu} but in the context of higher curvature Gauss-Bonnet terms.  We motivate an effective 4D low energy action that describes all the possible mixing terms that one may encounter between the two light states in the model, the radion and the Higgs.  We also derive the parametric size of these mixing terms.  In this context let us briefly survey the possible localization \nof the Higgs, what this implies for the radion-Higgs mixing \nin the theory, and the possibility of a Higgs as a PNGB of a shift symmetry.\n\n\\subsection{ The brane Higgs scenario}\n\nIn this case one can simply write the Higgs part of the Lagrangian as follows:\n\\begin{equation}\n S_{brane} = \\int d^4x \\sqrt{|\\gamma(r(x))|}\\left[ |{\\mathcal{D}} H|^2 - V(H) + \\xi R_4 H^{\\dagger}H \\right] \\,,\n\\end{equation}\nwhere $\\gamma$ is the induced metric on the boundary. After the Higgs gets a vev $v$, one can perform a Taylor expansion of the potential,\n\\begin{equation}\n V(H) = \\sum \\left. \\frac{\\delta^n V(H)}{\\delta H^n}\\right|_{H\\rightarrow v} h^n.\n\\end{equation}\nThe mass mixing term that can arise from the $n=1$ term in the above equation vanishes exactly due to the minimization condition. No mixing of any type arises from the kinetic term, as $\\partial_\\mu v = 0$.  This is the reason for the absence of any mass mixing in brane Higgs models. Only kinetic mixing via the usual term $\\xi R_4 H^{\\dagger}H$ is expected.\n\n\\subsection{ The bulk Higgs scenario}\\label{sec:bulkhiggs}\n\n Let us now consider a scenario where the Higgs and the SM fields can access the 5D bulk. We use this model as a tool to motivate our effective action in section \\ref{sec:effaction} and therefore we briefly describe the process of EWSB and Higgs mass generation.  Technical details of the calculation that are similar to those of~\\cite{Cacciapaglia:2006mz} are deferred to appendix~\\ref{app:details}.  In this case the full Higgs-radion action may be written as\n %\n\\begin{align} \\label{eq:action}\n  S_{bulk} & = \\int_0^Ld^5x\\,\\sqrt{g}\\left[\\left(\\frac{M^3}{2}+{\\xi}H^{\\dagger}H\\right)R_5+{\\vert}D_MH\\vert^2-V(H)\\right] \\notag \\\\\n  & \\quad -\\sum_{\\alpha=0,1}{\\int}d^4x\\,\\sqrt{\\gamma}\\bigg[\\left(M^3+2{\\xi}H^{\\dagger}H\\right)[K]+\\lambda^\\alpha(H)\\bigg],\n\\end{align}\nwhere $V(H)=-6k^2M^3+c^2k^2|H|^2$ is the 5D bulk potential ($c$ a dimensionless localization parameter), $\\lambda^{\\alpha}(H)$ are the 4D brane potentials, $\\gamma$ is the induced metric, and $[K]$ denotes the jump in the extrinsic curvature across the brane.  Note that in adding the direct coupling between the Higgs and the scalar curvature in the bulk, we must also modify the Gibbons-Hawking term to ensure the correct cancellation of boundary terms.  EWSB is induced on the IR brane by taking\n\\begin{equation}\n\\lambda^{1}(H)=\\frac{1}{2}\\frac{\\tilde{\\lambda}}{k^2}\\left(|H|^2-\\frac{\\tilde{v}^2_{IR}k^3}{2}\\right)^2\\label{IRpotential},\n\\end{equation}\nwhere $\\tilde{\\lambda}$ and $\\tilde{v}_{IR}$ are dimensionless quantities. On the UV brane, we simply add a mass term\n\\begin{equation}\n\\lambda^{0}(H)=m_{UV}|H|^2.\n\\label{eq:UVpotential}\\end{equation}\n\nTo simplify our analysis, we assume that the Higgs back reaction on the metric is negligible.  This requires that the Higgs vev satisfy\n\\begin{equation} \\label{eq:backreaction}\n\\vert\\xi\\vert v^2\\ll M^3,\\qquad \\vert v'^2-c^2k^2v^2 + 16 \\xi A' v \\, v' \\vert\\ll 12 A'{}^2 M^3 .\n\\end{equation}\nThe explicit mixing terms of Eq.~\\eqref{eq:action} contribute to the effective bulk and brane masses for the Higgs.  It is straightforward to solve for the Higgs vev $v(y)$.  Expressing it in terms of the physical observable $v_{ew}$, we find\n\\begin{equation}\nv(y)=\\sqrt{2(1+\\beta)k} \\, e^{ky}e^{(1+\\beta)k(y-L)}v_{ew}\\label{vev},\n\\end{equation}\nwhere $\\beta^2 = 4 + c^2 + 20 \\xi$.  The explicit relation between $v_{ew}$ and the 5D parameters is\n\\begin{equation}\nv^2_{ew}\\approx\\frac{\\tilde{\\lambda}\\tilde{v}^2_{IR} + 16 \\xi-2(2+\\beta)}{2(1+\\beta)\\tilde{\\lambda}} \\,\\tilde{k}^2 ,\\label{v1}\n\\end{equation}\nwhere $\\tilde{k} \\equiv k e^{-kL}$ and we have neglected terms suppressed by additional powers of $e^{-kL}$.  Inserting our expression for $v(y)$ into Eq.\\eqref{eq:backreaction}, we find that the back-reaction is negligible for $O(1)$ values of $\\xi$, $\\beta$, and $c$, provided that both $k\/M<1$ and $v_{ew}\/\\tilde{k} < 1$.\n\nThe Higgs fluctuation $h(x, y)={\\mathcal{H}}(y)h(x)$, with mass $m_h$, has a more complex form.  In the limit that the Higgs mass is small compared to the RS scale $\\tilde{k}$, we find that the profile is approximately proportional to the vev:\n\\begin{equation}\n{\\mathcal{H}}(y)=\\sqrt{2(1+\\beta)k} \\, e^{ky}e^{(1+\\beta)k(y-L)} + \\mathcal{O}(m_h^2\/\\tilde{k}^2) .\\label{fluctuation}\n\\end{equation}\nUsing the IR b.c. one also can determine the mass $m_h$. The resultant equation is complicated in the general case.  However, in our limiting case $m_h \\ll \\tilde{k}$, one can obtain an approximate analytical expression for the lightest mode given by\n\\begin{equation}\nm^2_h\\approx 4 (1+ \\beta)^2 \\tilde{\\lambda} v_{ew}^2 . \\label{mhiggs}\n\\end{equation}\n\nTo investigate the mass mixing induced by the bulk Lagrangian Eq.~(\\ref{eq:action}), we expand the scalar curvature using the $AdS_5$ metric and the replacement $F(x,y)=F(y)r(x)$:\n\\begin{align}\n R_5 &= [20 A'(y) - 8A''(y)] - 2 e^{2A} F(y) \\, \\partial^2 r(x) \\notag \\\\\n & \\quad + [-80 F(y) A'(y)^2 + 56 A'(y)F'(y) + 32 F(y)A''(y) -8 F''(y)]r(x) + \\mathcal{O}\\bigl( r(x) \\bigr)^2, \\notag \\\\\n \\left[K\\right] &= 4 A'(y) + \\mathcal{O}\\bigl( r(x) \\bigr)^2. \\label{scalarcurvature}\n\\end{align}\nNow using Eq.~\\eqref{radionprofile} and $A(y)\\sim ky$ we find that the expressions reduce to\n\\begin{equation} \\label{eq:curvkin}\n R_5= 20k^2 - 2 e^{2A} F(y) \\, \\partial^2 r(x)~~\\text{and}~~ [K] = 4k.\n\\end{equation}\nThe non-derivative terms linear in the radion vanish.  There could be a residual mass mixing that arises from the product of the constant terms in Eq.~\\eqref{eq:curvkin} with the linear fluctuation in the volume element.  However, as discussed below Eq.~\\eqref{eq:backreaction}, these constant terms are effective bulk and brane masses for the Higgs, and are more naturally associated with the mixing from the potentials.  Indeed, one can explicitly redefine the Lagrangian mass parameters to absorb these constant terms:\n\\begin{equation} \\label{eq:redefpot}\nc^2\\rightarrow c^2-20\\xi,\\qquad\n\\tilde{v}_{IR}^2\\rightarrow\\tilde{v}_{IR}^2-\\frac{16\\xi}{\\tilde{\\lambda}},\\qquad\nm_{UV}\\rightarrow m_{UV}+8\\xi k.\n\\end{equation}\nThis will naturally lead to modifications to the definition of $\\beta$, and the relation between $v_{ew}$ and the Lagrangian parameters.  Finally we compute the mass mixing that might arise from the potential terms in the bulk and on the brane and the kinetic term in the bulk,\n\\begin{align} \\label{mass_mixing}\n-\\int d^5 x\\sqrt{g} \\, c^2 k^2 |H|^2 &\\,\\to\\, 2(\\beta^2-4)\\frac{v_{ew}}{\\Lambda_r}\\tilde{k}^2 \\, h(x)r(x), && \\text{[Bulk potential]} \n\\notag \\\\\n-\\int d^4x \\sqrt{\\gamma} \\, \\lambda^{1}(H) &\\,\\to\\, -8(1+\\beta)(2+\\beta)\\frac{v_{ew}}{\\Lambda_r}\\tilde{k}^2 \\, h(x) r(x) , && \\text{[IR brane potential]}\n\\notag \\\\\n\\int d^5 x\\sqrt{g} \\, g^{55}D_5H^\\dagger D_5H &\\,\\to\\, 6(2+\\beta)^2\\frac{v_{ew}}{\\Lambda_r}\\tilde{k}^2 \\, h(x)r(x). && \\text{[Higgs kinetic term]}\n\\end{align}\nWe have neglected the UV potential as the Higgs is localized near the IR brane.\\footnote{One can show that the contribution from the UV potential cancels with additional exponentially suppressed terms that have been omitted in Eq.~\\eqref{mass_mixing}.}  We find that these contributions cancel exactly and leave us with no mass mixing between the Higgs and the radion.\n\nThe derivative terms in Eq.~\\eqref{eq:curvkin} lead to a kinetic mixing, as in the brane Higgs case.  A quantitative difference from the brane scenario is that the size of the induced mixing is $\\beta$-dependent.  Specifically,\n\\begin{equation}\n  \\int d^5 x \\, \\sqrt{g} \\, \\xi \\, R_5 H^\\dagger H \\to 2 \\xi \\frac{1+\\beta}{2+\\beta} \\, \\frac{v_{ew}}{\\Lambda_r} \\, (\\partial^\\mu h(x)) (\\partial_\\mu r(x)) \\, .\n\\end{equation}\nThe mixing term also gives contributions to the radion kinetic term.  One contribution arises when the linear derivative term combines with the linear term in $\\sqrt{g}$.  Another contribution of the same order comes from the terms in $R_5$ quadratic in the radion.  The net result is\n\\begin{equation}\n  \\int d^5 x \\, \\sqrt{g} \\, \\xi \\, R_5 H^\\dagger H \\to 3 \\xi \\frac{1+\\beta}{3+\\beta} \\, \\frac{v_{ew}^2}{\\Lambda_r^2} \\, (\\partial^\\mu r(x)) (\\partial_\\mu r(x)) \\,. \n\\end{equation}\n\n\n\\oldstuff{\nWith this assumption, the explicit mixing terms of Eq.~\\eqref{eq:action} contribute to the effective bulk and brane masses for the Higgs.  It is convenient to absorb these through a redefinition of the bulk and boundary potentials\n\\begin{equation} \\label{eq:redefpot}\nc^2\\rightarrow c^2-20\\xi,\\qquad\n\\tilde{v}_{IR}^2\\rightarrow\\tilde{v}_{IR}^2-\\frac{16\\xi}{\\tilde{\\lambda}},\\qquad\nm_{UV}\\rightarrow m_{UV}+8\\xi k.\n\\end{equation}\nIt is straightforward to solve for the Higgs vev $v(y)$.  Expressing it in terms of the physical observable $v_{ew}$, we find\n\\begin{equation}\nv(y)=\\sqrt{2(1+\\beta)k} \\, e^{ky}e^{(1+\\beta)k(y-L)}v_{ew}\\label{vev},\n\\end{equation}\nwhere $\\beta^2 = 4 + c^2$.  The explicit relation between $v_{ew}$ and the 5D parameters is\n\\begin{equation}\nv^2_{ew}\\approx\\frac{(\\tilde{\\lambda}\\tilde{v}^2_{IR}-2(2+\\beta))}{2(1+\\beta)\\tilde{\\lambda}} \\,\\tilde{k}^2 .\\label{v1}\n\\end{equation}\nInserting our expression for $v(y)$ into Eq.\\eqref{eq:backreaction}, we find that the back-reaction is negligible for $O(1)$ values of $\\xi$, $\\beta$, $c$, provided that $k\/M<1$ and $v_{ew}< \\tilde{k} \\equiv k e^{-kL}$.\n\nThe Higgs fluctuation $h(x, y)={\\mathcal{H}}(y)h(x)$, with mass $m_h$, has a more complex form.  In the limit that the Higgs mass is small compared to the RS scale $\\tilde{k}$, we find that the profile is approximately proportional to the vev:\n\\begin{equation}\n{\\mathcal{H}}(y)=\\sqrt{2(1+\\beta)k} \\, e^{ky}e^{(1+\\beta)k(y-L)}\\label{fluctuation}.\n\\end{equation}\nUsing the IR b.c. one also can determine the mass $m_h$. The resultant equation is complicated in the general case.  However, in our limiting case one can obtain an approximate analytical expression for the lightest mode given by\n\\begin{equation}\nm^2_h\\approx 4\\frac{(1+\\beta)}{(2+\\beta)} \\bigl( \\tilde{\\lambda}\\tilde{v}^2_{IR}-(4+2\\beta) \\bigr) \\, \\tilde{k}.\\label{mhiggs}\n\\end{equation}\nTo investigate the mass mixing induced by the bulk Lagrangian Eq.~(\\ref{eq:action}), we expand the scalar curvature using the $AdS_5$ metric and the replacement $F(x,y)=F(y)r(x)$:\n\\begin{align}\n R_5 &= [20 A'(y) - 8A''(y)] - 2 e^{2A} F(y) \\, \\partial^2 r(x) \\notag \\\\\n & \\quad + [-80 F(y) A'(y)^2 + 56 A'(y)F'(y) + 32 F(y)A''(y) -8 F''(y)]r(x) + \\mathcal{O}\\bigl( r(x) \\bigr)^2, \\notag \\\\\n \\left[K\\right] &= 4 A'(y) + \\mathcal{O}\\bigl( r(x) \\bigr)^2. \\label{scalarcurvature}\n\\end{align}\nNow using Eq.~\\eqref{radionprofile} and $A(y)\\sim ky$ we find that the expressions reduce to\n\\begin{equation} \\label{eq:curvkin}\n R_5= 20k^2 - 2 e^{2A} F(y) \\, \\partial^2 r(x)~~\\text{and}~~ [K] = 4k.\n\\end{equation}\nThe non-derivative terms linear in the radion vanish.  As discussed previously, the constant part of the curvature can be absorbed into the bulk and brane potentials, $V(H,H^{\\dagger}) \\rightarrow V(H,H^{\\dagger}) - \\xi R_5 H^{\\dagger}H$ and $\\lambda^{\\alpha}(H,H^{\\dagger}) \\rightarrow \\lambda^{\\alpha}(H,H^{\\dagger}) + 2 \\xi [K] H^{\\dagger}H.$ Therefore no mass mixing is derived from the curvature terms.  Finally we compute the mass mixing that might arise from the potential terms in the bulk and on the brane and the kinetic term in the bulk,\n\\begin{align} \\label{mass_mixing}\n-\\int d^5 x\\sqrt{g} \\, c^2 k^2 |H|^2 &\\,\\to\\, 2(\\beta^2-4)\\frac{v_{ew}}{\\Lambda_r}\\tilde{k}^2 \\, h(x)r(x), && \\text{[Bulk potential]} \n\\notag \\\\\n-\\int d^4x \\sqrt{\\gamma} \\, \\lambda^{1}(H) &\\,\\to\\, -8(1+\\beta)(2+\\beta)\\frac{v_{ew}}{\\Lambda_r}\\tilde{k}^2 \\, h(x) r(x) , && \\text{[IR brane potential]}\n\\notag \\\\\n\\int d^5 x\\sqrt{g} \\, g^{55}D_5H^\\dagger D_5H &\\,\\to\\, 6(2+\\beta)^2\\frac{v_{ew}}{\\Lambda_r}\\tilde{k}^2 \\, h(x)r(x). && \\text{[Higgs kinetic term]}\n\\end{align}\nWe have neglected the UV potential as the Higgs is localized near the IR brane.\\footnote{One can show that the contribution from the UV potential cancels with additional exponentially suppressed terms that have been omitted in Eq.~\\eqref{mass_mixing}.}  We find that these contributions cancel exactly and leave us with no mass mixing between the Higgs and the radion.\n\nThe derivative terms in Eq.~\\eqref{eq:curvkin} lead to a kinetic mixing, as in the brane Higgs case.  A quantitative difference from the brane scenario is that the size of the induced mixing is $\\beta$-dependent.  Specifically,\n\\begin{equation}\n  \\int d^5 x \\, \\sqrt{g} \\, \\xi \\, R_5 H^\\dagger H \\to 2 \\xi \\frac{1+\\beta}{2+\\beta} \\, \\frac{v_{ew}}{\\Lambda_r} \\, (\\partial^\\mu h(x)) (\\partial_\\mu r(x)) \\, .\n\\end{equation}\nThe mixing term also gives contributions to the radion kinetic term.  One contribution arises when the linear derivative term combines with the linear term in $\\sqrt{g}$.  Another contribution of the same order comes from the terms in $R_5$ quadratic in the radion.  The net result is\n\\begin{equation}\n  \\int d^5 x \\, \\sqrt{g} \\, \\xi \\, R_5 H^\\dagger H \\to 3 \\xi \\frac{1+\\beta}{3+\\beta} \\, \\frac{v_{ew}^2}{\\Lambda_r^2} \\, (\\partial^\\mu r(x)) (\\partial_\\mu r(x)) \\,. \n\\end{equation}\n}\n\\subsection{Bulk Higgs with back reaction}\\label{sec:backreaction}\n\nIn the above discussion we did not consider the back reaction of the Higgs and the radion on the metric.  This will modify the bulk profiles of the Higgs, the Higgs vev and the radion. The Higgs back reaction can be assumed to be small as already argued; even if we include its effect, it can at most induce a mass mixing proportional to the Higgs mass $ \\sim m_h^2 v_{ew}\/\\Lambda_r$.  A mass mixing of this order can also arise if we include the differences between the Higgs and Higgs vev bulk profiles $v(y) \\neq {\\mathcal{H}}(y)$; that is, if we expand the Bessel functions in Eq.~\\eqref{eq:bessexp} to include sub-leading terms in $\\epsilon$. \n\nA larger contribution to the mass mixing may arise due to the back reaction of the radion.  Let us assume that the radius stabilizing mechanism results in a small perturbation in the bulk profile of the fields. We can write the following ansatz for the perturbed radion bulk profile and the metric:\n\\begin{align}\n F(y)&\\sim  N_r e^{2ky}(1+l^2 f(y)) ,\\notag \\\\\n A(y) &\\sim  ky + \\frac{l^2}{6}e^{-2uy},\n\\end{align}\nwhere $uL = \\phi_T\/\\phi_P$;  $\\phi_{T(P)}$ is the radion vev on the TeV (Planck) brane introduced to stabilize the bulk; and $l^2=\\phi_P\/\\sqrt{2M^{3}}.$ The equation of motion for the radion field can be solved using the above ansatz as an expansion in $u\/k=\\epsilon \\sim 1\/37$~\\cite{Csaki:2000zn}.  Expanding up to $\\epsilon^2$ we obtain\n\\begin{equation}\n  f(y) = \\frac{1}{3} \\left( (1 - \\epsilon)e^{-2uy} + \\epsilon^2 \\left( e^{-2ky} - e^{2k(y-L)} \\right) \\right)  \\,.\n\\end{equation}\nOne can now solve for the normalization factor for the radion at this order of the expansion,\n\\begin{equation}\n N_r = \\frac{1}{\\Lambda_r} \\left( 1+ e^{-2uL} \\frac{l^2}{6} (-1+\\epsilon + 2\\epsilon^2)\\right) .\n\\end{equation}\nSolving for the Higgs vev in the same approximation yields,\n\\begin{equation}\n v(y) = B e^{(2+\\beta)ky}\\left( 1 + \\frac{l^2}{3} \\, \\frac{2+\\beta}{\\beta} \\, \\biggl( 1+ \\frac{\\epsilon}{\\beta} + \\frac{\\epsilon^2}{\\beta^2} \\biggr)e^{-2\\epsilon ky}\\right),\n\\end{equation}\nwhere $B$ is given by,\n\\begin{eqnarray}\n B^2&=& 2kv_{ew}^2(1+\\beta)e^{-2(1+\\beta)kL}\\nonumber\\\\\n &\\times&\\left(1+ \\frac{l^2}{3\\beta^3}\\left( -(4+\\beta)\\beta^2 + \\frac{(\\beta(\\beta + 8) +4)\\beta}{\\beta +1}\n \\epsilon - \\frac{\\beta(5\\beta^3 +18\\beta +14)+4}{(\\beta + 1)^2} \\epsilon^2\\right) \\right) .\n\\end{eqnarray}\nFinally we will assume that,\n\\begin{equation}\n h(x,y) = h(x)\\left( \\frac{v(y)}{v_{ew}} + {\\mathcal{O}}(m_h^2) \\right)\n\\end{equation}\nThus including the radion back reaction, the Higgs-radion mixing action at leading order can now be written as,\n\\begin{equation}\n S_{h-r} = \\int d^4x\\left[ -\\xi \\frac{2(1+\\beta)}{2+\\beta}\\frac{v_{ew}}{\\Lambda_r} h(x) \\partial_{\\mu}\n \\partial^{\\mu}r(x) + \\left(\\xi \\frac{2(7+4\\beta)}{2+\\beta} \n -\\frac{2(1+\\beta)}{\\beta} \\right)\\frac{v_{ew}}{\\Lambda_r}m_r^2 h(x) r(x)   \\right],\\label{massmix}\n\\end{equation}\nwhere $m_r$ is the radion mass given by\\cite{Csaki:2000zn},\n\\begin{equation}\n m_r^2 = \\frac{8}{3} l^2 (k\\epsilon)^2e^{-2kL}. \n\\end{equation}\nAs expected we find that the mass mixing terms arising from the radion back reaction are proportional to the radion mass.\n\n\\subsection{Composite Higgs models}\n\nAs mentioned in the introduction, the 5D analogue of the PNGB composite Higgs is the GHU scenario where the Higgs is identified as the fifth component of a 5D gauge boson  $A_M=(A_\\mu,A_5)$ belonging to the coset group $G\/H$. The higher-dimensional gauge symmetry translates to a 4D shift symmetry of the Higgs.  In a slice of $AdS_5$, the $A_5$ sector of the gauge boson kinetic term of the bulk Lagrangian is\n\\begin{eqnarray}\n    &-&\\frac{1}{2}\\int d^4 x\\, dy~e^{-2ky} \\left[(\\partial A_5)^2 -2\n       \\eta^{\\mu\\nu}\\partial_\\mu A_5 \\partial_5 A_\\nu \\right] + \\dots~ ~~\\underrightarrow{\\mbox{gauge-fixing}}\\nonumber\\\\\n       &-&\\frac{1}{2}\\int d^4 x\\, dy~e^{+2ky} (\\partial_\\mu A_5^{(0)}(x))^2 \n     + \\dots~.\n\\end{eqnarray}\nNotice that the higher-dimensional gauge symmetry prevents a tree-level mass for $A_5$ both in the bulk and on the brane.  Also, the antisymmetric nature of the field strength tensor prevents a term like $|\\partial_y A_5(y,x)|^2$.  This immediately implies that a composite Higgs cannot have mass mixing with the radion even when the back reaction is considered.  The only possible mixing can be introduced on the brane after the shift symmetry is explicitly broken by the Yukawa and SM gauge interactions to develop a potential. The relevant brane term reads,\n\\begin{equation}\n \\left. S_{CH} \\right|_{h-r} = \\int d^4x \\, \\xi_4 R_4 H^{\\dagger} H. \n\\end{equation}\nOne can estimate the size of $\\xi_4$ by noticing that PNGB potentials are generated at loop level primarily through the top Yukawa which is also responsible for the Higgs developing a potential. Naive dimensional analysis suggests that \n\\begin{equation}\n\\xi_4 \\sim \\frac{m_h^2}{f^2}\\,\\Gamma(v_{ew}\/f),\n\\end{equation}\nwhere $f$ is the compositeness scale given by $ke^{-kL}$ and $\\Gamma(v_{ew}\/f)$ is a generic function of $v_{ew}\/f$. Thus, we expect the kinetic mixing induced by this term to be very small. \n\n\n\\section{Effective action}\\label{sec:effaction}\n\nUp to this stage we have worked with a 5D warped scenario, considering two particular examples of EWSB, in both of which the Higgs resides in the bulk of the extra dimension. In this way we have been able to determine the possible induced mixing terms between the radion and the Higgs. Though we have determined these mixing terms for a particular scenario we expect their dependence on physical quantities to be general. In fact, from the 4D point of view through the $AdS\/CFT$ correspondence, we are describing a scenario of a conformal sector that is spontaneously broken leading to a light pseudo-Nambu-Goldstone boson known as the dilaton. This light state can mix with the other light state in the theory, the Higgs, via  the conformally covariant generalization of the gauge covariant derivative\\cite{Salam:1970qk,Vecchi:2010gj}:\n\\begin{equation}\n\\left(D_{\\mu}-\\Delta \\frac{\\partial_{\\mu} r(x)}{r(x)}\\right)H(x)+(1-6\\xi)H^{\\dagger}D_{\\mu}H\\frac{\\partial^{\\mu} r(x)}{r(x)}\\,,\n\\end{equation}\nwhere $\\Delta$ is the Higgs conformal weight, $D_{\\mu}$ is the gauge covariant derivative and we have included an additional term as suggested in Ref.~\\cite{Vecchi:2010gj} in order to account for the breaking of the special conformal symmetries, which in the 5D picture corresponds to the case $\\xi\\neq 1\/6$.  This interaction leads to kinetic mixing as found in the previous section. This mixing is always present due to the remnant shift symmetry of the model, and it is the only possible type of mixing allowed  when the CFT is broken spontaneously, as we also saw in our simplified 5D calculation.  An explicit breaking of the conformal symmetry is signalled by the presence of a non-vanishing dilaton mass and consequently the possibility of a mass mixing term between the dilaton and the Higgs field. This is represented in the 5D picture by the deformation from $AdS_5$ space due to back reaction effects responsible for the stabilization of the extra dimension and thus, for the generation of the radion mass. As we \nsaw, this explicit breaking of the conformal symmetry leads to mass mixing between the radion and the Higgs in the 5D picture as described in Eq.~(\\ref{massmix}).\n\nIt then becomes clear that from a pure 4D perspective, we can represent the most general effective phenomenological Lagrangian describing the light degrees of freedom of a spontaneously broken conformal sector by,\n\\begin{eqnarray}\\label{effact}\n{ \\mathcal{L}}_{eff}&=& \\frac{1}{2}\\partial_{\\mu} h(x)\\partial^{\\mu} h(x) - \\frac{1}{2} m_h^2h(x)^2 + \\frac{1}{2}\\left(1+c_2\\frac{v_{ew}^2}{\\Lambda_r^2}\\right)\\partial_{\\mu} r(x)\\partial^{\\mu} r(x) \\nonumber\\\\ \n&-& \\frac{1}{2} m_r^2r(x)^2 - c_1 \\frac{v_{ew}}{\\Lambda_r}  \\partial_{\\mu} h(x)\\partial^{\\mu} r(x) -c_3 \\frac{v_{ew}}{\\Lambda_r} m_r^2 h(x)r(x)\\,,\n\\end{eqnarray}\nwhere $c_1$, $c_2$ and $c_3$ are $\\mathcal{O}(1)$ numerical coefficients, and we use the terms radion\/dilaton interchangeably. From this point onwards we focus on this phenomenological Lagrangian to describe the possible mixing scenarios that may arise:\n\\begin{enumerate}\n \\item The no mass mixing scenario, $c_3=0$. From the 5D point of view, this case corresponds to a pure $AdS_5$ slice where the back reaction on the geometry from the radion potential that stabilizes the extra dimension can be neglected. Strictly speaking, it is not compatible to have a massive radion and no mass mixing unless a tuning of the parameters is involved such that $c_3=0$. From the 4D point of view, this corresponds to no explicit conformal breaking parameter in the dilaton self interactions and thus to a CFT that is not badly broken.\n\\item The generic scenario where $c_3,c_1 \\neq 0$ corresponds from the 5D point of view to considering the leading back reaction contributions of the radion potential and from the 4D point of view to explicit conformal breaking terms in the dilaton potential.\n\\item The gauge-Higgs unification\/pseudo-Nambu-Goldstone composite Higgs 5D\/4D scenarios correspond to $c_1\\ll 1$ and $c_3 = 0$ when explicit sources of conformal breaking are neglected.\n\\end{enumerate}\nDespite the fact that a brane or a bulk Higgs may enter in the same mixing category,  the phenomenology can very different due to the way in which in the conformal breaking is felt as we will see in the next section. For the study of the radion-Higgs mixing and its effect on both the Higgs and radion phenomenology at colliders we shall consider $c_1,c_2$ and $c_3$  as  free parameters. We will see in the next section that the GHU\/PNGB composite Higgs scenario reduces phenomenologically to the case of a brane Higgs with $c_1 \\ll 1$, and has therefore been covered by previous radion studies \\cite{Desai:2013pga}.  Thus we focus our scans on covering all possible values for $c_1,c_2$ and $c_3$ for a bulk scalar Higgs, which provides phenomenologically distinct signatures with respect to the brane Higgs case.\n\nOne can diagonalize the kinetic term in Eq.~\\eqref{effact} by  going to a new basis $h=h'+c_1 (v_{ew}\/\\Lambda_r) r'\/Z$ and $r=r'\/Z$, where\n\\begin{equation}\nZ^2=1+(c_2+c_1^2)\\frac{v_{ew}^2}{\\Lambda_r^2} \\,.\n\\end{equation}\nThis transformation decouples the kinetic mixing but introduces additional mass mixing terms. The mass matrix in the basis $(r',h')$ then takes the form\n\\begin{equation}\nM   \n=\n\\begin{pmatrix}\nM_{11}  & M_{12}   \\\\\nM_{12}  & M_{22}\n\\end{pmatrix} = \n\\begin{pmatrix}\n  \\frac{m_r^2}{Z^2}+\\frac{1}{Z^2}\\frac{v_{ew}^2}{\\Lambda_r^2}(c_1^2 m_h^2+2c_1 c_3 m_r^2) &    \\frac{1}{Z}\\frac{v_{ew}}{\\Lambda_r}(c_1 m_h^2+c_3m_r^2)\\\\\n \\frac{1}{Z}\\frac{v_{ew}}{\\Lambda_r}(c_1 m_h^2+c_3m_r^2)  & m_h^2\n\\end{pmatrix}\\,.\n\\end{equation}\nThe mass eigenbasis is obtained by the orthogonal transformation\n\\begin{equation}\n\\begin{pmatrix}\nr'  \\\\\nh'\n\\end{pmatrix}\n= \\begin{pmatrix}\n U_{r,-} &    U_{r,+}\\\\\n U_{h,-} & U_{h,+}\n\\end{pmatrix}\n\\, \\begin{pmatrix}\n\\phi_{-}  \\\\\n\\phi_{+}\n\\end{pmatrix} \\,.\n\\end{equation}\nwhere $\\Delta=\\sqrt{(M_{11}-M_{22})^2+4M_{12}^2}$ and\n\\begin{align}\nU_{r,-}&=\\frac{M_{11}-M_{22}-\\Delta}{\\sqrt{(M_{11}-M_{22}-\\Delta)^2+4M_{12}^2}}\\,, & U_{r,+} & =\\frac{M_{11}-M_{22}+\\Delta}{\\sqrt{(M_{11}-M_{22}+\\Delta)^2+4M_{12}^2}}\\,,\\nonumber \\\\\nU_{h,-}&=\\frac{2M_{12}}{\\sqrt{(M_{11}-M_{22}-\\Delta)^2+4M_{12}^2}}\\,, & U_{h,+} & =\\frac{2M_{12}}{\\sqrt{(M_{11}-M_{22}+\\Delta)^2+4M_{12}^2}}\\,.\n\\end{align}\nThere are correspondingly two eigenstates; a lighter one $\\phi_{-}=U_{r,-} r'+U_{h,-} h'$ and a heavier one $\\phi_{+}=U_{r,+} r'+U_{h,+} h'$, with masses:\n\\begin{equation}\nm^2_{\\phi_{\\pm}}=\\frac{1}{2}(M_{11}+M_{22}\\pm\\Delta)\\,.\n\\end{equation}\nThe gauge basis is related to the mass basis according to:\n\\begin{equation} \\label{estates}\nr=\\frac{1}{Z}(U_{r,+}\\phi_{+}+U_{r,-}\\phi_{-})\\,,\\qquad h=(U_{h,+}+\\frac{c_1}{Z}\\frac{v_{ew}}{\\Lambda_r}U_{r,+})\\phi_{+}+(U_{h,-}+\\frac{c_1}{Z}\\frac{v_{ew}}{\\Lambda_r}U_{r,-})\\phi_{-}\\,.\n\\end{equation}\n\n\n\\section{Higgs and Radion couplings, mixing and branching ratios} \\label{sec:couplings}\n\n\\subsection{Higgs and Radion couplings}\n\nThough we motivated our effective theory by studying a particular 5D scenario, we ultimately focused on an effective 4D picture wherein we consider two types of Higgs sector: i) the Higgs is identified with a light scalar doublet charged under the gauge group $SU(2)_L\\times U(1)_Y$; or ii) the Higgs field is identified with a composite PNGB of an enlarged broken global group that contains $SU(2)_L\\times U(1)_Y$ as a subgroup. In both cases there is an associated conformal sector that is spontaneously broken at an energy scale $f$ and that in our effective theory translates into the existence of a possible light state; the dilaton. One may be worried about possible contributions to the Higgs couplings arising from mixing or loop-effects involving resonances of the conformal sector.  However, notice that in case i) the only  symmetry additional to those already found in the SM is the spontaneously broken conformal symmetry.  We expect any possible additional composite resonances  besides the dilaton to \nhave masses of the order $m_{ress}\\sim g_{\\rho} f$, with $g_{\\rho}\\gg 1$ the strong coupling from the conformal sector, making their effects on the Higgs couplings strongly suppressed. In case ii) due to the enlarged global group in which SM particles are embedded and due to the shift symmetry protection of the Higgs, there is a relationship between the Higgs mass and light top fermionic resonances of the form $m_{h}^2\\propto m_{t}^2 m_{Q}^2\/f$.  Therefore in order to reproduce a light Higgs mass,  one usually finds the existence of light fermionic resonances that couple strongly to the Higgs, with masses $m_{Q}\\sim g_{\\psi} f\\ll g_{\\rho} f$.  This can have significant effects, in particular for Higgs couplings to gluons or photons. It has been shown  nonetheless that due to the pseudo-Nambu-Goldstone nature of the Higgs, the resonant fermionic loop contributions  cancel  against the top quark modified Yukawa coupling, and lead to modifications in the coupling to gluons that are suppressed by the ratio $v^2\/\nf^2\\lesssim 0.01$ \\cite{Montull:2013mla}.  Therefore, in the two Higgs scenarios considered, we do not expect sizeable deviations of the Higgs couplings from their SM values, and thus for simplicity we restrict the couplings to SM values.\\footnote{In the case of generic warped extra dimensional scenarios the mass scale of the lowest lying KK fermions $m_{KK} \\lesssim \\Lambda_r.$  A naive estimate of the of shift in the Higgs coupling to gluons due to the KK towers of the SM fermions is as follows,\n\\[ \\frac{\\delta \\Gamma^{KK}_{gg}}{\\Gamma^{SM}_{gg}} \\sim 4 C(r_{NP})N_{f}\\sum_n \n \\frac{v}{m^{(n)}_{KK}}\\frac{\\partial m^{(n)}_{KK}}{\\partial v} \\sim {\\mathcal{O}(1)} \\left(\\frac{v}{ke^{-\\pi kL}}\\right)^2,\\]\n where $C(r_{NP})$ is the quadratic Casimir of the KK states and $N_{f}=6$. This translates into a lower limit on the mass of the lightest KK state that may be as large as 3.2~TeV for a $20 \\%$ shift in the decay width, which is the resolution of current experimental data. A detailed calculation of this is rather model dependent \\cite{Bhattacharyya:2009nb} and beyond the mandate of this paper.} \n\nAllowing for the possibility of a bulk Higgs implies that some of the known radion couplings to SM fields are modified, in particular those involving radion couplings to the Higgs field itself as well as to massive gauge bosons. We use the 5D language as an easy tool to calculate the couplings and assume a given warp factor $kL$ that solves the hierarchy problem, though our results are general with the replacement $\\Lambda_r=f$. As was shown in Ref.~\\cite{Csaki:2007ns}, the bulk radion couples at linear order to SM fields through the  bulk stress energy tensor as\n\\begin{equation}\nS_{radion}=\\int d^4x dz \\sqrt{g} \\,F(x,z)\\left[\\Theta^{M}_{M}-3 g_{zz}\\Theta^{zz}\\right]\\label{rcoupling},\n\\end{equation}\nwhere the conformal coordinate $z$ is related to the extra-dimensional coordinate $y$ as $dy=e^{-A}dz$, and $\\Theta^{MN}$ is the bulk stress energy tensor which can be written as\n\\begin{equation}\n\\Theta^{MN}=-\\frac{2}{\\sqrt{g}}\\frac{\\delta(\\mathcal{L}_{matter}\\sqrt{g})}{\\delta g_{MN}}=\n-2\\frac{\\delta(\\mathcal{L}_{matter})}{\\delta g_{MN}}+g^{MN}\\mathcal{L}_{matter} \\,.\n\\end{equation}\nFocusing on the coupling to SM gauge bosons (massive or massless), using Eq.~(\\ref{rcoupling}), one can easily show that due to the bulk kinetic terms for the gauge fields, there will always be a non-vanishing coupling of the form\n\\begin{equation}\nS_{radion}=\\int d^4x dy \\left(-\\frac{1}{2}\\right)F(x,y)F_{\\mu\\nu}F^{\\mu\\nu}=-\\int d^{4}x \\frac{r(x)}{4\\Lambda_r}\\frac{1}{kL}F_{\\mu\\nu}F^{\\mu\\nu},\n\\end{equation}\nwhere we used that in this case $\\mathcal{L}_{matter}=-1\/4F_{MN}F^{MN}$ and therefore $\\Theta^{MN}=-F^{MA}F^N_{A}+\\frac{1}{4}g^{MN}F_{AB}F^{AB}$. As was argued in \\cite{Csaki:2007ns}, the fact that this tree level coupling is non-vanishing implies that loop effects merely renormalize this tree-level operator. Therefore, loop effects are prominent on the branes where no tree-level coupling is allowed, being stronger on the IR brane where the radion is usually closely localized. This provides the main mechanism of radion production through gluon fusion as is usual in radion scenarios. We refer the reader to Ref.~\\cite{Csaki:2007ns} for the appropriate expressions for the radion-digluon and radion-diphoton couplings, including fermion and gauge boson loops as well as QCD and QED trace anomalies respectively.\n\nIn addition, via electroweak symmetry breaking (EWSB), there is in principle a possibly large additional coupling of the radion to a pair of massive gauge bosons, which is dominant in the case of a brane-localized Higgs.  As is well-known, the gauge bosons acquire their mass through the kinetic term of the Higgs field, which in the case of a bulk Higgs scalar leads to mass terms for the gauge bosons of the form\n\\begin{equation}\n\\mathcal{L}_{matter}=D_{M}H^{\\dagger}D^{M}H\\to m_{W}^2 W^{+}_{\\mu}W^{\\mu, -}+\\frac{1}{2}m_{Z}^2 Z_{\\mu}Z^{\\mu}.\n\\end{equation}\nIt follows that the contribution to the stress energy tensor is $\\Theta^{MN}=-2 D^{M}HD^{N}H^{\\dagger}+g^{MN}D_AH^{\\dagger}D^{A}H$, which implies that $\\Theta^{M}_{M}=3D^{M}HD_{M}H^{\\dagger}=3e^{2A}D^{\\mu}HD_{\\mu}H^{\\dagger}$, where the last index is contracted using the Minkowski metric. Now $\\Theta^{zz}=g^{zz}D_{A}HD^{A}H^{\\dagger}$, and therefore $-3g_{zz}\\Theta^{zz}=-3 e^{2A}D^{\\mu}HD_{\\mu}H^{\\dagger}$, which exactly compensates the contribution from $\\Theta^{M}_{M}$. Thus the linear radion coupling to the electroweak gauge boson mass terms vanishes in the case of a bulk Higgs. This result can also be checked by simply expanding the metric in its spin-0 fluctuations in the matter action\n\\begin{align}\n\\mathcal{S}_{matter}& =\\int d^4x dy\\sqrt{g}(D_{\\mu}H^{\\dagger}D^{\\mu}H)\\notag \\\\\n&=\\int d^4x dy \\, e^{-4(A(y)+F(x,y))}(1+2F(x,y)) \\, e^{2(A(y)+F(x,y))}D_{\\mu}H^{\\dagger}D^{\\mu}H\\notag\\\\\n&\\approx \\int d^4x dy \\, (1-4F^2(x,y)+\\mathcal{O}(F(x,y)^3)) \\, e^{-2A(y)}D_{\\mu}H^{\\dagger}D^{\\mu}H,\n\\end{align}\nwhere the index on the r.h.s is contracted using the Minkowski metric.  Therefore we also see in this way  that the coupling vanishes. Notice that this result is general for the kinetic term of any scalar. We can understand this result from the 4D point of view as follows: as we just noticed, the vanishing of this particular coupling is geometrical from the 5D point of view. As a matter of fact we can take both the UV and IR branes to infinity, and the results would still hold in pure $AdS_5$-space. In that particular case, it is clear that the conformal symmetry is exact.  If we look at the 4D picture this implies that the 4D-analogue of the radion, the dilaton field, can only couple derivatively to conformally invariant operators, in particular to $D_{\\mu}\\Phi D^{\\mu}\\Phi$, where $\\Phi$ is a 4D-scalar field. Therefore from Lorentz invariance we see that no linear coupling can be written that derivatively couples the radion to $D_{\\mu}\\Phi D^{\\mu}\\Phi$. This has important consequences for the radion \nphenomenology when the Higgs is a scalar in the bulk, since then its coupling to pairs of massive SM gauge bosons only comes from Eq.~(\\ref{rcoupling}) and is highly suppressed. \n\nIn the case of gauge-Higgs unification scenarios,  the Higgs field is identified with the fifth component $A_5(x,y)$ of a gauge field belonging to the coset $G\/H$ of an enlarged gauge group $G$ that is broken down to the subgroup $H$ via boundary conditions. In that case the equivalent of the scalar kinetic term is given by\n\\begin{equation}\n\\mathcal{S}_{matter}=\\int d^4x dy \\sqrt{g} \\, {\\rm Tr}[F^a_{\\mu 5}F^{a,\\mu 5}],\n\\end{equation}\nwhere the index $a\\in G$. Due to the extra index in the kinetic term, there is a non-vanishing radion coupling proportional to the EWSB induced masses\n\\begin{align}\n\\mathcal{S}_{matter}&=\\int d^4x dy \\, e^{-4(A(y)+F(x,y))}(1+2F(x,y)) \\, e^{2(A(y)+F(x,y))}\\frac{1}{(1+2F(x,y))^2} \\, {\\rm Tr}[F^a_{\\mu 5}F^{a,\\mu 5}]\\notag\\\\\n&\\approx \\int d^4x dy \\, e^{-2A(y)}(1-4F(x,y)+\\mathcal{O}(F(x,y)^2)) \\, {\\rm Tr}[F^a_{\\mu 5}F^{a,\\mu 5}],\n\\end{align}\nwhere the index on the r.h.s is contracted using the Minkowski metric. Thus, in these kinds of scenarios the radion coupling to massive SM gauge bosons is similar to that encountered for a localized Higgs scalar on the IR brane.\n\nAnother potential difference with respect to the brane Higgs scenario may arise in the  Yukawa induced SM fermion-radion interactions with the Higgs field which tend to dominate for heavy fermions with respect to other radion-fermion interactions that are momentum suppressed. For that reason we focus on the term\n\\begin{equation}\n\\Delta\\mathcal{L}_{Y}=-\\int d^4x dy \\sqrt{g}\\, Y_{5}\\left[H \\bar{f}f+h.c.\\right], \\label{Yukawa}\n\\end{equation}\nwhere $Y_{5}$ is the 5D Yukawa coupling. We again expand the spin-0 fluctuations of the metric and use that the left-handed and right-handed fermion well-normalized zero mode profiles are given by\n\\begin{equation}\nf_{L}(y)=\\frac{e^{(\\frac{1}{2}-c_L)ky}}{N_{L}}\\;,\\qquad f_{R}(y)=\\frac{e^{(\\frac{1}{2}+c_R)ky}}{N_{R}},\n\\end{equation} \nwhere $f_{L}(y)$ and $f_{R}(y)$ satisfy\n\\begin{equation}\n\\int_{0}^{L}dy f^2_{L,R}(y)=1 \\qquad \\longrightarrow \\qquad N_{L,R}=\\sqrt{\\frac{e^{(1\\mp2c_{L,R})kL}-1}{(1\\mp2c_{L,R})k}}\\,.\n\\end{equation} \nThe upper and lower signs correspond to $N_L$ and $N_R$ respectively, while $c_{L,R}$ are the fermion bulk mass parameters defined by $M_{L,R}=c_{L,R}k$. Using Eq.~(\\ref{vev}) for the Higgs vev, we can obtain an expression for the SM fermion masses by integrating the zero-mode profiles for the fermions and the Higgs vev along the extra dimension. In that case we see that we can express the fermion mass as\n\\begin{eqnarray}\nm_f &=&\\int_{0}^{L} dy \\, e^{-A(y)} \\, f_{L}(y)f_{R}(y)v(y)Y_{5}=\\nonumber\\\\\n&=& \\frac{1}{N_R}\\frac{1}{N_{L}}\\sqrt{2(1+\\beta)k} \\, v_{ew}e^{-(1+\\beta)kL}\\frac{(e^{(2-c_L+c_R+\\beta)kL}-1)}{(2-c_L+c_R+\\beta)k}Y_5\\,. \\label{fermionmass}\n\\end{eqnarray}\nThe interaction Eq.~(\\ref{Yukawa}), once expanded in the spin-0 fluctuation of the metric, takes the form\n\\begin{align}\n-\\int d^4x dy \\, e^{-A(y)}\\, (-2F(y)) &\\, Y_5 \\, f_{L}(y) \\, f_{R}(y) \\, v(y) \\, (r(x) \\bar{f}^0(x) f^0(x)+h.c.)\\notag\\\\\n&\\approx  \\frac{2 m_f}{\\Lambda_r}\\frac{(2-c_{L}+c_{R}+\\beta)}{(4-c_L+c_R+\\beta)}\\int d^4 x \\, (r(x)\\bar{f}^0(x) f^0(x)+h.c.)\\,,\n\\end{align}\nwhere in the last line we assume that the fermion and Higgs profiles are IR localized and satisfy $1-c_L+c_R+\\beta>0$. So contrary to the gauge-boson case, we notice that the coupling of the radion to, in particular, the top quark can be non-negligible, similar to the case with a localized Higgs field.\n\n\nFinally we look at the coupling of the radion to two Higgs. For this coupling there is a kinetic mixing contribution coming from $\\sqrt{g}R_5 H^{\\dagger}H$ as well as contributions from the Higgs kinetic term, bulk Higgs mass $\\sqrt{g} c^2 k^2H^{\\dagger}H$ and important boundary contributions from the IR-brane potential $\\sqrt{g_4}\\lambda_{IR}(H)$.  The Higgs kinetic and bulk mass contributions cancel against some of the IR-brane contributions and after replacing $\\tilde{\\lambda}$ in terms of $m_h^2$ and $v^2_{ew}$ using Eq.~(\\ref{mhiggs}), one can write the radion-diHiggs coupling in the form\n\\begin{equation}\n\\int d^4 x \\frac{1}{\\Lambda_r}\\left(2m_h^2-\\frac{c_1}{2}m_r^2\\right)r(x)h(x)^2. \\label{radiondiHiggs}\n\\end{equation}\nWe have also used the radion equation of motion $\\Box r(x)=-m_r^2 r(x)$. Given Eq.~(\\ref{radiondiHiggs}), we do not expect large differences arising in comparison with the brane localized Higgs counterpart.\n\nTo summarize, after studying the radion couplings to SM particles, we expect the largest modifications in the phenomenology of the bulk scalar Higgs scenario to arise due to the vanishing of the radion-massive diboson coupling proportional to the gauge boson mass. We list for completeness in Table~\\ref{couplingsgauge} the most relevant couplings of the unmixed Higgs and radion states, where $\\tau_{i,(h,r)}=4 m_i^2\/m_{(h,r)}^2$, $F_{1\/2}$ and $F_{1}$ are the usual integrals over fermion and gauge boson states running in the loop and  $b_{QED}=-11\/3$ and $b_{QCD}=7$ are the $\\beta$-function coefficients.\n\\begin{table}[h]\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline\n\\rule{0mm}{4mm}\n   & $h(x)$ & $r(x)$\\\\[0.3em]\n\\hline\n\\rule{0mm}{5mm}\n$f\\bar{f}$ & $-\\frac{m_f}{v}$ & $\\frac{m_f}{\\Lambda_r}$\\\\ [0.3em]\n\\hline\n\\rule{0mm}{5mm}\n$WW$ & $\\frac{2m_W^2}{v}$ & $-\\frac{2}{\\Lambda_r}\\frac{1}{kL}$\\\\ [0.3em]\n\\hline\n\\rule{0mm}{5mm}\n$ZZ$ & $\\frac{m_Z^2}{v}$ & $-\\frac{1}{\\Lambda_r}\\frac{1}{kL}$\\\\ [0.3em]\n\\hline\n\\rule{0mm}{5mm}\n$\\gamma\\gamma$ & $\\frac{1}{v}\\left(F_{1}(\\tau_{W,h})+\\frac{4}{3}F_{1\/2}(\\tau_{t,h})\\right)\\frac{\\alpha_{EM}}{2\\pi}$ &  $-\\frac{1}{\\Lambda_r}\\left(\\frac{1}{kL}+\\left[b_{QED}-F_{1}(\\tau_{W,r})-\\frac{4}{3}F_{1\/2}(\\tau_{t,r})\\right]\\frac{\\alpha_{EM}}{2\\pi}\\right)$\\\\ [0.3em]\n\\hline\n\\rule{0mm}{5mm}\n$gg$ & $\\frac{1}{v}\\frac{\\alpha_{3}}{4\\pi}F_{1\/2}(\\tau_{t,h})$ &  $-\\frac{1}{\\Lambda_r}\\left(\\frac{1}{kL}+\\left[b_{QCD}-\\frac{1}{2}F_{1\/2}(\\tau_{t,r})\\right]\\frac{\\alpha_{3}}{2\\pi}\\right)$\\\\ [0.3em]\n\\hline\n\\end{tabular}\n\\caption{Phenomenologically relevant couplings of the gauge states $h(x)$ and $r(x)$ to SM particles.}\n\\end{center}\n\\label{couplingsgauge}\n\\end{table}\n\n\\subsection{ Mixing and branching ratios}\n\nMost of the interactions between the radion and SM particles, except those with massive gauge bosons and to the Higgs itself, have the same structure as those of the SM Higgs to fermions and gauge bosons.  So  one can easily obtain most of the decay rates of the mixed states by inspecting the well-known expressions for the Higgs decay rates (see for example \\cite{Djouadi:2005gi}) and using the replacements: $m_h \\to m_{\\phi_{\\pm}}$ and  $g_{h}\\to g_{\\pm}$, where from Eq.~(\\ref{estates}),\n\\begin{equation}\ng_{\\pm}=\\left(U_{h,\\pm}+\\frac{c_1}{Z}\\frac{v_{ew}}{\\Lambda_r}U_{r,\\pm}\\right)g_{h}+\\frac{1}{Z}U_{r,\\pm}\\,g_{r}\\,,\n\\end{equation}\nwith $g_h$ and $g_r$ the Higgs and radion couplings to SM particles respectively. \n\nThe interactions that have a structure different than those of the Higgs to SM particles are those of the mixed states to massive gauge bosons and among the mixed states themselves. In this case, the decay rate of the mixed states into massive gauge bosons can be written as\n\\begin{eqnarray}\n\\Gamma_{\\phi_{\\pm}WW}&=&\\frac{m_{\\phi_{\\pm}}}{32\\pi}\\sqrt{1-4\\frac{m^2_W}{m^2_{\\phi_{\\pm}}}}\\times\\left[\\frac{U^2_{r,\\pm}}{Z^2}\\frac{g^2_{rWW}}{4}m^2_{\\phi_{\\pm}}\\left(1-4\\frac{m^2_W}{m^2_{\\phi_{\\pm}}}+6\\frac{m^4_W}{m^4_{\\phi_{\\pm}}}\\right)\\right.\\nonumber\\\\\n&+&\\left. \\frac{U_{r,\\pm}}{Z}\\left(U_{h,\\pm}+\\frac{c_1}{Z}\\frac{v_{ew}}{\\Lambda_r}U_{r,\\pm}\\right)\\frac{3}{2}g_{rWW}g_{hWW}\\left(1-2\\frac{m^2_W}{m^2_{\\phi_{\\pm}}}\\right)\\right.\\nonumber\\\\\n&+&\\left.2\\left(U_{h,\\pm}+\\frac{c_1}{Z}\\frac{v_{ew}}{\\Lambda_r}U_{r,\\pm}\\right)^2 \\frac{g_{hWW}^2}{4 m^4_W}m^2_{\\phi_{\\pm}}\\left(1-4\\frac{m^2_{W}}{m^2_{\\phi_{\\pm}}}+12\\frac{m^4_W}{m^4_{\\phi_{\\pm}}}\\right)\\right], \\label{WWdecay}\n\\end{eqnarray}\nwhere $g_{rWW}$ and $g_{hWW}$ are among the couplings listed in Table \\ref{couplingsgauge}, and for decays into Z pairs one needs to divide Eq.~(\\ref{WWdecay}) by 2, replace $m_W \\to m_Z$, $g_{rWW}\\to 2 g_{rZZ}$ and $g_{hWW}\\to 2 g_{hZZ}$.\n\nUsing Eq.~(\\ref{radiondiHiggs}) and assuming that $\\phi_{+}$ is mostly radion while $\\phi_{-}$ is mostly Higgs, as experimental constraints seem to suggest, we can calculate the decay rate of $\\phi_{+}$ to a pair of $\\phi_{-}$ states,\n\\begin{eqnarray}\n\\Gamma_{\\phi_{+}\\phi_{-}\\phi_{-}}&=&\\frac{m^3_{\\phi_{+}}}{8\\pi \\Lambda_r^2}\\sqrt{1-4\\frac{m^2_{\\phi_{-}}}{m^2_{\\phi_{+}}}}\\times\\left[\\frac{U_{r,+}}{Z}\\left(U_{h,-}+\\frac{c_1}{Z}\\frac{v_{ew}}{\\Lambda_r}U_{r,-}\\right)^2 \\left(2\\frac{m^2_h}{m^2_{\\phi_{+}}}-\\frac{c_1}{2}\\right)\\right.\\nonumber\\\\\n&+&\\left.\\left(U_{h,+}+\\frac{c_1}{Z}\\frac{v_{ew}}{\\Lambda_r}U_{r,+}\\right)\\left(U_{h,-}+\\frac{c_1}{Z}\\frac{v_{ew}}{\\Lambda_r}U_{r,-}\\right)^2\\left(-\\frac{m_h^2}{2v_{ew}}\\right)\\frac{\\Lambda_r}{m^2_{\\phi_{+}}}\\right]^2.\n\\end{eqnarray}\n\n Now that we have all the relevant decay rates, we display in Figs.~\\ref{fig:BR_nomix} and \\ref{fig:BRmix} the branching fractions of $\\phi_+$ as a function of $m_{\\phi_{+}}$ for different values of $c_1=c_2=c_3$. In the case of no-mixing ($c_1=c_2=c_3=0$) where $\\phi_{+}=r$ and $\\phi_{-}=h$, and the results are independent of $\\Lambda_r$, notice that for $m_{r}\\gg m_{h}$  the dominant decay channels are $t\\bar{t}$, $gg$ and $hh$. As already mentioned, decays to massive dibosons only go through their kinetic terms as in the $\\gamma\\gamma$ channel and tend to be suppressed\\footnote{In contrast to the $gg$ channel where the QCD trace anomaly dominates, in the $\\gamma\\gamma$ channel the anomaly contribution is sub-dominant with respect to the conformal $1\/kL$ contribution.}. Thus we expect final state multijets, pairs of b-jets and possibly leptons plus missing energy. Depending on the mass difference between $m_r$ and $m_h$, we could have fat-jets if the decay $h\\to b\\bar{b}$ is very boosted. For radion masses \nslightly larger than 125 GeV, $m_{r}\\gtrsim m_h$, $gg$ dominates with $b\\bar{b}$ the second most important decay channel, thus we expect multijets in the final states, which can be hard to differentiate from the SM QCD background found at the LHC at those energies. It is interesting to note that the diphoton channel can have a branching fraction comparable to the SM Higgs for this range of masses and furthermore remains relevant out to higher masses, making it an appealing discovery channel in the small mixing scenario. As shown in Fig.~\\ref{fig:BRmix}, once the mixing increases WW and ZZ rapidly become more relevant branching fractions, and at $c_1=c_2=c_3=1$ they dominate over all regions of $m_r > m_h$, relegating the other decay branching fractions to be below 10$\\%$.  For smaller mixing, $c_1=c_2=c_3=0.1$, decays into $gg$, $b\\bar{b}$ and $\\phi_{-}\\phi_{-}$ are still relevant, with $gg$ dominant for low $m_{\\phi_{+}}$, decays into pairs of $\\phi_{-}$\nimportant in a small region at intermediate values of $m_{\\phi_{+}}$, and $t\\bar{t}$ dominating at large values of $m_{\\phi_{+}}$. Here we also observe a sharp drop in the branching fraction to $\\phi_{-}\\phi_{-}$ near $m_{\\phi_{+}}\\sim750$~GeV due to a cancellation between the various contributions to the partial width. As the mixing is increased, this cancellation occurs at smaller values of $m_{\\phi_{+}}$ and eventually moves below the $\\phi_{-}\\phi_{-}$ threshold and is not observed at $c_1=c_2=c_3=1$.\n\n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics[height=5cm]{figs\/BR_nomix_new.pdf}\n\\end{center}\n\\caption{Branching ratios for $\\phi_+$ as a function of mass with $c_1=c_2=c_3=0$, independent of $\\Lambda_r$. }\n\\label{fig:BR_nomix}\n\\end{figure}\n\n\\begin{figure}[h]\n\\begin{minipage}[b]{0.5\\linewidth}\n\\begin{center}\n\\includegraphics[height=5cm]{figs\/BR_c-01_3TeV_new.pdf}\n\\end{center}\n\\end{minipage}\n\\begin{minipage}[b]{0.5\\linewidth}\n\\begin{center}\n\\includegraphics[height=5cm]{figs\/BR_c-1_3TeV_new.pdf}\n\\end{center}\n\\end{minipage}\n\\caption{Branching ratios for $\\phi_+$ as a function of mass for $\\Lambda_r=3$ TeV. The left and right panels are for $c_1=c_2=c_3=0.1$ and $c_1=c_2=c_3=1$ respectively.}\n\\label{fig:BRmix}\n\\end{figure}\n\n\n\\section{Constraints from LHC searches}\n\\label{sec:expconstraints}\n\nStarting with the effective Lagrangian Eq.~\\eqref{effact}, we are now in a position to investigate the constraints on the allowed parameter space. With the discovery at the LHC of a new Higgs-like scalar, we consider the case where the lightest eigenstate, $\\phi_-$, is identified with this 125 GeV resonance. Measurements of the 125 GeV Higgs signal strengths as well as direct searches for the heavier eigenstate, $\\phi_+$, can then be used to constrain the allowed parameter space for models which can be described by Eq.~\\eqref{effact}.\n\nThe effective Lagrangian we are considering contains six parameters; the mass scales $m_h$, $m_r$, $\\Lambda_r$, and the $\\mathcal{O}(1)$ dimensionless parameters $c_1$, $c_2$ and $c_3$. One can immediately eliminate $m_h$ by requiring the mass of the lightest eigenstate to be 125 GeV. In addition, we expect $c_2$ to have a very small effect on the phenomenology since the relevant term in the Lagrangian is suppressed by an additional factor of $v_{ew}\/\\Lambda_r$. Therefore we choose to fix $c_2=1$ before scanning over the remaining 4-dimensional parameter space. We perform a random scan with flat priors over the mass of the radion gauge state, $m_r$, from 160 GeV to 1500 GeV and the kinetic and mass mixing coefficients, $c_1$ and $c_3$, from -3 to 3, while considering fixed values of 1, 3 and 5 TeV for the scale of the radion couplings, $\\Lambda_r$. We also note that there is a theoretical bound on $c_1$ in order to ensure that we do not encounter a ghost-like kinetic term for $\\phi_+$. For example when $c_\n3=0$ and $\\Lambda_r=1$ TeV this gives a bound of $\\vert c_1 \\vert\\lesssim4$.\n\nSince we have chosen to identify the lightest eigenstate, $\\phi_-$, with the 125 GeV Higgs, we impose the constraints from the measured Higgs signal strengths in the $\\gamma\\gamma$, $ZZ^{(*)}\\rightarrow 4l$, $WW^{(*)}\\rightarrow l\\nu l\\nu$, $b\\bar{b}$ and $\\tau\\bar{\\tau}$ decay channels. We focus on the dominant gluon-gluon fusion (ggF) production mode in all channels, with the exception of $b\\bar{b}$ where the best measurements are obtained by considering production in association with a W or Z boson (VH). In the case of gluon fusion, the signal strength is defined in the narrow width approximation by\n\\begin{equation}\n\\mu^{ggF}_X=\\frac{\\Gamma(\\phi_-\\rightarrow gg)}{\\Gamma(H_{SM}\\rightarrow gg)}\\frac{Br(\\phi_-\\rightarrow X)}{Br(H_{SM}\\rightarrow X)}.\n\\end{equation}\nWe use the combined ATLAS, CMS and Tevatron best fit values for the signal strengths given in \\cite{Belanger:2013xza}, which are shown in Table \\ref{sigstrength}, and require that the signal strength for the $\\phi_-$ state satisfy these bounds at the 1-sigma level. \n\\begin{table}\n\\begin{center} \n\\begin{tabular}[h]{|c|c|} \n\\hline\nChannel & $\\mu_X$ \\\\ \\hline\n$\\gamma\\gamma$ & $0.98\\pm 0.28$ \\\\ \\hline\n$VV$ & $0.91\\pm 0.16$ \\\\ \\hline\n$b\\bar{b}$ & $0.97\\pm 0.38$ \\\\ \\hline\n$\\tau\\bar{\\tau}$ & $1.07\\pm 0.71$ \\\\ \\hline\n\\end{tabular}\n\\caption{Best fit values for the Higgs signal strengths in various decay channels at 125 GeV \\cite{Belanger:2013xza}.}\\label{sigstrength}\n\\end{center}\n\\end{table}\n\nHowever, for masses $125<m_{\\phi_+}<160$ GeV, one must carefully consider the contribution of both states to the measured signal strength in the $WW^{(*)}$ channel, since unlike $\\gamma\\gamma$ and $ZZ^{(*)}$ the final state is not fully reconstructible. Additionally, interference effects must be taken into account if the two states have a very small mass separation. We therefore restrict $m_r > 160$ GeV, allowing us to consider the two states separately in the $WW$ channel.\n\nWe must also consider the possibility that, when kinematically allowed, the 125 GeV state may be produced via the decay $\\phi_+\\rightarrow\\phi_-\\phi_-$, which will result in an enhancement in the signal strengths for $\\phi_-$. In the case of the $WW^{(*)}$ analysis, such events will not contribute significantly due to vetoes on additional leptons and jets. On the other hand, the $\\gamma\\gamma$ and $ZZ^{(*)}$ analyses are quite inclusive and this additional contribution to the production cross section can be important. In fact, in certain regions of parameter space this process can become the dominant production mechanism for $\\phi_-$. In this case we define the signal strength as\n\\begin{equation}\n\\mu^{ggF}_X=\\left(\\frac{\\Gamma(\\phi_- \\rightarrow gg)}{\\Gamma(H_{SM}\\rightarrow gg)}+\\frac{2\\sigma_{ggF}(pp\\rightarrow \\phi_+ \\rightarrow \\phi_- \\phi_-)}{\\sigma_{ggF}(pp\\rightarrow H_{SM})}\\right)\\frac{Br(\\phi_- \\rightarrow X)}{Br(H_{SM}\\rightarrow X)}.\n\\end{equation}\nIn addition to the constraints on the 125 GeV eigenstate, the ATLAS and CMS Higgs searches can also be used to constrain the heavier eigenstate. We therefore require that the $\\phi_+$ state satisfies the exclusion limits from the CMS $H\\rightarrow WW \\rightarrow 2l2\\nu$ \\cite{CMS-PAS-HIG-13-003} and $H \\rightarrow ZZ \\rightarrow 4l$ \\cite{CMS-PAS-HIG-13-002} searches and the ATLAS high mass $H \\rightarrow WW \\rightarrow e\\nu\\mu\\nu$ search \\cite{ATLAS-CONF-2013-067}. The Higgs searches in the remaining channels ($\\gamma\\gamma$, $b\\bar{b}$ and $\\tau\\bar{\\tau}$ ) currently only provide constraints for masses below $\\sim150$ GeV. Finally, we also impose the additional constraints provided by the CMS semi-leptonic $t\\bar{t}$ resonance search \\cite{Chatrchyan:2013lca} in the 500 GeV to 1 TeV mass range.\n\nThere are in principle other searches performed at the LHC which could be adapted to our particular model, for example the searches for resonant $ZZ$ production in the dilepton plus dijet channel \\cite{CMS-PAS-EXO-12-022} and resonant $WW$ production in the lepton plus dijet channel \\cite{CMS-PAS-EXO-12-021}. These searches focus on dibosons produced by KK graviton decay and thus cannot be directly translated to our model without determining the signal acceptance via a Monte Carlo simulation of our signal with appropriate selection cuts. Since this would go beyond the intended scope of the paper, we leave these particular collider studies for subsequent work. While we do not expect these searches to currently constrain our model, they will become important at the 14TeV-LHC. The high mass diphoton \\cite{Aad:2012cy} and dijet \\cite{CMS-PAS-EXO-12-059} searches may also be able to provide constraints in the future. \n\n\n\\section{Radion-Higgs phenomenology for LHC14}\n\nWe performed a scan of 200,000 points for each value of $\\Lambda_r$, imposing the above experimental constraints on the $\\phi_-$ and $\\phi_+$ states. We find that the current experimental constraints already rule out a significant fraction of the parameter space, in particular at low values of $\\Lambda_r$ and small masses, $m_+$. Fig.~\\ref{fig:h+} shows the fraction of the $\\phi_+$ mass eigenstate in the Higgs gauge eigenstate, $h_+=U_{h,+}+\\frac{c_1}{Z}\\frac{v_{ew}}{\\Lambda_r}U_{r,+}$, as a function of the mass. This is a useful variable for characterizing the extent of the mixing between the two states. We note that $h_+$ can be greater than one due to the non-unitary transformation resulting from the kinetic mixing. The red points in Fig.~\\ref{fig:h+} are excluded by measurements of the 125 GeV Higgs signal strengths, while the black points satisfy these constraints but are ruled out by direct searches for the heavier state. The green points pass all of the current experimental bounds. The top panel is \nfor $\\Lambda_r=1$ TeV, while the bottom left and right panels are for values of $\\Lambda_r=3,5$~TeV respectively. \n\nWe see that for $\\Lambda_r=1$~TeV virtually all of the points are ruled out, with the exception of a few points with very small mixing. In the 250 to 350~GeV range, this is due to enhanced production of the 125~GeV state via $\\phi_+\\rightarrow\\phi_-\\phi_-$, as discussed previously. The remaining points which satisfy the Higgs signal strength bounds are excluded by searches for $\\phi_+$ in the $WW$ and $ZZ$ channels, as well as the $t\\bar{t}$ channel above 500 GeV. In the $\\Lambda_r=3$~TeV case we find that, as expected, a significantly larger fraction of the points survive the experimental constraints. Below 500~GeV the bounds from $WW$ and $ZZ$ searches still rule out most of the points with large mixing, while between 450 and 900~GeV we find that they also disfavour negative values of $h+$. This is the result of constructive interference between the Higgs and radion couplings to the top quark, which enhances the $\\phi_+$ gluon fusion cross section for negative $h_+$. For masses above 1~TeV there are no \nconstraints on $\\phi_+$ from current searches. Furthermore, notice that only the red points extend to larger values of $h_+$, which indicates that for large mixing one is unable to satisfy the Higgs signal strength constraints independently of the $\\phi_{+}$ mass. Finally, for $\\Lambda_r=5$ TeV there are once again significantly more allowed points for masses below 1~TeV, although negative values of $h_+$ are disfavoured by $WW$ and $ZZ$ searches between 250 and 600~GeV.\n\nUsing these results we can also derive bounds on the parameters of our effective Lagrangian, in particular $c_1$ and $c_3$. For $\\Lambda_r=1$~TeV we find that $-0.2<c_3<0.04$, while the constraints are somewhat weaker for $\\Lambda_r=3$~TeV, giving $-2.1<c_3<0.6$. These bounds are of course also dependent on the value of $m_r$ and can be significantly stronger, particularly for lower masses. Considering $c_1$ on the other hand, for $\\Lambda_r=1$~TeV we find $-0.2<c_1<0.3$, while for $\\Lambda_r=3$~TeV $c_1$ is unconstrained for values of $m_r > 1$~TeV but for masses below 450 GeV we obtain a bound of $-0.7<c_1<2.7$.\n\n\\begin{figure}[h]\n\\begin{minipage}[b]{\\linewidth}\n\\begin{center}\n\\includegraphics[height=6cm]{figs\/h+_m+_1000_new.png}\n\\end{center}\n\\end{minipage}\n\\begin{minipage}[b]{0.5\\linewidth}\n\\begin{center}\n\\includegraphics[height=6cm]{figs\/h+_m+_3000_new.png}\n\\end{center}\n\\end{minipage}\n\\begin{minipage}[b]{0.5\\linewidth}\n\\begin{center}\n\\includegraphics[height=6cm]{figs\/h+_m+_5000_new.png}\n\\end{center}\n\\end{minipage}\n\\caption{The fraction of the $\\phi_+$ mass eigenstate in the Higgs gauge eigenstate, $h+$, as a function of the mass. The red (dark grey) points are excluded by measurements of the 125 GeV Higgs signal strengths, while the black points satisfy these constraints but are ruled out by direct searches for $\\phi_+$. The green (light grey) points pass all of the current experimental bounds. The top panel is for $\\Lambda_r=1$~TeV, while the bottom left and right panels are for values of $\\Lambda_r=3,5$~TeV respectively.}\n\\label{fig:h+}\n\\end{figure}\n\n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics[height=7cm]{figs\/gamma_m+_new.png}\n\\end{center}\n\\caption{Gluon fusion cross section times branching ratio for $\\phi_+\\rightarrow \\gamma\\gamma$ as a function of mass. The black, blue (dark grey) and cyan (light grey) points are for $\\Lambda_r=$~1, 3 and 5 TeV respectively.}\n\\label{fig:gamma}\n\\end{figure}\n\nFinally, we investigate the phenomenology of the regions of parameter space which are allowed by current measurements and discuss the prospects for future searches during the next run of the LHC. We plot in Fig.~\\ref{fig:gamma} the diphoton cross-section due to a $\\phi_{+}$ produced via gluon fusion at a centre-of-mass energy of 14 TeV, as a function of $m_{\\phi_{+}}$. In this and subsequent plots all points satisfy the experimental constraints discussed in section \\ref{sec:expconstraints}. The black, blue and cyan points correspond to $\\Lambda_r=$~1, 3 and 5 TeV respectively. First of all, notice that the cross-section tends to decrease for larger $m_{\\phi_{+}}$, as expected due to the mass suppression in the gluon fusion $\\phi_{+}$ production. We concentrate first on the analysis of the $\\Lambda_r=1$~TeV (black) points. As mentioned above, the lack of points in the 250--350 GeV mass range can be attributed to the contribution of $\\phi_{+}$ decays to $\\phi_{-}$ pair-production. This constraint becomes \nsuppressed for larger values of $\\Lambda_{r}$, and for larger $m_{\\phi_{+}}$ due to the reduction in the $\\phi_{+}$ production cross section. Similarly, the second empty region is related to the $t\\bar{t}$ constraints that kick in at an invariant mass $m_{t\\bar{t}}\\approx 500$~GeV and which can again be evaded by increasing $\\Lambda_r$. \n\nAnother feature that stands out is the relatively large diphoton cross-sections attained for $m_{\\phi_{+}}\\in [160, 250]$~GeV. Recall that the points in this region correspond to the case of small mixing and therefore the branching ratios of $\\phi_{+}$ are dominated by $gg$ and $b\\bar{b}$. However, any signal in these channels will be buried under the large QCD background found at the LHC. On the other hand, the clean diphoton signal remains competitive, even overtaking the well-known SM Higgs diphoton cross-section for the same mass range. This can be clearly understood from the fact that $\\phi_{+}$ has an enhanced coupling to gluons via the trace anomaly, increasing the production cross section. The diphoton channel is therefore the most promising search channel in this mass range and even extending up to the $t\\bar{t}$ threshold since, unlike the SM Higgs, the branching fraction to photons does not drop off at higher masses due to the conformal contribution to the coupling. We therefore strongly encourage \nthe CMS and ATLAS collaborations to extend their diphoton searches to invariant masses above the current $m_{\\gamma\\gamma}=150$~GeV bound. \n\n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics[height=7cm]{figs\/tt_m+_new.png}\n\\end{center}\n\\caption{Gluon fusion cross section times branching ratio for $\\phi_+\\rightarrow t\\bar{t}$ as a function of mass. The black, blue (dark grey) and cyan (light grey) points are for $\\Lambda_r=$~1, 3 and 5 TeV respectively.}\n\\label{fig:tt}\n\\end{figure}\n\nFig.~\\ref{fig:tt} shows a similar plot of the cross section for a $\\phi_{+}$ produced via gluon fusion and then decaying to $t\\bar{t}$, as a function of $m_{\\phi_{+}}$. While this search channel currently only provides constraints for $\\Lambda_r=1$~TeV, we expect it to become an important channel for masses $m_{\\phi_{+}}>500$~GeV with additional integrated luminosity. It provides sensitivity to scenarios with small mixing, where the branching fraction to $t\\bar{t}$ dominates. It is particularly sensitive to cases where the mixing parameters in our effective Lagrangian are negative, since this results in an enhanced coupling to $t\\bar{t}$ due to the Higgs and radion couplings to the top quark combining constructively. Searches in the $t\\bar{t}$ channel will also be important in the high mass region, $m_{t\\bar{t}}\\gtrsim 1$~TeV, where the decay products are highly boosted and may be collimated into a single jet. Such boosted topologies are already considered by current searches at high invariant mass\\cite{\nChatrchyan:2013lca}, although do not currently provide constraints on our model. \n\n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics[height=7cm]{figs\/ZZ_m+_new.png}\n\\end{center}\n\\caption{Gluon fusion cross section times branching ratio for $\\phi_+\\rightarrow ZZ$ as a function of mass. The black, blue (dark grey) and cyan (light grey) points are for $\\Lambda_r=$~1, 3 and 5 TeV respectively.}\n\\label{fig:ZZ}\n\\end{figure}\n\n Finally, in Fig.~\\ref{fig:ZZ} we show the cross section times branching ratio for $\\phi_{+}$ decaying to $ZZ$ as a function of $m_{\\phi_{+}}$. Again one can clearly see the regions below 1 TeV, and in particular below 500 GeV, where searches in this channel are already restricting the allowed parameter space, even for larger values of $\\Lambda_r=5$~TeV. We also note that there are a significant number of points with relatively large cross sections, $\\sim 0.1$ pb, for $m_{\\phi_{+}}\\gtrsim 1$~TeV. These points correspond to cases where there is a large mixing, since as discussed in section~\\ref{sec:couplings}, the radion coupling to massive gauge bosons is suppressed when the Higgs is placed in the bulk. On the other hand there are a large number of points with smaller mixing where the cross section is highly suppressed. This ability to suppress the signal in the $ZZ$ (and $WW$) channels provides a distinct difference from the commonly considered brane Higgs scenarios. Hence, while the $ZZ$ channel has \nsensitivity across the entire mass range considered, other channels will be essential to probe the full parameter space. In conclusion we note that the various searches are in fact complementary, with the $ZZ$\/$WW$ channels providing the best sensitivity in cases with large mixing, while the $\\gamma\\gamma$ and $t\\bar{t}$ channels are important to probe cases where the mixing is small.\n\n\n\\section{Conclusions}\nA light scalar field, associated with the radius stabilization of a compactified extra dimension, is a generic prediction of warped 5D models. In the effective 4D picture this maps to a pseudo-Nambu-Goldstone mode associated with the spontaneous breaking of the conformal symmetry.  The phenomenology of the radion is sensitive to the 5D configuration. In the case of the brane Higgs or the Gauge-Higgs unification scenario, the IR brane assumes a physical significance. In the former picture it is the location of the Higgs, while in the latter it plays a crucial role in breaking of the 5D gauge symmetry through twisted boundary conditions. The existence of the IR brane breaks the conformal symmetry spontaneously, but the presence of a localized Higgs, or the twisted boundary conditions in the GHU case, leads to an explicit breaking of the conformal symmetry. This in turn implies a direct coupling of the radion to the massive gauge bosons which dominates its phenomenology. On the other hand,  we find that in the \nbulk Higgs case,  where the IR brane can be technically pushed to infinity,  the coupling to the massive gauge bosons are suppressed thus providing a significantly different phenomenological scenario.\n\nIn this paper we have surveyed 5D scenarios such as the brane Higgs, bulk Higgs and the GHU scenario. Leading contributions from the back reaction of bulk fields that stabilize the extra-dimension were considered. We find that the bulk Higgs scenario provides a distinct and rich phenomenology at colliders. We derived the most generic 4D effective action of the radion\/dilaton-Higgs sector for the bulk SM configuration. The relevant couplings of the radion and the bulk Higgs were then computed. The radion coupling to the massive gauge bosons gets suppressed as the radion-Higgs mixing decreases. Thus a relatively unmixed light radion can evade existing experimental searches which are heavily dependent on it decaying to massive gauge bosons. We performed an extensive scan of the parameter space to uncover regions that pass all existing collider bounds with the identification of a light mostly Higgs-like state and a heavier mostly radion-like state.\n\nWe find that radion masses as light as 160 GeV are allowed and may have remained hidden in the existing searches. For masses above 250 GeV, decays of the heaviest radion-like state into pairs of light Higgs-like states can contribute to their production by up to 30$\\%$. We find that the heaviest mostly radion-like state can be divided into several categories depending on its mass and the extent of the mixing. Below 250 GeV the surviving region corresponds to an almost pure radion-like state with suppressed couplings to massive gauge bosons. The $\\gamma\\gamma$ channel may be the most sensitive in this region and potentially remain viable at higher masses. Above 500 GeV, both the $t\\bar{t}$ and diboson channels will be important at the LHC 14 TeV, in cases of small and large mixing respectively. Beyond $\\Lambda_r =1$ TeV scale a large mixing between the radion and the Higgs may be tolerated by the present data. We find that the diphoton, diboson and $t\\bar{t}$ channels are complementary and can be used to \nexplore large regions of the parameter space. In light of this we urge our experimental colleagues to extend their $\\gamma\\gamma$ analysis to higher mass scales beyond 150 GeV.\n\n\n\\section*{Acknowledgements}\n\nWe would like to thank Tony Gherghetta for helpful discussions and comments on the manuscript, as well as Hiroshi de Sandes for helpful discussions. This work was supported by the Australian Research Council.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction and statement of results}\n\nLet $n$ be a positive integer.  A \\textit{partition} of $n$ is a weakly decreasing sequence of positive integers that sum to $n$. The number of partitions of $n$ is denoted by $p(n)$. For example, one has $p(4) = 5$, since the relevant partitions are \n\\begin{align*}\n    4, \\qquad 3+1, \\qquad 2+2, \\qquad 2+1+1, \\qquad 1+1+1+1. \n\\end{align*}\nWhen $\\lambda_1 + \\cdots + \\lambda_r = n$, the $\\lambda_j$ are called the \\textit{parts} of the partition $\\lambda = (\\lambda_1, ..., \\lambda_r)$, and we write $\\lambda \\vdash n$ to denote that $\\lambda$ is a partition of $n$. The partition function has no elementary closed formula, nor does it satisfy any finite order recurrence. However, when defining $p(0) := 1$, its generating function has the following product expansion\n\\begin{align}\n\\label{partitionproduct} \\sum_{n \\geq 0} p(n)q^n = \\prod_{k \\geq 1} \\frac{1}{1-q^k} = \\frac{q^{\\frac{1}{24}}}{\\eta(\\tau)},\n\\end{align}\nwhere as usual $q := e^{2\\pi i \\tau}$ and $\\eta(\\tau)$ denotes the Dedekind eta function. In \\cite{hardyramanujan}, Hardy and Ramanujan used \\eqref{partitionproduct} to show the asymptotic formula \n\\begin{align}\n\\label{partitionasy} p(n) \\sim \\frac{1}{4\\sqrt{3} n} \\exp\\left( \\pi \\sqrt{\\frac{2n}{3}}\\right), \\qquad n \\rightarrow \\infty.\n\\end{align}\n\nFor their proof they introduced the circle method, certainly one of the most useful tools in modern analytic number theory. The now so-called Hardy--Ramanujan circle method uses modular type transformations to obtain a divergent asymptotic expansion whose truncations approximate $p(n)$ up to small errors. A later refinement by Rademacher \\cite{Rademacher}, exploiting the modularity of $\\eta(\\tau)$, provides a convergent series for $p(n)$.\n\nIn this work we study the distribution of ordinary partitions whose number of parts are congruent to some residue class $a$ modulo $b$.\\footnote{A similar sounding, but entirely different problem is to study the total number of parts that are all congruent to $a$ modulo $b$.  This problem was studied in detail by Beckwith--Mertens \\cite{BeckwithMertens2,BeckwithMertens1} for ordinary partitions and recently by Craig \\cite{Craig} for distinct parts partitions.} The number of such partitions $\\lambda \\vdash n$ is denoted by $p(a,b,n)$.\\footnote{Note that the number of partitions $\\lambda \\vdash n$ with largest part $\\ell(\\lambda)$ equals the number of partitions with number of parts $\\ell(\\lambda)$ (see also \\cite{andrewsbook}, Ch. 1), so the results of this paper can be reformulated taking number of parts into account instead.} It is well-known \nthat the numbers $p(a,b,n)$ are asymptotically equidistributed; i.e., \n\\begin{align} \\label{pequa}\n    p(a,b,n) \\sim \\frac{p(n)}{b}, \\qquad n \\to \\infty. \n\\end{align}\nThe proof of \\eqref{pequa} begins by writing the generating function for $p(a,b,n)$ in terms of non-modular eta-products twisted with roots of unity modulo $b$ which is a direct consequence of the orthogonality of roots of unity:\n\\begin{align} \\label{pgen}\n    \\sum_{n \\geq 0} p(a,b,n)q^n = \\frac{1}{b} \\left( \\frac{q^{\\frac{1}{24}}}{\\eta(\\tau)} + \\sum_{b-1 \\geq j \\geq 1}\\frac{\\zeta_b^{-ja}}{ \\left(\\zeta_b^jq; q\\right)_\\infty}\\right),\n\\end{align}\nwhere $(a;q)_\\infty := \\prod_{n \\geq 0} (1-aq^n)$ denotes the usual $q$-Pochhammer symbol and $\\zeta_b := e^{\\frac{2\\pi i}{b}}$. Since the first term does not depend on $a$ and dominates the other summands, \\eqref{pequa} can be seen as a corollary of \\eqref{pgen}. Similar results have also been proved for related statistics. For example, the rank of a partition is defined to be the largest part minus the number of parts; Males \\cite{Males} showed that the Dyson rank function $N(a,b,n)$ (the number of partitions with rank congruent to $a$ modulo $b$) is asymptotically equidistributed. Males' proof uses Ingham's Tauberian theorem \\cite{Ingham} and exploits the modularity of the generating function of $N(a,b,n)$, which is given in terms of twisted generalizations of one of Ramanujan's famous mock theta functions. \nIn contrast, the twisted eta-products in \\eqref{pgen} lack modularity.\n\n\n\n\n\n\n\nIf we now consider differences, $p(a_1,b,n)-p(a_2,b,n)$, the main terms in \\eqref{pgen} cancel and the behavior must be determined by secondary terms. In the following example we look at the differences of two modulo 5 partition functions. \n\n\\begin{example}\nConsider the case $a_1 = 1$, $a_2 = 4$ and $b = 5$. The $q$-series of the differences has the following oscillating shape \n\\begin{align*}\n    \\sum_{n \\geq 0} \\left(p(1,5,n) - p(4,5,n)\\right)q^n  = \\ &  q+q^2+q^3 -q^7-2 q^8 -3 q^9-4 q^{10} -4 q^{11}-5 q^{12} -6 q^{13}-7 q^{14} \\\\ \n    &-7 q^{15}-7 q^{16}  - \\cdots + 2q^{22} + \\cdots + 109q^{40} + \\cdots + 11q^{48} - 24q^{49} \\\\ \n    \\vspace{1cm}\n    &- \\cdots - 1998q^{75} - \\cdots - 266q^{85} + 163q^{86} + \\cdots + 40511 q^{120} + \\cdots \\\\ \n    \\vspace{1cm}\n    &+ 3701 q^{133} -3587 q^{134} - \\cdots .\n\\end{align*} \n\n\\begin{figure}[H]\n         \\centering\n         \\includegraphics[width=120mm,height= 55mm]{1-4-5-log.png}\n        \\caption{For $b= 5$, $a_1 = 1$, and $a_2=4$, we plot  the difference $p(1,5,n)-p(4,5,n)$ with log-scaling. The abrupt vertical changes in the graph indicate the location of the sign changes in the sequence. }\n\\label{fig:log145}\n\\end{figure}\n\\end{example}\n\nOur first result predicts this oscillation as follows.  As usual, we define the dilogarithm for $|z|\\leq 1$ by the generating series\n$$\n\\mathrm{Li}_2(z):=\\sum_{n \\geq 1} \\frac{z^n}{n^2}.\n$$\nThroughout we use the principle branch of the complex square root and logarithm.\n\\begin{theorem} \\label{ThmA} Let $b \\geq 5$ be an integer. Then for any two residue classes $a_1 \\not\\equiv a_2 \\pmod{b}$, we have\n\\begin{align*}\n    \\frac{p(a_1,b,n) - p(a_2,b,n)}{B n^{-\\frac34} \\exp\\left(2\\lambda_1 \\sqrt{n}\\right)} = \\cos\\left(\\beta + 2\\lambda_2 \\sqrt{n}\\right) + o(1),\n\\end{align*}\nas $n \\to \\infty$, where\\footnote{Here and throughout we take the principal branch of the square-root and upcoming logarithms.} $\\lambda_1 + i\\lambda_2 := \\sqrt{\\mathrm{Li}_2(\\zeta_b)}$ and $B > 0$ and $0 \\leq \\beta < 2\\pi$ are implicitly defined by \n\\begin{align*}\n    Be^{i\\beta} := \\frac{1}{b}(\\zeta_b^{-a_1} - \\zeta_b^{-a_2}) \\sqrt{\\frac{(1 - \\zeta_b)(\\lambda_1 + i\\lambda_2)}{\\pi}}.\n\\end{align*}\n\\end{theorem}\nA more general version of Theorem \\ref{ThmA} holds for values $b \\geq 2$, see Theorem \\ref{T:simpledifferences}, where the special cases $b \\in \\{2,3,4\\}$ have to be treated slightly differently.  Figure 2 shows that this prediction is surprisingly accurate even for small $n$.\n\\begin{figure}[H]\n         \\centering\n         \\includegraphics[width=120mm,height= 70mm]{1-4-5normalized.png}\n       \n\\label{fig:difffigintro}\n\n\\caption{The plot shows the sign changes of $p(1,5,n)-p(4,5,n)$. The blue dots depict the function $\\frac{p(1,5,n)-p(4,5,n)}{Bn^{-\\frac34}e^{2\\lambda_1\\sqrt{n}}}$ and the red line is the asymptotic prediction  $\\cos\\left(\\beta + 2\\lambda_2 \\sqrt{n}\\right)$. The approximate values of the constants are $B \\approx 0.23268$, $\\beta \\approx 1.4758$, $\\lambda_1 \\approx 0.72984$, and $\\lambda_2\\approx 0.68327$.}\n\\end{figure}\n\n\n\n\n\n\n\n\n The proof makes use of \\eqref{pgen} and a detailed study of the coefficients $\\sum_{n \\geq 0} Q_n(\\zeta)q^n := (\\zeta q; q)^{-1}_\\infty$ when $\\zeta$ is a root of unity.  Prompted by a question of Stanley, a study of the polynomials $Q_n(\\zeta)$ and their complex zeroes was undertaken in a series of papers by Boyer, Goh, Keith and Parry (see \\cite{Boyergoh,Boyergoh2,Boyerkeith,Boyerparry,Parry}), and the functions $(\\zeta q; q)^{-1}_\\infty$ have also been studied in recent work of Bringmann, Craig, Males, and Ono \\cite{BrigmannOnoMales} in the context of distribution of homology of Hilbert schemes and $t$-hook lengths.  Asymptotics for $Q_n(\\zeta)$ were studied by Wright \\cite{Wright} when $\\zeta$ is any positive real number, and then by  Boyer and Goh \\cite{Boyergoh,Boyergoh2} for $|\\zeta|\\neq 1$.  Our results essentially complete this study, proving asymptotics when $\\zeta$ is any root of unity.  \n \n We use the circle method in the form of Parry \\cite{Parry} as a template; however, significant technical effort is required to bound minor arcs that one does not encounter when $|\\zeta|\\neq 1$.  For example, we have to overcome the fact that when $\\zeta$ is a root of unity, the series representation of the polylogarithm $\\mathrm{Li}_s(\\zeta)$ does not converge for $\\mathrm{Re}(s) < 0$. \n \n \n Asymptotics in the case that $b \\geq 5$ are as follows, and a general version with the sporadic cases $b \\in \\{2,3,4\\}$ is stated in Theorem \\ref{T:twistedetaproduct}.\n\\begin{theorem} \\label{ThmB} Let $b \\geq 5$. Then we have\n\\begin{align*}\n    Q_n\\left(\\zeta_b\\right) \\sim \\frac{\\sqrt{1-\\zeta_b}\\mathrm{Li}_2\\left(\\zeta_b\\right)^{\\frac14}}{2\\sqrt{\\pi}n^{\\frac34}}\\exp\\left( 2\\sqrt{\\mathrm{Li}_2\\left(\\zeta_b\\right)}\\sqrt{n}\\right), \\qquad n \\to \\infty.\n\\end{align*}\n\\end{theorem}\n  \n\n\n \\begin{remark} Our techniques for bounding minor arcs seem not to readily apply when $|\\zeta|=1$ and $\\zeta$ is not a root of unity, so we leave it as an open problem to prove asymptotic formulas for $Q_n(\\zeta)$ in this case.  Boyer and Goh \\cite{Boyergoh} prove that the unit circle is part of the {\\it zero attractor} of the polynomials $Q_n(\\zeta)$, and it follows from their results that asymptotic formulas for $Q_n(\\zeta)$ cannot be uniform on any subset of $\\mathbb{C}$ which is an open neighborhood of an arc of the unit circle.\n \n Furthermore, note that taking $\\zeta \\to 1$ in Theorem \\ref{ThmB} does not recover the Hardy--Ramanujan asymptotic formula \\eqref{partitionasy}.\n \\end{remark}\n\n\nThe above results can be further developed to linear combinations of $p(a,b,n)$ (where $b$ is fixed). Each relevant combination $\\sum_{0 \\leq a < b} c_a p(a,b,n)$ corresponds to a polynomial \\newline $P(x) := \\sum_{0 \\leq j < b} c_a x^a$ via $p(a,b,n) \\mapsto x^a$. Perhaps the most combinatorially interesting cases are $c_a \\in \\{0, \\pm1 \\}$; i.e., differences of partition numbers. This means that for any two nonempty disjoint subsets $S_1, S_2 \\subset [0, b-1]$ of integers, we consider the differences \n\\begin{align*}\n    \\sum_{a \\in S_1} p(a,b,n) - \\sum_{a \\in S_2} p(a,b,n).\n\\end{align*}\n\nThe asymptotic behavior of these differences is described in Theorem \\ref{T:differenceswithsets}. When choosing the coefficients $c_a$ properly we can reduce the growth of the difference terms by canceling main terms. By doing so, we see that actually all formulas of Theorem \\ref{ThmB} are required (as well as the sporadic cases described in Theorem \\ref{T:twistedetaproduct}). In contrast, one can deduce formula \\eqref{pequa} by only elementary means without a thorough analysis of the coefficients $Q_n(\\zeta)$. \n\n\n\nMoreover, for families of partition numbers, one can consider growth and sign changes simultaneously.  Of special interest here is the fact that any shift of $(S_1, S_2)$ to $(S_1+r,S_2+r)$ changes the ``phase\" but not the ``amplitude\" of the asymptotic terms. The following example demonstrates this fact.\n\n\\begin{example}\\label{Ex:mod12combs} Let $b = 12$. For the sets $S_1 := \\{1,2,5\\}$ and $S_2 := \\{0,3,4\\}$, we find \\newline $P_{S_1, S_2}(x) = x^5-x^4-x^3+x^2+x-1= (x-1)\\Phi_{12}(x)$, where $\\Phi_{12}(x)$ is the 12th cyclotomic polynomial. The corresponding difference of partition numbers is\n\\begin{align*}\n    p(5,12,n) - p(4,12,n) - p(3,12,n) + p(2,12,n) + p(1,12,n) - p(0,12,n).\n\\end{align*}\nBy shifting the sets with integers $0 \\leq r \\leq 6$, we find that, more generally, all differences \n\\begin{align*}\n    \\Delta_r(n) & := p(5+r,12,n) - p(4+r,12,n) - p(3+r,12,n)\\\\&\\hspace{4cm}  + p(2+r,12,n) + p(1+r,12,n) - p(r,12,n)\n\\end{align*}\nhave the same growth in their amplitudes but have different phases of sign changes. Since $ P_{S_1, S_2}(x)$ has zeros $\\{1, \\pm \\zeta_{12}, \\pm \\zeta^5_{12}\\}$, the dominating term in the asymptotic expansion is induced by the root of unity $\\zeta_6$. In fact, we obtain \n\\begin{align} \\label{Deltar}\n    \\frac{\\Delta_r(n)}{An^{-\\frac34}\\exp\\left(2\\lambda_1 \\sqrt{n}\\right)} = \\cos\\left(\\alpha - \\frac{2\\pi r}{6} + 2\\lambda_2 \\sqrt{n} \\right) + o(1),\n\\end{align}\nwith $\\lambda_1 + i\\lambda_2 = \\sqrt{\\mathrm{Li}_2(\\zeta_6)}$, where $A > 0$ and $\\alpha \\in [0,2\\pi)$ are defined by \n$$Ae^{i\\alpha} = \\frac{\\left(1 - i\\sqrt{3}\\right)^{\\frac32}}{12\\sqrt{2\\pi}} \\mathrm{Li}_2(\\zeta_6)^{\\frac{1}{4}}.$$\nNote that $A$, $\\alpha$, $\\lambda_1$ and $\\lambda_2$ all do not depend on the choice of $r$.  One can then asymptotically describe the regions of $n$, where \n\n$$\n    p(5,12,n) + p(2,12,n) + p(1,12,n) > p(4,12,n) + p(3,12,n) + p(0,12,n), \n$$\nand vice versa, using formula \\eqref{Deltar}. Additionally, since $\\mathrm{Re}(\\sqrt{\\mathrm{Li}_2(\\zeta_6)}) < \\mathrm{Re}(\\sqrt{\\mathrm{Li}_2(\\zeta_{12})})$, we note with the help of Theorem \\ref{ThmA} that\n\\begin{align*}\n    \\limsup_{n \\to \\infty} \\left| \\frac{p(a_1, 12, n) - p(a_2, 12, n)}{n^{-\\frac{3}{4}}\\exp\\left(2\\mathrm{Re}(\\mathrm{Li}_2(\\zeta_6))\\sqrt{n}\\right)}\\right| = \\infty.\n\\end{align*}\nThis implies some form of cancellation within the higher differences $\\Delta_r(n)$, that ``exceeds\" that of simple differences modulo $12$.  \\end{example} \n\nIn contrast to Example \\ref{Ex:mod12combs}, when $b$ is prime, one cannot decrease the order of growth below simple differences using any rational combination of the $p(a,b,n)$.  This is shown in Section 3.\n\n\n\n\n\nThe paper is organized as follows. In Section 2, we collect some classic analytical tools and prove some key lemmas. This includes a careful study of the dilogarithm function $\\mathrm{Li}_2(z)$ for values $|z|=1$. In Section 3, we state our main result, Theorem \\ref{T:twistedetaproduct}, and applications.  We prove Theorem \\ref{T:twistedetaproduct} in Sections 4 and 5 using the circle method.  Section 5 deals with the primary difficulty of bounding the minor arcs.\n \n\n\n\\section*{Acknowledgements}\nWe would like to thank Kathrin Bringmann, Joshua Males, Caner Nazaroglu, Ken Ono and Wadim Zudilin for useful discussions and for making comments on an earlier version of this paper.  We are grateful to the referees for their detailed comments that improved the exposition.\n\nThe first author is partially supported by the SFB\/TRR 191 ``Symplectic Structures in Geometry, Algebra and Dynamics'', funded by the DFG (Projektnummer 281071066 TRR 191).\n\nThe second author is partially supported by the Alfried Krupp prize. \n\n\\section{Preliminaries} \n\nWe will need several analytical results in this work, which we collect in this section. Much of the items here are discussed in works such as \\cite{Bringmannbook,BMJS,CaTir,IwanKow,Pinsky,Asymptbook}. The reader can skip this section and refer back to it as needed as we work through the proofs of our main theorems. \n\n\\subsection{Classical asymptotic analysis and integration formulas}\nA first tool is the well known Laplace's method for studying limits of definite integrals with oscillation, which we will use for evaluating Cauchy-type integrals.\n\\begin{theorem}[Laplace's method, see Section 1.1.5 of \\cite{Pinsky}]\\label{laplacemethod}\n   Let $A,B: [a,b]\\to \\mathbb{C}$ be continuous functions. Suppose $x\\neq x_0 \\in [a,b]$ such that $\\mathrm{Re}(B(x))<\\mathrm{Re}(B(x_0)),$ and that \n   \\begin{align*}\n       \\lim_{x\\to x_0}\\frac{B(x)-B(x_0)}{(x-x_0)^2} = -k\\in \\mathbb{C},\n   \\end{align*}\n   with $\\mathrm{Re}(k)>0.$ Then as $t \\to \\infty$\n   \\begin{align*}\n       \\int^b_{a}A(x)e^{tB(x)}dx = e^{tB(x_0)}\\left(A(x_0)\\sqrt{\\frac{\\pi}{tk}}+o\\left(\\frac{1}{\\sqrt{t}}\\right)\\right).\n   \\end{align*}\n\\end{theorem}\nWe are ultimately interested in how the coefficients of a series $S(q):= \\sum_{n\\geq 0}a(n)q^n$ grow as $n\\to \\infty$. The classical Euler--Maclaurin summation formulas can be applied in many cases to link the growth of $a(n)$ to the growth of $S(q)$ as $q$ approaches the unit circle. We state the Euler--Maclaurin summation formulas in two different forms. \n\n\\begin{theorem} [classical Euler--Maclaurin summation, see p. 66 of \\cite{IwanKow}]\\label{T:EulerMac}\n    Let $\\{x\\}:=x - \\lfloor x \\rfloor$ denote the fractional part of $x$. For $N \\in \\mathbb{N}$ and $f:[1, \\infty) \\to \\mathbb{C}$ a continuously differentiable function, we have\n    $$\n    \\sum_{1 \\leq n \\leq N} f(n)=\\int_1^N f(x)dx+\\frac{1}{2}(f(N)+f(1))+\\int_1^N f'(x)\\left(\\{x\\}-\\frac{1}{2}\\right)dx.\n    $$\n\\end{theorem}\n\nWe use a second formulation, due to Bringmann--Mahlburg--Jennings-Shaffer, to study the asymptotics of series with a complex variable approaching 0 within a fixed cone in the right-half plane.  It is not stated in \\cite{BMJS}, but one can conclude from the proof that Theorem \\ref{T:BMJS} is uniform in $0 \\leq a \\leq 1.$\n  \\begin{theorem}[uniform complex Euler--Maclaurin summation, \\cite{BMJS}, Theorem 1.2] \\label{T:BMJS}\n      Suppose $0\\leq \\theta < \\frac{\\pi}{2}$ and suppose that $f:\\mathbb{C}\\to \\mathbb{C}$ is holomorphic in a domain containing $\\{re^{i\\alpha}: |\\alpha| \\leq \\theta\\}$ with derivatives of sufficient decay; i.e., there is an $\\varepsilon >0$ such that for all $m$ $f^{(m)}(z) \\ll z^{-1-\\varepsilon}$ as $z \\to \\infty$.  Then uniformly for $a \\in [0,1]$, we have\n      $$\n      \\sum_{\\ell \\geq 0} f(w(\\ell+a))=\\frac{1}{w}\\int_0^{\\infty} f(w)dw -\\sum_{n=0}^{N-1} \\frac{f^{(n)}(0)B_{n+1}(a)}{(n+1)!}w^n+O_N\\left(w^{N}\\right),\n      $$\n      uniformly as $w \\to 0$ in $\\mathrm{Arg}(w)\\leq \\theta$.\n  \\end{theorem}\n  \n  To identify a constant term in our asymptotic formula, we cite the following integral calculation of Bringmann, Craig, Males and Ono.\n\\begin{lemma}[\\cite{BrigmannOnoMales}, Lemma 2.3]\\label{L:Bringmannintegral}\nFor $a \\in \\mathbb{R}^+,$\n\\begin{align*}\n    \\int_0^{\\infty} \\left(\\frac{e^{-ax}}{x(1-e^{-x})}-\\frac{1}{x^2}-\\left(\\frac{1}{2}-a \\right) \\frac{e^{-ax}}{x} \\right)dx =\\log \\left(\\Gamma \\left(a \\right)\\right)+\\left(\\frac{1}{2}-a\\right)\\log\\left(a \\right)-\\frac{1}{2}\\log(2\\pi).\n\\end{align*}\n\\end{lemma}\n\nFinally, we will use Abel partial summation extensively when bounding the twisted eta-products on the minor arcs.\n\n  \\begin{proposition}[Abel partial summation, see p. 3 of \\cite{Tenenbaum}]\\label{P:Abelpartialsummation}\nLet $N \\in \\mathbb{N}_0$ and $M \\in \\mathbb{N}$. For sequences $\\{a_n\\}_{n \\geq N}$, $\\{b_n\\}_{n \\geq N}$ of complex numbers, if $A_n:=\\sum_{N < m \\leq n} a_m,$  then\n  $$\n  \\sum_{N < n \\leq N+M} a_nb_n=A_{N+M}b_{N+M}+\\sum_{N < n < N+M} A_n(b_n-b_{n+1}).\n  $$\n  \\end{proposition}\n\n\n\\subsection{Elementary bounds}\n  The following bound for differences of holomorphic functions will be used in conjunction with Abel partial summation during the course of the circle method. The proof of the following is a straightforward application of the fundamental theorem of calculus and the maximum modulus principle.\n\\begin{lemma} \\label{L:DifferenceEstimate} Let $f : U \\to \\mathbb{C}$ be a holomorphic function and $\\overline{B_r(c)} \\subset U$ a compact disk. Then, for all $a,b \\in B_r(c)$ with $a \\not= b$, we have \n\\begin{align*}\n    \\left| f(b) - f(a)\\right| \\leq \\max_{|z - c|=r} |f'(z)| |b-a|.\n\\end{align*}\n\n\\end{lemma}\n\n\nWe also need the following elementary maximum; for a proof see \\cite{Parry}, Lemma 5.2.\n\n\\begin{lemma}\\label{L:exponentialquotientmax}\nFor $a \\in \\left(-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right)$ and $b \\in \\mathbb{R}$, we have\n$$\n\\mathrm{Re}\\left(\\frac{e^{ia}}{1+ib} \\right)\\leq \\cos^2\\left(\\frac{a}{2}\\right),\n$$\nwith equality if and only if $b$ satisfies $\\mathrm{Arg}(1+ib)=\\frac{a}{2}.$\n\\end{lemma}\n\n\\subsection{Bounds for trigonometric series and the polylogarithm}\nWe recall that for complex numbers $s$ and $z$ with $|z| < 1$ the polylogarithm $\\mathrm{Li}_s(z)$ is defined by the series\n\\begin{align*}\n    \\mathrm{Li}_s(z) := \\sum_{n \\geq 1} \\frac{z^n}{n^s}.\n\\end{align*}\nWe are especially interested in the case $s=2$, where $\\mathrm{Li}_2(z)$ is called the dilogarithm. The appendix of a recent preprint of Boyer and Parry \\cite{Boyerparry} contains many useful results on the dilogarithm, including the following key lemma.\n\n\n\\iffalse\n\\begin{proposition}[see p. 1005 of \\cite{AbramowitzStegun}] \\label{P:Dilog} We have for all $0 \\leq \\theta < 2\\pi$\n\\begin{align*}\n    \\mathrm{Li}_2\\left(e^{i\\theta}\\right) = \\frac{\\theta^2}{4} - \\frac{\\pi \\theta}{2} + \\frac{\\pi^2}{6} - i \\int_0^\\theta \\log\\left| 2\\sin\\left( \\frac{t}{2}\\right) \\right| dt.\n\\end{align*}\n\\end{proposition}\n\nWe also need some understanding of the behavior of the function $\\theta \\mapsto \\mathrm{Re}(\\sqrt{\\mathrm{Li}_2(e^{2\\pi i\\theta})})$ on intervals, since its values appear as exponents in several asymptotic formulas. To overcome the difficulties with the square root, we use the following trick.\n\n\n\\begin{lemma} \\label{L:ReSqrtPrep} Let $I$ be an interval and let $f : I \\to \\mathbb{H}$ be a continuous function satisfying the following: \\\\\n\\textup{(1)} The induced function $|f| : I \\to \\mathbb{R}$ with $x \\mapsto |f(x)|$ is decreasing. \\\\\n\\textup{(2)} The induced function $\\psi : I \\to (0, \\pi)$ with $x \\mapsto \\mathrm{Arg}(f(x))$ is increasing. \\\\\nThen the function $g : I \\to \\mathbb{R}$ with $g(x) := \\mathrm{Re}(\\sqrt{f(x)})$ is decreasing, where we consider the principal part of the square root. \n\\end{lemma} \\label{L:RealpartRoot}\n\nWe use the above tools to prove the following lemma. We put \n$$\nH^{(s)}_n := \\sum_{1 \\leq k \\leq n} \\frac{1}{k^s}.\n$$\n\\fi \n\\begin{lemma}[Proposition 4, \\cite{Boyerparry}]\\label{L:dilogdecreasing}\nThe function $\\theta \\mapsto \\mathrm{Re} \\left(\\sqrt{\\textnormal{Li}_2(e^{2\\pi i \\theta})}\\right)$ is decreasing on the interval $[0,\\frac12].$\n\\end{lemma}\n\\iffalse\n\\begin{proof} We apply Lemma \\ref{L:ReSqrtPrep} and start by showing that $\\theta\\mapsto |\\textnormal{Li}_2(e^{2\\pi i \\theta})|$ is decreasing in the interval $(0,\\frac13)$. We have \n\\begin{align*}\n    \\left|\\textnormal{Li}_2\\left(e^{2\\pi i \\theta}\\right)\\right|^2 &= \\sum_{n,m>0} \\frac{\\sin(2\\pi \\theta n)\\sin(2\\pi \\theta m)+\\cos(2\\pi \\theta n)\\cos(2\\pi \\theta m)}{m^2n^2} \\\\ \n    & = \\sum_{n,m>0}\\frac{\\cos(2\\pi\\theta(n-m))}{m^2n^2} = \\frac{\\pi^4}{90} + 2 \\sum_{n \\geq 1} A_n \\cos(2\\pi \\theta n),\n\\end{align*}\nwhere $A_n := \\sum_{m \\geq 1} \\frac{1}{m^2(m+n)^2}$. Unsing the partial fraction decomposition \n\\begin{align*}\n    \\frac{1}{x^2(x+n)^2} = \\frac{2}{n^3 (n+x)}-\\frac{2}{n^3 x}+\\frac{1}{n^2 x^2}+\\frac{1}{n^2 (n+x)^2}\n\\end{align*}\nwe find\n\\begin{align*}\n    A_n = \\frac{\\pi^2}{3n^2} - \\frac{H_n^{(2)}}{n^2} - \\frac{2H_n}{n^3},\n\\end{align*}\nwhere $H_n = H^{(1)}_n$ is the $n$-th harmonic number. As $A_n = \\frac{\\pi^2}{3n^2} + O(\\frac{\\log(n)}{n^3})$, we can take the derivative term by term to obtain \n\\begin{align*}\n \\frac{d}{d\\theta} \\left|\\textnormal{Li}_2\\left(e^{2\\pi i \\theta}\\right)\\right|^2 = -2\\pi \\sum_{n \\geq 1} nA_n \\sin(2\\pi \\theta n). \n\\end{align*}\nWe show that the sum without the scaling factor $-2\\pi$ is positive in the interval $(0,\\frac13)$. Using partial summation, we obtain \n\\begin{align*}\n    \\sum_{n \\geq 1} nA_n \\sin(2\\pi \\theta n) & = \\sum_{n \\geq 1} \\left( \\sum_{n \\geq k \\geq 1} \\sin(2\\pi \\theta k) \\right) (nA_n - (n+1)A_{n+1}) \\\\\n    & = \\sum_{n \\geq 1} \\frac{\\sin(\\pi \\theta n) \\sin(\\pi \\theta (n+1))}{\\sin(\\pi \\theta)} (nA_n - (n+1)A_{n+1}).\n\\end{align*}\nSince $(A_1 - 2A_2) \\sin(2\\pi \\theta)$ is positive for $0 < \\theta < \\frac13$, we are left with the sum $\\sum_{n \\geq 2}$. Using Abel partial summation again, we find \n\\begin{align*}\n  &\\sum_{n \\geq 2} \\frac{\\sin(\\pi \\theta n) \\sin(\\pi \\theta (n+1))}{\\sin(\\pi \\theta)} (nA_n - (n+1)A_{n+1}) \\\\\n  & = \\frac{1}{\\sin(\\pi \\theta)}\\sum_{n \\geq 2} \\left( \\sum_{n \\geq k \\geq 2}\\sin(\\pi \\theta k) \\sin(\\pi \\theta (k+1)) \\right) (nA_n - 2(n+1)A_{n+1} + A_{n+2}).\n\\end{align*}\nBy the trigonometric identity \n\\begin{align*}\n  \\sin(\\pi \\theta k) \\sin(\\pi \\theta (k+1)) + \\sin(\\pi \\theta (k+1)) \\sin(\\pi \\theta (k+2)) = 2 \\sin^2(\\pi \\theta (k+1)) \\cos\\left( \\pi \\theta\\right)\n\\end{align*}\nwe see that for odd $n$\n\\begin{align*}\n    \\sum_{n \\geq k \\geq 2}\\sin(\\pi \\theta k) \\sin(\\pi \\theta (k+1)) \\geq 0\n\\end{align*}\non $(0, \\frac13)$, and for even $n$\n\\begin{align*}\n    \\sum_{n \\geq k \\geq 2}\\sin(\\pi \\theta k) \\sin(\\pi \\theta (k+1)) = \\sin(2 \\pi \\theta) \\sin(3\\pi \\theta) + \\sum_{n \\geq k \\geq 3} \\sin(\\pi \\theta k) \\sin(\\pi \\theta (k+1)) \\geq 0\n\\end{align*}\non $(0, \\frac13)$. On the other hand, a straightforward calculation shows \n\\begin{align*}\n    & nA_n - 2(n+1)A_{n+1} + (n+2)A_{n+2} \\geq \\frac{9}{4n^3} - \\frac{12}{n^{\\frac{7}{2}}}\n    \\end{align*}\nfor $n \\geq 10$, and the last term is positive for all $n \\geq 29$. The finite cases $n = 2, ..., 28$ can easily seen numerically to be positive.\n\n\\par\nWe now show that the function $\\theta\\mapsto \\text{Arg}(\\text{Li}_2(e(\\theta))$ is increasing on the interval $(0,\\frac{1}{3})$. We abbreviate $x := \\mathrm{Re}(\\mathrm{Li}_2(e(\\theta)))$ and $y := \\mathrm{Im}(\\mathrm{Li}_2(e(\\theta)))$ as functions of $\\theta$. We compute \n\\begin{align*}\n    \\frac{d}{d\\theta}\\text{Arg}\\left(\\textnormal{Li}_2\\left(e^{2\\pi i \\theta}\\right)\\right) & = \\frac{1}{1+\\frac{y^2}{x^2}}\\left(\\frac{y'}{x}-\\frac{yx'}{x^2}\\right)= \\frac{1}{\\left|\\textnormal{Li}_2\\left(e^{2\\pi i \\theta}\\right)\\right|^2}\\left(y'x-yx'\\right) \\\\\n    & = \\frac{2\\pi}{\\left|\\textnormal{Li}_2\\left(e^{2\\pi i \\theta}\\right)\\right|^2} \\left( \\zeta(3) + \\sum_{n,m \\geq 1} \\left( \\frac{1}{m(m+n)^2} + \\frac{1}{n(n+m)^2}\\right) \\cos(2\\pi \\theta (n-m))\\right) \\\\\n    & = \\frac{2\\pi}{\\left|\\textnormal{Li}_2\\left(e^{2\\pi i \\theta}\\right)\\right|^2} \\left( \\zeta(3) + \\sum_{n \\geq 1} \\frac{H^{(2)}_n}{n} \\cos(2\\pi \\theta n)\\right). \n\\end{align*}\nSince the corresponding products of partial sums $y'_N x_N - y_N x'_N$ converge to $y'x - yx'$ in the observed interval, and for fixed $n$ the coefficients $\\frac{H^{(2)}_n}{n}$ stay unchanged as $N$ is sufficiently large, the final expression converges to $\\frac{d}{d\\theta}\\text{Arg}(\\text{Li}_2(e^{2\\pi i \\theta})$. The term $2\\pi|\\textnormal{Li}_2(e^{2\\pi i \\theta})|^{-2}$ is clearly positive. So we are left to show \n\\begin{align*}\n\\sum_{n \\geq 1} \\frac{H^{(2)}_n}{n} \\cos(2\\pi \\theta n) > - \\zeta(3)\n\\end{align*}\nfor all $0 < \\theta < \\frac13$. Using Abel partial summation, we find with Proposition \\ref{P:Dilog}\n\\begin{align*}\n\\sum_{n \\geq 1} \\frac{H^{(2)}_n}{n} \\cos(2\\pi \\theta n) & = - \\frac{\\pi^2}{6} \\log(2|\\sin(\\pi \\theta)|) - \\left( \\frac{\\pi^2}{6} - 1\\right) \\cos(2\\pi \\theta) \\\\ \n& \\hspace{5cm} - \\sum_{n \\geq 1} \\left( \\sum_{n \\geq k \\geq 2} \\frac{\\cos(2\\pi \\theta k)}{k}\\right)\\frac{1}{(n+1)^2}.\n\\end{align*}\nNow, since $|\\sum_{n \\geq k \\geq 2} \\frac{\\cos(2\\pi \\theta k)}{k}| < H_n - 1$ in the range $0 < \\theta < \\frac13$, we find\n\\begin{align}\n \\nonumber \\sum_{n \\geq 1} \\frac{H^{(2)}_n}{n} \\cos(2\\pi \\theta n) & \\geq - \\frac{\\pi^2}{6} \\log(2|\\sin(\\pi \\theta)|) - \\left( \\frac{\\pi^2}{6} - 1\\right) \\cos(2\\pi \\theta) - \\sum_{n \\geq 1} \\frac{H_n - 1}{(n+1)^2} \\\\\n \\label{eq:minimize} & = - \\frac{\\pi^2}{6} \\log(2|\\sin(\\pi \\theta)|) + \\left( \\frac{\\pi^2}{6} - 1\\right)(1 - \\cos(2\\pi \\theta)) - \\zeta(3).\n\\end{align}\nWe need to minimize the last expression on $(0, \\frac13)$. By taking the derivative, we conclude that the critical point(s) $\\theta_c$ satisfy the equation\n\\begin{align*}\n    \\cot(\\pi \\theta) = 2\\frac{\\zeta(2)-1}{\\zeta(2)}\\sin(2\\pi \\theta)= 4\\frac{\\zeta(2)-1}{\\zeta(2)}\\sin(\\pi\\theta)\\cos(\\pi\\theta),\n\\end{align*}\nwhich implies\n\\begin{align*}\n    \\sin(\\pi \\theta)= \\pm \\frac{1}{2}\\sqrt{\\frac{\\zeta(2)}{\\zeta(2)-1}}.\n\\end{align*}\nThus, the only critical point in $(0,\\frac13)$ is given by \n\\begin{align}\n    \\theta_c= \\frac{1}{\\pi}\\arcsin\\left(\\frac{1}{2}\\sqrt{\\frac{\\zeta(2)}{\\zeta(2)-1}}\\right).\n\\end{align}\nOne can easily check that this is a local minimum by the second derivative test. Substituting $\\theta_c$ into the last term of \\eqref{eq:minimize}, we find (for instance using a computer) that the output exceeds $-\\zeta(3)$, which completes the proof. \n \\end{proof}\n\\fi\n\nWe also need to consider the derivative of the function $\\theta \\mapsto \\mathrm{Li}_2(e^{2\\pi i\\theta})$ and its partial sums. Let \n\n\\begin{align*}\nG_M(\\theta) := \\sum_{1 \\leq m \\leq M} \\frac{e^{2\\pi i\\theta m}}{m}.\n\\end{align*}\nThen the following bound holds. \n\\begin{lemma} \\label{L:CosSumBound} We have, uniformly for $0 < \\theta < 1$, \n\t\\begin{align*}\n\t\\left|G_M(\\theta)\\right| \\ll \\log\\left(\\frac{1}{\\theta}\\right) + \\log\\left( \\frac{1}{1-\\theta}\\right), \\qquad M \\to \\infty. \n\t\\end{align*}\n\t\n\t\\end{lemma}\n\n\\begin{proof} Note that we have \n\t\\begin{align*}\n\tG_M(\\theta) = \\sum_{1 \\leq m \\leq M} \\frac{\\cos(2\\pi \\theta m)}{m} + i \\sum_{1 \\leq m \\leq M} \\frac{\\sin(2\\pi \\theta m)}{m},\n\t\\end{align*}\n\tand as it is well known that $\\sum_{1 \\leq m \\leq M} \\frac{\\sin(2\\pi \\theta m)}{m}$ is uniformly bounded in $\\mathbb{R}$ (see \\cite{Stein} on p. 94) we are left with the cosine sum. Let $0 < \\theta \\leq \\frac12$ and $M \\in \\mathbb{N}$. Consider the meromorphic function\n\t$$\n\th_\\theta(z) := \\frac{\\cos(2\\pi \\theta z)(\\cot(\\pi z)-i)}{2iz},\n\t$$\n\ttogether with the rectangle $R_M$ with vertices $\\frac{1}{2}-iM,\\frac{1}{2}+ \\frac{i}{\\theta}$, $\\frac{i}{\\theta} + M + \\frac12$, and $-iM + M + \\frac12$. Notice that in a punctured disk of radius $r<1$ centered at $k\\geq 1$, we have  $$ \th_\\theta(z) = \\frac{\\cos(2\\pi \\theta k)}{2ik}\\left(\\frac{1}{\\pi(z-k)}-i+O(z-k)\\right).$$ With the residue theorem we find \n\t\\begin{align*}\n\t\\oint_{\\partial R_M} h_\\theta(z) dz = 2\\pi i \\sum_{1 \\leq m \\leq M} \\mathrm{Res}_{z=m} h_\\theta(z) = \\sum_{1 \\leq m \\leq M} \\frac{\\cos(2\\pi \\theta m)}{m},  \n\t\\end{align*}\n\twhere the contour is taken once in positive direction. By the invariance of the function under the reflection $\\theta \\to 1 - \\theta$ it suffices to consider values $0 < \\theta \\leq \\frac12$. A straightforward calculation shows that the bottom side integrals are bounded uniformly in $0 < \\theta \\leq \\frac12$. Similarly, also using that $\\cot(\\pi z)$ is uniformly bounded on lines $\\{\\mathrm{Re}(z) \\in \\frac12 \\mathbb{Z} \\setminus \\mathbb{Z}\\}$ for the second part, one argues \n\t\\begin{align*} \n\t\\int_{M+\\frac12-Mi}^{M+\\frac12 + \\frac{i}{\\theta}} h_\\theta(z)dz = O(1) + \\int_{M+\\frac12}^{M+\\frac12 + \\frac{i}{\\theta}} h_\\theta(z)dz \\ll  \\int_{\\frac{1}{2}}^{\\frac{1}{2}+\\frac{i}{\\theta}} \\left| \\frac{dz}{z+M}\\right| \\ll \\log\\left( \\frac{1}{\\theta}\\right).     \n\t\\end{align*}\n A similar argument yields\n\t\\begin{align*}\n\t    \\int_{\\frac{1}{2}+\\frac{i}{\\theta}}^{\\frac{1}{2} - Mi} h_\\theta(z) dz \\ll \\log\\left( \\frac{1}{\\theta} \\right).\n\t\\end{align*}\n\t\n    For the rectangle top, note with the use of the substitution $z \\mapsto \\frac{z}{\\theta}$ we have\n\t\\begin{align} \\label{RectTopSplit}\n\t\\int_{M + \\frac12 + \\frac{i}{\\theta}}^{\\frac{1}{2}+\\frac{i}{\\theta}} h_\\theta(z) dz = \\int_{\\theta \\left(M + \\frac12\\right)+i}^{\\frac{\\theta}{2}+i} \\frac{\\cos(2\\pi z) (\\cot\\left( \\frac{\\pi z}{\\theta}\\right)+i)}{z} dz-2i \\int_{\\theta \\left(M + \\frac12\\right)+i}^{\\frac{\\theta}{2}+i}\\frac{\\cos(2\\pi z)}{z} dz.\n\t\\end{align}\n\tWith the Residue Theorem we obtain\n\t\t\\begin{align*}\n\t\\int_{\\frac{\\theta}{2}+i}^{\\theta(M+\\frac12) + i} = \\int_{\\frac{\\theta}{2}+i}^{i\\infty} + \\int_{\\theta(M+\\frac12) + i\\infty}^{\\theta(M+\\frac12) + i}.\n\t\\end{align*}\n\tand the bound $\\cos(2\\pi z)(\\cot\\left( \\frac{\\pi z}{\\theta}\\right) +i)= O(e^{-2\\pi \\mathrm{Im}(z)})$  as $\\mathrm{Im}(z) \\to \\infty$ (since $0 < \\theta \\leq \\frac12$) yields the uniform boundedness of the first integral in \\eqref{RectTopSplit}. The integral on the right hand side of \\eqref{RectTopSplit} can be bounded via standard contour integration, for instance, by using that $\\int_\\alpha^\\infty \\frac{\\cos(x)}{x} dx \\ll 1$ for all $\\alpha \\geq 1$. This completes the proof. \n\\end{proof}\n\n Lemma \\ref{L:CosSumBound} has the following important consequence.\n\n\\begin{lemma} \\label{L:Gmaxbound} Let $a$, $b$, $h$ and $k$ be positive integers, such that $\\gcd(a,b) = \\gcd(h,k) = 1$. We assume that $a$ and $b$ are fixed. Then we have\n\\begin{align*}\n    \\sum_{\\substack{1 \\leq j \\leq k \\\\ ak+bjh \\not\\equiv 0 \\pmod{bk}}} \\max_{m \\geq 1} \\left| G_m\\left( \\frac{a}{b} + \\frac{hj}{k}\\right) \\right| = O(k),\n\\end{align*}\nas $k \\to \\infty$, uniformly in $h$.\n\\end{lemma}\n\\begin{proof} The assumption $\\gcd(h,k)=1$ implies that the map $j \\mapsto hj$ is a bijection modulo $k$. One can show by elementary means that there is at most one $j_0$ such that $bk$ divides $ak+bj_0h$. First, we assume that such a $j_0$ exists. Using $G_m(x+1)=G_m(x)$, we first reorder the sum, then apply Lemma \\ref{L:CosSumBound} to obtain \n\\begin{align*}\n  \\sum_{\\substack{1 \\leq j \\leq k \\\\ j \\not= j_0}} \\max_{m \\geq 1} \\left| G_m\\left( \\frac{a}{b} + \\frac{hj}{k}\\right) \\right| = \\sum_{1 \\leq j \\leq k-1} \\max_{m \\geq 1} \\left| G_m\\left( \\frac{j}{k}\\right) \\right| &\\ll \\sum_{1 \\leq j \\leq k-1} \\left(\\log\\left(\\frac{k}{j}\\right)+\\log\\left(\\frac{k}{k-j}\\right)\\right) \\\\&= O(k)\n\\end{align*}\nby Stirling's formula. Now, assume that there is no such $j_0$. In this case we find $0 < \\alpha_{a,b,k} < b$, such that \n    \\begin{align*}\n        &\\sum_{1 \\leq j \\leq k} \\max_{m \\geq 1} \\left|G_m\\left(\\frac{a}{b}+\\frac{hj}{k}\\right)\\right| =\\max_{m \\geq 1} \\left|G_m\\left(\\frac{\\alpha_{a,b,k}}{bk}\\right)\\right|+\\max_{m \\geq 1} \\left|G_m\\left(\\frac{\\alpha_{a,b,k}}{bk}+1-\\frac{1}{k}\\right)\\right| \\\\&\\hspace{6cm} + \\sum_{1 \\leq j \\leq k-2} \\max_{m \\geq 1} \\left|G_m\\left(\\frac{\\alpha_{a,b,k}}{bk}+\\frac{j}{k}\\right)\\right|.\n    \\end{align*}\n    Using again Lemma \\ref{L:CosSumBound} and Stirling's formula, we obtain\n    \\begin{align*}\n    \\sum_{1 \\leq j \\leq k-2} \\max_{m \\geq 1} \\left|G_m\\left(\\frac{\\alpha_{a,b,k}}{bk}+\\frac{j}{k}\\right)\\right| &\\ll \\sum_{1 \\leq j \\leq k-2} \\left(\\log\\left(\\frac{k}{j}\\right)+\\log\\left(\\frac{k}{k-j}\\right)\\right) = O(k).\n    \\end{align*}\n    Since clearly \n    $$\\max_{m \\geq 1} \\left|G_m\\left(\\frac{\\alpha_{a,b,k}}{bk}\\right)\\right| + \\max_{m \\geq 1} \\left|G_m\\left(\\frac{\\alpha_{a,b,k}}{bk}+1-\\frac{1}{k}\\right)\\right| = O(\\log (k)),$$ the lemma follows.\n    \\end{proof}\n\n\n\n\\section{Main results and applications}\n\\subsection{Twisted eta-products}\n\nIn this section, we record the general asymptotic formula for $Q_n(\\zeta)$ where $\\zeta$ is any root of unity.  Note that $\\overline{Q_n(\\zeta)}=Q_n(\\overline{\\zeta})$, so it suffices to find asymptotic formulas for $\\zeta$ in the upper-half plane.  The following theorem of Boyer and Goh \\cite{Boyergoh} regarding the dilogarithm distinguishes several cases in our main theorem.  Following \\cite{Boyergoh}, we define\n$$\n\\Psi_k(\\theta):=\\mathrm{Re}\\left(\\frac{\\sqrt{\\mathrm{Li}_2(e^{ik \\theta})}}{k}\\right), \\qquad \\text{for $0 \\leq \\theta \\leq \\pi,$  }\n$$\nand\n$$0<\\theta_{13}<\\frac{2\\pi}{3}<\\theta_{23}<\\pi$$\nwhere each $\\theta_{jk}$ is a solution to $\\Psi_j\\left(\\theta\\right)=\\Psi_k\\left(\\theta\\right)$.\nHere,\n$$\n\\theta_{13}=2.06672\\dots , \\quad \\theta_{23}=2.36170\\dots.\n$$\nSince the values $\\theta_{13}$ and $\\theta_{23}$ arise as solutions to a non-algebraic equation, it is very unlikely that they are rational multiples of $\\pi$. Therefore, we will no longer consider them in future investigations. \n\\begin{theorem}[\\cite{Boyergoh}, discussion prior to Theorem 2]\\label{T:BoyerGoh}\nFor $0\\leq \\theta \\leq  \\pi$, we have\n$$\n\\max_{k \\geq 1} \\Psi_k(\\theta)=\\begin{cases} \\Psi_1(\\theta) & \\text{if $\\theta \\in [0,\\theta_{13}]$,} \\\\\n\\Psi_2(\\theta) & \\text{if $\\theta \\in [\\theta_{23},\\pi]$,}\n\\\\\n\\Psi_3(\\theta) &  \\text{if $\\theta \\in  [\\theta_{13},\\theta_{23}]$.}\\end{cases}\n$$\n\\end{theorem}\nFollowing \\cite{Parry}, define \n$$\n\\omega_{h,k}(z):=\\prod_{j=1}^k \\left(1-z \\zeta_k^{-jh}\\right)^{\\frac{j}{k}-\\frac{1}{2}}.\n$$\nWe have the following asymptotic formulas.\n\\begin{theorem}\\label{T:twistedetaproduct}\n\n\\textup{(1)} If $2\\pi \\frac{a}{b}\\in (0,\\theta_{13}),$ then\n$$\nQ_n\\left(\\zeta_b^a\\right) \\sim \\frac{\\sqrt{1-\\zeta_b^a}\\mathrm{Li}_2\\left(\\zeta_b^a\\right)^{\\frac14}}{2\\sqrt{\\pi}n^{\\frac34}}\\exp\\left({2\\sqrt{\\mathrm{Li}_2\\left(\\zeta_b^a\\right)}\\sqrt{n}}\\right), \\qquad n \\to \\infty.\n$$\n\\textup{(2)} If $2\\pi \\frac{a}{b}\\in (\\theta_{23},\\pi),$ then\n$$\nQ_n\\left(\\zeta_b^a\\right) \\sim \\frac{(-1)^n\\sqrt{1-\\zeta_b^a}\\mathrm{Li}_2\\left(\\zeta_b^{2a}\\right)^{\\frac14}}{2\\sqrt{2\\pi}n^{\\frac34}}\\exp\\left({\\sqrt{\\mathrm{Li}_2\\left(\\zeta_b^{2a}\\right)}\\sqrt{n}}\\right), \\qquad n \\to \\infty.\n$$\n\\textup{(3)} If $2\\pi \\frac{a}{b}\\in (\\theta_{13},\\theta_{23})\\setminus \\left\\{\\frac{2\\pi}{3}\\right\\},$ then\n$$\nQ_n\\left(\\zeta_b^a\\right) \\sim (\\zeta_3^{-n}\\omega_{1,3}(\\zeta_b^{a})+\\zeta_3^{-2n}\\omega_{2,3}(\\zeta_b^{a}))\\frac{\\mathrm{Li}_2(\\zeta_b^{3a})^{\\frac14}}{2\\sqrt{3\\pi}n^{\\frac34}}\\exp\\left(\\frac{2}{3}\\sqrt{\\mathrm{Li}_2(\\zeta_b^{3a})}\\sqrt{n}\\right), \\qquad n \\to \\infty.\n$$\n\\textup{(4)}  We have\n$$\n   Q_n\\left( \\zeta_3\\right)\\sim \\frac{\\zeta_3^{-2n}(1- \\zeta_3^2)^{\\frac16}(1- \\zeta_3)^{\\frac12}\\Gamma\\left(\\frac{1}{3}\\right)}{2(6\\pi n)^{\\frac23}}\\exp\\left( \\frac{2\\pi}{3}\\sqrt{\\frac{n}{6}}\\right), \\qquad n \\to \\infty.\n$$\n\\end{theorem}\n\nWe prove Theorem \\ref{T:twistedetaproduct} in Sections 4 and 5.\n\n\n\\begin{remark}\nRecall that we have the asymptotic formula \\eqref{partitionasy} for $Q_n(1)=p(n)$, whereas for $Q_n(-1)$, standard combinatorial methods give\n$$\n\\sum_{n \\geq 0} Q_n(-1)q^n=\\frac{1}{(-q;q)_{\\infty}}=\\frac{\\left(q;q\\right)_{\\infty}}{(q^2;q^2)_{\\infty}}=\\left(q;q^2\\right)_{\\infty}=\\sum_{n \\geq 0} (-1)^np_{\\mathcal{DO}}(n)q^n,\n$$\nwhere $p_{\\mathcal{DO}}(n)$ counts the number of partitions of $n$ into distinct odd parts.  An asymptotic formula for $p_{\\mathcal{DO}}(n)$ can be worked out using standard techniques. For example, Ingham's Tauberian theorem (see \\cite{BMJS}, Theorem 1.1) with the modularity of the Dedekind $\\eta$-function yields\n$$\nQ_n(-1)=(-1)^np_{\\mathcal{DO}}(n) \\sim \\frac{(-1)^n}{2(24)^{\\frac14}n^{\\frac34}}\\exp\\left(\\pi \\sqrt{\\frac{n}{6}}\\right).\n$$\nNote the lack of uniformity in the asymptotic formulas for $\\zeta$ near $\\pm 1$; in particular, the asymptotic formulas for $Q_n(1)$ and $Q_n(-1)$ cannot be obtained by taking $\\frac{a}{b} \\to \\pm 1$ in cases (1) and (2).\n\\end{remark}\n\n\\subsection{Applications to differences of partition functions}\nIn this section, we apply Theorem \\ref{T:twistedetaproduct} to differences of the partition functions $p(a,b,n)$, partitions of $n$ with number of parts congruent to $a$ modulo $b$.  The following elementary proposition relates the the numbers $p(a,b,n)$ to the coefficients $Q_n( \\zeta_b^{j})$.\n    \n    \\begin{proposition}\\label{P:pabnrewrite}\n    We have\n    $$\n    p(a,b,n)=\\frac{1}{b}\\sum_{0 \\leq j \\leq b-1} \\zeta_b^{-ja}Q_n\\left( \\zeta_b^{j}\\right).\n    $$\n    \\end{proposition}\n    \\begin{proof}\n    Using orthogonality, we can write the indicator functions of congruence classes as $$1_{x \\equiv a \\hspace{-.3cm} \\pmod{b}}= \\frac{1}{b}\\sum_{j=0}^{b-1} \\zeta_b^{-ja} \\zeta_b^{jx},$$ and by standard combinatorial techniques (see \\cite{andrewsbook}, Ch. 1) one has $$Q_n(z)=\\sum_{\\lambda \\vdash n} z^{\\ell(\\lambda)}.$$  Hence,\n    \\begin{align*}\n     p(a,b,n)=\\sum_{\\lambda \\vdash n} \\frac{1}{b}\\sum_{0 \\leq j \\leq b-1}  \\zeta_b^{-ja} \\zeta^{j\\ell(\\lambda)}_{b}&=\\frac{1}{b}\\sum_{0 \\leq j \\leq b-1}  \\zeta_b^{-ja}\\sum_{\\lambda \\vdash n}  \\left(\\zeta_b^{j}\\right)^{\\ell(\\lambda)} =\\frac{1}{b}\\sum_{0 \\leq j \\leq b-1}  \\zeta_b^{-ja} Q_n\\left( \\zeta_b^{j}\\right),\n    \\end{align*}\n    which completes the proof. \n    \\end{proof}\nThus, asymptotics for differences of $p(a,b,n)$ can be identified using the asymptotic formulas found for $Q_n(\\zeta)$ in Theorem \\ref{T:twistedetaproduct}, in particular the equidistribution of the largest part in congruence classes follows immediately: $\\frac{p(a,b,n)}{p(n)} \\sim \\frac{1}{b}.$  Furthermore, using the Hardy--Ramanujan--Rademacher exact formula for $p(n)$ (\\cite{andrewsbook}, Theorem 5.1) with Theorem \\ref{T:twistedetaproduct}, one can improve this in the various cases.  For example, for $b \\geq 5,$ we have\n$$\n\\lim_{n \\to \\infty}\\left(\\frac{b\\cdot p(a,b,n) - \\frac{2\\sqrt{3}}{24n-1}\\exp\\left(\\frac{\\pi\\sqrt{24n-1}}{6}\\right)\\left(1-\\frac{6}{\\pi\\sqrt{24n-1}} \\right)}{An^{-\\frac34}\\exp(2\\lambda_1\\sqrt{n})}\n-\\cos\\left(\\alpha-\\frac{2\\pi a}{b}+2\\lambda_2\\sqrt{n}\\right)\\right)=0,\n$$\nwhere $\\lambda_1+i\\lambda_2=\\sqrt{\\mathrm{Li}_2( \\zeta_b)},$ $A \\geq 0,$ and $\\alpha \\in [0,2\\pi)$ are defined by\n$$\nAe^{i\\alpha}=\\sqrt{\\frac{(\\lambda_1+i\\lambda_2)(1- \\zeta_b^a)}{\\pi}}.\n$$\n\nWe record a number of results below in the same vein.  Considering simple differences, $p(a_1,b,n)-p(a_2,b,n),$ it follows from Proposition \\ref{P:pabnrewrite} that when rewriting each $p(a,b,n)$ in terms of $Q_n$ the two summands $Q_n(1)=p(n)$ cancel.  With a few exceptions for $b=4$, the dominant terms are always $Q_n(\\zeta_b)$ and $Q_n(\\zeta_b^{b-1})$.\n\n\\begin{theorem}\\label{T:simpledifferences}\nLet $0 \\leq a_1 < a_2 \\leq b-1.$ \\\\\n\\textup{(1)} For $b=2,$ we have $p(0,2,n)-p(1,2,n)=Q_n(-1).$ \\\\\n\\textup{(2)}  For $b=3$, we have \n    $$\n    \\frac{p(a_1,3,n)-p(a_2,3,n)}{A_{a_1,a_2}n^{-\\frac23}\\exp\\left(\\frac{2\\pi}{3}\\sqrt{\\frac{n}{6}}\\right)} = \\cos\\left(\\alpha_{a_1,a_2}-\\frac{4\\pi n}{3}\\right) + o(1),\n    $$\n    where $A_{a_1,a_2} \\geq 0$ and $\\alpha_{a_1,a_2} \\in [0,2\\pi)$ are defined by\n    $$\n    A_{a_1,a_2}e^{i\\alpha_{a_1,a_2}}=( \\zeta_3^{-a_1}- \\zeta_3^{-a_2})(1- \\zeta_3^{2})^{\\frac16}(1- \\zeta_3)^{\\frac12}\\frac{\\Gamma\\left(\\frac{1}{3}\\right)}{3(6\\pi)^{\\frac23}}.\n    $$\n    \\textup{(3)} For $b=4,$ and $a_1,a_2$ of opposite parity, we have $$p(a_1,4,n)-p(a_2,4,n) \\sim \\frac{(-1)^{a_1} - (-1)^{a_2}}{4}Q_n(-1).$$\n    \\textup{(4)} For $b \\geq 5$, or for $b=4$ and $a_1,a_2$ of the same parity, we have\n$$\n\\frac{p(a_1,b,n)-p(a_2,b,n)}{B_{a_1,a_2,b}n^{-\\frac34}\\exp(2\\lambda_1\\sqrt{n})}=\\cos\\left(\\beta_{a_1,a_2,b}+2\\lambda_2\\sqrt{n} \\right) + o(1),\n$$\nwhere $\\lambda_1+i\\lambda_2=\\sqrt{\\mathrm{Li}_2( \\zeta_b)}$, $B_{a_1,a_2,b} \\geq 0$ and $\\beta_{a_1,a_2,b} \\in [0,2 \\pi)$ are defined by\n    $$\n    B_{a_1,a_2,b}e^{i\\beta_{a_1,a_2,b}}=\\frac{\\left( \\zeta_b^{-a_1}- \\zeta_b^{-a_2}\\right)}{b}\\sqrt{\\frac{(1- \\zeta_b)(\\lambda_1+i\\lambda_2)}{\\pi}}.\n    $$\n\n\\end{theorem}\n\n\\begin{proof}\nWhen $b=2$, Theorem \\ref{T:simpledifferences} follows from Proposition \\ref{P:pabnrewrite}.  Let $b \\geq 5.$  By Proposition \\ref{P:pabnrewrite}, it follows that\n$$\np(a_1,b,n)-p(a_2,b,n)=\\frac{1}{b}\\mathrm{Re}\\left(  (\\zeta_b^{-a_1} - \\zeta_{b}^{-a_2})Q_n( \\zeta_b)\\right)+\\frac{1}{b}\\sum_{1 \\leq j \\leq b-2} (\\zeta_b^{-ja_1} - \\zeta_b^{-ja_2})Q_n\\left( \\zeta_b^{j}\\right).\n$$\nUpon dividing both sides by $B_{a_1,a_2,b} n^{-\\frac34} \\exp(2\\lambda_1\\sqrt{n})$, Lemma \\ref{L:dilogdecreasing} implies that the sum on the right is $O(e^{-c\\sqrt{n}})$, for some $c>0,$ and it then follows from Theorem \\ref{T:twistedetaproduct} that\n\\begin{align} \\label{analogforfuture}\n\\frac{p(a_1,b,n)-p(a_2,b,n)}{B_{a_1,a_2,b}n^{-\\frac34}\\exp\\left(2\\lambda_1\\sqrt{n}\\right)}=\\mathrm{Re}\\left(e^{i\\left(\\beta_{a_1,a_2,b}+2\\lambda_2\\sqrt{n}\\right)}\\right)+o(1)+o\\left(e^{-c\\sqrt{n}} \\right),\n\\end{align}\nwhich gives the claim of Theorem \\ref{T:simpledifferences}.  \n\nThe other cases are proved similarly by noting that Lemma \\ref{L:dilogdecreasing} and Theorem \\ref{T:twistedetaproduct} imply that the $Q_n( \\zeta_b)$ and $Q_n( \\zeta_b^{-1})$ terms always dominate $Q_n( \\zeta_b^{j})$ for $j \\neq \\pm 1,$ except in the case that $b=4$, where $Q_n(-1)$ dominates when $a_1,a_2$ have opposite parity.  But $Q_n(-1)$ vanishes from the sum in Proposition \\ref{P:pabnrewrite} when $b=4$ and $a_1,a_2$ have the same parity, which leads to the third case in Theorem \\ref{T:simpledifferences}.\n\\end{proof}\n\n\n\nMore generally, if $P_{\\bold{v}}(x):=\\sum_{0 \\leq a \\leq b-1} v_ax^a \\in \\mathbb{R}[x]$ with $\\bold{v}:= (v_0,...,v_{b-1})\\in \\mathbb{R}^b$, then Theorem \\ref{T:twistedetaproduct} implies asymptotic formulas for any weighted count\n$\n\\sum_{a=0}^{b-1}v_ap(a,b,n).\n$\nTo state our general theorem, we let\n\n\n\n\n\\begin{multicols}{2}\n$$\nL(e^{i\\theta}):=\\begin{cases}\\sqrt{\\mathrm{Li}_2(e^{i\\theta})} & \\text{if $0 \\leq \\theta < \\theta_{13}$,} \\\\\n\\frac{\\sqrt{\\mathrm{Li}_2(e^{3i\\theta})}}{3} & \\text{if $\\theta_{13} < \\theta < \\theta_{23}$,} \\\\\n\\frac{\\sqrt{\\mathrm{Li}_2(e^{2i\\theta})}}{2} & \\text{if $\\theta_{23} < \\theta \\leq \\pi$.} \\end{cases}\n$$\nLet $\\mathcal{Z}(P_{\\bold{v}})$ be the roots of $P_{\\bold{v}}$, and let \\newline $\\lambda_1+i\\lambda_2=L( \\zeta_b^{a_0})$ for $a_0 \\leq \\frac{b}{2}$, whenever\n$$\n\\mathrm{Re}\\left(L( \\zeta_b^{a_0})\\right)=\\max_{\\substack{0 \\leq a \\leq \\frac{b}{2} \\\\  \\zeta_b^a\\notin \\mathcal{Z}(P_{\\bold{v}})}} \\mathrm{Re} \\left(L( \\zeta_b^a)\\right).\n$$\n\\begin{figure}[H]\n    \\centering\n    \\includegraphics[width = 70mm]{realdilogexponent.png} \\caption{$\\mathrm{Re}(L(e^{i\\theta}))$ for $0\\leq \\theta \\leq \\pi.$}\n    \\label{fig:my_label}\n\\end{figure}\n\\end{multicols}\n\n\\begin{theorem}\\label{T:genericrealsums}\nWith notation as above, we have the following asymptotic formulas. \\\\\n    \\textup{(1)} If $a_0=0,$ then $\\sum_{0 \\leq a \\leq b-1} v_ap(a,b,n) \\sim \\frac{P_{{\\bf v}}(1)}{b}p(n).$ \\\\\n    \\textup{(2)} If $0 < 2 \\pi \\frac{a_0}{b} < \\theta_{13},$ then\n    $$\n     \\frac{\\sum_{0 \\leq a \\leq b-1}v_ap(a,b,n)}{A_{a_0,b,\\bold{v}} n^{-\\frac{3}{4}} \\exp(2\\lambda_1\\sqrt{n})} = \\cos\\left(\\alpha_{a_0,b,\\bold{v}}+2\\lambda_2\\sqrt{n} \\right) + o(1),\n    $$\n    where $A_{a_0,b,\\bold{v}} \\geq 0$ and $\\alpha_{a_0,b,\\bold{v}} \\in [0,2\\pi)$ are defined by\n    $$\n    A_{a_0,b,\\bold{v}} \\cdot e^{i \\alpha_{a_0,b,\\bold{v}}}= \\frac{P_{\\bold{v}}( \\zeta_b^{-a_0})}{b}\\sqrt{\\frac{(\\lambda_1+i\\lambda_2)(1- \\zeta_b^{a_0})}{\\pi}}.\n    $$\n    \\textup{(3)} If $\\theta_{13} < 2 \\pi \\frac{a_0}{b} < \\theta_{23}$ and $a_0 \\neq \\frac{b}{3},$ then\n    \\begin{align*}\n    & \\frac{\\sum_{0 \\leq a \\leq b-1}v_ap(a,b,n)}{A_{a_0,b,\\bold{v}} n^{-\\frac{3}{4}} \\exp(2\\lambda_1\\sqrt{n})} = B_{a_0,b}\\cos\\left(\\alpha_{a_0,b,\\bold{v}}+\\beta_{a_0,b}-\\frac{2\\pi n}{3} + 2 \\lambda_2\\sqrt{n}\\right) \\\\ & \\hspace{3cm} + C_{a_0,b}\\cos\\left(\\alpha_{a_0,b,\\bold{v}}+\\gamma_{a_0,b}-\\frac{4\\pi n}{3} + 2 \\lambda_2\\sqrt{n}\\right) + o(1),\n    \\end{align*}\n    where $B_{a_0,b},C_{a_0,b} \\geq 0$ and $\\beta_{a_0,b},\\gamma_{a_0,b} \\in [0,2\\pi)$ are defined by\n    $$\n    B_{a_0,b}e^{i\\beta_{a_0,b}} = \\omega_{1,3}( \\zeta_b^{a_0}),\n    $$\n    $$\n    C_{a_0,b}e^{i\\gamma_{a_0,b}}= \\omega_{2,3}( \\zeta_b^{a_0}).\n    $$\n    \\textup{(4)} If $a_0=\\frac{b}{3}$, then\n    $$\n    \\frac{b\\sum_{0 \\leq a \\leq b-1}v_ap(a,b,n)}{D_{\\bold{v}} n^{-\\frac23} \\exp\\left(\\frac{2\\pi}{3}\\sqrt{\\frac{n}{6}}\\right)} = \\cos\\left(\\delta_{\\bold{v}}-\\frac{4\\pi n}{3}\\right) + o(1),\n    $$\n    where $D_{\\bold{v}} \\geq 0$ and $\\delta_{\\bold{v}} \\in [0,2\\pi)$ are defined by\n    $$\n    D_{\\bold{v}} \\cdot e^{i\\delta_{\\bold{v}}}=\\frac{(1- \\zeta_3^{2})^{\\frac16}(1- \\zeta_3)^{\\frac12}\\Gamma(\\frac13)}{2(6\\pi)^{\\frac23}}P_{\\bold{v}}\\left( \\zeta_3^{-1}\\right).\n    $$\n    \\textup{(5)} If $\\theta_{23} < 2 \\pi \\frac{a_0}{b} < \\pi$, then\n    $$\n     \\frac{\\sum_{0 \\leq a \\leq b-1}c_vp(a,b,n)}{A_{a_0,b,\\bold{v}} n^{-\\frac34}\\exp\\left(2\\lambda_1\\sqrt{n}\\right)} = \\cos\\left(\\alpha_{a_0,b,\\bold{v}}+\\pi n+2\\lambda_2\\sqrt{n} \\right) + o(1).\n    $$\n    \\textup{(6)} If $a_0=\\frac{b}{2},$ then $\\sum_{0 \\leq a \\leq b-1} (-1)^a v_ap(a,b,n) \\sim \\frac{P_{\\bold{v}}(-1)}{b}Q_n(-1).$\n\\end{theorem}\n\\begin{proof}\n     Theorem \\ref{T:genericrealsums} is proved similarly to Theorem \\ref{T:simpledifferences}. For Cases (1) and (6), the asymptotic formula for $Q_n(1) \\sim p(n)$ and Proposition \\ref{P:pabnrewrite} directly implies\n     \\begin{align*}\\sum_{0 \\leq a \\leq b-1} v_ap(a,b,n) &\\sim \\frac{1}{b}(v_0Q_n(1) + v_1Q_n(1)+...+v_{b-1}Q_n(1)) = \\frac{P_{\\textbf{v}}(1)p(n)}{b},\\\\ \\sum_{0 \\leq a \\leq b-1}(-1)^a v_ap(a,b,n) &\\sim \\frac{1}{b}(v_0Q_n(-1) - v_1Q_n(-1)+...+(-1)^{b-1}v_{b-1}Q_n(-1)) \\\\ &= \\frac{P_{\\textbf{v}}(-1)Q_n(-1)}{b},\n     \\end{align*}\nfor Cases (1) and (6) respectively.  \n   \\par For Cases (2), (3), and (5), the asymptotic main term (using that $\\overline{Q_n(\\zeta)} = Q_n(\\overline{\\zeta})$) is\n    $$p(a,b,n) \\sim \\frac{1}{b}\\left(\\zeta^{-a_0 a}_bQ_n(\\zeta^{a_0}_b)+\\overline{\\zeta^{-a_oa}_b{Q_n(\\zeta^{a_0}_b)}}\\right) = \\frac{2}{b}\\mathrm{Re}\\left(\\zeta^{-a_0 a}_bQ_n(\\zeta^{a_0}_b)\\right). $$\n    The proof then follows by applying Theorem \\ref{T:twistedetaproduct} and dividing by the appropriate normalizing factors in analog to Equation \\eqref{analogforfuture}.\n    \\par For case (4), there is only one main term in the sum for $$p(a,b,n)\\sim \\zeta^{-\\frac{a}{3}}Q_n\\left(\\zeta^{\\frac{1}{3}}\\right).$$ Applying Theorem \\ref{T:twistedetaproduct} and the analog to Equation \\eqref{analogforfuture} again proves the claim.\n\\end{proof}\n\nOne application of the above theorem generalizes Theorem \\ref{T:simpledifferences} to differences of partitions with number of parts modulo $b$ in one of two disjoint sets of residue classes $S_1, S_2 \\subset [0,b-1]$.  That is, we consider\n$$\nP_{S_1,S_2}(x):=\\sum_{a \\in S_1} x^a-\\sum_{a \\in S_2} x^a, \n$$\nand prove a more explicit version of Theorem \\ref{T:genericrealsums} in this case.  Since $P_{S_1,S_2}(x)$ is a polynomial of degree at most $b-1$ with integer coefficients, there must exist some $d \\mid b$ such that $ \\zeta_d \\notin \\mathcal{Z}(P_{S_1,S_2}),$ otherwise $P_{S_1,S_2}$ would be divisible by $\\prod_{d \\mid b} \\Phi_{d}(x)=x^b-1,$ where $\\Phi_d$ is the $d$-th cyclotomic polynomial, a contradiction.\n\n\n\\begin{theorem}\\label{T:differenceswithsets}\nLet $b \\geq 2$ and let $S_1, S_2 \\subset [0,b-1]$ be disjoint subsets of integers.  If $|S_1| \\neq  |S_2|,$ then \n$$\\sum_{a \\in S_1}p(a,b,n)-\\sum_{a \\in S_2}p(a,b,n) \\sim \\frac{(|S_1|-|S_2|)p(n)}{b}.$$  \nOtherwise, if $|S_1|=| S_2|$, then we have the following cases.  Let $d_0$ be the largest integer such that $d_0 \\mid b$ and $ \\zeta_{d_0} \\notin \\mathcal{Z}(P_{S_1,S_2}).$ \\\\\n    \\textup{(1)} If $d_0\\geq 5$ or if $d_0=4$ and $-1 \\in \\mathcal{Z}(P_{S_1,S_2})$, then\n    $$\n    \\frac{\\sum_{a \\in S_1} p(a,b,n)-\\sum_{a \\in S_2} p(a,b,n)}{A_{d_0,S_1,S_2} n^{-\\frac34} \\exp(2\\lambda_1\\sqrt{n})} = \\cos\\left(\\alpha_{d_0,S_1,S_2}+2\\lambda_2\\sqrt{n}\\right) + o(1),\n    $$\n    where $\\lambda_1+i\\lambda_2=\\sqrt{\\mathrm{Li}_2( \\zeta_{d_0})}$, $A_{d_0,S_1,S_2}\\geq 0$ and $\\alpha_{d_0,S_1,S_2} \\in [0,2\\pi)$ are defined by\n    $$\n    A_{d_0,S_1,S_2} \\cdot e^{i\\alpha_{d_0,S_1,S_2}}=\\frac{P_{S_1,S_2}\\left( \\zeta_{d_0}^{-1}\\right)}{b}\\sqrt{\\frac{(\\lambda_1+i\\lambda_2)(1- \\zeta_{d_0})}{\\pi}}.\n    $$\n    \\textup{(2)}  If $d_0=4$ or $3$ with $b$ even, and $-1 \\notin \\mathcal{Z}(P_{S_1,S_2})$, we have the following allowable sets:\n    \\begin{itemize}\n\\item If $d_0 = 4$ and $(k_1+k_2)\\not\\equiv 0 \\pmod{2}$,\n    \\begin{align*}\n     S_1\\times S_2&= \\{a: a\\leq b-1, \\; a\\equiv k_1 \\pmod{4}\\}\\times\\{a: a\\leq b-1, \\; a\\equiv k_2 \\pmod{4}\\}.\n    \\end{align*}\n \n\\item If $d_0=3$, $b$ is even and $k_1 \\not\\equiv k_2 \\pmod{2},$\n\\begin{align*}\n    S_1\\times S_2 &= \\{a: a\\leq b-1,\\; a\\equiv k_1 \\pmod{2}\\}\\times\\{a: a\\leq b-1,\\; a\\equiv k_2 \\pmod{2}\\}.\n\\end{align*}\n\n\\end{itemize}\nThe asymptotic formulas are then given by\n    $$\n    \\sum_{a \\in S_1}p(a,b,n)-\\sum_{a \\in S_2} p(a,b,n) \\sim \\frac{N_{S_1,S_2}}{b}Q_n(-1),$$\n    where\n    $$\n    N_{S_1,S_2}=\\begin{cases} (-1)^{k_1}b& \\textnormal{if}\\;d_0=3,\\; b \\; \\textnormal{even},\\\\  (-1)^{k_1}\\frac{b}{2} & \\textnormal{if}\\;d_0=4.\\end{cases}\n    $$\n    \\textup{(3)}  If $d_0=3$, $b$ is even and $-1 \\in \\mathcal{Z}(P_{S_1,S_2})$, or $d_0=3$ and $b$ is odd, we have the following sets $S_1$ and $S_2$:\n    \\begin{itemize}\n        \\item If $b$ is odd, $S_1$ and $S_2$ must contain distinct residue classes modulo $3$.\n        \\item If $b$ is even, \n        \\begin{align*}\n            S_1\\times S_2 &= \\{a: a\\leq b-1,\\; a\\equiv k_1 \\;\\textnormal{or}\\; k_2 \\pmod{6}\\}\\times\\{a: a\\leq b-2,\\; a\\equiv k_3\\; \\textnormal{or}\\; k_4 \\pmod{6}\\},\n        \\end{align*}\n        where \n\\begin{align*}\n    (k_1,k_2,k_3,k_4) &= (0,3,2,5),\\; (2,5,0,3),\\; (1,4,2,5),\\; (2,5,1,4),\n    (1,3,1,4),\\; \\textnormal{or}\\;  (1,4,1,3).\n\\end{align*}\n    \\end{itemize}\nThe asymptotic formula is then given by\n    $$\n    \\sum_{a \\in S_1} p(a,b,n)-\\sum_{a \\in S_2} p(a,b,n) \\sim \\frac{2}{b}\\mathrm{Re}\\left(Q_n(\\zeta_3)P_{S_1,S_2}\\left(\\zeta^{-1}_3\\right)\\right). $$\n\\textup{(4)}  If $d_0=2,$ then for some $a_1, a_2$ of opposite parity we have \n$$ (S_1,S_2)=\\{a \\equiv a_1 \\pmod{2}\\} \\times \\{a \\equiv a_2 \\pmod{2}\\}$$\n and\n    $$\n    \\sum_{a \\in S_1}p(a,b,n)-\\sum_{a \\in S_2} p(a,b,n) \\sim (-1)^{a_1}Q_n(-1).$$  \n  \n\\end{theorem}\n\n\\begin{proof}[Proof sketch of Theorem \\ref{T:differenceswithsets}]\nThe asymptotic analysis is similar to the proof of Theorem \\ref{T:simpledifferences}, since Lemma \\ref{L:dilogdecreasing} and Theorem \\ref{T:twistedetaproduct} imply that the sequence $Q_n( \\zeta_d)$, ranked from in asymptotic order from least to greatest, is\n$$\nQ_n( \\zeta_3), \\ Q_n(i), \\ Q_n(-1), \\ Q_n(\\zeta_5), \\ Q_n(\\zeta_6), \\dots, Q_n(1)=p(n).\n$$\nThus, for example in case (3), the asymptotic behavior of $\\sum_{a \\in S_1} p(a,b,n) - \\sum_{a \\in S_2} p(a,b,n)$ is determined by $Q_n( \\zeta_3)$ and $Q_n( \\zeta_3^{-1})$ since all other $Q_n( \\zeta_b^a)$ vanish in $P_{S_1,S_2}( \\zeta_{b}^{-j})Q_n( \\zeta_b^{j})$.  Furthermore, in this case we must have\n$$\n\\frac{x^{b}-1}{\\Phi_3(x)} \\mid P_{S_1,S_2}(x),\n$$\nand $\\deg (P_{S_1,S_2}(x))\\leq b-1$.  Since\n$$\n\\frac{x^{b}-1}{\\Phi_3(x)}=x^{b-2}-x^{b-3}+x^{b-5}-x^{b-6}+ \\dots + x^{4}-x^3+x-1,\n$$\nthis leads directly to the possible sets $S_1$ and $S_2$ described in case 3.  Finally, note that, given $S_1$ and $S_2$ defined in terms of $a_1$ and $a_2$ modulo $b$, we have\n$$\nP_{S_1,S_2}\\left( \\zeta_3^{-1}\\right)=\\sum_{\\substack{0 \\leq a \\leq b \\\\a \\equiv a_1 \\pmod{3}}}  \\zeta_{3}^{-a}-\\sum_{\\substack{0 \\leq a \\leq b \\\\ a \\equiv a_2 \\pmod{3}}}  \\zeta_{3}^{-a}=\\frac{b}{3}( \\zeta_3^{-a_1}- \\zeta_3^{-a_2}).\n$$  This is taken into account in the definition of the constant $B_{S_1,S_2}.$ The other cases are proved similarly.\n\\end{proof}\n\nWe make a few remarks. \n\\begin{remark} \\label{R:differenceremark}\n\n\\textup{(1)} Theorem \\ref{T:differenceswithsets} case (1), in combination with Lemma \\ref{L:dilogdecreasing}, shows that one can reduce the growth of the amplitudes in the differences exponentially, as long as the corresponding polynomial $P_{S_1, S_2}$ vanishes at the crucial roots of unity. But the options for such types of cancellation strongly depend on $b$. For example, if $b$ is a prime number, there is not even a rational combination (except for the trivial combination) such that the amplitudes of $\\sum_{0 \\leq a < b} v_a p(a,b,n)$ grow exponentially less than any simple difference $p(a_1,b,n) - p(a_2,b,n)$. The simple algebraic reason behind this is that the minimal polynomial of $\\zeta_b$ has degree $b-1$ in this case. It would be interesting to find a purely combinatorial interpretation for this fact. \\\\\n\n\\textup{(2)} Note that if we shift the residue classes in $S_1$ and $S_2$ by some integer $r$, and then take least residues modulo $b$ to compute $P_{S_1+r,S_2+r}(x)$, then this polynomial has the same roots of unity as $P_{S_1,S_2}(x)$, and so \n$$\n\\sum_{a \\in S_1+r}p(a,b,n)-\\sum_{a \\in S_2+r}p(a,b,n)\n$$\nalways has the same asymptotic behavior in Theorem \\ref{T:differenceswithsets} as $\\sum_{a \\in S_1}p(a,b,n)-\\sum_{a \\in S_2}p(a,b,n).$ At the same time, the phase in the cosine changes. Indeed, we obtain \n\\begin{align} \\label{E:phaseshift}\n        \\frac{\\sum_{a \\in S_1+r} p(a,b,n)-\\sum_{a \\in S_2+r} p(a,b,n)}{A_{d_0,S_1,S_2} n^{-\\frac34}\\exp\\left(2\\lambda_1\\sqrt{n}\\right)} = \\cos\\left(\\alpha_{d_0,S_1,S_2} - \\frac{2\\pi r}{d_0} +2\\lambda_2\\sqrt{n}\\right) + o(1),\n\\end{align}\nwhere all the constants are the same as in Theorem \\ref{T:differenceswithsets} (1).  One can further use trigonometric identities to obtain a wider class of more classical asymptotic formulas, for instance regarding squared partition differences. Indeed, if $4|d_0$ in \\eqref{E:phaseshift}, one finds using $\\sin^2(x) + \\cos^2(x) = 1$, as $n \\to \\infty$,\n\\begin{align*}\n    & \\left( \\sum_{a \\in S_1} p(a,b,n)-\\sum_{a \\in S_2} p(a,b,n) \\right)^2 + \\left( \\sum_{a \\in S_1+\\frac{d_0}{4}} p(a,b,n)-\\sum_{a \\in S_2+\\frac{d_0}{4}} p(a,b,n) \\right)^2  \\\\\n    & \\hspace{8.5cm} \\sim A_{d_0,S_1,S_2}^2 n^{-\\frac32}\\exp\\left(4\\lambda_1\\sqrt{n}\\right).\n\\end{align*}\n\n\\textup{(3)} Cases 3 and 4 in Theorem \\ref{T:differenceswithsets} show that for $d_0\\in\\{2,3\\}$, there are finitely many sets $S_1$ and $S_2$ such that the asymptotic behavior of  $\\sum_{a \\in S_1}p(a,b,n)-\\sum_{a \\in S_2}p(a,b,n)$ is determined by $Q_n( \\zeta_{d_0})$, and that the number of such sets is independent of $b$.  In fact this is true for any $d_0$, and we leave it as an open problem to describe the sets $S_1,S_2$ in general.  The sets $S_1$ and $S_2$ need not each consist of one congruence class each modulo $d_0,$ for example with $b=10$, the polynomial $P_{\\{1,3,6,8\\},\\{0,2,5,7\\}}(x)$ has $d_0=5.$ \n\\end{remark}\n\n\n\n\\subsection{Examples} In this section, we provide some examples. \n\n\\begin{example} Let $b=6$, and consider the difference $p(1,6,n) - p(5,6,n)$. Then according to Theorem \\ref{T:simpledifferences}, we obtain\n\\begin{align} \\label{E:p6explicit}\n    \\frac{p(1,6,n) - p(5,6,n)}{Bn^{-\\frac34} \\exp\\left(2\\lambda_1 \\sqrt{n}\\right)} = \\cos\\left( \\beta + 2\\lambda_2 \\sqrt{n}\\right) + o(1), \n\\end{align}\nwhere $\\lambda_1 + i\\lambda_2 = \\sqrt{\\mathrm{Li}_2(\\zeta_6)}$, and $B > 0$ and $\\beta \\in [0, 2\\pi)$ are given implicitely by \n\\begin{align*}\n    Be^{i\\beta} = \\frac{\\zeta_6^{-1} - \\zeta_6^{-5}}{6} \\sqrt{\\frac{(1-\\zeta_6) (\\lambda_1 + i \\lambda_2)}{\\pi}} = \\frac{i}{\\sqrt{12 \\pi}} \\sqrt{\\left( \\frac12 - i\\frac{\\sqrt{3}}{2}\\right) \\sqrt{\\mathrm{Li}_2(\\zeta_6)}}.  \n\\end{align*}\nNote that this implies (choosing $B$ to be the absolute value of the right hand side of the equation above)\n\\begin{align}\n    \\label{E:lambda1} \\lambda_1 & = 0.81408 \\ldots, \\qquad \\lambda_2 = 0.62336 \\ldots, \\\\\n    \\nonumber    B & = 0.23268 \\ldots, \\qquad \\hspace{1.4mm} \\beta = 1.37394 \\ldots.\n\\end{align}\nConsidering the first 900 coefficients numerically yields \n$$ M := \\{7, 26, 59, 104, 162, 233, 316, 412, 521, 642, 776, ...\\},$$ \nwhich are the highest indices until a change of signs in the sequence $p(1,6,n) - p(5,6,n)$. We can compare this exact result to the prediction of formula \\eqref{E:p6explicit}. By considering the roots of the cosine, we find that it changes signs approximately at \n$$M' := \\{7, 27, 59, 104, 162, 233, 316, 412, 521, 642, 777, ...\\}.$$\nNote that in the first eleven cases, only case two with $27$ and case eleven with $777$ give slightly wrong predictions. \n\n\\begin{figure}[H]\n         \\centering\n         \\includegraphics[width=120mm, height= 70mm]{1-5-6normalized.png}\n       \n        \\caption{The plot shows the sign changes of $p(1,6,n)-p(5,6,n)$ (in blue dots) and the estimated sign changes (the red line).}\n\\label{fig:difffigintro}\n\n\\end{figure}\n\n\n\n\\end{example}\nThe next example refers to higher differences of partition functions. \n\\begin{example} Again, we consider the case $b=6$. In the spirit of Theorem \\ref{T:differenceswithsets} we want to consider multi-termed differences. To do so, we need two subsets $S_1, S_2 \\subset \\mathbb{Z}\/6\\mathbb{Z}$, such that the corresponding nontrivial polynomial $P_{S_1, S_2}(x)$ of degree at most 5 vanishes at as many roots of unity around $x=1$ as possible. We first note that\n\\begin{align*}\n    (x-1)\\Phi_6(x) = (x-1)\\left(x^2 - x + 1\\right) = x^3 - 2x^2 + 2x - 1.\n\\end{align*}\nIn this case, we obtain a weighted difference and no subsets can be found for a growth reduction to an exponent induced by $\\mathrm{Li}_2(\\zeta_3)$. We continue by trying to eliminate also the 3rd roots of unity; i.e., with \n\\begin{align*}\n    (x-1)\\Phi_6(x)\\Phi_3(x) = x^5 - x^4 + x^3 - x^2 + x - 1.\n\\end{align*}\nThis is exactly the case (4) of Theorem \\ref{T:differenceswithsets}. As a result, setting $S_1 := \\{1,3,5\\}$ and $S_2 := \\{0,2,4\\}$, we find, as $n \\to \\infty$,\n\\begin{align*}\n    \\sum_{0 \\leq a \\leq 5} (-1)^{a+1} p(a,6,n) \\sim - Q_n(-1) \\sim \\frac{(-1)^{n+1}}{2(24)^{\\frac14} n^{\\frac34}} \\exp\\left( \\pi \\sqrt{\\frac{n}{6}}\\right).\n\\end{align*}\nAlso note that $\\frac{\\pi}{\\sqrt{6}} = 1.2825 \\ldots$ is much smaller then the exponent $2\\lambda_1 = 1.6281 \\ldots$ in \\eqref{E:p6explicit}, compare also \\eqref{E:lambda1}. \n\\end{example}\nFinally, we give an application of Remark \\ref{R:differenceremark}.\n\n\\begin{example} In light of Equation \\eqref{E:phaseshift}, we can choose $r$ such that the cosine becomes a sine on the right hand side. Using Pythagoras' Theorem, and considering the case $b=8$ and $r=2$, we obtain an asymptotic formula without oscillating terms. Indeed, according to Theorem \\ref{T:simpledifferences} (4) and Remark \\ref{R:differenceremark}, respectively, we obtain for residue classes $a_1 \\not= a_2$ that\n\\begin{align*}\n    (p(a_1, 8, n) - p(a_2, 8, n))^2 + (p(a_1+2,8,n) - p(a_2+2,8,n))^2 \\sim B_{a_1,a_2,8}^2 n^{-\\frac32} \\exp\\left( 4\\lambda_1 \\sqrt{n}\\right).\n\\end{align*}\nThere is no difficulty to extend this type of asymptotic formula for higher differences in the spirit of Theorem \\ref{T:differenceswithsets} (1).\n\\end{example}\n\n\\section{Proof of Theorem \\ref{T:twistedetaproduct}}\\label{proofofmainthm} \nSince the asymptotic formulas for $Q_n(1)$ and $Q_n(-1)$ are well-known, we assume throughout that $1 \\leq a < \\frac{b}{2}$ with $\\gcd(a,b)=1$ and $b \\geq 3,$ since $\\overline{Q_n(\\zeta)} = Q_n(\\overline{\\zeta})$.   \n\nThe setup follows the standard Hardy--Ramanujan circle method, expressing $Q_n(\\zeta)$ as a contour integral about 0 and breaking the contour apart with the sequence of Farey fractions of order $N.$  For facts about the Farey sequence, we refer the reader to Chapter 3 of \\cite{HardyWright}.  Much of the analysis in this section closely follows \\cite{Parry} after assuming the technical Lemmas \\ref{L:Esmallkbound} and \\ref{L:Elargekbound} which we prove in the next section.  \n\n\nLet $N=\\lfloor \\delta \\sqrt{n} \\rfloor$, for some $\\delta>0$ to be chosen independently of $n$ and small enough during the course of the proof.  Let $\\mathcal{F}_N$ be the sequence of Farey fractions of order $N$ with mediants $\\theta_{h,k}'$ and $\\theta_{h,k}''$ at $\\frac{h}{k}$.  We write \\begin{equation}\\label{E:tthetadef} t_{\\theta}:=t_n- 2 \\pi i \\theta, \\qquad \\text{where} \\qquad t_n\\sqrt{n}:=\\frac{\\sqrt{\\mathrm{Li}_2\\left(\\zeta_b^{ak_0}\\right)}}{k_0},\\end{equation} with $k_0 \\in \\{1,2,3\\}$ according to whether we are in case (1), (2) or (3).  \n\n\n  By Cauchy's integral formula, we have\n\\begin{align*}\n    Q_n\\left(\\zeta_b^a\\right)&=\\int_{0}^{1} \\left(\\zeta_b^ae^{-t_n+2\\pi i \\theta};e^{-t_n+2\\pi i \\theta}\\right)_{\\infty}^{-1}e^{nt_n-2 \\pi i n \\theta} d \\theta \\\\\n    &=\\sum_{\\frac{h}{k} \\in \\mathcal{F}_N } \\zeta_k^{-hn}  \\int_{-\\theta_{h,k}'}^{\\theta_{h,k}''} \\exp\\left(\\frac{\\mathrm{Li}_2\\left(\\zeta_b^{ak}\\right)}{k^2t_{\\theta}} +nt_{\\theta} + E_{h,k}(\\zeta_b^a,t_{\\theta})\\right)d\\theta,\n\\end{align*}\nwhere\n\\begin{align*}E_{h,k}(z,t):=& \\ \\mathrm{Log}\\left( \\left(z \\zeta_k^h e^{-t};\\zeta_k^h  e^{-t}\\right)_{\\infty}^{-1}\\right)-\\frac{\\mathrm{Li}_2\\left(z^k\\right)}{k^2t}.\\end{align*}\n\nWe will show that the integral(s) where $k=k_0$ dominate, that is they are the {\\it major arcs}, and all the other integrals are exponentially smaller, that is they are {\\it minor arcs}.  The $E_{h,k}$ will be shown to be error terms on all arcs; the following gives the growth of the $E_{h,k}$ up to $o(1)$ on each of the possible major arcs.\n\n\\begin{lemma}\\label{L:Efixedkbound}\n\\textup{(1)} For $2\\pi \\frac{a}{b} \\in (0, \\theta_{13})$ and $-\\theta_{0,1}' \\leq \\theta \\leq \\theta_{0,1}''$, we have\n$$\nE_{0,1}(\\zeta_b^a,t_{\\theta})= \\mathrm{Log}\\left(\\omega_{0,1}\\left(\\zeta_b^a\\right)\\right)+o(1).\n$$\n\\textup{(2)} For $2\\pi \\frac{a}{b} \\in (\\theta_{23}, \\pi)$ and $-\\theta_{1,2}' \\leq \\theta \\leq \\theta_{1,2}''$, we have\n$$\nE_{1,2}(\\zeta_b^a,t_{\\theta})= \\mathrm{Log}\\left(\\omega_{1,2}\\left(\\zeta_b^a\\right)\\right)+o(1).\n$$\n\\textup{(3)} For $2\\pi \\frac{a}{b} \\in (\\theta_{13},\\theta_{23})\\setminus \\left\\{\\frac{2\\pi}{3}\\right\\}$ and $-\\theta_{1,3}' \\leq \\theta \\leq \\theta_{1,3}''$, we have\n$$\nE_{1,3}(\\zeta_b^a,t_{\\theta})= \\mathrm{Log} \\left(\\omega_{1,3}(\\zeta_b^a)\\right) + o(1),\n$$\nand for  $-\\theta_{2,3}' \\leq \\theta \\leq \\theta_{2,3}''$, we have\n$$\n E_{2,3}(\\zeta_b^a,t_{\\theta})= \\mathrm{Log} \\left(\\omega_{2,3}(\\zeta_b^a)\\right) + o(1).\n$$\n\\textup{(4)} For $\\frac{a}{b}=\\frac{1}{3}$ and $-\\theta_{1,3}' \\leq \\theta \\leq \\theta_{1,3}''$, we have\n\\begin{align*}\n& E_{1,3}(\\zeta_3,t_{\\theta})=\\mathrm{Log}\\left(t_{\\theta}^{\\frac16}\\right)+\\mathrm{Log}\\left( \\left(1-\\zeta_3^2\\right)^{-\\frac16}\\left(1-\\zeta_3\\right)^{\\frac12} \\right)+\\log\\left(\\Gamma\\left(\\frac{2}{3}\\right)\\right)\\\\ & \\qquad \\hspace{3cm} +\\frac{1}{6}\\log\\left(3\\right) -\\frac{1}{2}\\log(2\\pi)+ o(1),\n\\end{align*} \nand for $-\\theta_{2,3}' \\leq \\theta \\leq \\theta_{2,3}''$, we have \n\\begin{align*}\n& E_{2,3}(\\zeta_3,t_{\\theta})=\\mathrm{Log}\\left(t_{\\theta}^{-\\frac16}\\right)+\\mathrm{Log}\\left( \\left(1-\\zeta_3^2\\right)^{\\frac16}(1-\\zeta_3)^{\\frac12} \\right)+\\log\\left(\\Gamma\\left(\\frac{1}{3}\\right)\\right)\\\\ & \\qquad \\hspace{3cm} +\\frac{1}{6}\\log\\left(\\frac{1}{3}\\right) -\\frac{1}{2}\\log(2\\pi)+ o(1).\n\\end{align*}\n\\end{lemma}\n\n\n\nThe next two lemmas give uniform bounds on $E_{h,k}$ to be applied on the minor arcs.  The proofs are quite intricate and are provided in the next section. We assume throughout that $0<\\varepsilon\\leq\\frac{1}{4}$.\n\n\\begin{lemma}\\label{L:Esmallkbound}\nUniformly for $k \\leq n^{\\varepsilon}$ and $-\\theta_{h,k}' \\leq \\theta \\leq \\theta_{h,k}''$, we have\n$$\nE_{h,k}(\\zeta_b^a,t_{\\theta})=O\\left(n^{3\\varepsilon-\\frac{1}{2}}\\right)+O\\left(n^{\\varepsilon}\\right).\n$$\n\\end{lemma}\nThe next lemma treats the case of large denominators. \n\\begin{lemma}\\label{L:Elargekbound}\nUniformly for $k \\geq n^{\\varepsilon}$ and $-\\theta_{h,k}' \\leq \\theta \\leq \\theta_{h,k}''$, we have\n$$\nE_{h,k}(\\zeta_b^a,t_{\\theta})=O\\left(N\\right).\n$$\n\\end{lemma}\n\nWe postpone the proofs of Lemmas \\ref{L:Efixedkbound}--\\ref{L:Elargekbound} until Section 5.  With these key lemmas in hand, the proof of Theorem \\ref{T:twistedetaproduct} follows \\cite{Parry} closely.\n\n\\begin{proof}[Proof of Theorem \\ref{T:twistedetaproduct}]\n{\\it Cases (1), (2) and (3).} Assume $\\frac{a}{b} \\neq \\frac{1}{3}.$\nWe write\n$$\n\\lambda_1+i\\lambda_2:=\\frac{\\sqrt{\\mathrm{Li}_2(\\zeta_b^{ak_0})}}{k_0}.\n$$\nIt follows from the choice $0 < \\varepsilon \\leq \\frac14$, Lemmas \\ref{L:Esmallkbound} and \\ref{L:Elargekbound} that $E_{h,k}(\\zeta_b^a,t_{\\theta})=\\delta O(\\sqrt{n})$ uniformly.  Using this and Lemma \\ref{L:Efixedkbound}, we have\n\\begin{align}\n    &e^{-2\\lambda_1\\sqrt{n}}Q_n\\left(\\zeta_b^a \\right) \\nonumber \\\\\n    &=\\sum_{\\substack{h \\\\ \\frac{h}{k_0} \\in \\mathcal{F}_N}} \\zeta_{k_0}^{-hn}\\omega_{h,k_0}(\\zeta_b^a)\\int_{-\\theta_{h,k_0}'}^{\\theta_{h,k_0}''} \\exp\\left(-2\\lambda_1\\sqrt{n}+\\frac{(\\lambda_1+i\\lambda_2)^2}{t_{\\theta}}+nt_{\\theta} + o(1)\\right)d\\theta \\nonumber  \\\\\n    & \\ \\ \\ +\\sum_{\\substack{\\frac{h}{k} \\in \\mathcal{F}_N \\\\ k \\neq k_0}} \\zeta_{k}^{-hn}  \\int_{-\\theta_{h,k}'}^{\\theta_{h,k}''} \\exp\\left(-2\\lambda_1\\sqrt{n}+\\frac{\\mathrm{Li}_2\\left(\\zeta_b^{ak}\\right)}{k^2t_{\\theta}} +nt_{\\theta} + \\delta O\\left(\\sqrt{n}\\right)\\right)d\\theta. \\label{E:Q_nmajorandminorarcs}\n\\end{align}\nRecalling \\eqref{E:tthetadef}, we rewrite the first term in \\eqref{E:Q_nmajorandminorarcs} as\n\\begin{align*}\n    &\\sum_{\\substack{1 \\leq h < k_0 \\\\ (h,k)=1}}\\zeta_{k_0}^{-hn}\\omega_{h,k_0}\\left(\\zeta_b^a \\right)\\exp\\left(i2\\lambda_2\\sqrt{n}\\right) \\int_{-\\theta_{h,k_0}'}^{\\theta_{h,k_0}''} \\exp\\left( \\sqrt{n}\\left(\\frac{\\lambda_1+i\\lambda_2}{1-\\frac{2\\pi i \\theta \\sqrt{n}}{\\lambda_1+i\\lambda_2}}-(\\lambda_1+i\\lambda_2) \\right) - 2 \\pi in\\theta \\right) d \\theta.\n\\end{align*}\nWe can estimate the mediants as $\\frac{1}{\\sqrt{n}}\\ll \\theta_{h,k_0}', \\theta_{h,k_0}'' \\ll \\frac{1}{\\sqrt{n}}$ and setting $\\theta \\mapsto \\theta n^{-\\frac12}$, the above integral is asymptotic to\n\\begin{equation}\\label{E:majorarclaplaceint}\n\\frac{1}{n^{\\frac12}}\\int_{-c}^{c}\n\\exp\\left( \\sqrt{n}\\left(\\frac{\\lambda_1+i\\lambda_2}{1-\\frac{2\\pi i  \\theta}{\\lambda_1+i\\lambda_2}}-(\\lambda_1+i\\lambda_2) -2 \\pi i \\theta\\right)  \\right) d \\theta=:\\frac{1}{n^{\\frac12}}\\int_{-c}^ce^{\\sqrt{n}B(\\theta)}d\\theta,\\end{equation}   \nfor some $c>0$, say.  We claim that we can apply Theorem \\ref{laplacemethod} with $x_0 \\mapsto 0,$ $A(x) \\mapsto 1$ and $B$ as above.  Here, $B(0)=0$ and expanding the geometric series gives\n$$\nB(\\theta)=-\\frac{4 \\pi^2}{\\lambda_1+i\\lambda_2}\\theta^2+o\\left(\\theta^2\\right), \\qquad \\theta \\to 0,\n$$\nwith $\\mathrm{Re}\\left(\\frac{4 \\pi^2}{\\lambda_1+i\\lambda_2} \\right) > 0$.  Finally, we claim that $\\mathrm{Re}(B(\\theta)) \\leq 0$ with equality if and only if $\\theta=0.$   Indeed, \n$$\n\\mathrm{Re}(B(\\theta))=\\mathrm{Re}\\left(\\frac{\\lambda_1+i\\lambda_2}{1-\\frac{2\\pi i \\theta}{\\lambda_1+i\\lambda_2}}\\right)-\\lambda_1 \n=\\frac{|\\lambda_1+i\\lambda_2|^2}{\\lambda_1}\\mathrm{Re}\\left(\\frac{e^{i\\psi}}{1+i\\left(\\frac{\\lambda_2}{\\lambda_1}-\\frac{2\\pi \\theta}{\\lambda_1}\\right)} \\right)-\\lambda_1,\n$$\nwhere $\\lambda_1+i\\lambda_2=\\left|\\lambda_1+i\\lambda_2 \\right|e^{i\\frac{\\psi}{2}}$ and $\\psi \\in \\left(-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right).$  Lemma \\ref{L:exponentialquotientmax} applies to show\n$$\n\\mathrm{Re}(B(\\theta)) \\leq \\frac{|\\lambda_1+i\\lambda_2|^2}{\\lambda_1}\\cos^2\\left(\\frac{\\psi}{2}\\right)-\\lambda_1=\\frac{\\lambda_1^2}{\\lambda_1}-\\lambda_1=0,\n$$\nwith equality if and only if\n$$\n\\mathrm{Arg}\\left(1+i\\left(\\frac{\\lambda_2}{\\lambda_1}-\\frac{2\\pi\\theta}{\\lambda_1}\\right)\\right)=\\frac{\\psi}{2}=\\mathrm{Arg}\\left(\\lambda_1+i\\lambda_2\\right),\n$$\nthus if and only if $\\theta=0,$ as claimed.  Now by Theorem \\ref{laplacemethod}, we conclude that \\eqref{E:majorarclaplaceint} is asymptotic to\n$$\n\\frac{\\sqrt{\\lambda_1+i\\lambda_2}}{2\\sqrt{\\pi}n^{\\frac34}},\n$$\nand overall\n\\begin{align*}\n    &\\sum_{\\substack{1 \\leq h < k_0 \\\\ (h,k)=1}}\\zeta_{k_0}^{-hn}\\omega_{h,k_0}\\left(\\zeta_b^a\\right) \\times \\int_{-\\theta_{h,k_0}'}^{\\theta_{h,k_0}''} \\exp\\left( -2\\lambda_1\\sqrt{n} +\\frac{(\\lambda_1+i\\lambda_2)^2}{\\frac{\\lambda_1+i\\lambda_2}{\\sqrt{n}}-2 \\pi i \\theta} +\\sqrt{n}(\\lambda_1+i\\lambda_2)-2 \\pi i n\\theta \\right) d \\theta \\\\\n    &\\hspace{4cm} \\sim \\frac{\\sqrt{\\lambda_1+i\\lambda_2}}{2\\sqrt{\\pi}n^{\\frac34}}e^{2i\\lambda_2\\sqrt{n}}\\sum_{\\substack{1 \\leq h < k_0 \\\\ (h,k_0)=1}} \\zeta_{k_0}^{-hn}\\omega_{h,k_0}\\left(\\zeta_b^a\\right).\n\\end{align*}\nWhen the $e^{2\\lambda_1\\sqrt{n}}$ is brought back to the right-hand side, this is the right-hand side of Theorem \\ref{T:twistedetaproduct}.\n\nFor $k\\neq k_0$, we follow Parry in Lemma 5.2 of \\cite{Parry} and write\n\\begin{align*}\n    \\mathrm{Re}\\left(\\frac{\\mathrm{Li}_2\\left(\\zeta_b^{ak}\\right)}{k^2t_{\\theta}} + nt_{\\theta}\\right) &=\\lambda_1\\sqrt{n}\\left(\\frac{\\left|\\mathrm{Li}_2\\left(\\zeta_b^{ak}\\right)\\right|}{k^2\\lambda_1^2} \\mathrm{Re}\\left(\\frac{e^{i\\psi_k}}{1+i\\left(\\frac{\\lambda_2}{\\lambda_1}-\\frac{2\\pi\\theta\\sqrt{n}}{\\lambda_1}\\right)}\\right)+1\\right),\n\\end{align*}\nwhere $\\psi_k$ satisfies $\\mathrm{Li}_2(\\zeta_b^{ak})=|\\mathrm{Li}_2(\\zeta_b^{ak})|e^{i\\psi_k}.$  Arguing as for the major arcs, the expression $\\mathrm{Re}(\\cdot)$ above is at most $\\cos^2\\left(\\frac{\\psi_k}{2}\\right)$.   Now let\n$$\n\\Delta:= \\inf_{k \\neq k_0}\\left(1-\\left(\\mathrm{Re}\\left(\\frac{\\sqrt{\\mathrm{Li}_2(\\zeta_b^{ak})}}{k\\lambda_1}\\right)\\right)^2\\right) >0.\n$$\nThen\n$$\n    \\mathrm{Re}\\left(\\frac{\\mathrm{Li}_2(\\zeta_b^{ak})}{k^2t_{\\theta}} + nt_{\\theta}\\right) \\leq \\lambda_1\\sqrt{n}\\left(\\frac{\\left|\\mathrm{Li}_2\\left(\\zeta_b^{ak}\\right)\\right|}{k^2\\lambda_1^2}\\cos^2\\left(\\frac{\\psi_k}{2}\\right)+1\\right)\\leq \\lambda_1 \\sqrt{n}(2-\\Delta).\n$$\nThus,\n\\begin{align*}\n    &\\left|\\sum_{\\substack{\\frac{h}{k} \\in \\mathcal{F}_N \\\\ k \\neq k_0}} \\zeta_{k}^{-hn}  \\int_{-\\theta_{h,k}'}^{\\theta_{h,k}''}\\exp\\left(-2\\lambda_1\\sqrt{n}+\\frac{\\mathrm{Li}_2(z^k)}{k^2t_{\\theta}} +nt_{\\theta} + \\delta O(\\sqrt{n})\\right)d\\theta\\right| \\leq \\exp\\left(-\\lambda_1\\Delta \\sqrt{n}+ \\delta O\\left(\\sqrt{n}\\right) \\right).\n\\end{align*}\nWe can choose $\\delta$ small enough so that the constant in the exponential is negative, and the minor arcs are exponentially smaller than the major arc(s).  This completes the proof of cases (1), (2) and (3).\n\nFor case (4), we have $\\lambda_1+i\\lambda_2=\\lambda_1=\\frac{\\sqrt{\\mathrm{Li}_2(1)}}{3}=\\frac{\\pi}{3\\sqrt{6}}$.  Exactly as in case (3) the minor arcs are those with $k \\neq 3$, and these are shown to be exponentially smaller than for $k_0=3$.  Thus, by Lemma \\ref{L:Efixedkbound} part (4), we have\n\\begin{align*}\n    e^{-2\\lambda_1\\sqrt{n}}Q_n(\\zeta_3) &= \\zeta_3^{-n}C_{1,3} \\int_{-\\theta_{1,3}'}^{\\theta_{1,3}''} t_{\\theta}^{\\frac16} \\exp\\left(-2\\lambda_1\\sqrt{n}+\\frac{\\lambda_1^2}{t_{\\theta}}+nt_{\\theta}+o(1) \\right)d \\theta \\nonumber \\\\\n    & \\quad + \\zeta^{-2n}_3C_{2,3} \\int_{-\\theta_{2,3}'}^{\\theta_{2,3}''} t_{\\theta}^{-\\frac16} \\exp\\left(-2\\lambda_1\\sqrt{n}+\\frac{\\lambda_1^2}{t_{\\theta}}+nt_{\\theta}+o(1) \\right)d \\theta,\n\\end{align*}\nwhere\n\\begin{align*}\n    C_{1,3}&:=\\left(1-\\zeta_3^2\\right)^{-\\frac{1}{6}}(1-\\zeta_3)^{\\frac{1}{2}}\\Gamma\\left(\\frac{2}{3}\\right) \\frac{3^{\\frac{1}{6}}}{\\sqrt{2\\pi}}, \\hspace{1cm} C_{2,3}&:=\\left(1-\\zeta_3^2\\right)^{\\frac{1}{6}}(1-\\zeta_3)^{\\frac{1}{2}}\\Gamma\\left(\\frac{1}{3}\\right) \\frac{1}{3^{\\frac{1}{6}}\\sqrt{2\\pi}}.\n\\end{align*}\nNoting\n$$\nt_{\\theta}=\\frac{\\pi}{3\\sqrt{6n}}\\left(1-6i\\sqrt{6n}\\theta\\right),\n$$\nwe have\n\\begin{align}\n \\nonumber\n    \\begin{split}\n    &e^{-2\\lambda_1\\sqrt{n}}Q_n(\\zeta_3)\n    \\end{split}\\\\\n      \\nonumber\n    \\begin{split}\n     &=\\zeta_3^{-n}C_{1,3}\\frac{(\\pi)^{\\frac16}}{3^{\\frac16}(6n)^{\\frac{1}{12}}} \\int_{-\\theta_{1,3}'}^{\\theta_{1,3}''} \\left(1-6i\\sqrt{6n}\\theta\\right)^{\\frac16} \\exp\\left(-2\\lambda_1\\sqrt{n}+\\frac{\\lambda_1^2}{t_{\\theta}}+nt_{\\theta}+o(1) \\right)d \\theta \n    \\end{split}\\\\ \n    \\begin{split}\\label{e13majorarcsint2b} \n& + \\zeta^{-2n}_3C_{2,3}\\frac{3^{\\frac16}(6n)^{\\frac{1}{12}}}{(\\pi)^{\\frac16}} \\int_{-\\theta_{2,3}'}^{\\theta_{2,3}''} \\left(1-6i\\sqrt{6n}\\theta\\right)^{-\\frac16} \\exp\\left(-2\\lambda_1\\sqrt{n}+\\frac{\\lambda_1^2}{t_{\\theta}}+nt_{\\theta}+o(1) \\right)d \\theta.\n    \\end{split}\n\\end{align}\nSetting $\\theta \\mapsto \\theta n^{-\\frac12}$ and arguing as before, both integrals are asymptotic to\n$$\n\\frac{\\sqrt{\\lambda_1}}{2\\sqrt{\\pi}n^{\\frac34}}=\\frac{1}{2^{\\frac54}3^{\\frac34}n^{\\frac34}}.\n$$\nHence, the second term in \\eqref{e13majorarcsint2b} dominates, and gives the claimed asymptotic formula.\n\\end{proof}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n  \n  \n  \n  \n  \n  \n  \n  \n  \\section{Proof of Lemmas \\ref{L:Efixedkbound}, \\ref{L:Esmallkbound}, and \\ref{L:Elargekbound} }\\label{minorarcbounds}\n\nWe prove Lemma \\ref{L:Esmallkbound} first then make use of these ideas in the proof of Lemma \\ref{L:Efixedkbound}. We finish the section by proving Lemma \\ref{L:Elargekbound}.\n\\subsection{Proof of Lemma \\ref{L:Esmallkbound} } We rewrite $E_{h,k}$ as a sum of two functions: a function to which we can apply Euler--Maclaurin summation, and another to which we apply the tools in Proposition \\ref{P:Abelpartialsummation} and Lemma \\ref{L:CosSumBound}.\n\\begin{lemma}\\label{L:Ehkcase1rewrite}\nFor $\\mathrm{Re}(t)>0$ and $z=\\zeta_b^a,$ we have\n\\begin{align}\n\\label{E:Ehkcase2rewrite1} E_{h,k}(z,t)&=\\sum_{\\substack{1 \\leq m \\leq bk \\\\ 1 \\leq j \\leq k}}  \\zeta_b^{ma} \\zeta_k^{jmh}kt\\sum_{\\ell \\geq 0} g_{j,k}\\left(t(bk^2 \\ell + km) \\right)\n + \\mathrm{Log} \\left(\\prod_{j=1}^k \\left(1-\\zeta_b^{a} \\zeta_k^{-jh}e^{-jt}\\right)^{-\\frac{1}{2}+\\frac{j}{k}}\\right),\n\\end{align}\n  where\n  $$\n  g_{j,k}(w):=\\frac{e^{-\\frac{j}{k}w}}{w(1-e^{-w})}-\\frac{1}{w^2}-\\left(\\frac{1}{2}-\\frac{j}{k} \\right)\\frac{e^{-\\frac{j}{k}w}}{w}.\n  $$\n\\end{lemma}\n\\begin{proof}\nIn $E_{h,k}$, we expand the logarithm using its Taylor series as\n  \\begin{align*}\n    \\mathrm{Log}\\left(\\zeta_b^{a} \\zeta_k^{h}e^{-t}; \\zeta_k^{h}e^{-t}\\right)_{\\infty}^{-1}\n    &=\\sum_{\\substack{\\nu \\geq 1 \\\\ \\ell \\geq 1}} \\frac{ \\zeta_b^{\\ell a} \\zeta_k^{\\ell \\nu h}e^{-\\ell \\nu t}}{\\ell} =\\sum_{\\substack{1 \\leq j \\leq k \\\\ 1 \\leq m \\leq bk}}\\sum_{\\substack{\\nu \\geq 0 \\\\ \\ell \\geq 0}} \\frac{\\zeta_{bk}^{m(ka+bjh)}e^{-(bk\\ell+m) (\\nu k + j)t}}{bk\\ell+m} \\\\\n     &=\\sum_{\\substack{1 \\leq j \\leq k \\\\ 1 \\leq m \\leq bk}}\\zeta_{b}^{ma}\\zeta_{k}^{mjh}\\sum_{\\ell \\geq 0} \\frac{e^{-jt(bk\\ell+m)}}{(bk\\ell+m)(1-e^{-t(bk^2\\ell+km)})}.\n  \\end{align*}\n  This corresponds to the left term in $g_{j,k}.$\n  For the middle term in $g_{j,k}$, we compute (using $\\gcd(h,k)=1$)\n $$\n      \\sum_{\\substack{1 \\leq j \\leq k \\\\ 1 \\leq m \\leq bk}}\\zeta_{b}^{ma}\\zeta_{k}^{mjh}kt\\sum_{\\ell \\geq 0} \\frac{1}{t^2(bk^2\\ell +km)^2}  =\\frac{k^2}{t}\\sum_{\\substack{1 \\leq m \\leq bk \\\\ m \\equiv 0 \\pmod{k}}}\\sum_{\\ell \\geq 0} \\zeta_{b}^{ma}\\frac{1}{(bk^2\\ell+mk)^2}  =\\frac{1}{tk^2} \\mathrm{Li}_2\\left(\\zeta_{b}^{ka} \\right).\n$$\n  \n  Finally, it is simple to show that the logarithm of the product in \\eqref{E:Ehkcase2rewrite1} cancels with the sum of the right term in $g_{j,k}$, simply by expanding the logarithm into its Taylor series.\n\\end{proof}\n\nWe estimate the first term in \\eqref{E:Ehkcase2rewrite1} using Euler--Maclaurin summation.  First we need a technical definition.  Since $\\textnormal{gcd}(h,k) =1$, there is at most one $j_0$ in the sum in \\eqref{E:Ehkcase2rewrite1} for which $\\zeta_{b}^{a}\\zeta_{k}^{j_0h}=1;$ i.e., such that $ak+bj_0h\\equiv 0 \\pmod{bk}.$ Define\n$$\n\\mathcal{S}_{a,b}:= \\{(h,k) \\in \\mathbb{N}^2 : \\text{there exists $j_0 \\in [1,k]$ with $ak + j_0b h \\equiv 0 \\pmod{bk}$}\\}.\n$$\n\n  \n   \n   \n   \n  \n   \n    \n  \n   \n\n\n\n\n\n\\begin{lemma}\\label{L:gjksmallbound} Let $j_0$ be as above.  For $k \\leq n^{\\varepsilon}$ and $-\\theta_{h,k}' \\leq \\theta \\leq \\theta_{h,k}''$, we have\n  \\begin{align*}\n  &\\sum_{\\substack{1 \\leq m \\leq bk \\\\ 1 \\leq j \\leq k}}  \\zeta_b^{ma} \\zeta_k^{jmh}kt_{\\theta}\\sum_{\\ell \\geq 0} g_{j,k}\\left(t_{\\theta}(bk^2 \\ell + km) \\right)\\\\&=\\left(\\log \\left(\\Gamma\\left(\\frac{j_0}{k}\\right)\\right)+\\left(\\frac{1}{2}-\\frac{j_0}{k}\\right)\\log\\left(\\frac{j_0}{k}\\right)-\\frac{1}{2}\\log(2 \\pi)\\right)1_{(h,k) \\in \\mathcal{S}_{a,b}} +O\\left(\\frac{k^3}{\\sqrt{n}}\\right)+O\\left(\\frac{k^5}{n}\\right).\n  \\end{align*}\n\\end{lemma}\n\n\\begin{proof}\nNote that the function $g_{j,k}(w)$ is holomorphic at 0 and in any cone $|\\mathrm{Arg}(w)| \\leq \\frac{\\pi}{2} - \\eta.$  Also, $\\theta_{h,k}', \\theta_{h,k}'' \\leq \\frac{1}{kN}=O\\left(\\frac{1}{\\sqrt{n}}\\right)$ implies that $t_{\\theta}$ lies in such a fixed cone (see also \\cite{andrewsbook} on p. 75).  Thus, we can apply Theorem \\ref{T:BMJS} to $g_{j,d}(z)$ with $w\\mapsto t_{\\theta}bk^2$, $a\\mapsto \\frac{m}{bk},$ and $N \\mapsto 0$,\n  \\begin{align*}\n  \\sum_{\\ell \\geq 0} g_{j,k}\\left(t_{\\theta}bk^2\\left(\\ell+\\frac{m}{bk}\\right)\\right)&=\\frac{1}{t_{\\theta}bk^2}\\int_0^{\\infty} g_{j,k}(w)dw-\\left(\\frac{1}{12}-\\frac{j^2}{2k^2}\\right)\\left(\\frac{1}{2}-\\frac{m}{bk}\\right)+O\\left(\\frac{k^2}{\\sqrt{n}}\\right).\n  \\end{align*}\n  When summing the $O$-term, we get\n  $$\n  \\sum_{\\substack{1 \\leq m \\leq bk \\\\ 1 \\leq j \\leq k}} kt_{\\theta} O\\left(\\frac{k^2}{\\sqrt{n}}\\right)=O\\left(\\frac{k^5}{n} \\right),\n  $$\n  where we used the fact that $t_{\\theta}$ lies in a cone. Summing first over $m$ gives\n  $$\n  \\sum_{1 \\leq m \\leq bk} \\zeta_{b}^{ma} \\zeta_k^{jmh}\\left(\\frac{1}{12}-\\frac{j^2}{2k^2}\\right)\\left(\\frac{1}{2}-\\frac{m}{bk}\\right)= O\\left(k\\right)\n\n  $$\n  \n  Hence,\n  \\begin{align*}\n      &\\sum_{\\substack{1 \\leq m \\leq bk \\\\ 1 \\leq j \\leq k}}  \\zeta_b^{ma} \\zeta_k^{jmh}kt_{\\theta}\\sum_{\\ell \\geq 0} g_{j,k}\\left(t_{\\theta}(bk^2 \\ell + km) \\right)\\\\%&=\\left(\\int_0^{\\infty} g_{j_0,k}(w)dw-bk^2t_{\\theta}\\left(\\frac{1}{12}-\\frac{j_0^2}{2k^2} \\right)\\left(\\frac{1}{2}-\\frac{j_0}{k} \\right)\\right)1_{k \\in \\mathcal{S}_{a,b}}+O\\left(\\frac{k^5}{n}\\right) \\\\\n      &=\\left(\\int_0^{\\infty} g_{j_0,k}(w)dw\\right)1_{(h,k) \\in \\mathcal{S}_{a,b}}+O\\left(\\frac{k^3}{\\sqrt{n}}\\right) +O\\left(\\frac{k^2}{\\sqrt{n}}\\right)+O\\left(\\frac{k^5}{n}\\right) \\\\\n      &=\\left(\\log \\Gamma\\left(\\frac{j_0}{k}\\right)+\\left(\\frac{1}{2}-\\frac{j_0}{k}\\right)\\log\\left(\\frac{j_0}{k}\\right)-\\frac{1}{2}\\log(2 \\pi)\\right)1_{(h,k) \\in \\mathcal{S}_{a,b}} +O\\left(\\frac{k^3}{\\sqrt{n}}\\right)+O\\left(\\frac{k^5}{n}\\right),\n  \\end{align*}\nwhere the last step follows by  by Lemma \\ref{L:Bringmannintegral}. If $\\varepsilon <\\frac{1}{4},$ then the terms $O\\left(\\frac{k^3}{\\sqrt{n}}\\right)$ and $O\\left(\\frac{k^5}{n}\\right)$ are smaller than $\\sqrt{n}$ as needed since $N = O(\\delta \\sqrt{n})$ where $\\delta$ is chosen small and independently of $n$.\n\\iffalse\nNote that the function $g_{j,k}(w)$ is holomorphic at 0 and in any cone $|\\mathrm{Arg}(w)| \\leq \\frac{\\pi}{2} - \\eta.$  Also, $\\theta_{h,k}', \\theta_{h,k}'' \\leq \\frac{1}{2N}=O\\left(\\frac{1}{\\sqrt{n}}\\right)$ implies that $t_{\\theta}$ lies in such a fixed cone.  Thus, we can apply Theorem \\ref{T:BMJS} to $g_{j,d}(z)$ with $w\\mapsto t_{\\theta}bk^2$, $a\\mapsto \\frac{m}{bk},$ and $N \\mapsto 0$,\n  \\begin{align*}\n  \\sum_{\\ell \\geq 0} g_{j,k}\\left(t_{\\theta}bk^2\\left(\\ell+\\frac{m}{bk}\\right)\\right)&=\\frac{1}{t_{\\theta}bk^2}\\int_0^{\\infty} g_{j,k}(w)dw-\\left(\\frac{1}{12}-\\frac{j^2}{2k^2}\\right)\\left(\\frac{1}{2}-\\frac{j}{k}\\right)+O\\left(\\frac{k^2}{\\sqrt{n}}\\right),\n  \\end{align*}\n  for a constant independent of $j$ and $m$.\n  When summing the $O$-term, we get\n  $$\n  \\sum_{\\substack{1 \\leq m \\leq bk \\\\ 1 \\leq j \\leq k}} kt_{\\theta} O\\left(\\frac{k^2}{\\sqrt{n}}\\right)=O\\left(\\frac{k^5}{n} \\right),\n  $$\n  where we used the fact that $t_{\\theta}$ lies in a cone.  The other terms are independent of $m$, and so summing first over $m$ gives\n  $$\n  \\sum_{1 \\leq m \\leq bk} \\zeta_{b}^{ma} \\zeta_k^{jmh}=\\begin{cases} bk & \\text{if $j=j_0$ and $k \\in \\mathcal{S}_{a,b,k}$,} \\\\\n 0 & \\text{otherwise.} \\end{cases}\n  $$\n  \n  Hence,\n  \\begin{align*}\n      &\\sum_{\\substack{1 \\leq m \\leq bk \\\\ 1 \\leq j \\leq k}}  \\zeta_b^{ma} \\zeta_k^{jmh}kt_{\\theta}\\sum_{\\ell \\geq 0} g_{j,k}\\left(t_{\\theta}(bk^2 \\ell + km) \\right)\\\\&=\\left(\\int_0^{\\infty} g_{j_0,k}(w)dw-bk^2t_{\\theta}\\left(\\frac{1}{12}-\\frac{j_0^2}{2k^2} \\right)\\left(\\frac{1}{2}-\\frac{j_0}{k} \\right)\\right)1_{k \\in \\mathcal{S}_{a,b,k}}+O\\left(\\frac{k^5}{n}\\right) \\\\\n      &=\\left(\\int_0^{\\infty} g_{j_0,k}(w)dw\\right)1_{k \\in \\mathcal{S}_{a,b,k}}+O\\left(\\frac{k^2}{\\sqrt{n}}\\right)+O\\left(\\frac{k^5}{n}\\right) \\\\\n      &=\\left(\\log \\Gamma\\left(\\frac{j_0}{k}\\right)+\\left(\\frac{1}{2}-\\frac{j_0}{k}\\right)\\log\\left(\\frac{j_0}{k}\\right)-\\frac{1}{2}\\log(2 \\pi)\\right)1_{k \\in \\mathcal{S}_{a,b,k}} +O\\left(\\frac{k^2}{\\sqrt{n}}\\right)+O\\left(\\frac{k^5}{n}\\right),\n  \\end{align*}\n  by Lemma \\ref{L:Bringmannintegral}, as claimed.\n \n  \\fi\n\\end{proof}\nIt remains to estimate the product term in \\eqref{E:Ehkcase2rewrite}.\n\\begin{lemma}\\label{L:TheProduct}\n  Uniformly for $k \\leq n^{\\varepsilon}$ and $-\\theta_{h,k} \\leq \\theta \\leq \\theta_{h,k}''$, we have\n  $$\n  \\mathrm{Log}\\left(\\prod_{j=1}^k \\left(1-\\zeta_b^{a} \\zeta_k^{-jh}e^{-jt_{\\theta}}\\right)^{-\\frac{1}{2}+\\frac{j}{k}}\\right) = O\\left(n^{\\varepsilon}\\right).\n  $$\n\\end{lemma}\n\n\n    \n    \\begin{proof}\n    Recall the sums $G_m$ defined in Lemma \\ref{L:CosSumBound}.  Using the Taylor expansion for the logarithm followed by Proposition  \\ref{P:Abelpartialsummation}, we write\n    \\begin{align*}\n    \\left|\\mathrm{Log} \\left(\\prod_{j=1}^k \\left(1-\\zeta_b^{a} \\zeta_k^{-jh}e^{-jt_{\\theta}}\\right)^{-\\frac{1}{2}+\\frac{j}{k}}\\right) \\right|&=\n     \\left|\\sum_{j=1}^k\\left(\\frac{1}{2}-\\frac{j}{k}\\right)\\sum_{m \\geq 1} \\frac{ \\zeta_{bk}^{m(ak+bjh)}}{m}e^{-jmt_{\\theta}} \\right|\\\\&=\\left|\\sum_{j=1}^k\\left(\\frac{1}{2}-\\frac{j}{k}\\right)(1-e^{-jt_{\\theta}})\\sum_{m \\geq 1} G_m\\left(\\frac{ak+bhj}{bk}\\right)e^{-mjt_{\\theta}}\\right|.\n    \\end{align*}\n    It is elementary to show that at most one of $\\{ak+bjh\\}_{1 \\leq j \\leq k}$ is divisible by $bk$.  Suppose that this happens at $j_0$ (if it never happens, then the argument is similar).  Then $G_m\\left(\\frac{ak+bhj_0}{bk}\\right)=H_m$, the $m$-th harmonic number.  Applying the formula $\\sum_{m \\geq 1} H_mx^m=\\frac{-\\log(1-x)}{1-x}$, the above is\n    \n    \n    \\begin{align*}\n    &\\ll \\left|1-e^{-j_0t_{\\theta}}\\right|\\sum_{m \\geq 1} H_m e^{-mj_0\\mathrm{Re}(t_{\\theta})}+ \\sum_{\\substack{1 \\leq j \\leq k \\\\ j \\neq j_0}} \\left|1-e^{-jt_{\\theta}}\\right|\\max_{m \\geq 1} \\left| G_m\\left(\\frac{a}{b}+\\frac{hj}{k}\\right) \\right|\\sum_{m \\geq 1} e^{-mj\\mathrm{Re}(t_{\\theta})} \\\\\n    &\\ll \\left|\\log\\left(1-e^{-j_0t_{\\theta}}\\right)\\right|\\frac{|1-e^{-j_0t_{\\theta}}|}{1-e^{-j_0\\mathrm{Re}(t_{\\theta})}}+ \\sum_{\\substack{1 \\leq j \\leq k \\\\ j \\neq j_0}} \\frac{\\left|1-e^{-jt_{\\theta}}\\right|}{1-e^{-j\\mathrm{Re}(t_{\\theta})}}\\max_{m \\geq 1} \\left| G_m\\left(\\frac{a}{b}+\\frac{hj}{k}\\right) \\right|.\n    \\end{align*}\n    The fact that $t_{\\theta}$ lies in a cone $|\\mathrm{Arg}(t_{\\theta})|\\leq \\frac{\\pi}{2}-\\eta$ with $j \\leq k \\leq n^{\\varepsilon}<\\sqrt{n}$ gives\n    $$\\frac{\\left|1-e^{-jt_{\\theta}}\\right|}{1-e^{-j\\mathrm{Re}(t_{\\theta})}}= O \\left( \\frac{|t_{\\theta}|}{\\mathrm{Re}(t_{\\theta})}\\right) =O(1).$$\n     Thus, using Lemma \\ref{L:Gmaxbound}\n    \\begin{align*}\n    \\left|\\mathrm{Log} \\left(\\prod_{j=1}^k \\left(1-\\zeta_b^{a} \\zeta_k^{-jh}e^{-jt_{\\theta}}\\right)^{-\\frac{1}{2}+\\frac{j}{k}}\\right) \\right|&=O(\\log( n))+O\\left(\\sum_{\\substack{1 \\leq j \\leq k \\\\ j \\neq j_0}} \\max_{m \\geq 1} \\left|G_m\\left(\\frac{a}{b}+\\frac{hj}{k}\\right)\\right|\\right) \\\\ &=O(\\log (n))+O(k)=O(n^{\\varepsilon}),\n    \\end{align*}\n    as claimed.\n   \\end{proof}\n   \n   Lemma \\ref{L:Esmallkbound} now follows from Lemmas \\ref{L:Ehkcase1rewrite}, \\ref{L:gjksmallbound} and  \\ref{L:TheProduct}  by recalling that $k\\leq n^{\\varepsilon}$ where $0 < \\varepsilon \\leq \\frac{1}{4}$:\n   \\begin{align*}\n       E_{h,k}(\\zeta^a_b,t_\\theta) &= \\left(\\log \\left(\\Gamma\\left(\\frac{j_0}{k}\\right)\\right)+\\left(\\frac{1}{2}-\\frac{j_0}{k}\\right)\\log\\left(\\frac{j_0}{k}\\right)-\\frac{1}{2}\\log(2 \\pi)\\right)1_{(h,k) \\in \\mathcal{S}_{a,b}}\\\\ &\\hspace{5mm}+O\\left(\\frac{k^3}{\\sqrt{n}}\\right)+O\\left(\\frac{k^5}{n}\\right)+ O\\left(n^\\varepsilon\\right)\\\\\n       &\\ll \\log(n) + n^{3\\varepsilon-\\frac{1}{2}}+n^\\varepsilon = O\\left(n^{3\\varepsilon-\\frac{1}{2}}\\right)+ O\\left(n^\\varepsilon\\right).\n   \\end{align*}\n   \n   \\subsection{Proof of Lemma  \\ref{L:Efixedkbound}} To prove Lemma \\ref{L:Efixedkbound}, we need an elementary fact about the sets $\\mathcal{S}_{a,b}$.\n   \\begin{lemma}\\label{L:Sabknonempty}\n     Let $1 \\leq a < \\frac{b}{2}$ with $\\gcd(a,b)=1$ and $b \\geq 3$.  Then $(1,1)\\not \\in \\mathcal{S}_{a,b}$, $(h,2)\\not\\in \\mathcal{S}_{a,b}$, and $(h,3)\\in \\mathcal{S}_{a,b}$ if and only if $(a,b) =(1,3)$.\n   \\end{lemma}\n   \\begin{proof}\n   We prove the case $(h,k) = (h,2)$ and note that the remaining cases are analogous. We have that $ (h,2) \\in S_{a,b}$   if and only if $2b$ divides $2a+b$ or $2a+2b$.  Clearly, $2b \\nmid (2a+2b)$, and since $2a+b < 3b < 2 \\cdot (2b)$,\n   $$\n   2b \\mid (2a+b) \\iff 2a+b=2b \\iff 2a=b \\iff (a,b)=(1,2),\n   $$\n   which is a contradiction.\n   \\end{proof}\n   \n   \n   \\begin{proof}[Proof of Lemma \\ref{L:Efixedkbound}]\n   Cases (1), (2) and (3) are simple consequences of Lemmas \\ref{L:Ehkcase1rewrite} and \\ref{L:gjksmallbound} and \\ref{L:Sabknonempty}.  For case (4), we suppose $\\zeta= \\zeta_3$.  Then one finds $j_0(1,3,1,3)=2$ and Lemmas \\ref{L:Ehkcase1rewrite} and  \\ref{L:gjksmallbound} imply \n   \\begin{align*}\n E_{1,3}( \\zeta_3,t_{\\theta}) & =\\mathrm{Log}\\left(\\prod_{j=1}^3\\left(1- \\zeta_3 \\zeta_3^{j}e^{-jt_{\\theta}}\\right)^{-\\frac{1}{2}+\\frac{j}{3}}\\right)+\\log \\left(\\Gamma\\left(\\frac{2}{3}\\right)\\right)-\\frac{1}{6}\\log\\left(\\frac{2}{3}\\right)-\\frac{1}{2}\\log(2\\pi)+o(1)\\\\\n &=\\mathrm{Log}\\left(t_{\\theta}^{\\frac{1}{6}}\\right)+\\mathrm{Log}\\left(\\frac{(1- \\zeta_3)^{\\frac12}}{(1- \\zeta_3^2)^{\\frac16}} \\right)+\\log\\left( \\Gamma\\left(\\frac{1}{3}\\right)\\right)+\\frac{1}{6}\\log\\left(3\\right)-\\frac{1}{2}\\log(2\\pi)+o(1) \n ,\n   \\end{align*}\n   as claimed, whereas $j_0(1,3,2,3)=1$, and so\n   \\begin{align*}\n       &E_{2,3}(\\zeta_b^{a},t_{\\theta}) =\\log \\prod_{j=1}^3\\left(1- \\zeta_3 \\zeta_3^{2j}e^{-jt_{\\theta}}\\right)^{-\\frac{1}{2}+\\frac{j}{3}}+\\log \\Gamma\\left(\\frac{1}{3}\\right) + \\frac{1}{6}\\log\\left(\\frac{1}{3}\\right) - \\frac{1}{2}\\log(2 \\pi)+o(1) \\\\\n       &=\\log\\left(t_{\\theta}^{-\\frac16}\\right)+\\log\\left( \\left(1- \\zeta_3^2\\right)^{\\frac16}(1- \\zeta_3)^{\\frac12} \\right)+\\log\\Gamma\\left(\\frac{1}{3}\\right)+\\frac{1}{6}\\log\\left(\\frac{1}{3}\\right)  -\\frac{1}{2}\\log(2\\pi)+ o(1),\n   \\end{align*}\n   as claimed.\n   \\end{proof}\n   \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\subsection{Proof of Lemma \\ref{L:Elargekbound}} In preparation for the proof of Lemma \\ref{L:Elargekbound}, we rewrite $E_{h,k}$ as in Lemma \\ref{L:Ehkcase1rewrite}, this time using only the first two terms of $g_{j,k}$.  The proof is analogous.\n\\begin{lemma}\\label{L:Ehkcase2rewrite}\nFor $\\mathrm{Re}(t)>0$ and $z=\\zeta_b^{a},$ we have\n\\begin{equation}\\label{E:Ehkcase2rewrite}\nE_{h,k}(z,t)=\\sum_{\\substack{1 \\leq m \\leq bk \\\\ 1 \\leq j \\leq k}}  \\zeta_b^{ma} \\zeta_k^{jmh}kt\\sum_{\\ell \\geq 0} \\widetilde{g}_{j,k}\\left(t\\left(bk^2 \\ell + km\\right) \\right),\\end{equation}\n  where\n  $$\n  \\widetilde{g}_{j,k}(w):=\\frac{e^{-\\frac{j}{k}w}}{w(1-e^{-w})}-\\frac{1}{w^2}.\n  $$\n\\end{lemma}\nWe will need to estimate the sum in \\eqref{E:Ehkcase2rewrite} separately for $\\ell \\geq 1$ and $\\ell=0.$  For $\\ell \\geq 1$, we can first compute the sum on $j$ as\n  $$\n  \\sum_{1\\leq j \\leq k} \\zeta_k^{jmh}\\widetilde{g}_{j,k}(z)=\\frac{ \\zeta_{k}^{mh}e^{-\\frac{z}{k}}}{z(1- \\zeta_{k}^{mh}e^{-\\frac{z}{k}})}-\\frac{k}{z^2} \\cdot 1_{k \\mid m}.\n  $$\n  Thus, writing $m=\\nu k$ with $1 \\leq \\nu \\leq b$ when $k \\mid m$, we have\n  \n  \\begin{align*}\n     &\\sum_{\\substack{1 \\leq m \\leq bk \\\\ 1 \\leq j \\leq k}}  \\zeta_b^{ma} \\zeta_k^{jmh}kt\\sum_{\\ell \\geq 1} \\widetilde{g}_{j,k}\\left(t(bk^2 \\ell + km) \\right) \\\\\n     &=t\\sum_{\\nu=1}^b \\zeta_{b}^{\\nu ka}\\sum_{\\ell \\geq 1} f_1\\left(bkt\\left(\\ell + \\frac{\\nu}{b}\\right)\\right)+t\\sum_{\\substack{1 \\leq m \\leq bk \\\\ k \\nmid m}} \\zeta_{b}^{ma}\\sum_{\\ell \\geq 1} f_2\\left(bkt\\left(\\ell + \\frac{m}{bk}\\right)\\right) =:S_1+S_2,\n  \\end{align*}\n say, where\n  $$\n  f_1(z):=\\frac{e^{-z}}{z(1-e^{-z})}-\\frac{1}{z^2}\n  $$\n  and\n  $$\n  f_2(z):=\\frac{ \\zeta_{k}^{mh}e^{-z}}{z(1- \\zeta_{k}^{mh}e^{-z})}.\n  $$\n \\begin{lemma}\\label{L:S1bound}\n   For $k \\geq n^{\\varepsilon}$, $-\\theta_{h,k}' \\leq \\theta \\leq \\theta_{h,k}''$ and $t \\mapsto t_{\\theta}$, we have $|S_1|=O\\left(\\log(n)\\right)$.\n \\end{lemma}\n \\begin{proof}\n \n\n  We use Theorem \\ref{T:EulerMac} (with $N \\to \\infty$) to write\n  \\begin{align*}\n  \\sum_{\\ell \\geq 1} f_1\\left(bkt_{\\theta}\\left(\\ell + \\frac{\\nu}{b}\\right)\\right)&=\\frac{f_1\\left(bkt_{\\theta}\\left(1+\\frac{\\nu}{b}\\right)\\right)}{2}+\\int_1^{\\infty}f_1\\left(bkt_{\\theta}\\left(x+\\frac{\\nu}{b}\\right)\\right)dx \\\\& \\quad +bkt_{\\theta}\\int_1^{\\infty}f_1'\\left(bkt_{\\theta}\\left(x+\\frac{\\nu}{b}\\right)\\right)\\left(\\{x\\}-\\frac{1}{2}\\right)dx \\\\\n  &=\\frac{f_1\\left(kt_{\\theta}\\left(b+\\nu\\right)\\right)}{2}+\\frac{1}{bkt_{\\theta}}\\int_{kt_{\\theta}(b+\\nu)}^{\\infty}f_1\\left(z\\right)dz \\\\& \\quad +\\int_{kt_{\\theta}(b+\\nu)}^{\\infty}f_1'\\left(z\\right)\\left(\\left\\{\\frac{z-\\frac{\\nu}{b}}{bkt_{\\theta}}\\right\\}-\\frac{1}{2}\\right)dz.\n  \\end{align*}\n  Here, $f_1(z) \\ll \\frac{1}{z}$ as $z \\to 0,$ thus\n  $$\n  f_1\\left(kt_{\\theta}(b+\\nu)\\right)=O\\left(\\frac{1}{k|t_{\\theta}|} \\right).\n  $$\n  Furthermore $\\int_{t\\cdot \\frac{c}{|t|}}^{t\\infty} f_1(z)dz=O(1)$ for $|\\mathrm{Arg}(t)|\\leq \\frac{\\pi}{2}-\\eta,$ uniformly for any $\\eta, c>0.$  As noted before, $t_{\\theta}$ lies in such a cone, so\n $$\n      \\frac{1}{bkt_{\\theta}}\\int_{kt_{\\theta}(b+\\nu)}^{\\infty}f_1\\left(z\\right)dz\n      =O\\left(\\frac{1}{k|t_{\\theta}|}\\int_{kt_{\\theta}(b+\\nu)}^{t_\\theta\\frac{2b}{|t_\\theta|}}\\frac{1}{z}dz\\right) =O\\left(\\frac{|\\log(kt_{\\theta})|}{k|t_{\\theta}|}\\right).\n  $$\n  Similarly, one has\n  $$\n  f_1'(z)=-\\frac{e^{-z}}{z(1-e^{-z})}-\\frac{e^{-z}}{z^2(1-e^{-z})}-\\frac{e^{-2z}}{z(1-e^{-z})^2}+\\frac{2}{z^3},\n  $$\n  so  $\\int_{t\\cdot \\frac{c}{|t|}}^{t\\infty} f'_1(z)dz=O(1)$ for $|\\mathrm{Arg}(t)|\\leq \\frac{\\pi}{2}-\\eta,$ for any $\\eta, c>0.$  And one has $f_1'(z) \\ll \\frac{1}{z^2}$ as $z \\to 0,$ thus\n \\begin{align*}\n     \\int_{kt_{\\theta}(b+\\nu)}^{\\infty}f_1'\\left(z\\right)\\left(\\left\\{\\frac{z-\\frac{\\nu}{b}}{bkt_{\\theta}}\\right\\}-\\frac{1}{2}\\right)dz &=O\\left(\\int_{kt_{\\theta}(b+\\nu)}^{t_{\\theta}\\frac{2b}{|t_{\\theta}|}} \\frac{1}{z^2} dz \\right) =O\\left(\\frac{1}{k|t_{\\theta}|}\\right).\n \\end{align*}\n The above bounds are all clearly uniform in $1 \\leq \\nu \\leq b$, thus overall\n $$\n |S_1| = \\sum_{\\substack{1 \\leq m \\leq bk \\\\ k \\nmid m}}|t_{\\theta}|O\\left(\\frac{|\\log kt_{\\theta}|}{k|t_{\\theta}|}\\right)=O\\left(|\\log (kt_{\\theta})|\\right)=O(\\log n),\n $$\nas claimed.\n  \\end{proof}\n\\begin{lemma}\\label{L:S2bound}\n  For $k \\geq n^{\\varepsilon}$, $-\\theta_{h,k}' \\leq \\theta \\leq \\theta_{h,k}''$ and $t \\mapsto t_{\\theta}$, we have $|S_2|=O\\left(n^{\\frac12-\\varepsilon}\\right)$.\n\\end{lemma}\n\\begin{proof}\nFor $\\mathrm{Re}(z)>0$, we see immediately that\n  $$\n  |f_2(z)|\\leq \\frac{e^{-\\mathrm{Re}(z)}}{\\mathrm{Re}(z)(1-e^{-\\mathrm{Re}(z)})}=:\\tilde{f_2}(\\mathrm{Re}(z)). \n  $$\n  Thus, since $\\tilde{f_2}$ is decreasing, we have\n  $$\n  |S_2| \\leq |t_{\\theta}|bk \\sum_{\\ell \\geq 1} \\tilde{f_2}\\left(bk\\mathrm{Re}(t_{\\theta})\\ell\\right) \n  \\leq \\frac{|t_{\\theta}|}{\\mathrm{Re}(t_{\\theta})}\\left(\\int_{bk\\mathrm{Re}(t_{\\theta})}^{\\infty} \\tilde{f_2}(x)dx + bk\\mathrm{Re}(t_{\\theta}) \\tilde{f_2}(bk\\mathrm{Re}(t_{\\theta}))  \\right),\n  $$\n  by integral comparison.  We can bound the right term as\n  $$\n bk\\mathrm{Re}(t_{\\theta}) \\tilde{f_2}(bk\\mathrm{Re}(t_{\\theta}))=\\frac{1}{e^{bk\\mathrm{Re}(t_{\\theta})}-1}\\leq \\frac{1}{bk\\mathrm{Re}(t_{\\theta})}.\n  $$\n  Furthermore, as $\\eta \\to 0^+$, we have\n  $$\n  \\int_{\\eta}^{\\infty} \\tilde{f_2}(x)dx = O(1)+\\int_{\\eta}^1 \\frac{e^{-x}}{x(1-e^{-x})}dx \\leq O(1)+\\int_{\\eta}^1 \\frac{1}{x^2}dx=O\\left(\\frac{1}{\\eta}\\right).\n  $$\n  Hence, overall,\n  $$\n  |S_2| = O\\left(\\frac{1}{k\\mathrm{Re}(t_{\\theta})}\\right)=O\\left(\\frac{\\sqrt{n}}{k}\\right)=O\\left(n^{\\frac12-\\varepsilon} \\right),\n  $$\n  as claimed.\n\\end{proof}\n\nIt remains to estimate the double sum \\eqref{E:Ehkcase2rewrite} for the term $\\ell=0;$ i.e., \n\\begin{equation*\n    \\sum_{\\substack{1 \\leq m \\leq bk \\\\ 1 \\leq j \\leq k}} \\zeta_{b}^{ma} \\zeta_k^{jmh} \\frac{\\phi_{\\frac{j}{k}}(tkm)}{m}, \n\\end{equation*}\nwhere\n\\begin{align*} \n\\phi_a(w):=\\frac{e^{-aw}}{1-e^{-w}}- \\frac{1}{w}.\n\\end{align*}\nNote that $\\phi_a$ is holomorphic at 0 and in the cone $|\\mathrm{Arg}(w)| \\leq \\frac{\\pi}{2}- \\eta,$ for any $\\eta>0.$  We apply Lemma \\ref{SmallRadiusEstimate} to $\\phi_a$ to bound differences as follows.\n\n\\begin{lemma} \\label{SmallRadiusEstimate} Let $x$ be a complex number with positive imaginary part and $|x| \\leq 1$. Then there is a constant $c > 0$ independent from $a$ and $x$, such that for all $m \\leq \\frac{1}{|x|}$ we have\n\\begin{align*}\n\\left| \\phi_a(xm) - \\phi_a(x(m+1))\\right| \\leq c|x|.\n\\end{align*}\n\\end{lemma}\n\\begin{proof} The function $\\phi_a(z)$ is holomorphic in $B_3(0)$. The functions $\\phi_a'(z)$ are uniformly bounded on $\\overline{B_{\\frac52}(0)} \\subset B_3(0)$. Indeed, we have uniformly in $a$\n\\begin{align*}\n    & \\max_{|z| \\leq \\frac52} |\\phi'_a(z)| = \\max_{|z| = \\frac{5}{2}} |\\phi'_a(z)| \\leq \\max_{|z| = \\frac52} \\left| \\frac{e^{-az-z}}{(1-e^{-z})^2}\\right| + \\max_{|z| = \\frac52} \\left| \\frac{ae^{-az}}{1-e^{-z}}\\right| + \\max_{|z| = \\frac52} \\left| \\frac{1}{z^2}\\right| \\ll 1.\n\\end{align*} \nOn the other hand, by Lemma \\ref{L:DifferenceEstimate} applied to $f = \\phi_a$, $U = B_3(0)$, and $\\overline{B_{\\frac52}(0)} \\subset U$, we find, since $|xm| \\leq 1$ and $|x(m+1)| \\leq |mx| + |x| \\leq 2$\n\\begin{align*}\n|\\phi_a(xm+x) - \\phi_a(mx)| \\leq \\max_{|z| \\leq \\frac52} |\\phi'_a(z)| |xm + x - xm| = c|x|,    \\end{align*}\nwhere $c$ does not depend on $0 < a \\leq 1$. \\end{proof}\nWe also require the following lemma for large values of $m$, whose proof is a straightforward calculation using that the denominators of the first term in $\\phi_a(w)$ are bounded away from 0. \n\\begin{lemma} \\label{LargeRadiusEstimate} Let $x$ be a complex number with positive imaginary part. Then all $m > \\frac{1}{|x|}$ we have\n\\begin{align*}\n\\left| \\phi_a(xm) - \\phi_a(x(m+1))\\right| \\ll \\frac{1}{|x|m(m+1)} + |x|e^{-m\\mathrm{Re}(x)} + a|x| e^{-am\\mathrm{Re}(x)}.\n\\end{align*}\n\\end{lemma}\n\n\n\n\n\n\n\n\n\n\nThe following lemma, when combined with Lemmas \\ref{L:Ehkcase2rewrite}--\\ref{L:S2bound}, completes the proof of Lemma \\ref{L:Elargekbound}, and thus that of Theorem \\ref{T:twistedetaproduct}.\n\\begin{lemma}\\label{L:l=0rewriteterm1}\nFor $ n^{\\varepsilon} \\leq k \\leq N$ and $-\\theta_{h,k}' \\leq \\theta \\leq \\theta_{h,k}''$, we have\n$$\n\\sum_{\\substack{1 \\leq m \\leq bk \\\\ 1 \\leq j \\leq k}}\\zeta_b^{ma}\\zeta_{k}^{jmh}\\frac{\\phi_{\\frac{j}{k}}(t_{\\theta}km)}{m}=O(k).\n$$\n\\end{lemma}\n\n\\begin{proof} Let $x := kt_{\\theta}$ and $a := \\frac{j}{k}$. Note that we have $0 < a \\leq 1$,  $\\mathrm{Re}(x) > 0$, and $\\frac{|x|}{\\mathrm{Re}(x)} \\ll 1$ uniformly in $k$.  We use Abel partial summation and split the sum into two parts:\n    \\begin{align*}\n        \\sum_{\\substack{1 \\leq m \\leq bk \\\\ 1 \\leq j \\leq k}} = \\sum_{j=1}^k \\left( \\sum_{0 < m \\leq \\min\\left\\{bk, \\frac{1}{|x|}\\right\\}} + \\sum_{\\min\\left\\{bk, \\frac{1}{|x|}\\right\\} < m \\leq bk}\\right).\n    \\end{align*}\n    In the case $|x| > 1$, the first sum is empty, so we can assume $|x| \\leq 1$. We first find with Proposition \\ref{P:Abelpartialsummation} that\n    \\begin{align*}\n         \\sum_{m \\leq \\min\\left\\{bk, \\frac{1}{|x|}\\right\\}}  \\zeta_{bk}^{m(ak+hjb)}\\frac{1}{m}\\phi_a(xm) &= G_{\\min\\left\\{bk, \\frac{1}{|x|}\\right\\}}\\left( \\frac{a}{b} + \\frac{hj}{k} \\right) \\phi_a\\left( x \\min\\left\\{bk, \\Big\\lfloor \\frac{1}{|x|} \\Big\\rfloor \\right\\} \\right) \\\\\n        & + \\sum_{m \\leq \\min\\left\\{bk, \\frac{1}{|x|}\\right\\} - 1} G_{m}\\left( \\frac{a}{b} + \\frac{hj}{k} \\right) \\left( \\phi_a(mx) - \\phi_a((m+1)x)\\right).\n    \\end{align*}\n    It follows that with Lemma \\ref{SmallRadiusEstimate}\n    \\begin{align*}\n    & \\left| \\sum_{j=1}^k \\sum_{m \\leq \\min\\left\\{bk, \\frac{1}{|x|}\\right\\}} \\zeta_b^{ma}\\zeta_k^{mhj}\\cdot \\frac{1}{m}\\phi_a(mx) \\right|  \\leq \\sum_{j=1}^k \\left|G_{\\min\\left\\{bk, \\frac{1}{|x|}\\right\\}}\\left( \\frac{a}{b} + \\frac{hj}{k} \\right)\\right| \\left| \\phi_a\\left( x \\min\\left\\{bk, \\Big\\lfloor\\frac{1}{|x|}\\Big\\rfloor \\right\\}  \\right) \\right| \\\\\n    & \\hspace{3cm} + \\left| \\sum_{j=1}^k \\sum_{0 < m \\leq \\min\\left\\{bk, \\frac{1}{|x|}\\right\\}} G_{m}\\left( \\frac{a}{b} + \\frac{hj}{k} \\right) \\left( \\phi_a(mx) - \\phi_a((m+1)x)\\right) \\right| \\\\\n    & \\ll \\sum_{j=1}^k \\left|G_{\\min\\left\\{bk, \\frac{1}{|x|}\\right\\}}\\left( \\frac{a}{b} + \\frac{hj}{k} \\right)\\right| + \\sum_{j=1}^k \\max_{m=1,..., \\min\\left\\{bk, \\frac{1}{|x|}\\right\\}} \\left|G_{m}\\left( \\frac{a}{b} + \\frac{hj}{k} \\right)\\right| \\sum_{0 < m \\leq \\frac{1}{|x|}} |x| = O(k),\n    \\end{align*}\n    where we used Lemma \\ref{L:Gmaxbound} and $G_{bk}(1) = H_{bk} = O(\\log(k))$ in the last step. Similarly, we find with Lemma \\ref{LargeRadiusEstimate} (without loss of generality we assume $\\frac{1}{|x|} < bk$)\n    \\begin{align*}\n        & \\left| \\sum_{j=1}^k \\sum_{\\frac{1}{|x|} < m \\leq bk} \\zeta_b^{ma}\\zeta_{k}^{mhj}\\cdot \\frac{1}{m}\\phi_a(mx) \\right| \\\\\n        & \\ll \\sum_{j=1}^k \\left| G_{bk}\\left( \\frac{a}{b} + \\frac{hj}{k}\\right) \\right| \\left| \\phi_a\\left( x bk \\right) \\right| + \\left| \\sum_{j=1}^k \\sum_{\\frac{1}{|x|} < m \\leq bk} G_{m}\\left( \\frac{a}{b} + \\frac{hj}{k} \\right) \\left( \\phi_a(mx) - \\phi_a((m+1)x)\\right) \\right| \\\\\n        & \\ll O(k) + \\sum_{j=1}^k \\max_{m=\\frac{1}{|x|},..., bk} \\left|G_{m}\\left( \\frac{a}{b} + \\frac{hj}{k} \\right)\\right| \\sum_{\\frac{1}{|x|} < m \\leq bk} \\left( \\frac{1}{|x|m(m+1)} + |x| e^{-m \\mathrm{Re}(x)} + a|x|e^{-am\\mathrm{Re}(x)} \\right). \n    \\end{align*}\n    Note that we uniformly have $\\phi_a(xbk) \\ll 1$ (as $1 \\ll |xbk|$ and $x$ is part of a fixed cone \\newline $|\\mathrm{Arg}(x)|\\leq \\frac{\\pi}{2}-\\eta$) as well as \n    \\begin{align*}\n    \\sum_{\\frac{1}{|x|} < m \\leq bk} \\frac{1}{|x|m(m+1)} & \\leq \\sum_{\\frac{1}{|x|} < m < \\infty} \\frac{1}{|x|m(m+1)} \\ll 1\n    \\end{align*}\n    and\n    \\begin{align*}\n    \\sum_{\\frac{1}{|x|} < m \\leq bk} |x| e^{-m \\mathrm{Re}(x)} & \\leq \\frac{|x|}{1-e^{-\\mathrm{Re}(x)}} \\ll 1,\n    \\end{align*}\n     as $\\frac{|x|}{\\mathrm{Re}(x)} \\ll 1, |x| \\ll 1.$ Similarly,\n     \n    \\begin{align*}\n    \\sum_{\\frac{1}{|x|} < m \\leq bk} a|x| e^{-am \\mathrm{Re}(x)} & \\ll 1.\n    \\end{align*}\n    As a result, using Lemma \\ref{L:Gmaxbound} (again up to at most one summand in $O(\\log(k))$),\n        \\begin{align*}\n        \\left| \\sum_{j=1}^k \\sum_{\\frac{1}{|x|} < m \\leq bk} \\zeta_b^{ma}\\zeta_{k}^{mhj}\\cdot \\frac{1}{m}\\phi_a(mx) \\right| & \\ll O(k) + \\sum_{j=1}^k \\max_{m=\\frac{1}{|x|},..., bk} \\left|G_{m}\\left( \\frac{a}{b} + \\frac{hj}{k} \\right)\\right| = O(k),\n        \\end{align*}\n       as claimed. \n    \\end{proof}\n    \n    \\section*{Data Availability Statement} Data sharing not applicable to this article as no data sets\nwere generated or analysed during the current study.\n\n\\section*{Conflict of Interest Statement} There are no conflicts of interest for the current study.\n   \n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\n\tDecays of the $\\chi_{c0}$, $\\chi_{c1}$, and $\\chi_{c2}$ states \nare not as well studied \nexperimentally and theoretically as those of other charmonium states.  \nThese states have charge-conjugation eigenvalue $C = +1$, in contrast to\nthe better-studied $C = -1$ states $J\/\\psi$ and $\\psi(2S)$.  Their decay\nproducts thus will differ from those of $J\/\\psi$ and $\\psi(2S)$, and may\nprovide complementary information on states containing light quarks\nand gluons.\nIt is possible that the color-octet mechanism,\n$c \\bar c g \\to 2(q \\bar q)$, could have large effects on the observed\ndecay pattern of the $\\chi_{cJ}$ states~\\cite{quarkoniumreview}.\nAssuming that $\\chi_{cJ}$ are the $^3P_J$ $c\\bar{c}$ bound states\none would expect that $\\chi_{c0}$ and $\\chi_{c2}$ with $J^{PC}$ quantum numbers\n$0^{++}$ and $2^{++}$ decay to light quarks via two gluons~\\cite{Zhao}.\nMeasurement of any possible $\\chi_{cJ}$ hadronic decays provides\nvaluable information on possible glueball dynamics.\nThus knowledge of any hadronic decay channels for these\nstates is valuable.\n\n\tCLEO has gathered a large sample of $e^+e^- \\to \\psi(2S)$ events,\nwhich leads to copious production of the $\\chi_{cJ}$ states in\nradiative decays of the $\\psi(2S)$.\nThe $\\psi(2S)$ branching fractions\nhave been recently measured \\cite{chicbf} with high precision:\n\\begin{equation}\n\\label{eqn:br_chic0}\n    {\\mathcal B}(\\psi(2S)\\to\\gamma \\chi_{c0}) = (9.22\\pm 0.11\\pm 0.46)\\%;\n\\end{equation}\n\\begin{equation}\n\\label{eqn:br_chic1}\n    {\\mathcal B}(\\psi(2S)\\to\\gamma \\chi_{c1}) = (9.07\\pm 0.11\\pm 0.54)\\%;\n\\end{equation}\n\\begin{equation}\n\\label{eqn:br_chic2}\n    {\\mathcal B}(\\psi(2S)\\to\\gamma \\chi_{c2}) = (9.33\\pm 0.14\\pm 0.61)\\%.\n\\end{equation}\nWe describe\na study of selected three-body hadronic decay modes of the\n$\\chi_{cJ}$ to two charged and one neutral hadron.\nThis is not an exhaustive study of $\\chi_{cJ}$ hadronic decays;\nwe do not even comprehensively cover all possible $h^+h^-h^0$ decays,\nbut simply take a first look\nat the rich structure of $\\chi_{cJ}$ decays in our initial\n$\\psi(2S)$ data sets.  A subset of these modes has\nbeen investigated by BES~\\cite{BES}.\nWith the CLEO III detector configuration~\\cite{CLEOIII}, \nwe have recorded an integrated luminosity of \n2.57~pb$^{-1}$ and the number of $\\psi(2S)$ events\nis $1.56 \\times 10^6$.\nWith the CLEO-c detector configuration~\\cite{CLEOc} we have recorded\n2.89~pb$^{-1}$, and the number\nof events is $1.52 \\times 10^6$. The apparent mis-match of luminosities \nand event totals is due to different beam energy spreads for the two data sets.  \n\n\n\\section{Measurement of the branching fractions}\n\n\tOur basic technique is an exclusive whole-event analysis searching\nfor $\\psi(2S)\\to\\gamma\\chi_{cJ}$ followed by a three body\ndecay of the $\\chi_{cJ}$ to $\\pi^+\\pi^-\\eta$, $K^+K^-\\eta$, $p{\\bar p}\\eta$,\n$\\pi^+\\pi^-\\eta^\\prime$, $K^+K^-\\pi^0$, $p{\\bar p}\\pi^0$, $\\pi^+K^-K^0_{\\rm S}$, or\n$K^+{\\bar p}\\Lambda$.  A photon\ncandidate is combined with three hadrons and their 4-momentum sum constrained\nto the known total beam energy and the initial momentum caused by the two \nbeams crossing at a small angle taking into account the measured errors on\nthe reconstructed charged tracks, neutral hadron, and transition\nphoton.  We cut on the $\\chi^2$ of this fit, which has four degrees of freedom,\nas it strongly discriminates between background and signal.  \nFor most modes we select events with an event 4-momentum fit \n$\\chi^2$ less than 25, but\nbackground from $\\psi(2S)\\to J\/\\psi\\pi^0\\pi^0$ followed by charged \ntwo-body decays of the $J\/\\psi$, with one of the $\\pi^0$\ndecay photons lost, fakes $\\psi(2S)\\to\\gamma\\chi_{cJ}\\to \\gamma p{\\bar p}\\pi^0$.\nFor this mode the cut on $\\chi^2$ is tightened to 12.  The\nefficiency of this cut is $\\approx$ 95\\% for all modes except\n$p{\\bar p}\\pi^0$, where it is $\\approx$ 80\\%.  \n\nEfficiencies\nand backgrounds are studied in a GEANT-based simulation~\\cite{cleog} of\nthe detector response to $e^+e^- \\to \\psi(2S)$ events.\nOur simulated sample is roughly ten times our data sample.\nThe radiated photon is generated according to an\nangular distribution of $ 1 + \\lambda \\cos^2\\theta$,\nwhere $\\theta$ is the radiated photon angle \nrelative to the positron beam axis. \nAn E1 transition, as expected for $\\psi(2S) \\to \\gamma\\chi_{cJ}$,\nimplies $\\lambda=1,-1\/3,+1\/13$ for $J=0,1,2$ particles. \nThe efficiencies we quote use this simulation,\nand differ from efficiencies using $\\lambda=0$ by up to a few percent.\n\n\tPhoton candidates are selected by their \nenergy depositions in the CsI crystal calorimeter.\nThey have a transverse shape consistent with that expected for an electromagnetic\nshower without a charged track pointing toward it.  \nThey are required to have an energy of at least 30 MeV.  \nPhoton candidates that are used to make\nneutral particles further must\nhave an energy of more than 50 MeV if they are not in the barrel, $|\\cos\\theta_\\gamma| > 0.82$,\nof our calorimeter. The $\\pi^0 \\to \\gamma\\gamma$ and $\\eta \\to \\gamma\\gamma$\ncandidates are formed from two-photon candidates that are kinematically fit to\nthe known resonance masses\nusing the event vertex position, determined using charged tracks constrained to\nthe beam spot.  We select events with a $\\chi^2$ from the kinematic mass\nfit with one degree of freedom of less than 10.\nTransition photon candidates are vetoed if they form a\n$\\pi^0$ or $\\eta$ candidate when paired with a second photon candidate.\n\n\nWe also reconstruct the $\\eta \\to \\pi^+\\pi^-\\pi^0$ mode combining\ntwo charged pions with a $\\pi^0 \\to \\gamma\\gamma$ candidate, increasing the \nnumber of $\\eta$ candidates  \nby about 25\\%.  The same sort of kinematic mass fit\nas used for $\\pi^0$'s and $\\eta \\to \\gamma\\gamma$\nis applied to this mode, and again we select those giving a $\\chi^2$\nof less than 10.\nSimilarly we combine the mass-constrained $\\eta$ candidates together with two charged pions to \nmake $\\eta^{\\prime}$ candidates, mass-constrain them, and select those with $\\chi^2 < 10$. \nIn addition, we include the decay mode $\\eta^{\\prime} \\to \\gamma \\rho$. \nHere the background is potentially high because of the large \nnumber of noise photons, so we require \n$E_{\\rm photon} > 200$~MeV. In addition, we require the $\\pi^+\\pi^-$ mass\nto be within 100~MeV\/c$^2$ of the mean $\\rho$ mass.  \n\nCharged tracks satisfy standard requirements \\cite{HadronicBF} that they\nbe of good fit quality. \nThose coming from the origin must have an impact parameter\nwith respect to the beam spot less than the\ngreater of $(5.0-3.8\\cdot p)$~mm and 1.2~mm, where $p$ is the measured\ntrack momentum in GeV\/c.\nThe $K^0_S \\to \\pi^+\\pi^-$ and $\\Lambda \\to p\\pi^-$ candidates\nare formed from good-quality tracks that are constrained to come\nfrom a common vertex.\nThe $K^0_S$ flight path is required to be greater than 5~mm and the \n$\\Lambda$ flight path greater than 3~mm.  The mass cut around the $K^0_S$ mass is \n$\\pm 10$~MeV\/c$^2$, and around the $\\Lambda$ mass $\\pm 5$~MeV\/c$^2$,\nboth about three times the resolution.\nEvents with only the exact number of selected tracks\nare accepted.\nThis selection is very efficient, $>$99.9\\%, for events\npassing all other requirements.\n\n\tPions are required to have specific ionization,\n$dE\/dx$, in the main drift chamber within four standard\ndeviations of the expected value for\na real pion at the measured momentum. \nFor kaons and protons, a combined $dE\/dx$ and RICH\n(ring imaging Cherenkov counter) \nlikelihood is formed and kaons are required\nto be more kaon-like than pion- or proton-like, \nand similarly for protons.\nCross feed between hadron species is negligible after all\nother requirements. \n\nIn modes comprising only two charged particles, \nthere are some extra cuts to eliminate QED background which\nproduce charged leptons in the final state.\nEvents are rejected if the sum over all the charged\ntracks produces a penetration into the muon system of more\nthan five nuclear interaction lengths.\nEvents are rejected if any track has $0.92<E\/p<1.05$ and it\nhas a $dE\/dx$ consistent with an electron.\nThis latter cut is not used for $p\\bar{p}$ \nmodes because anti-protons tend to deposit all their\nenergy in the calorimeter.  These cuts are essentially 100\\% efficient\nfor the signal,\nand ensure this QED background is negligible.\n\nThe efficiencies averaged over the CLEO~III and CLEO-c\ndata sets for each mode including the branching fractions\n$\\eta \\to \\gamma\\gamma$, $\\eta \\to \\pi^+\\pi^-\\pi^0$, and $\\eta^\\prime \\to \\eta\\pi^+\\pi^-$~\\cite{pdg}\nare given in Tables~\\ref{tab:BRfits0}-\\ref{tab:BRfits2} for\n$\\chi_{c0}$,\n$\\chi_{c1}$, and\n$\\chi_{c2}$ respectively.\n\\begin{figure}\n\\begin{minipage}[t]{75mm}\n\\includegraphics*[width=72mm]{3540806-001.eps}\n\\caption{Mass distribution for candidate $\\chi_{cJ} \\to \\pi^+\\pi^-\\eta$ events.\n         The displayed fit is described in the text.}\n\\label{fig:pipieta}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[t]{75mm}\n\\includegraphics*[width=72mm]{3540806-002.eps}\n\\caption{Mass distribution for candidate $\\chi_{cJ} \\to K^+K^-\\eta$ events.\n         The displayed fit is described in the text.}\n\\label{fig:KKeta}\n\\end{minipage}\n\\begin{minipage}[t]{75mm}\n\\includegraphics*[width=72mm]{3540806-003.eps}\n\\caption{Mass distribution for candidate $\\chi_{cJ} \\to p{\\bar p}\\eta$ events.\n         The displayed fit is described in the text.}\n\\label{fig:ppbeta}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[t]{75mm}\n\\includegraphics*[width=72mm]{3540806-004.eps}\n\\caption{Mass distribution for candidate $\\chi_{cJ} \\to \\pi^+\\pi^-\\eta^\\prime$ events.\n         The displayed fit is described in the text.}\n\\label{fig:pipietaP}\n\\end{minipage}\n\\end{figure}\n\\begin{figure}\n\\begin{minipage}[t]{75mm}\n\\includegraphics*[width=72mm]{3540806-005.eps}\n\\caption{Mass distribution for candidate $\\chi_{cJ} \\to K^+K^-\\pi^0$ events.\n         The displayed fit is described in the text.}\n\\label{fig:KKpi0}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[t]{75mm}\n\\includegraphics*[width=72mm]{3540806-006.eps}\n\\caption{Mass distribution for candidate $\\chi_{cJ} \\to p {\\bar p} \\pi^0$ events.\n         The displayed fit is described in the text.}\n\\label{fig:ppbpi0}\n\\end{minipage}\n\\begin{minipage}[t]{75mm}\n\\includegraphics*[width=72mm]{3540806-007.eps}\n\\caption{Mass distribution for candidate $\\chi_{cJ} \\to K^0_{\\rm S}K^-\\pi^+$ events.\n         The displayed fit is described in the text.}\n\\label{fig:piKKs}\n\\end{minipage}\n\\hfill\n\\begin{minipage}[t]{75mm}\n\\includegraphics*[width=72mm]{3540806-008.eps}\n\\caption{Mass distribution for candidate $\\chi_{cJ} \\to K^+{\\bar p}\\Lambda$ events.\n         The displayed fit is described in the text.}\n\\label{fig:Kpblam}\n\\end{minipage}\n\\end{figure}\nFigures \\ref{fig:pipieta}-\\ref{fig:Kpblam} show the mass\ndistributions for the eight $\\chi_{cJ}$ decay modes selected by\nthe analysis described above.  Signals are evident in all\nthree $\\chi_{cJ}$ states, but not in all the modes.  Backgrounds\nare small.  The mass distributions are fit to three signal shapes,\nBreit-Wigners convolved with Gaussian detector resolutions, and a linear\nbackground.  The $\\chi_{cJ}$ masses and intrinsic \nwidths are fixed at the values from the Particle\nData Group compilation~\\cite{pdg}.  The detector resolution is taken\nfrom the simulation discussed above.  The simulation\nproperly takes into account the amount of data in \nthe two detector configurations, and the distribution\nof different decay modes we have observed.  We approximate\nthe resolution with a single Gaussian distribution, and variations\nare considered in the determination of systematic uncertainty.\nThe detector resolution dominates for the $\\chi_{c1}$ and $\\chi_{c2}$,\nbut is similar to the intrinsic width of the $\\chi_{c0}$.\nThe fits are displayed in Figures \\ref{fig:pipieta}-\\ref{fig:Kpblam}\nand summarized in Tables~\\ref{tab:BRfits0}-\\ref{tab:BRfits2}.\n\\begin{table}\n\\caption{Parameters used and results of fits to the $\\chi_{cJ}$\n         mass distributions of Figures~\\ref{fig:pipieta}-\\ref{fig:Kpblam} for the $\\chi_{c0}$\n         signal. The\n         fit is described in the text and the yield error is only statistical.\n         If no significant signal is observed we also show an upper limit at 90\\% confidence level.}\n\\begin{tabular}{l|c|c|l}\n\\hline \\hline\nMode                     & Efficiency (\\%) & Resolution (MeV) & Yield \\\\ \\hline\n$\\pi^+\\pi^-\\eta$         & 18.2            & 6.23             & $4.2\\pm4.1$ ($<10.6$) \\\\\n$K^+K^-\\eta$             & 13.8            & 6.10             & $3.1\\pm2.7$ ($<9.3$) \\\\\n$p{\\bar p}\\eta$          & 16.1            & 5.42             & $17.7^{+5.2}_{-4.8}$ \\\\\n$\\pi^+\\pi^-\\eta^\\prime$  &  8.0            & 4.38             & $2.0\\pm3.8$ ($<8.5$) \\\\\n$K^+K^-\\pi^0$            & 27.6            & 6.47             & $-3.3\\pm2.7$ ($<4.7$)\\\\\n$p{\\bar p}\\pi^0$         & 27.8            & 5.80             & $46.4^{+8.0}_{-7.2}$ \\\\\n$\\pi^+K^-K^0_{\\rm S}$    & 19.8            & 4.75             & $0.0\\pm1.0$ ($<2.7$) \\\\\n$K^+{\\bar p}\\Lambda$     & 16.8            & 4.38             & $51.3^{+8.1}_{-7.4}$ \\\\\n\\hline \\hline\n\\end{tabular}\n\\label{tab:BRfits0} \n\\end{table}\n\\begin{table}\n\\caption{Parameters used and results of fits to the $\\chi_{cJ}$\n         mass distributions of Figures~\\ref{fig:pipieta}-\\ref{fig:Kpblam} for the $\\chi_{c1}$\n         signal. The\n         fit is described in the text and the yield error is only statistical.\n         If no significant signal is observed we also show an upper limit at 90\\% confidence level.}\n\\begin{tabular}{l|c|c|l}\n\\hline \\hline\nMode                     & Efficiency (\\%) & Resolution (MeV) & Yield \\\\ \\hline\n$\\pi^+\\pi^-\\eta$         & 18.8            & 5.85             & $255^{+17}_{-16}$    \\\\\n$K^+K^-\\eta$             & 14.6            & 5.66             & $14.1^{+4.6}_{-3.9}$ \\\\\n$p{\\bar p}\\eta$          & 17.7            & 5.41             & $3.2\\pm2.3$ ($<7.6$) \\\\\n$\\pi^+\\pi^-\\eta^\\prime$  &  8.5            & 4.37             & $57.6^{+8.4}_{-7.7}$ \\\\\n$K^+K^-\\pi^0$            & 29.2            & 6.79             & $157\\pm13$           \\\\\n$p{\\bar p}\\pi^0$         & 30.1            & 5.23             & $9.9^{+3.8}_{-3.2}$  \\\\\n$\\pi^+K^-K^0_{\\rm S}$    & 20.6            & 4.37             & $249\\pm16$           \\\\\n$K^+{\\bar p}\\Lambda$     & 17.7            & 4.38             & $16.3^{+4.7}_{-4.0}$ \\\\\n\\hline \\hline\n\\end{tabular}\n\\label{tab:BRfits1}\n\\end{table}\n\\begin{table}\n\\caption{Parameters used and results of fits to the $\\chi_{cJ}$\n         mass distributions of Figures~\\ref{fig:pipieta}-\\ref{fig:Kpblam} for the $\\chi_{c2}$\n         signal. The\n         fit is described in the text and the yield error is only statistical.\n         If no significant signal is observed we also show an upper limit at 90\\% confidence level.}\n\\begin{tabular}{l|c|c|l}\n\\hline \\hline\nMode                     & Efficiency (\\%) & Resolution (MeV) & Yield \\\\ \\hline\n$\\pi^+\\pi^-\\eta$         & 18.5            & 5.58             & $26.2^{+6.4}_{-5.7}$  \\\\\n$K^+K^-\\eta$             & 14.6            & 5.53             & $6.9\\pm2.9$ ($<12.5$)\\\\\n$p{\\bar p}\\eta$          & 17.2            & 5.08             & $9.5^{+3.8}_{-3.0}$   \\\\\n$\\pi^+\\pi^-\\eta^\\prime$  &  8.5            & 4.32             & $12.4^{+4.8}_{-4.1}$  \\\\\n$K^+K^-\\pi^0$            & 27.5            & 6.85             & $24.8^{+5.8}_{-5.1}$  \\\\\n$p{\\bar p}\\pi^0$         & 29.3            & 5.10             & $37.1^{+6.7}_{-6.1}$  \\\\\n$\\pi^+K^-K^0_{\\rm S}$    & 20.2            & 4.45             & $36.8^{+6.6}_{-5.9}$  \\\\\n$K^+{\\bar p}\\Lambda$     & 17.5            & 4.32             & $42.1^{+7.2}_{-6.5}$  \\\\\n\\hline \\hline\n\\end{tabular}\n\\label{tab:BRfits2}\n\\end{table}\nNote that for the $\\chi_{c0}$ in Table~\\ref{tab:BRfits0} the five modes for which no\nsignificant signal is found (yield less than three standard deviations from zero)\nare forbidden by parity conservation.\n\n\tWe consider various sources of systematic uncertainties on the yields.\nWe varied the fitting procedure by allowing the $\\chi_{cJ}$ masses and intrinsic widths\nto float.  The fitted masses and widths agree with the values from the Particle\nData Group~\\cite{pdg}, and we take the maximum variation in the observed yields, \n$\\pm$4\\%, as a systematic\nuncertainty from the fit procedure.  Allowing a curvature term to the background\nhas a negligible effect.\nFor modes with large yields we can break up the sample into CLEO~III and CLEO-c\ndata sets, and fit with resolutions and efficiencies appropriate for the individual\ndata sets.  We note that the separate data sets give consistent \nefficiency-corrected \nyields and the summed yield differs by 2\\% from the standard procedure,\nwhich is small\ncompared to the $\\pm$8\\% statistical uncertainty.  We take this as the systematic\nuncertainty from our resolution model.  From studies of other processes\nwe assign a $\\pm$0.7\\% uncertainty for the efficiency of finding each charged\ntrack, $\\pm$4.0\\% for the $\\gamma\\gamma$ resonances, $\\pm$2.0\\% for each extra photon,\n$\\pm$1.3\\% for the particle identification for each $K$ and $p$, $\\pm$2.0\\% for\nsecondary vertex finding, and $\\pm$3.0\\% from the statistical uncertainty\non the efficiency determined from the simulation.  We study the cut on the $\\chi^2$\nof the event 4-momentum kinematic fit in the three large yield $\\chi_{c1}$ signals\nby removing the $\\chi^2$ cut, selecting events around the $\\chi_{c1}$\nmass peak, subtracting a low-mass side band, the only one available, and \ncomparing the simulated $\\chi^2$ distribution for signal events with the data\ndistribution.  This comparison is shown in Figure~\\ref{fig:chi2}.  The agreement\n\\begin{figure}\n\\includegraphics*[width=160mm]{3540806-009.eps}\n\\caption{Distribution of the $\\chi^2$ for the event 4-momentum kinematic fit\n         shown here with a $\\chi_{c1}$ mass cut and sideband subtraction.  \n         Plot (a) is the $\\pi^+\\pi^-\\eta$ mode, (b) is the $K^+K^-\\pi^0$ mode,\n         and (c) is the $\\pi^+K^-K^0_{\\rm S}$ mode.  \n         The data are shown by points and the simulation of signal events is\n                        shown by the solid line normalized to have the same area.}\n\\label{fig:chi2}\n\\end{figure}\nbetween the data and simulation is good, and comparing the inefficiency introduced\nby our cut on the 4-momentum kinematic fit $\\chi^2$ between the data and the simulation\nwe assign a $\\pm$3.5\\% uncertainty on the efficiency due to uncertainty in modeling\nthis $\\chi^2$ distribution.  \nThe simulation was generated assuming three-body phase-space for the $\\chi_{cJ}$ decay products. \nDeviations from this are to be expected.  Based on the results of the Dalitz plot analyses\ndiscussed below we correct the efficiency in the \n$\\chi_{c1} \\to \\pi^+ \\pi^-\\eta $, \n$\\chi_{c1} \\to K^+K^-\\pi^0$, and\n$\\chi_{c1} \\to K^-\\pi^+K^0_S$ \nmodes by a relative $-2.2$\\%, $-1.5$\\%, and $+6$\\% respectively \nto account for the change\nin the efficiency caused by the deviation from a uniform phase space distribution\nof decay products to what we actually observe.  \nWe apply an additional\n$\\pm5$\\% uncertainty on all other modes to account for the effect of resonant sub-structure\non the efficiency.  The total systematic uncertainty is mode dependent, but is roughly\n10\\%; it is higher for modes with many photons in the final state and lower for those with\nonly one.\n\nTo calculate $\\chi_{cJ}$ branching fractions, we use previous CLEO measurements\nfor the $\\psi(2S)\\to\\gamma\\chi_{cJ}$\nbranching fractions from Equations~\\ref{eqn:br_chic0}-\\ref{eqn:br_chic2}\n\\cite{chicbf}.  \nThe uncertainties on these branching fractions\nare included in the systematic uncertainty on the $\\chi_{cJ}$ branching fractions we report.\nAlso there is a 3\\% uncertainty on the number of $\\psi(2S)$ produced.\nResults for the three-body branching fractions are shown in \nTable~\\ref{tab:Branching_fractions}.  Where the yields do not show clear signals\n\\begin{table}\n\\caption{\\label{tab:Branching_fractions}\nBranching fractions in\nunits of 10$^{-3}$.  Uncertainties are statistical,\nsystematic due to detector effects plus analysis methods,\nand a separate systematic due to uncertainties in the $\\psi(2S)$ branching\nfractions.  Limits are at the 90\\% confidence level.}\n\\begin{tabular}{l|c|c|c}\n\\hline \\hline\nMode &$\\chi_{c0}$ & $\\chi_{c1}$ & $\\chi_{c2}$ \\\\\n\\hline\n$\\pi^+\\pi^-\\eta $         & $<0.21$  \n                          & $5.0 \\pm 0.3 \\pm 0.4 \\pm 0.3$ \n                          & $0.49\\pm 0.12\\pm 0.05\\pm 0.03$ \\\\\n$K^+K^-\\eta$              & $<0.24$  \n                          & $0.34\\pm 0.10\\pm 0.03\\pm 0.02$ \n                          & $<0.33$                        \\\\\n$p\\bar{p}\\eta$            & $0.39\\pm 0.11\\pm 0.04\\pm 0.02$  \n                          & $<0.16$ \n                          & $0.19\\pm 0.07\\pm 0.02\\pm 0.01$ \\\\\n$\\pi^+\\pi^-\\eta^{\\prime}$ & $<0.38$  \n                          & $2.4 \\pm 0.4  \\pm0.2 \\pm 0.2$     \n                          & $0.51\\pm 0.18 \\pm0.05\\pm 0.03$ \\\\\n$K^+K^-\\pi^0$             & $<0.06$  \n                          & $1.95\\pm 0.16\\pm 0.18\\pm 0.14$ \n                          & $0.31\\pm 0.07\\pm 0.03\\pm 0.02$ \\\\\n$p\\bar{p}\\pi^0$           & $0.59\\pm 0.10\\pm 0.07\\pm 0.03$ \n                          & $0.12\\pm 0.05\\pm 0.01\\pm 0.01$ \n                          & $0.44\\pm 0.08\\pm 0.04\\pm 0.03$ \\\\\n$\\pi^+K^-\\overline{K}^0$  & $<0.10$  \n                          & $8.1 \\pm 0.6 \\pm 0.6 \\pm 0.5$ \n                          & $1.3 \\pm 0.2 \\pm 0.1 \\pm 0.1$  \\\\\n$K^+ \\bar{p}\\Lambda$      & $1.07\\pm 0.17\\pm 0.10\\pm 0.06$ \n                          & $0.33\\pm 0.09\\pm 0.03\\pm 0.02$ \n                          & $0.85\\pm 0.14\\pm 0.08\\pm 0.06$ \\\\ \n\\hline \\hline\n\\end{tabular}\n\\end{table}\nwe calculate 90\\% confidence level upper limits using the yield \ncentral values with the statistical errors from the yield fits\ncombined in quadrature with the systematic uncertainties on the \nefficiencies and other branching fractions.  We assume\nthe uncertainty is distributed as a Gaussian and the upper limit \nis the branching fraction value at which 90\\% of the\nintegrated area of the Gaussian falls below.  We exclude the \nunphysical region, negative branching fractions, for this\nupper limit calculation.  We note that the ratio of rates obtained \nfrom isospin symmetry\n(see Appendix~\\ref{sec:Clebsch-Gordan},\nEquations~\\ref{eqn:case_width} and~\\ref{eqn:case_width_for_a0}),\nexpected to be 4.0, is\nconsistent with our measurement:\n\\begin{equation} \\label{eqn:ratio_of_rates}\n  \\frac{\\Gamma(\\chi_{c1}\\to \\pi^+K^-K^0)\n       +\\Gamma(\\chi_{c1}\\to \\pi^-K^+\\overline{K}^0) }\n       {\\Gamma(\\chi_{c1}\\to K^+K^-\\pi^0)}\n       = 4.2 \\pm 0.7.\n\\end{equation}\nOur results are consistent with branching fractions and upper limits\nin the $\\pi^+K^-K^0_{\\rm S}$ and $\\pi^+\\pi^-\\eta$ modes\nfrom BES~\\cite{BES}, but more precise.\n\n\n\\section{Substructure analysis}\n\nWe perform a Dalitz plot analysis on the modes with the highest statistics,\n$\\chi_{c1} \\to \\pi^+ \\pi^-\\eta $, $\\chi_{c1} \\to K^+K^-\\pi^0$, and\n$\\chi_{c1} \\to \\pi^+K^-K^0_S$, to study the two-body substructure.\nFor the Dalitz analysis only those\nevents within 10 MeV, roughly two standard deviations, of the \nobserved $\\chi_{c1}$ signal peak mean in the specific mode\nare accepted.  For $\\chi_{c1} \\to \\pi^+ \\pi^-\\eta$ there are 228 events in\nthis region and the signal fit finds 224.2 signal events and 5.1 \ncombinatorial background. For $\\chi_{c1} \\to K^+K^-\\pi^0 $ there are\n137 events accepted with the fit finding 137.8 signal and 2.4 background\nevents, and for $\\chi_{c1} \\to \\pi^+K^-K^0_S$, the numbers\nare 234 events, of which 233.2 are signal and 0.8 are background. In all\ncases the contribution from the tail of the $\\chi_{c2}$ is less than \none event.\n\nAn unbinned maximum likelihood fit is used \nin order to perform the Dalitz plot analysis \\cite{cleodalitz}. \nIn order to assess the fit quality we use an adaptive binning technique \n\\cite{D0-K0SETAPI0} and calculate a probability for Pearson statistics.\nEfficiencies are determined with simulated event samples \nfor the $\\chi_{c1}$ decay generated uniformly in phase space,\nand run through the analysis procedure described above.\nThe efficiency across the Dalitz plots is fit to a two-dimensional\npolynomial of third order in the Dalitz plot variables.  The fits are\nof good-quality and the efficiency is generally flat across the \nDalitz plot.  \n\nWhen fitting the data small contributions from backgrounds are neglected. \nWe are examining the $e^+e^- \\to \\psi(2S) \\to \\gamma \\chi_{c1}$ process.\nIn such a decay the $\\chi_{c1}$ should be polarized.  In principle\na complete analysis would take into account the angle of the photon\nwith respect to the $e^+e^-$ beams' collision axis\nand decompose the $\\chi_{c1}$ decay into\nits partial waves.  We use a simple model to \nanalyze our data sample which is adequate for seeing the largest\ncontributions to the substructure in our small sample.\nWe take the Dalitz plot matrix element $|{\\mathcal M}|^2$\nto be a sum of non-interfering resonances,\n\\begin{equation}\n  \\label{eqn:sumofresonances}\n        |{\\mathcal M}|^2 = \\sum_R |A_R|^2 \\cdot \\Omega_R^2 .\n\\end{equation}\nThe quantity $A_R(m)$ represents the amplitude\nof each resonance contribution with angular distributions $\\Omega_R^2$\ntaken from Ref.~\\cite{Filippini-Fontana-Rotondi} as shown in \nTable~\\ref{tab:angular_distributions}.\n\\begin{table}[!htb]\n\\caption{\\label{tab:angular_distributions} Angular distributions from \n         Ref.~\\cite{Filippini-Fontana-Rotondi} used in the present analysis. \n         The notation follows the original publication.\n         We assume the decay of a particle with spin $J$ \n         ($J=1$ for $\\chi_{c1}$ in our case)\n         to the resonance $R$ of spin $j$ and a pseudoscalar particle \n         with relative orbital momentum $L$. \n         The angle $\\theta$ is the resonance decay angle with respect to\n         the pseudoscalar particle in the resonance's rest frame.\n         The term $z^2=\\gamma_R^2-1$ is a relativistic correction factor, where  \n         $\\gamma_R$ is the resonance Lorentz factor in the $\\chi_{c1}$ rest frame.}\n\\begin{center}\n\\begin{tabular}{c|c}\n\\hline \\hline\n$J \\to j+L$ & Angular distribution, $\\Omega^2_R$ \\\\\n\\hline\n1$\\to$0+1 & uniform \\\\\n1$\\to$1+0 & $1 + z^2\\cos^2\\theta$ \\\\\n1$\\to$1+2 & $1 + (3 + 4 z^2)\\cos^2\\theta$ \\\\\n1$\\to$2+1 & $(1+z^2) \\big[1 + 3\\cos^2\\theta + 9 z^2 (\\cos^2\\theta - 1\/3)^2 \\big]$ \\\\\n\\hline \\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\\\\ Narrow resonances are described with a Breit-Wigner amplitude\n\\begin{equation}\n  \\label{eqn:BW}\n A_R(m) = \\frac{a_R}{m_R^2 - m^2 - im \\Gamma_{R,~\\mathrm{total}}(m)}.\n\\end{equation}\nThe $a_R$ coefficients are fit parameters giving the amplitudes of the resonance \nwith spin $j$- and mass-dependent width\n\\begin{equation}\n  \\label{eqn:mGamma}\n    m \\Gamma_{R,~\\mathrm{total}}(m) = \\sum_f {\\mathcal B}(R \\to f)\\cdot m_R\\Gamma_{R}\n                               \\bigg(\\frac{p}{p_R}\\bigg)^{2j+1}\n                                     \\frac{m_R}{m},\n\\end{equation}\nwhere the \nresonance mass $m_R$, width $\\Gamma_{R}$, and branching ratio ${\\mathcal B}(R \\to f)$\ninto the final state $f$ are taken from previous experiments \\cite{pdg};\n$p$ and $p_R$ are the decay products' momenta in the resonance rest frame\nand its value at $m=m_R$.\nFor the scalar resonance $a_0(980)$ we use a Flatt\\'e parameterization\nin the style of the Crystal Barrel Collaboration~\\cite{CBarrel_a0_980}, \n\\begin{equation}\n  \\label{eqn:Flatte}\n A_{a_0(980)}(m) = \\frac{a_{a_0(980)}}{ m_R^2 - m^2 - i[\n                                                g^2_{\\eta\\pi} \\rho_{\\eta\\pi}(m)\n                                              + g^2_{\\bar{K}K} \\rho_{\\bar{K}K}(m)\n                                             ]\n                            },\n\\end{equation}\nwhere $m_R$, $g_{\\eta\\pi}$, and $g_{\\bar{K}K}$ are the resonance mass\nand coupling constants, $m$ is the invariant mass of the resonance final state, and\n$\\rho_{ab}(m)$ is a phase space factor for the particular final state. \nWe use the $a_0(980)$ line-shape parameters from Table~\\ref{tab:scalar_parameters}.\nSimilar details of the $f_0(980)$ parameterization\nare unimportant as it is used only in systematic studies.\n\nFor low-mass $\\pi^+\\pi^-$($\\sigma$) and  $K\\pi$($\\kappa$) $S$-wave contributions\nwe choose a parameterization with a complex pole $m_R$~\\cite{Oller_2005}, \n  \\begin{equation}\n  \\label{eqn:Oller}\n         A_R(m) = \\frac{a_R}{m_R^2 - m^2},\n  \\end{equation}\nwith $m_\\sigma = (470 - i 220)$ MeV and $m_\\kappa = (710 - i 310)$ MeV,\nwhich is adequate for our small sample.\n\n\tFigure~\\ref{fig:pipietadalitz} shows the Dalitz plot\nand three projections for $\\chi_{c1} \\to \\pi^+\\pi^-\\eta$.\n\\begin{figure}\n\\includegraphics*[width=150mm]{3540806-010.eps}\n\\caption{(a) Dalitz plot, (b)--(d) projections on the three mass squared combinations\n         for $\\chi_{c1} \\to \\pi^+\\pi^-\\eta$.  The displayed fit projections\n         are described in the text.}\n\\label{fig:pipietadalitz}\n\\end{figure}\nThere are clear contributions from $a_0(980)^\\pm \\pi^\\mp$ and $f_2(1270) \\eta$ intermediate states,\nand significant accumulation of events at low $\\pi^+\\pi^-$ mass.\nNote that the $a_0(980)$ can contribute in two decay modes to the Dalitz plot.  \nAn isospin Clebsch-Gordan decomposition for this decay,\ngiven in Appendix~\\ref{sec:Clebsch-Gordan}, Equation~\\ref{eqn:case_C_intermediate}, shows that \namplitudes and strong phases of both charge-conjugated states should be equal.  \nThe overall amplitude normalization is\narbitrary and we set\n$a_{a_0(980)^+} = a_{a_0(980)^-} = 1$.\nAll other fit components are defined relative\nto this choice.\n\nOur initial fit to this mode includes only $a_0(980)^\\pm \\pi^\\mp$ and $f_2(1270) \\eta$\ncontributions, but has a vanishing probability of 0.1\\% for describing the data\ndue to the accumulation of events at low $\\pi^+\\pi^-$ mass.\nTo account for this we try $K^0_S$, $f_0(980)$, $\\rho(770)$, and $\\sigma$ resonances.\nOnly the $\\rho(770)$ and the $\\sigma$ give high fit probability. \nHowever the decay $\\chi_{c1} \\to \\rho(770) \\eta$ is $C$-forbidden,\nand the low-mass distribution is not well represented by the $\\rho(770)$, which\nonly gives an acceptable fit due to its large width and \nthe limited statistics of our sample. \nThe $\\sigma$ describes well the low $\\pi^+\\pi^-$ mass spectrum,\nand we describe the Dalitz plot with \n$a_0(980)^\\pm \\pi^\\mp$, $f_2(1270) \\eta$, and $\\sigma \\eta$ contributions.\nTable~\\ref{tab:pipietadalitz} gives the results of this fit, which has a \nprobability to match the data of 66\\%.\nThe angular distributions for $a_0(980)^\\pm$ and $\\sigma$ meson decays are uniform, \nand for $f_{2}(1270)$ are taken from \nTable~\\ref{tab:angular_distributions} for quantum numbers $JjL=121$.\nWe assume that a possible contribution from $L=3$ is small and it is neglected.\n\\begin{table}[!htb]\n\\caption{\\label{tab:scalar_parameters}  Resonance parameters\n                            in the $\\chi_{c1} \\to \\eta\\pi^+\\pi^-$ mode\n                            comparing their nominal value to fit values\n                            when individual resonance parameters\n                            are allowed to float. }\n\\begin{center}\n\\begin{tabular}{c|c|c}\n\\hline \\hline\nParameter                       & Nominal Value & When Floating \\\\\n\\hline\n$m(a_0(980))$,  MeV\/c$^2$       &  999          &  1002$\\pm$18 \\\\\n$g_{\\eta\\pi}$,  MeV\/c$^2$       &  620          &  637$\\pm$49  \\\\\n$g_{K\\bar{K}}$, MeV\/c$^2$       &  500          &  523$\\pm$154 \\\\\n\\hline\n${\\rm Re}(m_\\sigma)$, MeV\/c$^2$ &  470          &  511$\\pm$28  \\\\\n${\\rm Im}(m_\\sigma)$, MeV\/c$^2$ &--220          &--102$\\pm$50  \\\\\n\\hline \\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\\begin{table}\n\\caption{Fit results for $\\chi_{c1} \\to \\eta\\pi^+\\pi^-$ Dalitz plot analysis.  The uncertainties\n         are statistical and systematic.\n         Allowing for interference among the resonances changes the fit fractions\n         by as much as 20\\% in absolute terms as discussed in the text.\n        }\n\\begin{tabular}{l|c|c}\n\\hline \\hline\nMode                   & $a_R$                    & Fit Fraction (\\%)  \\\\ \\hline\n$a_0(980)^\\pm \\pi^\\mp$ & 1                        & $75.1\\pm3.5\\pm4.3$ \\\\\n$f_2(1270) \\eta$       & $0.103\\pm0.014\\pm0.005$  & $14.4\\pm3.1\\pm1.9$ \\\\    \n$\\sigma \\eta$          & $0.41\\pm0.05\\pm0.10$     & $10.5\\pm2.4\\pm1.2$ \\\\\n\\hline \\hline\n\\end{tabular}\n\\label{tab:pipietadalitz} \n\\end{table}\nThe systematic uncertainties shown in the table were obtained from\nvariations to this nominal fit as discussed below. \nWe allow the 2D-efficiency to vary with its polynomial coefficients\nconstrained by the results of the fit to the simulated\nevents; the mass of the $a_0(980)$ and its coupling constants are allowed to float,\nthe parameters of the $\\sigma$-pole are allowed to float, \nand we allow additional contributions\nfrom $\\rho(770) \\eta$, $f_0(980) \\eta$, $K^0_S \\eta$, and $\\pi_1(1400) \\pi$.\nThe results of allowing the resonance parameters to float as compared\nto their fixed values used in the nominal fit are shown in Table~\\ref{tab:scalar_parameters}.\nFor the additional contributions we do\nnot observe amplitudes that are significant and we limit their \nindividual fit fractions\nto roughly less than 5\\% of the Dalitz plot.\nWe note that with higher statistics this mode\nmay offer one of the best measurements of the parameters of the $a_0(980)$.\nThese results are consistent with the substructure analysis of this mode \nby BES~\\cite{BES}.\n\nThe Dalitz plot for $\\chi_{c1} \\to K^+K^-\\pi^0$ decay and\nits projections are shown in Figure~\\ref{fig:KKpi0dalitz}, and\n\\begin{figure}\n\\includegraphics*[width=150mm]{3540806-011.eps}\n\\caption{(a) Dalitz plot, (b)--(d) projections on the three mass squared combinations\n         for $\\chi_{c1} \\to K^+K^-\\pi^0$.  The displayed fit projections\n         are described in the text. \n         The contribution from $\\pi^0K^-$ resonances are not shown. They look\n         similar to the $\\pi^0K^+$ resonance components for the relevant projections.}\n\\label{fig:KKpi0dalitz}\n\\end{figure}\nfor $\\chi_{c1} \\to \\pi^+K^-K^0_S$ in Figure~\\ref{fig:piKK0dalitz}.\n\\begin{figure}\n\\includegraphics*[width=150mm]{3540806-012.eps}\n\\caption{(a) Dalitz plot, (b)--(d) projections on the three mass squared combinations\n         for $\\chi_{c1} \\to \\pi^+K^-K^0_S$.  The displayed fit projections\n         are described in the text.\n         The $\\pi^+ K^-$ resonances are not shown. They look\n         similar to the $\\pi^+ K^0_S$  resonance components for the relevant projections.}\n\\label{fig:piKK0dalitz}\n\\end{figure}\nWe do a combined Dalitz plot analysis to these modes taking advantage\nof isospin symmetry.  An isospin Clebsch-Gordan decomposition for these decays,\ndescribed in Appendix~\\ref{sec:Clebsch-Gordan}, \nshows that these two Dalitz plots should have \nthe same set of amplitudes for all  \n$K^*\\overline{K}$ and $a_0(980)\\pi$ intermediate states. \nThe relative factor $-\\sqrt{2}$\nbetween the two Dalitz plot amplitudes does not matter due to the \nindividual normalization of their probability density functions.\nIn the combined fit to these two Dalitz plots, \nwe use the following constraints on the amplitudes:\n$a_{K^{*}} \\equiv a_{K^{*+}} = a_{K^{*-}} = a_{K^{*0}} = a_{\\overline{K}^{*0}}$,\nand \n$a_{a(980)} \\equiv a_{a(980)^+} = a_{a(980)^-} = a_{a(980)^0}$.\nThe overall amplitude normalization is arbitrary and\nwe set $a_{K^*(892)} = 1$.\n\nVisual inspection shows apparent\ncontributions from $K^*(892)^\\pm K^\\mp$, $K^*(892)^0K^0_S$,\n$K^*(1430)^\\pm K^\\mp$, $K^*(1430)^0K^0_S$, \n$a_0(980)^0\\pi^0$, and $a_0(980)^\\pm\\pi^\\mp$.\nIt is not clear if the $K^*(1430)$ are $K^*_0$ or $K^*_2$, and many\nother $K\\pi$ and $KK$ resonances can possibly contribute.  \nThe angular distribution for scalar resonance decays is always taken as uniform.\nThe shape for $K^*(892)K$ is taken from \nTable~\\ref{tab:angular_distributions} for quantum numbers $JjL=110$.\nWe also modeled this contribution with the $JjL=112$ angular distribution\nwith the difference taken as a systematic uncertainty.\nThe shape for $K_2^*(1430)K$ is taken for quantum numbers $JjL=121$,\nwith a possible contribution from $L=3$ ignored.\nOur best fit result is shown in Table~\\ref{tab:KKpiDalitz}, displaying\n\\begin{table}[!htb]\n\\caption{Results of the combined fits to the \n$\\chi_{c1} \\to K^+ K^- \\pi^0$ and $\\chi_{c1} \\to \\pi K K^0_S$ Dalitz plots.\n         Allowing for interference among the resonances changes the fit fractions\n         by as much as 15\\% in absolute terms as discussed in the text.}\n\\begin{tabular}{l|c|c}\n\\hline \\hline\nMode                   & $a_R$                    & Fit Fraction (\\%)   \\\\ \\hline\n$K^*(892)K$            & 1                        & $31.4\\pm2.2\\pm1.7$  \\\\\n$K^*_0(1430)K$         & $3.8\\pm0.4\\pm0.2$        & $30.4\\pm3.5\\pm3.7$ \\\\\n$K^*_2(1430)K$         & $0.44\\pm0.06\\pm0.04$     & $23.1\\pm3.4\\pm7.1$  \\\\\n$a_0(980)\\pi$          & $6.1\\pm0.6\\pm0.6$        & $15.1\\pm2.7\\pm1.5$  \\\\\n\\hline \\hline\n\\end{tabular}\n\\label{tab:KKpiDalitz}\n\\end{table}\nstatistical and systematic errors.  \nThis fit has a good probability of matching the data, 73\\%,\nand agrees with fits done to the separate Dalitz plots not taking advantage of\nisospin symmetry. The addition of a $\\kappa K$ contribution\ndoes not improve the fit probability and the amplitude $a_{\\kappa}$\nis statistically significant only at the four standard deviation level.\nSimilar behavior is noted for a non-resonant contribution.\nSystematic uncertainties are evaluated by observing deviations from the\nnominal fit as described above for the $\\chi_{c1} \\to \\pi^+\\pi^-\\eta$ analysis.\nWhen systematics are taken into account neither the $\\kappa K$ nor\nnon-resonant contribution has a fit fraction significant at the three\nstandard deviation level.  Their individual contributions are limited to\nless than roughly 10\\% of the Dalitz plot.\nThese observations are consistent with those by\nBES~\\cite{BES} in the $\\pi^+K^-K^0_{\\rm S}$ mode.\n\nWhile this model of the contributions to the Dalitz\nplots gives a good description of the data it is clearly\nincomplete.  There should be interference among the resonances,\nwhich the simple approach of Equation~\\ref{eqn:sumofresonances}\ndoes not take into account. \nTo quantify the effect of interference we have repeated the Dalitz\nanalyses using a ``quasi-coherent'' \n(note that $\\Omega_R^2$ is always positively-defined)\nsum of amplitudes with floating complex weighting factors instead of $a_R$.\nThis causes the\nfit fractions to change by as much as $\\sim$20\\% absolutely \nin the $\\eta\\pi\\pi$ analysis\nand $\\sim$15\\% absolutely in the $K\\overline{K}\\pi$ analysis.\nWith more data a study of the $\\chi_{c1}$ decay substructure\ntaking into account the effect of $\\chi_{c1}$ polarization,\nusing the orientation of the $\\chi_{c1}$ decay plane with respect to the $\\chi_{c1}$\nflight direction,\nin a partial wave analysis would be a complete description of these decays.\nThe matrix element amplitudes should include the partial wave dependent\nangular distributions and interference effects among the resonances.\nSee Ref.~\\cite{BES_PWA_formalism} for appropriate prescriptions.\n\n\\section{Summary}\n\nWe have searched for and studied selected three-body hadronic decays\nof the $\\chi_{c0}$, $\\chi_{c1}$, and $\\chi_{c2}$ produced in radiative decays\nof the $\\psi(2S)$ in $e^+e^-$ collisions observed with the CLEO detector.  \nMany of the channels covered in this analyses are observed or limited for\nthe first time.  Our observations and branching fraction limits are summarized in\nTable~\\ref{tab:Branching_fractions}.\nIn $\\chi_{c1} \\to \\pi^+\\pi^-\\eta$ we have studied the resonant\nsubstructure using\na Dalitz plot analysis simply modeling the resonance contributions\nas non-interfering amplitudes.\nOur results are summarized in Table~\\ref{tab:pipietadalitz}.\nWe observe clear signals for the $a_0(980)^\\pm \\pi^\\mp$ and $f_2(1270)\\eta$\nintermediate states,\nand a low-mass $\\pi^+\\pi^-$ enhancement.\nSimilarly for $\\chi_{c1} \\to K\\overline{K}\\pi$ our results are summarized\nin Table~\\ref{tab:KKpiDalitz}, assuming, based on isospin, that\nthe $\\pi K K^0_S$ and $K^+K^-\\pi^0$ plots are identical.\nWe observe $K^*(892) K$, $K^*_2(1430)K$ and likely $a_0(980)\\pi$ \ncontributions in the $K \\overline{K} \\pi$ Dalitz plots.\nOther conclusions about S-wave contributions are likely\nmodel-dependent.\n\n\n\\section{Acknowledgments}\nWe gratefully acknowledge the effort of the CESR staff\nin providing us with excellent luminosity and running conditions.\nD.~Cronin-Hennessy and A.~Ryd thank the A.P.~Sloan Foundation.\nThis work was supported by the National Science Foundation,\nthe U.S. Department of Energy, and\nthe Natural Sciences and Engineering Research Council of Canada.\n\n\n\\section{Appendix: Clebsch-Gordan decomposition for $\\chi_{c1}$}\n\\label{sec:Clebsch-Gordan}\n\nIn order to constrain amplitudes and phases in $\\chi_{c1}$ decays\nwe use a Clebsch-Gordan decomposition\nof the $\\chi_{c1}$ (the state with $|I=0,I_Z=0\\rangle$) for possible \nisospin subsystems:\n\\begin{equation} \\label{eqn:Kpi}\n    \\chi_{c1} \\to (K \\pi)_{I=1\/2} {\\overline K},\n\\end{equation}\n\\begin{equation} \\label{eqn:Kbarpi}\n    \\chi_{c1} \\to ({\\overline K} \\pi)_{I=1\/2} K,\n\\end{equation}\n\\begin{equation} \\label{eqn:KKbar}\n    \\chi_{c1} \\to (K {\\overline K})_{I=1} \\pi.\n\\end{equation}\nBelow we use the\nClebsch-Gordan decomposition rules, $|J,M\\rangle = \\sum_f c_f |m_1,m_2\\rangle_f$\nfrom Ref.~\\cite{pdg}. \n\n\\subsection{Clebsch-Gordan decomposition for $K^* \\to K\\pi$ decays}\n\nWe assume that $K^*$ mesons with I=1\/2 form two isodoublets: \n($K^{*+}$, $K^{*0}$) and ($\\overline{K}^{*0}$, $K^{*-}$) \nwith ($I_Z=\\frac{1}{2}$,$I_Z=-\\frac{1}{2}$) respectively.\nThe Clebsch-Gordan decomposition rules for $\\mathbf{ 1 \\times \\frac{1}{2} }$ isospin\nstates are:\n\n\n\n\\begin{equation} \\label{eqn:Kstar+}\n     K^{*+}\n            = \\sqrt{\\frac{2}{3}} \\pi^+K^0 \n            - \\sqrt{\\frac{1}{3}} \\pi^0 K^+,\n\\end{equation}\n\\begin{equation} \\label{eqn:Kstar0}\n     K^{*0}\n            = \\sqrt{\\frac{1}{3}} \\pi^0K^0 \n            - \\sqrt{\\frac{2}{3}} \\pi^- K^+,\n\\end{equation}\n\\begin{equation} \\label{eqn:Kstar0bar}\n     \\overline{K}^{*0}\n           \n            = \\sqrt{\\frac{2}{3}} \\pi^+K^- \n            - \\sqrt{\\frac{1}{3}} \\pi^0 \\overline{K}^0,\n\\end{equation}\n\\begin{equation} \\label{eqn:Kstar-}\n     K^{*-}\n            = \\sqrt{\\frac{1}{3}} \\pi^0K^- \n            - \\sqrt{\\frac{2}{3}} \\pi^- \\overline{K}^0.\n\\end{equation}\n\n\\subsection{Cases of $\\chi_{c1} \\to (K \\pi)_{I=1\/2} {\\overline K}$ and  \n                     $\\chi_{c1} \\to ({\\overline K} \\pi)_{I=1\/2} K$  decays }\n\\label{ref:Kpi_I05}\nFor $\\chi_{c1} \\to K^*\\overline{K}$ and \n    $\\chi_{c1} \\to \\overline{K}^* K$ modes we use the \n$\\mathbf{ \\frac{1}{2} \\times \\frac{1}{2} }$ rule: \n\\begin{equation} \\label{eqn:case_A}\n     \\chi_{c1} = \\frac{1}{\\sqrt{2}}(K^{*+} K^- - K^{*0} \\overline{K}^0),\n\\end{equation}\n\\begin{equation} \\label{eqn:case_B}\n     \\chi_{c1} = \\frac{1}{\\sqrt{2}}(\\overline{K}^{*0}K^0 - K^{*-} K^+).\n\\end{equation}\n\n\nCombining Equations~\\ref{eqn:case_A} and \\ref{eqn:case_B} \nwith Equations~\\ref{eqn:Kstar+}-\\ref{eqn:Kstar-} we get\n\\begin{equation} \\label{eqn:case_A_FS}\n     \\chi_{c1}\\sqrt{2} =\n               \\sqrt{\\frac{2}{3}} \\bigg[ (\\pi^+K^0)K^- + (\\pi^-K^+)\\overline{K}^0 \\bigg]\n             - \\sqrt{\\frac{1}{3}} \\bigg[ (\\pi^0K^+)K^- + (\\pi^0K^0)\\overline{K}^0 \\bigg],\n\\end{equation}\n\\begin{equation} \\label{eqn:case_B_FS}\n     \\chi_{c1}\\sqrt{2} = \n               \\sqrt{\\frac{2}{3}} \\bigg[ (\\pi^+K^-)K^0 + (\\pi^-\\overline{K}^0)K^+ \\bigg]\n             - \\sqrt{\\frac{1}{3}} \\bigg[ (\\pi^0K^-)K^+ + (\\pi^0\\overline{K}^0)K^0 \\bigg].\n\\end{equation}\nAssuming charge symmetry the amplitudes in \nEquations~\\ref{eqn:case_A_FS} and \\ref{eqn:case_B_FS} should be equal.\nFrom these equations we get the ratio of rates:\n\\begin{equation} \\label{eqn:case_rate_R1}\n    \\Gamma(\\chi_{c1}\\to \\pi^+K^-K^0) \/\n    \\Gamma(\\chi_{c1}\\to K^+K^-\\pi^0) = 2, \n\\end{equation}\n\\begin{equation} \\label{eqn:case_rate_R2}\n    \\Gamma(\\chi_{c1}\\to \\pi^-K^+\\overline{K}^0) \/\n    \\Gamma(\\chi_{c1}\\to K^+K^-\\pi^0) = 2,\n\\end{equation}\nor their sum\n\\begin{equation} \\label{eqn:case_width}\n             \\Gamma(\\chi_{c1}\\to \\pi^+K^-K^0)\n           + \\Gamma(\\chi_{c1}\\to \\pi^-K^+\\overline{K}^0) \n   = 4 \\cdot \\Gamma(\\chi_{c1}\\to K^+K^-\\pi^0).\n\\end{equation}\n\n\\subsection{Case of $\\chi_{c1} \\to (K {\\overline K})_{I=1} \\pi$ decay}\n\\label{ref:KK_I1}\n\nFor $\\chi_{c1} \\to a\\pi$ modes we use the $\\mathbf{ 1\\times 1 }$ rule: \n\\begin{equation} \\label{eqn:case_C_intermediate}\n     \\chi_{c1} = \\frac{1}{\\sqrt{3}}(a^+\\pi^- - a^0\\pi^0 + a^-\\pi^+)\n\\end{equation}\nFor $a\\to K{\\overline K}$ we use the $\\mathbf{\\frac{1}{2} \\times \\frac{1}{2}}$ rules:\n\\begin{equation} \\label{eqn:case_a+}\n         a^+ = K^+ \\overline{K}^0,\n\\end{equation}\n\\begin{equation} \\label{eqn:case_a0}\n         a^0 = \\frac{1}{\\sqrt{2}} (K^+ K^- + K^0 \\overline{K}^0),\n\\end{equation}\n\\begin{equation} \\label{eqn:case_a-}\n         a^- = K^0 K^-.\n\\end{equation}\nCombining Equation~\\ref{eqn:case_C_intermediate} \nwith Equations~\\ref{eqn:case_a+}-\\ref{eqn:case_a-} we get\n\n\\begin{equation} \\label{eqn:case_C}\n     \\chi_{c1}\\sqrt{3} = \n                      (K^+ \\overline{K}^0)\\pi^- \n                    - \\frac{1}{\\sqrt{2}} \\bigg[(K^+ K^-)\\pi^0  + (K^0 \\overline{K}^0)\\pi^0 \\bigg]\n                    + (K^0 K^-)\\pi^+.\n\\end{equation}\n\nFrom Equation~\\ref{eqn:case_C} we get the ratio\nof rates:\n\\begin{equation} \\label{eqn:case_rate_R1_for_a0}\n    \\Gamma(\\chi_{c1}\\to \\pi^+K^-K^0) \/\n    \\Gamma(\\chi_{c1}\\to K^+K^-\\pi^0) = 2, \n\\end{equation}\n\\begin{equation} \\label{eqn:case_rate_R2_for_a0}\n    \\Gamma(\\chi_{c1}\\to \\pi^-K^+\\overline{K}^0) \/\n    \\Gamma(\\chi_{c1}\\to K^+K^-\\pi^0) = 2,\n\\end{equation}\nor their sum\n\\begin{equation} \\label{eqn:case_width_for_a0}\n             \\Gamma(\\chi_{c1}\\to \\pi^+K^-K^0)\n           + \\Gamma(\\chi_{c1}\\to \\pi^-K^+\\overline{K}^0) \n   = 4 \\cdot \\Gamma(\\chi_{c1}\\to K^+K^-\\pi^0).\n\\end{equation}\n\n\\subsection{Consequences for Dalitz plot analysis}\n\nComparing \nEquations~\\ref{eqn:case_rate_R1}-\\ref{eqn:case_width}\nfor intermediate states with $K^*$ \nand\nEquations~\\ref{eqn:case_rate_R1_for_a0}-\\ref{eqn:case_width_for_a0}\nfor intermediate states with $a(980)$,\nwe note that they are identical.\nThus observations of $\\pi^+K^-K^0$ and \ncharge conjugated $\\pi^-K^+\\overline{K}^0$ final states \non the same Dalitz plot will yield the certain ratio\nbetween $K^*$ and $a(980)$ amplitudes for the $\\pi K K^0_S$ Dalitz plot.\nThe same ratio between $K^*$ and $a(980)$ amplitudes \nis expected for the $K^+K^-\\pi^0$ Dalitz plot. \nThis isospin analysis implies that these two Dalitz plots, \n$\\pi K K^0_S$ and $K^+K^-\\pi^0$,\ncan be parametrized using a common set of parameters for each \n$K^*$ and $a(980)$ intermediate state.\nFrom Equations~\\ref{eqn:case_A_FS}, \\ref{eqn:case_B_FS} we can\nwrite equations between decay amplitudes with $K^*$ mesons\n\\[\n{\\rm for~} \\pi K K^0_S:~~~  \n           a_{K^{*+}K^- \\to K^0K\\pi} \n         = a_{K^{*-}K^+ \\to K^0K\\pi} \n         = a_{K^{*0}\\overline{K}^0 \\to K^0K\\pi}\n         = a_{\\overline{K}^{*0}K^0 \\to K^0K\\pi}\n         =\n\\]\n\\begin{equation}\n   \\label{eqn:ampl_kstar}\n\\hspace{-20mm}\n{\\rm for~} K^+K^-\\pi^0:~~~~~\n         = -\\frac{1}{\\sqrt{2}} a_{K^{*+}K^- \\to K^+K^-\\pi^0}\n         = -\\frac{1}{\\sqrt{2}} a_{K^{*-}K^+ \\to K^+K^-\\pi^0},\n\\end{equation}\nwhere the signs assume equal phases\n\\begin{equation}\n \\phi_{K^{*+}} = \\phi_{K^{*-}} = \\phi_{K^{*0}} = \\phi_{\\overline{K}^{*0}}.\n\\end{equation}\nSimilar equations between amplitudes with $a_0(980)$ can be obtained\nfrom Equation~\\ref{eqn:case_C}\n\\[\n{\\rm for~} \\pi K K^0_S:~~~ \n           a_{a(980)^+\\pi^- \\to \\pi K K^0} \n         = a_{a(980)^-\\pi^+ \\to \\pi K K^0}\n         =\n\\]\n\\begin{equation}\n   \\label{eqn:ampl_a0_980}\n\\hspace{-13mm}\n{\\rm for~} K^+K^-\\pi^0:~~~\n         = -\\frac{1}{\\sqrt{2}}a_{a(980)^0\\pi^0 \\to K^+K^-\\pi^0},  \n\\end{equation}\nassuming equal phases\n\\begin{equation}\n \\phi_{a(980)^+} = \\phi_{a(980)^-} = \\phi_{a(980)^0}.\n\\end{equation}\nEquations~\\ref{eqn:ampl_kstar} and \\ref{eqn:ampl_a0_980} predict that \nthe ratio of amplitudes between these two Dalitz plots is $-\\sqrt{2}$.\nThis relative factor does not matter, because each Dalitz plot\nis normalized separately.\nIn the combined fit we ignore this $-\\sqrt{2}$ factor \nbetween the amplitudes \nin the $\\pi K K^0_S$ and $K^+K^-\\pi^0$ Dalitz plots, and use\ncommon fit parameters for each of $K^{*}$ mesons and $a_0(980)$ intermediate states   \n\\begin{equation}\n a_{K^{*}} \\equiv a_{K^{*+}} = a_{K^{*-}} = a_{K^{*0}} = a_{\\overline{K}^{*0}},\n\\end{equation}\n\\begin{equation}\n a_{a(980)} \\equiv a_{a(980)^+} = a_{a(980)^-} = a_{a(980)^0}.\n\\end{equation}\n\nIn Sections~\\ref{ref:KK_I1} and \\ref{ref:Kpi_I05} we have checked an isospin symmetry\nbetween $\\pi K K^0$ and $K^+K^-\\pi^0$ decays\nfor two particular intermediate states. \nHowever, this symmetry is valid independently of\nhow the amplitudes are decomposed into two-body sub-amplitudes, and thus\nshould be valid for all points on the Dalitz plot.\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Conclusion and Future Work}\nIn this paper, we presented the state-of-the-art results in the morphosyntactic tagging task for Modern Standard Arabic and three Arabic dialects that differ in terms of linguistic properties and resource availability.\nWe conducted different experiments to examine the performance of pre-trained LMs under different fine-tuning setups.\nWe showed that the factored model outperforms the unfactored model in low-resource settings; however, this gap diminishes as the data size increases.\nAdditionally, high-quality morphological analyzers proved to be helpful, especially in low-resource settings.\nOur results also show that fine-tuning using datasets from other dialects followed by fine-tuning using the target dialect is beneficial for low-resource settings.  \nOur systems outperform previously published SOTA on this task.\n\nIn the future, we plan to investigate continued training further and find other ways where we can utilize resources and datasets for low-resourced dialects.\nWe also intend to explore other architectures for morphosyntactic tagging using multi-task learning in the context of pre-trained LMs, as well as work on the task of automatic lemmatization.\nWe also plan to integrate some of our best models as part of the Python open-source Arabic NLP toolkit CAMeL~Tools~\\cite{obeid-etal-2020-camel}.\n\n\\section{Ethical Considerations}\nThe experiments reported in this work rely on previously published datasets described in Section~\\ref{subsec:resources}.\nWe used the CAMeLBERT models along with morphosyntactically annotated datasets to build our morphosyntactic taggers, which is in line with their intended use.\nOur work is on core and generic NLP technologies that can be potentially used with malicious intent, for example, as part of the pipeline.\nTo ensure reproducibility, we make our code publicly available.\nThe details on the datasets and training are described in Appendix~\\ref{sec:appendix}.\nGiven the focus of this paper and the available resources, we recognize the limitations of our findings in terms of applicability to different genres, styles, and other languages.\n\n\n\\section*{Acknowledgment}\nThis work was carried out on the High Performance Computing resources at New York University Abu Dhabi.\nWe thank anonymous reviewers for their insightful suggestions and comments.\nWe thank Bashar Alhafni and Ossama Obeid for their assistance with the codebase and the helpful discussions.\n\n\n\\section{Introduction}\nFine-tuning pre-trained language models like BERT~\\cite{devlin2019bert} has achieved great success in a wide variety of natural language processing (NLP) tasks, e.g., sentiment analysis~\\cite{abu-farha-etal-2021-overview}, question answering~\\cite{antoun-etal-2020-arabert}, named entity recognition~\\cite{ghaddar2022jaber}, and dialect identification~\\cite{abdelali2021pretraining}. \nPre-trained LMs have also been used for enabling technologies such as part-of-speech (POS) tagging \\cite{Lan:2020:empirical,khalifa-etal-2021-self,inoue:2021:interplay} to produce features for downstream processes.\nPrevious POS tagging results using pre-trained LMs focused on core POS tagsets;\nhowever, it is still not clear how these models perform on the full morphosyntactic tagging task of very morphologically rich languages, where the size of the full tagset can be in the thousands.\nOne such language is Arabic, where lemmas inflect to a large number of forms through different combinations of morphological features and cliticization.\nAdditionally, Arabic orthography omits the vast majority of its optional diacritical marks which increases morphosyntactic ambiguity.\n\n\nA third challenge for Arabic is its numerous variants.\nModern Standard Arabic (MSA) is the primarily written variety used in formal settings.\nDialectal Arabic (DA), by contrast, is the primarily spoken unstandardized variant.\nMSA and different DAs, e.g., Gulf (GLF), Egyptian (EGY), and Levantine (LEV), vary in terms of their grammar and lexicon to the point of impeding system usability cross-dialectally \\cite{Habash:2012:morphological}.\nFurthermore, these variants currently differ in the degree of data availability: MSA is the highest resourced variant, followed by GLF and EGY, and then LEV.\n\nIn this paper, we explore different training setups for fine-tuning Arabic pre-trained language models in the complex morphosyntactic tagging task \nfor four Arabic variants (MSA, GLF, EGY, and LEV) under controlled experimental settings.\n\nWe aim to answer the following questions:\n\\begin{itemize}\n    \\item How does the size of the fine-tuning data affect the performance?\n    \\item What kind of tagset scheme is suitable for modeling morphosyntactic features?\n    \\item Is there any additional value of using external linguistic resources?\n    \\item How can we make use of annotated data in some  dialects to improve performance in another low-resourced dialect?\n\\end{itemize}\n\nOur system\\footnote{We make our models and data publicly available at \\url{https:\/\/github.com\/CAMeL-Lab\/CAMeLBERT_morphosyntactic_tagger}.}\nachieves state-of-the-art (SOTA) performance in full morphosyntactic tagging accuracy in all the variants we study, resulting in 2.6\\% absolute improvement over previous SOTA in MSA, 2.8\\% in GLF, 1.6\\% in EGY, and 8.3\\% in LEV.\n\\section{Arabic Language and Resources}\n\n\\subsection{Arabic and its Dialects}\nMSA is the primarily written form of Arabic used in official media communications, official documents, news, and education. \nIn contrast, the primarily spoken varieties of Arabic are its dialects.\nArabic dialects vary among themselves and can be categorized at different levels of regional classifications \\cite{Salameh:2018:fine-grained}.\nThey are also different from MSA in most linguistic aspects (namely phonology, morphology, and syntax).\nMoreover, dialects have no official status despite being widely used in different means of daily communication --  spoken as well as increasingly written on social media.\nIn this work, we focus on MSA, Gulf Arabic (GLF), Egyptian Arabic (EGY), and Levantine Arabic (LEV). \n\n\\subsection{Orthography} \nIn this paper, we focus on Arabic written in Arabic script for MSA and DA.\n\\vocalize\nAn important feature of Arabic orthography is the omission of diacritical marks which are mostly used to indicate short vowels and consonantal doubling.\nThis omission introduces ambiguity to the text, e.g., the word <ktb>~\\emph{ktb}\\footnote{Arabic transliteration is presented in the HSB scheme \\cite{Habash:2007:arabic-transliteration}.}\ncould mean `to write' (<katab>~\\emph{katab}) or `books' (<kutub>~\\emph{kutub}) among other readings.\n\\novocalize\n\nUnlike MSA, Arabic dialects have no official standard orthography.\nDepending on the writer, words are sometimes spelled phonetically or closer to an MSA spelling through cognates or a mix of both.\nIt has been found that in extreme cases a word can have more than 20 different spellings \\cite{Habash:2018:unified}.\nThis results in highly inconsistent and sparse datasets and models.\nThe Conventional Orthography for Dialectal Arabic (CODA) \\cite{Habash:2018:unified} has been proposed and used in manual annotations of many datasets including some of those used in this paper.\nIdeally, the process of morphological disambiguation should take raw text as input, as this is more authentic than conventionalized spelling.\nWe follow this principle for EGY and LEV where analyses are paired with the raw text.\nHowever, the GLF dataset analyses are linked to the CODA version only, since orthographic conventionalization was applied as an independent step during manual data annotations and there are no simple direct mappings between the raw text and the analyses \\cite{Khalifa:2018:morphologically}.\n\n\\subsection{Morphology} Arabic is a morphologically rich language where a single lemma inflects to a large number of forms through different combinations of morphological features (gender, number, person, case, state, mood, voice, aspect) and cliticization (prepositions, conjunctions, determiners, pronominal objects, and possessives).\nAs some of the morphological features are primarily expressed with optional diacritical marks, orthographic ambiguity results in different morphological analyses, e.g., MSA can have up to 12 analyses per word (out-of-context) on average \\cite{Pasha:2014:madamira}.\nMSA and DA differ in the degree of morphological complexity, for example, MSA retains nominal case and verbal mood features; but these are absent in DA.\nOn the other hand, many dialects take more clitics than MSA,\ne.g., the <^s>+~+<mA> {\\it mA+~+{{\\v{s}}}} negation circumclitic structure found in EGY and not MSA \\cite{Habash:2012:morphological}.\n\n\\vocalize\nTable~\\ref{tab:example} shows different possible readings for the word <.hfydk> \\emph{Hfydk} among MSA, EGY, GLF, and LEV.\nRows (a) to (i) are different inflections for case or possessive pronouns or both of the lemma <.hafiyd> \\emph{Hafiyd} `grandchild' for all variants.\nRows (j) and (k) show different readings that are inflections of the verb lemma <fAd> \\emph{fAd} `to benefit', the inflections are for different object pronouns.\nNote that even between the different POS inflections words can sound and look exactly the same, this shows the degree of morphological complexity and ambiguity in Arabic and its dialects.\n\n\\subsection{Resources}\n\\label{subsec:resources}\n\n\\begin{table}[t!]\n\\centering\n\\includegraphics[scale=0.69]{table2_resource}\n\\caption{\nAn overview of the current status of the data and morphological analyzers used in this work.\n} \n\\label{tab:overview}\n\\end{table}\n\nIn this work, we use datasets that have been fully annotated for morphological features and cliticization among other lexical features such as lemmas.\nWe use the Penn Arabic Treebank for MSA~\\cite{Maamouri:2004:patb}, ARZTB~\\cite{Maamouri:2012:arz} for EGY, the Gumar corpus~\\cite{Khalifa:2018:morphologically} for GLF, and the Curras corpus~\\cite{Jarrar:2014:building} for LEV.\nWe also use morphological analyzers that provide out-of-context analyses for a given word, those analyzers provide the same set of features that are seen in the annotated data.\nFor MSA we use the SAMA database \\cite{Graff:2009:standard}, and for EGY we use CALIMA \\cite{Habash:2012:morphological}.\nBoth GLF and LEV do not have morphological analyzers, instead, we use automatically generated analyzers from their training data using paradigm completion as described in \\citet{Eskander:2013:automatic-extraction,Eskander:2016:creating} and \\citet{khalifa-etal-2020-morphological}.\nThe quality and coverage of analyzers, in general, can differ depending on how they were created.\nManually created analyzers (MSA and EGY in this work) tend to have a better quality and lexical coverage over automatically created ones (GLF and LEV in this work).\nThe quality of automatically generated analyzers is also highly dependent on the quality and size of the training data used to create them.\n\nTable~\\ref{tab:overview} shows the overall state of the resources for each dialect studied in this work.\nIn terms of the size of fully annotated corpora in tokens, MSA is approximately three times larger than GLF and EGY and 11 times larger than LEV.\nBoth MSA and GLF have consistent orthography whereas EGY and LEV are more noisy.\nWhen it comes to external morphological analyzers, only MSA and EGY have manually created and checked morphological analyzers, while both GLF and LEV have analyzers created automatically.\nThis contrast of resource availability allows us to study how challenging the morphosyntactic tagging task can be in different real-world situations.\n\\section{Related Work}\nArabic morphological modeling proved to be useful in a number of downstream NLP tasks such as machine translation  \\cite{Sadat:2006:combination,ElKholy:2012:orthographic}\nspeech synthesis \\cite{halabi2016modern}, dependency parsing \\cite{Marton:2013:dependency}, sentiment analysis \\cite{Baly:2017:sentiment}, and gender reinflection \\cite{alhafni-etal-2020-gender}.\nWe expect all of these applications and others to benefit from improvements in morphosyntactic tagging.\n\nThere have been multiple approaches to morphological modeling for Arabic.\nThose approaches differ depending on the target tagset (POS vs full morphology) and the availability of linguistic resources.\nWhen it comes to MSA and DA full morphological tagging, MADAMIRA \\cite{Pasha:2014:madamira} trained separate SVM taggers for each morphological feature (including cliticization) and selected the most probable answer provided by an external morphological analyzer all in one step for both MSA and EGY.\nAMIRA \\cite{Diab:2004:automatic} on the other hand used a cascading approach where it performed POS tagging after automatically segmenting the text.\n\nA more recent similar approach to MADAMIRA was introduced by \\newcite{Zalmout:2017:dont} but using a neural architecture instead.\n\\newcite{Inoue:2017:joint} presented a multitask neural architecture that jointly models individual morphological features for MSA.\n\\newcite{zalmout-habash-2019-adversarial} extended \\newcite{Zalmout:2017:dont}'s work using multitask learning and adversarial training for full morphological tagging in MSA and EGY.\nSimilarly, \\newcite{zalmout-habash-2020-joint} proposed an approach where they jointly model lemmas, diacritized forms, and morphosyntactic features, providing the current state-of-the-art in MSA.\nThe same approach was used in \\newcite{khalifa-etal-2020-morphological}, where they focused on the effect of the size of the data and the available linguistic resources and the impact on the overall performance on morphosyntactic tagging for GLF.\n\\newcite{zalmout2020} provides the current state-of-the-art performance in LEV by extending \\newcite{khalifa-etal-2020-morphological}'s work to LEV.\n\nAnother line of research that works with DA includes \\newcite{Darwish:2018:multi-dialect}, where they presented a multi-dialectal CRF POS tagger, using a small set of 350 manually annotated tweets for each of EGY, GLF, LEV, and Maghrebi Arabic \\cite{samih-etal-2017-learning}.\nWe do not evaluate on their data because their task is defined as shallow morpheme segmentation and tagging; this is quite different from, and not easily mappable to, our task, where we disambiguate morphosyntactic features of the whole word without identifying its morpheme segments.\nAdditionally, their tagset includes social media specific tags, such as HASH, EMOT, and MENTION, which are not in any of the large standard dataset and analyzers we study in this paper.\n\nPre-trained LM-based efforts in Arabic morphosyntactic tagging are relatively limited and either assume gold segmentation or only produce core POS tags.\n\\newcite{kondratyuk-2019-cross} leveraged the multilingual BERT model with additional word-level and character-level LSTM layers for lemmatization and morphological tagging, assuming gold segmentation.\nThey reported the results for the SIGMORPHON 2019 Shared Task~\\cite{mccarthy-etal-2019-sigmorphon}, which includes MSA.\n\\newcite{inoue:2021:interplay} reported POS tagging results in MSA, GLF, and EGY using BERT models pre-trained on Arabic text with various pre-training configurations.\nThey do not assume pre-segmentation of the text, however, they only consider the core POS tag, rather than the fully specified morphosyntactic tag.\n\\newcite{khalifa-etal-2021-self} proposed a self-training approach for core POS tagging where they iteratively improve the model by incorporating the predicted examples into the training set used for fine-tuning.\n\nIn this paper, we work with full morphosyntactic modeling on unsegmented text in four different variants of Arabic: MSA, GLF, EGY, and LEV.\nFurthermore, we explore the behavior of the pre-trained LM with respect to fine-tuning data size under different training setups.\nGiven the available resources, we recognize our results' limitations in terms of applicability to different genres and styles, as well as noisy social media text and Roman script Arabic text \\cite{Darwish:2014:arabizi}.\n\n\\section{Methodology}\n\n\\subsection{Morphosyntactic Tagging with Pre-trained LMs}\nTo obtain a fully specified morphosyntactic tag sequence, we build a classifier for each morphosyntactic feature independently, inspired by MADAMIRA.\nUnlike MADAMIRA where they use an SVM classifier, we use two pre-trained LM based classifiers: CAMeLBERT-Mix for DA and CAMeLBERT-MSA for MSA~\\cite{inoue:2021:interplay}.\nIn selecting these pre-trained language models, we considered the results from \\newcite{inoue:2021:interplay} who showed that CAMeLBERT-Mix, their largest Arabic BERT model by training data size,  gives the best results on DA tasks.  \nCAMeLBERT-MSA, which  outperforms  CAMeLBERT-Mix on MSA tasks, is only second to AraBERT~\\cite{antoun-etal-2020-arabert}, but since it was created under the same setting as CAMeLBERT-Mix, it minimizes experimental variations in our study.\\footnote{\nWe leave engineering optimization using other pre-trained language models to future work.}\nFollowing the work of \\newcite{devlin2019bert}, fine-tuning the CAMeLBERT models is done by appending a linear layer on top of its architecture.\nWe use the representation of the first sub-token as an input to the linear layer.\n\n\\subsection{Factored and Unfactored Tagset}\nOne of the challenges of the morphosyntactic tagging is the large size of the full tagset due to morphological complexity of the language, where a complete single tag is a concatenation of all the morphosyntactic features.\nFor example, MSA and EGY data have approximately 2,000 unique complete tags in the training data, whereas GLF and LEV have around 1,400 and 1,000 tags, respectively. These are not the full tagsets as there are many feature combinations that are not seen in the data.\n\nMADAMIRA's basic approach is to use a factored feature tagset that comprises multiple tags, each representing a corresponding morphosyntactic category.\\footnote{\nFor example, the tagset for MSA comprises POS (34 tags), per (4), gen (3), num (5), asp (4), vox (4), mod (5), stt (5), cas (5), prc3 (3), prc2 (9), prc1 (17), prc0 (7), enc0 (48).\n}\nThis approach remedies the issue of the large tagset size by dividing it into multiple sub-tagsets of small sizes, however, it may produce inconsistent tag combinations.\n\nAlternatively, one can combine the individual tags into a single tag.\nThis approach has the advantage of guaranteeing the consistency of morphosyntactic feature combinations.\nHowever, it may not be optimal in terms of tag coverage due to a large number of unseen tags in the test data in addition to the large space of classes.\n\nTo determine which approach is most suitable for modeling, we build morphosyntactic taggers with both the factored tagset and the unfactored tagset for each variant.\nAdditionally, we explore the effect of the training data size for both settings.\n\n\\subsection{Retagging via Morphological Analyzers}\n\\label{subsec:retagging}\nIn previous efforts~\\cite{Zalmout:2017:dont,khalifa-etal-2020-morphological}, it has been shown that lexical resources such as morphological analyzers can boost the performance of morphosyntactic tagging through an in-context ranking of out-of-context answers provided by the analyzer.\n\nIn this work, we follow their approach, where we use the morphological analyzers as a later step after tagging with the fine-tuned pre-trained model.\nWe use the analyzers described in Section~\\ref{subsec:resources} to provide out-of-context analyses.\nFor each word, the analyzer may provide more than one answer.\\footnote{Both the MSA and EGY analyzers provide backoff modes.\nWe use the recommended setting by \\newcite{Zalmout:2017:dont}.\nFor GLF and LEV analyzers we keep the original predictions if no answer is returned.}\nThe analyses are then ranked based on the unweighted sum of successful matches between the values of the predictions from the individual taggers and those provided by the analyzer.\nTo break ties during the ranking, we take the weighted sum of the probability of the \\emph{unfactored} feature tag and the product of the probabilities of all the individual tags as follows:\n\n\n\\begin{equation}\n\\frac{1}{2}P(t_{unfactored})+ \\frac{1}{2}\\prod_{m \\in M}P(t_{m})\n\\label{eq:tie1}\n\\end{equation}\nwhere $t$ is the tag for the feature $m$ and $M$ is the set of morphosyntactic features.\nThe probabilities are obtained through unigram models based on the respective training data split.\n\n\\subsection{Merged and Continued Training}\nMorphosyntactic modeling for DA is especially challenging because of  data scarcity.\nAmong the datasets that we use, LEV is the least resourced variant, having 11 times less training data than MSA.\nTherefore, we want to investigate an optimal approach to utilize data from other variants to improve upon the performance of morphosyntactic tagging for LEV.\n\nIn this work, we experiment with the following two settings:\n(a) we merge all the datasets together and fine-tune a pre-trained LM on the merged datasets in a single step; and \n(b) similar to \\newcite{zalmout2020}, we start fine-tuning a pre-trained LM on a mix of high-resource datasets (MSA, GLF, and EGY), and then continue fine-tuning on a low-resource dataset (LEV).\n\\section{Experiments}\n\\label{sec:experiments}\n\\subsection{Experimental Settings}\n\\label{subsec:experimental_settings}\n\\paragraph{Data}\nTo be able to compare with previous SOTA \\cite{zalmout-habash-2020-joint,zalmout-habash-2019-adversarial,khalifa-etal-2020-morphological,zalmout2020}, we follow the same conventions they used for data splits: MSA and EGY \\cite{Diab:2013:ldc}, GLF \\cite{Khalifa:2018:morphologically}, and LEV \\cite{Eskander:2016:creating}.\nIn Table \\ref{tab:data_split}, we show the statistics of our datasets.\n\n\\begin{table}[t!]\n\\centering\n\\includegraphics[width=0.33\\textwidth]{table3_corpus}\n\\caption{\nStatistics on TRAIN, TUNE, DEV, and TEST for each variant in terms of number of words.\n} \n\\label{tab:data_split}\n\\end{table}\n\n\\begin{table*}[t!]\n\\centering\n\\includegraphics[scale=0.69]{table4_main}\n\\caption{\n\\textsc{DEV} results on a learning curve of the training data size.\nMorph refers to the model with an additional step of retagging using a morphological analyzer.\nWe bold the best score for each variant.\nUnderlined scores denote that the differences between those scores and the best scores are statistically insignificant with McNemar's test ($p< 0.05$).\n}\n\\label{tab:table4_main}\n\\end{table*}\n\n\\paragraph{Fine-tuning}\nWe fine-tuned the CAMeLBERT models \\cite{inoue:2021:interplay} on each morphosyntactic tagging task.\nFollowing their recommendation, we used CAMeLBERT-MSA for MSA and CAMeLBERT-Mix for the dialects.\nWe used Hugging~Face's transformers~\\cite{wolf2020huggingfaces} for implementation.\nWe trained our models for 10 epochs with a learning rate of 5e-5, a batch size of 32, and a maximum sequence length of 512.\nWe pick the best checkpoint based on TUNE and report results on DEV and TEST from a single run.\n\n\\paragraph{Learning Curve}\nTo investigate the effect of fine-tuning data sizes, we randomly sample training examples on a scale of 5k, 10k, 20k, 40k, 80k, 120k, and 150k tokens.\nWe use 150k, 120k, and 40k since they are comparable to the number of tokens in GLF, EGY, and LEV datasets, respectively.\nThis allows us to measure the performance difference across different dialects in a controlled manner.\nThis also gives us insight into the amount of annotated data required to achieve a certain performance, which is useful when creating annotated resources for new dialects.\nWe use this setup in all the reported experiments.\n\n\\paragraph{Pre-processing for Merged and Continued Training}\nAlthough the different datasets provide the same set of morphosyntactic features, there exist some inconsistencies between them.\nThe datasets were annotated by different groups using slightly different annotation guidelines, therefore, we need to bring all the feature values into a common space with LEV.\nWe performed the following steps to address those inconsistencies:\n(a) we drop the \\textit{stt, cas, mod, vox, enc1}, and \\textit{enc2} features;\n(b) we remove the diactization from the lexical parts of the proclitic features, e.g., the conjunction +\\<w> {\\it w+} realized as \\emph{wa\\_conj} in MSA and \\emph{wi\\_conj} in EGY both maps to \\emph{w\\_conj} in LEV; and\n(c) for certain POS classes some features have default values in case they are not present, those default values were different for different datasets. Thus, we mapped those default values to match whatever was specified as default in LEV.\nWe only performed these modifications for the experiments on merged and continued training.\n\n\\paragraph{Evaluation Metrics}\nWe compute the accuracy in terms of the core POS and the combined morphosyntactic features (\\textbf{\\textsc{ALL TAGS}}).\nFor MSA, we use 14 features, which are \\textit{pos, per, gen, num, asp, vox, mod, stt, cas, prc3, prc2, prc1, prc0}, and \\textit{enc0}.\nFor dialects, we use 16 features, where we include \\textit{enc1} and \\textit{enc2} in addition to the 14 features used in MSA.\nIn the merged and continued training setup, we use a reduced set of\n10 features, \\textit{pos, per, gen, num, asp, prc3, prc2, prc1, prc0}, and \\textit{enc0}, which we refer to as \\textbf{\\textsc{ALL TAGS 10}}.\n\n\\subsection{Results}\n\\paragraph{Factored vs Unfactored Models}\nTable \\ref{tab:table4_main} shows the DEV results for the models trained with the factored and unfactored tagset (henceforth, factored and unfactored models, respectively) on a learning curve of the training data size.\nIn the extremely low-resource setting of 5k tokens in the \\textsc{ALL TAGS} metric, we observe that factored models consistently outperform unfactored models across all the variants (15.9\\% absolute increase on average).\nIn particular, MSA benefited most with a 32.1\\% absolute increase, followed by EGY (12.5\\%), GLF (12.0\\%), and LEV (7.1\\%).\n\nHowever, this gap shrinks as the data size increases.\nFor instance in MSA, the differences between the scores of the factored model and the unfactored model become statistically insignificant by McNemar's test~\\cite{McNemar1947} with $p<0.05$ when trained on the full data.\nThis is presumably due to the decrease in the number of unseen unfactored tags in DEV.\nIn fact, 3.9\\% of the unfactored tags in DEV are not seen in TRAIN in the 5k setting, whereas only 0.1\\% of tags are unseen in DEV when we use the full data.\n\nThe factored model performs better than the unfactored model across all the data sizes in MSA and LEV.\nThe EGY and GLF models follow a similar pattern in the low resourced settings, however, the unfactored models begin to perform better than the factored ones from 20k for EGY and 40k for GLF.\nOur results suggest that the factored tagset is optimal compared to the unfactored tagset, especially in low-resource settings.\n\n\\paragraph{Retagging with Morphological Analyzer}\nWe observe that the use of a morphological analyzer consistently improves the performance of both unfactored and factored models across all the different training data sizes in MSA and EGY in \\textsc{ALL TAGS}.\nThe value of a morphological analyzer is especially apparent in the very low resourced setting (5k), with an increase of 20.2\\% (MSA) and 11.8\\% (EGY) in the unfactored model and 11.2\\% (MSA) and 9.2\\% (EGY) in the factored model.\nHowever, the effect of retagging with a morphological analyzer diminishes as the data size increases, yet providing a performance gain of 0.4\\% in the unfactored model with the analyzer and 0.5\\% in its factored counterpart in the high resourced setting in MSA.\n\nSimilarly, we observe an increase in performance when we include a morphological analyzer in the very low-resourced settings in GLF and LEV.\nHowever, as we increase the training data size, the use of a morphological analyzer starts to hurt the performance at 40k in GLF and 10k in LEV in the unfactored model and 20k in GLF and 10k in LEV in the factored model.\nWe observe here that the quality of the analyzer has direct implications on the performance. The analyzers used for MSA and EGY are of higher quality since they were manually created and checked, whereas GLF and LEV analyzers are impacted by the quality and size of the annotated data used to create them. This is also consistent with the findings of \\newcite{khalifa-etal-2020-morphological}.\n\n\\begin{table*}[t!]\n\\centering\n\\includegraphics[scale=0.69]{table5_comparison}\n\\caption{\nDEV and TEST results of our systems and previously published systems on the same datasets.\n} \n\\label{tab:table5_comparison}\n\\end{table*}\n\n\\paragraph{Comparison with Previous SOTA Systems}\nTable \\ref{tab:table5_comparison} shows DEV and TEST results for our models and a number of previously published state-of-the-art morphosyntactic tagging systems.\nFor our models, we use the best systems in terms of \\textsc{ALL TAGS} metric, namely, the factored model with a morphological analyzer for MSA and EGY, the unfactored model for GLF, and the factored model for LEV.\nFor existing models, we report the best results from \\newcite{zalmout-habash-2020-joint} (ZH'20) for MSA, \\newcite{khalifa-etal-2020-morphological} (K'20) for GLF, \\newcite{zalmout-habash-2019-adversarial} (ZH'19) for EGY,\nand \\newcite{zalmout2020} (Z'20) for LEV.\n\nSince some of these systems do not report on all of the features that we report on, but rather on different subsets of them, we include in the table our results when matched with their features (\\textsc{ALL TAGS*} in Table~\\ref{tab:table5_comparison}).\nThere is no difference for MSA; however the \\textsc{ALL~TAGS*} setting for EGY and LEV excludes \\textit{enc1} and \\textit{enc2}. As for GLF,  \\textsc{ALL~TAGS*} consists of only 10 features: \\textit{pos, asp, per, gen, num, prc0, prc1, prc2, prc3,} and \\textit{enc0}.\n\nWe observe that our models consistently outperform the existing systems in all variants.\nOur model achieves 2.6\\% absolute improvement over the state-of-the-art system in MSA, 2.8\\% in GLF, 1.6\\% in EGY, and 8.3\\% in LEV.\n\n\\begin{table*}[t!]\n\\centering\n\\includegraphics[scale=0.69]{table6_strategy}\n\\caption{\n\\textsc{DEV} and \\textsc{TEST} results on LEV for the merged training setup (MERGED) and the continued training setup (CONTINUED).\nSINGLE refers to the model trained only on LEV.\n} \n\\label{tab:table6_strategy}\n\\end{table*}\n\n\\paragraph{Merged and Continued Training}\nTable \\ref{tab:table6_strategy} shows the results on LEV for the merged and the continued training setups.\nWe use the factored model without the analyzer as it was the best setup in the experiments presented so far.\nThe results for merged training are consistently below those for the baseline across different data sizes, even though they have access to more data.\nThis is most likely a result of the disproportionately small size of the LEV dataset when compared to the other variants.\n\nIn contrast, the results for continued training show consistent improvements over the LEV-only baseline model.\nContinued training provides a substantial increase in performance, especially in the very low resourced setting with only 5k tokens, giving 3.6\\% absolute improvement over the baseline on the DEV set.\nOur results show that continued training from the model trained on high-resourced dialects is very beneficial with lower amounts of training data.\nThese results are not directly comparable to the previous SOTA because of the different training data and metric used.\n\n\\subsection{Error Analysis}\n\\paragraph{OOV}\nTo better understand the effect of different training setups, we examine the performance of our models on out-of-vocabulary (OOV) tokens alone.\nHere, we observe a stronger and more consistent pattern.\nThe \\textit{average} difference between the best model and the weakest model in ALL TAGS across variants is larger in OOV tokens (6.7\\%) than in all tokens (2.3\\%).\nOn OOV tokens, the factored model with a morphological analyzer consistently performs best in all the data sizes for all the variants except for LEV.\nIn LEV, however, the same model without the morphological analyzer outperforms the one with the analyzer.\nThis is presumably due to the orthographic inconsistency in the data along with the quality of the morphological analyzer as discussed in Section~\\ref{subsec:resources}.\n\n\\begin{table*}[ht!]\n\\centering\n\\includegraphics[scale=0.69]{table7_error_analysis.pdf}\n\\caption{\nThe number and percentage of specific feature errors among the ALL TAGS errors in the best systems on the DEV set.\n} \n\\label{tab:table_error_analysis}\n\\end{table*}\n\n\\paragraph{Error Statistics}\nTable \\ref{tab:table_error_analysis} presents the number and percentage of specific feature errors among the ALL TAGS errors in the best systems on the DEV set.\nOn average, there are two feature prediction failures within an unfactored tag across the different variants.\nWe observe that MSA and DA exhibit different error patterns:\nIn MSA, case is the largest error contributor among other features, which is consistent with the previous findings along the line~\\cite{zalmout-habash-2020-joint}, whereas in dialects, POS is the largest error contributor.\n\nAmong the POS errors, the most common error type is mislabeling a nominal tag with a different nominal tag, at 44.2\\% of the errors in GLF, 67.3\\% in EGY, and 57.8\\% in LEV, while this type of error is more dominant in MSA (80.8\\%).\nMislabeling nominals with verbs is more common in DA at 23.1\\% in GLF, 13.0\\% in EGY, and 20.1\\% in LEV, compared to MSA (7.7\\%).\n\nThe core morphological features such as \\textit{per, gen, num}, and \\textit{asp} have a higher percentage of errors in DA than in MSA.\nAnother noticeable difference is \\textit{enc0} feature (MSA $\\sim$2\\% vs DA on average $\\sim$17\\%).\nThis is likely due to label distribution differences in pronominal enclitics: MSA has a highly skewed distribution with 90\\%, 1\\%, and 9\\% ratio for 3rd, 2nd and 1st persons as expected in MSA news genre.\nIn comparison, DA has less skew with 50\\%, 17\\%, and 32\\% respectively, which increases the likelihood of error. \n\nAmong the three dialects, we observe similar patterns in terms of feature error contribution, especially for GLF and LEV with a correlation coefficient of 0.93.\nHowever, in EGY specifically, we observe a high percentage of errors in \\textit{mod, vox, stt}, and \\textit{cas}, partly due to the difference and inconsistency in annotation schemes.\n\n\\novocalize\nWe also found some gold errors which affect all of the systems we compared (previous SOTA and ours).\nFor example, there are cases where genitive diptotes are annotated as accusative,\\footnote{For more information on Arabic morphology in a computational context, see \\newcite{Habash:2010:introduction}.} e.g., the word <'iyrAn>~\\emph{{{\\v{A}}}yrAn} `Iran' in the context <fy 'iyrAn> ~\\emph{fy {{\\v{A}}}yrAn} `in Iran'.\nAs the results on Arabic morphosyntactic disambiguation are reaching new heights, it may be useful for the community using these resources to revisit their annotations.\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
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+{"text":"\\section{Introduction}\n \nComputational fluid dynamics (CFD) has proven to be a very effective research tool in a very wide variety of disciplines, including engineering, science, medicine and more \\cite{CFD1995}. For its applications in  turbulent flows, however, the range of the temporal \\&  spatial scales is too broad to be captured by brute force direct numerical simulations (DNS) \\cite{Davidson2015}. Large eddy simulation (LES) provides an alternative, by filtering the small-scale scales of transport and concentrating on the larger scale energy containing eddies \\cite{Sagaut05}. By this filtering, LES can be conducted on coarser grids as compared to those required by DNS. The penalty, understandably, is that LES generated data are of lower accuracy  compared to DNS. Appraisal of LES predictions and assessments of its fidelity as compared to DNS, have been of interest in the turbulence research community for the past several decades \\cite{givi1989model,pope2001turbulent}. The objective of the present work is to build a new data-driven methodology to reconstruct DNS from LES data, which facilitates a more robust means of LES appraisal. \n\n\nMachine learning, including super-resolution methods~\\cite{Cheo2003SR}, have shown great success in reconstructing high-resolution data in a variety of commercial applications. For example, convolutional neural networks (CNNs) and their extensions, e.g., SRCNN~\\cite{dong2014learning}, RCAN~\\cite{zhang2018image}, and SRGAN~\\cite{ledig2017photo}, have proven very effective in directly mapping low-resolution images to high-resolution images. The effectiveness of these methods mainly come from the power of CNNs in automatically extracting representative spatial features through deep layers. An alternative solution is to consider super-resolution as an inverse modeling problem~\\cite{geiss2020invertible,mccann2017convolutional} with the constraints that the down-sampled version of the underlying high-resolution data should be consistent to the observed low-resolution data. \n\n\n\\begin{figure}[t]\n\\centering  \n\\subfigure[LES]{\n\\label{Fig.sub.1}\n\\includegraphics[width=4.1cm,height = 4.1cm]{les.png}}\\subfigure[DNS]{\n\\label{Fig.sub.2}\n\\includegraphics[width=4.1cm,height = 4.1cm]{dns.png}}\n\\caption{An example slice of Large Eddy Simulation (LES) and its corresponding Direct Numerical Simulation (DNS). This example is used to show the \nthe difference between LES and DNS at certain spatial locations and certain time steps. }\n\\label{Sample}\n\\end{figure}\n\nSuper-resolution techniques are starting to be used in turbulence research \\cite{liu2020deep,xie2018tempogan,fukami2019super}. However, there are several major challenges that must be overcome, before they can be employed for routine applications. \nFirst, turbulent flow data often exhibit significant variability. In the absence of underlying physical processes, machine learning models are prone to learning spurious patterns that fit statistical characteristics of available training data collected from a specific time period, but cannot generalize to other time intervals. This can be further exacerbated by limited training data. \nSecond, existing super-resolution algorithms could have degraded performance in CFD because of the huge information loss caused by the large resolution gap. For example, LES data can be of more than 8 times lower resolution compared to DNS data along each axis. Hence, standard statistical interpolation methods may fail to capture fine-level flow dynamics resulting from underlying physical relationships and constraints. Third, existing machine learning  models are not designed to deal with the discrepancy between\ndifferent simulation strategies (i.e. LES, DNS and\/or others). In general, the available simulations at a coarser resolution are not simply a down-sampled version of high-resolution simulations. Consider the examples in Fig.~\\ref{Sample}. It is obvious that the LES predictions on the coarser grids do not capture the flow patterns as compared to high-resolution DNS.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\begin{figure*}[htbp]\n\\begin{center}\n\\includegraphics[width = 1.03\\linewidth]{architecture.png}\n\\end{center}\n\\caption{The architecture of the proposed PGSRN model and different components in the loss function. Since the degradation structure is used for computing both the degradation loss and the GAN loss, we use the black arrows and grey arrows in the degradation process to show the flow for computing the degradation loss and GAN loss, respectively.}\n\\label{fig:tf_plot}\n\\end{figure*}\n\n\n\n\nIn this work, we develop a new method, termed Physics-Guided Super-Resolution Network (PGSRN)$\\footnote{The source code for the PGSRN model presented in this study is available online at link: \\url{https:\/\/drive.google.com\/drive\/folders\/1w6j3pNzVqZ7Q9P7ZpnTsVNmvnfJXnxh_?usp=sharing}}$, to improve the reconstruction of high-resolution turbulent flow data. This development is by leveraging known physical constraints and explicitly exploring the discrepancy \\& the consistency between different simulations. First, we generalize the loss function of the super-resolution model by incorporating the divergence-free velocity-field  constraint as required in incompressible flows.  Second, we introduce a hierarchical\ngenerative architecture by decomposing the data reconstruction into two steps:  (i)  transform low-resolution flow data into a down-sampled version of high-resolution data, and (ii) reconstruct high-resolution flow data from the down-sampled version. Step (i) allows explicitly modeling the data discrepancy due to different simulation methods used to generate low-resolution and high-resolution data. Step (ii) is to recover the fine-level details of flow data. Finally, we introduce a degradation process to further regularize reconstructed data by imposing the consistency between different simulations. Here we represent the degradation process by a forward model (by framing super-resolution as an inverse problem) that maps high-resolution data to low-resolution data. The forward model output of reconstructed data can then be compared against low-resolution simulations for consistency assessment. We further extend the degradation process as a feature extractor and introduce an adversarial loss on the extracted features from high-resolution data, which helps improve the modeling of fine-level fluid dynamics.  \n\nFor the purpose of demonstration, we consider a variant of the Taylor-Green vortex (TGV) \\cite{brachet1984taylor}.  This is a three-dimensional incompressible flow and is simulated within a box with periodic boundary conditions. The TGV provides a suitable setting for our demonstration as it exhibits several salient features of turbulent transport. In this flow, the original vortex collapses into turbulent worm-like structures which become progressively more turbulent until viscosity eventually dissipates the large scale vortical structures. \nWe compare our proposed method against several existing super-resolution algorithms to reconstruct DNS data of TGV. \nWe also demonstrate the effectiveness of each component in our proposed method by showing the improvement both qualitatively and quantitatively. \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\u00a0\u00a0\u00a0\u00a0\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\section{Methodology}\n\nThe goal of our work is to achieve an end-to-end reconstruction mechanism from low-resolution LES data, denoted by $\\textbf{X}_{LR}$ to high-resolution DNS data $\\textbf{X}_{HR}$.  In Fig.~\\ref{fig:tf_plot}, we show the overall structure of the methodology. The model has two components, the generative process and the degradation process. These are described here, in order: \n\n\\subsection{Hierarchical Generative Process}\n\n\nThe generative process aims to map \u00a0$\\textbf{X}_{LR}$ to $\\textbf{X}_{HR}$. It contains multiple residual blocks and each block consists of convolutional layers~\\cite{o2015introduction}, batch normalization layers~\\cite{ioffe2015batch}, and parametric ReLUs following previous literature~\\cite{he2015delving}. The generative process outputs a reconstructed data $\\textbf{X}_{SR}$, and then the model is  optimized to reduce the difference between obtained $\\textbf{X}_{SR}$ and provided high resolution data $\\textbf{X}_{HR}$. Such a difference is represented as a reconstruction loss $\\mathcal{L}_\\text{recon}(\\textbf{X}_{SR},\\textbf{X}_{HR})$, which can be implemented as mean squared loss (MSE),  perceptual loss or other loss functions that measure the difference between two sets of data. In this work, we use the mean squared loss as we do not observe significant improvement using other loss functions.\n\n\n\\subsubsection{Hierarchical Structure}\nWe also build a hierarchical generative structure to decompose the information gap between low-resolution and high-resolution data and explicitly capture their difference. In particular, we consider two types of information loss from high-resolution data to low-resolution data: 1) the discrepancy caused by different simulation methods used to generate data of different scales, and 2) the loss of fine-level information due to the reduced resolution.\n\n\n\nGiven the input low-resolution data $\\textbf{X}_{LR}\\in \\mathbb{R}^{H\\times W\\times C}$ ($H$ and $W$ are spatial dimensions while $C$ is the number of physical variables), we use a hierarchical structure to extract intermediate data representation before generating high-resolution data of size ${KH\\times KW\\times C}$. In particular, we create multiple middle layers $\\{\\textbf{h}_1, \\textbf{h}_2,. . . \\textbf{h}_m\\}$. Here the first middle layer $\\textbf{h}_1$ is used to extract a down-sampled version of the high-resolution data $\\textbf{X}_{HR}$, which is of size $H\\times W$ (same with input low-resolution data).  By introducing this layer, the model can explicitly capture the discrepancy between simulation strategies used for generating the input data $\\textbf{X}_{LR}$  (i.e., LES) and target data $\\textbf{X}_{HR}$ (i.e., DNS) on the same resolution.  We introduce another loss on this middle layer to reduce the difference between extracted information from $\\textbf{h}_1$ and the down-sampled $\\textbf{X}_{HR}$.  \nSpecifically, the model first transforms the hidden layer $\\textbf{h}_1$ into a reconstructed flow data of size $H\\times W\\times C$ via a function $g(\\cdot)$ and then compare $g(\\textbf{h}_1)$ against the down-sampled version of $\\textbf{X}_{HR}$.\nMore formally, this loss is expressed as:\n\\begin{equation}\n\\mathcal{L}_{h1} = \\text{MSE}(g(\\textbf{h}_1),\\textbf{X}^{\\text{down}_1}_{HR}),\n\\end{equation}\nwhere $\\textbf{X}^{\\text{down}_1}_{HR}$ represents the down-sampled version of $\\textbf{X}_{HR}$ of size $H\\times W$. \nWe implement the function $g(\\cdot)$ using convolutional layers and fully connected layers. \n\nWe can define additional losses on other intermediate layers $\\textbf{h}_2,...,\\textbf{h}_m$ by comparing down-sampled $\\textbf{X}_{HR}$ using different down-sampling rates. Specifically, we represent the loss of the hierarchical generative process as follows:\n\\begin{equation}\n\\begin{aligned}\n    \\mathcal{L}_{hier} &= \\alpha_1\\mathcal{L}_\\text{recon}(\\textbf{X}_{SR},\\textbf{X}_{HR})+ \\alpha_2\\sum_{i=1}^{m}\\mathcal{L}_{hi} \\\\\n    \\mathcal{L}_{hi} &= \\sum_{i=1}^m \\text{MSE}(g(\\textbf{h}_i),\\textbf{X}^{\\text{down}_i}_{HR})\/m,\n\\end{aligned}\n\\end{equation}\nwhere $\\textbf{X}^{\\text{down}_i}_{HR}$ is the down-sampled $\\textbf{X}_{HR}$ of size $k_iH\\times k_iW$, and $1=k_1<k_2<...<k_m<K$, and $\\alpha_1$ and $\\alpha_2$ are hyper-parameters to control the balance between the reconstruction loss on the predicted $\\textbf{X}_{SR}$ and the loss on the middle layers. \n\nIt is noteworthy that we only implement a two-dimensional super-resolution process in our tests, i.e., to increase the spatial dimensions from $H\\times W$ to $KH\\times KW$. For 3-D flow data, LES simulations often have coarser resolutions along two directions while keeping the other dimension to be the same. Hence, we can use the same method to reconstruct DNS simulations of size $KH\\times KW\\times D$ ($D$ for depths) using LES simulations of size $H\\times W\\times D$.\nThe method presented herein can also be easily extended to include a three-dimensional convolutional filter if DNS simulations have higher resolution along all the three directions. \n\n\n\n\n\n\n\n\n\n\n\n\\subsubsection{Physical Loss}\nWe further regularize the generative process by leveraging the physical constraints.\nThese constraints can potentially reduce the size of the hypothesis space to be physically consistent, which helps extract more generalizable patterns and reduce the data required for training.\n\n\nSpecifically, we incorporate the inherent physical relationship.\nHere we represent the  velocity vector ${\\bf V}({\\bf x},t) $ along 3-D dimensions $({\\bf x}\\equiv x,y,z$),  by $u,\\ v,$ and $w$, respectively. The flow is incompressible; thus, the  velocity field is divergence-free: \n\\begin{equation}\n\\nabla \\cdot {\\bf V}= \\frac{\\partial u}{\\partial x} + \\frac{\\partial v}{\\partial y} + \\frac{\\partial w}{\\partial z} = 0.\n\\end{equation}\nLet ($u$, $v$, $w$) be included as three channels in $\\textbf{X}_{LR}$ and $\\textbf{X}_{HR}$. We use a second-order central finite difference approximation to estimate the partial derivatives.\nWe employ this divergent free property as an additional physical loss in the training process. \n\\begin{equation}\n\\mathcal{L}_\\text{Phy} = \\sum_{(x,y,z)}\\left[\\nabla \\cdot \\hat{\\bf V} ({\\bf x},t)\\right]^2\/N,\n\\end{equation}\nwhere $N$ is the number of spatial locations in the high-resolution data,  and $\\hat{\\bf V}$ represents the reconstructed velocity field at high resolution. \nBy minimizing $\\mathcal{L}_\\text{Phy}$ on the velocity field, we penalize the reconstructed high-resolution flow data that significantly violate the divergence-free property. Such regularization can help reduce the search space for model parameters such that the reconstructed high-resolution data follow the divergence-free property which is enforced in incompressible flows. \n\n\n\n\n\n\n\n\n\n\n\n\\subsection{Degradation Process} \n\n\n\nGiven a low-resolution flow data sample, there can be multiple high-resolution samples that correspond to this low-resolution input. The generative process aims to find the mapping from low-resolution to high-resolution data that fit all the training samples, but are also prone to overfitting due to the large  high-resolution data space. On the other hand, given any high-resolution flow data samples, it would be much easier to learn a forward mapping which produces a unique correspondence at the coarser resolution. Here, we introduce a reverse degradation process to further regularize the model by considering the reconstruction as an inverse problem. Note that the degradation process cannot address the challenge of one-to-many correspondence from low-resolution to high-resolution data, but it can help eliminate reconstructed \nhigh-resolution flow data that are not consistent\nto the given low-resolution simulations. \nSuch a degradation process is also helpful for capturing the discrepancy between simulation strategies used to generate data of different scales.\n\n\nWe create a forward model (in reverse modeling) $f(\\cdot)$ that maps \nhigh-resolution $\\textbf{X}_{HR}$ to low-resolution $\\textbf{X}_{LR}$.  We implement this forward model by using stacked convolutional layers and batch normalization layers (see Fig.~\\ref{fig:tf_plot}).  Then we introduce an additional degradation loss to ensure the consistency between the given low-resolution data $\\textbf{X}_{LR}$, and the low resolution data obtained from the reconstructed $\\textbf{X}_{SR}$ through the forward model, i.e., $f(\\textbf{X}_{SR};\\theta_\\text{deg})$, where $\\theta_\\text{deg}$ represents model parameters in the forward model.  In particular, we implement the degradation loss as follows:\n\n\\begin{equation}\n    \\mathcal{L}_\\text{deg} = \\text{MSE}(\\textbf{X}_{LR},f(\\textbf{X}_{SR};\\theta_\\text{deg}))\n\\end{equation}\n\n\n\n\n\nThe parameters of the forward model in the degradation process are estimated by minimizing the degradation loss. Moreover, we introduce the additional GAN loss~\\cite{goodfellow2014generative} by sharing the architecture of the forward model and the discriminator used in the GAN-based model. In particular, the GAN loss is defined on the extracted features by further extending the forward model, as shown in Fig.~\\ref{fig:tf_plot}. The GAN-based loss has been shown to improve the performance of extracting high-resolution textures in super-resolution tasks~\\cite{Cheo2003SR}. \n\n\n\n\nFormally, the loss function of the degradation process is:\n\\begin{equation}\n\\mathcal{L}_{D} = \\beta_1 \\mathcal{L}_\\text{deg} + \\beta_2 \\mathcal{L}_\\text{GAN,disc}, \n\\end{equation}\nwhere $\\mathcal{L}_\\text{GAN,disc}$ is the discriminator loss used in SRGAN~\\cite{ledig2017photo}, $\\beta_1$ and $\\beta_2$ are hyper-parameters. \n\n\nThe generative process needs to be optimized in conjunction with the degradation process. In particular, it is optimized by minimizing the combination of reconstruction loss (including middle layers) in the hierarchical structure, the physical Loss, degradation loss, and the GAN loss (the generator part). The overall loss for the generative process is:\n\\begin{equation}\n\\begin{aligned}\n\\mathcal{L}_{G} &= \\alpha_1\\mathcal{L}_\\text{recon}(\\textbf{X}_{SR},\\textbf{X}_{HR})+ \\alpha_2\\sum_{i=1}^{m+1}\\mathcal{L}_{hi} + \\alpha_3 \\mathcal{L}_\\text{Phy}\\\\\n&+\\alpha_4 \\mathcal{L}_\\text{deg}+\\alpha_5 \\mathcal{L}_\\text{GAN,gen},\n\\end{aligned}\n\\end{equation}\nwhere\n$\\mathcal{L}_\\text{GAN,gen}$ is the standard generator loss in\nGAN~\\cite{ledig2017photo}. We have also explored other extensions of GAN-based loss functions, such as Wasserstein GAN~\\cite{arjovsky2017wasserstein} and Wasserstein GAN-GP~\\cite{gulrajani2017improved} but did not observe significant improvement. The hyper-parameters \\{$\\alpha_{1:5}$\\} are used to control the weight of each component. We discuss the selection of these parameters in Section~\\ref{sec:exp}\n\n\n\n\n\n\n\n\\section{Experiment}\n\\label{sec:exp}\n\nIn this section, we first introduce the dataset and  experimental settings. Then we evaluate the performance of our proposed method in reconstructing DNS data.\n\n\n\\subsection{Experiment Setting}\nWe consider two experiments: single-snapshot  and cross-time. The former is designed to verify the ability of the proposed method in reconstructing a new data portion over space , and the latter is for evaluation of the methodology for data reconstruction over time.\n\n\\subsubsection{Dataset}\n\nThe TGV is produced by solution of the constant density Navier-Stokes equation:\n\n\\begin{equation}\n    \\frac{\\partial \\textbf{V}}{\\partial t} + (\\textbf{V}. \\nabla) \\textbf{V} = \\frac{-1}{\\rho} \\nabla p + \\nu \\Delta \\textbf{V},\n\\end{equation}\nwhere $\\rho ({\\bf x},t)$ and $p ({\\bf x},t)$ denote the fluid density and the thermodynamic pressure, respectively. \nThe evolution of the TGV includes enhancement of vorticity stretching and the consequent production of small-scale eddies. Initially, large vortices are placed in a cubic periodic domain of $[-\\pi,\\pi]$ (in all three-directions), with initial conditions:\n\\begin{eqnarray}\nu (x,y,z,0) &=& \\sin(x) \\cos(y) \\cos(z) \\\\ v(x,y,z,t) &=& - \\cos(x)\\sin(y)\\cos(z) \\\\ w(x,y,z,t) &=& 0.    \n\\end{eqnarray}\nThen the value of the Reynolds number is set to $Re=1600$.  \nWe have LES and DNS results of TGV at several times steps.  \nFor each time step, we consider the three-components of the velocity along the $x$, $y$ and $z$ axis, denoted by  $u$, $v$ and $w$, respectively.\nOur objective is to reconstruct the DNS results of\nthe velocity field $(u,v,w)$ using LES data.  In particular, $\\textbf{X}_{LR}$ represents the LES predicted values of the velocity field while the target $\\textbf{X}_{HR}$ represents the DNS results of the velocity field. \nHere both LES and DNS data are generated along 65 grid points along the $z$ axis under equal intervals. The LES and DNS  are conducted on 32-by-32 and 128-by-128 grid points, respectively,\nalong the $xy$\ndirections. Hence, the DNS data is of 4 times higher resolution compared to LES data.  \n\n\n\\subsubsection{Evaluation Metrics}\nWe evaluate the performance of DNS reconstruction  using two different metrics, root mean squared error (RMSE) and structural similarity index measure (SSIM)~\\cite{wang2004image}. We use RMSE to measure the difference (error) between reconstructed data and target DNS data. The lower value of RMSE indicates better reconstruction performance.\nSSIM  is used to appraise the similarity between reconstructed data and target DNS on three aspects, luminance, contrast and overall structure.\n\n\n\\subsubsection{Baselines}\nWe compare the performance of PGSRN method against several existing  methods that have been widely used for image super-resolution and turbulent flow downscaling. Specifically, we implement SRCNN~\\cite{dong2014learning}, RCAN~\\cite{zhang2018image}, SRGAN~\\cite{ledig2017photo}, and a popular dynamic fluid downscaling method: DCS\/MS~\\cite{fukami2019super} as baselines. \n\nTo better verify the effectiveness of each component in our proposed method, we further compare PGSRN with two of its variants: PGSRN-P and PGSRN-H as described below.\n\n\n\\textit{The variant with only physical Loss (PGSRN-P): } To show the effectiveness of the physical loss, we remove the degradation Loss and hierarchical loss (in middle layers) from the Hierarchical Generative Process. We name this method as  PGSRN-P.\n\n\\textit{The variant with physical loss + hierarchical generative process (PGSRN-H):} In this baseline, we  remove only the degradation loss from the PGSRN method, and we name this baseline as PGSRN-H.\n\nBy comparing PGSRN-P and SRGAN, we hope to show the improvement by incorporating the physical loss. We can further verify the effectiveness of the hierarchical loss by comparing PGSRN-P and PGSRN-H. Finally, the comparison between PGSRN-H and the complete version of PGSRN can show the effectiveness of using the degradation loss. \n\n\n\n\\begin{figure*} [!h]\n\\centering\n\\subfigure[LES. ]{ \\label{fig:a}\n\\includegraphics[width=0.3\\columnwidth]{les12.png}\n}\\hspace{5mm}\n\\subfigure[Upsampling.$\\backslash$ 0.505]{ \\label{fig:b}\n\\includegraphics[width=0.3\\columnwidth]{lesup12.png}\n}\\hspace{5mm}\n\\subfigure[DCS\/MS.$\\backslash$ 0.640]{ \\label{fig:b}\n\\includegraphics[width=0.3\\columnwidth]{dcs12.png}\n}\\hspace{5mm}\n\\subfigure[SRCNN.$\\backslash$ 0.643]{ \\label{fig:b}\n\\includegraphics[width=0.3\\columnwidth]{srcnn12.png}\n}\\hspace{5mm}\n\\subfigure[RCAN.$\\backslash$ 0.565]{ \\label{fig:b}\n\\includegraphics[width=0.3\\columnwidth]{rcan12.png}\n}\n\n\n\\subfigure[SRGAN.$\\backslash$ 0.659]{ \\label{fig:b}\n\\includegraphics[width=0.3\\columnwidth]{gan12u.png}\n}\\hspace{5mm}\n\\subfigure[PGSRN-P.$\\backslash$ 0.710]{ \\label{fig:b}\n\\includegraphics[width=0.3\\columnwidth]{noDM12.png}\n}\\hspace{5mm}\n\\subfigure[PGSRN-H.$\\backslash$ 0.712]{ \\label{fig:b}\n\\includegraphics[width=0.3\\columnwidth]{noD12.png}\n}\\hspace{5mm}\n\\subfigure[PGSRN.$\\backslash$ 0.762]{ \\label{fig:b}\n\\includegraphics[width=0.3\\columnwidth]{our12.png}\n}\\hspace{5mm}\n\\subfigure[Target DNS.]{ \\label{fig:b}\n\n\\includegraphics[width=0.3\\columnwidth]{dns12.png}\n}\n\\vspace{.08in}\n\\caption{Reconstructed $u$ channel by each method on a sample testing slice along the $z$ dimension in the single-snapshot experiment. We also show the SSIM value for each reconstructed data.}\n\\vspace{.1in}\n\\label{fig:tf_plot1}\n\\end{figure*}\n\n\n\\begin{table}[!t]\n\\small\n\\newcommand{\\tabincell}[2]{\\begin{tabular}{@{}#1@{}}#2\\end{tabular}}\n\\centering\n\\caption{Reconstruction performance (measured by RMSE and SSIM) on $(u,v,w)$ channels by different methods in the single-snapshot experiment.}\n\\begin{tabular}{l|cccc}\n\\hline\n\\textbf{Method} & RMSE & SSIM &  \\\\ \\hline \nSRCNN & (0.086, 0.089, 0.106) &(0.833, 0.833, 0.764)&\\\\\nRCAN & (0.096, 0.095, 0.109) &(0.745, 0.741, 0.645)&\\\\ \nDSC\/MS & (0.096, 0.095, 0.106) &(0.828, 0.826, 0.729)&\\\\\nSRGAN & (0.089, 0.078, 0.085) &(0.837, 0.834, 0.751)&\\\\   \n\\hline\nPGSRN-P & (0.076, 0.075, 0.075)   & (0.845, 0.846, 0.781)&\\\\ \nPGSRN-H & (0.077, 0.074, 0.070) &(0.844, 0.844, 0.800)&\\\\\nPGSRN & (0.064, 0.061, 0.066) &(0.875, 0.877, 0.838)&\\\\\n\\hline\n\\end{tabular}\n\\label{fig:table1}\n\\end{table}\n\n\\subsubsection{Experimental Design}\n\nWe evaluate the performance of our proposed method in two different scenarios. First, we consider the case in which part of flow data is missing at a specific time. For example, the high-resolution flow data is available at certain points along the $z$ axis but not available at other points. We can use the model trained using available data to reconstruct high-resolution DNS data for the remaining locations.\nWe refer to this test as a single-snapshot experiment since the training and testing are conducted at the same time step.\nIn this test, we use the 5-fold cross validation method to divide 65 data slices into five parts and each part has 13 slices. Each time we use four folds (i.e., 52 slides) for training and use the remaining one fold (i.e., 13 slides) for testing.\n\nSecond, we conduct cross-time experiments to study how the proposed method helps simulate flows in a dynamic scenario. \nIn particular, we use data from  20 consecutive time steps  as the training data, and then test the model in the next 20 time steps.\nThis is a challenging task since dynamic fluid is changing over time following complex non-linear patterns (driven by Navier-Stokes equation~\\cite{foias2001navier}). Hence, the model trained from available data may not be able to generalize to future data that look very different with training data.\n\n\n\n\n\n\n\n\n\n\n\n\\subsubsection{Training Settings}\nData normalization is performed on both training and testing datasets, to normalize input LES variables to the range [0,1]. Then, the model is trained by ADAM optimizer~\\cite{kingma2014adam_arxiv}  with $\\beta_1$ = 0.5, $\\beta_2$ = 0.999. The initial learning rate is set to 0.0002 and iterations are 500 epochs.\nAll the $\\alpha_{i}$ ($i=1$ to 5) values are set to 1. We use Tensorflow 1.15 and Keras to implement our models with Titan Xp GPU.\n\n\n\n\n\n\\begin{table}[!t]\n\\small\n\\newcommand{\\tabincell}[2]{\\begin{tabular}{@{}#1@{}}#2\\end{tabular}}\n\\centering\n\\caption{Reconstruction performance on $(u,v,w)$ channels by RMSE and SSIM in the cross-time experiment.\nThe performance is measured at a time step which is 5 seconds apart from the last time step in training data.\n}\n\\begin{tabular}{l|cccc}\n\\hline\n\\textbf{Method} & RMSE & SSIM &  \\\\ \\hline \nSRCNN&(0.089, 0.089, 0.122) &(0.890, 0.889, 0.848)&\\\\ \nRCAN& (0.073, 0.073, 0.093)&(0.875, 0.874, 0.837)&\\\\ \nDSC\/MS&(0.095, 0.098, 0.131) &0.881, 0.879, 0.822)&\\\\\nSRGAN& (0.086, 0.087, 0.096) &(0.897, 0.901, 0.860)&\\\\ \n\n\\hline\nPGSRN-P&(0.086, 0.082, 0.095)&(0.903, 0.909, 0.876)&\\\\ \nPGSRN-H&(0.083, 0.081, 0.093) &(0.907, 0.908, 0.870)&\\\\\nPGSRN&(0.076, 0.072, 0.086) &(0.920, 0.922, 0.896)&\\\\\n\\hline\n\\end{tabular}\n\\label{fig:table2}\n\\end{table}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\subsection{Single-Snapshot Experiment}\n\n\n\\textbf{Quantitative Results.}\nTable.~\\ref{fig:table1} shows quantitative comparisons amongst all the methods.\nWhen comparing our proposed PGSRN method with baseline methods, our proposed PGSRN performs the best on both evaluation ways, obtaining lowest RMSE value and highest SSIM values. According to this table, the proposed method PGSRN in general outperforms other baselines for velocity components \\{$u$, $v$, $w$\\} in terms of both RMSE and SSIM. \n\nBy comparing SRGAN  and  SRCNN, we show the improvement by using the GAN loss. Furthermore, the comparison amongst SRGAN, PGSRN-P, PGSRN-H, and PGSRN shows the effectiveness of incorporating each component (physical loss, hierarchical loss, degradation) of the proposed method. In particular, the incorporation of physical loss and degradation loss brings the most significant performance improvement in terms of RMSE and SSIM. \n\n\nAlthough the baseline DSC\/MS was developed in the context of turbulent flow downscaling, it has been  successful only when tested towards reconstructing DNS data using down-sampled DNS data. This method does not work well in our test because it does not take into account the discrepancy between LES and DNS results.\n\n\n\n\n\\textbf{Visual Results.} In Fig.~\\ref{fig:tf_plot1}, we show an example of high-resolution flow data (128-by-128 on a specified $z$ value) reconstructed by each method. We observe that LES results on this slice do not capture some fine-level details of DNS. The DCS\/MS, SRCNN, and RCAN methods also do not capture such fine-level information. In contrast, SRGAN can obtain higher SSIM value compared to these methods, and it can be further improved by incorporating physical loss, hierarchical loss, and the degradation loss. By visually inspecting reconstructed data over multiple slices, we find that the incorporation of the physical in general helps eliminate artifacts that are physically inconsistent (e.g., the red circled areas in Fig.~\\ref{fig:tf_plot1} (f)). The use of degradation loss generally helps better match the magnitude of the reconstructed data to the target DNS. \nFor most slices for which LES exhibits obvious differences with DNS data, the SSIM value of PGSRN is more than 10$\\%$ higher than all the other existing algorithms.\n\n\n\\subsection{Cross-Time Experiment}\n\n\\textbf{Quantitative Results.} In this experiment, we compare the same set of existing methods as in the previous single-snapshot experiment. In Table~\\ref{fig:table2}, we show the quantitative results at the 5th time step in the testing set, which is five seconds apart from the last time step in the training set. We select this time step to show the performance in short-term prediction while we will show more results at different time steps later in the temporal analysis.\n\n\nWe can observe similar results that our proposed PGSRN outperforms other methods by a considerable margin. We also notice that RCAN method achieves good  RMSE in this test, e.g., RCAN has smaller RMSE than PGSRN in reconstructing velocity components $u$ and $v$. This shows that the machine learning model with a more complex (and carefully designed) forward process has a better chance at matching with the target data. However, the success of RCAN is limited in capturing the overall structure of flows as observed from its lower SSIM values compared with other methods. \n\n\n\n\\textbf{Temporal Analysis.} \nIn the temporal analysis, we show the change of performance as we reconstruct DNS data over 20 time steps after the training data.  \nWe show the performance of cross-time prediction in terms of RMSE and SSIM  in Fig.~\\ref{fig:tf_plot3} and Fig.~\\ref{fig:tf_plot4}, respectively. We have several observations from these figures: (1) With larger time intervals between training data and prediction data, the performance (in terms of both RMSE and SSIM) becomes worse. In general, our method still has better performance than other methods.  (2) RCAN has achieved better RMSE than the proposed method for reconstructing $u$ and $v$ channels, especially during the first 10 time steps. However, our method has much better SSIM compared to RCAN.   (3) After 15 time steps, the performance (SSIM\/RMSE) tends to be stable;   (4)  Although our proposed PGSRN method achieves better RMSE and SSIM than other methods, the reconstructed data is of very low quality when the time gap is large. We will show some examples in the visual results. \n\n\n\n\n\\begin{figure*} [!h]\n\\centering\n\\subfigure[$u$ Channel.]{ \\label{fig:a}{}\n\\includegraphics[width=0.32\\linewidth]{RMSE_plot_u.png}\n}\\hspace{-0.2in}\n\\subfigure[$v$ Channel.]{ \\label{fig:b}{}\n\\includegraphics[width=0.32\\linewidth]{RMSE_plot_v.png}\n}\\hspace{-0.2in}\n\\subfigure[$w$ Channel.]{ \\label{fig:b}{}\n\\includegraphics[width=0.32\\linewidth]{RMSE_plot_w.png}\n}\n\\vspace{.05in}\n\\caption{Change of RMSE values produced by different models from the 1st to 20th time steps in the cross-time experiment.}\n\\label{fig:tf_plot3}\n\\end{figure*}\n\n\n\\begin{figure*} [!h]\n\\centering\n\\subfigure[$u$ Channel.]{ \\label{fig:a}{}\n\\includegraphics[width=0.32\\linewidth]{SSIM_plot_u.png}\n}\\hspace{-0.2in}\n\\subfigure[$v$ Channel.]{ \\label{fig:b}{}\n\\includegraphics[width=0.32\\linewidth]{SSIM_plot_v.png}\n}\\hspace{-0.2in}\n\\subfigure[$w$ Channel.]{ \\label{fig:b}{}\n\\includegraphics[width=0.32\\linewidth]{SSIM_plot_w.png}\n}\n\\vspace{.05in}\n\\caption{Change of SSIM values produced by different models from the 1st to 20th time steps in the cross-time experiment.}\n\\label{fig:tf_plot4}\n\\end{figure*}\n\n\n\\textbf{Visual Results.} In Fig.~\\ref{fig:tf_plot2}, we show the reconstructed data at multiple time steps (1st time step, 5th time step,  10th time step and 20th time step) after the training period. For each time step, we only show the slice of the $w$ component at a specified $z$ value.\nAt the 1st step, both our method and other methods can obtain ideal reconstruction results. This is because the test data is similar to the training data at the last time step. According to reported SSIM values, our proposed method is slightly better than other baseline methods. At the 5th time step,\nour proposed PGSRN method performs much better than other methods. This confirms that our method can effectively eliminate the differences between input picture and ground truth picture, \naccurately fine-level capture textures and patterns (e.g., see red circled areas), reduce color amplitude difference, and thus achieve much better performance. At the 10th and 20th time steps, since the testing data is very different from training data,\nneither our method nor other methods can provide good reconstruction results.\n\n\nOne potential limitation of our proposed method and other methods is that they mainly focus on the reconstruction using the spatial information, and pay less attention to  temporal dependencies. Hence, these models may not fully capture fluid dynamics transport over time. After a sufficiently long time gap, the dynamic flow data can become very different from the data used in model training.\nHence, it is difficult for either our proposed methods or other state-of-the-art methods to obtain a relative positive consequence. We will keep this as our future work to further preserve long-term consistency to underlying fluid dynamics (e.g., by following the Navier-Stokes equation).\n\n\\textbf{Validation based on Physical Metrics.} We also show the performance of cross-time prediction in terms of Reynolds stress~\\cite{Nawab2020}, which is considered an important metric for studying the property of turbulence. In particular, Reynolds stress is computed as: \n\\begin{equation}\n \\mathcal{R}_{ab} = \\overline{ab} - \\bar{a}\\bar{b}   \n\\end{equation}\nwhere $a$ and $b$ represent any velocity variables\nfrom $(u, v, w)$, and $\\bar{a}$ represents the mean value of variable $a$ over the entire field.\n\n\n\nIn Fig.~\\ref{fig:tf_plot6}, we show the Reynolds stress of target DNS and Reynolds stress of reconstructed flow data by RCAN, SRGAN, and our method over time. Ideally, high-quality reconstruction should have Reynolds stress similar to that of the DNS data. However, this may not be true in practice since\ndifferent flow data can have the similar Reynolds stress values and the super-resolution model does not directly optimize the similarity of Reynolds stress during the training process.\nIn this figure, we observe that SRGAN performs poorly since its Reynolds stress values are far away from those of the DNS data. Our method PGSRN performs similarly to RCAN on estimating the three components of Reynolds stresses. \nHowever, there is still a large discrepancy between our method and the real DNS data in terms of Reynolds stresses. Sophisticated machine learning models are prone to produce artificial factors in reconstructed flow resulting in unreliable Reynolds stress. In the future, we will pursue optimizing the super-resolution model by including physical metrics in the training objective. \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\begin{figure*} [!h]\n\\centering\n\\subfigure[DCS\/MS.$\\backslash$ 0.749]{ \\label{fig:a}\n\\includegraphics[width=0.15\\linewidth]{dcs71_13w.png}\n}\\hspace{5mm}\n\\subfigure[SRCNN.$\\backslash$ 0.839]{ \\label{fig:b}\n\\includegraphics[width=0.15\\linewidth]{srcnn71_13w.png}\n}\\hspace{5mm}\n\\subfigure[SRGAN.$\\backslash$ 0.858]{ \\label{fig:c}\n\\includegraphics[width=0.15\\linewidth]{gan71_13w.png}\n}\\hspace{5mm}\n\\subfigure[PGSRN.$\\backslash$ 0.886]{ \\label{fig:d}\n\\includegraphics[width=0.15\\linewidth]{our71_13w.png}\n}\\hspace{5mm}\n\\subfigure[Target DNS.]{ \\label{fig:e}\n\\includegraphics[width=0.15\\linewidth]{dns71_13w.png}\n}\\hspace{5mm}\n\\subfigure[DCS\/MS.$\\backslash$ 0.715]{ \\label{fig:a}\n\\includegraphics[width=0.15\\linewidth]{dcs75_10w.png}\n}\\hspace{5mm}\n\\subfigure[SRCNN.$\\backslash$ 0.724]{ \\label{fig:b}\n\\includegraphics[width=0.15\\linewidth]{srcnn.png}\n}\\hspace{5mm}\n\\subfigure[SRGAN.$\\backslash$ 0.802]{ \\label{fig:b}\n\\includegraphics[width=0.15\\linewidth]{gan.png}\n}\\hspace{5mm}\n\\subfigure[PGSRN.$\\backslash$ 0.857]{ \\label{fig:b}\n\\includegraphics[width=0.15\\linewidth]{our.png}\n}\\hspace{5mm}\n\\subfigure[Target DNS.]{ \\label{fig:b}\n\\includegraphics[width=0.15\\linewidth]{dns10.png}\n}\\hspace{5mm}\n\\subfigure[DCS\/MS.$\\backslash$ 0.597]{ \\label{fig:a}\n\\includegraphics[width=0.15\\linewidth]{dcs80_12w.png}\n}\\hspace{5mm}\n\\subfigure[SRCNN.$\\backslash$ 0.642]{ \\label{fig:b}\n\\includegraphics[width=0.15\\linewidth]{srcnn80_12w.png}\n}\\hspace{5mm}\n\\subfigure[SRGAN.$\\backslash$ 0.658]{ \\label{fig:b}\n\\includegraphics[width=0.15\\linewidth]{gan80_12w.png}\n}\\hspace{5mm}\n\\subfigure[PGSRN.$\\backslash$ 0.688]{ \\label{fig:b}\n\\includegraphics[width=0.15\\linewidth]{our80_12w.png}\n}\\hspace{5mm}\n\\subfigure[Target DNS.]{ \\label{fig:b}\n\\includegraphics[width=0.15\\linewidth]{dns80_12w.png}\n}\\hspace{5mm}\n\\subfigure[DCS\/MS.$\\backslash$ 0.656]{ \\label{fig:a}\n\\includegraphics[width=0.15\\linewidth]{dcs90_8w.png}\n}\\hspace{5mm}\n\\subfigure[SRCNN.$\\backslash$ 0.670]{ \\label{fig:b}\n\\includegraphics[width=0.15\\linewidth]{srcnn90_8w.png}\n}\\hspace{5mm}\n\\subfigure[SRGAN.$\\backslash$ 0.728]{ \\label{fig:b}\n\\includegraphics[width=0.15\\linewidth]{gan90_8w.png}\n}\\hspace{5mm}\n\\subfigure[PGSRN.$\\backslash$ 0.756]{ \\label{fig:b}\n\\includegraphics[width=0.15\\linewidth]{our90_8w.png}\n}\\hspace{5mm}\n\\subfigure[Target DNS.]{ \\label{fig:b}\n\\includegraphics[width=0.15\\linewidth]{dns90_8w.png}\n}\n\\vspace{.05in}\n\\caption{Reconstructed $w$ channel by each method on a sample testing slice along the $z$ dimension in the cross-time experiment. We show the reconstruction results at the 1st time step, 5th time step, 10th time step and 20th time step in (a)-(e), (f)-(j), (k)-(o) and (p)-(t), respectively.  We also show the SSIM value for each reconstructed data.}\n\\label{fig:tf_plot2}\n\\end{figure*}\n\n\n\n\n\n\n\\subsection{Parameter Sensitivity}\nWe also test the performance of the proposed method using different hyper-parameters in the loss function. In particular, we report the RMSE achieved by our method in reconstructing the three velocity components $\\{u,v,w\\}$ when varying the weights of physical loss ($\\alpha_{3}$) and degradation loss($\\alpha_{4}$),\nas shown in Fig.~\\ref{fig:tf_plot5}. When we change the value of one hyper-parameter, we keep all the other $\\alpha_i$ values as 1.\n\nFor the value of $\\alpha_3$, when it increases from 0 to 1, the model gets better performance due to the contribution of physical regularization. However, as we keep increasing the value of $\\alpha_3$, especially when it is greater than 3, the model starts to produce worse performance. In the physical loss, we use the finite difference approximation for the divergence and thus the simulations may not strictly follow this regularization. When we set a larger $\\alpha_3$ value, the training process is dominated by the physical loss while paying less attention to other loss terms, which leads to a degraded reconstruction performance. \n\n\n\nFor the weight of the degradation loss, we can observe similar patterns that the model performs better when $\\alpha_4$ increases from 0 to 1. Unlike the physical loss, when we further increase the value of $\\alpha_4$, the performance is relatively stable. The performance becomes worse when we increase $\\alpha_4$ from 1 to 5, but becomes better from 5 to 10. \n\n\n\n\n\n\n \n\n\n\n\n\\begin{figure*} [!t]\n\\centering\n\\subfigure[$\\mathcal{R}_{uv}$.]{ \\label{fig:a}{}\n\\includegraphics[width=0.32\\linewidth]{Reynold_plot_uv.png}\n}\\hspace{-0.2in}\n\\subfigure[$\\mathcal{R}_{uw}$]{ \\label{fig:b}{}\n\\includegraphics[width=0.32\\linewidth]{Reynold_plot_uw.png}\n}\\hspace{-0.2in}\n\\subfigure[$\\mathcal{R}_{vw}$.]{ \\label{fig:b}{}\n\\includegraphics[width=0.32\\linewidth]{Reynold_plot_vw.png}\n}\n\\vspace{.05in}\n\\caption{Change of Reynolds Stress values produced by the reference DNS and different models from the 1st to 20th time steps in the cross-time experiment.}\n\\label{fig:tf_plot6}\n\\end{figure*}\n\\begin{figure*} [!t]\n\\centering\n\\subfigure[The value of $\\alpha_3$.]{ \\label{fig:a}{}\n\\includegraphics[width=0.51\\linewidth]{RMSE_plot_alphaP.png}\n}\\hspace{-0.5in}\n\\subfigure[The value of $\\alpha_4$.]{ \\label{fig:b}{}\n\\includegraphics[width=0.51\\linewidth]{RMSE_plot_alphaD.png}\n}\n\n\\caption{Change of RMSE as we adjust the hyper-parameters in the loss function. (a) The variation of performance (RMSE) with different values of  $\\alpha_{3}$, i.e., the weight for the physical loss. (b) The variation of performance (RMSE) with different values of  $\\alpha_{4}$, i.e., the weight for the degradation loss.}\n\\label{fig:tf_plot5}\n\\end{figure*}\n\n\n\n\n\n\n\n\\section{Related Work}\nIn this section, we introduce related literature on several topics. We start with existing super-resolution methods that are widely used in computer vision, which is followed by their adaptations to the problem of turbulent flow simulations. Finally, we  discuss existing works on incorporating physical relationships into the loss function of machine learning models. \n\n\n\n\n\\subsection{Machine Learning for Super-resolution in Computer Vision}\n\n\nResearchers have developed many deep learning-based methods for single image super resolution (SISR) in computer vision. The neural network structures, such as convolutional network layers, are known to be able to extract spatial contextual information that is needed for recovering  high-resolution data. The recent advances in GAN-based methods also enables better extracting high-resolution textures that are similar to target data. \n\n\nOne of the earliest models that uses deep convolutional networks for SISR problem is SRCNN~\\cite{dong2014learning}. SRCNN can directly learn the end-to-end mapping between coarse-resolution and high-resolution images using a series of convolutional layers.\nCompared to SRCNN, Residual Channel Attention Network (RCAN)~\\cite{zhang2018image} uses a very deep trainable structure with additional skip-connection layers.  The intuition of RCAN is to  bypass the abundant low-frequency information and focus more on the relevant information. The skip-connections are also known to improve the stability of the optimization process for deep neural networks. Moreover, RCAN\nrescales features of each channel to fully explore  the interdependencies among channels.\nRecently, there are also other popular methods based on residual structures such as HDRN~\\cite{Duong2021}, SAN~\\cite{Dai2019}, RDN~\\cite{zhang2018residual}, CARN~\\cite{ahn2018fast}, and DRRN~\\cite{Tai2017}.\n\n\n\n\nAnother popular super-resolution model is the SRGAN model~\\cite{ledig2017photo}, which employs generative adversarial network (GAN) for the SISR problem.  SRGAN model not only stacks the deep residual network to build a deeper generative network for image super resolution, but also introduces\na discriminator network to distinguish reconstructed images and real images using an adversarial loss function. The ultimate goal is to train the generative network such that the reconstructed images cannot be easily distinguished by the discriminator.\nCompared with other models, one major advantage of the SRGAN model is that the discriminator can help extract representative features from high-resolution data and enforce such features in the reconstructed images. \nRecently, there are also other extensions to the SRGAN method that further improve the performance~\\cite{chen2017fsrnet,wang2018recovering, wang2018esrgan,karras2018progressive,gan8759375,cheng2021mfagan,Long2021}. \n\n\nThese super-resolution methods have shown success in benchmark image datasets, but they are not designed for capturing complex patterns amongst multiple physical variables and the discrepancy between different simulation methods. Hence, they may lead to unsatisfactory performance in reconstructing flow data, especially when the resolution ratio between input data and target data is large. \n\n\n\\subsection{Machine Learning for Reconstructing Flow Data} Given the importance of simulating high-resolution flows, there is a surge of interest in using super-resolution techniques for reconstructing high-resolution flow data. \nFukami et al.~\\cite{fukami2019super} propose an improved CNN-based hybrid DSC\/MS model by extracting patterns from multiple scales. This method has been shown to produce good performance on reconstructing the turbulent velocity and vorticity fields from extremely low-resolution input data. This model has also shown success to handle spatio-temporal super resolution analysis in turbulent flow~\\cite{Fukami_2020}.\n\nSimilarly, Liu et al.~\\cite{liu2020deep} also propose another CNN-based model MTPC to simultaneously handle spatial and temporal information in turbulent flow simultaneously to fully capture features in different time ranges.\nThere are also other approaches that are inspired by GAN. For example, Xie et al. \\cite{xie2018tempogan} introduce tempoGAN, which augments a general adversarial network with an additional discriminator network along with additional loss function terms that preserve temporal coherence in the generation of physics-based simulations of fluid flow.  Deng et al.~\\cite{Deng2019SuperresolutionRO} demonstrate that both SRGAN and ESRGAN~\\cite{wang2018esrgan} can\nproduce good reconstruction of  high-resolution turbulent flow in their datasets.\n\n\nMost of these existing methods on reconstructing flow data still rely on simple CNN-based structure and do not leveraging recent advances in the super-resolution. Hence, they are limited in their capacity to extract complex non-linear relationships. Moreover, most of these approaches have only shown success in data reconstruction using a down-sampled version of the target data. These methods do not take into account the discrepancy of different simulations (e.g., LES and DNS) and thus may have degraded performance in our problem. \n\n\n\n\n\\subsection{Physics-based Loss Function}\n\nWhen applied to scientific problems, standard machine learning models can fail to capture complex relationships amongst physical variables, especially when provided with limited observation data. This is one reason for their failure to generalize to scenarios not encountered in training data. Hence, researchers are beginning to incorporate physical knowledge into loss functions to help machine learning models capture generalizable dynamic patterns consistent with established physical relationships.\n\n\n\n\n\n\nThe use of physical-based loss functions have already shown promising results in a variety of scientific disciplines. In a recent survey~\\cite{willard2020integrating}, Willard et al. summarize existing literature and approaches for incorporating scientific knowledge into machine learning models. For example, in lake water temperature modeling, Karpatne et al.~\\cite{karpatne2017physics} propose an additional physics-based penalty based on known monotonic physical  relationship to guarantee that the density of water at lower depth is always greater than the density of water in any depths above.\nThen, Jia et al.~\\cite{jia2019sdm2} and Read et al.~\\cite{read2019process} further extended this work by including an additional penalty term on violating the law of energy conservation. In the problem related to vortex induced vibrations, Kahana et al.~\\cite{Adar2020physical} apply an additional loss function to ensure the physical consistency in the time evolution of waves, which has been used in an inverse problem about distinguishing an underwater obstacle's location from acoustic measurements. This additional physical-based loss function has been shown to improve the prediction results and makes the model more robust. \n\nAnother application is to solve the PDEs of dynamical systems. Researchers commonly use physical-based loss functions for the mandatory compliance with the governing equation in the loss function. Raissi et al.~\\cite{raissi2019physics} develop data-efficient spatial-temporal function approximators to solve PDEs and estimate PDE parameters. \nSimilarly,an encoder-decoder is proposed by Zhu et al.~\\cite{Zhu2019physical} to predict transient PDE by controlling PDE constraints.\n\n\n\n\n\n\\section{Discussion and Future works}\nIn this paper, we develop a new data-driven method PGSRN that leverages physical relationships to fully explore the reconstruction gaps between coarse-resolution and high-resolution simulations of fluid dynamics. Specifically, we leverage the underlying physical relationships to regularize the relationships amongst velocity components in flow data. To further explore the correspondence and discrepancy between DNS and LES data, we also  build the hierarchical generative process and introduce the degradation process. \nWe have demonstrated the effectiveness of our proposed method in reconstructing DNS of flow data from coarse-resolution LES data\nthrough both single-snapshot  and cross-time experiments. Compared with existing methods, the proposed method can better recover fine-level fluid patterns that are missing from coarse-resolution LES data, and thus produce better performance in both tests. We have also shown that all the components introduced in our proposed method are helpful in the reconstruction process. \n\n\n\n\n\nAlthough our method has been developed in the context of simulating fluid dynamics, the involved techniques can be widely used for other important scientific problems. For example,  simulations of cloud-resolving models (CRM) at sub-kilometer horizontal resolution are critical for effectively representing boundary-layer eddies and low clouds. However, it is not feasible to generate simulations at such fine resolution even with the most powerful commuters expected to be available in the near future. Hence, the method developed in this paper can provide a great potential for reconstructing high-resolution simulations.  \n\n\n\n\n\nAdditionally, as shown in the cross-time experiment, our method remains limited in reconstructing long-term data. This requires new mechanisms to enforce underlying physical processes on fluid dynamics (e.g., Navier-Stokes equation). Furthermore, we plan to introduce other related parameters besides velocity (e.g., mass and pressure) to supplement and further optimize our model. Last, we also will introduce other domain's metrics (e.g., Reynolds Stress and Kinetic Energy~\\cite{Nawab2020}) as the training loss to enhance the trustworthiness of the model when it is deployed for long-term and large-scale simulations. We will purse these directions in our future work. \n\n\n\n\n\\bibliographystyle{IEEEtran}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section*{Introduction}\nSuperdense coding \\cite{bennett1992} is one of the simplest examples showing the power of quantum entanglement. It allows one to transmit two bits of classical information by sending only one qubit if a maximally entangled state is initially shared by the sender and receiver. It has been studied theoretically \\cite{barenco1995, hausladen1996, bose2000, bowen2001, hiroshima2001, ziman2003, bruss2004, mozes2005} as well as experimentally \\cite{mattle1996, fang2000, mizuno2005}.\n\nQuantum teleportation \\cite{bennett1993} is another intriguing example utilizing the power of quantum entanglement. It is a protocol to transmit an unknown quantum state using classical communication and an initially shared maximally entangled state. In fact, the equivalence of quantum teleportation and superdense coding with maximally entangled states has been proven \\cite{werner2001}. \n\nControlled dense coding \\cite{hao2001, jing2003} and controlled quantum teleportation \\cite{karlsson1998} have been proposed as extensions of superdense coding and quantum teleportation. The standard dense coding and quantum teleportation involve only two parties, a sender and a receiver, and assume that they share a maximally entangled state in advance. In controlled dense coding and teleportation, a third party participates in the protocol as a controller, and a tripartite entangled state is shared among the three parties. The controller in each protocol can control the channel capacity and the teleportation fidelity of the other two parties, respectively. Recently, the concepts of control power (CP) and minimal control power (MCP) of the controlled teleportation have been suggested to quantify how much teleportation fidelity can be controlled by the controller \\cite{li2014, li2015, jeong2016, hop2016}. CP is defined as the difference between teleportation fidelities with and without the controller's assistance. MCP is defined as the minimal value of CP among all possible permutations of the three qubits. Similarly, CP has been defined in controlled remote state preparation schemes as well \\cite{li2016}.\n\nMotivated by the similarity between quantum teleportation and superdense coding, we here define CP and MCP of controlled dense coding of three-qubit states to quantify how much the dense coding channel capacity can be controlled by the controller. We also calculate CP and MCP for two representative tripartite entangled states: the extended Greenberger-Horne-Zeilinger (GHZ) state and the generalized $W$ state. We show that the standard GHZ state and the standard $W$ state have maximal MCP values for each class, which implies that MCP can be a candidate to capture the genuine tripartite entanglement of pure states. We also find the lower and upper bounds and analyze the properties in terms of genuine tripartite entanglement.\n\nThis paper is organized as follows: First, we review the controlled dense coding scheme and define CP and MCP for controlled dense coding. Then we calculate CP and MCP for important three-qubit states such as the extended GHZ states and generalized $W$ states. Furthermore, we investigate the properties of MCP in terms of genuine tripartite entanglement. Finally, we summarize and conclude the study.\n\n\\section*{Results}\n\\subsection*{Controlled dense coding and minimal control power}\n\\label{sec:cdc}\nIn the standard scenario of superdense coding \\cite{bennett1992}, the sender, Alice, and the receiver, Bob, initially share a Bell state, and Alice encodes classical information by performing a local operation on her qubit and then sends it to Bob. After receiving her qubit, Bob performs a two-qubit measurement so that he can recover the classical information that Alice wants to transmit. Thus, Alice is able to transmit two classical bits by sending one qubit of a Bell state that is initially shared between them. Indeed, partially entangled states can be used in the dense coding scheme instead of maximally entangled states, and the number of bits that Alice can transmit to Bob using general two-qubit state $\\rho_{12}$ can be quantified by the dense coding channel capacity \\cite{bowen2001, bruss2004}\n\\begin{equation}\nC(\\rho_{12})=1+S(\\rho_2)-S(\\rho_{12})\\label{cc1}\n\\end{equation}\nwhere Alice has the first qubit, Bob the second, and $S(\\rho)=-\\text{Tr}(\\rho \\log_2\\rho)$ is the von Neumann entropy. It is easy to confirm that the dense coding channel capacity of a Bell state is 2 bits. Note that, in this paper, $C(\\rho_{jk})$ means the channel capacity when Alice has the $j$th qubit, Bob the $k$th qubit, and $C(\\rho_{12})=C(\\rho_{21})$ for a pure state $\\rho_{12}$.\n\nIn the controlled dense coding scenario \\cite{hao2001}, there is another party, Charlie, who plays the role as a controller, and the three parties share a three-qubit state $\\rho_{123}$. To maximize the channel capacity between Alice and Bob, Charlie measures his qubit on an optimal basis that maximizes the average dense coding channel capacity and broadcasts the measurement outcome to Alice and Bob. After receiving the measurement outcome, Alice and Bob perform the dense coding scheme. We define the controlled dense coding channel capacity that Alice and Bob can achieve using this protocol as,\n\\begin{align}\nC^{jkl}_{CD}&(\\rho_{123})=\\max_U[\\langle 0|U\\rho_j U^\\dagger|0\\rangle C(\\rho^0_{kl})+\\langle 1|U\\rho_jU^\\dagger|1\\rangle C(\\rho^1_{kl})], \\label{cc2}\n\\end{align}\nwhere Charlie, Alice, and Bob have the $j$th, $k$th, and $l$th qubit, respectively ($j,k,$ and $l$ are distinct numbers in $\\{1,2,3\\}$). The maximum is taken over all $2 \\times 2$ unitary matrices $U$, which correspond to Charlie's choice of measurement basis. $\\rho_j=\\text{Tr}_{kl}(\\rho_{123})$ and $\\rho_{kl}^i$ is the quantum state that Alice and Bob share when Charlie's measurement outcome is $i$, where $i\\in\\{0,1\\}$.\n\nOn the other hand, we now consider the channel capacity that Alice and Bob achieve without Charlie's assistance. In this case, the quantum state that Alice and Bob share is the reduced density operator of Alice and Bob, $\\rho_{kl}=\\text{Tr}_j (\\rho_{123})$ where Alice and Bob have the $k$th and $l$th qubit, respectively. Thus, the channel capacity without Charlie's assistance is given by $C(\\rho_{kl})$, which we will denote by $C_j(\\rho_{kl})$ to specify Charlie's qubit. Finally, we define the CP of Charlie as the difference between the channel capacities with and without Charlie's assistance,\n\\begin{equation}\nP^{jkl} (\\rho_{123})\\equiv C_{CD}^{jkl}-C_j(\\rho_{kl})\n\\end{equation}\nand also define the minimal control power (MCP) \n\\begin{align}\nP(\\rho_{123})\\equiv \\min_{j,k,l}  P^{jkl} (\\rho_{123})\n\\end{align}\nwhere the minimum is taken over all possible permutation of $\\{j,k,l\\}$. MCP is defined in the same way as for controlled teleportation \\cite{jeong2016} by replacing teleportation fidelity with channel capacity.\n\n\\subsection*{Examples}\n\\label{sec:ex}\nBefore we investigate the properties of MCP, let us calculate the MCPs of certain three-qubit states such as the extended GHZ states and generalized $W$ states \\cite{acin2001}.\n\\subsubsection*{Extended GHZ states}\nLet $|\\psi_{\\text{eGHZ}}\\rangle_{123}$ be a state defined by\n\\begin{equation}\n|\\psi_{\\text{eGHZ}}\\rangle_{123}=\\lambda_1|000\\rangle+\\lambda_2|110\\rangle+\\lambda_3|111\\rangle,\n\\end{equation}\nwhere the coefficients $\\lambda_i\\geq0$ and $\\sum_i\\lambda_i^2=1$ \\cite{acin2001}. The state $|\\psi_{\\text{eGHZ}}\\rangle$ is here called an extended GHZ state and $\\psi_{\\text{eGHZ}}=|\\psi_{\\text{eGHZ}}\\rangle\\langle\\psi_{\\text{eGHZ}}|_{123}$. Note that the extended GHZ states are invariant under the interchange of the first and second qubit.\n\nTo calculate CP, we need to obtain the channel capacities with and without Charlie's assistance for each permutation of $\\{j, k, l\\}$. The channel capacities with assistance can be obtained as follows:\n\\begin{align}\nC^{123}_{CD}(\\psi_{\\text{eGHZ}})&=C^{132}_{CD}=C^{213}_{CD}=C^{231}_{CD}=1+h\\bigg(\\frac{1+\\sqrt{1-4 \\lambda_1^2\\lambda_3^2}}{2}\\bigg), \\label{cc1} \\\\\nC^{312}_{CD}(\\psi_{\\text{eGHZ}})&=C^{321}_{CD}=1+h(\\lambda_1^2), \\label{cc2}\n\\end{align}\nwhere $h(x)\\equiv-x \\log_2 x-(1-x) \\log_2 (1-x)$ is the binary entropy function. We have only two distinct values of the channel capacities with assistance because the extended GHZ states are invariant under the interchange of the first and second qubit and $C(\\rho_{jk}^i)=C(\\rho_{kj}^i)$ for pure states. An interesting fact about the extended GHZ states is that Charlie's measurement basis that maximizes the average channel capacity is always $\\{(|0\\rangle+|1\\rangle)\/\\sqrt{2},(|0\\rangle-|1\\rangle)\/\\sqrt{2}\\}$, regardless of the values of $\\lambda_i$'s.\n\nThe channel capacities without assistance also can be obtained as:\n\\begin{align}\nC_3(\\rho_{12})&=C_3(\\rho_{21})=1+h(\\lambda_1^2)-h\\bigg(\\frac{1+\\sqrt{1-4\\lambda_1^2\\lambda_3^2}}{2}\\bigg), \\label{c1} \\\\\nC_1(\\rho_{23})&=C_2(\\rho_{13})=1-h(\\lambda_1^2)+h\\bigg(\\frac{1+\\sqrt{1-4\\lambda_1^2\\lambda_3^2}}{2}\\bigg), \\label{c2} \\\\\nC_2(\\rho_{31})&=C_1(\\rho_{32})=1. \\label{c3} \n\\end{align}\nThus, the CPs are given by\n\\begin{align}\nP^{123}(\\psi_{\\text{eGHZ}})&=P^{213}=h(\\lambda_1^2), \\\\\nP^{132}(\\psi_{\\text{eGHZ}})&=P^{231}=P^{312}=P^{321}=h\\bigg(\\frac{1+\\sqrt{1-4 \\lambda_1^2 \\lambda_3^2}}{2}\\bigg). \n\\end{align}\nSince $h\\big(\\frac{1+\\sqrt{1-4 \\lambda_1^2 \\lambda_3^2}}{2}\\big)\\leq h(\\lambda_1^2)=h\\big(\\frac{1+\\sqrt{1-4 \\lambda_1^2(\\lambda_2^2+\\lambda_3^2)}}{2}\\big)$, MCP of the extended GHZ states is\n\\begin{equation}\nP(\\psi_{\\text{eGHZ}})=h\\bigg(\\frac{1+\\sqrt{1-4 \\lambda_1^2 \\lambda_3^2}}{2}\\bigg) \\label{ghz}\n\\end{equation}\nwhich has the maximum value 1 if and only if $\\lambda_1^2=1\/2$ and $\\lambda_3^2=1\/2$, i.e., when the state is the standard GHZ state, $(|000\\rangle+|111\\rangle)\/\\sqrt{2}$. In addition, MCP is zero if and only if $\\lambda_1=0$ or $\\lambda_3=0$, i.e., the state is biseparable or fully separable \\cite{acin2001-2,dur2000}. These facts imply that MCP is closely related to the genuine tripartite entanglement of pure states. To investigate the meaning of the result in terms of the tripartite entanglement, let us consider the three-tangle $\\tau$ \\cite{coffman2000, dur2000}, which is defined for a pure three-qubit state $|\\psi\\rangle_{123}$ as\n\\begin{equation}\n\\tau=\\mathcal{C}^2_{j(kl)}-\\mathcal{C}_{jk}^2-\\mathcal{C}_{jl}^2,\n\\end{equation}\nwhere $\\mathcal{C}_{jk}=\\mathcal{C}(\\rho_{jk})=\\mathcal{C}(\\text{Tr}_l(\\psi_{123}))$, $\\mathcal{C}_{j(kl)}=\\mathcal{C}(\\psi_{j(kl)})$, $\\psi_{123}=|\\psi\\rangle\\langle\\psi|_{123}$, and $\\mathcal{C}$ is Wootters' concurrence \\cite{hill1997,wootters1998}. The three-tangle for the extended GHZ states is calculated as\n\\begin{equation}\n\\tau=4 \\lambda_1^2 \\lambda_3^2.\n\\end{equation}\nThus, MCP is a monotonically increasing function of the three-tangle $\\tau$,\n\\begin{equation}\nP(\\psi_{\\text{eGHZ}})=h\\bigg(\\frac{1+\\sqrt{1-\\tau}}{2}\\bigg).\n\\end{equation}\nIndeed, the three-tangle $\\tau$ is known as a value that quantifies genuine tripartite entanglement. Therefore, MCP can also be used to quantify the genuine tripartite entanglement for extended GHZ states. Note that MCP of the controlled teleportation is also a monotonically increasing function of the three-tangle \\cite{jeong2016}.\n\nIn the special case that $\\lambda_2=0$, the state $|\\psi_{\\text{eGHZ}}\\rangle$ is reduced to generalized GHZ states,\n\\begin{equation}\n|\\psi_{\\text{gGHZ}}\\rangle_{123}=\\lambda_1|000\\rangle+\\lambda_3|111\\rangle.\n\\end{equation}\nUsing $\\lambda_1^2+\\lambda_3^2=1$, we can simplify channel capacities with Charlie's assistance in equations~\\eqref{cc1},\\eqref{cc2} as\n\\begin{align}\nC^{ijk}_{CD}=1+h(\\lambda_1^2),\n\\end{align}\nand channel capacities without Charlie's assistance in equations~\\eqref{c1},\\eqref{c2},\\eqref{c3} as\n\\begin{align}\nC_i(\\rho_{jk})=1,\n\\end{align}\nfor all $i,j,k$.\nThus, MCP of generalized GHZ states can be obtained as\n\\begin{equation}\nP(\\psi_{\\text{gGHZ}})=h(\\lambda_1^2).\n\\end{equation}\nThe difference between channel capacities with and without Charlie's assistance and MCP for generalized GHZ states are shown in Fig. \\ref{capacity}. The figure shows how much channel capacity is affected by controller's assistance for generalized GHZ states.\n\nFor another special case ($\\lambda_1=1\/\\sqrt{2}$),\n\\begin{equation}\n|\\psi_{\\text{MS}}\\rangle_{123}=\\frac{1}{\\sqrt{2}}|000\\rangle+\\lambda_2|110\\rangle+\\lambda_3|111\\rangle,\n\\end{equation}\ncalled the maximal slice states \\cite{carteret2000}, MCP is given by\n\\begin{equation}\nP(\\psi_{\\text{MS}})=h\\bigg(\\frac{1+\\sqrt{2}\\lambda_2}{2}\\bigg).\n\\end{equation}\n\n\\begin{figure}\n\\centering\n\\begin{minipage}[h]{0.45\\linewidth}\n\\includegraphics[width=\\linewidth]{Jeong-1}\n\\end{minipage}\n\\caption{\\textbf{Channel capacities with and without Charlie's assistance and MCP for generalized GHZ states}. The solid curve represents channel capacities with Charlie's assistance, the dotted line those without Charlie's assistance, and dashed curve MCP of generalized GHZ states. The shaded region represents the amount of channel capacity controlled by Charlie.\n}\\label{capacity}\n\\end{figure}\n\n\\subsubsection*{Generalized $W$ states}\nLet $|\\psi_{\\text{g}W}\\rangle$ be a state defined by\n\\begin{equation}\n|\\psi_{\\text{g}W}\\rangle_{123}=\\lambda_1|100\\rangle+\\lambda_2|010\\rangle+\\lambda_3|001\\rangle,\n\\end{equation}\nwhere the coefficients $\\lambda_i\\geq0$ and $\\sum_i\\lambda_i^2=1$ \\cite{acin2001}. The state $|\\psi_{\\text{g}W}\\rangle$ is here called a generalized $W$ state and $\\psi_{\\text{g}W}=|\\psi_{\\text{g}W}\\rangle\\langle\\psi_{\\text{g}W}|_{123}$.\nThe MCP of generalized $W$ states is calculated in the same way as before. First, the channel capacity with assistance is\n\\begin{equation}\nC^{jkl}_{CD}(\\psi_{\\text{g}W})=1+(\\lambda_k^2+\\lambda_l^2)h\\bigg(\\frac{\\lambda_1^2}{\\lambda_k^2+\\lambda_l^2}\\bigg).\n\\end{equation}\nIn contrast to the case of extended GHZ states, the measurement basis that maximizes the channel capacity is $\\{|0\\rangle,|1\\rangle\\}$, regardless of the values of $\\lambda_i$'s.\nThe channel capacity without assistance is\n\\begin{equation}\nC_j(\\rho_{kl})=1+h(\\lambda_l^2)-h(\\lambda_j^2).\n\\end{equation}\nAfter simplification, the CPs can be obtained as\n\\begin{equation}\nP^{jkl}(\\psi_{\\text{g}W})=(\\lambda_j^2+\\lambda_k^2)h\\bigg(\\frac{\\lambda_j^2}{\\lambda_j^2+\\lambda_k^2}\\bigg),\n\\end{equation}\nand, thus, MCP can be written as\n\\begin{align}\nP(\\psi_{\\text{g}W})&=\\min_{j,k,l}\\bigg[(\\lambda_j^2+\\lambda_k^2)h\\bigg(\\frac{\\lambda_j^2}{\\lambda_j^2+\\lambda_k^2}\\bigg)\\bigg]  =(\\lambda_j^2+\\lambda_k^2)h\\bigg(\\frac{\\lambda_j^2}{\\lambda_j^2+\\lambda_k^2}\\bigg) \\quad \\text{if } \\max\\{\\lambda_j^2,\\lambda_k^2,\\lambda_l^2\\}=\\lambda_l^2. \n\\end{align}\nIt is easily checked that MCP of a generalized $W$ state is zero if and only if one $\\lambda_i$ is zero, i.e., the state is biseparable or fully separable. In addition, we prove that the standard $W$ state, $(|100\\rangle+|010\\rangle+|001\\rangle)\/\\sqrt{3}$, has maximal MCP among the generalized $W$ states as follows.\n\n\\begin{prop}\nLet $\\psi_{W}$ be the standard $W$ state, i.e., $\\psi_{W}=\\psi_{\\text{g}W}$ with $\\lambda_1=\\lambda_2=\\lambda_3=1\/\\sqrt{3}$. For any generalized $W$ state $\\psi_{\\text{g}W}$,\n\\begin{equation}\nP(\\psi_{\\text{g}W})\\leq\\frac{2}{3}=P(\\psi_{W}).\n\\end{equation}\n\\end{prop}\n\n\\begin{proof}\nSuppose that there exists a generalized $W$ state such that $P(\\psi_{\\text{g}W})>\\frac{2}{3}$, that is\n\\begin{equation}\n(\\lambda_j^2+\\lambda_k^2)h\\bigg(\\frac{\\lambda_j^2}{\\lambda_j^2+\\lambda_k^2}\\bigg)>\\frac{2}{3},\n\\end{equation}\nfor all distinct $j, k, l$ in $\\{1,2,3\\}$. Since the binary entropy is bounded from above by 1, i.e., $h(x)\\leq 1$ for all $x\\in[0,1]$, we have\n\\begin{equation}\n\\lambda_j^2+\\lambda_k^2>\\frac{2}{3},\n\\end{equation}\nfor all distinct $j, k, l$. This is, however, contradicting the normalization condition $\\lambda_1^2+\\lambda_2^2+\\lambda_3^2=1$.\n\\end{proof}\n\n\\begin{figure}\n\\centering\n\\begin{minipage}[h]{0.9\\linewidth}\n\\includegraphics[width=\\linewidth]{Jeong-2}\n\\end{minipage}\n\\caption{\\textbf{MCPs of randomly generated extended $W$ states.} (a) MCPs of randomly generated extended $W$ states plotted against $\\lambda_0^2$. The solid curve corresponds to MCPs of extended $W$ states that have $\\lambda_1=\\lambda_2=\\lambda_3$ with $\\lambda_0^2$'s given. (b) MCPs of randomly generated extended $W$ states plotted against $\\lambda_1^2$. The solid curve corresponds to the MCPs of extended $W$ states that have $\\lambda_0=0$ and $\\lambda_2=\\lambda_3$ with $\\lambda_1^2$'s given.\n}\\label{numerical}\n\\end{figure}\n\nLet us now consider more general states, the extended $W$ states \\cite{dur2000},\n\\begin{equation}\n|\\psi_{\\text{e}W}\\rangle_{123}=\\lambda_0|000\\rangle+\\lambda_1|100\\rangle+\\lambda_2|010\\rangle+\\lambda_3|001\\rangle,\n\\end{equation}\nwhere $\\lambda_i\\geq0$ and $\\sum_i\\lambda_i^2=1$. Although MCP for a given extended $W$ state can be calculated easily, it is not easy to obtain an analytic expression for arbitrary extended $W$ states. Nevertheless, we generated $10^5$ extended $W$ states randomly and calculated their MCPs, and no extended $W$ state has been found that has a larger MCP than that of the standard $W$ state, $2\/3$, which is shown in Fig.~\\ref{numerical}. Furthermore, we can see from Fig.~\\ref{numerical}(a) that for a given $\\lambda_0^2$, no extended $W$ state has been found that has a larger MCP than that of the extended $W$ state with $\\lambda_1=\\lambda_2=\\lambda_3$. We also conclude that MCP of the extended $W$ states with $\\lambda_1=\\lambda_2=\\lambda_3$ is a monotonically decreasing function of $\\lambda_0^2$. In addition, we also plot the same data against $\\lambda_1^2$, which is shown in Fig.~\\ref{numerical}(b). From the figure, we can also see that for a given $\\lambda_1^2$, no extended $W$ state has been found that has a larger MCP than that of the extended $W$ state with $\\lambda_2=\\lambda_3$ and $\\lambda_0=0$.\n\n\\subsection*{Properties of minimal control power} \\label{sec:pro}\nIn this section, we investigate properties of MCP in terms of genuine tripartite entanglement. Before we start to introduce the properties of MCP, let us rewrite equation~\\eqref{cc2} as\n\n\\begin{equation}\nC^{jkl}_{CD}(\\rho_{123})=1+\\max_\\mathcal{E} \\bigg[\\sum_{i=0}^1 p_i[S(\\rho_l^i)-S(\\rho_{kl}^i)]\\bigg]\n\\end{equation}\nwhere the maximum is taken over all possible ensembles $\\mathcal{E}=\\{p_i,\\rho^i_{kl}\\}$ satisfying $\\sum_{i=0}^1 p_i \\rho^i_{kl}=\\rho_{kl}$, which corresponds to maximization over all Charlie's possible measurement basis \\cite{hughston1993}. Thus, CP also can be written as\n\\begin{align}\nP^{jkl}(\\rho_{123})&=\\max_\\mathcal{E}\\bigg[\\sum_{i=0}^1 p_i[S(\\rho_l^i)-S(\\rho_{kl}^i)]\\bigg]-S(\\rho_l)+S(\\rho_{kl})=\\max_\\mathcal{E}\\bigg[\\sum_{i=0}^1 p_i I(k\\rangle l|\\rho_{kl}^i)\\bigg]-I(k\\rangle l|\\rho_{kl}), \n\\end{align}\nwhere we have used the definition of the coherent information, $I(k\\rangle l|\\rho_{kl})=S(\\rho_l)-S(\\rho_{kl})$, which is also known as a negative quantum conditional entropy \\cite{wilde2013, nielsen2010}. Using the properties of the von Neumann entropy and convexity of coherent information, we can prove the following proposition.\n\n\\begin{prop} For general three-qubit states $\\rho_{123}$, which can be mixed or pure,\n\\begin{equation}\n0\\leq P(\\rho_{123}) \\leq 1.\n\\end{equation}\n\\end{prop}\n\nBefore we start to prove the proposition, we review the inequalities for the von Neumann entropy of the mixture of quantum states $\\rho_i$ \\cite{nielsen2010},\n\\begin{equation}\n\\sum_i p_i S(\\rho_i)\\leq S\\bigg(\\sum_i p_i \\rho_i \\bigg)\\leq \\sum_i p_i S(\\rho_i)+h(p_i), \\label{entropy}\n\\end{equation}\nwhere the equality of the first inequality holds if and only if all the states $\\rho_i$ for which $p_i>0$ are identical, and the equality of the second inequality holds if and only if the states $\\rho_i$ have support on orthogonal subspaces.\n\n\\begin{proof}\nLet us prove the lower bound first. It can be shown that CP of $\\rho_{123}$ is non-negative by using the convexity of the coherent information \\cite{wilde2013, nielsen2010},\n\\begin{equation}\nP^{jkl}(\\rho_{123})=\\max_\\mathcal{E} \\bigg[\\sum_{i=0}^1 p_i I(k\\rangle l|\\rho_{kl}^i)-I(k\\rangle l|\\rho_{kl})\\bigg]\\geq 0. \\label{convex}\n\\end{equation}\nThus, MCP is also non-negative, $P(\\rho_{123})\\geq 0$.\nFor the upper bound, using equation~\\eqref{entropy}, we obtain for CP that\n\\begin{align}\nP^{jkl}(\\rho_{123})=\\max_\\mathcal{E} \\bigg[\\sum_{i=0}^1 p_i[S(\\rho^i_l)-S(\\rho^i_{kl})]\\bigg]-S(\\rho_l)+S(\\rho_{kl})\\leq\\max_\\mathcal{E}\\bigg[-\\sum_{i=0}^1 p_i S(\\rho^i_{kl})\\bigg]+S(\\rho_{kl})\\leq \\max_\\mathcal{E}h(p_i) \\leq 1. \\label{upper}\n\\end{align}\nIt is clear that MCP also has the same upper bound.\n\\end{proof}\n\nWe have found the lower and upper bounds of MCP of general three-qubit states. Now, let us investigate the conditions for pure states that attain the bounds by proving following two propositions.\n\n\\begin{prop}\nFor pure states $\\rho_{123}$, $P(\\rho_{123})=0$ if and only if $\\rho_{123}$ is biseparable or fully separable.\n\\end{prop}\n\n\\begin{proof}\nLet $\\rho_{123}=|\\psi\\rangle\\langle\\psi|_{123}$. If $\\rho_{123}$ is biseparable or fully separable, it is clear that when Charlie has the separated qubit, CP is zero, and thus MCP is zero. Let us now assume that $P(\\rho_{123})=0$. Thus, there exists $\\{j,k,l\\}$ such that $P^{jkl}(\\rho_{123})=0$. We set $\\{j,k,l\\}=\\{3,1,2\\}$ without loss of generality. Equation~\\eqref{convex} implies that for any ensemble $\\{p_i,\\rho_{12}^i\\}$ that satisfies $\\sum_ip_i\\rho_{12}^i=\\rho_{12}$,\n\\begin{align}\n\\sum_i p_i I(1\\rangle 2|\\rho_{12}^i)-I(1\\rangle 2|\\rho_{12})=\\sum_i p_iS(\\rho_2^i)-S(\\rho_2)+S(\\rho_{12})=0\n\\end{align}\nbecause the maximum is zero. Let us write the state in a Schmidt decomposition form $|\\psi\\rangle_{123}=\\sum_i\\sqrt{\\mu_i}|\\psi^i\\rangle_{12}|i\\rangle_3$, and let us assume that $\\mu_i\\neq 0$ because $|\\psi\\rangle_{123}$ is trivially biseparable or fully separable if $\\mu_0=0$ or $\\mu_1=0$. Then, it is easy to obtain\n that $S(\\rho_{12})=h(\\mu_0)$. Furthermore, an ensemble set $\\{p_i=\\mu_i,\\rho_{12}^{i*}=|\\psi^i\\rangle\\langle\\psi^i|_{12}\\}$ should satisfy that\n\\begin{align}\n\\sum_i\\mu_iS(\\rho_2^{i*})-S(\\rho_2)+h(\\mu_0)=0\n\\end{align}\nwhere $\\rho_2^{i*}=\\text{Tr}_1(\\rho_{12}^{i*})$. Therefore, $\\rho_2^{0*}$ and $\\rho_2^{1*}$ are orthogonal; thus we denote $\\rho_2^{0*}=|0\\rangle\\langle0|_2$ and $\\rho_2^{1*}=|1\\rangle\\langle1|_2$ without loss of generality. Thus, the state can be rewritten as $|\\psi\\rangle_{123}=\\sqrt{\\mu_0}|\\phi^0\\rangle_1|00\\rangle_{23}+\\sqrt{\\mu_1}|\\phi^{1}\\rangle_1|11\\rangle_{23}$ where $\\langle0|1\\rangle=0$, but $|\\phi^{0}\\rangle$ and $|\\phi^{1}\\rangle$ are not necessarily orthogonal. Then, $S(\\rho_2)=h(\\mu_0)$ so that $\\sum_ip_iS(\\rho_2^i)=0$ for any ensemble that satisfies $\\sum_ip_i\\rho_{12}^i=\\rho_{12}$. Now, let us choose another ensemble set $\\{p_i^{**}=1\/2,\\rho_{12}^{i**}=|\\phi^{\\pm}\\rangle\\langle\\phi^{\\pm}|_{12}\\}$ where $|\\phi^{\\pm}\\rangle_{12}=\\sqrt{\\mu_0}|\\phi^0\\rangle_1|0\\rangle_2\\pm\\sqrt{\\mu_1}|\\phi^1\\rangle_1|1\\rangle_2$. Since $\\sum_i p_i^{**}S(\\rho_2^{i**})=0$ should be satisfied, we require that $|\\phi^0\\rangle_1=|\\phi^1\\rangle_1$. Thus, the first qubit is separated, i.e., $|\\psi\\rangle_{123}$ is biseparable.\n\\end{proof}\n\n\\begin{prop}\nFor pure states $\\rho_{123}$, $P(\\rho_{123})=1$ if and only if $\\rho_{123}$ is the standard GHZ state.\n\\end{prop}\n\n\\begin{proof}\nWe have already shown that MCP of the standard GHZ state is 1 from equation~\\eqref{ghz}. Now, let us assume that MCP of a pure three-qubit state $\\rho_{123}$ is 1 so that the CPs of $\\rho_{123}$ for any $\\{j,k,l\\}$ are 1. Note that since $S(\\rho_{kl}^i)=0$ for pure states $\\rho_{123}$, CP can be written as $P^{jkl}=\\max_\\mathcal{E}[\\sum_i p_iS(\\rho_l^{i})]-S(\\rho_l)+S(\\rho_{kl})$. To prove that a pure state $\\rho_{123}$ that attains the upper bound should be the standard GHZ state, we need to prove that the measurement basis of Charlie that maximizes $P^{jkl}$ also maximizes $P^{jlk}$ and vice versa. Let $\\mathcal{E}^*=\\{p_i^*,\\rho^{i*}_{kl}\\}$ be an ensemble that maximizes $\\sum_i p_iS(\\rho_l^{i})$ and $\\rho_l^{i*}=\\text{Tr}_k (\\rho_{kl}^{i*})$, and let $\\mathcal{E}^{**}=\\{p_i^{**},\\rho^{i**}_{kl}\\}$ be an ensemble that maximizes $\\sum_i p_iS(\\rho_k^{i})$ and $\\rho_k^{i**}=\\text{Tr}_l (\\rho_{kl}^{i**})$. Using that $S(\\rho_l^{i*})=S(\\rho_k^{i*})$ and $S(\\rho_l^{i**})=S(\\rho_k^{i**})$ for pure states $\\rho_{kl}^{i*}$ and $\\rho_{kl}^{i**}$, we have\n\\begin{align}\n&\\sum_{i=0}^1p_i^{**}S(\\rho_l^{i**})\\leq\\sum_{i=0}^1p_i^*S(\\rho_l^{i*})=\\sum_{i=0}^1p_i^*S(\\rho_k^{i*}), \\\\\n&\\sum_{i=0}^1p_i^*S(\\rho_k^{i*})\\leq\\sum_{i=0}^1p_i^{**}S(\\rho_k^{i**})=\\sum_{i=0}^1p_i^{**}S(\\rho_l^{i**}).\n\\end{align}\nThus, we have $\\sum_ip_{i}^*S(\\rho_l^{i*})=\\sum_ip_{i}^{**}S(\\rho_l^{i**})$ and $\\sum_ip_{i}^*S(\\rho_k^{i*})=\\sum_ip_i^{**}S(\\rho_k^{i**})$, which means that both ensembles $\\mathcal{E}^*$ and $\\mathcal{E}^{**}$ maximize $\\sum_i p_iS(\\rho_k^{i})$ and $\\sum_i p_iS(\\rho_l^{i})$. Therefore, the measurement basis of Charlie that maximizes $P^{jkl}$ also maximizes $P^{jlk}$ and vice versa.\n\nLet us start to prove that if $P(\\rho_{123})=1$, where $\\rho_{123}=|\\psi\\rangle\\langle\\psi|_{123}$, then $\\rho_{123}$ is the standard GHZ state. Since the equality of the last inequality in equation~\\eqref{upper} holds if and only if $p_i=1\/2$, we can write $|\\psi\\rangle_{123}$, up to a local unitary transformation, as\n\\begin{equation}\n|\\psi\\rangle_{123}=\\frac{1}{\\sqrt{2}}(|\\psi^0\\rangle_{12}|\\phi_0\\rangle_3+|\\psi^1\\rangle_{12}|\\phi_1\\rangle_3), \n\\end{equation}\nwhere we have chosen $\\{j,k,l\\}=\\{3,1,2\\}$ without loss of generality, and $\\{|\\phi_0\\rangle, |\\phi_1\\rangle\\}$ is a measurement basis of Charlie that maximizes both $P^{312}$ and $P^{321}$. In addition, $\\langle \\psi^0|\\psi^1\\rangle=0$ because the equality of the second inequality in equation~\\eqref{upper} holds. Let us write $|\\psi^0\\rangle_{12}=\\sum_i \\sqrt{\\lambda_i}|i\\rangle_1|i\\rangle_2$ and $|\\psi^1\\rangle_{12}=\\sum_i \\sqrt{\\mu_i}|\\bar{i}\\rangle_1|\\bar{i}\\rangle_2$. Note that since the equality of the first inequality in equation~\\eqref{upper} holds if and only if $\\rho_l^0=\\rho_l^1$, we have $\\rho_2^0=\\rho_2^1=\\rho_2$. Since we can choose $\\{j,k,l\\}=\\{3,2,1\\}$, we also have $\\rho_1^0=\\rho_1^1=\\rho_1$. Thus,\n\\begin{align}\n\\rho_1^0=&\\sum_i \\lambda_i |i\\rangle_1\\langle i|=\\sum_i \\mu_i|\\bar{i}\\rangle_1\\langle\\bar{i}|=\\rho_1^1, \\\\\n\\rho_2^0=&\\sum_i \\lambda_i |i\\rangle_2\\langle i|=\\sum_i \\mu_i|\\bar{i}\\rangle_2\\langle\\bar{i}|=\\rho_2^1.\n\\end{align}\nSince the eigen-decomposition of $\\rho_1$ and $\\rho_2$ is unique, we require (i) $\\lambda_i=\\mu_i, |i\\rangle_1=|\\bar{i}\\rangle_1$, and $|i\\rangle_2=|\\bar{i}\\rangle_2$, or (ii) $\\lambda_i=\\mu_i=1\/2$. However, the condition (i) contradicts $\\langle\\psi^0|\\psi^1\\rangle=0$. Thus, we can only require condition (ii), which gives us that $|\\psi^0\\rangle$ and $|\\psi^1\\rangle$ are two orthogonal Bell states. Hence, $|\\psi\\rangle_{123}$ is the standard GHZ state up to a local unitary operation.\n\\end{proof}\n\n\\section*{Discussion}\n\\label{sec:con}\nWe have considered controlled dense coding and defined its CP and MCP. We have also calculated MCPs for several important pure three-qubit states such as the extended GHZ states and generalized $W$ states. We found that MCP of the  extended GHZ states is a monotonically increasing function of the three-tangle of the states, which quantifies genuine tripartite entanglement. We also found that the standard GHZ state uniquely achieves the maximal value of MCP among the extended GHZ states, so does the standard $W$ state among the generalized $W$ states. \n\nAlthough the extended $W$ states have a genuine tripartite entanglement, the three-tangle of the extended $W$ states vanishes \\cite{dur2000}. Based on the operational meaning of MCP, the three-party entanglement of the extended $W$ states can be witnessed by MCP as we have discussed in this paper. Thus, MCP can be used to quantify the three-party entanglement of the extended $W$ states.\n\nWe also found the lower and upper bounds of MCP for general three-qubit states. In addition, we proved that for pure states $\\rho_{123}$, the equality of the lower bound holds if and only if the three-qubit state is biseparable or fully separable and that the equality of the upper bound holds if and only if the three-qubit state is the standard GHZ state. These properties imply that not only does MCP have an operational meaning in the controlled dense coding scenario but also that it can capture the genuine tripartite entanglement of three-qubit pure states. We remark that it is possible for a separable mixed three-qubit state to attain the maximal value of MCP, for example, $\\rho_{123}=\\frac{1}{4}(|000\\rangle\\langle000|+|110\\rangle\\langle110|+|011\\rangle\\langle011|+|101\\rangle\\langle101|)$. Furthermore, it also means that there exists a mixed state whose MCP is not zero even though the state is fully separable. The interpretation is that both classical and quantum correlations of mixed three-qubit states $\\rho_{123}$ are captured by MCP. Thus, in future work, it would be worth analyzing the relation between MCP and genuine tripartite quantum and classical correlations.\n\nEven though we have analyzed discrete variable controlled dense coding only, it is worth mentioning generalization to continuous variable (CV) systems. In fact,  CV dense coding and CV controlled dense coding have been studied \\cite{braunstein2000, loock2000, jing2003, jing2002}. In order to perform CV dense coding, a two-mode squeezed vacuum is shared by Alice and Bob, and Alice encodes CV information by displacing her beam and sends it to Bob, followed by Bob's joint measurement of quadrature variables. For controlled dense coding, a GHZ-like state of CV is shared among Alice, Bob and Charlie, and Charlie performs homodyne detection on his beam. The  result of the homodyne measurement is then sent to Alice, and Alice and Bob perform CV dense coding using Charlie's measurement result. In fact, it was shown that channel capacities with and without Charlie's assistance are different \\cite{jing2002}. At a first glance, it seems possible to define the CP and MCP of CV controlled dense coding in a similar manner. However, channel capacity of CV dense coding and that of discrete variable have some differences. The channel capacity of CV dense coding requires certain constraints to prevent it from diverging, which are not required for discrete variable dense coding. In addition, the channel capacities that we have defined for discrete variable controlled dense coding are the optimal ones for given states so that it can be interpreted as an intrinsic property of the state, whereas optimal channel capacities of CV states are not known in general. Thus, in order to define CP and MCP properly and generalize our results to CV systems, it is required to find a general expression of the optimal channel capacity for a given CV state. It would be an interesting future work to  generalize the CP and MCP of discrete variable controlled dense coding to CV controlled dense coding.\n\n\\section*{Acknowledgements} The authors thank Chae-Yeun Park, Hyukjoon Kwon, and Seok Hyung Lee for valuable discussions. This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No.\\ 2010-0018295) and by the KIST Institutional Program (Project No.\\ 2E26680-16-P025).\n\n\\section*{Author Contributions} C.O. and K.J. conceived the idea and proposed the study. C.O. and H.K. performed the calculations and the proofs. C.O. and H.J. analyzed and interpreted the results. All authors contributed to discussions, reviewed the manuscript, and agreed with the submission.\n\n\\section*{Competing Financial Interests} The authors declare that they have no competing financial interests.\n\n\\bibliographystyle{naturemag}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nThe Laser Interferometry Gravitational-wave Observatory's successful detection \\cite{2016PhRvL.116f1102A} of gravitational waves (GW) in the tens to thousands Hertz frequency range heralds in the era of gravitational wave astronomy, allowing us to probe deeper into the depth of the cosmos and the core regions of violent astrophysical events. Just as with electromagnetic observations, GW messengers populate a broad frequency range, and projects are currently underway to detect them in the segments of: around $10^{-16}$Hz through the B-mode polarization of the Cosmic Microwave Background, nanohertz band via pulsar timing arrays, millihertz range by space-based laser interferometers, and upto about $10^4$ Hertz with a network of second generation ground-based interferometers. \n\nIn comparison, activities in the higher frequency ($>100k$Hz) end of the spectrum have been relatively subdued. One of the reasons is that the relevant GW sources have been less certain, so there is a chance that this corner of the GW universe is simply quiet. However, most of the speculative sources proposed so far are intimately tied into fundamental physics (e.g. of cosmological \\cite{Grischuk,Maggiore00,1999PhRvD..60l3511G,2007PhRvL..98f1302G,Easther07,Caprini09a,Copeland09,\nCaldwell96,Leblond09} and braneworld \\cite{Seahra05,Clarkson07} origins), and so a detection in this frequency regime may yield important insights, while null results would still be interesting in terms of constraining exotic models.  Another reason for the lack of interest is that our technology has not been sufficiently advanced to make the current detector designs sensitive enough to make the detection of such speculative sources likely (see e.g. Ref.~\\cite{2008PhRvL.101j1101A,2006CQGra..23.6185C}). However, rapid progresses in potentially relevant experimental capabilities are being made in the fields of controlled fusion and laboratory astrophysics. In addition, the wavelengths of high frequency gravitational waves (HFGW) are such that they impose less of a demand on the physical size of the detectors. Therefore, the cost-benefit ratio may eventually justify a new generation of detectors being built to listen for such signals, and it is consequently useful to maintain an active investigation into their design options (see e.g.~\\cite{TiltInPrep}). \n\nAs high HFGWs need to be converted into e.g., electromagnetic (EM) signals, in order for us to take a readout, the very core of the design problem is then to find a physical process that achieves this conversion most efficiently. The options explored so far concentrate on GW interacting with a static magnetic field, with or without a background electromagnetic wave (EMW) at the same frequency as the GW \\cite{Gertsenshtein62,1966PhRv..142..825Z,1972GReGr...3..401B,1983MNRAS.204..485C,2000CQGra..17.2525C,2006CQGra..23.6185C,Li:2009zzy}. \nIn such investigations, the presence of the magnetic field is vital for mediating the coupling between the GW and the EMW, and a curved background spacetime can also serve as the catalyst. More interestingly for our present study though, it has been noted that currents enabled by the presence of a plasma can also greatly enhance the coupling \\cite{1983PhRvD..28.2382M,1990ApJ...362..584M,1998CQGra..15.3655G,1999PhRvL..82.3012B,2000ApJ...536..875M,2000PhRvE..62.8493S,2001A&A...377..701P,2003PhRvD..68d4017S,Duez2005}, through their being disturbed by the GW. It is therefore interesting to examine the possibility of replacing the vacuum electromagnetic field with a strongly magnetized tenuous plasma as the quiescent configuration (in a stationary solution of the so-called force-free electrodynamics, thus no background radiation). In previous studies involving magnetized plasma\/fluid, while detailed equations of motion are written down and some estimates on the amplitude of induced plasma waves (PW) are made, analytical solutions relevant for HFGW detection are generally lacking, and a precise evaluation of the coupling strength and a depiction of the characteristics, such as the associated charges and currents, of the induced radiation remain illusive (we note that explicit solutions are given by Ref.~\\cite{2003PhRvD..68d4017S} for the EMW to GW conversion, but not vice versa, which is noted to be more complicated, and Ref.~\\cite{Duez2005} offers standing but not travelling wave solutions). \n\nIn this paper, we leverage some recent advances in modelling plasma dynamics in curved spacetimes to find simple and explicit analytical solutions, and show that unfortunately, the temporally averaged Poynting flux associated with the PW induced by the HFGW is no stronger than their vacuum counterparts. The introduction of the plasma however allows for the existence of currents, whose amplitudes depend on that of the GW linearly, and makes possible more sensitive detectors of the ammeter type. It is beyond the scope of this paper to design a technologically viable detector though, and therefore the parameter choices are somewhat arbitrary. We hope our demonstration of the potential enhancement in sensitivity through plasma injection, as well as the introduction of the user-friendly analytical solutions, would solicit interest from experts and lead to more detailed studies. We also mention that although not discussed in any detail below, our analytical solutions may also be applied to the beginning of the GW's journey, namely to study their EM counterparts generated by the GWs themselves inside magnetospheres of compact objects. A large body of excellent literature (see last paragraph for references) already exist on this subject, and we refer interested readers to them for potential applications of our results. \n\nWe derive the equations governing the coupling between the GW and the PW in Sec.~\\ref{sec:Eqs}, and analyse properties of the conversion process that they encode in Sec.~\\ref{sec:Ana}. In particular, we clarify what kinds of GW excite which types of PW, providing discussions from a physical point of view. We then discuss general solutions to these equations in Sec.~\\ref{sec:Gen}, and concentrate on a particular one that's relevant for HFGW detection in Sec.~\\ref{sec:Sol}. We further sketch the case for a potential detector design in Sec.~\\ref{sec:Det}, before concluding with a discussion in Sec.~\\ref{sec:Dis}. Unless otherwise stated, the formulae below are expressed in geometrized units where $G=c=\\epsilon_0=1$. Boldface letters are used to represent three or four dimensional vectors and tensors, with specific assignments made clear from context. \n\n\\section{The force-free equations} \\label{sec:Eqs}\nAnalytical solutions describing the interaction between a GW and a magnetized fluid has been worked out in Ref.~\\cite{Duez2005} for the case of a standing GW, and used to test a magnetohydrodynamics code. For the sake of HFGW detection, we need a description of induced PW converted from a travelling GW, and we solve for it under the assumption that the plasma's mass density is negligible in its contribution to the overall stress-energy tensor as compared to the electromagnetic field itself, or in other words we assume that the plasma is tenuous. Such a situation is described by the so-called ``force-free electrodynamics\", frequently invoked when examining astrophysical environments \\cite{Goldreich:1969sb,1977MNRAS.179..433B}. \nMore specifically, the inertia-less plasma particles do not have a tendency to preserve their previous states of motion, and thus require no separate kinetic equations (the state of the magnetized plasma is sufficiently described with only the electric and magnetic fields). A plasma particle's movement is instead governed entirely by the requirement that it experiences vanishing 4-force density (or else it would be infinitely accelerated), i.e.  \n\\begin{eqnarray} \\label{eq:FFECond}\nF_{ab}j^b =0 \\,,\n\\end{eqnarray}\nwhere $j^b$ is the 4-current density due to the plasma particles' motion. Enforcing this condition on the currents that act as the source terms in the usual Maxwell's equations leads to the force-free equations, in which the presence of the plasma manifests as nonlinear modifications \\cite{Zhang:2015aga}. \n\nIn this particular limit of magnetohydrodynamics, the propagation speed of the plasma waves are that of the speed of light, therefore optimal for creating resonant conditions where phase coherence with the GW is maintained for as long as possibly, allowing for consistent draining (as opposed to periodically feeding back in) of energy from GW to generate as large an EM signal as possible. Adopting the force-free assumption also allows us to take advantage of some technologies that have recently become available \\cite{Gralla:2014yja}, resulting in our being able to find closed-form solutions. \n\nSpecifically, let us assume that the spacetime is initially flat and there is an uniform magnetic field along the $z$ direction, which is described by the field 2-form (the Faraday tensor)\n\\begin{equation} \\label{eq:BG}\nF_0 = B_0 dx \\wedge dy\\,.\n\\end{equation}\nIn the flat spacetime, the background solution as given by Eq.~\\eqref{eq:BG} carries no current, so the force-free condition is satisfied trivially. However, once metric perturbations are introduced (metric becomes $\\eta_{ab}+h_{ab}$, where $\\eta_{ab}$ denotes the Minkowski values), a background current appears, taking the value of \n\\begin{eqnarray} \\label{eq:BGCurrent}\nj_0^a = B_0\\begin{pmatrix} \n\\partial_y h_{tx}-\\partial_x h_{ty} \\\\\n\\partial_t h_{ty}-\\partial_z h_{yz} -\\frac{1}{2}\\partial_y\\left( h_{tt}+h_{xx}+h_{yy}-h_{zz}\\right) \\\\\n-\\partial_t h_{tx}+\\partial_z h_{xz} +\\frac{1}{2}\\partial_x\\left( h_{tt}+h_{xx}+h_{yy}-h_{zz}\\right) \\\\\n\\partial_x h_{yz}-\\partial_y h_{xz}\n\\end{pmatrix} \\,. \n\\end{eqnarray}\nConsequently, $F_{0ab} j_0^b \\neq 0$ in a curved spacetime and that Eq.~\\eqref{eq:BG} ceases to be a valid force-free solution. The PWs then emerge to restore force-freeness, and the now PW-added field $2$-form can be written as \n\\begin{equation} \\label{eq:Faraday}\nF = B_0 \\,d\\,\\Big(x+ \\alpha(t,x,y,z)\\Big) \\wedge d\\,\\Big(y+ \\beta(t,x,y,z)\\Big)\\,,\n\\end{equation}\nwhereby the terms $x+\\alpha$ and $y+\\beta$ are called Euler potentials. That such a decomposition of the field 2-form is possible is established in Refs.~\\cite{1997PhRvE..56.2181U,1997PhRvE..56.2198U,Gralla:2014yja}. The force-free equations of motion can then be transcribed into the exterior calculus language as  \\cite{Gralla:2014yja}\n\\begin{eqnarray} \\label{eq:FFEEqRaw}\n(dx+ d \\alpha )\\wedge d*F=0, \\quad \n(dy+ d \\beta)\\wedge d*F=0\\,,\n\\end{eqnarray}\nwherein the spacetime curvature enters only through the Hodge dual operator $*$ (see Appendix \\ref{sec:AppHodge} for details), a fact that significantly simplifies formalism.\nTo make further progress, let us define, as in \\cite{2016ApJ...817..183Y}, the auxiliary variables\n\\begin{eqnarray} \\label{eq:Defpsi}\n\\psi_1 = \\partial_x \\beta -\\partial_y \\alpha, \\quad \\psi_2 = \\partial_y \\beta+ \\partial_x \\alpha, \n\\end{eqnarray}\nturning the explicit form of the equations \\eqref{eq:FFEEqRaw} (keeping to linear order in metric perturbation) into \n\\begin{align}\\label{Eq:psiEqs}\n \\left(-\\partial^2_t+\\partial^2_z\\right)\\psi_1 =& \\frac{\\partial^2 h_{tx}}{\\partial t \\partial y}-\\frac{\\partial^2 h_{ty}}{\\partial t \\partial x}+\\frac{\\partial^2 h_{yz}}{\\partial z \\partial x}-\\frac{\\partial^2 h_{xz}}{\\partial z \\partial y}\\,, \\nonumber \\\\\n\\left(-\\partial^2_t+\\partial^2_x+\\partial^2_y+\\partial^2_z\\right) \\psi_2 =&\n\\frac{1}{2} \\left(\\partial^2_x+\\partial^2_y\\right)\\left(h_{tt}+h_{xx}+h_{yy}-h_{zz}\\right)\n\\notag\\\\\n& \n+\\frac{\\partial^2 h_{yz}}{\\partial y \\partial z}\n+\\frac{\\partial^2 h_{xz}}{\\partial x \\partial z}-\\frac{\\partial^2 h_{yt}}{\\partial y \\partial t}-\\frac{\\partial^2 h_{xt}}{\\partial x \\partial t}\\,.\n\\end{align}\nThe quantity $\\psi_1$ that propagates along the $z$ direction (see the left hand side of Eq.~\\ref{Eq:psiEqs}) then depicts waves climbing the magnetic field lines or the Alfv\\'en waves, while $\\psi_2$ describes the fast-magnetosonic waves \\cite{2016ApJ...817..183Y}. \n\nFor the purpose of our study, we specialize to a sinusoidal plane gravitational wave, with a uniform transverse profile, propagating in a direction in the $x-z$ plane that extends an angle $\\chi$ with the $z$ axis (for a more generic wave profile, both along and transverse to the propagation direction, see Appendix \\ref{sec:GenericTrain}). \nWe define the amplitudes $h_{\\times}$ and $h_+$ for the cross and plus polarizations (and will use $h$ when distinguishing between them is not necessary), such that in an adapted coordinates system $(t, x',y,z')$ where the GW travels along the $z'$ axis (i.e. spatially rotated against the original coordinates around the $y$ axis by the angle $\\chi$), the metric perturbation takes on the familiar form of\n\\begin{eqnarray}\nh_{a'b'} =\\begin{pmatrix} \n 0 & 0 & 0 & 0 \\\\\n 0 & h_+ & h_{\\times} & 0 \\\\\n 0 & h_{\\times} & -h_+ & 0 \\\\\n 0 & 0 & 0 & 0 \n\\end{pmatrix}\n\\cos\\Big(\\phi_0-\\omega(t-z')\\Big)\\,.\n\\end{eqnarray}\nTransferring back to the original coordinate system where the magnetic field is along the $z$ axis, and in which we will carry out our computations, we then have \n\\begin{eqnarray} \\label{eq:GWperb}\nh_{ab} = \\begin{pmatrix}\n 0 & 0 & 0 & 0 \\\\\n 0 & h_+\\cos ^2\\chi   & h_{\\times} \\cos \\chi  & (h_+\/2)\\sin 2\\chi  \\\\\n 0 & h_{\\times} \\cos \\chi   & -h_+ & h_{\\times} \\sin \\chi   \\\\\n 0 & (h_+\/2)\\sin 2\\chi  & h_{\\times} \\sin \\chi   & h_+ \\sin ^2\\chi  \\end{pmatrix} \\cos\\xi\\,,\n\\end{eqnarray}\nwhere $\\xi \\equiv \\phi_0-\\omega(t +x \\sin \\chi- z \\cos \\chi )$. The force free equations \\eqref{Eq:psiEqs} then become\n\\begin{align}\n&-\\frac{\\partial ^2\\psi _1}{\\partial t^2}+\\frac{\\partial ^2\\psi _1}{\\partial z^2} \\label{eq:FFE1}\n=\n h_{\\times} \\omega ^2\\sin ^2 \\chi   \\cos \\chi   \\cos \\xi\\,, \\\\\n&-\\frac{\\partial ^2\\psi _2}{\\partial t^2}+\\frac{\\partial ^2\\psi _2}{\\partial x^2}+\\frac{\\partial ^2\\psi _2}{\\partial y^2}+\\frac{\\partial ^2\\psi _2}{\\partial z^2}\n=\nh_{+} \\omega ^2\\sin ^2 \\chi   \\cos  \\xi\\,. \\label{eq:FFE2}\n\\end{align}\nNote that in our derivations above, we have ignored the back-reaction of the electromagnetic field on the metric, which is suppressed by a factor of $G\/c^4$ in SI units (and by a corresponding suppression of the EM field strengths when transferring into geometrized units). \n\n\\section{The selection rules} \\label{sec:Ana}\nWe see that the Euler potential formalism allows us to write down very simple equations \\eqref{eq:FFE1} and \\eqref{eq:FFE2}, from which we can glean answers to important questions such as which types of GW excite which types of PW. We in fact have a fairly clean dichotomy: \ncross-polarized GWs excite the Alfv\\'en waves, while \nplus-polarized GWs excite fast-magnetosonic waves. \n\nThe intuitive reasons behind these simple rules are encoded in Eq.~\\eqref{eq:BGCurrent}, which represents the EM effects of immersing the background magnetic field in a curved spacetime. Such effects are the intermediate agents responsible for driving the PWs. \nMore precisely, the force-free condition demands that\n(to leading order in metric perturbation, and thus also $\\alpha$ and $\\beta$) \n\\begin{eqnarray} \\label{eq:CurrentCancellation}\nF_{0ab} j^{(1)b} = F_{0ab} \\left(\\delta j^b + j_0^b\\right) = 0\\,,\n\\end{eqnarray}\nwhere $\\delta j =* (d*\\delta F)$, with \n\\begin{eqnarray} \\label{eq:deltaF}\n\\delta F \\equiv B_0(dx\\wedge d\\beta+ d\\alpha \\wedge dy)\\,\n\\end{eqnarray}\nbeing the leading order perturbation to the field two-form. In essence then, PWs need to be produced in order to provide a current $\\delta j^a$ that cancels out (the troublesome components of) the GW-generated background $j_0^a$. \nFurthermore, we note that $j_0^{z}$ is not an active component in Eq.~\\eqref{eq:CurrentCancellation}, as $F_{0xy}=-F_{0yx}$ are the only non-vanishing components of ${\\bf F}_0$, so only $j_0^{x}$ and $j_0^{y}$ need to be neutralized (currents in the $x-y$ plane experience a Lorentz force from the background magnetic field in the $z$ direction). In contrast, the component $j^{(1)z}$ does not need to vanish, even at leading order, a fact that we will use later to propose HFGW detectors of the ammeter type. The fast-magnetosonic and Alfv\\'en waves split the task of current-neutralization between them. Comparing Eq.~\\eqref{eq:BGCurrent}\nwith Eq.~\\eqref{Eq:psiEqs}, we see that the source to the fast-magnetosonic wave $\\psi_2$ is simply $(\\partial_x j_0^y - \\partial_y j_0^x)\/B_0$, while the source to the Alfv\\'en wave $\\psi_1$ is $-(\\partial_x j_0^x + \\partial_y j_0^y)\/B_0$. We examine the two types of waves in turn.\n\nThe general characteristic of a magnetosonic wave in any magnetized plasma is that it has a tendency (but not absolutely enforced by the operator on the left hand side of Eq.~\\eqref{eq:FFE2}) to travel in the direction perpendicular to the background magnetic field ${\\bf B}_0$, with its associated perturbation to the magnetic field $\\delta {\\bf B}$ having a component along ${\\bf B}_0$ (see e.g.~\\cite{PlasmaBook} and also Eq.~\\eqref{eq:MagB} below).\nTherefore, $\\delta B^z$ is a good quantitative representation for the fast-magnetosonic waves. Substituting into Eq.~\\eqref{eq:deltaF} the two terms $\\partial_y\\beta$ and $\\partial_x \\alpha$ of Eq.~\\eqref{eq:Defpsi} that combine into $\\psi_2$, we see that they in fact give us $\\delta B^z = B_0 \\psi_2$ (obeyed by our specific fast-magnetosonic wave solution presented in Sec.~\\ref{sec:Sol}, see Eqs.~\\eqref{eq:Solpsi2} and \\eqref{eq:MagB} below). \n\nWith regard to polarization, because $\\psi_2$ is essentially $\\delta B^z$, the GWs effective at inducing fast-magnetosonic waves would be the ones that are capable of coupling to the background magnetic field in such a way as to generate a $\\delta B^z$ by introducing currents onto the $x-y$ plane. From Eq.~\\eqref{eq:BGCurrent}, the diagonal entries in $h_{ab}$ are obviously adapt at this task, and according to Eq.~\\eqref{eq:GWperb}, they correspond to the plus polarization. There are also other terms in $j_0^x$ and $j_0^y$, including a $h_{yz}$ that corresponds to the cross polarization. However, with our long wave train without $y$ dependence, the $j_0^x$ introduced by this term has no variation in the $y$ direction and is thus incapable of producing $\\delta B^z$. When a more complicated wave profile is introduced, such as that in Eq.~\\eqref{eq:GenericFFE2} of Appendix \\ref{sec:GenericTrain}, both polarizations are activated, but the general rule still applies, namely that \n\\begin{itemize}\n\\item GWs effective at introducing a current that rescales the background magnetic field would be efficient in inducing fast-magnetosonic waves. \n\\end{itemize}\n\n\nThe Alfv\\'en waves on the other hand, are restricted to propagate along the background magnetic field (see the left hand side of Eq.~\\eqref{eq:FFE1}), and are characterized by the presence of an accompanying dynamical current component flowing in the same direction (see e.g.~\\cite{2016arXiv160309693G,Brennan:2013jla,Yang:2014zva}). \nTherefore, GWs that can produce a dynamical current (as opposed to a constant flux) in the $z$ direction are better ``impedance matched'' \nand more effective at feeding energy into Alfv\\'en waves.\nIndeed, although the source term to $\\psi_1$ in Eq.~\\eqref{Eq:psiEqs} is derived by combining $j_0^x$ and $j_0^y$, the particularities of the combination is such that the source term turns out to be simply $\\partial_z j^z_0$ (ignoring the shift coordinate freedom terms like $h_{tx}$ that do not appear for GWs, see Eq.~\\eqref{eq:GWperb}). From Eqs.~\\eqref{eq:BGCurrent} and \\eqref{eq:GWperb}, we see that $h_{\\times}$ entering through $h_{yz}$ satisfies this requirement, with the lack of $y$ dependence once again suppressing the other polarization hidden in $h_{xz}$. Just as with the fast-magnetosonic waves, more complicated wave profiles allowed in Eq.~\\eqref{eq:GenericFFE1} re-activates $h_{+}$. In summary, a more general rule is that \n\\begin{itemize}\n\\item GWs that introduce variable currents along the background magnetic field direction would be more efficient at eliciting Alfv\\'en waves.\n\\end{itemize} \n\n \n\n\\section{The general solutions} \\label{sec:Gen}\nWe hope that the intuitive guidelines of Sec.~\\ref{sec:Ana} would prove useful in more complicated situations, e.g., ones involving secondary EM radiation coming from compact celestial objects. In such cases, the $j_0^a$ currents from immersing a background EM field in curved spacetimes are straightforward to compute as well, without the need to solve any equations (they are simply $*(d*F_0)$). One can then apply the rules of Sec.~\\ref{sec:Ana} to predict the GW-induced PW content without having to solve the FFE equations. Nevertheless, for more quantitative predictions, detailed solutions are sought, and we present a recipe for acquiring general solutions in this section. \n\nWe begin by noting that the selection rules do not mean a particular type of modes can not exist in the absence of the correct type of GW. In the absence of a source term, the homogeneous force-free equations can still be solved, and the resulting $\\psi_1$ or $\\psi_2$ represent waves being injected at the boundaries of the magnetized regions, and simply traverse such regions as their flat-spacetime counterparts would, without drawing energy from the GW. Such solutions are useful when superposed onto the so-called particular solutions to the inhomogeneous equations when constructing general solutions. The inhomogeneous solutions are more complicated to obtain, but fortunately, we have treated the relativistic effects perturbatively. Specifically, the metric perturbations have all been placed onto the right hand side of the force-free equations, leaving us with simple flat spacetime partial differential operators for the principal part of these equations, for whom the Green's functions are well-known. This allows us to adopt standard Green's function methods to solve them, not only for the long sinusoidal wave trains as assumed for Eqs.~\\eqref{eq:FFE1} and \\eqref{eq:FFE2}, but also the more complicated cases of Appendix \\ref{sec:GenericTrain}.  \n\nLet the source terms on the right hand sides of Eqs.~\\eqref{eq:FFE1} and \\eqref{eq:FFE2} be denoted by $\\mathcal{S}_1$ and $\\mathcal{S}_2$, then the particular solutions to the inhomogeneous equations are \n\\begin{eqnarray} \\label{eq:Green}\n\\psi_1({\\bf x'}) &=& \\int \\mathcal{G}_1(\\Delta'_t,\\Delta'_z) \\mathcal{S}_1({\\bf x''})\\ dt''\\, dz'' \\,,\\\\\n\\psi_2({\\bf x'}) &=& \\int  \\mathcal{G}_2({\\bf x''}-{\\bf x'}) \\mathcal{S}_2 ({\\bf x''}) d^4 x''\\,, \n\\end{eqnarray}\nwhere $\\Delta'_z \\equiv z'-z''$, $\\Delta'_t \\equiv t'-t''$, and $\\mathcal{G}_{1\/2}$ are the Green's functions. The integrations are to be carried out over the entire vessel containing the magnetized plasma. Homogeneous solutions (satisfying the FFE equations with $\\mathcal{S}_{1\/2}=0$) can then be superposed onto the results in order to satisfy desired boundary and initial conditions. Because we have decoupled the equations for the Alfv\\'en and fast-magnetosonic waves, their boundary conditions can be imposed separately. As already mentioned, these homogeneous solutions are simply freely propagating waves that behave as if they are in flat spacetime, and do not interact with the GW. Therefore, fixing boundary conditions is not important when studying the GW to PW conversion process, and they do not determine which type of PW is induced by the GW. They are however required if one is to compute the observables such as energy fluxes or currents, to be measured by HFGW detectors, because freely propagating waves injected at the boundaries contaminate these quantities. We will discuss this further in Sec.~\\ref{sec:Sol}. \nReturning to the particular solution, the Green's functions are those of the flat spacetime, specifically \n\\begin{eqnarray}\n\\mathcal{G}_1(z'',t'';z',t')&=&\\frac{1}{2}\\Theta(\\Delta'_t)\\Theta(\\Delta'_t+\\Delta'_z)\\Theta(\\Delta'_t-\\Delta'_z)\\,, \\label{eq:G1}\\\\\n\\mathcal{G}_2({\\bf x''}; {\\bf x'}) &=& \\frac{\\delta(t'-(t''-R))}{4 \\pi R}\\,,\n\\end{eqnarray}\nwhere $R\\equiv |{\\bf x}''-{\\bf x}'|$, and $\\Theta$ are the Heaviside step functions. \n\nFor simpler $\\mathcal{S}_{1\/2}$ such as those appearing on the right hand sides of Eqs.~\\eqref{eq:FFE1} and \\eqref{eq:FFE2}, closed-form solutions for $\\psi_{1\/2}$ exist. We will be examining a closed-form particular solution for $\\psi_2$ in Sec.~\\ref{sec:Sol} in quite some detail, so here, we present only a solution for $\\psi_1$. Assuming the interaction between the GW and the magnetized plasma begins at $t_0$, and that the $z$ extent of the plasma container is sufficiently large that at the time $t'$ concerned, all the regions where $\\mathcal{G}_1 >0$ are included within, then we have \n\\begin{eqnarray}\n\\psi_1 &=& 2 h_{\\times} \\Bigg[\\sin ^2\\frac{\\chi }{2} \\sin \\left(\\Delta _0 \\omega  \\cos ^2\\frac{\\chi }{2}\\right) \\sin \\left(\\hat{\\xi}+\\frac{1}{2} \\omega  \\Delta_0 \\cos \\chi \\right)\n\\notag \\\\\n&&-\\cos ^2\\frac{\\chi }{2} \\sin \\left(\\Delta _0 \\omega  \\sin ^2\\frac{\\chi }{2}\\right) \\sin \\left(\\hat{\\xi}-\\frac{1}{2} \\Delta _0 \\omega  \\cos \\chi \\right)\\Bigg]\\,, \\notag \\\\\n\\hat{\\xi} &\\equiv& \\phi_0-\\frac{1}{2} \\omega  (t_0+t')-x' \\omega  \\sin \\chi +\\omega  z' \\cos \\chi\\,,  \\label{eq:psi1Sol}\n\\end{eqnarray}\nwhere also $\\Delta_0\\equiv t'-t_0$.\n\nGiven the solutions for $\\psi_{1\/2}$, we will then need to reconstruct the original $\\alpha$ and $\\beta$ perturbation functions before we can compute the EM fields. From Eq.~\\eqref{eq:Defpsi}, we deduce that these quantities satisfy the two-dimensional elliptic equations \n\\begin{eqnarray}\n\\left(\\frac{\\partial^2}{\\partial x^2}+\\frac{\\partial^2}{\\partial y^2} \\right)\\alpha &=& -\\frac{\\partial \\psi_1}{\\partial y} + \\frac{\\partial \\psi_2}{\\partial x}\\,, \\label{eq:AlphaFrompsi}\n\\\\\n\\left(\\frac{\\partial^2}{\\partial x^2}+\\frac{\\partial^2}{\\partial y^2} \\right)\\beta &=& \\frac{\\partial \\psi_1}{\\partial x} + \\frac{\\partial \\psi_2}{\\partial y}\\,. \n\\end{eqnarray}\nOnce again, we have a Green's function giving us the particular solution\n\\begin{equation}\n\\alpha =\\int\\frac{\\ln |\\rho-\\rho'|}{2 \\pi} \\mathcal{S}_{\\alpha}(\\rho')\\,d^2 \\rho \\,, \n\\end{equation}\nwhere $\\rho$ denotes locations on the $x-y$ plane, $\\mathcal{S}_{\\alpha}$ represents the right hand side of Eq.~\\eqref{eq:AlphaFrompsi}, and a similar solution exists for $\\beta$. A further integration by parts allows us to write \n\\begin{eqnarray}\n\\alpha({\\bf x}) &=& \\int dx' dy' \\frac{\\Delta_x\\psi_2(x',y',z)-\\Delta_y\\psi_1(x',y',z)}{2 \\pi [\\Delta_x^2+\\Delta_y^2]}\\,, \\\\\n\\beta({\\bf x}) &=& \\int dx' dy' \\frac{\\Delta_x\\psi_1(x',y',z)+\\Delta_y\\psi_2(x',y',z)}{2 \\pi [\\Delta_x^2+\\Delta_x^2]}\\,,\n\\end{eqnarray}\nwhereby $\\Delta_x\\equiv x-x'$ and $\\Delta_y \\equiv y-y'$. It turns out that symbolic manipulation software such as \\verb!Mathematica! are capable of generating closed-form expressions for $\\alpha$ and $\\beta$ that correspond to the $\\psi_1$ given by Eq.~\\eqref{eq:psi1Sol}. The expressions are too long and tedious to be reproduced here, but the integrands are straightforward to input. On the other hand, the closed-form fast-magnetosonic wave we examine in the next section will have simple expressions for $\\alpha$, $\\beta$, as well as the Faraday tensor.  \n\n\nWe have (here and in the next section) thus given closed-form particular solutions to both of the inhomogeneous Eqs.~\\eqref{eq:FFE1} and \\eqref{eq:FFE2}, which can be combined with homogeneous solutions to generate general solutions satisfying different boundary and initial conditions. For more complicated $\\mathcal{S}_{1\/2}$ than considered in this paper, numerical integrations can be utilized to yield the various quantities.\n\n\\section{The accumulative solutions} \\label{sec:Sol}\nIn this section, we specialize to an exact solution that resembles the vacuum inverse-Gertsenshtein effect most closely, and is therefore the most relevant for HFGW detection. \nEqs.~\\eqref{eq:FFE1} and \\eqref{eq:FFE2} are simple enough that we can isolate such interesting solutions straight away. We expect efficient GW to PW conversion to be more likely when the two types of waves can co-move in the same direction and  retain a constant relative phase. For the Alfv\\'en waves, the intrinsic propagation direction is along the $z$ axis, but the source term on the right hand side of Eq.~\\eqref{eq:FFE1} vanishes when $\\chi=0$. There is however no restriction on the propagation direction for the fast-magnetosonic waves, and therefore we concentrate on this variety. \nMore specifically, we search for solutions that depict the following scenario: that the GW travelling in the direction determined by $\\chi$ excites a fast-magnetosonic wave moving in the same direction, which continues to siphon energy off of the GW while it propagates. Indeed, the following ansatz \n\\begin{eqnarray} \\label{eq:Solpsi2Raw}\n\\psi_2 = \\frac{\\zeta}{4} h_{+} \\omega \\sin^2\\chi \\sin  \\xi\\,,\n\\end{eqnarray}\nsolves Eq.~\\eqref{eq:FFE2}, where $\\zeta = t-x \\sin \\chi +z \\cos \\chi$ is the ``advanced'' time (with $\\xi$ being the retarded time) that measures distance along the propagation direction. Therefore, the PW grows linearly in amplitude as it propagates, and it is in this sense we term the solution ``accumulative\". \n\n\\begin{figure}[t,b]\n\\includegraphics[width=0.95\\columnwidth]{Setup2.pdf}\n\\caption{A schematic depiction of the interactions. The plasma and a strong magnetic field (black arrows) in the $z$ direction is contained between the two green screens. The GW (black wiggles) traverses the magnetic field orthogonally from the right. A fast-magnetosonic wave (red wiggles) is induced which grows linearly over distance along $-x$, resulting in a small Poynting flux being registered on the left screen.  \n}\n\\label{fig:Setup}\n\\end{figure}\n\nBelow, we will concentrate on this type of growing solutions and elucidate their properties, which would be useful if actual experimental apparatus is to be designed to exploit it in the detection of HFGW. We also note that the source term on the right hand side of Eq.~\\eqref{eq:FFE2} is the largest when $\\chi=\\pi\/2$ (GW propagating along the magnetic field generates no current \\cite{1983PhRvD..28.2382M,1990ApJ...362..584M}), and we will assume this value for the experimental setup. We will however retain $\\chi$ in our formulae in order to present as generic a solution as possible, to facilitate application to other occasions. Schematically, we trap a strongly magnetised plasma in-between two screens as depicted in green in Fig.~\\ref{fig:Setup} (for simplicity, we will set $x=0$ on the right screen where the GW first comes into contact with the plasma), and examine the PW generated by the GW in that region. \nFor comparison, we mention that a growing vacuum EMW would similarly be induced by the GW if the plasma is evacuated from the magnetized region. This phenomenon is commonly termed the inverse-Gertsenshtein effect \\cite{Gertsenshtein62,Lupanov67,1977PhRvD..16.2915D}, and ours is essentially a force-free version of it. \n\nBefore we compute the relevant field quantities, a few remarks regarding the growing solutions for $\\psi_2$ are in order. First of all, the advanced time $\\zeta$ has an arbitrary initial value. Taking the transformation $\\zeta \\rightarrow \\zeta+\\zeta_0$ with a constant $\\zeta_0$ will simply introduce an additional contribution that solves the homogeneous part of Eq.~\\eqref{eq:FFE2}. Physically, the value of $\\zeta_0$ is determined by the initial condition at wherever the GW begins to interact with the plasma, and whether there has already been a seed wave present then. Furthermore, the $\\zeta$ in Eq.~\\eqref{eq:Solpsi2Raw} can be broken into components, and the segmental expressions falling out such as \n\\begin{eqnarray}\n\\psi_2 = \\frac{t}{2} h_{+} \\omega \\sin  \\xi \\sin^2\\chi \\,,\n\\end{eqnarray}\nalso solve Eq.~\\eqref{eq:FFE2}. These solutions represent essentially the same physics of amplitude growth during concurrent GW-PW propagation (along null geodesics of constant $\\xi$), but with a rescaling and a geodesic-dependent translation of the affine parameter $\\zeta$. Which particular form of the growing solutions to use obviously depends on the boundary conditions we wish to impose, and as we will enforce a no-initial Poynting flux condition on the entrance screen at $x=0$, it turns out that the most convenient choice is of the form\n\\begin{eqnarray} \n\\psi_2= -\\frac{x}{2}  h_+  \\omega \\sin \\xi \\sin\\chi\\,.\n\\end{eqnarray}\n\nNote that we have the freedom to add freely propagating waves (solutions to the homogeneous part of Eq.~\\ref{eq:FFE2}) to the solution to help enforce boundary and initial conditions. In order to avoid being overly restrictive, given that we do not know of the detailed properties of the would-be detectors, and the initial conditions for their interaction with GWs, we look for steady state solutions representing the plasma after interacting with a long GW train for a significant amount of time, and only impose the boundary condition that the screen at $x=0$ does not inject any Poynting flux into the cavity, so that flux registered on the left screen comes from the GW conversion. \nBecause we do not enforce boundary conditions on the other surfaces of the plasma cavity, our solution will not be unique, we instead examine a representative solution, given by \n\\begin{eqnarray} \n\\psi_2= -\\frac{1}{2} h_+ \\Big(\\cos \\xi +x \\omega  \\sin \\xi  \\sin \\chi \\Big) \\,. \\label{eq:Solpsi2} \n\\end{eqnarray}\n\nWith Eq.~\\eqref{eq:Solpsi2} and the assumption that $\\psi_1=0$, the solutions to Eq.~\\eqref{eq:Defpsi} are easy to obtain by inspection, giving us\n\\begin{eqnarray} \\label{eq:alphabeta}\n\\alpha= -\\frac{x}{2} h_+ \\cos \\xi  \\,, \\quad  \\beta=0\\,,\n\\end{eqnarray} \nwhich indeed satisfy the original equations \\eqref{eq:AlphaEq} and \\eqref{eq:BetaEq} for these entities. We caution that solution \\eqref{eq:alphabeta} is valid only when either $h_{\\times} = 0$, or $\\chi=\\pi\/2$, or $\\chi=0$. This is because our solution corresponds to $\\psi_1=0$, but a vanishing $\\psi_1$ is only a solution to Eq.~\\eqref{eq:FFE1} when the right hand side of that equation vanishes. For compactness, we will not display the equations for each case separately, but readers should bear in mind this constraint when applying the formulae below. \n\nSubstituting Eq.~\\eqref{eq:alphabeta} into Eq.~\\eqref{eq:Faraday} for the Faraday tensor, we can subsequently compute the electric field ${\\bf E}$ through \n$E^a = F^{ab}\\tau_b$, where $\\tau_b$ is the time-like one form orthogonal to spatial slices of constant $t$, and magnetic field $B^d = (1\/2)\\epsilon^{abcd}F_{ab}\\tau_c$, as well as the Poynting vector ${\\bf P}={\\bf E}\\times {\\bf B}$ (we adopt the convention that $\\epsilon^{0123}=-1$, so $\\epsilon^{123}=\\tau_a\\epsilon^{a123}=1$ in the Minkowski limit). We use perturbed metric for the computation, but keep the results upto only linear order in $h$, which are (all contravariant spatial vectors)\n\\begin{eqnarray}\n{\\bf E}^{(1)}&=& \n\\frac{x}{2} B_0   h_+ \\omega \\sin \\xi \n\\begin{pmatrix} 0 \\\\ 1 \\\\ 0\\end{pmatrix}\n\\,, \n\\quad \n{\\bf B}^{(0)}= \nB_0\\begin{pmatrix} 0 \\\\ 0 \\\\\n1\\end{pmatrix} \\,,\n\\label{eq:ElecE} \\\\\n\\notag \\\\\n{\\bf B}^{(1)}&=& -\\frac{1}{2} B_0 h_+ \\cos \\xi\n\\begin{pmatrix} 0 \\\\ 0 \\\\ 1\\end{pmatrix} \n-\\frac{x}{2} B_0 h_+ \\omega  \\sin \\xi\n\\begin{pmatrix}  \\cos \\chi \\\\ 0 \\\\\n\\sin \\chi \\end{pmatrix}\n\\,, \\label{eq:MagB} \\\\\n{\\bf P}^{(1)}&=& \\frac{x}{2} B_0^2 h_+ \\omega  \\sin \\xi \\begin{pmatrix} 1\\\\0\\\\0 \\end{pmatrix} \n\\,, \\label{eq:Power}\n\\end{eqnarray}\nwhere we note that for our steady state solution, there is a component in ${\\bf B}^{(1)}$ that does not grow linearly in $x$. Nevertheless, there is no first order Poynting flux at $x=0$. In more details, the ${\\bf P}^{(1)}$ above is produced by crossing the induced electric field with the background magnetic field . This first order flux oscillates between going in the positive and negative $x$ directions, and would not contribute to a temporally integrated signal. A consistent flux (without periodic sign reversals causing nearly cancelling positive and negative accumulations) associated with a propagating wave on the other hand, comes from the second term of\n\\begin{align}\n\\mathcal{P}^{(2)} \\equiv {\\bf E}^{(1)} \\times {\\bf B}^{(1)} \n=& -\\frac{x}{8} B_0^2 h_+^2 \\omega  \\sin 2\\xi \\begin{pmatrix} 1 \\\\ 0 \\\\0 \\end{pmatrix} \n\\notag \\\\ \n&- \\frac{x^2}{4} B_0^2  h_+^2 \\omega^2 \\sin ^2\\xi\n\\begin{pmatrix} \\sin \\chi \\\\ 0 \\\\ -\\cos \\chi \\end{pmatrix}\\,.\n\\end{align}\nWe caution that $\\mathcal{P}^{(2)}$ does not constitute the entirety of the second order Poynting flux ${\\bf P}^{(2)}$, as there is a contribution from the second order ${\\bf E}^{(2)}$ crossing with the background ${\\bf B}^{(0)}$. The examination of such a term is beyond the scope of our current investigation, but it may nevertheless contain a part that does not average out over time. \n\nWith PWs, charges and currents are allowed, which can be computed by simply noting that half of the Maxwell's equations are given by $d*{\\bf F}={\\bf J}$, where ${\\bf J}$ is the current 3-form, relating to the usual $4$-current density $j^a$ (zeroth component being the charge density $\\rho$) via $j^a = (1\/3!)\\epsilon^{abcd} J_{bcd}$. To first order in metric perturbation, we have \n\\begin{eqnarray} \\label{eq:Current}\n\\rho^{(1)} = 0\\,, \\quad \n{\\bf j}^{(1)}= B_0  h_{\\times} \\omega \\sin \\xi  \\sin \\chi  \\begin{pmatrix}  \\cos \\chi  \\\\ 0 \\\\  \\sin \\chi \\end{pmatrix} \\,, \n\\end{eqnarray}\nwhere the cross polarization $h_{\\times}$ is introduced, and $h_+$ removed, when taking the Hodge dual to obtain $*{\\bf F}$. When $\\chi=\\pi\/2$ so we can have $h_{\\times} \\neq 0$, the nonvanishing last row of ${\\bf j}^{(1)}$ is simply $j_0^z$ (see Eq.~\\eqref{eq:BGCurrent}) that does not need to be removed by the PWs (see discussion in Sec.~\\ref{sec:Ana}). We also do not need to be concerned with $h_{\\times}$ generating Alfv\\'en waves, as the source term in Eq.~\\eqref{eq:FFE1} vanishes when $\\chi=\\pi\/2$.\nNow that we have the explicit expression for $j^a$, it is easy to verify that Eq.~\\eqref{eq:FFECond} is indeed satisfied. \n\n\\section{The high frequency gravitational wave detector} \n\\label{sec:Det}\n\nIn the absence of a GW, the plasma will be quiescent, with microwave detectors on the left hand screen registering no Poynting flux. When a GW wave train traverses the magnetic field orthogonally, a fast-magnetosonic wave is produced, which grows in amplitude as it propagates. Such a wave is described by Eq.~\\eqref{eq:Solpsi2}.  The dominant instantaneous energy flux recorded on the left screen at $x=-L$ is subsequently given by Eq.~\\eqref{eq:Power}, which when translated into SI units becomes (unit of $P$ is watts per square meter)\n\\begin{align}\\label{eq:SignalAmpInst}\nP_x^{(1)}=2.0\\times 10^{-12} B_{10}^2 L_{10} \\omega _{\\text{GHz}} h_{+-30} \\sin \\xi \\,,\n\\end{align}\nwhere \n\\begin{eqnarray}\nB_{10}&=&B_0\/(10\\text{Tesla})\\,, \\,\\, h_{+-30} = h_+\/10^{-30}\\,, \\,\\, h_{\\times-30} = h_{\\times}\/10^{-30}\\,, \\notag \\\\  L_{10}&=&L\/(10 \\text{m})\\,, \\,\\, \\omega _{\\text{GHz}} = \\omega\/(5\\times 10^9 \\text{Hz})\\,,\n\\end{eqnarray}\nare dimensionless rescaled quantities normalized by typical values (experimentally reasonable and commonly shared across different HFGW source predictions) \\cite{Li:2009zzy}. \nThe time-averaged flux due to the propagating wave on the other hand, appears at the next order, and evaluates to\n\\begin{align}\\label{eq:SignalAmpAvg}\n\\langle \\mathcal{P}_x^{(2)}\\rangle  =-8.3\\times 10^{-41} B_{10}^2 L_{10}^2 \\omega _{\\text{GHz}}^2 h_{+-30}^2 \\sin \\chi\\,.\n\\end{align}\nWe notice that, as typical for HFGW detection, higher frequencies can compensate for low strains \\cite{1674-1056-22-12-120402}.\n\nThe time-averaged flux \\eqref{eq:SignalAmpAvg} is at the $\\mathcal{O}(h^2)$ order, thus comparable to the vacuum inverse-Gertsenshtein effect \\cite{Li:2009zzy}. In addition, we do not expect the remaining part of ${\\bf P}^{(2)}$ from ${\\bf E}^{(2)}\\times {\\bf B}^{(0)}$ to provide significant enhancements, as that term would also be proportional to $B_{10}^2 h_{-30}^2$ and would unlikely contain much higher powers of $\\omega_{\\text{GHz}}$ ($L_{10}$ shares the same power for dimensional reasons). This is because even with new second order source terms being introduced into the right hand sides of Eq.~\\eqref{Eq:psiEqs}, the differential operators would still contain only two derivatives in order for the dimensions to match up, therefore we do not have extra derivatives to bring out additional factors of $\\omega$. Furthermore, numerical factors appearing in our geometrized unit computations are all of moderate values, often arising from combinatorics tied down to the $3+1$ dimensionality of our spacetime, so there is unlikely significant boosts from large newly emerging coefficients in the second order computations. In contrast, the state of art photodetector sensitivity circa 2012 is $10^{-22}$W \\cite{Cruise:2012zz}. Consequently, detecting this temporally averaged flux is not feasible. \n\nHowever, we notice that the instantaneous flux \\eqref{eq:SignalAmpInst} is at $\\mathcal{O}(h)$ and is comfortably measurable from a purely power amplitude point of view, provided that the detector is located inside of the magnetized region. With previous detector designs searching for GW to vacuum EMW conversions, the photodetectors are placed outside of the screens that are presumed transparent to the EMW (see Fig.~2 in Ref.~\\cite{Cruise:2012zz}), even though a similar first order effect should be present in that case as well (see e.g. Eq.~1 of Ref.~\\cite{1674-1056-22-12-120402}). This may be due to concerns regarding the effect of the magnetic field on the photodetector (although this issue appears manageable \\cite{Beznosko:2005sy}), or uncertainty in whether a photodetector is capable of registering such a rapidly sloshing energy flux. After all, Eq.~\\eqref{eq:SignalAmpInst} does not represent a steady stream of photons moving towards either the positive or the negative $x$ direction. \n\nWith PWs however, there is an accompanying current, also at $\\mathcal{O}(h)$, due to the kinetic motion of the plasma particles, which may be more readily detectable given that no photon to current conversion is required. Specifically, currents flowing in either direction is permitted, and a direct measurement of the first order effect simply as a high frequency alternating current may be possible. We have computed the current and charge densities for the growing solution, given by Eq.~\\eqref{eq:Current}, which in SI units takes the value of (with units of amperes per square meter, and we set $\\chi=\\pi\/2$ so $h_{\\times}$ does not need to vanish)\n\\begin{align}\n{\\bf j}^{(1)} = 1.3\\times 10^{-22} B_{10} h_{\\times -30} \\omega _{\\text{GHz}} \n\\sin \\xi \n\\begin{pmatrix} 0 \\\\ 0 \\\\ 1 \\end{pmatrix}\\,. \n\\end{align}\nThe dependence of the current density on $x$ through $\\xi$ means that the current collector would likely need to be stratified along the $x$ direction, with signals from adjacent stripes (each of half a wavelength, or $3\\pi\/(50\\omega_{\\text{GHz}})$ meters) aggregated by subtraction instead of addition, to ensure that positive and negative contributions in the current density do not cancel out. This may also help subtract out some of the background stray noise currents. If we manage to construct a current collecting area of ten meters by ten meters, and perhaps increase the target frequency range (note $\\omega_{\\text{GHz}}$ is angular frequency) and\/or magnetic field strength, we can bring the total current to the atto ($10^{-18}$) ampere regime, for which measurement equipments are already available at the turn of the century \\cite{measurementbook}, and the state of the art may be even more sensitive.  \n\n\\section{Discussion \\label{sec:Dis}}\nIn this paper, we have studied the force-free version of the inverse-Gertsenshtein effect, and obtained explicit solutions, allowing us to compute the first order currents that were not present in the vacuum case, offering possibly a new avenue for detecting HFGW. Specifically, we have considered a quiescent background configuration, where the magnetic field is constant in space and time. There is no background electric field, Poynting flux, or current density present in the absence of a GW. We then target nascent electrical current or Poynting flux converted from the GW for detection. \n\nIn other words, our consideration has been restricted to detectors of the ``conversion\" type \\cite{Cruise:2012zz,Gertsenshtein62,Lupanov67,1970NCimB..70..129B,DeLogi:1977qe,Cruise:2012zz}. Our computation shows that temporally averaged Poynting flux for the induced PW is at the $\\mathcal{O}(h^2)$ order, which turns out to be the same for the vacuum cases, and thus the introduction of plasma is unlikely to lead to feasible detectors of the traditional photodetection design. \nIn previous literature, more complicated designs termed \nthe ``geometric\" types \\cite{1978PhLA...68..165P,\n1972GReGr...3..401B,\n1976GReGr...7..583B,\n1974NCimB..19..105T,\n1966PhRv..142..825Z,\n1975PThPh..54.1309T,\n1993ApJ...418..202F,\n1968AnPhy..47..173C,\n1971PhRvL..26.1398B,\n1975GReGr...6..329B,\n1983MNRAS.204..485C,\n2000CQGra..17.2525C,\nCruise06,\nLi:2009zzy} have also been proposed. With such detectors, effects depending on the GW amplitude at the first order is seen in e.g., the polarization state or frequency, of a strong background EMW. Such more subtle characteristics of a EMW tends to be relatively difficult to measure however, and the demand on the purity of the background EMW is also high, so one faces not only a detection problem, but also a generation one. In contrast, the current associated with the PW also appears at the $\\mathcal{O}(h)$ order, but requires fewer intermediate stages before a signal readout can be taken, in addition to needing no nontrivial backgrounds. So introducing plasma may perhaps lead to more sensitive ammeter designs of the conversion type. \n\nAlthough beyond the scope of this paper, one may of course also consider geometric type force-free detectors, where background Alfv\\'en or fast-magnetosonic wave pulses are launched through the plasma cavity, and emerge altered by the GW. \nThe examination of such design choices should be carried out in conjunction with an investigation into technological options, and the general method introduced here should be adaptable to such studies. \n\nLastly, we note that although there is no background current or Poynting flux in theory, the motion of the plasma particles may not conform to force-free electrodynamics perfectly in practical situations, or vibrations of the apparatus may launch unwanted waves (sound wave conversion). Therefore, some level of stray background radiation and current is to be expected, which is likely stochastic. On the other hand, although we have used a clean monochromatic long GW train for analysis, the predicted HFGW signals are also mostly stochastic, and the standard method for analysing such signals is by examining the correlation between readouts from two detectors placed in close proximity \\cite{Cruise06}. This poses certain technical challenges, for example, the local vibrations at the two detectors would also be correlated. In addition, the usual gravity gradient noise etc., all need to be carefully investigated, and so in the end, the noise budget, instead of device sensitivity, may well prove to be the limiting factor for the ammeter detectors. \n\n\\acknowledgements\nWe thank Hao Wen for discussions regarding HFGW detector noises, and an anonymous referee for helpful suggestions that led to the introduction of Secs.~\\ref{sec:Ana} and \\ref{sec:Gen}. F.~Z.~is supported by the National Natural Science Foundation of China grants 11443008 and 11503003, Fundamental Research Funds for the Central Universities grant No.~2015KJJCB06, and a Returned Overseas Chinese Scholars Foundation grant. \n\n \n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\\label{sec:intro}\nThe promise of Digital Agriculture is to feed the growing population of the world with  a smaller footprint---less irrigation, agrochemicals, and space. There has long been talk of using computing technologies to make that promise a reality. Yet, this has not come to pass for several reasons, three of which are relevant to our discussion here. \\textit{First}, the sensors to capture fine-grained spatial and temporal data are either not available, are expensive, or are error-prone. \\textit{Second}, the ML platforms are not flexible enough to cater to the varied needs of the different farms. \\textit{Third}, the computing equipment is not available, such as to run fast analytics at the edge, and the wireless communication is unreliable, sparse, or not available at the bandwidth required.\n\nIn the digital agriculture model, equipments such as field cameras, temperature sensors, humidity monitoring sensors, and aerial drones are deployed for data acquisition. These generate streaming, often real-time data, which can be harnessed to guide production decisions, support preventive maintenance of equipment, develop intelligent logistics, and diversify risk management methods, thereby optimizing the efficiency of resource allocation. There is still a large room for improvement, considering the relative lag of agricultural digitization vis-\\`a-vis scarce resources for feeding the world.\n\nIn {\\sc Orpheus}\\xspace, we describe an end-to-end production pipeline of sensing-actuation, transport, and analytics to enable timely actions in digital agriculture toward sustainable agricultural practices. It brings together deploying low-cost energy-saving sensors in a ``living lab'' setting, wireless networking and information theory, applied data analytics, and domain expertise in digital agriculture. We demonstrate {\\sc Orpheus}\\xspace in operational farm settings --- at Purdue's experimental farms (Agronomy Center for Research and Education (ACRE) and Throckmorton Purdue Agricultural Center (TPAC)) and commercial production farms in counties in the vicinity of Purdue, such as Benton and Warren counties. Our vision is logically organized into three categories --- {\\bf Sense} (sensor deployment in the living lab environment, Fig.~\\ref{fig:nitrate},~\\ref{fig:soil-2}), {\\bf Transport} (wireless networking, Fig.~\\ref{fig:topology}), and {\\bf Analyze} (anomaly detection notifications, database aggregation, and dashboard for visualization, Fig.~\\ref{fig:grafana},~\\ref{fig:website},~\\ref{fig:pdr})\\footnote{We make a subset of the data collected from our living lab testbed available for broad research use at~\\cite{purduewhin-sensor-list}. We exclude all data that is privately owned and released by the data owner.}. \n\n\n\\begin{figure*}[htbp]\n    \\centering\n    \\includegraphics[width=0.85\\textwidth]{Figures\/topology.png}\n    \\caption{\n   \n  \n    {Three-layer IoT network topology of our living testbed: SNs, Gateway, and the backend servers. The SNs and LoRa Gateways form an LPWAN using LoRa wireless connection at the edge.\n    The LoRa Gateways upload the data collected from the SNs to the backend over TCP\/IP, or forward it to a nearby LoRaWAN Gateway, depending on the availability of Internet access.}\n   \n   \n    Finally, data visualization is built using a Grafana dashboard based on the data at the backend server.}\n    \\label{fig:topology}\n    \\vspace{-1em}\n\\end{figure*}\n\n\\noindent In {\\sc Orpheus}\\xspace, we make the following contributions:\n\\begin{enumerate}[leftmargin=1em]\n    \\item We have deployed a living testbed with dozens of low-power sensors, deployed in a 3-county region, \n   \n   \n    in northern and central Indiana. We show an end-to-end IoT network building scheme in real farms. See our network topology in Fig.~\\ref{fig:topology}. Our network consists of: the edge part that uses SNs (sensor networks, {\\em i.e.,}\\xspace network of embedded devices with sensors) to collect data, and the Gateway nodes, which gather data from all the local SNs. Then, gateway(s) will send all the data to a central server where we have a frontend to visualize the data. We use long-range wireless communication (specifically LoRa) to send data from the SNs to the gateway, which can be miles apart, forming an LPWAN (low-power wide area network or simply LPN, {\\em i.e.,}\\xspace low-power network). Our SNs are power-saving and field-environment resistant, allowing for collection of data over months using standard batteries. Our experience is that these SNs last for 3-5 months on 4 AAA batteries, which we plan on reducing further using our data reduction algorithm, as described in our system---Ambrosia~\\cite{suryavansh2021ambrosia}.\n   \n    We call this real IoT network a \\textit{living testbed} for use in downstream applications, such as approximate computer vision applications to monitor crop health, or livestock monitoring.\n    \\item We also built an embedded testbed in our lab that consists of System-on-Chips (SoCs) from NVIDIA, used for benchmarking various lightweight IoT and object detection protocols~\\cite{chaterji2020cloud, emdl2021} for use in surveillance in our experimental farms, {\\em e.g.,}\\xspace in livestock monitoring~\\cite{suryavansh2021ambrosia}.  \n   \n   \n   \n    We leverage heterogeneous edge devices, as follows, in our testbed: \\textit{NVIDIA Jetson Nano}, which has 4GB memory, and a 128-core Maxwell GPU; \\textit{NVIDIA Jetson TX2}, which has 8GB memory, and a 256-core Pascal GPU; \\textit{NVIDIA Jetson Xavier NX}, which has a 8GB memory, and a 384-core Volta GPU with 48 Tensor cores; and NVIDIA Jetson AGX Xavier, which has 32GB memory and 512-core Volta GPU. These Jetson-class devices~\\cite{nano,tx2,xaviernx,agxxavier} feature compute-constrained, ML-capable GPUs, and range in price from \\$100 to \\$700.\n    We use this testbed to perform computer vision tasks ranging from object classification to object detection to apply to digital agriculture scenarios. Further, drones can be used as data ferries for opportunistically offloading data from the SNs to the gateway nodes in the case of sparse or intermittent connectivity or for offloading large volumes of data. In addition, drones can be equipped with additional embedded devices as payloads to do custom-object detection using our specialized embedded computer vision software~\\cite{emdl2021}, such as ApproxNet for object classification~\\cite{xu2019approxnet} and ApproxDet for object detection~\\cite{xu2020approxdet}.\n    \\item We bring out insights about the three aspects of IoT---\\textit{Sense, Transport, and Analyze}---realized through actual (farm) deployments. These insights can serve to enable further efforts both in research and in development of production IoT networks. \n    \\end{enumerate}\n   \n   \n  \n  \n\n\n\n    \n    \n\n\n\n\n\n\n\n\n\\begin{comment}\nSolchip was interested in partnering with Purdue & WHIN, so is a good \"tech company\" to vet, so to speak.\nhttps:\/\/sol-chip.com\/sensors\/\n\nSolchip contact comes from WHIN. Solchip is ``LoRa-fying'' their weather stations.\nComparatively - in very casual terms, FarmBeats is yoyo \u2026 you're on your own.\n\nhttps:\/\/www.davisinstruments.com\/enviromonitor\/#gateway -- solchip's box\n\nhttps:\/\/thelightbug.com \u2014 this is the one that is used for one my collaborators' trackers .. we haven't used these but have data from these\n\nhttps:\/\/store.rakwireless.com\/collections\/wisnode\/products\/rak7204-lpwan-environmental-node\n\nhttps:\/\/www.davisinstruments.com\/product_documents\/weather\/EM-sensors.pdf\n\nhttps:\/\/www.digikey.com\/en\/products\/detail\/tektelic-communications-inc\/T0005247\/11203700\nhttps:\/\/www.digikey.com\/en\/products\/detail\/tektelic-communications-inc\/T0004855\/11203703\n\nhttps:\/\/store.rakwireless.com\/collections\/wisnode\/products\/rak7205-lpwan-tracker-node?variant=27837945413732\nhttps:\/\/thelightbug.com \u2014 this is the one that is used for one my collaborators' trackers .. we haven't used these but have data from these\nhttps:\/\/store.rakwireless.com\/collections\/wisnode\/products\/rak7204-lpwan-environmental-node\n\nhttps:\/\/www.davisinstruments.com\/enviromonitor\/#gateway\nhttps:\/\/www.davisinstruments.com\/product_documents\/weather\/EM-sensors.pdf\n\\end{comment}\n\\section{Looking Ahead}\n\\label{sec:looking-ahead}\n\\noindent Big data and precision agriculture will likely be a disruptive force in the farm economy over the medium to long-term range. Digital agriculture, with the incorporation of IoT-based technologies, presents the ability to evaluate a system at multiple levels (individual, local, regional, and global) and generate tools that allow for improved decision making in every sub-process related to digital agriculture.\n\n\\begin{comment}\nAn important focus of the paper is on the convergence of IoT and ML on the one side and agricultural sustainability on the other. The ability to track virtually every farm activity through ubiquitous and inexpensive sensors has spurred efforts to increase sustainability and can be verified and certified by third-parties. \nFor example, there are already commercial efforts to monetize on-farm carbon sequestration for farms using regenerative practices~\\cite{indigoag}. Blockchain technology promises to increase sustainability and ensure food safety by authenticating information across the food system~\\cite{nagaraj2019panel}. In additional to privacy concerns, adoption of precision agriculture and big data is limited by the availability of broadband internet in rural areas~\\cite{whitacre2014connected}. Thus, looking at the policy angle, integrated farm equipment and sensors pipe data up to the cloud in real time meaning farmers are more reliant on upload speeds than the typical user. The societal returns to rural broadband are large though immediate private gains are often unclear. This suggests that high-speed internet will be under-supplied in the market and stresses a role for governmental support. This has been argued by federal government sources like USDA~\\cite{usda-broadband-2019} as well state government sources, such as in Indiana~\\cite{grant2018broadband}. \n\\end{comment}\n\\begin{comment}\n\\noindent Big data and precision agriculture will likely be a disruptive force in the farm economy over the medium to long-term. Technological advancements have led to farm consolidation in the past. Newer and more efficient tools reduce per-unit costs, allowing small and mid-size farms to become more profitable and therefore more prevalent. Moreover, economies of scale---the ability of large firms to spread investment costs over many units of production---allow large operations to exploit precision agriculture and big data tools earlier, potentially accelerating the consolidation trend~\\cite{coble2016advancing}. As mechanization continues and farm operations become more digitized, their labor needs will reduce and will become specialized. This could mitigate the so-called ``brain drain'' impacting many rural communities in the U.S.~\\cite{artz2003brain}. \n\nThe ability to track virtually every farm activity through ubiquitous and inexpensive sensors means that efforts to increase sustainability can be verified and certified by third-parties. \nFor example, there are already commercial efforts to monetize on-farm carbon sequestration for farms using regenerative practices~\\cite{indigoag}. Blockchain technology promises to increase sustainability and ensure food safety by authenticating information across the food system. In additional to privacy concerns, adoption of precision agriculture and big data is limited by the availability of broadband internet in rural areas~\\cite{whitacre2014connected}. Integrated farm equipment and sensors pipe data up to the cloud in real time meaning farmers are more reliant on upload speeds than the typical user. The societal returns to rural broadband are large though immediate private gains are often unclear. This suggests that high-speed internet will be under-supplied in the market and implying a role for external support. This has been argued by federal government sources like USDA~\\cite{usda-broadband-2019} as well state government sources, such as in Indiana~\\cite{grant2018broadband}. \n\\end{comment}\n\\section{Implementation of the Living Testbed of IoT Nodes}\n\\label{sec:living-testbed}\n{Here, we describe the components and technologies to set up the living testbed. First, we describe each of the components in Fig.~\\ref{fig:topology}, followed by how these components are integrated into our three-layer architecture.}\n\n\\subsection{{Components of sensor nodes (SNs)}}\n\\label{subsec:sensor-node}\n\\begin{figure}[htb]\n    \\centering\n    \\includegraphics[width=0.9\\columnwidth]{Figures\/node.jpg}\n    \\caption{Packaged SNs connected with soil, and nitrate sensors. Location: Purdue University main campus.}\n    \\label{fig:node}\n\\end{figure}\n\n\\noindent{\\customsec{Embedded Boards for our Digital Agriculture Application}}\nThe following features are considered while designing the SN (shown in Fig.~\\ref{fig:node}) for our living lab: 1) Durability; 2) Energy efficiency; 3) Ruggedized packaging.\nFig.~\\ref{fig:pcb} shows the printed circuit board (PCB) used for our SN. The most important component is the HM200 module from HuWoMobility~\\cite{HuWoMobility}. It includes a Nordic nRF52832 SoC~\\cite{nRF52832} (with a 512 KB Flash and 64 KB RAM) and a Semtech SX1262 chip~\\cite{SX1262}, allowing both Bluetooth Low Energy (BLE) and LoRa wireless communication protocols, respectively. Fig.~\\ref{fig:pcb_design} shows the block diagram of the custom PCB used in our testbed.\nSX1262 has the following features: a) designed for a long battery life---only 4.2 mA of active current consumption; b) transmits up to +15dBm, with a highly efficient integrated power amplifier; c) supports LoRa modulation and LoRaWAN protocols, which makes the model configurable to satisfy different application demands; d) continuous frequency coverage from 150MHz to 960MHz allows the support of all major sub-GHz ISM bands around the world. Besides the microcontroller module, our SN includes an on-board temperature and humidity sensor HDC2010~\\cite{hdc2010} from Texas Instruments, one antenna port for LoRa, and one port for BLE.\nIn addition, 8 sensor ports can be connected with 4 nitrate sensors and 4 soil sensors.\n\n\\begin{figure}[htb]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/pcb.png}\n    \\caption{Embedded board (sensor node) with LoRa and BLE modules, on-board temperature \\& humidity sensors (HDC2010), 2 antenna ports---the 915MHz port for LoRa and the 2.4GHz port for BLE---8 sensor ports to connect with external sensors, the ADC module converts the analog signal from nitrate sensors to a digital signal, and the LEDs are for functional checking.}\n    \\label{fig:pcb}\n\\end{figure}\n\n\\begin{figure}[htb]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/pcb_design.png}\n    \\caption{Block diagram of the embedded board for SN.}\n    \\label{fig:pcb_design}\n\\end{figure}\n\n\\customsec{On-board Temperature \\& Humidity Sensor}\nThe HDC2010 is an integrated humidity and temperature sensor that offers high precision measurements with low power consumption in an ultra-compact Wafer-Level Chip Scale Package. The HDC2010 includes a heating element to dissipate condensation and moisture, improving its reliability. It is also resilient against dirt, dust, and other environmental contaminants. Moreover, the HDC2010 digital features provide programmable interrupt thresholds that support alerts and device wakeups, without needing a microcontroller to continuously track the system. The HDC2010 supports operation from -40\u00b0C to +125\u00b0C, with a temperature accuracy of 0.2\u00b0C, and 0\\% to 100\\% relative humidity with an accuracy of 2\\%, which could satisfy a vast number of environmental monitoring IoT applications.\n\n\n\\noindent{\\textbf{Nitrate Sensor:}}\nOur node can be connected with, at most, 4 (in-house developed) nitrate sensors (see Fig.~\\ref{fig:nitrate} and Fig.~\\ref{fig:nitrate-2}), and 4 soil moisture sensors, respectively.\nThe nitrate sensors are flexible, screen-printed, detecting nitrate levels in the water. The sensors are comprised of reference and sensing electrodes. The electrodes are fabricated by printing silver ink onto a polyethylene terephthalate substrate. The sensing electrode is coated with an ion-selective membrane, which is selective to nitrate ions, and the rest of the sensor is passivated with a silicone solution. The reference electrodes are passivated at the sensing area. The difference between the nitrate-sensitive electrode and a reference electrode is used to determine the nitrate concentration~\\cite{jiang2019wireless}.\n\n\n\n\\begin{figure}[htbp]\n    \\centering\n    \\begin{minipage}[t]{0.47\\columnwidth}\n    \\centering\n    \\includegraphics[width=\\textwidth]{Figures\/nitrate.jpg}\n    \\caption{Nitrate sensor of a sensor node in a farm drain tile. A tile drainage system consisting of a network of underground pipes allowing subsurface water to move out from between soil particles into the tile line.}\n    \\label{fig:nitrate}\n    \\end{minipage}\n    \\hspace{0.02\\linewidth}\n    \\begin{minipage}[t]{0.47\\columnwidth}\n    \\centering\n    \\includegraphics[width=\\textwidth]{Figures\/nitrate-2.jpg}\n    \\caption{Nitrate sensor of a sensor node in a water quality field station~\\cite{wqfs} at Purdue's experimental farm---Agronomy Center for Research and Education (ACRE). The water is collected using a drainage system.}\n    \\label{fig:nitrate-2}\n    \\end{minipage}\n\\end{figure}\n\n\\customsec{TEROS 12 Soil Sensor}\nWe used a commercial soil moisture sensor TEROS 12~\\cite{teros},  as shown in (Fig.~\\ref{fig:soil}; Fig.~\\ref{fig:soil-2}). The TEROS 12 sensor for soil moisture, temperature, and electrical conductivity is reliable, easy-to-use, robust, yet economical. It incorporates METER's~\\cite{meter} 70 MHz trademark circuitry with a durable epoxy filling and firmly attached, sharpened stainless steel needles that can slide quickly into the soil. The probe is resistant to salts, preventing sensor degradation. It features very low power consumption, and offers improved accuracy over a longer period of time with a high resolution.\n\n\n\n\\begin{figure}[htbp]\n    \\centering\n    \\begin{minipage}[t]{0.47\\columnwidth}\n    \\centering\n    \\includegraphics[width=\\textwidth]{Figures\/soil.jpg}\n    \\caption{TEROS 12 Soil Moisture Sensor from METER~\\cite{meter}.}\n    \\label{fig:soil}\n    \\end{minipage}\n    \\hspace{0.02\\linewidth}\n    \\begin{minipage}[t]{0.47\\columnwidth}\n    \\centering\n    \\includegraphics[width=\\textwidth]{Figures\/soil-2.jpg}\n    \\caption{TEROS 12 SN placed at 15 cm depth.}\n    \\label{fig:soil-2}\n    \\end{minipage}\n\\end{figure}\n\n\n\\customsec{Enclosure}\nThe enclosure for the SN can achieve the IP67 Standard, which ruggedizing it. \nIP stands for ``Ingress Protection'' and is the International Protection Marking per IEC standard 60529.\n{The most common use of an IP rating is to show how protected a product is from a solid or liquid entering the product.}\nThe first digit indicates the level of protection a product has from a solid, {\\em e.g.,}\\xspace dust. The second digit indicates the level of protection from liquid intrusion in certain volumes, pressures, or temperatures. So, a sensor that is IP67 rated will remain protected and fully operational in most industrial applications, including those where it is exposed to water spray, rain, debris, etc. The ``6'' indicates the sensor is completely protected against solid objects from entering the sensor, including dust, while the ``7'' indicates the sensor can be completely submerged in 1 meter of water for up to 30 minutes before the moisture penetrates the housing.\nAn example of the deployed sensor is shown in Fig.~\\ref{fig:node-example} and Fig.~\\ref{fig:node-example-2} where the SN keeps working, even after being coated in ice in winter. \n\n\n\n\\begin{figure}[htbp]\n    \\centering\n    \\begin{minipage}[t]{0.47\\columnwidth}\n    \\centering\n    \\includegraphics[width=\\textwidth]{Figures\/node-example.png}\n    \\caption{SN with antenna extension deployed during summer.}\n    \\label{fig:node-example}\n    \\end{minipage}\n    \\hspace{0.02\\linewidth}\n    \\begin{minipage}[t]{0.47\\columnwidth}\n    \\centering\n    \\includegraphics[width=\\textwidth]{Figures\/node-example-2.png}\n    \\caption{The IP67 enclosure providing protection in winter.}\n    \\label{fig:node-example-2}\n    \\end{minipage}\n\\end{figure}\n\n\\subsection{Gateway}\n\\label{subsec:gateway}\nThe Gateway has two main functions: collecting the data from SNs deployed in the field and uploading the data to the backend database server.\nFirst, the Gateway collects the SN's measurements using LoRa modulation. Then, it backs up the data locally before transferring the readings to the backend over a TCP\/IP connection.\nIn cases of low network connectivity, the Gateway uses a multi-hop approach. Here, the Gateway forwards the data to a nearby LoRaWAN Gateway---using the LoRaWAN protocol---transferring the readings to the backend through TCP\/IP. We use this multi-hop setup in our LoRaWAN deployments, as shown in Fig.~\\ref{fig:multiple-hop}.\n\\begin{comment}\n\\newtext{Depending on the functionality, we can distinguish two types of Gateways: LoRa Gateways or LoRaWAN Gateways. The former --- LoRa Gateways --- collect readings from SNs using LoRa modulation. Then it transfer the measurements to the backend through ethernet cable, WiFi, or a LoRaWAN Gateway. The latter --- LoRaWAN Gateways --- is a standard LoRaWAN Gateway follow LoRaWAN protocol that can receiver signal from either LoRaWAN SNs or our LoRa Gateway.\nWe use LoRaWAN Gateways in our IoT network where an wired or short range Internet connection is not accessible from the LoRa Gateway.\nThus, \\emph{LoRa} deployments are the ones where the SN networks are connected to a LoRa Gateway, and \\emph{LoRaWAN} deployments are the ones where the SNs and LoRa Gateway are connected to a LoRaWAN Gateway.\nWe use Raspberry Pi~\\cite{pi} as our LoRa Gateway in our current deployments.}\n\\end{comment}\nWe built our LoRa Gateway using a Raspberry Pi. The device is equipped with a LoStik transceiver that supports LoRa modulation for reception and transmission, as well as an LPWAN concentrator, compatible with the LoRaWAN protocol. The LoStik is used to collect the measurements from the SNs, and the LPWAN concentrator allows multi-hop routing using LoRaWAN specification.\n\n\\customsec{Raspberry Pi}\nRaspberry Pis are lightweight and popular edge devices, varying in price from \\$35 to \\$140, and with an easily programmable interface for custom applications.\nRaspberry Pi (RPi) 4 Model B, shown in Fig.~\\ref{fig:gateway}(a), has a 1.5 GHz 64-bit quad core ARM Cortex-A72 processor, on-board 802.11ac WiFi, full gigabit Ethernet. The RPi 4 is powered via a USB-C port, enabling additional power to its downstream peripherals.\nThe operating system, RPi OS, is a Debian-based Linux distribution. The Gateway software runs on the RPi, which we manage remotely using SSH (Secure Shell) and VNC (Virtual Network Computing) protocols.\n\n\\customsec{LoStik}\n\\begin{comment}\nLoStik~\\cite{lostik} is a LoRa development tool as shown in Fig.~\\ref{fig:gateway}(b). The LoStik is affixed on top of the RN2903 or RN2483  LoRa Technology Transceiver Module. \nThe LoStik is an opensource USB dongle that plugs into any computer or device and connects it to the LoRa network.\n\\end{comment}\nThe LoStik~\\cite{lostik} is a USB LoRa device, as shown in Fig.~\\ref{fig:gateway}(b). The LoStik is based on the RN2903\/RN2483 LoRa Modules by Microchip, which enables seamless connectivity with LoRa\/LoRaWAN compliant devices. The USB dongle is affixed into the Raspberry Pi to provide a single communication channel to receive and send LoRa packets.\n\n\\customsec{LPWAN Concentrator}\nA LPWAN Concentrator module based on Semtech SX1302 enables integration of the RPi with other network equipment with LPWAN capabilities. The Concentrator can detect uninterrupted packets at 8 different spreading factors, providing 10 channels with continuous demodulation.\n\n\\begin{figure}[htb]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/gateway.png}\n    \\caption{(a) RPi 4 Model B, (b) LoStik Module with USB port, (c) LoRa Gateway: RPi and LoStik in an IP65 enclosure.}\n    \\label{fig:gateway}\n    \\vspace{-2mm}\n\\end{figure}\n\n\\subsection{Backend Server} \n\\label{subsec:backend-server}\nWe support our backend on a server with the following specifications: 8 Intel(R) Xeon(R) W-2123 CPU cores at 3.60GHz, NVIDIA Quadro P400 with 256 Pascal CUDA cores and 2 GB of GPU memory, 32GB Memory, 3TB Disk, using Ubuntu 18.04.4 LTS. This server provides the following software components: a NoSQL database and a Web Server (frontend) for \\emph{LoRa} deployments, and a time-series database and application server for \\emph{LoRaWAN} deployments.\n\n\\customsec{Databases}\nSpecifically for \\emph{LoRa}, we use MongoDB to store all the data collected from rural or urban areas.\nMongoDB is a NoSQL database that organizes data collection in JSON-like documents. The dynamic nature of data collected on the field requires a schemaless database like MongoDB. \nIn the meanwhile, for \\emph{LoRaWAN}, we use InfluxDB, a time-series database.\nThese databases are specifically built to handle metrics and time-stamped events. Furthermore, the data is indexed by the SN's identifier, which is useful to query the measurements from the visualization layer. We plan to integrate our autotuning software for increasing the performance of these databases both in conventional~\\cite{rafiki, sophia, optimuscloud} and serverless environments~\\cite{mahgoub2021sonic}.\n\n\\customsec{Application Server}\nThe application server is part of the LoRaWAN stack. \nThe server handles the LoRaWAN application layer, including handling join requests and session keys, uplink data decryption and payload decoding, downlink queuing, and data encryption. \nWe use ChirpStack~\\cite{chirpstack}, an open source solution, for our IoT network. ChirpStack provides a RESTful API and a Web interface to manage users, organizations, applications, and devices related to the LoRaWAN network. \nChirpstack, for example, can inventory and manage all LoRaWAN SNs deployed, configure gateways connected to the IoT network, and monitor the SN condition.\n\n\\customsec{Web\/Visualization Server}\nWe also built a website on a Web server using Django, a high-level Python Web framework.\nThe website allows the user to query the measurements and visualize them on charts or download them in a CSV file for offline analysis.\nA visualization layer for LoRaWAN deployments stored in the InfluxDB time-series database is also included in our IoT network.\nWe use Grafana~\\cite{grafana}, an open-source platform for monitoring and observability, which allows the user to query and visualize the data in dynamic dashboards. Moreover, the user can define alerts' rules to monitor changes.\n\n\\subsection{Three-layer IoT Network Architecture} \n\\label{subsec:network}\nIn this section, we describe our three-layer IoT network architecture. As we can see in Fig.~\\ref{fig:topology}, we use different technologies, including wireless communication and wired communication, to assemble the whole network. \nIn the bottom layer, the SNs send data to the Gateway through either LoRa or BLE. Then, the Gateway uploads the collected data to the backend server using a secure connection over TCP\/IP or LoRaWAN. Finally, the end-user can visualize, in real-time, the measurements collected from the field.\n{Next, we describe the three layers of our architecture.}\n\n\\begin{comment}\nAs you can see in Fig.~\\ref{fig:topology}, we build a three layer IoT network to collect data from the bottom layer--SNs to the Gateway, and then transfer all of the data to the cloud. When we build our network, we use different technologies including wireless communication and wire communication to assemble the whole network. The SNs send data to the Gateway through LoRa or BLE wireless connection, the Gateway can be a Raspberry Pi or a Mini-PC connected with a LoStik module. Then the Gateway connect to the Internet through WiFi, and then upload all the data collected at the edge to the database server through Hypertext Transfer Protocol Secure (HTTPS) connection. All the data is stored in MongoDB on the server. Finally, we have a website build by Django that can do real-time data visualization.\n\\end{comment}\n\n\\subsubsection{First Layer: Data Collection}\n\\label{subsubsec:data-collection}\nWhen building our IoT network, we face multiple decisions regarding the communication protocol between SNs and Gateway and among the SNs themselves, {\\em e.g.,}\\xspace a mesh network proposed in~\\cite{jiang2020hybrid}. If nodes are close to each other (1 to 100 meters), Wireless Local Area Network (WLAN) protocol, such as Bluetooth, WiFi, and ZigBee, are more suitable. In contrast, for long-range communications (a few kilometers in urban areas to over 10 km in rural areas), we need LPWAN protocols. Table~\\ref{tab:protocol} presents an overview of some of the most relevant LPWAN available standards: LoRaWAN, Narrow Band IoT (NB-IoT), and Sigfox.\n\n\\begin{comment}\nDepending on different scenario, we have two choices to send data from the SNs to the Gateway, one method is using LoRa and the other is using BLE. When we are building a IoT network, we have multiple choices of communication protocols to choose: The first group is Wireless local area network (WLAN) protocols: Bluetooth, WiFi, ZigBee, etc, these protocol are suitable to build local area network which are mostly short distance (1-100 meters) wireless communication. The second group is Low Power Wide Area Network (LPWAN) protocols for long range (A few kilometers in urban areas to over 10 km in rural area) wireless communication, {\\em e.g.,}\\xspace LoRa, NB-IoT, Sigfox, etc. We would like to introduce some wireless communication protocols that can be used to build LPWAN in Table.~\\ref{tab:protocol}.\n\\end{comment}\n\n\\begin{table*}[h!]\n    \\small\n    \\centering\n    \\caption{Specification of LPWAN protocols: LoRaWAN, NB-IoT, and Sigfox.}\n   \n    \\begin{tabularx}{\\textwidth}{|>{\\raggedright\\arraybackslash}X\n    |>{\\centering\\arraybackslash}X\n    |>{\\centering\\arraybackslash}X\n    |>{\\centering\\arraybackslash}X|}\n    \\hline\n    \\textbf{Protocols} & \\textbf{LoRaWAN} & \\textbf{NB-IoT} & \\textbf{Sigfox} \\\\ \n    \\hline\n    \\hline\n    Spectrum & Unlicensed ISM radio bands & Licensed LTE frequency bands & Unlicensed ISM radio bands \\\\\n    \\hline\n    Bandwidth & 125 or 250kHz & 180kHz & 192Hz \\\\\n    \\hline\n    Max data rate & 5.5kbps & 127kbps & 100bps \\\\\n    \\hline\n    Max messages\/day & 30 seconds air-time per device per day & Unlimited & Uplink: 140, Downlink: 4\\\\\n    \\hline\n    Max payload length & 242 bytes & 1,600 bytes & 12 bytes\\\\\n    \\hline\n    Range & Urban: 2-5 km, Rural: 10-15 km & Urban: 1 km, Rural: 10 km& Urban: 3-10 km, Rural: 30-40 km\\\\\n    \\hline\n    Interference immunity & High & Low & High \\\\\n    \\hline\n    Authentication \\& encryption & AES 128 bit & 3GPP (128 to 256 bit) & N\/A \\\\\n    \\hline\n    Cost & Device (\\$4-\\$6), Own network infrastructure (\\$400-\\$1000), Network operation and maintenance & Device (\\$6-\\$12), SIM card (\\$1-\\$2), Subscription fees (\\$5-\\$30)& Device (\\$5-\\$10), Subscription fees (\\$8-\\$12)\\\\\n    \\hline\n    \\end{tabularx}\n    \\label{tab:protocol}\n\\end{table*}\n\n\\customsec{LoRaWAN}\nIt is one of the most promising LPWAN solutions and is currently gaining traction to support IoT applications and services based on the LoRa radio modulation technology. LoRa modulation adopts the frequency-shift keying (FSK) and Chirp Spread Spectrum (CSS) operating at 868 MHz (Europe) and 915 MHz (North America) ISM band, promising ranges upto 20-25 km. LoRa also supports an Adaptive Data Rate (ADR) from 300 bps to 50 kbps for a 125 kHz bandwidth and supports configurable chirp duration (spreading factor) to maximize both the battery life of each device and the overall capacity available through the system. LoRaWAN defines the MAC communication protocol and the system architecture for the network. It uses a hub-and-spoke topology in which every LoRa node can communicate directly with the Gateway module.\n\n\\customsec{NB-IoT}\nThe 3rd Generation Partnership Project (3GPP) is a joint initiative of Asia, Europe, and North America telecommunications standardization organizations to produce global specifications for the Universal Mobile Telecommunication System (UMTS). 3GPP standardized a set of low cost and low complexity devices targeting Machine-Type-Communications (MTC) in Release 13. In particular, 3GPP addresses the IoT market using a threefold approach by standardizing the enhanced Machine Type Communications (eMTC), the NB-IoT (Narrowband IoT), and the EC-GSM-IoT. Specifically, NB-IoT can operate in a system bandwidth as narrow as 200 kHz and supports deployment in spectrum originally intended for GSM or LTE. It also supports a minimum device bandwidth of only 3.75 kHz. This design affords NB-IoT an energy efficient operation, while coexisting with existing GSM and LTE network, reducing deployment costs~\\cite{narrowband2017}. \n\n\\customsec{Sigfox} \nSigfox is a proprietary Ultra Narrow Band (UNB) LPWAN solution that operates in the 869 MHz (Europe) and 915 MHz (North America) bands, with an extremely narrow bandwidth (100Hz). It is based on Random Frequency and Time Division Multiple Access (RFTDMA) and achieves a data rate of around 100 bps in the uplink, with a maximum packet payload of 12 Bytes. However, Sigfox limits the amount of data per device in the network to 14 packets\/day. These limitations, together with a business model where Sigfox owns the network, have shifted the interest to LoRaWAN, which is considered more flexible and open.\n\nAs we can see, none of the previous LPWAN protocols is a perfect scheme. However, considering our application is a local ad-hoc network designed for digital agriculture, LoRa modulation presents a reasonable solution. Its low energy consumption, long-range, privacy features, and flexibility~\\cite{devalal2018lora, sinha2017survey} fit our needs. \nSimilar to the hybrid LPWAN proposed in~\\cite{jiang2020hybrid}, we choose LoRa over LoRaWAN to support a broader coverage since the latter only supports a star\ntopology---SNs connected directly to the Gateway.  Nevertheless, in urban areas or widespread rural areas, a mesh network can extend the IoT network coverage. \nFig.~\\ref{fig:gateway}(c) shows a deployed Gateway consisting of a Raspberry Pi and LoStik in an IP56 enclosure~\\cite{pi-package}, ruggedizing it. The configuration of the Gateway can be customized depending on the deployed area. For instance, the spreading factor can vary from 7 to 12, where a higher value denotes a broader coverage.\n\n\\subsubsection{Second Layer: Data Upload}\n\\label{subsubsec:data-upload}\nAfter collecting data from SNs to the Gateway, we need to upload the respective measurements to the backend servers. \n{Considering that the Gateway may not be in the range of any network with Internet access (either through a wired or wireless connection), we have two possible scenarios. }\nIf the Gateway has Internet access, the Gateway uploads the measurements using a Transport Layer Security (TLS), or formerly, Secure Sockets Layer (SSL). In contrast, in the second scenario, the Gateway relies on LoRaWAN to forward the collected readings to a nearby Gateway with Internet access. \nAs described earlier, LoRaWAN uses AES (Advanced Encryption Standard), with a symmetric key of 128 bits to encrypt the data.\n\n\\subsubsection{Third Layer: Data Persistence and Visualization}\n\\label{subsubsec:data-visualization}\n\n\\begin{figure*}[h!]\n    \\centering\n    \\begin{adjustbox}{varwidth=0.85\\textwidth,margin=0 {\\abovecaptionskip} 0 0, frame=0.25pt }\n    \\includegraphics[width=\\textwidth]{Figures\/grafana-temp-example-white-big.png}\n    \\end{adjustbox}\n    \\caption{Grafana dashboards including the temperature and humidity of 5 different SNs of our IoT network deployment.}\n    \\label{fig:grafana}\n   \\vspace{1em}\n\\end{figure*}\n\nOur backend includes the following open-source servers: a NoSQL database (MongoDB), an application server (ChirpStack), a time-series database (influxDB), and a visualization server (Grafana). The NoSQL database stores the measurements uploaded through the network. The user can visualize these readings using a frontend website (Django framework). \nThe frontend provides access to the data and allows to export it in a CSV format for further analysis outside of our platform.\nOn the other hand, the application server coordinates the communication with the LoRaWAN gateways deployed in the field. This server is integrated with a time-series database, influxDB, specially useful to store real-time data. Finally, the user can access the measurements using a Grafana server Fig.~\\ref{fig:grafana}, which provides a flexible interface to query, visualize, and analyze the measurements.\n\n\n\\begin{comment}\n\\edgardo{5\/14: Fig.~\\ref{fig:grafana--testing} -- this is just a temporal test}\n\\begin{figure}[h!]\n    \\centering\n    \\begin{adjustbox}{varwidth=.49\\textwidth,margin=0 {\\abovecaptionskip} 0 0, frame=0.25pt }\n    \\includegraphics[width=\\textwidth]{Figures\/grafana-temp-example-white-big.png}\n    \\end{adjustbox}\n    \\caption{Dashboard in Grafana including the temperature and humidity of 5 different SNs of our real IoT network deployment in the state of Indiana.}\n    \\label{fig:grafana--testing}\n\\end{figure}\n\\end{comment}\n\\section{Emulated Testbed}\n\\label{sec:lab-testbed}\n\n\n\n\n\\begin{figure}[htb]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/testbed.png}\n    \\caption{Heterogeneous testbed using NVIDIA Jetson devices and Raspberry Pis in a local area network (LAN).}\n    \\vspace{-2mm}\n    \\label{fig:testbed}\n\\end{figure}\nIn addition to our living testbed, we also set up an emulated heterogeneous testbed in our lab using NVIDIA Jetson-class devices. The setup is shown in Fig.~\\ref{fig:testbed}.\nHaving an emulated testbed allows us to fine-tune the hardware-software interactions of the system in a controlled lab environment. Ironing out the kinks, stress testing, and proactively implementing additional layers of redundancy will result in a more resilient field deployment.\nArguably, the most important benefit is that it allows us to fast-forward new feature implementation, major system changes, and prototyping.\n\n\\subsection{Devices}\n\\label{subsec:jetson-devices}\nTable~\\ref{tab:jetson} summarizes the specification of the NVIDIA devices in our emulated testbed.\nBesides, they could be deployed in the field or be carried on an aerial drone if we require a mobile high-performance SN.\n\n\\begin{table*}[h!]\n    \\centering\n    \\small\n    \\caption{Comparison between Jetson modules: Nano, TX2, Xavier NX, and AGX Xavier.}\n    \\begin{tabularx}{\\textwidth}{|>{\\hsize=.6\\hsize\\raggedright\\arraybackslash}X\n    |>{\\hsize=.68\\hsize\\centering\\arraybackslash}X\n    |>{\\hsize=.68\\hsize\\centering\\arraybackslash}X\n    |>{\\hsize=.68\\hsize\\centering\\arraybackslash}X\n    |>{\\hsize=.68\\hsize\\centering\\arraybackslash}X\n    |>{\\hsize=.68\\hsize\\centering\\arraybackslash}X|}\n    \\hline\n    \\textbf{Models} & \\textbf{Raspberry Pi 4B} & \\textbf{Nano} & \\textbf{TX2} & \\textbf{Xavier NX} & \\textbf{AGX Xavier}\\\\ \n    \\hline\n    \\hline\n    CPU & Broadcom BCM2711, Quad core Cortex-A72 (ARM v8) 64-bit SoC @ 1.5GHz & Quad-Core ARM Cortex-A57 MPCore @ 1.5GHz & Dual-Core NVIDIA Denver 2 64-Bit CPU and Quad-Core ARM Cortex-A57 MPCore processor @ 2.0GHz & 6-core NVIDIA Carmel ARMv8.2 64-bit CPU 6MB L2 + 4MB L3 @ 1.9GHz & 8-core NVIDIA Carmel Armv8.2 64-bit CPU 8MB L2 + 4MB L3 @ 2.3GHz\\\\\n    \\hline\n    GPU & Broadcom VideoCore VI @ 500MHz & 128-core NVIDIA Maxwell GPU @ 921MHz & 256-core NVIDIA Pascal GPU @ 1300MHz & 384-core NVIDIA Volta GPU with 48 Tensor Cores @ 1100MHz & 512-core NVIDIA Volta GPU with 64 Tensor Cores @ 1377MHz\\\\\n    \\hline\n    Memory & 2GB, 4G or 8GB 32-bit LPDDR4 @ 3200MHz - 25.6GB\/s & 4 GB 64-bit LPDDR4 @ 1600MHz - 25.6GB\/s & 8 GB 128-bit LPDDR4 @ 1866MHz - 59.7GB\/s & 8 GB 128-bit LPDDR4x @ 1600MHz - 51.2GB\/s & 32 GB 256-bit LPDDR4x @ 2133MHz - 136.5GB\/s \\\\\n    \\hline\n    Storage & MicroSD & 16 GB eMMC + MicroSD & 32 GB eMMC + MicroSD & 16 GB eMMC + MicroSD & 32 GB eMMC + MicroSD\\\\\n    \\hline\n    Power modes & 15W & 5W\/10W & 7.5W\/15W & 10W\/15W & 10W\/15W\/30W\\\\\n    \\hline\n    DL Accelerator & - & - & - & 2x NVDLA Engines & 2x NVDLA Engines \\\\\n    \\hline\n    AI Performance & 32 GFLOPS & 472 GFLOPS & 1.33 TFLOPS & 21 TOPS & 32 TOPS \\\\\n    \\hline\n    Price & \\$55 - \\$100 & \\$100 & \\$400 & \\$400 & \\$700 \\\\\n    \\hline\n    \\end{tabularx}\n    \\label{tab:jetson}\n   \n\\end{table*}\n\n\\noindent{\\customsec{Jetson Nano}}\nNVIDIA Jetson Nano is an embedded system-on-module (SoM) including an integrated 128-core Maxwell GPU, quad-core ARM A57 64-bit CPU, 4GB LPDDR4 memory, along with support for MIPI CSI-2 and PCIe Gen2 high-speed I\/O. Jetson Nano runs Linux and provides 472 GFLOPS of FP16 compute performance with 5-10W of power consumption.\n\\noindent{\\customsec{Jetson TX2}}\nNVIDIA Jetson TX2 is an embedded SoM with dual-core NVIDIA Denver2 + quad-core ARM Cortex-A57, 8GB 128-bit LPDDR4 and integrated 256-core Pascal GPU. Jetson TX2 runs Linux and provides greater than 1TFLOPS of FP16 compute performance in less than 7.5 watts of power.\n\\noindent{\\customsec{Jetson Xavier NX}}\nNVIDIA Jetson Xavier NX is an embedded SoM including an integrated 384-core Volta GPU with Tensor Cores, dual Deep Learning Accelerators (DLAs), 6-core NVIDIA Carmel ARMv8.2 CPU, 8GB 128-bit LPDDR4x with 51.2GB\/s of memory bandwidth, hardware video codecs, and high-speed I\/O including PCIe Gen 3\/4, 14 camera lanes of MIPI CSI-2. Jetson Xavier NX runs Linux and provides up to 21 TeraOPS (TOPS) of compute performance in user-configurable 10\/15W power profiles.\n\\noindent{\\customsec{Jetson AGX Xavier}}\nNVIDIA Jetson AGX Xavier is an embedded SoM including an integrated Volta GPU with Tensor Cores, dual DLAs, octal-core NVIDIA Carmel ARMv8.2 CPU, 32GB 256-bit LPDDR4x with 137GB\/s of memory bandwidth, and 650Gbps of high-speed I\/O including PCIe Gen 4 and 16 camera lanes of MIPI CSI-2. Jetson AGX Xavier runs Linux and provides 32 TOPS of compute performance in user-configurable 10\/15\/30W power profiles.\n\n\\begin{comment}\n\\customsec{Server}\nThe server can be one machine from the testbed or a independent desktop server.\n\\pengcheng{Will comment this subsection if there is no major input.}\n\\edgardo{(2\/15) Can we use this server for the workload manager (SLURM)? Besides, is there any tasks that requires of a \"server\"? (for example, maybe an ML algorithm requires some \"server\" processing)}\n\\end{comment}\n\n\\subsection{SLURM}\n\\label{subsec:slurm}\nSLURM is an open-source distributed computing workload manager. SLURM allows multiple devices to work in parallel on a single task, as long as the application is written to execute in parallel mode. \nIn the context of this paper, SLURM acts as a resource scheduler for the emulated testbed. We pre-train ML models on more powerful devices at the edge or cloud. \nThen SLURM could allow us to run inference on embedded devices in the field, resulting in system with significantly less data transferring.\nTraditionally, SLURM is most prevalent in x86 architecture builds, and only recently began gaining traction in the ARM world. With significant numbers of ARM SoCs being deployed, we expect that ARM-based distributed computing will see significant adoption.\nSLURM is used to manage ML training tasks on distributed GPU clusters~\\cite{awan2019scalable, campos2017distributed}, parallelizing the training process.\nIn our testbed, we leverage SLURM to distribute the inference task on multiple heterogeneous Jetson devices to accelerate the prediction process. Main challenge with this is finding the sweet spot of task distribution across multiple devices while keeping resource management, storage I\/O, and power consumption overhead to a minimum.\nAnother benefit of distributing a task across multiple devices is hardware redundancy, increasing the system's reliability. For example, if we rely on a single device to do the object detection task, a hardware failure will kill the system. However, if we spread the task across multiple devices, the system will only fail if all of the devices concurrently go offline.\nFinally, idle standby time can be leveraged to divert workloads to idle devices for resource efficiency.\n\n\n\\subsection{Tegrastats}\n\\label{subsec:tegrastats}\n\n\\begin{figure}[t!]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/energy_new.png}\n    \\caption{Jetson TX2's instantaneous power consumption vs DVFS setting of the GPU module while profiling ApproxDet's~\\cite{xu2020approxdet} 40 approximation branches. The current power consumption of the board is directly influenced by the DVFS setting of the GPU module while running object detection tasks.}\n    \\label{fig:energy}\n    \\vspace{-5mm}\n\\end{figure}\n\nThe Jetson series products provide the {\\em tegrastats} utility~\\cite{tegrastats}, which reports important memory, processor, and disk usage information. This utility can be easily accessed by running the command ``sudo tegrastats.'' The detailed information includes RAM usage, CPU utilization for each core, GPU utilization, power consumption for main hardware modules, etc. \nThe output can be observed in real time, or piped to a file for future analysis. In our experiments, we use the information from {\\em tegrastats} to analyze the relationship between power consumption, and the intensity of computation tasks. We also use it to observe the change of CPU and GPU utilization when specific operations are performed. Fig.~\\ref{fig:energy} shows an example of our profiling experiments of the current power consumption of ApproxDet's 40 execution branches~\\cite{xu2020approxdet}. ApproxDet performs {\\em approximate} video object detection, in a way that adapts to changes in content characteristics and changes in contention levels. This experiment is done on ImageNet Large Scale Visual Recognition Challenge 2015 validation dataset\nwhen we use different Dynamic voltage and frequency scaling (DVFS) settings for the GPU module. The values for DVFS settings of the GPU module are provided by NVIDIA in the NVIDIA Jetson Linux Developer Guide~\\cite{nvidia-doc}. \n{The instantaneous power information is collected by using {\\em tegrastats}.}\nAs seen from the figure, with increasing frequency setting of the GPU module, the mean and median values of current power of the TX2 board keep increasing while running ApproxDet's execution branches. Another observation is that the variance of the energy consumption also increases as GPU frequency increases. That is because with a higher GPU frequency, a greater number branches can run (including the heavyweight branches, which may not have been possible at lower frequencies), resulting in greater variability because of the higher spread of the (possible) approximation branches.\nFurther, we can tune the DVFS settings of CPU, GPU, and memory modules separately based on the API that the Jetson platform provides. \nThis means the user can configure each module independently based on the application requirements (accuracy, latency, and energy).  \n\n\\begin{figure}[htbp]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/jtop.png}\n    \\caption{Jetson stats' GUI shows detailed working status information for each hardware module on the device.}\n    \\label{fig:jtop}\n   \\vspace{-2em}\n\\end{figure}\n\nBased on the {\\em tegrastats} utility, an open-source tool named {\\em Jetson stats}~\\cite{jtop} \nhas been developed. It is a package for monitoring and controlling NVIDIA Jetson devices, showing various component-level performance statistics. GUI variant allows tweaking of various hardware settings. Fig.~\\ref{fig:jtop} is an example of running {\\em Jetson stats} on one of TX2 boards in our testbed. By observing the displayed values, we can easily observe the utilization levels of CPU, GPU, and memory. For example, if a GPU-intensive memory task is launched, the GPU frequency and utilization will become high. The temperature and power increases can also be observed.\n\n\n\\subsection{Drones}\n\\label{subsec:drones}\nOur embedded testbed is augmented with aerial drones~\\cite{dronet21}. These complement the ground nodes in two ways. First, the drones periodically fly over the covered regions, and collect data that may have been missed due to communication holes. This interval can range from hourly to once a day. Drone-based data ferrying can help in areas with limited, or no wireless connectivity. This can happen due to physical conditions, such as growth of corn stalks, resulting in a loss of communication of nodes in the network chain.\nThere is a protocol programmed into the SNs\nto send buffered data to the drones when drones indicate being within communication range. This form of data ferrying is well known in the literature~\\cite{pu2019route} and works in our context as there can be short to long periods of network disconnection for some of the nodes. A second enabling factor is that much of the data also does {\\em not} have strict latency requirements and can afford periodic visits by the drones. \n Another use case is an on-demand summoning of a drone by the SNs. An SN has a limited computational capacity and can summon a drone when it senses that some event is unfolding that needs heavyweight processing such as streaming video analytics, object localization, object detection, or face recognition, resulting the actuated ``descent'' of the drone for higher precision. An SN can, through the regular (low bandwidth) LoRa channel, send a request to the backend server to dispatch a single, or multiple drones. The drone with a GPU-enabled embedded board can reach the SN, and perform the heavyweight analytics task for the time for which the event is happening. The raw video data does not need to be communicated over long ranges, but only over a short-range high bandwidth channel like BLE. Further, we have done preliminary work to optimize the drone coverage with a swarm of drones~\\cite{dronet21}. We allow the drone to change its height to optimize the precision versus coverage when a swarm of drones is deployed in a farm (for on-demand data ferrying from the ground sensors). Overall, we have observed that the precision of the computer vision workload is a function of the drone height, rather than the drone speed.\n\n\n\n\n\n\\begin{comment}\n\\somali{Old text from PW}\nWe also have two types of DJI drones for expanding the IoT network into the air. By doing some development on these drones, we can make them serve as a gateways to collect data from the SNs. For some applications that do not need the real time data or someplace that is hard to do the deployment with a static Gateway, the drone could serve as a mobile Gateway. For example, the drone can carry the LoRa Gateway (Raspberry Pi + LoStik) and fly through the farm to collect data twice a day; once in the morning, and once in the afternoon.\n\\pengcheng{Add the specification for the drones; add a figure of how will it work. Should I edit the figure 1 with our future work? That way it is more intuitive.}\n\\end{comment}\n\\section{Implementation and Evaluation}\n\\label{sec:implementation}\nThis section describes the techniques and challenges of the deployment of {\\sc Orpheus}\\xspace in production farms in northern and central Indiana and on Purdue campus.\n\\subsection{Deployment}\n\\label{subsec:deployment}\n\\begin{figure}[htb]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/map_deployed.png}\n    \\caption{{\\sc Orpheus}\\xspace's IoT deployment map in Northern and Central Indiana: Purdue Main Campus, Purdue ACRE, Ivy Tech Community College, Throckmorton-Purdue Agricultural Center (TPAC), and commercial farms in Benton and Warren Counties.}\n    \\label{fig:map_deployed}\n\\end{figure}\nAs can be observed in Fig.~\\ref{fig:map_deployed}, we deployed a living testbed of IoT nodes in urban areas (Purdue University main campus, West Lafayette) and rural areas (Purdue's experimental farms and commercial farms) across Indiana. \n\\begin{figure}[htb]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/field_deployment.png}\n    \\caption{Deployment at a farm in Benton County: The SN is equipped with two TEROS 12 sensors and sends measurements to the LoRa Gateway inside the farmer's house via LoRa.}\n    \\label{fig:field_deployment}\n\\end{figure}\nShown in Fig.~\\ref{fig:field_deployment}, an SN is set beside the cornfields, while the LoRa Gateway is located inside a house with a clear line-of-sight (LoS) propagation from the node. The SN is equipped with two TEROS 12 soil sensors, buried underneath the soil, to detect changes in the volumetric water content (VWC) at 12 and 6 inches depth, respectively. Each SN is capable of collecting the temperature and the relative humidity level using the on-board HDC2010 sensor included in the nodes, as described in Section~\\ref{subsec:sensor-node}. \n\n\nSNs transmit the measurements periodically to the nearest Gateway using the LoRa communication protocol. \nGateway receives the measurements and forwards them to the central database servers, as described in Section~\\ref{subsubsec:data-upload}. \nAs a contingency, the Gateway also stores the measurements locally in case of network failure.\n\\begin{figure}[htbp]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/receiver_output.png}\n    \\caption{Readings on the Gateway: SN ID, firmware version, time stamp for received message, battery level, temperature, humidity, soil nitrate level, soil dielectric, conductivity, temperature, VWC.}\n    \\label{fig:receiver_output}\n   \n\\end{figure}\n\n\\begin{figure*}[htbp]\n    \\centering\n    \\includegraphics[width=0.85\\textwidth]{Figures\/website.png}\n   \n    \\caption{Website for SN readings, which include information such as SN ID, Location, GPS coordinates, last seen time, and the battery level. The website also allows to directly plot the data online or download it in .csv format.}\n   \n   \n    \\label{fig:website}\n    \\vspace{-1em}\n\\end{figure*}\n\n\nFig.~\\ref{fig:receiver_output} shows an example of the output generated on a\nLoRa Gateway each time it receives the measurements. Primary information is received date and SN ID. Secondary information includes specific measurements for each metric: humidity, temperature, nitrate level, soil dielectric permittivity, conductivity, and VWC.\nOnce data is stored in the database server, it can be visualized from the frontend, as can be seen in Fig.~\\ref{fig:website}. On the website, a user can see detailed location for the SN with its GPS coordinates, the last-seen time---a timestamp for the latest message, and the sensor installation information ({\\em e.g.,}\\xspace which sensor ports have been activated and when). We also provide the functionality \\textit{Graph Data} for a user to plot the sensor measurements by choosing the date range and the sensor to use; {\\em e.g.,}\\xspace in Fig.~\\ref{fig:website}, we plot the temperature and humidity data. Finally, user can also download the raw data within a date range for further analysis using the \\textit{Export Raw Data} function.\n\n\n\n\\begin{figure}[htbp]\n    \\vspace{-3mm}\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/soil-rain.png}\n    \\caption{{Soil VWC (\\%) at different depths (12'' and 6'', respectively) and rain events (inches) in the nearby location.}}\n    \\label{fig:soil-rain}\n\\end{figure}\n\n{In Fig.~\\ref{fig:soil-rain}, we show an example of combined analysis using our collected soil VWC data and the open source data from WHIN weather stations on rain events. Both data were collected from June 1, 2021 to August 13, 2021. Our soil sensor data has an interval of 30 minutes and the rain events' data from WHIN's weather station has an interval of 15 minutes. The WHIN weather station is 5.8 miles away from our soil sensor node in a rural area, which we believe, share the same weather patterns, including temperature, rainfall, etc. The X-axis represents the time, synchronized across the two locations. \nThe left Y-axis is VWC (Volumetric Water Content) of soil sensors at two different depths (12 inches and 6 inches). The right Y-axis is the cumulative rainfall in the last 15 minutes. There are some insights we get from the figure:\n\\vspace{-2mm}\n\\begin{enumerate}[leftmargin=1em]\n    \\item As expected, the soil VWC measurements always follow the changes in rainfall in direction and magnitude. \n    \\item The soil at greater depths has higher VWC. \n\\end{enumerate}\n}\n\n\n\n\\subsection{IoT Network Monitoring and Troubleshooting}\n\\label{subsec:network-monitoring}\n\n\\begin{comment}\n\\end{comment}\n\n\\noindent{\\customsec{Data Filtering}}\nData collected in the field can become corrupted before it gets stored in the backend database. This can happen either due to malfunction of device sensors, or signal interference during wireless communication. Our IoT network uses different filters at both, edge and cloud, to achieve end-to-end data integrity. These filters prevent anomalous data from reaching the front end which is the Data Visualization layer of {{\\sc Orpheus}\\xspace}, as shown in Fig.~\\ref{fig:website}.\nWe use in-lab experiments to determine the threshold for each metric. For example, humidity measurement's reasonable range is between 0\\% to 100\\%; soil VWC's reasonable range is between 0 to 0.7, based on our experiment calculations.\n\n\\begin{comment}\n\\somali{what techniques?}\n\\pengcheng{Changed to \"filters at both edge and cloud\". And added an explanation \"These filters can tell the anomaly data that is out of range, thus do not show it on the front end.\"}\n\\end{comment}\n\n\\begin{figure}[htbp]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/email.png}\n    \\caption{Email notification format from Network Monitoring and Anomaly Detection (NMAD), including: SN ID, location, last-seen time, number of messages received in a single day, mean and standard deviation of the measurements collected ({\\em e.g.,}\\xspace nitrate level, temperature, battery level). The red cell indicates that there is no recorded reading from the SN in the last 24 hours.}\n   \n   \n    \\label{fig:email}\n    \\vspace{-2mm}\n\\end{figure}\n\n\n\n\n\n\n\\customsec{Network Monitoring and Anomaly Detection}\n\\begin{comment}\nProduction networks require \\rev{constant} monitoring and anomaly detection in several layers of the system. Network traffic monitoring, and data integrity checks ensure long uptime, and maintenance-free operation. Data anomalies can occur from natural causes, and not necessarily from a security breaches. Larger networks require greater amount of sensor node monitoring automation. Out of necessity, and as a part of {{\\sc Orpheus}\\xspace}, we developed NMAD, a server daemon that checks the status of the SNs deployed in the live testbed and sends daily reports or notifications to the system managers.\n\nThe NMAD pulls the measurements from the database server and checks for possible anomalies in the SNs. The notifications, whose frequency can be customized ({\\em e.g.,}\\xspace \\rev{hourly, daily}), includes the mean and standard deviation for every measurement. Fig.~\\ref{fig:email} shows an example of the email notifications. \n\\rev{If the NMAD detects a possible malfunctioning SN that has not been communicating with the Gateway in the last day, it highlights the node in the email notification.}\n\\end{comment}\n\n{Production networks require constant monitoring and anomaly detection in several layers of the system. Network traffic monitoring and data integrity checks ensure long uptime and maintenance-free operation. Data anomalies can occur from natural causes ({\\em e.g.,}\\xspace data drift) and not necessarily from a security breach. Out of necessity, and as a part of {\\sc Orpheus}\\xspace, we developed NMAD, a server daemon that checks the status of the SNs deployed in the live testbed and sends reports or notifications to the system managers. Fig.~\\ref{fig:email} shows an example of the email notifications. \nThe notifications, whose frequency can be customized   ({\\em e.g.,}\\xspace hourly, daily), include the mean and standard deviation for every measurement. Moreover, the report highlights possible anomalies in the SNs. As an example, NMAD flags as anomaly any SN that has not communicated any reading in the last 24 hours.}\n{We are including additional features in the NMAD, such as (near-real time) anomaly detection for new data based on the patterns from the existing data.}\n\n\n\n\n\\begin{figure}[htbp]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/pdr.png}\n    \\caption{Packet Delivery Ratio (PDR), Packet Error Ratio (PER), and Packet Miss Ratio (PMR) over 7 days in our living testbed.}\n   \n   \n   \n   \n    \\label{fig:pdr}\n\\end{figure}\n\n\n\\subsection{Network Stability of Large-Scale Deployment}\n\\label{subsec:network-stability}\n{We evaluate {\\sc Orpheus}\\xspace in terms of the stability of the network based on the following metrics: (a) Packet Delivery Ratio (PDR); (b) Packet Error Ratio (PER); and (c) Packet Miss Ratio (PMR).}\nWe report on network measurements from a sample selection of nodes from our living testbed. This includes measurements from farms (ACRE, Ivy Tech Community College, Warren County, and Benton County) and urban areas (Purdue Main Campus). During one week, February 23, 2021 to March 2, 2021, we analyzed the readings collected from these SNs in terms of PDR, PER, and PMR.\nWe calculate PDR, PMR, and PER as follows:\n \n\\begin{equation}\n\\small\n\\label{eq:pdr}\n  PDR = \\frac{\\#\\ of\\ Received\\ Normal\\ Messages}{Expected\\ \\#\\ of\\ Messages}\n\\end{equation}\n\n\\begin{equation}\n\\small\n\\label{eq:per}\n  PER = \\frac{\\#\\ of\\ Received\\ Error\\ Messages}{Expected\\ \\#\\ of\\ Messages}\n\\end{equation}\n\n\\begin{equation}\n\\small\n\\label{eq:pmr}\n  PMR = \\frac{\\#\\ of\\ Missing\\ Messages}{Expected\\ \\#\\ of\\ Messages}\n\\end{equation}\n\n\nWhere \\begin{small}$PDR + PMR + PER = 1.0$\\end{small}. Fig.~\\ref{fig:pdr} summarizes the network stability profile. \n\\begin{comment}\nFig~\\ref{fig:pdr} shows the network stability of large-scale deployment in 4 farms (ACRE, Ivy Tech, Warren County, Benton County) and one urban area (Purdue Main Campus).\nThe data includes one week of measurements, from 2\/23\/2021 to 3\/2\/2021. \n\\end{comment}\nThe communication interval for each SN is 30 minutes.\nWe use this interval to calculate the anticipated number of received messages in one week as: 7 * 24 * 60 \/ 30 $\\approx$ 336.\n\nAs can be seen from Fig.~\\ref{fig:pdr}, SN 56 has a higher PER than the rest of SNs. This is\nbecause of an anomaly where the post with the sensor had fallen to the ground, directly measuring a higher moisture level. SN \\#9 is deployed in an urban area with high building density, with a resultant high PMR. With respect SN \\#71, the slightly high PER and PMR is because there is a slope in the terrain between the SN and the gateway node, affecting the data transmission. The data collected by our living testbed is available at~\\cite{purduewhin-sensor-list}.\n\n\n\n\\subsection{Network Stability of Two-Hop Deployment in Urban Area}\n{Because a building on the path can obstruct the signal, LoS propagation is critical when deploying LoRa devices (usually low-power wireless devices) in urban environments.\nIn addition, the signal will be attenuated with the reciprocal square of distance~\\cite{mahapatra2016experimental}.\nIn practice, however, the LoS wireless propagation path is not always possible, especially in built urban environments. In order to establish an LoS wireless connection in a city, a Gateway or the nodes have to be deployed at heights, such as a building's roof or on a tall utility tower. Because of these constraints, the LoRa network's real communication range is often substantially lower than the theoretical value (5 km in urban area vs 20 km in rural area).\nOur testbed provides a multiple-hop network to tackle this difficulty. \nThrough a LoRa wireless connection, an SN transmits messages to a LoRa Gateway, which then forwards the messages to the LoRaWAN Gateway. We employ hybrid protocols because using LoRa for the first hop allows us to customize our local network. By using LoRaWAN for the second hop connection, we will be able to leverage the previously installed LoRaWAN Gateway and benefit from the standardization of the LoRaWAN protocol.\nThe signal is captured and amplified in the middle point---the LoRa Gateway---enabling us to communicate the data in a reliable manner to the LoRaWAN Gateway.}\n{Fig.~\\ref{fig:multiple-hop} shows the deployment map of our experiments on the Purdue campus.\nWe would like to send the signal from Wang Hall (about 21 meters above the ground) to Flex Lab (about 7 meters above the ground). However, a signal path wireless connection does not work because the buildings between them block the signal. By using our multi-hop network, first, the node sends the signal to the LoRa Gateway, located at the Hockmeyer building (about 13 meters above the ground). The LoRa Gateway collects the data, stores it locally, and then forwards it to Flex Lab by using LoRaWAN modulation. \nTo evaluate the network quality, we measure the PDR, PER, and PMR for the two individual links, and then, the end-to-end connection. Results can be seen in Table~\\ref{tab:multiple-hop}. \n\\begin{table}[h!]\n    \\centering\n    \\caption{Multiple Hop Network Stability.}\n    \\begin{tabular}{|p{2.8cm}|p{1cm}|p{1cm}|p{1cm}|}\n    \\hline\n    \\textbf{Steps} & \\textbf{PDR} & \\textbf{PER} & \\textbf{PMR} \\\\ \n    \\hline\\hline\n    Node to LoRa Gateway & 62.15\\% & 7.64\\% & 30.21\\% \\\\\n    \\hline\n    LoRa Gateway to LoRaWAN Gateway & 88.27\\% & 8.94\\%  & 2.79\\% \\\\\n    \\hline\n    End-to-end & 54.86\\% & 5.56\\% & 39.58\\% \\\\\n    \\hline\n    \\end{tabular}\n    \\label{tab:multiple-hop}\n\\end{table}\nThe first hop achieves a relatively low PDR and high PMR compared to the second hop because the propagation path for the first hop is not a perfect LoS propagation; its distance (1.25km) is much larger than the second hop (187m). The second hop is a clear LoS propagation, resulting in a higher PDR. In a real-world urban area, our multiple-hop network achieves over 55\\% PDR, which a typical LoRaWAN single-hop network cannot.}\n\n\\begin{figure}[htbp]\n    \\centering\n    \\includegraphics[width=0.9\\columnwidth]{Figures\/multiple-hop.png}\n    \\caption{Purdue campus multiple-hop network map.}\n    \\label{fig:multiple-hop}\n   \n\\end{figure}\n\n\n\\section{Big Data Frameworks to the Rescue}\n\\label{sec:big-data}\n\\noindent Here, we will discuss the popular frameworks through which we will invoke the ML algorithms in our living testbed. This will involve open-source frameworks such as Apache Spark, streaming data processing frameworks such as Apache Flink, and techniques for distributing the ML processing among nodes in a cluster, both on-premise~\\cite{sophia, rafiki} and in a conventional cloud~\\cite{optimuscloud} or serverless environment~\\cite{mahgoub2021sonic}, such as for video analytics workloads~\\cite{xu2019approxnet, xu2020approxdet}. Serverless computing has become a promising cloud model where cloud providers run the servers and manage all administrative tasks ({\\em e.g.,}\\xspace scaling, capacity planning, etc.), while users focus on the application logic~\\cite{schleier2021serverless}.\nDue to its elasticity and ease-of-use, serverless computing is becoming increasingly popular for advanced streaming workflows such as data processing pipelines~\\cite{pu2019shuffling}, ML pipelines~\\cite{muller2020lambada}, and video analytics~\\cite{fouladi2017encoding, ao2018sprocket, xu2020approxdet}. Major cloud providers have recently introduced serverless {\\em workflow} services such as AWS Step Functions, Azure Durable Functions, and Google Cloud Composer, where applications are composed of a sequence of execution stages, which can be represented as a DAG~\\cite{pu2019shuffling,elgamal2018costless}. DAG nodes\ncorrespond to serverless functions ($\\lambda$s) and edges represent the flow of data between dependent $\\lambda$s, as designed in our system, SONIC~\\cite{mahgoub2021sonic}. The serverless abstraction is attractive in this domain because \nthe computation is often \\textit{event driven}, {\\em e.g.,}\\xspace when a particular sensor is triggered, say to detect the sound of an oncoming combine. Thus, compute nodes \\textit{do not} need to be active all the time but can be ``turned on\" at the right time  to process an event. \nThe system owner (who is typically not a computer scientist) \nis not responsible for making subtle resource provisioning decisions. A Reinforcement Learning (RL)-based solution can be attached to the serverless execution to make decisions such as how much memory to allocate to any container in the serverless execution. We have productively used such RL-based orchestration for controlling physical operations (in a manufacturing floor setting) in prior work~\\cite{thomas2018minerva}. Another reason serverless appears attractive in this domain is that the owner is only charged based on the number of events processed, rather than for a length of time. This should make it economically attractive for this domain where event-driven processing is the norm. \n\nThis infrastructure is in preparation for deployment of SNs within a farm and then connecting SNs across farms to form a federated setting. In the federated setting, with the privacy transforms, data acquisition and analysis can be done while maintaining anonymity using well-known techniques such as secure multi-party computation (MPC), especially their efficient variants~\\cite{damgaard2013practical, ben2008fairplaymp}. \nSuch techniques will guarantee that individual bad actors cannot break the confidentiality properties of our solution. Rather, only if greater than a threshold of the participants become bad actors will the system become vulnerable. This is feasible because today there exist ``push-button\" solutions for MPC and our domain for many scenarios does not need very low latency (the baseline solutions in MPC are known to be slow). \n\n\\noindent{\\customsec{Streaming data processing}}\nSince most of the data obtained in digital agriculture is real time, stream processing is preferred over batch processing. This adds several constraints: {\\em first}, the data analytics code has to function at a rate at least as fast as the rate at which data is being generated; {\\em second}, it has to calculate statistics (such as, range for normalization of data) without access to the entire data and based on some look-ahead window based on the workload dynamism (for example, for a more dynamic workload, the look-ahead window will be lower for higher accuracy, plus the algorithm should be configured for some degree of error handling); and {\\em third}, the code has to have the right input-output interfaces so that it can ingest streaming data and output its results in a stream. Now we consider some popular open source streaming analytics frameworks---Apache Spark Streaming (\\url{https:\/\/spark.apache.org\/streaming\/}), Apache Storm (\\url{http:\/\/storm.apache.org\/}), and Apache Flink (\\url{https:\/\/flink.apache.org\/}). These differ in the ways in which they can transform the data stream, {\\em i.e.,}\\xspace the kinds of operators that they support, the latency of processing, the programming languages they support, etc. \n\\cite{carbone2015apache} provides an open-source stream processing framework. Flink, however, does not provide its own  data storage and needs to be supplemented by frameworks that do, {\\em e.g.,}\\xspace Kafka~\\cite{garg2013apache} or Cassandra~\\cite{cassandra2014apache}. Apache Spark~\\cite{zaharia2016apache} is an alternative that can also be used for data parallelism. \n\n\\noindent{\\customsec{Batch data processing} }\nThere are some data analytics applications that need batch processing in this domain. This includes analytics that will be processed for strategic decision-making, without any real-time requirement. Batch data processing is done through data warehousing tools~\\cite{chaudhuri1997overview, nargesian2019data} and analytics frameworks like Spark (as opposed to Spark-Streaming) that can ingest data from such warehouses. The ease of this mode of processing is that the analytics code can access the entire data in one shot. The challenge with this mode of processing is the large volumes of data. To fit within the resources of the compute nodes, the data has to be segmented and the analytics code then runs on the segmented data. \n\\begin{comment}\n\\noindent{\\customsec{Open-source frameworks}} Open-source frameworks provide extensive customization and allow collaboration. These two properties, among many, make them more preferable. \\cite{hashem2015rise} provides an overview of the existing challenges and solutions to handling big data. Hadoop is one such open-source framework that can process large datasets~\\cite{shvachko2010hadoop}, we have also made an open-source version of Apache-Spark available for distributed SVM approaches~\\cite{ghoshal2015ensemble, ghoshal2018distributed}. It functions on map-reduce programming models. Several warehousing solutions built on Hadoop such as Hive~\\cite{thusoo2009hive} are also available. Apache Drill is another open-source framework that provides interactive analysis of big data~\\cite{hausenblas2013apache}. \\cite{chandarana2014big} provides a comparative study of three open-source frameworks, Hadoop, Drill, and the Project Storm. \n\\end{comment}\n\n\\section{Democratizing AI for Farmers}\n\\label{sec:democratizing-ai}\n\\noindent This will require the accessibility of state-of-the-art wireless, database, and ML technologies to farms---even small-scale farms---deploying leading-edge analytics and broadband modalities to gather data from farms ({\\em e.g.,}\\xspace FarmBeats, AirBand technologies, Open Ag Data Alliance APIs).\nThis will cover the commercial angle of deploying and operating a system and the foundational (and often open-source) technologies that they build upon, such as, TV whitespace spectrum being used to upload high volume data.\nTo bring the benefits of digital agriculture, and the ML driven insights to the farmers, we need to make these systems\naffordable. However, existing digital agriculture solutions are expensive for two key reasons. \n\n\\underline{First}, is the limited broadband connectivity in rural farms. The sensors, drones, and tractors need to send data to the\ncloud to train the ML models, and the insights need to be conveyed to\nthe farmer's devices. Even in the US, around 20 million rural Americans\ndo not have broadband access~\\cite{fc2019eighth}. And a large part of\nfarmland does not have access either.\nTo bridge this digital divide, we need to come up with innovative\nsolutions to bring broadband Internet in the farms. One such promising\ntechnology is the TV White Spaces technology, which refers to unused TV\nchannels~\\cite{bahl2009white}. There is abundant unused TV channels in\nfarms, which can be used to send and receive data in farms. Wireless\nsignals also propagate smoothly in the TV frequencies, and are ideal for connecting farms. Satellite-based Internet access also holds promise, where low-earth orbit (LEO) satellites could enable low-cost backhaul connectivity.\n\n\\underline{Second}, the reason for expensive digital agriculture solutions is the lack of platforms for innovation that are opensource and interoperable. Data acquisition\nsystems are proprietary, and hence getting data from the farm for research is not easy. There is also a dearth of clean data from farms that can be used for building ML models. \nWe propose the building of open-source APIs, and data\nrepositories. These APIs, such as the one from Open Ag Data Alliance,\nafford researchers and startups a platform to prototype their\ninnovation. Similarly, a cloud-based data repository, for example with\ndrone imagery and satellite data from research farms, will enable\nresearchers to train new models. It will also create a\nbenchmarking dataset to evaluate new innovations before\nbringing it to the growers. \n\n\\section{Limitations}\n\\label{sec:limitation}\n\\noindent{Here we acknowledge the key limitations of our initial work setting up practical testbeds:}\n\\begin{itemize}\n    \\item Our solution still needs human intervention such as replacing batteries for SN, and stable power supply for LoRa gateways, which limit the places where we can deploy them.\n    \\item The bandwidth of LoRa is relatively low such that we cannot transmit complex data ({\\em e.g.,}\\xspace image data, audio data). We can also use 4G and 5G here to transmit data from the SNs to the gateway because they have broader bandwidth, better suited for video feeds, sound feeds, and images.\n    \\item We need to deploy and maintain our own LoRa and LoRaWAN gateway, which could be quite expensive in short-term. NB-IoT could be a alternative choice, but NB-IoT will have a monthly payment. \n    \\somali{put some specifics, what are the plans like -- data volumes to prices and for which vendors, otherwise this is not suitable to put in technical writing}.\n   \n\\end{itemize}\n\\section{Conclusion and Future Work}\n\\label{sec:conclusion}\nWe have built a low-energy, durable, flexible, long-range, low-cost IoT Network. And have inclusive implementation and troubleshooting examples.\nFor future work, we are aiming to develop smart, self-maintainable, sustainable sensor devices and network.\n\n\n\\noindent{\\customsec{Smart and Sustainable Node \\& Gateway}}\n\\begin{itemize}\n    \\item Problem: Currently, the SNs need to be powered by batteries. The Gateway can only be put somewhere where have a power supply and Internet access. And need a quite much effort to maintain them.\n    \\item Our solution: The overall feature of our solution is that they don't need any human evolving works after the first time deployment. Since the number of IoT devices and networks will explode in the future, sustainable devices and networks is a good point we can emphasize. \n    \\item Indesign node + Solar panel (The Indesign node is powered by 4 AAA batteries now, if we can replace the batteries with a solar panel, then we don't need to go to the field to replace the batteries manually.)\n    \\item Raspberry-Pi + Solar panel + Camera to serve as a camera SN in the field to do object detection. The detection target could be saboteurs, animals, diseases of crops, or if the height of crops is in anticipation. The traditional camera does not have the ability to analyze the video in the field and needs quite larger network bandwidth to upload the video to the cloud which is very power consuming. By using our method, we can collect the data in the field and directly analyze the video in the field, and only send the results back to the cloud. Since we will have limited power by using the solar panel, we can also incorporate approximate calculation here to save power. And for agriculture application, latency should not be a problem, 5 frames per second should be enough.\n    \\item A drone carrying Jetson Nano to do object detection. After the drone collected all the data, it can send the data to the Edge Server (a more powerful machine could be Xavier NX\n\\end{itemize}\n\n\\textbf{Improvement on Network:}\n\\begin{itemize}\n    \\item Expand longer coverage by combining LoRa and NB-IoT on a single Raspberry-Pi (It will serve as a relay station between SNs and NB-IoT base station, and this is to solve the coverage issue)\n    \\item An intelligent offloading scheme on the Gateway. We can do data analysis on the Raspberry-Pi directly and only send back the result to the cloud (decreasing the data need to be upload to the cloud).\n\\end{itemize}\n\n\n\n\n\n\n\\section{Discussion}\n\\label{sec:discussion}\nHere are some valuable experiences we have learned from the deployment of {\\sc Orpheus}\\xspace:\n\\begin{itemize}\n    \\item Since we are using electronic devices to build an IoT network, ruggedizing them to operate outdoors in agriculture settings is vital. Besides, robust firmware to support these devices is also critical. What's more, higher-compute gateway nodes and a backend database server with an in-memory database and application server ({\\em e.g.,}\\xspace Redis), and ability to offload from the SNs or gateway nodes to the cloud-hosted databases is required~\\cite{chaterji2021lattice, jiang2020hybrid, chaterji2020cloud}. Such cloud-hosted databases can serve to aggregate the data from multiple farms, and within each farm, from multiple SNs.\n    \\item When we build the whole end-to-end data collecting and visualization pipeline, data transmission and storage are important. Setting up multiple anchor points in the pipeline will be a good solution to avoid missing data and data tampering. This is accomplished by storing our data in both the gateway nodes and backend servers for groundtruthing and online updates.\n    Further, daily connectivity, and data integrity checks need to be performed to  ensure resiliency of the workflow loop.\n    \\item When building a large-scale IoT network architecture, modular design is a good approach, which allows one to divide the system into discrete scalable and reusable modules.\n    In our living lab, the SNs are designed by following the LoRa protocol so that the wireless communication in the field is done by using LoRa, the Raspberry Pi, and LoStik module serving as the Gateway. Raspberry Pi can potentially be replaced by more powerful devices, {\\em e.g.,}\\xspace Jetsons, at the gateway.\n    The Jetson-class devices can do the heavyweight computation, such as, computing a frequency spectrum of the values and identifying anomalies from them. \n       \n   \n    \n   Next, we use standard TCP\/IP protocol connecting the Gateway to the Internet. Finally, our website is developed using the Django framework. MongoDB stores all of the data, and acts as an interface between the cloud website, and the edge LPWAN.\n    \\item This is a real-world implementation work, which is subjected to drastic weather and frequently shifting landscape, affecting wireless communication performance, {\\em e.g.,}\\xspace the height of the corn stalks in a corn field can reduce the packet reception ratio between the SNs and the Gateway. \n   \n    \\end{itemize}\n\\section{Conclusion and Future Work}\n\\label{sec:conclusion}\nWe have deployed three models for testing and refining {\\sc Orpheus}\\xspace. The \\textit{first model} consists of a living lab with real, ruggedized sensors deployed in fields and networking innovations for low end-to-end latency. This is for more latency-sensitive tasks, such as near-live actuation of sensors on applicator for farm supplements and site-specific variable rate treatments. Further, there are multiple-hop networks connecting the sensor nodes on the farm and then aggregated at the gateway server at the farmer's house. This aggregation could be using a Raspberry Pi or a more compute-heavy mobile GPU-enabled, Jetson-class device. The \\textit{second model} consists of an embedded testbed consisting of leading-edge embedded devices in the Jetson class of mobile GPUs.\nSpecifically, three embedded devices are currently used in our embedded testbed to benchmark heavy video object detection algorithms, useful for applications in our living lab. The devices are the \\textit{Jetson TX2}, \\textit{Jetson Xavier NX}, and \\textit{Jetson AGX Xavier}, with different levels of CPU, GPU, and memory capacity. The relation between their computational capacities is Jetson TX2 $<$ Jetson Xavier NX $<$ Jetson AGX Xavier. \\textit{Finally}, we enable opportunistic data ferrying, using drones. This is for traffic that is delay tolerant. The drones perform fly-by over the farm and are able to detect sensor feeds beamed to them from the ground sensor nodes (or sensor nodes on poles) in the living testbed. This enables them to carry high-bandwidth video, sound, or image feeds from the static nodes to the gateway node(s). The drones can also be used for temporal surveillance of the fields where gathered image feeds (over time intervals) can be used for a temporal health scan of the fields. In our current implementation, we use LoRa and LoRaWAN gateways for aggregating the multi-modal sensor data. In alternate settings, these could be replaced by NB-IoT with some infrastructure and recurring costs.\n\nOur living lab testbed across different scenarios is an enabler for usable data collection and analytics from farms, even small-scale farms. This will require a careful adaptation of wireless, database, and ML technologies for the digital agriculture scenario and orchestration of these individual technology elements into a usable and low-cost end-to-end system, as described in Lattice~\\cite{chaterji2021lattice}. There is momentum behind this through projects like FarmBeats, AirBand technologies, and Open Ag Data Alliance. \nWe hope that our work by providing an exemplar instantiation will accelerate this movement.\n\n\n\n\n\n\\section{#1}\\vspace{-4pt}}\n\n\n\n\\newif\\ifdraft\n\\drafttrue\n\n\\usepackage{comment}\n\n\\newcommand{\\pengcheng}[1]{\\ifdraft{\\textcolor{magenta}{\\textbf{PW:} #1}}\\fi}\n\\newcommand{\\somali}[1]{\\ifdraft{\\textcolor{red}{SC: #1}}\\fi}\n\\newcommand{\\saurabh}[1]{\\ifdraft{\\textcolor{orange}{SB: #1}}\\fi}\n\\newcommand{\\edgardo}[1]{\\ifdraft{\\textcolor{blue}{\\textbf{EB:} #1}}\\fi}\n\\newcommand{\\tom}[1]{\\ifdraft{\\textcolor{brown}{\\textbf{TR:} #1}}\\fi}\n\\newcommand{\\question}[1]{\\ifdraft{\\textcolor{red}{Q: #1}}\\fi}\n\\newcommand{\\Ourtodo}[1]{\\ifdraft{\\textcolor{blue}{TODO: #1}}\\fi}\n\n\\newcommand{\\newtext}[1]{\\ifdraft{\\textcolor{red}{#1}}\\else{#1}\\fi}\n\\newcommand{\\rev}[1]{\\ifdraft{\\textcolor{blue}{#1}}\\else{#1}\\fi}\n\\newcommand{\\revreviewed}[1]{\\ifdraft{\\textcolor{brown}{#1}}\\else{#1}\\fi}\n\n\n\\newcommand{{\\em i.e.,}\\xspace}{{\\em i.e.,}\\xspace}\n\\newcommand{{\\em et al.}\\xspace}{{\\em et al.}\\xspace}\n\\newcommand{{\\em e.g.,}\\xspace}{{\\em e.g.,}\\xspace}\n\n\\newcommand{\\customsec}[1]{\\noindent{\\textbf{{#1}:}}}\n\n\\newcommand{{\\sc Orpheus}\\xspace}{{\\sc Orpheus}\\xspace}\n\\newcommand{{\\em Orpheus} is the God of supernatural music and can energize even lifeless rocks and trees to dance in enchantment. We envision our living lab to bring to fruition data analytics technologies, such as those tested on our embedded testbed, to transform IoT-enabled agriculture. \\xspace}{{\\em Orpheus} is the God of supernatural music and can energize even lifeless rocks and trees to dance in enchantment. We envision our living lab to bring to fruition data analytics technologies, such as those tested on our embedded testbed, to transform IoT-enabled agriculture. \\xspace}\n\n\\usepackage[font={bf,footnotesize},labelsep=colon,justification=justified]{caption}\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\n\\section{Fast-oopsi, a brief view}\n\nOopsi, from vogelstein \\cite{vogelstein2010oopsi,vogelstein2010fast}, is a family of optimal optical spike inference algorithms. Here, we focus on the development of the fast-oopsi, which was originally published in \\cite{vogelstein2010fast}. We will port the MATLAB implementation to python. Sec \\ref{sec:model}, \\ref{sec:bayes}, \\ref{fast-oopsi:bayes}, \\ref{fast-oopsi:solver} and \\ref{fast-oopsi:parameters} are digests from the original paper by vogelstein \\cite{vogelstein2010oopsi}.\n\nThe python implementation, \\textcolor{red}{\\textbf{py-oopsi}}, can be obtained at \\textcolor{red}{\\url{https:\/\/github.com\/liubenyuan\/py-oopsi}}.\n\n\\section{Calcium fluorescence model}\n\\label{sec:model}\n\nLet $\\ve{F}$ be a one-dimensional fluorescence trace. At time $t$, the fluorescence measurement $F_t$ is a linear Gaussian function of the intracellular calcium concentration $[\\ensuremath{\\mathrm{Ca}}^{2+}]_t$ at that time:\n\\begin{equation}\n    F_t = \\alpha [\\ensuremath{\\mathrm{Ca}}^{2+}]_t + \\beta + e_t, \\qquad e_t\\sim\\mathcal{N}(0,\\sigma^2)\n\\end{equation}\n$\\alpha$ determines the scale of the signal, $\\beta$ absorbs the offset. $\\alpha$ and $\\beta$ may be learned independently per neuron. The noise $e_t$ is assumed to be i.i.d distributed.\n\nThe calcium concentration jumps $A$ $\\mu$M after each spike and decays back down to baseline $C_b$ $\\mu$M, with time constant $\\tau$,\n\\begin{equation}\n    [\\ensuremath{\\mathrm{Ca}}^{2+}]_{t+1} = (1-\\Delta\/\\tau)[\\ensuremath{\\mathrm{Ca}}^{2+}]_t + (\\Delta\/\\tau)C_b + An_t,\n\\end{equation}\nwhere $\\Delta$ is the frame interval. The scale $A$ and $\\alpha$, baseline $C_b$ and $\\beta$ are not identifiable, therefore, we may let $A=1$ and $C_b=0$ without loss of generality. $n_t$ indicates the number of times the neuron spiked in time $t$, we may also write it as a delta function $\\delta_t$.\n\nFinally, letting $\\gamma=(1-\\Delta\/\\tau)$, we have\n\\begin{equation}\n    C_{t} = \\gamma C_{t-1} + n_t\n\\end{equation}\nand (the filtering model)\n\\begin{equation}\n    C[z] = \\frac{1}{1-\\gamma z^{-1}} N[z]\n\\end{equation}\nNote that $C_t$ does not refer to the absolute intracellular concentration, but rather, a relative measure\\cite{vogelstein2010fast}. The simulated calcium trace can be generated if we synthetically generate $n_t$ from a probability distribution. To complete the generative model, we assume spikes are sampled according to a Poisson distribution,\n\\begin{equation}\n    n_t \\sim \\text{Poisson}(\\lambda\\Delta)\n\\end{equation}\nwhere $\\lambda\\Delta$ is the expected firing rate per bin, $\\Delta$ is included to ensure that the expected firing rate is independent of the frame rate\\cite{vogelstein2010fast}.\n\n\\section{Bayes Model}\n\\label{sec:bayes}\nWe aim to find the most likely spike trains $\\hat{\\ve{n}}$ given the fluorescence $\\ve{F}$,\n\\begin{equation}\\label{eq:n_map0}\n    \\hat{\\ve{n}} = \\operatornamewithlimits{arg\\,max}_{n_t\\in\\mathcal{N}_0,\\forall t} p(\\ve{n}|\\ve{F})\n\\end{equation}\nUsing Bayes' rule,\n\\begin{equation}\n    p(\\ve{n}|\\ve{F}) = \\frac{1}{p(\\ve{F})}\\cdot p(\\ve{F}|\\ve{n})p(\\ve{n})\n\\end{equation}\ngiven that $p(\\ve{F})$ merely scales the results, we rewrite \\eqref{eq:n_map0} as,\n\\begin{equation}\n    \\hat{\\ve{n}} = \\operatornamewithlimits{arg\\,max}_{n_t\\in\\mathcal{N}_0,\\forall t} p(\\ve{F}|\\ve{n})p(\\ve{n})\n\\end{equation}\nand we already have,\n\\begin{align}\n    p(\\ve{F}|\\ve{n}) &= p(\\ve{F}|\\ve{C}) = \\prod p(F_t|C_t), \\\\\n    p(\\ve{n}) &= \\prod p(n_t),\n\\end{align}\nwhere,\n\\begin{align}\n    p(F_t|C_t) &= \\mathcal{N}(\\alpha C_t + \\beta,\\sigma^2), \\\\\n    p(n_t) &= \\mathrm{Poisson}(\\lambda\\Delta)\n\\end{align}\nThe Poisson distribution penalize sparsity (a sparse prior).\n\nFinally, we have the cost function,\n\\begin{align}\n    \\hat{\\ve{n}} &= \\operatornamewithlimits{arg\\,max}_{n_t\\in\\mathcal{N}_0} \\prod_{t=1}^{T} \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left\\{ -\\frac{1}{2}\\frac{(F_t - \\alpha C_t - \\beta)^2}{\\sigma^2}\\right\\} \\frac{\\exp\\left\\{ -\\lambda\\Delta \\right\\}(\\lambda\\Delta)^{n_t}}{n_t!} \\\\\n                 &= \\operatornamewithlimits{arg\\,max}_{n_t\\in\\mathcal{N}_0} \\sum_{t=1}^{T} -\\frac{1}{2\\sigma^2}(F_t - \\alpha C_t - \\beta)^2 + n_t\\ln \\lambda\\Delta - \\ln n_t!\n\\end{align}\nHowever, solving for this discretized optimization problem is computational intractable.\n\n\\section{Approximate Bayes Filter}\n\\label{fast-oopsi:bayes}\n\nWe can approximate the Poisson distribution with an exponential distribution of the same mean,\n\\begin{equation}\n    \\frac{\\exp\\{-\\lambda\\Delta\\}(\\lambda\\Delta)^{n_t}}{n_t!} \\rightarrow (\\lambda\\Delta)\\exp\\{-n_t\\lambda\\Delta\\}\n\\end{equation}\nand consequently,\n\\begin{equation}\n    \\hat{\\ve{n}} = \\operatornamewithlimits{arg\\,max}_{n_t>0} \\sum_{t=1}^{T} -\\frac{1}{2\\sigma^2}(F_t - \\alpha C_t - \\beta)^2 - n_t\\lambda\\Delta\n\\end{equation}\nnote that $n_t\\in\\mathcal{N}_0$ has been replaced by $n_t>0$, since exponential distribution can yield any nonnegative number\\cite{vogelstein2010fast}. The exponential approximation imposes a sparsening effect, and also, it makes the optimization problem concave in $\\ve{C}$, meaning that any gradient descent algorithm guarantees achieving \\textbf{the global maxima} (because there are no local minima).\n\nWe may further drop the constraint (nonnegative) by adopting \\textbf{interior point} method,\n\\begin{equation}\n    \\hat{\\ve{n}} = \\operatornamewithlimits{arg\\,max}_{n_t} \\sum_{t=1}^{T} -\\frac{1}{2\\sigma^2}(F_t - \\alpha C_t - \\beta)^2 - n_t\\lambda\\Delta + z\\ln n_t\n\\end{equation}\nwhere we add a weighted barrier term that approaches $-\\infty$ as $n_t$ approaches zero, by solving for a series of $z$ going down to nearly zero. The goal is to efficiently solve,\n\\begin{equation}\n    \\hat{\\ve{C}} = \\operatornamewithlimits{arg\\,max}_{C} \\sum_{t=1}^{T} -\\frac{1}{2\\sigma^2}(F_t - \\alpha C_t - \\beta)^2 - (C_t - \\gamma C_{t-1})\\lambda\\Delta + z\\ln (C_t - \\gamma C_{t-1})\n\\end{equation}\nthis cost function is twice differentiable, one can use the Newton-Raphson technique to ascend the surface.\n\n\\section{Matrix Notation and the Newton-Raphson solver}\n\\label{fast-oopsi:solver}\nTo proceed, we have\n\\begin{equation}\n    \\ve{M}\\ve{C} =\n    \\begin{bmatrix}\n        -\\lambda & 1 & 0 & 0 & \\cdots & 0 \\\\\n        0 & -\\lambda & 1 & 0 & \\cdots & 0 \\\\\n        \\vdots & \\ddots & \\ddots & \\ddots & \\ddots & \\vdots \\\\\n        0 & \\cdots & 0 & -\\lambda & 1 & 0 \\\\\n        0 & \\cdots & 0 & 0 & -\\lambda & 1\n    \\end{bmatrix}\n    \\begin{bmatrix}\n        C_1 \\\\\n        C_2 \\\\\n        \\vdots \\\\\n        C_{T-1} \\\\\n        C_{T}\n    \\end{bmatrix} =\n    \\begin{bmatrix}\n        n_1 \\\\\n        n_2 \\\\\n        \\vdots \\\\\n        n_{T-1}\n    \\end{bmatrix}\n\\end{equation}\n$\\ve{M}$ is a $(T-1)\\times T$ matrix. Now letting $\\ve{1}$ be a $(T-1)\\times 1$ column vector, $\\bm{\\lambda} = (\\lambda\\Delta)\\ve{1}$, $\\bm{\\alpha}$ and $\\bm{\\beta}$ a $T$-dimensional vector, $\\odot$ to indicate element-wise operations, then \\footnote{contrary to \\cite{vogelstein2010fast}, but alike \\textbf{fast-oopsi.m}, we choose $\\ve{M}$ as a sparse $T\\times T$ matrix, and $\\ve{1}$ as $T\\times 1$ column vector. Therefore we have $n_0=C_0$, we will correct $n_0=\\epsilon$ after convergence.}\n\\begin{equation}\n    \\hat{\\ve{C}} = \\operatornamewithlimits{arg\\,max}_{\\ve{MC}\\geq_{\\odot}\\ve{0}} -\\frac{1}{2\\sigma^2}\\norm{\\ve{F}-\\bm{\\alpha}\\ve{C}-\\bm{\\beta}}_2^2 - (\\ve{MC})^T\\bm{\\lambda} + z\\ln_{\\odot} (\\ve{MC})^T\\ve{1}\n\\end{equation}\n\nWe instead iteratively minimize the cost function $\\mathcal{L}$ (called \\textit{post} in our python implementation) where,\n\\begin{equation}\n    \\hat{\\ve{C}}_z = \\operatornamewithlimits{arg\\,min}_{\\ve{C}} \\mathcal{L}, \\quad \\mathcal{L}= \\frac{1}{2\\sigma^2}\\norm{\\ve{F}-\\bm{\\alpha}\\ve{C}-\\bm{\\beta}}_2^2 + (\\ve{MC})^T\\bm{\\lambda} - z\\ln_{\\odot} (\\ve{MC})^T\\ve{1}\n\\end{equation}\n$\\mathcal{L}$ is \\textbf{convex}, when using Newton-Raphson method to \\textbf{descend} a surface, one iteratively computes the gradient $\\ve{g}=\\nabla\\mathcal{L}$ (first derivative) and Hessian $\\ve{H}=\\nabla^2\\mathcal{L}$ (second derivative) of the argument to be optimized. Then, $\\ve{C} = \\ve{C} - s\\ve{d}$, where $s$ is the step size and $\\ve{d}$ is the step direction by solving $\\ve{H}\\ve{d} = \\ve{g}$. The gradient and Hessian, with respect to $\\ve{C}$, are\n\\begin{align}\n    \\ve{g} &= -\\frac{\\bm{\\alpha}}{\\sigma^2} (\\ve{F} - \\bm{\\alpha}\\ve{C} - \\bm{\\beta}) + \\ve{M}^T\\bm{\\lambda} - z\\ve{M}^T(\\ve{MC})_{\\odot}^{-1} \\\\\n    \\ve{H} &= \\frac{\\alpha^2}{\\sigma^2}\\ve{I} + z\\ve{M}^T(\\ve{MC})_{\\odot}^{-2}\\ve{M}\n\\end{align}\n$s$ is found via \\textbf{backtracking linesearches}. $\\ve{M}$ is bidiagonal, so $\\ve{H}$ is tridiagonal, $\\ve{d} = \\ve{H}^{-1}\\ve{g}$ can be efficiently implemented in matlab by assuming $\\ve{H}$ is a sparse matrix. In python, we may use sparse linsolvers (linsolve.spsolve) to efficiently find $\\ve{d}$. Once $\\hat{\\ve{C}}$ is obtained, it is a simple linear transform to obtain $\\hat{\\ve{n}}$, via $\\hat{\\ve{n}}=\\ve{M}\\hat{\\ve{C}}$. We will normalize $\\ve{n}$ by $\\ve{n}=\\ve{n}\/\\mathrm{max}(\\ve{n})$ after convergence.\n\n\\section{Parameters initialize and update}\n\\label{fast-oopsi:parameters}\n\nThe parameters $\\bm{\\theta}=\\{\\alpha,\\beta,\\sigma,\\gamma,\\lambda\\}$ are unknown. We may use pseudo expectation-maximization method,\n(1), initialize the parameters, (2) recursively computes $\\hat{\\ve{n}}$ and updating $\\bm{\\theta}$ given the new $\\hat{\\ve{n}}$ until the convergence is met.\n\nThe scale of $\\ve{F}$ relative to $\\ve{n}$ is arbitrary, therefore, $\\ve{F}$ is firstly \\textit{detrended}, and then \\textit{linearly mapped} between $0$ and $1$.\n\\begin{equation}\n    \\ve{F} = \\mathrm{detrend}(\\ve{F}), \\quad \\ve{F}=(\\ve{F} - F_{min}) \/ (F_{max} - F_{min}),\n\\end{equation}\nNext, because spiking is sparse in many experimental settings, $\\ve{F}$ tends to be around baseline, $\\beta$ is set to the median of $\\ve{F}$. We use median absolute deviation (MAD) and correction factor $K$, as a robust normal scale estimator of $\\ve{F}$ where $K=1.4826$. Previous works showed that the results $\\hat{\\ve{n}}$ and $\\hat{\\ve{C}}_z$ are robust to minor variations in the time constant, we let $\\gamma=1-\\Delta$. Finally, $\\lambda$ is set to $1$Hz, which is between baseline and evoked spike rate for data of interest \\footnote{corrections to \\cite{vogelstein2010fast}: 1), add detrend to $\\ve{F}$, 2), $K=1.4826$ and it is multiplied (not divided by) $\\mathrm{MAD}(\\ve{F})$.}.\n\\begin{align}\n    \\alpha &= 1, \\\\\n    \\beta &= \\mathrm{median}(\\ve{F}), \\\\\n    \\sigma &= \\mathrm{MAD}(\\ve{F})\\cdot K = \\mathrm{median}(\\abs{\\ve{F} - \\beta})\\cdot K, \\quad K = 1.4826 \\\\\n    \\gamma &= 1 - \\Delta\/(1 \\mathrm{sec}), \\\\\n    \\lambda &= 1 \\mathrm{Hz}\n\\end{align}\n\nThen, given $\\hat{\\ve{C}}$ and $\\hat{\\ve{n}}$, we may (approximately) update $\\bm{\\theta}$ by,\n\\begin{equation}\n    \\hat{\\bm{\\theta}} \\approx \\operatornamewithlimits{arg\\,max}_{\\bm{\\theta}} p(\\ve{F},\\hat{\\ve{C}}|\\bm{\\theta}) = \\operatornamewithlimits{arg\\,max}_{\\bm{\\theta}} \\ln p(\\ve{F}|\\hat{\\ve{C}};\\{\\alpha,\\beta,\\sigma\\}) + \\ln p(\\hat{\\ve{n}}|\\lambda)\n\\end{equation}\nwhere,\n\\begin{align}\n    \\hat{\\lambda} &= \\operatornamewithlimits{arg\\,max}_{\\lambda>0} \\sum_{i=1}^T \\left[ \\ln(\\lambda\\Delta) + \\hat{n_t}\\lambda\\Delta \\right] \\\\\n    \\{\\hat{\\alpha},\\hat{\\beta},\\hat{\\sigma}\\} &= \\operatornamewithlimits{arg\\,max}_{\\alpha,\\beta,\\sigma >0}\\sum_{i=1}^T \\left[ -\\frac{1}{2}\\ln(2\\pi\\sigma^2) - \\frac{1}{2}\\left( \\frac{F_t - \\alpha C_t - \\beta}{\\sigma} \\right)^2 \\right]\n\\end{align}\nWe have (by taking the derivatives and letting them equal zero),\n\\begin{align}\n    \\hat{\\lambda} &= \\frac{T}{\\Delta \\sum_t n_t}, \\\\\n    \\hat{\\alpha} &= 1, \\\\\n    \\hat{\\beta} &= \\frac{\\sum_t (F_t - C_t)}{T}, \\\\\n    \\hat{\\sigma}^2 &= \\frac{\\sum_t (F_t - C_t - \\beta)^2}{T} = \\frac{\\norm{\\ve{F} - \\ve{C} - \\bm{\\beta}}_2^2}{T}\n\\end{align}\nwhere $\\hat{\\lambda}$ is the inverse of the inferred firing rate, $\\hat{\\alpha}$ can be set to $1.0$ because the scale of $\\ve{C}$ is arbitrary, $\\hat{\\beta}$ is the mean bias, $\\hat{\\sigma}$ is the root-mean-square of the residual error.\n\n\\section{Implementation of oopsi}\nMatlab implementation is available, here we focus on the python migrant, and correct some typos in \\cite{vogelstein2010fast} as needed. The python code itself explains all, see \\ref{fast-oopsi:bayes}, \\ref{fast-oopsi:solver}, and \\ref{fast-oopsi:parameters} for detailed documentary. Pseudo code can be found in Algo \\ref{algo:fast-oopsi}. Algo \\ref{algo:oopsi_est_map} describe the subroutine \\textbf{MAP}, Algo \\ref{algo:oopsi_est_par} describe the subroutine \\textbf{update}.\n\\begin{algorithm}[htbp]\n    \\caption{Pseudo code (python) for fast-oopsi}\\label{algo:fast-oopsi}\n    \\begin{algorithmic}[1]\n        \\STATE Initialize parameters $\\ve{P}$: $\\ve{F}=\\mathrm{detrend}(\\ve{F})$, $\\ve{F}=(\\ve{F}-\\mathrm{min}(\\ve{F}))\/(\\mathrm{max}(\\ve{F})-\\mathrm{min}(\\ve{F}))$, $\\alpha=1.0$, $\\beta=\\mathrm{median}(\\ve{F})$, $\\lambda=1.0$, $\\gamma=1-\\Delta$, $\\sigma=\\mathrm{MAD}(\\ve{F})\\cdot 1.4826$, $T=\\mathrm{len}(\\ve{F})$\n        \\STATE one-shot Newton-Raphson $\\ve{n}$, $\\ve{C}$, $\\mathcal{L}$ = MAP($\\ve{F}$,$\\ve{P}$), see Algo \\ref{algo:oopsi_est_map}.\n        \\FOR{$i$ in $1\\cdots\\mathrm{iterMax}$}\n        \\STATE update parameters $\\ve{P}$ = update($\\ve{n}$,$\\ve{C}$,$\\ve{F}$,$\\ve{P}$), see Algo \\ref{algo:oopsi_est_par}.\n        \\STATE iterative through $\\ve{n}$, $\\ve{C}$, $\\mathcal{L}$ = MAP($\\ve{F}$,$\\ve{P}$),\n        \\STATE let $\\mathcal{L}^{(k)}=\\{\\mathcal{L}_1,\\cdots,\\mathcal{L}_k\\}$\n        \\IF{$\\abs{\\frac{\\mathcal{L}_i-\\mathcal{L}_{i-1}}{\\mathcal{L}_i}}<\\mathrm{ltol}$ or $\\mathrm{any}(\\abs{\\mathcal{L}^{(i)}-\\mathcal{L}_i})<\\mathrm{gtol}$}\n        \\STATE break\n        \\ENDIF\n        \\ENDFOR\n    \\end{algorithmic}\n\\end{algorithm}\n\n\\begin{algorithm}[htbp]\n    \\caption{Pseudo code of subroutine \\textit{MAP}}\\label{algo:oopsi_est_map}\n    \\begin{algorithmic}[1]\n        \\STATE Initialize $\\ve{n}=0.01\\ve{1}$\n        \\STATE Initialize $\\ve{C}(z) = 1\/(1-\\gamma) \\ve{N}(z)$\n        \\STATE Initialize $\\bm{\\lambda}=\\lambda\\Delta \\ve{1}$\n        \\FOR{$z=1.0$, $z>1e-13$, $z=z\/10$}\n            \\STATE calculate $\\mathcal{L}_z$\n            \\WHILE{$s>1e-3$ or $\\norm{\\ve{d}}>5e-2$}\n            \\STATE Calculate $\\ve{g}$, $\\ve{H}$ and $\\ve{d}=\\mathrm{spsolve}(\\ve{H},\\ve{g})$\n            \\STATE Find $s$ : $\\ve{h}=-\\ve{n}\/(\\ve{M}\\ve{d})$, $s=\\min (0.99\\ve{s}[\\ve{s}>0],1.0)$\n            \\STATE Initialize $\\mathcal{L}_s=\\mathcal{L}_z + 1$\n                \\WHILE{$\\mathcal{L}_s>\\mathcal{L}_z + 1e-7$}\n                \\STATE $\\ve{C}=\\ve{C}+s\\ve{d}$\n                \\STATE $\\ve{n}=\\ve{MC}$\n                \\STATE update $\\mathcal{L}_s$\n                \\STATE decrease $s=s\/5.0$\n                \\IF{$s<1e-20$}\n                \\STATE break\n                \\ENDIF\n                \\ENDWHILE\n            \\ENDWHILE\n        \\ENDFOR\n    \\end{algorithmic}\n\\end{algorithm}\n\n\\begin{algorithm}[htbp]\n    \\caption{Pseudo code of subroutine \\textit{update}}\\label{algo:oopsi_est_par}\n    \\begin{algorithmic}[1]\n        \\STATE $\\alpha=1.0$\n        \\STATE $\\beta=\\sum_i (F_i-C_i)\/T$\n        \\STATE $\\sigma^2=\\norm{\\ve{F}-\\alpha\\ve{C}-\\beta}_2^2\/T$\n        \\STATE $\\lambda=T \/ (\\Delta\\sum_i n_i)$\n    \\end{algorithmic}\n\\end{algorithm}\n\n\\section{Wiener filter (linear regression, simple convex optimization)}\nIn the wiener filter, we approximate the Poisson distribution with a Gaussian distribution,\n\\begin{equation}\n    p(n_t) \\sim \\mathcal{N}(\\lambda\\Delta,\\lambda\\Delta)\n\\end{equation}\nthen, the MAP estimator yields,\n\\begin{equation}\n    \\hat{\\ve{n}} = \\operatornamewithlimits{arg\\,max}_{n_t} \\sum_{t=1}^T \\left[ -\\frac{1}{2\\sigma^2}(F_t - \\alpha C_t -\\beta)^2 -\\frac{1}{2\\lambda\\Delta}(n_t - \\lambda\\Delta)^2 \\right]\n\\end{equation}\nand its matrix notation,\n\\begin{equation}\n    \\hat{\\ve{C}} = \\operatornamewithlimits{arg\\,max}_{\\ve{C}} -\\frac{1}{2\\sigma^2}\\norm{\\ve{F} - \\alpha\\ve{C} - \\beta\\ve{1}}_2^2 - \\frac{1}{2\\lambda\\Delta}\\norm{\\ve{MC}-\\lambda\\Delta\\ve{1}}_2^2\n\\end{equation}\nwhich is \\textbf{quadratic}, \\textbf{concave} in $\\ve{C}$.\n\nFinally, we aim to optimize (minimize, \\textbf{quadratic}, \\textbf{convex} optimization),\n\\begin{equation}\n    \\hat{\\ve{C}} = \\operatornamewithlimits{arg\\,min}_{\\ve{C}} \\mathcal{L}, \\quad \\mathcal{L}= \\frac{1}{2\\sigma^2}\\norm{\\ve{F} - \\alpha\\ve{C} - \\beta\\ve{1}}_2^2 + \\frac{1}{2\\lambda\\Delta}\\norm{\\ve{MC}-\\lambda\\Delta\\ve{1}}_2^2\n\\end{equation}\nwhere $\\mathcal{L}$ is \\textbf{convex} in $\\ve{C}$. Using Newton-Raphson update, we find $\\ve{C}=\\ve{C}-\\ve{d}$, $\\ve{H}\\ve{d}=\\ve{g}$ and $\\ve{g}=\\nabla \\mathcal{L}$, $\\ve{H}=\\nabla^2\\mathcal{L}$. The gradient $\\ve{g}$ and Hessian $\\ve{H}$ are,\n\\begin{align}\n    \\ve{g} &= -\\frac{\\alpha}{\\sigma^2}(\\ve{F}-\\alpha\\ve{C}-\\beta\\ve{1}) + \\frac{1}{\\lambda\\Delta}\\left[ \\ve{M}^T(\\ve{MC}) + \\lambda\\Delta\\ve{M}^T\\ve{1}\\right] \\\\\n    \\ve{H} &= \\frac{\\alpha^2}{\\sigma^2}\\ve{I} + \\frac{1}{\\lambda\\Delta}\\ve{M}^T\\ve{M}\n\\end{align}\nIn the python implementation, we let $\\alpha=1.0$ and $\\beta=0.0$. Pseudo code can be found in Algo \\ref{algo:fast-wiener}.\n\\begin{algorithm}[htbp]\n    \\caption{Pseudo code (python) for wiener filter}\\label{algo:fast-wiener}\n    \\begin{algorithmic}[1]\n        \\STATE Initialize $\\ve{F}=(\\ve{F}-\\mathrm{mean}(\\ve{F}))\/\\mathrm{max}(\\abs{\\ve{F}})$, $\\sigma=0.1\\norm{\\ve{F}}_2$\n        \\STATE Calculate $\\mathcal{L}_0$\n        \\FOR{$i$ in $1\\cdots$ iterMax}\n        \\STATE Calculate $\\ve{g}$, $\\ve{H}$ and $\\ve{d}=\\mathrm{spsolve}(\\ve{H},\\ve{g})$\n        \\STATE Calculate $\\ve{C}=\\ve{C} - \\ve{d}$\n        \\STATE Calculate $\\mathcal{L}_i$\n        \\IF{$\\mathcal{L}_{i}<\\mathcal{L}_{i-1}+\\mathrm{gtol}$}\n        \\STATE $\\ve{n}=\\ve{N}$\n        \\STATE $\\sigma=\\sqrt{\\norm{\\ve{F}-\\ve{C}}_2^2\/T}$\n        \\ENDIF\n        \\ENDFOR\n        \\STATE $\\ve{n}=\\ve{n}\/\\mathrm{max}(\\ve{n})$\n    \\end{algorithmic}\n\\end{algorithm}\n\n\\section{Simulation Results}\nWe generated synthetic calcium traces with $T=2000$, $\\Delta=20$ms, $\\lambda=0.1$, $\\tau=1.5$. Randomized noise were added with $0.2$ standard deviation. Py-oopsi and wiener filter are used to reconstruct the spikes from calcium fluorescence, where only $\\Delta$ is known a prior. The results are shown in Figure \\ref{fig:demo}\n\n\\begin{figure}[htbp]\n    \\centering\n    \\includegraphics[width=5in]{demo}\n    \\caption{Reconstruct spikes from calcium fluorescence. (a) The synthetic calcium trace. (b), (c), (d) are reconstructed spikes by py-oopsi, wiener filter and discretized binning, respectively.}\n    \\label{fig:demo}\n\\end{figure}\n\n\n\n\\ifCLASSOPTIONcaptionsoff\n  \\newpage\n\\fi\n\n\\bibliographystyle{IEEEtran}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
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+{"text":"\\section{Introduction and preliminaries}\n\n\\subsection{Homomorphisms and derivations}\n\nThe study of additive mappings from a ring into another ring which\npreserve squares was initiated by G.~Ancochea in \\cite{Anc42} in\nconnection with problems arising in projective geometry. Later,\nthese results were strengthened by (among others) Kaplansky\n\\cite{Kap} and Jacobson--Rickart \\cite{JR}.\n\n Let $R, R'$ be rings, the mapping $\\varphi:R\\rightarrow R'$ is called a \\emph{homomorphism} if\n\\[\n \\varphi(a+b)=\\varphi(a)+\\varphi(b)\n\\qquad \\left(a, b\\in R\\right)\n\\]\nand\n\\[\n \\varphi(ab)=\\varphi(a)\\varphi(b)\n\\qquad \\left(a, b\\in R\\right).\n\\]\nFurthermore, the function $\\varphi:R\\to R'$ is an\n\\emph{anti-homomorphism} if\n\\[\n \\varphi(a+b)=\\varphi(a)+\\varphi(b)\n\\qquad \\left(a, b\\in R\\right)\n\\]\nand\n\\[\n \\varphi(ab)=\\varphi(b)\\varphi(a)\n\\qquad \\left(a, b\\in R\\right).\n\\]\n\nHenceforth, $\\mathbb{N}$ will denote the set of the positive\nintegers. Let $n\\in\\mathbb{N}, n\\geq 2$ be fixed. \nThe function $\\varphi:R\\rightarrow R'$ is called an $n$-Jordan\nhomomorphism if\n\\[\n\\varphi(a+b)=\\varphi(a)+\\varphi(b) \\qquad \\left(a, b\\in R\\right)\n\\]\nand\n\\[\n \\varphi(a^{n})=\\varphi(a)^{n}\n\\qquad \\left(a\\in R\\right).\n\\]\nFinally, we remark that in case $n=2$ we speak about homomorphisms\nand Jordan homomorphisms, respectively. It was G.~Ancochea who\nfirstly dealt with the connection of Jordan homomorphisms and\nhomomorphisms, see \\cite{Anc42}. These results were\ngeneralized and extended in several ways, see for instance\n\\cite{JR}, \\cite{Kap}, \\cite{Zel68}. \n\n\nLet $n\\in\\mathbb{N}$, we say that a ring $R$ is \\emph{of\ncharacteristic larger than $n$} if $n!x=0$ implies that $x=0$. The\nring $R$ is termed to be a \\emph{prime ring} if\n$ a, b\\in R$ and $aRb=\\left\\{0\\right\\}$ imply that either $a=0$ or $b=0$. \nIn \\cite{Her} I.N.~Herstein proved that \nif $\\varphi$ is a Jordan homomorphism of a ring $R$\n\\emph{onto} a prime ring $R'$ of characteristic different from $2$\nand $3$, then either $\\varphi$ is a homomorphism or an\nanti-homomorphism.\n\n\nFurthermore, in the above-mentioned paper \\cite{Her}, \nnot only Jordan homomorphisms but also $n$-Jordan\nmappings were considered and he proved the following statement. \n\\begin{thm}\nLet $\\varphi$ be an $n$-Jordan\nhomomorphism from a ring $R$ \\textbf{onto} a prime ring $R'$ and assume that $R'$ has \ncharacteristic larger than $n$, suppose further that $R$ has a unit\nelement. Then $\\varphi=\\varepsilon\\tau$ where $\\tau$ is either a\nhomomorphism or an anti-homomorphism and $\\varepsilon$  is an\n$(n-1)$st root of unity lying in the center of $R'$.\n\\end{thm}\n\n\nBesides homomorphisms, derivations also play a key role in the theory of rings and fields. Concerning this notion, we will follow \\cite[Chapter 14]{Kuc}. \n\nLet $Q$ be a ring and let $P$ be a subring of $Q$.\nA function $d\\colon P\\rightarrow Q$ is called a \\emph{derivation}\\index{derivation} if it is additive,\ni.e. \n\\[\nd(x+y)=d(x)+d(y)\n\\quad\n\\left(x, y\\in P\\right)\n\\]\nand also satisfies the so-called \\emph{Leibniz rule}\\index{Leibniz rule}, i.e.  equation\n\\[\nd(xy)=d(x)y+xd(y)\n\\quad\n\\left(x, y\\in P\\right). \n\\]\n\nFundamental examples for derivations are the following ones. \n\n\nLet $\\mathbb{F}$ be a field, and let in the above definition $P=Q=\\mathbb{F}[x]$\nbe the ring of polynomials with coefficients from $\\mathbb{F}$. For a polynomial\n$p\\in\\mathbb{F}[x]$, $p(x)=\\sum_{k=0}^{n}a_{k}x^{k}$, define the function\n$f\\colon \\mathbb{F}[x]\\rightarrow\\mathbb{F}[x]$ as\n\\[\nf(p)=p',\n\\]\nwhere $p'(x)=\\sum_{k=1}^{n}ka_{k}x^{k-1}$ is the derivative of the polynomial $p$.\nThen the function $f$ clearly fulfills\n\\[\nf(p+q)=f(p)+f(q)\n\\]\nand\n\\[\nf(pq)=pf(q)+qf(p)\n\\]\nfor all $p, q\\in\\mathbb{F}[x]$. Hence $f$ is a derivation.\n\n\n\n Let $(\\mathbb{F}, +, \\cdot)$ be a field, and suppose that we are given a derivation \n $f\\colon \\mathbb{F}\\to \\mathbb{F}$. We define the mapping $f_{0}\\colon \\mathbb{F}[x]\\to \\mathbb{F}[x]$ in the following way. \nIf $p\\in \\mathbb{F}[x]$ has the form \n\\[\n p(x)=\\sum_{k=0}^{n}a_{k}x^{k}, \n\\]\nthen let \n\\[\n f_{0}(p)= p^{f}(x)=\\sum_{k=0}^{n}f(a_{k})x^{k}. \n\\]\nThen $f_{0}\\colon \\mathbb{F}[x]\\to \\mathbb{F}[x]$ is a derivation. \n\n\nIt is well-known that in case of additive functions, Hamel bases play an important role. \nAs \\cite[Theorem 14.2.1]{Kuc} shows in case of derivations, algebraic bases are fundamental. \n\n\\begin{thm}\\label{T14.2.1}\nLet $(\\mathbb{K}, +,\\cdot)$ be a field of characteristic zero, let $(\\mathbb{F}, +,\\cdot)$\nbe a subfield of $(\\mathbb{K}, +,\\cdot)$, let $S$ be an algebraic base of $\\mathbb{K}$ over $\\mathbb{F}$,\nif it exists, and let $S=\\emptyset$ otherwise.\nLet $f\\colon \\mathbb{F}\\to \\mathbb{K}$ be a derivation.\nThen, for every function $u\\colon S\\to \\mathbb{K}$,\nthere exists a unique derivation $g\\colon \\mathbb{K}\\to \\mathbb{K}$\nsuch that $g \\vert_{\\mathbb{F}}=f$ and $g \\vert_{S}=u$.\n\\end{thm}\n\n\n\n\n\n\n\\subsection{The symmetrization method}\n\nWhile proving our results, the so-called Polarization formula for multi-additive functions and the symmetrization method will play a key role. In this subsection the most important notations and statements are summarized. Here we follow the monograph \\cite{Sze91}. \n\n\n\\begin{dfn}\n Let $G, S$ be commutative semigroups, $n\\in \\mathbb{N}$ and let $A\\colon G^{n}\\to S$ be a function.\n We say that $A$ is \\emph{$n$-additive} if it is a homomorphism of $G$ into $S$ in each variable.\n If $n=1$ or $n=2$ then the function $A$ is simply termed to be \\emph{additive}\n or \\emph{bi-additive}, respectively.\n\\end{dfn}\n\nThe \\emph{diagonalization} or \\emph{trace} of an $n$-additive\nfunction $A\\colon G^{n}\\to S$ is defined as\n \\[\n  A^{\\ast}(x)=A\\left(x, \\ldots, x\\right)\n  \\qquad\n  \\left(x\\in G\\right).\n \\]\nAs a direct consequence of the definition each $n$-additive function\n$A\\colon G^{n}\\to S$ satisfies\n\\[\n A(x_{1}, \\ldots, x_{i-1}, kx_{i}, x_{i+1}, \\ldots, x_n)\n =\n kA(x_{1}, \\ldots, x_{i-1}, x_{i}, x_{i+1}, \\ldots, x_{n})\n \\qquad \n \\left(x_{1}, \\ldots, x_{n}\\in G\\right)\n\\]\nfor all $i=1, \\ldots, n$, where $k\\in \\mathbb{N}$ is arbitrary. The\nsame identity holds for any $k\\in \\mathbb{Z}$ provided that $G$ and\n$S$ are groups, and for $k\\in \\mathbb{Q}$, provided that $G$ and $S$\nare linear spaces over the rationals. For the diagonalization of $A$\nwe have\n\\[\n A^{\\ast}(kx)=k^{n}A^{\\ast}(x)\n \\qquad\n \\left(x\\in G\\right).\n\\]\n\nThe above notion can also be extended for the case $n=0$ by letting \n$G^{0}=G$ and by calling $0$-additive any constant function from $G$ to $S$. \n\nOne of the most important theoretical results concerning\nmultiadditive functions is the so-called \\emph{Polarization\nformula}, that briefly expresses that every $n$-additive symmetric\nfunction is \\emph{uniquely} determined by its diagonalization under\nsome conditions on the domain as well as on the range. Suppose that\n$G$ is a commutative semigroup and $S$ is a commutative group. The\naction of the {\\emph{difference operator}} $\\Delta$ on a function\n$f\\colon G\\to S$ is defined by the formula\n\\[\\Delta_y f(x)=f(x+y)-f(x)\n\\qquad\n\\left(x, y\\in G\\right). \\]\nNote that the addition in the argument of the function is the\noperation of the semigroup $G$ and the subtraction means the inverse\nof the operation of the group $S$.\n\n\\begin{thm}[Polarization formula]\\label{Thm_polarization}\n Suppose that $G$ is a commutative semigroup, $S$ is a commutative group, $n\\in \\mathbb{N}$.\n If $A\\colon G^{n}\\to S$ is a symmetric, $n$-additive function, then for all\n $x, y_{1}, \\ldots, y_{m}\\in G$ we have\n \\[\n  \\Delta_{y_{1}, \\ldots, y_{m}}A^{\\ast}(x)=\n  \\left\\{\n  \\begin{array}{rcl}\n   0 & \\text{ if} & m>n \\\\\n   n!A(y_{1}, \\ldots, y_{m}) & \\text{ if}& m=n.\n  \\end{array}\n  \\right.\n \\]\n\n\\end{thm}\n\n\\begin{cor}\n Suppose that $G$ is a commutative semigroup, $S$ is a commutative group, $n\\in \\mathbb{N}$.\n If $A\\colon G^{n}\\to S$ is a symmetric, $n$-additive function, then for all $x, y\\in G$\n \\[\n  \\Delta^{n}_{y}A^{\\ast}(x)=n!A^{\\ast}(y).\n\\]\n\\end{cor}\n\n\\begin{lem}\n\\label{mainfact}\n  Let $n\\in \\mathbb{N}$ and suppose that the multiplication by $n!$ is surjective in the commutative semigroup $G$ or injective in the commutative group $S$. Then for any symmetric, $n$-additive function $A\\colon G^{n}\\to S$, $A^{\\ast}\\equiv 0$ implies that\n  $A$ is identically zero, as well.\n\\end{lem}\n\n\n\\begin{dfn}\n Let $G$ and $S$ be commutative semigroups, a function $p\\colon G\\to S$ is called a \\emph{generalized polynomial} from $G$ to $S$ if it has a representation as the sum of diagonalizations of symmetric multi-additive functions from $G$ to $S$. In other words, a function $p\\colon G\\to S$ is a \n generalized polynomial if and only if, it has a representation \n \\[\n  p= \\sum_{k=0}^{n}A^{\\ast}_{k}, \n \\]\nwhere $n$ is a nonnegative integer and $A_{k}\\colon G^{k}\\to S$ is a symmetric, $k$-additive function for each \n$k=0, 1, \\ldots, n$. In this case we also say that $p$ is a generalized polynomial \\emph{of degree at most $n$}. \n\nLet $n$ be a nonnegative integer, functions $p_{n}\\colon G\\to S$ of the form \n\\[\n p_{n}= A_{n}^{\\ast}, \n\\]\nwhere $A_{n}\\colon G^{n}\\to S$ are the so-called \\emph{generalized monomials of degree $n$}. \n\\end{dfn}\n\n\\begin{rem}\n Obviously, generalized monomials \nof degree $0$ are constant functions and generalized monomials of degree $1$ are additive functions. \n\n Furthermore, generalized monomials of degree $2$ will be termed \\emph{quadratic functions}. \n\\end{rem}\n\n\n\n\n\\subsection{Polynomial functions}\n\n\nAs Laczkovich \\cite{Lac04} enlightens, on groups there are several polynomial notions. One of them is that we introduced in subsection 1.2, that is the notion of generalized polynomials. \nAs we will see in the forthcoming sections, not only this notion, but also that of \\emph{(normal) polynomials} will be important. The definitions and results recalled here can be found in \\cite{Sze91}. \n\nThroughout this subsection $G$ is assumed to be  a commutative group (written additively).\n\n\\begin{dfn}\n{\\it Polynomials} are elements of the algebra generated by additive\nfunctions over $G$. Namely, if $n$ is a positive integer,\n$P\\colon\\mathbb{C}^{n}\\to \\mathbb{C}$ is a (classical) complex\npolynomial in\n $n$ variables and $a_{k}\\colon G\\to \\mathbb{C}\\; (k=1, \\ldots, n)$ are additive functions, then the function\n \\[\n  x\\longmapsto P(a_{1}(x), \\ldots, a_{n}(x))\n \\]\nis a polynomial and, also conversely, every polynomial can be\nrepresented in such a form.\n\\end{dfn}\n\n\\begin{rem}\n For the sake of easier distinction, at some places polynomials will be called normal polynomials. \n\\end{rem}\n\n\n\n\n\\begin{rem}\n We recall that the elements of $\\mathbb{N}^{n}$ for any positive integer $n$ are called\n ($n$-dimensional) \\emph{multi-indices}.\n Addition, multiplication and inequalities between multi-indices of the same dimension are defined component-wise.\n Further, we define $x^{\\alpha}$ for any $n$-dimensional multi-index $\\alpha$ and for any\n $x=(x_{1}, \\ldots, x_{n})$ in $\\mathbb{C}^{n}$ by\n \\[\n  x^{\\alpha}=\\prod_{i=1}^{n}x_{i}^{\\alpha_{i}}\n \\]\nwhere we always adopt the convention $0^{0}=1$. We also use the\nnotation $\\left|\\alpha\\right|= \\alpha_{1}+\\cdots+\\alpha_{n}$. With\nthese notations any polynomial of degree at most $N$ on the\ncommutative semigroup $G$ has the form\n\\[\n p(x)= \\sum_{\\left|\\alpha\\right|\\leq N}c_{\\alpha}a(x)^{\\alpha}\n \\qquad\n \\left(x\\in G\\right),\n\\]\nwhere $c_{\\alpha}\\in \\mathbb{C}$ and $a=(a_1, \\dots, a_n) \\colon\nG\\to \\mathbb{C}^{n}$ is an additive function. Furthermore, the\n\\emph{homogeneous term of degree $k$} of $p$ is\n\\[\n \\sum_{\\left|\\alpha\\right|=k}c_{\\alpha}a(x)^{\\alpha} .\n\\]\n\\end{rem}\n\n\n\\begin{lem}[Lemma 2.7 of \\cite{Sze91}]\\label{L_lin_dep}\n Let $G$ be a commutative group,\n $n$ be a positive integer and let\n \\[\n  a=\\left(a_{1}, \\ldots, a_{n}\\right),\n \\]\nwhere $a_{1}, \\ldots, a_{n}$ are linearly independent complex valued\nadditive functions defined on $G$. Then the monomials\n$\\left\\{a^{\\alpha}\\right\\}$ for different multi-indices are linearly\nindependent.\n\\end{lem}\n\n\\begin{dfn}\nA function $m\\colon G\\to \\mathbb{C}$ is called an \\emph{exponential}\nfunction if it satisfies\n\\[\n m(x+y)=m(x)m(y)\n \\qquad\n \\left(x,y\\in G\\right).\n\\]\nFurthermore, on an  \\emph{exponential polynomial} we mean a linear\ncombination of functions of the form $p \\cdot m$, where $p$ is a\npolynomial and $m$ is an exponential function.\n\\end{dfn}\n\n\n\n\\begin{dfn}\n Let $G$ be an Abelian group and $V\\subseteq \\mathbb{C}^G$ a set of functions. We say that $V$ is {\\it translation invariant} if for every $f\\in V$ the function $\\tau_{g}f\\in V$ also holds for all $g\\in G$, where\n \\[\n  \\tau_{g}f(h)= f(h+g)\n  \\qquad\n  \\left(h\\in G\\right).\n \\]\n \\end{dfn}\n\n \n In view of Theorem 10.1 of Sz\\'ekelyhidi \\cite{Sze91}, any finite dimensional translation invariant linear \n space of complex valued functions on a commutative group consists of exponential polynomials. \n This implies that if $G$ is a commutative group, then any function \n $f\\colon G\\to \\mathbb{C}$, satisfying the functional equation \n \\[\n  f(x+y)= \\sum_{i=1}^{n}g_{i}(x)h_{i}(y) \n  \\qquad \n  \\left(x, y\\in G\\right)\n \\]\nfor some positive integer $n$ and functions $g_{i}, h_{i}\\colon G\\to \\mathbb{C}$ ($i=1, \\ldots, n$), \nis an exponential polynomial of degree at most $n$. \n \n\nThis enlightens the connection between generalized polynomials and polynomials. It is easy to see that \neach polynomial, that is, any function of the form \n\\[\n  x\\longmapsto P(a_{1}(x), \\ldots, a_{n}(x)), \n \\]\nwhere $n$ is a positive integer,\n$P\\colon\\mathbb{C}^{n}\\to \\mathbb{C}$ is a (classical) complex\npolynomial in\n $n$ variables and $a_{k}\\colon G\\to \\mathbb{C}\\; (k=1, \\ldots, n)$ are additive functions, is a generalized polynomial. The converse however is in general not true. A complex-valued generalized polynomial $p$ defined on a commutative group $G$ is a polynomial \\emph{if and only if} its variety (the linear space spanned by its translates) is of \\emph{finite} dimension. \nTo make the situation more clear, here we also recall Theorem 13.4 from Sz\\'ekelyhidi \\cite{Sze14}. \n \n \\begin{thm}\\label{thm_torsion}\n  The torsion free rank of a commutative group is finite \\emph{if and only if} every generalized polynomial on the group is a polynomial. \n \\end{thm}\n\n \n\\section{Results}\n\nIn this section $\\mathbb{F}$ is assumed to be a field with $\\mathrm{char}(\\mathbb{F})=0$.  \nLet further $n$ be a positive integer and $P\\in \\mathbb{F}[x]$ and $Q\\in \\mathbb{C}[x]$ be polynomials. Our aim is to prove characterization theorems for generalized polynomials $f\\colon \\mathbb{F}\\to \\mathbb{C}$ of degree at most $n$ that also fulfill equation \n\\[\n f(P(x))= Q(f(x))\n\\]\nfor each $x\\in \\mathbb{F}$. \n\n\nBefore presenting the results of this paper, we note that related problems have already been considered by Z.~Boros and E.~Garda--M\\'{a}ty\\'{a}s in \\cite{BorGar18, BorGar20, Gar19} and also by M.~Amou in \\cite{Amo20}. In these papers the authors consider monomial functions $f, g\\colon\\mathbb{R}\\to \\mathbb{R}$ of degree $n$, where $n\\in \\mathbb{N}$, $n\\geq 2$, which satisfy the conditional equation \n\\[\n x^{n}f(y)=y^{n}g(x)\n\\]\nfor all points $(x, y)$ on a specified planar curve. \n\nRoughly speaking, the following lemmata tell us that the problem investigated in this paper is meaningful in the sense that for any positive integer $n$, there \\emph{do exist} generalized polynomials of degree at most $n$ that satisfy the above identity. \n\n\n\\begin{lem}\\label{lemma3}\n Let $\\mathbb{F}$ be a field with $\\mathrm{char}(\\mathbb{F})=0$, $n$ be a positive integer and \n $\\varphi_{1}, \\ldots, \\varphi_{n}\\colon \\mathbb{F}\\to \\mathbb{C}$ be homomorphisms. Define the function $f$ on \n $\\mathbb{F}$ by \n \\[\n  f(x)= \\varphi_{1}(x)\\cdots \\varphi_{n}(x)\n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right). \n \\]\nThen the following statements hold true. \n\\begin{enumerate}[(i)]\n \\item The function $f\\colon \\mathbb{F}\\to \\mathbb{C}$ is a generalized polynomial of degree $n$. \n \\item The function $f\\colon \\mathbb{F}\\to \\mathbb{C}$ is a polynomial of degree $n$.\n \\item For any positive integer $k$, we have \n \\[\n  f(x^{k})=f(x)^{k} \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right). \n \\] \n\\end{enumerate}\n\\end{lem}\n\n\\begin{proof}\n Firstly, observe that the function $f$ defined on $\\mathbb{F}$ by \n \\[\n  f(x)= \\varphi_{1}(x)\\cdots \\varphi_{n}(x)\n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right)\n \\]\nis the trace of the symmetric $n$-additive mapping $F$ defined by \n\\[\n F(x_{1}, \\ldots, x_{n}) = \\frac{1}{n!}\\sum_{\\sigma\\in \\mathscr{S}_{n}}\\varphi_{1}(x_{\\sigma(1)})\\cdots \\varphi_{n}(x_{\\sigma(n)}) \n \\qquad \n \\left(x \\in \\mathbb{F}\\right). \n\\]\nThus $f$ is a generalized monomial of degree $n$. \nSecondly, in view of the definition of the function $f$ we immediately get that it is also a monomial of degree $n$. Indeed, let \n\\[\n P(x_{1}, \\ldots, x_{n})= x_{1}\\cdots x_{n} \n \\qquad \n \\left(x\\in \\mathbb{C}\\right)\n\\]\nand then $f$ can be written as $f= P\\circ \\varphi$, where $\\varphi\\colon \\mathbb{F}\\to \\mathbb{C}^{n}$ is \n\\[\n \\varphi(x)= \\left(\\varphi_{1}(x), \\ldots, \\varphi_{n}(x)\\right) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\nThirdly, recall that in case $\\varphi$ is a homomorphism between $\\mathbb{F}$ and $\\mathbb{C}$, then \nwe also have \n\\[\n\\varphi(x^{k}) = \\varphi(x)^{k}\n\\]\nfor each $x\\in \\mathbb{K}$. Therefore, \n\\[\n f(x^{k}) = \\varphi_{1}(x^{k})\\cdots \\varphi_{n}(x^{k}) = \\varphi_{1}(x)^{k}\\cdots \\varphi_{n}(x)^{k} \n =\n \\left(\\varphi_{1}(x)\\cdots\\varphi_{n}(x)\\right)^{k}\n = f(x)^{k} \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\n\\end{proof}\n\n\n\\begin{lem}\\label{lemma4}\n Let $\\mathbb{F}\\subset \\mathbb{C}$ be a field\n and $d\\colon \\mathbb{F}\\to \\mathbb{C}$ be a derivation and consider the function \n $f\\colon \\mathbb{F}\\to \\mathbb{C}$ defined by \n \\[\n  f(x)= d(x^{n}) \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right). \n \\]\nThen the following statements are satisfied. \n\\begin{enumerate}[(i)]\n \\item The function $f\\colon \\mathbb{F}\\to \\mathbb{C}$ is a generalized polynomial of degree $n$. \n \\item The function $f\\colon \\mathbb{F}\\to \\mathbb{C}$ is a polynomial of degree $n$.\n \\item For any positive integer $k\\geq 2$, we have \n \\[\n  f(x^{k})=kx^{(k-1)n}f(x)\n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right). \n \\] \n\\end{enumerate}\n\\end{lem}\n\n\n\\begin{proof}\n Let $\\mathbb{F}\\subset \\mathbb{C}$ be a field and  \n $d\\colon \\mathbb{F}\\to \\mathbb{C}$ be a derivation and let us consider the function \n $f\\colon \\mathbb{F}\\to \\mathbb{C}$ defined through \n \\[\n  f(x)= d(x^{n}) \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right). \n \\]\nObserve that in this case the function $F_{n}\\colon \\mathbb{F}^{n}\\to \\mathbb{C}$ \ndefined by \n\\[\n F_{n}(x_{1}, \\ldots, x_{n})= d\\left(x_{1}\\cdots x_{n}\\right) \n \\qquad \n \\left(x_{1}, \\ldots, x_{n}\\in \\mathbb{F}\\right)\n\\]\nis a symmetric and $n$-additive function. Furthermore, its trace is $f$, showing that $f$ is a generalized monomial of degree $n$. \n\nAt the same time, since $d$ is a derivation, we also have that \n\\[\n d(x^{n})= nx^{n-1}d(x) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right), \n\\]\nyielding that \n\\[\n f(x)= nx^{n-1}d(x)= P(x, d(x)) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right), \n\\]\nwith the two-variable complex polynomial\n\\[\n P(x, y)= nx^{n-1}y \n \\qquad \n \\left(x, y\\in \\mathbb{C}\\right). \n\\]\nTherefore, $f$ is a monomial of degree $n$. \n\nFinally, let $k\\geq 2$  be a positive integer. Then \n\\[\n f(x^{k})= d\\left((x^{k})^{n}\\right)= d(x^{kn})= kn x^{kn-1}d(x)\n =\n kx^{(k-1)n}\\cdot \\left(nx^{n-1}d(x)\\right)= kx^{(k-1)n}f(x) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\n\\end{proof}\n\n\n\n\\begin{lem}\\label{lemma5}\n Let $n$ and $k$ be positive integers, $\\alpha\\in \\mathbb{N}^{n}$ be an n-dimensional multi-index, $\\mathbb{F}$ be a field with $\\mathrm{char}(\\mathbb{F})=0$ and \n $a_{1}, \\ldots, a_{n}\\colon \\mathbb{F} \\allowbreak\\to \\mathbb{C}$ be additive functions and \n $a=(a_{1}, \\ldots, a_{n})$. Then the mapping \n \\[\n  \\mathbb{F}\\ni x\\longmapsto a^{\\alpha}(x^{k})\n \\]\nis a generalized monomial of degree $|\\alpha|\\cdot k$. \n\\end{lem}\n\n\\begin{proof}\n Let $n$ and $k$ be positive integers, $\\alpha\\in \\mathbb{N}^{n}$ be an $n$-dimensional multi-index and \n $a_{1}, \\ldots, a_{n}\\colon \\mathbb{F} \\allowbreak\\to \\mathbb{C}$ be additive functions. \n If $\\alpha= (\\alpha_{1}, \\ldots, \\alpha_{n})$, then the function \n \\[\n \\mathbb{F}\\ni  x\\longmapsto a_{1}^{\\alpha_{1}}(x^{k})\\cdots a_{n}^{\\alpha_{n}}(x^{k}) \n \\]\nis the trace of the $|\\alpha|\\cdot k$-additive function $F$ defined by \n\\[\n F(x_{1, 1}, \\ldots, x_{\\alpha_{n}, k})= \n \\prod_{i=1}^{n}\\prod_{j=1}^{\\alpha_{i}}a_{i}(x_{j, 1}\\cdots x_{j, k}). \n\\]\n\\end{proof}\n\nLet $\\mathbb{F}$ be a field and denote $\\mathbb{F}^{\\times}$ the multiplicative group of the nonzero elements of $\\mathbb{F}$. \nObviously, every (normal) polynomial $p\\colon \\mathbb{F}^{\\times}\\to \\mathbb{C}$ is a generalized polynomial, too. Furthermore, in view of Theorem \\ref{thm_torsion} we know that these are the only generalized polynomials if the torsion free rank of $\\mathbb{F}^{\\times}$ is finite. For example if we take \n$\\mathbb{F}=\\mathbb{Q}$ (the field of the rationals), then this is the case. While for larger fields, the same does not hold in general. Despite Theorem \\ref{thm_torsion} gives an elegant criterion for the above problem, with the aid of this result it is not too easy to imagine how generalized polynomials look like. From one hand, this is the purpose of the remark below. \n\n\n\\begin{rem}\\label{rem3}\n Notice that the above lemma cannot be in general strengthened. To see this let \n $a\\colon \\mathbb{F}\\to \\mathbb{C}$ be a non-identically zero additive function. \n As the following proposition shows, the mapping \n \\[\n  \\mathbb{F} \\ni x\\longmapsto a(x^{2})\n \\]\n is a generalized monomial of degree two that is not necessarily a (normal) monomial. \n \\end{rem}\n \n \\begin{prop}\n  Let $\\mathbb{F}\\subset \\mathbb{C}$ be a field and $a\\colon \\mathbb{F}\\to\\mathbb{C}$ be a non-identically zero additive function. The mapping \n  \\[\n  \\mathbb{F} \\ni x\\longmapsto a(x^{2})\n  \\]\n  is a monomial of degree two if and only if \n  \\[\n   a(x)= \\varphi(d(x))+a(1)\\cdot \\varphi(x)\n   \\qquad \n   \\left(x\\in \\mathbb{F}\\right)\n  \\]\nor \n\\[\n a(x)= \\alpha \\varphi_{1}(x)+\\beta \\varphi_{2}(x) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right), \n\\]\nwhere $\\alpha, \\beta$ are complex constants, $d\\colon \\mathbb{F}\\to \\mathbb{C}$ is a non-identically zero derivation and $\\varphi, \\varphi_{1}, \\varphi_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$ are homorphisms such that $\\varphi_{1}$ and $\\varphi_{2}$ are linearly independent. \n \\end{prop}\n\n \n\\begin{proof} \n Let $\\mathbb{F}\\subset \\mathbb{C}$ be a field and $a\\colon \\mathbb{F}\\to\\mathbb{C}$ be a non-identically zero additive function.\nAssume that the mapping appearing in the proposition is a monomial of degree two. Then there exist linearly independent additive functions \n$a_{1}, a_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$ and complex constants $\\alpha_{i, j}$, $i, j=1, 2$ such that \n\\[\n a(x^{2})= \\alpha_{1, 1}a_{1}(x)^{2}+(\\alpha_{1, 2}+\\alpha_{2, 1})a_{1}(x)a_{2}(x)+\\alpha_{2, 2}a_{2}(x)^{2}\n\\]\nfor each $x\\in \\mathbb{F}$. Since both sides of the above identity are traces of symmetric bi-additive functions, we can use the Polarization Formula to get that \n\\[\n a(xy)= \\alpha_{1, 1}a_{1}(x)a_{1}(y)+\\frac{\\alpha_{1, 2}+\\alpha_{2, 1}}{2}\\left(a_{1}(x)a_{2}(y)+a_{1}(y)a_{2}(x)\\right)+\\alpha_{2, 2}a_{2}(x)a_{2}(y)\n\\]\nis fulfilled by any $x, y\\in \\mathbb{F}$. \nAfter some rearrangement, we have \n\\[\n a(xy)\n = a_{1}(x) \\cdot \\left(\\alpha_{1, 1}a_{1}(y)+\\frac{\\alpha_{1, 2}+\\alpha_{2, 1}}{2}a_{2}(y)+\n \\right)\n +a_{2}(x)\\cdot \\left(\\frac{\\alpha_{1, 2}+\\alpha_{2, 1}}{2} a_{1}(y)+\\alpha_{2, 2}a_{2}(y)\\right)\n\\]\nfor all $x, y\\in \\mathbb{F}$, which is a Levi-Civita equation on $\\mathbb{F}^{\\times}$ (on the multiplicative group of the non-zero elements of $\\mathbb{F}$). Applying the result of \\cite[pages 93--94]{Sze91}, we deduce that there exist complex constants $\\alpha, \\beta$, an additive function \n$l\\colon \\mathbb{F}^{\\times}\\to \\mathbb{C}$ and exponentials $m, m_{1}, m_{2}\\colon \\mathbb{F}^{\\times}\\to \\mathbb{C}$, $m_{1}$ and $m_{2}$ are linearly independent such that \n\\[\n a(x)= (\\alpha l(x)+\\beta) m(x) \n \\qquad \n \\left(x\\in \\mathbb{F}^{\\times}\\right)\n\\]\nor \n\\[\n a(x)= m_{1}(x)+m_{2}(x) \n \\qquad \n \\left(x\\in \\mathbb{F}^{\\times}\\right). \n\\]\nRecall that on the group $\\mathbb{F}^{\\times}$ multiplication as group operation is considered. Therefore these functions fulfill the following identities: \n\\[\n l(xy)= l(x)+l(y) \n \\qquad \n \\left(x, y\\in \\mathbb{F}^{\\times}\\right)\n\\]\nand \n\\[\n m(xy)= m(x)m(y) \n \\qquad \n \\left(x, y\\in \\mathbb{F}^{\\times}\\right)\n\\]\nas well as \n\\[\n m_{i}(xy)= m_{i}(x)m_{i}(y) \n \\qquad \n \\left(x, y\\in \\mathbb{F}^{\\times}, i=1, 2\\right). \n\\]\nAt the same time, the mapping $a$ was assumed to be additive, thus in the above representation we have \n\\[\n   a(x)=\\varphi(d(x))+ a(1)\\cdot\\varphi(x) \n   \\qquad \n   \\left(x\\in \\mathbb{F}\\right)\n  \\]\nor \n\\[\n a(x)= \\alpha \\varphi_{1}(x)+\\beta \\varphi_{2}(x) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right), \n\\]\nwhere $\\alpha, \\beta$ are complex constants, $d\\colon \\mathbb{F}\\to \\mathbb{C}$ is a non-identically zero derivation and $\\varphi, \\varphi_{1}, \\varphi_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$ are homomorphisms such that $\\varphi_{1}$ and $\\varphi_{2}$ are linearly independent. \n\nThe converse is obvious. \n\\end{proof} \n\n\n\\begin{rem}\n The proof of the previous proposition can be a starting point of further investigations. More precisely, if $n$ is a positive integer, $a\\colon \\mathbb{F}\\to \\mathbb{C}$ is a non-identically zero additive function and the mapping \n  \\[\n  \\mathbb{F} \\ni x\\longmapsto a(x^{2})\n  \\]\n  is a monomial of degree $n$, then there exist linearly independent additive functions \n  $a_{1}, \\ldots, a_{n}\\colon \\mathbb{F}\\to \\mathbb{C}$ and complex constants $\\alpha_{i, j}$, $i, j=1, \\ldots, n$ such that \n  \\[\n   a(x^{2})= \\sum_{i, j=1}^{n}\\alpha_{i, j}a_{i}(x)a_{j}(x) \n   \\qquad \n   \\left(x\\in \\mathbb{F}\\right). \n  \\]\nSince both sides of the above identity are traces of symmetric bi-additive functions, we can use the Polarization Formula to get that\n\\[\n a(xy)= \\sum_{i, j=1}^{n}\\frac{\\alpha_{i, j}+\\alpha_{j, i}}{2}\\left(a_{i}(x)a_{j}(y)+a_{j}(x)a_{i}(y)\\right)\n = \\sum_{i=1}^{n}\\widetilde{a_{i}}(x)\\widetilde{a_{j}}(y)\n\\]\nfor all $x, y\\in \\mathbb{F}^{\\times}$ which is a Levi-Civita equation on the group $\\mathbb{F}^{\\times}$. In other words, the mapping $a$ as a function restricted to the multiplicative group $\\mathbb{F}^{\\times}$, is a normal exponential polynomial of degree $n$. In view of the results of \\cite[page 43 and page 79]{Sze91}, \n\\[\n a(x)= \\sum_{j=1}^{k}P_{j}\\left(l_{j, 1}(x), l_{j, 2}(x), \\ldots, l_{j, n_{j}-1}(x)\\right)m_{j}(x) \n \\qquad \n \\left(x\\in \\mathbb{F}^{\\times}\\right), \n\\]\nwhere $k, n_{1}, \\ldots, n_{k}$ are positive integers, $m_{1}, \\ldots, m_{k}$ are different, non-zero com\\-plex-valued exponentials on the group $\\mathbb{F}^{\\times}$, further \n$\\left\\{l_{j, 1}, \\ldots, l_{j, n_{j}-1} \\right\\}$ are sets of linearly independent, com\\-plex-valued additive functions defined on $\\mathbb{F}^{\\times}$ for $j=1, \\ldots, k$ and \n$P_{j}\\colon \\mathbb{C}^{n_{j}-1}\\to \\mathbb{C}$ are complex polynomials of degree at most $n_{j}-1$ and in $n_{j}-1$ variables for each $j=1, \\ldots, k$. \n\nWe conjecture that as a continuation, a result of Kiss--Laczkovich \\cite{KisLac18} might be useful. According to Theorem 1.1 of this paper, $a\\colon \\mathbb{F}\\to \\mathbb{C}$ is an additive function with $a(1)=0$ and \n$D\/j$, as a map from the group $\\mathbb{F}^{\\times}$ to $\\mathbb{C}$, is a generalized polynomial of degree at most $n$ if and only if $a$ is a derivation of order at most $n$. Here $j$ denotes the identity map from $\\mathbb{F}$ to $\\mathbb{C}$. \n\\end{rem}\n\n\\begin{ex}\n Let $d\\colon \\mathbb{C}\\to \\mathbb{C}$ be a non-identically zero derivation. Due to Theorem \\ref{T14.2.1} such a mapping does exist. Furthermore, due to Theorem 14.5.1 of \\cite{Kuc}, there exist non-trivial endomorphisms of $\\mathbb{C}$ (trivial endomorphisms are meant the identically zero and the identity mapping, resp.). Let $\\varphi\\colon \\mathbb{C}\\to \\mathbb{C}$ be a non-trivial endomorphism. Then the mapping $a$ defined on $\\mathbb{C}$ by \n \\[\n  a(x)= d(x)+\\varphi(x) \n  \\qquad \n  \\left(C\\right)\n \\]\nis clearly additive and we have \n\\[\n a(x^2)= d(x^{2})+\\varphi(x^{2})= 2xd(x)+\\varphi(x)^{2} \n \\qquad \n \\left(x\\in \\mathbb{F}\\right), \n\\]\nshowing that the mapping \n\\[\n \\mathbb{C} \\ni x \\longmapsto a(x^{2})\n\\]\nis a generalized polynomial of degree exactly two and it is a (normal) polynomial of degree exactly \nthree. \n\nNote that the situation changes if the domain is the real field. Indeed, all homomorphisms \n$\\varphi\\colon \\mathbb{R}\\to \\mathbb{C}$ are trivial, i.e. they are either identically zero or they coincide with the identity map. Therefore if $d\\colon \\mathbb{R}\\to \\mathbb{C}$ is a non-identically zero derivation and we define \n\\[\n a(x)= d(x)+x \n \\qquad \n \\left(x\\in \\mathbb{R}\\right),\n\\]\nthen the mapping \\[\n \\mathbb{C} \\ni x \\longmapsto a(x^{2})\n\\]\nis a polynomial of degree exactly two. \n\\end{ex}\n\n\n\\begin{rem}\nFrom the above thoughts we obtain that if $a\\colon \\mathbb{F}\\to \\mathbb{C}$ is an additive function such that the mapping \n\\[\n \\mathbb{F} \\ni x \\longmapsto a(x^{2})\n\\]\nis a generalized monomial which is not a monomial, then for all positive integer $k\\geq 2$, the mapping \n\\[\n \\mathbb{F} \\ni x \\longmapsto a(x^{k})\n\\]\nis also a generalized monomial which is not a monomial. \n\nIndeed, observe that the above mapping is the trace of the symmetric and $k$-additive function $A_{k}$ defined on $\\mathbb{F}^{k}$ by \n\\[\n A_{k}(x_{1}, \\ldots, x_{k})= a(x_{1}\\cdots x_{k}) \n \\qquad \n \\left(x_{1}, \\ldots, x_{k}\\in \\mathbb{F}\\right). \n\\]\n\nIf there would exist a positive integer $k>2$ such that the mapping \n\\[\n \\mathbb{F} \\ni x \\longmapsto a(x^{k})\n\\]\nwould be a monomial, then all the translates of this mapping would also be generalized monomials, as well. \nBy the Polarization formula, we have  \n\\[\n \\Delta_{y}^{2}\\Delta^{k-2}_{1}a(x^{k})= k!A(y, y, 1, \\ldots, 1)= k!a(y^{2}) \n \\qquad \n \\left(x, y\\in \\mathbb{F}\\right). \n\\]\nFrom this we would deduce that the mapping \n\\[\n \\mathbb{F} \\ni y \\longmapsto a(y^{2})\n\\]\nis a monomial of degree two, which is a contradiction. \n\\end{rem}\n\n\n\\begin{lem}\\label{lemma_6}\n Let $k$ and $n$ be positive integers and $f\\colon \\mathbb{F}\\to \\mathbb{C}$ be a generalized monomial of degree n, where $\\mathbb{F}$ is assumed to be a field with $\\mathrm{char}(\\mathbb{F})=0$. Then the mapping \n \\[\n  \\mathbb{F} \\ni x \\longmapsto f(x^{k})\n \\]\nis a generalized monomial of degree $n\\cdot k$. \n\\end{lem}\n\n\\begin{proof}\n Since $f\\colon \\mathbb{F}\\to \\mathbb{C}$ is a generalized monomial of degree $n$, there exists an \n $n$-additive function $F_{n}\\colon \\mathbb{F}^{n}\\to \\mathbb{C}$ such that its trace is the function $f$. In this case, the mapping \n $F_{nk}\\colon \\mathbb{F}^{nk}\\to \\mathbb{C}$ defined by \n \\begin{multline*}\n  F_{nk}(x_{1, 1}, \\ldots, x_{n, k}) =\n  F_{n}(x_{1, 1} \\cdots x_{1, k}, x_{2, 1} \\cdots x_{2, k}, \\ldots, x_{n, 1} \\cdots x_{n, k})\n  \\\\\n  \\left(x_{i, j}\\in \\mathbb{F}, i=1, \\ldots, n, j=1, \\ldots, k\\right)\n \\end{multline*}\nis an $(n\\cdot k)$-additive function whose trace is \n\\[\n F_{nk}(x, \\ldots, x)= F_{n}(x^{k}, \\ldots, x^{k})= f(x^{k})\n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\n\\end{proof}\n\n\\begin{rem}\n The above lemma with a different proof can be found among others in \\cite{AicMoo21}. \n\\end{rem}\n\n\nNow we turn to deal with the main problem of this paper, which is the following. \nAssume $\\mathbb{F}$ to be a field. \nLet further $P\\in \\mathbb{F}[x]$ and $Q\\in \\mathbb{C}[x]$ be polynomials. Our aim is to prove characterization theorems for quadratic functions $f\\colon \\mathbb{F}\\to \\mathbb{C}$ that also fulfill equation \n\\[\n f(P(x))= Q(f(x))\n\\]\nfor each $x\\in \\mathbb{F}$. \n\n\nAs for the difficulty of the problem, it is an important condition that the function $f$ is supposed to be quadratic (that is, it is a \\emph{generalized} monomial of degree two). As the statement below shows, \nalthough the result is the same, the proof is much easier for normal monomials of degree two. \n\n\\begin{prop}\\label{Prop1}\n Let $\\mathbb{F}$ be a field with $\\mathrm{char}(\\mathbb{F})=0$ and $f\\colon \\mathbb{F}\\to \\mathbb{C}$ be a quadratic function that can be represented as \n \\[\n  f(x)= a_{1}(x)a_{2}(x) \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right)\n \\]\n with the aid of the additive functions $a_{1}, a_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$. \nThen equation \n \\begin{equation}\\label{Eq1_simp}\n  f(x^{2})= f(x)^{2}\n \\end{equation}\nholds for each $x\\in \\mathbb{F}$ \\emph{if and only if} there exist complex-valued non-trivial homomorphisms  $\\varphi_{1}, \\varphi_{2}$ defined on $\\mathbb{F}$ such that \n\\[\n f(x)= f(1)\\cdot \\varphi_{1}(x)\\varphi_{2}(x)\n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\nFurthermore, \n\\begin{enumerate}[(A)]\n \\item either $f(1)=0$ and then $f$ is identically zero;\n \\item or $f(1)=1$. \n\\end{enumerate}\n\\end{prop}\n\n\\begin{proof}\n Assume $\\mathbb{F}$ be a field and $f\\colon \\mathbb{F}\\to \\mathbb{C}$ be a quadratic function that can be represented as \n \\[\n  f(x)= a_{1}(x)a_{2}(x) \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right)\n \\]\n with the aid of the additive functions $a_{1}, a_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$. \n Then equation \\eqref{Eq1_simp} in terms of the additive functions $a_{1}$ and $a_{2}$ is \n \\[\n  a_{1}(x^{2})a_{2}(x^{2})= a_{1}(x)^{2}a_{2}(x)^{2} \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right). \n \\]\nSince both sides of this identity are traces of symmetric, $4$-additive functions, a simple application of the Polarization Formula leads to \n\\begin{multline}\\label{Eq1_simp_sym}\n a_{1}(xy)a_{2}(uv)+a_{1}(xu)a_{2}(yv)+a_{1}(xv)a_{2}(yu)\n \\\\\n +a_{1}(yu)a_{2}(xv)+a_{1}(yv)a_{2}(xu)+a_{1}(ux)a_{2}(xy)\n \\\\\n =\n a_{1}(x)a_{1}(y)a_{2}(u)a_{2}(v)+a_{1}(x)a_{1}(u)a_{2}(y)a_{2}(v)+a_{1}(x)a_{1}(v)a_{2}(y)a_{2}(u)\n \\\\\n +a_{1}(y)a_{1}(u)a_{2}(x)a_{2}(v)+a_{1}(y)a_{1}(v)a_{2}(x)a_{2}(u)+a_{1}(u)a_{1}(x)a_{2}(x)a_{2}(y)\n \\\\\n (x, y, u, v\\in \\mathbb{F}). \n\\end{multline}\nFrom this, with the substitution $x=y=u=v=1$, we immediately get that \n\\[\n a_{1}(1)\\,a_{2}(1)\\,\\left(a_{1}(1)\\,a_{2}(1)-1\\right)=0\n\\]\nand with the substitution $y=u=v=1$, \n\\[\n \\left(a_{1}(1)\\,a_{2}(1)-1\\right)\\,\\left(a_{1}(1)\\,a_{2}(x)+a_{2}(\n 1)\\,a_{1}(x)\\right)=0\n\\]\ncan be deduced for all $x\\in \\mathbb{F}$. \nAssume first that $a_{1}(1)\\,a_{2}(1)-1\\neq 0$, then $a_{1}(1)=0$ or $a_{2}(1)=0$. If $a_{1}(1)=0$, then \n\\begin{enumerate}[(A)]\n \\item either $a_{2}(1)\\neq 0$ and the above identity reduces to \n \\[\n  a_{2}(1)a_{1}(x)=0 \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right). \n \\]\nIn other words $a_{1}$ is the identically zero function. In this case $f$ is identically zero, too. \n\\item or $a_{2}(1)=0$ and from \\eqref{Eq1_simp_sym} we get that \n\\begin{multline*}\n a_{1}(1)\\,a_{2}(x\\,y)+a_{2}(1)\\,a_{1}(x\\,y)+\\left(\\left(2-2\\,a_{1}(\n 1)\\,a_{2}(1)\\right)\\,a_{1}(x)-a_{1}(1)^2\\,a_{2}(x)\\right)\\,a_{2}(y)\n \\\\\n +\n \\left(\\left(2-2\\,a_{1}(1)\\,a_{2}(1)\\right)\\,a_{2}(x)-a_{2}(1)^2\\,a_{\n 1}(x)\\right)\\,a_{1}(y)=0\n\\end{multline*}\nfor all $x, y\\in \\mathbb{F}$, that is, \n\\[\n a_{1}(x)\\,a_{2}(y)+a_{2}(x)\\,a_{1}(y)=0 \n \\qquad \n \\left(x, y\\in \\mathbb{F}\\right). \n\\]\nFrom this, \n\\[\n a_{1}(x)a_{2}(x)=0\n\\]\nfollows for all $x\\in \\mathbb{F}$, that is, $f$ is the identically zero function.\n\\end{enumerate}\nTherefore, from now on $a_{1}(1)\\,a_{2}(1)-1=0$ can be supposed. Note that without the loss of generality we can (and we do) assume that $a_{1}(1)=a_{2}(1)=1$. In this case equation \n\\eqref{Eq1_simp_sym} implies that \n\\[\n a_{2}(x\\,y)+a_{1}(x\\,y)=a_{2}(x)\\,a_{2}(y)+a_{1}(x)\\,a_{1}(y)\n\\]\nfor all $x, y\\in \\mathbb{F}$. From this we deduce that either \n\\begin{enumerate}[(A)]\n \\item $\\left\\{a_{1}, a_{2}\\right\\}$ is linearly dependent, that is \n \\[\n  a_{2}=ca_{1}(x) \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right), \n \\]\nfrom which we get that $a_{1}\\equiv a_{2}$, since $a_{1}(1)=a_{2}(1)$. If so, then equation \\eqref{Eq1_simp} reduces to \n\\[\n a(x^{2})^{2}= \\kappa a(x)^{4} \n \\qquad \n \\left(x\\in \\mathbb{F}\\right), \n\\]\nthat is $a$ is a homomorphism and \n\\[\n f(x)= f(1)a(x)^{2} \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\n\\item or $\\left\\{a_{1}, a_{2}\\right\\}$ is linearly independent. Then due to \\cite[pages 93-94]{Sze91}\n\\[\n a_{i}(x)= (\\alpha_{i}l(x)+\\beta_{i})m(x) \n \\qquad \n \\left(x\\in \\mathbb{F}^{\\times}, i=1, 2\\right)\n\\]\nor \n\\[\n a_{i}(x)= \\alpha_{i}m_{1}(x)+\\beta_{i}m_{2}(x) \n \\qquad \n \\left(x\\in \\mathbb{F}^{\\times}, i=1, 2\\right), \n\\]\nwhere $l\\colon \\mathbb{F}^{\\times}\\to \\mathbb{C}$ is a logarithmic function, \n$m, m_{1}, m_{2}\\colon \\mathbb{F}^{\\times}\\to \\mathbb{C}$ are multiplicative functions and \n$\\alpha_{1}, \\alpha_{2}$ and $\\beta_{1}, \\beta_{2}$ are complex constants. \n\nSubstituting the first form into equation \\eqref{Eq1_simp}, $\\alpha_{1}=0$ and $\\alpha_{2}=0$. That is, $a_{1}$ and $a_{2}$ are constant multiples of a (nonzero) homomorphism. This means that there exists linearly independent homomorphisms $\\varphi_{1}, \\varphi_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$ such that \n\\[\n f(x)= f(1)\\varphi_{1}(x)\\varphi_{2}(x) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\nFinally, if we substitute the second form into \\eqref{Eq1_simp} then we get (among others) that \n\\[\n \\begin{array}{rcl}\n \\alpha_{1}\\alpha_{2}(1-\\alpha_{1}\\alpha_{2})&=&0\\\\\n  \\beta_{1}\\beta_{2}(1-\\beta_{1}\\beta_{2})&=&0\n \\end{array}\n\\]\nIf we would have $\\beta_{1}\\beta_{2}=1$, then the remaining equations, that is, \n\\[\n \\begin{array}{rcl}\n  \\alpha_{1}\\beta_{1}\\beta_{2}^{2}+\\alpha_{2}\\beta_{1}^{2}\\beta_{2}&=&0\\\\\n  \\alpha_{1}^{2}\\alpha_{2}\\beta_{2}+\\alpha_{1}\\beta_{2}^{2}\\beta_{1}&=&0\\\\\n  \\alpha_{1}\\beta_{2}+\\beta_{1}\\alpha_{2}-\\alpha_{1}^{2}\\beta_{2}^{2}-\\beta_{1}^{2}\\alpha_{2}-4\\alpha_{1}\\alpha_{2}\\beta_{1}\\beta_{2}&=&0\n \\end{array}\n\\]\nwould lead to a contradiction. The same concerns the case $\\alpha_{1}\\alpha_{2}=1$. \n\nThis means however that $\\alpha_{1}\\alpha_{2}=0$ and $\\beta_{1}\\beta_{2}=0$, that is, either $f$ is the \nidentically zero function, or there exists homomorphisms $\\varphi_{1}, \\varphi_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$ such that \n\\[\n f(x)=f(1)\\varphi_{1}(x)\\varphi_{2}(x) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\n\\end{enumerate}\n\\end{proof}\n\n\n\\begin{rem}\n Roughly speaking the above statement says that among polynomials whose variety is at most two-dimensional, the solutions $f\\colon \\mathbb{F}\\to \\mathbb{C}$ of equation \\eqref{Eq1_simp} are of the form \n \\[\n  f(x)= f(1)\\varphi_{1}(x)\\varphi_{2}(x) \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right), \n \\]\nwith appropriate homomorphisms $\\varphi_{1}, \\varphi_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$. \n\nLet now $n$ be a fixed positive integer. \nIn the general case, that is, if $f\\colon \\mathbb{F}\\to \\mathbb{C}$ is a quadratic function whose variety is at most $n$-dimensional, then we have \n\\[\n f(x)=\\sum_{p, q=1}^{n}a_{p}(x)a_{q}(x) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right), \n\\]\nwith certain additive functions $a_{1}, \\ldots, a_{n}\\colon \\mathbb{F}\\to \\mathbb{C}$. \nIn this situation equation \\eqref{Eq1_simp} can be investigated with an analogous argument as in the proof of Proposition \\ref{Prop1}. \n\\end{rem}\n\n\nThe starting point of study of equation \\eqref{Eq1} among quadratic functions is the theorem below that can be found in \\cite{GseKisVin19}. Here we also recall its proof to enlighten the way to the general case. \n\n\\begin{thm}\\label{THM_main}\n Let $\\mathbb{F}$ be a field with $\\mathrm{char}(\\mathbb{F})=0$ and $f\\colon \\mathbb{F}\\to \\mathbb{C}$ be a quadratic function. \n Then equation \n \\begin{equation}\\label{Eq1}\n  f(x^{2})= f(x)^{2}\n \\end{equation}\nholds for each $x\\in \\mathbb{F}$ \\emph{if and only if} there exist non-trivial homomorphisms $\\varphi_{1}, \\varphi_{2}\\colon \\allowbreak \\mathbb{F}\\to \\mathbb{C}$ such that \n\\[\n f(x)= f(1)\\cdot \\varphi_{1}(x)\\varphi_{2}(x)\n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\nFurthermore, \n\\begin{enumerate}[(A)]\n \\item either $f(1)=0$ and then $f$ is identically zero;\n \\item or $f(1)=1$. \n\\end{enumerate}\n\n\\end{thm}\n\n\\begin{proof}\n Since $f$ is a generalized monomial of degree $2$, there exists a\nsymmetric bi-additive function $F_{2}\\colon \\mathbb{F}^{2}\\allowbreak\n\\to \\mathbb{C}$ so that\n\\[\n F_{2}(x, x)= f(x)\n \\qquad\n \\left(x\\in \\mathbb{F}\\right).\n\\]\nDefine the symmetric $4$-additive mapping $F_{4}\\colon\n\\mathbb{F}^{4}\\to \\mathbb{C}$ through\n\\begin{multline*}\n F_{4}(x_{1}, x_{2}, x_{3}, x_{4})\n =\n F_{2}(x_{1}x_{2}, x_{3}x_{4})\n +  F_{2}(x_{1}x_{3}, x_{2}x_{4})\n + F_{2}(x_{1}x_{4}, x_{2}x_{3})\n \\\\\n -F_{2}(x_{1}, x_{2})F(x_{3}, x_{4})\n -F_{2}(x_{1}, x_{3})F(x_{2}, x_{4})\n -F_{2}(x_{1}, x_{4})F(x_{2}, x_{3})\n \\\\\n \\left(x_{1}, x_{2}, x_{3}, x_{4}\\in \\mathbb{F}\\right).\n\\end{multline*}\nSince\n\\[\n F_{4}(x, x, x, x)= 3 \\left(F_{2}(x^{2}, x^{2})-F_{2}(x, x)^{2}\\right)=3 \\left(f(x^{2})-f(x)^{2}\\right)=0\n \\qquad\n \\left(x\\in \\mathbb{F}\\right),\n\\]\nthe mapping $F_{4}$ has to be identically zero on\n$\\mathbb{F}^{4}$. Therefore, especially\n\\[\n0=F_{4}(1, 1, 1, 1)= 3F_{2}(1, 1)-3F_{2}(1, 1)^{2},\n\\]\nyielding that either $F_{2}(1, 1)=0$ or $F_{2}(1, 1)=1$. Moreover,\n\\[\n 0= F_{4}(x, 1, 1, 1) =\n 3F_{2}\\left(x , 1\\right)-3F_{2}\\left(1 , 1\\right)F_{2}\\left(x , 1\\right)\n \\qquad\n \\left(x\\in \\mathbb{F}\\right),\n\\]\nfrom which either $F_{2}(1, 1)=1$ or $F_{2}(x, 1)=0$ follows for any $x\\in\n\\mathbb{F}$.\n\nUsing that\n\\[\n 0= F_{4}(x, x, 1, 1)\n =\n F_{2}(x^2 , 1)-F_{2}\\left(1 , 1\\right)\\,F_{2}\\left(x , x\\right)+2F_{2} \\left(x , x\\right)-2F^2_{2}\\left(x , 1\\right)\n \\qquad \n \\left(x\\in \\mathbb{F}\\right),\n\\]\nwe obtain that\n\\[\n \\left(F_{2}(1, 1)-2\\right)F_{2}\\left(x , x\\right)= F_{2}(x^2 , 1)-2F^2_{2}\\left(x , 1\\right)\n \\qquad\n \\left(x\\in \\mathbb{F}\\right).\n\\]\nNow, if $F_{2}(1, 1)=0$, then according to the above identities $F_{2}(x,\n1)=0 $ would follow for all $x\\in \\mathbb{F}$. Since $F_{4}(x,\nx, 1, 1)=0$ is also fulfilled by any $x\\in \\mathbb{F}$, this\nimmediately implies that\n\\[\n -2f(x)=-2F_{2}(x, x)= F_{2}(x^{2}, 1)-F_{2}(x, 1)^{2}=0\n \\qquad\n \\left(x\\in \\mathbb{F}\\right),\n\\]\ni.e., $f$ is identically zero.\n\nIn case $F_{2}(1, 1)\\neq 0$, then necessarily $F_{2}(1, 1)=1$ from which\n\\[\n -F_{2}(x, x)= F_{2}(x^{2}, 1)-2F_{2}(x, 1)^{2}\n \\qquad\n \\left(x\\in \\mathbb{F}\\right).\n\\]\nDefine the non-identically zero additive function $a\\colon\n\\mathbb{F}\\to \\mathbb{C}$ by\n\\[\n a(x)=F_{2}(x, 1)\n \\qquad\n \\left(x\\in \\mathbb{F}\\right)\n\\]\nto get that\n\\[\n f(x)=F_{2}(x, x)= -F_{2}(x^{2}, 1)+2F_{2}(x, 1)^{2}= 2a(x)^{2} -a(x^{2})\n \\qquad\n \\left(x\\in \\mathbb{F}\\right).\n\\]\nSince $F_{4}(x, x, x, x)=0$ has to hold, the additive function\n$a\\colon \\mathbb{F}\\to \\mathbb{C}$ has to fulfill identity\n\\begin{equation}\\label{Eq3}\n -a(x^4)+a^2(x^2)+4a^2(x)a(x^2)-4a^4(x)=0\n \\qquad\n \\left(x\\in \\mathbb{F}\\right)\n\\end{equation}\ntoo.\n\nIn what follows, we will show that the additive function $a$ is of a\nrather special form.\n\nIndeed,\n\\[\n 0= F_{4}(x, y, z, 1)\n \\qquad\n \\left(x, y, z\\in \\mathbb{F}\\right)\n\\]\nmeans that $a$ has to fulfill equation\n\\[\n a(x)a(yz)+a(y)a(xz)+a(z)a(xy)= 2a(x)a(y)a(z)+a(xyz)\n \\qquad\n \\left(x, y, z\\in \\mathbb{F}\\right)\n\\]\nLet now $z^{\\ast}\\in \\mathbb{F}$ be arbitrarily fixed to have\n\\[\n a(x)a(yz^{\\ast})+a(y)a(xz^{\\ast})+a(z^{\\ast})a(xy)= 2a(x)a(y)a(z^{\\ast})+a(xyz^{\\ast})\n \\qquad\n \\left(x, y, z\\in \\mathbb{F}\\right).\n\\]\nDefine the additive function $A\\colon \\mathbb{F}\\to \\mathbb{C}$ by\n\\[\n A(x)=a(xz^{\\ast})-a(z^{\\ast})a(x)\n \\qquad\n \\left(x\\in \\mathbb{F}\\right)\n\\]\nto receive that\n\\[\n A(xy)=a(x)A(y)+a(y)A(x)\n \\qquad\n \\left(x, y\\in \\mathbb{F}\\right),\n \\]\n which is a special convolution type functional equation.\nDue to Theorem 12.2 of \\cite{Sze91}, we get that\n\\begin{enumerate}[(a)]\n \\item the function $A$ is identically zero under any choice of $z^{\\ast}$, implying that $a$ has to be multiplicative.\n Note that $a$ is additive, too. Thus, for the quadratic mapping $f\\colon \\mathbb{F}\\to \\mathbb{C}$ there exists a\n homomorphism $\\varphi\\colon \\mathbb{F}\\to \\mathbb{C}$ such that\n \\[\n  f(x)=\\varphi(x)^{2}\n  \\qquad\n  \\left(x\\in \\mathbb{F}\\right).\n \\]\n\n\\item or there exists multiplicative functions $m_{1}, m_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$\nand a complex constant $\\alpha$ such that\n\\[\n a(x)=\\frac{m_{1}(x)+m_{2}(x)}{2}\n \\qquad\n \\left(x\\in \\mathbb{F}\\right)\n\\]\nand\n\\[\n A(x)=\\alpha \\left(m_{1}(x)-m_{2}(x)\\right)\n  \\qquad\n \\left(x\\in \\mathbb{F}\\right).\n\\]\nDue to the additivity of $a$, in view of the definition of the\nmapping $A$, we get that $A$ is additive, too.\n\nThis however means that both the maps $m_{1}+m_{2}$ and\n$m_{1}-m_{2}$ are additive, from which the additivity of $m_{1}$ and\n$m_{2}$ follows, yielding that they are in fact homomorphisms.\n\nSince\n\\[\n F_{2}(x, x)= f(x)= 2a(x)^{2}-a(x^{2})\n \\qquad\n \\left(x\\in \\mathbb{F}\\right),\n\\]\nwe obtain for the quadratic function $f\\colon \\mathbb{F}\\to\n\\mathbb{C}$ that there exist homomorphisms $\\varphi_{1},\n\\varphi_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$ such that\n\\[\n f(x)=\\varphi_{1}(x)\\varphi_{2}(x)\n \\qquad\n \\left(x\\in \\mathbb{F}\\right).\n\\]\n\\end{enumerate}\nSumming up, we received the following: identity\n\\[\n f(x^{2})= f(x)^{2}\n \\qquad\n \\left(x\\in \\mathbb{F}\\right)\n\\]\nholds for the quadratic function $f\\colon \\mathbb{F}\\to \\mathbb{C}$\nif and only if there exist homomorphisms $\\varphi_{1},\n\\varphi_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$ such that\n\\[\n f(x)=f(1)\\cdot\\varphi_{1}(x)\\varphi_{2}(x)\n \\qquad\n \\left(x\\in \\mathbb{F}\\right).\n\\]\n\\end{proof}\n\n\n\\begin{cor}\n Let $n\\geq 2$ be a positive integer, $\\mathbb{F}$ be a field with $\\mathrm{char}(\\mathbb{F})=0$ and $f\\colon \\mathbb{F}\\to \\mathbb{C}$ be a quadratic function. \n Then equation \n \\begin{equation}\\label{Eq2}\n  f(x^{n})= f(x)^{n}\n \\end{equation}\nholds for each $x\\in \\mathbb{F}$ \\emph{if and only if} there exist  homomorphisms $\\varphi_{1}, \\varphi_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$ such that \n\\[\n f(x)= f(1)\\cdot \\varphi_{1}(x)\\varphi_{2}(x) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right), \n\\]\nfurthermore either $f(1)=0$ and then $f$ is identically zero, or $f(1)$ is an $(n-1)$\\textsuperscript{st} root of unity. \n\\end{cor}\n\n\\begin{proof}\n In case $n=2$, then in view of the previous theorem, there is nothing to prove. \n Thus $n>2$ can be supposed subsequently. \n \nLet $\\mathbb{F}$ be a field with $\\mathrm{char}(\\mathbb{F})=0$, $\\varphi_{1}, \\varphi_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$ be homomorphisms and \n$\\lambda\\in \\mathbb{C}$ be such that either $\\lambda$ is zero, or it is an $(n-1)$\\textsuperscript{st} root of unity. \nDefine the function $f\\colon \\mathbb{F}\\to \\mathbb{C}$ by \n\\[\nf(x)= \\lambda \\varphi_{1}(x)\\varphi_{2}(x) \n\\qquad \n\\left(x\\in \\mathbb{F}\\right). \n\\]\nSince every homomorphism is additive, Lemma \\ref{lemma3} immediately yields that $f$ is a quadratic function and we also have \n\\[\n f(x^{n})= \\lambda\\varphi_{1}(x^{n})\\varphi_{2}(x^{n})= \\lambda \\varphi_{1}(x)^{n}\\varphi_{2}(x)^{n}\n = \\lambda^{n}\\varphi_{1}(x)^{n}\\varphi_{2}(x)^{n}=  \\left(\\lambda \\varphi_{1}(x)\\varphi_{2}(x)\\right)^{n}\n =f(x)^{n}\n\\]\nfor each $x\\in \\mathbb{F}$, since $\\lambda= \\lambda^{n}$. \n  \nConversely, let $f\\colon \\mathbb{F}\\to \\mathbb{C}$ be a quadratic function such that we additionally have that \n  \\[\n   f(x^{n})= f(x)^{n}\n  \\]\nfor all $x\\in \\mathbb{F}$. Since $f$ is a quadratic function, there exists a symmetric, bi-additive function $F_{2}\\colon \\mathbb{F}^{2}\\to \\mathbb{C}$ such that \n\\[\n f(x)= F_{2}(x, x) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\nEquation \\eqref{Eq2} with $x=1$ immediately yields that \n\\[\n f(1)=f(1)^{n}, \n\\]\nthat is, $F(1, 1)= f(1)$ is either zero, or it is an $(n-1)$\\textsuperscript{st} root of unity. \n\nFurthermore, equation \\eqref{Eq2} in terms of the function $F_{2}$ is \n\\[\n F_{2}(x^{n}, x^{n})= F_{2}(x, x)^{n} \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\nObserve that both the sides of the above identity are traces of symmetric and $2n$-additive functions, namely we have \n\\[\n \\frac{1}{(2n)!}\\sum_{\\sigma\\in \\mathscr{S}_{2n}}F_{2}(x_{\\sigma(1)}\\cdots x_{\\sigma(n)}, x_{\\sigma(n+1)} \\cdots x_{\\sigma(2n)})\n =\n \\frac{1}{(2n!)} \\sum_{\\sigma \\in \\mathscr{S}_{2n}}F_{2}(x_{\\sigma(1)}, x_{\\sigma(2)})\\cdots F_{2}(x_{\\sigma(2n-1)}, x_{\\sigma(2n)})\n\\]\nfor all $x_{1}, \\ldots, x_{2n}\\in \\mathbb{F}$. \nThis identity with the substitution \n\\[\n x_{1}= x, \\; x_{2}=x \\quad x_{i}=1 \\quad \\text{for } i=3, \\ldots, 2n\n\\]\nyields that there are complex constants $\\alpha$ and $\\beta$ depending only on $F_{2}(1, 1)$ such that \n\\[\n f(x)=F_{2}(x, x)= \\alpha a(x^{2})+\\beta a(x)^{2} \n \\qquad \n \\left(x\\in \\mathbb{F}\\right), \n\\]\nwhere the additive function $a\\colon \\mathbb{F}\\to \\mathbb{C}$ is defined by \n\\[\n a(x)= F_{2}(x, 1) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\nWriting this form back into equation \\eqref{Eq2}, we deduce \n\\[\n \\alpha a(x^{2n})+\\beta a(x^{n})^{2}= \\left(\\alpha a(x^{2})+\\beta a(x)^{2}\\right)^{n} \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\nAgain, both the sides of this identity are traces of symmetric and $2n$-additive functions, therefore \n\\begin{multline*}\n \\frac{1}{(2n)!} \\sum_{\\sigma\\in \\mathscr{S}_{2n}} \\left[\\alpha a(x_{\\sigma(1)} \\cdots x_{\\sigma_{(2n)}})+\\beta a(x_{\\sigma_{(1)}} \\cdots x_{\\sigma_{(n)}})a(x_{\\sigma(n+1)} \\cdots x_{\\sigma(n)})\\right]\n\\\\= \n\\frac{1}{(2n)!} \\sum_{\\sigma\\in \\mathscr{S}_{2n}} \\prod_{k=0}^{n-1}(\\alpha a(x_{\\sigma(2k+1)}x_{\\sigma(2k+2)})+\\beta a(x_{\\sigma(2k+1)})a(x_{\\sigma(2k+2)}))\n\\end{multline*}\nfor each $x_{1}, \\ldots, x_{2n}\\in \\mathbb{F}$. Let now $x, y, z\\in \\mathbb{F}$ be arbitrary, then this identity with the substitutions \n\\[\n x_{1}=x, \\, x_{2}=y,\\, x_{3}=z \\quad  \\text{and} \\quad x_{i}=0 \\quad \\text{for} \\quad 4\\leq i \\leq 2n\n\\]\nleads to \n\\[\n Aa(xyz)+Ba(xy)a(z)+Ca(xz)a(y)\n +Da(yz)a(x)+Ea(x)a(y)a(z)=0 \n \\qquad \n \\left(x, y, z\\in \\mathbb{F}\\right), \n\\]\nthat is a similar equation that appear in the proof of Theorem \\ref{THM_main}. With an analogous thread we get that $a$ can be written as a sum of two homomorphisms that finally implies for the function $f$ that there are homomorphisms $\\varphi_{1}, \\varphi_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$ such that \n\\[\n f(x)= f(1)\\varphi_{1}(x)\\varphi_{2}(x) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right), \n\\]\nwhere $f(1)$ is either zero, or it is an $(n-1)$\\textsuperscript{st} root of unity. \n\\end{proof}\n\n\n\\section{Open problems and further perspectives}\n\n\nAs it is written at the beginning of the second section, the main aim of this paper was to \nprove characterization theorems for generalized polynomials $f\\colon \\mathbb{F}\\to \\mathbb{C}$ of degree at most $n$ that also fulfill equation \n\\[\n f(P(x))= Q(f(x))\n\\]\nfor each $x\\in \\mathbb{F}$, \nwhere $n$ is a positive integer and $P\\in \\mathbb{F}[x]$ and $Q\\in \\mathbb{C}[x]$ are polynomials. \nThe results presented in connection with this problem can be considered as initial steps. Thus we close this paper with several open questions and we would like to give some perspectives, too. \n\n\\begin{rem}\n Clearly, it is enough to consider the case $\\deg (P)=\\deg(Q)$. Indeed, if \n $f\\colon \\mathbb{F}\\to \\mathbb{C}$ is a generalized monomial of degree $n$, the due to Lemma \\ref{lemma_6}, the mappings \n \\[\n  \\mathbb{F}\\ni x \\longmapsto f(P(x)) \n  \\quad \n  \\text{and}\n  \\quad \n  \\mathbb{F}\\ni x \\longmapsto Q(f(x)) \n \\]\nare generalized polynomials of degree $n\\cdot \\deg(P)$ and $n\\cdot \\deg(Q)$, respectively. Furthermore, \nthey coincide at each point $x\\in \\mathbb{F}$. However, this is only possible if $\\deg (P)=\\deg(Q)$. \n\\end{rem}\n\nIn the second section, we studied only quadratic functions, i.e., generalized monomials of degree two. Therefore, we formulate the following. \n\n\\begin{opp}\nLet  $n\\in \\mathbb{N}$, $n\\geq 2$ and $P\\in \\mathbb{F}[x]$ and $Q\\in \\mathbb{C}[x]$ be polynomials of degree at least two and $f\\colon \\mathbb{F}\\to \\mathbb{C}$ be a generalized monomial of degree $n$. Prove or disprove that if \n\\[\n f(P(x))= Q(f(x)) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right), \n\\]\nthen and only then there exist homomorphisms $\\varphi_{1}, \\ldots, \\varphi_{n}\\colon \\mathbb{F}\\to \\mathbb{C}$ such that \n\\[\n f(x)= f(1)\\cdot \\varphi_{1}(x)\\cdots \\varphi_{n}(x)\n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\n\n\\end{opp}\n\n\n\\begin{opp}\n It might be promising to consider firstly the case \n \\[\n  P(x)= Q(x)=x^{2} \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right), \n \\]\n because as the results of the previous section show, hopefully, the case \n \\[\n  P(x)= Q(x)=x^{n} \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right)\n \\]\n where $n>2$, leads back to the case $n=2$. \n\\end{opp}\n\n\\begin{opp}\n In the special case we considered the above general problem, it turned our that the solutions of the functional equations are always (normal) monomials. Additionally, we also showed that the proof is much easier if we know this, see Proposition \\ref{Prop1}. We conjecture that this is true in general, too. Thus, prove or disprove that if the generalized monomial $f\\colon \\mathbb{F}\\to \\mathbb{C}$ solves equation \n \\[\n f(P(x))= Q(f(x)) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right), \n\\]\nthen $f$ is a monomial. \n\\end{opp}\n\n\n\\begin{rem}\n The above problem is clearly meaningful for polynomials $P$ and $Q$ with degree one. At the same time, in this case we cannot expect representations similar to that ones that appeared in the statements proved in the second section. Here we consider only the case quadratic functions. Accordingly, assume that for the quadratic function $f\\colon \\mathbb{F}\\to \\mathbb{C}$ equation \n \\[\n  f(ax+b)= Af(x)+B \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right), \n \\]\nwith some $a, b\\in \\mathbb{F}$ and $A, B\\in \\mathbb{C}$. Let us denote $F\\colon \\mathbb{F}^{2}\\to \\mathbb{C}$ the uniquely determined symmetric, bi-additive function whose trace is $f$. With $x=0$ we immediately get that $f(b)=F(b, b)=B$. \nFurthermore, \n\\[\n F(ax+b, ax+b)=AF(x, x)+F(b, b)\n \\qquad \n \\left(x, \\in \\mathbb{F}\\right), \n\\]\nthat is, \n\\[\n F(ax, ax)+2F(ax, b)+F(b, b)= AF(x, x)+F(b, b)\n \\qquad \n \\left(x, \\in \\mathbb{F}\\right), \n\\]\nor after some simplification \n\\[\n \\left(F(ax, ax)-AF(x, x)\\right)+2F(ax, b)= 0\n\\]\nfor all $x\\in \\mathbb{F}$. Since the left hand side of this equation is a generalized polynomial of degree two which has to be identically zero, all of its monomial terms should vanish. \nThis means from one hand that \n\\[\n F(ax, b)=0\n \\qquad \n \\left(x\\in \\mathbb{F}\\right), \n\\]\nespecially, $f(b, b)=B=0$. On the other hand, we also have \n\\[\n F(ax, ax)=AF(x, x)\n \\qquad \n \\left(x\\in \\mathbb{F}\\right), \n\\]\nfrom this however \n\\[\n F(ax, ay)=AF(x, y)\n \\qquad \n \\left(x, y\\in \\mathbb{F}\\right), \n\\]\nfollows, that is, the symmetric, bi-additive function is \\emph{semi-homogeneous}. \nFrom \\cite[Theorem 3]{GseKisVin20} it is known that a non-identically zero, symmetric and bi-additive function \n$F$ fulfilling the above semi-homogeneity exists if and only if there are injective homomorphism \n$\\delta_{1}, \\delta_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$ such that \n\\[\n \\delta_{1}(a)\\delta_{2}(a)= A. \n\\]\nSumming up, if $f\\colon \\mathbb{F}\\to \\mathbb{C}$ is a non-identically zero quadratic function such that \n\\[\n  f(ax+b)= Af(x)+B \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right), \n \\]\nwith some $a, b\\in \\mathbb{F}$ and $A, B\\in \\mathbb{C}$, then \n\\begin{enumerate}[(i)]\n \\item $B=0$\n \\item for the uniquely determined symmetric and bi-additive function $F\\colon \\mathbb{F}^{2}\\to \\mathbb{C}$, identity\n \\[\n  F(ax, b)=0\n \\]\nis satisfied for all $x\\in \\mathbb{F}$. \n\\item there are injective homomorphism \n$\\delta_{1}, \\delta_{2}\\colon \\mathbb{F}\\to \\mathbb{C}$ such that \n\\[\n \\delta_{1}(a)\\delta_{2}(a)= A. \n\\]\n\\end{enumerate}\n\n\nObserve that for instance with $b=0$, with arbitrary fixed $a\\in \\mathbb{Q}$ and with \n$A=a^{2}$ the above identity is fulfilled by \\emph{any} quadratic function $f\\colon \\mathbb{F}\\to \\mathbb{C}$ (this is obviously consistent with the fact that quadratic functions are $\\mathbb{Q}$-homogeneous of degree two). This shows that in this case we do not get in general any information for the form of the involved quadratic function $f$. With an analogous method, we obtain the same for higher order generalized monomials. \n\\end{rem}\n\n\n\n\\begin{opp}\n In this paper only equations with one unknown function were considered. At the same time, the investigated problem can clearly be extended: let \n $P\\in \\mathbb{F}[x]$ and $Q\\in \\mathbb{C}[x]$ be polynomials, $f, g\\colon \\mathbb{F}\\to \\mathbb{C}$ be generalized polynomials (of possibly \\emph{different order}) \n such that $\\deg(f)\\deg(P)=\\deg(g)\\deg(Q)$. Prove or disprove that if \n \\[\n  f(P(x))= Q(g(x)) \n \\]\nholds for all $x\\in \\mathbb{F}$, then $f$ and $g$ can be represented as products of homomorphisms. \n\\end{opp}\n\n\\begin{rem}\n A particularly interesting and presumably the simplest case of the following problem is when $\\deg(g)=1$, i.e., when $g\\colon \\mathbb{F}\\to \\mathbb{C}$ is an additive function. \n \\end{rem}\n \n In connection to this problem we prove the following special case, which is expected to be successfully applied in the general case as well. \n \n \\begin{prop}\n  Let $\\mathbb{F}$ be a field with $\\mathrm{char}(\\mathbb{F})=0$, $f\\colon \\mathbb{F}\\to \\mathbb{C}$ be a quadratic function and $a\\colon \\mathbb{F}\\to \\mathbb{C}$ be an additive function. Then equation \n  \\[\n  f(x^{2})= a(x)^{4} \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right)\n \\]\n holds if and only if here exists a homomorphism $\\varphi\\colon \\mathbb{F}\\to \\mathbb{C}$ such that \n\\[\n a(x)=a(1)\\varphi(x) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right)\n\\]\nand \n\\[\n f(x)= a(1)^{4}\\varphi(x)^{2}\n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\n\\end{prop}\n\n\\begin{proof} \n Assume that $f\\colon \\mathbb{F}\\to \\mathbb{C}$ is a quadratic, while $a\\colon \\mathbb{F}\\to\\mathbb{C}$ is an additive function such that \n \\[\n  f(x^{2})= a(x)^{4} \n  \\qquad \n  \\left(x\\in \\mathbb{F}\\right). \n \\]\nSince both the sides of this equation are traces of symmetric, $4$-additive functions, we obtain that \n\\[\n \\frac{1}{3}\\left[F(x_1 x_2, x_3 x_4)+F(x_1 x_3, x_2 x_4)+F(x_1 x_4, x_2 x_3)\\right]\n = a(x_1)a(x_2)a(x_3)a(x_4) \n \\qquad\n \\left(x_1, x_2, x_3, x_4\\in \\mathbb{F}\\right). \n\\]\nHere $F\\colon \\mathbb{F}\\times \\mathbb{F}\\to \\mathbb{C}$ is the uniquely determined symmetric, bi-additive function for which $F(x, x)= f(x)$ is satisfied for all $x\\in \\mathbb{F}$. \n\nThis identity implies especially that \n\\[\n f(1)=F(1, 1)=a(1)^{4} \n \\qquad \n \\text{and}\n \\qquad \n F(x, 1)=a(1)^{3}a(x) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\nFurthermore, we also have \n\\[\n 2F(x, y)= 3a(1)^{2}a(x)a(y)-F(xy, 1) \n \\qquad \n \\left(x, y\\in \\mathbb{F}\\right). \n\\]\nThus, \n\\[\n 2F(x, y)=3a(1)^{2}a(x)a(y)-a(1)^{3}a(xy) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\nIn other words, \n\\[\n f(x)= \\frac{3}{2}a(1)^{2}a(x)^{2}-\\frac{1}{2}a(1)^{3}a(x^{2})  \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\nSubstituting this back into the original equation we get that the additive function $a\\colon \\mathbb{F}\\to \\mathbb{C}$ has to fulfill \n\\[\n a(x)^{4}= \\frac{3}{2}a(1)^{2}a(x^{2})^{2}-\\frac{1}{2}a(1)^{3}a(x^{4})  \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\]\nAgain, after symmetrization or after applying \\cite[Theorem 15]{GseKisVin19}, we derive that there exists a homomorphism \n$\\varphi\\colon \\mathbb{F}\\to \\mathbb{C}$ such that \n\\[\n a(x)=a(1)\\varphi(x) \n \\qquad \n \\left(x\\in \\mathbb{F}\\right)\n\\]\nand \n\\begin{multline*}\n f(x)= \\frac{3}{2}a(1)^{2}a(x)^{2}-\\frac{1}{2}a(1)^{3}a(x^{2})\n \\\\\n = \n \\frac{3}{2}a(1)^{2}a(1)^{2}\\varphi(x)^{2}-\\frac{1}{2}a(1)^{3}a(1)\\varphi(x^{2})\n =\n a(1)^{4}\\varphi(x)^{2} \n \\qquad \n \\left(x\\in \\mathbb{F}\\right). \n\\end{multline*}\n\\end{proof}\n\n\\begin{rem}\nUsing the ideas of the results of the third section, the case \n\\[\n f(x^{n})= a(x)^{2n} \n \\qquad \n \\left(x\\in \\mathbb{F}\\right)\n\\]\nwhere $n$ is a fixed positive integer, can be reduced to the above studied case. \n\\end{rem}\n\n\n\\begin{rem}\n Observe that during the proof of Lemmas \\ref{lemma3}, \\ref{lemma5}, \\ref{lemma_6} the fact that we considered complex-valued mappings, was not used at all. We remark that these statements as well as their proofs are exactly the same for functions defined on a field $\\mathbb{F}$ and mapping to another field $\\mathbb{K}$. \n \n The situation is slightly different in case of Lemma \\ref{lemma4}, since in that case derivations are involved. Nevertheless, Lemma \\ref{lemma4} also holds true (with an unchanged proof) for mappings defined on $\\mathbb{F}$ and having values in $\\mathbb{K}$, where $\\mathbb{F}\\subset \\mathbb{K}$ are fields. \n\\end{rem}\n\n\n\\begin{rem}\n We would also like to clarify why we considered only complex-valued functions. Obviously, the investigated problems are meaningful in a much more general setting. The importance of this condition lies in our method. Namely, in each case we showed firstly that the involved mappings $f\\colon \\mathbb{F}\\to \\mathbb{C}$ are exponential polynomials of the multiplicative group $\\mathbb{F}^{\\times}$. This enabled us to describe the unknown function completely. This method however relies on the notion of exponential polynomials and the theory of this notion is well-developed only for complex-valued mappings. Maybe with a different approach the general case can also be handled. \n \n The assumption that the field $\\mathbb{F}$ has to have zero characteristic is caused by the limitations of the Polarization formula, since $n$-additive functions are uniquely determined by their diagonalizations only if the characteristic of the domain is large enough or zero. \n\\end{rem}\n\n\n\\begin{opp}\n Let $\\mathbb{F}$ and $\\mathbb{K}$ be fields, $n$ be a positive integer, $P\\in \\mathbb{F}[x]$ and $Q\\in \\mathbb{K}[x]$ be polynomials. Determine those generalized monomials $f, g\\colon \\mathbb{F}\\to \\mathbb{K}$ of degree at most $n$ that also fulfill equation \n\\[\n f(P(x))= Q(f(x))\n\\]\nfor each $x\\in \\mathbb{F}$. \n\nA particularly interesting case of this problem is when at least one of the fields $\\mathbb{F}$ and $\\mathbb{K}$ has finite characteristic. \n\\end{opp}\n\n\n\n\n\\begin{ackn}\n The author would like to thank Professor \\textsc{Jos\u00e9 Mar\u00eda Almira} (University of Murcia, Spain) and Professor \\textsc{Rezs\u0151 Lovas} (University of Debrecen, Hungary) for their generous help and valuable comments that improved the quality of the paper. \n \n Project No.~K134191 has been implemented with the support provided by the National Research, Development and Innovation Fund of Hungary, financed under the K\\_20 funding scheme. The research of the author has partially been carried out with the help of the Project 2019-2.1.11-T\u00c9T-2019-00049, which has been implemented with the support provided from the National Research, Development and Innovation Fund of Hungary, financed under the T\u00c9T funding scheme.\n\\end{ackn}\n\n\n\n\n \\bibliographystyle{plain}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nA deep connection between glass\ntransition in molecular glass formers,  structural arrest in\ncolloidal systems, and  jamming transition in granular media\n\\cite{coniglio,LN,OHern1,Danna,Mehta,OHern2} has often been stressed in the\npast few years. In spite of the fact that these systems are very\ndifferent one from each other, varying suitably the control\nparameters, a slowdown and a subsequent structural arrest in a\nsolid-like disordered state are found in each of them. In\n\\cite{LN,OHern2} a possible phase diagram for jamming is\nsuggested, which takes into account the fact that jamming is\nobtained either raising the volume fraction or lowering the\ntemperature or lowering the applied stress. Colloidal suspensions\nand molecular glass formers are both thermal systems,\nand it is commonly accepted that both colloidal glass transition\nand molecular glass transition are of the same type despite of the\nfact that  different control parameters may drive the transition.\nThe case of granular materials is instead very different: They are\nathermal systems, since the thermal fluctuations are significantly\nless than the gravitational energy and the system cannot explore\nthe phase space without any external driving. Nevertheless an\nexceedingly slowing down is observed when a granular material is\nshaken at low shaking amplitude, or flows under a low shear\nstress, with strong analogies with the slowing down observed in\nglass formers. Experimental and numerical studies\n\\cite{Danna,OHern2,NCH,Mehta} have confirmed this connection,\nhowever its precise nature is still unclear \\cite{OHern1,OHern2}.\n\nIn the present paper in order to study this connection we apply a\nstatistical mechanics approach to granular media. This approach,\nwhich has been extensively developed in previous works \\cite{e1, fnc}, is\nbased on an elaboration of the original ideas suggested by\nEdwards \\cite{Edwards}. The basic assumption is that for a granular\nsystem subject to an external drive (e. g. tapping), after having\nreached stationarity, time averages coincide with suitable\nensemble averages over the ``mechanically stable\" states. We have\nshown \\cite{fnc} that this assumption works for different lattice\nmodels namely that a generalized Gibbs distribution of the stable\nstates describes with good approximation the stationary state\nattained by the system under tapping dynamics. Here each tap\nconsists in raising the bath temperature to a finite value (called\ntap amplitude) and, after a lapse of time (called tap duration)\nquenching the bath temperature back to zero. By cyclically\nrepeating the process  the system explores the space of the\nmechanically stable states.\n\nWe thus consider one of the above lattice model for which the\nstatistical mechanics approach works. The model is made up of hard\nspheres under gravity. Then we apply standard statistical\nmechanics methods in order to investigate analytically the\nexistence and the nature of a possible jamming transition. More\nprecisely we consider the Bethe-Peierls approximation using the\ncavity method \\cite{MP,Biroli}: By changing the control parameter\na phase transition from a fluid to a crystal is found, and, when\ncrystallization is avoided, a glassy phase appears. The nature of\nthis glassy phase is analogous to that found in mean field models\nfor glass formers \\cite{Kurchan, Biroli, PC03}: In particular we\nobserve a dynamical transition, where an exponentially high number\nof metastable states appears, and at a lower temperature a\nthermodynamic discontinuous phase transition to a glassy state. A\nbrief account of these calculations was given in a previous\nLetter \\cite{epl}. We also studied \\cite{epl} the model in\n$3d$ by means of numerical simulations, and we found that the\nmodel under taps has a transition from a fluid to a crystal, in a\nvery good agreement with he mean field approximation. However the\nnumerical simulation was not suitable to study the glass\ntransition since the model showed a strong tendency towards\ncrystallization.\n\nFor this reason we study here a variant of the model \\cite{PC03}\nwhich has the virtue of avoiding crystallization. We find that the\nsystem under gravity evolved by Monte Carlo taps presents features\ncharacteristic of real granular media \\cite{Bideau, Clement}, and\nat low tap amplitudes a dynamical transition with properties\nrecalling those of usual glass formers. In particular we observe a\ndynamical non linear susceptibility with a maximum at increasing\ntime: This behavior, typical of glass formers, is usually\ninterpreted as the sign of dynamic heterogeneities in the system.\n\nIn conclusions the results confirm early\nspeculations about the deep connection between the jamming\ntransition in granular\nmedia and the glass transition in usual glass formers, giving moreover a\nprecise interpretation to its nature.\n\n\n\nIn Sect. \\ref{meanfield} the mean field phase diagram is discussed. The details\nof calculations are presented in App.s \\ref{app1} and \\ref{app2}. In particular\nin App. \\ref{app2} the self-consistency equations obtained using the cavity\nmethod are shown.  In Sect. \\ref{hardsphere} the $3d$ model is presented and the\nnumerical results are shown.\n\n\\section{Mean field solution in the Bethe-Peierls approximation}\n\\label{meanfield}\nThe model is a monodisperse hard sphere system (with diameter $\\sqrt{2} a_0$)\nunder gravity, constrained to move\non the sites of a cubic lattice of spacing $a_0=1$. The Hamiltonian is given by:\n\\begin{equation}\n{\\cal H} = {\\cal H}_{HC} + mg \\sum_i n_i  z_i\n\\label{H1}\n\\end{equation}\nwhere $z_i$ is the height of site $i$, $g=1$ is the gravity acceleration,\n$m=1$ the grain mass, $n_i\\in\\{0,1\\}$ is the occupancy variable\n(absence or presence of a grain on site $i$)\nand ${\\cal H}_{HC}(\\{n_i\\})$ is the hard core term\npreventing two nearest neighbor sites being simultaneously occupied.\n\nWe have shown in previous papers \\cite{fnc} that\nthe model, Eq.~(\\ref{H1}), evolving by means of a tap dynamics can be described\nin good approximation by\na generalized Gibbs distribution of the ``mechanically stable'' states (i.e.\nthe states where the system is found at rest).  In particular the weight of a\ngiven state, $\\{n_i\\}$, is:\n\\begin{equation}\n\\mbox{e}^{-\\beta H(\\{n_i\\})}{\\cdot} \\Pi(\\{n_i\\}),\n\\end{equation}\nwhere $T_{conf} = \\beta^{-1}$ is a thermodynamic parameter,\ncalled ``configurational temperature'', characterizing the distribution.\nThe operator $\\Pi(\\{n_i\\})$ selects mechanically stable states:\n$\\Pi(\\{n_i\\})=1$ if $\\{n_i\\}$ is ``stable'', or else $\\Pi(\\{n_i\\})=0$.\nThe system partition function is thus the following \\cite{fnc}:\\begin{equation}\n{\\cal Z} =\\sum_{\\{n_i\\}} \\mbox{e}^{-\\beta H(\\{n_i\\})}{\\cdot} \\Pi(\\{n_i\\})\n\\label{Z}\n\\end{equation}\nwhere the sum runs over all microstates, $\\{n_i\\}$.\n\nIn the present section we show the phase diagram of the model, Eq.~(\\ref{H1}),\nobtained using a mean field theory in the Bethe-Peierls approximation (see\n\\cite{MP, Biroli} and ref.s therein),\nbased on a random graph (plotted in Fig.~\\ref{Blattice})\nwhich keeps into account that the gravity breaks up the symmetry along the $z$\naxis. This lattice is made up by $H$ horizontal layers\n(i.e., $z\\in\\{1,...,H\\}$).\nEach layer is a random graph of connectivity, $k-1=3$. Each site in layer\n$z$ is also\nconnected to its homologous site in $z-1$ and $z+1$\n(the total connectivity is thus $k+1$).\nLocally the graph has a tree-like structure but there\nare loops whose length is of order $\\ln N$, insuring geometric frustration.\nIn the thermodynamic limit only very long loops are present.\nThe details of calculations are given in appendices~\\ref{app1} and~\\ref{app2}\n(see also Ref.s~\\cite{epl, prl} where this mean field theory was\nfirst introduced).\n\n\\begin{figure}[ht]\n\\centerline{\n\\psfig{figure=fig4.eps,width=6cm,height=4cm,angle=0}\n}\n\\vspace{-.3cm}\n\\caption{In the mean field approximation,\nthe grains are located on a Bethe lattice, sketched in the figure,\nwhere each horizontal layer is a random graph of given connectivity.\nHomologous sites on neighboring layers are also linked and the overall\nconnectivity, $c$, of the vertices is $c\\equiv k+1=5$.}\n\\label{Blattice}\n\\end{figure}\nWe solve the recurrence equations found in the Bethe-Peierls approximation in\nthree cases: 1) A fluid-like homogeneous phase; 2) a crystalline-like\nphase characterized by the breakdown of the horizontal translational\ninvariance; 3)  a glassy phase described by a $1$-step Replica Symmetry\nBreaking (1RSB).  The details of the calculations are shown in Appendices.\n\nThe results of the calculations are summarized in Fig.~\\ref{phi_T}, where the\nbulk density at equilibrium, $\\Phi\\equiv N_s\/(2\\langle z\\rangle-1)$\n\\cite{notadens}\n(where $\\langle z\\rangle$ is the average height)\nis plotted as a function of the configurational temperature, $T_{conf}$, for a\ngiven value of the number of grains per unit surface, $N_s$.\nWe found that at high $T_{conf}$\na homogeneous solution corresponding to the fluid-like phase is found.\nBy lowering $T_{conf}$ at $T_m$\na phase transition to a crystal phase (an anti-ferromagnetic solution with a\nbreakdown of the translation invariance) occurs.\nThe fluid phase still exist below $T_m$ as a metastable phase\ncorresponding to a supercooled fluid when crystallization\nis avoided. Finally a 1RSB solution (found with the cavity\nmethod \\cite{MP}), characterized by the presence of a large number of\nlocal minima in the free energy \\cite{MP}, appears\nat $T_D$, and becomes stable at a lower point $T_K$, where\na thermodynamic transition from the supercooled fluid\nto a 1RSB glassy phase takes place.\nThe temperature $T_D$, which is interpreted in mean field\nas the location of a  dynamical transition where the relaxation time diverges,\nin real systems might instead correspond to a crossover in the dynamics\n(see \\cite{Kurchan, Biroli, Toninelli} and Ref.s therein).\n$\\Phi(T_{conf})$ has a shape very similar to that observed in the\n``reversible regime'' of tap experiments \\cite{Knight,Bideau}.\nThe location of the glass transition, $T_K$, corresponds\nto a cusp in the function $\\Phi(T_{conf})$. The dynamical crossover point $T_D$\nmight  correspond to the position of a characteristic shaking amplitude\n$\\Gamma^*$ found in experiments and simulations where the ``irreversible''\nand ``reversible'' regimes approximately meet.\n\n\\begin{figure}[ht]\n\\vspace{-0.5cm}\n\\begin{center}\n\\mbox{\\epsfysize=8cm\\epsfbox{compaction.eps}}\n\\end{center}\n\\caption{ The density, $\\Phi\\equiv N_s\/(2\\langle z \\rangle-1)$,\nfor $N_s=0.6$ as a function of $T_{conf}$. $\\Phi_{max}$ is the maximum density\nreached by the system in the crystal phase.}\n\\label{phi_T}\n\\end{figure}\n\nIn Fig.~\\ref{MFPD} the phase diagram obtained by varying $N_s$ is shown. The\ndashed vertical line in figure corresponds to the value of $N_s$ chosen in\nFig.~\\ref{phi_T}.\n\\begin{figure}[ht]\n\\centerline{\n\\psfig{figure=fig1.ps,width=6cm,angle=-90}}\n\\caption{The system mean field phase diagram is plotted in the plane\nof its two control parameters $(T_{conf},N_s)$.}\n\\label{MFPD}\n\\end{figure}\n\nThe model, Eq.~(\\ref{H1}), simulated in $3d$ by means of Monte Carlo tap\ndynamics \\cite{epl} presents a transition from a fluid  to a crystal\nas predicted by the mean field approximation, density profiles in good\nagreement with the mean field ones, and in the fluid phase a large increase of\nthe relaxation time as a function of the inverse tap amplitude.\nIn the following section we study a more complex model for hard spheres,\nwhere an internal degree of freedom allows to\navoid crystallization \\cite{PC03}.\n\n\\section{Hard spheres with an internal degree of freedom}\n\\label{hardsphere}\nThe Hamiltonian of the model is\n\\begin{equation}\n{\\cal H}  =\\sum_{\\langle ij \\rangle} n_i n_j \\phi_{ij}(\\sigma_i,\\sigma_j)\n+ mg \\sum_i n_i  z_i,\n\\label{H2}\n\\end{equation}\nwhere $z_i$ is the height of site $i$, $g=1$ is the gravity acceleration,\n$m=1$ the grain mass, $n_i\\in\\{0,1\\}$ is the occupancy variable (absence\nor presence of a grain on site $i$), $\\sigma_i\\in\\{1,\\ldots,q\\}$ represents the\ninternal degree of freedom  (which we call spin), and\n$\\phi_{ij}(\\sigma_i,\\sigma_j)$ is the interaction energy between spins.\nDifferent values of the spin correspond to different positions of the\nparticle inside the cell.  It is reasonable that a few number\nof internal states might be enough to catch the main features\nof real systems.\n\nAs in Ref.~\\cite{PC03} we study a  simple realization of the model\ndescribed by Eq.~(\\ref{H2}). Interpreting the spin as position of the particle\nin the cell, our choice can be easily visualized in $2d$, as shown in Fig.~\n\\ref{fig-model}. We\npartition the space in square cells, and subdivide each cell into four\ninternal positions (namely $q=4$). When a cell is occupied by a particle in any\ngiven position, a hard-core repulsion excludes the presence of\nparticles in some of the internal states of the neighboring\ncells (namely the interaction $\\phi_{ij}(\\sigma_i, \\sigma_j)$ is chosen zero\nif the\npositions $\\sigma_i$ and $\\sigma_j$ are ``compatible'', and infinite otherwise).\nThis choice can be interpreted as a coarse grained version of a\nhard sphere system in the continuum.  In $3d$ we subdivide the\nspace into cubic cells, and considers six internal positions\ninstead of four.\n\n\\begin{figure}[ht!]\n\\hspace{-1cm}\\centerline{\\mbox{\\epsfysize=6cm\\epsfbox{MODELLO.eps}}}\n\\vspace{-2.5cm}\n\\caption{The model in two dimensions: the space is partitioned in square cells,\nand each cell can be occupied by at most one particle\nin anyone of the four shown positions (little circles). A particle in\nany given position (large shaded circle) excludes the presence of\nparticles in any of the black colored positions.}\n\\label{fig-model}\n\\end{figure}\n\\begin{figure}[ht]\n\\begin{center}\n\\mbox{\\epsfysize=7cm\\epsfbox{phi.eps}}\n\\end{center}\n\\vspace{-0.5cm}\n\\caption{The bulk density, $\\Phi\\equiv N\/L^2(2\\langle z\\rangle-1)$,\nis plotted as function of $T_\\Gamma$ for $\\tau_0=10~MCsteps\/particle$. The empty\ncircles correspond to stationary states, and the black stars to out of\nstationarity ones. $\\Phi_{max}$ is the maximum density reached by the system in\nthe crystal phase, $\\Phi_{max}=6\/7$.}\n\\label{phi}\n\\end{figure}\n\\begin{figure}[ht]\n\\begin{center}\n\\mbox{\\epsfysize=7cm\\epsfbox{prof.eps}}\n\\end{center}\n\\vspace{-0.5cm}\n\\caption{The density profile, $\\sigma (z)$, as function of the height, $z$, for\n$T_\\Gamma=~0.20$ and $\\tau_0=10~MCsteps\/particle$.}\n\\label{prof}\n\\end{figure}\n\nIn the Monte Carlo simulations, $N=~433$ grains are confined in a $3d$ box\nof linear size $L=~12$ (i.e. $N_s=~3$), between hard walls in the vertical\ndirection and with periodic boundary\nconditions in the horizontal directions.  We perform a standard Metropolis\nalgorithm on the system.  The particles,  initially prepared in a random\nconfiguration, are subject to taps, each one followed by a\nrelaxation process. During a tap, for a time $\\tau_0$ (called tap\nduration), the temperature is set to the value $T_{\\Gamma}$ (called tap\namplitude), so that particles have a finite probability, $p_{up}\\sim\ne^{-mg\/T_{\\Gamma}}$, to move upwards. During the relaxation the\ntemperature is set to zero, so that particles can only reduce the energy,\nand therefore can move only downwards. The relaxation stops when the\nsystem has reached a blocked state, where no grain can move downwards.\nOur measurements are performed at this stage when\nthe shake is off and the system is at rest. The time, $t$,\nis the number of taps applied to the system.\n\nIn the following the tap duration is fixed, $\\tau_0=10 MCsteps\/particle$, and\ndifferent tap amplitudes, $T_\\Gamma$, are considered.\nIn Fig.~\\ref{phi} the bulk density, $\\Phi \\equiv N\/\nL^2(2\\langle z \\rangle-1)$, is plotted as a function of $T_\\Gamma$:\n$\\Phi(T_\\Gamma)$ has a shape resembling that found in the\n``reversible regime'' of tap experiments \\cite{Knight, Bideau}, and moreover\nvery similar to that\nobtained in the mean field calculations and shown in Fig.~\\ref{phi_T}.\nAt low shaking amplitudes (corresponding to high bulk densities) a strong\ngrowth of the equilibration time (i.e. the time necessary to reach stationarity)\nis observed, and for the lowest values here considered (the black stars in\nFig.~\\ref{phi}) the system remains out of stationarity. In this region the\ndensity profile, $\\sigma (z)\\equiv 1\/L^2\\sum_i n_i(z)$ (where the sum $\\sum_i$\nis done over the sites $i$ in the layer $z=~1, \\dots, L$ \\cite{notapart}),\nis almost constant until a given layer and sharply decays to zero (see Fig.\n~\\ref{prof}), as found in real granular media \\cite{Clement}.\nIn conclusions the system here studied presents a jamming transition at low\ntap amplitudes as found in real granular media.\n\nIn order to test the predictions of the mean field calculations,\nin the following we measure quantities usually important in the\nstudy of glass transition: The relaxation functions, the\nrelaxation time\nand the dynamical susceptibility, connected to the presence a\ndynamical correlation length.\n\n\nIn particular we calculate the two-time autocorrelation\nfunctions:\n\\begin{equation}\nC(t,t_w)=\\frac{1}{N}\\sum_i\\overline{ n_i(t)n_i(t_w) \\vec {\\sigma} _i(t){\\cdot}\n\\vec{\\sigma} _i(t_w)},\n\\end{equation}\nwhere $\\vec {\\sigma} _i$ are unit length vectors, pointing\nin one of the six coordinate directions, representing the position of the\nparticles inside the cell; the average $\\overline{(\\ldots)} $ is done over\n$16-32$ different\nrealizations of the model obtained varying the random number generator in\nthe simulations, and the errors are calculated as the fluctuations\nover this statistical ensemble.\nFor values of $t_w$ long enough, the system\nreaches a stationary state, where the time translation invariance is\nrecovered, i.e., $C(t,t_w)=C(t-t_w)$.\nIn this time region, by averaging $C(t',t_w)$\nover $t'$ and $t_w$ such that $t=t'-t_w$ is fixed, we calculate\nthe ``equilibrium'' autocorrelation functions\n\\begin{equation}\n\\langle q(t) \\rangle= \\langle C(t'-t_w) \\rangle,\n\\end{equation}\nand the dynamical non linear susceptibility\n\\begin{equation}\n\\chi(t)=\\langle q(t)^2 \\rangle - \\langle q(t) \\rangle^2.\n\\end{equation}\nAs shown in Fig.~\\ref{tti}, at low values of the tap amplitudes, $T_\\Gamma$,\ntwo-step decays appear, well fitted in the intermediate time region,\nby the $\\beta-$correlator predicted by the mode coupling theory for \nsupercooled liquids \\cite{mct, notaMCT} (the continuous\ncurve in Fig.~\\ref{tti}), and at long time by stretched exponentials (the dashed\ncurve in figure).\n\\begin{figure}[ht]\n\\begin{center}\n\\mbox{\\epsfysize=7cm\\epsfbox{relax.eps}}\n\\end{center}\n\\vspace{-0.5cm}\n\\caption{The ``equilibrium'' autocorrelation function, $\\langle q(t) \\rangle$,\nplotted as function\nof $t$, for tap amplitudes $T_\\Gamma=~0.60,~0.50,~0.425,\n~0.40,~0.385,~0.365,~ 0.36$  (from bottom to top). The continuous line in\nfigure is the $\\beta-$correlator of the mode coupling theory \nwith exponent parameters\n$a=~0.30$ and $b=~0.52$.  The dashed line is a stretched exponential $\\propto\nexp[-(t\/\\tau)^\\beta]$ with $\\beta=~0.70$.}\n\\label{tti}\n\\end{figure}\nThe relaxation time, $\\tau$, is defined as $\\langle q(\\tau)\n\\rangle \\sim 0.1$. \n\nIn Fig.~\\ref{tau_phi} the relaxation time, $\\tau$, is plotted as a function of \nthe density, $\\Phi$. As found in many glass forming liquids, $\\tau(\\Phi)$ is \nwell fitted by a Vogel-Fulcher for the entire range, even if we can identify a \nfirst region where $\\tau(\\Phi)$ is fitted with good approximation by a power \nlaw. The power law divergence can be interpreted as a mean field behavior, \nfollowed by a hopping regime.\nNote that the model, Eq.~(\\ref{H2}), studied in absence of gravity\nby means the usual Monte Carlo Metropolis \\cite{PC03}, exhibits a\ndivergence of the relaxation time as a power law, and no crossover\nto a hopping regime is observed. We suggest that in the present\ncase the tap dynamics favors the equilibration\nvia hopping precesses.\n\n\\begin{figure}[ht]\n\\begin{center}\n\\mbox{\\epsfysize=7cm\\epsfbox{tau_phi.eps}}\n\\end{center}\n\\vspace{-0.5cm}\n\\caption{The relaxation time, $\\tau$, as function of the bulk\ndensity, $\\Phi$. The continuous line is a Vogel-Fulcher,\n$e^{A\/(\\Phi_c-\\Phi)}$,with $\\Phi_c=0.81\\pm 0.01$ and $A=0.49\\pm 0.10$. The \ndashed line is a power law, $(\\Phi_D-\\Phi)^{-\\gamma_1}$, with\n$\\Phi_D=0.76\\pm 0.01$ and $\\gamma_1=2.04\\pm 0.10$.}\n\\label{tau_phi}\n\\end{figure}\n\\begin{figure}[ht]\n\\begin{center}\n\\mbox{\\epsfysize=7cm\\epsfbox{tau.eps}}\n\\end{center}\n\\vspace{-0.5cm} \\caption{The relaxation time, $\\tau$, as function\nof the tap amplitude inverse, $T_\\Gamma^{-1}$. The dashed line\nis a power law, $(T_\\Gamma-T_D)^{-\\gamma_2}$, with\n$T_D=0.40\\pm 0.01$ and $\\gamma_2=1.52\\pm 0.10$. The continuous line\nis an Arrhenius fit, $e^{A\/T_\\Gamma}$, with $A=17.4\\pm 0.5$ (the data in this \nregion are also well fitted by both a super-Arrhenius and\nVogel-Fulcher laws).}\n\\label{figure3}\n\\end{figure}\nIn Fig.~\\ref{figure3} the relaxation time, $\\tau$, is plotted as a function of \nthe tap amplitude, $T_\\Gamma$: A clear crossover\nfrom a power law to a different regime is again observed around a\ntap amplitude $T_D$, corresponding to the value of the density, $\\Phi(T_D)\n\\simeq \\Phi_D$, where a similar crossover has been found in Fig.~\\ref{tau_phi}.\n\nThe divergence of the relaxation time at vanishing tap amplitude\nis consistent with the experimental data of Philippe\nand Bideau \\cite{Bideau} and D'Anna {\\em et al.} \\cite{Danna}. \nTheir findings are in fact consistent with an Arrhenius\nbehavior as function of the experimental tap\namplitude intensity. However a direct comparison with our data is not\npossible since we do not know the relation between the\nexperimental tap amplitude and the tap amplitude in our simulations.\nA more direct comparison would be possible if the experimental data \nwere plotted as function of the bulk density, as we did in Fig.~\\ref{tau_phi}.\n\nThe dynamical non linear susceptibility, $\\chi(t)$, plotted in\nFig.~\\ref{chi} at different $T_\\Gamma$, exhibits a maximum at a\ntime, $t^*(T_\\Gamma)$. The presence of a maximum in the  dynamical non linear\nsusceptibility is typical of glassy systems \\cite{franz, glotzer}.\nIn particular the value of the maximum, $\\chi(t^*)$, diverges in\nthe $p$-spin model \\cite{franz} as the dynamical transition is\napproached from above, signaling the presence of a diverging\ndynamical correlation length.\nIn the present case the value of the maximum increases as $T_\\Gamma$\ndecreases (except at very low $T_\\Gamma$ where the maximum seems to\ndecrease \\cite{nota_max}). The growth of $\\chi(t^*)$ in our model \nsuggests the presence of a growing\ndynamical length also in granular media.\n\n\n\\begin{figure}[ht]\n\\begin{center}\n\\mbox{\\epsfysize=7cm\\epsfbox{susc.eps}}\n\\end{center}\n\\vspace{-0.5cm}\n\\caption{The dynamical non linear susceptibility, $\\chi(t)$, (normalized by\n$\\chi(t_0)$, the value at $t_0=1$) as a function of $t$, for tap amplitudes\n$T_\\Gamma=\n0.60,~0.50,~0.425, ~0.41, ~0.40,~0.385, 0.3825$  (from left to right).}\n\\label{chi}\n\\end{figure}\n\n\\section{Conclusions}\n\nIn conclusions using standard methods of statistical mechanics we\nhave investigated  the jamming transition in a model for granular\nmedia. We have shown a deep connection  between the jamming\ntransition in granular media and the glass transition in usual\nglass formers. As in usual glass formers the mean field\ncalculations obtained using a statistical mechanics approach to\ngranular media predict a dynamical transition at a finite\ntemperature, $T_D$, and, at a  lower temperature, $T_K$, a\nthermodynamics discontinuous phase transition to a glass phase. In\nfinite dimensions 1) the dynamical transition becomes only a\ndynamical crossover as also found in usual glass formers\n\\cite{Kurchan, Biroli,Toninelli} (here the relaxation time,\n$\\tau$, as a function of both the density and the tap amplitude,  \npresents a crossover\nfrom a power law to a different regime); and 2) the thermodynamics\ntransition temperature, $T_K$, seems to go to zero (the relaxation\ntime, $\\tau$, seems to diverge only at $T_\\Gamma\\simeq 0$, even if a\nvery low value of the transition temperature is consistent with\nthe data).\n\n\\begin{acknowledgments}\nWe would like to thank M. Pica Ciamarra for many interesting discussions and \nsuggestions. Work supported by EU Network Number  MRTN-CT-2003-504712, \nMIUR-PRIN 2002, MIUR-FIRB 2002, CRdC-AMRA, INFM-PCI.\n\\end{acknowledgments}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Methodology}\\label{sec:methodology}\n\nIn the following, we will present a general formulation of the fragment molecular orbital (FMO) LC-TD-DFTB. As a starting point, we review the theory behind LC-TD-DFTB\\cite{humeniuk_long-range_2015, lutsker_implementation_2015}. This is followed by the formulation of the FMO-ansatz for the description of the electronic ground state. Subsequently, we present how the molecular orbitals of the total system can be calculated and introduce a theoretical approach for calculating electronically excited states. This is concluded with a description of the necessary Hamiltonian matrix elements and the computational procedure that is used in our implementation. \nThroughout the paper we use atomic units and the following notation convention: atoms are denoted as uppercase letters from A-H and molecular fragments from I-Z without indices. Uppercase letters with indices denote matrix elements and bold uppercase letters matrices. For molecular orbital (atomic orbital) indices lowercase (greek) letters are used. \nIt should be noted that in the following we use the terms fragment and monomer synonymously to refer to a molecular unit. Likewise, we use (molecular) cluster and aggregate synonymously to refer to a large number of molecular units that are not covalently linked. \n\n\\subsection{Long-range corrected DFTB (LC-DFTB)}\nAs shown previously, the formalism of LC-DFTB can be derived by a Taylor expansion of a long-range corrected full density functional (e.g. LC-PBE) around a reference density that is given by a sum of atomic densities, as described in detail elsewhere \\cite{humeniuk_long-range_2015, lutsker_implementation_2015}. In the following, we will only provide a brief summary of the working equations. After employing the usual tight-binding (TB) approximations\\cite{elstner_self-consistent-charge_1998} the total energy in SCC LC-DFTB is given by:\n\\begin{align}\nE=& \\sum_{\\mu \\nu} P_{\\mu \\nu} H_{\\mu \\nu}^{0}  \\tag{band structure energy}\\\\\n&+ \\frac{1}{2} \\sum_{\\mu, \\sigma, \\lambda, \\nu} \\Delta P_{\\mu \\sigma} \\Delta P_{\\lambda \\nu}(\\mu \\sigma \\mid \\lambda \\nu) \\tag{Coulomb energy} \\\\\n&-\\frac{1}{4} \\sum_{\\mu, \\sigma, \\lambda, \\nu} \\Delta P_{\\mu \\sigma}  \\Delta P_{\\lambda \\nu}(\\mu \\lambda \\mid \\sigma \\nu)_{\\operatorname{lr}}\\tag{exchange energy}\\\\\n& + \\sum_{A, B} V_{A B}^{\\mathrm{rep}}\\left(R_{A B}\\right)\\tag{repulsion energy} \n\\label{eq:dftb_energy}\n\\end{align}\nHere $P_{\\mu \\nu}$ denotes the electron density matrix elements and $H_{\\mu \\nu}^{0}$ the one-electron Hamiltonian matrix elements. The electron density difference matrix is defined as $\\Delta \\mathbf{P} = \\mathbf{P} - \\mathbf{P}^0$, where $\\mathbf{P}^0$ is the diagonal reference electron density matrix. The deviation of the Mulliken charge $q_A$ on Atom A from the charge of the neutral Atom $q^0_A$ is given by\n\\begin{align}\n    \\Delta q_A &= q_A - q^0_A \\\\\n    &= \\sum_{\\mu \\in A} \\sum_{\\nu} \\left[\\mathbf{P}_{\\mu\\nu} S_{\\mu\\nu} - \\mathbf{P}^0_{\\mu\\nu} S_{\\mu\\nu} \\right],\n\\end{align}\nwhere $S_{\\mu\\nu}$ represents a matrix element of the overlap matrix.\n\nApplying the tight-binding approximations to the two-electron integrals in the Coulomb and exchange part of the energy and neglecting all 3- and 4-center integrals gives the following expressions: \n\\begin{align*}\n(\\mu \\lambda \\mid \\sigma \\nu) &=\\iint \\phi_{\\mu}(r_1) \\phi_{\\lambda}(r_1) \\frac{1}{r_{12}} \\phi_{\\sigma}(r_2) \\phi_{\\nu}(r_2) \\mathrm{d} 1 \\mathrm{d} 2 \\\\\n& \\approx \\sum_{A, B} \\gamma_{A B} q_{A}^{\\mu \\lambda} q_{B}^{\\sigma \\nu}  \\numberthis{}{}\n\\label{eq:2e_approx_ao}\n\\end{align*}\nwith the transition charges on atom $A$ (in the atomic orbital basis) defined as\n\\begin{equation}\nq_{A}^{\\mu \\lambda}=\\frac{1}{2}(\\delta(\\mu \\in A)+\\delta(\\lambda \\in A)) S_{\\mu \\nu}\n\\label{eq:q_between_aos}\n\\end{equation}\nThe $\\bm{\\gamma}$-matrices for charge fluctuation interactions can be calculated assuming that the charge fluctuations can be represented by spherical Gaussian functions, leading to\n\\begin{equation}\n\\gamma_{A B}=\\frac{\\operatorname{erf}\\left(C_{A B} R\\right)}{R},\n\\label{eq:gamma}\n\\end{equation}\nwhere $R$ is the distance between the atomic centers $A$ and $B$ and $C_{A B}=(2\\left(\\sigma_A^2+\\sigma_B^2\\right))^{-\\frac{1}{2}}$ depends on the widths $\\sigma_A$ and $\\sigma_B$ of the charge clouds on the two atoms. The widths are determined by the atom-specific Hubbard parameters $U_A$ as $\\sigma_A= (\\sqrt{\\pi} U_A)^{\\frac{1}{2}}$.\nIn LC-DFTB the Coulomb potential is separated into a long-range and a short range part where the position of the smooth transition between the two regimes is controlled by the long-range radius $R_{\\mathrm{lr}}$\n\\begin{equation}\n\\frac{1}{r}=\\underbrace{\\frac{1-\\operatorname{erf}\\left(\\frac{r}{R_{\\mathrm{lr}}}\\right)}{r}}_{\\text {short range }}+\\underbrace{\\frac{\\operatorname{erf}\\left(\\frac{r}{R_{\\mathrm{lr}}}\\right)}{r}}_{\\text {long range }}.\n\\end{equation}\nThe short range term is already included by the local exchange-correlation functional employed in LC-DFTB. The electron integrals of the screened Coulomb potential for the long-range contribution can be calculated as \n\\begin{align*}\n(\\mu \\lambda \\mid \\sigma \\nu)_{\\mathrm{lr}} &=\\iint \\phi_{\\mu}(r_1) \\phi_{\\lambda}(r_1) \\frac{\\operatorname{erf}\\left(\\frac{r_{12}}{R_{\\mathrm{lr}}}\\right)}{r_{12}} \\phi_{\\sigma}(r_2) \\phi_{\\nu}(r_2) \\mathrm{d} 1 \\mathrm{d} 2 \\\\\n& \\approx \\sum_{A, B} \\gamma_{A B}^{\\operatorname{lr}} q_{A}^{\\mu \\lambda} q_{B}^{\\sigma \\nu}. \\numberthis{}{}\n\\label{eq:2e_approx_ao_lr}\n\\end{align*}\n The long-range $\\gamma$-matrix is defined similarly to the $\\gamma$-matrix in eq. \\ref{eq:gamma},\n\\begin{equation}\n\\gamma_{A B}^{\\operatorname{lr}}=\\frac{\\operatorname{erf}\\left(C_{A B}^{\\mathrm{lr}} R\\right)}{R},\n\\end{equation}\nwhere\n\\begin{equation}\nC_{A B}^{\\mathrm{lr}}=\\frac{1}{\\sqrt{2\\left(\\sigma_A^2+\\sigma_B^2+\\frac{1}{2} R_{\\mathrm{lr}}^2\\right)}}\n\\end{equation}\ndepends on the range-separation parameter $R_{\\mathrm{lr}}$.\nThe transformation of the two-electron repulsion integrals into molecular orbital (MO) basis leads to the following expressions:\n\\begin{equation}\n    (pq \\mid rs ) \\approx \\sum_{A} \\sum_{B} q_{A}^{pq} \\gamma_{AB} q_{B}^{rs}\n    \\label{eq:2e_approx_mo}\n\\end{equation}\nand \n\\begin{equation}\n    (pq \\mid rs )_{\\mathrm{lr}} \\approx \\sum_{A} \\sum_{B} q_{A}^{pq} \\gamma_{AB}^{\\mathrm{lr}} q_{B}^{rs}\n    \\label{eq:2e_approx_mo_lr}\n\\end{equation}\nThe atom-centered transition charges between MOs are defined as: \n\\begin{equation}\nq_{A}^{i j}=\\frac{1}{2} \\sum_{\\mu \\in A} \\sum_{\\nu}\\left(c_{\\mu}^{i} c_{\\nu}^{j}+c_{\\nu}^{i} c_{\\mu}^{j}\\right) S_{\\mu \\nu}\n\\label{eq:q_between_mos}\n\\end{equation}\nVariational minimization of the LC-DFTB energy with respect to the molecular orbitals leads to the corresponding Hamiltonian, that is defined as: \n\\begin{align*}\nH_{\\mu \\nu}^{\\mathrm{SCC}} &=H_{\\mu \\nu}^{0}+\\frac{1}{2} S_{\\mu \\nu} \\sum_{C}\\left(\\gamma_{A C}+\\gamma_{B C}\\right) \\Delta q_{C} \\\\\n&-\\frac{1}{8} \\sum \\Delta P_{\\alpha \\beta} S_{\\mu \\alpha} S_{\\beta \\nu}\\left(\\gamma_{\\mu \\beta}^{\\mathrm{lr}}+\\gamma_{\\mu \\nu}^{\\mathrm{lr}}+\\gamma_{\\alpha \\beta}^{\\mathrm{lr}}+\\gamma_{\\alpha \\nu}^{\\mathrm{lr}}\\right) \\numberthis{}{} \\label{eq:scc_hamiltonian}\n\\end{align*}\nThe ground state MOs and their energy are obtained by a self consistent procedure for solving the following general eigenvalue problem\n\\begin{equation}\n    \\mathbf{Hc} = \\epsilon\\mathbf{Sc}\n\\end{equation}\n\nBeing a semiempirical theory, (LC)-DFTB is heavily dependent on a parametrization for the electronic Hamiltonian, $H_{\\mu \\nu}^{0}$, the overlap matrix $S_{\\mu \\nu}$ and the repulsive potentials  $V_{A B}^{\\mathrm{rep}}$. The parametrization usually starts with the computation of pseudoorbitals, the tabulation of Slater-Koster files and ends with the fitting of repulsive potentials \\cite{elstner_density_2014,koskinen_density-functional_2009,spiegelman_density-functional_2020}. A benchmark of the used LC-DFTB parametrization for organic and biological molecules is given in Ref.\\cite{vuong_parametrization_2018}.\n\n\n\\subsection{Fragment molecular orbital LC-DFTB (FMO-LC-DFTB)}\nThe fragment molecular orbital method in combination with DFTB was developed by Nishimoto, Fedorov and Irle\\cite{nishimoto_density-functional_2014}. Recently, it was adopted to LC-DFTB by Niehaus and Irle\\cite{vuong_fragment_2019} and this theory forms the basis for our ground-state calculations. Therefore, we will only restate the most important equations in the following and refer to Ref. \\cite{nishimoto_density-functional_2014} and Ref. \\cite{vuong_fragment_2019} for a more detailed description. Only the case of molecular clusters --- molecules that are not covalently connected --- is considered in this work, and therefore, we do not introduce the hybrid orbital projection operator \\cite{nakano_fragment_2000}.\nThe total energy of the entire system in the self-consistent FMO-LC-DFTB is given by\n\\begin{equation}\nE=\\sum_{I}^{N} E_{I}+ \\frac{1}{2} \\sum_{I}^{N} \\sum_{J}^N \\left(E_{I J}-E_{I}-E_{J}\\right).\n\\label{eq:fmo_energy}\n\\end{equation}\nHere $E_I$ ($E_J$) are the energies of fragment $I$ ($J$) and $E_{IJ}$ is the energy of the pair $IJ$. The total number of fragments is denoted as $N$, while we will use $N_I$ for the number of atoms in fragment $I$. \nThe energies $E_X$ where $X$ is either $I$ or $IJ$ can be further separated into a part that depends only on the isolated molecule and another one that accounts for the environment of the molecule:\n\\begin{equation}\nE_{X}=E_{X}^{\\prime}+E_{X}^{\\mathrm{em}}\n\\label{eq:frag_energy}\n\\end{equation}\nThe former is the so-called internal energy, $E_{X}^{\\prime}$, which is equivalent to the total energy calculated in conventional LC-DFTB of entity $X$. The embedding energy, $E_{X}^{\\mathrm{em}}$, accounts for the Coulomb interaction between the entity $X$ and all other fragments: \n\\begin{equation}\nE_{X}^{\\mathrm{em}}=\\sum_{A \\in X} \\sum_{K \\neq X}^{N} \\sum_{C \\in K} \\gamma_{A C} \\Delta q_{A}^{X} \\Delta q_{C}^{K}\n\\label{eq:embedding_energy_frag}\n\\end{equation}\nInserting eq. \\ref{eq:frag_energy} and eq. \\ref{eq:embedding_energy} in eq. \\ref{eq:fmo_energy} allows to rewrite the total FMO energy as: \n\\begin{equation}\\label{eq:total_fmo_energy}\nE=\\sum_{I}^{N} E_{I}^{\\prime}+ \\frac{1}{2} \\sum_{I}^{N} \\sum_{J}^N \\left(E_{I J}^{\\prime}-E_{I}^{\\prime}-E_{J}^{\\prime}\\right)+ \\frac{1}{2} \\sum_{I}^{N} \\sum_{J}^{N} \\Delta E_{I J}^{\\mathrm{em}}\n\\end{equation}\nThe last term on the r.h.s. is the difference in embedding energy of the pair and corresponding embedded but noninteracting monomers. \n\\begin{equation}\\label{eq:embedding_energy}\n\\Delta E_{I J}^{\\mathrm{em}} = E_{I J}^{\\mathrm{em}} - E_{I}^{\\mathrm{em}} - E_{J}^{\\mathrm{em}} = \\sum_{A \\in I J} \\sum_{K \\neq I, J}^{N} \\sum_{C \\in K} \\gamma_{A C} \\Delta \\Delta q_{A}^{I J} \\Delta q_{C}^{K}\n\\end{equation}\nHere $\\Delta \\Delta q_{A}^{I J}$ denotes the difference between charges of pair $IJ$ and charges of fragments $I$ and $J$ for atom $A$:\n\\begin{align}\n\\Delta \\Delta q_{A}^{I J}   &= \\Delta q_{A}^{I J} - ( \\Delta q_{A}^{I} \\oplus \\Delta q_{A}^{J}) \\\\\n\\Delta q_{A}^{I} \\oplus \\Delta q_{A}^{J}  &= \\Delta q_{A}^{I}  \\text { for } A \\in I \\text { and } A \\notin J,\\\\\n                            &= \\Delta q_{A}^{J} \\text { for } A \\in J \\text { and } A \\notin I, \n\\end{align}\nWe employ the electrostatic dimer (ES-DIM) approximation \\cite{nakano_fragment_2002} for pairs, in which the fragments are so far separated, that their orbital overlap will be zero. The energy of the far-separated pairs is given by \n\\begin{equation}\\label{eq:esdim_energy}\nE_{I J}^{\\prime} = E_I^{\\prime}+E_J^{\\prime}+\\sum_{A \\in I} \\sum_{B \\in J} \\gamma_{A B} \\Delta q_A^I \\Delta q_B^J.\n\\end{equation}\nIt should be noted that although it is possible to separate the total energy into internal and embedding energies, the tight-binding Hamiltonian of an entity (\\textit{cf.} eq. \\ref{eq:scc_hamiltonian}) also depends on the electron density or, more specifically, the charges of all the other fragments\n\\begin{equation}\\label{eq:fragment_hamiltonian}\nH_{\\mu \\nu}^{X}=H_{\\mu \\nu}^{S C C, X}+V_{\\mu \\nu}^{X}\n\\end{equation}\nwhere, $V_{\\mu \\nu}^{X}$, is the electrostatic potential (ESP) that acts on fragment $X$ and is defined as: \n\\begin{equation}\n    V_{\\mu \\nu}^{X} = \\frac{1}{2} S_{\\mu \\nu}^X \\sum_{K \\notin I}^N \\sum_{C \\in K}^{N_K} \\left(\\gamma_{A C}+\\gamma_{B C}\\right) \\Delta q_{C} \\label{eq:electrostatic_potential}\n\\end{equation}\nThis makes it necessary to perform the SCC iterations for fragments self-consistently so that one iteration step per fragment is made to update all charges simultaneously. The obtained self-consistent charges are afterwards used for the calculation of the SCC iterations on pairs for which the ES-DIM approximation is not used. \\\\\n\nCalculating the electronic ground state in the context of FMO(-DFTB) allows one to make accurate calculations of the energy, but one does not obtain MOs of the entire system. Instead, one obtains only the MOs for each of the fragments and all fragment pairs that are not affected by the ES-DIM approximation. \nSince they are obtained by independent calculations such MOs are not orthogonal. However, it is possible, as shown by Tsuneyuki \\textit{et al.} \\cite{tsuneyuki_molecular_2009}, to construct orthogonal MOs for the whole system and to transform the Hamiltonian into such basis by using L\u00f6wdin's approach\\cite{lowdin_nonorthogonality_1950}\n\\begin{equation}\\label{LCMO_fock_4}\n    \\mathbf{H}^{\\prime}=\\mathbf{S}^{-1 \/ 2} \\mathbf{H}^{\\mathrm{LCMO}} \\mathbf{S}^{-1 \/ 2}.\n\\end{equation}\nSince the computation of the matrix inverse of the total overlap is computationally demanding and the overlap matrix in the basis of the fragments and pairs is almost diagonal, we approximate it in first order by\n\\begin{equation}\n    \\mathbf{S}^{-1 \/ 2} \\approx \\frac{3}{2} \\mathbf{1} - \\frac{1}{2} \\mathbf{S}\n    \\label{eq:invers_S_approx}\n\\end{equation}\nwhere the overlap matrix matrix elements are given by\n\\begin{equation}\n    S_{pq}^{IJ} = \\langle \\varphi_p^I | \\varphi_q^J \\rangle\n\\end{equation}\nand $\\varphi_p^I$ is the $p$-th MO of fragment $I$. \nThe Hamiltonian of the whole system, $\\mathbf{H}^{\\mathrm{LCMO}}$, can be constructed from the Hamiltonian matrices of the corresponding fragments and pairs as\n\\begin{equation}\\label{LCMO_fock_1}\n    \\mathbf{H}^{\\mathrm{LCMO}}=\\sum_{I}^N \\oplus \\mathbf{H}^{I}+ \\frac{1}{2} \\sum_{I}^N \\sum_{J \\neq I}^N \\oplus\\left(\\mathbf{H}^{I J}-\\mathbf{H}^{I} \\oplus \\mathbf{H}^{J}\\right).\n\\end{equation}\nThe $\\oplus$ sign indicates that each block in the total Hamiltonian matrix is filled with the Hamiltonian of the corresponding fragment ($\\mathbf{H}^{I}$) or fragment pair ($\\mathbf{H}^{IJ}$). \n\nIn contrast to the diagonal Hamiltonian matrix of the fragments \n\\begin{equation}\\label{LCMO_fock_2}\n  \\epsilon_{a}^X    =  \\delta_{a b} H^X_{a b},\n\\end{equation}\nwhere $\\epsilon_{a}$ is the $a$-th MO energy of fragment $X$, the Hamiltonian of pair $IJ$ accounts for the fact that the MOs between the fragments might not be strictly orthogonal\n\\begin{equation}\\label{LCMO_fock_3}\n    H^{IJ}_{ab} = \\sum_{r} \\epsilon_{r}^{IJ} \\langle \\varphi_a^I \\mid \\varphi_r^{IJ} \\rangle \\langle \\varphi_b^J \\mid \\varphi_r^{IJ} \\rangle \n\\end{equation}\nwhere the sum runs over all MOs of the pair $IJ$. Of course, it would now be possible to determine the eigenvectors of the Hamiltonian and thereby obtain the molecular orbitals of the entire system. In principle, once the MOs of the whole system are available, the excited states could be calculated using standard TD-DFTB procedure. While this seems straightforward, the disadvantage is that the calculation of the excited states are as costly as in a non-FMO approach and one would lose the scalability of the method. \n\n\\subsection{Excited states in the frame of FMO-LC-DFTB}\\label{sec:quasi_diabatic_states}\nAn alternative way to compute excited states in the framework of the FMO-Ansatz is motivated by the idea that an excited state wavefunction of the whole system can be expressed as a linear combination of basis states of the respective fragments and fragment pairs. Since we restrict ourselves to the interaction between two fragments in FMO, we also use only locally excited (LE) states on one fragment and charge-transfer (CT) states between two fragments as basis states. The electronic excited state wavefunction, $|\\Psi\\rangle$, of a large molecule assembly can then be expressed as \n\\begin{equation}\n\\left|\\Psi\\right\\rangle=\\sum_{I}^N \\sum_{m}^{N_{\\mathrm{LE}}} c_I^m \\left|\\mathrm{LE}_I^m \\right\\rangle+ \\sum_{I}^{N} \\sum_{J \\neq I}^{N} \\sum_{m}^{N_{\\mathrm{CT}}} c_{I\\rightarrow J}^m \\left| \\mathrm{CT}_{I \\to J}^{m}\\right\\rangle    \n\\label{eq:es_wf}\n\\end{equation}\nwhere the coefficients for fragment LE and CT configuration state functions (CSFs) are given by $c_I^m$ and $c_{I\\rightarrow J}^m$, respectively. The coefficients are obtained by solving the eigenvalue problem $\\mathbf{Hc} = \\mathbf{Ec}$. Notice that we assume that the basis states are orthogonal such that $\\mathbf{S} = \\mathbf{1}$. However, in the calculation of the Hamiltonian matrix elements the overlap matrix is explicitly included. This is in line with other semi-empirical methods that employ the same approximation. On the basis of FMO Hartree-Fock theory this approach was introduced by Fujita and Mochizuki\\cite{fujita_development_2018}. However, we will show that our definition of the CT states differs and how this impacts not only the energies but also the scaling of the method. \nThe ansatz in eq. \\ref{eq:es_wf} allows one to choose the energetically lowest basis states by setting the number of LE states per fragment ($N_{\\mathrm{LE}}$) and the number of CT states per pair ($N_{\\mathrm{CT}}$) to appropriate values. The number of eigenvalues for the corresponding eigenvalue problem then is given by $N \\cdot N_{\\mathrm{LE}} + (N^2 - N) \\cdot N_{\\mathrm{CT}}$. Furthermore, since these basis states are per definition locally excited or charge-transfer states the adiabatic states' eigenvectors (cf. \\ref{eq:es_wf}) contain the state character information. In principle, it would also be possible to extend this approach to doubly or even higher excited states.  \\\\\nThe LE states, $\\left|\\mathrm{LE}_{\\mathrm{I}}^m\\right\\rangle$, are calculated as singly excited states of a fragment. We restrict ourselves in this work to singlet  states, but it should be noted that this approach can be extended to triplet excited states in a straightforward way. The $m$-th excited state (S$_m$) on fragment $I$ defines the following LE basis state: \n\\begin{align}\n    \\left|\\mathrm{LE}_{\\mathrm{I}}^m\\right\\rangle &= \\sum_{i \\in I}\\sum_{a \\in I} T_{i a}^{m(I)}\\frac{1}{2}\\left(a_{\\mathrm{Ia}, \\alpha}^{\\dagger} a_{\\mathrm{Ii}, \\alpha}+a_{\\mathrm{Ia}, \\beta}^{\\dagger} a_{\\mathrm{Ii}, \\beta}\\right)|G\\rangle \\\\\n    &= \\sum_{i \\in I}\\sum_{a \\in I}  T_{i a}^{m(I)} | \\Phi_{I}^{i\\to a} \\rangle\n    \\label{eq:LE_states}\n\\end{align}\nHere, $a_{I a, \\alpha}^{\\dagger}$ and $a_{I a, \\beta}$ are the creation and annihilation operators of the $\\alpha$ and $\\beta$ spin electron in the $a$th orbital of fragment $I$, and $|G\\rangle$ is the ground-state wavefunction.\n$\\mathbf{T}^{m(I)}$ is the one-particle transition density matrix of the $m$-th excited state of fragment $I$ in the MO basis and $|\\Phi_{I}^{i\\to a} \\rangle$ is the configuration state function of the excitation from the occupied orbital $i$ to the virtual orbital $a$ on fragment $I$.\\\\\nSimilarly, the $m$-th intermolecular CT state from fragment $I$ (hole) to fragment $J$ (particle) can be defined as: \n\\begin{align}\n    \\left|\\mathrm{CT}_{I \\to J}^{m}\\right\\rangle &=\\sum_{i \\in I}\\sum_{a \\in J} T_{i a}^{m(IJ)} \\frac{1}{2}\\left(a_{\\mathrm{Ja}, \\alpha}^{\\dagger} a_{\\mathrm{Ii}, \\alpha}+a_{\\mathrm{Ja}, \\beta}^{\\dagger} a_{\\mathrm{Ii}, \\beta}\\right)|G\\rangle \\\\\n    &= \\sum_{i \\in I}\\sum_{a \\in J} T_{i a}^{m(IJ)} | \\Phi_{I \\to J}^{i\\to a} \\rangle\n    \\label{eq:CT_states}\n\\end{align}\nThe transition between the fragments $I$ and $J$ is restricted to the occupied orbitals of monomer $I$ and the virtual orbitals of monomer $J$. The definition of the CT state differs to the approach of Fujita and Mochizuki\\cite{fujita_development_2018} as they use the following  single configuration state function as a CT state\n\\begin{equation}\n    \\left|\\mathrm{CT}_{I \\to J}^{i \\to a}\\right\\rangle=\\frac{1}{2}\\left(a_{\\mathrm{Ja}, \\alpha}^{\\dagger} a_{\\mathrm{Ii}, \\alpha}+a_{\\mathrm{Ja}, \\beta}^{\\dagger} a_{\\mathrm{Ii}, \\beta}\\right)|G\\rangle =  | \\Phi_{I \\to J}^{i\\to a} \\rangle.\n    \\label{eq:CT_states_fujita}\n\\end{equation}\nBoth approaches have their merits, and we will briefly explain below why we define CT states as shown in equation \\ref{eq:CT_states}. The latter necessitates solving the CIS matrix for the lowest $N_{\\mathrm{CT}}$ charge-transfer states of each pair. Therefore, the construction of the basis states will no longer scale linearly with the number of fragments but quadratically. Nevertheless, this approach has the advantage that all electronic couplings between CT states on a pair are omitted since these are eigenstates of the pair. Furthermore, in both approaches, a restriction of the considered CT states or occupied and virtual orbitals is necessary. Using equation \\ref{eq:CT_states}, we can choose to use the $N_{\\mathrm{CT}}$ lowest energy CT states and ensure that all relevant orbitals for these states are considered, whereas with eq. \\ref{eq:CT_states_fujita}, the selection of states is made by considering $N_{\\mathrm{hole}}$ occupied and  $N_{\\mathrm{particle}}$ virtual MOs. A higher number of included orbitals quickly leads to very large eigenvalue problems as the number of considered CT states scales with $(N^2 - N) \\cdot N_{\\mathrm{hole}} \\cdot N_{\\mathrm{particle}}$. We will show in section \\ref{sec:accuracy_excited_states} how the accuracy of the excitation energies and the computational scaling depend on using either eq. \\ref{eq:CT_states} or \\ref{eq:CT_states_fujita} for the definition of charge-transfer states and that the usage of eq. \\ref{eq:CT_states} is generally preferable. \n\n\\subsection{Hamiltonian matrix elements}\\label{sec:DiabaticHamiltonian}\nThe definition of basis states in eq. \\ref{eq:LE_states} and \\ref{eq:CT_states} allows to express the matrix elements of the system Hamiltonian. We will first focus on the excitation energies (diagonal matrix elements) of LE and CT states. The energies are calculated by a LC-DFTB\\xspace calculation of the fragment (pair)\n in the framework of linear-response LC-TD-DFT, which was adapted to tight-binding DFT by Niehaus \\textit{et al.}\\cite{niehaus_tight-binding_2001} and has been extended to include the LC correction by some of us\\cite{humeniuk_long-range_2015}. In linear-response TD-DFT excited states are computed by solving the non-Hermitian eigenvalue problem \n\\begin{equation}\n    \\left(\\begin{array}{ll}\n\\mathbf{A} & \\mathbf{B} \\\\\n\\mathbf{B} & \\mathbf{A}\n\\end{array}\\right)\\left(\\begin{array}{l}\n\\mathbf{X} \\\\\n\\mathbf{Y}\n\\end{array}\\right)=\\bm{\\omega}\\left(\\begin{array}{cc}\n\\mathbf{1} & 0 \\\\\n0 & -\\mathbf{1}\n\\end{array}\\right)\\left(\\begin{array}{l}\n\\mathbf{X} \\\\\n\\mathbf{Y}.\n\\end{array}\\right)\\label{eq:Casida}\n\\end{equation}\nIn the framework of LC-TD-DFTB\\xspace the matrices $\\mathbf{A}$ and $\\mathbf{B}$ are defined as\\cite{humeniuk_long-range_2015}\n\\begin{align}\n    A_{i a, j b} &=\\delta_{i j} \\delta_{a b}\\left(\\epsilon_a-\\epsilon_i\\right)+2 \\sum_{A}\\sum_{B} q^{ia}_A \\gamma_{AB} q_B^{jb} - \\sum_{A} \\sum_{B} q^{ij}_A \\gamma_{AB}^{\\mathrm{lr}} q^{ab}_B \\\\\n    B_{i a, j b} &= 2 \\sum_{A}\\sum_{B} q^{ia}_A \\gamma_{AB} q_B^{jb} - \\sum_{A} \\sum_{B} q^{ib}_A \\gamma_{AB}^{\\mathrm{lr}} q^{aj}_B,\n\\end{align}\nwhere $\\epsilon_i$ is the energy of the $i$-th molecular orbital. The orbital energies $\\epsilon_i$ are represented by the diagonal elements of the orthogonalized total Hamiltonian $H^\\prime_{ii}$. Using the Tamm-Dancoff (TDA) approximation ($\\mathbf{B} = 0$), eq. (\\ref{eq:Casida}) is reduced to a simple Hermitian eigenvalue problem\n\\begin{equation}\n    \\mathbf{A} \\mathbf{X} = \\bm{\\omega} \\mathbf{X},\n\\end{equation}\nwhich can be solved iteratively for the lowest eigenvalues by employing the algorithm developed by Davidson\\cite{davidson_iterative_1975}. This is in principle equivalent to the configuration interaction singles (CIS) procedure. The energies of the CT states are calculated in analogy to the local excitations, where the excitations are restricted to the transition from the occupied orbitals of one monomer to the virtual orbitals of the other one.\n\nTo calculate the off-diagonal matrix elements of the Hamiltonian, the couplings between the basis states are required.\nIn accordance with Ref. \\cite{fujita_development_2018}, the Hamiltonian can be split into one electron\n\\begin{equation}\\label{One_electron_hamiltonian}\n    \\langle \\Phi_{I \\to J}^{i\\to a}|H_{1e}|\\Phi_{K \\to L}^{j \\to b} \\rangle = \\delta_{I K} \\delta_{i j} H_{a b}^{\\prime}-\\delta_{J L } \\delta_{a b} H_{i j}^{\\prime}\n\\end{equation}\nand two-electron contributions\n\\begin{equation}\\label{two_electron_hamiltonian}\n    \\langle \\Phi_{I \\to J}^{i\\to a} | H_{2 e} |\\Phi_{K \\to L}^{j \\to b} \\rangle =2\\left(i^{(I)} a^{(J)} \\mid j^{(K)} b^{(L)}\\right)-\\left(i^{(I)} j^{(K)} \\mid a^{(J)} b^{(L)}\\right),\n\\end{equation}\nwhich were derived using the usual Slater-Condon rules. The two-electron coupling matrix elements of the Hamiltonian require the calculation of the four-center electron repulsion integrals (\\textit{cf}. eq. \\ref{two_electron_hamiltonian}). In contrast to the work of Fujita and Mochizuki\\cite{fujita_development_2018}, the off-diagonal elements between the basis states that involve three or four fragments are not neglected.\n\n\n\\subsubsection{LE-LE matrix elements}\n The coupling between locally excited states is given only by the two-electron part, as the one electron coupling between locally excited states vanish due to the Slater-Condon rule,\n\\begin{align*}\n\\left\\langle \\mathrm{LE}_{I}^{m}\\left|H \\right| \\mathrm{LE}_{J }^{n}\\right\\rangle &=\\sum_{ia \\in I} \\sum_{jb \\in J} T_{i a}^{m(I)} T_{jb}^{n(J)}[2(i a \\mid j b) \\\\\n &-(ij \\mid ab)] \\label{le_le_coulomb} \\numberthis{}{}  \\\\\n\\approx& 2 \\sum_{A\\in I} \\sum_{B \\in J} q_{\\mathrm{tr}, A}^{m(I)} \\gamma_{AB} q_{\\mathrm{tr}, B}^{n(J)}\\\\\n-& \\sum_{A\\in IJ} \\sum_{B \\in IJ} \n\\sum_{ia \\in I} \\sum_{jb \\in J} T_{i a}^{(\\mathrm{Im})} T_{jb}^{(J n)} q_{A}^{ij} \\gamma_{AB}^{\\mathrm{lr}} q_{B}^{ab}, \\numberthis{}{} \\label{le_le_coupling}\n\\end{align*}\nwhere\n\\begin{equation}\n    q_{\\mathrm{tr}, A}^{m(I)} = \\sum_{ia} q_{A}^{ia} T_{i a}^{m(I)} \n\\end{equation}\nis the transition charge of the $m$-th excited state of the fragment $I$ on atom $A$. $q_{A}^{ij}$ and $q_{B}^{ab}$ are the atom-centered transition charges between the occupied and virtual orbitals of the two monomer fragements $I$ and $J$ (\\textit{cf}. eq. (\\ref{eq:q_between_mos})). The first term of the LE-LE coupling (\\textit{cf}. eq. \\ref{le_le_coulomb}) characterizes the Coulomb interaction between the transition densities of the respective excitations. The second term represents the exchange interaction.\nIn the case of LE states on far separated fragments, fragment pairs for which the ES-DIM approximation is used, the exchange contribution can be neglected as the overlap between both states will be zero: \n\\begin{equation}\n    \\left\\langle \\mathrm{LE}_{I}^{m}\\left|H\\right| \\mathrm{LE}_{J }^{n}\\right\\rangle \\approx 2 \\sum_{A\\in I} \\sum_{B \\in J} q_{\\mathrm{tr}, A}^{m(I)} \\gamma_{AB} q_{\\mathrm{tr}, B}^{n(J)}\n\\end{equation}\nTherefore, only the long-range Coulomb interaction is taken into account in this case. \n\n\\subsubsection{LE-CT matrix elements}\nThe Hamiltonian matrix elements between an LE state on fragment $I$ and a CT state which is formed by linear combination of holes on fragment $J$ and electrons on fragment $K$ contains a one-electron part\n\\begin{align*} \n    \\left\\langle\\mathrm{\\mathrm{LE}}_{I}^{m}\\left|H_{1 e}\\right| \\mathrm{CT}_{J \\to K}^{n}\\right\\rangle = & \\delta_{I J} \\sum_{ia \\in I}\\sum_{b \\in K} T_{ia}^{m(I)} T_{ib}^{n(IK)} H_{a b}^{\\prime} \\\\ &-\\delta_{I K}\n    \\sum_{ia \\in I}\\sum_{j \\in J} T_{i a}^{m(I)}T_{ja}^{n(JI)} H_{i j}^{\\prime}\n    \\label{eq:LE_CT_1e_coupling_2} \\numberthis{}{}\n\\end{align*}\nas well as a contribution from the two-electron interaction\n\\begin{align*}\n\\left\\langle \\mathrm{LE}_{\\mathrm{I}}^m\\left|H_{2 e}\\right| \\mathrm{CT}_{J \\to K}^{n}\\right\\rangle &= \\sum_{ia \\in I} \\sum_{j \\in J} \\sum_{b \\in K}  T_{i a}^{m(I)} T_{j b}^{n(JK)} [2(i a \\mid jb ) \\\\ &-( i j \\mid ab )] \\numberthis{}{} \\\\\n\\approx 2\\sum_{A \\in I}\\sum_{B \\in JK}& q_{\\mathrm{tr}, A}^{m(I)} \\gamma_{AB} q_{\\mathrm{tr}, B}^{n(JK)} \\\\\n- \\sum_{A \\in IJ}\\sum_{B \\in IK\n} &\\sum_{ia \\in I}  \\sum_{j \\in J}\\sum_{b \\in K}T_{ia}^{m(I)} T_{jb}^{n(JK)} q_{A}^{ij} \\gamma_{AB}^{\\mathrm{lr}} q_{B}^{ab}. \\label{le_ct_coupling} \\numberthis{}{}\n\\end{align*}\nThe first and second term in eq. \\ref{le_ct_coupling} correspond to the Coulomb and exchange interaction between the transition densities of the LE and CT state. The one-electron contribution is only non-zero if the CT state shares one of its fragment with the LE state and if the other fragment is in spatial proximity, so that the ES-DIM approximation is not used, because otherwise the matrix element $H_{pq}^{\\prime}$ will be zero. If both fragments of the CT state are far apart (ES-DIM approx.) from the fragment of the LE state then the exchange term of eq. \\ref{le_ct_coupling} will be zero and is neglected. In this case the matrix element becomes\n\\begin{equation}\n    \\left\\langle \\mathrm{LE}_{\\mathrm{I}}^m\\left|H\\right| \\mathrm{CT}_{J \\to K}^{n}\\right\\rangle  \n\\approx 2\\sum_{A \\in I}\\sum_{B \\in JK} q_{\\mathrm{tr}, A}^{m(I)} \\gamma_{AB} q_{\\mathrm{tr}, B}^{n(JK)}\n\\end{equation}\nand only the Coulomb interaction is calculated. \n\n\n\\subsubsection{CT-CT matrix elements}\nThe one-electron CT--CT coupling vanishes for $I \\neq K$ or $K \\neq L$ (\\textit{cf}. eq. \\ref{One_electron_hamiltonian}), and thus, is reduced to the diagonal contributions, which are included in the LC-TD-DFTB calculation of the CT state. \nThe two-electron off-diagonal coupling between two charge-transfer states is given by\n\\begin{align*}\n&\\left\\langle \\mathrm{CT}_{I \\to J}^{m(IJ)}\\left|H \\right| \\mathrm{CT}_{K \\to L}^{n (KL)}\\right\\rangle = \\\\ \n&\\sum_{i \\in I}\\sum_{a \\in J}\\sum_{j \\in K}\\sum_{b \\in L} T_{ia}^{m(IJ)} T_{jb}^{n(KL)}  [2(i a \\mid j b) -(i j \\mid a b)] \\numberthis{}{} \\\\\n&\\approx 2 \\sum_{A\\in IJ} \\sum_{B \\in KL} q_{\\mathrm{tr}, A}^{m(IJ)} \\gamma_{AB} q_{\\mathrm{tr}, B}^{n(KL)}\\\\\n&- \\sum_{i \\in I}\\sum_{a \\in J}\\sum_{j \\in K}\\sum_{b \\in L} \\sum_{A \\in IK} \\sum_{B \\in JL} T_{ia}^{m(IJ)} T_{jb}^{n(KL)}q_{A}^{ij} \\gamma_{AB}^{\\mathrm{lr}} q_{B}^{ab} \\numberthis{}{} \\label{ct_ct_coupling}\n\\end{align*}\nAs shown for the LE-LE and LE-CT matrix elements, we also neglect the exchange part of the coupling for the CT-CT couplings in case if either fragment $I$ and $K$ or $J$ and $L$ are different fragments that are far apart. Thus in this case the matrix element simplifies to\n\\begin{equation}\n    \\left\\langle \\mathrm{CT}_{I \\to J}^{m(IJ)}\\left|H\\right| \\mathrm{CT}_{K \\to L}^{n (KL)}\\right\\rangle \n\\approx 2 \\sum_{A\\in IJ} \\sum_{B \\in KL} q_{\\mathrm{tr}, A}^{m(IJ)} \\gamma_{AB} q_{\\mathrm{tr}, B}^{n(KL)} \\label{eq:CT_CT_ESDIM}\n\\end{equation}\n\n\\section{Computational procedure}\\label{sec:computational_procedure}\n\\begin{figure}[tbh!]\n    \\centering\n    \\includegraphics[width=\\linewidth]{pictures\/figure_1.pdf}\n    \\caption{Flowchart of the computational procedure of the entire FMO-LC-TDDFTB\\xspace calculation.}\n    \\label{flowchart}\n\\end{figure}\nHerein, the sequence of the steps necessary to carry out a FMO-LC-TDDFTB\\xspace calculation is briefly summarized. The flowchart displayed in Fig. \\ref{flowchart} shows the \norder of the different steps of a FMO-LC-TDDFTB\\xspace calculation and how the various parts of the calculation are connected. \n\nIn the first step, the input geometry is partitioned into the different monomer, pair and ES-DIM pair fragments. The ES-DIM approximation\\cite{nakano_fragment_2002} is applied if the closest distance between two fragments exceeds the threshold value of twice the sum of the van der Waals radii of the closest atoms. \n\nSubsequently, the coupled lc-DFTB SCC iterations of the monomer fragments are performed until the convergence of all monomer calculations is achieved. As the electrostatic potential between all monomer fragments is required to calculate the monomer Hamiltonian (\\textit{cf.} eq. \\ref{eq:fragment_hamiltonian}), the SCC iterations for all fragments are computed simultaneously in order to update the charges of all monomers in each step. The final self-consistent charges are stored, as they are necessary for the calculation of the pair, ES-DIM pair and embedding energies. The Anderson acceleration is used to speed up the convergence of the SCC routine \\cite{anderson_iterative_1965,zhang_globally_2020}. \n\nThen, using the electrostatic potential between all fragments (\\textit{cf}. eq. \\ref{eq:electrostatic_potential}) obtained from the previous step, the pair energies are calculated. The charges of the pair fragments are stored so that they can be used in the calculation of the embedding energy. The ES-DIM pair energy (\\textit{cf}. eq. \\ref{eq:esdim_energy}) and the embedding energy (\\textit{cf}. eq. \\ref{eq:embedding_energy}) are determined, using the charges of the monomer and pair fragments obtained from the previous SCC routines. The results of the fragment calculations are combined according to eq. (\\ref{eq:total_fmo_energy}), which yields the ground-state energy  of the FMO-LC-TDDFTB\\xspace approach.\n\nThereafter, the LCMO-Hamiltonian matrix is built according to eq. \\ref{LCMO_fock_4}--\\ref{LCMO_fock_3}, using the orbital energies, orbital coefficients and overlap matrices of the fragments. The $\\mathbf{H'}$ matrix is obtained by subsequent L\u00f6wdin orthogonalization. In order to construct the LE and CT basis states, LC-TD-DFTB\\xspace excited state calculations are performed for both the monomers, the pairs and the ES-DIM pairs, where the orbital energies of the respective fragments are replaced by the diagonal matrix elements of the $\\mathbf{H'}$ matrix. \n\nSubsequently, the off-diagonal matrix elements of the Hamiltonian are calculated according to the expressions for the couplings between the LE and CT states  given in eq. \\ref{le_le_coupling} -- \\ref{eq:CT_CT_ESDIM}. \nAs the calculation of the exchange terms in the eq. (\\ref{le_le_coupling}), (\\ref{le_ct_coupling}) and (\\ref{ct_ct_coupling}) includes all possible transitions between the orbitals of the monomer pairs, a screening of the one-particle transition density matrices $\\mathbf{T}$ was introduced, where only matrix elements over a certain threshold are considered. Thus, the number of transitions is limited to the actually contributing occupied and virtual orbitals of the fragments. \n\nAt the end of the FMO-LC-TDDFTB\\xspace calculation, the Davidson diagonalization is utilized to obtain the excited state energies and coefficients, which are then used to calculate the oscillator strengths.\n\nThe LC-TD-DFTB\\xspace and FMO-LC-TDDFTB\\xspace methods were implemented in our own software package DIALECT, which is available on Github\\cite{noauthor_dialect_2022}. \n\nAll calculations regarding the benchmarks and scaling tests were performed on a single core of a computing node with dual E5-2680 Xeon CPUs (2.4 GHz, 14 cores each), 188 Gb of DDR4 memory and a SATA hard drive. \n\nThe DFTB parameter set ob2-split\\cite{vuong_parametrization_2018} was employed in all calculations. In the case of the benchmark calculations, a long-range radius of 3.03~$a_0$ was used. In order to compensate the overestimation of the charge-transfer energies in the pentacene clusters, IP-EA tuning\\cite{stein_reliable_2009} was employed and an optimized long-range radius was used for these systems. This procedure will be described in greater detail in section \\ref{ch:pentacene_application}.\n\nThe Mercury\\cite{macrae_it_2020} program was employed to generate the various clusters of the anthracene, pentacene and perylen bisimide systems from their respective crystal structures\\cite{mason_crystallography_1964,holmes_nature_1999,lin_halochromic_2011}.\n\nIn case of the scans of potential energy curves of the pyrene dimer, the DFT-D3 dispersion correction\\cite{grimme_consistent_2010,grimme_effect_2011} was calculated using the simple-dftd3\\cite{ehlert_simple-dftd3_2021} program and the ob2-split dispersion parameters\\cite{vuong_parametrization_2018}.\n\\begin{figure*}[tb]\n    \\centering\n    \\includegraphics[width=\\linewidth]{pictures\/figure_2.pdf}\n    \\caption{(a) Potential energy curves of the ground state and the first 6 excited states of the pyren dimer along the $\\pi$--$\\pi$ stacking coordinate $R_z$. (b) Potential energy curves of the ground state and the first 4 excited states along the parallel shift coordinate $R_x$ at a $\\pi$--$\\pi$ stacking distance of 3.1 \\AA{}. (c) The contributions of the locally excited and charge transfer states to the excited states shown in b) for different values of $R_x$. For each monomer 20 local excitations and for each pair 15 charge-transfer states were used.}\n    \\label{dimer_scan}\n\\end{figure*}\n\\section{Results}\\label{sec:results}\n\\subsection{Accuracy of FMO-LC-TDDFTB\\xspace excited states}\\label{sec:accuracy_excited_states}\nThe accuracy of the FMO-LC-TDDFTB\\xspace methodology is evaluated calculating the excitation energies of $\\pi$-stacked dimers\nof pyrene. The potential energy curves of the first 6 excited states were calculated  as a function of the $\\pi$--$\\pi$ stacking distance $R_z$ and the parallel shift coordinate $R_x$. As a reference we performed calculations with the conventional LC-TD-DFTB\\xspace approach. The main purpose of this comparison is to test the FMO approach and the validity of the employed approximations and not to benchmark the general performance. The latter has been thoroughly benchmarked in previous works.\\cite{vuong_parametrization_2018, bold_benchmark_2020, fihey_performances_2019} In the case of the FMO-LC-TDDFTB\\xspace calculation, 20 locally excited states for each monomer and 15 charge-transfer states for each pair were included. In Fig. \\ref{dimer_scan}a, the electronic state energies of the FMO-LC-TDDFTB\\xspace and LC-TD-DFTB\\xspace methods are shown for a scan of the $\\pi$--$\\pi$ stacking distance $R_z$. While there is a slight deviation from the LC-TD-DFTB\\xspace energies at distances from 2.75~\\AA{} to 3.0~\\AA{}, the deviation between the two methods decreases with increasing interfragment distances. From a distance of 3.5~\\AA{} onwards, the results of the FMO-LC-TDDFTB\\xspace calculation show an excellent agreement with the LC-TD-DFTB\\xspace energies. Below distances of 2.75~\\AA{}, which already belong to the repulsive part of the potential energy curves, the deviation from the reference LC-TD-DFTB\\xspace calculation results from the non-orthogonality of the MOs.\n\nFig. \\ref{dimer_scan}b shows the potential energy curves of the pyrene dimer for a scan of the parallel shift coordinate $R_x$ at a $\\pi$--$\\pi$ stacking distance of 3.1~\\AA{}. Here, the results of the FMO-LC-TDDFTB\\xspace calculation are in good agreement with the LC-TD-DFTB\\xspace reference. \n\nAs the excited state Hamiltonian is constructed using LEs and CTs as basis states, the analysis of the excited state composition becomes easily accessible. The contributions of the LE and CT states to the first 4 excited states for different parallel shift distances are shown in Fig. \\ref{dimer_scan}c. As the shift along $R_x$ decreases, the contribution of the charge-transfer states increases. While the S$_1$, S$_2$ and S$_3$ state show CT character of up to 30\\%, 20\\% and 12\\%, the $S_4$ onlyconsists of local excitations for all $R_x$ values.\n\nIn addition, the influence of the number of basis states on the accuracy of the excited states energies was investigated. To this end, the mean absolute errors (MAEs) of the first 6 excited states were calculated for different numbers of LE and CT states. Table \\ref{Tab:MAE_pyrene_scan} shows the MAEs of the molecular aggregate for $\\pi$--$\\pi$ stacking distances of 2.5, 2.75, 3.0, 3.5, 4.0 and 5.0 \\AA{}. The results confirm that the accuracy of the excited state energies of the dimer calculated at the FMO-LC-TDDFTB\\xspace level is satisfactory. At an intermolecular distance of 4.0 \\AA{} the errors are as small as 2.7--5.6~meV. At 3.5~\\AA{}, the MAEs are 4.8--9.9 meV, showing a an almost perfect agreement to the LC-TD-DFTB\\xspace energies.\n\n\\begin{table}[tbh]\n\\centering\n\\caption{Mean absolute errors (MAEs) of the first 6 excited states for the pyrene dimer at various interplanar distances $R_z$ and number of basis states.}\n\\label{Tab:MAE_pyrene_scan}\n\\setlength\\tabcolsep{6.5pt}\n\\begin{tabular}{@{}cc|rrrrrr@{}}\n\\toprule\n     &      & \\multicolumn{6}{c}{MAE \/ meV}        \\\\ \\midrule\nN$_{\\mathrm{LE}}$ & N$_{\\mathrm{CT}}$ & 2.5 \\AA{}& 2.75 \\AA{} & 3.0 \\AA{}  & 3.5 \\AA{}& 4.0 \\AA{}& 5.0 \\AA{}\\\\ \\midrule\n5    & 5    & 433.7 & 136.4& 34.5  & 9.9 & 5.6 & 2.5 \\\\\n10   & 5    & 406.8 & 118.2& 23.7 & 5.9 & 3.2 & 1.4 \\\\\n10   & 10   & 192.9 & 74.2 & 21.6  & 5.6 & 3.2 & 1.4 \\\\\n15   & 10   & 194.6 & 73.7 & 21.6  & 5.6 & 3.2 & 1.4 \\\\\n20   & 15   & 186.2 & 72.7& 21.9  & 5.6 & 3.2 & 1.4 \\\\\n30   & 20   & 178.4 & 71.0& 20.6  & 4.8 & 2.7 & 1.2 \\\\ \\bottomrule\n\\end{tabular}\n\\end{table}\nAs expected, increasing the number of basis states improves the accuracy of the excited states energies. However, Table \\ref{Tab:MAE_pyrene_scan} shows that a further increase from 20 LE and 15 CT to 30 LE and 20 CT states yields only a marginal improvement of the MAEs as the additional states have a negligible electronic coupling to the first 6 excited states.\nAt all physically relevant intermolecular separations, the FMO-LC-TDDFTB\\xspace method almost perfectly reproduces the PES for the pyrene dimer. The deviations start to be visible at distances around 3~\\AA{}. Below 2.75~\\AA{}, which is already in the strongly repulsive part of the potential, the non-orthogonality of the MOs causes the deviation from the results of the LC-TD-DFTB\\xspace reference as the error in the couplings between the LE and CT states increases. Nevertheless, at distances at around 2.75~\\AA{} the MAEs are still relatively small; thus, the model should be sufficient for most physically realistic situations.\n\nTo evaluate the accuracy of our implementation of the charge-transfer states (\\textit{cf.} eq. \\ref{eq:CT_states}) in comparison to the approach of Fujita \\textit{et al.}\\cite{fujita_development_2018} (\\textit{cf.} eq. \\ref{eq:CT_states_fujita}), the mean absolute errors of the first 40 excited states from the LC-TD-DFTB\\xspace reference of a $\\pi$-stacked system of four pyrene monomers were calculated within both implementations. Fig. \\ref{ct_comparison} shows the results for stacking distances of 3.5 and 4.0 \\AA{}. For both methods, the number of LE states was set to 10 and the number of CT states was varied. As explained in section \\ref{sec:quasi_diabatic_states}, in our implementation, the dimension of the Hamiltonian grows linearly as we consider the lowest $N_{\\mathrm{CT}}$ states, and in the case of of Fujita's and Mochizuki's approach, the dimension of the Hamiltonian grows quadratically as all transitions between $N_{\\mathrm{hole}}$ occupied and $N_{\\mathrm{particle}}$ virtual orbitals are considered as separate CT states. As the amount of the charge-transfer states is increased for both implementations, the MAEs decrease in value. While both approaches achieve approximately the same accuracy, our method necessitates a much smaller size of the Hamiltonian. \n\n\\begin{figure}[h!]\n    \\centering\n    \\includegraphics[width=\\linewidth]{pictures\/figure_3.pdf}\n    \\caption{Comparison of the MAEs of both implementations of the charge-transfer states according to eq. (\\ref{eq:CT_states}) and (\\ref{eq:CT_states_fujita}) for different amounts of CT states at $\\pi$--$\\pi$ stacking distances of 3.5 and 4.0~\\AA{} for a system of four stacked pyrene molecules.}\n    \\label{ct_comparison}\n\\end{figure}\n\\begin{figure}[bth!]\n    \\centering\n    \\includegraphics[width=\\linewidth]{pictures\/figure_4.pdf}\n    \\caption{Simulated absorption spectra of an anthracene cluster containing 48 fragments (1152 atoms). The transitions to the first 40 excited states of the system were convolved using a Lorentzian line shape with a broadening of 2~meV. Two LE states and one CT state were used for each monomer and pair, respectively.}\n    \\label{spectrum_tda_vs_fmo}\n\\end{figure}\n\nIn order to investigate the accuracy of the FMO-LC-TDDFTB\\xspace method regarding the energies and oscillator strengths of larger systems, we compared the absorption spectra of an anthracene cluster composed of 48 fragments (1152 atoms) including the first 40 excited states for both theoretical methods. The basis was constructed using two LE states for each monomer and one CT state for each pair. The individual vertical transitions were convolved using a Lorentzian line-shape function with a width of 2~meV. The comparison between the calculated spectra is depicted in Fig. \\ref{spectrum_tda_vs_fmo} and shows a slight blue shift of the FMO-LC-TDDFTB\\xspace energies by about 20--30 meV. However, since the general error in TD-DFT and, in particular, in LC-TD-DFTB\\xspace excitation energies is on the order of 0.5~eV\\cite{vuong_parametrization_2018, fihey_performances_2019}, the additional error due to the FMO approach is hardly significant. Aside from slightly underestimating the intensity of the first peak, our approach could sufficiently reproduce the anthracene cluster's LC-TD-DFTB\\xspace absorption spectrum.\n\n\\subsection{Computational scaling of FMO-LC-TDDFTB\\xspace}\nTo investigate the computational efficiency of the developed method for the calculation of excited states, we compare the wall times of the method against conventional LC-TD-DFTB\\xspace for anthracene clusters containing up to 360 fragments (8640 atoms). In the case of the LC-TD-DFTB\\xspace approach, the number of fragments was limited to 48 (1152 atoms) due to the rapid increase in computational demand. For each cluster, the first 40 excited singlet states were calculated, and as in the previous anthracene calculation (\\textit{cf.} Fig. \\ref{spectrum_tda_vs_fmo}) two LE states per monomer and one CT state per pair were used for FMO-LC-TDDFTB\\xspace computations.\nThe wall times of the FMO-LC-TDDFTB\\xspace and LC-TD-DFTB\\xspace calculations are compared in Fig. \\ref{wall_time_fmo_vs_dftb}. In the case of the anthracene cluster containing 48 fragments (1152 atoms), a speedup factor of approx. $1.5\\times 10^4$ was achieved. Whereas the LC-TD-DFTB\\xspace calculation, using a full active space, took almost 11 days, the fragment approach finished in 60~seconds. \n\n\\begin{figure}[tbh!]\n    \\centering\n    \\includegraphics[width=\\linewidth]{pictures\/figure_5.pdf}\n    \\caption{Wall time comparison for an excited state calculation of anthracene clusters of different size between FMO-LC-TDDFTB\\xspace and LC-TD-DFTB\\xspace. The difference between using all molecular orbitals for the active and a reduced active space of only considering 20~\\% of the MOs is also shown.}\n    \\label{wall_time_fmo_vs_dftb}\n\\end{figure}\n\nFurthermore, we analyzed the timings of the LC-TD-DFTB\\xspace method using only 20~\\% of the active orbital space. As expected, this reduction in size of the $\\mathbf{A}$ matrix in the TDA-DFTB approach significantly accelerates the computation of excited states for the anthracene cluster consisting of 48 fragments which took 6293~seconds. However, the FMO-LC-TDDFTB\\xspace approach is still around 100 times faster for this system and the speedup grows to factor of more than 200 for the next bigger anthracene cluster containing 70 fragments (1680~atoms). \nIt should be noted that a restriction of the active spaces only lowers the prefactor of the method and not scaling. In addition, the restriction of the active orbitals leads to a loss of accuracy in (LC)-TD-DFTB as shown in Fig. \\ref{spectrum_tda_vs_truncated_tda}. While the energies and oscillator strength of FMO-LC-TDDFTB\\xspace with only two LE states and one CT state has shown a good agreement with LC-TD-DFTB\\xspace, the reduction of the active orbital space to 20~\\% leads to significantly larger errors of around 150~meV.\n\n\\begin{figure}[bth!]\n    \\centering\n    \\includegraphics[width=\\linewidth]{pictures\/figure_6.pdf}\n    \\caption{Simulated absorption spectrum (LC-TD-DFTB\\xspace: black, LC-TD-DFTB\\xspace with 20~\\% active space: blue) of an anthracene cluster containing 48 fragments (1152 atoms). The transition to the first 40 excited states of the system were convolved using a Lorentzian line shape with a broadening of 2~meV.}\n    \\label{spectrum_tda_vs_truncated_tda}\n\\end{figure}\n\n\\begin{figure*}[bth!]\n    \\centering\n    \\includegraphics[width=\\linewidth]{pictures\/figure_7.pdf}\n    \\caption{Timings of the FMO-LC-TDDFTB\\xspace excited state calculations for various a) anthracene and b) perylene bisimide clusters. The runtime scaling in relation to the system size is shown for different parts of the calculation on the right hand side of each figure. }\n    \\label{log_scaling}\n\\end{figure*}\n\nIn order to gain an insight into the time requirements of the different steps involved in a FMO-LC-TDDFTB\\xspace calculation, the total wall times have been split into separate parts. Fig. \\ref{log_scaling}a shows the timings of five steps: \n\\begin{enumerate}\n    \\item SCC: ground-state calculation of the entire systems\n    \\item $\\bm{H^{\\prime}}$ matrix: construction and L\u00f6wdin orthogonalization of the Hamiltonian matrix according to eq. \\ref{LCMO_fock_4} --\\ref{LCMO_fock_3}\n    \\item Basis states: calculation of LE and CT basis states of individual fragments and pairs according to section \\ref{sec:DiabaticHamiltonian}\n    \\item Couplings: computation of one- and two-electron coupling matrix elements between all LE and CT states according to eq. \\ref{le_le_coupling} -- \\ref{eq:CT_CT_ESDIM}\n    \\item Davidson: diagonalization of the Hamiltonian using the iterative Davidson procedure. \n\\end{enumerate}\n\nIn addition, the asymptotic scaling of the respective parts of the calculation was evaluated. With the increase in the size of the anthracene clusters, the Hamiltonian size grows up to a dimension of $129960^2$ for the system of 360 fragments (8640~atoms). Thus, the most time demanding steps are the calculation of the electronic couplings between the basis states and the following diagonalization for the lowest eigenvalues, which scale with factors of $\\mathcal{O}(N^{3.6})$ and $\\mathcal{O}(N^{5.1})$, respectively. The SCC routine implemented in our code shows the same nearly linear scaling of $\\mathcal{O}(N^{1.1})$, which has been reported previously\\cite{nishimoto_density-functional_2014}.\nAs the construction of the Fock matrix is limited by the scaling of the matrix multiplications during the L\u00f6wdin orthogonalization, it scales with a factor of $\\mathcal{O}(N^{2.9})$. Compared to the other parts of the calculation, the scaling of the construction of the basis states is negligible with a factor of $\\mathcal{O}(N^{1.9})$. \nThe combination of all steps of the procedure results in an effective scaling of $\\mathcal{O}(N^{3.4})$ for the total run time.\n\nA molecular system involving larger fragments was investigated to verify the effective scaling of the FMO-LC-TDDFTB\\xspace method. To this end, different clusters of substituted perylene bisimides (PBIs), where each monomer contains 142 atoms, were created, and the first 40 singlet excited states were calculated. Herefore, a basis of 2 locally excited states for each monomer and one charge-transfer state for each pair was employed. As shown in Fig. \\ref{log_scaling}b, the asymptotic scaling of the FMO approach remained approximately the same, if the Davidson diagonalization and the electronic couplings are excluded. Since the PBI clusters consist of distinctly less monomers than the anthracene clusters, the Hamiltonian is also significantly smaller. Subsequently, the fit of the scaling, which is strongly determined by the timings of the bigger clusters, results in smaller factors for the PBI systems, and thus, the total run time only scales with a factor of $\\mathcal{O}(N^{2.2})$. \nAs the system size grows above 100 fragments (approx. 15000 atoms), the calculation of the Hamiltonian becomes the most time consuming factor of the whole calculation.\nSubsequently, a further increase in the number of fragments would also result in a higher effective scaling factor as the Hamiltonian grows and the calculation of the couplings becomes the dominant aspect. \n\n\n\\subsection{Application to Pentacene} \\label{ch:pentacene_application}\nAfter demonstrating that FMO-LC-TDDFTB\\xspace can simulate excited states and absorption spectra with significantly reduced effort and, in return, at nearly the same accuracy as LC-TD-DFTB\\xspace, we wish to show the scope of possible applications by performing calculations on large pentacene clusters which serve as a model for bulk pentacene. This system has recently gained a lot of experimental and theoretical attention since it serves as a prototype for organic materials whose properties are determined by an interplay between local (Frenkel) and CT excitations.\\cite{zimmerman_mechanism_2011,zirzlmeier_singlet_2015,beljonne_charge-transfer_2013}\nThe FMO-LC-TDDFTB\\xspace method was used to simulate the absorption spectrum of pentacene clusters of different sizes, which were generated from crystal structure data. As a first step, an adjustment of the long-range radius was required since the energies of the pentacene aggregates' charge-transfer states are overestimated with the default radius of 3.03 $a_0$. Subsequently, ionization potential and electron affinity (IP-EA) tuning\\cite{stein_reliable_2009} were employed to estimate a reasonable value for the long-range radius by minimizing the following expression\n\\begin{equation}\n    (\\mathrm{IP}-\\epsilon_{\\mathrm{HOMO}})^2+(\\epsilon_{\\mathrm{LUMO}}-\\mathrm{EA})^2.\n\\end{equation}\nA scan of the radius yielded a minimum value of 6.875~$a_0$ as the optimal long-range radius which was used for all subsequent pentacene simulations. The ionization potential of 6.59~eV and the electron affinity of 1.35~eV were taken from experimental data of pentacene \\cite{coropceanu_hole-_2002,crocker_electron_1993}. A value of 6.67~eV and 1.77~eV  was obtained using the optimally tuned radius for $\\epsilon_{\\mathrm{HOMO}}$ and $\\epsilon_{\\mathrm{LUMO}}$, respectively.\n\\begin{figure}[bth!]\n    \\centering\n    \\includegraphics[width=\\linewidth]{pictures\/figure_8.pdf}\n    \\caption{Comparison between the experimental spectrum of a pentacene film \\cite{hammer_influence_2021} and the oscillator strengths of the FMO-LC-TDDFTB\\xspace calculation of pentacene clusters of various sizes. The energies of the clusters are red-shifted by 0.7 eV.}\n    \\label{pentacene_spectrum_vs_exp}\n\\end{figure}\n\nFor each of the pentacene clusters, which contain up to 319 fragments (11484 atoms), a calculation of the singlet excited state energies was performed. The basis states were constructed using three LE states for each monomer and one CT state for each pair. Depending on the system size, up to 3000 excited states have been calculated. The comparison between the experimental spectrum of a pentacene film\\cite{hammer_influence_2021} and our results is shown in Fig, \\ref{pentacene_spectrum_vs_exp}. The calculated oscillator strengths of the different pentacene clusters have been convolved with a Lorentzian line shape function of 10 meV width. In addition, the spectra were red-shifted by 0.7 eV to compensate for the error of the absorption energy. In the literature similar shifts are used even in the case of TD-DFT.\\cite{green_excitonic_2021, hoche_excimer_2021, rohr_exciton_2018} \n\nOverall, the calculated oscillator strengths for the first two bands of the absorption spectrum are in good agreement with the experimental spectrum. As the size of the pentacene clusters increases, the intensity of the first band grows in strength, while the oscillator strength of the second band shows a slight decrease in magnitude. Comparing the third and fourth absorption bands of the spectra, the deviation in the energy and intensity are apparent. While the intensity of the third peak is overestimated by a factor of two, the magnitude of the forth band is severely underestimated by FMO-LC-TDDFTB\\xspace. However, these discrepancies may partially stem from the fact that the influence of the vibrational modes is fully neglected in the present theory, which play a significant role in the case of the pentacene clusters.\\cite{benkyi_calculation_2019,craciunescu_accurate_2022, qian_herzbergteller_2020}\n\nStudying the excited states of large molecular systems leads to the question of how many monomers in a cluster contribute to an excited state. To this end, the participation numbers of the natural transition orbitals (NTOs)\\cite{luzanov_application_1976,luzanov_interpretation_1980} of the excited states of the pentacene clusters were calculated according to the expression\n\\begin{equation}\n    \\mathrm{PR}_{\\mathrm{NTO}}=\\frac{\\left(\\sum_i \\lambda_i\\right)^2}{\\sum_i \\lambda_i^2},\n\\end{equation}\nwhere $\\lambda_i$ are singular values which were obtained by a singular value decomposition (SVD) of the transition density matrix between the electronic ground state and a singlet excited state \\cite{plasser_new_2014}. Due to the fact that the pentacene monomers in the crystal structure all share the same internal coordinates, the locally excited states of the various monomers are nearly degenerate, which results in unrealistically high participation numbers for a perfectly arranged structure. In order to model the structural disorder that is present in a real system, we optimized the monomer geometry in the ground state using LC-DFTB\\xspace and sampled coordinates of the monomers from the ground-state canonical harmonic Wigner distribution.\\cite{bonacic-koutecky_theoretical_2005}\nSubsequently, the NTO participation numbers were calculated for the singlet excited states. In order to interpret the data, which showed strongly fluctuating participation numbers of the various states, the simple moving average was calculated by convolving the data with a rectangular window function. To guarantee a consistent approach, the width of the window was chosen to be 20\\% of the complete number of data points of the respective system. The resulting participation numbers of the different pentacene clusters are shown in Fig.~\\ref{participation_numbers}. \n\n\\begin{figure}[tbh!]\n    \\centering\n    \\includegraphics[width=\\linewidth]{pictures\/figure_9.pdf}\n    \\caption{Average participation numbers of the excited states of the Wigner-sampled pentacene clusters.}\n    \\label{participation_numbers}\n\\end{figure}\n\nAs expected, as the size of the pentacene clusters increases, the number of monomers contributing to the excited states grows. However, a convergence of the participation numbers would also be expected after a specific system size is reached. \nIn the case of the pentacene aggregates, the increase in the average participation number seems to be slowing down gradually.\n\\begin{figure}[tb!]\n    \\centering\n    \\includegraphics[scale=0.074]{pictures\/figure_10_a.png}\n    \\includegraphics[scale=0.074]{pictures\/figure_10_b.png}\n    \\caption{Particle and hole density (hole: blue, particle: red) of an excited state of the Wigner sampled pentacene cluster.\n    The state represents a high participation number of the system. The isovalue of the plot is 0.0001.\n    }\n    \\label{particle_hole_density}\n\\end{figure}\n\nIn order to visualize electron and hole delocalization the particle and hole density of a chosen pentacene system, containing 99 fragments (3564 atoms), was computed. The densities, which are shown in Fig. \\ref{particle_hole_density}, were selected due to their relative large participation number of 22.7. Both local excitations and charge-transfer states are discernible.\n\nThus, we have proven the applicability of our method to large molecular systems. The FMO-LC-TDDFTB\\xspace method is sufficient to estimate the excited state properties of molecular aggregates and can be used to analyze the composition of the excited states.\n\n\\section{Introduction}\nIn materials science, solid-state physics, biochemistry and many other branches of molecular sciences, the study of excited states is essential for understanding photochemical and photophysical processes as well as the function of molecular materials. Simulations of the excited state properties necessitate an accurate description of the electronic structure of molecular systems, which was first accomplished with ab-initio quantum chemical methods\\cite{friesner_new_1991,gonzalez_progress_2012}.\n\nHowever, investigating excited states of extended systems in the framework of the ab-initio approach requires very long calculation times due to the high computational scaling with the system size. With the development of the time-dependent density functional theory (TD-DFT), a reasonably fast method of calculating the excited state properties of relatively large molecular systems (over 100 atoms) became available \\cite{casida_time-dependent_1995,casida_progress_2012,laurent_td-dft_2013}. \nNew developments of approximative methods for the prediction of the nature of the excited states, including linear-scaling TD-DFT\\cite{wu_linear-scaling_2011}, subsystem density functional theory\\cite{jacob_subsystem_2014} and multilayer QM\/MM approaches (ONIOM)\\cite{dapprich_new_1999,vreven_combining_2006}, have further increased the applicability of TD-DFT to large polyatomic systems. However, despite the multitude of recent developments, the calculation of the excited states of molecular systems consisting of thousand atoms or more is still not possible even with TD-DFT.\n\nThe semiempirical quantum mechanical (SQM) methods, which approximate the wavefunction or density functional based methods, provide a further alternative for investigating the excited states of molecular systems. In the various SQM theories, a minimal basis set is used and the electronic integrals are approximated by the partial or complete neglect of the differential overlap between the atomic basis functions, which leads to a sizable increase in the computational efficiency  \\cite{thiel_semiempirical_2014,christensen_semiempirical_2016}. Whereas these approaches have been studied extensively in the 1970s--1990s\\cite{dewar_ground_1977,dewar_development_1985,stewart_optimization_1989,kolb_beyond_1993,thiel_extension_1996,weber_orthogonalization_2000}, the development of the self-consistent charge (SCC) density functional tight-binding (DFTB) method\\cite{porezag_construction_1995,seifert_calculations_1996,elstner_self-consistent-charge_1998} has renewed the interest in semiempirical approaches in the last 20 years. Niehaus \\textit{et al.}\\cite{niehaus_tight-binding_2001} adapted the time-dependent density functional theory to the tight-binding formalism, enabling the calculation of excited state properties of large molecular assemblies of hundreds of atoms. The introduction of long-range corrections to the DFTB framework facilitated the investigation of excited state properties of molecular systems involving charge-transfer states \\cite{niehaus_importance_2005,humeniuk_long-range_2015,lutsker_implementation_2015}. The DFTB and TD-DFTB methods have been implemented in various software packages including DFTB+\\cite{hourahine_dftb_2020}, DFTBaby\\cite{humeniuk_dftbaby_2017}, ADF\\cite{te_velde_chemistry_2001}, CP2K\\cite{hutter_cp2k_2014}, and hotbit\\cite{koskinen_density-functional_2009}, which can be employed to predict the excited state properties of polyatomic systems of over 1000 atoms. \n\nRecently, Grimme developed the simplified Tamm-Dancoff approximation\\cite{grimme_simplified_2013} (sTDA) for the calculation of excited-state spectra of large molecules, which is based on a ground state DFT calculation, followed by the semiempirical treatment of the integrals involved in the linear-response TD-DFT calculation, similar to the TD-DFTB approach. Furthermore, this method was extended to the tight-binding formalism (sTDA-xTB)\\cite{grimme_ultra-fast_2016} by the parametrization of the ground-state Hamiltonian to reduce the computational requirements of the previous models. Further developments of this approach include the GFN-xTB methods by Grimme and coworkers, which can be employed to predict the ground state properties and structures of a multitude of molecular systems \\cite{grimme_robust_2017,bannwarth_gfn2-xtbaccurate_2019,bannwarth_extended_2021}. Additional notable semiempirical methods, which can be used to predict the excited state properties of large molecular systems are MNDO\\cite{dewar_ground_1977}, AM1\\cite{dewar_development_1985}, PMx\\cite{stewart_optimization_1989} and OMx\\cite{weber_orthogonalization_2000}. \n\nThe computational efficiency and applicability of all above methods can be further enhanced by using fragmentation-based approaches allowing the simulation of large molecular systems of over a million atoms. Prominent examples include the fragment molecular orbital\\cite{kitaura_fragment_1999,nakano_fragment_2000,nakano_fragment_2002,fedorov_multilayer_2005,mochizuki_configuration_2005,tsuneyuki_molecular_2009,brorsen_fully_2011,fujino_fragment_2015,tanaka_electron-correlated_2014} (FMO) method and the divide-and-conquer\\cite{yoshikawa_novel_2013,nishizawa_three_2016,nakai_development_2017,yoshikawa_gpuaccelerated_2019,nishimura_quantum_2021} (DC) scheme. In these fragmentation approaches, a partitioning scheme divides the system into multiple fragments. The properties of the complete system are then obtained by combining the results of the different fragments. In the case of the FMO method, the energy of the fragments -- the monomers and fragment pairs -- is calculated iteratively while considering the electrostatic embedding potential (ESP) resulting from the interaction of all fragments. The number of fragment pairs is determined by the closest atomic interfragment distance. The FMO and the DC approach have previously been employed to investigate complex molecular systems, such as proteins\\cite{sawada_role_2010}, polymers\\cite{nakata_derivatives_2014} or optoelectronic materials\\cite{uratani_simulating_2020}. Furthermore, Nishimoto, Fedorov and Irle combined the FMO method with the density functional tight-binding approach (FMO-DFTB) to enable the study of even larger systems \\cite{nishimoto_density-functional_2014,nishimoto_fmo-dftb_2021}. The FMO-DFTB method has been extended to include analytical ground-state gradients\\cite{nishimoto_large-scale_2015}, the polarizable continuum model\\cite{nishimoto_fragment_2016}, periodic boundary conditions\\cite{nishimoto_fragment_2021}, the long-range correction\\cite{vuong_fragment_2019} and many other theoretical concepts\\cite{nishimoto_third-order_2015,nishimoto_three-body_2017,nishimoto_adaptive_2018,fedorov_partition_2020}. It has been succesfully employed to study the properties of large molecular systems, such as the charge transport in covalent organic frameworks \\cite{kitoh-nishioka_multiscale_2017,kitoh-nishioka_linear_2021}.\n\nWhile these fragmentation-based methods provide excellent tools to calculate the ground state properties of molecular aggregates, the study of excited states is limited to only local excitations within the fragments\\cite{komoto_development_2019,komoto_large-scale_2020,uratani_fast_2020,uratani_non-adiabatic_2020,uratani_trajectory_2021}. Recently, several approaches have been developed to investigate the excited states properties of molecular clusters using an excitonic Hamiltonian, consisting of local excitations (LEs) and charge-transfer states (CTs)\\cite{green_excitonic_2021,li_ab_2017,wen_fragmentation-based_2017}. Fujita and Mochizuki combined the multilayer FMO\\cite{fedorov_multilayer_2005} and the transition density fragment interaction\\cite{fujimoto_transition-density-fragment_2012,fujimoto_theoretical_2013} method and introduced an excitonic Hamiltonian to calculate nonlocal excitations in molecular clusters. A basis consisting of fragment configuration state functions (CSFs), which define the locally excited and charge-transfer states, is used to construct the Hamiltonian\\cite{fujita_development_2018}. \n\nIn this work, we combine the FMO-LC-DFTB method with the construction of an excitonic Hamiltonian to calculate the excited states of large molecular systems consisting of hundreds of molecules. As a basis for the description of the excited states of large molecular assemblies, we use locally excited and charge-transfer states, which are calculated for monomers and pair dimers employing the LC-TD-DFTB\\xspace approach. While the diagonal elements of the Hamiltonian are represented by the energies of the basis states, the couplings between the basis states, which represent the off-diagonal matrix elements of the Hamiltonian, are calculated by utilizing the tight-binding formalism for the two-electron four-center integrals. The excited state energies of the full system are given by the diagonalization of the excitonic Hamiltonian. \nThe accuracy and the efficiency of the proposed theory has been tested by the comparison with the full LC-TD-DFTB\\xspace method for molecular dimers and large assemblies of molecules. The effective computational scaling was determined by the calculation of large clusters of anthracene and perylene bisimide aggregates. In addition, the applicability of our approach was confirmed by the calculation of the excited state properties of pentacene crystal models. The FMO-LC-TDDFTB\\xspace method was implemented in our own software package \\mbox{DIALECT}\\cite{noauthor_dialect_2022}, which is publicly available on Github and was written in the Rust programming language. \n\nAlthough Rust is still a very young language --- with the first stable version (1.0) released in 2015 ---  its potential for scientific computing applications becomes increasingly apparent\\cite{perkel_why_2020}. The Rust programming language does not only have a strong focus on the code and memory safety, but also shows performance comparable to the C, C++ and Fortran languages. Additionally, Rust offers in our opinion a friendlier syntax and provides a strongly growing repository of development tools. Therefore, we expect Rust to gain high popularity also in the field of quantum chemistry in the coming years.\n\nThe present work is structured as follows: In Sec. \\ref{sec:methodology}, the methodological framework of our approach is outlined. Subsequently, in Sec. \\ref{sec:computational_procedure}, the computational procedure and the different steps of a FMO-LC-TDDFTB\\xspace calculation are illustrated. The application of the proposed theory to pentacene and the results of the benchmark calculations regarding the accuracy and the effective scaling of the FMO-LC-TDDFTB\\xspace method are presented in Sec. \\ref{sec:results}. Finally, the conclusions and outlook are given in Sec. \\ref{sec:conclusions}.\n\\section{Conclusions and outlook}\\label{sec:conclusions}\nIn this work, we have developed a new method to calculate the excited states in large molecular assemblies, consisting of hundreds of molecules. \nTo this end, we based our approach on the fragment orbital density-functional tight-binding method\\cite{nishimoto_density-functional_2014,vuong_fragment_2019} (FMO-DFTB) and employed an excitonic Hamiltonian constructed from locally excited and charge-transfer configuration state functions.\nOur method has been implemented in the software package DIALECT, publicly available on Github\\cite{noauthor_dialect_2022}.\n\nWe have proven that the accuracy of the proposed theory is sufficient to reproduce the excited state LC-TD-DFTB\\xspace potential energy curves of $\\pi$--stacked molecular pyrene dimers. The mean absolute errors are below 80 meV at all physically relevant intermolecular separations for the pyrene systems, showing that for distances of 2.75 \\AA \\text{ } and above, our method produces satisfactory results. The applicability of the present theory was confirmed by the calculation of the excited state energies and oscillator strengths of a large anthracene cluster. The spectrum of the FMO-LC-TDDFTB\\xspace approach was in good agreement with the LC-TD-DFTB\\xspace reference. \n\nThe comparison of the wall times of the LC-TD-DFTB\\xspace and FMO-LC-TDDFTB\\xspace calculation showed excellent speedup factors for different anthracene cluster sizes of up to $1.5\\times 10^4$. In addition, the computational effective scaling of the proposed theory was evaluated for molecular aggregates involving differently sized monomers. The results showed that in the case of small monomers, the scaling is highly dependent on the calculation of the matrix elements of the Hamiltonian. However, if larger monomers like the substituted perylene bisimide are to be considered, the calculation of the matrix elements of the Hamiltonian only becomes the dominant factor of the effective scaling after the systems grows to a size of over 15000 atoms. The effective scaling of the anthracene and PBI systems was determined as $\\mathcal{O}(N^{3.4})$ and $\\mathcal{O}(N^{2.2})$, respectively.\n\nAt last, the application of our method to pentacene crystals confirmed its validity to large molecular systems. The calculated spectra of the pentacene clusters showed reasonable agreement to the experimental reference spectrum. We were able to analyze the number of monomers that contribute to the excited states of the system by calculating the NTO participation numbers, which were verified by the particle and hole density of a chosen pentacene cluster.\n\nIn the future, we plan to extend our approach to quantum-classical dynamics simulations of large molecular systems, like organic semiconductors or optoelectronic materials. To this end, we will implement the analytical gradients of the excited states to enable the investigation of exciton dynamics and charge transport simulations. Concerning the efficiency, graph theory methods will be used to accelerate the diagonalization of the Hamiltonian by partitioning the matrices involved in the Davidson algorithm into separate blocks, and thus reduce the dimensionality of the problem. In addition, we intend to apply the parametrization of the DFTB framework to a wider range of elements to facilitate the investigation of different molecular systems.\n\\section*{Conflicts of interest}\n\\vspace*{-2ex}\nThere are no conflicts to declare.\n\\section*{Acknowledgments}\n\\vspace*{-2ex}\nWe gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft via the grants MI1236\/6-1 and MI1236\/7-1.\n\\section*{Data availability}\n\\vspace*{-2ex}\nThe data that support the findings of this study are available on Github under \\url{https:\/\/github.com\/mitric-lab\/Data_for_FMO-LC-TDDFTB}.\n\\section*{References}\n\\vspace*{-2ex}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nOne of the important subjects in elementary particle physics is to understand the basic properties of hadronic matter described by Quantum Chromodynamics (QCD).\nThe phase diagram and equation of state of QCD have been investigated both theoretically and experimentally.\nA number of studies indicate that QCD at finite temperature and finite density has various phases such as the quark-gluon plasma phase with effective chiral symmetry and the color superconductivity phase.\n\nInvestigating QCD vacuum need non-perturbative method due to strong interactions of QCD.\nVarious non-perturbative methods are employed in order to study the phase structure of QCD.\nLattice gauge simulation is very powerful because it is the first principle calculation respecting the gauge symmetry.\nHowever it is difficult to maintain the chiral symmetry on the lattice.\nThe even more difficult problem which is known as the sign problem occurs at finite chemical potential because the Dirac operator becomes complex. \n\nOther non-perturbative methods, such as the mean-field approximation (MFA), the Schwinger-Dyson equations (SDE) or the large-$N$ expansion, have been applied to QCD.\nThese methods do not have the difficulty of maintaining the chiral symmetry nor the sign problem.\nHowever, their approximations break the gauge symmetry and its systematic improvement is not easy.\n\nIn this paper, we study the dynamical chiral symmetry breaking (D$\\chi$SB) by using the functional renormalization group (FRG), another non-perturbative method~\\cite{Aoki:2000wm,Pawlowski:2005xe,Gies:2006wv,Wegner:1972ih,Polchinski:1983gv,Wetterich:1992yh}.\nThe main idea of the FRG is solving the effective action $\\Gamma_\\Lambda$ generated by the integration of fluctuations with higher momentum modes $\\Lambda < |p| <\\Lambda _0$ where $\\Lambda$ is the infrared (IR) cut-off scale and the bare action is defined at the initial scale $\\Lambda_0$.\nThe evolution of the effective action with decreasing the IR cut-off scale is described by the functional differential equation, so-called the Wetterich equation~\\cite{Wetterich:1992yh,Morris:1993qb},\n\\begin{align}\n\\partial_t \\Gamma_\\Lambda =\\frac{1}{2} {\\rm STr} \n\\left\\{ \\left[ \\frac{\\overrightarrow \\delta}{\\delta \\Phi} \\Gamma_\\Lambda \\frac{\\overleftarrow \\delta}{\\delta \\Phi} +R_\\Lambda \\right] ^{-1}\\cdot (\\partial _tR_\\Lambda) \\right\\}.\n\\end{align}\nThis equation itself is exact. However, we cannot solve it exactly.\nTherefore we solve the effective action in the truncated theory space.\nThe improvement of approximation can be done by enlarging the theory space, which are easier and more systematic than the case of the MFA or the SDE.\n\nThe D$\\chi$SB has been investigated by using low energy effective models such as the Nambu--Jona-Lasinio (NJL) model~\\cite{Nambu:1961tp,Nambu:1961fr,Hatsuda:1994pi,Kodama:1999if,Shimizube:2003bv,Braun:2011pp,Braun:2011fw,Braun:2012zq} which is described by the four-Fermi interactions. \nRe-bosonization methods~\\cite{Aoki:1999dw,Gies:2001nw,Gies:2002hq} are often applied in order to obtain the physical quantities in macro scale from the interactions in micro scale via the FRG.\nIn such analyses, however, the theory space is widely expanded and the analysis becomes highly complicated.\nRecently, a new method called the ``weak solution'' is proposed in order to evaluate the macro physical values without re-bosonization.\nSo far, the weak solution method can be applied to a specific type of the approximated FRG equation corresponding to the Fermionic large-$N$ leading approximation.\n\nIn this paper we analyze the NJL model at finite temperature and finite density without re-bosonization method nor weak solution method.\nOur theory space and quantum corrections included can not be treated by the weak solution method up to the present.\nWe compare the behaviors of the RG flows of the four-Fermi coupling constant between the large-$N$ leading approximation and that beyond it.\nWe actually evaluate the RG flows of the inverse four-Fermi coupling constant although its physical and mathematical ground is not completely clear.\nIn this manner we define macro physics beyond the MFA in the NJL model.\nHowever our method does not allows us to evaluate a critical endpoint in the phase diagram. \nOur work aims to motivate future studies of phase diagrams including the first order phase transition.\n\nThis paper is organized as follows: In section \\ref{section2} we briefly explain the NJL model in view of FRG and our analysis method.\nThe RG equations of the four Fermi coupling constant are numerically analyzed at finite temperature and density in section \\ref{section3}.\nSummary and Discussion are given in section \\ref{section5}.\n\\section{Nambu--Jona-Lasinio model in view of FRG}\\label{section2}\nIn this paper, we study the NJL model as a low energy effective model of QCD. \nThe NJL Lagrangian is given by\n\\begin{align} \n{\\mathcal L}_{\\rm NJL}={\\bar \\psi}i{\\Slash \\partial}\\psi \n\t\t\t\t\t\t+\\frac{G}{2N}\\{ ({\\bar \\psi}\\psi)^2 + ({\\bar \\psi}i\\gamma_5\\psi)^2\\} ,\n\\end{align}\nwhere $G$ is the four-Fermi coupling constant and $N$ is the number of degrees of freedom for the Dirac Fermion ${\\bar \\psi}$, $\\psi$.\nThe four-Fermi interactions are generated by the QCD gauge interactions.\nThis Lagrangian is invariant under the chiral U(1) transformation:~$\\psi \\to e^{i\\gamma^5\\theta}\\psi$.\nIn present paper, we analyze the ${\\rm U}(1)_L \\times {\\rm U}(1)_R$ symmetric system to study basic structures and behaivors of the four-Fermi interaction at finite temperature and density.\nThe four-Fermi coupling constant in the effective action corresponds to the chiral fluctuation: $G \\sim \\langle ({\\bar \\psi}\\psi)^2\\rangle $.\nTherefore, the divergence of the four-Fermi coupling constant in the course of RG flow means the signal of the D$\\chi$SB as the second order phase transition. \n\nThe RG flow equation of the four-Fermi coupling constant for the $4d$ sharp cut-off scheme in the large-$N$ leading approximation is given by\n\\begin{align}\n\\partial _t g=-2g+2g^2\n\\end{align}\nwhere $t$ is the dimensionless RG scale defined by $t=\\log (\\Lambda_0\/\\Lambda)$, and $g=G\\Lambda^2\/4\\pi^2$ is the dimensionless four-Fermi coupling constant~\\cite{Aoki:1999dv}. \nThis RG equation has an ultraviolet fixed point $g^\\ast =1$. \nWhen we solve this equation with an initial value $g_0>1$, the RG flow diverges at the following finite scale,\n\\begin{align}\nt_{\\rm c}=\\frac{1}{2}\\log \\left( \\frac{g_0}{g_0-1} \\right) .\n\\end{align} \nWe cannot solve the RG flow after $t_{\\rm c}$ because of this divergence. \nRecently, the ``weak solution'' method~\\cite{Aoki:2014ola} is introduced in order to define the flows after this divergence of $g$. \nIn this section, we propose another analysis method to evaluate the RG flow of $g$. \\\\\n\\indent We define the RG flow equation of the inverse four-Fermi coupling constant, ${\\tilde g}=1\/g$, and we have the RG flow equation of ${\\tilde g}$ as follows,\n\\begin{align}\n\\label{rgeqgs}\n\\partial _t {\\tilde g}=2{\\tilde g}-2.\n\\end{align}\nThe solution of this equation is \n\\begin{align}\n{\\tilde g}(t)=({\\tilde g}_0-1)e^{2t}+1.\n\\end{align} \nThe flow with an initial value ${\\tilde g}_0<1$ reaches zero at $t_{\\rm c}$, ${\\tilde g}(t_{\\rm c})=0$, which corresponds to the divergence of $g$.\nIn order to interpret the RG flow with negative ${\\tilde g}$ values, the Euclidean NJL action is bosonized,\n\\begin{align}\nS_{\\rm NJL}=\\int d^4x \\left[\n{\\bar \\psi}({\\Slash \\partial} +\\gamma_0\\mu)\\psi -\\frac{h^2}{G}(\\sigma ^2+\\pi^2)-h{\\bar \\psi}(\\sigma+i\\gamma _5\\pi)\\psi\n\\right],\n\\end{align}\nwhere $h$ is the Yukawa coupling constant and, $\\sigma$ and $\\pi$ are auxiliary fields.\nThe inverse four-Fermi coupling constant corresponds to the mass of the mesonic potential:\n\\begin{align}\\label{mandg}\nm^2=\\frac{h^2}{G}\n\\end{align}\nTherefore the negative RG flow of ${\\tilde g}$ might indicate that the curvature of the mesonic potential at the origin becomes negative and the potential takes a double-well shape, thus, D$\\chi$SB develops.\nSuch a crude treatment has turned out to be right in case when the weak solution can be defined~\\cite{Aoki:2014ola}.  \nThis simple analysis method follows the RG flow after D$\\chi$SB and reach the IR limit $\\Lambda \\to 0$. \nIn the next section, this method is applied to the NJL model at finite temperature and finite density. \n\n\\section{The RG flow at finite temperature and density}\\label{section3}\n\\subsection{RG flow equations of the four-Fermi coupling constant}\n\nWe analyze the Euclidean effective action in the local potential approximation~\\cite{Hasenfratz:1985dm},\n\\begin{align}\\label{eaa}\n\\Gamma_\\Lambda[\\psi,{\\bar \\psi}]=\n\\int _0^\\beta d \\tau\n\\int d^3x\n\t\t\t\t\t\t\t\\left[{\\bar \\psi}({\\Slash \\partial}+\\mu)\\psi \n\t\t\t\t\t\t-\\frac{G}{2N}\\{ ({\\bar \\psi}\\psi)^2 + ({\\bar \\psi}i\\gamma_5\\psi)^2\\} \\right],\n\\end{align}\nwhere $\\beta$ is the inverse temperature $1\/T$ and $\\mu$ is the chemical potential.\nThe evolution of $\\Gamma_\\Lambda$ is described by the Wetterich equation. In this case it reads,\n\\begin{align}\n\\partial _t \\Gamma_\\Lambda[\\psi,{\\bar \\psi}]\n=-{\\rm Tr}\\left[ \\frac{\\partial _tR_\\Lambda}{\\Gamma^{(1,1)}_\\Lambda+R_\\Lambda} \\right],\n\\end{align}\nwhere $\\partial _t=-\\Lambda \\frac{\\partial}{\\partial \\Lambda}$ and $R_\\Lambda$ is the cut-off profile function for the momentum of Fermion defined in Appendix~\\ref{thresholdapp}.\nWe introduce the simple notation,\n\\begin{align}\n\\Gamma_\\Lambda^{(1,1)}=\\frac{\\overrightarrow \\delta}{\\delta {\\Psi}^{\\rm T}(-p)}\\Gamma_\\Lambda \\frac{\\overleftarrow \\delta}{\\delta \\Psi(p)},\n\\end{align}\nwith $\\Psi^{\\rm T}(-p):=(\\psi^{\\rm T}(-p),{\\bar \\psi}(p))$ and\n$$\n\\Psi(p):=\n\\begin{pmatrix}\n\\psi(p)\\\\\n{\\bar \\psi}^{\\rm T}(-p)\n\\end{pmatrix}.\n$$\nThe ``Tr'' denotes sum over momenta and internal indices.\n\\begin{figure}\n\\begin{center}\n\\includegraphics[width=150mm]{4fermi.eps}\n\\end{center}\n\\caption{The quantum corrections to the four-Fermi interactions. The diagram surrounded by the dashed line is the large-$N$ leading term. The arrow denote the direction of particle number flow.}\n\\label{fourFermi}\n\\end{figure}\n\nLet us briefly explain how to introduce the RG flow equation of the four-Fermi coupling constant.\nThe modified inverse propagator $\\Gamma^{(1,1)}_\\Lambda+R_\\Lambda$ can be divided into the field-independent part and the field-dependent part,\n\\begin{align}\n\\Gamma^{(1,1)}_\\Lambda+R_\\Lambda ={\\mathcal S}_\\Lambda+{\\mathcal V}_\\Lambda[\\Psi],\n\\end{align}\nwith\n\\begin{align}\n{\\mathcal S}_\\Lambda :=\n\\begin{pmatrix}\n0\t&\t-i{\\Slash p}^{-}{}^ {\\rm T}\\\\\n-i{\\Slash p}^{+}\t&\t0\n\\end{pmatrix},\n\\end{align}\nand\n\\begin{align}\n{\\mathcal V}_\\Lambda \n&:=\\frac{\\overrightarrow \\delta}{\\delta {\\Psi}^{\\rm T}}\n\\left[\n-\\frac{G}{2N}\\{ ({\\bar \\psi}\\psi)^2 + ({\\bar \\psi}i\\gamma_5\\psi)^2\\} \n\\right]\n\\frac{\\overleftarrow \\delta}{\\delta \\Psi} \\nonumber \\\\\n&=\\frac{G}{N}\n\\begin{pmatrix}\n{\\mathcal C}\t&\t {\\mathcal A}^{\\rm T} + {\\mathcal B}^{\\rm T} \\\\\n{\\mathcal A} + {\\mathcal B}\t&\t{\\mathcal D}\n\\end{pmatrix},\n\\end{align}\nwhere we employ the following notations\n\\begin{align}\n{\\Slash p}^{+}& = {\\Slash p}+i\\mu\\gamma_0\t+{\\bvec {\\Slash p}}r_\\Lambda({\\bvec p})\n=\\left( p_0 +i\\mu ,{\\bvec p}(1+r_\\Lambda({\\bvec p})) \\right)_\\mu \\gamma_\\mu, \\\\\n{\\Slash p}^{-}& = {\\Slash p}-i\\mu \\gamma_0 + {\\bvec {\\Slash p}}r_\\Lambda({\\bvec p})\n=\\left( p_0 -i\\mu ,{\\bvec p}(1+r_\\Lambda({\\bvec p})) \\right)_\\mu \\gamma_\\mu,  \\nonumber \\\\\n{\\mathcal A}&= - \\{ \\delta_{ij} ({\\bar \\psi}\\psi) + i\\gamma^5_{ij}({\\bar \\psi}i\\gamma_5\\psi)\\} ,\\\\\n{\\mathcal B}&= -\\{ \\psi_i  {\\bar \\psi}_j + (i\\gamma_5\\psi)_i ({\\bar \\psi}i\\gamma^5)_j \\} , \\\\\n{\\mathcal C}&=  \\{ \\bar \\psi_i  {\\bar \\psi}_j +(\\bar \\psi i\\gamma_5)_i ({\\bar \\psi}i\\gamma^5)_j \\} ,\\\\\n{\\mathcal D}&=  \\{ \\psi_i  \\psi _j + (i\\gamma_5 \\psi )_i ( i\\gamma^5 \\psi)_j \\}.\n\\end{align}\nIn order to obtain the RG flow equation, we power expand the Wetterich equation with respect to ${\\mathcal V}_\\Lambda[\\Psi]$ as follows,\n\\begin{align}\n\\nonumber\n\\partial_t\\Gamma_\\Lambda\n&=-{\\rm Tr}[{\\tilde \\partial}_t~{\\rm ln}({\\mathcal S}_\\Lambda+{\\mathcal V}_\\Lambda[\\Psi])]\\\\\n\\label{modwet}\n&=-{\\rm Tr}[{\\tilde \\partial}_t~{\\rm ln}({\\mathcal S}_\\Lambda)]\n+{\\rm Tr}[{\\tilde \\partial}_t({\\mathcal S}_\\Lambda^{-1}{\\mathcal V}_\\Lambda[\\Psi])]\n-\\frac{1}{2}{\\rm Tr}[{\\tilde \\partial}_t({\\mathcal S}_\\Lambda^{-1}{\\mathcal V}_\\Lambda[\\Psi])^2]+\\cdots ,\n\\end{align}\nwhere ${\\tilde \\partial}_t$ acts only on the $\\Lambda$ dependence of function $R_\\Lambda$.\nWe evaluate the third term as follow:\n\\begin{align}\n-\\frac{1}{2}{\\rm Tr}[{\\tilde \\partial}_t({\\mathcal S}_\\Lambda^{-1}{\\mathcal V}_\\Lambda[\\Psi])^2]\n=\\frac{1}{2}\\int \\frac{d^4p}{(2\\pi)^4} {\\tilde \\partial}_t\\left[\\frac{1}{(p^+)^2} + \\frac{1}{(p^-)^2} \\right] \\frac{G^2}{N^2}\n\\left({\\rm tr}[\\gamma_\\mu {\\mathcal A}\\gamma_\\mu {\\mathcal A}]\\right) + \\cdots,\n\\end{align}\nwhere ${\\rm tr}[\\gamma_\\mu {\\mathcal A}\\gamma_\\mu {\\mathcal A}] = ({\\rm tr}[{\\bvec 1}_{\\rm spinor}]\\times  {\\rm tr}[{\\bvec 1}_{\\rm flavor}]) {\\mathcal O}_{\\rm 4Fermi}  =4N\\{ ({\\bar \\psi}\\psi)^2 + ({\\bar \\psi}i\\gamma_5\\psi)^2\\} $.\nThis term yields factor $N$, thus it is the large-$N$ leading term.\nOther terms including the operators ${\\mathcal B}$, ${\\mathcal C}$ and ${\\mathcal D}$ do not yield it.\nFor example, \n\\begin{align}\\label{example4}\n{\\rm tr}[\\gamma_\\mu\n {\\mathcal D}\\gamma_\\mu^{\\rm T} {\\mathcal C}]\n&={\\rm tr}[ (\\gamma_\\mu)_{ij} \n\\{ \\psi_j \\psi _k + (i\\gamma_5 \\psi )_j ( i\\gamma^5 \\psi)_k \\} \n(\\gamma_\\mu ^{\\rm T})_{kl}\n\\{ \\bar \\psi_l  {\\bar \\psi}_m +(\\bar \\psi i\\gamma_5)_l ({\\bar \\psi}i\\gamma^5)_m \\}\n] \\nonumber\\\\\n&=2\\{ ({\\bar \\psi}\\gamma_\\mu \\psi)^2 - ({\\bar \\psi}\\gamma_5\\gamma_\\mu\\psi)^2 \\}.\n\\end{align}\nUsing the Fierz transformation, we obtain the opertator $({\\bar \\psi}\\psi)^2 + ({\\bar \\psi}i\\gamma_5\\psi)^2$.\nAlthough the nonleading terms yields not only the scalar-type operator but also other four-Fermi operators such as a vector-type operator $({\\bar \\psi}\\gamma_\\mu \\psi)^2 + ({\\bar \\psi}\\gamma_5\\gamma_\\mu\\psi)^2$, these terms are dropped in our truncated theory space. \nThe possible ways of contraction between the operators are exhibited by the Feynman diagrams as shown in Fig.~\\ref{fourFermi}.\nIn particular , the first diagram in the dashed box is the large-$N$ leading term.\nThe large-$N$ leading approximation neglects other diagrams than the first one.\n\\begin{figure}\n\\begin{center}\n\\includegraphics[width=80mm]{NJLladders.eps}\n\\includegraphics[width=80mm]{NJLnonladders.eps}\n\\end{center}\n\\caption{The threshold functions $I_0$ (left) and $I_1$ (right) on ${\\tilde T}-{\\tilde \\mu}$ plane. }\n\\label{threshold}\n\\end{figure}\n\n\\indent We obtain the RG flow equation of the dimensionless four-Fermi coupling constant, \n\\begin{align}\\label{njlfinitetmuln}\n\\partial _t g&=-2g+\\frac{1}{3}\\{ 4I_0({\\tilde T},{\\tilde \\mu})-\\frac{1}{N}I_1({\\tilde T},{\\tilde \\mu})\\} g^2,\n\\end{align}\nwhere the rescaled temperature ${\\tilde T}=T\/\\Lambda$ and rescaled chemical potential ${\\tilde \\mu}=\\mu\/\\Lambda$, obeys the following equations respectively, \n\\begin{align}\n\\partial _t {\\tilde T}&={\\tilde T},\\\\\n\\partial _t {\\tilde \\mu}&={\\tilde \\mu}.\n\\end{align}\nThe ``form factor'' $I_0$ and $I_1$ are the threshold functions of ${\\tilde T}$ and ${\\tilde \\mu}$, which are given by the shell mode momentum integration of the large-$N$ leading term and the third diagram in Fig.~\\ref{fourFermi}, respectively, and they are defined in Appendix~\\ref{thresholdapp}.\nThe second and fourth diagrams in Fig.~\\ref{fourFermi} do not contribute to the RG flow equation of $g$ in the truncated effective action~(\\ref{eaa}).\nWe adopted the $3d$ optimized cut-off function~\\cite{Litim:2001up,Litim:2006ag} as the regulator function $R_\\Lambda$ which makes it easy to integrate in momentum space with the Matsubara summation~(see Appendix.~\\ref{thresholdapp}).\nThe large-$N$ leading approximated equation can be obtained by taking the limit $N\\to \\infty$, which makes $I_1$ term vanish. \n\nLet us now discuss the RG flows at finite temperature and density in a qualitative manner. \nFirst, we discuss the fixed point structure of the RG equation.\nThe non-trivial fixed point is given by\n\\begin{align}\ng^\\ast=\\frac{6}{4I_0({\\tilde T},{\\tilde \\mu})-\\displaystyle \\frac{1}{N}I_1({\\tilde T},{\\tilde \\mu})},\n\\end{align}\nhence, the fixed point moves with the RG evolutions of dimensionless temperature and density.\nWhen the threshold functions at finite temperature and density are smaller than these with the vanishing temperature and density, we obtain $g^\\ast_{T\\neq 0, \\mu\\neq 0}>g^\\ast_{T=0,\\mu=0}$.\nThus, the chiral symmetry tends to be restored by thermal and finite density effects.\n\nSecond, we briefly discuss the effects of the large-$N$ nonleading term at vanishing temperature and density. By taking the limit $T\\to 0$ and $\\mu\\to 0$, we obtain\n\\begin{align}\n\\partial_t g=-2g+\\frac{1}{3}\\left( 4-\\frac{1}{N}\\right) g^2,\n\\end{align}\nwhere the factor $4$ in the leading term is caused by the trace of the spinor space. \nNote that the difference of coefficients, $\\frac{4}{3}g^2$ here compared with $2g^2$ in Eq.~(\\ref{rgeqgs}), comes out of the difference of cut-off schemes.\nThe nonleading term has negative sign, and it suppresses D$\\chi$SB. \n\nFinally, we discuss finite temperature and density effects.\nWe show the threshold functions on ${\\tilde T}-{\\tilde \\mu}$ plane in Fig.~\\ref{threshold}.\nThe solutions of the RG equations of ${\\tilde T}$ and ${\\tilde \\mu}$ become simply the exponentially-growing solutions with increasing $t$, thus, the ratio ${\\tilde \\mu}\/{\\tilde T}$ is a scale independent constant, $\\mu\/T$.\nTherefore the RG flows of ${\\tilde T}$ and ${\\tilde \\mu}$ move on the straight line with the slope $\\mu\/T$ on ${\\tilde T}-{\\tilde \\mu}$ plane.\nNote that the threshold functions $I_0$ and $I_1$ with the vanishing temperature have the singular point at the Fermi surface $\\Lambda=\\mu$:\n\\begin{align}\nI_0(0,{\\tilde \\mu})&=1-\\theta({\\tilde \\mu}-1)-\\delta ({\\tilde \\mu}-1),\\\\\nI_1(0,{\\tilde \\mu})&=\\frac{1}{2(1+{\\tilde \\mu})^2}+\\frac{1}{(1-{\\tilde \\mu})^2}\\left( \\frac{1}{2}-\\theta({\\tilde \\mu}-1)\\right) +\\frac{1}{1-{\\tilde \\mu}}\\delta ({\\tilde \\mu}-1),\n\\end{align}\nwhere $\\theta({\\tilde \\mu}-1)$ is the step function.\nThe function $I_0$ at finite dimensionless chemical potential and the vanishing temperature is constant and positive value.\nIn particular, this function vanishes in the region $\\Lambda \\le \\mu$.\nOn the other hand, the function $I_1$ depends on ${\\tilde \\mu}$ in arbitrary scale. \nFurthermore, this function becomes quite large at the Fermi surface, therefore, the large-$N$ nonleading term is stronger than the leading term.\nThis means that the RG flow of the four Fermi coupling constant with the large-$N$ nonleading term tends to go to positive infinity at low temperature and high density.\nIn the next section, we numerically evaluate the RG flow equations.\n\n\\subsection{Numerical analysis}\n\\begin{figure}\n\\begin{center}\n\\includegraphics[width=160mm]{flow.eps}\n\\end{center}\n\\caption{The RG flows in case of the large-$N$ leading at ${\\tilde \\mu}=0.4$ (left) and the large-$N$ nonleading with $N=1$ at ${\\tilde \\mu}=0.22$ (right). }\n\\label{flows}\n\\end{figure}\nWe solve the RG flow equations of the inverse four-Fermi coupling constant ${\\tilde g}$. \nThe numerical results of the RG flows on ${\\tilde g}-{\\tilde \\mu}$ plane are shown in Fig.~\\ref{flows}. \nThe left-hand side panel and the right-hand side panel are the large-$N$ leading approximation case and the nonleading extended case, respectively.\nHere, we used the initial value: ${\\tilde g}=0.3$ where the RG flow at the vanishing temperature and density goes to the negative region in the IR limit. \nFirst, let us discuss the large-$N$ leading case.\nThe RG flows of $\\tilde g$ at higher temperature cases ($T=0.2 \\Lambda_0$ and $T=0.15\\Lambda_0$) go to positive infinity. \nThe flow at $T=0.1\\Lambda_0$ goes to negative region crossing the origin ${\\tilde g}=0$, and comes back to positive region. \nEventually, this flow goes to positive infinity at the IR scale.\nThe RG flows at lower temperature cases ($T=0.01\\Lambda_0$ and $T=0.001\\Lambda_0$) go to negative region at the IR limit.\n\nThese flows can be evaluated only by the RG equation for the inverse four-Fermi coupling constant.\nIf we solve the RG equation for the four-Fermi coupling constant Eq.~(\\ref{njlfinitetmuln}), these flows stop in the middle of the RG scale.\nSolving the RG equations of the inverse four-Fermi coupling constant is useful to discuss the flows after D$\\chi$SB, although it is not strictly authorized for large-$N$ nonleading case.\nIt should be noted that to discuss RG flows towards positive infinity at IR scale do not always imply the restoration of the chiral symmetry.\nThe RG flow of the inverse four-Fermi coupling constant corresponds to the curvature at origin of the effective potential with respect to the expectation value $\\sigma \\sim \\langle {\\bar \\psi}\\psi \\rangle$.\nIn case of the first order phase transition, the curvature at origin may remain positive, even after the D$\\chi$SB. \nWe cannot distinguish between the restoration of chiral symmetry and the first order D$\\chi$SB.\nIn other words, we see the effective potential only at the neighborhood of origin.\nThe chiral phase transition including the first order phase transition should be investigated by searching the global minima of the effective potential by using the weak solution method or the re-bosonization method. \nAlthough our method can be applied only to the second order phase transition, our results may be used as references for advanced analysis of the chiral phase transition.\n\nSecond, let us discuss the nonleading extended case. \nThe RG flows at low temperature~($T=0.01\\Lambda_0$ and $T=0.001\\Lambda_0$) go to positive infinity at the IR limit.\nThese behaviors are quite different from the large-$N$ leading case.\nThe large-$N$ nonleading term becomes larger than the leading term because the threshold function $I_1$ has the singularity at $\\mu=\\Lambda$.\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[width=130mm]{phase.eps}\n\\end{center}\n\\caption{The chiral phase structure given by the large-$N$ leading case (blue and green line) and nonleading case (red and pink line). We used ${\\tilde g}_0=0.3$ as the initial value and $N=1$ for the nonleading case. \nThe phase boundaries assume the second order phase transition.}\n\\label{phase}\n\\end{figure}\nThe chiral phase diagram on ${\\mu\/\\Lambda_0}-T\/\\Lambda_0$ plane is shown in Fig.~\\ref{phase}.\nWe show the phase boundaries evaluated by the blowup solution of Eq.~\\eqref{njlfinitetmuln} and the RG equation of the inverse four-Fermi coupling constant.\nHere we call the solution of the RG equation for the inverse four-Fermi coupling constant simply the inverse solution.\n\nFirst, we discuss the difference of phase boundaries between the blowup solution case and the inverse solution case.\nSince the blowup solution stops the RG flow in the midst of scale, we cannot evaluate it after the chiral symmetry breaking.\nThen we notice that the phase boundary with the inverse solution is correct.\nIn high temeperature and low density region, both boundaries become same.\nBy contrast, in low temperature and high density region, the phase boundaris evaluated by the blowup solutions become larger than the inverse solutions.\nThat is, it is especially important to evaluate the RG equation of the inverse four-Fermi coupling constant in this region.\n\nNext, we discuss the difference of phase boundaries with the inverse solution between the large-$N$ leading case and nonleading case.\nThe D$\\chi$SB region becomes smaller in case of the large-$N$ nonleading. \nWe find drastic difference of phase boundaries at low temperature and high density region since the large-$N$ nonleading effect strongly suppresses the D$\\chi$SB as we previously mentioned.\nThe chiral susceptibility, the curvature at the origin of mesonic potential $m^2\\sim 1\/\\langle ({\\bar \\psi}\\psi)^2 \\rangle$, is sensitive to the nonleading effects at low temperature and high density.\n\nNote that the phase boundaries shown in Fig.~\\ref{phase} denote second order phase transition. \nAs mentioned below Eq.~\\eqref{mandg}, the inverse four-Fermi coupling constant corresponds to the curvature of the effective potential at the origin and its RG equation describes the change of the curvature.\nIn the present work, the phase boundary is determined by the sign of the inverse four-Fermi coupling constant in IR limit.\nThe broken phase potential with double well form has the negative curvature of the effective potential at the origin.\nThe symmetric phase has a single well form and the positive curvature of the effective potential at the origin.\nThus, the change from the negative curvature to the positive curvature mean the second order phase transition at least near the origin.\nOne of important statements in our study is that these pictures can be described by the RG flow of the inverse four-Fermi coupling constant.\n\nOn the other hand, when the first order phase transition occurs, there might be no global minimum at the origin of the effective potential even in case that the curvature of the effective potential at the origin changes to be positive.\nTherefore, it does not always mean we evaluate the global minimum of the effective potential in the present work.\nThat is, there is possibility of occurring the first order phase transition at larger density region than the second order boundary evaluated in present paper.\n\n\n\n\n\\section{summary and discussion}\\label{section5}\n\\begin{figure}\n\\begin{center}\n\\includegraphics[width=80mm]{yukawa.eps}\n\\end{center}\n\\caption{The quantum corrections to the four-Fermi interactions generated by the Yukawa interaction. The crossed ladder diagram (right) at the zero temperature and finite density has the singularity at the Fermi surface.}\n\\label{yukawa}\n\\end{figure}\nIn this work, we have studied the RG flows of the four-Fermi coupling constant in NJL model at finite temperature and density by using the FRG. \nWe solved the RG equations of the inverse four-Fermi coupling constant.\nThis manner allows to integrate the equation up to the IR scale without the difficulties of the divergence.\nWe have investigated the impact of the large-$N$ nonleading term on the RG flow equation. \nThe large-$N$ nonleading term has the singularity at the Fermi surface scale $\\Lambda=\\mu$ with the vanishing temperature, i.e. the quantum fluctuation due to the large-$N$ nonleading term becomes quite large, which makes the system more symmetric, as seen in Fig.~\\ref{phase} \n\nIn this analysis, the second order phase transition is investigated. \nIn order to investigate the first order phase transition with the critical end point in the NJL model, the global minima of the effective potential with respect to the chiral order parameter must be studied by using more technical methods such as the re-bosonization method or the weak solution method.\nCurrently, since the weak solution method can be applied to only the Fermionic large-$N$ approximated case,  we need to employ the re-bosonization method.\nFor example, a truncated effective action of the NJL model with bosonization is given by\n\\begin{align}\\nonumber\n\\Gamma _{\\Lambda}[\\psi, {\\bar \\psi}, \\phi]=\\int^{1\/T}_0d\\tau \\int d^3x \n& \\left\\{ Z_{\\psi,\\Lambda}{\\bar \\psi}({\\Slash \\partial} + \\mu \\gamma _0)\\psi \n+{\\bar h_{\\Lambda}}{\\bar \\psi}(\\sigma +i{\\vec \\tau}\\cdot {\\vec \\pi}\\gamma _5)\\psi \n\\right. \\\\\n\\label{bosoef}\n&+\\left. \\frac{G_\\Lambda}{2}[({\\bar \\psi}\\psi)^2+({\\bar \\psi}i\\tau^i\\gamma_5 \\psi)^2]\n+\\frac{Z_{\\phi,\\Lambda}}{2}(\\partial _{\\mu}\\phi^i)^2\n+U_{\\Lambda}(\\phi^2)\\right\\},\n\\end{align}\nwhere $\\phi^i=(\\sigma,{\\bvec \\pi})$.\nThe four-Fermi interaction is generated by the Yukawa interaction in this action through the diagrams shown in Fig.~\\ref{yukawa}.\nThe contribution from the crossed ladder diagram at finite density has the singularity at the Fermi surface.\nThe impact of this singularity to the chiral phase diagram on $T-\\mu$ plane should be investigated.\nThe paper~\\cite{Braun:2014ata,Mitter:2014wpa} which study QCD at vanishing temperature and density by using re-bosonization method indicates that the Yukawa coupling constant always gets the same value in the IR scale, i.e. the Yukawa coupling constant at the IR scale does not depend on the initial values. However, the impact of the singularity to the phase boundary is non-trivial.\nThe analysis of the effective action (\\ref{bosoef}) will be presented elsewhere.\n\nOn the other hand, the weak solution method is also powerful to analyze the dynamical chiral symmetry breaking~\\cite{Aoki:2014ola}.\nThis method is just developing to apply to many systems.\nTherefore, the present work becomes one of valuable benchmarks.\nWe are going to clearly discuss the relation between our results obtained in this paper and the phase diagram given by the weak solution method in future works.\n\n\n\\section*{Acknowledgements}\nWe thank Kenji Fukushima, Akira Onishi, Jan. M. Pawlowski, Fabian Rannecke, Daisuke Sato and Motoi Tachibana for discussions and valuable comments.\nM. Y. thanks the Yukawa Institute for Theoretical physics, Kyoto University.\nDiscussions during the YITP workshop YITP-T-13-05 on ``New Frontiers in QCD'' were useful to complete this work. \nM. Y. is supported by a Grant-in-Aid for JSPS Fellows (No.~25-5332). \nK-I. A. is supported by JSPS Grant-in-Aid for Challenging Exploratory Research (No.~25610103).\n\n\\begin{appendix}\n\\section{Threshold functions}\\label{thresholdapp}\nIn this appendix, we show the threshold functions which are obtained by the shell mode integration.\nWe first introduce the cut-off profile function $R_\\Lambda(p)$.\nIn case of finite temperature and density, we employ the $3d$ optimized cut-off function~\\cite{Litim:2001up,Litim:2006ag},\n\\begin{align}\\nonumber\nR_\\Lambda({\\bvec p})\n\t&=i{\\Slash {\\bvec p}}\\left( \\frac{\\Lambda}{|{\\bvec p}|} -1\\right) \\theta (1-|{\\bvec p}|\/\\Lambda)\\\\\n\t&=:i{\\Slash {\\bvec p}}~r_\\Lambda({\\bvec p}),\n\\end{align}\nwhere $\\theta (1-|{\\bvec p}|\/\\Lambda)$ is the Heaviside step function,\n\\begin{align}\n\\theta (1-|{\\bvec p}|\/\\Lambda)\n=\n\\begin{cases}\n1\t&\t(|{\\bvec p}|<\\Lambda),\\\\\n0\t&\t(|{\\bvec p}|>\\Lambda).\n\\end{cases}\n\\end{align}\n\nWe define the following threshold functions,\n\\begin{align}\n{\\hat I}_0(T,\\mu;\\Lambda) \n&=T\\sum ^{\\infty}_{n=-\\infty}\\int \\frac{d^3p}{(2\\pi)^3}{\\tilde \\partial}_t\n\\frac{1}{[(p_0+i\\mu)^2+{\\bvec p}^2(1+r_\\Lambda({\\bvec p}))^2]},\\\\\n{\\hat I}_1(T,\\mu;\\Lambda) \n&=T\\sum ^{\\infty}_{n=-\\infty}\\int \\frac{d^3p}{(2\\pi)^3}{\\tilde \\partial}_t\n\\frac{(p_0+i\\mu)(p_0-i\\mu)+{{\\bvec p}}^2(1+r_\\Lambda({\\bvec p}))^2}{[(p_0+i\\mu)^2+{{\\bvec p}}^2(1+r_\\Lambda({\\bvec p}))^2][(p_0-i\\mu)^2+{{\\bvec p}}^2(1+r_\\Lambda({\\bvec p}))^2]},\n\\end{align}\nwhere ${\\tilde \\partial}_t=\\partial _tr_\\Lambda\\cdot \\partial _{r} $ and $p_0=(2n+1)\\pi T$.\nWe can analytically calculate the above integration and summation and we obtain\n\\begin{align}\n\\nonumber\n{\\hat I}_0(T,\\mu;\\Lambda) \n&=\\frac{\\Lambda^2}{3} \n\\left. \\left[ \\left( \\frac{1}{2}-n_+\\right) + \\left( \\frac{1}{2}-n_-\\right)\t+\\frac{\\partial}{\\partial \\omega}[n_++n_-]\\right]\\right| _{\\omega\\to 1}\\\\\n&=\\frac{\\Lambda^2}{3} I_0({\\tilde T},{\\tilde \\mu}),\\\\\n\\nonumber\n{\\hat I}_1(T,\\mu;\\Lambda) \n&=\\frac{\\Lambda^2}{3}\n\\left. \\left[ \\frac{1}{(1+{\\tilde \\mu})^2} \\left( \\frac{1}{2}-n_+\\right) + \\frac{1}{(1-{\\tilde \\mu})^2}\\left( \\frac{1}{2}-n_-\\right)\t+\\frac{1}{1+{\\tilde \\mu}}\\frac{\\partial}{\\partial \\omega}n_+   +\\frac{1}{1-{\\tilde \\mu}}\\frac{\\partial}{\\partial \\omega}n_-\\right]\\right| _{\\omega\\to 1}\\\\\n&=\\frac{\\Lambda^2}{3} I_1({\\tilde T},{\\tilde \\mu}).\n\\end{align}\nHere we have used the formula,\n\\begin{align}\n\\sum^{\\infty}_{n=-\\infty}\\frac{1}{(2n+1)^2\\pi^2+\\beta^2E_\\pm^2}\n=\\frac{1}{\\beta E_\\pm}\\left( \\frac{1}{2}-n_\\pm\\right),\n\\end{align}\nwhere $n_\\pm$ is the Fermi-Dirac distribution function:\n\\begin{align}\nn_\\pm=\\frac{1}{\\exp(\\beta E_\\pm)+1}\n\\end{align}\nwith $E_\\pm=\\Lambda\\pm \\mu$ and $\\beta =1\/T$.\n\n\\end{appendix}\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Acknowledgments}\n We thank Shailesh Chandrasekharan, Robert Ott, Arnab Sen, and Uwe-Jens Wiese for useful discussions. This work was supported by the Simons Collaboration on UltraQuantum Matter, which is a grant from the Simons Foundation (651440, P.Z.). D.B.~acknowledges support by the German Research Foundation (DFG), Grant ID BA 5847\/2-1. This work is part of and supported by the Interdisciplinary Center Q@TN \u2014 Quantum Science and Technologies at Trento, the DFG Collaborative Research Centre SFB 1225 (ISOQUANT), the Provincia Autonoma di Trento, and the ERC Starting Grant StrEnQTh (Project- ID 804305).\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
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+{"text":"\\section{Introduction}\n\\label{intro}\n\n\nThe idea of four-dimensional harmonic oscillator as a tool for universal description of  the Regge spectrum of hadron masses was formulated long time ago by Feynman,  Kislinger, and Ravndal~\\cite{Feynman}  and later  re-entered  the  discussion about quark confinement  several times  in  various ways. In particular,  Leutwyler and Stern  developed  the formalism devoted to the  covariant description of bilocal meson-like fields  combined with the idea of harmonic confinement~\\cite{Leutwyler:1977vz,Leutwyler:1977vy, Leutwyler:1977pv, Leutwyler:1977cs, Leutwyler:1978uk}.    In recent years,  the approaches to confinement based on the soft wall AdS\/QCD model with harmonic potential demonstrated an impressive phenomenological success.  \n\n\n\n\nThe approach to QCD vacuum and hadronization presented here  has been developed in a series of papers~\\cite{EN, EN1,NK1,NK4,NK6,NV,NV1}. It   clearly \nincorporates the idea of harmonic confinement both in terms of elementary color charged fields and the composite colorless  hadron fields. The distinctive feature of the approach is that it links the concept of harmonic confinement  and Regge character of hadron mass spectrum to the specific class of nonperturbative gluon configurations -- almost everywhere homogeneous Abelian (anti-)self-dual gluon fields. \nA  close interrelation of the   Abelian (anti-)self-dual fields and the hadronization based on harmonic confinement   can be read off the  papers~\\cite{Pagels, Minkowski, Leutwyler1, Leutwyler2,  Leutwyler:1977vz,Leutwyler:1977vy, Leutwyler:1977pv, Leutwyler:1977cs, Leutwyler:1978uk}.\nIn brief,  the line of arguments is as follows (for more detailed exposition see~\\cite{NV,NV1}). \n\nAn important starting point is due to the  observation of  Pagels and Tomboulis~\\cite{Pagels} that Abelian self-dual fields describe a  medium that is  infinitely stiff to small gauge field fluctuations, i.e. the  wave solutions for the effective quantum equations of motion are absent. This feature was interpreted as suggestive of confinement of color. \nStrong argumentation in favour of the Abelian (anti-)self-dual homogeneous field as a candidate for the global nontrivial minimum of the effective action originates from the papers \\cite{Minkowski,Leutwyler2,NG2011,Pawlowski,George:2012sb}.   Leutwyler has shown  that the constant gauge field is stable   against small quantum fluctuations only if it is Abelian (anti-)self-dual covariantly constant field  \\cite{Minkowski,Leutwyler2}. Nonperturbative calculation of the effective potential within the functional renormalization group \\cite{Pawlowski} supported the earlier one-loop results on existence of the nontrivial minimum of the effective action for the Abelian (anti-)self-dual field. \n\n\n\n\\begin{figure}\n\\centering\n\\sidecaption\n\\includegraphics[width=0.35\\textwidth]{effpot_xiomega}\n\\caption{Effective potential  as a function of the angle $\\omega$ between chromomagnetic and chromoelectric field  and the mixing angle $\\xi$  in the Cartan subalgebra. The minima in the dark gray regions correspond to the Abelian  (anti-)self-dual  configurations and form a periodic  structure labelled  by integer indices $(kl)$  in Eq.~\\eqref{minima} (for more details see  \\cite{NK1,NG2011,NV}).\\label{effpotxiomega}}\n\\end{figure}\n\\begin{figure}[h!]\n\\centering\n\\sidecaption\n\\includegraphics[width=.2\\textwidth]{cube1}\\includegraphics[width=.175\\textwidth]{cube2}\n\\caption{Topological charge density for domain wall networks with different values of the wall width. The left picture is an example of confining almost everywhere homogeneous Abelian (anti-)self-dual fields. Red (blue) color corresponds to the self-dual field (anti-self-dual), green -- pure chromomagnetic field. The right plot represents the case of preferably pure chromomagnetic field when the topological charge density is nearly zero and color charged quasiparticles can be excited thus indicating deconfinement (for more details see \\cite{NV}).\\label{cubes}}\n\\end{figure}\n\nThe eigenvalues of the Dirac and Klein-Gordon operators in the presence of Abelian self-dual field are purely discrete, and the corresponding eigenfunctions  of quarks and gluons charged with respect to the  background  are of the bound state type. This is a consequence of the \nfact that these operators contain the four-dimensional harmonic oscillator.   Eigenmodes  of the color charged fields have no (quasi-)particle interpretation but describe field fluctuations decaying in space and time. The consequence of this property is  that the momentum representation of the translation invariant part of the propagator of the color charged field in the background of homogeneous  (anti-)self-dual Abelian gauge field is an entire analytical function. \nThe absence of pole in the propagator was treated as the absence of the particle interpretation of the charged field~\\cite{Leutwyler1}. \n However,  neither the homogeneous Abelian (anti-)self-dual\nfield itself nor  the form of gluon propagator in the presence of this background\nhad the clue to linear quark-antiquark potential.  Nevertheless, the analytic structure of the gluon and quark propagators and assumption about the randomness of the background field ensemble led both to the area law for static quarks and the Regge spectrum for light hadrons.\n\nThe model of hadronization developed in~\\cite{EN1,EN, NV,NV1} indicated that the spectrum of mesons displayed the Regge character  both with respect to total angular momentum  and radial quantum number of the meson.  The  reason for confinement of a single quark and Regge spectrum of mesons turned out to be the same -- the analytic properties of quark and gluon propagators.  In this formalism any meson looks much more like  a complicated collective excitation of a medium (QCD vacuum) involving quark, antiquark and gluon fields than a nonrelativistic quantum mechanical bound state of charged  particles (quark and anti-quark) due to some potential interaction between them. Within this relativistic quantum field description the Regge spectrum of color neutral collective modes appeared as a \"medium effect\" as well as the suppression (confinement) of a color charged elementary modes.  \n\nThese observations have almost completed the quark confinement picture based on the random almost everywhere homogeneous Abelian (anti-)self-dual fields. Self-duality of the fields plays the crucial role in this picture. This random field ensemble represents a medium where the color charged elementary excitations exist as quickly decaying in space and time field fluctuations but the collective colorless excitations (mesons) can propagate as plain waves (particles).  Besides this dynamical color charge confinement,  a correct complete picture must include the limit of  static quark-antiquark pair with the area law for the temporal Wilson loop. In order to explore this aspect an  explicit construction of the random domain ensemble was suggested in paper~\\cite{NK1}, and the area law for the Wilson loop was demonstrated by the explicit calculation. Randomness of the ensemble (in line with \\cite{Olesen7}) and (anti-)self-duality of the fields are crucial for this result.  \n\n\n\n\n\n The  character of meson wave functions   in hadronization approach~\\cite{EN1} is fixed by the form of the gluon propagator in the  background  of  specific  vacuum gluon configurations.     These wave functions  are  very similar to the wave functions of the soft wall AdS\/QCD with  quadratic dilaton profile and Leutwyler-Stern formalism. In all three cases one deals with the generalized Laguerre polynomials as characteristic for the radial meson excitations. Another interesting observation is that the form of Euclidean gluon and quark propagators in the presence of the Abelian (anti-)self-dual background  are in qualitative agreement with the  decoupling scenario of the infra-red behaviour of the propagators  in Dyson-Schwinger equations (DSE) and functional renormalization group (FRG) approaches and  lattice QCD results for the Landau gauge propagators.\n \n \n \n \n \n\n \nThe next section  is devoted to motivation of the approach based on the domain wall network gluon configurations.  xt of the spontaneous chiral symmetry breaking by the background field and four-fermion interaction.  \nThe structure of the effective meson action  and the results  for the  masses, transition and decay constants of various mesons   are presented in  section \\ref{section2}. \n In the  last section  we outline the relation of  gluon propagator in the model under consideration to  the results of FRG and DSE.  \n\n\n\n\\begin{figure}[h!]\n\\centering\n\\includegraphics[scale=.8]{two-loop}\\\\\n\\includegraphics[scale=.8]{n-loop}\n\\caption{Diagrammatic representation of nonlocal meson vertex functions. Light grey denotes averaging over background field, dark grey denotes correlation of loop diagrams by background field.\\label{diagrams}}\n\\end{figure}\n\n\n\\begin{figure}[h]\n\\centering\n\\sidecaption\n\\includegraphics[width=9cm,clip]{spectra}\n\\caption{The masses of various radially excited mesons. The same  values of parameters  were used for all\nmesons shown in the figure. }\n\\label{fig-masses}      \n\\end{figure}\n\n\n\n\n\\section{Scalar gluon condensate and the effective action of QCD}\n\\label{section1}\n\n\n\nThe  phenomenological basis of the present approach is the assumption about existence of nonzero gluon condensates in QCD, first of all -- the scalar  condensate $\\langle g^2F^2\\rangle$.  In order to incorporate this condensate into the  functional integral approach to quantization of QCD one has to choose appropriate  conditions for  the functional space of gluon fields $A_\\mu^a$ to be integrated over (see, e.g., Ref.\\cite{faddeev}). \nBesides the formal mathematical  content, these conditions play the role of substantial physical input  which, together with the classical action of QCD, complements the statement of the quantization problem. In other words, starting with  the very basic  representation of the Euclidean  functional integral for QCD, \none has to specify integration spaces $\\mathcal{F}_A$ for gluon and  $\\Psi$ for quark fields. \nBearing in mind a nontrivial QCD vacuum structure encoded in various condensates, one have to define  $\\mathcal{F}_A$  permitting  gluon fields with nonzero classical action density.\nThe gauge fields $A$ that satisfy this condition  have a potential to provide the vacuum with the whole variety of  condensates.\n\n\nAn analytical approach to definition and calculation of the functional integral can be based on separation of gluon modes  $B_\\mu^a$ responsible for nonzero  condensates  from the small perturbations $Q_\\mu^a$. This separation must be supplemented with gauge fixing.  Background gauge fixing condition $D(B)Q=0$ is the most natural choice. To perform separation, one inserts identity\n\\begin{equation*}\n1=\\int\\limits_{{\\cal B}}DB \\Phi[A,B]\\int\\limits_{{\\cal Q}} DQ\\int\\limits_{\\Omega}D\\omega \\delta[A^\\omega-Q^\\omega-B^\\omega]\n \\delta[D(B^\\omega)Q^\\omega]\n\\end{equation*}\nin the functional integral and arrives at \n\\begin{eqnarray*}\nZ &=&N'\\int\\limits_{{\\cal B}}DB \\int\\limits_{\\Psi} D\\psi D\\bar\\psi\\int\\limits_{{\\cal Q}} DQ \\det[\\mathcal{D}(B)\\mathcal{D}(B+Q)]\n\\delta[\\mathcal{D}(B)Q]e^{-S_{\\rm QCD}[B+Q,\\psi, \\bar\\psi]}\\\\\n&=&\\int\\limits_\\mathcal{B}DB \\exp\\{-S_\\mathrm{eff}[B]\\}.\n\\end{eqnarray*}\n\n\n\\begin{table}[htbp]\n\\centering\n\\caption{Model parameters fitted to the masses of $\\pi,\\rho,K,K^*, \\eta', J\/\\psi,\\Upsilon$ and used in  calculation of all other meson masses, decay and transition constants.}\n{\\begin{tabular}{@{}ccccccc@{}}\n \\hline\n$m_{u\/d}$, MeV&$m_s$, MeV&$m_c$, MeV&$m_b$, MeV&$\\Lambda$, MeV&$\\alpha_s$&$R$, fm\\\\\n\\hline\n$145$&$376$&$1566$&$4879$&$416$&$3.45$&$1.12$\\\\\n\\hline\n\\end{tabular}}\n\\label{values_of_parameters}\n\\end{table}\n\n\nThus defined quantum effective action $S_\\text{eff}[B]$ has a physical meaning of the free energy of the quantum field system in the presence of the background  gluon field $B_\\mu ^a$.  In the limit $V\\to \\infty$  global minima of  $S_\\text{eff}[B]$ determine the class of  gauge field configurations  representing  the equilibrium state (vacuum) of the system. Quite reliable argumentation in favour of (almost everywhere) homogeneous Abelian  (anti-)self-dual fields as dominating vacuum configurations in pure gluodynamics was put forward by many authors~\\cite{Pagels,Leutwyler2}.  \nAs it has already been mentioned in Introduction, nonperturbative calculation of QCD quantum effective action  within the functional renormalization group approach \\cite{Pawlowski} supported the  one-loop result \\cite{Pagels,Minkowski,Leutwyler2} and indicated the existence of a minimum of the effective potential for nonzero value of Abelian (anti-)self-dual homogeneous gluon field.\n\n\n\\begin{table}[h]\n\\centering\n\\caption{Decay and transition constants of various  pseudoscalar and vector mesons calculated through the diagrams shown  in Figs.~\\ref{weak_decay_diagrams} and \\ref{g_rho_gamma_diagrams}. }\n{\\begin{tabular}{@{}cccc|cccc@{}} \\hline\nMeson&$n$&$f_P^{\\rm exp}$&$f_P$&Meson&$n$&$g_{V\\gamma}$ \n\\cite{PDG}&$g_{V\\gamma}$\\\\\n&&(MeV)& (MeV)&&&\\\\\n\\hline\n$\\pi$      &0 &130 \\cite{PDG}        &140 & $\\rho$&0&0.2&0.2 \\\\\n$\\pi(1300)$&1 &                      &29 & $\\rho$&1&&0.053 \\\\\n\\hline\n$K$        &0 &156 \\cite{PDG}        &175  & $\\omega$&0&0.059&0.067\\\\\n$K(1460)$  &1 &                      &27   & $\\omega$&1&&0.018\\\\\n\\hline\n$D$        &0 &205 \\cite{PDG}        &212  & $\\phi$&0&0.074&0.071\\\\\n$D$        &1 &                      &51   & $\\phi$&1&&0.02\\\\\n\\hline\n$D_s$      &0 &258 \\cite{PDG}        &274  & $J\/\\psi$&0&0.09&0.06\\\\\n$D_s$      &1 &                      &57  & $J\/\\psi$&1&&0.015\\\\\n\\hline\n$B$        &0 &191 \\cite{PDG}        &187  & $\\Upsilon$&0&0.025&0.014\\\\\n$B$        &1 &                      &55   & $\\Upsilon$&1&&0.0019\\\\\n\\hline\n$B_s$      &0 &253 \\cite{Chiu:2007bc}&248  &  & &\\\\\n$B_s$      &1 &                      &68   &  & &\\\\\n\\hline\n$B_c$      &0 &489 \\cite{Chiu:2007bc}&434  &  & &\\\\\n$B_c$      &1 &                  &135  & &&\\\\\n\\hline\n\\end{tabular}\n\\label{constants}}\n\\end{table}\n\n\n\nGinzburg-Landau (GL) approach to the quantum effective action indicated a possibility of the domain wall network formation in  QCD vacuum resulting in the  dominating vacuum gluon configuration seen as an ensemble of densely  packed lumps of covariantly constant Abelian (anti-)self-dual field \\cite{NK1,NG2011,NV,George:2012sb}. Nonzero scalar gluon condensate $\\langle g^2F^a_{\\mu\\nu}F^a_{\\mu\\nu}\\rangle$ \npostulated by the effective potential\nleads \nto the existence  of twelve discrete degenerate global minima of the effective action (see Fig.\\ref{effpotxiomega}), \n\\begin{eqnarray}\n&&\\breve A_{\\mu}\\in\\left\\{\\breve B^{(kl)}_{\\mu}| \\  k=0,1,\\dots,5; \\  l=0,1\\right\\}, \\ \\\n\\breve B^{(kl)}_{\\mu}  = -\\frac{1}{2}\\breve n_k B^{(l)}_{\\mu\\nu}x_\\nu, \n\\nonumber\\\\\n && \\tilde B^{(l)}_{\\mu\\nu}=\\frac{1}{2}\\varepsilon_{\\mu\\nu\\alpha\\beta} B^{(l)}_{\\alpha\\beta}=(-1)^l B^{(l)}_{\\mu\\nu},\n\\ \n\\breve n_k = T^3\\ \\cos\\left(\\xi_k\\right) + T^8\\ \\sin\\left(\\xi_k\\right),\n\\ \\\n\\xi_k=\\frac{2k+1}{6}\\pi,\n\\label{minima}\n\\end{eqnarray}\nwhere $l=0$ and $l=1$ correspond to the self-dual and anti-self-dual field respectively,  matrix $\\breve{n}_k$ belongs to Cartan subalgebra of $su(3)$ with six values of the angle $\\xi_k$ corresponding to the boundaries of the Weyl chambers in the root space of $su(3)$. \nThe minima are connected by the parity and Weyl group reflections.  \nTheir existence indicates that the system is prone to the domain wall formation.  To demonstrate the simplest example of domain wall interpolating between the self-dual and anti-self-dual Abelian configurations, one allows  the angle  $\\omega$ between chromomagnetic and chromoelectric fields to vary from point to point in $R^4$  and restricts other degrees of freedom of gluon field to their vacuum values.\nIn this case Ginsburg-Landau Lagrangian  leads  to the  sine-Gordon equation for  $\\omega$ with the standard\n kink solution (for details see Ref.~\\cite{NG2011,NV}).\nAway from the kink location vacuum  field is almost self-dual ($\\omega=0$) or anti-self-dual ($\\omega=\\pi$).  Exactly at the wall it becomes purely chromomagnetic ($\\omega=\\pi\/2$).  Domain wall network is constructed  by means of the kink superposition. \nTopological charge density distribution for a network of domain walls with different width is illustrated in Fig.\\ref{cubes}. \n\n\n\n\n\n\nBased on this construction, the measure of integration over the background field $B_\\mu^a$ can be constructively represented as the infinite dimensional (in the infinite volume) integral over the parameters  of $N\\to\\infty$ domain walls in the network:  their positions, orientations and widths, with the weight  determined by the effective action.  The  explicit construction of the  domain wall network is the most recent development of the \nformalism that have been studied in the series of papers \\cite{EN,EN1,NK1,NK4,NK6}, in which the domain wall defects in the homogeneous Abelian (anti-)self-dual field were taken into account either implicitly or \nin an  explicit but simplified form with the spherical domains.  The practical calculations in the next sections will be done within combined implementation of domain model given in paper~\\cite{NK4}: propagators in the quark loops are taken in the approximation of the homogeneous background field and the quark loops are averaged over    the background field,  the correlators of the  background field  are calculated in the spherical domain approximation.\n\n\n\n\n\n\\begin{figure}\\centering\n\\sidecaption\n\\includegraphics[scale=.9]{f_P}\n\\hspace*{5mm}\\caption{Diagrams contributing to leptonic decay constants $f_P$. \\label{weak_decay_diagrams}}\n\\end{figure}\n\n\\begin{figure}\\centering\n\\sidecaption\n\\includegraphics[scale=.9]{V-gamma}\n\\hspace*{5mm}\\caption{Diagrams contributing to $V\\to\\gamma$ transition constants \n$g_{V\\gamma}$.\\label{g_rho_gamma_diagrams}}\n\\end{figure}\n\n\n\n\n\n\\section{Meson properties}\n\\label{section2}\n\n\n\n The truncated QCD functional integral can be rewritten in terms of the   composite colorless meson fields $\\phi_{\\cal Q}$ by means of  the standard bosonization procedure: introduce the auxiliary meson fields, integrate out the quark fields, perform the orthogonal transformation of the auxiliary fields that diagonalizes the quadratic part of the action and, finally, rescale the  meson fields to provide the correct residue of the meson propagator at the pole corresponding to its physical mass (if any).  \nMore details can be found in Ref.~\\cite{EN,EN1,NK4}. \nThe result can be written in the following compact form~\\cite{NV1}\n\\begin{eqnarray}\n&&Z={\\cal N}\n\\int D\\phi_{\\cal Q}\n\\exp\\left\\{-\\frac{\\Lambda^2}{2}\\frac{h^2_{\\cal Q}}{g^2 C^2_{ \\mathcal Q}}\\int d^4x \n\\phi^2_{\\cal Q}(x)\n-\\sum\\limits_{k=2}^\\infty\\frac{1}{k}W_k[\\phi]\\right\\},\n\\label{meson_pf}\\\\\n&&W_k[\\phi]=\n\\sum\\limits_{{\\cal Q}_1\\dots{\\cal Q}_k}h_{{\\cal Q}_1}\\dots h_{{\\cal Q}_k}\n\\int d^4x_1\\dots\\int d^4x_k\n\\Phi_{{\\cal Q}_1}(x_1)\\dots \\Phi_{{\\cal Q}_k}(x_k)\n\\Gamma^{(k)}_{{\\cal Q}_1\\dots{\\cal Q}_k}(x_1,\\dots,x_k),\n\\label{effective_meson_action}\n\\\\\n &&\\Phi_{{\\cal Q}}(x)=\\int \\frac{d^4p}{(2\\pi)^4}e^{ipx}{\\mathcal O}_{{\\mathcal Q}{\\mathcal Q}'}(p)\\tilde\\phi_{{\\mathcal Q}'}(p), \\  .\n \\label{Pphi}\n\\end{eqnarray}\nwhere condensed index $\\mathcal{Q}$ denotes all relevant meson quantum numbers and indices. Integration variables $\\phi_{\\mathcal Q}$ in the functional integral \\eqref{meson_pf} correspond to the physical meson fields that diagonalize the quadratic part of the effective meson action \\eqref{effective_meson_action} in momentum representation, which is achieved by means of orthogonal transformation ${\\mathcal O}(p)$.\n\n\n\n\\begin{figure}\n\\begin{centering}\n\\sidecaption\n\\includegraphics[width=0.3\\textwidth]{gluon_prp_dr}\n\\caption{Momentum dependence of the gluon  dressing function  without (solid line)  and with (dashed line) accounting for the running of the strong coupling constant $\\alpha_s(p)$  (dotted line). The dashed line qualitatively reproduces the shape of the Landau gauge dressing function of gluons calculated within the functional renormalization group~\\cite{Jan2015} and  Lattice QCD~\\cite{Bowman, Ilgenfritz} as well as a part of the input gluon propagator used in the approaches based on combined  Dyson-Schwinger and Bethe-Salpeter equations~\\cite{Fischer:2014xha,Dorkin:2014lxa}.  \\label{gluon_fig}}\n\\end{centering}\n\\end{figure}\n\n\n\nInteractions between physical meson fields  $\\phi_{\\mathcal Q}$ are  described  by  $k$-point nonlocal vertices $\\Gamma^{(k)}_{\\mathcal{Q}_1\\dots \\mathcal{Q}_2}$. subsequently tuned to the physical meson representation by means of  corresponding orthogonal transformations ${\\mathcal O}(p)$. \nAs is illustrated in Fig.~\\ref{diagrams},  vertices $\\Gamma^{(k)}$ are expressed \\textit{via}  1-loop  diagrams  $G^{(k)}_{{\\cal Q}_1\\dots{\\cal Q}_k}$ which include  nonlocal quark-meson vertices  and quark propagators (for their explicit analytical form see~\\cite{NV1}).\n\nThe mass spectrum $M_\\mathcal{Q}$  of mesons  and quark-meson coupling constants  $h_{\\cal Q}$ are determined by the quadratic part of the effective meson action \\textit{via} equations\n\\begin{equation*}\n1=\n\\frac{g^2}{\\Lambda^2}C^2_{\\cal Q}\\tilde \\Pi_{\\cal Q}(-M^2_{\\cal Q}|B),\n\\  \\\nh^{-2}_{\\cal Q}=\n\\frac{d}{dp^2}\\tilde\\Pi_{\\cal Q}(p^2)|_{p^2=-M^2_{\\cal Q}}, \n\\end{equation*}\nwhere $\\tilde\\Pi_{\\cal Q}(p^2)$ is the diagonalized two-point correlator $\\tilde\\Gamma^{(2)}_{\\cal QQ'}(p)$  put on mass shell.\nAbove  definition  of the meson-quark coupling constant $h_{\\cal Q}$ provides correct residue at the pole. \n\nThe results of calculations are shown in Fig.~\\ref{fig-masses} and Table~\\ref{constants}.\nAn overall accuracy of description is 10-15 percent in the lowest order calculation\n achieved with the minimal for QCD  set of parameters: infrared limits of renormalized strong coupling constant $\\alpha_s$ and quark masses $m_f$, scalar gluon condensate $\\langle g^2F^2\\rangle$ as a fundamental scale of QCD\n and topological susceptibility of pure QCD without quarks.  This last parameter can be related to the mean size $R$ of  domains. \n \n\\section{Discussion}\n\\label{section3}\n\nIt is interesting to take a look at the properties of gluon propagator in the present approach  in view of the known functional form of quark  and Landau gauge gluon propagators calculated within the functional renormalization group, Lattice QCD and Dyson-Schwinger equations \\cite{Bowman,Ilgenfritz,Jan2015,Fischer:2014xha,Dorkin:2014lxa}.  \nAs it can be seen from  Fig.~\\ref{gluon_fig} the shape of the gluon dressing function in the background field under consideration is in qualitative agreement with the known results of functional RG, DSE and lattice QCD. \nFor more detailed comparison  we refer to the paper~\\cite{NV1}.\n\nFor conclusion we would like to outline few  problems to be addressed within the domain model of QCD vacuum. The most important conceptual question relates to identification of a  mechanism for stabilization of a  finite mean size of domains. Our preliminary estimates  indicated that the competition between gluon and ghost contributions and the  contribution of the quark lowest eigenvalues  to the free energy density of the finite domain  could lead to the appropriate stabilization. This issue has to be studied carefully.    Another important for phenomenological applications problem is the  accurate description of the $n-$pont correlators in the random domain wall network ensemble which can be achieved by numerical methods. Random spherical domain ensemble is a rather rough approximation, and it has to be improved. \nDomain model of QCD vacuum offers an appealing way to study the deconfinement transition in terms of the explicit degrees of freedom which are active or suppressed in different regimes (high energy density, high baryon charge density, strong electromagnetic fields). A preliminary consideration of the relevant features of the model can be found in \\cite{NV}.\n\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\n    Anyons are emergent quasi-particles that exist in two-dimensional condensed matter systems and whose exchange statistics generalize that of Bosons and Fermions. These particles have spurred much interest due to their potential applications for quantum computation. \n    In particular, it was found that with certain types of non-Abelian anyons, a universal quantum computation can be performed by braiding and fusing these particles \\cite{freedman2002modular, freedman2002simulation, kitaev2003fault}. \n    An intriguing benefit of this paradigm is that, due to their topological nature, computations are intrinsically robust to perturbations at zero temperature. \n    At non-zero temperature, however, thermal anyonic excitations can corrupt the computation by performing non-trivial braids with the computational anyons. \n    Since systems exhibiting anyonic excitations have a spectral gap $\\Delta$, this source of errors can be suppressed to some extent at temperatures $T \\ll \\Delta\/k_B$ as the density of thermal anyons scales as $e^{-\\Delta\/k_B T}$.\n    Alas, this passive protection does not suffice, because the presence of thermal anyons is unavoidable at non-zero temperatures when scaling up the size of computations. \n    Therefore, proficient active error correction schemes for non-Abelian models are paramount for the realization of topological quantum computers. \n\n    Besides their envisaged use for topological quantum computation, topologically ordered systems (i.e., those that support anyonic excitations on top of their ground space) are also of much interest for quantum error correction. \n    In particular, one of the characteristics of such systems is a robust ground space degeneracy, which allows one to use their ground space as the code space of an error correcting code. \n    This realization led to the discovery of topological quantum error correcting codes, which encode logical quantum states in topologically ordered states of a system of qudits (typically arranged on a two-dimensional lattice). \n    %\n    Since their discovery in the 90s, most research has focused exclusively on Abelian topological codes such as the surface code and the color code \\cite{bravyi1998quantum, dennis2002topological, kitaev2003fault, wang2009threshold, fowler2012surface, wootton2012high, anwar2014fast, bravyi2014efficient, wootton2015simple, andrist2015error}, which admit an elegant characterization in terms of the stabilizer formalism \\cite{gottesman1997stabilizer}.\n    Due to their geometrical locality and high error thresholds, these codes are considered to be promising candidates for protecting quantum information from noise in error-corrected quantum computers.\n    One of the drawbacks of Abelian topological codes, however, is that they do not allow one to execute a universal set of logical gates in a protected fashion in two dimensions. Hence, they must be supplemented with additional protocols such as magic state distillation \\cite{bravyi2005universal} or code switching to higher-dimensional codes \\cite{kubica2015universal, bombin2016dimensional} , which introduce a large space-time overhead \\cite{campbell2017roads}. \n    %\n    Alternatively, there exist non-Abelian topological codes which do not suffer from this inherent limitation, and are able to perform a universal gate set natively within their code space in two dimensions \\cite{freedman2002modular}. The trade-off is that such codes go beyond the stabilizer formalism and are therefore very hard to simulate classically.\n\n    While active error correction in Abelian anyon models and Abelian topological codes has been studied extensively, quantum error correction based on non-Abelian anyon models has not enjoyed the same focus. Nevertheless, important progress has been made over the last decade, including both analytical proofs and numerical demonstrations of threshold behavior for various non-Abelian topological error correcting codes \\cite{hutter2016continuous, wootton2014error, brell2014thermalization, burton2017classical, schotte2022quantum}. Moreover, syndrome extraction circuits for such non-Abelian string-net codes have been developed in recent years \\cite{Bonesteel:2012fl, schotte2022quantum}. In addition, state preparation for non-Abelian codes based on the Kitaev quantum double models via measurements has also been proposed recently for the experimental implementation on qubit lattices \\cite{verresen2021efficiently, tantivasadakarn2022shortest}, although further development is still needed in the context of fault-tolerant state preparation.  Notably,  previous studies in this field already include codes based on the Fibonacci anyon model, which is universal for quantum computation \\cite{burton2017classical, schotte2022quantum}. In particular, a quantum memory of qubits supporting doubled Fibonacci anyonic excitations was found to have a threshold that lies remarkably close to that of the surface code under similar assumptions \\cite{schotte2022quantum}.\n\n    These results, however, all assume perfect syndrome measurements, which are topological charge measurements in this context. As we aim to model more realistic scenarios, we must take faulty measurements into consideration. \n    Again, much is known in the case of Abelian topological codes \\cite{harrington, dennis2002topological, raussendorf2007fault, fowler2009high, watson2015fast, herold2017cellular}. \n    For their non-Abelian counterparts, one key result stands out: in Ref.~\\cite{dauphinais2017fault} a proof was formulated that topological codes based on non-cyclic anyon models admit a error correction thresholds with faulty topological charge measurements.\n   \n    While this result is remarkable, non-cyclic anyon models are not universal for quantum computation, and it remains an open question whether similar claims can be made for universal models. \n    \t\n\t\n    In this work, we take a step towards demonstrating that fault-tolerance is indeed possible for universal non-Abelian topological codes. To this end, we define a quantum memory constructed as a two-dimensional model of Fibonacci anyons on a torus. We study active continuous quantum error correction on this model in the presence of thermal noise represented by pair-creation processes, and with faulty syndrome measurements. \n\t%\n\tThe correction procedure is based on the cellular automaton decoders originating in the works of G\u00e1cs \\cite{gacs1986reliable} and Harrington \\cite{harrington}, and further studied in the context of non-Abelian models in Ref.~\\cite{dauphinais2017fault}. \n\tThrough numerical simulations, we study how the average memory lifetime changes with the error rate. The results indicate that this code is indeed fault-tolerant, which is strong evidence for the existence of fault-tolerant universal non-Abelian codes.\n\n \n\tThe structure of this work is as follows.\n\tIn Sec.~\\ref{sec:code} we introduce the topological Fibonacci code. We then describe the details of the noise model in Sec.~\\ref{sec:noise} and introduce the cellular automaton decoder in Sec.~\\ref{sec:decoder}. \n\tWe proceed by giving an outline of the numerical simulations performed in this work in Sec.~\\ref{sec:simulation}.\n\tFinally, we present the corresponding numerical results in Sec.~\\ref{sec:results} and conclude with a discussion in Sec.~\\ref{sec:discussion}. \n\t\n\t\\section{The Fibonacci code} \\label{sec:code}\n\t\n\n\tWe consider a two-dimensional model comprised of hexagonal tiles laid out on the surface of a torus. The resulting geometry can be represented as an $ L \\times L $ hexagonal lattice with periodic boundary conditions in both directions (Fig.~\\ref{fig:pair-creation}). Each of these hexagonal tiles can contain an excitation known as a \\emph{Fibonacci anyon}.\n\t\n\n\tAnyons are point-like quasi-particle excitations which can be characterized algebraically in terms of a unitary modular tensor category (UMTC). A thorough description of anyon models using UMTCs goes beyond the scope of this work, however, some details are given in Sec.~\\ref{sec:anyons}. \n\tFor now, it is sufficient to state that an anyon model specifies a set of anyon labels, also referred to as particle types, which can fuse according to a specific set of fusion rules.\n\tThe Fibonacci anyon model considered in this work contains two labels, $ \\mathbf{1} $ and $ \\tau $, which obey the fusion rules\n\t\\begin{equation}\\label{eq:fusion_rules}\n\t\t\\mathbf{1} \\times \\mathbf{1} = \\mathbf{1}\\,, \\quad \\mathbf{1} \\times \\tau = \\tau \\times \\mathbf{1} = \\tau\\,, \\quad \\tau \\times \\tau = \\mathbf{1} + \\tau\\,.\n\t\\end{equation}\n\t\n\tIn general, one can associate a vector space to a given set of anyons, where the basis vectors are labeled by the different ways in which the anyons can fuse. This fusion space has a topological degeneracy, and can therefore be used to robustly encode quantum information. In particular, for the Fibonacci anyon model the anyonic vacuum on a two-dimensional torus has a twofold degeneracy \\cite{pfeifer2012translation}. Starting from our two-dimensional model, we can therefore define an error correcting code whose code space is identified with the anyonic vacuum on the torus and which encodes a single logical qubit.\n\tA basis for this code space can be defined using Wilson line operators along the homologically non-trivial cycles $ x $ and $ y $ shown in \\figref{fig:torus}:\n\t\\begin{equation}\\label{eq:basis}\n\t    \\begin{array}{l}\n\t        W^a_x \\ket{\\mathbf{1}}_x = \\frac{S_{a\\mathbf{1}}}{S_{\\mathbf{1} \\mathbf{1}}} \\ket{\\mathbf{1}}_x\\,,\\\\\n\t\t W^a_x \\ket{\\tau}_x = \\frac{S_{a\\tau}}{S_{\\mathbf{1} \\tau}} \\ket{\\tau}_x\\,, \n\t    \\end{array}\n\t\t\\qquad  a \\in \\{\\mathbf{1},\\tau\\} \\,,\n\t\\end{equation}\n\tWe note that a different basis, $ \\{\\ket{0}_y, \\ket{1}_y\\} $, can be defined analogously by swapping the $ x $ and $ y $ labels above, where the two bases are related through the modular $ S $ matrix $ S_{ab} = \\!\\!\\phantom{a}_y\\!\\braket{a|b}_x$.\n\tFor the Fibonacci anyon model its numerical values are\n\t\\begin{equation}\\label{eq:S}\n\t\tS = \\dfrac{1}{\\sqrt{1+\\phi^2}} \n\t\t\\begin{pmatrix}\n\t\t\t1 & \\phi \\\\\n\t\t\t\\phi & -1\n\t\t\\end{pmatrix}\\,,\n\t\\end{equation}\n\twhere $ \\phi = \\dfrac{1 + \\sqrt{5}}{2} $.\n\n \n\n\t\n\t\\begin{figure}\n\t\t\\centering\n\t\t\\includegraphics[width=0.7\\linewidth]{fig\/torus}\n\t\t\\caption{The two homologically non-trivial cycles on a torus.}\n\t\t\\label{fig:torus}\n\t\\end{figure}\n\t\n\tThe action of the mapping class group on the anyonic vacuum then corresponds to unitary operations on the code space. For the Fibonacci category, any logical unitary operator can be realized in this way, up to arbitrary precision \\cite{freedman2002modular}. Therefore, the quantum error correcting code defined above natively supports universal quantum computation. \n\t\n\tErrors in this code appear as spurious anyonic excitations, which can corrupt the encoded information if their world lines between creation and re-annihilation are topologically non-trivial, i.e., form a non-contractible cycle \\footnote{Note that a pair of Fibonacci anyons can also fuse to a single non-trivial anyon when one member of the pair has been transported along a non-trivial cycle. Since the resulting state is no longer in the code space, this does not constitute a logical operation on the encoded information. However, one can show that the encoded information is irrevocably lost in case of such an event \\cite{wootton2014error}.}. The objective of error correction is then to systematically remove these spurious excitations, without corrupting the quantum memory in the process.\n\tThis correction is performed in an active and continuous manner, and can be broken down into a series of discrete steps. At each step, a suitable recovery operation is performed based on a measured list of positions and types of the excitations, called the error syndrome.\n\t\n\tWe conclude this section by noting that the numerical simulation of the error-correction process requires the introduction of some additional manipulations on fusion states of multiple Fibonacci anyons. As these are technical details that do not contribute to the intuition of the procedure, we defer their definition to Sec.~\\ref{sec:anyons}.\n\t\n\t\n\t\n\t\\section{Noise model and correctability} \\label{sec:noise}\n\t\n\tHaving defined our model and code space, we now turn to the description of the noise model used in our simulations.\n\tWe model continuous active error correction in our Fibonacci code as a sequence of time steps, where each time step itself consists of three parts: the application of pair-creation noise, faulty syndrome measurement, and error correction respectively. \n\t\n\tAt each time step, first, for each edge of the hexagonal lattice graph a pair of anyons is created across this edge with a probability $ p $. Immediately after each pair creation event, the resulting charge in the two affected tiles is sampled, effectively collapsing all superpositions of anyonic charge within each tile to either $\\mathbf{1}$ or $\\tau$. After the pair creation noise has been applied, faulty syndrome extraction is simulated by generating a list of the anyon charge in all tiles, and flipping each outcome individually with a probability $ q $. In addition to the charges that are correctly detected, the resulting faulty syndrome can contain both \\enquote{ghost defects} (indicating a non-trivial charge when none is truly present) and \\enquote{missing defects} (failing to report a true non-trivial charge).\n\tFinally, this faulty syndrome is passed to a decoder, introduced in the following section, which then performs a set of local operations based on the current (and past) syndrome information in an attempt to move the system back towards the initial state.\n\t\n\tAfter each time step, the current state of the system is copied and it is checked whether it is still correctable. This is done by passing the copy to a clustering decoder \\cite{brell2014thermalization, burton2017classical, schotte2022quantum} and simulating a decoding procedure with perfect syndrome measurements starting from this given initial state. If this perfect decoding is successful, the memory is considered intact and the simulation is continued. If perfect decoding is unsuccessful, the memory is considered corrupted and the simulation is aborted. The memory lifetime is then defined as the number of time steps after which a perfect clustering decoder can no longer successfully restore the initial state.\n\t\n    \\begin{figure}\n\t\t\\centering\n\t\t\\begin{subfigure}{.58\\linewidth}\n\t\t\t\\centering\n\t\t\t\\includegraphics[width=1\\linewidth]{fig\/hex_lattice_noise}\n\t\t\t\\caption{}\n\t\t\\end{subfigure}\n\t\t\\hfill\n\t\t\\begin{subfigure}{.4\\linewidth}\n\t\t\t\\centering\n\t\t\t\\includegraphics[width=.95\\linewidth]{fig\/dual_lattice_noise}\n\t\t\t\\caption{}\n\t\t\\end{subfigure}\n\t\t\\caption{(a) Pair-creation events creating anyonic excitations in neighboring tiles. The dotted ellipse represents a collapse to the total charge of the anyons it contains. A ghost defect is shown in blue, a missing defect is highlighted in orange with a cross. (b) The outcome of this noise process represented on the decoding graph. Note that the missing defect (highlighted in orange) will (by definition) not be visible in the syndrome.}\n\t\t\\label{fig:pair-creation}\n\t\\end{figure}\n\t\n\tFor a given pair of tiles which share an edge, the process of pair creation across this edge corresponds to the matrix elements\n\t\\begin{equation}\n\t\t\\bra{a'\\!,b'\\!;c'}U_{\\text{pc}}\\ket{a,b;c} = \\delta_{c,c'} F^{a a 1}_{\\tau\\tau a'} F^{a'\\!\\tau a}_{b \\, c \\, b'}\\,,\n\t\\end{equation}\n\twhere we have used the $ F $-symbols of the Fibonacci category, given in \\eqref{eq:Fib_F_symbols_nontriv}. Here, $ \\ket{a,b;c} $ represents the state where the affected tiles have anyon charges $ a $ and $ b $, respectively, with total charge $ c $.  This then defines the probability distribution according to which outcomes $ a' $ and $ b' $ are sampled. \n\t%\n\tSince our noise model does not allow any superposition in the anyonic charge of individual tiles, it should be considered semi-classical rather than fully quantum-mechanical. Note, however, that this does not render our model completely classical. Indeed, superpositions in the total charge $ c $ of the affected tiles are an inherent part of the state evolution that cannot be captured faithfully by any classical probabilistic process.  \n\tFurthermore, while the extreme decoherence assumption for the anyon charge in individual tiles greatly simplifies the numerical simulation outlined in this work, it was argued in Ref.~\\cite{brell2014thermalization} that this decoherence is unlikely to have any tangible influence on the observed memory lifetimes, as the essential topological nature of the noise processes is still captured correctly.\n\t\n\tWe note that this type of noise can be understood as originating from the connection to a thermal bath with inverse temperature  $ \\beta = 1\/(k_B T) $ determined by the error rate $ p $ through the relation\n\t\\begin{equation}\\label{key}\n\t\t\\dfrac{p}{1-p} = \\e^{-\\beta \\Delta}\\,.\n\t\\end{equation}\n\tHere, $ \\Delta $ represents the energy required to create a pair of anyonic excitations and place them in neighboring tiles.\n\t\n\tTo conclude this section, we emphasize that in the case of non-Abelian error correction, even decoding with perfect syndrome measurements is still an inherently stochastic procedure due to the indeterminacy of anyonic charge measurements. This means that perfect decoding can sometimes either be successful or unsuccessful even starting from the same initial state. Our definition of the memory lifetime therefore simply corresponds to a statistical estimate of the actual memory lifetime. \n\t%\n\tFurthermore, it is not known which decoder is optimal for the Fibonacci code. Hence, the choice for the clustering decoder to verify the correctability of states is, in a way, an arbitrary one. This choice, however, is motivated by the recent discovery that the clustering decoder yields high thresholds for a related error correcting code exhibiting doubled Fibonacci anyonic excitations, and performed significantly better in this context than decoders based on a perfect matching strategy \\cite{schotte2022quantum}.\n\tIn any case, one should keep in mind that the memory lifetime as defined above, does not represent the true memory lifetime. Instead the sub-optimal verification process entails that it merely provides us with a lower bound on the true value.\n\t\n\t\n\t\\section{Harrington's cellular automaton decoder} \\label{sec:decoder}\n\n\tThe model described above is paired with a decoder which is a straight-forward adaptation of the cellular automaton decoder introduced in Ref.~\\cite{harrington}.\n\tPreviously, this decoder has also been used for a similar phenomenological model of Ising anyons in Ref.~\\cite{dauphinais2017fault}, where the existence of an error correction threshold was proven analytically.\n\tAt each time step during the error correction simulation, based on the reported measurement outcomes in the faulty syndrome, the decoding algorithm will apply local transition rules to fuse neighboring anyons or to move anyons to neighboring tiles.\n\t\n\n\tIntuitively these transition rules work as follows. The lattice is divided into square colonies of size $Q \\times Q$. At each time step, the transition rules will attempt to fuse neighboring non-trivial anyons, as observed in the faulty syndrome. If a non-trivial anyon has no neighbors, the transition rules will move it to the center of its colony. \n\tAt larger timescales, higher-level transition rules are applied on a renormalized lattice where anyons located at colony centers will be fused with anyons at neighboring colony centers, or moved toward the center of their respective super-colonies, which consist of $Q \\times Q$ colonies. This renormalization scheme is then continued at higher levels until eventually the $ Q^n \\times Q^n $ super-colony covers the entire lattice for some integer $ n $. \n\tTo ensure the latter is possible, we will always assume that the linear lattice size satisfies $L= Q^n$ for some integer $ n $.\n\tAn example of these processes is shown in \\figref{fig:transition_rules}.\n\t\n\tTo describe the action of the decoding algorithm more precisely, we will define its action at different renormalization levels $ k $. \n\tThe level-0 transition rules are those already discussed above and are applied at every time step based on the reported faulty syndrome obtained from the most recent round of faulty measurements. The transition rules are applied to one location at a time and take into consideration only the anyon content of that site and of its eight neighbors. \n\tA detailed definition of these rules is given in App. \\ref{sec:transition_rules}.\n\tWhen an anyon is moved from a site $ l $ to a neighboring site $ l' $, the (true) anyon content of site $ l $ is fused with that of site $ l' $ and the resulting charge is placed on site $ l' $ while the charge of site $ l $ is restored to the vacuum. This happens irrespective of whether or not the syndrome for both sites was correct. \n\tHence, when the decoder attempts to move a ghost defect (a trivial charge misidentified as a non-trivial one) to a neighboring site, this process does not create additional excitations. This does not, however, mean that mistaking a trivial charge for a non-trivial one has no negative consequences. Indeed, these wrong syndromes may cause the decoder to stretch out existing errors. \n\n\t\n\tThe level-1 transition rules are not applied in every time step, but only when $ t $ is a multiple of a parameter called the \\emph{work period}, which we will denote by $ U $. We require that $ U = b^2 $ for some positive integer $ b $. \n\tOne should think of $ U $ as the time scale at which a coarse-graining is performed. \n\tLevel-1 transition rules act at on a coarse-grained lattice where the sites correspond to the centers of the level-0 colonies, and these are grouped into level-1 colonies of size $ Q^2 \\times Q^2 $. \n\tHence, the actions determined by the level-1 transition rules involve pairs of level-0 colony centers separated by a distance $ Q $. An example of such a move is provided in \\figref{fig:transition_4}.\t\n\tThe transition rules themselves are nearly identical to the level-0 rules, but are based on two sets of level-1 syndromes $ s_{1,c} $ and $ s_{1,n} $ (defined below) rather than one. For a site $ l $ (which is a level-0 colony center), the transition rules use $ s_{1,c}(l) $ as the anyon content of site, while the anyon content of its neighbors (that is, the neighboring level-0 colony centers) is taken to be $ s_{1,n}(l') $.\t\n\t\n\tThe definitions of the level-1 syndromes $ s_{1,c} $ and $ s_{1,n} $ require a pair of variables $ f_c, f_n \\in [0,1]$. \n\tIntuitively these variables serve as detection thresholds for the level-1 syndromes by determining the fraction of measurements that must return a non-trivial outcome at a site before it qualifies as a non-trivial level-1 syndrome. \n\tThe proper definition, however, is slightly more complicated and uses a coarse-grained counting method. \n\tBelow, we give the precise definition of $ s_{1,c} $,  the definition of $ s_{1,n} $ is entirely analogous (using $ f_n $ instead of $ f_c $). \n\tWe start by dividing the work period $ U = b^2 $, into $ b $ intervals of $ b $ time steps each.\n\tFor each of these intervals, we say a non-trivial syndrome is present at a colony center $ l $ if a non-trivial charge was reported there for at least $ f_c b $ of the $ b $ time steps in the interval. \n\tWhen at least $ f_c b $ of the $ b $ intervals have a non-trivial syndrome, $ s_{1,c}(l) $ is set to one.\n\tA visual example of this coarse-grained counting procedure is shown in \\figref{fig:binning}.\n\t\n\t\\begin{figure}[h]\n\t\t\\vspace{.5cm}\n\t\t\\centering\n\t\t\\includegraphics[width=\\linewidth]{fig\/level-n_syndrome} \n\t\t\\caption{A visual example of the coarse-grained counting procedure to determine the level-1 syndrome for a level-0 colony center. The row of dots represent $ U $ time steps, divided in $ b $ intervals of size $ b $. The time steps during which a non-trivial measurement outcome was reported are indicated by the colored dots. The crosses in the second row indicate in which intervals the fraction of non-trivial measurement outcomes is equal to or higher than $ f_c $.  }\n\t\t\\label{fig:binning}\n\t\\end{figure}\n\n\tThe motivation for using two types of syndromes for $ k>0 $ is as follows. Suppose that an error spans across two neighboring colonies, which we will label $ \\rho $ and $ \\rho' $. The level-0 transition rules will transport all resulting anyons to the respective colony centers, where they can now be acted upon by level-1 transition rules at the end of the work period. Imagine that a non-trivial anyon is now present at both colony centers. When considering the level-1 transition rules acting on $ \\rho $, there are four possible scenarios for the syndromes $ s_{1,c}(\\rho) $ and $ s_{1,n}(\\rho') $. In case $ s_{1,c}(\\rho) = 0 $, the transition rules act trivially on $ \\rho $. If both $ s_{1,c}(\\rho) = 1 $ and $ s_{1,n}(\\rho') = 1 $ then the transition rules will be applied correctly and the anyons will be fused. \n\tHowever, if $ s_{1,c}(\\rho) = 1 $ but $ s_{1,n}(\\rho') = 0 $, the transition rules may move the anyon in $ \\rho $ away from $ \\rho' $, thereby increasing the weight of the error.\n\tHence, it is desirable to set $ f_c > f_n $ to decrease the odds that when a level-k syndrome reports an non-trivial anyon at a colony center, the level-k syndrome for its neighbors are false negatives. \n\tWe must be careful not to set $ f_c $ too high or $ f_n $ too low, however. If we choose $ f_c $ to high, low-weight errors could cause $ s_{1,c} $ to never report any non-trivial charges, delaying any necessary corrections. Similarly, setting $ f_n $ too low will result in low-weight error triggering many false positives for $ s_{1,n} $, which can cause the decoder to make wrong decisions. \n\t\n\tLevel-$ k $ transition rules are applied when $ t \\mod U^k = 0 $. They operate on a renormalized lattice that uses the centers of level-$ (k-1) $ colonies as sites, and groups these into level-$ k $ colonies of size $ Q^k \\times Q^k $. The level-$ k $ syndromes $ s_{k,c} $ and $ s_{k,n} $ are determined by the coarse-grained counting method described above, using $ b^k $ intervals of $ b^k $ time steps each. \n\tFor linear system size $ L $, k ranges from 0 to $ k_{\\text{max}} = \\log_Q(L) $.\n\t\n\t\n\tIt is important to note that non-Abelian anyons do not allow for instantaneous moves. \n\tIndeed, while one can construct a unitary string operator for Abelian anyons, no such operator can be constructed for the non-Abelian case. \n\tThis discrepancy can be traced back to the fact that fusion outcomes are non-deterministic for non-Abelian anyons, implying it is not possible to move an non-Abelian anyon by annihilating it with one member of a particle-antiparticle pair (as is done in e.g., the surface code).\n\t\n\tTherefore, the actions determined by level-$k$ transition rules, for $k>0$ cannot be applied withing a single time step. Instead, they will be broken up into a sequence of moves involving only pairs of neighboring sites which will be applied in $Q^k$ consecutive time steps. \n\tWe further limit the model by requiring that the number recovery operations affecting a single tile in the lattice (or site in the decoding graph), is no greater than one in each time step. \n\tThis allows all recovery operations applied in one time step to be performed in parallel. \n\tHence, we must define a hierarchy determining which actions (moves or fusions between neighboring tiles) get prioritized based on the renormalization level from which they originated. In our case, it was opted to always prioritize correction processes from the highest renormalization level \\footnote{Note that if one were to prioritize the level-0 corrections, higher-level correction could never be completed, as they would be undone immediately after their first action is applied.}\n\t\n\tIt was argued in \\cite{dauphinais2017fault} that the prohibition of instantaneous corrections would likely not influence the threshold behavior other than slightly lowering the memory lifetimes relative to a hypothetical case where this restriction is dropped. We explicitly verify this claim for our Fibonacci model below in Sec.~\\ref{sec:results}.\n\t\n\t\\begin{figure}[h]\n\t\t\\centering\n\t\t\\begin{subfigure}{.45\\linewidth}\n\t\t\t\\includegraphics[width=\\linewidth]{fig\/transition_rules_example1}\n\t\t\t\\caption{}\n\t\t\t\\label{fig:transition_1}\n\t\t\\end{subfigure}\n\t\t\\hfill\n\t\t\\begin{subfigure}{.45\\linewidth}\n\t\t\t\\includegraphics[width=\\linewidth]{fig\/transition_rules_example2}\n\t\t\t\\caption{}\n\t\t\t\\label{fig:transition_2}\n\t\t\\end{subfigure}\n\t\t\\hfill\n\t\t\\begin{subfigure}{.45\\linewidth}\n\t\t\t\\includegraphics[width=\\linewidth]{fig\/transition_rules_example3}\n\t\t\t\\caption{}\n\t\t\t\\label{fig:transition_3}\n\t\t\\end{subfigure}\n\t\t\\hfill\n\t\t\\begin{subfigure}{.45\\linewidth}\n\t\t\t\\includegraphics[width=\\linewidth]{fig\/transition_rules_example4}\n\t\t\t\\caption{}\n\t\t\t\\label{fig:transition_4}\n\t\t\\end{subfigure}\n\t\t\\caption{Illustration of the transition rules on the decoding graph. The gray disks represent non-trivial syndromes, and the blue arrows represent the actions suggested by the decoder. The blue dotted lines represent the $3\\times3$ colonies. (a-c) show a sequence of level-0 transition rules and possible outcomes of those actions. In (d) non-trivial anyons have been transported to two neighboring colony centers, the blue arrow represent a level-1 transition which could be applied at the end of the work period.}\n\t\t\\label{fig:transition_rules}\n\t\\end{figure}\n\t\n\t\\begin{figure}[h]\n\t\t\\centering\n\t\t\\hfill\n\t\t\\begin{subfigure}{.45\\linewidth}\n\t\t\t\\includegraphics[width=\\linewidth]{fig\/dual_lattice_colonies}\n\t\t\t\\caption{}\n\t\t\t\\label{fig:colonies1}\n\t\t\\end{subfigure}\n\t\t\\hfill\n\t\t\\begin{subfigure}{.45\\linewidth}\n\t\t\t\\includegraphics[width=\\linewidth]{fig\/dual_lattice_colonies_2}\n\t\t\t\\caption{}\n\t\t\t\\label{fig:colonies2}\n\t\t\\end{subfigure}\n\t\t\\hfill\n\t\t\\begin{subfigure}{.45\\linewidth}\n\t\t\t\\includegraphics[width=\\linewidth]{fig\/dual_lattice_colonies_3}\n\t\t\t\\caption{}\n\t\t\t\\label{fig:colonies3}\n\t\t\\end{subfigure}\n\t\t\\hfill\n\t\t\\caption{(a) Level-0 colonies of size $Q\\times Q$. (b) Level-1 colonies defined as $Q\\times Q$ level-0 colonies. (c) Renormalized lattice used for the level-1 transition rules. }\n\t\t\\label{fig:colonies}\n\t\\end{figure}\n\t\n\t\n\t\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\t\n\t\\section{Outline of the simulation} \\label{sec:simulation}\n\t\n\tThe goal of this work is to numerically determine a fault-tolerant error threshold for the error correcting code defined in Sec.~\\ref{sec:code} with pair-creation noise and measurement noise as outlined in Sec.~\\ref{sec:noise}, and with the cellular automaton decoder introduced in Sec.~\\ref{sec:decoder}.\n\tThis is achieved by performing Monte-Carlo simulations to determine the average memory lifetime for a range of system sizes and error rates. \n\tThese results then allow one to estimate the value of the error threshold. \n\t\n\tA single Monte-Carlo sample (with some fixed values for the noise strength $p$ and the measurement error rate $q$) is obtained as follows.\n\tFirst, the state of the system is initialized as a ground state (i.e.: containing no anyons).\n\tThen a sequence of time steps is performed consisting of the application of pair-creation noise with rate $p$, a round of faulty syndrome measurements with error probability $q$, and finally a sequence of recovery operations. \n\tAt the end of each time step, it is verified whether or not the state is considered correctable, according to the criteria specified in Sec.~\\ref{sec:noise}. \n\tThis sequence of time steps is continued until one of the following three outcomes occurs: (1) The largest connected group of anyons grows too large, rendering its classical simulation intractable \\footnote{Note that such cases are likely to correspond configurations in which the initial state cannot be recovered.}; \n\t(2) A noise process or recovery operation induces a logical error by fusing a pair of anyons along a path that forms a non-contractible loop when combined with their fusion tree;\n\t(3) The verification procedure at the end of a time step fails. \n\tThe memory lifetime is then set as the number of time steps that were completed.\n\tThe course of a single Monte-Carlo sample in the simulation is summarized as pseudo-code in Alg. \\ref{alg:decoder}.\n\t\n\t\\begin{algorithm}[H]\n\t\t\\caption{Numerical simulation} \\label{alg:decoder}\n\t\t\\begin{algorithmic}\n\t\t\t\\State initialize state\n\t\t\t\\State $t = 0$\n\t\t\t\\While{correctable with clustering decoder $\\And$ no logical errors made}  \n\t\t\t\\State $t \\gets t+1$\n\t\t\t\n\t\t\t\\State apply pair-creation noise\n\t\t\t\\State perform faulty measurements\n\t\t\t\\For{$k = 0: k_{\\text{max}} $}\n\t\t\t\\If{$t\\!\\mod U^k = 0$}\n\t\t\t\\State update level-$ k $ syndromes\n\t\t\t\\State apply level-$ k $ transition rules\n\t\t\t\\EndIf\n\t\t\t\\EndFor\t\t\t\t\t\t\t\t\t\t\n\t\t\t\\EndWhile\n\t\t\t\\State memory lifetime = t\n\t\t\\end{algorithmic}\n\t\\end{algorithm}\n\t\n\\section{Numerical results}\\label{sec:results}\n\t\n\tThe Monte Carlo simulation described above were performed for various system sizes with $ p = q  $. \n\tThe following parameters were used:\n\t\\begin{align*}\n\t\tQ &= 3\\,,\\\\\n\t\tb &= 7\\,,\\\\\n\t\tF_c &= 0.7\\,,\\\\\n\t\tF_n &= 0.2\\,. \\\\ \n\t\\end{align*}\n\tThe resulting average memory lifetimes for $ L = 3 $, $ L = 9 $ and $ L = 27 $ are shown below in \\figref{fig:results}.\n\t\n\t\\begin{figure*}[t]\n\t    \\centering\n    \t\\begin{subfigure}[t]{.49\\textwidth}\n    \t\t\\centering\n    \t\t\\includegraphics[trim={.8cm 7.3cm .5cm 6cm},clip,width=1.0\\linewidth]{results.pdf}\n    \t\t\\caption{Average memory lifetime in function of the error strength, with $ p = q $, for various system sizes. Each data point represents the average over 1000 Monte Carlo samples. The blue line shows the coherence time of a single physical qubit. \n    \t\tThe average memory lifetimes for $ p \\leq 10^{-3}  $ were fitted to a function of the form $ f(p) \\sim p^{-a} $. The results for $ L = 3 $, $ L = 9 $ and $ L = 27 $ are shown as the green, yellow and red lines respectively. }\n    \t\t\\label{fig:results}\n    \t\\end{subfigure}\n\t    \\begin{subfigure}[t]{.49\\textwidth}\n    \t\t\\centering\n    \t\t\\includegraphics[trim={.8cm 7.3cm .5cm 6cm},clip,width=1.0\\linewidth]{results_instant.pdf}\n    \t\t\\caption{Average lifetime in function of the error strength with $ p = q $ for various system sizes and (unphysical) \\emph{instantaneous} corrections. Each data point represents the average over 1000 Monte Carlo samples. The blue line shows the coherence time of a single physical qubit. }\n    \t\t\\label{fig:results_instant}\n    \t\\end{subfigure}\n\t    \\caption{}\n\t    \\label{fig:results_both}\n\t\\end{figure*}\n\t\n\tThese results clearly indicate that the code presented in this work is indeed fault-tolerant. Furthermore, while the current data is not sufficient to demonstrate a clear-cut fault-tolerant threshold, it still exhibits threshold behavior and is remarkably similar to the results previously obtained for the toric code \\cite{harrington} and the Ising topological code \\cite{dauphinais2017fault}.\n\tWe estimate that the fault-tolerant threshold for the Fibonacci topological with pair-creation noise and measurement noise lies between $p=10^{-4}$ and $p=5\\cdot 10^{-4}$, which corresponds to an inverse temperature between $\\beta = 9.2 \/\\Delta $ and $\\beta = 7.6 \/\\Delta$. \n\tThis is comparable to the threshold found for the Ising topological code \\cite{dauphinais2017fault}, and only one order of magnitude below that for the surface code under similar circumstances \\cite{harrington}.\n\n\tFor physical error rates near $p=q=10^{-4}$, corresponding to a temperature $1\/\\beta$ one order of magnitude below the spectral gap, a code of linear size $L=27$ yields logical error rates of the order $10^{-8}$.\n\t\n\t\n\tA second round of simulations was performed to determine average memory lifetimes with the assumption that all corrections happen instantaneously. \n\tWhile this is akin to the Abelian topological codes, where distant anyons can be fused using unitary string-operators, this scenario is unphysical for non-Abelian anyons as they do not admit unitary string-operators. \n\tNevertheless, it is worth studying to which extend the results in \\figref{fig:results} are influenced by the restriction to non-instantaneous recovery operations.\n\tIn Ref.~\\cite{dauphinais2017fault} it was conjectured that allowing instantaneous corrections does not significantly change the qualitative behavior of the average memory lifetimes as a function of the error rate, but mostly just increases the memory lifetimes.\n\tOur results, shown in  \\figref{fig:results_instant}, confirm this hypothesis. \n\t\n\t\n\t\\section{Discussion and outlook}\\label{sec:discussion}\n    The results presented in this work demonstrate that fault-tolerant error correction is possible for non-Abelian topological quantum error correcting codes supporting a universal logical gate set within their code space.  \n    For a code consisting of Fibonacci anyons in hexagonal tiles on a two-dimensional torus, subjected to pair creation noise and measurement noise, we demonstrated that the cellular automaton decoder detailed in this work is fault-tolerant. \n    In particular, for physical error rates $p\\leq10^{-3}$, it was found that the logical memory lifetime surpasses the physical coherence time for all system sizes.\n    When interpreting the pair-creation noise as resulting from a non-zero temperature, this pseudo-threshold corresponds to an inverse temperature $\\beta = 6.9\/\\Delta$, where $\\Delta$ is the energy required to create a pair of Fibonacci anyons.\n    Furthermore, our results suggest that this code admits a fault-tolerant quantum error correction threshold around $p = 10^{-4}$, or $\\beta = 9.2 \/ \\Delta$, which is similar to the fault-tolerant threshold found for the Ising topological code \\cite{dauphinais2017fault}. \n    \n     \n\tSeveral future research directions present themselves.\n\tFirst, more research on a possible fault-tolerant threshold is necessary.\n\n    Wile the numeric results presented in this work provide a strong indication that a fault-tolerant error correction threshold exists, they do not conclusively prove its existence, nor do they provide a precise estimate of its value. \n\tHence, an important open problem is the formulation of a mathematical proof of its existence. \n\tSuch proofs were previously formulated for the toric code \\cite{harrington} and for non-cyclic non-Abelian anyon models such as in the Ising topological code \\cite{dauphinais2017fault}. \n\tDue to the cyclic nature of Fibonacci anyons (or any universal anyon model), however, the existing proofs are not sufficient.\n\t\n\tSecond, it would be interesting to study different decoders in an identical setting. This includes both different cellular-automaton decoders such as those in Refs.~\\cite{herold2015cellular, herold2017cellular}, as well as new decoders tailored to the Fibonacci topological code. \n\t\n\tThird, while this work demonstrates that the Fibonacci topological code can be operated fault-tolerantly as a quantum memory, results regarding its use for fault-tolerant quantum computing are still lacking. \n\tWe envisage that fault-tolerant topological quantum computing at non-zero temperatures could be achieved by combining the code and decoding procedure presented in this work with the scheme for performing Dehn twists presented in Refs.~\\cite{PhysRevLett.125.050502, PhysRevB.102.075105, Lavasani2019universal}.   Alternatively, one can also perform transversal logical gates in a folded Fibonacci code \\cite{Zhu:2017tr}.\n\n\t\n\tFinally, it would be of great interest to expand the current results to microscopic models for non-Abelian topological quantum error correction, such as the Fibonacci Turaev-Viro code \\cite{schotte2022quantum}.\n\t\n\t\\section*{Acknowledgments}\n\tThe authors would like to thank Guillaume Dauphinais and Jim Harrington for enlightening discussions on the cellular automaton decoder. \n\tThe computational resources (Stevin Supercomputer Infrastructure) and services used in this work were provided by the Flemish Supercomputer Center (VSC), funded by Ghent University, the Research Foundation Flanders (FWO), and the Flemish Government. \n\tAS was supported by a fellowship of the Belgian American Educational Foundation. LB was supported by a PhD fellowship from the FWO. GZ was supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Co-design Center for Quantum Advantage (C2QA) under contract number DE-SC0012704.\n\t\n\t","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nData is collected on anything, at any time, and in any location. A study by IBM~\\cite{ibm2020} found that in 2020, 40~trillion gigabytes (40~zettabytes) were generated.\nThe majority of data in the digital realm, however, is unstructured, making it impossible for humans to process it in its entirety and leaving businesses struggling to manage such massive amounts of data. As a result, one of today's major issues for businesses is extracting information and value from data contained in information systems.\n\nProcess Mining~(PM)~\\cite{van2016process} is a relatively new area of research that lies between process modeling and analysis, machine learning, and data mining.\nIt is an umbrella term for a family of techniques to facilitate the analysis of operational processes by extracting knowledge from event logs in symbolic form, typically in the form of process models.\nAn event log serves as the input to PM algorithms, which is essentially a database of events where each event has\n(1) a case id: a unique identifier for a particular process instance,\n(2) an activity: description of the event that is occurring, and\n(3) a timestamp: timestamp of the activity execution.\nResources, expenses, and other event-related attributes may also be integrated by some techniques.\nPM techniques mostly address three tasks:\n(1) process discovery: transform the event log into a process model which describes the underlying process generating such data: common techniques include the alpha algorithm, heuristic miner, or inductive miner~\\cite{van2004},\n(2) conformance checking: analyse discrepancies between an event log and an existing process model to detect deviations, for quality checking or risk management~\\cite{Munoz},\n(3) process enhancement: improve the existing model's performance in terms of specific process performance metrics \\cite{enhance}.\n\nThe initial focus of PM was the analysis of \\textit{historical} event data to generate a process model.\nThese monitoring systems are reactive in nature, allowing users to detect a violation only after it has occurred.\nIn contrast, \nPredictive Process Mining~(PPM)\nor Predictive Process Monitoring~\\cite{maggi2013}\naims for forward-looking forms of PM with predictive qualities.\nIt is a field that combines machine learning with process mining, aiming for specific tasks such as\npredicting \n\\textit{next activity}, \\textit{activity suffix}, \\textit{next timestamp}, \\textit{remaining time}, \\textit{attributes}, \\textit{attribute suffix}, and \\textit{outcome} of running cases.\nMost tasks can be modeled as classification problems, except \\textit{next timestamp} and \\textit{remaining time} prediction tasks, which are regression problems.\nSome approaches which have been used in this realm are based on\nrecurrent neural networks~(RNNs) or Long-short term memory~(LSTMs)\n\\cite{EVERMANN2017129,tax2017predictive,nguyen2020time}.\nAlternatives are based on \nAutoencoders~\\cite{mehdiyev2020novel} and Convolutional neural networks~\\cite{pasquadibisceglie2019using}.\nMore recently, Transformer~\\cite{vaswani2017} models have gained a lot attention due to their overwhelming success in computer vision~\\cite{dosovitskiy2020image} and natural language processing~\\cite{devlin2018bert}.\nInspired by their success, recent approaches proposed a Transformer-based model for process data \\cite{bukhsh2021}.\nA more detailed overview on different models for the  aforementioned tasks is covered in the survey~\\cite{rama2021deep}.\n\nPrevious work in PPM faces a few challenges:\nunclear training\/test set splits and pre-processing schemes, which leads to noticeably different findings and challenges w.r.t\\ reproducibility~\\cite{weytjens2021}.\nSince datasets often contain duplicates which are not respected by the evaluation schemes,  results are often confounded.\nIn this work, we investigate the capability of important classical ML technologies as well as modern Transformers on a variety of benchmark sets with clear train\/test splits, duplicates respected, and different types of representation for classical schemes.\nMore importantly, we do not treat the methods\nas opaque schemes, but rather rely on feature relevance determination and attention mechanisms to highlight the most important factors for each model.\nThis is in line with previous approaches such as \n\\cite{harl2020explainable}, which \nvisualizes the feature relevances of a gated graph neural network\nor\n\\cite{hsieh2021dice4el} which enhances next activity prediction using LSTMs with counterfactual explanations for wrongly classified samples.\nYet both approaches evaluate the behavior on a single\nand specific dataset only.\nIn our approach, we systematically investigate relevant ML models for different approaches and representations under the umbrella of explainability. In this way, we demonstrate how, in many cases, the presence of\nspecific events can easily fool the system into relying on `trivial' signals. When these are removed, ML models reveal not only high quality behavior but also intriguing insights into the relevance of more subtle signals or sequences. \n\\paragraph*{Contributions}\nOur contribution is twofold:\na systematic study of the behavior of diverse ML models with \ntrain-test split respecting the peculiarities of  datasets in PM and appropriate pre-processing,\nwhich prevent troubles due to data leakage.\nSecond, we utilize eXplainable Artificial Intelligence~(XAI) techniques to compute and visualize the most crucial features.\nOur code is open source and available at~\\url{https:\/\/github.com\/rizavelioglu\/ml4prom}.\n\nThe remainder of this work is structured as follows:\nIn Section~\\ref{methodology}, we present the peculiarities of the datasets and our methodology.\nIn Section~\\ref{experiments}, we present experiments and results.\nIn Section~\\ref{conclusion}, we conclude our contribution and discuss potential directions for future work.\n\n\n\\section{Methodology}\\label{methodology}\nIn this section we describe the datasets and how they are pre-processed to be utilized for binary classification, and highlight a few  domain-specific peculiarities which have to be taken into account.\nThen we introduce both classical ML models as well as the state-of-the-art Transformer model used subsequently.\nLastly, we present the XAI techniques applied.\n\n\\subsection{Data}\nWe focus on five widely used datasets which come from a variety of domains including loan applications, road traffic management, and healthcare. These datasets are benchmarks from PM and are also accessible within the well-known ProM tools~\\cite{VanDongen2005}, with the exception of healthcare, which contains personal data. Each dataset has been labeled in order to assess explainability and put them in the ML context. The variety of datasets enables us to check the robustness of our methodology across a wide range of domains. To apply ML classifiers to event data, we first transform the data into a format that resembles a binary classification problem. We present five real-life event logs, each with its own evaluation criterion for a prediction task (referred to as the positive\/negative subpart of the logs), and thereafter explain how they are transformed for the task.\n\\paragraph*{BPIC 2017\\_application+offer~\\cite{vanDongen2017}:} a loan application process of a Dutch financial institute that covers \\num{31509}~cases. Each case represents a loan application and every application has an outcome: positive if the offer is accepted and negative if rejected.\n\\paragraph*{BPIC 2018\\_application~\\cite{vanDongen2018}:} an agricultural grant-application process of the European Union that contains \\num{43809}~applications over a period of three years together with their duration.\n\\paragraph*{Traffic Fine Management~\\cite{deLeoni2015}:} an event log of an information system managing road traffic fines by the Italian government, with fines being payed or not\n\\paragraph*{COVID~\\cite{pegoraro2022analyzing}:} a dataset of COVID-19 patients hospitalized at an intensive care unit\nconsisting of 216 cases, of which 196 are complete cases~(patients have been released either dead or alive) and 20 ongoing cases~(partial process traces) that were being treated in the COVID unit at the time data was exported. \n\\paragraph*{Hospital Billing~\\cite{Mannhardt2017}:} an event log of the billing of medical services that have been provided by a regional hospital. Each trace in the event log keeps track of the actions taken to bill a group of medical services. A randomly selected sample of \\num{100000}~process instances make up the event log.\n\n\n\\subsection{Encoding}\n\nTable~\\ref{table:dataset} shows the rules used to label the samples as well as important statistics. One \ncharacteristic of typical PM datasets is that \nthey can contain a large number of duplicates, \\textit{i}.\\textit{e}.\\ observations of the same process.\nFor example, \\texttt{Hospital} dataset contains \\num{41343} and \\num{58653} traces in positive and negative classes, respectively. Out of those traces only \\num{306} and \\num{884} are unique.\nIn addition, the top-\\num{10} most frequent traces make up the \\num{95.3}\\% and \\num{89.7}\\% of the whole traces.\nHence such data are challenging for ML due to a narrow variety. In addition, duplicates need to be accounted for in evaluation to avoid information leakage.\n\n\\begin{table}\n    \\centering\n    \\caption{Datasets statistics and the rules used to generate binary classification task~(L\\textsuperscript{+}\/L\\textsuperscript{-} represent positive\/negative logs, respectively).\n    The statistics are the number of traces, the number of unique traces, the percentage of unique traces, and lastly the cumulative percentage of the top-10 most frequent traces.}\n    \\label{table:dataset}\n    \\footnotesize\n\\begin{tabular}{c@{\\hskip 4mm}l@{\\hskip 4mm}l@{\\hskip 4mm}S[table-format = 5.0]@{\\hskip 4mm}S[table-format = 4.0]@{\\hskip 2mm}S[table-format = 2.1]@{\\hskip 2mm}S[table-format = 2.1]} \\toprule\n{Dataset}          & {Class}       & \\multicolumn{1}{c}{{Classification Criteria}} & {traces} & {uniq.} & {uniq.\/\\%} & {top-10\\%}    \\\\ \n\\toprule\n\\multirow{2}{*}{BPIC17}   & L\\textsuperscript{+} & without activity `A\\_incomplete'                     & 16506               & 529    & 3.2    & 83.5    \\\\\n                          & L\\textsuperscript{-} & with activity `A\\_incomplete'                        & 15003               & 2101   & 14.0   & 51.5    \\\\\n\\midrule\n\\multirow{2}{*}{Traffic}  & L\\textsuperscript{+} & end activity `Payment'                               & 67201               & 122    & 0.2    & 99.1    \\\\\n                          & L\\textsuperscript{-} & end activity not `Payment'                           & 83169               & 109    & 0.1    & 99.2    \\\\\n\\midrule\n\\multirow{2}{*}{COVID}    & L\\textsuperscript{+} & with activity `Discharge alive'                      & 136                  & 33    & 24.0   & 74.3    \\\\\n                          & L\\textsuperscript{-} & with activity `Discharge dead'                       & 60                   & 20    & 33.0   & 83.3    \\\\\n\\midrule\n\\multirow{2}{*}{BPIC18}   & L\\textsuperscript{+} & duration less than 9 months                          & 27966               & 1081   & 3.9    & 57.7    \\\\\n                          & L\\textsuperscript{-} & duration more than 9 months                          & 15843               & 477    & 3.0    & 82.1    \\\\\n\\midrule\n\\multirow{2}{*}{Hospital} & L\\textsuperscript{+} & duration less than 3 months                          & 41343               & 306    & 0.7    & 95.3   \\\\\n                          & L\\textsuperscript{-} & duration more than 3 months                          & 58653               & 884    & 1.5    & 89.7   \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\n\\sloppy \nData consist of sequences of symbolic events of different length. For each of these datasets we compute \\(n\\)-grams for \\(n \\in \\{1, 2, 3\\}\\) to encode traces in vectorial form  for classic ML models. Unigrams~(n=1) encode occurrence of events, bigrams~(n=2) encode  two subsequent events and trigrams~(n=3) encode three subsequent events. \nTransformer models can directly deal with sequences. The network learns a vector embedding for each event within a trace.\nThis has the advantage of avoiding problems caused by the high-dimensionality of one-hot encoding method, for example.\n\n\\subsection{Models}\nUsing these representations, we train a variety of models, including Logistic Regression~(LR), Decision Tree~(DT), Random Forest~(RF), Gradient Boosting~(GB), and Transformer models. We only present the LR, DT and Transformer models because the findings do not vary significantly. We selected LR and DT due to their widespread use and overall high performance for classification problems \\cite{fernandezdelgado2014hundred}, and we selected Transformer models due to their propensity for learning complex patterns.\nThe type of encoding used in this case limits the amount of information that is accessible because only a portion of the sequential structure is represented. Conversely, transformer models can easily handle sequential data.\nWe use models as proposed in the works~\\cite{vaswani2017,bukhsh2021}.\n\n\\subsection{XAI}\nSince our primary concern is not the classification performance of our trained models, but rather whether ML models can capture underlying regularities, we employ XAI techniques to gain insight into which relationships between events in the data are used by the  models \\cite{molnar2022}.\nUnlike many explanation approaches such as LIME~\\cite{lime}, LRP~\\cite{lrp}, we are interested in global explanations rather than explanations of single decisions. This is because our goal is not to comprehend the ML model, but rather to gain understanding of the key components of the PM as a whole, which can enable users to enhance processes. As an example, one may anticipate altered process behavior if they come across a specific activity, such as `Discharge dead' in COVID dataset, which was identified as crucial for the ML model.\nAs a result, we strive for global explanations and, more specifically, we employ a number of well-established feature selection methods for both linear and non-linear settings, including LR with LASSO as a linear model with strong mathematical guarantees~\\cite{lasso}, DT as a non-linear model with efficient Mean Decrease in Impurity~(MDI) and permutation importance~\\cite{understandingrf} that takes into account non-linear relations between features to determine the relevances, and Transformer model equipped with an attention mechanism that highlights complex relationships.\nAttention mechanisms are technically local explanations. We utilize them to see if highly flexible non-linear explanations provide more complex relations than global feature importance measures.\n\nAs a first result of the analysis, feature selection methods immediately reveal a potential source of information leakage:\nLeaving the datasets as they are, \nthe algorithms rely on attributes that directly encode the class label but provide no additional insight into the process.\nTable~\\ref{table:dataset_biased_feats} shows the detected features that are removed from the logs to avoid such trivial outcomes.\nAll of the listed events exist only in their respective class, \\textit{e}.\\textit{g}.\\ `A\\_Incomplete' is present only in L\\textsuperscript{-} but not in L\\textsuperscript{+}, except `Payment' where the event is present in both classes. Therefore, we removed the event only if it is the last event in a trace from L\\textsuperscript{+}, as that is the source of leakage~(see Table~\\ref{table:dataset}).\n\n\\begin{table}[tb]\n    \\centering\n    \\caption{Datasets with features that leak label information.}\n    \\label{table:dataset_biased_feats}\n    \\footnotesize\n\\begin{tabular}{l@{\\hskip 4mm}l@{\\hskip 4mm}l@{\\hskip 4mm}} \\toprule\nDataset                 & Class                   & \\multicolumn{1}{c}{{Biased feature}} \\\\\n\\toprule\nBPIC17                  & L\\textsuperscript{-}    & `A\\_Incomplete'              \\\\\n\\midrule\n\\multirow{2}{*}{Traffic}& L\\textsuperscript{-}    & `Send for Credit Collection' \\\\\n                        & L\\textsuperscript{+}    & `Payment'            \\\\\n\\midrule\n\\multirow{2}{*}{COVID}  & L\\textsuperscript{-}    & `Discharge dead'             \\\\\n                        & L\\textsuperscript{+}    & `Discharge alive'            \\\\\n\\bottomrule\n\\end{tabular}\n\\end{table}\n\n\n\\section{Experimental Results}\\label{experiments}\nIn this section we present the data pre-processing pipeline used to transform all five datasets for training. Then, we present the evaluation metric used as well as the model design and training on each dataset. Finally, we present the scores of different approaches on the binary classification task and the resulting feature relevances. To save space, we limit ourselves to the \\texttt{BPIC17} dataset; results for the other datasets can be found in the GitHub repository.\n\n\\subsection{Data Split and Pre-Processing}\nFor simplicity, we only consider event names to encode traces and no other attributes, \\textit{e}.\\textit{g}.\\ timestamp, or resource of an event. After computing unique traces we randomly sample from them to construct train\/test sets with a ratio of \\num{70}\\%\/\\num{30}\\%, respectively. As the datasets are highly imbalanced, we sample class-wise from data--preserving the proportion of classes both in train and test sets. To account for frequency of traces, we keep the duplicate traces in train set while removing the ones in test set. \n\nWe apply minimal pre-processing to data at hand. First, we remove the biased features from traces. Then we add \\texttt{<start>} and \\texttt{<end>} tokens to the input to explicitly define the beginning and the end of traces. To have a fixed-length input, the traces that are shorter than the longest trace in an event log are padded with the \\texttt{<pad>} token. We then build a token dictionary consisting of unique event names in an event log and the aforementioned special tokens. Finally, the tokens in the input are replaced by their unique integer values stored in the dictionary.\n\n\\subsection{Evaluation Metric} \nBecause the datasets are highly imbalanced, we measure performance using the area under the receiver operating characteristic curve~(AUROC)~\\cite{Bradley1997auc}. ROC analysis does not favor models that outperform the majority class while under-performing the minority class, which is desirable when working with imbalanced data~\\cite[p.~27]{mehdiyev2020novel}.\nThe area under the curve of a binary classifier\nis the probability that a classifier would rank a randomly chosen positive instance higher than a randomly chosen negative one, which is given by the following equation:\n  \\begin{equation}\n        \\texttt{AUROC} = \\int_{x=\\infty}^{-\\infty} \\texttt{TPR}(T) \\texttt{FPR}^{'}(T)dT\n  \\end{equation}\n\\texttt{AUROC} ranges from \\num{0} to \\num{1}, with an uninformative classifier~(random classifier) producing a result of \\num{0.5}.\n\n\\subsection{Model Design and Training}\nFor ML models we utilize scikit-learn~\\cite{pedregosa2011scikit} and initialize the models with default parameters.\nFor logistic regression, we employ regularization by  a L1 penalty term(\\texttt{penalty} hyper-parameter) with regularization strength~(\\texttt{C} hyper-parameter). We use repeated stratified \\textit{k}-fold cross-validation~(CV) \nto evaluate and train a model across a number of iterations. \nThe number of repeats is \\num{50}, and the number of splits $\\textit{k}=5$, yielding \\num{250} models being trained. The reported metric is then the average of all scores computed.\n\nFor Transformer model, following~\\cite{bukhsh2021}, we chose the embedding dimension as \\num{36}, \\textit{i}.\\textit{e}.\\ each trace is represented by a point in \\num{36}-dimensional space. Since Transformer disregards the positional information of events in traces, we add positional encoding to token embedding which have the same dimensions. During training, the model learns to pay attention to input embedding as well as positional encoding in an end-to-end fashion. The embedding outputs are then fed to a multi-head attention block with $h=6$ heads. On the final layer of the attention block, we aggregate features using a global average pooling followed by a dropout at a rate of \\num{0.1}. Then, we employ a dense layer with ReLU activation of \\num{64} hidden units and a dropout at a rate of \\num{0.1}. Finally, we use a dense layer with sigmoid activation that outputs a value between \\num{0} and \\num{1}, which is interpreted as the ``\\textit{probability}'' of a trace belonging to positive~(desirable) class. We train the model for \\num{50} epochs with ADAM optimizer~\\cite{adam2014}, a learning rate of \\num{1e-3}, and batch size of \\num{16}.\n\n\\subsection{Results}\n\n\\subsubsection{Predictive Accuracy}\n\nWe report the experimental results for the binary classification task. Table~\\ref{table:results} reports the \\texttt{AUROC} scores of models on \\texttt{BPIC17, Traffic}, and \\texttt{COVID} datasets, where there are some features leaking the label information. Here the perfect score is achieved as the models correctly discover the biased features, as expected. However, the Transformer model and the ML models with \\num{1}-gram on \\texttt{Traffic} dataset do not achieve the perfect score on the test set. This is due to the fact that the biased feature--`Payment'--appears in both of the classes. Therefore, \\num{1}-gram encoding is not capable of leaking the information. The Transformer model also fails to discover the bias. On the other hand, models achieve the expected results with the \\num{2}-gram and \\num{3}-gram encoding because those encoding types explicitly define the biased feature: as \\texttt{<end>} token added to traces, the feature \\texttt{(Payment, <end>)} in \\num{2}-gram and \\texttt{(Payment, <end>, <PAD>)} in \\num{3}-gram would leak the label information~(positive class if last event is `Payment', negative class otherwise).\n\n\\begin{table}\n    \\centering\n    \\caption{AUROC scores on datasets \\textit{with} and \\textit{without} biased features using different encoding methods and models. The values inside the parenthesis represent the score on the hold-out test set, whereas others represent the score on the training set.}\n    \\label{table:results}\n    \\footnotesize\n    \\resizebox{\\linewidth}{!}{\n\\begin{tabular}{ll lll lll} \\toprule\n                              &                      & \\multicolumn{3}{c}{\\textbf{with biased features}}                         & \\multicolumn{3}{c}{\\textbf{without biased features}} \\\\ \\cmidrule(lr){3-5} \\cmidrule(lr){6-8}\n\\textbf{Dataset}              & \\textbf{Encoding} \\hspace{2mm} & \\textbf{LR}      & \\textbf{DT} & \\textbf{Transformer} \\hspace{2mm} & \\textbf{LR}       & \\textbf{DT} & \\textbf{Transformer} \\\\ \n\\toprule\n\\multirow{4}{*}{BPIC17}       & integer              & -                & -                               & 100.(100.)           & -                 & -                               & 97.3(97.3)          \\\\\n                              & 1-gram               & 100.(100.)       & 100.(100.)                      & -                    & 89.0(81.3)        & 89.5(76.0)                      & -                   \\\\\n                              & 2-gram               & 100.(100.)       & 100.(99.9)                      & -                  & \\textbf{97.4(97.9)} & 97.3(93.5)                      & -                   \\\\\n                              & 3-gram               & 100.(100.)       & 99.9(99.8)                      & -                    & 97.4(97.8)        & 97.3(91.7)                      & -                   \\\\ \n\\midrule\n\\multirow{4}{*}{Traffic}      & integer              & -                & -                               & 100.(98.4)           & -                 & -                               & \\textbf{63.9(53.5)}   \\\\\n                              & 1-gram               & 100.(93.3)       & 100.(92.2)                      & -                    & 61.5(36.8)        & 61.5(52.7)                      & -                     \\\\\n                              & 2-gram               & 100.(100.)       & 100.(100.)                      & -                    & 63.8(45.5)        & 63.9(49.8)                      & -                     \\\\\n                              & 3-gram               & 100.(100.)       & 100.(100.)                      & -                    & 63.8(48.1)        & 63.9(52.3)                      & -                     \\\\ \n\\midrule\n\\multirow{4}{*}{COVID}        & integer              & -                & -                               & 90.9(100.)           & -                 & -                               & \\textbf{74.8(94.2)}   \\\\\n                              & 1-gram               & 100.(100.)       & 100.(100.)                      & -                    & 67.3(75.0)        & 69.6(68.3)                      & -                      \\\\\n                              & 2-gram               & 100.(100.)       & 99.9(100.)                      & -                    & 89.3(61.7)        & 85.4(85.0)                      & -                      \\\\\n                              & 3-gram               & 99.9(96.7)       & 98.1(66.7)                      & -                    & 90.4(48.3)        & 85.5(76.7)                      & -                      \\\\ \n\\midrule\n\\multirow{4}{*}{BPIC18}       & integer              & -                & -                               & -                    & -                 & -                               & 98.6(81.2)            \\\\\n                              & 1-gram               & -                & -                               & -                    & 97.5(77.9)        & 97.5(78.5)                      & -                       \\\\\n                              & 2-gram               & -                & -                               & -                  & \\textbf{98.4(87.3)} & 98.2(84.5)                      & -                       \\\\\n                              & 3-gram               & -                & -                               & -                  & \\textbf{98.4(87.3)} & 98.2(81.5)                      & -                        \\\\ \n\\midrule\n\\multirow{4}{*}{Hospital}     & integer              & -                & -                               & -                    & -                 & -                               & \\textbf{92.4(78.7)}     \\\\\n                              & 1-gram               & -                & -                               & -                    & 91.8(73.9)        & 92.3(56.2)                      & -                        \\\\\n                              & 2-gram               & -                & -                               & -                    & 92.5(70.5)        & 92.7(52.5)                      & -                        \\\\\n                              & 3-gram               & -                & -                               & -                    & 92.6(66.0)        & 92.6(48.5)                      & -                        \\\\\n\\bottomrule\n\\end{tabular}}\n\\end{table}\n\nTable~\\ref{table:results} also reports the \\texttt{AUROC} scores of models on all of the five real-life event logs, where the biased features are removed from \\texttt{BPIC17, Traffic}, and \\texttt{COVID} datasets. For \\texttt{BPIC17} and \\texttt{COVID} datasets the scores worsen but the results are still promising, hinting that the processes, sequences of events, maintain valuable information for the task even though the distinct\/biased features are removed. \nThe different amount of information in different encoding is mirrored by the results: \\num{1}-gram achieves the worst results compared to \\num{2}-gram and \\num{3}-gram, as it only incorporates single events, whereas \\num{2}-gram and \\num{3}-gram incorporates event pairs. None of those methods integrate order information, while Transformer model learns this information during training. We observe that Transformer model successfully captures the relations between events as well as the order information and outperforms other models in \\texttt{Traffic} and \\texttt{COVID} datasets, whereas in \\texttt{BPIC17} it receives a comparable result. On the other hand, we observe that the scores for \\texttt{BPIC17} and \\texttt{COVID} datasets do not fluctuate as much as it does for \\texttt{Traffic} dataset when compared to biased scores represented in Table~\\ref{table:results}. This is due to the fact that after removing the biased feature in \\texttt{Traffic} dataset, some traces in both classes become identical. \n\n\n\n\n\\subsubsection{Feature Relevances}\n\n\\begin{figure}\n    \\centering\n    \\includegraphics[width=.55\\textwidth]{figures\/BPIC17-LR-unbiased.pdf}\n    \\vspace{-2mm}\n    \\caption{Relevance of features as considered by the logistic regression model. \n    A high positive\/negative value indicates a considerable contribution towards predicting the positive\/negative label, \\textit{i}.\\textit{e}. desirable\/undesirable event trace.}\n    \\label{fig:relevances-unbiased-logistic-regression}\n\\end{figure}\n\nWe present the relevances of features taken into account by our trained logistic regression model in Figure~\\ref{fig:relevances-unbiased-logistic-regression}. We find that `A\\_Validating' contributes the most towards predicting an undesirable trace, whereas `O\\_Refused' contributes most to predict a desirable trace. Other events have significantly lower impact on the predictions. Interestingly, the special tokens, \\textit{i}.\\textit{e}. \\texttt{<pad>}, \\texttt{<start>}, and \\texttt{<end>} affect the predictions when they should not, despite the fact that their influence is negligible. In addition, some features have no effect on the predictions, \\textit{e}.\\textit{g}.\\ `A\\_Denied', `A\\_Cancelled'.\n\n\n\\begin{figure}\n    \\centering\n    \\includegraphics[width=\\textwidth]{figures\/BPIC17-DT-unbiased.pdf}\n    \\vspace{-6mm}\n    \\caption{Relevance of features as considered by decision tree model.\n    \\textbf{Left}: Relevances according to MDI:\n    A high value indicates a considerable contribution towards deciding between the positive and negative label.\n    \\textbf{Right}: Relevances according to the permutation importance calculated on the test set, \\textit{i}.\\textit{e}.\n    how much shuffling a given feature negatively impacts the performance of the decision tree.\n    }\n    \\label{fig:relevances-unbiased-decision-tree}\n\\end{figure}\n\n\nIn Figure~\\ref{fig:relevances-unbiased-decision-tree} we show the feature relevances that our trained decision tree model considers. Based on the MDI value~(left figure) the most relevant feature is `A\\_Validating', followed by `O\\_Refused', `A\\_Submitted', and `O\\_Cancelled' with significantly lower impact. Based on the permutation feature importance~(right figure) the most relevant features are `A\\_Validating', and `O\\_Refused', where the rest of the features have no effect on the prediction performance, which aligns well with the relevances of LR model.\n\n\\begin{figure}\n     \\centering\n     \\begin{subfigure}[b]{0.4\\textwidth}\n         \\centering\n         \\includegraphics[width=\\textwidth]{figures\/bpic17-attention.png}\n       \n         \\label{fig:y equals x}\n     \\end{subfigure}\n     \\hfill\n     \\begin{subfigure}[b]{0.5\\textwidth}\n         \\centering\n         \\includegraphics[width=\\textwidth]{figures\/bpic17-attention_avg.pdf}\n       \n         \\label{fig:three sin x}\n     \\end{subfigure}\n     \\vspace{-5mm}\n        \\caption{\n        \\textbf{Left}: Relevance of features as considered by transformer model for one randomly selected event trace. The thickness of a line connecting two features indicates the intensity of attention in between, whereas the color represents one of the six different attention heads. \n        \\textbf{Right}: Normalized attention scores which are averaged among all attention heads and all traces in test set.}\n        \\label{fig:relevances-unbiased-transformer}\n\\end{figure}\n\nFigure~\\ref{fig:relevances-unbiased-transformer} visualizes the attention scores of six attention heads for a given trace, as well as normalized attention scores over all attention heads and test samples. We observe that, regardless of where it appears in the trace, the events mostly attend to `A\\_Validating' event for the aforementioned trace. In addition, some events focus on `O\\_Sent' in some heads, which differs from the other models. The normalized attention scores, however, demonstrates that not all traces exhibit this behavior. The plot also highlights features whose importances overlap with other models' results. In summary, all models agree on the most relevant features.\n\n\n\\section{Conclusion}\\label{conclusion}\nWe have demonstrated how to prepare process data in such a way that it can be used to train classic and modern -- state-of-the-art -- ML classifiers.\nAll our trained models exhibit high classification performance, \\textit{i}.\\textit{e}.\\ they are capable of learning the underlying regularity of the observed processes, whereby Transformers benefit from the fact that the full sequence information is available, unlike \\textit{e}.\\textit{g}.\\ 1-gram representations. XAI technologies prevent pitfalls such as information leakage by explicit encoding of the predicted event, and reveal insights into the relevance of events or sequences of events, respectively.\nThese insights enable a further exploration of crucial aspects of the processes, which is useful \\textit{e}.\\textit{g}.\\ for the improvement or correction of undesired process outcomes.\n\nFuture research could investigate the effects of various model architectures and encoding schemes on the outcomes of feature relevances. Another potential research direction might be to study the impact of adding further event attributes on the learnt representations.\n\n\n\\bibliographystyle{splncs04}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{#1}\\setcounter{equation}{0}}\n\\renewcommand{\\baselinestretch}{1.2}\n\n\n\\newcommand{\\langle 0|}{\\langle 0|}\n\\newcommand{|0\\rangle }{|0\\rangle }\n\\newcommand{\\frac{1}{2}\\,(1+\\!\\!\\not{\\!v})}{\\frac{1}{2}\\,(1+\\!\\!\\not{\\!v})}\n\\newcommand{\\langle aFF\\rangle}{\\langle aFF\\rangle}\n\\newcommand{e^{\\,gf^{abc}z^\\tau \\int_0^1 dt A^c_\\tau(x+tz)}}{e^{\\,gf^{abc}z^\\tau \\int_0^1 dt A^c_\\tau(x+tz)}}\n\n\\begin{document}\n\n\n\n\\date{\\small (December 1998)}\n\n\\author{\n{\\normalsize\\bf H.~G.~Dosch, M.~Eidem\\\"uller and M.~Jamin\\footnote{Heisenberg\n fellow} } \\\\\n\\ \\\\\n{\\small\\sl Institut f\\\"ur Theoretische Physik, Universit\\\"at Heidelberg,} \\\\\n{\\small\\sl Philosophenweg 16, D-69120 Heidelberg, Germany}\\\\\n}\n\n\\title{\n{\\small\\sf\n\\rightline{HD-THEP-98-51}\n\\rightline{hep-ph\/9812417}\n}\n\\bigskip\n\\bigskip\n{\\Huge\\bf QCD sum rule analysis of \\\\\n the field strength correlator \\\\}\n}\n\n\\maketitle\n\\thispagestyle{empty}\n\n\n\\begin{abstract}\n\\noindent\nThe gauge invariant two-point correlator for the gluon field strength tensor\nis analysed by means of the QCD sum rule method. To this end, we make use of\na relation of this correlator to a two-point function for a quark-gluon\nhybrid in the limit of the quark mass going to infinity. From the sum rules\na relation between the gluon correlation length and the gluon condensate is\nobtained. We briefly compare our results to recent determinations of the\nfield strength correlator on the lattice.\n\\end{abstract}\n\n\\vspace{1cm}\nPACS numbers: 14.70.Dj, 12.38.Bx, 11.10.Gh, 12.40.Ee\n\nKeywords: Gluons, perturbation theory, renormalisation, QCD vacuum\n\n\n\\newpage\n\\setcounter{page}{1}\n\n\n\n\n\\newsection{Introduction}\n\nThe gauge invariant non-local gluon field strength correlator plays an\nimportant r\\^ole in non-perturbative approaches to QCD \\cite{svz:79,vol:79,\nleu:81,sim:88,dos:94}. It is the basic ingredient in the model of the\nstochastic vacuum (MSV) \\cite{dos:87,ds:88} and in the description of high\nenergy hadron-hadron scattering \\cite{nr:84,ln:87,kd:90,dfk:94}. In the\nspectrum of heavy quark bound states it governs the effect of the gluon\ncondensate on the level splittings \\cite{gro:82,cgo:86,kdb:92,sty:95} and\nit is useful for the determination of the spin dependent parts in the\nheavy quark potential \\cite{sd:88,sim:89}.\n\nIts next-to-leading order correction in perturbative QCD has been calculated\nrecently by two of the authors \\cite{ej:98}. The correlator has also been\nmeasured on the lattice in pure gauge theory and full QCD using the cooling\nmethod \\cite{gmp:97,egm:97} and by making the assumptions of the MSV from\nlattice calculations of the heavy quark potentials \\cite{bbv:98}. The lattice\nanalyses found that for distances $z$ of the gluon field strength larger than\nroughly $0.4\\,{\\rm fm}$ an exponential decaying term dominates yielding a\ncorrelation length of approximately $0.2\\,{\\rm fm}$. On the other hand the\nshort distances are dominated by the perturbative $1\/z^4$ behaviour. Recently,\nthe field strength correlator has also been calculated in the framework of\nexact renormalisation group equations \\cite{elw:98}.\n\nThe gauge invariant gluon field strength correlator can be related to\na correlator of a colour singlet current composed of a (fictitious)\ninfinitely heavy octet quark and the gluon field strength tensor. This\nfact has already been employed in ref. \\cite{ej:98} in order to apply the\nmachinery developed in the Heavy Quark Effective Theory\\footnote{For a\nreview on HQET as well as original references the reader is referred to\n\\cite{neu:94}.} (HQET) for calculating the perturbative corrections. In this\npaper we again use this relation in order to apply QCD sum rule techniques \\cite{svz:79}\nto the correlator in question. The sum rule analysis can be used to estimate\nthe correlation length of the field strength correlator using as ingredients\nthe value of the gluon condensate and the results for the perturbative\ncalculation.\n\nOur paper is organised as follows. In the next section we discuss again the\nrelation of the field strength correlator and the corresponding heavy quark\ncurrent correlator. In section~3 we set up the different contributions\nneeded for the sum rule analysis and in section~4 we present our results\ntogether with a comparison with recent lattice determinations of the\nfield strength correlator. Finally, in section~5, we end with some conclusions\nand an outlook.\n\n\n\n\\newsection{The field strength correlator}\n\nThe gauge invariant two-point correlation function of the QCD field strength\ntensor $F^a_{\\mu\\nu}(x)$ in the adjoint representation can be defined as\n\\begin{equation}\n\\label{eq:2.1}\n{\\cal D}_{\\mu\\nu\\rho\\sigma}(z) \\; \\equiv \\; \\langle 0|T\\{g_s^2 F^a_{\\mu\\nu}(y)\n{\\cal P}e^{\\,gf^{abc}z^\\tau \\int_0^1 dt A^c_\\tau(x+tz)} F^b_{\\rho\\sigma}(x)\\}|0\\rangle \\,,\n\\end{equation}\nwhere the field strength $F^a_{\\mu\\nu}=\\partial_\\mu A^a_\\nu-\\partial_\\nu\nA^a_\\mu+gf^{abc}A^b_\\mu A^c_\\nu$, $z=y-x$ and ${\\cal P}$ denotes path\nordering of the exponential. In general, the gauge invariant field strength\ncorrelator could be defined with an arbitrary gauge string connecting the\nend points $x$ and $y$, but in this work we shall restrict ourselves to\na straight line. Only for that case the relation to HQET is possible.\nFrom the Lorentz structure of the field strength correlator it follows\nthat the correlator can be parametrised in terms of two scalar functions\n${\\cal D}(z^2)$ and ${\\cal D}_1(z^2)$ \\cite{ds:88}:\n\\begin{eqnarray}\n\\label{eq:2.2}\n{\\cal D}_{\\mu\\nu\\rho\\sigma}(z) & = & \\Big[\\,g_{\\mu\\rho}g_{\\nu\\sigma}-\ng_{\\mu\\sigma}g_{\\nu\\rho}\\,\\Big]\\Big(\\,{\\cal D}(z^2)+{\\cal D}_1(z^2)\\,\\Big) \\nonumber \\\\\n\\vbox{\\vskip 8mm}\n& & \\hspace{-3.9mm} +\\,\\Big[\\,g_{\\mu\\rho}z_\\nu z_\\sigma-g_{\\mu\\sigma}\nz_\\nu z_\\rho-g_{\\nu\\rho} z_\\mu z_\\sigma+g_{\\nu\\sigma}z_\\mu z_\\rho\n\\,\\Big]\\,\\frac{\\partial{\\cal D}_1(z^2)}{\\partial z^2} \\,.\n\\end{eqnarray}\nThe invariant function ${\\cal D}(z^2)$ can only occur in a non-abelian gauge\ntheory or an abelian one with monopoles. In the MSV it is responsible for\nconfinement and the formation of a string.\n\nThe correlator ${\\cal D}_{\\mu\\nu\\rho\\sigma}(z)$ can be related to the correlator\nof a local, gauge invariant current composed of an infinitely heavy quark\nfield in the octet representation, $h^a(x)$, and the gluon field strength\ntensor \\cite{eid:97,ej:98}. The current in question takes the form\n$(g_s h^a F^a_{\\mu\\nu})(x)$. Analogously to HQET the heavy octet-quark field\nis constructed from the field $Q^a$ with a finite mass $m_Q$ in the limit\n\\begin{equation}\n\\label{eq:2.3}\nh^a(x) \\; = \\; \\lim_{m_Q\\rightarrow\\infty}\\,\\frac{1}{2}\\,(1+\\!\\!\\not{\\!v})\\,e^{im_Qvx}Q^a(x) \\,,\n\\end{equation}\nwith $v$ being the four-velocity of the heavy quark. \nThe propagator of the free heavy quark field $h^a_0(x)$ in coordinate\nspace is given by\n\\begin{equation}\n\\label{eq:2.4}\nS(z) \\; = \\; \\langle 0| T\\{h^a_0(y)\\bar{h}^b_0(x)\\} |0\\rangle  \\; = \\; \\delta^{ab}\n\\frac{1}{v^0}\\,\\theta(z^0)\\,\\delta\\Big({\\bf z}-\\frac{z^0}{v^0}{\\bf v}\\Big) \\,,\n\\end{equation}\nwhere  $v^0$ is the zero-component of the velocity.\nThe correlator of the full field can be obtained by integrating out only\nthe heavy quark and leaving the expectation value with respect to the\ngauge field:\n\\begin{equation}\n\\label{eq:2.5}\n\\langle 0| T\\{h^a(y)\\bar{h}^b(x)\\} |0\\rangle  \\; = \\;\n S(z)\\,\\langle 0| {\\cal P}e^{\\,gf^{abc}z^\\tau \\int_0^1 dt A^c_\\tau(x+tz)} |0\\rangle  \\,.\n\\end{equation}\nThe gauge string is left after the elimination of the heavy quarks from the\ninteraction term of adjoint quarks with the colour potential\n\\begin{equation}\n\\label{eq:2.6}\n{\\cal L}_{int} \\; = \\; -\\,ig_s f_{abc} v^\\mu \\bar{h}^a(x) A_\\mu^c(x) h^b(x) \\,.\n\\end{equation}\nThe physical picture of this result is a heavy quark moving from point\n$x$ to $y$ with a four-velocity $v$, acquiring a phase proportional to the\npath-ordered exponential. \nThe limit of $m_Q\\rightarrow\\infty$ is necessary in order to constrain the\nheavy quark on a straight line and in order to decouple the spin interactions.\nThe same relation also holds for quarks in the fundamental representation\nwith the appropriate replacements in the exponential.\n\nThe equation \\eqn{eq:2.5} allows to establish a relation between the field\nstrength correlator \\eqn{eq:2.1} and the correlator for the colourless\nheavy quark current.\nBy integrating out the heavy degrees of freedom and using \\eqn{eq:2.5} we\narrive at\n\\begin{eqnarray}\n\\label{eq:2.8}\n\\widetilde{\\cal D}_{\\mu\\nu\\rho\\sigma}(z)\n& \\equiv & \\langle 0| T\\{g_s^2 F^a_{\\mu\\nu}(y)h^a(y)F^b_{\\rho\\sigma}(x)\\bar{h}^b(x)\n\\}|0\\rangle  \\nonumber \\\\\n& = & S(z) \\, D_{\\mu\\nu\\rho\\sigma}(z) \\,.\n\\end{eqnarray}\nWe may view the composite operator $(g_s h^a F^a_{\\mu\\nu})(x)$ as an\ninterpolating field of colourless quark gluon hybrids and evaluate\n$\\widetilde{\\cal D}_{\\mu\\nu\\rho\\sigma}(z)$ by introducing these as intermediate states\nin the absorption part of $\\widetilde{\\cal D}_{\\mu\\nu\\rho\\sigma}(z)$. The lowest lying\nstate will govern the long-range behaviour and hence the inverse of its\nenergy is the correlation length.\n\nOur next aim is to evaluate this correlator in the framework of QCD sum rules\n\\cite{svz:79} and in that way obtain information on the correlation length\nof the gluon field strength correlator.\nFor the sum rule analysis it is preferable to work with the correlator in\nmomentum space. Thus we define\n\\begin{equation}\n\\label{eq:2.9}\n\\widetilde{\\cal D}_{\\mu\\nu\\rho\\sigma}(w) \\; = \\; i \\int dz \\, e^{iqz} \\langle 0|\nT\\{g_s^2 F^a_{\\mu\\nu}(y)h^a(y) F^b_{\\rho\\sigma}(x)\\bar{h}^b(x)\\}|0\\rangle  \\,,\n\\end{equation}\nwhere the residual heavy quark momentum is $w=vq$. Similar to the Lorentz\ndecomposition of the coordinate space correlator ${\\cal D}_{\\mu\\nu\\rho\\sigma}(z)$\ninto scalar functions ${\\cal D}(z^2)$ and ${\\cal D}_1(z^2)$, eq.~\\eqn{eq:2.2},\nwe can write the momentum space correlator as follows: \n\\begin{eqnarray}\n\\label{eq:2.10}\n\\widetilde{\\cal D}_{\\mu\\nu\\rho\\sigma}(w) & = & \\Big[\\,g_{\\mu\\rho}g_{\\nu\\sigma}-\ng_{\\mu\\sigma}g_{\\nu\\rho}\\,\\Big]\\Big(\\,\\widetilde{\\cal D}(w)+\\widetilde{\\cal D}_1(w)\\,\\Big) \\nonumber \\\\\n\\vbox{\\vskip 8mm}\n& & \\hspace{-3.9mm} +\\,\\Big[\\,g_{\\mu\\rho}v_\\nu v_\\sigma-g_{\\mu\\sigma}\nv_\\nu v_\\rho-g_{\\nu\\rho} v_\\mu v_\\sigma+g_{\\nu\\sigma}v_\\mu v_\\rho\n\\,\\Big]\\,\\widetilde{\\cal D}_*(w) \\,.\n\\end{eqnarray}\nThe functions $\\widetilde{\\cal D}(w)$ and $\\widetilde{\\cal D}_1(w)$ are the Fourier transforms of\n$S(z)\\,{\\cal D}(z^2)$ and $S(z)\\,{\\cal D}_1(z^2)$ respectively, the function\n$\\widetilde{\\cal D}_*(w)$ is the Fourier transform of\n$S(z)z^2\\partial {\\cal D}_1(z^2)\/\\partial z^2$.\n\nFor our purpose of isolating intermediate states of the correlator\n\\eqn{eq:2.9} a decomposition according to an $O_3$ classification is more\nappropriate than the decomposition of eq.~\\eqn{eq:2.10}. Since the spin of\nthe heavy quark decouples, we only have to consider the gluon spin. The\nsix-component field can be decomposed into tensor structures depending on the\nonly two external vectors in the game; the four-velocity $v_\\mu$ and the\npolarisation vector of the gluon $e_\\mu$. This leads to the two Lorentz\nstructures for the hadronic matrix elements\n\\begin{eqnarray}\n\\label{eq:2.11}\n\\langle 0| (g_s F^a_{\\mu\\nu} h^a)(0)| H^{-}\\rangle & = &\nf^-\\,(v_\\mu e_\\nu-v_\\nu e_\\mu) \\,, \\\\\n\\vbox{\\vskip 6mm}\n\\langle 0| (g_s F^a_{\\mu\\nu} h^a)(0)| H^{+}\\rangle & = &\nf^+\\,\\varepsilon_{\\mu\\nu\\lambda\\kappa}v^\\lambda e^\\kappa \\,,\n\\end{eqnarray}\nwhere $H^\\mp$ are hadronic states with the same quantum numbers as the\ncomposite current. In the rest frame ${\\bf v}=0$, the first structure\ntransforms as a 3-vector and thus $H^-$ corresponds to a $1^-$ state whereas\nthe second structure transforms as an axialvector and $H^+$ corresponds to a\n$1^+$ state.\n\nThrough appropriate projections the two quantum numbers can be singled\nout from the correlator $\\widetilde{\\cal D}_{\\mu\\nu\\rho\\sigma}(w)$. Hence, we define\n\\begin{eqnarray}\n\\label{eq:2.13}\n\\widetilde{\\cal D}^-(w) & \\equiv & g^{\\mu\\rho}v^\\nu v^\\sigma \\, \\widetilde{\\cal D}_{\\mu\\nu\\rho\\sigma}(w)\n\\; = \\; 3\\,\\Big(\\widetilde{\\cal D}(w)+\\widetilde{\\cal D}_1(w)+\\widetilde{\\cal D}_*(w)\\Big) \\,, \\\\\n\\vbox{\\vskip 6mm}\n\\label{eq:2.14}\n\\widetilde{\\cal D}^+(w) & \\equiv & (g^{\\mu\\rho}g^{\\nu\\sigma}-2\\,g^{\\mu\\rho}v^\\nu v^\\sigma) \\,\n\\widetilde{\\cal D}_{\\mu\\nu\\rho\\sigma}(w) \\; = \\; 6\\,\\Big(\\widetilde{\\cal D}(w)+\\widetilde{\\cal D}_1(w)\\Big) \\,.\n\\end{eqnarray}\nThe Fourier transforms of the functions $\\widetilde{\\cal D}^-(w)$ and $\\widetilde{\\cal D}^+(w)$ are\nup to the factor $S(z)$ the invariant functions ${\\cal D}_\\parallel(z^2)$ and\n${\\cal D}_\\perp(z^2)$ respectively which have been used in the lattice\ncalculations of refs.~\\cite{gmp:97,egm:97}.\n\nUnder the assumption of quark-hadron duality which is usually made for\nsum rule analyses \\cite{svz:79}, we model the correlators by\na contribution from the lowest lying resonances plus the perturbative\ncontinuum above a threshold $s_0$. Inserting the matrix elements and\nperforming the heavy quark phase space integrals one obtains\n\\begin{equation}\n\\label{eq:2.15}\n\\widetilde{\\cal D}^\\mp(w) \\; = \\; \\frac{\\kappa^\\mp\\,|f^\\mp|^2}{w-E^\\mp+i\\epsilon} +\n\\int\\limits_{s_0^\\mp}^\\infty d\\lambda \\, \\frac{\\rho^\\mp(\\lambda)}\n{\\lambda-w-i\\epsilon} \\,,\n\\end{equation}\nwhere $\\kappa^-\\!=1$, $\\kappa^+\\!=-2$ and $E$ represents the energy\nof the glue around the heavy quark. The spectral densities are defined by\n$\\rho^\\mp(\\lambda)\\equiv 1\/\\pi\\,{\\rm Im}\\,\\widetilde{\\cal D}^\\mp(\\lambda+i\\epsilon)$ and are\nknown at the next-to-leading order \\cite{ej:98}. Explicit expressions will\nbe given in the next section.\n\nAfter Fourier transformation to coordinate space the above representation\nreads:\n\\begin{eqnarray}\n\\label{eq:2.16}\n\\widetilde{\\cal D}(z) & = & -i \\int \\frac{d^4 q}{(2 \\pi)^4} \\, e^{-iqz}\\,\\widetilde{\\cal D}(w) \\nonumber \\\\\n& = & \\biggl\\{-\\kappa\\,|f|^2 e^{-iE|z|} + \\int\\limits_{s_0}^\\infty d\\lambda \\,\n\\rho(\\lambda) \\, e^{-i\\lambda |z|} \\biggr\\} \\, S(z) \\,,\n\\end{eqnarray}\nwhere the factorisation of the heavy quark propagator can be seen explicitely.\nThe inverse correlation length is found to be given by $E$.\n\n\n\n\\newsection{The sum rules}\n\nThe {\\em phenomenological side} of the sum rules has already been given by\neq.~\\eqn{eq:2.15}. In this section, we shall present the {\\em theoretical side}\nof the sum rules which arises from calculating the correlator of\neq.~\\eqn{eq:2.9} in the framework of the operator product expansion\n\\cite{svz:79,wil:69}.\n\nIn coordinate space the purely perturbative contribution up to the\nnext-to-leading order in the strong coupling constant has been calculated\nin ref.~\\cite{ej:98}. Here we give the corresponding results in momentum\nspace for $\\widetilde{\\cal D}^\\mp(w)$:\n\\begin{equation}\n\\label{eq:3.1}\n\\widetilde{\\cal D}^\\mp_{PT}(w) \\; = \\; (-w)^3\\, a\\,\\Big[\\, p_{10}^\\mp+p_{11}^\\mp L +\na\\, (p_{20}^\\mp+p_{21}^\\mp L+p_{22}^\\mp L^2) \\,\\Big] \\,,\n\\end{equation}\nwhere $a\\equiv\\alpha_s\/\\pi$, $L=\\ln(-2w\/\\mu)$ and the coefficients\n$p_{ij}^\\mp$ are given explicitly in the appendix. From this result one can\nimmediately calculate the corresponding spectral functions:\n\\begin{equation}\n\\label{eq:3.2}\n\\rho^\\mp(\\lambda) \\; = \\; \\lambda^3\\,a\\, \\biggl[\\, p_{11}^\\mp +\na \\,\\biggl(p_{21}^\\mp +  2\\,p_{22}^\\mp\\ln \\frac{2 \\lambda}{\\mu}\\biggr)\n\\,\\biggr] \\,,\n\\end{equation}\nwhere $\\lambda$ has to be greater zero. Essential for the sum rule analysis\nare the contributions coming from\nthe condensates. The correlation function is expanded in powers of $1\/w$\ncorresponding to higher and higher dimensional condensates. In our case\nthe dimension three condensate $\\langle\\bar{h}h\\rangle$ vanishes since\nthe quark mass is infinite. The lowest nonvanishing term is the gluon\ncondensate of dimension four:\n\\begin{equation}\n\\label{eq:3.3}\n\\widetilde{\\cal D}^-_{FF}(w) \\; = \\; -\\,\\frac{\\pi^2}{w}\\langle aFF\\rangle \\,, \\qquad\n\\widetilde{\\cal D}^+_{FF}(w) \\; = \\; -\\,\\frac{2\\pi^2}{w}\\langle aFF\\rangle \\,.\n\\end{equation}\nThe next condensate contribution would be of dimension six, but we shall\nneglect all higher condensate contributions in this work and restrict\nourselves to the gluon condensate.\n\nIn order to suppress contributions in the dispersion integral coming from\nhigher exited states and from higher dimensional condensates, it is convenient\nto apply a Borel transformation $\\widehat{B}_T$ with $T$ being the Borel variable\n\\cite{svz:79}. Some useful formulae for the Borel transformation are also\ncollected in the appendix. For the phenomenological side of the sum rules,\neq.~\\eqn{eq:2.15}, we then find\n\\begin{equation}\n\\label{eq:3.4}\n\\widehat{{\\cal D}}^\\mp(T) \\; = \\; -\\,\\kappa^\\mp\\,|f^\\mp|^2 \\,e^{-E^\\mp\/T} +\n\\int\\limits_{s_0^\\mp}^\\infty d\\lambda\\,\\rho^\\mp(\\lambda)\\,e^{-\\lambda\/T} \\,.\n\\end{equation}\nFor the perturbative contribution it is convenient to apply the following\nidentity:\n\\begin{equation}\n\\label{eq:3.5}\n\\widehat{B}_T \\,\\widetilde{\\cal D}(w) \\; = \\; T^4 \\,\\widehat{B}_T \\left(\\frac{d}{dw}\\right)^{\\!4}\n\\widetilde{\\cal D}(w) \\,,\n\\end{equation}\nfrom which we obtain\n\\begin{equation}\n\\label{eq:3.6}\n\\widehat{{\\cal D}}^\\mp_{PT}(T) \\; = \\; 6\\, T^4\\, a\\,\\biggl[\\, p_{11}^\\mp + a \\,\\biggl(\np_{21}^\\mp+ \\frac{1}{3}\\,\\Gamma'(4)\\, p_{22}^\\mp +  2\\,p_{22}^\\mp \\ln\n\\frac{2T}{\\mu}\\biggr) \\,\\biggr] \\,,\n\\end{equation}\nwhere $\\gamma_E$ is Eulers constant and $\\Gamma'(4)=11-6\\gamma_E$.\nThe Borel transformed expression for the gluon condensate contribution\nis found to be:\n\\begin{equation}\n\\label{eq:3.7}\n\\widehat{{\\cal D}}^-_{FF} \\; = \\;   \\pi^2 \\langle aFF\\rangle \\,, \\qquad\n\\widehat{{\\cal D}}^+_{FF} \\; = \\; 2 \\pi^2 \\langle aFF\\rangle \\,.\n\\end{equation}\nAfter Borel transformation, the correlators satisfy homogeneous\nrenormalisation group equations. Thus we can improve the perturbative\nexpressions by resumming the logarithmic contributions. The perturbative\ncontribution is then expressed in terms of the running coupling\n$a(2T)$:\n\\begin{equation}\n\\label{eq:3.8}\n\\widehat{{\\cal D}}^\\mp_{PT}(T) \\; = \\; 6\\, T^4 \\left(\\frac{a(2T)}{a(\\mu)}\\right)^\n{-\\gamma_1^\\mp\/\\beta_1} \\!a(2T)\\,\\left[\\, p_{11}^\\mp + a\\,\\left(\\,p_{21}^\\mp\n+\\frac{1}{3}\\,\\Gamma'(4)\\,p_{22}^\\mp\\right) \\,\\right] \\,,\n\\end{equation}\nwhere $\\beta_1=11\/2-n_f\/3$ is the first coefficient of the QCD\n$\\beta$-function. Reexpanding and comparing with eq.~\\eqn{eq:3.6},\nthe anomalous dimensions $\\gamma_1^\\mp$ are found to be\n$\\gamma_1^\\mp=2\\,p_{22}^\\mp\/p_{11}^\\mp+\\beta_1$, or explicitly\n\\begin{equation}\n\\label{eq:3.9}\n\\gamma_1^- \\; = \\; 0 \\,, \\qquad\n\\gamma_1^+ \\; = \\; 3 \\,.\n\\end{equation}\nLet us note that the correlator $\\widehat{{\\cal D}}^-(T)$ which corresponds to the\nvector intermediate state does not depend on the renormalisation scale $\\mu$\nat this order.\n\nFor the continuum contribution we first evaluate the integral with the\ngeneral formula \\cite{jm:95} which makes the numerical analysis easier:\n\\begin{equation}\n\\label{eq:3.10}\n\\int\\limits_{s_0}^\\infty d\\lambda\\,\\lambda^{\\alpha-1}\\ln^n \\frac{2\\lambda}{\\mu}\ne^{-\\lambda\/T} \\; = \\; T^\\alpha \\sum_{k=0}^{n} {n\\choose k} \\ln^k\\frac{2T}{\\mu}\n\\left[\\frac{\\partial^{n-k}}{\\partial\\alpha^{n-k}}\\Gamma\\left(\\alpha,\\frac{s_0}\n{T}\\right)\\right] \\,,\n\\end{equation}\nsome formulae for the incomplete $\\Gamma$-function $\\Gamma(\\alpha,x)$ are\ngiven in the appendix. We then obtain\n\\begin{eqnarray}\n\\label{eq:3.11}\n\\chi^\\mp(T,s_0) & = & \\int\\limits_{s_0}^\\infty d\\lambda\\,\\rho^\\mp(\\lambda) \\,\ne^{-\\lambda\/T} \\; = \\; T^4\\,a\\,\\Biggl\\{\\,p_{11}^\\mp \\,\\Gamma\\left(4,\n\\frac{s_0}{T}\\right) \\\\\n\\vbox{\\vskip 8mm}\n& & +\\,a\\left[\\,\\left(\\,p_{21}^\\mp+2\\,p_{22}^\\mp\\ln\\frac{2T}\n{\\mu}\\right)\\Gamma\\left(4,\\frac{s_0}{T}\\right) + 2\\,p_{22}^\\mp\\Gamma'\n\\left(4,\\frac{s_0}{T}\\right)\\,\\right]\\,\\Biggr\\} \\,, \\nonumber\n\\end{eqnarray}\nand after renormalisation group improvement\n\\begin{eqnarray}\n\\label{eq:3.12}\n\\chi^\\mp(T,s_0) & = & T^4 \\left(\\frac{a(2T)}{a(\\mu)}\\right)^{-\\gamma_1^\\mp\/\n\\beta_1}\\!a(2T)\\,\\Biggl\\{\\,p_{11}^\\mp \\,\\Gamma\\left(4,\\frac{s_0}{T}\\right)\n\\hspace{30mm} \\nonumber \\\\\n\\vbox{\\vskip 8mm}\n& & +\\;a \\left[\\,p_{21}^\\mp\\,\\Gamma\\left(4,\\frac{s_0}{T}\\right)+2\\,p_{22}^\\mp\n\\,\\Gamma'\\left(4,\\frac{s_0}{T}\\right)\\,\\right]\\,\\Biggr\\} \\,.\n\\end{eqnarray}\nIn the limit $s_0\\rightarrow 0$, eq.~\\eqn{eq:3.12} agrees with eq.\n\\eqn{eq:3.8} as it should.\n\n\n\n\n\\newsection{Numerical analysis}\n\nAfter equating the phenomenological and the theoretical part we end up with\nthe sum rule\n\\begin{equation}\n\\label{eq:4.1}\nK^\\mp(T) \\; \\equiv \\; -\\,\\kappa^\\mp |f^\\mp|^2 e^{-E^\\mp\/T} \\; = \\;\n\\widehat{\\cal D}_{FF}^\\mp + \\widehat{\\cal D}_{PT}^\\mp(T)-\\chi^\\mp(T,s_0) \\,,\n\\end{equation}\nwhere $\\kappa^-= 1$ and $\\kappa^+=-2$. In order to estimate the binding\nenergy we derive as an immediate consequence of \\eqn{eq:4.1}:\n\\begin{equation}\n\\label{eq:4.2}\nE^\\mp \\; = \\; -\\,\\frac{\\partial}{\\partial(1\/T)}\\,\\ln K^\\mp \\; = \\;\n-\\,\\frac{\\frac{\\partial}{\\partial(1\/T)}\\Big(\\widehat{\\cal D}_{PT}^\\mp(T)-\\chi^\\mp(T,s_0)\n\\Big)}{\\Big(\\widehat{\\cal D}_{FF}^\\mp + \\widehat{\\cal D}_{PT}^\\mp(T)-\\chi^\\mp(T,s_0)\\Big)} \\,.\n\\end{equation}\nThe derivative can also be given analytically if we first derive with respect\nto $T$ and then perform the resummation of the logarithms. We thus find\n\\begin{eqnarray}\n\\label{eq:4.3}\n\\lefteqn{\\frac{\\partial}{\\partial (1\/T)} \\left(\\widehat{\\cal D}^\\mp_{PT}(T) -\n\\chi^\\mp(T,s_0)\\right) \\; =} \\nonumber \\\\\n& & -\\,T^5 \\left(\\frac{a(2T)}{a(\\mu)}\\right)^{-\\gamma_1^\\mp\/\\beta_1}\\!\\!\na(2T)\\,\\Bigg\\{\\, p_{11}^\\mp \\left(\\Gamma(5)-\\Gamma\\left(5,\\frac{s_0}{T}\\right)\n\\right) \\nonumber \\\\\n& & +\\,a\\,\\Bigg[\\,p_{21}^\\mp \\left(\\Gamma(5)-\\Gamma\\left(5,\\frac{s_0}{T}\\right)\n\\right) +  2\\,p_{22}^\\mp \\left(\\Gamma'(5)-\\Gamma'\\left(5,\\frac{s_0}{T}\\right)\n\\right)\\Bigg]\\Bigg\\} \\,.\n\\end{eqnarray}\nWe note that the different signs of the perturbative and non-perturbative\nterms in the $1^-$ state lead to a stabilisation for the energy sum rule,\nwhereas the equal sign in the $1^+$ state destabilises the sum rule.\n\nLet us begin our numerical analysis with the case for three light quark\nflavours. As our input parameters we use $\\langle aFF\\rangle = 0.024 \\pm 0.012 \\,\\mbox{\\rm GeV}^4$\nand $\\Lambda_{3fl} = 325 \\,\\mbox{\\rm MeV}$. In principle, the coupling constant at\nnext-to-leading order could be evaluated at any scale $\\mu$. As our central\nvalue in the numerical analysis we have chosen $\\mu = 2 \\,\\mbox{\\rm GeV}$.\nFor the energy $E^-$ of the $1^-$ state we obtain the\nbest stability for a continuum threshold $s_0 = 1.7 \\,\\mbox{\\rm GeV}$ in the range\n$T \\geq 0.7 \\,\\mbox{\\rm GeV}$ with an energy $E^- \\approx 1.4 \\,\\mbox{\\rm GeV}$. To estimate\nthe errors we have varied the scale $\\mu$ as well as the continuum\nthreshold $s_0$. In figure~1 we have displayed the energy $E^-$ as a\nfunction of the Borel parameter $T$ for $\\mu=1\\,\\mbox{\\rm GeV}$ (dashed lines),\n$2\\,\\mbox{\\rm GeV}$ (solid lines) and $4\\,\\mbox{\\rm GeV}$ (dotted lines). The corresponding\nvalues of the continuum threshold are $s_0=1.5\\pm0.2\\,\\mbox{\\rm GeV}$, $1.7\\pm0.2\\,\\mbox{\\rm GeV}$\nand $1.9\\pm0.2\\,\\mbox{\\rm GeV}$ respectively. The central values have been chosen\nin order to obtain maximal stability for the sum rule.\n\n\\begin{figure}[thb]\n\\vspace{0.2cm}\n\\centerline{\n\\rotate[r]{\n\\epsfysize=13cm\n\\epsffile{Em.eps} }}\n\\caption[]{The energy $E^-$ as a function of the Borel-parameter $T$\nfor three different renormalisation scales $\\mu$ and continuum\nthresholds $s_0$.\nDashed curves $\\mu=1\\,\\mbox{\\rm GeV}$: lowest $s_0=1.3\\,\\mbox{\\rm GeV}$, middle $s_0=1.5\\,\\mbox{\\rm GeV}$,\nupper $s_0=1.7\\,\\mbox{\\rm GeV}$.\nSolid curves $\\mu=2\\,\\mbox{\\rm GeV}$: lowest $s_0=1.5\\,\\mbox{\\rm GeV}$, middle $s_0=1.7\\,\\mbox{\\rm GeV}$,\nupper $s_0=1.9\\,\\mbox{\\rm GeV}$.\nDotted curves $\\mu=4\\,\\mbox{\\rm GeV}$: lowest $s_0=1.7\\,\\mbox{\\rm GeV}$, middle $s_0=1.9\\,\\mbox{\\rm GeV}$,\nupper $s_0=2.1\\,\\mbox{\\rm GeV}$.\n\\label{fig:1}}\n\\end{figure}\n\nLarger values of $s_0$ always increase $E$ but at the same time the stability\nregion shrinks and goes to smaller values of $T$. However, even at\n$T = 0.7 \\,\\mbox{\\rm GeV}$ the influence of the higher resonances expressed through\nthe continuum model  $\\chi^-(T)$ is very large:\n$\\chi^-(0.7)\/{\\cal D}^-_{PT}(0.7) \\approx 0.75$. For $s_0 = 2.1 \\,\\mbox{\\rm GeV}$, we have\na small stability region around $T = 0.65 \\,\\mbox{\\rm GeV}$\nyielding $E^- = 1.6 \\,\\mbox{\\rm GeV}$. Here the influence of the continuum model is\naround tolerable 50\\%, the perturbative corrections and the choice of the\nrenormalisation scale become however more important there.\n\nAnother source of uncertainty is the value of the gluon condensate. For the\nvalue $\\langle aFF\\rangle = 0.012 \\,\\mbox{\\rm GeV}^4$, originally obtained by \\cite{svz:79}, we\nfind $E^- = 1.2 \\,\\mbox{\\rm GeV}$ at $s_0 = 1.5 \\,\\mbox{\\rm GeV}$, whereas for\n$\\langle aFF\\rangle = 0.036 \\,\\mbox{\\rm GeV}^4$ we obtain $E^- = 1.8 \\,\\mbox{\\rm GeV}$ at $s_0 = 2.4 \\,\\mbox{\\rm GeV}$. \nWe therefore conclude from the sum rules for the above mentioned parameters\nan energy $E^-$ and a correlation length $a^-$ of:\n\\begin{equation}\nE^-_{3fl} \\; = \\; 1.5 \\pm 0.4 \\;\\mbox{\\rm GeV} \\qquad {\\rm and} \\qquad\na^-_{3fl} \\; = \\; 0.13^{+0.05}_{-0.02} \\;\\mbox{\\rm fm} \\,.\n\\end{equation}\n\nThe main sources of uncertainty are the value of the gluon condensate and the\ncontinuum contribution. Though the perturbative two-loop contributions to\nthe sum rule are very large, their influence on the value of $E^-$ is not so\ndramatic. The corrections tend to cancel in the ratio of eq. \\eqn{eq:4.2}.\nIf one determines the energy from the sum rule just containing the lowest\norder perturbation theory and chooses as the scale for $\\alpha_s$ the\napproximate value of the energy one finds for $\\langle aFF\\rangle = 0.024 \\,\\mbox{\\rm GeV}^4$ the\nvalue $E^- = 1.9 \\,\\mbox{\\rm GeV}$.\n\nIn a world without light quarks, i.e. $n_f = 0$, the main influence on the\nsum rule is the expected change of the gluon condensate which might increase\nby a factor two to three \\cite{nsvz:84}. If we perform an analysis as above,\nwe get for $\\Lambda_{0fl} = 250 \\,\\mbox{\\rm MeV}$ \\cite{lue:98},\n$\\langle aFF\\rangle = 0.048 \\pm 0.024 \\,\\mbox{\\rm GeV}^4$ and $s_0 = 2.3 \\,\\mbox{\\rm GeV}$ an energy and\ncorrelation length of \n\\begin{equation}\nE^-_{0fl} \\; = \\; 1.9 \\pm 0.5 \\;\\mbox{\\rm GeV} \\qquad {\\rm and} \\qquad\na^-_{0fl} \\; = \\; 0.11^{+0.04}_{-0.02} \\;\\mbox{\\rm fm} \\,.\n\\end{equation}\n\nFor $E^+$, the energy of the axial vector state, we obtain no stable sum rule.\nAlthough the expressions for $E^-$ and $E^+$ are equal in lowest order\nperturbation theory, higher order perturbative contributions and the gluon\ncondensate lead to a splitting in such a way that for the same values of\n$s_0$ and $T$ the resulting value for $E^-$ is higher than that for $E^+$.\n\n\n\n\\newsection{Summary and conclusions}\n\nThe analysis of the gauge invariant gluon field strength correlator\nby QCD sum rule methods allows to establish a relation between the gluon \ncondensate and the correlation length. In order to apply the sum rule\ntechnique which consists in the comparison of a phenomenological Ansatz\nwith a theoretical expression obtained from the operator product expansion\nwe interpret the gluon correlator as the correlator of two colour \nneutral hybrid states composed of a (fictitious) heavy quark transforming\nunder the adjoint representation and the gluon field. The former serves as\nthe source for the gauge string in the correlator.\n\nIn this approach the decomposition in two invariant functions $D^+$ and \n$D^-$ is more appropriate than the decomposition of eq. \\eqn{eq:2.2},\nsince $D^-$ receives only contributions from $1^-$ and $D^+$ from\n$1^+$ intermediate states (ignoring the decoupled spin of the heavy\noctet quark). Therefore these functions show simple exponential behaviour\nat large distances and {\\em not} $D$ and $D_1$. The perturbative expressions\nfor $D^+$ and $D^-$ are nearly degenerate, but the gluon condensate\ncontributes with different sign. It stabilises the sum rule for $D^-$ and\ndestabilises for $D^+$.\n\nThe value of the binding energy for the lowest intermediate $1^-$ state\n(the inverse correlation length of the correlator) with three flavours is\ndetermined to be $E^-_{3fl} = 1\/a^-_{3fl} \\approx 1.5 \\pm 0.4 \\,\\mbox{\\rm GeV}$ and\nwith zero flavours to be $E^-_{0fl} = 1\/a^-_{0fl} \\approx 1.9 \\pm 0.5 \\,\\mbox{\\rm GeV}$.\nThe main sources of uncertainty are the choice of the continuum threshold\n$s_0$ and the value of the gluon condensate. \n\nThough we find no stable sum rule for the axial vector state we have from\nthe difference of the expressions for the $1^-$ and $1^+$ state strong\nevidence for the counterintuitive result that the $1^+$ state is lighter\nthan the vector state. \n\nThe gauge invariant gluon correlator has been calculated on the lattice using\nthe cooling technique \\cite{gmp:97,egm:97}. There, the analysis has been made\nby assuming at large distances an exponential behaviour for the invariant\nfunctions $D$ and $D_1$, which in light of the present investigation seems\nless justified than the same Ansatz for the functions $D^-$ and $D^+$. The\nresults of the lattice calculation are in qualitative, but not quantitative\nagreement with the sum rule results. The lattice researchers find correlation\nlengths for $D$ and $D_1$, $a$ and $a_1$, which are degenerate within the\nerrors. The computations have been done in quenched QCD and with four dynamic\nflavours of staggered fermions at a bare quark mass of $d\\cdot m_q = 0.01$\nwhere $d$ denotes the lattice spacing. They found \\cite{egm:97}:\n\\begin{eqnarray}\n& & E^- \\; = \\; E^+ \\; = \\; \\frac{1}{a} \\; = \\; 0.90\\pm 0.14 \\;\\mbox{\\rm GeV}\n\\qquad \\mbox{for 0 flavours and} \\nonumber \\\\\n\\vbox{\\vskip 8mm}\n& & E^- \\; = \\; E^+ \\; = \\; \\frac{1}{a} \\; = \\; 0.58\\pm 0.10 \\;\\mbox{\\rm GeV}\n\\qquad  \\mbox{for 4 flavours.}\n\\end{eqnarray}\n\nA preliminary analysis of the lattice data based on an exponential behaviour\nfor $D^+$ and $D^-$ \\cite{meg:98} leaves the values essentially unchanged but\nindicates a splitting of $E^+$ and $E^-$ in the same direction as proposed\nby the sum rules! The reader should also note the increase of the correlation\nlength from zero to four flavours which is predicted by the sum rules as well\nwhere it is mainly due to the decrease of the gluon condensate.\n\nIn another approach \\cite{bbv:98} the exponential behaviour of the functions\n$D^+$ and $D^* = z^2\\partial\/\\partial z^2 D_1$ for quenched QCD could be\nextracted by analysing field insertions into a Wilson loop and assuming\nfactorisation as in the model of the stochastic vacuum \\cite{dos:87,ds:88}.\nThe resulting values for the correlation lengths are smaller than those of\nthe direct lattice calculations \\cite{bbv:98} and thus compare more\nfavourably with our results:\n\\begin{equation}\nE^+ \\; = \\; \\frac{1}{a^+} \\; = \\; 1.64 \\,\\mbox{\\rm GeV}\n\\quad \\mbox{and} \\quad\nE^* \\; = \\; \\frac{1}{a^*} \\; = \\; 1.04 \\,\\mbox{\\rm GeV}\n\\quad \\mbox{for 0 flavours.} \n\\end{equation}\n\nThe sum rule analysis shows that the state investigated here namely a gluon\nconfined by an octet source has a much higher energy than the corresponding\nstate in HQET. A similar analysis of a light quark bound by a source in the\nfundamental representation \\cite{bbbd:92} yielded an energy which is by a\nfactor 2 to 4 smaller. This is to be expected on general grounds \\cite{nsvz:84}\nsince the case treated here is nearer to a glueball than to a heavy meson.\n\n\n\\newpage \\noindent\n{\\Large\\bf Acknowledgements}\n\n\\vspace{3mm} \\noindent\nThe authors would like to thank N. Brambilla, D. Gromes, E. Meggiolaro\nand A. Vairo for interesting discussions. M. Eidem\\\"uller thanks the\nLandesgraduiertenf\\\"orderung at the University of Heidelberg for support\nand M. Jamin would like to thank the Deutsche Forschungsgemeinschaft for\ntheir support.\n\n\n \n\\vspace{6mm} \\noindent\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{INTRODUCTION}\n\\label{sec:intro} \n\nTwisted light is a light beam with intrinsic orbital angular momentum (OAM) in the direction of motion; for reviews, see~\\cite{2011AdOP....3..161Y,Bliokh:2015doa}.   The components of the vector potential that are transverse to the overall propagation direction of the beam can be given by~\\cite{2019PhRvA..99b3845Q}\n\\begin{equation}\n\\vec A_\\perp(\\vec r, t) =  A_0 \\hat \\epsilon_\\Lambda \\,  e^{i(k_z z-\\omega t)}\\,  e^{i \\ell \\phi} \\,J_\\ell(\\kappa \\rho)   \\,.\n\\end{equation}\n$A_0$ is a normalization constant, $\\hat\\epsilon$ is a polarization vector which can be made more specific as  $\\hat\\epsilon_\\Lambda$ for circular polarization $\\Lambda = \\pm 1$.  In wave number space, or momentum space quantum mechanically, it is a superposition of plane wave states all with the same longitudinal momentum $k_z$ and the same magnitude transverse momentum $\\kappa$ but varying azimuthal directions.  The phase $e^{i \\ell \\phi}$ makes the orbital angular momentum in the direction of motion be $\\ell$ (or $\\ell \\hbar$), and the total angular momentum is $m_\\gamma = \\ell + \\Lambda$.\nThe swirling wavefront, in addition to longitudinal momentum, has transverse momentum components that can twist objects in its path or give them sideways kicks.  \n\nThe expressions that give the momentum and angular momentum densities are obtained from the energy-momentum tensor~\\cite{Jauch:1976ava,Bjorken:1965zz}.\nUsing the electromagnetic Lagrangian \n$L = -\nF_{\\alpha\\beta} F^{\\alpha\\beta}\/(4\\mu_0)$ and the canonical or Noether procedure gives the canonical energy-momentum tensor\n\\begin{equation}\n    T^{\\mu\\nu} =\t- \\frac{1}{\\mu_0} F^{\\mu\\alpha} \\partial^\\nu \\! A_\\alpha - g^{\\mu\\nu} L    \\,.\n\\end{equation}\nIt is not symmetric in its two indices.  Aside from aesthetics, the field equation in General Relativity requires a symmetric energy-momentum tensor.  It can be symmetrized by adding a total derivative~\\cite{1940Phy.....7..449B,rosenfeld1940energy}, whereby spatial integrals over the energy-momentum tensor remain unchanged.  Doing so gives the Belinfante tensor\n\\begin{equation}\n    \\theta^{\\mu\\nu} = - \\frac{1}{\\mu_0} F^{\\mu\\alpha} F^\\nu_{\\ \\alpha} -\tg^{\\mu\\nu} L    \\,.\n\\end{equation}\nThe momentum densities $\\vec {\\mathcal P}$ are obtained from $T^{0i}\\!\\,\/c$ or $\\theta^{0i}\\!\\,\/c$,  and are\n\\begin{equation}\n    \\vec {\\mathcal P} = \n\t\t\t \\epsilon_0 \\vec E \\cdot (\\vec\\nabla) \\vec A\t\\,,\t\t\\quad \\text{canonical}\\ \n\\end{equation}\nor  \n\\begin{equation}\n    \\vec {\\mathcal P} = \n\t\t\t \\epsilon_0 \\vec E \\times \\vec B\t\t\\,,\t\t\\quad \\ \t\\text{Belinfante}.\n\\end{equation}\nIn general, they are numerically distinct.\nThe related results for angular momentum density $\\vec {\\mathcal J}$ are\n\\begin{align}\n\\vec {\\mathcal J} = \\left\\{\n\t\t\t\\begin{array}{l}\n\t\\epsilon_0 \\vec E \\cdot (\\vec r \\times \\vec\\nabla) \\vec A\t+ \\epsilon_0 \\vec E \\times \\vec A\n\t\t\\,,\t\t\\quad\\, \\text{canonical},\t\\\\\n\t\t\t \\epsilon_0 \\, \\vec r \\times ( \\vec E \\times \\vec B )\t\t\\,,\t\t\n\t\t\\qquad\\qquad\\qquad\t\\text{Belinfante}.\t\t\n\t\t\t\\end{array}\n\\right.\n\\end{align}\nAgain, the two expressions differ by just a total derivative.  But they do differ locally, so do not lead to the same torque upon small test objects.\n\nInterestingly, an alternative way to obtain the momentum density of electromagnetic field is to infer it from forces on small dielectrics calculated from Lorentz force law~\\cite{2009PhRvL.102k3602A}.  The momentum density obtained this way agrees with the canonical result.  Further discussions of momentum density   definitions can be found in~\\cite{Bliokh:2015doa,2013EJPh...34.1337B,1978OptCo..24..185H,2019PhRvA..99f3832W,2014OExpr..22.6586O,2002PhRvL..88e3601O,2003PhRvL..91i3602G}.\n\n\\section{Angular and transverse momentum density tests}\n\nWe will discuss some predictions for making objects spin by shining twisted light upon them, thinking in one case in terms of the torque generated by absorbing the electromagnetic angular momentum, and in another case in terms of the sideways kick, sometimes called the superkick~\\cite{2013JOpt...15l5701B}, given to individual particles in a system.\n\nOne specific result for the $z$-component (averaged over time) of the angular momentum density, plotted versus radius or the distance $\\rho$ out from the vortex axis, is shown in Fig.~\\ref{fig:example}.  In this figure, the projected total angular momentum of the field is $m_\\gamma=2$ and the circular polarization is $\\Lambda=\\sigma_z = 1$.  One sees significant  differences between the canonical and Belinfante results at most radii.\n\n\n   \\begin{figure} [b]\n   \\begin{center}\n   \\begin{tabular}{c}\n   \\includegraphics[height=5cm]{ang_mom_dens_i21}\n   \\end{tabular}\n   \\end{center}\n   \\caption[example] \n   { \\label{fig:example} \nAngular momentum density on a ring of radius $\\rho$ for a twisted light beam of total angular momentum $m_\\gamma =2$  and circular polarization $\\sigma_z =1$, with angular frequency $\\omega$ and $A_0$ normalizing the strength of the beam's electric field.  The pitch angle $\\theta_k$ is $\\arctan(\\kappa\/k_z)$.\nThe Belinfante case has regions where the angular momentum density swirls in a direction opposite to the overall angular momentum.}\n   \\end{figure} \n\n\n\\paragraph{One test:  twisted light on a cylindrical shell.}\n\nGiven the plot just mentioned, we will consider shining a twisted beam on a cylindrical shell, or hollow cylinder.  (Note that the torque on a filled cylinder would be an integrated torque, which is the about the same for the two cases, depending on the radius of the cylinder.)\n\n\nLet the cylinder and beam axes be coincident, Fig.~\\ref{fig:hollow} and the torque on shell will be proportional to angular momentum absorbed from beam at radius of cylinder.\n\n\n   \\begin{figure} [ht]\n   \\begin{center}\n   \\begin{tabular}{c} \n   \\includegraphics[height=4.5cm]{TwLIght_Cylind_SGi}\n\t\\end{tabular}\n\t\\end{center}\n   \\caption[example] \n   { \\label{fig:hollow} \nTwisted light hitting a hollow cylinder, with axes coincident.}\n   \\end{figure} \n   \n\nFor radius $\\rho = 2 \\,\\mu\\text{m} \\approx 2.74 \\,\\lambda$ and other selected parameters, and cylindrical shell sitting in a kerosine bath (the viscous drag is calculable~\\cite{1995PhRvL..75..826H,1996PhRvA..54.1593F}), terminal rotation frequency is\n\\begin{equation}\n    f  \\approx\n0.55   \\text{\\,Hz} ,\t\n\\quad \\text{canonical} , \n\\end{equation}\nor\n\\begin{equation}\n    f  \\approx  \n0.23   \\text{\\,Hz} ,\t\n\\quad \\text{Belinfante}.\n\\end{equation}\nThe other parameters used in this example are  $\\lambda = 0.729 \\,\\mu$m, power in beam = 4 mW, the beam put inside a Gaussian envelope of width 10 $\\lambda$,  thickness of shell = 0.5 $\\mu$m,  length of cylinder = 2  $\\mu$m, density of shell material twice water.\n\n\n\\paragraph{Another test: a two-ion rotor.}\n\nWe will study this case in terms of the effect of transverse momentum kicks, or superkicks, upon atoms constrained to move in a circle.  \n\nConsider a rotor has two $^{40}$Ca ions constrained to revolve in a circular path in a plane.  The atoms are well constrained to stay in the plane, and their radius from the center of the circle is well fixed, but they are free to revolve in a circle about the center.  Such a rotor exists, and is described in~\\cite{2019PhRvL.123m3202U}, but has not been used for the present purpose.  \n\n\n   \\begin{figure} [ht]\n   \\begin{center}\n   \\begin{tabular}{c} \n   \\includegraphics[height=4cm]{CaRotori}\n\t\\end{tabular}\n\t\\end{center}\n   \\caption[example] \n   { \\label{fig:carotor} \nA two-ion Calcium rotor.}\n   \\end{figure} \n   \n\nShine the beam perpendicular to plane of the rotor with vortex line passing thru its center. The beam can excite either ground state ion, and the ion receives one transverse momentum kick per lifetime of the excited state.  This will give a force $dp_\\perp\/dt$,  and a torque, and an angular acceleration.\nThe transverse momentum kick per absorption depends on the ratio of the momentum density and photon number density, and the numerator and denominator of this ratio give a simple result for the canonical case,\n\\begin{equation}\n    p_{\\perp} = \n\t\t \\frac{  \\ell \\, \\hbar} {\\rho}\n\t\t\\qquad \\qquad \\quad \\, \\text{canonical},\n\\end{equation}\nand\n\\begin{equation}\n    p_{\\perp} = \n\t\t\t\\hbar \\kappa \n\t\t\t\\displaystyle  \\frac{ J_{\\ell+\\Lambda}(\\kappa \\rho) }{ J_{\\ell}(\\kappa \\rho) }\n\t\t\t \\qquad \\text{Belinfante}\t.\n\\end{equation}\nAgain, $\\Lambda$ is the photon helicity; a plot of the anticipated angular acceleration for $\\Lambda = 1$ and $\\ell = 1$ is shown in Fig.~\\ref{fig:accel}.\nThe plot was made using the $4s_{1\/2}  \\to 4p_{3\/2}$ or $4p_{1\/2}$ transitions, where the excited state is not metastable but has a fast spontaneous\ndecay. The situation is analogous to laser cooling~\\cite{1975OptCo..13...68H}:\nthe spontaneous decay is isotropic so statistically there\nis no momentum kick in the decay, but the excitation\nalways involves a momentum kick in the same azimuthal\ndirection. \nThe predicted angular accelerations are wildly different, as Fig.~\\ref{fig:accel} shows.\n\n\n\n   \\begin{figure} [t]\n   \\begin{center}\n   \\begin{tabular}{c} \n   \\includegraphics[height=5cm]{rotortwistedacceli.pdf}\n\t\\end{tabular}\n\t\\end{center}\n   \\caption[example] \n   { \\label{fig:accel} \nCalculated angular acceleration for a two-ion Calcium rotor of varying radii, with further description in the text.}\n   \\end{figure} \n   \n\n\n\n\\section{Closing remarks}\n\\label{sec:closing}\n\n\n\nMore details and additional situations contrasting the canonical and Belinfante momentum and angular momentum density expressions can be found in~\\cite{Afanasev:2022vgl}.  \n\nThe canonical and the Belinfante versions of the electromagnetic energy-momentum tensor are by design the same for integrated quantities such as the total momentum or total angular momentum of the field.  However,  point by point in space they are different, and on small test objects they give different results in  calculations of the force or torque from electromagnetic waves striking them.  The differences are only apparent if the light has a structured wave front, and we have worked out examples using the particular example of twisted photons.  In certain regions the differences are especially dramatic.  Not discussed here are tractor beam effects in the Belinfante case, discussed in~\\cite{Afanasev:2022vgl} and also noticed in~\\cite{Novitsky:07}.  However, the dramatic tractor beam effects lie in limited spatial regions and are sensitive to details of the beam preparation. On the other hand, the dramatic torque differences which we have focused on in this talk are robust and exist over broad spatial regions and could well be confirmed or denied experimentally using ringlike or end-weighted rotor\n\n\\section*{Addendum}\n\n\\paragraph{Single particle off-axis in vortex beam.}  At the conference it was also possible to show a third test of the possible angular momentum densities.  This was to put a small test particle off-axis in a twisted photon beam, whence the transverse momentum absorption or the superkick would cause the particle to revolve about the vortex axis.\n\nSuch an experiment was actually performed nearly two decades ago~\\cite{2003PhRvL..91i3602G}, but measurements were made only at the maxima of the ringlike intensity profile of the twisted beam wavefront.  It happens that the difference between the predictions of the canonical and Belinfante angular momentum is proportional to the derivative of the intensity with respect to distance from the axis~\\cite{Afanasev:2022vgl}.  Hence the predictions of the two possibilities are the same at the points where measurements were made.  \n\n\n   \\begin{figure} [t]\n   \\begin{center}\n   \\begin{tabular}{c} \n   \\includegraphics[height=6cm]{Garces2breali.pdf}\n\t\\end{tabular}\n\t\\end{center}\n   \\caption[example] \n   { \\label{fig:revolution} \nCalculated angular acceleration for a two-ion Calcium rotor of varying radii, with further description in the text.}\n   \\end{figure} \n   \n\nFig.~\\ref{fig:revolution} shows the predictions of the Belinfante and canonical angular momentum densities for the off-axis test particle, given as its revolution frequency (for a certain laser power and for $\\ell=2$ and $\\Lambda=1$) plotted vs.~the distance from the vortex axis cubed, as in~\\cite{2003PhRvL..91i3602G}.   The dots show the radii where measurements have been made.  Clearly the predictions are significantly different and measurements with the test particle held at different radii could be quite decisive.  \n\n\\acknowledgments\n \nWe thank Elliot Leader for stimulating conversations.  A.A. thanks the US Army Research Office Grant W911NF-19-1-0022 for support, C.E.C. thanks the National Science Foundation (USA) for support under grant PHY-1812326, and A. M. thanks the SERB-POWER Fellowship, Department of Science and Technology, Govt. of India  for support.  \n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
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+{"text":"\\section{Quark-meson model}\nIn order to map out the phase diagrams, we employ\nthe quark-meson model as \nan effective low-energy model of QCD.\nThe Minkowski Lagrangian including\n$\\mu_u$ and $\\mu_d$ reads\n\\begin{eqnarray} \\nonumber\n{\\cal L}&=&\n{1\\over2}\\left[(\\partial_{\\mu}\\sigma)(\\partial^{\\mu}\\sigma)\n+(\\partial_{\\mu} \\pi_3)(\\partial^{\\mu} \\pi_3)\n\\right]\n+(\\partial_{\\mu}+2i\\mu_I\\delta_{\\mu}^0)\\pi^+(\\partial^{\\mu}-2i\\mu_I\\delta_{0}^{\\mu})\n\\pi^-\n\\nonumber-{1\\over2}m^2(\\sigma^2+\\pi_3^2\n\\\\ &&\n+2\\pi^+\\pi^-)\n-{\\lambda\\over24}(\\sigma^2+\\pi_3^2+2\\pi^+\\pi^-)^2\n+h\\sigma+\\bar{\\psi}\\left[\ni\/\\!\\!\\!\\!\\partial\n+\\mu_f\n\\gamma^0\n-g(\\sigma+i\\gamma^5{\\boldsymbol\\tau}\\cdot{\\boldsymbol\\pi})\\right]\\psi\\;.\n\\label{lag}\n\\end{eqnarray}\nWe will in the following allow for an inhomogeneous chiral condensate,\nseveral different ans\\\"atze have been discussed in the literature, for\nexample a chiral-density wave (CDW) and a chiral soliton\nlattice\nWe choose the simplest ansatz, namely that of a CDW,\n\\begin{eqnarray}\\nonumber\n\\sigma=\\phi_0\\cos(qz)\\;,\\hspace{0.5cm}\n\\pi_1=\\pi_0\n\\;,\\hspace{0.5cm}\n\\pi_2=0\n\\;,\\hspace{0.5cm}\n\\pi_3=\\phi_0\\sin(qz)\\;,\n\\end{eqnarray}\nwhere $\\phi_0$ is the magnitude of the chiral condesate, $q$ is a wavevector,\nand $\\pi_0$ is a homogeneous pion condensate.\nBelow we will express the effective potential using\nthe variables $\\Delta=g\\phi_0$ and $\\rho=g\\pi_0$.\n\nThere are two technical details I would like to\nbriefly mention, namely that of parameter fixing and regulator artefacts.\nIn mean-field calculations it is common to determine the\nparameters of the Lagrangian at tree level. However, this is inconsistent.\nOne must determine the parameters to the same accuracy as one is calculating\nthe effective potential. We are calculating the effective potential\nto one loop in the large-$N_c$ limit, which means that we integrate\nover the fermions, but treat the mesons at tree level.\nConsequently, we must determine the parameters in Eq. (\\ref{lag})\nin the same approximation. If one determines the\nparameters at tree level and the effective potential in the one-loop\nlarge-$N_c$ approximation, the onset of BEC will not be at\n$\\mu_I={1\\over2}m_{\\pi}$, in fact in some case there are substantial\ndeviations from this exact result. This point has been ignored in most\ncalculations to date.\nSecondly,\nin calculations using the NJL model, one is typically using a hard\nmomentum cutoff. In cases with inhomogeneous phases, this leads to an\nasymmetry in the states included due to the sign of $q$ in the\ndifferent quark dispersion relations. This leads to a $q$-dependent\neffective potential even in the limit $\\Delta\\rightarrow0$. This is\ninconsistent and one must typically subtract a  $q$-dependent term\nto remedy this.\nIn the present calculations in the QM model,\nwe are using dimensional regularization.\nWe have explicitly checked that the effective potential is consistent, i.e.\nit is independent of the wavevector $q$ in the limit\n$\\Delta\\rightarrow0$.\n\nLet us return to the QM Lagrangian (\\ref{lag}).\nThe quark energies are\n\\begin{eqnarray}\\nonumber\n  E_u^{\\pm}&=&E(\\pm q,-\\mu_I)\\;,\n\\hspace{0.5cm}\nE_d^{\\pm}=E(\\pm q,\\mu_I)\\;,\n\\hspace{0.5cm}\nE_{\\bar{u}}^{\\pm}=E(\\pm q,\\mu_I)\\;,\n\\hspace{0.5cm}E_{\\bar{d}}^{\\pm}=E(\\pm q,-\\mu_I)\\;, \n\\end{eqnarray}\nwhere\n\\begin{eqnarray}\nE(q,\\mu_I)&=&\n\\left[\n\\left(\\sqrt{p_{\\perp}^2+\n\\left(\\sqrt{p_{\\parallel}^2+\\Delta^2}+{q\\over2}\\right)^2}+\n{\\mu_I}\\right)^2\n+\\rho^2\\right]^{1\\over2}\\;.\n\\end{eqnarray}\nNote in particular that the quark energies depend on the isospin chemical\npotential.\nAfter regularization and renormalization, the zero-temperature part of the\neffective potential\ncan be expressed in terms of the physical meson masses and the pion-decay\nconstant as~\\footnote{We have been combining the on-shell and\n  $\\overline{\\rm MS}$\nschemes~\\cite{patrick}.}\n\\begin{eqnarray}\\nonumber\nV_{\\rm 1-loop}&=&\n{1\\over2}f_{\\pi}^2q^2\n\\left\\{1-\\dfrac{4 m_q^2N_c}{(4\\pi)^2f_\\pi^2}\n\\left[\\log\\mbox{$\\Delta^2+\\rho^2\\over m_q^2$}\n  +F(m_\\pi^2)+m_\\pi^2F^{\\prime}(m_\\pi^2)\n  \\right]\n\\right\\}{\\Delta^2\\over m_q^2}\n\\\\ && \\nonumber\n+\\dfrac{3}{4}m_\\pi^2 f_\\pi^2\n\\left\\{1-\\dfrac{4 m_q^2N_c}{(4\\pi)^2f_\\pi^2}m_\\pi^2F^{\\prime}(m_\\pi^2)\n\\right\\}\\dfrac{\\Delta^2+\\rho^2}{m_q^2}\n\\\\ \\nonumber &&\n -\\dfrac{1}{4}m_\\sigma^2 f_\\pi^2\n\\left\\{\n1 +\\dfrac{4 m_q^2N_c}{(4\\pi)^2f_\\pi^2}\n\\left[ \\left(1-\\mbox{$4m_q^2\\over m_\\sigma^2$}\n\\right)F(m_\\sigma^2)\n +\\dfrac{4m_q^2}{m_\\sigma^2}\n-F(m_\\pi^2)-m_\\pi^2F^{\\prime}(m_\\pi^2)\n\\right]\\right\\}\\dfrac{\\Delta^2+\\rho^2}{m_q^2} \n\\\\ \\nonumber &&\n-2\\mu_I^2f_\\pi^2\n\\left\\{1-\\dfrac{4 m_q^2N_c}{(4\\pi)^2f_\\pi^2}\n\\left[\\log\\mbox{$\\Delta^2+\\rho^2\\over m_q^2$}\n+F(m_\\pi^2)+m_\\pi^2F^{\\prime}(m_\\pi^2)\\right]\n\\right\\}{\\rho^2\\over m_q^2}\n\\\\ \\nonumber\n & & + \\dfrac{1}{8}m_\\sigma^2 f_\\pi^2\n\\Bigg\\{ 1 -\\dfrac{4 m_q^2  N_c}{(4\\pi)^2f_\\pi^2}\\Bigg[\n\\dfrac{4m_q^2}{m_\\sigma^2}\n\\left( \n\\log\\mbox{$\\Delta^2+\\rho^2\\over m_q^2$}\n-\\mbox{$3\\over2$}\n\\right) -\\left( 1 -\\mbox{$4m_q^2\\over m_\\sigma^2$}\\right)F(m_\\sigma^2)\n\\\\ &&\\nonumber\n+F(m_\\pi^2)+m_\\pi^2F^{\\prime}(m_\\pi^2)\\Bigg]\\Bigg\\}\n\\dfrac{(\\Delta^2+\\rho^2)^2}{m_q^4}\n- \\dfrac{1}{8}m_\\pi^2 f_\\pi^2\n\\left[1-\\dfrac{4 m_q^2N_c}{(4\\pi)^2f_\\pi^2}m_\\pi^2F^{\\prime}(m_\\pi^2)\\right]\n\\dfrac{(\\Delta^2+\\rho^2)^2}{m_q^4}\n\\\\ &&\n-m_\\pi^2f_\\pi^2\\left[\n1-\\dfrac{4 m_q^2  N_c}{(4\\pi)^2f_\\pi^2}m_\\pi^2F^{\\prime}(m_\\pi^2)\n\\right]\\dfrac{\\Delta}{m_q}\\delta_{q,0}\n+V_{\\rm fin}\\;,\n\\label{fullb}\n\\end{eqnarray}\nwhere  $V_{\\rm fin}$ is a finite term that must be evaluated numerically.\nThe linear term is responsible for explicit\nchiral symmetry breaking. It only contributes when $q=0$, i.e. in the\nhomogeneous case; for nonzero $q$ this term averages to zero over\na sufficiently large spatial volume of the system.\nThe finite-temperature part of the one-loop effective potential is\n\\begin{eqnarray}\nV_{T}&=&-2N_cT\\int_p\\bigg\\{\n\\log\\Big[1+e^{-\\beta(E_{u}-\\mu)}\\Big]\n+\\log\\Big[1+e^{-\\beta(E_{\\bar{u}}+\\mu)}\\Big]\n\\bigg\\}\n+{u\\leftrightarrow d}\\;.\n\\label{fd}\n\\end{eqnarray}\n\\section{Coupling to the Polyakov loop}\nThe Wilson line which wraps all the way around in imaginary time\nis defined as\n\\bq\nL({\\bf x})&=&{\\cal P}\\exp\\left[\ni\\int_0^{\\beta}d\\tau A_4({\\bf x},\\tau)\n\\right]\\;,\n\\label{ldef}\n\\end{eqnarray}\nwhere ${\\cal P}$ is time ordering.\nThe Wilson line is not gauge invariant, but taking the trace of it\ngives a gauge-invariant object, namely the Polyakov loop ${\\rm Tr}\\,L$.\nThe Polyakov loop is, however, not invariant under the socalled center\nsymmetry of the (pure glue) QCD Lagrangian, but transforms as \n${\\rm Tr}\\,L\\rightarrow e^{i{n\\over N_c}}{\\rm Tr }\\,L$, where $n=0,1,2...N_c-1$ and\n$e^{i{n\\over N_c}}$ is one of\nthe $N_c$  roots of unity. A nonzero expectation value of the\nPolyakov loop therefore signals the breaking of the center symmetry.\nThe expectation value of the correlator of Polyakov loop and its conjugate\nis related to the free energy of a quark and an antiquark.\nEmploying cluster decomposition, the expectation value of the Polyakov\nloop itself is related to the free energy of a single quark;\nA vanishing value of ${\\rm Tr}\\,L$ corresponds to an infinite free energy\nof a single quark and a vanishing value of\n${\\rm Tr}\\,L^{\\dagger}$ corresponds to an infinite free energy\nof an antiquark, and therefore signals confinement.\nIf we denote by $\\Phi$ the expectation value of \n${\\rm Tr}\\,L$ and $\\bar{\\Phi}$ of ${\\rm Tr}\\,L^{\\dagger}$,\nthe medium contribution reads\n  \\begin{eqnarray}\\nonumber\nV_T&=&-2T\\int{d^3p\\over(2\\pi)^3}\n\\bigg\\{\n    {\\rm Tr}\\log\\Big[1+3(\\Phi+\\bar{\\Phi}e^{-\\beta(E_u-\\mu)})\n      e^{-\\beta(E_u-\\mu)}+e^{-3\\beta(E_u-\\mu)}\\Big]\n\\\\ \n&&+{\\rm Tr}\\log\\Big[1+3(\\bar{\\Phi}+\\Phi e^{-\\beta(E_{\\bar{u}}+\\mu)})\n  e^{-\\beta(E_{\\bar{u}}+\\mu)}\n+e^{-3\\beta(E_{\\bar{u}}+\\mu)}\\Big]\n\\bigg\\}\n+{u\\leftrightarrow d}\n\\;.\n\\end{eqnarray} \nWe note that the symmetry between $\\Phi$ and $\\bar{\\Phi}$ implies\n$\\Phi=\\bar{\\Phi}$.\nThe expression for $V_T$ is also manifestly\nreal, reflecting that there is no sign problem at finite $\\mu_I$ and zero\n$\\mu_B$. Finally, for $\\Phi=\\bar{\\Phi}=1$, we recover the standard\nexpression for the fermionic contribution (\\ref{fd}) for $N_c=3$.\n\nWe also need to introduce a potential ${\\cal U}$ from the glue sector.\nThe terms are constructed from $\\Phi$ and $\\bar{\\Phi}$ such that\nit satisfies the symmetries. There are several such potentials\non the market. We choose the following logarithmic potential~\\cite{ratti2}\n\\begin{eqnarray}\n{{\\cal U}\\over {T^4}}&=&-{1\\over2}a \\Phi\\bar{\\Phi} + b\n\\log\\left[ 1 - 6\\Phi\\bar{\\Phi} +4(\\Phi^3 +\\bar{\\Phi}^3) -3(\\Phi\\bar{\\Phi})^2\n\\right]\\;,\n\\label{pglog}\n\\end{eqnarray}\nwith\n$a = 3.51 -2.47\\left({T_0\\over T}\\right) +15.2\\left({T_0\\over T}\\right)^2$\nand $b = -1.75\\left({T_0\\over T}\\right)^3$\\;.\nThe parameters are determined such that the potential reproduces the\npressure for pure-glue QCD as calculated on the lattice for temperatures\naround the critical temperature. Since the critical temperature depends\non the number of flavors $n_f$ and $\\mu_I$, one can refine\nthe potential by making $T_0$ dependent on these parameters,\n$T_0(N_f,\\mu_I)=T_{\\tau}e^{-1\/(\\alpha_0b(\\mu_I))}$ with\n$b(\\mu_I)={1\\over6\\pi}(11N_c-2N_f)-b_{\\mu_I}{\\mu_I^2\\over T_{\\tau}^2}$\nand $T_{\\tau}=1.77\\;\\text{GeV}$ and $\\alpha_0 = 0.304$\nare determined such that the transition temperature for pure glue at $\\mu_I=0$\nis $T_0=270$ MeV~\\cite{pawlow}. \nIn the numerical work, we use \n$m_{\\pi}=140$ MeV, $m_{\\sigma}=500$ MeV, $\\Delta=300$ MeV, and $f_{\\pi}=93$ MeV.\n\n\n\n\n\n\n\n\n\\section{Phase diagram in the $\\mu$-$\\mu_I$ plane}\nWe first discuss the results for the phase diagram in the $\\mu$-$\\mu_I$ plane\nat $T=0$  in the chiral limit, which\nis shown in the left panel of Fig.~\\ref{pionphase2}.\nDashed lines indicate first-order transitions while solid lines indicate\nsecond-order transitions. The black dot indicates the\nendpoint of the first-order line.\nThe vacuum phase is part of the $\\mu$-axis (recall that in the chiral limit,\nthe onset of pion condensation is at $\\mu_I=0$), ranging from $\\mu=0$\nto $\\mu=300$ MeV. In this phase all the thermodynamic functions are independent\nof the quark chemical potentials.\nIn the region to the left of the blue line, there is a nonzero pion condensate\nwhich is independent of $\\mu$.\nIn the wedge-like shaped region between the blue and green\nlines, there is a phase with a $\\mu$-dependent pion condensate and\na vanishing chiral condensate. In this phase the isospin and\nquark densities are nonzero. In the region between the green and red lines,\nwe have an inhomogeneous phase with a nonzero wavevector $q$. In this\nphase, the pion condensate is zero; thus there is no coexistence of\nan inhomogeneous chiral condensate and a homogeneous pion condensate.\nFinally,  the  region  to  the  right  of  red,  blue,\nand green line segments is the symmetric phase, where\n$\\Delta=\\rho=q=0$. The  blue  dot  marks  the  Lifshitz\npoint where the homogeneous, inhomogeneous and chi-\nrally symmetric phases connect.\nIn the right panel of Fig.~\\ref{pionphase2}, we show \nthe pion condensate $\\rho$ (green line),\nthe magnitude of the chiral condensate $\\Delta$ (blue line), and the\nwavevector $q$ (red line) as functions of $\\mu$ for fixed $\\mu_I=5$ MeV.\nThis corresponds to a horizontal line in the phase diagram.\n\n\\begin{figure}[htb]\n\\begin{center}\n  \\includegraphics[width=0.45\\textwidth]{phaseinhom.pdf}\n\\includegraphics[width=0.45\\textwidth]{10.pdf}\n\\caption{Phase diagram in the chiral limit (left) and $\\rho$, $\\Delta$, and\n  $q$ as functions of $\\mu$ for $\\mu_I=5$ MeV (right). See main text for\n  details.}\n\\label{pionphase2}\n\\end{center}\n\\end{figure}\n\n\nIn the left panel of Fig.~\\ref{bondary}, we show the\nwindow of inhomogeneous chiral condensate for $\\mu_I=0$, i.e. on the\n$\\mu$-axis as a function of the pion mass.\nThe inhomogeneous phase ceases to exist for pion masses larger than\n$37.1$ MeV and so is not present at the physical point\nThis is contrast to the QM study in Ref.~\\cite{nickel} where an\ninhomogeneous phase is found at the physical point.\nHowever, in that paper the parameters were\ndetermined at tree level, which may explain the difference with\nthe results presented here.\nThe question of inhomogeneous phases in QCD was also addressed by\nBuballa at this meeting using the NJL model, in particular\ndiscussing the role of the quark masses~\\cite{bubi}.\nPerforming a Ginzburg-Landau analysis, they find an inhomogeneous\nphase which\nshrinks with increasing quark mass, but survives at the physical point.\n\n\\begin{figure}[htb]\n\\begin{center}\n  \\includegraphics[width=0.44\\textwidth]{boundary.pdf}\n  \\includegraphics[width=0.44\\textwidth]{pionphase.pdf}\n\\end{center}\n\\caption{Window of inhomogeneous phase as a function of the pion mass\n  for $\\mu_I=0$ (left) and the homogeneous phase diagram at the physical\npoint (right).}\n\\label{bondary}\n\\end{figure}\n\nIn the right panel of\nFig. \\ref{bondary}, we show the phase diagram at the physical point.\nThe thermodynamic observables are independent\nof $\\mu$ and $\\mu_I$ in the region bounded by the \n$\\mu_I$ and $\\mu$ axes, and the straight lines given by \n$\\mu+\\mu_I=gf_{\\pi}=m_q$ (blue line) and $\\mu_I=\\mu_i^c={1\\over2}m_{\\pi}$\n(red line).\nWe therefore refer to this as the vacuum phase.\nThe red line shows the phase boundary between a phase with\n$\\rho=0$ and a pion-condensed phase. The transition is second order\nwhen the red line is solid and first order when it is dashed. The\nsolid dot indicates the position of the critical end point where the\nfirst-order line ends, and is located at\n$(\\mu, \\mu_I) = (264,91)$ MeV. The green line indicates the boundary\nbetween a chirally broken phase and a phase where chiral symmetry \nis approximately restored. This line is defined by the inflection point\nof the chiral condensate in the $\\mu$-direction.\nThe region bounded by the three lines is a phase\nwith chiral symmetry breaking but no pion condensate. The \neffective potential depends on $\\mu$ and $\\mu_I$ and therefore\nthe quark and isospin densities are nonzero.\n\n\n\\section{Phase diagram in the $\\mu_I$-$T$ plane}\n\n\n\n\n\\begin{figure}[!htb]\n\\begin{center}\n  \\includegraphics[width=0.45\\textwidth]{phasePQMlog.pdf}\n \n  \\includegraphics[width=0.45\\textwidth]{PD_final.pdf}\n  \\end{center}\n\\caption{Phase diagram in the $\\mu_I$-$T$ plane from the PQM model\n(left) and from the lattice simulations of Refs.~\\cite{gergy1,gergy2,gergy3}.}\n\\label{pionphase}\n\\end{figure}\nIn the left panel of Fig.~\\ref{pionphase},\nwe show the phase diagram in the $\\mu_I$-$T$ diagram\nresulting from our PQM model calculation. The green line indicates\nthe transition to a pion-condensed phase, where the $O(2)$-symmetry associated\nwith the conservation of the third component of the isospin is broken.\nThis transition is second order everywhere. At $T=0$ this transition takes\nplace at $\\mu_I={1\\over2}m_{\\pi}$ by construction.\nThe chiral transition line is in blue, while the transition line for the\ndeconfinement transition is in red.\nIn the noncondensed phase, these coincide.\nWhen these lines meet the BEC line, \nthey depart and the former coincides the BEC line.\nThe transition line for deconfinement penetrates into condensed phase.\nFinally, the dashed line indicates the BEC-BCS crossover defined by\nthe condition $\\Delta>\\mu_I$, i.e. when the dispersion relations for the \n$u$-quark and $\\bar{d}$-quark\nno longer have their minima at $p=0$, but rather at $p=\\sqrt{\\Delta^2-\\mu_I^2}$.\nIn the right panel of Fig.~\\ref{pionphase}, we see the lattice results of\nRefs.~\\cite{gergy1,gergy2,gergy3}.\nThe blue band indicates the chiral crossover. \nWithin the uncertainty it coincides with \nthe deconfinement transition. The green band indicates\nthe second-order transition to a Bose-Einstein condensed state. The three\ntransition meet at the yellow point. Their simulations also indicate\nthat the deconfinement transition temperature\ndecreases and the transition line smoothly penetrates into the\npion-condensed phase.\n\n\\section{Summary}\nI would like to finish this talk by highlighting our main results and\nthe comparison with lattice results from Refs.~\\cite{gergy1,gergy2,gergy3}.\n\n\\begin{enumerate}\n\\item Rich phase diagrams. Inhomogeneous chiral condensate excluded\nfor $m_{\\pi}>37.1$ MeV.\n\n\\item No inhomogeneous chiral condensate coexists with a\n  homogeneous pion condensate.\n\\item Good agreement between lattice simulations and model calculations:\n\\begin{enumerate}\n\\item Second-order transition to a BEC state, which is in the\n$O(2)$ universality class.\nAt $T=0$, onset of pion condensation at exactly $\\mu_I^c={1\\over2}m_{\\pi}$.  \n\\item BEC and chiral transition lines merge at large $\\mu_I$.\n\\item The deconfinement transition smoothly penetrates\ninto the BEC phase.\n\\end{enumerate}\n\\end{enumerate}\n\n\n\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nSince the discovery of the first transiting exoplanet, HD 209458b \\citepads{2000ApJ...529L..41H,2000ApJ...529L..45C}, the {transit method} has become the most successful detection method, surpassing the combined detection counts of all other methods (see Fig.~\\ref{Fig_methods}) and giving rise to the most thoroughly characterized exoplanets at present. \n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[width=10cm]{Fig_methods.pdf}\n\n\\caption{The fractions by which various detection methods contributed to the accumulated sample of known planets is shown, for years since 1995. At the end of 1995, only five planets were known, three from {pulsar timing} and two from radial velocities. Between 1996 and 2013, the sample of known planets was dominated by those discovered with radial velocities, while in 2018, 78\\% of all known planets had been discovered by transits. Based on data from the NASA Exoplanet Archive in Feb. 2018, and using its classification by discovery methods. 'Timing' includes planets found by pulsar timing, {eclipse timing}, or {transit timing}. Other detection methods ({astrometry}, orbital brightness variation) generate only a very small contribution that is barely visible at the bottom of the graph, for years following 2010.}\n \\label{Fig_methods}\n\\end{center}\n\\end{figure}\n\nThe detection of planetary transits is among the oldest planet detection methods; together with the {radial velocity} (RV) method it was proposed in \\citeyearads{1952Obs....72..199S} in a brief paper by {Otto Struve}. The early years of exoplanet discoveries were however dominated by planets found by RVs, and prior to the 1999 discovery of transits on {HD 209458}, the transit method was not considered overly promising by the community at large. For example, a \\citeyearads{1996jpl..reptQ....E} (Elachi et al.) NASA Road Map for the Exploration of Neighboring Planetary Systems (ExNPS) revises in some detail the potential of RV, astrometry and microlensing detections, with a recommended focusing onto space interferometry, while transits were considered only cursory.\nConsequently, activities to advance transit detections were rather limited; most notable are early proposals for a spaced based transit-search by {Borucki}, Koch and collaborators (\\citeads{1985ApJ...291..852B,1996JGR...101.9297K,1997ASPC..119..153B}) and the {TEP project}, a search for transiting planets around the eclipsing binary {CM Draconis} that had started in 1994 (\\citeads{1998A&A...338..479D,2000ApJ...535..338D}). The discovery of the first transiting planets, with some of them like HD 209458b already known from RV detections, quickly led  to intense activity to more deeply characterize them, mainly from multi-color photometry (e.g. \\citeads{2000ApJ...540L..45J,2001NewA....6...51D}) or from spectroscopy during transits (e.g. \\citeads{2000A&A...359L..13Q,2002ApJ...568..377C,2004MNRAS.353L...1S}); to provide the community with efficient transit fitting routines (e.g. \\citeads{2002ApJ...580L.171M}; for more see below), or to extract the most useful set of physical parameters from transit lightcurves  \\citepads{2003ApJ...585.1038S}.\n\nThe first detections of transits also provided a strong motivation towards the set-up of dedicated transit searches, which soon led to the first planet discoveries by that method, namely {OGLE-TR-56b}  \\citepads{2003Natur.421..507K} and further planets by the OGLE-III survey, followed by {TrES-1} \\citepads{2004ApJ...613L.153A}, which was the first transit-discovery on a bright host star. Transits were therefore established as a valid method to find new planets. \n\nCentral to the method's acceptance was also the fact that planets discovered by transits across bright host stars permit the extraction of a wealth of information from further observations. Transiting planets orbiting bright host-stars, such as HD 209458b, HD 189733 \\citepads{2005A&A...444L..15B}, WASP-33b \\citepads{2006MNRAS.372.1117C,2010MNRAS.407..507C}, or the terrestrial planet 55 Cnc e \\citepads{2004ApJ...614L..81M,2011ApJ...737L..18W} are presently the planets about which we have the most detailed knowledge. Besides RV observations for the mass and orbit determinations, further characterization may advance with the following techniques: transit photometry with increased precision or in different wavelengths; transit photometry to derive transit timing variations (TTVs); spectroscopic observations during transits (transmission spectroscopy; line-profile tomography of exoplanet transits; {Rossiter-McLauglin effect}). Furthermore, the presence of transits --  strictly speaking primary transits of a planet in front of its central star -- usually implies the presence of {secondary eclipses} or occultations, when a planet disappears behind its central star. These eclipses, as well as phase curves of a planet's brightness in dependence of its orbital position, might be observable as well.\n\nGiven the modest instrumental requirements to perform such transit searches on bright star samples -- both HD209458b's transits and the planet TReS-1 were found with a telescope of only 10cm diameter --  the first years of the 21st century saw numerous teams attempting to start their own transit surveys. Also, for the two space-based surveys that were launched a few years later, {CoRoT} and {Kepler}, it is unlikely that they would have received the necessary approvals without the prior ground-based discovery of transiting planets. The enthusiasm for transit search projects at that time is well represented by a paper by \\citetads{2003ASPC..294..361H} \n which lists 23 transit surveys that were being prepared or already operating. Its title 'Hot Jupiters Galore' also typifies the expectation that significant numbers of transiting exoplanets will be found in the near future: Summing all 23 surveys, Horne predicted a rate of 191 planet detections per month.  \n  In reality, advances were much slower, with none of these surveys  reaching the predicted productivity. By the end of 2007, before the first discoveries from the CoRoT space mission \\citepads{2008A&A...482L..17B,2008A&A...482L..21A}, only 27 planets had been found through transit searches. This slower advance can be traced to two issues that revealed themselves only during the course of the first surveys: The amount of survey time required under real conditions was higher than expected, and the presence of {red noises} decreased sensitivity to transit-like events (see later in this chapter). Once these issues got understood and accounted for, some of these ground-based surveys became very productive, and both WASP and HAT\/HATS have detected over 100 planets to date. The next major advances based on the transit method arrived with the launch of the space missions CoRoT in 2006 and Kepler in 2009. These led to the discoveries of transiting terrestrial-sized planets ({CoRoT-7b} by \\citeads{2009A&A...506..287L}, {Kepler-10b} by \\citeads{2011ApJ...729...27B}); to planets in the temperate regime ({CoRoT-9b}, \\citeads{2010Natur.464..384D}); to transiting {multi-planet systems} \\citepads{2011Natur.470...53L} and to a huge amount of transiting planets that permit a deeper analysis of planet abundances in a very large part of the radius - period (or Teff) parameter space. In the following, an introduction is given on the methodology of the transit detection and its surveys, as well as an overview about the principal projects that implement these surveys.\n  \n\\section{Fundamentals of the transit method}\n\n\\begin{figure}[t]\n\\includegraphics[width=\\textwidth]{Fig_transito_v2.png}\n\\caption{Outline of the transit of an exoplanet, with the main quantities used to describe the orbital configuration, from the observables given in the lower solid curve (the observed light curve), to the model representations from the observer's point of view (central panel) or other view points (top panels). See the text for details.  }\n\\label{fig:fig_tran}       \n\\end{figure}\n\nA schematic view of a transit event is given in Figure~\\ref{fig:fig_tran}, where the bottom part represents the observed flux of the system. As the planet passes in front of the star, its flux diminishes by a fractional denoted as $\\Delta F$. Under the assumptions of negligible flux from the planet and of spherical shapes of the star and planet, $\\Delta F$ is given by the ratio of the areas of the planet and the star:\n\n\\begin{equation}\n\\Delta F \\approx \\left(\\frac{R_p}{R_s}\\right)^2 = k^2\n\\end{equation}\n\nwhere $R_p$ is the radius of the planet, $R_s$ the radius of the star, and $k$ is the radius ratio. The total duration of the transit event is represented as $t_T$, and the time of totality, in which the entire planet disk is in front of the stellar disk (the time between \\emph{second} and \\emph{third} contacts, using eclipse terminology) is given by $t_F$, during which the light curve is relatively flat. Using basic geometry, the work by \\citetads{2003ApJ...585.1038S} derived analytic expressions that relate these observables to the orbital parameters. In particular, the {impact parameter} $b$, defined as the minimal projected distance to the center of the stellar disc during the transit, can be expressed as:\n\n\\begin{equation}\nb\\equiv \\frac{a}{R_s}\\cos i=\\Big\\{\\frac{(1-k)^2-[\\sin^2(t_F\\pi\/P)\/\\sin^2(t_T\\pi\/P)](1+k)^2\n}{\\cos^2(t_F\\pi\/P)\/\\cos^2(t_T\\pi\/P)}\\Big\\}^{1\/2}\n\\end{equation}\n\nwhere $a$ is the orbital semimajor axis, $i$ the orbital inclination, and $P$ the orbital period. A commonly used quantity that can be obtained from photometric data alone is the so-called scale of the system, or the ratio between the semimajor axis and the radius of the star:\n\n\\begin{equation}\\label{transit_distance}\n\\frac{a}{R_s}=\\frac{1}{\\tan(t_T\\pi\/P)}\\sqrt{(1+k)^2-b^2}\n\\end{equation}\n\nwhich, using {Kepler laws} of motion and making the reasonable approximations of the mass of the planet being much smaller than the mass of its host star, and a spherical shape for the star, can be transformed into a measurement of the mean {stellar density}:\n\n\\begin{equation}\n\\rho_s = \\frac{3\\pi}{GP^2}\\left(\\frac{a}{R_s}\\right)^3\n\\end{equation}\n\n This measurement and its comparison with the stellar density estimated by other means (through spectroscopy, mass-radius relations, or asteroseismology) has often been used as a way to prioritise the best transit candidates from a survey (\\citealt{2003ApJ...585.1038S,Tingley:2011aa,Kipping:2014ab}). In the previous equations we have assumed circular orbits for simplicity; a derivation of equivalent equations including the eccentricity terms can be found in \\citeauthor{Tingley:2011aa} (2011, with a correction in Eq. 15 of \\citealt{Parviainen:2013aa}). \n\nWhile the previous expressions allow quick estimates of the major parameters of an observed transit, more sophisticated derivations using the formalisms of \\citetads{2002ApJ...580L.171M} or \\citetads{2006A&A...450.1231G} are commonly used for their more precise derivation. This is in part due to a subtle effect visible in Figure~\\ref{fig:fig_tran}: the {limb-darkening} of the star, that manifests itself as a non-uniform brightness of the stellar disk. The limb-darkening of the star makes it challenging to determine the moments of \\emph{second} and \\emph{contact} of the transit, and to precisely measure $\\Delta F$. For more detailed introductions into the parameters that can be measured from transits, we refer to \\citetads{2010exop.book...55W} and \\citetads{2010trex.book.....H}.\n\n\\subsection{Detection probability}\n\nThe geometric probability to observe a planet in transit is given by \\citepads{2010exop.book...55W}:\n\n\\begin{equation}\np_{tra} = \\left(\\frac{R_s\\pm R_p}{a}\\right)\\left(\\frac{1+e\\sin \\omega}{1-e^2}\\right)\n\\end{equation}\n \nwhere the $+$ sign is used to include grazing transits, and the $-$ sign refers to the probability of full transits, that have \\emph{second} and \\emph{third} contacts. For a typical hot Jupiter with a semimajor axis of 0.05~AU this is on the order of 10\\%, while for a Earth at 1~AU it goes down to 0.5\\%. This geometric obstacle is the main handicap of the transit method, since the majority of existing planet systems will not display transits.\n\n\\subsection{False Positives}\n\nA transit-shaped event in a light curve is not always caused by a transiting planet, as there are a number of astrophysical configurations that can lead to similar signatures. These are the so-called false positives in transit searches, which have been a nuisance of transit surveys since their beginning. One example of a {false positive} would be a stellar eclipsing binary in an apparent sky position that is so close to a brighter single star that the light of both objects falls within the same photometric aperture of a detector: the deep eclipses of the eclipsing binary are diluted due to the flux of the brighter star, and a shallower eclipse is observed in the light curve, with a very similar shape to a transiting planet. More complete descriptions of the types of false positives that affect transit searches, and their expected frequencies, can be found in \\cite{Brown:2003aa, Alonso:2004ab,Almenara:2009aa, Santerne:2013aa}. \n\nTo detect false positives and to confirm the planetary nature of a list of candidates provided by a transit survey, a series of follow-up observations are required (e.g. \\citealt{Latham:2003aa,Alonso:2004ab, Latham:2007aa, Latham:2008aa, Deeg:2009aa, Moutou:2013aa, Gunther:2017aa}), which apply to both  ground-based or space-based surveys. Traditionally, the  \\emph{confirmation} that a transit signal is caused by a planet takes place when its mass is measured with high precision RV measurements. In some cases, particularly with planets orbiting faint host stars, or for the confirmation of the smallest planets, the achievable RV precision is insufficient to measure the planet's mass. As these cases are of high interest, for example, planets with similar sizes as the Earth orbiting inside the habitable zone of its host star, statistical techniques have been developed to estimate the probability of the observed signals being due to planets relative to every other source of false positive we know of. In this case, the planets are known as \\emph{validated}. Current {validation} procedures use the fact that astrophysical false positives scenarios have very low probabilities when several transiting signals are seen on the same star \\citep{Lissauer:2012aa}, or they use all the available information (observables and knowledge of the galactic population and stellar evolution) to compare the probabilities of a signal due to a transiting planet vs. anything else. A few examples of validation studies are \\cite{Torres:2011aa,Morton:2012aa,Lissauer:2014aa,2014ApJ...784...45\n,Diaz:2014aa,Torres:2015aa,2016ApJ...822...86M,Torres:2017aa}, some of which use one of the current state-of-the-art validation procedures: \\tt{ {BLENDER}}\\rm, \\tt{{VESPA}}\\rm, and \\tt{{PASTIS}}\\rm.   \n\nFinally, some false positives may be due to artifacts of the red noise or other instrumental effects, even in the most precise surveys to date (e.g. \\citealt{Coughlin:2014aa}). In a few cases planets that were previously validated have been disproved after an independent analysis \\citep{Cabrera:2017aa, Shporer:2017ac}, which should generate some caution about the use of results from validations, which are statistical by design. \n\n\n\\section{Transit Surveys: factors affecting their design}\n\nThe task of surveying a stellar sample for the presence  of transiting planets must overcome the inherent inefficiencies of the transit method: The planets need to be aligned correctly (see previous section) and the observations must be made when transits occur. The expected abundances of the desired planet catch must be taken into account and their transits need to be detectable with sufficient {photometric precision}. Furthermore, transit-like events (false positives) may arise from other astrophysical as well as  instrumental sources and means to identify them need to be provided. The success of a transit-detection experiment must take these factors into account, which are discussed in the following\n\n\\runinhead{Sample size}\nThe probability $p_{tr}$ for transits to occur in a given random-oriented system is between a few percent for Hot Jupiters and less than 0.1\\% for cool giant planets. In order to achieve a reasonable probability that $N$ transiting system will be found in a given stellar field, the number of surveyed stars (that is, stars for which light curves with sufficient precision for transit detection are obtained) should be at least $N_\\mathrm{survey} \\approx N\/(p_\\mathrm{tra}\\  f) $, where $f$ is the fractional abundance of the detectable planet population in the stellar sample. For surveys of Hot Jupiters, with $f \\approx 1\\% $ of main-sequence (MS) stars \\citepads{2012ApJ...753..160W,2011arXiv1109.2497M\n, this leads to minimum samples of 2000 MS stars to expect a single transit discovery. Given that most stars in the bright samples of small-telescope surveys are not on the MS, sample sizes of 5000 - 10000 targets are however more appropriate. Survey fields that provide sufficient numbers of suitable stars, by brightness and by  desired stellar type, need therefore be defined. The size of the sample is then given by the size of the field of view ({\\it fov}) and by the spatial density of suitable target stars, which depends  on the precision of the detector (primarily depending on the telescope aperture)  and on the location of the stellar fields. Also, in most surveys, sample size is increased through successive observations of different fields.\n\n\\runinhead{Temporal coverage}\nAt any given moment, the probability for the observation of a transit of a correctly aligned system is $p \\approx t_T\/ P$, where $t_T$ is the duration of a transit and $P$ the orbital period. This probability goes from 5-8\\% for {Ultra-short periodic planets} over 2-3\\% for typical {Hot Jupiter} systems to 0.15\\% for an Earth-Sun alike. For an estimation of the number of transits for a given sample at a given time, we need to multiply this probability and the probability for correct alignment with the abundance of detectable planets. \nTo determine a planet's period, of course at least two transits need to be observed.  The requirement to observe three transit-like events that are periodic has however been habitual in ground-based observations, which are prone to produce transit-like events from meteorologic and other non-astronomic causes. Furthermore, for an increased S\/N of transit detections, especially towards the detection of smaller planets, as well as towards a more precise derivation of physical parameters, the rule is 'the more transits, the better'. Continuous observational coverage is the most time-efficient way to achieve the observation of a minimum number  transits (e.g. $N_\\mathrm{tr,min} > 3$) for a given system. However, only space missions are able to observe nearly continuously over timescale of weeks, which is the only way to ascertain that transiting planets above some size threshold and below some maximum period are being detected with near-certainty. Ground-based surveys, with their interruptions from the day\/night cycle and from meteorological incidences, can only seek reasonable {\\it probabilities} (but no certainty) to catch a desired number of transits from a given planet. The principal factor that determines the number of observed transits in a given discontinuous light curve is a planet's orbital phase (at some reference time, such as the begin of observations) or its epoch (the time when one of its transits occurs); both are of course unknown prior to a planet's discovery. An example of the effect of phase on the number of observed transits in discontinuous data is shown in Fig.~\\ref{Fig_phase_coverage}. As a rough rule, in order to achieve reasonable detection probabilities (e.g. $\\geq 70\\%$) for typical Hot Jupiters ($P= 3-4 d$) with a requirement of 3 observed transits, surveys should cover a stellar field for at least 300h. \n\\begin{figure}\n\\begin{center}\n\\includegraphics[width=10cm]{Fig_phase_coverage.pdf}\n\n\\caption{The expected number of transits by a a test-planet\nwith a period of 5 days that would have been\nobserved in a ground-based lightcurve covering 617 hrs (= 25.7 d). The clockwise direction is the planet's phase at some time of reference and the radial\ndistance gives the number of transits that would have been observed at each phase. Achieving that the large majority of the potential phases would produce at least 3 transits required an observational coverage that was much longer than 3 times the orbital period. Adapted from \\citetads{1998A&A...338..479D}.}\n \\label{Fig_phase_coverage}\n\\end{center}\n\\end{figure}\n\n\n\n\\runinhead{Transit detection precision}\nA basic version of the S\/N of a single transit is given by the ratio \n\\begin{equation}\\label{transit_SN}\n(S\/N)_{tr} \\approx  \\Delta F \/ \\sigma_\\mathrm{lc} \\ ,\n\\end{equation}\nwhere $\\Delta F$ is the fractional flux-loss during a transit and $\\sigma_\\mathrm{lc}$ is the fractional noise of the light curve on the timescale of the transit-duration $T_T$. This noise is composed of various sources,most notably photon noise from the target and the surrounding sky background, Cosmic Ray hits, CCD read noise and flat-fielding or {jitter} noises (which arise from variations of the positions or shapes of stellar point spread functions on detectors whose sensitivity is not uniform). For ground-based surveys, we also have to add variations from atmospheric transparency and {scintillation} noise. \nFig.~\\ref{Fig_rms_NGTS} shows the scatter over 1 hour time-scales from the most precise space-based survey, Kepler, and from NGTS, one of the leading ground-based ones. \n\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[width=11.5cm]{Fig_kepler_NGTS.pdf}\n\\caption{Comparison of precision of between Kepler (grey points) and NGTS (violet points). Given is the lightcurves' rms scatter on a 1h time-scale. The magnitudes for NGTS are in the I-band; for Kepler they are in its own system. The Kepler noises are from long-cadence (0.5h cycle time) curves of Q1 targets \\citepads{2010ApJ...713L.120J} and scaled by $\\sqrt{1\/2}$ towards the 1h time-scale. The NGTS data are from 695 hours of monitoring with a 12 s cadence, rebinned to exposure times of 1 h, from \\citetads{Wheatley:2017ab}. The difference between NGTS and Kepler precision would be reduced by a factor of $\\sqrt{950\/200} \\approx 2.2$ if the different aperture sizes are taken into account. The precision for the brightest NGTS targets is limited by scintillation noise, which is independent of the targets' brightness.}\n \\label{Fig_rms_NGTS}\n\\end{center}\n\\end{figure}\n\nEarly estimates for planet detection yields assumed commonly a white-noise scaling from the point-to-point scatter of an observed light curve to the usually much longer duration of a transit. In practice, red or {correlated noises} degrade the precision of nearly all photometric time-series over longer time-scales, as was first shown by \\citetads{2006MNRAS.373..231P},\nbased on data from the OGLE-III transit survey. \nOnly the space-based data from the Kepler mission uphold a white-noise scaling from their acquisition cycle of 30 minutes to a transit-like duration of 6 hrs (\\citeads{2010ApJ...713L.120J\n; see \\citeads{2011ApJS..197....6G}\nfor more details on Kepler's noise properties). The CoRoT mission, in contrary to Kepler on a low Earth orbit, produced light curves that on time-scales of 2h were already about twice as noisy as would be the result of a white-noise scaling from their acquisition cycle of 8.5 minutes \\citepads{2009A&A...506..425A}.\nAt least as strongly affected are ground-based surveys, with the principal culprit being the nightly airmass variation, which is on a similar time-scale as the duration of most transits. Correlated noises have been the principal source for the early overestimations of detection yields. In the case of SuperWASP, recognizing their influence led to a revision of detection yields and to an increase in temporal coverage early in its operational phase \\citepads{2006MNRAS.373.1151S}. For surveys that attempt to detect  shallow transits, brightness variations due to the sample stars' activity might also be of concern. The demonstration that this variability does not prevent the detection of terrestrial planets of solar-like stars \\citepads{2002ApJ...575..493J} was an important advance during the development of the Kepler mission. \\citetads{2004A&A...414.1139A}\nfound then that K stars are the most promising targets for transit surveys, while the surveys' performance drops\nsignificantly for stars earlier than G and younger than 2.0 Gyr. \nFor a quantitative discussion of the factors that influence the yield of transit surveys, we refer to \\citet{Beatty:2008aa}. \n\nAlgorithms to dampen red noises and other systematic effects have been developed to either 'clean' directly a lightcurve from their influences or as part of a detection algorithm, thereby increasing its sensitivity for transit-like features. Examples are the pre-whitening employed in the Kepler pipeline \\citepads{2010SPIE.7740E..0DJ\n, the cleaning of Corot lightcurves \\citepads{2015sf2a.conf..277G} or the widely used {SYSREM} \\citepads{2005MNRAS.356.1466T} and TFA \\citepads{2005MNRAS.356..557K} algorithms.\n\n\n\n\\runinhead {Brightness of the sample: Rejection of false positives and characterisation of the planet catch}\nAs mentioned, a large number of transit surveys was initiated in the first years of the 21st century, after the discovery of the first transiting planets. These early efforts were aimed about equally at deep surveys of small fields using larger (1m and more) telescopes and at shallow surveys with small instruments having fields of view. The surveys with larger telescopes, including early projects with Hubble Space Telescope (\\citeads{2000ApJ...545L..47G}, on the {47 Tucanae} globular cluster,  and the {SWEEPS} survey by \\citeads{2006Natur.443..534S}), were met however with limited success, with the most productive one becoming the OGLE-III \\citepads{2003AcA....53..291U} survey using a dedicated 1m telescope. Besides the difficulties to get access to the required large facilities to perform a deep survey over a sufficiently long time, a major drawback of such surveys is the faintness of the sample. RV verifications or further observational  refinements of their transit detections are either impossible, or if possible at all, they likely require the largest existing telescope facilities.\n\nFor example, from the SWEEPS survey that targeted the Sagittarius I window of the Galactic bulge with the Hubble Space Telescope, \\citetads{2006Natur.443..534S} report the detection of transits on 16 targets. Their faintness of V=18.8 to 26.2 as well as crowding permitted however only for two of them (SWEEPS-04 and 11) a confirmation as planets, based on RVs taken with the 8m VLT. All other SWEEPS detections have remained in candidate status until the present. We also note the comparatively small impact (relative to brighter targets) of the very large number of planets on the fainter end of the Kepler mission's sample (\\citeads{2014ApJ...784...45R}\nwith 815 planets, \\citeads{2016ApJ...822...86M}\nwith 1284 planets). These planets count only with probabilistic validations, and their principal usefulness are statistical studies on planet abundances across their known parameters (radius, period, central star type, planet multiplicity). The brightness of a target sample is therefore a very valuable parameter towards the science return of a transit survey! \n\nThe most common follow-up observations of transit detections are RV measurements, which do not only prove (or disprove) a planet's existence beyond reasonable doubt, but also greatly improve our knowledge about them, providing masses, orbital eccentricity and occasionally, also the detection of further non-transiting planets in the same system. In practise, from the RV follow-up of numerous candidates for the Kepler, K2 and CoRoT missions, we found that a magnitude of $\\approx$ 14.5 is a soft limit for their routinary follow-up. This is due to that brightness being near the limit for RV measurements at several relatively well-accessible mid-sized telescopes with appropriate instrumentation (e.g. the FIES instrument on the 2.5m Nordic Optical Telescope, or the HARPS instruments on the 3.6m Telescopio Nazionale Galileo (TNG) and on the ESO 3.6m telescope). \n  \nOn transiting systems of bright central stars, a host of further possibilities to examine these systems opens up - such as observation of the Rossiter Mc-Laughlin effect, transit spectroscopy, secondary eclipse measurements or the detection of phase curves (see the Handbook's Section on Exoplanet Characterization). For this reason -- increased knowledge about the discovered systems -- both of the upcoming space-based transit surveys, TESS and PLATO, will focus on samples that are brighter than those of Kepler and CoRoT, while ground-based surveys continue with their efforts to find transiting planets principally on bright, or on special types of target stars.\n\n\\section{Transit detection in light curves}\nEfficient recognition of transit-like features in light curves is a central part of any transit detection experiment. This task is usually performed in two steps. In the first one, detection statistical values that describe the likelihood of a light curve to contain a transit-like event are assigned. These might also be expressed as a function of a candidate planet's size, period and further parameters. In the second step, these statistical values are evaluated and those candidates that deserve closer investigation are extracted. We reproduce here a description of this step in the Kepler pipeline, from \\citetads{2010SPIE.7740E..0DJ}:\n\"Light curves whose maximum folded {detection statistic} exceeds 7.1$\\sigma$ are designated Threshold Crossing Events (TCEs) and subjected to a suite of diagnostic tests in Data Validation (DV) to fit a planetary model to the data and to establish or break confidence in the planetary nature of the transit-like events\". \nThe threshold value for the extraction of candidates needs to be  chosen with care, as it must provide a balance between the number of false positives -- which increases to unmanageable levels if the threshold is too low --  and the risk to miss detections of true planets if the threshold is too high.\n\nAs representative transit detection methods and algorithms we mention here the early work on matched-filter detection algorithms by \\citetads{1996Icar..119..244J\n, which provided the basics for the transit detection of the early TEP observing project as well as for the Kepler mission; the widely used box least-squares ({BLS) algorithm} \\citepads{Kovacs:2002xf} with derivatives (e.g. \\citeads{2006MNRAS.373..799C\n) or algorithms using wavelets (e.g. \\citeads{2007A&A...467.1345R})\n\nFor the second step of a detection procedure, the evaluation of a transit candidate as a planet-like event, usually a more detailed modelling (or fitting) of the light curve of the presumed transit is performed. The \\citetads{2002ApJ...580L.171M}\nalgorithm or the analytical eclipsing formulae by \\citetads{2006A&A...450.1231G}\nare widely used basic transit modellers that have also been integrated into several transit fitting packages.\n\n\n\\begin{table*}\n\n\\begin{sideways}\n\\begin{minipage}{20.5cm}\n   \n   \\caption{Selected transit surveys}\n   \\label{table1}\n   \\includegraphics[width=\\columnwidth]{table1.pdf}\n   \\end{minipage}\n\\end{sideways}\n\\end{table*}\n\n\\section{Transit surveys: past, current and future projects}\nThe {Extrasolar Planets Encyclopedia} ( \\url{http:\/\/www.exoplanet.eu\/research\/}) lists currently web-sites of 39 planet search projects that indicate 'transits' as a principal observing method.  These projects include finished ones, currently operating ones, projects that are in various preparation stages, as well as projects or proposals that have never moved beyond some design phase. It includes also some projects that aren't dedicated to the discovery, but to the follow-up of  transiting planets, such as ESA's CHEOPS space mission. In Table 1 and in the following notes we provide an overview over a selection of well-known transit detection surveys. The columns of Table 1 have the following meaning:\\\\\n\\begin{description}\n\\item[years:] Indicates the years of operation.\n\\item[config:] Instrument configuration, with the aperture diameters of individual optical units (cam = camera)\n\\item[{\\it fov}$_\\mathrm{single}$:] The sky area in deg$^2$ covered by a single optical unit of the detection experiment.\n\\item[{\\it fov}$_\\mathrm{instr}$:] The sky area in deg$^2$ that is covered simultaneously be the experiment at a single site in its usual operating mode. Only given if there are multiple optical units at a site.\n\\item[$N_{pl}$:] Count of planet detections in February 2018, based on the number of planets carrying an instrument's designation in the name. Planets labeled with other designations, such as HD or GJ numbers, are missed.\n\\item[R$_{05}$, R$_{50}$, R$_{95}$:] 5th, 50th (median) and 95th percentiles of the radii of the detected planets. If $N_{pl} \\leq$ 20, the smallest and largest planets are given.\n\\item[m$_{05}$, m$_{50}$, m$_{95}$:] Similar to the previous, but indicating the V-mag brightness of the detected systems.\n\\end{description}\nPlanet counts, radii and magnitudes are from the Encyclopedia of Extrasolar Planets and from the {NASA Exoplanet Explorer}. Below, some notes are provided for the transit surveys listed in Table 1.  \n\n\\runinhead{{OGLE}-III} The {Optical Gravitational Lensing Experiment} has been implemented in four phases, with the fourth one operational at present. OGLE is dedicated to the detection of substellar objects from microlensing, except for its third phase (OGLE-III, \\citeads{2003AcA....53..291U}), when the observing procedure of the 1m OGLE telescope at Las Campanas Observatory was modified to enable the detection of transits. OGLE-TR-56 was the first planet discovered in a transit search, with a posterior verification from RV follow-up \\citepads{2003Natur.421..507K}.\n\n\\runinhead{{TrES}} The `{Trans-Atlantic Exoplanet Survey}' was the first  project with instruments that were specifically designed and  dedicated for transit surveying. Its first telescope, originally named STARE, was used in the 1999 discovery of the transits of HD 209458b during tests at the High Altitude Observatory at Boulder. In 2001, it was relocated to Teide Observatory, Tenerife, where a systematic transit search began. Since 2003, the project operated under the TrES name, after the merger with two other projects using similar instrumentation, namely PSST at Lowell Observatory and the Sleuth Project at Palomar Observatory \\citepads{2008PhDT........70O}. The principal success of TrES was the detection of the first transiting planets orbiting bright stars (TrES 1, \\citeads{2004ApJ...613L.153A}; TrES 2 \\citeads{2006ApJ...651L..61O}) by a dedicated survey. TrES was discontinued in 2010.\n\n\\runinhead{{XO}} This survey started in 2003 at a single site, with a second phase observing from three sites from 2012-2014. The CCDs are read in time-delayed integration (TDI): pixels are read continuously while stars move along columns on the detector, owing to a slewing motion of the telescope. This setup enlarges the effective field of view and results in stripes of $7^\\circ$ x  $43^\\circ$ that are acquired during each single exposure.\n\n\\runinhead{{HAT}} This denominator ({Hungarian-made Automated Telescope}) encompasses two surveys: For one, since 2003 {HATnet} operates seven CCD cameras with 110mm apertures on individual mounts, with five of them at Fred Lawrence Whipple Observatory at Mount Hopkins in Arizona and two at Mauna Kea Observatory in Hawaii. For another, {HATSouth} \\citepads{2013PASP..125..154B} is a network across three sites in the southern hemisphere that is able to track stars continuously over longer time-spans. Since 2009, it operates at the Las Campanas Observatory (Chile), at the High Energy Stereoscopic System site (Namibia), and at the Siding Spring Observatory (Australia). Each of these sites contains two mounts, with each of them holding four Takahashi astrographs with individual apertures of 180 mm. The HAT consortium is also advancing the {HATPI} Project of an all-sky camera consisting of 63 optical units on a single mount.\n\n\\runinhead{{WASP}} ({Wide Angle Search for Planets}, see \\citeads{2006PASP..118.1407P} for an instrument description; Smith et al.  \\citeyearads{2014CoSka..43..500S}\nfor a review). This consortium operates two instruments: {SuperWASP}-North, since 2004 at Roque de los Muchachos Observatory on the Canary Island of La Palma, and {WASP-South}, since 2006 at the South African Astronomical Observatory. A predecessor instrument, WASP0, was operated during the year 2000 on La Palma. SuperWASP-North is an array of 8 cameras covering 480 degrees of sky with each exposure; WASP-South is a close copy of it. WASP is currently the ground based search that has detected the most planets, among them several (such as WASP-3b, 12b, 43b) that stand out for their excellent suitability for deeper characterization work, due to their short orbital period and\/or large size.\n\n\\runinhead{{Kelt}} The `{Kilodegree Extremely Little Telescope}' has to date been the most successful survey using very wide field detectors (with a {\\it fov} of $26^\\circ$ x $26^\\circ$) with  commercial photographic optics of short focal length. Kelt-North operates since 2005 from Winer Observatory, Arizona, and KELT-South since 2009 from Sutherland, South Africa. Both instruments use a CCD camera with an 80mm\/f1.8 Mamya lens.\n\n\n\n\\runinhead{{NGTS}} The {Next-Generation Transit Survey} \\citepads{2013EPJWC..4713002W,Wheatley:2017ab} is operated by a consortium of seven institutions from Chile, Germany, Switzerland, and the United Kingdom. After testing in La Palma and at Geneva Observatory, operations started in 2016 at ESO's Paranal Observatory. NGTS employs an automated array of twelve 20-centimeter f\/2.8 telescopes on independent mounts, sensitive to orange to near-infrared wavelengths (600 \u2013- 900 nm). It is a successor project to WASP that achieves significantly better photometric precision (Fig~\\ref{Fig_NGTS_WASP}), but with a  focus on late type stars. Its first planet discovery has been the most massive planet known to transit an M-dwarf \\citepads{2017arXiv171011099B}. Simulations for a 4-year survey predict the discovery of about 240 planets, among them about 20 planets of 4 $R_\\mathrm{Earth}$  or less \\citepads{2017MNRAS.465.3379G}\n\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[width=7cm]{Fig_NGTS_WASP.pdf}\n\n\\caption{Single transit observations of the hot Jupiter WASP-\n4b with one NGTS telescope unit (top) and WASP (bottom). From \\citetads{Wheatley:2017ab}, reproduced with permission.}\n \\label{Fig_NGTS_WASP}\n\\end{center}\n\\end{figure}\n\n\\runinhead{CoRoT} Named after `{Convection Rotation and Transits}', this was the first space mission dedicated to exoplanets. Launched in December 2006 by the French space agency {CNES} and partners into a low polar orbit for a survey lasting initially 4 years, it surveyed 163 665 targets distributed over 26 stellar fields in two opposite regions in the galactic plane, with survey coverages lasting between 21 and 152 days \\citep{megapaper}. In May 2009, its first data processing unit failed and CoRoT's {\\it fov} was reduced to half, while the failure of the other unit in Nov. 2012 caused the end of the mission. Its most emblematic discovery was CoroT-7b, the first transiting terrestrial  planet \\citepads{2009A&A...506..287L\n\n\\runinhead{Kepler} This NASA mission was launched in 2009 into an Earth trailing orbit, for a mission of 4 years to survey a single field of 170,000 stars, principally for the presence of Earth-sized planets. Kepler has discovered the majority of currently known exoplanets, with discoveries that have revolutionized the field of exoplanets. In contrary to the planets found by any other transit survey, only a small fraction (3\\%) of Kepler planets are Jupiter-sized ($ \\geq 0.9 R_{jup}$), while the vast majority are Earth or Super-Earth sized ones. Science operations under the 'Kepler' denomination ended in May 2013 when two of the spacecraft's reaction wheels failed and its pointing become unreliable.\n \n\\runinhead{{K2}} In March 2014, the Kepler spacecraft was returned into service under the K2 name. Its observing mode was adapted to  the reduced number of reaction wheels, surveying fields near the ecliptic plane for about 80 days each \\citepads{2014PASP..126..398H}. Planets found by K2 have a rather similar size-distribution to Kepler, albeit with a somewhat larger fraction of Giant planets (8\\% are larger than  0.9R$_{jup}$). K2 is expected to end around Oct. 2018, when the spacecraft runs out of fuel. \n  \n\\runinhead{{TESS}} The `{Transiting Exoplanets Survey Satellite}' by {NASA} aims to scan about 85\\% of the entire sky for transits across relatively bright stars \\citepads{2015JATIS...1a4003R}. Most areas will be covered by pointings lasting 28 days. The spacecraft harbors 4 wide-field telescopes that cover jointly a stripe of the sky of 24$^\\circ$ by 96$^\\circ$. TESS is expected for launch in spring 2018 into an elliptical orbit with a 13.7-day period in a 2:1 resonance with the Moon's orbit, for a mission of 2 years.\n\n\\runinhead{{PLATO}} This {ESA} mission, named after '{PLAnetary Transits and Oscillation of stars}', is expected to be launched in 2026 into an orbit around the L2 point, to perform during at least 4 years a  survey of several large sky-areas \\citep{2014ExA....38..249R}. The mission's core sample are 15\\ 000 stars of $ 8 \\leq m_V \\leq 11$ while a secondary `statistical' sample includes 245\\ 000 targets up to $m_V \\approx 16 $. PLATO will have four groups of detectors, each with six cameras that all point to the same {\\it fov}. Between the groups there is a partial overlap due to which areas near the center of the common {\\it fov} will be covered by all 24 cameras while outer zones will be covered by 6 or 12 cameras only. Two additional \"fast\" cameras with rapid cycle-times and color-filters will survey the brightest stars of 4 -\u2013 8 $m_V$.\n\n\\subsection{Surveys for planets of low-mass stars}\n\nSeveral surveys, which are not listed in Table 1, have been designed specifically for the detection of planets around {low mass stars}, and in particular, {M-stars}. Given the difficulties to detect planets in the {habitable zone} of solar-like stars, planet-searches around such stars provide an alternative path for the detection of potentially habitable planets (e.g. \\citeads{2007AsBio...7...85S}).\nTheir small size permits that terrestrial planets produce transits that are deep enough to be observable from moderate ground-based instruments. Also, the habitable zone around these stars corresponds to orbital periods of a few days to weeks, making habitable planets' transits shorter, more frequent, and hence easier to detect than for solar-type stars. Disadvantages of low-mass stars as targets are however a flux variability that is exhibited by most of them, and the sparsity of such stars with sufficient apparent brightness. As a consequence, these detection projects are not performed as wide-field surveys, but as searches that point to selected target stars, which are covered sequentially. As such, these projects cover relatively few targets and have only a small planet catch, but may provide discoveries of large impact towards our knowledge of potentially habitable planets.\n\n\\runinhead{{MEarth}} This project operates since 2008 eight 40 cm telecopes at Mount Hopkins, Arizona, and since 2014 a similar setup at Cerro Tololo, Chile \\citepads{2012AJ....144..145B}.  MEarth has discovered several small planets, among them LHS1140b, a  planet of 1.4 $R_\\mathrm{Earth}$ in the habitable zone of an M dwarf at a distance of 10.5 parsec \\citepads{2017Natur.544..333D}.\n\n\\runinhead{{TRAPPIST} \/ {SPECULOOS}}  The `TRAnsiting Planets and PlanetesImals Small Telescope' survey consists of two 60 cm robotic telescopes, one operting since 2010 at ESO's La Silla Observatory, Chile, and one since 2016 at Oukaimden Observatory, Marocco. It has the dual objective of transit detection and the study of comets and other small bodies in the Solar System \\citepads{2014acm..conf..240J}. Its outstanding discovery has been the TRAPPIST-1 system of seven planets, with some of them in the habitable zone, around an ultra-cool M8 dwarf at a distance of 12 parsec \\citepads{2017Natur.542..456G}. TRAPPIST is also a prototype of the SPECULOOS (Search for habitable Planets EClipsing ULtra-cOOl Stars) project, whose first phase will consist of four 1m robotic telescopes at ESO's Paranal Observatory.\n\n\\section{Conclusion}\n\nIn the year 2003, K. Horne predicted the success of transit surveys in a paper entitled 'Hot Jupiters Galore'. It took longer than expected to get to that point, and required the understanding and resolution of several subtle issues affecting these surveys,\nbut today the paper's title has become reality and the discovery of transiting planets is common place. This applies not only to Hot Jupiters but also to planets across the entire size regime and has been a consequence of the continued refinement of observing techniques and of the development of new instruments, both ground and space based.\n\nAt the time of writing, the transit method is expected to remain the largest contributor towards the discovery of new planets and planet systems, with several ambitious ground and space-based searches under way. Planet systems found in transit searches will also continue to provide the motivation for the continued development of instruments and observing techniques, which take advantage of the opportunities for deeper insights that transiting systems offer. In that sense, systems found by transit surveys will continue as a basic nutritient of the field of exoplanet science. \n\nFor further reading about transits as a tool to detect and characterize exoplanets, we refer to the  reviews by \\citetads{2010exop.book...55W}\nand by \\citetads{2016ASSL..428...89C}\nand to a book dedicated to transiting exoplanets by \\citetads{2010trex.book.....H}.\n\n\n\n\\begin{acknowledgement}\nFinancial support by the Spanish Spanish Secretary of State for R\\&D\\&i (MINECO) is acknowledged by HD under the grant ESP2015-65712-C5-4-R and by RA for the Ram\u00f3n y Cajal program RYC-2010-06519, and the program RETOS ESP2014-57495-C2-1-R and ESP2016-80435-C2-2-R. This contribution has benefited from the use of the NASA Exoplanet Archive and the Extrasolar Planets Encyclopaedia and the authors acknowledge the people behind these tools.\n\\end{acknowledgement}\n\n\n\\bibliographystyle{spbasicHBexo} \n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section*{Acknowledgment}\nThis paper is supported by National Natural Science Fund for Distinguished Young Scholars (No. 61525201) and General Program of National Natural Science Foundation of China (61972006).\n\n\\bibliographystyle{model5-names}\n\n\\section{Framework}\n\\label{framework}\n\n\\begin{figure}\n\\includegraphics[width=0.48\\textwidth]{pic\/framework.png}\n\\caption{NLI2Code framework}\n\\label{fig-framework}\n\\end{figure}\nAs Figure \\ref{fig-framework} shows, the \\textsc{NLI2Code} framework consists of three components.\nIn the offline part, we construct a natural language interface as pairs of functional features and code patterns.\nIn the online part, the user solves tasks by selecting functional features and our synthesizer completes the corresponding code patterns into well-typed code snippets.\nIn the rest of this section, we will discuss the three components separately.\n\n\\subsection{Functional Feature Extractor}\nExtracting functional features is the first step in our framework.\nA functional feature is a brief description of certain library functionality in verb phrase form.\nNowadays, libraries typically provide multiple platforms for developers and users to communicate, such as mailing lists, issue tracker system, and posts from online forums like Stack Overflow.\nThese communication records are the natural corpus to extract functional features because they contain rich information about how libraries are used.\nIn our framework, all verb phrases from the discussions are considered as candidate functional features.\nWe issue two challenges to get usable functional features:\n\\begin{itemize}\n\\item Noises. As Figure \\ref{fig-so} shows, phrases like \\emph{want to} and \\emph{try many things} are unrelated to library functionalities and have little semantic information. Such phrases should be pruned off. \n\\item Diversity. Functionalities could be expressed in different ways. \\textit{e.g.} \\emph{set an Excel cell color} and \\emph{set the color of an Excel cell} in Figure \\ref{fig-so}.\nFurthermore, users could use different words which makes the phrases lexically different. \\textit{e.g.} \\emph{change the cell color}.\nSuch phrases with the same semantic information need to be clustered and normalized.\nOtherwise, the generated natural language interface will be verbose and repetitive.\n\\end{itemize}\n\nIn this work, we applied a filtering pipeline to remove noise phrases, considering stop words, the structure, and the context of the phrases.\nTo cluster similar phrases, we designed a normal form to extract the core action and objects in verb phrases.\nAfter normalization, phrases with the same content or merely lexically different are merged.\nHere we define two important properties for the extracted functional features:\n\\begin{itemize}\n\\item Accurate: Each functional feature should clearly correspond to certain library functionality.\n\\item Complete: The set of all functional features should cover the library functionalities as much as possible.\n\\end{itemize}\n\n\\begin{figure}\n\\includegraphics[width=0.45\\textwidth]{pic\/so.png}\n\\caption{Functional features in Stack Overflow}\n\\label{fig-so}\n\\end{figure}\n\n\\subsection{Code Pattern Miner}\nFunctional features organize library functionalities in a list of verb phrases.\nAlthough many posts from the user forums naturally provide code examples, these examples usually cannot be reused as-it.\nIn fact, most code examples are only intended to describe the main idea of a solution to the original question, which could be difficult to be understood by others \\citep{DBLP:conf\/icsm\/TreudeR17}.\nFurthermore, a recent analysis shows that online code examples usually have quality problems such as missing control constructs and incorrect order of API calls \\citep{api-misuse}.\nAnother analysis on 914,974 Java code snippets from Stack Overflow shows that only 3.89\\% of them are parsable \\citep{compilable}.\n\nA practical way to improve the quality of code examples is to detect similar API usage in a larger codebase.\nA code pattern is a code template describing that in a certain usage scenario, some API elements are frequently called together.\nCompared to a single code example in the original post, a code pattern exploits the commonalities among similar programs, which reduces the risk of unknown consequences.\nMoreover, code patterns naturally hint users which part of the code to modify because they leave variations among the programs as unfilled parts.\nCommon variations include hard-coded strings and magic numbers.\nA common procedure for code pattern mining is as follows:\n\\begin{itemize}\n\\item construct a code corpus\n\\item abstract code into a certain data structure (\\textit{e.g.}, call sequence, abstract syntax tree, data flow graph)\n\\item apply the corresponding frequent pattern mining algorithm on the corpus and transform the frequent items back to code\n\\end{itemize}\n\n\\subsection{Synthesizer}\nCode patterns are incomplete because they usually miss local information.\nExisting IDEs (Integrated Development Environment) usually provide a simple code completion feature.\nHowever, such completion typically only considers one step of computation, which means that the recommendation result is a single variable or method.\nIn fact, a missing parameter may require a method chain to get the desired result.\nFurthermore, each method in the chain may require new parameters to synthesize.\nThese efforts suggest a general direction for the synthesizer in \\textsc{NLI2Code}:\ngiven a programming context $\\Gamma$ and the desired type $\\tau$, synthesize the entire type-correct expression with type $\\tau$ from the context.\nFormally, find expression $e$ such that $\\Gamma\\vdash e: \\tau$.\n\nWe conclude two solutions for the synthesizer.\nThe first one is called the type-directed search \\citep{PLDI12:completion, insynth}, which enumerates all possible expressions with the desired type.\nSince the searching space is usually large, heuristic functions are often used to guide the search process.\nThe second solution recommends expressions according to the statistical analysis of a large code corpus.\nTo synthesize the desired expression, users can benefit if they are recommended with expressions frequently used under a similar context. \n\nTo understand the potential and feasibility of our framework, we instantiated it as a tool \\textsc{NLI4j} to reuse Java libraries.\nIn the following three sections, we will separately introduce our implementation of the three components.\n\\subsection{RQ1: Filtering Pipeline}\nAs the first step of our algorithm, \\textsc{NLI4j} extracts all the verb phrases from user discussions and then select functional features by filtering unrelated phrases.\nThis subsection discusses the output of our filtering pipeline on the labeled dataset \\textit{$SO_{small}$}.\n\n\\subsubsection{Methodology}\nWe first combine all the three filters (\\textit{i.e.} stop word filter, context filter, and structure filter) to filter verb phrases.\nThe results are compared to the manually labeled results on the dataset \\textit{$SO_{small}$}.\nWe automatically compare the results with a script that simply matches the textual contents.\nTo avoid the mistakes caused by trivial details in natural language (\\textit{e.g.} tenses of verbs, the plural form), instead of asking the annotator to label the benchmarks from scratch, \nwe provide the extracted verb phrases and let the annotator select the functional features from the phrases.\nIf the provided phrases already missed certain functional features, the verdict of this sentence will be a failure even before comparison. \n\nFurthermore, to evaluate the importance of each filter, we created three new filtering pipelines by removing one filter at a time.\nThen, we evaluated the three modified pipelines using the same script.\n\n\\subsubsection{Results}\nFrom the 500 sentences, our extractor extracted 1,360 verb phrases using the Stanford NLP toolkit.\nWe fed the phrases to our filter pipeline and got 315 functional features.\nFor 93\\% (465 out of 500) sentences, the automatically extracted functional features matched the labeled ones in the benchmark.\nOur tool missed 41 functional features and gave 12 wrong features in the remaining 35 sentences.\nTable \\ref{label-result} summarizes details of the results for each library.\nFor each library, we list 1). the number of verb phrases mined from the sentences, 2). the number of functional features after filtering, and 3). the number of sentences which the filtered results match the benchmarks.\nFrom the result, we did not notice significant variations between different libraries.\nHowever, it is possible that our fixed stop words can cause some false negatives when a new library is specified, since a stop word could be a domain-specific concept or action for the new library.\nIn that case, a customized stop word list is recommended.\n\n\\begin{table}\n    \\centering\n    \\caption{Filtering results for the five libraries}\n    \\vspace{0.2cm}\n    \\label{label-result}\n    \\begin{tabular}{l  r  r  r}\n        \\hline\n        \\multirow{2}*{\\textbf{\\footnotesize Library}} & \\multirow{2}*{\\textbf{\\footnotesize \\# Phrases}} & \\multirow{2}*{\\textbf{\\footnotesize \\# Features}} & \\textbf{\\footnotesize \\# Correct} \\\\ \n        & & & \\textbf{\\footnotesize Sentences} \\\\\n        \\hline\n        jsoup & 245 & 55 & 96 \\\\\n        apache-poi & 277 & 81 & 92 \\\\\n        neo4j & 290 & 75 & 87 \\\\\n        deeplearning4j & 284 & 68 & 96 \\\\\n        eclipse-jdt & 264 & 36 & 94 \\\\\n        \\hline\n        \\bfseries all & \\bfseries 1,360 & \\bfseries 315 & \\bfseries 465 \\\\\n        \\hline\n    \\end{tabular}\n\\end{table}\n\nWe checked each of the 35 failed sentences and summarized two main reasons for the mistakes, which resulted in both missing and wrong functional features:\n\\begin{itemize}\n    \\item \\emph{Preprocessing of natural language.}\n    We found in more than half of the failed sentences, the NLP toolkit did not produce the correct verb phrase list as expected.\n    \\item \\emph{Tangled votes.}\n    Some phrases were upvoted and downvoted at the same time, and our current weights for the filters lead to a wrong decision for these phrases.\n\\end{itemize}\n\nThe first reason is an external factor to our tool.\nWe found the Stanford NLP toolkit sometimes failed to split the sentences correctly when the punctuation characters are not correctly used.\nAlso, a common case for failed POS tagging is when verbs appear at the beginning of sentences.\nFor the second reason, as there were both upvotes and downvotes in our filter pipeline, sometimes they are tangled and bring mistakes in the functional feature recognition.\nFor example, the phrase \\emph{``return the node of the highest score''} was missing from the sentence \\emph{``With Cypher, I'm trying to return the node of the highest score.\"} because it was downvoted for using a stop word \\emph{return} and upvoted for the context (with a preceding Q\\&A expression \\emph{I'd like to}).\nMachine learning approaches could help in such a scenario by assigning proper weights for the three filters (all one point in our current implementation).\nHowever, consider the small size of the annotated sentences and the fact that the current algorithm is accurate for most sentences, we did not apply machine learning approaches at present.\n\nTo evaluate the importance of each filter, we create three new filtering pipelines by removing one filter at a time.\nThe results are displayed in the first three rows of Table \\ref{tab-modified} and the last row combines all the three filters.\nWhen the stop word filter is removed, the number of wrong features rapidly raises to 478 as the first row shows.\nThe context filter upvotes the verb phrases following Q\\&A expressions, as a result, the filter pipeline tends to give a lower score for each phrase after removing this filter.\nAs the second row shows, the number of missing features without the context filter is the largest.\nThe third row depicts the result for removing the structure filter, which also brings more incorrect features.\n\n\\begin{table}\n    \\centering\n    \\caption{Results for different combinations of the three filters}\n    \\label{tab-modified}\n    \\vspace{0.2cm}\n    \\begin{tabular}{l  r  r  r}\n        \\hline\n        \\textbf{\\footnotesize Filter} & \\textbf{\\footnotesize \\#Correct} & \\textbf{\\footnotesize \\#Wrong} & \\textbf{\\footnotesize \\#Missing}\\\\\n        \\textbf{\\footnotesize Combinition} & \\textbf{\\footnotesize Sentences} & \\textbf{\\footnotesize Features} & \\textbf{\\footnotesize Features}\\\\\n        \\hline\n        context+structure & 120 & 478 & 21 \\\\\n        word+structure & 414 & 10 & 103 \\\\\n        word+context & 389 & 97 & 36 \\\\\n        \\hline\n        all filters & 465 & 12 & 41\\\\\n        \\hline\n    \\end{tabular}\n\\end{table}\n\n\\mybox{\\emph{Answer for RQ1:} \nOn a labeled dataset containing five hundred sentences, our filtering pipeline correctly filters\n unrelated verb phrases for 465 (93\\%) sentences. All the three filters contribute to the performance\n and the stop word filter is proved to be the vital factor. }\n\n\\subsection{Controlled Experiment}\nWe conducted a controlled experiment on the library \\texttt{apache-poi} to see whether our tool can improve the efficiency of reusing libraries in real-world programming.\nWe also recorded the ranking of the expressions accepted by users to evaluate the performance of our synthesizer.\n\\subsubsection{Methodology}\n\\begin{figure*}\n\\centering\n\\includegraphics[width=0.95\\textwidth]{pic\/study_ui.png}\n\\caption{UI for our controlled experiment. The user is invoking a functional feature.}\n\\label{fig-ui}\n\\end{figure*}\nTo evaluate the utility and effectiveness of programming with \\textsc{NLI4j}, we invited 8 participants to solve real-world programming tasks using the tool.\nAll the participants were familiar with the Java programming language and were divided into two groups.\nThe newcomer group consisted of five participants new to the library \\texttt{apache-poi}.\nThe rest three participants once built client projects with \\texttt{apache-poi} and they formed the expert group.\nThe logic and usage of \\textsc{NLI4j} were briefly introduced to all the participants in advance.\n\nWe prepared five specific programming tasks for the participants to solve.\nPrototypes of the tasks were randomly picked from an online tutorial website\\footnote{https:\/\/www.tutorialspoint.com\/apache\\_poi}.\nWe concretized the tasks for two reasons.\nFirst, some tasks require specific configurations to be automatically validated. \nFor example, we concretized the task \\emph{``create blank workbook''} by specifying the file name and the path to save it.\nSecond, some tasks in the tutorial are supposed to teach users how to manipulate a class for multiple subtasks. Separating the subtasks makes it more executable for composing solutions and validators.\nTable \\ref{tab-tasks} lists the tasks with a brief description and the number of API elements invoked in the code example from the tutorial.\nOn average, one task in our experiment invokes 5.4 API elements.\nFigure \\ref{fig-ui} shows the user interface of our controlled experiment.\nEach task has three components: a task description with a detailed hint, a solution file with some pre-defined variables, and a validator program.\nAll tasks consider the fill-in-the-blanks approach, which meant the participants needed to fill the solution file by implementing the missing functions.\nA task is considered to be accomplished if the validator returns the accepted page.\nThe tool for our controlled experiment is available in the published online artifacts.\n\n\\begin{table}\n    \\caption{Five tasks for participants to solve with \\textsc{Apache-POI}}\n    \\vspace{0.2cm}\n    \\begin{tabular}{c|l|c}\n    \\hline\n    \\bfseries Id & \\bfseries Task description & \\bfseries \\#invoked APIs\\\\\n    \\hline\n    1 & create blank workbook & 4\\\\\n    2 & write into a spreadsheet & 3\\\\\n    3 & set cell color & 6\\\\\n    4 & set italic font and font color & 7\\\\\n    5 & create hyperlink to URL & 7\\\\\n    \\hline\n    \\end{tabular}\n    \\label{tab-tasks}\n\\end{table}\n\nWe allowed all participants to visit online resources such as Q\\&A forums and search engines when solving tasks, but we recorded the number of pages they opened in the process.\nTwo settings were configured for the coding environment, one equipped with the \\textsc{NLI4j} plugin and the other without it.\nParticipants were assigned at random to each programming task and each coding environment, and thus there was no proper balance.\nNo participants were assigned to the same task with different coding environments.\nFor the participants who used \\textsc{NLI4j}, their interaction with the plugin was recorded.\nRecall that our synthesizer would recommend synthesized expressions to users, we recorded whether the user accepted the recommendation and the ranking of the expression that they used.\nFinally, the overall task duration and the number of websites viewed was recorded to facilitate data analysis.\n\n\\subsubsection{Results}\n\nTable \\ref{tab-user} shows the results of the controlled experiment.\nColumns (1) and (2) display the participant's index and the reported programming expertise (N stands for the newcomer, and E for the expert).\nColumns (3) and (4) display the task and the code environment (STD stands for the standard IDE and NLI stands for the IDE equipped with \\textsc{NLI4j} plugin).\nFinally, Column (5) refers to the overall duration of the task, and Column (6) displays the number of web pages the participant opened for the task.\n\n\\begin{table}[htb]\n    \\centering\n    \\scriptsize\n    \\caption{Summary of experiment results}\n    \\label{results}\n    \\centering\n    \\begin{tabular}{c|c|c|l|c|c}\n    \\hline\n    \\bfseries (1) & \\bfseries (2) & \\bfseries (3) & \\bfseries (4) & \\bfseries (5) & \\bfseries (6)\\\\\n    \\bfseries Id & \\bfseries Expertise & \\bfseries Task & \\bfseries Environment & \\bfseries Time(s) & \\bfseries \\#Pages\\\\\n    \\hline\n    \\multirow{5}{*}{1} & \\multirow{5}{*}{N} & 1 & NLI & 144 & 0 \\\\ \\cline{3-6} \n    &  & 2 & STD & 377 & 4 \\\\ \\cline{3-6}\n    &  & 3 & NLI & 180 & 2 \\\\ \\cline{3-6} \n    &  & 4 & STD & 520 & 6 \\\\ \\cline{3-6} \n    &  & 5 & STD & 1021 & 8 \\\\ \\hline\n    \\multirow{5}{*}{2} & \\multirow{5}{*}{N} & 1 & STD & 212 & 2 \\\\ \\cline{3-6} \n    &  & 2 & STD & 419 & 4 \\\\ \\cline{3-6} \n    &  & 3 & NLI & 306 & 3 \\\\ \\cline{3-6} \n    &  & 4 & NLI & 729 & 5 \\\\ \\cline{3-6} \n    &  & 5 & STD & 741 & 9 \\\\ \\hline\n    \\multirow{5}{*}{3} & \\multirow{5}{*}{N} & 1 & NLI & 165 & 0 \\\\ \\cline{3-6} \n    &  & 2 & NLI & 265 & 2 \\\\ \\cline{3-6} \n    &  & 3 & STD & 764 & 10 \\\\ \\cline{3-6} \n    &  & 4 & STD & 1189 & 10 \\\\ \\cline{3-6} \n    &  & 5 & STD & 812 & 7 \\\\ \\hline\n    \\multirow{5}{*}{4} & \\multirow{5}{*}{N} & 1 & STD & 315 & 5 \\\\ \\cline{3-6} \n    &  & 2 & NLI & 197 & 2 \\\\ \\cline{3-6} \n    &  & 3 & STD & 610 & 6 \\\\ \\cline{3-6} \n    &  & 4 & NLI & 576 & 3 \\\\ \\cline{3-6} \n    &  & 5 & NLI & 382 & 3 \\\\ \\hline\n    \\multirow{5}{*}{5} & \\multirow{5}{*}{N} & 1 & NLI & 190 & 0 \\\\ \\cline{3-6} \n    &  & 2 & STD & 598 & 8 \\\\ \\cline{3-6} \n    &  & 3 & NLI & 247 & 3 \\\\ \\cline{3-6} \n    &  & 4 & STD & 1186 & 5 \\\\ \\cline{3-6} \n    &  & 5 & NLI & 431 & 5 \\\\ \\hline\n    \\multirow{5}{*}{6} & \\multirow{5}{*}{E} & 1 & NLI & 90 & 0 \\\\ \\cline{3-6} \n    &  & 2 & STD & 197 & 2 \\\\ \\cline{3-6} \n    &  & 3 & NLI & 91 & 0 \\\\ \\cline{3-6} \n    &  & 4 & NLI & 410 & 1 \\\\ \\cline{3-6} \n    &  & 5 & STD & 547 & 1 \\\\ \\hline\n    \\multirow{5}{*}{7} & \\multirow{5}{*}{E} & 1 & STD & 122 & 1 \\\\ \\cline{3-6} \n    &  & 2 & NLI & 109 & 2 \\\\  \\cline{3-6} \n    &  & 3 & STD & 169 & 1 \\\\  \\cline{3-6} \n    &  & 4 & STD & 623 & 4 \\\\  \\cline{3-6} \n    &  & 5 & NLI & 315 & 0 \\\\  \\hline\n    \\multirow{5}{*}{8} & \\multirow{5}{*}{E} & 1 & STD & 176 & 1 \\\\ \\cline{3-6} \n    &  & 2 & NLI & 138 & 0 \\\\  \\cline{3-6} \n    &  & 3 & STD & 201 & 1 \\\\  \\cline{3-6} \n    &  & 4 & NLI & 484 & 5 \\\\  \\cline{3-6} \n    &  & 5 & NLI & 206 & 0 \\\\  \\hline\n    \\end{tabular}\n    \\label{tab-user}\n\\end{table}\n\nFigures \\ref{fig-compare1} and \\ref{fig-compare2} summarize the data from Table \\ref{tab-user} for newcomers. \nIt compares the average time (minutes) used and the number of web pages opened by the newcomers between two coding environments.\nOn average, newcomers without \\textsc{NLI4j} spent 674 seconds and visited 6.5 web pages for each task, which is significantly larger than the number for participants using the plugin (317.7 seconds and 2.3 pages).\nNotice that when newcomers using \\textsc{NLI4j} met the first task (\\emph{create blank workbook}), all of them solved the task without referring to any web sources.\n\n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=0.44\\textwidth]{pic\/compare1.png}\n\\caption{Comparison between the average time newcomers spent in two coding environments\\label{fig-compare1}}\n\\end{figure}\n\n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=0.44\\textwidth]{pic\/compare2.png}\n\\caption{Comparison between the average number of web pages newcomers visited in two coding environments} \n\\label{fig-compare2}\n\\end{figure}\n\nHowever, such a difference is not that obvious in the expert group.\nOn average, an expert with \\textsc{NLI4j} solved a task in 230.3 seconds, an expert without \\textsc{NLI4j} solved a task in 290.7 seconds.\nFrom later communication with the three experts, we found they were familiar with how to read and search library documentation, which can explain the number of web pages they opened was much smaller than the newcomer group.\nHowever, all of the three experts confirmed the plugin is convenient when they forgot how to use a certain API.\nMany participants reported that when they used the plugin, they could accomplish most tasks without external information and the visited web pages were only to confirm the solution.\n\nFor participants who solved tasks with \\textsc{NLI4j}, we also asked them to record the rankings of the expressions they chose to complete the code patterns.\nWe wanted to know whether our synthesizer recommended useful expressions to the participants.\nTable \\ref{tab-interaction} shows the result, the second column lists the number of interactions for each task.\nAn interaction means there is a missing variable for users to provide or select from the list of recommended expressions.\nWe use two metrics, \\textit{i.e.} MRR (Mean Reciprocal Rank) and Hit@1 to evaluate the quality of the recommendation.\nOur synthesizer could not recommend useful expressions if the missing part must be specified by users.\nFor example, the only interaction in the first task is the name of the workbook, which could be any valid string.\n\\textsc{NLI4j} failed to recommend the desired string and get 0 for both MRR and Hit@1 metrics.\nActually, among all 13 interactions for the tasks, such conditions (arbitrary values of built-in types) happened 5 times.\nFor all the other interactions, \\textsc{NLI4j} successfully recommended the desired expressions at a top-2 position.\nIn the third task, all four desired variables were recommended as the first choice.\nOn average, each task requires 2.6 interactions and the average MRR value is 0.54 and the value for Hit@1 is 0.46.\n\n\\begin{table}\n\\centering\n\\caption{Recommendation performance of the synthesizer\\label{tab-interaction}}\n\\begin{tabular}{c c c c}\n\\hline\n\\bfseries Task ID & \\bfseries \\#Interactions & \\bfseries MRR & \\bfseries Hit@1\\\\\n\\hline\n1 & 1 & 0 & 0\\\\\n2 & 2 & 0.25 & 0\\\\\n3 & 4 & 1.00 & 1.00\\\\\n4 & 4 & 0.375 & 0.25\\\\\n5 & 2 & 0.50 & 0.50\\\\\n\\hline\n\\bfseries Average & \\bfseries 2.6 & \\bfseries 0.54 & \\bfseries 0.46\\\\\n\\hline\n\\end{tabular}\n\\end{table}\n    \n\n\\subsubsection{Discussion}\nAll participants were asked to fill a simple survey after the controlled experiment.\nThe survey form is available in our published artifacts.\nForm the survey result, we can see all participants agree that using \\textsc{NLI4j} could improve their coding efficiency.\nWhen asked to compare the input form of functional features with free-form natural language, most participants (6 out of 8) reported that they preferred functional features.\nHowever, some participants raised the concern that for those functions not included in functional features, they could only turn to the free-form queries.\nBesides, one of our participants mentioned that although free-form queries are flexible, however, composing such queries from scratch could be difficult for a newcomer.\nHe mentioned that some hint like auto-completion or our functional features would be very helpful when users described their requirements.\n\nWe also asked the participants to compare code patterns used in \\textsc{NLI4j} with concrete code examples.\nOverall, most of the participants (5 out of 8) preferred code patterns with two main reasons. \nFirst, code patterns gave a more clear hint for where to modify.\nSecond, participants believed that code patterns had higher quality and were more reliable since they were mined from multiple concrete examples.\n\n\\mybox{\\emph{Answer for RQ4:}\nThe result of the controlled experiment shows that \\textsc{NLI4j} can save half of the coding time for newcomers of a library.\nFor experienced developers, \\textsc{NLI4j} can play the role of a prompter when they forget the usage of certain APIs.\nGiven a programming context, the recommended expressions from our synthesizer can effectively help developers fill the missing parts.\n}\n\\section{Extracting Functional Features}\n\\label{feature}\n\\begin{figure*}[!htb]\n\\centering\n\\includegraphics[width=\\textwidth]{pic\/task-workflow.png}\n\\caption{The process of extracting functional features}\n\\label{fig-task}\n\\end{figure*}\nAs the first component of \\textsc{NLI2Code}, we need a list of functional features to summarize frequently-used library functionalities.\nRecall that a functional feature is defined as a brief description of certain functionality in verb phrase form.\nGiven a library, our extractor takes Stack Overflow threads as input and outputs the functional feature list.\n\nFigure \\ref{fig-task} shows the workflow of our approach to extract functional features.\nWe firstly extract verb phrases from Stack Overflow threads by leveraging the syntax parsing techniques.\nThen, a set of heuristic rules is used to filter out unlikely phrases.\nConsidering that the same functionality can be expressed in different ways, we propose a normalized functional feature representation grammar to ensure the correct clustering of phrases.\nAt last, a frequent subgraph mining algorithm gSpan \\citep{gSpan} is applied to mine functional features from the clustered phrases.\n\n\n\\subsection{Candidate Functional Features}\n\nOur data source is the Q\\&A threads from Stack Overflow containing the specific tags, such as \\textit{``apache-poi''} for the POI project.\nAccording to the definition, we extract all verb phrases as candidate functional features.\nSimilar to the state-of-the-art works, we use Stanford NLP toolkits \\citep{stanford-nlp} to extract verb phrases from the raw data.\nA big problem for applying NLP tools to software documentation is that there are many code-like terms, which are error-prone in the POS (Part-of-Speech) tagging and might cause failure in the syntax tree parsing.\nThus, we replace the code-like terms with special placeholders to ensure the correct POS tagging.\nFor reproducibility, we briefly explain how we recognize code-like terms here.\nStack Overflow threads usually label code fragments with consecutive $<pre><code>$ tags or $<code>$ tag for the inline code elements.\nFor those code-like terms that are not annotated with HTML tags, we employ a set of regular expressions, which is provided by \\cite{task1} to identify them from the natural language content.\n\nAfter the preprocessing, we split the natural language text into sentences and feed each sentence to the Stanford NLP toolkit.\nThe toolkit returns a tree-structured parsing result.\nFigure \\ref{fig-syntaxtree} displays the parsing tree of a long sentence, which contains seven verb phrases (subtrees tagged with VP).\nAll the verb phrases from the parsing tree are extracted and form the initial candidate functional features, which will be filtered by a filtering pipeline.\nThe pipeline filters out phrases not related to library functions, for example, in the sentence from Figure \\ref{fig-syntaxtree}, only one phrase out of seven subtrees is valuable, which is the seventh phrase \\emph{set up the print area for the excel file}. \n\n\\subsection{Filtering Pipeline}\nThe filtering pipeline consists of three rule-based phrase filters.\nIf a phrase matches the rule of a filter, one piece of evidence will be added to the phrase.\nA piece of evidence might be counted as one vote up or one vote down or veto to accept the phrase.\nThen we collect all the evidence added to a phrase and count the vote.\nIntuitionally, we remove a phrase when the upvotes are less than the downvotes.\n\nThe first filter is based on a handcrafting stop word list.\nWe downvote three types of verb phrases because they are not likely to appear in a meaningful functional feature: \n\\begin{itemize}\n\\item Special grammatical ingredients such as auxiliary verbs (\\textit{e.g.}, be, do, have), modal verbs and pronouns usually do not have actual meanings.\n\\item Q\\&A special words. The sentences from Stack Overflow often contain trivial words for describing the questioners' requirements (\\textit{e.g.}, ask, try, need).\n\\item Programming special terms. Some programming terms, keywords in programs, or development special words are usually not part of valid functional features. (\\textit{e.g.}, extend, return and stack trace).\n\\end{itemize}\n\nThe second filter judges the phrases based on information from the context.\nThough the phrases containing Q\\&A special expressions are considered invalid, the phrases following some special Q\\&A expressions are very likely to refer to the library functionalities.\nFor example, in Figure \\ref{fig-syntaxtree}, the 5th verb phrase \\emph{\"need to ...\"} should be filtered, but the 7th verb phrase \\emph{\"set up the print areas for the excel file\"} following the Q\\&A phrase \\emph{\"need to\"} is a functional feature.\nFor each phrase, we analyze its preceding content in the same sentence.\nIf we find a match with Q\\&A special expressions before the phrase, we upvote the phrase.\n\nThe third filter is based on the structure of the phrase in the syntax tree.\nWe use syntactic structure characteristics to filter out invalid verb phrases.\nFor example, the 3rd and the 6th phrases in Figure \\ref{fig-syntaxtree} do not contain any verbs as direct children and will be filtered out with the structural filter.\nBesides, there are usually some complex sub-clauses in the verb phrase.\nWe hope to keep our generated features as concise as possible, therefore we remove the sub-clauses.\nAnother important purpose of filtering parse tree structures is to get the candidate phrases ready for the later normalization.\nThe structural filter ensures the phrase candidates are compatible with the normal form.\n\n\\subsection{Phrase Normalization}\nTo cluster verb phrases with similar meaning, we define the normal form of feature phrases as Table \\ref{bnf} shows.\nThe symbol ``[]\" denotes that a component is optional.\nGenerally speaking, a functional feature consists of at least an \\emph{Action} and an \\emph{Object}, which could be modified by a \\emph{Condition} (usually a prepositional phrase).\n\n\\begin{table}[htbp]\n\\caption{The normal form of feature phrases}\n\\label{bnf}\n\\centering\n\\begin{tabular}{l l l}\n\\hline\nFeature & ::= & Action Object [Condition]\\\\\nAction & ::= & verb [particle]\\\\\nObject & ::= & dt adj noun\\\\\nCondition & ::= & prep [verb] Object\\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\nOur pilot study summarizes the common parsing tree types that are compatible with our normal form.\nTo put this straight, Table \\ref{transformrule} lists 6 types and their transformation rules to the normal form.\nCase \\#1 is the most common case, denotes the verb phrases that consist of a verb and a noun phrase.\nParticles for the intransitive verbs are presented in case \\#2.\nCase \\#3 is another popular case that contains a verb, noun phrase (NP), and prepositional phrase (PP).\nCase \\#4 denotes the verb phrases that do not contain a direct noun phrase.\nCase \\#5 is for the noun phrases that consist of a word chain headed by a noun.\nCase \\#6 is a typical prepositional phrase.\n\n\\begin{table*}[htbp]\n    \\centering\n    \\scriptsize\n    \\caption{Transformation rules for common types of verb phrases\\label{transformrule}}\n    \\begin{tabular}{l l l l}\n    \\hline\n    \\bfseries ID & \\bfseries Grammar pattern & \\bfseries Phrase example & \\bfseries Transformation rule to normal form\\\\\n    \\hline\n    \\multirow{2}{*}{1}&\\multirow{2}{*}{VP:=VB NP}&get the cached formula value & \\multirow{2}{*}{VB:=verb; NP:=Object}\\\\\n    & & VP(VB)(NP(DT)(JJ)(NN)(NN)) &\\\\\n    \\hline\n    \\multirow{2}{*}{2}&\\multirow{2}{*}{VP:=VB PRT NP}&set up the print areas & VB:=verb;PRT:=particle;\\\\\n    & & VP(VB)(PRT(RP))(NP(DT)(NN)(NN)) & NP:=Object\\\\\n    \\hline\n    \\multirow{2}{*}{3}&\\multirow{2}{*}{VP:=VB NP PP}&delete documents from lucene index & VB:=verb;NP:=Object;\\\\\n    & & VP(VB)(NP(NN))(PP(IN)(NP(NN)(NN))) & PP:=Condition\\\\\n    \\hline\n    \\multirow{2}{*}{4}&\\multirow{2}{*}{VP:=VB PP}&iterate through the terms in a document & VB:=verb;IN(in PP):=particle;\\\\\n    & & VP(VB)(PP(IN)(NP(NP(DT)(NN))(PP(IN)(NP(DT)(NN))))) & NP(in PP):=Object\\\\\n    \\hline\n    5&NP:=word NN&Case \\#1-\\#3& Map word to dt adj noun in Object\\\\\n    \\hline\n    \\multirow{2}{*}{6}&\\multirow{2}{*}{PP:=IN NP}& \\multirow{2}{*}{Case \\#3-\\#4} & IN ::= prep (in Condition);\\\\\n    & & & NP ::= Object (in Condition)\\\\\n    \\hline\n    \\end{tabular}\n\\end{table*}\n\nAfter normalization, we rebuild the tree representation for the phrase and apply \\emph{gSpan} algorithm to mine frequent subgraphs as our final functional features.\nFurthermore, we merge two phrases if they share the same objects and their action words are synonyms judged by WordNet \\footnote{We use APIs from nltk.corpus.wordnet}.\nFigure \\ref{cluster} explains why normalization is necessary.\nFigure \\ref{cluster}.(a) is the parse tree of the verb phrase \\emph{set the print area} and Figure \\ref{cluster}.(b) depicts another candidate phrase \\emph{set up the print areas for the excel file}.\nThe original parsing trees contain many detailed grammatical ingredients, which prevent us from mining valuable common subgraphs.\nThe two largest common subgraphs between tree (a) and tree (b) are (VP (VB set) (NP)) (in red color and bold font) and (NP (DT the) (NN print)) (in blue color and underscored), which are meaningless.\nIn contrast, Figure \\ref{cluster}.(c) and Figure \\ref{cluster}.(d) are rebuilt from our normalized phrases, which omit unnecessary details like POS tags and unify the structures of the top layers.\nTheir common parts (in red and bold font) show us a reasonable result.\n\n\\begin{figure}[htb]\n    \\centering\n    \\includegraphics[width=0.43\\textwidth]{pic\/syntax-tree.png}\n    \\caption{The parsing tree of a long sentence. The seventh verb phrase is a functional feature and the others need to be filtered.}\n    \\label{fig-syntaxtree}\n\\end{figure}\n    \n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=0.43\\textwidth]{pic\/cluster.png}\n\\caption{Comparison between parse tree and normalized tree in mining frequent subtrees}\n\\label{cluster}\n\\end{figure}\n    \n\n\n\\section{Introduction}\n\\label{intro}\n\nTo implement certain functionality, developers often reuse existing libraries with the corresponding APIs.\nYet discovering the correct subset of the APIs is a major obstacle for the API users \\citep{api-hard2}.\nThe obstacle not only comes from the large size of APIs, furthermore, a real-world programming task usually requires the cooperation of multiple APIs, and each API invocation should follow strict specifications.\nFor example, for a simple functionality like ``\\textit{set color for an Excel cell}\", the desired API usage sequence using \\texttt{apache-poi} is as follows:\n\\begin{equation}\\nonumber\n    \\begin{split}\n    &Workbook.createCellStyle();\\\\\n    &CellStyle.setFillBackgroundColor(short);\\\\\n    &CellStyle.setFillForegroundColor(short);\\\\\n    &CellStyle.setFillPattern(FillPatternType);\\\\\n    &Cell.setCellStyle(CellStyle);\n    \\end{split}\n\\end{equation}\n\nTo address the issue, we promoted the concept of NLI (Natural Language Interface) for library reuse \\citep{DBLP:conf\/icsr\/ShenXZZW19}.\nWith NLI, users reuse library functionalities with high-level natural language descriptions instead of directly manipulating the detailed APIs.\nFigure \\ref{mps} summarizes the key steps of how Alice, a Java programmer, reuses the library \\texttt{apache-poi} with NLI.\nAs Figure \\ref{mps}.(a) shows, Alice starts from selecting the desired functionality from a list of natural language descriptions, which is \\emph{set cell color} in this case.\nAfter the selection, the functionality is mapped to its corresponding implementation, which is a built-in code template in NLI.\nAs Figure \\ref{mps}.(b) shows, Alice needs to provide three parameters (\\textit{i.e.} specific background color, foreground color and fill pattern) to fill the template.\nEach parameter to provide is annotated with an example expression in grey font, which is recommended by a synthesizer.\nIn fact, there are more than three missing parameters in the code template, the synthesizer has automatically created trivial ones from the current context (\\textit{e.g.} creating a \\textit{Workbook} object with the constructor).\nAfter Alice fills the parameters, a well-typed code snippet is synthesized and inserted into the editor (as Figure \\ref{mps}.(c) shows), which perfectly solves Alice's task.\n\n\\begin{figure}[!htb]\n    \\centering\n    \\subfigure[User types or selects the desired functional feature]{\n    \\begin{minipage}{8cm}\n    \\centering\n    \\includegraphics[width=\\textwidth]{pic\/mps-alias.png}\n    \\vspace{0.1cm}\n    \\end{minipage}\n    }\n    \\centering\n    \\subfigure[The code pattern exposes three parameters for user]{\n    \\begin{minipage}{8cm}\n    \\centering\n    \\includegraphics[width=\\textwidth]{pic\/mps-param.png}\n    \\vspace{0.1cm}\n    \\end{minipage}\n    }\n    \\centering\n    \\subfigure[The synthesized code snippet for the functional feature]{\n    \\begin{minipage}{8cm}\n    \\vspace{0.2cm}\n    \\includegraphics[width=\\textwidth]{pic\/mps-code.png}\n    \\end{minipage}\n    }\n    \\caption{Application of NLI for reusing \\texttt{apache-poi}}\n    \\label{mps}\n\\end{figure}\n\nFor the library reuse problem, we highlight the benefits of NLI from two aspects.\nThe first benefit is the query composition.\nIf the developer is not familiar with the library, it could be difficult to compose a high-quality query which accurately describes the desired functionality.\nFor example, Table \\ref{qa} displays a post\\footnote{https:\/\/stackoverflow.com\/questions\/53052931} from Stack Overflow.\nThe post title mistakenly mentioned the concept ``\\textit{background color}'', while the accepted answer shows the user actually desired ``\\textit{foreground color}''.\nIn NLI, we summarize the library functionalities into functional features.\nWe conjecture that, compared to composing free-form queries, the mechanism of selecting functional features is easier and can make users more confident about the results.\nThe second benefit is code quality.\nAn illustrative code example can help developers quickly understand how to implement certain functionality.\nHowever, many online code examples are only intended to express the main idea of a solution instead of being reused as-it.\nPrevious studies \\citep{DBLP:conf\/icsm\/TreudeR17, api-misuse} show that online code examples are often not self-explanatory and may have quality problems such as incorrect order of API calls.\nAs Table \\ref{qa} shows, the code snippet in the accepted answer contains only one API, which is not a complete solution for the task.\nIn NLI, we mine code patterns by exploring more usage examples of the API.\nOur hypothesis is that unveiling how APIs are used in similar program contexts could improve the code quality.\n\n\\begin{table}[t]\n    \\centering\n    \\caption{An example post from Stack Overflow}\n    \\label{qa}\n    \\begin{tabular}{p{0.46\\textwidth}}\n    \\hline\n    \\textbf{Title: Apache-POI : How to set background color of a cell when creating spreadsheet?}\\\\\n    \\hline\n    \\textbf{Question: } In Apache POI 4.0, I want to set an Excel cell background color.\n    But all I get are black cells. I've tried many things, but result is always the same.\n    How can I set the background color of an Excel cell in Apache POI 4.0 ?\\\\\n    \\hline\n    \\textbf{Answer: }Try to use below code for background style:\\\\\n    \\small{setFillForegroundColor(IndexedColors.YELLOW.getIndex());}\\\\\n    \\hline\n    \\end{tabular}\n\\end{table}\n\nTo construct and use NLI, we designed an abstract framework \\textsc{NLI2Code}, which consists of three components: a functional feature extractor, a code pattern miner, and a synthesizer.\n\\emph{Functional features} are natural language descriptions of the library functionalities.\nIn this paper, we instantiated the extractor by mining Stack Overflow since a previous survey shows it is the first option for most developers to search for programming solutions \\citep{uclsurvey}.\nIn the second component, we try to match each functional feature with a \\emph{code pattern}, which is a code template mined from multiple implementations of the feature.\nAs code patterns usually lack customized information such as local parameters, a \\emph{synthesizer} is supposed to complete them into compilable snippets.\nThe missing parameters could be synthesized from the current programming context or provided by the user.\nFinally, \\textsc{NLI2Code} combines the three components and generates well-typed code snippets for users.\n\nAround the central concept \\textsc{NLI}, the main contributions of this paper are:\n\\begin{itemize}\n\\item an algorithm to extract verb phrases describing library functionalities from Stack Overflow.\n\\item an approach to mine code patterns, with a self-designed intermediate representation for Java to eliminate coding style differences.\n\\item an instantiation of \\textsc{NLI2Code} to reuse Java libraries, with evaluation on real-world tasks to prove the feasibility of the framework.\n\\end{itemize}\n\nThe remainder of the paper is organized as follows.\nSection \\ref{framework} demonstrates the abstract framework \\textsc{NLI2Code}.\nSections \\ref{feature}, \\ref{pattern} and \\ref{synthesizer} explain our implementation of the framework, which is available from our online artifacts \\footnote{https:\/\/github.com\/nli2code\/jss-artifact}.\nIn Section \\ref{evaluation}, we conduct several experiments to check the accuracy of our algorithms and apply a controlled experiment to explain how \\textsc{NLI2Code} works in real-world development.\nSection \\ref{related} introduces the related work.\nSection \\ref{conclusion} briefly summarizes this paper.\n\\section{Synthesizer}\n\\label{synthesizer}\nAs the last component of our framework, the synthesizer completes the skeleton code into a well-typed code snippet under the current programming context.\nWe explain the details in this section for reproducibility, but we do not claim the synthesizer as a contribution.\n\nConsider each hole in the skeleton code is annotated with the corresponding type, the synthesis problem can be stated as: \ngiven a programming context, how to create an expression with the desired type $\\tau$.\nHere are the three strategies we use:\n\\begin{itemize}\n\\item pick a variable of $\\tau$ from the current context\n\\item call the constructor function of $\\tau$ \n\\item invoke a method chain and the return type of the last method is $\\tau$ \n\\end{itemize}\n\nThe last strategy is a search process. Figure \\ref{search-tree} displays an example of the search tree.\nEach node in the tree is an API type from the library and an edge connects two nodes if they are separately the caller and the return type of a method.\nThe root of the tree is the type of a declared variable and the leaves are the target type.\nA path from the root to a leaf represents a method chain which returns the desired type.\nAs Figure \\ref{search-tree} shows, there are four method chains to create a variable with type \\textit{``Cell''} from the starting type \\textit{``Workbook''}.\nDuring the search, we also considered type casting between types by analyzing the inheritance between APIs.\n\n\\begin{figure}[htb]\n    \\centering\n    \\includegraphics[width=0.42\\textwidth]{pic\/search-tree.png}\n    \\caption{Type-directed search tree}\n    \\label{search-tree}\n\\end{figure}\n\nTo guide the search process, we define a cost model as the heuristic rule.\nThe model evaluates the goodness of different ways for variable synthesis by mapping them to integers.\nUsing existing variables in context is encouraged, with zero cost.\nIf there are multiple variables with the same type, we choose the one created most recently due to software localness.\nIf a variable is the return value of a certain method, it costs 2 when the method is a constructor and 1 for else.\nThe process for variable synthesis could be recursive, which means in the process of synthesizing the current variable, the invocations require parameters that are not in the context.\nOur cost model adds the costs for synthesizing these parameters to the total cost.\n\n\\begin{equation}\n\\begin{aligned}\ncost(t) = 0,\\quad t\\ in\\ context\\ or\\ t\\ is\\ constant\n\\end{aligned}\n\\end{equation}\n\\begin{equation}\n\\begin{aligned}\ncost(f(t_1, t_2, ..., t_k)) =\nprice(f) + \\sum_{i=1}^{k}{cost(t_i)}\n\\end{aligned}\n\\end{equation}\n\\begin{equation}\n\\begin{aligned}\nprice(f) =\n\\begin{cases}\n2& \\text{f is constructor}\\\\\n1& \\text{else}\n\\end{cases}\n\\end{aligned}\n\\end{equation}\n\nIf two expressions get the same score under the cost model, we break the tie by referring to the code corpus. \nRecall that each skeleton code comes from a code corpus, we first select instances of the skeleton code from the corpus.\nFor each instance, we extract the variable to fill the hole and locate the definition of the variable by analyzing the \\textit{``def-use''} relationship.\nThe process of extraction can be recursive because the definition of a variable may use other undeclared variables.\nThe recursion terminates when we find all definitions of the variables or we meet a variable defined outside the current method body (\\textit{i.e.}, parameters of the method, global variables).\nAs a result, from each instance in the corpus, we extract an expression (\\textit{i.e.}, a method chain) to fill the hole. \nFor the two synthesized expressions with the same score, we calculate their frequency in the expressions extracted from the corpus and recommend them in the order of decreasing frequency.\n\\subsection{RQ2: Functional Features}\nIn this subsection, we generate functional features for each library from the dataset \\textit{$SO_{large}$}.\nOur benchmark is the lists of functionality descriptions from the official tutorials.\nThe evaluation checks both 1). whether each functional feature is accurate, and 2). whether each functionality in the tutorial is covered.\n\n\\subsubsection{Methodology}\nGiven the Stack Overflow corpus of a library, the output of our functional feature extractor is a list of functional features in verb phrase form.\n\nTo evaluate the accuracy, we ask two annotators to rate the extracted functional features.\nThey are requested to give a score for each feature: two points for an actual library functionality, one point for a likely functionality that requires further information to make it clear, zero point for a meaningless phrase.\nTwo annotators mark the functional features separately and afterwards discuss to reach an agreement.\nWe count all the ratings by annotators and calculate the average score for all the functional features.\n\nTo evaluate the completeness, we ask the annotators to review the functionalities in the benchmark one by one and judge whether the functionality is included in our generated functional features.\nAgain, we ask the annotators to give a score for each functionality.\nIf a functionality is included in our generated features, our result gets two points.\nIf our output includes a similar functional feature but not precise, our result gets one point.\nOtherwise, our result gets zero point for the functionality.\n\n\\subsubsection{Results}\n\nTable \\ref{tab-task1} displays the results for the accuracy of the functional features.\nThe first column is the name of the library and the second column is the number of the normalized functional features extracted from the \\textit{$SO_{large}$} dataset.\nThe third column lists the number of functional features marked with three different scores and the last column is the average score for all the functional features in this library.\nAs the last row shows, for a total of 531 functional features, 282 (53.1\\%) of them are annotated with two points, 176 (33.1\\%) are annotated with 1 point and the remaining 73 (13.7\\%) are irrelevant to library functionalities.\nThe average score shows that our functional features get approximately 1.39 points out of two.\n\nTable \\ref{tab-task2} displays the results for the completeness of the functional features.\nInstead of rating a functional feature, we rate each functionality from the official tutorial in Table \\ref{tab-task2}.\nThe result shows that our generated functional features can cover 86.3\\% (82 out of 95, 66.3\\% with two points, 20.0\\% with one point) of the functionalities in the benchmark.\nFor the functions which get one point, our annotators reported that the majority of them are caused by the fact that the tutorial summarizes several tasks into one functionality.\nFor example, the last function in the tutorial of \\texttt{apache-poi} is \\textit{``cells with multiple styles''}, which mentioned three tasks (setting color, font and cell style) at the same time.\nThere is little chance that a user will discuss the three functionalities together in a verb phrase.\nWe carefully analyzed all the 13 missing functionalities (rated as zero point) by manually searching them on Stack Overflow.\nAs a result, seven of them are never mentioned on Stack Overflow, the rest six functionalities are discussed fewer than three times in the whole corpus.\nSince we only keep the frequent normalized syntax trees during normalizing functional features, phrases with low frequency will not be included in our final result.\n\nThe results show a little fluctuation among different libraries, especially for the completeness.\nIn Table \\ref{tab-task2}, the \\texttt{eclipse-jdt} library gets the highest score of 2.00, while the \\texttt{deeplearning4j} library is rated the lowest (1.09 points).\nThe fluctuation comes from the different sizes of related threads on Stack Overflow.\nIn fact, as Table \\ref{so-dataset}, the number of threads under the tag \\texttt{deeplearning4j} is the smallest in our dataset.\nThe small size of discussions obviously affects the completeness of functional features, which is an external threat to our algorithm.\n\n\\begin{table}[t]  \n    \\centering\n    \\caption{Accuracy of the generated functional features}  \n    \\vspace{0.2cm}\n    \\label{tab-task1}\n    \\begin{tabular}{l c p{0.5cm}<{\\centering} p{0.5cm}<{\\centering} p{0.5cm}<{\\centering} c c}\n    \\hline\n    \\multirow{2}*{\\textbf{\\footnotesize Library}} & \\multirow{2}*{\\textbf{\\footnotesize \\# Features}} & \\multicolumn{3}{c}{\\textbf{\\footnotesize Score}} & \\multirow{2}*{\\textbf{\\footnotesize Average}} \\\\ \n    \\cline{3-5}\n    & & 2 & 1 & 0 & \\textbf{\\footnotesize Score} \\\\\n    \\hline \n    jsoup & 86 & 41 & 27 & 18 & 1.26\\\\\n    apache-poi & 190 & 116 & 48 & 26 & 1.47\\\\\n    neo4j & 119 & 61 & 40 & 18 & 1.36\\\\\n    dl4j & 33 & 16 & 14 & 3 & 1.39\\\\\n    eclipse-jdt & 103 & 48 & 47 & 8 & 1.39\\\\\n    \\hline\n    {\\bfseries all} & {\\bfseries 531} & {\\bfseries 282} & {\\bfseries 176} & {\\bfseries 73} & {\\bfseries 1.39} \\\\\n    \\hline\n    \\end{tabular}\n\\end{table}\n\n\\begin{table}[t]  \n\\centering\n\\caption{Completeness of the generated functional features}\n\\vspace{0.2cm}\n\\label{tab-task2}\n\\begin{tabular}{l c p{0.5cm}<{\\centering} p{0.5cm}<{\\centering} p{0.5cm}<{\\centering} c}\n    \\hline\n    \\multirow{2}*{\\textbf{\\footnotesize Library}} & \\multirow{2}*{\\textbf{\\footnotesize \\# Functions}} & \\multicolumn{3}{c}{\\textbf{\\footnotesize Score}} & \\multirow{2}*{\\textbf{\\footnotesize Average}} \\\\ \n    \\cline{3-5}\n    & & 2 & 1 & 0 & \\textbf{\\footnotesize Score} \\\\\n    \\hline\n    jsoup & 13 & 10 & 3 & 0 & 1.77 \\\\\n    apache-poi & 46 & 30 & 12 & 4 & 1.56\\\\\n    neo4j & 9 & 7 & 1 & 1 & 1.67 \\\\\n    dl4j & 21 & 10 & 3 & 8 & 1.09 \\\\\n    eclipse-jdt & 6 & 6 & 0 & 0 & 2.00\\\\\n    \\hline\n    {\\bfseries all} & {\\bfseries 95} & {\\bfseries 63} & {\\bfseries 19} & {\\bfseries 13} & {\\bfseries 1.52} \\\\\n    \\hline\n\\end{tabular}\n\\end{table}\n\n\\mybox{\\emph{Answer for RQ2:} \nBy comparing the functional features with the official tutorials,\n we found that 86.2\\% (458 out of 531) functional features are accurate.\n Furthermore, the features can cover 86.3\\%(82 out of 95) of the functionalities listed in the official tutorials.\n}\n\n\n\\section{Conclusion}\n\\label{conclusion}\nThis paper promotes the concept of NLI (Natural Language Interface) for library reuse.\nTo construct and use NLI, we design a framework with three components (\\textit{i.e.}, functional feature extractor, code pattern miner, and synthesizer).\nWe instantiate the three components as a tool \\textsc{NLI4j} to reuse Java libraries.\nThe accuracy of our extracted functional features is 86.2\\% and can cover 86.3\\% of functionalities provided by the official tutorials.\nBy comparing with existing code pattern miner, \\textsc{NLI4j} can mine more accurate and complete code patterns.\nFinally, a controlled experiment with eight participants on five real-world tasks shows that our tool can save half of the coding time for newcomers of the library.\nFrom the practical perspective, our framework promotes the efficiency of reusing libraries.\nFrom the academic perspective, our framework lays out a design space of building the natural language interface for libraries, which would hopefully inspire research in this area.\n\n\\section{Evaluation}\n\\label{evaluation}\n\nIn this section, we evaluate \\textsc{NLI4J} from three perspectives, corresponding to the three components of the framework.\nFirst, to evaluate the accuracy and completeness of the functional features, we compare the extracted functional features with the library functionalities provided by the official tutorials.\nSecond, to evaluate the quality of code patterns, we use the code examples from the official tutorials as benchmarks and compare our mining algorithm with two existing pattern mining tools \\citep{OOPSLA15, api-misuse}.\nThird, we evaluate the synthesizer with a controlled experiment on \\texttt{apache-poi}.\nIn the study, we implement an IDE plugin by putting all the three components together and investigate whether the plugin could save programmers' time to solve real-world tasks.\n\nOur research questions are as follows:\n\\begin{itemize}\n    \\item \\textit{$RQ_1:$ How well does our filtering pipeline perform on selecting functional features from user discussions?}\n    This question aims at accessing whether our filtering pipeline is effective to filter unrelated verb phrases.\n    Furthermore, we investigate the importance of each filter in the process.\n    \\item \\textit{$RQ_2:$ To what extent is \\textsc{NLI4j} able to provide accurate and complete functional features?}\n    This question evaluates the accuracy and completeness of the normalized functional features.\n    Here, accuracy refers to each functional feature should clearly correspond to a functionality.\n    The completeness refers to the capability of the generated functional features to cover frequently-used library functionalities.\n    \\item \\textit{$RQ_3:$ How does our code pattern mining algorithm perform compared to existing mining tools?}\n    This research question is related to the quality of the mined code patterns.\n    Given the same codebase, we compare our mined code patterns with two existing mining algorithms, which separately abstract source code into syntax trees and sequences.\n    \\item \\textit{$RQ_4:$ To what extent is \\textsc{NLI4j} able to promote the efficiency to solve real-world programming tasks?}\n    Finally, this research question directly investigates the usefulness of \\textsc{NLI4j} in real-world development.\n\n\\end{itemize}\n\nIn the following, we first introduce our datasets and benchmarks.\nThen, for each research question, we detail our evaluation methodology and results in an individual subsection.\n\n\\input{sections\/6a_datasets}\n\\input{sections\/6b_label}\n\\input{sections\/6c_feature}\n\\input{sections\/6d_pattern}\n\\input{sections\/6e_userstudy}\n\\input{sections\/6f_threats}\n\n\\section{Related Work}\n\\label{related}\nThe idea of \\textsc{NLI2Code} contributes to the large body of work on API comprehension and software reuse.\nIn addition, each of the three components has benefited from related work in the corresponding domain, which will be summarized in this section separately.\n\n\\subsection{Information extraction from software artifacts}\nSeveral researchers have succeeded in extracting high-quality software specifications from software artifacts using NLP techniques.\n\\cite{zhong09} proposed an approach for inferring specifications from API documentation by detecting actions and resources through machine learning.\nTheir evaluation showed relatively high precision, recall, and F-scores for five software libraries, and indicated potential uses in bug detection.\n\\cite{concept} presented an NLP-based approach to extract and organize concepts from software identifiers in a WordNet-like structure through tokenization, part-of-speech tagging, dependency sorting, and lexical expansion.\n\\cite{api-tutorial} introduced an approach to select relevant tutorial fragments for APIs, which combined the topic model and the PageRank algorithm.\nMore closely to our goal, summarizing software artifacts with functional explanations, \\cite{faq} designed an approach to extract FAQs from mailing lists and forums.\nThe approach applied the LDA algorithm to extract topic models from the data which are used for the creation of topic-specific FAQs.\n\\cite{task1} defined the concept of task as a specific programming action that has been described in the documentation.\nIndexing long documents with high-level tasks can help users quickly locate the part they care about.\nFurthermore, \\cite{task2code} developed a tool that can map tasks to code snippets from Stack Overflow answers.\nIn \\textsc{NLI2Code}, we normalize the free-form tasks into a set of pre-defined functional features and enhance concrete code examples into abstract code patterns, considering the quality of Stack Overflow code examples are controversial \\citep{api-misuse}. \n\n\\subsection{Code pattern mining}\nCode patterns are abstract code examples with metavariables or other components to be completed by users.\nModern IDEs usually integrate relevant features to define widely-used code patterns, such as live template feature in IntelliJ IDEA and SnipMatch in Eclipse.\nSeveral studies \\citep{api2, api3} applied statistical methods to automatically mine code patterns since source code was shown to be highly repetitive \\citep{naturalness}.\nThe common workflow for code pattern mining first abstracts source code into a well-designed data structure and then apply the corresponding frequent pattern mining algorithm.\n\\cite{fse14:idiom} presented \\textsc{Haggis}, a system for mining code patterns that was built on techniques from statistical natural language processing.\n\\textsc{Haggis} transformed source code into abstract syntax trees and applied Bayesian probabilistic tree substitution technique to get code patterns.\nThe mined patterns were proved to be accurate and meaningful and the author mentioned part of the patterns were accepted by the Eclipse SnipMatch project.\nTo detect API misuse in online forums, \\cite{api-misuse} developed a tool \\textsc{ExampleCheck} to compare API usages in the forum with code patterns mined from large codebases.\nThe authors designed a data structure called the structured call sequence, which enriched API invocations with syntax like guard conditions and control flow statements.\nSuch enrichment is vital because most API misuses in online code examples suffer from missing guard conditions and exception handling and \\textsc{ExampleCheck} could effectively find these misuses.\n\nCompared with existing works, which are designed to solve a particular problem, \\textsc{NLI2Code} is designed as an abstract framework, which does not specify the approach to mine code patterns.\nCode abstraction designed in existing tools may rely on properties of their problems and cannot be easily generalized to others.\n\n\\subsection{Program synthesis from natural language}\nProgram synthesis is the task of automatically finding a program in the underlying programming language that satisfies the user intent expressed in the form of some specification \\citep{synthesis-overview}.\nThis problem has been considered the holy grail of computer science since the inceptions of AI in the 1950s.\nProgram synthesis works diverse in the form of specification, including partial data structures \\citep{pbp}, test cases \\citep{pbe}, natural language \\citep{t2api, keyword} and their combination \\citep{IJCAI15}.\nDespite its ambiguity, the natural language specification is the most flexible one and requires the smallest effort to compose.\nExisting synthesis tools with natural language input either recommend related APIs \\citep{demomatch, ASE17:bot} or compilable snippets \\citep{usage}.\n\\cite{OOPSLA15} defined a free-form specification that allowed users to write natural language queries and use names of local variables.\nGiven a specification, they mapped it to a method and expanded the method with a PCFG model trained from large codebases.\n\\cite{codehint} developed a dynamic and interactive program synthesis tool \\textsc{CodeHint}, which was integrated into the Eclipse IDE.\n\\textsc{CodeHint} allowed users to execute the recommended code snippets and refine the snippets iteratively.\n\n\\subsection{Datasets and Benchmarks}\nTo answer the research questions, we collect data for five Java libraries:\nan html extraction library (\\texttt{jsoup}), a source code parser (\\texttt{eclipse-jdt}), \na library manipulating Microsoft documents (\\texttt{apache-poi}), a deep learning toolkit (\\texttt{deeplearning4j}) and a graph database platform (\\texttt{neo4j}).\nIn addition to being widely used, these five libraries cover different domains of programming, from the front-end html parsing to the back-end database manipulation.\n\nTo construct NLI for a given library, our tool requires 1). related threads from Stack Overflow, and 2). client code reusing the library APIs.\n\nStack Overflow provides a tag for each of the five libraries (\\textit{e.g.} tag \\textit{``jsoup''} for the \\texttt{jsoup} library).\nFor each library, we crawl all the threads containing tag \\textit{``java''} and the library-specific tag.\nSince our functional feature extractor processes a single sentence at a time, we extract textual contents of the threads and split the text into sentences using the Stanford NLP toolkit.\nThe sentences form our first dataset \\textit{$SO_{large}$}.\nTable \\ref{so-dataset} lists the number of the threads and the split sentences in \\textit{$SO_{large}$}.\nFurthermore, we extract a smaller dataset \\textit{$SO_{small}$} by randomly sampling 100 sentences for each of the five libraries.\nDuring the sampling, we remove sentences that are shorter than 15 characters, since such sentences are usually mistakenly split and seldom contain functional features.\nAs a result, the dataset \\textit{$SO_{small}$} contains 500 sentences.\nBased on our theoretical definition of the extraction process, the first author manually labels the functional features for each sentence in \\textit{$SO_{small}$}.\n\nFor client code, we build the dataset by downloading all the client repositories using the Github APIs \\footnote{https:\/\/api.github.com\/search\/repositories}.\nGiven a library, the query we used is restricted as follows: the body is the name of the library (\\textit{e.g.}, jsoup), the programming language is specified as Java, and each repository should have at least five stars.\nTable \\ref{client-dataset} lists the number of the client repositories we download and the number of the source files from the repositories.\n\nTo evaluate the generated NLI, a list of library functionalities and their implementations are required as benchmarks.\nWe turn to the official tutorial for each of the five libraries.\nThe names of the tutorials vary between libraries, (\\textit{e.g.} cookbook, developers' guide), and we organize each tutorial as a list of functionalities.\nEach functionality is a pair consisting of a concise description and a code example.\nWe filter the functionalities with too long code examples (\\textit{i.e.} more than 20 lines of code after removing the comments) because instead of discussing a specific feature, such long examples are more likely to describe a topic or a complete procedure to reuse the library.\nAfter the filtering, we treat all the left official functionalities as benchmarks in our evaluation.\nFor each library, Table \\ref{benchmarks} lists the number of the functionalities and the average lines of a code example (LoC) in the benchmarks.\n\n\\begin{table}\n    \\centering \\caption{Overview of the Stack Overflow dataset}\n    \\vspace{0.2cm}\n    \\label{so-dataset}\n    \\begin{tabular}{l r r}\n        \\hline\n        \\textbf{\\footnotesize Library} & \\textbf{\\footnotesize \\# Threads} & \\textbf{\\footnotesize \\# Sentences}\\\\\n        \\hline\n        jsoup & 649 & 2,780\\\\\n        apache-poi & 2,496 & 8,046\\\\\n        neo4j & 1,600 & 8,144\\\\\n        deeplearning4j & 290 & 1,310\\\\\n        eclipse-jdt & 805 & 3,461\\\\\n        \\hline\n        \\bfseries all & \\bfseries 5,840 & \\bfseries 23,741\\\\\n        \\hline\n    \\end{tabular}\n\\end{table}\n\n\\begin{table}\n    \\centering\n    \\caption{Overview of the client code dataset}\n    \\vspace{0.2cm}\n    \\label{client-dataset}\n    \\begin{tabular}{l r r}\n        \\hline\n        \\textbf{\\footnotesize Library} & \\textbf{\\footnotesize \\# Repositories} & \\textbf{\\footnotesize \\# Source Files}\\\\\n        \\hline\n        jsoup & 119 & 5,077\\\\\n        apache-poi & 239 & 21,601\\\\\n        neo4j & 291 & 37,428\\\\\n        deeplearning4j & 48 & 7,470\\\\\n        eclipse-jdt & 26 & 34,254\\\\\n        \\hline\n        \\bfseries all & \\bfseries 723& \\bfseries 105,830\\\\\n        \\hline\n    \\end{tabular}\n\\end{table}\n\n\\begin{table}[!htb]\n    \\centering\n    \\caption{Benchmarks from the offcial tutorials}\n    \\vspace{0.2cm}\n    \\label{benchmarks}\n    \\begin{tabular}{l r r}\n        \\hline\n        \\textbf{\\footnotesize Library} & \\textbf{\\footnotesize \\# Functionalities} & \\textbf{\\footnotesize Average LoC}\\\\\n        \\hline\n        jsoup & 13 & 4.1\\\\\n        apache-poi & 46 & 12.3\\\\\n        neo4j & 9 & 2.9 \\\\\n        deeplearning4j & 21 & 10.9\\\\\n        eclipse-jdt & 6 & 18.0\\\\\n        \\hline\n        \\bfseries all & \\bfseries 95 & \\bfseries 10.3\\\\\n        \\hline\n    \\end{tabular}\n\\end{table}\n\\subsection{RQ3: Code Pattern}\nIn this section, we focus on evaluating the performance of our code pattern mining algorithm.\nWe start the evaluation from some examples and then compare our miner with two existing pattern mining tools.\n\n\\subsubsection{Examples}\n\nFigure \\ref{fig-patternexp} shows five code patterns that \\textsc{NLI4j} mines.\nA symbol with $\\$$ denotes that there is a missing part in the code pattern.\nTo be more specific, a $<\\$HOLE>$ represents a missing variable and a $<\\$BODY>$ represents a missing code block.\nThe reader will observe the immediate usefulness of the code patterns for learning API usage.\n\n\\begin{figure}[t]\n\\begin{lstlisting}[language=Java]\n\/\/ parse text from html\nDocument document_1 = Jsoup.parse(<$HOLE1>);\ndocument_1.select(<$HOLE2>).first().text();\n\\end{lstlisting}\n\n\\begin{lstlisting}[language=Java]\n\/\/ create an embedded database\nGraphDatabaseFactory factory_1 = \n    new GraphDatabaseFactory();\nGraphDatabaseService service_1 = \n    factory_1.newEmbeddedDatabase(<$HOLE1>);\n\\end{lstlisting}\n\n\\begin{lstlisting}[language=Java]\n\/\/ configure a network\nMultiLayerConfiguration configuration_1 =\n    new NeuralNetConfiguration.Builder()\n    .seed(<$HOLE1>).iterations(<$HOLE2>)\n    .list().layer(<$HOLE3>).build();\n\\end{lstlisting}\n\n\\begin{lstlisting}[language=Java]\n\/\/ merge cells\nCellRangeAddress address_1 = new\n    CellRangeAddress(\n    <$HOLE1>, <$HOLE2>,\n    <$HOLE3>, <$HOLE4>\n);\n<$HOLE5>.addMergedRegion(address_1);\n\\end{lstlisting}\n\n\\begin{lstlisting}[language=Java]\n\/\/ save workbook\nWorkbook wb_1 = new HSSFWorkbook();\ntry {\n    wb.write(<$HOLE1>);\n} catch (IOException e) { <$BODY> }\n\\end{lstlisting}\n\n\\caption{Example code patterns for functional features\\label{fig-patternexp}}\n\\end{figure}\n\n\nAs Figure \\ref{fig-patternexp} shows, a code pattern usually describes the frequent combination of API elements.\nThe fourth code pattern (\\textit{i.e., ``merge cells''}) denotes that a cell region is managed by the class $CellRangeAddress$, which is usually invoked with another method $addMergedRegion$.\nTo instantiate a $CellRangeAddress$ object, four parameters are required to specify the left top and the right bottom corners of the region.\nSome patterns contain control flow statements besides API invocations, such as the last example \\textit{``save workbook''} in Figure \\ref{fig-patternexp}.\nThe code pattern not only summarizes the correct APIs to invoke, but also hints that the method $write$ needs to handle an exception.\nThe specific way to handle the exception is left to the user in a $<\\$BODY>$ block.\n\n\\subsubsection{Methodology}\n\nTo evaluate the performance of our pattern mining algorithm, we use code examples from the official tutorials as the benchmark.\nFrom the total 95 functionalities in the benchmarks, we first remove the 13 functionalities that are not covered by our functional features (\\textit{i.e.} the functionalities with zero point in Table \\ref{tab-task2}).\nThen we removed another 13 functionalities because our algorithm failed to match a correct API from the corresponding functional feature.\nTable \\ref{pattern-dataset} shows the 69 left functionalities.\n\n\\begin{table}[htb]\n    \\centering\n    \\caption{The number of functionalities to mine code patterns}\n    \\vspace{0.2cm}\n    \\label{pattern-dataset}\n    \\begin{tabular}{l r r}\n        \\hline\n        \\multirow{2}*{\\textbf{\\footnotesize Library}} & \\textbf{\\footnotesize \\# Covered} & \\textbf{\\footnotesize \\# Functions to}\\\\ \n        & \\textbf{\\footnotesize Functions} & \\textbf{\\footnotesize Mine Patterns} \\\\\n        \\hline\n        jsoup & 13 & 12\\\\\n        apache-poi & 42 & 36\\\\\n        neo4j & 8 & 7\\\\\n        deeplearning4j & 13 & 10\\\\\n        eclipse-jdt & 6 & 4\\\\\n        \\hline\n        \\bfseries all & \\bfseries 82 & \\bfseries 69\\\\\n        \\hline\n    \\end{tabular}\n\\end{table}\n\nAs there is no universal metric to measure the quality of code patterns, we approximated the quality by calculating the \\emph{Jaccard distance}.\nTo be more specific, we built a set of the invoked APIs in the code pattern and another set of the invoked APIs in the official example.\nJaccard distance is the metric to calculate the differences between two sets as follows:\n\\begin{equation}\ndis(X,Y)=1-\\frac{|X\\cap Y|}{|X\\cup Y|}\n\\end{equation}\n\nWe compare our pattern mining algorithm with two existing tools, \\textit{i.e.}, \\textsc{anyCode} and \\textsc{ExampleCheck}.\n\\textsc{anyCode} expands an API element into a Java expression with a pre-trained PCFG (Probabilistic Context Free Grammar) model.\nThe second tool \\textsc{ExampleCheck} is designed to check API misuse from the Stack Overflow.\nThe rationale behind is to compare API examples from Stack Overflow with the mined API usage patterns from Github.\nWe choose the two tools because their abstractions for source code are representative. \n\\textsc{anyCode} abstracts code into tree-based structure PCFG, and \\textsc{ExampleCheck} abstracts code into the sequence structure SCS (\\textit{i.e.}, Structured Call Sequence).\nTo make the comparison meaningful, we configure the settings for all three tools as follows:\n\\begin{itemize}\n    \\item \\textit{The same codebase.}\n    All three tools are provided with the same codebase, which is all the usage examples for a given API. On average, the codebase for each API contains 217 source code files.\n    \\item \\textit{The same threshold.}\n    We set the threshold (5\\%) for the minimum frequency of a pattern to be mined from the codebase.\n\\end{itemize}\n\n\\subsubsection{Results}\nTable \\ref{pattern-result} shows the results of the experiments.\nGiven a tool and a library, we list the average Jaccard distance between the mined code patterns and the code examples from the benchmarks.\nOverall, \\textsc{NLI4j} achieves the minimum average Jaccard distance (0.29), which proves the code patterns mined by our tool are more similar to the official code examples.\nIn the experiment, we found that \\textsc{anyCode} can only synthesize quite short patterns.\nSome code examples in our benchmark contain more than ten API invocations, as a result, the performance of \\textsc{anyCode} on these cases are not as good as the other two tools.\n\\textsc{ExampleCheck} and \\textsc{NLI4j} can generate more complete and complex code patterns.\nHowever, as we explained before, in such cases, the sequence structure \\textsc{ExampleCheck} used is too strict for pattern mining.\nFor example, for the color setting task in Apache POI, we found that two APIs (\\textit{i.e.}, \\textit{``setFillForegroundColor''} and \\textit{``setFillPattern''}) could be swapped.\nHowever, swapping two APIs will result in two different subsequences for \\textsc{ExampleCheck} and it failed to produce the complete pattern.\n\nBesides, we observed the fluctuation among different libraries.\nFor \\texttt{deeplearning4j} and \\texttt{eclipse-jdt}, we found the Jaccard distances of all the three tools are significantly larger than the rest three libraries.\nIn fact, we found the style of API usage varies among different libraries.\nFor example, \\texttt{deeplearning4j} often requires a long method chain to configure the network from all aspects.\nHowever, users of \\texttt{deeplearning4j} may skip some aspects in their client code, as a result, the mined patterns are visibly shorter than the official code examples.\nFor \\texttt{eclipse-jdt}, many functionalities of the library apply the visitor pattern (a design pattern). \nAll the code abstractions of the three tools are designed to analyze code snippets inside a method, which could not represent the visitor pattern well.\n\n\\begin{table}\n    \\centering\n    \\caption{Comparison of three pattern mining tools}\n    \\vspace{0.2cm}\n    \\label{pattern-result}\n    \\begin{tabular}{l  c  c  c}\n        \\hline\n        \\textbf{\\footnotesize Library} & \\textbf{\\footnotesize anyCode} & \\textbf{\\footnotesize ExampleCheck} & \\textbf{\\footnotesize NLI4j} \\\\\n        \\hline\n        jsoup & 0.33 & 0.23 & 0.15 \\\\\n        apache-poi & 0.42 & 0.27 & 0.21 \\\\\n        neo4j & 0.35 & 0.29 & 0.29 \\\\\n        deeplearning4j & 0.79 & 0.68 & 0.56 \\\\\n        eclipse-jdt & 0.85 & 0.81 & 0.81 \\\\\n        \\hline\n        \\bfseries Average & \\bfseries 0.48 & \\bfseries 0.36 & \\bfseries 0.29 \\\\\n        \\hline\n    \\end{tabular}\n\\end{table}\n\n\\mybox{\\emph{Answer for RQ3:} \n    Given the same codebase, our generated code patterns are more complete and accurate than two existing pattern mining tools.\n}\n\n\\subsection{Threats to Validity}\n\\textbf{Internal validity: }\nOur four research questions covered the key steps in constructing NLI (\\textit{i.e.}, functional feature extraction, code pattern mining, and the synthesizer).\nHowever, we could not evaluate all the details in the implementation because our framework has a quite long workflow.\nFor example, we did not discuss parameter tuning for our frequent pattern mining algorithm.\nIn our current implementation, we set the frequency threshold as 5\\% to mine code patterns and it works well on our datasets.\nHowever, the best threshold may vary under different datasets.\n\nFor the case study, although we have considered the help of \\textsc{NLI4j} varies for different users.\nThe total number of participants is relatively small. We plan to put our tool in the daily development of developers and collect more user data in our future work.\n\n\\textbf{External validity: }\nWe selected five libraries from different domains, which covered the front-end parsing tool, the back-end database, and popular toolkits.\nThe evaluation shows that our tool can mine accurate functional features (accuracy of 86.2\\%) and high-quality code patterns.\nHowever, since our tool is feature-oriented, its performance on libraries with clear features are usually better than the libraries which are designed as frameworks.\nFurthermore, API invocation is not the only way of library reuse. \nSome libraries heavily rely on other design or syntax, such as design patterns and annotations (\\textit{e.g.}, the OGM mechanism in \\textit{neo4j}).\nThus, the first external validity is the generalization of our framework to other libraries.\n\nWe carefully chose the datasets in our experiment so the findings could be generalized as much as possible.\nWe selected Stack Overflow to extract functional features because it is one of the most popular platforms to search for programming tasks \\citep{uclsurvey}.\nThere are a lot of discussions about API usage from the site, and many previous studies encourage us to select it as the corpus (\\textit{e.g.}, \\citep{treude16, examplestack}). \nNonetheless, not all the libraries are active on Stack Overflow.\nAlthough most of our design is not specific to Stack Overflow, the performance may differ when other forms of user discussions are used as input.\nRegarding the codebase for mining code patterns, we downloaded all repositories with at least 5 stars from Github and the number of source code files is more than 105K.\nIn our experiment, we found a code corpus containing one hundred files is good enough to mine high-quality patterns.\nHowever, we only evaluated on Java APIs and it may not be representative to all the languages and libraries.\n\n\\section{Mining Code Patterns}\n\\label{pattern}\nAfter getting the list of functional features, we map the features to their implementation.\nAlthough Stack Overflow often provides direct code snippets along with the descriptions, such examples are usually incomplete (\\textit{i.e.} only mentioned the key APIs instead of the complete solution) and may have quality problems such as incorrect order of API calls \\citep{api-misuse}.\nTo augment these code examples, our main idea is to unveil what has been done in more similar programs.\nTo be specific, we first map each functional feature to a related API and construct a code corpus containing usage examples of the API.\nThen, we abstract each code example in the corpus into a data flow graph and apply existing frequent subgraph mining algorithm to mine the patterns.\nFinally, we transform the mined patterns (\\textit{i.e.}, frequent subgraphs) back to the text-form code.\n\n\\subsection{Code Corpus Construction}\nWe first match each functional feature with a related API and then construct a code corpus by searching usage examples of the API.\nThe rationale behind this design decision is that although code snippets on Stack Overflow suffer the quality problems, they often mentioned the correct API to use.\nSuch APIs could be a starting point to find the complete solution.\n\nGiven a functional feature, we view all the code elements mentioned in the same Stack Overflow thread (\\textit{i.e.}, contents inside the $<code>$ tag) as candidate APIs to match.\nThe metric we use to select the related API is based on the lexical similarity.\nFirst, we split the API names according to the camel-case rule and stem the splitted tokens.\nFor each API, we calculate the number of overlapped tokens between its name and the functional feature. (\\textit{e.g.}, the number is 2 for the API \\textit{``setFillForegroundColor''} and the feature \\textit{``set cell color''} since the overlapped tokens are \\textit{``set''} and \\textit{``color''}).\nThe API with the most overlapped tokens is selected as the matched one and we break the tie by counting the occurrence number of certain API in the thread.\n\nAfter selecting a related API, we further extract usage examples of the API from client repositories downloaded from Github in advance.\nIf a source code file from the repositories contains the desired API, we add it to the corpus.\n\n\\subsection{Code Abstraction}\n\n\\begin{figure}[htb]\n\\lstset{language=Java}\n\\begin{lstlisting}\n\/\/ snippet 1\nstyle.setFillForegroundColor(short);\nstyle.setFillPattern(SOLID_FOREGROUND);\n\/\/ snippet 2\nstyle.setFillPattern(SOLID_FOREGROUND);\nstyle.setFillForegroundColor(short);\n\\end{lstlisting}\n\\caption{Example snippets where the sequence model fails}\n\\label{poi-order}\n\\end{figure}\n    \n\\begin{figure}[htb]\n    \\centering\n    \\includegraphics[width=0.45\\textwidth]{pic\/dataflow-graph.png}\n    \\caption{An example data flow graph with type annotations}\n    \\label{fig-dataflow}\n\\end{figure}\n\n\\begin{figure*}[htb]\n    \\centering\n    \\includegraphics[width=0.9\\textwidth]{pic\/bnf.png}\n    \\caption{Grammar of intermediate representation for Java code}\n    \\label{fig-bnf}\n\\end{figure*}\n\nSource code can be viewed as plain text, however, such simple representation is sensitive to trivial differences (\\textit{e.g.}, variable names, indentations) and affects the performance of pattern mining.\nThus, before applying the frequent pattern mining algorithm on the constructed code corpus, we need to abstract the code into a certain data structure.\nCommon abstractions include the AST (abstract syntax tree) and the method call sequence.\nAs the natural representation of source code, the AST is sensitive to the coding style differences (\\textit{e.g.}, using different keywords \\textit{``for''} and \\textit{``while''} to implement loops).\nRecently, \\citep{swim, api-misuse} applied the \\textit{structured call sequence} as the code abstraction to mine API-centric code patterns.\nThe sequence model allows users to define the interested parts of code such as API invocations and guard conditions.\nHowever, sometimes changing the order of certain API calls does not affect the program behavior.\nFor example, the two snippets in Figure \\ref{poi-order} behave in the same way.\nIn this case, the sequence model is too sensitive to capture the complete pattern.\n\nCompared to the AST and method call sequence, the graph model is more expressive to describe interactions between variables \\citep{nguyen2009graph}.\nIn this paper, we augment the data flow graphs by annotating the data nodes with API types.\nVertices in a data flow graph can be divided into data and operations.\nTo better fit the library reuse problem, we annotate each data node with the corresponding API type name.\nFigure \\ref{fig-dataflow} displays the same dataflow graph generated for the two snippets from Figure \\ref{poi-order}.\nThe annotations \\textit{``CellStyle''} and \\textit{``FillPatternType''} are API types from the library \\texttt{apache-poi}.\nAlso, the different order of method invocations did not affect their abstractions because they share the same data flow.\n\nWe follow the common workflow to generate data flow graphs from source code.\nFirst, we generate a self-designed intermediate representation (IR) from Java code.\nThe IR is independent of the source language and is designed to be conducive for further processing.\nSecond, we generate control flow graphs from the IR, furthermore, the graphs are refined into the static single assignment (SSA) form.\nThird, the control flow graphs are transformed into the data flow graphs.\nThe last two steps are the implementation of existing algorithms \\citep{DBLP:conf\/cc\/BraunBHLMZ13} and won't be discussed here.\nThe rest of this subsection will discuss our self-designed IR, which is shown in Figure \\ref{fig-bnf}.\n\n\\begin{figure}[htb]\n\\lstset{language=Java}\n\\begin{lstlisting}\n\/\/ for-each style iteration\nfor (String s: lst) {\n    cnt++; foo(cnt, s);\n}\n\/\/ iterator style iteration\nIterator<String> iter = lst.iterator();\nwhile (iter.hasNext()) {\n    cnt += 1; foo(cnt, iter.next());\n}\n\\end{lstlisting}\n\\caption{Two example snippets of different coding styles}\n\\label{fig-codingstyle}\n\\end{figure}\n\nThere are two reasons to design our own intermediate representation:\nFirst, most existing tools to generate Java IR behave poorly on the incomplete code snippets.\n\\textit{e.g.}, The famous tool \\textsc{Soot}\\footnote{https:\/\/github.com\/Sable\/soot} requires all dependencies of the current file to generate the corresponding intermediate code.\nWhile our tool only requires that the input snippets can be taken as a compilation unit, which can be a method without the wrapper class, or even just a block containing several method invocations.\nSecond, the syntax of Java is complex, there are multiple ways to write code sharing the same behavior.\nAs Figure \\ref{fig-codingstyle} shows, to increments a variable, one can write \\emph{cnt++} or \\emph{cnt += 1}.\nTo iterate a list of strings, a for-each loop or an iterator are both correct.\nSuch details have not been normalized in existing tools, while our IR can eliminate some common coding style differences.\nAs a result, the two snippets will result in the same representation in our intermediate code.\nTo be specific, both increment operations are represented by $\\langle PstOp\\rangle$`++' defined in Figure \\ref{fig-bnf}.\n\nAfter generating data flow graphs for the corpus, we apply gSpan algorithm again to mine frequent subgraphs as code patterns.\n\n\\subsection{Skeleton Code}\nAs the last step of pattern mining, we recover the graph-form code patterns into the skeleton code.\n\\begin{mydef}\n    Skeleton code is an incomplete syntax tree, which is obtained by removing trees rooted at $v_1, v_2, ..., v_n$ from a complete syntax tree.\n    Each $v_i$ is a node from the complete syntax tree and we name such nodes as holes in the skeleton code.\n\\end{mydef}\nFor example, Figure \\ref{fig-skeletontree} is the skeleton code recovered from the graph in Figure \\ref{fig-dataflow}.\nNodes wrapped in the dotted line are holes in the syntax tree.\nFigure \\ref{fig-skeleton} shows the text form of the skeleton code.\n\n\\begin{figure}[htb]\n    \\centering\n    \\includegraphics[width=0.45\\textwidth]{pic\/skeleton-tree.png}\n    \\caption{Example skeleton code}\n    \\label{fig-skeletontree}\n\\end{figure}\n\n\\begin{figure}[htb]\n\\lstset{language=Java}\n\\begin{lstlisting}\n<HOLE1>.setFillForegroundColor(<HOLE2>);\nFillPatternType fillPatternType1 = \n    FillPatternType.SOLOD_FOREGROUND;\n<HOLE1>.setFillPattern(fillPatternType1);\n\\end{lstlisting}\n\\caption{Text-form of the example skeleton code}\n\\label{fig-skeleton}\n\\end{figure}\n\nDuring the generation of data flow graphs, we record the corresponding nodes from the syntax tree.\nTo construct the skeleton code from a data flow graph, we first list all the tree nodes included in the graph.\nThen we randomly select a syntax tree of the original source code and search the least common ancestor (LCA) of the nodes in the tree.\nAfter the search, we recover a complete syntax tree containing all the nodes from the graph.\nNaturally, the missing parts (\\textit{i.e.}, nodes not covered by the graph) in the recovered syntax tree become holes in the skeleton code.","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nAnalogue systems are used to test theories of predicted phenomena that are hard to observe directly \\cite{georgescu2014quantum_s}. Hawking \\cite{hawking1974black, hawking1975particle} predicted black-holes to thermally radiate from the quantum vacuum. Its measurement is unlikely, having a temperature inversely related to the black-hole mass. Stellar and heavier black-holes' radiation is much weaker than the cosmic microwave background (CMB) fluctuations \\cite{CMB_pedestrians,HawkingTemp}. Hypothetical microscopic primordial black-holes might emit significant Hawking radiation \\cite{halzen1991gamma}, but it is highly model-dependent, with rates seriously bounded by the lack of its observation \\cite{alexandreas1993new, fichtel1994search, linton2006new}. \n\nVolovik and Unruh \\cite{volovik2003universe, unruh1981experimental} have shown that a transonic fluid flow is analogous to the space-time geometry surrounding a black-hole, and should emit sound waves analogous to Hawking radiation. \n\nWave kinematics control the Hawking process, which appears in the presence of an effective horizon \\cite{visser1998acoustic, visser2003essential}. Black-hole dynamics and Einstein equations of gravity are not an essential requirement. The analogue of the event horizon is the surface separating the subsonic and supersonic flows. The surface gravity determines the strength of Hawking radiation and is analogous to the flow acceleration at the horizon. The horizon should also last long enough such that the modes of Hawking radiation will have well defined frequencies \\cite{visser2003essential}. \n\nMany analogues have been proposed \\cite{barcelo2011analogue, barcelo2019analogue} with realisations using water waves \\cite{rousseaux2008observation, jannes2011experimental, weinfurtner2011measurement, euve2015wave, euve2016observation, torres2017rotational}, Bose-Einstein condensates (BEC) \\cite{lahav2010realization, steinhauer2014observation, steinhauer2016observation, de2019observation}, and optics \\cite{philbin2008fiber, belgiorno2010hawking, rubino2012negative,elazar2012all,nguyen2015acoustic, bekenstein2015optical, bekenstein2017control, drori2019observation}. The analogues gave new perspectives in both gravity and the analogue systems \\cite{barcelo2011analogue}, extending Hawking's theory to wave dynamics in moving media. The universality of the Hawking effect shows it persists in real-world scenarios, where complicated dynamics replace simplified and possibly fine-tuned theories. Hawking's original derivation seems questionable, since the radiation originates from infinitely high frequencies, neglecting unknown high energy physics (known as the 'trans-Planckian problem'). The microscopic physics of the analogue systems is well known, allowing to test the role of high frequencies in Hawking predictions \\cite{jacobson1991black,unruh1995sonic}.\n\nThis paper discusses the optical analogues that use a refractive index perturbation to establish an artificial black-hole horizon. Extensive reviews of analogue gravity exist \\cite{barcelo2011analogue, barcelo2019analogue}, but they pay little attention to optical analogues and substantial progress was made after their publication. Additional useful resources include Refs. \\cite{daniele2018hawking,faccio2013analogue, leonhardt2010essential,unruh2007quantum}. This paper aims to present the main experiments that transformed the optical analogues from simple ideas to established reality. It aims to do so in the light of the recent developments, but in terms of hands-on physics. We believe that experiments reach the state where their data may lead the way for new questions and discoveries in the physics of Hawking radiation. \n\n\nSection 2. briefly describes early proposals for optical analogues using slow light and why they could not materialise. Transformation optics is also mentioned, where stationary dielectrics are viewed to change the spatial parts of the metric.\nSection 3. explains the standard theory of optical analogues discussed in this paper and the first demonstration of optical horizons. Further measurements of the frequency shift at group velocity horizons are briefly discussed, and additional related work is mentioned. \nSection 4. focuses on attempts in bulk optics rather than optical fibres, stressing the roles of group-velocity and phase-velocity \\cite{milonni2004fast} horizons. \nSection 5. discusses the first measurements of negative frequencies in optics, a phenomenon closely related to the Hawking effect. Its theory is also presented and shortly explained.\nSection 6. considers additional interpretations of the optical horizon. Theory and experiments are shown to directly relate the effect to cascaded four-wave mixing, but analysis in the time domain seems to be unavoidable. The use of temporal analogues of reflection and refraction, and numerical solutions are also mentioned. \nSection 7. discusses the first demonstration of stimulated Hawking radiation in an optical analogue, and lessons learnt from it. \nSection 8. concludes the paper with a brief outlook to the future.\n\n\\section{Early attempts}\n\nFresnel's drag \\cite{Fresnel} was an ether-based theory of light propagation in transparent media, 'confirmed' by Fizeau \\cite{fizeau}. The drag effect is just a relativistic velocity addition\\cite{rindler2006relativity}, but Fresnel's wrong theory was based on correct intuition of velocity addition. The ether was replaced by the space-time geometry and the quantum vacuum, which continued to have an intimate connection to moving media and produce puzzling phenomena \\cite{hawking1974black,hawking1975particle, fulling1973nonuniqueness,davies1975scalar,unruh1976notes}. Analogue gravity took this connection a step further, but despite theoretical progress in the 1990's, no practical realization of analogue black-holes was suggested at that time \\cite{barcelo2011analogue}.\n\nTechnology drove ideas in the right directions (optics and Bose-Einstein condensates) around the year 2000 \\cite{leonhardt1999optics,leonhardt2000slow_PRL, leonhardt2002slow_nature, garay2000sonic,garay2001sonic}. In optics, Leonhardt and Piwnicki \\cite{leonhardt1999optics,leonhardt2000slow_PRL, leonhardt2002slow_nature} suggested to slow down light such that its medium could be moved in super-luminal velocities and form a horizon. These ideas used the technology of 'slow light' \\cite{hau1999Slow_light_1,kash1999ultraslow}, where incredibly low group velocities are produced using electromagnetically induced transparency (EIT, see Fig.~\\ref{fig3}a). However, the phase velocity of 'slow light' is fast, preventing the crucial formation of a phase velocity horizon (where the media moves at the phase velocity of light. See below) \\cite{unruh2003slow}. Another problem with realising these ideas is the narrow bandwidth of light that can be slowed \\cite{unruh2003slow}, and severe absorption around it \\cite{milonni2004fast}. The inevitable conclusion was to move the medium in relativistic velocities.\n\nDespite missing key concepts of Hawking radiation, these ideas have pushed analogue gravity forward and beyond the scope of relativity (or relativitists). They showed that an analogue black-hole metric can be made in optics. Similarly, stationary dielectrics mimic spatial geometries. This interpretation inspired transformation optics, and the development of meta-materials technology extended the range of practical geometries \\cite{leonhardt2006optical, pendry2006controlling, leonhardt2006general, chen2010transformation, leonhardt2010geometry, xu2015conformal}. \n\n\\section{Changing a reference frame}\n\n\\begin{figure}[t!]\n\t\\centering\\includegraphics[width=0.9\\textwidth]{Fig1.pdf}\n\t\n\t\\caption{Main optical analogue concepts. \\textbf{(a)} A black-hole emit Hawking radiation from its event horizon: positive norm waves escape outside, while negative norm waves drift towards its singularity. The surface gravity $\\kappa$ represented by a falling weight determines the radiation's strength. \\textbf{(b)} The medium seems to flow in the pulse co-moving frame with its group velocity $u$. A pair of black-hole and white-hole horizons are formed due to nonlinear refraction index being proportional to the pulse local intensity. Positive frequency probe light is shifted, and negative frequency waves are formed at both horizons according to the dispersion relation (see Fig.~\\ref{fig2}). The magnitude of the Hawking effect is determined by the pulse steepness, being analogous to the surface gravity at the horizon (see text).}\n\t\\label{fig1}\n\\end{figure}\n\n\nThe groups of Leonhardt and K{\\\"o}nig \\cite{philbin2008fiber} started a new approach that follows a simple idea \\cite{Leonhardt2005Invent}: light itself travels at the speed of light. A light pulse (also denoted pump) travels in a dielectric medium with group velocity $u$ . In the reference frame co-moving with the pulse ('the co-moving frame'), the medium seems to flow in the opposite direction with velocity magnitude $\\left|u\\right|$ (Fig.~\\ref{fig1}b). Probe light of a different frequency differ in velocity due to dispersion. The nonlinear Kerr effect \\cite{boyd2003nonlinear} slows down the probe upon interaction with the pulse\\footnote{This has a similar effect to the flow acceleration in the fluid analogues, changing the probe velocity relative to the flow.} -- the refractive index change as $n=n_0+n_2 I$, where $n_0$ is the linear refractive index, $n_2$ is a parameter being typically  $10^{-16}\\text{cm}^2\/\\text{W}$ \\cite{boyd2003nonlinear}, and $I$ is the light intensity. A group velocity horizon forms where the probe group velocity obey $v_g=\\left|u\\right|$, blocking the probe from further entering the pump. A black-hole horizon is formed in the leading end of the pump, where the flow is directed into the pulse. Its time reversal, a white-hole horizon with outward flow, is formed in the pump trailing end \\cite{philbin2008fiber, belgiorno2011dielectric}.\n\nIf the pump is slowly varying \\cite{visser2003essential}, the probe co-moving (and Doppler shifted) frequency, \n\\begin{equation}\\label{dopplerEq}\n\\omega'=\\gamma \\left(1-n \\frac{u}{c}\\right) \\omega,\n\\end{equation}\nis conserved. Here $\\gamma=\\left(1-u^2\/c^2\\right)^{-1\/2}$ is the Lorentz factor, $c$ is the vacuum speed of light, $n$ is the refraction index, and $\\omega$ is the probe frequency in the laboratory frame. Photon pairs of Hawking radiation are produced at each horizon: one with positive $\\omega'$, and its negative partner with $-\\omega'$ \\cite{leonhardt2010essential, leonhardt2012analytical}. For positive $\\omega$, $\\omega'$ is positive only if the probe phase velocity, $v_\\phi$, is greater than $|u|$. A phase velocity horizon forms where $v_\\phi=\\left|u\\right|$ so $\\omega'=0$. The Hawking radiation outgoing from the horizon mix incoming radiation of positive and negative frequencies \\cite{leonhardt2010essential}. Quantum mechanically, it is described by a Bogoliubov transformation \n\\begin{equation}\\label{BogoliubovEq}\n\\hat{b}_\\pm=\\alpha \\hat{a}_\\pm + \\beta \\hat{a}^\\dagger_\\mp \\quad;\\quad |\\alpha|^2-|\\beta|^2=1,\n\\end{equation}\nwhere the sign of the operators equals the sign of $\\omega'$. Time dependent annihilation and creation operators for incoming modes, $\\hat{a}_\\pm,\\hat{a}^\\dagger_\\mp$ mix to form annihilation operators for outgoing modes, $\\hat{b}_\\pm$. This extracts metric energy (pump energy) to amplify the radiation, thus spontaneously creating outgoing radiation from incoming vacuum \\cite{leonhardt2010essential, drori2019observation}. The transformation parameters, $\\alpha$ and $\\beta$, give the flux of Hawking radiation. When neglecting dispersion, the radiation effective temperature is proportional to the analogue of the surface gravity -- the steepness of the pulse (giving the probe velocity gradient in the co-moving frame \\cite{visser2003essential, leonhardt2010essential}, which is related to the refractive index (and pulse intensity) gradient or rate of change \\cite{philbin2008fiber,leonhardt2010essential,belgiorno2011dielectric}).\n\nIn \\cite{philbin2008fiber}, an optical fibre called a photonic crystal fibre (PCF) provided both the desired dispersion (Fig.~\\ref{fig2}) and nonlinearity. Its unique structure guided light in a very small region -- the fibre's core \\cite{russell2003photonic, Agrawal_NLFO}. This increased the light intensity and the fibre's nonlinear response. Its nonlinear parameter was $\\gamma\\left(\\omega_0\\right) = \\omega_0 n_2 \/c A_\\text{eff} = 0.1 \\text{W}^{-1}\\text{m}^{-1}$ at $\\omega_0$ corresponding to $\\SI{780}{\\nano\\meter}$ wavelength, where $A_\\text{eff}$ is the fibre effective mode area and $\\epsilon_0$ is the vacuum permittivity \\cite{Agrawal_NLFO}. The fibre's structure was engineered to change its dispersion relation, $n(w)$, to have two points with matching group velocities \\cite{Agrawal_NLFO}: one in a normal dispersion region, where $n(w)$ is increasing; and another in an anomalous dispersion region, where $n(w)$ is decreasing. The anomalous dispersion included the pump spectra, generated by a Ti:Sapphire mode-locked laser. Self-phase modulation (SPM) due to the nonlinear refraction index counteracted the anomalous dispersion and formed stable solitons \\cite{Agrawal_NLFO}.\n\n\n\\begin{figure}[t!]\n\t\\centering\\includegraphics[width=0.9\\textwidth]{Fig2.pdf}\n\t\n\t\\caption{Schematic Doppler curve of the fibre optic analogue with phase matching conditions. Frequency $\\omega'$ at the reference frame co-moving with the pump pulse is plotted against the laboratory frequency $\\omega$ (Eq.~\\ref{dopplerEq}). The pump pulse is in a local minima, where the dispersion is anomalous. The phase matching condition of dispersive waves (DW) corresponds to conservation of $\\omega'_\\text{pump}$ (upper dotted line). Negative frequency resonant radiation (NRR) conserve $-\\omega'_\\text{pump}$ (lower dotted line. See also Fig.~\\ref{fig3}d,\\ref{fig3}f). Probe light (black-diamond) is red-shifted (white diamond) at black-hole horizon, conserving its co-moving frequency $\\omega'_\\text{probe}$ (upper solid line). At the white-hole horizon the probe (now white diamond) is blue-shifted (black diamond), as seen also in Fig.~\\ref{fig3}b. At the local maxima the group-velocity matches that of the pump, $u$. Negative Hawking radiation (NHR) conserve $-\\omega'_\\text{probe}$ (lower solid line. See also Fig.~\\ref{fig3}f). The phase horizon (PH), where the phase velocity equals $u$, corresponds to $\\omega'=0$. \n\t}\n\t\\label{fig2}\n\\end{figure}\n\n\n\nThe solitons in \\cite{philbin2008fiber} created horizons. Continuous wave (CW) probe was added to the fibre, being red-detuned from the frequency of matching group velocity (white diamond in Fig.~\\ref{fig2}). The fast probe mainly interacted with the pump trailing end, gradually slowed down, and blue-shifted (frequency up-conversion, see Fig.~\\ref{fig3}b). This pump-probe interaction is known as cross phase modulation (XPM), and induces chirp that depends on the pump pulse shape \\cite{Agrawal_NLFO}. If $\\delta n=n_2 I$ is large enough to form a horizon, the shifting probe become slower than the pulse and they separate. In the co-moving frame the probe is reflected (Fig.~\\ref{fig1}b) while conserving its co-moving frequency $\\omega'_\\text{probe}$, but not $\\omega$ (Fig.~\\ref{fig2}). This reflection demonstrated the existence of optical horizons \\cite{philbin2008fiber}. \n\nPhilbin et.al. \\cite{philbin2008fiber} used $\\SI{70}{\\femto\\second}$ duration FWHM (full width at half maximum), $\\SI{800}{\\nano\\meter}$ carrier wavelength pulses with peak power of about $\\SI{50}{\\watt}$. The PCF was $\\SI{1.5}{\\meter}$ long with core diameter smaller than $\\SI{2}{\\micro\\meter}$. The CW probe was tunable around $\\SI{1500}{\\nano\\meter}$ wavelength with $\\SI{100}{} - \\SI{600}{\\micro\\watt}$ power. Pump power was kept low to maintain a stable single soliton and reduce high-order nonlinearities, such as the Raman effect \\cite{Agrawal_NLFO}. Self-steepening was hoped to realize high Hawking temperatures. \n\nThis set-up achieved a mere $10^{-3}$ percent efficiency for probe shifting. Only $10^{-4}$ of the CW probe power was expected to interact with the pump over the $\\SI{1.5}{\\meter}$ fibre, and another order of magnitude reduction was attributed to tunnelling of the probe through the narrow pump barrier \\cite{philbin2008fiber}. While clearly showing probe blue-shifting at the white-hole horizon, this set-up could not produce detectable negative frequency partners. It was unclear whether they should form around the phase velocity horizon, where $\\omega'=0$, or around the supported frequency $-\\omega'_\\text{in}$ (Fig.~\\ref{fig2}).\n\nChoudhary and k{\\\"o}nig \\cite{choudhary2012efficient} reported probe red-shifting and studied its tunnelling. They used similar experimental parameters to \\cite{philbin2008fiber}, with tuneable $\\SI{50}{\\femto\\second}$ pump pulses and visible CW probe at $\\SI{532}{\\nano\\meter}$ (to avoid the difficulty of synchronisation). Tunnelling was minimal for probe detuning up to twice the soliton bandwidth (relative to the matching frequency), but limited pump-probe interaction kept the conversion efficiency small. Tartara \\cite{tartara2012frequency} derived both pump and probe from the same $\\SI{105}{\\femto\\second}$ source and propagated them in a $\\SI{1.1}{\\meter}$ fibre, demonstrating conversion efficiencies of tens of percents. An optical parametric amplifier produced the tuneable probe.\n\nThe Raman effect cause the pump to decelerate, and was shown to only slightly change the shifted probe spectra \\cite{robertson2010frequency}. Shifting of dispersive waves \\cite{wang2015optical,bendahmane2015observation} and trapping the probe light \\cite{nishizawa2002pulse, nishizawa2002characteristics, gorbach2007light ,hill2009evolution, wang2013soliton} were also related to the Raman effect. An optical 'black-hole laser' that use both the white and black-hole horizons was predicted and analysed \\cite{corley1999black , leonhardt2007black , faccio2012optical, gaona2017theory, bermudez2018resonant}. The horizon dynamics was also related to the formation of optical rogue waves and champion solitons \\cite{solli2007optical, demircan2012rogue , demircan2014rogue, pickartz2016adiabatic},  and the ability to form all-optical transistors \\cite{demircan2011controlling}. Similar 'front-induced transitions' were studied in other areas of photonics \\cite{gaafar2019front}, and the quest for measuring analogue Hawking radiation continued.\n\n\\section{Horizonless emissions}\nFaccio's group realized optical phase velocity horizons, without a group velocity horizon, in bulk optics \\cite{belgiorno2010hawking, rubino2011experimental}. They constructed pulses of super-luminal group velocities, by using their three dimensional nature \\cite{faccio2007conical}. A pulsed Bessel beam is one such example. It is composed of infinitely many plane waves on a cone with a constant angle $\\theta$ with the propagation axis. It can be made with an axicon lens \\cite{faccio2007conical}. At the apex of the cone, the plane waves interfere to form a bright spot that moves with super-luminal velocity that depends on $\\theta$. Belgiorno et al. \\cite{belgiorno2010hawking} used super-luminal pulses that travelled as narrow and powerful filaments inside fused silica. Looking perpendicularly to their propagation direction, they detected radiation around the phase velocity horizon -- where the radiation phase velocity matched the pulses group velocity (Fig.~\\ref{fig3}c). They could not measure along the propagation direction, because vast radiation was produced by the powerful pulses there (peak intensity was as high as $10^{13}\\text{W}\/\\text{cm}^2$ centred at $\\SI{1055}{\\nano\\meter}$ wavelength). \n\nSpurious radiation was a key issue even for observation at 90 degrees. Special care was taken to tune the radiation into spectral windows of minimal noise. Correctly identifying all the signals in such a set-up is another major challenge. Concerns were raised \\cite{schutzhold2010comment, unruh2012hawking, liberati2012quantum} and in-depth analysis related the radiation to a horizonless super-luminal perturbation, possibly linked to Hawking radiation \\cite{petev2013blackbody, finazzi2014spontaneous}. This work stressed the importance of a blocking group velocity horizon to the Hawking effect. Thermal Hawking radiation was predicted for super-luminal pulses in materials with linear dispersion at low energies (like diamond) \\cite{petev2013blackbody, finazzi2014spontaneous}, but is yet to be measured. \n\nLeonhardt and Rosenberg \\cite{leonhardt2019cherenkov} related the emission in \\cite{belgiorno2010hawking} to the physics of Cherenkov radiation\\footnote{Not to be confused with dispersive waves \\cite{akhmediev1995cherenkov}} in a surprising way. The pulse was modelled as a super-luminal light bullet \\cite{silberberg1990collapse}, and found to behave like a moving magnetic dipole that is predicted to emit Cherenkov radiation with a discontinuous spectrum \\cite{frank1942doppler, frank1984vavilov}. This discontinuity is exactly at the phase horizon -- where the effective dipole velocity equals the phase velocity of light and $\\omega'=0$ (Fig.~\\ref{fig2}). Interferences turn the discontinuity into a peak if the dipole is an extended object, like the light bullet.\n\n\\section{The role of negative frequencies}\nNegative frequencies are an integral part of Hawking radiation and can also appear as dispersive waves. Solitons emit dispersive waves (also known as resonant radiation) at a shifted frequency when disturbed by higher order dispersion. Non-dispersive three dimensional light bullets emit similar radiation \\cite{faccio2007conical}. Both emissions can be viewed to originate from self-scattering of the pulse by its nonlinear refractive index barrier. Conservation of momentum dictates the emitted frequency through a phase matching condition \\cite{dudley2006, Agrawal_NLFO}. In the reference frame co-moving with the stable pulse, this condition becomes a conservation of energy, given by the pulse co-moving frequency, $\\omega'_\\text{pulse}$ (Fig.~\\ref{fig2}). The frequency shifting at optical horizons extends this picture to the scattering of probe light. The prediction of negative Hawking modes suggested that negative dispersive waves should similarly appear. Rubino et al. \\cite{rubino2012negative} had measured this negative-frequency resonant radiation (NRR) after it was neglected and disregarded for a long time. This required very rapid (non-adiabatic) temporal changes of the pulse envelope.\n\nIntense pulses created NRR through steep shocks in two ways \\cite{rubino2012negative}: $\\SI{7}{\\femto\\second}$ high order solitons \\cite{Agrawal_NLFO} of about $\\SI{300}{\\pico\\joule}$ energy and $\\SI{800}{\\nano\\meter}$ carrier wavelength were placed in $\\SI{5}{\\milli\\meter}$ PCFs; and pulsed Bessel beams of $\\SI{60}{\\femto\\second}$ duration, about $\\SI{20}{\\micro\\joule}$ energy and $\\SI{800}{\\nano\\meter}$ carrier wavelength were sent through a $\\SI{2}{\\centi\\meter}$ long bulk calcium fluoride ($\\text{CaF}_2$), as seen in Fig.~\\ref{fig3}d. Despite NRR was seen both in optical fibres and in bulk, further work was needed to exclude other possible mechanisms for the effect -- contributions due to high order spatial modes, and possible interactions between the complex pulse and additional radiation.\n\nRubino et al. \\cite{rubino2012soliton} later used a relativistic scattering potential to directly explain NRR formation, and Petev et al. \\cite{petev2013blackbody} further related it to Hawking radiation. Conforti et al. \\cite{conforti2013negative} extended the theory to pulses in materials of normal dispersion (where the pulse experience dispersive broadening) and dominating second order nonlinearity, which effectively creates a nonlinear refractive index. The same conditions for phase matching and non-adiabatic temporal evolution were found. Analytic derivation of the NRR \\cite{conforti2013interaction} directly related it to interactions between fields and their conjugates (or the mixing of positive and negative frequency modes). It further strengthened the connection between NRR and Hawking radiation, which originate from a Bogoliubov transformation that mixes creation and annihilation operators \\cite{leonhardt2010essential, leonhardt2012analytical}. McLenaghan and K{\\\"o}nig \\cite{mclenaghan2014few} studied NRR for different PCF lengths and input chirps, and inferred UV propagation loss of $\\sim 2\\text{dB\/mm}$. We stress that the negative frequency (and negative norm) of the Hawking modes beyond the horizon is key to the Hawking amplification process \\cite{leonhardt2010essential}, extracting energy from the background metric in accordance to a Bogoliubov transformation.\n\n\\section{'It's just optics'}\nHawking radiation is a universal geometric effect that emerge due to conversion of modes at a horizon, regardless of the microscopic physics that create the background space-time geometry \\cite{visser2003essential}. The same (generalized) derivation applies for both astrophysical black-holes and analogue systems \\cite{visser2003essential, philbin2008fiber,finazzi2013quantum, jacquet2015quantum, bermudez2016hawking, linder2016derivation, jacquet2018_Thessis,jacquet2019analytical}. This established universality proved insightful for both gravity and optics (arguably solving the trans-Planckian problem and discovering negative frequencies in optics are two examples \\cite{barcelo2011analogue, barcelo2019analogue}). However, some researchers from both the optics and gravity (or quantum field theory on curved space-times) communities are still not comfortable with analogue Hawking radiation, claiming that the effect is 'just optics' \\footnote{The author have personally encountered such allegations from both communities, and believe that they partially originate from not separating 'gravity', predicted to create the black-hole event horizon, and 'kinematics', which are responsible for the Hawking effect once a horizon is formed \\cite{visser2003essential}.}. Such claims do not undermine (analogue) Hawking radiation, but complete our understanding of it. It's also possible to directly explain the effect using the underlying microscopic physics -- unknown quantum gravity for real black-holes, and nonlinear optics for the optical analogues.\n\nThe classical dynamics at optical horizons can be captured using numerical solutions that take into account the entire electric field (including negative frequencies), the dispersion relation and all nonlinearities \\cite{Agrawal_NLFO, amiranashvili2016hamiltonian, bermudez2016propagation, Raul2020inpress}. These are extensions and alternatives for solving the usual generalised nonlinear Schr{\\\"o}dinger equation (GNLSE), which is used extensively in standard descriptions of ultrafast nonlinear fibre optics \\cite{Agrawal_NLFO, dudley2006, skryabin2010colloquium}. \n\nAnother approach directly relates the phenomena to discrete photonic interactions. It uses cascaded four-wave mixing of discrete spectra, and takes the continuum limit for comparison \\cite{webb2014nonlinear, erkintalo2012cascaded}. A CW probe and a pair of beating quasi-CWs (of $\\SI{1}{\\nano\\second}$ duration) positioned symmetrically around the pump central frequency were being mixed continuously (Fig.~\\ref{fig3}e). At each step of the cascaded process, the probe shifted by the pair's detuning, and all three generated an equidistant frequency comb. A resonant amplification was produced at the frequency corresponding to conservation of $\\omega'_\\text{probe}$. Similar amplification appeared at the dispersive wave resonance, at $\\omega'_\\text{pump}$. The experiments used low cascade orders ($\\text{n}=5-7$ for the probe shift and about $\\text{n}=15$ for the dispersive waves) and were supported by numerical analysis. This picture shows how energy is being transferred from the pump to the shifting probe, by effectively absorbing pump photons of one frequency and emitting at another. The cascaded four wave mixing also details the back reaction mechanism, where the pump undergoes spectral recoil. \n\nThe studies \\cite{webb2014nonlinear, erkintalo2012cascaded} addressed the relevant phase matching conditions, but the efficiency of the cascaded process was found only in \\cite{webb2014efficiency}, for dispersive waves. Remarkably, it showed that the known concepts from horizon physics are crucial ingredients even when the pump is made of beating quasi-CWs that form a frequency comb: the mixing was analysed using (temporal) soliton fission dynamics, being efficient only when the frequency spacing between the CWs effectively generated compressing (non-adiabatic) high order solitons. The frequency-domain analysis was intractable for high cascade orders. The maximally compressed beat cycle corresponded to about $\\SI{102}{\\femto\\second}$ duration FWHM in the efficient regime, of high cascading orders. Conversion efficiencies of $10^{-4}$ over a $\\SI{100}{\\meter}$ fibre were reported.\n\nThe generation of NRR in media with quadratic nonlinearity was also related to a cascading process \\cite{conforti2013negative}, which must also be the case for cubic materials. However, negative frequencies were not demonstrated yet using a beating CW pump. It would be interesting to test how the cascading mixing behaves as it reaches negative frequencies, past the phase velocity horizon. \n\nTemporal analogues of reflection and refraction \\cite{plansinis2015temporal, plansinis2018cross} are also used to explain the frequency shifts at optical horizons. It compares the frequency change due to XPM to the wave number change during refraction. The reflection at the horizon is analogous to total internal reflection. The tunnelling through the refractive index barrier is compared to frustrated total internal reflection, where an evanescent wave extends beyond the pulse and tunnels through. The optical horizon can be seen as a temporal beam splitter for probe light (acting also as an amplifier when considering negative frequencies as well). \n\nComparing the mode mixing and squeezing of parametric amplification \\cite{gerryKnight2005QO} to the Hawking effect is also useful \\cite{leonhardt2010essential}. The origin of the two phenomena is completely different, and even in the optical analogue, simple down conversion obey different phase matching conditions that conserve total lab frequency \\cite{boyd2003nonlinear,Agrawal_NLFO} and cannot explain Hawking radiation. However, the two share intuition and the Bogoliubov transformation between incoming and outgoing modes. In both cases a pump creates 'signal' and 'idler' waves: the vacuum spontaneously generates quantum emissions, while stimulating the effect with classical light amplifies the effect for specific modes.\n\n\\section{Observing stimulated Hawking radiation}\nSpontaneous Hawking radiation originate from the quantum vacuum. Classical laser fields can replace the vacuum and stimulate the effect. Drori et al. \\cite{drori2019observation} observed stimulated negative Hawking radiation in an optical analogue (Fig.~\\ref{fig3}f). The idea of \\cite{philbin2008fiber} was used, but with more suitable pump pulses and a pulsed probe. Analysis of the fibre dispersion (schematically seen in Fig.~\\ref{fig2}) and simulations of the experiment allowed to optimise the experimental parameters. The pump was a high order few-cycle soliton that compressed and collapsed due to soliton fission \\cite{Agrawal_NLFO}. Its peak power reached a few hundred kilo-watts, with $\\SI{800}{\\nano\\meter}$ central wavelength. Very non-adiabatic dynamics generated NRR in the mid UV (Fig.~\\ref{fig3}f), at the negative of the pump co-moving frequency, $-\\omega'_\\text{pump}$. This ensured the formation of steep refractive index variations, increasing the analogous surface gravity and reducing the probability of probe tunnelling. The probe was derived from the pump's laser, and was generated through cascaded Raman scattering in a meter long PCF. Negative prechirp was used to enhance the Raman induced frequency shift \\cite{Rosenberg2020RIFS}, whose wavelength was continuously tuned up to $\\SI{1650}{\\nano\\meter}$ by varying the input power. Peak powers were around $\\SI{1}{\\kilo\\watt}$. \n\nEfficient and broad-band probe frequency shifts at the horizon accompanied negative Hawking radiation in the mid-UV, conserving the probe co-moving frequency $\\omega'_\\text{probe}$ and its conjugate $-\\omega'_\\text{probe}$, respectively. Since the fibre had strong dispersion, with different notions for phase and group velocity horizons, the spectrum was not Planckian \\cite{drori2019observation, leonhardt2012analytical, bermudez2016hawking}. Varying $\\omega'_\\text{probe}$, both signals shifted according to theory, supporting the correct interpretation of the negative Hawking radiation. By this, also the interpretation of the NRR was supported, and its analytic theory \\cite{conforti2013interaction} was generalised to include the Hawking process \\cite{Raul2020inpress}. Linear relation was verified between the probe power and that of the negative Hawking signals up to a point where the signal saturated. This saturation was related to a back-reaction of the probe on the pulse, which is a prerequisite for Hawking radiation (since its energy is drawn from the pump, or the black-hole that curves the metric). It also slightly reduced the magnitude of the NRR (Fig.~\\ref{fig3}f). \n\nThe rate of spontaneous Hawking emission was estimated based on the magnitude of the stimulated effect \\cite{drori2019observation}. It was found to be too low for measurement in the system used, calling to design an improved setup. The predicted spontaneous effect is minuscule and is overwhelmed by the noise in the system, which for the negative Hawking radiation is dominated by fluctuations of the overlapping NRR. The multi-mode nature of the PCF in the UV \\cite{Agrawal_NLFO} was found to reduce the observed signal power by up to four orders of magnitude.\n\nThe experiment \\cite{drori2019observation} showed how robust the Hawking effect is: it appeared despite the extreme nonlinear dynamics of the collapsing soliton. Since time in the co-moving frame is related to the propagation distance along the fibre, rapid variations in the pump profile do not violate the required slow evolution of the metric as long as they appear over a length scale much larger than the Hawking radiation wavelength \\cite{visser2003essential}. As such, pump deceleration due to the Raman effect could be accounted by simply correcting its central frequency. \n\n\n\\begin{figure}[!]\n\t\\centering\\includegraphics[width=0.9\\textwidth]{Fig3.pdf}\n\t\\caption{Central measurements. \\textbf{(a)} Schematic absorption (dotted line) and refractive index (solid line) for generating 'slow light' using electromagnetically induced transparency (EIT), as the inset depicts. The refractive index has small but rapid variation at the narrow resonance. The slow group velocity is inversely related to this steep change \\cite{hau1999Slow_light_1, kash1999ultraslow}. \\textbf{(b)} Frequency blue-shift of probe light at fibre optical white-hole event horizon. \\SI{70}{\\femto\\second} pump solitons were used in \\SI{1.5}{\\meter} long nonlinear PCF. A small fraction of CW probe at $\\omega_1$ is converted to $\\omega_2$, conserving its co-moving frequency, $\\omega'_\\text{probe}$. From \\cite{philbin2008fiber}; reprinted with permission from \\href{https:\/\/doi.org\/10.1126\/science.1153625}{\\textcopyright2008 AAAS}. \\textbf{(c)} Horizonless emissions from a Bessel filament creating a super-luminal refractive index perturbation in bulk silica \\cite{belgiorno2010hawking, petev2013blackbody}. The radiation was seen around the phase velocity horizon (where $\\omega'=0$) and increased with pump energy (in \\SI{}{\\micro \\joule}). The wavelength shift (black line) and broadening was in agreement with the increased nonlinear refractive index. From \\cite{belgiorno2010hawking}; reprinted with permission from \\href{https:\/\/doi.org\/10.1103\/PhysRevLett.105.203901}{\\textcopyright2010 APS} \\textbf{(d)} Negative-frequency resonant radiation (NRR) in bulk $\\text{CaF}_2$. \\SI{16}{\\micro\\joule} Bessel pump beam at \\SI{800}{\\nano\\meter} created dispersive-waves (around \\SI{600}{\\nano\\meter}) and NRR (around \\SI{350}{\\nano\\meter}) under highly non-adiabatic temporal evolution. From \\cite{rubino2012negative}; reprinted with permission from \\href{https:\/\/doi.org\/10.1103\/PhysRevLett.108.253901}{\\textcopyright2012 APS}. \\textbf{(e)} Comparison of frequency translation induced by a pump soliton (orange curve) and a pair of quasi-CW fields (purple curve). Probe light is being blue-shifted ('Idler') in a similar way in both cases, relating the effect to cascaded four-wave mixing. Similar dispersive-waves (DW) are also seen. From \\cite{webb2014nonlinear}; reprinted with permission from \\href{https:\/\/doi.org\/10.1038\/ncomms5969}{\\textcopyright2014 Springer Nature}. \\textbf{(f)} Negative frequency stimulated Hawking radiation. A compressing high-order few-cycle soliton \\cite{drori2019observation} generated horizons and NRR (green dotted-dashed curve). When a pulsed probe at \\SI{1450}{\\nano\\meter} interacted with the black-hole horizon, it red shifted (not shown) and produced negative Hawking radiation that overlapped the NRR (black solid curve). Subtracting the NRR revealed the UV Hawking signal (blue curve with 2$\\sigma$ error bars). From \\cite{drori2019observation}; reprinted with permission from \\href{https:\/\/doi.org\/10.1103\/PhysRevLett.122.010404}{\\textcopyright2019 APS}.\n\t} \n\t\\label{fig3}\n\\end{figure}\n\n\n\\section{Beyond the horizon?}\nAnalogue gravity in optics has come a long way: from erroneous visionary ideas, to careful analysis of experimental demonstrations. It drove new research directions and understandings in optics. The reality of optical horizons and negative frequencies became clear, and multiple optical interpretations made their physics more tangible. The crucial role of dispersion was stressed, determining the Hawking spectrum (Fig.~\\ref{fig2}). A group velocity horizon is blocking the radiation modes and allow their efficient conversion. A phase velocity horizon marks the support of non-trivial negative frequency modes, that allow for the Hawking amplification. The optical and other analogues, especially in water waves and BECs, provide extensive insights for gravity through concrete real-world examples. The universality of the Hawking effect separates it from gravity and high-energy physics, and emphasises the central role of classical fields to the process. This hints to more possibilities in gravity \\cite{barcelo2019analogue} and in optics \\cite{leonhardt2015cosmology}, even before going fully quantum. \n\nThe main challenge for observing the spontaneous (quantum) effect in optics is its low power. Noise from spurious radiation makes matters worse. Using knowledge from the stimulated effect \\cite{drori2019observation} could help overcome these challenges.\n\nThe demonstrated robustness of the Hawking effect is calling for new experiments to lead the way. Our increased confidence in the interpretation of the results allows to further separate from the traditional scheme of Hawking radiation, developing bolder questions and ideas. Optical technologies allow to realise wild ideas and to study them with high precision. We call for more cross-fertilisation between research of the different black-hole analogues, which might open new horizons in these fields.\n\n\\enlargethispage{20pt}\n\n\\section{Funding}\nFellowship of the Sustainability and Energy Research Initiative (SAERI) program, the Weizmann Institute of Science; European Research Council; and the Israel Science Foundation.\n\n\\section{Acknowledgements}\nI am grateful for discussions and comments from David Bermudez, Jonathan Drori and Ulf Leonhardt. I acknowledge valuable discussions with the participants of the scientific meeting 'The next generation of analogue gravity experiments' at the Royal Society (London, December 2019), and thank its organizers: Maxime Jacquet, Silke Weinfurtner and Friedrich K{\\\"o}nig.\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Frames and kinematics}\n\\section{Conventions}\n\\label{a:conv}\n\nIn this Appendix we discuss our light-cone conventions and notation. We start by reviewing the Fourier transform, the light-cone basis vectors for the longitudinal Minkowksi subspace, and the tensors needed to discuss parton and hadron dynamics in the transverse subspace. We then turn to  the conventions for the integration over the suppressed momentum component used to define the TMD fragmentation correlator and the fully inclusive jet correlators, and for the Dirac traces (or projections) needed to define the related TMD functions. For completeness, we also include a short discussion of the parton distribution correlator restricted to the spin-independent case. \n\n\n\\subsection{Fourier transform}\n\nIn order to be consistent with a large share of the literature dealing with TMD parton distribution and fragmentation functions \n(e.g. Refs.~\\cite{Bacchetta:2006tn,Mulders:2016pln,Levelt:1993ac,Mulders:1995dh}), we define the Fourier transform with a $1\/(2\\pi)^4$ factor for space-time four vector integrations, see {\\it e.g.} the definition of $\\Xi(k;\\omega)$ in Eq.~\\eqref{e:invariant_quark_correlator}. Correspondingly, we do not include such factor in four-momentum integrations, contrary to, {\\it e.g.}, Refs.~\\cite{Bjorken:1965zz,Roberts:2015lja,Roberts:2007jh,Siringo:2016jrc,Solis:2019fzm}. This, in particular, results in an additional $1\/(2\\pi)^4$ factor in Eq.~\\eqref{e:Feyn_spec_rep} and~\\eqref{e:SF_mass} with respect to the definitions in Refs.~\\cite{Bjorken:1965zz,Roberts:2015lja,Roberts:2007jh}.\n\n\\subsection{Light-cone coordinates and transverse space}\n\nIn a given reference frame, we collect the space-time components of a four-vector $a^\\mu$ inside round parentheses, $a^\\mu=(a^0,a^1,a^2,a^3)$, with $a^0$ the time coordinate. \nWe define the light-cone $\\pm$ components of the $a$ vector as\n\\begin{align}\n  a^{\\pm} = \\frac{1}{\\sqrt{2}} (a^0 \\pm a^3) \n\\end{align}\nand collect these inside square brackets: $a^\\mu = [a^-,a^+,\\vect{a}_T]$, with $\\vect{a}_T=(a^1,a^2)$ being the 2-dimensional components in transverse space. \nWe also define the transverse four-vector as $a_T^\\mu = [0,0,\\vect{a}_T]$, such that $a_T^2 = -\\vect{a}_T^2$. \nNamely, the norm of $\\vect{a}_T$ is taken according to the Euclidean metric $\\delta_T^{ij}=\\text{diag}(1,1)$, whereas the norm of $a_T$ is calculated using the Minkowski metric $g^{\\mu\\nu}=\\text{diag}(1,-1,-1,-1)$. \nNote that, in this paper, we consider highly boosted quarks and hadrons with dominant momentum component along the negative 3-axis, namely along the negative light-cone direction. Hence, we grouped the light-cone components inside the square parenthesis starting with the minus component.\n\nThe light-cone basis vectors are defined as:\n\\begin{equation}\n\\label{e:def_np_nm}\nn_{\\pm} = \\frac{1}{\\sqrt{2}} (1,0,0,\\pm 1) \\ \\ , \n\\end{equation}\nsuch that $n_+^2 = n_-^2 =0$, $n_+^\\mu n_{-\\mu} = 1$, and $a^\\pm = a^\\mu {n_\\mp}_\\mu$.  Upon considering a specific process, the basis vectors $n_{\\pm}^\\mu$ can be determined by physical quantities. For example, in inclusive deep-inelastic scattering one can choose the four-momentum of the target and virtual photon to lie in the plus-minus plane; in semi-inclusive processes the tagged hadron's momentum can replace either one, typically the photon's momentum. In semi-inclusive electron-positron annihilation into two hadrons, one typically chooses the four-momenta of both tagged hadrons. In this paper, however, we consider quark propagation and fragmentation independently of any specific process, and will study the Lorentz transformation between the different frames in which the quark hadronization mechanism can be studied (see Appendix~\\ref{a:frame_dep}). \n\nFollowing Ref.~\\cite{Bacchetta:2006tn,Mulders:2016pln}, the transverse projector, $g_T^{\\mu\\nu}$, and the transverse anti-symmetric tensor, $\\epsilon_T^{\\mu\\nu}$, are defined as:\n\\begin{align}\n\\label{e:gT_def}\ng_T^{\\mu\\nu} & \\equiv g^{\\mu\\nu} - n_+^{ \\{ \\mu} n_-^{\\nu \\} } \\\\ \n\\label{e:epsT_def}\n\\epsilon_T^{\\mu\\nu} & \\equiv \\epsilon^{\\mu \\nu \\rho \\sigma} {n_-}_\\rho {n_+}_\\sigma  \\equiv \\epsilon^{\\mu \\nu + -} \\ ,\n\\end{align}\nwhere $g^{\\mu\\nu}$ is the Minkowski metric, $\\epsilon^{\\mu\\nu\\rho\\sigma}$ is the totally anti-symmetric Levi-Civita tensor (with $\\epsilon^{0123}=1$).\nNote that $g_T^{\\mu\\nu} a_\\nu = a_T^\\mu$ projects a four-vector onto its transverse component, and $\\epsilon_T^{\\mu\\nu} a_\\nu = \\epsilon_T^{\\mu\\nu} a_{T\\nu}$ rotates that component by 90 degrees in the transverse plane.\n\nIn the paper we also make use of the correspondence between symmetric traceless tensors of definite rank and complex numbers, detailed in Ref.~\\cite{Boer:2016xqr}. Its essence is the possibility to trade an uncontracted rank-$m$ tensor with a complex number. For a rank-$m$ tensor $T$ built out of a single transverse vector $\\vect{a}_T$, this reads:\n\\begin{equation}\n  \\label{e:SST_C}\n  T^{i_1 \\cdots i_m}(\\vect{a}_T) \\rightarrow \\frac{1}{2^{m-1}}\\ \n  |\\vect{a}_T|^m\\ e^{\\pm \\i m \\phi} \\ ,\n\\end{equation}\nwhere $\\phi$ is the polar angle associated to $\\vect{a}_T$ in the transverse plane. The rank $m$ of the tensor is reflected in the power of the modulus and in the phase of the complex number.\n\n\nA useful consequence of this correspondence is that expressions proportional to $T^{i_1 \\cdots i_m}$ vanish upon integration over $\\vect{a}_T$, due to the angular part of the integration measure.\nIn our analysis we apply this correspondence to the following rank-2 tensor, built out of the hadron's transverse momentum $P_T$~\\cite{Boer:2016xqr,vanDaal:2016glj}:\n\\begin{equation}\n\\label{e:STT2_Php}\nP_T^{ij} \\ \\equiv\\ P_T^i P_T^j + \\frac{\\vect{P}_T^2}{2} g_T^{ij} \\ .\n\\end{equation} \n\n\n\n\\subsection{Parton distribution correlator}\nThe TMD parton distribution correlator and its Dirac projections are defined as:\n\\begin{equation*}\n\\label{e:proj_int_Phi}\n\\refstepcounter{equation}\n\\Phi(x,p_T)\\ \\equiv \\int_{-\\infty}^{+\\infty} dp^- \\Phi(p, P)_{\\begin{subarray}{l} p^+=xP^+ \\\\  \\end{subarray}}\\,\n= \\int dp^-\\, \\text{Disc} [ \\Phi(p, P) ]_{\\begin{subarray}{l} p^+=xP^+ \\\\  \\end{subarray}} \n\\ , \\ \\ \\ \\ \\ \\ \\ \n\\Phi^{[\\Gamma]}(x,p_T)\\ \\equiv\\ \\text{Tr} \\bigg[ \\Phi(x,p_T) \\frac{\\Gamma}{2} \\bigg] \\ ,\n\\eqno{(\\theequation \\textit{a,b})}\n\\end{equation*}\nwhere the unintegrated $\\Phi$ quark distribution correlator is defined as~\\cite{Bacchetta:2006tn,Mulders:1995dh,Echevarria:2016scs}:\n\\begin{equation*}\n\\Phi_{ij}(p,P) = \\int \\frac{d^4 \\xi}{(2\\pi)^4} e^{\\i p \\cdot \\xi}\\, \\text{Tr}_c \n\\langle P|  \n{\\cal T} \\big[ \\overline{\\psi}_j(0) W_2(0,\\infty) \\big] \\, \n{\\cal \\overline{T}} \\big[ W_1(\\infty,\\xi) \\psi_i(\\xi) \\big] \\, \n|P \\rangle  \\, .\n\\end{equation*}\nIn the previous equations $p$ is the quark momentum, $P$ is the hadronic momentum, $x=p^+\/P^+$ is the parton fractional momentum in the dominant direction. In Eq.~\\eqref{e:proj_int_Phi}(b), the ``Tr'' operator ``Tr'' without subscripts indicates to a Dirac trace,  the $1\/2$ factor is explained in Section 6.7 and 6.8 of Ref.~\\cite{Collins:2011zzd}, and $\\Gamma$ is a generic Dirac matrix;  for example, $\\Gamma=\\gamma^+$ is associated to the unpolarized TMD $f_1$, and the matrices associated to the other TMDs can be found in  \\cite{Bacchetta:2006tn}.\nIn the spirit of Feynman rules, the Dirac trace operator ``$\\text{Tr}$'' corresponds to the {\\it sum} over the polarization states of the quark in the final state. \nThe analogous color trace $\\text{Tr}_c$, corresponding to a sum over the color configurations, is included in the definition of the correlator $\\Phi$. \n\nAssuming that the correlators have the standard analiticity properties of the scattering amplitudes, the integration over the suppressed momentum component used to define the TMD correlators can be performed by complex contour deformation. Depending on the value of $x$, one can then replace the integral of the unintegrated correlator by the integral of its $s$-channel or $u$-channel discontinuity, denoted by ``Disc'' \n~\\cite{Jaffe:1983hp,Boer:1998im,Diehl:2003ny,Gamberg:2010uw}. These correspond, respectively to a quark distribution ($0 \\leq x \\leq 1$), and to an antiquark distribution  ($-1 \\leq x \\leq 0$). \n\n\n\n\\subsection{Parton fragmentation correlator}\n\nThe TMD fragmentation correlator in the parton frame and its Dirac projections are defined as:\n\n\\begin{equation*}\n\\label{e:proj_int_Delta}\n\\refstepcounter{equation}\n\\Delta(z,P_T) \\equiv  \\int_{-\\infty}^{+\\infty} \\frac{dk^+}{2z}\\, \\Delta(k, P)_{\\begin{subarray}{l} P^-= zk^- \\\\  \\end{subarray}}\n= \\int \\frac{dk^+}{2z}\\, \\text{Disc}\\, [ \\Delta(k, P) ]_{\\begin{subarray}{l} P^-= zk^- \\\\  \\end{subarray}}\n\\ , \\ \\ \\ \\ \\ \\ \\\n\\Delta^{[\\Gamma]}(z,P_T)\\ \\equiv\\ \\text{Tr} \\bigg[ \\Delta(z,P_T) \\frac{\\Gamma}{2} \\bigg] \\ ,\n\\eqno{(\\theequation \\textit{a,b})}\n\\end{equation*}\nwith the unintegrated quark correlator $\\Delta(k,P)$ defined in Eq.~\\eqref{e:1hDelta_corr}. \nHere $k$ is the momentum of the fragmenting quark, $P$ is the momentum of the produced hadron, and $z=P^-\/k^-$ is the hadron's fractional momentum in the dominant momentum direction. \nThe $1\/2$ factor in Eq.~\\eqref{e:proj_int_Delta}(b) arises in the same way as in Eq.~\\eqref{e:proj_int_Phi}(b). \nIn Eq.~\\eqref{e:proj_int_Delta}(a), the $1\/z$ factor comes from the normalization of the hadronic states (see Ref.~\\cite{Collins:1981uw} and Section 12.4 in Ref.~\\cite{Collins:2011zzd}). \nThe trace operator in this case has an additional $1\/2$ factor which appears in Eq.~\\eqref{e:proj_int_Delta}(a), since it corresponds to an {\\it average} over the quark polarizations in the initial state. \nA color trace Tr$_c\/N_c$, that in the same way corresponds to an average over the hadron's color configurations, is already included in the definition of the unintegrated correlator $\\Delta(k,P)$. \n\nNote that in the fragmentation case we integrate over the suppressed partonic plus component even if the correlator has a probabilistic interpretation in terms of the hadronic variables. This is because the integration is always performed with respect to the momentum components of the object that in a process would enter the hard interaction in a process, namely the parton.\n\n\n\\subsection{Fully inclusive jet correlator}\nIn analogy with Eqs.~\\eqref{e:proj_int_Delta}, the TMD inclusive jet correlator and its Dirac projections are defined as:\n\\begin{equation*}\n\\label{e:proj_int_J}\n\\refstepcounter{equation}\nJ(k^-,k_T)\\, \\equiv\\ \\frac{1}{2} \\int dk^+  \\, \\Xi(k) \n\\ , \\ \\ \\ \\ \\ \\ \\ \\ \\\nJ^{[\\Gamma]}(k^-,k_T)\\, \\equiv\\  \\text{Tr} \\bigg[ J(k^-,k_T) \\frac{\\Gamma}{2} \\bigg] \\ .\n\\eqno{(\\theequation \\textit{a,b})}\n\\end{equation*}\nFor consistency with Ref.~\\cite{Sterman:1986aj}, the discontinuity has been inserted directly in the definition of the unintegrated jet correlator~\\eqref{e:invariant_quark_correlator}, or equivalently \\eqref{e:invariant_quark_correlator_W}, where we also included the color trace Tr$_c\/N_c$ corresponding to an average over the initial state color configurations. \nNote that there is no $1\/k^-$ prefactor, at variance with Ref.~\\cite{Accardi:2008ne}.\n\n\n\n\n\n\n\\section{Frame transformations}\n\\label{a:frame_dep}\n\n\nIn this appendix we discuss the dependence of the fragmentation functions and of the associated momentum sum rules on the frame chosen to study the hadronization mechanism.\n\nWe will consider, in particular, two cases: the hadron frame used to define the TMD fragmentation functions \\cite{Collins:2011zzd,Bacchetta:2006tn}, and the parton frame used in the main text to derive the momentum sum rules. Either frame is defined by a specific choice of basis four-vectors $n_{-(f)}$, $n_{+(f)}, n_{1(f)}, n_{2(f)}$, that identify the light-cone plus and minus directions and the two directions orthogonal to these, with an index $f=h,p$ explicitly referring to the hadron and parton frames, respectively. The basis vectors are not only utilized to define the corresponding coordinate system, but also to decompose the fragmentation correlator in terms of Fragmentation Functions, whose definition, consequently, depends on the choice of frame. In this appendix, therefore, we will consistently use the $h$ and $p$ subscripts to explicitly distinguish between quantities defined in one or the other frame. Note, however, that in the main text we dispensed from this notation.\n\\newline\\indent\nAs discussed in Section~\\ref{ss:1h_inclusive_FF}, the hadron frame is defined such that the momentum of the hadron under consideration has no transverse component ($\\vect{P}_{Th}=0$); and the parton frame is such that the quark's momentum has no transverse component ($\\vect{k}_{Tp}=0$). \nIn the main body of this paper, we connected the fragmentation correlator and the quark propagator through a correlator-level sum rule that integrated over all hadron momenta. Hence only the quark's momentum is available to define the frame, and we could only choose to work in the parton frame. When discussing the fragmentation correlator, however, both frames are possible, with the hadron frame being the conventional choice~\\cite{Collins:2011zzd,Bacchetta:2006tn}. As a consequence, the FFs functions defined in the TMD literature, and here generically denoted by $X_h$, differ from the fragmentation functions entering the sum rules for the parton-frame $X_p$ FFs summarized in Section~\\ref{ss:1h_inclusive_FF}, where the $p$ index was dropped for simplicity. It is the purpose of this Appendix to derive the rules for transforming one set of FFs, and their corresponding sum rules and Equation of Motion relations, into the other. \n\n\\subsection{Parton and hadron frames}\n\\label{ss:p_h_frames}\n\nWe will first consider the Lorentz transformation from the parton frame to the hadron frame. The transformation is completely determined by requiring that \n(1) the parton transverse momentum in the parton frame $\\vect{k}_{Tp}$ be zero,  \n(2) the minus component be invariant, and \n(3) the norm of any four-vector be invariant. \nThe matrix associated to this transformation reads, in light-cone coordinates~\\cite{Levelt:1993ac,Collins:2011zzd}:\n\\begin{equation}\n  \\label{e:p_to_h_frame}\n \n  {\\cal M}_{h \\leftarrow p} = \n  \\begin{bmatrix}\n  1 & 0 & 0 \\\\\n  \\frac{\\vect{k}_{Th}^2}{2(k^-)^2} & 1 & \\frac{\\vect{k}_{Th}}{k^-} \\\\\n  \\frac{\\vect{k}_{Th}}{k^-} & 0 & 1\n  \\end{bmatrix}\n  \\,  ,\n\\end{equation}\nwhere $\\vect{k}_{Th}$ is the (Euclidean 2D) transverse momentum of the quark in the hadron frame. \nThe hadron frame components $a_h^\\mu$ of the vector $a$ can then be obtained from the parton frame components by\n\\begin{align}\n   a_h^\\mu = {({\\cal M}_{h \\leftarrow p})^\\mu}_\\nu \\, a_p^\\nu \\ .\n\\end{align}\nAs the minus component is invariant, we will omit the subscript identifying the frame whenever little risk of misunderstanding occurs. The inverse transformation matrix ${\\cal M}_{p \\leftarrow h}$ from the hadron to the parton frame can be simply obtained by replacing $\\vect{k}_{Th} \\rightarrow - \\vect{k}_{Th}$ in Eq.~\\eqref{e:p_to_h_frame}.\n\nFrom Eq.~\\eqref{e:p_to_h_frame} one can see that the transverse momentum $\\vect{P}_{Tp}$ of the hadron in the parton frame and the transverse momentum $\\vect{k}_{Th}$ of the quark in the hadron frame are related by\n\\begin{equation}\n\\label{e:PTp_kTh_rel}\n\\vect{P}_{Tp} = -z\\, \\vect{k}_{Th} \\, ,\n\\end{equation}\nwhile the hadron's collinear momentum fraction relative to the quark is invariant between the two considered frames because of the invariance of the minus components of the momenta:\n\\begin{align}\n\\label{e:z_inv}\n  z = \\frac{P^-_p}{k^-_p} = \\frac{P^-_h}{k^-_h} \\ .\n\\end{align}\n\nLet us now consider the transformation of the different ingredients in the Dirac decomposition of the TMD fragmentation correlator, that defines the fragmentation functions (see, for example, Eq.~\\eqref{e:1hDelta_TMDcorr_param} for the decomposition in the parton frame).  \nTo start with, the metric tensor $g^{\\mu\\nu}$ is Lorentz-invariant by definition, and the Levi-Civita tensor $\\epsilon^{\\mu\\nu\\rho\\sigma}$ is invariant, as well, since the transformation ${\\cal M}_{h \\leftarrow p}$ belongs to the orthochronus Lorentz group (det ${\\cal M}_{h \\leftarrow p} = 1$). \n\nThe transformation of the transverse $g_T^{\\mu\\nu}$ and $\\epsilon_T^{\\mu\\nu}$ tensors are, instead, more complex, and we need to first address the relation between the basis vectors defining the two frames under consideration.\nLet's consider first the hadron frame basis vectors, which can be expressed in hadron-frame coordinates as ${n_-}_{(h)}^\\mu = [1,0,\\vect{0}_T]_h$, ${n_+}_{(h)}^\\mu = [0,1,\\vect{0}_T]_h$ and $n_{i(h)}^\\mu = [0,1,\\vect{e}_i]_h$, where $\\vect{e}_1 = (1,0)$ and $\\vect{e}_2=(0,1)$, and $i=1,2$ a transverse index. We also collect the transverse basis vectors $n_{i(h)}$ into a 2D transverse vector, $\\vect{n}_{T(h)} \\equiv (n_{1(h)},n_{2(h)})$. The parton frame basis vectors are analogously defined in parton frame coordinates. \nOne can easily show that \n\\begin{subequations}\n\\label{e:n_transf}\n\\begin{numcases}{}\nn_{-(h)}^\\mu = n_{-(p)}^\\mu\n  - \\frac{1}{k^-} \\vect{k}_{Th} \\cdot \\vect{n}_{T(p)}^\\mu \n  + \\frac12 \\frac{\\vect{k}_{Th}^2}{(k^-)^2} n_{+(p)}^\\mu\n  & \\label{e:n_minus_transf} \\\\\nn_{+(h)}^\\mu = n_{+(p)}^\\mu\n  & \\label{e:n_plus_transf} \\\\\n\\vect{n}_{T(h)}^\\mu = \\vect{n}_{T(p)}^\\mu - \\frac{\\vect{k}_{Th}}{k^-} n_{+(p)}^\\mu \\ ,\n  & \\label{e:n_T_transf}     \n\\end{numcases}\n\\end{subequations}\nIt is then not difficult to obtain\n\\begin{align}\n  \\label{e:gT_transf}\ng_{T(h)}^{\\mu\\nu} & = g_{T(p)}^{\\mu\\nu} + \\frac{1}{k^-} \\vect{k}_{Th} \\cdot \\vect{n}_{T(p)}^{\\{\\mu} n_{+(p)}^{\\nu\\}} - \\frac{\\vect{k}_{Th}^2}{(k^-)^2} n_{+(p)}^\\mu n_{+(p)}^\\nu\\\\\n  \\label{e:epsT_trans}\n\\epsilon_{T(h)}^{\\mu\\nu} & = \\epsilon_{T(p)}^{\\mu\\nu} - \\frac{1}{k^-} \\epsilon^{\\mu\\nu\\rho\\sigma} \\vect{k}_{Th} \\cdot \\vect{n}_{T(p)\\rho} \\, n_{+(p)\\sigma} \\ .\n\\end{align}\nWhile neither tensor is actually Lorentz invariant in itself, the breaking terms are at least of $O(1\/k^-)$.\nIn our application to the Lorentz  transformation of the fragmentation correlator $\\Delta$, we only need these tensors contracted with $k_\\nu$, with a much simpler transformation: \n\\begin{align}\n\\label{e:nTdot_transf}\ng_{T(h)}^{\\mu\\nu} k_\\nu & = -\\frac{1}{z} g_{T(p)}^{\\mu\\nu} P_\\nu - \\frac{\\vect{P}_{Tp}^2}{z^2k^-} n_{+(p)}^\\mu  \n\\\\\n\\label{e:epsTdot_transf}\n\\epsilon_{T(h)}^{\\mu\\nu} k_\\nu & = -\\frac{1}{z} \\epsilon_{T(p)}^{\\mu\\nu} P_\\nu \\ .\n\\end{align}\nNote that Eq.~\\eqref{e:nTdot_transf} generalizes Eq.~\\eqref{e:PTp_kTh_rel} to the four vector case. \nFinally, the first four Dirac matrices transform as any other four-vector: \n\\begin{subequations}\n\\label{e:gammamu_transf}\n\\begin{numcases}{}\n\\gamma_h^- = \\gamma_p^- \\equiv \\gamma^- \n& \\label{e:gammaminus_transf} \\\\\n\\gamma_h^+ = \\gamma_p^+ \n+ \\frac{\\vect{k}_{Th}^2}{2(k^-)^2}\\, \\gamma^- \n+ \\frac{\\vect{k}_{Th} \\cdot \\vect{\\gamma}_{Tp}}{k^-}  \n& \\label{e:gammaplus_transf} \\\\\n\\vect{\\gamma}_{Th} = \\vect{\\gamma}_{Tp} + \\frac{\\vect{k}_{Th}}{k^-}\\, \\gamma^- \\ ,\n& \\label{e:gammaT_transf}     \n\\end{numcases}\n\\end{subequations}\nwith $\\gamma_5 = \\varepsilon_{\\mu\\nu\\rho\\sigma} \\gamma^\\mu \\gamma^\\nu\\gamma^\\rho \\gamma^\\sigma$ invariant because such is the Levi-Civita tensor and we are working in 4 dimensions \\cite{Collins:1984xc}.\n\n\nWe now have all the tools to understand what happens to the fragmentation functions, the Equation of Motion relations (EOMs), and the momentum sum rules when changing frames.\n\n\n\n\\subsection{Transformation of the fragmentation functions}\n\\label{ss:FFtransforms}\n\nAs discussed, the TMD fragmentation functions are conventionally defined by decomposing the TMD fragmentation correlator in terms of the light cone basis vectors of the hadron frame~\\cite{Bacchetta:2006tn}: \n\\begin{align}\n\\label{e:1hDelta_TMDcorr_param_hadron_frame}\n{\\Delta}_{(h)}(z,k_{T(h)}) & = \n\\frac{1}{2} \\slashed{n}_{-(h)} D_{1h}(z,k_{Th}^2) + \n\\i \\frac{ \\big[ \\slashed{k}_{T(h)}, \\slashed{n}_{-(h)} \\big]}{4 M} H_{1h}^{\\perp}(z,k_{Th}^2) + \n\\frac{M}{2 P^-} E_h(z,k_{Th}^2) \\\\\n\\nonumber & \n+ \\frac{\\slashed{k}_{T(h)}}{2 P^-} D_h^{\\perp}(z,k_{Th}^2) \n+ \\frac{\\i M}{4 P^-} \\big[ \\slashed{n}_{-(h)}, \\slashed{n}_{+(h)} \\big] H_h(z,k_{Th}^2) \n+ \\frac{1}{2 P^-} \\gamma_5\\, \\epsilon_{T(h)}^{\\rho\\sigma}\\, \\gamma_{\\rho}\\, {k_\\sigma} \\, G_h^{\\perp}(z,k_{Th}^2) \\ .\n\\end{align}\nNote that we omitted the frame subscript for the frame-independent quantities, and that $\\slashed{k}_{T(h)} = \\gamma_\\mu\\, g_{T(h)}^{\\mu\\nu} k_\\nu$. We have also dropped the flavor index on the mass $M$ to avoid confusion with the frame subscript $h$, and used $k_{Th}^2=k_{T(h)}^\\mu k\\big._{T(h)\\mu}$ as a shorthand in the argument of the fragmentation functions. \n\nIt is now important to realize that the TMD correlator $\\Delta_{(h)}(z,k_{Th}^2) \\equiv (2z)^{-1} \\int dk_h^+ \\Delta(k,P)$ is invariant under Lorentz trasformations, such as the hadron to parton frame transformation under discussion in this appendix, that connect frames with the same light-cone plus axis. Explicitly,\n\\begin{align}\n\\label{e:Delta_h_vs_p}\n    \\Delta_{(p)}(z,P_{Tp}^2) =  \\Delta_{(h)}(z,k_{Th}^2) \\ ,\n\\end{align}\nwhere the TMD correlator $\\Delta_{(p)} = (2z)^{-1} \\int dk_p^+ \\Delta(k,P)$ is decomposed in terms of the parton-frame light-cone basis vectors, see Eq.~\\eqref{e:1hDelta_TMDcorr_param} in the main text. This can be seen in two steps. First, notice that the integration over $dk^+$ is Lorentz invariant because the minus and transverse components are fixed. Then, look at the definition \\eqref{e:1hDelta_ampl} of the unintegrated $\\Delta^h(k,P)$: on the one hand, there are no open Lorentz indexes; on the other hand, the light-cone plus vectors associated  with the $B_i$ functions is the same in the considered frames.\n\n\nSchematically, the Dirac projections that define the FFs take the form\n\\begin{equation}\n\\label{e:inv_traces}\n  X_f \\sim \\text{Tr}\\Big[ \\Delta_{\\text{TMD}}\\, \\Gamma_{(f)} \\Big] \\ ,\n\\end{equation}\nwhere $\\Gamma_{(f)}$ is a suitable contraction of the Dirac matrices and the light-cone basis vectors for a given frame $f$, see for example \nEqs.~\\eqref{e:sumrule_D1},~\\eqref{e:sumrule_E},~\\eqref{e:sumrule_H},~\\eqref{e:sumrule_H1p},~\\eqref{e:sumrule_Dp},~\\eqref{e:sumrule_Gp}.  \nWhen  performing a Lorentz transformation, one needs to keep all the involved vectors unchanged. Under this condition, the traces in Eq.~\\eqref{e:inv_traces} are Lorentz invariant. If one changes the basis vectors, though, one obtains a {\\em different} definition of fragmentation functions, and one can study how these different fragmentation functions transform into one another.\n\nSpecifically, let's consider the transformation between the hadron-frame FFs introduced in this appendix, and the parton-frame FFs discussed in the main text. This can be obtained by decomposing, with the help of Eq.~\\eqref{e:n_transf}, the $n_{(h)}$ vectors in Eq.~\\eqref{e:Delta_h_vs_p} on the parton-frame light-cone basis, and transforming the transverse momentum components according to Eq.~\\eqref{e:PTp_kTh_rel}. The parton frame FFs can then be projected out utilizing the $\\Gamma_{(p)}$ functions, or, more simply, obtained by matching the corresponding Dirac structures in Eq.~\\eqref{e:Delta_h_vs_p}. One finds \n\\begin{align}\n\\label{e:Dperp_transf}\n& D_p^\\perp(z,P_{Tp}^2) = D_h^\\perp(z,k_{Th}^2) - z\\, D_{1h}(z,k_{Th}^2) \\equiv {\\widetilde D}_h^\\perp(z,k_{Th}^2) \\, , \\\\\n\\label{e:H_transf} \n& H_p(z,P_{Tp}^2) = H_h(z,k_{Th}^2) -z\\, \\frac{k_{Th}^2}{M^2}\\, H_{1h}^\\perp(z,k_{Th}^2) \\equiv {\\widetilde H}_h(z,k_{Th}^2) \\,  ,\n\\end{align}\nwhile all other fragmentation functions do not mix\\footnote{For the $G^\\perp$function, this is actually true only when summing over the hadron spins.}:\n\\begin{align}\n  \\label{e:p_to_h_genericFF}\n  X_p (z,P_{Tp}^2) = X_h(z,k_{Th}^2) \\ .\n\\end{align}\nIn practice, the change of basis vectors mixes the twist-2 FFs in the hadron frame ($D_{1h}$ and $H_{1h}^\\perp$) with two other twist-3 FFs ($D_h^\\perp$ and $H_h$) through the off-diagonal terms in Eq.~\\eqref{e:p_to_h_frame} proportional to $1\/k^- \\sim 1\/P_h^-$. The other FFs do not mix under this change of basis.  \n\nThe identification of the r.h.s. of Eqs.~\\eqref{e:Dperp_transf} and~\\eqref{e:H_transf} with the ${\\widetilde D}_h$ and ${\\widetilde H}_h$ functions requires one to use the hadron frame EOM relations discussed in Ref.~\\cite{Bacchetta:2006tn}. It is important to remark that these tilde-functions are among the functions that parametrize the dynamical twist-3 quark-gluon-quark correlator $\\Delta_A^\\alpha$~\\cite{Bacchetta:2006tn}. Hence, Eqs.~\\eqref{e:Dperp_transf} and~\\eqref{e:H_transf} imply that the distinction between kinematical and dynamical twist-3 is, for certain functions, frame-dependent, and the transformation ${\\cal M}_{h \\leftarrow p}$ actually maps a kinematical twist-3 quantity into a dynamical one. A similar version of the transformation~\\eqref{e:Dperp_transf} for $D^\\perp$ was already discussed in Ref.~\\cite{Levelt:1993ac}, whereas the transformation~\\eqref{e:H_transf} for $H$ is, to our knowledge, new.\n\nBefore moving to collinear functions, it is worthwhile remarking an important, but potentially confusing difference between our notation (derived e.g. from Ref.~\\cite{Bacchetta:2006tn}) and that of, {\\em e.g.}, Refs~\\cite{Metz:2016swz,Collins:2011zzd}. In the hadron frame, the natural transverse momentum variable for a FF is $k_{Th}$, as we have used in this Appendix. However, the physical interpretation of a FF should be given in the partonic frame. Hence, reading Eq.~\\eqref{e:p_to_h_genericFF} from right to left, and utilizing Eq.~\\eqref{e:PTp_kTh_rel}, we find \n\\begin{align}\n     X_h(z,k_{Th}^2) = X_p (z,z^2 k_{Th}^2)\\ .\n\\end{align}\nIn other words, the hadron frame FFs depend on the $z^2 k_{Th}^2$ combination, rather than $k_{Th}^2$ alone. This justifies using $z^2 k_{Th}^2$ as argument of $X_h$ as done in e.g.  Refs~\\cite{Metz:2016swz,Collins:2011zzd}. An important consequence is that, if one wishes to use a Gaussian approximation for the transverse momentum dependence of the FFs in the hadron frame, this should read $X_h(z,k_{Th}^2) \\approx D(z) \\exp\\big[-z^2 \\vect{k}_{Th}^2\/(\\Delta^2)\\big]$, where $\\Delta^2$ is the variance, and $D$ a function of $z$ alone. \n\nThe collinear FFs are usually defined in the parton frame as integrals of the TMD FFs over the transverse momentum (see Refs.~\\cite{Bacchetta:2006tn,Metz:2016swz}). The definition in the hadron frame follows, if one requires the collinear FFs to be frame independent. \nExplicitly,\n\\begin{equation}\n\\label{e:D1_coll_def}\nX_{p}(z) \\equiv \\int d^2 \\vect{P}_{Tp}\\, X_{p}(z,P_{Tp}^2)   \\, ,\n\\quad \\quad \\quad \nX_{h}(z) \\equiv z^2 \\int d^2 \\vect{k}_{Th}\\, X_{h}(z,k_{Th}^2) \\ ,\n\\end{equation}\nand it is easy to see that \n\\begin{align}\n  \\label{e:coll_FF_lorentz}   \n  X_{p}(z)=X_{h}(z)\n \\end{align}\nfor FFs that do not mix under Lorentz transformations.\nFollowing the standard conventions discussed in Refs.~\\cite{Bacchetta:2006tn,Metz:2016swz}, the first transverse moments are defined in the parton and hadron frames as\n\\begin{equation}\n\\label{e:first_mom} \nX_p^{(1)}(z) \\equiv \\int d^2 \\vect{P}_{Tp}\\, \\frac{\\vect{P}_{Tp}^2}{2 z^2 M^2}\\, X_p(z,P_{Tp}^2) \\, ,\n\\quad \\quad \\quad \nX_h^{(1)}(z) \\equiv z^2\\, \\int d^2 \\vect{k}_{Th}\\, \\frac{\\vect{k}_{Th}^2}{2M^2}\\, X_h(z,k_{Th}^2) \\, .\n\\end{equation} \nThese also do not mix, $X^{(1)}_{p}(z)=X^{(1)}_{h}(z)$, except for the $D^\\perp$ and $H$ functions.\n\n\n\n\n\\subsection{Transformation of the EOMs}\n\nThe EOMs allow one to relate twist-2 fragmentation functions with kinematical and dynamical twist-3 fragmentation functions. \nThey can be obtained by applying the Dirac equation $(i\\slashed{D}(\\xi) - m)\\psi(\\xi)=0$ to the fragmentation correlator and projecting on the good quark components. The resulting relation between the twist-2 and twist-3 fragmentation correlators is Lorentz covariant, as seen in Eq. (3.53) of Ref.~\\cite{Bacchetta:2006tn}, which is given in the hadron frame.  \nUsing the transformation~\\eqref{e:p_to_h_frame} it is possible to show that the EOMs are frame invariant up to terms suppressed by powers of $M\/P^-$, which can be kinematically neglected in a frame boosted to high values of $P^-$ such as we are considereing in this paper~\\cite{Bacchetta:2006tn}. \nThus, in order to derive the EOMs in the parton frame, one simply needs to apply the replacement rule~\\eqref{e:PTp_kTh_rel} for the transverse momenta to the hadron frame EOMs given in Ref.~\\cite{Bacchetta:2006tn}:  \n\\begin{equation}\n  \\label{e:eom_p_frame}\n  \\begin{aligned}\n  & E_p = \\widetilde{E}_p + z \\frac{m_{q0}}{M} D_{1p} \n  &\\quad\\quad& D_p^{\\perp} = \\widetilde{D}_p^{\\perp} + z D_{1p} \\\\\n  & H_p = \\widetilde{H}_p - \\frac{\\vect{P}_{Tp}^2}{z M^2}   H_{1p}^\\perp\n  && G_p^{\\perp} = \\widetilde{G}_p^{\\perp} + z \\frac{m_{q0}}{M}   H_{1p}^{\\perp\\,} \\ .\n  \\end{aligned}\n\\end {equation}\nThese are the EOMs utilized in Section~\\ref{ss:qgq_sumrules}, but are written with an explicit $p$ frame subscript. \n\n\n\\subsection{Transformation of the sum rules}\n\nWe now discuss the frame (in)dependence of the momentum sum rules for the fragmentation functions. \n\nLet us start from the rank $0$ sum rules for the $D_1$ and $E$ fragmentation functions, derived in Section~\\ref{ss:mu_minus} in the parton frame.  \nThe Dirac matrices that project these functions out of the fragmentation correlator are, respectively, the $\\gamma^-$ and ${\\mathbb 1}$ matrices. Since these are invariant under the ${\\cal M}_{h \\leftarrow p}$ transformation, also the momentum sum rules for $D_1$ and $E$ are invariant. \n\nThe transformation of the rank $0$ parton frame sum rule for $H$ is less straightforward, because of its mixing with the Collins function $H_1^\\perp$, and it is instructive to look at the latter first. The projection matrix for $H_1^\\perp$ is $\\Gamma = \\i \\sigma^{i-}\\gamma_5$, which renders the RHS of the master sum rule~\\eqref{e:sumrule_transverse} equal zero. Moreover this matrix is frame independent,  because the extra term from Eq.~\\eqref{e:gammaT_transf} cancels in the commutator that defines $\\sigma^{i-}$. Accordingly, the rank $1$ sum rule for $H_1^\\perp$ is Lorentz-invariant. As a consequence of Eq.~\\eqref{e:H_transf}, also the sum rule for $H$ is, despite the fact that this FF mixes with the Collins function under Lorentz transformations. \n\nThe other two FFs appearing in the rank $1$ sum rules discussed in Section~\\ref{ss:mu_transverse} are $G^\\perp$ and $D^\\perp$. \nThe projection matrix for $G^\\perp$ is $\\Gamma = \\gamma_T^i\\, \\gamma_5$, such that the RHS of the sum rule is zero, as well. Differently from the sum rule for the Collins function, this matrix does get an extra term proportional to $\\gamma^- \\gamma_5$ under Lorentz transformation, which is however only related to polarized FFs. Since the sum rules can only be obtained after summing over the hadronic polarizations, this extra term does not contribute and the sum rule for $G^\\perp$ is Lorentz invariant. \n\nThe sum rule for $D^\\perp$ in the parton frame involves the hadronic transverse momentum rescaled by the collinear momentum fraction averaged over the kinematics and summed over the produced hadrons and their spin. \nIt is therefore useful to introduce the notion of the average of a momentum-dependent $O_p=O_p(z,P_{Tp}^2)$ observable in the parton frame  as:\n\\begin{equation}\n\\label{e:def_average_pframe}\n\\langle O_p \\rangle = \\sum_{H, S} \\int dz\\, d^2 \\vect{P}_{Tp}\\, O_p(z,P_{Tp}^2)\\, z\\, D_{1}^{H}(z,P_{Tp}^2) \\ ,\n\\end{equation}\nwhere, at variance with the main text, we used an upper case hadronic $H$ flavor index to distinguish this from the hadronic frame index (this definition can also be extended to a flavor dependent observable $O^H$, but we suppressed that index for clarity).  \nThe average operator is Lorentz invariant if we define this for a hadron frame observable $O_h=O_h(z,k_{Th}^2)$ as\n\\begin{equation}\n\\label{e:def_average_hframe}\n\\langle O_h \\rangle \\equiv \\sum_{H, S} \\int dz\\, d^2 \\vect{k}_{Th}\\, O_h(z,k_{Th}^2)\\, z^3\\, D_{1}^{H}(z,k_{Th}^2) \\, .\n\\end{equation}\nNow, one can calculate the hadron frame sum rule for $D^\\perp$ by applying the ${\\cal M}_{h \\leftarrow p}$ Lorentz transformation and the mixing relation~\\eqref{e:Dperp_transf} to the parton frame sum rule~\\eqref{e:pframe_sumrule_Dp_Dpt}$a$. \nUtilizing the EOMs in the two frames, it is also possible to obtain the hadron frame sum rule for $\\widetilde{D}^\\perp$. The result of these manipulation is given in Table~\\ref{t:sum_rules_Dperp},  where we collect and compare the $D^\\perp$ and $\\widetilde{D}^\\perp$ sum rules in either frame, expressed in terms of the average  defined in Eqs.~\\eqref{e:def_average_pframe} and~\\eqref{e:def_average_hframe}.\n\n\\begin{table}\n\\small\n \\centering\n\\begin{tabular}{|c||c|c|}\n  \\hline\n  \\multicolumn{1}{|c||}{\\ frame\\ \\ } & \n  \\multicolumn{1}{c|}{\\ $\\displaystyle 2 \\sum_{H,S} \\int dz\\, M_H^2\\, {D}_f^{H\\perp(1)}(z)$\\ \\ } & \n  \\multicolumn{1}{c|}{\\ $\\displaystyle 2 \\sum_{H,S} \\int dz\\, M_H^2\\, \\widetilde{D}_f^{H\\perp(1)}(z)$\\ \\ } \\\\\n  \\hline\n  \\hline\n          &   &  \\\\ \n$f = p$ & 0 & $\\langle P_{Tp}^2\/z^2 \\rangle$ \\\\              \n          &   &  \\\\ \n$f =  h$ & $\\langle \\vect{k}_{Th}^2 \\rangle$ & 0  \\\\                      \n          &   &  \\\\ \n\\hline\n\\end{tabular}\n\\caption{Sum rules for the $D^\\perp$ and $\\widetilde{D}^\\perp$ twist-3 FFs in the parton frame ($f = p$) and in the hadron frame ($f =  h$). The flavor index is denoted by an uppercase $H$ to distinguish this from the lowercase $h$ frame index.}\n\\label{t:sum_rules_Dperp}\n\\end{table} \n\nOne can notice an interesting symmetry between the results obtained in the parton and in the hadron frames. \nIn the parton frame, the twist-3 $\\widetilde{D}^\\perp$ sum rule measures the average squared hadronic transverse momentum dynamically generated during the hadronization process scaled by a factor $1\/z$, while the $D^\\perp$ sum rule is trivial. \nIn the hadron frame, instead, it is the twist-2 sum rule for $D^\\perp$ that measures the dynamical generation of transverse momentum. In this case the averaged quantity is formally the transverse partonic momentum as seen by the hadron. \nWhile different in form, the two averages measure the same quantity, as is obvious from Eq.~\\eqref{e:PTp_kTh_rel}. The formal frame dependence of the $D^\\perp$ and $\\widetilde D^\\perp$ sum rules is a consequence of the  fact that these FFs enter the fragmentation correlator with a coefficient proportional to the transverse momentum, and of the Lorentz transformation properties of the latter. \n\n\n\n\n\n\n\n\n\n\n\n\\end{appendix}\n\n\n\\section{The fully inclusive jet correlator and its spectral decomposition}\n\\label{s:jetcor}\n\n\n\\subsection{The inclusive jet correlator}\n\nLet us start by considering the unintegrated \ninclusive quark-to-jet correlator~\\cite{Sterman:1986aj,Chen:2006vd,Collins:2007ph,Accardi:2008ne,Accardi:2017pmi,Accardi:2019luo} \n\\begin{align}\n  \\label{e:invariant_quark_correlator}\n  \\Xi_{ij}(k;w) = \\text{Disc} \\int \\frac{d^4 \\xi}{(2\\pi)^4} e^{\\i k \\cdot \\xi} \\,\n    \\frac{\\text{Tr}_c}{N_c}\\, {\\langle\\Omega|} \n    \\big[\\, {\\cal T}\\, W_1(\\infty,\\xi;w) \\psi_i(\\xi) \\big]\\, \n    \\big[\\, {\\cal \\overline{T}}\\, {\\overline{\\psi}}_j(0) W_2(0,\\infty;w) \\big] \n    {|\\Omega\\rangle} \\ ,  \n\\end{align}\nwhere ${|\\Omega\\rangle}$ is the interacting vacuum state of QCD, $\\psi$ the quark field, $W_{1,2}$ are Wilson lines that ensure the gauge invariance of the correlator, and $w$ is an external vector that determines the direction of their paths, as discussed in detail later. ${\\cal T}$ represents the time ordering operator for the fields whereas ${\\cal \\overline{T}}$ represents the anti time ordering operator~\\cite{Collins:2011zzd,Echevarria:2016scs}, and for sake of brevity we omit the flavor index of the quark fields and of $\\Xi$ (but all the results in this paper should be understood to be flavor-dependent). The color trace of the correlator will be shortly discussed in detail.\n\nThe definition~\\eqref{e:invariant_quark_correlator} clarifies and refines the definitions previously advanced in Refs.~\\cite{Accardi:2008ne,Accardi:2017pmi,Accardi:2019luo}. \nIn particular, with the present definition, the jet correlator naturally emerges at the right hand side of the master sum rule~\\eqref{e:master_sum_rule}, that we will derive in the next section and connects the single inclusive quark fragmentation process to the propagation  and inclusive fragmentation of a quark discussed in this Section. \nA diagrammatic interpretation of Eq.~\\eqref{e:invariant_quark_correlator} is given in Figure~\\ref{f:cut_diagrams}(a), where the vertical cut line represents the discontinuity, ``Disc'', in Eq.~\\eqref{e:invariant_quark_correlator}, or, in other words, a sum over all quark hadronization products~\\cite{Sterman:1986aj}. In fact, inserting a completeness between the square brackets in Eq.~\\eqref{e:invariant_quark_correlator}, one can interpret the jet correlator as the square of the sum of all possible quark-to-hadron transition amplitudes. \n\n\\begin{figure}[tb]\n\\centering\n\\begin{tabular}{ccc}\n\\includegraphics[width=0.32\\linewidth,valign=b]{Xi_cut.png}\n& \\hspace{2cm} &\t\n\\includegraphics[width=0.32\\linewidth,valign=b]{Delta_cut.png}\n\\\\ & & \\\\ \n(a) & & (b)\n\\end{tabular}\n\\caption{\nDiagrammatic interpretations of (a) the fully inclusive jet correlator of Eqs.~\\eqref{e:invariant_quark_correlator} and \\eqref{e:invariant_quark_correlator_W}, and (b) the single-hadron fragmentation correlator \\eqref{e:1hDelta_corr}. The black solid line corresponds to the hadronizing quark with momentum $k$, the black dashed line to the produced hadron with momentum $P_h$ and spin $S_h$. The yellow blob corresponds to the unobserved hadronization products. The vertical thin dashed line is the cut that puts the (unobserved) particles on the mass shell (see Appendix~\\ref{a:conv}).\n}\n\\label{f:cut_diagrams}\n\\end{figure}\n\n\nThe color-averaging of the initial-state quark, implemented as Tr$_c[\\dots]\/N_c$, has a crucial role, since it mimicks the color neutralization that has to take place in order to be able to consider the discontinuity, which corresponds to having on-shell intermediate states (see, {\\it e.g.}, Ref.~\\cite{Roberts:2015lja}, Section~2.4.). Furthermore, the color average is essential for the spectral representation of the jet correlator to be developed in Section~\\ref{ss:spectr_dec}.  Finally, color averaging is also important in view of the sum rule discussion of Section~\\ref{s:1h_rules} and, more in general, for using the inclusive jet correlator in factorization theorems at large Bjorken $x$~\\cite{Chen:2006vd}. When calculating Dirac traces, we will also average over the quark's polarization states as detailed in Appendix~\\ref{a:conv}. \n\nOn the physics side, the correlator $\\Xi$\ncaptures the hadronization of a quark including {\\em all} the products of the hadronization process. We call this the ``fully inclusive'' jet correlator\\footnote{Other names used in the literature for the same correlator are ``jet distribution\"~\\cite{Sterman:1986aj} and ``jet factor\"~\\cite{Collins:2007ph}. Its Dirac projections have also been called  ``(final state) jet functions\"~\\cite{Accardi:2008ne,Chen:2006vd,Chay:2013zya}.} \nin order to stress that none of the jet's constituents is actually reconstructed -- hence the absence of a definition for a jet axis and radius, contrary to other semi-inclusive definition of jets. In the following, when using for simplicity the term ``jet''(or ``inclusive jet'') correlator, we will always refer to this fully inclusive jet correlator.\nThe inclusiveness of $\\Xi$ will also be evident when relating this to the correlator for the hadronization of a quark into a single hadron by the sum rule we will prove in Section~\\ref{s:1h_rules}. Finally, when inserting $\\Xi$ in a DIS diagram~\\cite{Accardi:2008ne,Accardi:2017pmi}, which can be justified at large values of Bjorken $x$ where 4-momentum conservation limits the amount of transverse momentum available to final state hadrons \\cite{Sterman:1986aj,Chen:2006vd,Accardi:2018gmh}, the jet in question can be identified with the current jet. \n\nIt is also interesting to remark that, taking into account the properties of the color trace and after a specific choice for the path of the Wilson line (to be discussed next), the correlator $\\Xi$ can be expressed as the discontinuity of the gauge-invariant quark propagator, whose spectral decomposition has been studied in Ref.~\\cite{Yamagishi:1986bj} for the case of a straight Wilson line connecting $0$ to $\\xi$. In this paper, we will discuss instead the spectral representation for the case of Wilson lines running along staple-like contours -- which are the natural paths arising in QCD factorization theorems -- and use this in applications involving correlators integrated along one light-cone direction.\n\n\n\n\n\n\n\\subsubsection{Wilson line structure}\n\\label{sss:link_structure}\n\nWe work in a reference frame specified by two light-like unit vectors $n_+$ and $n_-$ such that $n_+^2 = n_-^2 = 0$ and $n_+\\cdot n_- = 1$. Any other vector $a^\\mu$ can then be specified in light-cone coordinates as $a=[a^-,a^+,\\vect{a}_T]$, with $a^\\pm = a\\cdot n_\\mp$, and $\\vect{a}_T$ the 2-dimensional coordinates of $a$ transverse with respect to the $(n_+,n_-)$ plane, see Appendix~\\ref{a:conv}. We also assume the quark to be highly boosted in the negative $z$ direction, so that the minus component of its momentum is dominant, $k^- \\gg |\\vect{k}_T| \\gg k^+$. \nWhen the jet correlator is included in the calculation of a physical process, $n_+$ and $n_-$ can be determined by the kinematics of that process; for example, in DIS one can choose these to be coplanar with the hadron and virtual photon momenta, with $n_-$ aligned with the latter \\cite{Accardi:2008ne,Accardi:2017pmi}. However, in this paper we study the jet correlator as a theoretical object in its own right. \n\n\\begin{figure\n\\centering\n\\begin{tabular}{ccccc}\n\\includegraphics[width=0.31\\textwidth]{W2W1_generic.pdf}\n& \\hspace{0.15cm} &\n\\includegraphics[width=0.31\\textwidth]{W_generic.pdf}\n& \\hspace{0.15cm} &\n\\includegraphics[width=0.31\\textwidth]{W_TMD.pdf}\n\\\\\n\\quad\\ (a) & & \\quad\\ (b) & & \\quad\\ (c)  \n\\\\ \n\\end{tabular}\n\\caption{Staple-like Wilson line paths for the jet correlator $\\Xi(k;w=n_+)$: \n(a) $W_2(0,\\infty;w=n_+)$ (red) and $W_1(\\infty,\\xi;w=n_+)$ (blue); \n(b) the combined Wilson line $W(0,\\xi;w=n_+)$; \n(c) the TMD Wilson line $W_{TMD}(\\xi^+,\\vect{\\xi}_T)$.\n}\n\\label{f:W_paths}\n\\end{figure}\n\n\n\n\\begin{comment}\n\\begin{figure}[t]\n  \\centering\n  \\textbf{(a)}\\includegraphics[width=0.3\\linewidth,valign=b]{fig_W1-general.png}\n  \\hfill\n  \\textbf{(b)}\\includegraphics[width=0.3\\linewidth,valign=b]{fig_W2-nplus.png}\n  \\hfill\n  \\textbf{(c)}\\includegraphics[width=0.3\\linewidth,valign=b]{fig_W3-tmd.png}\n\\caption{Staple-like Wilson line paths for the quark correlator $\\Xi(k;v)$: (a) For a generic direction $v$; (b) For a light-cone $v=n_+$; (c) For TMD correlators, where $\\xi^-=0$. \n\\AScom{Change this figure into the one with the $\\{ n_+, n_- \\}$ plane.} }\n\\label{f:W_paths}\n\\end{figure}\n\\begin{figure}[t]\n\\centering\n\\includegraphics[width=0.5\\linewidth]{Wpath}\n\\caption{The chosen path for the Wilson line $W_2(0,\\infty)$ in the unintegrated jet correlator $\\Xi(k,n_+)$ can be understood as the limit $\\overline{t} \\to +\\infty$ of the link in the figure. \\AScom{I have to introduce $\\overline{t}$ in the figure.} The arrows pointing out of the page represent the two-dimensional transverse plane. \\AScom{Add a similar figure for $W_1(\\infty,\\xi)$?}}\n\\label{f:W_paths}\n\\end{figure}\n\\end{comment}\n\n\nWe restrict our attention to a class of Wilson lines that reproduces the paths determined by the TMD factorization theorems for quark-initiated hard scattering processes, when $\\Xi$ is integrated over the sub-dominant momentum components $k^+$~\\cite{Collins:2008ht,Collins:2011zzd} (or even in the fully unintegrated factorization proposed in Ref.~\\cite{Collins:2007ph}). \nFor simplicity, we also restrict the discussion to the case $w=n_+$, even though no substantial impediment arises in the treatment of slightly off-the-light-cone Wilson lines. \nTo be specific, \nwe take $W_2$ to run first from 0 to infinity along the plus light-cone direction,   \nthen to infinity in the transverse plane, \nand eventually to infinity again along the minus light-cone direction, see Figure~\\ref{f:W_paths}(a).\nAnalogously, $W_1$  \nruns from infinity backwards in the minus direction until it reaches $[\\xi^-,\\infty^+,\\vect{\\infty}_T$], \nthen in the transverse direction until $[\\xi^-,\\infty^+,\\vect{\\xi}_T]$, \nand eventually reaching $\\xi = [\\xi^-,\\xi^+,\\vect{\\xi}_T]$ along the plus direction \n(see Figure~\\ref{f:W_paths}(a)).  \nExplicitly, \n\\begin{align}\n\\label{e:W2_antitime}\nW_2(0,\\infty;n_+) & =\\, \n{\\cal U}_{n_+}[0^-, 0^+, \\vect{0}_T; 0^-, \\infty^+, \\vect{0}_T]\\,\\,\n{\\cal U}_{v_T}[0^-, \\infty^+, \\vect{0}_T; 0^-, \\infty^+, \\vect{\\infty}_T]\\, \\, \n{\\cal U}_{n_-}[0^-, \\infty^+, \\vect{\\infty}_T; \\infty^-, \\infty^+, \\vect{\\infty}_T]\\, ,\n\\\\\n\\label{e:W1_time}\nW_1(\\infty,\\xi;n_+) &=\\,\n{\\cal U}_{n_-}[\\infty^-, \\infty^+, \\vect{\\infty}_T; \\xi^-, \\infty^+, \\vect{\\infty}_T]\\,\\, \n{\\cal U}_{v_T}[\\xi^-, \\infty^+, \\vect{\\infty}_T; \\xi^-, \\infty^+, \\vect{\\xi}_T]\\,\\,\n{\\cal U}_{n_+}[\\xi^-, \\infty^+, \\vect{\\xi}_T; \\xi^-, \\xi^+, \\vect{\\xi}_T]\\, , \n\\end{align}\nwith  ${\\cal U}_v$ representing the Wilson operator along a half-line starting from $a$ in the $v$ direction, {\\it i.e.},\n\\begin{align}\n  {\\cal U}_v[a;\\infty] = {\\cal P} \\exp \\Big( -\\i g \\int_0^\\infty ds\\,  v^\\mu A_\\mu(a+sv) \\Big) \\, ,\n\\end{align}\nwhere ${\\cal P}$ denotes the path-ordering operator, and the square brackets emphasizes the straightness of the path. We will comment upon other possible choices of paths below. \n\n\nFrom the definitions~\\eqref{e:W2_antitime} and \\eqref{e:W1_time}, one can see that $W_2$ is automatically anti time ordered, and $W_1$, time ordered. Namely, with our choice of paths, ${\\cal \\overline{T}} {\\cal P} \\equiv {\\cal P}$ and ${\\cal T} {\\cal P} \\equiv {\\cal P}$. \nOwing to this specific choice for the Wilson lines and thanks to the color trace and to the absence of intermediate states, we can also perform a cyclic permutation of the fields in Eq.~\\eqref{e:invariant_quark_correlator} and combine the two Wilson operators $W_{1,2}$ into the single, staple-like operator \n\\begin{align}\n  W(0,\\xi;n_+) = W_2(0,\\infty;n_+) W_1(\\infty,\\xi;n_+) \n\\end{align}\nillustrated in Figure~\\ref{f:W_paths}(b), so that\n\\begin{align}\n  \\label{e:invariant_quark_correlator_W}\n  \\Xi_{ij}(k;n_+) = \\text{Disc} \\int \\frac{d^4 \\xi}{(2\\pi)^4} e^{\\i k \\cdot \\xi} \\,\n  \\frac{\\text{Tr}_c}{N_c}\\, {\\langle\\Omega|} \\psi_i(\\xi) {\\overline{\\psi}}_j(0) W(0,\\xi;n_+) {|\\Omega\\rangle} \\, .\n\\end{align}\nThe jet correlator can thus also be written as the discontinuity of a gauge invariant quark propagator. \n\nUpon setting $\\xi^-=0$, that corresponds to integrating the correlator over the $k^+$ component, we obtain the staple-like $W_{TMD}$ Wilson line \nutilized to define TMD distributions: \n\\begin{align}\n\\label{e:W_np_TMD}\n  W_{TMD}(\\xi^+, \\vect{\\xi}_T) & \\equiv W(0,\\xi;n_+)|_{\\xi^-=0} \\nonumber \\\\\n  & = \n    {\\cal U}_{n_+}[0^-, 0^+, \\vect{0}_T; 0^-, \\infty^+, \\vect{0}_T] \\ \n    {\\cal U}_{v_T}[0^-, \\infty^+, \\vect{0}_T; 0^-, \\infty^+, \\vect{\\xi}_T] \\\n    {\\cal U}_{n_+} [0^-, \\infty^+, \\vect{\\xi}_T; 0^-, \\xi^+, \\vect{\\xi}_T] \\ , \n\\end{align}\nsee Figure~\\ref{f:W_paths}(c).  \nNote that, even without choosing a specific form for $W_{1,2}$, the integration over $k^+$ renders the (anti-)time ordering on the light cone  equivalent to the path ordering, since $\\xi^+$ becomes proportional to the time variable. \nSetting also $\\vect{\\xi}_T=0$, which corresponds to furthermore integrating $\\Xi$ over the transverse momentum $\\vect{k}_T$, one would finally obtain the collinear Wilson line  $W_{coll}(\\xi^+) \\equiv W_{TMD}(\\xi^+,\\vect{0}_T)={\\cal U}[0^-, 0^+, \\vect{0}_T; 0^-, \\xi^+, \\vect{0}_T]$, running along the light-like segment from $0^+$ to $\\xi^+$.\n\n\nIt is important to remark that the results discussed in this paper hold true also for a larger class of Wilson lines. In order to drop the ${\\cal T}$ and ${\\cal \\overline{T}}$ time-ordering operators and rewrite the jet correlator as a gauge invariant quark propagator, one only needs to ensure that the time variable increases along the path that goes from 0 to $\\infty$, and decreases when going from $\\infty$ to $\\xi$. This clearly restricts the class of Wilson lines available, but not overmuch. \nFor example, one could \nconsider off-the-light-cone lines, with $w \\neq n_+$ slightly tilted away from the plus light-cone direction, \nor adopt L-shaped lines reaching infinity along $n_+$ and then moving to infinity simultaneously along the minus and transverse directions. \nFurthermore, we will need $W$ in Eq.~\\eqref{e:invariant_quark_correlator_W} to reduce to the identity matrix when $\\xi \\to 0$, hence in that limit the path of the Wilson line should not contain loops. The straight line and the staple-like Wilson line that enter in collinear and TMD factorization belong to this category. \n\n\n\n\n\n\n\n\\subsubsection{Dirac structure}\n\\label{sss:dirac_structure}\n\nThe correlator $\\Xi$ can be decomposed on a basis of Dirac matrices,\n$\n  \\big\\{ {\\mathbb 1}, \\gamma_5, \\gamma^\\mu, \\gamma^\\mu \\gamma_5,\n    \\i\\sigma^{\\mu\\nu} \\gamma_5   \\big\\} ,\n$\nwhere $\\i$ is the imaginary unit, ${\\mathbb 1}$ the identity matrix, \n$\\gamma_5 = \\i \\epsilon^{\\mu\\nu\\rho\\sigma}\\gamma_\\mu\\gamma_\\nu\\gamma_\\rho\\gamma_\\sigma$,  $\\epsilon^{\\mu\\nu\\rho\\sigma}$ the totally antisymmetric tensor of rank 4, \nand $\\sigma^{\\mu\\nu} = (\\i\/2) [ \\gamma^\\mu,\\gamma^\\nu ]$. \nAssuming invariance under Lorentz and parity transformations, we can parametrize $\\Xi$ as:\n\\begin{align}\n  \\Xi(k;n_+) = \\Lambda A_1 {\\mathbb 1} + A_3 \\slashed{k}\n    + \\frac{\\Lambda^2}{k \\cdot n_+} B_1 \\slashed{n}_+\n    + \\frac{\\Lambda}{k \\cdot n_+} B_3 \\sigma_{\\mu\\nu} k^\\mu n_+^\\nu \\ .\n  \\label{e:jet_ampl}\n\\end{align}\nThe amplitudes\n$A_i$ and $B_i$ are, in principle, functions of all the Lorentz scalars that one can build with the available Lorentz vectors, $k \\cdot n_+$ and $k^2$~\\cite{Mulders:1995dh,Bacchetta:2000jk,Boer:2016xqr}. \nThe vector $n_+$ is available as the vector specifying the direction of the Wilson line.\nThe subscripts differ from the conventions discussed in Refs.~\\cite{Accardi:2017pmi,Accardi:2018gmh}, but have been chosen such that they match the customary decomposition of the fragmentation correlator to be discussed in Section~\\ref{ss:1h_inclusive_FF}. \nWe have also introduced a power-counting scale $\\Lambda = O(\\Lambda_{\\text{QCD}})$\nthat defines an ``operational'' twist expansion for the correlator in powers of $\\Lambda\/k^-$, where we assume a large boost in the $k^-$ direction so that $k^+ = (k^2+\\vect{k}_T^2)\/2k^- \\ll |\\vect{k}_T| \\ll k^-$, with $\\vect{k}_T \\sim O(\\Lambda)$ and $k^+,k^2\\sim O(\\Lambda^2)$. \nThis expansion is analogous to that used in Ref.~\\cite{Bacchetta:2004zf,Bacchetta:2006tn} for the single-hadron fragmentation correlator, and further discussed in Section~\\ref{ss:1h_inclusive_FF}. Its relation with the rigorous twist expansion of local operators in the Operator Product Expansion formalism is discussed, {\\it e.g..}, in Ref.~\\cite{Jaffe:1996zw}. \n\nThe twist expansion of the inclusive jet correlator can be made explicit by writing Eq.~\\eqref{e:jet_ampl} in terms of the light-cone Dirac matrices $\\gamma^\\pm = \\slashed{n}_\\mp$:\n\\begin{align}\n  \\Xi(k;n_+) = k^-  A_3 \\, \\gamma^+\n    + \\Lambda\\left( A_1\\, {\\mathbb 1}\n      + A_3\\, \\frac{\\slashed{k}_T}{\\Lambda}\n      + \\frac{\\i}{2} B_3\\, [\\gamma^+,\\gamma^-] \\right)\n    + \\frac{\\Lambda^2}{k^-} \\left( B_1\\, \\gamma^-   \n      + A_3 \\frac{k^2+\\vect{k}_T^2}{2\\Lambda^2}\\, \\gamma^-  \n      + B_3 \\frac{\\i}{2\\Lambda}[\\slashed{k}_T, \\gamma^-] \\right)  \\ .\n  \\label{e:Xi_twist_dec}\n\\end{align}\nThe amplitudes $A_{1,3}$ and $B_{1,3}$ can be projected out by tracing $\\Xi$ multiplied by suitable Dirac matrices.\nWe report here only the non-zero traces and group these according to the power counting with which they contribute to Eq.~\\eqref{e:Xi_twist_dec}: \\\\\n\\begin{itemize}\n\n\\item\n  Twist-2 structures - $O(k^-)$:\n  \\begin{align}\n    \\label{e:trace_gm}\n    \\text{Tr}[\\Xi\\, \\gamma^-] & = 4 A_3 k^- \n   \n   \n   \n   \n  \\end{align}\n\n\\item\n  Twist-3 structures - $O(\\Lambda)$:\n  \\begin{align}\n    \\label{e:trace_1}\n    \\text{Tr}[\\Xi\\, {\\mathbb 1}] & = 4 \\Lambda A_1 \\\\\n    \\label{e:trace_gi}\n    \\text{Tr}[\\Xi\\, \\gamma^i] & = 4 A_3 k_T^i \\\\\n   \n   \n   \n   \n   \n   \n    \\label{e:trace_isigmaijg5}\n    \\text{Tr}[\\Xi\\, \\i \\sigma^{ij} \\gamma_5] \n   \n                             & = -4\\Lambda B_3 \\epsilon_T^{ij} \n  \\end{align}\n\n\\item\n  Twist-4 structures - $O(\\Lambda^2\/k^-)$:\n  \\begin{align}\n    \\label{e:trace_gp}\n    \\text{Tr}[\\Xi\\, \\gamma^+] \n       & = 4 A_3 \\frac{k^2 + \\vect{k}_T^2}{2k^-} + \\frac{4\\Lambda^2}{k^-} B_1 \\\\\n   \n   \n    \\label{e:trace_isigmaipg5}\n    \\text{Tr}[\\Xi\\, \\i \\sigma^{i+} \\gamma_5] \n       & = 4 \\frac{\\Lambda}{k^-} B_3 \\epsilon_T^{ij} {k_T}_j \n  \\end{align}\n\n\\end{itemize}\nIn these formulas, the  $\\epsilon_T^{ij}=\\epsilon^{ij\\mu\\nu}n_{-\\mu}n_{+\\nu}$ tensor is the projection of the completely antysimmetric tensor in the transverse plane, and $i,j=1,2$ are transverse Lorentz indices (see Appendix~\\ref{a:conv}). \n\nWe note that the trace in Eq.~\\eqref{e:trace_gm} corresponds to the inclusive jet function $J$ defined in e.g. Ref.~\\cite{Procura:2009vm,Jain:2011xz}. \nAs we shall see in Sec.~\\ref{ss:spectr_dec}, the amplitudes $A_3$ and $A_1$ are also directly related to the chiral even and chiral odd spectral functions of the quark propagator, respectively.\n\nMoreover, \nnote that the Dirac structure associated to the amplitude $B_3$ is time-reversal odd (T-odd)~\\cite{Mulders:1995dh,Bacchetta:2000jk,Mulders:2016pln,Accardi:2017pmi}. \nIn the correlator that defines parton distribution functions, the T-odd structures are generated by the presence of the gauge link in the transverse plane.  \nSince the partonic poles vanish in the correlator that defines fragmentation functions, the T-odd FFs are generated by the interchange of {\\em in-} and {\\em out-}states induced by a time-reversal transformation rather then by the link structure~\\cite{Pijlman:2006vm,Bomhof:2004aw,Boer:2003cm,Meissner:2008yf,Metz:2016swz,Gamberg:2008yt,Gamberg:2010uw}. For this reason the FFs are universal, contrary to TMD PDFs. \nAs shown in Section~\\ref{ss:sum_operator}, the inclusive jet correlator is related to the fragmentation correlator via an on-shell integration over the hadronic momenta and a sum over all the possible hadronic final states. Since there are no {\\em out-}states in Eq.~\\eqref{e:invariant_quark_correlator}, we conclude that T-odd structures cannot be present in $\\Xi$, namely\n\\begin{align}\n\\label{e:B3_zero}\n  B_3 = 0 \\ .   \n\\end{align}\nThis further simplifies Eq.~\\eqref{e:Xi_twist_dec} and its Dirac projections in Eq.~\\eqref{e:trace_isigmaijg5} and Eq.~\\eqref{e:trace_isigmaipg5}. We will briefly return to this point also in the next subsection.\n\n\n\n\\subsection{Convolution representation and spectral decomposition}\n\\label{ss:spectr_dec}\n\nWe aim now at deriving a spectral representation for the inclusive jet correlator \\eqref{e:invariant_quark_correlator}, or, equivalently, for the the gauge invariant quark propagator \\eqref{e:invariant_quark_correlator_W}. \n\nThe first step is to rewrite Eq.\\eqref{e:invariant_quark_correlator_W} as a convolution of a quark bilinear $\\i \\widetilde S$ and the Fourier transform $\\widetilde W$ of the Wilson line,\n\\begin{align}\n  \\label{eq:convolution_Xi}\n  \\Xi_{ij}(k;n_+) = \\text{Disc} \\int d^4p\\, \\frac{\\text{Tr}_c}{N_c}\\,  {\\langle\\Omega|} \\i \\widetilde S_{ij}(p) \\widetilde W(k-p;n_+) {|\\Omega\\rangle} \\ ,\n\\end{align}\nwhere \n\\begin{align}\n\\label{e:def_tildeS}\n\\i \\widetilde S_{ij}(p) & = \\int \\frac{d^4\\xi}{(2\\pi)^4}\\, e^{\\i\\xi \\cdot p}\\, \\psi_i(\\xi) {\\overline{\\psi}}_j(0)\\, , \\\\\n\\label{e:def_tildeW}\n\\widetilde W(k-p;n_+) & = \\int \\frac{d^4\\xi}{(2\\pi)^4}\\, e^{\\i\\xi \\cdot (k-p)}\\, W(0,\\xi;n_+) \\ .\n\\end{align}\nNote that this convolution representation does not, in itself, depend on the choice of the path for the Wilson line and it is thus generally valid for the study of gauge invariant quark propagators. A careful choice of Wilson line within the generic class discussed in Section~\\ref{sss:link_structure} is only needed when relating the gauge invariant propagator to the inclusive jet correlator \\eqref{e:invariant_quark_correlator}. \n\n\n\nThe convolution representation becomes very useful in combination with the spectral decomposition of the quark bilinear.  The vacuum expectation value of the operator $\\i \\widetilde S$ is, indeed, the retarded\/advanced (according to the sign of $\\xi^0$) quark propagator, for which there exist spectral representations~\\cite{Bjorken:1965zz}. However, in this paper, we are rather interested in the jet correlator integrated over the sub-dominant $k^+$ component of the quark momentum, and we can, in fact, work with the simpler spectral representation of the Feynman quark propagator. To this end, we introduce the following \\textit{\\it auxiliary} unintegrated correlator:\n\\begin{align}\n\\label{e:Xiprime}\n\\Xi^\\prime_{ij}(k;n_+) = \\text{Disc} \\int \\frac{d^4 \\xi}{(2\\pi)^4} e^{\\i k \\cdot \\xi} \\,\n\\frac{\\text{Tr}_c}{N_c}\\, {\\langle\\Omega|}\\, {\\cal T} \\big[ \\psi_i(\\xi) {\\overline{\\psi}}_j(0) \\big]\\, W(0,\\xi;n_+) {|\\Omega\\rangle} \\, ,   \n\\end{align}\nwhere\nonly the quark bilinear operator is time ordered.  In Section~\\ref{ss:TMD_J_corr}, we will show that under the Wilson line choice discussed in Section~\\ref{sss:link_structure}, the $\\Xi$ and $\\Xi^\\prime$ correlators integrated over $k^+$ are, in fact, identical, and we can equivalently work with the latter.\n\nThe convolution representation of $\\Xi^\\prime$ is obtained from Eq.~\\eqref{eq:convolution_Xi} by replacing $\\i \\widetilde S$ with $\\i \\widetilde S^\\prime$, defined as \n\\begin{equation}\n\\label{e:def_tildeSF}\n\\i \\widetilde S^\\prime_{ij}(p) = \\int \\frac{d^4\\xi}{(2\\pi)^4}\\, e^{\\i\\xi \\cdot p}\\,\n{\\cal T} \\big[ \\psi_i(\\xi) {\\overline{\\psi}}_j(0) \\big] \\, .\n\\end{equation}\nThis operator can be given a Dirac decomposition assuming invariance under Lorentz and parity transformations~\\cite{Bjorken:1965zz}:\n\\begin{align}\n\\i \\widetilde S^\\prime_{ij}(p) = \\hat s_3(p^2) \\slashed{p}_{ij} + \\sqrt{p^2} \\hat s_1(p^2) {\\mathbb 1}_{ij} \\ ,\n\\label{e:quark_bilinear_decomp}\n\\end{align}\nwhere, for simplicity, we omitted an overall identity matrix in color space, and we can call $\\hat{s}_{1,3}$ {\\it spectral operators} for reasons that will become clear shortly. \nThe correlator $\\Xi^\\prime$ can then be written as\n\\begin{align}\n\\label{e:spectral_convolution}\n\\Xi^\\prime_{ij}(k;n_+) = \\text{Disc} \\int d^4p\\, \\frac{\\text{Tr}_c}{N_c}\\, \n{\\langle\\Omega|} \n\\Big[\\hat s_3(p^2) \\slashed{p}_{ij} + \\sqrt{p^2} \\hat s_1(p^2) {\\mathbb 1}_{ij} \\Big]  \n\\widetilde W(k-p;n_+)\\, \n{|\\Omega\\rangle} \\ .\n\\end{align}\nWe can obtain a connection with the K\\\"allen-Lehman spectral representation of the quark propagator~\\cite{Bjorken:1965zz,Weinberg:1995mt,Accardi:2008ne,Accardi:2019luo} by noticing that the Feynman propagator for the quark in momentum space is given by the expectation value of $\\i \\widetilde S^\\prime$ on the interacting vacuum. In turn, the Feynman propagator can be written as a superposition of propagators for (multi)particle states of invariant mass $\\mu$~\\cite{Bjorken:1965zz,Weinberg:1995mt}:\n\\begin{equation}\n\\label{e:Feyn_spec_rep}\n\\frac{\\text{Tr}_c}{N_c}\\, {\\langle\\Omega|} \\i \\widetilde S^\\prime(p) {|\\Omega\\rangle} = \\frac{1}{(2\\pi)^4} \\int_{-\\infty}^{+\\infty} d\\mu^2 \n\\Big\\{ \\slashed{p}\\, \\rho_3(\\mu^2) + \\sqrt{\\mu^2}\\, \\rho_1(\\mu^2) \\Big\\}\\, \n\\theta(\\mu^2)\\,\n\\frac{\\i}{p^2-\\mu^2+ \\i \\epsilon} \\ ,\n\\end{equation}\nwhere the theta function ensures that the spectral functions $\\rho_{1,3}$ contribute to the integral only at time-like momenta.\\footnote{In Eq.~\\eqref{e:Feyn_spec_rep}, there is an extra $(2\\pi)^{-4}$ factor with respect to Refs.~\\cite{Bjorken:1965zz,Accardi:2008ne,Accardi:2017pmi} because of the normalization of Eq.~\\eqref{e:invariant_quark_correlator}, which is customary in the literature dealing with TMD parton distribution and fragmentation functions and the associated non-local operators (see {\\em e.g.} Ref.~\\cite{Bacchetta:2006tn}).} \nAs a consequence of the canonical commutation relations, the spectral function $\\rho_{3}$ satisfies~\\cite{Zwicky:2016lka,Weinberg:1995mt}\n\\begin{equation}\n  \\int_0^{+\\infty} d\\mu^2 \\rho_3(\\mu^2) = 1 \\ .\n\\label{e:rho13_positivity_rho3sumrule}\n\\end{equation}This function can then be interpreted as the probability distribution for a quark to fragment into a multi-particle state of invariant mass $\\mu^2$. The $\\rho_1$ spectral function does not  satisfy any normalization condition, but, as we will show in Section~\\ref{sss:zeta_calc}, is related to the \nmass density of the quark hadronization products. \nCare is, however, needed with these interpretations since the positivity of $\\rho_3$ (along with that of $\\rho_1$) is not guaranteed in a confined theory. \n\nNote that, when working in an axial gauge $v \\cdot A=0$ as we will do in Section~\\ref{s:1h_rules}, we should also add a structure proportional to $\\slashed v$ to the decomposition in Eq.~\\eqref{e:quark_bilinear_decomp} and to the term in curly brackets in Eq.~\\eqref{e:Feyn_spec_rep}, see also Ref.~\\cite{Yamagishi:1986bj}. However, in our explicit calculations we will adopt the light-cone gauge, where $v=n_+$, and the additional, gauge-fixing term would only contribute at twist-4 level. Since in this work we limit the applications of our formalism to FF sum rules up to the twist-3 level, for sake of simplicity we have not explicitly written the gauge-fixing term in Eq.~\\eqref{e:Feyn_spec_rep}, but we will briefly return on its role in Section~\\ref{ss:TMDjet_recap}.  \n\n\n\n\n\nThe discontinuity in Eq.~\\eqref{e:spectral_convolution} is completely determined by the discontinuity of  Eq.~\\eqref{e:Feyn_spec_rep}. To calculate the latter, we employ the Cutkosky rule~\\cite{Cutkosky:1960sp,Bloch:2015efx,Zwicky:2016lka}, by which one simply needs to replace\n\\begin{equation}\n\\label{e:Cutkosky_rule}\n\\frac{1}{p^2-\\mu^2 + \\i \\epsilon} \\longrightarrow -2\\pi \\i\\, \\delta(p^2 - \\mu^2)\\, \\theta(p^0) \n\\end{equation}\nat the right hand side of that equation. Namely, as the multiparticle state of invariant mass $\\mu^2$ passes the cut, this can be thought of as a set of on-shell particles with positive energy. We thus obtain:\n\\begin{align}\n\\nonumber\n\\text{Disc}\\, \\frac{\\text{Tr}_c}{N_c}\\, {\\langle\\Omega|} \\i \\widetilde S^\\prime(p) {|\\Omega\\rangle} & = \\frac{1}{(2\\pi)^3} \\int_{-\\infty}^{+\\infty} d\\mu^2 \n\\big\\{ \\slashed{p}\\, \\rho_3(\\mu^2) + \\sqrt{\\mu^2}\\, \\rho_1(\\mu^2) \\big\\}\\, \n\\theta(\\mu^2)\\,\n\\delta(p^2 - \\mu^2)\\, \\theta(p^0) \\\\\n\\label{e:cut_Feyn_spec_rep}\n& = \\frac{1}{(2\\pi)^3}\\, \\big\\{ \\slashed{p}\\, \\rho_3(p^2) + \\sqrt{p^2}\\, \\rho_1(p^2) \\big\\}\\, \n\\underbrace{\\theta(p^2)\\, \\theta(p^0)}_{=\\theta(p^2)\\, \\theta(p^-)} \n\\end{align}\nFinally, using the operator decomposition for $\\i \\widetilde S^\\prime$ given in Eq.~\\eqref{e:quark_bilinear_decomp}, we obtain the spectral representation for the discontinuity of the expectation values of the operators $\\hat{s}_{1,3}$: \n\\begin{equation}\n\\label{e:spec_rep_s13}\n(2\\pi)^{3}\\, \\text{Disc}\\, \\frac{\\text{Tr}_c}{N_c}\\, {\\langle\\Omega|} \\hat{s}_{1,3}(p^2) {|\\Omega\\rangle} =  \\rho_{1,3}(p^2)\\, \\theta(p^2)\\, \\theta(p^-) \\ .\n\\end{equation}\nIt is in this sense, that we can refer to $\\hat s_{1,3}$ as spectral operators. \n\nNote that Eqs.~\\eqref{e:cut_Feyn_spec_rep} and~\\eqref{e:spec_rep_s13} provide a spectral representation for the quark propagator ${\\langle\\Omega|} \\i \\widetilde{S}^\\prime {|\\Omega\\rangle}$ without a Wilson line insertion. It is the purpose of the convolution representation in Eq.~\\eqref{e:spectral_convolution}, supplemented by Eq.~\\eqref{e:spec_rep_s13} to provide a spectral representation for $\\Xi^\\prime(k;n_+)$. Its application to the calculation of the $k^+$-integrated jet correlator is discussed in the next Section.\n\n\n\n\n\n\\subsection{The TMD inclusive jet correlator}\n\\label{ss:TMD_J_corr}\n\nWhen integrating the inclusive jet correlator over the suppressed $k^+$ quark momentum component, one obtains the TMD inclusive  jet correlator $J$~\\cite{Accardi:2019luo},\n\\begin{align}\n\\label{e:J_TMDcorr}\n  J_{ij}(k^-,\\vect{k}_T;n_+)\n    & \\equiv \\frac{1}{2} \\int dk^+\\, \\Xi_{ij}(k;n_+) \\nonumber \\\\\n    & = \\frac{1}{2}\\ \\text{Disc} \\int \\frac{d\\xi^+ d^2 \\vect{\\xi}_T}{(2\\pi)^3}\\,\n      e^{\\i k \\cdot \\xi} \\frac{\\text{Tr}_c}{N_c}\n      {\\langle\\Omega|} \\psi_i(\\xi) {\\overline{\\psi}}_j(0) W(0,\\xi;n_+) \n     \n      {|\\Omega\\rangle}_{|_{\\xi^-=0}} \\ ,\n\\end{align}\nwhere the $1\/2$ normalization factor is justified in Appendix~\\ref{a:conv}, and the integrand is now restricted to $\\xi^-=0$.\n\nThe TMD jet correlator can be decomposed in Dirac structures, with coefficients that can be determined by integrating the projections of $\\Xi$ given in Eqs.~\\eqref{e:trace_gm}-\\eqref{e:trace_isigmaipg5}. \nFollowing the arguments discussed in Appendix~\\ref{a:conv} and using Eq.~\\eqref{e:proj_int_J}, we define the projection of $J$ to be:\n\\begin{equation}\n\\label{e:def_proj}\nJ^{[\\Gamma]} \\ \\equiv\\ {\\rm Tr}\\bigg[ J\\, \\frac{\\Gamma}{2} \\bigg] = \n\\frac{1}{2} \\int dk^+ {\\rm Tr} \\bigg[ \\Xi\\, \\frac{\\Gamma}{2} \\bigg] = \n\\frac{1}{4} \\int dk^+ {\\rm Tr} \\big[ \\Xi\\, \\Gamma \\big] \\ .\n\\end{equation}\nFor twist-2 structures we have:\n\\begin{align}\n\\label{e:trace_J_gm}\nJ^{[\\gamma^-]} & =\n\\frac{1}{2} \\int dk^2 A_3(k^2,k^-) \n\\ \\equiv\\ \\alpha(k^-) \\ .\n\\end{align}\nFor twist-3 structures we have:\n\\begin{align}\n\\label{e:trace_J_id}\n& J^{[{\\mathbb 1}]} = \n\\frac{\\Lambda}{2k^-} \\int dk^2 A_1(k^2,k^-) \n\\ \\equiv\\ \\frac{\\Lambda}{k^-} \\zeta(k^-)  \\\\\n\\label{e:trace_J_gi}\n& J^{[\\gamma^i]} = \n\\frac{k_T^i}{2k^-} \\int dk^2 A_3(k^2,k^-) \n= \\frac{\\Lambda}{k^-} \\alpha(k^-) \\frac{k_T^i}{\\Lambda}  \\\\\n\\label{e:trace_J_isigmaijg5}\n& J^{[\\i \\sigma^{ij} \\gamma_5]} =\n- \\frac{\\Lambda}{2k^-} \\epsilon_T^{ij} \\int dk^2 B_3(k^2,k^-) \n\\ \\equiv\\ - \\frac{\\Lambda}{k^-} \\epsilon_T^{ij} \\eta(k^-) \\ .\n\\end{align}\nFor twist-4 structures we have:\n\\begin{align}\n\\label{e:trace_J_gp}\nJ^{[\\gamma^+]} & =\n\\frac{\\Lambda^2}{2(k^-)^2} \\int dk^2 \\bigg[ A_3(k^2,k^-) \\frac{k^2+\\vect{k}_T^2}{2\\Lambda^2} + B_1(k^2,k^-) \\bigg] \n\\ \\equiv\\ \\frac{\\Lambda^2}{(k^-)^2} \\omega(k^-,\\vect{k}_T^2) \n\\end{align}\n\\begin{align}\n\\label{e:trace_J_isigmaipg5}\nJ^{[\\i \\sigma^{i+} \\gamma_5]} & =\n\\frac{\\Lambda^2}{2(k^-)^2} \\epsilon_T^{ij} \\frac{{k_T}_j}{\\Lambda} \\int dk^2 B_3(k^2,k^-)\n= \\frac{\\Lambda^2}{(k^-)^2} \\epsilon_T^{ij} \\frac{{k_T}_j}{\\Lambda} \\eta(k^-) \\ .\n\\end{align}\nBecause of the integration over $k^2$, all the functions defined in the previous equations depend only on $k^-$, apart from $\\omega$ which has an additional dependence on $\\vect{k}_T^2$ that we will discuss in Section~\\ref{sss:omega_calc}.\nThe TMD jet correlator can then be given a twist decomposition in Dirac space as follows: \n\\begin{align}\n\\label{e:J_Dirac}\nJ(k^-,\\vect{k}_T;n_+) & = \n\\frac{1}{2} \\alpha(k^-) \\gamma^+ \\\\ \n\\nonumber\n& + \\frac{\\Lambda}{2k^-} \\left[ \\zeta(k^-) {\\mathbb 1}  \n\t\t\t\t\t\t\t\t\t\t\t    + \\alpha(k^-) \\frac{\\slashed{k}_T}{\\Lambda} \n\t\t\t\t\t\t\t\t\t\t\t    \t+ \\eta(k^-) \\sigma_{\\mu\\nu} n_-^\\mu n_+^\\mu \\right] \\\\\n\\nonumber\n& + \\frac{\\Lambda^2}{2(k^-)^2} \\left[ \\omega(k^-,\\vect{k}_T^2) \\gamma^-\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t+ \\frac{1}{\\Lambda} \\eta(k^-) \\sigma_{\\mu\\nu} k_T^\\mu n_+^\\nu \\right] \\ . \t\n\\end{align}\nSince $B_3 = 0$, according to time-reversal symmetry arguments, we obtain $\\eta(k^-) = 0$ and thus the correlator $J$ simplifies to:\n\\begin{equation}\n\\label{e:J_Dirac_noeta}\nJ(k^-,\\vect{k}_T;n_+) = \n\\frac{1}{2} \\alpha(k^-) \\gamma^+ \n+ \\frac{\\Lambda}{2k^-} \\left[ \\zeta(k^-) {\\mathbb 1}  \n\t\t\t\t\t\t\t\t\t\t\t    + \\alpha(k^-) \\frac{\\slashed{k}_T}{\\Lambda} \\right] \\\\\n+ \\frac{\\Lambda^2}{2(k^-)^2} \\left[ \\omega(k^-,\\vect{k}_T^2) \\gamma^- \\right] \\ . \t\n\\end{equation}\nNote that one could also explicitly factor a $\\theta(k^-)$ function out of $\\alpha$, $\\zeta$, and $\\omega$. \nThe positivity of $k^-$ is indeed guaranteed in any gauge by four-momentum conservation, if one assumes that the particles in the final state all have physical four-momenta. \n\nThe explicit calculation of the coefficients in Eq.~\\eqref{e:J_Dirac_noeta} can be carried out with the aid of the convolutional spectral representation discussed in Section~\\ref{ss:spectr_dec}. Indeed, recall that in Eq.~\\eqref{e:J_TMDcorr} the integrand is restricted to the light front $\\xi^-=0$, so that $\\xi^2 = -\\vect{\\xi}_T^2 < 0$ is space-like. Under this condition, the fermion fields anticommute and $ {\\cal T} \\big[\\psi_i(\\xi) {\\overline{\\psi}}_j(0)\\big] = \\psi(\\xi){\\overline{\\psi}}(0)$.\nThus, the integrated version of the correlators $\\Xi$ and $\\Xi^\\prime$ are equivalent,\n\\begin{equation}\n\\label{e:J_intXi_intXiprime}\nJ_{ij}(k^-,\\vect{k}_T;n_+) = \\frac{1}{2} \\int dk^+\\, \\Xi_{ij}(k;n_+) \n\\equiv \\frac{1}{2} \\int dk^+\\, \\Xi^\\prime_{ij}(k;n_+) \\, .\n\\end{equation}\nand one can utilize formulas \\eqref{e:spectral_convolution} and \\eqref{e:spec_rep_s13} in the calculation of the jet correlator coefficient. This task is carried out in the light-cone gauge in the next three susbsections. \n\n\n\n\n\\subsubsection{Calculation of the twist-2 $\\alpha$ coefficient}\n\\label{sss:alpha_calc}\n\nUsing the definition of $\\alpha$ given in Eq.~\\eqref{e:trace_J_gm}, the equivalence Eq.~\\eqref{e:J_intXi_intXiprime} between the $\\Xi$ and $\\Xi^\\prime$ integrated correlators, and the convolution representation for $\\Xi^\\prime$, we find: \n\\begin{align}\n\\label{e:alpha_calc_1}\n\\alpha(k^-) & \n= \\int dk^+\\, \\text{Disc} \\int_{\\mathbf M} d^4p\\, \\frac{\\text{Tr}_c}{N_c} {\\langle\\Omega|} \\hat{s}_3(p^2) p^- \\widetilde W(k-p) {|\\Omega\\rangle} \\\\\n\\nonumber\n& = \\frac{1}{2}\\, \\text{Disc} \\int_{\\mathbf R} dp^2 \\int_{\\mathbf R} dp^- \\frac{\\text{Tr}_c}{N_c} \n{\\langle\\Omega|} \\hat{s}_3(p^2) \\int \\frac{d\\xi^+}{2\\pi} e^{\\i \\xi^+ (k^- - p^-)} \nW_{coll}(\\xi^+) {|\\Omega\\rangle} \\ ,\n\\end{align}\nwhere the integration domain for $p$ is the whole Minkowski space ($\\mathbf M$) and we decompose the integral as $d^4p =  dp^2\\, d^2\\vect{p}_T\\, dp^-\/2p^-$. \nFrom the first to the second line we used Eq.~\\eqref{e:def_tildeW} and performed the integrations over $k^+$ and $\\vect{p}_T$, fixing $\\xi^-=0$ and $\\vect{\\xi}_T=0$ so that the staple-shaped Wilson line reduces to the straight gauge link in the $n_+$ collinear direction, {\\it i.e.}, $W_{coll}(\\xi^+)$. Next, we choose the light-cone gauge $A^-=0$ so that the collinear Wilson line reduces to the unity matrix in color space. Finally, performing the integration over $\\xi^+$ we obtain:\n\\begin{align}\n\\label{e:alpha_calc_2}\n\\nonumber\n\\alpha(k^-) & \\overset{lcg}{=} \\text{Disc} \\int_{\\mathbf R} dp^2 \\int_{\\mathbf R} \\frac{dp^-}{2} \\frac{\\text{Tr}_c}{N_c}\\, {\\langle\\Omega|} \\hat{s}_3(p^2) {|\\Omega\\rangle} \\delta(k^- - p^-) \n= \\int_{\\mathbf R} dp^2 \\int_{\\mathbf R} \\frac{dp^-}{2} \\delta(k^- - p^-) \\{ (2\\pi)^{-3} \\rho_3(p^2) \\theta(p^2) \\theta(p^-) \\} \\\\\n& = \\frac{1}{2(2\\pi)^3} \\bigg\\{ \\int_0^{+\\infty} dp^2 \\rho_3(p^2) \\bigg\\} \\theta(k^-) = \\frac{\\theta(k^-)}{2(2\\pi)^3} \\ ,\n\\end{align}\nwhere $lcg$ stresses the use of the light-cone gauge. In the second step we used the representation for the spectral operator $\\hat{s}_3$ given in Eq.~\\eqref{e:spec_rep_s13}, and in the last one we used the normalization property for $\\rho_3$ given in Eq.~\\eqref{e:rho13_positivity_rho3sumrule}. We remark that the only dependence on $k^-$ resides in the theta function, and that this result hold, in fact, in any gauge beacuse of the invariance of the jet correlator, hence of the coefficients of its Dirac decomposition. The theta function, which is due to four momentum conservation, and the accompanying numerical coefficients determined by the convention used in the definition of the correlators, also appear in the calculation of the higher-twist $\\zeta$ and $\\omega$ coefficients to be discussed next. \n\n\n\\subsubsection{Calculation of the twist-3 $\\zeta$ coefficient}\n\\label{sss:zeta_calc}\n\nThe $\\zeta$ coefficient defined in Eq.~\\eqref{e:trace_J_id} is proportional to the trace of the gauge invariant TMD jet correlator $J$. \nFactoring out the $\\theta(k^-)$ function, we can thus write\n\\begin{align}\n  \\zeta(k^-) = \\frac{\\theta(k^-)}{2(2\\pi)^3\\Lambda} M_j \\ ,\n\\end{align}\nwhere $M_j$ is a {\\it gauge-invariant} mass term. $M_j$ is in fact independent of $k^-$, and can be interpreted as the inclusive jet's (or the color-averaged dressed quark's) mass, as we will presently show.  \n\nThe calculation of $\\zeta$ in the light-cone gauge follows closely the procedure outlined in the calculation of $\\alpha$. We start from the definition of $\\zeta$ given in Eq.~\\eqref{e:trace_J_id}, use the convolution representation \\eqref{e:spectral_convolution} for the jet correlator, and obtain\n\\begin{align}\n\\label{e:zeta_calc_1}\n\\zeta(k^-) & \n= \\frac{k^-}{4\\Lambda} \\int dk^+\\, \\text{Disc} \\int_{\\mathbf M} d^4p\\, \\frac{\\text{Tr}_c}{N_c} {\\langle\\Omega|} \\sqrt{p^2} \\hat{s}_1(p^2) 4 \\widetilde W(k-p) {|\\Omega\\rangle} \\\\ \n\\nonumber\n& = \\frac{k^-}{2\\Lambda}\\, \\text{Disc} \\int_{\\mathbf R} dp^2 \\int_{\\mathbf R} \\frac{dp^-}{p^-} \\frac{\\text{Tr}_c}{N_c} \n{\\langle\\Omega|} \\sqrt{p^2} \\hat{s}_1(p^2) \\int \\frac{d\\xi^+}{2\\pi} e^{\\i \\xi^+ (k^- - p^-)} W_{coll}(\\xi^+) {|\\Omega\\rangle} \\ , \n\\end{align}\nwhere the integrations have been performed as in the case of $\\alpha$. In particular the integration over $\\vect{p}_T$ has projected the Wilson line on the light cone, leaving us once more with $W_{coll}(\\xi^+)$. \nImposing the light-cone $A \\cdot n_+ = 0$ gauge and integrating over $\\xi^+$, we obtain:\n\\begin{align}\n\\label{e:zeta_calc_2}\n\\zeta(k^-) & \\overset{lcg}{=} \\frac{k^-}{2\\Lambda} \\text{Disc} \\int_{\\mathbf R} dp^2 \\int_{\\mathbf R} \\frac{dp^-}{p^-} \n\\frac{\\text{Tr}_c}{N_c}\\, {\\langle\\Omega|} \\sqrt{p^2} \\hat{s}_1(p^2) {|\\Omega\\rangle} \\delta(k^- - p^-) \\\\\n\\nonumber\n& = \\frac{k^-}{2\\Lambda} \\int_{\\mathbf R} dp^2 \\int_{\\mathbf R} \\frac{dp^-}{p^-} \\delta(k^- - p^-) \\sqrt{p^2} \n\\{ (2\\pi)^{-3} \\rho_1^{}(p^2) \\theta(p^2) \\theta(p^-) \\} \n = \\frac{\\theta(k^-)}{2(2\\pi)^3\\Lambda} \\bigg\\{ \\int_0^{+\\infty} dp^2 \\sqrt{p^2} \\rho_1^{}(p^2) \\bigg\\} \\ ,\n  \n\\end{align}\nwhere, in going from the first to the second line, we used the representation for the spectral operator $\\hat{s}_1$ given in Eq.~\\eqref{e:spec_rep_s13\n\nThis calculation shows that the gauge-invariant jet mass $M_j$ has a particularly simple form when choosing the light-cone gauge, being completely determined by the first moment of the ``chiral-odd'' spectral function $\\rho_1^{}$:\n\\begin{equation}\n  \\label{e:Mj_lcg}\n   M_j  \\overset{lcg}{=} \\int_0^{+\\infty} d\\mu^2\\, \\sqrt{\\mu^2}\\, \\rho_1^{}(\\mu^2) \\ .\n\\end{equation}\nThe integral at the right hand side is summing over all the discontinuities of the quark propagator. In this gauge, therefore, $M_j$ can be interpreted as the average mass generated by chirality-flipping processes during the quark's fragmentation, and therefore called ``jet mass'' as proposed in Ref.~\\cite{Accardi:2017pmi}. We will elaborate further on this interpretation in Section~\\ref{ss:TMDjet_recap}.  \nIn closing, it is important to remark, that although the explicit dependence of $M_j$ on $\\rho_1$ may depend on the choice of gauge,  its numerical value is in fact gauge invariant - and, in particular, independent of $k^-$ as anticipated.\n\n\\subsubsection{Calculation of the twist-4 $\\omega$ coefficient}\n\\label{sss:omega_calc}\n\nThe calculation of the twist-4 $\\omega$ coefficient is more complex than for the $\\alpha$ and $\\zeta$ coefficients, although the main ideas and techniques discussed in the previous two subsection also apply to this case. \nSince this coefficient appears in Eq.~\\eqref{e:J_Dirac_noeta} at twist 4 only, it will not contribute to the fragmentation function sum rules discussed in Section~\\ref{s:1h_rules}, that are for now derived up to twist 3. For this reason, we leave a full study of the $\\omega$ coefficient for future work, and here we outline its general properties.\n\nFrom the definition of $\\omega$ in Eq.~\\eqref{e:trace_J_gp} and using the convolution representation in Eq.~\\eqref{e:spectral_convolution} the $\\omega$ coefficient reads:\n\\begin{align}\n\\label{e:omega_calc_1}\n\\nonumber \n\\omega(k^-,\\vect{k}_T^2) & = \\bigg(\\frac{k^-}{\\Lambda}\\bigg)^2 \n\\int dk^+\\, \\text{Disc} \\int_{\\mathbf M} d^4p\\, \\frac{\\text{Tr}_c}{N_c} {\\langle\\Omega|} \\hat{s}_3(p^2)\n\\frac{p^2+\\vect{p}_T^2}{2p^-} \\widetilde W(k-p) {|\\Omega\\rangle}\\\\ \n   & \\equiv\\ \\langle\\!\\langle \\frac{p^2}{(p^-)^2} \\rangle\\!\\rangle\n      + \\langle\\!\\langle \\frac{\\vect{p}_T^2}{(p^-)^2} \\rangle\\!\\rangle \\ .\n\\end{align}\n\n\n\n\n\n\nThe integral involving $p^2$ in Eq.\\eqref{e:omega_calc_1} can be calculated following the same procedure used for the $\\zeta$ coefficient. One obtains\n\\begin{equation}\n\\label{e:omega_avp2}\n  \\langle\\!\\langle \\frac{p^2}{(p^-)^2} \\rangle\\!\\rangle = \\frac{\\theta(k^-)}{4 \\Lambda^2 (2\\pi)^3} \\, \\mu_j^2 \\ ,\n\\end{equation}\nwhere the $\\theta(k^-)$ function arises as for the $\\alpha$ and $\\zeta$ coefficients, and (similarly to $M_j$) $\\mu_j^2$ has a particularly simple form in the light-cone gauge:\n\\begin{equation}\n  \\label{e:Kj2_lcg} \n   \\mu_j^2 \\overset{lcg}{=} \\int_0^{+\\infty} d\\mu^2\\, \\mu^2\\, \\rho_3^{}(\\mu^2) \\ .\n\\end{equation}Unlike $M_j$, however, this is not gauge-invariant.  Given the properties of $\\rho_3$ in Eq.~\\eqref{e:rho13_positivity_rho3sumrule}, $\\mu_j^2$ can be interpreted as the average invariant mass squared directly generated by the quark as it fragments into the final state\\footnote{One has to be careful, though, with this interpretation since the positivity of $\\rho_3$ is not guaranteed in a confined theory.}. \n\nThe calculation of the $\\langle\\!\\langle \\vect{p}_T^2 \/ (p^-)^2 \\rangle\\!\\rangle$ term is more involved because one cannot immediately integrate over $\\vect{p}_T$ and project the integrand on the light cone. To achieve that, one needs first to remove the explicit dependence of the integrand on $\\vect{p}_T^2$ using\n\\begin{equation}\n\\label{e:pT2_deriv}\n  \\vect{p}_T^2\\, e^{\\i \\vect{\\xi}_T \\cdot (\\vect{p}_T - \\vect{k}_T)}\n  = \\bigg( -\\frac{\\partial}{\\partial \\vect{\\xi}_T^\\alpha}\n    \\frac{\\partial}{\\partial {\\vect{\\xi}_T}_\\alpha} \n    -2\\i \\vect{k}_T^\\alpha \\frac{\\partial}{\\partial \\vect{\\xi}_T^\\alpha} \n    + \\vect{k}_T^2 \\bigg)\\, e^{\\i \\vect{\\xi}_T \\cdot (\\vect{p}_T - \\vect{k}_T)} \\ .\n\\end{equation}\nOne then obtains\n\\begin{align}\n\\label{e:omega_avpT2}\n  \\langle\\!\\langle \\frac{\\vect{p}_T^2}{(p^-)^2} \\rangle\\!\\rangle \n   \n   \n    = \\frac{\\theta(k^-)}{4 \\Lambda^2 (2\\pi)^3} \\,\n    \\Big( \\vect{k}_T^2 + \\tau_j^2 \\Big) \\ ,\n\\end{align}\nwhere \n\\begin{align}\n\\label{e:Tjdef}\n\\theta(k^-) \\, \\tau_j^2 = (2\\pi)^3 (k^-)^2\\, \\text{Disc} \n  & \\int_{\\mathbf M} d^4 p\\, \\frac{\\text{Tr}_c}{N_c} \\frac{1}{(p^-)^2} {\\langle\\Omega|} \\hat{s}_3(p^2) \n  \\int \\frac{d\\xi^+ d^2\\vect{\\xi}_T}{(2\\pi)^3} e^{\\i \\xi^+ (k^- - p^-)} \\\\\n\\nonumber\n& \\times \\bigg( -\\frac{\\partial}{\\partial \\vect{\\xi}_T^\\alpha} \\frac{\\partial}{\\partial {\\vect{\\xi}_T}_\\alpha} \n-2\\i \\vect{k}_T^\\alpha \\frac{\\partial}{\\partial \\vect{\\xi}_T^\\alpha} \\bigg) \ne^{\\i \\xi_T \\cdot (\\vect{p}_T - \\vect{k}_T)} W_{TMD}(\\xi^+, \\xi_T) {|\\Omega\\rangle} \\ .\n\\end{align}\nThe $\\vect{k}_T^2$ term in Eq.\\eqref{e:omega_avpT2} is a purely kinematical effect of the initial parton's  non-zero transverse momentum. The $\\tau_j^2$ term can be interpreted \nas the average squared transverse momentum of the fragmented hadrons relative to the quark axis. This quantity also characterizes the jet's transverse shape: the larger $\\tau_j^2$ the less aligned the final state is to the initial quark; in this sense, we can call $\\tau_j^2$ the ``jet broadening\" parameter. \n\n\n\n\n\n\n\n\\begin{comment}\n\\ \\\\ \\tocless\\subsubsection{Calculation of the twist-4 $\\omega$ coefficient}\n\\label{sss:omega_calc}\n\n\\AScom{Let's see what to do with this section.} \nThe calculation of the twist-4 $\\omega$ coefficient is more complex than for the $\\alpha$ and $\\zeta$ coefficients, although the main ideas and techniques discussed in the previous two subsection also apply to this case. \nSince this appears only at twist-4 in Eq.~\\eqref{e:J_Dirac_noeta}, it will not contribute to the momentum sum rules for fragmentation functions discussed in Section~\\ref{s:1h_rules}, that are for now limited to twist-3. For this reason, we leave a full study of the $\\omega$ coefficient for future work, and here we simply outline its general properties.\n\nAs for $\\zeta$, we first factor out a $\\theta(k^-)$ function from the gauge invariant $\\omega$ coefficient, \n\\begin{align}\n  \\omega(k^-,\\vect{k}_T^2) = \\frac{\\theta(k^-)}{4(2\\pi)^3 \\Lambda^2}\n    \\Big( \\vect{k}_T^2 + K_j^2(k^-,\\vect{k}_T^2) \\Big) \\ ,\n\\end{align}\nwhere the {\\it gauge-invariant} $K_j^2$ term can be interpreted as the jet's virtuality, generalizing the free quark's squared four momentum $k^2=m_{0q}^2$, as discussed in more detail in Section~\\ref{ss:TMDjet_recap}.\nAgain, the reason for the chosen normalization will be clear after performing the explicit calculation in the light-cone gauge.\n\nThen, we look at the definition of $\\omega$ given in Eq.~\\eqref{e:trace_J_gp}, and using the convolution representation in Eq.~\\eqref{e:spectral_convolution} we obtain\n\\begin{align}\n\\label{e:omega_calc_1}\n  \\omega(k^-,\\vect{k}_T^2)\n    & = \\bigg(\\frac{k^-}{\\Lambda}\\bigg)^2 \n      \\int dk^+ \\text{Disc} \\int_M d^4p \\frac{\\text{Tr}_c}{N_c} {\\langle\\Omega|} \\hat{s}_3(p^2)\n      \\frac{p^2+\\vect{p}_T^2}{2p^-} \\widetilde W(k-p) {|\\Omega\\rangle}\\ \n    \\equiv\\ \\langle\\!\\langle p^2\/(p^-)^2 \\rangle\\!\\rangle\n      + \\langle\\!\\langle \\vect{p}_T^2\/(p^-)^2 \\rangle\\!\\rangle \\ ,\n\\end{align}\nwhere the two average values at the right hand side can be, in principle, functions of $k^-$ and $\\vect{k}_T^2$.\nThe additional $p^-$ factors at the denominator\ncome from the the light-cone form of the integration measure, that reads $d^4p=d^2\\vect{p}_T\\, dp^2\\, dp^-\/2p^-$.\nNote also that for simplicity, as discussed in Section~\\ref{ss:spectr_dec}, we refrain from an explicit treatment of the additional light-cone gauge fixing term.\n\nThe first contribution in Eq.~\\eqref{e:omega_calc_1} can be calculated following the same procedure used for the $\\zeta$ coefficient. Using again the light-cone gauge we find:\n\\begin{equation}\n\\label{e:omega_avp2}\n  \\langle\\!\\langle p^2\/(p^-)^2 \\rangle\\!\\rangle = \\frac{\\theta(k^-)}{4 \\Lambda^2 (2\\pi)^3} \\, \\mu_j^2 \\ ,\n\\end{equation}\nwhere $\\mu_j^2$ has a particularly simple form in the light-cone gauge,\n\\begin{equation}\n  \\label{e:Kj2_lcg}\n   \\mu_j^2 = \\int_0^{+\\infty} d\\mu^2\\, \\mu^2\\, \\rho_3^{}(\\mu^2) \\ .\n\\end{equation}\nGiven the properties of $\\rho_3$ in Eq.~\\eqref{e:rho13_positivity_rho3sumrule}, this can be interpreted as the average invariant mass squared directly generated by the quark as it fragments into the final state\\footnote{One has to be careful though, as the positivity of $\\rho_3$ is not guaranteed in a confined theory.}. Unlike $M_j$, however, this term is not the only one contributing to the jet's virtuality $K_j^2$ and therefore it is {\\it not} gauge-invariant. \\AScom{Option 0: stop here} \n\nThe calculation of the $\\langle\\!\\langle \\vect{p}_T^2 \/ (p^-)^2 \\rangle\\!\\rangle$ term is more involved because one cannot immediately integrate over $\\vect{p}_T$ and project the integrand on the light cone. To achieve that, one needs first to remove the explicit dependence of the integrand on $\\vect{p}_T^2$ using\n\\begin{equation}\n\\label{e:pT2_deriv}\n  \\vect{p}_T^2\\, e^{i \\vect{\\xi}_T \\cdot (\\vect{p}_T - \\vect{k}_T)}\n  = \\bigg( -\\frac{\\partial}{\\partial \\vect{\\xi}_T^\\alpha}\n    \\frac{\\partial}{\\partial {\\vect{\\xi}_T}_\\alpha} \n    -2\\i \\vect{k}_T^\\alpha \\frac{\\partial}{\\partial \\vect{\\xi}_T^\\alpha} \n    + \\vect{k}_T^2 \\bigg)\\, e^{i \\vect{\\xi}_T \\cdot (\\vect{p}_T - \\vect{k}_T)} \\ .\n\\end{equation}\nOne then obtains\n\\begin{align}\n\\label{e:omega_avpT2}\n  \\langle\\!\\langle \\vect{p}_T^2\/(p^-)^2 \\rangle\\!\\rangle \n   \n   \n    = \\frac{\\theta(k^-)}{4 \\Lambda^2 (2\\pi)^3} \\,\n    \\Big( \\vect{k}_T^2 + \\tau_j^2 \\Big) \\ ,\n\\end{align}\nwhere \n\\begin{align}\n\\label{e:Tjdef}\n\\theta(k^-) \\, \\tau_j^2 = (2\\pi)^3 (k^-)^2\\, \\text{Disc} \n  & \\int_{M} d^4 p \\frac{\\text{Tr}_c}{N_c} \\frac{1}{(p^-)^2} {\\langle\\Omega|} \\hat{s}_3(p^2) \n  \\int \\frac{d\\xi^+ d^2\\vect{\\xi}_T}{(2\\pi)^3} e^{i \\xi^+ (k^- - p^-)} \\\\\n\\nonumber\n& \\times \\bigg( -\\frac{\\partial}{\\partial \\vect{\\xi}_T^\\alpha} \\frac{\\partial}{\\partial {\\vect{\\xi}_T}_\\alpha} \n-2\\i \\vect{k}_T^\\alpha \\frac{\\partial}{\\partial \\vect{\\xi}_T^\\alpha} \\bigg) \ne^{i \\xi_T \\cdot (\\vect{p}_T - \\vect{k}_T)} W_{TMD}(\\xi^+, \\xi_T) {|\\Omega\\rangle} \\ .\n\\end{align}\nTo complete the calculation of $\\tau_j^2$, one would need to integrate by parts, compute the first and the second derivative of the Wilson line~\\cite{LewisLicht:2008mv,Lorce:2012ce} with respect to the transverse component, and pay attention to the border terms. We defer this study to future work. \nHere we simply note the $\\tau_j^2$ is the only place where (in the chosen light-cone gauge) the Wilson line contributes to the TMD jet correlator. Furthermore, from the decomposition~\\eqref{e:omega_avpT2} and~\\eqref{e:Tjdef}, $\\tau_j^2$ can also be interpreted as the final state transverse momentum broadening of the jet compared to the fragmenting quark's transverse momentum.\n\n\\AScom{Include below equation anyway.}  Collecting all the pieces, we obtain\n\\begin{align}\n\\label{e:omega_summ}\n  \\omega(k^-,\\vect{k}_T^2) =  \\frac{\\theta(k^-)}{4 \\Lambda^2 (2\\pi)^3} \\,\n   \n   \n    \\Big( \\vect{k}_T^2 + \\mu_j^2 + \\tau_j^2 + \\textit{g.f.t.} \\Big)\\ ,\n\\end{align}\nwith the gauge invariant jet virtuality\n\\begin{align}\n  K_j^2 = {\\mu_j^2 + \\tau_j^2 + \\textit{g.f.t.}}\n\\end{align}\nreceiving contributions from the quark's fragmentation process, from the jet's interaction with the Wilson line, and from the ``gauge fixing term'' $g.f.t.$ term that symbolically represents the potential contributions from a structure proportional to $\\slashed{n}_+$ in Eq.~\\eqref{e:Feyn_spec_rep}.\nIt is the sum of these three terms that is gauge invariant.\n\\end{comment}\n\n\n\n\n\n\\subsection{Summary and interpretation of $\\boldmath M_j$}\n\\label{ss:TMDjet_recap}\n\n\\begin{comment}\nInserting the expressions of the $\\alpha$, $\\zeta$, $\\omega$ coefficients in Eq.~\\eqref{e:J_Dirac_noeta} we obtain the following decomposition for the TMD jet correlator:\n\\begin{align}\n\\label{e:J_Dirac_explicit}\n  J(k^-,\\vect{k}_T;n_+)\n    = \\frac{\\theta(k^-)}{4(2\\pi)^3\\, k^-} \\, \n    \\bigg\\{ k^-\\, \\gamma^+ + \\slashed{k}_T + M_j {\\mathbb 1} + \\frac{\\mu_j^2 + \\vect{k}_T^2}{2k^-} \\gamma^- \\bigg\\} \n   \n  + \\frac{\\theta(k^-)}{4(2\\pi)^3} \\,\n  \\frac{ \\tau_j^2 + \\textit{g.f.t.}}{2 (k^-)^2} \\, \\gamma^- \\ .\n\\end{align}\nThe expression in brackets generalizes the familiar term appearing in the free quark propagator:\n\\begin{align}\n  \\slashed{k} + m = k^-\\, \\gamma^+ + \\slashed{k}_T + m {\\mathbb 1}\n    +  \\frac{m^2 + \\vect{k}_T^2}{2k^-}\\, \\gamma^- \\ . \n\\end{align}\nWe can see that the current quark mass generalizes to the jet mass, $m \\rightsquigarrow M_j$,\nand the mass shell generalizes to the jet's invariant mass, $m^2 \\rightsquigarrow \\mu_j^2$. Conversely, using the non-interacting propagator's spectral functions $\\rho_{1,3} \\propto \\delta(\\mu^2-m^2)$ in Eqs.~\\eqref{e:Kj2_lcg} and \\eqref{e:Mj_lcg}, we obtain  $M_j^{n.i.}=m$ and $\\mu_j^{2,n.i.}=m^2$. Of the remaining terms, $\\tau_j^2$ is a consequence of the Wilson line included in the definition of the gauge-invariant jet correlator, and in the light-cone gauge it is the only contribution due to the Wilson line. \n\nOverall, the jet propagator \\eqref{e:J_Dirac_explicit} can be thought as a propagating particle of mass $M_j$, that is however off the mass shell because its virtuality $K_j^2 = \\mu_j^2  + \\tau_j^2 + \\textit{g.f.t.}$ is in general different from $M_j^2$. However, it may be dangerous to push this interpretation beyond the kinematic level, because the jet mass cannot necessarily be interpreted as a pole mass.\n\\end{comment}\n\n\n\nInserting the expressions of the $\\alpha$, $\\zeta$, $\\omega$ coefficients in Eq.~\\eqref{e:J_Dirac_noeta} we obtain the following decomposition for the TMD jet correlator:\n\\begin{align}\n\\label{e:J_Dirac_explicit}\n  J(k^-,\\vect{k}_T;n_+)\n    = \\frac{\\theta(k^-)}{4(2\\pi)^3\\, k^-} \\, \n    \\bigg\\{ k^-\\, \\gamma^+ + \\slashed{k}_T + M_j {\\mathbb 1} + \\frac{K_j^2 + \\vect{k}_T^2}{2k^-} \\gamma^- \\bigg\\} \\ ,\n\\end{align}\nwith the ``jet virtuality''\n\\begin{align}\n  K_j^2 = {\\mu_j^2 + \\tau_j^2 + \\textit{g.f.t.}}\n\\end{align}\nreceiving contributions from the invariant mass directly produced in the quark fragmentation process ($\\mu_j^2$, Eq.\\eqref{e:Kj2_lcg}), from the final state jet broadening ($\\tau_j^2$, Eq.\\eqref{e:Tjdef}), and from a gauge fixing term [$g.f.t.$]. The latter symbolically represents the potential contributions from a structure proportional to $\\slashed{v} = \\slashed{n}_+$ in Eq.~\\eqref{e:quark_bilinear_decomp} and~\\eqref{e:Feyn_spec_rep}, that, as discussed, we do not consider further in this article. As it happens to the jet mass $M_j$~\\eqref{e:Mj_lcg} the jet virtuality $K_j^2$ is also a gauge invariant quantity. \n\nThe expression in brackets in Eq.~\\eqref{e:J_Dirac_explicit} generalizes the familiar term appearing in the numerator of the free quark propagator:\n\\begin{align}\n  \\slashed{k} + m = k^-\\, \\gamma^+ + \\slashed{k}_T + m {\\mathbb 1}\n    +  \\frac{m^2 + \\vect{k}_T^2}{2k^-}\\, \\gamma^- \\ . \n\\end{align}We can see that the current quark mass generalizes to the jet mass, $m \\rightsquigarrow M_j$, and the mass shell generalizes to the jet's virtuality, $m^2 \\rightsquigarrow K_j^2$. Conversely, using the non-interacting propagator's spectral functions $\\rho_{1,3} \\propto \\delta(\\mu^2-m^2)$ in Eqs.~\\eqref{e:Kj2_lcg}, we obtain $M_j=m$; furthermore, neglecting the contribution of the Wilson line and the gauge fixing term, we obtain $K_j^2=m^2$. \n\nOverall, the jet correlator~\\eqref{e:J_Dirac_explicit} can be thought as a propagating particle of mass $M_j$, that is however off the mass shell because its virtuality $K_j^2 = \\mu_j^2  + \\tau_j^2 + \\textit{g.f.t.}$ is in general different from $M_j^2$. However, it may be dangerous to push this interpretation beyond the kinematic level, because the jet mass cannot necessarily be interpreted as a pole mass.\nIn fact, let us consider the non-perturbative Feynman quark propagator in momentum space expressed in terms of a renormalization factor $Z(p^2)$ and a mass function $M(p^2)$~\\cite{Roberts:2007jh,Roberts:2015lja,Siringo:2016jrc,Zwicky:2016lka,Solis:2019fzm})\\footnote{As for the spectral representation in Eq.~\\eqref{e:Feyn_spec_rep}, there is an additional $1\/(2\\pi)^4$ factor with respect to the expression given in e.g. Refs.~\\cite{Roberts:2007jh,Roberts:2015lja,Siringo:2016jrc,Zwicky:2016lka,Solis:2019fzm} in order to match the convention for the Fourier transform used in Eq.~\\eqref{e:invariant_quark_correlator}.}:\n\\begin{equation}\n\\label{e:SF_mass}    \n\\i S_F(p) =  \\frac{\\i Z(p^2)}{(2\\pi)^4 [\\slashed{p} - M(p^2)]} \\, . \n\\end{equation}\nBy comparing this expression with the spectral representation for the Feynman propagator presented in Eq.~\\eqref{e:Feyn_spec_rep} with $p^0>0$ and using the definition~\\eqref{e:Mj_lcg} of $M_j$ in the light-cone gauge, we find that\n\\begin{align}\n\\label{e:relation_Mj_M}\nM_j \\overset{lcg}{=} \\int_{-\\infty}^{+\\infty} dp^2\\, \\theta(p^2)\\, \\sqrt{p^2}\\, \\rho_1(p^2) = \n\\frac{\\i}{2\\pi} \\int_{-\\infty}^{+\\infty} dp^2\\, \\text{Disc}\\, \\frac{Z(p^2) M(p^2)}{p^2 - M^2(p^2)} \\, . \n\\end{align}\nThis equation relates the gauge-invariant and scale-dependent jet mass $M_j$ in the light-cone gauge and the gauge-dependent and scale-invariant mass function $M(p^2)$.  \nThe scale dependence of the jet mass is provided by the (implicit) scale dependence of the renormalized spectral function $\\rho_1$ on the one hand, and on the other hand is accounted for by the $Z(p^2)$ renormalization function~\\cite{Roberts:2015lja,Roberts:2007jh,Solis:2019fzm}. \nIf the propagator $\\i S_F$ in Eq.~\\eqref{e:SF_mass} had a single pole \nat $p^2=M^2(p^2)\\equiv M^2_p$\nand no branch cut, \nby a simple application of Cutkosky's rule one would obtain $M_j = Z(M_p^2)\\, M_p$ -- i.e., the jet mass could be identified with the renormalized pole mass. In general, however, $M_j$ is summing all the discontinuities of the non-perturbative propagator, hence also over the mass spectrum continuum, and can be different from zero even if no pole, in fact, exists. A more universal interpretation of $M_j$ can be obtained by considering the jet correlator as represented in Eq.~\\eqref{e:invariant_quark_correlator}. $M_j$ can then be thought as the sum over the masses of all physical states overlapping with a quark, weighted by the amplitude squared of that particular quark to multi-hadron state transition.\n\n\nFrom a heuristic point of view, \none can think \nof $M_j$ as a gauge-invariant mass scale that characterizes the physics of a {\\em color-averaged} (or {\\em color-screened}) dressed quark. \nIn light of this interpretation, it is possible to subtract from $M_j$ the current quark mass component responsible for the explicit breaking of the chiral symmetry, and isolate a dynamical component generated by quark-gluon interactions and responsible for the dynamical breaking of the chiral symmetry. \nThis suggest the decomposition\n\\begin{equation}\n\\label{e:Mj_decomp}\nM_j = m + m^{\\text{corr}} \\, ,\n\\end{equation} \nwhere $m$ is the current quark mass, $m^{\\text{corr}}$ is the dynamical mass, and all terms have an implicit renormalization scale dependence. In perturbation theory $m^{\\text{corr}}_{\\text{pert}} \\propto m$ vanishes in the chiral $m \\rightarrow 0$ limit. Thus the dynamical mass $m^{\\text{corr}} = M_j - m$ can also be thought as an order parameter for dynamical chiral symmetry breaking. \nAs will be discussed in details in Section~\\ref{s:1h_rules}, the decomposition~\\eqref{e:Mj_decomp} is also particularly meaningful in light of the equations of motion that relate the twist-2 and twist-3 fragmentation functions, and we will see that this mass is quantitatively related to quark-gluon-quark correlations. For this reason in the following we will refer to it as the {\\em correlation mass}. \n\nCrucially, all this discussion is not merely of theoretical interest\nbecause, in fact $M_j$ and $m^{\\text{corr}}$ can couple to the target's transversity PDF in inclusive DIS processes \\cite{Accardi:2008ne},\nand can furthermore be related to the chiral-odd twist-3 fragmentation functions $E^h$ and $\\widetilde{E}^h$ by momentum sum rules measurable in semi-inclusive processes~\\cite{Accardi:2017pmi,Accardi:2019luo}. \nWe are therefore offered the possibility of comparing calculations of the quark spectral functions, nowadays directly possible in Minkowski space~\\cite{Solis:2019fzm,Siringo:2016jrc}, to experimentally measurable quantities: this is a non-trivial feature in the case of particles such as quarks that do not appear in the physical spectrum of the theory because of color confinement. \n\nIn summary, when investigating the transition of a quark propagating in the QCD vacuum into a set of detectable hadrons in terms of the higher-twist components of the jet correlator~\\eqref{e:J_Dirac_explicit}, one is provided with a with a rather concrete window on color confinement and the dynamical generation of mass. We will revisit these points in Section~\\ref{sss:DCSB}, after an in-depth discussion of the connection of the inclusive jet correlator with the single-inclusive fragmentation correlator, and the ensuing fragmentation function sum rules.\n\n\n\n\n\n\n\\section{Introduction}\n\\label{s:intro}\n\nOne of the crucial properties of the strong force is confinement, namely the fact that color charged partons seemingly cannot exist as free particles outside of hadrons. As a consequence, any individual parton struck in a high-energy scattering process and extracted from its parent hadron must transform into at least one hadron -- in technical language, it must ``hadronize''.\nDuring this process, a struck light quark, such as an up, down or strange, initially propagates as a high-energy but nearly massless colored particle, radiating by chromodynamic {\\it bremsstrahlung} a number of other gluons and light quark-antiquark pairs (the radiation of heavy quarks such as the charm and the bottom is suppressed in proportion to their much higher mass, and can be ignored for the purposes of this discussion). \nBefore reaching the experimental detectors, however, this system of colored, nearly massles particles will turn into a number of massive, color neutral hadrons such as pions, kaons and protons (with overall color charge conservation guaranteed, arguably, by soft final state interactions with the remnant of the parton's parent hadron). Hadronization is thus quite clearly and tightly connected to parton propagation, color charge neutralization, and dynamical generation of the mass, spin, and size of hadrons. However, the exact details of this parton-to-hadrons transition are poorly known. It is the purpose of this article to shed new light on these.\n\nUnraveling hadronization dynamics is not only of fundamental importance to understand the emergence and nature of massive visible matter, but also an essential tool in hadron tomography studies at current and future facilities, including the 12 GeV program at Jefferson Lab~\\cite{Dudek:2012vr} and a future US-based Electron-Ion Collider~\\cite{Accardi:2012qut,Aidala:2020mzt}. For example, in Semi-Inclusive Deep Inelastic Scattering (SIDIS), measuring the transverse momentum of one of the final state hadrons can crucially provide a handle into the transverse motion of its parent quarks and gluons inside the hadron target~\\cite{Angeles-Martinez:2015sea,Rogers:2015sqa,Bacchetta:2016ccz,Scimemi:2019mlf,Bacchetta:2019sam,Grewal:2020hoc,Bacchetta:2017gcc,Scimemi:2019cmh,Signori:2013mda,Anselmino:2013lza,Boglione:2014oea,Collins:2016hqq,Echevarria:2018qyi}. Understanding the hadronization mechanism is therefore critically important to quantitatively connect the initial, short-scale lepton-quark scattering hidden by confinement, with the measurable properties of hadrons as they hit the detectors.\nHadronization and, more in general, hadron structure are also very important for high-energy physics as they are among the biggest sources of uncertainty in the determination of Standard Model parameters~\\cite{Webber:1999ui,Bozzi:2011ww,Quackenbush:2015yra,Bozzi:2015zja,CarloniCalame:2016ouw,Bacchetta:2018lna,Bozzi:2019vnl,Martinez:2019mwt} and the searches for physics beyond the Standard Model at the LHC~\\cite{Gao:2017yyd,Rojo:2015acz}. \nUnderstanding hadronization is also essential for the study of cold and hot nuclear matter properties by means of jet quenching measurements in electron-nucleus and heavy ion collisions \\cite{Accardi:2009qv, Arratia:2019vju}.\n\nIn high-energy collisions with a large four-momentum transfer, factorization theorems in Quantum Chromodynamics (QCD) allow one to separate the short-distance partonic scattering from the long-distance, non perturbative dynamics that binds the partons inside the target and detected particles~\\cite{Parisi:1979se,Collins:1981uk,Collins:1989gx,Catani:2000vq,Becher:2010tm,GarciaEchevarria:2011rb,Collins:2011zzd,Echevarria:2012js, Chiu:2012ir,Rogers:2015sqa}. \nIn this context, hadronization can be mapped -- and then utilized as a tool -- by means of fragmentation functions (FFs) that quantify the transmutation of a parton into one or more hadrons. FFs can be ``collinear'', namely, depending only on the ratio of the longitudinal momenta of the hadron and the parton, or ``trasverse-momentum-dependent'' (TMD), meaning they depend on both the longitudinal and transverse hadron momentum components.\n\nThe fragmentation functions can be determined by means of global QCD fits of hard semi-inclusive collisions. Collinear FFs for unpolarized hadrons are relatively well determined~\\cite{Sato:2016wqj,Bertone:2017tyb,deFlorian:2014xna}, but there is currently no fit available for leading-twist polarized collinear FFs, such as the transversity FF $H_1$. The observation of a polarized hyperon in the final state could, however, shed light on the twist-3 collinear sector~\\cite{Gamberg:2018fwy,Kanazawa:2015jxa}. In the transverse momentum sector, some information is available on the Collins TMD FF, among the polarized ones, as this involves polarized quarks but unpolarized hadrons~\\cite{Kang:2015msa,Kang:2017btw,DAlesio:2017bvu,Anselmino:2013vqa,Anselmino:2015sxa,Anselmino:2015fty}. Lastly, while unpolarized TMD FFs are so far poorly known~\\cite{Matevosyan:2011vj,Bentz:2016rav,Boglione:2017jlh}, present and forthcoming data from the {\\tt BELLE} and {\\tt BES-III} collaborations~\\cite{Garzia:2016kqk,Seidl:2019jei,Seidl:2019FFtalk} will soon allow one to perform fits of these FFs, as well~\\cite{Bacchetta:2015ora,Moffat:2019pci}. A comprehensive review on the theory and phenomenology of fragmentation functions, including di-hadron FFs and gluon FFs, can be found in Ref.~\\cite{Metz:2016swz}.\n\nThe behavior of the fragmentation functions can be usefully constrained in a global QCD fit utilizing suitable sum rules~\\cite{Jimenez-Delgado:2013sma}.\nA number of sum rules for single-hadron FFs are  documented in literature~\\cite{Collins:1981uw,Jaffe:1993xb,Mulders:1995dh,Schafer:1999kn,Bacchetta:2006tn,Meissner:2010cc,Accardi:2017pmi}, starting from the well known momentum sum rule for the unpolarized $D_1$ fragmentation function originally introduced in Ref.~\\cite{Collins:1981uw}. A few have also been proposed for di-hadron FFs~\\cite{Konishi:1979cb,deFlorian:2003cg,Majumder:2004br,Metz:2016swz}.\nAs we will see, however, the interest of FF sum rules also extends beyond their application to phenomenological fits, since a few of these are also sensitive to aspects of the non-perturbative QCD dynamics, such as the dynamics of mass generation.\n\n\n\nThe aim of this paper is to develop a field-theoretical formalism enabling us to take a fresh look at quark propagation and hadronization in the QCD vacuum.\nOur strategy is to establish an operator-level master sum rule connecting the quark-to-hadron fragmentation correlator, that describes the transition of a quark into a hadron and an unobserved remnant ~\\cite{Mulders:1995dh,Bacchetta:2006tn}, with the ``fully inclusive jet correlator'', that describes the fragmentation of a quark into an unobserved jet of particles~\\cite{Sterman:1986aj,Collins:2007ph,Accardi:2008ne,Accardi:2017pmi}. \nWe do this by generalizing the techniques utilized in Ref.~\\cite{Meissner:2010cc}. \nWe will then systematically exploit this correlator-level sum rule, and derive a complete set of sum rules for hadron spin independent fragmentation functions up to the twist-3 level. Results for selected Dirac structures have already been presented in Ref.~\\cite{Accardi:2019luo}; in this work, that also provides full details of our approach, we complete the set of twist-3 sum rules (some of which generalize known results) and comment on their theoretical and phenomenological implications.\n\nWe would like to stress already here that, while the fully inclusive jet correlator also finds an application in the QCD factorization of, {\\em e.g.}, inclusive DIS scattering at large values of the Bjorken $x$ variable~\\cite{Sterman:1986aj,Becher:2006nr,Becher:2006mr,Collins:2007ph,Accardi:2008ne,Accardi:2017pmi,Accardi:2018gmh,Manohar:2003vb,Manohar:2005az,Chen:2006vd,Chay:2005rz,Chay:2013zya}, in this paper we consider this correlator as a theoretical object of intrinsic interest, and as a tool to derive the aforementioned sum rules, {\\it independently} of any scattering process in which it may find application. \nIn fact, as we will see, the inclusive jet correlator can be rewritten as the gauge invariant propagator of a color-averaged quark, and the generation of intermediate hadronic states analyzed in terms of the quark's K\\\"allen-Lehmann spectral functions. The dynamics of mass generation in the quark hadronization process can thus be explicitly connected in a gauge invariant way to the propagation of a quark in the QCD vacuum. \n\nIn Section~\\ref{s:jetcor} we perform a spectral analysis of the jet correlator, that will yield a gauge invariant decomposition in terms of the jet's momentum $k$, its mass $M_j$, and its virtuality $K_j^2$ plus terms associated with the Wilson line that renders the correlator gauge invariant. The starting point of this analysis is the convolutional spectral representation of the gauge invariant quark propagator proposed in Ref.~\\cite{Accardi:2019luo}, see Eq.~\\eqref{e:spectral_convolution}. \nWe believe that this spectral representation can also find application beyond the present paper, for example \nin the study of the gauge independence of objects such as the virtuality-dependent parton distributions of Ref.~\\cite{Radyushkin:2016hsy}, that are playing an increasingly important role in the direct lattice QCD calculation of PDFs in momentum space~\\cite{Orginos:2017kos,Joo:2019jct}. \n\nAll the coefficients in the inclusive jet correlator's decomposition are gauge invariant. In particular, this allows us to identify $M_j$ with, and propose a gauge invariant definition of, the mass of a dressed quark. This mass can be calculated in the light-cone gauge as an integral involving the chiral-odd spectral function of the quark propagator (see Section~\\ref{ss:spectr_dec} and Section~\\ref{ss:TMD_J_corr}), and can be considered as an order parameter for the dynamical breaking of chiral symmetry (see Section~\\ref{ss:TMDjet_recap}).\n\nIn Section~\\ref{s:1h_rules}, we derive the master sum rule connecting the unintegrated single-hadron fragmentation correlator to the inclusive jet correlator, see  Eq.~\\eqref{e:master_sum_rule}, and from this obtain momentum sum rules for FFs up to twist 3 by suitable Dirac projections. These sum rules are summarized in Section~\\ref{ss:sumrules_summary}, where we extensively comment on their theoretical and phenomenological implications. \nIn particular, we find that the jet mass can be expressed as the sum of the current quark mass, $m$, and an interaction-dependent mass, $m^{\\rm corr}$, which enter, respectively, at the right hand side of the sum rules for the collinear twist-3 $E$ and $\\widetilde E$ FFs, see Section~\\ref{ss:qgq_sumrules}. Measurements of these fragmentation functions, therefore, provide one with a concrete way to experimental probe the the mass generation mechanism in QCD, and to study the dynamical breaking of the chiral symmetry. Furthermore, the $E$ and $\\widetilde E$ sum rules provide a way to separate the contribution of each hadron flavor to the overall jet mass, giving one even more insight on these processes.\n\nFinally, in Section~\\ref{s:conclusions} we summarize the results and discuss possible extensions of our work, and in the appendices\nwe provide details about our conventions and the Lorentz transformations of the fragmentation and inclusive jet correlators.\n\n\n\n\n\n\n\\section{Momentum sum rules for single-hadron fragmentation functions}\n\\label{s:1h_rules}\n\n\n\n\n\nIn this section, we will establish a sum rule at the correlator level between the single-hadron fragmentation correlator and the inclusive jet correlator, and systematically exploit this to derive explicit sum rules for fragmentation functions up to the twist-3 level. We will recover known sum rules, and derive a number of new ones. As we will discuss, the interest of these sum rules also extends beyond their application to phenomenological fits. \n\n\n\\subsection{The single-hadron fragmentation correlator}\n\\label{ss:1h_inclusive_FF}\n\nThe unintegrated correlator describing the fragmentation of a quark into a single hadron (or ``single-inclusive\" correlator) is defined as~\\cite{Mulders:1995dh,Goeke:2003az,Bacchetta:2006tn,Meissner:2007rx,Mulders:2016pln,Metz:2016swz,Echevarria:2016scs}\n\\begin{align}\n  \\label{e:1hDelta_corr}\n  & \\Delta^h_{ij}(k,P,S) = \\sum_X \\int \\frac{d^4 \\xi}{(2\\pi)^4} e^{\\i k \\cdot \\xi} \\frac{\\text{Tr}_c}{N_c} {\\langle\\Omega|} \n  {\\cal T} \\big[ W_1(\\infty,\\xi) \\psi_i(\\xi) \\big] \\, \n  |P S X \\rangle \n  \\langle P S X| \\, \n  {\\cal \\overline{T}} \\big[ \\overline{\\psi}_j(0) W_2(0,\\infty) \\big] {|\\Omega\\rangle}\\, ,\n\\end{align}\nwhere $k$ is the quark's four-momentum, $h$ is an identified hadron with four-momentum $P$ and spin $S$, and $X$ represents the quantum numbers of all unobserved hadrons in the final state. \nThe vector $S^\\mu$ is the covariant spin vector associated to the Bloch representation for a hadron with spin $1\/2$~\\cite{Bacchetta:2006tn,Mulders:1995dh}. \nThe remarks given in Section~\\ref{s:jetcor} about the importance of the color average for the definition of the inclusive jet correlator also apply to the fragmentation correlator~\\eqref{e:1hDelta_corr}. A diagrammatic interpretation is given in Figure~\\ref{f:cut_diagrams}(b).\n\nIn the following we will deal only with the correlator describing the fragmentation of a quark into an unpolarized or spinless hadron $\\Delta^h(k,P)$, which is defined as a sum of the polarization-dependent correlator over the polarization of the identified hadron:\n\\begin{align}\n  \\label{e:1hDelta_corr_unpol}\n  & \\Delta^h_{ij}(k,P) = \\sum_{S} \\Delta^h_{ij}(k,P,S) \\ .\n\\end{align}Letting the sum over $S$ act on the right hand side of Eq.~\\eqref{e:1hDelta_corr}, one obtains an explicit definition by substituting $|PSX\\rangle \\langle PSX|$ with $|PX\\rangle \\langle PX|$ in that equation.\n\nLet us now focus on the structure of the $| P X \\rangle$ final state. This is composed of one identified hadron $h$ with momentum $P$ and a remnant $X$. Following the approach of Ref.~\\cite{Levelt:1993ac}, we assume that:\n\\begin{equation}\n\\label{e:completeness_X}\n\\sum_X | X \\rangle \\langle X | = {\\mathbb 1} = \\sum_{n=0}^{+\\infty} {\\mathbb 1}_n \\ .\n\\end{equation}\nThe first equality in Eq.~\\eqref{e:completeness_X} is the completeness relation for the {$|X\\rangle$} states, {\\it i.e.}, the resolution of the identity in terms of the projectors $| X \\rangle \\langle X |$. The second equality decomposes the identity as a sum of identity operators ${\\mathbb 1}_n$ acting in the sub-space spanned by $n$--hadron states. These can be explicitly represented as \n\\begin{equation}\n\\label{e:def_1n}\n{\\mathbb 1}_n = \\frac{1}{n!} \\int d\\widetilde{K}_1 \\cdots d\\widetilde{K}_n \na^\\dagger(K_1) \\cdots a^\\dagger(K_n) \n{|\\Omega\\rangle} {\\langle\\Omega|}\na(K_1) \\cdots a(K_n) \\ ,\n\\end{equation}\nwhere, for ease of notation we combined the momentum $K_i$ and flavor $h_i$ of the $i$-th unobserved hadron into a single $\\widetilde K_i$ variable, and $a(\\widetilde K_i)$, $a^\\dagger(\\widetilde K_i)$ are the associated annihilation and creation operators. The integration reads $\\int d\\widetilde K_i \\equiv \\sum_{h_i} \\int d^3K_i \/ [(2\\pi)^3 2 E_i]$, and as before a sum over the hadron spin is understood when the corresponding index is not explicitly written.\nUsing Eqs.~\\eqref{e:completeness_X} and \\eqref{e:def_1n}, we can recast the sum over the projectors $|PX\\rangle \\langle PX|$ as:\n\\begin{align}\n\\nonumber\n\\sum_X | P X \\rangle \\langle P X | & = | P \\rangle \\langle P | \n+ \\int d\\widetilde K_1 a^\\dagger(\\widetilde K_1) | P \\rangle \\langle P | a(\\widetilde K_1) \n+ \\frac{1}{2} \\int d\\widetilde K_1 d\\widetilde K_2 a^\\dagger(\\widetilde K_1) a^\\dagger(\\widetilde K_2) | P \\rangle \\langle P | a(\\widetilde K_1) a(\\widetilde K_2) + \\cdots \\\\\n\\label{e:1h_proj_to_op} &  = a_h^\\dagger \\bigg(  \\sum_{n=0}^{+\\infty} {\\mathbb 1}_n  \\bigg) a_h = a_h^\\dagger a_h \\ , \n\\end{align}\nwhere we have used $a^\\dagger(\\widetilde K_i) {|\\Omega\\rangle} = | \\widetilde K_i \\rangle$, and $a_h^\\dagger {|\\Omega\\rangle} = |P \\rangle$ creates the identified hadron $h$ from the vacuum.\nUsing Eq.~\\eqref{e:1h_proj_to_op}, we obtain\n\\begin{equation}\n\\label{e:1hDelta_aa}\n\\Delta^h_{ij}(k,P) = \\int \\frac{d^4 \\xi}{(2\\pi)^4} e^{\\i k \\cdot \\xi} \\frac{\\text{Tr}_c}{N_c} {\\langle\\Omega|} \n{\\cal T} \\big[ W_1(\\infty,\\xi) \\psi_i(\\xi) \\big] \\, \n(a_h^\\dagger a_h) \\,\n{\\cal \\overline{T}} \\big[ \\overline{\\psi}_j(0) W_2(0,\\infty) \\big] \\, \n{|\\Omega\\rangle} \\ , \n\\end{equation}\nwhere it is understood that $a_h = a_h(P,S)$ and the same for $a_h^\\dagger$. \nFor brevity of notation, in the following we work with the same Wilson lines $W_{1,2}$ we have chosen for the inclusive jet correlator $\\Xi$ and drop the (anti)time-ordering operators.\nThe expansion of this correlator on a basis of Dirac structures can be obtained from the one given in Refs.~\\cite{Bacchetta:2004zf,Goeke:2005hb} for the distribution correlator by replacing the target hadron momentum with the produced hadron momentum, the target mass with the produced hadron mass, by interchanging $n_-$ with $n_+$, and neglecting the structures related to the polarization of the produced hadron:  \n\\begin{align}\n\\label{e:1hDelta_ampl}\n\\Delta^h(k, P) \n&= M_h A_1 {\\mathbb 1} + A_2 \\slashed{P} + A_3 \\slashed{k} + \\frac{A_4}{M_h} \\sigma_{\\mu\\nu} P^\\mu k^\\nu + \\\\\n\\nonumber & + \\frac{M_h^2}{P \\cdot n_+} B_1 \\slashed{n}_+ + \n\\frac{M_h}{P \\cdot n_+} B_2 \\sigma_{\\mu\\nu} P^\\mu {n_+^\\nu} + \n\\frac{M_h}{P \\cdot n_+} B_3 \\sigma_{\\mu\\nu} k^\\mu n_+^\\nu +\n{\\frac{1}{P \\cdot n_+}\\, B_4\\, \\epsilon_{\\mu\\nu\\rho\\sigma}\\, \\gamma^\\mu\\, \\gamma_5\\, P^\\nu\\, k^\\rho\\, n_+^\\sigma} \\ .\n\\end{align}The amplitudes $A_i$ and $B_i$ are functions of the Lorentz scalars $k \\cdot n_+$, $k \\cdot P$, $k^2$. The terms proportional to $n_+$ originate from the path defining the Wilson lines $W_{1,2}$, that provides one additional vector beside $k$ and $P$ with which to carry out the decomposition. These terms generate TMD and collinear structures that appear only at subleading twist~\\cite{Mulders:1995dh,Mulders:2016pln,Bacchetta:2006tn}. \nIn keeping with the conventions of \\cite{Bacchetta:2006tn}, we have introduced a power-counting scale $M_h$ equal to the mass of the identified hadron. This choice is not mandatory, and only affects the normalization of the above defined amplitudes and of the related fragmentation functions to be introduced below. For example, a flavor-independent choice of scale, such as $\\Lambda$ used for the jet expansion of the inclusive jet correlator in Eq.~\\eqref{e:Xi_twist_dec},  would slightly simplify a number of the sum rules to be discussed later. However the present choice of $M_h$ not only agrees with most of the literature on TMD FFs, but also suggests interesting physical interpretations for these sum rules. \nIt is also of interest to note that, formally, Eq.~\\eqref{e:jet_ampl} for the decomposition of the inclusive correlator $\\Xi(k;n_+)$ can be obtained from Eq.~\\eqref{e:1hDelta_ampl} by replacing the hadron four-momentum $P$ with the parton four-momentum $k$, and by replacing the hadron mass $M_h$ with the power counting scale $\\Lambda$.\n\nThe fragmentation process can be studied either in the parton or in the hadron frame~\\cite{Collins:2011zzd,Levelt:1993ac}. The Lorentz transformation between these and its consequences are discussed in detail in Appendix~\\ref{a:frame_dep}\\footnote{See also Ref.~\\cite{Mulders:2016pln} and Section~12.4.1 in Ref.~\\cite{Collins:2011zzd}.}. \nIn the parton frame, defined such that the parton's transverse momentum $\\vect{k}_T=0$, one can interpret the fragmentation correlator as the probability density for the quark to fragment into a hadron of a given flavor $h$ and momentum $P$, with $\\vect{P}_T$ generically non zero \\cite{Collins:2011zzd,Metz:2016swz}. \nThe parton frame, however, turns out not to be convenient in derivations of factorization theorems and calculations of semi-inclusive cross sections: the partonic momenta are integrated over, and the parton frame axes are not fixed (see Chap. 12 in Ref.~\\cite{Collins:2011zzd}). In this case, it is preferable to utilize the hadron frame, where the experimentally observable hadron's 3-momentum determines the $z$ direction, so that $\\vect{P}_T=0$. In this frame, it is the quark's transverse momentum that, in general, has a non-zero value. \n\nSince we are not dealing with a specific scattering process and we want to connect the fragmentation correlator to the invariant quark propagator, we choose to work from now on in the parton frame. \nNamely, we consider a base in Minkowski space composed of the light-cone $n_+$ and $n_-$ vectors such that $k=k^+ n_+ + k^- n_-$, and two transverse four-vectors $n_1$ and $n_2$. \nThis basis not only determines the coordinates of any four-vector under consideration, but will also be used to define a set of parton-frame TMD fragmentation functions, as we will discuss next.\n\n\nIn calculations of semi-inclusive hadron production cross sections one deals with the fragmentation correlator integrated over the subdominant quark momentum component $k^+$. \nAccording to the convention outlined in Appendix~\\ref{a:conv} this is defined as \n\\begin{align}\n\\label{eq:integratedFFcorr}\n\\Delta^h(z,P_T) \\equiv \\frac{1}{2z} \\in\ndk^+ \\, \\Delta^h(k, P)_{k^- = P^-\/z } \\ ,\n\\end{align} \nwhich corresponds to:\n\\begin{equation}\n\\label{e:1hDelta_TMDcorr}\n\\Delta^h_{ij}(z,P_T) = \\frac{1}{2z} \\int \\frac{d \\xi^+ d^2 \\vect{\\xi}_T}{(2\\pi)^3} e^{\\i k^- \\xi^+} \n\\frac{\\text{Tr}_c}{N_c}\\, \\text{Disc}\\, {\\langle\\Omega|} \nW_1(\\infty,\\xi) \\psi_i(\\xi) (a_h^\\dagger a_h) \\overline{\\psi}_j(0) W_2(0,\\infty)  \n{|\\Omega\\rangle}_{\\begin{subarray}{l} \\xi^-=0 \\\\ k^- = P^-\/z \\end{subarray}}  \\ . \n\\end{equation}\nIn the parton frame, this can be expanded in Dirac structures and parametrized in terms of TMD FFs up to twist 3 as: \n\\begin{align}\n\\label{e:1hDelta_TMDcorr_param}\n\\Delta^h(z,P_T) & = \n\\frac{1}{2} \\slashed{n}_- D^h_1(z,P_T^2)  \n- \\i \\frac{ \\big[ \\slashed{P}_T, \\slashed{n}_- \\big]}{4 z M_h} H_1^{\\perp\\, h}(z,P_T^2)\n+ \\frac{M_h}{2 P^-} E^h(z,P_T^2) \n\\\\\n\\nonumber & \n- \\frac{\\slashed{P}_T}{2 z P^-} D^{\\perp\\, h}(z,P_T^2) \n+ \\frac{\\i M_h}{4 P^-} \\big[ \\slashed{n}_-, \\slashed{n}_+ \\big] H^h(z,P_T^2)\n- \\frac{1}{2 z P^-} \\gamma_5 \\epsilon_T^{\\rho\\sigma} \\gamma_\\rho {P_T}_\\sigma G^{\\perp\\, h}(z,P_T^2) \\ ,\n\\end{align}\nwhere the Dirac structures and the TMDs explicitly depend on the hadron momentum $P_T$. It is important to note that this decomposition of the TMD fragmentation correlator depends on the choice of the light cone basis vectors, in our case the parton-frame basis discussed above, even though for simplicity of notation no explicit index is introduced to remind us of this fact.\nIn Refs.~\\cite{Mulders:1995dh,Bacchetta:2006tn,Metz:2016swz} an analogous decomposition is given, instead, in the hadron frame, as is standard procedure in the TMD literature. \nThe relation between the hadron- and parton-frame decomposition, and therefore between the hadron- and parton-frame TMD fragmentation functions, is discussed in detail in Appendix~\\ref{a:frame_dep}. \n\nEq.~\\eqref{e:1hDelta_TMDcorr_param} can be also re-arranged as a sum of terms with definite rank in $P_T$~\\cite{Boer:2016xqr}:\n\\begin{equation}\n\\label{e:1hDelta_r0_r1}\n\\Delta^h(z,P_T) = \\Delta_0^h(z,P_T^2) + {P_T}_\\alpha\\, \\Delta_1^{h\\, \\alpha}(z,P_T^2) \\, , \n\\end{equation}\nwhere\n\\begin{align}\n\\label{e:1hDelta_r0}\n& \\Delta_0^h(z,P_T^2) = \n\\frac{1}{2} \\slashed{n}_- D^h_1(z,P_T^2) + \n\\frac{M_h}{2 P^-} E^h(z,P_T^2) + \n\\frac{\\i M_h}{4 P^-} \\big[ \\slashed{n}_-, \\slashed{n}_+ \\big] H^h(z,P_T^2) \\, , \\\\\n\\label{e:1hDelta_r1}\n& \\Delta_1^{h\\, \\alpha}(z,P_T^2) = \n- \\i \\frac{ \\big[ \\gamma_T^\\alpha, \\slashed{n}_- \\big]}{4 z M_h} H_1^{\\perp\\, h}(z,P_T^2)\n- \\frac{\\gamma_T^\\alpha}{2 z P^-} D^{\\perp\\, h}(z,P_T^2) \n- \\frac{1}{2 z P^-} \\gamma_5 \\epsilon_T^{\\rho\\alpha} \\gamma_\\rho G^{\\perp\\, h}(z,P_T^2) \\, .\n\\end{align}\nThe subscript $0,1$ refers to the rank in $P_T$ of the associated structures~\\cite{Boer:2016xqr} and, in the following, we will collectively refer to $D_1^h$, $E^h$, $H^h$ as the rank 0 TMD FFs, and to $H_1^{\\perp\\, h}$, $D^{\\perp\\, h}$, $G^{\\perp\\, h}$ as the rank 1 TMD FFs. \nFrom Eq.~\\eqref{e:1hDelta_r0_r1} one can see that~\\cite{Bacchetta:2006tn}\n\\begin{equation}\n\\label{e:1hDelta_integrated}\n\\Delta^h(z) = \\int d^2 \\vect{P}_T\\, \\Delta^h(z,P_T) = \\int d^2 \\vect{P}_T\\, \\Delta_0^h(z,P_T) \\, , \n\\end{equation}\nwhere the collinear fragmentation correlator $\\Delta^h(z)$ is defined as\n\\begin{equation}\n\\label{e:1hDelta_coll_op}\n\\Delta^h_{ij}(z) = \\frac{z}{2} \\int \\frac{d \\xi^+ }{2\\pi} e^{\\i \\xi^+ P^-\/z} \n\\frac{\\text{Tr}_c}{N_c}\\, \\text{Disc}\\, {\\langle\\Omega|} \nW_1(\\infty,\\xi) \\psi_i(\\xi) (a_h^\\dagger a_h) \\overline{\\psi}_j(0) W_2(0,\\infty)  \n{|\\Omega\\rangle}_{\\begin{subarray}{l} \\xi^-=\\vect{\\xi}_T=0 \\\\ P_T=0 \n\\end{subarray}}  \\ . \n\\end{equation}\nMoreover, $\\Delta(z)$ can be parametrized as~\\cite{Bacchetta:2006tn}:\n\\begin{equation}\n\\label{e:1hDelta_coll}\n\\Delta^h(z) = \n\\frac{1}{2} \\slashed{n}_- D^h_1(z) + \n\\frac{M_h}{2 P^-} E^h(z) + \n\\frac{\\i M_h}{4 P^-} \\big[ \\slashed{n}_-, \\slashed{n}_+ \\big] H^h(z) \\, .\n\\end{equation}\nThe rank-1 term $\\Delta_1^{h\\, \\alpha}(z,P_T^2)$ in Eq.~\\eqref{e:1hDelta_r0_r1} does not contribute at the collinear level~\\eqref{e:1hDelta_integrated} since the explicit ${P_T}_\\alpha$ factor sets the associated integral over $\\vect{P}_T$ to zero. \nFor this reason, we will only be able to derive constraints on the integral of rank-0 TMD FFs, but not of rank-1 FFs (see Section~\\ref{ss:mu_transverse}). On the contrary, by weighting $\\Delta^h(z,P_T)$ by $P_T^\\alpha$ and integrating over the transverse momentum one can obtain sum rules for the first moment of rank-1 TMD FFs. \nNote that Eq.~\\eqref{e:1hDelta_integrated}, relating the collinear correlator to the TMD correlator integrated over $\\vect{P}_T$, is only valid for bare, {\\it i.e.}, non-renormalized fields in perturbative QCD~\\cite{Collins:2011zzd}.\\footnote{The identification of an integrated TMD FF with the corresponding collinear FF is also valid in certain models of QCD, where the integration over the transverse momentum can be regularized introducing a phenomenological scale to suppress the large momentum region. An example is the parton model in Gaussian approximation~\\cite{Signori:2013mda,Anselmino:2013lza}. Other examples include the spectator diquark model~\\cite{Bacchetta:2008af} and the Nambu--Jona-Lasinio model~\\cite{Matevosyan:2011vj}.} \nThe same is also true when one identifies the integrated TMD FFs $f = D_1^h, E^h, H^h$ with their collinear counterparts in Eq.~\\eqref{e:1hDelta_coll}, \\textit{i.e.}, takes $f(z) \\ \\equiv\\ \\int d^2 \\vect{P}_T f(z,P_T^2)$.\n\n\n\\subsection{Connection between the fragmentation and jet correlators}\n\\label{ss:sum_operator}\n\nWe can now discuss a momentum sum rule connecting the unintegrated single-hadron fragmentation correlator to the inclusive jet correlator.\nWe work in the context of field theory, taking inspiration from, but generalizing, the strategy outlined in Ref.~\\cite{Meissner:2010cc}.\nIn particular, the authors of that reference directly manipulate the $k^+$-integrated TMD correlator, withouth the notion of the jet correlator, and limit their attention to a restricted number of Dirac structures.\nInstead, we prove the sum rule at the level of unintegrated correlators, then specialize this to the TMD correlators, and from there derive the sum rules for the fragmentation functions. As a result, we are able to extend the formalism to include all twist-2 and twist-3 FFs. Let us also stress from the outset that, as discussed in Ref.~\\cite{Meissner:2010cc}, the proof is only valid for unpolarized correlators and FFs. In the polarized case one would just obtain trivial identities.\nThe methods utilized here have also  been used in Ref.~\\cite{Anselmino:2011ss} to prove momentum sum rules for the quark fracture functions and reduce these to parton distribution functions,  but without considering Wilson line insertions as we do, instead, in this paper. \n\nOur starting point are the definitions of the unintegrated correlators $\\Xi$ and $\\Delta^h$ in Eq.~\\eqref{e:invariant_quark_correlator} and Eq.~\\eqref{e:1hDelta_corr}, respectively. \nLet us then consider the following quantity:\n\\begin{equation}\n\\label{e:average_Ph}\n\\sum_h \\sum_{S} \n\\int \\frac{d^4 P}{(2\\pi)^4}\\, (2\\pi) \\delta(P^2 - M_h^2) \nP^\\mu \\Delta^h(k,P,S)  \\, .\n\\end{equation}\nThe integration is performed in Minkowski space over the on-shell momentum $P$ of the detected hadron with mass $M_h$, and the sum extends to all hadron spin states and species. Eq.~\\eqref{e:average_Ph} can be loosely understood as providing one with the average four-momentum of the produced hadrons, if one considers $\\Delta$ as a probability distribution in hadron momentum and spin. This interpretation becomes explicit in the parton frame for the $\\gamma^+$ projection of the $k^+$-integrated $\\Delta$ correlator \\cite{Mulders:2016pln}. \n\nLet us now introduce the $\\hat {\\vect P}_h^\\mu$ hadronic momentum operator associated to the vector $P^\\mu$ of the identified hadron in the framework of second quantization~\\cite{Weinberg:1995mt,Collins:1981uw}:\n\\begin{equation}\n\\label{e:Ph_op_1}\n\\hat{\\vect{P}}_h^\\mu = \\sum_{S} \\int \\frac{dP^- d^2 \\vect{P}_T}{2P^- (2\\pi)^3} P^\\mu\\, \\hat{a}_h^\\dagger(P,S) \\hat{a}_h(P,S) \n\\end{equation}\nas well as the inclusive $\\hat{\\vect P}^\\mu$ momentum operator, that also appears in Eq.~(4.25) of Ref.~\\cite{Collins:1981uw} and in Ref.~\\cite{Meissner:2010cc}:\n\\begin{equation}\n\\label{e:P_op_1}\n\\hat{\\vect{P}}^\\mu = \\sum_h \\hat{\\vect{P}}_h^\\mu \\ . \n\\end{equation}\nUsing Eqs.~\\eqref{e:Ph_op_1} and \\eqref{e:P_op_1}, the average four-momentum defined in Eq.~\\eqref{e:average_Ph} can be further manipulated:\n\\begin{align}\n\\label{e:unintegrated_sum_rule}\n\\nonumber\n\\sum_{h\\, S} \n\\int \\frac{d^4 P}{(2\\pi)^4}\\, (2\\pi) \\delta(P^2 - M_h^2) \nP^\\mu \\Delta^h(k,P,S)  & = \n\\sum_{h\\, S} \n\\int \\frac{dP^- d^2 \\vect{P}_T}{(2\\pi)^3 2P^-} P^\\mu \n\\int \\frac{d^4 \\xi}{(2\\pi)^4} e^{\\i k \\cdot \\xi} \n{\\langle\\Omega|} W_1 \\psi_i(\\xi)(a_h^\\dagger a_h) \\overline{\\psi}_j(0) W_2 {|\\Omega\\rangle} \\\\\n& = \\int \\frac{d^4 \\xi}{(2\\pi)^4} e^{\\i k \\cdot \\xi} \n{\\langle\\Omega|} W_1(\\infty,\\xi) \\psi_i(\\xi) \\hat{\\vect{P}}^\\mu\\, \\overline{\\psi}_j(0) W_2(0,\\infty) {|\\Omega\\rangle} \\\\\n\\nonumber\n& = \\int \\frac{d^4 \\xi}{(2\\pi)^4} e^{\\i k \\cdot \\xi} \\,\n\\i \\frac{\\partial}{\\partial \\xi_\\mu}\n\\bigg\\{ {\\langle\\Omega|} W_1(\\infty,\\xi) \\psi_i(\\xi) \\overline{\\psi}_j(0) W_2(0,\\infty) {|\\Omega\\rangle} \\bigg\\} \\ ,\n\\end{align}\nwhere, for brevity, we have omitted the color traces. The last step can be justified as follows:\n\\begin{align}\n\\label{e:comm_prop_P}\n{\\langle\\Omega|} W(\\infty,\\xi) \\psi(\\xi) \\hat{\\vect{P}}^\\mu & = \n{\\langle\\Omega|} \\big[ W(\\infty,\\xi) \\psi(\\xi)\\, , \\hat{\\vect{P}}^\\mu \\big] = \n{\\langle\\Omega|} W(\\infty,\\xi) \\big[ \\psi(\\xi)\\, , \\hat{\\vect{P}}^\\mu \\big] + \n{\\langle\\Omega|} \\big[ W(\\infty,\\xi)\\, , \\hat{\\vect{P}}^\\mu \\big] \\psi(\\xi) \\\\\n\\nonumber\n& = {\\langle\\Omega|} W(\\infty,\\xi) \\bigg( \\i \\frac{\\partial}{\\partial \\xi_\\mu} \\psi(\\xi) \\bigg) + \n{\\langle\\Omega|} \\bigg( \\i \\frac{\\partial}{\\partial \\xi_\\mu} W(\\infty,\\xi) \\bigg) \\psi(\\xi) = \n\\i \\frac{\\partial}{\\partial \\xi_\\mu} \\bigg\\{ {\\langle\\Omega|} W(\\infty,\\xi) \\psi(\\xi) \\bigg\\} \\ . \n\\end{align}\nFinally,  \nintegrating by parts, we obtain the master result of this section,\n\\begin{equation}\n\\label{e:master_sum_rule}\n\\sum_h \\sum_{S} \n\\int \\frac{d^4 P}{(2\\pi)^4}\\, (2\\pi) \\delta(P^2 - M_h^2) \nP^\\mu \\Delta^h(k,P,S) = \nk^\\mu\\, \\Xi^{n.c.}(k) \\ , \n\\end{equation}\nwhere the boundary terms have vanished because of the boundary conditions for the fermionic fields, and the {\\it n.c. (no cut)} label at the r.h.s. means that we are not calculating the discontinuity of the inclusive jet correlator. \nIt is important to notice that the derivation of Eq.~\\eqref{e:master_sum_rule} holds true even with the (anti)time-ordering operators explicit, namely the specified choice for $W_{1,2}$ is not a necessary condition for the sum rule (but it is necessary for the spectral representation of $\\Xi$ discussed in Section~\\ref{ss:spectr_dec}).\n\nThe master sum rule~\\eqref{e:master_sum_rule} encodes the connection between the quark-to-single-hadron fragmentation correlator and the jet correlator without the discontinuity, which coincides with the gauge invariant color averaged dressed quark propagator. The Dirac projections of its discontinuity give rise to the sum rules for collinear and TMD fragmentation functions that will be discussed in detail in the remainder of this section.\nNote that, since Eq.~\\eqref{e:master_sum_rule} involves a sum over the hadron spins, all the polarized structures in the $\\Delta^h$ correlator vanish. Thus, we will be able to prove sum rules for unpolarized fragmentation functions only. \nPreliminary results on these FF sum rules have been presented at various conferences~\\cite{Accardi:2018gmh}, and the unpolarized case has been discussed in Ref.~\\cite{Accardi:2019luo}. \n\n\n\n\\subsection{Sum rules for rank 0 fragmentation functions}\n\\label{ss:mu_minus}\n\nWe now specialize the master sum rule~\\eqref{e:master_sum_rule} to the TMD case in the parton frame. We start with the rank 0 term, defined in Eq.~\\eqref{e:1hDelta_r0_r1}, which can be selected by choosing $\\mu=-$.\nWe then consider the discontinuity of the sum rule, integrate both sides on the suppressed plus component of the partonic momentum, and choose the parton frame ($k_T = 0$).\nWe also exploit the relation\n\\begin{equation}\n\\label{e:measure}\n\\int \\frac{d^4 P}{(2\\pi)^3} \\delta(P^2 - M_h^2) = \n\\int \\frac{dP^- d^2 \\vect{P}_T}{2P^- (2\\pi)^3} = \n\\int \\frac{dz d^2 \\vect{P}_T}{2z (2\\pi)^3} \\ ,\n\\end{equation}\nand obtain: \n\\begin{equation}\n\\label{e:long_sr_operator_1}\n\\sum_{h\\, S} \\int \\frac{dz d^2 \\vect{P}_T}{2z (2\\pi)^3} P^- \\int dk^+ \\,\n\\text{Disc}\\, [\\Delta^h(k,P,S)]_{\\begin{subarray}{l} P^- = z k^- \\\\ k_T = 0 \\end{subarray}} = \nk^- \\int dk^+\\, \\text{Disc}\\, [\\Xi^{n.c.}(k)]_{k_T = 0} \\ .\n\\end{equation}\nThis equation can be rewritten in terms of the collinear fragmentation correlator~\\eqref{e:1hDelta_integrated} and the jet correlator Eq.~\\eqref{e:J_TMDcorr}.  \nThe result is:\n\\begin{align}\n\\label{e:long_sr_operator_2}\n\\sum_{h\\, S} \\int dz\\, z\\, \\Delta^h(z) = \n\\sum_{h\\, S} \\int dz\\, d^2 \\vect{P}_T \\, z\\, \\Delta_0^h(z,P_T) = \n2(2\\pi)^3 J(k^-,\\vect{0}_T) \\ .\n\\end{align}\nNote that only the hadron spin-independent part of $\\Delta^h(z)$ survives in~\\eqref{e:long_sr_operator_2}. \nConsidering now the Dirac projections of the correlators on both sides, we can turn this into momentum sum rules for the collinear FFs in Eq.~\\eqref{e:1hDelta_coll}. \nThere are, in general, 9 Dirac projections $\\Delta^{[\\Gamma]}$ and $J^{[\\Gamma]}$ \ninvolving twist-2 and twist-3 functions, of which only three are relevant for the rank 0 case:\\footnote{The structures $\\Gamma=\\{ \\gamma^-\\gamma_5 ,\\, \\i\\gamma_5 ,\\,  \\i\\sigma^{-+}\\gamma_5 \\}$ project polarized TMD fragmentation functions out of $\\Delta$. Since we are summing over the hadron polarization states in Eq.~\\eqref{e:average_Ph}, these contributions vanish; on the contrary, these structure do not appear in $J$ from the very beginning because of parity invariance. The projections for the other 3 Dirac structures $\\Gamma=\\{ \\i\\sigma^{i-}\\gamma_5 ,\\, \\gamma^i ,\\, \\gamma^i\\gamma_5 \\}$ produce the trivial result $0=0$.} \n\\begin{align}\n\\label{e:sumrule_D1}\n[\\, \\Gamma = \\slashed{n}_+ \\, ] \\ \\ \\ \\ \n& \\sum_{h\\, S} \\int dz  z\\,  D_1^{h}(z) = 1 \\ ,\t\\\\\n\\label{e:sumrule_E}\n[\\, \\Gamma = {\\mathbb 1} \\, ] \\ \\ \\ \\\n& \\sum_{h\\, S} \\int dz M_h E^{h}(z) = M_j \\ , \\\\\n\\label{e:sumrule_H}\n[\\, \\Gamma = \\i \\sigma^{\\mu\\nu} {n_i}_\\mu {n_j}_\\nu \\gamma_5  \\, ] \\ \\ \\ \\ \n& \\sum_{h\\, S} \\int dz  M_h H^{h}(z) = 0 \\ .\n\\end{align} \nTo obtain the result for the collinear $D_1$ and $E$ FFs we have used Eq.~\\eqref{e:alpha_calc_2} and~\\eqref{e:zeta_calc_2} with $\\theta(k^-)=1$ because $k^-$ is positive by four momentum conservation ($k^-$ is equal to the sum of the minus momenta of all produced hadrons, and these are physical on-shell particles). \n\nRenormalization is known to preserve Eq.~\\eqref{e:sumrule_D1}~\\cite{Collins:1981uw,Collins:2011zzd}.\nThe renormalization of $E^h(z)$ and its moments has been discussed in Refs.~\\cite{Belitsky:1996hg,Belitsky:1997ay} at leading order in the strong coupling and in the large $N_c$ limit, using the light-cone gauge and neglecting current quark mass contributions. \nOne can then infer an approximate evolution equation for $M_j$.\nInstead, the renormalization of $H^h$, which is directly connected to a three-parton correlation function~\\cite{Metz:2016swz}, has not yet been addressed to our knowledge.\nNevertheless, the derivations of these sum rules are rooted in the conservation of the partonic four-momentum encoded in Eq.~\\eqref{e:master_sum_rule} and in the symmetry properties of the correlators $\\Xi$ and $\\Delta^h$. Therefore, we expect Eqs.\\eqref{e:sumrule_D1}-\\eqref{e:sumrule_H} and all the other sum rules discussed in this paper to be valid \\emph{in form} also at the renormalized level in perturbative QCD.    \n\n\n\n\nThe normalization~\\eqref{e:rho13_positivity_rho3sumrule} of the spectral function $\\rho_3$ -- which is a direct consequence of the equal-time anticommutation relations for the fermion fields~\\cite{Weinberg:1995mt,Solis:2019fzm} -- is crucial to obtain the well-known {\\it momentum sum rule}~\\eqref{e:sumrule_D1} for the unpolarized fragmentation function $D_1^h$, that was originally proven without reference to the jet correlator~\\cite{Collins:1981uw,Mulders:1995dh}. \nAn experimental verification of this sum rule is therefore also an indirect check of the validity of the K\\\"allen-Lehman spectral representation. \nIt is also interesting to note that Eq.~\\eqref{e:sumrule_D1} allows one to write the unpolarized ``inclusive jet function'' and ``energy-energy correlation jet function'' introduced in the context of Soft Collinear Effective Theory as, respectively, the matching coefficients of the fragmenting jet functions onto the collinear FFs~\\cite{Procura:2009vm,Jain:2011xz} and of the TMD FFs onto the collinear FFs~\\cite{Moult:2018jzp,Luo:2019hmp}.\n\n\nThe chiral-odd sum rule~\\eqref{e:sumrule_E}, that generalizes the one discussed in Ref.~\\cite{Jaffe:1993xb,Jaffe:1996zw}, can be called {\\em ``mass sum rule''} because of its physical interpretation: the non-perturbative jet mass $M_j$ corresponds to the sum of the masses of all possible particles produced in the hadronization of the quark, weighted by the chiral-odd collinear twist-3 fragmentation function $E^h(z)$. \nIn looser terms, $M_j$ can be interpreted as the average mass of the hadronization products.\n\nFinally, the sum rule~\\eqref{e:sumrule_H} is, to our knowledge, new.\n\n\n\n\n\\subsection{Sum rules for rank 1 fragmentation functions}\n\\label{ss:mu_transverse}\n\nLet us now specify the master sum rule to the case of the rank 1 correlator $\\Delta_{1}^{h\\, \\alpha}(z,P_T)$ defined in Eq.~\\eqref{e:1hDelta_r1}. This can be selected by choosing  $\\mu = \\alpha = 1,2$ in Eq.~\\eqref{e:master_sum_rule}. Since we are working in the parton frame  \nwhere $k_T=0$, this reads:\n\\begin{equation}\n\\label{e:sumrule_transverse}\n\\sum_{h\\, {S}} \\int dz\\ d^2 \\vect{P}_T\\, P_T^\\alpha\\, \\Delta^h(z,P_T) = \n\\sum_{h\\, {S}} \\int dz\\ d^2 \\vect{P}_T\\, P_T^\\alpha\\, {P_T}_\\rho\\, \\Delta_1^{h\\, \\rho}(z,P_T) =\n0 \\, . \n\\end{equation}\nThis result can also be achieved directly from Eq.~\\eqref{e:unintegrated_sum_rule} choosing the parton frame, performing the integration explicitly with $\\mu$ transverse index, and assuming that the fermion fields vanish at the boundary of space~\\cite{Meissner:2010cc}. \n\nUsing the correspondence between symmetric traceless tensors built with the transverse momentum and complex numbers outlined in Appendix~\\ref{a:conv} and Ref.~\\cite{Boer:2016xqr}, and the relation~\\cite{Bacchetta:2006tn,Mulders:2016pln}\n\\begin{equation}\n\\label{e:NT_eps_relation}\nP_T^{[ \\alpha} \\epsilon_T^{\\rho\\sigma ]} {P_T}_\\rho = P_T^2 \\epsilon_T^{\\alpha\\rho} \\ ,\n\\end{equation}\nwe can calculate the Dirac projections of Eq.~\\eqref{e:sumrule_transverse}, based on the parametrization given in Eq.~\\eqref{e:1hDelta_r1}. The result reads\n\\begin{align}\n\\label{e:sumrule_H1p}\n[\\, \\Gamma = -\\i \\sigma^{\\mu\\nu} {n_i}_\\mu {n_+}_\\nu \\gamma_5 \\, ] \\ \\ \\ \\ \n& \\sum_{h\\, S} \\int dz z M_h\\, H_1^{\\perp\\, (1)\\, h}(z) = 0 \\ , \\\\\n\\label{e:sumrule_Dp}\n[\\, \\Gamma = -\\slashed{n}_i \\, ] \\ \\ \\ \\ \n& \\sum_{h\\, S} \\int dz M_h^2\\, D^{\\perp\\, (1)\\, h}(z) = 0 \\ , \\\\\n\\label{e:sumrule_Gp}\n[\\, \\Gamma = -\\slashed{n}_i \\gamma_5 \\, ] \\ \\ \\ \\ \n& \\sum_{h\\, S} \\int dz M_h^2\\, G^{\\perp\\, (1)\\, h}(z) = 0 \\ , \n\\end{align}\nwhere we defined the first $P_T$-moment of a generic fragmentation function $D$ as (see Appendix~\\ref{a:frame_dep}): \n\\begin{equation}\n\\label{e:def_Php_mom}\nD^{(1)}(z) = \\int d^2 \\vect{P}_T \\frac{\\vect{P}_T^2}{2 z^2 M_h^2} D(z,P_T^2) \\ .\n\\end{equation}\nAs in Section~\\ref{ss:mu_minus}, the remaining Dirac projections yield the trivial result $0=0$. The sum rule~\\eqref{e:sumrule_H1p} for $H_1^{\\perp\\, h}$ is also known as the Sch\\\"afer-Teryaev sum rule~\\cite{Schafer:1999kn,Meissner:2010cc}. \nWe already discussed the sum rule for $D^{\\perp\\, h}$ in Ref.~\\cite{Accardi:2019luo}, and that for $G^{\\perp\\, h}$ is new.\nThe QCD evolution of the first moment of $H_1^{\\perp\\, h}$ has been discussed in Ref.~\\cite{Kang:2010xv}, but no statement is available on the validity of the Sch\\\"afer-Teryaev sum rule under renormalization. Nevertheless, the sum rule for the T-odd FFs, $H_1^{\\perp\\, h}$, $G^{\\perp\\, h}$, and $H^h$, is a result of the absence of T-odd terms in the inclusive jet correlator, a feature that should be preserved under renormalization, too. Checking this by explicit calculation remains an interesting exercise for the future.\n\n\n\n\\subsection{Sum rules for dynamical twist-3 fragmentation functions}\n\\label{ss:qgq_sumrules}\n\nLet us now consider the equations of motion relations (EOMs) which relate twist-2 and twist-3 fragmentation functions in the parton frame:\n\\begin{align}\n  \\label{e:eom_E}\n  & E^h = \\widetilde{E}^h + z \\frac{m}{M_h} D^h_1 \\\\\n  \\label{e:eom_H}\n  & H^h = \\widetilde{H}^h - \\frac{\\vect{P}_T^2}{z M_h^2} H_1^{\\perp\\, h} \\\\\n  \\label{e:eom_Dp}\n  & D^{\\perp\\, h} = \\widetilde{D}^{\\perp\\, h} + z D^h_1 \\\\\n  \\label{e:eom_Gp}\n  & G^{\\perp\\, h} = \\widetilde{G}^{\\perp\\, h} + z \\frac{m}{M_h} H_1^{\\perp\\, h} \\ ,\n\\end{align}\nwhere the functions with a tilde parametrize the twist-3 $\\widetilde{\\Delta}_A^\\alpha$ quark-gluon-quark correlator~\\cite{Bacchetta:2006tn}, and $m$ is the current mass of the specific quark considered. These relations, that are a consequence of the Dirac equation for the quark field, have been originally presented in the hadron frame~\\cite{Tangerman:1994bb,Mulders:1995dh} (see also Ref.~\\cite{Bacchetta:2006tn}) and in Appendix~\\ref{a:frame_dep} we discuss their transformation to the parton frame. \n\nThe Eqs.~\\eqref{e:eom_E}-\\eqref{e:eom_Gp} allow us to investigate the momentum sum rules for the ``dynamical\" twist-3 FFs (those with a tilde) without explicitly working with  the quark-gluon-quark fragmentation correlator $\\widetilde{\\Delta}_A^\\alpha$ and the quark-gluon-quark inclusive jet correlator $\\widetilde{J}_A^\\alpha$ introduced in Ref.~\\cite{Accardi:2017pmi}.\nIndeed, combining the four EOMs with the sum rules discussed in Section~\\ref{ss:mu_minus} and Section~\\ref{ss:mu_transverse} we obtain\n\\begin{align}\n\\label{e:sumrule_Et}\n& \\sum_{h\\, S} \\int dz M_h \\widetilde{E}^{h}(z) = M_j - m = m^{\\text{corr}}\\\\\n\\label{e:sumrule_Ht}\n& \\sum_{h\\, S} \\int dz M_h \\widetilde{H}^{h}(z) = 0 \\\\\n\\label{e:sumrule_Dtp}\n& \\sum_{h\\, S} \\int dz M_h^2 \\widetilde{D}^{\\perp\\, (1)\\, h}(z) = \n- \\sum_{h\\, S} \\int dz z\\, M_h^2 D_1^{(1)\\, h}(z) \\ \\equiv\\\n\\frac{1}{2} \\langle P_{T}^2 \/ z^2 \\rangle \\\\\n\\label{e:sumrule_Gtp}\n& \\sum_{h\\, S} \\int dz M_h^2 \\widetilde{G}^{\\perp\\, (1)\\, h}(z) = 0 \\ ,\n\\end{align}\nwhich provide a complete set of sum rules for the four unpolarized dynamical twist-3 FFs. As with the twist-2 case, no sum rule can be established for polarized FFs.\n\nEq.~\\eqref{e:sumrule_Et} is the generalization of the sum rule $\\int dz \\widetilde{E} = 0$ discussed in Ref.~\\cite{Bacchetta:2006tn}. \nThis generalization is based on the fact that the jet mass $M_j$ differs in general from the current quark mass by an amount $m^{\\text{corr}}$ (the correlation mass introduced in Eq.~\\eqref{e:Mj_decomp}) which we argued is non-perturbatively generated by quark-gluon-quark correlations and the dynamical breaking of the chiral symmetry. In the FF correlator $\\widetilde{\\Delta}_A^\\alpha$, the chiral odd component of these correlations is parametrized by the $\\widetilde E$ function~\\cite{Bacchetta:2006tn}, that also provides a flavor decomposition for $m^{\\text{corr}}$ through Eq.~\\eqref{e:flav_mqcorr}. See Section~\\ref{ss:sumrules_summary} for a deeper discussion of this point. \n\nThe sum rule~\\eqref{e:sumrule_Dtp} connects the first moment of the twist-3 $\\widetilde D^\\perp$ FF to the average squared transverse momentum acquired by unpolarized hadrons fragmented from an unpolarized quark~\\cite{Accardi:2019luo} (for the definition of the average operator see Appendix~\\ref{a:frame_dep}). Therefore, this sum rule also probes the nature of the non-perturbative hadronization process in analogy with the way the sum rule for $\\widetilde E$ probes the nature of the vacuum. \nSimilar relations exist in literature, see e.g. Eq.~(76) in Ref.~\\cite{Metz:2016swz}, which connects a three-parton FF, the first moment of the Collins FF, and the average transverse momentum of an unpolarized hadron fragmenting from a transversely polarized quark. Another example is the relation between the average transverse momentum of an unpolarized quark in a transversely polarized hadron and the Qiu-Sterman function~\\cite{Qiu:1991pp,Qiu:2020oqr}. \n\nIt is finally worthwhile remarking that the sum rules for $D^\\perp$ and $\\widetilde{D}^\\perp$ are frame dependent because such are the involved transverse momenta. On the contrary, all other sum rules are frame independent. Appendix~\\ref{a:frame_dep} discusses these features in details.\n\n\n\n\n\\section{Sum rules compendium and discussion}\n\\label{ss:sumrules_summary}\n\nWe collect here for convenience the complete set of sum rules for twist-2 and twist-3 FFs scattered throughout Section~\\ref{s:1h_rules}, and remind that all fragmentation functions implicitly depend on the quark flavor, omitted for sake of simplicity.\nAt twist 2,\n\\begin{align}\n\\label{e:pframe_sumrule_D1}\n& \\sum_{h\\, S} \\int dz\\, z\\, D_1^{h}(z) = 1 \\, , \\\\\n\\label{e:pframe_sumrule_H1p}\n& \\sum_{h\\, S} \\int dz\\, z\\, M_h H_1^{\\perp\\, (1)\\, h}(z) = 0 \\, .\n\\end{align}\nAt twist 3,\n\\gdef\\thesubequation{\\theequation \\textit{a,b}}\n\\begin{subeqnarray}\n\\label{e:pframe_sumrule_E_Et}\n& \\ \\ \\displaystyle \\sum_{h\\, S} \\int dz\\, M_h\\, E^{h}(z) = M_j\\, , \\qquad \\ \\\n& \\sum_{h\\, S} \\int dz\\, M_h\\, \\widetilde{E}^{h}(z) = M_j - m = m^{\\text{corr}}\\, , \\\\\n\\refstepcounter{equation}\n\\label{e:pframe_sumrule_H_Ht}\n& \\displaystyle \\sum_{h\\, S} \\int dz\\, M_h\\, H^{h}(z) = 0\\, , \\qquad \\ \\ \n& \\sum_{h\\, S} \\int dz\\, M_h\\, \\widetilde{H}^{h}(z) = 0\\, , \\\\\n\\refstepcounter{equation}\n\\label{e:pframe_sumrule_Dp_Dpt}\n& \\ \\ \\ \\ \\ \\ \\displaystyle\\sum_{h\\, S} \\int dz\\, M_h^2\\,  D^{\\perp\\, (1)\\, h}(z) = 0\\, , \\qquad \\ \\  \n& \\sum_{h\\, S} \\int dz\\, M_h^2\\, \\widetilde{D}^{\\perp\\, (1)\\, h}(z) = \\frac{1}{2} \\langle P_{T}^2 \/ z^2 \\rangle\\, , \\\\\n\\refstepcounter{equation}\n\\label{e:pframe_sumrule_Gp_Gpt}\n& \\ \\ \\ \\ \\ \\ \\displaystyle\\sum_{h\\, S} \\int dz\\, M_h^2\\, G^{\\perp\\, (1)\\, h}(z) = 0\\, , \\qquad \\ \\  \n& \\sum_{h\\, S} \\int dz\\, M_h^2\\, \\widetilde{G}^{\\perp\\, (1)\\, h}(z) = 0 \\, .\n\\end{subeqnarray}\n\nThe sum rules~\\eqref{e:pframe_sumrule_D1},~\\eqref{e:pframe_sumrule_H1p} and~\\eqref{e:pframe_sumrule_H_Ht}$b$ were already known in literature~\\cite{Collins:1981uw,Mulders:1995dh,Meissner:2010cc,Schafer:1999kn,Bacchetta:2006tn}, with the latter proven here for the first time at the correlator level. \nIt's interesting to notice that the sum rules for the T-odd FFs $H^h$, $H_1^{\\perp\\, h}$, $G^{\\perp\\, h}$ are a consequence of the absence of T-odd terms in the inclusive jet correlator~\\eqref{e:invariant_quark_correlator} (see Eq.~\\eqref{e:B3_zero}). Being the consequence of time-reversal symmetry, this feature is frame-independent (see Appendix~\\ref{a:frame_dep}).\nThe sum rules~\\eqref{e:pframe_sumrule_E_Et} for $E$ and $\\widetilde E$ have been originally discussed in Ref.~\\cite{Jaffe:1996zw}, but here extended to the non-perturbative domain (we will have more to say about these shortly). \nAll others are, to the best of our knowledge, novel results\\footnote{A partial proof was discussed in Ref.~\\cite{Accardi:2019luo} and at various conferences, see for example Ref.~\\cite{Accardi:2018gmh}.}. \\\\ \n\n\nAs we will discuss below, these sum rules are generically useful as constraints in phenomenological fits where experimental data is scarce, and when developing fragmentation models.\nThe non-zero sum rules, however, have a significance that goes well beyond that. \nTo start with, we have shown that the $D_1$ sum rule is theoretically linked to the normalization property~\\eqref{e:rho13_positivity_rho3sumrule} of the chiral-even $\\rho_3$ spectral function, and, thus, to the equal-time anticommutation relations for the fermion fields. Hence its experimental verification also entails an indirect check of the validity of the K\\\"allen-Lehman spectral representation. \nThe sum rules~\\eqref{e:pframe_sumrule_E_Et} for $E$ and $\\widetilde E$, and~\\eqref{e:pframe_sumrule_Dp_Dpt}$b$ for $\\widetilde D^\\perp$ are also noteworthy because, unlike the others, they are sensitive to aspects of the non perturbative dynamics of QCD: respectively, the dynamical mass generation in the QCD vacuum, and the transverse momentum generation in the fragmentation process~\\cite{Accardi:2019luo}. \n\nOur proof has been developed in the parton frame in order to connect to the inclusive jet correlator, that cannot be defined in the hadron frame.\nMost of the sum rules are nonetheless frame independent, as detailed in Appendix~\\ref{a:frame_dep}. The only exceptions are the sum rules~\\eqref{e:pframe_sumrule_Dp_Dpt} for $D^\\perp$ and $\\widetilde{D}^\\perp$, that in the hadron frame exchange the role of the kinematic and dynamical twist-3 functions. In that frame, it is the first moment of the $D^{\\perp h}$ functions that are sensitive to the transverse momentum of the fragmented hadrons, whereas the first moment of the $\\widetilde{D}^{\\perp h}$ functions sum up to zero. \n\nFinally, note that our proofs are at present valid only for unrenormalized FFs. However, the arguments we utilized are rooted in the conservation of the partonic four-momentum encoded in Eq.~\\eqref{e:master_sum_rule}, and on the symmetry properties of the correlators $\\Xi$ and $\\Delta^h$. For this reason, we expect all momentum sum rules to be valid in form also at the renormalized level. \nIn fact: renormalization is known to preserve Eq.~\\eqref{e:pframe_sumrule_D1}~\\cite{Collins:2011zzd,Collins:1981uw}; \nthe evolution of $E(z)$ and $M_j$ can be inferred from the results presented in Refs.~\\cite{Belitsky:1996hg,Belitsky:1997ay}; it could also be argued that the sum rules for the T-odd FFs are preserved under renormalization due to the absence of T-odd terms in the inclusive jet correlator, but explicit calculations are needed to corroborate this hypothesis and to understand the behavior of all the other sum rules.  \n\n\n\n\n\\subsection{Dynamical chiral symmetry breaking}\n\\label{sss:DCSB}\n\nThe mass sum rules~\\eqref{e:pframe_sumrule_E_Et} are of particular interest, because they shed additional light on the QCD mass generation mechanism already explored in Section~\\ref{s:jetcor} in terms of the jet correlator $J$ and its chiral odd component. As discussed in Section~\\ref{ss:TMDjet_recap}, the jet mass $M_j=m+m^{\\text{corr}}$ quantifies the dressing of a quark as it propagates in the QCD vacuum. Here we suggest that, whereas the current quark mass $m$ is the component of $M_j$ that explicitly breaks the chiral symmetry, it is the  $m^{\\text{corr}}$ correlation mass component that can be considered a theoretically solid order parameter for its dynamically breaking.  That this is the case is supported by the following arguments, highlighting the central role played by quark-gluon interactions in generating $m^{corr}$, and how this is intrinsically connected to the properties of the QCD vacuum. \n\nOverall, the correlation mass can vanish in two circumstances, where the neglect of quark-gluon-quark correlations is achieved in different ways. In the first case, one can invoke the ``Wandzura-Wilczek (WW) approximation'', which consists in neglecting the twist-3 ``tilde'' functions, that parametrize the strength of quark-gluon-quark correlations, compared to the twist-2 and twist-3 functions without a tilde, that describe quark-quark correlations. In other words, this approximation consists in neglecting the role of gluons except in the dressing of the quark-quark correlators, and setting the ``tilde'' functions to zero~\\cite{Bastami:2018xqd}\\footnote{The WW appriximation takes its name from the fact that one is in fact utilizing simplified form of the Wandzura-Wilczek-type relations, originally introduced and discussed in Ref.~\\cite{Wandzura:1977qf}, that relate twist-2 and twist-3 functions. While in some processes the neglect of quark-gluon-quark interactions leads to phenomenologically successful comparisons to experimental data \\cite{Bastami:2018xqd}, this assumption is not a priori justified in all circumstances~\\cite{Accardi:2017pmi}. In particular, one needs to make sure that the dominant quark-quark terms do not cancel in the observable of interest. For example, in our case, a WW approximation applied to Eq.~\\eqref{e:sumrule_Dtp} would amount to predicting no transverse momentum in the fragmentation process, $\\langle P_{T}^2 \/ z^2 \\rangle = 0$, which is clearly not the case.}\nThus, $M_j \\overset{\\,_{WW}}{=} m$ and $m^{\\text{corr}} \\overset{\\,_{WW}}{=} 0$, as can be easily seen by setting $\\widetilde E = 0$ in Eq.~\\eqref{e:eom_E} and using the sum rules~\\eqref{e:sumrule_D1} and~\\eqref{e:sumrule_E}. (An application of the same WW approximation to the sum rule~\\eqref{e:sumrule_Et} consistently provides one with the identity $0=0$.)\nAnother case in which the dynamical mass $m^{\\text{corr}}$ vanishes is when the non-interacting vacuum $|0 \\rangle$ of the theory is used in place of the interacting one ${|\\Omega\\rangle}$~\\cite{Peskin:1995ev}, so that one cannot fully contract the $\\psi A_T^\\alpha \\bar\\psi$ operator that defines $\\widetilde E$ unless the interaction terms in the Lagrangian are taken into account, effectively causing $\\widetilde E = 0$ as in the WW approximation. \n\nFurthermore, one can decompose the chiral-odd spectral function $\\rho_1$ into a pole part, with an isolated singularity at the (renormalized) current mass value $\\mu^2=m^2$, and a remnant $\\overline\\rho_1$ (see, {\\it e.g.}, Ref.~\\cite{Solis:2019fzm}):\n\\begin{align}\n  \\rho_1(\\mu^2) = \\delta(\\mu^2-m^2) + \\overline\\rho_1(\\mu^2) \\ .\n\\end{align}\nThis singularity, in fact cannot appear in the full, non-perturbative propagator because quarks are not physical states of the theory; rather, it originates from a perturbative treatment of a the propagating quark considered as an asymptotic field while in reality it is not. \nNext, combining the $E$ and $\\widetilde E$ sum rule with the EOM relation~\\eqref{e:eom_E} one sees that\n\\begin{align}\n\\label{e:nonpole_rho1_mcorr}\n\tm^{\\text{corr}} \\overset{lcg}{=} \\int d\\mu^2 \\sqrt{\\mu^2}  \\, \\overline\\rho_1(\\mu^2) \\ .\n\\end{align}\nTherefore, the perturbative pole \nis effectively removed in the sum rule for $\\widetilde E$, and from the spectral decomposition of the correlation mass. This is all the more interesting, because it is the twist-3 $\\widetilde E$ function rather than $E$, that contributes to hadroproduction DIS processes, whence the sum rules can be experimentally measured~\\cite{Bacchetta:2006tn}.\n\nFinally,  the $\\widetilde E$ sum rule also provides one with a hadronic flavor decomposition of the correlation mass: \n\\begin{equation}\n\\label{e:flav_mqcorr}\nm^{\\text{corr}} = \\sum_{h,S} \\int dz M_h\\, \\widetilde{E}^{h}(z) \n  \\equiv \\sum_h \\, m_h^{\\text{corr}} \\ ,\n\\end{equation}\nwhere each $m_h^{\\text{corr}} = \\sum_{S} \\int dz M_h\\, \\widetilde{E}^{h}(z)$ quantifies the contribution to the interaction-dependent part of the jet mass associated to the hadronization into a specific hadron $h$. One can therefore envisage investigating the separate role of baryon and light mesons in the dynamical chiral symmetry breaking process, with the pions and kaons expected to become massless in the chiral limit due to the Goldstone theorem, and obtain a more fine-grained picture of the spontaneous generation of mass in QCD.\nAs a starter, calculations of $E$ and $\\widetilde{E}$ in models which incorporate the dynamical breaking of the chiral symmetry, for example such as in treatments combining the Nambu--Jona-Lasinio model~\\cite{Ito:2009zc,Matevosyan:2011vj,Bentz:2016rav} \nThe full set of sum rules provided in this article could be used to constrain and refine these calculations, and a comparison with even a limited amount of experimental data on $\\widetilde E$ would provide the model with the dynamical input necessary to explore with confidence the chiral limit via Eq.~\\eqref{e:flav_mqcorr}.  \n\n\n\\subsection{Phenomenology}\n\\label{sss:pheno}\n\nThese sum rules can be of phenomenological relevance in the studies of hard scattering process with hadrons in the final states, \nfor example, semi-inclusive deep-inelastic scattering (SIDIS) and electron-positron annihilation into one or two hadrons, \nas well as hadroproduction in hadronic collisions at both fixed target and collider facilities~\\cite{Hadjidakis:2018ifr,Aidala:2019pit}).\n\n\nThe leading-twist TMD FFs $D_1$ and $H_1^\\perp$ can be observed in \nSIDIS procceses, considering specific angular modulations of the cross section at low transverse momentum~\\cite{Bacchetta:2006tn}. \n\nThe dynamical twist-3 FFs ($\\widetilde E$, $\\widetilde H$, $\\widetilde D^\\perp$, $\\widetilde G^\\perp$) appear in the SIDIS cross section at order $1\/Q$, where $Q$ is the hard scale of the process. As it turns out, these are the only twist-3 FFs contributing to the cross section in a frame where the azimuthal angles refer to the axis given by the four-momenta of the target nucleon and the photon, rather than of the target nucleon and the detected hadron~\\cite{Bacchetta:2006tn}.\nIn such a frame, their kinematic twist-3 counterparts (those without a tilde in their symbol) do not contribute to the  cross section, but can be obtained from the former by use of the equation of motion relations \\eqref{e:eom_E}-\\eqref{e:eom_Gp}. \nThe role of twist-3 FFs in other semi-inclusive processes is reviewed in Ref.~\\cite{Metz:2016swz}. \nIn general, to access these fragmentation functions one needs to calculate cross sections at least to twist-3 level, and, in the case of the chiral-odd $E$ and $\\widetilde E$ FFs, to combine these with another chiral-odd distribution or fragmentation function.\n\n\nThe possibility to experimentally observe the tilde functions in semi-inclusive processes is particularly interesting for the case of $\\widetilde E$, which contributes to the determination of the interaction-dependent correlation mass $m^{\\text{corr}}$ and its flavor decomposition through the sum rule \\eqref{e:pframe_sumrule_E_Et}. This is not, however, the only experimental window on $m^{\\text{corr}}$. For example, as discussed in Ref.~\\cite{Accardi:2017pmi,Accardi:2018gmh}, the correlation mass $m^{\\text{corr}}$ also contributes coupled to the collinear transversity PDFs to the inclusive DIS $g_2$ structure function at large Bjorken $x_B$. Likewise, the correlation mass couples to the collinear transversity FF $H_1$ in single hadron production of, say, the self-polarizing $\\Lambda$ particle in semi-inclusive $e^+e^-$ collisions. Likewise, it can couple to the dihadron $H_1^\\sphericalangle$ FF in the case of same-hemisphere double hadron production. \n\nAs one can see, the experimental information we are after is scattered among a umber of diverse observables and process. One way to gather it in a consistent fashion is to perform ``universal'' QCD fits of a suitable subsets of PDFs and FFs. One possibility is to simultaneously fit $m^{\\text{corr}}$, the collinear transversity PDFs $h_1$, and the collinear dihadron $H_1^\\sphericalangle$. The needed processes are longitudinal-transverse asymmetries in inclusive DIS ($\\propto m^{\\text{corr}}\\, h_1 $~\\cite{Accardi:2017pmi}), \ndi-hadron production in SIDIS ($\\propto h_1 H_1^\\sphericalangle$~\\cite{Radici:2015mwa,Radici:2018iag}), the Artru-Collins asymmetry in double di-hadron production in electron-positron annihilation ($\\propto H_1^\\sphericalangle H_1^\\sphericalangle$~\\cite{Matevosyan:2018icf}), and semi-inclusive same-side dihadron production ($\\propto m^\\text{corr} H_1^\\sphericalangle$~\\cite{Accardi:2017pmi}). This kind of universal QCD analysis, seeking to numerically fit several non perturbative functions at once, is numerically very demanding in terms of raw computational power and stability of the fitting algorithms. Nonetheless its feasibility has been recently demonstrated in a series of works by the JAM collaboration~\\cite{Ethier:2017zbq,Lin:2017stx,Sato:2019yez}. \n\nIn order to properly separate perturbative and non-perturbative contributions, these observables should be addressed in the context of the associated factorization theorems. In this respect, resummed perturbative QCD and Soft-Collinear Effective Theories (SCET) provide the needed tools. Namely, the inclusive jet correlator $\\Xi$ emerges, {\\em e.g.}, in the factorization of the so-called end-point region of DIS processes at large $x$~\\cite{Becher:2006mr,Becher:2006nr,Chen:2006vd,Sterman:1986aj,Chay:2005rz}, where the final state invariant mass $Q(1-x) \\sim \\Lambda_{\\text{QCD}}$, and $Q$ is the hard momentum transfer. Those analyses should be extended to the chiral-odd components of the jet correlator, and also applied to SIDIS and $e^+e^-$ annihilation into one or two hadrons.\n\n\n\n\\begin{comment}\n\\tocless\n\\subsubsection{Flavor decomposition and chiral limit of the correlation mass}\n\nFormally it is possible to give a decomposition of the correlation mass in the hadronic flavor, which can have applications also at the phenomenological level:\n\\begin{equation}\n\\label{e:flav_mqcorr}\nm_q^{\\text{corr}} = \\sum_h m_{q,\\, h}^{\\text{corr}}\\ \\ , \\ \\ \\ \\ \\ \\ \\ \\ \\\nm_{q,\\, h}^{\\text{corr}} \\equiv \\sum_{S} \\int dz M_h \\widetilde{E}^{h}(z) \\ ,\n\\end{equation}\nwhere each contribution to $m_q^{\\text{corr}}$ is the normalization of the associated $\\widetilde E$ function multiplied by the hadron mass and summed over the hadronic polarization. Each $m_{q,\\, h}^{\\text{corr}}$ quantifies the contribution to the interaction-dependent part of the quark mass associated to the hadronization into a specific hadron $h$. \n\nIt is then instructive to consider the chiral limit of each flavor contribution, and therefore of $M_j$ and $m_q^{\\text{corr}}$. \nFor hadrons which are massive in the chiral limit, the associated jet mass and the correlation mass are, in principle, non-vanishing. \nFor the pions in the chiral limit, instead,  $m_\\pi \\to 0$ due to the Goldstone theorem. But even in a theory with only pions, we cannot a priori exclude that the LHS of the mass sum rule~\\eqref{e:sumrule_E} is non-zero.\nFor example: the presence of $M_h$ in Eq.~\\eqref{e:1hDelta_TMDcorr_param} in the coefficients of the Dirac expansion is artificial and could be modified in the chiral limit. \nAccordingly, also $M_j$ and $m_q^{\\text{corr}}$ could be non-zero.\n\\AAcom{Questa discussione (e anche le seguenti) non l'ho molto capita. Mi sa che e' meglio discuterne un po' a voce, cosi' mi spieghi.} \\AScom{Ne parliamo.}\n\nBecause of its non-vanishing value in the chiral limit, $m_q^{\\text{corr}}$ could be an order parameter for the dynamical breaking of the chiral symmetry. \n\nIn the event in which the LHS of Eq.~\\eqref{e:sumrule_E} vanishes in the chiral limit and in the pion sector, \nalso $M_j$ has to vanish in the same limit. A sufficient condition for that is $m_q^{\\text{corr}} \\sim (m_{q0})^c$, where $c$ is a positive number. Namely, also the correlation mass would be proportional to the current quark mass. \nThis would imply that, in general, the contribution to the jet mass associated to a light quark fragmenting into a pion is small. \nMoreover, the correlation mass could not be considered, in general, an order parameter for the dynamical breaking of the chiral symmetry.\n \n\nIf the LHS of Eq.~\\eqref{e:sumrule_E} vanishes in the chiral limit, the contribution $m_{q,\\, \\pi}^{\\text{corr}}$ could be small when $q$ is a light quark, but sizeable in all the other cases. \nIn the same scenario, the sum rules $\\int dz E = 0$ given in Ref.~\\cite{Jaffe:1993xb,Jaffe:1996zw} and $\\int dz \\widetilde{E} = 0$ given in Ref.~\\cite{Bacchetta:2006tn}, which were presented without any connection to the inclusive jet correlator, are justified for the fragmentation of a light quark into a pion in the chiral limit.\\\\\n\n\n\nOverall, the total correlation mass can vanish in two circumstances, where the neglect of quark-gluon-quark correlations is achieved in different ways. In the first case, one can invoke the ``Wandzura-Wilczek (WW) approximation''~\\cite{Bastami:2018xqd}, that is assume that the ``tilde'' fragmentation functions are negligible compared to their twist-2 counterparts, \nand set the former to zero\\footnote{The so-called ``Wandzura-Wilczek'' approximation consists in utilizing a simplified form of the Wandzura-Wilczek-type relations, introduced and discussed in Ref.~\\cite{Wandzura:1977qf,Bacchetta:2006tn}, that relate twist-2 and twist-3 functions. While in some processes this leads to phenomenologically successful comparisons to experimental data, the assumption is not a priori justified in all circumstances~\\cite{Bastami:2018xqd,Accardi:2017pmi}. In particular, one needs to make sure that the dominant quark-quark terms do not cancel in the observable of interest. For example, in our case, a WW approximation applied to Eq.~\\eqref{e:sumrule_Dtp} would amount to predicting no transverse momentum in the fragmentation process, $\\langle P_{pT}^2 \/ z^2 \\rangle = 0$, which is clearly not the case.}.\nThus, $M_j^{WW} = m_{q0}$ and $m_q^{corr\\, WW} = 0$, as can be easily seen by setting $\\widetilde E = 0$ in Eq.~\\eqref{e:eom_E} and using the sum rules~\\eqref{e:sumrule_D1} and~\\eqref{e:sumrule_E}. Applying the same WW approximation to the sum rule~\\eqref{e:sumrule_Et} consistently provides the identity $0=0$.\nAnother case in which the dynamical mass $m_q^{\\text{corr}}$ vanishes is the one in which the non-interacting vacuum $|0 \\rangle$ of the theory is used in place of the interacting one ${|\\Omega\\rangle}$~\\cite{Peskin:1995ev}, so that one cannot fully contract the $\\psi A_T^\\alpha \\bar\\psi$ operator, effectively causing $\\widetilde E = 0$ as in the WW approximation \n\\AScom{Alberto, controlla che questa cosa del vuoto non-interagente sia ok}.  \nThese observations suggest that the interaction-dependent correlation mass is intrinsically connected to the properties of the QCD vacuum. \n\\end{comment}\n\n\n\\begin{comment}\n\\tocless\\subsubsection{Chiral limit and flavor decomposition of the correlation mass}\n\nIt is instructive to study the chiral limit of the $M_j$ and $m_q^{\\text{corr}}$. \nWithin this limit and in a theory with only pions, the LHS of the mass sum rule~\\eqref{e:sumrule_E} vanishes, since in the chiral limit $m_\\pi \\to 0$ due to the Goldstone nature of the pion. Moreove, we expect physical quantities to be smooth functions of $m_\\pi$ in the chiral limit, which prevents $E \\sim m_\\pi^{-1}$. \nAccordingly, also $M_j$ has to vanish in the chiral limit of such a theory. A sufficient condition for that is $m_q^{\\text{corr}} \\sim (m_{q0})^c$, where $c$ is a positive number. Namely, also the correlation mass would be proportional to the current quark mass. \nThis implies that, in general, the contribution to the jet mass associated to a light quark fragmenting into a pion is small. \nMoreover, the vanishing of $M_j$ in the pion sector in the chiral limit prevents us from concluding that $M_j$ is, in general, an order parameter for the dynamical breaking of the chiral symmetry.\nNonetheless, for hadrons which are massive in the chiral limit, the jet mass and the correlation mass are, in principle, non-vanishing. \nThis suggest a decomposition of the correlation mass in the hadronic flavor:\n\\begin{equation}\n\\label{e:flav_mqcorr}\nm_q^{\\text{corr}} = \\sum_h m_{q,\\, h}^{\\text{corr}}\\ \\ , \\ \\ \\ \\ \\ \\ \\ \\ \\\nm_{q,\\, h}^{\\text{corr}} \\equiv \\sum_{S} \\int dz M_h \\widetilde{E}^{h}(z) \\ ,\n\\end{equation}\nwhere each contribution to $m_q^{\\text{corr}}$ is the normalization of the associated $\\widetilde E$ function multiplied by the hadron mass and summed over the polarization. Each $m_{q,\\, h}^{\\text{corr}}$ quantifies the contribution to the interaction-dependent part of the quark mass associated to the hadronization into a specific hadron $h$. As we have argued, the contribution $m_{q,\\, \\pi}^{\\text{corr}}$ is small when $q$ is a light quark, but can be sizeable in all the other cases. \n\nWe now recognize that the sum rules $\\int dz E = 0$ given in Ref.~\\cite{Jaffe:1993xb,Jaffe:1996zw} and $\\int dz \\widetilde{E} = 0$ given in Ref.~\\cite{Bacchetta:2006tn}, which were presented without any connection to the inclusive jet correlator, are justified only for the fragmentation of a light quark into a pion and also for the fragmentation of a heavy quark into a pion in the chiral limit.\\\\\n\n\n\nOverall, the total correlation mass can vanish in two circumstances, where the neglect of quark-gluon-quark correlations is achieved in different ways. In the first case, one can invoke the ``Wandzura-Wilczek (WW) approximation''~\\cite{Bastami:2018xqd}, that is assume that the ``tilde'' fragmentation functions are negligible compared to their twist-2 counterparts, \nand set the former to zero\\footnote{The so-called ``Wandzura-Wilczek'' approximation consists in utilizing for one's purposes a simplified form of the Wandzura-Wilczek-type relations, introduced and discussed Ref.~\\cite{Wandzura:1977qf,Bacchetta:2006tn}, that relate twist-2 and twist-3 functions. While in some processes this leads to phenomenologically successful comparisons to experimental data, the assumption is not a priori justified in all circumstances~\\cite{Bastami:2018xqd,Accardi:2017pmi}. In particular, one needs to make sure that the dominant quark-quark terms do not cancel in the observable of interest. For example, in our case, a WW approximation applied to Eq.~\\eqref{e:sumrule_Dtp} would amount to predicting no transverse momentum in the fragmentation process, $\\langle \\vect{P}_{h\\perp}^2 \/ z \\rangle = 0$, which is clearly not the case. }.\nThus, $M_j^{WW} = m_{q0}$ and $m_q^{corr\\, WW} = 0$, as can be easily seen by setting $\\widetilde E = 0$ in Eq.~\\eqref{e:eom_E} and using the sum rules~\\eqref{e:sumrule_D1} and~\\eqref{e:sumrule_E}. Applying the same WW approximation to the sum rule~\\eqref{e:sumrule_Et} consistently provides the identity $0=0$.\nAnother case in which the dynamical mass $m_q^{\\text{corr}}$ vanishes is the one in which the non-interacting vacuum $|0 \\rangle$ of the theory is used in place of the interacting one ${|\\Omega\\rangle}$~\\cite{Peskin:1995ev}, so that one cannot fully contract the $\\psi A \\bar\\psi$ operator, effectively causing $\\widetilde E = 0$ as in the WW approximation.\nThese observations suggest that the interaction-dependent correlation mass is intrinsically connected to the properties of the QCD vacuum, whose nature can be experimentally probed, at least in principle, through the sum rule \\eqref{e:sumrule_Et}.\n\\end{comment}\n\n\\section{Summary and outlook}\n\\label{s:conclusions}\n\n\nIn this paper we have studied the properties of the fully inclusive jet correlator~\\eqref{e:invariant_quark_correlator} introduced and in, {\\em e.g.}, Ref.~\\cite{Sterman:1986aj,Chen:2006vd,Collins:2007ph,Accardi:2008ne,Accardi:2017pmi,Accardi:2019luo}. \nIn particular, in Section~\\ref{sss:link_structure} we have have presented a gauge-invariant definition for this correlator, and discussed a specific class of Wilson lines (staple-like) that allows one to re-write this as the gauge-invariant quark propagator~\\eqref{e:invariant_quark_correlator_W}.\nMoreover, in Section~\\ref{sss:dirac_structure} we have decomposed the fully inclusive jet correlator in Dirac structures, and organized the various terms according to their suppression in powers of $\\Lambda\/k^-$, where $\\Lambda$ is a generic hadronic scale and $k^-$ the dominant light-cone component of the quark momentum. \n\nAs a byproduct of the Dirac decomposition of the jet correlator, we have provided a gauge invariant definition for the inclusive jet mass $M_j$, an object which encodes the physics of the hadronizing color-averaged dressed quark. \nThis mass can be decomposed in terms of the current quark mass and a dynamical component generated by nonperturbative quark-gluon-quark correlations (see Eq.~\\eqref{e:Mj_decomp}). \nNew non-perturbative effects induced by this mass and its dynamical component can emerge at the twist-3 level, for example in inclusive deep-inelastic scattering at the level of the $g_2$ structure function~\\cite{Accardi:2017pmi,Accardi:2018gmh}, and potentially in semi-inclusive DIS, in semi-inclusive annihilation into one or two hadrons, and in hadronic collisions (see Section~\\ref{sss:pheno}).\n\nIn Section~\\ref{ss:spectr_dec}, we have developed a spectral representation for the gauge-invariant quark propagator, and we have connected the jet's mass and virtuality to the chiral-odd and even spectral functions, respectively. In particular, in the light-cone gauge the jet mass reduces to the first moment of the chiral odd spectral function, which provides a link to non-perturbative treatments of the quark propagator and in particular to the properties of the associated mass function~\\cite{Siringo:2016jrc,Solis:2019fzm,Roberts:2007jh,Roberts:2015lja}, see Section~\\ref{ss:TMDjet_recap}. In analogy with the role played by the dressed quark mass and the mass function, the dynamical component of the jet mass can be interpreted as an order parameter for the dynamical breaking of the chiral symmetry (see Section~\\ref{ss:TMDjet_recap} and Section~\\ref{sss:DCSB}). \n\nIn Section~\\ref{s:1h_rules}, we have presented a connection at the operator level between the single-hadron fragmentation correlator~\\eqref{e:1hDelta_corr} and the fully inclusive jet correlator~\\eqref{e:invariant_quark_correlator}. This connection, encoded in the master sum rule~\\eqref{e:master_sum_rule}, provides an explicit link between the propagation of the quark and the fully inclusive limit of its hadronization. The chosen class of Wilson lines allows one to connect these operators to matrix elements accessible in high-energy scattering experiments.\nIn fact, from the master sum rule~\\eqref{e:master_sum_rule} we have derived momentum sum rules for the fragmentation functions of quarks into unpolarized hadrons up to twist 3, confirming sum rules already known in the literature and proposing new ones (see Section~\\ref{ss:sumrules_summary}). \nAmong the others, the novel sum rules for the $\\widetilde E$ and the $\\widetilde{D}^\\perp$ FFs have a dynamical interpretation: the RHS of this sum rules corresponds, respectively, to the mass and the average squared transverse momentum generated during the fully inclusive hadronization of a nearly massless quark.\n\nMoreover, we have connected the sum rules for the $D_1$ and the $E$ FFs to the integral of the quark's chiral-even and chiral-odd spectral functions, whose integrals become experimentally measurable quantities (see Eq.~\\eqref{e:sumrule_D1} and Eq.~\\eqref{e:sumrule_E}, respectively). \nAs a result, the sum rule for the unpolarized $D_1$ FF acquires a new deep interpretation, which goes beyond conservation of the collinear quark momentum: the RHS of the momentum sum rule for $D_1$ is precisely the normalization of the chiral-even $\\rho_3$ spectral function, whose value only depends on the equal-time (anti)commutation relations for the fields involved~\\cite{Weinberg:1995mt,Solis:2019fzm}. \nThe mass sum rules for the $E$ and $\\widetilde E$ FFs, instead, provide us with \na way to constrain the chiral-odd $\\rho_1$ spectral function, or, equivalently, to measure the color-screened dressed quark mass $M_j$ and its dynamical component $m^{\\rm corr}$, respectively.\nWe believe that the possibility to experimentally access quantities connected to the dynamical breaking of the chiral symmetry in QCD is one of the most important outcomes of this paper.\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
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+{"text":"\\section{Introduction}\n\\label{sec:intro}\nThe World Health Organization (WHO) declared the SARS-CoV-2 (Covid-19) outbreak in Wuhan to be a pandemic on March 11, 2020.\nSince then, Covid-19 has become a serious global health threat due to its rapid spread, transmission through asymptomatic infected individuals and complex epidemiological dynamics.\nAs of May 2021, already more than 3 million lives have been lost due to the virus. The spread of SARS-CoV-2 has thus far been extremely difficult to contain. \\\\\nBy the end of 2020, the successful development of effective vaccines and the onset of their widespread distribution in most of the world's countries, was hailed as the decisive mean to contain the pandemic.\nHowever, important questions linger on whether the vaccination effort will succeed in effectively eradicating the disease.\nThe appearance and wide spread of more contagious SARS-Cov-2 strains, the onset and scale of the vaccine deployment and high levels of vaccine hesitancy\/denial in the society, are among the key factors hindering the vaccination effort and the achievement of herd immunity. \nModeling the impact of these key factors on the  evolution of the pandemic is of critical importance for assessing the vaccination effectiveness against it.\\\\\nIn studying past epidemics, scientists have systematically applied ''random mixing'' compartmental\nmodels which assume that an infectious individual can spread the disease to any susceptible member of the population before becoming recovered or removed, \nas originally considered by Kermack and McKendrick~\\cite{Kermack_1927}. These models constrain the total population in compartments by considering stages of the infection and flows among them.\n\nIn the present study we propose a new model named SAIVR, which incorporates two important characteristics of the Covid-19 epidemic, namely the considerable transmission of the disease by asymptomatic infected individuals and the vaccination campaign with World Health Organization (WHO) approved vaccines. \nMore recent modeling approaches involve agent-based simulations ~\\cite{Kaxiras_2020}, heterogeneous social networks ~\\cite{Barthelemy_2005, Ferrari_2006, Volz_2008, Tagliazucchi_2020, Vespignani_2018, Zhang_2016}, and Bayesian inference models \\cite{Groendyke_2011}.\nAlthough a large number of research studies are currently investigating the Covid-19 epidemiological characteristics ~\\cite{Sanche_2020, Li_2020,Imai_2020, Rothe_2020,  Wynants_2020, Koh2020, Riccardo2020, khalili2020, Jie2020}, we believe that a simple but efficient model, which can capture the basics of the complex behavior of the pandemic including the vaccine roll-out, can offer useful guidance for the pandemic's near-term and longer-term evolution. \nBy using a recently developed semi-supervised machine learning approach \\cite{Flamant, Marios_2020, Paticchio_NIPS} we  systematically reproduced the pandemic dynamics during the 2021 spring in several different countries.  \nWe then used the model to assess the importance of a rapid vaccination campaign to prevent future outbreaks driven by more infectious variants.\n\\\\\n\nThe work is organized as follows. In Sec.~\\ref{sec:SAIVR} we introduce the SAIVR model and its parameters. The machine learning approach that we used to reproduce the infectious curves of 27 selected countries\/states is thoroughly described in Sec.~\\ref{sec:NN}. In Sec.~\\ref{sec:future_scenarios} we study future scenarios involving more infectious variants making quantitative arguments on how they might affect herd immunity.\nSec.~\\ref{sec:Conclusions} is devoted to concluding remarks.\n\n\\section{The SAIVR model}  \\label{sec:SAIVR}\n\nOne of the first attempts to mathematically describe the spread of an infectious disease is due to Kermack and McKendrick~\\cite{Kermack_1927}. In 1927 they introduced the so-called Susceptible-Infectious-Removed (SIR) model.\nThe SIR model describes the dynamics of a (fixed) population of $N$ individuals split into three compartments:\n\\begin{itemize}\n\\item\n$S(t)$ is the Susceptible compartment that counts the number of individuals susceptible but still not infected by the disease;\n\\item\n$I(t)$ is the Infectious compartment that counts the number of infectious individuals;\n\\item\n$R(t)$ is the Removed compartment. It represents the number of those who can no longer be infected either because they recovered and gained long-term immunity or because they passed away.\n\\end{itemize}\n\n\\begin{figure*}[h]\n\\begin{center}\n\\includegraphics[width=0.95\\textwidth]{SAIVR_sketch.pdf}\n\\caption{\nIllustration of the SAIVR model compartments and their inter-dependencies denoted by incoming and outgoing arrows and relevant flow parameters.\n}\n\\label{fig:SAIVR_schematic}\n\\end{center}\n\\end{figure*}\n\nThe model involves two positive parameters, $\\beta$ and $\\gamma$ which govern the flow from one compartment to the other:\\\\\n- $\\beta$ is the transmission rate or effective contact rate of the disease: \nan infected individual comes into contact with $\\beta$ other individuals per unit time \n(the fraction that are susceptible to contracting the disease is $S\/N$); \\\\\n- $\\gamma$ is the removal rate. $\\gamma^{-1}$  is the mean \nnumber of days who is infected spends in the Infectious compartment.\\\\\nThe SIR model obeys the following system of ordinary differential equations (ODE):\n\\begin{subequations}\n\\label{eq:SIR}\n\\begin{align}\n\\frac{dI}{dt} &= \\beta I \\frac{S}{N} - \\gamma I  \n\\label{eq:SIR_I}\n\\\\\n\\frac{dS}{dt} &= - \\beta I \\frac{S}{N} \n\\label{eq:SIR_S}\n\\\\\n\\frac{dR}{dt} &= \\gamma I \n\\label{eq:SIR_R}\n\\end{align}\n\\end{subequations}\n\n\nAlthough the SIR model has been adopted\nto study epidemic outbreaks in many previous works \\cite{Saito_SIR, Fang_SIR, Smirnova_SIR, Alanazi_SIR, Palladino_SIR, Cooper_SIR, Kaxiras_2020}, it lacks few important aspects of the current ongoing pandemic.\nFirst of all, it has been reported ~\\cite{Asymptomatic_1, Asymptomatic_2} that an important fraction of those who are carrying the virus is asymptomatic. Since they often avoid contact tracing due to the absence of symptoms, they can spread the disease while remaining undetected.\n Furthermore, in December 2020 a global vaccination campaign has started. Vaccinating is a safe way to transfer people from the Susceptible to the Removed compartment bypassing the Infectious one thus reducing the likelihood of an outbreak.\\\\\n\nThe SAIVR model extends the SIR model by incorporating the two aforementioned   additional compartments:\n\\begin{itemize}\n\\item\n$A(t)$ is the Asymptomatic\/Undetected compartment that counts the number of those individuals that despite being infected are not tested\/traced. This mainly occurs to those who recover from the infection without suffering any symptoms.\n\n\\item\n$V(t)$ is the Vaccinated compartment. It takes into account those that have received a vaccine shot but are still not fully immunized by it.\n\n\\end{itemize}\n\nThe SAIVR model ODEs read:\n\\begin{subequations}\n\\label{eq:SAIVR}\n\\begin{align}\n\\frac{dI}{dt} &= \\beta_1 I \\frac{S}{N}  + \\alpha_2 A \\frac{S}{N} + \\zeta I \\frac{V}{N} - \\gamma I\n\\label{eq:SAIVR_I}\n\\\\\n\\frac{dA}{dt} &=  \\alpha_1 A \\frac{S}{N}   + \\beta_2 I \\frac{S}{N} + \\eta A \\frac{V}{N} - \\gamma A\n\\label{eq:SAIVR_A}\n\\\\\n\\frac{dS}{dt} &=   - \\beta I \\frac{S}{N} - \\alpha A \\frac{S}{N} - \\delta \\frac{S}{N} + (1-\\lambda) \\epsilon V\n\\label{eq:SAIVR_S}\n\\\\\n\\frac{dV}{dt} &=  \\delta \\frac{S}{N}- \\eta A \\frac{V}{N} - \\zeta I \\frac{V}{N}  - \\epsilon V\n\\label{eq:SAIVR_S}\n\\\\\n\\frac{dR}{dt} &= \\gamma I + \\gamma A + \\lambda \\epsilon V\n\\label{eq:SAIVR_R}\n\\end{align}\n\\end{subequations}\n\nThe compartment inter-dependencies and flow are presented in Fig. \\ref{fig:SAIVR_schematic}. \nThe parameters of the SAIVR model  are the following:\\\\\n- $\\beta_1$ describes the rate at which individuals are exposed to symptomatic infection. An infected symptomatic individual comes into contact and infects $\\beta_1$ susceptible individuals per unit time; \\\\\n- $\\alpha_1$ is the asymptomatic infection rate. An infected asymptomatic individual comes into contact with $\\alpha_1$ susceptible individuals per unit time;  \\\\\n- $\\beta_2$ describes the rate at which susceptible individuals become asymptomatic infected after entering in contact with a symptomatic individual; \\\\\n- $\\alpha_2$ describes the rate at which who's susceptible becomes symptomatic after entering in contact with an asymptomatic individual; \\\\\n- $\\gamma$ retains the same meaning as in the SIR model, representing the mean removal rate.  $\\gamma^{-1}$ is the mean \namount of time individuals spend either in the Infectious or Asymptomatic compartments;\\\\\n- $\\zeta$ is the rate at which a vaccinated (but still not immune) individual enters in contact with a symptomatic infectious; \\\\\n- $\\eta$ describes the transmission rate at which who's asymptomatic comes into contact and infects vaccinated (but still not immune) individuals; \\\\\n- $\\delta$ is the first shot vaccination rate;\\\\\n- $\\lambda$ is the vaccine efficacy; \\\\ \n- $\\epsilon^{-1}$ is the mean \namount of time an individual spends in the Vaccinated compartment before reaching immunity and moving to the Removed compartment.\\\\\\\\\nCountries and states do not respond to the disease as static entities passively facing the pandemic. They react by actively imposing (and relaxing) restrictive measures, learning how to effectively treat the infected, adjusting social interactions and by launching vaccination campaigns. Finally, the virus itself evolves in more infectious variants ~\\cite{2021_variants}.\\\\\nCountry-specific parameters can be obtained by fitting the SAIVR model to a selected infectious wave occurred in a given country.\nSAIVR has 14 adjustable parameters or initial conditions that needs to be estimated; given the scarcity of data (only the infectious and vaccinated populations are known) optimizing them presents a challenging problem. To address this, we either fixed some of them or employed a novel fitting method based on semi-supervised neural networks, which we present in the following section.\n\n\\section{Solving the SAIVR model with Neural Networks}\\label{sec:NN}\n\n\\begin{figure*}[h]\n\\begin{center}\n\\includegraphics[width=1.0\\textwidth]{NN_sketch.pdf}\n\\caption{ Semi-supervised network architecture. During the unsupervised procedure (blue box), a time sequence $t$, a set of initial conditions $\\mathcal{Z}_0$ and parameter bundles $\\Theta$ are fed as an input to a 6 layers fully connected network (FCN).\nThe output of the network $\\mathcal{Z}_{NN}$ is multiplied by a function $f(t)$ to become a tentative parametric solution $\\hat{\\mathcal{Z}}(t)$ of the system of ODE in Eq.~\\ref{eq:SAIVR}. \nThe quality of $\\hat{\\mathcal{Z}}(t)$ is probed by the loss function $\\mathcal{L}$.\nWhen the network has learned the solutions, the inverse problem is then solved (red box).\nAn optimization algorithm selects the initial conditions and parameters in the bundle that best fit a given data-set. The loss $\\mathcal{L}_{inv}$ depends on the infectious population of a given country\/state $I_{Data}$ during the time sequence $t$.\n}\n\\label{fig:NN_sketch}\n\\end{center}\n\\end{figure*}\n\n\n\nIn order to apply the SAIVR model we need a realistic estimate of the parameters and initial conditions for the system of Eqs.~\\ref{eq:SAIVR}.\nTo obtain them we employed machine learning, a powerful method which has been extensively used for disease modeling \\cite{Amazon, Yang_SEIR, Zou_NN, Paticchio_NIPS} and dynamical system forecasting \\cite{Gallinari_NN, Chen_NN,Flamant}.\nOur approach employs a semi-supervised procedure which determines the optimal set of initial conditions and parameters of the SAIVR model, yielding solutions that best fit a given data-set.\nA sketch of this procedure is shown in Fig.~\\ref{fig:NN_sketch}.\n\n\\subsection{Unsupervised learning} \\label{sec:unsupervised}\nThe unsupervised part (blue box) consists of a data-free Neural Network (NN) that is trained to discover solutions for an ODE system of the form:\n\\begin{equation}\n    \\frac{d\\mathcal{Z}}{dt} = g(\\mathcal{Z}), \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\; \\mathcal{Z}(t=0) = \\mathcal{Z}_0\n\\end{equation}\nwhere $\\mathcal{Z} = (S(t),A(t),I(t),V(t),R(t))$ and $g(\\mathcal{Z})$ is given in Eqs.\\ref{eq:SAIVR}.\nThe NN takes as an input a time sequence $t$, a set of initial conditions $\\mathcal{Z}_0$, and modeling parameters $\\Theta$.\\\\\nAs we'll see in the following, $t$ is the set of days involved in a given epidemic wave going from $t_0$ to $t_0 + \\Delta t$, $Z_0$ are the initial compartment populations and $\\Theta$ some parameters of the SAIVR model.\nThe initial conditions and parameters are randomly sampled at each iteration $n$ over predefined intervals called bundles \\cite{Flamant, Paticchio_NIPS}, so that the network learns an entire family of solutions.\nThe inputs propagate through the network until an output vector $\\mathcal{Z}_{NN}$ of the same dimensions as the target solutions $\\mathcal{Z}$ is produced.\nThe learned solutions $\\hat{\\mathcal{Z}}$ satisfy\nthe initial conditions identically by considering parametric solutions of the form:\n\\begin{equation}\n\\hat{\\mathcal{Z}} = \\mathcal{Z}_0 + f(t) (\\mathcal{Z}_{NN} - \\mathcal{Z}_0   )\n\\end{equation}\nwhere $f(t) =1- e^{-t}$ \\cite{Marios_2020}.\nThe loss function:\n\\begin{equation}\n\\label{eq:loss_de}\n\\mathcal{L} = \\bigg \\langle \\left( \\frac{d\\mathcal{Z}}{dt} - g(\\mathcal{Z})\\right) ^2 \\bigg  \\rangle\n\\end{equation}\nsolely depends on the network predictions averaged ($\\langle .. \\rangle$) over all the iterations $n$, providing an unsupervised learning framework. \nTime derivatives are computed using the automatic-differentiation and back-propagation techniques \\cite{automatic_differentiation}.\n\n\\subsection{Fitting a dataset}\n\\label{sec:fitting_method}\nOnce the NN is trained to provide solutions for the system of Eq. \\ref{eq:SAIVR}, its weights and biases are fixed and the trained network  is used to develop a supervised pipeline for the estimation of the initial conditions and parameters, leading to solutions $\\tilde{\\mathcal{Z}}(t)$ that fit given data.\nThis procedure is illustrated in the red box in Fig.~\\ref{fig:NN_sketch}. \nA solution $\\hat{\\mathcal{Z}}$ is generated by the network starting from $\\bar{\\mathcal{Z}_0}$ and $\\bar{\\Theta}$ randomly selected in the bundles. A stochastic gradient descent optimizer then adjusts $\\bar{\\mathcal{Z}_0}$ and $\\bar{\\Theta}$ in order to minimize the loss function:\n\\begin{equation}\n\\label{eq:loss_inv}\n\\mathcal{L}_{inv} = \\bigg \\langle \\left( \\tilde{I}(t) - I_{Data}(t) \\right) ^2 \\bigg \\rangle \n\\end{equation}\nwhere $I_{Data}(t)$ is the infectious population of a given country\/state and $\\tilde{I}(t)$ is its NN fit.\n\n\\subsection{Applying the method to real data}\n\\label{sec:fitting}\nWe used this method to reproduce the most recent Covid-19 waves in 27 countries or states.\nTo test the generality of the model we selected epidemic waves that occurred in a broad range of geopolitical conditions, restrictive measures, time periods and vaccination efforts.\nThe bundles and fixed parameters used during the unsupervised training of the network are listed in Table.~\\ref{tab:parameters}.\n\nWe found that the model is weakly sensitive on the choice of most parameters and thus, we kept some of them fixed during the training. \nThe value of the vaccine efficacy $\\lambda$ is based on Refs.\\cite{Polack, Baden_2020}, where a vaccine efficacy of $94.8\\%$ and $94.1\\%$ is reported for the Pfizer-BioNTech and Moderna mRNA vaccines.\nThe $V \\rightarrow I$ and $V \\rightarrow A$ rates $\\zeta$ and $\\eta$\nare derived by considering the order-of-magnitude ratio of the infected individuals in the vaccinated and placebo cohorts of Ref.~\\cite{Polack}, with\n$\\beta_2$ and $\\alpha_2$ set to $0.001$ and $0.01$ respectively, which are in order-of-magnitude agreement with the aforementioned results of the clinical trials.\nThe $V \\rightarrow R$ rate $\\epsilon$ is the inverse time an individual takes to acquire vaccine protection after the first shot. \nWe set it to $\\epsilon^{-1} = 21$ to reflect the fact that the second shot of vaccines is usually administered about three weeks after the first one.\n\n\n\\begin{figure*}[h]\n\\begin{center}\n\\includegraphics[width=1.0\\textwidth]{vaccinated_countries_fit2.pdf}\n\\caption{ Infectious population percentage (red dots) of some selected countries in which a high percentage of their population has received a vaccine shot. The infectious population is expressed as a function of time (days). The date at which the wave began is pointed out on the horizontal axis. The neural network fits and predictions are shown by black solid and dashed lines respectively. \n}\n\\label{fig:vaccinated_countries_fit}\n\\end{center}\n\\end{figure*}\n\n\n\\begin{table*\n\\begin{center}\n\\caption{Bundles and fixed parameters}\n\\begin{tabular}{cccccccc}\n$I_0$ & $A_0$ & $V_0$ & $R_0$ & $\\beta_1$ & $\\gamma$ & $\\alpha_1$ & $\\delta$ \\\\\n\\midrule\n$[0.1~\\%, 2~\\%]$ & $[0.1~\\%, 2~\\%]$ & $[0~\\%, 60~\\%]$ & $[0~\\%, 30~\\%]$ & $[0.1, 0.25]$ & $[0.07, 0.12]$  &  $[0.1, 0.25]$ & $[0, 0.03]$ \\\\\n\\end{tabular}\n\n\n\\begin{tabular}{cccccccc}\n$\\epsilon$ & $\\lambda$ & $\\eta$ & $\\zeta$ & $\\beta_2$  & $\\alpha_2$  \\\\\n\\midrule\n1\/21 & 0.95 & 1e-2 & 5e-3 & 1e-3  &  1e-2  \\\\\n\\end{tabular}\n\\label{tab:parameters}\n\\end{center}\n\n\\end{table*}\n\n\n\\begin{figure*}[h]\n\\begin{center}\n\\includegraphics[width=1.0\\textwidth]{US_states_fit.pdf}\n\\caption{\nInfectious population percentage (red dots) of ten selected US states. The infectious population is expressed as a function of time (days). The date at which the wave began is pointed out on the horizontal axis. The neural network fits and predictions are shown by black solid and dashed lines respectively.\n }\n\\label{fig:US_states_fit}\n\\end{center}\n\\end{figure*}\n\nThe remaining parameters $\\Theta = (\\alpha_1, \\beta_1, \\delta, \\gamma)$ strongly depend on what kind of restrictive measures are taken or how fast the vaccination campaign is, i.e. they are country dependent. We therefore selected them in bundles so that the network could learn solutions corresponding to a broad range of parameters and fit multiple countries.\nThe decay rate $\\gamma$ is the inverse of the removal time which is about 1-2 weeks \\cite{Recovery_time}.\nThe main symptomatic infection rate $\\beta_1$ was sampled in an interval consistent with previous reports \\cite{Kaxiras_2020}.\nThe earlier estimates that $80\\%$ of infected population is asymptomatic has been considered\ntoo high and have since been revised down  ~\\cite{Asymptomatic_1, Asymptomatic_2}; the initial studies estimating this proportion were\nlimited by heterogeneity in case definitions, incomplete symptom assessment,\nand inadequate retrospective and prospective follow-up of symptoms. We selected the main asymptomatic infection rate $\\alpha_1$ to be varying in the same interval of $\\beta_1$.  The first shot vaccination rate $\\delta$ was selected based on known vaccination reports (see \\ref{sec:matsmethod}).\\\\\nFinally, the initial condition bundles $\\mathcal{Z}_0 = (S_0,A_0,I_0,V_0,R_0)$ are defined over broad intervals able to cover the expected ($S,A,I,V,R$) populations at any given time for all the cases considered. Although the initial infected population $I_0$ is known, we still included it in the set of quantities to be fit by the network. We found that by doing so, the network generalizes better improving the fit of a given epidemic wave.\n\nWe then performed the fitting procedure described in \\ref{sec:fitting_method} using the infectious populations of 27 countries\/states. The data (including the number of vaccine shots administered) is retrieved from the `Our World in Data' GitHub repository \\cite{OWID}.\nStrictly speaking, the Infectious population of the SAIVR model is the amount of people that are actively infected by the virus on a given day, a number that should not be confused with the daily new cases. As such, it was computed as the difference between the total number of cases and of recovered\/dead individuals.\n\nWe first applied the method to study the most recent Covid-19 wave in  some of the countries with the fastest vaccination campaigns and that managed to inoculate the first shot in at least $30\\%$ of their population.\nFig.~\\ref{fig:vaccinated_countries_fit} presents real data (red points), fits (black solid line), and some predictions (black dashed line) for the infectious populations of Israel, UK, Hungary, France, Romania and Serbia.\nWe also studied the USA, although due to the large size of the country we focused only on the largest states or those with the highest vaccination rates in the first quarter 2021, see Fig.~\\ref{fig:US_states_fit}.\nTo assess the generality of the model and the fitting procedure, we applied it to other 12 countries spread throughout the world and which had at the end of spring 2021 a high number of cases.\nThe corresponding fits are shown in Figs. S1-S2 of the \\textbf{Supplementary Material}.\nAs can be seen, the model is able to well reproduce all these epidemic curves despite missing some abrupt and rapid events that can be captured by more sophisticated multiple-wave models \\cite{Kaxiras_2020}.\nAll the parameters determined by the network can be found in the \\textbf{Supplementary Material};   their values are  within the bundles of Table.~\\ref{tab:parameters}.\nIn particular, $\\gamma$ was found in the $~ 10-12$ days range, $\\beta_1$ oscillating in  $[0.14-0.19]$ while alpha was more volatile.\n\\\\\n\n\n\n\n\\section{Insights on the future: vaccine hesitancy, herd immunity and new variants}\n\n\\begin{figure}[h]\n\\includegraphics[width=1.0\\textwidth]{hesitancy.pdf}\n\\caption{Total infected population as a function of vaccination rate,  vaccine efficacy and vaccine denial population percentage. Results are obtained by numerically solving the SAIVR model for $I_0 = 10^{-5} N_{pop}$ and $A_0 = 0.2 \\times I_0$, where $N_{pop} = 10^6$.\nThe parameters of the model used are those obtained by applying machine learning on the epidemic curves. \\\\\na) Infected population vs. vaccination rate $\\delta$ and vaccine efficacy $\\lambda$.\\\\\nb) Infected population as a function of the percentage of the population that avoids getting vaccinated and the vaccine rate $\\delta$.\n}\n\\label{fig:hesitancy}\n\\end{figure}\n\n\n\\label{sec:future_scenarios}\nIn this section we use the results of the analysis performed in the previous section to study how the vaccination campaign is affecting the pandemic and its future evolution.\nUnless otherwise specified, we set $\\beta_1 = 0.16$, $\\alpha_1 = 0.2$ and $\\gamma = 1\/12$, the average values retrieved from fitting real data. \nWe start by pointing out how the vaccine efficacy is a key factor in halting the spread of the virus and how hesitancy is challenging the vaccination campaigns.\nFinally, we discuss the concept of herd immunity and how it is affected by more infectious Covid-19 variants.\n\n\\subsection{Vaccination efficacy and hesitancy}\n\nFigure \\ref{fig:hesitancy} presents the total infected ($I + A$) population under increasing values of vaccination onset times ($T_0$), vaccination daily rates ($\\delta$), vaccine efficacy ($\\lambda$) and of vaccine hesitancy\/denial population percentage. \nIn the top panel, total infected population  is shown as a function of the vaccination rate $\\delta$ and vaccine efficacy $\\lambda$. As can be seen, even vaccines with a relatively low efficacy can rapidly reduce the infected population.\nIn Fig.~\\ref{fig:hesitancy} b) we show how the number of those infected evolves as a function of $\\delta$ and the percentage of population that avoids getting vaccinated.\nThese findings suggest that vaccine hesitancy, which accounts for a significant proportion of the population might seriously threaten the reach of herd immunity, especially if the situation is worsened by the appearance of more infectious Covid-19 strains.\n\n\\subsection{Herd immunity and new Covid-19 variants}\n\n\n\\begin{figure*}[h]\n\\includegraphics[width=1.0\\textwidth]{future_scenaria.pdf}\n\\caption{\n{\\bf Top row}: Time evolution of epidemics following the introduction of infected individuals in a population that has been already vaccinated at 50$\\%$ (left panel), 60$\\%$ (middle panel), and 70$\\%$ (right panel), with permanent immunity and no further vaccine roll-out, for four different numbers of newly infected individuals ($I_0 = 1 - 0.001 \\%$ of total population, the color code is presented in the legends). Results are obtained from numerically solving the SAIVR model for $\\beta_1 = 0.16$, $\\alpha_1=0.20$, which represent the average of the countries' fitted values (see text for details and for the values of the other parameters). \n{\\bf Middle row}: Same as in top row but with $\\beta_1 = 0.25$, $\\alpha_1=0.25$, which represent a more contagious Covid-19 variant. As is shown, vaccinated coverage of $50\\%$ and $60\\%$ cannot prevent the resurgence of outbreaks.\n{\\bf Bottom row}: Same as in middle row, but with ongoing vaccination roll-out with rate $\\delta = 0.001$, per day, as it is shown, a continuing vaccine roll-out lowers the intensity of the resurgent waves and prevents the resurgence of subsequent outbreaks.\n}\n\\label{fig:future_scenarios}\n\\end{figure*}\n\nThe achievement of herd immunity has been hailed as the ultimate goal of a successful vaccination campaign.\n`Herd immunity', also known as `population immunity', is the indirect protection from an infectious disease that happens when a sufficient portion of the population is immune either through vaccination or immunity developed through previous infection.\nOnce the herd immunity threshold is met, the spread of the infectious disease is kept under control, current outbreaks will extinguish and endemic transmission of the pathogen will be interrupted. \nEarlier estimates of the threshold found values of about $60-70 \\%$ of the population \\cite{Howard_herd,Chowdhury2020,Aguas2020}. \nIn reality, highly transmissible strains tend to increase the threshold value, possibly keeping this goal out of reach.\nFurthermore, persistent hesitancy about vaccines makes vaccinating more than the $60 - 65\\%$ of the population unlikely even in countries which are at the global forefront of the vaccination effort.\n\nWe quantitatively investigate the likelihood of incurring resurgent Covid-19 epidemics after having immunized $50\\%$, $60\\%$, and $70\\%$ of the population, under different new infection introductions, Covid-19 variants and ongoing vaccine deployment pace.\nHerd immunity protection is affected by the initial value of the removed population ($R_0$ at $t=0$), which comprises both recovered as well as fully vaccinated individuals, assuming permanent immunity for both cases. In each scenario, we study  the epidemic evolution after the introduction of a cluster of newly infected individuals in the population. $I_0$ represents the newly infected load at $t=0$ ($I_0 = 1\\%, 0.1\\%, 0.01\\%, 0.001\\%$ of the total population).\n\nIn the first part of the study we considered the less infectious variants spreading during the 2021 spring by using the parameters retrieved in Sec.~\\ref{sec:fitting}.\nThe second scenario involves a more infectious Covid-19 strain such as the Delta variant, which has been reported to be able to spread the virus more efficiently  \\cite{Delta_variant}.\nFinally, we explore cases that involve or not further (continuing) vaccine roll-outs. \n\nFigure ~\\ref{fig:future_scenarios} presents the results obtained by numerically solving the SAIVR model for the aforementioned cases. The top row presents the time evolution of an outbreak in a population where the 50$\\%$ (left panel), 60$\\%$ (middle panel), and 70$\\%$ (right panel) of the individuals have been immunized, for different numbers of initially infected individuals $I_0$. Results are obtained by solving the SAIVR model for $\\beta_1 = 0.16$, $\\alpha_1=0.20$, and $\\gamma = 1\/12$; the average values obtained for the countries considered in Sec.~\\ref{sec:fitting} and listed in \\textbf{Supplementary Material}.\nAs it can be seen, when the immune portion of the population is only $50\\%$, the outbreaks are contained but not eradicated as the virus spreads in low intensity waves \nmaking the disease endemic. Given the contagiousness of the less infectious variants, an immunity threshold larger than $60\\%$ is enough to eradicate the disease.\\\\\nThe middle row of Fig.~\\ref{fig:future_scenarios} presents the evolution of outbreaks driven by a more contagious variant; here $\\beta_1 = 0.25$, and $\\alpha_1=0.25$. As it is shown, if the immunized portion of the population is only $50\\%$ or $60\\%$, the resurgence of outbreaks cannot be prevented ($60\\%$ immunity protection makes the disease endemic). Only when the $70\\%$ of the population is immunized the disease is eradicated. \\\\\nIn both the top and the middle rows, the vaccine deployment is not taking place during the outbreaks. The bottom row instead considers the highly infectious variant disease evolution but with constant vaccine roll-out (with rate $\\delta = 0.001$).\n As it can be seen, since even after getting only the first vaccine shot individuals are partially protected, continuing the vaccine administration rapidly lowers the intensity of the resurgent waves and helps preventing subsequent outbreaks. \n\nAlthough recent reports on highly infectious variants claim that the efficacy of most vaccines is still about $90 \\%$ in preventing serious illnesses ~\\cite{Delta_vaccine}, it is still not clear their performance on halting asymptomatic transmission.\nIn this study, we assumed that the vaccine efficacy on protecting from more infectious variants is the same as for the less infectious ones.\nDespite this optimistic assumption, the herd immunity threshold is moved to higher values by simply increasing the infection rates.\n\n\\section{Discussion} \\label{sec:Conclusions}\nCompartmental models are efficient tools to deal with the time evolution of disease outbreaks. They provide us with useful intuition on the impact of non-pharmaceutical intervention in decreasing the number of infectious incidence rates.\\\\\nIn this work, we have augmented the classic SIR model with the ability to accommodate asymptomatic transmission and vaccinated individuals.\nThe SAIVR model is a straightforward deterministic model, which does not take into consideration age, gender or geographic clustering.\nDespite this, its simplicity and the insights it offers on how key epidemiological variables affect individuals are among its main strengths. \nIts power also lies in the fact that, as factors such new variants are added to the model, it is easy to adjust its parameters and provide with best fit curves between the data and the model predictions.\\\\\nSince the inclusion of the Asymptomatic and Vaccinated compartments enlarged the number of parameters and initial conditions of the model, we employed a novel semi-supervised framework to estimate most of them.\nAn unsupervised neural network solves the model's differential equations over a range of parameters and initial conditions. A supervised approach then incorporates data and determines the optimal initial conditions and modeling parameters that best fit the 27 epidemic curves considered.\nAs expected due to the heterogeneity of the countries sample,\nthe resulting parameters fit are dissimilar although they follow similar trends.\\\\\nWe used these results to shed light on the impact of the vaccination campaign on the future of the pandemic.\nWe pointed out how vaccine hesitancy is one of the most important hurdles of the campaign and further efforts should be done to support people and give them correct information about vaccines. \nBecause of this, vaccinating the critical number of people that have to be immune in order to prevent future outbreaks (i.e. herd immunity), is likely to be out of reach. Widely circulating coronavirus variants are also a threat as they move the herd immunity threshold to higher values.\nThis points out the importance of rapidly reducing the infection rate by any means, such as\nby imposing restrictive measures in case highly infective new variants appears before the herd immunity threshold is reached.\nThese results manifest the need for continuing the vaccination effort and the drive for achieving high vaccination coverage in order to contain outbreaks generated by new and possibly more infectious variants.\\\\\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n{\\bf Data availability}\\\\\nThe code used to perform the fitting is available on GitHub \\cite{Github_Mattia}. All study data are either included in the article and\nsupporting information or available in Ref.~\\cite{OWID}. \\\\\n\n{\\bf Author Contribution}\\\\\nE.K. conceived the proposed model and supervised the study.  M.A, G.N. and M.M. designed the code. M.A. and G.N. performed numerical experiments, collected data and analyzed the results. M.A. wrote the initial\ndraft of the manuscript. All authors critically revised, improved, and reviewed the manuscript in various\nways, and gave final approval for publication.\\\\\n\n{\\bf Competing interests}\\\\\nThe authors declare no competing interest.\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nLet $U$ be an open set in \\textbf{C}$^n$ which contains 0, $f$ be\na holomorphic function defined on $U$, $f_p$ is the germ of $f$ at\npoint $p\\in U$.\\\\\n\nFor any two holomorphic functions $g,h$ defined on $U$,if\n$g_0,h_0$ are relatively prime with each other, then with the help\nof resultants, we know that $g,h$ are relatively prime with each\nother nearby. Precisely to say, that means their exists an open\nneighborhood $V\\subset U$ of 0, such that for any point $q\\in V$,\n$g_q$ and $h_q$ are relatively prime with each other. In this\nsense, we can say that \\textbf{Being co-prime is a stable\nproperty.}\\\\\n\nCan we say \\textbf{Irreducibility is a stable property}?In the\ncase of dimension 2, the answer is positive, and the proof is\neasy. But in the case of dimension 3, I will present a polynomial\nas counter-example.\n\n\n\\section{Proof for the Case of Dimension 2}\n\\textbf{Statement}: For any holomorphic function $f=f(z_1,z_2)$ on\n$U\\subset$ \\textbf{C}$^2$($0\\in U$), and the germ of f at origin\nis irreducible, then their exists an open neighborhood $V\\subset\nU$ of 0, such that for any point $q\\in V$, $f_q$ is\nirreducible.(\\textbf{Remark}:If $f(p)\\neq 0$, the $f$ is irreducible at $p$. So we only need to care about zero points of $f$.)\\\\\\\\\n\\textbf{Proof:} Without the loss of generality, we can assume\n$f(0,z_2)$ is not identically 0 near the origin, and $f(0,0)=0$.\\\\\\\\\nlet $w=z_2^d+e_1(z_1)z_2^{d-1}+\\cdots+e_{d-1}(z_1)+e_d(z_1)$ be a\nWeierstrass polynomial of $f$ near 0.\\\\\\\\\nBecause $w$ is irreducible at 0, so $w$ and $\\frac{\\partial\nw}{\\partial z_2}$ are relatively prime near 0. Then the resultant\nof $w$ and $\\frac{\\partial w}{\\partial z_2}$ is not zero. Then the\ncommon zero loci of $w$ and $\\frac{\\partial w}{\\partial z_2}$ are\ndiscrete near 0.\\\\\\\\\nFrom above, we know that their exists an open set $V(0\\in V\\subset\nU)$, such that in ${\\bf U}$, (0,0) is the only zero point of $w$ which\nis POSSIBLE to be singular.(since for other points in $q\\in U$,\n$\\frac{\\partial w}{\\partial z_2}(p)\\neq 0$ ).We can conclude that\nat any zero point  $p(p\\neq 0)$ of $w$ in $V$,$w$ is a local\ncomplex parameter near $p$. Since $w$ is a local complex parameter\nnear $p$, then the germ of $w$ at $p$ is irreducible.\\\\\\\\\nFinally, because $w$ is a Weierstrass polynomial of $f$ at 0, then\nwe know that in $V$, the irreducibility of $f$ is as the same as t\nthat of $w$.\\hfill$\\Box$\\medskip\n\n\n\n\n\n\n\n\\section{A Counter Example in Dimension 3} \\label{se:C0}\nIn the case of dimension 3, the statement should be:\\\\\\\\\n\\textbf{Statement}: For any holomorphic function\n$f=f(z_1,z_2,z_3)$ on $U\\subset$ \\textbf{C}$^3$($0\\in U$), and the\ngerm of f at origin is irreducible, then their exists an open\nneighborhood $V\\subset U$ of 0, such that for any point $q\\in V$,\n$f_q$ is irreducible.\\\\\\\\\nBut unfortunately, this statement is not true.In this section, I\nwill present, a polynomial of three variables,\nas a counter example.\\\\\\\\\nThis polynomial is $f=z_3^2-z_1z_2^2$.\\\\\\\\\n\n\\subsection{Irreducibility of $f$ at origin}\nObviously, near 0, $f$ is a Weierstrass polynomial of itself(we\nchoose $z_3$ as the polynomial variable).Now, we will show the\nirreducibility at origin by means of contradiction. \\\\\\\\\nIf $f$ is not irreducible at origin, then its Weierstrass\npolynomial is decomposable at origin as a Weierstrass\nPolynomial.Assume that,near origin,\n$f=(z_3-g_(z_1,z_2))(z_3-h(z_1,z_2))$, here $g,h$ are holomorphic\nfunctions of variable $z_1,z_2$ near 0, and g(0,0)=h(0,0)=0.\\\\\\\\\nFrom the factorization $f=(z_3-g_(z_1,z_2))(z_3-h(z_1,z_2))$, we\nknow that $g+h=0,gh=-z_1z_2^2$, which implies $g^2=z_1z_2^2$ near\n0.\\\\\\\\\nBut if $g^2=z_1z_2^2$ near 0. Then for some $\\varepsilon\\in$\n\\textbf{C} whose norm is small enough,\n$g^2(z_1,\\varepsilon)=\\varepsilon ^2 z_1$ near 0. But just from\nelementary knowledge of functions of one complex variable, we know\nthis is not possible.\\\\\\\\ From argument above, we know $f$ is\nirreducible at origin.\n\n\\subsection{Further Argument}\nAt point $p=(z,0,0)(z\\neq 0)$, we know that $f(p)=0$, and easily\nwe can factorize $f$ as $f=(z_3+z_2r)(z_3-z_2r)$ near $p$, here\n$r$ is a one-variable holomorphic function such that $r^2=z_1$\nnear $(z,0,0)$(Because z is not 0, so we can take square-root of\n$z_1$ near by.).\\\\\\\\\nFrom the argument in \\textbf{3.2}, we know that, in any\nneighborhood $U$ of origin, there EXISTS some point $p$ such that\n$f$ is not irreducible at $p$. This fact can destroy our statement\nat the beginning of this section.\n\n\n\n\n\\end{document}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction and statement of results}\n\nFor a simple loopless graph $G = (V(G),E(G))$ and a graph $H = (V(H),E(H))$ (possibly with loops, but without multi-edges), an {\\em $H$-coloring} of $G$ is an adjacency-preserving map $f:V(G) \\to V(H)$ (that is, a map satisfying $f(x) \\sim_H f(y)$ whenever $x\\sim_G y$). Denote by $\\hom(G,H)$ the number of $H$-colorings of $G$.\n\nThe notion of $H$-coloring has been the focus of extensive research in recent years. Lov\\'asz's monograph \\cite{Lovasz} explores natural connections to graph limits, quasi-randomness and property testing. Many important graph notions can be encoded via homomorphisms --- for example, {\\em proper $q$-coloring} using $H=K_q$ (the complete graph on $q$ vertices), and {\\em independent} (or {\\em stable}) {\\em sets} using $H=H_{\\text{ind}}$ (an edge with one looped endvertex). The language of $H$-coloring is also ideally suited for the mathematical study of hard-constraint spin models from statistical physics (see e.g. \\cite{BrightwellWinkler}). Particularly relevant to the present paper is the Widom-Rowlinson model of the occupation of space by $k$ mutually repulsive particles, which is encoded as an $H$-coloring by using the graph $H = H_{\\rm WR}(k)$ which has loops on every vertex of $K_{1,k}$ (the star on $k+1$ vertices). Note that the original Widom-Rowlinson model \\cite{WidomRowlinson} has $k=2$.\n\nMany authors have addressed the following extremal enumerative question for $H$-coloring: given a family ${\\mathcal G}$ of graphs, and a graph $H$, which $G \\in {\\mathcal G}$ maximizes or minimizes ${\\rm hom}(G,H)$? This question can be traced back to Birkhoff's attacks on the 4-color theorem, but recent attention on it owes more to Wilf and (independently) Linial's mid-1980's query as to which $n$-vertex, $m$-edge graph admits the most proper $q$-colorings (i.e. has the most $K_q$-colorings). For a survey of the wide variety of results and conjectures on the extremal enumerative $H$-coloring question, see \\cite{Cutler}.\n\nA focus of the present paper is the extremal enumerative $H$-coloring question for the family $\\calT(n)$, the set of all trees on $n$ vertices. This family has two natural candidates for extremality, namely the path $P_n$ and the star $K_{1,n-1}$, and indeed in \\cite{ProdingerTichy} Prodinger and Tichy showed that these two are\nextremal for the count of independent sets in trees: for all $T \\in \\calT(n)$,\n\\begin{equation} \\label{inq-PT}\n\\hom(P_n,H_{\\text{ind}}) \\leq \\hom(T,H_{\\text{ind}}) \\leq \\hom(K_{1,n-1},H_{\\text{ind}}).\n\\end{equation}\nThe Hoffman-London matrix inequality (see e.g. \\cite{Hoffman,London,Sidorenko2}) is equivalent to the statement that $\\hom(P_n,H) \\leq \\hom(K_{1,n-1},H)$ for \\emph{all} $H$ and $n$; a significant generalization of this due to Sidorenko \\cite{Sidorenko} (see also \\cite{CsikvariLin} for a short proof) shows that the right-hand inequality of (\\ref{inq-PT}) extends to arbitrary $H$.\n\\begin{theorem}[Sidorenko] \\label{thm-siderenko}\nFix $H$ and $n \\geq 1$.  Then for any $T \\in \\calT(n)$,\n\\[\n\\hom(T,H) \\leq \\hom(K_{1,n-1},H).\n\\]\n\\end{theorem}\nIn other words, the star admits not just the most independent sets among $n$-vertex trees, but also the most $H$-colorings for arbitrary $H$. Two points are worth noting here. First, since deleting edges in a graph cannot decrease the number of $H$-colorings, Theorem \\ref{thm-siderenko} shows that among all connected graphs on $n$ vertices, $K_{1,n-1}$ admits the most $H$-colorings. Second, if we extend $\\calT(n)$ instead to the family of graphs on $n$ vertices with minimum degree at least $1$ and consider even $n$, then as shown by the first author \\cite{Engbers} the number of $H$-colorings is maximized either by the star or by the graph consisting of a union of disjoint edges.\n\nThe left-hand side of (\\ref{inq-PT}) turns out {\\em not} to generalize to arbitrary $H$: Csikv\\'{a}ri and Lin \\cite{CsikvariLin}, following earlier work of Leontovich \\cite{Leontovich}, exhibit a (large) tree $H$ and a tree $E_7$ on seven vertices such that $\\hom(E_7,H) < \\hom(P_7,H)$, and raise the natural question of characterizing those $H$ for which $\\hom(P_n,H) \\leq \\hom(T,H)$ holds for all $n$ and all $T \\in \\calT(n)$.\n\nOur first result gives a partial answer to this question. Before stating it, we need to establish a convention concerning degrees of vertices in graphs with loops.\n\n\\medskip\n\n\\noindent \\textbf{Convention:} For all graphs in this paper, the degree of a vertex $v$ is the number of neighbors\nof\n$v$, i.e., $d(v) = |\\{w : v \\sim w\\}|$. In particular, a loop on a vertex\nadds one to the degree.  We let $\\Delta$ denote the maximum degree of $H$.\n\nWe also let $G^{\\circ}$ denote the graph obtained from $G$ by adding loops to every vertex in $G$.\n\n\\begin{theorem} \\label{thm-minfortrees}\nLet $n\\geq 1$ and let $H$ be a regular graph.  For an integer $\\ell \\geq 1$, let $H^{\\circ}(\\ell)$ be the join of $H$ and $K_{\\ell}^{\\circ}$. \nThen for any $T \\in \\calT(n)$,\n\\[\n\\hom(P_n,H^{\\circ}(\\ell)) \\leq \\hom(T,H^{\\circ}(\\ell)).\n\\]\nEquality occurs if and only if $T = P_n$ or $H^{\\circ}(\\ell) = K_{q}^{\\circ}$ for some $q \\geq \\ell$. \n\\end{theorem}\nNotice that the result also holds for $H$ where each component is of the form $H^{\\circ}(\\ell)$. Theorem \\ref{thm-minfortrees} generalizes the left-hand side of (\\ref{inq-PT}), as $H_{\\text{ind}}$ is the join of $K_1$ and $K_{1}^{\\circ}$, \nand our proof is a generalization of the inductive approach used in \\cite{ProdingerTichy}.\n\nSince the Widom-Rowlinson graph $H_{\\rm WR}(k)$ can be constructed from the disjoint union of $k$ looped vertices by the addition of a single looped dominating vertex, an immediate corollary of Theorem \\ref{thm-minfortrees} is that for all $n \\geq 1$,\n\\[\n\\hom(P_n,H_{\\rm WR}(k)) \\leq \\hom(T,H_{\\rm WR}(k)).\n\\]\nfor all $T \\in \\calT(n)$. We also note in passing that Theorem \\ref{thm-minfortrees} may be interpreted in terms of partial $H$-colorings of $G$ (that is, $H$-colorings of induced subgraphs of $G$ that need not be extendable to $H$-colorings of $G$). Specifically, when $\\ell=1$ the theorem says that if $H$ is regular, then among all $n$-vertex trees none admits fewer partial $H$-colorings than $P_n$.\n\nOur second result is a new proof of Sidorenko's theorem, valid for sufficiently large $n$.\n\\begin{theorem} \\label{thm-maxfortrees}\nThere is a constant $c_H$ such that if $n \\geq c_H$ and $T \\in \\calT(n)$ then\n\\[\n\\hom(T,H) \\leq \\hom(K_{1,n-1},H)\n\\]\nwith equality if and only if $H$ is regular or $T = K_{1,n-1}$.\n\\end{theorem}\n\nWhile Theorem \\ref{thm-maxfortrees} is weaker than Theorem \\ref{thm-siderenko} in that it only holds for $n \\geq c_H$, it is noteworthy for two reasons.  Firstly, our proof for non-regular $H$ uses a stability technique --- we show that if a tree is not structurally close to a star (specifically, if it has a long path), then it admits significantly fewer $H$-colorings than the star, and if it is structurally almost a star but has some blemishes, then again it admits fewer $H$-colorings. Secondly, the proof is less tree-dependent than Sidorenko's, and so the ideas used may be applicable in other settings. We illustrate this by considering the extremal enumerative question for $H$-colorings of $2$-connected graphs. Let $\\calC_2(n)$ denote the set of $2$-connected graphs on $n$ vertices, and let $K_{a,b}$ be the complete bipartite graph with $a$ and $b$ vertices in the two color sets. Also, for graph $H$ with maximum degree $\\Delta$, denote by $s(H)$ the number of ordered pairs $(i,j)$ of vertices of $H$ satisfying $|N(i) \\cap N(j)| = \\Delta$. The special case $H=H_{\\text{ind}}$ of the following was established by Hua and Zhang \\cite{HuaZhang}.\n\\begin{theorem} \\label{thm-2connected}\nFor non-regular connected $H$ there is a constant $c_H$ such that if $n \\geq c_H$ and $G \\in \\calC_2(n)$ then\n\\[\n\\hom(G,H) \\leq \\hom(K_{2,n-2},H)\n\\]\nwith equality if and only if $G=K_{2,n-2}$.\n\nFor $\\Delta$-regular $H$ the same conclusion holds whenever $s(H) \\geq 2\\Delta^2 + 1$ (when $H$ is loopless and bipartite) or $s(H) \\geq \\Delta^2+1$ (otherwise).\n\\end{theorem}\nFor regular $H$ we have $s(H) \\geq |V(H)|$ (consider ordered pairs of the form $(i,i)$), so an immediate corollary in this case is that if $|V(H)| \\geq 2\\Delta^2+1$ (when $H$ is loopless and bipartite) or if $|V(H)| \\geq \\Delta^2+1$ (otherwise) then for all large $n$ the unique $2$-connected graph with the most $H$-colorings is $K_{2,n-2}$. Note that the bounds on $s(H)$ in the $\\Delta$-regular case are tight with respect to the characterization of uniqueness: when $H=K_{\\Delta}^{\\circ}$ we have $\\hom(G,H) = \\Delta^n$ for {\\em all} $n$-vertex $G$, and here $s(H)=\\Delta^2$, and when $H=K_{\\Delta, \\Delta}$ (a loopless bipartite graph) we have $\\hom(G,H) = 2\\Delta^n \\cdot \\textbf{1}_{\\{\\text{$G$ bipartite}\\}}$ for all $n$-vertex connected graphs $G$, and here $s(H)=2\\Delta^2$.\n\nSince all $G \\in \\calC_2(n)$ are connected, the restriction to connected $H$ is natural.  Unlike with Theorem \\ref{thm-maxfortrees}, the restriction to non-regular $H$ is somewhat significant here. In particular, there are examples of regular graphs $H$ such that for all large $n$, there are graphs in $\\calC_2(n)$ that admit more $H$-colorings than $K_{2,n-2}$ (and so there is no direct analog of Theorem \\ref{thm-siderenko} in the world of $2$-connected graphs). One such example is $H=K_3$; it is easily checked that ${\\rm hom}(C_n,K_3)>{\\rm hom}(K_{2,n-2},K_3)$ for all $n \\geq 6$ (where $C_n$ is the cycle on $n$ vertices).  \nMore generally, we have the following.\n\\begin{theorem} \\label{thm-2conn-cycles}\nLet $n \\geq 3$ and $q \\geq 3$ be given.  Then for any $G \\in \\calC_2(n)$, \n\\[\n\\hom(G,K_q) \\leq \\hom(C_n,K_q),\n\\]\nwith equality if and only if $G=C_n$, unless $q=3$ and $n=5$ in which case $G=K_{2,3}$ also achieves equality.\n\nThe same conclusion holds with $\\calC_2(n)$ replaced by the larger family of $2$-edge-connected graphs on $n$ vertices.\n\\end{theorem}\n\n\nIn the setting of Theorem \\ref{thm-2conn-cycles} it turns out that no extra complications are introduced in moving from $2$-connected to $2$-edge-connected. We do not, however, currently see a way to extend Theorem \\ref{thm-2connected} to this larger family. In particular, the key structural lemma given in Corollary \\ref{cor-P3} does not generalize to the family of 2-edge-connected graphs. \n\nThe rest of the paper is laid out as follows. The proof of Theorem \\ref{thm-minfortrees} is given in Section \\ref{sec-minfortrees}. We prove Theorem \\ref{thm-maxfortrees} in Section \\ref{sec-maxfortrees}, and use similar ideas to then prove Theorem \\ref{thm-2connected} in Section \\ref{sec-2connected}. The proof of Theorem \\ref{thm-2conn-cycles} is given in Section \\ref{sec-2conn-cycles}. Finally, we end with a number of open questions in Section \\ref{sec-concluding remarks}. \n\n\n\\section{Proof of Theorem \\ref{thm-minfortrees}} \\label{sec-minfortrees}\n\nLet $H$ be a $\\Delta$-regular graph, and let $H^{\\circ}(\\ell)$ be the join of $H$ and $K_{\\ell}^{\\circ}$. \nUsing induction on $n$, we will show something a little stronger than Theorem \\ref{thm-minfortrees}, namely that for any $n$-vertex \\emph{forest} $F$, $\\hom(F,H^{\\circ}(\\ell)) \\geq \\hom(P_n,H^{\\circ}(\\ell))$, with equality if and only if either $H^{\\circ}(\\ell)$ is a complete looped graph, or $F=P_n$. We will first prove the inequality, and then address the cases of equality.\n\nFor $n \\leq 4$, the only forest $F$ on $n$ vertices that is not a subgraph of $P_n$ (and so for which $\\hom(F,H^{\\circ}(\\ell))\\geq \\hom(P_n,H^{\\circ}(\\ell))$ is immediate) is $F=K_{1,n-1}$; but in this case the required inequality follows directly from the Hoffman-London inequality \\cite{Hoffman,London}.\n\nSo now fix $n \\geq 5$, and let $F$ be a forest on $n$ vertices. In what follows, for $x \\in V(F)$ and $i \\in V(H^{\\circ}(\\ell))$ we write $\\hom(F,H^{\\circ}(\\ell) | x \\mapsto i)$ for the number of homomorphisms from $F$ to $H^{\\circ}(\\ell)$ that map $x$ to $i$.\nAlso, we'll assume that $H^{\\circ}(\\ell)$ has $q+\\ell$ vertices, say $V(H^{\\circ}(\\ell)) = \\{1,\\ldots,q, \\ldots,q+\\ell\\}$, with the looped dominating vertices being $q+1,\\ldots,q+\\ell$.\n\nLet $x$ be a leaf in $F$, with unique neighbor $y$ (note that we may assume that $F$ has an edge, because the desired inequality is trivial otherwise).\nFor each $i  \\in \\{1,\\ldots,q+\\ell\\}$,\n\\begin{equation} \\label{eqn-restrict}\n \\hom(F,H^{\\circ}(\\ell) | x \\mapsto i) = \\sum_{j \\sim i} \\hom(F-x,H^{\\circ}(\\ell) | y \\mapsto j),\n\\end{equation}\nwhich in particular implies $\\hom(F,H^{\\circ}(\\ell) | x \\mapsto k) = \\hom(F-x,H^{\\circ}(\\ell))$ if $k \\in \\{q+1,\\ldots,q+\\ell\\}$.\nSo\n\\begin{eqnarray*}\n\\hom(F,H^{\\circ}(\\ell)) &=& \\sum_{i=1}^{q+\\ell} \\hom(F,H^{\\circ}(\\ell) | x \\mapsto i) \\\\\n&=& \\ell \\hom(F-x,H^{\\circ}(\\ell)) + \\sum_{i=1}^{q} \\sum_{j\\sim i} \\hom(F-x,H^{\\circ}(\\ell) | y \\mapsto j)\\\\\n&=& \\ell \\hom(F-x,H^{\\circ}(\\ell)) + \\sum_{j=q+1}^{q+\\ell} q\\hom(F-x,H^{\\circ}(\\ell) | y \\mapsto j) \\\\\n&& \\qquad + \\sum_{j=1}^{q} d_{H}(j) \\hom(F-x,H^{\\circ}(\\ell) | y \\mapsto j)\\\\\n&=& \\ell \\hom(F-x,H^{\\circ}(\\ell)) + \\sum_{j=q+1}^{q+\\ell} (q-\\Delta) \\hom(F-x,H^{\\circ}(\\ell) | y \\mapsto j) \\\\\n&& \\qquad + \\Delta\\sum_{j=1}^{q+\\ell} \\hom(F-x,H^{\\circ}(\\ell) | y \\mapsto j)\\\\\n&=& (q-\\Delta)\\hom(F-x-y,H^{\\circ}(\\ell)) + (\\Delta+\\ell) \\hom(F-x,H^{\\circ}(\\ell)).\n\\end{eqnarray*}\n\nIf $F=P_n$ then $F-x=P_{n-1}$ and $F-x-y=P_{n-2}$.  Therefore, by induction, we have\n\\begin{eqnarray*}\n\\hom(F,H^{\\circ}(\\ell)) &=& (q-\\Delta)\\hom(F-x-y,H^{\\circ}(\\ell)) + (\\Delta+\\ell)\\hom(F-x,H^{\\circ}(\\ell))\\\\\n&\\geq& (q-\\Delta)\\hom(P_{n-2},H^{\\circ}(\\ell)) + (\\Delta+\\ell)\\hom(P_{n-1},H^{\\circ}(\\ell))\\\\\n&=& \\hom(P_{n},H^{\\circ}(\\ell)).\n\\end{eqnarray*}\n\nWhen can we achieve equality?  If $H^{\\circ}(\\ell)$ is the complete looped graph, then we have equality for all $F$. So we may assume that $H^{\\circ}(\\ell)$ is not a complete looped graph, and that in particular there are $i, j \\in V(H^{\\circ}(\\ell))$ with $i \\not \\sim j$.\nNow consider an $F$ with more than one component, and let $u$ and $v$ be vertices of $F$ in different components. Using the looped dominating vertices of $H^{\\circ}(\\ell)$ we may construct an $H^{\\circ}(\\ell)$-coloring of $F$ in which $u$ is colored $i$ and $v$ is colored $j$. This is not a valid $H^{\\circ}(\\ell)$-coloring of the forest obtained from $F$ by adding the edge $uv$. It follows that there is a tree $T$ on $n$ vertices with $\\hom(F,H^{\\circ}(\\ell)) > \\hom(T,H^{\\circ}(\\ell))$.\nThe proof of the Hoffman-London inequality ($\\hom(K_{1,n-1},H) \\geq \\hom(P_n,H)$) given in \\cite{Sidorenko2} in fact shows strict inequality for $H^{\\circ}(\\ell)$ that is not a complete looped graph; since strict inequality holds for the base cases $n \\leq 4$, the inductive proof therefore gives strict inequality unless $F-x=P_{n-1}$ and $F-x-y=P_{n-2}$, which implies $F=P_n$.\n\n\n\n\\section{Proof of Theorem \\ref{thm-maxfortrees}} \\label{sec-maxfortrees}\nFirst, notice that for $\\Delta$-regular $H$ we have ${\\rm hom}(T,H) = |V(H)| \\Delta^{n-1}$ for all $T \\in \\calT(n)$, as can be seen by fixing the color on one vertex and iteratively coloring away from that vertex. \nTherefore the goal for the remainder of this section is to show that for non-regular $H$ there is a constant $c_H$ such that if $n \\geq c_H$ and $T \\in \\calT(n)$ then\n\\[\n\\hom(T,H) \\leq \\hom(K_{1,n-1},H),\n\\]\nwith equality if and only if $T = K_{1,n-1}$.\nRecall that a loop in $H$ will count \\emph{once} toward the degree of a vertex $v \\in V(H)$ and $\\Delta$ denotes the maximum degree of $H$.  If $H$ has components $H_1,\\ldots,H_s$ then $\\hom(G,H)= \\hom(G,H_1) + \\cdots + \\hom(G,H_s)$, so we may assume that $H$ is connected.\n\nLet $V_{=\\Delta} \\subset V(H)$ be the set of vertices in $H$ with degree $\\Delta$.  By coloring the center of the star with a color from $V_{=\\Delta}$, we have\n\\[\n\\hom(K_{1,n-1},H) \\geq |V_{=\\Delta}|\\Delta^{n-1}.\n\\]\nWe will show that if $n \\geq c_H$ and $T \\neq K_{1,n-1}$, then $\\hom(T,H) < |V_{=\\Delta}|\\Delta^{n-1}$. We use the following lemma, which will also be needed in the proof of Theorem \\ref{thm-2connected}.\n\n\\begin{lemma}\\label{lem-no long paths}\nFor non-regular $H$ there exists a constant $\\ell_H$ such that if $k \\geq \\ell_H$, then $\\hom(P_{k},H) < \\Delta^{k-2}$.\n\\end{lemma}\n\n\\begin{proof}\nLet $A$ denote the adjacency matrix of $H$, which is a symmetric non-negative matrix.  \nSince an $H$-coloring of $P_k$ is exactly a walk of length $k$ through $H$, we have\n\\begin{equation} \\label{eq-homs-lin-alg-count}\n\\hom(P_k,H) = \\sum_{i,j} (A^k)_{ij} \\leq |V(H)|^2\\max_{i,j} (A^k)_{ij}.\n\\end{equation}\nBy the Perron-Frobenius theorem (see e.g. \\cite[Theorem 1.5]{Seneta}), the largest eigenvalue $\\lambda$ of $A$ has a strictly positive eigenvector ${\\bf x}$, for which it holds that $A^k \\textbf{x} = \\lambda^k \\textbf{x}$. Considering the row of $A^k$ containing $\\max_{i,j} \\left( A^k \\right)_{ij}$, it follows that $\\max_{i,j} \\left( A^k \\right)_{ij} \\leq c_1 \\lambda^k$ for some constant $c_1$. Combining this with (\\ref{eq-homs-lin-alg-count}) we find that $\\hom(P_k,H) \\leq |V(H)|^2 c_1 \\lambda^k$.\nSince $H$ is not regular, we have $\\lambda < \\Delta$, and so the lemma follows.\n\\end{proof}\n\nWe use Lemma \\ref{lem-no long paths} to show that any tree $T$ containing $P_k$ as a subgraph, for $k \\geq \\ell_H$, has $\\hom(T,H) < |V_{=\\Delta}|\\Delta^{n-1}$. Indeed, by first coloring the path and then iteratively coloring the rest of the tree we obtain\n\\[\n\\hom(T,H) < \\Delta^{k-2} \\Delta^{n-k} < |V_{=\\Delta}|\\Delta^{n-1}.\n\\]\n(The bound $\\hom(P_k,H) < \\Delta^{k-2}$ will be necessary for the proof of Theorem \\ref{thm-2connected}; here  the weaker bound $\\hom(P_k,H) < |V_{=\\Delta}|\\Delta^{k-1}$ would suffice.)\n\nSo suppose that $T$ does not contain a path of length $\\ell_H$.\nNotice that for $n>2^{c+1}$ there are at most\n\\[\n1+n^{1\/(c+1)}+n^{2\/(c+1)}+\\cdots + n^{c\/(c+1)} < n\n\\]\nvertices in a rooted tree with depth at most $c$ and each vertex having degree at most $n^{1\/(c+1)}$. Because of this, there exists a constant $c_2>0$ (which depends on $\\ell_H$, but is independent of $n$) and \na vertex $v \\in T$ with $d(v) \\geq n^{c_2}$. \nSince $T \\neq K_{1,n-1}$ we have $d(v) < n-1$ and so some neighbor $w$ of $v$ is adjacent to a vertex in $V(T) \\setminus (\\{v\\} \\cup N(v))$.\nAs $H$ is connected and not regular, there is an $i \\in V(H)$ with $d_H(i) = \\Delta$ and $d_H(j) \\leq \\Delta-1$ for some neighbor $j$ of $i$.\n\nThe number of $H$-colorings of $T$ that don't color $v$ with a vertex of degree $\\Delta$ is at most\n\\begin{equation} \\label{eqn-cols1}\n|V(H)| (\\Delta-1)^{n^{c_2}}\\Delta^{n-1-n^{c_2}} \\leq |V(H)|e^{-n^{c_2}\/\\Delta}  \\Delta^{n-1}.\n\\end{equation}\nThe number of $H$-colorings that color $v$ with a vertex of degree $\\Delta$ different from $i$ is at most\n\\begin{equation} \\label{eqn-cols2}\n(|V_{=\\Delta}| -1) \\Delta^{n-1},\n\\end{equation}\nand the number of $H$-colorings that color $v$ with $i$ and $w$ with a color different from $j$ is at most\n\\begin{equation} \\label{eqn-cols3}\n(\\Delta-1)\\Delta^{n-2} = \\left(1-\\frac{1}{\\Delta}\\right) \\Delta^{n-1}.\n\\end{equation}\nFinally, the number of $H$-colorings that color $v$ with $i$ and $w$ with $j$ is at most\n\\begin{equation} \\label{eqn-cols4}\n(\\Delta-1)\\Delta^{n-3} = \\left(\\frac{1}{\\Delta} - \\frac{1}{\\Delta^2}\\right) \\Delta^{n-1},\n\\end{equation}\nsince the degree of $j$ is at most $\\Delta-1$ and $w$ is adjacent to a vertex in $V(T) \\setminus (\\{v\\} \\cup N(v))$, which can be colored with one of the at most $\\Delta-1$ neighbors of $j$.\nCombining (\\ref{eqn-cols1}), (\\ref{eqn-cols2}), (\\ref{eqn-cols3}), and (\\ref{eqn-cols4}) we obtain\n\\[\n\\hom(T,H) \\leq   \\left( |V_{=\\Delta}| - \\frac{1}{\\Delta^2} + |V(H)|e^{-n^{c_2}\/\\Delta} \\right) \\Delta^{n-1} < |V_{=\\Delta}|\\Delta^{n-1},\n\\]\nthe final inequality valid as long as $n \\geq c_H$.\n\n\n\\section{Proof of Theorem \\ref{thm-2connected}} \\label{sec-2connected}\n\nHere we build on the approach used in the proof of Theorem \\ref{thm-maxfortrees} to tackle the family of $n$-vertex $2$-connected graphs $\\calC_2(n)$.\n\nIn order to proceed, we will need a structural characterization of $2$-connected graphs. In the definition below we abuse standard notation a little, by allowing the endpoints of a path to perhaps coincide.\n\\begin{definition}\nAn \\emph{ear} on a graph $G$ is a path whose endpoints are vertices of $G$, but which otherwise is vertex-disjoint from $G$. An ear is an \\emph{open ear} \nif the endpoints of the path are distinct. \nAn \\emph{(open) ear decomposition} of a graph $G$ is a partition\nof the edge set of $G$ into parts $Q_0, Q_1,\\ldots Q_\\ell$\nsuch that $Q_0$ is a cycle and $Q_i$ for $1 \\leq i \\leq \\ell$ is an (open) ear on $Q_0 \\cup \\cdots \\cup Q_{i-1}$.\n\\end{definition}\n\n\\begin{theorem}[Whitney \\cite{Whitney}]\nA graph is $2$-connected if and only if it admits an open ear decomposition.\n\\end{theorem}\n\nSince removing edges from a graph does not decrease the count of $H$-colorings, we will assume in the proof of Theorem \\ref{thm-2connected} that we are working with a \\emph{minimally $2$-connected graph} $G$, meaning that $G$ is $2$-connected and for any edge $e$ we have that $G-e$ is not $2$-connected. A characterization of these graphs is the following, which can be found in \\cite{Dirac}.\n\\begin{theorem} \\label{thm-nochord}\nA $2$-connected graph $G$ is minimally $2$-connected if and only if no cycle in $G$ has a chord.\n\\end{theorem}\n\n\\begin{corollary}\\label{cor-P3}\nLet $G$ be a minimally $2$-connected graph. There is an open ear decomposition $Q_0, \\ldots, Q_\\ell$ of $G$, and a $c$ satisfying $1 \\leq c \\leq \\ell$, with the property that each of $Q_1$ up to $Q_c$ are paths on at least four vertices, and each of $Q_{c+1}$ through $Q_\\ell$ are paths on three vertices with endpoints in $\\cup_{k=1}^c Q_k$.\n\\end{corollary}\n\n\\begin{proof}\nLet $Q_0, \\ldots, Q_\\ell$ be an open ear decomposition of $G$. If any of the $Q_k$, $1 \\leq k \\leq \\ell$, is a path on two vertices, its removal leads to an open ear decomposition of a proper spanning subgraph of $G$, contradicting the minimality of $G$. So we may assume that each of $Q_1$ through $Q_\\ell$ is a path on at least three vertices. We claim that if $Q_i$ is a path on exactly three vertices, then the degree 2 vertex in $Q_i$ also has degree 2 in $G$; from this the corollary easily follows.\n\nTo verify the claim, let $Q_i$ be on vertices $x, a$ and $y$, with $a$ the vertex of degree 2, and suppose, for a contradiction, that there is some $Q_j$, $j > i$, that has endpoints $a$ and $z$ (the latter of which may be one of $x$, $y$). In $\\cup_{k=1}^{i-1} Q_k$ there is a cycle $C$ containing both $x$ and $y$, and in  $\\cup_{k=1}^{j-1} Q_k$ there is a path $P$ from $z$ to $C$ that intersects $C$ only once. Now consider the cycle $C'$ that starts at $a$, follows $Q_j$ to $z$, follows $P$ to $C$, follows $C$ until it has met both $x$ and $y$ (meeting $y$ second, without loss of generality), and finishes along the edge $ya$. The edge $xa$ is a chord of this cycle, giving us the desired contradiction.\n\\end{proof}\n\nThe next lemma follows from results that appear in \\cite{Engbers}, specifically Lemma 5.3 and the proof of Corollary 5.4 of that reference.\n\n\\begin{lemma}\\label{lem-col paths}\nSuppose $H$ is not $K_{\\Delta,\\Delta}$ or $K_{\\Delta}^{\\circ}$ (the complete looped graph). Then for any two vertices $i$, $j$ of $H$ and for $k\\geq 4$ there are at most $(\\Delta^2-1)\\Delta^{k-4}$ $H$-colorings of $P_k$ that map the initial vertex of the path to $i$ and the terminal vertex to $j$.\n\\end{lemma}\n\n\\begin{remark}\nCorollary 5.4 in \\cite{Engbers} gives a bound of $\\Delta^{k-2}$ for a smaller class of $H$, which is simply for convenience.  The proof given actually delivers a bound of $(\\Delta^2-1)\\Delta^{k-4}$ for all $H$ except $K_{\\Delta,\\Delta}$ and $K_{\\Delta}^{\\circ}$. \n\\end{remark}\n\n\\begin{proof}[Proof of Theorem \\ref{thm-2connected}]\n\nWe begin with the proof for a non-regular connected graph $H$, and then consider regular $H$ and describe the necessary modifications needed in the proof.\n\nLet $H$ be non-regular and connected. We will first show that for all sufficiently large $n$ and all minimally $2$-connected graphs $G$ that are different from $K_{2,n-2}$ we have $\\hom(G,H) < \\hom(K_{2,n-2},H)$, and we will then address the cases of equality when $G$ is allowed to be not minimal.\nAn easy lower bound on the number of $H$-colorings of $K_{2,n-2}$ is\n$$\n\\hom(K_{2,n-2},H) \\geq s(H)\\Delta^{n-2} \\geq \\Delta^{n-2},\n$$\nwhere $s(H)$ is the number of ordered pairs $(i,j)$ of (not necessarily distinct) vertices in $V(H)$ with the property that $|N(i) \\cap N(j)|=\\Delta$. For the first inequality, consider coloring the vertices in the partition class of size $2$ of $K_{2,n-2}$ with colors $i$ and $j$, and for the second note that the pair $(i,i)$, where $i$ is any vertex of degree $\\Delta$, is counted by $s(H)$.\n\nSuppose that $G$ contains a path on $k\\geq \\ell_H$ vertices (with $\\ell_H$ as given by Lemma \\ref{lem-no long paths}). By first coloring this path and then iteratively coloring the remaining vertices we have (using Lemma \\ref{lem-no long paths}) $\\hom(G,H) < \\Delta^{k-2} \\Delta^{n-k} = \\Delta^{n-2}$. We may therefore assume that $G$ contains no path on $k \\geq \\ell_H$ vertices.\n\nConsider now an open ear decomposition of $G$ satisfying the conclusions of Corollary \\ref{cor-P3}. Since $G$ contains no path on $\\ell_H$ vertices, we have that there is some constant (independent of $n$) that bounds the lengths of each of the $Q_i$, and so $\\ell$, the number of open ears in the decomposition, satisfies $\\ell=\\Omega(n)$.\nWe now show that $c$, the number of paths in the open ear decomposition that have at least four vertices, may be taken to be at most a constant (independent of $n$). Coloring $Q_0$ first, then coloring each of $Q_1$ through $Q_{c}$, and then iteratively coloring the rest of $G$, Lemma \\ref{lem-col paths} yields\n\\begin{eqnarray*}\n\\hom(G,H) & \\leq & |V(H)|\\Delta^{|Q_0|-1}(\\Delta^2-1)^{c} \\Delta^{\\left(\\sum_{i=1}^{c} |Q_i|\\right)-4c}\\Delta^{\\ell-c} \\\\\n& \\leq & \\frac{|V(H)|}{\\Delta}\\left(1-\\frac{1}{\\Delta^2}\\right)^{c} \\Delta^n\n\\end{eqnarray*}\n(noting that $n=|Q_0| + \\left(\\left(\\sum_{i=1}^{c} |Q_i|\\right)-2c\\right) + (\\ell-c)$). Unless $c$ is a constant, this quantity falls below the trivial lower bound on $\\hom(K_{2,n-2},H)$ for all sufficiently large $n$.\n\nNow since there are only constantly many vertices in the graph $G'$ with open ear decomposition $Q_0, \\ldots, Q_{c}$, and $G$ is obtained by adding the remaining vertices to $G'$, each joined to exactly two vertices of $G'$, it follows by the pigeonhole principle that for some constant $c'$ \nthere is a pair of vertices $w_1$, $w_2$ in $G$ with at least $c' n$ common neighbors, all among the middle vertices of the $Q_i$ for $i \\geq {c}+1$.\n(Notice that this makes $G$ ``close'' to $K_{2,n-2}$ in the same sense that in the proof of Theorem \\ref{thm-maxfortrees} a tree with a vertex of degree $\\Omega(n)$ was ``close'' to $K_{1,n-1}$.)\n\nWe count the number of $H$-colorings of $G$ by first considering those in which $w_1$ is colored $i$ and $w_2$ is colored $j$, for some pair $i, j \\in V(H)$ with $|N(i) \\cap N(j)| < \\Delta$. There are at most\n\\begin{equation} \\label{small-common-nhood}\n|V(H)|^2(\\Delta-1)^{c' n}\\Delta^{n-2-c' n}\n\\end{equation}\nsuch $H$-colorings. Next, we count the number of $H$-colorings of $G$ in which $w_1$ is colored $i$ and $w_2$ is colored $j$, for some pair $i,j \\in V(H)$ with $|N(i) \\cap N(j)| = \\Delta$. We argue that in $G'$ (the graph with open ear decomposition $Q_0, \\ldots, Q_{c}$) there must be a path $P$ on at least $4$ vertices with endpoints $w_1$ and $w_2$. \nTo see this, note that since $G \\neq K_{2,n-2}$ there must be some vertex $v\\in G'$ so that $v \\neq w_1$, $v \\neq w_2$, and $v \\notin N(w_1) \\cap N(w_2)$. Choose a cycle in $G'$ containing $v$ and $w_1$, and find a path from $w_2$ to that cycle (the path will be trivial if $w_2$ is on the cycle). From this structure we find such a path $P$, and it must have at least $4$ vertices as $v \\notin N(w_1) \\cap N(w_2)$.\n\nColoring $G$ by first coloring $w_1$ and $w_2$, then the vertices of $P$, and finally the rest of the graph, we find by Lemma \\ref{lem-col paths} that the number of\n$H$-colorings of $G$ in which $w_1$ is colored $i$ and $w_2$ is colored $j$, for some pair $i,j \\in V(H)$ with $|N(i) \\cap N(j)| = \\Delta$ is at most\n\\begin{equation} \\label{large-common-nhood}\ns(H)\\left(1-\\frac{1}{\\Delta^2}\\right)\\Delta^{n-2}.\n\\end{equation}\nCombining (\\ref{small-common-nhood}) and (\\ref{large-common-nhood}) we have\n\\begin{eqnarray*}\n\\hom(G,H) &\\leq& |V(H)|^2\\Delta^{n-2}\\left(\\frac{\\Delta-1}{\\Delta}\\right)^{c' n} + s(H)\\left(1-\\frac{1}{\\Delta^2}\\right) \\Delta^{n-2}\\\\\n&<& s(H)\\Delta^{n-2}\\\\\n&\\leq& \\hom(K_{2,n-2},H),\n\\end{eqnarray*}\nwith the strict inequality valid for all sufficiently large $n$.\n\n\n\\medskip\n\nWe have shown that for non-regular connected $H$, $K_{2,n-2}$ is the unique minimally $2$-connected $n$-vertex graph maximizing the number of $H$-colorings. We now complete the proof of Theorem \\ref{thm-2connected} for non-regular connected $H$ by showing that if \n$G$ is an $n$-vertex $2$-connected graph that is not minimally $2$-connected then $\\hom(G,H) < \\hom(K_{2,n-2},H)$.  Suppose for the sake of contradiction that $\\hom(G,H) = \\hom(K_{2,n-2},H)$. Since deleting edges from $G$ cannot decrease the count of $H$-colorings, the uniqueness of $K_{2,n-2}$ among minimally $2$-connected graphs shows that $K_{2,n-2}$ is the only minimally $2$-connected graph that is a subgraph of $G$, and in particular we may assume that $G$ is obtained from $K_{2,n-2}$ by adding a single edge, necessarily inside one partition class of $K_{2,n-2}$. Since $K_{2,n-2}$ is a subgraph of $G$, all $H$-colorings of $G$ are $H$-colorings of $K_{2,n-2}$.\n\nSuppose that $i$ and $j$ are distinct adjacent vertices of $H$. The $H$-coloring of $K_{2,n-2}$ that maps one partition class to $i$ and the other to $j$ must also be an $H$-coloring of $G$, which implies that both $i$ and $j$ must be looped. By similar reasoning, if $i$ and $j$ are adjacent in $H$, and also $j$ and $k$, then $i$ and $k$ must be adjacent. It follows that $H$ is a disjoint union of fully looped complete graphs, and so if connected must be a single complete looped graph (and therefore is regular), which is a contradiction.     \n\n\\medskip\n\nNow we turn to regular connected $H$ satisfying $s(H) \\geq 2\\Delta^2+1$ (if $H$ is loopless and bipartite) or $s(H) \\geq \\Delta^2+1$ (otherwise). For these $H$, Lemma \\ref{lem-no long paths} does not apply. We will argue, however, that there is still an $\\ell_H$ such that if $2$-connected $n$-vertex $G$ has an open ear decomposition in which any of the added paths $Q_i$, $i \\geq 1$, has at least $\\ell_H$ vertices then $G$ has fewer $H$-colorings than $K_{2,n-2}$. Once we have established this, the proof proceeds exactly as in the non-regular case.\n\nWe begin by establishing that $G$ has no long cycles; we will use the easy fact that the number of $H$-colorings of a $k$-cycle is the sum of the $k$th powers of the eigenvalues of the adjacency matrix of $H$. By the Perron-Frobenius theorem there is exactly one eigenvalue of the adjacency matrix of $H$ equal to $\\Delta$, and a second one equal to $-\\Delta$ if and only if $H$ is loopless and bipartite, with the remaining eigenvalues having absolute value strictly less than $\\Delta$. It follows that the number of $H$-colorings of a $k$-cycle is, for large enough $k$, less than $(2+\\frac{1}{\\Delta^2})\\Delta^k$ (if $H$ is loopless and bipartite) or $(1+\\frac{1}{\\Delta^2})\\Delta^k$ (otherwise). If $G$ has such a cycle then by coloring the cycle first and then coloring the remaining vertices sequentially, bounding the number of options for the color of each vertex by $\\Delta$, we get that the number of $H$-colorings of $G$ falls below the trivial lower bound on ${\\rm hom}(K_{2,n-2},H)$ of $s(H)\\Delta^{n-2}$.\n\nNow if a $2$-connected $G$ has an open ear decomposition with an added path $Q_i$, $i \\geq 1$, on at least $\\ell_H$ vertices, then it has a cycle of length at least $\\ell_H$, since the endpoints of $Q_i$ are joined by a path in $Q_0\\cup \\ldots \\cup Q_{i-1}$.\n\n\\end{proof}\n\n\n\\section{Proof of Theorem \\ref{thm-2conn-cycles}} \\label{sec-2conn-cycles}\n\nIn this section we show that for all $q \\geq 3$ and $n \\geq 3$, among $n$-vertex $2$-edge-connected graphs, and therefore among the subfamily of $n$-vertex $2$-connected graphs, the cycle $C_n$ uniquely (up to one small exception) admits the greatest number of proper $q$-colorings (that is,  $K_q$-colorings). The result is trivial for $n=3$ and easily verified directly for $n=4$, so throughout we assume $n \\geq 5$.\n\nWe will use the following characterization of $2$-edge-connected graphs, due to Robbins (see Section \\ref{sec-2connected} for the definition of ear decomposition).\n\n\\begin{theorem}[Robbins \\cite{Robbins}]\nA graph is $2$-edge-connected if and only if it admits an ear decomposition.\n\\end{theorem}\n\nNotice that we are trying to show that $C_n$, which is the unique graph constructed with a trivial ear decomposition $Q_0=C_n$, maximizes $\\hom(G,K_q)$. To do this, we aim to show that almost any time a $2$-edge-connected graph contains a cycle and a path that meets the cycle only at the endpoints (which is what results after the first added ear in an ear decomposition for $G \\neq C_n$), we can produce an upper bound on $\\hom(G,K_q)$ which is smaller than $\\hom(C_n,K_q)$; we will then deal with the exceptional cases by hand. The proof will initially consider an arbitrary fixed cycle and a path joined to that cycle at its endpoints in $G$ (but independent of a particular ear decomposition of $G$), and will begin by producing an upper bound on $\\hom(G,K_q)$ based on the lengths of the path and cycle. \n\nLet $G \\neq C_n$ be an $n$-vertex $2$-edge-connected graph, and let $C$ be a non-Hamiltonian cycle in $G$ of length $\\ell$.\nSince $\\ell < n$ and $G$ is $2$-edge-connected, there is a path $P$ on at least $3$ vertices that meets $C$ only at its endpoints. \n\nSuppose first that $P$ contains $m+2$ vertices, where $m \\geq 2$ (so there are $m$ vertices on $P$ outside of the vertices of $C$). Color $G$ by first coloring $C$, then $P$, and then the rest of the graph. Using  $\\hom(C_{\\ell},K_q) = (q-1)^{\\ell} + (-1)^{\\ell} (q-1)$ and Lemma \\ref{lem-col paths}, we have\n\\begin{eqnarray*}\n\\hom(G,K_q) &\\leq& \\left((q-1)^{\\ell} + (-1)^{\\ell} (q-1)\\right) \\left[ \\left( (q-1)^{2} -1\\right) (q-1)^{m-2} \\right] (q-1)^{n-m-\\ell}\\\\\n&=& (q-1)^n - (q-1)^{n-2} + (-1)^{\\ell} (q-1)^{n-\\ell+1} - (-1)^{\\ell} (q-1)^{n-\\ell-1}\\\\\n&\\leq& (q-1)^n - (q-1)^{n-2} + (q-1)^{n-\\ell+1} - (q-1)^{n-\\ell-1}\\\\\n&\\leq& \\hom(C_n,K_q).\n\\end{eqnarray*}\nSince the last inequality is strict for $\\ell > 3$ and the second-to-last inequality is strict for all odd $\\ell$, the chain of inequalities is strict for all $\\ell \\geq 3$. \nIn other words, if $G$ contains any cycle $C$ and a path $P$ on at least $4$ vertices that meets $C$ only at its endpoints, then $\\hom(G,K_q) < \\hom(C_n,K_q)$.\n\nSuppose next that all the paths on at least three vertices that meet $C$ only at their endpoints have exactly three vertices. If $\\ell \\geq 5$, or if $\\ell=4$ and there is such a path that joins two adjacent vertices of the cycle, then using just the vertices and edges of $C$ and one such path $P$ we can easily find a new cycle $C'$\nand a path $P'$ on at least four vertices that only meets $C'$ at it endpoints, and so $\\hom(G,K_q) < \\hom(C_n,K_q)$ as before.\n\nIt remains to find an upper bound for those $2$-edge-connected graphs (apart from $C_n$) that do not have any of the following:\n\\begin{itemize}\n\\item[(a)] a cycle of any length with a path on at least $4$ vertices that only meets the cycle at its endpoints;\n\\item[(b)] a cycle of length at least $5$ and a path on $3$ vertices that only meets the cycle at its endpoints; or\n\\item[(c)] a cycle of length $4$ with a path of length $3$ that only meets the cycle at its endpoints, and those endpoints are two adjacent vertices of the cycle.\n\\end{itemize}\n\nRecall that we are assuming $n \\geq 5$. For the remaining graphs, notice that if $Q_0$ is a cycle of length $3$, then $Q_0 \\cup Q_1$, where $Q_1$ is a path on three vertices (by (a) above), must contain a cycle of length $4$. \nIn fact, in this case this cycle will use vertices from both $Q_0$ and $Q_1$.\nTherefore, we need not separately analyze the situation where $C$ is a cycle of length $3$ among the remaining graphs. \nIn particular, this means that there is one final case to consider: $C$ has length $\\ell=4$, and $P$ is a path on $3$ vertices that only meets $C$ at its endpoints, and the endpoints of $P$ are non-adjacent vertices of $C$.  In this case, $C$ and $P$ form a copy of $K_{2,3}$, and we color this copy of $K_{2,3}$ first and then the rest of $G$.  This gives \n$$\n\\hom(G,K_q) \\leq \\left( q(q-1)^3 + q(q-1)(q-2)^3\\right) (q-1)^{n-5}.\n$$\nFor $n \\geq 6$, some algebra shows that the right-hand side above is strictly less than $\\hom(C_n,K_q)$, and also for $n=5$ and $q > 3$. For $n=5$ and $q=3$ we have equality, and so in this case $\\hom(G,K_3) \\leq \\hom(C_5,K_3)$ with equality only if $G$ has the same number of proper $3$-colorings as $K_{2,3}$ and has $K_{2,3}$ as a subgraph; this can only happen if $G=K_{2,3}$ (using a similar argument as the one given in the proof of the cases of equality for Theorem \\ref{thm-2connected}).\n\n\\section{Concluding Remarks}\\label{sec-concluding remarks}\nIn this section, we highlight a few questions related to the work in this article.\n\n\\begin{question}\nWhich graphs $H$ have the property that the path on $n$ vertices is the tree that minimizes the number of $H$-colorings?\n\\end{question}\n\nSince the star maximizes the number of $H$-colorings among trees, it is natural to repeat the maximization question among trees with some prescribed bound on the maximum degree.  Some results (for strongly biregular $H$) are obtained in \\cite{Ray}.\n\n\\begin{question}\nFor a fixed non-regular $H$ and positive integer $\\Delta$, which tree on $n$ vertices with maximum degree $\\Delta$ has the most $H$-colorings?\n\\end{question}\n\nThere are still open questions about regular $H$ in the family of $2$-connected graphs. In particular, we have seen that $K_{2,n-2}$ and $C_n$ are $2$-connected graphs that have the most $H$-colorings for some $H$. \n\n\\begin{question}\nWhat are the necessary and sufficient conditions on $H$ so that $K_{2,n-2}$ is the unique 2-connected graph that has the most $H$-colorings?\n\\end{question}\n\n\\begin{question}\nAre $C_n$ and $K_{2,n-2}$ the only $2$-connected graphs that uniquely maximize the number of $H$-colorings for some $H$?\n\\end{question}\n\nFinally, it would be natural to try to extend these results to $k$-connected graphs and to $k$-edge-connected graphs. \n\n\\begin{question}\\label{q-kconn}\nLet $H$ be fixed.  Which $k$-connected graph has the most $H$-colorings? Which $k$-edge-connected graph has the most number of $H$-colorings?\n\\end{question}\nSome results related to Question \\ref{q-kconn} for graphs with fixed minimum degree $\\delta$ can be found in \\cite{Engbers}, with $K_{\\delta,n-\\delta}$ shown to be the graph with the most $H$-colorings in this family. We remark that family of connected graphs with fixed minimum degree $\\delta$ has been considered very recently in \\cite{Engbers1}, where it is shown that for connected non-regular $H$ and all large enough $n$, again $K_{\\delta,n-\\delta}$ is the unique maximizer of the count of $H$-colorings. The question for regular $H$ remains fairly open.\n\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\\label{Sec:Intro}\nSurfaces with features from macro~\\cite{Candela} to nanoscale~\\cite{Bhushan} can be found both in\nnature and in industrial products. Such features cause light scattering and diffraction\nand, therefore, they impact the visual appearance of objects. Among the phenomena related to light\nscattering and diffraction there are many non-exotic effects which can be experienced in\neveryday life: reflection of light from, or transmission trough, a rough surface~\\cite{Stover,Simonsen2010};\ndiffraction through apertures~\\cite{BornWolf}~(holes in the window blinds) or from or through\na transparent\/opaque material of a particular shape (Mie scattering~\\cite{Cohen1982}); diffraction\nfrom periodic structures (diffraction gratings~\\cite{Loewen1997}, photonic crystals~\\cite{Joannopoulos}).\nIn textbooks these phenomena are often considered a separate phenomenon  and often restricted to a\nparticular range of parameters. For instance, ``diffraction grating'' analysis is almost\nexclusively applied to periodic structures for which the lattice constants are comparable to the\nwavelength of the incident light, which for visible light, corresponds to roughly \\num{0.5}--\\SI{2}{\\micro\\meter}.\nMeanwhile, the habit of considering only specific cases of light scattering and diffraction for a particular range of\nparameters may lead to an incorrect approach to the characterization of samples and thus to inaccurate or even incorrect \ninterpretation of experimental data.\n\nPeriodic patterns with lattice constants from tens to hundreds of micrometers exhibit hundreds\nto thousands of (propagating) diffraction orders when the sample is illuminated by visible light. Such structures are by no\nmeans efficient diffraction gratings. Yet, as will be shown in this paper, they can still produce a\nnoticeable effect on the optical properties of the samples and thus their visual appearances. Moreover,\nif several feeble optical effects are brought together they can impact significantly the optical\nresponse of the surfaces.\n\nMeasurements of gloss and haze are often the first step in the experimental characterization of the\noptical properties of samples which scatter light due to surface patterns or volume disorder. The simple\nintegral optical properties --- haze and gloss --- allow a distinction of the light that is reflected\/transmitted specularly\nby the sample  from the light that is scattered diffusely by it.\nHowever, the actual spectral and angular distributions of the intensity of the scattered light can be rather\ncomplex. Despite the convenience of haze and gloss in terms of the simplicity of measurement and speed,\nsuch integral properties may misguide the interpretation, especially if such measurements \ncontain the artifacts related to the diffraction of light.\n\n\\smallskip\nThe rest of this paper is organized in the following way. Section~\\ref{Sec:Methods} presents the samples that we will study in this work and the instruments used to perform the angle-resolved intensity measurements. Such and other results are presented in Sec.~\\ref{Sec:Results} where we also discuss and interpret the various features that are present in them. In particular, in this section, we discuss origin of the different types of circular intensity fringes that the angle-resolved transmitted intensity distributions possess. The haze of the samples, both directly measured, and obtained on the basis of the angle-resolved measurements are also discussed here [Sec.~\\ref{Sec:Results}.\\ref{Sec:Haze}]. Finally the conclusions that can be drawn from this work are presented in Sec.~\\ref{Sec:Concusions}. \n  \n\\section{Materials and Methods}\n\\label{Sec:Methods}\n\n\\subsection{Description of the samples}\n\\label{Sec:samples}\nThe studied samples consist of \\SI[product-units=power]{5 x 5}{\\cm} glass slides covered by an array of cylindrical silica micropillars [Fig.~\\ref{Fig:2}]; all cylinders had the height $h=\\SI{10}{\\micro\\meter}$ while their diameter were $d=\\SI{10}{\\micro\\meter}$, \\SI{20}{\\micro\\meter} or \\SI{40}{\\micro\\meter}. Both regular and random arrays were studied. The regular arrays were either hexagonal or square, for which the lattice vectors are $\\vec{a}_1= a\\vecUnit{x}$ [both cases] and $\\vec{a}_2 = (a\/2)[-\\vecUnit{x} + \\sqrt{3}\\vecUnit{y}]$~[hexagonal] or $\\vec{a}_2 = a \\vecUnit{y}$~[square], where $\\vecUnit{x}$ and $\\vecUnit{y}$ are orthogonal unit vectors in the sample plane (the $xy$-plane). The lattice constant $a$ of the regular arrays varied from \\SIrange{20}{80}{\\micro\\meter}~[Fig.~\\ref{Fig:2}]. The surface coverage $\\rho$ is defined as the ratio between the areas of the base of one micropillar to the area of a unit cell. If the diameter of the micropillars is denoted $d$, one finds that for a hexagonal array  \n$\\rho = (\\pi\/2\\sqrt{3})(d\/a)^2$ while for a square array $\\rho=(\\pi\/4)(d\/a)^2$~\\cite{Turbil2016}.\nFor instance, for pillars of diameter  \\SI{10}{\\micro\\meter} arranged in a hexagonal array the previously given values of $a$ correspond to the surface coverage between $\\rho=\\SI{1.4}{\\percent}$ ($a=\\SI{80}{\\micro\\meter}$) and \\SI{22.7}{\\percent} ($a=\\SI{20}{\\micro\\meter}$). Random arrays were produced to have the same surface coverage as the regular arrays for the same type of micropillars. To this end, the centers of the pillars were chosen to be uniformly distributed in such a way that two pillars could not be closer to each other than a minimum center-to-center distance (\\SI{20}{\\micro\\meter}). About a \\SI{300}{nm} thick residual silica layer between the glass surface and the base of the pillars provided an adhesion layer for the pillars to the surface of the substrate~[Fig.~\\ref{Fig:2}]. The thickness of the glass substrates was \\SI{2}{mm} for the majority of samples, and \\SI{1}{mm} for samples measured with the multimodal microscope. All the samples were produced in sol-gel silica by the use of  the nanoimprinting technique (for detailed description see Ref.~\\cite{Dubov2013}).\n\n\n\\begin{figure}[tbhp]\n  \\begin{center}\n    \\centering\n    \\includegraphics[width=0.6\\columnwidth]{Figure_1}\n    \\caption{Scanning electron microscope image of a cross-section of the sample taken at grazing incidence. The height of all micropillars used in this study was $h=\\SI{10}{\\micro\\meter}$. }\n    \\label{Fig:2}\n  \\end{center}\n\\end{figure}\n\n\n\n\n\n\n\n\n\n\\subsection{Optical measurements}\n\n\nConventional integral haze and gloss measurements were used in this study together with two\nfacilities for angle-resolved measurements: OMS4 goniospectrophotometer (commercialized\nby OPTIS) and a home-made multimodal imaging (Mueller) polarimetric microscope.\nBoth angle-resolved setups allow for the measurements of the optical intensity response of the\nsample. Since the two instruments are based on very different optical configurations, we\ndecided to use them both to verify the consistency of the results and to identify the presence\nof possible artifacts due to the instrument response functions. Despite of the fact that the two\ninstruments also allowed for the measurement of the state of polarization of the transmitted or\nreflected light~\\cite{Yoo2017}, this paper focuses on the angular distribution in the far field of the intensity\ntransmitted through the sample regardless of its polarization.\n\n\nThe integral optical properties, haze and gloss, were obtained by the use of a \n\\textit{hazemeter} (BYK Gardner Haze-gard plus) for measurements in transmission and a\n\\textit{glossmeter} (Enrichsen -- Pico Glossemaster Model 500) for measurements in reflection.\n\nBeing a goniospectrophotometer device, OMS4 consists of the sample holder and two\narms where one of the arms have a set of light sources installed and the other a photomultiplicator detector. The\nsample holder and detector arm can be moved automatically with the help of one and two\nprecise motors, respectively. This allows to scan the whole angular region around the sample and thus,\nto measure the angular intensity distributions of the reflected or transmitted light, at any angle of incidence in the\nrange of $\\theta_i\\in[\\ang{0}; \\ang{85}]$.\n\nIn this study OMS4 was used in transmission mode to  measure the angular distribution of the transmitted intensity; the angular resolution was \\ang{0.5} around the specular direction. Measurements were performed with three coherent laser sources~(RGB) and an incoherent Xenon lamp light with or without color filters. The bidirectional\ntransmittance distribution function~(BTDF)~\\cite{Bartell1981} of the samples was collected for\nthe polar angles of incidence $\\theta_i=\\ang{0}$, \\ang{10}, \\ang{30} and \\ang{60}. A related function, the differential transmission coefficient~(DTC)~\\cite{Hetland}, is obtained by multiplying the BTDF by the cosine of the polar angle of transmission~[$\\cos\\theta_t$].\nThe contour plots of the DTC, obtained in this way from data measured by OMS4, were plotted with the SPEOS software package produced by OPTIS.\n\n\n\\smallskip\nThe main difference between the goniospectrophotometer and the multimodal\npolarimetric microscope is the absence of moving parts in the latter system. The multimodal\nmicroscope can be operated in two imaging modes, real plane and Fourier (or conjugate\nspace) plane imaging modes. In real plane imaging mode the microscope produces images of the studied\nsample, while in Fourier imaging mode the images correspond to the angular distribution of\nlight transmitted or reflected by the sample. The optical configuration of the multimodal\nmicroscope is sketched in Fig.~\\ref{Fig:3}. The instrument was coupled to a laser emitting green light\nat a wavelength of \\SI{533}{nm} with a spectral width of less than \\SI{2}{nm}. Speckle effects due to the\ncoherence of the laser were minimized using a vibrating rough membrane (Laser Speckle\nreducer from Optotune) just in front of the laser source. The microscope was mounted in\nthe transmission configuration; the sample was located between two identical microscope\nobjectives (one for imaging and another one for illumination). The microscope objectives can be\nselected to have different magnifications; $50\\times$, $20\\times$, $10\\times$, and $5\\times$\ndepending on the required resolution and a numerical aperture.\n\n\n\n\n\\begin{figure}[tbhp]\n  \\begin{center}\n    \\centering\n    \\includegraphics[width=0.85\\columnwidth]{Figure_2}\n    \\caption{Schematic illustration of the multimodal (Mueller) microscope in the\n      transmission configuration. The positions of the conjugate images corresponding to the back-focal\n      planes~(BFP) of the two objectives, as well as the conjugate planes of the sample in the\n      illumination and imaging arm are shown. Also indicated are the positions of the retractable Bertrand lens, the\n      light source, and the detection camera.}\n    \\label{Fig:3}\n  \\end{center}\n\\end{figure}\n\n\n\nThanks to the use of a series of relay lenses, it is possible to create conjugate images of the\nback-focal planes (BFP) of the objectives in both the illumination and imaging parts.\nTherefore, we can insert apertures in the conjugate plane of the BFP of the illuminating\nobjective with different shapes and sizes to simultaneously control the direction and the\nangular aperture of the illuminating beam. Analogously, the insertion of a pinhole or polar mask\nat the conjugate plane of the BFP of the imaging microscope objective, allows controlling the\ndirection and aperture of the detected scattered beam.\n\n\nThe direction of the illuminating beam is defined by the mean polar angle of incidence\n$\\left<\\theta_i\\right> = \\arcsin(D\/f)$.\nHere $f$ is the focal length of the microscope objective and  $D$ the off-axis distance measured from the\ncenter of the pinhole to the optical axis of the microscope. For instance, if a pinhole is placed in the plane conjugated to the illuminating objective BFP,\nand, this same pinhole is shifted to a given distance to the optical axis, then the sample can be\nilluminated with an oblique incidence. When the pinhole is aligned with the microscope\noptical axis, the sample is illuminated at normal incidence.\n\n\n\nMoreover, once the average polar angle $\\left<\\theta_i\\right>$  is known, the divergence (div in radians) of the\nillumination, or alternatively the imaging beam, can be expressed as a function of the\ncorresponding pinhole diameter $\\phi_{\\textrm{pin}}$, the focal length of microscope objective $f$, and the mean\npolar angle according to:\n\\begin{align}\n \\textrm{div}\n  &=\n    \\frac{\\phi_{\\textrm{pin}}}{f \\cos \\left<\\theta_i\\right>}.\n  \\label{eq:6}\n\\end{align}\nThe relay lens system also provides a conjugate of the object plane (the sample) in both; the\nillumination and the imaging arms, therefore, the use of pinholes or polar masks in those\nplanes, helps to define the shape and size of the illuminated and imaged area of the sample,\nor, in other words, the field of view (FOV). The insertion of a Bertrand lens in the optical\npath of the microscope allows to easily switching between the real and the Fourier imaging\nmodes~\\cite{Kurvits2015}.\n\n\n\\section{Results and discussions}\n\\label{Sec:Results}\n\nFirst in this section we are concerned with angle-resolved measurements for both the regular and the random arrays of micropillars and the discussion of the features that such data show. Later we address the integral optical properties of the samples, like haze and gloss. This will be done by direct measurements of haze, but also by calculations based on the angle-resolved measurements that we performed.\n\n\n\n\\subsection{Angle-resolved measurements}\n\\label{SubSec:3B}\n\nIn standard scatterometry measurements, such as BTDF or DTC measurements, the direction of illumination\nand detection are both selected by moving the goniometric arms on which the source and the\ndetector are mounted, respectively. In the multimodal microscope, however, the control of the\ndirection of the beam in both the illumination and the imaging arm is obtained by the use of pinholes\nplaced at different positions in the conjugate planes~(BFP) of the microscope objective as\npreviously discussed. These intrinsic differences in how the measurements are performed\nwith these two setups make a comparison of the obtained data very interesting.\n\n\n\nFigure~\\ref{Fig:5}  presents contour plots of the angular distribution of the normalized DTCs obtained for a sample of a hexagonal array of micropillars and measured by either the goniospectrophotometer[Figs.~\\ref{Fig:5}(a)--(b)] or the microscope [Fig.~\\ref{Fig:5}(c)]. The normalization was done with respect to the maximum value of the angular dependent DTC, which in our case, was found in the direction of specular transmission.\n\nWe first start by discussing the measurements performed with the  goniospectrophotometer. In the outer brown region of Figs.~\\ref{Fig:5}(a) and ~\\ref{Fig:5}(b) no measurements were performed since either the detector arm covered for the source (around $\\phi_t=\\ang{0}$ in  Fig.~\\ref{Fig:5}(a)) or the angular region being inaccessible to the detector due to the physical dimensions of the support on which the setup is mounted (around $\\phi_t=\\ang{270}$ in Figs.~\\ref{Fig:5}(a) and \\ref{Fig:5}(b)). The specular direction of transmission in Fig.~\\ref{Fig:5}, and in the preceding experimental results to be presented, is at $(\\theta_t, \\phi_t)=(\\theta_i,\\phi_i-\\ang{180})=(\\theta_i,\\ang{0})$. The sample consisted of cylindrical pillars of diameter $d=\\SI{10}{\\micro\\meter}$ and the lattice constant was $a=\\SI{30}{\\micro\\meter}$~[$\\rho=\\SI{10}{\\percent}$]. The angles of incidence assumed in obtaining the results in Fig.~\\ref{Fig:5}(a) were $(\\theta_i,\\phi_i)=(\\ang{0},\\ang{180})$ while in Figs.~\\ref{Fig:5}(b)--(c) the angles of incidence were $(\\theta_i,\\phi_i)=(\\ang{30},\\ang{180})$. In obtaining the results in\nFigs.~\\ref{Fig:5}(a)--(b) the illuminating source consisted of a Xenon lamp to which  a \\SI{10}{nm}-wide spectral filter centered at \\SI{535}{nm} was applied; a laser source of wavelength $\\lambda=\\SI{533}{nm}$ was used to obtain the results presented in Fig.~\\ref{Fig:5}(c). All the transmitted light, independent of polarization, was detected. It is challenging to accurately align the micro-patterned sample in the macroscopic setup so therefore the azimuthal angle of incidence may show slight deviations from $\\phi_i=\\ang{180}$. It should be mentioned that for the  case of regular arrays of micropillars we for all experiments tried to align the samples so that the plane of incidence contains the lattice vector $\\vec{a}_1$. \n\n\n\n\n\\begin{figure}[tbhp]\n  \\begin{center}\n    \\centering\n    \\includegraphics[width=0.8\\columnwidth]{Figure_3}\n    \\caption{\n      The angular distribution of the DTCs,  normalized by their maximum values, and measured with\n      (a)~a goniospectrophotometer and (b)~a multimodal microscope in the Fourier plane imaging mode.\n      In both cases, the polar angle of incidence was $\\theta_i=\\ang{30}$ and the sample consisted of a hexagonal array of cylindrical micropillars\n      of diameter $d=\\SI{10}{\\micro\\meter}$, height $h=\\SI{10}{\\micro\\meter}$, and the lattice constant was $a= \\SI{30}{\\micro\\meter}$.\n      The measurements were performed at wavelengths (a)~\\SI{535}{nm} and (b)~\\SI{533}{nm}. In panel~(b) the angular aperture of the\n      illuminating beam was \\ang{10}. The angular distribution of the measured DTCs contain three main features (as marked in each of the panels):\n      (1)~a specular peak and diffraction orders; (2)~a diffuse ring; and (3)~concentric patterns.\n      The inset in panel~(a) shows the details around the specular direction of an angular width of $\\pm\\ang{20}$. The regions of polar angles of transmission over which the measurements were performed were $\\theta_t\\leq\\ang{85}$~[Figs.~\\ref{Fig:5}(a)--(b)] and $\\theta_t\\leq\\ang{45}$~[Fig.~\\ref{Fig:5}(c)].}\n    \\label{Fig:5}\n  \\end{center}\n\\end{figure}\n\n\n\nSeveral interesting features should be observed from the results presented in Fig.~\\ref{Fig:5}. First, specular\npeaks of high transmitted intensity are observed in the measurements at $(\\theta_t,\\phi_t)=(\\theta_i, \\ang{0})$,\nand the transmitted intensities drop off away from this direction.\n\nSecond, the measurements have sufficient angular resolution to allow for the observation of the dense pattern of propagating diffractive orders; this is most apparent from Fig.~\\ref{Fig:5}(a) and the region marked~(1) in Fig.~\\ref{Fig:5}(b) where the diffraction orders appears like small dots.\nThe positions of the propagating diffractive orders are determined by the grating equation which states that the lateral wavevector of transmission is given by\n\\begin{align}\n  \\pvec{q}^{(m)} = \\pvec{k}+\\vec{G}_m,\n  \\label{eq:grating_equation}  \n\\end{align}\nwhere $\\vec{G}_m=m_1\\vec{b}_1+m_2\\vec{b}_2$ is a vector defined in terms of the primitive lattice vectors $\\vec{b}_i$  of the reciprocal lattice, and $m=\\{m_1,m_2\\}$ denotes a set of two integers~[$m_i\\in\\mathbb{Z}$] defining a diffractive order. The primitive lattice vectors $\\vec{b}_j$ are obtained from the relations $\\vec{a}_i\\cdot \\vec{b}_j= 2\\pi \\delta_{ij}$. For a hexagonal array of lattice vectors $\\vec{a}_i$ defined in Sec.~\\ref{Sec:Methods}.\\ref{Sec:samples}, we obtain the primitive lattice vectors  $\\vec{b}_1=(2\\pi\/a)[\\vecUnit{x}+\\vecUnit{y}\/\\sqrt{3}]$ and $\\vec{b}_2=(2\\pi\/a)[2 \\vecUnit{y}\/\\sqrt{3}]$.\nThe  wavevector $\\pvec{q}^{(m)}$ of the diffractive order characterized by $m$ and the angles $(\\theta_t^{(m)},\\phi_t^{(m)})$ is defined in terms of the angles of transmission as $\\pvec{q}=(\\omega\/c)\\sin\\theta_t(\\cos\\phi_t,\\sin\\phi_t,0)$ with $(\\theta_t,\\phi_t)=(\\theta_t^{(m)},\\phi_t^{(m)})$ where  $\\omega\/c=2\\pi\/\\lambda$ is the vacuum wave number. The wavevector $\\pvec{k}$ of the incident light is defined in a similar manner but in terms of the angles of incidence $(\\theta_i,\\phi_i-\\ang{180})$. \nThe polar angles of transmission $\\theta_t^{(m)}$ for the diffractive order characterized by $m$ is therefore obtained from the relation $q_\\parallel^{(m)}=(\\omega\/c)\\sin\\theta_t^{(m)}$ and the corresponding azimuthal angle of transmission from the orientation of the unit vector $\\pvecUnit{q}^{(m)}$. \nIn this way we calculated the angular positions of the various diffractive orders indicated in Fig.~\\ref{Fig:5}(a) as black dots; this figure displays a good agreement between the measured and the theoretically predicted angular positions of the diffractive orders.    \n\n\n\n\nThird, and probably most unexpected and interesting, are the additional complex angular patterns that are visible in the DTC for non-normal incidence~[Figs.~\\ref{Fig:5}(b)--(c)] and which are further away from the specular directions. These features are marked~(2) and (3) in Fig.~\\ref{Fig:5}(b). The first of these features, refers to  the \\textit{circular structure} of high transmitted intensity seen in this figure. In the following we will simply refer to it as a ``halo''. The circular halo is centered at the direction of normal transmission~[$\\theta_t=\\ang{0}$]  and it contains the direction of specular transmission $(\\theta_t,\\phi_t)=(\\theta_i,\\ang{0})$. This means that the angular position of the halo is defined by the equation $\\theta_t=\\theta_i$ (which is also the  angular radius of the circular structure). This has the consequence that the halo is predicted to disappear, or coincide with the specular, for light that is incident normally onto the micropillar array. \nThat this is indeed the case, can be observed from Fig.~\\ref{Fig:5}(a), where the measured data do not show any apparent signs of a halo. Further discussion and details about the halo will be provided in Sec.~\\ref{Sec:Results}.\\ref{SubSec:3B1}.\n\n\nThe features marked~(3) in Fig.~\\ref{Fig:5}(b) refer to the ``intensity oscillations'', or \\textit{fringes}, observed in the angular distribution of the DTC  in the angular region around the specular direction that also is outside the halo. As will be discussed in greater detail in Sec.~\\ref{Sec:Results}.\\ref{SubSec:3B3}, these fringes belong to two distinct classes of \\textit{concentric patterns}: (i)~those circular fringes that are concentric to the specular direction of transmission and (ii) those  patterns that are concentric to the normal direction of transmission $(\\theta_t,\\phi_t)=(\\ang{0},\\ang{0})$ [the ``origin'']. The former class of fringes are, for instance, readily observed within a \\ang{10} cone around the specular direction of transmission in Figs.~\\ref{Fig:5}(a)--(b), while the latter class is particularly visible for larger polar angles of transmission Fig.~\\ref{Fig:5}(a).\n\n\\smallskip\nWe now turn to the measurement performed by the multimodal microscope. Figure~\\ref{Fig:5}(c) presents the result for the angular distribution of the normalized DTC obtained in this way when light was incident at the polar angle of incidence $\\theta_i = \\ang{30}$ on a hexagonal array of micropillars of the same kind as used to produce the results in Figs.~\\ref{Fig:5}(a)--(b).\nThe microscope measurement was performed for the range of polar angles of transmission $\\theta_t\\leq \\ang{45}$ and all azimuthal angles of transmission $\\phi_t$ with no aperture restriction imposed in the imaging arm.  Moreover, the wavelength of the incident light was $\\lambda = \\SI{533}{nm}$. This is \\SI{2}{nm} less than the wavelength used to perform the measurements with the goniospectrophotometer, but we believe that this minor difference in wavelength will not cause any significant difference in the obtained results. The four concentric dashed circles seen in Fig.~\\ref{Fig:5}(c) indicate the polar angles of transmission $\\theta_t=\\ang{10}$, \\ang{20}, \\ang{30} and \\ang{40} (from inner to outer). The white circular area in this figure represents the region around the specular direction.\n\n\nThe angular aperture, $\\Theta$, or in other words, the maximum polar angle that can be measured by the multimodal microscope is $\\sim\\ang{45}$. This value is given by the numerical aperture~(NA) of the objective of the microscope used, which in our case was identical to the  magnification $50\\times$ and an NA of \\num{0.85}. In this case the minimum available thickness of the glass substrate on which the cylinders were deposited was \\SI{1}{mm}. In consequence, using objectives with higher NA and thereby working distance much smaller than \\SI{1}{mm}, was not possible in this study.\n\n\nThe angular dependence of the normalized DTC measured with the multimodal microscope is, for the same angles of incidence, \nsimilar to the same quantity  measured with the goniospectrophotometer.\nAn additional analogy between the images taken with the goniospectrophotometer\nand the multimodal microscope is the fact that the diffracted orders are also visible in the\nimage taken with the multimodal microscope as an ensemble of regularly spaced spots (light\nblue) clearly seen on a dark blue background.\nIn the image taken with the goniospectrophotometer the intensity oscillations that are due to scattering are easily seen to be located for polar angles of transmission  $\\theta_t >\\theta_i$ (on the right of the specular spot). Unfortunately, in the image taken by the multimodal microscope, this angular region of high contrast falls outside the measured area because the polar angle of the incident beam is close to the maximum aperture accepted by the microscope objective used for the measurements.\n\n\n\n\n\n\n\n\\subsubsection{Diffraction orders due to the regular array of pillars}\n\\label{SubSec:3B1}\n\nNow we will more closely inspect the intensities and positions of some of the propagating diffractive orders that the hexagonal arrays of micropillars give rise to. Such results will in part provide information on the quality and consistency of the measurements. The results reported in Fig.~\\ref{Fig:5} where obtained using narrow band sources. Therefore, to facilitate a more direct comparison of the measured results to those predicted from the grating equation, Eq.~\\eqref{eq:grating_equation}, and to study the dependence on the wavelength of the incident light, we performed measurements in the plane of incidence by the use of a laser source of wavelength $\\lambda$ in vacuum.\nFigure~\\ref{Fig:6}(a) presents the dependence of the out-of-plane transmitted intensity measured with the goniospectrophotometer for hexagonal arrays defined by three values of the lattice constant $a$ for normal incidence [$(\\theta_i,\\phi_i)=(\\ang{0},\\ang{0})$] and wavelength $\\lambda=\\SI{513}{nm}$. The angular positions of the diffractive peaks are in good agreement with the predictions from the grating equation~\\eqref{eq:grating_equation} indicated by the black vertical dashed lines (for $m=\\{0,m_2\\}$ with $m_2=0,\\pm 1$) in the figure. Furthermore, the gray shaded region represents the $\\theta_t\\leq\\ang{2.5}$ used in the definition of haze.\nAlso good agreement is obtained between the measured data for $a=\\SI{30}{\\micro\\meter}$ and the result obtained from standard diffraction theory when the polar angle of incidence is changed~[Fig.~\\ref{Fig:6}(b)] or wavelength of the incident light is changed~[Fig.~\\ref{Fig:6}(c)]. The latter results presented in these figures as black dashed lines are obtained on the basis of Eq.~\\eqref{eq:grating_equation}.\nBased on the results in Fig.~\\ref{Fig:6} [and Fig.~\\ref{Fig:5}(a)] we conclude that our angular dependent measurements are able to resolve well the densely packed diffractive orders of the regular arrays give rise to; at least this was the case for the values of the lattice constant $a\\leq \\SI{80}{\\micro\\meter}$ that we considered.\n\n\n\\begin{figure}[tbhp]\n  \\begin{center}\n    \\centering\n\t\t\\includegraphics[width=0.99\\columnwidth]{Figure_4}\n        \\caption{The out-of-plane dependence of the DTCs measured by the goniospectrophotometer for hexagonal arrays of micropillars ($d=\\SI{10}{\\micro\\meter}$) illuminated by a laser source of wavelength $\\lambda$. \n          (a) The angular dependence of the out-of-plane DTCs for a set of three values of the lattice constants $a$ for $\\theta_i=\\ang{0}$ and $\\lambda=\\SI{513}{nm}$;\n          the dependence of the polar angle of transmission $\\theta_t^{(m)}$ for $m=\\{0,m_2\\}$ (out-of-plane) obtained experimentally (filled symbols) as a function of (b)~the polar angle of incidence $\\theta_i$ for $\\lambda=\\SI{513}{nm}$; or   (c)~the wavelength $\\lambda$ for normal incidence [$\\theta_i =\\ang{0}$]. In panels~(b) and (c) the lattice constant was $a=\\SI{30}{\\micro\\meter}$ and $m_2=0,\\pm 1$.\n          The plane of incident was chosen so that the lattice vectors $\\vec{a}_1$ lies in this plane.\n      The dashed black lines represent the theoretic values for the polar angle of diffraction $\\theta_t^{(m)}$ obtained on the basis of Eq.~\\protect\\eqref{eq:grating_equation}. The shaded gray areas in panel~(a) represent the regions for which $\\theta_t\\leq \\ang{2.5}$. } \n    \\label{Fig:6}\n  \\end{center}\n\\end{figure}\n    \n\\subsubsection{The diffuse ring or halo: impact of the polar angle of incidence}\n\n\nNext we turn to a discussion of the physical origin and the properties of the halo that is so distinctly present in Fig.~\\ref{Fig:5}. To this end, we first investigate if the halo is exclusive to the regular arrays of micropillars or if it also is present in the light transmitted through random arrays of micropillars of similar surface densities. Second, we study how the intensity at the position of the halo $\\theta_t=\\theta_i$ varies with azimuthal angle when we change the polar angle of incidence $\\theta_i$. Figure~\\ref{Fig:8} presents contour plots for the angular distribution of the DTCs, measured with the goniospectrophotometer, and normalized by their maximum values for a set of polar angles of incidence. The samples were patterned by either a random array of micropillars  or a hexagonal array of micropillars. All the  micropillars were assumed to be identical and characterized by the diameter $d=\\SI{10}{\\micro\\meter}$. Both samples were produced to have a surface coverage of about \\SI{10}{\\percent} which for the an hexagonal array corresponds to the lattice constant $a=\\SI{30}{\\micro\\meter}$. The source used to illuminate these samples was light from a Xenon lamp, filtered at the center wavelength $\\lambda=\\SI{535}{nm}$ by a window of \\SI{10}{nm} spectral width, that was unpolarized. The subplots of Fig.~\\ref{Fig:8} correspond to the polar angles of incidence $\\theta_i=\\ang{10}$, \\ang{30} and \\ang{60} and in all cases  the azimuthal angle of incidence was $\\phi_i=\\ang{180}$~(top-down in Fig.~\\ref{Fig:8}). As expected, the measured data show a reflection symmetry with respect to the plane of incidence. Therefore, for reasons of convenience, we have combined the presentation of the results for the random and regular arrays for the same surface coverage. This is done in such a way that the upper halves of each of the subplots in Fig.~\\ref{Fig:8} [$\\ang{0}<\\phi_t<\\ang{180}$] represents the normalized DTCs for the random arrays, while the lower halves [$\\ang{180}<\\phi_t<\\ang{360}$] present the corresponding results for the regular array. The various insets in Fig.~\\ref{Fig:8} present the details in an angular region around the direction of specular transmission. The first striking observation to be made from the results presented in Fig.~\\ref{Fig:8} is how similar the angular intensity distributions for the random and the regular arrays of micropillars are. Of course, the transmitted intensity distributions for the random array do not display diffractive orders as is the case for the intensity distributions for the regular array. Hence, it is the intensity envelopes of the latter data sets that are similar to the corresponding intensity distributions obtained for the random array. \n\nBefore further discussing the several interesting features that can be observed in the measurements reported in Fig.~\\ref{Fig:8}, we present additional measurements obtained by the multimodal microscope in Fig.~\\ref{Fig:9} for the same random array used in obtaining the results presented in Fig.~\\ref{Fig:8}.  In particular, Fig.~\\ref{Fig:9} shows results for polar angles of incidence $\\theta_t=\\ang{0}$, \\ang{10}, \\ang{20} and \\ang{30} and without any angular restriction in the\ncollection arm of the microscope [\\textit{i.e.} $\\theta_t\\leq\\ang{45}$]. Again one finds that the intensity patterns measured with the microscope agree rather well with the corresponding  results obtained with the goniospectrophotometer.\nIt should be remarked that, located at the lower right edges of Figs.~\\ref{Fig:9}(a)--(c), one can see a few irregular spots~(in yellow)  These features we believe to be due to  contamination present on the surfaces of the optical elements of the microscope and they are only visible when the intensity measurement requires an extremely high dynamic range. These irregular features are therefore artifacts and must not be considered as part of the light scattered by the sample.\n\nThe results presented in Figs.~\\ref{Fig:8} and \\ref{Fig:9} show explicitly that halos are present in the angular distribution of  the transmitted intensities for \\textit{both} regular and random arrays of micropillars if $\\theta_i\\neq \\ang{0}$. Furthermore, for both array types we find that the polar angle of transmission defining the halo is related to the polar angle of incidence by the relation $\\theta_t=\\theta_i$, which for our geometry, also is the polar angle of the specular direction of transmission. These results suggest that the presence of the halo is related to individual micropillars and their cylindrical shape rather than to how they are arranged on the surface of the substrate.\n\n\\begin{figure}[tbhp]\n  \\begin{center}\n    \\centering\n    \\includegraphics[width=0.75\\columnwidth]{Figure_5}\n    \\caption{The angular dependence of the DTCs for the polar angles of incidence (a)~$\\theta_i=\\ang{10}$, (b)~\\ang{30} and (c)~\\ang{60} measured with the  goniospectrophotometer and normalized by their maximum values (found in the specular direction). The insets zoom in on $\\pm\\ang{15}$ angular regions around the specular directions. The samples consisted of a random array of micropillars~(upper halfs) or a hexagonal regular array of micropillars~(lower halfs). All micropilars were characterized by a diameter and a height of $d=\\SI{10}{\\micro\\meter}$ and $h=\\SI{10}{\\micro\\meter}$, respectively. The surface coverage of the two arrays were approximately \\SI{10}{\\percent} which for the regular array corresponds to the lattice constant of $a=\\SI{30}{\\micro\\meter}$. In the case of the regular array, one aimed for the plane of incidence to be aligned with one of the lattice vectors $\\vec{a}_i$ ($i=1,2$). The source of the incident light was a Xenon lamp filtered around the center wavelength $\\lambda=\\SI{535}{nm}$ by a window of width \\SI{10}{nm}. The dashed grid circles are placed at multiples of $\\theta_t=\\ang{10}$.} \n    \\label{Fig:8}\n  \\end{center}\n\\end{figure}\n\n\n\n\n\n\\smallskip\nThe origin of the halo can in fact be understood within the framework of either the extended Mie theory for non-spherical particles~\\cite{Cohen1982} or the Debye series approach~\\cite{Xu2010}. According to the later formalism, the origin of the halo can be attributed to rays which have been directly transmitted \nthrough the microsized cylinders (like in an optical fiber), or which have been directly reflected (or scattered) by the outer surface of the cylinders.\nA detailed analysis of the halo and its origin will be presented in a separate publication using polarization dependent measurements. This study will be based on polarization sensitive measurements and it concludes that the halo is a consequence of reflection and\/or transmission of light by \\textit{individual} cylinders, and not due to, for instance, multiple reflections or the excitation of leaky guided modes in the glass slide (substrate).\n\n\n\\begin{figure}[tbhp]\n  \\begin{center}\n    \\centering\n    \\includegraphics[width=0.99\\columnwidth]{Figure_6}\n    \\caption{The far-field distribution of the normalized total intensity transmitted\n      through a glass substrate patterned with a random array of micropillars of a  surface coverage of \\SI{10}{\\percent}. \n      The measurements were performed by the multimodal microscope in the in Fourier imaging mode.\n      The polar angle of incidence of the illuminating beam was assumed to be \n      (a) $\\theta_i=\\ang{0}$; (b) \\ang{10}; (c) \\ang{20}; and (d) \\ang{30}.\n      The angular aperture of the illumination beam was set to \\ang{10} in all cases and the measurements were performed for the wavelength $\\lambda=\\SI{533}{nm}$.}\n    \\label{Fig:9}\n  \\end{center}\n\\end{figure}\n\n\n\n  \n\n\n\\subsubsection{Concentric circular fringes}\n\\label{SubSec:3B3}\n\nDuring the discussion of the results presented in  Figs.~\\ref{Fig:5}(a)--(b), we observed two classes of concentric circular intensity patterns; \\textit{class~1 fringes} are concentric about the direction defined by $\\theta_t=\\ang{0}$ while \\textit{class~2 fringes} are centered around the direction of specular transmission $(\\theta_t,\\phi_t)=(\\theta_i,\\ang{0})$. The azimuthally symmetric circular fringes that are centered at $\\theta_t=\\ang{0}$ are readily observed in Fig.~\\ref{Fig:10}(a) for sufficiently large values of $\\theta_t$; these are the class~1 fringes for this configuration. In particular what is presented in Fig.~\\ref{Fig:10}(a) are the angle-resolved DTCs for normal incidence obtained for two square arrays of micropillars where the micropillars of the first had diameter  $d=\\SI{40}{\\micro\\meter}$~(upper half)  and the second $d=\\SI{20}{\\micro\\meter}$~(lower half). The lattice constants were rather different for the two arrays and defined by $a=2d$. In both cases the heights of the micropillars  were $h=\\SI{10}{\\micro\\meter}$. The surface coverage of square lattices is given by $\\rho =(\\pi\/4)(d\/a)^2$ and hence the two square arrays had the same surface coverage~[$\\rho=\\pi\/16$]. A careful inspection and comparison of the results in the upper and lower halves of Fig.~\\ref{Fig:10}(a) reveals that the (class~1) fringes for the two samples are rather similar even if the size of the  micropillars and the lattice constants were different for the two samples. Furthermore, when the illumination is oblique, the azimuthal symmetry of these fringes is lost, as seen in Fig.~\\ref{Fig:8}, for instance, but the fringes remain centered at $\\theta_t=\\ang{0}$.It should be noted that class~1 fringes are also present in the intensity of the light transmitted through random arrays of micropillars~[Fig.~\\ref{Fig:8}; upper halves]. In particular, for normal and oblique incidence, for random and regular arrays of micropillars, and for different sizes of micropillars, we find that the polar angle separation between two consecutive maxima of the fringes is of the order \\ang{10}.\n\n\nThese results seem to rule out a specific size of the mircropillars, or the sample being periodic or random, as the main reason for the fringes pattern that we observe. Instead we believe that the origin of the class~1 fringes in the transmitted intensities can be attributed to guiding of light inside the sample. To support this interpretation we conducted an additional experiment, in which we remeasured the angle-resolved DTC for normal incidence for the sample used to produce the results in Fig.~\\ref{Fig:5}~[hexagonal array of micropillars defined by $d=\\SI{10}{\\micro\\meter}$ and $a=\\SI{30}{\\micro\\meter}$]. However, in this additional experiment, the front and back sides of the sample were covered by a piece of black paper with the hole in the center each, where a hole of \\SI{3}{cm} diameter was aligned with the incident beam on each side of sample. The diameter of the hole was chosen to be larger than the full width of the incident beam in order to allow the transmission of the direct beam, but, at the same time, partially block the light presumably partially guided inside the sample. By partially we mean that light is not perfectly confined inside the glass substrate as it would be in an ideal waveguide. The guided light modes in the glass are converted to radiative modes because the faces of the substrate are neither infinite nor perfectly smooth. Roughness and micropillars contribute to convert guided modes to radiative ones. The result for the angular distribution of the DTCs, with and without the black cover paper (on both the front and back side), are presented in Fig.~\\ref{Fig:10}(b) as the upper half and lower halves, respectively. A comparison of these two data sets show clearly that the class~1 fringes vanish, or at least are significantly suppressed, when the sample has the black front and back covers. This finding we take as a direct confirmation that guiding of light in the sample is what causes the class~1 circular fringes.   \n\n\n\n\n\\smallskip\nAdditional fringes, which are of another type than those we just discussed, are observed in the intensity transmitted through regular or random arrays of micropillars that are concentric about the direction of specular transmission. For instance, in the insets to Figs~\\ref{Fig:8}(a) and \\ref{Fig:10}(a), showing the details around the specular direction of transmission, they are seen for smaller values of $\\theta_t-\\theta_i$ (and $\\phi_t-\\phi_i-\\ang{180}$), and these fringes are examples of the class~2 fringes. Note that such fringes are also seen in Fig.~\\ref{Fig:5}(b). The class~2 fringes are in the measured data superimposed on the class~1 fringes so that it can be challenging to distinguish them in certain cases. However, the frequency of the class~2 fringes is typically found to be significantly higher than the frequency for the class~1 fringes. The class~2 fringes do depend on the size of the micropillars which contrasts what we found for the class~1 fringes. For instance, the upper and lower halves of Fig.~\\ref{Fig:10}(a) compare DTCs for regular arrays of micropillars of different sizes (and lattice constants); the diameters of the micropillars were $d$=\\SI{20}{\\micro\\meter} and $d$=\\SI{40}{\\micro\\meter}, respectively. From the inset to this figure it is found that the polar angle separation between consecutive fringes close to the specular direction is smallest for the array consisting of micropillars of the largest diameter. Furthermore, the class~2 fringes, like their class~1 counterparts, can be observed for both regular and random arrays of micropillars. In Fig.~\\ref{Fig:8}(b), the class~2 fringes are observed clearly as oscillations along the halo for both the random and regular array, and the angular distance between them are of the same order for both cases. These results we take as indications that the class~2 fringes are related to the size of the micropillars, not to how they are organized along the surface of the substrate.\n\nThe results for the class~2 fringes for normal incidence presented in Figs.~\\ref{Fig:10}(a)--(b) we rationalize in the following way. The normally incident light of wavelength $\\lambda$ is assumed to couple into the micropillars of diameter $d\\sim\\num{E1}\\lambda$. This guided light will be radiated into the glass slide by the open-ended circular waveguide giving rise to an Airy like diffraction pattern predicted by Fraunhofer diffraction~\\cite{BornWolf}. Taking a circular aperture, for simplicity, the\nexpression for the normalized transmitted intensity distribution of the diffracted light reads~\\cite{BornWolf}\n\\begin{align}\n  \\bar{I}(\\theta_t)\n  &=\n    \\left(\n    \\frac{ 2 \\, \\mathtt{J}_1\\!\\!\\left(\\pi\\frac{d}{\\lambda}\\sin\\theta_t \\right)\n    }{\n    \\pi\\frac{d}{\\lambda}\\sin\\theta_t\n    }\n    \\right)^2,\n  \\label{eq:4}\n\\end{align}\nwhere $\\mathtt{J}_1$ denotes the Bessel function of the first kind and order one, and $d$ denotes the diameter of the aperture that we will set equal the diameter of the micropillars~\\cite{BornWolf}. Such normalized intensity distributions are shown on Fig.~\\ref{Fig:10}(c) for diameter $d=\\SI{10}{\\micro\\meter}$, \\SI{20}{\\micro\\meter} and \\SI{40}{\\micro\\meter}, respectively. The frequency of the oscillations observed in the transmitted intensities in the region around the specular direction of transmission are clearly different for the two samples considered in Fig.~\\ref{Fig:10}(a), and the trend that one finds, is in agreement with the prediction of Eq.~\\eqref{eq:4} [see also Fig.~\\ref{Fig:10}(c)].  This demonstrates the high sensitivity of the angular position and intensity of the oscillations to the size of the cylinders, which is in good agreement with the predictions made on the basis of the Fraunhofer diffraction formalism. A direct comparison of the measurements and the Airy patterns is not straightforward for samples with a regular array of pillars, since the Airy pattern is modulated by the presence of diffraction orders.\n\n\n\n\\begin{figure}[tbhp]\n  \\begin{center}\n    \\centering\n    \\includegraphics[width=0.85\\columnwidth]{Figure_7}\n    \\caption{Angle-resolved DTCs for (a)~square or (b)~hexagonal arrays of supported micropillars obtained for normal incidence~[$\\theta_i=\\ang{0}$]. \n      The illumination was done with a Xenon lamp filtered at the center wavelength $\\lambda=\\SI{535}{nm}$ by a window of width \\SI{10}{nm}.\n      (a)~The diameters of the micropillars and the lattice constants of the square arrays were  $d=\\SI{40}{\\micro\\meter}$ and $a=\\SI{80}{\\micro\\meter}$ (upper half); and  \n      $d=\\SI{20}{\\micro\\meter}$ and $a=\\SI{40}{\\micro\\meter}$~(lower half). (b) An hexagonal array of micropillars defined by  $d=\\SI{10}{\\micro\\meter}$ and $a=\\SI{30}{\\micro\\meter}$ measured with~(upper half) and without~(lower half) a black cover on both front and back sides. Each cover had a SI{3}{cm} hole in diameter that was big enough to not interact with the incident beam, and was aligned with the incident beam. (c) Airy patterns from Eq.~\\eqref{eq:4} for circular apertures of diameter\n      \\SI{10}{\\micro\\meter}, \\SI{20}{\\micro\\meter} and \\SI{40}{\\micro\\meter}, respectively.}\n   \n    \\label{Fig:10}\n  \\end{center}\n\\end{figure}\n\n\\subsection{Haze and gloss}\n\\label{Sec:Haze}\n\n\nTwo of the most commonly used  integral optical measurements are haze and gloss. \nAccording to the two standards, ISO 14782:1999~\\cite{ISO1} and ASTM D1003-13~\\cite{ASTM1}, haze is defined as the percentage of\ntransmitted intensity, passing through a specimen, which deviates from the specular direction of transmission by  more\nthan 0.044 rad (\\ang{2.5})~\\cite{Simonsen2009}. Similarly, gloss is defined as the total intensity scattered inside a small angular region about the specular direction normalized by the intensity that is scattered by a standard sample; this ratio defines the ``gloss unit'' scale. According to the standards\nISO~2813:2014~\\cite{ISO2} and ASTM~D523-14~\\cite{ASTM2}, gloss can be measured at three different polar angles of incidence: $\\theta_i=\\ang{20}$, \\ang{60} and \\ang{80}~\\cite{Simonsen2005}.\n\n\nWe will now discuss the haze and gloss values that can be obtained for our supported regular and random arrays of micropillars. The gloss measurements that we report were performed in reflection for a polar angle of incidence of $\\theta_i=\\ang{20}$, while haze was measured in transmission for normal incidence~[$\\theta_i=\\ang{0}$].\nFigure~\\ref{Fig:4} presents the experimental values obtained for haze and gloss~(filled symbols) as functions of the surface coverage of the supported arrays by the use a hazemeter and a glossmeter. These results were obtained by keeping the diameter of the pillars constant at $d=\\SI{10}{\\micro\\meter}$ and changing the lattice constant of the hexagonal array between $a=\\SI{20}{\\micro\\meter}$ and \\SI{80}{\\micro\\meter}.\nWe also performed measurements of haze and gloss for some samples of random arrays of micropillars [open symbols in Fig.~\\ref{Fig:4}], and only minor differences  were found between values of these quantities obtained for regular and random arrays of the same surface coverage. From the results presented in Fig.~\\ref{Fig:4} it is observed that the overall trend is that haze (in transmission) is an increasing (and approximately linear) function of the surface coverage while gloss decreases as \nfunction of the same quantity. The increase in haze with surface coverage indicates an increase in the amount of light transmitted away from the specular direction by more than \\ang{2.5}. This observation is consistent with the decreasing level of measured gloss for the same samples. It is tempting to interpret this observation as a decrease in the specular component of the transmitted intensity with increasing surface coverage, while, at the same time, the diffuse component increases.\n\n\n\\begin{figure}[tbhp]\n  \\begin{center}\n    \\centering\n    \\includegraphics[width=0.99\\columnwidth]{Figure_8}\n    \\caption{Measured haze and gloss values for hexagonal arrays of micropillars~(filled symbols) or random arrays of micropillars~(open symbols). The gloss values were measured with the glossmeter~(Enrichsen -- Pico Glossemaster Model 500) in reflection at $\\theta_i=\\ang{20}$. The haze values were obtained by a hazemeter~(BYK Gardner Haze-gard plus) in transmission at $\\theta_i=\\ang{0}$. The diameter and height of all micropillars were both \\SI{10}{\\micro\\meter}.}\n    \\label{Fig:4}\n  \\end{center}\n\\end{figure}\n\n\n\nWhen the angular dependency  of the DTC is integrated over the full solid angle of transmission~[$\\mathrm{d}\\Omega_t=\\sin\\theta_t\\,\\mathrm{d}\\theta_t\\mathrm{d}\\phi_t$], the transmittance of the sample is obtained~\\cite{Hetland}. To calculate the haze of a sample from the angular distribution of the DTC measured for a given angle of incidence, one proceeds in the following way. First one performs a solid angle integration of the DTC over an angular region around the specular direction of transmission $(\\theta_t,\\phi_t)=(\\theta_i,\\phi_i-\\ang{180})$ defined by $|\\theta_t -\\theta_i| \\leq \\Delta\\theta_t$. For given angles of incidence, the haze of the sample is calculated by first dividing the result obtained in this way by the transmittance and then subtracting the resulting ratio from unity~(see Ref.~\\cite{Simonsen2009}).\nWe have chosen  $\\Delta\\theta_t=\\ang{2.5}$ to be consistent with the standard, and what is assumed in the construction of the hazemeter. \n\n \nFigure~\\ref{Fig:7} compares the haze values calculated in this way from the angle-resolved DTC measurements with the values obtained by direct haze measurements performed on the same samples of hexagonal arrays in transmission and at normal incidence; in such calculations, the missing data points were set to zero. One finds good agreement between haze values measured directly and values calculated from the measured angle-resolved DTC data. This testifies to the consistency of the angle-resolved measurements and their normalization. For instance, the haze values calculated from the angle-resolved DTC data are \\SI{18}{\\percent} for lattice constant a=\\SI{20}{\\micro\\meter} (or surface coverage $\\rho$=\\SI{23}{\\percent}); \\SI{9}{\\percent} for a=\\SI{30}{\\micro\\meter} [$\\rho$=\\SI{10}{\\percent}]; and \\SI{2}{\\percent} for a=\\SI{60}{\\micro\\meter} [$\\rho$=\\SI{3}{\\percent}]. These values should be compared to the corresponding measured haze values for the same samples which are \\SI{20}{\\percent}, \\SI{8}{\\percent} and \\SI{4}{\\percent}, respectively. An increase of the lattice constant $a$, or equivalently, a decrease of the surface coverage $\\rho$, cause more of the diffractive orders to end up inside a cone of angular width $\\Delta\\theta_t$ about the specular direction, and hence, the value of haze to drop. Yet, transmission efficiencies of individual diffraction orders are naively expected to decay with increasing lattice constant and increasing order. Therefore, for sufficiently large lattice constant, a further increase of it will only marginally affect the resulting haze value. However, for smaller lattice constants, for which only a few diffractive orders fall inside $\\Delta \\theta_t < \\ang{2.5}$, this is no longer the case. Therefore, from haze values measured with a hazemeter alone, we are not able to distinguish a regular array from a random array if the surface coverage is sufficiently large. For reasons of comparison, Fig.~\\ref{Fig:7} also reports results for the calculations assuming $\\Delta\\theta_t=\\ang{1}$ a value suggested as more realistic in a recent study on the angular width of specular beams~\\cite{Leloup2016}. As expected, when using this value for $\\Delta\\theta_t$, the calculation procedure results in values that are higher than the haze values for the same sample. However, the interesting observation is not that one gets larger values, but how much larger the obtained values are. For small values of the surface coverage, or larger lattice constants, the difference between the results obtained when using these two values for  $\\Delta\\theta_t$ in the calculation of haze are not very dramatic. However, for the larger values of the surface coverage the differences increase. \n\n\\begin{figure}[tbhp]\n  \\begin{center}\n    \\centering\n    \\includegraphics[width=0.95\\columnwidth]{Figure_9}\n    \\caption{Comparison of the haze values for hexagonal arrays obtained with the hazemeter (direct measurements) and those calculated from angular resolved DTC data as functions of the surface coverage. The DTC data used in obtaining these results were measured at normal incidence by the use of the goniospectrophotometer. The measurement configuration was identical (accept for the angles of incidence) to what was used in obtaining the results in Fig.~\\ref{Fig:5}(a). The way that haze was calculated from such data is described in the main text. The value of the polar angular interval  $\\Delta\\theta_t$  assumed in such calculations are given in the legend. It is noted that the value $\\Delta\\theta_t=\\ang{2.5}$ corresponds to the norm of haze measurements. The diameter and height of all micropillars were both \\SI{10}{\\micro\\meter}.}\n    \\label{Fig:7}\n  \\end{center}\n\\end{figure}\n\n\\smallskip\nWhen the visual aspect of an object is to be taken into account, the particularities of the human eye, rather than those of a artificial detector, must be considered. For instance the angular resolution of the human eye is about \\ang{0.03}~\\cite{Zettler1976}.\nIf haze is intended to quantify the fraction of transmitted intensity that is transmitted away from the specular direction (of transmission), the use of the value $\\Delta \\theta_t=\\ang{2.5}$, which is perfect for a number of industrial needs is far too large when it comes to discuss human visual perception of the optical response of 1D or 2D gratings.\n\n For the sake of illustration, let us restrict ourselves to a one-dimensional grating at normal incidence for which the polar angle of the propagating diffractive orders in transmission is given by $\\sin\\theta_m=m(\\lambda\/a)$ with $m$ and an integer ($m\\in\\mathbb{Z}$) and $m=0$ corresponds to specular transmission. For this system, the number of propagating diffracted orders in transmission is (red curve in Fig.~\\ref{Fig:1}) $N = 2 \\left \\lfloor{\\frac{a}{\\lambda}}\\right \\rfloor  + 1$,\nwhere $\\left \\lfloor{x}\\right \\rfloor$ denotes the floor function of $x$ which returns the greatest integer less than or equal to its argument $x$. At normal incidence the two first diffractive orders are symmetric about the specular direction and correspond to the polar angles of transmissions $\\pm\\theta_1$.\nFigure~\\ref{Fig:1} illustrates the variation of the angle of the first diffracted order $\\theta_1$ under the assumption of normal incidence [$\\theta_i=\\ang{0}$]. The green solid line in this figure corresponds to an illumination  wavelength of $\\lambda=\\SI{500}{nm}$ while the green area around this line  represents the variation due to the whole visible range of wavelengths from \\SIrange{380}{780}{nm}. Moreover, the red solid curve in Fig.~\\ref{Fig:1} illustrates the total number of diffraction orders in such system.\n\nFor a lattice constant of about a=\\SI{9}{\\micro\\meter} and an illuminating  wavelength  of $\\lambda=\\SI{380}{nm}$, the first diffracted order will enter into the ``specular'' area of the haze measurement. Starting from this wavelength (and higher) the haze measurements, as a measure of the fraction of transmitted intensity away from the specular direction,  are biased (unshaded region of Fig.~\\ref{Fig:1}). For lattice constants all the way up to $a=\\SI{1}{mm}$ a human observer will be able to distinguish specular transmission from the first diffraction order. These results hints towards a not optimal definition of haze for gratings of long  periods compared to the wavelength of visible light. According to our discussion, when the visual aspect of gratings with large periods matters, a haze definition making use of smaller angular spread around the specular direction than the actual 2.5\u00b0 defined in the norms, would provide objective haze values which would be in agreement with the subjective experience of the human eye.\n\n\\begin{figure}[tbhp]\n  \\begin{center}\n    \\centering\n    \\includegraphics[width=0.9\\columnwidth]{Figure_10}\n    \\caption{Normally incident light~[$\\theta_i=\\ang{0}$] diffracted through a surface consisting of a one-dimensional grating of lattice constant $a$. The green line shows the angle of diffraction $\\theta_1$ of the first diffraction order [$m=1$], while the red line represents the total number of propagating diffracted orders $N$, both obtained by assuming the wavelength $\\lambda=\\SI{500}{nm}$ for the incident light. The corresponding green and red shaded areas (around the solid lines of the same color) represent  the variations of these two quantities due to the wavelength of the incident light varying over the visible range \\num{380}--\\SI{780}{nm}. The blue horizontal line corresponds to the smallest diffraction angle~[\\ang{2.5}] for which the diffracted light in transmission contributes to haze. Haze measurements for lattice constants smaller than approximately \\SI{9}{\\micro\\meter} receive contribution from all higher order diffractive orders for which $m\\neq 0$. However, for larger lattice constants not \\textrm{all} such higher orders will contribute. \n      For comparison, the horizontal red dashed line corresponds the limit of angular resolution of the human eye.\n    } \n    \\label{Fig:1}\n  \\end{center}\n\\end{figure}\n\n\n\n\n\n\n\n\n\n\n\n\\section{Conclusions}\n\\label{Sec:Concusions}\n\nWe report experimental results for the angle-resolved transmitted intensity measurements for a set of regular or random arrays of dielectric micropillars in the low coverage limit that are supported by thin index matched glass slides. The regular arrays were characterized lattice constants in the range from $a=\\SI{20}{\\micro\\meter}$ to \\SI{80}{\\micro\\meter}. The measurements were performed by either a goniospectrophotometer or a multimodal imaging polarimetric microscope and the two sets of measurements gave comparable results. On the basis of experimental data obtained in this way, it is demonstrated that for identical micropillars, the mean differential transmission coefficients for the random arrays agree well with the envelope of the same quantity for the regular array under the assumption that the surface coverage is the same. Moreover, we find that the angle-resolved measurements display unique diffractive features that are due to properties of single micropillars and not to how they are organized along the surface. Finally we perform a comparison of direct measurements of haze in transmission for our structured samples with what can can calculated from the angle-resolved transmitted intensity measurements. Good agreement between the two types of results are found which testifies to the accuracy of the angle-resolved measurements that we report. However, we find that for larger surface coverage, haze values alone can not be used to distinguish regular and random arrays of micropillars.  \n\n\n\\bigskip\n\\textbf{Acknowledgments}\nWe thank Gael Obein, Guillaume Ged, Sebastien Noygues and Emmanuel Garre for valuable discussions.\n\nFrench National Research Agency (ANR-15-CHIN-0003; IDEX Paris-Saclay ANR-11-IDEX-0003-02)\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\chapter*{Acknowledgements}\nI would like to thank my supervisor, Prof. Meir Feder, for his devoted mentoring throughout my research. Without Meir's enthusiasm, curiosity and endless support, this thesis could not have been what it is now. His depth as an information theorist, his broad-mindedness as a scientist and his openheartedness inspired me all along the way. I am grateful for having given the opportunity to walk this path with him.\n\nI would also like to thank Or Ordentlich and Yuval Lomnitz for their interest and insights, which helped me tackle some of the most challenging problems in my research.\n\n\\cleardoublepage\n\n\\begin{abstract}\nIn this study we consider rateless coding over discrete memoryless channels (DMC) with feedback. Unlike traditional fixed-rate codes, in rateless codes each codeword in infinitely long, and the decoding time depends on the confidence level of the decoder. Using rateless codes along with sequential decoding, and allowing a fixed probability of error at the decoder, we obtain results for several communication scenarios. The results shown here are non-asymptotic, in the sense that the size of the message set is finite.\n\nFirst we consider the transmission of equiprobable messages using rateless codes over a DMC, where the decoder knows the channel law. We obtain an achievable rate for a fixed error probability and a finite message set. We show that as the message set size grows, the achievable rate approaches the optimum rate for this setting. We then consider the \\emph{universal} case, in which the channel law is unknown to the decoder. We introduce a novel decoder that uses a mixture probability assignment instead of the unknown channel law, and obtain an achievable rate for this case.\n\nFinally, we extend the scope for more advanced settings. We use different flavors of the rateless coding scheme for joint source-channel coding, coding with side-information and a combination of the two with universal coding, which yields a communication scheme that does not require any information on the source, the channel, or the amount the side information at the receiver.\n\\end{abstract}\n\n\\cleardoublepage\n\n\\pagestyle{plain}\n\\pagenumbering{roman}\n\n\\tableofcontents\n\\singlespace\n\\listoffigures\n\n\\cleardoublepage\n\n\\baselineskip0.7cm\n\n\\pagestyle{plain}\n\\pagenumbering{arabic}\n\n\\chapter{Introduction}\n\\section{Background} \\label{sec:Background}\nIn traditional channel coding schemes the code rate, which is the ratio between the lengths of the encoder's input and output blocks, is an integral part of the code definition. If one of $M$ messages is to be encoded at rate $R$, then the corresponding codeword has length $n=(\\log M)\/R$. Provided that the rate is chosen properly, the error probability decreases as $M$ grows. The capacity of the channel $C$ is defined as the largest value of $R$ for which the error probability can vanish.\n\nAn alternative approach to fixed-rate channel coding is \\emph{rateless codes}. In this approach, we abandon the basic assumption of a fixed coding rate, and allow the codeword length, and hence also the rate, to depend on the channel conditions. When the encoder wants to send a certain message, it starts transmitting symbols from an infinite-length codeword. The decoder receives the symbols that passed through the channel and when it is confident enough about the message, it makes a decision. Perhaps the simplest example of a rateless code is the following (see e.g. \\cite[Ch.3]{Nadav} or \\cite[Ch.7]{Cover}). Suppose that we have a binary erasure channel (BEC) with erasure probability $\\delta$. Suppose also that noiseless feedback exists, i.e. the encoder at time instant $n$ has an access to the outputs of the channel at times $1,\\ldots,n-1$. We use a simple repetition coding, in which each binary symbol is retransmitted until the decoder receives an unerased symbol. Since the erasure probability is $\\delta$, the expected number of transmissions until an unerased symbol is received is $1\/(1-\\delta)$. This transmission time implies a rate of $1-\\delta$, which is exactly the capacity of the binary erasure channel. This simple setting exemplifies some important concepts of rateless codes. First, the transmission time is not fixed, but rather is a random variable (geometrically-distributed in the above case); second, when the length of the transmission is set dynamically, the error probability may be controllable. In this case the transmission is only terminated once the decoder \\emph{knows} what message has been transmitted, so the error probability of this coding scheme is zero; third, the code design is rate-independent. In fact, this code can be used for any binary erasure channel; fourth, the continuity of the transmission requires feedback to the encoder. Indeed, as we shall see in this thesis, when rateless codes are used for point-to-point communication, some form of feedback, which can be limited to decision feedback, must exist to enable continuity. However, rateless codes are also invaluable for other settings such as multicast or broadcast communications, in which the existence of feedback is not explicitly required. Shulman \\cite{Nadav} introduced the concept of \\emph{Static Broadcasting}, in which the transmitter sends a message to multiple users, and each user remains connected until it retrieved enough symbols to make a confident decision. This scheme does not require feedback; the user remains online only as much as it needs, and the rate is determined according to the time the user spent online.\n\nIn this thesis we assume a discrete memoryless channel (DMC) with feedback, and devise rateless coding schemes which allow a small (but fixed) error probability $\\epsilon$. We investigate the dependence between the rate, the error probability and the size of the message set. The entire analysis is done for a finite message set, and we show that when the size of the message set is taken to infinity, our results agree with classic results from coding theory. We also investigate the rate of convergence to these results. We start by building a simple rateless coding scheme for a known channel. The motivation for this method is due to Wald's analysis (see \\cite[Ch.3]{Wald}), where he demonstrated that the Sequential Probability Ratio Test (SPRT) performs like the most powerful test in terms of error probabilities, while using about half the samples on average.\n\nBuilding on the rateless coding scheme devised for the case of known channel, we obtain a \\emph{universal} channel coding scheme that does not require channel knowledge at the receiver. Unlike previous results on universal decoding, the results here are non-asymptotic and are valid for an arbitrary message set size. We then extend the coding scheme to joint source-channel coding, and show that optimal rate is achievable even when the encoder is uninformed on the source statistics. Next, we use a rateless coding scheme for source coding with side information at the receiver and show that the Slepian-Wolf rate for this scenario is achievable even when the encoder is unaware of the amount of side information. Finally, we show how to combine the above-mentioned techniques with universal source coding, to obtain a scheme that can operate when the statistics of both the source and the channel are unknown, potentially using side information that is obscure to the encoder.\n\nOur work follows previous results discovered by Shulman \\cite{Nadav} for the universal case, where the decoder is ignorant of the channel law. In particular, a sequential version of the maximal mutual information (MMI) decoder \\cite{CsiszarKorner} is used for universal channel decoding and joint-source channel coding, including the case of side information at the decoder. However, the results in \\cite{Nadav} are asymptotic in the size of the message set, while the analysis here is made for a fixed size of the message set. For the case of known channel, the decoder used here can be viewed as the counterpart of the sequential MMI decoder that uses the channel law rather than the empirical mutual information. This scheme has been originally introduced by Polyanskiy in \\cite{PPV}, where it is proven to achieve the best variable-length coding rate. While the analysis in \\cite{PPV} concentrates on finding the best achievable size of the message set with a constraint on the average decoding time, in this paper we seek the optimum decoding time for a fixed size of the message set. More importantly, the analysis introduced here is then extended naturally to apply for the case of unknown channel, where we use a novel universal decoder, as well as for joint source-channel coding with and without side information at the receiver.\n\n\\section{Thesis Outline} \\label{sec:Outline}\nThe rest of the thesis is organized as follows. In Chapter \\ref{ch:DefinitionsAndNotation} we define rateless codes and provide related definitions and notation. In Chapter \\ref{ch:PreviousResults} we survey previous results related to universal communication and rateless codes. In Chapter \\ref{ch:KnownChannel} we treat the case of known channel, for which we obtain an achievable rate using rateless codes. We also prove a converse theorem showing that this rate is asymptotically optimal, and we analyze the rate of convergence. The case of unknown channel is examined in Chapter \\ref{ch:UnknownChannel}, where we develop a universal decoder and analyze its performance for a general DMC. In Chapter \\ref{ch:Extensions} we extend the coding scheme for the case of message sets with non-equiprobable messages, and we also show how rateless coding can be used for problems with side information. Chapter \\ref{ch:Summary} concludes the thesis.\n\n\\chapter{Definitions and Notation}\n\\label{ch:DefinitionsAndNotation}\nThroughout this thesis, random variables will be denoted by capital letters and their realizations by the corresponding lowercase letters. Vectors are denoted by superscript that indicate their length, for instance $X^n = [X_1,\\ldots,X_n]$. Unless otherwise stated, all logarithms are taken to the base of 2. We focus on communication over a discrete memoryless channel (DMC) characterized by a transition probability $p(y|x)$, $x \\in \\mathcal{X} , y \\in \\mathcal{Y}$, where $\\mathcal{X}$ and $\\mathcal{Y}$ are the input and output alphabets of the channel, respectively. With a slight abuse of notation, we use $p(\\cdot|\\cdot)$ also to denote the joint transition probabilities of the channel, thus $p(y^n|x^n) = \\prod_{i=1}^n p(y_i|x_i)$. The capacity of the channel (in bits per channel use) in conventionally defined as $C = \\max_{q(x)}I(X;Y)$, where $I(X;Y)$ is the mutual information between the input of the channel and its output, and the maximization is over all channel input priors $q(x)$. If $|\\mathcal{X}| = |\\mathcal{Y}|$, and $p(y|x)=1$ if $x=y$ and $p(y|x)=0$ otherwise, then the channel is said to be noiseless, and in that case $C = \\log |\\mathcal{X}|$. We also assume that a noiseless feedback exists from the receiver to the transmitter.\n\nA rateless code has the following elements:\n\\begin{enumerate}\n\\item Message set $\\mathcal{W}$ containing $M$ messages. Without the loss of generality we assume that $\\mathcal{W}=\\{1,\\ldots,M\\}$, with corresponding probabilities $\\pi(1),\\ldots,\\pi(M)$. Occasionally, we define $K=\\log M$ as the number of bits conveyed in a message.\n\\item Codebook $\\mathcal{C} = \\{\\mathbf{c}_i\\}_{i=1}^M$, where each codeword $\\mathbf{c}_i \\in \\mathcal{X}^\\infty$ is generated by drawing i.i.d. symbols according to a prior $q(x), x\\in\\mathcal{X}$.\n\\item Set of encoding functions $f_n:\\mathcal{W} \\rightarrow \\mathcal{X}$, $n \\geq 1$.\n\\item Set of decoding function $g_n:\\mathcal{Y}^n \\rightarrow \\mathcal{W} \\cup \\{0\\}$, $n \\geq 1$.\n\\end{enumerate}\nUnlike conventional codes, for which the rate is a fundamental property, the above description does not specify a working rate--hence the term \\emph{rateless code}. To encode a message $w \\in \\mathcal{W}$, the encoder starts transmitting the codeword $\\mathbf{c}_w$ over the channel. Upon receiving each channel output, the decoder can either decide on one of the messages $\\hat{w}$ or decide to wait for further channel outputs, returning `$0$'. Through feedback, the decoder's decision is known to the encoder, which correspondingly decides whether to transmit further symbols from $\\mathbf{c}_w$ or to proceed to the next message. We note that two different forms of feedback can be assumed here: channel feedback and decision feedback. In channel feedback, the encoder at time instance $t$ observes $Y^{t-1}$, the channel outputs so far, and by imitating the decoder's operation it becomes aware of any decision made by the decoder. In decision feedback, the encoder is only informed that a decision has been made, and it can proceed to the next message. While channel feedback requires no intervention from the decoder in the feedback process, it essentially assumes that the feedback channel has the same bandwidth as the main channel. Decision feedback, in contrast, requires only one feedback bit per symbol.\n\nWe conclude this section with a few definitions required for the next sections.\n\\begin{definition} \\label{def:StoppingTime}\nA \\emph{stopping time} $T$ of a rateless code is a random variable defined as\n\\begin{equation} \\label{eq:StoppingTimeDef}\n    T = \\min\\{n: g_n(Y^n) \\neq 0\\}\n\\end{equation}\n\\end{definition}\n\\begin{definition} \\label{def:EffectiveRate}\nAn \\emph{effective rate} $R$ of a rateless code is defined as\n\\begin{equation} \\label{eq:EffectiveRateDef}\n    R = \\frac{\\log M}{\\E\\{T\\}}\n\\end{equation}\nwhere $\\E\\{T\\}=\\E_q \\{ \\E_p \\{T\\}\\}$, i.e. the averaging is done over all possible codebooks and channel realizations.\n\\end{definition}\nUsing the definition of stopping time, we can define the error event as the case in which the decoder stops, deciding on the wrong message. The error event conditioned on a particular message is defined as\n\\begin{equation} \\label{eq:EmDef}\n    E_w = \\{\\hat{W} \\neq w \\ | \\ W = w \\}\n\\end{equation}\nwhere $\\hat{W}=g_{_T}(Y^T)$.\nThe average error probability for the entire message set is therefore\n\\begin{equation} \\label{eq:PeDef}\n    P_e = \\sum_{w=1}^M \\pi(w) \\cdot \\Pr\\{E_w\\}\n\\end{equation}\n\\begin{definition}\nFor a given DMC, an $(R,M,\\epsilon)$-code is a rateless code with effective rate $R$, containing $M$ messages and error probability $P_e \\leq \\epsilon$.\n\\end{definition}\n\n\\chapter{Previous Results}\n\\label{ch:PreviousResults}\nAs noted, the rateless coding scheme is a special case of communication over a channel with feedback. Shannon \\cite{ShannonZEC} proved that the capacity of a DMC is not increased by adding feedback. However, adding feedback \\emph{can} increase the zero-error capacity of the channel. In his well known paper, Burnashev \\cite{Burnashev} investigated the effect of feedback in communication over a DMC by analyzing the error exponent of such channel. Introducing the notion of random transmission time, Burnashev obtained a bound on the mean transmission time for a fixed error probability, from which he derived the error exponent\\footnote{Referred to as \\emph{reliability function}.} for a DMC with feedback. He also proved a converse theorem showing that the expected transmission time, hence also the error exponent, are asymptotically optimal. (That is, they coincide with the results of the converse theorem as the size of the message set grows to infinity.) The main result of \\cite{Burnashev} is the following theorem.\n\\begin{untheorem}[Burnashev \\cite{Burnashev}]\nThe optimum error exponent for a DMC with noiseless feedback is\n\\begin{equation}\\label{eq:BurnasheErrorExp}\n    \\lim_{M \\to \\infty} -\\frac{1}{\\E\\{T\\}} \\log P_e = C_1\\left(1 - \\frac{R}{C} \\right), \\qquad 0 \\leq R \\leq C\n\\end{equation}\nwhere $T$ is the transmission time, $R$ is defined in \\eqref{eq:EffectiveRateDef} and\n\\begin{equation}\\label{eq:C1Def}\n    C_1 \\triangleq \\max_{(x,x') \\in \\mathcal{X} \\times \\mathcal{X}} D\\left(p(\\cdot|x)||p(\\cdot|x')\\right)\n\\end{equation}\n\\end{untheorem}\n\nExamining \\eqref{eq:BurnasheErrorExp} we can observe that whenever $R \\geq C$, the error exponent vanishes, which concurs with Shannon's result \\cite{ShannonZEC}. Moreover, whenever the channel has at least two inputs that are completely distinguishable from one another, i.e. $p(y|x)>0$ and $p(y|x')=0$ for some $x,x' \\in \\mathcal{X}$ and $y \\in \\mathcal{Y}$, it holds that $D\\left(p(\\cdot|x)||p(\\cdot|x')\\right) \\to \\infty$ and hence also $C_1 \\to \\infty$ for that channel. Therefore, the error exponent in that case is infinite at \\emph{every} rate below the channel capacity, which implies that the zero-error capacity coincides with the channel capacity $C$.\n\nAlso for the case feedback channels, Shulman \\cite{Nadav} developed a coding scheme providing reliable communication over an unknown channel, without compromising the rate. Introducing the concept of \\emph{static broadcasting}, which is based on random codebook and universal sequential decoder, he demonstrated that it is possible to achieve vanishing error probability at rate that tends to the capacity of the channel as the size of the message set grows indefinitely. Furthermore, Shulman showed that even if the statistics of the information source is unknown to the transmitter, this scheme achieves the optimal decoding length that would have been achieved if the source were compressed by an optimal source-encoder and the channel were known at both ends. More formally, if $K$ information bits of a source $S$ were to be transmitted over an unknown channel $W$, then the average decoding length satisfies\n\\begin{equation}\\label{eq:DecodingLengthNadav}\n    \\lim_{K \\to \\infty} \\frac{\\E\\{T\\}}{K} = \\frac{H(S)}{I(P;W)}\n\\end{equation}\nwhere $P$ is the codebook generation prior and $I(P;W)$ is the mutual information between the input and the output of the channel $W$ when the input is drawn according to distribution $P$.\n\nShulman also used the coding scheme for source-encoding of correlated sources. He demonstrated that using static broadcasting, it is possible to achieve the Slepian-Wolf optimal rate region. Combining all into one communication scheme, the achievable decoding length is\n\\begin{equation}\\label{eq:DecodingLengthNadav}\n    \\lim_{K \\to \\infty} \\frac{\\E\\{T\\}}{K} = \\frac{H(S|Z)}{I(P;W)}\n\\end{equation}\nwhere $Z$ is the side information at the decoder. Shulman's work has been the main inspiration for this research.\n\nFor the case of unknown channel, Tchamkerten and Telatar in \\cite{Telatar} used a rateless coding scheme similar to the one defined in Chapter \\ref{ch:DefinitionsAndNotation}, where the stopping condition is that the mutual information between (at least) one of the codewords and the channel output sequence exceeds a certain time-dependent threshold. The authors proved that this scheme can achieve the capacity of a general DMC.\\footnote{Since no assumption has been made on the capacity-achieving prior, authors only demonstrated that the rate approaches $I(PQ)$, where $P$ is the codebook generation prior and $Q$ is the transition probability of the channel.} Moreover, they demonstrated that for the class of binary symmetric channel with crossover probabilities $L \\in [0,1\/2)$, this coding scheme can achieve Burnashev's exponent at a rate bounded by any fraction of the channel capacity. The latter result is obtained by using a second coding phase, in which the transmitter indicates whether the decoder's decision is correct (an \\emph{Ack\/Nack} phase). Tchamkerten and Telatar also demonstrated that for the class of $Z$ channels with parameter $L \\in [0,1)$, the achievable rate can be arbitrarily close to the channel capacity, while the error exponent is infinite. The latter result also coincides with Burnashev's exponent ($C_1$ in \\eqref{eq:BurnasheErrorExp} is infinite in this case), since error-free communication is attainable for the $Z$ channel.\n\nWe note that all the above-mentioned results were asymptotic in the size of the message set. Recently, Polyanskiy, Poor and Verd{\\'u} in \\cite{PPV} introduced non-asymptotic results for communication over DMC with feedback. Through the use of variable-rate coding and sequential decoding they obtained upper and lower bounds for the maximal message set size for fixed bounds on the error probability and mean decoding length. The authors showed that for an error probability constraint $P_e \\leq \\epsilon$ and mean decoding length constraint $\\E \\{T\\} \\leq \\ell$, the maximal message set size $M^*(\\ell,\\epsilon)$ satisfies\n\\begin{equation}\\label{eq:PolyanskiyUpperLower}\n    \\frac{\\ell C}{1-\\epsilon} - \\log \\ell + O(1) \\leq \\log M^*(\\ell,\\epsilon) \\leq \\frac{\\ell C}{1-\\epsilon} + O(1)\n\\end{equation}\nThe setting of \\cite{PPV}, as well as the coding scheme, is similar to the one defined later in Chapter \\ref{ch:KnownChannel}. However, while in \\cite{PPV} the optimization is on $M$, for fixed $\\epsilon$ and $\\ell$, we fix $\\epsilon$ and $M$ and find the optimum mean decoding length. The analysis is slightly different, but the results of Chapter \\ref{ch:KnownChannel} comply with \\cite{PPV}. The analysis in Chapter \\ref{ch:KnownChannel}, coming next, lays the ground for the derivation of our novel results for the case of unknown channel.\n\n\\chapter{Rateless Coding -- Known Channel}\n\\label{ch:KnownChannel}\n\\section{Sequential Decoder} \\label{sec:SequentialDecoder}\nWe begin by introducing a rateless coding scheme for noisy channels and analyzing its effective rate, under certain constraints on the size of the message set and the error probability. As will be shown in the sequel, the effective rate is closely related to the channel capacity $C$. More precisely, we will show that under the conventional setting, in which the size message set is taken to infinity, the effective rate coincides with the capacity of the channel.\n\nConsider a discrete memoryless source with a set of $M$ equiprobable messages, i.e. $\\pi(i)=1\/M$, $i=1,\\ldots,M$. We use a rateless code as defined in Section \\ref{ch:DefinitionsAndNotation}, where each codeword $\\mathbf{c}_i$, $i=1,\\ldots,M$ is generated by drawing i.i.d. symbols according to $q(x)$, the capacity-achieving prior of the channel. The source of randomness generating the codewords is shared by the encoder and the decoder, so that the codebook in known at both ends. The decoder uses the following decision rule:\n\\begin{equation} \\label{eq:ChannelDecoderLin}\n    g_n(y^n)= \\begin{cases}\n                w, \\ \\prod_{k=1}^n p(c_{w,k}|y_k) \\geq A \\cdot \\prod_{k=1}^n q(c_{w,k}) \\\\\n                0, \\ \\text{if no such $w$ exists}\n              \\end{cases}\n\\end{equation}\nwhere $\\{c_{w,k}\\}_{k=1}^{\\infty}$ are the symbols in $\\mathbf{c}_w$. If the threshold crossing condition in \\eqref{eq:ChannelDecoderLin} is satisfied by more than one codeword, we randomly choose one of them and declare an error. We note here that similar decoders have been proposed by Polyanskiy \\cite{PPV} and Burnashev \\cite[Ch.3]{Burnashev}.\nThe decision rule at \\eqref{eq:ChannelDecoderLin} can be equivalently written as\n\\begin{equation} \\label{eq:ChannelDecoderLog}\n    g_n(y^n)= \\begin{cases}\n                w, \\ z_{w,1}+\\ldots+z_{w,n} \\geq a \\\\\n                0, \\ \\text{if no such $w$ exists}\n              \\end{cases}\n\\end{equation}\nwhere\n\\begin{equation}\n    z_{w,k} = \\log \\frac{p(c_{w,k}|y_k)}{q(c_{w,k})}, \\qquad k=1,\\ldots,n\n\\end{equation}\nand we define $a = \\log A$.\n\nThe above-described coding scheme can be summarized as follows. Having selected a message, the encoder starts transmitting an infinite-length random codeword corresponding to that message. The decoder sequentially receives symbols from this codeword that passed through the channel, and at each time instant $k$ calculates $z_{w,k}$ for $w={1,\\ldots,M}$. It then updates a set of $M$ accumulators, each corresponding to a possible message, and checks whether any of those crossed a prescribed threshold $a$. If neither of the counters crossed the threshold, `$0$' is returned and the decoder waits for the next channel output; if exactly one counter crossed the threshold, the decoder makes a decision; and if more that one threshold crossing occurred, an error is declared. In the two latter cases, the encoder proceeds to the next codeword.\n\nFor the above-described scheme we have the following theorem.\n\\begin{theorem} \\label{Theorem1}\nFor the decoder in \\eqref{eq:ChannelDecoderLog} with $P_e \\leq \\epsilon$, the following effective rate is achievable:\n\\begin{equation}\n    R = \\frac{C}{1+ \\frac{C - \\log \\epsilon}{\\log M}} \\label{eq:AchievableRateChannelDec}\n\\end{equation}\n\\end{theorem}\n\n\\begin{proof}\nSince $T$ is a stopping time of the i.i.d. sequence $Z_1,Z_2,\\ldots$, Wald's equation \\cite{Wald} implies\n\\begin{equation} \\label{eq:ETForWald}\n    \\E\\{T\\} = \\frac{\\E \\{Z_1 + \\ldots + Z_T\\}}{\\E\\{Z\\}},\n\\end{equation}\nwhere $\\E\\{Z\\}$ is the expectation of a single sample $Z_i$. If $X_i$ and $Y_i$ are input and output of the channel, respectively, then by the definition of $Z_i$ we have\n\\begin{equation} \\label{eq:EZForWald}\n    \\E\\{Z\\} = \\E\\{Z_i\\} = \\E \\left\\{\\frac{p(X_i|Y_i)}{q(X_i)}\\right\\} = C.\n\\end{equation}\nFurthermore, since the stopping condition was not fulfilled time instant $T-1$ we have\n\\begin{equation}\n    Z_1 + \\ldots + Z_{T-1} < a\n\\end{equation}\nwhich implies\n\\begin{equation} \\label{eq:SumZForWald}\n    Z_1 + \\ldots + Z_T < a + Z_T\n\\end{equation}\nCombining \\eqref{eq:ETForWald}, \\eqref{eq:EZForWald} and \\eqref{eq:SumZForWald} we obtain\n\\begin{equation} \\label{eq:WaldC}\n    \\E\\{T\\} < \\frac{a+C}{C}.\n\\end{equation}\n\nWe now tune the threshold parameter $a$ to meet the error probability requirement. Suppose that the stopping time of the correct codeword is $T_w$. An error occurs if a competing codeword $\\mathbf{c}_{w'}$, independent of $\\{Y_k\\}_{k=1}^{\\infty}$, crosses the threshold before $\\mathbf{c}_w$ does. Thus,\n\\begin{align}\n    \\Pr \\{E_w\\} &= \\Pr \\left\\{ \\bigcup_{w' \\neq w} \\bigcup_{t=1}^{T_w}\n    \\left\\{ \\frac{\\prod_{k=1}^{t} p(C_{w',k}|Y_k)}{\\prod_{k=1}^{t} q(C_{w',k})} > A \\right\\} \\right\\} \\\\\n                &\\leq (M-1) \\Pr \\left\\{ \\bigcup_{t=1}^{T_w}\n    \\left\\{ \\frac{\\prod_{k=1}^{t} p(X_k|Y_k)}{\\prod_{k=1}^{t} q(X_k)} > A \\right\\} \\right\\} \\label{eq:ErrorProbUB} \\\\\n                &\\leq (M-1) \\Pr \\left\\{ \\bigcup_{t=1}^{\\infty}\n    \\left\\{ \\frac{\\prod_{k=1}^{t} p(X_k|Y_k)}{\\prod_{k=1}^{t} q(X_k)} > A \\right\\} \\right\\} \\label{eq:ErrorProbInf}\n\\end{align}\nwhere \\eqref{eq:ErrorProbUB} follows from the union bound for an arbitrary series $\\{X_k\\}_{k=1}^{\\infty}$ drawn i.i.d. from $q(x)$, independently of $\\{Y_k\\}_{k=1}^{\\infty}$. Note that the bound in \\eqref{eq:ErrorProbInf} represents the probability that a randomly-chosen codeword will exceed the threshold at any time instant. Define a sequence of random variables\n\\begin{equation}\\label{eq:uidef}\n    U_t = \\begin{cases}\n                \\frac{p(X_t|Y_t)}{q(X_t)}, \\ \\prod_{k=1}^{t-1} U_k \\leq A \\\\\n                1, \\ \\text{otherwise}\n              \\end{cases}\n\\end{equation}\nIf at instant $t$ the threshold at \\eqref{eq:ErrorProbInf} is exceeded for the first time, then we have $U_k=p(X_k|Y_k)\/q(X_k)$ for $k=1,\\ldots,t$ and $U_k=1$ for all $k>t$. Therefore, it is easy to see that\n\\begin{equation}\n    \\bigcup_{t=1}^{\\infty}\n    \\left\\{ \\frac{\\prod_{k=1}^{t} p(X_k|Y_k)}{\\prod_{k=1}^{t} q(X_k)} > A \\right\\}\n    \\Leftrightarrow \\prod_{t=1}^{\\infty} U_t > A\n\\end{equation}\nWe can also see that $\\E\\{U_t\\}=1$ for \\emph{all} $t$ because\n\\begin{equation*}\n    \\E \\left\\{ U_t|\\prod_{k=1}^{t-1} U_k > A \\right\\} = 1\n\\end{equation*}\nsince $U_t = 1$ deterministically in this case, and\n\\begin{align}\n    \\E \\left\\{ U_t|\\prod_{k=1}^{t-1} U_k \\leq A \\right\\} &= \\E \\left\\{ \\frac{p(X_t|Y_t)}{q(X_t)} \\right\\} \\\\\n    &= \\E \\left\\{ \\E \\left\\{ \\frac{p(X_t|Y_t)}{q(X_t)}|Y_t \\right\\} \\right\\} \\\\\n    &= \\E \\left\\{ \\sum_{x \\in \\mathcal{X}} \\frac{p(x|Y_t)}{q(x)} \\cdot q(x) \\right\\} \\label{eq:IndependentX} \\\\\n    &= 1\n\\end{align}\nwhere \\eqref{eq:IndependentX} follows since $X_t$ and $Y_t$ are independent. For an arbitrary $N$ we have\n\\begin{align}\\label{eq:ProdU}\n    \\E \\left\\{\\prod_{t=1}^N U_t \\right\\} &= \\E \\left\\{ \\E \\left\\{\\prod_{t=1}^N U_t | \\prod_{t=1}^{N-1} U_t \\right\\} \\right\\} \\\\\n    &= \\E \\{ U_N \\} \\cdot \\E \\left\\{\\prod_{t=1}^{N-1} U_t \\right\\} \\\\\n    &= \\E \\left\\{\\prod_{t=1}^{N-1} U_t \\right\\} = \\ldots = \\E\\{U_1\\} = 1\n\\end{align}\nSince the above holds for all $N$, we also have\n\\begin{equation}\\label{eq:InfProdU}\n    \\E \\left\\{\\prod_{t=1}^\\infty U_t \\right\\} = 1\n\\end{equation}\nReturning to \\eqref{eq:ErrorProbInf}, we get\n\\begin{align}\n   \\Pr \\{E_w\\} &\\leq  (M-1) \\Pr \\left\\{ \\bigcup_{t=1}^{\\infty}\n    \\left\\{ \\frac{\\prod_{k=1}^{t} p(X_k|Y_k)}{\\prod_{k=1}^{t} q(X_k)} > A \\right\\} \\right\\} \\label{eq:BoundErrorProbKnownCh} \\\\\n    &= (M-1) \\Pr \\left\\{ \\prod_{t=1}^{\\infty} U_t > A \\right\\} \\\\\n    &\\leq \\frac{M-1}{A} \\label{eq:Markov}\n\\end{align}\nwhere \\eqref{eq:Markov} follows from \\eqref{eq:InfProdU} and Markov's Inequality.\nSince the above holds for all $w \\in \\mathcal{W}$, we also have\n\\begin{equation}\n    P_e \\leq \\frac{M-1}{A}\n\\end{equation}\n\nBy choosing $a = \\log M - \\log \\epsilon $, or equivalently $A = M\/\\epsilon$, we secure that $P_e < \\epsilon$. Substituting $a$ into \\eqref{eq:WaldC} and using Definition \\ref{def:EffectiveRate}, we obtain \\eqref{eq:AchievableRateChannelDec}.\n\\end{proof}\n\nIt is important to note that the encoding operation is independent of the working rate; the encoder needs to know the channel law only to generate the codebook. However, if the channel is known to belong to a family for which the capacity-achieving prior is known (e.g. the uniform prior for symmetric channel), then the optimal rate can be achieved even when the encoder is uninformed on the channel law. Furthermore, from a practical point of view, using the uniform prior instead of the capacity-achieving prior is known to perform relatively well in many cases. For instance, using a uniform prior in a binary channel will lose at most 6\\% of the capacity (see \\cite[Ch.5]{Nadav}).\n\n\\section{Coding Theorem for Known Channel} \\label{sec:CodingThmKnownChannel}\nWe will now use the coding scheme developed in Section \\ref{sec:SequentialDecoder} to prove the main result for rateless channel coding. For a fixed error probability, we will obtain an achievable rate using rateless codes. Then, we will prove that this rate is within $O(\\log \\log M \/ \\log M)$ from the optimal rate achievable with this error probability. Before we get to the main theorem, we prove the following lemma, which facilitates some refinement in the achievable rate.\n\n\\begin{lemma} \\label{Lemma1}\nSuppose that an $(R,M,\\epsilon)$-code exists for a DMC. Then for any $0<\\alpha<1$, there also exists an $(R',M,\\epsilon')$-code for the same channel, where\n\\begin{eqnarray}\n    R' & = & (1-\\alpha)^{-1}R \\\\\n    \\epsilon' & = & \\alpha + \\epsilon - \\alpha \\epsilon\n\\end{eqnarray}\n\n\\end{lemma}\n\n\\begin{proof}\nTo show that the triplet $(R',M,\\epsilon')$ is achievable, we use the original code with randomized decision-making at the decoder. For each transmitted message, the decoder either terminates the transmission immediately and declares an error, with probability $\\alpha$, or uses the original decision rule. Denote the stopping time of the original decoder and the modified one by $T$ and $T'$, respectively. The expected decision time of the modified decoder is\n\\begin{equation}\n    \\E\\{T'\\} = (1-\\alpha) \\E\\{T\\},\n\\end{equation}\nwhich implies\n\\begin{equation}\n    R' = (1-\\alpha)^{-1} R.\n\\end{equation}\nThe error event in the modified scheme is a union of two non-mutually-exclusive events: error in the original decoder and the event of early termination. The probability of this union is\n\\begin{equation}\n    \\epsilon' = \\alpha + \\epsilon - \\alpha \\epsilon.\n\\end{equation}\nFinally, we note that the number of messages in the codebook remains unchanged---which completes the proof of the lemma.\n\\end{proof}\n\n\\begin{theorem}\nFor rateless codes, the following rate is achievable:\n\\begin{equation} \\label{eq:AchievableRate}\n   R' = \\begin{cases}\n                \\frac{1 - 1\/\\log M}{1+ \\frac{C + \\log \\log M}{\\log M}} \\cdot \\frac{C}{1-\\epsilon} & \\epsilon > 1\/\\log M \\\\\n                \\frac{C}{1+ \\frac{C - \\log \\epsilon}{\\log M}} & \\epsilon \\leq 1\/\\log M \\\\\n              \\end{cases}\n\\end{equation}\n\\end{theorem}\n\nWe note that if $\\epsilon$ is fixed and $M$ is large enough so that $\\epsilon > 1\/\\log M$, the achievable rate has the following asymptotics:\n\\begin{equation} \\label{eq:AchievableRateAsym}\n    R' = \\frac{C}{1-\\epsilon} \\cdot \\left(1 - O \\left( \\frac{\\log \\log M}{\\log M} \\right) \\right)\n\\end{equation}\n\\begin{proof}\nTheorem \\ref{Theorem1} implies that the triplet $(R,M,\\delta)$ is achievable for all $0 < \\delta < 1$, where\n\\begin{equation}\n    R = \\frac{C}{1+ \\frac{C - \\log \\delta}{\\log M}}\n\\end{equation}\nBy Lemma \\ref{Lemma1}, we can also achieve $(R',M,\\delta')$, where\n\\begin{eqnarray}\n    R' & = & \\frac{C}{(1-\\alpha)\\left(1+ \\frac{C - \\log \\delta}{\\log M}\\right)} \\\\\n    \\delta' & = & \\alpha + \\delta - \\alpha \\delta\n\\end{eqnarray}\nfor all $0 < \\alpha < 1$. By choosing\n\\begin{equation}\n    \\alpha = \\frac{\\epsilon - \\delta}{1 - \\delta}\n\\end{equation}\nwe obtain\n\\begin{eqnarray}\n    R' & = & \\frac{1 - \\delta}{1+ \\frac{C - \\log \\delta}{\\log M}} \\cdot \\frac{C}{1-\\epsilon} \\\\\n    \\delta' & = & \\epsilon\n\\end{eqnarray}\nSince the foregoing analysis holds for all $0 < \\delta < \\epsilon$, we can choose $\\delta = \\min\\{\\epsilon, 1\/\\log M\\}$ to obtain \\eqref{eq:AchievableRate}.\n\\end{proof}\n\n\\begin{remark}\nIf $\\epsilon \\leq 1\/ \\log M$, the choice $\\delta = \\epsilon$ implies $\\alpha = 0$, that is, no randomization at the decoder. This result could be anticipated, since the randomized decoder trades rate for reliability: it obtains a better effective rate with some compromise on the error probability. Hence, whenever the error probability constraint is more important than the working rate -- randomization can only worsen matters.\n\\end{remark}\n\n\\section{Error Exponent}\nTheorem 2 in the previous section provides a relation between the working rate and the allowed error probability. We will now investigate this dependency in the regime of low error probability by developing the error exponent induced by this coding scheme. Assuming that a low error probability is required, randomization at the decoder is inapplicable, so \\eqref{eq:AchievableRate} can be rewritten as\n\\begin{equation}\n    - \\frac{R}{\\log M} \\log \\epsilon = C - R - \\frac{CR}{\\log M}\n\\end{equation}\n\nRecall that $R = \\log M \/ \\E\\{T\\}$, so\n\\begin{equation}\n    - \\frac{\\log \\epsilon}{\\E\\{T\\}} = C - R - \\frac{CR}{\\log M} \\triangleq E(R)\n\\end{equation}\n\nWe can see that the error exponent is a \\emph{linear} function of the rate, which is also the case in Burnashev's analysis \\eqref{eq:BurnasheErrorExp} (albeit with a different coefficient). Furthermore, as $M$ grows, the error exponent converges to $C-R$ and the convergence is dominated by a term of order $O(1\/\\log M)$, or $O(1\/K)$. This term can be interpreted as a penalty for using a finite message set.\n\n\\section{Weak Converse}\nIn the previous section we have seen that if we use a codebook with $M$ messages and allow an error probability $P_e \\leq \\epsilon$, then we can achieve an effective rate with the following asymptotics:\n\\begin{equation}\n    R' = \\frac{C}{1-\\epsilon} \\cdot \\left(1 - O \\left( \\frac{\\log \\log M}{\\log M} \\right) \\right)\n\\end{equation}\n\nWe will now prove that under the above constraints on the message set and the error probability, the best achievable rate has the same asymptotics. In other words, the achievable rate at \\eqref{eq:AchievableRate} converges to the optimal rate, and the convergence is dominated by a term of order $O(1\/\\log M)$.\n\n\\begin{theorem}\nGiven a decoder with random \\footnote{Fixed stopping time is a private case of random stopping time, in which $T$ takes only one value.} stopping time $T$, any rate for which the probability of error does not exceed $\\epsilon$ satisfies\n\\begin{equation}\n    R' \\leq \\frac{C}{1-\\epsilon} \\cdot \\left(1 + O \\left( \\frac{1}{\\log M} \\right) \\right).\n\\end{equation}\n\\end{theorem}\n\n\\begin{proof}\nDefine\n\\begin{equation}\n    \\mu(n) = H(W|Y^n) + nC.\n\\end{equation}\nBy \\cite[Lemma 2]{Burnashev}) we have\n\\begin{equation}\n    \\E \\{\\mu(n+1)|Y^n\\} - \\mu(n) = \\E \\{H(W|Y^{n+1})-H(W|Y^n)|Y^n\\} + C \\geq 0\n\\end{equation}\nwhich implies that $\\mu(n)$ is a submartingale with respect to the process $\\{Y_k\\}_{k=1}^{\\infty}$. Therefore we have\n\\begin{align}\n    \\log M &= H(W) = \\mu(0) \\nonumber \\\\\n           &\\leq \\E \\{\\mu(T)\\} \\nonumber \\\\\n           &= \\E \\{H(W|Y^T)\\} + C \\cdot \\E\\{T\\} \\label{eq:SubmartingalIneq}\n\\end{align}\nFurthermore, by \\cite[Lemma 1]{Burnashev} we have\n\\begin{align}\n    \\E\\{H(W|Y^T)\\} &\\leq h \\left(P_e\\right) + P_e \\cdot \\log (M-1) \\nonumber \\\\\n             &< 1 + \\epsilon \\cdot \\log M \\label{eq:Fano}\n\\end{align}\nwhere \\eqref{eq:Fano} follows from the requirement $P_e \\leq \\epsilon$, and from an upper bound on the binary entropy function. Combining \\eqref{eq:SubmartingalIneq} and \\eqref{eq:Fano} we obtain\n\\begin{equation} \\label{eq:BoundLogM}\n    \\log M < 1 + \\epsilon \\cdot \\log M + C \\cdot \\E\\{T\\}\n\\end{equation}\nwhich implies\n\\begin{equation} \\label{eq:RPrimeWithET}\n    R' = \\frac{\\log M}{\\E\\{T\\}} < \\frac{C}{1-\\epsilon} \\cdot \\left(1 + \\frac{1}{C \\cdot \\E\\{T\\}}\\right)\n\\end{equation}\nFurthermore, from \\eqref{eq:BoundLogM} we can see that\n\\begin{equation}\n    C \\cdot \\E\\{T\\} > (1 - \\epsilon) \\cdot \\log M - 1\n\\end{equation}\nand therefore \\eqref{eq:RPrimeWithET} can be replaced by\n\\begin{equation}\n    R' = \\frac{\\log M}{\\E\\{T\\}} \\leq \\frac{C}{1-\\epsilon} \\cdot \\left(1 + O\\left(\\frac{1}{\\log M}\\right)\\right) \\label{eq:UpperBound}\n\\end{equation}\n\\end{proof}\n\n\\begin{remark}\nWhile \\eqref{eq:AchievableRate} approaches \\eqref{eq:UpperBound} for large $M$, the upper bound is not tight for a finite $M$. Note that the converse used here is ``weak'', in that it is based on Fano's inequality, which is known to be loose in many cases. We conjecture that a strong converse can be found, which will be tighter (i.e. closer to \\eqref{eq:AchievableRate}) even in the non-asymptotic realm.\n\\end{remark}\n\n\\begin{remark}\nEquation \\eqref{eq:AchievableRateAsym}, the achievable rate, is essentially equivalent to the left-hand side of \\cite[Eq.18]{PPV}, and equation \\eqref{eq:UpperBound}, the upper bound on the rate, is equivalent to the right-hand side of that equation. Note, however, that the formulation is slightly different: in \\cite{PPV} size of the message set $M$ is optimized with constraint on the maximal transmission time, while here $M$ is fixed and the transmission time is minimized.\n\\end{remark}\n\n\\section{Further Discussions}\n\\subsection{Application for Gaussian Channels}\nWhile the analysis in Sections \\ref{sec:SequentialDecoder} and \\ref{sec:CodingThmKnownChannel} is done for discrete channels, it can be easily extended to memoryless Gaussian channels. Suppose that $X_t$ and $Y_t$ are the input and output of an additive white Gaussian noise channel at time instant $t$, i.e.\n\\begin{equation} \\label{eq:AWGNDef}\n    Y_t = X_t + V_t, \\qquad t=1,2,\\ldots\n\\end{equation}\nwhere $\\{V_t\\}_{t=1}^\\infty$ is a sequence of i.i.d. Gaussian RV's with zero mean and a known variance. The encoding and the decoding processes, as well as the expression for the resulting effective rate, are similar to those of the DMC, where $q(\\cdot)$ is the codebook generation PDF and $p(\\cdot|\\cdot)$ is the transition PDF of the backward channel.\n\nSpecifically, consider the above-described setting where $V_k \\sim N(0,\\theta)$. Suppose that the codebook is Gaussian with power constraint $P$, i.e. $C_{m,k} \\sim N(0,P)$ for all $m,k$. (Here again, $C_{m,k}$ is the $k$-th symbol of the $m$-th codeword.) The decoding rule is given by \\eqref{eq:ChannelDecoderLin}, where\n\\begin{align}\n    p(x|y) &= \\left( 2\\pi \\condvar \\right)^{-1\/2} \\exp \\left\\{ -\\frac{1}{2 \\cdot \\condvar} \\left( x - \\Wiener \\cdot y \\right)^2 \\right\\} \\\\\n    q(x) &= \\left( 2\\pi P \\right)^{-1\/2} \\exp \\left\\{ -\\frac{x^2}{2P} \\right\\}\n\\end{align}\nThe effective rate of the decoder is given in \\eqref{eq:AchievableRateChannelDec}, where\n\\begin{equation}\n    C = \\frac{1}{2} \\log \\left( 1 + \\frac{P}{\\theta}\\right)\n\\end{equation}\n\n\\subsection{Limited Feedback Channel}\nIn the forgoing analysis, we assumed that the feedback channel must be used once per each main channel use. In practice, however, it may be desirable to reduce the amount of data transmitted over the feedback channel. For instance, in the case of broadcasting to multiple users, the upstream channel may have a more stringent bandwidth constraint as it must be accessed by all users. It is therefore interesting to see how lowering the frequency of the feedback affects the performance of the rateless coding scheme. Suppose that we want to use the feedback channel only once per $s$ received symbols. The maximal number of excess symbols transmitted over the main channel (i.e. the number of symbols transmitted after a decoder without feedback limitation would acknowledge the message) is $s-1$, which implies an effective rate of\n\\begin{equation}\\label{eq:RateLimitedFB}\n    R = \\frac{C}{1+ \\frac{(s-1)C - \\log \\epsilon}{\\log M}}\n\\end{equation}\nFrom \\eqref{eq:RateLimitedFB} we see that limiting the feedback frequency has negligible effect if either $s \\ll (-\\log \\epsilon)\/C$ or $s \\ll (\\log M)\/C$. In the former case, the required confidence level is high, and in the latter case the messages are long. That is, in both cases the codewords are long with respect to the capacity of the channel, which implies long transmission time. Therefore, in both cases the excess decoding time is small compared to the entire transmission length, and the effect of the limiting the feedback is negligible.\n\n\\chapter{Rateless Coding -- Unknown Channel}\n\\label{ch:UnknownChannel}\nIn Chapter \\ref{ch:KnownChannel} we assumed that the communication channel, characterized by $p(y|x)$, is known at the receiver end. Assume now, that the underlying channel is unknown to the receiver. The capacity of the channel is known to be achievable in this scenario using sequential versions of the Maximal Mutual Information (MMI) decoder \\cite{Nadav}, \\cite{Telatar}. However, while these schemes provide reliable communication at rate equal to the channel capacity, they assume that the size of the message set $M$ is infinite. In this chapter we try to answer the question whether universal communication is feasible with a finite message set, and if it is, what rates are achievable? As we shall see shortly, it is possible to achieve reliable communication over an unknown channel even when the message set is finite, and we can also bound the rate degradation due to lack of information about the channel law.\n\n\\section{Achievable Rate for an Unknown Channel} \\label{sec:RateUnknownChannel}\nSuppose that we wish to communicate over a DMC with unknown (backward) transition probabilities\n\\begin{equation}\n    \\theta_{ij} = \\Pr\\{X=i|Y=j\\}, \\qquad i = 1,\\ldots,|\\mathcal{X}| \\qquad j = 1,\\ldots,|\\mathcal{Y}|\n\\end{equation} \\label{eq:ThetaParamsDef}\nWe use a coding scheme similar to the one described in Chapter \\ref{ch:KnownChannel} with the following modification. Instead of using the true transition probability $p_{\\tv}(x^t|y^t)$, which is unknown to the decoder, we use a \\emph{universal} probability assignment defined as\n\\begin{equation}\\label{eq:UniversalProb}\n    p_U (x^t|y^t) \\triangleq \\int_{\\Lambda} w(\\tv') p_{\\tv'} (x^t|y^t) d\\tv'\n\\end{equation}\nwhere\n\\begin{equation}\n    \\Lambda = \\left\\{\\tv' \\in [0,1]^{\\XY} \\ | \\ \\sum_{i=1}^{|\\mathcal{X}|} \\theta'_{ij} = 1, \\quad j = 1,\\ldots,|\\mathcal{Y}|\\right\\}\n\\end{equation}\nand the weight function $w(\\cdot)$ is chosen to be Jeffreys Prior \\footnote{This is also a special case of Dirichlet Distribution.}, i.e.\n\\begin{equation} \\label{eq:JeffreysPrior}\n    w(\\tv') = \\frac{1}{\\BXY \\sqrt{\\prod_{i,j} \\theta'_{ij}}}\n\\end{equation}\nwhere\n\\begin{equation} \\label{eq:DefBXY}\n    \\BXY = \\int_{\\Lambda} \\frac{d\\tv'}{\\sqrt{\\prod_{i,j} \\theta_{ij}}}\n\\end{equation}\n\n\\begin{remark}\nWhile the unknown channel is usually characterized by a set of transition probabilities\n\\begin{equation*}\n    \\tilde{\\theta}_{ij} = \\Pr\\{Y=j|X=i\\}, \\qquad i = 1,\\ldots,|\\mathcal{X}| \\qquad j = 1,\\ldots,|\\mathcal{Y}|\n\\end{equation*}\nthe entire derivation here is done for the \\emph{backward} channel parameterization given in \\eqref{eq:ThetaParamsDef}. However, this does not need to bother us since the entire analysis assumes a known input prior $q(x)$, and therefore given $\\{\\tilde{\\theta}_{ij}\\}$, the parameters in \\eqref{eq:ThetaParamsDef} are well-defined. Moreover, the region $\\tilde{\\Lambda}$, induced by $\\{\\tilde{\\theta}_{ij}\\}$ and $q(x)$, is clearly contained in the region $\\Lambda$. Therefore, if a coding scheme is universal with respect to all possible realizations of the backward channel, it is also universal w.r.t. all possible realizations of the forward channel.\n\\end{remark}\n\nThe universal probability assignment implies the following decoding rule, which is the universal counterpart of \\eqref{eq:ChannelDecoderLin}:\n\\begin{equation} \\label{eq:ChannelDecoderUnv}\n    g_n(y^n)= \\begin{cases}\n                w, \\ p_U(\\mathbf{c}_w|y^n) \\geq A \\cdot q(\\mathbf{c}_w) \\\\\n                0, \\ \\text{if no such $w$ exists}\n              \\end{cases}\n\\end{equation}\n\nIn Chapter \\ref{ch:KnownChannel} we used Wald's Identity to bound the expected transmission time, thereby obtaining an effective rate for the sequential decoder. Unfortunately, in the universal case $p_U(\\cdot|\\cdot)$ is not necessarily multiplicative, so $\\log p_U(\\cdot|\\cdot)$ cannot be expressed as the sum of i.i.d. random variables. Therefore, the expected transmission time in the universal case cannot be calculated directly by applying Wald's identity. Nevertheless, as we shall see shortly, we can use the results for the known channel case to obtain an upper bound for the transmission time in the universal case.\n\nThe following lemma shows that given two sequences $x^t$ and $y^t$, the universal metric cannot be too far from the conditional probability assignment that is optimally fitted to $x^t$ and $y^t$.\n\\begin{lemma} \\label{thm:UnvProbLemma}\nFor any two series $x^t$ and $y^t$ we have\n\\begin{equation}\n    \\log \\frac{p_{\\htv} (x^t|y^t)}{p_U (x^t|y^t)} \\leq \\frac{\\left(\\XX-1\\right)\\YY}{2} \\log \\frac{t}{2\\pi} + \\YY \\Lkappa_{\\XX} + \\left( \\frac{\\XX^2 \\YY}{4} + \\frac{\\XY}{2} \\right) \\log e\n\\end{equation}\nwhere\n\\begin{equation} \\label{eq:ThetaOpt}\n    \\htv = \\arg \\max_{\\tv' \\in \\Lambda} p_{\\tv'} (x^t|y^t)\n\\end{equation}\nand we define\n\\begin{equation}\n    \\Lkappa_{\\XX} = \\log \\frac{\\Gamma(1\/2)^{\\XX}}{\\Gamma(\\XX\/2)}\n\\end{equation}\n\\end{lemma}\n\n\\begin{proof}\nNote that\n\\begin{align}\n    p_{\\htv}(x^t|y^t)&= \\max_{\\{\\theta_{i,j}\\}} \\prod_{i,j} \\theta_{i,j}^{N(x^t,y^t;i,j)} \\\\\n             &= \\max_{\\{\\theta_{i,1}\\}} \\prod_i \\theta_{i,1}^{N(x^t,y^t;i,1)} \\cdot \\max_{\\{\\theta_{i,2}\\}} \\prod_i \\theta_{i,2}^{N(x^t,y^t;i,2)} \\cdot \\ldots \\cdot\n             \\max_{\\{\\theta_{i,\\YY}\\}} \\prod_i \\theta_{i,\\YY}^{N(x^t,y^t;i,\\YY)}\n\\end{align}\nwhere\n\\begin{equation} \\label{eq:NxyDef}\n    N(x^t,y^t;i,j) = \\left| \\left\\{k \\ : \\ (x_k,y_k)=(i,j) \\right\\} \\right|\n\\end{equation}\nSince both $w(\\cdot)$ and $p_{\\tv}$ are multiplicative functions, we also have\n\\begin{align}\n    p_U (x^t|y^t) &= \\int_{\\Lambda} w(\\tv') p_{\\tv'} (x^t|y^t) d\\tv' \\\\\n                  &= \\int_{\\tilde{\\Lambda}} w(\\tilde{\\tv}) \\prod_i \\tilde{\\theta}_i^{N(x^t,y^t;i,1)} d\\tilde{\\tv} \\cdot \\int_{\\tilde{\\Lambda}} w(\\tilde{\\tv}) \\prod_i \\tilde{\\theta}_i^{N(x^t,y^t;i,2)} d\\tilde{\\tv} \\cdot \\ldots \\\\\n                  & \\cdot \\int_{\\tilde{\\Lambda}} w(\\tilde{\\tv}) \\prod_i \\tilde{\\theta}_i^{N(x^t,y^t;i,\\YY)} d\\tilde{\\tv}\n\\end{align}\nwhere\n\\begin{equation}\n    \\tilde{\\Lambda} = \\left\\{\\tilde{\\tv} \\in [0,1]^{\\XX} \\ | \\ \\sum_{i=1}^{|\\mathcal{X}|} \\tilde{\\theta}_i = 1, \\right\\}\n\\end{equation}\n\nFrom \\cite[Lemma 1]{Barron} we know that\n\\begin{equation}\\label{eq:BarronsIneq}\n    \\log \\frac{\\max_{\\{\\theta_{i,j}\\}} \\prod_i \\theta_{i,j}^{N(x^t,y^t;i,j)}}{\\int_{\\tilde{\\Lambda}} w(\\tilde{\\tv}) \\prod_i \\tilde{\\theta}_{i,j}^{N(x^t,y^t;i,j)} d\\tilde{\\tv}} \\leq \\frac{\\XX-1}{2} \\log \\frac{t}{2\\pi} + \\Lkappa_{\\XX} + \\left( \\frac{\\XX^2}{4} + \\frac{\\XX}{2} \\right) \\log e\n\\end{equation}\nfor all $j = 1,\\ldots,\\YY$. Thus, we obtain\n\\begin{align}\n    \\log \\frac{p_{\\htv} (x^t|y^t)}{p_U (x^t|y^t)} &= \\log \\prod_j \\frac{\\max_{\\{\\theta_{i,j}\\}} \\prod_i \\theta_{i,j}^{N(x^t,y^t;i,j)}}{\\int_{\\tilde{\\Lambda}} w(\\tilde{\\tv}) \\prod_i \\tilde{\\theta}_{i,j}^{N(x^t,y^t;i,j)} d\\tilde{\\tv}} \\\\\n    &\\leq \\frac{\\left(\\XX-1\\right)\\YY}{2} \\log \\frac{t}{2\\pi} + \\YY \\Lkappa_{\\XX} + \\left( \\frac{\\XX^2 \\YY}{4} + \\frac{\\XY}{2} \\right) \\log e \\\\\n    &=\\frac{\\left(\\XX-1\\right)\\YY}{2} \\log t + \\beta\n\\end{align}\nwhere we define\n\\begin{equation}\\label{eq:BetaDef}\n    \\beta \\triangleq \\YY \\Lkappa_{\\XX} + \\left( \\frac{\\XX^2 \\YY}{4} + \\frac{\\XY}{2} \\right) \\log e - \\frac{\\left(\\XX-1\\right)\\YY}{2} \\log (2\\pi)\n\\end{equation}\n\\end{proof}\n\nWe are now ready to prove the main theorem for rateless coding over an unknown channel.\n\n\\begin{theorem} \\label{thm:UnvRate}\nFor the decoder in \\ref{eq:ChannelDecoderUnv} with $P_e \\leq \\epsilon$, the following effective rate is achievable:\n\\begin{equation}\\label{eq:UnvEffectiveRate}\n    R = \\frac{C \\left( 1 - \\frac{\\hXY}{\\log M \\ln 2} \\right)}{1 + \\frac{C + \\beta - \\log \\epsilon + \\frac{\\XY}{2} \\left( \\log \\log M - \\log C - \\frac{1}{\\ln 2} \\right)}{\\log M}}\n\\end{equation}\n\\end{theorem}\n\n\\begin{proof}\nThe stopping time in the above-described scheme is\n\\begin{equation} \\label{eq:StoppingTimeUnv}\n    T = \\min \\left\\{ t: \\frac{p_U (x^t|y^t)}{\\prod_{k=1}^t q(x_k)} > A \\right\\}\n\\end{equation}\nsince\n\\begin{equation}\n    \\log p_U (x^t|y^t) = \\log p_{\\tv} (x^t|y^t) - \\log \\frac{p_{\\tv} (x^t|y^t)}{p_U (x^t|y^t)}\n\\end{equation}\nwe have\n\\begin{align}\n    T &= \\min \\left\\{ t: \\frac{p_U (x^t|y^t)}{\\prod_{k=1}^t q(x_k)} > A \\right\\} \\\\\n      &= \\min \\left\\{ t: \\log \\frac{ \\prod_{k=1}^t p_{\\tv} (x_k|y_k)}{\\prod_{k=1}^t q(x_k)} > \\log A + \\log \\frac{p_{\\tv} (x^t|y^t)}{p_U (x^t|y^t)} \\right\\} \\\\\n      &\\leq \\min \\left\\{ t: \\log \\frac{ \\prod_{k=1}^t p_{\\tv} (x_k|y_k)}{\\prod_{k=1}^t q(x_k)} > \\log A + \\log \\frac{p_{\\htv} (x^t|y^t)}{p_U (x^t|y^t)} \\right\\} \\label{eq:ThetaOptUse} \\\\\n      &< \\min \\left\\{ t: \\sum_{k=1}^t \\log \\frac{p_{\\tv}(x_k|y_k)}{q(x_k)} > \\log A + \\frac{\\XY}{2} \\log t + \\beta \\right\\} \\label{eq:UnvProbLemmaUse}\n\\end{align}\nwhere \\eqref{eq:ThetaOptUse} follows since $p_{\\htv} (x_k|y_k) \\geq p_{\\tv} (x_k|y_k)$ by definition \\eqref{eq:ThetaOpt} and \\eqref{eq:UnvProbLemmaUse} follows from Lemma \\ref{thm:UnvProbLemma}.\n\nFrom the same considerations as in the proof of Theorem \\ref{Theorem1}, at the stopping time $T$ we necessarily have\n\\begin{equation} \\label{eq:UnvStoppingTimeCond}\n    \\sum_{k=1}^T \\log \\frac{p_{\\tv}(X_k|Y_k)}{q(X_k)} \\leq a + \\frac{\\XY}{2} \\log T + \\beta + \\log \\frac{p_{\\tv}(X_T|Y_T)}{q(X_T)}\n\\end{equation}\nwhere we define $a = \\log A$. By \\eqref{eq:UnvStoppingTimeCond} and Wald's Identity,\n\\begin{align}\n    \\E \\{T\\} &= \\frac{\\E \\left\\{\\sum_{k=1}^T \\log \\frac{p_{\\tv}(X_k|Y_k)}{q(X_k)}\\right\\}}{\\E\\left\\{\\log \\frac{p_{\\tv}(X|Y)}{q(X)}\\right\\}} \\\\\n    &\\leq \\frac{a + \\frac{\\XY}{2} \\cdot \\E\\{\\log T\\} + \\beta + C}{C} \\label{eq:BoundWithLog}\n\\end{align}\nSince $\\log_2 u \\leq \\frac{u}{v \\ln 2} + \\log_2 v - \\frac{1}{\\ln 2}$ for all $u,v>0$, \\eqref{eq:BoundWithLog} implies\n\\begin{equation}\n    \\E \\{T\\} \\leq \\frac{a + \\frac{\\XY}{2} \\left( \\log v - \\frac{1}{\\ln 2} \\right) + \\beta + C}{C \\left( 1 - \\frac{\\hXY}{C \\cdot v\\ln 2} \\right)}\n\\end{equation}\n\nFor $v = \\frac{\\log M}{C}$  we obtain\n\\begin{equation} \\label{eq:UnvExpStoppingTime}\n    \\E \\{T\\} \\leq \\frac{a + \\frac{\\XY}{2} \\left( \\log \\log M - \\log C - \\frac{1}{\\ln 2} \\right) + \\beta + C}{C \\left( 1 - \\frac{\\hXY}{\\log M \\ln 2} \\right)}\n\\end{equation}\nwhich corresponds to the following effective rate:\n\\begin{equation}\\label{eq:UnvEffectiveRateParam}\n    R = \\frac{C \\log M \\left( 1 - \\frac{\\hXY}{\\log M \\ln 2} \\right)}{a + \\frac{\\XY}{2} \\left( \\log \\log M - \\log C - \\frac{1}{\\ln 2} \\right) + \\beta + C}\n\\end{equation}\n\nSimilarly to the derivation in Chapter \\ref{ch:KnownChannel}, we bound the error probability by\n\\begin{equation*} \\label{eq:ErrorProbUnv}\n    \\Pr \\{E_w\\} \\leq (M-1) \\Pr \\left\\{ \\bigcup_{t=1}^{\\infty}\n    \\left\\{ \\frac{p_U(X^t|Y^t)}{q(X^t)} > A \\right\\} \\right\\}\n\\end{equation*}\nwhere $\\{X_k\\}_{k=1}^{\\infty}$ and $\\{Y_k\\}_{k=1}^{\\infty}$ are independent sequences. Define\n\\begin{equation}\\label{eq:uidef}\n    \\Phi_t = \\begin{cases}\n                \\frac{p_U(X^t|Y^t)}{p_U(X^{t-1}|Y^{t-1}) \\cdot q(X_t)}, \\ \\prod_{k=1}^{t-1} \\Phi_k \\leq A \\\\\n                1, \\ \\text{otherwise}\n              \\end{cases}\n\\end{equation}\nWe can see that\n\\begin{equation}\n    \\bigcup_{t=1}^{\\infty}\n    \\left\\{ \\frac{p_U(X^t|Y^t)}{q(X^t)} > A \\right\\}\n    \\Leftrightarrow \\prod_{t=1}^{\\infty} \\Phi_t > A\n\\end{equation}\nFurthermore, we can see that $\\E\\{\\Phi_t\\}=1$ for all $t$ since\n\\begin{equation*}\n    \\E \\left\\{ \\Phi_t | \\prod_{k=1}^{t-1} \\Phi_k > A \\right\\} = 1\n\\end{equation*}\nand\n\\begin{align}\n    \\E \\left\\{ \\Phi_t | \\prod_{k=1}^{t-1} \\Phi_k \\leq A \\right\\}\n    &= \\E \\left\\{ \\frac{p_U(X^t|Y^t)}{p_U(X^{t-1}|Y^{t-1}) \\cdot q(X_t)} \\right\\} \\\\\n    &= \\E \\left\\{ \\E \\left\\{ \\frac{p_U(X^t|Y^t)}{p_U(X^{t-1}|Y^{t-1}) \\cdot q(X_t)} | X^{t-1}, Y^t \\right\\} \\right\\} \\\\\n    &= \\E \\left\\{ \\frac{ \\E \\left\\{ \\int_{\\Lambda} w(\\tv') \\frac{p_{\\tv'} (x^t|y^t)}{q(x_t)} d\\tv' | X^{t-1}, Y^t \\right\\}}{\\int_{\\Lambda} w(\\tv') p_{\\tv'} (x^{t-1}|y^{t-1}) d\\tv'} \\right\\} \\\\\n    &= \\E \\left\\{ \\frac{ \\sum_{x_t \\in \\mathcal{X}} q(x_t) \\int_{\\Lambda} w(\\tv') \\frac{p_{\\tv'} (x^t|y^t)}{q(x_t)} d\\tv'}{\\int_{\\Lambda} w(\\tv') p_{\\tv'} (x^{t-1}|y^{t-1}) d\\tv'} \\right\\} \\\\\n    &= \\E \\left\\{ \\frac{ \\int_{\\Lambda} w(\\tv') \\sum_{x_t \\in \\mathcal{X}} p_{\\tv'} (x^t|y^t) d\\tv' }{\\int_{\\Lambda} w(\\tv') p_{\\tv'} (x^{t-1}|y^{t-1}) d\\tv'} \\right\\} \\\\\n    &= \\E \\left\\{ \\frac{ \\int_{\\Lambda} w(\\tv') p_{\\tv'} (x^{t-1}|y^{t-1}) d\\tv' }{\\int_{\\Lambda} w(\\tv') p_{\\tv'} (x^{t-1}|y^{t-1}) d\\tv'} \\right\\} = 1\n\\end{align}\nFor an arbitrary $N$ we have\n\\begin{align}\\label{eq:ProdPhi}\n    \\E \\left\\{\\prod_{t=1}^N \\Phi_t \\right\\} &= \\E \\left\\{ \\E \\left\\{\\prod_{t=1}^N \\Phi_t | \\prod_{t=1}^{N-1} \\Phi_t \\right\\} \\right\\} \\\\\n    &= \\E \\{ \\Phi_N \\} \\cdot \\E \\left\\{\\prod_{t=1}^{N-1} \\Phi_t \\right\\} \\\\\n    &= \\E \\left\\{\\prod_{t=1}^{N-1} \\Phi_t \\right\\} = \\ldots = 1\n\\end{align}\nSince the above holds for all $N$, we also have\n\\begin{equation}\\label{eq:InfProdPhi}\n    \\E \\left\\{\\prod_{t=1}^\\infty \\Phi_t \\right\\} = 1\n\\end{equation}\nThus, similarly to the case of known channel, the error probability can be bounded by\n\\begin{align}\n   \\Pr \\{E_w\\} &\\leq (M-1) \\Pr \\left\\{ \\bigcup_{t=1}^{\\infty}\n    \\left\\{ \\frac{p_U(X^t|Y^t)}{q(X^t)} > A \\right\\} \\right\\} \\label{eq:BoundErrorProbUnknownCh}\\\\\n    &= (M-1) \\Pr \\left\\{ \\prod_{t=1}^{\\infty} \\Phi_t > A \\right\\} \\leq \\frac{M-1}{A}\n\\end{align}\nHere again, we choose $A = M\/\\epsilon$ to obtain $P_e < \\epsilon$. Substituting $a = \\log A = \\log M - \\log \\epsilon$ into \\eqref{eq:UnvEffectiveRateParam} we finally get \\eqref{eq:UnvEffectiveRate}.\n\\end{proof}\n\n\\begin{remark}\nInterestingly, the upper bound on the error probability in \\eqref{eq:BoundErrorProbKnownCh}, obtained when the decoder uses the known channel law $p(x|y)$, applies for an arbitrary probability assignment $p_U(x|y)$, where the only required constraint is that the latter integrates to unity.\n\\end{remark}\n\n\\begin{remark}\nAs in the case of known channel, we can use randomized decoder here to obtain the following rate:\n\\begin{equation}\\label{eq:UnvEffectiveRateRand}\n    R = \\frac{C \\left( 1 - \\frac{\\hXY}{\\log M \\ln 2} \\right)}{1 + \\frac{C + \\beta - \\log \\delta + \\frac{\\XY}{2} \\left( \\log \\log M - \\log C - \\frac{1}{\\ln 2} \\right)}{\\log M}} \\cdot \\frac{1-\\delta}{1-\\epsilon}\n\\end{equation}\nfor all $0 < \\delta < \\epsilon$. As we mentioned in Section \\ref{sec:CodingThmKnownChannel}, if the required error probability is small, randomization should not be applied. However, if the error probability constraint is loose enough, a better rate may be obtained by optimizing delta in \\eqref{eq:UnvEffectiveRateRand}.\n\\end{remark}\n\n \\section{Discussion}\n \\subsection{Comparison to the Known Channel Case}\n Having obtained achievable rates for the cases of both known and unknown channels, it is interesting to compare these results and evaluate the rate degradation due to the unknown channel. For the case of a known channel, the effective rate at \\eqref{eq:AchievableRateChannelDec} can be approximated by\n \\begin{equation}\n    R \\thickapprox C \\left(1 - \\frac{C- \\log \\epsilon}{\\log M} \\right)\n \\end{equation}\n\n For the case of unknown channel, we can approximate \\eqref{eq:UnvEffectiveRate} by\n \\begin{align}\n    R_U &\\thickapprox C \\left(1 - \\frac{C- \\log \\epsilon}{\\log M} \\right) \\nonumber \\\\\n      &- C \\left( \\frac{\\XY}{2} \\frac{\\log \\log M}{\\log M} + \\frac{(\\hXY-1)\/\\ln 2 + \\beta + \\log C}{\\log M} \\right) + O \\left( \\frac{1}{\\log^2 M}\\right)\n \\end{align}\n\n Hence, the penalty for lack of channel knowledge amounts to\n \\begin{align} \\label{eq:RateDegradation}\n    R-R_U &= C \\left( \\frac{\\XY}{2} \\frac{\\log \\log M}{\\log M} + \\frac{(\\hXY-1)\/\\ln 2 + \\beta + \\log C}{\\log M} \\right) \\\\\n          &+ O \\left( \\frac{1}{\\log^2 M}\\right) \\nonumber\n \\end{align}\n\n The leading term in the latter expression behaves as $O(\\log \\log M \/ \\log M) = O(\\log K\/K)$, factorized by the product of the cardinalities of input and output of the channel. It is interesting to compare this result with known results from universal source coding, where the \\emph{redundancy}\\footnote{The excess of the average codeword length above the entropy of the source.} is dominated by the cardinality of the alphabet of the source \\cite{UnvPrediction}, and a term that behaves as $O(\\log n\/n)$, where $n$ is the source length.\n\n \\subsection{Induced Error Exponent}\n Let us now examine Theorem \\ref{thm:UnvRate} in light of the previous results. Equation \\eqref{eq:UnvEffectiveRate} implies the following error exponent:\n \\begin{equation}\\label{eq:UnvErrorExp}\n    - \\frac{\\log \\epsilon}{\\E\\{T\\}} = C - R - \\frac{\\XY}{2} \\cdot \\frac{\\log \\log M}{\\log M} + O\\left(\\frac{1}{\\log M}\\right)\n \\end{equation}\n As in the case of a known channel, we see that the error exponent is a linear function of the rate, but an additional term of order $O(\\log \\log M \/ \\log M)$ is added. Here again, we interpret this term as a penalty for the lack of channel knowledge at the receiver. Furthermore, by taking $M \\to \\infty$, we can also see that \\eqref{eq:UnvErrorExp} coincides with \\cite[Proposition 1]{Telatar}.\n\n \\subsection{Training and Channel Estimation}\n In many practical applications, communication over an unknown channel is done by means of channel estimation. In this approach, the transmission includes predefined \\emph{training} signals, which are known to the receiver and are used to estimate the channel parameters. As an alternative to the universal communication scheme introduced in this chapter, we can use the following method. Prior to any message transmission, the transmitter sends a training sequence, which the receiver uses to estimate the channel. After the training phase, the transmitter sends the message. The receiver uses the \\emph{estimated} channel parameters to decode the message, using, for instance, the decoding rule at \\eqref{eq:ChannelDecoderLog}. A drawback from this approach is that even after the channel estimation phase, the residual error in the estimated channel parameters will degrade the performance of the decoder. Furthermore, enhancement of the channel estimation accuracy requires long training sequences, which will introduce non-negligible overhead to the transmission time. Clearly, using training will not lead to the convergence rate of \\eqref{eq:RateDegradation}.\n\n\\chapter{Extensions}\n\\label{ch:Extensions}\n\\section{Joint Source-Channel Coding} \\label{sec:JointSC}\nIn the previous chapters we assumed that the messages conveyed over the channel were equiprobable, which is the case if, for instance, the source of information has been compressed and the message $W$ is the output of the source encoder. Assume now, that the messages have arbitrary probabilities ${\\pi(1),\\ldots,\\pi(M)}$. Each message now contains a different amount of information, which would translate into different codeword length at the output of the source encoder. However, in rateless codes the codeword assigned to each message is always infinite, and the actual codeword length is determined by the decoder. (The effective length of the message depends on the decoder's stopping time.) It is therefore tempting to use rateless codes for an uncompressed source and try to achieve good compression rate and reliable communication simultaneously. To simplify matters, we begin by tackling the case of known channel and postpone the analysis for unknown channel to Section \\ref{sec:CompleteUnv}. We use the following generalized version of the encoder \\eqref{eq:ChannelDecoderLog}.\n\\begin{equation} \\label{eq:JointScDec}\n    g_n(y^n)= \\begin{cases}\n                w, \\ z_{w,1}+\\ldots+z_{w,n} \\geq a_w \\\\\n                0, \\ \\text{if no such $w$ exists}\n              \\end{cases}\n\\end{equation}\nwhere $a_w$ is a threshold that depends on the message $w$, and we define $a_w= \\log A_w$. Repeating the derivation for the error probability done in the previous section, we get by Markov's inequality\n\\begin{equation}\n    \\Pr\\{E_w\\} \\leq \\sum_{w' \\neq w} \\frac{1}{A_{w'}}\n\\end{equation}\nBy choosing\n\\begin{equation}\n    A_w  = \\frac{1}{\\epsilon \\cdot \\pi(w)} \\qquad \\forall w \\in \\mathcal{W}\n\\end{equation}\nwe get a uniform bound on the error probability\n\\begin{equation}\n    \\Pr\\{E_w\\} \\leq \\epsilon \\cdot \\sum_{w' \\neq w} \\pi(w') \\leq \\epsilon\n\\end{equation}\nwhich also implies\n\\begin{equation}\n    P_e \\leq \\epsilon\n\\end{equation}\n\nThus, for an appropriate choice of message-dependent threshold values, the average probability of error for the entire message set is bounded by $\\epsilon$. Recall, however, that the effective rate depends on the threshold value and therefore needs to be reexamined here. When different thresholds are used for different messages, the stopping time depends on which message crosses the threshold. We can therefore use Wald's equation \\eqref{eq:WaldC} conditioned on the true message:\n\\begin{equation}\n    \\E\\{T|W=w\\} \\leq \\frac{a_w + C}{C}\n\\end{equation}\nwhere\n\\begin{equation}\n    a_w = \\log A_w = - \\log \\pi(w) - \\log \\epsilon\n\\end{equation}\nAveraging on the entire message set, we have\n\\begin{align}\n    \\E\\{T\\} &= \\E\\{\\E\\{T|W\\}\\} \\leq \\frac{\\E\\{a_{_W}\\} + C}{C} \\nonumber \\\\\n            &= \\frac{\\E\\{- \\log \\pi(W)\\} - \\log \\epsilon + C}{C} \\nonumber \\\\\n            &= \\frac{H(W) - \\log \\epsilon + C}{C} \\label{eq:JointScET}\n\\end{align}\nwhere $H(W)$ is the entropy rate of the source in bits per symbol. Let us now examine \\eqref{eq:JointScET} in a practical setting. Suppose the we wish to convey blocks of $K$ source bits with fixed probability of error $\\epsilon > 0$. Since every source symbol contains $\\log M$ bits, $K \/ \\log M$ source symbols will be needed. Thus, the rate at which source bits can be conveyed over the channel will be\n\\begin{align}\n    R &= \\frac{K}{\\E\\{T\\}} \\geq \\frac{K \\cdot C}{\\frac{K \\cdot H(W)}{\\log M} - \\log \\epsilon + C} \\\\\n      &= \\frac{C}{\\mathscr{H}(W) + \\frac{C - \\log \\epsilon}{K}} \\\\\n      &= \\frac{C}{\\mathscr{H}(W)} \\cdot \\frac{1}{1 + \\frac{C - \\log \\epsilon}{\\mathscr{H}(W) \\cdot K}} \\\\\n      &= \\frac{C}{\\mathscr{H}(W)} \\cdot \\left(1 - O \\left( \\frac{1}{K} \\right) \\right) \\label{eq:JointScRateAsym}\n\\end{align}\nwhere we define $\\mathscr{H}(W)=H(W)\/ \\log M$ as the per-bit entropy of the source.\n\nNote that the encoder used here, as well as the codebook, are the same ones defined in Chapter \\ref{ch:DefinitionsAndNotation} and the only change is in the definition of the decoder. The encoder is uninformed on the statistics of the source or the capacity of the channel, yet the rate approaches the optimum rate achievable by an informed encoder. We note the practical implication of such scheme: the compression algorithms can be implemented and maintained at the decoder, while the encoder remains simple and source-independent.\n\n\\section{Source Coding with Side Information} \\label{sec:SI}\nSuppose now, that the source of information emits independent pairs of messages $(W_1,W_2) \\in \\mathcal{W}_1 \\times \\mathcal{W}_2$ according to a probability distribution $\\pi_{_{W_1,W_2}}(w_1,w_2)$, which are encoded separately and pass through a noiseless channel. Suppose that $R_1$ and $R_2$ are the coding rates of $W_1$ and $W_2$, respectively. By Slepian-Wolf theorem, if $W_1$ is encoded with rate $R_1 \\geq H(W_1)$, then $W_2$ can be encoded independently with $R_2 = H(W_2|W_1)$. (This rate pair is a corner point in the achievable rate region.) We will now show that using rateless codes, we can approach this rate with some redundancy due to the usage of finite message set. The encoder of $W_1$ assigns to each message in $\\mathcal{W}_1$ an infinite codeword $\\mathbf{c}_{w_1} \\in \\{0,1\\}^\\infty$, $w_1 = 1,\\ldots,|\\mathcal{W}_1|$, and transmits it over the channel. The encoder of $W_2$ operates similarly to that of $W_1$ and independently of it, with codewords $\\mathbf{d}_{w_2} \\in \\{0,1\\}^\\infty$, $w_2 = 1,\\ldots,|\\mathcal{W}_2|$. The codewords are assumed to be i.i.d.\\ Bernoulli$(1\/2)$ sequences. To reconstruct $W_1$, the decoder can use the decision rule \\eqref{eq:JointScDec}, to to obtain an error probability of\n\\begin{equation} \\label{eq:BoundErrorW1}\n    \\Pr\\{\\hat{W_1} \\neq W_1\\} \\leq \\frac{\\epsilon}{2}\n\\end{equation}\nSince binary code is used and the channel is noiseless, we have $C=1$, so \\eqref{eq:JointScET} implies that the expected transmission time for $W_1$ satisfies\n\\begin{equation} \\label{eq:SlepianWolfR1}\n    R_1 = \\E\\{T_1\\} \\leq \\ H(W) - \\log \\frac{\\epsilon}{2} + 1\n\\end{equation}\nNote that the coding rate is defined here as the average codeword length for the message set. Therefore, the effective rate equals the expected transmission time, rather than its reciprocal as in channel coding.\n\nHaving decoded message $W_1$, the decoder uses the following decision rule to reconstruct $W_2$:\n\\begin{equation}\n    g^{(2)}_n(y^n,w_1)= \\begin{cases}\n                w_2, \\ z_{w_2,1}+\\ldots+z_{w_2,n} \\geq a(w_1,w_2) \\\\\n                0,   \\ \\text{if no such $w_2$ exists}\n              \\end{cases}\n\\end{equation}\nwhere\n\\begin{equation}\n    z_{w_2,k} = \\log \\frac{p(y_k|d_{w_2,k})}{p(y_k)}, \\qquad k=1,\\ldots,n\n\\end{equation}\nSimilar derivation for the error probability as in Section \\ref{sec:JointSC} yields\n\\begin{equation}\n    \\Pr\\{\\hat{W_2} \\neq w_2 \\ | \\ W_1 = w_1, W_2 = w_2 \\} \\leq \\sum_{w_2' \\neq w_2} \\frac{1}{A(w_1,w_2)}\n\\end{equation}\nWe choose\n\\begin{equation}\n    A(w_1,w_2) = \\frac{1}{\\epsilon\/2 \\cdot \\pi_{_{W_2|W_1}}(w_2|w_1)}\n\\end{equation}\nso that\n\\begin{equation}\n    \\Pr\\{\\hat{W_2} \\neq w_2 \\ | \\ W_1 = w_1, W_2 = w_2 \\} \\leq \\epsilon\/2 \\cdot \\sum_{w_2' \\neq w_2} \\pi_{_{W_2|W_1}}(w_2|w_1) \\leq \\frac{\\epsilon}{2}\n\\end{equation}\nTherefore,\n\\begin{equation} \\label{eq:BoundErrorW2}\n    \\Pr\\{\\hat{W_2} \\neq W_2\\} \\leq \\frac{\\epsilon}{2}\n\\end{equation}\nUsing \\eqref{eq:BoundErrorW1}, \\eqref{eq:BoundErrorW2} and the union bound, we have\n\\begin{equation}\n    \\Pr\\{\\hat{W_1} \\neq W_1 \\bigcup \\hat{W_2} \\neq W_2\\} \\leq \\epsilon\n\\end{equation}\n\nSince $a(w_1,w_2) = - \\log \\epsilon\/2 - \\log \\pi_{_{W_2|W_1}}(w_2|w_1)$, we can use Wald's equation for the stopping time of decoding $W_2$ to obtain\n\\begin{align}\n    R_2 &= \\E\\{T_2\\} = \\E\\{\\E\\{T_2|W_1,W_2\\}\\} \\nonumber \\\\\n        &\\leq \\E\\{a(W_1,W_2)\\} + 1 \\nonumber \\\\\n        &= \\E\\{- \\log \\pi_{_{W_2|W_1}}(W_2|W_1)\\} - \\log \\frac{\\epsilon}{2} + 1 \\nonumber \\\\\n        &= H(W_2|W_1) - \\log \\frac{\\epsilon}{2} + 1 \\label{eq:SlepianWolfR2}\n\\end{align}\n\nCombining \\eqref{eq:SlepianWolfR1} and \\eqref{eq:SlepianWolfR2}, we get\n\\begin{equation} \\label{eq:SlepianWolfSumRate}\n    R_1 + R_2 = H(W_1,W_2) - 2 \\log \\frac{\\epsilon}{2} + 2\n\\end{equation}\n\nSimilarly to Section \\ref{sec:JointSC}, if we take blocks of $K$ source bits and a fixed error probability $\\epsilon > 0$, we obtain\n\\begin{equation}\n    R_1 + R_2 = H(W_1,W_2) \\cdot \\left(1 + O \\left( \\frac{1}{K} \\right) \\right)\n\\end{equation}\n\n\\section{Complete Universality} \\label{sec:CompleteUnv}\n\nWe now consider the case of joint source-channel coding of an unknown source over an unknown channel, with an unknown amount of side-information at the receiver. Initially, we bring together the results of the previous sections to obtain a communication scheme for a source with unknown statistics over an unknown channel. As a straightforward generalization of the universal source coding scheme in Section \\ref{sec:RateUnknownChannel}, we use a fusion of the decoders \\eqref{eq:ChannelDecoderUnv} and \\eqref{eq:JointScDec}, i.e.\n\\begin{equation} \\label{eq:JointScUnvDec}\ng_n(y^n)= \\begin{cases}\n            w, \\ p_U(\\mathbf{c}_w|y^n) \\geq A_w \\cdot q(\\mathbf{c}_w) \\\\\n            0, \\ \\text{if no such $w$ exists}\n          \\end{cases}\n\\end{equation}\nwhere\n\\begin{equation}\\label{eq:Aw}\n    A_w = \\frac{1}{\\epsilon \\cdot \\pi(w)}\n\\end{equation}\nSimilar derivation to those done at Sections \\ref{sec:RateUnknownChannel} and \\ref{sec:JointSC} yields the following rate for an uncompressed source $W \\in \\{1,\\ldots,M\\}$ over an unknown channel with capacity $C$:\n\\begin{equation}\\label{eq:JointScUnvRate}\n    R = \\frac{C \\left( 1 - \\frac{\\hXY}{\\log M \\ln 2} \\right)}{\\mathscr{H}(W) + \\frac{C + \\beta - \\log \\epsilon + \\frac{\\XY}{2} \\left( \\log \\log M - \\log C - \\frac{1}{\\ln 2} \\right)}{\\log M}}\n\\end{equation}\nwhere $\\mathscr{H}(W)$ is defined in Section \\ref{sec:JointSC}. We note that while the encoder can be ignorant of the source statistic, the decoder needs to know $\\pi(w), \\ w \\in \\mathcal{W}$.\n\nWe now go one step further and assume that the decoder has no knowledge of the statistics of the source or the channel. Suppose that the source $S$ generates sequences of $L$ symbols from an alphabet $\\mathcal{S}$, drawn i.i.d. according to set of $|\\mathcal{S}|$ unknown probabilities $\\gv$. Each sequence is encoded as one message, hence $M = |\\mathcal{S}|^L$. Instead of using the set of thresholds \\eqref{eq:Aw}, which depends on the unknown probabilities, we use a universal probability measure \\cite{UnvPrediction}\n\\begin{equation}\n    \\ph(s^L) = \\int u(\\gv) \\pi_{\\gv}(s^L)\n\\end{equation}\nso that\n\\begin{equation}\n    a_w = \\log A_w = -\\log \\epsilon -\\log \\ph (s^L)\n\\end{equation}\nIf the weight function $u(\\cdot)$ is chosen to be Jeffreys prior, we get (see \\cite[Eq.17]{UnvPrediction})\n\\begin{equation}\n    \\E\\{a_w\\} = -\\log \\epsilon + H(W) + \\frac{|\\mathcal{S}|-1}{2} \\log \\frac{L}{2 \\pi e} + O(1)\n\\end{equation}\nHence, similarly to \\eqref{eq:JointScUnvRate} we can achieve the following rate\n\\begin{equation}\\label{eq:CompUnvRate}\n    R = \\frac{C \\left( 1 - \\frac{\\hXY}{\\log M \\ln 2} \\right)}{\\hat{\\mathscr{H}}(W) + \\frac{C + \\beta - \\log \\epsilon + \\frac{\\XY}{2} \\left( \\log \\log M - \\log C - \\frac{1}{\\ln 2} \\right)}{\\log M}}\n\\end{equation}\nwhere\n\\begin{equation}\n    \\hat{\\mathscr{H}}(W) = \\mathscr{H}(W) + \\frac{|\\mathcal{S}|-1}{2} \\frac{\\log L}{\\log M} + O\\left(\\frac{1}{\\log M}\\right)\n\\end{equation}\nRecall that $L = \\log_{|\\mathcal{S}|} M$, so\n\\begin{equation}\\label{eq:EmpEntropy}\n    \\hat{\\mathscr{H}}(W) = \\mathscr{H}(W) + \\frac{|\\mathcal{S}|-1}{2} \\frac{\\log \\log M}{\\log M} + O\\left(\\frac{1}{\\log M}\\right)\n\\end{equation}\nBy plugging \\eqref{eq:EmpEntropy} into \\eqref{eq:CompUnvRate} we get\n\\begin{equation}\\label{eq:CompUnvRateAsym}\n    R = \\frac{C}{\\mathscr{H}(W)} \\cdot \\left(1 - O \\left( \\frac{\\log K}{K} \\right) \\right) + O \\left( \\frac{1}{K} \\right)\n\\end{equation}\nwhere $K = \\log M$ is the number of encoded bits. Comparing \\eqref{eq:CompUnvRateAsym} to \\eqref{eq:JointScRateAsym}, we see that the leading term is unchanged and equals the optimal rate achievable by separated source-channel coding. However, the lack of information affects the rate of convergence, which is now dominated by a $O \\left( \\frac{\\log K}{K} \\right)$ term, as opposed to $O \\left( \\frac{1}{K} \\right)$ for an informed decoder.\n\nThe implications of the latter result are far-reaching. We have shown that even if the statistics of both the channel and the source are unknown to the decoder, rateless coding not only achieves the best source-channel coding rate as $M \\to \\infty$, but it also has the same asymptotics of a rateless scheme with an informed decoder. This observation has been made in \\cite[Ch.4]{Nadav} for infinitely large message sets. The results obtained here coincide with those of \\cite{Nadav}, and also quantify the redundancy caused by the lack of information on the source and the channel, and by the use of finite blocks.\n\n\\subsection*{Unknown Side Information at the Decoder}\nSimilarly to Section \\ref{sec:SI}, if the source contains side information $V$ that is known non-causally at the decoder, we can further improve the communication rate. Combining the technique from Section \\ref{sec:SI} with the derivation above, we obtain the following rate for universal joint source-channel coding with side information at the decoder:\n\\begin{equation}\\label{eq:CompUnvRateSI}\n    R = \\frac{C}{\\mathscr{H}(W|V)} \\cdot \\left(1 - O \\left( \\frac{\\log K}{K} \\right) \\right) + O \\left( \\frac{1}{K} \\right)\n\\end{equation}\nwhere $\\mathscr{H}(W|V)$ is the conditional entropy of the source $W$ given the side information $V$, normalized by $\\log M$. Since $\\mathscr{H}(W|V) \\leq \\mathscr{H}(W)$, the side information improves the rate, even if the encoder is uninformed on the amount (or the existence) of the side information.\n\n\\chapter{Summary}\n\\label{ch:Summary}\nIn this study we developed and analyzed several communication schemes that are all based on the concept of \\emph{rateless codes}. In rateless codes, each codeword has an infinite length and the decoding length is dynamically determined by the confidence level of the decoder. Throughout this study, we allowed the coding schemes to have a fixed error probability, while aiming to achieve shortest mean transmission time, or equivalently, the highest rate. This approach is different than the prevalent one, in which the communication rate is held fixed and the codebook is enlarged indefinitely so that the error probability vanishes. We demonstrated how rateless codes, combined with sequential decoding, can be used in basic communication scenarios such as communication over a DMC, but can also be used to solve more complex problems, such as communication over an unknown channel. The decoding methods introduced here enabled us to obtain results for finite message set, while previous studies were restricted to asymptotic results.\n\nWe began by describing rateless codes and surveyed some previous results related to such coding schemes. Then, we introduced the sequential decoder that uses a known channel law. Using Wald's theory and the notion of stopping time, we obtained an upper bound for the mean transmission time for a fixed error probability, and the resulting effective rate is shown to approach to the capacity of the channel as the size of the message set, $M$, grows. We also obtained an upper bound for the rate for a fixed error probability. The upper bound is not tight for small $M$, but it converges to the achievable rate as $M \\to \\infty$. We conjecture that a stronger converse can be found, which will be tighter also in the non-asymptotic realm. Although we developed the above-mentioned scheme for a DMC, we also demonstrated that it is applicable in a memoryless Gaussian channel.\n\nFor the case of an unknown channel we introduced a novel decoding metric. Unlike previous studies, the universal decoding metric in not based on empirical mutual information, but on a mixture probability assignment. For an appropriate choice of mixture, we were able to bound the difference between the universal metric and the one used by an informed decoder. Thus, we used the results obtained for an informed decoder to upper bound the mean transmission time in the universal case.\n\nWe then applied rateless coding to more advanced scenarios. We showed how with only a minor change in the sequential decoder, we can easily use rateless codes as a joint source-channel coding scheme. We also used rateless coding for source coding with side information, obtaining the optimum Slepian-Wolf rate for this setting. Finally, we combined the techniques for universal channel coding, joint source-channel coding and source coding with side information and demonstrated that even without any information on the source, the channel or the amount (or even the existence) of side information---reliable communication is feasible, and the rate can be analyzed even for a finite message set.\n\n\\bibliographystyle{IEEETran}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
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+{"text":"\\section{Introduction} \\label{sec:intro}\nThe branch-and-bound scheme, invented by Land and Doig~\\cite{land1960automatic}, is the method of choice for solving mixed integer linear programs (MILP) by all modern state-of-the-art  MILP solvers. \n\nWe present a quick outline of this well-known method below; see ~\\cite{wolsey1999integer,conforti2014integer} for more discussion on the branch-and-bound method. The optimal objective function value of the linear programming (LP) relaxation of a given MILP provides a dual bound (upper\/lower bound for maximization-type\/minimization-type objective respectively) on the optimal objective function value of the MILP. This LP relaxation corresponds to the root node of the branch-and-bound tree. In order to improve this bound and to find feasible solutions, after solving the LP corresponding to a node, the feasible region of the LP  is partitioned into two sub-problems which correspond to the child nodes of the given node. Such a partitioning of the feasible region for binary MILPs is usually accomplished in practice by selecting a variable $x_j$ that is currently fractional and adding the constraint $x_j =0$ to one of the child nodes and the constraint $x_j =1$ to the other child node. The process of partitioning the feasible regions of the LP at a node continues recursively for the child nodes (thus forming a tree) and is stopped (sometimes referred to as pruning a node), if one of the following conditions hold: (i) the LP at the node is infeasible, (ii) the LP's optimal solution is integer feasible, or (iii) the LP's optimal objective function value is worse than an already known integer feasible solution. The procedure terminates when all nodes have been pruned. \n\nGiven an underlying LP solver, formally speaking, the \\emph{branch-and-bound algorithm} is well-defined by fixing two rules:\n\\begin{itemize}\n\\item Rule for selecting an open node to be branched on next and,\n\\item Rule for deciding the variable to branch on.\n\\end{itemize} \nIt is natural to measure the efficiency of a branch-and-bound algorithm by the number of nodes (corresponding to number of LPs solved) in the tree, i.e., lesser the number of nodes, faster the algorithm. \n\n\\paragraph{Selecting an open node to branch on next (node selection rule).}\nIt is well established~\\cite{wolsey1999integer} that the \\emph{worst-bound rule} (i.e., select node with the maximum LP optimal objective function value for a maximization-type MILP or select node with minimum LP optimal objective function value for a minimization-type MILP) for selecting the next node to branch on, leads to small branch-and-bound trees. The intuition behind this is the following: one cannot ignore the node with worst-bound if one wants to solve the MILP. Thus, it is best to select to branch on it first.  In the rest of the paper, we always assume to use the worst-bound rule.\n\n\\paragraph{Deciding which variable to branch on (variable selection rule).} Given that the rule for selecting the node to be branched on is well-understood, much of the research in the area of branch-and-bound algorithms has focused on the topic of deciding the variable to branch on -- see for example~\\cite{healy1964multiple,dakin1965tree,driebeek1966algorithm, benichou1971experiments,mitra1973investigation,forrest1974practical,breu1974branch,gauthier1977experiments,land1979computer,eckstein1994parallel,applegate1995finding,linderoth1999computational,achterberg2005branching}. Most of the above work develops various intricate greedy rules for determining the branching variable. \nA popular concept is that of \\emph{pseudocost branching}: the value of pseudocost (variable with largest pseudocost gets branched on) keeps a history of the success (in terms of improving dual bound) of the variables on which branching has already been done. Many of the papers cited above differ in how pseudocost is initialized and updated during the course of the branch-and-bound tree. Other successful methods like \\emph{hybrid branching} and \\emph{reliability branching}~\\cite{achterberg2005branching} are combinations of pseudocost branching and \\emph{full strong-branching}, that we discuss next.\n\nThe focus of this work is \\emph{full strong-branching}~\\cite{applegate1995finding}, henceforth referred to as strong-branching for simplicity. This rule works as follows: branching on all the current fractional variables is computed (i.e., the child nodes are solved for every choice of fractional variable) and improvement measured in the left and right child node. Branching is now done on the variable with the most `combined improvement', where the combined improvement is computed as a `score' function of the left and right improvement.\nFormally, let $z$ be the optimal objective function value of the LP at a given node, and let $z^{0}_j$ and $z^{1}_j$ be the optimal objective function values of the LPs corresponding to the child nodes where the variable $x_j$ is set to $0$ and $1$ respectively; we define $\\Delta^{+}_j := z - z^1_j$ and $\\Delta^{-}_j := z - z^0_j$ (assuming the MILP's objective function is of maximizing-type). Note that  $\\Delta^+_j = +\\infty$ is the child node with $x_j$ set to $0$ is infeasible. Similarly for $\\Delta^-_j$. Two common  score functions used  are:\n$$\\textup{score}_{L}(j) = (1 - \\mu)\\cdot \\textup{min} \\{\\Delta^{-}_j , \\Delta^{+}_j \\} + \\mu \\cdot \\textup{max} \\{\\Delta^{-}_j , \\Delta^{+}_j \\}$$\nand\n$$\\text{score}_{P}(j) = \\max(\\Delta^+_j, \\epsilon) \\cdot \\max(\\Delta^-_j, \\epsilon),$$\nwhere the first score is recommended in~\\cite{linderoth1999computational,achterberg2005branching} (the paper~\\cite{achterberg2005branching} recommends using $\\mu  = 1\/6$) and the second score function is recommended in~\\cite{achterberg2007constraint}, where $\\epsilon >0$ is chosen close to $0$ (for example, $\\epsilon = 10^{-6}$) to break ties. We will refer to the first score function as the \\textit{linear score function} and the second score function as the \\textit{product score function}. Finally, the variable selected to branch on belongs to the set:\n$$\\arg \\max_{j} \\{\\textup{score}(j)\\}.$$\nEmpirically, strong-branching is well-known to produce significantly smaller branch-and-bound trees~\\cite{achterberg2005branching} compared to all other known techniques, but is extremely expensive to implement as one has to solve $2K$ LPs where $K$ is the number of fractional variables for making just one branching decision. This experimentally observed fact is so well established in the literature that almost all recent methods to improve upon branching decisions are based on using \\emph{machine learning techniques to mimic strong-branching} that avoid solving the $2K$ LPs, see for example~\\cite{khalil2016learning,lodi2017learning,alvarez2017machine,balcan2018learning,gasse2019exact,gupta2020hybrid,nair2020solving}. Finally, see~\\cite{le2017abstract} that describes a more sophisticated way to decide the branching variable based on left and right improvement rather than a static `score' function.\n\n\\subsection{Our contributions}\n\nAs explained in the previous section, empirically it is well understood that strong-branching produces very small trees in comparison to other rules. However, to the best of our knowledge there is \\emph{no understanding of how good strong-branching is in absolute terms.} In particular, we would like to answer questions such as: \n\\begin{itemize}\n\\item How large is the tree produced by strong-branching in comparison to the smallest possible branch-and-bound tree for a given instance? Answering this question may lead us to finding better rules. \n\\item A more refined line of questioning: Intuitively, we do not expect strong-branching to work well for all types of MILP models and instances. On the other hand, it may be possible that for some classes of MILPs strong-branching based branch-and-bound tree may be quite close to the smallest possible branch-and-bound tree. It would be, therefore, very useful to understand the performance of strong-branching vis-\\'a-vis different classes of instances.    \n\\end{itemize}\nIn this paper, we attempt an analysis of the performance of the strong-branching rule -- both from a theoretical and a computational perspective, keeping in mind the above questions.  \n\\begin{itemize}\n\\item Strong branching is provably good: We show that for the vertex cover problem, the strong-branching rule has several benefits. First, we present a fixed parameter-type (FPT) result that uses the additive gap between the IP's and the LP's optimal objective function value to bound the size of the branch-and-bound tree using strong-branching. \n\nNemhauser and Trotter~\\cite{nemhauser1975vertex} proved that one may fix variables that are integral in the optimal solution of the LP relaxation of vertex cover and still find an optimal solution to the IP. Note that in the branch-and-bound tree, every node corresponds to a sub-graph of the original vertex-cover instance, and thus, ideally we would like to continue to use the Nemhauser-Trotter property at each node. Instead of designing a specialized implementation of branch-and-bound algorithm (where we fix variables that have an integer value in the LP optimal solution at each node), our second result is to show that strong-branching naturally incorporates ``fixing\" the integral variables of the LP solution recursively and consistently thoughout the branch-and-bound tree. \n\nFinally, we construct an instance where strong-branching yields a branch-and-bound tree that is exponential-times smaller than a branch-and-bound tree generated using a very reasonable alternative variable selection rule. \n\\item Strong branching is provably bad: We present a class of instances where the size of the strong-branching based branch-and-bound tree is exponentially larger than a special branch-and-bound tree that solves these instances. In fact, the result we prove is stronger -- we show that if we only branch on variables that are fractional, then the size of the branch-and-bound tree is exponentially larger than the given special branch-and-bound tree to solve these instances. This special branch-and-bound tree branches on variables that are integral in the optimal LP solutions at certain nodes.\n\\item Computational evaluation of the size of strong-branching based branch-and-bound tree against the ``optimal\" branch-and-bound tree\\footnote{We write ``optimal\" branch-and-bound tree with quotes, since the size of the optimal branch-and-bound tree depends not only on the branching decisions taken at each node, but also on the properties of the LP solver. We discuss this issue in detail in Section \\ref{sec:main}.}: We first present a dynamic programming algorithm for generating the optimal branch-and-bound tree whose running time is $\\text{poly}(\\text{data}(\\mathcal{I})) \\cdot 3^{O(n)}$ where $n$ is the number of binary variables. Then we conduct experiments on various types of instances like the lot-sizing problem and its variants, packing IPs, covering IPs,  chance constrainted IPs, vertex cover, etc., to understand how much larger is the size of the strong-branching based branch-and-bound tree  in comparison to the optimal branch-and-bound tree. The main take-away from these experiments is that for all these instances, the size of the strong-branching based branch-and-bound tree is within a factor of two of the size of the optimal branch-and-bound tree. \n\\end{itemize}\n\nTo the best of our knowledge, this is the first such study of this kind on strong-branching, that provides a better understanding of why strong-branching often performs so well in practice, and gives insight into when an instance may be challenging for strong-branching. \n\nThe rest of the paper is organized in the following fashion. In Section~\\ref{sec:main} we formally present all our theoretical and computational results.  In Section~\\ref{sec:vertexcoverproof} and Section~\\ref{sec:bdg_ex}, we present proofs of the theoretical results presented in Section~\\ref{sec:main}. In Section~\\ref{sec:computing_opt} we present the details of the dynamic programming algorithm mentioned above. Finally, in Section~\\ref{sec:experiments} we present all the details of our computational experiments. \n\n\n\\section{Main results}\\label{sec:main}\n\\subsection{Theoretical results}\\label{sec:theo}\nNote that in this section (Section~\\ref{sec:theo}), whenever we refer to strong-branching, we assume that it has been used in conjunction with the product score function~\\cite{achterberg2007constraint} $\\text{score}_{P}$, where $\\epsilon = 0$ and we use the convention that $0\\cdot \\infty = 0$. Finally, we refer to the \\textit{size} of a branch-and-bound tree to denote its number of nodes; we note that in any binary tree, the number of nodes is at most $2\\ell + 1$, where $\\ell$ is the number of leaves. \n\n\\subsubsection{Strong branching works well for vertex cover}\nThere are simple MILPs that require exponential size branch-and-bound trees \\cite{jeroslow1974trivial,chvatal1980hard,dey2021lower, jiang2021complexity,dadush2020complexity}. A common way to meaningfully analyze an algorithm with exponential worst-case performance is to show its performance with respect to some parameter \\cite{roughgarden2019beyond, cygan2015parameterized}. Arguably the most well-studied problem in parameterized complexity is \\textit{vertex cover}.\n\\begin{definition}[Vertex cover]\\label{def:vc_ip}\nThe vertex cover problem over a graph $G = (V, E)$ can be expressed as the following integer program (IP)\n\\begin{equation*}\n\\begin{array}{ll@{}ll}\n\\text{min} & \\displaystyle\\sum\\limits_{v \\in V} x_v & \\\\\n\\text{s.t.}   &x_u + x_v \\geq 1, & \\quad uv \\in E \\\\\n              &x_v \\in \\{0,1\\}, & \\quad v \\in V\n\\end{array}\n\\end{equation*}\nGiven an instance $\\mathcal{I}$ of this IP, we let $L(\\mathcal{I})$ denote its LP relaxation (i.e. when the variable constraints instead are $x_v \\in [0,1]$). We denote the optimal objective function value of an instance by $\\textup{OPT}(\\mathcal{I})$ and the optimal objective function value of its LP relaxation by $\\textup{OPT}(L(\\mathcal{I}))$. We denote its additive integrality gap $\\Gamma(\\mathcal{I}) := \\textup{OPT}(\\mathcal{I}) - \\textup{OPT}(L(\\mathcal{I}))$. For results pertaining to vertex cover, we use $n$ to denote the number of vertices (i.e. $n := |V|$).\n\\end{definition}\n\n\\paragraph{Upper bound on the size of branch-and-bound tree using strong-branching.}\n\nLet $\\mathcal{T}_S(\\mathcal{I})$ represent a branch-and-bound tree for solving instance $\\mathcal{I}$ using strong-branching. Unfortunately, the number of nodes in this tree depends not only on the node selection rule and variable selection rule, but also on the underlying LP solver as well. For example, a solver may report an integral solution at a given node and allow us to prune the node. Another solver might report a different optimal solution to the LP, which is not integral. Therefore, we will be careful to not refer to \\emph{the branch-and-bound tree generated by strong-branching}. Instead, we will use $\\mathcal{T}_S(\\mathcal{I})$ to represent \\emph{some branch-and-bound tree generated by strong-branching}. As such, we conduct a parameterized analysis of strong-branching as an algorithm for vertex cover. \n\nWe show an upper bound on strong-branching for vertex cover parameterized by its additive integrality gap $\\Gamma(\\mathcal{I})$.\n\\begin{theorem}\\label{thm:vc_fpt}\nLet $\\mathcal{I}$ be any instance of vertex cover. Assume we break ties within the worst-bound rule for node selection rule by selecting a node with the largest depth.  Let $\\mathcal{T}_S(\\mathcal{I})$ be {some branch-and-bound tree generated by strong-branching} with the above version of worst-bound node selection rule that solves $\\mathcal{I}$. Then independent of the underlying LP solver used, \n$$|\\mathcal{T}_S (\\mathcal{I})| \\leq  2^{2\\Gamma(\\mathcal{I}) + 2} + \\mathcal{O}(n).$$\n\\end{theorem}\nMoreover, this bound is tight within an multiplicative factor of $2$ and additive factor of $\\mathcal{O}(n)$. \n\\begin{remark}\\label{rem:tight}\nThere is an instance $\\mathcal{I}$ of vertex cover such that {any} branch-and-bound tree that solves $\\mathcal{I}$ has size $2^{2\\Gamma(\\mathcal{I}) +1} -1$.  \n\\end{remark}\nThis is the instance of $m$ disjoint triangles presented in \\cite{basu2020complexity}. Note that the smallest vertex cover in this instance has value $2m$ while the optimal solution to the LP relaxation has value $\\frac{3}{2}m$, therefore $\\Gamma(\\mathcal{I}) = \\frac{1}{2}m$. It follows from the discussion in \\cite{basu2020complexity}, that all branch-and-bound trees for this instance have $2^m $ leaves, i.e., at least $2^{m +1} - 1$ nodes. \n\nWe note that the result of Theorem~\\ref{thm:vc_fpt} matches the classic upper bound using bounded search trees; see Theorem 3.8 of \\cite{cygan2015parameterized}.\n\nWe present the proof of Theorem~\\ref{thm:vc_fpt} in Section \\ref{sec:fpt}. \n\n\\paragraph{Strong branching and persistency.}\n\nNemhauser and Trotter~\\cite{nemhauser1975vertex} prove the following property regarding the LP relaxation of vertex cover. \n\\begin{fact}[Persistency; Theorem 2 of \\cite{nemhauser1975vertex}]\\label{fact:persistency}\nLet $\\mathcal{I}$ be an instance of vertex cover, $\\hat{x}$ be an optimal solution of $L(\\mathcal{I})$ and $I$ be the set of variables on which $\\hat{x}$ is integer (i.e. $I = \\{j : \\hat{x}_j \\in \\{0,1\\} \\}$). Then, there exists an optimal solution $\\hat{y}$ to $\\mathcal{I}$ such that $\\hat{y}$ agrees with $\\hat{x}$ on all of its integer components (i.e. $\\hat{y}_j = \\hat{x}_j$ for all $j \\in I$). \n\\end{fact}\n\nOne way to use this property is to use it as a pre-solve routine, i.e., fix variables that are integral in the optimal solution of the LP relaxation, and then work with the sub-graph induced by the vertices with value $\\frac{1}{2}$ in the optimal solution of the LP. (The extreme points of the LP relaxation of the vertex cover problem are half integral~\\cite{nemhauser1974properties}.)\nHowever, note that in the branch-and-bound tree, every node corresponds to a sub-graph of the original vertex-cover instance, and thus, ideally we would like to continue to use the Nemhauser-Trotter property at each node. Instead of designing a specialized implementation of branch-and-bound algorithm (where we fix variables that have an integer value in the LP optimal solution at each node), we show that strong-branching naturally incorporates ``fixing\" the integral variables of the optimal solution of LP at each node recursively throughout the branch-and-bound tree. In fact, it does even better in the following sense: due to dual degeneracy, there may be  alternative linear programming optimal solutions with different corresponding sets of variables being integral. Strong branching ``avoids branching\" on all the variables that are integral in any of the alternative optimal LP solutions, i.e., strong-branching is not fooled by the LP solver.  \n\nIn order to present our results, we need to define the notion of \\emph{maximal set of integer variables} and present some properties regarding this set of variables. \n\n\\begin{fact}[Lemma 1 in \\cite{picard1977integer}]\\label{fact:max_idx}\nConsider instance of vertex cover and its LP relaxation. Let $x^1, x^2$ be two optimal solutions to this LP relaxation and let $I^1, I^2 \\subseteq [n]$ be the indices of the integer valued variables in $x^1, x^2$ respectively. Then, there exists an optimal solution of the LP relaxation, $\\hat{x}$,  such that the set of integer valued variables in $\\hat{x}$ is $I = I^1 \\cup I^2$.\n\\end{fact}\n\nBased on the above fact we obtain the following observation: Given a vertex cover instance, if we examine all the maximal optimal solutions of the linear programming relaxation in terms of the number of integral components, then all such maximal solutions have integrality in one unique subset $I \\subseteq [n]$ of indices. Given an instance of vertex cover $\\mathcal{I}$, we call this subset the \\emph{maximal set of integer variables} and denote as $I(\\mathcal{I})$.  Fact~\\ref{fact:persistency} then implies that there exists an optimal solution to the vertex-cover instance where the  \\emph{maximal set of integer variables} are fixed to integer values from the corresponding values of an maximal optimal solution of the LP relaxation. \n\nAs discussed before, in a branch-and-bound tree, each node corresponds to a vertex cover instance on a sub-graph. Therefore, we can define the notion of maximal set of integer variables at a given node $N$, which we denote as $I(\\mathcal{I}, N)$. Given an instance of vertex cover $\\mathcal{I}$, we refer to $\\mathcal{TP}(\\mathcal{I})$ as a partial branch-and-bound tree for $\\mathcal{I}$ if all the nodes of $\\mathcal{TP}(\\mathcal{I})$ cannot be pruned. For such a partial branch-and-bound tree, we use $\\mathcal{TP}^B(\\mathcal{I})$ to refer to the dual bound that one can infer from the partial tree. \n\nThe strength of strong-branching with regards to the maximal set of integer variables at a node $N$ is explained by the next result: Let $j$ belong to the maximal set of integer variables at node $N$. If the LP solver returns an optimal solution with $x_j$ integral, then clearly we do not branch on this variable. However, if the LP solver returns an optimal solution where $x_j$ is fractional and we decide on branching on this variable  based on strong-branching, then it must be that we have ``nearly solved\" the instance, i.e., the dual bound that can be inferred from the partial tree must be equal to the optimal objective function value of the instance.  Formally we have the following:\n\n\\begin{proposition}\\label{prop:makekernelsense}\nLet $\\mathcal{I}$ be any instance of vertex cover. Assume we break ties within the worst-bound rule for node selection by selecting a node with the largest depth. Consider a partial tree $\\mathcal{TP}_S$ generated by strong-branching with the above version of worst-bound node selection rule. Let $N$ be a node of this tree that is not pruned. If $j \\in I(\\mathcal{I},N)$ and we decide to branch on variable $x_j$ at node $N$ (using strong-branching), then \n\\begin{enumerate}\n\\item $\\mathcal{TP}_S^B(\\mathcal{I}) = \\textup{OPT}(\\mathcal{I})$.\n\\item After branching on $x_j$, we need to branch another $\\mathcal{O}(n)$ times to find an integral optimal solution. \n\\end{enumerate}\n\\end{proposition}\n\nThe above result shows that  we ``almost never\" branch on maximal set of integer variables at a node if we use strong-branching. However, after branching on a variable that is not in the maximal set of integer variables, what happens to the set of maximal set of integer variables at the child nodes? A very favorable property would be if the  maximal set of integer variables of the parent node is inherited by the child nodes.  Otherwise, while we may not branch on $x_j$ where $j \\in I(\\mathcal{I},N)$ at node $N$, but we may end up branching on $j$ for a child $N'$ of $N$ --- in other words, we are then not really ``fixing\" variable $x_j$.  As it turns out the above bad scenario does not occur. Formally we have the following:\n\n\\begin{theorem}\\label{thm:nt-monot}\nLet $\\mathcal{I}$ be an instance of vertex cover. Consider any internal node $N$ of $\\mathcal{T}_S(\\mathcal{I})$ \nand let $N'$ be a child node of $N$ that results from branching on $x_v$ where $v \\not \\in I(\\mathcal{I}, N)$. Then, $I(\\mathcal{I}, N) \\subset I(\\mathcal{I}, N')$.\n\\end{theorem}\n\n\nTherefore, using Proposition~\\ref{prop:makekernelsense} and Theorem~\\ref{thm:nt-monot} together, we can conclude that when using strong-branching, we are essentially repeatedly using Nemhauser-Trotter property recursively and consistenly through-out the branch-and-bound tree: If $j$ is in the maximal set of integer variables at node $N$, it continues to remain in the maximal set of integer variables for all the child nodes of $N$; and we do not branch on such a variable $x_j$ at node $N$ or any of its children unless the instance is essentially solved (i.e., dual bound inferred from the tree equals the values of the IP). \n\nHere we present an example to illustrate that there are variable selection rules for which the property described in Theorem \\ref{thm:nt-monot} does not hold. See the instance $\\mathcal{I}^*$ shown in Figure \\ref{fig:monoton_ex}. Consider the following partial branch-and-bound tree, letting $N$ denote the root node. Observe that there is an optimal LP solution that sets $x_a = x_c = 1$ and $x_b = x_d = 0$; therefore, $I(\\mathcal{I}^*, N) = \\{a, b, c, d\\}$. However, suppose that an adversarial LP solver returns the optimal basic feasible solution $x_a = x_b = x_c = x_d = \\frac{1}{2}$. Suppose we branch on $x_b$ and consider the sub-problem resulting from $x_b = 1$, which we denote $N'$. The unique optimal solution to $N'$ sets $x_b = 1$ and $x_a = x_c = x_d = \\frac{1}{2}$; therefore, $I(\\mathcal{I}^*, N') = \\{b\\} \\subset I(\\mathcal{I}^*, N)$. In fact, this example can be easily extended to that of Theorem \\ref{thm:sep_example} (see below) to show that this variable selection rule similarly results in an exponentially larger branch-and-bound tree as compared to one that is obtained by strong-branching. \n\n\\begin{figure}[ht]\n\\centering\n\\includegraphics[width=0.4\\textwidth]{diamond.png}\n\\caption{Instance $\\mathcal{I}^*$: example illustrating that the property of Theorem \\ref{thm:nt-monot} is not true for every variable selection rule.}\n\\label{fig:monoton_ex}\n\\end{figure}\n\nWe present proof of Proposition~\\ref{prop:makekernelsense} and Theorem~\\ref{thm:nt-monot} in Section~\\ref{sec:kernels}.\n\n\\paragraph{Superiority of strong-branching.}\nThere are very few papers that give upper bounds on sizes of branch-and-bound tree (when we use 0-1 branching)~\\cite{dey2021branch,borst2021integrality}. These papers show that certain class of IPs with random data can be solved using polynomial-size branch-and-tree with high probability. However, these results do not depend on the variable selection rule used. Theorem~\\ref{thm:vc_fpt} above is the first result of its kind that we are aware of, which uses a specific variable selection rule to prove upper bounds on size of branch-and-bound tree. To further highlight the importance of strong-branching in obtaining this upper bound result, we next show that if we do not use the strong-branching rule and we have an ``adversarial\" LP solver, then we may need exponentially larger trees to solve the instance.\n\nIn particular, we next demonstrate the superiority of strong-branching by comparing it with another variable selection rule for the vertex cover problem (which we call the \\emph{greedy-rule}) when the LP solver is adversarial, i.e. the LP solver always gives the most fractional extreme point solution. The greedy-rule for variable selection is intuitive and natural for vertex cover:  branch on the vertex with most fractional neighbors. Since setting such a vertex to $0$ would enforce all of its fractional neighbors to be $1$, one might think this rule provides the most ``local improvement''.\n\n\\begin{theorem}\\label{thm:sep_example}\nConsider an LP solver with the following property: Among all optimal extreme point solutions, it reports an optimal extreme point with maximal number of fractional components. Given an instance $\\mathcal{I}$ and the above LP solver, let $\\mathcal{T}_S(\\mathcal{I})$ and $\\mathcal{T}_G(\\mathcal{I})$ be some branch-and-bound trees that solves instance $\\mathcal{I}$ obtained using the strong-branching rule and the greedy rule respectively. \n\nThere is an instance $\\mathcal{I}^*$ of vertex cover such that \n$$|\\mathcal{T}_G(\\mathcal{I}^*)| \\geq 2^{\\Omega(n)} \\cdot |\\mathcal{T}_S(\\mathcal{I}^*)|$$ \nand furthermore \n$$|\\mathcal{T}_G(\\mathcal{I}^*)| \\geq 2^{\\text{cst}\\cdot \\Gamma(\\mathcal{I}^*)}$$ \nwhere $\\text{cst}$ is a constant strictly greater than $2$.\n\\end{theorem}\n\n\nWe present the proof of Theorem~\\ref{thm:sep_example} in Section~\\ref{sec:sb_greedy_ex}.\n\n\\subsubsection{Strong branching does not work well for some instances}\nNext we present a negative result regarding strong-branching, showing that strong-branching based branch-and-bound tree can have an exponential times as many nodes as compared to number of nodes in an alternative tree. In fact, the example shows something even stronger: any tree that branches only on variables fractional in the current nodes optimal solution will have exponential size, while an alternative tree has linear size.\n\nWe begin by showing a seemingly surprising result about the existence of an extended formulation for any binary IP, that leads to a linear size branch-and-bound tree. \n\n\\begin{proposition}\\label{prop:bdg_ub}\nFor any integer program $\\mathcal{I}$ with $n$ binary variables, there is an equivalent integer program that uses an extended formulation of the feasible region of $\\mathcal{I}$ with $2n$ binary variables, which we refer to as $BDG(\\mathcal{I})$, that has the following property: there exists a branch and bound tree $\\mathcal{T}^*(BDG(\\mathcal{I}))$ that solves the instance $BDG(\\mathcal{I})$ and $|\\mathcal{T}^*(BDG(\\mathcal{I}))| \\leq 4n + 1$.\n\\end{proposition}\n\nThe extended formulation corresponding to $BDG(\\mathcal{I})$ used in Proposition~\\ref{prop:bdg_ub} was first introduced in~\\cite{bodur2017cutting} to show that every binary integer program has an extended formulation with split rank of $1$. We also remark here that Proposition~\\ref{prop:bdg_ub} does not imply that the decision version of binary IPs is in \\emph{co-NP}. This is because the $BDG(\\mathcal{I})$  formulation may be of exponential-size in comparison to the original formulation. \n\nIn  Corollary~\\ref{cor:bdg_lb} below, we take the cross-polytope~\\cite{dey2021lower} and apply\n the extended formulation of Proposition~\\ref{prop:bdg_ub} to obtain an example where strong-branching based branch-and-bound tree can have an exponential times as many nodes as compared to number of nodes in an alternative tree.\n\\begin{corollary}\\label{cor:bdg_lb}\nThere exists an instance $\\mathcal{I}^*$ with $2n$ binary variables, such that the following holds: Let $\\mathcal{T}(\\mathcal{I}^*)$ be any tree that solves $\\mathcal{I}^*$ satisfying the following property: if $x$ is the optimal solution to an internal node $N$ of $\\mathcal{T}(\\mathcal{I}^*)$, then the variable $j$ branched on at $N$ must be such that $x_j \\in (0,1)$. Then, $|\\mathcal{T}(\\mathcal{I}^*)| \\geq 2^{n +1} - 1$.   In particular, if $\\mathcal{T}_S(\\mathcal{I}^*)$ is a branch-and-bound tree generated using strong-branching that solve $\\mathcal{I}^*$, then $|\\mathcal{T}_S(\\mathcal{I}^*)| \\geq 2^{n +1} - 1$.  On the other hand,  there exists a tree $\\mathcal{T}^*$ that solves $\\mathcal{I}^*$ such that $|\\mathcal{T}^*(\\mathcal{I}^*)| \\leq 4n + 1$.\n\\end{corollary}\n\n\n\n\n\nTypically, when implementing a branch-and-bound algorithm, one might be inclined to restrict the algorithm to branch on variables that are fractional in the current optimal solution. Therefore the above example is counter-intuitive in that it shows there can be a significant separation between branch-and-bound trees that are restricted to branch on variables that are fractional in the current optimal solution and branch-and-bound trees that are allowed to branch on integer valued variables. To our knowledge, this is the first such explicit example in the literature.\n\nWe present a proof of Proposition~\\ref{prop:bdg_ub} and Corollary \\ref{cor:bdg_lb} in  Section \\ref{sec:bdg_ex}.\n\\subsection{Computational results}\nIn the previous section, we have shown that strong-branching works well for vertex cover and on the other hand, strong-branching can sometimes produce exponentially larger trees than alternative trees to solve an instance.  However, in general it seems very difficult to analyze strong-branching for general MILPs on a case-to-case basis. Moreover, we would really like to answer the question: how good is the strong-branching based branch-and-bound tree in comparison to the optimal tree? We try and answer this question computationally in this section.\n\n\\paragraph{Optimal branch-and-bound tree.}\nWe begin with a discussion of an ``optimal branch-and-bound tree\" for a given instance\n\nFirst note that it is clear that the optimal branch-and bound tree uses the worst bound rule for node selection~\\cite{wolsey1999integer}. Moreover, we will consider branching on all variables at a given node, whether it is integral or not in the optimal solution of the LP relaxation. Since we are using the worst bound rule for node selection, we only branch on nodes whose objective function value is at least as good as that of the MILP optimal objective function value, i.e. (i) any node those optimal objective value is strictly better than the MILP optimal objective function must be branched on, (ii)  similarly, any node those optimal objective value is strictly less than the MILP optimal objective function will never be branched on.\n\nNow consider a node whose LP optimal objective function value is equal to that of the MILP optimal objective function value. There are two possible scenarios:\n\\begin{itemize}\n\\item The optimal face of this LP is integral, i.e., all the vertices of the optimal face are integer feasible and therefore the LP solver (like simplex) is guaranteed to find an integral solution and prune the node.\n\\item At least one vertex of the optimal face is fractional. In this case, depending on whether the LP solver returns an integral vertex or not, we are able to prune the node or not. Moreover, if we arrive at a fractional vertex, then depending on properties of other nodes and how we break ties for node selection among nodes with same objective function value, we may or may not end up branching on this node. \n\\end{itemize}\nIn other words, in the second case, the size of tree may depend on the type of optimal vertex reported by the LP solver. In order to simplify our analysis and to remove all ambiguity regarding the definition of the optimal branch-and-bound tree, we make the following assumption for results presented in this section.\n\n\\begin{assumption}\\label{assum:int}\nWe assume that if there exists an optimal solution to the LP relaxation at a given node that is integral,  then the LP solver finds it. \n\\end{assumption}\n\n\\begin{observation}\\label{obs:assumption}\nWhen using an LP solver which satisfies Assumption \\ref{assum:int}, a branch-and-bound tree using the worst bound rule  never branches on a node whose optimal objective function value is equal to that of the IP solver. \n\\end{observation}\nProof of Observation~\\ref{obs:assumption} is presented in Section~\\ref{sec:opttreewelldefined}.\nThe above observation clearly makes the notion of ``optimal branch-and-bound tree\" for a given instance well-defined: Restricting to any face of the zero-one cube (corresponding to branching-constraints), we precisely know if this node will be pruned or not. Thus, for a given set of branching-decision there is a deterministic number of nodes to solve the MILP, leading to an well-defined optimal number of nodes to solve an instance.\n\n\\paragraph{Dynamic programming algorithm for finding the optimal branch-and-bound tree.}\n\nIn Section~\\ref{sec:dpalgo} we present a dynamic programming (DP) algorithm that computes an optimal branch-and-bound tree for a given instance under Assumption~\\ref{assum:int} for the LP solver. \n\\begin{theorem}\\label{thm:DP}\nUnder Assumption~\\ref{assum:int}, there exists an algorithm with running time $\\textup{poly}(data)\\cdot3^{O(n)}$ time to compute an optimal branch-and-bound tree for any binary MILP instance $\\mathcal{I}$ defined on $n$ binary variables. \n\\end{theorem}\n\nSection~\\ref{sec:dpalgo} also presents some computational enhancements (like exploiting parallel computing) to improve the wall clock run time of the DP algorithm.\n\n\\paragraph{Computationally comparison of various variable selection rules against the optimal branch-and-bound tree.}\n\nWe conduct the first study comparing branch-and-bound trees employing different variable selection rules to the optimal branch-and-bound tree.  Detailed results are presented in Section~\\ref{sec:experiments}.\n\n\nWe consider the following variable selection rules: strong-branching with linear score function, strong-branching with product score function, most infeasible, and random. We evaluate the performance of these rules on a wide range of problems: multidimensional variants of knapsack problem (packing-type, covering-type, and mixed packing and cover instances), lot-sizing and variants, vertex cover, chance constraint programming (CCP) models for multi-period power planning and portfolio optimization, and stable set on a bipartite graph with knapsack sides constraint (100 instances for each model). Note that all these instances have up to $20$ binary variables since we are unable to run the DP algorithm of Theorem~\\ref{thm:DP} for larger instances. See Section~\\ref{sec: Data generation} for a detailed description of all these instances. \n\nWe present a discussion of all our results (together with tables and explanatory figures) in Section~\\ref{sec:compres}. Here are some of our notable findings on sizes of branch-and-bound tree trees:\n\\begin{itemize}\n    \\item Random consistently performs the worst.\n    \\item Strong branching \\textit{almost} always performs the best. Strong branching is out-performed by most-infeasible branching strategy on the CCP multi-period power planning problem.\n    \\item While the performance of two variants of strong-branching is comparable on all problems considered in this study, strong branching with product score function (SB-P) dominates over strong branching with linear score function (SB-L) on 8 out of 10 problems, although by a small margin.\n    \\item The geometric mean of branch-and-bound tree size using strong-branching remains less than twice the size of optimal branch-and-bound tree for all problems considered in this study.\n\\end{itemize}\nFinally, see Figure \\ref{fig:gmratio} for a summary of the computational results. It is clear that while strong-branching does quite well (within a factor of $2$), there is clearly scope for coming up with better rules for deciding branching variables, for example for problems such as CCP multi-period power planning problem. It would be interesting to see if one can use machine learning techniques to learn from the optimal branch-and-bound trees.\n\n\\begin{figure}[ht]\n    \\centering\n    \\includegraphics[width=0.8\\linewidth]{Charts\/gmRatio.png}\n    \\caption{Ratio of geometric mean of branch-and-bound tree sizes to geometric mean of optimal tree sizes over all instances of a problem for various branching strategies. ``Rand\" stands for random, ``Most Inf\" stands for most infeasible, ``SB-P\" stands for strong-branching with product score function, and ``SB-L\" stands for strong-branching with linear score function.}\n    \\label{fig:gmratio}\n\\end{figure}\n\nIn previous section (see Corollary~\\ref{cor:bdg_lb}), we have seen an example where strong-branching performs badly while alternative branch-and-bound tree that has exponentially lesser nodes, branches on integer variables. So a natural question we would like to understand is the percentage of times the optimal branch-and-bound tree branches on integer variables for the various instances. These results are presented in Table~\\ref{tab:ratio}.  We note that there are multiple optimal trees. So it may be possible that these exists other optimal trees with a slightly different number of branchings on integer variables.  \n\nHere are some of our notable findings:\n\\begin{itemize}\n\\item Strong branching does relatively poorly on knapsack which has a high fraction of integer branchings in the optimal tree and it does very well on Lot-sizing where the optimal tree rarely branches on integers. So it would appear consistent with our hypothesis that more branchings on integer variables in the optimal tree implies strong-branching performs poorly.\n\\item However, in the case of CCP multi-period power planning problem, strong-branching has a relatively poor performance, yet the optimal tree almost always branches on fractional values. \n\\item Finally, for stable set on bipartite graph with knapsack side constraint, strong-branching does very well in spite of a lot of integer branchings in the optimal tree. \n\\end{itemize}\n\n\\begin{table}[ht]\n\n\\begin{center}\\small\n\n\\caption{Summary of average tree sizes (geometric) and percentage of branching on integral variable in optimal tree for all problems across 100 instances}\\label{tab:ratio}\n\n\n\\begin{tabular}{lrrrrrr}\n\n\n\nProblem                                    & Opt Tree & SB-L   & SB-P   & Most inf & Rand   & \\% Int Branch \\\\\n        \t\n\\cline{1-7}\n\nMulti-dimensional Packing   Knapsack       & 25.44    & 41.24  & 40.88  & 51.01    & 60.20  & 48\\%                                       \\\\\n\nMulti-dimensional Covering   Knapsack      & 24.48    & 38.11  & 37.98  & 47.87    & 55.19  & 50\\%                                       \\\\\n\nMix Packing + Covering Knapsack            & 10.18    & 13.78  & 13.77  & 14.99    & 17.61  & 48\\%                                       \\\\\n\nLot-sizing                                 & 109.68   & 132.71 & 128.90 & 453.61   & 640.65 & 0.2\\%                                       \\\\\n\nConstrained Lot-sizing                     & 98.44    & 126.84 & 121.58 & 321.61   & 608.48 & 0.1\\%                                       \\\\\n\nBig-bucket Lot-sizing                      & 83.77    & 113.72 & 110.08 & 273.14   & 365.87 & 1\\%                                       \\\\\n\nCCP Power Planning                         & 38.69    & 68.63  & 70.37  & 55.85    & 337.97 & 0.9\\%                                       \\\\\n\nCCP Portfolio Optimization                 & 96.59    & 170.81 & 168.85 & 205.82   & 653.21 & 4\\%                                       \\\\\n\nStable Set on Bipartite Graph +   Knapsack & 132.93   & 174.13 & 183.93 & 176.54   & 189.92 & 48\\%                                       \\\\\n\nMinimum Vertex Cover                       & 6.99     & 9.10   & 8.98   & 12.02    & 12.04  & 0\\%                \\\\                     \n\\cline{1-7}\n\\end{tabular}\n\n\n\\end{center}\n\\end{table}\n\n\nIn other words, there does not seem to be a direct relationship between the performance of strong-branching and the number of branching on integer variable of the optimal branch-and-bound tree. \n\nFinally we end this section with a word of caution regarding over-interpreting the computational results above: As mentioned above, due of the exponential nature of the DP algorithm to compute the optimal branch-and-bound tree, computational experiments could be performed only on relatively smaller problem sizes with up to 20 binary variables. Some of the observations derived here may not extrapolate to larger instances. \n\n\\section{Analysis of Strong Branching for Vertex Cover}\\label{sec:vertexcoverproof}\n\n\n\n\\subsection{Proof of Theorem~\\ref{thm:vc_fpt}.}\\label{sec:fpt}\n\n\n Throughout this section, we use $N_{j, 0}$ to denote the child node of $N$ that results from the branch $x_j = 0$; we use $N_{j, 1}$ similarly.\n\nThroughout this section we make the following assumptions. Let $\\mathcal{I}$ be any instance of vertex cover. Assume we break ties within the worst-bound rule for node selection rule by selecting a node with the largest depth.  Let $\\mathcal{T}_S(\\mathcal{I})$ be \\emph{some branch-and-bound tree generated by strong-branching} with the above version of worst-bound node selection rule that solver $\\mathcal{I}$. Moreover, all results are independent of the underlying LP solver used.\n\nWe will require two preliminary results for the proof of Theorem~\\ref{thm:vc_fpt}.\n\n\\begin{lemma}\\label{lem:branch_frac}\nLet $N$ be a node of $\\mathcal{T}_S(\\mathcal{I})$ with optimal objective value  less than $\\textup{OPT}(\\mathcal{I})$. Then strong-branching will branch on $v \\not \\in I(\\mathcal{I}, N)$ at node $N$ and $N_{v, 0}, N_{v, 1}$ have optimal value at least $\\frac{1}{2}$ more than that of $N$. \n\\end{lemma}\n\n\\begin{proof}\nSince $N$ has optimal objective value less than $\\textup{OPT}(\\mathcal{I})$, the LP relaxation at $N$ must not have an optimal solution that is integer. Note that if at $N$ we branch on $x_u$ where $u \\in I(\\mathcal{I}, N)$, it must hold that, at least one of $N_{u, 0}$ or $N_{u, 1}$ have optimal value the same as $N$. Therefore, $\\text{score}_{P}(u) = 0$. We now show that there exists $v \\in [n]$ such that $\\text{score}_{P}(v) > 0$. If there is no optimal solution to $N$ that is integer, then $I(\\mathcal{I}, N) \\not = [n]$ by Fact \\ref{fact:max_idx}. Therefore, there exists a $v \\not \\in I(\\mathcal{I}, N)$ such that $x_v = \\frac{1}{2}$ in every optimal solution to $N$. It follows that fixing $x_v \\in \\{0,1\\}$ must result in a feasible solution to $N$ that has strictly greater value, and so branching on $x_v$ at $N$ leads to child nodes $N_{v, 0}$ and $N_{v, 1}$ where both have optimal value more than that of $N$. Further, since $N_{v, 0}$ and $N_{v, 1}$ have objective value strictly more than $N$ and all basic feasible solutions are half-integral, it holds that $N_{v,0}$ and $N_{v, 1}$ have objective value at least $\\frac{1}{2}$ more than $N$. \n\\end{proof}\n\n\\begin{lemma}\\label{lem:branch_int}\nLet $N$ be a node of $\\mathcal{T}_S(\\mathcal{I})$ with an optimal LP solution that is integer. Then the sub-tree rooted at $N$ will have size $\\mathcal{O}(n)$, where it finds an integer optimal solution. \n\\end{lemma}\n\n\\begin{proof}\nLet $y \\in \\{0,1\\}^n$ be an optimal solution to the LP of node $N$. If the LP solver returns an integer solution, we are done. Suppose not, and suppose we branch on some variable $v$, and without loss of generality let $y_v = 0$. Then, of course $N_{v, 0}$ will have $y$ as an optimal solution and therefore have value $\\textup{OPT}(\\mathcal{I})$. If $N_{v, 1}$ has value greater than $ \\textup{OPT}(\\mathcal{I})$, this node gets pruned by bound and we continue by branching on $N_{v, 0}$ since it is now the open node with largest depth. Suppose instead $N_{v, 1}$ has value $\\textup{OPT}(\\mathcal{I})$. Then, we argue in the next paragraph that there is an optimal solution to the LP corresponding to $N$ that is integer feasible, denote $z$, with $z_v = 1$; in this case we can break the tie between $N_{v, 0}, N_{v, 1}$ arbitrarily. Then, for every node $N'$ in the sub-tree rooted at $N$, either one child of $N'$ has value greater than $\\textup{OPT}(\\mathcal{I})$ and is pruned by bound, or both children of $N'$ have optimal solutions that are integer. In the second case, only one of these two children will ever be branched on, since we break ties by branching on the node with largest depth, and therefore will find an integer solution before revisiting a shallower node. The result of the lemma follows.\n\nHere we argue that if $N_{v,1}$ has a LP optimal objective function value $\\textup{OPT}(\\mathcal{I})$, then there is an optimal solution to the LP corresponding to $N$ that is integral, denote $z$, with $z_v = 1$. Let $x'$ denote any optimal solution of $N_{v,1}$ and observe that $x',y$ are both optimal solutions to $N$. It follows from the proof of Lemma 1 in \\cite{picard1977integer} that: given two half-integral optimal solutions $x', y$, there exists an optimal solution $z$ constructed as follows:\n$$ z_j = \\begin{cases}\n1 & \\text{ if } x'_j = 1 \\text{ or } x'_j = \\frac{1}{2}, y_j = 1\\\\\n0 & \\text{ if } x'_j = 0 \\text{ or } x'_j = \\frac{1}{2}, y_j = 0 \\\\\n\\frac{1}{2} & \\text{ if } x'_j = y_j = \\frac{1}{2}\n\\end{cases}\n$$\nIn particular,~\\cite{picard1977integer} shows that that $z$ constructed as above is feasible and satisfies, $\\sum_{j}z_j = \\sum_{j}x'_j = \\sum_{j}y_j$. Clearly $z_v = x'_v = 1$ and since $y \\in \\{0,1\\}^n$, it follows that $z \\in \\{0,1\\}^n$ and is an optimal solution of the LP corresponding to $N$. \n\\end{proof}\n\n\n\\begingroup\n\\def\\ref{thm:DP}{\\ref{thm:vc_fpt}}\n\\begin{theorem}\nLet $\\mathcal{I}$ be any instance of vertex cover. Assume we break ties within the worst-bound rule for node selection rule by selecting a node with the largest depth.  Let $\\mathcal{T}_S(\\mathcal{I})$ be \\emph{some branch-and-bound tree generated by strong-branching} with the above version of worst-bound node selection rule that solver $\\mathcal{I}$. Then independent of the underlying LP solver used, \n$$|\\mathcal{T}_S (\\mathcal{I})| \\leq 2^{2\\Gamma(\\mathcal{I}) + 2} + \\mathcal{O}(n).$$\n\\end{theorem}\n\\addtocounter{theorem}{-1}\n\\endgroup\n\n\\begin{proof}\nFix any branch-and-bound tree (using strong-branching) for $\\mathcal{I}$. Let $N$ be a node at depth $2\\Gamma(\\mathcal{I}) + 1$. Suppose that no ancestor of $N$ had an optimal LP solution that was integer; it follows from Lemma \\ref{lem:branch_frac} that $N$ has optimal objective value at least $\\textup{OPT}(\\mathcal{I}) + \\frac{1}{2}$. Denote the set of such nodes $\\mathcal{N}_{\\text{no ancestor}}$ and note that these nodes are pruned by bound.  Observe all other nodes (if any) at depth $2\\Gamma(\\mathcal{I}) + 1$ do have such an ancestor. Let $\\mathcal{N}_{\\text{integer}}$ denote the set of nodes at depth $\\leq 2\\Gamma(\\mathcal{I})$ that have an optimal solution that is integer, but none of its ancestors have an optimal solution that is integer. Finally, observe that $|\\mathcal{N}_{\\text{no ancestor}}| + |\\mathcal{N}_{\\text{integer}}| \\leq 2^{2\\Gamma(\\mathcal{I}) + 1}$. We conclude the proof by observing that Lemma \\ref{lem:branch_int} gives: if $N$ is the node in $\\mathcal{N}_{\\text{integer}}$ with largest depth, then the sub-tree rooted at $N$ has size $\\mathcal{O}(n)$ where it finds an integer solution with value $\\textup{OPT}(\\mathcal{I})$. Therefore, no other nodes in $\\mathcal{N}_{\\text{integer}}$ will be branched on. Since the number of leaves in this tree is at most $2^{2\\Gamma(\\mathcal{I}) + 1} + \\mathcal{O}(n)$, the result of the theorem follows. \n\n\\end{proof}\n\n\n\n\n\\subsection{Proof of Proposition~\\ref{prop:makekernelsense} and Theorem~\\ref{thm:nt-monot}.}\\label{sec:kernels}\n\n\\begingroup\n\\def\\ref{prop:bdg_ub}{\\ref{prop:makekernelsense}}\n\\begin{proposition}\nLet $\\mathcal{I}$ be any instance of vertex cover. Assume we break ties within the worst-bound rule for node selection by selecting a node with the largest depth. Consider a partial tree $\\mathcal{TP}_S$ generated by strong-branching with the above version of worst-bound node selection rule. Let $N$ be a node of this tree that is not pruned. If $j \\in I(\\mathcal{I},N)$ and we decide to branch on variable $x_j$ at node $N$ (using strong-branching), then \n\\begin{enumerate}\n\\item $\\mathcal{TP}_S^B(\\mathcal{I}) = \\textup{OPT}(\\mathcal{I})$.\n\\item After branching on $x_j$, we need to branch another $\\mathcal{O}(n)$ times to find an integral optimal solution. \n\\end{enumerate}\n\\end{proposition}\n\\addtocounter{proposition}{-1}\n\\endgroup\n\n\\begin{proof}\nWe begin by proving property 1. Suppose for sake of contradiction, there exists an open node $N'$ in $\\mathcal{TP}_S^B(\\mathcal{I})$ with optimal objective value less than $ \\textup{OPT}(\\mathcal{I})$. It follows from the worst-bound rule and Lemma \\ref{lem:branch_frac} that strong-branching will choose to branch on $j'$ at $N'$ with $j' \\not\\in I(\\mathcal{I}, N')$. Thus $j'$ and $N'$ are not the same as $j$ and $N$, giving the desired contradiction.\n\nProperty 2 follows directly from Lemma \\ref{lem:branch_int} and the fact that $I(\\mathcal{I},N) = [n]$, since otherwise strong-branching would branch on some $j \\not \\in I(\\mathcal{I},N)$. \n\\end{proof}\n\n\n\\begingroup\n\\def\\ref{thm:DP}{\\ref{thm:nt-monot}}\n\\begin{theorem}\nLet $\\mathcal{I}$ be an instance of vertex cover. Consider any internal node $N$ of $\\mathcal{T}_S(\\mathcal{I})$  and let $N'$ be a child node of $N$ that results from branching on $x_v$ where $v \\not \\in I(\\mathcal{I}, N)$. Then, $I(\\mathcal{I}, N) \\subset I(\\mathcal{I}, N')$.\n\\end{theorem}\n\\addtocounter{theorem}{-1}\n\\endgroup\n\n\n\\begin{proof}\nThroughout this proof, we use $N_{j, 0}$ to denote the child node of $N$ that results from the branch $x_j = 0$; we use $N_{j, 1}$ similarly. We use $\\delta(S)$ to denote the neighbors of any subset of vertices $S \\subseteq V$. Also, throughout the proof, let $x^*$ be an optimal solution to $N$ with maximal set of integer components (i.e. $x^*_j \\in \\{0,1\\}$ for all $j \\in I(\\mathcal{I}, N)$).\n\nWe will first consider the child $N_{v, 1}$. Consider the solution $y$ to $N_{v, 1}$ constructed from $x^*$ as follows: $y$ takes the same values as $x^*$, but $y_v = 1$ instead of $\\frac{1}{2}$. Note that this is feasible for $N_{v, 1}$. Since $v \\not \\in I(\\mathcal{I}, N)$ we have that $x_v = \\frac{1}{2}$ in every optimal solution to $N$. In other words, optimal objective function value of $N_{v,1}$ is at least $\\frac{1}{2}$ more than that of $N$. Also, $\\ip{1}{y} = \\ip{1}{x^*} + \\frac{1}{2}$, and so, $y$ is an optimal solution to $N_{v, 1}$. So $I(\\mathcal{I}, N) \\subset I(\\mathcal{I}, N')$ follows in the case of $N' = N_{v, 1}$. \n\nWe will now consider the child $N_{v, 0}$. Let $V_1^* = \\{u \\in V : x^*_u = 1\\}$ and $V_0^*$ be defined similarly. We will need the following technical result later in the proof.\n\n\\begin{lemma}\\label{lem:neighbors}\n$|\\delta(S) \\cap V_0^*| \\geq |S|$ for all $S \\subseteq V_1^*$. \n\\end{lemma}\n\n\\begin{proof}\nAssume, for the sake of contradiction, there is a subset $S \\subseteq V_1^*$ such that $|\\delta(S) \\cap V_0^*| < |S|$, then it must hold that $x^*$ is not an optimal solution. This is because, we can set all of $S$ and $\\delta(S) \\cap V_0^*$ to be $\\frac{1}{2}$. This remains feasible, since we are only decreasing the value of the vertices in $S$, but all of the vertices with value $0$ adjacent to these vertices are also being raised to $\\frac{1}{2}$. It also decreases the cost, since $\\frac{1}{2} (|\\delta(S) \\cap V_0^*| + |S|) < |S|$. \n\\end{proof}\n\nLet $x'$ be any optimal solution to LP corresponding to $N_{v, 0}$. Let $\\Phi = \\{u \\in V_1^* : x'_u \\not = 1 \\}$. We will construct a feasible solution $z$ such that $z_u = 1$ for all $u \\in V_1^*$ with cost no more than\nthat of $x'$. Note that since $\\delta(V_0^*) \\subseteq V_1^*$, this implies the existence of an optimal solution to $N_{v, 0}$ with the same integer variables as $x^*$ (since any optimal solution with all variables in $V_1^*$ set to $1$ will have all variables in $V_0^*$ set to $0$). \n\nWe begin by constructing an intermediate solution $y$. Notice $\\Phi$ can be partitioned into $\\Phi^0 = \\{u \\in \\Phi : x'_u = 0\\}$ and $\\Phi^{\\frac{1}{2}} = \\{u \\in \\Phi : x'_u = \\frac{1}{2}\\}$. Let $y$ be defined by setting the variables in $\\Phi^0$ to $\\frac{1}{2}$ and setting the variables in $\\delta(\\Phi^0) \\cap V_0^*$ to $\\frac{1}{2}$ (note that $x'_u = 1$ for all $u \\in \\delta(\\Phi^0) \\cap V_0^*$). This maintains feasibility, since the variables with decreasing value are a subset of $V_0^*$, which are only adjacent to vertices in $V_1^*$ which now all have value at least $\\frac{1}{2}$ in $y$. This also maintains optimality, since the cost increases by $\\frac{1}{2}|\\Phi^0|$ and decreases by $\\frac{1}{2}|\\delta(\\Phi^0) \\cap V_0^*|$, and by Lemma \\ref{lem:neighbors}, $|\\delta(\\Phi^0) \\cap V_0^*| \\geq |\\Phi^0|$. We now construct $z$ similarly, from this intermediate solution $y$. Notice now, that all variables in $\\Phi$ have value $\\frac{1}{2}$ in $y$. We construct $z$ by setting all of these variables to $1$ and setting all variables in $\\delta(\\Phi) \\cap V_0^*$ to $0$ (note that $y_u \\geq \\frac{1}{2}$ for all $u \\in \\delta(\\Phi) \\cap V_0^*$). This maintains feasibility, since the variables with decreasing value are a subset of $V_0^*$, which are adjacent only to vertices in $V_1^*$, which all have value at least $1$ in $z$. This also maintains optimality, since the cost increases by $\\frac{1}{2}|\\Phi|$ and decreases by at least $\\frac{1}{2}|\\delta(\\Phi) \\cap V_0^*|$, and by Lemma \\ref{lem:neighbors}, $|\\delta(\\Phi) \\cap V_0^*| \\geq |\\Phi|$. Finally, we note that $z$ maintains feasibility for $N_{v, 0}$, since $x'_v = 0$ and therefore $x'_u = 1$ for all $u \\in \\delta(v)$; since $\\delta(v) \\cap \\Phi =  \\emptyset$, all vertices $v$ and $\\delta(v)$ keep their value in $z$. This concludes the proof. \n\n\\end{proof}\n\n\n\n\\subsection{Proof of Theorem \\ref{thm:sep_example}.}\\label{sec:sb_greedy_ex}\n\nIn this section, we will demonstrate an instance of vertex cover where the worst tree can have $2^{\\Omega(n)}$ times as many nodes as the tree generated by strong-branching. Here we assume that the LP solver finds a basic feasible solution at every node, but the one with the \\textit{most} fractional components.\n\n\\paragraph{The instance.} Here we refer to a \\textit{triangle} as a $K_3$ and to a \\textit{diamond} as a $K_4$ minus an edge; see Figure \\ref{fig:graphs}. Let $G$ be a union of $m$ triangles and $\\frac{1}{2}m$ diamonds. We will consider the instance of finding the maximum unweighted vertex cover on $G$. Observe the following properties of this instance:\n\\begin{itemize}\n    \\item The number of vertices is $5m$.\n    \\item An optimal IP solution picks both vertices of degree $3$ in each diamond and any two vertices in each triangle, so the optimal IP value is $3m$. This also implies that, at the root node, the maximal set of integer variables $I$ is the set of vertices that make up the diamonds.\n    \\item An optimal LP solution sets all vertices to have value $\\frac{1}{2}$, so the optimal LP value is $\\frac{5}{2}m$. \n    \\item The additive integrality gap of the instance is then $\\frac{1}{2}m$. \n\\end{itemize}\n\n\\begin{figure}[ht]\n\\centering\n\\includegraphics[width=0.35\\textwidth]{triangle.png}\n\\hspace{0.08\\textwidth}\n\\includegraphics[width=0.4\\textwidth]{diamond.png}\n\\caption{We refer to the component on the \\textbf{left} as a \\textit{triangle} and the component on the \\textbf{right} as a \\textit{diamond}. We label the vertices of the diamond for ease of following the arguments of this section. }\n\\label{fig:graphs}\n\\end{figure}\n\n\\paragraph{Branching on a diamond.} Consider any diamond, and suppose all of its vertices are set to $\\frac{1}{2}$ in the LP optimal solution. Let $a$ be a vertex of degree $3$ and $b$ be a vertex of degree $2$; see Figure \\ref{fig:graphs}. First, we consider the case of branching on $a$. Setting $x_a = 0$, the only feasible solution is to set the three other vertices in the diamond to $1$. This increases the objective value by $1$. Setting $x_a = 1$, the only optimal solution sets $x_c = 1$ and $x_b = x_d = 0$. This results in no objective value change. Therefore, $\\text{score}_{P}(a) = 0$. Now, we consider the case of branching on $b$. Setting $x_b = 0$, any feasible solution sets $x_a = x_c = 1$ and the only optimal solution then sets $x_d = 0$. This results in no change to the objective value. Setting $x_v = 1$, the only optimal solution sets $x_a = x_c = x_d = \\frac{1}{2}$. This results in an objective value increase of $\\frac{1}{2}$. Therefore, $\\text{score}_{P}(b) = 0$. \n\n\\paragraph{Branching on a triangle.} Consider any triangle, and suppose all of its vertices are set to $\\frac{1}{2}$ in the LP optimal solution. Let $u$ be any vertex of the triangle. Setting $x_u = 0$, the only optimal solution is to set the other two vertices to $1$. This results in an objective value increase of $\\frac{1}{2}$. Setting $x_u = 1$, any optimal basic feasible solution sets one of the other two vertices to $1$ and the other to $0$. This results in an objective value increase of $\\frac{1}{2}$. Therefore, $\\text{score}_{P}(u) = \\frac{1}{4}$. \n\n\\paragraph{Strong branching.} Observe that, given an instance with at least one diamond with all of its vertices set to $\\frac{1}{2}$ and at least one triangle with all of its vertices set to $\\frac{1}{2}$, strong-branching will choose to branch on a vertex in such a triangle. Then, observe that each node on the $m$-th level of the strong-branching tree ''looks the same'': its LP optimal solution has an integer value for each vertex in every triangle, in particular, sets two vertices to $1$ and one vertex to $0$; and all other vertices (i.e. all vertices in the diamonds) are set to $\\frac{1}{2}$. Observe that each of these nodes has LP value the \\textit{same} as the optimal IP value. Since each node on the $m$-th level has an optimal solution that is integer, it follows from Lemma \\ref{lem:branch_int} that strong-branching results in a tree of size at most $2^{m + 1} + \\mathcal{O}(m)$.\n\n\\paragraph{A greedy rule.} Consider instead the \\textit{greedy} variable selection rule: branch on the vertex with most fractional neighbors. Observe that, given an instance with at least one diamond with all of its vertices set to $\\frac{1}{2}$ and at least one triangle with all of its vertices set to $\\frac{1}{2}$, greedy will choose to branch on a vertex with degree $3$ in such a diamond (without loss of generality, we assume its vertex $a$). Now, consider the nodes on the $\\frac{1}{2}m$-th level of the tree generated by greedy. Each node's optimal LP solution has an integer value for each vertex in every diamond, and all other vertices (i.e. all vertices in the triangles) are set to $\\frac{1}{2}$. In particular, consider any specific node on this level and suppose that, on the path from the root to this node in the tree, $k$ vertices are set to $1$ and $\\frac{1}{2}m - k$ vertices are set to $0$. Then, this node has objective value $\\textup{OPT}(L(\\mathcal{I})) + (\\frac{1}{2}m - k)$. Notice then that the sub-tree at this node will have to branch on $2k + 1$ triangles and the resulting $2^{2k + 1}$ leaves will have objective value $\\textup{OPT}(L(\\mathcal{I})) + (\\frac{1}{2}m - k) + \\frac{1}{2}(2k + 1) = \\textup{OPT}(L(\\mathcal{I})) + \\frac{1}{2}m + \\frac{1}{2} > \\textup{OPT}(\\mathcal{I})$ (branching on any fewer triangles will not allow the sub-tree to be pruned). On the $\\frac{1}{2}m$-th level, there are $\\binom{m\/2}{k}$ nodes with $k$ vertices set to $1$ on its path from the root. Then, the final number of nodes in the tree is more than\n\\begin{align*}\n    \\sum_{k = 1}^{m\/2} \\binom{m\/2}{k} 2^{2k}.\n\\end{align*}\nWe can bound this quantity using the Binomial Theorem. In particular, we use the form\n\\begin{align}\n    (x + y)^n  = \\sum_{k = 0}^n \\binom{n}{k} x^k y^{n - k}. \\label{eq:binom}\n\\end{align}\nPlugging $n = \\frac{1}{2}, x = 4, y = 1$ into (\\ref{eq:binom}), we have the bound \n\\begin{align}\n    \\sum_{k = 0}^{m\/2} \\binom{m\/2}{k} 4^k = 5^{m\/2} \\geq 2^{1.15 m}. \\label{eq:final_bound}\n\\end{align}\n\n\n\n\n\n\\section{Proof of Proposition \\ref{prop:bdg_ub} and Corollary \\ref{cor:bdg_lb}: A bad example}\\label{sec:bdg_ex}\n\n\\begingroup\n\\def\\ref{prop:bdg_ub}{\\ref{prop:bdg_ub}}\n\\begin{proposition}\nFor any integer program $\\mathcal{I}$ with $n$ binary variables, there is an equivalent integer program that uses an extended formulation of the feasible region of $\\mathcal{I}$ with $2n$ binary variables, which we refer to as $BDG(\\mathcal{I})$, that has the following property: there exists a branch and bound tree $\\mathcal{T}^*(BDG(\\mathcal{I}))$ that solves the instance $BDG(\\mathcal{I})$ and $|\\mathcal{T}^*(BDG(\\mathcal{I}))| \\leq 4n + 1$\n\\end{proposition}\n\\addtocounter{proposition}{-1}\n\\endgroup\n\n\\begin{proof}\nConsider the instance $\\mathcal{I}$:\n\\begin{align*}\n    \\textup{max} &\\quad c^{\\top}x  \\\\\n    \\textup{s.t.} &\\quad x \\in P,\\; x \\in \\{0, 1\\}^n.  \\tag{$\\mathcal{I}$}\n\\end{align*}\nwhere $P \\subseteq [0,1]^n$ is a polytope. In~\\cite{bodur2017cutting}, Bodur, Dash and Gunluk construct the  extended formulation $Q \\subseteq [0,1]^{2n}$ of $P$ as follows. For every vertex $x$ of $P$, construct a vertex $(x, y)$ of $Q$ where\n$$y_i = \\begin{cases}\n1 & \\text{ if } x_i \\in \\{0,1\\} \\\\\n0 & \\text{ if } x_i \\in (0,1)\n\\end{cases}.$$\nDefine $Q$ to be the convex hull of these vertices, we call this the \\emph{BDG extended formulation for $P$}. We construct the equivalent IP, $BDG(\\mathcal{I})$,  as follows:\n\\begin{align*}\n    \\textup{max} &\\quad c^{\\top}x  \\\\\n    \\textup{s.t.} &\\quad (x, y) \\in Q ,\\; x \\in \\{0, 1\\}^n,\\; y \\in \\{0, 1\\}^. \\tag{$\\textup{BDG}(\\mathcal{I})$}\n\\end{align*}\n\nFor any IP $\\mathcal{I}$, there exists a branch-and-bound tree with at most $4n + 1$ nodes that solves $BDG(\\mathcal{I})$. However, this tree does not remove the current LP optimal fractional point when branching. See Figure \\ref{fig:bdg}. \n\n\\begin{figure}[h]\n    \\centering\n    \\includegraphics[width=12cm]{bdg_fig.png}\n    \\caption{Branch-and-bound on BDG extended formulation}\n    \\label{fig:bdg}\n\\end{figure}\n\n\n\nThis follows since, by the definition of $Q$, all of its vertices that have $y_j = 0$ must have $x_j \\in (0,1)$. Therefore, the branch that has $y_j = 0$ and $x_j = 0$ (and similarly $x_j = 1$) must be empty. Also, note that the branch that has $y_1 = 1, ..., y_n = 1$ must be integral. \n\\end{proof}\n\n\\begingroup\n\\def\\ref{cor:bdg_lb}{\\ref{cor:bdg_lb}}\n\\begin{corollary}\nThere exists an instance $\\mathcal{I}^*$ with $2n$ binary variables, such that the following holds: Let $\\mathcal{T}(\\mathcal{I}^*)$ be any tree that solves $\\mathcal{I}^*$ satisfying the following property: if $x$ is the optimal solution to an internal node $N$ of $\\mathcal{T}(\\mathcal{I}^*)$, then the variable $j$ branched on at $N$ must be such that $x_j \\in (0,1)$. Then, $|\\mathcal{T}(\\mathcal{I}^*)| \\geq 2^{n +1} -1$.   In particular, if $\\mathcal{T}_S(\\mathcal{I}^*)$ is a branch-and-bound tree generated using strong-branching that solve $\\mathcal{I}^*$, then $|\\mathcal{T}_S(\\mathcal{I}^*)| \\geq 2^{n +1} - 1$.  On the other hand,  there exists a tree $\\mathcal{T}^*$ that solves $\\mathcal{I}^*$ such that $|\\mathcal{T}^*(\\mathcal{I}^*)| \\leq 4n + 1$.\n\\end{corollary}\n\\addtocounter{corollary}{-1}\n\\endgroup\n\n\\begin{proof}\nNote that the $y$ variables are not fractional in any vertex of $Q$. So when the tree of Figure \\ref{fig:bdg} branches on a $y$ variable, it does not remove the current LP optimal fractional point (because it does not remove any vertex of $Q$). \n\nNow suppose we restrict ourselves to branching on a variable that does remove the current optimal point. Such a tree would only branch on $x$ variables (i.e. the original variables). Then, if $P$ is the $n$-dimensional cross polytope~\\cite{dey2021lower}, and $Q$ is its BDG extended formulation, we know that branching on only the $x$ variables will require a tree of size at least $2^{n +1} -1$, as shown in \\cite{dey2021lower}. \n\nThe final statement follows from Proposition~\\ref{prop:bdg_ub}.\n\\end{proof}\n\n\n\n\n\n\n\\section{Computing an optimal branch-and-bound tree}\\label{sec:computing_opt}\n\\subsection{Proof of Observation~\\ref{obs:assumption}.}\\label{sec:opttreewelldefined}\n\\begingroup\n\\def\\ref{obs:assumption}{\\ref{obs:assumption}}\n\\begin{observation}\nWhen using an LP solver which satisfies Assumption \\ref{assum:int}, a branch-and-bound tree using the worst bound rule  never branches on a node whose optimal objective function value is equal to that of the IP solver. \n\\end{observation}\n\\addtocounter{observation}{-1}\n\\endgroup\n\n\\begin{proof}\nConsider a linear program at a node whose optimal function value is equal to that of the MILP optimal objective function value. There are two cases to consider. Case 1: if there exists an integral optimal solution to the LP relaxation at a given node, then the LP solver finds it and the node is pruned. Case 2: If not, then this node does not contain an integral solution with objective function value equal to that of the MILP optimal objective function value. This implies that there must exist another node whose feasible region contains an integer feasible solution with the same objective function value as that of the MILP optimal objective function value. In particular, this implies that there must exist a node whose optimal linear programming solution is such an  integer feasible solution. Since the LP solver will discover this solution before branching on the current node, we will never branch on the current node.\n\\end{proof}\n\n \n\\subsection{The dynamic programming algorithm to compute optimal branch-and-bound tree.} \\label{sec:dpalgo}\nWe will now present the algorithm to compute the size of an optimal branch-and-bound tree for a fixed IP $\\max_{x \\in P \\cap \\{0,1\\}^n}\\ip{c}{x}$ under Assumption~\\ref{assum:int}. Let $\\mathcal{F}$ denote the set of faces of $[0,1]^n$ and note that each face can be defined as a string in $\\{ \\star , 0,  1\\}^n$. For example, $(0, \\star  ,1)$ denotes the face $\\{x \\in [0, 1]^3 : x_1 = 0, x_3 = 1\\}$. Thus, $|\\mathcal{F}| = 3^n$. Also, $\\mathcal{F}$, is in one-to-one correspondence with all the possible nodes in the branch-and-bound tree. Let $\\overline{\\textup{OPT}}(F)$ denote the size of the optimal branch-and-bound tree for the sub-problem restricted to $F$, i.e., $\\max_{x \\in F \\cap P \\cap \\{0,1\\}^n}\\ip{c}{x}$.  \n\nBased on Assumption~\\ref{assum:int} and Observation~\\ref{obs:assumption},  with the WDB rule for node selection, a node in the branch-and-bound tree is pruned if and only if it is either infeasible, or the optimal objective function value of its LP relaxation is less than or equal to the optimal MILP optimal objective value. In Phase-1 of our algorithm (Algorithm \\ref{dpalgo}), this fact is used to identify nodes that are pruned by infeasibility or by bound, thus, $\\overline{\\textup{OPT}}(F) = 0$ for corresponding faces.\n\nNow, given a face $F$ that is not pruned in the branch-and-bound tree, and variable $x_j$ that is free in $F$, define $F_{j,0}, F_{j,1}$ to be the faces of $F$ that result from fixing $x_j$ to $0$ and $1$ respectively, i.e. $F_{j, 0} = \\{x \\in F : x_j = 0\\}$. The fact that the optimal sub-tree at the node corresponding to $F$ branches on the variable that produces two child nodes having the smallest optimal sub-trees, leads to the following recurrence relation, \n$$\\overline{\\textup{OPT}}(F) = 1 + \\min_{j \\in J_F} \\left\\{\\overline{\\textup{OPT}}(F_{j, 0}) + \\overline{\\textup{OPT}}(F_{j,1}) \\right\\},$$ \nwhere $J_F$ denotes the set of variables that are free in $F$. We use this recurrence relation in the bottom-up computation of $\\overline{\\textup{OPT}}(F)$ for the remaining faces (i.e. faces where  $\\overline{\\textup{OPT}}(F) \\neq 0$) in $\\mathcal{F}$ as Phase-2 of the algorithm. Thus, it can be inductively seen that the algorithm is correct. Additionally, the actual branch-and-bound tree can be found by storing $\\arg \\min_j \\left\\{\\overline{\\textup{OPT}}(F_{j, 0}) + \\overline{\\textup{OPT}}(F_{j,1})\\right\\}$ at every iteration. \n\n\\begin{algorithm}\n\\caption{Computing Optimal Branch-and-bound Tree} \\label{dpalgo}\n\\begin{algorithmic}[1]\n\\Statex \\textbf{Phase-1:} Pruning by Infeasibility or Bound\n\\State Solve $\\max_{x \\in P \\cap \\{0,1\\}^n}\\ip{c}{x}$; let $x^*$ be the solution\n\\State Initialise: $\\mathcal{S} \\leftarrow \\mathcal{F}$\n\\For{$F$ in $\\mathcal{S}$}\n    \\State Solve $\\max_{x \\in F \\cap P} \\ip{c}{x}$; let $x_F^*$ be the optimal solution ($x_F^* = \\emptyset$ if LP is infeasible)\n    \\If {$x_F^* = \\emptyset$ \\textbf{or} $\\ip{c}{x_F^*} \\le \\ip{c}{x^*}$ }\n        \\State $\\overline{\\textup{OPT}}(F) \\leftarrow 0$\n        \\State $\\mathcal{S} \\leftarrow \\mathcal{S} \\setminus \\{F\\}$\n    \\EndIf\n\\EndFor\n\\Statex\n\\Statex\n\\textbf{Phase-2:} Recursive bottom-up computation\n\\State Sort $\\mathcal{S}$ in order of increasing dimension\n\\For{$F$ in $\\mathcal{S}$}\n    \\State $\\overline{\\textup{OPT}}(F) \\leftarrow 1 + \\min_j (\\overline{\\textup{OPT}}(F_{j, 0}) + \\overline{\\textup{OPT}}(F_{j,1}))$\n\\EndFor\n\\State  \\textbf{return} $\\overline{\\textup{OPT}}([0,1]^n)$\n\\end{algorithmic}\n\\end{algorithm}\n\n\n\\textcolor{black}{Notice it takes $2^{O(n)}$ time to execute line 1 and $\\textup{poly}( data)$ time to execute line 3 of Algorithm \\ref{dpalgo} for a particular face, where $\\textup{poly}(data)$ is the running time for solving an LP.  Therefore, Phase I takes at most $2^{O(n)} + \\textup{poly}(data) \\cdot 3^n$ time.\nAlso notice Phase-2 takes $n \\cdot 3^n$ time; this is because line 11 of Algorithm \\ref{dpalgo} takes at most $n$ comparisons. So, in total Phase-1 and Phase-2 take $ 2^{O(n)} + (\\textup{poly}(data) + n) \\cdot 3^n = \\textup{poly}(data)\\cdot3^{O(n)}$ time. }\n\n\n\n\\subsection{Implementation enhancements}\n\\paragraph{Cascading 0-nodes} Observe that for $F_1, F_2 \\in \\mathcal{F}$ such that $F_2 \\subset F_1$, if $\\overline{\\textup{OPT}}(F_1) = 0$, then $\\overline{\\textup{OPT}}(F_2) = 0$ as well. Thus,  at the start of Phase-1, faces in $\\mathcal{F}$ are arranged in decreasing order of their dimension and upon finding a face, $F_1$, that is infeasible or pruned by bound, all other faces that are contained in $F_1$ can be removed from $\\mathcal{S}$.\n\n\\paragraph{Parallelization} Phase-1 of the proposed algorithm can be directly parallelized, as each face can be independently solved. However, to benefit from Cascading 0-nodes, we group faces that have the same values from $\\{0, 1, \\star\\}$ for the first $n_1$ dimensions and run Phase-1 for the resulting $3^{n_1}$ groups independently. Note that this also reduces peak memory usage as all $3^n$ faces in $\\mathcal{F}$ are not required to be generated at the start of the algorithm and the remaining $n - n_1$ dimensions are generated on the fly for each group. In our experiments, we set $n_1 = \\lfloor \\frac{n}{2} \\rfloor$. In addition, this manner of grouping also enables the LP solver to benefit from smaller incremental changes between consecutive faces. \n\n\\section{Computational Experiments} \\label{sec:experiments}\nWe evaluate the following branching strategies on problems mentioned in Section \\ref{sec: Data generation} by comparing the number of branching to the optimal number of branching computed using the  dynamic programming based algorithm presented in Section \\ref{sec:dpalgo}. Recall the definition of $\\Delta^+_j, \\Delta^-_j$ from Section \\ref{sec:intro}. \n\\begin{itemize}\n\\item \\textbf{SB-L}: Strong branching where branching candidates are compared using a convex combination of the maximum and minimum. The scoring function used is $$ \\text{score}_L(j) = \\frac{5}{6} \\min(\\Delta^+_j, \\Delta^-_j) + \\frac{1}{6} \\max(\\Delta^+_j, \\Delta^-_j).$$\n\\item \\textbf{SB-P}: Strong branching where the product of improvements is used to score branching candidates. Thus, the scoring function is, $$\\text{score}_P(j) = \\max(\\Delta^+_j, \\epsilon) \\cdot \\max(\\Delta^-_j, \\epsilon),$$ where $\\epsilon > 0$ is small. For the computations presented in this section, $\\epsilon$ is chosen to be $10^{-4}.$\n\\item \\textbf{Most-Inf}: Most infeasible branching where the variable with fractional value closest to 0.5 is selected for branching\n\\item \\textbf{Rand}: Branching variable is randomly chosen from variables with fractional values.\n\\end{itemize}\n\\subsection{Instance Generation} \\label{sec: Data generation}\nIn this section, we discuss the problems considered for computational experiments and the details of generating randomized instances.\n\n\\subsubsection{Multidimensional Variants of Knapsack Problem}\nWe consider packing problems, covering problems and general problems with multiple covering and packing inequalities. Let $I_p$ and $I_c$ represent the set of indices corresponding to packing and covering constraints respectively. The general formulation is as follows,\n\\begin{eqnarray*}\n&\\textup{max}& {c^{\\top}}{x} \\\\\n&\\textup{s.t.} &a_i^{\\top} x \\leq b_i  \\ \\forall \\ i \\in I_p \\\\\n&& a_i^{\\top} x \\geq b_i \\ \\forall \\ i \\in I_c \\\\\n&& x \\in \\{0, 1\\}^n.\n\\end{eqnarray*}\nFor the experiments in this paper, $n =  20$  is considered. The constraint matrix is generated randomly while incorporating sparsity. Each element $a_{ij}$ is $0$ with probability $p = 0.25$. Otherwise, a random integer selected uniformly from the set $\\{1, 2, \\dots, 200\\}$ otherwise. The capacity parameter $b_i$ is $50\\%$ of the sum of weights of the constraint, rounded down to integer value. The objective function is dependent on the number of packing and covering constraints as follows, \n\\begin{itemize}\n\\item $K-P5$ is a purely packing type problem with $5$ constraints ($I_p = 5, I_c = 0$). We thus choose a non negative vector for the objective function, and each component $c_i$, is independently selected from the set $\\{1, 2, \\dots, 200\\}$ with uniform probability.\n\\item $K-C5$ is a purely covering type problem with $5$ constraints ($I_p = 0, I_c = 5$). Each component of the objective, $c_i$, is independently selected from the set $\\{-200, \\dots, -2, -1\\}$ with uniform probability.\n\\item$ K-G22$ is a general MILP with $2$ packing-type and $2$ covering-type knapsack like constraints ($I_p~=~I_c~=~2$). Each component of the objective, $c_i$, is independently selected from the set $\\{-100, \\hdots, 100\\}$ with uniform probability.\n\\end{itemize}\n\n\\subsubsection{Lot-sizing Problem and Variants}\nWe consider the classical lot-sizing problem of determining production volumes while minimizing production cost, fixed cost of production and inventory holding cost across the planning horizon. The MILP model for the lot-sizing problem with $n$ time periods is as follows,\n\\begin{eqnarray}\n& \\textup{min} & \\sum_{i=1}^{n} \\left( c_i \\, x_i + f_i \\, y_i \\right ) +   \\sum_{i=1}^{n -1} h_i \\, s_i  \\label{lotsize:obj} \\\\\n&\\textup{s.t.}& {x_1}{ = s_1 + d_1}{} \\label{lotsize:flow0} \\\\\n&& s_{i-1} + x_{i} = d_{i} + s_{i}  \\ \\forall \\ i \\in \\{2, \\dots, n\\}  \\label{lotsize:flow} \\\\\n&& s_{n-1} + x_n = d_n \\label{lotsize: flown}\\\\\n&& x_i \\le \\left(\\sum_{j=i}^n d_j \\right) \\, y_i \\ \\forall \\ i \\in \\{1, \\hdots, n\\} \\label{lotsize: x-y} \\\\\n&& x \\in  \\mathbb{R}^n_+, \\ s \\in  \\mathbb{R}^{n -1}_+, \\  y \\in  \\{0, 1\\}^n.\n\\end{eqnarray}\nwhere variable $x_i$ is the quantity produced in period $i$ and $y_i$ is a binary variable with value $1$  if production occurs in period $i$ and $0$ otherwise. Lastly variable $s_i$ is the inventory at the end of period $i$. Unit cost of production for each period, $c_i$, is independently and uniformly sampled from $\\{1, \\hdots, 10\\}$, fixed cost of production, $f_i$, from $\\{200, \\hdots, 400\\}$ and unit inventory holding cost $h_i$ from $\\{1, \\hdots, 10\\}$. Similarly, the demand for each time period, $d_i$ is independent and uniformly distributed in $\\{0, \\hdots, 100\\}$. In our computational experiments, we consider problems with $n=17$.\n\\paragraph*{Capacitated Lot-sizing}\nIn the capacitated lot-sizing problem, the maximum quantity produced in every time period is constrained. Let parameter $u_i$ denote the upper-bound on the quantity that can be produced in period $i$. In our experiments, $u_i$ are sampled uniformly and independently from $\\{150, \\hdots, 250\\}$. All other parameters are generated in the same was as the uncapacitated problem. Equation (\\ref{lotsize: x-y}) is thus replaced with the constraint, \n\\begin{equation*}\nx_i \\le u_i \\, y_i, \\qquad \\forall i \\in \\{1, \\hdots, n\\}\n\\end{equation*}\n\\paragraph*{Big-bucket Lot-sizing}\nThe last variant of lot-sizing problem that we consider is the big-bucket lot-sizing problem where resources are shared amongst multiple products~\\cite{quadt2008capacitated}. We do not consider unit cost of production here. On the other hand, set up time and processing time are considered to be constrained. \nThe following are the parameters of the corresponding MILP model,\\\\ \\\\\n\\begin{tabular}{l l}\n$P$ & Number of products, $\\mathcal{P} = \\{1, \\hdots, P\\}$ \\\\\n$T$ & Number of time periods, $\\mathcal{T} = \\{1, \\hdots, T\\}$ \\\\\n$f_i^p$ & Fixed cost of producing product $p$ in period $i$ \\\\\n$h_i^p$ & Inventory holding cost of product $p$ in period $i$ \\\\\n$t_i^{s, p}$ & Set up time of product $p$ in period $i$ \\\\\n$t_i^{u, p}$ & Processing time per unit of product $p$ in period $i$ \\\\\n$C_i$ & Time available in period $i$ \\\\\n$z^p$ & Initial inventory of product $p$ at the beginning of planning horizon. \\\\\n\\end{tabular}\n\\newline \\newline The variables used to model the problem are following,\\\\ \\\\\n\\begin{tabular}{l l}\n$x_i^p$ & Quantity product $p$ produced in period $i$ \\\\\n$s_i^p$ & Quantity of product $p$ stored as inventory at the end of period $i$ \\\\\n$y_i^p$ & Binary variable indicating if product $p$ was produced in period $i$ ($y_i^p = 1$ if $x_i^p > 0$)\\\\\n\\end{tabular}\n\\newline \\newline The MILP model used for the big-bucket lot-sizing problem is described below.\n\\begin{eqnarray*}\n&\\textup{min} &  \\sum_{i \\in \\mathcal{T}} \\sum_{p \\in \\mathcal{P}} \\left(f^p_i \\, y^p_i + h^p_i \\, s^p_i \\right) \\label{bblotsize: obj} \\\\\n& \\textup{s.t.} & s^p_0 = z^p, \\ p \\in \\mathcal{P}  \\label{bblotsize: s_init}\\\\\n&& s^p_T = 0, \\ p \\in \\mathcal{P} \\label{bblotsize: s_fin} \\\\\n&& s^p_{i-1} + x^p_{i}  = d^p_{i} + s^p_{i},  i \\in \\mathcal{T},  p \\in \\mathcal{P} \\label{bblotsize: flow} \\\\\n&& x^p_i  \\leq \\left(\\sum_{j=i}^n d^p_j \\right) \\, y^p_i, i \\in \\mathcal{T}, p \\in \\mathcal{P} \\label{bblotsize: x-y} \\\\\n&& \\sum_{p \\in \\mathcal{P}} \\left( t^{s,p}_i \\, y^p_i + t^{u,p}_i \\, x^p_i \\right) \\leq C_i,  i \\in \\mathcal{T} \\label{bblotsize: cap} \\\\\n&& x^p_i \\in  \\mathbb{R}_+, s^p_i \\in  \\mathbb{R}_+, y^p_i \\in  \\{0, 1\\},\\quad i \\in \\mathcal{T}, p \\in \\mathcal{P}.\n\\end{eqnarray*}\nIn our experiments, we consider problems with 9 time periods ($T=9$) and 2 products ($P=2$). Parameters corresponding to demand, fixed cost of production and inventory holding cost are generated as described in the context of previous variants. Set up time for a product in a each period, $t^{s, p}_i$ is independently sampled from $\\{200, \\hdots, 500\\}$ with equal probability, unit processing time $t^{u, p}_i$ from $\\{1, \\hdots, 10\\}$ and time limitation $C_i$ from $\\{1000 P, \\hdots, 2000 P\\}$. Initial inventory for each product $z^p$ is similarly sampled from $\\{0, \\hdots, 200\\}$.\n\n\\subsubsection{Minimum Vertex Cover}\nThe vertex cover problem on graphs $G = (V, E)$ concerns with identifying the smallest possible subset $V'$ of $V$, such that for every edge in $E$, at least one of its endpoints is included in $V'$. It is formulated as follows, \n\\begin{eqnarray*}\n&\\textup{min}& \\sum_{i \\in V} x_i \\\\\n&\\textup{s.t.}& x_i + x_j \\ge 1, \\qquad \\forall (i, j) \\in E \\\\\n&& x \\in \\{0,1\\}^{|V|}\n\\end{eqnarray*}\nWe generated random graphs for the vertex cover problem using the \\emph{Erd{\\H o}s-R{\\'e}nyi model}, i.e., the graph $G = (V, E)$  is constructed using \ntwo parameters; $N$ indicating the number of nodes and $p$ representing the probability with which each edge of the complete graph on $V$ is independently included in the set $E$. For our computational experiments, we consider graphs with $N=20$ and $p=0.75.$\n\n\n\n\n\n\\subsubsection{Chance Constraint Programming - Multiperiod Power Planning}\n\nWe consider the problem of expanding the electric power capacity~\\cite{bertsimas1997introduction} of a state by constructing new coal and nuclear power plant to meet with the electricity demand of the state for a time horizon of $T$ periods. Once constructed, coal plants are operational for $T_c$ time periods and nuclear plants for $T_n$ time periods. Legal restrictions mandate that fraction of nuclear power should be at most $f$ of the total capacity. Capital cost incurred for the construction of coal and nuclear power plants operational from the beginning of time period $t$ are $c_t$ and $n_t$ respectively per megawatt of power capacity. The objective is to minimize the total capital cost of construction. Further, the demand is stochastic and defined on probability space $(\\Omega, \\mathcal{F}, \\mathbb{P})$. Approximated by the sample approximation approach, $\\Omega = \\{\\omega_1, \\hdots, \\omega_N\\}$ is assumed to be a finite sample space. It is required that the probability of the event where the demand is not satisfied be at most $\\epsilon$. The deterministic formulation of the problem as an MILP is as follows, \n\\paragraph*{Parameters\\\\ \\\\}\n\\begin{tabular}{ l l }\n$T$ & Number of time periods, $\\mathcal{T} = \\{1, \\hdots, T\\}$ \\\\\n$N$ & Size of sample space $\\Omega$,  $\\mathcal{N} = \\{1, \\hdots, N\\}$\\\\\n$c_t$ & Capital cost per MW for coal plant operational from period $t$\\\\  \n$n_t$ & Capital cost per MW for nuclear plant operational from period $t$ \\\\\n$T_c$ & Lifespan of a coal power plant \\\\ \n$T_n$ & Lifespan of a nuclear power plant \\\\\n$f$ & Upper bound on nuclear capacity as a fraction of total capacity \\\\\n$e_t$ & Electric capacity from existing resources in period $t$ \\\\\n$d^i_t$ & Electricity demand (in MW) in period t corresponding to outcome $\\omega_i$\\\\\n$p_i$ & Probability of outcome $\\omega_i$\\\\\n$\\epsilon$ & Upper bound on the probability that the demand is satisfied\n\\end{tabular}\n\n\\paragraph*{Variables\\\\ \\\\}\n\\begin{tabular}{l l}\n$x_t$ & Power capacity (in MW) of coal plants operational starting at period $t$ \\\\\n$y_t$ & Power capacity (in MW) of coal plants operational starting at period $t$ \\\\\n$u_t$ & Total coal power capacity (in MW) in period $t$ \\\\\n$v_t$ & Total nuclear power capacity (in MW) in period $t$ \\\\\n$z_i$ & Binary variable indicating if demand is not satisfied for outcome $\\omega_i$\n\\end{tabular}\n\n\\paragraph*{Model - CCP Power Planning}\n\\begin{eqnarray}\n&\\textup{min}& \\sum_{t=1}^{T} (c_t \\, x_t + n_t \\, y_t)  \\label{ccp power: obj} \\\\\n& \\textup{s.t.} & u_t = \\sum_{\\textup{max}\\{1, \\, t-T_c+1\\} }^t x_s, \\quad t \\in \\mathcal{T} \\label{ccp power: sum coal} \\\\\n&& v_t = \\sum_{\\textup{max}\\{1, \\, t-T_n+1\\}}^t y_s,\\quad  t \\in \\mathcal{T} \\label{ccp power: sum nucl} \\\\\n&& (1-f) \\, u_t - f \\, v_t  \\le f \\, e_t, \\quad t \\in \\mathcal{T} \\label{ccp power: nuc lim}  \\\\\n&&u_t + v_t \\ge (d^i_t - e_t)(1-z_i), \\quad t, i \\in \\mathcal{T} \\times\\mathcal{N} \\label{ccp power: demand} \\\\\n&& \\sum_{i = 1}^n z_i \\, p_i \\le \\epsilon \\label{ccp power: epsilon} \\\\\n&& x_t, y_t, u_t, v_t \\in \\mathbb{R}_+, \\quad t \\in \\mathcal{T} \\\\\n&& z_i  \\in \\{0, 1\\}, \\quad i \\in \\mathcal{N}.\n\\end{eqnarray}\nThe objective function (\\ref{ccp power: obj}) minimizes total capital expenditure of constructing power plants. Equations (\\ref{ccp power: sum coal}) and (\\ref{ccp power: sum nucl}) compute total coal and nuclear power capacity for a given time period from active power plants based on their lifespan. Equation (\\ref{ccp power: nuc lim}) enforces the regulatory limit on nuclear capacity is satisfied. Equations (\\ref{ccp power: demand}) and (\\ref{ccp power: epsilon}) ensure that the outcomes for which the demand is not satisfied has probability at most $\\epsilon$.\n\nFor the experiments in Section \\ref{sec:experiments}, we generate instances with $T = 30$ and $N = 20$ which corresponds to 30 time periods and 20 outcomes in sample space. Parameters $d^i_t$ are independent random integers uniformly distributed \nin $\\{300, \\hdots, 700\\}$. Similarly, $c_t$ are uniformly distributed in $\\{100, \\hdots, 300\\}$ and $n_t$ in $\\{100, \\hdots, 200\\}$. Electric capacity from existing resources for the first period, $e_1$ is a random integer in $\\{100, \\hdots, 500 \\}$. Capacity from existing resources is then modelled to decline by a factor of $r$ in every subsequent period where $r$ is uniformly distributed in $[0.7, 1)$, ie. $e_i = e_1\\,r^{i-1}$. Lifespan of coal and nuclear power plants are $15$ and $10$ periods respectively. Nuclear capacity is constrained to be at most 20\\% of total capacity. All outcomes in $\\Omega$ are equally probable with $p_i = 0.05$ and demand satisfiability can be violated with a probability of at most $0.2$.\n\n\\subsubsection{Chance Constraint Programming - Portfolio Optimization}\nWe consider the probabilistically-constrained portfolio optimization problem for $n$ asset types, approximated by the sample approximation approach~\\cite{pagnoncelli2009computational}, where the constraint on overall return may be violated for at most $k$ out of the $m$ samples. The MILP formulation of this problem is as follows:\n\\begin{eqnarray*}\n&\\textup{min} &\\sum_{i = 1}^n x_i \\\\\n&\\textup{s.t.} & a_i^T x + r z_i\\ge r, \\quad \\forall i = 1, \\hdots, m \\\\\n&& \\sum_{i=1}^m z_i \\le k \\\\\n&& x \\in \\mathbb{R}^n_+, \\, z \\in \\{0,1\\}^m. \n\\end{eqnarray*}\nWe sample scenarios from the distribution presented in~\\cite{qiu2014covering}, which is shown to be computationally difficult to solve. Each component of the constraint matrix, $a_{ij}$ is independently sampled from a uniform distribution in $[0.8, 1.5]$ and $r$ is equal to $1.1$. For our experiments, we set $n=30$, $m=20$ and $k=4$.\n\n\\subsubsection{Stable Set Polytope on Bipartite Graph With Knapsack Constraint}\nStable set polytope corresponding to a bipartite graph is known to have a totally unimodular matrix and thus integral vertices. We consider the problem of solving a maximization problem on the stable set polytope of a bipartite graph where the optimal extreme point is cut off with a knapsack constraint with the same coefficients as the objective function. The details of model are explained below.  A bipartite graph $G = (N, E)$ is generated for a $n$ nodes and $m$ edges as follows. The partition of $N = N_1 \\cup N_2$ is generated, by setting $N_1$ as a randomly selected subset of $\\lfloor f n \\rfloor$ nodes and $N_2$ as its complement, where $f$ is sampled from a uniform distribution over $[0.3, 0.5]$. From the $N_1 \\times N_2$ possible edges, $m$ are then randomly selected to form set $E$. Lastly, each component $c_i$ of the objective function is a randomly selected integer from 1 to 50. In our experiments, we consider instances with $20$ nodes and $30$ edges.\nLet $\\delta^*$ be the objective function value of the corresponding maximum weight stable set problem, \n\\begin{eqnarray}\n&\\textup{max}& \\sum_{i=1}^n c_i \\, x_i  \\label{stable set ip}\\\\\n&\\textup{s.t.}& x_i + x_j \\le 1,\\quad \\forall i, j \\in E \\label{stable set ip2}\\\\\n&& x \\in \\{0, 1\\}^m .\\label{stable set ip3}\n\\end{eqnarray}\nThe following constraint is then added to (\\ref{stable set ip})- (\\ref{stable set ip3}),\n\\begin{equation}\n\\sum_{i=1}^n c_i \\, x_i \\le r\\delta^*\n\\end{equation}\nwhere $r$ is uniformly distributed in $[0.75, 0.9]$.\n\n\\subsection{Results}\\label{sec:compres}\nWe present some preliminary results of various variable selection rules in comparison to optimal tree. $\\textup{SB-L}$ stands for strong-branching with linear score, $\\textup{SB-P}$ stands for strong-branching with product score, $\\textup{Most infeasible}$ is selecting the variable with fractionality closest to $0.5$, and $\\textup{Random}$ just selects a variable randomly from a list of fractional variables. \n\nFigure~\\ref{fig:gmratio} shows a comparison of branching strategies based on the ratio of geometric mean of BB tree sizes to geometric mean of optimal tree sizes over all instances of the problem.\n\nFigure~\\ref{fig:performance1} shows performance profiles. The way to read the plots is the following: Consider the yellow curve for multi row packing problem. The point $(80\\%, 0.3)$ means that in the case of using the most infeasible rule for multi row packing problem, $0.3\\times 100 = 30$ instances out of 100, have branch-and-bound trees that have at most 80\\% more nodes than the optimal branch-and-bound tree. The x-axis represents percentage differences in size of the BB tree in comparison to the optimal BB tree. The y-axis is the cumulative frequency of instances. \n\nTables~1 through 12 present the number of nodes for all the instances we tested and all the variable selection rules. \n\n\\subsubsection{Discussion On Findings}\nIt is clear from the Fig.~\\ref{fig:gmratio}-\\ref{fig:performance1} and Tables 1 through 12 that random always performs the worst. However, contrary to expectation strong-branching is not always the best and is out-performed by most-infeasible branching strategy on the CCP Multiperiod Power Planning problem. Yet, as seen in Fig.~\\ref{fig:gmratio}, the geometric mean of tree size for strong-branching remains less than twice of the optimal tree for all problems considered in this study. The overall geometric mean of optimal tree size of instances across all problems is 42.65, whereas the same for SB-L, SB-P, most infeasible branching and random branching is 61.47, 61.09, 90.19 and 145.37 respectively. While the performance of two variants of strong-branching is comparable on all problems considered in this study, SB-P dominates over SB-L on 8 out of 10 problems, although by a small margin.\n\nStrong branching is near optimal for the lot-sizing instances and performs exceptionally well on all other lot sizing variants as well. This is an interesting result considering that the tree sizes of the other two strategies can be significantly larger for almost all instances as seen in Fig~\\ref{fig:scatter_lotsizing}. Thus, this indicates that very large branch-and-bound trees exist for the problem, but strong-branching is indeed effective at finding an effective branching strategy. This is in contrast to the problem of Stable Set on Bipartite Graphs with additional knapsack constraint, where all strategies have comparable performance as seen in Fig~\\ref{fig:scatter_TUcutoff}. In comparison with the optimal tree, it performs worst on Chance Constraint Programming problems. The performance of random branching is also worst for CCP problems, thus making these an interesting class of problems for which better variable selection rules could be discovered. \n\n\n\n\\bibliographystyle{plain}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Framework, model and main ideas}\nReal-world systems often consist of interacting agents\nthat may develop a collective behavior (e.g. \\cite{alb-bar, bar-alb, new, hof}):\nin neuroscience the brain is an active network\nwhere billions of neurons interact in various ways in the cellular\ncircuits; many studies in biology focus on the interactions between\ndifferent sub-systems; social sciences and economics deal with\nindividuals that take decisions under the influence of other\nindividuals, and also in engineering and computer science ``consensus\nproblems'', understood as the ability of interacting dynamic agents to\nreach a common asymptotic stable state, play a crucial role.\nIn all these frameworks, an usual phenomenon is the {\\em synchronization},\nthat could be roughly defined as the tendency of different interacting\nagents to adopt a common behavior. Taking into account various\nfeatures of these systems, several research works employed agent-based\nmodels in order to analyze how macro-level collective behaviors arise\nas products of the micro-level processes of interaction among the\nagents of the system (we refer to \\cite{are} for a detailed and well\nstructured survey on this topic, rich of examples and references). The\nmain goals of these researches are twofold: (i) to understand\nwhether and when a (complete or partial) synchronization in a\ndynamical system of interacting agents can emerge and (ii) to\nanalyze the interplay between the network topology of the\ninteractions among the agents and the dynamics followed by the agents.\n\\\\\n\n\\indent This work is placed in the stream of scientific literature\nthat studies systems of {\\em interacting urn models} (e.g.~\\cite{ale-ghi,\n  ben, che-luc, cir, cri-dai-min, dai-lou-min, lau2, lau1, lima,\n  mar-val, pag-sec, sah}) and their variants and generalizations\n(e.g.~\\cite{ale-cri-ghi, cri-dai-lou-min}). Specifically, our work deals with\nthe class of the so-called {\\em interacting reinforced stochastic processes}\nconsidered in~\\cite{ale-cri-ghi, cri-dai-lou-min}.\nGenerally speaking, by reinforcement in a\nstochastic dynamics we mean any mechanism for which the probability\nthat a given event occurs has an increasing dependence on the number\nof times that events of the same type occurred in the past. This {\\em\n  ``self-reinforcing property''}, also known as {\\em ``preferential\n  attachment rule''}, is a key feature governing the dynamics of many\nbiological, economic and social systems (see, e.g. \\cite{pem}).  The best\nknown example of reinforced stochastic process is the standard\nP\\`{o}lya's urn \\cite{egg-pol,mah}, which has been widely studied and\ngeneralized (some recent variants can be found in \\cite{ale-ghi-pag,\n  ale-ghi-vid, aoudia-perron, ber-cri-pra-rig-barriere,\n  cal-che-cri-pam, chen-kuba, collevecchio, cri-ipergeom, ghi-pag14,\n  ghi-vid-ros, laru-page}).  \\\\\n\n\\indent We consider a system of $N\\geq1$ interacting reinforced\nstochastic processes $\\{X^j=(X_{n,j})_{n\\geq 1}:\\, 1 \\leq j\\leq N\\}$\npositioned at the vertices of a {\\em weighted directed graph} $G=(V,\\,\nE,\\, W)$, where $V:=\\{1,...,N\\}$ denotes the set of vertices,\n$E\\underline{\\subset} V\\times V$ the set of edges and\n$W=[w_{h,j}]_{h,j\\in V\\times V}$ the weighted adjacency matrix with\n$w_{h,j}\\geq 0$ for each pair of vertices.  The presence of the edge\n$(h,j)\\in E$ indicates a ``direct influence'' that the vertex $h$ has\non the vertex $j$ and it corresponds to a strictly positive element\n$w_{h,j}$ of $W$ that represents a weight quantifying this influence.\nWe assume the weights to be normalized so that $\\sum_{h=1}^N\nw_{h,j}=1$ for each $j\\in V$.  For any $n\\geq 1$, we assume the random\nvariables $\\{X_{n,j}:\\,j\\in V\\}$ to take values in $\\{0,1\\}$ and hence\nthey can be interpreted as ``two-modality actions'' that the agents of\nthe network can adopt at time $n$. Formally, the interaction between\nthe processes $\\{X^j:\\,j\\in V\\}$ is modeled as follows: for any $n\\geq\n0$, the random variables $\\{X_{n+1,j}:\\,j\\in V\\}$ are conditionally\nindependent given ${\\mathcal F}_{n}$ with\n\\begin{equation}\\label{interacting-1-intro}\nP(X_{n+1,j}=1\\, |\\, {\\mathcal F}_n)=\\sum_{h=1}^N w_{h,j} Z_{n,h},\n\\end{equation}\nand, for each $h\\in V$,\n\\begin{equation}\\label{interacting-2-intro}\nZ_{n,h}=(1-r_{n-1})Z_{n-1,h}+r_{n-1}X_{n,h},\n\\end{equation}\nwhere $Z_{0,h}$ are random variables with values in $[0,1]$,\n${\\mathcal F}_n:=\\sigma(Z_{0,h}: h\\in V)\\vee \\sigma(X_{k,j}:\\, 1\\leq\nk\\leq n,\\,j\\in V )$ and $0\\leq r_n<1$ are real numbers such that\n\\begin{equation}\\label{ass-r-intro}\n\\lim_n n^{\\gamma} r_n=c>0\\qquad\\hbox{with } 1\/2<\\gamma\\leq 1.\n\\end{equation}\n(We refer to \\cite{cri-dai-lou-min} for a discussion on the case\n$0<\\gamma \\leq 1\/2$, for which we have a different asymptotic\nbehavior of the model that is out of the scope of this research\nwork.) For example, if at each vertex $j\\in V$ we have a standard\nP\\'olya's urn, with initial composition given by the pair $(a,b)$,\nthen we have $r_n=(a+b+n+1)^{-1}$ and so $\\gamma=c=1$.  Each random\nvariable $Z_{n,h}$ takes values in $[0,1]$ and it can be interpreted\nas the ``personal inclination'' of the agent $h$ of adopting ``action\n1'', so that the probability that the agent $j$ adopts ``action 1'' at\ntime $(n+1)$ depends on its personal inclination $Z_{n,j}$ and on the\ninclinations $Z_{n,h}$, with $h\\neq j$, of the other agents at time\n$n$ according to the ``influence-weights'' $w_{h,j}$.\\\\\n\n\\indent The previous quoted papers \\cite{ale-cri-ghi, cri-dai-lou-min,\n  cri-dai-min, dai-lou-min} are all focused on the asymptotic\nbehavior of the stochastic processes of the ``personal inclinations''\n$\\{Z^j=(Z_{n,j})_n:\\, j\\in V \\}$ of the agents. On the contrary, in this\nwork we focus on the average of times in which the agents adopt\n``action 1'', i.e. we study the stochastic processes of the {\\em\n  empirical means} $\\{N^j=(N_{n,j})_{n}:\\, j\\in V\\}$ defined,\nfor each $j\\in V$, as $N^j_0:=0$ and, for any $n\\geq 1$,\n\\begin{equation}\\label{medie-empiriche-intro}\nN_{n,j}:=\\frac{1}{n}\\sum_{k=1}^{n} X_{k,j}\\,.\n\\end{equation}\nSince $(1\/n)\\sum_{k=1}^{n-1}X_{k,j}=(1-1\/n)N_{n-1,j}$, the dynamics of\neach process $N^j$ can be written as follows:\n\\begin{equation}\\label{interacting-N}\nN_{n,j}=\\left(1-\\frac{1}{n}\\right)N_{n-1,j}+\\frac{1}{n}X_{n,j}.\n\\end{equation}\nFurthermore, the above dynamics \\eqref{interacting-1-intro},\n\\eqref{interacting-2-intro} and \\eqref{interacting-N} can be expressed\nin a compact form, using the random vectors\n$\\mathbf{X}_{n}:=(X_{n,1},\\dots,X_{n,N})^{\\top}$ for $n\\geq 1$,\n$\\mathbf{N}_{n}:=(N_{n,1},\\dots,N_{n,N})^{\\top}$ and\n$\\mathbf{Z}_{n}:=(Z_{n,1},\\dots,Z_{n,N})^{\\top}$ for $n\\geq 0$, as:\n\\begin{equation}\\label{eq:dynamic-0}\nE[\\mathbf{X}_{n+1}|\\mathcal{F}_{n}]=W^{\\top}\\,\\mathbf{Z}_{n}\\,,\n\\end{equation}\nwhere $W^{\\top}\\mathbf{1}=\\mathbf{1}$ by the normalization of the\nweights, and\n\\begin{equation}\\label{eq:dynamic}\n\\left\\{\\begin{aligned}\n&\\mathbf{Z}_{n}\\ =\\\n\\left(1-r_{n-1}\\right)\\mathbf{Z}_{n-1}\\ +\\ r_{n-1}\\mathbf{X}_{n},\\\\\n&\\mathbf{N}_{n}\\ =\\\n\\left(1-\\frac{1}{n}\\right)\\mathbf{N}_{n-1}\\ +\\ \\frac{1}{n}\\mathbf{X}_{n}.\n\\end{aligned}\\right.\n\\end{equation}\n\n\\indent In the framework described above, under\n  suitable assumptions, we prove that all the stochastic processes\n  $N^j=(N_{n,j})_n$, with $j\\in V$, converge almost surely to the same\n  limit random variable (in other words, we prove their almost sure\n  synchronization), which is also the common limit random variable of\n  the stochastic processes $Z^j=(Z_{n,j})_n$, say $Z_{\\infty}$ (see\n  Theorem~\\ref{th:sincro}).  From an applicative point of view, the\n  almost sure synchronization of the stochastic processes $N^j$ means\n  that, with probability $1$, the percentages of times that the agents\n  of the system adopt the ``action 1'' tend to the same random value\n  $Z_{\\infty}$. Moreover, we provide some Central Limit Theorems\n  (CLTs) in the sense of stable convergence, in which the asymptotic\n  variances and covariances are expressed as functions of the\n  eigen-structure of the weighted adjacency matrix $W$ and of the\n  parameters $\\gamma,\\, c$ governing the asymptotic behavior of the\n  sequence $(r_n)_n$ (see Theorem~\\ref{thm:asymptotics_theta_gamma},\n  Theorem~\\ref{thm:N_1_gamma_1}, Theorem~\\ref{thm:asymptotics_theta_1}\n  and Theorem~\\ref{thm:asymptotics_Z_1_star}). These convergence\n  results are also discussed from the point of view of the\n  statistical applications. In particular, they lead to the\n  construction of asymptotic confidence intervals for the common limit\n  random variable $Z_{\\infty}$ based on the random variables $X_{n,j}$\n  through the empirical means \\eqref{medie-empiriche-intro}, that\n  specifically require neither the knowledge of the initial random\n  variables $\\{Z_{0,j}:\\, j\\in V\\}$ nor of the exact expression of\n  the sequence $(r_n)_n$. For the case $\\gamma=1$, that for instance\n  includes the case of interacting standard P\\'olya's urns, we also\n  provide a statistical test, based on the random variables $X_{n,j}$\n  through the empirical means \\eqref{medie-empiriche-intro}, to make\n  inference on the weighted adjacency matrix $W$ of the network. The\n  fact that the confidence intervals and the inferential procedures\n  presented in this work are based on $X_{n,j}$, instead of $Z_{n,j}$\n  as done in~\\cite{ale-cri-ghi}, represents a great improvement in any\n  area of application, since the ``actions'' $X_{n,j}$ adopted by the\n  agents of the network are much more likely to be observed than their\n  ``personal inclinations'' $Z_{n,j}$ of adopting these actions.\\\\\n\n\\indent The proofs of the given CLTs are a substantial part of\nthis work and we believe that it is worth spending some words on the\nmain tools employed and technical issues faced.  The essential idea is\nto decompose the stochastic process $(\\mathbf{N}_{n})_n$ into the sum\nof two terms, where the first one converges, at the rate\n$n^{\\gamma-1\/2}$ for each $1\/2<\\gamma\\leq 1$, stably in the strong\nsense with respect to the filtration $(\\mathcal{F}_n)_n$ toward a\ncertain Gaussian kernel, and the second term is an\n$(\\mathcal{F}_n)$-adapted stochastic process that converges stably to\na suitable Gaussian kernel, with the corresponding rate and argument\nrequired for the proof different according to the value of $\\gamma$.\nIndeed, when $1\/2<\\gamma<1$, the second term converges stably at the\nsame rate as above, i.e.~$n^{\\gamma-1\/2}$, and in the proof we have a\ncertain remainder term that tends to zero in probability (see\nTheorem~\\ref{thm:asymptotics_theta_hat_gamma}). On the contrary, when\n$\\gamma=1$ and $N\\geq 2$ (the case $\\gamma=1, \\, N=1$ is similar to\nthe previous case $1\/2<\\gamma<1$), we do not have the convergence to\nzero of that remainder term (see\nRemark~\\ref{rem:different_approach_gamma_1}) and so we develop a\ncoupling technique based on the pair of random vectors\n$(\\mathbf{Z}_n,\\mathbf{N}_n)$. So doing, we determine two different\nrates for the convergence of the second term, depending on the second\nhighest real part ${\\mathcal Re}(\\lambda^*)$ of the eigenvalues of $W$\n(see Theorem~\\ref{thm:asymptotics_theta_hat_1} where the rate is\n$\\sqrt{n}$ and Theorem~\\ref{thm:asymptotics_theta_1_star} where the\nrate is $\\sqrt{n\/\\ln(n)}$). The contributions of the two terms are in\nparticular reflected in the analytic expressions of the asymptotic\ncovariance matrix of $\\mathbf{N}_{n}$ (see\nTheorem~\\ref{thm:asymptotics_theta_gamma},\nTheorem~\\ref{thm:asymptotics_theta_1} and\nTheorem~\\ref{thm:asymptotics_Z_1_star}), where there is a component\n$\\widetilde{\\Sigma}_{\\gamma}$ due to the first term (which is zero\nwhen the rate for the second term is $\\sqrt{n\/\\ln(n)}$, because the\ncontribution of the first term vanishes) and another component\ndue to the second term that is different in the various cases:\n$\\widehat{\\Gamma}_{\\gamma}$ when $1\/2<\\gamma<1$, and\n$\\widehat{\\Sigma}_{\\mathbf{N}\\mathbf{N}}$ or\n$\\widehat{\\Sigma}^{*}_{\\mathbf{N}\\mathbf{N}}$, according to the value\nof ${\\mathcal Re}(\\lambda^*)$, when $\\gamma=1$.\\\\\n\n\\indent Summing up, the main focus here concerns the asymptotic\nbehavior of the empirical means $({\\mathbf N}_n)_n$, that has not been\nsubject of study yet. Furthermore, although we recover some results on\n$(\\mathbf{Z}_n)_n$ proved in \\cite{ale-cri-ghi}, we point out that the\nexistence of joint central limit theorems for the pair\n$(\\mathbf{Z}_n,\\mathbf{N}_n)$ is not obvious because the ``discount\nfactors'' in the dynamics of the increments\n$(\\mathbf{Z}_{n}-\\mathbf{Z}_{n-1})_n$ and\n$(\\mathbf{N}_{n}-\\mathbf{N}_{n-1})_n$ are generally different. Indeed,\nas shown in~\\eqref{eq:dynamic}, these two stochastic processes follow\nthe dynamics\n\\begin{equation}\\label{eq-increments-intro}\n\\left\\{\n\\begin{aligned}\n&\\mathbf{Z}_{n}-\\mathbf{Z}_{n-1}\\ =\\\nr_{n-1}\\left(\\mathbf{X}_{n}-\\mathbf{Z}_{n-1}\\right),\\\\\n&\\mathbf{N}_{n}-\\mathbf{N}_{n-1}\\ =\\\n\\frac{1}{n}\\left(\\mathbf{X}_{n}-\\mathbf{N}_{n-1}\\right),\n\\end{aligned}\n\\right.\n\\end{equation}\nand so, when we assume $1\/2<\\gamma<1$, it could be surprising that\nthere exists a common convergence rate. In addition, we will show\nthat, when $1\/2<\\gamma<1$, the stochastic processes $N^j=(N_{n,j})_n$\nlocated at different vertices of the graph synchronize among each\nother faster than how they converge to the common random limit\n$Z_{\\infty}$, i.e.  for any pair of vertices $(j,h)$ with $j\\neq h$,\nthe velocity at which $(N_{n,j}-N_{n,h})_n$ converges almost surely to\nzero is higher than the one at which $N^j=(N_{n,j})_n$ and\n$N^h=(N_{h,n})_n$ converge almost surely to $Z_{\\infty}$.  At the\ncontrary, when $\\gamma=1$ the stochastic processes $N^j=(N_{n,j})_n$\nsynchronize and converge almost surely to $Z_{\\infty}$ at the same\nvelocity.  The same asymptotic behaviors characterize the stochastic\nprocesses $Z^j=(Z_{n,j})_n$, as proved also in~\\cite{ale-cri-ghi,\n  cri-dai-lou-min}.  However, while it is somehow guessable from\n\\eqref{eq-increments-intro} that the velocities of synchronization and\nconvergence for the processes $Z^j=(Z_{n,j})_n$ depend on the\nparameter $\\gamma$, it could be somehow unexpected that, although the\ndiscount factor of the increments $(\\mathbf{N}_{n}-\\mathbf{N}_{n-1})$\nis always $n^{-1}$, the corresponding velocities for the processes\n$N^j=(N_{n,j})_n$ also depend on $\\gamma$ and, in general, also these\nprocesses do not synchronize and converge to $Z_{\\infty}$ at the same\nvelocity.  As we will see, this fact is essentially due to their\ndependence on the process $(\\mathbf{Z}_{n})_n$, which is induced by\nthe process $(\\mathbf{X}_{n})_n$. It is worthwhile to note that\ndynamics similar to~\\eqref{eq-increments-intro} have already been\nconsidered in the Stochastic Approximation literature.  Specifically,\nin~\\cite{mok-pel} the authors established a CLT for a pair of\nrecursive procedures having two different step-sizes. However, this\nresult does not apply to our situation.  Indeed, the covariance\nmatrices $\\Sigma_\\mu$ and $\\Sigma_\\theta$ in their main result\n(Theorem~1) are deterministic, while the asymptotic covariance\nmatrices in our CLTs are random (as said before, they depend on the\nrandom variable $Z_\\infty$).  This is why we do not use the simple\nconvergence in distribution, but we employ the notion of stable\nconvergence, which is, among other things, essential for the\nconsidered statistical applications. Finally, in~\\cite{mok-pel}, the\nauthors find two different convergence rates, depending on the two\ndifferent step-sizes, while, as already said, we find a common\nconvergence rate.\\\\\n\n\\indent The rest of the paper is organized as follows. In Section\n\\ref{section_model} we describe the notation and the assumptions used\nalong the paper.  In Section \\ref{section_asymptotic_results} we\nillustrate our main results and we discuss some possible statistical\napplications. An interesting example of interacting system is also\nprovided in order to clarify the statement of the theorems and the\nrelated comments. Section \\ref{section_proofs} contains the proofs or\nthe main steps of the proofs (postponing some technical lemmas to\nAppendix \\ref{app-A}) of the presented results. For the reader's\nconvenience, Appendix \\ref{app-B} supplies a brief review on the\nnotion of stable convergence and its variants.\n\n\n\\section{Notation and assumptions}\\label{section_model}\n\nThroughout all the paper, we will adopt the same notation used in\n\\cite{ale-cri-ghi}.  In particular, we denote by ${\\mathcal Re}(z)$,\n${\\mathcal Im}(z)$, $\\overline{z}$ and $|z|$ the real part, the\nimaginary part, the conjugate and the modulus of a complex number $z$.\nThen, for a matrix $A$ with complex elements, we let $\\overline{A}$\nand $A^{\\top}$ be its conjugate and its transpose, while we indicate\nby $|A|$ the sum of the modulus of its elements. The identity matrix\nis denoted by $I$, independently of its dimension that will be clear\nfrom the context.  The spectrum of $A$, i.e.~the set of all the\neigenvalues of $A$ repeated with their multiplicity, is denoted by\n$Sp(A)$, while its sub-set containing the eigenvalues with maximum\nreal part is denoted by $\\lambda_{\\max}(A)$, i.e.  $\\lambda^*\\in\n\\lambda_{\\max}(A)$ whenever ${\\mathcal Re}(\\lambda^*)=\\max\\{ {\\mathcal\n  Re}(\\lambda):\\, \\lambda\\in Sp(A) \\}$.  Finally, we consider any\nvector $\\mathbf{v}$ as a matrix with only one column (so that all the\nabove notations apply to $\\mathbf{v}$) and we indicate by\n$\\|\\mathbf{v}\\|$ its norm, i.e. $ \\|\\mathbf{v} \\|^2 =\n\\overline{\\mathbf{v}}^{\\top}\\mathbf{v}$.  The vectors whose elements\nare all ones or zeros are denoted by $\\mathbf{1}$ and $\\mathbf{0}$,\nrespectively, independently of their dimension that will be clear from\nthe context.\\\\\n\n\\indent Throughout all the paper, we assume that the following\nconditions hold:\n\n\\begin{ass}\\label{ass:r_n}\nThere exist real constants $c>0$ and $1\/2<\\gamma\\leq 1$ such that\ncondition \\eqref{ass-r-intro} is satisfied, which can be rewritten as\n\\begin{equation}\\label{ass:condition_r_n_gamma}\nn^{\\gamma} r_n\\ =\\ c\\ +\\ o(1).\n\\end{equation}\nIn some results for $\\gamma=1$, we will require a slightly stricter\ncondition than~\\eqref{ass:condition_r_n_gamma}, that is:\n\\begin{equation}\\label{ass:condition_r_n_1}\nnr_n\\ =\\ c\\ +\\ O\\left(n^{-1}\\right).\n\\end{equation}\nWe will explicitly mention this assumption in the statement of the\ntheorems when it is required.\n\\end{ass}\n\n\\begin{ass\nThe weighted adjacency matrix $W$ is irreducible and diagonalizable.\n\\end{ass}\n\nThe irreducibility of $W$ reflects a situation in which all the\nvertices are connected among each others and hence there are no\nsub-systems with independent dynamics (see \\cite{ale-cri-ghi, ale-ghi}\nfor further details). The diagonalizability of $W$ allows us to find a\nnon-singular matrix $\\widetilde{U}$ such that\n$\\widetilde{U}^{\\top}W(\\widetilde{U}^{\\top})^{-1}$ is diagonal with\ncomplex elements $\\lambda_j\\in Sp(W)$.  Notice that each column\n$\\mathbf{u}_j$ of $\\widetilde{U}$ is a left eigenvector of $W$\nassociated to some eigenvalue $\\lambda_j$.  Without loss of\ngenerality, we set $\\|\\mathbf{u}_j\\|=1$.  Moreover, when the\nmultiplicity of some $\\lambda_j$ is bigger than one, we set the\ncorresponding eigenvectors to be orthogonal.  Then, if we define\n$\\widetilde{V}=(\\widetilde{U}^{\\top})^{-1}$, we have that each column\n$\\mathbf{v}_j$ of $\\widetilde{V}$ is a right eigenvector of $W$\nassociated to $\\lambda_j$ such that\n\\begin{equation}\\label{eq:relazioni-0}\n\\mathbf{u}_j^{\\top}\\,\\mathbf{v}_j=1,\\quad\\mbox{ and }\\qquad\n\\mathbf{u}_h^{\\top}\\,\\mathbf{v}_j=0,\\ \\forall h\\neq j.\n\\end{equation}\n\nThese constraints combined with the above assumptions on $W$\n(precisely, $w_{h,j}\\geq 0$, $W^{\\top}\\mathbf{1}=\\mathbf{1}$ and\nthe irreducibility) imply, by\nFrobenius-Perron Theorem, that $\\lambda_1:=1$ is an eigenvalue of $W$\nwith multiplicity one, $\\lambda_{\\max}(W)=\\{1\\}$ and\n\\begin{equation}\\label{eq:relazioni-1}\n\\mathbf{u}_1=N^{-1\/2}\\mathbf{1}, \\qquad\nN^{-1\/2}{\\mathbf 1}^{\\top}{\\mathbf v}_1=1\\qquad\n\\mbox{and}\\qquad\nv_{1,j}:=[\\mathbf{v}_1]_j>0\\;\\ \\forall 1\\leq j\\leq N.\n\\end{equation}\n\nWe use $U$ and $V$ to indicate the sub-matrices of\n$\\widetilde{U}$ and $\\widetilde{V}$, respectively, whose columns are\nthe left and the right eigenvectors of $W$ associated to\n$Sp(W)\\setminus \\{1\\}$, that is $\\{\\mathbf{u}_2,\\dots,\\mathbf{u}_N\\}$\nand $\\{\\mathbf{v}_2,\\dots,\\mathbf{v}_N\\}$, respectively, and, finally, we denote\nby $\\lambda^*$ an eigenvalue belonging to $Sp(W)\\setminus\\{1\\}$ such that\n$$\n{\\mathcal Re}(\\lambda^*)=\\max\\left\\{ {\\mathcal Re}(\\lambda_j):\\,\n\\lambda_j\\in Sp(W)\\setminus\\{1\\}\\right\\}.\n$$\nIn other words, if we denote by $D$ the diagonal matrix whose\nelements are $\\lambda_j\\in Sp(W)\\setminus\\{1\\}$, we have\n$\\lambda^*\\in \\lambda_{\\max}(D)$.\n\n\n\\section{Main results and discussion}\n\\label{section_asymptotic_results}\n\nIn this section, we present and discuss our main results concerning\nthe asymptotic behavior of the joint process\n$(\\mathbf{Z}_{n},\\mathbf{N}_{n})_n$.  We recall the assumptions stated\nin Section~\\ref{section_model} and we refer to Appendix \\ref{app-B}\nfor a brief review on the notion of stable convergence and its\nvariants.  \\\\\n\n\\indent We start by providing a first-order asymptotic result\nconcerning the almost sure convergence of the sequence of pairs\n$(\\mathbf{Z}_{n},\\mathbf{N}_{n})_n$.\n\\begin{theo}\\label{th:sincro}\nFor $N\\geq 1$, we have\n\\begin{equation*\n\\mathbf{N}_n\\ \\stackrel{a.s.}{\\longrightarrow}\\ Z_{\\infty}\\mathbf{1}\\,,\n\\end{equation*}\nwhere $Z_{\\infty}$ is the random variable with values in $[0,1]$\ndefined as the common almost sure limit of the stochastic processes\n$Z^j=(Z_{n,j})_n$. \\\\\n\\indent Moreover, the following statements hold true:\n\\begin{itemize}\n\\item[(i)] $P(Z_\\infty=z)=0$ for any $z\\in (0,1)$.\n\\item[(ii)] If we have\n  $P(\\bigcap_{j=1}^N\\{Z_{0,j}=0\\})+P(\\bigcap_{j=1}^N\\{Z_{0,j}=1\\})<1$,\n  then $P(0<Z_\\infty<1)>0$.\n\\end{itemize}\n\\end{theo}\nIn particular, this result states that, when $N\\geq 2$, all the\nstochastic processes $N^j=(N_{n,j})_n$, located at the different\nvertices $j\\in V$ of the graph, synchronize almost surely, i.e. all of\nthem converge almost surely toward the same random variable\n$Z_\\infty$. Moreover, this random variable is the same limit toward\nwhich all the stochastic processes $Z^j=(Z_{n,j})_n$ synchronize\nalmost surely (see Theorem 3.1 in~\\cite{ale-cri-ghi}). In addition, it\nis interesting to note that the synchronization holds true without any\nassumption on the initial configuration $\\mathbf{Z}_{0}$ and for any\nchoice of the weighted adjacency matrix $W$ with the required\nassumptions. Finally, note that the synchronization is induced along\ntime independently of the fixed size $N$ of the network, and so it\ndoes not require a large-scale limit (i.e. the limit for $N\\to\n+\\infty$), which is usual in statistical mechanics for the study of\ninteracting particle systems.\\\\\n\n\\indent We now focus on the second-order asymptotic results.\nSpecifically, we present joint central limit theorems for the sequence\nof pairs $(\\mathbf{Z}_{n},\\mathbf{N}_{n})_n$ in the sense of stable\nconvergence, that establish the rate of convergence to the limit\n$Z_{\\infty}\\mathbf{1}$ given in Theorem~\\ref{th:sincro} and the\nrelative asymptotic random covariance matrices.  First, we consider\nthe case $1\/2<\\gamma<1$:\n\\begin{theo}\\label{thm:asymptotics_theta_gamma}\nFor $N\\geq 1$ and $1\/2<\\gamma<1$, we have that\n\\begin{equation}\\label{eq:CLT_theta_gamma}\nn^{\\gamma-\\frac{1}{2}}\n\\begin{pmatrix}\n\\mathbf{Z}_n-Z_{\\infty}\\mathbf{1}\\\\\n\\mathbf{N}_n-Z_{\\infty}\\mathbf{1}\n\\end{pmatrix}\n{\\longrightarrow}\\\n\\mathcal{N} \\left(\\ \\mathbf{0}\\ ,\\ Z_{\\infty}(1-Z_{\\infty})\n\\begin{pmatrix}\n\\widetilde{\\Sigma}_{\\gamma} & \\widetilde{\\Sigma}_{\\gamma}\\\\\n\\widetilde{\\Sigma}_{\\gamma} & \\widetilde{\\Sigma}_{\\gamma}+\\widehat{\\Gamma}_{\\gamma}\n\\end{pmatrix}\\ \\right)\\ \\ \\ \\ stably,\n\\end{equation}\nwhere\n\\begin{equation}\\label{def:Sigmatilde_gamma}\n\\widetilde{\\Sigma}_{\\gamma}:=\n\\widetilde{\\sigma}_{\\gamma}^2{\\mathbf 1}{\\mathbf 1}^{\\top}\n\\qquad\\mbox{ and }\\qquad\n\\widetilde{\\sigma}_{\\gamma}^2:=\n\\frac{c^2\\,\\|\\mathbf{v}_1\\|^2}{N(2\\gamma-1)}\n>0,\n\\end{equation}\nand\n\\begin{equation}\\label{def:Sigmahat_NN_gamma}\n\\widehat{\\Gamma}_{\\gamma}:=\n\\widehat{\\sigma}_{\\gamma}^2{\\mathbf 1}{\\mathbf 1}^{\\top}\n\\qquad\\mbox{ and }\\qquad\n\\widehat{\\sigma}_{\\gamma}^2:=\n\\frac{c^2\\,\\|\\mathbf{v}_1\\|^2}{N (3-2\\gamma)}\n>0.\n\\end{equation}\n\\end{theo}\n\n\\begin{rem}\n\\rm Some considerations can be drawn by looking at the analytic\nexpressions of $\\widetilde{\\sigma}_{\\gamma}^2$ and\n$\\widehat{\\sigma}_{\\gamma}^2$ in~\\eqref{def:Sigmatilde_gamma}\nand~\\eqref{def:Sigmahat_NN_gamma}, respectively.  First, they are both\ndecreasing in $N$, so that the asymptotic variances are small when the\nnumber of vertices in the graph is large.  Second, they are both\nincreasing in $c$ and decreasing in $\\gamma$, which, recalling that\n$\\lim_n n^{\\gamma }r_n=c$, means that the faster is the convergence to\nzero of the sequence $(r_n)_n$, the lower are the values of the\nasymptotic variances $\\widetilde{\\sigma}_{\\gamma}^2$ and\n$\\widehat{\\sigma}_{\\gamma}^2$. Third, when $\\gamma$ is close to $1\/2$,\n$\\widetilde{\\sigma}_{\\gamma}^2$ becomes very large, while\n$\\widehat{\\sigma}_{\\gamma}^2$ remains bounded, and hence the processes\n$(\\mathbf{Z}_n-Z_{\\infty}\\mathbf{1})$ and\n$(\\mathbf{N}_n-Z_{\\infty}\\mathbf{1})$ become highly correlated.\nFinally, since we have\n$$\n1\\leq 1+\\|\\mathbf{v}_1-\\mathbf{u}_1\\|^2=\\|\\mathbf{v}_1\\|^2\\leq N,\n$$\nwe can obtain the following lower and upper bounds for\n$\\widetilde{\\sigma}_{\\gamma}^2$ and $\\widehat{\\sigma}_{\\gamma}^2$ (not\ndepending on $W$):\n$$\n\\frac{c^2}{N(2\\gamma-1)}\\leq\n\\widetilde{\\sigma}_{\\gamma}^2\\leq\\frac{c^2}{(2\\gamma-1)}\n\\quad\\hbox{and}\\quad\n\\frac{c^2}{N(3-2\\gamma)}\\leq\\widehat{\\sigma}_{\\gamma}^2\\leq\n\\frac{c^2}{(3-2\\gamma)}.\n$$ Notice that the lower bound is achieved when\n$\\mathbf{v}_1=\\mathbf{u}_1=N^{-1\/2}\\mathbf{1}$, i.e. when $W$ is\ndoubly stochastic.\n\\end{rem}\n\n\\begin{rem} \\rm\nNote that from~\\eqref{eq:CLT_theta_gamma} of\nTheorem~\\ref{thm:asymptotics_theta_gamma}, we get in particular that,\nfor any pair of vertices $(j,h)$ with $j\\neq h$,\n$n^{\\gamma-\\frac{1}{2}}(N_{n,j}-N_{n,h})$ converges to zero in\nprobability.  Indeed, denoting by $\\mathbf{e}_j$ the vector such that\n$e_{j,j}=1$ and $e_{j,i}=0$ for all $i\\neq j$, we have\n$\\mathbf{1}^{\\top}(\\mathbf{e}_j-\\mathbf{e}_h)=0$ and hence\n$(\\mathbf{e}_j-\\mathbf{e}_h)^{\\top}\\widetilde{\\Sigma}_{\\gamma}\n(\\mathbf{e}_j-\\mathbf{e}_h)=\n(\\mathbf{e}_j-\\mathbf{e}_h)^{\\top}\\widehat{\\Gamma}_{\\gamma}\n(\\mathbf{e}_j-\\mathbf{e}_h)=0$.  Therefore,\nTheorem~\\ref{thm:asymptotics_theta_gamma} implies that the velocity at\nwhich the stochastic processes $N^j=(N_{n,j})_n$, located at different\nvertices $j\\in V$, synchronize among each other is higher\nthan the one at which each of them converges almost surely to the\ncommon random limit $Z_{\\infty}$. The same asymptotic behavior is\nshown also by the stochastic processes $Z^j=(Z_{n,j})_n$ as shown\nin \\cite{ale-cri-ghi, cri-dai-lou-min}.\n\\end{rem}\n\nFor $\\gamma=1$ we need to distinguish the case $N=1$ and the case\n$N\\geq 2$.  Indeed, in the second case we can have different\nconvergence rates according to the value of ${\\mathcal Re}(\\lambda^*)$.\nMore precisely, we have the following results:\n\\begin{theo}\\label{thm:N_1_gamma_1}\nFor $N=1$ and $\\gamma=1$, we have that\n\\begin{equation*\n\\sqrt{n}\n\\begin{pmatrix}\nZ_n-Z_{\\infty}\\\\\nN_n-Z_{\\infty}\n\\end{pmatrix}\n{\\longrightarrow}\\\n\\mathcal{N}\n\\left(\n\\ \\mathbf{0}\\ ,\\ Z_{\\infty}(1-Z_{\\infty})\n\\begin{pmatrix}\nc^2 & c^2\\\\\nc^2 & c^2+(c-1)^2\n\\end{pmatrix}\n\\ \\right)\\ \\ \\ \\ stably.\n\\end{equation*}\n\\end{theo}\n\n\\begin{theo}\\label{thm:asymptotics_theta_1}\nFor $N\\geq 2$, $\\gamma=1$ and ${\\mathcal\n  Re}(\\lambda^{*})<1-(2c)^{-1}$, under\ncondition~\\eqref{ass:condition_r_n_1}, we have that\n\\begin{equation}\\label{eq:CLT_theta_1}\n\\sqrt{n}\n\\begin{pmatrix}\n\\mathbf{Z}_n-Z_{\\infty}\\mathbf{1}\\\\\n\\mathbf{N}_n-Z_{\\infty}\\mathbf{1}\n\\end{pmatrix}\n{\\longrightarrow}\\\n\\mathcal{N} \\left(\\ \\mathbf{0}\\ ,\\ Z_{\\infty}(1-Z_{\\infty})\n\\begin{pmatrix}\n\\widetilde{\\Sigma}_1+\\widehat{\\Sigma}_{\\mathbf{ZZ}}\n& \\widetilde{\\Sigma}_1+\\widehat{\\Sigma}_{\\mathbf{ZN}}\\\\\n\\widetilde{\\Sigma}_1+\\widehat{\\Sigma}_{\\mathbf{ZN}}^{\\top}\n& \\widetilde{\\Sigma}_1+\\widehat{\\Sigma}_{\\mathbf{NN}}\n\\end{pmatrix}\\ \\right)\\ \\ \\ \\ stably,\n\\end{equation}\nwhere $\\widetilde{\\Sigma}_1$ is defined as\nin~\\eqref{def:Sigmatilde_gamma} with $\\gamma=1$, and\n\\begin{equation}\\label{def:Sigmahat_ZZ_1}\n\\widehat{\\Sigma}_{\\mathbf{ZZ}}:=U\\widehat{S}_{\\mathbf{ZZ}}U^{\\top},\\qquad\\mbox{with}\n\\end{equation}\n\\begin{equation}\\label{def:Shat_ZZ}\n[\\widehat{S}_{\\mathbf{ZZ}}]_{h,j}\\ :=\\\n\\frac{c^2}{c(2-\\lambda_h-\\lambda_j)-1}(\\mathbf{v}_{h}^{\\top}\\mathbf{v}_{j}),\\\n2\\leq h,j\\leq N;\n\\end{equation}\n\\begin{equation}\\label{def:Sigmahat_NN_1}\n\\widehat{\\Sigma}_{\\mathbf{NN}}:=\n\\widetilde{U}\\widehat{S}_{\\mathbf{NN}}\\widetilde{U}^{\\top},\n\\qquad\\mbox{with}\n\\end{equation}\n\\begin{equation}\\label{def:Shat_NN_1}\n[\\widehat{S}_{\\mathbf{NN}}]_{1,1}:=(c-1)^2\\|\\mathbf{v}_{1}\\|^2,\\qquad\n[\\widehat{S}_{\\mathbf{NN}}]_{1,j}=[\\widehat{S}_{\\mathbf{NN}}]_{j,1}:=\n\\left(\\frac{1-c}{1-\\lambda_j}\\right)(\\mathbf{v}_{1}^{\\top}\\mathbf{v}_{j}),\\\n2\\leq j\\leq N,\n\\end{equation}\n\\begin{equation}\\label{def:Shat_NN_2}\n[\\widehat{S}_{\\mathbf{NN}}]_{h,j}\\ :=\\\n\\frac{1+(c-1)[(1-\\lambda_h)^{-1}+(1-\\lambda_j)^{-1}]}{c(2-\\lambda_h-\\lambda_j)-1}\n(\\mathbf{v}_{h}^{\\top}\\mathbf{v}_{j}),\\ 2\\leq h,j\\leq N;\n\\end{equation}\n\\begin{equation}\\label{def:Sigmahat_ZN_1}\n\\widehat{\\Sigma}_{\\mathbf{ZN}}:=U\\widehat{S}_{\\mathbf{ZN}}\\widetilde{U}^{\\top},\n\\qquad\\mbox{with}\n\\end{equation}\n\\begin{equation}\\label{def:Shat_ZN_1}\n[\\widehat{S}_{\\mathbf{ZN}}]_{h,1}:=\\left(\\frac{1-c}{1-\\lambda_h}\\right)\n(\\mathbf{v}_{h}^{\\top}\\mathbf{v}_{1}),\\ 2\\leq h\\leq N,\n\\end{equation}\n\\begin{equation}\\label{def:Shat_ZN_2}\n[\\widehat{S}_{\\mathbf{ZN}}]_{h,j}\\ :=\\\n\\frac{c+(c-1)(1-\\lambda_h)^{-1}}{c(2-\\lambda_h-\\lambda_j)- 1}\n(\\mathbf{v}_{h}^{\\top}\\mathbf{v}_{j}),\\ 2\\leq h,j\\leq N.\n\\end{equation}\n\\end{theo}\n\nThe condition ${\\mathcal Re}(\\lambda^{*})<1-(2c)^{-1}$ in the above\nTheorem~\\ref{thm:asymptotics_theta_1} is the analogous of the one\ntypically required for the CLTs in the Stochastic Approximation\nframework (e.g. \\cite{konda, mok-pel, pel}). However, we deal with a\nrandom limit $Z_\\infty$ and random asymptotic covariances and our\nproofs are not based on that results, but we employ different\narguments. Moreover, in the next theorem, we analyze also the case\n${\\mathcal Re}(\\lambda^{*})=1-(2c)^{-1}$.\n\n\\begin{theo}\\label{thm:asymptotics_Z_1_star}\nFor $N\\geq 2$, $\\gamma=1$ and ${\\mathcal\n  Re}(\\lambda^{*})=1-(2c)^{-1}$, under\ncondition~\\eqref{ass:condition_r_n_1}, we have that\n\\begin{equation}\\label{eq:CLT_theta_1_star}\n\\sqrt{\\frac{n}{\\ln(n)}}\n\\begin{pmatrix}\n\\mathbf{Z}_n-Z_{\\infty}\\mathbf{1}\\\\\n\\mathbf{N}_n-Z_{\\infty}\\mathbf{1}\n\\end{pmatrix}\n{\\longrightarrow}\\\n\\mathcal{N} \\left(\\ \\mathbf{0}\\ ,\\ Z_{\\infty}(1-Z_{\\infty})\n\\begin{pmatrix}\n\\widehat{\\Sigma}^{*}_{\\mathbf{ZZ}} & \\widehat{\\Sigma}^{*}_{\\mathbf{ZN}}\\\\\n\\widehat{\\Sigma}_{\\mathbf{ZN}}^{*\\top} & \\widehat{\\Sigma}^{*}_{\\mathbf{NN}}\n\\end{pmatrix}\\\n\\right)\\ \\ \\ \\ stably,\n\\end{equation}\nwhere\n\\begin{equation}\\label{def:Sigmahat_ZZ_1_star}\n\\widehat{\\Sigma}^{*}_{\\mathbf{ZZ}}:=\nU\\widehat{S}^{*}_{\\mathbf{ZZ}}U^{\\top},\\qquad\\mbox{with}\n\\end{equation}\n\\begin{equation}\\label{def:Shat_ZZ_star}\n[\\widehat{S}^{*}_{\\mathbf{ZZ}}]_{h,j}\\ :=\\\nc^2(\\mathbf{v}_{h}^{\\top}\\mathbf{v}_{j})\\ind_{\\{c(2-\\lambda_h-\\lambda_j)=1\\}},\\\n2\\leq h,j\\leq N;\n\\end{equation}\n\\begin{equation}\\label{def:Sigmahat_NN_1_star}\n\\widehat{\\Sigma}^{*}_{\\mathbf{NN}}:=\nU\\widehat{S}^{*}_{\\mathbf{NN}}U^{\\top},\\qquad\\mbox{with}\n\\end{equation}\n\\begin{equation}\\label{def:Shat_NN_star}\n[\\widehat{S}^{*}_{\\mathbf{NN}}]_{h,j}\\ :=\\\n\\frac{\\lambda_h\\lambda_j}{(1-\\lambda_h)(1-\\lambda_j)}\n(\\mathbf{v}_{h}^{\\top}\\mathbf{v}_{j})\\ind_{\\{c(2-\\lambda_h-\\lambda_j)=1\\}},\\\n2\\leq h,j\\leq N;\n\\end{equation}\n\\begin{equation}\\label{def:Sigmahat_ZN_1_star}\n\\widehat{\\Sigma}^{*}_{\\mathbf{ZN}}:=\nU\\widehat{S}^{*}_{\\mathbf{ZN}}U^{\\top},\\qquad\\mbox{with}\n\\end{equation}\n\\begin{equation}\\label{def:Shat_ZN_star}\n[\\widehat{S}^{*}_{\\mathbf{ZN}}]_{h,j}\\ :=\\\n\\frac{c\\lambda_j}{1-\\lambda_h}(\\mathbf{v}_{h}^{\\top}\\mathbf{v}_{j})\n\\ind_{\\{c(2-\\lambda_h-\\lambda_j)=1\\}},\\ 2\\leq h,j\\leq N.\n\\end{equation}\n\\end{theo}\n\n\\begin{rem\n \\rm The central limit theorem only for the stochastic process\n $(\\mathbf{Z}_n)_n$ can be established in the case ${\\mathcal\n   Re}(\\lambda^*)<1-(2c)^{-1}$ replacing\n condition~\\eqref{ass:condition_r_n_1} with the more general\n assumption~\\eqref{ass:condition_r_n_gamma} (see Theorem 3.2 in~\\cite{ale-cri-ghi}).\n However, condition~\\eqref{ass:condition_r_n_1} is essential in our\n proof of the central limit theorem for the joint stochastic process\n $(\\mathbf{Z}_n, \\mathbf{N}_n)_n$ as stated in\n Theorem~\\ref{thm:asymptotics_theta_1}.\n\\end{rem}\n\n\\begin{rem}\n\\rm From Theorem~\\ref{thm:asymptotics_theta_1} and\nTheorem~\\ref{thm:asymptotics_Z_1_star} we get that, when $N\\geq 2$ and\n$\\gamma=1$, for any pair of vertices $(j,h)$ with $j\\neq h$, the\ndifference $(N_{n,j}-N_{n,h})$ converges almost surely to zero with\nthe same velocity at which each process $N^j=(N_{n,j})$ converges\nalmost surely to $Z_{\\infty}$.  (The same asymptotic behavior is shown\nalso by the stochastic processes $Z^j=(Z_{n,j})_n$ as provided in\n\\cite{ale-cri-ghi, cri-dai-lou-min}.)  Indeed, although\n$\\widetilde{\\Sigma}_{1}(\\mathbf{e}_j-\\mathbf{e}_h)=\\mathbf{0}$ and\n$\\mathbf{u}_1^{\\top}(\\mathbf{e}_j-\\mathbf{e}_h)=0$, we have\n$U^{\\top}(\\mathbf{e}_j-\\mathbf{e}_h)\\neq\\mathbf{0}$ and hence,\nsetting $\\mathbf{u}_{j,h}:=U^{\\top}(\\mathbf{e}_j-\\mathbf{e}_h)$ and\n$\\widetilde{\\mathbf{u}}_{j,h}:=\n\\widetilde{U}^{\\top}(\\mathbf{e}_j-\\mathbf{e}_h)=(0,\\mathbf{u}_{j,h})^{\\top}$,\nfor ${\\mathcal Re}(\\lambda^{*})<1-(2c)^{-1}$ by~\\eqref{eq:CLT_theta_1}\nwe have\n\\begin{equation*}\n\\sqrt{n}\n\\begin{pmatrix}\nZ_{n,j}-Z_{n,h}\\\\\nN_{n,j}-N_{n,h}\n\\end{pmatrix}\n{\\longrightarrow}\\\n\\mathcal{N} \\left(\\ \\mathbf{0}\\ ,\\ Z_{\\infty}(1-Z_{\\infty})\n\\begin{pmatrix}\n\\mathbf{u}^{\\top}\\widehat{S}_{\\mathbf{ZZ}}\\mathbf{u}_{j,h}\n& \\mathbf{u}_{j,h}^{\\top}\\widehat{S}_{\\mathbf{ZN}}\\widetilde{\\mathbf{u}}_{j,h}\\\\\n\\widetilde{\\mathbf{u}}_{j,h}^{\\top}\\widehat{S}_{\\mathbf{ZN}}^{\\top}\\mathbf{u}_{j,h}\n& \\widetilde{\\mathbf{u}}_{j,h}^{\\top}\\widehat{S}_{\\mathbf{NN}}\n\\widetilde{\\mathbf{u}}_{j,h}\n\\end{pmatrix}\\ \\right)\\ \\ \\ \\ \\hbox{stably};\n\\end{equation*}\nwhile for ${\\mathcal Re}(\\lambda^{*})=1-(2c)^{-1}$\nby~\\eqref{eq:CLT_theta_1_star} we have\n\\begin{equation*}\n\\sqrt{\\frac{n}{\\ln(n)}}\n\\begin{pmatrix}\nZ_{n,j}-Z_{n,h}\\\\\nN_{n,j}-N_{n,h}\n\\end{pmatrix}\n{\\longrightarrow}\\\n\\mathcal{N} \\left(\\ \\mathbf{0}\\ ,\\ Z_{\\infty}(1-Z_{\\infty})\n\\begin{pmatrix}\n\\mathbf{u}_{j,h}^{\\top}\\widehat{S}^{*}_{\\mathbf{ZZ}}\\mathbf{u}_{j,h}\n& \\mathbf{u}_{j,h}^{\\top}\\widehat{S}^{*}_{\\mathbf{ZN}}\\mathbf{u}_{j,h}\\\\\n\\mathbf{u}_{j,h}^{\\top}\\widehat{S}_{\\mathbf{ZN}}^{*\\top}\\mathbf{u}_{j,h}\n& \\mathbf{u}_{j,h}^{\\top}\\widehat{S}^{*}_{\\mathbf{NN}}\\mathbf{u}_{j,h}\n\\end{pmatrix}\\\n\\right)\\ \\ \\ \\ \\hbox{stably}.\n\\end{equation*}\nNotice that the only elements $[\\widehat{S}_{\\mathbf{NN}}]_{h,j}$ that\ncount in the above limit relations are those with $2\\leq h,j\\leq N$.\nThen, from~\\eqref{def:Sigmahat_NN_1} we can see that these elements\nremain bounded for any value of $c$, while\nfrom~\\eqref{def:Sigmahat_ZZ_1} we can see that the elements of\n$\\widehat{S}_{\\mathbf{ZZ}}$ are increasing in $c$. (The same\nconsiderations can be made for the elements of the matrices\n$\\widehat{S}^{*}_{\\mathbf{NN}}$ and $\\widehat{S}^{*}_{\\mathbf{ZZ}}$,\nbut in this case the value of $c$ is uniquely determined by\n${\\mathcal Re}(\\lambda^*)$).  As a consequence, for large values of\n$c$, the asymptotic variance of $(N_{n,j}-N_{n,h})$ becomes negligible\nwith respect to the one of $(Z_{n,j}-Z_{n,h})$.  Therefore, when\n$N\\geq 2$ and $\\gamma=1$, the synchronization between the empirical\nmeans $N^j=(N_{n,j})_n$, located at different vertices $j\\in V$,\nis more accurate than the synchronization between the\nstochastic processes $Z^j=(Z_{n,j})_n$.\n\\end{rem}\n\nAn interesting example of interacting system is provided by the {\\em\n  ``mean-field interaction''}, already considered\nin~\\cite{ale-cri-ghi, cri-dai-lou-min, cri-dai-min,\n  dai-lou-min}. Naturally, all the weighted adjacency matrices\nintroduced and analyzed in \\cite{ale-cri-ghi} can be considered as\nwell.\n\n\\begin{example}\\label{ex:mean_field}\\rm\nThe mean-field interaction can be expressed in terms of a\nparticular weighted adjacency matrix $W$ as follows: for any $1\\leq h,\nj\\leq N$ (here we consider only the true ``interacting case'', that is\n$N\\geq 2$)\n\\begin{equation}\\label{def:W_crimaldi}\nw_{h,j}\\ =\\ \\frac{\\alpha}{N}\\ +\\ \\delta_{h,j}(1-\\alpha)\n\\qquad\\mbox{with } \\alpha\\in [0,1],\n\\end{equation}\nwhere $\\delta_{h,j}$ is equal to $1$ when $h=j$ and to $0$\notherwise. Note that $W$ in~\\eqref{def:W_crimaldi} is irreducible for\n$\\alpha>0$ and so we are going to consider this case. Since $W$ is\ndoubly stochastic, we have ${\\mathbf v}_1={\\mathbf\n  u}_1=N^{-1\/2}\\mathbf{1}$.  Thus, for $1\/2<\\gamma<1$, we have\n$$\n\\widetilde{\\sigma}_{\\gamma}^2=\\frac{c^2}{N(2\\gamma-1)}\n\\quad \\hbox{and} \\quad\n\\widehat{\\sigma}_{\\gamma}^2=\\frac{c^2}{N(3-2\\gamma)}.\n$$\nFurthermore, we have $\\lambda_j=1-\\alpha$ for all\n$\\lambda_j\\in Sp(W)\\setminus\\{1\\}$ and, consequently, the conditions\n${\\mathcal Re}(\\lambda^*)<1-(2c)^{-1}$ or ${\\mathcal\n  Re}(\\lambda^*)=1-(2c)^{-1}$ required in the previous results when\n$\\gamma=1$ correspond to the conditions $2c\\alpha>1$ or $2c\\alpha=1$.\nFinally, since $W$ is also symmetric, we have $U=V$ and so\n$U^{\\top}U=V^{\\top}V=I$ and\n$UU^{\\top}=VV^{\\top}=(I-N^{-1}\\mathbf{1}\\mathbf{1}^{\\top})$. Therefore,\nfor the case $\\gamma=1$ and $2c\\alpha>1$, we obtain:\n\\begin{itemize}\n\\item[(i)] $\\widehat{S}_{\\mathbf{ZZ}}=\\frac{c^2}{2c\\alpha-1}I$;\n\\item[(ii)] $[\\widehat{S}_{\\mathbf{NN}}]_{1,1}=(c-1)^2$ and\n  $[\\widehat{S}_{\\mathbf{NN}}]_{j,j}=\\frac{1+2(c-1)\\alpha^{-1}}{2c\\alpha-1}$\n  for $2\\leq j\\leq N$, while $[\\widehat{S}_{\\mathbf{NN}}]_{h,j}=0$ for any\n  $h\\neq j$, $1\\leq h,j\\leq N$;\n\\item[(iii)]\n  $[\\widehat{S}_{\\mathbf{ZN}}]_{j,j}=\\frac{c+(c-1)\\alpha^{-1}}{2c\\alpha-1}$\n  for $2\\leq j\\leq N$, while $[\\widehat{S}_{\\mathbf{ZN}}]_{h,j}=0$ for any\n  $h\\neq j$, $2\\leq h\\leq N$ and $1\\leq j\\leq N$.\n\\end{itemize}\nFinally, when $\\gamma=1$ and $2c\\alpha=1$, we get:\n\\begin{itemize}\n\\item[(i)] $\\widehat{S}^{*}_{\\mathbf{ZZ}}=c^2I$;\n\\item[(ii)] $\\widehat{S}^{*}_{\\mathbf{NN}}=\\frac{(1-\\alpha)^2}{\\alpha^2} I$;\n\\item[(iii)] $\\widehat{S}^{*}_{\\mathbf{ZN}}=\\frac{c(1-\\alpha)}{\\alpha} I$. \\qed\n\\end{itemize}\n\\end{example}\n\n\\subsection{Some comments on statistical applications}\n\\label{section_statistics}\n\nThe first statistical tool that can be derived from the previous\nconvergence results is the construction of asymptotic confidence\nintervals for the limit random variable $Z_{\\infty}$.  This issue has\nbeen already considered in~\\cite{ale-cri-ghi}, where from the central\nlimit theorem for\n$\\widetilde{Z}_{n}:=N^{-1\/2}\\,\\mathbf{v}_1^{\\top}\\,\\mathbf{Z}_{n}$\n(recalled here in the following\nTheorem~\\ref{thm:asymptotics_Z_tilde}), a confidence interval with\napproximate level $(1-\\theta)$ is obtained for any $1\/2<\\gamma\\leq 1$\nas:\n\\begin{equation}\\label{eq:confidence_interval_Z_inf_based_Z}\nCI_{1-\\theta}(Z_{\\infty})\\ =\\\n\\widetilde{Z}_{n}\\ \\pm\\ \\frac{z_{\\theta}}{n^{\\gamma-1\/2}}\n\\sqrt{\\widetilde{Z}_n(1-\\widetilde{Z}_n)\\widetilde{\\sigma}_{\\gamma}^2},\n\\end{equation}\nwhere $\\widetilde{\\sigma}_{\\gamma}^2$ is defined as\nin~\\eqref{def:Sigmatilde_gamma} (also for $\\gamma=1$) and $z_\\theta$\nis such that ${\\mathcal N}(0,1)(z_\\theta,+\\infty)=\\theta\/2$. We note\nthat the construction of the above interval requires to know the\nfollowing quantities:\n\\begin{itemize}\n\\item[(i)] $N$: the number of vertices in the network;\n\\item[(ii)] $\\mathbf{v}_1$: the right eigenvector of $W$ associated to\n  $\\lambda_1=1$ (note that it is not required to know the whole weighted\n  adjacency matrix $W$, e.g.  we have\n  $\\mathbf{v}_1=\\mathbf{u}_1=N^{-1\/2}\\mathbf{1}$ for any doubly\n  stochastic matrix);\n\\item[(iii)] $\\gamma$ and $c$: the parameters that describe the\n  first-order asymptotic approximation of the sequence $(r_n)_n$\n(see Assumption \\ref{ass:r_n}).\n\\end{itemize}\nIn addition, the asymptotic confidence interval\nin~\\eqref{eq:confidence_interval_Z_inf_based_Z} requires the\nobservation of $\\widetilde{Z}_{n}$, and so of $Z_{n,j}$ for any $j\\in V$.\nHowever, this requirement may not be feasible in practical\napplications since the initial random variables $Z_{0,j}$ and the\nexact expression of the sequence $(r_n)_n$ are typically unknown.\nFor instance, if at each vertex $j\\in V$ we have a standard P\\`olya's\nurn with initial composition given by the pair $(a,b)$, then we have\n$Z_{0,j}=a\/(a+b)$ and $r_n=(a+b+n+1)^{-1}$ and hence, when the initial\ncomposition is unknown, we have neither $Z_{0,j}$ nor the exact\nvalue of $r_n$, but we can get $\\gamma=c=1$. To face this problem,\nhere we propose asymptotic confidence intervals for $Z_\\infty$ that do\nnot require the observation of $Z_{n,j}$, but are based on the\nempirical means $N_{n,j}=\\sum_{k=1}^{n}X_{k,j}\/n$, where the random\nvariables $X_{k,j}$ are typically observable. To this aim, we consider\nthe convergence results presented in\nSection~\\ref{section_asymptotic_results} on the asymptotic behavior of\n$\\mathbf{N}_n$.  \\\\\n\n\\indent We first focus on the case $1\/2<\\gamma<1$ and we construct an\nasymptotic confidence interval for $Z_{\\infty}$ based on the empirical\nmeans $N_{n,j}$, with $j\\in V$, and the quantities in\n(i)-(ii)-(iii). Indeed, setting\n$\\widetilde{N}_n:=N^{-1\/2}\\mathbf{v}_1^{\\top}\\mathbf{N}_n$ and using\nthe relation\n$\\mathbf{v}_1^{\\top}\\mathbf{u}_1=N^{-1\/2}\\mathbf{v}_1^{\\top}\\mathbf{1}=1$\n(see~\\eqref{eq:relazioni-1}),\nfrom Theorem~\\ref{thm:asymptotics_theta_gamma} we obtain that\n$$\nn^{\\gamma-1\/2}(\\widetilde{N}_n-Z_{\\infty}){\\longrightarrow}\\\n\\mathcal{N}\\left(\\ 0\\ ,\\\nZ_{\\infty}(1-Z_{\\infty})(\\widetilde{\\sigma}_{\\gamma}^2+\\widehat{\\sigma}_{\\gamma}^2)\\\n\\right)\\ \\ \\ \\ \\ \\ \\ \\hbox{stably},\n$$\nwhere $\\widetilde{\\sigma}_{\\gamma}^2$ and $\\widehat{\\sigma}_{\\gamma}^2$\nare defined in~\\eqref{def:Sigmatilde_gamma}\nand~\\eqref{def:Sigmahat_NN_gamma}, respectively.\nThen, for $1\/2<\\gamma<1$, we have the following confidence interval\nwith approximate level $(1-\\theta)$:\n\\begin{equation*}\nCI_{1-\\theta}(Z_{\\infty})\\ =\\\n\\widetilde{N}_n\\ \\pm\\ \\frac{z_{\\theta}}{n^{\\gamma-1\/2}}\n\\sqrt{\\widetilde{N}_n(1-\\widetilde{N}_n)\n(\\widetilde{\\sigma}_{\\gamma}^2+\\widehat{\\sigma}_{\\gamma}^2)}.\n\\end{equation*}\n\n\\indent Analogously, for $\\gamma=1$ and $N=1$, from Theorem\n\\ref{thm:N_1_gamma_1} we get\n\\begin{equation*}\nCI_{1-\\theta}(Z_{\\infty})\\ =\\\nN_n\\ \\pm\\ \\frac{z_{\\theta}}{\\sqrt{n}}\n\\sqrt{N_n(1-N_n)\n(c^2+(c-1)^2)}.\n\\end{equation*}\n\n\\indent When $\\gamma=1$ and $N\\geq 2$, we have to distinguish two\ncases according to the value of ${\\mathcal Re}(\\lambda^*)$. Thus, in this\ncase, the construction of suitable asymptotic confidence intervals for\n$Z_\\infty$ requires also the knowledge of ${\\mathcal Re}(\\lambda^*)$.\nSpecifically, when ${\\mathcal Re}(\\lambda^*)<1-(2c)^{-1}$, from\nTheorem~\\ref{thm:asymptotics_theta_1}, using the relations\n$\\mathbf{v}_1^{\\top}\\mathbf{u}_1=1$ and\n$\\mathbf{v}_1^{\\top}U=\\mathbf{0}$ (see~\\eqref{eq:relazioni-0}), we\nobtain that\n$$\n\\sqrt{n}(\\widetilde{N}_n-Z_{\\infty}){\\longrightarrow}\\\n\\mathcal{N}\\left(\\ 0\\ ,\\ Z_{\\infty}(1-Z_{\\infty})\n(\\widetilde{\\sigma}_{1}^2+N^{-1}[\\widehat{S}_{\\mathbf{NN}}]_{1,1})\\\n\\right)\\ \\ \\ \\ \\ \\ \\ \\hbox{stably},\n$$\nwhere $\\widetilde{\\sigma}_{1}^2=c^2\\|\\mathbf{v}_1\\|^2\/N$ and\n$[\\widehat{S}_{\\mathbf{NN}}]_{1,1}=(c-1)^2\\|\\mathbf{v}_1\\|^2$.  Hence,\nin this case we find:\n\\begin{equation*}\nCI_{1-\\theta}(Z_{\\infty})\\ =\\\n\\widetilde{N}_n\\ \\pm\\ \\frac{z_{\\theta}}{\\sqrt{n}}\n\\!\\sqrt{\\widetilde{N}_n(1-\\widetilde{N}_n)\n\\!\\left(\\textstyle{\\frac{(c^2+(c-1)^2)\\|\\mathbf{v}_1\\|^2}{N}}\\right)}.\n\\end{equation*}\nNote that analogous asymptotic confidence intervals for $Z_{\\infty}$\ncan be constructed replacing $\\widetilde{N}_n$ by another real\nstochastic processes $(\\mathbf{a}^{\\top}\\mathbf{N}_n)_n$, where\n$\\mathbf{a}\\in\\mathbb{R}^N$ and\n$\\mathbf{a}^{\\top}\\mathbf{1}=1$.  \\\\ \\indent Finally, when ${\\mathcal\n  Re}(\\lambda^*)=1-(2c)^{-1}$, we can not use $\\widetilde{N}_n$ since,\nby Theorem \\ref{thm:asymptotics_Z_1_star} and the fact that\n$\\mathbf{v}_1^{\\top}U=\\mathbf{0}$, we have\n$\\sqrt{n\/\\ln(n)}(\\widetilde{N}_n-Z_{\\infty})\\to 0$ in probability.\nTherefore, in this case we need to replace the vector $\\mathbf{v}_1$\nby another vector $\\mathbf{a}\\in\\mathbb{R}^N$ with\n$\\mathbf{a}^{\\top}\\mathbf{1}=1$ and $\\mathbf{a}^{\\top}U\\neq\n\\mathbf{0}$.\n\n\\begin{example}\\rm\nIn the case of a system with $N\\geq 2$ and mean-field interaction (see\nExample~\\ref{ex:mean_field}), we get the following asymptotic\nconfidence intervals for $Z_{\\infty}$ with approximate level\n$(1-\\theta)$:\n\\begin{itemize}\n\\item[(i)] when $1\/2<\\gamma<1$, setting\n  $\\widetilde{N}_n=N^{-1}\\mathbf{1}^{\\top}\\mathbf{N}_n$, we have\n\\begin{equation*}\nCI_{1-\\theta}(Z_{\\infty})\\ =\\\n\\widetilde{N}_n\\ \\pm\\ \\frac{z_{\\theta}}{n^{\\gamma-1\/2}}\n\\sqrt{\\widetilde{N}_n(1-\\widetilde{N}_n)\\frac{2c^2}{N(2\\gamma-1)(3-2\\gamma)}};\n\\end{equation*}\n\\item[(ii)] when $\\gamma=1$ and $2c\\alpha>1$, setting\n  $\\widetilde{N}_n=N^{-1}\\mathbf{1}^{\\top}\\mathbf{N}_n$, we have\n\\begin{equation*}\nCI_{1-\\theta}(Z_{\\infty})\\ =\\\n\\widetilde{N}_n \\pm\\ \\frac{z_{\\theta}}{\\sqrt{n}}\n\\sqrt{\\widetilde{N}_n(1-\\widetilde{N}_n)\\frac{c^2+(c-1)^2}{N}};\n\\end{equation*}\n\\item[(iii)] when $\\gamma=1$ and $2c\\alpha=1$, setting\n  $\\widetilde{N}^a_n:=\\mathbf{a}^{\\top}\\mathbf{N}_n$ with\n  $\\mathbf{a}^{\\top}\\mathbf{1}=1$ and\n  $\\mathbf{a}\\neq N^{-1}\\mathbf{1}$, we have\n\\begin{equation*}\nCI_{1-\\theta}(Z_{\\infty})\\ =\\\n\\widetilde{N}^a_n \\pm\\ z_{\\theta} \\sqrt{ \\frac{\\ln(n)}{n} }\n\\sqrt{\\widetilde{N}^a_n(1-\\widetilde{N}^a_n)}\n\\frac{(1-\\alpha)}{\\alpha}\\|\\mathbf{a}-N^{-1}\\mathbf{1}\\|,\n\\end{equation*}\nwhere the last term follows by recalling that\n$UU^{\\top}=I-N^{-1}\\mathbf{1}\\mathbf{1}^{\\top}$ and\nnoticing that\n$$\n\\mathbf{a}^{\\top}UU^{\\top}\\mathbf{a}=\n\\mathbf{a}^{\\top}(I-N^{-1}\\mathbf{1}\\mathbf{1}^{\\top})\\mathbf{a}\n=\\|\\mathbf{a}\\|^2-N^{-1}=\\|\\mathbf{a}-N^{-1}\\mathbf{1}\\|^2\n$$\n(where for the last two equalities we used that\n$\\mathbf{a}^{\\top}\\mathbf{1}=1$).\n\\end{itemize}\n\\qed\n\\end{example}\n\n\n\\indent Another possible statistical application of the convergence\nresults of Section~\\ref{section_asymptotic_results} concerns the\ninference on the weighted adjacency matrix $W$ based on the empirical\nmeans $N_{n,j}$, with $j\\in V$, instead of the random variables\n$Z_{n,j}$ as done in~\\cite{ale-cri-ghi}.  Let us assume $N\\geq 2$ (the\nproper ``interacting'' case).  We propose to construct testing\nprocedures based on the multi-dimensional real stochastic process\n$(UV^{\\top}\\mathbf{N}_n)_n$. Indeed, we note that it converges to\n$\\mathbf{0}$ almost surely because\n$\\mathbf{N}_n\\stackrel{a.s.}{\\longrightarrow}Z_{\\infty}\\mathbf{1}$ and\n$V^{\\top}\\mathbf{1}=\\mathbf{0}$ (since~\\eqref{eq:relazioni-0} and\n\\eqref{eq:relazioni-1}). Moreover, when $\\gamma=1$ and ${\\mathcal\n  Re}(\\lambda^*)<1-(2c)^{-1}$, from\nTheorem~\\ref{thm:asymptotics_theta_1} we get that\n$$\n\\sqrt{n}UV^{\\top}\\mathbf{N}_n{\\longrightarrow}\\\n\\mathcal{N} \\left(\\ \\mathbf{0}\\ ,\\\nZ_{\\infty}(1-Z_{\\infty})U[\\widehat{S}_{\\mathbf{NN}}]_{(-1)}U^{\\top}\\ \\right)\n\\ \\ \\ \\ \\ \\ \\\n\\hbox{stably},\n$$\nwhere $[\\widehat{S}_{\\mathbf{NN}}]_{(-1)}$ denotes the square sub-matrix\nobtained from $\\widehat{S}_{\\mathbf{NN}}$ removing its first row and its\nfirst column.\\\\\nAnalogously, when $\\gamma=1$ and\n${\\mathcal Re}(\\lambda^*)=1-(2c)^{-1}$, from\nTheorem~\\ref{thm:asymptotics_Z_1_star} we get that\n$$\n\\sqrt{\\frac{n}{\\ln(n)}} UV^{\\top}\\mathbf{N}_n{\\longrightarrow}\\\n\\mathcal{N} \\left(\\ \\mathbf{0}\\ ,\\\nZ_{\\infty}(1-Z_{\\infty})\\widehat{\\Sigma}^{*}_{\\mathbf{NN}}\\ \\right)\n\\ \\ \\ \\ \\ \\ \\\n\\hbox{stably}.\n$$\nRemember that the case $\\gamma=1$ includes, for instance, systems\nof interacting P\\'olya's urns.\n\n\\begin{example}\\rm\nIn the case of $N\\geq 2$ and mean-field interaction (see\nExample~\\ref{ex:mean_field}), recalling that $U=V$,\n$UU^{\\top}=(I-N^{-1}\\mathbf{1}\\mathbf{1}^{\\top})$,\n$[\\widehat{S}_{\\mathbf{NN}}]_{(-1)}=\\frac{1+2(c-1)\\alpha^{-1}}{2c\\alpha-1}I$\nand\n$\\widehat{\\Sigma}^{*}_{\\mathbf{NN}}=\\frac{(1-\\alpha)^2}{\\alpha^2}UU^{\\top}$,\nwe obtain that:\n\\begin{itemize}\n\\item[(i)] when $\\gamma=1$ and $2c\\alpha>1$,\n$$\n\\sqrt{n}(I-N^{-1}\\mathbf{1}\\mathbf{1}^{\\top})\\mathbf{N}_n{\\longrightarrow}\\\n\\mathcal{N} \\left(\\ \\mathbf{0}\\ ,\\\nZ_{\\infty}(1-Z_{\\infty})\n\\frac{1+2(c-1)\\alpha^{-1}}{2c\\alpha-1}\n(I-N^{-1}\\mathbf{1}\\mathbf{1}^{\\top})\\\n\\right)\\ \\ \\ \\ \\ \\ \\\n\\hbox{stably};\n$$\n\\item[(ii)] when $\\gamma=1$ and $2c\\alpha=1$,\n$$\n\\sqrt{\\frac{n}{\\ln(n)}}(I-N^{-1}\\mathbf{1}\\mathbf{1}^{\\top})\n\\mathbf{N}_n{\\longrightarrow}\\\n\\mathcal{N} \\left(\\ \\mathbf{0}\\ ,\\\nZ_{\\infty}(1-Z_{\\infty})\n\\frac{(1-\\alpha)^2}{\\alpha^2}\n(I-N^{-1}\\mathbf{1}\\mathbf{1}^{\\top})\\ \\right)\n\\ \\ \\ \\ \\ \\ \\\n\\hbox{stably}.\n$$\n\\end{itemize}\nIn this framework, it may be of interest to test whether the unknown\nparameter $\\alpha$ can be assumed to be equal to a specific value\n$\\alpha_0\\in (0,1]$, i.e. we may be interested in a statistical test\n  of the type:\n$$\nH_0:\\, W=W_{\\alpha_0}\\qquad\\mbox{ vs} \\qquad\nH_1:\\, W=W_{\\alpha}\\ \\mbox{for some }\\alpha\\in (0,1]\\setminus\\{\\alpha_0\\}.\n$$\nTo this purpose, assuming $2c\\alpha_0\\geq 1$ and setting\n$\\widetilde{N}_n:=N^{-1}\\mathbf{1}^{\\top}\\mathbf{N}_n$, we note that:\n\\begin{itemize}\n\\item[(i)] for $\\gamma=1$ and $2c\\alpha_0>1$, under $H_0$ we have that\n$$n\\left[\\widetilde{N}_n(1-\\widetilde{N}_n)\\right]^{-1}\n\\frac{2c\\alpha_0-1}{1+2(c-1)\\alpha_0^{-1}}\\,\n\\mathbf{N}_n^{\\top}(I-N^{-1}\\mathbf{1}\\mathbf{1}^{\\top})\\mathbf{N}_n\n\\stackrel{d}\\sim\\chi^2_{N-1};\n$$\n\\item[(ii)] for $\\gamma=1$ and $2c\\alpha_0=1$, under $H_0$ we have that\n  $$\\frac{n}{\\ln(n)}\\left[\\widetilde{N}_n(1-\\widetilde{N}_n)\\right]^{-1}\n  \\frac{\\alpha_0^2}{(1-\\alpha_0)^2}\\,\n\\mathbf{N}_n^{\\top}(I-N^{-1}\\mathbf{1}\\mathbf{1}^{\\top})\\mathbf{N}_n\n\\stackrel{d}\\sim\\chi^2_{N-1}.$$\n\\end{itemize}\nConcerning the distribution of the above quantities for $\\alpha\\neq \\alpha_0$,\nsince the eigenvectors of $W$ do not depend on $\\alpha$, we have that,\nfor any fixed $\\alpha\\in (0,1]\\setminus\\{\\alpha_0\\}$, under the hypothesis\n  $\\{W=W_{\\alpha}\\}\\subset H_1$, we have that:\n\\begin{itemize}\n\\item[(i)] for $\\gamma=1$, $2c\\alpha_0>1$ and\nfor any $\\alpha\\neq\\alpha_0$ such that $2c\\alpha>1$,\n$$\\frac{n}{\\widetilde{N}_n(1-\\widetilde{N}_n)}\n\\frac{2c\\alpha_0-1}{1+2(c-1)\\alpha_0^{-1}}\n\\mathbf{N}_n^{\\top}(I-N^{-1}\\mathbf{1}\\mathbf{1}^{\\top})\\mathbf{N}_n\n\\stackrel{d}\\sim\n\\left(\\frac{2c\\alpha_0-1}{2c\\alpha-1}\\right)\n\\left(\\frac{1+2(c-1)\\alpha^{-1}}{1+2(c-1)\\alpha_0^{-1}}\\right)\\chi^2_{N-1};$$\nwhile, if $2c\\alpha=1$, the above quantity\nconverges in probability to infinity;\n\\item[(ii)] for $\\gamma=1$, $2c\\alpha_0=1$ and for any $\\alpha$ such that\n$2c\\alpha>1$ (which obviously implies $\\alpha\\neq\\alpha_0$), we have\n$$\\frac{n}{\\ln(n)}\\left[\\widetilde{N}_n(1-\\widetilde{N}_n)\\right]^{-1}\n  \\frac{\\alpha_0^2}{(1-\\alpha_0)^2}\\,\n\\mathbf{N}_n^{\\top}(I-N^{-1}\\mathbf{1}\\mathbf{1}^{\\top})\\mathbf{N}_n\n\\stackrel{P}{\\longrightarrow}0.$$\n\\end{itemize}\n\\qed\n\\end{example}\n\nThe case $1\/2<\\gamma<1$ requires further future investigation. Indeed,\nsince $V^{\\top}\\mathbf{1}=\\mathbf{0}$ (by~\\eqref{eq:relazioni-0} and\n\\eqref{eq:relazioni-1}), from\nTheorem~\\ref{thm:asymptotics_theta_gamma} we obtain that\n$n^{\\gamma-\\frac{1}{2}} UV^{\\top}\\mathbf{N}_n\\to \\mathbf{0}$ in\nprobability.  Then, a central limit theorem for\n$UV^{\\top}\\mathbf{N}_n$ with the exact convergence rate (if exists) is\nneedful. In this paper, as we will see more ahead in\nRemark~\\ref{rem:O_gamma_2}, by the computations done in the proofs of\nSection~\\ref{section_proofs} we can only affirm that $n^{e}\nUV^{\\top}\\mathbf{N}_n\\to \\mathbf{0}$ in probability for all\n$e<\\gamma\/2$ and, when $e=\\gamma\/2$, the random vector $n^{e}\nUV^{\\top}\\mathbf{N}_n$ is the sum of a term converging to zero in\nprobability and a term bounded in $L^1$.  Therefore, further analysis\non the asymptotic behavior of $n^{\\gamma\/2}UV^{\\top}\\mathbf{N}_n$\nresults to be interesting for future developments.\n\n\\section{Proofs}\\label{section_proofs}\n\nThis section contains all the proofs of the results presented in the\nprevious Section~\\ref{section_asymptotic_results}.\n\n\\subsection{Preliminary relations and results}\n\nWe start by recalling that, given the eigen-structure of $W$ described\nin Section~\\ref{section_model}, the matrix ${\\mathbf\n  u}_1{\\mathbf v}_1^{\\top}$ has real elements and\nthe following relations hold:\n\\begin{equation}\\label{eq:relazioni-2}\nV^{\\top}\\,\\mathbf{u}_1=U^{\\top}\\,\\mathbf{v}_1=\\mathbf{0},\\quad\nV^{\\top}\\,U=U^{\\top}\\,V=I\\quad\\mbox{and}\\quad\nI={\\mathbf u}_1{\\mathbf v}_1^{\\top} + UV^{\\top},\n\\end{equation}\nwhich implies that the matrix $UV^{\\top}$ has real elements. Moreover,\nusing the matrix $D$ defined in Section~\\ref{section_model}, we can\ndecompose the matrix $W^{\\top}$ as follows:\n\\begin{equation}\\label{eq:decomposition-matrix}\nW^{\\top}\\ =\\ {\\mathbf u}_1{\\mathbf v}_1^{\\top}\\ +\\ UDV^{\\top}.\n\\end{equation}\n\n\\indent Now, in order to understand the asymptotic behavior of the\nstochastic processes $(\\mathbf{Z}_{n})_n$ and $(\\mathbf{N}_{n})_n$,\nlet us express the dynamics~\\eqref{eq:dynamic} as follows:\n\\begin{equation}\\label{eq:dynamic_SA}\n\\left\\{\\begin{aligned}\n&\\mathbf{Z}_{n+1}-\\mathbf{Z}_{n}\\ =\\ -r_n\\left(I-W^{\\top}\\right)\\mathbf{Z}_{n}\\\n+\\ r_n\\Delta\\mathbf{M}_{n+1},\\\\\n&\\mathbf{N}_{n+1}-\\mathbf{N}_{n}\\ =\\\n-\\frac{1}{n+1}\\left(\\mathbf{N}_{n}-W^{\\top}\\mathbf{Z}_{n}\\right)\\\n+\\ \\frac{1}{n+1}\\Delta\\mathbf{M}_{n+1},\n\\end{aligned}\\right.\n\\end{equation}\nwhere\n$\\Delta\\mathbf{M}_{n+1}=(\\mathbf{X}_{n+1}-W^{\\top}\\mathbf{Z}_{n})$ is\na martingale increment with respect to the filtration~${\\mathcal\n  F}:=({\\mathcal F}_{n})_n$. Furthermore, we decompose the stochastic\nprocess $(\\mathbf{Z}_{n})_n$ as\n\\begin{equation}\\label{eq:decomposition_Z}\n\\mathbf{Z}_{n}=\\widetilde{Z}_n\\mathbf{1} + \\widehat{\\mathbf{Z}}_{n}\n=\\sqrt{N}\\widetilde{Z}_n \\mathbf{u}_1 + \\widehat{\\mathbf{Z}}_{n},\n\\;\\mbox{where}\\;\n\\left\\{\n\\begin{aligned}\n&\\widetilde{Z}_{n}:=N^{-1\/2}\\,\\mathbf{v}_1^{\\top}\\,\\mathbf{Z}_{n}, \\\\\n&\\widehat{\\mathbf{Z}}_{n}:={\\mathbf Z}_n-{\\mathbf 1}{\\widetilde Z}_n\n=(I-\\mathbf{u}_1\\mathbf{v}_1^{\\top})\\mathbf{Z}_n\n=U\\,V^{\\top}\\,\\mathbf{Z}_{n};\n\\end{aligned}\n\\right.\n\\end{equation}\nwhile we decompose the stochastic process $(\\mathbf{N}_{n})_n$ as\n\\begin{equation}\\label{eq:decomposition_N}\n\\mathbf{N}_{n}=\\widetilde{Z}_n\\mathbf{1} + \\widehat{\\mathbf{N}}_{n}\n=\\sqrt{N}\\widetilde{Z}_n \\mathbf{u}_1 + \\widehat{\\mathbf{N}}_{n},\n\\qquad\\mbox{where}\\qquad\n\\widehat{\\mathbf{N}}_{n}:={\\mathbf N}_n-{\\widetilde Z}_n{\\mathbf 1}.\n\\end{equation}\nThen, the asymptotic behavior of the joint stochastic process\n$(\\mathbf{Z}_{n},\\mathbf{N}_{n})_n$ is obtained by establishing the asymptotic\nbehavior of $(\\widetilde{Z}_{n})_n$ and of\n$(\\widehat{\\mathbf{Z}}_{n},\\widehat{\\mathbf{N}}_{n})_n$.\n\n\\begin{rem\n\\rm In the particular case when $W$ is doubly stochastic, we have\n$\\mathbf{v}_1=\\mathbf{u}_1=N^{-1\/2}\\mathbf{1}$.\nAs a consequence, we have\n\\begin{equation*\n\\widetilde{Z}_{n}=N^{-1}\\mathbf{1}^{\\top}\\mathbf{Z}_{n}\n=N^{-1}\\sum_{j=1}^N Z_{n,j},\n\\end{equation*}\nwhich represents the average of the stochastic processes $Z_{n,j}$,\nwith $j\\in V$, in the network, and\n$$\n\\widehat{\\mathbf{Z}}_{n}=\n\\left(I-N^{-1}\\mathbf{1}\\mathbf{1}^{\\top}\\right)\\mathbf{Z}_n\n\\quad\\hbox{and}\\quad\n\\widehat{\\mathbf{N}}_n=\\mathbf{N}_n-N^{-1}\\mathbf{1}\\mathbf{1}^{\\top}\\mathbf{Z}_n.\n$$ Notice that the assumed normalization\n$W^{\\top}\\mathbf{1}=\\mathbf{1}$ implies that symmetric matrices $W$\nare also doubly stochastic. Therefore, the above equalities hold for\nany undirected graph for which $W$ is symmetric by definition.\n\\end{rem}\n\nConcerning the real-valued stochastic process $(\\widetilde{Z}_{n})_n$,\nfrom~\\cite[Section 4.2]{ale-cri-ghi} we have that it is an $\\mathcal F$-martingale\nwith values in $[0,1]$ and its dynamics can be expressed as follows:\n\\begin{equation}\\label{eq:dynamic_SA_tilde}\n\\widetilde{Z}_{n+1}-\\widetilde{Z}_{n}\\ =\\\nN^{-1\/2} r_n\\left(\\mathbf{v}_1^{\\top}\\Delta\\mathbf{M}_{n+1}\\right).\n\\end{equation}\nIn particular, we have that ${\\widetilde\n  Z}_n\\stackrel{a.s.}\\longrightarrow Z_{\\infty}$ and\nin~\\cite{ale-cri-ghi} the following central limit theorem for\n$(\\widetilde{Z}_{n})_n$ is esta\\-bli\\-shed:\n\n\\begin{theo}\\cite[Theorem 4.2]{ale-cri-ghi}\\label{thm:asymptotics_Z_tilde}\nFor $N\\geq 1$ and $1\/2<\\gamma\\leq 1$, we have\n\\begin{equation*\nn^{\\gamma-\\frac{1}{2}}\n\\left(\\widetilde{Z}_{n}-Z_{\\infty}\\right)\\\n{\\longrightarrow}\\\n\\mathcal{N}\n\\left(\\ 0\\ ,\\ \\widetilde{\\sigma}_{\\gamma}^2\\,Z_{\\infty}(1-Z_{\\infty})\\ \\right)\\\n\\ \\ \\ stably,\n\\end{equation*}\nwhere $\\widetilde{\\sigma}_{\\gamma}^2$ is defined as\nin~\\eqref{def:Sigmatilde_gamma} (also for $\\gamma=1$).  The above\nconvergence is also in the sense of the almost sure conditional\nconvergence w.r.t.~${\\mathcal F}$.\n\\end{theo}\n\nConcerning the multi-dimensional real stochastic process\n$(\\widehat{\\mathbf{Z}}_n)_n$, we\nfirstly recall the relation\n\\begin{equation}\\label{rel-tecnica-i}\nW^{\\top}\\widehat{\\mathbf{Z}}_{n}\\ =\\ UDV^{\\top}\\widehat{\\mathbf{Z}}_{n},\n\\end{equation}\nwhich is due to \\eqref{eq:relazioni-2} and\n\\eqref{eq:decomposition-matrix}, and, moreover, we recall that\nfrom~\\cite[Section 4.2]{ale-cri-ghi} we have the dynamics\n\\begin{equation}\\label{eq:dynamic_SA_hat}\n\\widehat{\\mathbf{Z}}_{n+1}-\\widehat{\\mathbf{Z}}_{n}=\n-r_nU(I-D)V^{\\top}\\widehat{\\mathbf{Z}}_{n} + r_n UV^{\\top}\\,\\Delta\\mathbf{M}_{n+1}\n\\end{equation}\nand $\\widehat{\\mathbf{Z}}_n\\stackrel{a.s.}\\longrightarrow \\mathbf{0}$.\n\\\\\n\n\\indent Finally, concerning the multi-dimensional real stochastic process\n$(\\widehat{\\mathbf{N}}_n)_n$, using~\\eqref{eq:dynamic_SA},\n\\eqref{eq:decomposition_Z}, \\eqref{eq:decomposition_N} and the\nassumption $W^{\\top}\\mathbf{1}=\\mathbf{1}$ (which implies\n$W^{\\top}\\mathbf{Z}_n=\\widetilde{Z}_n\\mathbf{1}+W^{\\top}\\widehat{\\mathbf{Z}}_n$),\nwe obtain the dynamics:\n\\begin{equation}\\label{eq:dynamic_SA_N_hat}\n\\widehat{\\mathbf{N}}_{n+1}-\\widehat{\\mathbf{N}}_{n}=\n-\\frac{1}{n+1}(\\widehat{\\mathbf{N}}_{n}-W^{\\top}\\widehat{\\mathbf{Z}}_{n}) +\n\\frac{1}{n+1}\n\\Delta\\mathbf{M}_{n+1}-(\\widetilde{Z}_{n+1}-\\widetilde{Z}_n)\\mathbf{1}.\n\\end{equation}\n\n\n\\subsection{Proof of Theorem \\ref{th:sincro}\n(Almost sure synchronization of the empirical means)}\n\nWe recall that in \\cite[Theorem 3.1]{ale-cri-ghi}, by\ndecomposition~\\eqref{eq:decomposition_Z}, i.e. $\\mathbf{Z}_{n}\n=\\widetilde{Z}_n\\mathbf{1}+\\widehat{\\mathbf{Z}}_{n}$, and combining\n${\\widetilde Z}_n\\stackrel{a.s.}\\longrightarrow Z_{\\infty}$ and\n$\\widehat{\\mathbf{Z}}_n\\stackrel{a.s.}\\longrightarrow \\mathbf{0}$,\nit is proved that\n$\\mathbf{Z}_{n}\\stackrel{a.s.}\\longrightarrow Z_{\\infty}\\mathbf{1}$.\nAs a consequence, using\n$W^{\\top}\\mathbf{1}=\\mathbf{1}$ and~\\eqref{eq:dynamic-0}, we obtain\n$E[\\mathbf{X}_{n}|{\\mathcal F}_{n-1}]\\stackrel{a.s.}\\longrightarrow\nZ_{\\infty}\\mathbf{1}$ and, applying Lemma~\\ref{lemma-serie-rv} (with\n$c_k=k$, $v_{n,k}=k\/n$ and $\\eta=1$), we get that $\\mathbf{N}_n\n\\stackrel{a.s.}\\longrightarrow\\ Z_{\\infty}\\mathbf{1}$.  This concludes\nthe proof of the first part of the theorem, concerning the\nsynchronization result.  For the second part, that is the results on\nthe limit random variable $Z_\\infty$, we refer to\n\\cite[Theorem 3.5 and Theorem 3.6]{ale-cri-ghi}. \\qed \\\\\n\n\\indent Note that, by the synchronization result for $(Z_n)$, we can state that\n\\begin{equation}\\label{eq:multidim-limite-conditional-M}\nE[(\\Delta{\\mathbf M}_{n+1})(\\Delta{\\mathbf M}_{n+1})^{\\top}\n\\,|\\,{\\mathcal F}_n]\n\\stackrel{a.s.}\\longrightarrow Z_{\\infty}(1-Z_{\\infty})I.\n\\end{equation}\nIndeed, since $\\{X_{n+1,j}:\\, j=1,\\dots, N\\}$ are conditionally independent\ngiven $\\mathcal{F}_n$, we have\n\\begin{equation}\\label{eq:covar-conditional-M}\nE[\\Delta{M}_{n+1,h}\\Delta{M}_{n+1,j}\\,|\\,{\\mathcal F}_n]=0\\quad\n\\mbox{ for } h\\neq j;\n\\end{equation}\nwhile, for each $j$, using the normalization $W^{\\top}{\\mathbf\n  1}={\\mathbf 1}$, we have\n\\begin{equation}\\label{eq:var-conditional-M}\nE[(\\Delta{M}_{n+1,j})^2\\,|\\,{\\mathcal F}_n]=\n\\left(\\sum_{h=1}^N w_{h,j}Z_{n,h}\\right)\n\\left(1-\\sum_{h=1}^N w_{h,j}Z_{n,h}\\right)\n\\stackrel{a.s.}\\longrightarrow Z_{\\infty}(1-Z_{\\infty}).\n\\end{equation}\n\n\\subsection{Proof of Theorem \\ref{thm:asymptotics_theta_gamma}\n(CLT for $({\\mathbf Z}_n,{\\mathbf N}_n)_n$ in the case $1\/2<\\gamma<1$)}\n\nIn order to prove Theorem \\ref{thm:asymptotics_theta_gamma}, we need\nto provide the asymptotic behavior of the stochastic processes\n$(\\widehat{\\mathbf{Z}}_{n})_n$ and\n$(\\widehat{\\mathbf{N}}_{n})_n$. First of all, we recall that\n$\\widehat{\\mathbf{Z}}_{n}=0$ for each $n$ when $N=1$ and, for $N\\geq\n2$ and $1\/2<\\gamma<1$, we have from \\cite[Theorem 4.3]{ale-cri-ghi} that\n\\begin{equation}\\label{eq:CLT_Z_hat_gamma}\nn^{\\frac{\\gamma}{2}}\\,\\widehat{\\mathbf{Z}}_{n}\\longrightarrow\\\n\\mathcal{N}\\left( \\mathbf{0} ,\nZ_{\\infty}(1-Z_{\\infty})\\widehat{\\Sigma}_{\\gamma}\\right)\n\\ \\ \\ \\ \\hbox{stably},\n\\end{equation}\nwhere\n\\begin{equation*\n\\widehat{\\Sigma}_{\\gamma}:=U\\widehat{S}_{\\gamma}U^{\\top}\n\\qquad\\mbox{ and }\\qquad\n[\\widehat{S}_{\\gamma}]_{h,j}:=\n\\frac{c}{2-(\\lambda_h+\\lambda_j)} (\\mathbf{v}_{h}^{\\top}\\mathbf{v}_{j})\\\n\\mbox{ with }\\ 2\\leq h,j\\leq N.\n\\end{equation*}\nMoreover, looking at the proof of \\eqref{eq:CLT_Z_hat_gamma} in\n\\cite{ale-cri-ghi}, it is easy to realize that for $N\\geq 2$ and\n$1\/2<\\gamma<1$ we have $\\lim_n\nn^{\\gamma}E\\left[\\,\\|\\widehat{\\mathbf{Z}}_n\\|^2\\,\\right]=C$, where $C$\nis a suitable constant in $(0,+\\infty)$, and so, recalling that\n$\\widehat{\\mathbf{Z}}_n=0$ for each $n$ when $N=1$, we can affirm\nthat, for every $N\\geq 1$ and $1\/2<\\gamma<1$, we have that\n\\begin{equation}\\label{eq:L2_Z_hat}\nE\\left[\\,\\|\\widehat{\\mathbf{Z}}_n\\|^2\\,\\right]=O( n^{-\\gamma} ).\n\\end{equation}\nRegarding the stochastic process $(\\widehat{\\mathbf{N}}_{n})_n$, we\nare going to prove the following convergence result:\n\n\\begin{theo}\\label{thm:asymptotics_theta_hat_gamma}\nFor $N\\geq 1$ and $1\/2<\\gamma<1$, we have that\n\\begin{equation}\\label{eq:CLT_N_hat_gamma}\nn^{\\gamma -\\frac{1}{2}}\\,\\widehat{\\mathbf{N}}_{n}\\ \\stackrel{d}\\longrightarrow\\\n\\mathcal{N}\\left(\\mathbf{0},\nZ_{\\infty}(1-Z_\\infty)\\widehat{\\Gamma}_{\\gamma}\\right)\n\\ \\ \\ \\ stably,\n\\end{equation}\nwhere $\\widehat{\\Gamma}_{\\gamma}$ is the matrix defined in\n\\eqref{def:Sigmahat_NN_gamma}.\n\\end{theo}\n\\begin{proof}\nWe observe that by means of~\\eqref{eq:dynamic_SA_N_hat}  we can write\n$$n(\\widehat{\\mathbf{N}}_{n}-\\widehat{\\mathbf{N}}_{n-1})=\n-\\widehat{\\mathbf{N}}_{n-1}+W^{\\top}\\widehat{\\mathbf{Z}}_{n-1} +\n\\Delta\\mathbf{M}_{n}+n(\\widetilde{Z}_{n-1}-\\widetilde{Z}_n)\\mathbf{1}.$$\nThen, using the relation\n$$\nn(\\widehat{\\mathbf{N}}_{n}-\\widehat{\\mathbf{N}}_{n-1})+\n\\widehat{\\mathbf{N}}_{n-1}\n\\ =\\ n\\widehat{\\mathbf{N}}_{n}-(n-1)\\widehat{\\mathbf{N}}_{n-1},\n$$\nwe obtain that\n$$n\\widehat{\\mathbf{N}}_{n}=\\sum_{k=1}^n\n\\left[k\\widehat{\\mathbf{N}}_{k}-(k-1)\n  \\widehat{\\mathbf{N}}_{k-1}\\right] =\nW^{\\top}\\sum_{k=1}^n\\widehat{\\mathbf{Z}}_{k-1}\n+\n\\sum_{k=1}^n\\left[\\Delta\\mathbf{M}_{k}+k(\\widetilde{Z}_{k-1}-\\widetilde{Z}_k)\n  \\mathbf{1}\\right].\n$$\nNow, we set $e:=\\gamma-1\/2>0$ for each\n$1\/2<\\gamma<1$ and hence from the above expression we get\n$n^e\\widehat{\\mathbf{N}}_n = t_n\\sum_{k=1}^n {\\mathbf T}_{k}+ W^{\\top}{\\mathbf\n  Q}_{n}$, where $t_n:=1\/n^{(1-e)}$, ${\\mathbf\n  Q}_{n}:=t_n\\sum_{k=1}^n \\widehat{\\mathbf{Z}}_{k-1}$\nand\n$${\\mathbf T}_{k}:=\n\\Delta\\mathbf{M}_k+\nk\\left(\\widetilde{Z}_{k-1}-\\widetilde{Z}_k\\right){\\mathbf 1}\n=\\Delta\\mathbf{M}_k\n-N^{-1\/2}kr_k\\left(\\mathbf{v}_1^{\\top}\\Delta\\mathbf{M}_k\\right)\\mathbf{1}.\n$$\nThe idea of the proof is to study separately the two terms\n$$\nt_n\\sum_{k=1}^n {\\mathbf T}_{k}\\qquad\\mbox{and}\\qquad {\\mathbf Q}_{n}\\,.\n$$\nMore precisely, we are going to prove that the first term converges\nstably to the desired Gaussian kernel, while the second term converges\nin probability to zero.\n\\\\\n\n\\noindent {\\em First step: the convergence result for $t_n\\sum_{k=1}^n {\\mathbf\n    T}_{k}$.}\\\\\n\\noindent We note that $(\\mathbf{T}_{k})_{1\\leq k\\leq n}$ is a\nmartingale difference array with respect to ${\\mathcal F}$. Therefore,\nwe want to apply Theorem~\\ref{thm:triangular} (with $k_n=n$,\n$\\mathbf{T}_{n,k}=\\mathbf{T}_k$ and ${\\mathcal G}_{n,k}={\\mathcal\n  F}_k$). To this purpose, we observe that condition~(c1) is obviously\nsatisfied and so we have to prove only conditions~(c2) and~(c3).\n\\\\\n\n\\indent Regarding condition~(c2), we note that\n\n\\begin{multline*}\n\\sum_{k=1}^n {\\mathbf T}_k{\\mathbf T}_k^{\\top}\n=\n\\sum_{k=1}^n \\Delta\\mathbf{M}_k(\\Delta\\mathbf{M}_k)^{\\top}\n+\nN^{-1}\\sum_{k=1}^n k^2r_k^2\\left(\\mathbf{v}_1^{\\top}\\Delta\\mathbf{M}_k\\right)^2\n\\mathbf{1}\\mathbf{1}^{\\top}\\\\\n-N^{-1\/2}\\sum_{k=1}^n kr_k \\left(\\mathbf{v}_1^{\\top}\\Delta\\mathbf{M}_k\\right)\n\\Delta\\mathbf{M}_k\\mathbf{1}^{\\top}\n-N^{-1\/2}\\sum_{k=1}^n kr_k \\left(\\mathbf{v}_1^{\\top}\\Delta\\mathbf{M}_k\\right)\n\\mathbf{1}(\\Delta\\mathbf{M}_k)^{\\top}.\n\\end{multline*}\nThe convergence rate of each of the four terms will be determined in the\nfollowing.\n\\\\\n\n\\indent By~\\eqref{eq:multidim-limite-conditional-M}\nand~Lemma~\\ref{lemma-serie-rv}\n(with $c_k=k$, $v_{n,k}=k\/n$ and $\\eta=1$),\nfor the first term, we obtain that\n\\begin{equation*\nn^{-1}\\sum_{k=1}^n \\Delta\\mathbf{M}_k(\\Delta\\mathbf{M}_k)^{\\top}\n\\stackrel{a.s.}\\longrightarrow  Z_{\\infty}(1-Z_{\\infty})I\\,.\n\\end{equation*}\nMoreover, regarding the second term, by \\eqref{relazione-nota} we\nhave that\n\\begin{equation*}\n\\lim_n n^{-2(1-e)} \\sum_{k=1}^n k^2 r_k^2=\nc^2 \\lim_n n^{-2(1-e)} \\sum_{k=1}^n \\frac{1}{k^{1-2(1-e)}}=\n\\frac{c^2}{2(1-e)}\n\\end{equation*}\nand, since by \\eqref{eq:covar-conditional-M} and\n\\eqref{eq:var-conditional-M} we have that\n\\begin{equation*}\nE\\left[\\left(\\mathbf{v}_1^{\\top}\\Delta\\mathbf{M}_k\\right)^2\\,|\\,\n{\\mathcal F}_{k-1}\\right]\n=\\sum_{j=1}^N v_{1,j}^2 E\\left[(\\Delta M_{k,j})^2|{\\mathcal F}_{k-1}\\right]\n\\stackrel{a.s.}\\longrightarrow\n\\|\\mathbf{v}_1\\|^2 Z_{\\infty}(1-Z_{\\infty})\\,,\n\\end{equation*}\nby~Lemma~\\ref{lemma-serie-rv} again (with $c_k=k$,\n$v_{n,k}=k^3r_k^2\/n^{2(1-e)}$ and $\\eta=\\frac{c^2}{2(1-e)}$), we\nobtain that\n\\begin{equation*\nn^{-2(1-e)}\\,N^{-1}\n\\sum_{k=1}^n k^2r_k^2\\left(\\mathbf{v}_1^{\\top}\\Delta\\mathbf{M}_k\\right)^2\n\\mathbf{1}\\mathbf{1}^{\\top}\n\\stackrel{a.s.}\\longrightarrow\n\\frac{c^2}{2(1-e)N}\\|\\mathbf{v}_1\\|^2 Z_{\\infty}(1-Z_{\\infty})\n\\mathbf{1}\\mathbf{1}^{\\top}\\,.\n\\end{equation*}\nFurthermore, concerning the third term, by \\eqref{relazione-nota} we\nhave that\n\\begin{equation*}\n\\lim_n n^{-(1+\\frac{1}{2}-e)}\\sum_{k=1}^n k r_k=\nc\\lim_n n^{-(1+\\frac{1}{2}-e)}\\sum_{k=1}^n k^{\\frac{1}{2}-e}=\n\\frac{c}{1+\\frac{1}{2}-e}\\,.\n\\end{equation*}\nOn the other hand, by means of~\\eqref{eq:covar-conditional-M} and\n\\eqref{eq:var-conditional-M}, we have that\n\\begin{equation*}\nE\\Big[\\Big(\\mathbf{v}_1^{\\top}\\Delta\\mathbf{M}_k\\Big)\n\\Delta\\mathbf{M}_k\\mathbf{1}^{\\top}\\,|\\,\n{\\mathcal F}_{k-1}\\Big]\n=E\\Big[\\Big(\\sum_{j=1}^N v_{1,j}\\Delta M_{k,j}\\Big)\n\\Delta\\mathbf{M}_k\\mathbf{1}^{\\top}\\,|\\,\n{\\mathcal F}_{k-1}\\Big]\n\\stackrel{a.s.}\\longrightarrow\n\\mathbf{v}_1\\mathbf{1}^{\\top} Z_{\\infty}(1-Z_{\\infty}),\n\\end{equation*}\nand so, by~Lemma~\\ref{lemma-serie-rv} again (with $c_k=k$,\n$v_{n,k}=k r_k\/n^{1+\\frac{1}{2}-e}$ and $\\eta=\\frac{c}{(1+1\/2-e)}$),\nit follows\n\\begin{equation*\n n^{-(1+\\frac{1}{2}-e)}\\,\nN^{-1\/2}\\sum_{k=1}^n kr_k \\left(\\mathbf{v}_1^{\\top}\\Delta\\mathbf{M}_k\\right)\n\\Delta\\mathbf{M}_k\\mathbf{1}^{\\top}\n\\stackrel{a.s.}\\longrightarrow\n\\frac{c}{(1+1\/2-e)\\sqrt{N}}Z_{\\infty}(1-Z_{\\infty})\\mathbf{v}_1\\mathbf{1}^{\\top}\\,.\n\\end{equation*}\nFinally, for the convergence of the fourth term, we can argue as we\nhave just done for the third one. Indeed, observing that,\nby~\\eqref{eq:covar-conditional-M} and \\eqref{eq:var-conditional-M}, we\nhave that\n\\begin{equation*}\nE\\Big[\\Big(\\mathbf{v}_1^{\\top}\\Delta\\mathbf{M}_k\\Big)\n\\mathbf{1}(\\Delta\\mathbf{M}_k)^{\\top}\\,|\\,\n{\\mathcal F}_{k-1}\\Big]\n=E\\Big[\\mathbf{1}\\Big(\\sum_{j=1}^N v_{1,j}\\Delta M_{k,j}\\Big)\n(\\Delta\\mathbf{M}_k)^{\\top}\\,|\\,\n{\\mathcal F}_{k-1}\\Big]\n\\stackrel{a.s.}\\longrightarrow\n\\mathbf{1}\\mathbf{v}_1^{\\top} Z_{\\infty}(1-Z_{\\infty})\\,,\n\\end{equation*}\nwe get\n\\begin{equation*\n n^{-(1+\\frac{1}{2}-e)}\\,N^{-1\/2}\n\\sum_{k=1}^n kr_k \\left(\\mathbf{v}_1^{\\top}\\Delta\\mathbf{M}_k\\right)\n\\mathbf{1}(\\Delta\\mathbf{M}_k)^{\\top}\n\\stackrel{a.s.}\\longrightarrow\n\\frac{c}{(1+1\/2-e)\\sqrt{N}} Z_{\\infty}(1-Z_{\\infty})\\mathbf{1}\\mathbf{v}_1^{\\top}\\,.\n\\end{equation*}\nSumming up, since for $1\/2<\\gamma<1$ we have $2(1-e)>1$ and\n$2(1-e)>1+1\/2-e$, we obtain that\n\\begin{equation}\\label{var-asin-gamma}\n\\begin{split}\nt_n^2\\sum_{k=1}^n {\\mathbf T}_k{\\mathbf T}_k^{\\top}\n=\n\\frac{1}{n^{2(1-e)}}\\sum_{k=1}^n {\\mathbf T}_k{\\mathbf T}_k^{\\top}\n&\\stackrel{a.s.}\\longrightarrow\n0+\\frac{c^2}{N}\\|\\mathbf{v}_1\\|^2 \\frac{1}{2(1-e)} Z_{\\infty}(1-Z_{\\infty})\n\\mathbf{1}\\mathbf{1}^{\\top}\n-0-0\n\\\\\n&= Z_{\\infty}(1-Z_\\infty)\\widehat{\\Gamma}_{\\gamma}\\,.\n\\end{split}\n\\end{equation}\n\\indent Regarding condition~(c3), we note that\n\\begin{equation*}\nt_n \\sup_{1\\leq k\\leq n} |\\mathbf{T}_k|=\n\\frac{1}{n^{1-e}} \\sup_{1\\leq k\\leq n} O(k^{1-\\gamma})\n= O(1\/n^{\\gamma-e})=O(1\/\\sqrt{n})\\longrightarrow 0\\,.\n\\end{equation*}\nTherefore also this condition is satisfied and we can conclude that\n$t_n\\sum_{k=1}^n {\\mathbf T}_{k}$ converges stably to the Gaussian\nkernel with mean zero and random covariance matrix given by\n\\eqref{var-asin-gamma}.\n\\\\\n\n\\noindent{\\em Second step: the convergence result for $\\mathbf{Q}_n$.}\\\\\n\\noindent We aim at proving that $\\mathbf{Q}_n$ converges in\nprobability to zero, that is each component $Q_{n,j}$ converges in\nprobability to zero. To this purpose, we note that\n\\begin{equation*}\nE\\left[\\,|Q_{n,j}|\\,\\right]\n\\leq\nt_n\\sum_{k=1}^n\nE\\left\\{\\, | \\widehat{Z}_{k-1,j} |\\, \\right\\}\n\\leq\nt_n\\sum_{k=1}^n\n\\sqrt{\nE\\left[\\, (\\widehat{Z}_{k-1,j})^2 \\,\\right]\n}\n\\leq t_n\\sum_{k=1}^n\n\\sqrt{\nE\\left[\\, \\| \\widehat{\\mathbf{Z}}_{k-1} \\|^2 \\,\\right]\n}\n\\,.\n\\end{equation*}\n\nTherefore, recalling that, for $1\/2<\\gamma<1$, we have $E\\left[\n  \\|\\widehat{\\mathbf{Z}}_n\\|^2\\right]=O(n^{-\\gamma})$ (see\n\\eqref{eq:L2_Z_hat}), we can conclude by \\eqref{relazione-nota} that\n$$\nE[\\,|Q_{n,j}|\\,]=O\\Big(t_n\\sum_{k=1}^n k^{-\\gamma\/2}\\Big)\n\\!=\\!\nO\\Big(n^{-(1-e)}\\sum_{k=1}^n \\frac{1}{k^{1-(1-\\gamma\/2)}}\\Big)\n\\!=\\!\nO\\Big(n^{-1+e+1-\\gamma\/2}\\Big)\n\\!=\\!\nO\\Big(\\frac{1}{n^{(1-\\gamma)\/2}}\\Big)\n\\!\\to\\! 0\\,.\n$$\n\\end{proof}\n\nNow, the proof of Theorem \\ref{thm:asymptotics_theta_gamma} follows\nfrom the previous result, together with\nTheorem~\\ref{thm:asymptotics_Z_tilde} and Theorem~\\ref{blocco}.\n\\\\\n\n{\\it Proof of Theorem \\ref{thm:asymptotics_theta_gamma}.} By\nTheorem~\\ref{thm:asymptotics_Z_tilde}, we have that\n\\begin{equation*}\nn^{\\gamma -\\frac{1}{2}}(\\widetilde{Z}_n-Z_\\infty)\\mathbf{1}\n\\longrightarrow {\\mathcal N}\\big(\\mathbf{0},\nZ_{\\infty}(1-Z_{\\infty})\\widetilde{\\Sigma}_\\gamma\\big)\n\\ \\ \\ \\hbox{stably in the strong sense}.\n\\end{equation*}\nThus, from Theorem \\ref{thm:asymptotics_theta_hat_gamma}, applying\nTheorem~\\ref{blocco}, we obtain that\n$$\nn^{\\gamma -\\frac{1}{2}}\n\\left({\\mathbf N}_n-\\widetilde{Z}_n{\\mathbf 1},\n(\\widetilde{Z}_n-Z_\\infty)\\mathbf{1}\n\\right)\n\\longrightarrow\n\\mathcal{N}\\left(\\mathbf{0},\nZ_\\infty(1-Z_\\infty)\\widehat{\\Gamma}_\\gamma\\right)\n\\otimes\n{\\mathcal N}\\left(\\mathbf{0},\nZ_{\\infty}(1-Z_{\\infty})\\widetilde{\\Sigma}_\\gamma\\right)\n\\ \\ \\ \\hbox{stably}.\n$$\nIn order to conclude, it is enough to observe that\n$$\nn^{\\gamma -\\frac{1}{2}}\n\\left(\n\\mathbf{Z}_n-Z_{\\infty}\\mathbf{1},\n{\\mathbf N}_n-Z_{\\infty}\\mathbf{1}\n\\right)\n=\\Phi\\left(\nn^{\\gamma -\\frac{1}{2}}\n(\\mathbf{N}_n-\\widetilde{Z}_n\\mathbf{1}),\nn^{\\gamma -\\frac{1}{2}}\n(\\widetilde{Z}_n-Z_{\\infty})\\mathbf{1}\n\\right)\n+\\frac{1}{ n^{(1-\\gamma)\/2} }\n\\left(\nn^{ \\frac{\\gamma}{2} } \\widehat{\\mathbf Z}_n, \\mathbf{0}\n\\right)\\,,\n$$\nwhere $\\Phi(x,y)=(y, x+y)$ and the last term converges in\nprobability to zero (since $\\widehat{\\mathbf Z}_n=0$ for each $n$ when\n$N=1$ and since \\eqref{eq:CLT_Z_hat_gamma} when $N\\geq 2$).\n\\qed\n\n\\begin{rem}\\label{rem:O_gamma_2}\n\\rm\nWith reference to the statistical applications discussed in\nSubsection \\ref{section_statistics}, we recall that, since\n$V^{\\top}\\mathbf{1}=\\mathbf{0}$ (by \\eqref{eq:relazioni-2}), we have\n$UV^{\\top}\\mathbf{N}_n=UV^{\\top}\\widehat{\\mathbf{N}}_n$ and\n$V^{\\top}\\widehat{\\Gamma}_{\\gamma}V$ is the null matrix, and so\nfrom~\\eqref{eq:CLT_N_hat_gamma} we can get that $n^{\\gamma\n  -\\frac{1}{2}}UV^{\\top}\\mathbf{N}_{n}\\stackrel{P}\\to \\mathbf{0}$ for\n$1\/2<\\gamma<1$.  More precisely, following the arguments in the proof\nof Theorem~\\ref{thm:asymptotics_theta_hat_gamma}, it is possible to\nshow that, when $1\/2<\\gamma<1$, we have\n$n^{e}UV^{\\top}\\mathbf{N}_{n}\\stackrel{P}\\to \\mathbf{0}$ for each $e<\\gamma\/2$.\nIndeed, from \\eqref{eq:dynamic_SA_N_hat}, together with\n\\eqref{rel-tecnica-i} and again the relation\n$V^{\\top}\\mathbf{1}=\\mathbf{0}$, we obtain\n$$ n(UV^{\\top}\\mathbf{N}_{n}-UV^{\\top}\\mathbf{N}_{n-1})=\n-UV^{\\top}\\mathbf{N}_{n-1}+W^{\\top}\\widehat{\\mathbf{Z}}_{n-1} +\nUV^{\\top}\\Delta\\mathbf{M}_{n}$$ and hence, setting $t_n:=1\/n^{1-e}$,\n$\\mathbf{T}_k:=UV^{\\top}\\Delta\\mathbf{M}_k$ and\n$\\mathbf{Q}_n:=t_n\\sum_{k=1}^n\\widehat{\\mathbf{Z}}_{k-1}$, we get\n$$\nn^e UV^{\\top}\\mathbf{N}_n=t_n\\sum_{k=1}^n \\mathbf{T}_k+ W^{\\top}\\mathbf{Q}_n\n=\\frac{1}{ n^{\\frac{1}{2}-e} }\n\\frac{1}{\\sqrt{n}}\\sum_{k=1}^n T_k+ W^{\\top}\\mathbf{Q}_n,\n$$ where $\\frac{1}{\\sqrt{n}}\\sum_{k=1}^n \\mathbf{T}_k$ converges\nstably to the Gaussian kernel $\\mathcal{N}(\\mathbf{0},\nZ_{\\infty}(1-Z_\\infty)UV^{\\top}VU^{\\top})$ and\n$E[\\,|\\mathbf{Q}_n|\\,]=O( t_nn^{1-\\frac{\\gamma}{2}} )=O( n^{-(\n  \\frac{\\gamma}{2}-e)} ).$ From these relations, we can also conclude\nthat for $1\/2<\\gamma<1$ and $e=\\gamma\/2$, we have that $n^e\nUV^{\\top}\\mathbf{N}_n$ is the sum of a term converging to zero in\nprobability and a term bounded in $L^1$. Therefore the asymptotic\nbehavior of $n^{\\gamma\/2}UV^{\\top}\\mathbf{N}_n$ needs further\ninvestigation.\n\\end{rem}\n\n\n\\subsection{Proof of Theorem \\ref{thm:N_1_gamma_1}\n(CLT for $({\\mathbf Z}_n,{\\mathbf N}_n)_n$ in the case $N=1$ and $\\gamma=1$)}\n\nThe proof in the case $N=1$ and $\\gamma=1$ is similar to the one for\n$1\/2<\\gamma<1$. Indeed, using the same arguments as in the proof of\nTheorem \\ref{thm:asymptotics_theta_hat_gamma}, together with the facts\nthat $\\widetilde{Z}_n=Z_n$, $\\widehat{\\mathbf Z}_n=0$ for each $n$,\n$\\mathbf{v}_1=v_{1,1}=1$ and $2(1-e)=1+1\/2-e=1$, we obtain that\n\\begin{equation*}\n\\sqrt{n}(N_n-Z_n)=\\sqrt{n}\\,\\widehat{N}_{n}\n\\ \\longrightarrow\\\n\\mathcal{N}\\left(0,  Z_{\\infty}(1-Z_\\infty)(c-1)^2\\right)\n\\ \\ \\ \\ \\hbox{stably}.\n\\end{equation*}\nOn the other hand, by Theorem~\\ref{thm:asymptotics_Z_tilde}, we have that\n\\begin{equation*}\n\\sqrt{n}(Z_n-Z_\\infty)=\\sqrt{n}(\\widetilde{Z}_n-Z_\\infty)\n\\longrightarrow {\\mathcal N}\\big(0,\nZ_{\\infty}(1-Z_{\\infty})c^2\\big)\n\\ \\ \\ \\hbox{stably in the strong sense}.\n\\end{equation*}\nThus, applying Theorem~\\ref{blocco}, we obtain\n$$\n\\sqrt{n}\n\\left(N_n-Z_n, Z_n-Z_\\infty\\right)\n\\longrightarrow\n\\mathcal{N}\\left(0,\nZ_\\infty(1-Z_\\infty) (c-1)^2\\right)\n\\otimes\n{\\mathcal N}\\left(0,\nZ_{\\infty}(1-Z_{\\infty})c^2\\right)\n\\ \\ \\ \\hbox{stably}.\n$$\nIn order to conclude, it is enough to observe that\n$$\n\\sqrt{n}\n\\left(Z_n-Z_{\\infty}, N_n-Z_{\\infty}\\right)\n=\\Phi\\left(\n\\sqrt{n}(N_n-Z_n), \\sqrt{n}(Z_n-Z_{\\infty})\n\\right)\\,,\n$$\nwhere $\\Phi(x,y)=(y, x+y)$.\n\\qed\n\n\\begin{rem}\\label{rem:different_approach_gamma_1}\n\\rm Looking at the arguments of the proof of\nTheorem~\\ref{thm:asymptotics_theta_hat_gamma} with $N\\geq 2$ and\n$\\gamma=1$, we find\n$E\\left[\\,|\\mathbf{Q}_n|\\,\\right]=O\\left(\\frac{1}{n^{(1-\\gamma)\/2}}\\right)=O(1)$\nand so, from this relation, we can not conclude that $\\mathbf{Q}_n$\nconverges to zero in probability. Therefore part of the proof of\nTheorem~\\ref{thm:asymptotics_theta_hat_gamma} does not work when\n$N\\geq 2$ and $\\gamma=1$. Moreover, since $\\mathbf{Q}_n=\\sum_{k=1}^n\n\\widehat{\\mathbf{Z}}_{k-1}\/\\sqrt{n}$ and, from \\cite[Theorem\n  4.3]{ale-cri-ghi}, we know that, when $N\\geq 2$ and $\\gamma=1$, the\nrate of convergence of $\\widehat{\\mathbf{Z}}_n$ is $\\sqrt{n}$ or\n$\\sqrt{n\/\\ln(n)}$ according to the value of ${\\mathcal\n  Re}(\\lambda^*)$, we may conjecture that, for $N\\geq 2$ and\n$\\gamma=1$, $\\mathbf{Q}_{n}$ generally does not converge in\nprobability to zero.  This fact leads us to a complete different\napproach to the proofs of Theorem~\\ref{thm:asymptotics_theta_1} and\nTheorem~\\ref{thm:asymptotics_Z_1_star} concerning the case $N\\geq 2$\nand $\\gamma=1$, that will be developed in the next sections.\n\\end{rem}\n\n\\subsection{Proof of Theorem \\ref{thm:asymptotics_theta_1}\n(CLT for $({\\mathbf Z}_n,{\\mathbf N}_n)_n$ in the case $N\\geq 2$, $\\gamma=1$\nand ${\\mathcal Re}(\\lambda^{*})<1-(2c)^{-1}$)}\n\nIn order to prove Theorem \\ref{thm:asymptotics_theta_1}, we need the\nfollowing convergence result on $(\\widehat{\\mathbf{Z}}_n,\n\\widehat{\\mathbf{N}}_n)_n$:\n\n\\begin{theo}\\label{thm:asymptotics_theta_hat_1}\nLet $N\\geq 2$, $\\gamma=1$ and ${\\mathcal R}e(\\lambda^{*})<1-(2c)^{-1}$.\nThen, under condition~\\eqref{ass:condition_r_n_1}, we have that\n\\begin{equation*\n\\sqrt{n}\n\\begin{pmatrix}\n\\widehat{\\mathbf{Z}}_n\\\\\n\\widehat{\\mathbf{N}}_n\n\\end{pmatrix}\n{\\longrightarrow}\\\n\\mathcal{N} \\left(\\ \\mathbf{0}\\ ,\\ Z_{\\infty}(1-Z_{\\infty})\n\\begin{pmatrix}\n\\widehat{\\Sigma}_{\\mathbf{ZZ}} & \\widehat{\\Sigma}_{\\mathbf{ZN}}\\\\\n\\widehat{\\Sigma}_{\\mathbf{ZN}}^{\\top} & \\widehat{\\Sigma}_{\\mathbf{NN}}\n\\end{pmatrix}\\ \\right)\\ \\ \\ \\ stably,\n\\end{equation*}\nwhere $\\widehat{\\Sigma}_{\\mathbf{ZZ}}$, $\\widehat{\\Sigma}_{\\mathbf{NN}}$ and\n$\\widehat{\\Sigma}_{\\mathbf{ZN}}$ are the matrices defined\nin~\\eqref{def:Sigmahat_ZZ_1},~\\eqref{def:Sigmahat_NN_1}\nand~\\eqref{def:Sigmahat_ZN_1}, respectively.\n\\end{theo}\n\n\\begin{proof}\nFirst we use \\eqref{rel-tecnica-i} in~\\eqref{eq:dynamic_SA_N_hat} and\nwe replace the term $(\\widetilde{Z}_n-\\widetilde{Z}_{n-1})$\nin~\\eqref{eq:dynamic_SA_N_hat} as shown\nin~\\eqref{eq:dynamic_SA_tilde}, so that we obtain\n$$\\widehat{\\mathbf{N}}_n-\\widehat{\\mathbf{N}}_{n-1}=\n\\frac{1}{n}(-\\widehat{\\mathbf{N}}_{n-1}\n+UDV^{\\top}\\widehat{\\mathbf{Z}}_{n-1}+\\Delta\\mathbf{M}_n)\\\n-r_{n-1}N^{-1\/2}\\mathbf{v}_1^{\\top}\\Delta\\mathbf{M}_n\\mathbf{1}.\n$$\nThen, if we define the remainder term as\n\\begin{equation}\\label{def:R_n}\n\\mathbf{R}_n\\ :=\\\n\\Big(\\frac{1}{nr_{n-1}}-\\frac{1}{c}\\Big)\n(-\\widehat{\\mathbf{N}}_{n-1}\n+UDV^{\\top}\\widehat{\\mathbf{Z}}_{n-1}+\\Delta\\mathbf{M}_n),\n\\end{equation}\nwe can rewrite the above dynamics of $\\widehat{\\mathbf{N}}_n$ as follows:\n\\begin{equation}\\label{eq:dynamic_SA_N_hat_proof}\n\\widehat{\\mathbf{N}}_n=(1-r_{n-1}c^{-1})\\widehat{\\mathbf{N}}_{n-1}\n+r_{n-1} c^{-1}UDV^{\\top}\\widehat{\\mathbf{Z}}_{n-1}\n+r_{n-1}[c^{-1}I-N^{-1\/2}\\mathbf{1}\\mathbf{v}_1^{\\top}]\\Delta\\mathbf{M}_n\n+r_{n-1}\\mathbf{R}_n.\n\\end{equation}\nThen, setting\n$\\boldsymbol{\\theta}_n:=\n(\\widehat{\\mathbf{Z}}_{n},\\widehat{\\mathbf{N}}_{n})^{\\top}$,\n$\\Delta\\mathbf{M}_{\\theta,n}:=(\\Delta\\mathbf{M}_n,\\Delta\\mathbf{M}_n)^{\\top}$\nand $\\mathbf{R}_{\\theta,n}:=(\\mathbf{0},\\mathbf{R}_n)^{\\top}$, which\nare vectors of dimension $2N$, and combining~\\eqref{eq:dynamic_SA_hat}\nand~\\eqref{eq:dynamic_SA_N_hat_proof}, we can write\n$$\n\\boldsymbol{\\theta}_{n+1}=\n(I-r_nQ)\\boldsymbol{\\theta}_{n}+\nr_n(R\\Delta\\mathbf{M}_{\\theta,n+1}+\\mathbf{R}_{\\theta,n+1}),\n$$\nwhere\n\\begin{equation*\nQ:=\\begin{pmatrix}\nU(I-D)V^{\\top} & 0 \\\\\n-c^{-1}UDV^{\\top} & c^{-1}I\n\\end{pmatrix},\n\\end{equation*}\nand (recalling~that $\\mathbf{u}_1=N^{-1\/2}\\mathbf{1}$ and\n$I=\\mathbf{u}_1\\mathbf{v}_1^{\\top}+UV^{\\top}$ by\n\\eqref{eq:relazioni-1} and~\\eqref{eq:relazioni-2})\n\\begin{equation}\\label{def:R-irene}\nR:=\\begin{pmatrix}\nUV^{\\top} & 0\\\\\n0 & (c^{-1}-1)\\mathbf{u}_1\\mathbf{v}_1^{\\top}+c^{-1}UV^{\\top}\n\\end{pmatrix}.\n\\end{equation}\nNow, we will prove that $\\sqrt{n}\\boldsymbol{\\theta}_{n}$ converges stably\nto the desired Gaussian kernel.  To this end, the first step is to define\nthe $(2N)\\times(2N-1)$ matrices\n\\[U_{\\theta}:=\\begin{pmatrix}\nU & 0 \\\\\n0 & \\widetilde{U}\n\\end{pmatrix}=\\begin{pmatrix}\nU & \\mathbf{0} & 0 \\\\\n0 & \\mathbf{u}_1 & U\n\\end{pmatrix}\n\\qquad\\mbox{and}\\qquad\nV_{\\theta}:=\\begin{pmatrix}\nV & 0  \\\\\n0 & \\widetilde{V}\n\\end{pmatrix}=\\begin{pmatrix}\nV & \\mathbf{0} & 0 \\\\\n0 & \\mathbf{v}_1 & V\n\\end{pmatrix},\\]\nand observe that from~\\eqref{eq:relazioni-2} we have\n$V_{\\theta}^{\\top}U_{\\theta}=I$ and\n\\begin{equation*}\nU_{\\theta}V_{\\theta}^{\\top}=\n\\begin{pmatrix}\nUV^{\\top} & 0  \\\\\n0 & I\n\\end{pmatrix}.\n\\end{equation*}\nThen, defining the $(2N)\\times(2N-1)$ matrices\n\\begin{equation}\\label{def:S_Q_S_R}\nS_Q:=\\begin{pmatrix}\n(I-D) & \\mathbf{0} & 0\\\\\n\\mathbf{0}^{\\top} & c^{-1} & \\mathbf{0}^{\\top}\\\\\n-c^{-1}D & \\mathbf{0} & Ic^{-1}\n\\end{pmatrix}\n\\qquad\\hbox{and}\\qquad\nS_R:=\\begin{pmatrix}\nI & \\mathbf{0} & 0\\\\\n\\mathbf{0}^{\\top} & c^{-1}-1 & \\mathbf{0}^{\\top}\\\\\n0 & \\mathbf{0} & c^{-1}I\n\\end{pmatrix},\n\\end{equation}\nwe have that $Q=U_{\\theta}S_QV_{\\theta}^{\\top}$\nand $R=U_{\\theta}S_R V_{\\theta}^{\\top}$.\nFrom the above relations on $U_{\\theta}$ and $V_{\\theta}$,\nwe get that\n$U_{\\theta}V_{\\theta}^{\\top}\\boldsymbol{\\theta}_n=\\boldsymbol{\\theta}_n$ and hence\nwe can write\n$$\n\\boldsymbol{\\theta}_{n+1}=\nU_{\\theta}\\left[I-r_nS_Q\\right]V_{\\theta}^{\\top}\\boldsymbol{\\theta}_n\n+r_nR\\Delta\\mathbf{M}_{\\theta, n+1}+r_n\\mathbf{R}_{\\theta,n+1}.\n$$ Let us now set $\\alpha_j:=1-\\lambda_j\\in\\mathbb{C}$ with\n$\\lambda_j\\in Sp(W)\\setminus \\{1\\}=Sp(D)$ and recall that ${\\mathcal\n  Re}(\\alpha_j)>0$ for each $j$ since ${\\mathcal Re}(\\lambda_j)<1$ for\neach $j$.  Then, if we take an integer $m_0\\geq 2$ large enough such\nthat ${\\mathcal Re}(\\alpha_j) r_n<1$ for all $j$ and $n\\geq m_0$, we\ncan write\n\\begin{equation}\\label{eq:theta-irene}\n\\boldsymbol{\\theta}_{n+1}=\nC_{m_0,n}\\boldsymbol{\\theta}_{m_0}+\n\\sum_{k=m_0}^nC_{k+1,n}r_kR\\Delta\\mathbf{M}_{\\theta,k+1}+\n\\sum_{k=m_0}^nC_{k+1,n}r_k\\mathbf{R}_{\\theta,k+1}\n\\quad\\hbox{for } n\\geq m_0,\n\\end{equation}\nwhere\n\\begin{equation}\\label{def:C_k_n_A_k_n}\n\\begin{split}\n&C_{k+1,n}:=U_{\\theta}A_{k+1,n}V_{\\theta}^{\\top}\n\\quad\\hbox{for } m_0-1\\leq k\\leq n,\n\\\\\n&A_{k+1,n}:=\n\\begin{cases}\n\\prod_{m=k+1}^n\\left[I-r_mS_Q\\right]=\\begin{pmatrix}\nA^{11}_{k+1,n} & \\mathbf{0} & 0\\\\\n\\mathbf{0}^{\\top} & a^{22}_{k+1,n} & \\mathbf{0}^{\\top}\\\\\nA^{31}_{k+1,n} & \\mathbf{0} & A^{33}_{k+1,n}\n\\end{pmatrix}\n\\;&\\hbox{for } m_0\\!-\\!1\\!\\leq\\! k\\!\\leq\\! n\\!-\\!1\n\\\\\nI\\;&\\hbox{for } k\\!=\\!n.\n\\end{cases}\n\\end{split}\n\\end{equation}\nNotice that the blocks $A^{11}_{k+1,n}$, $A^{31}_{k+1,n}$ and\n$A^{33}_{k+1,n}$ are all diagonal $(N-1)\\times(N-1)$ matrices.  In\nparticular, setting for any $x\\in\\mathbb{C}$, $p_{m_0-1}(x):=1$ and\n$p_{k}(x):=\\prod_{m=m_0}^{k}(1-r_mx)$ for $k\\geq m_0$ and\n$F_{k+1,n}(x):=p_{n}(x)\/p_{k}(x)$ for $m_0-1\\leq k\\leq n-1$, from\nLemma~\\ref{lem:terms_in_A_k_n} we get\n\\begin{equation}\\label{def:terms_in_A_k_n}\\begin{aligned}\n&[A^{11}_{k+1,n}]_{jj}\\ =\\ F_{k+1,n}(\\alpha_j),\\\\\n&[A^{33}_{k+1,n}]_{jj}\\ =\\ a^{22}_{k+1,n}\\ =\\ F_{k+1,n}(c^{-1}),\\\\\n&[A^{31}_{k+1,n}]_{jj}\\ =\\ \\left\\{\\begin{aligned}\n&\\left(\\frac{1-\\alpha_j}{c\\alpha_j-1}\\right)\n(F_{k+1,n}(c^{-1})-F_{k+1,n}(\\alpha_j)),\\ &\\hbox{for } c\\alpha_j\\neq 1,\\\\\n&(1-c^{-1})F_{k+1,n}(c^{-1})\\ln\\left(\\frac{n}{k}\\right)+O(n^{-1}),\\\n&\\hbox{for } c\\alpha_j=1.\n\\end{aligned}\\right.\n\\end{aligned}\\end{equation}\n\nFinally, we rewrite \\eqref{eq:theta-irene} as\n\\begin{equation}\\label{eq:dynamic_SA_theta_proof}\n\\boldsymbol{\\theta}_{n+1}=C_{m_0,n}\\boldsymbol{\\theta}_{m_0}+\n\\sum_{k=m_0}^n {\\mathbf T}_{n,k}+\\boldsymbol{\\rho}_{n},\\qquad\\mbox{where}\n\\qquad \\left\\{\n\\begin{aligned}\n&{\\mathbf T}_{n,k}:=r_k C_{k+1,n} R\\Delta{\\mathbf M}_{\\theta,k+1},\\\\\n&\\boldsymbol{\\rho}_{n}:=\\sum_{k=m_0}^nr_k C_{k+1,n} {\\mathbf R}_{\\theta,k+1}.\n\\end{aligned}\\right.\\end{equation}\nand, in the sequel of the proof, we will establish the asymptotic\nbehavior of $\\boldsymbol{\\theta}_{n}$ by studying separately the terms\n$C_{m_0,n}\\boldsymbol{\\theta}_{m_0}$, $\\sum_{k=m_0}^n {\\mathbf\n  T}_{n,k}$ and $\\boldsymbol{\\rho}_{n}$.\\\\\n\n\\indent Let us use the symbol $^*$ for the quantities\n$a_{\\alpha_j}:={\\mathcal Re}(\\alpha_j)$ and $p_{n}(\\alpha_j)$\ncorresponding to $\\alpha^*=\\alpha_j=1-\\lambda_j$ with\n$\\lambda_j=\\lambda^*\\in \\lambda_{\\max}(D)$. Now, we note that, as a\nconsequence of \\eqref{def:C_k_n_A_k_n}, \\eqref{def:terms_in_A_k_n}\nand Lemma~\\ref{lemma-tecnico_1}, we have\n\\begin{equation}\\label{eq-corretta}\n\\begin{split}\n|A_{k+1,n}|&=O\\left(\\frac{|p_n^*|}{|p_k^*|}\\right)\n+O\\left(\\frac{k}{n}\\right)+O\\left(\\frac{k}{n}\\ln\\left(\\frac{n}{k}\\right)\\right)\n+O\\left(\\frac{1}{n}\\right)\\\\\n&\\hbox{(where the last two terms are present when\nthere exists $j$ such that $c\\alpha_j=1$)}\n\\\\\n&=O\\left(\\frac{|p_n^*|}{|p_k^*|}\\right)\n+O\\left(\\frac{k}{n}\\ln(n)\\right)\n=\nO\\left( \\Big(\\frac{k}{n}\\Big)^{ca^*} \\right)\n+O\\left(\\frac{k}{n}\\ln(n)\\right)\n\\quad\\hbox{for } m_0-1\\leq k\\leq n-1.\n\\end{split}\n\\end{equation}\nTherefore, we get that $\\sqrt{n}\n|C_{m_0,n}\\boldsymbol{\\theta}_{m_0}|\\rightarrow 0$ almost surely \n because $ca^*>1\/2$ by assumption.\\\\\n\n\\indent Concerning the term $\\boldsymbol{\\rho}_{n}$, notice that\nby~\\eqref{ass:condition_r_n_1} and~\\eqref{def:R_n} we have that\n$|\\mathbf{R}_k|=O(k^{-1})$ and, by \\eqref{eq-corretta}, we have that\n\\begin{equation*}\n|C_{k+1,n}|\\ =\\  O\\Big(\\ \\Big(\\frac{k}{n}\\Big)^{ca^*}\\ \\Big)\n+O\\Big(\\ \\frac{k}{n}\\ln(n)\\ \\Big)\n\\quad\\hbox{for } m_0\\leq k\\leq n-1.\n\\end{equation*}\nTherefore, since $\\boldsymbol{\\rho}_{n}=\\sum_{k=m_0}^nr_k C_{k+1,n}\n{\\mathbf R}_{\\theta,k+1}=\\sum_{k=m_0}^{n-1} r_k C_{k+1,n}{\\mathbf\n  R}_{\\theta,k+1} +r_nC_{n+1,n}{\\mathbf R}_{\\theta,n+1}$, it follows (by\n\\eqref{relazione-nota}) that\n\\begin{equation*}\n\\sqrt{n}|\\boldsymbol{\\rho}_{n}|\\ =\\\nO\\Big( n^{1\/2-c a^*}\n\\sum_{k=m_0}^{n-1} k^{-(2-c a^*)}\\Big)\n+\nO\\big( n^{-1\/2} \\ln(n)^2 \\big)\n+\nO\\big(n^{-3\/2}\\big)\n\\longrightarrow 0\\quad \\hbox{a.s.}\\,,\n\\end{equation*}\nbecause $ca^*>1\/2$.\n\\\\\n\n\\indent We now focus on the asymptotic behavior of the second term.\nSpecifically, we aim at pro\\-ving that $\\sqrt{n}\\sum_{k=m_0}^n{\\mathbf\n  T}_{n,k}$ converges stably to the suitable Gaussian kernel.  For this\npurpose, we set ${\\mathcal G}_{n,k}={\\mathcal F}_{k+1}$, and consider\nTheorem~\\ref{thm:triangular} (recall that ${\\mathbf T}_{n,k}$ are real\nrandom vectors).  Given the fact that condition $(c1)$ of\nTheorem~\\ref{thm:triangular} is obviously satisfied, we will check\nonly conditions $(c2)$ and $(c3)$.  \\\\\n\nRegarding condition $(c2)$, since the relation\n$V_{\\theta}^{\\top}U_{\\theta}=I$ implies $V_{\\theta}^{\\top}R=S_R\nV_{\\theta}^{\\top}$, we have that\n\\begin{align*}\n\\sum_{k=m_0}^n (\\sqrt{n}\\mathbf{T}_{n,k})(\\sqrt{n}\\mathbf{T}_{n,k})^{\\top}\n& = n\\sum_{k=m_0}^n r_k^2\nC_{k+1,n}R\n(\\Delta{\\mathbf M}_{\\theta,k+1})(\\Delta{\\mathbf M}_{\\theta,k+1})^{\\top}RC_{k+1,n}^{\\top}\n\\\\\n&= U_{\\theta} \\left(n\\sum_{k=m_0}^n r_k^2\nA_{k+1,n}\\,V_{\\theta}^{\\top}\\,R\n(\\Delta{\\mathbf M}_{\\theta,k+1})(\\Delta{\\mathbf M}_{\\theta,k+1})^{\\top}R\\,\nV_{\\theta}\\,A^{\\top}_{k+1,n}\n\\right) U_{\\theta}^{\\top}\\\\\n&= U_{\\theta} \\left(n\\sum_{k=m_0}^n r_k^2\nA_{k+1,n}S_R\\,V_{\\theta}^{\\top}\\,(\\Delta{\\mathbf M}_{\\theta,k+1})\n(\\Delta{\\mathbf M}_{\\theta,k+1})^{\\top}\\,\nV_{\\theta}\\, S_RA^{\\top}_{k+1,n}\n\\right) U_{\\theta}^{\\top}.\n\\end{align*}\nTherefore, it is enough to study the convergence of\n\\begin{equation*}\nn\\sum_{k=m_0}^n r_k^2\nA_{k+1,n}S_R\\,V_{\\theta}^{\\top}\\,\n(\\Delta{\\mathbf M}_{\\theta,k+1})(\\Delta{\\mathbf M}_{\\theta,k+1})^{\\top}\\,\nV_{\\theta}\\, S_RA^{\\top}_{k+1,n}.\n\\end{equation*}\nMoreover, since $O(nr_n^2)=O(n^{-1})\\to 0$ the last term in the above sum is negligible as $n$ increase to infinity,\nand hence it is enough to study the convergence of\n\\begin{equation}\\label{step_proof-irene}\nn\\sum_{k=m_0}^{n-1} r_k^2\nA_{k+1,n}S_R\\,V_{\\theta}^{\\top}\\,\n(\\Delta{\\mathbf M}_{\\theta,k+1})(\\Delta{\\mathbf M}_{\\theta,k+1})^{\\top}\\,\nV_{\\theta}\\, S_RA^{\\top}_{k+1,n}.\n\\end{equation}\nTo this purpose, setting\n$B_{\\theta,k+1}:=V_{\\theta}^{\\top}\\,(\\Delta{\\mathbf\n    M}_{\\theta,k+1})(\\Delta{\\mathbf\n    M}_{\\theta,k+1})^{\\top}\\,V_{\\theta}$,\n$B_{k+1}:=V^{\\top}\\,(\\Delta{\\mathbf M}_{k+1})(\\Delta{\\mathbf\n    M}_{k+1})^{\\top}\\,V$,\n$\\mathbf{b}_{k+1}:=V^{\\top}\\,(\\Delta{\\mathbf M}_{k+1})(\\Delta{\\mathbf\n    M}_{k+1})^{\\top}\\,\\mathbf{v}_1$ and\n$b_{k+1}:=\\mathbf{v}_1^{\\top}\\,(\\Delta{\\mathbf\n    M}_{k+1})(\\Delta{\\mathbf M}_{k+1})^{\\top}\\,\\mathbf{v}_1$, we\nobserve that\n\\begin{equation}\\label{def:B_matrix}\nB_{\\theta,k+1}=\\begin{pmatrix}\nB_{k+1} & \\mathbf{b}_{k+1} & B_{k+1}\\\\\n\\mathbf{b}_{k+1}^{\\top} & b_{k+1} & \\mathbf{b}_{k+1}^{\\top}\\\\\nB_{k+1} & \\mathbf{b}_{k+1} & B_{k+1}\n\\end{pmatrix}.\n\\end{equation}\nSince in $B_{\\theta,k+1}$ the first and the third row and column of\nblocks are the same, in~\\eqref{step_proof-irene} the\n$(2N-1)\\times(2N-1)$ matrix $(A_{k+1,n}S_R)$ can be rewritten as a\ndiagonal matrix with the following diagonal blocks:\n$A^{1}_{k+1,n}:=A^{11}_{k+1,n}$,\n$A^{3}_{k+1,n}:=(A^{31}_{k+1,n}+c^{-1}A^{33}_{k+1,n})$ and\n$a^{2}_{k+1,n}:=(c^{-1}-1)a^{22}_{k+1,n}$.  Hence, the expression\nin~\\eqref{step_proof-irene} can be rewritten as\n\\begin{equation}\\label{eq:matrix}\nn\\sum_{k=m_0}^{n-1} r_k^2\n\\begin{pmatrix}\nA^{1}_{k+1,n}B_{k+1}A^{1}_{k+1,n} & a^{2}_{k+1,n}A^{1}_{k+1,n}\\mathbf{b}_{k+1}\n& A^{1}_{k+1,n}B_{k+1}A^{3}_{k+1,n}\\\\\na^{2}_{k+1,n}\\mathbf{b}_{k+1}^{\\top}A^{1}_{k+1,n} & (a^{2}_{k+1,n})^2b_{k+1}\n& a^{2}_{k+1,n}\\mathbf{b}_{k+1}^{\\top}A^{3}_{k+1,n}\\\\\nA^{3}_{k+1,n}B_{k+1}A^{1}_{k+1,n} & a^{2}_{k+1,n}A^{3}_{k+1,n}\\mathbf{b}_{k+1}\n& A^{3}_{k+1,n}B_{k+1}A^{3}_{k+1,n}\n\\end{pmatrix}.\\end{equation}\nThe elements of $A^{1}_{k+1,n}$, $a^{2}_{k+1,n}$ and $A^{3}_{k+1,n}$ in the above matrix\ncan be rewritten in terms of $F_{k+1,n}(\\cdot)$, by~\\eqref{def:terms_in_A_k_n}, in the following way:\n\\begin{equation}\\label{def:terms_in_A_k_n_B_k}\n\\begin{aligned}\n&[A^{1}_{k+1,n}]_{jj}=F_{k+1,n}(\\alpha_j),\\\\\n&a^{2}_{k+1,n}=(c^{-1}-1)F_{k+1,n}(c^{-1}),\\\\\n&[A^{3}_{k+1,n}]_{jj}=\n\\left\\{\\begin{aligned}\n&\\frac{1}{c\\alpha_j-1}\n\\left[(1-c^{-1})F_{k+1,n}(c^{-1})-(1-\\alpha_j)F_{k+1,n}(\\alpha_j)\\right],\\\n&\\hbox{for } c\\alpha_j\\neq 1,\\\\\n&\\left[(1-c^{-1})\\ln\\left(\\frac{n}{k}\\right)+c^{-1}\\right]F_{k+1,n}(c^{-1})\n+O(n^{-1}),\\\n&\\hbox{for } c\\alpha_j=1.\n\\end{aligned}\n\\right.\n\\end{aligned}\n\\end{equation}\nHence, the almost sure convergences\nof all the elements in~\\eqref{eq:matrix} can be obtained by combining the\nresults of the following limits:\n\\begin{equation}\\label{eq:results_limits}\n\\begin{aligned}\n&n\\sum_{k=m_0}^{n-1} r_k^2 \\beta_{k+1}\nF_{k+1,n}(x)F_{k+1,n}(y)\\\n\\stackrel{a.s}\\longrightarrow\\\n\\beta\\frac{c^2}{c(x+y)-1},\n\\\\\n&n\\sum_{k=m_0}^{n-1} r_k^2 \\beta_{k+1}\n\\ln\\left(\\frac{n}{k}\\right)F_{k+1,n}(x)F_{k+1,n}(y)\\\n\\stackrel{a.s}\\longrightarrow\\\n\\beta\\frac{c^2}{(c(x+y)-1)^2},\n\\\\\n&n\\sum_{k=m_0}^{n-1} r_k^2 \\beta_{k+1}\n\\ln^2\\left(\\frac{n}{k}\\right)F_{k+1,n}(x)F_{k+1,n}(y)\\\n\\stackrel{a.s}\\longrightarrow\\\n\\beta\\frac{2c^2}{(c(x+y)-1)^3},\n\\end{aligned}\n\\end{equation}\nfor certain complex numbers $x,y\\in\\{\\alpha_j,\\, 2\\leq j\\leq N\\}$\n(remember that, by the assumption ${\\mathcal Re}(\\lambda^*)<1\n-(2c)^{-1}$, we have $c(a_x+a_y)>1$ with $a_x:={\\mathcal Re}(x)$ and\n$a_y:={\\mathcal Re}(y)$), a suitable sequence of random variables\n$\\beta_{k}\\in\\{[B_{k}]_{h,j},[\\mathbf{b}_{k}]_{j},b_{k};\\,\n2\\leq h,j\\leq N\\}$ and some random variable $\\beta$.  Indeed,\nusing~Lemma~\\ref{lemma-tecnico_1} and relation \\eqref{relazione-nota},\nwe have\n\\begin{itemize}\n\\item[(1)] $n\\sum_{k=m_0}^{n-1}r_k^2|\\beta_{k+1}|O(n^{-2})\\ =\\\nO(n^{-1})\\sum_{k=m_0}^{n-1}O(k^{-2})\\ \\rightarrow 0 $;\n\\item[(2)] $n\\ln(n)\\sum_{k=m_0}^{n-1}r_k^2|\\beta_{k+1}|O(n^{-1})|F_{k+1,n}(c^{-1})|\\ =\\\nO(n^{-1}\\ln(n))\\sum_{k=m_0}^{n-1}O(k^{-1})\\ \\rightarrow 0$;\n\\item[(3)] $n\\sum_{k=m_0}^{n-1}r_k^2|\\beta_{k+1}|O(n^{-1})|F_{k+1,n}(y)|\\ =\\\nO(n^{-ca_y})\\sum_{k=m_0}^{n-1}O(k^{-(2-ca_y)})\\ \\rightarrow 0$.\n\\\\\n\\end{itemize}\n\n\\indent In order to prove the convergences\nin~\\eqref{eq:results_limits}, we will apply Lemma \\ref{lemma-serie-rv}\nto each of the three limits.  Indeed, each quantity\nin~\\eqref{eq:results_limits} can be written as $\\sum_{k=m_0}^{n-1}\nv^{(e)}_{n,k}Y_k\/c_k$, where\n$$\nY_k=\\beta_{k+1},\n\\quad\nc_k=\\frac{1}{kr_k^2}\n\\quad\\mbox{and }\\quad\nv^{(e)}_{n,k}=\\left(\\frac{n}{k}\\right)\\ln^e\n\\left(\\frac{n}{k}\\right)F_{k+1,n}(x)F_{k+1,n}(y),\n\\quad\\mbox{ for }e\\in\\{0,1,2\\},\n$$\nsatisfy the assumptions of Lemma \\ref{lemma-serie-rv}.\nMore precisely, setting ${\\mathcal H}_n={\\mathcal F}_{n+1}$ we have\n\\begin{equation*}\n\\begin{split}\nE[Y_n\\,|\\,{\\mathcal H }_{n-1}] =\nE[\\beta_{n+1}\\, |\\, {\\mathcal F}_n]\n\\ \\stackrel{a.s}\\longrightarrow\\ \\beta,\n\\end{split}\n\\end{equation*}\nbecause, by \\eqref{eq:multidim-limite-conditional-M}, we get that\n\\begin{equation*}\n\\begin{split}\n&E[B_{n+1}\\,|\\,{\\mathcal F }_{n}]\\\n=\\\nV^{\\top}E[(\\Delta{\\mathbf M}_{n+1})\n(\\Delta{\\mathbf M}_{n+1})^{\\top}\\,|\\,{\\mathcal F}_n] V\\\n\\stackrel{a.s}\\longrightarrow\\ (V^{\\top}V)Z_{\\infty}(1-Z_{\\infty}),\n\\\\\n&E[\\mathbf{b}_{n+1}\\,|\\,{\\mathcal F }_{n}]\\\n=\\ V^{\\top}E[(\\Delta{\\mathbf M}_{n+1})\n(\\Delta{\\mathbf M}_{n+1})^{\\top}\\,|\\,{\\mathcal F}_n] \\mathbf{v}_1\\\n\\stackrel{a.s}\\longrightarrow\\ (V^{\\top}\\mathbf{v}_1)Z_{\\infty}(1-Z_{\\infty}),\n\\\\\n&E[b_{n+1}\\,|\\,{\\mathcal F }_{n}]\\\n=\\ \\mathbf{v}_1^{\\top}E[(\\Delta{\\mathbf M}_{n+1})\n(\\Delta{\\mathbf M}_{n+1})^{\\top}\\,|\\,{\\mathcal F}_n]\\mathbf{v}_1\n\\stackrel{a.s}\\longrightarrow\\ \\|\\mathbf{v}_1\\|^2Z_{\\infty}(1-Z_{\\infty}).\n\\end{split}\n\\end{equation*}\nMoreover, we have\n$$\n\\sum_{k}\\frac{ E[\\,|Y_k|^2] }{ c_k^2 }=\\sum_k E[\\,|Y_k|^2]r_k^4 k^2=\n\\sum_k r_k^4 O(k^{2})=\\sum_k O(1\/k^{2})<+\\infty.\n$$\nIn addition, since\n$|v^{(e)}_{n,k}|\/c_k= n r_k^2\\ln^e(n\/k)|F_{k+1,n}(x)F_{k+1,n}(y)|$,\nfrom~\\eqref{affermazione3} in Lemma~\\ref{lemma-tecnico_2} (with $u=1$)\nit follows that $\\sum_{k=m_0}^{n-1}\\frac{|v^{(e)}_{n,k}|}{c_k}=O(1)$.\nAnalogously, using again Lemma~\\ref{lemma-tecnico_2}, we can prove that\n$\\sum_{k=m_0}^{n-1}|v^{(e)}_{n,k}-v^{(e)}_{n,k-1}|=O(1)$ since by\nRemark~\\ref{rem:relations_diff_v} we have\n\\[\n\\left\\{\\begin{aligned}\n&|v^{(e)}_{n,k}-v^{(e)}_{n,k-1}|\\ =\\\nO\\Big(nr_k^2\\frac{|p_n(x)||p_n(y)|}{|p_k(x)||p_k(y)|}\\Big),\\\n&\\hbox{for } e=0,\\\\\n&|v^{(e)}_{n,k}-v^{(e)}_{n,k-1}|\\ =\\\nO\\Big(nr_k^2(\\ln(n\/k)+1)\\frac{|p_n(x)||p_n(y)|}{|p_k(x)||p_k(y)|}\\Big),\n\\ &\\hbox{for } e=1,\\\\\n&|v^{(e)}_{n,k}-v^{(e)}_{n,k-1}|\\ =\\\nO\\Big(\nnr_k^2(\\ln^2(n\/k)+\\ln(n\/k))\\frac{|p_n(x)||p_n(y)|}{|p_k(x)||p_k(y)|}\n\\Big),\n\\ &\\hbox{for } e=2.\n\\end{aligned}\\right.\n\\]\nHence, condition~\\eqref{cond-serie-rv-2} in Lemma \\ref{lemma-serie-rv}\nis satisfied and so, in order to apply this lemma, it only remains to\nprove condition~\\eqref{cond-serie-rv-1}.  To this end, we get the\nvalues of $\\lim_n\\sum_{k=m_0}^n v^{(e)}_{n,k}\/c_k$ by\n\\eqref{affermazione2} in Lemma \\ref{lemma-tecnico_2}, and we observe\nthat $\\lim_n v^{(e)}_{n,n}=s\\in\\{0,1\\}$ and, for a fixed $k$,\n$\\lim_n|v^{(e)}_{n,k}|=0$ since by~Lemma \\ref{lemma-tecnico_1} we have\n$|p_n(x)p_n(y)|=O(n^{-c(a_x+a_y)})=o((n\\ln^e(n))^{-1})$.\\\\\n\nNow that we have proved the convergences in~\\eqref{eq:results_limits},\nwe can use the relations in~\\eqref{def:terms_in_A_k_n_B_k} to compute\nthe almost sure limits of all the elements in~\\eqref{eq:matrix}.  The\nresults are listed below, while the technical computations are\nreported in\nAppendix~\\ref{subsubsection_appendix_technical_computation_1}.\n\\begin{itemize}\n\\item $n\\sum_{k=m_0}^{n-1} r_k^2 [A^{1}_{k+1,n}B_{k+1}A^{1}_{k+1,n}]_{h,j}\\stackrel{a.s}\\longrightarrow\n\\frac{c^2}{c(\\alpha_h+\\alpha_j)-1}(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty});$\n\\item $n\\sum_{k=m_0}^{n-1} r_k^2 [A^{3}_{k+1,n}B_{k+1}A^{3}_{k+1,n}]_{h,j}\\stackrel{a.s}\\longrightarrow\n\\frac{1+(c-1)(\\alpha_h^{-1}+\\alpha_j^{-1})}{c(\\alpha_h+\\alpha_j)-1}(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty})$;\n\\item $n\\sum_{k=m_0}^{n-1} r_k^2 (a^{2}_{k+1,n})^2b_{k+1}\\stackrel{a.s}\\longrightarrow (c-1)^2\\|\\mathbf{v}_1\\|^2Z_{\\infty}(1-Z_{\\infty})$;\n\\item $n\\sum_{k=m_0}^{n-1} r_k^2 [A^{1}_{k+1,n}B_{k+1}A^{3}_{k+1,n}]_{h,j}\\stackrel{a.s}\\longrightarrow\n\\frac{\\alpha_h^{-1}(c-1)+c}{c(\\alpha_h+\\alpha_j)-1}(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty})$;\n\\item $n\\sum_{k=m_0}^{n-1} r_k^2 a^{2}_{k+1,n}[\\mathbf{b}_{k+1}^{\\top}A^{1}_{k+1,n}]_{j}\\stackrel{a.s}\\longrightarrow\n\\frac{1-c}{\\alpha_j}(\\mathbf{v}_1^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty})$;\n\\item $n\\sum_{k=m_0}^{n-1} r_k^2 a^{2}_{k+1,n}[\\mathbf{b}_{k+1}^{\\top}A^{3}_{k+1,n}]_{j}\\stackrel{a.s}\\longrightarrow\n\\frac{1-c}{\\alpha_j}(\\mathbf{v}_1^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty})$.\n\\end{itemize}\n\nHence, recalling the definitions of the matrices\n$\\widehat{S}_{\\mathbf{ZZ}}, \\widehat{S}_{\\mathbf{NN}}$ and\n$\\widehat{S}_{\\mathbf{ZN}}$ given in~\\eqref{def:Shat_ZZ},\n\\eqref{def:Shat_NN_1}, \\eqref{def:Shat_NN_2}, \\eqref{def:Shat_ZN_1}\nand \\eqref{def:Shat_ZN_2}, we obtain \n\\begin{equation*}\\begin{aligned}\n&Z_\\infty(1-Z_\\infty)\\widehat{S}_{\\mathbf{ZZ}}\\ =\\\na.s.-\\lim_{n\\rightarrow\\infty}n\\sum_{k=m_0}^{n-1} r_k^2A^{1}_{k+1,n}B_{k+1}A^{1}_{k+1,n},\\\\\n&Z_\\infty(1-Z_\\infty)\\widehat{S}_{\\mathbf{NN}}\\ =\\\na.s.-\\lim_{n\\rightarrow\\infty}n\\sum_{k=m_0}^{n-1} r_k^2\n\\begin{pmatrix}\n(a^{2}_{k+1,n})^2b_{k+1} & a^{2}_{k+1,n}\\mathbf{b}_{k+1}^{\\top}A^{3}_{k+1,n}\\\\\na^{2}_{k+1,n}A^{3}_{k+1,n}\\mathbf{b}_{k+1} & A^{3}_{k+1,n}B_{k+1}A^{3}_{k+1,n}\n\\end{pmatrix},\\\\\n&Z_\\infty(1-Z_\\infty)\\widehat{S}_{\\mathbf{ZN}}\\ =\\\na.s.-\\lim_{n\\rightarrow\\infty}n\\sum_{k=m_0}^{n-1} r_k^2\n\\begin{pmatrix}\na^{2}_{k+1,n}A^{1}_{k+1,n}\\mathbf{b}_{k+1} & A^{1}_{k+1,n}B_{k+1}A^{3}_{k+1,n}\n\\end{pmatrix}.\n\\end{aligned}\n\\end{equation*}\nTherefore, using~\\eqref{eq:matrix}, we can state that\n$$\\sum_{k=m_0}^n (\\sqrt{n}\\mathbf{T}_{n,k})(\\sqrt{n}\\mathbf{T}_{n,k})^{\\top}\\\n\\stackrel{a.s.}\\longrightarrow\\ \nZ_\\infty(1-Z_\\infty)\nU_{\\theta}\\begin{pmatrix}\n\\widehat{S}_{\\mathbf{ZZ}} & \\widehat{S}_{\\mathbf{ZN}}\\\\\n\\widehat{S}_{\\mathbf{ZN}}^{\\top} & \\widehat{S}_{\\mathbf{NN}}\n\\end{pmatrix}U^{\\top}_{\\theta}\\ =\\ \nZ_\\infty(1-Z_\\infty)\n\\begin{pmatrix}\nU\\widehat{S}_{\\mathbf{ZZ}}U^{\\top} & U\\widehat{S}_{\\mathbf{ZN}}\\widetilde{U}^{\\top}\\\\\n\\widetilde{U}\\widehat{S}_{\\mathbf{ZN}}^{\\top}U^{\\top}\n& \\widetilde{U}\\widehat{S}_{\\mathbf{NN}}\\widetilde{U}^{\\top}\n\\end{pmatrix},$$\nwhere the last matrix coincides with the one in the statement of the\ntheorem because of~\\eqref{def:Sigmahat_ZZ_1},\n\\eqref{def:Sigmahat_NN_1} and \\eqref{def:Sigmahat_ZN_1}.  \n\\\\\n\n\\indent Regarding condition $(c_3)$, we observe that, using the\ninequalities\n$$\n|{\\mathbf T}_{n,k}|=r_k |C_{k+1,n}R\\Delta{\\mathbf M}_{\\theta,k+1}|\\leq\nr_k |U||A_{k+1,n}||V^{\\top}||R||\\Delta{\\mathbf M}_{\\theta,k+1}| \\leq K r_k |A_{k+1,n}|,\n$$\nwith a suitable constant $K$, we find for any $u>1$\n\\begin{equation*}\n\\begin{split}\n\\big(\\sup_{m_0\\leq k\\leq n}|\\sqrt{n}\\mathbf{T}_{n,k}|\\big)^{2u}\n&\\leq n^{u} \\!\\sum_{k=m_0}^{n-1} |\\mathbf{T}_{n,k}|^{2u} \n+ n^{u} |\\mathbf{T}_{n,n}|^{2u}\\\\\n&=\nn^{u} O\\left(|p_{n}^*|^{2u}\\sum_{k=m_0}^{n-1} \\frac{r_k^{2u}}{|p_{k}^*|^{2u}}\\right)\n+ O\\Big( \\frac{\\ln(n)^{2u}}{n^{u-1}} \\Big)\n+ n^{u} O(r_n^{2u}),\n\\end{split}\n\\end{equation*}\nwhere, for the last equality, we have used \\eqref{eq-corretta}.  Now,\nsince $2ca^*>1$, by \\eqref{affermazione3} in Lemma\n\\ref{lemma-tecnico_2} (with $x=y=\\alpha^*=1-\\lambda^*$, $e=0$ and\n$u>1$), we have\n\\begin{equation*}\n|p_{n}^*|^{2u}\\sum_{k=m_0}^{n-1} \\frac{r_k^{2u}}{|p_{k}^*|^{2u}}\\ =\n\\begin{cases}\nO(n^{-2uca^*})\\quad &\\hbox{for } 2uca^*<2u-1,\\\\\nO(n^{-(2u-1)}\\ln(n))\\quad &\\hbox{for } 2uca^*=2u-1,\\\\\nO(n^{-(2u-1)})\\quad &\\hbox{for } 2uca^*>2u-1,\n\\end{cases}\n\\end{equation*}\n\\noindent which, in particular, implies $(\\sup_{m_0\\leq k\\leq\n  n}|\\sqrt{n}\\mathbf{T}_{n,k}|)^{2u}\\stackrel{L^1}\\longrightarrow 0$ for any\n$u>1$.  As a consequence of the above convergence to zero, condition\n(c3) of Theorem~\\ref{thm:triangular} holds true.  \\\\\n\nSumming up, all the conditions required by\nTheorem~\\ref{thm:triangular} are satisfied and so we can apply this\ntheorem and obtain the stable convergence of $\\sqrt{n}\\sum_{k=m_0}^n\n\\mathbf{T}_{n,k}$ to the Gaussian kernel with random covariance matrix defined\nin Theorem~\\ref{thm:asymptotics_theta_hat_1}.\n\\end{proof}\n\nNow, we are ready to prove Theorem \\ref{thm:asymptotics_theta_1}.\n\\\\\n\n{\\it Proof of Theorem \\ref{thm:asymptotics_theta_1}.} By\nTheorem~\\ref{thm:asymptotics_Z_tilde}, we have that\n\\begin{equation*}\n\\sqrt{n}(\\widetilde{Z}_n-Z_\\infty)\\mathbf{1}\n\\longrightarrow {\\mathcal N}\\big(\\mathbf{0},\nZ_{\\infty}(1-Z_{\\infty})\\widetilde{\\Sigma}_\\gamma\\big)\n\\ \\ \\ \\hbox{stably in the strong sense}.\n\\end{equation*}\nThus, from Theorem \\ref{thm:asymptotics_theta_hat_1}, applying\nTheorem~\\ref{blocco}, we obtain that\n$$\n\\sqrt{n}\n\\left(\n\\begin{pmatrix}\n{\\mathbf Z}_n - \\widetilde{Z}_n{\\mathbf 1}\\\\\n{\\mathbf N}_n - \\widetilde{Z}_n{\\mathbf 1}\n\\end{pmatrix},\n(\\widetilde{Z}_n-Z_\\infty)\\mathbf{1}\n\\right)\n\\longrightarrow\n\\mathcal{N}\\left(\\mathbf{0},\nZ_\\infty(1-Z_\\infty)\n\\begin{pmatrix}\n\\widehat{\\Sigma}_{\\mathbf{ZZ}} & \\widehat{\\Sigma}_{\\mathbf{ZN}}\\\\\n\\widehat{\\Sigma}_{\\mathbf{ZN}}^{\\top} & \\widehat{\\Sigma}_{\\mathbf{NN}}\n\\end{pmatrix}\n\\right)\n\\otimes\n{\\mathcal N}\\left(\\mathbf{0},\nZ_{\\infty}(1-Z_{\\infty})\\widetilde{\\Sigma}_\\gamma\\right)\n$$\nstably.  In order to conclude, it is enough to observe that\n$$\n\\sqrt{n }\n\\begin{pmatrix}\n\\mathbf{Z}_n-Z_{\\infty}\\mathbf{1}\\\\\n{\\mathbf N}_n-Z_{\\infty}\\mathbf{1}\n\\end{pmatrix}\n=\\Phi\n\\left(\n{\\mathbf Z}_n - \\widetilde{Z}_n{\\mathbf 1},\n{\\mathbf N}_n - \\widetilde{Z}_n{\\mathbf 1},\n(\\widetilde{Z}_n-Z_\\infty)\\mathbf{1}\n\\right)\\,,\n$$\nwhere $\\Phi(x,y,z)=(x+z, y+z)^{\\top}$.\n\\qed\n\n\\subsection{Proof of Theorem \\ref{thm:asymptotics_Z_1_star}\n(CLT for $({\\mathbf Z}_n,{\\mathbf N}_n)_n$ in the case $N\\geq 2$, $\\gamma=1$\nand ${\\mathcal Re}(\\lambda^{*})=1-(2c)^{-1}$)}\n\nAs above, in order to prove Theorem \\ref{thm:asymptotics_Z_1_star}, we\nneed the following convergence result on\n$(\\widehat{\\mathbf{Z}}_n, \\widehat{\\mathbf{N}}_n)_n$:\n\n\\begin{theo}\\label{thm:asymptotics_theta_1_star}\nLet $N\\geq 2$, $\\gamma=1$ and ${\\mathcal Re}(\\lambda^{*})=1-(2c)^{-1}$.\nThen, under condition~\\eqref{ass:condition_r_n_1}, we have that\n\\begin{equation*}\n\\sqrt{\\frac{n}{\\ln(n)}}\n\\begin{pmatrix}\n\\widehat{\\mathbf{Z}}_n\\\\\n\\widehat{\\mathbf{N}}_n\n\\end{pmatrix}\n{\\longrightarrow}\\\n\\mathcal{N} \\left(\\ \\mathbf{0}\\ ,\\ Z_{\\infty}(1-Z_{\\infty})\n\\begin{pmatrix}\n\\widehat{\\Sigma}^{*}_{\\mathbf{ZZ}} & \\widehat{\\Sigma}^{*}_{\\mathbf{ZN}}\\\\\n\\widehat{\\Sigma}_{\\mathbf{ZN}}^{*\\top} & \\widehat{\\Sigma}^{*}_{\\mathbf{NN}}\n\\end{pmatrix}\\\n\\right)\\ \\ \\ \\ stably,\n\\end{equation*}\nwhere $\\widehat{\\Sigma}^{*}_{\\mathbf{ZZ}}$, $\\widehat{\\Sigma}^{*}_{\\mathbf{NN}}$ and\n$\\widehat{\\Sigma}^{*}_{\\mathbf{ZN}}$ are the matrices defined\nin~\\eqref{def:Sigmahat_ZZ_1_star},~\\eqref{def:Sigmahat_NN_1_star}\nand~\\eqref{def:Sigmahat_ZN_1_star}, respectively.\n\\end{theo}\n\n\\begin{proof} The proof of Theorem~\\ref{thm:asymptotics_theta_1_star} follows\nanalogous arguments to those used in\nTheorem~\\ref{thm:asymptotics_theta_hat_1}.  In particular, consider\nthe joint dynamics of $\\boldsymbol{\\theta}_n:=\n(\\widehat{\\mathbf{Z}}_{n},\\widehat{\\mathbf{N}}_{n})^{\\top}$ defined\nin~\\eqref{eq:dynamic_SA_theta_proof} as follows:\n$$\\boldsymbol{\\theta}_{n+1}=\nC_{m_0,n}\\boldsymbol{\\theta}_{m_0}+\n\\sum_{k=m_0}^n {\\mathbf T}_{n,k}+\\boldsymbol{\\rho}_{n},\\qquad\\mbox{where}\n\\qquad \\left\\{\n\\begin{aligned}\n&{\\mathbf T}_{n,k}=r_k C_{k+1,n} R\\Delta{\\mathbf M}_{\\theta,k+1},\\\\\n&\\boldsymbol{\\rho}_{n}=\\sum_{k=m_0}^nr_k C_{k+1,n} {\\mathbf R}_{\\theta,k+1},\n\\end{aligned}\\right.$$\nwhere $C_{k+1,n}$ is defined\nin~\\eqref{def:C_k_n_A_k_n}, $R$ is defined in\n\\eqref{def:R-irene},\n$\\Delta\\mathbf{M}_{\\theta,n}=(\\Delta\\mathbf{M}_n,\\Delta\\mathbf{M}_n)^{\\top}$ and\n$\\mathbf{R}_{\\theta,n}=(\\mathbf{0},\\mathbf{R}_n)^{\\top}$ with\n$\\mathbf{R}_n$ defined in~\\eqref{def:R_n}.  Then, we are going to prove that\n$\\sqrt{n\/\\ln(n)}\\sum_{k=m_0}^n {\\mathbf T}_{n,k}$ converges stably to the desired\nGaussian kernel, while $\\sqrt{n\/\\ln(n)}|C_{m_0,n}\\boldsymbol{\\theta}_{m_0}|$ and\n$\\sqrt{n\/\\ln(n)}|\\boldsymbol{\\rho}_{n}|$ converge almost surely to zero.\n\\\\\n\nFirst, note that by \\eqref{eq-corretta}, we have that\n\\begin{equation}\\label{eq-corretta-2}\n\\begin{split}\n|A_{k+1,n}|&=O\\left(\\frac{|p_n^*|}{|p_k^*|}\\right)\n+O\\left(\\frac{k}{n}\\ln(n)\\right)\n=O\\left( \\Big(\\frac{k}{n}\\Big)^{ca^*} \\right)\n+O\\left(\\frac{k}{n}\\ln(n)\\right)\n\\\\\n&=O\\left( \\Big(\\frac{k}{n}\\Big)^{1\/2} \\right)\n+O\\left(\\frac{k}{n}\\ln(n)\\right)\n\\quad\\hbox{for } m_0-1\\leq k\\leq n-1,\n\\end{split}\n\\end{equation}\nwhere, as before, the symbol $^*$ refers to the quantities\n$a_{\\alpha_j}:={\\mathcal Re}(\\alpha_j)$ and $p_n(\\alpha_j)$\ncorresponding to $\\alpha^*=\\alpha_j=1-\\lambda_j$ with\n$\\lambda_j=\\lambda^*\\in \\lambda_{\\max}(D)$, and hence the last passage\nfollows since $ca^*=1\/2$ by assumption. As a consequence, we obtain\n\\begin{equation*\n|C_{m_0,n}\\boldsymbol{\\theta}_{m_0}|\\ =\\\nO\\left(n^{-1\/2}\\right) +O\\left(\\frac{\\ln(n)}{n}\\right)\n\\end{equation*}\nand so  $\\sqrt{n\/\\ln(n)} |C_{m_0,n}\\boldsymbol{\\theta}_{m_0}|\\rightarrow0$\nalmost surely.\\\\\n\n\\indent Concerning the term $\\boldsymbol{\\rho}_{n}$, notice that\nby~\\eqref{ass:condition_r_n_1} and~\\eqref{def:R_n} we have that\n$|\\mathbf{R}_k|=O(k^{-1})$ and, by \\eqref{eq-corretta-2}, we have that\n\\begin{equation*}\n|C_{k+1,n}|\\ =\\ O\\left(\\ \\left(\\frac{k}{n}\\right)^{1\/2}\\ \\right)\n+O\\left(\\frac{k}{n}\\ln(n)\\right)\n\\quad\\hbox{for } m_0\\leq k\\leq n-1.\n\\end{equation*}\nTherefore, since $\\boldsymbol{\\rho}_{n}=\\sum_{k=m_0}^nr_k C_{k+1,n}\n{\\mathbf R}_{\\theta,k+1}=\\sum_{k=m_0}^{n-1} r_k C_{k+1,n} {\\mathbf\n  R}_{\\theta,k+1} + r_nC_{n+1,n}{\\mathbf R}_{\\theta,n+1}$, it follows\n(by \\eqref{relazione-nota}) that\n\\begin{equation*}\n\\sqrt{n\/\\ln(n)}|\\boldsymbol{\\rho}_{n}|\\ =\\\nO\\left( 1\/\\sqrt{\\ln(n)}\n\\sum_{k=m_0}^{n-1} k^{-3\/2}\n\\right)\n+\nO\\left( n^{-1\/2} \\ln(n)^{3\/2} \\right)\n+\nO\\left(n^{-3\/2} \\ln(n)^{-1\/2}\\right)\n\\longrightarrow 0\\quad \\hbox{a.s.}\\,.\n\\end{equation*}\n\n\\indent We now focus on the proof of the fact that\n$\\sqrt{n\/\\ln(n)}\\sum_{k=m_0}^n{\\mathbf T}_{n,k}$ converges stably to the \nsuitable Gaussian kernel.  For this purpose, we set ${\\mathcal\n  G}_{n,k}={\\mathcal F}_{k+1}$, and consider\nTheorem~\\ref{thm:triangular}.  Given the fact that condition $(c1)$ of\nTheorem~\\ref{thm:triangular} is obviously satisfied, we will check\nonly conditions $(c2)$ and $(c3)$.\\\\\n\nRegarding condition $(c2)$, from the computations seen in the proof of\nTheorem~\\ref{thm:asymptotics_theta_hat_1} and using the fact that\n$O(nr_n^2\/\\ln(n))=O(n^{-1}\/\\ln(n))\\to 0$, we have\n\\[\\begin{aligned}\n&a.s.-\\lim_n\\sum_{k=m_0}^n \\left(\\sqrt{\\frac{n}{\\ln(n)}}\\mathbf{T}_{n,k}\\right)\n\\left(\\sqrt{\\frac{n}{\\ln(n)}}\\mathbf{T}_{n,k}\\right)^{\\top}\\\n=\\\\\n&U_{\\theta}\\left(a.s.-\\lim_n\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2\nA_{k+1,n}S_R\\,V_{\\theta}^{\\top}\n\\,(\\Delta{\\mathbf M}_{\\theta,k+1})(\\Delta{\\mathbf M}_{\\theta,k+1})^{\\top}\\,\nV_{\\theta}\\, S_RA^{\\top}_{k+1,n}\\right)U_{\\theta}^{\\top}.\n\\end{aligned}\n\\]\nThen, setting $B_{\\theta,k+1}$ as in~\\eqref{def:B_matrix},\nthe limit of the above expression can be obtain by studying the\nconvergence of the following matrix:\n\\begin{equation}\\label{eq:matrix_star}\n\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2\n\\begin{pmatrix}\nA^{1}_{k+1,n}B_{k+1}A^{1}_{k+1,n} & a^{2}_{k+1,n}A^{1}_{k+1,n}\\mathbf{b}_{k+1}\n& A^{1}_{k+1,n}B_{k+1}A^{3}_{k+1,n}\\\\\na^{2}_{k+1,n}\\mathbf{b}_{k+1}^{\\top}A^{1}_{k+1,n} & (a^{2}_{k+1,n})^2b_{k+1}\n& a^{2}_{k+1,n}\\mathbf{b}_{k+1}^{\\top}A^{3}_{k+1,n}\\\\\nA^{3}_{k+1,n}B_{k+1}A^{1}_{k+1,n} & a^{2}_{k+1,n}A^{3}_{k+1,n}\\mathbf{b}_{k+1}\n& A^{3}_{k+1,n}B_{k+1}A^{3}_{k+1,n}\n\\end{pmatrix},\\end{equation}\nwhere $A^{1}_{k+1,n},a^{2}_{k+1,n},A^{3}_{k+1,n}$ are defined\nin~\\eqref{def:terms_in_A_k_n_B_k}.  Notice that the almost sure convergences\nof all the elements in~\\eqref{eq:matrix_star} can be obtained by\ncombining the results of the following limits:\n\\begin{equation}\\label{eq:results_limit_star}\n\\begin{split}\n&\\frac{n}{\\ln(n)}\n\\sum_{k=m_0}^{n-1} r_k^2 \\beta_{k+1}\n\\ln^e\\left(\\frac{n}{k}\\right)F_{k+1,n}(x)F_{k+1,n}(y)\\\n\\stackrel{a.s}\\longrightarrow\\ 0,\n\\quad\\hbox{with } c(a_x+a_y)>1\\,\\hbox{and}\\,\ne=0,1,2,\\\\\n&\\frac{n}{\\ln(n)}\n\\sum_{k=m_0}^{n-1} r_k^2 \\beta_{k+1}\nF_{k+1,n}(x)F_{k+1,n}(y)\\\n\\stackrel{a.s}\\longrightarrow\\\n\\left\\{\\begin{aligned}\n&c^2\\beta\\ &\\mbox{ if }c(a_x+a_y)=1\\mbox{ and }b_x+b_y=0,\\\\\n&0\\ &\\mbox{ if }c(a_x+a_y)=1\\mbox{ and }b_x+b_y\\neq0,\n\\end{aligned}\\right.\n\\end{split}\n\\end{equation}\nfor certain complex numbers $x,y\\in\\{\\alpha_j,\\,2\\leq j\\leq N\\}$ with\n$a_x:={\\mathcal Re}(x)$, $b_x:={\\mathcal Im}(x)$, $a_y:={\\mathcal Re}(y)$\nand $b_y:={\\mathcal Im}(y)$ (remember that, by the assumption on\n${\\mathcal Re}(\\lambda^*)$, we can have both cases $c(a_x+a_y)>1$ and\n$c(a_x+a_y)=1$), a suitable sequence of random variables\n$\\beta_{k}\\in\\{[B_{k}]_{h,j},[\\mathbf{b}_{k}]_{j},b_{k};\\, 2\\leq\nh,j\\leq N\\}$ and some random variable $\\beta$.  \\\\\n\nIn order to prove the convergence in \\eqref{eq:results_limit_star} for the\ncase $c(a_x+a_y)>1$, we can use the convergences in~\\eqref{eq:results_limits}\nestablished in the proof of Theorem~\\ref{thm:asymptotics_theta_hat_1};\nwhile for the case $c(a_x+a_y)=1$ we can apply Lemma\n\\ref{lemma-serie-rv} since each quantity\nin~\\eqref{eq:results_limit_star} can be written as $\\sum_{k=m_0}^{n-1}\nv_{n,k}Y_k\/c_k$, where\n$$\nY_k=\\beta_{k+1},\n\\quad\nc_k=\\frac{1}{kr_k^2}\n\\quad\\mbox{and }\\quad\nv_{n,k}=\\frac{1}{\\ln(n)}\\left(\\frac{n}{k}\\right)F_{k+1,n}(x)F_{k+1,n}(y)\n$$\nsatisfy the assumptions of Lemma \\ref{lemma-serie-rv}.  Indeed,\nsimilarly as in the proof of Theorem~\\ref{thm:asymptotics_theta_hat_1},\nwe have\n$$\n\\sum_{k}\\frac{ E[\\,|Y_k|^2] }{ c_k^2 }<+\\infty,\\;\nE[[B_{k+1}]_{h,j}|{\\mathcal F}_n] \\stackrel{a.s}\\rightarrow\n(\\mathbf{v}_h^{\\top}\\mathbf{v}_j),\\;\nE[[\\mathbf{b}_{k+1}]_{j}|{\\mathcal F}_n]\n\\stackrel{a.s}\\rightarrow (\\mathbf{v}_j^{\\top}\\mathbf{v}_1)\n\\;\\hbox{and }\nE[b_{k+1}|{\\mathcal F}_n] \\stackrel{a.s}\\rightarrow\n\\|\\mathbf{v}_1\\|^2.$$\nIn addition, since\n$|v_{n,k}|\/c_k=(n\/\\ln(n))r_k^2|F_{k+1,n}(x)F_{k+1,n}(y)|$,\nfrom~\\eqref{affermazione3_log} in Lemma~\\ref{lemma-tecnico_2} (with\n$u=1$) it follows that\n$\\sum_{k=m_0}^{n-1}\\frac{|v_{n,k}|}{c_k}=O(1)$.  Moreover, we\nhave that $\\sum_{k=m_0}^{n-1}|v_{n,k}-v_{n,k-1}|=O(1)$ since by\nRemark~\\ref{rem:relations_diff_v} we have\n\\[|v_{n,k}-v_{n,k-1}|\\ =\\ \\left\\{\\begin{aligned}\n&O(k^{-1}\/\\ln(n))\\ &\\mbox{ if }b_x+b_y \\neq 0,\\\\\n&O(k^{-2}\/\\ln(n))\\ &\\mbox{ if }b_x+b_y = 0.\n\\end{aligned}\\right.\\]\nHence, condition~\\eqref{cond-serie-rv-2} of Lemma \\ref{lemma-serie-rv}\nis satisfied and so, in order to apply this lemma, it only remains to\nprove condition~\\eqref{cond-serie-rv-1}.  To this end, we get the\nvalue of $\\lim_n\\sum_{k=m_0}^{n-1} v_{n,k}\/c_k$ from\n\\eqref{affermazione2_log} in Lemma \\ref{lemma-tecnico_2}, and we\nobserve that $\\lim_n v_{n,n}=0$ and, for a fixed $k$,\n$\\lim_n|v_{n,k}|=0$ since by Lemma~\\ref{lemma-tecnico_1} we have\n$|p_n(x)p_n(y)|=O(n^{-1})$.\\\\\n\nNow that we have proved the convergences\nin~\\eqref{eq:results_limit_star}, we can use the relations\nin~\\eqref{def:terms_in_A_k_n_B_k} to compute the almost sure limits of\nall the elements in~\\eqref{eq:matrix_star}.  The results are listed\nbelow, while the technical computations are reported in\nAppendix~\\ref{subsubsection_appendix_technical_computation_1_star}.\n\\begin{itemize}\n\\item $\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2[A^{1}_{k+1,n}B_{k+1}A^{1}_{k+1,n}]_{h,j}\\stackrel{a.s}\\longrightarrow\n(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty})c^2\\ind_{\\{b_{\\alpha_h}+b_{\\alpha_j}=0\\}}$;\n\\item $\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2 [A^{3}_{k+1,n}B_{k+1}A^{3}_{k+1,n}]_{h,j}\\stackrel{a.s}\\longrightarrow\n(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty})\\frac{(\\alpha_h-1)(\\alpha_j-1)}{\\alpha_h\\alpha_j}\\ind_{\\{ b_{\\alpha_h}+b_{\\alpha_j}=0\\}}$;\n\\item $\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2b_{k+1}(a^{2}_{k+1,n})^2\\stackrel{a.s}\\longrightarrow0$;\n\\item $\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2[A^{1}_{k+1,n}B_{k+1}A^{3}_{k+1,n}]_{h,j}\\stackrel{a.s}\\longrightarrow\n(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty})\\frac{c(1-\\alpha_j)}{\\alpha_h}\\ind_{\\{b_{\\alpha_h}+b_{\\alpha_j}=0\\}}$;\n\\item $\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2 a^{2}_{k+1,n}[\\mathbf{b}_{k+1}^{\\top}A^{1}_{k+1,n}]_{j}\\stackrel{a.s}\\longrightarrow0$;\n\\item $\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2 a^{2}_{k+1,n}[\\mathbf{b}_{k+1}^{\\top}A^{3}_{k+1,n}]_{j}\\stackrel{a.s}\\longrightarrow0$.\n\\end{itemize}\n\nHence, recalling the definitions of the matrices\n$\\widehat{S}^{*}_{\\mathbf{ZZ}}, \\widehat{S}^{*}_{\\mathbf{NN}}$ and\n$\\widehat{S}^{*}_{\\mathbf{ZN}}$ given in~\\eqref{def:Shat_ZZ_star},\n\\eqref{def:Shat_NN_star} and \\eqref{def:Shat_ZN_star}, we obtain \n\\begin{equation*}\\begin{aligned}\n&Z_\\infty(1-Z_\\infty)\\widehat{S}^{*}_{\\mathbf{ZZ}}\\ =\\\na.s.-\\lim_{n\\rightarrow\\infty}n\\sum_{k=m_0}^{n-1} r_k^2A^{1}_{k+1,n}B_{k+1}A^{1}_{k+1,n},\\\\\n&Z_\\infty(1-Z_\\infty)\\widehat{S}^{*}_{\\mathbf{NN}}\\ =\\\na.s.-\\lim_{n\\rightarrow\\infty}n\\sum_{k=m_0}^{n-1} r_k^2A^{3}_{k+1,n}B_{k+1}A^{3}_{k+1,n},\\\\\n&Z_\\infty(1-Z_\\infty)\\widehat{S}^{*}_{\\mathbf{ZN}}\\ =\\\na.s.-\\lim_{n\\rightarrow\\infty}n\\sum_{k=m_0}^{n-1} r_k^2A^{1}_{k+1,n}B_{k+1}A^{3}_{k+1,n}.\n\\end{aligned}\n\\end{equation*}\nTherefore, using~\\eqref{eq:matrix_star}, we can state that\n\\begin{equation*}\n\\begin{split}\n\\sum_{k=m_0}^n\n\\left(\\sqrt{\\frac{n}{\\ln(n)}}\\mathbf{T}_{n,k}\\right)\n\\left(\\sqrt{\\frac{n}{\\ln(n)}}\\mathbf{T}_{n,k}\\right)^{\\top}\n&\\ \\stackrel{a.s.}\\longrightarrow\\\nZ_\\infty(1-Z_\\infty)\nU_{\\theta}\n\\begin{pmatrix}\n\\widehat{S}^{*}_{\\mathbf{ZZ}} & \\mathbf{0} & \\widehat{S}^{*}_{\\mathbf{ZN}}\\\\\n\\mathbf{0}^{\\top} & 0 &  \\mathbf{0}^{\\top}\\\\\n\\widehat{S}_{\\mathbf{ZN}}^{*\\top} & \\mathbf{0} & \\widehat{S}^{*}_{\\mathbf{NN}}\n\\end{pmatrix}\nU^{\\top}_{\\theta}\n\\\\\n&\\ =\\\nZ_\\infty(1-Z_\\infty)\n\\begin{pmatrix}\nU\\widehat{S}^{*}_{\\mathbf{ZZ}}U^{\\top} & U\\widehat{S}^{*}_{\\mathbf{ZN}}U^{\\top}\\\\\nU\\widehat{S}_{\\mathbf{ZN}}^{*\\top}U^{\\top} & U\\widehat{S}^{*}_{\\mathbf{NN}}U^{\\top}\n\\end{pmatrix},\n\\end{split}\n\\end{equation*}\nwhere the last matrix coincides with the one in the statement of\nthe theorem because of~\\eqref{def:Sigmahat_ZZ_1_star},\n\\eqref{def:Sigmahat_NN_1_star} and \\eqref{def:Sigmahat_ZN_1_star}. \n\\\\\n\n\\indent Regarding condition $(c_3)$, we observe that, using the\ninequalities\n$$\n|{\\mathbf T}_{n,k}|=r_k |C_{k+1,n}R\\Delta{\\mathbf M}_{\\theta,k+1}|\\leq\nr_k |U||A_{k+1,n}||V^{\\top}||R||\\Delta{\\mathbf M}_{\\theta,k+1}| \\leq\nK r_k |A_{k+1,n}|,\n$$\nwith a suitable constant $K$, we find for any $u>1$\n\\begin{align*}\n\\left(\\sup_{m_0\\leq k\\leq\n    n}\\Big|\\sqrt{\\frac{n}{\\ln(n)}}\\mathbf{T}_{n,k}\\Big|\\right)^{2u} &\\leq\n  \\left(\\frac{n}{\\ln(n)}\\right)^{u} \\sum_{k=m_0}^{n-1}\n  |\\mathbf{T}_{n,k}|^{2u} + \\left(\\frac{n}{\\ln(n)}\\right)^{u}\n  |\\mathbf{T}_{n,n}|^{2u}\n  \\\\ &= \\left(\\frac{n}{\\ln(n)}\\right)^{u}\n  O\\left(|p_{n}^*|^{2u} \\sum_{k=m_0}^{n-1}\n  \\frac{r_k^{2u}}{|p_{k}^*|^{2u}}\\right)\n+\nO\\left(\\frac{\\ln(n)^{u}}{n^{u-1}}\\right)\n+\n \\left(\\frac{n}{\\ln(n)}\\right)^{u} O(r_n^{2u}),\n\\end{align*}\nwhere, for the last equality, we have used \\eqref{eq-corretta-2}. Now,\nsince $2ca^*=1$, by \\eqref{affermazione3_log} in Lemma\n\\ref{lemma-tecnico_2} (with $x=y=\\alpha^*=1-\\lambda^*$ and $u>1$), we\nhave\n\\begin{equation*}\n|p_{n}^*|^{2u}\\sum_{k=m_0}^{n-1}\n\\frac{r_k^{2u}}{|p_{k}^*|^{2u}}\\ =\\ O(n^{-u}),\n\\end{equation*}\nwhich, in particular, implies $(\\sup_{m_0\\leq k\\leq\n  n}|\\sqrt{(n\/\\ln(n))}\\mathbf{T}_{n,k}|)^{2u}\\stackrel{L^1}\\longrightarrow0$\nfor any $u>1$.  As a consequence of the above convergence to zero,\ncondition (c3) of Theorem~\\ref{thm:triangular} holds true.  \\\\\n\nSumming up, all the conditions required by\nTheorem~\\ref{thm:triangular} are satisfied and so we can apply this\ntheorem and obtain the stable convergence of\n$\\sqrt{n\/\\ln(n)}\\sum_{k=m_0}^n \\mathbf{T}_{n,k}$ to the Gaussian\nkernel with random covariance matrix defined in\nTheorem~\\ref{thm:asymptotics_theta_1_star}.\n\\end{proof}\n\nNow, we are ready to prove Theorem \\ref{thm:asymptotics_Z_1_star}.\n\\\\\n\n{\\it Proof of Theorem \\ref{thm:asymptotics_Z_1_star}.} By\nTheorem~\\ref{thm:asymptotics_Z_tilde}, we have that\n\\begin{equation*}\n\\sqrt{n}(\\widetilde{Z}_n-Z_\\infty)\n\\longrightarrow {\\mathcal N}\\big(0,\nZ_{\\infty}(1-Z_{\\infty})\\widetilde{\\sigma}_\\gamma^2\\big)\n\\ \\ \\ \\hbox{stably}.\n\\end{equation*}\nMoreover, from Theorem \\ref{thm:asymptotics_theta_1_star}, we have that\n$$\n\\sqrt{\\frac{n}{\\ln(n)}}\n\\begin{pmatrix}\n{\\mathbf{Z}}_n-\\widetilde{Z}_n\\mathbf{1}\\\\\n{\\mathbf{N}}_n-\\widetilde{Z}_n\\mathbf{1}\n\\end{pmatrix}\n{\\longrightarrow}\\\n\\mathcal{N} \\left(\\ \\mathbf{0}\\ ,\\ Z_{\\infty}(1-Z_{\\infty})\n\\begin{pmatrix}\n\\widehat{\\Sigma}^{*}_{\\mathbf{ZZ}} & \\widehat{\\Sigma}^{*}_{\\mathbf{ZN}}\\\\\n\\widehat{\\Sigma}_{\\mathbf{ZN}}^{*\\top} & \\widehat{\\Sigma}^{*}_{\\mathbf{NN}}\n\\end{pmatrix}\\\n\\right)\\ \\ \\ \\ \\hbox{stably}.\n$$\nIn order to conclude, it is enough to observe that\n\\begin{equation*}\n\\sqrt{\\frac{n}{\\ln(n)}}\n\\begin{pmatrix}\n\\mathbf{Z}_n-Z_{\\infty}\\mathbf{1}\\\\\n\\mathbf{N}_n-Z_{\\infty}\\mathbf{1}\n\\end{pmatrix}\n=\n\\sqrt{\\frac{n}{\\ln(n)}}\n\\begin{pmatrix}\n{\\mathbf{Z}}_n-\\widetilde{Z}_n\\mathbf{1}\\\\\n{\\mathbf{N}}_n-\\widetilde{Z}_n\\mathbf{1}\n\\end{pmatrix}\n+\n\\sqrt{\\frac{1}{\\ln(n)}}\\sqrt{n}\n(\\widetilde{Z}_n-Z_{\\infty})\n\\begin{pmatrix}\n\\mathbf{1}\\\\\n\\mathbf{1}\n\\end{pmatrix},\n\\end{equation*}\nwhere the last term converges in probability to zero.\n\\qed\n\n\\begin{center}\n{\\bf Acknowledgments}\n\\end{center}\n\n\\noindent Irene Crimaldi and Andrea Ghiglietti are members of the\nItalian group ``Gruppo Nazionale per l'Analisi Matematica, la\nProbabilit\\`a e le loro Applicazioni (GNAMPA)'' of the Italian\nInstitute ``Istituto Nazionale di Alta Matematica (INdAM)''.\\\\ Giacomo\nAletti is a member of the Italian group ``Gruppo Nazionale per il\nCalcolo Scientifico (GNCS)'' of the Italian Institute ``Istituto\nNazionale di Alta Matematica (INdAM)''.\n\n\\newpage\n\\appendi\n\n\\begin{center}\n\\huge{{\\bf Appendix}}\n\\end{center}\n\n\\section{Some technical results}\\label{app-A}\n\nIn all the sequel, given $(a_n)_n, (b_n)_n$ two sequences of real\nnumbers with $b_n\\geq 0$, the notation $a_n=O(b_n)$ means $|a_n|\\leq C\nb_n$ for a suitable constant $C>0$ and $n$ large enough.  Therefore,\nif we also have $a_n^{-1}=O(b_n^{-1})$, then $C'b_n\\leq |a_n|\\leq C\nb_n$ for suitable constants $C,C'>0$ and $n$ large enough. Moreover,\ngiven $(z_n)_n, (z'_n)_n$ two sequences of complex numbers, with\n$z'_n\\neq 0$, the notation $z_n=o(z'_n)$ means $\\lim_n z_n\/z'_n=0$.\n\n\\subsection{Asymptotic results for sums of complex numbers}\n\nWe start recalling an extension of the Toeplitz lemma (see\n\\cite{lin-ros}) to complex numbers provided in \\cite{ale-cri-ghi},\nfrom which we get useful technical results employed in our proofs.\n\n\\begin{lem}{\\cite[Lemma A.2]{ale-cri-ghi}}\\label{toeplitz-lemma-complex} \n(Generalized Toeplitz lemma)\\\\\nLet $\\{z_{n,k}:\\, 1\\leq k\\leq k_n\\}$ be a\ntriangular array of complex numbers such that\n\\begin{itemize}\n\\item[i)] $\\lim_n z_{n,k}=0$ for each fixed $k$;\n\\item[ii)] $\\lim_n \\sum_{k=1}^{k_n} z_{n,k}=s\\in\\{0,1\\}$;\n\\item[iii)] $\\sum_{k=1}^{k_n} |z_{n,k}|=O(1)$.\n\\end{itemize}\nLet $(w_n)_n$ be a sequence of complex numbers with $\\lim_n\nw_n=w\\in{\\mathbb C}$. Then, we have $\\lim_n \\sum_{k=1}^{k_n}\nz_{n,k}w_k=s w$.\n\\end{lem}\n\nFrom this lemma we can easily get the following corollary, which\nslightly extends the generalized version of the Kronecker lemma\nprovided in \\cite[Corollary A.3]{ale-cri-ghi}:\n\n\\begin{cor}\\label{kronecker-complex} (Generalized Kronecker lemma)\\\\\nLet $\\{v_{n,k}:1\\leq k\\leq n\\}$ and $(z_n)_n$ be respectively a\ntriangular array and a sequence of complex numbers such that\n $v_{n,k}\\neq 0$ and\n$$\n\\lim_n v_{n,k}=0,\\quad\\lim_n v_{n,n}\\;\\hbox{exists finite},\\quad\n\\sum_{k=1}^n \\left|v_{n,k}-v_{n,k-1}\\right|=O(1)\n$$\nand $\\sum_n z_n$ is convergent. Then\n$$\n\\lim_n \\sum_{k=1}^n v_{n,k}z_k=0.\n$$\n\\end{cor}\n\\begin{proof}\nWithout loss of generality, we can suppose $\\lim_n\nv_{n,n}=s\\in\\{0,1\\}$.  Set $w_n=\\sum_{k=n}^{+\\infty} z_k$ and observe\nthat, since $\\sum_n z_n$ is convergent, we have $\\lim_n w_n=w=0$ and,\nmoreover, we can write\n\\begin{equation*}\n\\sum_{k=1}^n v_{n,k}z_k\\ =\\ \\sum_{k=1}^n v_{n,k}(w_k-w_{k+1})\\\n=\\ \\sum_{k=2}^n (v_{n,k}-v_{n,k-1})w_k +v_{n,1}w_1-v_{n,n}w_{n+1}.\n\\end{equation*}\nThe second and the third term obviously converge to zero. In order to\nprove that the first term converges to zero, it is enough to apply\nLemma \\ref{toeplitz-lemma-complex} with $z_{n,k}=v_{n,k}-v_{n,k-1}$.\n\\end{proof}\n\nThe above corollary is useful to get the following result for complex\nrandom variables, which again slightly extends the version provided in\n\\cite[Lemma A.3]{ale-cri-ghi}:\n\n\\begin{lem}\\label{lemma-serie-rv}\nLet ${\\mathcal H}=({\\mathcal H}_n)_n$ be a filtration and\n$(Y_n)_n$ a $\\mathcal H$-adapted sequence of complex random variables\nsuch that $E[Y_{n}|{\\mathcal H}_{n-1}]\\to Y$ almost surely. Moreover,\nlet $(c_n)_n$ be a sequence of strictly positive real numbers such that\n$\\sum_n E\\left[|Y_n|^2\\right]\/c_n^2<+\\infty$ and let $\\{v_{n,k},1\\leq\nk\\leq n\\}$ be a triangular array of complex numbers such that\n$v_{n,k}\\neq 0$ and\n\\begin{equation}\\label{cond-serie-rv-1}\n\\lim_n v_{n,k}=0,\\quad\n\\lim_n v_{n,n}\\;\\hbox{exists finite},\\quad\n\\lim_n\\sum_{k=1}^n \\frac{v_{n,k}}{c_k}= \\eta\\in{\\mathbb C},\n\\end{equation}\n\\begin{equation}\\label{cond-serie-rv-2}\n\\sum_{k=1}^n\\frac{|v_{n,k}|}{c_k}=O(1),\n\\quad\n\\sum_{k=1}^n \\left|v_{n,k}-v_{n,k-1}\\right|=O(1).\n\\end{equation}\nThen $\\sum_{k=1}^n v_{n,k}Y_k\/c_k\\stackrel{a.s.}\\longrightarrow \\eta Y$.\n\\end{lem}\n\\begin{proof} Let $A$ be an event such that $P(A)=1$ and $\\lim_n\nE[Y_n|{\\mathcal H}_{n-1}](\\omega)=Y(\\omega)$ for each $\\omega\\in\nA$. Fix $\\omega \\in A$ and set $w_n=E[Y_n|{\\mathcal H}_{n-1}](\\omega)$\nand $w=Y(\\omega)$. If $\\eta\\neq 0$, applying Lemma\n\\ref{toeplitz-lemma-complex} to $z_{n,k}=v_{n,k}\/(c_k\\eta)$, $s=1$ and $w_n$,\nwe obtain\n$$\n\\lim_n \\sum_{k=1}^n v_{n,k}\\frac{E[Y_k|{\\mathcal H}_{k-1}](\\omega)}{c_k\\eta}=\nY(\\omega).\n$$\nIf $\\eta=0$,  applying Lemma\n\\ref{toeplitz-lemma-complex} to $z_{n,k}=v_{n,k}\/c_k$, $s=0$ and $w_n$,\nwe obtain\n$$\n\\lim_n \\sum_{k=1}^n v_{n,k}\\frac{E[Y_k|{\\mathcal H}_{k-1}](\\omega)}{c_k}=\n0.\n$$\nTherefore, for both cases, we have\n$$\n\\sum_{k=1}^n v_{n,k}\\frac{E[Y_k|{\\mathcal H}_{k-1}]}{c_k}\n\\stackrel{a.s.}\\longrightarrow \\eta Y.\n$$\n\nNow, consider the martingale $(M_n)_n$ defined by\n$$\nM_n=\\sum_{k=1}^n \\frac{Y_k-E[Y_k|{\\mathcal H}_{k-1}]}{c_k}.\n$$\nIt is bounded in $L^2$ since $\\sum_{k=1}^n\n\\frac{E[|Y_k|^2]}{c_k^2}<+\\infty$ by assumption and so it is almost surely\nconvergent, that means $$ \\sum_{k}\n\\frac{Y_k(\\omega)-E[Y_k|{\\mathcal H}_{k-1}](\\omega)}{c_k}<+\\infty\n$$ for $\\omega\\in B$ with $P(B)=1$. Therefore, fixing $\\omega\\in B$\nand setting $z_k=\\frac{Y_k(\\omega)-E[Y_k|{\\mathcal\n      H}_{k-1}](\\omega)}{c_k}$, by Corollary \\ref{kronecker-complex},\nwe get\n$$\n\\lim_n \\sum_{k=1}^n v_{n,k}\n\\frac{Y_k(\\omega)-E[Y_k|{\\mathcal H}_{k-1}](\\omega)}{c_k}\n=0\n$$\nand so\n$$\n\\sum_{k=1}^n v_{n,k}\n\\frac{Y_k-E[Y_k|{\\mathcal H}_{k-1}]}{c_k}\n\\stackrel{a.s.}\\longrightarrow 0.\n$$\nIn order to conclude, it is enough to observe that\n$$\n\\sum_{k=1}^n v_{n,k}\\frac{Y_k}{c_k}=\n\\sum_{k=1}^n v_{n,k}\\frac{Y_k-E[Y_k|{\\mathcal H}_{k-1}]}{c_k} +\n\\sum_{k=1}^n v_{n,k}\\frac{E[Y_k|{\\mathcal H}_{k-1}]}{c_k}.\n$$\n\\end{proof}\n\nWe conclude this subsection recalling the following well-known\nrelations for $a\\in{\\mathbb R}$:\n\\begin{equation}\\label{relazione-nota}\n\\sum_{k=1}^n\\frac{1}{k^{1-a}}=\n\\begin{cases}\n& O(1) \\quad\\mbox{for } a<0,\\\\\n& \\ln(n)+O(1) \\quad\\mbox{for } a=0,\\\\\n&a^{-1}\\, n^a + O(1) \\quad\\mbox{for } 0<a\\leq 1,\\\\\n&a^{-1}\\, n^{a} + O(n^{a-1}) \\quad\\mbox{for } a>1.\n\\end{cases}\n\\end{equation}\nMore precisely, in the case $a=0$, we have\n\\begin{equation}\\label{eulero_mascheroni}\nd_n=\\sum_{k=1}^n\\frac{1}{k}-\\ln(n)=\nd+O(n^{-1})\n\\end{equation}\nwhere $d$ denotes the Euler-Mascheroni constant.\n\n\\subsection{Asymptotic results for products of complex numbers}\n\nFix $\\gamma=1$ and $c>0$, and consider a sequence $(r_n)_n$ of\nreal numbers such that $0\\leq r_n<1$ for each $n$ and\n\\begin{equation}\\label{ass:condition_r_n_1_appendix}\nnr_n-c\\ =\\  O\\left(n^{-1}\\right).\n\\end{equation}\nObviously, we have $r_n>0$ for $n$ large enough and so in the sequel,\nwithout loss of generality, we will assume $0<r_n<1$ for all $n$.\n\\\\\n\n\\indent Let $x=a_x+i\\,b_x\\in{\\mathbb C}$ and\n$y=a_y+i\\,b_y\\in{\\mathbb C}$ with $a_x,a_y>0$ and $c(a_x+a_y)\\geq1$.\nDenote by $m_0\\geq 2$ an integer such that $\\max\\{a_x,\\,a_y\\}r_m<1$\nfor all $m\\geq m_0$ and set:\n$$\np_{m_0-1}(x):=1,\\quad\np_{n}(x):=\\prod_{m=m_0}^n (1-x r_m)\\; \\hbox{for } n\\geq m_0\n\\quad\\mbox{and}\\quad\nF_{k+1,n}(x):=\\frac{p_{n}(x)}{p_{k}(x)}\\; \\hbox{for } m_0-1\\leq k\\leq n-1.\n$$\n\nWe recall the following result, which has been proved in \\cite{ale-cri-ghi}:\n\\begin{lem}\\cite[Lemma A.4]{ale-cri-ghi}\\label{lemma-tecnico_1}\nWe have that\n\\begin{equation*\n|p_n(x)|\\ =\\ O\\left(n^{- ca_x}\\right)\\qquad\\mbox{and}\\qquad\n|p^{-1}_n(x)|\\ =\\ O\\left(n^{ca_x}\\right).\n\\end{equation*}\n\\end{lem}\n\nInspired by the computation done in\n\\cite{ale-cri-ghi,cri-dai-lou-min}, we can prove the following\nother technical result:\n\n\\begin{lem}\\label{lemma-tecnico_2}\n(i) When $c(a_x+a_y)=1$, we have\n\\begin{equation}\\label{affermazione2_log}\n\\lim_n \\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2 F_{k+1,n}(x)F_{k+1,n}(y)\\\n=\\\n\\left\\{\\begin{aligned}\n&c^2\\ &\\mbox{ if }b_x+b_y=0,\\\\\n&0\\ &\\mbox{ if } b_x+b_y\\neq 0;\n\\end{aligned}\\right.\\end{equation}\nwhile when $c(a_x+a_y)>1$, we have\n\\begin{equation}\\label{affermazione2}\\begin{aligned}\n&\\lim_n n\\sum_{k=m_0}^{n-1} r_k^2 F_{k+1,n}(x)F_{k+1,n}(y)\n\\ =\\\n\\frac{c^2}{c(x+y)-1},\\\\\n&\\lim_n n\\sum_{k=m_0}^{n-1} r_k^2 \\ln\\left(\\frac{n}{k}\\right)F_{k+1,n}(x)F_{k+1,n}(y)\n\\ =\\\n\\frac{c^2}{(c(x+y)-1)^2},\\\\\n&\\lim_n n\\sum_{k=m_0}^{n-1}r_k^2\\ln^2\\left(\\frac{n}{k}\\right)F_{k+1,n}(x)F_{k+1,n}(y)\n\\ = \\\n\\frac{2c^2}{(c(x+y)-1)^3}.\n\\end{aligned}\\end{equation}\n(ii) Moreover, for any $u\\geq 1$, we have:\\\\\n\\noindent when $c(a_x+a_y)=1$\n\\begin{equation}\\label{affermazione3_log}\n\\sum_{k=m_0}^{n-1} r_k^{2u}\\frac{|p_{n}(x)|^u|p_{n}(y)|^u}{|p_{k}(x)|^u|p_{k}(y)|^u}\n=\\left\\{\\begin{aligned}\n&O(\\ln(n)\/n)\\quad&\\mbox{for } u=1,\\\\\n&O\\left(n^{-u}\\right)\\quad&\\mbox{for } u>1;\n\\end{aligned}\\right.\n\\end{equation}\nwhile when $c(a_x+a_y)>1$ and $e\\in\\{0,1,2\\}$\n\\begin{equation}\\label{affermazione3}\n\\sum_{k=m_0}^{n-1} r_k^{2u}\\ln^{e u}\n\\left(\\frac{n}{k}\\right) \\frac{|p_{n}(x)|^u|p_{n}(y)|^u}{|p_{k}(x)|^u|p_{k}(y)|^u}\n=\\begin{cases}\nO(n^{-uc(a_x+a_y)}\\ln^{eu}(n))\\quad &\\hbox{for } uc(a_x+a_y)<2u-1,\\\\\nO(n^{-(2u-1)}\\ln^{eu+1}(n))\\quad &\\hbox{for } uc(a_x+a_y)=2u-1,\\\\\nO(n^{-(2u-1)})\\quad &\\hbox{for } uc(a_x+a_y)>2u-1\n\\end{cases}\n\\end{equation}\n(note that for $u=1$ only the third case is possible).\n\\end{lem}\n\n\\begin{proof} (i) First of all, let us notice that the limit\n\\eqref{affermazione2_log} and the first of the limits\n\\eqref{affermazione2} have already been proved\nin~\\cite[Eq. (A.11),(A.18)]{ale-cri-ghi}. Therefore, we can focus on\nthe second and the third limits in \\eqref{affermazione2}. To this end,\nlet us set\n$$\n\\mathcal{S}_{1,n}:=\\sum_{k=m_0}^{n-1} \\frac{r_k^2}{p_k(x)p_k(y)},\\qquad\n\\mathcal{S}_{2,n}:=\\sum_{k=m_0}^{n-1} \\frac{r_k^2\\ln(k)}{p_k(x)p_k(y)},\\qquad\n\\mathcal{S}_{3,n}:=\\sum_{k=m_0}^{n-1} \\frac{r_k^2\\ln^2(k)}{p_k(x)p_k(y)},\n$$\nso that, recalling the equality $F_{k+1,n}(x)=p_n(x)\/p_k(x)$, we can write:\n\n\\begin{equation*\n\\begin{aligned}\n&n\\sum_{k=m_0}^{n-1} r_k^2 F_{k+1,n}(x)F_{k+1,n}(y)=\nnp_n(x)p_n(y)\\mathcal{S}_{1,n},\\\\\n&n\\sum_{k=m_0}^{n-1} r_k^2 \\ln\\left(\\frac{n}{k}\\right)F_{k+1,n}(x)F_{k+1,n}(y)=\nnp_n(x)p_n(y)\\left(\\ln(n)\\mathcal{S}_{1,n}-\\mathcal{S}_{2,n}\\right),\\\\\n&n\\sum_{k=m_0}^{n-1} r_k^2 \\ln^2\\left(\\frac{n}{k}\\right)F_{k+1,n}(x)F_{k+1,n}(y)=\nnp_n(x)p_n(y)\n\\left(\\ln^2(n)\\mathcal{S}_{1,n}-2\\ln(n)\\mathcal{S}_{2,n}+\\mathcal{S}_{3,n}\\right).\n\\end{aligned}\n\\end{equation*}\nNow, set $G_{1,k}:=c^2\/[kp_{k}(x)p_{k}(y)]$ and recall that, as seen\nin~\\cite[Proof of Lemma A.5]{ale-cri-ghi}, when $c(a_x+a_y)>1$ we have\n\\begin{equation}\\label{irene1}\n\\Delta G_{1,k}\n=(c(x+y)-1)\\Delta\\mathcal{S}_{1,k}\n+O\\left(k^{-1} |\\Delta \\mathcal{S}_{1,k}| \\right).\n\\end{equation}\nUsing analogous arguments, we can set\n $G_{2,k}:=c^2\\ln(k)\/[kp_{k}(x)p_{k}(y)]$ and observe that we have:\n\\begin{equation*}\n\\begin{split}\n\\Delta G_{2,k}&=\\frac{c^2}{p_k(x)p_k(y)}\n\\left[\n\\left(\\frac{\\ln(k)}{k}-\\frac{\\ln(k-1)}{k-1}\\right)\n\\left(1-(x+y)r_k+r_k^2xy\\right) +\n\\frac{\\ln(k)}{k}\\left((x+y)r_k-r_k^2xy\\right)\\right]\n\\\\\n&=\\frac{c^2}{p_k(x)p_k(y)}\n\\left[\n\\left(-\\frac{\\ln(k)}{k^2}+\\frac{1}{k^2}+o(k^{-2})\\right)\n\\left(1-(x+y)r_k+r_k^2xy\\right) +\n\\frac{\\ln(k)}{k}\\left((x+y)r_k-r_k^2xy\\right)\n\\right]\n\\\\\n&=(c(x+y)-1)\\Delta \\mathcal{S}_{2,k}+\\Delta \\mathcal{S}_{1,k}\n+O(k^{-1} |\\Delta\\mathcal{S}_{2,k}|).\n\\end{split}\n\\end{equation*}\nTherefore, when $c(a_x+a_y)>1$, we obtain\n\\begin{equation}\\label{irene2}\n\\frac{\\Delta G_{2,k}}{c(x+y)-1}-\\Delta\\mathcal{S}_{2,k}\n=\\frac{\\Delta\\mathcal{S}_{1,k}}{c(x+y)-1}+\nO\\left(k^{-1}\\ln(k) |\\Delta\\mathcal{S}_{1,k}| \\right).\n\\end{equation}\nThe relations \\eqref{irene1}, \\eqref{irene2} and the first limit in\n\\eqref{affermazione2} imply\n\\begin{align*}\n\\lim_n & np_n(x)p_n(y)\n\\Big(\\ln(n) \\mathcal{S}_{1,n}-\\mathcal{S}_{2,n}\\Big)\n\\\\\n&=\\lim_n np_n(x)p_n(y)\n\\Big(\n\\frac{\\ln(n)G_{1,n}}{c(x+y)-1}-\\mathcal{S}_{2,n}\n\\Big)+\nO\\Big(\\ln(n)n |p_n(x)p_n(y)|\\sum_{k=m_0}^{n-1} k^{-1}|\\Delta\\mathcal{S}_{1,k}|\n\\Big)\n\\\\\n&= \\lim_n np_n(x)p_n(y)\n\\Big(\n\\frac{G_{2,n}}{c(x+y)-1}-\\mathcal{S}_{2,n}\n\\Big)\n\\\\\n&= (c(x+y)-1)^{-1}\n\\lim_n np_n(x)p_n(y)\\mathcal{S}_{1,n}+\nO\\Big(n |p_n(x)p_n(y)|\\sum_{k=m_0}^{n-1} k^{-1}\\ln(k)|\\Delta\\mathcal{S}_{1,k}|\n\\Big)\n\\\\\n&= (c(x+y)-1)^{-1}\n\\lim_n np_n(x)p_n(y)\\mathcal{S}_{1,n}=\\frac{c^2}{(c(x+1)-1)^2},\n\\end{align*}\nwhere we have used the fact that, by Lemma \\ref{lemma-tecnico_1} and\nrelation \\eqref{relazione-nota}, we have\n$$\nO\\Big(\\ln(n)n |p_n(x)p_n(y)|\n\\sum_{k=m_0}^{n-1} k^{-1}|\\Delta\\mathcal{S}_{1,k}|\\Big)\n=\nO\\Big(\\frac{\\ln(n)}{n^{c(a_x+a_y)-1}}\n\\sum_{k=m_0}^{n-1} \\frac{1}{k^{1-(c(a_x+a_y)-2)}}\n\\Big)\n\\longrightarrow 0.\n$$\n\nFor the last limit, we can set\n$G_{3,k}:=c^2\\ln^2(k)\/[kp_{k}(x)p_{k}(y)]$ and, similarly as above,\nobserve that we have:\n\\begin{equation*}\n\\begin{split}\n \\Delta G_{3,k}\n&=\\frac{c^2}{p_k(x)p_k(y)}\n\\left[\n\\left(\\frac{\\ln^2(k)}{k}-\\frac{\\ln^2(k-1)}{k-1}\\right)\n\\left(1-(x+y)r_k+r_k^2xy\\right) +\n\\frac{\\ln^2(k)}{k}\\left((x+y)r_k-r_k^2xy\\right)\n\\right]\n\\\\\n&=\\frac{c^2}{p_k(x)p_k(y)}\\times\n\\\\\n&\\left[\n\\left(-\\frac{\\ln^2(k)}{k^2}+2\\frac{\\ln(k)}{k^2}+O(k^{-3}\\ln^2(k))\\right)\n\\left(1-(x+y)r_k+r_k^2xy\\right)+\n\\frac{\\ln^2(k)}{k}\\left((x+y)r_k-r_k^2xy\\right)\n\\right]\n\\\\\n&=(c(x+y)-1)\\Delta \\mathcal{S}_{3,k}+2\\Delta \\mathcal{S}_{2,k}+\nO(k^{-1} |\\Delta\\mathcal{S}_{3,k}| ).\n\\end{split}\n\\end{equation*}\nTherefore, when $c(a_x+a_y)>1$, we obtain\n\\begin{equation}\\label{irene3}\n\\frac{\\Delta G_{3,k}}{c(x+y)-1}- \\Delta \\mathcal{S}_{3,k}\n=\\frac{2\\Delta \\mathcal{S}_{2,k}}{c(x+y)-1}\n+O(k^{-1}\\ln^2(k) |\\Delta\\mathcal{S}_{1,k}| ).\n\\end{equation}\nBy means of analogous computations as above, the relations\n\\eqref{irene1}, \\eqref{irene2}, \\eqref{irene3} and the\nalready proved second limit in \\eqref{affermazione2} imply\n\\begin{align*}\n\\lim_n & np_n(x)p_n(y)\n\\left(\\ln^2(n)\\mathcal{S}_{1,n}-2\\ln(n)\\mathcal{S}_{2,n}\n+\\mathcal{S}_{3,n}\\right)\n\\\\\n&= \\lim_n np_n(x)p_n(y)\n\\Big(\\frac{\\ln^2(n)G_{1,n}}{c(x+y)-1}\n-2\\ln(n)\\mathcal{S}_{2,n}+\\mathcal{S}_{3,n}\\Big)\n\\!+\\!O\\Big(\n\\ln^2(n)n |p_n(x)p_n(y)| \\sum_{k=m_0}^{n-1} k^{-1}|\\Delta\\mathcal{S}_{1,k}|\n\\Big)\n\\\\\n&= \\lim_n np_n(x)p_n(y)\n\\Big(\\frac{\\ln(n) G_{2,n}}{c(x+y)-1}\n-2\\ln(n)\\mathcal{S}_{2,n}+\\mathcal{S}_{3,n}\\Big)\n\\\\\n& = \\lim_n np_n(x)p_n(y)\n\\Big(\\frac{\\ln(n)G_{2,n}}{c(x+y)-1}\n-2\\frac{ \\ln(n)(G_{2,n}-\\mathcal{S}_{1,n}) }{c(x+y)-1}\n+\\mathcal{S}_{3,n}\\Big)\n\\\\\n& \\qquad + O\\Big(\n\\ln(n)n |p_n(x)p_n(y)|\n\\sum_{k=m_0}^{n-1} k^{-1}\\ln(k)|\\Delta\\mathcal{S}_{1,k}|\n\\Big)\n\\\\\n&= \\lim_n np_n(x)p_n(y)\n\\Big(\\frac{2\\ln(n)\\mathcal{S}_{1,n}}{c(x+y)-1}\n-\\frac{G_{3,n}}{c(x+y)-1}\n+\\mathcal{S}_{3,n}\\Big)\n\\\\\n& = \\frac{2}{c(x+y)-1}\\lim_n np_n(x)p_n(y)\n\\Big(\\ln(n)\\mathcal{S}_{1,n}-\\mathcal{S}_{2,n}\\Big)\n\\!+\\!O\\Big(n |p_n(x)p_n(y)|\n\\sum_{k=m_0}^{n-1} k^{-1}\\ln^2(k)|\\Delta\\mathcal{S}_{1,k}|\n\\Big)\n\\\\\n& = \\frac{2}{c(x+y)-1}\\lim_n np_n(x)p_n(y)\n\\Big(\\ln(n)\\mathcal{S}_{1,n}-\\mathcal{S}_{2,n}\\Big)=\n\\frac{2c^2}{(c(x+1)-1)^3},\n\\end{align*}\nwhere we have used the fact that, by Lemma \\ref{lemma-tecnico_1} and\nrelation \\eqref{relazione-nota}, we have\n$$\nO\\Big(\\ln^2(n) n |p_n(x)p_n(y)|\n\\sum_{k=m_0}^{n-1} k^{-1}|\\Delta\\mathcal{S}_{1,k}|\\Big)\n=\nO\\Big(\\frac{\\ln^2(n)}{n^{c(a_x+a_y)-1}}\n\\sum_{k=m_0}^{n-1} \\frac{1}{k^{1-(c(a_x+a_y)-2)}}\n\\Big)\n\\longrightarrow 0.\n$$\n\nii) For the second part of the proof, note that by\ncondition~\\eqref{ass:condition_r_n_1_appendix} on $(r_n)_n$, relation\n\\eqref{relazione-nota} and Lemma~\\ref{lemma-tecnico_1}, when\n$c(a_x+a_y)=1$, we have\n$$\n\\sum_{k=m_0}^{n-1} r_k^{2u}\n\\frac{|p_{n}(x)|^u|p_{n}(y)|^u}{|p_{k}(x)|^u|p_{k}(y)|^u}=\nO(n^{-u})\\sum_{k=m_0}^{n-1} O(k^{-u}) =\n\\left\\{\\begin{aligned}\n&O(\\ln(n)\/n)\\quad&\\mbox{for } u=1,\\\\\n&O\\left(n^{-u}\\right)\\quad&\\mbox{for } u>1.\n\\end{aligned}\\right.$$\nFor the case $c(a_x+a_y)>1$, note that for $u\\geq 1$ and\n$e\\in\\{0,1,2\\}$, we have\n\\[\\begin{aligned}\n&\\sum_{k=m_0}^{n-1} r_k^{2u}\\ln^{e u}\\Big(\\frac{n}{k}\\Big)\n\\frac{|p_{n}(x)|^u|p_{n}(y)|^u}{|p_{k}(x)|^u|p_{k}(y)|^u} =\n\\sum_{k=m_0}^{n-1} O(k^{-2u})\\ln^{e u}\\Big(\\frac{n}{k}\\Big)\nO\\Big(\\Big(\\frac{k}{n}\\Big)^{uc(a_x+a_y)}\\Big) =\\\\\n&n^{-2u}\\sum_{k=m_0}^{n-1} \\ln^{e u}\\Big(\\frac{n}{k}\\Big)\nO\\Big(\\Big(\\frac{k}{n}\\Big)^{u(c(a_x+a_y)-2)}\\Big).\n\\end{aligned}\\]\nThen, for $e=0$, using relation \\eqref{relazione-nota}, it is easy to\nsee that\n$$\nn^{-2u}\\sum_{k=m_0}^{n-1}O\\left(\\left(\\frac{k}{n}\\right)^{u(c(a_x+a_y)-2)}\\right)\n=\\begin{cases}\nO(n^{-uc(a_x+a_y)})\\quad &\\hbox{for } uc(a_x+a_y)<2u-1,\\\\\nO(n^{-(2u-1)}\\ln(n))\\quad &\\hbox{for } uc(a_x+a_y)=2u-1,\\\\\nO(n^{-(2u-1)})\\quad &\\hbox{for } uc(a_x+a_y)>2u-1\n\\end{cases}\n$$\n(note that for $u=1$ only the third case is possible).\n\\\\\n\n\\indent Now we consider the cases $e=1$ and $e=2$. Note that, setting\n$\\alpha:=2u-uc(a_x+a_y)\\in\\mathbb{R}$ and $\\beta:=eu\\geq1$, we have\nthat\n$$\n\\frac{1}{n}\\sum_{k=m_0}^{n-1} \\ln^{\\beta}\\Big(\\frac{n}{k}\\Big)\\,\nO\\Big(\\Big(\\frac{k}{n}\\Big)^{-\\alpha}\\Big)\n\\ =\\\nO(1)\\ +\\ O\\left(\\int_{\\frac{m_0-1}{n}}^{\\epsilon}x^{-\\alpha}\\ln^{\\beta}(x^{-1})dx\\right),\n$$\nwhere $\\epsilon\\in(0,1)$ has been chosen such that\n$g(x)=x^{-\\alpha}\\ln^{\\beta}(x^{-1})$ is monotone in $(0,\\epsilon]$ and we\n  recall that $(m_0-1)\\geq 1$. Then, we have that\n$$\n\\int_{\\frac{m_0-1}{n}}^{\\epsilon}x^{-\\alpha}\\ln^{\\beta}(x^{-1})dx\n=\\begin{cases}\nO(n^{\\alpha-1}\\ln^{\\beta}(n))\\quad &\\hbox{for } \\alpha>1\\\\\nO(\\ln^{\\beta+1}(n))\\quad &\\hbox{for } \\alpha=1,\\\\\nO(1)\\quad &\\hbox{for } \\alpha<1.\n\\end{cases}\n$$\nFinally, we can conclude that, for the cases $e=1$ and $e=2$, we have\n$$\nn^{-2u}\\sum_{k=m_0}^{n-1}\\ln^{e u}\\Big(\\frac{n}{k}\\Big)\nO\\Big(\\Big(\\frac{k}{n}\\Big)^{u(c(a_x+a_y)-2)}\\Big)\n=\\begin{cases}\nO(n^{-uc(a_x+a_y)}\\ln^{eu}(n))\\quad &\\hbox{for } uc(a_x+a_y)<2u-1,\\\\\nO(n^{-(2u-1)}\\ln^{eu+1}(n))\\quad &\\hbox{for } uc(a_x+a_y)=2u-1,\\\\\nO(n^{-(2u-1)})\\quad &\\hbox{for } uc(a_x+a_y)>2u-1\n\\end{cases}\n$$\n(note again that for $u=1$ only the third case is possible).\n\\end{proof}\n\n\\begin{rem}\\label{rem:relations_diff_v}\n\\rm Setting $v^{(e)}_{n,k}:=(n\/k)\\ln^e(n\/k)F_{k+1,n}(x)F_{k+1,n}(y)$\nfor any $e\\in\\{0,1,2\\}$ and $m_0-1\\leq k\\leq n-1$, and using the\nrelations \\eqref{irene1}, \\eqref{irene2}, \\eqref{irene3} found in the\nproof of Lemma~\\ref{lemma-tecnico_2}, for $c(a_x+a_y)>1$ we have:\n\\[\n\\begin{aligned}\n&|v^{(0)}_{n,k}-v^{(0)}_{n,k-1}|\\ =\\ n|p_n(x)p_n(y)|O(|\\Delta G_{1,k}|)\\ =\n\\ n|p_n(x)p_n(y)|O(|\\Delta \\mathcal{S}_{1,k}|)\\ =\\\nO\\Big(n r_k^2\\frac{|p_{n}(x)||p_{n}(y)|}{|p_{k}(x)||p_{k}(y)|}\\Big);\n\\\\\n&|v^{(1)}_{n,k}-v^{(1)}_{n,k-1}|\\ =\n\\ n|p_n(x)p_n(y)|O(|\\ln(n)\\Delta G_{1,k}-\\Delta G_{2,k}|) \\\\\n& \\quad = n|p_n(x)p_n(y)|O(|\\ln(n)\\Delta \\mathcal{S}_{1,k}-\\Delta \\mathcal{S}_{2,k}|\n+|\\Delta \\mathcal{S}_{1,k}|)\\ =\nO\\Big(nr_k^{2}\\left(\\ln\\left(\\frac{n}{k}\\right)+1\\right)\n\\frac{|p_{n}(x)||p_{n}(y)|}{|p_{k}(x)||p_{k}(y)|}\n\\Big);\n\\\\\n&|v^{(2)}_{n,k}-v^{(2)}_{n,k-1}|\\ =\\\nn|p_n(x)p_n(y)|O(|\\ln^2(n)\\Delta G_{1,k}-2\\ln(n)\\Delta G_{2,k}+\\Delta G_{3,k}|)\\\n\\\\\n&\\quad =n|p_n(x)p_n(y)|\nO\\left(\n|\\ln^2(n)\\Delta \\mathcal{S}_{1,k}-2\\ln(n)\\Delta\\mathcal{S}_{2,k}\n+\\Delta \\mathcal{S}_{3,k}|\n+|\\ln(n)\\Delta\\mathcal{S}_{1,k}-\\Delta\\mathcal{S}_{2,k}|\n\\right)\\\\\n&\\quad = O\\Big(\nnr_k^2\n\\Big(\\ln^2\\Big(\\frac{n}{k}\\Big)+\\ln\\Big(\\frac{n}{k}\\Big)\n\\Big) \\frac{|p_{n}(x)||p_{n}(y)|}{|p_{k}(x)||p_{k}(y)|}\n\\Big),\n\\end{aligned}\n\\]\nMoreover, setting $v_{n,k}:=v^{(0)}_{n,k}\/\\ln(n)$ for any $m_0-1\\leq\nk\\leq n-1$, in the case $c(a_x+a_y)=1$ we have:\n $|v_{n,k}-v_{n,k-1}|=O\\left(r_k^2 k\/\\ln(n)\\right)$ when $b_x+b_y\\neq 0$\nsince Lemma \\ref{lemma-tecnico_1} and\n$$|v^{(0)}_{n,k}-v^{(0)}_{n,k-1}|\\ =\\ n|p_n(x)p_n(y)|O(|\\Delta G_{1,k}|)\\ =\\\nn|p_n(x)p_n(y)|O(|\\Delta \\mathcal{S}_{1,k}|)\\ =\\\nO\\Big(nr_k^{2}\\frac{|p_{n}(x)||p_{n}(y)|}{|p_{k}(x)||p_{k}(y)|}\n\\Big);\n$$\nwhile $|v_{n,k}-v_{n,k-1}|=O\\left(r_k^{2}\/\\ln(n)\\right)$ when $b_x+b_y=0$ since\n Lemma \\ref{lemma-tecnico_1} and\n$$|v^{(0)}_{n,k}-v^{(0)}_{n,k-1}|\\ =\\ n|p_n(x)p_n(y)|O(|\\Delta G_{1,k}|)\\ =\\\nn|p_n(x)p_n(y)|O(k^{-1}|\\Delta \\mathcal{S}_{1,k}|)\\ =\\\nO\\Big(r_k^{2}\\frac{n|p_{n}(x)||p_{n}(y)|}{k|p_{k}(x)||p_{k}(y)|}\\Big).\n$$\n\\end{rem}\n\n\\subsection{Technical computations for the proofs of Theorem~\\ref{thm:asymptotics_theta_hat_1} and\nTheorem~\\ref{thm:asymptotics_theta_1_star}\n\nIn this subsection we collect some technical computations necessary for the proofs of\nTheorem~\\ref{thm:asymptotics_theta_hat_1} and Theorem~\\ref{thm:asymptotics_theta_1_star}.\nTherefore, the notation and the assumptions used here are the same as those used in these theorems.\\\\\n\nThe first technical result is the following:\n\n\\begin{lem}\\label{lem:terms_in_A_k_n}\nLet the matrix $A_{k+1,n}$ be defined as in~\\eqref{def:C_k_n_A_k_n}\nfor $m_0-1\\leq k\\leq n-1$.  Then, we have that\n\\begin{equation*}\\begin{aligned}\n&[A^{11}_{k+1,n}]_{jj}\\ =\\ F_{k+1,n}(\\alpha_j),\\\\\n&[A^{33}_{k+1,n}]_{jj}\\ =\\ a^{22}_{k+1,n}\\ =\\ F_{k+1,n}(c^{-1}),\\\\\n&[A^{31}_{k+1,n}]_{jj}\\ =\\\n\\begin{cases}\n\\left(\\frac{1-\\alpha_j}{c\\alpha_j-1}\\right)\n(F_{k+1,n}(c^{-1})-F_{k+1,n}(\\alpha_j)),\\ &\\hbox{for } c\\alpha_j\\neq 1,\\\\\n(1-c^{-1})F_{k+1,n}(c^{-1})\\ln\\left(\\frac{n}{k}\\right)+O(n^{-1}),\\\n&\\hbox{for } c\\alpha_j=1.\n\\end{cases}\n\\end{aligned}\\end{equation*}\n\\end{lem}\n\n\\begin{proof}\nBy means of~\\eqref{def:S_Q_S_R} and~\\eqref{def:C_k_n_A_k_n}, after\nstandard calculations, the elements in $A_{k+1,n}$ for $m_0-1\\leq\nk\\leq n-1$ can be written as follows:\n$[A^{11}_{k+1,n}]_{jj}=F_{k+1,n}(\\alpha_j)$, $[A^{33}_{k+1,n}]_{jj}=\na^{22}_{k+1,n}= F_{k+1,n}(c^{-1})$ and\n$$\n[A^{31}_{k+1,n}]_{jj}\\ =\\\n(1-\\alpha_j)\n\\frac{p_{n}(\\alpha_j)}{p_{k}(c^{-1})}\nS^j_{k+1,n},\n$$\nwhere\n\\begin{equation*}\nS^j_{k+1,n}:=\\sum_{l=k+1}^n\\Big(\\frac{r_lc^{-1}}{1-r_lc^{-1}}\\Big)X^j_{l}\n\\qquad\\mbox{and}\\qquad\nX^j_{l}:=\\frac{p_{l}(c^{-1})}{p_{l}(\\alpha_j)}.\n\\end{equation*}\nSetting $\\Delta X^j_{l}:=(X^j_{l}-X^j_{l-1})$, notice that we have\n$$\n\\Delta X^j_{l}\n=\\Big(\\frac{1-r_{l}c^{-1}}{1-r_{l}\\alpha_j}-1\\Big)X^j_{l-1}\n=(c\\alpha_j-1)\\Big(\\frac{r_lc^{-1}}{1-r_{l}\\alpha_j}\\Big)X^j_{l-1}\n=(c\\alpha_j-1)\\Big(\\frac{r_lc^{-1}}{1-r_lc^{-1}}\\Big)X^j_l.\n$$\nHence, in the case $c\\alpha_j\\neq 1$, we have that\n$$\n(X^j_{n}-X^j_{k})=\\sum_{l=k+1}^{n}\\Delta X^j_{l}\n=(c\\alpha_j-1)S^j_{k+1,n},\n$$\nwhich implies\n$$\nS^j_{k+1,n}=\n\\frac{X^j_{n}-X^j_{k}}{c\\alpha_j-1}=(c\\alpha_j-1)^{-1}\n\\Big(\\frac{p_{n}(c^{-1})}{p_{n}(\\alpha_j)}-\\frac{p_{k}(c^{-1})}{p_{k}(\\alpha_j)}\n\\Big).\n$$\nUsing the above expression of $S^j_{k+1,n}$ in the definition of\n$A^{31}_{k+1,n}$, we\nobtain (for $c\\alpha_j\\neq 1$) that\n\\[\n[A^{31}_{k+1,n}]_{jj}=\n\\frac{1-\\alpha_j}{c\\alpha_j-1}\n\\frac{p_{n}(\\alpha_j)}{p_{k}(c^{-1})}\n\\Big(\n\\frac{p_{n}(c^{-1})}{p_{n}(\\alpha_j)}-\\frac{p_{k}(c^{-1})}{p_{k}(\\alpha_j)}\n\\Big)=\n\\Big(\\frac{1-\\alpha_j}{c\\alpha_j-1}\\Big)\n\\Big(F_{k+1,n}(c^{-1})-F_{k+1,n}(\\alpha_j)\\Big).\n\\]\nWhen $c\\alpha_j=1$, observing that $X^j_{l}=1$ for any $l\\geq 1$ and\nusing condition~\\eqref{ass:condition_r_n_1_appendix} we get\n$$\nS^j_{k+1,n}\n=\n\\sum_{l=k+1}^{n}\\frac{r_lc^{-1}}{1-r_lc^{-1}}\n=\n\\sum_{l=k+1}^n \\frac{1}{l-1}+\\sum_{l=k+1}^nO\\Big(\\frac{1}{l^2}\\Big)\n=\n\\sum_{l=k}^n\\frac{1}{l}-\\frac{1}{n}+O\\Big(\\sum_{l\\geq k}\\frac{1}{l^2}\\Big)\n=\n\\sum_{l=k}^n \\frac{1}{l}+O(k^{-1}),\n$$\nwhere, for the last equality, we have used the fact that $k<n$ and\n$\\sum_{l\\geq k}1\/l^2=O(1\/k)$. Then, using \\eqref{eulero_mascheroni} for $a=0$,\nwe have\n$$\\sum_{l=k}^n \\frac{1}{l}=\\ln\\Big(\\frac{n}{k}\\Big)+d_n-d_k=\n\\ln\\Big(\\frac{n}{k}\\Big)+O(n^{-1})-O(k^{-1})=\n\\ln\\Big(\\frac{n}{k}\\Big)+O(k^{-1})\n$$\n(where the last passage follows again by the fact that $k<n$).\nFinally, since Lemma~\\ref{lemma-tecnico_1} we have\n$|F_{k+1,n}(c^{-1})|=O(k\/n)$, we obtain (for $c\\alpha_j=1$) that\n$$\n[A^{31}_{k+1,n}]_{jj}\n=\n(1-c^{-1})\\frac{p_n(c^{-1})}{p_k(c^{-1})}\n\\Big(\\ln(n\/k)+O(1\/k)\\Big)\n=\n(1-c^{-1})F_{k+1,n}(c^{-1})\\ln\\Big(\\frac{n}{k}\\Big)+O(n^{-1}).\n$$\n\\end{proof}\n\n\\subsubsection{Computations for the almost sure limits of the elements in \\eqref{eq:matrix}}\\label{subsubsection_appendix_technical_computation_1}\n\n\\begin{itemize}\n\\item\n\\textit{$a.s.-\\lim_{n}n\\sum_{k=m_0}^{n-1} r_k^2 [A^{1}_{k+1,n}B_{k+1}A^{1}_{k+1,n}]_{h,j}$}:\\\\\nBy using the first limit in~\\eqref{eq:results_limits}, we have\n\\begin{multline*}\nn\\sum_{k=m_0}^{n-1} r_k^2 [B_{k+1}]_{h,j}[A^{1}_{k+1,n}]_{h,h}[A^{1}_{k+1,n}]_{j,j} =\\\nn\\sum_{k=m_0}^{n-1} r_k^2 [B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(\\alpha_j)\\\\\n\\stackrel{a.s}\\longrightarrow\\\n\\frac{c^2}{c(\\alpha_h+\\alpha_j)-1}(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)\nZ_{\\infty}(1-Z_{\\infty}).\n\\end{multline*}\n\\item\n\\textit{$a.s.-\\lim_{n}n\\sum_{k=m_0}^{n-1} r_k^2\n  [A^{3}_{k+1,n}B_{k+1}A^{3}_{k+1,n}]_{h,j}$}:\\\\\nFirst, note that when\n$c\\alpha_h\\neq 1$ and $c\\alpha_j\\neq 1$, we have that\n$n\\sum_{k=m_0}^{n-1}\nr_k^2[B_{k+1}]_{h,j}[A^{3}_{k+1,n}]_{h,h}[A^{3}_{k+1,n}]_{j,j}$ has the\nsame limit as\n\\begin{multline*}\n\\frac{(1-c^{-1})^2}{(c\\alpha_h-1)(c\\alpha_j-1)}\n\\,n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F^2_{k+1,n}(c^{-1})\\\\\n\\begin{aligned}\n&+\n\\ \\frac{(1-\\alpha_h)(1-\\alpha_j)}{(c\\alpha_h-1)(c\\alpha_j-1)}\n\\,n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(\\alpha_j)\\\\\n&-\\frac{(1-\\alpha_h)(1-c^{-1})}{(c\\alpha_h-1)(c\\alpha_j-1)}\n\\,n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(c^{-1})\\\\\n&-\\frac{(1-\\alpha_j)(1-c^{-1})}{(c\\alpha_h-1)(c\\alpha_j-1)}\n\\,n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_j)F_{k+1,n}(c^{-1}).\n\\end{aligned}\n\\end{multline*}\nThen, when $c\\alpha_h\\neq 1$ and $c\\alpha_j\\neq 1$, using the first\nlimit in~\\eqref{eq:results_limits} we obtain, after some standard\ncalculations,\n$$\nn\\sum_{k=m_0}^{n-1} r_k^2 [B_{k+1}]_{h,j}[A^{3}_{k+1,n}]_{h,h}[A^{3}_{k+1,n}]_{j,j}\\\n\\stackrel{a.s}\\longrightarrow\\\n\\frac{1+(c-1)(\\alpha_h^{-1}+\\alpha_j^{-1})}\n{c(\\alpha_h+\\alpha_j)-1}(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty}).\n$$\nWhen $c\\alpha_h=c\\alpha_j=1$, we have that $n\\sum_{k=m_0}^{n-1}\nr_k^2[B_{k+1}]_{h,j}[A^{3}_{k+1,n}]_{h,h}[A^{3}_{k+1,n}]_{j,j}$ has the\nsame limit as\n\\begin{multline*}\n(1-c^{-1})^2\\,n\\sum_{k=m_0}^{n-1} \\ln^2(n\/k)r_k^2[B_{k+1}]_{h,j}F^2_{k+1,n}(c^{-1})\\\\\n\\begin{aligned}\n&+2c^{-1}(1-c^{-1})\\,n\\sum_{k=m_0}^{n-1} \\ln(n\/k)r_k^2[B_{k+1}]_{h,j}F^2_{k+1,n}(c^{-1})\n\\\\\n&+ c^{-2}\\,n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F^2_{k+1,n}(c^{-1}),\n\\end{aligned}\n\\end{multline*}\nfrom which, using the three limits in~\\eqref{eq:results_limits}, we\nobtain\n$$n\\sum_{k=m_0}^{n-1} r_k^2 [B_{k+1}]_{h,j}[A^{3}_{k+1,n}]_{h,h}[A^{3}_{k+1,n}]_{j,j}\\\n\\stackrel{a.s}\\longrightarrow\\\n(1+2c(c-1))(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty}).\n$$\nFinally, when $c\\alpha_h\\neq 1$ and $c\\alpha_j=1$, we have that\n$n\\sum_{k=m_0}^{n-1}\nr_k^2[B_{k+1}]_{h,j}[A^{3}_{k+1,n}]_{h,h}[A^{3}_{k+1,n}]_{j,j}$ has the\nsame limit as\n\\begin{multline*}\n\\frac{(1-c^{-1})^2}{(c\\alpha_h-1)}\\,\nn\\sum_{k=m_0}^{n-1} \\ln(n\/k)r_k^2[B_{k+1}]_{h,j}F^2_{k+1,n}(c^{-1})\\\\\n\\begin{aligned}\n&+\\frac{c^{-1}(1-c^{-1})}{(c\\alpha_h-1)}\\,\nn\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F^2_{k+1,n}(c^{-1})\\\\\n&-\\frac{(1-\\alpha_h)(1-c^{-1})}{(c\\alpha_h-1)}\\,\nn\\sum_{k=m_0}^{n-1} \\ln(n\/k)r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(c^{-1})\\\\\n&-\\frac{c^{-1}(1-\\alpha_h)}{(c\\alpha_h-1)}\\,\nn\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(c^{-1}),\n\\end{aligned}\n\\end{multline*}\nwhich implies, using the first two limits in~\\eqref{eq:results_limits}, that\n$$\nn\\sum_{k=m_0}^{n-1} r_k^2 [B_{k+1}]_{h,j}[A^{3}_{k+1,n}]_{h,h}[A^{3}_{k+1,n}]_{j,j}\\\n\\stackrel{a.s}\\longrightarrow\\\n\\frac{1+(c-1)(c+\\alpha_h^{-1})}\n{c\\alpha_h}(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty}).\n$$\nThe case $c\\alpha_h=1$ and $c\\alpha_j\\neq1$ is\nanalogous. Therefore, we can summarize the limits in all the above\ncases with the formula:\n$$\n\\frac{1+(c-1)(\\alpha_h^{-1}+\\alpha_j^{-1})}\n{c(\\alpha_h+\\alpha_j)-1}(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty}).\n$$\n\\item\n\\textit{$a.s.-\\lim_{n}n\\sum_{k=m_0}^{n-1} r_k^2 (a^{2}_{k+1,n})^2b_{k+1}$}:\n\\\\\nUsing the first limit in~\\eqref{eq:results_limits}, we have\n$$\nn\\sum_{k=m_0}^{n-1} r_k^2 (a^{2}_{k+1,n})^2b_{k+1}\\ =\\\n(c^{-1}-1)^2n\\sum_{k=m_0}^{n-1} r_k^2 b_{k+1}F^2_{k+1,n}(c^{-1})\\\n\\stackrel{a.s}\\longrightarrow\\ (c-1)^2\\|\\mathbf{v}_1\\|^2Z_{\\infty}(1-Z_{\\infty}).\n$$\n\\item\n\\textit{$a.s.-\\lim_{n}n\\sum_{k=m_0}^{n-1} r_k^2 [A^{1}_{k+1,n}B_{k+1}A^{3}_{k+1,n}]_{h,j}$}:\n\\\\\nFirst, when $c\\alpha_j\\neq 1$ notice that\n$n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}[A^{1}_{k+1,n}]_{h,h}[A^{3}_{k+1,n}]_{j,j}$\nhas the same limit as\n\\[\n\\frac{1-c^{-1}}{c\\alpha_j-1}\\!\nn\\!\\sum_{k=m_0}^{n-1}\\! r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(c^{-1})\n-\\frac{1-\\alpha_j}{c\\alpha_j-1}\nn\\!\\sum_{k=m_0}^{n-1}\\! r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(\\alpha_j),\n\\]\nand hence, after standard calculations, we obtain\n$$\nn\\sum_{k=m_0}^{n-1} r_k^2 [B_{k+1}]_{h,j}[A^{1}_{k+1,n}]_{h,h}[A^{3}_{k+1,n}]_{j,j}\\\n\\stackrel{a.s}\\longrightarrow\\\n\\frac{\\alpha_h^{-1}(c-1)+c}\n{c(\\alpha_h+\\alpha_j)-1}(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty}).\n$$\nWhen $c\\alpha_j=1$, $n\\sum_{k=m_0}^{n-1}\nr_k^2[B_{k+1}]_{h,j}[A^{1}_{k+1,n}]_{h,h}[A^{3}_{k+1,n}]_{j,j}$ has the\nsame limit as\n\\[\n(1-c^{-1})\nn\\sum_{k=m_0}^{n-1} \\ln(n\/k)r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(c^{-1})\n+ c^{-1}n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(c^{-1}),\n\\]\nand hence\n$$\nn\\sum_{k=m_0}^{n-1} r_k^2 [B_{k+1}]_{h,j}[A^{1}_{k+1,n}]_{h,h}[A^{3}_{k+1,n}]_{j,j}\\\n\\stackrel{a.s}\\longrightarrow\\\n\\frac{\\alpha_h^{-1}(c-1)+c}{c\\alpha_h}(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)\nZ_{\\infty}(1-Z_{\\infty}).$$\nTherefore we can summarize the limits of the above two cases with the formula\n$$\n\\frac{\\alpha_h^{-1}(c-1)+c}\n{c(\\alpha_h+\\alpha_j)-1}(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty}).\n$$\n\\item\n\\textit{$a.s.-\\lim_{n}n\\sum_{k=m_0}^{n-1} r_k^2\n  a^{2}_{k+1,n}[\\mathbf{b}_{k+1}^{\\top}A^{1}_{k+1,n}]_{j}$}: \\\\\nNotice\nthat\n$$\nn\\sum_{k=m_0}^{n-1} r_k^2\n[\\mathbf{b}_{k+1}]_j[A^{1}_{k+1,n}]_{jj}a^{2}_{k+1,n}=\n(c^{-1}-1)n\\sum_{k=m_0}^{n-1} r_k^2\n[\\mathbf{b}_{k+1}]_jF_{k+1,n}(\\alpha_j)F_{k+1,n}(c^{-1}),\n$$\nwhich implies that\n$$\nn\\sum_{k=m_0}^{n-1} r_k^2 [\\mathbf{b}_{k+1}]_j[A^{1}_{k+1,n}]_{jj}a^{2}_{k+1,n}\\\n\\stackrel{a.s}\\longrightarrow\\\n\\frac{1-c}{\\alpha_j}(\\mathbf{v}_1^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty}).\n$$\n\\item\n\\textit{$a.s.-\\lim_{n}n\\sum_{k=m_0}^{n-1} r_k^2\n  a^{2}_{k+1,n}[\\mathbf{b}_{k+1}^{\\top}A^{3}_{k+1,n}]_{j}$}:\n\\\\\nFirst,\nwhen $c\\alpha_j\\neq 1$, notice that\\\\ $n\\sum_{k=m_0}^{n-1}\nr_k^2[\\mathbf{b}_{k+1}]_j[A^{3}_{k+1,n}]_{jj}a^{2}_{k+1,n}$ has the\nsame limit as\n\\[\n\\begin{aligned}\n&\\frac{(1-c^{-1})(1-\\alpha_j)}{c\\alpha_j-1}\nn\\sum_{k=m_0}^{n-1} r_k^2[\\mathbf{b}_{k+1}]_jF_{k+1,n}(\\alpha_j)F_{k+1,n}(c^{-1})\\\\\n&- \\frac{(1-c^{-1})^2}{c\\alpha_j-1}n\n\\sum_{k=m_0}^{n-1} r_k^2[\\mathbf{b}_{k+1}]_j F_{k+1,n}^2(c^{-1}),\n\\end{aligned}\n\\]\nwhich implies after some calculations\n$$n\\sum_{k=m_0}^{n-1} r_k^2 [\\mathbf{b}_{k+1}]_j[A^{3}_{k+1,n}]_{jj}a^{2}_{k+1,n}\\\n\\stackrel{a.s}\\longrightarrow\\\n\\frac{1-c}{\\alpha_j}(\\mathbf{v}_1^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty}).\n$$\nWhen $c\\alpha_j=1$, $n\\sum_{k=m_0}^{n-1}\nr_k^2[\\mathbf{b}_{k+1}]_j[A^{3}_{k+1,n}]_{jj}a^{2}_{k+1,n}$ has the\nsame limit as\n\\[\n-(1-c^{-1})^2n\\sum_{k=m_0}^{n-1}\\ln(n\/k)r_k^2[\\mathbf{b}_{k+1}]_jF^2_{k+1,n}(c^{-1})\n-c^{-1}(1-c^{-1})n\\sum_{k=m_0}^{n-1} r_k^2[\\mathbf{b}_{k+1}]_jF^2_{k+1,n}(c^{-1}),\n\\]\nfrom which we can obtain\n$$\nn\\sum_{k=m_0}^{n-1} r_k^2[\\mathbf{b}_{k+1}]_j[A^{3}_{k+1,n}]_{jj}a^{2}_{k+1,n}\\\n\\stackrel{a.s}\\longrightarrow\\\nc(1-c)(\\mathbf{v}_1^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty}).\n$$\nTherefore, we can summarize the limits of the above two cases with the formula\n$$\n\\frac{1-c}{\\alpha_j}(\\mathbf{v}_1^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty}).\n$$\n\\end{itemize}\n\n\\subsubsection{Computations for the almost sure limits of the elements in~\\eqref{eq:matrix_star}}\\label{subsubsection_appendix_technical_computation_1_star}\n\n\\begin{itemize}\n\\item\n\\textit{$a.s.-\\lim_{n}\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2\n  [A^{1}_{k+1,n}B_{k+1}A^{1}_{k+1,n}]_{h,j}$}: \\\\\nBy\nusing~\\eqref{eq:results_limit_star}, we have\n\\begin{multline*}\n\\frac{n}{\\ln(n)}\n\\sum_{k=m_0}^{n-1} r_k^2 [B_{k+1}]_{h,j}[A^{1}_{k+1,n}]_{h,h}[A^{1}_{k+1,n}]_{j,j}\n=\n\\frac{n}{\\ln(n)}\n\\sum_{k=m_0}^{n-1} r_k^2 [B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(\\alpha_j)\n\\\\\n\\stackrel{a.s}\\longrightarrow\n(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty})\n\\begin{cases}\nc^2\\ &\\mbox{ if }b_{\\alpha_h}+b_{\\alpha_j}=0,\\\\\n0\\ &\\mbox{ if }b_{\\alpha_h}+b_{\\alpha_j}\\neq 0.\n\\end{cases}\n\\end{multline*}\n\\item\n\\textit{$a.s.-\\lim_{n}\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2\n  [A^{3}_{k+1,n}B_{k+1}A^{3}_{k+1,n}]_{h,j}$}:\\\\\nSince\n$c(\\alpha_h+\\alpha_j)=1$ implies $c\\alpha_h\\neq 1$ and $c\\alpha_j\\neq\n1$, we have that\n$$\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}\n[A^{3}_{k+1,n}]_{h,h}[A^{3}_{k+1,n}]_{j,j}$$\nhas the same limit as\n\\begin{multline*}\n\\frac{(1-c^{-1})^2}{(c\\alpha_h-1)(c\\alpha_j-1)}\\,\n\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F^2_{k+1,n}(c^{-1})\\\\\n\\begin{aligned}\n&+\\ \\frac{(1-\\alpha_h)(1-\\alpha_j)}{(c\\alpha_h-1)(c\\alpha_j-1)}\\,\n\\frac{n}{\\ln(n)}\n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(\\alpha_j)\\\\\n&-\\frac{(1-\\alpha_h)(1-c^{-1})}{(c\\alpha_h-1)(c\\alpha_j-1)}\\,\n\\frac{n}{\\ln(n)}\n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(c^{-1})\\\\\n&-\\frac{(1-\\alpha_j)(1-c^{-1})}{(c\\alpha_h-1)(c\\alpha_j-1)}\\,\n\\frac{n}{\\ln(n)}\n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_j)F_{k+1,n}(c^{-1}),\n\\end{aligned}\n\\end{multline*}\nwhich is equal to\n$$\no(1) + \\left(\\frac{(\\alpha_h-1)(\\alpha_j-1)}{c^2\\alpha_h\\alpha_j}\\right)\n\\frac{n}{\\ln(n)}\n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(\\alpha_j).\n$$\nHence, we have that\n\\begin{multline*}\n\\frac{n}{\\ln(n)}\n\\sum_{k=m_0}^{n-1} r_k^2 [B_{k+1}]_{h,j}[A^{3}_{k+1,n}]_{h,h}[A^{3}_{k+1,n}]_{j,j}\\\n\\\\\n\\stackrel{a.s}\\longrightarrow\n(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)Z_{\\infty}(1-Z_{\\infty})\n\\begin{cases}\n\\frac{(\\alpha_h-1)(\\alpha_j-1)}{\\alpha_h\\alpha_j}\\\n&\\mbox{ if }b_{\\alpha_h}+b_{\\alpha_j}=0,\\\\\n0\\\n&\\mbox{ if }b_{\\alpha_h}+b_{\\alpha_j}\\neq 0.\n\\end{cases}\n\\end{multline*}\n\\item\n\\textit{$a.s.-\\lim_{n}\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2b_{k+1}\n  (a^{2}_{k+1,n})^2$}: \\\\\nSince the calculations are analogous to those in\nSubsection~\\ref{subsubsection_appendix_technical_computation_1}, we\nhave $$\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2 b_{k+1}(a^{2}_{k+1,n})^2\n\\stackrel{a.s}\\longrightarrow 0.$$\n\\item\n\\textit{$a.s.-\\lim_{n}\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2\n  [A^{1}_{k+1,n}B_{k+1}A^{3}_{k+1,n}]_{h,j}$}:\\\\\nSince $c(\\alpha_h+\\alpha_j)=1$ implies $c\\alpha_j\\neq 1$, we have that\n$$\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1}\nr_k^2[B_{k+1}]_{h,j}[A^{1}_{k+1,n}]_{h,h}[A^{3}_{k+1,n}]_{j,j}$$ has the\nsame limit as\n\\begin{align*}\n\\left(\\frac{1-c^{-1}}{c\\alpha_j-1}\\right)&\n\\frac{n}{\\ln(n)}\n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(c^{-1})\n\\\\\n&\\qquad\\qquad- \\left(\\frac{1-\\alpha_j}{c\\alpha_j-1}\\right)\n\\frac{n}{\\ln(n)}\n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(\\alpha_j)\n\\\\\n&=o(1)- \\left(\\frac{1-\\alpha_j}{c\\alpha_j-1}\\right)\n\\frac{n}{\\ln(n)}\n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}F_{k+1,n}(\\alpha_h)F_{k+1,n}(\\alpha_j).\n\\end{align*}\nHence, we have\n\\begin{multline*}\n\\frac{n}{\\ln(n)}\n\\sum_{k=m_0}^{n-1} r_k^2[B_{k+1}]_{h,j}[A^{1}_{k+1,n}]_{h,h}[A^{3}_{k+1,n}]_{j,j}\\\\\n\\stackrel{a.s}\\longrightarrow\n(\\mathbf{v}_h^{\\top}\\mathbf{v}_j)\nZ_{\\infty}(1-Z_{\\infty})\n\\begin{cases}\n\\frac{c^2(\\alpha_j-1)}{c\\alpha_j-1}=\n\\frac{c(1-\\alpha_j)}{\\alpha_h}\\\n&\\mbox{ if }b_{\\alpha_h}+b_{\\alpha_j}=0,\\\\\n0\\\n&\\mbox{ if } b_{\\alpha_h}+b_{\\alpha_j}\\neq 0.\n\\end{cases}\n\\end{multline*}\n\\item\n\\textit{$a.s.-\\lim_{n}\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2\n  a^{2}_{k+1,n}[\\mathbf{b}_{k+1}^{\\top}A^{1}_{k+1,n}]_{j}$}:\\\\\nSince\nthe calculations are analogous to those in Subsection~\\ref{subsubsection_appendix_technical_computation_1}, we\nhave $$\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2\n[\\mathbf{b}_{k+1}]_ja^{2}_{k+1,n}[A^{1}_{k+1,n}]_{jj}\n\\stackrel{a.s}\\longrightarrow 0.$$\n\\item\n\\textit{$a.s.-\\lim_{n}\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2\n  a^{2}_{k+1,n}[\\mathbf{b}_{k+1}^{\\top}A^{3}_{k+1,n}]_{j}$}:\\\\\nSince\nthe calculations are analogous to those in Subsection~\\ref{subsubsection_appendix_technical_computation_1}, we\nhave $$\\frac{n}{\\ln(n)}\\sum_{k=m_0}^{n-1} r_k^2\n[\\mathbf{b}_{k+1}]_ja^{2}_{k+1,n}[A^{3}_{k+1,n}]_{jj}\n\\stackrel{a.s}\\longrightarrow0.$$\n\\end{itemize}\n\n\\section{Stable convergence and its variants}\\label{app-B}\n\nThis brief appendix contains some basic definitions and results\nconcerning stable convergence and its variants. For more details, we\nrefer the reader to \\cite{crimaldi-2009, crimaldi-libro,\n  cri-let-pra-2007, hall-1980} and the references therein.\\\\\n\n\\indent Let $(\\Omega, {\\mathcal A}, P)$ be a probability space, and let\n$S$ be a Polish space, endowed with its Borel $\\sigma$-field. A {\\em\n  kernel} on $S$, or a random probability measure on $S$, is a\ncollection $K=\\{K(\\omega):\\, \\omega\\in\\Omega\\}$ of probability\nmeasures on the Borel $\\sigma$-field of $S$ such that, for each\nbounded Borel real function $f$ on $S$, the map\n$$\n\\omega\\mapsto\nK\\!f(\\omega)=\\int f (x)\\, K(\\omega)(dx)\n$$\nis $\\mathcal A$-measurable. Given a sub-$\\sigma$-field $\\mathcal H$ of\n$\\mathcal A$, a kernel $K$ is said $\\mathcal H$-measurable if all the\nabove random variables $K\\!f$ are $\\mathcal H$-measurable.\\\\\n\n\\indent On $(\\Omega, {\\mathcal A},P)$, let $(Y_n)_n$ be a sequence of\n$S$-valued random variables, let $\\mathcal H$ be a sub-$\\sigma$-field\nof $\\mathcal A$, and let $K$ be a $\\mathcal H$-measurable kernel on\n$S$. Then we say that $Y_n$ converges {\\em $\\mathcal H$-stably} to\n$K$, and we write $Y_n\\longrightarrow K$ ${\\mathcal H}$-stably, if\n$$\nP(Y_n \\in \\cdot \\,|\\, H)\\stackrel{weakly}\\longrightarrow\nE\\left[K(\\cdot)\\,|\\, H \\right]\n\\qquad\\hbox{for all } H\\in{\\mathcal H}\\; \\hbox{with } P(H) > 0,\n$$where $K(\\cdot)$ denotes the random variable\n  defined, for each Borel set $B$ of $S$, as $\\omega\\mapsto\n  K\\!I_B(\\omega)=K(\\omega)(B)$.  In the case when ${\\mathcal\n  H}={\\mathcal A}$, we simply say that $Y_n$ converges {\\em stably} to\n$K$ and we write $Y_n\\longrightarrow K$ stably. Clearly, if\n$Y_n\\longrightarrow K$ ${\\mathcal H}$-stably, then $Y_n$ converges in\ndistribution to the probability distribution $E[K(\\cdot)]$. Moreover,\nthe $\\mathcal H$-stable convergence of $Y_n$ to $K$ can be stated in\nterms of the following convergence of conditional expectations:\n\\begin{equation}\\label{def-stable}\nE[f(Y_n)\\,|\\, {\\mathcal H}]\\stackrel{\\sigma(L^1,\\, L^{\\infty})}\\longrightarrow\nK\\!f\n\\end{equation}\nfor each bounded continuous real function $f$ on $S$. \\\\\n\n\\indent In \\cite{cri-let-pra-2007} the notion of $\\mathcal H$-stable\nconvergence is firstly generalized in a natural way replacing in\n(\\ref{def-stable}) the single sub-$\\sigma$-field $\\mathcal H$ by a\ncollection ${\\mathcal G}=({\\mathcal G}_n)_n$ (called conditioning\nsystem) of sub-$\\sigma$-fields of $\\mathcal A$ and then it is\nstrengthened by substituting the convergence in\n$\\sigma(L^1,L^{\\infty})$ by the one in probability (i.e. in $L^1$,\nsince $f$ is bounded). Hence, according to \\cite{cri-let-pra-2007}, we\nsay that $Y_n$ converges to $K$ {\\em stably in the strong sense}, with\nrespect to ${\\mathcal G}=({\\mathcal G}_n)_n$, if\n\\begin{equation}\\label{def-stable-strong}\nE\\left[f(Y_n)\\,|\\,{\\mathcal G}_n\\right]\\stackrel{P}\\longrightarrow K\\!f\n\\end{equation}\nfor each bounded continuous real function $f$ on $S$.\\\\\n\n\\indent Finally, a strengthening of the stable convergence in the\nstrong sense can be naturally obtained if in (\\ref{def-stable-strong})\nwe replace the convergence in probability by the almost sure\nconvergence: given a conditioning system ${\\mathcal G}=({\\mathcal\n  G}_n)_n$, we say that $Y_n$ converges to $K$ in the sense of the\n{\\em almost sure conditional convergence}, with respect to ${\\mathcal\n  G}$, if\n\\begin{equation*\nE\\left[f(Y_n)\\,|\\,{\\mathcal G}_n\\right]\\stackrel{a.s.}\\longrightarrow K\\!f\n\\end{equation*}\nfor each bounded continuous real function $f$ on\n  $S$. The almost sure conditional convergence has been introduced in\n  \\cite{crimaldi-2009} and, subsequently, employed by others in the\n  urn model literature (e.g. \\cite{aletti-2009, z}).  \\\\\n\nWe now conclude this section recalling two convergence results that we\nneed in our proofs. \\\\\n\nFrom \\cite[Proposition~3.1]{cri-pra}, we can get the following\nresult.\n\n\\begin{theo}\\label{thm:triangular}\nLet $({\\mathbf T}_{n,k})_{n\\geq 1, 1\\leq k\\leq k_n}$ be a triangular\narray of $d$-dimensional real random vectors, such that, for each\nfixed $n$, the finite sequence $({\\mathbf T}_{n,k})_{1\\leq k\\leq k_n}$\nis a martingale difference array with respect to a given filtration\n$({\\mathcal G}_{n,k})_{k\\geq 0}$. Moreover, let $(t_n)_n$ be a\nsequence of real numbers and assume that the following\nconditions hold:\n\\begin{itemize}\n\\item[(c1)] ${\\mathcal G}_{n,k}{\\underline{\\subset}} {\\mathcal G}_{n+1,\n  k}$ for each $n$ and $1\\leq k\\leq k_n$;\n\\item[(c2)] $\\sum_{k=1}^{k_n} (t_n{\\mathbf\n  T}_{n,k})(t_n{\\mathbf T}_{n,k})^{\\top}=t_n^2\\sum_{k=1}^{k_n} {\\mathbf\n  T}_{n,k}{\\mathbf T}_{n,k}^{\\top} \\stackrel{P}\\longrightarrow \\Sigma$,\n  where $\\Sigma$ is a random positive semi\\-defi\\-ni\\-te matrix;\n\\item[(c3)] $\\sup_{1\\leq k\\leq k_n} |t_n{\\mathbf T}_{n,k}|\n\\stackrel{L^1}\\longrightarrow 0$.\n\\end{itemize}\nThen $t_n\\sum_{k=1}^{k_n}{\\mathbf T}_{n,k}$ converges stably to the\nGaussian kernel ${\\mathcal N}(\\mathbf{0}, \\Sigma)$.\n\\end{theo}\n\nThe following result combines together stable convergence and \nstable convergence in the strong sense.\n\n\\begin{theo}\\cite[Lemma 1]{ber-cri-pra-rig}\\label{blocco}\nSuppose that $C_n$ and $D_n$ are $S$-valued random variables, that $M$\nand $N$ are kernels on $S$, and that ${\\mathcal G}=({\\mathcal G}_n)_n$\nis a filtration satisfying for all $n$\n$$\n\\sigma(C_n)\\underline\\subset{\\mathcal G}_n\\quad\\hbox{and }\\quad\n\\sigma(D_n)\\underline\\subset\n\\sigma\\left({\\textstyle\\bigcup_n}{\\mathcal G}_n\\right)\n$$\n\n\\noindent If $C_n$ stably converges to $M$ and $D_n$ converges to $N$\nstably in the strong sense, with respect to $\\mathcal G$, then\n$$\n(C_n, D_n)\\longrightarrow M \\otimes N \\qquad\\hbox{stably}.\n$$\n(Here, $M\\otimes N$ is the kernel on $S\\times S$ such that $(M\n\\otimes N )(\\omega) = M(\\omega) \\otimes N(\\omega)$ for all $\\omega$.)\n\\end{theo}\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\\subsection{The full water waves system above a flat bottom} \nWe are interested in the long time behavior of the $3D$ water waves system  for suitably small initial data in the flat bottom  setting. \n\nThe water waves system describes the evolution of an  inviscid incompressible fluid with constant density (e.g., water) inside a time dependent  water region   $\\Omega(t)$, which has a free interface $\\Gamma(t)$  and a fixed flat bottom $\\Sigma$.  Above the domain $\\Omega(t)$, it is vacuum. \n\n\nWithout loss of generality, we normalize  the depth of $\\Omega(t)$ to be $1$. In the Eulerian coordinates system,   we can represent the domain ``$\\Omega(t)$'', the interface ``$\\Gamma(t)$'' and the bottom ``$\\Sigma$''  as follows, \n\\[\n\\Omega(t):= \\{(x,y): x\\in \\mathbb{R}^2, -1\\leq y\\leq \\,h(t,x)\\},\\]\n\\[ \\Gamma(t):= \\{(x,y): x\\in \\mathbb{R}^2, y= \\,h(t,x)\\}, \\quad \\Sigma :=\\{(x,y): x\\in \\mathbb{R}^2, y=-1\\}.\n\\]\nWe remark that, for the case we are considering, the size of $h(t,\\cdot)$ will be small all   time.\n\nWe assume that the velocity field is  irrotational. The evolution of fluid is subjected to the gravity effect or the surface tension effect. We can describe the evolution of fluid   by the Euler equation as follows, \n\\begin{equation}\n\\left\\{\\begin{array}{l}\n\\partial_t u + u\\cdot \\nabla u =-\\nabla p -g(0,0,1),\\\\\n\\\\\n\\nabla\\cdot u =0,\\,\\, \\nabla \\times u =0, \\,\\,u(0)=u_0,\\\\\n\\end{array}\\right.\n\\end{equation}\nwhere  ``$g$'' denotes the gravity effect constant.\n\n\nMoreover, we have following boundary conditions,\n\\begin{equation}\\label{boundaryconditions}\n\\left\\{\\begin{array}{lr}\nu\\cdot \\vec{\\mathbf{n}}=0 & \\textup{on\\,\\,$\\Sigma$},\\\\\n\nP=\\sigma H(h) & \\textup{on\\,\\, $\\Gamma(t),$}\\\\\n\n\\partial_t + u\\cdot\\nabla \\textup{tangents to $\\cup_{t} \\Gamma(t)$} & \\textup{on\\, $\\Gamma(t)$,}\n\\end{array}\\right.\n\\end{equation}\nwhere $\\sigma$ denotes the surface tension coefficient and ``$H(h)$ '' denotes the mean curvature of the interface, which is given as follows,\n\\[\nH(h)= \\nabla\\cdot \\Big(\\frac{\\nabla h}{\\sqrt{1+|\\nabla h|^2}}\\Big).\n\\]\n\nThe first boundary condition in (\\ref{boundaryconditions}) means that the fluid cannot go through the fixed bottom. The second boundary condition in (\\ref{boundaryconditions})  comes from the Young-Laplace equation for the pressure. The third boundary condition in (\\ref{boundaryconditions}) represents the kinematic boundary condition, which says that the free interface moves with the normal component of the velocity.\n\n\nRecall that the velocity field is irrotational.  Hence, we can represent it in terms of a velocity potential $\\phi$. We use $\\psi$ to denote the restriction of the velocity potential on the boundary $\\Gamma(t)$, i.e., $\\psi(t,x):=\\phi(t,x,\\,h(t,x))$. From the  incompressible condition and boundary conditions, we can derive the following Laplace equation with two boundary conditions: Neumann type on the bottom and Dirichlet type on the interface,\n\\begin{equation}\\label{harmoniceqn}\n(\\Delta_x + \\partial_y^2)\\phi=0, \\quad \\frac{\\partial \\phi}{\\partial \\vec{\\mathbf{n}}}\\big|_{\\Sigma}=0, \\quad \\phi\\big|_{\\Gamma(t)} = \\psi.\n\\end{equation}\n\nHence, we can reduce (for example, see \\cite{zakharov}) the motion of fluid inside the water region $\\Omega(t)$ to the  evolution of height $\\,h$ and the restricted velocity potential $\\psi$ on the interface $\\Gamma(t)$   as follows,\n\\begin{equation}\\label{fullsystem}\n\\left\\{\\begin{array}{l}\n\\partial_t \\,h= G(\\,h)\\psi,\\\\\n\\\\\n\\partial_t \\psi = - g h + \\sigma H(h) - \\frac{1}{2} |\\nabla \\psi|^2 + \\displaystyle{\\frac{(G(\\,h)\\psi + \\nabla \\,h\\cdot\\nabla \\psi)^2}{2(1+ |\\nabla\\,h|^2)}},\n\\end{array}\\right.\n\\end{equation}\nwhere $G(\\,h)\\psi= \\sqrt{1+|\\nabla\\,h|^2}\\mathcal{N}(\\,h)\\psi$  and $\\mathcal{N}(\\,h)\\psi$ is the Dirichlet-Neumann operator on the interface.\n\n The system (\\ref{fullsystem}) has the following conservation law\n\\[\n\\mathcal{H}(\\,h(t),\\psi(t)) := \\Big[ \\int \\frac{1}{2}\\psi(t) G(\\,h(t))\\psi(t) +\\frac{g}{2}  |\\,h(t)|^2 + \\frac{\\sigma |\\nabla h(t)|^2}{1+\\sqrt{1+|\\nabla h(t)|^2}}\\Big]= \\mathcal{H}(\\,h(0), \\psi(0)).\n\\] \n\nIntuitively speaking, after diagonalizing the system (\\ref{fullsystem}), we find ourself dealing with the following type of  quasilinear dispersive  equation,\n\\begin{equation}\\label{dispersivefullsystem}\n(\\partial_t + i \\widetilde{\\Lambda}) u = \\mathcal{N}(u, \\nabla u),\\quad \\widetilde{\\Lambda} = \\sqrt{|\\nabla| \\tanh(|\\nabla|)(g+\\sigma |\\nabla|^2)}, \\quad u = \\,h + i \\widetilde{\\Lambda}^{-1} |\\nabla|\\tanh{|\\nabla|}\\psi,\n\\end{equation}\n\\begin{equation}\\label{diagonalizedvariable}\n u: \\mathbb{R}_t \\times \\mathbb{R}_x^2\\longrightarrow \\mathbb{C}.\n\\end{equation}\nReaders can temporarily take (\\ref{dispersivefullsystem})   as granted. It would be much clearer after we obtain the linear term of the Dirichlet-Neumann operator, which is $|\\nabla|\\tanh|\\nabla| \\psi$, in section \\ref{DNoperator}. \n\n \n\\subsection{Motivation and the main result of this paper.}\n Note that  the best decay rate that one can expect for a $2D$ dispersive equation is $1\/t$, which is critical to establish the global regularity for small initial data.  \n\n  To know the long time behavior,  it is crucial  to know what type of quadratic term we are dealing with.   Unfortunately, to the best of author's knowledge, there is no previous work that addresses this issue. It  motivates us to study this problem in this paper.\n\nTo identify the quadratic terms, it requires more careful analysis of the Dirichlet-Neumann operator in the flat bottom setting. Note that the water waves system  in the Eulerian coordinates  formulation (\\ref{fullsystem}) is dimensionless.  Since we don't want to limit our scope to the $3$D setting, in this paper,  we will identify structures inside the Dirichlet-Neumann operator as many as possible. \n\n\nTo help readers understand what they will read about the  Dirichlet-Neumann operator in this paper, we   summarize and explain several important properties of  the  Dirichlet-Neumann operator here.  Those understandings will play   important roles in the long time behavior. They are listed as follows,\n\n  \n(i) Unlike the infinite depth setting,   in the flat bottom setting, we don't have   the null structure in the low frequency part.\n  More precisely, if the frequencies of two inputs are $1$ and $0$ respectively, then   the size of symbol is ``$1$'' (flat bottom setting)  instead of ``$0$''(infinite depth setting).\n\n We remark that the principle symbol  of the  Dirichlet-Neumann operator  in the flat bottom setting is still same as in the infinite depth setting. Intuitively speaking, the high frequency parts of the  Dirichlet-Neumann operator in  two setting are almost same.\n\n\n   (ii)   We give the explicit  formula of the quadratic terms of the Dirichlet-Neumann operator, which provides the first step to study the long time behavior of (\\ref{dispersivefullsystem}).\n\n(iii) We formulate the cubic and higher order terms of Dirichlet-Neumann operator   in a fixed point type formulation, which provides a good way to control the high order terms over time. \n\n\n\nAs a starting point and an example, we study  a specific  setting  of the water waves  system (\\ref{fullsystem}), which is the gravity water waves system. More precisely, we consider the gravity effect and neglect the surface tension effect.  After normalizing the gravity effect constant ``$g$ ''to be ``$1$'',  the system (\\ref{fullsystem}) is reduced as follows,\n\\begin{equation}\\label{waterwave}\n\\left\\{\\begin{array}{l}\n\\partial_t \\,h= G(\\,h)\\psi,\\\\\n \n\\partial_t \\psi = -  h  - \\frac{1}{2} |\\nabla \\psi|^2 + \\displaystyle{\\frac{(G(\\,h)\\psi + \\nabla \\,h\\cdot\\nabla \\psi)^2}{2(1+ |\\nabla\\,h|^2)}}.\n\\end{array}\\right.\n\\end{equation}\n\nCorrespondingly, the diagonalized equation  (\\ref{dispersivefullsystem})    is reduced to the \n    quasilinear dispersive  equation as follows,\n\\begin{equation}\\label{dispersive}\n(\\partial_t + i \\Lambda) u = \\mathcal{N}(u, \\nabla u),\\quad \\Lambda = \\sqrt{|\\nabla| \\tanh(|\\nabla|)}, \\quad u = \\,h + i\\Lambda \\psi.\n\\end{equation}\n\nFor the water waves system in the flat bottom setting, a typical issue is that the phases are  highly degenerated at the low frequency part. For example, we   consider a   phase associated with  a quadratic term  of (\\ref{dispersive}) as follows,\n\\[\n\\Lambda(|\\xi|) -\\Lambda(|\\xi-\\eta|)+\\Lambda(|\\eta|) \\approx [|\\xi|-|\\xi-\\eta|+|\\eta|] -\\frac{1}{6}\\big( |\\xi|^3 -|\\xi-\\eta|^3 +|\\eta|^3 \\big), \\quad    |\\eta|\\leq |\\xi|\\sim |\\xi-\\eta|\\ll 1.\n\\]\n\nWhen   ``$\\xi$'' and ``$-\\eta$'' are in the same direction, above phase is of size $|\\xi|^2|\\eta|$, which is highly degenerated.  Because of this issue, generally speaking, it is not hopeful to prove the sharp  $1\/t$ decay rate of the nonlinear  solution over time. As a result, a rough energy estimate is not sufficient to control the growth of energy in the long run. \n\n\nTo get around this issue, instead of working too hard, it turns out that there is a relatively simple way to control the growth of energy. It relies on the   two observations for the system (\\ref{waterwave}) as follows,\n\n (i) We can derive a new $L^2-L^\\infty$ type   energy estimate    after carefully analyzing     the structures inside the quadratic terms  in (\\ref{waterwave}). The input inside quadratic terms is not roughly putted in $L^\\infty$ but in a weaker $L^\\infty$ type space, which has derivatives in front.  See (\\ref{energyestimate}).\n\n  (ii)  The derivatives at low frequency part compensate  the decay rate of the solution of (\\ref{waterwave}).  We can prove that the solution with some derivatives in front decays sharply, despite the fact that the solution itself may not have sharp decay rate. The proof of this fact involves a very delicate Fourier analysis. For those interested readers, please refer to \\cite{wang2} for more details. \n\n \n\n\n\nBefore stating our main result, we define our  main function spaces as follows, \n\\begin{equation}\\label{equation1}\n\\| f \\|_{\\widetilde{W^\\gamma}}:= \\sum_{k \\geq 0, k\\in \\mathbb{Z}}2^{\\gamma k} \\|P_{k} f\\|_{L^\\infty} + \\| P_{\\leq 0} f\\|_{L^\\infty},\n\\end{equation}\n\\begin{equation}\\label{equation2}\n\\| f \\|_{\\widehat{W^{\\gamma,\\alpha}}}:= \\sum_{ k\\in \\mathbb{Z}}(2^{\\alpha k}+2^{\\gamma k}) \\|P_{k} f\\|_{L^\\infty}, \\quad 0\\leq \\alpha \\leq \\gamma, \\quad \\| f\\|_{\\widehat{W^\\gamma}}:= \\| f \\|_{\\widehat{W^{\\gamma,0}}}.\n\\end{equation}\n\n\\begin{theorem}\\label{maintheorem}\nLet $0< \\delta < c$,    $  \\alpha\\in(0,1]$, and $N_0\\geq 6$, where  $c$ is some sufficiently small constant.  If the initial data $(\\,h_0, \\Lambda \\psi_0)\\in H^{N_0+1\/2}(\\mathbb{R}^2)\\times H^{N_0}(\\mathbb{R}^2)$  satisfies the   smallness condition as follows,\n\\begin{equation}\\label{smallnesscondition}\n\\| (h_0, \\Lambda\\psi_0)\\|_{\\widetilde{W^4}} \\leq \\delta, \n\\end{equation}\nthen there exists $T > 0$ such that the system \\textup{(\\ref{waterwave})} has a unique solution $(\\,h, \\Lambda\\psi)\\in C^{0}\\big([0,T]; H^{N_0}(\\mathbb{R}^2)\\times H^{N_0}(\\mathbb{R}^2)\\big)$. Moreover, we have a new type of energy estimate in the time interval of existence as follows,\n\\begin{equation}\\label{energyestimate}\n\\frac{d}{d t}E_{N_0}(t)\\lesssim_{N_0}  \\big[ \\|(\\,h, \\Lambda\\psi)(t)\\|_{\\widehat{W^{4,\\alpha}}} + \\| (\\,h, \\Lambda\\psi)(t)\\|_{\\widehat{W^4}}^2\\big] E_{N_0}(t),\n\\end{equation}\nwhere the energy $E_{N_0}(t)$ is defined in \\textup{(\\ref{energyfunction})}. The size of energy is comparable to $\\|(\\,h, \\Lambda\\psi)(t)\\|_{H^{N_0}}^2$.\n\\end{theorem}\n\n\n\n\n\n\n\\begin{remark}\nNote that smallness condition is not assumed  in  \\cite{alazard1, alazard2,alazard3, lannes}  to derive the local wellposedness. For the \npurpose of obtaining global solution, we impose the  smallness condition (\\ref{smallnesscondition})   to derive (\\ref{energyestimate}) as our main goal, which is the first step to obtain global existence for small initial data. \n\\end{remark}\n\n\nIn our second paper \\cite{wang2}, base  on the results we obtained in this paper, we show  that the solution of the system (\\ref{waterwave}) globally exists and scatters to a linear solution. We will study the long time behaviors of the water waves system (\\ref{fullsystem}) in other settings  in the future. For example, the capillary waves system and the gravity-capillary waves system. We expect that the results we obtained in this paper  will be very helpful to the future study of water waves system in the flat bottom setting. \n\n\\subsection{Previous results.}  To be concise,  we mainly discuss works on the local behavior of the water waves system in this subsection.   For more detailed discussion on the long time behavior, please refer to the introduction  of our second paper \\cite{wang2} and references therein. \n\n\n Starting from the work of Nalimov \\cite{nalimov} and Yoshihara \\cite{yosihara}, there are considerable amount of works on the local theory of the water waves system. In the framework of Sobolev spaces and without smallness assumptions on the initial data, the local wellposedness was first obtained by Wu \\cite{wu1, wu2} for the gravity waves system.  The local wellposedness was also obtained when the surface tension effect is   effective  by Beyer-G\\\"unther  \\cite{beyer}. Later, different methods were developed and many important results were obtained to improve our understanding on the local behavior of the water waves system.  Among many of them, we mention the following works:  Christodoulou-Lindblad \\cite{christodoulou}, Ambrose-Masmoudi \\cite{ambrose}, Lannes \\cite{lannes}, Shatah-Zeng \\cite{shatah1}, Coutand-Shkoller \\cite{coutand1}, Alazard-Burq-Zuily \\cite{alazard1, alazard2, alazard3}. Interested readers may refer there and the references therein for more details. \n\n \nRoughly speaking,  the local existence of the water waves system (\\ref{fullsystem}) holds even when the initial interface  has a unbounded curvature and  the   bottom   is very rough. A fixed length separation between the interface and the bottom is sufficient.  See the works of Alazard-Burq-Zuily \\cite{alazard1, alazard2, alazard3} and Lannes \\cite{lannes} for more details and more precise descriptions.\n\n \\subsection{Main ideas and the outline of this paper}\nTo prove our main theorem, we have to pay attentions to both the low frequency part and the high frequency part. \n\nFor the high frequency part, due to the quasilinear nature of the gravity waves system (\\ref{waterwave}), we have to get around the difficulty of losing  one derivative. Thanks to the work of Lannes \\cite{lannes}, the work of Alazard-M\\'etivier \\cite{alazard4} and the works of  Alazard-Burq-Zuily \\cite{alazard1, alazard2, alazard3}, we can utilize the  paralinearization method to get around the potential loss of one derivative. However, for their purposes, only the high frequency part has been paid attentions in their works.  In this paper, we will  do the paralinearization process   and pay special attentions to the low frequency part at the same time. \n\nFor the low frequency part, more  careful estimates of the Dirichlet-Neumann operator are necessary and essential. Since it is not straightforward to see the fact  that we can gain ``$\\alpha$ ''derivatives for the input that is putted in $L^\\infty-$ type space. For example, for the quadratic term   $\\nabla h \\cdot \\nabla \\psi$ of the Dirichlet-Neumann operator, it is problematic to gain $\\alpha$ derivatives  when $\\psi$ has smaller frequency   because   the total number of derivatives of $\\psi$ in (\\ref{energyestimate})   is  $1+\\alpha$  at the low frequency part  when the input $\\psi$ of the quadratic terms is putted in $L^\\infty$. \n\n\n\n \n\n To close the argument,  we will use the hidden structures inside the system (\\ref{waterwave}) for different scenarios.  Without involving too many details, we give two examples as follows to explain the main ideas behind. (i) When $\\psi$ has a smaller frequency inside $\\nabla h\\cdot \\nabla \\psi$, we can use the hidden symmetry  to move one derivative from $\\nabla h$ to  $\\nabla \\psi$ during energy estimate, hence we have two derivatives in total for $\\psi$. (ii) For some terms, e.g., the good remainder term of  the paralinearization  process,  we can lower their regularities to $L^2$. Hence, we can  put $\\nabla\\psi$ in $L^2$  and  put $\\nabla\\,h$ in $L^\\infty$, as a result the desire estimate (\\ref{energyestimate}) also  holds for this case.\n\n\n\n\n\\vspace{1\\baselineskip}\n\n\\noindent \\textbf{Outline:\\quad }In section \\ref{preliminary}, we introduce   notations and give a quick summary of the paradifferential calculus. In section \\ref{DNoperator}, we study various properties of the Dirichlet-Neumann operator. In section \\ref{parasymm}, we use the paralinearization method to show the good structures inside the system (\\ref{waterwave}), which   help us to find   good substitution   variables. In section \\ref{energyestimatesection}, we  prove the new energy estimate (\\ref{energyestimate}) by using the symmetries inside the  equations satisfied by the  good substitution variables. In the appendix, we   calculate explicitly the quadratic terms of good remainder terms. It aims to help readers   understand the fact that we can gain  gain ``$\\alpha$ ''derivatives in (\\ref{energyestimate}) for the inputs  of quadratic terms, which are putted\t in the $L^\\infty-$ type space.\n\n\n\\vspace{1\\baselineskip}\n\\noindent \\textbf{Acknowledgement} \\quad I thank my Ph.D. advisor Alexandru Ionescu for many helpful discussions and suggestions. The first version of manuscript was done when I was visiting Fudan University and BICMR, Peking University. I thank Prof. Zhen Lei and BICMR for their warm hospitalities during the visits.\n\\section{Preliminary}\\label{preliminary}\n\n\\subsection{Notations} For any two numbers $A$ and $B$, we use  $A\\lesssim B$ and $B\\gtrsim A$ to denote  $A\\leq C B$, where $C$ is an absolute constant. We use   $A\\lesssim_{\\epsilon} B$ to denote $A\\leq C_{\\epsilon} B$, where  constant $C_{\\epsilon}$ depends on $\\epsilon$. For an integer $k\\in\\mathbb{Z}$, we use $k_{+}$ to denote $\\max\\{k,0\\}$ and   use $k_{-}$ to denote $\\min\\{k,0\\}$.\n\nThroughout this paper, we will abuse the notation of $``\\Lambda\"$. When  there is no lower script associated with $\\Lambda$, then  $\\Lambda:=\\sqrt{\\tanh(|\\nabla|)|\\nabla|}$, which is the linear operator associated with the  system (\\ref{dispersive}). For $p\\in \\mathbb{N}_{+}$, we  use   $\\Lambda_{p}(\\mathcal{N})$ to denote the $p$-th order terms of a nonlinearity $\\mathcal{N}$  when a Taylor expansion  for the nonlinearity $\\mathcal{N}$ is available.   For example, $\\Lambda_{2}[\\mathcal{N}]$ denotes the quadratic term of $\\mathcal{N}$.   We also use   $\\Lambda_{\\geq p}[\\mathcal{N}]$ to denote the $p$-th  and higher orders terms. More precisely, $\\Lambda_{\\geq p}[\\mathcal{N}]:=\\sum_{q\\geq p}\\Lambda_{q}[\\mathcal{N}]$.  In this paper, \n the Taylor expansion and $\\Lambda_{p}[\\cdot]$  are in terms of $\\,``h\"$ and $``\\psi\"$ when there is no special annotation.\n\n\nWe fix an even smooth function $\\tilde{\\psi}:\\mathbb{R} \\rightarrow [0,1]$, which is supported in $[-3\/2,3\/2]$ and equals to $1$ in $[-5\/4, 5\/4]$. For any $k\\in \\mathbb{Z}$, define\n\\[\n\\psi_{k}(x) := \\tilde{\\psi}(x\/2^k) -\\tilde{\\psi}(x\/2^{k-1}), \\quad \\psi_{\\leq k}(x):= \\tilde{\\psi}(x\/2^k), \\quad \\psi_{\\geq k}(x):= 1-\\psi_{\\leq k-1}(x).\n\\]\nDenote the projection operators $P_{k}$, $P_{\\leq k}$ and $P_{\\geq k}$ by the Fourier multipliers $\\psi_{k},$ $\\psi_{\\leq k}$ and $\\psi_{\\geq k }$ respectively. For a well defined function $f$, we will also use the notation $f_{k}$ to abbreviate $P_{k} f$.\n\n\n\n The Fourier transform is defined as follows, \n\\[\n\\mathcal{F}(f)(\\xi) = \\int_{\\mathbb{R}^2} e^{-i x\\cdot \\xi} f (x) d x. \n\\] \n For two well defined functions $f$ and $g$ and  a bilinear form  $Q(f,g)$, we will use the convention that the symbol $q(\\cdot, \\cdot)$ of $Q(\\cdot, \\cdot)$  is defined in the following sense throughout this paper,\n\\begin{equation}\n\\mathcal{F}[Q(f,g)](\\xi)= \\frac{1}{4\\pi^2} \\int_{\\mathbb{R}^2} \\widehat{f}(\\xi-\\eta)\\widehat{g}(\\eta)q(\\xi-\\eta, \\eta) d \\eta. \n\\end{equation}\nMeanwhile, for a trilinear form $C(f, g, h)$, its symbol $c(\\cdot, \\cdot, \\cdot)$ is defined in the following sense, \n\\[\n\\mathcal{F}[C(f,g,h)](\\xi) =  \\frac{1}{16\\pi^4} \\int_{\\mathbb{R}^2}\\int_{\\mathbb{R}^2} \\widehat{f}(\\xi-\\eta)\\widehat{g}(\\eta-\\sigma) \\widehat{h}(\\sigma) c(\\xi-\\eta, \\eta-\\sigma, \\sigma) d \\eta d \\sigma.\n\\]\n\n\\subsection{Multilinear estimate}\n\n\nWe define a class of symbol and its associated norms as follows,\n\\[\n\\mathcal{S}^\\infty:=\\{ m: \\mathbb{R}^4\\,\\textup{or}\\, \\mathbb{R}^6 \\rightarrow \\mathbb{C}, m\\,\\textup{is continuous and }  \\quad \\| \\mathcal{F}^{-1}(m)\\|_{L^1} < \\infty\\},\n\\]\n\\[\n\\| m\\|_{\\mathcal{S}^\\infty}:=\\|\\mathcal{F}^{-1}(m)\\|_{L^1}, \\quad \\|m(\\xi,\\eta)\\|_{\\mathcal{S}^\\infty_{k,k_1,k_2}}:=\\|m(\\xi, \\eta)\\psi_k(\\xi)\\psi_{k_1}(\\xi-\\eta)\\psi_{k_2}(\\eta)\\|_{\\mathcal{S}^\\infty},\n\\]\n\\[\n \\|m(\\xi,\\eta,\\sigma)\\|_{\\mathcal{S}^\\infty_{k,k_1,k_2,k_3}}:=\\|m(\\xi, \\eta,\\sigma)\\psi_k(\\xi)\\psi_{k_1}(\\xi-\\eta)\\psi_{k_2}(\\eta-\\sigma)\\psi_{k_3}(\\sigma)\\|_{\\mathcal{S}^\\infty}.\n\\]\n\n\\begin{lemma}\\label{multilinearestimate}\nAssume that $m$, $m'\\in S^\\infty$, $p, q, r, s \\in[1, \\infty]$ , then the following estimates hold for  well defined functions $f(x), g(x)$, and $h(x)$, \n\\begin{equation}\\label{productofsymbol}\n\\| m\\cdot m'\\|_{S^\\infty} \\lesssim \\| m \\|_{S^\\infty}\\| m'\\|_{S^\\infty},\n\\end{equation}\n\\begin{equation}\\label{bilinearesetimate}\n\\Big\\| \\mathcal{F}^{-1}\\big[\\int_{\\mathbb{R}^2} m(\\xi, \\eta) \\widehat{f}(\\xi-\\eta) \\widehat{g}(\\eta) d \\eta\\big]\\Big\\|_{L^p} \\lesssim \\| m\\|_{\\mathcal{S}^\\infty}\\| f \\|_{L^q}\\| g \\|_{L^r}  \\quad \\textup{if}\\,\\,\\, \\frac{1}{p} = \\frac{1}{q} + \\frac{1}{r},\n\\end{equation}\n\\begin{equation}\\label{trilinearesetimate}\n\\Big\\| \\mathcal{F}^{-1}\\big[\\int_{\\mathbb{R}^2}\\int_{\\mathbb{R}^2} m'(\\xi, \\eta,\\sigma) \\widehat{f}(\\xi-\\eta) \\widehat{h}(\\sigma) \\widehat{g}(\\eta-\\sigma)  d \\eta d\\sigma\\big] \\Big\\|_{L^{p}} \\lesssim \\|m'\\|_{\\mathcal{S}^\\infty} \\| f \\|_{L^q}\\| g \\|_{L^r} \\| h\\|_{L^s},\\,\\, \\end{equation}\nwhere $ \\displaystyle{\\frac{1}{p} = \\frac{1}{q} + \\frac{1}{r} + \\frac{1}{s}}.$\n\\end{lemma}\n\n\nTo estimate the $\\mathcal{S}^{\\infty}_{k,k_1,k_2}$ norm  and the $\\mathcal{S}^{\\infty}_{k,k_1,k_2,k_3}$ norm  of symbols, we   constantly use the following lemma . \n\\begin{lemma}\\label{Snorm}\nFor $i\\in\\{1,2,3\\}, $ if $f:\\mathbb{R}^{2i}\\rightarrow \\mathbb{C}$ is a smooth function and $k_1,\\cdots, k_i\\in\\mathbb{Z}$, then the following estimate holds,\n\\begin{equation}\\label{eqn61001}\n\\| \\int_{\\mathbb{R}^{2i}} f(\\xi_1,\\cdots, \\xi_i) \\prod_{j=1}^{i} e^{i x_j\\cdot \\xi_j} \\psi_{k_j}(\\xi_j) d \\xi_1\\cdots  d\\xi_i \\|_{L^1_{x_1, \\cdots, x_i}} \\lesssim \\sum_{m=0}^{i+1}\\sum_{j=1}^i 2^{m k_j}\\|\\partial_{\\xi_j}^m f\\|_{L^\\infty} .\n \\end{equation}\n\\end{lemma}\n\\begin{proof}\nThe case when $i=1,3$ can be estimated in the same way as the case when $i=2$. We only do the case $i=2$ in details here. Through scaling, it is  sufficient to prove above estimate for the case when $k_1=k_2=0$. From Plancherel theorem, we have the following two estimates, \n\\[\n \\| \\int_{\\mathbb{R}^{2i}} f(\\xi_1,\\xi_2) e^{i (x_1\\cdot \\xi_1+ x_2\\cdot \\xi_2)} \\psi_{0}(\\xi_1) \\psi_{0}(\\xi_2) d \\xi_1 d\\xi_2 \\|_{L^2_{x_1, x_2}}\\lesssim \\| f(\\xi_1, \\xi_2)\\|_{L^\\infty_{\\xi_1, \\xi_2}},\n\\]\n\\[\n \\| (|x_1|+|x_2|)^3 \\int_{\\mathbb{R}^{2i}} f(\\xi_1,\\xi_2) e^{i (x_1\\cdot \\xi_1+ x_2\\cdot \\xi_2)} \\psi_{0}(\\xi_1) \\psi_{0}(\\xi_2) d \\xi_1 d\\xi_2 \\|_{L^2_{x_1, x_2}}\\lesssim  \\sum_{m=0}^3\\big[\\|\\partial_{\\xi_1}^m f\\|_{L^\\infty} + \\| \\partial_{\\xi_2}^m f \\|_{L^\\infty}\\big],\n\\]\nwhich are sufficient to finish the proof of (\\ref{eqn61001}).\n\\end{proof}\n\n\\subsection{Paradifferential calculus}\nIn this subsection, we discuss some necessary background materials of the paradifferential calculus. For more details and related topics, please refer to \\cite{para} and references therein.\n\\begin{definition}\nGiven $\\rho\\in \\mathbb{N}_{+}, \\rho \\geq 0$ and $m\\in \\mathbb{R}$, we use $\\Gamma^{m}_{\\rho}(\\mathbb{R}^2)$  to denote the space of locally bounded functions $a(x,\\xi)$ on $\\mathbb{R}^2\\times (\\mathbb{R}^2\/\\{0\\})$, which are $C^{\\infty}$ with respect to $\\xi$ for $\\xi\\neq 0 $. Moreover, they satisfy the following estimate, \n\\[\n\\forall |\\xi|\\geq 1\/2, \\| \\partial_{\\xi}^{\\alpha} a(\\cdot, \\xi)\\|_{W^{\\rho, \\infty}}\\lesssim_{\\alpha} (1+|\\xi|)^{m-|\\alpha|}, \\quad \\alpha\\in \\mathbb{N}^2,\n\\]\nwhere $W^{\\rho, \\infty}$ is the usual Sobolev space. Note that $W^{\\rho, \\infty}$ contains the spaces $\\widetilde{W^\\rho}$ and $\\widehat{W^{\\rho, \\alpha}}$, which are defined in (\\ref{equation1}) and (\\ref{equation2}),  as subspaces.\n\\end{definition}\n\n\\begin{remark}\n$\\rho$ in above definitions is not necessary an integer, but the integer case is sufficient for our purpose.\n\\end{remark}\n\n\\begin{definition}\n\\begin{enumerate}\n\\item[(i)] We use   $\\dot{\\Gamma}^{m}_{\\rho}(\\mathbb{R}^2)$ to denote the subspace of $\\Gamma^{m}_{\\rho}(\\mathbb{R}^2)$, which consists of symbols that are homogeneous of degree $m$ in $\\xi.$ \\\\\n\\item[(ii)] If $a= \\displaystyle{\\sum_{0\\leq j < \\rho} a^{(m-j)}}$, where $a^{(m-j)}\\in \\dot{\\Gamma}^{m-j}_{\\rho-j}(\\mathbb{R}^2)$, then we say $a^{(m)}$ is the principal symbol of $a$.\\\\\n\\item[(iii)] An operator $T$ is said to be of order $m$, $m\\in \\mathbb{R}$, if for all $\\mu\\in\\mathbb{R}$, it's bounded from $H^{\\mu}(\\mathbb{R}^2)$ to $H^{\\mu-m}(\\mathbb{R}^2)$. We use $S^{m}$ to denote the set of all operators of order m.\n\\end{enumerate}\n\\end{definition}\nFor symbol $a\\in \\Gamma^{m}_{\\rho}$, we can define its norm as follows,\n\\[\nM^{m}_{\\rho}(a):= \\sup_{|\\alpha|\\leq 2+\\rho} \\sup_{|\\xi|\\geq 1\/2} \\| (1+|\\xi|)^{|\\alpha|-m}\\partial_{\\xi}^{\\alpha} a (\\cdot, \\xi)\\|_{W^{\\rho, \\infty}}.\n\\]\n\n\n\n\nFor  \n$a, f\\in L^2$ and  a pseudo differential operator $\\tilde{a}(x,\\xi)$, we define the operator $T_{a} f$ and $T_{\\tilde{a}} f$ as follows,\n \\begin{equation}\\label{eqn1001}\nT_a f = \\mathcal{F}^{-1}[\\int_{\\mathbb{R}} \\widehat{a}(\\xi-\\eta) \\theta(\\xi-\\eta, \\eta)\\widehat{f}(\\eta) d \\eta]\n,\\,\\, T_{\\tilde{a}} f = \\mathcal{F}^{-1} [ \\int_{\\mathbb{R}} \\mathcal{F}_x(\\tilde{a})(\\xi-\\eta,\\eta) \\theta(\\xi-\\eta,\\eta)\\widehat{f}(\\eta) d \\eta  ],\n\\end{equation}\nwhere the cut-off function  $\\theta(\\xi-\\eta, \\eta) $ is defined as follows,\n\\[\n\\theta(\\xi-\\eta, \\eta) = \\left\\{\\begin{array}{ll}\n1 & \\textup{when}\\,\\,|\\xi-\\eta|\\leq 2^{-10} |\\eta|, |\\eta| \\geq 1,\\\\\n0 & \\textup{when}\\,\\, |\\xi-\\eta| \\geq 2^{10} |\\eta|\\,\\, \\textup{or $|\\eta|\\leq 1$}.\\\\\n\\end{array}\\right.\n\\]\nFor two well defined functions $a$ and $b$, we have the   paraproduct decomposition as follows,\n\\begin{equation}\\label{equation340}\na b = T_a b + T_b a + \\mathcal{R}(a,b),\n\\end{equation}\nwhere $\\mathcal{R}(a,b)$ contains those terms in which $a$ and $b$ have comparable size of frequencies or the frequency of output is less than ``$1$''.\n\n\n We have the following composition lemma for paradifferential operators. It can be found, for example, in \\cite{ alazard1,para}.\n\\begin{lemma}\\label{composi}\nLet $m\\in \\mathbb{R}$ and $\\rho >0$. If given symbols $a\\in \\Gamma_{\\rho}^{m}(\\mathbb{R}^d)$ and $b\\in\\Gamma_{\\rho}^{m'}(\\mathbb{R}^d)$,  we   define\n\\[\na\\sharp b = \\sum_{|\\alpha|< \\rho} \\frac{1}{i^{|\\alpha|} \\alpha!} \\partial_{\\xi}^{\\alpha} a \\partial_{x}^{\\alpha}b,\n\\]\nthen for all $\\mu\\in\\mathbb{R}$, there exists a constant $K$ such that \n\\begin{equation}\\label{eqn700}\n\\| T_a T_b - T_{a\\sharp b}\\|_{H^{\\mu}\\rightarrow H^{\\mu-m-m'+\\rho}} \\leq K M^{m}_{\\rho}(a) M^{m'}_{\\rho}(b).\n\\end{equation}\n\\end{lemma}\n\\begin{remark}\nIt may be too early to give this remark here, but we think that it is a good idea to  keep the following simple observation in mind,   which will be very helpful to see the equivalence relations later. The simple observation is that if the  symbols $a$ and $b$ are all depends on $\\nabla\\,h$ instead of $\\,h$, then the rough estimate (\\ref{eqn700}) is sufficient to gain one derivative at low frequency part. \n\n\\end{remark}\n\n\\begin{lemma}\\label{adjoint}\n Let $m\\in \\mathbb{R}$,  $\\rho >0$ and  $a\\in \\Gamma^{m}_{\\rho}(\\mathbb{R}^d)$. If we use $(T_{a})^{\\ast}$ to denote the adjoint operator of $T_a$ and use $\\bar{\na}$ to denote   the complex conjugate of $a$, then  $(T_{a})^{\\ast}- T_{a^{\\ast}}$ is of order $m-\\rho$, where\n\\[\na^{\\ast} = \\sum_{|\\alpha|< \\rho} \\frac{1}{i^{|\\alpha|} \\alpha !} \\partial_{\\xi}^{\\alpha} \\partial_{x}^{\\alpha} \\bar{a}.\n\\]\nMoreover, the operator norm of $(T_{a})^{\\ast} - T_{a^{\\ast}}$ is bounded by $M^{m}_{\\rho}(a).$\n\\end{lemma}\n\\begin{proof}\nSee \\cite{alazard1}[Theorem 3.10].\n\\end{proof}\n\\begin{remark}\nIn most  applications of Lemma \\ref{adjoint}, we have $m\\leq 1$. If we let $\\rho=1$ in above lemma, then it's easy to see $a^{\\ast}= \\bar{a}$. If moreover  $a$ is real, then $a^{\\ast}=\\bar{a}=a$. \n\\end{remark}\n\n\n\\section{Dirichlet-Neumann operator}\\label{DNoperator}\n\n\nThe main goal of this section is to study various properties of the Dirichlet-Neumann operator, which provide a foundation to do the process of paralinearization and symmetrization in section \\ref{parasymm} and obtain the new energy estimate (\\ref{energyestimate}) in section \\ref{energyestimatesection}.  The study of the Dirichlet-Neumann operator is mainly reduced to study the velocity potential inside the water region $\\Omega(t)$.\n\n\n\n\n\n\n\n\nRecall the smallness condition (\\ref{smallnesscondition}) of the initial data.  From the local wellposedness result of the gravity waves system (\\ref{waterwave}), we know that there exists a   positive time $T$, such that the following estimate holds, \n\\begin{equation}\\label{smallnessestimate}\n\\sup_{t\\in[0,T]} \\| (h, \\Lambda\\psi)(t)\\|_{\\widetilde{W^4}}\\leq 2\\delta,\n\\end{equation}\nwhich means that the $L^\\infty$ norm of solution remains small in the time interval $[0,T].$ Throughout the rest of this paper, we restrict ourself to the time interval $[0,T].$\n\n\n\\subsection{Type I formulation of the Laplace equation (\\ref{harmoniceqn})}\n\n\n\n\nIn this subsection, we   reduce the Laplace equation  (\\ref{harmoniceqn})  into a favorable formulation such that we can solve it and identify the fixed point type structure inside the Laplace equation, which further enables us to estimate the Dirichlet-Neumann operator.  \n\n\nWe   do change of variables and map the water region $\\Omega(t)$ to the strip $\\mathcal{S}:=\\mathbb{R}^2\\times[-1,0]$ as follows,\n\\[\n(x,y)\\rightarrow (x,z), \\quad z: = \\displaystyle{\\frac{y-h(t,x)}{h(t,x)+1}}.\n\\]\nVery naturally, the inverse of transformation is given as follows, \n\\[\ny= h + (h+1)z.\n\\]\n\nDefine the velocity potential in the $(x,z)$ coordinate system as $\\varphi(x,z):= \\phi(x, h+ (h+1)z)$. From direct computations, we have    the following identities, \n\\begin{equation}\\label{eqn640}\n\\phi(x,y)= \\varphi(x, \\frac{y-h}{1+h}), \\quad \\partial_y \\phi = \\frac{\\partial_z\\varphi }{1+h},\\quad \\partial_y^2 \\phi = \\frac{\\partial_z^2 \\varphi}{(1+h)^2},\n\\end{equation}\n\\begin{equation}\\label{eqn641}\n\\partial_{x_i}  \\phi = \\partial_{x_i} \\varphi + \\partial_z \\varphi \\big[\\frac{-\\partial_{x_i}h}{1+h}- \\frac{(y-h)\\partial_{x_i} h}{(1+h)^2}\\big] = \\partial_{x_i}\\varphi - \\frac{(y+1)\\partial_{x_i}h}{(1+h)^2}\\partial_z\\varphi,\n\\end{equation}\n\\[\\partial_{x_i}^2 \\phi = \\partial_{x_i}^2 \\varphi - 2 \\frac{(y+1)\\partial_{x_i} h}{(1+ h)^2}\\partial_z\\partial_{x_i}\\varphi + [\\frac{-(y+1)\\partial_{x_i}^2 h}{(1+ h)^2} + 2\\frac{(y+1)(\\partial_{x_i} h)^2}{(1+ h)^3}] \\partial_z\\varphi + \\frac{(y+1)^2(\\partial_{x_i} h)^2}{(1+h)^4} \\partial_z^2\\varphi.\n\\]\nFrom above identities and (\\ref{harmoniceqn}), it's easy to derive the following equation,\n\\begin{equation}\\label{changeco1}\n(\\Delta_{x}+\\partial_y^2)\\phi = 0 \\Longrightarrow P_{x,z}\\varphi:=[ \\Delta_{x}+ \\tilde{a}\\partial_z^2 +  \\tilde{b}\\cdot \\nabla \\partial_z + \\tilde{c}\\partial_z ] \\varphi=0, \n\\end{equation}\nwhere\n\\begin{equation}\\label{coeff}\n\\tilde{a}= \\frac{(y+1)^2|\\nabla h|^2}{(1+h)^4}  + \\frac{1}{(1+h)^2}=\\frac{1+(z+1)^2|\\nabla h|^2}{(1+h)^2},\n\\end{equation}\n\\begin{equation}\\label{coeff1}\n\\tilde{b}=- 2 \\frac{(y+1)\\nabla h}{(1+h)^2} = \\frac{-2(z+1)\\nabla h}{1+h},\\quad \\tilde{c}= \\frac{-(z+1)\\Delta_{x} h}{(1+h)} + 2\\frac{(z+1)|\\nabla h|^2}{(1+h)^2}. \n\\end{equation}\n\nTo sum up, we can reduce the Laplace equation (\\ref{harmoniceqn}) with two boundary conditions    in terms of  ``$\\varphi$'' as follows,\n\\begin{equation}\\label{harmonic}\nP_{x,z} \\varphi =0, \\quad \\varphi\\big|_{z=0}=\\psi, \\quad \\partial_z\\varphi\\big|_{z=-1} = 0, \\quad (x,z)\\in \\mathbb{R}^2\\times [-1,0].\n\\end{equation}\n\n\\subsection{Type II formulation of the Laplace equation (\\ref{harmoniceqn}) }\\label{type2}\nIn this subsection, we reduce the Laplace equation (\\ref{harmoniceqn}) into another favorable formulation, which will be used  to do the paralinearization of the Dirichlet-Neumann operator in subsection \\ref{paralinearDN}.  \n\nWe remark that we don't use the type I formulation (\\ref{harmonic}) to do the paralinearization process because the coefficients $\\tilde{a}, \\tilde{b}, \\tilde{c}$ in (\\ref{coeff}) and (\\ref{coeff1})  are very complicated, which complicate the paralinearization process and prevent us to see clearly the principle symbol of the Dirichlet-Neumann operator. \n\n\n\n\n\n\nRecall the smallness condition (\\ref{smallnessestimate}). Since  the height of interface  is very small, we know that  there exists a curve parallel to the interface $\\Gamma(t)$ with depth  $1\/2$ inside $\\Omega(t)$. More precisely, we have\n\\[\n\\Omega_1(t):=\\{(x,y): x\\in \\mathbb{R}^2, \\quad \\,h(t,x)-1\/2\\leq y \\leq \\,h(t,x)\\}, \\quad \\Omega_1(t) \\subset \\Omega(t).\n\\]\n  Define \n \\begin{equation}\\label{region2}\n\\Omega_2(t):=\\{(x,y): x\\in \\mathbb{R}^2, \\quad \\,h(t,x)-1\/4\\leq y \\leq \\,h(t,x)\\}, \\quad \\Omega_2(t)\\subset \\Omega_1(t) \\subset \\Omega(t),\n\\end{equation}\n\\begin{equation}\\label{ee1}\n\\tilde{\\phi}(x,y):= \\chi(y-\\,h(t,x)) \\phi(x,y), \\quad (x,y)\\in \\Omega_1(t),\n \\quad \\chi(z)=1\\, \\textup{if $z\\geq -1\/4$}, \\textit{supp}(\\chi)\\subset [-1\/2,0],\\end{equation}\nwhere $\\chi(x)$  is a fixed Schwarz function. \n\nRecall the Laplace equation (\\ref{harmoniceqn}). From   (\\ref{ee1}), it is easy to derive the  following identities\n\\begin{equation}\\label{cutoffharmonic}\n\\Delta_{x,y}\\tilde{\\phi} = \\tilde{g}:= \\Delta_{x,y}[\\chi \\phi ]- \\chi \\Delta_{x,y}\\phi, \\quad (x,y)\\in \\Omega_1(t),\n\\end{equation}\n\\[\n\\tilde{\\phi}(x,y)= {\\phi}(x,y),\\quad \\tilde{g}(x,y)=0, \\quad (x,y)\\in \\Omega_2(t).\n\\]\n\n\n\nWe can map the water region $\\Omega_1(t)$ to the strip $\\mathcal{S}':=\\mathbb{R}^2 \\times [-1\/2,0]$ by changing the coordinate system as follows, \n\\[\n(x, y)\\rightarrow (x, w),\\quad w:= y-\\,h(t,x).\n\\]\nDefine the velocity potential in the $(x,w)$ coordinate system as  $\\Phi(x,w):= \\tilde{\\phi}(x, \\omega+\\,h(t,x)).$ Hence $\\tilde{\\phi}(x,y)= \\Phi(x,y -\\,h(t,x))$. From (\\ref{cutoffharmonic}), it's easy to verify that the following equality holds, \n\\begin{equation}\\label{changco2}\n\\mathcal{P}_{x,w} \\Phi:=[ \\Delta_{x}+ a'\\partial_w^2 +  b'\\cdot \\nabla \\partial_w + c'\\partial_w ]\\Phi = g'(x,w):= \\tilde{g}(x,\\omega+ h(t,x)), \n\\end{equation}\nwhere\n\\begin{equation}\\label{coeff2}\na'= 1 + |\\nabla \\,h|^2, \\quad b'= -2\\nabla \\,h, \\quad c'= -\\Delta \\,h. \n\\end{equation}\n\n \n\n\\begin{remark}\nFrom  (\\ref{coeff}),  (\\ref{coeff1}), and (\\ref{coeff2}), it is easy to see that the coefficients in the equation (\\ref{changco2}) satisfied by ``$\\Phi$''  are much easier and more favorable than the coefficients in  the equation (\\ref{changeco1}) satisfied by ``$\\varphi$''.  However, the equation (\\ref{changco2})  satisfied by $\\Phi$ cannot be used as the starting point because we don't know the   estimates of $\\Phi$ at the first place. \n\\end{remark}\n\n\n\nFrom above definitions,   the following identities hold inside the water region $\\Omega_2(t)$ (see (\\ref{region2})) and its corresponding regions in the new coordinate systems,\n\\[\n\\Phi(x,w)= \\varphi(x,\\frac{w}{1+\\,h}), \\quad \\varphi(x,z)= \\Phi(x,(1+\\,h)z),\\quad  (x,w)\\in \\mathbb{R}^2\\times[-1\/4, 0],\n\\]\n\\begin{equation}\\label{eqq4}\n\\partial_{x_i}\\Phi = \\partial_{x_i}\\varphi -\\frac{w \\partial_z\\varphi \\partial_{x_i} h }{(1+h)^2}\n\\quad \\partial_{w} \\Phi = \\frac{\\partial_{z}\\varphi}{1+\\,h}.\n\\end{equation}\n\n\n\n\nFrom (\\ref{eqn640}) and (\\ref{eqq4}), the Dirichlet-Neumann operator $G( h)\\psi $ in terms of ``$\\varphi$'' and ``$\\Phi$''  and  the quadratic term of $G(\\,h)\\psi$  are given as follows,\n\\begin{equation}\\label{DN1}\nG( h)\\psi = [-\\nabla\\,h\\cdot\\nabla \\phi + \\partial_y\\phi]\\big|_{y=\\,h} = \\frac{1+|\\nabla \\,h|^2}{1+\\,h} \\partial_z \\varphi \\big|_{z=0} -\\nabla\\psi \\cdot \\nabla \\,h,\\quad \n\\end{equation}\n\\begin{equation}\\label{DN2}\nG(h)\\psi=(1+|\\nabla \\,h|^2) \\partial_{w}\\Phi\\big|_{w=0} - \\nabla\\,h \\cdot \\nabla\\psi,\n\\end{equation}\n\\begin{equation}\\label{quadraticformula}\n\\Lambda_{2}[G(\\,h)\\psi]= \\Lambda_{2}[\\partial_z\\varphi\\big|_{z=0}] - \\Lambda_1[\\partial_z\\varphi\\big|_{z=0}]\\,h - \\nabla\\psi \\cdot \\nabla \\,h. \n\\end{equation}\n\n\n \n\\subsection{A fixed point type formulation for the Dirichlet-Neumann operator} In this subsection, our main goal is   to obtain basic estimates of the Dirichlet-Neumann operator with special attention to the low frequency part, which will further help us to obtain a new energy estimate. \n\nTo this end, we  study the reduced Laplace equation (\\ref{harmonic}) and formulate $\\nabla_{x,z}\\varphi$ into a fixed point type formulation, which enables us to use a fixed point type argument. \n\nWe first rewrite the equation (\\ref{harmonic}). After moving all nonlinear terms to the right hand, we can rewrite the  equation (\\ref{harmonic}) as follows,\n\\begin{equation}\\label{eqq40}\n\\partial_z^2\\varphi + \\Delta_x\\varphi = (\\partial_z -|\\nabla|)(\\partial_z +|\\nabla|) \\varphi= g(z) := (1-\\tilde{a})\\partial_z^2 \\varphi - \\tilde{b}\\cdot \\nabla \\partial_z \\varphi - \\tilde{c}\\partial_z\\varphi.\n\\end{equation}\n\n\nNow, we will solve $\\varphi(z)$ from (\\ref{eqq40}) by treating ``$g(z)$''  in (\\ref{eqq40})  as a given nonlinearity.  Define $\\tilde{h}(x,z):= (\\partial_z - |\\nabla|)\\varphi$. Very naturally, we have\n\\begin{equation}\n\\left\\{\\begin{array}{l}\n(\\partial_z + |\\nabla|)\\tilde{h} = g,\\\\\n\\\\\n(\\partial_z- |\\nabla|)\\varphi = \\tilde{h}, \\quad \\varphi\\big|_{z=0}=\\psi,\\partial_{z}\\varphi\\big|_{z=-1}=0.\\\\\n\\end{array}\\right.\n\\end{equation}\nWe can solve above system of equations with $\\tilde{h}(-1)$ to be determined as follows,\n\\[\n\\tilde{h}(z) = e^{-z|\\nabla|}\\tilde{h}(-1) + \\int_{-1}^{z} e^{-(z-z')|\\nabla|} g(z') d z',\\quad \n\\]\n\\[\n\\varphi(z) = e^{z|\\nabla|} \\varphi(0) + \\int_{0}^{z} e^{(z-z')|\\nabla|} \\tilde{h}(z') d z'\n= e^{z|\\nabla|}\\psi - \\int_{z}^{0} e^{(z-z')|\\nabla|} [ e^{-z'|\\nabla|} \\tilde{h}(-1)\\]\n\\[ + \\int_{-1}^{z'} e^{-(z'-s)|\\nabla|} g(s) d s] d z'\n=e^{z|\\nabla|}\\psi -\\frac{1}{2} |\\nabla|^{-1}[e^{-z|\\nabla|}- e^{z|\\nabla|} ]\\tilde{h}(-1)\\]\n\\[- \\int_{-1}^{z} \\int_{z}^{0} e^{(z+s-2z')|\\nabla|} g(s) d z' d s - \\int_{z}^{0} \\int_{s}^0 e^{(z+s-2z')|\\nabla|} g(s) d z' d s\n\\]\n\\begin{equation}\\label{eqn10}\n= e^{z|\\nabla|}\\psi -\\frac{1}{2}|\\nabla|^{-1}[e^{-z|\\nabla|}- e^{z|\\nabla|} ]\\tilde{h}(-1) +\\frac{1}{2} \\int_{-1}^{0} |\\nabla|^{-1}e^{(z+s)|\\nabla|} g(s) d s- \\frac{1}{2} \\int_{-1}^{0} |\\nabla|^{-1} e^{-|z-s||\\nabla|} g(s) d s. \n\\end{equation}\n\nThe unknown $\\tilde{h}(-1)$ is determined by the Neumann type boundary condition $\\partial_{z}\\varphi|_{z=-1}=0$. We calculate $\\partial_z \\varphi $ from the formula (\\ref{eqn10}) and have the following equality,\n\\[\n\\partial_z \\varphi = |\\nabla| e^{z|\\nabla|}\\psi  + \\frac{1}{2} [e^{z|\\nabla|} + e^{-z|\\nabla|}]\\tilde{h}(-1) + \\frac{1}{2} \\int_{-1}^{0} e^{(z+s)|\\nabla|} g(s) ds  - \\frac{1}{2} \\int_{-1}^{0} e^{-|z-s||\\nabla|} \\textup{sign}(s-z) g(s) d s.\n\\]\nAfter evaluating above equality at point $z=-1$, we have\n\\begin{equation}\n\\tilde{h}(-1)= - \\frac{2|\\nabla| e^{-|\\nabla|}\\psi}{e^{-|\\nabla|} + e^{|\\nabla|}} -\\int_{-1}^0 \\frac{e^{(s-1)|\\nabla|} - e^{-(s+1)|\\nabla|}}{e^{-|\\nabla|} + e^{|\\nabla|}} g(s)\\, d s ,\n\\end{equation}\nwhich further gives us \n\\begin{equation}\n\\partial_z \\varphi =  \\frac{e^{(z+1)|\\nabla|}- e^{-(z+1)|\\nabla|}}{e^{-|\\nabla|}+e^{|\\nabla|}} |\\nabla| \\psi -\\frac{1}{2} \\frac{e^{z|\\nabla|}+e^{-z|\\nabla|}}{e^{-|\\nabla|} +e^{|\\nabla|}} \\int_{-1}^0 [e^{(s-1)|\\nabla|}- e^{-(s+1)|\\nabla|}] g(s) \\, d s \n\\end{equation}\n\\begin{equation}\n+ \\frac{1}{2} \\int_{-1}^{0} e^{(z+s)|\\nabla|} g(s) ds  - \\frac{1}{2} \\int_{-1}^{0} e^{-|z-s||\\nabla|} \\textup{sign}(s-z) g(s) d s.\n\\end{equation}\nMoreover, we can reduce (\\ref{eqn10})    as follows, \n\\[\n\\varphi(z) = \\Big[ \\frac{e^{-(z+1)|\\nabla|}+ e^{(z+1)|\\nabla|}}{e^{-|\\nabla|} + e^{|\\nabla|}}\\Big]\\psi + \\frac{1}{2}|\\nabla|^{-1}\\frac{e^{-z|\\nabla|}- e^{z|\\nabla|} }{e^{-|\\nabla|} + e^{|\\nabla|}}\\int_{-1}^0 \\big[e^{(s-1)|\\nabla|} - e^{-(s+1)|\\nabla|}\\big] g(s)\\, d s\n\\]\n\\begin{equation}\\label{eqn11}\n+\\frac{1}{2} \\int_{-1}^{0} |\\nabla|^{-1}e^{(z+s)|\\nabla|} g(s) d s - \\frac{1}{2} \\int_{-1}^{0} |\\nabla|^{-1} e^{-|z-s||\\nabla|} g(s) d s. \n\\end{equation}\n\nHowever, we can not use the formulation  (\\ref{eqn11}) to estimate the velocity potential and the Dirichlet-Neumann operator because $g(z)$ actually depends on the  velocity potential $\\varphi(z)$, see (\\ref{eqq40}). \n\nTo get around this issue. we observe that there exists a    fixed point type structure inside $g(z)$. Recall (\\ref{eqq40}), (\\ref{coeff}), and (\\ref{coeff1}). Note that\n\\[\ng= \\partial_z [ \\frac{2\\,h+\\,h^2 - (z+1)^2 |\\nabla\\,h|^2}{(1+\\,h)^2} \\partial_z \\varphi +\\frac{2(z+1)\\nabla\\,h\\cdot \\nabla\\varphi}{1+\\,h}] - \\frac{2\\nabla \\,h \\cdot \\nabla\\varphi}{1+\\,h}  + \\frac{(z+1)\\Delta \\,h}{1+\\,h}\\partial_z \\varphi,\n\\]\nand\n\\[\n \\frac{(z+1)\\Delta \\,h}{1+\\,h}\\partial_z \\varphi = \\nabla \\cdot [\\frac{(z+1)\\nabla \\,h \\partial_z\\varphi}{1+\\,h}] + \\frac{(z+1)|\\nabla \\,h|^2 \\partial_z\\varphi}{(1+\\,h)^2} -\\partial_z[ \\frac{(z+1)\\nabla \\,h \\cdot \\nabla \\varphi}{1+\\,h} ] + \\frac{\\nabla \\,h\\cdot \\nabla \\varphi}{1+\\,h}.\n\\]\nHence, we can decompose the nonlinearity $g(z)$ into three parts as follows, \n\\begin{equation}\\label{eqq20}\ng(z)= \\partial_z g_1(z)+g_2(z) + \\nabla\\cdot g_3(z),\n\\end{equation}\n where\n\\begin{equation}\\label{eqn12}\ng_1(z) =  \\frac{2\\,h+\\,h^2 - (z+1)^2 |\\nabla\\,h|^2}{(1+\\,h)^2} \\partial_z \\varphi +\\frac{(z+1)\\nabla\\,h\\cdot \\nabla\\varphi}{1+\\,h},\\quad g_1(-1)=0,\n\\end{equation}\n\\begin{equation}\\label{eqn14}\ng_2(z) =\\frac{(z+1)|\\nabla \\,h|^2 \\partial_z\\varphi}{(1+\\,h)^2}  - \\frac{\\nabla \\,h \\cdot \\nabla\\varphi}{1+\\,h} ,\\quad g_3(z)= \\frac{(z+1)\\nabla \\,h \\partial_z\\varphi}{1+\\,h}.\n\\end{equation}\nTo simplify the notation, we define \n\\begin{equation}\\label{tildeeta}\n \\tilde{\\,h}_1:= \\frac{2\\,h+\\,h^2}{(1+\\,h)^2}, \\quad    \\tilde{h}_2:=\\frac{|\\nabla \\,h|^2}{(1+\\,h)^2}, \\quad \\tilde{h}_3:=  \\frac{\\nabla \\,h}{1+\\,h}.\n \\end{equation}\nAs a result, we have\n\\begin{equation}\\label{eqn782}\ng_1(z)=\\tilde{\\,h}_1 \\partial_z \\varphi - (z+1)^2 \\tilde{h}_2  \\partial_z\\varphi + (z+1) \\tilde{h}_3\\cdot \\nabla \\varphi,\n\\end{equation}\n\\begin{equation}\\label{eqn783}\ng_2(z)=  (z+1) \\tilde{h}_2\\partial_z \\varphi - \\tilde{h}_3\\cdot \\nabla \\varphi, \\quad g_3(z)=(z+1)   \\tilde{h}_3 \\partial_z \\varphi.\n\\end{equation}\nNote that $g_1(z)$, $g_2(z)$, and $g_3(z)$ are all linear with respect to $\\nabla_{x,z}\\varphi(z)$.\n\n\n    After decomposing  $g(s)$ in (\\ref{eqn11}) into three parts: ``$\\partial_s g_1 $'', ``$g_2$'' and ``$\\nabla\\cdot g_3$'', we  do integration by parts in ``$s$'' to move the derivative ``$\\partial_s$'' in front of   ``$\\partial_s g_1$'' around.  As a result,   the following equality holds, \n\\[\n\\varphi(z)=\\Big[ \\frac{e^{-(z+1)|\\nabla|}+ e^{(z+1)|\\nabla|}}{e^{-|\\nabla|} + e^{|\\nabla|}}\\Big]\\psi + \\frac{1}{2}|\\nabla|^{-1}\\frac{e^{-z|\\nabla|}- e^{z|\\nabla|} }{e^{-|\\nabla|} + e^{|\\nabla|}}\\int_{-1}^0 \\big[e^{(s-1)|\\nabla|}  (g_2 +\\nabla\\cdot g_3 -|\\nabla| g_1)  \\]\n\\[- e^{-(s+1)|\\nabla|}(g_2 + \\nabla \\cdot g_3+|\\nabla| g_1)  \\big] d s +\\frac{1}{2} \\int_{-1}^{0} |\\nabla|^{-1}e^{(z+s)|\\nabla|} [g_2 +\\nabla\\cdot g_3 -|\\nabla| g_1] d s\n\\]\n\\begin{equation}\\label{solution}\n  - \\frac{1}{2} \\int_{-1}^{0} |\\nabla|^{-1} e^{-|z-s||\\nabla|} [g_2 +\\nabla\\cdot g_3 -\\textup{sign}(z-s)|\\nabla| g_1] d s. \n\\end{equation}\nNow, we know that the nonlinearity in (\\ref{solution}) is linear with respect to $\\nabla_{x,z}\\varphi$. \n\nTo see the fixed point type structure of $\\nabla_{x,z}\\varphi$, we take the derivative  ``$\\nabla_{x,z}$'' on the both hand  sides of (\\ref{solution}). As a result,  we   derive the  fixed point type formulation for $\\nabla_{x,z}\\varphi$ as follows, \n\\[\n\\nabla_{x,z}\\varphi = \\Bigg[ \\Big[ \\frac{e^{-(z+1)|\\nabla|}+ e^{(z+1)|\\nabla|}}{e^{-|\\nabla|} + e^{|\\nabla|}}\\Big]\\nabla\\psi ,  \\frac{e^{(z+1)|\\nabla|}- e^{-(z+1)|\\nabla|}}{e^{-|\\nabla|}+e^{|\\nabla|}} |\\nabla| \\psi\\Bigg] + \\]\n\\[\n\\Bigg[\\frac{1}{2} \\frac{\\nabla}{|\\nabla|}\\frac{e^{-z|\\nabla|}- e^{z|\\nabla|} }{e^{-|\\nabla|} + e^{|\\nabla|}}\\int_{-1}^0  \\big[e^{(s-1)|\\nabla|}  (g_2 + \\nabla \\cdot g_3  -|\\nabla| g_1)  - e^{-(s+1)|\\nabla|}(g_2 + \\nabla \\cdot g_3+|\\nabla| g_1) \\big] d s,\\]\n\\[ -\\frac{1}{2} \\frac{e^{z|\\nabla|}+e^{-z|\\nabla|}}{e^{-|\\nabla|} +e^{|\\nabla|}} \\int_{-1}^0  \\big[e^{(s-1)|\\nabla|}  (g_2+\\nabla \\cdot g_3 -|\\nabla| g_1)  - e^{-(s+1)|\\nabla|}(g_2 +\\nabla\\cdot g_3 +|\\nabla| g_1) \\big] d s \n  \\Bigg] + \n\\]\n\\[\n\\Bigg[ \\frac{1}{2} \\int_{-1}^{0} \\frac{\\nabla}{|\\nabla|}e^{(z+s)|\\nabla|} [g_2+ \\nabla \\cdot g_3-|\\nabla| g_1] d s - \\frac{1}{2} \\int_{-1}^{0} \\frac{\\nabla}{|\\nabla|} e^{-|z-s||\\nabla|} [g_2+ \\nabla \\cdot g_3- \\textup{sign}(z-s)|\\nabla| g_1] d s,\\]\n\\begin{equation}\\label{fixedpoint2}\n\\frac{1}{2} \\int_{-1}^{0} e^{(z+s)|\\nabla|} [g_2+ \\nabla \\cdot g_3-|\\nabla| g_1] ds  - \\frac{1}{2} \\int_{-1}^{0} e^{-|z-s||\\nabla|}  [\\textup{sign}(s-z)(g_2+ \\nabla \\cdot g_3) + |\\nabla| g_1]d s\\Bigg]+ [\\mathbf{0}, g_1(z)].\\end{equation}\nTo simplify the notation, we define  operators as follows,\n\\begin{equation}\\label{equation300}\nK_1(z,s):=\\Big[ \\frac{\\nabla}{2|\\nabla|}\\frac{e^{-z|\\nabla|}- e^{z|\\nabla|} }{e^{-|\\nabla|} + e^{|\\nabla|}}e^{(s-1)|\\nabla|} +\\frac{\\nabla}{2|\\nabla|}e^{(z+s)|\\nabla|} ,  -\\frac{1}{2} \\frac{e^{z|\\nabla|}+e^{-z|\\nabla|}}{e^{-|\\nabla|} +e^{|\\nabla|}}e^{(s-1)|\\nabla|} + \\frac{1}{2}e^{(z+s)|\\nabla|}  \\Big],\n\\end{equation}\n\\begin{equation}\\label{equation301}\nK_2(z,s):= \\Big[ \\frac{\\nabla}{2|\\nabla|}\\frac{e^{-z|\\nabla|}- e^{z|\\nabla|} }{e^{-|\\nabla|} + e^{|\\nabla|}}e^{-(s+1)|\\nabla|}\\,\\, , \\,\\,\n  -\\frac{1}{2} \\frac{e^{z|\\nabla|}+e^{-z|\\nabla|}}{e^{-|\\nabla|} +e^{|\\nabla|}} e^{-(s+1)|\\nabla|} \\Big],\n\\end{equation}\n\\begin{equation}\\label{equation302}\nK_3(z,s)= \\Big[  \\frac{\\nabla}{2|\\nabla|}e^{-|z-s||\\nabla|} \\,\\, , \\,\\, \\frac{1}{2}e^{-|z-s||\\nabla|}\\textup{sign($s-z$)}\\Big].\n\\end{equation}\nWith above operators, we can rewrite (\\ref{fixedpoint2}) as follows,\n\\[\\nabla_{x,z}\\varphi = \\Bigg[ \\Big[ \\frac{e^{-(z+1)|\\nabla|}+ e^{(z+1)|\\nabla|}}{e^{-|\\nabla|} + e^{|\\nabla|}}\\Big]\\nabla\\psi ,  \\frac{e^{(z+1)|\\nabla|}- e^{-(z+1)|\\nabla|}}{e^{-|\\nabla|}+e^{|\\nabla|}} |\\nabla| \\psi\\Bigg] + [\\mathbf{0}, g_1(z)]+ \\]\n\\[\n+\\int_{-1}^{0} [K_1(z,s)-K_2(z,s)-K_3(z,s)](g_2(s)+\\nabla \\cdot g_3(s))  ds \\]\n\\begin{equation}\\label{fixedpoint}\n+\\int_{-1}^{0} K_3(z,s)|\\nabla|\\textup{sign($z-s$)}g_1(s)  -|\\nabla| [K_1(z,s) +K_2(z,s)]g_1(s)\\, d  s.\n\\end{equation}\n  \nTo make sure that we can close the fixed point type argument, we need to check the boundednesses of operators $K_i(z,s)$ such that the issue of losing derivative doesn't exist. More precisely,   the following Lemma holds.\n\n \n\\begin{lemma}\\label{integraloperator}\nFor $k, \\gamma \\geq 0$, we have the following estimates, \n\\begin{equation}\\label{eqn2300}\n\\sum_{i=1,2,3}\\| \\int_{-1}^{0} K_i(z,s)\\nabla g(s) ds \\|_{L^\\infty_z H^k} + \\| \\int_{-1}^{0} K_i(z,s) g(s) ds\\|_{L^\\infty_z H^k} \\lesssim \\|g(z)\\|_{L^\\infty_z H^k},\n\\end{equation}\n\\[\n\\sum_{i=1,2,3}\\| \\int_{-1}^{0} K_i(z,s)\\nabla g(s) ds\\|_{L^\\infty_z \\widetilde{W^\\gamma}}\n\\]\n\\begin{equation}\\label{eqn2301}\n + \\| \\int_{-1}^{0} [K_1(z,s)-K_2(z,s)-K_3(z,s)] g(s) ds \\|_{L^\\infty_z\\widetilde{W^\\gamma}} \\lesssim \\| g(z)\\|_{L^\\infty_z \\widetilde{W^\\gamma}}.\n\\end{equation}\n\\end{lemma}\n\\begin{proof}\nWe first prove the desired estimate (\\ref{eqn2300}).\nRecall (\\ref{equation300}), (\\ref{equation301}), and (\\ref{equation302}). From   Lemma \\ref{Snorm},   the following estimates hold,\t\n\\begin{equation}\\label{equation330}\n\\sup_{z,s\\in[-1,0]}\\|\\mathcal{F}^{-1}[\\mathcal{F}\\big([K_1(z,s)-K_2(z,s)-K_3(z,s)-[0,(1-\\textup{sign($s-z$)})\/2]]\\big)(\\xi)\\psi_{k_1}(\\xi)] \\|_{L^1} \\lesssim 2^{k_{1,-}},  \n\\end{equation}\n\\begin{equation}\\label{equation320}\n\\sup_{z,s\\in[-1,0]}\\sum_{i=1,2,3}\\|\\mathcal{F}^{-1}[\\mathcal{F}\\big(K_i(z,s)\\big)(\\xi)\\psi_{k_1}(\\xi)] \\|_{L^1} \\lesssim 1. \n\\end{equation}\n\nWe will use above estimates for the case when $k_1< 0$. However, when $k_1\\geq 0$, we can not use the estimate  (\\ref{equation320}) directly to estimate the left hand side of (\\ref{eqn2300}), otherwise\t we lose one derivative. An  important observation is that the integration with respect to ``$s$'' actually compensates the loss.\n\n For any fixed $k\\geq 0, k\\in \\mathbb{Z}$, we have the following formulation in terms of kernel,\n\\begin{equation}\\label{equation331}\n\\int_{-1}^{0} K_i(z,s)\\nabla P_k[g(s)] ds  = \\int_{-1}^0\\int_{\\mathbb{R}^2} K_{i;k}(z,s,y) g(s,x-y) d y d s, \\quad \n\\end{equation}\nwhere\n\\[\nK_{i;k}(z,s,y) = \\int_{\\mathbb{R}^2} e^{i y \\cdot \\xi} \\mathcal{F}(K_1(z,s))(\\xi)\\psi_k(\\xi) \\xi d \\xi.\n\\]\nAfter integration by parts in $\\xi$ many times, the following point-wise estimate holds for $i\\in\\{1,2,3\\}$,\n\\begin{equation}\\label{equation332}\n|K_{i;k}(z,s,y)| \\lesssim 2^{3k} \\big( 1 +2^k |y| + 2^k|z-s| \\big)^{-10},\n\\end{equation}\nwhich further implies that the kernel ``$K_{i;k}(z,s,y)$'' belongs to $L^1_{s,y}$ for fixed $z$.\nTherefore, from (\\ref{equation320}) and (\\ref{equation332}), the following estimate holds, \n\\[\n\\big|\\textup{The left hand side of (\\ref{eqn2300})}\\big|^2 \\lesssim \\sum_{k_1\\leq 0} \\| P_{k_1}[g(z)]\\|_{L^\\infty_z L^2}^2 + \\sum_{i=1,2,3} \\sum_{k_1\\geq 0 }  2^{2kk_1} \\| K_{i;k_1}(z,s)\\|_{L^1_{s,y}}^2\\]\n\\[\\times \\| P_{k_1}[g(z)]\\|_{L^\\infty_z L^2}^2   \\lesssim \\| g(z)\\|_{L^\\infty_z H^k}^2. \n\\]\n Hence finishing the proof of (\\ref{eqn2300}).  Very similarly, from (\\ref{equation330}), (\\ref{equation320}), and (\\ref{equation332}), our desired estimate (\\ref{eqn2301}) follows in the same way.  \n\\end{proof}\n\n \n\n\nFrom (\\ref{fixedpoint}) and estimates in Lemma \\ref{integraloperator}, now, it is clear that we can estimate $\\nabla_{x,z}\\varphi$ by using a fixed point type argument.  \n\nHowever, if we do it roughly, then the resulted estimate will not tell the difference between $\\nabla_x \\varphi$ and $\\partial_z \\varphi$. To  capture the fact that $\\partial_z \\varphi$ actually has two derivatives at the low frequency part while $\\nabla_x \\varphi$ only has one derivative, we \tdecompose  $\\nabla_{x,z}\\varphi$ as follows, \n\\begin{equation}\\label{eqq51}\n\\nabla_{x,z}\\varphi = \\Lambda_{1}[\\nabla_{x,z}\\varphi] + \\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi].\n\\end{equation}\nFrom (\\ref{fixedpoint}), it's easy to see that  $ \\Lambda_{1}[\\nabla_{x,z}\\varphi]$ is given as follows, \n \\begin{equation}\\label{eqn773}\n \\Lambda_{1}[\\nabla_{x,z}\\varphi]= \\Bigg[ \\Big[ \\frac{e^{-(z+1)|\\nabla|}+ e^{(z+1)|\\nabla|}}{e^{-|\\nabla|} + e^{|\\nabla|}}\\Big]\\nabla\\psi ,  \\frac{e^{(z+1)|\\nabla|}- e^{-(z+1)|\\nabla|}}{e^{-|\\nabla|}+e^{|\\nabla|}} |\\nabla| \\psi\\Bigg].\n \\end{equation}\nFrom (\\ref{eqn773}), it is easy to see that $\\Lambda_{1}[\\partial_z \\varphi]$ has two derivatives at the low frequency part. Now, the goal  is reduced to estimate  $\\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi]$, which is done again by a fixed-point type argument.\n\n \n\nRecall (\\ref{fixedpoint}). To identify the   fixed point type structure inside $\\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi]$, it is sufficient to reformulate $\\Lambda_{\\geq 2}[g_i(z)], i \\in \\{1,2,3\\}$.\n\n Recall (\\ref{eqn782}) and (\\ref{eqn783}). After using the decomposition (\\ref{eqq51})  for $\\nabla_{x,z}\\varphi$ in  $g_{i}(z), i \\in \\{1,2,3\\}$, we have the decomposition of  $\\Lambda_{\\geq 2}[g_i(z)], i \\in \\{1,2,3\\}$, as follows,\n\\begin{equation}\\label{eqn2001}\n\\Lambda_{\\geq 2}[g_1(z)] = \\tilde{\\,h}_1 \\Lambda_{\\geq 2}[\\partial_z \\varphi] - (z+1)^2  \\tilde{\\,h}_2 \\Lambda_{\\geq 2}[\\partial_z\\varphi] + (z+1) \\tilde{\\,h}_3\\cdot\\Lambda_{\\geq 2}[ \\nabla \\varphi]\n\\end{equation}\n\\begin{equation}\\label{eqn2002}\n+ \\tilde{\\,h}_1 \\Lambda_{1}[\\partial_z \\varphi] - (z+1)^2  \\tilde{\\,h}_2 \\Lambda_{1}[\\partial_z\\varphi] + (z+1)  \\tilde{\\,h}_3\\cdot \\Lambda_{1}[ \\nabla \\varphi],\n\\end{equation}\n\\begin{equation}\\label{eqn2003}\n\\Lambda_{\\geq 2}[g_2(z)]= (z+1)  \\tilde{\\,h}_2\\Lambda_{\\geq 2}[\\partial_z \\varphi] -   \\tilde{\\,h}_3\\cdot \\Lambda_{\\geq 2}[ \\nabla \\varphi]+  (z+1)   \\tilde{\\,h}_2\\Lambda_{1}[\\partial_z \\varphi] -  \\tilde{\\,h}_3\\cdot \\Lambda_{1}[\\nabla \\varphi],\n\\end{equation}\n\\begin{equation}\\label{eqn2004}\n\\Lambda_{\\geq 2}[g_3(z)]=(z+1)  \\tilde{\\,h}_3 \\Lambda_{\\geq 2}[\\partial_z \\varphi] + (z+1)  \\tilde{\\,h}_3 \\Lambda_{1}[\\partial_z \\varphi].\n\\end{equation}\n \nFrom (\\ref{eqn2002}), (\\ref{eqn2003}), and (\\ref{eqn2004}), now it is easy to see that there exists the fixed point type structure for $\\Lambda_{\\geq 2}[\\nabla_{x, z}\\varphi]$ in $\\Lambda_{\\geq 2}[g_i(z)], i \\in \\{1,2,3\\}$. From the standard fixed point type argument and the estimates in Lemma \\ref{integraloperator}, we obtain basic estimates for $\\Lambda_{\\geq 2}[\\nabla_{x, z}\\varphi]$, which further gives us a more precise estimate for $ \\nabla_{x, z}\\varphi $ from (\\ref{eqq51}).\n\n \n\nMore precisely, our main results in this subsection is summarized as follows,\n\\begin{lemma}\\label{Sobolevestimate}\nFor $\\gamma', k' \\geq 1$,  $0< \\delta \\ll 1 $, $\\alpha\\in(0,1],$ if $\\,h \\in \\widetilde{W^{\\gamma'}}\\cap H^{k'}$ satisfies the following smallness assumption:\n\\begin{equation}\\label{smallness}\n\\| \\,h\\|_{\\widetilde{W^{\\gamma'}}} < \\delta,\n \\end{equation}\n  then  the following $L^2-$ type estimate and $L^\\infty-$ type estimate of the velocity potential ``$\\varphi$'' hold,\n\\begin{equation}\\label{eqn2200}\n \\|\\nabla_{x,z}\\varphi\\|_{L^\\infty_z H^k}  \\lesssim \\| \\nabla\\psi\\|_{H^k} + \\| \\,h\\|_{H^{k+1}} \\| \\nabla\\psi\\|_{\\widetilde{W^0}},\\quad \n\\end{equation}\n\\begin{equation}\\label{eqn2201}\n\\| \\nabla_{x}\\varphi\\|_{L^\\infty_z \\widetilde{W^\\gamma}} \\lesssim \\| \\nabla \\psi \\|_{\\widetilde{W^{\\gamma}}} , \\quad \\| \\partial_z \\varphi\\|_{L^\\infty_z \\widetilde{W^{\\gamma}}}\\lesssim\\| \\nabla \\psi\\|_{\\widehat{W}^{\\gamma,\\alpha}}+  \\| \\,h\\|_{\\widetilde{W^{\\gamma+1}}} \\| \\nabla \\psi \\|_{\\widetilde{W^\\gamma}},\n\\end{equation}\n\\begin{equation}\\label{eqn2203}\n\\|\\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi]\\|_{L^\\infty_z\\widetilde{W^{\\gamma}}} \\lesssim \\| \\nabla\\psi\\|_{\\widetilde{W^\\gamma}}\\| \\,h\\|_{\\widetilde{W^{\\gamma+1}}},\n\\end{equation}\n\\begin{equation}\\label{eqn2202}\n\\| \\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi]\\|_{L^\\infty_z H^k} \\lesssim  \\| \\,h\\|_{\\widetilde{W^1}}\\| |\\nabla|\\psi\\|_{H^k} + \\| \\nabla \\psi\\|_{\\widetilde{W^0}}\\| \\,h\\|_{H^{k+1}},\n\\end{equation}\nwhere $k\\leq k'-1$ and $1\\leq \\gamma \\leq \\gamma'-1$. In above estimates, the range of $z$ for the $L^\\infty_z$ norm is  $[-1,0].$\n\\end{lemma}\n\n\n\\begin{proof}\nWe first estimate $\\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi]$. Recall (\\ref{fixedpoint}), (\\ref{eqn2001}), (\\ref{eqn2002}), (\\ref{eqn2003}) and (\\ref{eqn2004}). From estimate   (\\ref{eqn2301}) in Lemma \\ref{integraloperator},  the following estimate holds   \n\\[\n\\| \\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi]\\|_{L^\\infty_z \\widetilde{W^\\gamma}} \\lesssim \\|\\Lambda_{\\geq 2}[(g_1(z), g_2(z), g_3(z))] \\|_{L^\\infty_z \\widetilde{W^\\gamma}}\\]\n\\[\n\\lesssim \\| \\,h\\|_{\\widetilde{W^{\\gamma+1}}} \\| \\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi]\\|_{L^\\infty_z \\widetilde{W^\\gamma}} + \\|\\,h\\|_{\\widetilde{W^{\\gamma+1}}} \\|\\nabla\\psi\\|_{\\widetilde{W^\\gamma}}. \n\\]\nHence, from the smallness condition (\\ref{smallness}), we have\n\\begin{equation}\\label{Linfty}\n\\| \\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi]\\|_{L^\\infty_z \\widetilde{W^\\gamma}} \\lesssim \\| \\,h\\|_{\\widetilde{W^{\\gamma+1}}} \\| \\nabla\\psi\\|_{\\widetilde{W^\\gamma}}.\n\\end{equation}\nVery similarly, from estimate (\\ref{eqn2300}) in Lemma \\ref{integraloperator}, the following estimate holds,\n\\[\n\\| \\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi]\\|_{L^\\infty_z H^k} \\lesssim \\|\\Lambda_{\\geq 2}[(g_1(z), g_2(z), g_3(z))] \\|_{L^\\infty_z H^k}\\lesssim \\| \\,h\\|_{\\widetilde{W^1}} \\| \\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi]\\|_{L^\\infty_z H^k}\\]\n\\[\n + \\| \\,h\\|_{H^{k+1}} \\| \\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi]\\|_{L^\\infty_z \\widetilde{W^0}} + \\| \\,h\\|_{H^{k+1}}\\| \\nabla\\psi\\|_{\\widetilde{W^0}} + \\| \\nabla \\psi\\|_{H^{k}} \\| \\,h\\|_{\\widetilde{W^1}}\n\\]\n\\[\n\\lesssim \\| \\,h\\|_{\\widetilde{W^1}} \\| \\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi]\\|_{L^\\infty_z H^k} \n+ \\| \\,h\\|_{H^{k+1}}\\|\\nabla\\psi\\|_{\\widetilde{W^0}}(1+ \\| \\,h\\|_{\\widetilde{W^1}}) + \\| \\nabla \\psi\\|_{H^{k}} \\| \\,h\\|_{\\widetilde{W^1}}.\n\\]\nAgain, from the smallness assumption (\\ref{smallness}), we conclude\n\\begin{equation}\\label{L2type}\n\\| \\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi]\\|_{L^\\infty_z H^k} \\lesssim \\| \\,h\\|_{H^{k+1}}\\|\\nabla\\psi\\|_{\\widetilde{W^0}} + \\| \\nabla \\psi\\|_{H^{k}} \\| \\,h\\|_{\\widetilde{W^1}}.\n\\end{equation}\nFrom estimates (\\ref{Linfty}) and (\\ref{L2type}) and the explicit formulas of $\\Lambda_{1}[\\nabla_{x,z}\\varphi]$ in (\\ref{eqn773}), we have\n\\[\n\\| \\nabla_{x,z}\\varphi\\|_{L^\\infty H^k} \\lesssim \\| \\nabla\\psi\\|_{H^k} +  \\| \\,h\\|_{H^{k+1}}\\|\\nabla\\psi\\|_{\\widetilde{W^0}},\\quad\\|\\nabla_{x}\\varphi\\|_{L^\\infty_z \\widetilde{W^\\gamma}} \\lesssim \\|\\nabla\\psi\\|_{\\widetilde{W^\\gamma}},\n\\]\n\\[\n\\| \\partial_z \\varphi\\|_{L^\\infty_z \\widetilde{W^\\gamma}} \\lesssim \\| \\Lambda^2\\psi\\|_{\\widetilde{W^\\gamma}} + \\| \\,h\\|_{\\widetilde{W^{\\gamma+1}}} \\| \\nabla\\psi\\|_{\\widetilde{W^\\gamma}}\\lesssim \\|\\nabla\\psi\\|_{\\widehat{W}^{\\gamma, \\alpha}} + \\| \\,h\\|_{\\widetilde{W^{\\gamma+1}}} \\| \\nabla\\psi\\|_{\\widetilde{W^\\gamma}}.\n\\]\nHence  finishing the proof.\n\\end{proof}\n\n\n\\subsection{ The quadratic terms  of the Dirichlet-Neumann operator }\\label{secondorderexpansion} The content of this subsection is not related to the proof of our main theorem. However, it is crucial to the study of the long time behavior of the water waves system in the flat bottom.\n\n Generally speaking, the main enemies of the global existence of a $2D$ dispersive equation are the quadratic terms. The  first step is to know exactly what the enemies are. Surprisingly, as a byproduct of  the fixed point type formulation  (\\ref{fixedpoint}),  we can calculate explicitly the quadratic terms of the Dirichlet-Neumann operator.   \n\n \n\nMore precisely, the main result of this subsection is stated as follows,\n\\begin{lemma}\\label{quadraticterms}\nIn terms of $h$ and $\\psi$, the quadratic terms of   the Dirichlet-Neumann operator is given as follows,\n\\begin{equation}\\label{eqq345}\n\\Lambda_{2}[G(h)\\psi] = -\\nabla\\cdot( h \\nabla\\psi) - |\\nabla| \\tanh|\\nabla|( h |\\nabla| \\tanh|\\nabla| \\psi).\n\\end{equation}\n\\end{lemma}\n\n \n\\begin{remark}\nBefore we proceed to   prove above Lemma, we compare the main difference between the flat bottom setting, which is less studied, and the infinite depth setting, which is well studied recently. In the infinite depth setting, the quadratic terms of the Dirichlet-Neumann operator is given as follows,\n\\begin{equation}\\label{eqq259}\n\\textup{(Infinite depth setting)}\\qquad \\qquad  \\Lambda_{2}[G(h)\\psi] = -\\nabla\\cdot( h \\nabla\\psi) - |\\nabla|  ( h |\\nabla|   \\psi).\n\\end{equation}\n\nIf  the frequency  $ \\eta$   of ``$\\psi$'' is of size $1$ and the frequency  $ \\xi-\\eta$ of ``$h$''   is of size $0$, from (\\ref{eqq345}) and (\\ref{eqq259}),   \nit is easy to check the size of the symbol of quadratic terms as follows,\n\\[\n\\textup{symbol of quadratic term in the flat bottom:} \\quad \\xi\\cdot \\eta - |\\xi||\\eta| \\tanh|\\xi| \\tanh|\\eta| = \\frac{4|\\xi|^2}{(e^{|\\xi|}+e^{-|\\xi|})^2}\\sim 1,\n\\]\n\\[\n\\textup{symbol of quadratic term in the infinite depth setting:}\\qquad  -|\\xi||\\eta| + \\xi \\cdot \\eta =0.\n\\]\n That is to say, unlike the infinite depth setting, we don't have null structure at the low frequency part in  the flat bottom setting. As a result,  we expect much stronger nonlinear effect from the quadratic terms, which makes the global regularity problem in the flat bottom setting more delicate and more difficult than the infinite depth setting.\n\n\n \n \\end{remark}\n\n\\noindent \\textit{Proof of Lemma} \\ref{quadraticterms}.\\qquad Recall (\\ref{DN1}) and (\\ref{eqn773}). We have\n\\begin{equation}\\label{eqqn1}\n\\Lambda_{2}[G(h)\\psi]= \\Lambda_{2}[\\partial_z\\varphi\\big|_{z=0}] - h |\\nabla| \\tanh|\\nabla| \\psi - \\nabla h \\cdot \\nabla \\psi.\n\\end{equation}\nHence,  the problem is reduced to calculate explicitly the quadratic terms of $\\partial_z\\varphi\\big|_{z=0}$. Recall    (\\ref{fixedpoint}) , we have \n\\[\n\\Lambda_{2}[\\partial_z \\varphi \\big|_{z=0}] = -\\frac{1}{e^{|\\nabla|}+e^{-|\\nabla|}} \\int_{-1}^0 [e^{(s-1)|\\nabla|}-e^{-(s+1)|\\nabla|}] [\\Lambda_{2}[g_2+\\nabla\\cdot g_3]] ds \n\\]\n\\[\n+\\frac{1}{e^{|\\nabla|}+e^{-|\\nabla|}} \\int_{-1}^0 [e^{(s-1)|\\nabla|}+e^{-(s+1)|\\nabla|}] |\\nabla| [\\Lambda_{2}[g_1]] ds + \\int_{-1}^{0}e^{s|\\nabla|} \\Lambda_{2}[g_2+\\nabla\\cdot g_3-|\\nabla| g_1] d s + \\Lambda_{2}[g_1(0)]\n\\]\n\\begin{equation}\\label{eqn40}\n= \\int_{-1}^0 \\frac{e^{(s+1)|\\nabla|} + e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+ e^{-|\\nabla|}}\\Lambda_{2}[g_2+\\nabla\\cdot g_3] d s - \\int_{-1}^{0} \\frac{e^{(s+1)|\\nabla|} -e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+e^{-|\\nabla|}} |\\nabla|\\Lambda_{2}[g_1(s)] d s   + \\Lambda_{2}[g_1(0)].\n\\end{equation}\n From  (\\ref{eqn12}),  (\\ref{eqn14}), and (\\ref{eqn773}), it is easy to derive the following equalities, \n\\[\n\\Lambda_{2}[g_1(s)]= 2\\,h \\frac{e^{(s+1)|\\nabla|} -e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+e^{-|\\nabla|}}|\\nabla|\\psi + (s+1)\\nabla \\,h \\cdot \\nabla \\frac{e^{(s+1)|\\nabla|} + e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+e^{-|\\nabla|}}\\psi,\n\\]\n\\begin{equation}\\label{eqn2008}\n\\Lambda_{2}[g_1(0)] = 2  h |\\nabla|\\tanh|\\nabla|  \\psi + \\nabla \\,h\\cdot \\nabla \\psi,\n\\end{equation}\n\\[\n\\Lambda_{2}[g_2(s)]=  - \\nabla \\,h\\cdot \\nabla \\frac{e^{(s+1)|\\nabla|} + e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+e^{-|\\nabla|}}\\psi,\\quad \\Lambda_{2}[g_3(s)]=(s+1)\\nabla \\,h \\frac{e^{(s+1)|\\nabla|} -e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+e^{-|\\nabla|}}|\\nabla|\\psi.\n\\]\nAfter plugging above explicit formulas of $\\Lambda_2[g_i(z)]$, $i\\in\\{1,2,3\\}$, the goal is reduced to calculate explicitly the symbols of two integrals in (\\ref{eqn40}).  Define\n\\begin{equation}\\label{eqnn2}\nQ_1(\\,h,\\psi):=\n\\int_{-1}^{0} \\frac{e^{(s+1)|\\nabla|} + e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+ e^{-|\\nabla|}}\\Lambda_{2}[g_2+\\nabla\\cdot g_3] d s = Q_{1,1}(\\,h,\\psi)+ Q_{1,2}(\\,h, \\psi), \n\\end{equation}\n\\begin{equation}\\label{eqnn6}\nQ_2(\\,h, \\psi) = - \\int_{-1}^{0} \\frac{e^{(s+1)|\\nabla|} -e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+e^{-|\\nabla|}} |\\nabla|\\Lambda_{2}[g_1] d s= Q_{2,1}(\\,h, \\psi) + Q_{2,2}(\\,h,\\psi),\n\\end{equation}\nwhere\n\\[\nQ_{1,1}(\\,h, \\psi) = \\int_{-1}^{0} \\frac{e^{(s+1)|\\nabla|} + e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+ e^{-|\\nabla|}}\\Big[\n\\nabla \\cdot[(s+1)\\nabla \\,h \\frac{e^{(s+1)|\\nabla|} -e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+e^{-|\\nabla|}}|\\nabla|\\psi \\Big] d s,\n\\]\n\\[\nQ_{1,2}(\\,h, \\psi) = \\int_{-1}^{0} \\frac{e^{(s+1)|\\nabla|} + e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+ e^{-|\\nabla|}}\\Big[\n- \\nabla \\,h\\cdot \\nabla \\frac{e^{(s+1)|\\nabla|} + e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+e^{-|\\nabla|}}\\psi \\Big] d s,\n\\]\n\\[\nQ_{2,1}(\\,h,\\psi)= - \\int_{-1}^{0} \\frac{e^{(s+1)|\\nabla|} -e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+e^{-|\\nabla|}} |\\nabla|\\Big[2\\,h \\frac{e^{(s+1)|\\nabla|} -e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+e^{-|\\nabla|}}|\\nabla|\\psi\\Big] d  s,\n\\]\n\\[\nQ_{2,2}(\\,h, \\psi)= - \\int_{-1}^{0} \\frac{e^{(s+1)|\\nabla|} -e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+e^{-|\\nabla|}} |\\nabla|\\Big[(s+1)\\nabla \\,h \\cdot \\nabla \\frac{e^{(s+1)|\\nabla|} + e^{-(s+1)|\\nabla|}}{e^{|\\nabla|}+e^{-|\\nabla|}}\\psi\\Big] d  s.\n\\]\nThe   symbol $q_{i,j}(\\xi-\\eta, \\eta)$ of bilinear operator $Q_{i,j}(h, \\psi)$, $i,j\\in\\{1,2\\},$ is given as follows, \n\\[\nq_{1,1}(\\xi-\\eta,\\eta)= \\frac{-\\xi\\cdot (\\xi-\\eta)|\\eta|}{(e^{|\\xi|}+e^{-|\\xi|})(e^{|\\eta|}+e^{-|\\eta|})} \\int_{-1}^{0} (s+1)[e^{(s+1)|\\xi|} + e^{-(s+1)|\\xi|}][e^{(s+1)|\\eta|} - e^{-(s+1)|\\eta|}]  d s\n\\] \n\\[\n= \\frac{-\\xi\\cdot (\\xi-\\eta)|\\eta|}{(e^{|\\xi|}+e^{-|\\xi|})(e^{|\\eta|}+e^{-|\\eta|})}\\Big[\\frac{(|\\xi|+|\\eta|-1)e^{|\\xi|+|\\eta|}-(-|\\xi|-|\\eta|-1)e^{-|\\xi|-|\\eta|}}{(|\\xi|+|\\eta|)^2}\n\\]\n\\begin{equation}\\label{eqn42}\n+ \\frac{(|\\eta|-|\\xi|-1)e^{|\\eta|-|\\xi|}-(|\\xi|-|\\eta|-1)e^{|\\xi|-|\\eta|}}{(|\\xi|-|\\eta|)^2}\\Big],\n\\end{equation}\n\n\\[\nq_{1,2}(\\xi-\\eta,\\eta) = \\frac{(\\xi-\\eta)\\cdot \\eta}{(e^{|\\xi|}+e^{-|\\xi|})(e^{|\\eta|}+e^{-|\\eta|})} \\int_{-1}^{0}[e^{(s+1)|\\xi|} + e^{-(s+1)|\\xi|}][e^{(s+1)|\\eta|} +e^{-(s+1)|\\eta|}] d s  \n\\]\n\\begin{equation}\\label{eqnn3}\n= \\frac{(\\xi-\\eta)\\cdot \\eta}{(e^{|\\xi|}+e^{-|\\xi|})(e^{|\\eta|}+e^{-|\\eta|})} \\Big[ \\frac{e^{|\\xi|+|\\eta|}-e^{-|\\xi|-|\\eta|}}{|\\xi|+|\\eta|} + \\frac{e^{|\\xi|-|\\eta|} - e^{|\\eta|-|\\xi|}}{|\\xi|-|\\eta|} \\Big].\n\\end{equation}\n\\[\nq_{2,1}(\\xi-\\eta, \\eta) = \\frac{-2|\\xi||\\eta|}{(e^{|\\xi|}+e^{-|\\xi|})(e^{|\\eta|}+e^{-|\\eta|})}\\int_{-1}^0 [e^{(s+1)|\\xi|} - e^{-(s+1)|\\xi|}][e^{(s+1)|\\eta|} -e^{-(s+1)|\\eta|}]  d s\n\\]\n\\begin{equation}\\label{eqn80}\n= \\frac{-2|\\xi||\\eta|}{(e^{|\\xi|}+e^{-|\\xi|})(e^{|\\eta|}+e^{-|\\eta|})}\\Big[  \\frac{e^{|\\xi|+|\\eta|}-e^{-|\\xi|-|\\eta|}}{|\\xi|+|\\eta|} -  \\frac{e^{|\\xi|-|\\eta|} - e^{|\\eta|-|\\xi|}}{|\\xi|-|\\eta|} \n\\Big],\n\\end{equation}\n\\[\nq_{2,2}(\\xi-\\eta,\\eta)=  \\frac{|\\xi|(\\xi-\\eta)\\cdot \\eta}{(e^{|\\xi|}+e^{-|\\xi|})(e^{|\\eta|}+e^{-|\\eta|})} \\int_{-1}^0 (s+1)[e^{(s+1)|\\xi|}-e^{-(s+1)|\\xi|}][e^{(s+1)|\\eta|} + e^{-(s+1)|\\eta|}]  d s\n\\]\n\\[\n=  \\frac{|\\xi|(\\xi-\\eta)\\cdot \\eta}{(e^{|\\xi|}+e^{-|\\xi|})(e^{|\\eta|}+e^{-|\\eta|})}\\Big[\\frac{(|\\xi|+|\\eta|-1)e^{|\\xi|+|\\eta|}-(-|\\xi|-|\\eta|-1)e^{-|\\xi|-|\\eta|}}{(|\\xi|+|\\eta|)^2}\n\\]\n\\begin{equation}\\label{eqn81}\n- \\frac{(|\\eta|-|\\xi|-1)e^{|\\eta|-|\\xi|}-(|\\xi|-|\\eta|-1)e^{|\\xi|-|\\eta|}}{(|\\xi|-|\\eta|)^2}\\Big].\n\\end{equation}\n In above computations, we used the  following simple fact,\n\\[\n\\int_{-1}^{0} (s+1) e^{(s+1) a} d s = \\frac{1+(a-1)e^{a}}{a^2}.\n\\]\nFrom  (\\ref{eqqn1}), (\\ref{eqn40}), (\\ref{eqn2008}), (\\ref{eqnn2}) and (\\ref{eqnn6}), we have\n\\[\n\\Lambda_2[G(\\,h)\\psi]:=\\widetilde{Q}( h, \\psi)= Q_1(h,\\psi) + Q_2(h,\\psi) + h |\\nabla| \\tanh|\\nabla| \\psi.\n\\]\nTherefore, the symbol $\\tilde{q}(\\xi-\\eta, \\eta)$ of $\\widetilde{Q}( h, \\psi)$ is given as follows, \n\\[\n\\tilde{q}(\\xi-\\eta, \\eta)=\\sum_{i,j=1,2} q_{i,j}(\\xi-\\eta, \\eta) +\\frac{e^{|\\eta|} - e^{-|\\eta|}}{e^{|\\eta|}+e^{-|\\eta|}}|\\eta|. \n\\]\nAlthough above formulas look complicated, actually there are cancellations inside. Note that,\n\\[\n q_{1,2}(\\xi-\\eta, \\eta)  +  q_{2,1 }(\\xi-\\eta, \\eta) +\\frac{e^{|\\eta|} - e^{-|\\eta|}}{e^{|\\eta|}+e^{-|\\eta|}}|\\eta| \n\\]\n\\[\n= \\frac{\\xi\\cdot \\eta}{(e^{|\\xi|}+e^{-|\\xi|})(e^{|\\eta|}+e^{-|\\eta|})} \\Big[ \\frac{e^{|\\xi|+|\\eta|}-e^{-|\\xi|-|\\eta|}}{|\\xi|+|\\eta|}+ \\frac{e^{|\\xi|-|\\eta|} - e^{|\\eta|-|\\xi|}}{|\\xi|-|\\eta|} \\Big]  \n\\]\n\\begin{equation}\\label{eqn82}\n- \\frac{|\\xi||\\eta|}{(e^{|\\xi|}+e^{-|\\xi|})(e^{|\\eta|}+e^{-|\\eta|})}\\Big[ \\frac{[e^{|\\xi|+|\\eta|}-e^{-|\\xi|-|\\eta|}]}{|\\xi|+|\\eta|}- \\frac{e^{|\\xi|-|\\eta|}-e^{|\\eta|-|\\xi|}}{|\\xi|-|\\eta|}\\Big],\n\\end{equation}\n\\[\n q_{1,1}(\\xi-\\eta, \\eta)  +  q_{2,2 }(\\xi-\\eta, \\eta) \n\\] \n\\[\n=\\frac{ (-|\\xi||\\eta|+\\xi\\cdot\\eta)}{(e^{|\\xi|}+e^{-|\\xi|})(e^{|\\eta|}+e^{-|\\eta|})} \\frac{(|\\xi|+|\\eta|-1)e^{|\\xi|+|\\eta|}-(-|\\xi|-|\\eta|-1)e^{-|\\xi|-|\\eta|}}{(|\\xi|+|\\eta|) }\n\\]\n\\begin{equation}\\label{eqnn989}\n- \\frac{ ( \\xi||\\eta|+\\xi\\cdot\\eta)}{(e^{|\\xi|}+e^{-|\\xi|})(e^{|\\eta|}+e^{-|\\eta|})} \\frac{(|\\eta|-|\\xi|-1)e^{|\\eta|-|\\xi|}-(|\\xi|-|\\eta|-1)e^{|\\xi|-|\\eta|}}{(|\\xi|-|\\eta|) }\\Big].\n\\end{equation}\nFrom (\\ref{eqn82}) and (\\ref{eqnn989}),  now  it is easy to verify the following equality,\n \\begin{equation}\\label{eqnq929}\n\\tilde{q}(\\xi-\\eta, \\eta)= \\xi\\cdot \\eta - |\\xi||\\eta| \\tanh|\\xi|\\tanh|\\eta|.\n \\end{equation}\n Hence our desired equality (\\ref{eqq345}) holds.\n\n\\qed\n\n \n\\begin{lemma}\\label{symbol}\nFor $k_1,k_2,k\\in \\mathbb{Z}$,  the following estimate holds for the symbol of the quadratic terms of the Dirichlet-Neumann operator,\n\\begin{equation}\\label{eqn1202}\n\\| \\widetilde{q}(\\xi-\\eta, \\eta)\\|_{\\mathcal{S}^\\infty_{k,k_1,k_2}} \\lesssim 2^{k+k_2}.\n\\end{equation}\n\\end{lemma}\n\\begin{proof}\nFrom  (\\ref{eqnq929}) and the estimate in    Lemma \\ref{Snorm}, it is straightforward to derive above estimate. \n\\end{proof}\n\n\n\\subsection{A fixed point type formulation for $\\Lambda_{\\geq 3}[\\nabla_{x,z}\\varphi]$}\\label{fixedpointcubic} \nSame as in the previous subsection, the content of this subsection is not related to the proof of the main theorem but related to the future study of the long time behavior of the water waves system in different settings.\n\nAlthough, intuitively speaking, the quadratic terms are the leading terms for the dispersive equation (\\ref{dispersive}) in $2D$ case, one also has to control the cubic and higher order remainder terms to see that their effects are indeed small over time.  In this subsection, our goal is to formulate $\\Lambda_{\\geq 3}[\\nabla_{x,z}\\varphi]$ into a fixed point type formulation, which provides a good way to estimate the cubic and higher order remainder terms.\n\n\n\n Recall the fixed point type formulation of $\\nabla_{x,z}\\varphi$ in (\\ref{fixedpoint}), we truncate it at the cubic and higher level and have the following, \n\\[\n\\Lambda_{\\geq 3}[\\nabla_{x,z}\\varphi]=[\\mathbf{0}, \\Lambda_{\\geq 3}[g_1(z)]] +\n\\]\n\\[\n+\\int_{-1}^{0} [K_1(z,s)-K_2(z,s)-K_3(z,s)](\\Lambda_{\\geq 3}[g_2(s)]+\\nabla \\cdot \\Lambda_{\\geq 3}[g_3(s)])  ds \\]\n\\begin{equation}\\label{eqn68}\n+\\int_{-1}^{0} K_3(z,s)|\\nabla|\\textup{sign($z-s$)}\\Lambda_{\\geq 3}[g_1(s)]  -|\\nabla| [K_1(z,s) +K_2(z,s)]\\Lambda_{\\geq 3}[g_1(s)]\\, d  s.\n\\end{equation}\nRecall (\\ref{eqn782})  and (\\ref{eqn783}).  Similar to the decomposition we did in (\\ref{eqn2001}), (\\ref{eqn2002}), (\\ref{eqn2003}) and (\\ref{eqn2004}), we can separate  $\\Lambda_{\\geq 3}[g_i(z)]$, $i\\in\\{1,2,3\\}$, into two parts: (i) one of them contains $\\Lambda_{\\geq 3}[\\nabla_{x,z}\\varphi]$, in which lies the fixed point structure; (ii) the other part does not depend on $\\Lambda_{\\geq 3}[\\nabla_{x,z}\\varphi]$, which can be estimated directly. \n \n More precisely, we  decompose $\\Lambda_{\\geq 3}[g_i(z)], i\\in\\{1,2,3\\},$ as follows,\n\\begin{equation}\\label{eqn50}\n\\Lambda_{\\geq 3}[g_1(z)] = \\tilde{\\,h}_1 \\Lambda_{\\geq 3}[\\partial_z \\varphi] -  (z+1)^2  \\tilde{\\,h}_2 \\Lambda_{\n\\geq 3}[\\partial_z\\varphi] + (z+1) \\tilde{\\,h}_3\\cdot \\Lambda_{\\geq 3}[\\nabla \\varphi]\n\\end{equation}\n\\begin{equation}\\label{eqn2000}\n+\\sum_{i=1,2} \\Lambda_{\\geq 3-i}[\\tilde{\\,h}_1] \\Lambda_{  i}[\\partial_z \\varphi]  -  (z+1)^2  \\Lambda_{\\geq 3-i}[\\tilde{\\,h}_2 ] \\Lambda_{i}[\\partial_z\\varphi]  + (z+1) \\Lambda_{\\geq 3-i}[\\tilde{\\,h}_3]\\cdot \\Lambda_{i}[\\nabla \\varphi] ,\n\\end{equation}\n\\[\n\\Lambda_{\\geq 3}[g_2(z)] = (z+1)  \\tilde{\\,h}_2  \\Lambda_{\\geq 3}[\\partial_z \\varphi] - \\tilde{\\,h}_3\\cdot \\Lambda_{\\geq 3}[\\nabla \\varphi]\n\\]\n \\begin{equation}\\label{eqn790}\n+\\sum_{i=1,2}(z+1)\\Lambda_{\\geq 3-i}[ \\tilde{\\,h}_2] \\Lambda_{i}[\\partial_z \\varphi] -   \\Lambda_{\\geq 3-i}[\\tilde{\\,h}_3]\\cdot \\Lambda_{i }[\\nabla \\varphi] ,\n\\end{equation}\n\\begin{equation}\\label{eqn53}\n\\Lambda_{\\geq 3}[g_3(z)] =  (z+1)  \\tilde{\\,h}_3 \\Lambda_{\\geq 3}[\\partial_z \\varphi]  + \\sum_{i=1,2}( z+1)  \\Lambda_{\\geq 3-i}[\\tilde{\\,h}_3] \\Lambda_{ i}[\\partial_z \\varphi]  .\n\\end{equation}\nFrom (\\ref{tildeeta}), it is easy to verify that the following equalities hold,\n\\[\n\\Lambda_{\\geq 2}[\\tilde{h}_1]= h^2 -(2h+h^2) \\tilde{h}_1, \\quad \\Lambda_{\\geq 2}[\\tilde{h}_2]= \\tilde{h}_2,\\quad \\Lambda_{\\geq 2}[\\tilde{h}_3]= -h \\tilde{h}_3.\n\\]\n\n\nWe can summarize above decomposition as the following Lemma, \n\\begin{lemma}\nWe have\n\\[\n\\Lambda_{\\geq 3}[\\nabla_{x,z}\\varphi(z)] = \\sum_{i=1,2,3} C_z^i (\\,h, \\psi, \\tilde{\\,h}_i) + \\,h \\tilde{C}_z^i(\\,h, \\psi, \\tilde{\\,h}_i)+  T^i_z(\\tilde{\\,h}_i, \\Lambda_{\\geq 3}[\\nabla_{x,z}\\varphi]),\\]\n where $C^i_z$ and $\\tilde{C}_z^i$  are some trilinear operators and $ T^i_z$ is some bilinear operator. Assume that the corresponding symbols are   $c_z^i(\\cdot, \\cdot, \\cdot)$, $\\tilde{c}_z^i(\\cdot, \\cdot, \\cdot)$, and $t_z^i(\\cdot, \\cdot)$ respectively,  then   the following estimate holds,\n \\begin{equation}\\label{eqn2304}\n \\sup_{z\\in[-1,0]}\\sum_{i=1,2,3} \\|c_{z}^i(\\xi_1, \\xi_2, \\xi_3)\\|_{\\mathcal{S}^\\infty_{k,k_1,k_2,k_3}} + \\|\\tilde{c}_z(\\xi_1, \\xi_2,\\xi_3)\\|_{\\mathcal{S}^\\infty_{k,k_1,k_2,k_3}}  \\lesssim  2^{3\\max\\{k_1,k_2,k_3\\}_{+}},\n\\end{equation}\n\\begin{equation}\\label{eqn2306}\n\\sup_{z\\in[-1,0]} \\sum_{i=1,2,3} \\|t^{i}_z(\\xi_1,\\xi_2)\\|_{\\mathcal{S}^\\infty_{k,k_1,k_2}}  \\lesssim 2^{3\\max\\{k_1,k_2\\}_{+}}.\n\\end{equation}\n\n\\end{lemma}\n\\begin{proof}\nThe proof is   straightforward. From   Lemma \\ref{Snorm}, our desired estimates (\\ref{eqn2304}) and (\\ref{eqn2306}) can be derived by checking symbol of  each term inside the equations (\\ref{eqn68}), (\\ref{eqn2000}), (\\ref{eqn790}) and (\\ref{eqn53}). Note that there are at most three derivatives in total.\n\\end{proof}\n\n\n\n\n\\section{Paralinearization and symmetrization of the system}\\label{parasymm}\n\nSince the gravity waves system (\\ref{waterwave}) is quasilinear and lacks symmetric structures inside, we cannot use this system directly to do energy estimate because of the difficulty of losing one derivative.\n\nTo identity the hidden symmetries inside the gravity waves system (\\ref{waterwave}) and get around this losing derivative issue, we use the method of  paralinearization and symmmetrization, which was   introduced and studied in a series of works by Alazard-M\\'etivier \\cite{alazard4} and Alazard-Burq-Zuily \\cite{alazard1,alazard2,alazard3}. Interested readers may refer to those works for more details. Here, we  only briefly discuss this method here to help readers understand how this method works and get a sense of what they will read in this section.\n\nFor a fully nonlinear term, it is very hard to tell which part   actually loses derivatives and which part doesn't, which is clearly very important to get around the issue of losing derivatives. With the help of  the paralinearization process, we can identify the part that  actually loses derivatives, which is the real issue. In subsection \\ref{paralinearDN}, we will do the paralinearization process for the nonlinearity of equation satisfied by the height ``$h$'', which is the Dirichlet-Neumann operator. In subsection \\ref{paralinearvelocitypotential},   \nwe will do the paralinearization process for the nonlinearity of equation satisfied by the velocity potential ``$\\psi$''.\n\n\n\n\nKnow which part loses derivative is certainly very helpful, but it doesn't imply that we can get around the issue of losing derivatives because the original system lacks good symmetric structures. With the help of the symmetrization process, in subsection \\ref{symmetrizationsubsection}, we  identify good substitution variables such that the system of equations satisfied by the good substitution variables have requisite symmetries and moreover it has comparable size of energy as the original variables. Therefore, instead of doing energy estimate for the original variables, we do energy estimate for the good substitution variables.\n\n\n \n\n\n\\subsection{Paralinearization of the Dirichlet-Neumann operator}\\label{paralinearDN}\nIn this subsection, our main goal is to identify which part of the Dirichlet-Neumann operator actually loses derivatives by using the paralinearization method. In the mean time, we also pay attentions to the low frequency part for the purpose of proving our new energy estimate (\\ref{energyestimate}).\n\nMore precisely, the goal of this subsection is to prove the   Proposition as follows,\n \n\\begin{proposition}\\label{prop1}\nLet $k\\geq 6$, $\\alpha\\in(0,1]$. Assume that $(\\,h, \\Lambda \\psi)\\in H^{k}$ and $\\,h$ satisfies the smallness condition \\textup{(\\ref{smallness})}, then we have\n\\begin{equation}\\label{paralinear}\nG(\\,h)\\psi = T_{\\lambda} (\\psi - T_{B}\\,h) - T_{V}\\cdot \\nabla \\,h + F(\\,h) \\psi = \\Lambda^2(\\psi - T_{B} \\,h) + T_{\\lambda -|\\xi|}(\\psi-T_{B}\\,h) - T_{V}\\cdot \\nabla \\,h + \\widetilde{F}(\\,h)\\psi,\n\\end{equation}\nwhere\n\\begin{equation}\\label{principalsymbol}\n\\lambda:= \\sqrt{(1+|\\nabla \\,h|^2)|\\xi|^2 - (\\nabla \\,h \\cdot \\xi)^2 },\n\\end{equation}\n\\begin{equation}\\label{hvderivative}\nB \\overset{\\text{abbr}}{=} B(\\,h)\\psi =\\frac{G(\\,h)\\psi + \\nabla \\,h \\cdot \\nabla \\psi}{1+|\\nabla \\,h|^2},\\quad V\\overset{\\text{abbr}}{=} V(\\,h)\\psi= \\nabla \\psi - B \\nabla \\,h .\n\\end{equation}\nThe good remainder terms $F(\\,h)\\psi$ and $\\widetilde{F}(h)\\psi$ don't lose derivatives and they satisfy the following estimate,\n\\begin{equation}\\label{goodremainder}\n\\|\\Lambda_{\\geq 2}[ F(\\,h)\\psi]\\|_{H^{k}}+ \\|\\widetilde{ F}(\\,h)\\psi\\|_{H^{k}}\\lesssim_k \\big[\\|(\\,h, \\Lambda\\psi)\\|_{\\widehat{W^{4,\\alpha}}} + \\| (\\,h,\\Lambda\\psi)\\|_{\\widehat{W}^{4}}^2\\big]\n\\big[ \\|\\,h\\|_{H^k} + \\|\\nabla\\psi\\|_{H^{k-1}} \\big].\n\\end{equation}\n\n\\end{proposition}\n\n\\begin{remark}\nWe remark that, unlike the infinite depth setting, the good remainder term $F(\\,h)\\psi$ in (\\ref{paralinear}) actually contains a linear term, which is $[\\tanh(|\\nabla|)-1]|\\nabla|\\psi\\in H^{\\infty}$.\n\\end{remark}\n\n\n\n\n\n\nFor simplicity, we define the following equivalence relation. For two well defined nonlinearities   $A$ and $B$, which are nonlinear with respect to $\\,h$ and $\\psi$, we  denote\n\\[\nA\\thickapprox B, \\quad \\textup{if and only if $A-B$ is a good error term in the sense of (\\ref{gooderror})},\n\\]\n\\begin{equation}\\label{gooderror}\n\\|\\textup{good error term}\\|_{H^{k}}\\lesssim_{k} \\big[\\|(\\,h, \\Lambda\\psi)\\|_{\\widehat{W^{4,\\alpha}}} + \\| (\\,h,\\Lambda \\psi)\\|_{\\widehat{W}^{4}}^2\\big]\n\\big[ \\|\\,h\\|_{H^k} + \\|\\nabla\\psi\\|_{H^{k-1}} \\big],\\,\\, \\alpha\\in(0,1], k\\geq 0.\n\\end{equation}\n\nRecall (\\ref{DN2}). Note that, essentially speaking, the only fully nonlinear term inside the Dirichlet-Neumann operator $G(h)\\psi$ is $\\partial_w \\Phi\\big|_{w=0}$. So the task is reduced to identify which part of $\\partial_w \\Phi$ is actually losing derivative. \n\nTo this end, we will show that there exists a pseduo differential operator $A(x, \\xi)$ such that $\\partial_w \\Phi -T_A(\\Phi -T_{\\partial_w \\Phi} h)$ actually doesn't lose derivatives, where `` $\\Phi- T_{\\partial_w \\Phi}  h$'' is the so-called good unknown variable. This step is very nontrivial and technical. Unfortunately, to the best of my knowledge, there is no physical intuitive explanation available.   It relies  heavily on the study of good structures of the Laplace equation (\\ref{changco2}). We do this step in details in the subsubsection as follows.\n\n\n\\subsubsection{Paralinearization of the Laplace equation \\textup{(\\ref{changco2})} }\n\n\n\n Recall (\\ref{changco2}) and the fact that $g'(\\cdot, w)=0$ when $w\\in[-1\/4,0]$, we have\n\\begin{equation}\\label{eqn710}\n[ \\Delta_{x}+ a'\\partial_w^2 +  b'\\cdot \\nabla \\partial_w + c'\\partial_w ]\\Phi = 0,\n\\end{equation}\n\\[\na'= 1 + |\\nabla \\,h|^2\\thickapprox 1+2 T_{\\nabla \\,h}\\cdot \\nabla \\,h, \\quad b'= -2\\nabla \\,h, \\quad c'= -\\Delta \\,h.\n\\]\nWe remark that  $w$  is  also restricted inside $[-1\/4,0]$ in the rest of this paper.\n\nBefore proceeding to do the paralinearization process for (\\ref{eqn710}), we need some necessary estimates of $``\\Phi\"$. Essentially speaking, under certain smallness condition, the size of `'$\\Phi$'' is comparable to $``\\varphi\"$. Note that  we already have necessary estimates of $\\varphi$, see Lemma \\ref{Sobolevestimate}.\n More precisely,\nfrom definition of $\\Phi$ (see subsection \\ref{type2}) and estimates of $\\varphi$ in  Lemma \\ref{Sobolevestimate}, the following lemma holds,\n\\begin{lemma}\\label{IntermsofPhi}\nUnder the smallness estimate \\textup{(\\ref{smallnessestimate})}, we have the following estimates for $k\\geq 1,\\gamma \\leq 3,$\n\\begin{equation}\\label{eqn3123}\n\\sup_{w\\in[-1\/4, 0]} \\| \\nabla_{x,w}\\Phi\\|_{H^{k}}\\lesssim \\|\\nabla\\psi\\|_{H^k} + \\| \\,h\\|_{H^{k+1}}\\|\\nabla \\psi\\|_{\\widetilde{W^1}},\\end{equation}\n\\begin{equation}\\label{eqn3124}\n\\sup_{w\\in[-1\/4,0]}\\| \\nabla_{x}\\Phi\\|_{\\widetilde{W^\\gamma}} \\lesssim \\| \\nabla \\psi \\|_{\\widetilde{W^{\\gamma}}} , \\quad \\sup_{w\\in[-1\/4,0]}\\| \\partial_w \\Phi\\|_{\\widetilde{W^{\\gamma}}}\\lesssim \\| \\nabla \\psi\\|_{\\widehat{W}^{\\gamma,\\alpha}}+  \\| \\,h\\|_{\\widetilde{W^{\\gamma+1}}} \\| \\nabla \\psi \\|_{\\widetilde{W^\\gamma}},\n\\end{equation}\n\\begin{equation}\\label{eqn3125}\n\\sup_{w\\in[-1\/4,0]} \\| \\Lambda_{\\geq 2}[\\nabla_{x,w} \\Phi] \\|_{L^2}\\lesssim\\big[ \\|(\\,h,\\Lambda \\psi)\\|_{\\widehat{W^{2,\\alpha}}}+\\|(\\,h, \\Lambda \\psi)\\|_{\\widehat{W^2}}^2\\big]\\big[ \\|\\,h\\|_{H^1} + \\|\\nabla \\psi\\|_{L^2} \\big].\n\\end{equation}\n\\end{lemma}\n\\begin{proof}\nPostponed to the end of this subsection for the purpose of improving presentation.\n \\end{proof}\n\n\nAfter paralinearizing (\\ref{eqn710}), we have\n\\begin{equation}\\label{eqn712}\nP\\Phi + 2T_{\\partial_{w}^2 \\Phi} T_{\\nabla\\,h}\\cdot \\nabla \\,h -2 T_{\\nabla \\partial_{w}\\Phi} \\cdot \\nabla \\,h - T_{\\partial_w \\Phi} \\Delta \\,h \\thickapprox 0,\n\\end{equation}\nwhere\n\\begin{equation}\\label{operatorP}\nP:=[\\Delta + T_{a'}\\partial_{w}^2 + T_{b'\\cdot } \\nabla\\partial_w + T_{c'} \\partial_w].\n\\end{equation}\nTo see  why the equivalence relation (\\ref{eqn712}) holds, we mention that we can always put $\\nabla h$ in $L^\\infty$ and   put $\\partial_w\\Phi$ and $\\partial_w^2  \\Phi$ in $L^2$. \n\n Define $W:= \\Phi - T_{\\partial_w \\Phi}\\,h$. Same as in \\cite{alazard1}, we claim that $P W \\thickapprox 0$ when $w\\in[-1\/4,0]$.  After using (\\ref{equation340}) and the composition Lemma \\ref{composi}, the following equivalence relations hold, \n\\begin{equation}\\label{eqn720}\nP W \\thickapprox 0  \\Longleftrightarrow P [T_{\\partial_{w}\\Phi} \\,h] +  2T_{\\partial_{w}^2 \\Phi} T_{\\nabla\\,h}\\cdot \\nabla \\,h -2 T_{\\nabla \\partial_{w}\\Phi} \\cdot \\nabla \\,h - T_{\\partial_w \\Phi} \\Delta \\,h\\thickapprox  0,\n\\end{equation}\n\\begin{equation}\\label{eqn721}\n\\Longleftrightarrow \\big[T_{a'} T_{\\partial_{w}^3 \\Phi} \\,h + T_{b'}\\cdot \\nabla T_{\\partial_{w}^2\\Phi} \\,h + T_{c'}T_{\\partial_{w}^2\\Phi} \\,h + 2T_{\\nabla\\partial_w \\Phi} \\cdot \\nabla \\,h  \\big] + \\big[ 2 T_{\\partial_{w}^2 \\Phi} T_{\\nabla\\,h}\\cdot \\nabla \\,h -2 T_{\\nabla \\partial_{w}\\Phi} \\cdot \\nabla \\,h  \\big]\\thickapprox 0\n\\end{equation}\n\\begin{equation}\\label{eqn722}\n\\Longleftrightarrow  \\big[ T_{b'}\\cdot T_{\\partial_{w}^2 \\Phi}\\nabla \\,h +  2T_{\\nabla\\partial_w \\Phi} \\cdot \\nabla \\,h \\big] + \\big[ 2T_{\\partial_{w}^2 \\Phi} T_{\\nabla\\,h}\\cdot \\nabla \\,h -2 T_{\\nabla \\partial_{w}\\Phi} \\cdot \\nabla \\,h \\big]\\thickapprox 0\n\\end{equation}\n\\begin{equation}\\label{eqn723}\n\\Longleftrightarrow T_{[b'\\partial_{w}^2 \\Phi + 2\\partial_{w}^2\\Phi \\nabla \\,h ]}\\cdot \\nabla \\,h \\thickapprox 0 \\end{equation}\n\\begin{equation}\\label{eqn742}\n\\Longleftrightarrow 0 \\thickapprox 0, \\quad \\textup{as $b'=-2\\nabla \\,h$}.\n\\end{equation}\nObviously, (\\ref{eqn742}) holds. Hence, we can reverse the directions of all arrows back to conclude $P W \\thickapprox 0$. \n\n\\par Although tedious, it is  not  difficult to verify  all  ``$\\thickapprox$ \" equivalence relations  hold in above equations. As a typical example, we  give a detail proof of (\\ref{eqn721}) here. To prove (\\ref{eqn721}), it would be  sufficient to estimate $T_{\\Delta\\partial_{w}\\Phi} h$. From estimate (\\ref{eqn3124}) in Lemma \\ref{IntermsofPhi}, we have,\n\\[\n\\sup_{w\\in[-1\/4,0]} \\| T_{\\Delta \\partial_w \\Phi} \\,h\\|_{H^{k}}\n\\lesssim \\sup_{w\\in[-1\/4,0]} \\| \\,h\\|_{H^k} \\|\\partial_w\\Phi\\|_{\\widetilde{W^2}}\\lesssim [ \\|\\Lambda\\psi\\|_{\\widehat{W}^{4,\\alpha}} +\\|(\\,h,\\Lambda\\psi)\\|_{\\widehat{W}^4}^2]\\|\\,h\\|_{H^k}.\n\\]\nHence, the equivalence relation (\\ref{eqn721}) holds. All other equivalence relations can be obtained very similarly. \n\n\nThe next step is to decompose the equation $P W \\thickapprox 0$ into a forward evolution equation  and  a backward evolution equation, which shows that $\\partial_w W-T_A W  $ actually doesn't lose derivatives. Note that  $\\partial_w W-T_A W\\approx \\partial_w \\Phi -T_A(\\Phi -T_{\\partial_w \\Phi} h) $. Hence, our desired result is obtained.\n\nMore precisely, we have the following Lemma,   \n\\begin{lemma}\\label{decomp}\nThere exist two symbols $a=a(x,\\xi)$ and $A(x,\\xi)$ with \n\\[\na= a^{(1)}+ a^{(0)}, \\quad  A = A^{(1)} + A^{(0)}, \n\\]\nwhere\n\\[\na^{(1)}(x,\\xi)= \\frac{1}{1+|\\nabla \\,h|^2}(i \\nabla \\,h\\cdot \\xi - \\sqrt{(1+|\\nabla \\,h|^2)|\\xi|^2-(\\nabla\\,h \\cdot\\xi)^2}),\n\\]\n\\begin{equation}\\label{eqqq098}\nA^{(1)}(x,\\xi)=  \\frac{1}{1+|\\nabla \\,h|^2}(i \\nabla \\,h\\cdot \\xi + \\sqrt{(1+|\\nabla \\,h|^2)|\\xi|^2-(\\nabla\\,h \\cdot\\xi)^2}),\n\\end{equation}\n\\[\na^{(0)}(x,\\xi)= \\frac{1}{A^{(1)}- a^{(1)}}\\Big(i \\partial_{\\xi}a^{(1)}\\cdot \\partial_x A^{(1)} - \\frac{\\Delta \\,h \\,\\,a^{(1)}}{1+|\\nabla \\,h|^2}\\Big),\n\\]\n\\[\nA^{(0)}(x,\\xi)=  \\frac{1}{a^{(1)}- A^{(1)}}\\Big(i \\partial_{\\xi}a^{(1)}\\cdot \\partial_x A^{(1)} - \\frac{\\Delta \\,h \\,\\,A^{(1)}}{1+|\\nabla \\,h|^2}\\Big),\n\\]\nsuch that \n\\begin{equation}\\label{eqn1450}\nP = T_{a'}(\\partial_w - T_{a})(\\partial_w -T_{A})  + R_0 + R_1\\partial_w,\\quad a'(a+A)= i b'\\cdot \\xi + c',\n\\end{equation}\n\\begin{equation}\\label{eqn1452}\na'[a^{(1)}A^{(1)} + \\frac{1}{i} \\partial_{\\xi}a^{(1)} \\cdot\\partial_x A^{(1)} + a^{(1)} A^{(0)} + a^{(0)}A^{(1)}] = a'(a\\sharp A)= -|\\xi|^2, \n\\end{equation}\nwhere\n\\begin{equation}\\label{equation210}\nR_0 = T_{a'}T_{a}T_A - \\Delta, \\quad R_1 = - T_{a'} T_{a+A} + T_{b'}\\cdot \\nabla + T_{c'}.\n\\end{equation}\nMoreover, the following estimate holds for good error operators $R_0$ and $R_1$,\n\\begin{equation}\\label{errorestimate}\n\\| R_0 f \\|_{H^k} + \\| R_1 f\\|_{H^{k+1}}\\lesssim \\| \\nabla \\,h\\|_{\\widetilde{W^3}} \\| f\\|_{H^k}. \n\\end{equation}\n\\end{lemma}\n\\begin{proof}\nMost parts of above Lemma are cited directly from \\cite{alazard1}[Lemma 3.18]. Given the  a-priori decomposition (\\ref{eqn1450}), from (\\ref{operatorP}), we can calculate explicitly the formulas of  $R_0$ and $R_1$, which are given in  (\\ref{equation210}).  Note that  $a'$ doesn't depend on $\\xi$, from (\\ref{eqn1450}), (\\ref{eqn1452}) and (\\ref{equation210}), we have the following identities, \n\\[\nR_1= -T_{a'}T_{a+A} +T_{a'(a+A)}= -T_{a'}T_{a+A}+ T_{(a'\\sharp (a+A))},\\]\n\\[\nR_0= T_{a'}[T_{a}T_{A}-T_{a\\sharp A}] + T_{a'}T_{a\\sharp A} - T_{a'(a\\sharp A)}= T_{a'}[T_{a}T_{A}-T_{a\\sharp A}] + T_{(a'-1)}T_{a\\sharp A} - T_{(a'-1)\\sharp(a\\sharp A)} .\n\\]\nFrom explicit formulations of $a'$, $a$ and $A$, we can see that $a', a'-1\\in \\Gamma^{0}_2(\\mathbb{R}^2), a, A, a+A\\in \\Gamma^{1}_2(\\mathbb{R}^2)$, $a\\sharp A \\in \\Gamma^{2}_2(\\mathbb{R}^2)$.  The following estimates  on their symbolic bounds hold, \n\\[\nM^2_2(a\\sharp A)+M^{0}_{2}(a')\\lesssim 1,\\quad  M^{1}_2(a) +M^1_2(A) + M^1_2(a+A)\\lesssim \\|\\nabla \\,h\\|_{\\widetilde{W^3}}, \\quad M_2^0(a'-1) \\lesssim \\|\\nabla\\,h\\|_{\\widetilde{W^3}}^2.\n\\]\nFrom estimate (\\ref{eqn700}) in Lemma \\ref{composi}, we have\n\\[\n\\| R_1 f\\|_{H^{k+1}} \\lesssim M^{0}_2(a') M^{1}_2(a+A) \\| f\\|_{H^k}\\lesssim \\| \\nabla \\,h\\|_{\\widetilde{W^3}}\\|f\\|_{H^k},\n\\]\n\\[\n\\| R_0 f\\|_{H^k}\\lesssim \\big[M_2^0(a') M^1_2(a)M_2^1(A) + M_2^0(a'-1) M_2^2(a\\sharp A)\\big] \\| f\\|_{H^k} \\lesssim \\| \\nabla\\,h\\|_{\\widetilde{W^3}}^2 \\| f\\|_{H^k}.\n\\]\nHence finishing the proof of (\\ref{errorestimate}).\n \\end{proof}\nIn the following Lemma, we prove that $\\partial_w W - T_A W$ doesn't lose derivative.\n\\begin{lemma}\\label{doesntlosederivative}\nLet $A(x,\\xi)$ be defined in Lemma \\textup{\\ref{decomp}}, we have  the following estimate for $k\\geq 1,$\n\\begin{equation}\\label{eqqq675}\n\\| \\Lambda_{\\geq 2}\\big[(\\partial_w W - T_A W)\\big]\\big|_{w=0}\\|_{H^k}\\lesssim_k  \\big[\\|(\\,h, \\Lambda \\psi)\\|_{\\widehat{W^{4,\\alpha}}} +  \\|(\\,h, \\Lambda \\psi)\\|_{\\widehat{W^{4}}}^2 \\big]\\big[ \\|\\,h\\|_{H^k} +\\|\\nabla \\psi\\|_{H^{k-1}} \\big].\n\\end{equation}\n\\end{lemma}\n\\begin{proof}\n\n\nRecall that $P W \\thickapprox 0$ and the decomposition of operator $P$ in  (\\ref{eqn1450}), we have\n\\[\nT_{a'} (\\partial_w - T_a )(\\partial_w - T_{A}) W \\thickapprox - R_0 W - R_1 \\partial_w W, \n\\]\nwhich further gives us\n\\[\n(\\partial_w - T_a )(\\partial_w - T_{A}) W  \\thickapprox \\tilde{g}, \\]\nwhere\n\\[\n\\tilde{g}=T_{a'^{-1}}[- R_0 W - R_1 \\partial_w W] + [I- T_{a'^{-1}}T_{a'}](\\partial_w - T_a )(\\partial_w - T_{A}) W,\n\\]\n\\[\n= T_{a'^{-1}}[- R_0 W - R_1 \\partial_w W] + [I-T_{1}+ T_{(a'-1)(a'^{-1}-1)}-T_{(a'-1)}T_{(a'^{-1}-1)}](\\partial_w - T_a )(\\partial_w - T_{A}) W.\n\\]\nFrom estimate (\\ref{errorestimate}) in Lemma \\ref{decomp}, and the fact that $T_{(a'-1)(a'^{-1}-1)}-T_{(a'-1)}T_{(a'^{-1}-1)}$ is of order $-2$, we have\n\\[\n\\sup_{w\\in[-1\/4,0]} \\| \\Lambda_{\\geq 2}[\\tilde{g}(w)]\\|_{H^k} \\lesssim \\|\\nabla\\,h\\|_{\\widetilde{W^3}} \\big[ \\|P_{\\geq 1\/2}[W]\\|_{H^k}  + \\| \\partial_{w} W\\|_{H^{k-1}} \\big]\n\\]\n\\[\n\\lesssim \\big[\\|(\\,h, \\Lambda \\psi)\\|_{\\widehat{W^{4,\\alpha}}} +  \\|(\\,h, \\Lambda \\psi)\\|_{\\widehat{W^{4}}}^2 \\big]\\big[ \\|\\,h\\|_{H^k} +\\|\\nabla \\psi\\|_{H^{k-1}} \\big].\n\\]\n Note that $[\\partial_w^2 + \\Delta]\\Lambda_1[W(w)]=[\\partial_w^2 + \\Delta]\\Lambda_1[\\Phi(w)]=0 $ when $w\\in[-1\/4,0]$, see (\\ref{eqn710}). It's easy to see the following equivalence relation holds,\n\\begin{equation}\\label{eqn750}\n (\\partial_w - T_{a})\\Lambda_{\\geq 2}[(\\partial_w -T_{A}) W] + \\Lambda_{\\geq 2}[(\\partial_w - T_{a})\\Lambda_{1}[(\\partial_w -T_{A}) W] ] \\thickapprox \\Lambda_{\\geq 2}[\\tilde{g}].\n\\end{equation}\nNote that\n\\[\n\\Lambda_{1}[\\partial_w \\Phi]= \\Lambda_{1}[\\partial_z \\varphi(w\/(1+\\,h))]= \\frac{e^{(w+1)|\\nabla|}- e^{-(w+1)|\\nabla|}}{e^{-|\\nabla|}+e^{|\\nabla|}} |\\nabla| \\psi,\n\\]\n\\[\n\\Lambda_{1}[\\Phi]= \\Lambda_{1}[\\varphi(w\/(1+\\,h))]= \\frac{e^{-(w+1)|\\nabla|}+ e^{(w+1)|\\nabla|}}{e^{-|\\nabla|} + e^{|\\nabla|}}\\psi.\n\\]\nIt's easy to verify that,\n\\[\n\\Lambda_{1}[(\\partial_w -T_{A}) W] ]= \\Lambda_{1}[\\partial_w \\Phi - T_{|\\xi|}\\Phi] \\in H^{\\infty}, \n\\]\n\\[\n\\| \\Lambda_{\\geq 2}[(\\partial_w - T_{a})\\Lambda_{1}[(\\partial_w -T_{A}) W] ] \\|_{H^k}\\lesssim \\| \\nabla\\,h\\|_{\\widetilde{W^3}}\\| \\nabla \\psi\\|_{H^{k-1}}.\n\\]\nTherefore, from (\\ref{eqn750}), we have\n\\[\n (\\partial_w - T_{a})\\Lambda_{\\geq 2}[(\\partial_w -T_{A}) W] \\thickapprox \\Lambda_{\\geq 2}[\\tilde{g}].\n \\]\nWe reformulate above equation as follows,\n\\[\n(\\partial_w + T_{-a})\\Lambda_{\\geq 2}[(\\partial_w -T_{A}) W] = \\Lambda_{\\geq 2}[\\tilde{g}] + \\hat{g},\n\\]\nwhere \n\\[\n\\hat{g}= \\textup{error term from ``$\\thickapprox$ equivalence\" relation}.\n\\]\nRecall the precise formula of ``$a$'' in Lemma \\ref{decomp}, we know $-a$ satisfies the assumption of Lemma \\ref{elliptic}. We can first choose a series of constants $\\{\\tau_i\\}_{i=1}^k$ such that $\\tau_{i+1}= 4\\tau_{i}$ and $\\tau_{k}\\geq -1\/5$ and then keep iterating the estimate (\\ref{coreest1}). As a result, the following estimate holds, \n\\[\n \\| \\Lambda_{\\geq 2}[(\\partial_w -T_{A}) W\\big|_{w=0}]\\|_{H^{k}} \\lesssim_{k} \\sup_{w\\in[-1\/5,0]}\\big[\\| \\Lambda_{\\geq 2}[(\\partial_w -T_{A}) W(w,\\cdot)]\\|_{L^2}  + \\|\\tilde{g}(w)\\|_{H^{k-1+\\epsilon}}\n\\]\n\\begin{equation}\\label{eqn730}\n + \\| \\hat{g}(w)\\|_{H^{k-1+\\epsilon}}\\big]\\lesssim_k  \\big[\\|(\\,h, \\Lambda \\psi)\\|_{\\widehat{W^{4,\\alpha}}} +  \\|(\\,h, \\Lambda \\psi)\\|_{\\widehat{W^{4}}}^2 \\big]\\big[ \\|\\,h\\|_{H^k} +\\|\\nabla \\psi\\|_{H^{k-1}} \\big].\n\\end{equation}\n\\end{proof}\n\n\n\\begin{lemma}\\label{elliptic}\nLet $a\\in \\Gamma^{1}_{2}(\\mathbb{R}^2)$ and it satisfies the following assumption,\n$\nRe[a(x,\\xi)]\\geq c |\\xi|,$\nfor some positive constant $c$. If $u$ solves the following equation \n\\[\n(\\partial_w + T_a) u(w,\\cdot) = g(w,\\cdot),\n\\]\nthen we have the following estimate holds for  any fixed and sufficiently  small constant  $\\tau$, and arbitrarily small constant $\\epsilon >0.$\n\\begin{equation}\\label{coreest1}\n\\sup_{w\\in[\\tau,0]}\\| u(w)\\|_{H^{k}} \\lesssim M_2^1(a) \\frac{1+|\\tau|}{|\\tau|}\\big[ \\sup_{z\\in[4\\tau,0]} \\| u(w)\\|_{H^{k-2(1-\\epsilon)}} + \\sup_{z\\in[4\\tau, 0]} \\| g(z)\\|_{H^{\\mu-(1-\\epsilon)}}\\big].\n\\end{equation}\n\\end{lemma}\n\\begin{proof}\nA detailed proof can be found in \\cite{alazard}. Above result is the combination of \\cite{alazard}[Lemma 2.1.9] and the proof part of \\cite{alazard}[Lemma 2.1.10].\n\n\\end{proof}\n\n\n\\subsubsection{Paralinearization of Dirichlet-Neumann operator} In this subsubsection, we use the result we obtained in last subsubsection, which is the fact that $\\partial_w W-T_A W$ doesn't lose derivatives, to identify which part of the Dirichlet-Neumann operator loses derivatives. \n\n\nRecall  (\\ref{DN2}). For readers' convenience, we  rewrite it as follows,\n\\[\nG(\\,h)\\psi =\\big( (1+|\\nabla\\,h|^2)\\partial_w \\Phi - \\nabla \\,h \\cdot \\nabla \\Phi\\big) \\big|_{w=0}.\n\\]\nDefine\n\\[\n   \\uline{V}:= \\nabla \\Phi- \\partial_w \\Phi \\nabla \\,h,\\quad  \\uline{V}\\big|_{w=0}=V.\n\\]\n\nNow we   let $w$ be inside the range $[-1\/4,0]$ instead of restricting it at the boundary. By using (\\ref{equation340}) and   Lemma \\ref{composi}, we have the paralinearization result as follows,\n\\[\n(1+|\\nabla\\,h|^2)\\partial_w \\Phi - \\nabla \\,h \\cdot \\nabla \\Phi \\thickapprox T_{1+|\\nabla \\,h|^2}\\partial_w \\Phi + 2T_{\\partial_w \\Phi} T_{\\nabla \\,h}\\cdot \\nabla \\,h - T_{\\nabla \\,h} \\cdot \\nabla \\Phi - T_{\\nabla\\Phi}\\cdot \\nabla \\,h\n\\]\n\\[\n\\thickapprox T_{1+|\\nabla \\,h|^2}\\partial_w \\Phi + T_{2\\nabla\\,h \\partial_w \\Phi-\\nabla \\Phi}\\cdot \\nabla \\,h - T_{\\nabla \\,h}\\cdot \\nabla \\Phi\n\\]\n\\[\n= T_{1+|\\nabla \\,h|^2}\\partial_w (W+T_{\\partial_w \\Phi}\\,h)+ T_{2\\nabla\\,h \\partial_w \\Phi-\\nabla \\Phi}\\cdot \\nabla \\,h - T_{\\nabla \\,h}\\cdot \\nabla (W+T_{\\partial_w \\Phi}\\,h)\n\\]\n\\[\n\\thickapprox T_{1+|\\nabla\\,h|^2}\\partial_w W + T_{2\\nabla \\,h \\partial_w \\Phi-\\nabla\\Phi}\\cdot \\nabla \\,h - T_{\\nabla \\,h}\\cdot \\nabla W - T_{\\nabla \\,h \\partial_w \\Phi}\\cdot\\nabla \\,h \n= T_{1+|\\nabla \\,h|^2} \\partial_w W - T_{\\nabla \\,h}\\cdot \\nabla W - T_{\\uline{V}}\\cdot \\nabla \\,h,\n\\]\n\\[\n= T_{1+|\\nabla \\,h|^2}[\\partial_w W - T_A W]+ [T_{1+|\\nabla \\,h|^2} T_{A} - T_{\\nabla \\,h}\\cdot \\nabla] W - T_{\\uline{V}}\\cdot \\nabla \\,h,\n\\]\n\\begin{equation}\\label{eqn1520}\n= T_{\\lambda} W - T_{\\uline{V}}\\cdot \\nabla \\,h + T_{1+|\\nabla \\,h|^2}[\\partial_w W - T_A W] + R_2 W, \\quad R_2:= [T_{1+|\\nabla \\,h|^2} T_A - T_{(1+|\\nabla \\,h|^2)A^{(1)}}],\n\\end{equation}\nwhere $\\lambda$ is given in (\\ref{principalsymbol}). In (\\ref{eqn1520}), we used  the following identity,\n\\[\n\\lambda = (1+|\\nabla \\,h|^2) A^{(1)} - i \\xi\\cdot \\nabla \\,h,\n\\]\nwhere $A^{(1)} $ is given in (\\ref{eqqq098}). Note that \n\\[\nR_2 = T_{(1+|\\nabla\\,h|^2)} T_{A^{(0)}} + \\big[ T_{(1+|\\nabla\\,h|^2)} T_{A^{(1)}} - T_{(1+|\\nabla \\,h|^2)A^{(1)}}\\big] = T_{a'} T_{A^{0}} + \\big[ T_{(a'-1)} T_{A^{(1)}}- T_{(a'-1)\\sharp A^{(1)}} \\big].\n\\]\nNow,  it is  easy to see that $R_2$ is an operator of order $0$ with an upper  bound given by $\\| \\nabla \\,h\\|_{\\widetilde{W^3}}$. Hence, the following estimate holds, \n\\[\n\\| R_2 W\\big|_{w=0}\\|_{H^{k}}= \\| R_2 [P_{\\geq 1\/2}[W]\\big|_{w=0}]\\|_{H^{k}}\\lesssim \\| \\nabla \\,h\\|_{\\widetilde{W^{3}}}\\| P_{\\geq 1\/2}[\\psi - T_{B(\\,h)\\psi} \\,h]\\|_{H^{k}}\n\\]\n\\begin{equation}\\label{eqqq09876}\n\\lesssim \\big[\\|(\\,h, \\Lambda \\psi)\\|_{\\widehat{W^{4,\\alpha}}} +  \\|(\\,h, \\Lambda \\psi)\\|_{\\widehat{W^{4}}}^2 \\big]\\big[ \\|\\,h\\|_{H^k} +\\|\\nabla \\psi\\|_{H^{k-1}} \\big].\n\\end{equation}\nCombining (\\ref{eqn1520}), (\\ref{eqqq09876}), and   the estimate (\\ref{eqqq675}) in Lemma \\ref{doesntlosederivative}, it's easy to see Proposition \\ref{prop1} holds. \n\n\n\\vspace{1\\baselineskip} \n\nNow, we give the postpone proof  of Lemma \\textup{\\ref{IntermsofPhi}} as follows. \n\n\\vspace{1\\baselineskip}\n\n\\noindent\\textit{Proof of Lemma \\textup{\\ref{IntermsofPhi}}.\\quad}\nFor fixed $w\\in[-1\/4,0]$, it's easy to see $\\Phi(w)= \\varphi(w\/(1+\\,h(x)))$ and the  following identity holds, \n\\begin{equation}\\label{eqn3110}\n\\nabla_{x,w}\\Phi= \\nabla_{x,z}\\varphi(w\/(1+\\,h)) + [-w \\nabla\\,h \\partial_z\\varphi(w\/(1+\\,h))\/(1+\\,h)^2, -\\,h \\partial_z \\varphi(w\/(1+\\,h))\/(1+\\,h)].\n\\end{equation}\nTherefore, we know that the leading term of $\\nabla_{x,w}\\Phi(w)$ is $\\nabla_{x,z}\\varphi(w\/(1+\\,h))$.  Under the smallness estimate (\\ref{smallnessestimate}), to estimate $\\nabla_{x,w}\\Phi$, it's sufficient to estimate $\\nabla_{x,z}\\varphi(w\/(1+\\,h))$.  \n\nRecall the fixed point type formulation of $\\nabla_{x,z}\\varphi$ in (\\ref{fixedpoint}), we study the linear term on the right hand side of (\\ref{fixedpoint}) first.\n Denotes \n\\[\np_{\\pm}(w,x,\\xi):=  \\pm \\frac{e^{-(w+1)|\\xi|}(e^{\\,h(x)w|\\xi|\/(1+\\,h(x))}-1)}{e^{-|\\xi|} + e^{|\\xi|}}+\\frac{ e^{(w+1)|\\xi|}(e^{-\\,h(x)w|\\xi|\/(1+\\,h(x))}-1) }{e^{-|\\xi|} + e^{|\\xi|}},\n\\]\n\\[\n= \\sum_{n\\geq 1} \\frac{1}{n!} \\Big[ \\pm \\frac{e^{-(w+1)|\\xi|}}{e^{|\\xi|}+e^{-|\\xi|}} (w|\\xi|)^{n}\\Big(\\frac{\\,h(x)}{1+\\,h(x)}\\Big)^{n}  + \\frac{e^{|\\xi|}}{e^{|\\xi|}+e^{-|\\xi|}} e^{w|\\xi|}(w|\\xi|)^{n}\\Big( \\frac{\\,h(x)}{1+\\,h(x)} \\Big)^n\\Big]\n\\]\n\\[\n= \\sum_{n\\geq 1} \\frac{1}{n!} \\big[ \\pm f^1_{n}(w,\\xi) g_n(x) + f^2_n(w,\\xi) g_n(x) \\big],\n\\]\nwhere\n\\[\nf_n^1(w,\\xi):=\\frac{e^{-(w+1)|\\xi|}}{e^{|\\xi|}+e^{-|\\xi|}} (w|\\xi|)^{n},\\quad f_n^2(w,\\xi):=  \\frac{e^{|\\xi|}}{e^{|\\xi|}+e^{-|\\xi|}} e^{w|\\xi|}(w|\\xi|)^{n}, \\quad g_n(x) = \\Big( \\frac{\\,h(x)}{1+\\,h(x)}\\Big)^n.\n\\]\nIt's easy to verify the following identities hold,\n\\[\n\\Lambda_{1}[\\nabla_{x}\\varphi](x,w\/(1+\\,h(x)))= \\Lambda_{1}[\\nabla_{x}\\varphi](x,w)+ P_{1} \\psi(x,w),\n\\]\n\\[\n\\Lambda_{1}[\\partial_z\\varphi](x,w\/(1+\\,h(x))) = \\Lambda_{1}[\\partial_z\\varphi](x,w) \n+ P_2 \\psi (x,w),\n\\]\nwhere\n\\[\n P_{1} \\psi(x,w):=\\frac{1}{4\\pi^2}\\int_{\\mathbb{R}^2} e^{ix\\cdot \\xi }\\widehat{\\psi}(\\xi) i\\xi p_{+}(w,x,\\xi) d \\xi, \\quad  P_{2} \\psi(x,w)=\\frac{1}{4\\pi^2}\\int_{\\mathbb{R}^2} e^{ix\\cdot \\xi }\\widehat{\\psi}(\\xi) |\\xi| p_{-}(w,x,\\xi) d \\xi.\n\\]\n\nWe will show that, under the smallness estimate (\\ref{smallnessestimate}),  the size of $\\Lambda_{1}[\\nabla_{x,z}\\varphi](x,w\/(1+\\,h(x)))$ is almost same as the size of  $\\Lambda_{1}[\\nabla_{x,z}\\varphi](x,w)$. For $ k \\in \\mathbb{Z}$, we define \n\\begin{equation}\\label{eqn3103}\np_{\\pm, k}(w,x,\\xi)=\\frac{1}{4\\pi^2} \\int_{\\mathbb{R}^2 } e^{ix\\cdot \\sigma}\\mathcal{F}_{x}(p)(w,\\sigma, \\xi)\\psi_{k}(\\sigma) d\\sigma = \\frac{1}{4\\pi^2}\\sum_{n\\geq 1} \\frac{1}{n!}\\big[ \\pm f^1_{n}(w,\\xi)  + f^2_n(w,\\xi) \\big]P_{k}[g_{n}](x),\n\\end{equation}\n\\[\n P_{1,k} \\psi(x,w):=\\int_{\\mathbb{R}^2} e^{ix\\cdot \\xi }\\widehat{\\psi}(\\xi) i\\xi p_{+,k}(w,x,\\xi) d \\xi, \\quad   P_{2,k} \\psi(x,w)=\\int_{\\mathbb{R}^2} e^{ix\\cdot \\xi }\\widehat{\\psi}(\\xi) |\\xi| p_{-,k}(w,x,\\xi) d \\xi. \n\\]\nSince $P_{2}\\psi$ can be treated in the same way as $P_1 \\psi$,  we only estimate $P_1\\psi$ in details here. We have the following decomposition,\n\\[\nP_{1}\\psi = \\sum_{k_1, k_2\\in \\mathbb{Z}} P_{1,k_1} \\psi_{k_2} = \\mbox{I} + \\mbox{II}, \\quad \\mbox{I}= \\sum_{k_2 \\leq k_1 } P_{1,k_2} \\psi_{k_1}, \\quad \\mbox{II}= \\sum_{k_1 \\leq k_2} P_{1,k_2} \\psi_{k_1}.\n\\]\nFrom $L^2-L^\\infty$ type bilinear estimate (\\ref{bilinearesetimate}) in Lemma \\ref{multilinearestimate}, it's easy to see the following estimates hold,\n\\[\n\\| \\mbox{I} \\|_{H^{k}} \\lesssim \\Big(\\sum_{ k_1} 2^{2k_1 + 2k k_{1,+}} \\| P_{k_1}\\psi\\|_{L^2}^2   \\Big(\\sum_{n\\geq 1} \\frac{1}{n!} \\| P_{\\leq k_1} g_{n}\\|_{L^\\infty}\\Big)^2\\Big)^{1\/2} \\lesssim \\|\\nabla \\psi\\|_{H^{k}} \\| \\,h\\|_{\\widetilde{W^1}},\n\\]\n\\[\n\\|\\mbox{II}\\|_{H^s} \\lesssim  \\sum_{n\\geq 1} \\frac{1}{n!} \\sum_{k_2\\leq k_1} 2^{k_2 + k k_{1,+}}  \\| P_{k_1}  g_{n}\\|_{L^2} \\| P_{k_2}\\psi\\|_{L^\\infty} \\lesssim \\| \\,h\\|_{H^{s+1}} \\| \\nabla \\psi \\|_{\\widetilde{W^1}},\n\\]\n\\[\n\\| \\mbox{I} \\|_{\\widetilde{W^\\gamma}} \\lesssim \\|\\,h\\|_{\\widetilde{W^\\gamma}} \\|\\nabla\\psi\\|_{\\widetilde{W^\\gamma}},\\quad \\| \\mbox{II}\\|_{\\widetilde{W^\\gamma}} \\lesssim \\|\\,h\\|_{\\widetilde{W^\\gamma}} \\|\\nabla\\psi\\|_{\\widetilde{W^\\gamma}}.\n\\]\nTherefore\n\\[\n\\|\\Lambda_{1}[\\nabla_{x,z}\\varphi](x,w\/(1+\\,h(x)))\\|_{H^k} \\lesssim \\| \\nabla\\psi\\|_{H^k} + \\|\\,h\\|_{H^{k+1}} \\| \\nabla \\psi \\|_{\\widetilde{W}^{1}},\n\\]\n\\[\n\\|\\Lambda_{1}[\\nabla_{x}\\varphi](x,w\/(1+\\,h(x)))\\|_{\\widetilde{W^\\gamma}} \\lesssim \\|\\nabla\\psi \\|_{\\widetilde{W^\\gamma}} + \\|\\,h\\|_{\\widetilde{W^\\gamma}} \\|\\nabla\\psi\\|_{\\widetilde{W^\\gamma}}\\lesssim \\|\\nabla \\psi\\|_{\\widetilde{W^\\gamma}},\n\\]\n\\[\n\\|\\Lambda_{1}[\\partial_z \\varphi](x,w\/(1+\\,h(x)))\\|_{\\widetilde{W^\\gamma}} \\lesssim \\|\\Lambda^2\\psi \\|_{\\widetilde{W^{\\gamma}}} + \\|\\,h\\|_{\\widetilde{W^\\gamma}} \\|\\nabla\\psi \\|_{\\widetilde{W^\\gamma}}.\n\\]\nFrom above estimates and  (\\ref{eqn3110}), we conclude the following estimates,\n\\begin{equation}\\label{eqn3127}\n\\|\\Lambda_{1}[\\nabla_{x}\\Phi]\\|_{\\widetilde{W^\\gamma}}\\lesssim \\|\\nabla \\psi\\|_{\\widetilde{W^\\gamma}},\\quad \n\\|\\Lambda_{1}[\\partial_w \\Phi]\\|_{\\widetilde{W^\\gamma}} \\lesssim \\|\\Lambda^2\\psi \\|_{\\widetilde{W^{\\gamma}}} + \\|\\,h\\|_{\\widetilde{W^\\gamma}} \\|\\nabla\\psi \\|_{\\widetilde{W^\\gamma}},\n\\end{equation}\n\\[\n\\| \\Lambda_{1}[\\nabla_{x,w}\\Phi] \\|_{H^k} \\lesssim \\|\\Lambda_{1}[\\nabla_{x,z}\\varphi](x,w\/(1+\\,h)) \\|_{H^k} + \\|\\Lambda_{1}[\\nabla_{x,z}\\varphi](x,w\/(1+\\,h))  \\|_{\\widetilde{W^0}}\\|\\,h\\|_{H^{k+1}}\n\\]\n\\begin{equation}\\label{eqn3120}\n\\lesssim \\| \\nabla \\psi \\|_{H^k} + \\|\\,h\\|_{H^{k+1}}\\|\\nabla \\psi\\|_{\\widetilde{W^1}}.\n\\end{equation}\n\nFollowing a similar procedure, we can handle the integral part in (\\ref{fixedpoint}) in the same way.  Similar to what we did in the proof of Lemma \\ref{integraloperator},  we use the size of symbol directly when $|\\xi|\\leq 1$ and   estimate the associated kernel when $|\\xi|\\geq 1$. As a result, we have the following estimate,\n\\[\n\\|\\textup{All terms in the R.H.S. of (\\ref{fixedpoint}) except linear part}(x,w\/(1+\\,h(x)))\\|_{H^{k}}\n\\]\n\\[\n\\lesssim \\sum_{i=1,2,3}  \\| g_i(z,\\cdot)\\|_{L^\\infty_z H^k}  + \\| \\,h\\|_{H^{k+1}} \\| g_i(z,\\cdot)\\|_{L^\\infty_z \\widetilde{W^0}} \\lesssim \\|\\nabla\\psi \\|_{\\widetilde{W^0}}\\|\\,h\\|_{H^{k+1}} + \\| \\nabla\\psi\\|_{H^k} \\| \\,h\\|_{\\widetilde{W^0}}\n\\]\n\\begin{equation}\\label{eqn3121}\n\\lesssim \\|\\nabla\\psi \\|_{\\widetilde{W^0}}\\|\\,h\\|_{H^{k+1}} + \\| \\nabla\\psi\\|_{H^k} \\| \\,h\\|_{\\widetilde{W^0}}.\n\\end{equation}\n\\[\n\\|\\textup{All terms in the R.H.S. of (\\ref{fixedpoint}) except linear part}(x,w\/(1+\\,h(x)))\\|_{\\widetilde{W^\\gamma}}\n\\]\n\\begin{equation}\\label{equation346}\n\\lesssim \\sum_{i=1,2,3}\\| g_i(z,\\cdot)\\|_{L^\\infty_z \\widetilde{W^\\gamma}} \\lesssim \\|\\,h\\|_{\\widetilde{W^{\\gamma+1}}} \\|\\nabla\\psi\\|_{\\widetilde{W^\\gamma}}.\n\\end{equation}\nFrom (\\ref{eqn3110}), (\\ref{eqn3127}), (\\ref{eqn3120}), (\\ref{eqn3121}) and (\\ref{equation346}), now it's easy to see estimates (\\ref{eqn3123}) and (\\ref{eqn3124}) hold.\n\nNow, we proceed to prove (\\ref{eqn3125}). From (\\ref{eqn3110}) and the same procedure as above, we have the following estimate,\n\\[\n\\|\\Lambda_{\\geq 2}[\\nabla_{x,w}\\Phi]\\|_{L^2} \\lesssim \\|\\Lambda_{\\geq 2}[\\nabla_{x,z}\\varphi](x,w\/(1+\\,h(x)))\\|_{L^2}  + \\|\\,h\\|_{H^1} \\| \\partial_z\\varphi(x,w\/(1+\\,h(x)))\\|_{\\widetilde{W^0}}\n\\]\n\\begin{equation}\\label{eqn3200}\n\\lesssim \\| \\,h\\|_{H^1} \\big[\\|\\Lambda \\psi \\|_{\\widehat{W^{2,\\alpha}}} + \\|\\,h\\|_{\\widetilde{W^1}} \\|\\nabla \\psi\\|_{\\widetilde{W^1}} \\big] + \\sum_{i=1,2,3}\\|g_{i}\\|_{L^\\infty_z L^2}.\n\\end{equation}\nRecall (\\ref{eqn12}) and (\\ref{eqn14}). Note that   $\\nabla\\varphi$ appears together with $\\nabla h$ inside the quadratic terms of $g_i(z)$, $i\\in\\{1,2,3\\}$.  When estimating the $L^{\\infty}_{z} L^{2}$ norm of $g_{i}(z)$, $i\\in\\{1,2,3\\}$, we  always put $\\nabla\\varphi$ in $L^2$ and put $\\partial_{z}\\varphi$ in $L^\\infty$. As a result,  the following estimate holds, i.e., our desired estimate (\\ref{eqn3125}) holds,\n\\[\n(\\ref{eqn3200}) \\lesssim \\|\\,h\\|_{H^1}  \\|\\Lambda \\psi \\|_{\\widehat{W^{2,\\alpha}}} +  \\big[\\|(\\,h, \\Lambda\\psi)\\|_{\\widehat{W^{2,\\alpha}}}  + \\|(\\,h, \\Lambda\\psi)\\|_{\\widehat{W^2}}\\big] (\\|\\,h\\|_{H^1} +\\|\\nabla\\psi\\|_{L^2})\\]\n\\[\\lesssim \\big[\\|(\\,h, \\Lambda\\psi)\\|_{\\widehat{W^{2,\\alpha}}}  + \\|(\\,h, \\Lambda\\psi)\\|_{\\widehat{W^2}}\\big] (\\|\\,h\\|_{H^1} +\\|\\nabla\\psi\\|_{L^2} ).\n\\]\n\n\\qed\n\n\n\\subsection{Paralinearization of the equation satisfied by the velocity potential }\\label{paralinearvelocitypotential}\nIn this subsection, our main goal is to do  paralinearization  process for the nonlinearity of equation satisfied by  $\\psi$ in (\\ref{waterwave}), which shows which part of nonlinearity actually loses derivatives. \n\nMore precisely, the main result of this subsection is stated as the following Proposition, \n\\begin{proposition}\\label{para2}\nWe have the following paralinearization  for the nonlinearity of equation satisfied by $ \\psi,$\n\\begin{equation}\\label{eqn740}\n\\frac{1}{2} |\\nabla \\psi|^2 - \\frac{1}{2} \\frac{(\\nabla\\,h\\cdot \\nabla \\psi + G(\\,h)\\psi)^2}{1+|\\nabla \\,h|^2}\\thickapprox T_{V}\\cdot \\nabla[ \\psi -  T_{B(\\,h)\\psi} \\,h] - T_{B}G(\\,h)\\psi.\n\\end{equation}\n\\end{proposition}\n\n\\begin{proof}\nRecall that $V=\\nabla \\psi- \\nabla \\,h B$.  From (\\ref{equation340}) and the composition Lemma \\ref{composi}, we have\n\\[\n\\frac{1}{2} |\\nabla \\psi|^2 - \\frac{1}{2} \\frac{(\\nabla\\,h\\cdot \\nabla \\psi + G(\\,h)\\psi)^2}{1+|\\nabla \\,h|^2} = \\frac{1}{2} |\\nabla \\psi|^2 - \\frac{1}{2} (1+|\\nabla \\,h|^2) B^2\n\\]\n\\[\n= \\frac{1}{2} |V|^2 + V\\cdot \\nabla \\,h B + \\frac{1}{2} |\\nabla \\,h|^2 B^2 -   \\frac{1}{2} (1+|\\nabla \\,h|^2) B^2= \\frac{1}{2} |V|^2 + V\\cdot \\nabla \\,h B - \\frac{1}{2} B^2 \n\\]\n\\[\n\\thickapprox T_{V}\\cdot V + T_{B} (V\\cdot \\nabla \\,h) + T_{V\\cdot \\nabla \\,h} B - T_{B} B= T_{V}\\cdot V + T_{V\\cdot \\nabla \\,h} B - T_{B} G(\\,h)\\psi\n\\]\n\\[\n=T_{V}\\cdot \\nabla \\psi - T_{V}\\cdot (\\nabla \\,h B) + T_{V\\cdot \\nabla \\,h} B - T_{B} G(\\,h)\\psi\n\\]\n\\[\n\\thickapprox T_{V}\\cdot \\nabla \\psi  - T_{V}T_{B}\\cdot \\nabla \\,h -[ T_{V}\\cdot T_{\\nabla \\,h} - T_{V\\cdot \\nabla \\,h} ]B - T_{B} G(\\,h)\\psi\n\\]\n\\[\n\\thickapprox T_{V}\\cdot [\\nabla \\psi - T_{B}\\cdot \\nabla \\,h] - T_{B} G(\\,h)\\psi \\thickapprox T_{V}\\cdot \\nabla[ \\psi -  T_{B(\\,h)\\psi} \\,h] - T_{B} G(\\,h)\\psi.\n\\]\nHence, finishing  the proof of this proposition.\n\\end{proof}\n    \n\n\n\\subsection{Symmetrization of the full system}\\label{symmetrizationsubsection}\nBased on the paralinearization results we obtained in previous subsections,  in this subsection, we will find out the good substitution variables by doing the symmetrization process  such that the resulted system has requisite symmetric structures inside. \n\nDefine $\\omega=\\psi- T_{B(\\,h)\\psi} \\,h$, which is the so-called good unknown variable.   After combining the good decomposition  (\\ref{paralinear}) in Proposition \\ref{prop1} and the good decomposition (\\ref{eqn740}) in Proposition \\ref{para2}, we reduce the system of equation satisfied by $h $ and $\\psi$ to the system of equation satisfied by $h$ and $\\omega$ as follows, \n\\begin{equation}\\label{presym}\n\\left\\{\\begin{array}{l}\n\\partial_t \\,h  =\\Lambda^2 \\omega+ T_{\\lambda-|\\xi|} \\omega - T_{V}\\cdot \\nabla \\,h + \\widetilde{F}(\\,h)\\psi,\\\\\n\\\\\n\\partial_t \\omega= -T_{a} \\,h - T_{V}\\cdot \\nabla \\omega  + f',\n\\end{array}\\right.\n\\end{equation}\nwhere\n\\[\na:=1+\\partial_t B+V\\cdot \\nabla B,\n\\]\nwhich is the so-called Taylor coefficient  and $f'$ is a good error term  in the sense of estimate (\\ref{gooderror}).\n\n\n\nHowever,  the system (\\ref{presym}) cannot be used to do energy estimate.   When using the system (\\ref{presym}) to do the energy estimate, one might find that the following term loses one derivative and can't be simply treated,\n\\begin{equation}\\label{eqq2345}\n\\int_{\\mathbb{R}^2} \\partial_{x}^{N}\\,h \\partial_{x}^{N}[T_{\\lambda-|\\xi|} \\omega] + \\partial_{x}^{N}\\Lambda \\omega \\partial_x^N \\Lambda[-T_{a}\\,h], \\quad \\textup{where $N$ is the prescribed top derivative level.}\n\\end{equation}\n\nTo get around this difficulty,  we will symmetrize the system (\\ref{presym}) by following the same procedures in \\cite{alazard2}. Define \n\\begin{equation}\\label{transform}\nU_1 = \\,h + T_{\\alpha} \\,h, \\quad U_2 = \\Lambda [\\omega + T_{\\beta}\\omega]\\thickapprox [T_{\\sqrt{\\lambda}-|\\xi|^{1\/2}}\\omega] + \\Lambda \\omega, \\quad U:= U_1 + i U_2,\n\\end{equation}\nwhere\n\\begin{equation}\\label{taylorcoef}\n\\alpha= \\sqrt{a}-1,\\quad \\quad \\omega = \\psi - T_{B(\\,h)\\psi}\\,h, \\quad\n\\beta := \\sqrt{\\lambda\/|\\xi|}-1 =\\sqrt[4]{(1+|\\nabla \\,h|^2) - (\\nabla\\,h \\cdot \\xi\/|\\xi|)^2}-1.\n\\end{equation}\nNote that,\n\\[\n\\Lambda_{1}[ a ]= \\Lambda_{1}[\\partial_t \\Lambda^2 \\psi] =- \\Lambda^2 \\,h, \\quad \\Lambda_1[\\partial_t  a] = -\\Lambda^4 \\psi,\\quad \\Lambda_1[\\partial_{t} \\alpha] = -\\frac{1}{2}\\Lambda^4 \\psi,\\quad \\Lambda_1[\\alpha] = -\\frac{1}{2} \\Lambda^2 \\,h.\n\\]\n\nWe   take the estimates of the Taylor coefficient in Lemma \\ref{taylorcoefficient} as granted first. Then it is easy to see the following estimate and equivalence relations  hold,\n\\begin{equation}\\label{eqn5900}\n\\| (U_1, U_2)- (\\,h, \\Lambda\\psi)\\|_{H^{k}}\\lesssim \\| (h, \\Lambda \\psi)\\|_{\\widetilde{W^{3}}} \\|(\\,h, \\Lambda \\psi)\\|_{H^{k}}.\n\\end{equation}\n\\[\n\\partial_t U_1\\thickapprox\\Lambda^2 \\omega+  [T_{\\lambda-|\\xi|} \\omega] - T_{V}\\cdot \\nabla \\,h  + T_{\\partial_t \\alpha}\\,h + T_{\\alpha}[\\partial_t \\,h]\n\\]\n\\[\n\\thickapprox [\\Lambda^2 -T_{|\\xi|}] \\omega+  T_{\\lambda} \\omega - T_{V}\\cdot \\nabla U_1 + T_{V}\\cdot T_{\\alpha} \\nabla \\,h  + T_{\\alpha}\\big[  T_{\\lambda} \\omega - T_{V}\\cdot \\nabla \\,h \\big]\n\\]\n\\[\n\\thickapprox [\\Lambda^2 -T_{|\\xi|}] \\Lambda^{-1} U_2 + T_{\\lambda \\sqrt{a}}\\omega  - T_{V}\\cdot \\nabla U_1 \n\\thickapprox \\Lambda U_2 + [T_{\\sqrt{ \\lambda}\\alpha} T_{\\sqrt{\\lambda}}\\omega ]- T_{V}\\cdot \\nabla U_1\n\\]\n\\begin{equation}\\label{equation200}\n\\thickapprox \\Lambda U_2 + [T_{\\sqrt{\\lambda}\\alpha} U_2] - T_{V}\\cdot \\nabla U_1.\n\\end{equation}\n\\[\n\\partial_t U_2 \\thickapprox \\Lambda (1+T_{\\beta}) [-T_{a} \\,h - T_{V}\\cdot \\nabla \\omega] + \\Lambda T_{\\partial_t \\beta} \\omega \n\\thickapprox -\\Lambda U_1 - [T_{\\sqrt{\\lambda}} T_{\\alpha} U_1] - T_{V}\\cdot \\nabla T_{\\sqrt{\\lambda}} \\omega + T_{\\partial_t \\beta} \\Lambda \\omega\\]\n\\begin{equation}\\label{equation201}\n\\thickapprox -\\Lambda U_1 - [T_{\\sqrt{\\lambda}\\alpha} U_1] - T_{V}\\cdot \\nabla U_2 + T_{\\partial_t \\beta} U_2.\n\\end{equation}\nHence, the problematic terms in (\\ref{eqq2345}) becomes the following terms (modulo good error terms),\n\\begin{equation}\\label{eqq2122}\n\\int_{\\mathbb{R}^2} \\partial_{x}^{N} U_{1} \\partial_{x}^{N}[T_{\\sqrt{\\lambda}\\alpha} U_2] - \\partial_{x}^{N}U_{2} \\partial_x^N   [T_{\\sqrt{\\lambda}\\alpha} U_1], \\quad \\textup{where $N$ is the prescribed top derivative level.}\n\\end{equation}\nTherefore, we can move derivatives in (\\ref{eqq2122}) around such that this cubic term doesn't loss derivative. See (\\ref{eqnn9824}) for more details.\n\n\n\\subsection{Estimates of the Taylor coefficient} The main goal of this subsection is to obtain some basic estimates for the Taylor coefficient, which is a necessary part of the energy estimate.\n\n\n\n\n\\begin{lemma}\\label{taylorcoefficient}\nUnder the smallness estimate \\textup{(\\ref{smallnessestimate})}, we have the following estimates for $\\gamma\\leq 3, \\gamma_1\\leq 2$,\n\\[\n\\|a-1 \\|_{H^k}\\lesssim \\|\\nabla\\,h\\|_{H^k} + \\|(\\,h, \\nabla\\psi)\\|_{H^k}\\|(\\,h, \\nabla\\psi)\\|_{\\widetilde{W^2}},\n\\|a-1\\|_{\\widetilde{W^{\\gamma}}}\\lesssim \\|\\nabla\\,h\\|_{\\widetilde{W^\\gamma}} +  \\big[ \\| \\nabla\\psi\\|_{\\widetilde{W^{\\gamma+1}}} + \\|\\nabla\\,h\\|_{\\widetilde{W^{\\gamma}}}  \\big]^2,\n\\]\n\\[\n\\| \\partial_t a \\|_{H^k}\\lesssim \\|\\nabla \\psi\\|_{H^{k+1}} +\\|(\\,h, \\nabla\\psi)\\|_{\\widetilde{W^{3}}}  \\|(\\,h,\\nabla\\psi)\\|_{H^{k+1}},\n\\|\\partial_t a \\|_{\\widetilde{W^{\\gamma_1}}} \\lesssim  \\| \\Lambda^2\\psi \\|_{\\widetilde{W^{\\gamma_1+1}}} +  \\| (\\nabla\\,h, \\nabla\\psi)\\|_{\\widetilde{W^{\\gamma_1+1}}}^2.\n\\]\n\\end{lemma}\n\\begin{proof}\n\nRecall  (\\ref{hvderivative}), (\\ref{waterwave}), and\n\\[\na= 1 + V\\cdot\\nabla B + \\partial_t B,\\quad B=\\partial_z \\varphi\/(1+\\,h)\\big|_{z=0}.\n\\]\n To estimate $a$ and $\\partial_t a$,  it's sufficient to estimate $\\partial_z\\partial_t\\varphi$ and $\\partial_z\\partial_t^2\\varphi $. From the fixed point type formulation of $\\nabla_{x,z}\\varphi$ in (\\ref{fixedpoint}), we can derive the following equality, \n\\[\n\\nabla_{x,z}\\partial_t \\varphi = \\Bigg[ \\Big[ \\frac{e^{-(z+1)|\\nabla|}+ e^{(z+1)|\\nabla|}}{e^{-|\\nabla|} + e^{|\\nabla|}}\\Big]\\nabla\\partial_t \\psi ,  \\frac{e^{(z+1)|\\nabla|}- e^{-(z+1)|\\nabla|}}{e^{-|\\nabla|}+e^{|\\nabla|}} |\\nabla| \\partial_t\\psi\\Bigg] + [\\mathbf{0}, \\partial_t g_1(z)]+ \n\\]\n\\[\n+\\int_{-1}^{0} [K_1(z,s)-K_2(z,s)-K_3(z,s)](\\partial_t g_2(s)+\\nabla \\cdot \\partial_t g_3(s))  ds \\]\n\\begin{equation}\\label{eqn3300}\n+\\int_{-1}^{0} K_3(z,s)|\\nabla|\\textup{sign($z-s$)}\\partial_t g_1(s)  -|\\nabla| [K_1(z,s) +K_2(z,s)]\\partial_t g_1(s)\\, d  s.\n\\end{equation}\nFollowing the same fixed point type argument that we used in the proof of  Lemma \\ref{Sobolevestimate}, we can derive the following estimates,\n\\[\n\\| \\nabla_{x,z}\\partial_t \\varphi\\|_{L^\\infty_z \\widetilde{W^\\gamma}} \\lesssim  \\|\\nabla\\,h\\|_{\\widetilde{W^\\gamma}} +   \\| \\partial_t \\,h\\|_{\\widetilde{W^{\\gamma+1}}} \\|\\nabla_{x,z}\\varphi\\|_{L^\\infty_z \\widetilde{W^\\gamma}}\n\\]\n\\begin{equation}\\label{eqn3301}\n \\lesssim\n\\|\\nabla\\,h\\|_{\\widetilde{W^\\gamma}} +  \\big[ \\| \\nabla\\psi\\|_{\\widetilde{W^{\\gamma+1}}} + \\|\\nabla\\,h\\|_{\\widetilde{W^{\\gamma}}}  \\big]^2.\n\\end{equation}\n\\[\n\\| \\nabla_{x,z}\\partial_t \\varphi\\|_{L^\\infty_z H^k}\\lesssim \\| \\nabla \\partial_t \\psi \\|_{H^{k}} + \\|\\,h\\|_{H^{k+1}} \\| \\nabla_{x,z}\\partial_t \\varphi\\|_{\\widetilde{W^1}} +\\|\\partial_t \\,h\\|_{H^{k+1}} \\|\\nabla_{x,z}\\varphi\\|_{\\widetilde{W^{1}}}\n\\]\n\\[ + \\|\\partial_t\\,h\\|_{\\widetilde{W^1}} \\|\\nabla_{x,z}\\varphi\\|_{L^\\infty_z H^{k}}\\lesssim \\|\\nabla\\,h\\|_{H^{k}} + \\|(\\,h, \\nabla\\psi)\\|_{H^k}\\|(\\,h, \\nabla\\psi)\\|_{\\widetilde{W^2}}.\n\\]\n\nWe can take another time derivative at the both hands side of equation (\\ref{eqn3300}) to derive a fixed point type formulation for $\\nabla_{x,z}\\partial_t^2 \\varphi$. Following a similar argument, we can derive the following estimate, \n\\[\n\\|\\nabla_{x,z}\\partial_t^2 \\varphi\\|_{L^\\infty_z \\widetilde{W^\\gamma}} \\lesssim \\|\\partial_t^2\\psi \\|_{\\widetilde{W^{\\gamma +1}}} + \\|\\partial_t \\,h\\|_{\\widetilde{W^{\\gamma +1}}} \\| \\partial_t \\nabla_{x,z}\\varphi\\|_{L^\\infty_z \\widetilde{W^\\gamma} } + \\|\\partial_t^2\\,h \\|_{\\widetilde{W^{\\gamma +1}}} \\| \\nabla_{x,z}\\varphi\\|_{L^\\infty_z \\widetilde{W^\\gamma}}.\n\\]\nRecall the system of equations satisfied by $\\,h$ and $\\psi$ in (\\ref{waterwave}), we have\n\\[\n\\partial_t^2 h = \\partial_t G(h)\\psi = \\partial_t[(1+|\\nabla h|^2) B -\\nabla h \\cdot \\nabla \\psi],\n\\]\n\\[\n\\partial_t^2 \\psi = -\\partial_t \\,h + \\nabla\\psi \\cdot\\nabla\\partial_t \\psi + (1+|\\nabla\\,h|^2) B \\partial_t B + \\nabla\\,h\\cdot \\nabla\\partial_t \\,h B^2.\n\\]\nHence,\n\\[\n\\|\\partial_t^2\\psi\\|_{\\widetilde{W^{\\gamma+1}}} \\lesssim \\| \\Lambda^2\\psi \\|_{\\widetilde{W^{\\gamma+1}}} + \\big[ \\| \\nabla\\,h\\|_{\\widetilde{W^{\\gamma+1}}} + \\|\\nabla\\psi\\|_{\\widetilde{W^{\\gamma+1}}}\\big]^2.\n\\]\nCombining above estimate, (\\ref{eqn3301}) and (\\ref{eqn2201}) in Lemma \\ref{Sobolevestimate}, we have\n\\[\n\\|\\nabla_{x,z}\\partial_t^2 \\varphi\\|_{L^\\infty_z \\widetilde{W^\\gamma}} \\lesssim   \\| \\Lambda^2\\psi \\|_{\\widetilde{W^{\\gamma+1}}} + \\big[ \\| \\nabla\\,h\\|_{\\widetilde{W^{\\gamma+1}}} + \\|\\nabla\\psi\\|_{\\widetilde{W^{\\gamma+1}}}\\big]^2.\n\\]\nFollow the same argument, we derive the $L^2$ type estimate of $\\partial_t^2\\varphi$ as follows,\n\\[\n\\| \\nabla_{x,z}\\partial_t^2 \\varphi\\|_{L^\\infty_z H^k} \\lesssim \\| \\partial_t^2\\psi\\|_{H^{k+1}} + \\|\\partial_t \\,h\\|_{H^{k+1}}\\|\\nabla_{x,z}\\partial_t\\varphi\\|_{L^\\infty_z \\widetilde{W^1}} \n\\]\n\\[\n+ \\|\\partial_t \\,h\\|_{\\widetilde{W^1}} \\| \\nabla_{x,z}\\partial_t\\varphi\\|_{L^\\infty_z H^{k}}+ \\|\\partial_t^2\\,h\\|_{H^{k}} \\|\\nabla_{x,z}\\varphi\\|_{L^\\infty_z \\widetilde{W^1}} + \\|\\partial_t^2\\,h\\|_{\\widetilde{W^1}} \\|\\nabla_{x,z}\\varphi\\|_{L^\\infty_z H^k} \n\\]\n\\[\n+\\|\\,h\\|_{H^{k+1}} \\|\\partial_t^2 \\nabla_{x,z}\\varphi\\|_{L^\\infty_z \\widetilde{W^1}} +\\|\\,h\\|_{\\widetilde{W^1}} \\| \\nabla_{x,z}\\partial_t^2 \\varphi\\|_{L^\\infty_z H^k},\n\\]\nwhich further gives us the following estimate, \n\\[\n\\| \\nabla_{x,z}\\partial_t^2 \\varphi\\|_{L^\\infty_z H^k} \\lesssim \\|\\Lambda^2 \\psi\\|_{H^{k+1}} + \\|\\nabla\\,h\\|_{\\widetilde{W^2}} \\|\\Lambda^2\\psi\\|_{H^{k+1}} + \\|\\nabla\\psi \\|_{\\widetilde{W^2}} \\|\\,h\\|_{H^{k+1}}\n\\]\n\\[\n\\lesssim \\|\\nabla \\psi\\|_{H^{k+1}} + \\|(\\,h, \\nabla\\psi)\\|_{\\widetilde{W^{3}}}  \\|(\\,h,\\nabla\\psi)\\|_{H^{k+1}}.\n\\]\nTherefore, our desired estimates of the Taylor coefficient hold.\n\n \\end{proof}\n\n\n\\section{Energy estimate}\\label{energyestimatesection}\nThe main goal in this section is to prove our main Theorem \\ref{maintheorem}.   Since the energy of $(U_1,U_2)$ is comparable with  the energy of $(\\,h, \\Lambda \\psi)$ (see(\\ref{eqn5900})), it is sufficient to do energy estimate for the system of equations satisfied by $U_1$ and $U_2$. Let $N_0$ be the prescribed top regularity level.  From (\\ref{equation200}) and (\\ref{equation201}), we know that  the system of equations satisfied by $(U_1,U_2)$ reads as follows, \n\\begin{equation}\\label{system4}\n\\left\\{\\begin{array}{l}\n\\partial_t U_1 -\\Lambda U_2 = T_{\\sqrt{\\lambda}\\alpha} U_2 - T_{V\\cdot}\\nabla U_1 +\\mathcal{R}_1, \\\\\n\\\\\n\\partial_t U_2 + \\Lambda U_1 = -T_{\\sqrt{\\lambda}\\alpha} U_1 - T_{V}\\cdot \\nabla U_2 + \\mathcal{R}_2. \\ \\\\\n\\end{array}\\right.\n\\end{equation}\nThe precise formulations of good remainder terms $\\mathcal{R}_1$ and $\\mathcal{R}_2$ are not so important in the energy estimate part. From (\\ref{equation200}) and (\\ref{equation201}), we know that they are good error terms, i.e.,\n\\begin{equation}\\label{remainderenergy}\n\\| \\mathcal{R}_1\\|_{H^{N_0}} + \\| \\mathcal{R}_2\\|_{H^{N_0}} \\lesssim_{N_0} \\big[ \\|(\\,h, \\Lambda\\psi)\\|_{\\widehat{W^{4,\\alpha}}}  + \\|(\\,h, \\Lambda\\psi)\\|_{\\widehat{W^4}}^2\\big] \\|(\\eta,\\Lambda \\psi)\\|_{H^{N_0}}.\n\\end{equation}\nDefine the energy of $U_1$ and $U_2$ as follows,\n\\begin{equation}\\label{energyfunction}\nE_{N_0}(t):=\\frac{1}{2}\\Big[ \\|U_1\\|_{L^2}+\\|U_2\\|_{L^2} + \\sum_{k+j=N_0, 0\\leq k , j\\in \\mathbb{Z}} \\| \\partial_1^{k}\\partial_2^{j} U_1\\|_{L^2}^2 + \\|\\partial_1^{k}\\partial_2^{j}  U_2\\|_{L^2}^2\\Big].\n\\end{equation}\nFrom \n(\\ref{system4}), we have\n\\[\n\\Big|\\frac{d}{d t} E_{N_0}(t) \\Big|\\lesssim \\| (U_1, U_2)\\|_{H^{N_0}}\\| (\\mathcal{R}_1, \\mathcal{R}_2)\\|_{H^{N_0}}+ \\sum_{k+j=N_0, 0\\leq k , j\\in \\mathbb{Z}}  \\Big|\\int_{\\mathbb{R}^2}\\big[\\partial_1^{k}\\partial_2^{j}  U_1\\partial_1^{k}\\partial_2^{j} [-T_{V}\\cdot \\nabla U_1]  \n\\]\n\\[\n+ \\partial_1^{k}\\partial_2^{j}  U_2\\partial_1^{k}\\partial_2^{j} [-T_{V}\\cdot \\nabla U_2]\\big] d x \\Big|+ \\Big| \\int_{\\mathbb{R}^2} \\partial_1^{k}\\partial_2^{j}  U_1 \\partial_1^{k}\\partial_2^{j} ([ T_{\\sqrt{\\lambda}\\alpha} U_2]) -\\partial_1^{k}\\partial_2^{j}  U_2 \\partial_1^{k}\\partial_2^{j} ([T_{\\sqrt{\\lambda}\\alpha} U_1])\\Big|\n\\]\n\\[\n\\lesssim_{N_0} \\big[ \\| \\nabla V\\| _{\\widetilde{W}^{1}} + \\|(\\,h, \\Lambda\\psi)\\|_{\\widehat{W^{4,\\alpha}}}  + \\|(\\,h, \\Lambda\\psi)\\|_{\\widehat{W^4}}^2 \\big]\\|(U_1, U_2)\\|_{H^{N_0}}^2 + \\mathcal{E}_{N_0},\n\\]\n\\begin{equation}\\label{eqn811}\n\\lesssim_{N_0}  \\big[  \\|(\\,h, \\Lambda\\psi)\\|_{\\widehat{W^{4, \\alpha}}} + \\| (\\,h,\\Lambda\\psi)\\|_{\\widehat{W^{4}}}^2\\big]\\|(U_1, U_2)\\|_{H^{N_0}}^2 + \\mathcal{E}_{N_0},\n\\end{equation}\nwhere\n\\[\n\\mathcal{E}_{N_0} =  \\sum_{k+j=N_0, 0\\leq k , j\\in \\mathbb{Z}}\\Big|\\int_{\\mathbb{R}^2}\\Big[\\partial_1^{k}\\partial_2^{j} U_1  T_{\\sqrt{\\lambda}\\alpha} \\partial_1^{k}\\partial_2^{j} U_2 -\\partial_1^{k}\\partial_2^{j} U_2 T_{\\sqrt{\\lambda}\\alpha}  \\partial_1^{k}\\partial_2^{j}  U_1 \\Big]\\Big|\\]\n\\begin{equation}\\label{eqnn9824}\n= \\sum_{k+j=N_0, 0\\leq k , j\\in \\mathbb{Z}}\\Big|\\int_{\\mathbb{R}^2} \\Big[ \\partial_1^{k}\\partial_2^{j} U_1 \\big(T_{\\sqrt{\\lambda}\\alpha}  - (T_{\\sqrt{\\lambda}\\alpha})^{\\ast}\\big)\\partial_1^{k}\\partial_2^{j} U_2\\Big]\\Big|.\n\\end{equation}\nRecall that $\\sqrt{\\lambda}\\alpha\\in M^{1\/2}_1$ is a symbol of order $1\/2$. Note that it is real. Hence, from Lemma \\ref{adjoint}, we know that the symbol of the adjoint operator is itself, and operator $(T_{\\sqrt{\\lambda}\\alpha})^{\\ast} - T_{\\sqrt{\\lambda} \\alpha}$  is of order $-1\/2$. As a result,    the following estimate holds, \n\\begin{equation}\\label{eqn808}\n\\mathcal{E}_{N_0}\\lesssim M_{1}^{1\/2}(\\sqrt{\\lambda}\\alpha) \\| (U_1, U_2)\\|_{H^{N_0}}^2 \\lesssim \\| \\nabla \\,h\\|_{\\widetilde{W^2}}\\|(U_1, U_2)\\|_{H^{N_0}}^2.\n\\end{equation}\nCombining above estimate with (\\ref{eqn811}) and (\\ref{eqn5900}), we have\n\\[\n\\Big| \\frac{d}{d t} E_{N_0}(t) \\Big| \\lesssim_{N_0}   \\big[  \\|(\\,h, \\Lambda\\psi)\\|_{\\widehat{W^{4, \\alpha}}} + \\| (\\,h,\\Lambda\\psi)\\|_{\\widehat{W^{4}}}^2\\big]\\|(h, \\Lambda \\psi)\\|_{H^{N_0}}^2.\n\\]\n\n\n\\section*{Appendix: Quadratic terms of the good remainders}\\label{appendix}\n\nIn this section, we calculate explicitly the quadratics terms of the good reminder terms $\\mathcal{R}_1$ and $\\mathcal{R}_2$ \tto help readers to understand the fact that we can gain  one derivative  in the new energy estimate (\\ref{energyestimate}) for the inputs of quadratic terms, which are putted  in the $L^\\infty$ type space.     Recall (\\ref{transform}) and (\\ref{taylorcoef}). We have \n \\[\n\\Lambda_1[B]= \\Lambda^2 \\psi, \\quad \\Lambda_{1}[a]= \\Lambda_{1}[\\partial_t B]= -\\Lambda^2 h,\\quad \\Lambda_{1}[\\alpha]= -\\frac{1}{2} \\Lambda^2 h,\\quad \\Lambda_{1}[\\beta]=0.\n\\]\nRecall (\\ref{system4}). By using above definitions, we can reduce the equations satisfied by $U_1$ and $U_2$ to the equations satisfied by $h$ and $\\psi$ as follows,  \n\\begin{equation}\\label{eqn2}\n\\left\\{\\begin{array}{l}\n\\partial_t\\,h -\\Lambda^2\\psi = \\widetilde{Q}_1(\\,h, \\psi) + \\Lambda_{2}[\\mathcal{R}_1](\\,h, \\psi) + \\textup{cubic and higher}_1, \\\\\n\\\\\n\\partial_t \\Lambda \\psi + \\Lambda \\,h = \\widetilde{Q}_{2}(\\,h, \\psi) + \\Lambda_{2}[\\mathcal{R}_2](\\,h, \\psi) + \\textup{cubic and higher}_2,\\\\\n\\end{array}\\right.\n\\end{equation}\nwhere\n\\[\n\\widetilde{Q}_1(\\,h, \\psi)=-\\Lambda^2(T_{\\Lambda^2\\psi}\\,h) + \\frac{1}{2} T_{\\Lambda^2\\,h}\\Lambda^2\\psi + \\frac{1}{2} T_{\\Lambda^4\\psi}\\,h - \\frac{1}{2}(T_{\\Lambda^2\\,h} |\\nabla|^{1\/2}\\Lambda \\psi) - T_{\\nabla \\psi} \\cdot \\nabla \\,h,\n\\]\n\\[\n\\widetilde{Q}_2(\\,h, \\psi)= \\Lambda(T_{\\Lambda^2\\psi} \\Lambda^2\\psi-T_{\\Lambda^2\\,h}\\,h) +\\Lambda (\\frac{1}{2} T_{\\Lambda^2\\,h}\\,h) +\\frac{1}{2} ( T_{\\Lambda^2\\,h}|\\nabla|^{1\/2}\\,h) - T_{\\nabla\\psi}\\cdot \\nabla \\Lambda \\psi.\n\\]\nRecall   (\\ref{waterwave}) and (\\ref{eqq345}) in Lemma \\ref{quadraticterms}. We   have\n\\[\n\\Lambda_2[\\mathcal{R}_1](h, \\psi) = \\Lambda_{2}[G(h)\\psi]- \\widetilde{Q}_{1}(h, \\psi)= -\\nabla\\cdot\\big( T_{ h}\\nabla \\psi \\big)- \\nabla\\cdot\\mathcal{R}( h, \\nabla \\psi) -T_{\\Delta^2 \\psi} h -\\Lambda^{2}(T_{ h } \\Lambda^{2}\\psi )  \n\\]\n\\begin{equation}\\label{eqqqn1234}\n- \\Lambda^{2}\\mathcal{R}(h, \\Lambda^2 \\psi)+ \\frac{1}{2} T_{\\Lambda^2 h} \\Lambda (\\Lambda-|\\nabla|^{1\/2})\\psi -  \\frac{1}{2} T_{\\Lambda^4\\psi}\\,h,\n\\end{equation}\n\\[\n\\Lambda_{2}[\\mathcal{R}_2](h, \\psi) = \\Lambda\\big[ -\\frac{1}{2} |\\nabla\\psi |^2 + \\frac{1}{2} |\\Lambda^2\\psi|^2 \\big]- \\widetilde{Q}_2(h, \\psi) = \\Lambda(-T_{\\nabla \\psi}\\cdot \\nabla\\psi) + T_{\\nabla\\psi} \\cdot \\nabla\\Lambda  \\psi \n\\]\n\\begin{equation}\\label{eqnnqn1223}\n+ \\frac{1}{2}\\big(  -\\Lambda (T_{\\Lambda^2 h }  h)+ T_{\\Lambda^2 h} |\\nabla|^{1\/2} h    \\big)  -\\frac{1}{2}\\Lambda\\mathcal{R}(\\nabla \\psi, \\nabla \\psi) + \\frac{1}{2} \\Lambda\\mathcal{R}(\\Lambda^2 \\psi, \\Lambda^2 \\psi).\n\\end{equation}\nNote that \n\\begin{equation}\\label{difference}\n\\Lambda-|\\nabla|^{1\/2}= |\\nabla|^{1\/2}( \\sqrt{\\tanh|\\nabla|}-1)= \\frac{-2 e^{-|\\nabla|}|\\nabla|^{1\/2}}{(\\sqrt{\\tanh|\\nabla|}+1)(e^{|\\nabla|}+e^{-|\\nabla|})}.\n\\end{equation}\nNow, it is easy to see that  $\\Lambda_{2}[\\mathcal{R}_2](h, \\psi)$ and  $\\Lambda_{2}[\\mathcal{R}_2](h, \\psi)$ don't lose derivatives. It remains to check  that we can gain one derivative in the $L^\\infty$ type space. From (\\ref{eqqqn1234}) and (\\ref{eqnnqn1223}), it would be sufficient to check the following  term ,\n\\begin{equation}\\label{bulkterms}\n-\\nabla\\cdot \\big(T_{ h }  \\nabla \\psi \\big)  -\\Lambda^{2}(T_{ h } \\Lambda^{2}\\psi ).\n\\end{equation}\nThe corresponding symbol of above quadratic terms is given as follows,\n\\[\n\\xi\\cdot \\eta -|\\xi||\\eta|\\tanh |\\xi| \\tanh|\\eta|,\\quad |\\xi-\\eta|\\ll |\\xi|\\sim |\\eta|.\n\\]\nWe decompose this symbol  into two parts as follows, \n\\[\np_1(\\xi-\\eta, \\eta)=\\xi\\cdot \\eta - |\\xi||\\eta|=-\\frac{1}{2} |\\xi-\\eta|^2  + \\frac{1}{2} |\\xi|^2+ \\frac{1}{2}|\\eta|^2-|\\xi||\\eta|=-\\frac{1}{2} |\\xi-\\eta|^2 + \\frac{1}{2}(|\\xi|-|\\eta|)^2,\n\\]\n\\[\n  p_2(\\xi-\\eta, \\eta) = |\\xi||\\eta| \\big(1-\\tanh|\\xi|\\tanh|\\eta| \\big).\n\\]\nNow, it is clear that the first part of (\\ref{bulkterms}), which is determined by $p_1(\\xi-\\eta, \\eta)$, doesn't lose derivative and gain two derivatives for `` $h$''. For the second part of (\\ref{bulkterms}), which is determined by $p_2(\\xi-\\eta, \\eta)$, we can lower the regularity to $L^2$ such that we can put ``$  \\psi$''   in $L^\\infty$ and`` $h$'' in $L^2$. As a result, we can always gain one derivative for the inputs of quadratic terms that are putted in $L^\\infty$ type space.\n \n\n \n \n \n\n \n\n\n\n\n\n\n\n\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n \n\n\n\n\n\n\n\n\n\n\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nIt is well known that the current accelerated expansion of the universe, described very successfully by the cold dark matter (DM) model with a cosmological constant ($\\Lambda$CDM), \nis difficult to construct from the bottom--up in particle physics models beyond the standard model. More dramatically, \nit has recently been conjectured that de Sitter space cannot be embedded in string theory and that there are restrictions on the effective field \ntheory compatible with string theory \\cite{Obied:2018sgi}. These restrictions are called the swampland criteria and are given below. \nWhile this conjecture is currently under scrutiny, if true it would either imply that string theory, as currently understood, is wrong or that the current accelerated expansion is not due to a non-vanishing cosmological constant (or vacuum energy) but is driven by some other processes, either by modifications of gravity or new degrees of freedom in the matter sector (dark energy (DE)). Among the best studied \nmodels are quintessence fields, in which the expansion at late times is driven by a light scalar field \\cite{Wetterich:1987fm,Ratra:1987rm,Caldwell:1997ii,Zlatev:1998tr}. The swampland criteria on the effective potential $V$ of scalar fields are given by the following inequalities:\\footnote{Extensions of these criteria have been proposed in \\cite{Andriot:2018wzk,Ooguri:2018wrx,Andriot:2018mav}.}\n\\begin{equation} \\label{swampland1}\n M_{\\rm Pl}|\\nabla V| \\geq c V,\n\\end{equation}\nwhere the left hand side denotes the gradient of the potential, $M_{\\rm Pl}$ is the reduced Planck mass and $c\\sim {\\cal O}(1)$ is a constant. In addition, the field should not vary more than \nroughly one Planck unit throughout the history of the universe\n\\begin{equation}\\label{swampland2}\n\\Delta\\phi \\lesssim d~ M_{\\rm Pl}~,\n\\end{equation}\nwhere $d \\sim {\\cal O}(1)$, as otherwise light fields become important and the effective field theory becomes invalid (see \\cite{Palti:2019pca} for a recent review). The swampland criteria have sparked a lot of activity recently, because of their implications for inflation (see e.g. \\cite{Banerjee:2018qey,Achucarro:2018vey,Garg:2018reu, Kehagias:2018uem,Brahma:2018hrd,Dimopoulos:2018upl,Kinney:2018nny,Kinney:2018kew,Lin:2018kjm}) and dark energy (see e.g. \\cite{Agrawal:2018own,Chiang:2018jdg,Heisenberg:2018yae,Cicoli:2018kdo,Akrami:2018ylq,Heisenberg:2018rdu,Marsh:2018kub,DAmico:2018mnx,Han:2018yrk,Heckman:2018mxl,Olguin-Tejo:2018pfq,Colgain:2018wgk,Heckman:2019dsj,Brahma:2019kch}). \n\n\n\nIt has long been argued that a quintessence field should couple to other sectors, \nunless there is a symmetry which forbids this \\cite{Carroll:1998zi}. This is certainly the case for quintessence fields motivated from string theory, in which the fields usually determine coupling constants. In \\cite{Agrawal:2018own}, the authors argued that the field should at least couple to dark matter, given that the couplings to the standard model particles are strongly constrained. Theories with DE-DM couplings have been studied for some time and models like these are named 'coupled quintessence' \\cite{Wetterich:1994bg,Amendola:1999er}. These type of theories are already strongly constrained by current observations of the cosmic microwave background, large scale structures and the expansion history of the universe. As we will see below, for the simplest theories, the couplings allowed are very small. The strength of a fifth force mediated between two DM particles is constrained to be much less than that of gravity \\cite{vandeBruck:2017idm,Miranda:2017rdk}, if the coupling is constant. In this paper we argue that one class of models, which could be very relevant for the swampland picture, deserves further studies. In these models the fifth force between DM particles switches on at late times, when the quintessence field starts to roll down its potential energy. These theories can be reconciled with observations of the cosmic microwave background radiation (CMB) as well as large scale structures (LSS), but they predict an equation of state different from the cosmological constant (and in fact can mimic DE with an equation of state $w\\lesssim -1$) and an effective gravitational constant between DM particles considerably larger than Newton's constant $G_N$. We expect the predictions for structure formation and evolution in these models to deviate from $\\Lambda$CDM model on intermediate and smaller length scales. \n\nThe paper is organized as follows: in the next Section we study first the simplest types of models, based on a conformal coupling. We then modify the theory with a different coupling function which possesses a minimum. In Section 3 we further extend the class of models, allowing for derivative couplings. Our conclusions and an outlook are given in Section 4. \n\n\\section{The simplest models and an extension}\nA well studied effective field theory setup to introduce a coupling between dark matter and a scalar field $\\phi$, is the following. The gravitational field and the standard model field propagate under the influence of the \nmetric $g_{\\mu\\nu}$, whereas dark matter (DM) particles propagate on geodesic with respect to a second metric ${\\tilde g}_{\\mu\\nu}$. The gravitational field and the scalar field are described by the action\n\n\\begin{equation}\n{\\cal S} = \\int d^4 x \\sqrt{-g}\\left( \\frac{M_{\\rm Pl}^2}{2} {\\cal R} - \\frac{1}{2}g^{\\mu\\nu} \\partial_\\mu \\phi \\partial_\\nu\\phi - V(\\phi) \\right) ~,\n\\end{equation}\nwhere ${\\cal R}$ is the Ricci--scalar and $V(\\phi)$ the potential energy of $\\phi$. The action for the matter fields consists of \n\\begin{equation}\n{\\cal S}_{\\rm SM} = \\int d^4 x \\sqrt{-g} {\\cal L}_{\\rm SM}(g,\\Psi_i)\n\\end{equation}\nfor the standard model fields $\\Psi_i$ and \n\\begin{equation} \\label{DMaction}\n{\\cal S}_{\\rm DM} = \\int d^4 x \\sqrt{-{\\tilde g}} {\\cal L}_{\\rm DM}({\\tilde g},\\sigma)\n\\end{equation}\nfor the DM field $\\sigma.$ \\footnote{We assume here for simplicity that there is only one dark matter species. This doesn't have to be the case and in \\cite{Brookfield:2007au,Baldi:2012kt} examples of more complicated setups have been studied.} In what follows, we are interested in processes well after Big Bang Nucleosynthesis (BBN) and assume that dark matter consists of non--relativistic particles. \nIn the simplest case, the relationship between the two metrics is via a conformal transformation ${\\tilde g}_{\\mu\\nu} = C(\\phi) g_{\\mu\\nu}$, where $C(\\phi)$ is a generic function of $\\phi$. As a consequence, \nDM particles do not propagate on geodesics with respect to the metric $g_{\\mu\\nu}$ but there is an additional force, mediated by $\\phi$ acting on DM particles. For long--ranged forces, which in case of \nthe light quintessence fields we are considering here are of order of the horizon size, the effective Newton's constant is given by ($G_N$ is Newton's constant)\n\\begin{equation}\\label{effgrav}\nG_{{\\rm eff}} = G_N\\left( 1 + 2\\beta^2 \\right)~,\n\\end{equation}\nwith \n\\begin{equation} \\label{coupling}\n\\beta \\equiv \\frac{M_{\\rm Pl}}{2} \\left(\\frac{{\\rm d} \\ln C}{{\\rm d} \\phi} \\right)\n\\end{equation}\nis the coupling. From the perspective of the action, the \nmasses of the DM particles become field dependent with $m(\\phi) = m_0 \\sqrt{C(\\phi)}$, where $m_0$ is a bare mass parameter setting the overall mass scale of the DM particles (see e.g. \\cite{Fujii:2003pa}). This exchange of dark energy (DE) \nand non--relativistic DM implies that the DM density does not scale like baryons (for which the energy density $\\rho_b$ scales like $a^{-3}$, where $a$ is the scale factor describing the expansion of space), but depending on \nthe details of the energy exchange decays either faster or slower than baryons. The density of DM particles is given by $\\rho_c = m(\\phi)\/a^3$, resulting in the energy conservation \\cite{Wetterich:1994bg} \n\\begin{equation}\n\\dot \\rho_c + 3 H \\rho_c = \\frac{1}{2} \\frac{\\rm d \\ln C}{\\rm d \\phi} \\dot\\phi \\rho_c = M_{\\rm Pl}^{-1} \\beta \\dot\\phi \\rho_c,\n\\end{equation}\nwhere $H = \\dot a\/a$ is the expansion rate and the dot denotes the derivative with respect to cosmic time. This equation can be also obtained directly from the action (\\ref{DMaction}), where the energy momentum tensor for dark matter is defined as \n\\begin{equation}\nT_{\\mu\\nu} = -\\frac{2}{\\sqrt{-g}} \\frac{\\delta {\\cal S}_{\\rm DM}}{\\delta g^{\\mu\\nu}}, \n\\end{equation}\nand DM is modelled as a non--relativistic fluid. The evolution of the scalar field is given by\n\n\\begin{equation}\n\\ddot \\phi + 3H\\dot\\phi + V_{,\\phi} = - M_{\\rm Pl}^{-1}\\beta \\rho_c.\n\\end{equation}\n\nThe modified energy conservation equation implies that, in general, the ratio of the density parameter of baryons and DM $\\Omega_b\/\\Omega_{\\rm DM} = \\rho_b\/\\rho_{\\rm DM}$ at last scattering is different as it would be expected in the $\\Lambda$CDM model. As a consequence, in these theories the  \npositions and relative heights of the peaks and valleys in the CMB anisotropy power spectrum have changed compared to the $\\Lambda$CDM \nmodel \\cite{Mifsud:2017fsy}. \n\nFor concreteness, in this paper we will focus on the case of an exponential potential for the scalar field with $V(\\phi) = V_0 \\exp (-\\lambda\\phi\/M_{\\rm Pl})$. A widely studied example for the coupling is the case of ($\\alpha$ is constant)\n\\begin{equation} \\label{coupledquintessence}\nC(\\phi) = \\exp(2\\alpha\\phi\/M_{\\rm Pl}),\n\\end{equation}\nin which the coupling (\\ref{coupling}) is given by $\\beta=\\alpha$ and is constant \\cite{Wetterich:1994bg,Amendola:1999er}. For this particular choice, the effective gravitational coupling between two DM particles is enhanced by a constant factor $1 + 2 \\alpha^2$. \n\nConstraints coming from supernovae data, baryonic acoustic oscillations and large scale structures put  \nupper bounds on the parameter $\\alpha$ and $\\lambda$, which are roughly $\\alpha \\lesssim 0.05$ and $\\lambda \\lesssim 1$ at 2$\\sigma$ \\cite{vandeBruck:2017idm}. That means that the additional \nforce has to be $5\\times 10^{-3}$ smaller than gravity in this model. Given that $\\alpha$ is constrained to be very small, this model looks rather unattractive. \n\n\\subsubsection{Dark energy and the least coupling principle}\n\nWhile the coupling function (\\ref{coupledquintessence}) is well motivated, we will consider an appealing modification, in which the coupling function $C(\\phi)$ possesses a minimum. Since according to the swampland conjectures the evolution of the scalar field is below the Planck mass (see eq. (\\ref{swampland2})), we expand $C(\\phi)$ around its minimum at $\\phi_*$:\n\\begin{equation} \\label{conformalgrowing}\nC(\\phi) \\approx 1 + \\frac{1}{2M_{\\rm Pl}^2}\\alpha (\\phi - \\phi_*)^2 + {\\cal O} (( \\phi - \\phi_* )^3).\n\\end{equation}\nIn this paper we choose, without the loss of generality, $\\phi_* = 1 M_{\\rm Pl}$. Furthermore, we will choose $\\alpha$ to be positive, so that $\\phi_*$ is the minimum of the coupling function and not the maximum. Most of our calculations below assume $\\phi_{\\rm ini} = \\phi_*$, but we will briefly discuss the effect of a displacement from $\\phi_*$ in the very early universe as well as discuss two processes in the very early universe which drive the field towards $\\phi_*$. The case for coupling functions with minima in string theory has been discussed in \\cite{Damour:1994zq,Damour:1994ya} and in \\cite{Brax:2010gi} in the context of dark energy physics. \n\nSince the density of DM does not scale like $a^{-3}$, we define an effective energy density for DE as $\\rho_{DE} = \\rho_\\phi + \\rho_c - \\rho_{c,0}a^{-3}$. We have therefore split the part of $\\rho_c$, which does not scale $a^{-3}$ and included it in the energy density for the DE sector. As a result, the effective equation of state for DE is now given by \\cite{Das:2005yj}\n\n\\begin{figure}{\n\\includegraphics[scale=0.16]{fig1_uf_eos.pdf}\n\\includegraphics[scale=0.16]{fig1_lf_geff.pdf}\n\\caption{Upper figure: Evolution of the equation of state of dark energy $w_{\\rm DE}$, defined in Eq. (\\ref{weff}), for models M1 ($\\alpha = 3, \\lambda = 0.5$) and M2 ($\\alpha = 5, \\lambda = 0.6$). Lower figure: The evolution of the effective gravitational constant, defined in Eq. (\\ref{effgrav}), in both models.}\n}\n\\end{figure}\n\n\n\\begin{equation} \\label{weff}\nw_{\\rm DE} = \\frac{p_\\phi}{\\rho_{\\rm DE}} = \\frac{p_\\phi}{\\rho_\\phi + \\rho_c - \\rho_{c,0}a^{-3}},\n\\end{equation}\nwhere $\\rho_\\phi$ and $p_\\phi$ are the energy density and pressure of the scalar field, respectively. From the definition, $w_{\\rm DE,0} = \\left(p_\\phi\/ \\rho_\\phi\\right)_0=w_{\\phi,0}$ today in all models. In the uncoupled case, this expression becomes the standard expression $w_{\\rm DE} = w_\\phi = p_\\phi\/ \\rho_\\phi$ for all times. \n\nTo study numerically the background evolution as well as the evolution of cosmological perturbations, we have used a modified version of the CLASS code \\cite{Blas:2011rf,vandeBruck:2017idm}. We refer to \\cite{Mifsud:2017fsy} and references therein, where all relevant equations for the cosmological perturbations can be found. In the following, we will consider two parameter choices. The first model (M1) has the parameters $\\alpha = 3$ and $\\lambda = 0.5$, whereas in the second model (M2), we choose $\\alpha = 5.0$ and $\\lambda = 0.6$. And to be concrete in the examples, we fix the other cosmological parameter as follows ($h$ is the Hubble parameter today in units of 100 km s$^{-1}$Mpc$^{-1}$): Hubble parameter today $H_0 = 67.32$ km s$^{-1}$Mpc$^{-1}$, density parameter of baryons $\\Omega_b h^2 = 0.022383$, density parameter of dark matter $\\Omega_c h^2 = 0.12011$, spectral index $n_s = 0.96605$, scalar amplitude $\\ln(10^{10} A_s) = 3.0448$, optical depth $\\tau = 0.0543$. The evolution of the effective equation of state $w_{\\rm DE}$ for the scalar field is shown in the upper plot in Figure 1. In both models, the evolution of the scalar field is such that the variation $\\Delta\\phi <1 M_{\\rm Pl}$. \n\n\\begin{figure}\n\\includegraphics[scale=0.16]{fig2_eos.pdf}\n\\caption{Predictions for the equation of state $w_{\\rm DE}$ for fixed value of ($\\lambda = 0.6$) but different values for $\\alpha$: \nA: $\\alpha = 5$, B: $\\alpha = 3$ and C: $\\alpha = 0$ (uncoupled).}\n\\end{figure}\n\n\nThe evolution of the effective gravitational constant in both models is shown in the lower plot in Figure 1. As it can be seen from this figure, once the potential energy of the scalar field becomes dynamically important, the field starts to evolve and the coupling between DM and DE increases. As a result, a long--range fifth force between DM appears at a redshift of about $z\\approx 2$. In both models, the gravitational coupling between DM particles today is considerably larger than $G_N$. \n\nNote that the same value of $\\lambda$ does lead to different predictions of the equation of state today if $\\alpha$ is varied (see Figure 2). This is because while the field wants to roll down the potential to larger values of $\\phi$, its motion is hindered by the presence of the coupling, which grows as $\\phi$ gets larger. Thus, unlike in the uncoupled counterpart, the model discussed here may allow for slightly larger values of $\\lambda$. This strongly suggests that the couplings to DM thus help to alleviate the tension of the model with the swampland conjecture (\\ref{swampland1}). In table I, we show the results for $\\omega_{\\rm eff,0}$, $\\sigma_8$ and $G_{\\rm eff,0}\/G_{N}$ for different choices of $\\alpha$ but fixed $\\lambda = 0.6$. As it can be seen, the effective equation of state moves indeed towards $\\omega = -1$, but for very large values of $\\alpha$, the value of $\\sigma_8$ becomes larger. We will in future work compare the theory to cosmological data, but it is clear that large violations of the equivalence principle in the dark sector today are not necessarily disallowed by current cosmological observations. \n\n\\begin{table}[t] \n   \\label{tab:example}\n   \\small\n   \\centering\n   \\begin{tabular}{c c c c}\n   \\hline\\hline\n   \\textbf{$\\alpha$} & \\textbf{$\\omega_{\\rm DE,0}$} & \\textbf{$\\sigma_{8}$} & \\textbf{$G_{\\rm eff,0}\/G_{N}$} \\\\ \n   \\hline  \n   0  & -0.947 & 0.805 & 1 \\\\\n   3  & -0.962 & 0.799 & 1.09\\\\\n   5  & -0.969 & 0.799 & 1.19\\\\\n   10  & -0.979 & 0.801 & 1.46\\\\\n   50 & -0.995 & 0.821 & 2.91\\\\\n   \\hline\\hline\n   \\end{tabular}\n   \\caption{Values of the effective equation of state today ($\\omega_{\\rm DE,0}$), $\\sigma_8$ and $G_{\\rm eff,0}\/G_{N}$ today for fixed values of $\\lambda= 0.6$ but different values of the coupling parameter $\\alpha$. As it can be seen, the effective equation of state today approaches the cosmological constant value $\\omega = -1$ for larger values of $\\alpha$. The value of $\\sigma_8$  is large for large values of $\\alpha$, implying a stronger clustering of matter.}\n  \n\\end{table}\n\nThe predictions for the CMB anisotropies spectrum are shown in Figure 3, in which we compare models M1 and M2 to the $\\Lambda$CDM model. As it can be seen, both models M1 and M2 deviate only slightly from $\\Lambda$CDM, despite the effective gravitational coupling today being considerably larger. We will constrain the model with cosmological data in future work. Furthermore, it would be interesting to consider changes to the form of the potential, e.g. considering a double exponential \\cite{Barreiro:1999zs} or changing the kinetic term of the scalar field (e.g. see \\cite{Teixeira:2019tfi}). \n\n\n\\begin{figure}\n\\includegraphics[scale=0.16]{fig3_cls.pdf}\n\\caption{The CMB anisotropy power spectrum for models M1 and M2, compared to the $\\Lambda$CDM model.}\n\\end{figure}\n\n\\begin{figure}\n\\includegraphics[scale=0.16]{fig4_uf_pk.pdf}\n\\includegraphics[scale=0.16]{fig4_lf_geff.pdf}\n\\caption{Upper plot: The predictions for the linear matter power spectrum for different initial conditions for the scalar field. For both curves, we have chosen $\\lambda = 0.5$ and $\\alpha = 3$. Lower plot: Evolution of the effective gravitational constant $G_{\\rm eff}$ for different initial conditions for the scalar field. The evolution of $G_{\\rm eff}$ is essentially the same in both models for redshifts below $z=200$, but differs substantially at higher redshifts.}\n\\end{figure}\n\n\nWe end this section by addressing the initial conditions for the DE field. The model seems fine--tuned, in the sense that we have chosen the value of $\\phi$ in the very early universe to be at the extremum of the coupling function $C(\\phi)$. If the field would not be at the minimum $\\phi_*$ in the very early universe, the effective gravitational constant would be larger than $G_N$ early on. In this case, we find that the matter power spectrum is enhanced for small and intermediate wavenumbers $k$, as shown in Fig 4, where we fix $\\lambda$ and $\\alpha$, but vary $\\phi_{\\rm ini}$. We also show the evolution of the effective gravitational constant. The field starts at a value $\\phi_{\\rm ini}$ away from the minimum. As soon as the matter density becomes important, the coupling affects the evolution of the field and drives it towards the minimum $\\phi_*$. Once it has settled at the minimum, the evolution is the same as in a model for which $\\phi_{\\rm ini} = \\phi_*$. The enhanced gravitational constant in the late radiation dominated epoch results in an enhancement of the power spectrum and therefore larger values for $\\sigma_8$. \n\n\\subsubsection{Attractor mechanism in the very early universe}\n\nThere are two processes which drive the field towards the minimum of the coupling function $C(\\phi)$ in the very early universe. One mechanism is provided by inflation and the other one at the time dark matter becomes non--relativistic. \n\nLet us first consider a set of inflaton fields $\\chi_i$, which roll down their potential energy $U(\\chi_i)$. If $\\phi$ is coupled to the fields $\\chi_i$ in the same way as it is coupled to DM, then the action of the theory is\n\\begin{eqnarray}\\label{inflaaction}\n{\\cal S} = \\int d^4 x \\sqrt{-g} \\left[ \\frac{M_{\\rm Pl}^2}{2} R - \\frac{1}{2} g^{\\mu\\nu}\\partial_\\mu \\phi \\partial_\\nu\\phi - V(\\phi)\\right] \\nonumber \\\\\n+ \\sum_i \\int d^4 x \\sqrt{-\\tilde g} \\left[ - \\frac{1}{2} \\tilde{g}^{\\mu\\nu}\\partial_\\mu \\chi_i \\partial_\\nu\\chi_i - U(\\chi_i)\\right].\n\\end{eqnarray}\nWriting the action fully in terms of the metric $g_{\\mu\\nu}$, we find that\n\\begin{eqnarray}\n&{\\cal S}& = \\int d^4 x \\sqrt{-g} \\left[ \\frac{M_{\\rm Pl}^2}{2} R - \\frac{1}{2} g^{\\mu\\nu}\\partial_\\mu \\phi \\partial_\\nu\\phi \\right. \\nonumber \\\\\n&-& \\left.  \\left( C(\\phi) \\sum_i \\left( \\frac{1}{2} g^{\\mu\\nu}\\partial_\\mu \\chi_i \\partial_\\nu\\chi_i  \\right) - C^2(\\phi) U(\\chi_i) \\right) \\right],\n\\end{eqnarray}\nwhere we have neglected the dark energy potential $V(\\phi)$ since it plays no role in the very early universe. Theories of this kind have been studied for one field $\\chi$ in e.g. \\cite{DiMarco:2002eb}. The equations of motion for the fields are given by\n\\begin{eqnarray}\n\\ddot \\phi + 3H\\dot\\phi + \\frac{\\partial \\tilde U}{\\partial \\phi} = \\beta C(\\phi) \\sum_i \\dot\\chi_i^2 &=& \\frac{1}{2}\\frac{dC}{d\\phi}\\sum_i \\dot\\chi_i^2, \\\\\n\\ddot \\chi_i + (3H + 2\\beta\\dot\\phi)\\dot\\chi_i + \\frac{1}{C(\\phi)}\\frac{\\partial \\tilde U}{\\partial \\chi_i}  &=& 0.\n\\end{eqnarray}\n\nWe want to show that field $\\phi$ is driven very quickly to the minimum of the coupling function during inflation and it is sufficient to show this for one field as the addition of additional scalar fields in the action above drive the field even faster to the minimum. In the case of one inflaton field $\\chi$, the equations of motion for $\\chi$ and $\\phi$ are \n\\begin{eqnarray}\n\\ddot \\phi + 3H\\dot\\phi + \\frac{\\partial \\tilde U}{\\partial \\phi} = \\beta C(\\phi)\\dot\\chi^2, \\label{inf1}\\\\\n\\ddot \\chi + (3H + 2\\beta\\dot\\phi)\\dot\\chi + \\frac{1}{C(\\phi)}\\frac{\\partial \\tilde U}{\\partial \\chi} = 0 \\label{inf2},\n\\end{eqnarray}\nwhere we have defined $\\tilde U(\\phi,\\chi) = C^2(\\phi)U(\\chi)$. Noting that $\\partial \\tilde U\/ \\partial \\phi = 2 C' C U(\\chi)= 4 \\beta \\tilde U\/M_{\\rm Pl}$, we can see from the equation of motion for $\\phi$, that it is driven by the derivative of the coupling function. If this function has a minimum, the field will be driven towards it and eventually settle at this point\\footnote{For the coupling function in question, we have $\\beta\\approx \\alpha (\\phi - \\phi_*)\/2M_{\\rm Pl}$.}. To be concrete, we consider a model with a plateau potential (see e.g. \\cite{Kehagias:2018uem}), which is a model consistent with the swampland conjectures. We choose \n\\begin{equation}\\label{infexample}\nU(\\chi) = \\frac{U_0}{2} \\tanh^2 \\frac{b\\chi}{2M_{\\rm Pl}}.\n\\end{equation}\nFor this potential we solve the equations of motion (\\ref{inf1}) and (\\ref{inf2}), to show that $\\phi$ settles very quickly in the minimum of the coupling function. The minimum of $C(\\phi)$ is again to be chosen at $\\phi_* = 1 $M$_{\\rm Pl}$ and we displace the field from the minimum by a maximal amount consistent with the swampland distance conjecture and set $\\phi_{\\rm ini} = 2$M$_{\\rm Pl}$. We choose $\\chi_{\\rm ini} = 0.95$M$_{\\rm Pl}$. The result for the evolution of the fields is shown in Figure 5 for the first 10 e--folds (in that figure we have chosen $\\alpha =5$). As it can be seen, the DE field $\\phi$ indeed settles within the first couple of e--folds to the value $\\phi_*$, as expected. After that, $\\phi$ is a spectator field during inflation and inflation is purely driven by the field $\\chi$. In the case of several inflaton fields, the same will happen: $\\phi$ will settle quickly at the minimum and inflation is driven by the fields $\\chi_i$. \n\nThe field $\\phi$ will move away from $\\phi_*$ as soon as the potential $V(\\phi)$ becomes dynamically important in the late universe at a redshift $z\\approx 1$. The scenario above requires that $\\phi$ is coupled to at least one inflaton field as in the action (\\ref{inflaaction}). But, as just seen, it is a rather efficient attractor mechanism. \n\n\\begin{figure}\n\\includegraphics[scale=0.67]{inflaton_evolution.pdf}\n\\caption{The evolution of the inflaton field $\\chi$ and the DE field $\\phi$ during the first 10 e--folds during inflation, for the potential $U(\\chi)$ given by eq. (\\ref{infexample}). In this example, we have chosen $b=10$ and $U_0 = 10^{-5}M_{\\rm Pl}^4$ for the parameter in the potential and $\\alpha = 5$ in the coupling function. Inflation lasts more than 50 e--folds. The field $\\phi$ is driven quickly to the minimum value $\\phi_*$, whereas $\\chi$ rolls down its potential.}\n\\end{figure}\n\nLet us turn to a second mechanism which drives the field towards the minimum after inflation. In the very early universe, DM is initially non--relativistic and becomes in many scenarios non--relativistic before BBN at temperatures above MeV. In the case of DM with a general equation of state ($p_{\\rm DM}$ is the pressure of the DM fluid) $w_c = p_{\\rm DM}\/\\rho_{\\rm DM}$, the equations governing the energy density and the scalar field become \n\\begin{equation}\n\\dot \\rho_c + 3 H \\rho_c(1 + w_c) = M_{\\rm Pl}^{-1} \\beta \\dot\\phi \\rho_c(1-3w_c),\n\\end{equation}\nand \n\\begin{equation}\\label{KG}\n\\ddot \\phi + 3H\\dot\\phi + V_{,\\phi} = - M_{\\rm Pl}^{-1}\\beta \\rho_c(1-3w_c),\n\\end{equation}\nsince the conformally coupled scalar field couples to the trace of the DM energy momentum tensor. Initially, DM is relativistic and the trace of the energy--momentum tensor (nearly) vanishes. Assuming that the potential energy does not play a role, the field is heavily damped by the Hubble expansion. At a temperature $T\\sim m_{\\rm DM}$ ($m_{\\rm DM}$ is the mass of the DM particle), DM becomes quickly non--relativistic (which happens well before BBN for heavy DM particles) and the right--hand-side (RHS) of the Klein--Gordon equation does no longer vanish if the field is not at the minimum $\\phi_*$. The field gets a 'kick' and is then driven by the term on the RHS towards the minimum value of the function $\\beta$ (and hence $C(\\phi)$). Such a mechanism has been studied in \\cite {Damour:1993id} for scalar--tensor theories and in \\cite{Brax:2004qh} for chameleon theories. In scalar-tensor theories usually all matter species are universally coupled to the scalar degree of freedom and the field gets a kick whenever a species becomes non--relativistic. In the present theory, the field gets a kick only once if there is only one species of DM. This attractor mechanism is therefore not as efficient as in a universally coupled scalar--tensor theory. To show that the kick will displace the field by at most $1 M_{\\rm Pl}$, following \\cite{Brax:2004qh} (Appendix 2) we can estimate the displacement by approximating the RHS of the Klein--Gordon equation (\\ref{KG}) by a delta--function source, i.e. \n\n\\begin{equation}\n\\ddot \\phi + 3H\\dot\\phi + V_{,\\phi} \\approx - \\beta \\frac{g_{\\rm DM}}{g_*} H M_{\\rm Pl} \\delta(t - t_0),\n\\end{equation}\nwhere $g_{\\rm DM}$ is the number of internal degrees of freedom, $g_*$ is the effective number of relativistic degrees of freedom and $t_0$ is the time of the kick at which $T\\sim m_{\\rm DM}$. Integrating this equation one finds the displacement \\cite{Brax:2004qh} \n\n\\begin{equation}\\label{kick}\n\\frac{\\Delta \\phi}{M_{\\rm Pl}} \\approx -\\frac{g_{\\rm DM}}{g_*} \\beta_{t_0},\n\\end{equation}\nwhere the coupling function $\\beta$ is evaluated at the time $t_0$. The expression for $\\beta$ is \n\n\\begin{equation}\n\\beta = \\frac{ \\frac{\\alpha}{2}\\frac{\\phi-\\phi_*}{M_{\\rm Pl}}}{1 + \\frac{\\alpha}{2}\\left( \\frac{\\phi-\\phi_*}{M_{\\rm Pl}} \\right)^2 }~.\n\\end{equation}\n\nFor the extreme case that $\\phi$ is displaced from the minimum by one Planck unit ($\\phi - \\phi_* = 1 M_{\\rm Pl}$) at the time of the kick, we find that $|\\beta| \\leq 1$ for all values of $\\alpha$. For a heavy DM particle with $m_{\\rm DM} \\approx 10^2~$GeV, we have $g_{\\rm DM}\/g_* \\approx 10^{-2}$. For a somewhat lighter DM particle, $g_*$ might be somewhat smaller than 100 at the time when the particle becomes non--relativistic and the ratio $g_{\\rm DM}\/g_*$ may be pushed to be of order 0.1, but it is still well below one. Thus, the field is displaced by the kick by an amount much smaller than the Planck mass. If there were several DM species, the field gets a kick whenever a DM species becomes non--relativistic. The total displacement can be estimated from (\\ref{kick}) by summing up individual contributions. \n\nTo conclude, both during inflation and at the time when DM becomes non-relativistic the field is naturally driven towards the minimum of the coupling function $C(\\phi)$. This attractor mechanism is a rather attractive feature of the model just discussed. \n\n\n\\section{Derivative couplings}\nAmong the extensions of the theories discussed above are theories in which derivative couplings between DM and DE are allowed. A well motivated example of such a theory is in which the conformal transformation discussed above is extended to include a disformal term. That is, instead of a purely conformal relation between the metric $g$ and ${\\tilde g}$, we allow for a disformal relation of the form (the comma represents the derivative with respect to the coordinates) \n\\begin{equation}\n{\\tilde g}_{\\mu\\nu} = C(\\phi) g_{\\mu\\nu} + D(\\phi)\\phi_{,\\mu}\\phi_{,\\nu},\n\\end{equation}\nwhere the term containing the function $D(\\phi)$ is the disformal term. Such theories appear naturally in theories with branes, in which the disformal term originates from the induced metric on the brane containing \nthe DM particles. In general, the disformal coupling $D(\\phi)$ introduces a new mass scale into this theory. A specific, string-inspired set-up has been studied in \\cite{Koivisto:2013fta}, in which the \nfunctions $C$ and $D$ are of power-law form, dictated by the geometry of the higher-dimensional space. In \\cite{Zumalacarregui:2012us,vandeBruck:2015ida,vandeBruck:2016hpz,Mifsud:2017fsy,vandeBruck:2017idm}, the exponential form $D(\\phi) = M^{-4} \\exp(2\\gamma \\phi)$ has been studied in detail. \n\nAssuming a canonical kinetic term for the DE field, the effective coupling is now specified by the function \n\\begin{equation}\nQ=\\frac{C_{,\\phi}}{2C}T_{\\rm DM}+\\frac{D_{,\\phi}}{2C}T_{\\rm DM}^{\\mu\\nu}\\nabla_\\mu\\phi\\nabla_\\nu\\phi-\\nabla_\\mu\\left[\\frac{D}{C}T^{\\mu\\nu}_{\\rm DM}\\nabla_\\nu\\phi\\right],\n\\end{equation}\nwhere $T^{\\mu\\nu}_{\\rm DM}$ is the DM energy tensor and $T_{\\rm DM}$ its trace. In cosmology, $Q$ can be written as \n\\begin{equation}\n\\beta= -\\frac{Q}{\\rho_c} = M_{\\rm Pl} \\frac{C_{,\\phi} + D_{,\\phi}{\\dot\\phi}^2 - 2D\\left(\\frac{C_{,\\phi}}{C}{\\dot\\phi}^2 + V_{,\\phi} + 3H\\dot\\phi\\right)}{2\\left[C + D\\left(\\rho_c - {\\dot\\phi}^2\\right)\\right]} \n\\end{equation}\nfor a pressureless fluid. For the exponential potential and exponential couplings, it was shown in \\cite{vandeBruck:2015ida} that the coupling is very small in the early universe and until late in the matter dominated epoch, due to the suppression by the \ndenominator. At a redshift $z\\approx 3$, the coupling grows and DM particles begin to feel the force mediated by $\\phi$. In Figure 6 we show the evolution of the effective gravitational constant in a purely disformal model, in which $C(\\phi)=1$ and $D = 1\/M^4$ and an exponential potential. The choices shown are $M=2.5$ meV and $\\lambda = 0.5$ for model D1 and $M = 4$ meV and $\\lambda = 0.7$ for model D2. The choice of $\\lambda$ and the mass scale $M$ affect the behaviour of the effective gravitational constant substantially but both models are in the 2$\\sigma$ region of allowed parameter space \\cite{vandeBruck:2017idm}. We emphasize again that a growing effective gravitational constant is a prediction of these models, providing another motivation to search for equivalence principle violations in the dark sector. \n\n\\begin{figure}\n\\includegraphics[scale=0.7]{gravconst_disformal.pdf}\n\\caption{The evolution of the effective gravitational constant for the purely disformal models D1 ($M=2.5$ meV and $\\lambda = 0.5$) and D2 ($M = 4$ meV and $\\lambda = 0.7$.) }\n\\end{figure}\n\n\\section{Conclusions}\nIf the swampland conjectures survive further theoretical scrutiny, they will have considerable impact on modelling of dark energy and inflation within string theory. Current observations of the universe are in excellent agreement with the $\\Lambda$CDM model. In particular, the equation of state of DE inferred from observations is in very good agreement with the cosmological constant. \n\nIn this paper we have discussed the question of DM-DE couplings in the context of the swampland conjectures. In the well--studied case of the coupling specified by (\\ref{coupledquintessence}), the fifth force, which acts continuously throughout the history of the universe in this model, has to be much smaller than the gravitational force. We have argued and shown that another class of models is worth investigating, in which the fifth force between dark matter particles appears at redshifts when dark energy becomes dynamically important. We have discussed two models: one with purely conformal coupling and one which allows for disformal couplings. For the conformal coupling, we have studied the case of a coupling function which possesses a minimum. We have argued that the field is driven towards the minimum in the very early universe. In the very early universe, the DE field becomes essentially uncoupled from DM and is stuck at a fixed field value. This provides an explanation for the initial condition of the quintessence field. Deep inside the matter area, the potential energy drives the scalar field away from the minimum. Since the coupling no longer vanishes, a long--range fifth force between DM particles appears. Importantly, we have shown that since the motion of the quintessence field is slowed down by the matter coupling, larger values of $\\lambda$ for the exponential potential are potentially allowed by observations. On the other hand, the enhanced gravitational constant leads to larger predicted values for $\\sigma_8$ \\cite{Mifsud:2017fsy,vandeBruck:2017idm}. We will study the predictions and the constraints on the parameter of the theory in detail in future work. Finally, we have pointed out that time--varying couplings between DE and DM appears naturally in theories with derivative couplings, such as in disformally coupled models. In these modes the effective coupling is a function of the DM density as well as on the time--derivative of the scalar field. \n\nFor both types of theories, the inferred DE equation of state can mimic that of a tachyon field with $w\\lesssim -1$ at intermediate redshift, but the theory predicts that, today, $w\\geq-1$. It is therefore important to measure the DE equation of state for redshifts $0\\leq z \\leq 2$ to high accuracy. Since the effective gravitational coupling between two DM particles can today be substantially bigger than gravity alone, our work motivates searches for equivalence principle violations in the dark sector at various redshifts and in the non--linear regime \\cite{Baldi:2008ay}. One test has been suggested in \\cite{Kesden:2006vz}, using satellite galaxies which are tidally disrupted by the Milky Way. It would be worth investigating this test in the context of the theories discussed here. \n\n\\noindent {\\bf Acknowledgements} We are grateful to Jurgen Mifsud for providing us with the modified CLASS code \\cite{Blas:2011rf} and to Sebastian Trojanowski for useful discussions. CvdB is supported (in part) by the Lancaster-Manchester-Sheffield Consortium for Fundamental Physics under STFC grant: ST\/L000520\/1. CCT is supported by a studentship from the School of Mathematics and Statistics at the University of Sheffield.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nHigh resolution, high contrast imaging at optical and sub-millimeter wavelengths\nhas in recent years revealed that protoplanetary disks are highly structured.\nWhile some disks show complex non-axisymmetric structures, there are also\nnumerous disks that display multiple nearly perfect concentric ringlike\nstructures. The first and most prominent example was the disk around the star HL\nTau \\citep{2015ApJ...808L...3A}. Many other examples have since followed such as\nTW Hydra \\citep{2016ApJ...820L..40A,2017ApJ...837..132V}, RX J1615.3\n\\citep{2016A&A...595A.114D}, HD 97048 \\citep{2016A&A...595A.112G}, HD 163296\n\\citep{2016PhRvL.117y1101I} and HD 169142 \\citep{2015PASJ...67...83M,\n  2017A&A...600A..72F}. The rings are seen at submillimeter wavelength thermal\ndust emission as well as in optical\/near-infrared scattered light. These rings\nand gaps have been interpreted as resulting from newly formed planets opening up\ngaps within the disk \\citep[e.g.][]{2015MNRAS.454L..36G, 2015ApJ...806L..15K,\n  2015A&A...584A.110P}. This is an attractive scenario, because it would mean\nthat we are indirectly `seeing' the young planets as they are being formed in\ntheir birth-disk. However, since we do not yet have direct indications of these\nplanets, it is important to also investigate other explanations. Could these\nrings be caused by something entirely different altogether? And could this\n`something', though unrelated to already existing planets, still teach us\nsomething about the formation of planets?\n\nVarious non-planet-related explanations for these rings have been proposed.  In\nfact, their existence was predicted before their discovery, through a simple\nargument: It is known that dust aggregates of millimeter size and larger tend to\nradially drift toward the star on a very short time scale\n\\citep{1972fpp..conf..211W, 2007A&A...469.1169B}. If the disk lives a few\nmillions years, and the dust aggregates grow to the millimeter sizes inferred\nfrom millimeter-wave observations \\citep[e.g.][]{2016A&A...588A..53T}, then\nthese disks should by the time they are observed already have lost most of their\ndust particles. By contrast, we see large quantities of dust in these disks, so\nsomething must be holding up the dust, preventing it from taking part in the\nrapid radial drift mechanism. It was suggested by \\citet{2012A&A...538A.114P}\nthat perhaps a multitude of local ring-shaped gas pressure bumps in the disk\ncould trap the dust after it has grown to sizes of about a millimeter. The\nphysical mechanism behind this dust trapping is the well-known, and unavoidable\neffect, that dust particles tend to drift toward regions of increased gas\npressure \\citep[e.g.][]{1972fpp..conf..211W, 1976PThPh..56.1756A}. Or in other\nwords, that they drift in the direction of the gas pressure gradient $\\vec\\nabla\nP$. In smooth protoplanetary disks the gas pressure decreases with radius\n($\\partial_r P<0$), which is the reason for the inward drift of dust. But if the\ngas pressure has wiggles that are strong enough that they cause $\\partial_r P$\nto flip sign, then there will exist local pressure maxima for which $\\partial_r P=0$,\nand for which the dust drift is converging. In the absense of gas turbulence,\nall dust grains sufficiently close by would get trapped in these\ntraps. Turbulence can mix the small dust grains (that are most strongly coupled\nto the gas) out of the traps, so that they may, on average, continue to drift\ninward. The bigger dust particles, which are less coupled to the gas, may still\nremain trapped. It depends on the amplitude of the pressure bumps and the\nstrength of the turbulence, which grain sizes remain trapped and which not.\n\nWhile the origin of these gas pressure bumps was not addressed in\n\\citet{2012A&A...538A.114P}, it was shown that if they exist, and if they\nare strong enough, the radial drift paradoxon could be solved. As a direct\nconsequence, however, it was shown that high-resolution ALMA observations should\nthen be able to see these dust rings, and the predicted ALMA images bear\nstriking resemblance to HL Tau and similar sources.\n\nThis scenario does not, however, explain why these gas pressure bumps form\nin the first place. \\cite{2014ApJ...794...55T, 2016AJ....152..184T} propose an\nelegant scenario in which dust rings are formed through a secular gravitational\ninstability \\citep{2000orem.book...75W}. The idea is that if the dust density is\nhigh enough for a dust-driven gravitational instability to occur, the gas drag\nwill slow this process down. The slowness of this process allows the information\nabout the gravitational contraction to shear out and spread along azimuth, so\nthat grand-design rings are formed instead of gravitationally contracting\nclumps.  \\citet{2016AJ....152..184T} argue that as these rings contract further,\nthis eventually leads to planets being formed, which, in their turn, open up\ngaps in the dust distribution \\citep{2004A&A...425L...9P}. They suggest that the\nring-like structures could therefore be witnesses of both the initial and the\nfinal stages of planet formation.\n\nA completely different scenario was proposed by \\citet{2015ApJ...806L...7Z}, who\nargue that the locations of the rings suggest their association with the snow\nlines of a series of different volatile molecular species. A physical mechanism\nby which snow lines could lead to rings was worked out by\n\\citet{2016ApJ...821...82O}. The physics of ice sublimation and deposition near\nthese snow lines is complex, because it interacts strongly with the coagulation\nand fragmentation of dust aggregates, as well as with the radial drift and\nturbulent mixing in the disk \\citep[e.g.][]{2017A&A...600A.140S}.\n\n\\citet{2017MNRAS.467.1984G} propose an alternative scenario of spontaneous ring\nformation. In their model the radial drift of dust particles coupled to the dust\ncoagulation process tends to lead to ring-like regions of high dust\nconcentration and fast growth \\citep[see also][]{2016A&A...594A.105D}.  While\nthis might explain transition disks with a single dust ring, it may be more\ndifficult to explain the multi-ring structures discussed here.\n\nGlobal magnetohydrodynamical disk simulations with dead-zones also tend to\ncreate rings-shaped structures \\citep{2015A&A...574A..68F}, and zonal flows\n\\citep{2009ApJ...697.1269J}.\n\nIn this paper we investigate whether the viscous disk evolution could lead to\nthe spontaneous formation of rings. This idea is not new. For instance,\n\\citet{2005MNRAS.362..361W} show, using 2-D radiation-hydrodynamics models, that\na disk with an active surface layer, self-gravity and `dead' midplane region\ncould become viscously unstable and lead to the formation of several concentric\nrings. Our proposal is, however, based on a different physical driving\nmechanism. A version of this mechanism was already studied in a local box model\nby \\citet{2011IAUS..274...50J}.\n\nThe ring instability works as follows. If we perturb an otherwise\nsmooth disk with an infinitesimal-amplitude wiggle in the gas pressure (of the\nconcentric ring type), it will tend to cause a slight enhancement of the\ndust-to-gas ratio in these pressure enhancements. This is the same physical\nmechanism as for dust trapping, but we do not necessarily need a flip of sign of\n$\\partial_r P$ to cause this effect. It is just that the radial inward drift\nvelocity $|v_{\\mathrm{drift}}|$ of the dust is slightly increased on the outer\nside of the pressure enhancement and slightly reduced on the inner side, leading\nto a traffic-jam density enhancement effect. This effect works for big and small\ngrains alike. It is known that dust has a negative influence on the disk\nviscosity, if it is caused by the magnetorotational instability\n\\citep[e.g.][]{2000ApJ...543..486S, 2006A&A...445..205I, 2009ApJ...698.1122O,\n  2013ApJ...765..114D}. A viscous disk reacts to the resulting wiggle in\nthe viscosity $\\nu(r)$ by adapting the surface density $\\Sigma_g(r)$ such that\nthe steady-state\n\\begin{equation}\n\\Sigma_g(r)\\,\\nu(r) = \\mathrm{const}\\,,\n\\end{equation}\nis restored. So, whereever $\\nu$ is reduced, $\\Sigma_g$ is increased. This change \nin $\\Sigma_g(r)$ amplifies the initial perturbation, resulting in a positive feedback\nloop. We therefore expect an initial perturbation in the gas disk to be amplified\nby the combined effect of dust drift and the effect the dust has on the viscosity\nof the disk. This process is depicted in cartoon form in Fig.~\\ref{fig-cartoon}.\n\n\\begin{figure*}\n  \\centerline{\\includegraphics[width=0.94\\textwidth]{cartoon.png}}\n  \\caption{\\label{fig-cartoon}Mechanism of the ring\n    instability studied in this paper.}\n\\end{figure*}\n\nTo test whether this mechanism indeed works requires a linear perturbation\nanalysis. This is what we present in this paper.\n\nIn Section \\ref{sec-basic-equations} we give the basic equations that stand\nat the basis of our model. These are the standard viscous disk equations\ncoupled to a single dust component of a given Stokes number.\n\nThe linear perturbation analysis of the combined gas and dust system is rather\ncumbersome. So in Section \\ref{sec-pert-analy-simple} we first simplify the\nsystem of equations radically, so that the mechanism presents itself more\nclearly. In Section \\ref{sec-pert-analy-full} we then tackle the full\nset of equations, with some mathematics moved to the appendix. \n\n\n\n\\section{Basic disk equations and model assumptions}\n\\label{sec-basic-equations}\nThe standard viscous disk equations for the gas together with a single dust\ncomponent are:\n\\begin{eqnarray}\n\\frac{\\partial \\Sigma_{g}}{\\partial t} +\n  \\frac{1}{r}\\frac{\\partial}{\\partial r}\n  \\left(r\\Sigma_g v_{rg}\\right) &=& 0\\label{eq-gas-continuity}\\\\\n\\frac{\\partial \\Sigma_{d}}{\\partial t} +\n  \\frac{1}{r}\\frac{\\partial}{\\partial r}\n  \\left(r\\Sigma_d v_{rd}\\right) &=&\n  \\frac{1}{r}\\frac{\\partial}{\\partial r}\n  \\left(r{\\cal D}_d\\Sigma_g\\frac{\\partial}{\\partial r}\n  \\left(\\frac{\\Sigma_d}{\\Sigma_g}\\right)\\right)\\,.\\label{eq-dust-continuity}\n\\end{eqnarray}\nThe gas radial velocity is given by the usual viscous disk equation:\n\\begin{equation}\\label{eq-vr-gas}\n  v_{rg} = - \\frac{3}{\\Sigma_g\\sqrt{r}}\\frac{\\partial}{\\partial r}\n  \\left(\\Sigma_g\\nu\\sqrt{r}\\right)\\,,\n\\end{equation}\nwith the turbulent viscosity defined by\n\\begin{equation}\\label{eq-def-nu}\n\\nu = \\alpha \\frac{c_s^2}{\\Omega_K}\\,,\n\\end{equation}\nwhere $\\alpha$ is the usual alpha-turbulence parameter. The Kepler frequency is\n\\begin{equation}\\label{eq-omega-kepler}\n\\Omega_K=\\sqrt{\\frac{GM_{*}}{r^3}}\\,,\n\\end{equation}\nwith $G$ the gravitational constant and $M_*$ the stellar mass.  The isothermal\nsound speed squared is\n\\begin{equation}\\label{eq-cs2-in-temp}\nc_s^2 = \\frac{k_BT}{\\mu m_p}\\,,\n\\end{equation}\nwith $k_B$ the Boltzmann constant, $\\mu=2.3$ the mean molecular weight,\nand $m_p$ the proton mass. The vertical pressure scale height of the disk is\n\\begin{equation}\\label{eq-disk-hp}\nH_p = \\frac{c_s}{\\Omega_K}\\,.\n\\end{equation}\nThe dust diffusion constant is\n\\begin{equation}\\label{eq-cald-in-nu}\n  {\\cal D}_d = \\frac{1}{1+\\mathrm{St}^2}{\\cal D}_g =\n  \\frac{1}{1+\\mathrm{St}^2}\\frac{\\nu}{\\mathrm{Sc}}\\,,\n\\end{equation}\nwhere $\\mathrm{St}$ is the Stokes number of the dust and $\\mathrm{Sc}$ is the\nSchmidt number of the gas. The radial velocity of the dust is\n\\begin{equation}\\label{eq-vdust-1}\n  v_{rd} = \\frac{1}{1+\\mathrm{St}^2} v_{rg}\n  + \\frac{1}{\\mathrm{St}+\\mathrm{St}^{-1}}\\frac{1}{\\rho_g\\Omega_K}\n  \\frac{\\partial P_g}{\\partial r}\\,,\n\\end{equation}\nwhere $\\rho_g$ is the midplane gas density and $P_g\\equiv \\rho_g c_s^2$ is the\nmidplane gas pressure.\n\nThe $\\alpha$ determines the strength of the turbulence, and hence the strength\nof the viscosity and the dust diffusivity. In our analysis we allow the dust\nsurface density to affect the value of $\\alpha$: a higher dust concentration\nwill lead to a lower $\\alpha$ \\citep[e.g.][]{2000ApJ...543..486S, 2006A&A...445..205I, 2009ApJ...698.1122O,\n  2013ApJ...765..114D}. Since the \\revised{physics of magnetorotational\n  turbulence in non-ideal MHD is not yet fully understood},\nwe parameterize this effect. We consider the following\ngeneral prescription:\n\\begin{equation}\\label{eq-alpha-param}\n  \\alpha = \\alpha_1\\left(\\frac{\\Sigma_d}{\\Sigma_{d1}}\\right)^{\\phi_d}\n  \\left(\\frac{\\Sigma_g}{\\Sigma_{g1}}\\right)^{\\phi_g}\\,,\n\\end{equation}\nwhere $\\alpha_1$ is the unperturbed value of $\\alpha$, and likewise\n$\\Sigma_{d1}$ and $\\Sigma_{g1}$ are the unperturbed values of $\\Sigma_d$ and\n$\\Sigma_g$ respectively.  The parameters $\\phi_d$ and $\\phi_g$ are powerlaw\nindices that parameterize how $\\alpha$ depends on the change in dust and\/or gas\nsurface density. We focus on cases with $\\phi_d<0$, meaning that an increase\nin $\\Sigma_d\/\\Sigma_{d1}$ leads to a {\\em de}crease in $\\alpha$. The $\\phi_g$\nis used to allow for the following two cases of interest:\n\\begin{eqnarray}\n\\phi_g =& 0 & \\qquad \\hbox{(Case 1: $\\alpha$ depends on $\\Sigma_d$)} \\label{eq-case-1}\\\\\n\\phi_g =& -\\phi_d & \\qquad \\hbox{(Case 2: $\\alpha$ depends on $\\Sigma_d\/\\Sigma_g$)} \\label{eq-case-2}\n\\end{eqnarray}\nCase 1 could, at least in principle, allow for the expected instability even\nwithout dust drift relative to the gas, since without dust drift, $\\Sigma_d$\nwill necessarily increase if $\\Sigma_g$ does. In contrast, case 2 strictly\nrequires dust drift for the instability to operate, since lack of dust drift\nkeeps $\\Sigma_d\/\\Sigma_g$ constant.\n\n\n\n\\section{Simplified perturbation analysis}\n\\label{sec-pert-analy-simple}\nIt is cumbersome to perform the linear stability analysis for the full set of\nequations of Section \\ref{sec-basic-equations}, because these equations contain\nfactors $\\sqrt{r}$ and the like. We postpone this full analysis to Section\n\\ref{sec-pert-analy-full}. For now, let us first simplify the equations.\n\n\\subsection{Simplified equations}\nWe simplify the equations to the following form:\n\\begin{eqnarray}\n\\frac{\\partial \\Sigma_{g}}{\\partial t} +\n\\frac{1}{r_0}\\frac{\\partial}{\\partial x}\n  \\left(\\Sigma_g v_{xg}\\right) &=& 0\\,,\\label{eq-simpl-gas-continuity}\\\\\n\\frac{\\partial \\Sigma_{d}}{\\partial t} +\n\\frac{1}{r_0}\\frac{\\partial}{\\partial x}\n  \\left(\\Sigma_d v_{xd}\\right) &=&\n  \\frac{1}{r_0^2}\n  \\frac{\\partial}{\\partial x}\n  \\left({\\cal D}_d\\Sigma_g\\frac{\\partial}{\\partial x}\n  \\left(\\frac{\\Sigma_d}{\\Sigma_g}\\right)\\right)\\,,\\label{eq-simpl-dust-continuity}\n\\end{eqnarray}\nwhere $r_0$ is the radius at which we wish to locally carry out the perturbation\nanalysis, and $x$ is the dimensionless radial coordinate starting from that\nlocation:\n\\begin{equation}\nr = r_0 (1+x)\\,.\n\\end{equation}\nThe gas radial velocity formula (Eq.~\\ref{eq-vr-gas}) is simplified as:\n\\begin{equation}\\label{eq-simpl-vr-gas}\n  v_{xg} = - \\frac{3}{\\Sigma_gr_0}\\frac{\\partial(\\Sigma_g\\nu)}{\\partial x}\\,,\n\\end{equation}\nwith the viscosity still defined by Eq.~(\\ref{eq-def-nu}). However, for\nsimplicity $c_s$ and $\\Omega_K$ are now assumed be be constant. On the\nother hand, $\\alpha$ is allowed to depend on $x$, but only due to the\nperturbation. The radial velocity of the dust is given, in our simplified\ndescription, by\n\\begin{equation}\\label{eq-simpl-vdust-1}\n  v_{xd} = \\frac{1}{1+\\mathrm{St}^2} v_{xg}\n  + \\frac{1}{\\mathrm{St}+\\mathrm{St}^{-1}}\\frac{c_s^2}{\\Omega_Kr_0}\n  \\frac{\\partial\\ln \\Sigma_g}{\\partial x}\\,.\n\\end{equation}\nThe stationary solution is $\\Sigma_g=$constant, $\\Sigma_d=$constant and\n$\\alpha=$constant. This also yields $v_{xd}=v_{xg}=0$ for that stationary\nsolution. This stationary solution is the backdrop of our perturbation\nanalysis. \n\nNow we introduce an infinitesimal perturbation:\n\\begin{eqnarray}\n\\Sigma_g(x,t) &=& \\Sigma_{g1} (1+\\sigma_g(x,t))\\,,\\label{eq-simpl-sigma-g-pert}\\\\\n\\Sigma_d(x,t) &=& \\Sigma_{d1} (1+\\sigma_d(x,t))\\,,\\label{eq-simpl-sigma-d-pert}\n\\end{eqnarray}\nwhere $\\Sigma_{g1}$ and $\\Sigma_{d1}$ are the stationary (constant) solutions\nfor gas and dust, respectively. From here on the subscript $1$ denotes this\nstationary solution. We will also omit the $(x,t)$ notation, to not clutter the\nequations too much. The symbols $\\sigma_g$ and $\\sigma_d$ are the dimensionless\ninfinitesimal perturbations on the gas and the dust respectively. For the\n$\\alpha$, according to Eq.~(\\ref{eq-alpha-param}), we \nobtain, to leading order:\n\\begin{equation}\\label{eq-alpha-prescr}\n\\alpha = \\alpha_1 \\big(1+\\phi_d\\sigma_d+\\phi_g\\sigma_g\\big)\\,,\n\\end{equation}\non account of the fact that $|\\sigma_{d\/g}|\\ll 1$.\n\nInserting these formulae into Eqs.~(\\ref{eq-simpl-gas-continuity},\n\\ref{eq-simpl-dust-continuity}), and keeping in mind that both $v_{xg}$ and\n$v_{xd}$ are linear in the perturbations, and that we omit all terms\nof higher order in $\\sigma_{g\/d}$, we arrive, to leading order, at:\n\\begin{eqnarray}\n\\frac{\\partial \\sigma_{g}}{\\partial t} +\n  \\frac{1}{r_0}\\frac{\\partial v_{xg}}{\\partial x}\n   &=& 0\\,,\\label{eq-simpl-gas-continuity-1}\\\\\n\\frac{\\partial \\sigma_{d}}{\\partial t} +\n  \\frac{1}{r_0}\\frac{\\partial v_{xd}}{\\partial x}\n  &=&\n  \\frac{1}{r_0^2}{\\cal D}_d\n  \\frac{\\partial^2(\\sigma_d-\\sigma_g)}{\\partial x^2}\\,.\n  \\label{eq-simpl-dust-continuity-1}\n\\end{eqnarray}\nBy inserting Eqs.~(\\ref{eq-def-nu}, \\ref{eq-simpl-sigma-g-pert}) together with\nEq.~(\\ref{eq-alpha-prescr}) into Eq.~(\\ref{eq-simpl-vr-gas}), and assuming\nthat $c_s$ and $\\Omega_K$ are constant (see above), the radial velocity for the\ngas becomes\n\\begin{equation}\n  v_{xg} = - 3\\frac{\\nu_1}{r_0}\\left(\\frac{\\partial\\sigma_g}{\\partial x}\n  +\\frac{\\partial(\\phi_d\\sigma_d+\\phi_g\\sigma_g)}{\\partial x}\\right)\\,.\n\\end{equation}\nSimilarly that of the dust becomes\n\\begin{equation}\n\\begin{split}\n  v_{xd} =&\n  \\frac{1}{1+\\mathrm{St}^2}\\frac{\\nu_1}{r_0}\\bigg\\{\n  - 3\\left(\\frac{\\partial\\sigma_g}{\\partial x}\n  +\\frac{\\partial(\\phi_d\\sigma_d+\\phi_g\\sigma_g)}{\\partial x}\\right)\\\\\n&  \\qquad\\qquad\\quad\n  +\\frac{\\mathrm{St}}{\\alpha_1}\n  \\frac{\\partial\\sigma_g}{\\partial x}\\bigg\\}\\,.\\\\\n\\end{split}\n\\end{equation}\nInserting these into the continuity equations\n(Eqs.~\\ref{eq-simpl-gas-continuity-1},\n  \\ref{eq-simpl-dust-continuity-1}) yields\n\\begin{eqnarray}\n  \\frac{\\partial\\sigma_g}{\\partial t}\n  &=& 3\\frac{\\nu_1}{r_0^2}\\left(\\frac{\\partial^2\\sigma_g}{\\partial x^2}\n  +\\frac{\\partial^2(\\phi_d\\sigma_d+\\phi_g\\sigma_g)}{\\partial x^2}\\right)\\,,\\\\\n  \\frac{\\partial\\sigma_d}{\\partial t} &=&\n  \\frac{1}{1+\\mathrm{St}^2}\\frac{\\nu_1}{r_0^2}\\bigg\\{\n  3\\left(\\frac{\\partial^2\\sigma_g}{\\partial x^2}\n  +\\frac{\\partial^2(\\phi_d\\sigma_d+\\phi_g\\sigma_g)}{\\partial x^2}\\right)\n   \\nonumber\\\\\n & &  \\qquad\\qquad\\quad -\\frac{\\mathrm{St}}{\\alpha_1}\n  \\frac{\\partial^2\\sigma_g}{\\partial x^2}\\bigg\\}\n  + \\frac{1}{r_0^2}{\\cal D}_{d1}\n  \\frac{\\partial^2(\\sigma_d-\\sigma_g)}{\\partial x^2} \\,.\n\\end{eqnarray}\nNow let us assume the linear perturbations to be plane waves in space $x$ and\ntime $t$. Since we seek modes for which the dust and the gas perturbations\ngrowth due to their mutual coupling, we can assume a single spatial frequency\n$k$ and time frequency $\\omega$ for both modes:\n\\begin{eqnarray}\n\\sigma_g &=& A e^{i\\omega t-ikx}\\,,\\\\\n\\sigma_d &=& B e^{i\\omega t-ikx}\\,.\n\\end{eqnarray}\nThe complex amplitudes $A$ (for the gas) and $B$ (for the dust) can be\nset independently. Inserting this mode into the above set of equations yields:\n\\begin{eqnarray}\n  i\\omega A\n  &=& -3k^2 \\frac{\\nu_1}{r_0^2}\\left(A\n  +\\phi_d B+\\phi_gA\\right)\\,,\\\\\n  i\\omega B &=&\n  \\frac{-k^2}{1+\\mathrm{St}^2}\\frac{\\nu_1}{r_0^2}\\bigg\\{\n  3\\left(A\n  +\\phi_dB+\\phi_gA\\right)\n  -\\frac{\\mathrm{St}}{\\alpha_1}A\n   \\nonumber\\\\\n & & \\qquad\\qquad\\qquad +\\frac{1}{\\mathrm{Sc}}\n  (B-A)\\bigg\\}\\,,\n\\end{eqnarray}\n\\revised{where we made use of Eq.~(\\ref{eq-cald-in-nu}) to replace ${\\cal D}_{d1}$.}\nThis can be put into matrix form:\n\\begin{equation}\ni\\omega \\left(\\begin{matrix}\n  A\\\\\n  B\n\\end{matrix}\\right)\n=\\left(\\begin{matrix}\n  M_{aa} & M_{ab}\\\\\n  M_{ba} & M_{bb}\n\\end{matrix}\\right)\n\\left(\\begin{matrix}\n  A\\\\\n  B\n\\end{matrix}\\right)\\,,\n\\end{equation}\nwith\n\\begin{eqnarray}\n  M_{aa} &=& -3k^2\\frac{\\nu_1}{r_0^2}(1+\\phi_g)\\,, \\\\\n  M_{ab} &=& -3k^2\\frac{\\nu_1}{r_0^2}\\phi_d\\,, \\\\\n  M_{ba} &=& -3k^2\\frac{\\nu_1}{r_0^2}\n  \\frac{1}{1+\\mathrm{St}^2}\\left((1+\\phi_g)-\\frac{\\mathrm{St}}{3\\alpha_1}-\\frac{1}{3\\mathrm{Sc}}\\right)\\,,\\\\\n  M_{bb} &=& -3k^2\\frac{\\nu_1}{r_0^2}\n  \\frac{1}{1+\\mathrm{St}^2}\\left(\\phi_d+\\frac{1}{3\\mathrm{Sc}}\\right)\\,.\n\\end{eqnarray}\nThe eigenvalues of this matrix are found from:\n\\begin{equation}\\label{eq-gamma-pm}\n  \\begin{split}\n    \\Gamma_{\\pm} =& \\frac{1}{2}\\bigg((M_{aa}+M_{bb}) \\\\\n&   \\pm \\sqrt{(M_{aa}+M_{bb})^2-4(M_{aa}M_{bb}-M_{ba}M_{ab})}\\bigg)\\,.\n  \\end{split}\n\\end{equation}\nSo we have\n\\begin{equation}\\label{eq-iomega-from-gamma}\ni\\omega = \\Gamma_{\\pm}\\,.\n\\end{equation}\nThe solution is stable if\n\\begin{equation}\n\\mathrm{Re}(i\\omega) \\le 0\\,,\n\\end{equation}\nfor all possible \\revised{values of $k$. One can see that if this is true\/untrue\n  for one value of $k$, it is true\/untrue for all values of $k$, because $k$\n  only enters as a multiplicative factor. The above stability condition\n  requires that both $M_{aa}+M_{bb}<0$ and $M_{aa}M_{bb}>M_{ab}M_{ba}$.\n  These two conditions simplify to:}\n\\begin{eqnarray}\n  1+\\phi_g + \\frac{1}{1+\\mathrm{St}^2}\\left(\\phi_d + \\frac{1}{3\\mathrm{Sc}}\\right) &\\ge& 0\\,,\n\\label{eq-stability-criterion-simple-1}\\\\\n  1+\\phi_g + \\left(1 + \\frac{\\mathrm{St}}{\\alpha_1}\\,\\mathrm{Sc}\\right)\\phi_d &\\ge& 0\\,.\n\\label{eq-stability-criterion-simple-2}\n\\end{eqnarray}\n\\revised{Both conditions have to be fulfilled for the disk to be stable against\nthe dust-driven viscous instability. Otherwise it is unstable for all $k$.}\n\n\n\\subsection{Results for the growth rates}\\label{sec-results-simple}\nWe apply the model to the case of a young solar mass star ($M_{*}=M_\\odot$) with\nstill substantial luminosity ($L_{*}=10\\,L_\\odot$), to mimic the case of HL Tau\n\\citep{2015ApJ...808L...3A}. We perform the analysis at a radius of\n$r_0=60\\,\\mathrm{au}$. The Schmidt number of the gas is set to $\\mathrm{Sc}=1$.\nTo compute the temperature of the midplane gas we assume a simple irradiated\ndisk model, in which the irradiation angle is $\\varphi=0.05$. By setting the\nmidplane temperature to the effective temperature of the disk assuming thermal\nequilibrium we obtain $T=(\\varphi L_{*}\/(4\\pi r_0^2\\sigma_{\\mathrm{SB}}))^{1\/4}\n=43\\,\\mathrm{K}$, which is a very rough estimate of the disk temperature, but\nsufficient for the present purpose. The orbital time is 465 years. The vertical\npressure scale height of the disk is $H_p=c_s\/\\Omega_K=6\\,\\mathrm{au}$.  We now\napply the perturbation analysis for wave numbers $k$ corresponding to\ndimensionless wavelengths $\\lambda=2\\pi\/k$ in the range between the smallest\npossible wavelength $\\lambda=H_p\/r_0$ and the largest reasonable one\n$\\lambda=1$. The choice of $H_p\/r_0$ is the smallest wavelength is based on\nthe assumption that the turbulent viscosity in the disk cannot lead to\nradial structures that are narrower than about one vertical scale height. In\nthe current example this means that the smallest wavelength we should consider\nis $\\lambda=0.1$.\n\nWe now compute the growth rate\n\\begin{equation}\n\\Gamma = \\mathrm{Re}(i\\omega)\\,,\n\\end{equation}\nof each of these modes for a range of different dust particle sizes. We express\nthe dust particle size in terms of its Stokes number $\\mathrm{St}$ defined as\n$\\mathrm{St}=t_{\\mathrm{stop}}\/t_{\\mathrm{orbit}}$, where $t_{\\mathrm{stop}}$ is\nthe stopping time of the dust particle defined as\n$t_{\\mathrm{stop}}=f_{\\mathrm{fric}}\/m_{\\mathrm{grain}}|{\\bf\n  v}_{\\mathrm{grain}}-{\\bf v}_{\\mathrm{gas}}|$ where $f_{\\mathrm{fric}}$ is the\nfriction force between the gas and the dust particle, $m_{\\mathrm{grain}}$ is\nthe dust grain mass, and $|{\\bf v}_{\\mathrm{grain}}-{\\bf v}_{\\mathrm{gas}}|$ is\nthe absolute value of the velocity difference between the gas and the dust\nparticle. The precise translation between particle mass $m_{\\mathrm{grain}}$ and\nStokes number is not trivial to express, because it depends on much detailed\nphysics, such as the porosity or fractility of the dust aggregate, its size\ncompared to the gas mean free path, the gas density and temperature etc.  For\ntypical disk parameters a Stokes number of unity at 60 AU would correspond to a\ncompact silicate dust particle of about a centimeter or a decimeter, and is\nsmaller for smaller particles. We refer to the literature for an in-depth\ndiscussion of the relation between particle size and Stokes number \\citep[see\n  e.g.][]{2010A&A...513A..79B}. For our analysis only the Stokes number is\nrelevant.  The results of the present analysis are shown in\nFig.~(\\ref{fig-gammaorb-simple}).\n\\begin{figure}\n  \\centerline{\\includegraphics[width=0.52\\textwidth]{fig_gammaorb_simple.pdf}}\n  \\caption{\\label{fig-gammaorb-simple}Growth rate in units of the reciprocal\n    orbital time ($1\/t_{\\mathrm{orbit}}=\\Omega_K\/2\\pi$) of the dust-driven\n    viscous instability, as a function of dust particle size (expressed as\n    Stokes number $\\mathrm{St}$), according to the simplified analysis of\n    Section \\ref{sec-pert-analy-simple}. Dashed lines: case 1 (i.e.~$\\phi_g=0$),\n    solid lines: case 2 (i.e.~$\\phi_g=-\\phi_d$). The different lines show modes\n    of different dimensionless wavelength $\\lambda$ in the dimensionless\n    coordinate $x$, where $\\lambda=2\\pi\/k$. A dimensionless wavelength\n    $\\lambda=1$ means a wavelength as large as $r_0$. The parameters of the\n    model shown here are $\\phi_d=-1.0$, $\\alpha_1=10^{-4}$,\n    $M_{*}=1\\,M_{\\odot}$, $L_{*}=10\\,L_{\\odot}$, $r_0=60\\,\\mathrm{au}$,\n    $T=43,\\mathrm{K}$, $\\mathrm{Sc}=1$ (i.e.~$c_s=0.39\\,\\mathrm{km\/s}$ and\n    $t_{\\mathrm{orbit}}=465\\,\\mathrm{year}$).}\n\\end{figure}\n\nThe growth rate $\\Gamma=\\mathrm{Re}(i\\omega)$ is expressed in terms of the\nreciprocal orbital time scale. This means that if this value is larger than\nunity, the perturbation grows faster than the gas can orbit around the star.\nThis would not lead to `grand-design' rings, but instead to small arc-shaped\nclumps, because if a perturbation is triggered at some azimuthal position, the\ninformation about this event does not have time to propagate around the entire\norbit before the perturbation has grown to much larger amplitude. In other\nwords: to create global-scale rings we need a slow instability (a\n`secular instability'). It must be slow compared to the time it takes for a\nperturbation to shear out over $2\\pi$ in azimuth. This time scale depends on the\nradial width of the perturbation, which is related to the dimensionless\nwavelength $\\lambda$ of the unstable mode through $\\Delta r=r_0\\lambda$. Through\nkeplerian orbital dynamics we can then define this shear time scale\nas\n\\begin{equation}\\label{eq-time-shear}\nt_{\\mathrm{shear}} = \\frac{2}{3}\\frac{1}{\\lambda}\\,t_{\\mathrm{orbit}}\\,.\n\\end{equation}\nSo instead of comparing $\\Gamma$ to the reciprocal orbital time, we should\nexpress $\\Gamma$ in terms of $1\/t_{\\mathrm{shear}}$. If we do so, the curves for\nsmall $\\lambda$ will move up. The results are shown in\nFig.~\\ref{fig-gammalib-simple}. \n\\begin{figure}\n  \\centerline{\\includegraphics[width=0.52\\textwidth]{fig_gammalib_simple.pdf}}\n  \\caption{\\label{fig-gammalib-simple}Same as Fig.~\\ref{fig-gammaorb-simple},\n    but now with the growth rate $\\Gamma$ expressed in units of the reciprocal\n  shear time over a radial distance of $\\Delta r=r_0\\lambda$.}\n\\end{figure}\nWhereever the curve lies above unity, the growth is faster than the azimuthal\ncommunication. In that case small-scale arcs form instead of global scale\nrings. Wherever the curve lies sufficiently below unity but above zero (which in\nthis log-representation means that the curve is visible in the plot), the\nperturbation may lead to large scale rings. \n\nOne can also see that, for case 2 ($\\phi_g=-\\phi_d$, solid lines in the figure)\nthe instability does not operate for $\\mathrm{St}\\le 10^{-4}$ (for this\nset of model parameters), \\revised{consistent with Eqs.~(\\ref{eq-stability-criterion-simple-1},\n  \\ref{eq-stability-criterion-simple-2})}. This can be\nunderstood because for very small grains (small $\\mathrm{St}$) the dust is so\nwell-coupled to the gas that dust drift is virtually inhibited, meaning that\n$\\Sigma_d\/\\Sigma_g$ remains constant.\n\n\\revised{For both case 1 and case 2, however, the instability does not occur for\n  $\\mathrm{St}\\rightarrow 0$, i.e.\\ for the case in which the dust does not\n  drift at all. This changes if we set $\\phi_d<-1$. In\n  Fig.~\\ref{fig-gammalib-simple-phi2} the results for $\\phi_d=-2$ are shown\n  (both case 1 and case 2). Now, at least for case 1 ($\\phi_g=0$, dashed lines),\n  the instability even operates for $\\mathrm{St}\\rightarrow 0$, i.e.\\ without\n  dust drift. The reason is that the convergent flow of gas, dragging along the\n  dust with it, increases the gas and dust density enough to set the instability\n  in motion. We then recover the instability by \\citet{2015ApJ...815...99H}\n  and others. We discuss this in Section \\ref{sec-discussion}. \n}\n\n\\begin{figure}\n  \\centerline{\\includegraphics[width=0.52\\textwidth]{fig_gammalib_simple_phi2.pdf}}\n  \\caption{\\label{fig-gammalib-simple-phi2}Same as Fig.~\\ref{fig-gammalib-simple},\n    but now for $\\phi_d=-2$ instead of $\\phi_d=-1$.}\n\\end{figure}\n\nAs can be seen, however, the strongest growth occurs around Stokes numbers of\nunity, and for the shortest wavelength $\\lambda$. In this regime the growth rate\nis faster than $1\/t_{\\mathrm{shear}}$. In a disk with a grain size distribution\nspanning from tiny to large, this seems to suggest that the instability will be\nmainly driven by the comparetively large $\\mathrm{St}\\simeq 1$ grains, which\nwould then lead not to rings but to numerous small arcs. Perhaps these arcs\ncan later merge into large scale rings is something that cannot be studied\nusing this linear perturbation analysis.\n\nIn reality the situation is likely more subtle. In a disk with a dust size\ndistribution it is typically the smallest grains that are affecting\nthe $\\alpha$ the most, because the smallest grains have the largest total\nsurface area and can thus be most effective in removing free electrons and\nions from the gas. We therefore speculate that in spite of the strong\ngrowth rate for $\\mathrm{St}\\simeq 1$ particles that results from our\nanalysis, it is mostly the smallest dust grains that drive the instability,\nif at all. If most\/all of the dust has Stokes numbers below the cut-off\nfor case 1, then if case 1 is applicable the instability would not operate\nat all.\n\n\\subsection{A speculative scenario}\n\\label{sec-two-stage-scenario}\nLet us speculate about the following scenario: We assume that only relatively\nsmall dust affects the viscosity parameter $\\alpha$. From\nFig.~\\ref{fig-gammalib-simple} for, say, $\\mathrm{St}\\simeq 3\\times 10^{-4}$ the\ninstability is driven at a low enough rate, even for the smallest wavelengths,\nthat a set of global rings can form. As these rings grow in strength, we will\nenter into the non-linear regime. The radial derivative of the gas pressure will\nstart to display sign-changes, and thus form actual dust traps. Since the disk\nalso has large grains (even though they did not participate in the instability),\nthese large grains get trapped into the dust traps and form dense dust rings,\npossibly even dominating the local density over the gas density.\n\\revisedtwo{At this point the frictional back-reaction of the dust onto the \n  gas will have to be taken into account, and the streaming instability\n  \\citep{2007ApJ...662..627J} may set in within these dust rings. Also}\nthe self-gravity of the population of large grains may start to play a role.\nPerhaps a combination with the secular instability of\n\\citet{2016AJ....152..184T} could occur.  We are aware that these are mere\nspeculations, and more investigation (in particular: numerical modeling) is\nrequired.\n\nSo far we have only looked at the growth rates of the modes, not their spatial\npropagation. In other words, we looked at $\\mathrm{Re}(i\\omega)$ but not yet at\n$\\mathrm{Im}(i\\omega)$. The above speculative scenario is only possible if the\ninitial ring-instability occurs more or less {\\em in situ}, or in other words,\nthat it is not\na moving wave that is slowly amplifying but instead a standing wave that is\ngrowing in amplitude. To verify this we need to study the ratio\n$\\mathrm{Im}(i\\omega)\/\\mathrm{Re}(i\\omega)$ for all cases where\n$\\mathrm{Re}(i\\omega)>0$. For the simplified analysis of this section it\nturns out that $\\mathrm{Im}(i\\omega)=0$. The mode grows exactly\nin-situ, meaning that the above speculative scenario is plausible. \n\n\n\n\n\n\n\\section{Full perturbation analysis}\n\\label{sec-pert-analy-full}\nThe perturbation analysis for the full system of equations of Section\n\\ref{sec-basic-equations} is substantially more tedious than the simplified\nanalysis of Section \\ref{sec-pert-analy-simple}, but the results are overall\nconsistent with each other. There are also some simplifications that we keep:\nwe still assume that the Stokes number does not change with time and space, and\nthe same holds for the Schmidt number. In reality, for a given particle size\nthe Stokes number changes if the gas density changes. Such effects are not\nincluded.\n\n\\subsection{Stationary powerlaw solution}\n\\label{sec-stationary-solution}\nLet us assume the following Ansatz for the stationary solution:\n\\begin{eqnarray}\n\\Sigma_{g1}(r) &=& \\Sigma_{g0} \\left(\\frac{r}{r_0}\\right)^p\\,,\\label{eq-ansatz-sigmag}\\\\\n\\Sigma_{d1}(r) &=& \\Sigma_{d0} \\left(\\frac{r}{r_0}\\right)^p\\,,\\label{eq-ansatz-sigmad}\n\\end{eqnarray}\nwhere we deliberately took the same powerlaw index for both the dust and\nthe gas component. For the temperature profile we also assume a powerlaw\nof the form\n\\begin{equation}\\label{eq-ansatz-temp}\nT(r) = T_0 \\left(\\frac{r}{r_0}\\right)^q\\,.\n\\end{equation}\nThe isothermal sound speed $c_s$ follows from this temperature by\nEq.~(\\ref{eq-cs2-in-temp}).  The dimensionless vertical scale height $h$ is\ndefined as $h=H_p\/r$, where the scale height $H_p$ is given by\nEq.~(\\ref{eq-disk-hp}).\n\nThe radial gas velocity (Eq.~\\ref{eq-vr-gas}) becomes\n\\begin{equation}\\label{eq-vrg-as-dbllog-dir}\n  v_{rg} = -\\frac{3\\nu}{r} \\frac{\\partial\\ln(\\Sigma_g\\nu\\sqrt{r})}{\\partial \\ln r}\n  = -\\frac{3\\nu}{r}\\left(p+\\frac{1}{2}+\\frac{\\partial\\ln\\nu}{\\partial \\ln r}\\right)\\,,\n\\end{equation}\nwhere $\\nu$ is given by Eq.~(\\ref{eq-def-nu}). It can be aposteriori verified\nthat stationary powerlaw solutions only exist if the $\\alpha$ coefficient is\nindependent of radius, which we will, from here on, assume to be the case.\nWith Eq.~(\\ref{eq-def-nu}) we then obtain\n\\begin{equation}\\label{eq-vr-stationary_1}\n  v_{rg} = -\\frac{3\\nu}{r}\\left(p+q+2\\right)\\,.\n\\end{equation}\nInserting this into the gas continuity equation (Eq.~\\ref{eq-gas-continuity}),\nand setting the time-derivative to zero, yields $\\Sigma_g\\nu=$constant. This\nmeans (with Eqs.~\\ref{eq-def-nu}, \\ref{eq-omega-kepler}, \\ref{eq-cs2-in-temp},\n\\ref{eq-ansatz-temp}, \\ref{eq-ansatz-sigmag}) that\n\\begin{equation}\\label{eq-powerlaw-sum-steady}\np+q=-\\frac{3}{2}\\,.\n\\end{equation}\nInserting this into Eq.~(\\ref{eq-vr-stationary_1}) yields\n\\begin{equation}\\label{eq-vr-in-nu-r}\n  v_{rg} = -\\frac{3\\nu}{2r}\\,.\n\\end{equation}\n\nNow let us do the dust, Eq.~(\\ref{eq-dust-continuity}). Since by our Ansatz\n$\\Sigma_d(r)\/\\Sigma_g(r)$ is a constant (because both have the same powerlaw\nindex), the right-hand-side of Eq.~(\\ref{eq-dust-continuity}) is zero. This then\nimmediately means that $v_d(r)\/v_g(r)$ must also be a constant. If we now\nlook at the two terms in Eq.~(\\ref{eq-vdust-1}), and we assume that $v_d(r)$\nmust have the same radial powerlaw dependency as $v_g(r)$, then both terms in\nEq.~(\\ref{eq-vdust-1}) must have the same radial powerlaw dependency.  This\nmeans that $c_sh$ must have the same radial powerlaw dependency on $r$ as\n$v_{rg}$:\n\\begin{equation}\n  \\frac{d\\ln(c_sh)}{d\\ln r} = \\frac{d\\ln |v_{rg}|}{d\\ln r} = q+\\frac{1}{2}\\,,\n\\end{equation}\nwhere we used Eqs.~(\\ref{eq-vr-in-nu-r}, \\ref{eq-def-nu}) and the definition of\n$q$ (Eq.~\\ref{eq-ansatz-temp}) in the last\nstep. However, given that $c_sh=c_s^2\/\\Omega_Kr$ we already independently know that\n\\begin{equation}\\label{eq-dlncsh}\n  \\frac{d\\ln(c_sh)}{d\\ln r} = q+\\frac{1}{2}\\,,\n\\end{equation}\nwhich confirms that we indeed have a stationary powerlaw solution for both the\ndust and the gas. We can now calculate the ratio of the dust radial velocity to\nthe gas radial velocity using Eq.~(\\ref{eq-vdust-1}) with\nEq.~(\\ref{eq-ansatz-sigmag}):\n\\begin{equation}\\label{eq-vdust-vgas-stationary}\n\\begin{split}\n  v_{rd} &= \\frac{v_{rg}}{1+\\mathrm{St}^2} \n  + \\frac{c_sh}{\\mathrm{St}+\\mathrm{St}^{-1}}\n  \\left(p + \\frac{q-3}{2}\\right)\\\\\n  &= \\frac{1}{1+\\mathrm{St}^2}\\left[1+L\\left(p+\\frac{q-3}{2}\\right)\\right] \\;v_{rg}\\,,\n\\end{split}\n\\end{equation}\nwhere we define\n\\begin{equation}\\label{eq-definition-l}\nL\\equiv \\frac{\\mathrm{St}\\,c_s^2}{\\Omega_K\\,r\\,v_{rg}} = -\\frac{2}{3}\\frac{\\mathrm{St}}{\\alpha}\\,,\n\\end{equation}\nwhere in the last step we used the stationary solution for $v_{rg}$\n(Eq.~\\ref{eq-vr-in-nu-r}) and the equation for $\\nu$ (Eq.~\\ref{eq-def-nu}).\n\nIf we insert a standard example, $p=-1$, $q=-0.5$, then this becomes:\n\\begin{equation}\nv_{rd} = \\frac{1}{1+\\mathrm{St}^2}\\left[1+1.833\\,\\frac{\\mathrm{St}}{\\alpha}\\right] \\;v_{rg}\\,.\n\\end{equation}\n\n\\subsection{Linearization}\n\\label{sec-linearization}\nNow we impose a perturbation on the stationary solution. We introduce the\ncoordinate $x$:\n\\begin{equation}\nr=r_0e^x\\simeq r_0(1+x)\\,,\n\\end{equation}\nand the perturbations:\n\\begin{eqnarray}\n\\Sigma_g(r,t) &=& \\Sigma_{g1}(r) (1+\\sigma_g(x,t))\\,,\\label{eq-full-sigma-g-pert}\\\\\n\\Sigma_d(r,t) &=& \\Sigma_{d1}(r) (1+\\sigma_d(x,t))\\,,\\label{eq-full-sigma-d-pert}\n\\end{eqnarray}\nsimilar to Section \\ref{sec-pert-analy-simple}. Again, the subscript $1$ denotes\nthe stationary solution.  We keep the temperature and sound speed stationary\n(i.e.~static in time, but varying in space). The perturbations $\\sigma_d(x,t)$\nand $\\sigma_g(x,t)$ are allowed to affect $\\alpha(x,t)$. We use the same recipe\nfor $\\alpha$ as before (Eq.~\\ref{eq-alpha-param}).  To first order in the\nperturbations we can write:\n\\begin{eqnarray}\nd\\ln r            &=& dx\\,,\\label{eq-dlnr-dx}\\\\\nd\\ln\\Sigma_g(r,t) &=& d\\ln\\Sigma_{g1}(r) + d\\sigma_g(x,t) \\,,\\\\\nd\\ln\\Sigma_d(r,t) &=& d\\ln\\Sigma_{d1}(r) + d\\sigma_d(x,t) \\,,\\\\\nd\\ln\\left(\\frac{\\Sigma_d(r,t)}{\\Sigma_g(r,t)}\\right) &=&\n     d\\sigma_d(x,t) - d\\sigma_g(x,t)\\,,\\\\\nd\\ln\\alpha(r,t)   &=& \\phi_d\\,d\\sigma_d(x,t)+\\phi_g\\,d\\sigma_g(x,t)\\,,\\\\\nd\\ln\\nu(r,t)    &=& d\\ln\\nu_{1}(r) + \\phi_d\\,d\\sigma_d(x,t) \\nonumber\\\\\n& & + \\phi_g\\,d\\sigma_g(x,t)\\,.\\label{eq-differ-ln-nu}\n\\end{eqnarray}\nOr specifically for the double-logarithmic derivative with respect\nto $r$ we obtain (omitting the $(r,t)$ for notational convenience):\n\\begin{eqnarray}\n\\frac{\\partial\\ln\\Sigma_g}{\\partial\\ln r} &=& p + \\frac{\\partial\\sigma_g}{\\partial x} \\,,\\label{eq-dbllog-sigma-g}\\\\\n\\frac{\\partial\\ln\\Sigma_d}{\\partial\\ln r} &=& p + \\frac{\\partial \\sigma_d}{\\partial x} \\,,\\label{eq-dbllog-sigma-d} \\\\\n\\frac{\\partial\\ln(\\Sigma_d\/\\Sigma_g)}{\\partial\\ln r} &=&\n     \\frac{\\partial\\sigma_d}{\\partial x} - \\frac{\\partial\\sigma_g}{\\partial x}\\,,\\\\\n\\frac{\\partial\\ln\\alpha}{\\partial\\ln r} &=& \\phi_d\\,\\frac{\\partial\\sigma_d}{\\partial x}+\\phi_g\\,\\frac{\\partial\\sigma_g}{\\partial x}\\,,\\\\\n\\frac{\\partial\\ln\\nu}{\\partial\\ln r} &=& q+\\frac{3}{2} + \\phi_d\\,\\frac{\\partial\\sigma_d}{\\partial x}+ \\phi_g\\,\\frac{\\partial\\sigma_g}{\\partial x}\\,.\\label{eq-diff-ln-nu}\n\\end{eqnarray}\nThe gas velocity $v_{rg}$ (Eq.~\\ref{eq-vr-gas}) is now:\n\\begin{eqnarray}\n  v_{rg} &=& -\\frac{3\\nu}{r} \\frac{\\partial\\ln(\\Sigma_g\\nu\\sqrt{r})}{\\partial \\ln r}\\\\\n  &=& -\\frac{3\\nu}{2r}\\left(1+2(1+\\phi_g)\\frac{\\partial\\sigma_g}{\\partial x}+2\\phi_d\\frac{\\partial\\sigma_d}{\\partial x}\\right)\n\\,,\\label{eq-vrgin-nu-with-perturb}\n\\end{eqnarray}\nwhere we used Eqs.~(\\ref{eq-diff-ln-nu}, \\ref{eq-powerlaw-sum-steady}). The\ndust velocity $v_{rd}$ (Eq.~\\ref{eq-vdust-1}) becomes, using\nEqs.(\\ref{eq-omega-kepler}, \\ref{eq-cs2-in-temp}, \\ref{eq-disk-hp},\n\\ref{eq-ansatz-sigmag}, \\ref{eq-dbllog-sigma-g}) and the identities $h=H_p\/r$\nand $P=\\rho_gc_s^2$:\n\\begin{eqnarray}\n\\label{eq-vdust-2}\n  v_{rd} &=& \\frac{v_{rg}}{1+\\mathrm{St}^2} \n  + \\frac{c_sh}{\\mathrm{St}+\\mathrm{St}^{-1}}\n\\left(\\frac{\\partial \\ln \\Sigma_g}{\\partial \\ln r} + \\frac{q-3}{2}\\right)\\\\\n  &=& \\frac{v_{rg}}{1+\\mathrm{St}^2} \\left[1+\\frac{\\mathrm{St}\\,c_sh}{v_{rg}}\n    \\left(p+\\frac{\\partial \\sigma_g}{\\partial x} + \\frac{q-3}{2}\\right)\\right]\n\\,.\\label{eq-vrdin-nu-with-perturb}\n\\end{eqnarray}\nTo be able to use $v_{rg}$ and $v_{rd}$ in the viscous disk equations\nEqs.~(\\ref{eq-gas-continuity}, \\ref{eq-dust-continuity}), will be forced\nto compute their radial derivatives, which is where the cumbersome math\ncomes in. To keep things as orderly as possible, we rewrite\nEqs.~(\\ref{eq-gas-continuity}, \\ref{eq-dust-continuity}) into double-logarithmic\nform:\n\\begin{eqnarray}\n\\frac{\\partial\\ln \\Sigma_{g}}{\\partial t} +\n  \\frac{v_{rg}}{r}\\frac{\\partial\\ln(r\\Sigma_g |v_{rg}|)}{\\partial\\ln r}\n  &=& 0\\,,\\label{eq-gas-continuity-doublog}\\\\\n\\frac{\\partial\\ln \\Sigma_{d}}{\\partial t} +\n  \\frac{v_{rd}}{r}\\frac{\\partial\\ln(r\\Sigma_d |v_{rd}|)}{\\partial\\ln r}\n  &=& \\nonumber\\\\\n  \\frac{1}{r\\Sigma_d}\\frac{\\partial}{\\partial r}\n  \\bigg(r{\\cal D}_d & \\Sigma_d & \\frac{\\partial}{\\partial r}\n  \\ln\\bigg(\\frac{\\Sigma_d}{\\Sigma_g}\\bigg)\\bigg)\\,.\\label{eq-dust-continuity-doublog}\n\\end{eqnarray}\nThe double-logarithmic derivatives of $r\\Sigma_{g\/d}v_{r\\,g\/d}$ can, using\nEqs.~(\\ref{eq-dbllog-sigma-g}, \\ref{eq-dbllog-sigma-d}), be written out as\n\\begin{equation}\\label{eq-dlog-cons-term}\n  \\frac{\\partial\\ln(r\\Sigma_{g\/d} |v_{rg\/d}|)}{\\partial\\ln r}\n  = 1 + p + \\frac{\\partial\\sigma_{g\/d}}{\\partial x} +\n  \\frac{\\partial\\ln |v_{rg\/d}|}{\\partial\\ln r}\\,.\n\\end{equation}\nThe right-hand-side of Eq.~(\\ref{eq-dust-continuity-doublog}) can also\nbe written into the derivatives of the perturbations. To first order in\n$\\sigma_{g}$ and $\\sigma_{d}$ we get:\n\\begin{equation}\\label{eq-simplified-rhs}\n\\begin{split}\n  \\frac{1}{r\\Sigma_d}\\frac{\\partial}{\\partial r}\n  \\bigg(r{\\cal D}_d  \\Sigma_d & \\frac{\\partial}{\\partial r} \n  \\ln\\bigg(\\frac{\\Sigma_d}{\\Sigma_g}\\bigg)\\bigg)\\\\\n  &= \\frac{{\\cal D}_d}{r^2}\n  \\frac{\\partial^2 (\\sigma_d-\\sigma_g)}{\\partial x^2}\\,,\n\\end{split}\n\\end{equation}\nwhere we made use of the fact that $\\partial(\\sigma_d-\\sigma_g)\/\\partial x$ is\nalready first order in $\\sigma_{g}$ and $\\sigma_{d}$, and that $\\Sigma_d{\\cal\n  D}_d$ is, to first order in $\\sigma_{g}$ and $\\sigma_{d}$, constant. This is\nbecause the stationary solution (Section \\ref{sec-stationary-solution}) obeys\n$\\Sigma_{d1}{\\cal D}_d\\propto \\Sigma_{g1}\\nu$, which is constant.\n\nWhat remains to be done is to derive expressions for the double-logarithmic\nderivatives of the gas and dust velocities (Eqs.~\\ref{eq-vrgin-nu-with-perturb}\nand \\ref{eq-vrdin-nu-with-perturb}, respectively) used in\nEq.~(\\ref{eq-dlog-cons-term}). This is somewhat tedious algebra, which we defer\nto Appendix \\ref{app-dbllog-v}. After inserting the resulting expressions\n(Eqs.~\\ref{eq-dbllog-lin-der-vrg-2}, \\ref{eq-dbllog-lin-der-vrd-2}), into\nEq.~(\\ref{eq-dlog-cons-term}), we see that for both the gas and the dust version\nthe constant term $1+p$ drops out, and the expression of\nEq.~(\\ref{eq-dlog-cons-term}) becomes linear in the perturbations. This\ncancellation of the constant $1+p$ is not surprising, because it follows from\nthe fact that we start our perturbation analysis from the stationary solutions\nof Section \\ref{sec-stationary-solution}. Inserting the resulting gas- and\ndust-versions of Eq.~(\\ref{eq-dlog-cons-term}), together with\nEq.~(\\ref{eq-simplified-rhs}), into the continuity equations\nEqs.~(\\ref{eq-gas-continuity-doublog}, \\ref{eq-dust-continuity-doublog}), we\nfind the following set of equations:\n\\begin{eqnarray}\n  \\frac{\\partial\\sigma_g}{\\partial t}\n  &+&\\bigg[\n    \\tilde C_g\\frac{\\partial \\sigma_g}{\\partial x}\n   + \\tilde C_{gg}\\frac{\\partial^2\\sigma_g}{\\partial x^2}\n   + \\tilde C_{gd} \\,\\phi_d\\left(\n   \\frac{1}{2}\\frac{\\partial\\sigma_d}{\\partial x} + \\frac{\\partial^2\\sigma_d}{\\partial x^2}\\right)  \\nonumber\\\\\n   & & + \\tilde C_{gd} \\,\\phi_g\\left(\n  \\frac{1}{2}\\frac{\\partial\\sigma_g}{\\partial x} + \\frac{\\partial^2\\sigma_g}{\\partial x^2}\\right)\n  \\bigg] = 0 \\,,\\label{eq-cont-gas-lin-2}\\\\\n  \\frac{\\partial\\sigma_d}{\\partial t}\n  &+&\\bigg[\n    \\tilde C_d\\frac{\\partial \\sigma_d}{\\partial x}\n   + \\tilde C_{dg}\\frac{\\partial^2\\sigma_g}{\\partial x^2}\n   + \\tilde C_{dd} \\,\\phi_d\\left(\n  \\frac{1}{2}\\frac{\\partial\\sigma_d}{\\partial x} + \\frac{\\partial^2\\sigma_d}{\\partial x^2}\\right) \\nonumber\\\\\n& &    + \\tilde C_{dd} \\,\\phi_g\\left(\n  \\frac{1}{2}\\frac{\\partial\\sigma_g}{\\partial x} + \\frac{\\partial^2\\sigma_g}{\\partial x^2}\\right)\n  \\bigg] =\n \\tilde {\\cal D}_d\\,\n    \\frac{\\partial^2(\\sigma_d-\\sigma_g)}{\\partial x^2} \\,,\\label{eq-cont-dust-lin-2}\n\\end{eqnarray}\nwhere the tilde-symbols are defined as:\n\\begin{eqnarray}\n  \\tilde C_g &=&\\frac{v_{rg1}}{r}\\,,\\\\\n  \\tilde C_d &=&\\frac{v_{rd1}}{r}\\,,\\\\\n  \\tilde C_{gg} &=& \\frac{v_{rg1}}{r}C_{gg} \\,,\\\\\n  \\tilde C_{gd} &=& \\frac{v_{rg1}}{r}C_{gd} \\,,\\\\\n  \\tilde C_{dg} &=& \\frac{v_{rd1}}{r}C_{dg} \\,,\\\\\n  \\tilde C_{dd} &=& \\frac{v_{rd1}}{r}C_{dd} \\,,\\\\\n  \\tilde {\\cal D}_d &=& \\frac{1}{r^2}{\\cal D}_d\\,,\n\\end{eqnarray}\nwhere the symbols $C_{gg}$, $C_{gd}$, $C_{dg}$ and $C_{dd}$ are defined\nin Eqs.~(\\ref{eq-define-cgg}, \\ref{eq-define-cgd}, \\ref{eq-define-cdg},\n\\ref{eq-define-cdd}). We again insert trial functions\n\\begin{eqnarray}\n\\sigma_g &=& A e^{i\\omega t-ikx}\\,,\\\\\n\\sigma_d &=& B e^{i\\omega t-ikx}\\,,\n\\end{eqnarray}\nand obtain the matrix equation\n\\begin{equation}\ni\\omega \\left(\\begin{matrix}\n  A\\\\\n  B\n\\end{matrix}\\right)\n=\\left(\\begin{matrix}\n  M_{aa} & M_{ab}\\\\\n  M_{ba} & M_{bb}\n\\end{matrix}\\right)\n\\left(\\begin{matrix}\n  A\\\\\n  B\n\\end{matrix}\\right)\\,,\n\\end{equation}\nwith\n\\begin{eqnarray}\n  M_{aa} &=& ik\\tilde C_g+k^2\\tilde C_{gg} + \\left(\\tfrac{1}{2}ik+k^2\\right)\\tilde C_{gd}\\phi_g\\,,\\\\\n  M_{ab} &=& \\left(\\tfrac{1}{2}ik+k^2\\right)\\tilde C_{gd}\\phi_d \\,,\\\\\n  M_{ba} &=& k^2(\\tilde C_{dg}+\\tilde {\\cal D}_d) + \\left(\\tfrac{1}{2}ik+k^2\\right)\\tilde C_{dd}\\phi_g \\,,\\\\\n  M_{bb} &=& ik\\tilde C_d+ \\left(\\tfrac{1}{2}ik+k^2\\right)\\tilde C_{dd}\\phi_d \n  -k^2\\tilde{\\cal D}_d\\,.\n\\end{eqnarray}\nThe eigenvalues, and thereby the growth rates of the modes, follow \nfrom Eqs.~(\\ref{eq-gamma-pm}, \\ref{eq-iomega-from-gamma}).\n\n\\subsection{Results}\\label{sec-results-full}\nFor the same parameters as in Section \\ref{sec-results-simple} we\nplot the resulting growth rates for the full perturbation analysis.\nThe result is shown in Fig.~\\ref{fig-gammalib-full-simple} \\revised{for case 2}.\n\\begin{figure}\n  \\centerline{\\includegraphics[width=0.52\\textwidth]{fig_gammalib_full.pdf}}\n  \\caption{\\label{fig-gammalib-full-simple}Results for the full perturbation\n    analysis of Section \\ref{sec-pert-analy-full} (solid lines) compared to the\n    results of the simplified perturbation analysis of Section\n    \\ref{sec-pert-analy-simple} (dashed lines). Here case 2 is shown\n    ($\\phi_g=-\\phi_d$) with $\\phi_d=-1$. For the rest the figure is the same as\n    Fig.~\\ref{fig-gammalib-simple}. \\revised{If we would have plotted case 1\n      instead of case 2, the difference would only be that the curves would not\n      be cut off for $\\mathrm{St}\\lesssim 10^{-4}$, but would continue down to\n      $\\mathrm{St}\\rightarrow 0$ in the same fashion as the dashed lines in\n      Fig.~\\ref{fig-gammalib-simple}.}}\n\\end{figure}\nIt shows that for small enough particles and small enough wavelength $\\lambda$\nthe simple perturbation analysis of Section \\ref{sec-pert-analy-simple} agrees\nwell with the full perturbation analysis. \\revised{The same is true if we would\n  have plotted this diagram for case 1, the only difference to\n  Fig.~\\ref{fig-gammalib-full-simple} being, that the curves would continue down\n  to $\\mathrm{St}\\rightarrow 0$ as in Fig.~\\ref{fig-gammalib-simple}.} However,\nfor larger particles and\/or larger wavelength, the full perturbation analysis\nyields substantially weaker growth rates. But we see that for $\\lambda\\lesssim\n0.25$ the growth rates are nevertheless everywhere positive where the simplified\nanalysis predicts positive growth rates. Since we need the instability to be\nslow to obtain large scale rings, this is, in fact, advantageous for the\nmodel.\n\nAs we did for the simplified analysis of Section \\ref{sec-two-stage-scenario} we\nhave to verify if the initial ring-instability occurs more or less in situ.  To\nthis end we plot $\\mathrm{Im}(i\\omega)\/\\mathrm{Re}(i\\omega)$\n(Fig.~\\ref{fig-imre-full}). We see that, in contrast to the simplified analysis,\nthe imaginary component of $i\\omega$ is not zero. However, we see in the plot\nthat for most Stokes numbers of interest $\\mathrm{Im}(i\\omega)$ is sufficiently\nmuch smaller than $\\mathrm{Re}(i\\omega)$. That means that the growth can be\nconsidered to be sufficiently well in-situ for the speculative scenario of\nSection \\ref{sec-two-stage-scenario} to remain plausible.\n\\begin{figure}\n  \\centerline{\\includegraphics[width=0.52\\textwidth]{fig_imre_full.pdf}}\n  \\caption{\\label{fig-imre-full}Ratio of\n    $\\mathrm{Im}(i\\omega)\/\\mathrm{Re}(i\\omega)$ for the full perturbation\n    analysis. Dashed lines: case 1 ($\\phi_d=-1$, $\\phi_g=0$), solid lines: case\n    2 ($\\phi_d=-1$, $\\phi_g=1$).}\n\\end{figure}\n\n\n\n\\section{Discussion}\n\\label{sec-discussion}\n\\subsection{Limitations and speculations}\nThe linear stability analysis of this paper shows that, at least in principle,\nthe combination of viscous disk theory, radial drift of dust, and the negative\nfeedback of the dust on the viscosity, could lead to ring-shaped patterns in a\nprotoplanetary disk.\n\nThe linear growth rate depends on the size of the dust grains, or more\nprecisely: on their Stokes number. Depending on the prescription of the\nfeedback, the instability is inhibited for the very small Stokes numbers.  But\nfor Stokes numbers beyond a critical value, the growth rate increases with\nincreasing $\\mathrm{St}$. Around $\\mathrm{St}\\simeq 1$ the instability is\nsuppressed again. Fig.~\\ref{fig-gammalib-full-simple} shows the growth rates as\na function of $\\mathrm{St}$ for given wavelengths of the mode.\n\nNot surprisingly, the instability grows the quickest for the shortest wavelengths.\nThe shortest wavelength is expected to be the disk pressure scale height, which is\ntherefore expected to be the dominant mode.\n\nHowever, the feedback of the dust onto the viscosity of the gas is a\nsurface-area effect (dust grains removing free electrons and ions from the gas),\nso one should expect the feedback to be the strongest for the smallest\ngrains. In our model we did not include this effect: we took the same feedback\nrecipe (Eq.~\\ref{eq-alpha-param}) independent on grain size. We \nspeculate that if a disk contains a size distribution of dust, the smallest\ngrains with Stokes numbers still beyond the critical one, will be the ones\nthat drive the instability. Since the growth rate of the instability for such\ngrain sizes is substantially slower than the time a blob would be sheared out\ninto a ring (see Fig.~\\ref{fig-gammalib-full-simple}), the information about the\ngrowth of the instability can be communicated over the full $2\\pi$ azimuth of\nthe disk, so that a global ring is formed instead of a set of independent arcs.\n\nWith our model we cannot study what happens if the instability becomes\nnon-linear. Assuming we have a size distribution of dust grains, then, although\nonly the smaller grains drive the instability, also the larger grains will\nundergo density enhancements: they will do so even stronger than the\ninstability-driving smaller grains. Once the mode becomes so strong that rings\nof positive pressure gradient are produced, then the larger grains will\nget trapped. Turbulent mixing always leaks a few of these grains\nout of the traps, but on the whole, large grains would be trapped and produce\nlarge-amplitude rings \\revised{made from millimeter to centimeter size grains,}\nsimilar to what is seen with ALMA in many sources. \\revised{Our perturbation\n  analysis suggests that the shortest wavelengths grow the quickest. However,\n  viscous disk theory works on scales equal to or larger than the pressure\n  scale height. The spacing between the rings in the gas structure of the disk will therefore \n  be at least a pressure scale height. The large dust grains, however, could\n  conceivably get trapped in rings that are thinner than that.}\n\n\\revised{In this two-stage scenario (small grains triggering the rings, large\n  grains getting trapped) the rings have to be sustained. If the small grains\n  coagulate and become large, their ability to affect $\\alpha$ reduces, and the\n  rings may dissipate. Maybe this can be prevented through a bit of\n  fragmentation of the pebbles, producing fresh fine grained dust. Even for low\n  levels of turbulence the collision velocities of the pebbles may be relatively\n  high. The typical turbulent eddy velocity at the top of the Kolmogorov cascade\n  is $v_{\\mathrm{eddy}}=\\sqrt{\\alpha}c_s$.  With a temperature of, say, 100 K\n  one has $c_s=0.6\\,\\mathrm{km\/s}$. If the fragmentation velocity is 1 m\/s\n  \\citep[e.g.][]{2010A&A...513A..56G} one would need $\\alpha\\lesssim 3\\times\n  10^{-6}$ to prevent fragmentation. Anything above that would lead to the\n  production of small grains. It is therefore feasible that a sufficient amount\n  of small grains are continuously regenerated to keep the rings in place. On\n  the other hand, aggregates made up of icy grains are thought to be more\n  robust, and may fragment only at collision velocities of $\\sim\n  10\\,\\mathrm{m\/s}$, or even up to $\\sim 50\\,\\mathrm{m\/s}$, depending on\n  the size of the monomers of which they are made \\citep{2009ApJ...702.1490W}}\n\n\\revised{Dust aggregates are most likely porous or fractal. Large `pebbles'\n  may therefore still have rather large surface-to-mass ratios, and thus still\n  strongly affect the ionization degree of the disk. We would, however, also\n  observe them as if they were much smaller than they are, since also the\n  optical properties of such dust aggregates depend a lot on the surface-to-mass\n  ratio \\citep{2014A&A...568A..42K}. The `big grains' that we identify as\n  `big' due to their opacity slope at millimeter wavelengths therefore\n  presumably also have a relatively low surface-to-mass ratio, and thus have\n  little influence on the ionization degree of the disk. To have such big grains\n  arranged in rings, we really need this two-stage scenario, as the big grains\ncannot (according to our scenario) generate the rings themselves.}\n\n\\revised{There is, however, a big uncertainty with the model: the role of the vertical\nstructure. Small grains can be turbulently stirred to several pressure scale\nheights above the midplane, even for relatively low turbulent $\\alpha$. Is it\ntherefore still justified to assume that the wavelength of one pressure scale\nheight to be the strongest growing mode? Could it be that this would lead to\nsufficient radial smearing that larger wavelength modes dominate?\n\\citet{2011ApJ...742...65O} study the effect of the vertical structure on the\nviscosity of the disk. They conclude that the vertically averaged\nmagneto-turbulent viscosity only depends on the resistivity profile (and thereby\non the vertically averaged dust abundance) through three critical heights, and\nis largely insensitive to the details of the resistivity profile itself. This may mean\nthat the vertically averaged dust abundance has, in most parts of the disk, only\nlimited influence (S.~Okuzumi, priv.comm.). }\n\nMulti-wavelength\nobservations of the same sources can help answer these questions. For instance,\nfor TW Hydra both millimeter \\citep{2016ApJ...820L..40A} and H-band observations\n\\citep{2017ApJ...837..132V} exist. \\citet{2017ApJ...837..132V} study how the\nrings in the millimeter compare to the large scale rings in the H-band. Some\ncorrespondence is found, but overall the structures appear to be uncorrelated,\nwhich appears to argue against our model, at least for this source.\n\n\\subsection{On rings and the slowness of the instability}\n\\revised{As argued in this paper, for an instability to lead to ring-like structures\nrather than patchy\/clumpy structures in a disk, the instability has to be slower\nthan the shear. This is the case for the dust-driven viscous instability discussed\nin this paper. In hindsight this is not surprising, since the viscous time scale\nof the disk can be quite long. One can quantify this by considering a perturbation with\nradial width $W$ (i.e.~in our dimensionless form this is $W=\\lambda r$). If\nwe express $W$ in units of the pressure scale height, which is the narrowest\nviscous structures we can expect in the disk, we get}\n\\begin{equation}\nW=w H_p = w\\frac{c_s}{\\Omega_K}\\,,\n\\end{equation}\n\\revised{The viscous time scale for this perturbation is}\n\\begin{equation}\nt_{\\mathrm{visc}}=\\frac{W^2}{\\nu} = \\frac{w^2}{\\alpha\\Omega_K}\\,.\n\\end{equation}\n\\revised{The shear time (from Eq.~\\ref{eq-time-shear}) is}\n\\begin{equation}\nt_{\\mathrm{shear}} = \\frac{4\\pi}{3}\\frac{r}{wc_s}\\,.\n\\end{equation}\n\\revised{The condition for the instability to be slow enough then becomes}\n\\begin{equation}\n\\frac{t_{\\mathrm{visc}}}{t_{\\mathrm{shear}}} = \\frac{3}{4\\pi}\\frac{w^2}{\\alpha}\\frac{H_p}{r}\\gg 1\\,.\n\\end{equation}\n\\revised{The smallest possible value for $w$ is 1, which is also the fastest\n  growing mode. This shows that if $\\alpha$ is much smaller than the disk's\n  dimensionless thickness (aspect ratio), then the instability (if it exists) is\n  slow enough to create rings instead of patches. For a typical disk\n  $H_p\/r\\simeq 0.05\\cdots 0.1$ this means that $\\alpha\\ll 10^{-2}$ for the\n  instability to be slow enough.  Therefore we can conclude that, if the rings\n  seen in numerous disks are due to any form of viscous instability, the\n  viscosity of the disk must be substantially lower than the canonical value of\n  $10^{-2}$, or the instability must be slowed down by an even slower process\n  such as dust drift of small enough dust grains.}\n\n\n\\subsection{Comparison to earlier work}\nThe ring-instability we have investigated in this paper appears to have a\nrelation to the ring-instability found by \\citet{2005MNRAS.362..361W}. In their\nmodel the disk had an active surface layer and a passive (`dead') midplane\nlayer. If gas would accumulate at some radius, the surface density of the active\nlayer stays the same, but that of the dead layer increases. In a vertically\naveraged sense the viscosity thus gets reduced. This is mathematically identical\nto our case of $\\phi_d=-1$ and $\\phi_g=0$ (prescription 1,\nEqs.~\\ref{eq-alpha-param}, \\ref{eq-case-1}), with $\\mathrm{St}=0$. In our model,\nhowever, we do not find an instability for these parameters. However,\n\\citet{2005MNRAS.362..361W} include the effect of the perturbation on the disk\nmidplane temperature, which we do not. In our case we indeed get the instability\nif $\\phi_d<-1$.\n\n\\revised{\\citet{2015ApJ...815...99H} also studied the behavior of the\n  two-layered disk model. They find that if the effective $\\alpha$ of the\n  two-layered disk is simply an average of the active and dead layers (weighted\n  by their respective surface densities), then the disk remains stable. Our\n  model with $\\phi_d=-1$ and $\\phi_g=0$ (prescription 1) and $\\mathrm{St}=0$ (no\n  dust drift) confirms this. When they apply a more sophisticated effective\n  $\\alpha$ recipe, based on \\citet{2011ApJ...742...65O}, they find that the disk\n  becomes unstable near the dead zone outer edge, because that is where the\n  dependence of $\\alpha$ on $\\Sigma$ is the steepest. Our model confirms this,\n  because the more sophisticated $\\alpha$ recipe has a steeper dependence of\n  $\\alpha$ on $\\Sigma$, which would amount, in our work, to $\\phi_d<-1$ (again\n  taking $\\phi_g=0$ and $\\mathrm{St}=0$), which we confirm to lead to\n  instability. Our model is thus consistent with the earlier work by\n  \\citet{2015ApJ...815...99H}.  But by including dust drift our model is more\n  general.}\n\n\\revised{\\citet{2015A&A...574A..68F} perform 3-D full disk non-ideal MHD models\n  and find ringlike structures, too, although rather wide ones and only two of\n  them. But like \\citet{2015ApJ...815...99H}, this is unrelated to dust drift.}\n\n\\revised{Our dust-drift induced viscous instability is, however, very similar to\n  the instability found by \\cite{2011IAUS..274...50J}. While the analysis in\n  that paper is locally more detailed (including radial and azimuthal motions),\n  our linear stability analysis includes the radial gradients and the global\n  cylindrical geometry terms an is thus not just a local analysis. Furthermore\n  our analysis includes the radial drift, as well as the turbulent diffusion,\n  both of which play a key role in the mechanism. Moreover, we argue that the\n  slowness of the instability is critical in getting grand-design rings\n  rather than chaotic arc-shaped structures.}\n\n\\revised{The analysis in this paper} is\nby no means a proof of the feasibility of this scenario. It will require\ndetailed 2-D\/3-D viscous hydrodynamic disk modeling, and comparisons to\nobservations, to test this scenario.\n\n\\section{Conclusion}\n\\revised{In this paper we} show that it is conceivable that the combination\nof viscous disk theory, radial drift of dust, and the negative feedback of the\ndust on the viscosity, can produce (or at least trigger the formation of)\nring-shaped patterns in protoplanetary disks similar to what is seen in\nprotoplanetary disks at millimeter and optical\/near-infrared wavelengths. \n\\revised{From our present analysis we conclude:}\n\\begin{enumerate}\n\\item \\revised{Even without dust drift, if $\\partial \\ln\\alpha\/\\partial\\ln\\Sigma<-1$,\n  the disk is prone to the viscous ring instability. This is a conclusion\n  in agreement with work by \\citet{2015ApJ...815...99H}.}\n\\item \\revised{When dust grains are large enough to start drifting, yet small enough to\n  have a substantial influence on the viscosity of the disk (through their\n  ability to capture free electrons and ions from the gas), dust drift tends\n  to cause a feedback loop on the disk viscosity, leading to dust-rich regions\n  of low viscosity and dust-poor regions of high viscosity. In this way\n  dust drift can trigger the viscous instability even when the disk would\n  be stable otherwise ($\\partial \\ln\\alpha\/\\partial\\ln\\Sigma\\ge -1$). These\n  findings are consistent with \\cite{2011IAUS..274...50J}, and generalize them\n  to global disk accretion with generalized viscosity description.}\n\\item \\revised{The radial drift due to the global pressure gradient in the disk\n  does not suppress the instability for small grains, but does so for grains\n  with Stokes number near unity. The ring instability (viscous instability) must\n  therefore be driven by small enough grains. This also agrees with the issue\n  that small grains more easily affect the viscosity of the disk, because due to\n  their larger surface-to-mass ratio, they more easily capture free electrons\nand ions. }\n\\item \\revised{For grand-design rings to form, such as those observed in real\n  protoplanetary disks, rather than pseudo-random patchy structures, the\n  growth rate of the instability must be slower than the shear-out time scale.\n  Our analysis shows that this is generally the case, if the instability is\n  driven by small enough grains and\/or if the viscous $\\alpha\\ll 10^{-2}$.}\n\\item \\revised{If the grains are too small, they hardly drift. Whether\n  the disk is then stable or not depends strongly on the viscosity recipe.\n  We have identified two cases: case 1 in which the absolute value of the\n  dust density determines the viscous $\\alpha$ and case 2 in which the \n    ratio of dust-to-gas density determines the viscous $\\alpha$. For very\n  small grains, the disk becomes stable for case 2, but may still become\n  unstable for case 1, if the dependence of $\\alpha$ on $1\/\\Sigma$ is steep\n  enough.}\n\\item \\revised{Observations seem to show that the rings seen at millimeter\n  wavelengths are populated by relatively large rains. Since the viscous\n  ring instability seems to be driven by small grains, this may seem inconsistent\n  at first. We suggest that the initial rings are created by the viscous\n  instability, which then produces strong enough dust traps that the\n  larger grains get trapped and produce the ALMA images observed.}\n\\end{enumerate}\n\n\n\n\\begin{acknowledgements}\n  This research was supported by the Munich Institute for Astro- and Particle\n  Physics (MIAPP) of the DFG cluster of excellence ``Origin and Structure of the\n  Universe''. We thank Satoshi Okuzumi for interesting discussions regarding the\n  effect of the vertical structure. We thank the anonymous referee for insightful\n  comments which helped improve the manuscript.\n\\end{acknowledgements}\n\n\n\\begingroup\n\\bibliographystyle{aa}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
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+{"text":"\\section{Introduction}\n\\label{Sec:Intro}\nConsider a dynamic network in which nodes come and go, change abruptly or evolve, alone or in communities, and form connections accordingly. Our goal is to find a vector representation, $\\hat{\\+Y}_i^{(t)} \\in \\mathbb{R}^d$, for every node $i$ and time $t$, which could be used for a diversity of downstream analyses, such as clustering, time series analysis, classification, model selection and more. This problem is known as dynamic (or evolutionary) network (or graph) embedding, and a great number of scalable and empirically successful techniques have been put forward, with recent surveys by \\cite{xie2020survey,xue2021dynamic}. We consider, among these, a subset about which it is reasonable to try to establish a certain statistical guarantee.\n\nThe novelty of this paper is \\emph{not} to propose a new procedure. Instead, it is to demonstrate that an existing procedure, unfolded adjacency spectral embedding (UASE) \\cite{jonesrubindelanchy2021MRDPG}, has two important stability properties. Given a sequence of symmetric adjacency matrices $\\+A^{(1)}, \\ldots, \\+A^{(T)} \\in \\{0,1\\}^{n \\times n}$, where $\\+A^{(t)}_{ij} = 1$ if nodes $i$ and $j$ form an edge at time $t$, UASE computes the rank $d$ matrix factorisation of $\\+A := (\\+A^{(1)}|\\cdots|\\+A^{(T)})$ to obtain $\\+A  \\approx \\hat{\\+X} \\hat{\\+Y}^\\top$ using the singular value decomposition (precise details later). The matrix $\\hat{\\+Y} \\in \\mathbb{R}^{nT \\times d}$ contains, as rows, the desired representations  $\\hat{\\+Y}_1^{(1)}, \\ldots,\\hat{\\+Y}_n^{(1)}, \\ldots, \\hat{\\+Y}_1^{(T)}, \\ldots,\\hat{\\+Y}_n^{(T)}.$\n\n\nThe original motivation for UASE was to analyse multilayer (or multiplex) graphs under an appropriate extension of the random dot product graph model \\cite{jonesrubindelanchy2021MRDPG}. To evaluate UASE and other procedures on the task of dynamic network embedding, we instead consider the dynamic latent position model\n\\begin{align}\n\t\\+A^{(t)}_{ij} \\overset{ind}{\\sim} \\mathrm{Bernoulli}\\left(f\\left\\{\\+Z^{(t)}_i,\\+Z^{(t)}_j\\right\\}\\right), \\label{eq:latent_position_model}\n\\end{align}\nfor $1 \\leq i < j \\leq n$, $t \\in [T]$, where $\\+Z_i^{(t)} \\in \\mathbb{R}^k$ represents the unknown position of node $i$ at time $t$, and $f: \\mathbb{R}^{k} \\times \\mathbb{R}^k \\rightarrow [0,1]$ is a symmetric function. \n\nThis model is well-established \\cite{sarkar2005dynamic,lee2011latent,hoff2011hierarchical,hoff2011separable,robinson2012detecting,lee2013latent,durante2014nonparametric,sewell2015latent,friel2016interlocking,durante2017bayesian}, with recent reviews by \\cite{kim2018review} and \\cite{turnbull2020advancements}, and inference usually proceeds on the basis of a parametric model for $f$ (e.g. logistic in the latent position distance \\cite{sarkar2005dynamic}) and for the dynamics of $\\+Z_i^{(t)}$ (e.g. a Markov process \\cite{sarkar2005dynamic}). The model also includes the dynamic degree-corrected, mixed-membership and standard stochastic block models as special cases, which were studied in \\cite{xing2010state,yang2011detecting,ho2011evolving,liu2014persistent,xu2014dynamic,xu2015stochastic,matias2015statistical,bhattacharyya2018spectral,pensky2019spectral,keriven2020sparse}.\n\nTo make statistical sense of UASE under this latent position model, we must somehow connect its output $\\hat{\\+Y}_i^{(t)}$ to $\\+Z_i^{(t)}$. To this end we construct a canonical representative of $\\+Z_i^{(t)}$, denoted $\\+Y_i^{(t)}$, that UASE can be seen to estimate. Although we make some regularity assumptions on $f$ and the $\\+Z_i^{(t)}$, they are not modelled in an explicit, parametric way, and UASE can clearly be used in practice without having a specific model in mind. For example, we do not make a Markovian assumption on the evolution of $\\+Z_i^{(t)}$ and UASE can be used to uncover periodic behaviours. \n\n\nThe key purpose of imposing a dynamic latent position model is to allow us to put down certain embedding stability requirements. Using this framework, we can define precisely what we mean by two nodes, $i$ and $j$, behaving ``similarly'' at times $s$ and $t$ respectively. In such cases, ideally we would have $\\hat{\\+Y}_i^{(s)} \\approx\\hat{\\+Y}_j^{(t)}$. Two special cases are: to assign the same position, up to noise, to nodes behaving similarly at a given time (cross-sectional stability) and a constant position, up to noise, to a single node behaving similarly across different times (longitudinal stability).\n\n\nTo achieve both cross-sectional and longitudinal stability is generally elusive. We show that two plausible alternatives, omnibus \\cite{levin2017central} and independent embedding of each $\\+A^{(t)}$, alternately exhibit one form of stability and not the other. More generally, we find existing procedures \\cite{chi2007evolutionary,lin2008facetnet,scheinerman2010modeling,dunlavy2011temporal,zhu2016scalable,deng2016latent,liu2018global,chen2018exploiting,bhattacharyya2018spectral,pensky2019spectral,passino2019link,keriven2020sparse} tend to trade one type of stability off against the other, e.g. via user-specified cost functions. As a side-note, it could be observed that omnibus embedding is not being evaluated on a task for which it was designed, since in the theory of \\cite{levin2017central} the graphs are identically distributed. Because the technique is so different from the others, we still feel it makes an interesting addition.\n\nOur central contribution is to prove that UASE asymptotically provides both longitudinal and cross-sectional stability: for two nodes, $i$ and $j$, behaving similarly at times $s$ and $t$ respectively, we have $\\hat{\\+Y}_i^{(s)} \\approx\\hat{\\+Y}_j^{(t)}$ and, moreover, $\\hat{\\+Y}_i^{(s)}$ and $\\hat{\\+Y}_j^{(t)}$ have asymptotically equal error distribution. We emphasise that these properties hold without requiring any sort of global stability  --- the network could vary wildly over time but certain nodes still stay fixed. In the asymptotic regime considered, we have $n \\rightarrow \\infty$, but $T$ fixed so that, for example, our results are relevant to the case of two  large graphs. The alternative regime where $T \\rightarrow \\infty$ grows but $n$ is fixed is not easily handled by existing theory and to provide constant updates to UASE (or omnibus embedding) in a streaming context presents significant computational challenges.\n\n\n\nThe remainder of this article is structured as follows. Section~\\ref{Sec:Example} gives a pedagogical example demonstrating the cross-sectional and longitudinal stability of UASE in a two-step dynamic stochastic block model, while highlighting the instability of omnibus and independent spectral embedding. In Section~\\ref{Sec:Setup}, we prove a central limit theorem for UASE under a dynamic latent position model, and demonstrate that the distribution satisfies both stability conditions. In Section~\\ref{Sec:Comp}, we review the stability of other dynamic network embedding procedures.\nSection~\\ref{Sec:Data} presents an example of UASE applied to a dynamic network of social interactions in a French primary school, with a dynamic community detection example given in the main text and a further classification example provided in the Appendix. Section~\\ref{Sec:Concs} concludes.\n\n\n\\section{Motivating example}\n\\label{Sec:Example}\nSuppose it is of interest to uncover dynamic community structure, including communities changing, merging or splitting. The dynamic stochastic block model \\cite{yang2011detecting,xu2014dynamic} provides a simple explicit model for this, in which two nodes connect at a certain point in time with probability only dependent on their current community membership. Suppose that at times 1 and 2, we have the following inter-community link probability matrices,\n\\begin{equation*}\n    \\+B^{(1)} = \\left(\n    \t\\begin{matrix}\n     \t0.08 & 0.02 & 0.18 & 0.10 \\\\\n     \t0.02 & 0.20 & 0.04 & 0.10 \\\\\n     \t0.18 & 0.04 & 0.02 & 0.02 \\\\\n     \t0.10 & 0.10 & 0.02 & 0.06\n     \\end{matrix} \\right), \\quad\n    \\+B^{(2)} = \\left(\n        \\begin{matrix}\n     \t0.16 & 0.16 & 0.04 & 0.10 \\\\\n     \t0.16 & 0.16 & 0.04 & 0.10 \\\\\n     \t0.04 & 0.04 & 0.09 & 0.02 \\\\\n     \t0.10 & 0.10 & 0.02 & 0.06\n     \\end{matrix} \\right).\n\\end{equation*}\nAt time 1 there are four communities present, for example, a node of community 1 connects with a node of community 3 with probability 0.18. At time 2, this matrix changes so that communities 1 and 2 have merged, community 3 has moved, whereas community 4 is unchanged. For simplicity, in this example, the community membership of each node is fixed across time-steps.\n\nWe simulate a dynamic network from this model over these two time steps, on $n = 1000$ nodes, equally divided among the four communities and investigate the results of three embedding techniques: UASE, omnibus, and independent spectral embedding, displayed in Figure~\\ref{Fig:Embed_Comparison}. Note that the different techniques produce embeddings of different dimensions; UASE embeds into $d=4$ dimensions, omnibus embedding $\\tilde d=7$, while independent spectral embedding has $d_1=4$ and $d_2=3$. For visualisation, we show the leading two dimensions for each embedding. Given the dynamics described above, we contend that the following properties would be desirable:\n\\begin{enumerate}\n\\item \\emph{Cross-sectional stability}: The embeddings for communities 1 and 2 at time 2 are close.\n\\item \\emph{Longitudinal stability}: The embeddings for community 4 at times 1 and 2 are close.\n\\end{enumerate}\n\\begin{figure}[ht]\n\t\\centering\n\t\\includegraphics[width=0.80\\textwidth]{Embedding_Comparison.pdf}\n\t\\caption{First two dimensions of the embeddings for the adjacency matrices $\\+A^{(1)}$ and $\\+A^{(2)}$ using three different techniques: UASE, omnibus and separate embedding. The points are coloured according to true community membership, with the black dots showing the fitted community centroid and the ellipses a fitted 95\\% level Gaussian contour.}\n\t\\label{Fig:Embed_Comparison}\n\\end{figure}\nFigure~\\ref{Fig:Embed_Comparison} illustrates that UASE has both properties: the blue and orange point clouds merge at time 2, and the red point cloud has the same location \\emph{and} shape over the two time points. On the other hand, omnibus embedding only has longitudinal stability (the blue and orange point clouds don't merge at time 2), whereas independent spectral embedding only has cross-sectional stability (the red point cloud is at different locations over the two time points).\n\n\\section{Theoretical background and results}\n\\label{Sec:Setup}\nWe consider a sequence of random graphs distributed according to a dynamic latent position model, in which the latent position sequences $(\\+Z^{(t)}_i)_{t \\in [T]}$ (where we use the shorthand $[T] = \\{1,\\ldots,T\\}$) are independent of each other, and identically distributed according to a joint distribution $\\mathcal{F}$ on $\\mathcal{Z}^T$, for a bounded subset $\\mathcal{Z}$ of $\\mathbb{R}^k$. We emphasise that for a fixed $i$ the latent positions $\\+Z^{(t)}_i$ and $\\+Z^{(t')}_i$ may have different distributions --- we are imposing exchangeability over the nodes (invariance to node labelling), but not over time. \n\nBy extending the function $f$ to be zero outside of its domain of definition, we may view it as an element of $L^2(\\mathbb{R}^k \\times \\mathbb{R}^k)$, and consequently may define a compact, self-adjoint operator $A$ on $L^2(\\mathbb{R}^k)$ by setting \n\\begin{align}\n    Ag(x) = \\int_{\\mathbb{R}^k} f(x,y)g(y)dy\n\\end{align}\nfor all $g \\in L^2(\\mathbb{R}^k)$.  The operator $A$ has a---possibly infinite---sequence of non-zero eigenvalues $\\lambda_1 \\geq \\lambda_2 \\geq \\ldots$ with corresponding orthonormal eigenfunctions $u_1, u_2, \\ldots \\in L^2(\\mathbb{R}^k)$, such that $Au_j = \\lambda_ju_j$ (for further details, see for example \\cite{rubindelanchy2021manifold}).  We shall make the simplifying assumption that $A$ has a \\emph{finite} number of non-zero eigenvalues, in which case $f$ admits a canonical eigendecomposition \n\\begin{align}\n\tf(\\+x,\\+y) = \\sum_{i=1}^D \\lambda_i u_i(\\+x)u_i(\\+y),\n\\end{align}\nassumed to hold everywhere, where after relabelling we may assume that $|\\lambda_1| \\geq \\ldots \\geq |\\lambda_D|$.  \n\nSeveral families of functions satisfy the finite rank assumption $D < \\infty$, such as the multivariate polynomials \\cite{rubindelanchy2021manifold}. Moreover, several existing statistical models can be written as dynamic latent position network models in which $D < \\infty$, including the dynamic mixed membership, degree-corrected, and standard stochastic block models. To assume $D < \\infty$, more generally, is tantamount to a claim that, for large $n$, $\\+A^{(t)}$ has `low' approximate rank: an overwhelming proportion of its eigenvalues are close to zero. Large matrices with low approximate rank are routinely encountered across numerous disciplines, and the study \\cite{udell2019datamatrices} provides a hypothesis for this ``puzzling'' general observation. However, given a real network, we might reject the hypothesis that $f$ has low rank (we must then also reject any type of stochastic block model), for example on the basis of triangle counts \\cite{seshadhri2020triangles}. In such a setting, we anticipate that UASE is still consistent and stable if $d$ is allowed to grow sufficiently slowly with $n$ and there exist asymptotic results for adjacency spectral embedding, for the single graph case, showing convergence in Wasserstein distance under assumptions on eigenvalue decay which can be related to the smoothness of $f$ \\cite{lei2021network}. However, even if we could obtain such results for UASE, they would not be as powerful as those we present here for the finite rank case, where we show uniform consistency with asymptotic Gaussian error.\n\n\\begin{theorem}\\label{TRDPG_to_MRDPG} The adjacency matrices $\\+A^{(1)}, \\ldots, \\+A^{(T)}$ are jointly distributed according to a multilayer random dot product graph model.\n\\end{theorem}\n\nThe multilayer random dot product graph model (MRDPG, see \\cite{jonesrubindelanchy2021MRDPG}) is a multi-graph analogue of the generalised random dot product graph model \\cite{rubindelanchyetal2020GRDPG}, and is characterised by the existence of matrices $\\+\\Lambda^{(t)} \\in \\mathbb{R}^{d \\times d_t}$ and random matrices $\\+X \\in \\mathbb{R}^{n \\times d}$ and $\\+Y^{(t)} \\in \\mathbb{R}^{n \\times d_t}$ (generated according to some joint distribution $\\mathcal{G}$) such that \n\\begin{align}\n    \\+A^{(t)}_{ij} \\overset{ind}{\\sim} \\mathrm{Bernoulli}\\bigl(\\+X_i\\+\\Lambda^{(t)}\\+Y^{(t)\\top}_j\\bigr)\n\\end{align}\nfor each $t \\in [T]$ and $i,j \\in [n]$, where $\\+X_i$ and $\\+Y^{(t)}_j$ denote the $i$th and $j$th rows of $\\+X$ and $\\+Y^{(t)}$ respectively. \n\nWe refer the reader to the supplemental material for full details of the proof of Theorem \\ref{TRDPG_to_MRDPG}, but note that given knowledge of the function $f$ and the underlying distribution $\\mathcal{F}$ we can construct explicit maps $\\varphi: \\mathbb{R}^{Tk} \\to \\mathbb{R}^d$ and $\\varphi_t: \\mathbb{R}^k \\to \\mathbb{R}^{d_t}$, producing row vectors, and matrices $\\+\\Lambda^{(t)} \\in \\mathbb{R}^{d \\times d_t}$ such that \n\\begin{align}\n    f(\\+Z^{(t)}_i,\\+Z^{(t)}_j) = \\+X_i \\+\\Lambda^{(t)} \\+Y_j^{(t)\\top},\n\\end{align}\nwhere $\\+X_i = \\varphi(\\+Z_i), \\+Y^{(t)}_j = \\varphi_t(\\+Z_j^{(t)})$ and $\\+Z_i = (\\+Z^{(1)}_i|\\cdots|\\+Z^{(T)}_i) \\in \\mathbb{R}^{Tk}$, for each $t \\in [T]$ and $i, j \\in [n]$. Consequently, each Gram matrix \n\\begin{align}\n    \\+P^{(t)} = \\bigl(f(\\+Z^{(t)}_i,\\+Z^{(t)}_j)\\bigr)_{i,j \\in [n]}\n\\end{align}\nadmits a factorisation into a product of low-rank matrices, in which the matrix whose rows are the vectors $\\varphi(\\+Z_i)$ appears as a common factor.  The dimensions $d_t$ and $d$ are precisely the ranks of the matrices $\\+P^{(t)}$ and their concatenation $\\+P = (\\+P^{(1)}|\\cdots|\\+P^{(T)})$ respectively.  In the theory that follows we will assume that the dimension $d$ is known and fixed, whereas in practice we would usually have to estimate it (for example by using profile likelihood \\cite{zhu2006automatic}). \n\nWe can extend our model to incorporate a range of sparsity regimes by scaling the function $f$ by a sparsity factor $\\rho_n$, which we assume is either constant and equal to $1$, or else tends to zero as $n$ grows, corresponding to dense and sparse regimes respectively. When this factor is present, the maps $\\varphi$ and $\\varphi_t$ are scaled by a factor of $\\rho_n^{1\/2}$.  \n\nRealising our model as an MRDPG allows us to make precise statements about the asymptotic behaviour of the point clouds obtained through UASE.  In particular, it is the existence of a common factor in the decomposition of each of the Gram matrices $\\+P^{(t)}$ that gives rise to the stability properties previously demonstrated in the embeddings $\\hat{\\+Y}^{(t)}$, as this matrix in a sense acts as an anchor for the individual point clouds.\n\nIn \\cite{jonesrubindelanchy2021MRDPG} UASE is used to obtain \\emph{two} multi-graph embeddings; the algorithm below retains only one --- the `dynamic' component.\n\\vspace*{-0.1cm}\n\\begin{algorithm}[H]\n \\caption{Unfolded adjacency spectral embedding for dynamic networks}\\label{alg:spec}\n\\begin{algorithmic}[1]\n  \\Statex \\textbf{input} symmetric adjacency matrices $\\+A^{(1)}, \\ldots, \\+A^{(T)} \\in \\{0,1\\}^{n \\times n}$, embedding dimension $d$\n  \\State Form the matrix $\\+A = (\\+A^{(1)}|\\cdots|\\+A^{(T)}) \\in \\{0,1\\}^{n \\times Tn}$ (column concatenation)\n  \\State Compute the truncated singular value decomposition $\\+U_\\+A\\+\\Sigma_\\+A\\+V_\\+A^\\top$ of $\\+A$, where $\\+\\Sigma_\\+A$ contains the $d$ largest singular values of $\\+A$, and $\\+U_\\+A, \\+V_\\+A$ the corresponding left and right singular vectors\n  \\State Compute the right embedding $\\hat{\\+Y} = \\+V_\\+A\\+\\Sigma_\\+A^{1\/2} \\in \\mathbb{R}^{Tn \\times d}$ and create sub-embeddings $\\hat{\\+Y}^{(t)} \\in \\mathbb{R}^{n \\times d}$ where $\\hat{\\+Y} = (\\hat{\\+Y}^{(1)};\\ldots;\\hat{\\+Y}^{(T)})$ (row concatenation)\n  \\Statex \\Return node embeddings for each time period $\\hat{\\+Y}^{(1)},\\ldots,\\hat{\\+Y}^{(T)}$\n\\end{algorithmic}\n\\end{algorithm}\n\\vspace*{-0.1cm}\n\nReplacing $\\+A$ with $\\+P$ in this construction yields the \\emph{noise-free} embeddings $\\tilde{\\+Y}^{(t)}$, whose rows are known to be linear transformations of the vectors $\\varphi_t(\\+Z^{(t)}_i)$ (see the supplemental material for further details).  A desirable property of UASE is that since the matrices $\\+A^{(t)}$ follow an MRDPG model there exist known asymptotic distributional results for the  embeddings $\\hat{\\+Y}^{(t)}$.  In order to ensure the validity of these results, we will make the assumption that the sparsity factor $\\rho_n$ satisfies $\\rho_n = \\omega(n^{-1} \\log^c(n))$ for some universal constant $c > 1$.\n\nIn the results to follow, UASE is shown to be consistent and stable in a uniform sense, i.e. the maximum error of any position estimate goes to zero, under the assumption that the average network degree grows polylogarithmically in $n$. To achieve this for less than logarithmic growth would be impossible, by any algorithm, because it would violate the information-theoretic sparsity limit for perfect community recovery under the stochastic block model \\cite{abbe2017sbm}. In practice this means that the embedding will have high variance when the graphs have few edges. Several approaches have been proposed to make single graph embeddings more robust (e.g. to sparsity or heterogeneous degrees), such as based on the regularised Laplacian \\cite{amini2013pseudo} or non-backtracking matrices \\cite{krzakala2013spectral}, but it is an open and interesting question how to extend them to the dynamic graph setting to achieve both cross-sectional and longitudinal stability.\n\nThe first of our distributional results states that after applying an orthogonal transformation---which leaves the structure of the resulting point cloud intact---the embedded points $\\hat{\\+Y}^{(t)}_i$ converge in the Euclidean norm to the noise-free embedded points $\\tilde{\\+Y}^{(t)}_i$ as the graph size grows:\n\n\\begin{proposition}\\label{consistency} There exists a sequence of orthogonal matrices $\\tilde{\\+W} \\in \\mathrm{O}(d)$ such that \n\\begin{align}\n \\max_{i \\in \\{1,\\ldots,n\\}} \\bigl\\|\\hat{\\+Y}^{(t)}_i \\tilde{\\+W}- \\tilde{\\+Y}^{(t)}_i\\bigr\\| = \\mathrm{O}\\Bigl(\\tfrac{\\log^{1\/2}(n)}{\\rho_n^{1\/2}n^{1\/2}}\\Bigr)\n\\end{align} \nwith high probability for each $t$.\n\\end{proposition}\n\nThe matrices $\\tilde{\\+W}$ are unidentifiable in practice, but are defined to be the solution to the one-mode orthogonal Procrustes problem\n\\begin{align}\n\t\\tilde{\\+W} = \\argmin_{\\+Q \\in \\mathrm{O}(d)} \\|\\+U_\\+A \\+Q - \\+U_\\+P\\|_F^2 + \\|\\+V_\\+A \\+Q- \\+V_\\+P\\|_F^2,\n\\end{align} where $\\lVert \\cdot \\rVert^2_F$ denotes the Frobenius norm. We emphasise that the matrix $\\tilde{\\+W}$ is \\emph{the same} for each embedding, and so similar behaviour in the noise-free embeddings $\\tilde{\\+Y}^{(t)}$ is captured by UASE.\n\nOur second result states that after applying a \\emph{second} orthogonal transformation the above error converges in distribution to a fixed multivariate Gaussian distribution:\n\n\\begin{proposition}\\label{CLT} Let $\\zeta = (\\zeta_1|\\cdots|\\zeta_T) \\sim \\mathcal{F}$, and for $\\+z \\in \\mathcal{Z}$ define\n\\begin{align}\n\t\\+\\Sigma_t(\\+z) = \\left\\{\\begin{array}{cc}\\mathbb{E}_\\zeta\\Bigl[f(\\+z,\\zeta_t)\\bigl(1-f(\\+z,\\zeta_t)\\bigr) \\cdot \\varphi(\\zeta)^\\top\\varphi(\\zeta)\\Bigr]&\\mathrm{if~}\\rho_n = 1\\\\\n\t\\mathbb{E}_\\zeta\\Bigl[f(\\+z,\\zeta_t) \\cdot \\varphi(\\zeta)^\\top\\varphi(\\zeta)\\Bigr]&\\mathrm{if~}\\rho_n \\to 0.\\end{array}\\right..\n\\end{align} \nThen there exists a deterministic matrix $\\+R_* \\in \\mathbb{R}^{d \\times d}$ and a sequence of orthogonal matrices $\\+W \\in \\mathrm{O}(d)$ such that, given $\\+z \\in \\mathcal{Z}$, for all $\\+y \\in \\mathbb{R}^d$ and for any fixed $i \\in [n]$ and $t \\in [T]$, \n\\begin{align}\n\t\\mathbb{P}\\Bigl(n^{1\/2}(\\hat{\\+Y}^{(t)}_i  \\tilde{\\+W} - \\tilde{\\+Y}^{(t)}_i)\\+W \\leq \\+y ~|~ \\+Z^{(t)}_i = \\+z\\Bigr) \\to \\Phi\\bigl(\\+y,\\+R_*\\+\\Sigma_t(\\+z)\\+R_*^\\top\\bigr).\n\\end{align}\n\\end{proposition}\n\nAs in our previous results, the matrices $\\+W$ and $\\+R_*$ can be explicitly constructed given knowledge of the underlying function $f$ and distribution $\\mathcal{F}$ (again, we defer full details to the supplemental material). Note that as in Proposition \\ref{consistency}, both constructed matrices are common to \\emph{all} embeddings.\n\nWe can now demonstrate one of the key advantages that UASE holds over other embedding methods, namely that \\emph{UASE exhibits both cross-sectional and longitudinal stability}, in a sense that we shall now define.  We say that two space-time positions $(\\+z,t)$ and $(\\+z',t')$ are \\emph{exchangeable} if $f(\\+z,\\zeta_t) = f(\\+z',\\zeta_{t'})$ with probability one, where $\\zeta = (\\zeta_1|\\cdots|\\zeta_T) \\sim \\mathcal{F}$, and that the positions are \\emph{exchangeable up to degree} if $f(\\+z,\\zeta_t) = \\alpha f(\\+z',\\zeta_{t'})$ for some $\\alpha >0$.  Equivalently, $(\\+z,t)$ and $(\\+z',t')$ are exchangeable if conditional on $\\+Z^{(t)}_i = \\+z$ and $\\+Z^{(t')}_j = \\+z'$ the $i$th row of $\\+P^{(t)}$ and $j$th row of $\\+P^{(t')}$ are equal with probability one.\n\n\\begin{definition}\nGiven a generic method for dynamic network embedding, with output denoted $(\\hat{\\+Z}^{(t)}_i)_{i \\in [n]; t \\in [T]}$, define the following stability properties:\n\\begin{enumerate}\n    \\item \\emph{Cross-sectional stability:} Given exchangeable $(\\+z,t)$ and $(\\+z',t)$, $\\hat{\\+Z}^{(t)}_i$ and $\\hat{\\+Z}^{(t)}_j$ are asymptotically equal, with identical error distribution, conditional on $\\+Z^{(t)}_i = \\+z$ and $\\+Z^{(t)}_j = \\+z'$.\n    \\item \\emph{Longitudinal stability:} Given exchangeable $(\\+z,t)$ and $(\\+z,t')$, $\\hat{\\+Z}^{(t)}_i$ and $\\hat{\\+Z}^{(t')}_i$ are asymptotically equal, with identical error distribution, conditional on\n    $\\+Z^{(t)}_i = \\+Z^{(t')}_i = \\+z$.\n\\end{enumerate}\n\\end{definition}\n\n\nThe following result then shows that UASE exhibits both types of stability:\n\n\\begin{corollary}\\label{stability} Conditional on $\\+Z^{(t)}_i = \\+z$ and $\\+Z^{(t')}_j = \\+z'$, the following properties hold:\n\\begin{enumerate}\n    \\item If $(\\+z,t)$ and $(\\+z',t')$ are exchangeable then $\\hat{\\+Y}^{(t)}_i$ and $\\hat{\\+Y}^{(t')}_j$ are asymptotically equal, with identical error distribution.\n    \\item If $(\\+z,t)$ and $(\\+z',t')$ are exchangeable up to degree then $\\hat{\\+Y}^{(t)}_i$ and $\\alpha\\hat{\\+Y}^{(t')}_j$ are asymptotically equal and, under a sparse regime, their error distributions are equal up to scale, satisfying $\\+\\Sigma_t(\\+z) = \\alpha\\+\\Sigma_{t'}(\\+z')$. \n\\end{enumerate}\n\\end{corollary}\n\n\nWe can gain insight into our theoretical results by applying them in the context of common statistical models. Under the dynamic stochastic block model of Section~\\ref{Sec:Example}, a pair $(\\+z,t)$ and $(\\+z',t')$ are exchangeable if and only if the corresponding rows of $\\+B^{(t)}$ and $\\+B^{(t')}$ are identical.  Proposition \\ref{CLT} then predicts that the point cloud obtained via UASE should decompose into a finite number of \\emph{Gaussian} clusters, as we observe in Figure \\ref{Fig:Embed_Comparison}.  Moreover, when combined with Corollary \\ref{stability} the equality of the fourth rows of $\\+B^{(1)}$ and $\\+B^{(2)}$ implies that we should expect \\emph{identical} clusters (centre and shape) corresponding to the fourth community at both time points (indicating longitudinal stability) and similarly the equality of the first and second rows of $\\+B^{(2)}$ tells us that the communities should be indistinguishable at the second time point (indicating cross-sectional stability), behaviours we observe in Figure \\ref{Fig:Embed_Comparison}. Under degree-correction \\cite{karrer2011stochastic,liu2014persistent}, Corollary \\ref{stability} indicates that we should at least observe cross-sectional and longitudinal stability along `rays' representing communities, a behaviour that is exhibited in Figure \\ref{Fig:Primary_UASE}.\n\n\\section{Comparison}\n\\label{Sec:Comp}\nIn this section we investigate the stability properties of alternatives to UASE. Table~\\ref{tab:Algorithm_Comp} shows the stability of the three embedding algorithms described in Section~\\ref{Sec:Example} and two wider classes of algorithms, described below. \nFor alternatives to UASE, it will be considered sufficient to establish whether an embedding is stable when applied to the Gram matrices $\\+P^{(1)}, \\ldots, \\+P^{(T)}$. A method found to be unstable in this noise-free condition is not expected to be stable when the matrices are replaced by their noisy observations $\\+A^{(1)}, \\ldots, \\+A^{(T)}$.\n\n\n\\begin{table}[ht]\n  \\caption{Classes of dynamic network embedding algorithms: a brief description, the algorithm complexity and its cross-sectional\/longitudinal stability. In the three latter classes, one may replace $\\+A^{(t)}$ with other matrix representations of the graph (e.g. the normalised Laplacian). Further details in main text.}\n  \\label{tab:Algorithm_Comp}\n  \\centering\n  \\begin{tabular}{@{}lp{5.9cm}cc@{}}\n    \\toprule\n    \\textbf{Algorithm} & \\textbf{Description} & \\textbf{Complexity} & \\textbf{Stability} \\\\\n    \\midrule\n    \\addlinespace[-0em]\n    UASE \\cite{jonesrubindelanchy2021MRDPG} & Embed $\\+A = (\\+A^{(1)}| \\cdots | \\+A^{(T)})$ & $\\mathrm{O}(d T n^2)$ & Both \\\\\n    \\hline\n    Omnibus \\cite{levin2017central} & Embed $\\tilde{\\+A}$; $\\tilde{\\+A}_{s,t} = (\\+A^{(s)} + \\+A^{(t)})\/2$ & $\\mathrm{O}(\\tilde{d} T^2 n^2)$ & Longitudinal \\\\\n    \\hline\n    Independent & Embed $\\+A^{(t)}$ & $\\mathrm{O}(\\sum_t d_t n^2)$ & Cross-sectional \\\\\n    \\hline\n    Separate embedding & Embed $\\bar{\\+A}^{(t)} = \\sum_k w_k \\+A^{(t-k)}$ & & Neither \\\\\n    \\cite{scheinerman2010modeling,dunlavy2011temporal,bhattacharyya2018spectral,pensky2019spectral,passino2019link,keriven2020sparse} & & \\\\\n    \\hline\n    Joint embedding & $\\argmin_{\\hat{\\+Y}^{(1)}, \\ldots, \\hat{\\+Y}^{(T)}} \\alpha \\sum_t \\text{CS}(\\hat{\\+Y}^{(t)}, \\+A^{(t)})$ & & Neither \\\\\n    \\cite{lin2008facetnet,deng2016latent,zhu2016scalable,chen2018exploiting,liu2018global} & $\\qquad + (1 - \\alpha) \\sum_t \\text{CT}(\\hat{\\+Y}^{(t)}, \\hat{\\+Y}^{(t+1)})$ & & \\\\\n    \\addlinespace[-0em]\n    \\bottomrule\n  \\end{tabular}\n\\end{table}\n\nThe omnibus method computes the spectral embedding of the matrix $\\tilde{\\+A} \\in \\{0,1\\}^{nT \\times nT}$ where the block $\\tilde{\\+A}_{s,t} \\in \\mathbb{R}^{n \\times n}$ is given by $(\\+A^{(k)} + \\+A^{(\\ell)})\/2 \\in \\mathbb{R}^{n \\times n}$ and we denote by $\\tilde{\\+P} \\in [0,1]^{nT \\times nT}$ the noise-free counterpart of $\\tilde{\\+A}$. If $(\\+z, t)$ and $(\\+z, t')$ are exchangeable, then, conditional on $\\+Z^{(t)}_i =\\+Z^{(t')}_i = \\+z$, the rows $\\tilde{\\+P}_{n(t-1) + i}$ and $\\tilde{\\+P}_{n(t'-1) + i}$ are equal. However, if $(\\+z, t)$ and $(\\+z', t)$ are exchangeable, then, in general, $\\tilde{\\+P}_{n(t-1) + i} \\ne \\tilde{\\+P}_{n(t-1) + j}$ when $\\+Z^{(t)}_i = \\+z$ and $\\+Z^{(t)}_j = \\+z'$. One can demonstrate that two rows of $\\tilde{\\+P}$ are equal if and only if the corresponding nodes' embeddings are too. Therefore, omnibus embedding provides longitudinal but not cross-sectional stability\n\nIndependent adjacency spectral embedding computes the spectral embeddings of the matrices $\\+A^{(t)} \\in \\{0,1\\}^{n \\times n}$. If $(\\+z, t)$ and $(\\+z', t')$ are exchangeable, then, conditional on $\\+Z^{(t)}_i = \\+z$ and $\\+Z^{(t')}_j = \\+z'$, the rows $\\+P^{(t)}_i$ and $\\+P^{(t')}_j$ are equal. If $t=t'$ the embeddings of nodes $i$ and $j$ are equal, however, embeddings between different graphs are subject to (possibly indefinite) orthogonal transformations $\\+Q^{(t)}$ which, if $\\+P^{(t)} \\neq \\+P^{(t')}$, differ in a non-trivial way (i.e. \\emph{beyond} simply reflecting the ambiguity of choosing eigenvectors in the spectral decomposition of $\\+P^{(t)}$). Therefore, independent adjacency spectral embedding provides cross-sectional but not longitudinal stability. The same arguments extend to other independent embeddings\n\nSeparate embedding covers a collection of embedding techniques separately applied to time-averaged matrices, $\\bar{\\+A}^{(t)} = \\sum_k w_k \\+A^{(t-k)}$ where $w_k$ are non-negative weights, and $\\+A^{(t)}$ may be replaced by another matrix representation of the graph such as the normalised Laplacian. The weights may be constant, e.g. $w_k = 1\/t$ for all $k$ \\cite{scheinerman2010modeling,bhattacharyya2018spectral}, exponential forgetting factors $w_k = (1-\\lambda)^k$ \\cite{dunlavy2011temporal, keriven2020sparse}, chosen to produce a sliding window \\cite{pensky2019spectral}, based on a time series model \\cite{passino2019link}, and more. In general, temporal smoothing results in two nodes behaving identically at time $t$ being embedded differently if their past or future behaviours differ, whereas the act of embedding the matrices separately will result in the same issues of alignment encountered in independent adjacency spectral embedding. Therefore, those methods can have neither cross-sectional nor longitudinal stability, except in special cases where one can contrive to have one but not other (e.g., $w_0 = 1$ and $w_k = 0$, reducing to independent embedding).\nJoint embedding techniques generally aim to find an embedding to trade-off two costs: a `snapshot cost' (CS) measuring the goodness-of-fit to the observed $\\+A^{(t)}$, and a `temporal cost' (CT) penalising change over time. These are then combined into a single objective function, for example, as \\cite{liu2018global} (where we have replaced the normalised Laplacian by the adjacency matrix):\n\\begin{equation}\n  \\argmin_{\\breve{\\+A}^{(1)}, \\ldots, \\breve{\\+A}^{(T)}} \\alpha \\sum_{t=1}^T \\lVert \\+A^{(t)} - \\breve{\\+A}^{(t)}\\rVert^2_F + (1 - \\alpha) \\sum_{t=1}^{T-1} \\lVert \\breve{\\+A}^{(t)} - \\breve{\\+A}^{(t+1)}\\rVert^2_F, \\label{eq:gse}\n\\end{equation}\nwhere $\\alpha \\in [0,1]$, subject to a low rank constraint on $\\breve{\\+A}^{(1)}, \\ldots, \\breve{\\+A}^{(T)}$, where $\\hat{\\+Y}^{(t)}$ is the spectral embedding of $\\breve{\\+A}^{(t)}$. It is easy to see that a change affecting only a fraction of the nodes will result in a change of all node embeddings, precluding both cross-sectional and longitudinal stability (again apart from contrived cases, e.g. when $\\alpha = 1$). \n\nFor the complexity calculations, we assume a dense regime in which the $k$-truncated singular value decomposition of an $m$-by-$n$ matrix is $\\mathrm{O}(kmn)$ \\cite{gu1996efficient}. Independent embedding is more efficient than UASE, on account of $\\sum_t d_t \\le dT$, but UASE is more efficient than omnibus embedding, because of the linear versus quadratic growth in $T$, while $\\tilde{d} = \\rank(\\tilde{\\+P})$ is often larger than $d$.\n\n\\section{Real data}\n\\label{Sec:Data}\nThe Lyon primary school data set shows the social interactions at a French primary school over two days in October 2009 \\cite{stehle2011high}. The school consisted of 10 teachers and 241 students from five school years, each year divided into two classes. Face-to-face interactions were detected when radio-frequency identification devices worn by participants (10 teachers and 232 students gave consent to be included in the experiment) were in close proximity over an interval of 20 seconds and recorded as a pair of anonymous identifiers together with a timestamp. The data are available for download from the Network Repository website\\footnote{\\url{https:\/\/networkrepository.com}} \\cite{nr-aaai15}.\n\nA time series of networks was created by binning the data into hour-long windows over the two days, from 08:00 to 18:00 each day. If at least one interaction was observed between two people in a particular time window, an edge was created to connect the two nodes in the corresponding network. This results in a time series of graphs $\\+A^{(1)}, \\ldots, \\+A^{(20)}$ each with $n = 242$ nodes. Where a node is not active in a given time window, it is still included in the graph as an isolated node. This is compatible with the theory and method, and the node is embedded to the zero vector at that time point. \n\nGiven the unfolded adjacency matrix $\\+A = (\\+A^{(1)} | \\cdots | \\+A^{(20)})$, an estimated embedding dimension $\\hat{d} = 10$ was obtained using profile likelihood \\cite{zhu2006automatic} and we construct the embeddings $\\hat{\\+Y}^{(1)}, \\ldots, \\hat{\\+Y}^{(20)} \\in \\mathbb{R}^{n \\times 10}$, taking approximately five seconds on a 2017 MacBook Pro. Figure~\\ref{Fig:Primary_UASE} shows the first two dimensions of this embedding to visualise some of the structure in the data. Similar plots and discussion for both individual spectral embedding and omnibus embedding are given in the Appendix.\n\n\\begin{figure}[ht]\n\t\\centering\n\t\\includegraphics[width=\\textwidth]{Primary_School_Hour_UASE.pdf}\n\t\\caption{First two dimensions of the embeddings $\\hat{\\+Y}^{(1)}, \\ldots, \\hat{\\+Y}^{(20)}$ of the unfolded adjacency matrix $\\+A = (\\+A^{(1)} | \\cdots | \\+A^{(20)})$. The colours indicate different school years while the marker type distinguish the two school classes within each year.}\n\t\\label{Fig:Primary_UASE}\n\\end{figure}\n\nFrom this plot, we observe clustering of students in the same school class. For time windows corresponding to classroom time, for example, 09:00--10:00 and 15:00--16:00, the embedding forms rays of points in 10-dimensional space, with each ray broadly corresponding to a single school class. This is to be expected under a degree-corrected stochastic block model, and the distance along the ray is a measure of the node's activity level \\citep{lei2015consistency,lyzinski2014perfect,sanna2020spectral}. However, not all time windows exhibit this structure, for example, the different classes mix more during lunchtimes (time windows 12:00--13:00 and 13:00--14:00).\n\n\\subsection{Clustering}\nFollowing recommendations regarding community detection under a degree-corrected stochastic block model \\cite{sanna2020spectral}, we analyse UASE using spherical coordinates $\\+\\Theta^{(t)} \\in [0,2\\pi)^{n \\times 9}$, for $t \\in [T]$. Since UASE demonstrates cross-sectional and longitudinal stability, we can combine the embeddings into a single point cloud $\\+\\Theta = (\\+\\Theta^{(1) \\top} | \\cdots | \\+\\Theta^{(T) \\top})^\\top \\in \\mathbb{R}^{nT \\times 9}$ where each point represents a student or teacher in a particular time window. This allows us to detect people returning to a previous behaviour in the dynamic network. We fit a Gaussian mixture model with varying covariance matrices to the non-zero points in $\\+\\Theta$ with 20--50 clusters increasing in increments of 5, with 50 random initialisations, taking approximately five minutes on a 2017 MacBook Pro. Using the Bayesian Information Criterion, we select the best fitting model (30 clusters) and assign the maximum a posteriori Gaussian cluster membership to each student in each time window.\n\nFigure~\\ref{Fig:Primary_Clusters} shows how students in the ten classes move between these clusters over time. Each class has one or two clusters unique to it, for example, the majority of students in class 1A spend their classroom time (as opposed to break time) assigned to cluster 1 or cluster 25. This highlights the importance of longitudinal stability in UASE, as we are detecting points in the embedding returning to some part of latent space. \n\\begin{figure}[ht]\n\t\\centering\n\t\\includegraphics[width=\\textwidth]{Primary_School_Clusters_Labels.pdf}\n\t\\caption{Bar chart showing the Gaussian cluster assignment of school classes over time. The height of each coloured bar represents the proportion of students, in that class and at that time, assigned to the corresponding Gaussian cluster, the total available height representing 100\\%. If the coloured bars do not sum to the full available height, the difference represents the proportion of inactive students. For legibility, only bars representing over 35\\% of the class are labelled with the cluster number.}\n\t\\label{Fig:Primary_Clusters}\n\\end{figure}\n\nThere are also instances of multiple school classes being assigned the same cluster at the same time period, for example, on the morning of day 1, classes 5A and 5B are mainly in cluster 28 suggesting they are having a joint lesson, and we see this behaviour again on day 2 with classes 3A and 3B in cluster 20. In the lunchtime periods, particularly on day 1, the younger students (classes 1A--2B) mingle to form a larger cluster, as do the older students (classes 4A--5B), potentially explained by the cafeteria needing two sittings for lunch for space reasons \\cite{stehle2011high}. This highlights the importance of cross-sectional stability in UASE, as it allows the grouping of nodes behaving similarly in a specific time window, irrespective of their potentially different past and future behaviours. \n\n\\section{Conclusion}\n\\label{Sec:Concs}\nWe prove that an existing procedure, UASE, allows dynamic network embedding with longitudinal and cross-sectional stability guarantees. These properties make a range of subsequent spatio-temporal analyses possible using `off-the-shelf' techniques for clustering, time series analysis, classification and more. \n\n\n \\section*{Funding Transparency Statement} Andrew Jones and Patrick Rubin-Delanchy's research was supported by an Alan Turing Institute fellowship. Ian Gallagher's research was supported by an EPSRC PhD studentship. \n\\bibliographystyle{apalike}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction and main results}\n \nLet $(X, d_X)$ be a metric space $X$ with a distance function $d_X$. \nSuppose that $X$ has infinite diameter, i.e. the function $d_X$ is unbounded.\nThen one may ask what is the structure of the space $X$ \"at infinity\".\nIntuitively, structure at infinity is what is seen if one looks at\nthe space $X$ from an infinitely far point (see [Gr2]).\nM. Gromov suggested several ways to treat this notion rigorously.\nIn this paper we follow one of them.\n\n\\proclaim Definition 1.1.\n{\\rm Let $(X, d_X)$ be a metric space with an infinite diameter.\nA metric space $(T, d_T)$ can be} isometrically embedded at infinity {\\rm into\nthe space $X$ if for every point $t \\in T$ there exists an\ninfinite sequence $\\{x_t^i\\}$, $i=1,2,..$ of points in $X$,\nsuch that for some  fixed sequence of positive $\\varepsilon_i \\to 0$\n$$\\lim_{i\\to\\infty}\\varepsilon_i\\cdot d_X(x_{t_1}^i, x_{t_2}^i)=\nd_T(t_1, t_2) \n\\eqno (1.2)\n$$  \nfor every $t_1,t_2 \\in T$.}\n\nIn other words, to every point of the space\n$T$ we may put in correspondence a sequence of points in $X$ going to infinity,\nsuch that the ``normalized'' pairwise distances between the sequences in $X$\ntend to the distances between the corresponding points in $T$. \n\nThe Definition 1.1. somehow clarifies what the ``structure at infinity''\nmeans but it is still too difficult to work with it.\n\nIn order to proceed we need to define a certain \nclass of ``geometrically simpler'' metric\nspaces --- {\\it geodesic} metric spaces (see [Gr1], [GhH]):\n\n\\proclaim Definition 1.3.\n{\\rm Let $x_0,x_1$ be two points of the metric space $X$ and let  \n$a=d_X(x_0,x_1)$ be the distance between them. A} geodesic segment {\\rm in\n$X$ {\\rm connecting\n$x_0$ and $x_1$} is an isometric inclusion $g:\\lbrack 0,a \\rbrack \\to X$ such that\n$g(0)=x_0$, $g(a)=x_1$. The image of this inclusion sometimes is also \ncalled a geodesic segment.\nA metric space $X$ is} geodesic {\\rm if for every two points\n$x_1,x_2 \\in X$ there exists a \n(not necessarily unique) geodesic segment connecting these two points.}   \n\nFor example, every complete Riemannian manifold is a geodesic space\ndue to Hopf-Rinow theorem. All metric spaces which appear in this paper \nare geodesic.\n\n\\proclaim Definition 1.4.\n{\\rm A metric space $X_0$ is an} asymptotic subcone {\\rm of the space $X$\nif $X_0$ is geodesic and its every finite subset of points can be\nisometrically embedded at infinity into the space $X$.}\n \nAsymptotic subcones were introduced in [Gr1] in the context of \n{\\it hyperbolic}  metric spaces (see [Gr1], [GhH]). There are several\nequivalent formal definitions of a hyperbolic metric space but all of them\ndemand additional non--trivial geometric explanations.  \nWe are not presenting any of them \nthem here since throughout this paper we deal with the familiar \nLobachveskian (hyperbolic) plane which is  the most well--known\nexample of a hyperbolic metric space. \n\nIn fact, there is another very well--known class of hyperbolic\nspaces~--- these are $0$-hyperbolic spaces (see [Gr1], [GhH] for the\ndefinition of $\\delta$-hyperbolicity) , or {\\it real\ntrees}:\n\n\\proclaim Definition 1.5.\n{\\rm A metric space $X$  is a} real tree {\\rm if it satisfies the following\nconditions:\n\\noindent 1) For every two distinct \npoints of the space there exists a unique geodesic segment joining them.\n\\noindent 2)If two geodesic segments\n$[a,b], [b,c]$ have exactly one endpoint  $b$ in\ncommon,\ntheir union is also a geodesic segment.}\n \nReal trees play the key role in the asymptotic geometry of\nthe hyperbolic metric spaces.\nThere is a general theorem that every asymptotic\nsubcone of a hyperbolic space is a real tree (see [GhH]). \nMoreover, as it was stated by Gromov (see [Gr1], [GhH]), \nif every asymptotic subcone of a metric space is a real tree\nthan this space is hyperbolic. Therefore, one may define hyperbolic\nspaces as metric spaces whose all asymptotic subcones are real trees.\nFor the hyperbolic groups Gromov considered this definition as the \nmost intuitive ([Gr1]).\n\nThe property of being a real tree does not give a complete description\nof a metric space. Different real trees can be very much unlike each\nother. Therefore in order to describe asymptotic subcones of a particular\nhyperbolic metric space (a Lobachevskian plane in our case)\nit is not satisfactory to say they are just real trees,  a  far more \n``explicit'' construction is desirable.\n\nWe found  only one example of an asymptotic subcone of a hyperbolic\nplane in the literature --- a star--shaped tree formed by\n$k$ segments with a common vertex (see [GhH]). Clearly, the asymptotic\ngeometry of a hyperbolic plane is much richer.\nHyperbolic plane is a homogeneous metric space. It is quite natural\nto look for asymptotic subcones sharing this property. Such a subcone\nshould be real tree branching at every its point --- already an object \nwhich is quite\ndifficult to imagine. We also want our subcone to contain\nall ``simple'' examples of asymtotic subcones (it follows from the \nDefinition 1.4. that every geodesic subset of an asymptotic subcone \nof the space $X$ is itself an asymptotic subcone of $X$). As a criterion\nof ``simplicity'' we choose countability of the number of vertices of\nthe real tree:\n \n\\proclaim Definition 1.6.\n{\\rm A real tree is } thick {\\rm if it allows an isometric\ninclusion of any real tree with countably many vertices.}\n\nThus, we want to ``materialize'' an asymptotic subcone of a hyperbolic\nplane which is a homogeneous and thick real tree. The surprising fact is\nthat such a substantial part of the ``structure at infinity'' of the\nLobachevskian plane can be described as a certain simple functional\nspace.\n\n\\proclaim Definition 1.7.\n{\\rm Let $S$ be \nthe set of all continuous real functions $f(t)$ \ndefined on a finite interval \n$\\lbrack 0,\\rho \\rbrack$, $0 \\le \\rho< \\infty$ (each function has its\nown $\\rho$), such that \n$f(0)=0$ for all $f \\in S$.\nDefine the following metric on $S$: \n$$d_S(f_1,f_2)=(\\rho_1-s)+(\\rho_2-s),\n\\eqno(1.8)\n$$   \nwhere \n$[0,\\rho_i]$ is the domain of  the function $f_i$ , $i=1,2$ and\n$$s=\\sup \\lbrace t|f_1(t')=f_2(t') \n\\quad \\forall t' < t \n\\rbrace.\n$$ \nThis defines the} metric space S.\n{\\rm The number $s$ is called the} moment of segregation  \n{\\rm of the functions  $f_1(t), f_2(t)$.}\n\nLet us formulate the main result of our paper:\n\n\\proclaim Theorem 1.9.\nThe space $S$ is a thick real tree and a homogeneous metric\nspace. It is an asymptotic subcone of the hyperbolic plane.\n \nWe prove this theorem in the next two sections. In the last section\nwe show that the completion of an asymptotic subcone of a metric\nspace is itself an asymptotic subcone of a metric space\n(motivated by the fact that the space $S$ is non--complete). \nThe paper is completed by two appendices.\n\n\\medskip\n\n\\noindent {\\bf Remark 1.10.}\nMost of the results of the present paper were announced in \n[PSh]. Some constructions introduced here were used in [Sh] to describe\nthe {\\it asymptotic cone}, or the {\\it asymptotic space}  (see [Gr0], [Gr2]) \nof the Lobachevskian plane by means of non--standard analysis \n(see [D]).  \n\n\\medskip\n\n\\noindent{\\it Acknowledgements.}\nThe authors are grateful to M.~Gromov, L.~Poltero-\n\\noindent vich, V.~Buchstaber and A.~Vershik\nfor helpful discussions and support.\n\n\n\\bigskip\n\n\\bigskip\n\n\\bigskip\n\n\\bigskip\n\n\n\n\n\n\\section{Properties of the metric space $S$}\nIn this section we study some properties of the metric space $S$.\n\n\\proclaim Lemma 2.1.\nThe function $d_S$ defined by {\\rm ( 1.8)} is a metric. \n\n\\noindent {\\bf Proof.}\nWe need to check that the metric (1.8) satisfies the triangle inequality.\nLet $f_1,f_2,f_3$ be three functions in $S$, \n$\\rho_1, \\rho_2, \\rho_3$ be the lenghts of their domains and\n$s_{12}, s_{13},s_{23}$ be their segregation moments. \nWe may always assume that $s_{12} \\le s_{13} \\le s_{23}$\nThen clearly $s_{12}=s_{13}$. Therefore,\n$$d_S(f_1,f_2)+d_S(f_1,f_3)=2\\rho_1+\\rho_2+\\rho_3-4s_{12} \\ge\n\\rho_2+\\rho_3-2s_{12} \\ge \n$$\n$$\n\\ge \\rho_2+\\rho_3-2s_{23} = d_S(f_2,f_3).$$\nThe two other inequalities are proved similarly.\n\n\\medskip\n\n\\proclaim Lemma 2.2.\nThe space $S$ is a real tree.\n\n\\noindent {\\bf Proof.}\nLet $f_1, f_2 \\in S$ be two arbitrary functions, $\\rho_1, \\rho_2$ be their\ndomains and $s$ be their moment of segregation. By (1.8)\n$d_S(f_1,f_2)=\\rho_1+\\rho_2-2s$. \nConsider the following inclusion $g:\\lbrack 0,\\rho_1+\\rho_2-2s \\rbrack \\to X$:\n$$g(x)=\\cases{\n\\lbrace f_1(t),\\, 0\\le t\\le \\rho_1-x \\rbrace, 0\\le x\\le \\rho_1-s; \\cr\n\\lbrace f_2(t),\\, 0\\le t \\le x+2s-\\rho_1 \\rbrace, \\rho_1-s\\le x \\le \n\\rho_1+\\rho_2-2s.\\cr}\n \\eqno (2.3)\n$$\nThis inclusion is isometric and clearly unique with such property, therefore\nthe condition 1) of the Definition 1.5. is verified. In order to check the\ncondition 2) we note that any two geodesic segments $[f,g]$, $[g,h]$ may have \nexactly one point $g$ in common if and only if the function $h$ \nis the extension of the function $g$ and segregates from it not earlier \nthan from the function $f$,\nor, symmetrically,\nif the function $f$  is the extension of the function $g$ and segregates \nfrom it  not earlier than \nfrom the function $h$. In both cases the formula (2.3) implies that  \n$\\lbrack f,h \\rbrack$ is also a geodesic segment. \nTherefore $S$ is a real tree which completes the proof.   \n\n\\medskip\n\n\\proclaim Lemma 2.4.\nThe space  $S$ is a thick tree.\n\n\\noindent {\\bf Proof.} \nLet $T$ be an arbitrary real tree with countably many vertices. We ``brush''\nthis tree in the following way. Fix some isomorphism between natural\nnumbers and the set of all vertices. Let $a_{ij}$ be the distance between\nvertices corresponding to the numbers $i$ and $j$, and $\\lbrace k_n \\rbrace$ \nbe an infinite strictly increasing sequence of natural numbers.\nNow we build a mapping from $T$ into $S$. Let the vertex $1$ go to zero\n(by zero we denote the function defined \nand equal to 0 at the single point $0$).\nThe vertex $2$ goes to a linear function $f(t)=k_1t$ defined on the\ninterval $\\lbrack 0, a_{12} \\rbrack$. In order to find the image of the\nvertex $3$ we find from $a_{12}$, $a_{13}$ and \n$a_{23}$ where it branches from $1$ and $2$;\nlet $s_3$ be the abscissa of this point. Therefore on the interval\n$\\lbrack 0, s_3 \\rbrack$ it is already defined and on the interval\n$\\lbrack s_3, a_{13} \\rbrack$ we set it  to be linear \nwith the angular coefficient\n$k_2$ (the free term is found from continuity). \nRepeating the same inductive algorithm for all $n$ (if $n-1$ vertices\nare already built we find the abscissa  $s_n$ of its point of segregation\nfrom the already built tree and continue the function by setting it linear with\nthe coefficient $k_{n-1}$ on the interval  \n$\\lbrack s_n, a_{1n} \\rbrack$) we get an inclusion of $T$ into $S$.\nIt is isometric by construction since the sequence $\\lbrace k_n \\rbrace$ \nis strictly increasing  and hence segregation is defined correctly.\n\n\\medskip\n\nNow let us prove that the space $S$ is homogeneous, i.e. \nfor every two its points\nthere exists a one-to-one isometry moving one point to another.\n\n\\proclaim Lemma 2.5.\nThe metric space $S$ is homogeneous. \n\n\\noindent {\\bf Proof.}\nClearly it is sufficient to construct a one-to-one isometry $F$ which moves\nany function  to zero. \nDenote the preimage of zero by $f_0(t)$, let $[0,\\rho]$ be \nits domain. Let $f(t)$ be  any other function with the domain $[0,a+b]$, where\n$a$ is the moment of segregation of the functions $f_0(t), f(t)$.\nIf $a < \\rho$ then the image of $f$ is given by  the function \n$F(f(t))$,such that $F(f(t))=0$  on $\\lbrack 0,\\rho-a\\rbrack$ and  \n$F(f(t))=f(t-\\rho+2a)-f_0(a)$ on $\\lbrack \\rho-a,\\rho-a+b \\rbrack$.\nIf $a=\\rho$, i.e. the function $f$ is a ``continuation'' of $f_0$, the\nconstruction is more complicated. Let us choose some infinite sequence\nof continuous functions $\\lbrace g_n(t) \\rbrace$ such that $g_1(t)$\nis identically zero and for any two elements of this sequence\ntheir moment of segregation is zero. For example we can take the sequence\n$$g_n(t)=\\frac{(2^n-1)t}{2^n}, n=0,1,2,....$$\nConsider the function \n$F^*(f(t))=f(t+\\rho)-f_0(\\rho)$\ndefined on $\\lbrack 0,b \\rbrack$. If there exists $0<c\\le b$ such \nthat $F^*(f(t))=g_n(t)$ identically on $\\lbrack 0,c \\rbrack$ \nfor some $n\\ge 0$ then $F(f(t))=F^*(f(t))+g_{n+1}(t)$ on\n$\\lbrack 0,b \\rbrack$, otherwise simply $F(f(t))=F^*(f(t))$.\nOne can easily check that $F$ is indeed an isometry.\n\n\\medskip\n\nAs it was mentioned in the introduction, homogeneity is a very\nimportant feature of the space $S$ since we are interested in it\nas in the model of the asymptotic space of the hyperbolic plane,\nand such a model can not be considered ``good'' if it does not preserve\nsuch a fundamental property of the initial space. \nAt the same time the question about the relations between the isometries\nof $S$ and of the initial hyperbolic plane remains open.\n \n\\section{Asymptotic subcones of the hyperbolic plane}  \n\nLet $X$ be the hyperbolic plane. For the conveniency of computations we use \nits Poincare unit disc model  \n$$X=\\lbrace x \\in C : |x|<1 \\rbrace.$$ \n\nFor every point $x\\in X$, denote by $\\rho$ the non-Euclidean\ndistance between $x$ and $0$, the centre of $X$, and by $\\varphi$\nthe polar angle; thus, $(\\rho,\\varphi)$ are the non-Euclidean\npolar coordinates of the point $x$.\n\nThe Euclidean distance between $0$ and $x$ is denoted by $r$.\n\nThere is the following relation between $\\rho$\nand $r$ (see [Be]):\n$$r=\\frac{e^{\\rho}-1}{e^{\\rho}+1}.\n\\eqno(3.1)\n$$\n\n\nThe distance between the two points $x_1,x_2 \\in X$ is given by the\nformula ([Be]):\n$$d_X(x_1,x_2)=\\ln \\frac{|1-x_1\\overline{x_2}|+|x_1-x_2|}\n{|1-x_1\\overline{x_2}|-|x_1-x_2|}  \\eqno (3.2)$$\nWe rewrite this formula in Euclidean polar coordinates. If $x_1=(r_1,\\varphi_1)$,\n$x_2=(r_2,\\varphi_2)$ then the formula (3.2) transforms into the\nfollowing:\n$$d_X(x_1,x_2)=\\ln \\frac{\\sqrt{\\frac{1+(r_1r_2)^2-2r_1r_2\\cos(\\varphi_1-\\varphi_2)}\n{r_1^2+r_2^2-2r_1r_2\\cos(\\varphi_1-\\varphi_2)}}+1}\n{\\sqrt{\\frac{1+(r_1r_2)^2-2r_1r_2\\cos(\\varphi_1-\\varphi_2)}\n{r_1^2+r_2^2-2r_1r_2\\cos(\\varphi_1-\\varphi_2)}}-1}\n\\eqno (3.3)\n$$\n\nAfter a number of elementary transformations\nof (3.3) we get:\n$$d_X(x_1,x_2)=\\ln \\frac{1+A}{1-A}, \\eqno(3.4)$$\nwhere\n$$A^2=1-\\frac{8}{(2-\\beta^2)(t+1\/t)^2+\\beta^2(s+1\/s)^2},$$\n$$\n\\beta^2=1-\\cos(\\varphi_1-\\varphi_2),\\, s^2=e^{\\rho_1+\\rho_2},\\,t^2=e^{\\rho_1-\\rho_2}.\n$$  \n\nIn order to prove that the space $S$ is an asymptotic subcone of\nthe hyperbolic plane we introduce an auxilary metric space $D$:\n\n\\proclaim Definition 3.5.\n{\\rm Consider\nthe set of all real functions $f(t)$ \ndefined on a finite semi-interval \n$\\lbrack 0,\\rho)$, $0 \\le \\rho< \\infty$ ($\\rho$ also depends on the function),\nsuch that $f(0)=0$ and $f(t)=0$ everywhere but at a finite number of points.\nDenote the }metric space $D$ {\\rm by endowing this set with the metric\n$d_D$, whose expression is given by the formula (1.8).}\n\nThe space $D$ is also a real tree (the proof is exactly the same as \nof the Lemma 2.2.). In fact, it can be isometrically included into the\nspace $S$ but is not isometric it (and hence ``smaller'' than the space $S$).\nThis statement is proved in the Appendix A.\n\n\\proclaim Lemma 3.6.\nThe space $D$ is an asymptotic subcone of the hyperbolic plane.\n\n\\noindent{\\bf Proof.}\nLet $f_1(t), f_2(t)$ be two arbitrary  functions from $D$, let \n$\\rho_1 \\ge \\rho_2$ be\nthe lengths of their domains, $\\lbrace s_{i,1}, ..., s_{i,N_i}\\rbrace$\nbe their supports and $f_i(s_{i,k})=a_{i,k}$, $k=1,..N_i$,  $i=1,2$.  \nConsider the following two sequences of points of the hyperbolic plane:\n$x_i(n)=(\\rho_i(n), \\varphi_i(n))$, where $\\rho_i(n)=\\rho_i\/\\varepsilon_n$,  \n$\\varphi_i(n)=\\sum_{k=0}^{N_i} a_{i,k}e^{-s_{i,k}\/\\varepsilon_n}$, $i=1,2$,\nwhere $\\lbrace \\varepsilon_n \\rbrace$ is an arbitrary sequence of positive \nnumbers tending to zero.\nThen after a simple asymptotic analysis of the formula (3.4) we get \n \n$$\n\\lim_{n \\to \\infty} \\varepsilon_n d_X(x_1(n),x_2(n))= \\lim_{n \\to \\infty}\n\\varepsilon_n\\ln(e^{(\\rho_1-\\rho_2)\/\\varepsilon_n}+\ne^{-2s\/\\varepsilon_n}e^{(\\rho_1+\\rho_2)\\varepsilon_n})=\n$$\n$$\n=\\rho_1+\\rho_2-2s,\n$$\nwhere $s$ is exactly the moment of segregation of the functions \n$f_1(t), f_2(t)$. Therefore,\n$$\\lim_{n \\to \\infty}\\varepsilon_n d_X(x_1(n),x_2(n))=d_D(f_1,f_2).$$\nComparing this\nwith (1.2) and recalling that \n$D$ is a geodesic space being a real tree completes the proof of our lemma.\n\n\\medskip\nWe call $D$ the {\\it discrete subcone} of the hyperbolic plane.\n\nNow we are able to complete the proof of our main result.\n\n\\proclaim Theorem 3.7.\nThe space $S$ is an asymptotic subcone of the hyperbolic\nplane.\n\n\\noindent{\\bf Proof.}\nLet $f_k(t)$, $k=1,...,n$ be an arbitrary finite subset of the\nspace $S$. Denote by $[0,\\rho_k]$ the domains of the functions\n$f_k(t)$, $k=1,..n$ and by   \n$s_{k_1k_2}$ the moments of segregation of the\nfunctions $f_{k_1}$ and $f_{k_2}$,  $k_1,k_2=1,..n$.\nWe choose $\\frac{n(n-1)}{2}$ pairwise distinct \npoints $t^1_{k_1k_2}$ on the positive half-line\nsuch that\n$$ f_{k_1}(t_{k_1k_2}) \\not= f_{k_2}(t_{k_1k_2})\n\\quad {\\rm and} \\quad t^1_{k_1k_2}-s_{k_1k_2}< 1\/4 \n\\eqno(3.8)\n$$ \nfor every two different $k_1, k_2 = 1..n$ (the first condition should\nbe checked only if $t^1_{k_1k_2} \\le \\min(\\rho_{k_1},\\rho_{k_2})$\nsince otherwise it does not make sense).\nLet us put down these points in the growing order and denote the resulting \nordered set\nby $\\lbrace t^1_j \\rbrace$: $t^1_{j_1}> t^1_{j_2}$ for all $j_1>j_2$,\n$j_1,j_2=1,..\\frac{n(n-1)}{2}$.  \nTake an arbitrary sequence \nof positive numbers \n$\\lbrace \\varepsilon_i \\rbrace$, $i=1,2,..$\ntending  to zero. \nConsider the following sequences of points of the hyperbolic plane:\n\n$$x^1_{i,k}=(\\rho_k\/\\varepsilon_i, \\varphi^1_{i,k}(\\varepsilon_i)),$$\nwhere\n$$ \\varphi^1_{i,k}(\\varepsilon_i)= \\sum_{j=1}^{J^1_k} e^{-t^1_j\/\\varepsilon_i}\nf_k(t^1_j), \\qquad k=1,..,n ,$$\nwhere $J^1_k$  is the number of points $t^1_j$ which lie in the domain\n$ [0,\\rho_k]$ of the function $f_k$; if there are no such points set \n$\\varphi^1_{i,k}(\\varepsilon_i)\\equiv 0$.  \n\nDenote by $g^1_k(t)$, $k=1,...n$, the functions \nbelonging to the discrete subcone\n$D$ such that each $g^1_k(t)$ has the same domain $[0,\\rho_k]$ as $f_k(t)$ and\n$$\ng^1_k(t)=\\cases{f_k(t),\\quad  t=t^1_j, j=1,...J^1_k;\\cr\n0,\\quad  {\\rm otherwise}.\\cr}\n$$\n \nThen, by lemma 3.6 there exists a number \n$I_1$, such that for all $k_1,k_2=1,..n$:\n$$\n|\\varepsilon_{I_1} d_X (x^1_{I_1,k_1},x^1_{I_1,k_2})-\nd_D(g^1_{k_1},g^1_{k_2})| \\le 1\/2.\n\\eqno (3.9)\n$$ \nTherefore, by the choice of the points $t^1_{k_1k_2}$ we have:\n$$\n|\\varepsilon_{I_1} d_X (x^1_{I_1,k_1},x^1_{I_1,k_2})-\nd_S(f_{k_1},f_{k_2})| \\le \n$$\n$$\n\\le |\\varepsilon_{I_1} d_X (x^1_{I_1,k_1},x^1_{I_1,k_2})-\nd_D(g^1_{k_1},g^1_{k_2})|+|d_D(g^1_{k_1},g^1_{k_2})-d_S(f_{k_1},f_{k_2})|\\le\n$$\n$$\n\\le 1\/2+ 2|t^1_{k_1k_2}-s_{k_1k_2}|<1\/2+2\\cdot 1\/4 = 1.\n$$ \n\nNow we take new points $t^2_{k_1k_2}$ which satisfy the condition (3.8)\nwith $1\/8$ instead of $1\/4$ in the right--hand side and get the new set \nof points $\\lbrace t^2_j \\rbrace$, the new\nsequences $x^2_{i,k}$ and the new  functions\n$g^2_k(t) \\in D$, $k=1,..n$.\n\nSimilarly, there exists a number $I_2$, greater than $I_1$, such that\n$$\n|\\varepsilon_{I_2} d_X (x^2_{I_2,k_1},x^2_{I_2,k_2})-\nd_D(g^2_{k_1},g^2_{k_2})| \\le 1\/4\n$$\nfor all $k_1,k_2=1,..,n$, and therefore\n$$\n|\\varepsilon_{I_2} d_X (x^2_{I_2,k_1},x^2_{I_2,k_2})-\nd_S(f_{k_1},f_{k_2})| \\le 1\/4+2|t^2_{k_1k_2}-s_{k_1k_2}|<1\/2\n$$\nfor all $k_1,k_2=1,..,n$.\n\nContinuing this procedure (which is possible due to the Lemma 3.6. and\nthe assumption that $f_k(t)$ are\ncontinuous functions)\nwe get the sequence $\\lbrace I_N \\rbrace$, \n$I_N \\to \\infty$ as $N \\to \\infty$, \nthe sequences $\\lbrace {\\varepsilon_{I_N} \\rbrace \\to 0}$\n(or just  $\\lbrace \\varepsilon_N \\rbrace$),\n$\\lbrace x^N_{I_N,k} \\rbrace$  (or just $\\lbrace x_{N,k} \\rbrace$),\nand the functions $g^N_k(t) \\in D$, $k=1,..,n$\nsuch that \n$$\n|\\varepsilon_N d_X (x_{N,k_1},x_{N,k_2})-\nd_S(f_{k_1},f_{k_2})| \\le \n$$\n$$\n\\le\n|\\varepsilon_N d_X (x_{N,k_1},x_{N,k_2})-\nd_D(g^N_{k_1},g^N_{k_2})|+\n2|t^N_{k_1k_2}-s_{k_1k_2}|<\n$$\n$$\n< 1\/2^N+2 \\cdot 1\/2^{N+1}=1\/2^{N-1}\n$$\n\nThus we have proved that there exists a limit\n$$\n\\lim_{N \\to \\infty} \\varepsilon_N d_X(x_{N,k_1},x_{N,k_2})=\nd_S(f_{k_1},f_{k_2})\n$$\nfor all $k_1,k_2= 1,..,n.$\nTherefore $S$ is indeed an asymptotic subcone of the \nhyperbolic  plane.\n  \n\\smallskip\n\nThe Theorem 3.7. together with the Lemmas 2.2., 2.4. and 2.5.\ncompletes the proof of the Theorem 1.9.\n\nWe call $S$ the {\\it continuous subcone} of the hyperbolic plane.\nIn fact it is  an asymptotic subcone of an\ninfinitely narrow neighborhood of a single half-line on the hyperbolic plane,\nas follows from the construction of the discrete subcone $D$.\n\nSome modifications of the construction of the\ncontinous subcone $S$ are considered in the Appendix B.\n\n\\medskip\n\nWe would like to conclude this section with a simple corollary of\nthe main result  which however reflects the ``wealth''\nof the space $S$:\n\n\n\\proclaim Corollary 3.10.\nAny real tree with countably many vertices is an asymptotic subcone of \nthe hyperbolic plane.\n\n\\noindent{\\bf Proof.}\nIndeed, every geodesic subspace of an asymptotic subcone \nis itself an asymptotic subcone. Real trees are geodesic spaces\nand by Lemma 2.4 any\nreal tree with countably many vertices can be isometrically inluded into \nthe continuous subcone $S$.\nTherefore every such tree is an asymptotic subcone of the hyperbolic plane.\n  \n\\section{Completions of the asymptotic subcones}\n\nThe metric spaces $S$ and $D$ are non--complete           \nmetric spaces. For $D$ this is obvious;\nfor $S$ it follows from the following example.\nConsider a sequence $\\{f_k(t)\\}$ of functions, defined on the segment\n$[0,1-2^{-k}]$, and equal to  $f_k(t)=\\sin(1\/(1-t))$ on its domain of\ndefinition. Clearly, this sequence has no limit \nin the space $S$ as $k \\to \\infty$.\n\nTherefore, it is reasonable to consider the completion \n$\\bar S$ \nof the  \ncontinuous subcone $S$. \nThough it does not have such a simple functional description as the\noriginal one, it is  also an asymptotic subcone of the hyperbolic plane\ndue to the following  simple general theorem (since we could not find it in\nthe literature we found it appropriate to state it here):\n\n\\proclaim Theorem 4.1.\nA completion of an asymptotic subcone of a metric space is also\nan asymptotic subcone of this metric space.\n\n\\noindent {\\bf Proof.}\nLet $X$ be our metric space, $X_0$ --- its asymptotic subcone and $\\bar X_0$ \n--- the completion of $X_0$.\nLet $f_1,f_2,...,f_k$ be a finite number of points in $\\bar X_0$.\nBy definition, \n$$f_i=\\lim_{n \\to \\infty} \\varphi_i^n,$$ \nwhere $\\varphi_i^n \\in X_0$, $n \\in {\\bf N}$, $i=1,...,k$.\n \nChoose a number $N_1=N_1(1\/4)$ such that \n$$d_{\\bar X_0}(\\varphi_i^n,f_i)<1\/4\n$$ \nfor all $i=1,..,k$, $n \\ge N_1$.\nThen for all $l,m=1,..,k$ and $n \\ge N_1$ we get\n\n$$|d_{\\bar X_0}(f_l,f_m)-d_{X_0}(\\varphi_l^n,\\varphi_m^n)|\\le\nd_{\\bar X_0}(\\varphi_l^n,f_l)+d_{\\bar X_0}(\\varphi_m^n,f_m) <\n$$\n$$\n< \\frac{1}{4}+\\frac{1}{4}=\n\\frac{1}{2}\n\\eqno(4.2)\n$$ \n\nThe space $X_0$ is an asymptotic subcone of $X$. Therefore for its\nfinite subset $\\varphi_i^{N_1}$, $i=1,..,k$ there exists a \nsequence $\\{ \\varepsilon_j \\}$ of positive numbers tending to zero,\nand $k$ sequences of points of the space $X$,  \n$\\{ x_j^{i,N_1} \\}$, $i=1,..,k$,  such that for some $J_1=J_1(N_1,1\/2)$\n$$ |\\varepsilon_j d_X(x_j^{l,N_1},x_j^{m,N_1}) - \nd_{X_0}(\\varphi_l^{N_1},\\varphi_m^{N_1})| < \\frac{1}{2}\n\\qquad \\forall j\\ge J_1.\n\\eqno (4.3)\n$$\n\nTherefore, by (4.2) and (4.3) we get:\n$$ |\\varepsilon_{J_1} d_X(x_{J_1}^{l,N_1},x_{J_1}^{m,N_1}) - \nd_{\\bar X_0}(f_l, f_m)| < \\frac{1}{2} + \\frac{1}{2}=1\n$$\nfor all $l,m=1,..,k$.\n\n\nNext, we choose  $N_2=N_2(1\/8)$ and $J_2=J_2(N_2, 1\/4)$\nand similarly obtain\n$$ |\\varepsilon_{J_2} d_X(x_{J_2}^{l,N_2},x_{J_2}^{m,N_2}) - \nd_{\\bar X_0}(f_l, f_m)| < \\frac{1}{4} + \\frac{1}{4}=\\frac{1}{2}\n$$\nfor all $l,m=1,..,k$.\nLet us note that we can always choose $N_2$ and $J_2$ in such a way that\n$N_2 > N_1$ and $\\varepsilon_{J_2}< \\varepsilon_{J_1}\/2$. \n\nContinuing this procedure analogously we get \nthe sequence $\\{\\varepsilon_{J_r}\\}$ of positive numbers tending to zero \nand $k$ sequences of points in $X$, \n$\\{x_{J_r}^{i,N_r}\\}$, $i=1,..,k$, such that\n\n$$ |\\varepsilon_{J_r} d_X(x_{J_r}^{l,N_r},x_{J_r}^{m,N_r}) - \nd_{\\bar X_0}(f_l, f_m)| < \\frac{1}{2^r} + \\frac{1}{2^r}=\\frac{1}{2^{r-1}}\n$$\nfor all $l,m=1,..,k$,  which implies\n\n$$\\lim_{r \\to \\infty}\\varepsilon_{J_r} d_X(x_{J_r}^{l,N_r},x_{J_r}^{m,N_r})=\nd_{\\bar X_0}(f_l, f_m)|, \\quad l,m=1,..,k.\n\\eqno(4.4)\n$$\n \nThe relation (4.4) exactly means that $\\bar X_0$ is an asymptotic subcone\nof the metric space $X$, which completes the proof of the theorem. \n  \n\\bigskip\n\n\\section*{Appendix A}\n\nWe have shown that the spaces $S$ and $D$\nare real trees. These\ntrees are branching at every point and the cardinal number of \nthe set of their vertices is continuum (for $D$ this is\nclear and for $S$ it follows from the fact that every \ncontinuous function is defined by its values at the rational points). \nAs a metric space $S$ is ``larger'' than $D$, as it is shown by the following\n\n\\proclaim Lemma A.1.\nThe space $D$ can be isometrically included into the space \n$S$ but is not isometric to it.\n\n\\noindent {\\bf Proof.} \nLet us show that $D$ can be \nisometrically included into $S$.\nLet $\\gamma(t)$ be any element of $D$, \n$Z_\\gamma=\\lbrace a_1<a_2<..<a_N \\rbrace$ be the set  \nof  points where $\\gamma (t)$ is non-zero, \nand $[0,\\rho_0)$ be the domain of $\\gamma(t)$.\nSet $a_0=0$, $a_{N+1}=\\rho_0$.\nConsider the following map $F: D\\to S$: \n$$\nF[\\gamma(t)](t)=\\sum_{i=0}^k \\gamma(a_i)(t-a_i),\\, \\, a_k \\le t \\le a_{k+1},\\, \nk=0,..,N.\n\\eqno (A.2)\n$$\nIt is easy to see that $F$ is an isometric inclusion of $D$ into $S$.\n\nNow, assume that $\\Phi$ is a an isometric inclusion of\n$S$ into $D$ and let $\\Phi[f(t)](t)=\\gamma(t)$\nfor some $f(t)\\in S$  where $\\gamma(t)\\in D$ \nis defined as above.\n\nTake some $0<\\varepsilon_0 < \\rho_0-m_0$, where $m_0=a_N$, and consider two\nfunctions $g_1(t)$, $h_1(t)$ \nin the $\\varepsilon_0$-neighborhood of $f(t)$ in $S$, such that none\nof the functions $f(t)$, $g_1(t)$, $h_1(t)$\nis the extension of any of the other two. Denote\n$\\alpha_1(t)=\\Phi[g_1(t)](t)$, $\\beta_1(t)=\\Phi[h_1(t)](t)$. \n\nLet us show that \n$Z_\\gamma \\subset Z_{\\alpha_1}$, $Z_\\gamma \\subset Z_{\\beta_1}$.\nIf, for instance, $Z_\\gamma$ is not a subset of $Z_{\\alpha_1}$\nthen $d_D(\\gamma,\\alpha_1)\\ge \\rho_0-m_0>\\varepsilon_0$, \nwhich contradicts with the choice of $\\alpha_1(t)$; the similar argument\nis valid for $\\beta_1(t)$.  \nAt least one of these inclusions is proper; \nindeed, if $Z_{\\alpha_1}=Z_{\\beta_1}= Z_\\gamma$ then one \nof the functions $\\alpha_1(t)$,\n$\\beta_1(t)$, $\\gamma(t)$ is the  extension of the two others which is\nimpossible since $\\Phi$ is an isometry and none of the functions\n$f(t)$, $g_1(t)$, $h_1(t)$\nis the extension of any of the other two.\nLet this proper inclusion be $Z_\\gamma \\subseteq Z_{\\alpha_1}$ .\nThen the set $Z_{\\alpha_1}$ consists of at least $N+1$ points.\n\nRepeat this construction taking $g_1$ instead of $f$, and instead of  \n$\\varepsilon_0$ taking  \n$0< \\varepsilon_1< \\min(\\varepsilon_0\/2,\\rho_1-m_1)$, where\n$[0,\\rho_1)$ is the domain of $\\alpha_1(t)$ and \n$m_1$ is the maximal element in  $Z_{\\alpha_1}$.\nSimilarly, we shall get the new function $\\alpha_2(t) \\in D$ such that\n$Z_{\\alpha_2}$ consists of at least $N+2$ points.\n\nContinuing this procedure we obtain a sequence $\\lbrace g_i(t)\\rbrace$ in \n$S$ and the corresponding sequence $ \\lbrace \\alpha_i(t)\\rbrace$ in $D$ \nsuch that\n$Z_{\\alpha_i}$ consists of at least $N+i$ points.\nWhen $i \\to \\infty$ the functions $g_i(t) \\to g(t)$, where $g(t) \\in S $ since \n$\\varepsilon_i<\\varepsilon_0\/2^i$ for all $i=1,2,..$ and therefore\nthe length of  the domain of $g(t)$ is finite --- it is not greater than\n$r+2\\varepsilon_0$, where $r$ is the length of the domain of $f(t)$. \nConsider the image of $g(t)$ under the isometry $\\Phi$;\nit is equal to $\\alpha(t)=\\lim_{i\\to \\infty}\\alpha_i(t)$.\nBy our construction $Z_\\alpha \\supset Z_{\\alpha_i}$ for all $i=1,2,..$ ,\ntherefore $Z_\\alpha$ consists of an infinite number of points. \nBut this contradicts with the fact that $\\alpha(t) \\in D$,\nand hence $S$ and $D$ are non-isometric.\nThis completes the proof of our lemma.      \n \n\\section*{Appendix B}\n\nInstead of continuous functions with bounded\ndomain one could take generalized functions of bounded domain with the\ndistance defined by (1.8).\nSuch generalized functions are of finite order (see [GeS]), i.e. they\ncan be represented as finite sums of generalized derivatives of continuous\nfunctions. One may check that integration preserving the condition $f(0)=0$\nis an isometry with respect to our metric\n(compare this with the formula (A.2.) --- \nin fact we have represented each element\nof the discrete subcone $D$ as a finite sum of $\\delta$-functions and \nintergrated twice). Hence every space of all generalized\nfunctions of order less than some finite $m > 0$ is isometric to $S$:\nits isometric inclusion into $S$ is obtained  by integrating $m$ times\nevery its element as described above, \nand isometric inclusion of $S$ into such \nspace can be given by  an identical map.   \nSimilarly, if we take $C^m$-smooth functions,\nwe also get an isometric space. Therefore, all such functional spaces are\nisometric asymptotic subcones of the hyperbolic plane. \n\nThe construction of $S$ can be also generalized for\nthe Lobache\\noindent vskian  space of arbitrary dimension $n$. \nIn this case instead of  scalar functions one has to take \n$n$-component vector functions. \n\n\n\\bigskip\n\n\\bigskip\n\n\\bigskip\n\n\\bigskip\n\n\\medskip\n\n\\centerline{ {\\large\\bf References}}\n\n\\medskip\n\n\\noindent [Be] A. Beardon, The geometry of discrete groups, Springer--Verlag, \n1983.\n\n\\smallskip\n\n\\noindent  [D] M.~Davis, Applied Nonstandard Analysis, \nJ. Wiley \\& Sons, New York, 1977\n\n\\smallskip\n\n\\noindent [GeS] I.M. Gelfand, G.E. Shilov, \nGeneralized functions, Vol. 2, Academic Press, 1968. \n\n\\smallskip \n\n\\noindent [GhH] E. Ghys, P. de la Harpe, Sur le groupes hyperboliques apres\nMikhael Gromov, Birkh\\\"auser, 1990. \n\n\\smallskip\n\n\\noindent [Gr0] M. Gromov, Groups of polynomial growth and expanding\nmaps, IHES Math. Publ., N 53, 1981, 53-71.\n\n\\smallskip\n \n\\noindent [Gr1] M. Gromov, Hyperbolic Groups, in: Essays in group theory,\ned. S.M.Gersten, M.S.R.I. Publ. 8 , Springer--Verlag, 1987, 75-263.\n\n\\noindent [Gr2] M. Gromov, Asymptotic invariants of infinite groups, \nGeometric group theory. Vol. 2 (Sussex, 1991), London Math. Soc. Lecture\nNote Ser. 182, Cambridge Univ. Press, 1993, 1-295.\n\n\\smallskip\n\\noindent [PSh] I. Polterovich, A. Shnirelman, An asymptotic subcone       \nof the Lobachevskii plane as a space of functions, Russian Math. Surveys,  \nv. 52 No. 4, 1997, 842-843.                                                \n                                                                           \n                                                                           \n\\noindent [Sh]  A. Shnirelman, On the structure of  asymptotic space       \nof the Loba-\n\n\\noindent chevsky plane, 1-23, to appear in the Amer. J. Math.\n\n\n\\end{document}  \n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\n\n Carbon-rich stars ([C\/Fe] $\\ge$ +1.0) comprise a significant fraction of \nmetal-poor ([Fe\/H] $\\le$ $-$2.0) stars with estimates ranging from \n14 $\\pm$ 4\\% (Cohen et al. 2005) to 21 $\\pm$ 2\\% (Lucatello et al. 2005); \nthis fraction  increases with decreasing metallicity (Rossi, Beers and Sneden\n 1999). A large fraction of carbon-enhanced metal-poor stars exhibit\noverabundances of neutron-capture elements relative to iron.  Significant \ninsight into the  neutron-capture processes  taking place in the early \nGalaxy  can be derived from  chemical composition studies of  metal-poor \ncarbon-stars (Norris et al. 1997a 1997b, 2002; Bonifacio et al. 1998; \nHill et al. 2000; Aoki et al. 2002a,b;  Goswami et al. 2006, Aoki et al. 2007).\nHowever, formation mechanisms of these stars still remain poorly understood.\n The prime cause of the origin of C-N  stars is believed to be the third \ndredge-up during the AGB evolutionary phase of low to intermediate-mass \nstars; the origin of C-R stars as well as SC-type stars still remains \nunclear (Izzard et al. 2007, Zijlstra  2004). \n\n The population II  CH stars,  characterized by a strong G-band of CH and \ns-process elements play significant roles in probing the impact of s-process \nmechanisms in early Galactic chemical evolution. These stars are classified \ninto  two distinct types, the Late-type and the Early-type. This classification\n is  based on their  $^{12}$C\/$^{13}$C ratios; stars with a large value of\n $^{12}$C\/$^{13}$C ratio ( $\\ge$ 100) belong to  Late-type, and those\nwith values of $^{12}$C\/$^{13}$C ratio ($\\le$ 10) belong to  Early-type.\n The two groups  follow two distinct evolutionary paths. Late-type CH stars \nare further identified as intrinsic stars that  generate s-process elements \ninternally and the early-type CH stars as extrinsic stars; they receive \nthe s-process  elements via binary mass transfer. The chemical composition \nof early-type  CH stars, if remains unaltered, would   bear signatures \nof the nucleosynthesis  processes operating in the low-metallicity AGB stars.\n Abundance analysis of such stars can provide observational constraints for \ntheoretical modelling of $s-$process nucleosynthesis at very low-metallicity\n revealing the time of influence of this process on early Galactic Chemical\n Evolution (GCE). \n\nAlthough new large-aperture telescopes has substantially enhanced the number\n of target stars for which high spectral resolution data with high\n signal-to-noise ratio can be obtained,  literature  survey shows  not many \nCH stars have been studied in detail so far. A major difficulty is in \ndistinguishing these objects from other types of carbon stars. In  particular,\n Population I C-R, C-N and dwarf carbon stars  exhibit remarkably similar \nspectra with those of carbon giants. It is important to distinguish them \nfrom one another and  understand  the astrophysical implications  of each \nindividual class of stellar population. It is with this motivation  we have\nundertaken  to identify the  CH stellar content as well as different types\nin a sample of  stars  presented by  Christlieb et al. (2001b). Using low \nresolution spectral analysis we have classified the stars based on a set of\nspectral classification criteria. The present  work led \nto the detection of 36 potential CH star candidates among ninety two objects.\nCombining this result with  our previous studies we find ${\\sim}$ 37\\%  \n (of 243) objects are  potential CH star candidates.\nThis  set of objects  would make important targets for  detailed chemical \ncomposition  studies  based on high resolution spectroscopy.\n\nSelection of the program stars is outlined in section 2.  Observations \nand data reductions are described in section 3. In section 4 we  briefly \ndiscuss the main features and spectral characteristics  of C-stars.\n Description of the program stars spectra   and results are drawn in \nsection 5.  Conclusions are   presented in section 6. \n\n\\section {Selection of program stars}\n\nThe program stars belong to the list of 403  Faint High Latitude Carbon (FHLC) \nstars presented by Christlieb et al. (2001b) from  the database of \nHamburg\/ESO Survey (HES)  described by  Wisotzki et al. (2000).\nHamburg\/ESO Survey for carbon stars covers 6400 degree$^{2}$ limited by\n${\\delta}$ $\\le$ +2.5$^{0}$ and $\\|$b$\\|$ $\\ge$ 30$^{0}$. The magnitude limit\nis V ${\\sim}$ 16.5. The  wavelength range of the spectra is\n3200 to 5200 \\AA\\, \n at a resolution of 15 \\AA\\, at H$_{\\gamma}$. \nChristlieb et al. found a total of 403 FHLC stars in this survey by\n application of  an \nautomated procedure to the digitized spectra. \n\nThe identification of these objects as FHLC stars  was based on a \nmeasure of line indices - i.e. ratios of the mean photographic densities\n in the carbon molecular absorption features and the continuum band passes.\n The primary consideration is the presence of  strong  C$_{2}$ and CN \nmolecular bands shortward of 5200 \\AA\\,;  CH bands were not considered.\n\n At high galactic latitudes  different kinds of  carbon stars such as \nN-type carbon stars, dwarf carbon stars, CH-giants, warm  C-R stars\n etc. are known to  populate the region (Green et al. 1994). \nGoswami (2005)\nand Goswami et al. (2007) have conducted spectral classification of about 151\nobjects that belong to the FHLC stars sample offered\n by Christlieb et al. (2001b).  These studies are enhanced by\nmedium  resolution\nspectroscopic analysis  of an additional sample of ninety two objects\n observed during 2007 to 2009.\n\n\\section{Observations and Data Reduction}\nObservations were  carried out using the 2-m Himalayan Chandra Telescope (HCT)\n at the Indian Astronomical Observatory (IAO), Mt. Saraswati, Digpa-ratsa Ri,\n Hanle.  The spectrograph used is the Himalayan Faint Object Spectrograph\nCamera (HFOSC).  HFOSC is an optical imager cum a spectrograph for conducting \nlow and medium resolution grism spectroscopy\n(http:\/\/www.iiap.res.in\/centers\/iao).\nThe grism and the camera combination used for observation provided a \nspectral resolution of  $\\sim$ 1330( ${\\lambda\/\\delta\\lambda}$ );\nthe observed bandpass ran from about 3800 to 6800 \\AA\\,. All the objects\nlisted in Table 1 and 2 are observed during 2007 - 2009.  The B$_{J}$, V, B-V, \nU-B colours listed in the tables are taken from Christlieb et al.(2001b).\nDetermination of these values  are described in Wisotzki et al. (2000) \n and  Christlieb et al.(2001a).  B$_{J}$ magnitudes  are accurate to better \nthan ${\\pm}$0.2mag including zero point errors (Wisotzki et al. 2000).\nSpectra of  HD~182040, HD~26, HD~5223, HD~209621, Z~PSc, V460~Cyg and RV~Sct\n  used for comparison were obtained  during earlier observations using the \nsame observational set up.\nA few spectra  acquired using the OMR spectrograph at the cassegrain focus\nof the 2.3-m Vainu Bappu Telescope (VBT) at Kavalur, cover a wavelength \nrange 4000 - 6100 \\AA\\, at a resolution of ${\\sim}$1000.  With a 600 line\nmm$^{-1}$ grating, we get a dispersion of 2.6 \\AA\\, pixel$^{-1}$.\n\n \nObservations of  Th-Ar hollow cathode lamp taken immediately before and\nafter the stellar exposures provide the wavelength calibration. The CCD\ndata were reduced  using the IRAF software spectroscopic reduction  packages.\nFor each object two spectra were taken \nand  combined to increase the signal-to-noise ratio.\n\n\n{\\footnotesize\n\\begin{table*}\n\\centering\n{\\bf Table 1: HE stars with prominent C$_{2}$ molecular bands observed during 2007 - 2009 }\\\\\n\\tiny\n\\begin{tabular}{cccccccccccccc}\n\\hline\nStar No.   & RA(2000)$^{a}$ & DEC(2000)$^{a}$& $l$ & $b$ & B$_{J}^{a}$& V$^{a}$ & B-V$^{a}$  &  U-B$^{a}$ &J & H & K &    &Dt of Obs\\\\\n             &            &           &          &          &      &      &       &      &     &    &    &  &    \\\\\n\\hline\nHE 0008-1712 & 00 11 19.2 & -16 55 34 & 78.5866  & -76.2106 & 16.5 & 15.2 &  1.78 & 1.64 &  13.630 & 13.069 &  12.975 &  & 06.12.2008\\\\\n             &            &           &          &          &      &      &       &      &         &        &         &  &11.09.2008\\\\\nHE 0009-1824 & 00 12 18.5 & -18 07 55 & 75.8376  & -77.2654 & 16.5 & 15.7 &  1.09 & 0.58 &  14.080 & 13.724 &  13.665 &  & 12.09.2008    \\\\\nHE 0037-0654 & 00 40 02.0 & -06 38 13 & 114.8865 & -69.3303 & 16.4 & 15.5 &  1.19 & 0.58 &  14.146 & 13.708 &  13.724 &  & 11.09.2008   \\\\\nHE 0052-0543 & 00 55 00.0 & -05 27 02 & 125.3316 & -68.3057 & 16.5 & 15.0 &  1.95 & 1.74 &  12.952 & 12.241 &  12.086 &  & 12.09.2008    \\\\\nHE 0100-1619 & 01 02 41.6 & -16 03 01 & 136.7651 & -78.6185 & 15.9 & 14.7 &  1.54 & 1.28 &  13.114 & 12.537 &  12.476 &  & 21.11.2008 \\\\\n             &            &           &          &          &      &      &       &      &         &        &         &\n&12.09.2008\\\\\nHE 0136-1831 & 01 39 01.8 & -18 16 43 & 176.4932 & -75.9157 & 16.9 & 15.6 &  1.72 & 1.43 &  14.216 & 13.679 &  13.532 &  & 12.09.2008\\\\\nHE 0217+0056 & 02 20 23.5 & +01 10 39 & 163.6094 & -54.5125 & 16.3 & 14.6 &  2.35 & 2.25 &  11.276 & 10.271 &  9.833  &  & 22.11.2008\\\\\nHE 0225-0546 & 02 28 19.4 & -05 32 58 & 174.1738 & -58.4222 & 16.5 & 15.2 &  1.79 & 1.51 &  13.347 & 12.707 &  12.528 &  & 06.12.2008 \\\\\nHE 0228-0256 & 02 31 15.5 & -02 43 07 & 171.5942 & -55.8545 & 16.2 & 14.7 &  1.99 & 1.52 &  12.506 & 11.813 &  11.531 &  & 18.01.2009\\\\\nHE 0308-1612 & 03 10 27.1 & -16 00 41 & 201.1165 & -55.9582 & 12.5 &  --  &  --   &  --  &  10.027 & 9.475  &  9.331  &  & 21.11.2008\\\\\nHE 0420-1037 & 04 22 47.0 & -10 30 26 & 205.0454 & -37.7176 & 15.2 & 14.7 &  1.38 & 0.99 &  12.341 & 11.815 &  11.695 &  & 21.11.2008  \\\\\nHE 0945-0813 & 09 48 18.7 & -08 27 40 & 245.0790 & 33.1497 & 16.2 & 15.3  & 1.22 & 1.11  & 13.531 &  13.026  &     12.903  &  &  08.04.2007\\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &09.04.2007\\\\\nHE 0954+0137 & 09 57 19.2 & +01 23 00 & 237.1030 &  41.0018 & 16.6 & 15.7 & 1.18  & 0.32 &   --    &   --   &  --     &  & 21.11.2008\\\\\nHE 1011-0942 & 10 14 25.0 & -09 57 54 & 251.7699 &  36.8590 & 15.4 & 14.2 & 1.65  & 1.76 &  11.209 & 10.432 &  10.125 &  & 22.11.2008\\\\\nHE 1019-1136 & 10 22 14.7 & -11 51 39 & 255.1421 &  36.8087 & 15.2 & 13.9 & 1.84  & 2.29 &  10.005 & 9.031  &  8.488  &  & 06.02.2009  \\\\  \nHE 1027-2501 & 10 29 29.5 & -25 17 16 & 266.6832 &  27.4163 & 13.9 & 12.7 & 1.73  & 1.51 &  10.627 & 9.896 & 9.722    &  & 22.11.2008\\\\\nHE 1045-1434 & 10 47 44.1 & -14 50 23 & 263.5905 &  38.4049 & 15.5 & 14.6 &  1.23 & 0.96 &  12.935 & 12.449 & 12.244 &  &  09.04.2007\\\\\nHE 1051-0112 & 10 53 58.8 & -01 28 15 & 253.5294 &  49.7900 & 17.0 & 16.0 & 1.44  & 0.94 &  14.347 & 13.794 &  13.703 &  & 06.12.2008 \\\\\nHE 1102-2142 & 11 04 31.2 & -21 58 29 & 272.5241 &  34.5071 & 16.0 & 14.9 & 1.44 & 0.98  &  13.275 & 12.714 &  12.601 &  & 16.03.2009  \\\\\nHE 1110-0153 & 11 13 02.7 & -02 09 28 & 261.1493 &  52.4883 & 16.5 & 15.5 & 1.47 & 1.29  &  12.912 & 12.205 &  12.063 &  & 04.04.2009 \\\\\nHE 1116-1628 & 11 19 03.9 & -16 44 50 & 273.2181 &  40.7347 & 16.6 & 15.6 & 1.28 & 1.41  &  13.241 & 12.614 & 12.482  &  & 06.02.2009 \\\\\nHE 1119-1933 & 11 21 43.5 & -19 49 47 & 275.7342 &  38.2583 & 12.8 & 14.6 & 1.34 & 0.87  &  13.043 & 12.571 & 12.422  &  & 18.03.2009  \\\\\nHE 1120-2122 & 11 23 18.6 & -21 38 33 & 277.1276 &  36.7743 & 12.9 &  --  &  --  &  --   &  9.573  & 8.902  & 8.788   &  & 17.03.2009 \\\\\nHE 1123-2031 & 11 26 08.7 & -20 48 19 & 277.4490 &  37.8097 & 16.8 & 15.8 & 1.33 & 1.19  &  13.513 & 12.940 & 12.800  &  & 18.03.2009\\\\\nHE 1127-0604 & 11 29 36.8 & -06 20 51 & 269.3427 &  51.1090 & 16.8 & 15.9 & 1.23 & 0.87  &  14.594 & 14.087 & 14.027  &  & 18.01.2009 \\\\\nHE 1142-2601 & 11 44 52.9 & -26 18 29 & 284.8485 &  34.2157 & 13.9 & 13.0 & 1.28 & 1.07  &  11.218 & 10.675 & 10.539  &  \n& 04.04.2009\\\\\nHE 1145-1319 & 11 48 21.4 & -13 36 38 & 280.3756 &  46.4800 & 16.4 & 15.4 & 1.37 & 1.32  &  13.466 & 12.934 & 12.790  &  & 17.03.2009\\\\\n             &            &           &          &          &      &      &       &      &         &        &         &   &05.04.2009\\\\\nHE 1146-0151 & 11 49 02.3 & -02 08 11 & 273.2807 & 57.0990 & 14.9  & 14.2 & 0.96 & 0.97  &  12.929 & 12.400 & 12.262  &  & 16.03.2009\\\\\nHE 1157-1434 &  12 00 11.5 &  -14 50 50 & 284.8854  &   46.2211   &    16.1 &  13.8  &  1.62  &  1.41& 11.792   &  11.178  &     11.019    &   &  06.06.2007\\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &07.06.2007\\\\\nHE 1205-0521 & 12 07 53.  & -05 37 51 & 283.5026 & 55.5893 & 15.2 & 14.4 & 1.09  &0.48   & 12.434  & 11.988 &  11.806 &  & 04.04.2009\\\\\nHE 1205-2539 & 12 08 08.1 & -25 56 38 & 290.8957 & 35.9137 & 13.6 & 15.4 & 1.91  &1.72   & 12.313  & 12.665  & 12.540 &  & 17.03.2009 \\\\\nHE 1210-2636 & 12 12 59.7 & -26 53 22 & 292.4334 & 35.1974 & 13.8 & 12.6 & 1.65  &1.52   & --      &   --   &   --    &  & 06.05.2009\\\\\nHE 1228-0417 & 12 31 12.5 & -04 33 40 & 293.4045 & 57.9360 & 14.8 & 14.0 & 1.17  &0.96   &  12.406 &  11.969 & 11.818 &  & 04.04.2009\\\\\nHE 1230-0327 & 12 33 24.1 & -03 44 28 & 294.2159 & 58.8251 & 13.7 & 15.1 & 1.02  &0.80   &  13.683 &  13.224 & 13.100 &  & 17.03.2009\\\\\nHE 1238-0836 &  12 41 02.4 &  -08 53 06 & 298.5709  &   53.8987   &    13.1 &  --      &   --      & --     &    9.189  &   8.503   & 8.154  &    & 08.04.2007\\\\\nHE 1253-1859 & 12 56 38.4 & -19 15 32 & 304.6277 & 43.5957 & 13.7 & 12.9 & 1.09  &1.22   &  10.604 &  9.972  & 9.850  &  & 16.03.2009\\\\\nHE 1315-2035 & 13 17 57.4 & -20 50 53 & 311.2275 & 41.5961 & 16.7 & 15.7 & 1.35  &0.93   &  13.678 &  13.236 & 13.047 &  & 06.05.2009\\\\\nHE 1331-2558 & 13 34 20.1 & -26 13 38 & 314.7873 & 35.6550 & 13.9 & 16.0 & 1.53  &1.10   &  10.998 &  10.394 & 10.240 &  & 18.03.2009\\\\\nHE 1344-0411 & 13 47 25.7 & -04 26 04 & 328.2429 & 55.6614 & 16.3 & 14.9 & 2.02  &2.29   &  11.708 &  10.848 & 10.467 &  & 05.04.2009\\\\\nHE 1358-2508 & 14 01 12.3 & -25 22 39 & 322.8426 & 34.4322 & 13.2 & 12.3 & 1.25  &0.84   & 9.521  &   8.802  & 8.532  &  & 18.01.2009\\\\\nHE 1400-1113 & 14 03 39.8 & -11 28 04 & 329.7145 & 47.6129 & 16.0 & 15.2 & 1.19  &0.75   & 13.838  &  13.411 & 13.276 & \n& 17.03.2009\\\\\nHE 1404-0846 &  14 06 55.1 &  -09 00 58 & 332.3876  &   49.4897   &   15.3 &  14.2  &  1.52   & 1.29  &  12.435   &11.783& 11.681&   &  07.06.2007\\\\             \nHE 1405-0346 & 14 07 58.3 & -04 01 03 & 336.5341 & 53.7853 & 14.7 & 13.5 & 1.68  &1.28   & 11.608  &  11.068 & 10.903 & \n& 16.03.2009\\\\\nHE 1410-0125 & 14 13 24.7 & -01 39 54 & 340.6313 & 55.0908 &  --  &  --  &   --  &  --   & 10.360  &  9.770  & 9.651   & & 16.03.2009\\\\\n             &            &           &          &          &      &      &       &      &         &         &         & &11.06.2008\\\\\nHE 1418-0306 &14 20 57.1 & -03 19 54 & 341.7366  & 52.6618  &  --  & 13.0 &  1.66 & 1.11 &  10.505 & 9.767   &  9.505 &   &  09.04.2007\\\\   \nHE 1425-2052 & 14 28 39.5 & -21 06 05 & 331.4023 & 36.3382 & 13.6 & 12.7 & 1.27  &1.29   & 10.043  &  9.446   & 9.273  & & 17.03.2009\\\\\nHE 1428-1950 & 14 30 59.4 & -20 03 42 & 332.6046 & 37.0083 &  --  &  --  &  --    &  --  & 9.988   &  9.469  & 9.318   & & 06.02.2009\\\\\nHE 1429-1411 & 14 32 40.6 & -14 25 06 & 336.6322 & 41.7341 & 12.5 & 11.1  &1.99  &1.89   & 7.622   &  6.721  & 6.346   & & 06.02.2009\\\\\nHE 1430-0919 & 14 33 12.9 & -09 32 53 & 340.3560 & 45.7983 & 14.9 & 13.8  &1.46  &0.75   & 12.476  &  11.971 &  11.862 & & 18.03.2009 \\\\\n             &            &           &          &          &      &      &       &      &         &         &         & &09.05.2007\\\\\nHE 1431-0755 &  14 34 32.7 &  -08 08 37 & 341.8828  &   46.7820     & 14.6  & 13.5 &   1.51 &   1.44  &   11.283  & 10.605    &  10.422  &   &  08.05.2007\\\\ \nHE 1439-1338 & 14 42 26.4 & -13 51 18 & 339.7039 & 40.9588 & 14.5 & 13.5  &1.39  &0.97   & 10.810  &  10.112 &   9.836 & & 25.07.2008\\\\\n             &            &           &          &          &      &      &       &      &         &         &         & &09.04.2007\\\\\nHE~1440-1511 &  14 43 07.1  & -15 23 48 & 338.737   &   39.5765   & 14.6  & 13.8   & 1.13   & 0.87 &  12.238  & 11.757 & 11.606    &    &  09.05.2007  \\\\\nHE 1442-0058 &  14 44 48.9 &  -01 10 56 & 351.4558  &   50.6883    & 17.8  & 16.2  &  2.15  &  1.80 &  12.287   &   11.268    &   10.751   &   & 06.06.2007\\\\ \nHE 1447+0102 & 14 50 15.1 & +00 50 15 & 355.2263 & 51.2262 & 15.6 & 15.0  &0.90  &0.14   & 13.207  &  12.760 &  12.682 & & 12.09.2008\\\\\n             &            &           &          &          &      &      &       &      &         &         &         & &08.04.2007\\\\\nHE 1525-0516 & 15 27 52.2 & -05 27 04 & 358.1110 & 40.1019 & 16.8 & 15.8  &1.29  &1.14   & 13.972  &  13.479 &  13.314 & & 11.09.2008 \\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &07.06.2007\\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &08.06.2007\\\\\nHE 2114-0603 & 21 17 20.8 & -05 50 48 & 45.5467  & -34.9459& 16.7 & 15.4  &1.80  &1.58   & 12.472  &  11.786 &  11.615 & & 11.09.2008 \\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &09.05.2007\\\\\nHE 2144-1832 &  21 46 54.7 &  -18 18 15 & 34.6476 & -46.7834& 12.6 &   -- &   --  &   -- & --     & --       &  --     &   & 06.06.2007\\\\\nHE 2157-2125 &  22 00 25.5 &  -21 11 23 & 32.0715 &-50.7274 & 16.8 & 15.9 & 1.29  & 1.02 &  14.389&  13.980  & 13.742  &    & 08.06.2007\\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &12.09.2008\\\\\nHE 2211-0605 & 22 13 53.5 & -05 51 06 & 55.3066  & -46.9505& 16.0 & 15.1  &1.21  &1.01   & 13.383 &  12.875  &  12.727 & & 24.07.2008 \\\\\nHE 2213-0017 & 22 15 37.1 & -00 02 59 & 62.3019  & -43.8276& 16.4 & 14.6  &2.38  &2.52   & 10.860 &   9.832  &   9.351 & & 24.07.2008\\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &27.05.2007\\\\\nHE 2216-0202 & 22 18 47.5 & -01 47 36 & 61.0859  & -45.5370& 17.2 & 16.4  &1.01  &0.43   & 14.571 &  14.165  &  14.028 & & 06.12.2008\\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &11.09.1008\\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &24.07.2009\\\\\nHE 2222-2337 & 22 25 38.8 & -23 22 44 & 31.2015  & -56.9371& 17.1 & 15.7  &1.93  &1.84   & 13.535 &  12.837  &  12.664 & & 12.09.2008\\\\\nHE 2225-1401 & 22 28 10.7 & -13 46 23 & 47.4570  & -54.0483& 16.5 & 14.5  &2.72  &2.36   & 11.870 &  10.748  &  9.896  & & 21.11.2008\\\\\nHE 2228-0137 & 22 31 26.2 & -01 21 42 & 64.4957  & -47.7030& 15.8 & 14.7  &1.56  &1.20   & 12.301 &  11.715  &  11.589 & & 11.09.2008\\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &25.07.2009\\\\\nHE 2246-1312 & 22 49 26.4 & -12 56 35 & 53.2930  & -58.1569& 17.0 & 15.9  &1.56  &1.60   & 14.101 &  13.472  &  13.303 & & 11.09.2008\\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &25.07.2008\\\\\nHE 2255-1724 & 22 58 06.8 & -17 08 19 & 47.9045  & -62.0030& 16.1 &15.1   &1.45  &1.05   & 12.931 &  12.374  &  12.310 & & 11.09.2008\\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &25.07.2008\\\\\nHE 2305-1427 & 23 08 10.9 & -14 11 27 & 55.9986  & -62.6875& 16.4 &15.3   &1.41  &0.80   & 13.269 &  12.762  &  12.744 & & 25.07.2008\\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &10.10.2008\\\\\nHE 2334-1723 & 23 37 03.7 & -17 06 34 & 59.3241  & -70.1108& 16.1  &  15.1 &1.38   &1.48 & 13.583 &  13.119  &  12.977 & & 10.10.2008\\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &25.07.2008\\\\\nHE 2347-0658 & 23 49 56.3 & -06 41 55 & 84.5844  & -64.8865& 16.9 &16.0   &1.30  & 0.69  & 14.568 &  14.145  &  14.158 & & 11.09.2008 \\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &24.07.2008\\\\\nHE 2353-2314 & 23 55 44.0 & -22 58 09 & 48.1281  & -76.7257& 16.5 &15.2   &1.82  & 1.53  & 13.064 &  12.403  &  12.199 & & 25.07.2008  \\\\\n\\hline\n\\end{tabular}\n\n$^{a}$ From Christlieb et al. (2001b)\\\\\n\n\\end{table*}\n}\n\n\n{\\footnotesize\n\\begin{table*}\n\\centering\n{\\bf Table 2:  HE stars without prominent C$_{2}$ molecular bands observed during 2007 - 2009 }\\\\\n\\tiny\n\\begin{tabular}{cccccccccccccc}\n\\hline\nStar No.   & RA(2000)$^{a}$ & DEC(2000)$^{a}$& $l$ & $b$ & B$_{J}^{a}$& V$^{a}$ & B-V$^{a}$  &  U-B$^{a}$ &J & H & K &   mol. bands &Dt of Obs\\\\\n             &            &           &          &          &      &      &       &      &     &    &    &  &    \\\\\n\\hline\nHE 0422-2518 & 04 24 38.5 & -25 12 10 & 223.2761 & -42.4854 & 13.9 &  --  &  --   & --   & --      &  --    &   --    & CH, CN & 22.11.2008\\\\\nHE 0443-2523 & 04 45 17.7 & -25 17 48 & 224.9946 & -38.0024 & 13.8 & --   &    -- &  --  &  10.704 & 10.169 &  10.012 &  CH, CN & 06.12.2008 \\\\\nHE 0513-2008 & 05 15 14.9 & -20 04 59 & 221.6222 & -29.8139 & 13.2 & --   &  --   &  --  &  9.398  &  8.810 &  8.677  &  CH, CN& 18.01.2009\\\\\n             &            &           &          &          &      &      &       &      &         &        &         &  &22.11.2008\\\\\nHE 1027-2644 & 10 29 57.8 & -26 59 51 & 267.8862 &  26.0820 & 14.4 & 13.4 & 1.40  & 1.59 &  --     &  --    &   --    &        & 17.01.2009\\\\\nHE 1033-0059 & 10 36 34.0 & +00 43 39 & 246.4726 &   48.2458& 12.9 & 13.0 & 1.10  &  1.29 & 10.709 & 10.138 & 9.951   &  CH, CN & 09.04.2007\\\\\nHE 1036-2615 & 10 38 25.9 & -26 30 50 & 269.3336 &  27.5445 & 14.6 & 13.7 & 1.21  & 1.49 & --      &  --    &  --     &  CH, CN& 17.01.2009\\\\\nHE 1037-2644 & 10 40 02.3 & -27 00 36 & 269.9776 &  27.3253 & 14.3 & 13.4 & 1.33  & 1.38 & 11.360  & 10.776 & 10.662  &  CH, CN& 06.02.2009 \\\\\nHE 1056-1855 & 10 59 12.2 & -19 11 08 & 269.4843 &  36.2931 & 13.6 &  --  &  --   &  --  &  10.784 & 10.249 &  10.090 &  CH, CN& 22.11.2008  \\\\\nHE 1104-1442 & 11 06 30.3 & -14 58 56 & 268.5996 &  40.7912 &  --  & 13.7 &  1.31 & 1.16 & 12.217  & 11.568 &  11.470 & \nCH, CN  &  09.04.2007\\\\\nHE 1105-2736 & 11 07 44.7 & -27 52 35 & 276.5372 &  29.6271 & 14.1 & 13.2 & 1.30 & 1.23  &11.314   & 10.742 & 10.551  &  CH, CN& 17.03.2009\\\\\nHE 1112-2557 & 11 15 14.1 & -26 13 28 & 277.4416 &  31.8419 & 14.5 & 13.6 & 1.29 & 1.45  & 11.548  & 11.006 & 10.849  &  CH, CN& 06.05.2009\\\\\nHE 1150-2546 & 11 53 15.5 & -26 03 41 & 286.9462 & 34.9979 & 15.6  &  --  &  --  &   --  &   --     &  --   &  --     &  & 18.03.2009\\\\\nHE 1152-2432 & 11 54 35.0 & -24 48 44 & 286.8824 & 36.2813 &  --   &  --  &  --  &  --  &   9.413 & 8.833  &  8.686   &  CH, CN& 18.03.2009 \\\\\nHE 1229-1857 & 12 31 46.8 & -19 14 02 & 296.5412 & 43.3938 & 14.6  & 14.0 & 0.85  &0.73   &  12.124 &  11.569 & 11.459 &  CH, CN& 04.04.2009\\\\\nHE 1236-0036 & 12 39 25.4 & -00 52 58 & 296.5586 & 61.8402 &  16.5 &  13.5 & 0.92 & 0.94  &11.679   &  11.176 & 11.104 & CH, CN  &  08.05.2007\\\\ \nHE 1406-2016 & 14 09 44.1 & -20 30 57 & 326.6476 & 38.7233 & 15.1 & 14.2 & 1.28  &1.22   & 12.092  &  11.558 &  11.423 & CH, CN& 16.03.2009 \\\\\nHE 1420-1659 & 14 23 03.1 & -17 12 51 &332.7845  &39.8992  & 13.1   &  --  &  --   &  --   & 9.871   &  9.226  & 9.067 &\nCH, CN & 18.01.2009 \\\\\nHE 1514-0207 & 15 16 38.9 & -02 18 33 & 358.6655 & 44.2895 & 13.6 &  --   &  --  &  --   &  10.335 &  9.703  &  9.536  & CH, CN& 24.07.2008\\\\\nHE 2115-0709 & 21 17 42.1 & -06 57 11 & 44.4121  &-35.5571 & 15.1 & 16.2  & 1.68 &  1.70 &  12.673 &  12.000 &  11.808 & CH, CN &  07.06.2007\\\\\nHE 2121-0313 & 21 23 46.2 & -03 00 51 & 49.5147  & -34.9016& 14.9 & 13.9  &1.35  &1.47   & 11.304  &  10.718 &  10.592 & CH, CN& 11.06.2008 \\\\\nHE 2124-0408 & 21 27 06.8 & -03 55 22 & 49.0907  & -36.0859& 14.8 & 13.9  &1.26  &1.15   & 11.578  &  10.986 &  10.848 & CH, CN& 24.07.2008  \\\\\nHE 2205-1033 & 22 08 29.2 & -10 18 37 & 48.6453  & -48.1654& 12.8 &  --   &  --  &  --   & 9.732  &  9.178   &  8.980  & CH, CN& 24.07.2008\\\\\n\\hline\n\\end{tabular}\n$^{a}$ From Christlieb et al. (2001b)\\\\\n\n\\end{table*}\n}\n\n\n{\\footnotesize\n\\begin{table*}\n\\centering\n{\\bf Table 3: Potential CH star candidates}\\\\\n\\tiny\n\\begin{tabular}{cccccccccccccc}\n\\hline\nStar No.   & RA(2000)$^{a}$ & DEC(2000)$^{a}$& $l$ & $b$ & B$_{J}^{a}$& V$^{a}$ & B-V$^{a}$  &  U-B$^{a}$ &J & H & K & &Dt of Obs\\\\\n             &            &           &          &          &      &      &       &      &     &    &    &  &    \\\\\n\\hline\nHE 0008-1712 & 00 11 19.2 & -16 55 34 & 78.5866  & -76.2106 & 16.5 & 15.2 &  1.78 & 1.64 &  13.630 & 13.069 &  12.975 &  & 06.12.2008\\\\\n             &            &           &          &          &      &      &       &      &         &        &         &  &11.09.2008\\\\\nHE 0052-0543 & 00 55 00.0 & -05 27 02 & 125.3316 & -68.3057 & 16.5 & 15.0 &  1.95 & 1.74 &  12.952 & 12.241 &  12.086 &  & 12.09.2008    \\\\\nHE 0100-1619 & 01 02 41.6 & -16 03 01 & 136.7651 & -78.6185 & 15.9 & 14.7 &  1.54 & 1.28 &  13.114 & 12.537 &  12.476 &  & 21.11.2008 \\\\\n             &            &           &          &          &      &      &       &      &         &        &         &\n&12.09.2008\\\\\nHE 0136-1831 & 01 39 01.8 & -18 16 43 & 176.4932 & -75.9157 & 16.9 & 15.6 &  1.72 & 1.43 &  14.216 & 13.679 &  13.532 &  & 12.09.2008\\\\\nHE 0225-0546 & 02 28 19.4 & -05 32 58 & 174.1738 & -58.4222 & 16.5 & 15.2 &  1.79 & 1.51 &  13.347 & 12.707 &  12.528 &  & 06.12.2008 \\\\\nHE 0308-1612 & 03 10 27.1 & -16 00 41 & 201.1165 & -55.9582 & 12.5 & --   &  --   &  --  &  10.731 & 9.821  &  9.406  &  & 21.11.2008\\\\\nHE 0420-1037 & 04 22 47.0 & -10 30 26 & 205.0454 & -37.7176 & 15.2 & 14.7 &  1.38 & 0.99 &  12.341 & 11.815 &  11.695 &  & 21.11.2008  \\\\\nHE 1027-2501 & 10 29 29.5 & -25 17 16 & 266.6832 &  27.4163 & 13.9 & 12.7 & 1.73  & 1.51 & 10.627 & 9.896    & 9.722  &  & 22.11.2008\\\\\nHE 1045-1434 & 10 47 44.1 & -14 50 23 & 263.5905 &  38.4049 & 15.5 & 14.6 &  1.23 & 0.96 &  12.935 & 12.449 & 12.244 &  &  09.04.2007\\\\\nHE 1051-0112 & 10 53 58.8 & -01 28 15 & 253.5294 &  49.7900 & 17.0 & 16.0 & 1.44  & 0.94 &  14.347 & 13.794 &  13.703 &  & 06.12.2008 \\\\\nHE 1102-2142 & 11 04 31.2 & -21 58 29 & 272.5241 &  34.5071 & 16.0 & 14.9 & 1.44  & 0.98 &  13.275 & 12.714 &  12.601 &  & 16.03.2009  \\\\\nHE 1110-0153 & 11 13 02.7 & -02 09 28 & 261.1493 &  52.4883 & 16.5 & 15.5 & 1.47 & 1.29  &  12.912 & 12.205 &  12.063 &  & 04.04.2009 \\\\\nHE 1119-1933 & 11 21 43.5 & -19 49 47 & 275.7342 &  38.2583 & 12.8 & 14.6 & 1.34 & 0.87  &  13.043 & 12.571 & 12.422  &  & 18.03.2009  \\\\\nHE 1120-2122 & 11 23 18.6 & -21 38 33 & 277.1276 &  36.7743 & 12.9 &  --  &  --  &  --   &  9.573  & 8.902  & 8.788   &  & 17.03.2009 \\\\\nHE 1123-2031 & 11 26 08.7 & -20 48 19 & 277.4490 &  37.8097 & 16.8 & 15.8 & 1.33 & 1.19  &  13.513 & 12.940 & 12.800  &  & 18.03.2009\\\\\nHE 1142-2601 & 11 44 52.9 & -26 18 29 & 284.8485 &  34.2157 & 13.9 & 13.0 & 1.28 & 1.07  & 11.218  & 10.675 & 10.539  &  \n& 04.04.2009\\\\\nHE 1145-1319 & 11 48 21.4 & -13 36 38 & 280.3756 &  46.4800 & 16.4 & 15.4 & 1.37 & 1.32  &  13.466 & 12.934 & 12.790  &  & 17.03.2009\\\\\n             &            &           &          &          &      &      &       &      &         &        &         &\n&05.04.2009\\\\\nHE 1146-0151 & 11 49 02.3 & -02 08 11 & 273.2807 & 57.0990 & 14.9  & 14.2 & 0.96 & 0.97  &  12.929 & 12.400 & 12.262  &  & 16.03.2009\\\\\nHE 1157-1434 & 12 00 11.5 & -14 50 50 & 284.8854 & 46.2211 & 16.1  & 13.8 & 1.62 &  1.41 &  11.792 & 11.178 & 11.019  &  & 06.06.2007\\\\\n             &            &           &          &         &       &      &      &       &         &        &         &  &07.06.2007\\\\\nHE 1205-2539 & 12 08 08.1 & -25 56 38 & 290.8957 & 35.9137 & 13.6 & 15.4 & 1.91  &1.72   & 13.313 & 12.665  & 12.540  &  & 17.03.2009 \\\\\nHE 1210-2636 & 12 12 59.7 & -26 53 22 & 292.4334 & 35.1974 & 13.8 & 12.6 & 1.65  &1.52   &   --   &  --     &   --    &  & 06.05.2009\\\\\nHE 1228-0417 & 12 31 12.5 & -04 33 40 & 293.4045 & 57.9360 & 14.8 & 14.0 & 1.17  &0.96   &  12.406 &  11.969 & 11.818 &  & 04.04.2009\\\\\nHE 1253-1859 & 12 56 38.4 & -19 15 32 & 304.6277 & 43.5957 & 13.7 & 12.9 & 1.09  &1.22   &  10.60  &  9.972  & 9.850  &  & 16.03.2009\\\\\nHE 1331-2558 & 13 34 20.1 & -26 13 38 & 314.7873 & 35.6550 & 13.9 & 16.0 & 1.53  &1.10   &  10.998 &  10.394 & 10.240 &  & 18.03.2009\\\\\n& 17.03.2009\\\\\nHE 1404-0846 & 14 06 55.1 & -09 00 58 & 332.3876 & 49.4897 & 15.3 & 14.2 & 1.52  &1.29   &  12.435 &11.783   & 11.681&  & 07.06.2007\\\\             \nHE 1405-0346 & 14 07 58.3 & -04 01 03 & 336.5341 & 53.7853 & 14.7 & 13.5 & 1.68  &1.28   & 11.608  &  11.068 & 10.903 &  & 16.03.2009\\\\\nHE 1410-0125 & 14 13 24.7 & -01 39 54 & 340.6313 & 55.0908 & --   &  --  &  --   &  --   & 10.360  &  9.770  & 9.651   & & 16.03.2009\\\\\n             &            &           &          &          &      &      &       &      &         &         &         & &11.06.2008\\\\\nHE 1425-2052 & 14 28 39.5 & -21 06 05 & 331.4023 & 36.3382  & 13.6 & 12.7 & 1.27  &1.29   & 10.043 & 9.446   & 9.273   & & 17.03.2009\\\\\nHE 1431-0755 & 14 34 32.7 & -08 08 37 & 341.8828 & 46.7820  & 14.6 & 13.5 & 1.51  & 1.44  &  11.283  & 10.605 &  10.422 & & 08.05.2007\\\\ \nHE~1440-1511 & 14 43 07.1 & -15 23 48 & 338.737  & 39.5765  & 14.5 & 13.5 & 1.13  & 0.87  &  12.238  & 11.757 & 11.606 &  &  09.05.2007  \\\\\nHE 1447+0102 & 14 50 15.1 & +00 50 15 & 355.2263 & 51.2262  & 15.6 & 15.0 &  0.90 & 0.14  & 13.207   & 12.760 & 12.682 &  &   08.04.2007\\\\\nHE 1525-0516 & 15 27 52.2 & -05 27 04 & 358.1110 & 40.1019 & 16.8 & 15.8  &1.29  &1.14   & 13.972  &  13.479 &  13.314 & & 11.06.2008 \\\\\n             &            &           &          &          &      &      &       &      &         &         &         & &07.06.2007\\\\\n             &            &           &          &          &      &      &       &      &         &         &         & &08.06.2007\\\\\nHE 2114-0603 & 21 17 20.8 & -05 50 48 & 45.5467  & -34.9459& 16.7 & 15.4  &1.80  &1.58   & 12.472  &  11.786 &  11.615 & & 11.09.2008 \\\\\n             &            &           &          &          &      &      &       &      &         &         &         & &09.05.2007\\\\\nHE 2211-0605 & 22 13 53.5 & -05 51 06 & 55.3066  & -46.9505& 16.0 & 15.1  &1.21  &1.01   & 13.383 &  12.875  &  12.727 & & 24.07.2008 \\\\\nHE 2228-0137 & 22 31 26.2 & -01 21 42 & 64.4957  & -47.7030& 15.8 & 14.7  &1.56  &1.20   & 12.301 &  11.715  &  11.589 & & 11.09.2008\\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &25.07.2009\\\\\nHE 2246-1312 & 22 49 26.4 & -12 56 35 & 53.2930  & -58.1569& 17.0 & 15.9  &1.56  &1.60   & 14.101 &  13.472  &  13.303 & & 11.09.2008\\\\\n             &            &           &          &          &      &      &       &      &        &          &         & &25.07.2008\\\\\n\\hline\n\\end{tabular}\n\n$^{a}$ From Christlieb et al. (2001b)\\\\\n\n\\end{table*}\n}\n\n\\section { Characteristics of carbon stars and spectral classification}\n\n Spectral classification  helps reducing\n the number of stars to  be analyzed to a tractable number of\nprototype objects of different groups;  each group may be   correlated\nwith one or more physical parameters such as luminosity and temperature.\nAbundance anomalies  observed in carbon stars  cannot be explained on \nthe  basis of observed temperature and luminosity of the stars; \n it is therefore  difficult to \ndevise a classification scheme for carbon stars  based  on  only \nthese two physical parameters. \nMorgan-Keenan system  for carbon star classification (Keenan 1993)\ndivided  carbon stars into C-R, C-N and C-H sequence,\n with subclasses running to C-R6, C-N6 and C-H6\naccording to temperature criteria. In the old R-N system, CH stars\nthat were classified as R-peculiar are put in a separate class in the\nnew system. \nIn the following we  briefly  discuss  the main characteristics that place \ncarbon stars into different groups. Detailed discussions on  carbon stars are\navailable in literature  including Wallerstein and Knapp  (1998) and \nreferences therein.\n\nIn contemporary  stellar  classification schemes  assigning stars to\n `morphological groups' is  largely in practice. \nCarbon stars are  primarily  classified  based on the strength of carbon\nmolecular bands.  \n The C-N stars are characterized by strong depression \nof light in the violet part of the spectrum. The cause of rapidly weakening \ncontinuum below about 4500\\AA\\, is not fully established yet, but believed\nto be due to scattering by particulate matter. Oxygen-rich stars of similar \neffective temperatures do not show such weakening.\n C-N stars  are also  easily detected  for  their characteristic \ninfrared colours. The majority of C-N stars show ratios of $^{12}$C\/$^{13}$C \nin the range of  30 to 100 while in C-R stars this ratio ranges from\n 4 to 9 (Lambert et al. 1986). They have  lower temperatures and stronger \nmolecular bands than those of C-R stars. They are used as tracers of an \nintermediate age population in extragalactic objects.  \n\nCH stars are  characterised by the strong G-band of CH in their spectra. They\n form a group of warm stars of equivalent spectral\ntypes, G and K normal giants, but  show  weaker metallic lines.\nIn general, CH stars are high velocity objects, large radial velocities\nindicating that  they belong to the halo population of the Galaxy \n(McClure 1983, 1984, McClure \\& Woodsworth 1990).\n `CH-like' stars, \nwhere CH are less dominant have low space velocities (Yamashita 1975).\nFrom  radial velocity survey   CH stars are known  to be binaries. \nAccording to the models of  McClure (1983, 1984)  and   McClure \\& Woodsworth \n(1990) the CH binaries have orbital characteristics consistent with the\npresence of a white dwarf companion. Early type CH stars  are believed to \nhave conserved the products \nof the carbon rich primary received through mass transfer and survived until\nthe present in the Galactic halo.\nCH stars are not a homogeneous group of stars. They consist of two populations, \nthe most metal-poor ones have a spherical distribution and the ones slightly \nricher in metals are characterised by a flattened ellipsoidal distribution \n(Zinn 1985).  The ratio of the local density of CH stars was found to be \n ${\\sim}$ 30\\% of metal-poor giants  (Hartwick \\& Cowley 1985).\n\n Many C-R stars also show a quite strong  G band of CH  in their \nspectra. Hence, based only  on the strength of the G-band of  CH it is \nnot possible  to make a distinction between CH and C-R stars.\n In such cases the secondary \nP-branch head near 4342 \\AA\\, serves  as a more  useful indicator.\nThis is a well-defined feature in CH stars spectra in contrast\n to its appearance in C-R stars spectra (refer Fig 2, 3 of Goswami 2005).\nAnother  important  diagnostic  feature is  Ca I at 4226 \\AA\\, which  in \ncase of CH stars is weakened by the overlying  CH band \nsystems. In C-R star's spectra  this feature is  quite strong; usually  \nthe   line depth is  deeper \nthan the depth of the  CN molecular band around 4215 \\AA\\,.  \nThese spectral characteristics allow for an identification of the CH  and \nC-R stars even at  low resolution.  \n\nAbundances of neutron-capture  elements  can also be used as an useful \nindicator of spectral type. The abundances of  s-process elements  are nearly \nsolar in C-R stars (Dominy 1984); whereas the CH stars  show significantly \nenhanced abundances of the s-process  elements relative to iron \n(Lambert et al. 1986, Green and Margon 1994). Although, the  C-R  as well as \nCH stars have warmer temperatures than those of C-N stars and blue\/violet  \nlight is accessible \nto observation and atmospheric analysis, at low dispersion the \nnarrow lines are difficult to estimate and elemental abundances can not  be\ndetermined.   At low dispersion, therefore,  the `abundance criteria'\ncan not be used to  distinguish  the C-R stars from the  CH stars.\n Although the CH and \nC-R stars have similar range of temperatures, the distribution of CH stars \nplace most of them in the Galactic halo. The large radial velocities,\ntypically $\\sim$ 200 km s$^{-1}$  of the CH stars are indicative of their \nbeing halo objects (McClure 1983, 1984).\n \nC-J stars spectra  are characterized by strong  Merrill-Sanford (M-S) bands \nascribed to SiC$_{2}$  that appear in the wavelength region 4900 - 4977 \\AA\\,.\n The SiC$_{2}$ being a triatomic molecule, M-S bands are  expected to be the  \nstrongest in the coolest stars. SiC$_{2}$  and  C$_{3}$  have similar \nmolecular structures and  in many C stars  C$_{3}$ molecule is believed to be\nthe cause of ultraviolet depression (Lambert et al. 1986).\n These bands are absent in the spectra of known  CH stars. A few warmer C-N stars \nare known to exhibit the presence of M-S bands in their spectra. \n Strength of M-S bands are known to show a distinct correlation with  \ncarbon isotopic ratios; i.e., stars with higher $^{12}$C\/$^{13}$C ratios show\nweaker  M-S bands.  \n WZ Cas, V Aql \\& U Cam  are a few exceptions that  have low $^{13}$C  \nand  strong M-S bands (Barnbaum et al. 1996).\nStrong C-molecular bands but a weak CH band characterize the class of\nhydrogen deficient carbon stars. \n\nWe have classified the program stars guided by  the above  spectral \ncharacteristics.  In the present  sample of ninety two stars the  spectra\nof twenty two  objects are found  to not exhibit molecular bands of C$_{2}$.\n These objects are listed  in Table 2.\n Among the seventy    stars  that exhibit  strong carbon molecular bands\n (Table 1) thirty six  of them  are found to  show spectral characteristics \nof CH stars. \nThese potential CH star candidates are listed in Table 3. \n  In the following  we  discuss the spectral characteristics\nof the  individual  objects. \n\n\\section{ Results and Discussions}\n\n The spectra of the objects are primarily  examined in terms of the following  \nspectral characteristics.\\\\\n1. The strength (band depth) of the CH band around  4300 \\AA\\,.\\\\\n2. Prominance of the secondary P-branch head near 4342 \\AA\\,.\\\\\n3. Strength\/weakness  of the  Ca I feature at 4226 \\AA\\,.\\\\\n4. Isotopic band depths  of C$_{2}$ and CN,  in particular the Swan bands\n of $^{12}$C$^{13}$C and $^{13}$C$^{13}$C near 4700 \\AA\\,.\\\\\n5. Strengths of the other C$_{2}$ bands in the 6000 -6200 \\AA\\, region. \\\\\n6. The $^{13}$CN band near 6360 \\AA\\, and the other CN bands across the\n wavelength range.\\\\\n7. Presence\/absence of the  Merrill-Sandford bands around 4900 - 4977 \\AA\\, \nregion.\\\\\n8. Strength of the  Ba II features at 4554 \\AA\\, and 6496 \\AA\\,.\\\\\n\nThe   membership of a star in a particular  group is established  from a \ndifferential analysis of the program stars spectra with the spectra\nof  the comparison stars. Spectra of carbon stars  available in the \nlow resolution spectral atlas of carbon stars of  Barnbaum et al. (1996)\nare also consulted. \nIn Figure 1 we reproduce\n the spectra of the comparison stars in the wavelength region\n4000 - 6800 \\AA\\,; in figure 2 we show one example of HE stars spectra \nfrom the  present sample corresponding\nto each comparison star's spectrum in figure 1.\n\n\\begin{figure*}\n\\epsfxsize=14truecm\n\\epsffile{aruna_chstars_fig1.eps}\n\\caption{ The spectra of the comparison stars in the wavelength \nregion 3860 - 6800 \\AA\\,. Prominent features seen on the spectra are indicated.}\n\\label{Figure 1}\n\\end{figure*}\n\n\n\n\\begin{figure*}\n\\epsfxsize=14truecm\n\\epsffile{aruna_chstars_fig2.eps}\n\\caption{ An example of each of the HE stars corresponding to the \ncomparison stars presented in Figure 1, in the top to bottom sequence,\nin the wavelength region 3860 - 6800 \\AA\\,. The locations  of the\nprominent features  seen in the spectra are marked on the figure.\n}\n\\label{Figure 2}\n\\end{figure*}\n\n\\subsection { Location of the  candidate CH stars on (J-H) vs (H-K) plot}\n\nWe have  used JHK photometry as  supplementary diagnostics for stellar \nclassification. Figure 3 shows the locations of the candidate CH stars \nlisted in Table 3  on the (J-H) vs (H-K) plot.\n 2MASS JHK measurements of the stars  are available on-line at\nhttp:\/\/www.ipac.caltech.edu\/.\nThe thick box on the lower left represents the location of CH stars and the\nthin box on the upper right represents the location of C-N stars (Totten et\nal. 2000). \n Except two lying outside (shown with open squares in figure 3), the  locations \nof the   candidate CH  stars (shown with open circles) are well within the CH \nbox. This  supports  their identification  with the class of  CH stars. \nLocation of the  comparison  CH stars\nHD~26, HD~5223 and  HD~209621, C-R star  RV Sct, C-N stars V460~Cyg \nand  Z PSc,  are  shown by solid squares on the (J-H) vs (H-K) plot.\nAs described in the next section, we have  also used  2MASS JHK photometry \n to determine the effective temperatures of the objects.\n\n\n\\begin{figure*}\n\\epsfxsize=14truecm\n\\epsffile{aruna_chstars_fig3.eps}\n\\caption{\n A two colour  J-H versus H-K diagram of the candidate CH stars.\nThe thick box on the lower left represents the location of CH stars and the\nthin box on the upper right represents the location of C-N stars (Totten et\nal. 2000).  Majority of the  candidate CH stars\nlisted in Table 3  (represented by open circles) fall well\n within the CH box. The positions of the two outliers are shown with open\nsquares. C-N stars  found in our sample are represented by solid \ntriangles.  The location of the \ncomparison stars are labeled and marked with solid squares. Location of the \nthree dwarf carbon stars are indicated by open triangles.}\n\\label{Figure 3}\n\\end{figure*}\n\n\\subsection{ Effective temperatures of the program stars}\nSemiempirical temperature calibrations offered by Alonso et al. \n(1994, 1996, 1998)\nare used to derive priliminary temperature estimates of the program stars.\nThese authors used the infrared flux method to measure temperatures for a \nlarge number of lower main sequence stars and subgiants  to derive\n the calibrations. The calibrations relate T$_{eff}$ with Stromgren \nindices as well as [Fe\/H] and colours (V-B), (V-K), (J-H) and (J-K). The\ncalibrations  hold within a temperature and\nmetallicity range 4000 ${\\le}$ T$_{eff}$ ${\\le}$ 7000 K and\n-2.5 ${\\le}$ [Fe\/H] ${\\le}$ 0 . The estimated uncertainty in T$_{eff}$ \narising from different sources is ${\\sim}$90 K (Alonso et al. 1996).\nAlonso et al.  derived the T$_{eff}$ scales using   photometric data \nmeasured on  TCS system; 2MASS  JHK photometric data  are therefore\nconverted to the  TCS system using the conversion relations \nof  Ramirez and Melendez (2004).\nEstimation of T$_{eff}$ from  (J-H) \\&\n (V-K) temperature relations involve a metallicity term; (J-K) calibration\nrelation is independent of metallicity.\nWe have estimated the effective temperatures using  adopted metallicities\nshown in parenthesis in Table 4.\n (B-V) calibration,  normally used in case of normal stars  is  not \nconsidered as in the case of carbon stars the colour \n B-V depends on the \nchemical composition and metallicity in addition to T$_{eff}$. B-V colour \noften gives a  much lower value than the actual surface temperature of the \nstar due to the effect of CH molecular  absorption in the B band.\nWe have  assumed that the effects of reddening on the measured colours\nare  negligible.\n  \n\n\\subsection{ Isotopic ratio $^{12}$C\/$^{13}$C from molecular band depths}\n\n  Carbon isotopic ratios  $^{12}$C\/$^{13}$C,  widely used as  mixing \ndiagnostics  provide an important  probe of stellar evolution.  \nThese ratios  measured on low resoltuion spectra do  not give accurate \nresults  but provide  a fair indication of evolutionary states of the objects.\n\nWe have estimated  these ratios, whenever possible, using  the molecular band \ndepths  of (1,0) $^{12}$C$^{12}$C ${\\lambda}$4737 and\n(1,0) $^{12}$C$^{13}$C ${\\lambda}$4744.\nFor a majority of the  candidate CH  stars,\nthe ratios $^{12}$C\/$^{13}$C are found to be  ${\\le}$ 10.\nThese ratios  for  HD 26, HD 5223 and HD 209621 are respectively\n5.9, 6.1  and 8.8 (Goswami 2005).\n\nOur estimated ratios of  $^{12}$C\/$^{13}$C indicate that most of the candidate\nCH stars belong to the `early-type' category.\nThe low carbon isotope ratios imply that, in a binary system,\nthe material transferred from the now unseen companion has been mixed into\nthe CN burning region of the CH stars or constitute  a minor fraction of the\nenvelope mass of the CH stars. Low  isotopic ratios are  typical of stars\non their first ascent of the giant branch.\nThe $^{12}$C\/$^{13}$C ratios and the total carbon abundances decrease \ndue to the convection which dredges up the products of internal CNO cycle to \nstellar atmosphere as ascending RGB. If it reaches AGB stage,  fresh $^{12}$C \nmay be supplied from the internal He burning layer to stellar surface leading \nto an increase of  $^{12}$C\/$^{13}$C ratios  again. \n\n\\subsection{ Spectral characteristics of the  candidate CH  stars } \n\n\\begin{figure*}\n\\epsfxsize=14truecm\n\\epsffile{aruna_chstars_fig4.eps}\n\\caption{ A comparison of the spectra of three HE stars in the\nwavelength region 3870 - 5400 \\AA\\, with the spectrum of the comparison star\nHD~26. Prominent features  noticed in the spectra  are marked on the figure.\n}\n\\label{Figure 4}\n\\end{figure*}\n\n{\\bf HE~0420-1037, ~1102-2142, ~1142-2601, \n~1146-0151, ~1210-2636, ~1253-1859, ~1447+0102.~~ }\nThe spectra of these objects resemble closely the spectrum of HD~26.\nHD~26 is a known  classical CH star with effective temperature \n5170 K and log $g$ = 2.2 (Vantures 1992b). \n The temperatures of these objects as measured using JHK\nphotometric data range from 4200 to 5000 K.\n The locations of these objects are well within the CH box in figure 3.\nIn figure 4, we show as an example, a comparison of the spectra of three \nobjects HE~0420-1037, HE~1142-2601  and HE~1146-0151 with the spectrum \nof HD~26.\nWith marginal differences in the strengths of the molecular features,  the \nspectra of these \nthree objects show more or less a good match with their counterparts in HD~26. \nThe  CN  band around  4215 \\AA\\,  and the  C$_{2}$ band around  5165 \\AA\\, in \nthe spectra\nof HE~0420-1037 and HE~1146-0151 are marginally  stronger; the Na I D  \nfeature also \nappears stronger. The features due to Ca K and H appear with similar strengths.\nIn the spectrum of HE~1142-2601, the CN  band depth around  4215 \\AA\\,\n  and Ca II K and H line depths are deeper than their counterparts in  HD~26.\nThe Ca I line  at 4226 \\AA\\,  is detected with line depth weaker than the band \ndepth around 4215 \\AA\\,.  In HD~26,  the  Ca I 4226 \\AA\\, feature  is \nnot detected.\nThe object   HE~1253-1859  also have very similar spectrum with that of HD~26.\nThe  CN band around 4215 \\AA\\, and  carbon \nisotopic band around 4730 \\AA\\, are   stronger,  but the CH band, Ca II K and H \nfeatures are of similar strengths. The molecular bands around 5165 \\AA\\,  \nand 5635 \\AA\\,\n show an exact  match.  The lines due to Na  I D, Ba II at 6496 \\AA\\, and\n H$_{\\alpha}$ are seen equally strongly as in HD~26. \nThe Ca I feature at 4226 \\AA\\, could not be detected and the\n secondary P-branch head around 4342 \\AA\\, seems to be marginally \nweaker.  \n  In the  spectrum  of   HE~1102-2142 \nthe molecular  C$_{2}$ bands  around 4735, 5165 and 5635 \\AA\\,  are  slightly \ndeeper than those in HD~26. The  CN band around 4215\\AA\\, and the CH band \naround  4310 \\AA\\,  \nalso appear marginally stronger in the spectrum of  HE~1102-2142. The\nH$_{\\alpha}$  feature and the Ba~II line at 6496 \\AA\\, are  marginally weaker;\nthe feature due to Na I D\nappears with similar strength as in  HD~26.  H$_{\\beta}$ at 4856\\AA\\,\nis  clearly seen. The Ca I line at 4226 \\AA\\, is weakly detected.\nIn the spectrum of HE~1210-2636, the CN band around 4215 \\AA\\, and \nthe secondary P-branch head around 4342 \\AA\\, appear slightly stronger than \nin HD~26. The C$_{2}$ molecular band around 5165 \\AA\\, is also  slightly \nweaker.\nThe  carbon isotopic band  around 4733 \\AA\\, is marginally detectable. \nCa I  line at 4226 \\AA\\, could  not be \ndetected. Features due to Ca II K and  H and H$_{\\alpha}$ are  clearly detected.\n In the spectrum of  HE~1447+0102, the CN band around  4215 \\AA\\, is almost\nabsent. Strong well defined features due to Ca II K and\nH are seen.  Molecular bands around 4733,  5165, and  5635 \\AA\\,\n are distinctly seen to be stronger than their counterparts in HD~26. \nIn the redward of \n5700 \\AA\\,  no  molecular  bands are  detected. We assign these objects to \nthe CH group. \\\\\n\n\\begin{figure*}\n\\epsfxsize=14truecm\n\\epsffile{aruna_chstars_fig5.eps}\n\\caption{ A comparison of the spectra of three HE stars in the\nwavelength region 3870 - 5400 \\AA\\, with the spectrum of the comparison star\nHD~209621. Prominent features  noticed in the spectra  are marked on the figure.\n}\n\\label{Figure 5}\n\\end{figure*}\n{\\bf HE~0136-1831, ~0308-1612, ~1027-2501, ~1051-0112, ~1119-1933, ~1120-2122, \n~1123-2031, ~1145-1319,  ~1205-2539,  ~1331-2558, ~1404-0846, \n~1425-2052, ~1525-0516, ~2114-0603, ~2211-0605, \n~2228-0137, ~2246-1312.~~ } \nThe spectra of these objects resemble closely  the spectrum of HD~209621,\na  classical CH star  with effective temperature  ${\\sim}$  4400 K \n(Tsuji et al. 1991). The  effective temperatures estimated for this set \nof objects  using JHK \nphotometry range from 3948 K (HE~2114-0603) to 4675 K (HE~1119-1933). Their\nlocations on the J-H vs H-K plot are well within the CH box in figure 3.\nThree examples,  HE~0136-1831, HE~1027-2501 and HE~2228-0137  from this \nset are  shown in figure 5 together  with the spectrum of HD~209621.\nIn the spectrum of HE~0136-1831, the CN band around 4215 \\AA\\, is \nmarginally weaker and the carbon molecular \nbands around 4733 and 5635 \\AA\\,  are marginally stronger than those \nin HD~209621. All other features show a good match.  The spectrum of \nHE~1027-2501  also shows a  close match with the spectrum of HD~209621. \nExcept for the molecular bands around 4733, 5165 and 5635 \\AA\\, that appear \nmarginally weaker in the spectrum of HE~2228-0137 the spectrum of this\n object  bears a close resemblance with the spectrum of  HD~209621.\nThe spectrum of  HE~0308-1612  shows  weaker molecular bands around 5165 \\AA\\, \n and 5635 \\AA\\,. The CN band around 4215 \\AA\\, and  the carbon \nisotopic band around 4730 \\AA\\, are  of similar strengths. The CH band around \n4300 \\AA\\, and  Ca II K  and H  features are of similar depths.  The  lines \ndue to Na I D, Ba II at 6496 \\AA\\, and  H$_{\\alpha}$ are clearly noticed.\nThe Ca I feature at 4226 \\AA\\, could not be detected. \nThe spectrum of  HE~1051-0112 shows a weaker CN  band around 4215 \\AA\\,. The \nG-band \nof CH appears with  almost the  same strength   as in HD~209621. The secondary \nP-branch head around 4342 \\AA\\,  and  the bands around  4730 and 5635 \\AA\\, \nare  relatively stronger. Features due to Ca II K and H are barely detectable \nin the spectrum of this object. The molecular  band around 5165 \\AA\\, shows an \nexact match with its counterpart in HD~209621. The features due \nto H$_{\\alpha}$ and Na I D  are detected distinctly; the  Ba II feature at\n  6496 \\AA\\, is  marginally detected.\n\nIn the spectrum of HE~1119-1933, Ca II K and  H\nappear marginally stronger. The molecular band around 5365\\AA\\, appears \nmarginally \nweaker than in HD~209621.  The spectra of HE~1120-2122 and HE~1123-2031 are \nvery similar, both  exhibit a weaker CN band around 4215 \\AA\\,.\n All other features show a  good match with their counterparts in the spectrum \nof HD~209621.\nCa II K and H appear with almost  the same strength in the spectrum of \nHE~1120-2122 as in HD~209621. Ca I line at 4226 \\AA\\, is not detectable.\nThe spectra of HE~1123-2031, HE~1145-1319, HE~1205-2539, HE~1331-2558 \n are  noisy shortward of 4100 \\AA\\,\nand  the lines due to Ca II K and H  could not be clearly detected.\nCa I line at 4226 \\AA\\, is not detectable in these spectra.\nFeatures due to Na  I D, H$_{\\alpha}$, and Ba II at 6496 \\AA\\, are detected. \n In the spectrum of HE~1145-1319, C$_{2}$ molecular bands around 5635 and \n4733 \\AA\\,  are marginally deeper than those in HD~209621.  \nThe features redward of 4200 \\AA\\, in the spectrum of HE~1205-2539 show a good \nmatch with those in HD~209621. The molecular features in the spectrum \n of HE~1331-2558 are  also of similar strenths with those in HD~209621. \nExcept for the G-band of CH, all other molecular features are weaker in the \nspectrum of HE~1404-0846. The features due to Ca II K  and H are marginally \nstronger. The spectrum of HE~1404-0846 is noisy at the blue end.\n\nIn the spectrum of  HE~1425-2052 the G-band of CH  and  the C$_{2}$ band \naround 5635  \\AA\\,  are mildly stronger.\nThe rest of the features show a close  match   with their counterparts \nin HD~209621.\nThe  Ba II feature at 6496 \\AA\\,  appears with equal intensity  as that of\nH$_{\\alpha}$ feature. The feature due to Na  I D is clearly detected.\nIn the spectrum  of HE~1525-0516, H$_{\\alpha}$ and  Na I D features\n are detected with almost equal strength as  in HD~209621. \nThe spectrum of HE~2114-0603 shows a remarkably close  match with\nthe features in HD~209621 including those longward of 5700 \\AA\\,. However the\nfeatures due to Ca II K  and H that are seen very distinctly in the spectrum \nof HD~209621 could not be detected in the spectrum of HE~2114-0603;\nthe spectrum  is noisy blueward of 4000 \\AA\\,.\nIn the spectrum of  HE~2211-0605  the molecular\n features are weaker than their counterparts in  HD~209621 but stronger \nthan those in HD~26. The CH band  matches  exactly with the one in HD~209621.\n Ca II K and H appear with  almost  equal strengths as in HD~209621.\nThe spectrum of HE~2246-1312 shows a  weaker molecular band  around\nCN 4215 \\AA\\,. Other molecular bands appear with  almost of equal strengths \nas their counterparts in HD~209621.  The spectrum \nblueward of 4100  \\AA\\, is  noisy and \n Ca II K and H features could not be detected as  well defined features.\nThe spectrum obtained in  september 2008 has a better signal. \\\\\n\n\\begin{figure*}\n\\epsfxsize=14truecm\n\\epsffile{aruna_chstars_fig6.eps}\n\\caption{ A comparison of the spectra of three HE stars in the\nwavelength region 3880 - 5400 \\AA\\, with the spectrum of the comparison star\nHD~5223. Prominent features  noticed in the spectra  are marked on the figure.\n}\n\\label{Figure 6}\n\\end{figure*}\n\n {\\bf HE~0008-1712, ~0052-0543, ~0100-1619, ~0225-0546, ~1045-1434, \n~1110-0153, ~1157-1434, ~1228-0417, ~1405-0346, ~1410-0125, ~1431-0755,\n ~1440-1511.~~ }\nThe spectra of these objects closely resemble the spectrum of HD~5223, \na well-known classical CH star with effective temperature ${\\sim}$ 4500 K,\n log $g$ = 1.0 and metallicity [Fe\/H] = $-$2.06 (Goswami et al. 2006).\nThe effective temperatures of these objects  derived from J-K colour range \nfrom  about 3924 K (HE~0052-0543)  to 4795 K (HE~1228-0417).\nExcept for the two outliers  HE~1045-1434 and  HE~1228-0417 (represented \nwith open squares)  the locations  of this set of \nobjects are well within the CH box in figure 3.\n\nA comparison of  the spectra of HE~0008-1712, HE~0100-1619 and HE~1405-0346 \nwith the spectrum of HD~5223 is shown in figure 6.\nThe Ca I line at  4226 \\AA\\, is not detectable in any of these spectra.\nThe  CH band as well as other molecular bands  show a very good match.\nThe features due to Ca  II K and H  are seen with equal strength as in HD~5223.\nThe CN band around 4215 \\AA\\, in HE~0100-1619\nis slightly deeper. The bands longward of 5635 \\AA\\, are also  marginally \ndeeper.\nThis object HE~0100-1619 is also mentioned as a CH star in \nTotten et al. (2000). Heliocentric radial velocity of HE~0100-1619 as reported\n  by Bothun et al. (1991) is $-$142 km s$^{-1}$.\n\n The spectra of  HE~0052-0543 and HE~1110-0153 \nshow  stronger molecular bands than their counterparts in HD~5223.\nIn the spectrum of HE~0225-0546 the molecular  bands are  marginally stronger \nthan  in HD~5223. The molecular  features  above 5700 \\AA\\, seen  in these two\nspectra  are barely noticed in the spectrum of HD~5223.\nThe spectrum of HE~1157-1434 also show a good match with the spectrum of\nHD~5223 except for the molecular band  around 5635 \\AA\\, which is distinctly\n weaker in its spectrum.\nThe molecular features redward of  5700 \\AA\\, are  also noticed\nweakly  in the spectrum of this object.\n The spectrum of HE~1405-0346 shows a stronger  CN  band around\n4215 \\AA\\, as well as a stronger carbon molecular  band around 5635 \\AA\\,. \nThe secondary P-branch head near 4342 \\AA\\, is also stronger\nthan its counterpart in HD~5223. Other molecular bands around 4733 and  \n5165 \\AA\\,   show a  good match.  Ca  II K and H are seen as strongly as \nin HD~5223.\n The effective temperature of the object from J-K colour is 4391 K, slightly \nlower than the  effective temperature of HD~5223. \nIn the spectrum of HE~1410-0125 the molecular features are slightly shallower\nthan their counterparts in HD~5223. The CH band depth is however of  similar \nstrength.  The feature at  Ca I 4226 \\AA\\, is absent; the features due to \n Ca II K and H  are of similar strengths. The CN band around 4215 \\AA\\,  \nmatches  well with the CN feature in HD~5223.  The  radial velocity\nof this object  as quoted by Frebel et al. (2006) is  +80 Km s$^{-1}$. \nThe effective temperature  estimated using\n(J-K) calibation returns a value 4378 K for this object.\n\nThe spectrum of HE~1431-0755 is noisy blueward of 4000 \\AA\\,; the features of\n  Ca II K  and H   could not be   detected. The CH band around 4310 \\AA\\,  and\n the  CN band around  4215 \\AA\\, appear\n slightly stronger than their counterparts in HD~5223. \nOther C$_{2}$ molecular  bands present in the spectrum are narrower than their\ncounterparts in HD~5223. The spectrum redward of 5700 \\AA\\, shows molecular \nfeatures that are barely noticed in the spectrum of HD~5223.\nThe spectrum of HE~1440-1511 shows molecular bands with almost equal depths\nwith  those in HD~5223. Ca II  K and H features are however stronger than \ntheir counterparts in\nHD~5223.  The spectrum shows a  distinctly stronger feature due to Na I D. \nFeatures of \nH$_{\\alpha}$ and Ba II at 6496  \\AA\\, are of equal strengths. The spectrum  \nredward  of 5700 \\AA\\, shows a good match.\n\nIn the spectrum of HE~1228-0417 the  Ba II feature at 6496  \\AA\\, \nand H$_{\\alpha}$ are\nseen with equal strengths as in HD~5223. The part of the spectrum redward of\n5700 \\AA\\, shows a very good match. The Ca I line at 4226 \\AA\\, is not detected.\nThe feature due to Na I D  is clearly detected. Other carbon molecular features\naround 4730, 5165, and 5635 \\AA\\, appear marginally weaker than their \ncounterparts in HD~5223. The G-band of CH appears with almost equal \nstrength but  the CN band around 4215 \\AA\\, is marginally weaker than its \ncounterpart  in HD~5223.\n The effective temperature of the object estimated using  J-K colour \ncalibration is 4795 K, higher than the effective temperature of \nHD~5223 ${\\sim}$ 4500 K (Goswami et al. 2006). The location of this  object\noutside the CH box is not obvious from its low resolution spectra.\\\\\n\n\n\\begin{figure*}\n\\epsfxsize=14truecm\n\\epsffile{aruna_chstars_fig7.eps}\n\\caption{ The spectra of three  dwarf carbon stars in the\nwavelength region 4500 - 6800 \\AA\\,. Prominent features  noticed in the \nspectra  are marked on the figure.\n}\n\\label{Figure 7}\n\\end{figure*}\n\n{\\bf HE~0009-1824, ~1116-1628, ~1358-2508.~~} \n The spectra of these objects are illustrated in figure 7. \nThese three objects are known  dwarf carbon stars.\nThe effective  temperatures of HE~0009-1824, HE~1116-1628, HE~1358-2508\n  as estimated from (J-K) calibration are respectively 5530 K, 4224 K and \n3623 K. As expected, the molecular band depths are the  strongest  \nin HE~1358-2508, \nthe  coolest of the three objects; and weakest in HE~0009-1824.\nIn the  spectrum of HE~0009-1824 the CN band around \n4215 \\AA\\, is completely missing.\nThe features due to  Ca II K  and H   as well as the CN band near 3880 \\AA\\, \nare detected. The G-band of  CH  is strong but not as strong \nas it appears  in CH stars. \nThe secondary P-branch head near 4342 \\AA\\, is seen distinctly. Apart from \nthe absence of the  CN band around  4215 \\AA\\,  the \nspectrum of this object looks somewhat  similar to the spectrum\n of HD~209621. \nThe distance of this object as reported by Mauron et al. (2007) is 300 pc. \n\nThe spectra of HE~1116-1628 and HE~1358-2508  show characteristics of C-R star \nRV Sct with marginal differences in the  molecular band depths. \nIn the spectrum of HE~1358-2508, the CH  band is marginally stronger \nthan in  RV Sct. The C$_{2}$ molecular  bands are  stronger in the spectrum \nof this object. The CN  band around 4215\\AA\\, is  clearly detected.\nRatnatunga (1983) first proposed  this object   HE~1116-1628 to be a \ndwarf carbon\nstar. This object  is  also present in the list of dwarf carbon stars\nof  Lowrance et al. (2003). Mauron et al. (2007)  reported  the proper motions\n in ${\\alpha}$ and\n${\\delta}$ and their respective 1${\\sigma}$ errors in mas yr$^{-1}$ as\n$-23.5 \\pm 6.7$ and $+29.8 \\pm 4.6$. \n  The distances of HE~1116-1628 and HE~1358-2508 \nas reported by Mauron et al. (2007) are  170 pc and 270 pc respectively.\n Totten and Irwin (1998)  reported a radial velocity of $-69$ km s$^{-1}$\n for the object  HE~1116-1628.\nAll the  three objects have total proper motion ${\\mu}$ \n${\\ge}$ 30 mas yr$^{-1}$ (Mauron et al. 2007).\n\n  The locations  of the three dwarf carbon stars are \n indicated by open triangles in figure 3. Location of HE~0009-1824\nis on the left below the CH box, the location of HE~1358-2508 is on the\nright edge of the CH box and the location of HE~1116-1628 is  found to be \nwell inside the CH box. \n Dwarf carbon stars have anomalous infrared colours (Green et al. 1992 and \nWesterlund et al. 1995). In the conventional two colour JHK diagram\nthe locus of dwarf-carbon-stars colours is away  from the normal carbon-star\nlocus. The locus defined by  dwarf carbon stars is bounded by \n(J-H) ${\\le}$ 0.75\nand (H-K) ${\\ge}$ 0.25 (Westerlund et al. 1995). This condition is \nsatisfied by HE~1358-2508; however\nHE~0009-1824, and  HE~1116-1628 both have (H-K) colours less than the lower \nlimit of 0.25 mag set for dwarf carbon stars.\\\\\n\n\n\\begin{figure*}\n\\epsfxsize=14truecm\n\\epsffile{aruna_chstars_fig8.eps}\n\\caption{ A comparison of the spectra of  the candidate C-N stars with the\n spectrum of V460 Cyg in the wavelength region 4500 - 6800 \\AA\\,.\n The bandheads of the prominant molecular bands, Na I D and H$_{\\alpha}$ \nare marked on the figure.\n}\n\\label{Figure 8}\n\\end{figure*}\n\n\n{\\bf Candidate C-N stars:   HE~0217+0056, ~0228-0256, ~1019-1136, \n~1344-0411, ~1429-1411, ~1442-0058, ~2213-0017, ~2225-1401.~~}  \\\\\nThe spectra of these objects show a close resemblance with the spectrum of the\nC-N star Z PSc with similar strengths of CN and C$_{2}$ molecular\nbands across the wavelength regions. \nIn figure 3, the objects  HE~0217+0056, HE~1019-1136,  HE~1344-0411, \nHE~1429-1411, HE~1442-0058 and    HE~2213-0017 represented by solid triangles\n lie  well within the CN box.\nThe spectra  have  low flux   below  about 4400 \\AA\\,.\n The spectrum  of HE~1429-1411 is  similar to that  of Z PSc's spectrum,\n except that the  CN band around 4215 \\AA\\, is  marginally weaker in this star. \nThe  CH band is weakly detected in the spectrum of HE~1116-1628.  The molecular\nbands near  4735, 5135 and 5635  \\AA\\, are  noticed distinctly.   The feature\ndue to Na I D is strongly\ndetectable.  The Ba II line  at  6496 \\AA\\, is detectable\n but the  H$_{\\alpha}$ feature could not be detected. \nHE~1127-0604 has low flux below about 4200 \\AA\\,. The  CH band and \n C$_{2}$  molecular bands \naround 4735, 5165, 5635 \\AA\\, are detected. All the  features  in the spectrum \nare weaker than their counterparts in Z Psc. While features of \nCa II K and H are  detected, the CN band around 4215 \\AA\\, is  not clearly seen.\nThe spectrum of HE~2225-1401 has low flux below about  4700 \\AA\\,.\nThe strong C$_{2}$ molecular  bands around 5165, 5635 \\AA\\, appear\n stronger than their counterparts  in Z Psc. The spectrum of  HE~2225-1401 \nalthough have spectral characteristics of   C-N stars, its location in figure 3\n is  not within the CN  box. The  spectra of the objects\n HE~2213-0017, HE~1442-0058, HE~1344-0411  compare closest to the\nspectrum of C-N star V460 Cyg as illustrated in figure 8. \n\nThe objects  HE~0217+0056, HE~1019-1136, HE~1442-0058, HE~2213-0017 and \nHE~2225-1401 are  also  mentioned  as N-type stars   in the \nAPM survey of cool carbon stars in the Galactic halo (Totten \\& Irwin 1998).\nTotten et al. (2000) have provided proper motion measurements for \nthese objects.  The distances measured\nby these authors  assuming an average M$_{R}$ = $-$3.5 for these objects  are \nrespectively 24, 16, 43, 29 and 24 kpc. Heliocentric radial velocities  \nestimated by\nTotten \\& Irwin (1998) for these objects are respectively \n$-142 \\pm 3$, $126 \\pm 4$, $37 \\pm 4$, $-44 \\pm 3$, and $-113 \\pm 5$ \n km s$^{-1}$.\nHeliocentric radial velocity of   HE~0228-0256  is $-72$ km s$^{-1}$\n (Bothun et al. 1991).\\\\\n\n\n\n{\\bf HE~0945-0813, ~1011-0942,  ~1127-0604, ~1205-0521,  ~1238-0836, \n ~1418-0306, ~1428-1950,   ~1439-1338, ~2222-2337.~~ }\nThe spectra of these objects show characteristics of C-R stars. \n The spectra of HE~1011-0942,  HE~1205-0521, HE~1238-0836 match closest to \nthe spectrum of RV~Sct. The effective temperatures of the objects estimated\nusing (J-K) calibration range from 3521 K (HE~1238-0836) to 4875 K\n(HE~1127-0604).\n\nIn the spectra of HE~1238-0836 and HE~1428-1950 the CH band  around 4300 \\AA\\, \nis slightly  deeper than in RV~Sct. The molecular features in the redward of \n5700 \\AA\\, appear marginally weaker. \nIn the spectra of HE~0945-0813, the  CN band around 4215 \\AA\\, is \ndistinctly detected.  Ca I line at 4226 \\AA\\, which is generally very\nweak or absent in CH stars appears very strongly in the spectrum\nof this  object.  The feature due to Na I D   appears very strong.\nFeature due to the secondary P-branch head around 4342 \\AA\\,  is \n somewhat noticeable in  the spectrum of  HE~0945-0813. The lines due to \nBa II at 6496 \\AA\\, and\nH$_{\\alpha}$ are detected in both the spectra. The molecular bands around 4733, \n5165 and 5635 \\AA\\,  appear  strongly   in the spectrum of \nHE~0945-0813.  \nThe spectrum of HE~2222-2337  has low flux below about 4100 \\AA\\,.\nThe CH band does not appear as strong as it should be in C-R star's spectrum.\nThe  CN  band around 4215 \\AA\\, is marginally \ndetected. Other molecular  bands are of similar \nstrengths. The  molecular features redward of  5635  \\AA\\, are slightly weaker. \nWe place these objects in  the  C-R group.\\\\\n\n{\\bf  HE~0037-0654,  ~0954+0137,  ~1230-0327, ~1400-1113, ~ 1430-0919, \n~1447-0102, ~2157-2125, ~2216-0202,  ~2255-1724, ~2305-1427, ~2334-1723,\n ~2347-0658, ~2353-2314.~~}\nThe spectra of these objects are characterized by a  weak (or absent) CN band \naround 4215 \\AA\\,. Apart from this feature the spectra are somewhat similar\n to the  spectrum of HD~209621.\n\nThe spectrum of HE~1230-0327 shows a strong  G-band of CH\nand  a  distinct  secondary P-branch head near 4342 \\AA\\,. Ca I feature\nat 4226 \\AA\\, is not detected. The CN band around 4215 \\AA\\, is almost \nabsent. While\natomic lines of  Ca II K, H , H$_{\\alpha}$, Na  I D are distinctly seen,\n BaII line  at 6496 \\AA\\,  is marginally detected.\nThe spectra of   HE~0954+0137,  HE~1400-1113, \nHE ~1430-0919, HE~2255-1724 and  HE~2347-0658 look very similar to the spectrum\n of HE~1230-0327.\nIn the spectra  of these objects  the feature  due to the CN band \naround 4215 \\AA\\\nis marginally detectable. Weak molecular bands noticed in the \nspectrum of HD~209621 upward of 5700 \\AA\\, are  not observable in \nthese spectra. Compared to \n HD~209621, the molecular bands around 4733, 5165, and \n5635 \\AA\\, are slightly weaker in the spectra of these  objects. \nCa II K and H are detected almost with equal strength as in HD~209621. \n In the spectrum of HE~1430-0919 the  secondary P-branch head near  4342 \\AA\\,\n is  marginally weaker than  in HD~209621. While the molecular band  \naround 5165 \\AA\\ shows a good match, the \nbands around 4733 and 5635 \\AA\\, are marginally stronger. The spectrum \nin the redward of 5700 \\AA\\, resembles  the spectrum of HD~209621.\nFeatures due to Na I D, H$_{\\alpha}$ and Ba II line at  6496 \\AA\\, are detected.\nIn the spectrum of HE~1447+0102, the CN  band around 4215 \\AA\\, is almost\nabsent. Strong well defined  features  of Ca II K and H  are seen. \nThe C$_{2}$ molecular bands around 4733, 5165, 5635 \\AA\\, \n are distinctly present. No other molecular  bands are noticed longward of \n5700 \\AA\\,.\nThe spectra of HE~2305-1427 and  HE~2334-1723   show the  CN band around\n 4215 \\AA\\, with band depth almost half of that in HD~209621. \nAll other molecular features  match well  with their counterparts in the\nspectrum of  HD~209621. Weak\n molecular bands that  are noticed in the spectrum of HD~209621 upward \nof 5700 \\AA\\,\nare not noticeable in the spectra  of these two  objects. The features due to \nNa  I D, H$_{\\alpha}$ and Ba II at 6496 \\AA\\, could be detected.\nThe secondary P-branch head at 4223 \\AA\\,  is seen as distinctly as \nin HD~209621.\n\nIn the spectrum of HE~2353-2314, the CH band around 4300 \\AA\\, as well as the\n CN  band  around 4215 \\AA\\,\n are  marginally detected. The carbon molecular band around  5165 \\AA\\,  is \nclearly detected; the band around 5635 \\AA\\, is much  weaker. No other \nmolecular  bands or atomic lines are detectable.  \nIn the spectrum of  HE~2255-1724,  the CN band  around 4215 \\AA\\ is much \nweaker   \n than that in HD~209621. The CH band and Ca II K and H are of\nsimilar depths. The molecular bands around  4733, 5165, 5635 \\AA\\, are slightly \nweaker in this object.  Features of  Na I D,  Ba II line at 6496 \\AA\\,, and\n H$_{\\alpha}$  are distinctly seen. \n The molecular  bands longward of 5635 \\AA\\, are not detectable. \nThe spectrum acquired on  Sep 11, 2008 have a better signal. In the\n spectrum of HE~2334-1723, the CN band around 4215 \\AA\\,  is much weaker than \nin HD~209621; all other molecular  bands show a good match.\n The features due to Ca II K  and H also  show a good match.  No molecular  \nbands  are  detectable upward of 5700 \\AA\\,.\nIn the spectrum of HE~2347-0658 the CN band  around 4215 \\AA\\, is almost \nabsent. \nCa II K and H features and  carbon molecular bands around 4733, 5165, \n5635 \\AA\\\nshow a good match. Molecular  bands seen in HD~209621 upward of 5700 \\AA\\,\n are not detectable in the spectrum of this object.\n\n The spectrum of HE~1400-1113 is noisy  below about 4220 \\AA\\,. The CN band \naround 4215 \\AA\\,\ncould be marginally detected. Ca  II K and H  are detected as  weak features.\n A  strong  CH band around 4300 \\AA\\,  and the secondary  P-branch head \nnear 4342 \\AA\\,  are distinctly seen. Other molecular\n features have band depths \nmarginally weaker than their counterparts in HD~209621. Except  for \nNa  I D, Ba II at  6496 \\AA\\, and \nH$_{\\alpha}$ no other atomic lines are detected redward of 5670 \\AA\\,. \n\nThe spectrum of HE~1430-0919  also shows a very weak CN band around 4215 \\AA\\,. \nThe features\ndue to Ca II K and H are not detected. The G-band of CH around 4300 \\AA\\, is \nhowever very strong in the spectrum.\nThe spectrum of HE~2157-2125 shows  the CH band around 4300 \\AA\\, with almost \nequal \nstrength to its counterpart  in HD~209621. Features due to  Ca II K  and H \n and other \nmolecular features are  also seen with equal intensities.  However,  \nthe CN band around 4215 \\AA\\,  is much \nweaker than that in HD~209621. The spectrum obtained in October, 2008 has a\nbetter signal  than the spectra  obtained in  June and September, 2008.\n\n The spectrum of HE~0037-0654  looks very similar to the spectrum\nof HD~26; however, molecular  bands  of C$_{2}$ around 4730, 5165 and \n5635 \\AA\\, are marginally stronger than their counterparts in  HD~26. The\nCN band around 4215 \\AA\\, is barely detected, much  weaker than in HD~26.\n Ba II line at 6496 \\AA\\, is clearly detected. Strong lines \nof H$_{\\alpha}$ and Na  I D are   distinctly noticed. \nExcept for the features of  Ca II K  and H  which are much weaker,\nthe spectrum of HE~2216-0202 is  very similar to  the spectrum of  HD~26.\n The secondary \nP-branch head around 4342 \\AA\\,  is  much stronger than in HD~26. \nThe CN band around 4215 \\AA\\, is not\nobserved. The CH band at 4305 \\AA\\, is not  as strong as in HD~26. The molecular\nbands around  4733 \\AA\\, and   5236 \\AA\\, are  of similar depths. The carbon \nmolecular band around \n5635 \\AA\\, is weaker than the band around 5165 \\AA\\,. No molecular bands \nlongward of 5700 \\AA\\, are detectable. \n\nThe spectrum of HE~1315-2035 is  noisy blueward \nof 4200 \\AA\\,.  The G-band of CH and the  carbon  molecular  bands near \n 4733, 5165 and  5635 \\AA\\,  are   detected in the spectrum. The H$_{\\alpha}$  \nfeature  is  clearly  detected. The effective temperature of this object is \n4639 K as estimated  from  (J-K) colour calibration.\n\n{\\bf HE~1027-2644.~~} The spectra of HE~1027-2644 do not show presence \nof  any carbon molecular bands. The features due to  Ca  II K and H are \n not detected. The  G-band of CH is seen as a weak feature. \nFeatures due to Ca I at 4226 \\AA\\, and Na D I are \n  seen as strong features.  Ba II line at 6496 \\AA\\, and H$_{\\alpha}$ \nfeature are detected. 2MASS JHK photometry is not available for this object.\n\n\n\\begin{table}\n\\centering\n{\\bf Table 4: Estimated effective temperatures (T$_{eff}$) from \nsemi-empirical relations}\n\n\\begin{tabular}{|c|c|c|}\n\\hline\\noalign{\\smallskip}\nStar Name &    Teff(J-K)  &  Teff(J-H)  \\\\\n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\nHE0008-1712 &  4556.52& 4378.94(-0.5) \\\\\n            &         & 4446.43(-2.5)\\\\ \n            &         &                            \\\\\nHE0009-1824 &  5530.27& 5377.40(-0.5) \\\\ \n            &         & 5443.08(-2.5) \\\\\n            &         &                            \\\\\nHE0037-0654 &  5496.71& 4912.74(-0.5) \\\\ \n            &         & 4980.33(-2.5) \\\\\n            &         &                            \\\\\nHE0052-0543 &  3924.82 &3831.70(-0.5) \\\\ \n            &          &3896.64(-2.5) \\\\\n            &         &               \\\\\nHE0100-1619 &  4615.21 &4305.94(-0.5) \\\\\n            &          &4373.23(-2.5) \\\\\n            &         &                 \\\\\nHE0113+0110 &  4130.72 &3973.94(-0.5)  \\\\\n            &         & 4039.78(-2.5) \\\\\n            &         &                  \\\\\nHE0136-1831&   4459.39& 4493.10(-0.5)  \\\\\n           &          & 4560.81(-2.5) \\\\\n            &         &                \\\\\nHE0217+0056&   2794.61& 3053.31(-0.5) \\\\\n           &         &  3110.53(-2.5) \\\\\n            &         &                 \\\\\nHE0225-0546&   4051.67& 4086.82(-0.5) \\\\ \n            &         & 4153.25(-2.5) \\\\\n            &         &                \\\\\nHE0228-0256 &  3655.89& 3916.80(-0.5) \\\\ \n            &         &  3982.30(-2.5) \\\\\n            &         &                \\\\\nHE0308-1612 &  4420.27& 4428.17(-0.5)  \\\\\n           &          & 4495.77(-2.5)  \\\\\n            &         &                     \\\\\nHE0341-0314&   4119.26& 4336.67(-0.5) \\\\\n           &          & 4404.05(-2.5) \\\\\n            &         &                 \\\\\nHE0420-1037&   4587.42& 4534.65(-0.5) \\\\ \n           &         &  4602.42(-2.5) \\\\\n            &         &                \\\\\nHE0945-0813 &  4650.36& 4629.30(-0.5)  \\\\\n            &         & 4697.14 (-2.5) \\\\\n            &         &               \\\\\nHE1011-0942 & 3417.52& 3646.15(-0.5) \\\\\n            &         & 3709.67(-2.5) \\\\\n            &         &                \\\\\nHE1019-1136 &  2690.13 &3140.84(-0.5) \\\\\n            &         & 3199.16(-2.5)\\\\ \n            &         &                \\\\\nHE1028-2501 & 3824.73 & 3769.05(-0.5)  \\\\ \n            &         & 3833.54(-2.5)  \\\\\n            &         &                \\\\\nHE1045-1434   &4436.49& 4738.21(-0.5) \\\\ \n               &      & 4806.03(-2.5) \\\\\n            &         &                \\\\\nHE1051-0112  & 4594.34& 4411.69(-0.5) \\\\\n             &        & 4479.26(-2.5) \\\\\n            &         &               \\\\\nHE1102-2142  &4492.46& 4383.27(-0.5) \\\\\n             &       & 4450.77(-2.5)\\\\\n            &         &              \\\\\n\\noalign{\\smallskip}\\hline \n\\end{tabular}\n\n\\end{table}\n\n\\begin{table}\n\\centering\n{\\bf Table 4: Estimated effective temperatures (T$_{eff}$) from \nsemi-empirical relations (continued)}\n\n\\begin{tabular}{|c|c|c|}\n\\hline\\noalign{\\smallskip}\nStar Name &    Teff(J-K)  &  Teff(J-H)  \\\\\n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\nHE1110-0153 &  3969.89& 3842.74(-0.5)  \\\\\n            &         & 3907.75(-2.5) \\\\\n            &         &                  \\\\\nHE1116-1628 &  4224.43 &4125.85(-0.5) \\\\ \n            &         & 4192.46(-2.5)\\\\\n            &         &               \\\\\nHE1119-1933  & 4675.25& 4790.28(-0.5)\\\\ \n            &         & 4858.06(-2.5)  \\\\\n            &         &               \\\\\nHE1120-2122 &  4148.01& 3961.57(-0.5)\\\\\n            &         & 4027.33 (-2.5)\\\\\n            &         &                    \\\\\nHE1123-2031 &  4365.87& 4339.85(-0.5)   \\\\\n           &         &  4407.24(-2.5) \\\\\n            &         &                \\\\\nHE1127-0604 &  4875.50& 4604.60(-0.5) \\\\\n             &       &  4672.42(-2.5)  \\\\\n            &         &                  \\\\\nHE1142-2601 & 4475.87 & 4464.64(-0.5)   \\\\ \n            &         & 4532.31(-2.5)   \\\\\n            &         &                  \\\\\nHE1145-1319   &4485.81 &4514.13(-0.5)  \\\\\n             &      &   4581.87(-2.5) \\\\\n            &         &                \\\\\nHE1146-0151  & 4515.88& 4525.81(-0.5)  \\\\ \n             &       &  4593.57(-2.5)  \\\\\n            &         &                \\\\\nHE1157-1434 &  4182.97 &4181.08(-0.5) \\\\\n           &         &  4247.93(-2.5)\\\\\n            &         &                \\\\\nHE1205-0521 &  4650.36 &4927.12(-0.5)  \\\\\n            &        &  4994.67(-2.5)\\\\\n            &         &                \\\\\nHE1205-2539&  4182.97 & 4046.42(-0.5)   \\\\\n            &         &  4112.64(-2.5)  \\\\\n            &         &                    \\\\\nHE1228-0417 &  4795.85& 4964.09(-0.5) \\\\ \n           &          & 5031.55(-2.5)\\\\\n            &         &               \\\\\nHE1230-0327  & 4814.61& 4846.74(-0.5)  \\\\\n               &      & 4914.44(-2.5) \\\\\n            &         &               \\\\\nHE1238-0836&  3521.23 &  3954.13(-0.5)  \\\\\n           &          &  4019.85(-2.5)  \\\\\n            &         &                  \\\\\nHE1253-1859 &  4239.41& 4105.00(-0.5)  \\\\\n            &         & 4171.51(-2.5) \\\\\n            &         &                \\\\\nHE1315-2035 & 4639.76 &4949.26(-0.5) \\\\\n           &          & 5016.77(-2.5)  \\\\\n            &         &                 \\\\\nHE1318-1657 &  4423.50& 4612.48(-0.5)\\\\\n            &         & 4680.31(-2.5)  \\\\\n            &         &                   \\\\\nHE1331-2558  & 4227.41& 4218.84(-0.5) \\\\\n           &           &4285.84(-2.5)  \\\\\n            &         &                  \\\\\nHE1344-0411  & 3118.34 &3414.55(-0.5) \\\\\n            &          &3475.93(-2.5) \\\\ \n            &         &                \\\\\n\\noalign{\\smallskip}\\hline \n\\end{tabular}\n\n\\end{table}\n\n\\begin{table}\n\\centering\n{\\bf Table 4: Estimated effective temperatures (T$_{eff}$) from \nsemi-empirical relations (continued)}\n\n\\begin{tabular}{|c|c|c|}\n\\hline\\noalign{\\smallskip}\nStar Name &    Teff(J-K)  &  Teff(J-H)  \\\\\n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\nHE1358-2508&  3623.67&  3826.04(-0.5)   \\\\\n            &         &  3890.93(-2.5)  \\\\\n            &         &                 \\\\\nHE1400-1113 &  4894.81& 5010.94(-0.5) \\\\\n            &         & 5078.27(-2.5) \\\\\n            &         &                \\\\\nHE1404-0846 &  4239.40& 4027.25(-0.5)\\\\\n            &         & 4093.38(-2.5) \\\\\n            &         &                \\\\\nHE1405-0346  & 4391.32& 4484.40(-0.5) \\\\\n            &        &  4552.09(-2.5) \\\\\n            &         &                 \\\\\nHE1410-0125&  4378.56  &4266.53(-0.5) \\\\\n           &          & 4333.70(-2.5) \\\\\n            &         &              \\\\\nHE1418-0306 & 3598.71&  3761.98(-0.5) \\\\\n            &         & 3826.41(-2.5) \\\\\n            &         &                \\\\\nHE1425-2052&  4191.80 & 4250.49(-0.5)  \\\\\n           &          & 4317.60 (-2.5)  \\\\\n            &         &                  \\\\\nHE1428-1950 & 4505.82  &4573.18 (-0.5)\\\\\n            &         & 4640.98(-2.5) \\\\\n            &         &                \\\\\nHE1429-1411 & 3057.76 & 3302.55(-0.5)  \\\\\n            &        &  3362.74(-2.5)  \\\\\n            &         &                \\\\\nHE1430-0919 & 4700.38&  4625.80(-0.5) \\\\\n            &         & 4693.64(-2.5)\\\\\n            &         &                \\\\\nHE1431-0755 & 3937.98 & 3950.23(-0.5)\\\\\n             &        & 4015.92(-2.5)  \\\\\n            &         &                \\\\\nHE1432-2138 & 5074.94 & 5075.25(-0.5)\\\\\n            &         & 5142.38(-2.5) \\\\\n            &         &                     \\\\\nHE1439-1338 &3658.21  & 3898.38(-0.5)\\\\\n            &         & 3963.76(-2.5) \\\\\n            &         &                   \\\\\nHE1440-1511 & 4636.24  &4747.85(-0.5)\\\\\n            &         & 4815.66 (-2.5)\\\\\n            &         &               \\\\\nHE1442-0346 & 4622.20 & 4655.40(-0.5) \\\\\n            &         & 4723.24(-2.5)\\\\\n            &         &                \\\\\nHE1447+0102 & 5042.06 & 4893.55 (-0.5)\\\\\n            &         & 4961.18(-2.5) \\\\\n            &         &                \\\\\nHE1525-0516 & 4546.30 &4695.10 (-0.5)\\\\\n            &         & 4762.94(-2.5) \\\\\n            &         &                 \\\\\nHE2114-0603 & 3948.56 & 3919.97(-0.5)  \\\\\n            &         & 3985.48(-2.5) \\\\\n            &         &                \\\\\nHE2157-2125 & 4583.97 & 5135.81(-0.5)\\\\\n            &        &  5202.71(-2.5)\\\\ \n            &         &                \\\\\nHE2211-0605 & 4553.10 &4621.90(-0.5) \\\\ \n            &         & 4689.73(-2.5) \\\\ \n            &         &                \\\\\n\\noalign{\\smallskip}\\hline \n\\end{tabular}\n\\end{table}\n\n{\\footnotesize\n\\begin{table}\n\\centering\n{\\bf Table 4: Estimated effective temperatures (T$_{eff}$) from \nsemi-empirical relations (continued)}\n\n\\begin{tabular}{|c|c|c|}\n\\hline\\noalign{\\smallskip}\nStar Name &    Teff(J-K)  &  Teff(J-H)  \\\\\n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\nHE2213-0017 & 2701.10 & 3005.84(-0.5)\\\\ \n            &         & 3062.45(-2.5) \\\\ \n            &         &                  \\\\\nHE2216-0202 & 4969.45&  5122.15(-0.5) \\\\ \n            &         & 5189.11(-2.5) \\\\\n            &         &                  \\\\\nHE2222-2337 & 3911.73 & 3879.01(-0.5) \\\\ \n            &         & 3944.26(-2.5) \\\\ \n            &         &                 \\\\\nHE2225-1401 & 2169.18 & 2845.70(-0.5)\\\\ \n             &        & 2900.11(-2.5) \\\\ \n            &         &                \\\\\nHE2228-0137 & 4369.03 & 4284.06(-0.5) \\\\ \n            &        &  4351.28(-2.5) \\\\ \n            &         &                \\\\\nHE2246-1312 & 4110.70&  4125.95(-0.5) \\\\ \n            &        &  4192.57(-2.5)\\\\ \n            &         &                   \\\\\nHE2255-1724 & 4675.26&  4388.73(-0.5)\\\\ \n            &        &  4456.25(-2.5) \\\\ \n            &         &                  \\\\\nHE2305-1427 & 5042.06&  4594.23(-0.5) \\\\ \n            &        &  4662.05(-2.5) \\\\ \n            &         &                \\\\\nHE2334-1723 &4729.39 &4827.13 (-0.5) \\\\ \n             &        & 4894.87(-2.5) \\\\ \n            &         &                  \\\\\nHE2347-0658 & 5554.46 &4989.70(-0.5)  \\\\ \n            &         & 5057.10(-2.5) \\\\ \n            &         &               \\\\\nHE2353-2314 & 3927.44 &4014.92(-0.5)\\\\ \n            &         & 4080.98(-2.5)\\\\ \n\\noalign{\\smallskip}\\hline \n\\end{tabular}\n\nThe numbers inside the parentheses indicate the adopted metallicities [Fe\/H] \\\\\n\\end{table}\n}\n\n{\\footnotesize\n\\begin{table}\n\\centering\n{\\bf Table 5: Stars with   radial velocity estimates  }\n\\begin{tabular}{|c|c|c|}\n\\hline\\noalign{\\smallskip}\nStar Name &   $v_{\\rm r}$ km s$^{-1}$  &  Reference  \\\\\n\\noalign{\\smallskip}\\hline\\noalign{\\smallskip}\nHE~0100$-$1629 & $-$142.0              & 1   \\\\\nHE~0217$+$0056 & $-$142.0 ${\\pm}$ 3    & 2  \\\\\nHE~0228$-$0256 & $-$72.0               & 1   \\\\\nHE~1019$-$1136 & $-$126.0 ${\\pm}$ 4    & 2  \\\\\nHE~1105$-$2736 & $-$36.0 ${\\pm}$ 1.3    & 3  \\\\\nHE~1116$-$1628 & $-$69.0               & 2 \\\\\nHE~1152$-$0355 & $+$431.3 ${\\pm}$ 1.5 & 4  \\\\\nHE~1305$+$0007 & $+$217.8 ${\\pm}$ 1.5 & 4 \\\\\nHE~1410$-$0125 & $+$88.0 ${\\pm}$ 3     & 5    \\\\\nHE~1429$-$1411 & $-$90.0 ${\\pm}$ 1.5   & 6  \\\\\nHE~1442$-$0058 & $-$37.0 ${\\pm}$ 4     & 2   \\\\\nHE~2213$-$0017 & $-$44.0 ${\\pm}$ 3    & 2 \\\\\nHE~2225$-$1401 & $-$113.0 ${\\pm}$ 5    & 2  \\\\\nHD~26        & $+$217.8 ${\\pm}$ 1.5 & 6  \\\\\nHD~5223      & $-$244.9 ${\\pm}$ 1.5 & 4  \\\\\nHD~209621    &  $-$390.5 ${\\pm}$ 1.5 & 6  \\\\\n\\noalign{\\smallskip}\\hline \n\\end{tabular}\n\nReferences: 1: Bothun et al. (1991), 2: Totten \\& Irwin (1998), \n3: Zwitter et al. (2008), 4: Goswami et al. (2006), 5: Frebel et al. (2006), \n6: Goswami et al. (in preparation\n\\end{table}\n}\n\n\n\n\\section{Concluding Remarks}\n\nAn accurate assessment of the  fraction of CH stars can significantly aid \nour understanding of formation and evolution of heavy elements at low \nmetallicity. Another important issue is the role of low to intermediate-mass\nstars of the halo in the early Galactic chemical evolution. Thus large samples\nof faint high latitude  stars such as the one reported by Christlieb et al. \n(2001b)  that contain different types of carbon stars need to be analyzed to \nunderstand the astrophysical implications  of each individual type  of \nstellar population.  Our objective  in this study has been to identify the \nCH stars (as well as different type of stellar objects) in a selected sample \nof high  Galactic latitude field stars. The sample is  based on  our  \non-going  observational programs with HCT and VBT  on cool  stars. During \n2007 and 2009 we have acquired low resolution spectra for a large number of \nstars that included  about ninety two  objects from the Hamburg survey of \nChrisltieb et al. (2001b).\n\nThe  spectral classification criteria are those  presented in Goswami (2005).\nAmong the ninety two objects, the spectra of  seventy  objects are \ncharacterized by the presence of strong C$_{2}$ molecular bands. The spectra\nof  twenty two  objects show only a weak or moderate  G-band of CH and a CN \nband \naround 4215 \\AA\\,.  One object, HE~1027-2644 does not show presence of any \nmolecular bands in its spectrum. The spectral   analysis  led to the \ndetection of \nthirty six  potential CH star candidates.  Their locations on the two\ncolor J-H versus H-K diagram, estimated effective temperatures, and carbon\nisotopic ratios are in support of their classification with this class\nof objects. This set of objects  will make important targets for  subsequent\nchemical composition  studies  based on high resolution spectroscopy and for \nconfirmation of these objects with this class of identification.\n\n While identification of C-N and C-J type stars are relatively easy,  \nseparating C-R stars from CH stars is not so straightforward.\nThe two main properties, presence or absence of $s-$process elements and\nbinarity that differentiate early-R stars from CH stars, can\nbe known  only through detailed abundance studies that require high\nresolution spectroscopy and from long-term radial velocity monitoring.\n The faintness of these objects makes   high resolution spectroscopic\nstudies  arduous and time-consuming. As such, the method described in\nGoswami (2005) to distinguish a C-R from a CH star proved  quite\nuseful (Goswami et al. 2006).\nHigh resolution spectra will also allow for    an accurate \nmeasurement of $^{12}$C\/$^{13}$C ratios.  Based on medium resolution spectra,\n for  the potential CH star candidates,  we find a low (${\\le}$ 10)  \ncarbon isotopic ratios,  indicating that they belong \nto  the group of early-type CH stars.\n\nAbia et al. (2002) have shown that CH stars  cannot be formed above a \nthreshold metallicity, around Z $\\sim$ 0.4Z$_{\\odot}$.  According to \nDominy (1984), the metallicities of C-R stars  are either  solar or slightly \nsub-solar. C-R stars are believed to be Core Helium Burning (CHeB) \ncounterparts of CH stars in which $s-$process elements are either absent \nor not detectable (Izzard et al. 2007).  These authors  have predicted an \nearly-R\/CH ratio $\\sim$ 7\\%, at [Fe\/H] = -2.3, a metallicity typical of the\nGalactic halo.  This ratio  is derived considering only CHeB CH stars,  if \nCH giants and dwarfs are also considered, this ratio is likely to get much\nlower.\n\nWesterlund et al. (1995) defined dwarf carbon stars as having J-H ${\\le}$ 0.75,\n H-K ${\\ge}$ 0.25 mag. Among the three dwarf carbon stars in our sample the\n objects HE~1358-2508 occupies a region defined by these limits on J-H, H-K \nplane.  HE~0009-1824  and HE~1116-1628 however do not follow the JHK \ndefinition of dwarf carbon stars offered by Westerlund et al. (1995). It \nseems, these limits on J-H and H-K may  not be  very tight. Proper motions\nof these objects have been estimated by Mauron et al. (2007) and have \nplaced them as  dwarf carbon stars.\n\n The temperature estimates of the program stars derived using JHK-temperature\n calibration relations of Alonso et al. (1996), although varying over a wide \nrange,  provide a  preliminary temperature check for the program stars and \ncan  be \nused  as starting values in deriving atmospheric  parameters from high \nresolution spectra using model atmospheres. \n\nImportant information such as kinematic properties of the stars can be \nderived from radial velocity estimates.\nFrom low resolution spectra, radial velocities are generally computed using\n Fourier cross-correlation method. This method,\nwidely  employed, uses  the spectrum of a radial velocity standard as the \ntemplate spectrum.  Unfortunately, we could  not acquire spectra of radial \nvelocity standards that are usable for the present set of program stars \nunder study. \nEstimated radial velocities using a few atomic lines,\ndetectable on the low resolution spectra,  did not return consistent results.\nHowever,  a systematic estimation of radial velocities\nof the program stars using appropriate radial velocity standard templates\nwould be a worthwhile future program.\nRadial velocities of a few stars belonging to our program star list,\nthat are available in literature, are listed in Table 5.\n\nThe primary focus of  this work is CH stars; however, a  detailed discussion on\nthe objects of other  spectral types is also necessary and is under progress.\\\\\n\n {\\it Acknowledgement}\\\\\n We thank  the staff at IAO, VBO and at the remote control station  at CREST,\nHosakote for assistance during the observations.  This work made use of the\nSIMBAD astronomical database, operated at CDS, Strasbourg, France, and the\nNASA ADS, USA. Ms Drisya K. is a JRF in the DST project NO. SR\/S2\/HEP-09\/2007; \nfunding from the above mentioned project is greatfully acknowledged. \n\\\\\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nBiochemical reactions in cellular microdomains involve, in general,\na small number of molecules that can bind to agonist molecules,\nconfined in some subregions. A microdomain $\\Omega$ is defined as a\nbounded domain where a large fraction of the boundary $\\partial\\Omega_r$\nis reflective and a small part $\\partial\\Omega_a$ of it is absorptive,\nwhich allows molecules to enter or\/and exit. Under normal\nphysiological conditions, a molecule can be trapped inside a\nmicrodomain for a period long enough, compared to other time scales\nsuch as free diffusion or binding time. Because a molecule can be\ntrapped for a long time, many chemical bounds can be made, before it\nexits. From a physiological stand point, an interesting property of\nsuch  microdomain is that depending on the number of chemical bounds\nmade by a molecule, a cascade of chemical reactions can be\ninitiated, which ultimately affects some physiological properties.\nOur interest here is to estimate the number of chemical bounds made\nby a Brownian interacting molecule inside $\\Omega$. This number\ndepends on the geometry of the microdomain and the distribution of\nagonist molecules. We also provide an estimation of the mean time\nspent (Dwell time) by a molecule inside the microdomain, denoted by\n$E(\\tau_D)$. For that purpose, we derive an asymptotic formula for\nthe Dwell time, the mean and the variance of the number of bounds\nmade before the molecule exits, as the ratio\n$\\frac{|\\partial\\Omega_a|}{|\\partial\\Omega_r|}$ tends to zero. Finally, we\nderive a formula for the Dwell time of a molecule inside $\\Omega$,\nwhen a steady state flux of molecules is maintained fixed at the\nabsorbing boundary. The role of the flux is to fix the number of\nfree binding sites. Using the present method, we also obtain an\nestimate of the forward binding rate constant. Historically, the\ntheory of chemical reactions at a molecular level limited by\ndiffusion has been developed by many authors, to quote but a few\n\\cite{Wilemski,Perico,Agmon,Szabo1,Szabo2}: using the classical\ntheory of diffusion and interactions with binding sites, various\nrate constants were computed. Recently, using averaged equations,\nchemical reactions in microdomains have been described in\n\\cite{BereSmalhole,Berepartialflux}. Chemical reactions in closed\nmicrodomains were studied in \\cite{JChemPhys}, where we obtain, in\nparticular, some estimates on the mean of the variance of the\nnumber of bound molecules in a steady state regime. In \\cite{HS},\nan asymptotic estimate of the mean time it takes for a Brownian\nmolecule to escape an empty domain through small openings located\non the boundary, was obtained using a new type of singular\nperturbation problem. More specifically, if D denotes the\ndiffusion constant, $|\\Omega|$ the volume of the domain $\\Omega$\nand $\\varepsilon=\\frac{|\\partial \\Omega_a|}{|\\partial \\Omega|}<<1$ is the\nratio of the absorbing to the total boundary, then for\n$\\varepsilon$ small, the leading order term of the mean escape\ntime $\\tau(\\mbox{\\boldmath$x$})$ (for a molecule starting at position $\\mbox{\\boldmath$x$}$, far\nfrom the entrance) is given by\n\\begin{eqnarray}\\label{HolcSchuss}\n\\tau(\\mbox{\\boldmath$x$}) =\n\\frac{|\\Omega|}{\\pi D}\\log(\\frac1{\\varepsilon})+O(1).\n\\end{eqnarray}\nIn the first approximation, the mean time $\\tau(\\mbox{\\boldmath$x$})$ does not depend\non the initial position $\\mbox{\\boldmath$x$}$ and will be denoted by $\\tau$. In this\narticle, we obtain an explicit asymptotic estimation of the Dwell\ntime $E(\\tau_D)$ as a function of the characteristic sizes of the\ndomain $\\Omega$, the size of the small openings $\\partial \\Omega_a$, the\nnumber of the binding molecules. More specifically, $E(\\tau_D)$ is\ngiven by expression (\\ref{eq:formula_mean_mean}), which depends on\nthe mean time $\\mean{\\tau}$ to exit when no binding occurs, the mean\ntime $\\mean{T}$ to enter into the binding site area, $m_{\\delta}$\nthe mean probability to bind before exit and the backward binding\nrate $k_{-1}$. We get\n\\begin{equation}\\label{eq:formula_mean_meanintro}\nE(\\tau_D) = \\mean{\\tau}+\\frac{1-m_{\\delta}}{m_{\\delta}}\\left(\n\\mean{T}+\\frac{1}{k_{-1}}\\right).\n\\end{equation}\nIt is well known from the theory of chemical reactions that the\nbackward binding rate $k_{-1}$ depends only on the local\ninteractions between two interacting molecules. If $\\Delta E$\ndenotes the activation barrier, $kT_e$ is the energy due to the\ntemperature, the Arrhenius law states that: \\begin{eqnarray} k_{-1} = C\ne^{-\\frac{\\Delta E}{kT_e}},\n \\end{eqnarray}\nwhere C is a constant that depends on the temperature $T_e$, the\nelectrostatic potential barrier $\\Delta E$ generated by the\nbinding molecule and the friction coefficient \\cite{Schuss}. In\nthe first part of the paper, we derive equation\n(\\ref{eq:formula_mean_meanintro}) by counting the number of bounds\nbetween the Brownian molecule and the agonist molecules, before\nthe Brownian molecule exits the domain. In the second part, we\nderive some asymptotic estimates of the quantities $\\mean{T}$,\n$\\mean{\\tau}$ and $m_{\\delta}$ as a function of the geometry, when\nthe radius $\\delta$ of the binding site tends to zero. Although\nthe present computations are carried out in two dimensions, they\ncan be extended to dimension 3 by using the techniques developed\nin \\cite{SSHE}. Finally in the last part, we apply the present\ncomputations to study chemical reactions occurring in synaptic\nmicrodomains: the chemical reactions are the binding of receptors\nwith the scaffolding molecules. It is indeed of great interest to\nanalyze the mechanism that regulates the number and the type of\nreceptors at a synapse, because receptors control the synaptic\nweight. Any fluctuations of the number results in a variation of\nthe synaptic weight and affects the reliability of the synaptic\ntransmission. Moreover, certain experimental protocols have lead\nto a Long Term Potentiation of a synapse, a mechanism which is\nassociated with a change of the number and the type of certain\nreceptors \\cite{Bredt,Nicoll}. The regulation of synaptic\nplasticity is a fundamental process underlying learning and memory\n\\cite{Bredt,Nicoll} and recently, single molecule tracking has\nrevealed that the number of postsynaptic receptors, which\nparticipate to the synaptic transmission, is not fixed but it\nchanges due to constant traffick of receptors on the surface of\nneurons. Receptors move in and out from synaptic regions\n\\cite{Choquet} \\cite{Triller} and following these observations,\nmany questions have been raised: in particular, what determines\nthe time spent by a receptor inside a synapse? How receptors can\nbe stabilized inside a synapse? How long they stay inside synaptic\nmicrodomains? Such questions are partially answered in the present\npaper. In particular, our computation of the Dwell time of a\nreceptor inside a specific microdomain, called the Postsynaptic\ndensity (PSD) takes into account the interaction with the\nscaffolding molecules, which was ignored in \\cite{HS}.\n\n\\subsection{Molecular dynamics in a microdomain}\n{The dynamics of a molecule or a protein moving on the surface of\na cell is usually described in the Smoluchowsky limit (large\nfriction) of the Langevin equation \\cite{Schuss}: for a molecule\nof mass $m$, described by its position $X$ at time $t$, with a\nfriction coefficient $\\gamma$, moving inside a potential well $V$,\nthe Smoluchowsky limit of the Langevin equation is \\begin{eqnarray}\\label{SL}\n\\gamma \\dot{X}+\\nabla V(X)=\\sqrt{2\\gamma \\varepsilon_e}\\dot{w},\n \\end{eqnarray}\nwhere $\\varepsilon_e=\\frac{kT_e}{m}$ and $w$ is a Gaussian random\nvariable with variance 1 and mean 0. In a microdomain $\\Omega$,\nwhere a large fraction of the boundary is reflective $\\partial \\Omega_r$\nand a small part of it is absorptive $\\partial \\Omega_a$, the probability\ndensity function (pdf) $p$ to find $X$ at time $t$ in the surface\nelement $\\mbox{\\boldmath$x$}+d\\mbox{\\boldmath$x$}$ satisfies the Fokker-Planck Equation (FPE)\n\\begin{eqnarray}\\label{FPE} \\frac{\\partial p(\\mbox{\\boldmath$x$},t)}{ \\partial t} &=& D \\Delta p(\\mbox{\\boldmath$x$},t) -\n\\nabla\\cdot (\\nabla V(\\mbox{\\boldmath$x$})p(\\mbox{\\boldmath$x$},t)) \\hbox{ for } \\mbox{\\boldmath$x$} \\in \\Omega\\\\\n& & \\nonumber\\\\\n\\mbox{\\boldmath$J$}(\\mbox{\\boldmath$x$},t)\\cdot\\mbox{\\boldmath$n$}&=&0\\hbox{ for } \\mbox{\\boldmath$x$} \\in \\partial \\Omega_r \\\\\n& & \\nonumber\\\\\np(\\mbox{\\boldmath$x$},t)&=&0 \\hbox{ for } \\mbox{\\boldmath$x$} \\in \\partial \\Omega_a\n \\end{eqnarray}\nwhere $D=\\gamma \\varepsilon_e$ is the diffusion constant, $\\mbox{\\boldmath$n$}$ is\nthe external normal at the boundary, the flux $\\mbox{\\boldmath$J$}$ is given by\n\\begin{eqnarray} \\mbox{\\boldmath$J$}(\\mbox{\\boldmath$x$},t)=-D\\nabla p(\\mbox{\\boldmath$x$},t) +\\nabla V(\\mbox{\\boldmath$x$})p(\\mbox{\\boldmath$x$},t).\n \\end{eqnarray}\nWe denote by $t^{x}$ the first time the molecule arrives at the\nabsorbing boundary  $\\partial \\Omega_a$, when it started at position $\\mbox{\\boldmath$x$}$.\nIt is well known \\cite{Schuss} that the mean first passage is the\nexpectation of the time $t^{x}$ and is given by\n\\begin{eqnarray*}\nE^{\\mbox{\\boldmath$x$}}(t^{x})&=& \\int_{0}^{\\infty} t\\frac{d}{dt}\n Pr\\{ t^x<t \\}dt= \\int_0^{\\infty} Pr\\{t^x>t\\}dt\\\\\n           &=& \\int_0^{\\infty} \\int_{\\Omega} p(\\mbox{\\boldmath$y$},t|\\mbox{\\boldmath$x$})d\\mbox{\\boldmath$y$} dt,\n\\end{eqnarray*}\nwhere $p(\\mbox{\\boldmath$y$},t|\\mbox{\\boldmath$x$})$ is the pdf of the process $X$, conditioned on the\ninitial position $\\mbox{\\boldmath$x$}$, that is, as $t$ goes to zero, \\begin{eqnarray}\np(\\mbox{\\boldmath$y$},t|\\mbox{\\boldmath$x$})\\rightarrow \\delta(\\mbox{\\boldmath$x$}-\\mbox{\\boldmath$y$}),\n \\end{eqnarray}\nwhere $\\delta$ is the Delta-Dirac function. In equation (\\ref{FPE}),\n$V$ represents the potential wells generated by the binding\nmolecules inside the domain $\\Omega$. It is, in fact, the sum of the\nlocal potential wells, supported inside a ball of finite radius\ngenerated by the binding molecules. Usually the binding molecules\nare scattered inside the domain $\\Omega$, but in the present model\nwe replace the scattered distribution of binding molecules by a\nsimplified distribution, where we imagine that all the binding\nmolecules are located inside a compartment $D(\\delta)$ in $\\Omega$.\nIn the present description, the potential $V$ becomes an effective\npotential defined in $D(\\delta)$, whose characteristics should be\nsuch that the classical chemical reaction theory is recovered. More\nspecifically,  we can define the microdomain $\\Omega$ containing the\nbinding domain $D(\\delta)$, which replaces the domain with many\nscattered binding sites: this simplified domain made of two\ncompartments is called the homogenized microdomain and is described\nas (see figure 1)\n\\begin{enumerate}\n\\item An internal compartment, which is described as a disk\n$D(\\delta)$ of radius $\\delta$. This disk represents the region\nwhere the binding sites are located. Instead of using the dynamics\nassociated with equation (\\ref{SL}), we describe the entrance and\nthe exit of a molecule inside $D(\\delta)$ using a Poissonnian\ndescription, where the mean can be related to the properties of\nthe potential well. For that purpose, we recall that a chemical\nreaction with a binding molecule is described as the arrival of a\nBrownian molecule inside the disk $D(\\delta)$. The release process\nis modeled as the escape of the molecule from the potential well\n$V$ and is described by the chemical reaction \\begin{eqnarray} \\label{chem}\nR+S\n\\begin {array}{c}\n{k_1}\\\\\n\\rightleftharpoons \\\\\n{k_{-1}} \\end{array} RS \\end{eqnarray} where  $\\frac{1}{k_{-1}}$ is the mean\nbinding time and depends only on the local potential well, generated\nby the binding molecules \\cite{Tier84} \\cite{Schuss}.\n\\item An external compartment separated from the rest of the\nbiological environment by the boundary $\\partial \\Omega_r$, containing\nsmall openings $\\partial \\Omega_a$. Molecules can enter or exit through\nthe openings and thus can be exchanged with the rest of the\ncellular medium (see figure 1). The dynamics of a molecule in that\ncompartment is described as pure Brownian until it escapes.\n\\end{enumerate}\n\\begin{figure}[htbp]\\label{fig1}\n\\centerline{\\includegraphics[width=2.0in,height=1.9in]{Dwell_fig2.eps}}\n \\caption{Model of a cellular microdomain in two\ndimensions. The domain is a disk $D(R)$ of radius $R$, made of two\ncompartments: an inner disk $D(\\delta)$ of radius $\\delta$ and the\nannulus $A_\\delta=D(R)-D(\\delta)$. A molecule moves by Brownian\nmotion inside $A_\\delta$ until it hits $D(\\delta)$ or the\nabsorbing boundary $\\partial \\Omega_a$. When the Brownian molecule\nenters into $D(\\delta)$, which represents the domain of chemical\nreactions, while it reacts with an effective binding molecule\nduring a mean time (the inverse of the backward binding rate) its\nmovement in $D(\\delta)$ is frozen. The molecule is then released\nuniformly inside the annulus $A_\\delta=D(R)-D(\\delta)$. This\nscenario repeats until the molecule hits the absorbing boundary\n$\\partial \\Omega_a$, where the molecule is finally removed.}\n\\end{figure}\n\n\\subsection{Time spent by a molecule inside a disk containing a small opening}\nWe estimate asymptotically the Dwell time $E(\\tau_D)$ of a molecule\ninside a domain $\\Omega$, when the domain $\\Omega$ is a disk $D(R)$\nof radius $R$. The case of a general domain is left open. By\ndefinition, $E(\\tau_D)$ is the mean time to exit, averaged over an\ninitial uniform distribution. We make the following assumptions: the\nratio $\\varepsilon$ of the absorbing to the reflective boundary of\n$D(R)$ is small $<<1$. The absorbing (resp. reflecting) part is\ndenoted $\\partial\\Omega_a$ (resp. $\\partial\n\\Omega_r$). The computation of the Dwell time will be made using\nthe homogenization version of the domain, described in the\nprevious paragraph: the binding molecules are located in the small\nconcentric disk D($\\delta$), where $\\delta<<R$. Each time a\nmolecule enters into D($\\delta)$, it can be bound with a binding\nmolecule and will be released in the annulus\n$A_{\\delta}(R)=D(R)-D(\\delta)$. Since R is a fixed parameter, we\nwill denote the annulus by $A_{\\delta}$.\n We assume that the boundary $\\partial D(\\delta)$ is always absorbing.\n\\section{The Dwell Time $E(\\tau_D)$}\n The goal of this section is to derive a general expression of the Dwell time\n$E(\\tau_D)$. The movement of a molecule is described here as\nBrownian (see \\cite{Choquet1,Choquet} for the case of a synapse)\nwith a diffusion constant $D$ and $X^{\\mbox{\\boldmath$x$}}(t)$ is the position of a\nmolecule at time $t$ starting at position $\\mbox{\\boldmath$x$}$. $E(\\tau_D)$ is the\nmean time a molecule remains inside the domain $\\Omega$ before it\nexits, averaged over a uniform initial distribution inside the\nannulus $A_{\\delta}=D(R)-D(\\delta)$. Inside  $A_{\\delta}$, a\n molecule diffuses freely until it hits $\\partial D(\\delta)$. Inside $D(\\delta)$, a bound\n molecule is kept fixed for a mean time $\\frac1{k_{-1}}$, before being released inside\n $A_{\\delta}$ at a random position, distributed uniformly.\nTo estimate the Dwell time $E(\\tau_D)$, we first consider the\nDwell time $E(\\tau^{\\mbox{\\boldmath$x$}})$, conditioned on the initial position\nlocated inside $A_{\\delta}$. We do not consider here the entrance\nof the Brownian receptor inside the domain, which would require to\nuse a Langevin formulation of the dynamics \\cite{Schuss}. We\nderive a formula for $E(\\tau^{\\mbox{\\boldmath$x$}})$ by counting the number of\ntimes a molecule enters into $D(\\delta)$ before it exits: either a\nmolecule exits with no bindings or many bindings occur, before the\nreceptor leaves $D(R)$. Let $T^A_{\\mbox{\\boldmath$x$}}$ denote the first passage\ntime the trajectory $X^{\\mbox{\\boldmath$x$}}(t)$ hits the absorbing boundary\n$\\partial\\Omega_a$. Similarly we define by $T^S_{\\mbox{\\boldmath$x$}}$ the first passage\ntime of the trajectory $X^{\\mbox{\\boldmath$x$}}(t)$ to the boundary of $D(\\delta)$.\n  We define now the probability $p_{\\delta}(\\mbox{\\boldmath$x$})$ that a\ntrajectory $X^{\\mbox{\\boldmath$x$}}(t)$ leaves the domain $A_{\\delta}$ before\n any bounds occur, explicitly\n\\begin{eqnarray} p_{\\delta}(\\mbox{\\boldmath$x$})=\\Pr\\{T^A_{\\mbox{\\boldmath$x$}}<T^{S}_{\\mbox{\\boldmath$x$}}\\}. \\end{eqnarray}\n\\subsection{The general formula for the mean Dwell time $E(\\tau_D)$}\nTo estimate $E(\\tau_D)$, we consider the different random events\nrelated to the number of times\n the Brownian molecule enters into the region $A_{\\delta}$, before it exits.  $F^{\\mbox{\\boldmath$x$}}_0$ is the event that a\nreceptor exits the microdomain $A_{\\delta}$ when no bindings\noccur, starting at position $\\mbox{\\boldmath$x$}$. $F^{\\mbox{\\boldmath$x$}}_1$ is the event that a\nreceptor starting at $\\mbox{\\boldmath$x$}$, enters the domain $D(\\delta)$ only once\nand then exits without entering again in $D(\\delta)$. Similarly,\nwe define the event $F^{\\mbox{\\boldmath$x$}}_n$ that a receptor starting at\nposition $\\mbox{\\boldmath$x$}$ exits after exactly $n$ bounds. The probability that\nthe molecule has left the domain before time $t$ is\n$Pr\\{\\tau^{\\mbox{\\boldmath$x$}}<t\\}$. The mean time is given by \\begin{eqnarray}\nE(\\tau^{\\mbox{\\boldmath$x$}}) &=&\\int_{0}^{\\infty} t\\frac{d}{dt} Pr\\{\\tau^{\\mbox{\\boldmath$x$}}<t\\}dt\\\\\n          &=& \\sum_n\\int_{0}^{\\infty} t\\frac{d}{dt}\n          Pr\\{\\tau^{\\mbox{\\boldmath$x$}}<t,F^{\\mbox{\\boldmath$x$}}_n\\}dt.\n\\end{eqnarray} We use Bayes formula to get \\begin{eqnarray} \\label{mfpt}\nE(\\tau^{\\mbox{\\boldmath$x$}})=E(\\tau^{\\mbox{\\boldmath$x$}}|F^{\\mbox{\\boldmath$x$}}_0)\\Pr(F^{\\mbox{\\boldmath$x$}}_0)+E(\\tau^x|F^{\\mbox{\\boldmath$x$}}_1)\\Pr(F^{\\mbox{\\boldmath$x$}}_1)+E(\\tau^{\\mbox{\\boldmath$x$}}|F^{\\mbox{\\boldmath$x$}}_2)\\Pr(F^{\\mbox{\\boldmath$x$}}_2)+....\n\\end{eqnarray} where \\begin{eqnarray} E(\\tau^{\\mbox{\\boldmath$x$}}|F^{\\mbox{\\boldmath$x$}}_n) =\\int_{0}^{\\infty}\nt\\frac{d}{dt} Pr\\{\\tau^{\\mbox{\\boldmath$x$}}<t|F^{\\mbox{\\boldmath$x$}}_n\\}dt. \\end{eqnarray}\n$Pr\\{\\tau^{\\mbox{\\boldmath$x$}}<t|F^{\\mbox{\\boldmath$x$}}_n\\}$ is the probability that $\\tau^{\\mbox{\\boldmath$x$}}<t$\nconditioned to the event that exactly $n$ bounds are made before the\nmolecule exits the domain $D(R)$. When a molecule detaches from the\ndomain $D(\\delta)$, in this model, it is released inside the domain\n$A_{\\delta}$ according to a density distribution $\\rho(\\mbox{\\boldmath$x$})$:\nimmediately after the mean duration\n $\\frac1{k_{-1}}$, the molecule is released inside the volume element $\\mbox{\\boldmath$x$}+d\\mbox{\\boldmath$x$}$\n with a probability $\\rho(\\mbox{\\boldmath$x$})d\\mbox{\\boldmath$x$}$.\nTo compute the first term in equation (\\ref{mfpt}), we notice that\n\\begin{eqnarray} E(\\tau^x|F^{\\mbox{\\boldmath$x$}}_0)\\Pr(F^{\\mbox{\\boldmath$x$}}_0)\n=E(T^A_{\\mbox{\\boldmath$x$}}|T^{A}_{\\mbox{\\boldmath$x$}}<T^S_{\\mbox{\\boldmath$x$}}) p_{\\delta}(\\mbox{\\boldmath$x$}). \\end{eqnarray} The second\nterm $E(\\tau^{\\mbox{\\boldmath$x$}}|F^{\\mbox{\\boldmath$x$}}_1)\\Pr(F^{\\mbox{\\boldmath$x$}}_1)$ is the sum of two terms.\nFirst the mean time it takes for a molecule to reach the boundary\n$\\partial D(\\delta)$ and stays there for a mean time $\\frac1{k_{-1}}$ and\nsecond the mean time to go from a point $\\mbox{\\boldmath$x$}_1$, where the molecule\nstarts afresh, to the absorbing boundary. If we note that the\nprobability to reach $\\partial D(\\delta)$ before $\\partial\\Omega_a$ starting\nfrom $\\mbox{\\boldmath$x$}$ is $1-p_{\\delta}(\\mbox{\\boldmath$x$})$, then we have: \\begin{eqnarray*} & &\nE(\\tau^{\\mbox{\\boldmath$x$}}|F^{\\mbox{\\boldmath$x$}}_1)\\Pr(F^{\\mbox{\\boldmath$x$}}_1) =(1-p_{\\delta}(\\mbox{\\boldmath$x$}))\\times\\\\ & &\n\\left( (E\\{T^S_{\\mbox{\\boldmath$x$}}|T^S_{\\mbox{\\boldmath$x$}}<T^A_{\\mbox{\\boldmath$x$}}\\}+ \\frac1{k_{-1}})\n\\int_{A_{\\delta}} \\rho(\\mbox{\\boldmath$x$}_1)p_{\\delta}(\\mbox{\\boldmath$x$}_1)d\\mbox{\\boldmath$x$}_1 +\n\\int_{A_{\\delta}} E\\{T^A_{\\mbox{\\boldmath$x$}_1}|T^A_{\\mbox{\\boldmath$x$}_1}<T^S_{\\mbox{\\boldmath$x$}_1}\\}\n\\rho(\\mbox{\\boldmath$x$}_1)p_{\\delta}(\\mbox{\\boldmath$x$}_1)d\\mbox{\\boldmath$x$}_1 \\right). \\end{eqnarray*} Similarly, the\ngeneral term where exactly $k$ bounds are formed is computed, with\nthe notation \\begin{eqnarray} \\label{def-time}\nt^A(\\mbox{\\boldmath$x$})&=&E\\{T^A_{\\mbox{\\boldmath$x$}}|T^A_{\\mbox{\\boldmath$x$}}<T^S_{\\mbox{\\boldmath$x$}}\\}\\\\\n& &  \\nonumber \\\\\n t^S(\\mbox{\\boldmath$x$})&=& E\\{T^S_{\\mbox{\\boldmath$x$}}|T^S_{\\mbox{\\boldmath$x$}}<T^A_{\\mbox{\\boldmath$x$}}\\}. \\end{eqnarray}\n We get,\n\\begin{eqnarray*}\nE(\\tau^{\\mbox{\\boldmath$x$}}|F^{\\mbox{\\boldmath$x$}}_n)\\Pr(F^{\\mbox{\\boldmath$x$}}_n)\n&=&\\int_{A_{\\delta}}...\\int_{A_\\delta}\n\\left( \\sum_{i=0}^{n-1}t^{S}(\\mbox{\\boldmath$x$}_i)+\\frac{n}{k_{-1}}+t^A(\\mbox{\\boldmath$x$}_n) \\right)\\\\\n& & \\prod_{i=1}^{n-1}(1-p_{\\delta}(\\mbox{\\boldmath$x$}_i))\\rho(\\mbox{\\boldmath$x$}_i)(1-p_{\\delta}\n(\\mbox{\\boldmath$x$}))p_{\\delta} (\\mbox{\\boldmath$x$}_n)\\rho(\\mbox{\\boldmath$x$}_n)d\\mbox{\\boldmath$x$}_1\\ldots\nd\\mbox{\\boldmath$x$}_n.\\\\\n &=& (1-p_{\\delta}(\\mbox{\\boldmath$x$})) \\Big{\\{}t^S(\\mbox{\\boldmath$x$})(1-m_{\\delta})^{n-1}m_\\delta \\\\\n &+&(n-1) (1-m_{\\delta})^{n-2}m_\\delta\\int_{A_{\\delta}}t^S(\\mbox{\\boldmath$y$})(\\rho(\\mbox{\\boldmath$y$})-p_{\\delta}(\\mbox{\\boldmath$y$})\\rho(\\mbox{\\boldmath$y$}))d\\mbox{\\boldmath$y$} \\\\\n&+&\\frac{n}{k_{-1}}(1-m_{\\delta})^{n-1}m_\\delta+(1-m_{\\delta})^{n-1}\n\\int_{A_{\\delta}} t^A(\\mbox{\\boldmath$y$})p_{\\delta}(\\mbox{\\boldmath$y$})\\rho(\\mbox{\\boldmath$y$})d\\mbox{\\boldmath$y$} \\Big{\\}} \\end{eqnarray*}\nwhere\n\\begin{eqnarray*} m_{\\delta}= \\int_{A_{\\delta}}p_{\\delta}(\\mbox{\\boldmath$y$})\\rho(\\mbox{\\boldmath$y$})d\\mbox{\\boldmath$y$} .\\end{eqnarray*}\nFormula (\\ref{mfpt}) is in fact a geometric sum and using the\ngeneric expression of the series, we get \\begin{eqnarray}\\label{eq:mean_general}\nE(\\tau^{\\mbox{\\boldmath$x$}}) &=& t^A(\\mbox{\\boldmath$x$})\np_{\\delta}(\\mbox{\\boldmath$x$})+\\frac{1-p_{\\delta}(\\mbox{\\boldmath$x$})}{m_\\delta}\\Big{\\{}t^S(\\mbox{\\boldmath$x$})+\\int_{A_{\\delta}}t^A(\\mbox{\\boldmath$y$})\np_{\\delta}(\\mbox{\\boldmath$y$})\\rho(\\mbox{\\boldmath$y$})d\\mbox{\\boldmath$y$}\\\\\n&+& \\frac1{m_\\delta} (\\int_{A_{\\delta}}t^S(y)\n(\\rho(\\mbox{\\boldmath$y$})-p_{\\delta}(\\mbox{\\boldmath$y$})\\rho(\\mbox{\\boldmath$y$}))d\\mbox{\\boldmath$y$} +\\frac{1}{k_{-1}})\\Big{\\}}\n\\nonumber . \\end{eqnarray} When $\\rho$ is uniformly distributed, formula\n(\\ref{eq:mean_general}) can be simplified. Using that \\begin{eqnarray*}\nm_{\\delta}=\\frac{1}{|A_{\\delta}|}\\int_{A_{\\delta}}p_{\\delta}(\\mbox{\\boldmath$y$})d\\mbox{\\boldmath$y$},\n\\quad\\quad \\end{eqnarray*} where $|A_\\delta|$ is the volume of $A_\\delta$ and\nif we define the two mean times\n\\begin {equation}\\label{eq:tau} \\mean{\\tau}=\n\\frac{\\int_{A_{\\delta}} t^A(\\mbox{\\boldmath$x$}) p_{\\delta}(\\mbox{\\boldmath$x$}) d\\mbox{\\boldmath$x$}\n}{\\int_{A_{\\delta}}p_{\\delta}(\\mbox{\\boldmath$y$})d\\mbox{\\boldmath$y$}}\n\\end{equation}\nand\n\\begin{equation}\\label{eq:T}\n\\mean{T}= \\frac{\\int_{A_{\\delta}} t^S(\\mbox{\\boldmath$x$})(1- p_{\\delta}(\\mbox{\\boldmath$x$}))\nd\\mbox{\\boldmath$x$}}{\\int_{A_{\\delta}}(1-p_{\\delta}(\\mbox{\\boldmath$y$}))d\\mbox{\\boldmath$y$} },\n\\end{equation}\nthen the Dwell time $E(\\tau_D)$ is given by the average of\n$E(\\tau^{\\mbox{\\boldmath$x$}})$ with respect to the uniform distribution and we get\n\\begin{equation}\\label{eq:formula_mean_mean}\nE(\\tau_D) = \\mean{\\tau}+\\frac{1-m_{\\delta}}{m_{\\delta}}\\left(\n\\mean{T}+\\frac{1}{k_{-1}}\\right).\n\\end{equation}\n\\bigskip\nIn the next paragraphs we obtain an explicit asymptotic estimate\nof for component of formula (\\ref{eq:formula_mean_mean}).\n\n{\\noindent \\bf Remark.} It seems artificial to free a bounded\nmolecule not immediately at the boundary of the domain $D_{\\delta}$.\nBut in fact, the release process can be modeled by re-initiating the\nmolecule at the boundary of $D_{\\delta}$, otherwise it would\nimmediately return to a bounded state. To avoid this unrealistic\nbehavior, we have used the distribution function $\\rho(\\mbox{\\boldmath$y$})$ to model\nthe releasing process. A more accurate scenario  would require to\nuse a Langevin description, which accounts for the acceleration of\nthe molecule: when a molecule is released with a random Gaussian\ninitial velocity, it can travel up to a certain distance, before its\nvelocity reaches the value of mean thermal velocity of free\nmolecules.\n\\subsection{The mean number of bounds before exit}\nTo estimate the mean number of bounds made by a molecule before it\nexits, we use the analysis of the previous paragraph. The\nprobability that a molecule starting at $\\mbox{\\boldmath$x$}$ does not bind before\nexit is exactly $\\Pr(F^{\\mbox{\\boldmath$x$}}_0)$, while the probability that\nexactly $k$ bounds are made is $\\Pr(F^{\\mbox{\\boldmath$x$}}_k)$. We define the\naverage probability by \\begin{eqnarray*} \\Pr(F_k)=\\int_{A_{\\delta}}\n\\Pr(F^{\\mbox{\\boldmath$x$}}_k) \\rho(\\mbox{\\boldmath$x$})d\\mbox{\\boldmath$x$}. \\end{eqnarray*} The probability $\\Pr(F^{\\mbox{\\boldmath$x$}}_k)$\ncan be expressed in terms of the conditional probability $p$ as\nfollows \\begin{eqnarray*} \\Pr(F^{\\mbox{\\boldmath$x$}}_1)= \\int_{A_{\\delta}} p_{\\delta}(\\mbox{\\boldmath$y$})\n\\rho(\\mbox{\\boldmath$y$})d\\mbox{\\boldmath$y$} (1-p_{\\delta}(\\mbox{\\boldmath$x$})) \\end{eqnarray*} and the average probability\n$\\Pr(F_1)$ is given by \\begin{eqnarray*} \\Pr(F_1)= \\int_{A_{\\delta}}\n\\rho(\\mbox{\\boldmath$x$})\\Pr(F^{\\mbox{\\boldmath$x$}}_1)d\\mbox{\\boldmath$x$}=\\int_{A_{\\delta}} \\int_{A_{\\delta}}\np_{\\delta}(\\mbox{\\boldmath$y$}) \\rho(\\mbox{\\boldmath$y$})d\\mbox{\\boldmath$y$} \\rho(\\mbox{\\boldmath$x$})(1-p_{\\delta}(\\mbox{\\boldmath$x$})) d\\mbox{\\boldmath$x$} =\nm_{\\delta}(1-m_{\\delta}). \\end{eqnarray*} More generally, \\begin{eqnarray*} \\Pr(F_k)=\n\\int_{A_{\\delta}}...\\int_{A_{\\delta}}p_{\\delta}(\\mbox{\\boldmath$y$}_k)\n\\rho(\\mbox{\\boldmath$y$}_k)d\\mbox{\\boldmath$y$}_k (p_{\\delta}(\\mbox{\\boldmath$y$}_{k-1}) \\rho(\\mbox{\\boldmath$y$}_{k-1})dy_{k-1}) ...\n(1-p_{\\delta}(\\mbox{\\boldmath$y$}_1)) \\rho(\\mbox{\\boldmath$y$}_1)d\\mbox{\\boldmath$y$}_1 (1-p_{\\delta}(\\mbox{\\boldmath$x$})) \\end{eqnarray*} and\nafter some integrations we get\n \\begin{eqnarray*} \\Pr(F_k)=\nm_{\\delta}(1-m_{\\delta})^k. \\end{eqnarray*} The mean $M_b$ and the variance\n$V_b$ of the number of bounds before exit are given by the well\nknown formula of geometric probability, \\begin{eqnarray} \\label{mbb}\n M_b&=& \\sum k \\Pr(F_k)= \\sum km_{\\delta}(1-m_{\\delta})^k \\nonumber\\\\&=&\\frac{1-m_{\\delta}}{m_{\\delta}}\n=\\frac{\\int_{A_{\\delta}}(1-p_{\\delta}(\\mbox{\\boldmath$y$}))d\\mbox{\\boldmath$y$}}{\\int_{A_{\\delta}}p_{\\delta}(\\mbox{\\boldmath$y$})d\\mbox{\\boldmath$y$}} \\\\\nV_b&=& \\sum k^2 \\Pr(F_k)-(\\sum k \\Pr(F_k))^2\n=\\left(\\frac{1-m_{\\delta}}{m^2_{\\delta}}\\right). \\end{eqnarray} Later on we\nwill give\n an asymptotic expansion of $m_{\\delta},V_b$ and $M_b$ as a\nfunction of the parameter $\\delta$.\n\\section{Estimation of the probability\\\\ $p_{\\delta}(x)=Pr\\{T^a_{\\mbox{\\boldmath$x$}}<T^{S}_{\\mbox{\\boldmath$x$}}\\}.$}\nTo obtain an asymptotic expansion of the probability $p_{\\delta}(x)$\nthat a molecule exits before it enters into the domain $D(\\delta)$,\nthat is, before it binds to any binding sites, we use the notations\nof the previous section. $T_x^a $ denotes the first time a molecule\nstarting from $x$ hits the absorbing boundary. We assume that when a\nmolecule exits the domain $\\Omega$, it does not come back. $T_x^S$\nis the first time a molecule hits the inner circle $\\partial D(\\delta)$.\nThe probability\n$q_{\\delta}(\\mbox{\\boldmath$x$})=1-p_{\\delta}(\\mbox{\\boldmath$x$})=\\Pr\\{T^{S}_{\\mbox{\\boldmath$x$}}<T^{a}_{\\mbox{\\boldmath$x$}}\\}$ of\nthe event $T_{\\mbox{\\boldmath$x$}}^a>T_{\\mbox{\\boldmath$x$}}^S $ satisfies an elliptic partial\ndifferential equation \\cite{Karlin}, with mixed boundary conditions\ngiven by  \\begin{eqnarray} \\label{eq5}\n \\Delta q_{\\delta}&=&0\\mbox{ on }A_{\\delta} , \\\\\n \\frac{\\partial q_{\\delta}}{\\partial n}(\\mbox{\\boldmath$x$})&=&0\\mbox{ on }\\partial \\Omega _r , \\nonumber \\\\\n q_{\\delta}(\\mbox{\\boldmath$x$})&=&0\\mbox{ on }\\partial \\Omega_a ,\\nonumber\\\\\n q_{\\delta}(\\mbox{\\boldmath$x$})&=&1\\mbox{ on }\\partial D(\\delta), \\nonumber\n\\end{eqnarray} where $\\partial \\Omega _a $ is the small opening located on the\nexternal boundary of $\\Omega$, $\\partial \\Omega _r $ is the\nremaining part of the external boundary, which is reflecting. In\npolar coordinates $(r,\\theta)$, the portion of the boundary $\\partial\n\\Omega_a$ is parameterized by $|\\theta-\\pi|\\leq\\varepsilon$. By using the\nparticular geometry of the annulus $A_{\\delta}$, an explicit\n estimation of the solution can be obtained by using spectral methods, developed in the context\n of mixed boundary value problems \\cite{Sneddon,Fabrikant1,Fabrikant2}. Using the method of\nseparation of variables, the solution $q_{\\delta}$ of problem\n(\\ref{eq5}) has the general form \\begin{eqnarray}\n&&q_{\\delta}(r,\\theta)=\\frac{a_0}{2}+\\sum_{n=1}^{\\infty}\n\\Big[a_n\\Big( \\frac r R\\Big)^n+b_n\\Big(\\frac \\delta\nr\\Big)^n\\Big]\\cos(n\\theta)+\\alpha \\log\\Big(\\frac r\n\\delta\\Big).\\label{eq:series} \\end{eqnarray} We wish now to estimate the\ncoefficients $a_n$ and $b_n$. We denote $\\beta=\\frac{\\delta}{R}$.\nFrom the boundary conditions on\n $\\partial D(\\delta)$ and on $r=R$,  we get\n\\begin{eqnarray}\n \\frac{a_0}{2}+\\sum_{n=1}^\\infty\n\\Big[a_n\\Big(\\frac{\\delta}{R}\\Big)^n+b_n\\Big]\\cos(n\\theta)&=1,& \\label{bc1}\\\\\n\\sum_{n=1}^\\infty\nn\\Big[\\frac{a_n}{R}-\\frac{b_n}{R}\\beta^{n}\\Big]\\cos(n\\theta)+\n\\frac{\\alpha}{R}&=0&\\mbox{ for $|\\theta-\\pi|>\\varepsilon$}\\label{eq:ser1p}\\\\\n1+\\sum_{n=1}^\\infty \\Big[a_n+b_n\\beta^{n}\\Big]\\cos(n\\theta)-\\alpha\n\\log(\\beta)&=0&\\mbox{ for $|\\theta-\\pi|\\leq\\varepsilon$}\\label{eq:ser2p}.\n \\end{eqnarray}\nUsing equation (\\ref{bc1}), we get the following identities:\n \\begin{eqnarray*}\n&&a_0=2\\\\\n&& b_n=-a_n\\beta^n \\mbox{ for $n\\geq 1$}. \\end{eqnarray*} Using the\nidentities above and (\\ref{eq:ser1p}) and (\\ref{eq:ser2p}), we\nobtain the double series equations\n \\begin{eqnarray}\n&\\sum_{n=1}^\\infty\nn\\Big[\\frac{a_n}{R}+\\frac{a_n}{R}\\beta^{2n}\\Big]\\cos(n\\theta)+\n\\frac{\\alpha}{R}=0,&\\mbox{ for $|\\theta-\\pi|>\\varepsilon$}\\label{eq:ser1}\\\\\n&1+\\sum_{n=1}^\\infty\n\\Big[a_n-a_n\\beta^{2n}\\Big]\\cos(n\\theta)-\\alpha\n\\log(\\beta)=0,&\\mbox{ for $|\\theta-\\pi|\\leq\\varepsilon$.}\\label{eq:ser2}\n \\end{eqnarray}\nSubstituting $c_n=a_n(1+\\beta^{2n})$ and $H_n=\\frac{2\\beta^{2n}}{1-\\beta^{2n}}$\n equations (\\ref{eq:ser1}),(\\ref{eq:ser2}) have the following\n form\n \\begin{eqnarray}\n&\\frac{c_0}{2}+\\sum_{n=1}^\\infty \\frac{c_n}{1+H_n}\n\\cos(n\\theta) =0,&\\theta\\in [\\pi,\\pi-\\varepsilon]\\label{eq:gen1}\\\\\n&&\\nonumber\\\\\n &\\alpha+\\sum_{n=1}^\\infty n c_n\n\\cos(n\\theta)=0,&\\theta\\in[0,\\pi-\\varepsilon],\\label{eq:gen2} \\end{eqnarray} where\n\\begin{eqnarray}\\label{eq:c0} \\frac{c_0}{2}=1-\\alpha\\log(\\beta). \\end{eqnarray} The\nasymptotic solution of  equations (\\ref{eq:gen1})-(\\ref{eq:gen2})\nuses the double series expansion, developed in\n\\cite{Sneddon,Fabrikant1} and used in \\cite{HS} in the context of\na small opening asymptotic. In Appendix A, the general solution is\ngiven. By using these results, we have the following expression\nfor the coefficient $c_0$\n \\begin{eqnarray}\\label{eq:c0p}\n c_0=-2\\alpha\\Big[2\\log{\\frac 1\n \\varepsilon}+2\\log2+4\\beta^2+O(\\beta^2,\\varepsilon)\\Big].\n \\end{eqnarray}\nUsing equation (\\ref{eq:c0}) and (\\ref{eq:c0p}), we get the\nexpression \\begin{eqnarray} \\label{alpha}\n\\alpha=-\\frac1{\\Big(\\log(\\frac1{\\beta})+\\Big[2\\log{\\frac 1\n\\varepsilon}+2\\log2+4\\beta^2+O(\\beta^2,\\varepsilon)\\Big]\\Big)}. \\end{eqnarray} To remember\nthat $\\alpha$ depends on $\\beta$ and $\\varepsilon$, we denote it\n$\\alpha(\\beta,\\varepsilon)$.\nFor $\\epsilon$ fixed and $\\delta$ small, the other coefficients are\nestimated by using the expression of $c_n$ (given in the appendix)\nby \\begin{eqnarray} c_n=\\alpha(\\beta,\\varepsilon) \\tilde{c}_n=O(\\alpha(\\beta,\\varepsilon)),\n\\end{eqnarray} where $\\tilde{c}_n$ depends only on $n$ and \\begin{eqnarray}\na_n &= & \\frac{c_n}{1+\\beta^{2n}} \\sim O(\\alpha(\\beta,\\varepsilon))  \\\\\nb_n &=&-c_n\\beta^{n} \\sim O(\\alpha(\\beta,\\varepsilon)\\beta^{n}). \\end{eqnarray}\nThese estimates show for $\\delta$ small that the leading term of\n$q$ is given by : \\begin{eqnarray}\\label{eq:asymptotic q} q_{\\delta}(r,\\theta)\n= \\left\\{\n\\begin{array}{cc}\n1+\\alpha(\\beta,\\varepsilon) \\log(r\/\\delta) +O(\\beta) & \\hbox{ for } r \\sim \\delta \\\\\n&  \\label{midd}\\\\\n1+\\alpha(\\beta,\\varepsilon) \\log(r\/\\delta)+ O(\\alpha) & \\hbox{ for } r \\sim\nR.\n\\end{array}\n\\right. \\end{eqnarray} The probability $p_{\\delta}(\\mbox{\\boldmath$x$})$ that  $T_x^a<T_x^S $\nis given by $p_{\\delta}(\\mbox{\\boldmath$x$})=1-q_{\\delta}(\\mbox{\\boldmath$x$})$ and the average over a\nuniform distribution in formula (\\ref{eq:series}) using (\\ref{midd})\ngives \\begin{eqnarray} \\label{asym}\nm_{\\delta}=\\mean{p_{\\delta}}&=&\\frac{\\int_{A(\\delta)} p_{\\delta}(r,\\theta)rdrd\\theta}{\\int_{A(\\delta)} rdrd\\theta}\\nonumber \\\\\n&=& -2\\frac{\\int_{\\delta}^R\\alpha(\\beta,\\varepsilon) \\log(r\/\\delta) rdr}{R^2-\\delta^2} +O(\\beta)\\nonumber\\\\\n&=& -\\alpha\\log{\\frac 1 \\beta} +O(\\beta)\\\\\n&=& \\frac{\\log{\\frac 1 \\beta}}{\\log{\\frac 1 \\beta} +2\\log{\\frac 1\n\\varepsilon} +2\\ln2} +o(1). \\nonumber \\end{eqnarray}\n\nIn the appendix some properties of $p_{\\delta}$ are given when\n$\\delta$ is small, which will be useful for the next section. From\nexpression (\\ref{asym}), we  obtain the following asymptotic\nexpression for the mean and the variance of the number of bounds\n \\begin{eqnarray} \\label{mbbp}\n M_b &=&\\frac{1-m_{\\delta}}{m_{\\delta}}= \\frac{2\\log{\\frac 1 \\varepsilon} }{\\log{\\frac 1 \\beta}} +O(1)\\\\\nV_b &=&\\left(\\frac{1-m_{\\delta}}{m^2_{\\delta}}\\right)=2 \\left(\n\\frac{ (\\log\\frac 1 \\varepsilon) (\\log{\\frac 1 \\beta} +2 \\log{\\frac 1\n\\varepsilon}+2\\log{2})}{\\displaystyle(\\log{\\frac 1 \\beta})^2 } \\right)+O(1). \\end{eqnarray}\nThese expressions are valid for $\\varepsilon<<1$ fixed, but are uniform in\n$\\beta$ for $\\beta<<1$.\n\\section{Estimation of Mean First Passage Time \\\\ $E\\{T^A_{\\mbox{\\boldmath$x$}}|T^A_{\\mbox{\\boldmath$x$}}<T^S_{\\mbox{\\boldmath$x$}}\\}.$}\nIn this section, we give an asymptotic estimate of the mean time\nto hit $\\partial \\Omega_a$, denoted by $T^A_{\\mbox{\\boldmath$x$}}$, conditioned on the\nevent that $ \\{ T^A_{\\mbox{\\boldmath$x$}}<T^{S}_{\\mbox{\\boldmath$x$}} \\}$. As described in\n\\cite{Karlin}, the conditional process of a Brownian motion\nconditioned on $ \\{ T^A_{\\mbox{\\boldmath$x$}}<T^{S}_{\\mbox{\\boldmath$x$}} \\}$ satisfies the\nfollowing stochastic differential equation \\begin{eqnarray}\ndX^*(t)=2D\\frac{\\nabla p_{\\delta}(X^*(t))}{\np_{\\delta}(X^*(t))}dt+\\sqrt{2D}dW. \\end{eqnarray} On the outer boundary $\\partial\nD(R)$, the process $X^*$ is reflected (resp. absorbed) exactly\nwhere $X$ is reflected (resp. absorbed). We denote $t^A(\\mbox{\\boldmath$x$})=\nE\\{T^A_{\\mbox{\\boldmath$x$}}|T^A_{\\mbox{\\boldmath$x$}}<T^S_{\\mbox{\\boldmath$x$}}\\}$. It satisfies Dynkin's equation\n\\cite{Schuss} which here is a degenerated elliptic partial\ndifferential equation, with mixed boundary values:\n\\begin{eqnarray}\\label{eqfd}\nD p_{\\delta} \\Delta t^A +2D\\nabla t^A\\cdot \\nabla p_{\\delta}&=&-p_{\\delta}\\mbox{ on} A_{\\delta} ,\\\\\n \\frac{\\partial t^A }{\\partial n}(\\mbox{\\boldmath$x$})&=&0\\mbox{ on }\\partial \\Omega _r ,\\nonumber \\\\\n t^A (\\mbox{\\boldmath$x$})&=&0\\mbox{ on }\\partial \\Omega _a , \\nonumber\n\\end{eqnarray} where $\\partial \\Omega _r $, $\\partial \\Omega _a $ are\nrespectively the reflecting part and the absorbing part of the outer\nboundary. We remark that no boundary conditions are needed to be\ngiven in the inner circle $\\partial D(\\delta)$ because\n $\\nabla p\\cdot n=\\frac{\\partial p}{\\partial n}>0$ and this is exactly the Fichera conditions,\n discussed in \\cite{Fichera,Nirenberg}, where\nboundary conditions cannot be given.\n\\subsection{Asymptotic expansion of the mean first passage time}\nWhen the radius $\\delta $ of the inner circle is small, we obtain\nan explicit asymptotic expansion of the mean conditional time\n$t^A$, solution of equation (\\ref{eqfd}). We first derive an\nasymptotic solution by gluing two solutions: 1) when the initial\npoint $\\mbox{\\boldmath$x$}$ is far from the inner-circle, the solution looks like\nthe mean exit time when the drift term is set to zero. This\nsolution is called the outer-solution and has been estimated in\n\\cite{SSH2} with similar boundary conditions. 2) When the initial\npoint $\\mbox{\\boldmath$x$}$ is chosen near the inner-circle, the solution can be\napproximated by a radial function. The approximation is valid in a\nboundary layer and has to\n match the radial part of the outer-solution at least $C^1$ .\n\\subsection{Outer-solution}\nWe now provide a construction of the outer-solution to equation\n(\\ref{eqfd}). We start with the expansion of $p$, which depends on\nthe parameter $\\delta$.\n \\begin{eqnarray} p_{\\delta}(r,\\theta)=\n1-\\alpha(\\delta,\\epsilon)\\phi_{\\delta}(r,\\theta). \\end{eqnarray} By using\nthe appendix, we obtain the following expression \\begin{eqnarray}\n\\phi_{\\delta}(r,\\theta) =\\Big( \\sum_{n=1}^{\\infty}\n\\frac{\\tilde{c_n}}{1+\\beta^{2n}}\\Big[\\Big(\\frac r R\\Big)^n\n-\\Big(\\frac{\\delta \\beta} r\\Big)^n\\Big]\\cos(n\\theta)+\n\\log\\Big(\\frac rR\\Big)+4\\log(\\frac1 \\varepsilon)\\Big). \\end{eqnarray}\nEquation (\\ref{eqfd}) can be written outside the boundary layer:\n$U_{\\delta}=\\{ r| r_{\\delta} \\leq r \\leq R\\}$, \\begin{eqnarray}\\label{eqfdp1}\n& D (1-\\alpha(\\delta,\\epsilon)\\phi_{\\delta}(r,\\theta) ) \\Delta t^A\n-2\\alpha(\\delta,\\epsilon) \\nabla \\cdot\\phi_{\\delta}(r,\\theta)\n\\nabla t^A =-(1-\\alpha(\\delta,\\epsilon)\\phi_{\\delta}(r,\\theta) )\n\\mbox{ on\n} U_{\\delta} ,\\nonumber\\\\&\\\\\n& \\frac{\\partial  }{\\partial n}t^A(\\mbox{\\boldmath$x$})=0 \\mbox{ on }\\partial \\Omega _r ,\n\\mbox{ and }\n t^A (\\mbox{\\boldmath$x$})=0\\mbox{ on }\\partial \\Omega_a. \\nonumber\n\\end{eqnarray} We look for a regular asymptotic expansion of the solution :\n\\begin{eqnarray} \\label{expa} t^A(\\mbox{\\boldmath$x$})=u(\\mbox{\\boldmath$x$}) -\\alpha(\\delta,\\epsilon) u_{1}(\\mbox{\\boldmath$x$}) +\nO(\\alpha^2(\\delta,\\epsilon) ). \\end{eqnarray} Using expression (\\ref{expa})\nand\n the behavior of $p$ as $\\delta$ goes to zero,  in the closed domain $D(R)$ (see appendix), we\nobtain from equation (\\ref{eqfdp1}) that $u$ satisfies\n\\begin{eqnarray}\\label{eqfdp3}\nD \\Delta u &=&-1\\mbox{ on } D(R) ,\\\\\n \\frac{\\partial u }{\\partial n}&=&0\\mbox{ on }\\partial \\Omega _r ,\\nonumber \\\\\n  u&=&0\\mbox{ on }\\partial \\Omega _a.\\nonumber \\end{eqnarray}\nWe can now use the result of \\cite{HS,SSH2} to compute the leading\norder term of $u$. For $\\mbox{\\boldmath$x$}$ that does not belong to a boundary\nlayer near the absorbing boundary $\\partial\\Omega _a$, the asymptotic\nexpansion of $u$ is given by  \\begin{eqnarray} u(\\mbox{\\boldmath$x$})= \\frac{R^2}{D} \\big(\n\\ln(\\frac{1}{\\varepsilon})+ \\ln2 \\big)+ O(\\varepsilon) \\mbox{ on }\nU_{\\delta}. \\end{eqnarray}\n We conclude that $u$ does not depend on the variable $r$ and $\\theta$ at the first order\nin $\\delta$ and $\\epsilon$. Because $u$ is a solution of equation\n(\\ref{eqfdp3}), outside a boundary layer of $\\partial\\Omega _a$,    the\nderivatives $\\frac{\\partial u}{\\partial r }$ and $\\frac{\\partial u}{r\\partial \\theta }$\nare small at the first order in $\\delta$ and $\\epsilon$. We now\nconsider the first order term in $\\alpha$ in equation\n(\\ref{eqfdp1}), which satisfies the equation \\begin{eqnarray*} & D \\Delta u_1\n-2\\nabla \\phi\\nabla u = 0\\\\ &\\frac{\\partial u_1 }{\\partial\nn}(\\mbox{\\boldmath$x$})=0\\mbox{ on }\\partial \\Omega _r, \\mbox{ and }\n u_1 (\\mbox{\\boldmath$x$})= 0\\mbox{ on }\\partial \\Omega _a.\n  \\nonumber\n\\end{eqnarray*} Outside the boundary layer near $\\partial \\Omega _a$, the\nleading order term  is given by $ u_1 (\\mbox{\\boldmath$x$})= o(1)$ (for the variable\n$\\delta$). We get that \\begin{eqnarray} \\label{ext}\nt^A(\\mbox{\\boldmath$x$})&=& u(\\mbox{\\boldmath$x$}) +o(\\alpha(\\delta,\\epsilon) ) \\mbox{ on } U_{\\delta} \\nonumber \\\\\n       &=& \\frac{R^2}{D} \\big( \\ln(\\frac{1}{\\varepsilon})+ \\ln2 \\big)\n        +o(\\alpha(\\delta,\\epsilon) ) \\mbox{ on } U_{\\delta}.\n\\end{eqnarray}\n\\subsection{Asymptotic solution inside the boundary layer }\nWe now provide an asymptotic expansion of the mean time $t^A$\ninside the\n boundary layer $BL_{\\delta}=\\{\\delta<r<r_{\\delta}\\}$, where\n$r_{\\delta} = \\delta(1-\\frac1{\\alpha(\\delta,\\epsilon)})$. The size\nof the boundary layer is given by formula (\\ref{bbll}) in the\nappendix. To estimate $t^A$, we use the expression of the\nconditional probability $p_{\\delta}$. As described in the appendix\n(\\ref{Boundaryl}), it can be approximated by a radial function, so\nthat equation (\\ref{eqfd}) becomes \\begin{eqnarray}\\label{eqfdp} D \\left(\n(t^{A})''+\\frac{1}{r}(t^A)'\\right) +\\frac{2D}{p_{\\delta}}\n{(t^{A})}' \\frac{\\partial p_{\\delta}}{ \\partial r }&= &-1\\mbox{ on }\nBL_{\\delta}, \\end{eqnarray} and the function $\\tau$ has to be glued\ncontinuously at $r=r_{\\delta}$, using that \\begin{eqnarray}\np_{\\delta}(r,\\theta) = -\\frac{\\alpha(\\beta,\\varepsilon)}{\\delta} \\Big(r-\n\\delta \\Big) +\\alpha(\\beta,\\varepsilon)O\\Big(r- \\delta \\Big). \\end{eqnarray} The\nleading order term is  \\begin{eqnarray} \\frac{2D}{p_{\\delta}}\\frac{\\partial\np_{\\delta}}{ \\partial r }= \\frac{2D}{r-\\delta}, \\end{eqnarray}\nwe have \\begin{eqnarray}\\label{eqfd2} D ((t^A)''+\\frac{1}{r}(t^A)'\n+2\\frac{1}{r-\\delta}(t^A)') &=&-1\\mbox{ on } BL_{\\delta}. \\end{eqnarray} The\nsolution is given for $r> \\delta$ by\\begin{eqnarray} (t^A)'(\\mbox{\\boldmath$x$})\n=\\frac{1}{r(r-\\delta)^2}\\left(C\n-\\frac{1}{D}(\\frac{r^2\\delta^2}{2}-2\\delta\n\\frac{r^3}{3}+\\frac{r^4}{4}) \\right) \\end{eqnarray} where the constant is\nchosen such that the function $t^A$ is integrable. Thus  the\nnumerator vanishes for $r=\\delta$. Actually $r=\\delta$ has to be a\nthird order zero of the numerator and \\begin{eqnarray} (t^A)'(\\mbox{\\boldmath$x$})\n=-\\frac{r-\\delta}{4Dr} \\left(r+\\delta\/3\\right). \\end{eqnarray} Thus, \\begin{eqnarray}\nt^A(\\mbox{\\boldmath$x$}) =-\\frac{1}{4D} \\left(\\frac{r^2}{2}\n-\\frac{2r\\delta}{3}-\\frac{\\delta^2}{3} \\ln(r) +C \\right), \\end{eqnarray}\nwhere the constant $C$ is determined by the matching condition:\n\\begin{eqnarray} t^A(r_{\\delta}) =\\frac{R^2}{D} \\big(\n\\ln(\\frac{1}{\\varepsilon})+ \\ln2 \\big)+O(\\alpha^2(\\delta,\\epsilon)\n). \\end{eqnarray} We get \\begin{eqnarray} C \\approx\n-4R^2\\left(\\ln(\\frac{1}{\\varepsilon})+ \\ln2\\right)\n-\\frac{\\delta^2}{2\\alpha^2}, \\end{eqnarray} and for $\\mbox{\\boldmath$x$} \\in BL_{\\delta}$,\n\\begin{eqnarray} \\label{BL}t^A(\\mbox{\\boldmath$x$}) &=&\\frac{1}{D}\n\\left(R^2\\left(\\ln(\\frac{1}{\\varepsilon})+ \\ln2\n\\right)+\\frac{\\delta^2}{8\\alpha^2}- \\frac{r^2}{8}\n+\\frac{r\\delta}{6}+\\frac{\\delta^2}{12} \\ln(r)   \\right).\\nonumber\\\\\n\\end{eqnarray}\n\\subsection{Asymptotic estimate of the average Mean time $\\mean{\\tau}$}\nWe now compute asymptotically the mean time $\\mean{\\tau}$ defined in\nequation (\\ref{eq:tau}) by \\begin{eqnarray}\\label{eq:taur} \\mean{\\tau}=\n\\frac{\\int_{A_{\\delta}} t^A(\\mbox{\\boldmath$x$}) p_{\\delta}(\\mbox{\\boldmath$x$})\nd\\mbox{\\boldmath$x$}}{\\int_{A_{\\delta}}p_{\\delta}(\\mbox{\\boldmath$y$})d\\mbox{\\boldmath$y$}} =\n\\frac{\\mean{\\tau}_{A_{\\delta}}}{m_{\\delta}}, \\end{eqnarray}\n where we recall that $\n\\mean{\\tau}_{A_{\\delta}} = \\frac{1}{Vol({A_{\\delta}})}\n\\int_{A_{\\delta}} t^A(\\mbox{\\boldmath$x$}) p_{\\delta}(\\mbox{\\boldmath$x$}) d\\mbox{\\boldmath$x$}.$\n$Vol({A_{\\delta}})=\\pi(R^2-\\delta^2)$. To compute\n$\\mean{\\tau}_{A_{\\delta}}$, we decompose\n the domain $A_{\\delta}= BL_{\\delta} \\cup \\left(A_{\\delta}-BL_{\\delta}\\right)$. Using\nthe previous computations for the outer solution (\\ref{ext}) and\nthe boundary layer solution (\\ref{BL}), we compute each term\nseparately and we get: \\begin{eqnarray*} \\mean{\\tau}_{A_{\\delta}} =\nm_{\\delta}\\frac{R^2}{D} \\big( \\ln(\\frac{1}{\\varepsilon})+ \\ln2\n\\big)+\\frac{R^2\\beta^4}{9\\alpha^2D}+\n\\frac{R^2}{8D(-\\alpha)^3}\\ln(\\frac{-1}{\\alpha})R^2\\beta^4+\\frac{-\\delta^2\\alpha}{12DR^2}\n\\ln(\\frac{-\\delta}{\\alpha})\\ln(\\frac{-1}{\\alpha}).\\end{eqnarray*}\n By taking into account the leading order term only, using the expressions of\n$m_{\\delta}$ and $p$, we obtain after some computations that \\begin{eqnarray}\n\\label{tau}\\mean{\\tau}\\approx\\frac{R^2}{D} \\big(\n\\ln(\\frac{1}{\\varepsilon})+ \\ln2 \\big) -\n\\frac{R^2}{8D}\\ln(\\ln(\\frac{1}{\\beta}))\\ln^3(\\frac{1}{\\beta})\\beta^4\n.\\end{eqnarray} We conclude that the boundary layer has very little influence\non the leading order term at the order $\\alpha$.\n\\subsection{Computation of the mean time $\\mean{T}$ for a molecule to hit the boundary $\\partial D(\\delta)$ before exit}\nWe now provide an estimate of mean time it takes for a Brownian\nmolecule to enter into the binding site domain $D(\\delta)$, before\nexit. To estimate the mean time $\\mean{T}$, we observe that\n$E\\{T^S_{\\mbox{\\boldmath$x$}}|T^S_{\\mbox{\\boldmath$x$}}<T^A_{\\mbox{\\boldmath$x$}}\\}q_{\\delta}(\\mbox{\\boldmath$x$})+E\\{T^A_{\\mbox{\\boldmath$x$}}|T^A_{\\mbox{\\boldmath$x$}}<T^S_{\\mbox{\\boldmath$x$}}\\}p_{\\delta}(\\mbox{\\boldmath$x$})$\nis the mean time it takes for a Brownian molecule to exit the domain\n$\\Omega$ when it can either be absorbed in the inner disk or in the\nsmall absorbing boundary on the outer circle. If we denote the mean\ntime by \\begin{eqnarray}\\label{meantime}\n w(\\mbox{\\boldmath$x$})=E\\{T^S_{\\mbox{\\boldmath$x$}}|T^S_{\\mbox{\\boldmath$x$}}<T^A_{\\mbox{\\boldmath$x$}}\\}q_{\\delta}(\\mbox{\\boldmath$x$})+E\\{T^A_{\\mbox{\\boldmath$x$}}|T^A_{\\mbox{\\boldmath$x$}}<T^S_{\\mbox{\\boldmath$x$}}\\}p_{\\delta}(\\mbox{\\boldmath$x$})\n\\end{eqnarray} then  $w$ satisfies the following PDE \\cite{Schuss},\n \\begin{eqnarray*}\n \\Delta w&=&-\\frac{1}{D} \\mbox{ in } \\Omega\\\\\n w&=&0\\quad \\mbox{on } \\partial \\Omega_a \\cup \\partial \\Omega_\\delta \\\\\n \\frac{\\partial w}{\\partial n}&=&0\\quad \\mbox{on }\\partial \\Omega_r\\\\\n \\end{eqnarray*}\n We substitute $w(r,\\theta)=v(r,\\theta)+\\frac{R^2-r^2}{4D}$,\n and solve the problem for $v$, solution of\n \\begin{eqnarray*}\n \\Delta v=&0&\\quad\\mbox{ in } \\Omega\\\\\n v=&0&\\quad \\mbox{on } \\partial \\Omega_a \\\\\n \\frac{\\partial v}{\\partial n}=&\\frac{R}{2D}&\\quad\\mbox{on }\\partial \\Omega_r\\\\\nv=-&\\frac{R^2-\\delta^2}{4D}&\\quad\\mbox{on }\\partial \\Omega_\\delta.\n \\end{eqnarray*}\nWe proceed as in the previous section by expanding $v$ in Fourier\nSeries\\begin{eqnarray} &&v(r,\\theta)=\\frac{a_0}{2}+\\sum_{n=1}^{\\infty}\n\\Big[a_n\\Big( \\frac r R\\Big)^n+b_n\\Big(\\frac R\nr\\Big)^n\\Big]\\cos(n\\theta)+\\gamma \\log\\Big(\\frac r\nR\\Big).\\label{eq:seriesv}\\end{eqnarray} In a similar way as we estimated $p$\nand $q$ (described in appendix A), from the boundary conditions on\n$\\Omega_\\delta$ we get\n \\begin{eqnarray}\n\\frac{a_0}{2}+\\sum_{n=1}^\\infty \\left(a_n\\beta^n+b_n\\left(\\frac 1\n\\beta\\right)^n\\right)\\cos(n\\theta)+\\gamma \\log\n\\beta=-\\frac{R^2-\\delta^2}{4D} ,\\end{eqnarray} from which we get \\begin{eqnarray}\na_0&=&-\\frac{R^2-\\delta^2}{2D}-2\\gamma \\log\\beta \\label{eq:c0 1}\\\\\n-a_n\\beta^{2n}&=&b_n.\\nonumber\\end{eqnarray} With the definitions $c_0=a_0$,\n$c_n=a_n(1-\\beta^{2n})$, $H_n=\\frac{2\\beta^{2n}}{1-\\beta^{2n}}$\nthe boundary conditions on $\\partial\\Omega_r$,$\\partial\\Omega_a$ have the form\nof double series equations\n\\begin{eqnarray*} \\frac{c_0}{2}+\\sum_{n=1}^\\infty\n\\frac{c_n}{1+H_n}\\cos(n\\theta)=&0,&\\quad\\theta\\in[\\pi-\\varepsilon,\\pi]\\\\\n\\sum_{n=1}^\\infty n c_n\\cos(n\\theta)=&\n\\left(\\frac{R^2}{2D}-\\gamma\\right),&\\quad\\theta\\in[0,\\pi-\\varepsilon].\n\\end{eqnarray*} The solution of these equations follows the steps described in\nthe appendix and the asymptotic approximation of the coefficient\n$c_0$ is given by \\begin{eqnarray}\nc_0=2\\left(\\frac{R^2}{2D}-\\gamma\\right)\\left(2\\log \\frac 1 \\varepsilon\n+2\\log2 +O(\\beta^2)\\right). \\end{eqnarray} Using the last equation and\n(\\ref{eq:c0 1}) we obtain an equation for $\\gamma$\n$$-\\frac{R^2-\\delta^2}{2D}-2\\gamma \\log\\beta=2\\left(\\frac{R^2}{2D}-\\gamma\\right)\\left(2\\log \\frac 1 \\varepsilon\n+2\\log2 +O(\\beta^2,\\varepsilon)\\right),$$ which gives that\\begin{eqnarray}\\label{gamma}\n\\gamma=\\frac{R^2}{2D}\\frac{4\\log\\frac 1\n\\varepsilon+4\\log2+1+O(\\beta^2,\\varepsilon)}{2\\log\\frac 1 \\beta +4\\log\\frac 1\n\\varepsilon+4\\log2+O(\\beta^2)},\\end{eqnarray} and \\begin{eqnarray} c_0 =\n\\frac{R^2}{D}\\frac{(2\\log\\frac 1 \\beta-1)(2\\log\\frac 1 \\varepsilon\n+2\\ln2)}{2\\log\\frac 1 \\beta +4\\log\\frac 1 \\varepsilon+4\\log2+O(\\beta^2)}.\n\\end{eqnarray}\n\\subsection*{Remarks}\nAveraging $w$ with respect to a uniform distribution\n \\begin{eqnarray*}\n\\mean{w}&=&\\frac{1}{\\mbox{Vol}(A_\\delta)}\\int_0^{2\\pi}\\int_\\delta^R w(r,\\theta)rdrd\\theta\\\\\n&=&\\frac{1}{\\mbox{Vol}(A_\\delta)}2\\pi\\int_\\delta^R\n\\left(v(r,\\theta)+\\frac{R^2-r^2}{4D}\\right)rdr =\n\\frac{c_0-\\gamma}{2} + \\frac{R^2}{8D} \\\\ &=&\\frac{R^2}{2D}\\left(\n\\frac{(2\\log\\frac 1 \\beta-1)(\\log\\frac 1 \\varepsilon+ \\log 2)\n-\\frac12\\log\\frac 1 \\varepsilon - \\frac12\\log 2+\\frac{1}{4}\\log\\frac 1\n\\beta -\\frac{1}{4}+O(\\beta^2,\\varepsilon)}{\\log\\frac 1 \\beta +2\\log\\frac 1\n\\varepsilon+2\\log2+O(\\beta^2)} \\right).\n \\end{eqnarray*}\n When $\\beta\\to 0$, we obtain the mean time to exit for only one\n  small hole located on the boundary of the domain: this result agrees with\n  the result obtained in (\\cite{SSH2}, eq.(1.3)).\nIn the limit $\\delta<<\\varepsilon$, we have the following\napproximation for $\\mean{w}$,\n \\begin{eqnarray} \\label{ap1}\n \\mean{w}\\approx \\frac{R^2}{D}\\{(\\log\\frac 1\n\\varepsilon+ \\log 2)+\\frac18\\},\\end{eqnarray} while for $\\varepsilon<<\\delta$, we\nhave \\begin{eqnarray} \\label{ap2}\n \\mean{w}\\approx \\frac{R^2}{2D}\\{(\\log\\frac 1\n\\beta-\\frac12)-\\frac14\\}. \\end{eqnarray}\n\\subsection*{Final computations}\nTo compute $E(\\tau_D)$ it is sufficient to estimate the average\n$q(\\mbox{\\boldmath$x$})E\\{T^S_{x}|T^S_{\\mbox{\\boldmath$x$}}<T^A_{\\mbox{\\boldmath$x$}}\\}$ defined by equation\n(\\ref{eq:T}) \\begin{eqnarray}\\label{eq-T} \\mean{T}= \\frac{\\int_{A_{\\delta}}\nE\\{T^S_{\\mbox{\\boldmath$x$}}|T^S_{\\mbox{\\boldmath$x$}}<T^A_{\\mbox{\\boldmath$x$}}\\}q (\\mbox{\\boldmath$x$}) d\\mbox{\\boldmath$x$}}{\\int_{A_{\\delta}}q\n(\\mbox{\\boldmath$y$})d\\mbox{\\boldmath$y$} }. \\end{eqnarray}\n Starting from equation (\\ref{meantime}), we get\n\\begin{eqnarray*} q_{\\delta}(\\mbox{\\boldmath$x$})t^S(\\mbox{\\boldmath$x$}) &=&w(\\mbox{\\boldmath$x$})-p_{\\delta}(\\mbox{\\boldmath$x$})t^A(\\mbox{\\boldmath$x$})\n                       \n                       \n\\end{eqnarray*} thus, \\begin{eqnarray} \\mean{T}=\\frac{\\int_{A_{\\delta}}\nt^S(\\mbox{\\boldmath$x$})q_{\\delta}(\\mbox{\\boldmath$x$}) d\\mbox{\\boldmath$x$}}{|A_{\\delta}| (1-m_{\\delta})}=\n\\frac{\\mean{w}}{1-m_{\\delta}}\n-\\mean{\\tau}\\frac{m_{\\delta}}{1-m_{\\delta}}. \\end{eqnarray} Using expression\n(\\ref{asym}), we have \\begin{eqnarray}\n\\frac{1}{|A_{\\delta}|}\\int_{A_{\\delta}}q_{\\delta} (\\mbox{\\boldmath$y$})d\\mbox{\\boldmath$y$}\n=1-m_{\\delta}=\\frac{2\\ln(\\frac{1}{\\epsilon})+2\\ln\n2}{\\ln(\\frac{1}{\\beta})+2\\ln(\\frac{1}{\\epsilon})+2\\ln 2}+O(1).\n\\end{eqnarray} Finally, the expression of $\\mean{T}$ can be computed from\n(\\ref{ap1}) and (\\ref{tau}) and in the limit\n$\\delta<<\\varepsilon$, the leading order term is\n\\begin{eqnarray} \\label{T1}\n \\mean{T}\\approx \\frac{R^2}{16D(\\log\\frac 1 \\varepsilon+\\ln 2)}\\{\\log\\frac 1\n \\beta \\} \\hbox{ for } \\delta<<\\varepsilon.\n\\end{eqnarray}\nTo derive the final expression for the Dwell time, we gather\nthe computational results: using equation (\\ref{mbb}), we have\n\\begin{eqnarray} \\frac{ 1-m_{\\delta}}{m_{\\delta}} \\approx\n\\frac{2\\ln(\\frac1{\\epsilon})+2\\ln2}{\\ln(\\frac1{\\beta})}.\\end{eqnarray}\nFinally,  we obtain from equation  (\\ref{eq:formula_mean_mean})\nthat the dwell time in the approximation $\\delta<< \\varepsilon$,\n\n\\begin{eqnarray} \\label{dwell-f}\nE(\\tau_D) &=&\\mean{\\tau}\n+\\frac{1-m_{\\delta}}{m_{\\delta}}(\n\\mean{T}+\\frac{1}{k_{-1}})\\nonumber\\\\ & &  \\\\\n &\\approx& \\frac{R^2}{D}\n(\\ln(\\frac{1}{\\varepsilon})+\\ln\n2)+\\frac{2\\ln(\\frac{1}{\\epsilon})+2\\ln 2}{\\ln(\\frac{1}{\\beta})}\n\\left( \\frac{1}{k_{-1}} + \\frac{R^2}{16D(\\log\\frac 1 \\varepsilon+\\ln\n2)}\\{\\log\\frac 1 \\beta \\}\\right)+o(1).\\nonumber \\end{eqnarray} The expression\nof $E(\\tau_D) $ when $\\epsilon<<\\delta$ is more delicate and\ninvolves a different boundary layer analysis than the one given in\nthe appendix.\n\\section{Discussion and conclusion}\nIn this article, we have computed the mean time spent by a\nmolecule inside a microdomain $\\Omega$, when it can interact with\nsome binding sites, represented as a connected sub-domain\n$D(\\delta) \\subset \\Omega $. This simplified assumption ignores\nthe scattered distribution of the binding sites but leaves one\nfree parameter $\\delta$. A rational way to choose the radius\n$\\delta$ is to equal the length $2\\pi \\delta$ with the sum of the\npotential well boundary length of each binding site.\n\nMore generally, the problem of estimating the Dwell time of a\nmolecule in $\\Omega$ when there are already many other independent\nmolecules, is much more involved. The reason is that even if these\nmolecules are not interacting, they are coupled through the\ncompetition for the binding sites. However, if the mean number of\nbound receptors is fixed and the variance is small enough, the\nDwell time formula (\\ref{dwell-f}) can be applied, by choosing for\n$\\delta$, a value that is related to the amount of free binding\nsites available (see below). In general,  when the number of\nbounded molecules is fluctuating, a different model is needed to\naccount for the fluctuations. In that case, a different derivation\nof the Dwell time is needed.\n\\subsection{Receptor trafficking at synapses}\nThe explicit expression of the Dwell time can be used to describe\nreceptor dynamics at synapses. A synapse is a micro-contact between\ntwo neurons, involved in signal transmission. In the past decades\nexperimental observations have revealed that the molecular\ncomposition of the postsynaptic part of a synapse depends on the\nhistory of the neuronal activity\n\\cite{Nicoll,Bredt,Ehlers1,Choquet,Choquet1, Triller,Lee}.\nAlthough it is a difficult problem to predict the chemical\norganization of a synapse, it has been found experimentally that\nthe type and the number of receptors do not appear randomly, but\nare well regulated during specific synaptic plasticity protocols,\nsuch as Long Term Potentiation (LTP). During LTP \\cite{Nicoll},\nthe number and the type of receptors can change, whereas\nextra-synaptic receptors diffuse inside a specific microdomain\ncalled the postsynaptic density (PSD). Recently, the concept has\nemerged that receptors are constantly moving on the neuronal\nsurface, in and out of the synaptic domain \\cite{Triller}.\nMoreover, receptors are  also cycling between the cell surface and\nintracellular pools.  According to some recent experimental\nresults \\cite{Choquet}, the movement of the receptors at synapses\ncan be approximated by a random walk in the heterogeneous PSD.\nMoreover, it has been observed that receptors can become confined\nfor random times \\cite{Choquet} and can also be bound to\nscaffolding molecules. The PSD delimits a bounded domain $\\Omega$\ncontaining small openings at the boundary, where receptors can be\nexchanged with the rest of the dendrite. The PSD contains many\nfundamental molecules, scaffolding proteins, receptors, kinases,\nand many others required for the normal synaptic activity. The PSD\nis thus a place where the synaptic molecular machinery is\nconcentrated. Scaffolding molecules may be used to anchor\nreceptors and\/or to change the biophysical properties of\nreceptors. Because scaffolding molecules are scattered inside the\ndomain $\\Omega$, in the present model we have replaced the complex\norganization of the PSD by a homogenized domain (Figure 1). We can\napply the result of the first part of the present paper to obtain\nsome estimates of the mean time spent by a receptor inside the\nPSD, when it can bind with scaffolding molecules. Estimate\n(\\ref{dwell-f}) of the Dwell time $E(\\tau_D)$ depends on the size\n$\\delta$ of the scaffolding domain and is a good approximation\nwhen the amount of free scaffolding molecules is small $\\delta<<1$\nand when the corral barrier, measured by $\\varepsilon$, made by\nthe impenetrable molecules around the PSD, is also small.\n\n\\subsection{Dwell time of a single receptor in a synapse containing many other receptors}\nTo estimate the mean time a receptor stays inside the PSD, we\nconsider the case where the influx J of receptors entering the PSD\nis fixed. The Dwell time can be computed from formula\n(\\ref{dwell-f}) once the value of the radius $\\delta$ is known.\n$\\delta$ is indeed the radius of the disk containing the free\nscaffolding molecules. To obtain an estimate of $\\delta$, we\nconsider the dynamics where each injected receptor can escape with a\nrate $\\tau$, approximated by formula (\\ref{HolcSchuss}). When the\nnumber of injected receptors is balanced by the exiting one from the\nPSD, the total number of free receptors  inside the PSD is given by\n\\begin{eqnarray}\n[R]=J \\tau.\n\\end{eqnarray}\n(for a detailed analysis see \\cite{HT}). Under the steady state\nassumption, the number of free scaffolding molecules can be\nestimated by using the law of chemical reaction (\\ref{chem}) which\nsays that\n\\begin{eqnarray}\\label{chemReact}\nK=\\frac{[R-S]}{[R][S]},\n\\end{eqnarray}\nwhere $[R-S]$ is the number of bounds. $[R]$ (resp. $[S]$) the\nnumber of free receptors (resp. scaffolding molecules) $K$ is the\nequilibrium reaction constant per unit area. If $[S_0]$ denotes the\ninitial number of scaffolding molecules, the conservation of matter\n(the total number of scaffolding molecules is conserved) and\nequation\n\\ref{chemReact} implies that\n\\begin{eqnarray} \\label{conser}\n[S_0]&=&[S]+[R-S]=[S]+K [R][S]\\\\\n      &=&(1+K J\\tau)[S]\n\\end{eqnarray}\nThus, if $[S]$ (resp. $[S_0]$) occupies a surface $\\pi\n\\delta^2$, (resp.  $\\pi \\delta_0^2$), then\n\\begin{eqnarray} \\label{delta}\n\\delta = \\frac{\\delta _0}{\\sqrt{1+K J \\tau}}.\n\\end{eqnarray}\n$\\delta_0$ can be related to the concentration $c_0$ of scaffolding\nmolecules by $c_0=\\frac{[S_0]}{\\pi \\delta_0^2}$. To obtain the mean\ntime estimate, expression (\\ref{delta}) of $\\delta$ should be used\nin the Dwell time formula.\n\nExpression (\\ref{delta}) depends on the equilibrium constant $K$,\nwhich in fact depends implicitly of $\\delta$. Thus to provide a more\naccurate value of $\\delta$, we note that the forward binding rate\n$k_1$ represents the rate of arrival of a free receptor to a free\nbinding site and can be approximated by\n\\begin{eqnarray}\n k_1 \\approx\\frac{1}{\\mean{T}},\n\\end{eqnarray}\nwhere $\\mean{T}$ is given by equation (\\ref{eq-T}). Using the\nprevious considerations and the conservation law \\ref{conser}, we\nhave\n\\begin{eqnarray} \\label{conserp}\n[S_0]&=&[S]+[R-S]=[S]+K [R][S]\\\\\n      &=&(1+\\frac{J\\tau}{k_{-1}\\mean{T}})[S],\n\\end{eqnarray}\nwhere $\\tau$ is approximated by expression (\\ref{HolcSchuss}) and\n$\\mean{T}$ (\\ref{T1}) depends on $\\delta$, which is denoted by\n$\\mean{T}(\\delta)$. Using equation (\\ref{delta}), $\\delta$ is\nsolution of equation\n\\begin{eqnarray} \\label{eq-delta}\n\\delta = \\frac{\\delta _0}{\\sqrt{1+\\displaystyle{\\frac{J \\tau}{k_{-1}\\mean{T}(\\delta)}}}}.\n\\end{eqnarray}\nIn practice, the value of $\\delta$ obtained by solving equation\n(\\ref{eq-delta}) can now be used to estimate the Dwell time, the\nmean number of bounds and the other mean times.\n\nFinally, when the total number of receptors inside $\\Omega$ is\nsmall, the radius $\\delta$ cannot be approximated by a constant,\nrather it is fluctuating and in that case, the present approach\nneeds to be adapted. A variant model of the PSD has been proposed in\n\\cite{HT}, based on a Markovian approach, which uses an in- and\nout-flux of receptors. At steady state, under some approximations,\nsome estimates of the mean and the fluctuation of the total number\nof bound receptors are obtained, however the computations depend\non an a priori expression of the forward binding rate.\n\n\\section{Appendix}\n\\subsection{Solution of double series equation}\nIn this section we give the mathematical details needed to solve\nthe double series equation (\\ref{eq:gen1})-(\\ref{eq:gen2}). The\nmethod was already used in \\cite{SSH2},\\cite{Sneddon}. Starting\nwith the equations\n \\begin{eqnarray}\n&\\frac{c_0}{2}+\\sum_{n=1}^\\infty \\frac{c_n}{1+H_n}\n\\cos(n\\theta) =0,&\\theta\\in [\\pi,\\pi-\\varepsilon]\\label{eqA:gen1}\\\\\n&&\\nonumber\\\\\n &\\alpha+\\sum_{n=1}^\\infty n c_n\n\\cos(n\\theta)=0,&\\theta\\in[0,\\pi-\\varepsilon],\\label{eqA:gen2} \\end{eqnarray} we are\ninterested in computing  $\\alpha$  and the coefficients $\\{c_i\\}$.\nLet us define the function $h(\\theta)$  for $\\theta\\in[0,\\pi-\\varepsilon]$\nby\n\\begin{equation}\n\\frac{c_0}{2}+\\sum_{n=1}^\\infty \\frac{c_n}{1+H_n}\n\\cos(n\\theta)=\\cos\n(\\frac{\\theta}{2})\\int_\\theta^{\\pi-\\varepsilon}\\frac{h(t)}{\\sqrt{\\cos(\\theta)-\\cos(t)}}\n\\end{equation}\nUsing this definition and the Fourier coefficient formula\n(\\cite{SSH2})we can write\n\\begin{eqnarray} &c_n& = \\frac{1 + H_n}{\\sqrt 2} \\int_0^{\\pi-\\varepsilon} h(t)\n[P_n(\\cos (t)) + P_{n-1}(\\cos(t))] dt,\\label{eq:cn}\\\\\n&c_0&=\\sqrt{2}\\int_0^{\\pi-\\varepsilon}h(t)dt,\\label{eq:c00}\\end{eqnarray} where\n Mehler's identity for Legendre polynomials gives\n(\\cite {Sneddon} ch.2)\n\\[P_n(\\cos(u))=\\frac{\\sqrt {2}}{\\pi}\\int_0^u\\frac{\\cos(n+\\frac{1}{2})d\\theta}{\\sqrt{\\cos(\\theta)-\\cos(u)}}.\\]\nIntegrating equation (\\ref{eqA:gen2}), using the expression for\nthe coefficients (\\ref{eq:cn}) into the integrated equation and\nthe identity \\begin{eqnarray*}\n&\\frac{1}{\\sqrt{2}}\\sum_{n=1}^\\infty\\{P_n(\\cos(t))+P_{n-1}(\\cos(t))\\}\\sin(n\\theta)=\n\\frac{\\cos(\\frac{1}{2}\\theta)H(\\theta-t)}{\\sqrt{\\cos(t)-\\cos(\\theta)}},\n\\end{eqnarray*} where $H$ is the Heaviside function, we get the integral\nequation \\begin{eqnarray} &&\\int _0^\\theta\n\\frac{h(t)}{\\sqrt{\\cos(t)-\\cos(\\theta)}}+\\int_0^{\\pi-\\varepsilon}K_\\beta(\\theta,t)h(t)dt=\\frac{-\\alpha\\theta}{\\cos(\\frac{\\theta}{2})},\n\\label{eqA:int1}\\end{eqnarray} where the kernel function $K_\\beta$ is\n\\[K_\\beta(\\theta,s)=\\frac{1}{\\sqrt{2}\\cos(\\frac{\\theta}{2})}\\sum_{n=1}^\\infty H_n(P_n(\\cos(t)+P_n(\\cos(t))).\\]\nUsing the first elements in the infinite series we can give an\nasymptotic expansion to $K_\\beta$\n\\begin{equation}\nK_\\beta(t,s)=2\\beta^2\\cos^2(s)\\sin(t)+\\mbox{O}(\\beta^4).\n\\end{equation}\nEquation (\\ref{eqA:int1}) can be transformed according to the Abel\ntransform  \\begin{eqnarray*}\nf(x)&=&\\int_0^x\\frac{g(t)dt}{(p(x)-p(t))^q}\\\\\ng(t)&=& -\\frac{\\sin(\\pi\nq)}{\\pi}\\frac{d}{dt}\\int_0^t\\frac{p'(x)f(x)dx}{(p(x)-p(t))^{1-q}},\\end{eqnarray*}\n where $p(x)$ is monotonic increasing function. Transforming eq.(\\ref{eqA:int1}), with $q=\\frac{1}{2}$\n and $p(x)=-\\cos(x)$ we get\n\\begin{eqnarray}\nh(\\theta)-\\int_0^{\\pi-\\varepsilon}\\tilde{K}_\\beta(\\theta,t)h(t)dt=\\frac{1}{\\pi}\\frac{d}{d\\theta}\\int_0^\\theta\n\\frac{2\\alpha t \\sin(\\frac{1}{2}t)dt}{\\sqrt{\\cos t -\\cos\n\\theta)}}\\label{eqA:int2}\n \\end{eqnarray}\nwith\n$\\tilde{K}_\\beta(t,s)=-\\frac{1}{\\pi}\\frac{d}{dt}\\int_0^t\\frac{K_\\beta(u,s)\\sin(u))}{\\sqrt{\\cos(u)-\\cos(t)\n}}$. If we define\n$z(\\theta)=\\frac{1}{\\pi}\\frac{d}{d\\theta}\\int_0^\\theta \\frac{2\\alpha\nt \\sin(\\frac{1}{2}t)dt}{\\sqrt{\\cos t-\\cos \\theta}}$, then equation\n(\\ref{eqA:int1}) has the form $(I-\\tilde{K}_\\beta)h=z$. This is the\nFredholm integral equation, which can be approximated using the\ninfinite sum\n\\begin{eqnarray}\n\\label{expand}\nh=z+\\tilde{K}_\\beta z +\\tilde{K}^2_\\beta z+\\ldots\n\\end{eqnarray}\nComputing the first elements in the sum gives an approximation to\n$h(\\theta)$ which in turn, by substituting the approximation into\nthe expressions for $c_n$ gives an approximation for the\ncoefficients. To calculate $c_0$ up to $\\mbox{O}(\\varepsilon,\\beta^4)$ we\nhave to evaluate the integral\n\\[\\sqrt{2}\\left(\\int_0^{\\pi-\\varepsilon}z(t)dt+\\int_0^{\\pi-\\varepsilon}\\int_0^{\\pi-\\varepsilon}\\tilde{K(s,t)}_\\beta\nz(t) dtds\\right). \\] The computation is made in \\cite{SSH2} and\ngives\n\\[c_0\\approx 2\\alpha (2\\log \\frac{1}{\\varepsilon}+2\\log 2+4\\beta^2).\\]\n\\subsection{Properties of the conditional probability $p_{\\delta}$}\n\\subsubsection{Inside $A_{\\delta}$}\n$q_{\\delta}$ is solution of equation (\\ref{eq5}) and depends on\nthe parameter $\\delta$.\n\\begin{prop}\nThe sequence $p_{\\delta}$ converges uniformly to the constant 1,\non any compact set $K$ strictly contained in the domain\n$A_{\\delta}$. More specifically, for any $K \\subset A_{\\delta}$,\nthere exists a constant $C>0$ such that for all $r,\\theta \\in K$,\n \\begin{eqnarray*}\n|p_{\\delta}(r,\\theta)-1| &\\leq& C \\alpha(\\beta,\\varepsilon)  \\\\ \\\\\n|\\nabla p_{\\delta}(r,\\theta)| &\\leq&  C \\alpha(\\beta,\\varepsilon)\n \\end{eqnarray*}\nwhere $\\alpha(\\beta,\\varepsilon)$ is  defined by (\\ref{alpha}) and \\begin{eqnarray}\n0<\\alpha(\\beta,\\varepsilon)=\\alpha(\\frac{\\delta}{R},\\varepsilon)\\leq\n\\frac{C}{\\ln(\\frac1{\\delta})} \\end{eqnarray} which tends to zero when\n$\\delta$ goes to zero.\n\\end{prop}\n{\\noindent \\bf Proof.}\nTo estimate $p_{\\delta}$ we consider expression (\\ref{eq:series}),\nwhich can be written as \\begin{eqnarray*}\n&&-p_{\\delta}=q_{\\delta}(r,\\theta)-1=\\sum_{n=1}^{\\infty}\n\\frac{c_n}{1+\\beta^{2n}}\\Big[\\Big( \\frac r\nR\\Big)^n-\\Big(\\frac{\\delta \\beta}\nr\\Big)^n\\Big]\\cos(n\\theta)+\\alpha(\\beta,\\varepsilon) \\log\\Big(\\frac r\n\\delta\\Big).\\label{eq:seriesp} \\end{eqnarray*} where $\\alpha(\\beta,\\varepsilon)$ is\ngiven by expression  (\\ref{alpha}) and we recall that \\begin{eqnarray}\n\\label{coef2} &c_n& = \\frac{1 + H_n}{\\sqrt 2} \\int_0^{\\pi-\\varepsilon}\nh(t) P_n(\\cos (t)) + P_{n-1}(\\cos(t))] dt. \\end{eqnarray} By definition\n$H_n=O(\\beta^{2n})$ and $P_n$ is the Legendre polynomial. For\n$x\\in [-1,1]$ and all n, $|P_{n}(x)| \\leq 1$. Moreover,  using\nformula (\\ref{expand}), we obtain that \\begin{eqnarray} \\label{fomzp}\nh(t)=z(t)+O(\\beta^2)=-\\frac{2\\alpha}{\\pi}\\frac{d}{dt}\\int_0^t\\frac{u\n\\sin u}{\\sqrt{\\cos u-\\cos t}}du. \\end{eqnarray} Thus we conclude from the\nexplicit formula (\\ref{coef2}) that there exists a constant $C>0$\nsuch that for all $n$ \\begin{eqnarray} |c_n| \\leq C \\alpha(\\beta,\\varepsilon) \\end{eqnarray}\nwhich is independent of $n$. We denote\n$c_n=\\tilde{c_n}\\alpha(\\beta,\\varepsilon).$ We can now obtain the desired\nestimates. For $r_0<r<R_1<R$, we get, \\begin{eqnarray} \\label{express}\n1-p_{\\delta}(r,\\theta)=1+\\alpha(\\beta,\\varepsilon) \\Big(\n\\sum_{n=1}^{\\infty}\n\\frac{\\tilde{c_n}}{1+\\beta^{2n}}\\Big[\\Big(\\frac r\nR\\Big)^n-\\Big(\\frac{\\delta \\beta} r\\Big)^n\\Big]\\cos(n\\theta)+\n\\log\\Big(\\frac r \\delta\\Big)\\Big). \\end{eqnarray} Thus, \\begin{eqnarray}\n|1-p_{\\delta}(r,\\theta)|\\leq  I+ II, \\end{eqnarray} where \\begin{eqnarray}\nI \\leq |1-\\alpha(\\beta,\\varepsilon)\\log \\Big(\\frac{R_1}\\delta \\Big)| \\leq C \\frac{\\ln(R_1\/r_0)+O(1)}{\\ln(R\/\\delta)+O(1)}\\\\\nII\\leq \\alpha(\\beta,\\varepsilon) \\sum_{n=1}^{\\infty}  \\Big[\\Big(\n\\frac{R_1} R\\Big)^n+\\Big(\\frac{\\delta \\beta} {r_0}\n\\Big)^n\\Big]\\leq C \\alpha(\\beta,\\varepsilon). \\end{eqnarray} The last part of these\ninequalities uses the asymptotic expression of $\\alpha$ given by\nformula (\\ref{alpha}). These inequalities show that on any compact\nset of $A_{\\delta}$, $1-p_{\\delta}$ converges uniformly to zero at\na rate $\\frac1{\\ln(1\/\\delta)}$. Similarly, to estimate the\ngradient we estimate separately $|\\frac{\\partial p}{\\partial r}|$ and\n$|\\frac1{r}\\frac{\\partial p}{\\partial \\theta}|$. First, \\begin{eqnarray*} -\\frac{\\partial\np_{\\delta}}{\\partial r}(r,\\theta)=\\alpha(\\beta,\\varepsilon) \\Big(\n\\sum_{n=1}^{\\infty} \\frac{n\\tilde{c_n}}{1+\\beta^{2n}}\\Big[\\Big(\n\\frac{r^{n-1}}{R^n}\\Big)+\\Big(\\frac{(\\delta\n\\beta)^n}{r^{n+1}}\\Big) \\Big]\\cos(n\\theta)+ \\frac{1}{r} \\Big),\n\\end{eqnarray*} we get \\begin{eqnarray*} |\\frac{\\partial p_{\\delta}}{\\partial r}(r,\\theta)| \\leq\n|\\alpha(\\beta,\\varepsilon)| \\Big( \\sum_{n=1}^{\\infty} n \\Big[\\Big(\n\\frac{R_1^{n-1}}{R^n}\\Big)+\\Big(\\frac{(\\delta\n\\beta)^n}{r_o^{n+1}}\\Big) \\Big]+ \\frac{1}{r_0} \\Big)\\leq\nC|\\alpha(\\beta,\\varepsilon)| \\end{eqnarray*} and second, \\begin{eqnarray*} \\frac{1}{r}\\frac{\\partial\np_{\\delta}}{\\partial \\theta}(r,\\theta)=\\frac{\\alpha(\\beta,\\varepsilon)}{r}\n\\Big( \\sum_{n=1}^{\\infty}\n\\frac{\\tilde{c_n}}{1+\\beta^{2n}}\\Big[\\Big( \\frac r\nR\\Big)^n-\\Big(\\frac{\\delta \\beta} r\\Big)^n\\Big]n\\sin(n\\theta)\\Big)\n\\end{eqnarray*} and \\begin{eqnarray*} |\\frac1{r}\\frac{\\partial p}{\\partial \\theta}| \\leq\n|\\frac{\\alpha(\\beta,\\varepsilon)}{r_0}| \\Big( \\sum_{n=1}^{\\infty}\n\\Big[\\Big( \\frac {R_1} R\\Big)^n+\\Big(\\frac{\\delta \\beta}{r_0}\n\\Big)^n\\Big]n\\Big)\\leq C|\\alpha(\\beta,\\varepsilon)|. \\end{eqnarray*} \\quad\\hbox{\\hskip 4pt\\vrule width 5pt height 6pt depth 1.5pt}\n\\subsubsection{The boundary layer}\\label{Boundaryl}\nWe consider now the behavior of $p_{\\delta}$ near the the inner\ncircle $r=\\delta$, where $p_{\\delta}$ vanishes. We expect to see a\nboundary layer near the circle $r=\\delta$, as $\\delta$ goes to\nzero. $p_{\\delta}$  is a regular function and a Taylor expansion\nin the $r$-variable inside expression (\\ref{express}) gives that\n\\begin{eqnarray*} -p_{\\delta}(r,\\theta) = \\frac{\\alpha(\\beta,\\varepsilon)}{\\delta}\n\\Big(r- \\delta \\Big) + \\alpha(\\beta,\\varepsilon)  \\sum_{n=1}^{\\infty}\nn\\frac{\\tilde{c_n}}{1+\\beta^{2n}}\\Big[ 2R\n\\beta^{n-1}\\Big]\\cos(n\\theta)\\Big(r- \\delta \\Big)+O\\Big(r- \\delta\n\\Big)^2. \\end{eqnarray*} The leading order term is radial and we get\n\\begin{eqnarray}\\label{bbl} p_{\\delta}(r,\\theta) =\n-\\frac{\\alpha(\\beta,\\varepsilon)}{\\delta} \\Big(r- \\delta \\Big)\n+\\alpha(\\beta,\\varepsilon)O\\Big(r- \\delta \\Big). \\end{eqnarray} To estimate the\nsize of the boundary layer, we look at the value $r_{\\delta}$ such\nthat $p_{\\delta}$ is of the order one. Using the previous\napproximation of $p_{\\delta}$ (\\ref{bbl}) we get \\begin{eqnarray}\\label{bbll}\nr_{\\delta} &=&\n\\delta-\\frac{\\delta}{\\alpha(\\beta,\\varepsilon)}\\\\\n &=&  \\delta+ \\delta(\\ln\\frac{1}{\\delta}+2 \\ln\\frac{1}{\\varepsilon}+2\\ln2+\\ln\n R+O(\\beta^2)).\n \\end{eqnarray}\n\\subsubsection{Convergence of $p_{\\delta}$ in the neighborhood of $\\partial D(R)$}\nThe sequence of harmonic function  $p_{\\delta}$ converges\nuniformly on any compact set of $D(R)-\\{0\\}$ to the function 1. We\nshow now that this is also the case in the neighborhood of $\\partial\nD(R)$. We use the elliptic estimates given in \\cite{Gilbarg}\nderived at the boundary. We can also directly extend as a harmonic\nfunction $p_{\\delta}$ to a neighborhood $T$ of $D(R)$. We have\nthat \\begin{eqnarray} \\sup_{\\{x \\in K\\}} | \\nabla p_{\\delta}| \\leq C \\end{eqnarray} for\nany compact $K$ in $T$. By Ascoli's theorem, there exists a\nsubsequence of $p_{\\delta}$ converging in $C^{0,\\alpha}$. We\nconclude since $p_{\\delta}$ converges to 1 on any compact set of\n$D(R)-\\{0\\}$ that the sequence $p_{\\delta}$ converges to 1 on\n$T-\\{0\\}$ and is a weak solution of \\begin{eqnarray}\\label{eeqq}\n\\Delta u&=&0 \\mbox{ on } D(R)-{0} \\\\\n    u(x)&=&1 \\mbox{ on }\\partial \\Omega_a ,\\nonumber\\\\\n\\frac{\\partial u}{\\partial n}(x)&=& \\mbox{ on }\\partial D(\\delta), \\nonumber \\end{eqnarray}\nBecause $0\\leq u\\leq 1$, the solution can be extended up to 0 and\nthe only solution of equation (\\ref{eeqq}) is the constant 1. We\nconclude that the sequence $p_{\\delta}$ converges to the constant\none uniformly on $\\overline{D(R)}$.\\newpage\n\n\n\\bibliographystyle{amsplain}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nFor a very long time, network architectures have been inspired by the model called Three-Tier Architecture. This model is composed of three levels: Core, Distribution and Access. Server farms are just a special case of the Access level. The Distribution and Access levels form Building Blocks which are concentrated on the Core level. The objective is to size Building Blocks that will not grow beyond a threshold established in advance. Increasing the size of the network requires the addition of Building Blocks. The sizing of the Building Blocks and the connections between all the layers of the architecture uses the notion called over-subscription.\nAs explained in \\cite{1}, statistical considerations play a key role in the field of network Capacity Planning. It is intuitively obvious that, in the worst case, the results of provisioning lead to unnecessary waste and expense. It is also intuitively obvious that in a network with over-subscription there is a risk of not being able to provide adequate services to users if the ratio that is used is too aggressive.\nNetwork Capacity Planning is a field often based on empirical observations, trends, patterns and forecasts of network usage. In a domain subject to bursty traffic, it is difficult to derive precise link sizing parameters and it is common to see networks designed for worst-case usage scenarios. However, it is precisely the bursty nature of traffic that allows a statistical approach to be used in Capacity Planning. In other words, we exploit the fact that not everyone is online at the same time to make our network sizing decisions.\n\n\\section{Mathematical approach}\n\nAs proposed in \\cite{1}, it is possible to approach the subject from a statistical point of view. Assume a number \\emph{n} of \\emph{on\/off} type traffic sources that can use the network links. Each source generates a burst of traffic of up to \\emph{R} (bits per second) in a time interval of \\emph{T} seconds during its \\emph{on} period, then that source goes \\emph{off} for another period of \\emph{T} seconds, and finally the cycle repeats itself. Note that the source sends \\emph{RT} bits during the \\emph{on} period and that the number of bits per period is random.\nThe different sources are not synchronized in time (they can go \\emph{on} and \\emph{off} independently of each other) and their aggregated traffic is processed by the network links.\nWe can compute the statistical over-subscription for all the sources, using the following formula: \\[C=\\frac{R}{2}n+C_{\\epsilon}S_{max}\\sqrt{n}\\]\n\n\\pagebreak\n\nInto which:\n\n\\begin{itemize}\n    \\item \\emph{C} is the capacity of the link to forecast in bits\/s, if half of the sources are \\emph{on} at the same time.\n    \\item $nR$ corresponds to the maximum traffic in bits\/s, if all the sources are \\emph{on} at the same time.\n    \\item $\\frac{R}{2}n$ is the average traffic in bits\/s, from all sources aggregated assuming that only half are \\emph{on} at any one time.\n    \\item $C_{\\epsilon}$ corresponds to the QoS level which reflects the confidence interval with which it can be declared that the resulting capacity will not be exceeded by the traffic load.\n    \\item $\\epsilon=0.01$ corresponds to a confidence interval of $99\\%$ or $1-\\epsilon$, which gives $C_{\\epsilon}=2.575829303549$ according to the Normal Law table.\n    \\item $S_{max}=\\frac{R}{2\\sqrt{3}}$ is the standard deviation in bits\/s for a traffic source, where standard deviation is $\\sqrt{variance}$.\n\\end{itemize}\n\nConsider an example where $n=100$, $R=1,000,000\\,bit\/s$, $T=1\\,sec$ and $\\epsilon=0.01$.\n\n\\begin{align}\n\tC_{max}&=nR  \\nonumber\\\\\n\t&=100\\times1.000.000\\,bits\/s  \\nonumber\\\\\n\t&=100\\,Mbits\/s  \\nonumber\n\\end{align}\n\n\\begin{align}\n    S_{max}&=\\frac{R}{2\\sqrt{3}}  \\nonumber\\\\\n    &=\\frac{1.000.000\\,bits\/s}{3,46}  \\nonumber\\\\\n    &=289.017\\,bits\/s  \\nonumber\n\\end{align}\n\n\\begin{align}\n    C_{stat}&=\\frac{1.000.000\\,bits\/s}{2}\\times100+2,58\\times289.017\\,bits\/s\\times10 \\nonumber\\\\\n    &=50\\,Mbits\/s+7,5\\,Mbits\/s \\nonumber\\\\\n    &=57,5\\,Mbits\/s  \\nonumber\n\\end{align}\n\nIn this example, we can see that in the worst case provisioning, the link would require \\emph{100 Mbps} of capacity, while a link with capacity of around \\emph{60 Mbps} would be sufficient to support the volume of traffic, with a confidence level of $99\\%$ (i.e. we are convinced that $99\\%$ of the time, the total volume of traffic will not exceed \\emph{60 Mbits\/s}).\n\n\\section{Ratios approach}\n\n\\begin{figure}[H]\n\\centering\n\\includegraphics[width=0.8\\textwidth]{Three-Tier.png}\n\\caption{\\label{fig:ThreeTier}Three-Tier architecture}\n\\end{figure}\n\nIn a faster and more pragmatic way, good practices propose over-subscription ratios of \\emph{20:1} for the links between the Access level and the Distribution level, of \\emph{4:1} for the links between the Distribution level and the Core level and \\emph{1:1} for the links between the Access level of the server farms and the Core level. If congestion should occur on the interconnection links, the frames are queued and it is the QoS that can take over in order to prioritize critical flows.\nIf these rules are not respected, the algorithms used by the TCP protocol may see segment losses which will not allow them to take full advantage of the speeds available.\n\nIf it was always relatively obvious that the interconnection links between the Access level and Distribution level were at level 2, the links between the Distribution level and the Core level could be at level 2 or at level 3. The point of setting up routing was to ensure that all the links were used in parallel by seeking the shortest path or by distributing the load over all the paths of equivalent cost. In this case, setting up Layer 2 virtual networks through the architecture was less easy to achieve, although not impossible. The use of level 2 for the links between the Distribution level and the Core level made the architecture simpler, but did not make it possible to use all the links in active mode, since a protocol for avoiding Ethernet loop, such as the Spanning Tree would deactivate the links corresponding to the redundant paths.\n\nThe arrival of the aggregation of the Control Plane between several switches (stacking, virtualization, ...) has changed the vision of the three-level architecture, into which the Spanning Tree protocol no longer sees a redundant path. The duplicated links going up on two switches, whose control plane is merged, are aggregated together using the LACP IEEE 802.3ad protocol.\n\n\\begin{figure}[H]\n\\centering\n\\includegraphics[width=0.8\\textwidth]{Three-Tier-with-Control-Plane-aggregation.png}\n\\caption{\\label{fig:ThreeTierAggregation}Three-Tier architecture with aggregated Control Plane}\n\\end{figure}\n\nNot only are all the links active, which increases speeds and promotes over-subscription ratios, but in the event of the loss of one of them, the re-convergence times of the architecture can reach less than a second. This Subsecond Convergence architecture is more suited to the transport of UDP streams with strong constraints such as voice.\n\nThe consequence of changing application deployment, increased use of virtual machines, and redesigned storage has resulted in changing traffic patterns in the particular building block of server farms from predominantly client\/ server (north-south) to a significant level of server-to-server (east-west) flow. These changes in the flow matrix led to the rebirth, under the name of Leaf-Spine, of the architecture developed by Charles Clos within Bell Laboratories in the 1950s. In his document \\cite{2}, Charles Clos introduces the concept of a multi-stage switched network, the advantage of which is to allow connection between a large number of input and output ports with small intermediate switches. The mathematical model makes it possible to realize a totally non-blocking network like a crossbar switch. The demonstration is usually done with a three-stage system (Ingress Stage or Input Switches, Middle Stage or Intermediary Switches, and Egress Stage or Output Switches), but the Leaf-Spine model we use is represented on Two-Tier (as Charles Clos pointed out when entry points are also exit points), into which the Spine tier is the aggregation level and the Leaf tier represents the Access level.\n\n\\begin{figure}[H]\n\\centering\n\\includegraphics[width=0.8\\textwidth]{Leaf-Spine.png}\n\\caption{\\label{fig:LeafSpine}Leaf-Spine architecture}\n\\end{figure}\n\nIn this architecture, it is no longer necessary to merge the Control Plane of the Spine switches, but all the links must be active for the model to work. In order not to be subject to the use of a level 2 loop avoidance protocol such as the Spanning Tree, a dynamic routing protocol such as OSPF (Open Shortest Path First) makes it possible to create an architecture whose links are used in ECMP (Equal-Cost MultiPath). Routing protocols such as IS-IS (Intermediate System to Intermediate System) or BGP (Border Gateway Protocol) can also be implemented in this kind of architecture. We find the difficulty of propagation of level 2 virtual network through the whole architecture, which is circumvented by the encapsulation of Ethernet frames in UDP thanks to the use of the VXLAN protocol (Virtual eXtensible LAN \u2013 RFC 7348) which achieves a MAC-in-IP tunnel for the transport of level 2 virtual networks on a level 3 network (concept called Overlay Network as opposed to the supporting level 3 network which is called Underlay Network). The NVGRE protocol (Network Virtualization using Generic Routing Encapsulation \u2013 RFC 7637) is another Overlay technology allowing to build a layer 2 network on an infrastructure configured in layer 3.\n\nThe SPB (Shortest Path Bridging \u2013 IEEE 802.1aq) and TRILL (TRansparent Interconnection of Lots of Links \u2013 RFC 6325 corrected by RFCs 6327, 6439, 7172, 7177, 7357, 7179, 7180, 7455, 7780 and 7783) protocols have been proposed as an alternative to the Spanning Tree to be able to achieve this architecture entirely in level 2 with all the active links. Manufacturers make it possible to build this type of level 2 architecture for small to medium-sized networks.\n\n\\begin{figure}[H]\n\\centering\n\\includegraphics[width=0.8\\textwidth]{Clos-Network.png}\n\\caption{\\label{fig:ClosNetwork}3-stage Clos Network}\n\\end{figure}\n\nThe mathematical model can be extract from the Standford University course \\cite{3}. It can be shown that with $k \\geq n$, the Clos network can be non-blocking like a crossbar switch.\n\nFor the Leaf-Spine model to be non-blocking, it would be necessary that for each pair of ports, there is a path arrangement to connect the input port with the output port, which would require the use of a large amount of spine nodes and interconnecting links. At the Spine level, the over-subscription ratio is generally \\emph{1:1}, i.e. the speed of the aggregate links of a Leaf switch is equal to that of another Leaf switch so that that all received traffic can be resent in a non-blocking fashion. The over-subscription ratio of a leaf switch to a spine switch must be planned according to needs and it is generally considered that a ratio of \\emph{3:1} is acceptable. This could be write: \\[k \\geq \\frac{n}{3}\\]\nAs all the input and output links of a leaf can have different speeds, it is necessary to include variables to represent them, using \\emph{i} as output speed and \\emph{j} as input speed: \\[ik \\geq \\frac{jn}{3}\\]\n\n\\section{Ethernet performance background}\n\nThe IEEE (Institute of Electrical and Electronics Engineers) 802.3 Working Group develops standards for Ethernet networks. A number of active projects focus on different throughputs. A standard Ethernet frame consists of the following fields:\n\n\\begin{center}\n\\begin{tabular}{ l c c }\n    \\textbf{Frame Part} &\t\\textbf{Minimum Frame Size} &\t\\textbf{Maximum Frame Size} \\\\\n    Inter Frame Gap (96 ns)\\footnotemark[1] &\t12 Bytes &\t12 Bytes \\\\\n    MAC Preamble (+SFD) &\t8 Bytes &\t8 Bytes \\\\\n    MAC Destination Address &\t6 Bytes &\t6 Bytes \\\\\n    MAC Source Address &\t6 Bytes &\t6 Bytes \\\\\n    MAC Type (or length) &\t2 Bytes &\t2 Bytes \\\\\n    Payload (Network PDU) &\t46 Bytes &\t1500 Bytes \\\\\n    Check Sequence (CRC) &\t4 Bytes &\t4 Bytes \\\\\n    \\textbf{Total Frame Physical Size} &\t\\textbf{84 Bytes} &\t\\textbf{1,538 Bytes}\n\\end{tabular}\n\\end{center}\n\n\\footnotetext[1]{96 ns for Gigabit Ethernet and 9.6 ns for 10 Gigabit Ethernet}\n\nThe maximum capacity of an interface in frames per second, or speed, is calculated using the following formula: \\[Maximum Number of Frames per Second = \\frac{Ethernet Data Rate (bits per second)}{Total Frame Physical Size (bits)}\\]\n\nIf we take Gigabit Ethernet as an example, we get the following performance:\n\n\\begin{center}\n\\begin{tabular}{ c c }\n    \\begin{tabular}{@{}c@{}}\\textbf{Maximum Rate with} \\\\ \\textbf{Minimum Frame Size}\\end{tabular} &\t\\begin{tabular}{@{}c@{}}\\textbf{Maximum Rate with} \\\\ \\textbf{Maximum Frame Size}\\end{tabular} \\\\\n    $\\frac{1,000,000,000 \\, b\/s}{(84 \\, B \\times 8 \\, b\/B)} = 1,488,095 \\, f\/s$ &\t$\\frac{1,000,000,000 \\, b\/s}{(1,538 \\, B \\times 8 \\, b\/B)} = 81,274 \\, f\/s$\n\\end{tabular}\n\\end{center}\n\nTo compute the throughput of an Ethernet interface, the Inter Frame Gap and MAC Preamble fields are not taken into account, as they do not constitute useful information. The Check Sequence field may or may not be included in the calculation depending on how you see it. Therefore, our example of Gigabit Ethernet becomes:\n\n\\begin{center}\n\\begin{tabular}{ l c c }\n    \\begin{tabular}{@{}l@{}}\\textbf{Maximum Gigabit} \\\\ \\textbf{Bandwidth}\\end{tabular} &\t\\textbf{With CRC (4 Bytes)} &\t\\textbf{Without CRC} \\\\\n    \\begin{tabular}{@{}l@{}}Minimum Frame Size \\\\ (60 Bytes)\\end{tabular} & \\begin{tabular}{@{}c@{}}$1,488,095 \\, f\/s \\times (64 \\, B \\times 8 \\, b\/B)$ \\\\ $\\approx 762 \\, Mbps$\\end{tabular}  & \\begin{tabular}{@{}c@{}}$1,488,095 \\, f\/s \\times (60 \\, B \\times 8 \\, b\/B)$ \\\\  $\\approx 714 \\, Mbps$\\end{tabular} \\\\\n    \\begin{tabular}{@{}l@{}}Maximum Frame Size \\\\ (1514 Bytes)\\end{tabular} & \\begin{tabular}{c}$81,274 \\, f\/s \\times (1,518 \\, B \\times 8 \\, b\/B)$ \\\\ $\\approx 987 \\, Mbps$\\end{tabular}  & \\begin{tabular}{c}$81,274 \\, f\/s \\times (1,514 \\, B \\times 8 \\, b\/B)$ \\\\ $\\approx 984 \\, Mbps$\\end{tabular} \n\\end{tabular}\n\\end{center}\n\nApplied to 10 Gigabit Ethernet technology we can generates the following figures:\n\n\\begin{center}\n\\begin{tabular}{ c c }\n    \\begin{tabular}{@{}c@{}}\\textbf{Maximum Rate with} \\\\ \\textbf{Minimum Frame Size}\\end{tabular} &\t\\begin{tabular}{@{}c@{}}\\textbf{Maximum Rate with} \\\\ \\textbf{Maximum Frame Size}\\end{tabular} \\\\\n    $14,880,952 \\, f\/s$ &\t$812,743 \\, f\/s$\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\begin{tabular}{ l c c }\n    \\textbf{Maximum 10 Gigabit Bandwidth} &\t\\textbf{With CRC (4 Bytes)} &\t\\textbf{Without CRC} \\\\\n    Minimum Frame Size (60 Bytes) & $\\approx 7.62 \\, Gbps$  & $\\approx 7.14 \\, Gbps$ \\\\\n    Maximum Frame Size (1514 Bytes) & $\\approx 9.87 \\, Gbps$  & $\\approx  9.84 \\, Gbps$ \n\\end{tabular}\n\\end{center}\n\nThe size of an Ethernet frame can be increased by at least one Tag Id of 4 bytes due to the use of 802.1Q vlan. It is also possible to use a larger frame size, called Jumbo Frame, which can reach a total size of 9038 bytes.\n\n\\pagebreak\n\n\\section{TCP and UDP performance background}\n\nThe Payload field of the Ethernet frame contains the data that has been encapsulated in TCP or UDP, then in IP.\n\n\\begin{center}\n\\begin{tabular}{ l c c c c }\n    \\textbf{Frame Component} &&\t\\textbf{TCP} &&\t\\textbf{UDP} \\\\\n    Inter Frame Gap &&\t12 Bytes &&\t12 Bytes \\\\\n    MAC Preamble (+SFD) &&\t8 Bytes &&\t8 Bytes \\\\\n    MAC Destination Address &&\t6 Bytes &&\t6 Bytes \\\\\n    MAC Source Address &&\t6 Bytes &&\t6 Bytes \\\\\n    MAC Type (or length) &&\t2 Bytes &&\t2 Bytes \\\\\n    \\rowcolor{lightgray}\n    Payload (Network PDU) & IPv4 Header\t&\t20 Bytes & IPv4 Header &\t20 Bytes \\\\\n    \\rowcolor{lightgray}\n    46 - 1500 Bytes & TCP Header\t&\t20 Bytes & UDP Header &\t8 Bytes \\\\\n    \\rowcolor{lightgray}\n    & \\begin{tabular}{@{}c@{}}TCP options \\& \\\\ Data\/Padding\\end{tabular}\t&\t\\begin{tabular}{@{}c@{}}6 \u2013 1460 \\\\ Bytes\\end{tabular} & Data\/Padding &\t\\begin{tabular}{@{}c@{}}18 \u2013 1472 \\\\ Bytes\\end{tabular} \\\\\n    Check Sequence (CRC) &&\t4 Bytes &&\t4 Bytes \\\\\n    \\textbf{Total Frame Physical Size} & \\multicolumn{4}{c}{\\textbf{84 - 1,538 Bytes}}\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\begin{tabular}{ l c }\n    \\textbf{Gigabit Ethernet TCP\/IP \\& UDP\/IP Throughput} & \\\\\n    \\begin{tabular}{@{}l@{}}Max TCP\/IP Data Rate (84 Bytes Frames) and \\\\ Min TCP\/IP Packet (60 Bytes + 4 Bytes CRC)\\end{tabular}\t& \\begin{tabular}{@{}c@{}}$1,488,095 \\, f\/s \\times 6 \\, B\/f \\times 8 \\, b\/B$ \\\\ $\\approx 71 \\, Mbps$\\end{tabular} \\\\\n    \\begin{tabular}{@{}l@{}}Max TCP\/IP Data Rate (1538 Bytes Frames) and \\\\ Max TCP\/IP Packet (1514 Bytes + 4 Bytes CRC)\\end{tabular}\t& \\begin{tabular}{@{}c@{}}$81,274 \\, f\/s \\times 1,448 \\, B\/f \\times 8 \\, b\/B$ \\\\ $\\approx 941 \\, Mbps$\\end{tabular} \\\\\n    \\textbf{With TCP\/IP TimeStamp} & \\\\\n    \\begin{tabular}{@{}l@{}}Max TCP\/IP Data Rate (1538 Bytes Frames) and \\\\ Max TCP\/IP Packet (1514 Bytes + 4 Bytes CRC)\\end{tabular}\t& \\begin{tabular}{@{}c@{}}$81,274 \\, f\/s \\times 1,460 \\, B\/f \\times \\, 8 b\/B$ \\\\ $\\approx 949 \\, Mbps$\\end{tabular} \\\\\n    \\textbf{Without TCP\/IP TimeStamp} & \\\\\n    \\begin{tabular}{@{}l@{}}Max UDP\/IP Data Rate (84 Bytes Frames) and \\\\ Min UDP\/IP Packet (60 Bytes + 4 Bytes CRC)\\end{tabular}\t& \\begin{tabular}{@{}c@{}}$1,488,095 \\, f\/s \\times 18 \\, B\/f \\times 8 \\, b\/B$ \\\\ $\\approx 214 \\, Mbps$\\end{tabular} \\\\\n    \\begin{tabular}{@{}l@{}}Max UDP\/IP Data Rate (1538 Bytes Frames) and \\\\ Max UDP\/IP Packet (1514 Bytes + 4 Bytes CRC)\\end{tabular}\t& \\begin{tabular}{@{}c@{}}$81,274 \\, f\/s \\times 1,472 \\, B\/f \\times \\, 8 b\/B$ \\\\ $\\approx 957 \\, Mbps$\\end{tabular} \\\\\n\\end{tabular}\n\\end{center}\n\nTCP (Transmission Control Protocol) and UDP (User Datagram Protocol) are used to transfer data or packets over networks. TCP is connection oriented while UDP is connectionless. TCP transmission is more reliable, but slower because it checks for errors and maintains data order. UDP does not have an error checking mechanism that is why it is less reliable but faster in data transfer.\n\nThere are several implementations of TCP (Tahoe, Reno, Vegas, New Reno\u2026), but fundamentally the operation of TCP remains the same and is based on RFC 5681. It is worth knowing the implementation used on the system and change it if it turns out that it is not the most suitable for the intended use.\n\n\\begin{center}\n\\begin{tabular} { l c c l }\n    \\textbf{TCP variant} &\t\\textbf{Network} &\t\\textbf{Class} & \\textbf{Main features} \\\\\n    Reno & Standard & Loss-based & Standard TCP \\\\\n    Vegas & Standard & Delay-based & \\begin{tabular}{@{}l@{}}Proactive scheme \\\\ RTT and rate estimation\\end{tabular} \\\\\n    Veno & Wireless & Delay-based & \\begin{tabular}{@{}l@{}}Combine Reno and Vegas \\\\ Deal with random loss\\end{tabular} \\\\\n    Westwood & Wireless & Delay-based & Deal with \u00ab Large \u00bb dynamic channels \\\\\n    BIC & Long fat\\footnotemark[2] & Loss-based & Modification of congestion avoidance scheme \\\\\n    CUBIC & Long fat & Loss-based & Improved variant of BIC \\\\\n    HSTCP & Long fat & Loss-based & Modification of congestion avoidance scheme \\\\\n    Hybla & Long fat & Delay-based & Modification of congestion avoidance scheme \\\\\n    Scalable & Long fat & Loss-based & Modification of congestion avoidance scheme \\\\\n    Illinois & Long fat & Loss-Delay-based & Modification of congestion avoidance scheme \\\\\n    YeAH & Long fat & Delay-based & \\begin{tabular}{@{}l@{}}Two working modes for the congestion \\\\ avoidance phase: fast and slow\\end{tabular} \\\\\n    HTCP & Long fat & Delay-based & Modification of congestion avoidance scheme \\\\\n    LP & - & Delay-based & Variant for low priority flows \\\\\n\\end{tabular}\n\\end{center}    \n\n\\footnotetext[2]{High Latency}\n\n\\pagebreak\n\nThere are four fundamental congestion control algorithms: slow start, congestion avoidance, fast retransmit and fast recovery. The slow start and congestion avoidance algorithms must be used by the sender to control the amount of data injected into the network. To implement these algorithms, two variables are used: \\emph{cwnd} (sender side congestion window) and \\emph{rwnd} (receiver's advertised window). The \\emph{cwnd} variable is the amount of data the sender can transmit over the network before receiving an acknowledgment (ACK) and the \\emph{rwnd} variable is the limit on the receiver side. It is the minimum of these two variables which is taken as a reference in the data transmission. Another state variable: \\emph{ssthresh} (slow start threshold) is used to determine which of the two algorithms slow start or congestion avoidance should be used to control data transmission.\n\nThe slow start algorithm is used at startup or after a loss detected by the retransmission timer, to determine the available network capacity in order to avoid congestion. \\emph{IW} (Initial Window) is the initial value of \\emph{cwnd} and should be set using the following rules:\n\n\\begin{itemize}\n    \\item If $Sender \\, MSS > 2190 \\, bytes$ then $IW = 2 * SMSS \\, bytes$ and must not be greater than 2 segments\n    \\item If $(SMSS > 1095 \\, bytes) \\, and \\, (SMSS \\leq 2190 \\, bytes)$ then $IW = 3 * SMSS \\, bytes$ and must not be more than 3 segments\n    \\item If $SMSS \\leq 1095 \\, bytes$ then $IW = 4 * SMSS \\, bytes$ and should not be more than 4 segments\n\\end{itemize}\n\nThe initial value of \\emph{ssthresh} should be set to the size of the largest possible window (advertised window), but \\emph{ssthresh} should be reduced in response to congestion. The slow start algorithm is used when $cwnd < ssthresh$, while the congestion avoidance algorithm is used when $cwnd > ssthresh$. In the event of a tie, the issuer can choose which algorithm to use. During the slow start phase, TCP increments \\emph{cwnd} by at most \\emph{SMSS bytes} and slow start stops when \\emph{cwnd} reaches or exceeds \\emph{ssthresh}. It is recommended to augment \\emph{cwnd} in the following way: \\[cwnd \\mathrel{+}= min(N, SMSS)\\] with \\emph{N} being the number of bytes that were acknowledged in the last ACK.\n\nDuring the congestion avoidance phase, \\emph{cwnd} is increased by approximately one segment per RTT (Round-Trip Time) and the algorithm continues its work until congestion is detected. It is recommended to increase \\emph{cwnd} as follows and adjust each time an ACK is received: \\[cwnd \\mathrel{+}= SMSS \\times \\frac{SMSS}{cwnd}\\]\n\nWhen a transmitter detects the loss of a segment using the retransmission timer and this segment has not been retransmitted, the value of \\emph{ssthresh} must not be set beyond the value given by the equation: \\[ssthresh=max(\\frac{FlightSize}{2}, 2\\times SMSS)\\] with \\emph{FlightSize} being the amount of data waiting in the network.\n\nA receiver, in TCP, should immediately send a duplicate ACK when an out-of-order segment arrives, with the objective of informing the sender of what happened and requesting sending the segment again. The sender should use the fast retransmit algorithm to detect and repair the loss based on incoming duplicate ACKs. The algorithm uses the arrival of three duplicate ACKs as an indication that a segment has been lost. From then on, TCP performs a retransmission of the lost segment without waiting for the expiration of the retransmission timer. After transmission of the lost segment, the fast recovery algorithm takes over the transmission of new data until a non-duplicate ACK arrives. The implementation of the fast retransmit and fast recovery algorithms follows rules for positioning values for \\emph{cwnd} and \\emph{ssthresh}.\n\nIn a simplified way, the TCP throughput is calculated with the following formula: \\[Throughput = \\frac{Window Size}{RTT}\\]\n\nStudies have shown that it is necessary to take into account other parameters such as MSS (Maximum Segment Size) and packet loss. As explained in \\cite{4}, assuming that the network has a packet loss probability called \\emph{p}, the sender will be able to send an average of $\\frac{1}{p}$ packets before a packet loss. According to this model, \\emph{cwnd} will never exceed a maximum \\emph{W} (window expressing the number of segments that can be sent during an RTT), because at approximately $\\frac{1}{p}$ packets, a new packet loss will cause the division by two from \\emph{cwnd}. Therefore, the total quantity of data delivered at each cycle of $\\frac{1}{p}$ packets is given by: \\[\\frac{1}{p} = \\left( \\frac{W}{2} \\right) ^2 + \\frac{1}{2} \\left( \\frac{W}{2} \\right) ^2 = \\frac{3}{8} W^2\\]\n\nTherefore, $MSS \\times \\frac{3}{8} W^2$ bytes are emitted every $RTT \\times \\frac{W}{2}$ cycle.\n\nAs $W = \\sqrt{\\frac{8}{3p}}$ the bit rate is therefore:\n\n\\begin{align}\n\tThroughput &= \\frac{MSS \\times \\frac{3}{8} W^2}{RTT \\times \\frac{W}{2}}\\nonumber\\\\\n\t&= \\frac{\\frac{MSS}{p}}{RTT \\sqrt {\\frac{2}{3p}}}\\nonumber\\\\\n\t&= \\frac{MSS \\times \\sqrt{\\frac{3}{2}}}{RTT \\times \\sqrt{p}}\\nonumber\\\\\n\t&= \\frac{MSS \\times 1.22}{RTT \\times \\sqrt{p }}\\nonumber\n\\end{align}\n\nA study \\cite{5} compared different TCP implementations and highlighted the performance differences in situations where RTT and loss probability values vary. As a result, on a wired network, the TCP Hybla and TCP CUBIC implementations achieve very good performance while TCP Reno also performs well, but TCP-LP achieves the worst results. On a wireless network, the cards are redistributed and the TCP Reno, TCP BIC and TCP-LP implementations obtain the best results. On long distance networks with delay, such as satellite networks, the TCP CUBIC implementation performs best. Finally, the implementation that seems to behave homogeneously in all circumstances remains TCP Reno.\n\n\\bibliographystyle{alpha}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
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+{"text":"\\section{Introduction}\\label{intro}\n\nAssociation schemes~\\cite{BI,BCN} were first defined by Bose and Mesner~\\cite{BM} in the context of the design of experiments.\nPhilippe Delsarte used association schemes to unify the study \nof coding theory and design theory in his thesis~\\cite{PD}, where he derived his well-known linear programming bound which has since found many applications \nin combinatorics. There he identified two types of association schemes which were of particular interest: the so-called \n$P$-polynomial and $Q$-polynomial schemes. \nSchemes which are $P$-polynomial are precisely those arising from distance-regular graphs, and are well studied.\nIn particular, much effort has gone into the classification of distance-transitive graphs, the $P$-polynomial schemes \nwhich are the orbitals of a permutation group; and it is likely that all such examples are\nknown. Also well-studied are the schemes which are both $Q$-polynomial and\n$P$-polynomial. A well-known conjecture~\\cite[p.312]{BI} of Bannai and Ito is the following: for sufficiently\nlarge $d$, a primitive scheme is $P$-polynomial if and only if it is $Q$-polynomial.\n\nClassification efforts for $Q$-polynomial schemes are far less advanced than in the $P$-polynomial case; in particular it is likely that more\nexamples from permutation groups are yet to be found. The $Q$-polynomial property has no known combinatorial characterization, making their study more difficult. \nHowever, the list of known examples (see~\\cite{MMW,PW,VDMM}) indicates that these objects have interesting structure from the viewpoint\nof designs, lattices, coding theory and finite geometry.\n\nIn this paper, we give a new family of imprimitive $Q$-polynomial schemes with an\nunbounded number of classes. These schemes are formed by the orbitals of a group, giving a double cover of the scheme arising from the symplectic dual polar space graph. \nWe note that only one other family of imprimitive $Q$-polynomial schemes with an\nunbounded number of classes is known that is not $P$-polynomial, namely the bipartite doubles of the Hermitian dual polar space graphs, which are $Q$-bipartite and $Q$-antipodal.\nThe schemes in this paper are $Q$-bipartite, and have two $Q$-polynomial orderings.\nExcept when the field order $q$ is a square, the splitting field of these schemes is also\nirrational.  We note that this is the only known family of $Q$-polynomial schemes with\nunbounded number of classes and an irrational splitting field.\nIn the last section we give open parameters for hypothetical primitive $Q$-polynomial subschemes of this family. \n\nOur paper is organized as follows: Background material on Gaussian coefficients, two-graphs\nand double covers of graphs, are covered in Sections \\ref{gaussian}--\\ref{graphs}. In\nSection~\\ref{dual_polar} we recall the standard construction of the symplectic dual polar\ngraph $\\Gamma=\\Gamma(2n,q)$. There we also introduce the Maslov index, which we use in Section~\\ref{double_cover} to construct the double cover\n$\\widehat{\\Gamma}\\to\\Gamma$ when $q\\equiv1$ mod~4. In Section~\\ref{scheme} we construct a $(2n+1)$-class association scheme\n$\\mathcal{S}=\\mathcal{S}_{n,q}$ from $\\widehat{\\Gamma}$; and in Section~\\ref{Q-poly} we show that $\\mathcal{S}$ is\n$Q$-polynomial. The $P$-matrix of the scheme is constructed in Section~\\ref{P-matrix}.\nA particularly tantalizing open problem is the question whether $\\mathcal{S}$ is in general\nthe extended $Q$-bipartite double of a primitive $Q$-polynomial scheme; see Section~\\ref{subscheme}.\n\n\\section{Gaussian coefficients}\\label{gaussian}\n\nFor all integers $n,k$ we define the {\\em Gaussian coefficient\\\/}\n\\[\\gauss{n}k=\\gauss{n}k_q=\\begin{cases}\n\\frac{(q^n-1)(q^{n-1}-1)\\cdots(q^{n-k+1}-1)}{(q^k-1)(q^{k-1}-1)\\cdots(q-1)},\n&\\mbox{if\\ }k\\geqslant0;\\\\\n0,&\\mbox{if\\ }k<0.\n\\end{cases}\\]\nIn particular for $k=0$ the empty product gives $\\gauss{n}0=1$. In later sections, $q$ will be a fixed prime power; but here we may regard $q$ as an indeterminate, so that\nfor $n\\geqslant0$, after cancelling factors we find $\\gauss{n}k\\in{\\mathbb Z}[q]$; and specializing to\n$q=1$ gives the ordinary binomial coefficients $\\gauss{n}k_1=\\binom{n}k$. For general\n$n\\in{\\mathbb Z}$ we instead obtain a Laurent polynomial in $q$ with integer coefficients, i.e.\\ \n$\\gauss{n}k\\in{\\mathbb Z}[q,q^{-1}]$, as follows from conclusion (ii) of the following.\n\n\\begin{proposition}\\label{prop2.1}\nLet $n,k,\\ell\\in{\\mathbb Z}$. The Gaussian coefficients satisfy\n\\begin{itemize}\n\\item[(i)]$\\gauss{n}k=q^k\\gauss{n-1}k+\\gauss{n-1}{k-1}=\\gauss{n-1}k+q^{n-k}\\gauss{n-1}{k-1}$;\n\\item[(ii)]$\\gauss{-n}k=(-q^{-n})^k\\gauss{n+k-1}k$;\n\\item[(iii)]$\\gauss{n}k\\gauss{k}\\ell=\\gauss{n}\\ell\\gauss{n-\\ell}{k-\\ell}$;\n\\item[(iv)]$\\gauss{n}k=\\gauss{n}{n-k}$ whenever $0\\leqslant k\\leqslant n$.\\qed\n\\end{itemize}\n\\end{proposition}\nMost of the conclusions of Proposition~\\ref{prop2.1} are found in standard references such as~\\cite{A}. However, our definition of $\\gauss{n}k$ differs from the\nstandard definition found in most sources, which either leave $\\gauss{n}k$ undefined for $n<0$, or define it to be zero in that case.\nOur extension to all $n\\in{\\mathbb Z}$ means that the recurrence formulas~(i) hold for all integers $n,k$, unlike the `standard definition' which fails for $n=k=0$. Property~(i) plays a role in\nour later algebraic proofs using generating functions. In further defense of our definition,\nwe observe that it has become standard to extend the definition of binomial coefficients\n$\\binom{n}k$ so that $\\binom{-n}k=(-1)^k\\binom{n+k-1}k$ (see e.g.~\\cite[p.12]{A});\nand (ii) naturally generalizes this to Gaussian coefficients. We further note that (iii) holds for all $n,k\\in{\\mathbb Z}$\nwhether one takes the standard definition of $\\gauss{n}k$ or ours. The one advantage of\nthe standard definition is that it renders superfluous the extra restriction $0\\leqslant k\\leqslant n$\nin the symmetry condition~(iv). The interpretation of $\\gauss{n}k$ as the number of $k$-subspaces\nof an $n$-space over ${\\mathbb F}_q$ is valid for all $n\\geqslant0$.\n\nIn Section~\\ref{P-matrix} we will make use of the well-known generating polynomials\n\\[E_m(t)=\\prod_{i=0}^{m-1}(1+q^i t)=\\sum_{\\ell=0}^\\infty q^{\\binom{\\ell}2}\\gauss{m}\\ell t^\\ell\\quad\\mbox{for\\ }m=0,1,2,\\ldots;\\]\nnote that in the latter sum, the terms for $\\ell>m$ vanish, yielding $E_m(t)\\in{\\mathbb Z}[q,t]$ (or\nafter specializing to a fixed prime power $q$, we obtain $E_m(t)\\in{\\mathbb Z}[t]$).\nHere we see the usual binomial coefficient $\\binom{\\ell}2=\\frac12\\ell(\\ell-1)$. In Section~\\ref{P-matrix} we will make use of the following obvious relations:\n\n\\begin{proposition}\\label{prop2.2}\nFor all $m\\geqslant0$, the generating function $E_m(t)$ satisfies\n\\begin{itemize}\n\\item[(i)]$E_m(-q t)=\\frac{1- q^mt}{1-t} E_m(-t)$;\n\\item[(ii)]$E_m(q^2t)=\\frac{1+q^{m+1}t}{1+qt} E_m(qt)$; and\n\\item[(iii)]$E_m(r^3 t)=\\frac{1+rq^mt}{1+rt} E_m(rt)$ where $r=\\sqrt{q}$.\\qed\n\\end{itemize}\n\\end{proposition}\n\n\\section{Two-graphs and double covers of graphs}\n\\label{graphs}\n\nHere we describe the most basic connections between two-graphs and double covers of graphs; see \\cite{M,Se,BCN,Ta} for more details. Our notation is chosen to conform to that used in subsequent sections.\n\nLet $\\mathcal{V}$ be any set. Denote by $\\binom{\\mathcal{V}}k$ the collection of all $k$-subsets of $\\mathcal{V}$\n(i.e.\\ subsets of cardinality $k$). A {\\em two-graph on $\\mathcal{V}$\\\/} is a subset\n$\\Delta\\subseteq\\binom{\\mathcal{V}}3$ such that for\nevery 4-set $\\{x,y,z,w\\}\\in\\binom{\\mathcal{V}}4$, an even number, i.e.\\ 0, 2 or 4, of the triples\n$\\{x,y,z\\}$, $\\{x,y,w\\}$, $\\{x,z,w\\}$, $\\{y,z,w\\}$ is in $\\Delta$. If $\\Delta$ is a\ntwo-graph on $\\mathcal{V}$, then the complementary set of triples\n$\\overline\\Delta=\\bigl\\{\\{x,y,z\\}\\in\\binom\\V3:\\{x,y,z\\}\\notin\\Delta\\bigr\\}$ is also a\ntwo-graph, called the {\\em complementary two-graph on $\\mathcal{V}$\\\/}.\n\nA {\\em graph\\\/} on $\\mathcal{V}$ is a subset $\\Gamma\\subseteq\\binom\\V2$. Elements of\n$\\Gamma$ are called {\\em edges\\\/}.\nThe {\\em complete graph on $\\mathcal{V}$\\\/} is the graph $K_\\mathcal{V}$ with full edge set $\\binom{\\mathcal{V}}2$.\nIn general the complementary set of pairs\n$\\overline\\Gamma=\\bigl\\{\\{x,y\\}\\in\\binom\\V2:\\{x,y\\}\\notin\\Gamma\\bigr\\}$ is the\n{\\em complementary graph on $\\mathcal{V}$\\\/}.\n\nEvery graph on $\\mathcal{V}$ may be identified with a signing of the edges of the complete graph $K_\\mathcal{V}$, i.e.\\ a function $\\sigma:\\binom{\\mathcal{V}}2\\to\\{\\pm1\\}$. Under this correspondence, the graph corresponding to $\\sigma$ has as its edge set $\\sigma^{-1}(1)=\\bigl\\{\\{x,y\\}\\in\\binom{\\mathcal{V}}2:\\sigma(x,y)=1\\bigr\\}$. (Here we abbreviate\n$\\sigma(\\{x,y\\})=\\sigma(x,y)$.)\n\nGiven $\\Gamma$ and $\\sigma$ as above (which amounts to two graphs which may be\nentirely unrelated except for sharing the same vertex set $\\mathcal{V}$), we construct a new graph\n$\\widehat{\\Gamma}=\\widehat{\\Gamma}_\\sigma$ with vertex set $\\widehat{\\V}=\\mathcal{V}\\times\\{\\pm1\\}$ and adjacency relation defined by\n\\[(x,\\varepsilon)\\sim(y,\\varepsilon')\\;\\iff\\;x\\sim y\\mbox{\\ and\\ }\\varepsilon\\varepsilon'=\\sigma(x,y).\\]\n(Note that $(x,1)\\not\\sim(x,-1)$ since $\\Gamma$ has no loops.)\nThe map $(x,\\varepsilon)\\mapsto x$ is a {\\em double covering map\\\/} $\\theta:\\widehat{\\Gamma}\\to\\Gamma$, also called a {\\em double cover\\\/} or simply a {\\em cover\\\/}; and the {\\em fibers\\\/}\nof this map are the pairs $\\theta^{-1}(x)=\\{(x,1),(x,-1)\\}$ where $x\\in\\mathcal{V}$.\n(By definition, a {\\em covering map\\\/} of graphs is a graph homomorphism $\\theta:\\widehat{\\Gamma}\\to\\Gamma$ such that for any vertex $x\\in\\Gamma$, the preimage of the neighborhood graph $\\Gamma_x$ is isomorphic to a disjoint union of copies of $\\Gamma_x$; see e.g.~\\cite{GR}. `Double' refers to the condition that the covering map is\n2-to-1.) We also say that the vertices $(x,1)$ and $(x,-1)$ are {\\em antipodal\\\/}\nwith respect to the covering map. (Note that antipodal vertices must be at\ndistance${}\\geqslant2$; but we deviate from common custom by\n{\\em not requiring\\\/} pairs of antipodal vertices to be at maximal distance $\\diam\\widehat{\\Gamma}$.) We denote\nby $\\zeta$ the transposition interchanging antipodal vertices:\n$(x,1)\\stackrel\\zeta\\leftrightarrow(x,-1)$. Denote by\n$\\mathop{\\rm Aut}\\nolimits_\\zeta\\widehat{\\Gamma}\\leqslant\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}$\nthe subgroup consisting of all automorphisms of the graph $\\widehat{\\Gamma}$ which preserve the\nantipodality relation. In general, $\\mathop{\\rm Aut}\\nolimits_\\zeta\\widehat{\\Gamma}$ is the centralizer of $\\zeta$\nin the full automorphism group $\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}\\leqslant\\mathop{\\rm Sym}\\nolimits\\widehat{\\V}$; but in our case\nwe obtain equality $\\mathop{\\rm Aut}\\nolimits_\\zeta\\widehat{\\Gamma}=\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}$ (see\nLemma~\\ref{lemma5.4}).\nSimilarly, two covers $\\theta_i:\\widehat{\\Gamma}_i\\to\\Gamma$ of the\nsame graph $\\Gamma$ (for $i=1,2$) are {\\em equivalent\\\/} or {\\em isomorphic\\\/}\nif there is a graph isomorphism $\\rho:\\widehat{\\Gamma}_1\\to\\widehat{\\Gamma}_2$ which preserves\nantipodality, i.e.\\ $\\theta_1\\circ\\rho=\\theta_2$.\n\nGiven $\\sigma:\\binom{\\mathcal{V}}2\\to\\{\\pm1\\}$ as above, for every triple $\\{x,y,z\\}\\in\\binom{\\mathcal{V}}3$ we may define\n\\[\\sigma(x,y,z)=\\sigma(x,y)\\sigma(y,z)\\sigma(z,x)\\in\\{\\pm1\\}.\\]\nA triple $\\{x,y,z\\}\\in\\binom{\\mathcal{V}}3$ is called {\\em coherent\\\/} or {\\em non-coherent\\\/}\naccording as $\\sigma(x,y,z)=1$ or $-1$.\nThe set of all coherent triples forms a two-graph on $\\mathcal{V}$, denote by $\\Delta_\\sigma$; and\nthe set of non-coherent triples gives the complementary two-graph $\\overline{\\Delta}_\\sigma$.\n\nTwo sign functions $\\sigma_1,\\sigma_2:\\binom{\\mathcal{V}}2\\to\\{\\pm1\\}$ (or the corresponding graphs $\\sigma_1^{-1}(1)$, $\\sigma_2^{-1}(1)$ on $\\mathcal{V}$) are {\\em switching-equivalent\\\/}\nin the sense of Seidel~\\cite{Se} if there exists a map $f:\\mathcal{V}\\to\\{\\pm1\\}$ such that $\\sigma_2(x,y)=f(x)f(y)\\sigma_1(x,y)$ for all $\\{x,y\\}\\in\\binom{\\mathcal{V}}2$. We have\n$\\Delta_{\\sigma_1}=\\Delta_{\\sigma_2}$ iff $\\sigma_1$ and $\\sigma_2$ are\nswitching-equivalent. Assuming this holds,\nthen the corresponding covers $\\widehat{\\Gamma}_{\\sigma_1}$ and $\\widehat{\\Gamma}_{\\sigma_2}$\nare isomorphic via $(x,\\varepsilon)\\mapsto(x,f(x)\\varepsilon)$.\n\nIn the special case of the complete graph\n$\\Gamma=K_\\mathcal{V}$, the following three notions are equivalent (see \\cite[\\S1.5]{BCN}): two-graphs on $\\mathcal{V}$,\nswitching classes of graphs on $\\mathcal{V}$, and isomorphism classes of double covers of the complete graph $K_\\mathcal{V}$. For example given a double cover $\\widehat{K_\\mathcal{V}}\\to K_\\mathcal{V}$, the\ncorresponding two-graph is obtained as follows (see \\cite[p.488]{Se}): Each triple $\\{x,y,z\\}$ of distinct vertices in\n$\\mathcal{V}$ induces a triangle $K_{\\{x,y,z\\}}\\subseteq K_\\mathcal{V}$; and such a triple is coherent iff its preimage in $\\widehat{K_\\mathcal{V}}$ induces a pair of triangles, rather than a 6-cycle, in $\\widehat{K}_\\mathcal{V}$.\n\nAn {\\em automorphism of a two-graph $\\Delta$\\\/} is a permutation of the underlying\npoint set $\\mathcal{V}$ which preserves the set of coherent triples. We now relate $\\mathop{\\rm Aut}\\nolimits\\Delta$\nto the group $\\mathop{\\rm Aut}\\nolimits_\\zeta\\widehat{K}\\leqslant\\mathop{\\rm Aut}\\nolimits\\widehat{K}$ defined above for the associated double cover\n$\\widehat{K}\\to K$, where we abbreviate the complete graph $K_\\mathcal{V}=K$. The following is easy to verify (or see \\cite[\\S2]{Ta}, where this isomorphism is denoted $\\widehat{G}\/Z\\cong G$):\n\n\\begin{proposition}\\label{prop3.1}\nThe group $\\mathop{\\rm Aut}\\nolimits_\\zeta\\widehat{K}$ acts naturally on $\\Delta$, inducing the full automorphism group of $\\Delta$.\nThe kernel of this action is the central subgroup $\\langle\\zeta\\rangle$ of order~2; thus $(\\mathop{\\rm Aut}\\nolimits_\\zeta\\widehat{K})\/\\langle\\zeta\\rangle\\cong\\mathop{\\rm Aut}\\nolimits\\Delta$.\n\\end{proposition}\n\n\\section{Dual polar graphs of type $Sp(2n,q)$, $q$ odd}\n\\label{dual_polar}\n\nFix a finite field ${\\mathbb F}_q$ of odd prime power order $q$; an integer $n\\geqslant1$; a $2n$-dimensional vector space $V$ over ${\\mathbb F}_q$; and a symplectic (i.e.\\ nondegenerate alternating) bilinear form $B:V\\times V\\to{\\mathbb F}_q$. The {\\em symplectic group\\\/} $Sp(2n,q)$ consists of\nall {\\em(linear) isometries\\\/} of $B$, i.e.\n\\[Sp(2n,q)=\\{g\\in GL(V):B(x^g,y^g)=B(x,y)\\mbox{\\ for all\\ }x,y\\in V\\}.\\]\nThe group of all {\\em (linear) similarities\\\/} of $B$ is\n\\begin{align*}\nGSp(2n,q)&=\\{g\\in GL(V):\\mbox{for some nonzero\\ }\\mu\\in{\\mathbb F}_q\\mbox{\\ we have}\\\\ &\\qquad B(x^g,y^g)=\\mu B(x,y)\\mbox{\\ for all\\ }x,y\\in V\\};\n\\end{align*}\nsome other notations for this group are $GSp_n(q)$ in~\\cite{KL} or $CSp_n(q)$ in~\\cite[p.31]{BHR}.\nReplacing $GL(V)$ by $\\Gamma L(V)\\cong GL(V)\\rtimes\\mathop{\\rm Aut}\\nolimits{\\mathbb F}_q$, the group of all semilinear transformations of $V$, we obtain the group $\\Sigma Sp(2n,q)$ of\nall {\\em semi-isometries\\\/}, and\nthe group $\\Gamma Sp(2n,q)$ of all {\\em semi-similarities\\\/} of $B$, given by\n\\begin{align*}\n\\Sigma Sp(2n,q)&=\\{g\\in\\Gamma L(V):\\mbox{for some\\ }\\tau\\in\\mathop{\\rm Aut}\\nolimits{\\mathbb F}_q\\mbox{\\ we have}\\\\\n&\\qquad\\quad B(x^g,y^g)=B(x,y)^\\tau\\mbox{\\ for all\\ }x,y\\in V\\}\\\\\n&\\cong Sp(2n,q)\\rtimes\\mathop{\\rm Aut}\\nolimits{\\mathbb F}_q;\\\\\n\\Gamma Sp(2n,q)&=\\{g\\in\\Gamma L(V):\\mbox{for some nonzero\\ }\\mu\\in{\\mathbb F}_q\\mbox{\\ and\\ }\\tau\\in\\mathop{\\rm Aut}\\nolimits{\\mathbb F}_q\\\\\n&\\qquad\\quad\\mbox{we have\\ }B(x^g,y^g)=\\mu B(x,y)^\\tau\\mbox{\\ for all\\ }x,y\\in V\\}\\\\\n&\\cong GSp(2n,q)\\rtimes\\mathop{\\rm Aut}\\nolimits{\\mathbb F}_q.\n\\end{align*}\nThe projective versions of these groups are\n\\begin{align*}PSp(2n,q)&=Sp(2n,q)\/\\langle-I\\rangle,\\\\\nPGSp(2n,q)&=GSp(2n,q)\/Z,\\\\\nP\\Sigma Sp(2n,q)&=\\Sigma Sp(2n,q)\/\\langle-I\\rangle,\\\\\nP\\Gamma Sp(2n,q)&=\\Gamma Sp(2n,q)\/Z\n\\end{align*}\nwhere the central subgroup $Z$ of order $q-1$ consists of all scalar transformations $v\\mapsto\\lambda v$\nfor $0\\neq\\lambda\\in{\\mathbb F}_q$. We have\n\\[[P\\Gamma Sp(2n,q):P\\Sigma Sp(2n,q)]=[PGSp(2n,q):PSp(2n,q)]=2\\]\nwhere the nontrivial coset in both cases is represented by $h\\in GSp(2n,q)$\nsatisfying $B(u^h,v^h)=\\eta B(u,v)$ and $\\eta\\in{\\mathbb F}_q$ is a nonsquare.\n\nOur choice of notation for these groups, while not universal, is intended to conform\nreasonably with \\cite{Atlas,KL}. The group $P\\Gamma Sp(2n,q)$, for example, is denoted $PC\\Gamma Sp_n(q)$ in \\cite[p.31]{BHR}. It arises (see Theorem~\\ref{theorem4.1}) as the full automorphism\ngroup of the associated dual polar graph, which we now describe.\n\nDenote by $\\mathcal{V}$ be the collection of all maximal totally\nisotropic subspaces with respect to $B$, i.e.\\ \n\\[\\mathcal{V}=\\{X\\leqslant V:X^\\perp=X\\}\\]\nwhere by definition $X^\\perp=\\{v\\in V:B(x,v)=0\\mbox{\\ for all\\ }x\\in X\\}$. Members of\n$\\mathcal{V}$ are often called {\\em generators\\\/}, and every $X\\in\\mathcal{V}$ has dimension~$n$.\nDenote by $\\Gamma=\\Gamma(2n,q)$ the graph on $\\mathcal{V}$ where two vertices\n$X,Y\\in\\mathcal{V}$ are adjacent iff $X\\cap Y$ has codimension~1 in both $X$ and $Y$. More generally, the distance between $X$ and $Y$ in $\\Gamma$ is\n$d(X,Y)=k\\in\\{0,1,2,\\ldots,n\\}$ where the subspace $X\\cap Y$ has codimension $k$ in both $X$ and~$Y$. Let $\\Gamma_k$ denote the graph of the\ndistance-$k$ relation on $\\mathcal{V}$; i.e.\\ $\\Gamma_k$ has vertex set $\\mathcal{V}$ and two vertices $X,Y\\in\\mathcal{V}$ are adjacent in $\\Gamma_k$ iff $d(X,Y)=k$.\nThe graph $\\Gamma_1=\\Gamma$ is called the {\\em dual polar graph of type\\\/} Sp$(2n,q)$. It is {\\em distance\nregular\\\/}: given any two vertices $X,Y$ in $\\Gamma$ at distance $k\\in\\{0,1,2,\\ldots,n\\}$, the vertex $Y$ has $q^{\\binom{n-k}2}\\gauss{n}k$ neighbors $Z$ in $\\Gamma$, of which\n\\begin{align*}\na_k&=q^k-1\\mbox{\\ are at distance $k$ from\\ }X,\\\\\nb_k&=q^{k+1}\\gauss{n-k}1\\mbox{\\ are at distance $k+1$ from $X$, and}\\\\\nc_k&=\\gauss{k}1\\mbox{\\ are at distance $k-1$ from\\ }X;\n\\end{align*}\nsee \\cite[\\S9.4]{BCN}.\nThe edges of $\\Gamma_1,\\Gamma_2,\\ldots,\\Gamma_n$ partition the non-identical pairs\non $\\mathcal{V}$, viewed as the edges of the complete graph $K_\\mathcal{V}$; and together with the identity relation\n$\\Gamma_0=\\{(X,X):X\\in\\mathcal{V}\\}$ we obtain an $n$-class association scheme on $\\mathcal{V}$ (see Section~\\ref{scheme}). This scheme is $P$-polynomial since $\\Gamma$ is distance regular; see~\\cite{BCN}.\n\\begin{theorem}\\label{theorem4.1}\nFor $n\\geqslant2$, the full automorphism group of $\\Gamma=\\Gamma(2n,q)$ is the group $P\\Gamma Sp(2n,q)$ acting naturally on the projective space of $V$.\n\\end{theorem}\n\n\\begin{pf}\nSee \\cite[p.275]{BCN} (where this group is however denoted $P\\Sigma p(2n,q)$).\\qed\n\\end{pf}\nNote that when $n=1$, the dual polar graph $\\Gamma(2,q)$ is simply the complete graph\n$K_{q+1}$, whose full automorphism group is the symmetric group of degree $q+1$.\n\nFor use in Section~\\ref{double_cover} we record the following well-known fact. Although it follows easily from the axioms of polar geometry (or of near polygons), in the interest of self-containment we include a proof.\n\n\\begin{lemma}\\label{lemma4.2}\nThe `diamond' graph (as shown) is not an induced subgraph of the dual polar graph $\\Gamma$.\n\\end{lemma}\n\\[\\begin{tikzpicture}[scale=1.1]\n\\node at (-1,0) {$\\bullet$};\n\\node at (-1.25,0) {$X$};\n\\node at (0,.73) {$\\bullet$};\n\\node at (.22,.85) {$Y$};\n\\node at (0,-.73) {$\\bullet$};\n\\node at (.2,-.85) {$Z$};\n\\node at (1,0) {$\\bullet$};\n\\node at (1.3,0) {$W$};\n\\draw (-1,0) -- (0,.73) -- (1,0) -- (0,-.73) -- (-1,0);\n\\draw (0,.73) -- (0,-.73);\n\\end{tikzpicture}\\]\n\n\\begin{pf}If $X,Y,Z$ are mutually adjacent as shown, then $X\\cap Y$ and $X\\cap Z$ are distinct subspaces of codimension~1 in $X$, so $X=(X\\cap Y)+(X\\cap Z)$, whence $X\\subseteq Y+Z$. Thus $X=X^\\perp\\supseteq Y^\\perp\\cap Z^\\perp=Y\\cap Z$. Similarly,\n$W\\supseteq Y\\cap Z$. Now $X\\cap W$ contains a subspace of dimension $n{-}1$, contradicting $d(X,W)\\geqslant2$.\\qed\n\\end{pf}\n\nNow let $X$ be any $n$-dimensional vector space over ${\\mathbb F}_q$. An $n$-linear form $f:X^n\\to{\\mathbb F}_q$ (i.e.\\ linear in each argument whenever the other\n$n-1$ arguments are fixed) is {\\em alternating\\\/} if $f(x_1,x_2,\\ldots,x_n)=0$ whenever two $x_i$'s coincide; equivalently,\n$f(x_{1^\\tau},x_{2^\\tau},\\ldots,x_{n^\\tau})=-f(x_1,x_2,\\ldots,x_n)$ for every odd permutation $\\tau$ of the indices.\nThe space of all such alternating forms is one-dimensional, and is canonically identified with $(\\bigwedge^{\\mskip-2mu n}\\mskip-2mu X)^*$,\nthe dual space of $\\bigwedge^{\\mskip-2mu n}\\mskip-2mu X$. A {\\em determinant function on $X$\\\/} is any nonzero alternating form $X^n\\to{\\mathbb F}_q$. Since\n$\\dim(\\bigwedge^{\\mskip-2mu n}\\mskip-2mu X)^*=1$, a determinant function is determined up to nonzero scalar multiple.\n\nFix a choice of determinant function $\\delta_X$ for each $X\\in\\mathcal{V}$. Although these choices are not canonical, one may proceed by arbitrarily choosing a basis\n$\\psi_1,\\psi_2,\\ldots,\\psi_n$ for $X^*=\\mathop{\\rm Hom}\\nolimits(X,{\\mathbb F}_q)$; then we obtain a determinant function on $X$ by defining\n\\[\\delta_X(x_1,x_2,\\ldots,x_n)=\\det\\bigl(\\psi_i^*(x_j):1\\leqslant i,j\\leqslant n\\bigr).\\]\n\nWe need to define $\\sigma(X,Y)\\in\\{\\pm1\\}$ for any pair $X\\neq Y$ in $\\mathcal{V}$. Let $k\\in\\{1,2,\\ldots,n\\}$ be the codimension of $X\\cap Y$ in both\n$X$ and $Y$. Choose bases $x_1,x_2,\\ldots,x_n$ and $y_1,y_2,\\ldots,y_n$ for $X$ and $Y$ respectively, such that $x_i=y_i$ (for $k<i\\leqslant n$)\nis a common basis for $X\\cap Y$. (These bases depend on the choice of pair $(X,Y)$ and so are unrelated to any bases for $X$ and $Y$ used as a crutch\nfor constructing the corresponding determinant functions). Define\n\\[\\sigma(X,Y)=\\chi\\bigl(\\delta_X(x_1,x_2,\\ldots,x_n)\\delta_Y(y_1,y_2,\\ldots,y_n)\\det\\bigl[B(x_i,y_j):1\\leqslant i,j\\leqslant k\\bigr]\\bigr)\\]\nwhere $\\chi:{\\mathbb F}_q^{\\times}\\to\\{\\pm1\\}$ is the quadratic character:\n$\\chi(a)=1$ or $-1$ according as $a\\in{\\mathbb F}_q^{\\times}$ is a square or a nonsquare.\nThis definition is implicit in~\\cite{Th,KS}; and inspired by the literature, we refer to\n$\\sigma(X,Y)$ (or the ternary function $\\sigma(X,Y,Z)$ defined below) as the\n{\\em Maslov index\\\/}. Note that $B$ induces a nondegenerate bilinear form on the\n$2k$-space $(X+Y)\/(X\\cap Y)$, so that the $k\\times k$\nmatrix $\\bigl[B(x_i,y_j):1\\leqslant i,j\\leqslant k\\bigr]$ is nonsingular.\n\\bigskip\n\n\\begin{proposition}\\label{prop4.3}\nLet $X,Y\\in\\mathcal{V}$ at distance $d(X,Y)=k\\in\\{0,1,2,\\ldots,n\\}$.\n\\begin{itemize}\n\\item[(i)]The value of $\\sigma(X,Y)$ is independent of the choice of bases $x_i$ and $y_j$ as above.\n\\item[(ii)]Its dependence on the choice of determinant functions is expressed as follows:\nReplacing $\\delta_X$ by $c\\delta_X$ has the effect of multiplying $\\sigma(X,Y)$ by $\\chi(c)$.\n\\item[(iii)]$\\sigma(Y,X)=\\chi(-1)^k\\sigma(X,Y)=(-1)^{k(q-1)\/2}\\sigma(X,Y)$.\n\\item[(iv)]Let $g\\in\\Gamma Sp(2n,q)$, so that there exists a nonzero scalar $\\mu_g\\in{\\mathbb F}_q$\nand $\\tau_g\\in\\mathop{\\rm Aut}\\nolimits{\\mathbb F}_q$ satisfying $B(x^g,y^g)=\\mu_g B(x,y)^{\\tau_g}$ for all $x,y\\in Y$.\nThen there exist nonzero scalars $\\lambda_{g,U}\\in{\\mathbb F}_q$ for $U\\in\\mathcal{V}$, such that\n\\[\\sigma(X^g,Y^g)=\\chi\\bigl(\\mu_g^k\\lambda_{g,X}\\mskip1mu\\lambda_{g,Y}\\bigr)\\sigma(X,Y).\\]\n\\end{itemize}\n\\end{proposition}\n\n\\begin{pf}\nConsider a change of basis on $X\\cap Y$ specified by $x_i'=y_i'=\\sum_{k<j\\leqslant n}a_{ij}x_j$ where $A=\\bigl(a_{ij}:k<i,j\\leqslant n\\bigr)$\nis any invertible $(n-k)\\times(n-k)$ matrix. Then\n\\[\\delta_X(x_1,\\ldots,x_k,x_{k+1}',\\ldots,x_n')=(\\det A)\\delta_X(x_1,\\ldots,x_n)\\]\nand $\\delta_Y(y_1,\\ldots,y_n)$ is multiplied by the same factor, $\\det A$. The $(n-k)\\times (n-k)$ matrix $[B(x_i,y_j):k<i,j\\leqslant n]$ is unchanged, so the\nvalue of $\\sigma(X,Y)$ is multiplied by a net factor of $\\chi\\bigl((\\det A)^2\\bigr)=1$.\n\nNext consider replacing $x_1,\\ldots,x_k$ by $x_1',\\ldots,x_k'$ where\n\\[x_i'\\equiv\\sum_{1\\leqslant j\\leqslant k}a_{ij}x_j\\quad{\\rm mod\\ }(X\\cap Y)\\]\nfor $i=1,2,\\ldots,k$ where $A$ is an invertible $k\\times k$ matrix, and we leave the basis of $Y$ unchanged. Then\n\\[\\begin{array}{c}\n\\delta_X(x_1',\\ldots,x_k',x_{k+1},\\ldots,x_n)=(\\det A)\\delta_X(x_1,\\ldots,x_n);\\\\\n\\det\\bigl[B(x_i',y_j):1\\leqslant i,j\\leqslant k\\bigr]=(\\det A)\\det\\bigl[B(x_i,y_j):1\\leqslant i,j\\leqslant k\\bigr]\n\\end{array}\\]\nand the $\\delta_Y$ factor is unchanged; so once again, the value of $\\sigma(X,Y)$ is multiplied by $\\chi\\bigl((\\det A)^2\\bigr)=1$.\nThe same argument applies if $y_1,\\ldots,y_k$ are replaced by $y_1',\\ldots,y_k'$, and so~(i) follows. Conclusion~(ii) is clear.\n\nInterchanging $X$ and $Y$ has the effect of interchanging the $\\delta_X$ and $\\delta_Y$ factors, and replacing\n\\begin{multline*}\n\\bigl[B(x_i,y_j):1\\leqslant i,j\\leqslant k\\bigr]\\mapsto\\\\\n\\bigl[B(y_i,x_j):1\\leqslant i,j\\leqslant k\\bigr]=-\\bigl[B(x_i,y_j):1\\leqslant i,j\\leqslant k\\bigr].\n\\end{multline*}\nThe determinant of this matrix accrues a factor of $(-1)^k$, whence (iii) holds.\n\nLet $g\\in\\Gamma Sp(2n,q)$. There exists a nonzero $\\mu_g\\in{\\mathbb F}_q$ and\n$\\tau_g\\in\\mathop{\\rm Aut}\\nolimits{\\mathbb F}_q$ such that $(au+bv)^g=a^{\\tau_g}u^g+b^{\\tau_g}v^g$ and $B(u^g,v^g)=\\mu_g B(u,v)^{\\tau_g}$ for all\n$a,b\\in{\\mathbb F}_q$ and $u,v\\in V$. Now the map\n\\[X^n\\to{\\mathbb F}_q,\\quad(x_1,x_2,\\ldots,x_n)\\mapsto\\delta_{X^g}\\bigl(x_1^g,x_2^g,\\ldots,x_n^g\\bigr)^{\\tau_g^{-1}}\\]\nis a determinant function on $X$, so it is a scalar multiple of $\\delta_X(x_1,x_2,\\ldots,x_n)$. Hence there exists a nonzero scalar $\\lambda_X=\\lambda_{g,X}\\in{\\mathbb F}_q$ such that\n\\[\\delta_{X^g}\\bigl(x_1^g,x_2^g,\\ldots,x_n^g\\bigr)=\\lambda_{g,X}\\delta_X(x_1,x_2,\\ldots,x_n)^{\\tau_g}\\]\nfor all $x_1,x_2,\\ldots,x_n\\in X$.\n\nNow given $X,Y\\in\\mathcal{V}$ at distance $k$, fix bases $x_i,y_i$ as before; then\n\\begin{align*}\n\\sigma(X^g,Y^g)&=\\chi\\bigl(\\delta_{X^g}(x_1^g,x_2^g,\\ldots,x_n^g)\\delta_{Y^g}(y_1^g,y_2^g,\\ldots,y_n^g)\\\\\n&{\\mskip100mu}\\times\\det\\bigl[B(x_i^g,y_j^g):1\\leqslant i,j\\leqslant k\\bigr]\\bigr)\\\\\n&=\\chi\\bigl(\\lambda_{g,X}\\delta_X(x_1,x_2,\\ldots,x_n)^{\\tau_g}\\lambda_{g,Y}\\delta_Y(y_1,y_2,\\ldots,y_n)^{\\tau_g}\\\\\n&{\\mskip100mu}\\times\\det\\bigl[\\mu_g B(x_i,y_j)^{\\tau_g}:1\\leqslant i,j\\leqslant k\\bigr]\\bigr)\\\\\n&=\\chi\\bigl(\\mu_g^k\\lambda_{g,X}\\lambda_{g,Y}\\bigr)\\chi\\bigl(\\delta_X(x_1,x_2,\\ldots,x_n)^{\\tau_g}\\delta_Y(y_1,y_2,\\ldots,y_n)^{\\tau_g}\\\\\n&{\\mskip100mu}\\times\\det\\bigl[B(x_i,y_j):1\\leqslant i,j\\leqslant k\\bigr]^{\\tau_g}\\bigr)\\\\\n&=\\chi\\bigl(\\mu_g^k\\lambda_{g,X}\\mskip1mu\\lambda_{g,Y}\\bigr)\\sigma(X,Y)\n\\end{align*}\nsince $\\chi(a^\\tau)=\\chi(a)$. This proves (iv).\\qed\n\\end{pf}\n\nFor each triple $(X,Y,Z)$ with distinct $X,Y,Z\\in\\mathcal{V}$, define\n\\[\\sigma(X,Y,Z)=\\sigma(X,Y)\\sigma(Y,Z)\\sigma(Z,X)\\in\\{\\pm1\\}.\\]\nA triple $(X,Y,Z)$ of distinct elements of $\\mathcal{V}$ is {\\em coherent\\\/} or {\\em non-coherent\\\/}\naccording as $\\sigma(X,Y,Z)=1$ or $-1$.\n\n\\begin{theorem} \\label{theorem4.4}\nSuppose $q\\equiv1\\,$ mod~$4$. Then the set of coherent\ntriples forms a two-graph $\\Delta_\\sigma$ on $\\mathcal{V}$, invariant under $P\\Sigma Sp(2n,q)$.\n\\end{theorem}\n\n\\begin{pf}\nLet $X,Y,Z,W\\in\\mathcal{V}$ be distinct. Since $\\chi(-1)=1$, $(X,Y,Z)$ is coherent iff any permutation of its members yields a coherent triple; so\nthe set of coherent triples may be regarded as a collection of unordered triples $\\{X,Y,Z\\}$. Since\n\\begin{multline*}\n\\sigma(X,Y,Z)\\sigma(X,Y,W)\\sigma(X,Z,W)\\sigma(Y,Z,W)\\\\\n=\\sigma(X,Y)^2\\sigma(X,Z)^2\\cdots\\sigma(Z,W)^2=1,\n\\end{multline*}\nevenly many of the triples in $\\{X,Y,Z,W\\}$ are coherent. If $g\\in\\Gamma Sp(2n,q)$ with $B(x^g,y^g)=\\mu_g B(x,y)^{\\tau_g}$, then\n\\begin{align*}\n\\sigma(X^g,Y^g,Z^g)&=\\chi(\\mu_g^{d(X,Y)}\\lambda_{g,X}\\mskip1mu \\lambda_{g,Y})\\chi(\\mu_g^{d(Y,Z)}\\lambda_{g,Y}\\mskip1mu\\lambda_{g,Z})\\\\\n&\\phantom{{}={}}\\times\\chi(\\mu_g^{d(Z,X)}\\lambda_{g,Z}\\mskip1mu \\lambda_{g,X})\\sigma(X,Y,Z)\\\\\n\\phantom{\\sigma(X^g,Y^g,Z^g)}&=\\chi(\\mu_g)^{d(X,Y)+d(Y,Z)+d(Z,X)}\\sigma(X,Y,Z).\n\\end{align*}\nIn particular when $g\\in\\Sigma Sp(2n,q)$, $\\mu_g=1$ and $\\sigma(X^g,Y^g,Z^g)=\\sigma(X,Y,Z)$.\\qed\n\\end{pf}\n\nIf $q\\equiv3\\,$ mod~$4$, or $g\\in P\\Gamma Sp(2n,q)$ with $g\\notin P\\Sigma Sp(2n,q)$,\nthe situation is a little trickier: various subsets of the coherent triples form either two-graphs or skew two-graphs in the sense of \\cite{M},\ninvariant under $Sp(2n,q)$. We ignore this case here, and {\\em henceforth assume that\\\/}\n\\[q\\equiv1\\,\\hbox{\\ mod\\ }4.\\]\n\nWe next show that {\\em in a geodesic path, every triple of vertices is coherent.\\\/}\n\n\\begin{lemma} \\label{lemma4.5}\nSuppose $q\\equiv1\\,$ \\hbox{mod $4$}. Let $X,Y,Z\\in\\mathcal{V}$ such that $d(X,Y)=j$, $d(Y,Z)=k-j$ and $d(X,Z)=k$ where\n$1\\leqslant j<k\\leqslant n$. Then $\\sigma(X,Y,Z)=1$.\n\\end{lemma}\n\n\\begin{pf}\nChoose a hyperbolic basis $e_1,e_2,\\ldots,e_n,f_1,f_2,\\ldots,f_n$ for $V$, so that $B(e_i,e_j)=B(f_i,f_j)=0$ and $B(e_i,f_j)=\\delta_{ij}$.\nSince Sp$(2n,q)$ is transitive on triples of generators satisfying the given distance constraints, by Theorem~\\ref{theorem4.4} we may suppose that\n\\[\\begin{array}{c}\nX=\\langle e_1,e_2,\\ldots,e_n\\rangle,\\quad Y=\\langle f_1,f_2,\\ldots,f_j,e_{j+1},e_{j+2},\\ldots,e_n\\rangle,\\\\\nZ=\\langle f_1,f_2,\\ldots,f_k,e_{k+1},e_{k+2},\\ldots,e_n\\rangle.\n\\end{array}\\]\nWe choose the determinant function $\\delta_X$ on $X$ given by\n\\[\\delta_X(x_1,x_2,\\ldots,x_n)=\\det\\bigl[B(x_i,f_j)\\,:\\,1\\leqslant i,j\\leqslant n\\bigr]\\quad\\hbox{for\\ }x_1,x_2,\\ldots,x_n\\in X;\\]\nthis is nothing other than the determinant of the $n\\times n$ matrix whose columns are the coordinates of $x_1,\\ldots,x_n$ with respect to the\nbasis $e_1,e_2,\\ldots,e_n$. The determinant functions $\\delta_Y$, $\\delta_Z$ on $Y$ and on $Z$ are defined similarly, using the bases for $Y$ and on\n$Z$ listed above. The computation of $\\sigma(X,Z)$ is simplified by the fact that a basis for $X\\cap Z$ is $e_{k+1},e_{k+2},\\ldots,e_n$. We have\n\\[\\delta_X(e_1,e_2,\\ldots,e_n)=\\delta_Z(f_1,\\ldots,f_k,e_{k+1},\\ldots,e_n)=1\\]\nand $\\bigl[B(e_i,f_j)\\,:\\,1\\leqslant i,j\\leqslant k\\bigr]$ is a $k\\times k$ identity matrix, with determinant~1; thus $\\sigma(X,Z)=1$. Exactly the same reasoning\ngives $\\sigma(X,Y)=\\sigma(Y,Z)=1$, so $\\sigma(X,Y,Z)=1$.\\qed\n\\end{pf}\n\nIn the case of triples $X,Y,Z$ not lying on geodesic paths, however, $\\sigma$ (or its two-graph $\\Delta_\\sigma$) yields interesting nontrivial information. In particular, the restriction of $\\Delta_\\sigma$\nto partial spreads (sets of vertices of $\\Gamma$ mutually at distance $n$) was investigated in~\\cite[\\S6]{M}.\nHere we consider triangles in $\\Gamma$:\n\n\\begin{lemma}\\label{lemma4.6}\nSuppose $q\\equiv1\\,$ \\hbox{mod $4$}. Let $X,Y\\in\\mathcal{V}$ such that $d(X,Y)=1$, i.e.\\ $X$ and $Y$ are adjacent in $\\Gamma$.\nThere are $a_1=q{-}1$ common neighbors $Z$ of $X$ and $Y$ in $\\Gamma$; and exactly half of the resulting triples $(X,Y,Z)$ are coherent.\n\\end{lemma}\n\n\\begin{pf}\nChoose a hyperbolic basis $e_i,f_i$ as in the proof of Lemma~\\ref{lemma4.5}. Again without loss of generality,\n\\[X=\\langle e_1,e_2,\\ldots,e_n\\rangle,\\quad Y=\\langle f_1,e_2,\\ldots,e_n\\rangle,\\quad Z=\\langle e_1{+}\\alpha f_1,e_2,\\ldots,e_n\\rangle\\]\nwhere $0\\neq\\alpha\\in{\\mathbb F}_q$. The $q{-}1$ choices of $\\alpha$ give exactly the $q{-}1$ common neighbors of $X$ and $Y$ in $\\Gamma$.\nThese bases of $X,Y,Z$ give rise to natural choices of determinant functions $\\delta_X$,\n$\\delta_Y$, $\\delta_Z$ as described in the proof of Lemma~\\ref{lemma4.5}. When computing\n$\\sigma(X,Y),\\sigma(Y,Z),\\sigma(Z,X)$, we use $e_2,e_3,\\ldots,e_n$ as the basis of $X\\cap Y=X\\cap Z=Y\\cap Z$. Now\n\\[\\delta_X(e_1,e_2,\\ldots,e_n)=\\delta_Z(e_1{+}\\alpha f_1,e_2,\\ldots,e_n)=1\\]\nand $B(e_1,e_1{+}\\alpha f_1)=\\alpha$, so $\\sigma(X,Z)=\\chi(\\alpha)$. Similarly, $\\sigma(X,Y)=\\sigma(Y,Z)=1$ and\n\\[\\sigma(X,Y,Z)=\\chi(\\alpha).\\]\nSince exactly half the nonzero elements of ${\\mathbb F}_q$ are squares, the result follows.\\qed\n\\end{pf}\n\n\\begin{theorem}\\label{theorem4.7}\nSuppose $q\\equiv1\\,$ \\hbox{mod $4$}. Let $X,Y\\in\\mathcal{V}$ such that $d(X,Y)=k$. Then $Y$ has exactly $a_k=q^k{-}1$ neighbors $Z\\in\\mathcal{V}$\nat distance $k$ from $X$ in $\\Gamma$; and exactly half of the resulting triples $(X,Y,Z)$ are coherent.\n\\end{theorem}\n\n\\begin{pf}\nThe result holds for $k=1$ by Lemma~\\ref{lemma4.6}, so we may assume $k\\geqslant2$.\nGiven $X,Y\\in\\mathcal{V}$ with $d(X,Y)=k$, there are $\\gauss{k}1$ choices of hyperplane $H<Y$ containing $X\\cap Y$. Each such $H$ yields an Sp$(2,q)$-space\n$H^\\perp\/H$, which contains $q{+}1$ subspaces of the form $Z\/H$ with $Z\\in\\mathcal{V}$. One such $Z$ has distance $k{-}1$ from $X$, this being the subspace\n$W=(Y{\\cap}Z)+X\\cap(Y{+}Z)=(Y{+}Z)\\cap(X{+}(Y{\\cap}Z))$. If we exclude $W$ and $Y$ itself, this leaves exactly $q{-}1$ choices of $Z$ having the required\ndistances from $X$ and $Y$; and this gives $(q{-}1)\\gauss{k}1=q^k{-}1=a_k$ choices of $Z$, the full number. But for how many such $Z$ is the resulting\ntriple $(X,Y,Z)$ coherent? In each case $\\sigma(X,W,Y)=\\sigma(X,W,Z)=1$ by Lemma~\\ref{lemma4.5}; therefore $\\sigma(X,Y,Z)=\\sigma(W,Y,Z)$.\nBut by Lemma~\\ref{lemma4.6}, given\n$W,Y$ at distance~1, exactly half of the $q{-}1$ choices of $Z$ yield coherent triples $(W,Y,Z)$. Therefore among the $a_k=(q{-}1)\\gauss{k}1$ triples\n$(X,Y,Z)$ with fixed $X$ and $Y$, exactly $\\frac{q{-}1}{2}\\gauss{k}1=(q^k{-}1)\/2$ such triples are coherent.\\qed\n\\end{pf}\n\n\\section{The Double Cover $\\widehat{\\Gamma}\\to\\Gamma$}\n\\label{double_cover}\n\nThe resulting double cover $\\widehat{\\Gamma}=\\widehat{\\Gamma}(2n,q)\\to\\Gamma(2n,q)$ has vertex set $\\widehat{\\V}=\\mathcal{V}\\times\\{\\pm1\\}$ and adjacency relation\n\\[(X,\\varepsilon)\\sim(Y,\\varepsilon')\\qquad\\iff\\qquad d(X,Y)=1\\hbox{\\ and\\ }\\varepsilon\\varepsilon'=\\sigma(X,Y).\\]\nThe covering map is given by $(X,\\varepsilon)\\mapsto X$. \n\n\\begin{theorem} \\label{theorem5.1}\nEvery geodesic path\n\\[X_0\\sim X_1\\sim\\cdots\\sim X_k\\]\nin $\\Gamma$ (meaning that $d(X_i,X_j)=|j-i|$) lifts to exactly two paths\n\\[(X_0,\\varepsilon_0)\\sim(X_1,\\varepsilon_1)\\sim\\cdots\\sim(X_k,\\varepsilon_k)\\]\nin $\\widehat{\\Gamma}$, in which $\\varepsilon_k=\\varepsilon_0\\sigma(X_0,X_k)$ for each $k\\geqslant1$; thus any one of the $\\varepsilon_i$ determines all the others\nalong this path.\n\\end{theorem}\n\n\\begin{pf}\nWe have $\\varepsilon_1=\\varepsilon_0\\sigma(X_0,X_1)$ by definition of adjacency in $\\widehat{\\Gamma}$. Assuming that\n$\\varepsilon_i=\\varepsilon_0\\sigma(X_0,X_i)$ for some $i\\in\\{1,2,\\ldots,k{-}1\\}$,\n\\[\\varepsilon_{i+1}=\\varepsilon_i\\sigma(X_i,X_{i+1})=\\varepsilon_0\\sigma(X_0,X_i)\\sigma(X_i,X_{i+1})=\\varepsilon_0\\sigma(X_0,X_{i+1})\\]\nsince $\\sigma(X_0,X_i,X_{i+1})=1$ by Lemma~\\ref{lemma4.5}.\\qed\n\\end{pf}\n\n\\noindent However, not every geodesic path in $\\widehat{\\Gamma}$ is obtained by lifting a geodesic path in~$\\Gamma$. For example if $(X,Y,Z)$ is an incoherent\ntriangle in $\\Gamma$, say with $\\sigma(X,Y)=\\varepsilon$, $\\sigma(Y,Z)=\\varepsilon'$ and $\\sigma(X,Z)=-\\varepsilon\\varepsilon'$, then\n\\[(X,1)\\sim(Y,\\varepsilon)\\sim(Z,\\varepsilon\\varepsilon')\\sim(X,-1)\\]\nis a geodesic path of length~3 in $\\widehat{\\Gamma}$, obtained by lifting a closed path of length~3 (not a geodesic path) in~$\\Gamma$.\n\n\\begin{lemma} \\label{lemma5.2}\nLet $X_0\\sim X_1\\sim\\cdots\\sim X_k$ be a geodesic path of length $k\\geqslant1$ in $\\Gamma$, so that $d(X_i,X_j)=|j-i|$, and let\n$\\varepsilon,\\varepsilon'\\in\\{\\pm1\\}$. Then $(X_0,\\varepsilon)$ and $(X_k,\\varepsilon')$ have distance $k$ or $k{+}1$ in $\\widehat{\\Gamma}$, according\nas $\\sigma(X_0,X_k)=\\varepsilon\\varepsilon'$ or $-\\varepsilon\\varepsilon'$. In particular, the diameter of $\\widehat{\\Gamma}$ is $\\max\\{n{+}1,3\\}$.\n\\end{lemma}\n\n\\begin{pf}\nIf $\\sigma(X_0,X_k)=\\varepsilon\\varepsilon'$, then we have a path\n\\[(X_0,\\varepsilon_0)\\sim(X_1,\\varepsilon_1)\\sim\\cdots\\sim(X_k,\\varepsilon_k)\\]\nin $\\widehat{\\Gamma}$ where $\\varepsilon_i=\\varepsilon_0\\sigma(X_0,X_i)$ for $i=1,2,\\ldots,k$; in particular if $\\varepsilon_0=\\varepsilon$ then\n$\\varepsilon_k=\\varepsilon'$. Clearly this path in $\\widehat{\\Gamma}$ is shortest possible.\n\nNow suppose $\\sigma(X_0,X_k)=-\\varepsilon\\varepsilon'$. We first obtain a path\n\\[(X_0,\\varepsilon)\\sim(X_1,\\varepsilon_1)\\sim\\cdots\\sim(X_{k-1},\\varepsilon_{k-1})\\]\nin $\\widehat{\\Gamma}$ where $\\varepsilon_i=\\varepsilon_0\\sigma(X_0,X_i)$ for $i=1,2,\\ldots,k{-}1$. Let $Y\\in\\mathcal{V}$ be adjacent to both $X_{k-1}$ and $X_k$ in\n$\\Gamma$, such that $\\sigma(X_{k-1},Y,X_k)=-1$. (By Lemma~\\ref{lemma4.6}, there are $\\frac{q-1}{2}\\geqslant1$ choices of such $Y\\in\\mathcal{V}$.) Appending\n\\[(X_{k-1},\\varepsilon_{k-1})\\sim(Y,\\varepsilon'')\\sim(X_k,\\varepsilon'),\\]\nwhere $\\varepsilon''=\\varepsilon_{k-1}\\sigma(X_{k-1},Y)=\\varepsilon'\\sigma(Y,X_k)$, we obtain a path of length $k{+}1$ from $(X_0,\\varepsilon)$ to\n$(X_k,\\varepsilon')$ in $\\widehat{\\Gamma}$; once again this path is shortest possible.\\qed\n\\end{pf}\n\nThe fibers of the covering map $\\widehat{\\Gamma}\\to\\Gamma$ are the {\\it antipodal\\\/} pairs\n$\\{(X,1),(X,-1)\\}$ for $X\\in\\mathcal{V}$.\n\n\\begin{lemma}\\label{lemma5.3}\nLet $(X,\\varepsilon)$ and $(W,\\varepsilon')$ be any two vertices of $\\widehat{\\Gamma}$. Then\n$(X,\\varepsilon)$ and $(W,\\varepsilon')$ are antipodal iff they are at distance~3 in $\\widehat{\\Gamma}$ and are joined by exactly $\\frac12 q(q^n{-}1)$ paths of length~3 in $\\widehat{\\Gamma}$.\n\\end{lemma}\n\n\\begin{pf}Consider a typical antipodal pair $\\{(X,1),(X,-1)\\}$ where $X\\in\\mathcal{V}$. There exist $b_0=q\\gauss{n}1$ vertices $Y\\in\\mathcal{V}$ adjacent to $X$ in $\\Gamma$; and each such vertex $Y$ has $a_1=q{-}1$ neighbors $Z$ in common with $X$.\nBy Lemma~\\ref{lemma4.6}, exactly half of these choices of the vertex $Z$ yield coherent triples $(X,Y,Z)$. In particular, $X$ lies in exactly $b_0{\\cdot}\\frac12 a_1=\\frac12 q\\bigl(q^n-1)$ incoherent triples $(X,Y,Z)$, giving\nthe same number of paths $(X,1)\\sim(Y,\\varepsilon)\\sim(Z,\\varepsilon')\\sim(X,-1)$\nof length~3 in $\\widehat{\\Gamma}$. There is no path of length${}<3$ from $(X,1)$ to $(X,-1)$ in\n$\\widehat{\\Gamma}$, otherwise the covering map would give a closed\npath of length${}<3$ from $X$ to $X$ in $\\Gamma$. This shows that any two antipodal\nvertices $(X,1),(X,-1)$ are at distance~3 in $\\widehat{\\Gamma}$; and in each case there are exactly $\\frac12 q(q^n{-}1)$ geodesic paths from $(X,1)$ to $(X,-1)$.\n\nConversely, let $(X,\\varepsilon)$ and $(W,\\varepsilon')$ be any two vertices at distance~3 in\n$\\widehat{\\Gamma}$. By Lemma~\\ref{lemma5.2}, $d(X,W)\\in\\{0,2,3\\}$\nin $\\Gamma$. Consider first the case that $d(X,W)=3$; then by Theorem~\\ref{theorem5.1}, every geodesic path from $(X,\\varepsilon)$ to\n$(W,\\varepsilon')$ in $\\widehat{\\Gamma}$ arises from a unique geodesic path $X\\sim Y\\sim Z\\sim W$ in $\\Gamma$. There are exactly $c_3 c_2 c_1=(q^2{+}q{+}1)(q{+}1)$ such\ngeodesic paths from $X$ to $W$; and this number clearly cannot equal $\\frac12 q(q^n-1)$.\n\nNext suppose $d(X,W)=2$ in $\\Gamma$. For every geodesic path\n\\[(X,\\varepsilon)\\sim(Y,\\varepsilon'')\\sim(Z,\\varepsilon''')\\sim(W,\\varepsilon')\\]\nin $\\widehat{\\Gamma}$, we have $X\\sim Y\\sim Z\\sim W$ in $\\Gamma$. Further, the condition $d(X,W)=2$ requires either $X\\sim Z$ or $Y\\sim W$ (but {\\it not both,\\\/} by Lemma~\\ref{lemma4.2}). We first count\ngeodesic paths satisfying $X\\sim Z$, noting that the vertex $W$ has $c_2=q{+}1$ neighbors $Z$ in common with $X$; and in each case $\\sigma(X,Z,W)=1$ by Lemma~\\ref{lemma4.5}.\nMoreover $Z$ has $a_1=q{-}1$ neighbors $Y$ in common with $X$ (all of which satisfy $\\sigma(Y,Z,W)=1$, again by Lemma~\\ref{lemma4.5}). By the two-graph\ncondition, we have $\\sigma(X,Y,Z)=-1$ iff $\\sigma(X,Y,W)=-1$. By Lemma~\\ref{lemma4.6}, for each $Z$ there are exactly $\\frac12\\bigl(q{-}1\\bigr)$\nchoices of $Y$ satisfying the latter condition; and each such pair $(Y,Z)$ yields a unique geodesic path\n$(X,\\varepsilon)\\sim(Y,\\varepsilon'')\\sim(Z,\\varepsilon''')\\sim(W,\\varepsilon')$. We obtain\n$(q{+}1){\\cdot}\\frac12\\bigl(q{-}1\\bigr)=\\frac12\\bigl(q^2{-}1\\bigr)$ geodesic paths in this case. There are another $\\frac12\\bigl(q^2{-}1\\bigr)$ geodesic paths from $(X,\\varepsilon)$ to $(W,\\varepsilon')$ satisfying $Y\\sim W$, for a total of $q^2{-}1$ geodesic paths. Once again, this number cannot equal $\\frac12 q(q^n{-}1)$.\\qed\n\\end{pf}\n\n\\begin{lemma}\\label{lemma5.4}\n$\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}$ acts naturally on $\\Gamma$, with kernel $\\langle\\zeta\\rangle$,\ninducing a {\\em proper\\\/} subgroup $\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}\/\\langle\\zeta\\rangle<\\mathop{\\rm Aut}\\nolimits\\Gamma$.\n\\end{lemma}\n\n\\begin{pf}\nBy Lemma~\\ref{lemma5.3}, $\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}$ permutes fibres of the covering\nmap $\\widehat{\\Gamma}\\to\\Gamma$, and so $\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}$ acts naturally on $\\Gamma$.\nIt remains to be shown that the induced subgroup $\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}\/\\langle\\zeta\\rangle\\leqslant\\mathop{\\rm Aut}\\nolimits\\Gamma$ is proper.\n\nChoose a hyperbolic basis $e_1,e_2,\\ldots,e_n,f_1,f_2,\\ldots,f_n$ for $V$, so that\n$B(e_i,e_j)=B(f_i,f_j)=0$ and $B(e_i,f_j)=\\delta_{ij}$, and let $\\eta\\in{\\mathbb F}_q$ be a nonsquare.\nConsider the subspaces $X,Y,Z,Z'\\in\\mathcal{V}$ defined by $X=\\langle e_1,e_2,\\ldots,e_n\\rangle$,\n$Y=\\langle f_1,e_2,\\ldots,e_n\\rangle$, $Z=\\langle e_1{+}f_1,e_2,\\ldots,e_n\\rangle$ and\n$Z'=\\langle e_1{+}\\eta f_1,e_2,\\ldots,e_n\\rangle$. By straightforward computation,\n$\\sigma(X,Y,Z)=1$ and $\\sigma(X,Y,Z')=-1$. Now consider $g\\in GL(V)$ mapping our\noriginal ordered basis to the new ordered basis $e_1,\\eta e_2,\\ldots,\\eta e_n,\\eta f_1,f_2,\\ldots,f_n$ so that $B(u^g,v^g)=\\eta B(u,v)$ for all $u,v\\in V$; thus $g\\in GSp(2n,q)$\ninduces an automorphism of the dual polar graph $\\Gamma=\\Gamma(2n,q)$.\nHowever, $g$ maps the coherent triple $\\{X,Y,Z\\}$ to the non-coherent triple $\\{X,Y,Z'\\}$\nand so does not preserve $\\Delta_\\sigma$. If $g$ were induced by an automorphism of\n$\\widehat{\\Gamma}$, this automorphism would map $\\{X,Y,Z\\}\\times\\{\\pm1\\}$ to\n$\\{X,Y,Z'\\}\\times\\{\\pm1\\}$. However, the induced subgraphs of $\\widehat{\\Gamma}$ on these\ntwo 6-sets of vertices are not isomorphic (a pair of triangles and a 6-cycle, respectively;\nsee Section~\\ref{graphs}).\\qed\n\\end{pf}\n\nThe natural action of $\\Sigma Sp(2n,q)$ on $\\mathcal{V}$ lifts to an action on $\\widehat{\\V}$ as follows:\nLet $g\\in\\Sigma Sp(2n,q)$ with associated field automorphism $\\tau_g$ in the earlier notation of this section.\nGiven $(U,\\varepsilon)\\in\\widehat{\\V}$, the map\n\\[U^n\\to{\\mathbb F}_q,\\quad (u_1,u_2,\\ldots,u_n)\\mapsto\\delta_{U^g}(u_1^g,u_2^g,\\ldots,u_n^g)^{\\tau_g^{-1}}\\]\nis a determinant function; so there exists a nonzero constant $\\lambda_{g,U}\\in{\\mathbb F}_q$ such that\n\\[\\delta_{U^g}(u_1^g,u_2^g,\\ldots,u_n^g)=\\lambda_{g,U}\\delta_U(u_1,u_2,\\ldots,u_n)^{\\tau_g}.\\]\nDefine $(U,\\varepsilon)^g=(U^g,\\chi(\\lambda_{g,U})\\varepsilon)$. One easily checks that\nthis defines an action of $\\Sigma Sp(2n,q)$\non $\\widehat{\\V}$. The central element $-I\\in Sp(2n,q)$ fixes every $U\\in\\mathcal{V}$ and since\n\\[\\delta_U(-u_1,-u_2,\\ldots,-u_n)=(-1)^n\\delta_U(u_1,u_2,\\ldots,u_n)\\]\nwhere $\\chi(-1)^n=1$,\n$-I$ acts trivially on $\\widehat{\\V}$; thus $\\Sigma Sp(2n,q)$ induces a permutation group\n$P\\Sigma Sp(2n,q)$ on~$\\widehat{\\V}$. The transposition $\\zeta$ which exchanges antipodal\nvertices via $(U,1)\\stackrel\\zeta\\leftrightarrow(U,-1)$ is not induced by any element of\n$P\\Sigma Sp(2n,q)$ since $Z(P\\Sigma Sp(2n,q))=1$, so we obtain a permutation group\n$\\langle\\zeta\\rangle\\times P\\Sigma Sp(2n,q)$ acting faithfully on $\\widehat{\\V}$. We show that this\npermutation group preserves the graph $\\widehat{\\Gamma}$, and is in fact its full automorphism group:\n\n\\begin{theorem}\\label{theorem5.5}\n$\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}\\cong2\\times P\\Sigma Sp(2n,q)$ where this group acts as defined above.\nThe full automorphism group of the two-graph associated to $\\sigma$ is $\\mathop{\\rm Aut}\\nolimits\\Delta_\\sigma\\cong P\\Sigma Sp(2n,q)$.\n\\end{theorem}\n\n\\begin{pf}\nSuppose $(X,\\varepsilon)\\sim(Y,\\varepsilon')$ in $\\widehat{\\Gamma}$, so that\n$\\sigma(X,Y)=\\varepsilon\\varepsilon'$; and let $g\\in\\Sigma Sp(2n,q)$ with\n$\\tau_g\\in\\mathop{\\rm Aut}\\nolimits{\\mathbb F}_q$ as above. Then by Proposition~\\ref{prop4.3}(iv) we have\n\\[\\sigma(X^g,Y^g)=\\chi(\\lambda_{g,X}\\lambda_{g,Y})\\sigma(X,Y)\n=\\bigl(\\chi(\\lambda_{g,X})\\varepsilon\\bigr)\\bigl(\\chi(\\lambda_{g,Y})\\varepsilon'\\bigr)\\]\nso that by definition, $(X,\\varepsilon)^g\\sim(Y,\\varepsilon')^g$. Thus $P\\Sigma Sp(2n,q)$,\nacting on $\\widehat{\\Gamma}$ as defined above, preserves the graph $\\widehat{\\Gamma}$.\nIt is clear that the central factor $\\langle\\zeta\\rangle$ also preserves $\\widehat{\\Gamma}$,\nso that $\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}$ has a subgroup isomorphic to\n$\\langle\\zeta\\rangle\\times P\\Sigma Sp(2n,q)$. Moreover by Proposition~\\ref{prop3.1},\n$\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}\/\\langle\\zeta\\rangle\\cong\\mathop{\\rm Aut}\\nolimits\\Delta_\\sigma$. (We use the fact that by\nLemma~\\ref{lemma5.4}, $\\mathop{\\rm Aut}\\nolimits_\\zeta\\widehat{\\Gamma}=\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}$ in the notation\nof Proposition~\\ref{prop3.1}.)\n\nSuppose now that $n\\geqslant2$, so that $\\mathop{\\rm Aut}\\nolimits\\Gamma\\cong P\\Gamma Sp(2n,q)$ by\nTheorem~\\ref{theorem4.1}. By Lemma~\\ref{lemma5.4}, $\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}$\nacts on $\\Gamma$, inducing a group of automorphisms satisfying\n\\[P\\Sigma Sp(2n,q)\\leqslant\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}\/\\langle\\zeta\\rangle<P\\Gamma Sp(2n,q).\\]\nThis forces $\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}\\cong\\langle\\zeta\\rangle\\times P\\Sigma Sp(2n,q)$ and\n$\\mathop{\\rm Aut}\\nolimits\\Delta_\\sigma\\cong P\\Sigma Sp(2n,q)$.\n\nFinally suppose $n=1$, so that $\\Delta_\\sigma$ is the\nTaylor-Paley two-graph on $q+1$ vertices, with full automorphism group\n$\\mathop{\\rm Aut}\\nolimits\\Delta_\\sigma\\cong P\\Sigma Sp(2,q)=P\\Sigma L(2,q)$ by \\cite[Theorem 2]{Ta};\nsee also~\\cite[\\S4]{M}. As above, $\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}$ has a subgroup\nisomorphic to $\\langle\\zeta\\rangle\\times P\\Sigma Sp(2,q)$, and\n$\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}\/\\langle\\zeta\\rangle\\cong\\mathop{\\rm Aut}\\nolimits\\Delta_\\sigma\\cong P\\Sigma Sp(2,q)$,\nso we must have equality:\n$\\mathop{\\rm Aut}\\nolimits\\widehat{\\Gamma}\\cong2\\times P\\Sigma Sp(2,q)=2\\times P\\Sigma L(2,q)$.\\qed\n\\end{pf}\n\n\\section{The Association Scheme}\n\\label{scheme}\n\nFrom the double cover $\\widehat{\\Gamma}\\to\\Gamma$, we now construct association schemes.\nAs we will see in Section~\\ref{Q-poly}, this gives\na new family of $Q$-polynomial association schemes. We begin with the\nrelevant definitions, following \\cite[Chapter~2]{BCN}.\n\nLet $\\Omega$ be a finite set. A {\\em (symmetric) $d$-class association scheme on $\\Omega$\\\/} is a pair $(\\Omega,\\mathcal{R})$ such that\n\\begin{enumerate}\n\\item $\\mathcal{R}=\\{R_0,\\ldots,R_d\\}$ is a partition of $\\Omega\\times\\Omega$;\n\\item $R_0$ is the identity relation on $\\Omega$;\n\\item $R_i=R_i^{\\top}$ for $0\\leqslant i\\leqslant d$; and\n\\item there are constants $p_{ij}^k$ such that for any pair $(x,y)\\in R_k$, the number of $z \\in\\Omega$ such that $(x,z)\\in R_i$ and $(z,y)\\in R_j$ equals $p_{ij}^k$.\n\\end{enumerate}\nFor the rest of this paper, all association schemes are symmetric (i.e.\\ the third property above holds).\nEach relation $R_i$ has adjacency matrix $A_i$ defined by\n\\[(A_i)_{x,y}=\\begin{cases}\n1,&\\mbox{if\\ }(x,y)\\in R_i;\\\\\n0,&\\mbox{otherwise.}\n\\end{cases}\\]\nThe axioms above imply that $p_{ji}^k=p_{ij}^k$ and the matrices $A_0,\\ldots,A_d$ form an algebra of symmetric matrices satisfying\n$A_iA_j=\\sum_k p_{ij}^k A_k$. This matrix algebra is also closed under Schur (entrywise) multiplication, which we will denote by \n`$\\circ$'. This algebra is referred to as the {\\em Bose-Mesner algebra\\\/} ${\\mathfrak{A}}$ of the association scheme.  \n\nSince ${\\mathfrak{A}}$ is a commutative algebra consisting of symmetric matrices, its elements are simultaneously diagonalizable, and ${\\mathfrak{A}}$ has a second basis consisting of primitive idempotents $E_0,\\ldots,E_d$.  \nWe define the parameters $Q_{ij}$ by $E_j =\\frac{1}{|\\Omega|}\\sum_i Q_{ij}A_i$.  Similarly we define the parameters $P_{ij}$ by the relation \n$A_j=\\sum_i P_{ij} E_i$.  The matrix $P$ of parameters $P_{ij}$ is often referred to as the character table of the scheme.   \nThe matrix $Q$ of parameters $Q_{ij}$ satisfies $Q=|\\Omega|P^{-1}$. \n\nWe say an association scheme is {\\em$Q$-polynomial\\\/} if, after suitably reindexing its idempotents, \nthe idempotent $E_j$ is a degree $j$ polynomial in $E_1$ (where multiplication is done entrywise). This is equivalent to the condition\nthat the $j$th column of the $Q$-matrix is a degree $j$ polynomial of the column 1 of the $Q$-matrix (note that we start indexing the columns at 0).\n\nPermutation groups give many examples of association schemes.  Let $G$ be a transitive\npermutation group acting on a finite set $\\Omega$, and suppose the orbits of $G$ on\n$\\Omega\\times\\Omega$ happen to be symmetric relations; such a group is called {\\em generously transitive\\\/}).\nIt is not hard to check that the orbits of $G$ on $\\Omega\\times\\Omega$ form an association scheme. We will refer to these schemes as {\\em Schurian schemes\\\/}.\n\\bigskip\n\nWe will now construct a $(2n{+}1)$-class Schurian association scheme $\\mathcal{S}=\\mathcal{S}_{n,q}$ with vertex set $\\widehat{\\V}=\\mathcal{V}\\times\\{\\pm1\\}$ of cardinality\n$|\\widehat{\\V}|=2|\\mathcal{V}|=2q^{n^2}\\!\\prod_{i=1}^n(q^{2i}-1)$ using the Maslov index $\\sigma$\nand the double cover $\\widehat{\\Gamma}\\to\\Gamma$ (defined as in Section~\\ref{double_cover}).\nFor $k=0,1,2,\\ldots,n$, the $k$th and $(2n{+}1{-}k)$th relations are given by\n\\begin{align*}\nR_k&=\\{((X,\\varepsilon),(Y,\\varepsilon'))\\in\\widehat{\\V}\\times\\widehat{\\V}\\;:\\;d(X,Y)=k,\\;\\varepsilon\\varepsilon'=\\sigma(X,Y)\\};\\\\\nR_{2n+1-k}&=\\{((X,\\varepsilon),(Y,\\varepsilon'))\\in\\widehat{\\V}\\times\\widehat{\\V}\\;:\\;d(X,Y)=k,\\;\\varepsilon\\varepsilon'=-\\sigma(X,Y)\\}.\n\\end{align*}\nThese are symmetric relations which clearly partition $\\widehat{\\V}\\times\\widehat{\\V}$. In particular,\n$R_1$ is the adjacency relation of our graph $\\widehat{\\Gamma}$ of Section~\\ref{double_cover}; and the identity and antipodality relations are\n\\begin{align*}\nR_0&=\\{((X,\\varepsilon),(X,\\varepsilon)):X\\in\\mathcal{V},\\;\\varepsilon=\\pm1\\};\\\\\nR_{2n+1}&=\\{((X,\\varepsilon),(X,-\\varepsilon)):X\\in\\mathcal{V},\\;\\varepsilon=\\pm1\\}.\n\\end{align*}\nWe will write\n\\[(X,\\varepsilon)\\irel{i}(Y,\\varepsilon')\\iff((X,\\varepsilon),(Y,\\varepsilon'))\\in R_i\\,.\\]\nIn the following, the parameters $a_i,b_i,c_i$ are those of the dual polar graph $\\Gamma$\nas given in Section~\\ref{dual_polar}.\n\n\\begin{lemma}\\label{lemma6.1}\nLet $(X,\\varepsilon)\\irel{k}(Y,\\varepsilon')$ where $k\\in\\{0,1,2,\\ldots,2n{+}1\\}$. The number of $(Z,\\varepsilon'')\\in\\widehat{\\V}$\nsuch that $(X,\\varepsilon)\\irel{i}(Z,\\varepsilon'')\\irel{1}(Y,\\varepsilon')$ is\n\\[p_{i,1}^k=\\begin{cases}\nc_k=\\gauss{k}1,&\\mbox{if }\\,i=k{-}1\\leqslant n;\\\\\n\\noalign{\\smallskip}\n\\frac12 a_k=\\frac{1}{2}\\bigl(q^k-1),&\\mbox{if }\\,i=k;\\\\\n\\noalign{\\smallskip}\nb_k=q^{k+1}\\gauss{n-k}1,&\\mbox{if }\\,i=k{+}1\\leqslant n{+}2;\\\\\n\\noalign{\\smallskip}\nb_{2n+1-k}=q^{2n+2-k}\\gauss{k-n-1}1,&\\mbox{if }i=k{-}1\\geqslant n{-}1;\\\\\n\\noalign{\\smallskip}\n\\frac12 a_{2n+1-k}=\\frac{1}{2}\\bigl(q^{2n+1-k}-1),&\\mbox{if }\\,i=2n{+}1{-}k;\\\\\n\\noalign{\\smallskip}\nc_{2n+1-k}=\\gauss{2n+1-k}1,&\\mbox{if }\\,i=k{+}1\\geqslant n{+}1;\\\\\n\\noalign{\\smallskip}\n0,&\\hbox{otherwise.}\n\\end{cases}\\]\n\\end{lemma}\n\n\\begin{pf}(i) First suppose $d(X,Y)=k\\leqslant n$, so $\\varepsilon\\varepsilon'=\\sigma(X,Y)$. Then $(Z,\\varepsilon'')\\in\\widehat{\\V}$ satisfies\n$(X,\\varepsilon)\\irel{i}(Z,\\varepsilon'')\\irel{1}(Y,\\varepsilon')$ iff\n\\[\\begin{cases}\n\\mbox{\\qquad case (i.a)}\\\\\n\\hline\ni=d(X,Z)\\leqslant n\\\\\nd(Z,Y)=1\\\\\n\\varepsilon''=\\varepsilon\\sigma(X,Z)=\\varepsilon'\\sigma(Y,Z)\n\\end{cases}\\mbox{\\quad\\em or\\quad}\n\\begin{cases}\n\\mbox{\\qquad case (i.b)}\\\\\n\\hline\ni=2n{+}1{-}d(X,Z)\\geqslant n{+}1\\\\\nd(Z,Y)=1\\\\\n\\varepsilon''=-\\varepsilon\\sigma(X,Z)=\\varepsilon'\\sigma(Y,Z)\n\\end{cases}\\]\nMoreover, each such $(Z,\\varepsilon'')$ satisfies $d(X,Z)\\in\\{k{-}1,k,k{+}1\\}$ by the triangle inequality.\n\nThere are exactly $c_k=\\gauss{k}1$ choices of $Z\\in\\mathcal{V}$ satisfying $d(X,Z)=k{-}1$ and $d(Z,Y)=1$. Each such $Z$ yields a coherent\ntriple $(X,Y,Z)$ by Lemma~\\ref{lemma4.5}, so $\\varepsilon\\varepsilon'=\\sigma(X,Y)=\\sigma(X,Z)\\sigma(Y,Z)$. This yields $c_k$ pairs $(Z,\\varepsilon'')$,\nall of which satisfy~(i.a).\n\nThere are exactly $b_k=q^{k+1}\\gauss{n-k}1$ choices of $Z\\in\\mathcal{V}$ satisfying $d(X,Z)=k{+}1$ and $d(Z,Y)=1$. Each such $Z$ yields a coherent\ntriple $(X,Y,Z)$ by Lemma~\\ref{lemma4.5}, once again with $\\varepsilon\\varepsilon'=\\sigma(X,Y)=\\sigma(X,Z)\\sigma(Y,Z)$. This yields $b_k$ pairs $(Z,\\varepsilon'')$,\nall of which satisfy~(i.a).\n\nThere are exactly $a_k=q^k-1$ choices of $Z\\in\\mathcal{V}$ satisfying $d(X,Z)=k$ and $d(Z,Y)=1$. By Theorem~\\ref{theorem4.7}, exactly $a_k\/2$ of these $Z$ yield coherent\ntriples $(X,Y,Z)$, in which case $\\varepsilon\\varepsilon'=\\sigma(X,Y)=\\sigma(X,Z)\\sigma(Y,Z)$; this yields $a_k\/2$ pairs $(Z,\\varepsilon'')$\nsatisfying~(i.a). The remaining $a_k\/2$ of these $Z$ yield incoherent\ntriples $(X,Y,Z)$, with $\\varepsilon\\varepsilon'=\\sigma(X,Y)=-\\sigma(X,Z)\\sigma(Y,Z)$; and the resulting pairs $(Z,\\varepsilon'')$ satisfy~(i.b).\\qed\n\\end{pf}\n\nIn Section~\\ref{double_cover} we lifted the action of $P\\Sigma Sp(2n,q)$ on $\\mathcal{V}$, to a\ntransitive permutation action of $\\langle\\zeta\\rangle\\times P\\Sigma Sp(2n,q)$ on $\\widehat{\\V}$\n(below Lemma~\\ref{lemma5.4}). Theorem~\\ref{theorem5.5} shows\nthat this group preserves $R_1$ (the adjacency relation of the graph $\\widehat{\\Gamma}$).\nWe next show that this group preserves {\\em each\\\/} of the relations $R_i$, and\nso gives the full automorphism group of the scheme.\n\n\\begin{lemma}\\label{lemma6.2}\nThe diagonal action of $2\\times PSp(2n,q)$ on $\\widehat{\\V}\\times\\widehat{\\V}$ preserves each\nof the relations $R_i$. The same conclusion holds for the subgroup $2\\times P\\Sigma Sp(2n,q)$.\n\\end{lemma}\n\n\\begin{pf}\nClearly the central factor $(U,\\varepsilon)\\stackrel\\zeta\\leftrightarrow(U,-\\varepsilon)$ preserves each $R_i$.\nNow let $g\\in Sp(2n,q)$, and suppose\n$X,Y\\in\\mathcal{V}$ such that $d(X,Y)=k\\in\\{0,1,2,\\ldots,n\\}$. Also let $\\varepsilon,\\varepsilon'\\in\\{\\pm1\\}$, so that $((X,\\varepsilon),(Y,\\varepsilon'))\\in R_k$ or $R_{2n+1-k}$\naccording as $\\varepsilon\\varepsilon'\\sigma(X,Y)=1$ or $-1$.\nSince $g$ preserves distances in $\\Gamma$, $d(X^g,Y^g)=k$. Let $x_1,x_2,\\ldots,x_n$ and\n$y_1,y_2,\\ldots,y_n$ be bases for $X$ and $Y$ respectively, such that a basis for\n$X\\cap Y$ is formed by $x_{k+1}{=}y_{k+1}$, $x_{k+2}{=}y_{k+2}$, \\dots,\n$x_n{=}y_n$. Then $(X,\\varepsilon)^g=(X^g,\\chi(\\lambda_{g,X})\\varepsilon)$ and\n$(Y,\\varepsilon')^g=(Y^g,\\chi(\\lambda_{g,Y})\\varepsilon')$ where\n\\begin{align*}\n&\\chi(\\lambda_{g,X})\\varepsilon\\chi(\\lambda_{g,Y})\\varepsilon'\\sigma(X^g,Y^g)\\\\\n&\\qquad=\\varepsilon\\varepsilon'\\chi\\bigl(\\lambda_{g,X}\\delta_{X^g}(x_1^g,\\ldots,x_n^g)\\lambda_{g,Y}\\delta_{Y^g}(y_1^g,\\ldots,y_n^g)\\\\\n&\\qquad\\phantom{{}={}}\\times\\det\\bigl[B(x_i^g,y_j^g):1\\leqslant i,j\\leqslant k\\bigr]\\bigr)\\\\\n&\\qquad=\\varepsilon\\varepsilon'\\chi\\bigl(\\lambda_{g,X}^2\\lambda_{g,Y}^2\\delta_X(x_1,\\ldots,x_n)\\delta_Y(y_1,\\ldots,y_n)\\det\\bigl[B(x_i,y_j)\\,:\\,1\\leqslant i,j\\leqslant k\\bigr]\\bigr)\\\\\n&\\qquad=\\varepsilon\\varepsilon'\\sigma(X,Y).\n\\end{align*}\nIf this value is $1$, then both $(X,\\varepsilon)\\irel{k}(Y,\\varepsilon')$ and\n$(X,\\varepsilon)^g\\irel{k}(Y,\\varepsilon')^g$; but if the latter value is $-1$, then\n$(X,\\varepsilon)\\irel{\\scriptscriptstyle{2n{+}1{-}k}}(Y,\\varepsilon')$ and\n$(X,\\varepsilon)^g\\irel{\\scriptscriptstyle{2n{+}1{-}k}}(Y,\\varepsilon')^g$.\n\nThus $2\\times PSp(2n,q)$ preserves the relations $R_i$ as claimed. A similar argument\nholds for $2\\times P\\Sigma Sp(2n,q)$.\\qed\n\\end{pf}\n\nIt is easy to see that $\\langle\\zeta\\rangle\\times P\\Sigma Sp(2n,q)$ acts transitively on\neach $R_i$, and similarly for $\\langle\\zeta\\rangle\\times PSp(2n,q)$. This yields\n\n\\begin{theorem}\\label{theorem6.3}\nThe diagonal action of the group $2\\times PSp(2n,q)$ on $\\widehat{\\V}\\times\\widehat{\\V}$ has orbits $R_0$, $R_1$, \\dots, $R_{2n+1}$; so these form the relations of a $(2n+1)$-class Schurian association scheme. The same conclusion holds for $2\\times P\\Sigma Sp(2n,q)$,\nwhich is therefore the full automorphism group of the association scheme $\\mathcal{S}$.\\qed\n\\end{theorem}\n\n\\section{The $Q$-polynomial property}\n\\label{Q-poly}\n\nIn this section we will use some parameters of the scheme to prove that the association scheme $\\mathcal{S}$ is $Q$-polynomial.\nWe will benefit from the action of the $A_i$'s by left-multiplication on the Bose-Mesner algebra,\nresulting in matrices $L_i$ defined by $(L_i)_{kj}=p_{ij}^k$.\nIn particular, the parameter $p_{1j}^k$ of the scheme from Lemma~\\ref{lemma6.1}, is the $(k,j)$-entry of the matrix\n\\[L_1=\\begin{pmatrix}  \n0&b_0&0&0&0&\\cdots &0&0&0&0 \\\\\n1&\\frac{a_1}{2}&b_1&0&0&\\cdots &0&0&\\frac{a_1}{2}&0 \\\\\n0&c_2&\\frac{a_2}{2}&\\ddots&0&\\cdots &0&\\iddots&0&0 \\\\\n0&0&\\ddots&\\ddots&b_{d-1}&0&\\frac{a_{d-1}}{2}&0&0&0 \\\\\n0&0&0&c_d&\\frac{a_d}{2}&\\frac{a_d}{2} &0&0&0&0 \\\\\n0&0&0&0&\\frac{a_d}{2}&\\frac{a_d}{2} &c_d&0&0&0 \\\\\n0&0&0&\\frac{a_{d-1}}{2}&0&b_{d-1}&\\ddots&\\ddots&0&0 \\\\\n0&0&\\iddots&0&0&0 &\\ddots&\\frac{a_2}{2}&c_2&0 \\\\\n0&\\frac{a_1}{2}&0&0&0&0 &0&b_1&\\frac{a_1}{2}&1 \\\\\n0&0&0&0&0&0 &0&0&b_0&0\n\\end{pmatrix}.\\]\n\nAs it turns out, this matrix has distinct eigenvalues, which in turn will give us a great deal of information about the scheme.\nIn particular by \\cite[Proposition 2.2.2]{BCN}, the columns of $Q$ are right eigenvectors of $L_1$.\nWe will use the following generalization of \\cite[Theorem 8.1.1]{BCN} to prove that $\\mathcal{S}$ is $Q$-polynomial.\n\n\\begin{theorem}\\label{theorem7.1}\nSuppose  $A_i$ is a matrix in a $d$-class association scheme $(\\Omega,\\mathcal{R})$ with $d+1$ distinct eigenvalues.\nThen $(\\Omega,\\mathcal{R})$ is $Q$-polynomial if and only if there is a sequence of {\\em distinct\\\/} complex numbers $\\sigma_0,\\sigma_1,\\ldots,\\sigma_d$ and polynomials \n$s_0(x),s_1(x),\\ldots,s_d(x)$ of degree $0,1,\\ldots,d$, respectively, with\n\\[\\sum_j p_{ij}^k\\sigma_j^\\ell=s_\\ell(\\sigma_k)\\]\nfor $0 \\leqslant\\ell\\leqslant d$. Furthermore, the leading coefficients of the polynomials $s_0(x)$, $s_1(x)$, \\dots, $s_d(x)$ are precisely the eigenvalues of $A_i$ in a $Q$-polynomial ordering.\n\\end{theorem}\n\n\\begin{pf}\nWithout loss of generality we assume $A_1$ has this property.  Let $L_1$ be the corresponding intersection matrix.  Let \n$S,T$ be the $d+1$ by $d+1$ matrices with $S_{jk}=\\sigma_j^k$ and $T_{jk}$ equal to the coefficient of $x^j$ in the polynomial $s_k(x)$. Then the above statement is equivalent to \n$L_1 S=ST$.  Then $L_i$ is similar to $T$ and since $T$ is upper triangular, the diagonal entries of $T$ are precisely the eigenvalues of $L_1$. \nSince $T$ is an upper triangular matrix with distinct diagonal entries, an easy induction shows that it can be diagonalized by an upper triangular matrix.  Namely, there is an invertible matrix $U$ and a diagonal matrix $D$ with $D_{jj}=T_{jj}$ such that $U^{-1}TU=D$.\nThen $L_1(SU)=(SU)D$. This implies that the columns of $SU$ are eigenvectors of $L_1$, hence there is a diagonal matrix $D'$ such that $SUD'=Q$.\nSince the $j$th column of $SUD'$ is a degree $j$ polynomial of the first column of $T$, which is a linear combination of columns 0 and 1 of $SUD'$, it is clear that the $j$th column of $SUD'$ is a degree $j$ polynomial of the \nfirst column of $SUD'$.  This implies that the columns of $Q$ are in a given $Q$-polynomial ordering, which in turn implies that the ordering of the eigenvalues in $T$ is a $Q$-polynomial ordering.\\qed\n\\end{pf}\n\nThis leads to our main result:\n\n\\begin{theorem}\\label{theorem7.2}\nThe scheme $\\mathcal{S}$ is $Q$-polynomial. Furthermore, it has two $Q$-polynomial orderings.\n\\end{theorem}\n\n\\begin{pf}\nLet $r=\\sqrt{q}$ and $d=2n+1$. We define the sequence of polynomials\n\\[s_\\ell(x)=\\begin{cases}\nr^\\ell\\gauss{n-\\ell+1}{1}x^\\ell+\\frac{1}{r^{\\ell-2}}\\gauss{\\ell-1}{1}x^{\\ell-2},&\\mbox{for $\\ell$ odd};\\\\\n\\noalign{\\smallskip}\nr^\\ell\\left(\\gauss{n-\\ell+1}{1}-\\frac{1}{r^\\ell}\\right)x^\\ell+\\frac{1}{r^{\\ell-2}}\\left( \\gauss{\\ell-1}{1}+r^{\\ell-2} \\right)x^{\\ell-2},&\\mbox{for $\\ell$ even}\n\\end{cases}\\]\nand constants\n\\[\\sigma_j=\\begin{cases}\n\\frac{1}{r^j},&\\mbox{for\\ }0\\leqslant j\\leqslant n;\\\\\n-\\frac{1}{r^{2n+1-j}},&\\mbox{for\\ }n+1\\leqslant j\\leqslant2n+1.\n\\end{cases}\\]\nThe polynomials $s_0(x),\\ldots,s_{2n+1}(x)$ realize $\\sigma_0,\\ldots,\\sigma_{2n+1}$\nas a $Q$-sequence for $\\mathcal{S}$, as we proceed to show by direct computation.\nFor $k\\leqslant n$ we have $\\sum_j p_{1j}^k \\sigma_j^\\ell=c_k \\sigma_{k-1}^\\ell+\\frac{a_k}{2} \\sigma_{k}^\\ell+b_k \\sigma_{k+1}^\\ell+\\frac{a_k}{2} \\sigma_{2n+1-k}^\\ell $.\nFor odd $\\ell$ this reduces to\n\\begingroup\n\\allowdisplaybreaks\n\\begin{align*}\nc_k \\sigma_{k-1}^\\ell+b_k \\sigma_{k+1}^\\ell\n&=\\tfrac{1}{r^{(k-1)\\ell}}\\gauss{k}{1}+q\\left(\\gauss{k}{1}-\\gauss{n}{1}-\\gauss{k}{1} \\right)\\tfrac{1}{r^{(k+1)\\ell}}\\\\\n&=\\tfrac{1}{r^{(k+1)\\ell}}\\left(\\gauss{k}{1}q^\\ell+q\\bigl(\\gauss{n}{1}-\\gauss{k}{1}\\bigr)\\right)\\\\\n&=\\tfrac{1}{r^{(k+1)\\ell}}\\left(\\gauss{n+1}{1}-\\gauss{\\ell}{1}+\\gauss{k+\\ell}{1}- \\gauss{k+1}{1}\\right)\\\\\n&=\\tfrac{1}{r^{(k+1)\\ell}}\\left( \\gauss{n-\\ell+1}{1}r^{2\\ell}+\\gauss{\\ell-1}{1}r^{2(k+1)}\\right)\\\\\n&=r^\\ell\\gauss{n-\\ell+1}{1}\\tfrac{1}{r^{k\\ell}}+\\tfrac{1}{r^{\\ell-2}}\\gauss{\\ell-1}{1}\\tfrac{1}{r^{k(\\ell-2)}}\\\\\n&=s_\\ell(\\sigma_k),\n\\end{align*}\nwhereas for even $\\ell$ we have\n\\begin{align*}\n\\textstyle{\\sum_j p_{1j}^k \\sigma_j^\\ell}\n&=c_k\\sigma_{k-1}^\\ell+a_k \\sigma_{k}^\\ell+b_k \\sigma_{k+1}^\\ell\\\\\n&=\\gauss{k}{1}\\tfrac{1}{r^{(k-1)\\ell}}+(q-1)\\gauss{k}{1}\\tfrac{1}{r^{k\\ell}}+q\\left(\\gauss{k}{1}-\\gauss{n}{1}-\\gauss{k}{1}\\right)\\tfrac{1}{r^{(k+1)\\ell}}\\\\\n&=\\tfrac{1}{r^{(k+1)\\ell}}\\left(\\gauss{k}{1}q^{\\ell}+q\\bigl(\\gauss{n}{1}-\\gauss{k}{1}\\bigr)+r^{2k+\\ell}-r^\\ell\\right)\\\\\n&=\\tfrac{1}{r^{(k+1)\\ell}}\\left(\\gauss{n+1}{1}-\\gauss{\\ell}{1}+\\gauss{k+\\ell}{1}- \\gauss{k+1}{1}+r^{2k+\\ell}-r^\\ell\\right)\\\\\n&=\\tfrac{1}{r^{(k+1)\\ell}}\\left(\\gauss{n-\\ell+1}{1}r^{2\\ell}-r^\\ell+\\gauss{\\ell-1}{1}r^{2(k+1)}+r^{2k+\\ell}\\right)\\\\\n&=r^\\ell\\left(\\gauss{n-\\ell+1}{1}-\\tfrac{1}{r^\\ell}\\right)\\tfrac{1}{r^{k\\ell}}+\\tfrac{1}{r^{\\ell-2}}\\left(\\gauss{\\ell-1}{1}+r^{\\ell-2}\\right)\\tfrac{1}{r^{k(\\ell-2)}}\\\\\n&=s_\\ell(\\sigma_k).\n\\end{align*}\n\\endgroup\n\nNow we deal with $k\\geqslant n+1$, noting that\n\\[\\sum_j p_{1j}^k \\sigma_j^\\ell=b_{2n+1-k} \\sigma_{k-1}^\\ell+\\tfrac{a_{2n+1-k}}{2} \\sigma_{k}^\\ell+c_{2n+1-k} \\sigma_{k+1}^\\ell+\\tfrac{a_{2n+1-k}}{2} \\sigma_{2n+1-k}^\\ell.\\]\nFor odd $\\ell$ this reduces to\n\\begin{align*}\nb_{2n+1-k} \\sigma_{k-1}^\\ell+c_{2n+1-k} \\sigma_{k+1}^\\ell&=- b_{2n+1-k} \\sigma_{2n+2-k}^\\ell - c_{2n+1-k} \\sigma_{2n-k}^\\ell\\\\\n&=-s_\\ell( \\sigma_{2n+1-k})=s_\\ell(-\\sigma_{2n+1-k})=s_\\ell(\\sigma_{k}),\n\\end{align*}\nwhile for even $\\ell$ we obtain\n\\begin{align*}\nb_{2n+1-k}\\sigma_{k-1}^\\ell+{}&a_{2n+1-k}\\sigma_{k}^\\ell+c_{2n+1-k} \\sigma_{k+1}^\\ell\\\\\n&=b_{2n+1-k}\\sigma_{2n+2-k}^\\ell+a_{2n+1-k}\\sigma_{2n+1-k}^\\ell+c_{2n+1-k}\\sigma_{2n-k}^\\ell\\\\\n&=s_\\ell( \\sigma_{2n+1-k})=s_\\ell(-\\sigma_{2n+1-k})=s_\\ell(\\sigma_{k}).\n\\end{align*}\n\nFor nonsquare $q$ the splitting field of $\\mathcal{S}$ is irrational, implying that it is a quadratic extension of the rationals, namely \n$\\mathbb{Q}(r)$. The Galois group acts faithfully on the idempotents of the scheme, yielding a second $Q$-polynomial ordering.  \nThis second $Q$-polynomial ordering can also be obtained by replacing $r\\mapsto-r$ in both the $\\sigma_j$ and the polynomials $s_\\ell(x)$, showing that this second ordering exists for square $q$ as well. \\qed\n\\end{pf}\n\nWe note that by a result of Suzuki \\cite{SUZ}, $Q$-polynomial schemes can have at most two $Q$-polynomial orderings.\n\n\\section{The $P$-matrix}\n\\label{P-matrix}\n\nWe now compute the $P$-matrix of the scheme $\\mathcal{S}$, expressing it in terms of the auxiliary matrices $\\widetilde{P}$ and $\\widehat{P}$ whose entries are defined by\n\\begin{align*}\n\\widetilde{P}_{ij}&=\\sum\\limits_{l=0}^j (-1)^\\ell r^{j-2\\ell+(j-\\ell)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell};\\\\\n\\widehat{P}_{ij}&=\\sum\\limits_{\\ell=0}^j (-1)^\\ell r^{(j-\\ell)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell}.\n\\end{align*}\nBy \\cite[Proposition 2.2.2]{BCN}, the $P$-matrix is determined by the left-normalized left eigenvectors of $L_1$. We first show that the rows of $\\widetilde{P}$ and $\\widehat{P}$ are left\neigenvectors of the matrices defined by\n\\[M\\llap{$\\widetilde{\\phantom{D}}$}=\\begin{pmatrix}  \n0&b_0&&&&\\\\\n1&a_1&b_1&&&\\\\\n&c_2&a_2&\\smash\\ddots&&\\\\\n\\noalign{\\vskip-2pt}\n&&\\ddots&\\ddots&\\ddots&\\\\\n\\noalign{\\vskip-3pt}\n&&&\\ddots&a_{d-1}&b_{d-1}\\\\\n&&&&c_{d}&a_d\n\\end{pmatrix},\\quad\nM\\llap{$\\widehat{\\phantom{D}}$}=\\begin{pmatrix}  \n0&b_0&&&&\\\\\n1&0&b_1&&&\\\\\n\\noalign{\\vskip-4pt}\n&c_2&0&\\ddots&&\\\\\n\\noalign{\\vskip-2pt}\n&&\\ddots&\\ddots&\\ddots&\\\\\n\\noalign{\\vskip-5pt}\n&&&\\ddots&0&b_{d-1}\\\\\n&&&&c_{d}&0\n\\end{pmatrix}\\]\nrespectively. We will show that the corresponding diagonal forms are\n\\[\\widetilde{D}=\\diag(\\widetilde{P}_{i0},\\widetilde{P}_{i1},\\ldots,\\widetilde{P}_{in}),\\quad\\widehat{D}=\\diag(\\widehat{P}_{i0},\\widehat{P}_{i1},\\ldots,\\widehat{P}_{in}).\\]\nThe ordering we give to the eigenvectors of $M\\llap{$\\widetilde{\\phantom{D}}$}$ and $M\\llap{$\\widehat{\\phantom{D}}$}$ may seem arbitrary, but will be important later.\n\n\\begin{theorem}\\label{theorem8.1}\n$\\widetilde{P}M\\llap{$\\widetilde{\\phantom{D}}$}=\\widetilde{D}\\widetilde{P}$ and $\\widehat{P}M\\llap{$\\widehat{\\phantom{D}}$}=\\widehat{D}\\widehat{P}$.\n\\end{theorem}\n\n\\begin{pf}\nFix $i$ and let $v_i=(\\widetilde{P}_{i0},\\widetilde{P}_{i1},\\ldots,\\widetilde{P}_{in})$.\nWe must show that $v_iM\\llap{$\\widetilde{\\phantom{D}}$}=\\widetilde{P}_{i1}v_i$. In particular, we need to show the following recurrence holds for all $j$:\n\\begin{align*}\nb_{j-1}\\sum\\limits_{\\ell=0}^{j-1}(-1)^\\ell&r^{j-1-2\\ell +(j-1-\\ell)^2+\\ell^2}\n\\gauss{i}{\\ell}\\gauss{n-i}{j-1-\\ell} + a_j \\sum\\limits_{\\ell=0}^{j}(-1)^\\ell r^{j-2\\ell +(j-\\ell)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell}\\\\\n&\\qquad+c_{j+1}\\sum\\limits_{\\ell=0}^{j+1}(-1)^\\ell r^{j+1-2\\ell+(j+1-\\ell)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j+1-\\ell}\\\\\n&=\\widetilde{P}_{i1} \\sum\\limits_{\\ell=0}^j(-1)^\\ell r^{j-2\\ell+(j-\\ell)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell}.\n\\end{align*}\nMultiplying both sides by $q-1$ and substituting for $b_{j-1}, a_j$ and $c_{j+1}$, we find this is equivalent to showing that the quantity $z_j$, defined as follows, vanishes for all $j$:\n\\begin{align*}\nz_j={}&(q^{n+1}-q^j)\\sum\\limits_{\\ell=0}^{j-1}(-1)^\\ell r^{j-2\\ell-1+(j-\\ell-1)^2+\\ell^2} \\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell-1}\\\\\n&+(q-1)(q^j-1)\\sum\\limits_{\\ell=0}^{j}(-1)^\\ell r^{j-2\\ell+(j-\\ell)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell}\\\\\n&+(q^{j+1}-1) \\sum\\limits_{\\ell=0}^{j+1}(-1)^\\ell r^{ j-2\\ell+1+(j-\\ell+1)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell+1}\\\\\n&-\\bigl(q^i(q^{n-2i+1}-1)-q+1\\bigr)\\sum\\limits_{\\ell=0}^j (-1)^\\ell r^{ j-2\\ell+(j-\\ell)^2+\\ell^2} \\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell}.\n\\end{align*}\nThe second and last sums combine, simplifying to\n\\begin{align*}\nz_j={}&(q^{n+1}-q^j) \\sum\\limits_{\\ell=0}^{j-1} (-1)^\\ell r^{ j-2\\ell-1 +(j-\\ell-1)^2+\\ell^2} \\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell-1}\\\\\n&+\\bigl((q-1)q^{j}+q^i - q^{n-i+1}\\bigr) \\sum\\limits_{\\ell=0}^{j} (-1)^\\ell r^{ j-2\\ell +(j-\\ell)^2+\\ell^2} \\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell}\\\\\n&+(q^{j+1}-1) \\sum\\limits_{\\ell=0}^{j+1} (-1)^\\ell r^{ j-2\\ell+1 + (j-\\ell+1)^2+\\ell^2} \\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell+1}.\n\\end{align*}\nNow it suffices to show that the generating function $Z(t)=\\sum_{j=0}^\\infty z_j t^j$ vanishes. We first express $Z(t)$ in terms of the\npolynomials $E_m(t)$ defined in Section~\\ref{gaussian}.\nUsing Proposition~\\ref{prop2.2}(iii),\nwe are able to rewrite our generating function as $Z(t)=\\Sigma_1+\\Sigma_2+\\cdots+\\Sigma_6$ where\n\\begingroup\n\\allowdisplaybreaks\n\\begin{align*}\n\\Sigma_1&=q^{n+1}\\sum\\limits_{j=0}^{\\infty}\\sum\\limits_{\\ell=0}^{j-1}(-1)^\\ell r^{ j-2\\ell-1 +(j-\\ell-1)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell-1}t^j\\\\\n&=q^{n+1}tE_i(-t)E_{n-i}(qt);\\\\\n\\Sigma_2&=-\\sum\\limits_{j=0}^{\\infty}q^j\\sum\\limits_{\\ell=0}^{j-1}(-1)^\\ell r^{ j-2\\ell-1 +(j-\\ell-1)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell-1}t^j\\\\\n&=-qtE_i(-qt)E_{n-i}(q^2t);\\\\\n\\Sigma_3&=(q-1)\\sum\\limits_{j=0}^{\\infty}q^j\\sum\\limits_{\\ell=0}^{j+1}(-1)^\\ell r^{ j-2\\ell +(j-\\ell)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell}t^j\\\\\n&=(q-1)E_i(-qt)E_{n-i}(q^2t);\\\\\n\\Sigma_4&=(q^i - q^{n-i+1})\\sum\\limits_{j=0}^{\\infty}\\sum\\limits_{\\ell=0}^{j+1} (-1)^\\ell r^{ j-2\\ell+(j-\\ell)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell}t^j\\\\\n&=(q^i-q^{n-i+1})E_i(-t)E_{n-i}(qt);\\\\\n\\Sigma_5&=\\sum\\limits_{j=0}^{\\infty}q^{j+1}\\sum\\limits_{\\ell=0}^j(-1)^\\ell r^{ j-2\\ell+1 +(j-\\ell+1)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell+1}t^j\\\\\n&=\\tfrac{1}{t}E_i(-qt)E_{n-i}(q^2t);\\\\\n\\Sigma_6&=-\\sum\\limits_{j=0}^{\\infty}\\sum\\limits_{\\ell=0}^j (-1)^\\ell r^{ j-2\\ell+1 +(j-\\ell+1)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell+1}t^j\\\\\n&=-\\tfrac{1}{t}E_i(-t)E_{n-i}(qt).\n\\end{align*}\n\\endgroup\nUsing Proposition~\\ref{prop2.2}(i,ii), we find \n\\begin{align*}\nZ(t)&{}=\\Sigma_1+\\Sigma_2+ \\Sigma_3+\\Sigma_4+\\Sigma_5+\\Sigma_6\\\\\n&{}=\\Bigl(q^{n+1}t+q^i-q^{n-i+1}-\\tfrac{1}{t}\\\\\n&\\qquad{}+\\tfrac{(1-q^it)}{(1-t)}\\tfrac{(1+q^{n-i+1}t)}{(1+qt)}\\bigl(-qt+q-1+\\tfrac{1}{t}\\bigr)\\Bigr) E_i(-t) E_{n-i}(qt)=0\n\\end{align*}\nas required.\n\n\nThe strategy for showing $\\widehat{P}M\\llap{$\\widehat{\\phantom{D}}$}=\\widehat{D}\\widehat{P}$ is very similar but the details are sufficiently different that we provide the details here.\nFix $i$ and let $v_i=(\\widehat{P}_{i0},\\widehat{P}_{i1},\\ldots,\\widehat{P}_{in})$.\nWe must show that $v_iM\\llap{$\\widehat{\\phantom{D}}$}=\\widehat{P}_{i1}v_i$. In particular, we need to show the following recurrence holds for all $j$:\n\\[b_{j-1}\\sum\\limits_{\\ell=0}^{j-1} (-1)^\\ell r^{ (j-1-\\ell)^2+\\ell^2} \\gauss{i}{\\ell}\\gauss{n-i}{j-1-\\ell} + c_{j+1}\\sum\\limits_{\\ell=0}^{j+1} (-1)^\\ell r^{ (j+1-\\ell)^2+\\ell^2}  \\gauss{i}{\\ell}\\gauss{n-i}{j+1-\\ell}\\]\n\\[=\\widehat{P}_{i1} \\sum\\limits_{\\ell=0}^j (-1)^\\ell r^{ (j-\\ell)^2+\\ell^2} \\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell}.\\]\nMultiplying both sides by $q-1$ and substituting for $b_{j-1}, c_{j+1}$, we find this is equivalent to showing that the following is zero for all $j$: \n\\begin{align*}\nz_j={}&(q^{n+1}-q^j) \\sum\\limits_{\\ell=0}^{j-1} (-1)^\\ell r^{(j-\\ell-1)^2+\\ell^2} \\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell-1}\\\\\n&+(q^{j+1}-1) \\sum\\limits_{\\ell=0}^{j+1} (-1)^\\ell r^{(j-\\ell+1)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell+1}\\\\\n&-q^i(q^{2n-i}-1) \\sum\\limits_{\\ell=0}^j (-1)^\\ell r^{(j-\\ell)^2+\\ell^2}\\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell}.\n\\end{align*}\nAgain, it suffices to show that the generating function $Z(t)=\\sum_{j=0}^\\infty z_j t^j$ vanishes. As before, we first\nrewrite our generating function as $Z(t)=\\Sigma_1+\\Sigma_2+\\cdots+\\Sigma_6$ where\n\\begingroup\n\\allowdisplaybreaks\n\\begin{align*}\n\\Sigma_1&=q^{n+1} \\sum\\limits_{\\ell=0}^{j-1} (-1)^\\ell r^{ (j-\\ell-1)^2+\\ell^2} t^\\ell \\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell-1} t^m=q^{n+1}tE_i(-rt) E_{n-i}(rt);\\\\\n\\Sigma_2&=-q^{j} \\sum\\limits_{\\ell=0}^{j-1} (-1)^\\ell r^{ (j-\\ell-1)^2+\\ell^2}t^\\ell \\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell-1}t^m=-qtE_i(-r^3t) E_{n-i}(r^3t);\\\\\n\\Sigma_3&=q^{j+1} \\sum\\limits_{\\ell=0}^{j+1} (-1)^\\ell r^{ (j-\\ell+1)^2+\\ell^2}t^\\ell  \\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell+1}t^m=\\tfrac{1}{t}E_i(-r^3t) E_{n-i}(r^3t);\\\\\n\\Sigma_4&=-\\sum\\limits_{\\ell=0}^{j+1} (-1)^\\ell r^{ (j-\\ell+1)^2+\\ell^2}t^\\ell  \\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell+1}t^m=-\\tfrac{1}{t}E_i(-rt) E_{n-i}(rt);\\\\\n\\Sigma_5&=-rq^{2n} \\sum\\limits_{\\ell=0}^j (-1)^\\ell r^{ (j-\\ell)^2+\\ell^2}t^\\ell \\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell}t^m=-r q^{n-i}E_i(-rt) E_{n-i}(rt);\\\\\n\\Sigma_6&=rq^i \\sum\\limits_{\\ell=0}^j (-1)^\\ell r^{ (j-\\ell)^2+\\ell^2}t^\\ell \\gauss{i}{\\ell}\\gauss{n-i}{j-\\ell}t^m=r q^{i}E_i(-rt) E_{n-i}(rt)\n\\end{align*}\n\\endgroup\nin terms of the polynomials $E_m(t)$ defined\nin Section~\\ref{gaussian}. Using Proposition~\\ref{prop2.2}(iii), we find \n\\begin{align*}\nZ(t)&{}=\\Sigma_1+\\Sigma_2+\\Sigma_3+\\Sigma_4+\\Sigma_5+\\Sigma_6\\\\\n&=\\Bigl(q^{n+1}t-\\tfrac{1}{t}-rq^{n-i}+rq^i\\\\\n&\\qquad+\\bigl(\\tfrac{1}{t}-qt\\bigr)\\tfrac{(1-rq^it)(1+rq^{n-i}t)}{(1-rt)(1+rt)}\\Bigr)E_i(-rt) E_{n-i}(rt)=0\n\\end{align*}\nas required.\\qed\n\\end{pf} \n\n\\bigskip\n\n\\begin{corollary}\\label{corollary8.2}\nThe $P$-matrix of the $Q$-polynomial scheme $\\mathcal{S}$ is given by\n\\[\\begin{cases}\nP_{i,j}=P_{i,2n+1-j}=\\widetilde{P}_{\\frac{i}2,j}&\\mbox{for $i$ even, $0\\leqslant j\\leqslant n$;}\\\\\n\\noalign{\\smallskip}\nP_{i,j}=-P_{i,2n+1-j}=\\widehat{P}_{\\lfloor\\frac{i}2\\rfloor,j}&\\mbox{for $i$ odd, $0\\leqslant j\\leqslant n$.}\n\\end{cases}\\]\n\\end{corollary}\n\n\\begin{pf}\nIf $(v_0,\\ldots,v_n)$ is a left eigenvector of $M\\llap{$\\widetilde{\\phantom{D}}$}$ or $M\\llap{$\\widehat{\\phantom{D}}$}$, it is easily seen that\neither $(v_0,\\ldots,v_n, v_n,\\dots,v_0)$ or  \n$(v_0,\\ldots, v_n,-v_n,\\ldots,-v_0)$ is a left eigenvector of $L_1$, respectively.  The fact that this ordering of the eigenvalues of $L_1$ is a $Q$-polynomial ordering follows from Theorem~\\ref{theorem7.2}.\\qed\n\\end{pf}\n\n\\section{A hypothetical subscheme}\n\\label{subscheme}\n\nWe ask whether $\\mathcal{S}$ is the extended $Q$-bipartite double (in the sense of \\cite{MMW}) of a primitive $Q$-polynomial scheme.  \nWe investigated these parameters up to $n=20$ and found they satisfied the Krein conditions, had integral eigenvalue multiplicities and nonnegative integral $p^k_{ij}$, and satisfy the handshaking lemma for all square $q$.\nThis appears to give an infinite family of feasible parameters for primitive $Q$-polynomial schemes with an unbounded number of classes. \nDetailed parameters and a proof of feasibility will be given in a forthcoming paper of Eiichi Bannai and Jianmin Ma.\n\nWe give the smallest case below for which existence is unknown:\n\\bigskip\n\n\\[P=\\begin{pmatrix} \n 1 &  \\frac{r^4 + r^3 + r^2 + r}{2} &  \\frac{r^4 - r^3 + r^2 - r}{2} &  \\frac{r^6 + r^4}{2} &  \\frac{r^6 - r^4}{2} \\\\\n  1 &  \\frac{r^3 + r^2 + r - 1}{2} &  \\frac{-r^3 + r^2 - r - 1}{2} &  \\frac{r^4 - r^2}{2} &  \\frac{-r^4 - r^2}{2} \\\\\n  1 &  \\frac{r^2 - 1}{2} &  \\frac{r^2 - 1}{2} &  -r^2 &  0 \\\\\n  1 &  \\frac{-r^2 - 1}{2} &  \\frac{-r^2 - 1}{2} &  0 &  r^2 \\\\\n  1 &  \\frac{-r^3 - r^2 - r - 1}{2} &  \\frac{r^3 - r^2 + r - 1}{2} &  \\frac{r^4 + r^2}{2} &  \\frac{-r^4 + r^2}{2}\n \\end{pmatrix}\\]\n\n\\[Q= \\begin{pmatrix} \n 1 &  \\frac{r^4 - 1}{2} &  \\frac{r^6 + r^4 + r^2 + 1}{2} &  \\frac{r^6 - r^4 + r^2 - 1}{2} &  \\frac{r^4 + 1}{2} \\\\\n  1 &  \\frac{r^4 - 2r + 1}{2r} &  \\frac{r^5 - r^4 + r - 1}{2r} &  \\frac{-r^5 + r^4 - r + 1}{2r} &  \\frac{-r^4 - 1}{2r} \\\\\n  1 &  \\frac{-r^4 - 2r - 1}{2r} &  \\frac{r^5 + r^4 + r + 1}{2r} &  \\frac{-r^5 - r^4 - r - 1}{2r} &  \\frac{r^4 + 1}{2r} \\\\\n  1 &  \\frac{r^4 - 2r^2 + 1}{2r^2} &  \\frac{-r^4 - 1}{r^2} &  0 &  \\frac{r^4 + 1}{2r^2} \\\\\n  1 &  \\frac{-r^4 - 2r^2 - 1}{2r^2} &  0 &  \\frac{r^4 + 1}{r^2} &  \\frac{-r^4 - 1}{2r^2}\n\\end{pmatrix}\\]\n\n\\[L_0= \\begin{pmatrix} \n 1 &  0 &  0 &  0 &  0 \\\\\n  0 &  1 &  0 &  0 &  0 \\\\\n  0 &  0 &  1 &  0 &  0 \\\\\n  0 &  0 &  0 &  1 &  0 \\\\\n  0 &  0 &  0 &  0 &  1\n\\end{pmatrix}\\]\n\n\\[L_1= \\begin{pmatrix} \n 0 &  \\frac{r^4 + r^3 + r^2 + r}{2} &  0 &  0 &  0 \\\\\n  1 &  \\frac{r^2 + 2r - 3}{4} &  \\frac{r^2 - 1}{4} &  \\frac{r^4 + r^3}{2} &  0 \\\\\n  0 &  \\frac{r^2 + 2r + 1}{4} &  \\frac{r^2 - 1}{4} &  0 &  \\frac{r^4 + r^3}{2} \\\\\n  0 &  \\frac{r^2 + 2r + 1}{2} &  0 &  \\frac{r^4 + r^3 + r^2 - r - 2}{4} &  \\frac{r^4 + r^3 - r^2 - r}{4} \\\\\n  0 &  0 &  \\frac{r^2 + 1}{2} &  \\frac{r^4 + r^3 + r^2 + r}{4} &  \\frac{r^4 + r^3 - r^2 + r - 2}{4}\n\\end{pmatrix}\\]\n\n\\[L_2= \\begin{pmatrix} \n 0 &  0 &  \\frac{r^4 - r^3 + r^2 - r}{2} &  0 &  0 \\\\\n  0 &  \\frac{r^2 - 1}{4} &  \\frac{r^2 - 2r + 1}{4} &  0 &  \\frac{r^4 - r^3}{2} \\\\\n  1 &  \\frac{r^2 - 1}{4} &  \\frac{r^2 - 2r - 3}{4} &  \\frac{r^4 - r^3}{2} &  0 \\\\\n  0 &  0 &  \\frac{r^2 - 2r + 1}{2} &  \\frac{r^4 - r^3 + r^2 + r - 2}{4} &  \\frac{r^4 - r^3 - r^2 + r}{4} \\\\\n  0 &  \\frac{r^2 + 1}{2} &  0 &  \\frac{r^4 - r^3 + r^2 - r}{4} &  \\frac{r^4 - r^3 - r^2 - r - 2}{4}\n\\end{pmatrix}\\]\n\n\\[L_3= \\begin{pmatrix} \n 0 &  0 &  0 &  \\frac{r^6 + r^4}{2} &  0 \\\\\n  0 &  \\frac{r^4 + r^3}{2} &  0 &  \\frac{r^6 + r^4 - 2r^3}{4} &  \\frac{r^6 - r^4}{4} \\\\\n  0 &  0 &  \\frac{r^4 - r^3}{2} &  \\frac{r^6 + r^4 + 2r^3}{4} &  \\frac{r^6 - r^4}{4} \\\\\n  1 &  \\frac{r^4 + r^3 + r^2 - r - 2}{4} &  \\frac{r^4 - r^3 + r^2 + r - 2}{4} &  \\frac{r^6 + 2r^4 - 3r^2}{4} &  \\frac{r^6 - 2r^4 + r^2}{4} \\\\\n  0 &  \\frac{r^4 + r^3 + r^2 + r}{4} &  \\frac{r^4 - r^3 + r^2 - r}{4} &  \\frac{r^6 - r^2}{4} &  \\frac{r^6 - r^2}{4}\n\\end{pmatrix}\\]\n\n\\[L_4= \\begin{pmatrix} \n 0 &  0 &  0 &  0 &  \\frac{r^6 - r^4}{2} \\\\\n  0 &  0 &  \\frac{r^4 - r^3}{2} &  \\frac{r^6 - r^4}{4} &  \\frac{r^6 - 3r^4 + 2r^3}{4} \\\\\n  0 &  \\frac{r^4 + r^3}{2} &  0 &  \\frac{r^6 - r^4}{4} &  \\frac{r^6 - 3r^4 - 2r^3}{4} \\\\\n  0 &  \\frac{r^4 + r^3 - r^2 - r}{4} &  \\frac{r^4 - r^3 - r^2 + r}{4} &  \\frac{r^6 - 2r^4 + r^2}{4} &  \\frac{r^6 - 2r^4 + r^2}{4} \\\\\n  1 &  \\frac{r^4 + r^3 - r^2 + r - 2}{4} &  \\frac{r^4 - r^3 - r^2 - r - 2}{4} &  \\frac{r^6 - r^2}{4} &  \\frac{r^6 - 4r^4 + 3r^2}{4}\n\\end{pmatrix}\\]\n\n\\[L_0^*=\\begin{pmatrix}\n1&0&0&0&0\\\\\n0&1&0&0&0\\\\\n0&0&1&0&0\\\\\n0&0&0&1&0\\\\\n0&0&0&0&1\n\\end{pmatrix}\\]\n\n\\[L_1^*=\\begin{pmatrix}\n0&\\frac{r^4 - 1}{2}&0&0&0\\\\\n1&\\frac{r^6 - 5r^4 - 3r^2 - 1}{2(r^4 + r^2)} &\\frac{r^8 +2r^4 + 1}{2(r^4 + r^2)} &0&0\\\\\n0&\\frac{r^6 - r^4 + r^2 - 1}{2(r^4 + r^2)} &\\frac{r^8 - 4r^2 + 3}{4(r^4 + r^2)} &\\frac{r^6 - r^4 + r^2 - 1}{4r^2}&0\\\\\n0&0&\\frac{r^6 + r^4 + r^2 + 1}{4r^2}&\\frac{r^6 - 3r^4 - 3r^2 - 3}{4r^2}&\\frac{r^4 + 1}{2r^2}\\\\\n0&0&0&\\frac{r^6 - r^4 + r^2 - 1}{2r^2}&\\frac{r^4 - 2r^2 + 1}{2r^2}\n\\end{pmatrix}\\]\n\n\\[L_2^*=\\begin{pmatrix}\n0&0&\\frac{r^6 + r^4 + r^2 + 1}{2}&0&0\\\\\n0&\\frac{r^8 + 2r^4 + 1}{2(r^4 + r^2)} &\\frac{r^{10} + r^8 + 2r^6 - 2r^4 + r^2 - 3}{4(r^4 + r^2)} &\\frac{r^8 + 2r^4 + 1}{4r^2}&0\\\\\n1&\\frac{r^8 - 4r^2 + 3}{4(r^4 + r^2)} &\\frac{r^{10} + 3r^8 + 2r^6 - 2r^4 + r^2 - 5}{4(r^4 + r^2)} &\\frac{r^8 - 2r^6 + 2r^4 - 2r^2 + 1}{4r^2}&\n\\frac{r^6 + r^4 + r^2 + 1}{4r^2}\\\\\n0&\\frac{r^6 + r^4 + r^2 + 1}{4r^2}&\\frac{r^8 - 1}{4r^2}&\\frac{r^8 + 2r^4 + 1}{4r^2}&\\frac{r^6 - r^4 + r^2 - 1}{4r^2}\\\\\n0&0&\\frac{r^8 + 2r^6 + 2r^4 + 2r^2 + 1}{4r^2}&\\frac{r^8 - 2r^6 + 2r^4 - 2r^2 + 1}{4r^2}&\\frac{r^6 - r^4 + r^2 - 1}{2r^2}\n\\end{pmatrix}\\]\n\n\\[L_3^*=\\begin{pmatrix}\n0&0&0&\\frac{r^6 - r^4 + r^2 - 1}{2}&0\\\\\n0&0&\\frac{r^8 + 2r^4 + 1}{4r^2}&\\frac{r^{10} - 3r^8 - 2r^6 - 6r^4 - 3r^2 - 3}{4(r^4 + r^2)} &\\frac{r^8 + 2r^4 + 1}{2(r^4 + r^2)} \\\\\n0&\\frac{r^6 - r^4 + r^2 - 1}{4r^2}&\\frac{r^8 - 2r^6 + 2r^4 - 2r^2 + 1}{4r^2}&\\frac{r^{10} - r^8 + 2r^6 - 2r^4 + r^2 - 1}{4(r^4 + r^2)} &\\frac{r^8 - 2r^6 + 2r^4 - 2r^2 + 1}{4(r^4 + r^2)} \\\\\n1&\\frac{r^6 - 3r^4 - 3r^2 - 3}{4r^2}&\\frac{r^8 + 2r^4 + 1}{4r^2}&\\frac{r^8 - 4r^6 + 4r^4 - 4r^2 + 3}{4r^2}&\\frac{r^6 - r^4 + r^2 - 1}{4r^2}\\\\\n0&\\frac{r^6 - r^4 + r^2 - 1}{2r^2}&\\frac{r^8 - 2r^6 + 2r^4 - 2r^2 + 1}{4r^2}&\\frac{r^8 - 2r^6 + 2r^4 - 2r^2 + 1}{4r^2}&0\n\\end{pmatrix}\\]\n\n\\[L_4^*=\\begin{pmatrix}\n0&0&0&0&\\frac{r^4+1}{2}\\\\\n0&0&0&\\frac{r^8 + 2r^4 + 1}{2(r^4 + r^2)} &\\frac{r^6 - r^4 + r^2 - 1}{2(r^4 + r^2)} \\\\\n0&0&\\frac{r^6 + r^4 + r^2 + 1}{4r^2}&\\frac{r^8 - 2r^6 + 2r^4 - 2r^2 + 1}{4(r^4 + r^2)} &\\frac{r^6 - r^4 + r^2 - 1}{2(r^4 + r^2)} \\\\\n0&\\frac{r^4 + 1}{2r^2}&\\frac{r^6 - r^4 + r^2 - 1}{4r^2}&\\frac{r^6 - r^4 + r^2 - 1}{4r^2}&0\\\\\n1&\\frac{r^4 - 2r^2 + 1}{2r^2}&\\frac{r^6 - r^4 + r^2 - 1}{2r^2}&0&0\n\\end{pmatrix}\\]\n\n\\section*{Acknowledgements}\n\nThis research was supported in part by NSF grant DMS-1400281. The software package\nMAGMA~\\cite{Magma} was instrumental in finding the initial examples \nof these schemes, as well as in computations related to verifying our proofs.\n\n\\section*{References}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nDue to asymptotic freedom, the large distance behavior of\n\\mbox{SU$(N)$}~gauge theories must be treated non-perturbatively.\nA convenient method is to put the model in a finite spatial box\nof length $L$ and calculate the low-lying energy eigenstates as\nfunction of $L$. Obviously the wave functionals of\nsuch states are concentrated at small $L$\nin the vacua of {\\em classical}\nconfiguration space. At larger $L$ they can spread out over low energy\nbarriers between these vacua. This spreading causes the breakdown\nof conventional perturbation theory.\n\nThis picture has been used~\\cite{LuKoBa,BaDa} for reduction of the\nfield theory to a finite dimensional system. The remaining degrees\nof freedom are expected to correspond to the set of vacua (called\nthe vacuum valley) and suitable paths over the barriers between\nvacua. One of the requirements on such paths is that they cross\na barrier at its lowest point. This point, a sphaleron~\\cite{Ta,KlMa},\nis defined through a mini-max procedure. One first finds the maximal\nenergy on a path connecting two vacua. Then one minimizes this maximum\nover the space of all such paths.\nIn local terms a sphaleron is\na saddle point of the energy functional with exactly one\nunstable mode.\n\nWell-known paths between two vacua are instantons~\\cite{BePo,BePoScTy},\ninterpreting Euclidean time as a path parameter. In the\nWKB-approximation the tunneling amplitude is dominated by paths near\ninstantons.\nTherefore it seems natural to assume that amongst the instanton paths\nthere is one which crosses a barrier at its lowest point, i.e. it\ngoes through a sphaleron. Let us assume that the set of instantons\n(called the instanton moduli-space) has a scale parameter $\\rho$.\nSince all instantons have the same Euclidean action, a dimensional\nargument easily shows that the maximal energy along the tunneling\npath goes as $1\/\\rho$. Hence it is likely that instantons with\nmaximal width, as set by $L$, go through a sphaleron.\n\nThe latter assumption was made in~\\cite{BaDa} for the following\nreasons.\nFirst, in a direct approach it is often easier to find\ninstantons than sphalerons. Then, if the assumption holds,\none can find all sphalerons via instantons. Second,\nfor small $L$ (high barriers) the spreading of a\nlow energy wave function is determined by tunneling. For large\n$L$ (low barriers) it is determined by classically allowed motion\nthrough a sphaleron. If the\nassumption does not hold, there is some range of $L$~values in\nwhich the most important paths between vacua change dramatically.\n\nThe conjecture that a sphaleron lies on an instanton path is\n{\\em in general} not true. For example, consider the two-dimensional\npotential $V(q_1,q_2)=(q_1^2-1)^2\\mbox{$((q_2^2-1)^2(2+q_2^2)+1)$}\n+(1+b^2\/q_2^2)^{-1}$ for small values of the parameter $b$.\nIt has vacua at $(\\pm 1, 0)$  with zero energy\nand (to leading order in $b$) sphalerons\nat $(0,\\pm 1)$ with energy 2. However, for small enough $b$\nthe instanton does not go through a sphaleron. Instead,\nit goes straight through the saddle point at $(0,0)$, which has\none unstable mode and energy 3. It is even possible that an\ninstanton goes through several saddle points with one unstable\nmode (we think of a one-dimensional example), in which only the\none with {\\em highest} energy would be a candidate sphaleron.\n\nThe above clearly shows that in field theory the conjecture\nneeds to be checked. For \\mbox{SU$(2)$}~gauge theory on a space-time\n$\\mbox{${\\rm T}^3$}\\times\\mbox{$[-\\half T, \\half T]$}$ we~\\cite{PeGoSnBa}\nhave developed a numerical procedure to find the widest\ninstantons (for $T\\rightarrow\\infty$). Subsequent numerical\ninvestigation~\\cite{GaBa} has shown that the widest instanton\ngoes through a saddle point with one unstable mode, like for\n\\mbox{SU$(2)$}\\ on a space-time $S^3\\times\\mbox{I$\\!$R}$~\\cite{BaDa}. It is\nlikely these saddle points are sphalerons. For the two-dimensional\n\\mbox{O$(3)\\,\\sigma$-model}, which is studied in the present paper, this can be\nproven rigorously.\n\nIt is well-known that this $\\sigma$-model shares with the\nfour-dimensional gauge theories features like renormalizability and\nasymptotic freedom. Another\nsimilarity is still more important to us now. Both models,\nwhen put in a spatial cube with periodic boundary conditions,\nhave vacuum valleys of nonzero dimension. This\ncan increase the number of\ninstantons, as they\nmust have endpoints in the vacuum valley. In this context\nwe also mention the\nabsence of instantons on compact\nspace-times \\mbox{${\\rm T}^3\\times {\\rm T}^1$}\\ and \\mbox{${\\rm T}^1\\times {\\rm T}^1$},\nrespectively~\\cite{BrBa,RiRo,MiSp}. This does not rule out\nthe existence of instantons on an\ninfinite time interval. It merely suggests the vacuum valley\ncannot be reached in a finite amount of time.\n\nThe outline of this paper is as follows: in\nsection~\\ref{sec:genform} we will set up a convenient formalism,\nwhich will be used in\nsection~\\ref{sec:stat} to derive all static solutions of the\nEuler-Lagrange equations. In particular we\nfind the vacuum valley and the\nsphaleron solutions. Section~\\ref{sec:inst} is devoted\nto constructing all instanton solutions and interpreting their\nmoduli-space. A scale parameter will emerge that relates the\ninstanton field at $t=+\\infty$ to that at $t=-\\infty$.\nWe conclude in section~\\ref{sec:concl} by\nputting our results in\nperspective with respect to the four-dimensional \\mbox{SU$(2)$}\\ case.\n\n\n\\section{The \\mbox{O$(3)\\,\\sigma$-model}\\ in general coordinates}\n\\label{sec:genform}\n\nThe action for the \\mbox{O$(3)\\,\\sigma$-model}\\ on a cylinder reads\n\\begin{equation}\nS[\\mbox{$\\vec{n}$}]=\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2}$}\\mbox{$\\int\\!\\!d^2x\\,\\,$} |\\partial_{\\mu}\\mbox{$\\vec{n}(x)$}|^2,\\ \\ \\ \\mbox{$\\vec{n}(x)$}\\in\\mbox{I$\\!$R}^3,\\ \\ \\\n|\\mbox{$\\vec{n}(x)$}|^2=1,\n\\label{eq:nact}\n\\end{equation}\nwhere the integration runs over space-time\n$\\{(x_2,x_1)\\in\\mbox{${\\rm T}^1\\times\\re$}\\}$. We use\noverall scale invariance to fix the length of the spatial 1-torus\n${\\rm T}^1$ (the circle) to be $2\\pi$. So $\\mbox{$\\vec{n}$}(x+2\\pi\\hat{e}_2)=\\mbox{$\\vec{n}$}(x)$.\nThe metric on space-time is Euclidean, and we use the summation\nconvention over repeated indices throughout.\n\nBy definition, $\\mbox{$\\vec{n}(x)$}\\in S^2$. If we use coordinates $v^i$ ($i=1,2$)\nand a metric $g_{ij}$ on $S^2$, \\refeq{nact} can be\nrewritten as\n\\begin{equation}\nS[v]=\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2}$}\\mbox{$\\int\\!\\!d^2x\\,\\,$} g_{ij}(v(x))\\partial_{\\mu} v^i(x)\\partial_{\\mu} v^j(x).\n\\label{eq:vact}\n\\end{equation}\nIn this paper we will use both\nspherical coordinates $(\\vartheta,\\varphi)$ and\nstereographic projection $(u_1,u_2)$ which will be paired as\n$u\\equiv u_1+i u_2$, with complex conjugate $\\bar{u}=u_1-i u_2$\n(c.f.~\\cite{BePo,RiRo}):\n\\begin{equation}\n\\mbox{$\\vec{n}$}=\\left(\\!\\!\\begin{array}{c}\\sin\\vartheta\\cos\\varphi \\\\\n\\sin\\vartheta\\sin\\varphi \\\\ \\cos\\vartheta\\end{array}\\!\\!\\right)=\n\\frac{1}{1+|u|^2}\\left(\\!\\!\\begin{array}{c}u+\\mbox{$\\bar{u}$} \\\\ (u-\\mbox{$\\bar{u}$})\/i\n\\\\ |u|^2-1\\end{array}\\!\\!\\right)\n\\label{eq:npar}\n\\end{equation}\n(hence $u=\\cot\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2}$}\\vartheta\\,e^{i\\varphi}$).\n\nIn section~\\ref{sec:stat} we will need the Euler-Lagrange\nequations and the Hessian of \\refeq{vact}. A\nstraightforward computation~\\cite{AlFrMu} gives (for vanishing\n$\\delta v(x_1\\rightarrow\\pm\\infty,x_2)$):\n\\begin{eqnarray}\nS[v+\\delta v]&=&S[v]+S^{(1)}[v,\\xi]+S^{(2)}[v,\\xi]+\\mbox{$\\cal O$}(\\xi^3),\n\\nonumber\\\\\nS^{(1)}[v,\\xi]&=&-\\mbox{$\\int\\!\\!d^2x\\,\\,$} \\left(D_{\\mu}\\partial_{\\mu} v\\right)_i\\xi^i,\n\\label{eq:pertact}\\\\\nS^{(2)}[v,\\xi]&=&\\mbox{$\\int\\!\\!d^2x\\,\\,$} \\xi^i\\mbox{$\\cal H$}_{ij}[v]\\xi^j,\\ \\ \\\n\\mbox{$\\cal H$}_{ij}[v]=-\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2}$}\\left(D_{\\mu}D_{\\mu}\\right)_{ij}+\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2}$} R_{kijl}\\partial_{\\mu}\nv^k\\partial_{\\mu} v^l.\n\\nonumber\n\\end{eqnarray}\nHere $\\xi=\\delta v+\\mbox{$\\cal O$}(\\delta v^2)$ is defined in such a way that it\ntransforms covariantly; see~\\cite{AlFrMu} for details. Since the\naction is a scalar, this guarantees that \\mbox{$\\cal H$}\\ is a tensor, as can be\nverified from the explicit form. Furthermore, $D_{\\mu}$ is\nthe covariant derivative and $R$ is the Riemann tensor, both at the\npoint $v$:\n\\begin{eqnarray}\n\\left(D_{\\mu}\\lambda\\right)_i&=&\\partial_{\\mu}\\lambda_i-{\\Gamma^j}_{ik}\\partial_{\\mu}\nv^k\\lambda_j,\\ \\ \\ \\mbox{(for any vector $\\lambda$)} \\nonumber\\\\\n\\Gamma_{kij}&=&\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2}$}\\left(\\hat{\\partial}_j g_{ik}+\\hat{\\partial}_i\ng_{jk}-\\hat{\\partial}_k g_{ij}\\right),\\ \\ \\\n(\\hat{\\partial}_i\\equiv\\frac{\\partial}{\\partial v^i})\n\\\\\n{R^l}_{ijk}&=&\\hat{\\partial}_j{\\Gamma^l}_{ik}-\\hat{\\partial}_k\n{\\Gamma^l}_{ij}\n+{\\Gamma^m}_{ik}{\\Gamma^l}_{mj}-{\\Gamma^m}_{ij}{\\Gamma^l}_{mk}.\n\\nonumber\n\\end{eqnarray}\nThe Euclidean action, \\refeq{vact}, is precisely half the\ntotal volume of \\mbox{$v(\\mbox{${\\rm T}^1\\times\\re$})\\subset S^2$}.\nThis action also naturally\noccurs in string theory (see e.g.~\\cite{GrScWi}). Therefore,\nextremizing the action (which amounts to putting $D_{\\mu}\\partial_{\\mu} v=0$,\n\\refeq{pertact}) gives a geodesic surface (in affine parametrization)\non the space $S^2$.\n\nFinally, it is important to introduce the winding number which\nmeasures the number of times \\mbox{${\\rm T}^1\\times\\re$}\\ is wrapped around $S^2$ by\n$v$ (and therefore is invariant under continuous deformations\nof $v$):\n\\begin{equation}\nQ[v]=-\\raisebox{.15ex}{\\scriptsize$\\frac{1}{8\\pi}$}\\mbox{$\\int\\!\\!d^2x\\,\\,$} \\varepsilon_{\\mu\\nu}\\mbox{$\\vec{n}$}\\cdot\\left(\\partial_{\\mu}\\mbox{$\\vec{n}$}\n\\times\\partial_{\\nu}\\mbox{$\\vec{n}$}\\right)=\\raisebox{.15ex}{\\scriptsize$\\frac{1}{8\\pi}$}\\mbox{$\\int\\!\\!d^2x\\,\\,$}\\varepsilon_{\\mu\\nu}\\partial_{\\mu}\\mbox{$\\vec{n}$}\\cdot\\left(\n\\mbox{$\\vec{n}$}\\times\\partial_{\\nu}\\mbox{$\\vec{n}$}\\right)=\\raisebox{.15ex}{\\scriptsize$\\frac{1}{8\\pi}$}\\mbox{$\\int\\!\\!d^2x\\,\\,$}\\varepsilon_{\\mu\\nu}g_{ij}\n\\partial_{\\mu} v^i\\lambda^j_{\\nu},\n\\label{eq:topch}\n\\end{equation}\nwhere $\\lambda^j_{\\nu}$ is the vector in the tangent space of $S^2$\n(at the point $v$) corresponding to $\\mbox{$\\vec{n}$}\\times\\partial_{\\nu}\\mbox{$\\vec{n}$}$; up to orientation\n$\\lambda_{\\nu}$ is defined by $g_{ij}\\lambda^i_{\\nu}\\lambda^j_{\\nu}=\ng_{ij}\\partial_{\\nu} v^i\\partial_{\\nu} v^j,\\;g_{ij}\\lambda^i_{\\nu}\\partial_{\\nu} v^j=0$ (no summations\nover $\\nu$). From this follows the well-known formula~\\cite{BePo}\n\\begin{equation}\nS=\\tilde{S}_{\\pm}\\mp4\\pi Q,\\ \\ \\ \\tilde{S}_{\\pm}[v]=\n\\raisebox{.15ex}{\\scriptsize$\\frac{1}{4}$}\\mbox{$\\int\\!\\!d^2x\\,\\,$} g_{ij}\\left(\\partial_{\\mu} v^i\\pm\\varepsilon_{\\mu\\nu}\n\\lambda^i_{\\nu}\\right)\n\\left(\\partial_{\\mu} v^j\\pm\\varepsilon_{\\mu\\rho}\\lambda^j_{\\rho}\\right).\n\\label{eq:niceact}\n\\end{equation}\nWe define an instanton to be a minimal action configuration in the\nsector $Q=+1$. Therefore it has action $4\\pi$ and satisfies the instanton\nequation\n\\begin{equation}\n\\partial_{\\mu} v^i=\\varepsilon_{\\mu\\nu}\\lambda^i_{\\nu}.\n\\label{eq:insteq}\n\\end{equation}\n\n\\section{Sphalerons, vacua and other static solutions}\n\\label{sec:stat}\n\nIn this section we study the potential, or energy functional,\nwhich is the action (\\ref{eq:vact}) restricted to space, i.e.\\\nwithout time-dependence and without integration over time:\n\\begin{equation}\nV[v]=\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2}$}\\int_{{\\rm T}^1}\\!\\!dx_2\\,\\, g_{ij}(v)\\partial_2 v^i\n\\partial_2 v^j.\\ \\ \\ (v=v(x_2))\n\\label{eq:pot}\n\\end{equation}\nThis is the geodesic action for a curve $v(x_2)$ on $S^2$.\nTherefore all static solutions of\nthe Euler-Lagrange equations, being extrema of \\refeq{pot}, are big\ncircles on $S^2$ (affinely parametrized by $x_2$). Remembering\nthe requirement $v(x_2+2\\pi)=v(x_2)$ we conclude that the most\ngeneral static solution reads (after an \\mbox{SO$(3)$}~rotation)\n\\begin{equation}\n\\mbox{$\\vec{n}$}_k(x_2)=\\left(\\begin{array}{c}\\cos(kx_2) \\\\\n\\sin(kx_2) \\\\ 0\\end{array}\\right),\\ \\ \\ k\\in{\\rm Z \\!\\! Z}.\n\\label{eq:statsol}\n\\end{equation}\nOne easily computes the energy\n\\begin{equation}\nV[\\mbox{$\\vec{n}$}_k]=\\pi k^2.\n\\label{eq:staten}\n\\end{equation}\nIn particular $\\mbox{$\\vec{n}$}_0$ is a classical vacuum. Due to \\mbox{SO$(3)$}~symmetry\nthe vacuum valley is isomorphic to $S^2$.\n\nNow we turn to the sphalerons. For this we have to determine the Hessian\nof the energy functional, \\refeq{pot}, at the field\n$\\mbox{$\\vec{n}$}_k$, \\refeq{statsol}. This is easy in spherical coordinates where\n\\refeq{statsol} reads\n$\\vartheta_k(x_2)=\\frac{\\pi}{2},\\;\\varphi_k(x_2)=kx_2$ and the metric is\ngiven by $(g_{ij})={\\rm diag}(1,\\sin^2\\vartheta)$.\nSubstituting these formulas in the static version of \\refeq{pertact}\nwe obtain\n\\begin{equation}\n\\mbox{$\\cal H$}[\\mbox{$\\vec{n}$}_k]=\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2}$}\\left(\\begin{array}{cc}-\\partial_2^2-k^2 & 0 \\\\ 0 &\n-\\partial_2^2\\end{array}\\right).\n\\end{equation}\nOne immediately sees that\n$k=\\pm1$ is the only solution with exactly one unstable mode\n($\\delta\\vartheta(x_2)=1$, $\\delta\\varphi(x_2)=0$).\nSo\\footnote{At this point we do not prove that these saddle points are\ntrue sphalerons in the mini-max sense. This proof\ncan be constructed easily with the results of the next section.}\n the sphaleron\nsolutions are given by $\\mbox{$\\vec{n}$}_1$\nand \\mbox{SO$(3)$}~transformations thereof. In particular $k\\rightarrow-k$ can\nbe undone by a rotation over $\\pi$ around any vector\n$\\mbox{$\\vec{n}$}_k(x_2)$ ($x_2$ fixed). Thus, sphaleron moduli-space\nis isomorphic to $\\mbox{SO$(3)$}$.\n\nOne can verify that\n\\mbox{SO$(3)$}~rotations are responsible for the 3 zero-modes of the\nHessian. Note that the sphaleron is invariant\nunder an $x_2$-translation in combination with a specific\n${\\rm SO}(2)\\subset\\mbox{SO$(3)$}$~rotation (in the case of \\refeq{statsol} around\nthe 3-axis). Therefore spatial translations do not give new sphaleron\nsolutions. Also one can check that the discrete symmetries\n$x_2\\rightarrow-x_2$ and $\\mbox{$\\vec{n}$}\\rightarrow-\\mbox{$\\vec{n}$}$ leave the sphaleron\nmoduli-space invariant.\n\n\\section{Instanton solutions}\n\\label{sec:inst}\n\\subsection{Construction of the solutions}\n\nIn stereographic projection~\\cite{BePo,RiRo} the instanton equation\n(\\ref{eq:insteq}) is particularly simple:\n\\begin{equation}\n\\mbox{$\\partial_{\\bar{z}}$} u=0.\n\\label{eq:analyt}\n\\end{equation}\nHere we have introduced complex coordinates on space-time, $z=x_1+ix_2$,\n$\\bar{z}=x_1-ix_2$, with derivatives $\\mbox{$\\partial_z$}=\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2}$}(\\partial_1-i\\partial_2)$,\n$\\mbox{$\\partial_{\\bar{z}}$}=\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2}$}(\\partial_1+i\\partial_2)$. The construction of instantons\nreduces to finding\nall analytic functions on \\mbox{${\\rm T}^1\\times\\re$}\\ with topological charge $Q=1$.\n\nSubstitution of \\refeq{npar} in \\refeq{topch} gives, for any $u$\nsatisfying \\refeq{analyt},\n\\begin{equation}\nQ[u]=\\raisebox{.15ex}{\\scriptsize$\\frac{1}{\\pi}$}\\intxD{\\mbox{\\scriptsize${\\rm T}^1\\times\\re$}\\,}\\frac{|\\mbox{$\\partial_z$} u|^2}{(1+|u|^2)^2}=\n-\\raisebox{.15ex}{\\scriptsize$\\frac{1}{\\pi}$}\\intxD{\\mbox{\\scriptsize${\\rm T}^1\\times\\re$}\\,}\\mbox{$\\partial_{\\bar{z}}$}\\left(\\frac{1}{1+|u|^2}\\frac{\\mbox{$\\partial_z$} u}{u}\\right).\n\\label{eq:utopch}\n\\end{equation}\nHandling carefully the poles of $\\frac{1}{1+|u|^2}\\frac{\\mbox{$\\partial_z$} u}{u}$,\ni.e.\\ the zeros of $u$, one finds\n\\begin{equation}\nQ[u]=-\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2\\pi}$}\\left(\\int_{x_1=\\infty} - \\int_{x_1=-\\infty}\\right)dx_2\\,\\,\n\\frac{1}{1+|u|^2}\\frac{\\mbox{$\\partial_z$} u}{u}+\\sum_i n_i,\n\\label{eq:nicetopch}\n\\end{equation}\nwhere the $x_2$~integrations run from $0$ to $2\\pi$ and $i$ runs over\nthe zeros of $u$, of degree $n_i\\in\\mbox{I$\\!$N}$. In order to simplify this\nformula, we observe that\nboth the kinetic and the potential term in the Lagrangian\nare semi-positive definite. Hence any finite-action configuration, in\nparticular an instanton, must\napproach a point in the vacuum valley for $x_1\\rightarrow\\pm\\infty$:\n$\\lim_{x_1\\rightarrow\\pm\\infty}u(z)=u_{\\pm}$. In the derivation below\nwe will assume that\n$0<|u_{\\pm}|<\\infty$, as can always be achieved by an\n\\mbox{SO$(3)$}~rotation\\footnote{This is equivalent to changing coordinates\non $S^2$ by shifting the pole used in stereographic\nprojection.}. Under this\nassumption \\refeq{nicetopch} reduces to $Q[u]=\\sum_i n_i$.\n\nNow we are fully prepared to determine all instanton solutions. The\nstrategy is first to find a class of solutions and then to prove no\nsolutions exist outside this class. In order to construct a\nsolution observe that\n\\begin{enumerate}\n\\item Since $e^{z+2\\pi i}=e^z$, any $u=h(e^z)$ ($h$ single-valued and\nanalytic) is a function on \\mbox{${\\rm T}^1\\times\\re$}\\ satisfying the instanton equation.\n\\item Under the above assumption any instanton can have only one zero\n$z_1$ of degree $n_1=1$.\n\\end{enumerate}\nA class of functions satisfying all requirements is\n\\begin{equation}\nu^{\\rm inst}_{a,b,c,d}(z)=-\\frac{c+d e^z}{a+b e^z},\n\\label{eq:inst}\n\\end{equation}\nwith certain restrictions on the complex coefficients $a,b,c,d$; note\nthat $u_{+}=-d\/b$, $u_{-}=-c\/a$ and $z_1=\\ln(-c\/d)$ (which is unique on\n\\mbox{${\\rm T}^1\\times\\re$}). So in order to satisfy the assumption $0<|u_{\\pm}|<\\infty$, we\nmust require $a,b,c,d\\not=0$. Also we must demand $a\/b\\not=c\/d$ as\notherwise the zero of $u^{\\rm inst}_{a,b,c,d}$ cancels against its\npole and we have a trivial solution with $Q=0$.\n\nTo prove that all instanton solutions are of the form (\\ref{eq:inst}) is\neasy: suppose $\\tilde{u}$ is an instanton. We can still assume\n$0<|\\tilde{u}_{\\pm}|<\\infty$, so $\\tilde{u}$ can have only\none zero of degree 1, say at $z=\\tilde{z}_1$. Now define a function\n$f$ by\n\\begin{equation}\n\\tilde{u}(z)=u^{\\rm inst}_{a,b,c,d}(z)f(z).\n\\nonumber\n\\end{equation}\nBy choosing $-c\/a=\\tilde{u}_{-}$, $-d\/b=\\tilde{u}_{+}$,\n$c\/d=-e^{\\tilde{z}_1}$ and imposing the\ninstanton requirements $\\mbox{$\\partial_{\\bar{z}}$} \\tilde{u}=0$, $Q[\\tilde{u}]=1$ and\n$\\tilde{u}(z+2\\pi i)=\\tilde{u}(z)$, that are already met by $u$, we\nsee that $f$ has to satisfy\n\\begin{equation}\n\\left\\{ \\begin{array}{l}\\mbox{$\\partial_{\\bar{z}}$} f=0 \\\\ \\lim_{{\\rm Re}(z)\\rightarrow\\pm\n\\infty}f(z)=1 \\\\ f(z+2\\pi i)=f(z) \\\\ f(z)\\not=0.\\end{array}\\right.\n\\label{eq:fisone}\n\\end{equation}\nThus, $1\/f$ is analytic and bounded on \\mbox{$l\\!\\!\\!$C}. By Liouville's theorem this\nimplies, using the second condition in\n\\refeq{fisone}, that $f(z)=1$. This completes the proof.\n\nFinally we drop the assumption $0<|u_{\\pm}|<\\infty$.\nTaking into account the boundary terms in\n\\refeq{nicetopch}, one finds that the only restriction on $(a,b,c,d)$ is\nthat $u^{\\rm inst}_{a,b,c,d}(z)$ is not constant, corresponding to\n\\begin{equation}\nad-bc\\not=0.\n\\label{eq:coefreq}\n\\end{equation}\nSo the class of instantons, \\refeq{inst}, is precisely the set of\nconformal mappings of $e^z$.\n\nWe end this part by noting that by the same line of argument each\nmulti-instanton with topological charge $Q$ can be written as\n$\\prod_{n=1}^Q u^{\\rm inst}_{a_n,b_n,c_n,d_n}$. For\n(multi-)anti-instantons one substitutes\n$z\\rightarrow\\bar{z}$.\n\n\\subsection{Physical interpretation of the moduli-space}\n\nIt is clear that the moduli-space has six real dimensions: $(a,b,c,d)\\in\n\\mbox{$l\\!\\!\\!$C}^4$ with the projective character $u^{\\rm\ninst}_{ga,gb,gc,gd}=u^{\\rm inst}_{a,b,c,d}$ for any $g\\in\\mbox{$l\\!\\!\\!$C}\\backslash\n\\{0\\}$ (while the set of coefficients not satisfying \\refeq{coefreq} has\nzero measure). A physical parametrization of this moduli-space is\n$(-c\/a,-d\/b,\\ln(-c\/d))$, corresponding to the starting point $u_{-}$ in\nthe\nvacuum valley $S^2$, the end point $u_{+}$ and a space-time translation\nparameter, which one can show to be in $1-1$~relation with the\ninstanton position (cf. \\refeq{instsol} below). The\ndisadvantage of this parametrization is that it leaves unclear what kind\nof manifold the moduli-space is; the parametrization is singular for\n$u_{-}=u_{+}$, since the requirement of \\refeq{coefreq} is not met in\nthis case. Note that this means that even for $T\\rightarrow\\infty$\nperiodic boundary conditions do not admit instanton solutions. We\nwill see below that $u_{-}\\rightarrow u_{+}$ corresponds to\n$\\rho\\rightarrow0$, where $\\rho$ is the instanton scale parameter.\n\nFor a better description of moduli-space it is necessary first to\nconsider the transformation of instantons under space-time translations\nand \\mbox{SO$(3)$}~rotations. We will see that most\ninstantons are not invariant under these symmetries which therefore give\nrise to five of the six dimensions of moduli-space. The interesting\nsixth parameter, not related to a symmetry of the action, will play the\nrole of a scale parameter, related to the geodesic distance between the\npoints $u_{\\pm}$ in the vacuum valley $S^2$.\n\n{}From \\refeq{inst} it is trivial to see that under a translation\n$z\\rightarrow z+z_0$, $(a,b,c,d)\\rightarrow(a,b e^{z_0},c,d e^{z_0})$.\nNote that \\refeq{coefreq} is therefore invariant under this shift, as\nit should be. Any continuous symmetry of the action must be present\nin the instanton moduli-space.\n\nThe effect of an \\mbox{SO$(3)$}~rotation is more difficult to derive, because\nwhile it acts linearly on \\mbox{$\\vec{n}$}, \\mbox{$\\vec{n}$}\\ and $u$ are related non-linearly\nby \\refeq{npar}. Nevertheless, one can show\nthat $(a,b,c,d)$ again transform linearly. After some effort one sees\nthat the rotation\n\\begin{equation}\n\\mbox{$\\vec{n}(x)$}\\rightarrow R\\mbox{$\\vec{n}(x)$},\\ \\ \\ R=e^{\\alpha_a L^a},\\ \\ \\ {L^a}_{ij}=\n-\\varepsilon_{aij},\\ \\ \\ (\\alpha_a\\in\\mbox{I$\\!$R})\n\\end{equation}\ninduces\n\\begin{equation}\n\\mbox{\\scriptsize $\\left(\\!\\!\\begin{array}{c}a\\\\ b\\\\ c\\\\ d\\end{array}\n\\!\\!\\right)$}\\rightarrow\n\\tilde{R}\\mbox{\\scriptsize $\\left(\\!\\!\\begin{array}{c}a\\\\ b\\\\ c\\\\ d\n\\end{array}\\!\\!\\right)$},\\ \\ \\\n\\tilde{R}=e^{\\alpha_a \\tilde{L}^a},\\ \\ \\ \\tilde{L}^a=-\\frac{i}{2}\\sigma^a\n\\otimes{\\bf 1},\\ \\ \\ {\\rm (i.e.\\ } \\tilde{L}^1= -\\frac{i}{2}\n\\mbox{\\scriptsize $\\left(\\!\\!\n\\begin{array}{cccc}0&0&1&0\\\\ 0&0&0&1\\\\ 1&0&0&0\\\\\n0&1&0&0\\end{array}\\!\\!\\right)$} {\\rm\\ etc.)}\n\\label{eq:rot}\n\\end{equation}\nwhere $\\sigma^a$ are the Pauli-matrices. Since $\\pm(a,b,c,d)$ are\nidentified, this is a representation of \\mbox{SO$(3)$}. Notice that only\n$(a,c)$ and $(b,d)$ mix. Hence both $|a|^2+|c|^2$ and\n$|b|^2+|d|^2$ are rotationally invariant, as is \\refeq{coefreq}.\n\nUsing the projective character of moduli-space, and an \\mbox{SO$(3)$}~rotation\n$\\tilde{R}$, it is always possible to bring\n$u^{\\rm inst}_{a,b,c,d}$ ($ad\\not= bc$) to the form\n$u^{\\rm inst}_{-1,0,\\tilde{c},\\tilde{d}}$ with $\\tilde{c}\\in\\mbox{I$\\!$R}$,\n$\\tilde{c}\\geq0$, $\\tilde{d}\\in\\mbox{$l\\!\\!\\!$C}\\backslash\\{0\\}$. If $\\tilde{c}>0$,\nthis fixes $\\tilde{R}$ completely. If\n$\\tilde{c}=0$, then $\\tilde{R}$ is only unique up to a factor\n$e^{\\alpha_3\\tilde{L}^3}$. This can be fixed by requiring\n$\\tilde{d}=|\\tilde{d}|$. Therefore, we can parametrize\n$u^{\\rm inst}_{a,b,c,d}$ uniquely by $\\tilde{R}$, $|\\tilde{d}|$ and\n$\\tilde{c}e^{i\\phi}$ ($\\tilde{c}\\geq0$). Here $\\phi={\\rm\nArg}(\\tilde{d})$ ($\\phi\\in[0,2\\pi)$) if $\\tilde{c}>0$ and $\\phi$ is\nundetermined if $\\tilde{c}=0$. We conclude that $(\\tilde{c},\\phi)$ can\nbe viewed as polar coordinates on $\\mbox{I$\\!$R}^2$. Furthermore, $|\\tilde{d}|\n>0$ due to \\refeq{coefreq}, so $\\ln|\\tilde{d}|\\in\\mbox{I$\\!$R}$. Thus the instanton\nmoduli space is isomorphic to $\\mbox{SO$(3)$}\\times\\mbox{I$\\!$R}^2\\times\\mbox{I$\\!$R}$. The discrete\nsymmetry transformations $\\mbox{$\\vec{n}$}\\rightarrow-\\mbox{$\\vec{n}$}$\n(in stereographic coordinates $u\\rightarrow-1\/\\bar{u}$),\n$x_2\\rightarrow-x_2$ or $x_1\\rightarrow-x_1$ make an instanton solution\nanti-analytic, and therefore are transformations from instanton\nmoduli-space into anti-instanton moduli-space. This should be compared\nto the sphaleron moduli space which is invariant under such discrete\ntransformations.\n\nNote that $\\tilde{d} e^z=e^{z+\\ln|\\tilde{d}|+i\\phi}$. So after an\n\\mbox{SO$(3)$}~rotation and a translation in space-time \\mbox{${\\rm T}^1\\times\\re$}, any instanton\nsolution can be brought to the form\n\\begin{equation}\nu^{\\rm inst}_c(z)\\equiv c+e^{z+\\ln(\\sqrt{1+c^2})+i\\pi}.\\ \\ \\ (c\\geq0)\n\\label{eq:instsol}\n\\end{equation}\nThe factor $e^{\\ln(\\sqrt{1+c^2})+i\\pi}=-\\sqrt{1+c^2}$ centers the\ninstanton around $z=0$ (see below). From the above equation it\nfollows that $\\lim_{x_1\\rightarrow\\infty}|u^{\\rm\ninst}_c(z)|=\\infty$ and $\\lim_{x_1\\rightarrow-\\infty}u^{\\rm\ninst}_c(z)=c$, hence\n(using \\refeq{npar}) this instanton `tunnels' from\n$(\\sin\\vartheta_{-},0, \\cos\\vartheta_{-})$ to $(0,0,1)$, with\n$\\cot\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2}$}\\vartheta_{-}=c$. Note that\n$\\theta_{-}$ is the geodesic distance between these vacua.\n\nLet us determine the instanton size $\\rho$ as function of\n$c=2{\\rm arccot}\\vartheta_{-}$. Substituting \\refeq{instsol} into the\nLagrangian density, which for an instanton in stereographic coordinates\nis $4\\pi$ times the integrand in \\refeq{utopch} (see\neqs.(\\ref{eq:niceact},\\ref{eq:insteq})), one obtains\n\\begin{equation}\n\\mbox{$\\cal L$}[u^{\\rm inst}_c](x_1,x_2)=4\\frac{|\\mbox{$\\partial_z$} u^{\\rm inst}_c|^2}{(1+|u^{\\rm\ninst}_c|^2)^2}=\\frac{1}{(\\sqrt{1+c^2}\\cosh x_1-c\\cos x_2)^2}.\n\\label{eq:instlagr}\n\\end{equation}\nThis function is plotted in fig.\\ref{fig:lagr} for different values of\n$c$. From the formula it is clear that $u^{\\rm inst}_c$ is\ncentered at $z=0$. Now consider the potential along the instanton path,\n\\begin{equation}\nV[u^{\\rm inst}_c](x_1)=\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2}$}\\int_0^{2\\pi}\\!\\!\ndx_2\\,\\,\\mbox{$\\cal L$}[u^{\\rm inst}_c](x_1,x_2).\n\\end{equation}\nThe factor $\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2}$}$ comes from the fact that the kinetic energy,\n$\\raisebox{.15ex}{\\scriptsize$\\frac{1}{2}$}\\int_{{\\rm T}^1}\\!dx_2\\, g_{ij}(v)\\partial_1v^i\\partial_1v^j$,\nis equal to the potential energy, \\refeq{pot} (this `self-duality'\nfollows from \\refeq{insteq}). We see that the potential is maximal at\n$x_1=0$ where it satisfies\n\\begin{equation}\nV^{\\max}_c\\equiv V[u^{\\rm inst}_c](0)=\\pi\\sqrt{1+c^2}.\n\\label{eq:insten}\n\\end{equation}\nSince all instantons have equal action, it is natural to define the\ninstanton size\n\\begin{equation}\n\\rho(c)\\equiv\\frac{\\pi}{V^{\\max}_c}=\\frac{1}{\\sqrt{1+c^2}}.\n\\label{eq:instrho}\n\\end{equation}\nNote however that for small $c$ there are two different scales; the\nshape of $\\mbox{$\\cal L$}[u^{\\rm inst}_c](x_1,x_2)$ is anisotropic (see\nfig.\\ref{fig:lagr}). Only for $c\\gg1$ and $x_1^2+x_2^2\\ll1$ the\nboundary effects disappear and $\\mbox{$\\cal L$}[u^{\\rm inst}_c](x_1,x_2)\\approx\n\\frac{4c^2}{(1+c^2(x_1^2+x_2^2))^2}$ becomes rotationally invariant.\n\nThe relationship between instantons and sphalerons is now also clear.\n{}From eqs.(\\ref{eq:insten},\\ref{eq:staten}) we see that only\n$u^{\\rm inst}_{c=0}$ can go through a sphaleron at the time of maximal\n$V[u^{\\rm inst}_c]$ (i.e.\\ $x_1=0$). Indeed this does happen, since\n\\refeq{instsol} gives $u^{\\rm inst}_{c=0}(x_1=0,x_2)=-e^{ix_2}$,\nwhich up to a rotation is just the sphaleron solution $\\mbox{$\\vec{n}$}_1$,\n\\refeq{statsol},\nin stereographic coordinates. As the instanton is a self-dual solution\nof the equations of motion, it has to follow streamlines of the energy\nfunctional. This explains why\n$\\partial_1 u^{\\rm inst}_{c=0}|_{x_1=0}=-\\exp(ix_2)$\ncorresponds to the unstable mode of the sphaleron solution.\n\nFinally note that\n$u^{\\rm inst}_{c=0}$, unlike $u^{\\rm inst}_{c>0}$, is a point in\ninstanton moduli-space that is symmetric under a joint\n${\\rm SO}(2)$~rotation $e^{\\alpha_{3}\\tilde{L}^3}$ and a spatial\ntranslation $x_2\\rightarrow x_2-\\alpha_3$. The sphaleron has of\ncourse the same symmetry, as mentioned in section~\\ref{sec:stat}.\nAlso a natural correspondence between sphaleron moduli-space \\mbox{SO$(3)$}\\\nand the subspace of widest instantons emerges. From the paragraph\nabove \\refeq{instsol} it follows that the latter is isomorphic to\n$\\mbox{SO$(3)$}\\times\\mbox{I$\\!$R}$, $\\mbox{I$\\!$R}$ corresponding to time translations.\n\\begin{figure}[t]\n\\epsfxsize=\\textwidth\n\\epsffile{fig.ps}\n\\caption{The Lagrangian densities of three instantons,\n\\protect\\refeq{instsol},\nwith from left to right $c=0,\\:0.25,\\:0.5$.}\n\\label{fig:lagr}\n\\end{figure}\n\n\\section{Conclusions}\n\\label{sec:concl}\n\nWe have proven that the \\mbox{O$(3)\\,\\sigma$-model}\\ on a space-time \\mbox{${\\rm T}^1\\times\\re$}\\ admits instantons.\nThe moduli-space is 6-dimensional ($\\mbox{SO$(3)$}\\times\\mbox{I$\\!$R}^2\\times\\mbox{I$\\!$R}$):\n3 parameters for \\mbox{SO$(3)$}, 2 for scaling and spatial translations, 1 for\ntime translations. It is possible to `tunnel' between any different\npoints $\\mbox{$\\vec{n}$}_{\\pm}$ in the vacuum valley ($S^2$),\nbut this gives no independent parameters. Three parameters describing\n$\\mbox{$\\vec{n}$}_{\\pm}$ can be removed by an \\mbox{SO$(3)$}~rotation, while\nthe fourth (the geodesic distance between the points) depends\nuniquely on the scale parameter $\\rho$. Instantons with maximum scale, as\nset by the extent of spatial ${\\rm T}^1$, satisfy $\\mbox{$\\vec{n}$}_{+}=-\\mbox{$\\vec{n}$}_{-}$. These,\nand only these, instantons go through sphalerons. None of the exotic\npossibilities sketched in the introduction take place in this model.\nOn the other hand,\n$\\rho\\rightarrow0$ corresponds to $\\mbox{$\\vec{n}$}_{+}\\rightarrow\\mbox{$\\vec{n}$}_{-}$. Exact\nequality cannot be reached. We think this peculiar size-dependence\nis important for improving on instanton gas calculations as\nin~\\cite{BeLu}. By doing a proper convolution with the vacuum wave\nfunction at $t\\rightarrow\\pm\\infty$ it might be possible to remove the\nwell-known UV divergence for $\\rho\\rightarrow0$, which was also\nencountered in recent numerical studies~\\cite{MiSp}.\n\nOur results do not admit a straightforward generalization to\n\\mbox{SU$(2)$}~gauge theory on a space-time \\mbox{${\\rm T}^3\\times\\re$}. In that model\nthe vacuum valley is isomorphic to \\mbox{${\\rm T}^3$}~\\cite{BaKo},\nwhich can be parametrized\nby three Polyakov lines $P_i$. Instantons again must have endpoints,\n$P_i^{\\pm}$, in the vacuum valley. For the special case\n$P_i^{+}=-P_i^{-}$ it has already been known for some time\nthat an 8-dimensional moduli-space exists. This anti-periodic\nsituation corresponds to time-like twist~\\cite{Ho}, which has been\nanalyzed~\\cite{BrMaTo} on any space-time $\\mbox{$[-\\half T, \\half T]$}\\times\\mbox{${\\rm T}^3$}$. For\n$T\\rightarrow\\infty$ it is very likely~\\cite{PeGoSnBa} that the\nmoduli-space includes a scale parameter. This is not the case\nfor the \\mbox{O$(3)\\,\\sigma$-model}\\ on a space-time \\mbox{${\\rm T}^1\\times\\re$}. We have just proven that\nanti-periodic boundary conditions, $\\mbox{$\\vec{n}$}_{+}=-\\mbox{$\\vec{n}$}_{-}$, fix the\ninstanton size\\footnote{We also note that no instantons exist\nwith anti-periodic boundary conditions in finite time $T$,\n\\mbox{$\\mbox{$\\vec{n}$}(x_1+T,x_2)=-\\mbox{$\\vec{n}$}(x_1,x_2)$}\n(while the winding number $Q$ is still a well-defined integer object).\nThe reason is simple: in stereographic coordinates anti-pbc read\n$u(z+T)=-1\/\\bar{u}(z)$, which is incompatible with the instanton\nequation $\\mbox{$\\partial_{\\bar{z}}$} u=0$.}. It would be nice to understand the cause of\nsuch different behavior\nbetween two models that are so similar in other respects. This might\nbe a starting point for finding new instanton parameters in \\mbox{SU$(2)$}~gauge\ntheory on \\mbox{${\\rm T}^3\\times\\re$}, by relaxing the condition $P_i^{+}=-P_i^{-}$.\n\n\\section{Acknowledgments}\n\nI am grateful to Pierre van Baal for fruitful discussions and for\ncarefully reading this manuscript. Also I thank Pieter Rijken for\nexpanding my knowledge of analytic functions, and Margarita\nGarc\\'{\\i}a P\\'{e}rez for discussions on various sphaleron-related\ntopics.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\\label{sec:1}\nThe combined MAXIMA-1 \\cite{MAXIMA-1} ,  BOOMERANG \\cite{BOOMERANG} , \nDASI \\cite{DASI} ,  COBE\/DMR Cosmic Microwave Background (CMB)\nobservations \\cite{COBE} ,  the recent WMAP data \\cite{SPERGEL} and\nSDSS\n \\cite{SDSS} imply that the\nUniverse is flat \\cite{flat01} and that most of the matter in\nthe Universe is dark, i.e. exotic.These results have been confirmed and improved\nby the recent WMAP data \\cite{WMAP06}. The deduced cosmological expansion is\nconsistent with  the luminosity distance as a function of redshift of distant supernovae \n\\cite{supernova1,supernova2,supernova3}.\nAccording to the scenario favored by the observations \nthere are various contributions to the energy content of our Universe.\nThe most accessible energy component is baryonic matter, which accounts for\n$\\sim 5\\%$ of the total energy density. A component that has\nnot been directly observed is cold dark matter (CDM)): a pressureless fluid that is\nresponsible for the growth of cosmological perturbations through\ngravitational instability. Its contribution to the total energy density is\nestimated at \n$\\sim 25\\%$. The dark matter is expected to become more abundant \nin extensive halos, that\nstretch up to 100--200 kpc from the center of galaxies.\nThe component with the biggest contribution to the energy density has\nan equation of state similar to that of a cosmological constant and is characterized as dark energy. \nThe ratio $w=p\/\\rho$ is negative and close to $-1$. \nThis component is responsible for $\\sim 70\\%$ of the total energy density \nand induces\nthe observed acceleration of the Universe \\cite{supernova1}$^-$\\cite{supernova3} . \nThe total energy density of our Universe \nis believed to take the critical value consistent with spatial flatness.\nAdditional indirect information about the existence of dark matter\ncomes from  the rotational curves \\cite{Jung} . The rotational velocity of an object increases so long\nis surrounded by matter. Once outside matter the velocity of rotation drops as the square root  of the \ndistance. Such observations are not possible in our own galaxy. The observations of other galaxies, \nsimilar to our own, indicate that the rotational velocities of objects outside the luminous matter\ndo not drop. So there must be a halo of dark matter out there.\n\nSince the non exotic component cannot exceed $40\\%$ of the CDM\n~\\cite {Benne} , there is room for exotic WIMP's (Weakly\nInteracting Massive Particles).\\\\\n  In fact the DAMA experiment ~\\cite {BERNA2} has claimed the observation of one signal in direct\ndetection of a WIMP, which with better statistics has subsequently\nbeen interpreted as a modulation signal \\cite{BERNA1} . These  data,\nhowever, if they are due to the coherent process, are not\nconsistent with other recent experiments, see e.g. EDELWEISS and\nCDMS \\cite{EDELWEISS} . It could still be interpreted as due to the\nspin cross section, but with a new interpretation of the extracted\nnucleon cross section. \n\nSince the WIMP  is expected to be very massive, $m_{\\chi} \\geq 30 GeV$, and\nextremely non relativistic with average kinetic energy $T \\leq 100 KeV$,\nit can be directly detected mainly via the recoiling\nof a nucleus  in the WIMP-nucleus elastic scattering.\n\nThe above developments are in line with particle physics considerations.\n\\begin{enumerate} \n\\item Dark matter in supersymmetric theories\\\\\nThe lightest supersymmetric particle (LSP) or neutralino\n is the most natural WIMP candidate. In the most favored scenarios the\nLSP can be simply described as a Majorana fermion, a linear \ncombination of the neutral components of the gauginos and Higgsinos\n\\cite{Jung}$^-$\\cite{Hab-Ka} . \n\n In order to compute the event rate one needs\n an effective Lagrangian at the elementary particle \n(quark) level obtained in the framework of supersymmetry \n~\\cite{Jung,ref2,Hab-Ka} .\n One starts with   \nrepresentative input in the restricted SUSY parameter space as described in\nthe literature, e.g. Ellis {\\it et al} \\cite{EOSS04} , Bottino {\\it et al} , \nKane {\\it et al} , Castano {\\it et al} and Arnowitt {\\it et al} \\cite{ref2} as well as elsewhere\n\\cite{GOODWIT}$^-$\\cite{UK01} .\nWe will not, however, elaborate on how one gets the needed parameters from\nsupersymmetry. \n\nEven though the SUSY WIMPs have been well studied, for tor the reader's convenience we will give a description  in sec. \\ref{sec:diagrams} of the basic \nSUSY ingredients needed to calculate LSP-nucleus scattering\n cross section.\n\n\\item  Kaluza-Klein (K-K) WIMPs. \\\\\nThese arise in  extensions of the standard model with compact extra dimensions. In\nsuch models  a tower of massive particles appear as Kaluza-Klein\nexcitations.\nIn this scheme the ordinary particles are associated with the zero\nmodes and are assigned K-K parity $+1$.\nIn models with Universal Extra Dimensions one can have\ncosmologically stable particles in the excited modes because of a\ndiscreet symmetry yielding  K-K parity $-1$ (see previous work \\cite{ST02a,ST02b,CFM02} as well as\nthe recent review by Servant\n\\cite{SERVANT}).\n \\\\The kinematics involved is similar to\nthat of the neutralino, leading to cross sections which are\nproportional $\\mu^2_r$, $\\mu_r$ being the WIMP-nucleus reduced\nmass. Furthermore the\n nuclear physics input\n  is independent of the WIMP mass, since for heavy WIMP $mu_r\\simeq Am_p$.\n   There are appear two differences compared to the\n  neutralino, though,  both related to its larger mass.\n  \\\\i) First the density\n  (number of particles per unit volume) of a WIMP\n falls inversely proportional to its mass. Thus,\n  if the WIMP's considered are much heavier than the nuclear\n targets, the corresponding event rate takes the form:\n  \\beq\n R(m_{WIMP})=R(A)\\frac{A \\mbox{ GeV\n}}{m_{WIMP}}\n \\label{eq:rate}\n \\eeq\n where $R(A)$ are the rates extracted from experiment up to WIMP\n masses of the order of the mass of the target.\n\\\\ii) Second the average WIMP energy is now  higher. In fact one\nfinds that $\\langle T_{WIMP}\\rangle =\\frac{3}{4}m_{WIMP}\n\\upsilon^2_0\\simeq 40 \\left ({m_{WIMP}}\/({100 \\mbox{\nGeV)}}\\right )$keV ($\\upsilon_0\\simeq 2.2\\times 10^5$km\/s).\n  Thus for a K-K WIMP with mass $1$ TeV, the average\nWIMP energy is $0.4$ MeV. Hence, due to the high velocity tail of\nthe velocity distribution,  one expects {\\bf an energy transfer to\nthe nucleus  in the MeV region. Thus many nuclear\n targets can now be excited by the WIMP-nucleus interaction and the de-excitation photons\n can be detected.}\n\n \n \\end{enumerate}\nIn addition to the particle model one needs the following  ingredients:\n\\begin{itemize}\n\\item A procedure in going from the quark to the nucleon level, i.e. a quark \nmodel for the nucleon. The results depend crucially on the content of the\nnucleon in quarks other than u and d. This is particularly true for the scalar\ncouplings as well as the isoscalar axial coupling ~\\cite{Dree}$^-$\\cite{Chen} . Such topics will be discussed in sec.\n\\ref{sec:nuc}.\n\\item computation of  the relevant nuclear matrix elements~\\cite{Ress}$^-$\\cite{SUHONEN03}\nusing as reliable as possible many body nuclear wave functions.\nBy putting as accurate nuclear physics input as possible, \none will be able to constrain the SUSY parameters as much as possible.\nThe situation is a bit simpler in the case of the scalar coupling, in which\ncase one only needs the nuclear form factor.\n\\item  Convolution with the LSP velocity Distribution.\nTo this end we will consider here  Maxwell-Boltzmann \\cite {Jung} (MB) velocity distributions, with an upper velocity cut off put in by hand. The characteristic velocity of the M-B distribution can be increased by\na factor $n$ ($\\upsilon_0\\rightarrow n \\upsilon_0,~n\\ge1 $)by considering the interaction of dark matter and dark energy \\cite{TETRVER06}.\n\nOther distributions are possible, such as\n  non symmetric ones,  like those \nof Drukier \\cite {Druk} and Green \\cite{GREEN02} , or non isothermal ones, e.g. those arising from late in-fall of   \ndark matter into our galaxy, like  Sikivie's caustic rings \\cite {SIKIVIE} . In any event in a proper treatment the velocity distribution ought to be consistent with the dark matter density as, e.g., in the context of the Eddington theory \\cite{OWVER} .\n\\end{itemize}\n\n\n\n Since the expected rates are extremely low or even undetectable\nwith present techniques, one would like to exploit the characteristic\nsignatures provided by the reaction. Such are: \n\\begin{enumerate}\n\\item The modulation\n effect, i.e the dependence of the event rate on the velocity of\nthe Earth \n\\item The directional event rate, which depends on the\n velocity of the sun around the galaxy as well as the the velocity\nof the Earth. \nhas recently begun to appear feasible by the planned experiments\n\\cite {UKDMC,DRIFT} .\n\\item Detection of signals other than nuclear recoils, such as\n\\begin{itemize}\n\\item Detection of $\\gamma$ rays following nuclear de-excitation, whenever possible \\cite{eji93,VQS04} .\nThis seems to become feasible for heavy WIMPs especially in connection with modified M-B distributions due to \nthe coupling of dark matter and dark energy ($\\langle T_{WIMP} \\rangle \\simeq n^2  40 \\left ({m_{WIMP}}\/({100 \\mbox{\nGeV})}\\right ),~n\\ge 1$keV)\n\\item Detection of ionization electrons produced directly in the LSP-nucleus collisions \\cite{VE05,MVE05} . \n\\item Observations of hard X-rays produced\\cite{EMV05} , when the inner shell electron holes produced as above are filled.\n\\end{itemize}\n\\end{enumerate}\n\n In all calculations we will, of course, include an appropriate \nnuclear form factor and take into account\nthe influence on the rates of the detector energy cut off.\nWe will present our results a function of the\nLSP mass, $m_{\\chi}$, in a way\nwhich can be easily understood by the experimentalists.\n\n\n\\section{The Feynman Diagrams Entering the Direct Detection of WIMPS.}\n\\label{sec:diagrams}\n\\subsection{The Feynman Diagrams involving the neutralino}\n\\label{sec:FEYLSP}\n The neutralino is perhaps the most viable WIMP candidate and has been extensively \nstudied (see, e.g., our recent review \\cite{JDV06}). Here we will give a very brief \nsummary of the most important aspects entering the direct neutralino searches.\n In currently favorable supergravity models the LSP is a linear\ncombination~\\cite{Jung} of the neutral four fermions \n${\\tilde B}, {\\tilde W}_3, {\\tilde H}_1$ and ${\\tilde H}_2$ \nwhich are the supersymmetric partners of the gauge bosons $B_\\mu$ and\n$W^3_\\mu$ and the Higgs scalars\n$H_1$ and $H_2$. Admixtures of s-neutrinos are expected to be negligible.\nThe relevant Feynman diagrams involve Z-exchange, s-quark exchange and Higgs \nexchange.\n\\subsubsection{The Z-exchange contribution.}\n\\label{sec:Z-exc}\nThe relevant Feynman diagram is shown in Fig. \\ref{LSPZH}. It does not lead to coherence, since $\\bar{\\Psi}\\gamma_{\\lambda}\\Psi=0$ for a Majorana fermion like the neutralino (the Majorana fermions do not\nhave electromagnetic properties). The coupling $\\bar{\\Psi}\\gamma_{\\lambda}\\gamma_5\\Psi$ yields negligible contribution for a non relativistic particle in the case of the spin independent cross section \\cite{JDV96}. It may be important in the case of the spin contribution, which arises\nfrom the axial current).\n\\begin{figure}\n\\psfig{file=zvec.ps,width=2.0in}\n\\psfig{file=higgs.ps,width=2.0in}\n\\caption{The LSP-quark interaction mediated by Z and Higgs exchange.}\n\\label{LSPZH}\n\\end{figure}\n\\subsubsection{The $s$-quark Mediated Interaction }\n\\label{sec:sq-exc}\nThe other interesting possibility arises from the other two components of\n$\\chi_1$, namely ${\\tilde B}$ and ${\\tilde W}_3$. Their corresponding\ncouplings to $s$-quarks (see Fig. \\ref{LSPSQVS} ) can be read from the appendix C4 of Ref.~\\cite{Hab-Ka} and our earlier review \\cite{JDV06}.\n\\begin{figure}\n\\begin{center}\n\\psfig{file=sqvec.ps,width=2.0in}\n\\psfig{file=sqsca.ps,width=2.0in}\n\\end{center}\n\\caption{The LSP-quark interaction mediated by s-quark exchange. Normally it yields V-A interaction \nwhich does not lead to coherence at the nuclear level. If, however, the isodoublet\n s-quark is admixed with isosinglet one to yield a scalar interaction at the quark level.}\n\\label{LSPSQVS}\n\\end{figure}\nNormally this contribution yields vector like contribution, i.e it does not lead to coherence. If,\nhowever, there exists mixing between the s-quarks with  isospin $1\/2$ ($\\tilde{q}_L$) and the isospin 0 ($\\tilde{q}_R$), the s-quark exchange \nmay lead to a scalar interaction at the quark level and hence to coherence over all nucleons\nat the nuclear level \\cite{JDV06}.\n\\subsubsection{The Intermediate Higgs Contribution}\n\\label{sec:Higgs-exc}\nThe most important contribution to coherent scattering can be achieved via the intermediate Higgs\nparticles which survive as physical particles. In supersymmetry there exist two such physical\nHiggs particles, one light $h$ with a mass $m_h\\leq$120 GeV and one heavy $H$ with mass $m_H$, which\n is much larger. The relevant interaction can arise out of the\nHiggs-Higgsino-gaugino interaction \\cite{JDV06} leading to a Feynman diagram shown in Fig.\n\\ref{LSPZH}. \n\nIn the case of the scalar interaction the resulting amplitude is proportional to the quark mass.\n \\subsection{The Feynman Diagrams involving the K-K WIMPs}\n\\label{sec:FEYKK}\n\n \\subsubsection{The Kaluza-Klein Boson as a dark matter candidate}\n \\label{KK}\n We will assume that the lightest exotic particle, which can serve as a dark matter candidate, is a gauge boson $B^{1}$\n having the same quantum numbers and couplings with the standard model gauge boson $B$, except that it has K-K parity\n $-1$. Thus its couplings must involve another negative K-K parity particle. In this work we will assume that such  a particle can be one of\n  the K-K quarks, partners of the ordinary quarks, but much heavier  \\cite{ST02a,ST02b,CFM02} .\n \\begin{itemize}\n\\item Intermediate K-K quarks.\\\\\nthis case the relevant\nFeynman diagrams are\n shown in fig. \\ref{fig:kkq}.\n \\begin{figure}\n\\psfig{file=kkqa.ps,width=2.2in}\n\\psfig{file=kkqb.ps,width=2.2in}\n \\caption{K-K quarks mediating the interaction of K-K gauge boson $B^{1}$ with quarks at tree\nlevel.}\n \\label{fig:kkq}\n  \\end{figure}\n\\\\The amplitude at the nucleon level can be written as:\n \\beq {\\cal M}_{coh}= \\Lambda(\\mbox{\\boldmath\n$\\epsilon^{*'}$}.\\mbox{\\boldmath $\\epsilon$})N\\left [\n\\frac{11+12\\tau_3}{54} \\frac{m_p\nm_W}{(m_{B^{(1)}})^2} f_1(\\Delta )+\\frac{1+\\tau_3}{3} \\frac{m_W}{\nm_{B^{(1)}}} f_2(\\Delta ) \\right ] N \\eeq\n$$\\Lambda=i 4 \\sqrt{2} G_F m_W \\tan^2{\\theta_W\n},f_1(\\Delta )=\\frac{1+\\Delta +\\Delta ^2 \/2}{\\Delta ^2(1+\\Delta\n\/2)^2},$$\n$$ f_2 (\\Delta )=\\frac{1+\\Delta }{\\Delta (1+\\Delta \/2)}~,\n~\\Delta =\\frac{m_{q^{(1)}}}{m_{B^{(1)}}}-1$$ We see that the\namplitude is very sensitive to the parameter $\\Delta $ (\"resonance\neffect\").\n\nIn going from the quark to the nucleon level the best procedure is\nto replace the quark energy by the constituent quark mass $\\simeq\n1\/3m_p$, as opposed to adopting  \\cite{ST02a,ST02b,CFM02} a procedure related to\nthe current mass encountered in the neutralino case \\cite{JDV06}.\n\n\n\n\nIn the case of the spin contribution we find at the nucleon level\nthat:\n\\barr {\\cal M}_{spin}&=& -i 4 \\sqrt{2} G_F m_W \\tan^2{\\theta_W\n}\\frac{1}{3} \\frac{m_p m_W}{(m_{B^{(1)}})^2} f_1(\\Delta )\ni(\\mbox{\\boldmath $\\epsilon^{*'}$}\\times \\mbox{\\boldmath\n$\\epsilon$}).\n\\nonumber\\\\\n&&\\left [ N\\mbox{\\boldmath $\\sigma$} (g_0+g_1 \\tau_3) N\n\\right ] \\earr\n$$g_0=\\frac{17}{18}\\Delta u+\\frac{5}{18} \\Delta d+\\frac{5}{18} \\Delta s~,\n~g_1=\\frac{17}{18}\\Delta u-\\frac{5}{18} \\Delta d$$\nfor the isoscalar and isovector quantities \\cite{JDV06}. The\nquantities $\\Delta_q$ are given by \\cite{JDV06}\n$$\\Delta u=0.78\\pm 0.02~,~\\Delta d=-0.48\\pm 0.02~,~\\Delta s=-0.15\\pm 0.02$$\nWe thus find $g_0=0.26~,~g_1=0.41\\Rightarrow\na_p=0.67~,~a_n=-0.15$.\n\\item Intermediate Higgs Scalars.\\\\\nThe corresponding\nFeynman diagram is shown in Fig. \\ref{fig:kkhz}\n   \\begin{figure}[!ht]\n\\psfig{file=kkh.eps,width=2.2in}\n\\psfig{file=kknu.eps,width=2.2in}\n \\caption{The Higgs H mediating interaction of K-K gauge boson $B^{1}$ with quarks at tree\nlevel (on the left). The Z-boson mediating the interaction of K-K\nneutrino $\\nu^{(1)}$ with quarks at tree level (on the right).}\n \\label{fig:kkhz}\n  \\end{figure}\nThe relevant amplitude is given by:\n  \\beq\n {\\cal M}_N(h)= -i~4 \\sqrt{2}G_F m^2_W \\tan^2{\\theta_W}~\\left [\\frac{1}{4}\\frac{m_p}{m^2_h}\n \\left (-\\mbox{\\boldmath\n$\\epsilon^{*'}$}.\\mbox{\\boldmath $\\epsilon$} \\right ) \\prec\nN|N\\succ  \\sum_q f_q\\right ]\n  \\eeq\n   In going from the quark to the nucleon level we follow a procedure analogous to that\n of the of the neutralino,\n  i.e.\n  $\\prec  N |m_q q \\bar{q}|N  \\succ  \\Rightarrow f_q m_p$\n\\end{itemize}\n  \\subsubsection{K-K neutrinos as dark matter candidates}\n  The other possibility is the dark matter candidate to be a heavy K-K neutrino.\n   We will distinguish the following cases:\n\\begin{itemize}\n\\item Process mediated by Z-exchange.\\\\\n\n The amplitude associated with the diagram of Fig. \\ref{fig:kkhz} becomes:\n\n\n\n  \\beq\n\n{\\cal M}_{\\nu^{(1)}}=-\\frac{1}{2 \\sqrt{2}}G_FJ^{\\lambda}(\\nu^{(1)}) J_{\\lambda}(NNZ)\n \\eeq\n with $J_{\\lambda}(NNZ)$ the standard nucleon neutral current and\n$$J_{\\lambda}(\\nu^{(1)})= \\bar{\\nu}^{(1)}\\gamma _{\\lambda\n}\\gamma_5\\nu^{(1)}~,~J_{\\lambda}(\\nu^{(1)})= \\bar{\\nu}^{(1)}\\gamma\n_{\\lambda }(1-\\gamma_5)\\nu^{(1)}$$\n for Majorana and Dirac neutrinos respectively.\n\\item Process mediated by right handed currents  via Z'-boson exchange.\\\\\n The process is similar to that exhibited by Fig. \\ref{fig:kkhz}, except that instead of Z we encounter Z', which is much\nheavier.  Assuming that the couplings of the $Z'$ are similar\nto those of $Z$, the above results apply except that now the\namplitudes are retarded by the multiplicative factor\n$\\kappa=m^2_{Z}\/m^2_{Z'}$\n\\item Process mediated by Higgs exchange.\\\\\n In this case in Fig \\ref{fig:kkhz} the Z is replaced by the Higgs particle.\n\n Proceeding as above we find that the amplitude at the nucleon level is:\n  \\beq\n {\\cal M}_{\\nu^{(1)}}(h)=\n-2 \\sqrt{2}G_F \\frac{m_p m_{\\nu^{(1)}}}{m_h^2}\n\\bar{\\nu}^{(1)}~\\nu^{(1)} \\prec N|N \\succ \\sum_q f_q\n \\eeq\n  In the evaluation of the parameters\n$f_q$ one encounters both theoretical and experimental errors.\n\\end{itemize}\n\\section{Other non SUSY Models}\n\\label{Zmodel}\n We should mention that there exist extensions of the standard model not motivated by symmetry. Such are:\n\\begin{itemize}\n\\item Models which introduce extra higgs particles and impose a discrete symmetry which leads to a \"parity\" \na la R-parity or K-K parity \\cite{MA06}.\n\\item Extensions of the standard model, which do not require a parity, but introduce high weak isospin\nmultiplets \\cite{CFA06} with Y=0. So the WIMP-nucleus interaction via Z-exchange at tree level is absent and the dominant contribution to the WIMP-nucleus scattering occurs at the one loop level.\n\\item Another interesting extension of the standard model is in the direction of tecnicolor \\cite{GKS06}. In this case the WIMP is\nthe neutral LTP (lightest neutral technibaryon).\n This is scalar particle, which couples to the quarks via derivative coupling\nthrough Z-exchange.\n\\end{itemize}\n\\section{Going from the Quark to the Nucleon Level} \n\\label{sec:nuc}\n In going from the quark to the nucleon level one has to be a bit more \ncareful in handling the quarks other than $u$ and $d$. This is especially true in the\ncase of the scalar interaction, since in this case the coupling \nof the WIMP to the quarks\nis proportional to their mass~\\cite{JDV06} .\nThus one has to consider in the nucleon not only\nsea quarks ($u {\\bar u}, d {\\bar d}$ and $s {\\bar s}$) but the heavier\nquarks as well due to QCD effects ~\\cite{Dree00} . \nThis way one obtains the scalar Higgs-nucleon\ncoupling by using  effective parameters $f_q$ defined as follows:\n\\beq\n\\Big<N| m_q \\bar{q}q|N \\Big> = f_q m_N\n\\label{fofq}\n\\eeq\nwhere $m_N$ is the nucleon mass. \n The parameters $f_q,~q=u,d,s$ can be obtained by chiral\nsymmetry breaking \nterms in relation to phase shift and dispersion analysis (for a recent review see\n\\cite{JDV06}). We like to emphasize here that since the current masses of the u and d \nquarks are small, the heavier quarks tend to dominate even though the probability of\nfinding them in the nucleus is quite small. In fact the s quark contribution may become dominant,\ne.g. allowed by the above analysis is the choice:\n$$f_d=0.046,f_u=0.025,f_s=0.400,f_c=0.050,f_b=0.055,f_t=0.095$$\n\n  The isoscalar and the isovector axial current in the case of K-K theories has already been discussed\n  above. In the case of the neutralino these\ncouplings at the nucleon level, $ f^0_A$, $f^1_A$, are obtained from the corresponding ones given by the SUSY\n models at the quark level, $ f^0_A(q)$, $f^1_A(q)$, via renormalization\ncoefficients $g^0_A$, $g_A^1$, i.e.\n$ f^0_A=g_A^0 f^0_A(q),f^1_A=g_A^1 f^1_A(q).$\nThe  renormalization coefficients are given terms of $\\Delta q$ defined above \\cite{JELLIS},\nvia the relations\n$$g_A^0=\\Delta u+\\Delta d+\\Delta s=0.77-0.49-0.15=0.13~,~g_A^1=\\Delta u-\\Delta d=1.26$$\nWe see that, barring very unusual circumstances at the quark level, the isoscalar contribution is\nnegligible. It is for this reason that one might prefer to work in the isospin basis.\n\\section{The allowed SUSY Parameter Space}\n\\label{sec:parameter}\n It is clear from the above discussion that the LSP-nucleon cross section depends, among other things,\non the parameters of supersymmetry.\n One starts with a set of parameters at the GUT scale and predicts the low energy\nobservables via the renormalization group equations (RGE). Conversely starting from the low energy phenomenology\none can constrain the input parameters at the GUT scale. \n The parameter space is the most crucial. In SUSY models derived from minimal SUGRA\nthe allowed parameter space is characterized at the GUT scale  by five \nparameters:\n\\begin{itemize}\n\\item two universal mass parameters, one for the scalars, $m_0$, and one for the\nfermions, $m_{1\/2}$.\n\\item $tan\\beta $, i.e the ratio of the Higgs expectation values, $\\left < H_2 \\right>\/\\left < H_1 \\right>$.\n\\item The trilinear coupling  $ A_0 $ (or  $ m^{pole}_t $)  and \n\\item The sign of $\\mu $ in the Higgs self-coupling  $\\mu H_1H_2$.\n\\end{itemize}\nThe experimental constraints \\cite{JDV06} restrict the values of the above\nparameters yielding the {\\bf allowed SUSY parameter space}.\n\\section{Event rates}\n\\label{sec:rates}\nThe differential non directional  rate can be written as\n\\begin{equation}\ndR_{undir} = \\frac{\\rho (0)}{m_{\\chi}} \\frac{m}{A m_N}\n d\\sigma (u,\\upsilon) | \\mbox{\\boldmath $\\upsilon$}|\n\\label{2.18}\n\\end{equation}\nwhere A is the nuclear mass number, \n$\\rho (0) \\approx 0.3 GeV\/cm^3$ is the WIMP density in our vicinity,\n m is the detector mass, \n $m_{\\chi}$ is the WIMP mass and $d\\sigma(u,\\upsilon )$ is the differential cross section.\n \n The directional differential rate, i.e. that obtained, if nuclei recoiling in the direction $\\hat{e}$ are \nobserved, is given by \\cite{JDVSPIN04,JDV06} :\n\\beq\ndR_{dir} = \\frac{\\rho (0)}{m_{\\chi}} \\frac{m}{A m_N}\n|\\upsilon| \\hat{\\upsilon}.\\hat{e} ~\\Theta(\\hat{\\upsilon}.\\hat{e})\n ~\\frac{1}{2 \\pi}~\nd\\sigma (u,\\upsilon\\\n\\nonumber \\delta(\\frac{\\sqrt{u}}{\\mu_r \\upsilon\n\\sqrt{2}}-\\hat{\\upsilon}.\\hat{e})\n \\label{2.20}\n\\eeq\nwhere $\\Theta(x)$ is the Heaviside function.\n\nThe differential cross section is given by:\n\\beq\nd\\sigma (u,\\upsilon)== \\frac{du}{2 (\\mu _r b\\upsilon )^2}\n [(\\bar{\\Sigma} _{S}F(u)^2\n                       +\\bar{\\Sigma} _{spin} F_{11}(u)]\n\\label{2.9}\n\\end{equation}\nwhere $ u$ the energy transfer $Q$ in dimensionless units given by\n\\begin{equation}\n u=\\frac{Q}{Q_0}~~,~~Q_{0}=[m_pAb]^{-2}=40A^{-4\/3}~MeV\n\\label{defineu}\n\\end{equation}\n with  $b$ is the nuclear (harmonic oscillator) size parameter. $F(u)$ is the\nnuclear form factor and $F_{11}(u)$ is the spin response function associated with\nthe isovector channel.\n\nThe scalar contribution is given by:\n\\begin{equation}\n\\bar{\\Sigma} _S  =  (\\frac{\\mu_r}{\\mu_r(p)})^2\n                           \\sigma^{S}_{p,\\chi^0} A^2\n \\left [\\frac{1+\\frac{f^1_S}{f^0_S}\\frac{2Z-A}{A}}{1+\\frac{f^1_S}{f^0_S}}\\right]^2\n\\approx  \\sigma^{S}_{N,\\chi^0} (\\frac{\\mu_r}{\\mu_r (p)})^2 A^2\n\\label{2.10}\n\\end{equation}\n(since the heavy quarks dominate the isovector contribution is\nnegligible). $\\sigma^S_{N,\\chi^0}$ is the LSP-nucleon scalar cross section.\n\nThe spin contribution is given by:\n\\begin{equation}\n\\bar{\\Sigma} _{spin}  =  (\\frac{\\mu_r}{\\mu_r(p)})^2\n                           \\sigma^{spin}_{p,\\chi^0}~\\zeta_{spin},\n\\zeta_{spin}= \\frac{1}{3(1+\\frac{f^0_A}{f^1_A})^2}S(u)\n\\label{2.10a}\n\\end{equation}\n\\begin{equation}\nS(u)\\approx S(0)=[(\\frac{f^0_A}{f^1_A} \\Omega_0(0))^2\n  +  2\\frac{f^0_A}{ f^1_A} \\Omega_0(0) \\Omega_1(0)+  \\Omega_1(0))^2  \\, ]\n\\label{s(u)}\n \\end{equation}\n The couplings $f^1_A$ ($f^0_A$) and the nuclear matrix elements $\\Omega_1(0)$ ($\\Omega_0(0)$) associated\n with the isovector (isoscalar) components are normalized so that, in the case\n of the proton at $u=0$, they yield $\\zeta_{spin}=1$.\n\n With these definitions in the proton neutron representation we get:\n\n\n\n\n \\beq\n \\zeta_{spin}= \\frac{1}{3}S^{'}(0)~,~S^{'}(0)=\\left[(\\frac{a_n}{a_p}\\Omega_n(0))^2+2 \\frac{a_n}{a_p}\\Omega_n(0) \\Omega_p(0)+\\Omega^2_p(0)\\right]\n \\label{Spn}\n \\eeq\n where $\\Omega_p(0)$ and $\\Omega_n(0)$ are the proton and neutron components of the static spin nuclear matrix elements. In extracting limits on the nucleon cross sections from the data we will find it convenient to\n write:\n \\begin{equation}\n                          \\sigma^{spin}_{p,\\chi^0}~\\zeta_{spin} =\\frac{\\Omega^2_p(0)}{3}|\\sqrt{\\sigma_p}+\\frac{\\Omega_n}{\\Omega_p} \\sqrt{\\sigma_n}\n e^{i \\delta}|^2\n\\label{2.10ab}\n\\end{equation}\n In Eq. (\\ref{2.10ab}) $\\delta$ the relative\nphase between the two amplitudes $a_p$ and $a_n$, which in most models is 0 or $\\pi$, i.e. one expects them to be relatively real.\n The static spin matrix elements are obtained in the context of a given nuclear model. Some such matrix elements of interest to the planned experiments  can be found in \\cite{JDV06}.\n \nThe spin ME are defined as follows:\n\\beq\n\\Omega_p(0)=\\sqrt{\\frac{J+1}{J}}\\prec J~J| \\sigma_z(p)|J~J\\succ ~~,~~\n\\Omega_n(0)=\\sqrt{\\frac{J+1}{J}}\\prec J~J| \\sigma_z(n)|J~J\\succ\n\\label{Omegapn}\n\\eeq\nwhere $J$ is the total angular momentum of the nucleus and $\\sigma_z=2 S_z$. The spin operator is defined by $S_z(p)=\\sum_{i=1}^{Z} S_z(i)$, i.e. a sum over all protons in the nucleus,  and\n$S_z(n)=\\sum_{i=1}^{N}S_z(i)$, i.e. a sum over all neutrons. Furthermore $\\Omega_0(0)=\\Omega_p(0)+\\Omega_n(0)~~,~~\\Omega_1(0)=\\Omega_p(0)-\\Omega_n(0)$\n\\section{The WIMP velocity distribution}\nTo obtain the total rates one must fold with WIMP velocity distribution and integrate  the\nabove expressions  over the\nenergy transfer from $Q_{min}$ determined by the detector energy cutoff to $Q_{max}$\ndetermined by the maximum LSP velocity (escape velocity, put in by hand in the\nMaxwellian distribution), i.e. $\\upsilon_{esc}=2.84~\\upsilon_0$ with  $\\upsilon_0$\nthe velocity of the sun around the center of the galaxy($229~Km\/s$).\n\nFor a given velocity distribution f(\\mbox{\\boldmath $\\upsilon$}$^{\\prime}$),\n with respect to the center of the galaxy,\none can find the velocity distribution in the Lab\nf(\\mbox{\\boldmath $\\upsilon$},\\mbox{\\boldmath $\\upsilon$}$_E$)\nby writing \n\\mbox{\\boldmath $\\upsilon$}$^{'}$=\n          \\mbox{\\boldmath $\\upsilon$}$ \\, + \\,$ \\mbox{\\boldmath $\\upsilon$}$_E \\, ,$\n\\mbox{\\boldmath $\\upsilon$}$_E$=\\mbox{\\boldmath $\\upsilon$}$_0$+\n \\mbox{\\boldmath $\\upsilon$}$_1$, with\n\\mbox{\\boldmath $\\upsilon$} $_1 \\,$ the  Earth's velocity\n around the sun.\n  \nIt is convenient to choose a coordinate system so  that\n $\\hat{x}$  is radially out in the plane of the galaxy,\n $\\hat{z}$ in the sun's direction of motion and \n $\\hat{y}=\\hat{z}\\times\\hat{x}$.\n\nSince the axis of the ecliptic  \nlies very close to the $x,y$ plane ($\\omega=186.3^0$) only  the angle\n $\\gamma=29.8^0$\nbecomes relevant.\nThus the velocity of the earth around the\nsun is given by \n\\begin{equation}\n\\mbox{\\boldmath $\\upsilon$}_E  = \\mbox{\\boldmath $\\upsilon$}_0 \\hat{z} +\n                                  \\mbox{\\boldmath $\\upsilon$}_1  \n(\\, sin{\\alpha} \\, {\\bf \\hat x}\n-cos {\\alpha} \\, cos{\\gamma} \\, {\\bf \\hat y}\n+ cos {\\alpha} \\, sin{\\gamma} \\, {\\bf \\hat z} \\,)\n\\label{3.6}  \n\\end{equation}\nwhere $\\alpha$ is  phase of the earth's orbital motion.\n\nThe WIMP velocity distribution f(\\mbox{\\boldmath $\\upsilon$}$^{\\prime}$) is not known. Many velocity distributions\nhave been used. The most common one is the M-B distribution with characteristic velocity $\\upsilon_0$ \nwith an upper bound $\\upsilon_{esc}=2.84 \\upsilon_0$. \n\\beq\nf(\\mbox{\\boldmath $\\upsilon$}^{\\prime})=\\frac{1}{(\\sqrt{\\pi}\\mbox{\\boldmath $\\upsilon_0$})^3}\ne^{-(\\mbox{\\boldmath $\\upsilon$}^{\\prime}\/\\mbox{\\boldmath $\\upsilon_0$})^2}\n\\label{fv}\n\\eeq\nModifications of this velocity distribution\nhave also been considered such as: i) Axially symmetric M-B distribution  \\cite {Druk,Verg00}. and ii) \nmodifications of the characteristic parameters of the M-B distribution by considering a coupling\nbetween dark matter and dark energy \\cite{TETRVER06} \n($\\upsilon_0 \\rightarrow n \\upsilon_0,\\upsilon_{esc}\\rightarrow n \\upsilon_{esc}$). Other possibilities are adiabatic velocity distribution following the Eddington approach \n\\cite{EDDIN}$^-$\\cite{VEROW06} ,\ncaustic rings \\cite{SIKIVI1}$^-$\\cite{Gelmini} and  Sagittarius dark matter \\cite{GREEN02} .\n  \nFor a given energy transfer the velocity $\\upsilon$ is constrained to be\n\\beq\n\\upsilon\\geq \\upsilon_{min}~,~\\upsilon_{min}= \\sqrt{\\frac{ Q A m_p}{2}}\\frac{1}{\\mu_r}.\n\\eeq\n\\section{The Direct detection rate}\nThe event rate for the coherent WIMP-nucleus elastic scattering is given by \\cite{Verg01,JDV03,JDVSPIN04,JDV06}:\n\\beq\nR= \\frac{\\rho (0)}{m_{\\chi^0}} \\frac{m}{m_p}~\n              \\sqrt{\\langle v^2 \\rangle } \\left [f_{coh}(A,\\mu_r(A)) \\sigma_{p,\\chi^0}^{S}+f_{spin}(A,\\mu_r(A))\\sigma _{p,\\chi^0}^{spin}~\\zeta_{spin} \\right]\n\\label{fullrate}\n\\eeq\nwith\n\\beq\nf_{coh}(A, \\mu_r(A))=\\frac{100\\mbox{GeV}}{m_{\\chi^0}}\\left[ \\frac{\\mu_r(A)}{\\mu_r(p)} \\right]^2 A~t_{coh}\\left(1+h_{coh}cos\\alpha \\right)\n\\eeq\n\\beq\nf_{spin}(A, \\mu_r(A))=\\left[ \\frac{\\mu_r(A)}{\\mu_r(p)} \\right]^2 \\frac{t_{spin}(A)}{A}t_{spin}\\left(1+h_{spin}cos\\alpha \\right)\n\\eeq\nwith $\\sigma_{p,\\chi^0}^{S}$ and $\\sigma _{p,\\chi^0}^{spin}$ the scalar and spin proton cross sections\n$~\\zeta_{spin}$ the nuclear spin ME. In the above expressions $h$ is the modulation amplitude.\n\n The number of events in time $t$ due to the scalar interaction, which leads to coherence, is:\n\\beq\n R\\simeq 1.60~10^{-3}\n\\frac{t}{1 \\mbox{y}} \\frac{\\rho(0)}{ {\\mbox0.3GeVcm^{-3}}}\n\\frac{m}{\\mbox{1Kg}}\\frac{ \\sqrt{\\langle\nv^2 \\rangle }}{280 {\\mbox kms^{-1}}}\\frac{\\sigma_{p,\\chi^0}^{S}}{10^{-6} \\mbox{ pb}} f_{coh}(A, \\mu_r(A))\n\\label{scalareventrate}\n\\eeq\nIn the above expression\n $m$ is the target mass, $A$ is the number of nucleons\nin the nucleus and $\\langle v^2 \\rangle$ is the average value of the square of the WIMP velocity.\n\nIn the case of the spin interaction we write:\n\\beq\n R\\simeq 16\n\\frac{t}{1 \\mbox{y}} \\frac{\\rho(0)}{ {\\mbox0.3GeVcm^{-3}}}\n\\frac{m}{\\mbox{1Kg}}\\frac{ \\sqrt{\\langle\nv^2 \\rangle }}{280 {\\mbox kms^{-1}}}\\frac{\\sigma_{p,\\chi^0}^{S}}{10^{-2} \\mbox{ pb}} f_{spin}(A, \\mu_r(A))\n\\label{spineventrate}\n\\eeq\nNote the different scale for the proton spin cross section.\nThe parameters $f_{coh}(A,\\mu_r(A))$, $f_{spin}(A,\\mu_r(A))$, which give the relative merit\n for the coherent and the spin contributions in the case of a nuclear\ntarget compared to those of the proton,  have already been  tabulated \\cite{JDV06}\n for energy cutoff $Q_{min}=0,~10$ keV. It is clear that for large A the coherent process is\nexpected to dominate unless for some reason the scalar proton cross section is very suppressed.\n\nIn the case of directional experiments the event rate is given\n by Eqs (\\ref{scalareventrate}) and (\\ref{spineventrate}) except that now:\n \\beq\nf_{coh}(A, \\mu_r(A))=\\frac{100\\mbox{GeV}}{m_{\\chi^0}}\\left[ \\frac{\\mu_r(A)}{\\mu_r(p)} \\right]^2 A\\frac{\\kappa}{2 \\pi}t_{coh}\\left(1+h_m(coh)cos{(\\alpha+\\alpha_m \\pi)} \\right)\n\\eeq\n\\beq\nf_{spin}(A, \\mu_r(A))=\\frac{100\\mbox{GeV}}{m_{\\chi^0}}\\left[ \\frac{\\mu_r(A)}{\\mu_r(p)} \\right]^2 \\frac{\\kappa}{2 \\pi}\\frac{t_{spin}}{A}\\left(1+h_m(spin)cos{(\\alpha+\\alpha_m \\pi)} \\right)\n\\eeq\nIn the above expressions $h_m$ is the modulation amplitude and $\\alpha _m$ the shift in the phase of the modulation (in units of $\\pi$) relative to the phase of the Earth. $\\kappa\/(2 \\pi)$, $\\kappa\\leq 1$, is the suppression factor entering due to the restriction of\nthe phase space.  $\\kappa$, $h_m$ and $\\alpha_m$ depend on the direction of observation. It is precisely this\ndependence as well as the large values of $h_m$, which can be exploited to reject background \\cite{JDV06}, that makes the directional experiments quite attractive in spite of the suppression factor relative to the standard\nexperiments.\n\\section{Bounds on the scalar proton cross section}\nUsing the above formalism one can obtain the quantities of interest $t$ and $h$ both for the standard as\nwell as the directional experiments. Due to lack of space we are not going to present the obtained results\nhere. The interested reader can find some of these results elsewhere \\cite{JDVSPIN04,JDV06} . Here we are \nsimply going to show how\none can employ such results to extract the nucleon cross section from the data.\nDue to space considerations we are not going to discuss the limits extracted from the data on the spin cross\nsections, since in this case one has to deal with two amplitudes (one for the proton and one for the neutron). We will only\nextract some limits imposed on the\nscalar nucleon cross section (the proton and neutron cross section are essentially the same).\nIn what follows we will employ for all targets \\cite{BCFS02}$^-$\\cite{PAVAN01} the limit of CDMS II for the Ge target \\cite{CDMSII04} ,\n i.e.  $<2.3$ events for \nan exposure of $52.5$ Kg-d with a threshold of $10$ keV. This event rate is similar to that for other systems \\cite{SGF05}. The thus obtained limits are exhibited in Fig. \\ref{b127.73}. For larger WIMP masses one can\nextrapolate these curves, assuming an increase as $\\sqrt{m_{\\chi}}$.\n\\begin{figure}\n\\rotatebox{90}{\\hspace{0.0cm} $\\sigma_p\\rightarrow 10^{-5}$pb}\n\\psfig{file=bcoh127.eps,width=2.0in}\n\\rotatebox{90}{\\hspace{0.0cm} $\\sigma_p\\rightarrow 10^{-5}$pb}\n\\psfig{file=bcoh73.eps,width=2.0in}\n\\hspace{-2.0cm} $m_{\\chi}\\rightarrow$ GeV\n\\caption{ The limits on the scalar proton cross section for A$=127$ on the left and A$=73$ on the right as functions of $m_{\\chi}$. The continuous (dashed) curves correspond to $Q_{min}=0~(10)$ keV respectively. Note that the advantage of the larger nuclear mass number of the A$=127$ system is counterbalanced by the favorable form factor dependence of the A$=73$ system.}\n \\label{b127.73}\n\\end{figure}\n\\section{Transitions to excited states}\nThe above formalism can easily be extended to cover transitions to excited states. Only the kinematics and \nthe nuclear physics is different. In other words one now needs:\n\\begin{itemize}\n\\item The inelastic scalar form factor.\\\\\n The transition amplitude is non zero due to the momentum transfer involved. The relevant multipolarities\n are determined by the spin and parity of the final state.\n \\item Spin induced transitions.\\\\\n In this case one can even have a Gamow-Teller like transition, if the final state is judiciously chosen.\n \\end{itemize}\n \n In the case of $^{127}I$ the static spin matrix element involving the first excited state around \n50 keV is twice as large compared to that of the\n ground state \\cite{VQS04}. The spin response function was assumed to be the same with that of the ground\n state. The results obtained \\cite{VQS04} are shown in Fig. \\ref{ratio}.\n \\begin{figure}\n\\begin{center}\n\\rotatebox{90}{\\hspace{1.0cm} {\\tiny BRR}$\\rightarrow$}\n\\includegraphics[height=.17\\textheight]{ratio0.eps}\n\n \\rotatebox{90}{\\hspace{1.0cm} {\\tiny BRR}$\\rightarrow$}\n\\includegraphics[height=.17\\textheight]{ratioQ.eps}\\\\\n \\hspace{0.0cm}$m_{LSP}\\rightarrow$ ($GeV$)\n \\caption{ The ratio of the rate to\nthe excited state divided by that of the ground state as a\nfunction of the LSP mass (in GeV) for $^{127}I$.\n We found that\nthe static spin matrix element of the transition from the ground\nto the excited state is a factor of 1.9 larger than that\ninvolving the ground state and assumed that the spin response functions\n$F_{11}(u)$ are the same. \nOn the left we show the results for $Q_{min}=0$ and on\nthe right for $Q_{min}=10~KeV$. \\label{ratio} }.\n\\end{center}\n\\end{figure}\nThese results are very encouraging, since, as we have mentioned, for heavier WIMPS like those involved\nin K-K theories, the branching ratios are expected to be much larger. Thus one may consider such\ntransitions, since the detection of de-excitation $\\gamma$ rays is much easier than the detection of\nrecoiling nuclei.\n\\section{Other non recoil experiments}\nAs we have already mentioned the nucleon recoil experiments are very hard. It is therefore necessary to consider\nother possibilities. One such possibility is to detect the electrons produced during the WIMP-nucleus \ncollisions \\cite{VE05,MVE05} employing detectors with low energy threshold with a high Z target. Better yet\none may attempt to detect the very hard X-rays generated when the inner shell electron holes are \nfilled \\cite{EMV05}. The relative X-ray to nucleon recoil probabilities $[Z \\sigma _K \/\\sigma _r]_i$, \nfor $i=L (m_{\\chi}\\leq \\mbox{100GeV}),~M(\\mbox{100 GeV}\\leq m_{\\chi}\\leq  \\mbox{200 GeV})$ and $H (m_{\\chi}\\simeq \\mbox{200 GeV})$ are shown in table \\ref{table:X-rays}. For even heavier WIMPs, like\nthose expected in K-K theories, the relative probability is expected to be even larger.\n\n\\begin{table}\n\\begin{center}\n\\caption{K X-ray cross sections relative to the nuclear recoil,\nrates and energies in WIMPs nuclear interactions with $^{131}$Xe.\n$[Z \\sigma _K \/\\sigma _r]_L, [Z \\sigma _K \/\\sigma _r]_M$ and $[Z\n\\sigma _K \/\\sigma _r]_H$ are the ratios for light (30 GeV), medium\n(100 GeV) and heavy (300 GeV) WIMPs.} \\label{t:2} \\vspace{0.5cm}\n\\label{table:X-rays}\n\\begin{tabular}{|ccccc|}\n\\hline K X-ray & $E_K(K_{ij})$ keV    & $[\\frac{Z\n\\sigma _K(K_{ij})}{\\sigma _r}]_{L}$ &  $[\\frac{Z \\sigma\n_K(K_{ij})}{\\sigma _r} ]_{M} $ & $[\\frac{Z \\sigma\n_K(K_{ij})}{\\sigma _r}]_{H} $ \\\\ \\hline\n K$_{\\alpha 2}$  & 29.5  & 0.0086 & 0.0560 & 0.0645 \\\\\n K$_{\\alpha 1}$ & 29.8  & 0.0160 & 0.1036 & 0.1196 \\\\\n K$_{\\beta 1}$  & 33.6   & 0.0047 & 0.0303 & 0.0350 \\\\\n K$_{\\beta 2}$  & 34.4   & 0.0010 & 0.0067 & 0.0077 \\\\\n\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\nThe K$_{\\alpha}$ and K$_{\\beta}$ lines can be\nseparated experimentally by using good energy-resolution\ndetectors, but the sum of all K lines can be measured in modest\nenergy-resolution experiments.\n\\section{Conclusions}\nWe examined the various signatures expected in the direct detection of WIMPs via their\ninteraction with nuclei. We specially considered WIMPs predicted in supersymmetric models (LSP or neutralino) as well as  theories with extra dimensions. We presented the formalism for the modulation \namplitude for non directional as well as directional experiments. We discussed the role played by\nnuclear physics on the extraction of the nucleon cross sections from the data. We also considered\nnon recoil experiments, such as measuring the $\\gamma$ rays following the de-excitation of the nucleus\nand\/or the hard X-rays after the de-excitation of the inner shell electron holes produced during the WIMP \nnucleus interaction. These are favored by very heavy MIMPs in the TeV region and velocity distributions\nexpected in models allowing interaction of dark matter and dark energy.\n\n{\\bf Acknowledgments}:\nThis work was supported in part by the European Union contract MRTN-CT-2004-503369.  Special thanks to Professor Raduta for support and hospitality during  the Predeal Summer School.\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nGravitational lensing of photons by black holes has received great attention in the last few years, mainly due to the increasing evidence of the presence of supermassive black holes at the center of galaxies. Theoretical studies of black hole lenses, both numerically and analytically, were made with Schwarzschild \\cite{virbha1, bozza1, schw}, Reissner--Nordstr\\\"{o}m \\cite{eiroto}, general spherically symmetric \\cite{bozza2, bozman1} and rotating \\cite{bozza3, rotating} geometries, and also for black holes coming from alternative theories \\cite{alternative} or braneworld cosmologies \\cite{braneworld}. Even naked singularities were considered as lenses \\cite{nakedsing}. Photons (or null mass particles) passing close enough to the photon sphere of the lens will have large deflection angles, and they can even make one or more turns around the deflector before reaching the observer. By this mechanism, two infinite sets of strong deflection images, one at each side of the lens, are produced. The presence of images with large deflection angles is not a new fact, since they were obtained already in 1959 for the Scharzschild spacetime \\cite{darwin}. The analytical study of these images is more simple if one adopts the strong deflection limit, which consists in a logarithmic approximation of the deflection angle, first obtained for the Schwarzschild metric \\cite{darwin}, revisited by several authors \\cite{old, bozza1},  extended to Reissner--Nordstr\\\"{o}m geometry \\cite{eiroto}, to general spherically symmetric spacetimes \\cite{bozza2} and to Kerr metric \\cite{bozza3}.  For some lensing configurations two weak deflection images are also obtained, which are analyzed by making a first order Taylor expansion of the deflection angle (weak deflection limit), as it is usually done for more standard astrophysical objects, such as stars and galaxies (see, e.g., \\cite{schneider}). Intermediate cases can be treated analytically by perturbative \\cite{perturba} or variational methods \\cite{amore}. A special configuration, where no weak deflection images are present, is when the source is in front of the lens instead of behind it, which is called retrolensing \\cite{retrolens}. Recently, the strong deflection limit was extended to include sources very close to the black hole \\cite{bozza4}.\\\\\n\nLensing of neutrinos have been previously studied by other authors. In Ref. \\cite {escribano}, gravitational lensing of neutrinos by stars and galaxies was analyzed, and in Ref. \\cite{mena}, the lensing effects of supernova neutrinos by the Galactic center black hole was considered, in the weak deflection limit. However, perhaps the most interesting cosmological sources of neutrinos from the point of view of lensing are transients associated with gamma-ray bursts (GRBs). It is expected that proton-photon interactions during the GRB will result into copious photopion production and hence neutrinos would be generated from the decay of charged pions and muons (e.g. \\cite{neutrinos, meszaros, dermer, murase}). Since GRBs occur frequently, say once per day, and can be detected at gamma-rays by SWIFT satellite and then the follow up of the afterglows usually allows the identification of the host galaxy and the corresponding redshift (see, e.g., \\cite{meszaros2}), they are outstanding candidates for lensing produced by massive black holes in the center of interposed galaxies. \\\\\n\nWe notice, however, that in the collapsar scenario for long GRBs \\cite{woosley1, woosley2} the jet not always is expected to be able to make its way through the star, so no observable gamma-ray emission would result in such cases \\cite{meszaros}. Nonetheless, the neutrino emission might be important. If the event is lensed, the neutrino signal should repeat and hence be identified, despite the absence of electromagnetic counterparts. \\\\\n\nIn this letter we investigate gravitational lensing of neutrinos by Schwarzschild black holes. We pay special attention to neutrino transients lensed by supermassive black holes located at the center of galaxies. In Section \\ref{pm} we present the expressions that give the positions and magnifications of the weak and strong deflection images, and in Section \\ref{td} we calculate the time delays between the arrival signals. Then, in Section \\ref{lnb}, we calculate the specific time delays produced by some interposed supermassive black holes for neutrino transient at a distance of $\\sim 10^{28}$ cm. Finally, in Section \\ref{conc}, a brief summary and the conclusions are presented.\n\n\\section{Positions and magnifications of the images}\\label{pm} \n\nNeutrinos have zero or negligible mass, so we assume that they follow null geodesics as photons do. We consider a point source of neutrinos, with angular diameter distance $D_{\\rm{os}}$ to the observer, behind a Schwarzschild black hole lens, placed at an angular diameter distance $D_{\\rm{ol}}$. The angular diameter distance between the lens and the source is dubbed $D_{\\rm{ls}}$. The optical axis is defined by the line that joins the observer with the deflector. The distances are very large compared to the Schwarzschild radius of the black hole and the angles are measured from the observer. We restrict our analysis to high alignment, which is more interesting from an astrophysical point of view, since the images are more prominent. Then the angular position of the source $\\beta $, taken positive here, is small. For this configuration, we have two weak deflection images and two infinite sets of strong deflection (also called relativistic \\cite{virbha1}) images. Neutrinos with closest approach distance $r_{0}$ much larger than the photon sphere radius $r_{\\rm{ps}}=3MG\/c^2$, which corresponds to the unstable circular orbit around the black hole\\footnote{For a complete study of the photon sphere in a spherically symmetric geometry see \\cite{atkinson}; and for a general definition of the photon surface in an arbitrary spacetime see \\cite{claudel}.}, will have a small deflection angle $\\alpha$, which can be approximated to first order in $1\/r_{0}$ by $\\alpha= 4GM\/(c^{2}r_{0})$ (weak deflection limit). Within this approximation, the lens equation has the form \\cite{schneider}\n\\begin{equation}\n\\beta =\\theta-\\frac{\\theta_{\\rm{E}}^{2}}{\\theta},\n\\label{pm1} \n\\end{equation}\nwhere $\\theta $ is the angular position of the image and $\\theta_{\\rm{E}}$ is the angular Einstein radius, given by\n\\begin{equation}\n\\theta_{\\rm{E}}=\\sqrt{\\frac{2R_{\\rm{s}}D_{\\rm{ls}}}{D_{\\rm{ol}}D_{\\rm{os}}}},\n\\label{pm2} \n\\end{equation} \nwith $R_{\\rm{s}}=2MG\/c^{2}$ the Schwarzschild radius of the lens. The lens equation has two solutions:\n\\begin{equation}\n\\theta_{\\rm{p},s}=\\frac{1}{2}\\left( \\beta\\pm\\sqrt{\\beta^{2}+4\\theta_{\\rm{E}}^{2}}\\right),\n\\label{pm3} \n\\end{equation} \nthat give the positions of the primary (upper sign) and the secondary (lower sign) images. The primary image lies inside the Einstein radius and the secondary image outside. When $\\beta =0$, instead of two images, an Einstein ring with radius $\\theta_{\\rm{E}}$ is obtained. Another important aspect is the magnification of the images, defined as the ratio between the observed and intrinsic fluxes of the source. As a consequence of the Liouville theorem in curved spacetimes \\cite{misner}, gravitational lensing preserves surface brightness for neutrinos and photons, so the magnifications of the images are given by the ratio of the solid angles subtended by the images and the source, which result in \\cite{schneider}:\n\\begin{equation}\n\\mu _{\\rm{p},s}=\\frac{1}{4}\\left( \\frac{\\beta}{\\sqrt{\\beta^{2}+4\\theta_{\\rm{E}}^{2}}}+\n\\frac{\\sqrt{\\beta^{2}+4\\theta_{\\rm{E}}^{2}}}{\\beta}\\pm 2 \\right),\n\\label{pm4} \n\\end{equation}\nwhere the plus sign corresponds to the primary image and the minus sign to the secondary one. If the position of the source $\\beta$ is close to zero, the magnifications of both images are large. If $\\beta =0$ the approximation of point source breaks down and the magnifications become infinite. It is not difficult to see that $\\mu _{\\rm{p}}>1$ for all $\\beta $, and $\\mu _{\\rm{s}}>1$ only if $\\beta \/\\theta_{\\rm{E}}< \\sqrt{(3\\sqrt{2}-4)\/2}\\approx 0.35$. When $\\beta \/\\theta_{\\rm{E}}$ is large we have that $\\mu _{\\rm{p}}\\approx 1$ and $\\mu _{\\rm{s}}\\approx 0$.\\\\\n\nBesides the weak deflection images, two infinite sets of relativistic images are formed by neutrinos that make one or more loops, in both directions of winding, around the black hole lens. For high alignment, the deflection angle corresponding to the relativistic images is close to an even number of $\\pi$, $\\alpha=\\pm (2n\\pi + \\Delta\\alpha_{n})$ with $0<\\Delta\\alpha_{n}\\ll 1$, the upper sign corresponding to one set of images and the lower one to the other set. The other angles involved are small, then the lens equation \\cite{virbha1}\\footnote{Eq. (\\ref{pm5a}) is valid for asymptotically flat spacetimes, with the source and the observer in the flat region; for more general lens equations see \\cite{lensequa}.} \n\\begin{equation}\n\\tan \\beta =\\tan \\theta -\\frac{D_{\\mathrm{ls}}}{D_{\\mathrm{os}}}\\left( \\tan\n\\theta + \\tan(\\alpha -\\theta )\\right),\n\\label{pm5a}\n\\end{equation}\ntakes the form \\cite{bozza1, bozza2}\n\\begin{equation}\n\\beta=\\theta \\mp \\frac{D_{\\rm{ls}}}{D_{\\rm{os}}}\\Delta\\alpha_{n}.\n\\label{pm5b}\n\\end{equation}\nIn the strong deflection limit, i.e. for trajectories passing close to the photon sphere of the black hole, the deflection angle can be approximated by a logarithmic function of the impact parameter $b$, defined as the perpendicular distance from the deflector to the asymptotic path at infinite. For the Schwarzschild geometry, it can be shown that \\cite{darwin, bozza1, bozza2}\n\\begin{equation}\n\\alpha =\\pm \\left[ -c_{1}\\ln \\left( \\frac{b}{b_{\\rm{ps}}}-1\\right)+ c_{2}\\right] +O(b-b_{\\rm{ps}}),\n\\label{pm6} \n\\end{equation} \nwith $c_{1}=1$, $c_{2}=\\ln [216(7-4\\sqrt{3})]-\\pi$ and $b_{\\rm{ps}}=\\sqrt{3}r_{\\rm{ps}} =3\\sqrt{3}R_{\\rm{s}}\/2$ the critical impact parameter. Neutrinos with impact parameter smaller than the critical value will spiral inside the photon sphere into the black hole, not reaching the observer, and those with $b$ larger than $b_{\\rm{ps}}$ will make one or more outward turns outside the photon sphere, finally getting to the observer. As in the case of photons, using that $b=\\sin D_{\\rm{ol}} \\theta \\approx \\theta D_{\\rm{ol}}$, inverting Eq. (\\ref{pm6}) and Taylor expanding it around $\\alpha =2n\\pi$ to obtain $\\Delta\\alpha_{n}$, then replacing the result in the lens equation (\\ref{pm5b}) and finally inverting it, the positions of the relativistic images can be approximated (keeping only the lower order terms) by \\cite{bozza1, bozza2}:\n\\begin{equation}\n\\theta_{n}=\\pm \\theta_{n}^{\\rm{E}}+\\frac{D_{\\rm{os}}b_{\\rm{ps}}}{D_{\\rm{ls}}D_{\\rm{ol}}c_{1}}e_{n}\\beta,\n\\label{pm7} \n\\end{equation} \nwhere\n\\begin{equation}\n e_{n}=e^{(c_{2}-2n\\pi)\/c_{1}},\n\\nonumber\n\\end{equation} \nand\n\\begin{equation}\n\\theta_{n}^{\\rm{E}}=\\frac{b_{\\rm{ps}}}{D_{\\rm{ol}}}\\left( 1- \\frac{D_{\\rm{os}}b_{\\rm{ps}}}{D_{\\rm{ls}}D_{\\rm{ol}}c_{1}}e_{n}\\right)(1+e_{n}),\n\\label{pm8} \n\\end{equation} \nis the $n$-th relativistic Einstein ring radius. For perfect alignment an infinite sequence of Einstein rings is obtained instead of point images. With the same considerations given above for the weak deflection images, the magnification of the $n$-th image has the same expression that was found previously for photons \\cite{bozza1, bozza2}:\n\\begin{equation}\n\\mu_{n}=\\frac{1}{\\beta}\\frac{b_{\\rm{ps}}^2D_{\\rm{os}}}{D_{\\rm{ol}}^2 D_{\\rm{ls}} c_{1}}(1+e_{n})e_{n},\n\\label{pm9} \n\\end{equation} \nfor both sets of relativistic images. The first image ($n=1$) is the strongest one and the others have magnifications that decrease exponentially with $n$. For a given source angle $\\beta$, the relativistic images are very faint compared with the weak deflection ones\\footnote{For example, if $\\beta \/\\theta_{\\rm{E}}\\ll 1$  we have that $\\mu_{1}\/\\mu_{\\rm{p}}\\propto (R_{\\rm{S}}\/D_{\\rm{ol}})^{3\/2}$, which is usually a very small number.}.\n\n\\section{Time delays}\\label{td} \n\nNeutrinos that form distinct images take different paths, resulting in time delays between the images. Considering again that neutrinos follow null geodesics as photons do, the time delay between the primary and the secondary images is given by \\cite{schneider}:\n\\begin{equation}\n\\Delta t_{\\rm{p,s}}=\\frac{2R_{\\rm{s}}}{c}(1+z_{\\rm{d}})\\left( \\frac{\\theta_{\\rm{s}}^{2}-\\theta_{\\rm{p}}^{2}}{2|\\theta_{\\rm{p}}\\theta_{\\rm{s}}|} +\\ln \\left|\\frac{\\theta_{\\rm{s}}}{\\theta_{\\rm{p}}}\\right|\\right),\n\\label{td1}\n\\end{equation}\nwhere $z_{\\rm{d}}$ is the redshift of the deflector. The last equation can be written in the form\n\\begin{equation}\n\\Delta t_{\\rm{p,s}}=\\frac{2R_{\\rm{s}}}{c}(1+z_{\\rm{d}})\\left( \\frac{-\\beta \\sqrt{\\beta^{2}+4\\theta_{\\rm{E}}^{2}}}{2\\theta_{\\rm{E}}^{2}}+\\ln \\left| \\frac{\\beta -\\sqrt{\\beta^{2}+4\\theta_{\\rm{E}}^{2}}}{\\beta +\\sqrt{\\beta^{2}+4\\theta_{\\rm{E}}^{2}}}\\right|\\right).\n\\label{td2}\n\\end{equation}\nWhen $\\beta =0$ there is no time delay. Large time delays can be obtained if $\\beta \/\\theta_{\\rm{E}}\\gg 1$, but in this case the magnification of the primary image is close to one and the secondary image is very faint. The optimal situation for a variable source is when $\\beta \/\\theta_{\\rm{E}}$ is small enough to have large magnifications of both images, but not too close to zero, so the time delay can be longer than the typical time scale of the transient source.\\\\\n\nIn the case of relativistic images, the time delay between the images formed at the same side of the lens is given by \\cite{bozman1}\\footnote{The expressions from Ref. \\cite{bozman1} have been rewritten here using physical units, adding the cosmological factor $1+z_{d}$ and expanding them to first order in the source position angle (measured from the observer instead of from the source).}:\n\\begin{equation}\n\\Delta t^{\\rm{s}}_{n,m}=\\frac{b_{\\rm{ps}}}{c}(1+z_{\\rm{d}})\\left[ 2\\pi (n-m)+2\\sqrt{2}(w_{m}-w_{n})\\pm \\dfrac{\\sqrt{2}D_{\\rm{os}}(w_{m}-w_{n})}{c_{1}D_{\\rm{ls}}}\\beta \\right] ,\n\\label{td3}\n\\end{equation}\nwhere\n\\begin{equation}\nw_{k}=e^{(c_{2}-2k\\pi)\/(2c_{1})},\n\\nonumber\n\\end{equation}\nand the upper\/lower sign corresponds if both images are on the same\/opposite side of the source. For the images at the opposite side of the lens we have \\cite{bozman1}:\n\\begin{equation}\n\\Delta t^{\\rm{o}}_{n,m}=\\frac{b_{\\rm{ps}}}{c}(1+z_{\\rm{d}})\\left[ 2\\pi (n-m)+2\\sqrt{2}(w_{m}-w_{n})+\\left(  \\dfrac{\\sqrt{2}D_{\\rm{os}}(w_{m}+w_{n})}{c_{1}D_{\\rm{ls}}}-\\frac{2D_{\\rm{os}}}{D_{\\rm{ls}}}\\right) \\beta \\right],\n\\label{td4}\n\\end{equation}\nwhere the image with winding number $n$ is on the same side of the source and the other one on the opposite side. The first term in Eqs. (\\ref{td3}) and (\\ref{td4}) is by large the most important one \\cite{bozman1}. The time delays between the relativistic images are longer than the time delay between the primary and the secondary images.\n\n\\section{Lensing of neutrino transients}\\label{lnb} \n\n\\begin{table}[t]\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\nGalaxy & Black hole mass ($M_{\\odot}$) & Distance (Mpc) & $\\theta_{\\rm{E}}$ (arcsec) & $\\Delta t_{\\rm{s,p}}$ (s)\\\\\n\\hline\nMilky Way & $2.8 \\times 10^{6}$ & $0.0085$ & $1.6$  & $11$ \\\\\n\\hline\nNGC0224   & $ 3.0\\times 10^{7}$ & $0.7$ & $0.6$  & $1.2\\times 10^{2}$\\\\\n\\hline\nNGC3115   & $ 2.0\\times 10^{9}$ & $8.4$ & $1.4$  & $7.9\\times 10^{3}$\\\\\n\\hline\nNGC3377   & $ 1.8\\times 10^{8}$ & $9.9$ & $0.4$  & $7.1\\times 10^{2}$\\\\\n\\hline\nNGC4486B   & $ 5.7\\times 10^{8}$ & $15.3$ & $0.5$  & $2.2\\times 10^{3}$\\\\\n\\hline\nNGC4486   & $ 3.3\\times 10^{9}$ & $15.3$ & $1.3$ & $1.3\\times 10^{4}$\\\\\n\\hline\nNGC4261   & $ 4.5\\times 10^{8}$ & $27.4$ & $0.4$ & $1.8\\times 10^{3}$\\\\\n\\hline\nNGC7052   & $ 3.3\\times 10^{8}$ & $58.7$ & $0.2$ & $1.3\\times 10^{3}$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\caption{Time delays between the weak deflection images of neutrino burst sources at a distance of $10^{28}$ cm. The lenses are supermassive black holes at the center of the galaxies indicated. The Schwarzschild geometry was adopted to model the black holes. The source angular position is $\\beta =0.1 \\, \\theta_{\\rm{E}}$, with $\\theta_{\\rm{E}}$ the angular Einstein radius. In this case, the angular positions of the primary and the secondary images are $\\theta_{\\rm{p}}=1.05 \\, \\theta_{\\rm{E}}$ and $\\theta_{\\rm{s}}=-0.95 \\, \\theta_{\\rm{E}}$, while their respective magnifications are $\\mu_{\\rm{p}}=5.5$ and $\\mu_{\\rm{s}}=4.5$.}\n\\label{table1}\n\\end{table}\n\n\\begin{table}[t]\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline\nGalaxy & Black hole mass ($M_{\\odot}$) & Distance (Mpc) & $\\theta_{\\rm{E}}$ (arcsec) & $\\Delta t_{\\rm{s,p}}$ (s)\\\\\n\\hline\nMilky Way & $2.8 \\times 10^{6}$ & $0.0085$ & 1.6 & $55$\\\\\n\\hline\nNGC0224   & $ 3.0\\times 10^{7}$ & $0.7$ &  0.6 & $6.0\\times 10^{2}$\\\\\n\\hline\nNGC3115   & $ 2.0\\times 10^{9}$ & $8.4$ & 1.4  & $4.0\\times 10^{4}$\\\\\n\\hline\nNGC3377   & $ 1.8\\times 10^{8}$ & $9.9$ & 0.4 & $3.6\\times 10^{3}$\\\\\n\\hline\nNGC4486B  & $ 5.7\\times 10^{8}$ & $15.3$ & 0.5  & $1.1\\times 10^{4}$\\\\\n\\hline\nNGC4486   & $ 3.3\\times 10^{9}$ & $15.3$ & 1.3  & $6.6\\times 10^{4}$\\\\\n\\hline\nNGC4261   & $ 4.5\\times 10^{8}$ & $27.4$ & 0.4  & $8.9\\times 10^{3}$\\\\\n\\hline\nNGC7052   & $ 3.3\\times 10^{8}$ & $58.7$ & $0.2$ & $6.6\\times 10^{3}$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\caption{Time delays between the weak deflection images of neutrino burst sources at a distance of $10^{28}$ cm. The lenses are supermassive black holes at the center of the galaxies indicated. The Schwarzschild geometry was adopted to model the black holes. The source angular position is $\\beta =0.5 \\, \\theta_{\\rm{E}}$, with $\\theta_{\\rm{E}}$ the angular Einstein radius. In this case, the angular positions of the primary and the secondary images are $\\theta_{\\rm{p}}=1.28 \\, \\theta_{\\rm{E}}$ and $\\theta_{\\rm{s}}=-0.78 \\, \\theta_{\\rm{E}}$, while their respective magnifications are $\\mu_{\\rm{p}}=1.6$ and $\\mu_{\\rm{s}}=0.6$.}\n\\label{table2}\n\\end{table}\n\nThe angular resolution of the primary and secondary images is beyond the capability of current and near future neutrino detectors, which is of the order of one tenth of a degree, but the temporal resolution of the images of individual transient events, which have typical durations in the range of $\\sim$10 s to 100 s for long GRBs \\cite{meszaros2}, is possible. As an example of this, we consider neutrino transients acting as possible sources situated at distances of the order of $10^{28}$ cm, with supermassive black holes at the center of interposed galaxies as lenses. Some results of our calculations for specific cases of lenses in the local universe ($z_{\\rm{d}}\\sim 0$) are shown in Tables \\ref{table1} and \\ref{table2}, with the masses and distances taken from Ref. \\cite{richstone}. We see that the separation between the primary and secondary images of neutrino transients is of the order of a second of arc, so they cannot be resolved. For suitable values of the parameters involved, the weak deflection images can be both magnified several times, with time delays of $10^2 - 10^4$ s, larger than the intrinsic time of variation of the sources. \\\\\n\nIf one fixes $\\beta \/\\theta_{\\rm{E}}$ to obtain from Eq. (\\ref{pm4}) the desired values of magnification of the images, it is clear from Eq. (\\ref{td2}) that the time delay increases linearly with the redshift of the lens. Then, with a typical source with redshift $z_{\\rm{s}}\\sim 1$, the values of time delays between the primary and the secondary images for lenses closer to the neutrino sources can be up to twice of those obtained in Tables \\ref{table1} and \\ref{table2}. But far lenses require better alignment to have large magnifications because $\\theta _{\\rm{E}}$ decreases with the distance to the lens.\\\\\n\nThroughout this letter we have assumed that the neutrinos move like photons in null geodesics, so the time delays do not depend on the energy of the neutrinos. The time lag between neutrinos with an energy $E_{\\nu}$ and a small mass $m_{\\nu}$ and photons travelling the same distance $d$ can be approximated by $\\Delta t\\approx (1\/2)(d\/c)(m_{\\nu}c^2\/E_{\\nu})^2$, which using $E_{\\nu} \\gtrsim 1$ TeV (for neutrinos associated with GRBs), $m_{\\nu}c^2 \\lesssim 1$ eV, $d \\sim 10^{28}$ cm,  gives $\\Delta t < 10^{-6}$ s. This time lag corresponds to a total travelling time of about $3 \\times 10^{17}$ s. Then, if neutrinos have mass, the time delays given in Tables \\ref{table1} and \\ref{table2}  should be modified in the same proportion, i.e. in less than one part in $10^{23}$. There is also observational evidence related to the supernova SN1987A which shows that the time delay due to the presence of the galaxy for photons and neutrinos with different energies is the same within a $0.5\\%$ or better accuracy \\cite{supernova}. All these justify our assumption, and the results obtained are excellent approximations if the neutrinos have sub-eV mass.\\\\\n\nConcerning the relativistic images, if we choose $\\beta \/\\theta_{\\rm{E}}=0.1$ as it was done in Table \\ref{table1}, we have from Eq. (\\ref{pm9}) that the magnification of the brightest image is $\\mu _{1}=1.1\\times 10^{-17}$ for the Galactic black hole and $\\mu _{1}=1.8\\times 10^{-22}$ for NGC4486. Similar values are obtained for the other black holes considered in Tables \\ref{table1} and \\ref{table2}. The other image magnifications decrease exponentially with $n$. To obtain magnifications about one or larger, a closer alignment is necessary, i.e. $\\beta \\sim b_{\\rm{ps}}\/d_{\\rm{ol}}$ instead of  $\\beta \\sim \\theta _{\\rm{E}}$. Then, while the primary and secondary images are amplified several times for $\\beta \/\\theta_{\\rm{E}}=0.1$, the strong deflection ones are highly demagnified. Using Eq. (\\ref{pm7}), it can be seen that the angular separation between the strong deflection images is of the order of micro arc seconds or less. The time delays between the relativistic images, given by Eqs. (\\ref{td3}) and (\\ref{td4}), can be large, but they are too faint to be detected. So, in what follows, we restrict ourselves to the weak deflection images.\\\\\n\nThe probability of supermassive black holes located at the center of galaxies in the line of sight to GRBs is not negligible because of the high-redshift of most GRBs. Moreover, optical spectroscopic observations can detect absorbing lines of the interposed galaxy in the afterglow, hence allowing a direct determination of the different distances involved in the scenario. In the case of choked GRBs, where only neutrinos are produced, the time delays and the relative magnifications of the signals could used for the unequivocal identifications of {\\sl dark} neutrino transients. A neutrino transient associated with a GRBs might have an fluence of several times $10^{-4}$ erg cm$^{-2}$ \\cite{dermer}. With a mild amplification as obtained for the parameters adopted in Tables \\ref{table1} and \\ref{table2}, this might imply the detection of a few neutrinos by a km$^{3}$-detector. Even if the signal-to-noise ratio is not at a high confidence level, the repetition of the signal on a time scale from minutes to hours from the same location in the sky would render the identification of the neutrino transient source unequivocal. If the detection of the GRB afterglow allows a clear determination of the redshifts involved, then Eqs. (\\ref{pm4}) and (\\ref{td2}) can be used to obtain an independent estimated of the central black hole mass in the interposed galaxy. \\\\\n\nThe analysis of current databases indicates that the space-time clustering of GRBs is only marginal, at the level of $5\\%$ or less \\cite{romero}, but as we have mentioned in the Introduction, choked collapsars can result in transient neutrino sources without electromagnetic counterparts, so the total number of neutrino transients that is affected by lensing effects could be significantly larger from what is inferred from GRB population studies. The detection of a single event could be of paramount importance for our understanding of physical processes governing the GRBs.\n\n\n\\section{Final remarks}\\label{conc} \n\nIn this letter we have shown that the primary and secondary images of neutrino transient sources lensed by supermassive black holes cannot be angularly resolved but they could be temporally resolved by next generation instruments. The relativistic images, instead, are too faint and packed to be detected. Thus, we have found that neutrino transients produced by long GRBs can act as sources for gravitational lensing when supermassive black holes are present in foreground galaxies. This sources would have a unique signature, that will allow an easy detection above the background despite a possible low signal-to-noise ratio: repetition. The neutrino fluence can be magnified, but more importantly, the arriving signal will repeat, leading to an unequivocal identification. We conclude that neutrino gravitational lensing can help to establish GRBs as sources of relativistic protons and neutrinos, as proposed by several authors \\cite{meszaros,dermer}.\n\n\\section*{Acknowledgments}\n\nE.F.E. is supported by UBA and CONICET. G.E.R. is supported by grants PIP 5375 (CONICET) and PICT 03-13291 BID 1728\/OC-AR (ANPCyT) and by the Ministerio de Educaci\\'on y Ciencia (Spain) under grant AYA 2007-68034-C03-01, FEDER funds.\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section*{Introduction}\nQuantum mechanics traditionally places the observer `outside' of the system being studied, and refers only to ensembles of data. \nThe theory does not refer to the primary data obtained in individual trials.  So standard quantum mechanics is incomplete for two\nreasons -- it excludes the primary observer \\emph{and} the primary data.  For a theory that claims to be a fundamental law of\nnature, it excludes too much of nature.\n\nStandard theory also makes a distinction between microscopic and macroscopic systems, and this is ambiguous at best.  In addition,\nif one tries to use a quantum mechanical superposition of states to define an ontology in an individual trial, and if a secondary\nobserver like Schr\\\"{o}dinger's cat is included in the system, then the result will not only be paradoxical, it will be wrong.  The\ncat is not in a dual state of consciousness at any time during that famous experiment.\n\nStandard quantum mechanics posits four auxiliary rules that lead to these unacceptable  results.  These rules (called the\n\\emph{sRules}) are: (\\textbf{1}) Quantum measurement occurs only when a quantum mechanical microscopic (or possibly mesoscopic)\nsystem engages a macroscopic measuring device.  (\\textbf{2}) Primary data is collected during individual trials of this kind in\nwhich single eigenvalues are chosen by a stochastic process.  (\\textbf{3}) This choice is followed by a state reduction (i.e., the\ncollapse) in which a stochastically chosen eigenvalue is the sole survivor.  And (\\textbf{4}), the probability of choosing a given\neigenvalue is equal to its square modulus (i.e., the Born rule).  These auxiliary rules are not contained in the Schr\\\"{o}dinger\nequation.  They are supplementary instructions that tell us how to use the Schr\\\"{o}dinger equation\\footnote{These are Copenhagen\nsRules.  There may be any number of variations.  Their essential feature is the Born Rule that establishes the \\emph{only} link\nbetween  observation and the symbols of the theory.}.\n\nOther auxiliary rules are possible -- rules that avoid the difficulties described above.  There are at least two such rule-sets\ncalled the \\emph{nRules} and the \\emph{oRules} that correctly relate Schr\\\"{o}dinger's equation to observation.  Both are\nontologically based, for they place the primary observer `inside' the system -- or at least they allow for that possibility.  With\neither of these rule-sets (as in classical physics) the observer of an external system can extend the system to include himself so\nhe can become a continuous part of the wider system.  That is not possible with the auxiliary rules of standard quantum mechanics,\nwhere the observer is only allowed to ``peek\" at the system from time to time. \n\nIn addition, the nRules provide an ontological description of individual trials, so they include the primary data obtained in each\ntrial.   They give us a running description of each trial.  They are sequentially deterministic except for the time interval between\nstochastic choices, inasmuch as they cannot predict when the next stochastic choice will occur. The nRules are more deterministic\nthan the sRules, but they are less deterministic than classical physics.  The oRules are the least deterministic.  Both\nthe nRules and the oRules present an ontology for individual trials that removes the ambiguity that is now associated with\nSchr\\\"{o}dinger's cat.\n\nThe proposed rule-sets do not make a fundamental distinction between microscopic and macroscopic things.  Each has four rules that\napply equally to all parts of nature.  As a result, both microscopic and macroscopic systems may be said to experience quantum\njumps; and in the nRule case, microscopic states can sometimes undergo state reduction.  Examples are given in this and related\npapers.  Neither one of the proposed rule-sets directly includes the Born Rule that connects probability with square modulus; for in\nboth cases, probability is introduced only through \\emph{probability current}.\n\nThis paper is concerned only with the nRules.  Their adequacy is demonstrated in a number of cases, and their properties (described\nabove) are made apparent.\n\n\n\n\n\n\n\n\n\\section*{Ontology and Epistemology}\n\nThe method of this paper differs from that of traditional quantum mechanics in that it sees the observer in an ontological rather\nthan an epistemological context.  Traditional or standard quantum theory (i.e., Copenhagen) places the observer outside of the\nsystem where operators and\/or operations are used to obtain information about the system.  This is the epistemological model shown\nin \\mbox{Fig.\\ 1}.  \n\n\\begin{figure}[h]\n\\centering\n\\includegraphics[scale=0.8]{aXnRulesFig1.eps}\n\\center{Figure 1: Epistemological Model (Copenhagen)}\n\\end{figure}\n\nThe large OP in Fig.\\ 1 might be a mathematical `operator' or a corresponding physical `operation'.  The observer makes a\nmeasurement by choosing a formal operator that is associated with a chosen laboratory operation.  As a result, the observer is\nforever outside of the observed system -- making operational choices.  The observer is forced to act apart from the system as one who\nposes theoretical and experimental questions to the system, and he can only get answers  through `instantaneous'\ncontacts with the system at a given time.  This model is both useful and epistemologically sound.  \n\n\tHowever, the special rules developed in this paper apply to the system by itself, independent of the possibility that an observer\nmay be inside, and disregarding everything on the outside.  This is the ontological model shown in \\mbox{Fig.\\ 2}.\n\n\\begin{figure}[h]\n\\centering\n\\includegraphics[scale=0.8]{aXnRulesFig2.eps}\n\\center{Figure 2: Ontological Model (requires special rules)}\n\\end{figure}\n\nA measurement occurring inside this system is not represented by a formal operator.  Rather, it is represented by a measuring\ndevice that is itself part of the system.  If the sub-system being measured is $S$ and a detector is $D$, then a measurement\ninteraction is given by $\\Phi = SD$.  If an observer joins the system in order to look at the detector, then the system becomes\n$\\Phi = SDB$, where $B$ is the brain state of the observer.  Contact between the observer and the observed is continuous in this\ncase.\n\nThe ontological model is able to place the observer inside the universe of things and give a full account of his conscious\nexperience there.  It is a departure from traditional quantum mechanics and has three defining characteristics:  (1) It includes\nobservations given by $\\Phi = SDB$ as described above, (2) it allows all conscious observations to be continuous, and (3) it rejects\nthe long-standing Born interpretation of quantum mechanics by introducing probability (only) through the notion of\n\\emph{probability current}. \n\nQuantum mechanical measurement is  said to refer to ensembles of observations but not to individual observations.  In this\npaper I propose a set of four \\emph{nRules (1-4)} that  apply to individual measurements in the ontological model.  I claim that\nthey are a consistent and complete set of rules that can give an ontological description of any individual measurement or\ninteraction in quantum mechanics.  These rules are not themselves a formal theory of measurement.  I make no attempt to understand\n\\emph{why} they work, but strive only to insure that they do work. Presumably, a formal theory can one day be found to explain these\nrules in the same way that atomic theory now explains the empirically discovered rules of atomic spectra, or in the way that current\ntheories of measurement aspire to merge with standard quantum mechanics, or make the neurological connection with conscious\nobservation.\n\n\n\n\n\n\n\n\\section*{The oRules}\n Other papers \\cite{RM1, RM2, RM3} propose another set of rules called the oRules (1-4).  These are similar to the nRules\nexcept that the basis states of reduction are confined to observer brain states, reflecting the views of Wigner and von Neumann. \nLike the nRules, they introduce probability through the notion of `probability current' rather than through square modulus, and they\naddress the state reduction of conscious individuals in an ontological context, thereby giving us an alternative quantum friendly\nontology.  In Ref.\\ 3 they are called simply the \\emph{rules (1-4)}.  Like the nRules, the oRules are not a formal theory of\nmeasurement  for they require a wider theoretical framework to be understood.  I do not finally choose one of the rule-sets or\npropose an explanatory theory.  I am only concerned with how state reduction might occur in each case.  For the above stated\nreasons, both of these rule-sets are more acceptable than the sRules; and so far as I am aware, there is no observation that can\ndistinguish between the two.\n\n\n\n\n\n\n\\section*{The Interaction: Particle and Detector}\n\n\t\tBefore introducing the nRules, we will apply  Schr\\\"{o}dinger's equation to a `microscopic' particle interacting with a\n`macroscopic' detector in order to see what difficulties arise.  These two objects are assumed to be initially independent and\ngiven by the equation \n \n\\begin{equation}\n\\Phi(t)=exp(-iHt)\\psi_i\\otimes d_i\n\\end{equation}\nwhere $\\psi_i$ is the initial particle state and $d_i$ is the initial detector state.  The particle is then allowed to pass over the\ndetector, where the two interact with a cross section that may or may not result in a capture.  After the interaction begins at a\ntime $t_0$, the state is an entanglement in which the particle variables and the detector variables are not separable.  \n\nThe first component of the resulting system is the detector $d_0$ in its ground state prior to capture, and the second, third, and\nfourth components are the detector in various states of capture   given by $d_w$, $d_{m}$, and $d_d$.  \n\\begin{equation}\n\\Phi(t \\ge t_0) =\\psi(t)d_0 + d_w(t) \\rightarrow d_{m}(t) \\rightarrow d_d(t)\n\\end{equation}\nwhere $d_w(t)$ represents the entire detector immediately after a capture when only the window side of the detector is affected, and\n$d_d(t)$ represents the entire detector when the result of a capture has worked its way through to the display side of the\ndetector.   The middle state $d_{m}(t)$ represents the entire detector during stages in between, when the effects of the capture\nhave found their way into the interior of the detector, but not as far as the display. \n\nThe state $\\psi(t)$ is a free particle as a function of time, including all the incoming and scattered components.  It does no harm\nand it is convenient to let $\\psi(t)$ carry the total time dependence of the first component, and to let $d_0$ be normalized\nthroughout The first component in Eq.\\ 2 is a superposition of all possible scattered waves of $\\psi(t)$ in\nproduct with all possible recoil states of the ground state detector, so $d_0$ is a spread of detector states including all the\nrecoil possibilities together with their correlated environments.  Subsequent components are also superpositions of this kind. \nThey include all of the recoil components of the detector that have captured the particle. \n  \nThere is a clear discontinuity or ``quantum jump\" between the two components $d_0$ and $d_w$ at the detector's window interface. \nThis discontinuity is represented by a ``plus\" sign and can only be bridged by a stochastic jump.  The remaining evolution from\n$d_w(t)$ to $d_d(t)$ is connected by ``arrows\"  and is continuous and classical.  These three detector states develop in time and\nmay be represented by the single component \n\\begin{displaymath}\nd_1(t) = d_w(t) \\rightarrow d_{m}(t)\\rightarrow d_d(t)\n\\end{displaymath}\n so\n\\begin{equation}\n\\Phi(t \\ge t_0)=\\psi(t)d_0 + d_1(t) \n\\end{equation}\nThe capture state $d_1(t)$ in Eq.\\ 3 is equal to zero at $t_0$ and increases with time\\footnote{Each component in Eq.\\ 3 has an\nattached environmental term $E_0$ and $E_1$ that is not shown.  These are orthogonal to one another, insuring local decoherence. \nBut even though Eq.\\ 3 may be decoherent locally, we  assume that the macroscopic states $d_0$ and $d_1$ are fully coherent when\n$E_0$ and $E_1$ are included.  So Eq.\\ 3 and others like it in this paper are understood to be coherent when universally\nconsidered.  We  call them ``superpositions\", reflecting their global rather than their local\nproperties.}$^,$\\footnote{Superpositions of macroscopic states have been found at low temperatures \\cite{JRF}.  The components of\nthese states are locally coherent for a measurable period of time.}$^,$\\footnote{Equation  3 can be written with coefficients\n$c_0(t)$ and $c_1(t)$ giving $\\Phi(t \\ge t_0) = c_0(t)\\psi(t)d_0 + c_1(t)d_1$, where the states $\\psi(t)$, $d_0$, and\n$d_1$ are normalized throughout.  We let $c_0(t)\\psi(t)$ in this expression be equal to $\\psi(t)$ in Eq.\\ 3, and let $c_1(t)d_1$ be\nequal to $d_1(t)$ in Eq.\\ 3.}$^,$\\footnote{It is important to realize that\nthe interaction Hamiltonian can only connect $\\psi(t)d_0$ with the window state $d_w(t)$, which is the \\emph{launch state} of the\nactivated detector.  It cannot pour probability current directly into a state that is more dynamically advanced, like $d_m(t)$ or\n$d_d(t)$.  Therefore, at every moment during the current flow, a new state $d_w(t)$ is launched, since the state that was launched\nimmediately before that time has moved on (dynamically) to become $d_m(t)$. This means that the component $d_1(t)$ in Eq.\\ 3 is  a\nsuperposition of a continuum of all the detector states that have been launched at all previous times during the interaction.  For\nthe time being we will ignore this complication and come back to it (in Footnote 6) after we have examined this case from the point\nof view of the nRules.}. \n\n\n\n\n\n\n\n\n\\section*{Add an Observer}\nAssume that an observer is looking at the detector in Eq. 1 from the beginning.  \n\\begin{displaymath}\n\\Phi(t)=exp(-iHt)\\psi_i\\otimes D_iB_i\n\\end{displaymath}\nwhere $B_i$ is the observer's initial brain state that is entangled with the detector $D_i$.  This brain is understood to\ninclude \\emph{only} higher order brain parts -- that is, the physiology of the brain that is directly associated with consciousness\nafter all image processing is complete.  All lower order physiology leading to $B_i$ is assumed to be part of the detector.  The\ndetector is now represented by a capital $D$, indicating that it includes the bare detector  \\emph{plus} the low-level\nphysiology of the observer.\n\nFollowing the interaction between the particle and the detector, we  have\n\\begin{eqnarray}\n\\Phi(t \\ge t_0) &=& \\psi(t)D_0B_0 + D_w(t)B_0 \\rightarrow D_{m}(t)B_0 \\rightarrow D_d(t)B_1 \\hspace{.5cm}  \\\\\n\\mbox{or} \\hspace{.5cm} \\Phi(t \\ge t_0) &=& \\psi(t)D_0B_0 + D_1(t)B_1 \\nonumber\n\\end{eqnarray}\nwhere $B_0$ is the observer's brain when the detector is observed to be in its ground state $D_0$, and $B_1$ is the brain when the\ndetector is observed (only at the display end) to be in its capture state $D_1$.   As before, a discontinuous quantum jump is\nrepresented by a plus sign, and the continuous evolution of a single component is represented by an arrow.  \n\nIf the interaction is long lived compared to the time it takes for the signal to travel through the detector in Eq.\\ 4 (as in the\ncase of a long lived radioactive decay), then the superposition in that equation might exist for a long time before a capture.  \nThis means that there can be two active brain states of this observer in superposition, where one sees the detector in its ground\nstate and the other simultaneously sees the detector in its capture state.  Equation 4 therefore invites a paradoxical\ninterpretation like that associated with Schr\\\"{o}dinger's cat.  This ambiguity cannot be allowed.  It is not acceptable on\nempirical grounds.  An observer who watches a detector in these circumstances will \\emph{not} experience dual states of\nconsciousness.  \n\nThe nRules of this paper must not only provide for a stochastic trigger that gives rise to a state reduction, and describe that\nreduction, they must also insure than an empirical ambiguity of this kind will not occur.  \n\n\n\n\n\n\n\\section*{The nRules}\n\tThe first rule establishes the existence of a stochastic trigger.  This is a property of the system that has nothing to do with\nthe kind of interaction taking place or its representation.  Apart from making a choice, the trigger by itself has no effect on\nanything.  It initiates a state reduction only when it is combined with nRules 2 and 3.\n\n\\vspace{.4cm}\n\n\\noindent\n\\textbf{nRule (1)}: \\emph{For any subsystem of n complete components in a system having a total square modulus equal to s, the\nprobability per unit time of a stochastic choice of one of those components at time t is given by $(\\Sigma_nJ_n)\/s$, where\nthe net probability current $J_n$ going into the $n^{th}$ component at that time is positive.}\n\n\\noindent\n[\\textbf{note}: A \\emph{complete component} is a solution of Schr\\\"{o}dinger's equation that includes all of the (symmetrized)\nobjects in the universe.  It is made up of \\emph{complete states} of those objects  including all their state variables.  If\n$\\psi(x_1, x_2)$ is a two particle system with inseparable variables $x_1$ and $x_2$, then $\\psi$ is considered to be a single \nobject.  All such  objects are included in a complete component.  A component that is a sum of\nless than  the full range of a variable (such as a partial Fourier expansion) is not complete. This is why representation does not\nmatter to the stochastic trigger.]\n\n\\noindent\n[\\textbf{note}: Functions are not normalized in this treatment.  Instead, probability currents are normalized at each moment of\ntime by dividing $J$ by the value of $s$ at each moment of time. \n\n\\vspace{.4cm}\n\nThe second rule specifies the conditions under which \\emph{ready states} appear in solutions of Schr\\\"{o}dinger's equation.\nThese are understood to be the basis states of a state reduction. Ready states are always ``underlined\" in this treatment.\n\n\\vspace{.4cm}\n\n\\noindent\n\\textbf{nRule (2)}: \\emph{If a noncyclic interaction produces complete components that are discontinuous with the initial \ncomponent, then all of the new states that appear in these components will be ready states.}\n\n\\noindent\n[\\textbf{note}: A cyclic interaction between two component is one that produces continuous oscillations.  A \\emph{noncyclic\ninteraction} goes in one direction only.\n\n\\noindent\n[\\textbf{note}: Continuous means continuous in all variables. Although solutions to Schr\\\"{o}dinger's equation change\ncontinuously in time, they can be \\emph{discontinuous} in other variables -- e.g., the separation between the $n^{th}$ and the $(n +\n1)^{th}$ orbit of an atom with no orbits in between.  A discontinuity  can also exist between macroscopic states that are locally\ndecoherent.   For instance, the displaced detector states $d_0$ (ground state) and $d_w$ (window capture state) appearing in\n\\mbox{Eq.\\ 2} are discontinuous with respect to detector variables.  There is no state in between.  Like atomic orbits, these\ndetector states are a `quantum jump' apart.]\n\n\\noindent\n[\\textbf{note}: The \\emph{initial component} is the first complete component that appears in a given solution of Schr\\\"{o}dinger's\nequation.  A  solution is defined by a specific set of boundary conditions.  So Eqs.\\ 1 and 3 are both included in the single\nsolution that contains the discontinuity between $d_0$ and $d_1$, where Eq.\\ 1 (together with its complete environment) is the\ninitial state.  However, boundary conditions change with the collapse of the wave function.  The   component that\nsurvives a collapse will be complete, and will be the initial component of the new solution.]\n\n\\noindent\n[\\textbf{note}: If a noncyclic interaction does not produce complete components that are discontinuous with the\ninitial component, then the Hamiltonian will develop the state in the usual way, independent of these rules.]\n\n\\vspace{.4cm}\n\nThe collapse of a wave function and the change of a ready state to a \\emph{realized} state is provided for by nRule (3).  If a\ncomplete state is not `ready' it will be called `realized'.  We therefore introduce dual state categories where ready\nstates are the basis states of a collapse.  They are on stand-by, ready to be stochastically chosen and converted by nRule (3) to\nrealized states.  In this paper, realized states are \\emph{not} underlined.    \n\n\\vspace{.4cm}\n\n\\noindent\n\\textbf{nRule (3)}: \\emph{If a component is stochastically chosen during an interaction, then all of the ready states that result\nfrom that interaction (using nRule 2)  will become realized, and all other components in the superposition will be immediately\nreduced to zero.}\n\n\\noindent\n[\\textbf{note}: The claim of an immediate (i.e., discontinuous) reduction is the simplest possible way to describe the collapse\nof the state function.  A collapse is brought about by an instantaneous change in the boundary conditions of the\nSchr\\\"{o}dinger equation, rather than by the introduction of a new `continuous' mechanism of some kind.]\n\n\n\\noindent\n[\\textbf{note}:  This collapse does not preserve normalization.  That does not alter probability of subsequent\nreductions because of the way probability per unit time is defined in nRule (1); that is, current $J$ is divided by the total square\nmodulus.  Again, currents are normalized in this treatment -- not functions.]\n\n\n\\noindent\n[\\textbf{note}: If the stochastic trigger selects a component that does not contain ready states, then there will be no nRule (3) \nstate reduction.]\n\n\\vspace{.4cm}\n\nOnly positive current going into a \\emph{ready component} (i.e., a component containing ready states) is physically meaningful\nbecause it represents positive probability.  A negative current (coming out of a ready component) is not physically meaningful and\nis not allowed by nRule (4).  Without this restriction, probability current might flow in-and-out of one ready component and into\nanother.  The same probability current  would then be `used' and `reused'.  Given  the above rules, this would \ndistort the total probability of a process.  If the nRules are to work, the total integrated positive current (divided by $s$) must\nbe no greater than 1.0.  To insure this we say     \n\n\\vspace{.4cm}\n\n\n\\noindent\n\\textbf{nRule (4)}: \\emph{A ready component cannot transmit probability current.}\n\n\\vspace{.4cm}\nAlthough it can receive current that increases its square modulus, a ready state is dynamically terminal.  It cannot develop beyond\nitself.  If a ready state $\\underline{S}_1(t)$ evolves from a state $S_0(t)$, then Schr\\\"{o}dinger's equation $H[S_0(t) +\n\\underline{S}_1(t)] = i\\hbar\\frac{d}{dt}[S_0(t) + \\underline{S}_1(t)]$ will change $\\underline{S}_1(t)$ in the usual way. \nHowever, nRule (4) will prevent the creation of a second order component.  The state $\\underline{S}_1(t)$ is time dependent because\nits square modulus increases \\emph{and} because it reflects the dynamical changes  coming from $S_0(t)$ at every moment of time, \nbut  it does not advance dynamically on its own.  It is the launch state of a new solution of Schr\\\"{o}dinger's equation if and when\nit is stochastically chosen, and it will contain all the initial conditions of that solution.  Those initial conditions are not\napplied until the moment of choice. \n\nWhile no theoretical reason can be given to explain Rule(4), its important consequences are demonstrated throughout the rest of\nthis paper.\n\n\n\n\n\n\n\n\n\n\n\n\\section*{Particle\/Detector Revisited}\nWhen the nRules are applied to the particle\/detector interaction, Eq.\\ 2 becomes \n\\begin{displaymath}\n\\Phi(t \\ge t_0) = \\psi(t)d_0 + \\underline{d}_w(t)\n\\end{displaymath}\nwhere the quantum jump (+ sign)  is discontinuous and noncyclic, where \\mbox{nRule (2)} requires that\n$\\underline{d}_w(t)$ is a ready state, and where the other components of the detector ($d_m$ and $d_d$) are zero because nRule (4)\nwill not allow $\\underline{d}_w(t)$ to pass current to them.  At $t_0$, the first component is maximum and the second is zero, but\n$\\underline{d}_w(t)$ increases in time because of the probability current flow from $\\psi(t)d_0$.  These components are\ncomplete because the environment of each (not shown) is assumed to be present.\n\n\tThe ready component in this equation is time dependent because of its increase in square modulus \\emph{and} because it duplicates\nthe moment-to-moment changes that occur within the detector (such as molecular changes) \\emph{although} it will not advance\ndynamically to $d_m$.  So long a $\\underline{d}_w(t)$ is a ready state, it will not pass current along to its successors.  As\nindicated above, it is a function that contains the boundary conditions of the next solution of Schr\\\"{o}dinger's equation -- that\nis, the `collapsed' solution that is realized when $\\underline{d}_w(t)$ is stochastically chosen.  So the effect of nRule (4) is to\nput the boundary conditions of the `next' solution on hold until there is a stochastic hit.  The nRules  then launch the new\nsolution with boundary conditions that are inherited at that moment from the old solution.  \n\n\t \tIf there is a stochastic hit at time $t_{sc}$, then a continuous classical evolution will give\n\\begin{displaymath}\n\\Phi(t\\ge t_{sc} > t_0)= d_w(t) \\rightarrow d_m(t) \\rightarrow d_d(t) \n\\end{displaymath}\nso the capture is eventually registered at the display end of the detector.\n\n\t If there is \\emph{no} stochastic hit on $\\underline{d}_w(t)$ it will become a \\emph{phantom} component.  A component is a phantom\nwhen there is no longer probability current flowing into it (in this case because the interaction is complete), and when there can\nbe no current flowing out of it because it is a ready component that complies with nRule (4).  A phantom component can be dropped\nout of the equation without consequence.  Doing so only changes the definition of the system -- it changes the total square modulus\n$s$ that normalizes the current in nRule (1).  This is the same kind of redefinition that occurs in standard practice when one\nchooses to renormalize a system at some new starting time.  Keeping a phantom is like keeping the initial system.  Because of nRule\n(3), kept phantoms are reduced to zero whenever another component is stochastically chosen.  \n\n\tThe nRules place this particle\/detector system in an ontological setting, for they give an \\emph{insider's} answer to the\nprobability question.  The nRules ask:  What is the probability that $\\underline{d}_w(t)$ will be stochastically chosen during the\nnext time interval $dt$; and then, what is the probability that it will be stochastically chosen during the time interval $dt$\nafter that, etc?  The nRules are always concerned with what happens next.  Probabilities that are associated with the second order\nstates like $d_m(t)$ and $d_d(t)$ are ruled out by nRule (4) until the fate of $\\underline{d}_w(t)$ is determined.  This is the\nmost important consequence of nRule (4) -- it does not allow a stochastic leap over the \\emph{next} (ready) state of the system. \nThe insider is concerned with the temporal ordering of states, and the nRules address that concern.\n\nIn contrast, the sRules ask:  What is the probability of finding $d_0$, $d_w$, $d_m$, or $d_d$ at some finite time $T$ after\n$t_0$?  This is an outsider's question.  It is the question asked by one who can only observer the system at distinct and finitely\nseparated times like $t_0$ and $T$.\n\n\n\n\n\n\n\n\n\n\n\\section*{Particle\/Detector\/Observer Revisited}\nTo see how the nRules carry out a particle capture when an observer is a witness, we apply them to the first row of Eq.\\ 4.  As\nbefore, this only affects the first two components\n\\begin{equation}\n\\Phi(t \\ge t_0)=\\psi(t)D_0B_0 + \\underline{D}_w(t)B_0 \n\\end{equation}\nbecause nRule (4) will not allow $\\underline{D}_w(t)$ to pass probability current to the other components.  Component\n$\\underline{D}_w(t)$ is `ready' because it is a discontinuous and noncyclic quantum jump away from $\\psi(t)D_0B_0$ and it is complete\nbecause it includes the (not shown) entangled environment.  Again, the time dependence of $\\underline{D}_w(t)$ does not\nrepresent a dynamical evolution beyond the changes given to it by the first component.  It does not evolve dynamically\non its own.  And again, the sub-0 on $B_0$ indicates an awareness of the ground state $D_0$ of the detector.  Since the second brain\nstate in Eq.\\ 5 is the same as the first, there is only one brain state $B_0$ in this superposition.  A cat-like ambiguity is\nthereby avoided.  Equation 5 now \\emph{replaces} Eq.\\ 4.   \n\n\tEquation 5 is the state of the system before there is a stochastic hit that produces a state reduction.  If there is a capture,\nthen there will be a stochastic hit on the second component of Eq.\\ 5 at a time $t_{sc}$. This will reduce the first component to\nzero according to nRule (3), and convert the ready state in the second component to a realized state.\n\\begin{displaymath}\n\\Phi(t = t_{sc} > t_0) = D_w(t)B_0\n\\end{displaymath}\nThe observer is still conscious of the detector's ground state in this equation because the capture has only affected the window end\nof the detector.  But after $t_{sc}$, a continuous evolution will produce\n\\begin{equation}\n\\Phi(t \\ge t_{sc} > t_0) = D_w(t)B_0 \\rightarrow D_{m}(t)B_0 \\rightarrow D_d(t)B_1\n\\end{equation}\nSince this equation represents a \\emph{single component} that evolves in time as shown, there is no time at which both $B_0$ and\n$B_1$ appear simultaneously.  There is therefore no cat-like ambiguity in this equation.\n\n\\vspace{.4cm}\n\n\tStandard quantum mechanics  gives us Eq.\\ 4 by the same logic that it gives us Schr\\\"{o}dinger's cat and\nEverett's many worlds.  \\mbox{Equation 4} (top or bottom row) is a single equation that simultaneously presents two different\nconscious brain states, resulting in an unacceptable ambiguity.  But with the nRules, each Schr\\\"{o}dinger solution is\nseparately grounded by its own stochastically selected boundary, allowing the rules to correctly and unambiguously predict the\ncontinuous experience of the observer in two stages.  This is accomplished by replacing `one' equation in \\mbox{Eq.\\ 4} with `two'\nequations in Eqs.\\ 5 and 6.   Equation 5 describes the state of the system \\emph{before} capture, and Eq.\\ 6 describes the state of\nthe system \\emph{after} capture.  Before and after are two \\emph{different} solutions to Schr\\\"{o}dinger's equation, specified by\ndifferent boundary conditions.  Remember we said that the stochastic trigger selects the new boundary that applies to the reduced\nstate.  So it is the stochastic event that separates the two solutions \\mbox{-- defining} before and after.  \n\n\t\tIf there is no stochastic hit on the second component in Eq.\\ 5 it will become a phantom component.  The new\nsystem is then just the first component of that equation.  This corresponds to the observer continuing to see the ground state\ndetector $D_0$, as he should in this \ncase\\footnote{Had the reasoning of Footnote 5 been applied to Eq.\\ 4, the component $D_1(t)B_1$\nwould be a superposition of the continuum of launch possibilities.  It would include a superposition of all the brain states $B_0$\nthat existed before the signal could have traveled through the detector to reach the brain, plus all the brain states $B_1$ that\nwere reached after that time.  This would have produced a massive cat-like paradox prior to a stochastic hit or state reduction of\nany kind.  However, the nRules also avoid this difficulty because they produce only \\emph{one} launch component\n$D_1(t_{sc})B_1$.}.\n\n\n\n\n\n\n\n\n\\section*{A Terminal Observation}\n\tAn observer who is inside a system must be able to confirm the validity of the Born rule that is normally applied from the\noutside.  To show this, suppose our observer is not aware of the detector during the interaction with the particle, but\nhe looks at the detector after  a time $t_f$ when the primary interaction is\ncomplete. Assume initial normalization equal to 1.0. During that interaction we have \n\\begin{equation}\n\\Phi(t_f > t \\ge t_0) = [\\psi(t)d_0 + \\underline{d}_w(t)]\\otimes X\n\\end{equation}\nwhere $X$ is the unknown state of the observer prior to the physiological \ninteraction. \n\nAssume there has \\emph{not} been a capture.  Then after the interaction is complete and before the observer looks at the detector\nwe have\n\\begin{displaymath}\n\\Phi(t \\ge t_f > t_0) = [\\psi(t)d_0 + \\underline{d}_w(t_f)]\\otimes X\n\\end{displaymath}\nwhere there is no longer a probability current flow inside the bracket. The second component in the bracket is therefore a\nphantom.  There is no current flowing into it, and none can flow out of it because of nRule (4).  So the equation is\nessentially   \n\\begin{displaymath}\n\\Phi(t \\ge t_f > t_0) = \\psi(t)d_0\\otimes X\n\\end{displaymath}\nWhen the observer finally observes the detector at $t_{ob}$ he will get\n\\begin{displaymath}\n\\Phi(t \\ge t_{ob} > t_f > t_0) = \\psi(t)d_0\\otimes X \\rightarrow \\psi(t)D_0B_0 \n\\end{displaymath}\nwhere the physiological process (represented by the arrow) carries $\\otimes X$ into $B_0$ and $d_0$ into $D_0$ by a continuous\nclassical progression leading from independence to entanglement.   This corresponds to the observer coming on board to witness\nthe detector in its ground state as he should when is no capture.  The probability of this happening (according to the sRules) is\nequal to the square modulus of $\\psi(t)d_0\\otimes X$ in Eq.\\ 7.\n\nIf the particle \\emph{is} captured during the primary interaction, there will be a stochastic hit on the second component inside\nthe bracket of Eq.\\ 7 at some time $t_{sc} < t_f$.  This results in a capture given by\n\\begin{displaymath}\n\\Phi(t_f > t = t_{sc} > t_0) = d_w(t)\\otimes X\n\\end{displaymath}\nafter which \n\\begin{displaymath}\n\\Phi(t_f > t \\ge  t_{sc} > t_0) = [d_w(t) \\rightarrow d_m(t) \\rightarrow d_d(t)]\\otimes X \n\\end{displaymath}\n\\begin{displaymath}\n\\Phi(t \\ge t_f >   t_{sc} > t_0) =  d_1(t)\\otimes X\n\\end{displaymath}\nas a result of the classical progression inside the detector.  When the observer does become aware of the detector at $t_{ob} > t_f$\nwe finally get\n\\begin{displaymath}\n\\Phi(t \\ge t_{ob} > t_f > t_{sc} > t_0) = d_1\\otimes X \\rightarrow D_1B_1\n\\end{displaymath}\nSo the observer comes on board to witness the detector in its capture state with a probability (according to the sRules) equal to\nthe square modulus of\n$\\underline{d}_w(t_f)\\otimes X$ in Eq.\\ 7.  The nRules therefore confirm the Born rule, in this case as a theorem.\n\n\n\n\n\n\n\\section*{An Intermediate Case}\n\t\tIn Eq.\\ 5 the observer is assumed to interact with the detector from the beginning.  Suppose that the incoming particle results\nfrom a long half-life decay, and that the observer's physiological involvement only \\emph{begins}  in the middle of the\nprimary interaction.  Before that time we will have\n\\begin{displaymath}\n\\Phi(t \\ge t_0) = [\\psi(t)d_0 + \\underline{d}_w(t)]\\otimes X\n\\end{displaymath}\nwhere again $X$ is the unknown brain state of the observer prior to the physiological interaction.  Primary probability current here\nflows between the detector components inside the bracket.  Let the physiological interaction begin at a time $t_{look}$ after\n$\\underline{d}_w(t)$ has gained some amplitude, and suppose it lasts for a period of time equal to $\\pi$.   Then\n\\begin{eqnarray}\n&\\Phi(t=t_{look} > t_0) = \\psi(t)d_0\\otimes X + \\underline{d}_w(t) \\otimes X&  \\\\\n&\\hspace{3.2cm}\\downarrow\\hspace{1.6cm}\\downarrow&\\nonumber\\\\\n&\\Phi(t=t_{look} + \\pi > t_{look} > t_0) = \\psi(t)D_0B_0 + \\underline{D}_w(t) B_0& \\nonumber\n\\end{eqnarray}\nwhere the arrows mean that the evolution from the first to the second row is classical and continuous. That evolution carries\n$\\otimes X$ into $B_0$ and $d_0$ into $D_0$ by a process that leads from independence to entanglement.  So while the second\ncomponent in each row gains square modulus because of the primary interaction (plus signs), the observer is simultaneously coming on\nboard by a continuous process (arrows).  \n\nThe second component at each moment of time during the physiological interaction in Eq.\\ 8 is the launch state of the new solution\nof the Schr\\\"{o}dinger equation -- if there is a stochastic hit at that moment.  This component establishes the boundary conditions\nof any  newly launched solution.   \n\nAfter the time $t_{ob} =  t_{look} + \\pi$ we can write Eq.\\ 8 as \n\\begin{equation}\n\\Phi(t \\ge t_{ob} > t_0) = \\psi(t)D_0B_0 + \\underline{D}_w(t)B_0\n\\end{equation}\nThis equation is identical with Eq.\\ 5; so from this moment on, it is as though the observer has been on board from the beginning.  \n\n  \tIf there is a subsequent capture at a time $t_{sc}$, this will become like Eq.\\ 6.\n\\begin{equation}\n\\Phi(t \\ge t_{sc} > t_{ob} > t_0) = D_w(t)B_0 \\rightarrow  D_m(t)B_0 \\rightarrow D_d(t)B_0\n\\end{equation}\n\n\tIf a stochastic hit occurs between $t_{look}$ and $t_{ob}$, then the ready component at that moment (the second component in Eq.\\\n8) will be chosen and made a realized state.  It will then proceed classically and continuously to $D_dB_1$ as in Eq.\\ 10. \n\n\n\n\n\n\n\n\n\n\\section*{A Second Observer}\nIf a second observer is standing by while the first observer interacts with the detector during the primary interaction, the state\nof the system will be\n\\begin{displaymath}\n\\Phi(t \\ge  t_0) = [\\psi(t)D_0B_0 + \\underline{D}_w(t)B_0]\\otimes X\n\\end{displaymath}\nwhere $X$ is an unknown state of the second observer prior to his interacting with the system.  The detector $D$ here includes the\nlow-level physiology of the first observer.  A further expansion of the detector will include the second observer's low-level\nphysiology when he comes on board.  The detector will then split into two parallel paths, one connecting to the first observer and\nthe other  connecting to the second observer.    When a product of brain states appears in the form $BB$ or $B\\otimes X$, the\nfirst term will refer to the first observer and the second to the second observer.  \n\t\nThe result of the second observer looking at the detector will be the same as that found for the first observer in the previous\nsection, except now the first observer will be present in each case.  In particular, the equations similar to \\mbox{Eqs.\\ 8, 9, and\n10} are now \n\\begin{eqnarray}\n&\\Phi(t=t_{look} + t) = \\psi(t)d_0\\otimes X + \\underline{d}_w(t) \\otimes X \\rightarrow& \\nonumber\\\\\n &\\Phi(t = t_{look} + \\pi > t_{look} > t_0) = [\\psi(t)D_0B_0B_0 + \\underline{D}_w(t)B_0B_0]&  \\nonumber\\\\\n&\\Phi(t \\ge t_{ob}  > t_0) = \\psi(t)D_0B_0B_0 + \\underline{D}_w(t)B_0B_0&  \\nonumber \\\\\n&\\Phi(t \\ge t_{sc} > t_{ob}  > t_0) = D_w(t)B_0B_0 \\rightarrow D_m(t)B_0B_0 \\rightarrow D_d(t)B_1B_1&  \\nonumber \n\\end{eqnarray}\nThese will all yield the same result for the new observer as they did for the old observer.  In no case will the nRules produce a\nresult like $B_1B_2$ or $B_2B_1$.\n\n\\vspace{.4cm}\n\nUp to this point we have seen how the nRules go about including observers inside a system in an ontological model.  These rules\ndescribe when and how the observer becomes conscious of measuring instruments, and replicate common empirical experience in these\nsituations. The nRules are also successfully applied in another paper \\cite{RM5}  where two versions of the Schr\\\"{o}dinger cat\nexperiment are examined.  In the first version a conscious cat is made unconscious by a stochastically initiated process; and in the\nsecond version an unconscious cat is made conscious by a stochastically initiated process. \n\nIn the following sections we turn attention to another problem -- the requirement that macroscopic states must appear in\ntheir normal sequence.   This sequencing chore represents a major application of nRule (4) that is best illustrated in the case of a\nmacroscopic counter.\n\n\n\n\n\n\n\n\n\\section*{A Counter}\n\nIf a beta counter that is exposed to a radioactive source is turned on at time $t_0$, its state function will be given by\n\\begin{displaymath}\n\\Phi(t \\ge   t_0) = C_0(t) + \\underline{C}_1(t)\\\n\\end{displaymath}\nwhere $C_0$ is a counter that reads zero counts, $C_1$ reads one count, and $C_2$ (not shown) reads two counts, etc.  The second\ncomponent $\\underline{C}_1(t)$ is zero at $t_0$ and increases in time.  The underline indicates that it is a ready state as\nrequired by nRule (2).  $C_2$ and higher states do not appear in this equation because \\mbox{nRule (4)} forbids current to leave\n$\\underline{C}_1(t)$.  Ignore the time required for the capture effects to go from the window to the display end of the counter.  \n\nThe $0^{th}$ and the $1^{st}$ components are the only ones that are initially active, where the current flow is $J_{01}$\nfrom the $0^{th}$ to the $1^{st}$ component.  The resulting distribution at some time $t$ before $t_{sc}$ is shown in Fig.\\ 3,\nwhere $t_{sc}$ is the time of a stochastic hit on the second component.  \n\n\\begin{figure}[h]\n\\centering\n\\includegraphics[scale=0.7]{aXnRulesFig3.eps}\n\\center{Figure 3: Square moduli before the first stochastic hit}\n\\end{figure}\n\nThis means that the $1^{st}$ component \\emph{will} be chosen because all of the current from the (say,\nnormalized) $0^{th}$ component will pore into the $1^{st}$ component making $\\int J_{01}dt = 1.0$.  Following the stochastic hit\non the $1^{st}$ component, there will be a collapse to that component because of \\mbox{nRule (3)}.  The first two dial readings\nwill therefore be sequential, going from 0 to 1 without skipping a step such as going directly from 0 to 2.  It is nRule (4) that\nenforces the no-skip behavior of a counter; for without it, any component in the superposition might be chosen as a result of\nprobability current flowing into it.    It is empirically mandated that these states should always follow in sequence without\nskipping a step. \n\n\\begin{figure}[h]\n\\centering\n\\includegraphics[scale=1.2]{aXnRulesFig4.eps}\n\\center{Figure 4: Square moduli before second hit}\n\\end{figure}\n\nWith the stochastic choice of the $1^{st}$ component at $t_{sc}$, the process will begin again as shown in \nFig.\\ 4.  This  leads with certainty to a stochastic choice of the $2^{nd}$ component.  That certainty is accomplished by the\nwording of nRule (1) that requires current normalization at each moment of time; that is, the  current  $J_{12}$ is divided by the\ntotal square modulus at each moment.  The total integral $\\int J_{12}dt$  is less than 1.0 in  Fig.\\ 4 because of the reduction that\noccurred in \\mbox{Fig.\\ 3};  but it is restored to 1.0 when divided by the (new) total square modulus.  It is therefore certain that\nthe $2^{nd}$ component will be chosen.\n\nAnd finally, with the choice of the $2^{nd}$ component, the process will resume again with current $J_{23}\/s$ going from the\n$2^{nd}$ to the $3^{rd}$ component.  This leads with certainty to a stochastic choice of the $3^{rd}$ component.  \n\n If an observer watches the counter from the beginning he will be able to see it go sequentially from $C_0$ to $C_1$, to $C_2$,\netc., for he is himself a continuous part of the system.  He does not have to `peek' intermittently like an\nepistemological observer who is not part of the system as has been said.  Although the empirical experience of the ontological\n(nRule) observer is different from the epistemological (sRule) observer, there is no contradiction between the two.  That's because\nthe nRules and the sRules answer two different questions about probability as previously noted.  The nRules ask: What is the\nprobability that the system will jump to the \\emph{next} counter state in the next differentially small increment of time; and the\nsRules ask: What it the probability that an outside observer will find the system in any one of its possible counter states if he\nlooks after some finite time $T$?  \n\n\n\n\n\n\n\n\n\n\\section*{The Parallel Case} \nNow imagine parallel states in which a quantum process may go either clockwise or counterclockwise as shown in Fig. 5.  Each\ncomponent includes a macroscopic piece of laboratory apparatus $A$, where the Hamiltonian provides for a discontinuous clockwise\ninteraction going from the $0^{th}$ to the $r^{th}$ state, and another one going from there to the final state $f$; as well as a\ncomparable counterclockwise interaction from the $0^{th}$ to the $l^{th}$ state and from there to the final \\mbox{state $f$}.  The\nHamiltonian does not provide a direct route from the $0^{th}$ to the final state, so the system will choose stochastically between a\nclockwise and a counterclockwise route.  Ready states $\\underline{A}_l$ and $\\underline{A}_r$ are the \\emph{eigenstates} of that\nchoice, and contain the boundary conditions for each separate path.\n\n\\begin{figure}[t]\n\\centering\n\\includegraphics[scale=0.8]{aXnRulesFig5.eps}\n\\center{Figure 5: Possible parallel decay routes}\n\\end{figure}\n\nWith nRule (4) in place, probability current cannot initially flow from either of the intermediate states to the final state, for\nthat would require current flow from a ready state.  The dashed lines in Fig.\\ 5 indicate the forbidden\ntransitions.  But once the state $\\underline{A}_l$ (or $\\underline{A}_r$) has been stochastically chosen, it will become a\nrealized state $A_l$ (or $A_r$) and a subsequent transition to $\\underline{A}_f$ can occur that realizes $A_f$.  \n\nThe effect of nRule (4) is therefore to force this macroscopic system into a classical sequence that goes either clockwise or\ncounterclockwise.  Without it, the system might make a  second order transition (through one of the intermediate states) to the final\nstate, without the intermediate state being realized.  The observer would then see the initial state followed by the final state,\nwithout knowing (in principle) which pathway was followed.  This is a familiar property of continuous microscopic evolution.  In\nHeisenberg's famous example formalized by Feynman, a microscopic particle observed at point $a$ and later at point $b$ will travel\nover a quantum mechanical superposition of all possible paths in between.  Without nRule (4), macroscopic objects facing\ndiscontinuous and noncyclic parallel choices would do the same thing.  But that should not occur.  The fourth nRule forces this\nparallel system into one or the other classical path, so it is not a quantum mechanical superposition of both paths.  \n\n\n\n\n\n\n\n\n\n\\section*{A Continuous Variable}\nIn the above examples nRule (4) guarantees that sequential discontinuous steps in a superposition are not passed over. \nIf the variable itself is classical and continuous, then continuous observation is possible without the\nnecessity of stochastic jumps.  In that case we do not need \\mbox{nRule (4)} or any of the \\mbox{nRules (1-4)}, for they do not\nprevent or in any way qualify the motion.  \n\nHowever, a classical variable may require a quantum mechanical jump-start.  For instance, the\nmechanical device that is used to  seal the fate of Schr\\\"{o}dinger's cat (e.g., a falling hammer) begins its motion with a\nstochastic hit.  That is, the decision to begin the motion (or not) is left to a $\\beta$-decay.  In this case \\mbox{nRule (4)}\nforces the motion to begin at the beginning, insuring that no value of the classical variable is passed over;  so the hammer\nwill always fall from its \\emph{initial} angle with the horizontal.   Without nRule (4), the hammer might begin its fall at some\nother angle because probability current will flow into angles other than the initial one.  \n\n\n\n\n\n\n\n\\section*{Microscopic Systems}\nThe discussion so far has been limited to experiments or procedures whose outcome is empirically known.  Our claim has been that the\nnRules are chosen to work without regard to a theory as to `why' they work.  Therefore, our attention has always gone to\nmacroscopic situations in which the results are directly available to conscious experience.  However, if the nRules are correct we\nwould also want know how they apply to microscopic systems, even though the predicted results in these cases are more\nspeculative.  In this section we will consider the implications of the nRules in three microscopic cases.  The important question to\nask in each case is: Under what circumstances will these rules result in a state reduction of a microscopic system?\n\n\n\n\\begin{displaymath}\n\\mbox{\\textbf{Case 1 -- spin states}}\n\\end{displaymath}\n\nNo state reduction will result from changing the representation.    In particular, replacing the\nspin state $+z$ with the sum of states $+x$ and $-x$ will not result in either one of the $x$-states becoming a ready state.  \n\n\tThis will be true for a spin $+z$ particle even if the common environment of $+x$ and $-x$ includes a magnetic field that is\ncontinuously applied in (say) the $x$-direction.  So long as the magnetic field  is the same for both $+x$ and $-x$, the result will\nbe the same (i.e., neither one will become a ready state).  \n\nMore generally, let the environments $E^p(t)$ of $+x$ and $E^n(t)$ of $-x$ change continuously over time such that\n\\begin{equation}\n\\Phi(\\tau > t \\ge t_0) = \\frac{1}{\\sqrt{2}}(+z)E^p(t) + \\frac{1}{\\sqrt{2}}(-z)E^n(t)\n\\end{equation}\nwhere $E^p(0) = E^n(0) = E$, and $E^p(\\tau) = E_+,  E^n(\\tau) = E_-$.  States $E_+$ and $E_-$ are the final environments of $+x$\nand $-x$ at a time $\\tau$ that will be either the time at which the process is complete, or  complete to some\ndesired extent.  It may be that the environments $E_+$ and $E_-$ are \\emph{similar} to $E$ and to each other (i.e., same temperature\nand pressure, same particles, same radiation field, etc.), but time will change $E_+$ and $E_-$ so they can no longer be\n\\emph{identical} with $E$ or with each other.  Of course, it might also be that $E_+$ and $E_-$ are not even similar \\mbox{to E}.\n\nTaking the first and last term in Eq.\\ 11 we write\n\\begin{eqnarray}\n\\Phi(\\tau > t \\ge t_0) &=& \\frac{1}{\\sqrt{2}}[(+z) + (-z)]E \\rightarrow \\frac{1}{\\sqrt{2}}[(+z)E_+ + (-z)E_-] \\\\\n&&   \\hspace{1cm}  t =t_ 0  \\hspace{2.8cm} t = \\tau  \\nonumber\n\\end{eqnarray}\nwhere the arrow indicates a continuous transition. Therefore, there will be \\emph{no state reduction} in this case.  It may be\nnoncyclic, but this process does not lead to a collapse of the wave to either $+x$ or $-x$.   \n\n\tFor example, if the magnetic field is non-homogeneous there will be a physical separation of the $+x$ and $-x$ states.  One will\nmove into a stronger magnetic field and the other will move into a weaker magnetic field.  Assuming that this field is continuously\n(i.e., classically) applied, there will be no ready state and no state reduction.  Ready states will appear only when the $+x$ and\n$-x$ components are picked up by different detectors at different locations, resulting in a \\emph{detector related} discontinuity. \nAccording to nRule (3), a state reduction can only occur if and when that happens.\n\n\tThere are many other `quantum' processes that are continuous and therefore not subject to stochastic reduction, such\nas scattering, interference, diffraction, and tunneling.  Vacuum fluctuations are cyclic. \n\n\\begin{displaymath}\n\\mbox{\\textbf{Case 2 -- Free neutron decay}}\n\\end{displaymath}\n\n\nA free neutron decay is written $\\Phi(t) = n(t) + \\underline{ep\\overline{\\nu}}(t)$, where the second component is zero at $t = 0$\nand increases in time as probability current flows into it.  This component contains three entangled particles  making a whole \nobject, where all three  are `ready' states as indicated by the underline \\mbox{(see nRule 2)}. Each component  is multiplied by a\nterm representing the environment (not shown).  Each  is complete for this reason and also because the variables of each particle\ntake on all of the values that are allowed by the boundary conditions.  Following \\mbox{nRule (3)} there will be a\nstochastic hit on $\\underline{ep\\overline{\\nu}(t)}$ at some time $t_{sc}$, reducing the system to the realized correlated states\n$ep\\overline{\\nu}(t_{sc})$.  \n\nSpecific values of, say, the electron's momentum are not stochastically chosen by this reduction because all possible values of\nmomentum are included in $ep\\overline{\\nu}(t_{sc})$ and its subsequent evolution.  For the electron's momentum to be determined in\na specific direction away from the decay site, a detector in that direction must be activated.  That will require another stochastic\nhit on the component that includes that detector.   \n\nThis case provides a good example of how  $\\underline{ep\\overline{\\nu}}(t)$ is a function time beyond its increase in square\nmodulus.  Assume that the neutron moves across the laboratory in a wave packet of finite width.  At each moment the ready component\n$\\underline{ep\\overline{\\nu}}(t)$ will ride with the packet, having the same size, shape, and group velocity.  It is the launch\ncomponent that contains the boundary conditions of the next solution of Schr\\\"{o}dinger's equation -- the solution that appears when\n$\\underline{ep\\overline{\\nu}}(t)$ is stochastically chosen at $t_{sc}$.  Before this `collapse', $\\underline{ep\\overline{\\nu}}(t)$\nis time dependent because it increases in square modulus \\emph{and} because it follows the motion of the neutron; however, nRule (4)\ninsures that it will not evolve dynamically beyond itself until it becomes a realized component at the time of  stochastic choice. \nThe neutron\n$n(t)$ will then disappear and the separate particles $e(t)p(t)\\overline{\\nu}(t)$ will spread out on their own, still\ncorrelated in conserved quantities.   \n\n\\begin{displaymath}\n\\mbox{\\textbf{Case 3 -- Atomic absorption and emission}}\n\\end{displaymath}\n\nIf an atom is raised to an excited state by a passing photons, the absorption part of this interaction is cyclic because the atom\nmight fall back to its ground state by a stimulated emission.  However, the excited state atom might also emit `another' photon by\nsimultaneous emission and that is noncyclic.  That could lead to a stochastic hit and collapse of the wave to the newly formed decay\nstate.  The  pulse of $N$ photons is represented by $\\gamma_N(t)$ in the first component of Eq.\\ 13, and the spontaneously emitted\nphoton is $\\underline{\\gamma}(t)$ in the third component. \n\n\\begin{equation} \n\\Phi(t \\ge t_0) = \\gamma_N(t)A_0(t) \\leftrightarrow \\gamma_{N-1}(t)A_1(t)+ \\gamma_{N-1}(t)\\underline{\\gamma}(t)\\underline{A}_0(t)\n\\end{equation}\nThe continuous (cyclic) oscillation is represented by the reversible arrow $\\leftrightarrow$ between the first and second\ncomponents.\n\nIf the incoming photons have a small cross section with the atom, the second component in Eq.\\ 13 will not fully discharge into the\nthird component.  In that case the latter will become a phantom that can be subsequently ignored.  There will be no collapse.  The\nsecond component will then dampen out and the first component, modified by the encounter, will be the only survivor.   \n\nOtherwise, there will be a stochastic hit on the third component at some time $t_{sc}$, resulting in \n\\begin{displaymath}\n\\Phi(t \\ge t_{sc} < t_0) = \\gamma_{N-1}(t)\\gamma(t)A_0(t)\n\\end{displaymath}  \nThe newly emitted photon $\\gamma(t)$ will evolve until it has a final pulse width $\\Delta T_f$ that is\nassociated with its final spread of energy $\\Delta E$.  There is no necessary relationship between $\\Delta T_f$ and the half-life\n$T_{1\/2}$ of the decay from the second to the third component in Eq.\\ 13.  There might be any number of influences affecting\n$T_{1\/2}$, including the number of photons in the stimulating pulse $\\gamma_N(t)$.  If there are no incoming photons, and if the\nexcited state $A_1(t)$ is realized by a quantum jump from a higher energy level at some stochastically chosen moment $t_{scc}$,\nthen \n\\begin{equation} \n\\Phi(t \\ge t_{scc}) = A_1(t)+ \\underline{\\gamma}(t)\\underline{A}_0(t)\n\\end{equation}\nwhere the second component is zero at $t_{scc}$ and increases in time.  The state $A_1(t)$  decays \\emph{only} into the\nsecond component in this equation; whereas in \\mbox{Eq.\\ 13} it shares time with the initial state\n$\\gamma_N(t)A_0(t)$.  In Eq. 13 the  average current flow into $\\underline{\\gamma}(t)\\underline{A}_0(t)$ is therefore decreased,\nso the half-life $T_{1\/2}$ of the spontaneous decay is increased.\n\nIn contrast, $\\Delta T_f$ is determined only by the time dependent solutions of the excited state $A_1(t)$.  So $\\Delta T_f$ is\nnot causally connected to $T_{1\/2}$.  The value of $\\Delta T_f$ is transmitted from $A_1(t)$ to the launch component\n$\\underline{\\gamma} (t)\\underline{A}_0(t)$ at each moment of time, setting the boundary conditions of that launch site at that\nmoment.  Therefore, it will not matter to the properties of the emitted photon (in particular $\\Delta T_f$) if a stochastic hit\non $\\underline{\\gamma}(t)\\underline{A}_0(t)$ in Eq.\\ 13 or Eq.\\ 14 aborts the decay before it is complete.\n\n\n\n\n\n\n\\section*{Decoherence}\nSuppose that two states $A$ and $B$ that are initially in coherent Rabi oscillation and are exposed to a phase disrupting\nenvironment.  This may be expressed by the equation\n\\begin{equation}\n\\Phi(\\tau > t \\ge t_0) = (A \\leftrightarrow B)E(t) \\rightarrow [AE_A(t) + BE_B(\\tau)] \n\\end{equation}\nwhere $A$ is at a higher energy level than $B$.  The right pointing arrow indicates a continuous process.  When the environments\n$E_A$ and $E_B$ are sufficiently different to be orthogonal, then states $A$ and $B$ in Eq.\\ 15 will become totally decoherent. \nStatistically, this leaves a local mixture of $A$ and $B$ with no current flow between them.  The subsequent \ndecay of $AE_A$ is generally much slower than decoherence, so decoherence will be essentially complete before there is a\nstochastic interruption.  Evidence for this is found in low temperature experiments \\cite{DV, YY} where Rabi oscillations undergo\ndecoherent decay without any sign of interruption due to state reduction.     \n\n\\vspace{.4cm}\n\nThe ammonia molecule is generally found in a partially decoherent state.  In a rarified atmosphere the molecule will most likely be\nin its symmetric coherent form $(A\\leftrightarrow B)$, where $A$ has the nitrogen atom on one side of the\nhydrogen plane, and $B$ has the nitrogen atom placed symmetrically on the other side.  This is the lowest energy state available to\nthe molecule.  In this case the states $A$ and $B$ (Eq.\\ 15) taken by themselves are equally energetic at a higher energy level.  \n  \nCollisions with other molecules in the environment will tend to destroy the coherence between $A$ and $B$, causing the ammonia\nmolecule to become decoherent to some extent.  This decoherence can be reversed by decreasing the pressure.  Since an ammonia\nmolecule wants to fall into its lowest energy level, it will tend to return to the symmetric  state when outside pressure\nis reduced.  In general, equilibrium can be found between a given environment and some degree of decoherence.    \n\n\tThe ammonia molecule  cannot assume the symmetric form $(A \\leftrightarrow B)$ if the environmental collisions are too frequent\n-- i.e., if the pressure exceeds about 0.5 atm.\\ at room temperature \\cite{JZ}.   At low pressures the molecule is a stable coherent\nsystem, and at high pressures it is a stable decoherent system.  It seems to change from a microscopic object to a macroscopic\nobject as a function of its environment.  This further supports the idea that the micro\/macroscopic distinction is not\nfundamental.  \n\n\\vspace{.4cm}\n\nTo accommodate the main example of this paper, which is a detector that may or may not capture a\nparticle, a more general form is adopted.  We now use time dependent coefficients $m(t)$ and $n(t)$, where $m(t_0) = 1, n(t_0) = 0$,\nand where $m(t)$ decreases in time keeping\n$m(t)^2 + n(t)^2 = 1$.  These coefficients describe the progress of the primary interaction, giving  \n\\begin{eqnarray}\n\\Phi(\\tau > t \\ge t_0) &=& [m(t)A + n(t)\\underline{B}]E \\rightarrow [m(t)AE_A(t) + n(t)\\underline{B}E_B(t)] \\nonumber\\\\\n&&   \\hspace{.95cm}  t = t_0  \\hspace{3.3cm} t = \\tau \\nonumber\n\\end{eqnarray} \nwhere the transitions \\emph{inside} the brackets are now discontinuous and noncyclc, making $\\underline{B}$ a ready state as\nrequired by nRule (2).  This can be written\n\\begin{eqnarray}\n\\Phi(t = t_0) &=& AE \\hspace{.5cm}\\mbox{(intial  component)}\\hspace{1.8cm} m(t_0) = 1 \\\\\n\\Phi(\\tau \\ge t \\ge t_0) &=&  AE \\rightarrow [m(t)AE^m(t) + n(t)\\underline{B}E^n(t)]\\hspace{.4cm}  m(t) \\rightarrow 0 \n\\nonumber\n\\end{eqnarray} \nSince state $\\underline{B}$ in this equation is a `ready' state and  the  primary current flows from $A$ to\n$\\underline{B}$ inside the  square bracket, $\\underline{B}$ is a candidate for state reduction according to nRule (3).  \n\n\tEquation 16 applied to our example in Eq.\\ 3 with $m(t)A = \\psi(t)d_0$ and $n(t)\\underline{B} = \\underline{d}_w(t)$ says that \ninitially coherent states $\\psi(t)d_0$ and $\\underline{d}_w$ rapidly become decoherent.  Because of the macroscopic nature of the\ndetector, decoherence at time $\\tau$ may be assumed to be complete, and the decay time from $t_0$ to $\\tau$ extremely short lived. \nThe  time for any newly created pair of macroscopic objects to approach full decoherence is so brief that it is not measurable in\npractice.  Still, we see that decoherence does not happen immediately when a new macroscopic state is  created.\n\n\n\n\n\n\n\n\\section*{Grounding the Schr\\\"{o}dinger Solutions}\n\tStandard quantum mechanics is not completely grounded because it does not recognize all of the boundary conditions (beyond \nthe initial conditions) that are stochastically chosen during the lifetime of the system.  With either one of the proposed\nrule-sets, every stochastic hit sets a new boundary (i.e., the chosen eigenvalue) for a new solution of Schr\\\"{o}dinger's equation. \nOn the other hand, traditional quantum theory accumulates all the possible solutions as though they were all simultaneously valid;\nand as a result, this model encourages bizarre speculations such as the many-world interpretation of Everett or the cat paradox of\nSchr\\\"{o}dinger.  With the proposed rule-sets, these empirical distortions disappear.  It is because standard quantum mechanics\nfails to respond to the system's ongoing state reductions that these fanciful excursions seem plausible.  \n\n\n\n\n\n\n\n\\section*{Limitation of the Born Rule}\nUsing the Born rule in standard theory, the observer can only record an observation at a given instant of time, and he must do so\nconsistently over an ensemble of observations.  He cannot himself become part of the system for any finite period of\ntime.  When discussing the Zeno effect it is said that continuous observation can be simulated by rapidly increasing the number of\ninstantaneous observations; but of course, that is not really  continuous.    \n\n\t On the other hand, the observer in an ontological model can \\emph{only} be continuously involved with the observed system.  Once\nhe is on board and fully conscious of a system, the observer can certainly try to remove himself ``immediately\".  However, that\neffort is not likely to result in a truly instantaneous conscious observation.    So the epistemological observer claims to make\ninstantaneous observations but cannot make continuous ones; and the ontological observer makes continuous observations but cannot\n(in practice) make instantaneous ones.  Evidently the Born rule would require the ontological observer to do something that cannot\nbe realistically done.  Epistemologically we can ignore this difficulty, but a consistent ontology should not match a continuous\nphysical process with continuous observation by using a discontinuous rule of correspondence.  Therefore, no ontological model\nshould  make fundamental use of the Born interpretation that places unrealistic demands on an observer.  \n\n\n\n\n\n\n\n\\section*{Status of the Rules}\nNo attempt has been made to relate conscious brain states to particular neurological configurations.  The nRules are an empirically\ndiscovered set of macro relationships that exist on another level than microphysiology, and there is no need to connect these two\ndomains.  These rules preside over physiological detail in the same way that thermodynamics presides over molecular detail.  It is\ndesirable to eventually connect these domains as thermodynamics is now connected to molecular motion; and hopefully, this is what a\ncovering theory will do.  But for the present we are left to investigate the rules by themselves without the benefit of a wider\ntheoretical understanding of state reduction or of conscious systems.  There are two rule-sets of this kind giving us two different\nquantum friendly ontologies -- the nRules of this paper and the oRules of Refs. 1-3.  \n  \n\\hspace{.4cm}\n\nThe question is, which if either of these two rule-sets is correct (or most correct)?  Without the availability of a wider\ntheoretical structure or a discriminating observation, there is no way to tell.  Reduction theories that are currently being\nconsidered may accommodate a conscious observer, but none are fully accepted.  So the search goes on for an extension of quantum\nmechanics that is sufficiently comprehensive to cover the collapse associated with an individual measurement.  I expect that\nany such theory will support one of the ontological rule-sets, so these rules might server as a guide for the construction of a\n\\mbox{wider theory}.  \n\n\n\n\\pagebreak\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
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+{"text":"\\section{Introduction} \n\nBhabha scattering is measured with remarkable precision at LEP1\/SLC \nenergies in two kinematical regions identified by the scattering angle: \nat small-angle for the luminosity monitoring and \nat large-angle for the measurements of the $Z$ properties. \n\\par\nSuch results require a continuous effort on the theoretical side to maintain \nthe theoretical error on the prediction within a comparable precision and \nto provide a tool for realistic comparisons with the experimental data \n(namely an event generator).\n\\par\nWe have already given in ~\\cite{NC92} the general description of our approach\nto the problem, \nwhile the features of the first version of our event generator BHAGEN are \ndescribed in ~\\cite{IJMP93}, with instructions on how to get the program \nand how to use it. In ~\\cite{PL94} we have considered the higher order \nQED corrections, including the most relevant contributions and estimating the \nomitted terms; in ~\\cite{PL94} a new version of our event generator, BHAGEN94, \nis also announced. \n\\par\nSeveral improvements have been made subsequently to BHAGEN94, in \norder to increase and control its precision, and \nin ~\\cite{CERN95-03} some results for small-angle \nBhabha scattering cross-section are presented with the label BG94-NEW \nand compared with the results from few other available \ncomputer programs: OLDBIS ~\\cite{OLDBIS}, LUMLOG ~\\cite{LUMLOG}, \nBHLUMI 2.01~\\cite{BHLUMI2} and 40THIEVES ~\\cite{40THIEVES}.\nThe conclusion from the comparisons with the above programs, and also from the\nuse of the new event generator BHAGEN-1PH, which contains the complete hard \nphoton matrix element ~\\cite{1PH}, is  that the hard photon part (even in the \nimproved version of BHAGEN94) deserves a more accurate treatment to achieve \nthe 0.1\\% precision, presently aimed at small-angle for luminosity monitoring. \nTo obtain such a result a new procedure and the code BHAGEN95 are developed. \nBHAGEN95 (available on request from the authors) is actually a collection of \nthree programs and in this paper we discuss\nin detail two of them, as the third one is already discussed separately \n~\\cite{1PH}.\nThe current precision for the cross-section is heavily dependent on the chosen \nevent selection and for our code can be estimated to be about 0.1\\%-0.2\\% for \ntypical experimental event selection at small-angle for LEP1\/SLC and LEP2 \nenergies.\nIn references ~\\cite{CERN96} and ~\\cite{BWG_LETT} our results are presented \nin a variety of different event selections and conditions \n(some of those preliminary results are updated in this discussion),\nand compared with the other presently available programs of similar\nprecision:\nBHLUMI 4.03 ~\\cite{BHLUMI4},\nOLDBIS+LUMLOG ~\\cite{OBI+LUMG}, \nSABSPV ~\\cite{SABSPV},\nNLLBHA ~\\cite{NLLBHA}.\n\nThe precision at large-angle depends on the beam energy and \nalso on the event selection used; in the worst case (beam energy a few GeV \nabove the $Z$ peak) can be safely estimated to be about 1\\%, \nmainly due to the raise of the incertitude coming from the second order leading \nlogarithmic correction in the $s-t$-interference terms, which are still \nunknown and usually are assumed to be the same as in the $s$-channel.\nFor the other energy ranges at LEP1\/SLC, and at LEP2,\none can expect with relatively loose cuts a typical accuracy of 0.5\\%,\nwhich can be usefully compared with the other presently available programs, \nin the conditions they are suited for: \nALIBABA ~\\cite{ALIBABA}, \nZFITTER ~\\cite{ZFITTER}, \nTOPAZ0 ~\\cite{TOPAZ0}, \nBHAGENE3 ~\\cite{BHAGENE}, \nUNIBAB ~\\cite{UNIBAB},\nBHWIDE ~\\cite{BHWIDE},\nSABSPV ~\\cite{SABSPV}.\n\n\\par\nThis paper goes through the following sections:\nimplementation of an improved energy distribution for the final photon \nemission in the resummed program BHAGEN94, in section 2;\nconstruction of the BG94-FO code, the \\Ord{\\alpha} version of the event \ngenerator BHAGEN94, in section 3;\nimplementation of necessary weak and QCD corrections in BHAGEN94 up\nto two loops, in section 4;\nconstruction of the BHAGEN95 code, in section 5;\ncomparisons at small-angle, in section 6; \ncomparisons at large-angle, in section 7; \nconclusions, in section 8.\n\\bigskip\n\n\\section{ Improved energy distribution for the final photon \nemission in the resummed program BHAGEN94.}\n\nIn the same notation as in \n~\\cite{NC92}, ~\\cite{IJMP93}, ~\\cite{PL94} and ~\\cite{CERN89},\nthe integrated cross-section is \n\\begin{equation}\n\\sigma(e^{+}e^{-} \\rightarrow  e^{+} e^{-} ) = \\int\\limits_{\\Delta\\Omega_-} d\\Omega_- \\quad\n{d\\tilde\\sigma(E_b,\\theta_-)\\over{d\\Omega_-}} \\ ,\n\\label{eq:s1}\n\\end{equation}\nwhere the dressed differential cross-section in our approach is \n\\begin{eqnarray}\n{d\\tilde\\sigma(E_b,\\theta_-)\\over{d\\Omega_-}} = \n&&\\int\\limits_{E_{min}}^{E_b} {d E^0_- \\over{E_b}} F^0(E_b,E^0_-,\\theta_-)\n  \\int\\limits_{E_{min}}^{E_b} {d E^0_+ \\over{E_b}} F^0(E_b,E^0_+,\\theta_+) \n\\nonumber \\\\\n&&\\int\\limits_{E_{min}}^{E_-} {d E'_-  \\over{E_-}} F'(E_-,E'_-,\\theta_-)\n  \\int\\limits_{E_{min}}^{E_+} {d E'_+  \\over{E_+}} F'(E_+,E'_+,\\theta_+) \n\\label{eq:s2} \\\\\n&&{d\\sigma(E^0_+,E^0_-,\\theta_-)\\over{d\\Omega_-}} \\quad \\Theta(cuts) \\ , \\nonumber \n\\end{eqnarray} \n$E_b$ is the beam energy, $\\theta_{\\pm}$ the scattering-angle of the electron \n(positron), $s=4E_b^2$ and $t_{\\pm}=-s \\sin^2{\\theta_{\\pm}\\over2}$.\nIn the laboratory system the electron (positron) energy after \ninitial radiation is $E^0_{\\pm}$, after the scattering is $E_{\\pm}$, \nafter the final radiation is $E'_{\\pm}$, and $E_{min}$ is the minimum energy \nfor the leptons.\n\\par\nIn terms of the variables in the LM-c.m.s. (the c.m.s. after initial radiation \nemitted collinearly to the initial direction, as introduced \nin ~\\cite{NC92}), the incoming fermion energy \n$E^*=\\sqrt{E^0_- E^0_+}$, the scattering angle $\\theta^*(E^0_-,E^0_+,\\theta_-)$ \nand the jacobian $\\left( {d\\Omega^* \\over{d\\Omega_-}} \\right)$,\nthe differential cross-section from Feynman diagrams, \\Ord{\\alpha} complete \nand up to \\Ord{\\alpha^2} leading logarithm, is written as\n\\begin{eqnarray}\n{d\\sigma(E^0_+,E^0_-,\\theta_-)\\over{d\\Omega_-}} = \n&& \\left( {d\\Omega^* \\over{d\\Omega_-}} \\right)\n   \\sum_{i=1}^{10} {{d\\bar\\sigma_0^{(i)}(E^*,\\theta^*)}\\over{d\\Omega^*}} \n\\label{eq:s3} \\\\\n&& \\left[ 1+\\delta_N^{(i)}(E_b,\\theta^*) \\right]\n   \\left[ 1 + \\tilde C^{(i)}(E^*,\\theta^*) \\right] \n   \\left[ 1+\\delta_N^{(i)}(E^*,\\theta^*) \\right]   \\nonumber \\ , \n\\end{eqnarray}\nwhere ${{d\\bar\\sigma_0^{(i)}(E^*,\\theta^*)}\\over{d\\Omega^*}}$ are the Born \ndifferential cross-sections for the various channels with vacuum polarization \ninsertions (Dyson resummed as in Eq.(2.6) of ~\\cite{NC92}),\n$\\delta^{(i)}_{N}(E, \\theta)$ (defined in Eq.(16) of ~\\cite{PL94}) \nare the leading logarithmic corrections up to \\Ord{\\alpha^2}, \nand $\\tilde C^{(i)}(E_b,\\theta_-)$ are the \\Ord{\\alpha} complete corrections \nafter subtraction of the terms already included in the previous corrections.\n\\par \nThe function $\\Theta(cuts)$ accounts for the rejection procedure, according to \nthe requested cuts on energies and angles.\n\\par \nAs usual,\n\\begin{eqnarray}\n\\beta(E,\\theta) &=& \\beta_e(E) +\\beta_{int}(\\theta) \\ , \\nonumber \\\\ \n\\beta_e(E) &=& 2 \\left({\\alpha\\over\\pi}\\right) \\left(\\ln {{4E^2}\\over{m_e^2}} -1\\right) \\ , \\\\\n\\beta_{int}(\\theta) &=& 4 \\left({\\alpha\\over\\pi}\\right) \\ln \\left( \\tan {\\theta \\over2} \\right) \\ ,\n\\nonumber \n\\end{eqnarray} \nwith $\\beta(E_b,\\theta_{\\pm}) \\simeq \\beta_e(\\sqrt{s}\/2)$ at large-angle and \n$\\beta(E_b,\\theta_{\\pm})  \\simeq \\beta_e(\\sqrt{-t_{\\pm}}\/2)$ at small-angle.\n\\par\nThe emission functions for initial $(F^0)$ and final $(F')$ emission \nin the notation of ~\\cite{PL94}, and using the results of ~\\cite{S+J}, are\n\\begin{eqnarray}\nF^0(E_b,E^0_{\\pm},\\theta_{\\pm}) &&= D^0(E_b,E^0_{\\pm},\\theta_{\\pm})\n\\Biggl\\{\n     {1\\over2} \\left( 1 + \\left( {E^0_{\\pm}\\over{E_b}} \\right)^2 \\right)\n     + A^0_m(E_b,E^0_{\\pm})    \n\\label{eq:s4} \\\\\n    &&+ {{\\beta(E_b,\\theta_{\\pm})}\\over 8}\n     \\left[ -{1\\over2}\n     \\left( 1 +3 \\left( {E^0_{\\pm}\\over{E_b}} \\right)^2 \\right)\n     \\ln \\left( {E^0_{\\pm}\\over{E_b}} \\right)\n    - \\left(1-{E^0_{\\pm}\\over{E_b}}\\right)^2\n     \\right] \\Biggr\\}  \\ , \\nonumber \n\\end{eqnarray}\nand\n\\begin{eqnarray}\nF'(E_{\\pm},E'_{\\pm},\\theta_{\\pm}) &&= D'(E_{\\pm},E'_{\\pm},\\theta_{\\pm})\n\\Biggl\\{\n     {1\\over2} \\left( 1 + \\left( {E'_{\\pm}\\over{E_{\\pm}}} \\right)^2 \\right)\n     + A'_m(E_{\\pm},E'_{\\pm}) \n\\label{eq:s5} \\\\\n    &&+ {{\\beta(E_{\\pm},\\theta_{\\pm})}\\over 8}\n     \\left[ -{1\\over2}\n     \\left( 1 +3 \\left( {E'_{\\pm}\\over{E_{\\pm}}} \\right)^2 \\right)\n     \\ln \\left( {E'_{\\pm}\\over{E_{\\pm}}} \\right)\n    - \\left(1-{E'_{\\pm}\\over{E_{\\pm}}}\\right)^2\n     \\right] \\Biggr\\}  \\ , \\nonumber \n\\end{eqnarray}\nwith\n\\begin{equation}\nA^0_m(E_b,E^0_{\\pm}) = {1\\over2} {{\\left( 1 - {{E^0_{\\pm}}\\over{E_b}} \\right)}^2\n \\over {\\ln \\left({{2E_b}\\over{m_e}}\\right)^2 - 1 } } \\ , \\quad\nA'_m(E_{\\pm},E'_{\\pm}) ={1\\over2}{{\\left(1-{{E'_{\\pm}}\\over{E_{\\pm}}} \\right)}^2\n \\over {\\ln \\left({{2E'_{\\pm}}\\over{m_e}}\\right)^2 - 1 } } \\ .\n\\end{equation}\nThe radiator functions for initial $(D^0)$ and final $(D')$ emission are\n\\begin{equation}\nD^0(E_b,E^0_{\\pm},\\theta_{\\pm}) = \\div12 \\beta(E_b,\\theta_{\\pm})\n\\left( 1-{E^0_{\\pm}\\over{E_b}} \\right)^{\\div12 \\beta(E_b,\\theta_{\\pm}) -1} \n\\label{eq:s6}\n\\end{equation}\nand\n\\begin{equation}\nD'(E_{\\pm},E'_{\\pm},\\theta_{\\pm}) = \\div12 \\beta(E'_{\\pm},\\theta_{\\pm})\n\\left( 1-{E'_{\\pm}\\over{E_{\\pm}}} \\right)^{\\div12 \\beta(E'_{\\pm},\\theta_{\\pm}) \n-1} \\ ,\n\\label{eq:s7}\n\\end{equation}\nnote that the leading logarithmic corrections, up to \\Ord{\\alpha^2}, \nhave been included in the factors $(1+\\delta_N^{(i)}(E,\\theta))$ of the expression \nin Eq.~(\\ref{eq:s3}). \n\nAs the differential cross-section in Eq.~(\\ref{eq:s3}) does not depend on \nfinal lepton energies $E'_{\\pm}$, in our previous formulations the \nintegrations on these variables were performed analytically, assuming the \nfurther simplification that in the expression for $D'$ in Eq.~(\\ref{eq:s7}) \nthe values for $\\beta(E'_{\\pm},\\theta_{\\pm})$ were taken constant at energy $E^*$,\ni.e. $\\beta(E^*,\\theta_{\\pm})$. \n\\par\nThe simplification allows the analytical integration \n\\begin{eqnarray}\n\\int\\limits_{E_{min}}^{E_-} {d E'_-  \\over{E_-}} F'(E_-,E'_-,\\theta_-) &=&\n\\Delta_-^{\\div12 \\beta(E^*,\\theta^*)} G(E^*,\\theta^*,\\Delta_-) \\ , \n\\label{eq:s8} \\\\\n\\int\\limits_{E_{min}}^{E_+} {d E'_+  \\over{E_+}} F'(E_+,E'_+,\\theta_+) &=&\n\\Delta_+^{\\div12 \\beta(E^*,\\theta^*)} G(E^*,\\theta^*,\\Delta_+) \\ ,\n\\label{eq:s9}\n\\end{eqnarray}\nwhere $\\Delta_{\\pm} = 1-E_{min}\/E_{\\pm}$ and the function \n$G(E^*,\\theta^*,\\Delta_{\\pm})$ is explicitly given in Eq.~(23) of ~\\cite{PL94}. \n\\par \nThe procedure is rather good for small values of $\\Delta_{\\pm}$, but the \nextension to larger and more realistic values, corresponding to harder photon \nemission, causes a loss in precision, which justifies the difference with\nBHLUMI 2.01~\\cite{BHLUMI2} and 40THIEVES ~\\cite{40THIEVES} amounting up to \n0.8\\%, as reported in ~\\cite{CERN95-03} for results under label BG94-OLD.\n\\par\nIn the new version of BHAGEN94 the $\\beta$ dependence on $E'_{\\pm}$ is kept\nand the integration (or generation) is done numerically without further \napproximations.\nThe new values (reported in ~\\cite{CERN95-03} under label BG94-NEW) \nreduce the difference with the above mentioned programs to about 0.25\\%.\n\\par\nThe new approach imply the generation of two more variables for the final \nfermion energies $E'_{\\pm}$, for the proper description of the peaks in \nEq.~(\\ref{eq:s7}) the variables $y'_{\\pm}$ are introduced\n\\begin{equation}\ny'_{\\pm} = \n\\left( 1-{E'_{\\pm}\\over{E_{\\pm}}} \\right)^{\\div12 \\beta(E_{\\pm},\\theta_{\\pm})}\\ .\n\\end{equation}\nTo generate within a unit volume, the variables are changed to \n$r'_{\\pm} \\in (0,1)$\n\\begin{equation}\ny'_{\\pm} = r'_{\\pm} \n\\left( 1-{E_{min}\\over{E_{\\pm}}} \\right)^{\\div12 \\beta(E_{\\pm},\\theta_{\\pm})}\\ .\n\\end{equation}\nNote that, even if in the generation procedure the function $\\beta$ is still \ntaken constant in energy, in the actual calculation the exact value is \ncomputed and used to determine the cross-section.\n\\bigskip\n\n\\section{ Construction of the BG94-FO generator.}\n\nWe have extracted from BHAGEN94 a first-order event generator \n\\ ---\\  i.e. including only corrections up to \\Ord{\\alpha} \\ ---\\ \nthat we call BG94-FO, \nkeeping as much as possible unchanged the structure of the program.\n\\par \nThat is achieved by analytically expanding in $\\alpha$ all the formulae \nand then keeping the \\Ord{\\alpha} terms only; the separation between soft and \nhard radiation is reintroduced through the small emitted energy fraction cut \n$\\epsilon$, whose size has to be of the order of the accepted error, \ntypically $\\epsilon \\le 10^{-4}$. \nTo allow the expansion in $\\alpha$, the integrations in Eq.~(\\ref{eq:s2}) are \nsplit into \n\\begin{equation}\n\\int\\limits_{E_{min}}^{E_b} {d E^0_{\\pm}} = \n\\int\\limits_{E_{min}}^{E_b(1-\\epsilon)} {d E^0_{\\pm}} \n         +\\int\\limits_{E_b(1-\\epsilon)}^{E_b} {d E^0_{\\pm}} \\ , \n\\end{equation}\nand\n\\begin{equation}\n\\int\\limits_{E_{min}}^{E_{\\pm}} {d E'_{\\pm}} =\n\\int\\limits_{E_{min}}^{E_{\\pm}(1-\\epsilon)} {d E'_{\\pm}} \n         +\\int\\limits_{E_{\\pm}(1-\\epsilon)}^{E_{\\pm}} {d E'_{\\pm}} \\ .\n\\end{equation}\nAll the resulting terms, which involve more than one integration in the hard \nphoton regions $(E_{min},E_b(1-\\epsilon))$ and $(E_{min},E_{\\pm}(1-\\epsilon))$, \nare omitted, being of higher order.\n\\par\nIn the soft photon regions \n$(E_b(1-\\epsilon),E_b)$ and $(E_{\\pm}(1-\\epsilon),E_{\\pm})$ \nand for smooth functions, \n$E^0_{\\pm}$ can be approximated by $E_b$ and $E'_{\\pm}$ by $E_{\\pm}$, \nwhile special care has to be devoted to the peaking behaviour of\nthe functions $D^0$ and $D'$.\nMoreover from the definition of $E^0_{\\pm}$ (Eq.~(3.6) of ~\\cite{NC92}) \none has that for \n$E^0_{\\pm} \\simeq E_b$ also $E_{\\pm} \\simeq E_b$, and $\\theta_+ = \\theta_-$, \nso Eq.~(\\ref{eq:s2}) becomes\n\\begin{eqnarray}\n{d\\tilde\\sigma(E_b,\\theta_-)\\over{d\\Omega_-}} &\\simeq& \n\\int\\limits_{E_b(1-\\epsilon)}^{E_b} {d E^0_- \\over{E_b}} D^0(E_b,E^0_-,\\theta_-)\n\\int\\limits_{E_b(1-\\epsilon)}^{E_b} {d E^0_+ \\over{E_b}} D^0(E_b,E^0_+,\\theta_-) \n\\nonumber \\\\\n& &\\int\\limits_{E_b(1-\\epsilon)}^{E_b} {d E'_-  \\over{E_b}} D'(E_b,E'_-,\\theta_-) \n   \\int\\limits_{E_b(1-\\epsilon)}^{E_b} {d E'_+  \\over{E_b}} D'(E_b,E'_+,\\theta_-) \n   {d\\sigma(E_b,E_b,\\theta_-)\\over{d\\Omega_-}} \n\\nonumber \\\\\n&+&\\int\\limits_{E_b(1-\\epsilon)}^{E_b}{d E^0_- \\over{E_b}}D^0(E_b,E^0_-,\\theta_-)\n   \\int\\limits_{E_b(1-\\epsilon)}^{E_b}{d E^0_+ \\over{E_b}}D^0(E_b,E^0_+,\\theta_-) \n\\nonumber \\\\\n& &\\int\\limits_{E_{min}}^{E_b(1-\\epsilon)} \n                           {d E'_-  \\over{E_b}} F'(E_b,E'_-,\\theta_-) \n   \\int\\limits_{E_b(1-\\epsilon)}^{E_b} {d E'_+  \\over{E_b}} D'(E_b,E'_+,\\theta_-) \n   {d\\sigma(E_b,E_b,\\theta_-)\\over{d\\Omega_-}} \n\\nonumber \\\\\n&+&\\int\\limits_{E_b(1-\\epsilon)}^{E_b}{d E^0_- \\over{E_b}}D^0(E_b,E^0_-,\\theta_-)\n   \\int\\limits_{E_b(1-\\epsilon)}^{E_b}{d E^0_+ \\over{E_b}}D^0(E_b,E^0_+,\\theta_-) \n\\\\\n& &\\int\\limits_{E_b(1-\\epsilon)}^{E_b} {d E'_-  \\over{E_b}} D'(E_b,E'_-,\\theta_-) \n   \\int\\limits_{E_{min}}^{E_b(1-\\epsilon)} \n                           {d E'_+  \\over{E_b}} F'(E_b,E'_+,\\theta_-) \n   {d\\sigma(E_b,E_b,\\theta_-)\\over{d\\Omega_-}} \n\\nonumber \\\\\n&+&\\int\\limits_{E_{min}}^{E_b(1-\\epsilon)} \n                           {d E^0_- \\over{E_b}} F^0(E_b,E^0_-,\\theta_-)\n\\int\\limits_{E_b(1-\\epsilon)}^{E_b} {d E^0_+ \\over{E_b}} D^0(E_b,E^0_+,\\theta_+) \n\\nonumber \\\\\n& &\\int\\limits_{E_-(1-\\epsilon)}^{E_-} {d E'_-  \\over{E_-}} D'(E_-,E'_-,\\theta_-) \n   \\int\\limits_{E_+(1-\\epsilon)}^{E_+} {d E'_+  \\over{E_+}} D'(E_+,E'_+,\\theta_+) \n   {d\\sigma(E_b,E^0_-,\\theta_-)\\over{d\\Omega_-}} \n\\nonumber \\\\\n&+&\\int\\limits_{E_b(1-\\epsilon)}^{E_b}{d E^0_- \\over{E_b}}D^0(E_b,E^0_-,\\theta_-)\n   \\int\\limits_{E_{min}}^{E_b(1-\\epsilon)} \n                           {d E^0_+ \\over{E_b}} F^0(E_b,E^0_+,\\theta_+) \n\\nonumber \\\\\n& &\\int\\limits_{E_-(1-\\epsilon)}^{E_-} {d E'_-  \\over{E_-}} D'(E_-,E'_-,\\theta_-) \n   \\int\\limits_{E_+(1-\\epsilon)}^{E_+} {d E'_+  \\over{E_+}} D'(E_+,E'_+,\\theta_+) \n   {d\\sigma(E^0_+,E_b,\\theta_-)\\over{d\\Omega_-}} \n\\nonumber \\ ,\n\\end{eqnarray}\nwhere the first term accounts for soft emission only, \nthe second and third account for hard emission from final electron or positron, \nthe fourth and fifth for hard emission from initial electron or positron.\nThe functions $F^0$ and $F'$ are now intended at \\Ord{\\alpha}, that is \nomitting the $\\beta$ term in curly braces of \nEq.~(\\ref{eq:s4}) and Eq.~(\\ref{eq:s5}).\n\\par\nThe analytical integration and subsequent expansion in $\\alpha$ can be easily \ndone for the initial radiation\n\\begin{equation}\n\\int\\limits_{E_b(1-\\epsilon)}^{E_b} \n{d E^0_{\\pm} \\over{E_b}} D^0(E_b,E^0_{\\pm},\\theta_{\\pm}) = \n\\epsilon^{\\div12 \\beta(E_b,\\theta_{\\pm})} = \n1 + {\\div12 \\beta(E_b,\\theta_{\\pm})} \\ln \\epsilon +{\\cal O}(\\alpha^2) \\ ,\n\\end{equation}\nand in the case of final radiation the result is similar, apart from \ncorrections of order $\\epsilon$ \n\\begin{equation}\n\\int\\limits_{E_b(1-\\epsilon)}^{E_b} \n{d E'_{\\pm} \\over{E_b}} D'(E_b,E'_{\\pm},\\theta_{\\pm}) = \n\\epsilon^{\\div12 \\beta(E_b,\\theta_{\\pm})} +{\\cal O}(\\epsilon) = \n1 + {\\div12 \\beta(E_b,\\theta_{\\pm})} \\ln \\epsilon +{\\cal O}(\\alpha^2) \n+{\\cal O}(\\epsilon) \\ .\n\\end{equation}\nIn Eq.~(\\ref{eq:s3}) the expansion in $\\alpha$ is performed and only \n\\Ord{\\alpha} terms are retained: the vacuum polarization contribution \n$\\delta^{(i)}_{VP}$ is defined in Eq.(2.3) of ~\\cite{NC92},\n$\\delta^{(i)}_{N}(E_b)$ is taken up to \\Ord{\\alpha} from Eq.(16) of \n~\\cite{PL94}, and $\\tilde C^{(i)}(E_b,\\theta_-)$, as indicated in\n~\\cite{PL94}, is the nonleading part of the \\Ord{\\alpha} correction\n$C^{(i)}(E_b,\\theta_-)$, given explicitly in ~\\cite{CERN89}. \nWhen an \\Ord{\\alpha} correction from above integrals occurs only the Born \ncross-section is retained, and if no longer necessary the transformation \nto LM-c.m.s. is released. \n\\par \nWith all that the cross-section at \\Ord{\\alpha} becomes \n\\begin{eqnarray}\n&&{d\\tilde\\sigma(E_b,\\theta_-)\\over{d\\Omega_-}} \\simeq\n   \\sum_{i=1}^{10} {d\\sigma_0^{(i)}(E_b,\\theta_-) \\over{d\\Omega_-}}\n   \\Biggl\\{ 1 +2 \\beta(E_b,\\theta_-) \\ln\\epsilon\n   +\\delta^{(i)}_{VP} +2 \\delta^{(i)}_{N}(E_b) + \\tilde C^{(i)}(E_b,\\theta_-) \n\\nonumber \\\\\n&&+\\int_{E_{min}}^{E_b(1-\\epsilon)} {d E'_- \\over{E_b -E'_-}}\n{{\\beta(E'_-,\\theta_-)}\\over{4}} \n\\left[ 1 +\\left({E'_-\\over{E_b}}\\right)^2 \n+{\\left(1-{E'_-\\over{E_b}}\\right)^2 \\over{\\ln (2E'_-\/m_e)^2 -1}} \\right] \n\\nonumber \\\\\n&&+\\int_{E_{min}}^{E_b(1-\\epsilon)} {d E'_+ \\over{E_b -E'_+}}\n{{\\beta(E'_+,\\theta_-)}\\over{4}} \n\\left[ 1 +\\left({E'_+\\over{E_b}}\\right)^2 \n+{\\left(1-{E'_+\\over{E_b}}\\right)^2 \\over{\\ln (2E'_+\/m_e)^2 -1}} \\right] \n\\Biggr\\} \\label{eq:fo1} \\\\\n&&+\\int_{E_{min}}^{E_b(1-\\epsilon)} {d E^0_- \\over{E_b -E^0_-}} \n{{\\beta(E_b,\\theta_-)}\\over{4}} \n\\left[ 1 +\\left({E^0_-\\over{E_b}}\\right)^2 \n+{\\left(1-{E^0_-\\over{E_b}}\\right)^2 \\over{\\ln ({2E_b}\/m_e)^2 -1}} \\right] \n   {d\\sigma_0(E_b,E^0_-,\\theta_-)\\over{d\\Omega_-}} \n\\nonumber \\\\\n&&+\\int_{E_{min}}^{E_b(1-\\epsilon)} {d E^0_+ \\over{E_b -E^0_+}} \n{{\\beta(E_b,\\theta_+)}\\over{4}} \n\\left[ 1 +\\left({E^0_+\\over{E_b}}\\right)^2 \n+{\\left(1-{E^0_+\\over{E_b}}\\right)^2 \\over{\\ln ({2E_b}\/m_e)^2 -1}} \\right] \n   {d\\sigma_0(E_b,E^0_+,\\theta_-)\\over{d\\Omega_-}} \n\\nonumber \\ ,\n\\end{eqnarray}\nwhere \n\\begin{equation}\n{d\\sigma_0(E_b,E^0_{\\pm},\\theta_-)\\over{d\\Omega_-}} =\n\\left( {d\\Omega^* \\over{d\\Omega_-}} \\right)\n   \\sum_{i=1}^{10} {d\\sigma_0^{(i)}(E^*,\\theta^*) \\over{d\\Omega^*}}\n\\end{equation}\nwith accordingly $E^*=\\sqrt{E_b E^0_{\\pm}}$ and \n$\\theta^*=\\theta^*(E_b,E^0_{\\pm},\\theta_-)$. \n\\par\nIn Eq.~(\\ref{eq:fo1}) the last two lines are due to hard initial emission, \nthe second and third lines are due to hard final emission; in the approximation \nof constant $\\beta$ and symmetrical cuts, the hard final emission contributions \ncan be integrated analytically giving \n\\begin{equation}\n + \\beta(E_b,\\theta_-) \\left[ \\ln{\\Delta\\over{\\epsilon}} -\\Delta\n +{\\Delta^2 \\over{4}} {\\ln(s\/m_e^2) \\over{(\\ln(s\/m_e^2) -1)}} \\right] \n   \\sum_{i=1}^{10} {d\\sigma_0^{(i)}(E_b,\\theta_-) \\over{d\\Omega_-}} \\ ,\n\\label{eq:fo2} \\end{equation}\nwith $\\Delta = 1 -E_{min}\/E_b$.\nIn Table 1 of ~\\cite{CERN95-03} Eq.~(\\ref{eq:fo2}) is used to produce the \nresults presented under the label BG94-FO-OLD, which \ndiffer from the exact ones up to 0.87\\%, while the direct generation from \nEq.~(\\ref{eq:fo1}) gives the results under the label BG94-FO-NEW, which have \nonly up to 0.28\\% difference from the exact ones; these are under label OLDBIS \n~\\cite{OLDBIS} and BG94-FO-EXACT (obtained using BHAGEN-1PH ~\\cite{1PH} for\nthe hard photon emission part) and are well in agreement inside the OLDBIS \ntechnical precision of 0.02\\%. \n\\bigskip\n\n\\section{ Implementation of weak and QCD corrections.}\n\n\\def(v_e^2 + a_e^2){(v_e^2 + a_e^2)}\n\\def\\delta^{tZ}_{1}(+){\\delta^{tZ}_{1}(+)}\n\\def\\delta^{tZ}_{1}(-){\\delta^{tZ}_{1}(-)}\n\\def\\[(2s^2-1)]{\\left(2 \\ s_W^2 -1 \\right)}\n\\def{\\left(1+z\\right)}^2{{\\left(1+z\\right)}^2}\n\\def\\delta^{tZ}_{3}(+){\\delta^{tZ}_{3}(+)}\n\\def\\hbox{Re}\\left(\\chi(s)\\right){\\hbox{Re}\\left(\\chi(s)\\right)}\n\\def\\hbox{Im}\\left(\\chi(s)\\right){\\hbox{Im}\\left(\\chi(s)\\right)}\n\\def\\delta^{sZ}_{2}(+){\\delta^{sZ}_{2}(+)}\n\\def\\delta^{sZ}_{1}(+){\\delta^{sZ}_{1}(+)}\n\\def\\delta^{sZ}_{1}(-){\\delta^{sZ}_{1}(-)}\n\nThe previous versions of the program ~\\cite{NC92}, ~\\cite{IJMP93}, including \nthe latest BHAGEN94 ~\\cite{PL94}, did not contain the $Zee$ weak vertex \ncorrection, while the self energy corrections were included in an \napproximate form.\nFor an accuracy better than 1\\% at large-angle those complete corrections \n~\\cite{HOLLIK}, and also some higher order corrections ~\\cite{CERN95-03_2}\nare necessary. \nAfter their inclusion the error due to the neglected weak one loop corrections \nis about 0.06\\% around the $Z$ boson resonance (LEP1) and 0.1\\% at LEP2 \nenergies, so smaller than the other left over photonic corrections.\nThe use of the program at much higher energies (say 1 TeV) requires an update \nof the weak library for having a precision better than 2\\%.\n\nFor the one loop $Zee$ vertex corrections and  self-energy corrections \nwe use the results of ~\\cite{HOLLIK}, but we introduce the \nDyson resummation of the self energy, as described for $s$-channel in\n~\\cite{CERN89_1} (we do actually the Dyson resummation in all channels).\nThe higher orders corrections are included as outlined in ~\\cite{CERN95-03_2},\nusing the available results for weak ~\\cite{FLEISCHER} \nand QCD corrections ~\\cite{Kniehl}.\n\nFor completeness we report here the formulae of these corrections as they come\nusing our notation as in ~\\cite{NC92}, ~\\cite{IJMP93}, ~\\cite{PL94} and \n~\\cite{CERN89}.\n\nThe $\\tilde C^{(i)}(E^*,\\theta^*)$ for $(i=4,...,10)$ should be changed in \nthe following way\n\n\\begin{equation}\n   \\tilde C^{(i)}(E^*,\\theta^*) \\rightarrow \\tilde C^{(i)}(E^*,\\theta^*)\n   + C^{(i)}_{Z}(E^*,\\theta^*) \\ . \n\\end{equation}\n\nThe $C^{(i)}_{Z}(E^*,\\theta^*)$ are \n\n\\begin{equation}\n    C^{(4)}_Z ={\n        {   8  \\delta^{tZ}_{1}(+) s_W^4 + 2  \\delta^{tZ}_{1}(-) \\[(2s^2-1)]^2 }\n           \\over {(v_e^2 + a_e^2)}} \\ , \n\\label{eq:c4}\n\\end{equation}\n\n\\begin{eqnarray}\n   C^{(5)}_Z &=& {1 \\over {(v_e^2 + a_e^2) \\left( {\\left(1+z\\right)}^2 + 4(r_V-r_A)\\right) }}\n           {\\Bigl[ 8  \\delta^{tZ}_{1}(+) {\\left(1+z\\right)}^2 s_W^4} \\label{eq:c5} \\\\\n          & &{ + 2  \\delta^{tZ}_{1}(-) {\\left(1+z\\right)}^2 \\[(2s^2-1)]^2  + 32  \\delta^{tZ}_{3}(+) s_W^2\n      \\[(2s^2-1)] \\Bigr]} \\ , \\nonumber \n\\end{eqnarray}\n\n\\begin{eqnarray}\n   C^{(6)}_Z &=& { 1 \\over\n    {(v_e^2 + a_e^2)^2 \\left[{\\left(1+z\\right)}^2 (1+4r_V r_A) + 4 (1-4r_V r_A) \\right]}}\n        { \\Bigl[ 256 \\delta^{tZ}_{1}(+) {\\left(1+z\\right)}^2 s_W^8} \\nonumber\\\\ \n         & &{+ 16 \\delta^{tZ}_{1}(-) {\\left(1+z\\right)}^2 \\[(2s^2-1)]^4 \n            + 512 \\delta^{tZ}_{3}(+) s_W^4\n         \\[(2s^2-1)]^2 \\Bigr] } \\ , \n\\label{eq:c6}\n\\end{eqnarray}\n\n\\begin{eqnarray}\n    C^{(7)}_Z &=&{ {1} \\over { 2 (v_e^2 + a_e^2) \\Bigl( (1+z^2)r_V + 2 z r_A \\Bigr) } }\n      { \\Bigl[ \\Bigl( 8 (1-z^2) \\hbox{Re}(\\delta^{sZ}_{2}(+)) s_W^2 \\[(2s^2-1)]} \\nonumber\\\\ \n    & &{ + 8{\\left(1+z\\right)}^2 \\hbox{Re}(\\delta^{sZ}_{1}(+)) s_W^4 \n          + 2{\\left(1+z\\right)}^2 \\hbox{Re}(\\delta^{sZ}_{1}(-)) \\[(2s^2-1)]^2 \\Bigr) } \\label{eq:c7} \\\\ \n    & &{ +   {{\\hbox{Im}\\left(\\chi(s)\\right)}\\over{\\hbox{Re}\\left(\\chi(s)\\right)}}\n           \\Bigl(  - 8 (1-z^2) \\hbox{Im}(\\delta^{sZ}_{2}(+)) s_W^2 \\[(2s^2-1)]\n          - 8 {\\left(1+z\\right)}^2 \\hbox{Im}(\\delta^{sZ}_{1}(+)) s_W^4 } \\nonumber\\\\ \n    & &{  - 2{\\left(1+z\\right)}^2 \\hbox{Im}(\\delta^{sZ}_{1}(-)) \\[(2s^2-1)]^2 \\Bigr) \\Bigr] } \\ , \\nonumber \n\\end{eqnarray}\n\n\\begin{eqnarray}\n    C^{(8)}_Z &=& { 1 \\over {(v_e^2 + a_e^2)} }\n        {  \\Bigl[ 8 \\hbox{Re}(\\delta^{sZ}_{1}(+)) s_W^4\n                         + 2 \\hbox{Re}(\\delta^{sZ}_{1}(-)) \\[(2s^2-1)]^2 } \\label{eq:c8} \\\\ \n        & &{+ {{\\hbox{Im}\\left(\\chi(s)\\right)}\\over{\\hbox{Re}\\left(\\chi(s)\\right)}}  \\Bigl(  - 8 \\hbox{Im}(\\delta^{sZ}_{1}(+)) s_W^4\n        - 2 \\hbox{Im}(\\delta^{sZ}_{1}(-))\\[(2s^2-1)]^2 \\Bigr) \\Bigr] } \\ , \\nonumber \n\\end{eqnarray}\n\n\\begin{eqnarray}\n   C^{(9)}_Z &=& {1 \\over { {(v_e^2 + a_e^2)^2 } \\left(1+4 r_V r_A \\right)} }\n       {   \\Bigl[   128 \\delta^{tZ}_{1}(+) s_W^8\n           + 8 \\delta^{tZ}_{1}(-) \\[(2s^2-1)]^4} \\nonumber\\\\ \n        & &{ + 128 \\hbox{Re}(\\delta^{sZ}_{1}(+)) s_W^8\n           + 8 \\hbox{Re}(\\delta^{sZ}_{1}(-)) \\[(2s^2-1)]^4 } \\label{eq:c9} \\\\ \n        & &{ -{{\\hbox{Im}\\left(\\chi(s)\\right)}\\over{\\hbox{Re}\\left(\\chi(s)\\right)}}  \\Bigl( 128 \\hbox{Im}(\\delta^{sZ}_{1}(+)) s_W^8 \n          + 8 \\hbox{Im}(\\delta^{sZ}_{1}(-)) \\[(2s^2-1)]^4 \\Bigr) \\Bigr] } \\ ,\\nonumber  \n\\end{eqnarray}\n\n\\begin{eqnarray}\n  C^{(10)}_Z &=& { 1 \\over { (1+z^2) (v_e^2 + a_e^2)^2 + 8 z v_{e}^{2} a_{e}^{2} } }\n        {\\Bigl[ 128 {\\left(1+z\\right)}^2 \\hbox{Re}(\\delta^{sZ}_{1}(+)) s_W^8 } \\label{eq:c10} \\\\ \n    & &{+ 8 {\\left(1+z\\right)}^2 \\hbox{Re}(\\delta^{sZ}_{1}(-)) \\[(2s^2-1)]^4 \n    + 64 (1-z)^2 \\hbox{Re}(\\delta^{sZ}_{2}(+)) s_W^4 \\[(2s^2-1)]^2 \\Bigr] } \\ .\\nonumber  \n\\end{eqnarray}\n\nThe symbols used are \n\\begin{eqnarray}\n&&\\delta_{1}^{tZ}(\\pm)=\\delta_{1,w,V}^{tZ}(\\pm) \n   + {{2}\\over{g^Z_{\\pm}}} \\Pi^{\\gamma Z}(t) \\ ,\n  \\delta_{1}^{sZ}(\\pm)=\\delta_{1,w,V}^{sZ}(\\pm) \n   + {{2}\\over{g^Z_{\\pm}}} \\Pi^{\\gamma Z}(s) \\ , \\label{eq:cdef} \\\\\n&&\\delta_{2}^{sZ}(\\pm)=\\delta_{2,w,V}^{sZ}(\\pm) \n+ \\left( {{1}\\over{g^Z_{+}}} + {{1}\\over{g^Z_{-}}}\\right) \\Pi^{\\gamma Z}(s) \\ ,\n  \\delta_{3}^{tZ}(\\pm)=\\delta_{3,w,V}^{tZ}(\\pm) \n+ \\left({{1}\\over{g^Z_{+}}} + {{1}\\over{g^Z_{-}}}\\right) \\Pi^{\\gamma Z}(t) \\ ,\n\\nonumber  \\end{eqnarray}\nwhile functions $\\delta_{i,w,V}^{tZ}(\\pm)$, $\\delta_{i,w,V}^{sZ}(\\pm)$\n ($i=1,2,3$), $\\Pi^{\\gamma Z}(t)$ and constants $g^Z_{\\pm}$\nare defined in the second reference of ~\\cite{HOLLIK} in the same notation. \nAs usual we take \n\\begin{equation}\n {\\sin^2(\\theta_W) \\equiv s_W^2 = 1 - c_W^2  = 1-{{M_W^2}\\over{M_Z^2}} } \\ .\n\\label{eq:c11} \n\\end{equation}\n\nThe above formulae take into account the $Zee$ weak vertex corrections and \n$\\gamma Z$ mixing self energy contribution. \nTo include completely the $Z$ boson self energy corrections it is sufficient \nto change in our approach the two functions $\\chi(s)$ and $\\chi'(t)$. \nThe new ones are \n\\begin{eqnarray}\n  \\chi(s) &=& { {{1} \\over {16 s_W^2 c_W^2}} {{1}\\over{1+\\Pi^Z(s)}}\n   (v_e^2 + a_e^2) {{s}\\over{s-M_Z^2 +is\\Gamma_Z\/M_Z}} }\\ ,\n           \\label{eq:c12} \\\\  \n  \\chi'(t) &=& { {{1} \\over {32 s_W^2 c_W^2}} {{1}\\over{1+\\Pi^Z(t)}}\n   (v_e^2 + a_e^2) {{s}\\over{M_Z^2 -t}} } \\ ,\n           \\label{eq:c13} \n\\end{eqnarray}\nwhere \n$\\Pi^Z(s) = \\hbox{Re}[\\hat \\Sigma^Z(s)]\/(s-M_Z^2)$ and $\\hat \\Sigma^Z(s)$ \nis again defined in ~\\cite{HOLLIK}.\nAll the higher order corrections are included into the \n$\\Pi^Z$ and $\\Pi^{\\gamma Z}$ functions, and through them into the formulae\n~(\\ref{eq:c4}-\\ref{eq:cdef}) and ~(\\ref{eq:c12}-\\ref{eq:c13}), which remain\nunchanged.\n\nThe value of $s_W^2$ is calculated using Eq.~(\\ref{eq:c11}) with $M_Z$\nas an input parameter. In the code the value of $M_W$ can be supplied by \nthe user, or is calculated using the Fermi constant $G_F$ as an independent \nparameter.\nIn the latter case we implement the approach outlined in ~\\cite{CERN95-03_2},\nwhich allows to get the value of the $W$ boson mass with higher accuracy\nthan from its direct measurement.  \nFor this better precision it is necessary to include the already mentioned \nweak corrections up to two loops to the $\\Delta\\rho$ parameter \n~\\cite{FLEISCHER} and also the QCD corrections to the self energy functions of \nthe bosons (which are needed to properly calculate $\\Delta r$ ) ~\\cite{Kniehl}. \nChecking with the values of the $W$ boson mass presented in ~\\cite{CERN95-03_2} \nas a function of the mass of the top quark $m_t$ (at fixed values of \n$m_H=300$ GeV and $\\alpha_S(M_Z)=0.125$), we obtain a very good agreement \naround $m_t=175$ GeV (only a small difference (0.03\\%) is appreciable \nabove the unrealistic value $m_t$ = 225 GeV). \n\nActually the inclusion in BHAGEN94 (and as a consequence also in BHAGEN95) of \nthe higher order QCD corrections is done in an approximate form. \nIn particular for the first two fermion generations (u,d,s and c quarks, \nfor which the limit $s,-t \\gg m^2$ is valid, with $m$ the quark mass) \nwe use the multiplicative factor $(1+{{\\alpha_S}\\over \\pi}+...)$ \nin front of the contribution due to one quark loop in the self energy \nfunctions of the bosons. \nFor the $t,b$ doublet we use the approximated formulae, \npresented in ~\\cite{Kniehl}, \nfor the doublet contribution to $\\Delta r$ in the $M_W$ calculation.\nOn the contrary in the Bhabha cross-section calculations is necessary the \nknowledge of the separate contributions $\\Pi^Z$ and $\\Pi^{\\gamma Z}$ to the \nboson self energies, we use them in the form described in ~\\cite{CERN95-03_2} \n(BHM\/WOH approach), i.e. we include the leading $\\Delta\\rho^{HO}$ corrections. \nIn this way the corrections are\ncalculated in the point $s=M_Z^2$ and their $s,t$ dependance \n(which is known however only in the QCD two loop contribution) is not taken\ninto account. Also some known nonleading corrections are not included. \nAll this considered the approximation is sufficient to reach at large-angle \nthe projected accuracy of 0.5\\% in the cross-section calculations. \nMoreover other not included QED two loop corrections are expected to be \nmuch bigger than the left over QCD corrections, like the next to leading \ncorrection, which is not yet calculated, or the inferred leading term in \n$s-t$ channel interference, assumed to be identical to the $s$-channel.\n\\bigskip\n\n\\section{ The BHAGEN95 code. }\n\nBHAGEN95 is a collection of three programs to calculate the cross-section\nfor Bhabha scattering from small to large scattering angles at LEP1 and\nLEP2 energies.\nIn its present form the integrated cross-section $\\sigma({\\hbox{BHAGEN95}})$ \nfor a given selection of cuts is calculated as\n\\begin{eqnarray}\n        \\sigma({\\hbox{BHAGEN95}})\n                = \\sigma({\\hbox{BHAGEN94}})\n                -\\sigma^H({\\hbox{BH94-FO}})\n                +\\sigma^H({\\hbox{BHAGEN-1PH}}) \\ .\n       \\label{eq:cs}\n\\end{eqnarray}\n\n$\\sigma({\\hbox{BHAGEN94}})$ is the integrated cross-section, \nbased on leading \\Ord{\\alpha^2} exponentiated formulae,   \nobtained with the Monte Carlo event generator BHAGEN94, \nwith the implementations described in the previous sections 2 and 4.\nThe use of collinear kinematics of initial and final radiation leaves \nsome approximation in the angular distribution, which limits the accuracy\nparticularly in the region of hard photon emission, as remarked at the end of\nsection 2.\n\\par\n$\\sigma^H({\\hbox{BH94-FO}})$ is the integrated cross-section of\n\\Ord{\\alpha} for one hard photon emission, obtained selecting the appropriate \npart in the Monte Carlo event generator BH94-FO, the \\Ord{\\alpha} expansion \nof BHAGEN94 described in section 3.\n\\par\n$\\sigma^H({\\hbox{BHAGEN-1PH}})$ is the integrated cross-section obtained\nwith the one hard photon complete matrix element and exact kinematics,\nimplemented in the Monte Carlo event generator BHAGEN-1PH ~\\cite{1PH}.\n\\par\nThe subtraction of $\\sigma^H({\\hbox{BH94-FO}})$ and its substitution\nwith $\\sigma^H({\\hbox{BHAGEN-1PH}})$ is performed to reduce the error\nin the cross-section, coming from the approximation in the contribution \ndue to the one hard photon emission in BHAGEN94, as discussed in \n~\\cite{CERN95-03}.\nIn this way the one hard photon emission is treated exactly in BHAGEN95.\n\nThe choice of the energy threshold $\\epsilon$ (in units of the beam energy) \nfor a photon to be considered hard should not affect the difference between \n$\\sigma^H({\\hbox{BHAGEN-1PH}})$ and $\\sigma^H({\\hbox{BH94-FO}})$. \nHowever the approximate hard photon treatment in BH94-FO implies that a \ncorrection of the order of $\\epsilon$ is missing, so it is necessary to \nchoose $\\epsilon$ well below the desired accuracy, typically in the range \nof $10^{-5}-10^{-4}$.\nBut even so the difference is really independent on $\\epsilon$ only if \nthe soft photon treatment in BH94-FO is the same as in the exact program \nBHAGEN-1PH. This is indeed the case.\nIn fact changing $\\epsilon$ from $10^{-4}$ to $10^{-5}$ the separate \ncross-sections are growing about 20-30\\% for the event selections described \nin ~\\cite{CERN96}, while the difference is stable within statistical errors.\n\nThe three programs provide cross-sections, which are summed as in \nEq.~(\\ref{eq:cs}) or used to obtain other quantities, such as \nforward-backward asymmetry.\nAlthough the constituent programs are separately genuine event generators, \nthe discussed combination can be used for Monte Carlo integration only.\n\nAt small-angle we estimate the accuracy in the cross-section evaluation,\ndue to the uncontrolled higher orders terms \\Ord{\\alpha^2 L} and\n\\Ord{\\alpha^3 L^3} and to the incertitude in \\Ord{\\alpha^2 L^2} $s-t$\ninterference, to amount comprehensively to about 0.1\\%.\nThe further error, due to the approximate two hard photon contribution \n(strongly dependent on the imposed cuts) is estimated on the basis of the \ncalculated correction for the one hard photon contribution times \n$\\beta_e(s)\\simeq 0.1$, to account for the increase in perturbative order.\n\nIn Table \\ref{Tab1} are presented the values of the ratio $R$, defined as \n \\begin{eqnarray}\n         R  = 100 {{\\sigma^H({\\hbox{BHAGEN-1PH}})\n                -\\sigma^H({\\hbox{BH94-FO}}) } \\over\n                 {\\sigma({\\hbox{BHAGEN95}})}}\n                   \\ ,\n       \\label{eq:cs1}\n\\end{eqnarray}\nwhich is the correction (in \\%) introduced in BHAGEN95, to account for the \napproximation in the one hard photon contribution in BHAGEN94. \nThe correction is given for the event selections used in ~\\cite{CERN96}, \nin the same notation as for the $t$-channel comparison. \nAs already said, for $\\beta_e(s)\\simeq 0.1$ the same numbers in Table \n\\ref{Tab1} are an estimation (in per mil) of the inaccuracy, due to the \napproximate treatment of two hard photon emission.\nThe values in Table \\ref{Tab1} are acceptably small for cuts closer to the \nones in experiments,  which are of the angular asymmetric WN type, with \n$ 0.3 \\le z_{min} \\le 0.7 $, where $z_{min}$ is the energy threshold for the\nfinal clusters for accepting or rejecting the events. \nIndeed in such cases the (included) one hard photon \ncorrections are found to be below 1.4 \\% at LEP1, so that the corrections \nto two hard photon emissions are expected to be below 1.4 per mil. \nFor the values at $z_{min}=0.9$ and calorimetric event selection, \nthese corrections are expected to be much bigger (at a few per mil level).\n\nAll included we estimate at small-angle an accuracy of the order of\n0.1\\%-0.2\\% for typical experimental cuts for both LEP1 and LEP2 energies.\n\\par\nAt large-angle we estimate the accuracy of the \\Ord{\\alpha^2 L^2} $s-t$ \ninterference contribution up to 1\\% (depending on energy and cuts) at LEP1, \nbut much smaller at LEP2.\nThe error, coming from the approximate treatment of two hard photon emission,\nis estimated as explained above for the small-angle case, and is smaller for \nmore stringent acollinearity cut.\nAll included we estimate an accuracy of the order of 1\\% in the worst case\nat LEP1, when the beam energy is a few GeV above the $Z$ boson peak, while\ntypical accuracy for relatively loose cuts is 0.5\\%.\n\nThe three programs run separately.\nThey provide initialization and fiducial volume definition according to\ninput parameters, then starts the generation of events according to \nappropriate variables, which smooth the cross-section behavior.\nRejection is performed through the routine {\\tt TRIGGER}, where the special\ncuts can be implemented.\nThe programs stop when the requested number of accepted events is reached\nor alternatively when the requested accuracy is obtained.\n\nThe following data have to be provided in input:\nmass of the $Z$, mass of the top quark, mass of the Higgs, value of\n$\\alpha_S(M_Z)$, value of $\\Gamma_Z$, the beam energy $E_{beam}$, the\nminimum energy for final leptons $E_{min}$ (larger than 1 GeV), \nminimum and maximum angle for the scattered electron (positron) with \nthe initial electron (positron) direction, maximum acollinearity allowed \nbetween final electron and positron, number of accepted events to be produced, \nnumbers to initialize the random number generator.\nThe following possibilities are also provided: i) to switch on or off the \nleading contribution from virtual and soft emitted pairs ~\\cite{PL94},\nii) to calculate separately the different channel contributions (useful for \ntests), iii) the recording of the generated events of each component program \nin a separate file.\n\nFor \\Ord{\\alpha} programs the minimum and maximum energy allowed for the photon\nhas to be specified.\nThe input of BHAGEN-1PH requires also the maximum acoplanarity, \nand minimum angles of the emitted photon with initial \nand final fermion directions, if the contributions with the collinear photons\nare to be excluded.\n\nEach program returns the input parameters and the values of the cross-section\nobtained with weighted and unweighted events, with the relative statistical\nvariance (one standard deviation).\nOf course, due to the efficiency, the weighted cross-section is usually much\nmore precise than the unweighted one.\nThe total integrated cross-section is then calculated according to Eq.\n(\\ref{eq:cs}).\n\n\n\\begin{table}[!ht]\n\\centering\n\\begin{tabular}                            {|c|c|c|c|c|c|}\n\\hline\n$ z_{min} $\n& 0.1\n& 0.3\n& 0.5\n& 0.7\n& 0.9\n\\\\\n\\hline\n\\hline\n  BARE1(WW)  \n& \n& -0.24\n& -0.29\n& -0.23\n& -0.11\n\\\\\n\\hline\n  CALO1(WW)\n& \n& -0.46\n& -0.75\n& -1.15\n& -2.29\n\\\\\n\\hline\n  CALO2(WW)\n& -0.38\n& -0.60\n& -1.01\n& -1.66\n& -3.57\n\\\\\n\\hline\n  SICAL2(WW)\n& +0.35\n& +0.26\n& +0.005\n& -1.02\n& -3.34\n\\\\\n\\hline\n  CALO2(NN)\n& -0.54\n& -0.73\n& -1.06\n& -1.76\n& -3.66\n\\\\\n\\hline\n  CALO2(NW)\n& +0.01\n& -0.22\n& -0.64\n& -1.39\n& -3.40\n\\\\\n\\hline\n  CALO2(WW-all incl.)\n& -0.36\n& -0.57\n& -0.96\n& -1.59\n& -3.42\n\\\\\n\\hline\n  CALO2(NN-all incl.)\n& -0.52\n& -0.70\n& -1.02\n& -1.69\n& -3.51\n\\\\\n\\hline\n  CALO2(WN-all incl.)\n& +0.00\n& -0.21\n& -0.61\n& -1.33\n& -3.26\n\\\\\n\\hline\n\\hline\n  CALO3(NN)\n& -1.14\n& -1.29\n& -1.56\n& -2.19\n& -4.38\n\\\\\n\\hline\n  CALO3(NW)\n& -0.21\n& -0.41\n& -0.77\n& -1.61\n& -3.95\n\\\\\n\\hline\n  CALO2(WW)\n&  \n& -0.61\n& -1.02\n& -1.68\n& -3.62\n\\\\\n\\hline\n  SICAL2(WW)\n&  \n& +0.25\n& +0.04\n& -1.03\n& -3.40\n\\\\\n\\hline\n\\end{tabular}\n\\caption{\\small \nCorrection R, defined in Eq.~({\\protect\\ref{eq:cs1}}), due to the approximate \ntreatment of the one hard photon emission in BHAGEN94, in \\% of the BHAGEN95 \ncross-section. \nAll event selections are defined in ~\\protect\\cite{CERN96} in the same \nnotation. \nFirst 9 rows are for LEP1 and last 4 rows are for LEP2 energies.\nThe option 'all incl.' means that all possible contributions are included, \nwhile the remaining tests are done only for $t$-channel contributions with \nvacuum polarization switched off. }\n\\label{Tab1}\n\\end{table}\n\\bigskip\n\n\\section{ Comparisons at small-angle. }\n\nThe \\Ord{\\alpha} results are tested with other programs in ~\\cite{CERN95-03} \nfor bare event selection and in ~\\cite{CERN96} also for calorimetric event \nselection, where the precision of 0.03 \\% is confirmed, as a consequence \nof the agreement of different programs within statistical errors. \n\nIn ~\\cite{CERN95-03} the results of BHAGEN94, including the improvement \noutlined here in section 2, are presented for a comparison of the \ncross-section with the final electron and positron scattering \nangles $\\theta_\\pm$ in the range $3^{\\circ} \\leq \\theta_\\pm \\leq 8^{\\circ}$.\nFrom this comparison it is clear that we cannot reach a precision better than\n0.3\\% using only the structure function approach. \n\nTo have a better precision the code BHAGEN95 is settled, with the features \ndescribed in the previous section. \nSeveral preliminary results are already presented and compared in \n~\\cite{CERN96}, so we correct the few which are revised, but \nwe do not repeat here the unchanged ones. \n\nIn Fig. 16 of ~\\cite{CERN96}, in the comparison at small-angle \n($t$-channel only) the bare event selection case (BARE1, WW) shows \ngood agreement (almost inside the 0.1\\% box) \nup to $z_{min} = 0.9$ included among all the programs (BHAGEN95, \nBHLUMI 4.03 ~\\cite{BHLUMI4},\nOLDBIS+LUMLOG ~\\cite{OBI+LUMG}, \nSABSPV ~\\cite{SABSPV},\nNLLBHA ~\\cite{NLLBHA}).\n\nFor calorimetric event selections BHAGEN95 and OLDBIS+LUMLOG \nhave very close results for every event selection cut, but they \nagree (within 0.1\\% at LEP1 and 0.2\\% at LEP2) with BHLUMI and SABSPV \nonly for values of the parameters close to the real experimental ones \n(NW or WW, $0.3\\le z_{min} \\le 0.7$).\nThe difference is larger for more severe cuts (as in the NN case) and  \nfor $z_{min} = 0.9$. \n\nIt is proposed in ~\\cite{CERN96} that for OLDBIS+LUMLOG the difference is due \nto the so called 'classical limit' (i.e. zero radiation emission limit)\nwhich could be different in higher orders.\n\nFor BHAGEN95 we believe that the difference is due to the approximate \ntreatment of two hard photons illustrated in previous section, while the\n'classical limit' is sufficiently accurate.\nIn fact for calorimetric event selection, even for $z_{min} \\rightarrow 1.0$, \nthat limit is not approached, as almost collinear hard photons can join the\nfinal lepton in the cluster.\nThe 'classical limit' is approached only for BARE1 event selection, where\nall the programs are in substantial agreement even at $z_{min} =0.9$, \nand remarkably there the estimated error in BHAGEN95 on the basis of \nTable \\ref{Tab1} is only about 0.01 \\%.\nOn the contrary for calorimetric event selection and $z_{min} = 0.9$ \nhard photons are included within very stringent cuts on phase space, \nas the cluster opening is very narrow. \nThe structure function approach (used in the part of BHAGEN95 called BHAGEN94) \nfor this configuration is expected to be inaccurate, as it is not able to mimic \nvery sophisticated cuts.\n\nIn conclusion, at small-angle for the test cross-section called \n'$t$-channel only', the results of BHAGEN95 are in very good agreement \nwith those of OLDBIS+LUMLOG, and inside the errors also with those of \nBHLUMI and SABSPV. \nThe accuracy of BHAGEN95 is very much dependent on the event selection used, \nand is of the order of 0.1\\% - 0.2\\% for typical experimental cuts, \nwhile for more stringent cuts it can amount up to say 0.5\\%, with the \nsource of the error well understood.\n\nThe results for the complete cross-section of BHAGEN95, with all the other \ncontributions included, are presented and compared in Table 18 and in Fig. 17 \nof ~\\cite{CERN96}, repeated here in Fig. \\ref{fig:sical92asy-FG} for \ncompleteness\n\\footnote{The values of BHAGEN95 in Fig. 2 of ~\\cite{BWG_LETT} differ \n          slightly from the ones in ~\\cite{CERN96}, due to a second bug \n          introduced in the rush-fixing of a previous (actually inactive) \n          bug in the routine {\\tt TRIGGER}. \n          The corrected results confirm those already presented in \n          ~\\cite{CERN96}. }.\n\nIt is interesting to compare the difference $\\Delta\\sigma$ between the \ncomplete results (all included) of Table 18 and the '$t$-channel only' \nresults of Tables 14 and 16 of ~\\cite{CERN96} for BHLUMI and BHAGEN95 \n(for SABSPV values the comparison has no significance due to larger \nstatistical errors). \nIn Table \\ref{Tab2} are presented the values for different angular ranges \n(WW, NN, WN) and energy threshold $z_{min}$, taken from Table 18 of \n~\\cite{CERN96} for BHLUMI and calculated as indicated above for BHAGEN95.\n\nThe difference $\\Delta\\sigma$ is mainly due to vacuum polarization correction, \npresumably implemented in the same way in both programs, using also the \nparameterization in ~\\cite{VPH}, and to the $Z-\\gamma$ interference term.\nThis latter contribution at small-angle is in the range of 1 per mil of \nthe total cross-section, depending mostly on the angular range allowed and \nmuch less on the other details of the selection.\n\nIn the last column of Table \\ref{Tab2} is presented in per mil the variation \n \\begin{eqnarray}\n      V = 1000 {{\\Delta\\sigma({\\hbox{BHAGEN95}})\n                -\\Delta\\sigma({\\hbox{BHLUMI}}) } \\over\n                 {\\sigma({\\hbox{BHLUMI,all incl.}})}}\n                   \\ ,\n       \\label{eq:cs2}\n\\end{eqnarray}\nbetween the complete cross-section obtained with BHLUMI and the one obtained \nwith BHAGEN95, due to the difference in vacuum polarization implementation and \n$Z-\\gamma$ interference correction. \nIt can be seen that in the experimentally interesting region the variation \nis statistically significant, always positive and increasing with $z_{min}$, \nand it is almost up to 0.1\\%.\n\\begin{table}[!ht]\n\\centering\n\\begin{tabular}                            {|c|c|c|c|}\n\\hline\n$ z_{min} $\n& $\\Delta\\sigma$(BHLUMI,WW)\n& $\\Delta\\sigma$(BHAGEN95,WW)\n& V(WW)\n\\\\\n\\hline\n0.1\n&5.140(8) \n&5.203(11)\n&0.46(10)\n\\\\\n\\hline\n0.3\n&5.126(8)\n&5.197(14)\n&0.52(12)\n\\\\\n\\hline\n0.5\n&5.100(8)\n&5.195(14)\n&0.70(12)\n\\\\\n\\hline\n0.7\n&4.994(8)\n&5.125(16)\n&0.99(14)\n\\\\\n\\hline\n0.9\n&4.627(8)\n&4.821(16)\n&1.57(15)\n\\\\\n\\hline\n \n& $\\Delta\\sigma$(BHLUMI,NN)\n& $\\Delta\\sigma$(BHAGEN95,NN)\n& V(NN)\n\\\\\n\\hline\n0.1\n&3.751(7)\n&3.802(14)\n&0.51(16)\n\\\\\n\\hline\n0.3\n&3.742(7)\n&3.801(14)\n&0.60(16)\n\\\\\n\\hline\n0.5\n&3.728(7)\n&3.799(14)\n&0.72(16)\n\\\\\n\\hline\n0.7\n&3.678(7)\n&3.774(14)\n&0.99(16)\n\\\\\n\\hline\n0.9\n&3.430(7)\n&3.579(14)\n&1.64(18)\n\\\\\n\\hline\n\n& $\\Delta\\sigma$(BHLUMI,WN)\n& $\\Delta\\sigma$(BHAGEN95,WN)\n& V(WN)\n\\\\\n\\hline\n0.1\n&3.883(4)\n&3.920(13)\n&0.36(14)\n\\\\\n\\hline\n0.3\n&3.873(4)\n&3.919(13)\n&0.45(14)\n\\\\\n\\hline\n0.5\n&3.854(4)\n&3.916(13)\n&0.61(14)\n\\\\\n\\hline\n0.7\n&3.779(4)\n&3.869(13)\n&0.90(14)\n\\\\\n\\hline\n0.9\n&3.478(4)\n&3.624(14)\n&1.59(15)\n\\\\\n\\hline\n\\end{tabular}\n\\caption{\\small \nThe difference $\\Delta\\sigma$, in nb, between the complete cross-section \nand the '$t$-channel only' contribution, for BHLUMI and BHAGEN95, for several\nevent selections (WW, NN, and WN angular range), for $2E_b = 92.3$ GeV.\nIn the last column is the variation V, defined in \nEq.~({\\protect\\ref{eq:cs2}}),  \ngiving in per mil the difference due to vacuum polarization implementation and \n$Z-\\gamma$ interference correction of BHAGEN95 respect to BHLUMI. \nIn brackets is the statistical error on the last digits. } \n\\label{Tab2}\n\\end{table}\n\nIt seems difficult that the difference comes from vacuum polarization \nimplementation, so we have investigated the $Z-\\gamma$ interference \ncontribution. \n\nIn the next section are reported comparisons at large-angle: BHAGEN95 is in \na good agreement (about 0.5\\%) with the other programs (notably with \nALIBABA for BARE event selection), where the contribution of the $Z-\\gamma$ \ninterference term amounts up to half of the cross-section.\n\nThe accuracy of the $Z-\\gamma$ interference term included in BHLUMI is tested \nin ~\\cite{J+P+W}, relaying mostly on the comparison with the ALIBABA code, \nso we have obtained results in the same conditions for BHAGEN95 for comparison.\nThe results of ALIBABA and the Born cross-sections, to which the\nresults are normalized, were taken from ~\\cite{B+P92} for old generation \nluminometers (LCAL: larger angular range between $3.3^{\\circ}$ and \n$6.3^{\\circ}$) and from ~\\cite{B+P93} for new generation luminometers \n(SCAL: smaller angular range between $1.5^{\\circ}$ and $3.15^{\\circ}$, more\nsimilar to the ones used in ~\\cite{CERN96}), \nwhile the results of BHLUMI are taken from ~\\cite{J+P+W} in the same \nconditions. \nIn Table \\ref{Tab3} the results of ALIBABA, BHLUMI and BHAGEN95 \nin the SCAL angular range are inside the 0.01\\% difference, and in the LCAL \nangular range are inside the 0.05\\%.\nThis test is done for very loose cuts: no cut on photon energy and angles\nis applied and only the angular ranges of leptons are restricted.\nIn the results of Table \\ref{Tab2} the agreement between BHLUMI\nand BHAGEN95 is much better for the looser cuts, than for the more severe ones,\nand this could be the reason for the better agreement in Table \\ref{Tab2} .\n\nIt is however difficult to identify with certainty the source of the difference \nwithout a more detailed analysis, particularly if it comes from a different\nuse of the same electroweak parameters, but it would be necessary in case the \naccuracy has to be better than 0.1\\%.\n\\begin{table}[!ht]\n\\centering\n\\begin{tabular}                            {|c|c|c|c|c|c|c|}\n\\hline\n          &\n\\multicolumn{3}{|c|}{LCAL angular range}\n&\\multicolumn{3}{c|}{SCAL angular range} \\\\\n\\hline\n$ 2 E_b $ \n&BHAGEN95 \n&ALIBABA\n&BHLUMI\n&BHAGEN95\n&ALIBABA\n&BHLUMI\n\\\\\n\\hline\n89.661 \n&0.757\n&0.778\n&0.794\n&0.165\n&0.172\n&0.175\n\\\\\n\\hline\n90.036 \n&0.779\n&0.799\n&0.816\n&0.169\n&0.177\n&0.180\n\\\\\n\\hline\n90.411 \n&0.724\n&0.747\n&0.754\n&0.156\n&0.164\n&0.165\n\\\\\n\\hline\n90.786 \n&0.527\n&0.545\n&0.538\n&0.112\n&0.117\n&0.116\n\\\\\n\\hline\n91.161 \n&0.175\n&0.187\n&0.158\n&0.035\n&0.036\n&0.032\n\\\\\n\\hline\n91.563 \n&-0.206\n&-0.206\n&-0.247\n&-0.048\n&-0.050\n&-0.057\n\\\\\n\\hline\n91.911 \n&-0.473\n&-0.479\n&-0.521\n&-0.105\n&-0.110\n&-0.116\n\\\\\n\\hline\n92.286 \n&-0.602\n&-0.609\n&-0.647\n&-0.132\n&-0.136\n&-0.143\n\\\\\n\\hline\n92.661 \n&-0.642\n&-0.650\n&-0.678\n&-0.141\n&-0.145\n&-0.150\n\\\\\n\\hline\n\\end{tabular}\n\\caption{\\small \n$Z-\\gamma$ interference term (in \\% of Born cross-section)\n for BHAGEN95, ALIBABA and BHLUMI for two\ndifferent angular ranges (LCAL and SCAL) as a function of the beam energy. }\n\\label{Tab3}\n\\end{table}\n\\bigskip\n\n\\section{ Comparisons at large-angle. }\n\nAt large-angle some comparisons were presented for LEP1 and LEP2 energies \nin ~\\cite{CERN96}.\nHowever, as mentioned also there, the higher orders weak and QCD corrections \nwere just implemented in BHAGEN95 and the results were very preliminary. \nUnfortunately some bugs were present in the program and, after their \ncorrection and test, the new results of BHAGEN95 can now be compared with \nthe ones of the other programs \nALIBABA ~\\cite{ALIBABA}, \nTOPAZ0 ~\\cite{TOPAZ0}, \nBHAGENE3 ~\\cite{BHAGENE}, \nUNIBAB ~\\cite{UNIBAB},\nBHWIDE ~\\cite{BHWIDE},\nSABSPV ~\\cite{SABSPV}.\n\nWe report here the new results of BHAGEN95 in Fig. \\ref{fig:lab-lep1-bare} \nand Fig. \\ref{fig:lab-lep1-calo} for LEP1 and in Fig. \\ref{fig:lab-lep2-calo} \nfor LEP2 energies (corresponding respectively to Fig. 19, 20 and \nFig. 21 in ~\\cite{CERN96} in the same notation), for scattering angles \n$40^\\circ < \\theta_- < 140^\\circ$ and $0^\\circ < \\theta_+ < 180^\\circ$. \n\nWe estimate that at large-angle the accuracy of the program BHAGEN95 is 0.5\\% \neverywhere, except in the region of a few GeV above the $Z$ boson peak, \nwhere, due to the absence of the calculation of the leading \\Ord{\\alpha^2 L^2} \nterm in $s-t$ channel interference, it can be assumed to be up to 1\\% \n~\\cite{PL94}.\n\nIn Fig. \\ref{fig:lab-lep1-bare}, for LEP1 energy and BARE type event selection \nthe results of BHAGEN95 are in agreement with most of the programs inside 0.5\\% \nfor energies under and on top of the $Z$ boson peak, while above the resonance \nand with more stringent acollinearity cuts ($10^\\circ$) there is \na noticeable agreement with ALIBABA, but some difference from other programs, \nwhich however is still less than 1\\%. \nThe same pattern is kept for the calorimetric event selection CALO, \nshown in Fig. \\ref{fig:lab-lep1-calo}, where unfortunately results from \nALIBABA are no longer available. \n\nIn Fig. \\ref{fig:lab-lep2-calo}, for LEP2 energies and CALO event selection, \nthere is a remarkable clustering in a 2\\% interval of most of the programs.\n\\bigskip\n\n\\section{ Conclusions.} \n\nThe Monte Carlo integrator BHAGEN95 (available on request from the authors) \ncalculates the cross-section of the Bhabha scattering with continuity from \nsmall to large-angle and from LEP1 to LEP2 energies. \n\nThe program contains all the necessary corrections to provide results, \nfor typical experimental event selections, with the precision required \nto usefully compare with experimental measurements and other theoretical \nresults. \nWe estimate a precision of 0.1-0.2\\% at small-angle, in the angular range \nof the new generation of LEP luminometers, mainly due to the inaccuracy in\nin the two hard photon emission contribution. \nAt large-angle for both LEP1 and LEP2 energies, we estimate a precision of \n0.5\\% with the exception of the region of the beam energies a few GeV above \nthe $Z$ boson resonance, where the relevance of the still missing calculation \nof the leading \\Ord{\\alpha^2 L^2} radiative corrections to the $Z-\\gamma$ \ninterference term spoils the accuracy up to 1\\%, as in every other present \ncalculation.\n\nWe have performed a detailed comparison of the photonic and weak corrections \nfor both small-angle (angular range of the new generation of LEP luminometers) \nand large-angle Bhabha scattering. \n\nAt small-angle we obtain an agreement better than 0.02\\% at \\Ord{\\alpha} \nwith the program OLDBIS for every type of event selection. \nIn the comparison beyond the \\Ord{\\alpha}, but limited to the $t$-channel only, \nwith vacuum polarization and $Z-\\gamma$ interference switched off, the results \nof BHAGEN95 agree with the ones of OLDBIS+LUMLOG better than 0.03\\%, \nfor typical experimental event selection, and have a difference less than 0.1\\%\nwith BHLUMI and SABSPV in these conditions. \nFor event selections less realistic for experiments the results of BHAGEN95\n(and also of OLDBIS+LUMLOG) can differ from the ones of BHLUMI and SABSPV\nof a few per mil. We believe to understand the difference (at least in the \nBHAGEN95 case) as due to the inaccuracy in the two hard photon emission \ncontribution, which depends on the details of the event selection used and is \nsmaller for looser cuts. \nWhen all possible contributions are switched on the agreement between \nBHLUMI, SABSPV and BHAGEN95 is inside 0.1\\% for realistic experimental event\nselection, as presented in Fig. \\ref{fig:sical92asy-FG} (same as in Fig. 17 of \n~\\cite{CERN96}). \nThe better agreement in this case is due to a slightly larger (but less \nthan 0.1\\%) contribution of BHAGEN95, coming mainly from the implementation \nof the vacuum polarization and\/or $Z-\\gamma$ interference correction. \nWe have investigated this small difference, but it is impossible to \ndisentangle the contributions without ad hoc runs of all the compared programs.\n\nAt large-angle and in the LEP1 energy range the corrected results of BHAGEN95 \nare shown in Fig. \\ref{fig:lab-lep1-bare} and in Fig. \\ref{fig:lab-lep1-calo}; \nthe difference with the other results is \nwithin 0.5\\% around the $Z$ boson resonance, being bigger \nfor energies a few GeV above the peak, where BHAGEN95 is in agreement with\nALIBABA within 0.5\\% and within 1\\% with other codes.\n\nFor LEP2 energies although the differences between the codes are larger \n(up to 2\\% for the cluster of the results of TOPAZ0, BHWIDE, SABSPV and \nBHAGEN95), as shown in Fig. \\ref{fig:lab-lep2-calo}, the precision is \ncomparable with the foreseen experimental accuracy.\n\\bigskip\n\n\\noindent{\\bf Acknowledgments}\\par\nUseful conversations with the conveners (S.~Jadach and O.~Nicrosini) and \nall the members of the CERN Working Group of the Event Generators for Bhabha \nScattering are gratefully acknowledged. \nWe thank W.~Hollik for useful informations about the BHM\/WOH approach and \nW.~Beenakker about the ALIBABA parameters.\nOne of us (HC) is grateful to the Bologna Section of INFN and to the Department \nof Physics of Bologna University for support and kind hospitality.\n\\bigskip\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{S1.\\quad Symmetry constraints on the S-matrix}\n\nFirst, we consider $C_3$ rotation symmetry which preserves the valley. We find that\n\\begin{equation}\n\\mathcal S = C_3 \\mathcal S C_3^{-1},\n\\end{equation}\nwhere $C_3$ is a cyclic permutation $(a_1,a_1') \\rightarrow (a_2,a_2') \\rightarrow (a_3,a_3') \\rightarrow (a_1,a_1')$ of the incoming modes which are defined in Fig.\\ {\\color{red} 1}(b) of the main text, and similar for outgoing modes. Next, we discuss the effect of $C_2$ rotation symmetry and time-reversal symmetry $T$. As these symmetries do not conserve the valley, we need to consider both valleys:\n\\begin{equation}\n\\begin{pmatrix} b_K \\\\ b_{K'} \\end{pmatrix} = \\begin{pmatrix} \\mathcal S_K & 0 \\\\ 0 & \\mathcal S_{K'} \\end{pmatrix} \\begin{pmatrix} a_K \\\\ a_{K'} \\end{pmatrix}.\n\\end{equation}\nUnder $C_2$ rotation symmetry, we have\n\\begin{equation}\n\\begin{pmatrix} b_{K'} \\\\ b_K \\end{pmatrix} = \\begin{pmatrix} \\mathcal S_K & 0 \\\\ 0 & \\mathcal S_{K'} \\end{pmatrix} \\begin{pmatrix} a_{K'} \\\\ a_K \\end{pmatrix},\n\\end{equation}\nsuch that $\\mathcal S_{K'} = \\mathcal S_K$. On the other hand, under time-reversal symmetry we have\n\\begin{equation}\n\\begin{pmatrix} a_{K'}^* \\\\ a_K^* \\end{pmatrix} = \\begin{pmatrix} \\mathcal S_K & 0 \\\\ 0 & \\mathcal S_{K'} \\end{pmatrix} \\begin{pmatrix} b_{K'}^* \\\\ b_K^* \\end{pmatrix},\n\\end{equation}\nsuch that $\\mathcal S_{K'} = (\\mathcal S_K)^t$. Hence, the combination $C_2T$ enforces $\\mathcal S_K = (\\mathcal S_K)^t$.\n\n\\section{S2.\\quad S-matrix without forward scattering}\n\nThe $S$-matrix relates valley Hall states that propagate along AB\/BA domain walls at the scattering nodes (AA regions) such that $(b,b')^t = \\mathcal S (a, a')^t$ with $a,a'$ six incoming modes and $b,b'$ six outgoing modes where the prime distinguishes the two valley Hall states as illustrated in Fig.\\ {\\color{red} 1}(b) of the main text. In the absence of forward scattering, we find that the most general $S$-matrix consistent with unitarity and $C_3$ and $C_2T$ symmetry is given by\n\\begin{equation} \\label{eq:Smat1}\n\\mathcal S = e^{i\\varphi} \\begin{pmatrix}\n0 & e^{i \\phi} \\sqrt{P_{d1}} & e^{i \\phi} \\sqrt{P_{d1}} & 0 & \\sqrt{P_{d2R}} & -\\sqrt{P_{d2L}} \\\\\ne^{i \\phi} \\sqrt{P_{d1}} & 0 & e^{i \\phi} \\sqrt{P_{d1}} & -\\sqrt{P_{d2L}} & 0 & \\sqrt{P_{d2R}} \\\\\ne^{i \\phi} \\sqrt{P_{d1}} & e^{i \\phi} \\sqrt{P_{d1}} & 0 & \\sqrt{P_{d2R}} & -\\sqrt{P_{d2L}} & 0 \\\\\n0 & -\\sqrt{P_{d2L}} & \\sqrt{P_{d2R}} & 0 & -e^{-i\\phi} \\sqrt{P_{d1}} & -e^{-i\\phi} \\sqrt{P_{d1}} \\\\\n\\sqrt{P_{d2R}} & 0 & -\\sqrt{P_{d2L}} & -e^{-i\\phi} \\sqrt{P_{d1}} & 0 & -e^{-i\\phi} \\sqrt{P_{d1}} \\\\\n-\\sqrt{P_{d2L}} & \\sqrt{P_{d2R}} & 0 & -e^{-i\\phi} \\sqrt{P_{d1}} &-e^{-i\\phi} \\sqrt{P_{d1}} & 0\n\\end{pmatrix},\n\\end{equation}\nwith $\\varphi$ and $\\phi$ real phases, and with the conditions $2P_{d1}+P_{d2R}+P_{d2L}=1$ and $P_{d1}=\\sqrt{P_{d2R} P_{d2L}}$ which has two solutions. Either all probabilities are nonzero with $0<P_{d1} \\leq 1\/4$ the only independent parameter or $P_{d1}=0$ and either $P_{d2R}$ or $P_{d2L}$ zero, which is equivalent to what we call the zigzag regime below. Hence, we consider the former solution. In this case, the secular equations yields\n\\begin{equation} \\label{eq:secular1}\n1 - \\lambda^6 + \\lambda^2 \\left[ \\lambda^2 h(\\bm k) - h(\\bm k)^* \\right] \\left( 1 - 4 P_{d1} \\sin^2 \\phi \\right) + 2i \\lambda^3 ( 2 \\sqrt{P_{d1}} \\sin \\phi )^3=0,\n\\end{equation}\nwith $\\lambda = e^{i(El\/\\hbar v+\\varphi)}$ and $h(\\bm k)=e^{ik_1}+e^{ik_2}+e^{-i(k_1+k_2)}$. If we define $\\sin \\phi' = 2\\sqrt{P_{d1}} \\sin \\phi$, which always has a solution for $\\phi'$ since $0<P_{d1} \\leq 1\/4$, we can write the secular equation as \n\\begin{equation} \\label{eq:secular2}\n1 - \\lambda^6 + \\lambda^2 \\left[ \\lambda^2 h(\\bm k) - h(\\bm k)^* \\right] \\cos^2 \\phi' + 2i \\lambda^3 \\sin^3 \\phi'=0,\n\\end{equation}\nwhich is equivalent to the case $P_{d1}=P_{d2R}=P_{d2L}=1\/4$ and $\\phi \\rightarrow \\phi'$. Hence, it is reasonable to assume that $\\mathcal S(\\phi,P_{d1})$ is unitary equivalent to $\\mathcal S(\\phi',1\/4)$. The latter $S$-matrix is given in Eq.\\ ({\\color{red} 1}) of the main text where we drop the prime on $\\phi$ from now on. For general $\\phi$, Eq.\\ \\eqref{eq:secular2} has analytical solutions only at $\\bar \\Gamma$, in which case $h=3$ and we find\n\\begin{equation}\n\\lambda_{1\\pm} = \\pm e^{\\mp i \\phi}, \\qquad \\lambda_{2\\pm} = \\pm \\exp \\left[ \\pm i\\arctan \\left( \\frac{\\sin \\phi}{\\sqrt{4-\\sin^2\\phi}} \\right) \\right],\n\\end{equation}\nwhere the $\\lambda_{2\\pm}$ are doubly degenerate. Hence, for each network energy period $2\\pi \\hbar v\/l$, there are always two protected nodes at the $\\bar \\Gamma$ point. This is shown in Fig.\\ \\ref{fig:sfig1} where we show the network spectrum along high-symmetry lines of the moir\\'e Brillouin zone (MBZ) for several values of $\\phi$. The same statement also holds at $\\bar K$ and $\\bar K'$. Furthermore, when $\\phi\\neq n\\pi$ ($n \\in \\mathbb Z$), we find that the triple degeneracy at the $\\bar \\Gamma$, $\\bar K$, and $\\bar K'$ points of the MBZ is lifted, while the bands remain doubly degenerate at these points for all $\\phi$, even after including forward scattering, as these crossings are protected by $C_3$ and $C_2 T$ symmetry.\n\\begin{figure}\n\\centering\n\\includegraphics[width=\\linewidth]{sfig1}\n\\caption{Network spectrum in the absence of forward scattering over one energy period $2\\pi \\hbar v\/l$ along high-symmetry lines of the moir\\'e Brillouin zone with $\\varphi=-\\pi \\hbar v\/6l$. Solid (dashed) curves correspond to the $K$ ($K'$) valley.}\n\\label{fig:sfig1}\n\\end{figure}\n\nWe have shown that up to a unitary transformation, the most general $S$-matrix in the absence of forward scattering is given by $\\mathcal S(\\phi,1\/4)$ for which the left and right interchannel deflection amplitudes are equal. Hence we consider this case from now on and perform another unitary transformation\n\\begin{equation}\nU^\\dag \\mathcal S U = \\frac{e^{i\\varphi}}{2} \\begin{pmatrix}\ni \\sin \\phi \\, S^t & e^{-i\\phi} \\cos \\phi \\, S \\\\\ne^{i\\phi} \\cos \\phi \\, S^t & i \\sin \\phi \\, S\n\\end{pmatrix}, \\qquad S = \\begin{pmatrix} 0 & 1 & 0 \\\\ 0 & 0 & 1 \\\\ 1 & 0 & 0 \\end{pmatrix},\n\\end{equation}\nwhere $U = \\left[ \\mathds 1_6 + i \\sigma_y e^{i\\phi\\sigma_z} \\otimes \\mathds 1_3 \\right]\/\\sqrt{2}$ transforms $a,a' \\rightarrow a_\\pm= \\left( a\\pm a' e^{\\mp i\\phi} \\right) \/ \\sqrt{2}$ and similar for outgoing modes. We see that for $\\phi=n \\pi$ ($n \\in \\mathbb Z$),\n\\begin{equation}\nU^\\dag \\mathcal S U = \\frac{e^{i\\varphi}}{2} \\begin{pmatrix} 0 & S \\\\ S^t & 0 \\end{pmatrix},\n\\end{equation}\nsuch that scattering modes form three independent chiral zigzag channels. Furthermore, in this case we see from Eqs.\\ \\eqref{eq:secular1} and \\eqref{eq:secular2} that $\\phi'=\\phi$ such that the network supports chiral zigzag modes for any allowed values of the deflection probabilities. On the other hand, for $\\phi = (n+1\/2) \\pi$ ($n \\in \\mathbb Z$),\n\\begin{equation}\nU^\\dag \\mathcal S U = (-1)^n \\frac{ie^{i\\varphi}}{2} \\begin{pmatrix} S^t & 0 \\\\ 0 & S \\end{pmatrix},\n\\end{equation}\nsuch that scattering modes perform closed orbits around AB and BA domains.\n\n\\section{S3.\\quad S-matrix with forward scattering}\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=.3\\linewidth]{sfig2}\n\\caption{Scattering processes for the $S$-matrix in Eq.\\ \\eqref{eq:Smat2} and their probabilities.}\n\\label{fig:sfig2}\n\\end{figure}\nWhen we allow for forward scattering, the $S$-matrix can be written as\n\\begin{equation} \\label{eq:Smat2}\n\\mathcal S =\ne^{i\\varphi} \\begin{pmatrix}\ne^{i(\\phi+\\chi)} \\sqrt{P_{f1}} & e^{i\\phi} \\sqrt{P_{d1}} & e^{i\\phi} \\sqrt{P_{d1}} & -\\sqrt{P_{f2}} & \\sqrt{P_{d2}} & - \\sqrt{P_{d2}} \\\\\ne^{i\\phi} \\sqrt{P_{d1}} & e^{i(\\phi+\\chi)} \\sqrt{P_{f1}} & e^{i\\phi} \\sqrt{P_{d1}} & -\\sqrt{P_{d2}} & -\\sqrt{P_{f2}} & \\sqrt{P_{d2}} \\\\\ne^{i\\phi} \\sqrt{P_{d1}} & e^{i\\phi} \\sqrt{P_{d1}} & e^{i(\\phi+\\chi)} \\sqrt{P_{f1}} & \\sqrt{P_{d2}} & - \\sqrt{P_{d2}} & -\\sqrt{P_{f2}} \\\\\n-\\sqrt{P_{f2}} & -\\sqrt{P_{d2}} & \\sqrt{P_{d2}} & -e^{-i(\\phi+\\chi)} \\sqrt{P_{f1}} & -e^{-i\\phi} \\sqrt{P_{d1}} & -e^{-i\\phi} \\sqrt{P_{d1}} \\\\\n\\sqrt{P_{d2}} & -\\sqrt{P_{f2}} & -\\sqrt{P_{d2}} & -e^{-i\\phi} \\sqrt{P_{d1}} & -e^{-i(\\phi+\\chi)} \\sqrt{P_{f1}} & -e^{-i\\phi} \\sqrt{P_{d1}} \\\\\n-\\sqrt{P_{d2}} & \\sqrt{P_{d2}} & -\\sqrt{P_{f2}} & -e^{-i\\phi} \\sqrt{P_{d1}} & -e^{-i\\phi} \\sqrt{P_{d1}} & -e^{-i(\\phi+\\chi)} \\sqrt{P_{f1}}\n\\end{pmatrix},\n\\end{equation}\nwith $\\cos\\chi = \\left( P_{d2} - P_{d1} \\right) \/ 2 \\sqrt{P_{f1} P_{d1}}$ such that $\\chi$ is real, so that $2 \\sqrt{P_{f1} P_{d1}} \\geq | P_{d2}-P_{d1} |$. Note that when $P_{d2}=0$, this condition gives a lower bound on forward scattering $P_{f1} \\geq P_{d1}\/4$. Here, we assumed that the probability for intrachannel processes is the same for the two valley Hall states. Current conservation then requires $2(P_{d1} + P_{d2}) + P_{f1} + P_{f2} = 1$, where $P_{f1}$ ($P_{d1}$) and $P_{f2}$ ($P_{d2}$) are the probabilities for intra- and interchannel forward scattering (deflections), respectively, as illustrated in Fig.\\ \\ref{fig:sfig2}. We take the parameterization\n\\begin{equation}\nP_{f1} = (\\sin \\alpha_1 \\sin \\alpha_2)^2, \\quad P_{f2} = (\\sin \\alpha_1 \\cos \\alpha_2)^2, \\quad P_{d1} = \\frac{1}{2} (\\cos \\alpha_1 \\cos \\alpha_3)^2, \\quad P_{d2} = \\frac{1}{2} (\\cos \\alpha_1 \\sin \\alpha_3)^2,\n\\end{equation}\nwith $\\alpha_{1,2,3} \\in [0,\\pi\/2]$ under the condition that $\\chi$ is real. This condition is graphically represented in Fig.\\ \\ref{fig:sfig3} where we show $|\\delta_- = | \\sqrt{P_{d1}} - \\sqrt{P_{d2}} |$ for allowed $(\\alpha_1,\\alpha_3)$ and $\\alpha_2=\\pi\/2$ ($P_{f2}=0$). Reducing $\\alpha_2$ shrinks the allowed area, which in the figure corresponds to the area enclosed by the gray-scaled curves and the right-vertical axis.\n\\begin{figure}\n\\centering\n\\includegraphics[width=.6\\linewidth]{sfig3}\n\\caption{(color online) Scattering amplitude $|\\delta_-| = |\\sqrt{P_{d1}} - \\sqrt{P_{d2}}|$ between different zigzag modes for $\\phi=0$, in the $(\\alpha_1,\\alpha_3)$-plane where white regions are incompatible with unitarity for any $\\alpha_2$. The area enclosed by the gray-scaled curves and the right-vertical axis correspond to allowed $(\\alpha_1,\\alpha_3)$ for given $2\\alpha_2\/\\pi$ as denoted next to the curves.}\n\\label{fig:sfig3}\n\\end{figure}\n\nWhen chiral zigzag modes propagating along different directions remain decoupled ($\\phi=0$ and $P_{d1} = P_{d2}$), the Fermi surface is always nested and the density of states is constant, regardless of forward scattering, as demonstrated in the main text. We show the network bands along high-symmetry lines of the MBZ in Fig.\\ \\ref{fig:sfig4} for the case without and with forward scattering. On the other hand, when zigzag modes propagating along different directions are coupled ($P_{d1} \\neq P_{d2}$ or $\\phi\\neq0$) the network bands develop anti-crossings except at the $\\bar \\Gamma$, $\\bar K$, and $\\bar K'$ points of the MBZ, where crossings are protected by $C_3$ and $C_2T$, as shown in Fig.\\ {\\color{red} 5} of the main text.\n\\begin{figure}\n\\centering\n\\includegraphics[width=\\linewidth]{sfig4}\n\\caption{Network spectrum in the absence of coupling between different zigzag modes ($\\phi=0$ and $P_{d1}=P_{d2}$) over one energy period $2\\pi \\hbar v\/l$ along high-symmetry lines of the moir\\'e Brillouin zone as shown in the inset of Fig.\\ {\\color{red} 5}(a) with $\\varphi =-\\pi \\hbar v\/6l$. The bands are shown for $K$ (solid) and $K'$ (dashed) for (a) no forward scattering [Fig.\\ {\\color{red} 1}(c) of the main text], (b) $P_{f1}=0.02$ and $P_{f2}=0$ [Fig.\\ {\\color{red} 3}(b)  of the main text], and (c) $P_{f1}=0$ and $P_{f2}=0.02$ [Fig.\\ {\\color{red} 3}(c) of the main text].}\n\\label{fig:sfig4}\n\\end{figure}\n\n\\end{document} ","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\subsection{Crash of Memcached servers}\n\n\nIn these experiments, Memcached is stopped on a subset of the caching server nodes. An experiment has a total duration of 600 seconds. We have an initial phase of 200 seconds (\\emph{warm-up}), in which the system and the workload execute without faults; then, we have a second phase of 200 seconds (\\emph{fault-injection}), in which the fault is actually injected in the system; and a final phase of 200 seconds (\\emph{recovery}), in which the fault is removed from the system. Several experiments were performed by increasing the number of failed servers, to evaluate how this affects the behavior of the system and its fault tolerance mechanisms.\n\n\n\nWhen Memcached nodes crash, the three middleware platforms react in different ways. Client requests can experience three possible outcomes, as summarized in \\figurename{}~\\ref{fig:node_failure_results}: \\emph{done} (i.e., the key-value pair is correctly set or retrieved), \\emph{misses} (i.e., the key-value pair cannot be retrieved because of the fault, despite it is actually stored by the caching tier); \\emph{errors} (i.e., the middleware returns an error signal to the clients). \n\nBy using Twemproxy, we have cache misses both during the failure and the recovery phase (two values are reported in the cells of the table). Moreover, when the number of failed server is higher than 4, we observe a significant throughput decrease and latency increase, due to the timeouts required to activate the node ejection mechanism. We found that cache misses during the recovery phase are even more than during the fault-injection phase due to a redistribution of the keys in the nodes that are still alive.  \\figurename~\\ref{fig:misses} shows in detail this behaviour: after 200s a subset of memcached nodes are stopped and restarted after 200s. During the fault, the part of the keys are redistributed in the remaining nodes. Those keys are potential future cache misses during the recovery phase due to another change in the topology. This behavior happens because Twemproxy does not provide mechanisms for data replication that could mask data losses during node failures, and does not support online topology changes without redistributing keys among the nodes.\n\n\\begin{figure}[ht]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{figures\/Node_failure.pdf}\n    \\caption{Performance under Memcached crash failures}\n    \\label{fig:node_failure_results}\n\\end{figure}\n\n\\begin{figure}[ht]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{figures\/misses.pdf}\n    \\caption{Cache miss rate during experiments with crash of Memcached servers}\n    \\label{fig:misses}\n\\end{figure}\n\n\n\nMcrouter and Dynomite both support failure detection and data replication. Under the same conditions, Mcrouter is able to mask Memcached failures without significant latency and throughput variation when only 1-out-of-3 servers with the same data are crashed. If two nodes with the same data are crashed, there are timeouts errors, since the only alive server becomes overloaded. The unresponsive nodes are promptly detected and removed from the topology and thus we did not found effects on the latency, which remained stable up to 10 out of 30 node failures. Dynomite is also capable to mask node crashes. However, due to the specific peer-to-peer architecture of Dynomite, when the failed node is in the same rack of the coordinator, and the received responses from other racks are different (such as a cache miss and a cache value), the coordinator always replies with the local rack response \\cite{dynomiteConsistency} which is an error . Moreover, in case of two-out-of-three crashed nodes with the same data, all requests to these data experience a failure due to the impossibility to reach the quorum. Thus, differently from Mcrouter, the system does not suffer from an overload of the only available replica, but the clients can experience data unavailability (i.e., service errors).\n\n\n\n\n\n\n\n\n\\subsection{Unbalanced overloads of Memcached servers}\n\nIn this scenario, a subset of the caching servers experiences an overload, which does not simply cause a fail-stop behavior (such as crashes, which are explicitly notified by the OS), but degrades the performance of the servers without explicit failure notifications. In all of the middleware platforms, the data and the requests are distributed among nodes using a stateless and fixed scheme, by computing a deterministic hash function on the keys (\\emph{consistent hashing}). This approach selects a node (or a subset of nodes) only on the basis of the key, without considering the workload of the nodes across the datacenter. This can result in an uneven distribution of the workload, such as when most of the users' requests are on a specific resource (\\emph{hot-spot}), or when there is physical resource contention on specific nodes.\n\n\\begin{figure}[ht]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{figures\/Unbalanced_load.png}\n    \\caption{Performance under unbalanced overloads of Memcached nodes.}\n    \\label{fig:unbalanced_load_results}\n\\end{figure}\n\n\n\\figurename~\\ref{fig:unbalanced_load_results} shows the percentage of requests done for the three middleware platforms, when injecting overloads on an increasing number of caching servers. \nIn Twemproxy, the presence of unbalanced overloads significantly affects the performance, since these nodes are slowed-down, but are not enough to trigger the ejection mechanism and keys reallocation. It is interesting to note the absence of correlation between the number of failed servers and the number of timeouts errors. This means that having just one or several overloaded nodes has the same impact on performance. We looked at resource utilization metrics of the non-overloaded nodes, and found that these nodes are under-performing much below their normal load, despite they are not directly targeted by fault injection. \nThis behavior occurred because most of the requests in the Twemproxy queue were waiting on the network sockets opened towards the overloaded nodes, and could not be quickly re-sent to another node. Therefore, the effects of one faulty node propagate through the middleware to the whole caching tier.\n\nAmong the three middleware platforms, Mcrouter is the one most robust against unbalanced overloads, as there is no degradation of the rate of requests done (\\figurename{}~\\ref{fig:unbalanced_load_results}). The fault does not impact on the throughput and latency of the caching tier. Resource utilization remains stable in non-overloaded nodes, and only saturates on the overloaded ones. This behavior was due to the failover mechanism, which is able to detect the overloaded nodes, mark them as \\emph{soft TKO} as shown in the logs in \\figurename{}~\\ref{fig:logs}, and remove them from the list of routes. Thus, Mcrouter addresses both overloads and crashes of servers in a similar way. Thanks to the exclusion of failed servers, requests are directly sent to another node without any waiting time, thus achieving a stable latency.  Regardless of the pool of the overloaded nodes (in the same pool, or in different ones), performance is not affected. \n\\begin{figure*}[ht]\n    \\centering\n    \\includegraphics[width=0.9\\textwidth]{figures\/logs.pdf}\n    \\caption{Mcrouter logs during unbalancing overloads.}\n    \\label{fig:logs}\n\\end{figure*}\nInstead, when we inject an overload in two nodes with the same data, performance is inevitably degrades. In our experiments, throughput reduces by 85\\% and  latency grows by two orders of magnitude. The overloaded nodes alternate between states (active vs. \\emph{soft TKO}), with one node active and the other unavailable, and vice versa.\nThis behavior increases latency, since \\texttt{set} requests cause the middleware to wait for responses from an overloaded node to achieve a majority. In the case of \\texttt{get} requests, part of them are sent to an overloaded node.\n\n\n\n\\begin{figure*}[ht]\n    \\centering\n    \\includegraphics[width=0.9\\textwidth]{figures\/vcpu_unbalancing.pdf}\n    \\caption{Average vCPU usage before (blue) and after (red) unbalanced overload injection.}\n    \\label{fig:dynomite_unbalanced_cpu}\n\\end{figure*}\n\nDynomite is not able to properly manage unbalanced overloads. The average throughput decreases proportionally with the increase of overloaded servers (\\figurename{}~\\ref{fig:unbalanced_load_results}). In this middleware platform, the throughput degrades due to the high latency of requests processed by the overloaded servers. \\figurename~\\ref{fig:dynomite_unbalanced_cpu} shows the effects of the overload of two out of thirty servers on the cpu usage of the remaining nodes. In particular we observe a significant cpu usage reduction across the whole datastore cluster.\nRequests for a given key can experience a high or low latency, depending on whether an overloaded node is chosen among the nodes of the quorum.  Differently from the Twemproxy case, Dynomite does not propagate the effect of overloaded nodes to the remaining servers.\n\n\n\n\n\\subsection{Network link bottlenecks}\n\nIn these experiments, we inject faults in the caching tier by reducing the network bandwidth of a group of servers. In this case, the fault affects a group of Memcached servers that are hosted on the same host, to reproduce a fault (e.g., network congestion) happening at the infrastructure level. Restricting the bandwidth leads to a bottleneck in the network. \n\n\\begin{figure}[ht]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{figures\/Network_link_failure.png}\n    \\caption{Performance under network link bottlenecks.}\n    \\label{fig:link_failure_results}\n\\end{figure}\n\n\nIn Twemproxy, bottlenecks in a subset of connections affect the caching tier as a whole system, as the overall throughput and latency degrade, showed in \\figurename{}~\\ref{fig:link_failure_results}. The standard deviation of latency becomes an order of magnitude higher than the average, which indicates the unbalance of the latency for different requests. Since the latency does not increase for all requests, there are not enough timeouts to trigger the ejection mechanism. The throughput degrades to $20,000$ reqs\/sec, which represents a reduction of 82\\% when compared to $115,000$ reqs\/sec reached under a normal condition. As in the case of unbalanced overloads, in Twemproxy all nodes are impacted by the effects of the fault.\n\nNetwork bottlenecks are the only kind of fault that have an impact on the performance of Mcrouter. We have a sharp increase of latency, as shown in \\figurename{}~\\ref{fig:link_failure_results}, and a decrease of the throughput, with some requests that experience errors. The throughput decreases from $45,000$ reqs\/sec under normal conditions to $8,500$ under faults, and the average latency increases from $2.8$ ms to $142.3$ ms under faults.\n\nDynomite is able to manage the reduction of network bandwidth, as these faults are transparent to the clients. We found that there is no variation in throughput, and we do not have any request with errors. Comparing latency with vs. without faults (\\figurename{}~\\ref{fig:link_failure_results}), we notice a small increase of latency (from $2.8$ ms to $4.2$ ms under faults) which cannot be considered statistically significant. This behavior is due to the peer-to-peer architecture adopted by Dynomite. Indeed, one of the main advantages of the peer-to-peer architecture is that it increases tolerance to faults related to a specific connection. By creating several connections between nodes in a rack, the bandwidth reduction of few connections does not affect performance, since requests are forwarded to the other connections. Thus, this approach is effective at isolating the problem. The effects of the fault do not propagate across the system, which is why the performance of the caching tier as a whole is not significantly affected.\n\n\n\n\n\n\\subsection{Twitter Twemproxy}\n\nTwemproxy (aka Nutcracker) is a fast and light-weight proxy for the Memcached protocol. Twemproxy was developed by Twitter to reduce open connections towards cache nodes, by deploying a local proxy on every front-end node. Thanks to protocol pipelining and sharding, Twemproxy improves horizontal scalability of distributed caching. Twemproxy allows to create a pool of cache servers to distribute the data and to reduce the amount of connections. To send a request to any of those servers, the client contacts Twemproxy, which routes the request to a Memcached\nserver. The same Twemproxy instance can manage different pools, by setting different listening ports to each pool. The number of connections between the client and Twemproxy, and between Twemproxy and each server is set through a configuration file. It is interesting to note that the ``read my last write'' constraint does not necessarily hold true when Twemproxy is configured with more than one connection per server.\n\nTwemproxy shards data automatically across multiple servers. To decide the destination server for a request, a \\emph{request hashing} function is applied to the key of the request to select a shard; then, based on a chosen random distribution, the request is routed to a Memcached server in the shard. Twemproxy provides 12 different hash functions (i.e., \\texttt{one\\_at\\_a\\_time}, \\texttt{MD5}, \\texttt{CRC16}, \\texttt{CRC32}, \\texttt{FNV1\\_64}, etc.) and 3 different distributions (i.e., ketama, modula, random). It allows the application to use only part of the key (\\emph{hashtag}) to calculate the hash function. When the hashtag option is enabled, only part of the key is used as input for the hash function. This option allows the application to map different keys to the same server, as long as the part of the key within the tag is the same.\n\nWhen a failure occurs, Twemproxy provides a mechanism to exclude the failed server.\nIt detects the failure after a number of failed requests (set in a configuration file), ejects the failed server from the pool, and redistributes the key among the remaining servers. Client requests are routed to the active servers; at regular intervals, some requests are sent to the failed server to check its status. When the failed server returns active, it is added back to the pool and the key is distributed again. Twemproxy increases observability using logs and stats. Stats can be at the granularity of server pool or individual servers, through a monitoring port. In the configuration file, it is possible to define the monitoring port and the aggregation interval. Companies that use Twemproxy in production include Pinterest, Snapchat, Flikr and Yahoo!.\n\n\n\n\\subsection{Facebook Mcrouter}\n\nMcrouter is a Memcached protocol router to handle traffic to, from, and between thousands of cache servers across dozens of clusters, distributed at geographical scale. It is a key component of the cache infrastructure at Facebook and Instagram, where Mcrouter handles nearly 5 billion requests per second at peak. It uses the standard ASCII Memcached protocol to provide a transparent layer between clients and servers, and adds advanced features that make it more than a simple proxy.\n\nIn the Mcrouter terminology, a Memcached server is a \\emph{destination}, and a set of destinations is a \\emph{pool}. Mcrouter adopts a client\/server architecture: every Mcrouter instance communicates with several pools, without any communication between different pools. Several clients can connect to a single Mcrouter instance and share the outgoing connections, reducing the number of open connections. Looking at the Facebook infrastructure at a high level, one or more pools with Mcrouter instances and clients define a \\emph{cluster}, and clusters together create a \\emph{region}. Mcrouter is configured with a graph of small routing modules, called \\emph{route handles}, which share a common interface (route a request, return a reply), and which can be combined. The configuration can be changed online to adapt routing to a transient situation, such as adding and warming up a new node.\nSince the configuration is checked and loaded by a background thread, there is no extra latency from the client point of view.\n\nMcrouter supports sharding in order to adapt the datastore tier to the growth of data. The data distribution among servers is based on a key hash. In this way, different keys are evenly distributed across different destinations, and requests for the same key are served by the same destination. It is possible to choose between different hash functions (e.g., \\texttt{CH3}, weighted \\texttt{CH3}, or \\texttt{CRC32}). Keys in the same pool compete for the same amount of memory, and are evicted in the same way. \nMcrouter also provides a feature, namely \\emph{prefix routing}, that allows applications to control data distribution on different pools, by using different key prefixes. This feature is valuable since applications generate and store data of different complexity (e.g., caching the results of complex computations), and they can prevent cache misses on ``expensive'' data by using different prefixes than ``cheap'', so that they do not compete for the same memory space.\n\nMcrouter supports data replication. Read and write requests are managed in a different way: writes are replicated to all hosts in the pool, while reads are routed to a single replica, chosen separately for each client, to achieve a higher read rate.\nTo increase fault tolerance, Mcrouter also provides destination health monitoring and automatic failover. When a destination is marked as unresponsive, the incoming requests will be routed to another destination. At the same time, health check requests will be sent in the background, and as soon as a health check is successful, Mcrouter will send the requests to the original destination again. Mcrouter distinguishes between \\emph{soft errors} (e.g., data timeouts), which are tolerated to happen a few times in a row, and \\emph{hard errors} (e.g., connection refused), which cause a host to be marked unresponsive immediately.\nThe health monitoring parameters are set up through command line options. It is possible to define the number of data timeouts to declare a \\emph{soft TKO} (``technical knockout''), the maximum number of destinations allowed to be in soft TKO state at the same time, and the health check frequency. The health check requests (\\emph{TKO probes}) are sent with an exponentially increasing interval, whose initial and maximum length (in ms) is configurable. The actual intervals have an additional random jitter of up to 50\\% to avoid overloading a single failed host with TKO probes from different Mcrouters.\n\nMcrouter provides mechanisms to check the current configuration. Through an admin request, it is possible to verify what is the route of a specifc request. Given the operation and the key, the response from Mcrouter will be the server that owns the data. It is possible to get the route handle graph that a given request would traverse. These requests allow administrators to get insights on the actual state of the system, e.g., to show how the routing changes when a failure occurs.\n\n\n\n\\subsection{Netflix Dynomite}\n\nDynomite is a middleware solution implemented by Netflix. The main purpose of Dynomite is to transform a single server datastore into a peer-to-peer, clustered and linearly scalable system that preserves native client\/server protocols of the datastores, such as the Redis and Memcached protocols. \n\nA Dynomite cluster consists of multiple \\emph{data centers} (DC). A data center is a group of \\emph{racks}, and a rack is a group of \\emph{nodes}. Each rack consists of the entire dataset, which is partitioned across several nodes in that rack. A client can connect to any node on a Dynomite cluster when sending a request. If the node that receives the request owns the data, it gives the response; otherwise, the node forwards the request to the node that owns the data in the same rack. Dynomite is designed to be a sharding and replication layer. Sharding is achieved as in distributed hash tables \\cite{chi2017hashing,tanenbaum2007distributed}: \nRequest keys are hashed to obtain a \\emph{token} (an integer value); the range of all possible token values is partitioned among the nodes, by assigning to each node a unique token value; the keys that fall in the sub-range ending with the node's unique token are assigned to that node. \n\nTo achieve replication, datasets are replicated among all the racks. When a node receives a \\texttt{set} request, it acts as a coordinator, by writing data in the node of its rack which owns the token, and by forwarding the request to the corresponding nodes in other racks and data centers. \nEvery node knows the distribution of the token in the nodes of all data centers through to the configuration file. Using a similar technique for \\texttt{get} requests, it is possible to increase data availability and tolerate node failures. The configuration file defines the topology, the number of connections and the token range partitioning among the nodes. Moreover, it is possible to configure one of three confidence levels writes and reads: \n\n\\begin{itemize}\n\n\\item \\textbf{DC\\_ONE}: requests are propagated synchronously only in the local rack, and asynchronously replicated to other racks and regions;\n\n\\item \\textbf{DC\\_QUORUM}: requests are sent synchronously to a quorum of servers in the local data center, and asynchronously to the rest. This configuration writes to a set of nodes that forms a quorum. If responses are different, the first response that the coordinator received is returned;\n\n\\item \\textbf{DC\\_SAFE\\_QUORUM}: similar to DC\\_QUORUM, but data checksums have to match.\n\n\\end{itemize}\n\nDynomite makes the caching system tolerant to failures of one or few servers (i.e., less than the size of the quorum) through replication, but it does not provide any failover detection or online reconfiguration. This makes the system less dynamic. For example, to add a new node you have to recompute all tokens, update the configuration file, and restart all processes. Failover detection, token reconfiguration, and other features are provided from other components in the Dyno ecosystem, like Dynomite-manager or Dyno client. Dynomite provides REST APIs for checking the state of some parameters (e.g., the confidence level), but this does not include routing (i.e., where a key is stored or read from).\n\n\n\n\\subsection{Qualitative comparison of fault-tolerance mechanisms}\n\nBoth Mcrouter and Dynomite adopt replication as strategy to achieve transparent fault tolerance. Of course, this strategy has a major impact on performance, since a single request turns in multiple operations on several machines. Given the same settings (number of clients, connections, threads, etc.), the throughput of the caching system can significantly degrade when enabling replication: for example, if throughput without replication reaches $20,000$ reqs\/sec, it can settle to $5,500$ reqs\/sec when using a replication factor of three. \nThe same is not necessarily true for latency, which is of the same order of magnitude in all cases. Being able to use replication without affecting latency is the reason why major service providers are using this strategy despite lower throughput, since latency is the key performance indicator that mostly influences the Quality of Experience.\n\nMcrouter has a more complete failure management, as compared to the previous ones. It consists on monitoring the health state of destinations and detecting failures. By default, it converts all \\texttt{get} errors into cache misses, so that the application can still work even if there is no replication and a high amount of errors occur.\nSimilar considerations on misses and errors also apply for Twemproxy. When  keys are redistributed among nodes after a failure, Twemproxy turns the timeouts into cache misses. \n\nBoth Twemproxy and Mcrouter rely on knowledge about the infrastructure and its failures to be configured with appropriate values, e.g., for the frequency of monitoring, the timeouts, and the replication policies. The main factors driving the configuration are: the fault duration, the throughput, and the amount of data on each server. For example, if we have a throughput of 20k \\texttt{set} reqs\/sec, and 100k keys on each node, then all keys can be redistributed in 5 seconds and be again available. Thus, it is worth adopting redistribution when the throughput is high, the amount of data on each node is small, and the outage of faulty nodes is expected to b long.\n\nDynomite is fault-tolerant with some limitations. In particular, if the coordinator node fails (i.e., the node that first receives a request), there is no retry mechanism that sends the request to another node. Thus, coordinator failures are not tolerated. This is a deliberate design choice, since Dynomite is designed to be on the same host running a Memcached server, thus when the host fails, both Memcached and Dynomite fail. Furthermore, if the rack includes a failed node, the rack still continues to count towards the quorum, while the rack is excluded from the quorum when all its nodes are failed.\n\n\\subsection{Workload generation}\n\nTo generate a workload for the caching nodes and for the middleware platform, we need i)to create connections to send data requests, and ii) to collect performance metrics from the clients' perspective. We initially tried several publicly-available tools, but many proved not to be suitable for carrying out our experiments. \nThe first tool was the \\emph{CloudSuite Data Caching Benchmark} \\cite{cloudsuiterepo}, which is part of CloudSuite, a benchmark suite for cloud services. This tool does not support execution in the presence of failures (which we will deliberately force with fault injection), and stops making requests when a server fails. \nThen, we tried \\emph{Memaslap} \\cite{memaslap}, a load generation and benchmark tool for Memcached servers included in \\emph{libMemcached}. However, the format of requests generated by this tool are incompatible with Mcrouter. \nFor this reason, we developed our own tool, namely Mcrouter \\emph{Mcbench}. It is written in Python, uses the \\emph{aiomcache} library to create the connections and makes requests according to the Memcached protocol. Mcbench generates only \\texttt{set} (20\\%) and \\texttt{get} (80\\%) requests with random keys and values.\nThe tool can be configured with respect to the distribution of keys and values lengths; \nthe duration of the experiment; \nthe desired throughput; \nthe number of threads, clients and connections per server; \nthe list of servers where to forward requests.\n\nThe tool collects performance statistics about requests that are successful and failed, latency, and misses, aggregating them every second.\nTo warm up servers, we configure the tool to initially perform only \\texttt{set} requests. The random distribution of the keys is based on a real-world Twitter dataset from the CloudSuite Data Caching Benchmark \\cite{twitterdataset}. To create random distributions for a more intensive workload for large distributed systems, we scaled-up the Twitter dataset by a factor of ten, while preserving both the popularity and the distribution of object size, with alphanumeric variable-length keys. \nThe original dataset consumes 300MB (267,433 rows) of server memory, while the scaled dataset requires about 3GB (2,674,339 rows).\n\n\n\n\\subsection{Testbed configuration}\n\nThe experimental testbed was built on top of OpenStack, an open-source Infrastructure-as-a-Service (IaaS) cloud computing platform. \nThe experimental testbed consists of eight host machines SUPERMICRO (high density), equipped with two 8-Core 3.3Ghz Intel XEON CPUs (32 logic cores in total), 128GB RAM, two 500GB SATA HDD, four 1-Gbps Intel Ethernet NICs, and a NetApp Network Storage Array with 32TB of storage space and 4GB of SSD cache. The hosts are connected to three 1-Gbps Ethernet network switches, respectively for management, storage and VM network traffic. The testbed is managed with OpenStack Mitaka and the VMware ESXi 6.0 hypervisor. \n\n\\begin{table}\n\\centering\n\\protect\\caption{Configuration of the experimental testbed}\n\\label{tab:configuration}\n\n\\begin{tabular}{|p{1.5cm}|p{0.6cm}|p{5cm}|}\n\\hline \n\\textbf{Node Type} & \\textbf{\\# of nodes} & \\textbf{VM configuration}\\tabularnewline\n\\hline \n\\hline \n\\textbf{Controller Node} & 1 & 2 vCPU, 16GB RAM, 120 GB HDD\\tabularnewline\n\\hline \n\\textbf{Middleware Node}  & 7 & 4 vCPU, 4 GB RAM, 20 GB HDD\\tabularnewline\n\\hline \n\\textbf{Memcached Node} & 30 & 1 vCPU, 8 GB RAM, 20 GB HDD\\tabularnewline\n\\hline \n\\textbf{Workload generator}  & 7 & 4 vCPU, 8 GB RAM, 40 GB HDD\\tabularnewline\n\\hline \n\\textbf{\\emph{Total}} & \\emph{45} & \\emph{88 vCPU, 340 GB RAM, 1.14 TB HDD}\\tabularnewline\n\\hline \n\\end{tabular}\n\n\\end{table}\n\nThe system architecture detailed in Table \\ref{tab:configuration} consists of: \n\\begin{itemize}\n\\item one controller machine, which orchestrates the test and sends commands to the other machines; \n\\item seven workload generators, which send requests to the middleware platform;\n\\item seven middleware machines, which forward the requests to the Memcached servers;\n\\item thirty Memcached servers.\n\\end{itemize}\n\nThe connections between the middleware and the Memcached servers vary depending on the specific middleware. In the case of Twemproxy and Mcrouter, each instance of the middleware connects to all servers, as in \\figurename{}~\\ref{fig:topology1}. In Dynomite, each instance connects only to one node, since there as many Dynomite instances of Dynomite as the number of Memcached servers, as shown in \\figurename{}~\\ref{fig:topology2}. Therefore, in Dynomite there are fewer connections between the middleware and the Memcached servers, and the instances of the middleware communicate with each other to route the requests\n\n\\begin{figure}[ht]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{figures\/topology1.pdf}\n    \\caption{Twemproxy and Mcrouter topology}\n    \\label{fig:topology1}\n\\end{figure}\n\\begin{figure}[ht]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{figures\/topology2.pdf}\n    \\caption{Dynomite topology}\n    \\label{fig:topology2}\n\\end{figure}\n\n\nTo have a balanced load among the physical hosts, we equally divided the VMs in order to have one workload generator, one middleware and at most five Memcached servers on each physical host. \nFor Twemproxy, the dataset is divided among all thirty nodes; for Mcrouter and Dynomite, which support replication schemes, we have three pools\/racks, each composed of ten nodes among which the dataset is divided, thus with a replication factor of three. Thus, a $set$ operation is performed on three different nodes and a get operation in one node out of three. In case of a miss or of an error the operation is retried on the remaining nodes and it is returned the first valid response if any. If the middleware supports the quorum (i.e., in the case of Dynomite) the middleware should reply with an error if the reply does not reach the quorum of two valid responses.\nWe carried out a capacity test to define the maximum throughput that can be reached by the system. The maximum throughput is $18,500$ reqs\/sec per workload generator with Twemproxy, and $7,200$ reqs\/sec per workload generator with Mcrouter and Dynomite. We then calibrated the workload generator to have a throughput per workload generator of $16,500$ reqs\/sec for Twemproxy, and $6,500$ reqs\/sec for Mcrouter and Dynomite. The total number of requests served in the experiments are respectively $115,500$ reqs\/sec and $45,500$ reqs\/sec.\n\n\n\n\\section{Introduction}\n\\label{sec:introduction}\n\\input{tex\/introduction.tex}\n\n\\section{Middleware platforms for distributed caching}\n\\label{sec:fault_tolerance}\n\\input{tex\/fault_tolerance.tex}\n\n\\section{Experimental methodology and setup}\n\\label{sec:experiment}\n\\input{tex\/experiment.tex}\n\n\\section{Experimental results}\n\\label{sec:discussion}\n\\input{tex\/discussion.tex}\n\n\\section{Related work}\n\\label{sec:related}\n\\input{tex\/related.tex}\n\n\\section{Conclusion}\n\\label{sec:conclusion}\n\\input{tex\/conclusion.tex}\n\n\n\n\n\\bibliographystyle{IEEEtran}\n\n\\section{Introduction}\n\\label{sec:introduction}\n\\input{tex\/introduction.tex}\n\n\\section{Middleware platforms for distributed caching}\n\\label{sec:fault_tolerance}\n\\input{tex\/fault_tolerance.tex}\n\n\\section{Experimental methodology and setup}\n\\label{sec:experiment}\n\\input{tex\/experiment.tex}\n\n\\section{Experimental results}\n\\label{sec:discussion}\n\\input{tex\/discussion.tex}\n\n\\section{Related work}\n\\label{sec:related}\n\\input{tex\/related.tex}\n\n\\section{Conclusion}\n\\label{sec:conclusion}\n\\input{tex\/conclusion.tex}\n\n\n\n\n\\bibliographystyle{IEEEtran}\n\n\\subsection{Crash of Memcached servers}\n\n\nIn these experiments, Memcached is stopped on a subset of the caching server nodes. An experiment has a total duration of 600 seconds. We have an initial phase of 200 seconds (\\emph{warm-up}), in which the system and the workload execute without faults; then, we have a second phase of 200 seconds (\\emph{fault-injection}), in which the fault is actually injected in the system; and a final phase of 200 seconds (\\emph{recovery}), in which the fault is removed from the system. Several experiments were performed by increasing the number of failed servers, to evaluate how this affects the behavior of the system and its fault tolerance mechanisms.\n\n\n\nWhen Memcached nodes crash, the three middleware platforms react in different ways. Client requests can experience three possible outcomes, as summarized in \\figurename{}~\\ref{fig:node_failure_results}: \\emph{done} (i.e., the key-value pair is correctly set or retrieved), \\emph{misses} (i.e., the key-value pair cannot be retrieved because of the fault, despite it is actually stored by the caching tier); \\emph{errors} (i.e., the middleware returns an error signal to the clients). \n\nBy using Twemproxy, we have cache misses both during the failure and the recovery phase (two values are reported in the cells of the table). Moreover, when the number of failed server is higher than 4, we observe a significant throughput decrease and latency increase, due to the timeouts required to activate the node ejection mechanism. We found that cache misses during the recovery phase are even more than during the fault-injection phase due to a redistribution of the keys in the nodes that are still alive.  \\figurename~\\ref{fig:misses} shows in detail this behaviour: after 200s a subset of memcached nodes are stopped and restarted after 200s. During the fault, the part of the keys are redistributed in the remaining nodes. Those keys are potential future cache misses during the recovery phase due to another change in the topology. This behavior happens because Twemproxy does not provide mechanisms for data replication that could mask data losses during node failures, and does not support online topology changes without redistributing keys among the nodes.\n\n\\begin{figure}[ht]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{figures\/Node_failure.pdf}\n    \\caption{Performance under Memcached crash failures}\n    \\label{fig:node_failure_results}\n\\end{figure}\n\n\\begin{figure}[ht]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{figures\/misses.pdf}\n    \\caption{Cache miss rate during experiments with crash of Memcached servers}\n    \\label{fig:misses}\n\\end{figure}\n\n\n\nMcrouter and Dynomite both support failure detection and data replication. Under the same conditions, Mcrouter is able to mask Memcached failures without significant latency and throughput variation when only 1-out-of-3 servers with the same data are crashed. If two nodes with the same data are crashed, there are timeouts errors, since the only alive server becomes overloaded. The unresponsive nodes are promptly detected and removed from the topology and thus we did not found effects on the latency, which remained stable up to 10 out of 30 node failures. Dynomite is also capable to mask node crashes. However, due to the specific peer-to-peer architecture of Dynomite, when the failed node is in the same rack of the coordinator, and the received responses from other racks are different (such as a cache miss and a cache value), the coordinator always replies with the local rack response \\cite{dynomiteConsistency} which is an error . Moreover, in case of two-out-of-three crashed nodes with the same data, all requests to these data experience a failure due to the impossibility to reach the quorum. Thus, differently from Mcrouter, the system does not suffer from an overload of the only available replica, but the clients can experience data unavailability (i.e., service errors).\n\n\n\n\n\n\n\n\n\\subsection{Unbalanced overloads of Memcached servers}\n\nIn this scenario, a subset of the caching servers experiences an overload, which does not simply cause a fail-stop behavior (such as crashes, which are explicitly notified by the OS), but degrades the performance of the servers without explicit failure notifications. In all of the middleware platforms, the data and the requests are distributed among nodes using a stateless and fixed scheme, by computing a deterministic hash function on the keys (\\emph{consistent hashing}). This approach selects a node (or a subset of nodes) only on the basis of the key, without considering the workload of the nodes across the datacenter. This can result in an uneven distribution of the workload, such as when most of the users' requests are on a specific resource (\\emph{hot-spot}), or when there is physical resource contention on specific nodes.\n\n\\begin{figure}[ht]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{figures\/Unbalanced_load.png}\n    \\caption{Performance under unbalanced overloads of Memcached nodes.}\n    \\label{fig:unbalanced_load_results}\n\\end{figure}\n\n\n\\figurename~\\ref{fig:unbalanced_load_results} shows the percentage of requests done for the three middleware platforms, when injecting overloads on an increasing number of caching servers. \nIn Twemproxy, the presence of unbalanced overloads significantly affects the performance, since these nodes are slowed-down, but are not enough to trigger the ejection mechanism and keys reallocation. It is interesting to note the absence of correlation between the number of failed servers and the number of timeouts errors. This means that having just one or several overloaded nodes has the same impact on performance. We looked at resource utilization metrics of the non-overloaded nodes, and found that these nodes are under-performing much below their normal load, despite they are not directly targeted by fault injection. \nThis behavior occurred because most of the requests in the Twemproxy queue were waiting on the network sockets opened towards the overloaded nodes, and could not be quickly re-sent to another node. Therefore, the effects of one faulty node propagate through the middleware to the whole caching tier.\n\nAmong the three middleware platforms, Mcrouter is the one most robust against unbalanced overloads, as there is no degradation of the rate of requests done (\\figurename{}~\\ref{fig:unbalanced_load_results}). The fault does not impact on the throughput and latency of the caching tier. Resource utilization remains stable in non-overloaded nodes, and only saturates on the overloaded ones. This behavior was due to the failover mechanism, which is able to detect the overloaded nodes, mark them as \\emph{soft TKO} as shown in the logs in \\figurename{}~\\ref{fig:logs}, and remove them from the list of routes. Thus, Mcrouter addresses both overloads and crashes of servers in a similar way. Thanks to the exclusion of failed servers, requests are directly sent to another node without any waiting time, thus achieving a stable latency.  Regardless of the pool of the overloaded nodes (in the same pool, or in different ones), performance is not affected. \n\\begin{figure*}[ht]\n    \\centering\n    \\includegraphics[width=0.9\\textwidth]{figures\/logs.pdf}\n    \\caption{Mcrouter logs during unbalancing overloads.}\n    \\label{fig:logs}\n\\end{figure*}\nInstead, when we inject an overload in two nodes with the same data, performance is inevitably degrades. In our experiments, throughput reduces by 85\\% and  latency grows by two orders of magnitude. The overloaded nodes alternate between states (active vs. \\emph{soft TKO}), with one node active and the other unavailable, and vice versa.\nThis behavior increases latency, since \\texttt{set} requests cause the middleware to wait for responses from an overloaded node to achieve a majority. In the case of \\texttt{get} requests, part of them are sent to an overloaded node.\n\n\n\n\\begin{figure*}[ht]\n    \\centering\n    \\includegraphics[width=0.9\\textwidth]{figures\/vcpu_unbalancing.pdf}\n    \\caption{Average vCPU usage before (blue) and after (red) unbalanced overload injection.}\n    \\label{fig:dynomite_unbalanced_cpu}\n\\end{figure*}\n\nDynomite is not able to properly manage unbalanced overloads. The average throughput decreases proportionally with the increase of overloaded servers (\\figurename{}~\\ref{fig:unbalanced_load_results}). In this middleware platform, the throughput degrades due to the high latency of requests processed by the overloaded servers. \\figurename~\\ref{fig:dynomite_unbalanced_cpu} shows the effects of the overload of two out of thirty servers on the cpu usage of the remaining nodes. In particular we observe a significant cpu usage reduction across the whole datastore cluster.\nRequests for a given key can experience a high or low latency, depending on whether an overloaded node is chosen among the nodes of the quorum.  Differently from the Twemproxy case, Dynomite does not propagate the effect of overloaded nodes to the remaining servers.\n\n\n\n\n\\subsection{Network link bottlenecks}\n\nIn these experiments, we inject faults in the caching tier by reducing the network bandwidth of a group of servers. In this case, the fault affects a group of Memcached servers that are hosted on the same host, to reproduce a fault (e.g., network congestion) happening at the infrastructure level. Restricting the bandwidth leads to a bottleneck in the network. \n\n\\begin{figure}[ht]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{figures\/Network_link_failure.png}\n    \\caption{Performance under network link bottlenecks.}\n    \\label{fig:link_failure_results}\n\\end{figure}\n\n\nIn Twemproxy, bottlenecks in a subset of connections affect the caching tier as a whole system, as the overall throughput and latency degrade, showed in \\figurename{}~\\ref{fig:link_failure_results}. The standard deviation of latency becomes an order of magnitude higher than the average, which indicates the unbalance of the latency for different requests. Since the latency does not increase for all requests, there are not enough timeouts to trigger the ejection mechanism. The throughput degrades to $20,000$ reqs\/sec, which represents a reduction of 82\\% when compared to $115,000$ reqs\/sec reached under a normal condition. As in the case of unbalanced overloads, in Twemproxy all nodes are impacted by the effects of the fault.\n\nNetwork bottlenecks are the only kind of fault that have an impact on the performance of Mcrouter. We have a sharp increase of latency, as shown in \\figurename{}~\\ref{fig:link_failure_results}, and a decrease of the throughput, with some requests that experience errors. The throughput decreases from $45,000$ reqs\/sec under normal conditions to $8,500$ under faults, and the average latency increases from $2.8$ ms to $142.3$ ms under faults.\n\nDynomite is able to manage the reduction of network bandwidth, as these faults are transparent to the clients. We found that there is no variation in throughput, and we do not have any request with errors. Comparing latency with vs. without faults (\\figurename{}~\\ref{fig:link_failure_results}), we notice a small increase of latency (from $2.8$ ms to $4.2$ ms under faults) which cannot be considered statistically significant. This behavior is due to the peer-to-peer architecture adopted by Dynomite. Indeed, one of the main advantages of the peer-to-peer architecture is that it increases tolerance to faults related to a specific connection. By creating several connections between nodes in a rack, the bandwidth reduction of few connections does not affect performance, since requests are forwarded to the other connections. Thus, this approach is effective at isolating the problem. The effects of the fault do not propagate across the system, which is why the performance of the caching tier as a whole is not significantly affected.\n\n\n\n\n\n\\subsection{Twitter Twemproxy}\n\nTwemproxy (aka Nutcracker) is a fast and light-weight proxy for the Memcached protocol. Twemproxy was developed by Twitter to reduce open connections towards cache nodes, by deploying a local proxy on every front-end node. Thanks to protocol pipelining and sharding, Twemproxy improves horizontal scalability of distributed caching. Twemproxy allows to create a pool of cache servers to distribute the data and to reduce the amount of connections. To send a request to any of those servers, the client contacts Twemproxy, which routes the request to a Memcached\nserver. The same Twemproxy instance can manage different pools, by setting different listening ports to each pool. The number of connections between the client and Twemproxy, and between Twemproxy and each server is set through a configuration file. It is interesting to note that the ``read my last write'' constraint does not necessarily hold true when Twemproxy is configured with more than one connection per server.\n\nTwemproxy shards data automatically across multiple servers. To decide the destination server for a request, a \\emph{request hashing} function is applied to the key of the request to select a shard; then, based on a chosen random distribution, the request is routed to a Memcached server in the shard. Twemproxy provides 12 different hash functions (i.e., \\texttt{one\\_at\\_a\\_time}, \\texttt{MD5}, \\texttt{CRC16}, \\texttt{CRC32}, \\texttt{FNV1\\_64}, etc.) and 3 different distributions (i.e., ketama, modula, random). It allows the application to use only part of the key (\\emph{hashtag}) to calculate the hash function. When the hashtag option is enabled, only part of the key is used as input for the hash function. This option allows the application to map different keys to the same server, as long as the part of the key within the tag is the same.\n\nWhen a failure occurs, Twemproxy provides a mechanism to exclude the failed server.\nIt detects the failure after a number of failed requests (set in a configuration file), ejects the failed server from the pool, and redistributes the key among the remaining servers. Client requests are routed to the active servers; at regular intervals, some requests are sent to the failed server to check its status. When the failed server returns active, it is added back to the pool and the key is distributed again. Twemproxy increases observability using logs and stats. Stats can be at the granularity of server pool or individual servers, through a monitoring port. In the configuration file, it is possible to define the monitoring port and the aggregation interval. Companies that use Twemproxy in production include Pinterest, Snapchat, Flikr and Yahoo!.\n\n\n\n\\subsection{Facebook Mcrouter}\n\nMcrouter is a Memcached protocol router to handle traffic to, from, and between thousands of cache servers across dozens of clusters, distributed at geographical scale. It is a key component of the cache infrastructure at Facebook and Instagram, where Mcrouter handles nearly 5 billion requests per second at peak. It uses the standard ASCII Memcached protocol to provide a transparent layer between clients and servers, and adds advanced features that make it more than a simple proxy.\n\nIn the Mcrouter terminology, a Memcached server is a \\emph{destination}, and a set of destinations is a \\emph{pool}. Mcrouter adopts a client\/server architecture: every Mcrouter instance communicates with several pools, without any communication between different pools. Several clients can connect to a single Mcrouter instance and share the outgoing connections, reducing the number of open connections. Looking at the Facebook infrastructure at a high level, one or more pools with Mcrouter instances and clients define a \\emph{cluster}, and clusters together create a \\emph{region}. Mcrouter is configured with a graph of small routing modules, called \\emph{route handles}, which share a common interface (route a request, return a reply), and which can be combined. The configuration can be changed online to adapt routing to a transient situation, such as adding and warming up a new node.\nSince the configuration is checked and loaded by a background thread, there is no extra latency from the client point of view.\n\nMcrouter supports sharding in order to adapt the datastore tier to the growth of data. The data distribution among servers is based on a key hash. In this way, different keys are evenly distributed across different destinations, and requests for the same key are served by the same destination. It is possible to choose between different hash functions (e.g., \\texttt{CH3}, weighted \\texttt{CH3}, or \\texttt{CRC32}). Keys in the same pool compete for the same amount of memory, and are evicted in the same way. \nMcrouter also provides a feature, namely \\emph{prefix routing}, that allows applications to control data distribution on different pools, by using different key prefixes. This feature is valuable since applications generate and store data of different complexity (e.g., caching the results of complex computations), and they can prevent cache misses on ``expensive'' data by using different prefixes than ``cheap'', so that they do not compete for the same memory space.\n\nMcrouter supports data replication. Read and write requests are managed in a different way: writes are replicated to all hosts in the pool, while reads are routed to a single replica, chosen separately for each client, to achieve a higher read rate.\nTo increase fault tolerance, Mcrouter also provides destination health monitoring and automatic failover. When a destination is marked as unresponsive, the incoming requests will be routed to another destination. At the same time, health check requests will be sent in the background, and as soon as a health check is successful, Mcrouter will send the requests to the original destination again. Mcrouter distinguishes between \\emph{soft errors} (e.g., data timeouts), which are tolerated to happen a few times in a row, and \\emph{hard errors} (e.g., connection refused), which cause a host to be marked unresponsive immediately.\nThe health monitoring parameters are set up through command line options. It is possible to define the number of data timeouts to declare a \\emph{soft TKO} (``technical knockout''), the maximum number of destinations allowed to be in soft TKO state at the same time, and the health check frequency. The health check requests (\\emph{TKO probes}) are sent with an exponentially increasing interval, whose initial and maximum length (in ms) is configurable. The actual intervals have an additional random jitter of up to 50\\% to avoid overloading a single failed host with TKO probes from different Mcrouters.\n\nMcrouter provides mechanisms to check the current configuration. Through an admin request, it is possible to verify what is the route of a specifc request. Given the operation and the key, the response from Mcrouter will be the server that owns the data. It is possible to get the route handle graph that a given request would traverse. These requests allow administrators to get insights on the actual state of the system, e.g., to show how the routing changes when a failure occurs.\n\n\n\n\\subsection{Netflix Dynomite}\n\nDynomite is a middleware solution implemented by Netflix. The main purpose of Dynomite is to transform a single server datastore into a peer-to-peer, clustered and linearly scalable system that preserves native client\/server protocols of the datastores, such as the Redis and Memcached protocols. \n\nA Dynomite cluster consists of multiple \\emph{data centers} (DC). A data center is a group of \\emph{racks}, and a rack is a group of \\emph{nodes}. Each rack consists of the entire dataset, which is partitioned across several nodes in that rack. A client can connect to any node on a Dynomite cluster when sending a request. If the node that receives the request owns the data, it gives the response; otherwise, the node forwards the request to the node that owns the data in the same rack. Dynomite is designed to be a sharding and replication layer. Sharding is achieved as in distributed hash tables \\cite{chi2017hashing,tanenbaum2007distributed}: \nRequest keys are hashed to obtain a \\emph{token} (an integer value); the range of all possible token values is partitioned among the nodes, by assigning to each node a unique token value; the keys that fall in the sub-range ending with the node's unique token are assigned to that node. \n\nTo achieve replication, datasets are replicated among all the racks. When a node receives a \\texttt{set} request, it acts as a coordinator, by writing data in the node of its rack which owns the token, and by forwarding the request to the corresponding nodes in other racks and data centers. \nEvery node knows the distribution of the token in the nodes of all data centers through to the configuration file. Using a similar technique for \\texttt{get} requests, it is possible to increase data availability and tolerate node failures. The configuration file defines the topology, the number of connections and the token range partitioning among the nodes. Moreover, it is possible to configure one of three confidence levels writes and reads: \n\n\\begin{itemize}\n\n\\item \\textbf{DC\\_ONE}: requests are propagated synchronously only in the local rack, and asynchronously replicated to other racks and regions;\n\n\\item \\textbf{DC\\_QUORUM}: requests are sent synchronously to a quorum of servers in the local data center, and asynchronously to the rest. This configuration writes to a set of nodes that forms a quorum. If responses are different, the first response that the coordinator received is returned;\n\n\\item \\textbf{DC\\_SAFE\\_QUORUM}: similar to DC\\_QUORUM, but data checksums have to match.\n\n\\end{itemize}\n\nDynomite makes the caching system tolerant to failures of one or few servers (i.e., less than the size of the quorum) through replication, but it does not provide any failover detection or online reconfiguration. This makes the system less dynamic. For example, to add a new node you have to recompute all tokens, update the configuration file, and restart all processes. Failover detection, token reconfiguration, and other features are provided from other components in the Dyno ecosystem, like Dynomite-manager or Dyno client. Dynomite provides REST APIs for checking the state of some parameters (e.g., the confidence level), but this does not include routing (i.e., where a key is stored or read from).\n\n\n\n\\subsection{Qualitative comparison of fault-tolerance mechanisms}\n\nBoth Mcrouter and Dynomite adopt replication as strategy to achieve transparent fault tolerance. Of course, this strategy has a major impact on performance, since a single request turns in multiple operations on several machines. Given the same settings (number of clients, connections, threads, etc.), the throughput of the caching system can significantly degrade when enabling replication: for example, if throughput without replication reaches $20,000$ reqs\/sec, it can settle to $5,500$ reqs\/sec when using a replication factor of three. \nThe same is not necessarily true for latency, which is of the same order of magnitude in all cases. Being able to use replication without affecting latency is the reason why major service providers are using this strategy despite lower throughput, since latency is the key performance indicator that mostly influences the Quality of Experience.\n\nMcrouter has a more complete failure management, as compared to the previous ones. It consists on monitoring the health state of destinations and detecting failures. By default, it converts all \\texttt{get} errors into cache misses, so that the application can still work even if there is no replication and a high amount of errors occur.\nSimilar considerations on misses and errors also apply for Twemproxy. When  keys are redistributed among nodes after a failure, Twemproxy turns the timeouts into cache misses. \n\nBoth Twemproxy and Mcrouter rely on knowledge about the infrastructure and its failures to be configured with appropriate values, e.g., for the frequency of monitoring, the timeouts, and the replication policies. The main factors driving the configuration are: the fault duration, the throughput, and the amount of data on each server. For example, if we have a throughput of 20k \\texttt{set} reqs\/sec, and 100k keys on each node, then all keys can be redistributed in 5 seconds and be again available. Thus, it is worth adopting redistribution when the throughput is high, the amount of data on each node is small, and the outage of faulty nodes is expected to b long.\n\nDynomite is fault-tolerant with some limitations. In particular, if the coordinator node fails (i.e., the node that first receives a request), there is no retry mechanism that sends the request to another node. Thus, coordinator failures are not tolerated. This is a deliberate design choice, since Dynomite is designed to be on the same host running a Memcached server, thus when the host fails, both Memcached and Dynomite fail. Furthermore, if the rack includes a failed node, the rack still continues to count towards the quorum, while the rack is excluded from the quorum when all its nodes are failed.\n\n\\subsection{Workload generation}\n\nTo generate a workload for the caching nodes and for the middleware platform, we need i)to create connections to send data requests, and ii) to collect performance metrics from the clients' perspective. We initially tried several publicly-available tools, but many proved not to be suitable for carrying out our experiments. \nThe first tool was the \\emph{CloudSuite Data Caching Benchmark} \\cite{cloudsuiterepo}, which is part of CloudSuite, a benchmark suite for cloud services. This tool does not support execution in the presence of failures (which we will deliberately force with fault injection), and stops making requests when a server fails. \nThen, we tried \\emph{Memaslap} \\cite{memaslap}, a load generation and benchmark tool for Memcached servers included in \\emph{libMemcached}. However, the format of requests generated by this tool are incompatible with Mcrouter. \nFor this reason, we developed our own tool, namely Mcrouter \\emph{Mcbench}. It is written in Python, uses the \\emph{aiomcache} library to create the connections and makes requests according to the Memcached protocol. Mcbench generates only \\texttt{set} (20\\%) and \\texttt{get} (80\\%) requests with random keys and values.\nThe tool can be configured with respect to the distribution of keys and values lengths; \nthe duration of the experiment; \nthe desired throughput; \nthe number of threads, clients and connections per server; \nthe list of servers where to forward requests.\n\nThe tool collects performance statistics about requests that are successful and failed, latency, and misses, aggregating them every second.\nTo warm up servers, we configure the tool to initially perform only \\texttt{set} requests. The random distribution of the keys is based on a real-world Twitter dataset from the CloudSuite Data Caching Benchmark \\cite{twitterdataset}. To create random distributions for a more intensive workload for large distributed systems, we scaled-up the Twitter dataset by a factor of ten, while preserving both the popularity and the distribution of object size, with alphanumeric variable-length keys. \nThe original dataset consumes 300MB (267,433 rows) of server memory, while the scaled dataset requires about 3GB (2,674,339 rows).\n\n\n\n\\subsection{Testbed configuration}\n\nThe experimental testbed was built on top of OpenStack, an open-source Infrastructure-as-a-Service (IaaS) cloud computing platform. \nThe experimental testbed consists of eight host machines SUPERMICRO (high density), equipped with two 8-Core 3.3Ghz Intel XEON CPUs (32 logic cores in total), 128GB RAM, two 500GB SATA HDD, four 1-Gbps Intel Ethernet NICs, and a NetApp Network Storage Array with 32TB of storage space and 4GB of SSD cache. The hosts are connected to three 1-Gbps Ethernet network switches, respectively for management, storage and VM network traffic. The testbed is managed with OpenStack Mitaka and the VMware ESXi 6.0 hypervisor. \n\n\\begin{table}\n\\centering\n\\protect\\caption{Configuration of the experimental testbed}\n\\label{tab:configuration}\n\n\\begin{tabular}{|p{1.5cm}|p{0.6cm}|p{5cm}|}\n\\hline \n\\textbf{Node Type} & \\textbf{\\# of nodes} & \\textbf{VM configuration}\\tabularnewline\n\\hline \n\\hline \n\\textbf{Controller Node} & 1 & 2 vCPU, 16GB RAM, 120 GB HDD\\tabularnewline\n\\hline \n\\textbf{Middleware Node}  & 7 & 4 vCPU, 4 GB RAM, 20 GB HDD\\tabularnewline\n\\hline \n\\textbf{Memcached Node} & 30 & 1 vCPU, 8 GB RAM, 20 GB HDD\\tabularnewline\n\\hline \n\\textbf{Workload generator}  & 7 & 4 vCPU, 8 GB RAM, 40 GB HDD\\tabularnewline\n\\hline \n\\textbf{\\emph{Total}} & \\emph{45} & \\emph{88 vCPU, 340 GB RAM, 1.14 TB HDD}\\tabularnewline\n\\hline \n\\end{tabular}\n\n\\end{table}\n\nThe system architecture detailed in Table \\ref{tab:configuration} consists of: \n\\begin{itemize}\n\\item one controller machine, which orchestrates the test and sends commands to the other machines; \n\\item seven workload generators, which send requests to the middleware platform;\n\\item seven middleware machines, which forward the requests to the Memcached servers;\n\\item thirty Memcached servers.\n\\end{itemize}\n\nThe connections between the middleware and the Memcached servers vary depending on the specific middleware. In the case of Twemproxy and Mcrouter, each instance of the middleware connects to all servers, as in \\figurename{}~\\ref{fig:topology1}. In Dynomite, each instance connects only to one node, since there as many Dynomite instances of Dynomite as the number of Memcached servers, as shown in \\figurename{}~\\ref{fig:topology2}. Therefore, in Dynomite there are fewer connections between the middleware and the Memcached servers, and the instances of the middleware communicate with each other to route the requests\n\n\\begin{figure}[ht]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{figures\/topology1.pdf}\n    \\caption{Twemproxy and Mcrouter topology}\n    \\label{fig:topology1}\n\\end{figure}\n\\begin{figure}[ht]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{figures\/topology2.pdf}\n    \\caption{Dynomite topology}\n    \\label{fig:topology2}\n\\end{figure}\n\n\nTo have a balanced load among the physical hosts, we equally divided the VMs in order to have one workload generator, one middleware and at most five Memcached servers on each physical host. \nFor Twemproxy, the dataset is divided among all thirty nodes; for Mcrouter and Dynomite, which support replication schemes, we have three pools\/racks, each composed of ten nodes among which the dataset is divided, thus with a replication factor of three. Thus, a $set$ operation is performed on three different nodes and a get operation in one node out of three. In case of a miss or of an error the operation is retried on the remaining nodes and it is returned the first valid response if any. If the middleware supports the quorum (i.e., in the case of Dynomite) the middleware should reply with an error if the reply does not reach the quorum of two valid responses.\nWe carried out a capacity test to define the maximum throughput that can be reached by the system. The maximum throughput is $18,500$ reqs\/sec per workload generator with Twemproxy, and $7,200$ reqs\/sec per workload generator with Mcrouter and Dynomite. We then calibrated the workload generator to have a throughput per workload generator of $16,500$ reqs\/sec for Twemproxy, and $6,500$ reqs\/sec for Mcrouter and Dynomite. The total number of requests served in the experiments are respectively $115,500$ reqs\/sec and $45,500$ reqs\/sec.\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\n General Relativity \\cite{wald}, or in other words Einstein theory of gravity,  is recognized as one of the best physical theories -- with beautiful theoretical properties and significant phenomenological achievements. GR very well describes dynamics of the Solar System. It predicted several important phenomena that were confirmed: deflection of light by the Sun,\ngravitational light redshift, gravitational waves, gravitational lensing and black holes.\n\nDespite its extraordinary  success, GR should not be viewed as a final theory of gravity. For example, from the standard cosmological model, which assumes applicability  of GR to the universe as a whole,  follows that the universe is approximately made of 68\\% of dark energy (DE),  27\\% of dark matter (DM) and only  5\\% of visible (standard) matter.  However, DE and DM are not yet experimentally detected, and validity of GR at very large cosmic scales is not confirmed.  Even in the case of discovering DM and DE, there is still a sense to look for modifications of GR  that may mimic the same or similar effects as those of DE and DM. Also, cosmological solutions of GR, under rather general properties of the matter, contain singularity at the cosmic time $t = 0.$ In addition to these  mentioned  astrophysical and cosmological problems, there are also some problems that are pure theoretical and come from quantum gravity and string theory. Note also that there is no known  reliable theoretical principle that might show the right direction for valuable extension of GR. Because of all these shortages, there  are many approaches towards  possible  generalization of Einstein theory of gravity (for a review, see  \\cite{faraoni,clifton,nojiri,novello,nojiri1}).\n\n One of the current ways towards modification of GR  is nonlocal modified gravity, see e.g. \\cite{deser,woodard,maggiore,biswas1,biswas2,biswas3,biswas5,biswas4,biswas6,dragovich0,koshelev1a,koshelev1b,koshelev1,koshelev2,koshelev3,koshelev4,eliz,koivisto}.\nAll nonlocal gravity models contain the d'Alembert-Beltrami operator $\\Box$, that is  involved mainly in two ways: 1) in the form $\\Box^{-n}$ and 2)  as an analytic function\n$F (\\Box) = \\sum_{n=0}^{+\\infty} f_n \\Box^n$. Models with $\\Box^{-n}$ operator are introduced to investigate  the late cosmic time acceleration without its matter origin.  Some  of such models are given by the action\n\\begin{equation} \\label{1.1}\nS = \\frac{1}{16\\pi G} \\int \\sqrt{-g} \\left(R + \\mathcal{L}  \\right) \\, d^4x ,\n\\end{equation}\nwhere $\\mathcal{L} = R\\, f(\\Box^{-1}R)$ (see, e.g.  \\cite{nojiri,woodard,koivisto}), and  $ \\mathcal{L} = -\\frac{1}{6} m^2 R \\Box^{-2} R $ (see \\cite{maggiore} and references therein).\n\n An interesting and promising class of nonlocal gravity models, that have been recently considered,  is given by\n\\begin{equation} \\label{1.2}\nS = \\frac{1}{16 \\pi G}\\int_{\\mathcal{M}} \\sqrt{-g}\\, [R - 2\\Lambda + P(R)\\, \\mathcal{F}(\\Box)\\, Q(R)]\\, d^4x ,\n\\end{equation}\nwhere $\\mathcal{M}$ is a pseudo-Riemannian manifold of signature $(1,3)$ with metric $(g_{\\mu\\nu})$, $\\Lambda$ is the cosmological constant, $P(R)$ and $Q(R)$ are some differentiable functions of the Ricci scalar $R$, and $\\mathcal{F} (\\Box) = \\sum_{n=1}^{+\\infty} f_n \\Box^n$.\nMotivation to use this analytic nonlocal operator  comes from  ordinary and $p$-adic string theory (see \\cite{dragovich1} and references therein) and observation that some  analytic nonlocal operators\nmay improve renormalizability in some quantum gravity models, see \\cite{stelle,modesto1,modesto2}.\nTo have better insight into  effects, preliminary investigation of these models is usually without matter.\n\n Note again that action \\eqref{1.2} contains a class  of simple nonlocal extensions of GR, but still in rather general form. Usually researchers start by a particular expression for $P(R)$ and $Q(R)$ as differentiable functions of $R$, while $\\mathcal{F}(\\Box)$ is treated as an analytic function of operator $\\Box$, whose concrete form is not given at the beginning. For given $P(R)$ and $Q(R)$, the next step is derivation of equations of motion for metric tensor $g_{\\mu\\nu}$. To consider \\eqref{1.2} as nonlocal gravity model of interest for cosmology, equations of motion should have  some useful cosmological solutions. Existence of such (usually exact) cosmological solutions requires some restrictions on the function $\\mathcal{F} (\\Box) = \\sum_{n=1}^{+\\infty} f_n \\Box^n$, i.e. on its coefficients $f_n$, e.g. see \\cite{biswas1,biswas2,biswas3,biswas5,biswas4}. Then with these, and perhaps some additional, restrictions there is a possibility to construct the corresponding concrete function\n$\\mathcal {F} (\\Box)$. Since we do not know {\\it a priori} function $\\mathcal {F} (\\Box)$,  this approach is a reasonable\nway to get it.\n\n\n Concerning action \\eqref{1.2}, the most attention has been paid to the simple case when $P(R) = Q(R) = R$, e.g. see \\cite{biswas1,biswas2,koshelev1a,koshelev1b,koshelev2,dimitrijevic1,dimitrijevic2,dimitrijevic3,dimitrijevic4,dimitrijevic5,dimitrijevic6,\ndimitrijevic7,dimitrijevic8}.  This investigation started in \\cite{biswas1,biswas2} by successful attempt to find nonsingular bouncing\nsolution of the Big Bang singularity problem in standard cosmology. To find appropriate solution of equations of motion, the ansatz  $\\Box R = r R + s$ was used, where $r$ and $s$ are parameters that connect the solution and function $\\mathcal {F} (\\Box)$.   If also in this case cosmological constant $\\Lambda = 0$ then it is some kind of nonlocal generalization of the Starobinsky $R^2$ inflation model, whose various properties are studied in \\cite{koshelev1,koshelev2}.\n\nAnother very intriguing example of the nonlocal gravity  \\eqref{1.2} has $P(R) = Q(R) = \\sqrt{R - 2\\Lambda}$ \\cite{PLB}. One of its exact cosmological solutions is $a(t) = A t^{\\frac{2}{3}} e^{\\frac{\\Lambda}{14}t^2} , \\, \\Lambda \\neq 0, \\, k=0.$  This solution mimics properties similar to an interplay of the dark matter and the dark energy. Moreover, computed cosmological parameters are in a good agreement with astronomical observations.  It is worth noting that at the first glance appearance of $\\sqrt{R - 2 \\Lambda}$ in this model may look strange. However, it can be regarded as a natural nonlocal generalization of the standard local Lagrangian $R - 2 \\Lambda.$ Namely, one can introduce nonlocality as follows: $R - 2 \\Lambda = \\sqrt{R - 2 \\Lambda} \\, \\sqrt{R - 2 \\Lambda}\\ \\to \\ \\sqrt{R - 2 \\Lambda}\\, [1 + \\mathcal {F} (\\Box)] \\, \\sqrt{R - 2 \\Lambda}$.\n\nNonlocal gravity model which we investigate in this paper has $P(R) = Q(R) = R - 4 \\Lambda $,  and the action is given explicitly below in \\eqref{2.1}. As we will see, one of the exact cosmological solutions is $a(t) = A \\sqrt{t} e^{\\frac{\\Lambda}{4}t^2} , \\, \\Lambda \\neq 0, \\, k=0 ,$ which mimics an interplay between radiation and the dark energy.\n Nonlocal term $(R - 4\\Lambda)\\ \\mathcal {F} (\\Box) \\ (R - 4\\Lambda)$ in this model arose in the process of generalization of the above mentioned model with nonlocality $R\\ \\mathcal {F} (\\Box) \\ R $. The starting expression was $(R - R_0)\\ \\mathcal {F} (\\Box) \\ (R - R_0)$, where $R_0$ is a constant that may lead to some interesting  background solutions.\n\nSection 2 contains derivation of the equations of motion. Section 3 is devoted to the exact cosmological solutions. Some concluding remarks are in section 4.\n\n\\section{New Nonlocal Gravity Model}\n\nThe action of our nonlocal gravity model is\n\\begin{equation} \\label{2.1}\nS =  \\frac{1}{16\\pi G} \\int [ R- 2\\Lambda + (R-4\\Lambda) \\, \\mathcal{F}(\\Box) \\, (R-4\\Lambda) ] \\, \\sqrt{-g}\\; d^4x ,\n\\end{equation}\nwhere  $\\mathcal{F}(\\Box)= \\displaystyle \\sum_{n =1}^{\\infty} f_{n}\\, \\Box^{n}$\nand $\\Box = \\nabla_{\\mu}\\nabla^{\\mu}= \\frac{1}{\\sqrt{-g}}\\, \\partial_\\mu \\, (\\sqrt{-g}\\, g^{\\mu\\nu}\\, \\partial_\\nu )$ is the corresponding  d'Alembert-Beltrami operator.  In construction of \\eqref{2.1} we started from  action\n\\begin{equation} \\label{2.1a}\nS =  \\frac{1}{16\\pi G} \\int [ R- 2\\Lambda + (R-R_0) \\, \\mathcal{F}(\\Box) \\, (R-R_0) ] \\, \\sqrt{-g}\\; d^4x\n\\end{equation}\n and found that for $R_0 = 4 \\Lambda$ the corresponding equations of motion \\eqref{2.9} and \\eqref{2.10} give two interesting background solutions presented in subsections \\ref{sol-1} and \\ref{sol-2}.\n\n\n\\subsection{Equations of Motion}\n\nThe equations of motion for nonlocal gravity action \\eqref{1.2} are derived in \\cite{dimitrijevic9} and have the following form:\n\\begin{align} \\label{2.2}\n\\hat{G}_{\\mu\\nu} &= G_{\\mu\\nu} +\\Lambda g_{\\mu\\nu} -\\frac{1}{2} g_{\\mu\\nu} P(R)\\, \\mathcal{F}(\\Box)\\, Q(R) + \\big(R_{\\mu\\nu}  - K_{\\mu\\nu} \\big) W +\\frac{1}{2} \\Omega_{\\mu\\nu} = 0,\n\\end{align}\nwhere $\\hat{G}_{\\mu\\nu}$ is nonlocal version of Einstein's tensor, and\n\\begin{align}\nK_{\\mu\\nu} &= \\nabla_\\mu \\nabla_\\nu - g_{\\mu\\nu}\\Box , \\label{2.3} \\\\\n  W &= P'(R)\\, \\mathcal{F}(\\Box)\\, Q(R) + Q'(R)\\, \\mathcal{F}(\\Box)\\, P(R), \\label{2.4} \\\\\n  \\Omega_{\\mu\\nu} &= \\sum_{n=1}^{\\infty} f_n \\sum_{\\ell=0}^{n-1} S_{\\mu\\nu}\\big(\\Box^\\ell P(R),\\, \\Box^{n-1-\\ell}\\, Q(R)\\big) ,\n  \\label{2.5} \\\\ S_{\\mu\\nu}(A,B) &= g_{\\mu\\nu} \\nabla^\\alpha A \\nabla_\\alpha B + g_{\\mu\\nu} A \\Box B -2 \\nabla_\\mu A \\nabla_\\nu B  , \\label{2.5a}\n\\end{align}\nwhere $P'(R)$ and $Q'(R)$ are derivatives of $P(R)$ and $Q(R)$ with respect to R, respectively.\n\nFrom computation in detail, it follows\n\\begin{equation}\n\\triangledown^\\mu\\hat{G}_{\\mu\\nu} = 0  \\, .       \\label{2.6}\n\\end{equation}\n\n\nAction \\eqref{2.1} is particular case of \\eqref{1.2} and the corresponding equations of motion for model \\eqref{2.1} easily follow from \\eqref{2.2}, i.e. equations of motion are\n\\begin{align}\\label{2.7}\n&\\hat{G}_{\\mu\\nu} = G_{\\mu\\nu}+ \\Lambda g_{\\mu\\nu} -\\frac{1}{2}g_{\\mu\\nu} U \\mathcal{F}(\\Box)U + 2 (R_{\\mu\\nu}  - \\nabla_{\\mu}\\nabla_{\\nu} +   g_{\\mu\\nu}\\Box)\\mathcal{F}(\\Box) U \\nonumber \\\\\n & + \\frac{1}{2}\\sum_{n=1}^{+\\infty}f_{n}\\sum_{\\ell=0}^{n-1}\\Big\n(g_{\\mu\\nu}(g^{\\alpha\\beta}\\partial_{\\alpha}\\Box^{\\ell}U\n\\partial_{\\beta} \\Box^{n-1-\\ell}U + \\Box^{\\ell} U \\Box^{n-\\ell}U) \\nonumber \\\\\n& - 2 \\partial_{\\mu} \\Box^{\\ell}U \\partial_{\\nu}\\Box^{n-1-\\ell}U \\Big ) =  0,\n\\end{align}\nwhere $G_{\\mu\\nu} = R_{\\mu\\nu} - \\frac{1}{2} R g_{\\mu\\nu}$ is the Einstein tensor, and  $U = R - 4 \\Lambda$.\n\n\nIn the sequel of this paper, we are mainly interested in finding and investigating some exact cosmological solutions of \\eqref{2.7}.  Since the universe is homogeneous and isotropic at large scales, it has the\nFriedmann-Lema\\^{\\i}tre-Robertson-Walker (FLRW) metric\n\\begin{align}\nds^2 = - dt^2 + a^2(t)\\left(\\frac{dr^2}{1-k r^2} + r^2 d\\theta^2 + r^2 \\sin^2 \\theta d\\phi^2\\right), \\quad (c=1) , \\, \\, k= 0, \\pm 1 , \\label{2.8}\n\\end{align}\nwhere $a(t)$ is the cosmic scale factor.\n As a consequence of symmetries of the FLRW metric,\n \\eqref{2.7} can be reduced to  two independent differential equations and we take trace and 00-component, respectively:\n \\begin{align}\n&4\\Lambda - R  -2 U \\, \\mathcal{F}(\\Box) \\, U +  2(R\n + 3 \\Box )\\,  \\mathcal{F}(\\Box) \\, U  \\nonumber \\\\\n &+ \\sum_{n=1}^{+\\infty}f_{n}\n\\sum_{\\ell =0}^{n-1} \\Big( \\partial_{\\alpha}\\Box^{\\ell}\\, U \\partial^{\\alpha} \\Box^{n-1-\\ell}\\, U + 2\\Box^{\\ell}\\, U \\Box^{n-\\ell}\\, U \\Big)\n  = 0,  \\label{2.9}\n\\end{align}\n\\begin{align}\n &G_{00} - \\Lambda  + \\frac{1}{2} U \\, \\mathcal{F}(\\Box) \\, U  +  2 (R_{00} - \\partial_{0}\\partial_{0} - \\Box) \\,  \\mathcal{F}(\\Box) \\, U \\nonumber \\\\\n &- \\frac{1}{2} \\sum_{n=1}^{+\\infty} f_{n} \\sum_{\\ell =0}^{n-1}\\Big( \\partial_{\\alpha}\\Box^{\\ell}\\, U\n\\partial^{\\alpha} \\Box^{n-1-\\ell}\\, U + \\Box^{\\ell}\\, U \\Box^{n-\\ell}\\, U \\nonumber \\\\\n &+ 2 \\partial_{0} \\Box^{\\ell}\\, U \\partial_{0}\\Box^{n-1-\\ell}\\, U \\Big )  = 0 ,  \\label{2.10}\n\\end{align}\nwhere\n\\begin{equation}\n   R_{00} = - 3 \\frac{\\ddot{a}}{a} \\, , \\qquad   G_{00} = 3 \\frac{\\dot{a}^2  + k}{a^2} \\,  .     \\label{2.11}\n\\end{equation}\n\n\nEq. \\eqref{2.7} can be rewritten in the form\n\\begin{equation}\n\\hat{G}_{\\mu\\nu} = G_{\\mu\\nu}+ \\Lambda g_{\\mu\\nu} - 8 \\pi G \\hat{T}_{\\mu\\nu} = 0 \\, , \\label{2.12}\n\\end{equation}\nwhere $ \\hat{T}_{\\mu\\nu}$ can be regarded as a nonlocal gravity analog of the energy-momentum tensor in Einstein's gravity.\nThe corresponding Friedmann equations to \\eqref{2.12} are\n\\begin{equation}\n\\frac{\\ddot{a}}{a} = - \\frac{4\\pi G}{3} (\\bar{\\rho} + 3 \\bar{p}) + \\frac{\\Lambda}{3} \\,,  \\quad \\frac{\\dot{a}^2  + k}{a^2} = \\frac{8\\pi G}{3} \\bar{\\rho}\n+ \\frac{\\Lambda}{3} \\,,   \\label{2.13}\n\\end{equation}\nwhere $\\bar{\\rho}$ and $\\bar{p}$ play a role of the energy density and pressure of the dark side of the universe, respectively.\n The related equation of state is\n\\begin{equation}\n\\bar{p} (t) = \\bar{w}(t) \\, \\bar{\\rho} (t) .  \\label{2.14}\n\\end{equation}\n\n\\subsection{Ghost-free condition}\n\nThe spectrum can be found and a possibility to avoid ghost degrees of freedom can be studied by considering the second variation of the action. This task was accomplished in different settings. In paper \\cite{biswas6} it was done for an action which contains our action (\\ref{2.1}) as one of the terms. In paper \\cite{dimitrijevic4} analogous analysis was performed for generic functions $P(R)$ and $Q(R)$. The generic idea is that certain combinations containing the operator function ${\\mathcal F}(\\Box)$ form kinetic operators for scalar and tensor propagating degrees of freedom. Consequently such combinations must be equal to an exponent of an entire function. The latter has no zeros on the whole complex plane and as such does not result in poles in propagators yielding no new degrees of freedom. Detailed expressions and all the restrictions can be found in the above mentioned references.\n\n\n\\section{Cosmological Solutions}\n\n\nOur intention is to obtain some exact cosmological solutions of the equations of motion \\eqref{2.9} and \\eqref{2.10} in the form  $a(t) = A t^m e^{\\gamma \\ t^2}$, where $m$ and $\\gamma$ are some constants. At the beginning we take $U = R - R_0$ and $k = 0$ in the equations of motion. Thus we have three parameters $m,\\ \\gamma, \\ R_0$ that  have to be determined. We found that for $R_0 = 4\\ \\Lambda$ there are two pairs of solutions for $m$ and $\\gamma$: 1) $m = \\frac{1}{2} , \\, \\, \\gamma = \\frac{\\Lambda}{4}$ and 2) $m = 0 , \\, \\, \\gamma = \\Lambda$. These background solutions are presented below.\n\n\nRecall that  scalar curvature for the FLRW metric \\eqref{2.8} is\n\\begin{align}\nR (t) = 6\\Big(\\frac{\\ddot a}{a} + \\big(\\frac{\\dot a}{a}\\big)^2 +\\frac{k}{a^2}\\Big).   \\label{3.1}\n\\end{align}\n The d'Alembert-Beltrami operator $\\Box$  acts as $\\Box R = - \\frac{\\partial^2}{\\partial t^2} {R}-3 H \\frac{\\partial}{\\partial t} {R} ,$ where $H=  \\frac{\\dot{a}}{a}$ is the Hubble parameter.\n\n\nNote that the Minkowski space (a(t) = const.,\\ $R = \\Lambda = k = 0$) is  a solution of equations of motion \\eqref{2.9} and \\eqref{2.10}.\n\nIn what follows, we will present  and briefly discuss some exact cosmological solutions mainly with $\\Lambda \\neq 0 .$\n\n\n\\subsection{Cosmological solution $ a (t) = A \\, \\sqrt{t} \\, e^{\\frac{\\Lambda}{4} t^2}  \\,, \\,\\, k=0 $}\n\\label{sol-1}\n\nFor this solution we have\n\\begin{equation}\n\\dot{a}(t) = a(t) \\frac{1}{2} \\Big(t^{-1} + \\Lambda t  \\Big) , \\quad  \\ddot{a}(t) = a(t)\n\\frac{1}{4} \\Big(\\Lambda^2 t^2 + 4 \\Lambda - t^{-2} \\Big),  \\label{3.1a}\n\\end{equation}\nand scalar curvature \\eqref{3.1} becomes\n\\begin{equation} \\label{3.2}\nR(t) = 3 \\Lambda (\\Lambda t^2 + 3) .\n\\end{equation}\n\nThe Hubble parameter is\n\\begin{align}\n H(t) = \\frac{1}{2} \\big(  t^{-1} +  \\Lambda t \\big) , \\label{3.3}\n \\end{align}\n and its first part ($ \\frac{1}{2t}$) is the same as  for the radiation dominance in Einstein's gravity, while the second term\n ($\\frac{\\Lambda t}{2}$) can be related to the dark energy generated by cosmological constant $\\Lambda$. It is evident that this dark radiation is dominated at the small cosmic times and can be ignored compared to $\\Lambda$ term at  large times. At the present cosmic time $t_0 = 13.801 \\cdot 10^9$ yr and $\\Lambda = 0.98 \\cdot 10^{-35}\\ \\text{s}^{-2}$, both terms in \\eqref{3.3} are of the same order of magnitude and $H (t_0) = 100.2 \\ \\text{km\/s\/Mpc}$.  This value for the Hubble parameter is  larger than current Planck mission result $H_0 = (67.40 \\pm 0.50)$ km\/s\/Mpc \\cite{planck2018}. Hence this cosmological solution may be of interest for the early universe with radiation dominance and for far-future accelerated expansion.\n\n\n   There is useful equality\n\\begin{align}\n\\Box \\big(R - 4 \\Lambda\\big) =  - 3\\Lambda \\big(R - 4 \\Lambda \\big)    \\label{3.4}\n\\end{align}\nwhich leads to\n\\begin{align}\n\\mathcal{F}(\\Box) \\, \\big(R - 4 \\Lambda\\big) =  \\mathcal{F}\\big(- 3 \\Lambda\\big) \\, \\big(R - 4 \\Lambda\\big) .  \\label{3.5}\n\\end{align}\n$R_{00}$ and $G_{00}$ are:\n\\begin{align}\nR_{00} = \\frac{3}{4} \\big( t^{-2} - 4\\Lambda - \\Lambda^2 t^2 \\big) \\,, \\quad G_{00} =  \\frac{3}{4} \\big( t^{-1} + \\Lambda t \\big)^2 .  \\label{3.6}\n\\end{align}\n\nUsing equality $\\Box (R-4 \\Lambda)=-3 \\Lambda (R-4 \\Lambda)$, the trace equation \\eqref{2.9} becomes\n\\begin{align}\\label{trace:R-4Lambda- anzac}\n&4 \\Lambda -R- 10 \\Lambda(R-4 \\Lambda)\\mathcal{F}(-3 \\Lambda)+ \\big(-6 \\Lambda (R-4 \\Lambda)^{2}-\\dot{R}^{2}\\big)\\mathcal{F}'(-3 \\Lambda)=0.\n\\end{align}\n\nThe $00$ component of EOM \\eqref{2.10} becomes\n\\begin{align}\\label{00eq:R-4Lambda- anzac}\n&G_{00}- \\Lambda + (R-4 \\Lambda)\\mathcal{F}(-3 \\Lambda)(2 R_{00}+ \\frac{1}{2}R+ 4 \\Lambda)- 2 \\mathcal{F}(-3 \\Lambda)\\ddot{R}\\nonumber \\\\\n&+ \\frac{1}{2}\\big(3 \\Lambda (R-4 \\Lambda)^{2}-\\dot{R}^{2}\\big)\\mathcal{F}'(-3 \\Lambda)=0.\n\\end{align}\n\nSubstituting scalar curvature $R$ into the trace equation \\eqref{trace:R-4Lambda- anzac} we obtain\n\\begin{align}\n&4 \\Lambda - 3 \\Lambda ( 3+ \\Lambda t^{2})-10 \\Lambda^{2}(5 + 3 \\Lambda t^{2})\\mathcal{F}(-3 \\Lambda)\\nonumber \\\\\n&+ \\big(-6 \\Lambda^{3}(9 \\Lambda^{2}t^{4}+ 30 \\Lambda t^{2}+ 25)- 36 \\Lambda^{4}t^{2}\\big)\\mathcal{F}'(-3 \\Lambda)=0.\n\\end{align}\n\nSimilarly, the $00$ component of EOM \\eqref{00eq:R-4Lambda- anzac} becomes\n\\begin{align}\n&\\frac{3(1+\\Lambda t^{2})^{2}}{4 t^{2}}- \\Lambda + \\Lambda (5+ 3 \\Lambda t^{2})\\big(\\frac{3}{2t^{2}}+ \\frac{5}{2} \\Lambda \\big)\\mathcal{F}(-3 \\Lambda)\\nonumber \\\\\n&-12 \\Lambda^{2} \\mathcal{F}(-3 \\Lambda)+ \\frac{1}{2}\\big( 3 \\Lambda^{3}(9 \\Lambda^{2}t^{4}+ 30 \\Lambda t^{2}+ 25)- 36 \\Lambda^{4}t^{2}\\big)\\mathcal{F}'(-3 \\Lambda)=0.\n\\end{align}\n\n\nFinally, the solution of equations of motion \\eqref{2.9} and \\eqref{2.10} requires constraints\n\\begin{align}\n    \\mathcal{F} \\big(- 3\\Lambda \\big) = - \\frac{1}{10 \\Lambda} \\,,  \\quad   \\mathcal{F}' \\big(- 3\\Lambda \\big) = 0 \\, , \\quad \\Lambda \\neq 0 ,  \\label{3.7}\n\\end{align}\nwhich are satisfied by nonlocal operator\n\\begin{align}\n\\mathcal{F}(\\Box) = \\frac{\\Box}{30\\Lambda^2} \\exp{\\left(\\frac{\\Box}{3\\Lambda} + 1\\right)} . \\label{3.7a}\n\\end{align}\n\nFrom \\eqref{2.13} follows\n\\begin{equation}\n\\bar{\\rho} (t) = \\frac{3 t^{-2} + 3\\Lambda^2 t^2 + 2 \\Lambda}{32 \\pi G} \\,,    \\quad \\bar{p}(t) =  \\frac{t^{-2} -3 \\Lambda^2 t^2 - 6 \\Lambda}{32 \\pi G}  .   \\label{3.1.5a}\n\\end{equation}\n\nOne can easily conclude that\n\\begin{equation}\n\\bar{w} = \\frac{t^{-2} - 3\\Lambda^2 t^2 - 6\\Lambda}{3 t^{-2} + 3\\Lambda^2 t^2  + 2\\Lambda} \\to   \\begin{cases}\n-1 ,  \\, \\, t \\to \\infty \\\\\n\\frac{1}{3} , \\quad  t \\to  0 .   \\label{3.1.5b}\n\\end{cases}\n\\end{equation}\nFrom \\eqref{3.1.5b}, we see that parameter $\\bar{w}$ behaves: (i)   like 1\/3 at early times as for the case of radiation and (ii) like -1 as in the usual prediction for the late times  acceleration with cosmological constant $\\Lambda$.\n\n\n\n\n\n\\subsection{Cosmological solution $ a (t) = A  \\, e^{\\Lambda t^2} \\,, \\,\\, k=0  $}\n\\label{sol-2}\n\nFor this solution we have\n\\begin{align} \\label{3.2.1}\n&\\dot{a}(t) = a(t)\\ 2 \\Lambda t , \\quad \\ddot{a}(t) = a(t)\\ 2 \\Lambda \\big(2 \\Lambda t^2 + 1\\big) ,  \\\\\n&R(t) = 12 \\Lambda \\big(4 \\Lambda t^2 +1\\big) , \\quad H(t) =2 \\Lambda t , \\label{3.2.1a} \\\\\n&R_{00} = -6\\Lambda \\big(1 + 2\\Lambda t^2 \\big) \\ \\quad G_{00} = 12 \\Lambda^2 t^2 .\n\\end{align}\nThere are  useful equalities:\n\\begin{align} \\label{3.2.2}\n\\Box (R - 4\\Lambda) = - 12 \\Lambda (R - 4 \\Lambda) , \\quad  \\mathcal{F}(\\Box) (R -4 \\Lambda) = \\mathcal{F}(-12 \\Lambda) (R -4 \\Lambda) .\n\\end{align}\n\nUsing equalities  \\eqref{3.2.2},     \nthe trace equation \\eqref{2.9} becomes\n\\begin{align}  \\label{3.2.3}\n&4 \\Lambda -R- 64 \\Lambda(R-4 \\Lambda)\\mathcal{F}(-12 \\Lambda)+ \\big(-24 \\Lambda (R-4 \\Lambda)^{2}-\\dot{R}^{2}\\big)\\mathcal{F}'(-12 \\Lambda)=0.\n\\end{align}\n\nThe $00$ component of EOM \\eqref{2.10} is as follows:\n\\begin{align}  \\label{3.2.4}\n&G_{00}- \\Lambda + (R-4 \\Lambda)\\mathcal{F}(-12 \\Lambda)(2 R_{00}+ \\frac{1}{2}R+ 22 \\Lambda)- 2 \\mathcal{F}(-12 \\Lambda)\\ddot{R}\\nonumber \\\\\n&+ \\frac{1}{2}\\big(12 \\Lambda (R-4 \\Lambda)^{2}-\\dot{R}^{2}\\big)\\mathcal{F}'(-12 \\Lambda)=0.\n\\end{align}\n\nSubstituting scalar curvature $R$ \\eqref{3.2.1a} into the trace equation \\eqref{3.2.3} we obtain\n\\begin{align} \\label{3.2.5}\n&4 \\Lambda - 12 \\Lambda ( 1+ 4 \\Lambda t^{2})-512 \\Lambda^{2}(1 + 6 \\Lambda t^{2})\\mathcal{F}(-12 \\Lambda) \\nonumber \\\\\n&+ \\big(-1536 \\Lambda^{3}(36 \\Lambda^{2}t^{4}+ 12 \\Lambda t^{2}+ 1)- 9216 \\Lambda^{4}t^{2}\\big)\\mathcal{F}'(-12 \\Lambda)=0.\n\\end{align}\n\nSimilarly, the $00$ component of EOM \\eqref{3.2.4} becomes\n\\begin{align} \\label{3.2.6}\n&12 \\Lambda^{2}t^{2}- \\Lambda +8 \\Lambda ( 1+ 6 \\Lambda t^{2})\\big(2(-12 \\Lambda^{2}t^{2}-6\\Lambda)+ 6 \\Lambda (1 + 4 \\Lambda t^{2})+ 22 \\Lambda \\big)\\mathcal{F}(-12 \\Lambda)\\nonumber \\\\\n&-2\\mathcal{F}(-12 \\Lambda) 96 \\Lambda^{2}+ \\frac{1}{2}\\big( 768 \\Lambda^{3}(36 \\Lambda^{2}t^{4}+ 12 \\Lambda t^{2}+ 1)- 9216 \\Lambda^{4}t^{2}\\big)\\mathcal{F}'(-12 \\Lambda)=0.\n\\end{align}\n\n\nTo be satisfied, equations of motion \\eqref{2.9} and \\eqref{2.10} imply  conditions\n\\begin{align} \\label{3.2.7}\n    \\mathcal{F} \\big(- 12\\Lambda \\big) = - \\frac{1}{64 \\Lambda} \\,,  \\quad   \\mathcal{F}' \\big(- 12\\Lambda \\big) = 0 \\, , \\quad \\Lambda \\neq 0 ,\n\\end{align}\nthat can be realized by\n\\begin{align}\n\\mathcal{F}(\\Box) = \\frac{\\Box}{768\\Lambda^2} \\exp{\\left(\\frac{\\Box}{12\\Lambda} + 1\\right)} . \\label{3.2.7a}\n\\end{align}\n\n\n\nAccording to \\eqref{2.13} follows\n\\begin{equation}\n\\bar{\\rho}(t) = \\frac{\\Lambda \\big(12\\Lambda t^2 -1\\big)}{8\\pi G} \\,, \\quad \\bar{p}(t) = - \\frac{3\\Lambda \\big(4 \\Lambda t^2 +1   \\big)}{8\\pi G} . \\label{3.2.8}\n\\end{equation}\n\nThe corresponding $\\bar{w}$ parameter is\n\\begin{equation} \\label{3.2.9}\n\\bar{w} =  \\frac{ - 12\\Lambda t^2 - 3}{ 12\\Lambda t^2  - 1} \\to  \\begin{cases}\n-1 ,  \\, \\, t \\to \\infty \\\\\n3 , \\quad  t \\to  0 .\n\\end{cases}\n\\end{equation}\n\n\\bigskip\n\n\\subsection{Other vacuum solutions: $R (t)$ = const.}\n\nThe above two cosmological solutions have scalar curvature $R (t)$ dependent on time $t$.\nThere are also vacuum solutions with  $R = 4 \\Lambda$ that are the same as for Einstein's equations of motion.\nSince $\\Box (R -4 \\Lambda) = 0$, it is evident that such solutions satisfy equations of motion \\eqref{2.9} and \\eqref{2.10}\nwithout conditions of function $\\mathcal{F} (\\Box)$.\n\n\nIn addition to the already mentioned Minkowski space, there is another solution with $R(t) = 0$:\n\n Milne solution: $a(t) = t, \\ k= -1, \\ \\Lambda = 0 , \\ (c=1).$\n\nFrom our analysis follows that there are no other exact power law solutions of the form $a(t) = A t^\\alpha$ except  this Milne one.\n\n\n\\section{Concluding Remarks}\n\n\nIn this article, we have presented some exact cosmological solutions of nonlocal gravity model without matter given by\naction \\eqref{2.1}. Two of these solutions are valid only if  $\\Lambda \\neq 0 $. The solutions $a(t) = A \\sqrt{t} e^{\\frac{\\Lambda}{4} t^2}$ and $a(t) = A e^{\\Lambda t^2}$ are not contained in Einstein's gravity with  cosmological constant $\\Lambda$. The solution $a(t) = A \\sqrt{t} e^{\\frac{\\Lambda}{4} t^2}$ mimics interference between expansion with radiation $a(t) = A \\sqrt{t}$ and a dark energy $a(t) = A e^{\\frac{\\Lambda}{4} t^2} .$\n\nThe solution $a(t) = A e^{\\Lambda t^2}$ is a nonsingular bounce one and an even function of cosmic time.\nAn exact cosmological solution of the type $a(t) = A e^{\\alpha\\Lambda t^2}$, where $\\alpha$ is a number, appears  also\nat least in the following two models of \\eqref{1.2}: 1) $P(R) = Q (R) = R$  \\cite{koshelev1a} (see also \\cite{koshelev1b}), and 2) $P(R) = Q (R) = \\sqrt{R - 2\\Lambda}$ \\cite{PLB}. It would be interesting to investigate other possible models with this kind of solution.\n\nWith respect to the cosmological solutions $a(t) = A \\sqrt{t} e^{\\frac{\\Lambda}{4} t^2}$ and $a(t) = A e^{\\Lambda t^2}$,\nthe nonlocal analytic operator $\\mathcal{F}(\\Box)$ is presented by expressions \\eqref{3.7a} and\n\\eqref{3.2.7a}, respectively. Operator $\\mathcal{F}(\\Box)$ that takes into account both solutions\nshould have the form $\\mathcal{F}(\\Box) = a \\frac{u}{\\Lambda} \\exp(b u^3 + c u^2 + d u) ,$  where $a, b, c, d, $ are some definite constants and $u = \\Box\/\\Lambda $ is dimensionless operator. We do not introduce  an additional parameter like mass $M .$\n\n\nAccording to our solutions $a(t) = A \\sqrt{t} e^{\\frac{\\Lambda}{4} t^2}$  and $a(t) = A t^{\\frac{2}{3}} e^{\\frac{\\Lambda}{14} t^2}$ \\cite{PLB},\n it follows that effects of the dark radiation ($\\sqrt{t}$), the dark matter ($t^{\\frac{2}{3}}$) and the dark energy ($e^{\\alpha\\Lambda t^2}$) at the cosmic scale can be generated by suitable nonlocal gravity models. These findings should play\nuseful role in further research concerning  the universe evolution.\n\n\n\n\n\\section*{Funding}\n\n{This research is  partially  supported by the Ministry of Education, Science and Technological Development of  Republic of Serbia, grant No 174012.}\n\n\n\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nLattice QCD predicts that, under conditions of extremely high temperatures and energy densities, a phase transition or crossover from hadronic matter to a new form of matter, known as Quark Gluon Plasma (QGP) ~\\cite{QGP_bib}, will occur. The Relativistic Heavy Ion Collider (RHIC) was built to search for the QGP and to study its properties in laboratory through high-energy heavy-ion collisions~\\cite{starwhitepaper}. Many observables have been proposed to probe the QGP created in heavy-ion collisions. Among them, the $J\/\\psi$ suppression caused by the color-charge screening  in QGP is one of most important signatures ~\\cite{QGP_jpsi}.\n   \nOver the past twenty years, $J\/\\psi$ production in hot and dense medium has been a topic attracting growing interest. Suppression of $J\/\\psi$ production has been observed in various experimental measurements~\\cite{SPS_jpsi1,SPS_jpsi2,SPS_jpsi3,PHENIX_jpsi1}. A similar suppression pattern and magnitude of $J\/\\psi$ was observed at SPS and RHIC despite of huge collision energy difference. Furthermore, the $J\/\\psi$ is suppressed more in forward rapidity than that in midrapidity at RHIC 200 GeV Au$+$Au collisions ~\\cite{PHENIX_jpsi2}. These experimental observations suggest that, in addition to color screening, there exist other effects  contributing to the modification of $J\/\\psi$ production. Cold nuclear matter (CNM) effects, the combined contribution of finite $J\/\\psi$ formation time and finite space-time extent of QGP and recombination from uncorrelated c and $\\bar{c}$ in the medium may account for these contributions ~\\cite{10_zebo}. Among these contributions, the regeneration of $J\/\\psi$ from the recombination of c$\\bar{c}$ plays an important role  to explain the similar suppressions at SPS and RHIC. As the collision energy increases, the regeneration of $J\/\\psi$ from the larger charm quark density would also increase which partly compensates for the additional suppression from color-screening. The regeneration  also expects  a stronger suppression at forward rapidity at RHIC where the charm quark density is lower than that at midrapidity. At LHC, the $J\/\\psi$ is less suppressed in both mid-rapidity and forward rapidity than that at RHIC ~\\cite{LHC_jpsi1,LHC_jpsi2}, which may indicate that the regeneration contribution is dominant in the $J\/\\psi$ production at LHC energies.   Measurements of $J\/\\psi$  in different collision energies at the Solenoidal Tracker at RHIC (STAR)  can give us indications  on the balance of these mechanisms for $J\/\\psi$ production and medium properties. \n\n \nTo qualify the medium effects on the modification of $J\/\\psi$ production, the knowledge of  $J\/\\psi$ cross section and kinematics in $p+p$ collision  is crucial to offer a reference.  During RHIC year 2010, STAR has collected abundant events of Au$+$Au collisions at $\\sqrt{s_{NN}} = 39$ and 62.4 GeV, while the reference data in $p+p$ collisions is not in the schedule of RHIC run plan. As what we did in ref ~\\cite{upsilon_paper}, we study the world-wide data to obtain the $J\/\\psi$ reference at these collision energies.  \n\n\nIn this letter,we report an interpolation of the $p_{T}$-integrated and differential inclusive $J\/\\psi$ cross section in $p+p$ collisions at mid-rapidity to $\\sqrt{s} = $ 39 and 62.4 GeV. We establish a strategy to estimate the inclusive $J\/\\psi$ cross section and kinematics at certain energy points, which makes the calculation of the $J\/\\psi$ nuclear modification factors for any colliding system and energy at RHIC possible. The extrapolation is done in three steps. The first step is an energy interpolation of the existing total $J\/\\psi$ cross section measurements. The second step is the description of the energy evolution of the rapidity distribution. The last step is the evaluation of the energy evolution of the transverse momentum distribution. \n\\section{Available experimental results treatment}\nThe measurements of $J\/\\psi$ hadroproduction have been performed for about forty years. In such a long period, different experimental techniques have been utilized and different input information was available at the time of the measurements. Therefore, comparison of different experimental results on an equal footing needs an update of the published values on several common assumptions and aspects. For example, the branching ratio of $J\/\\psi \\rightarrow e^{+} e^{-}$ (or $\\mu^{+} \\mu^{-}$) have changed with time; the assumed functional forms for the $x_{F}$ and $p_{T}$ shapes, which can be used to infer the total $J\/\\psi$ production, are different in different measurements; and the treatment of the nuclear effects are not homogeneous. In this section, we update all the results with the current best knowledge of branching ratios, kinematics and nuclear effects.\n\nThe cross section for $J\/\\psi$ on a nuclear target is often characterized by a power law: \n\\begin{equation}\n\\label{eq1}\n\\sigma^{pA}_{J\/\\psi} = \\sigma_{J\/\\psi}^{pN} \\times A^{\\alpha} .\n\\end{equation} \nwhere $\\sigma_{pN}^{J\/\\psi}$ is the $J\/\\psi$ proton-nucleon cross section and $\\sigma_{pA}^{J\/\\psi}$ is the corresponding proton-nucleus cross section for a target of atomic mass number $A$. \n\n\\renewcommand{\\floatpagefraction}{0.75}\n\\begin{figure}[htbp]\n\\begin{center}\n\\includegraphics[keepaspectratio,width=0.45\\textwidth]{plotxfa.pdf}\n\\caption{(color online) Measurements of $\\alpha$ as a function of $x_{F}$ by various experiments in different collision energies. The solid curve represents the parametrization discussed in the text.}\n\\label{figure1}\n\\end{center}\n\\end{figure}\nThe dependence of $\\alpha$ on $x_{F}$ measured by NA3 ~\\cite{alpha_na3}, NA50 ~\\cite{alpha_na50}, E772 ~\\cite{alpha_E772}, E886 ~\\cite{alpha_E886} and HERA-B ~\\cite{alpha_HERA-B} is shown in Fig.~\\ref{figure1}, where $x_{F}$ is defined as $x_{F} = 2p_{z}\/\\sqrt{s}$ ($p_{z}$ is longitudinal momentum, along the beam direction.). No significant energy dependence of $\\alpha$ as a function of $x_{F}$ is observed within uncertainties, thus we assume it is independent of the cms-energy ($\\sqrt{s}$). The results of $J\/\\psi$ $\\alpha$ at $x_{F}>0$ can be represented for convenience by the simple parametrization shown as solid line in Fig.~\\ref{figure1}:    $\\alpha(x_{F}) =0.9503e^{-ln2(\\frac{x_{F}}{1.3846})^{1.8067}} $ . If an experiment has published cross sections of $J\/\\psi$ in proton nucleus collisions, Eq.~\\ref{eq1} and the solid curve in Fig.~\\ref{figure1} is applied to obtain the corresponding $J\/\\psi$ cross section in proton nucleon collisions. Some of the experimental measurements are only quoted for a limited phase-space. To obtain the total cross sections, the functional forms of $x_{F}$ and $p_{T}$ spectrum shapes utilized for extrapolation are: $d\\sigma\/dx_{F} = a \\times e^{-ln2(\\frac{x_{F}}{b})^{c}}$,and $d\\sigma\/dp_{T} = a \\times \\frac{p_{T}}{(1+b^{2}p_{T}^{2})^{c}}$ respectively, where a, b, and c are free parameters. As illustrated in Fig.~\\ref{E331_Fig}, these two functional forms describe the $x_{F}$ and $p_{T}$ spectra very well.  All the measurements are updated with the latest branching fractions ($5.961 \\pm 0.032\\%$ for $J\/\\psi \\rightarrow \\mu^{+} + \\mu^{-}$, $5.971 \\pm 0.032\\%$ for $J\/\\psi \\rightarrow e^{+}+e^{-}$) ~\\cite{PDG}. The treated results on $J\/\\psi$ cross sections are listed in Tab.~\\ref{table1}.They show a good overall consistency, even though some of them contradict with each other. For example, the two measurements (E331 and E444) at 20.6 GeV deviate from each other by roughly 2$\\sigma$. The E705 measurement at 23.8 GeV is higher than the UA6 one at 24.3 GeV by more than 2$\\sigma$.\n\n\\renewcommand{\\floatpagefraction}{0.75}\n\\begin{figure*}[htbp]\n\\begin{center}\n\\includegraphics[keepaspectratio,width=0.45\\textwidth]{drawE331pCpT.pdf}\n\\includegraphics[keepaspectratio,width=0.45\\textwidth]{drawE331pCxF.pdf}\n\\caption{(color online) Distributions of  $Ed\\sigma\/dp_{T}$ (left panel) and $Ed\\sigma\/dx_{F}$ (right panel) in $p+C$ collisions at $\\sqrt{s} = 20.6$ GeV measured by E331 collaboration ~\\cite{E331_1}. The solid lines are fit curves with the functional forms described in the text.}\n\\label{E331_Fig}\n\\end{center}\n\\end{figure*}\n\n\\renewcommand{\\floatpagefraction}{0.75}\n\\begin{table*}[htbp]\n\\newcommand{\\tabincell}\n\\centering\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline\nExperiment&Reaction&$\\sqrt{s}$ (GeV)&$\\sigma_{J\/\\psi}$ (nb\/nucleon)\\\\\n\\hline\n\\hline\nCERN-PS ~\\cite{CERN-PS}&p+A &6.8&0.732$\\pm$0.13\\\\\n\\hline\nWA39 ~\\cite{WA39}&p+p&8.7&2.35$\\pm$1.18\\\\\n\\hline\nIHEP ~\\cite{IHEP}&p+Be&11.5&21.63$\\pm$5.64\\\\\n\\hline\nE331 ~\\cite{E331}&p+Be&16.8&85.15$\\pm$21.30\\\\\n\\hline\nNA3 ~\\cite{alpha_na3}&p+Pt&16.8&95.0$\\pm$17.0\\\\\n\\hline\nNA3 ~\\cite{alpha_na3}&p+Pt&19.4&122.6$\\pm$21\\\\\n\\hline\nNA3 ~\\cite{alpha_na3}&p+p&19.4&120$\\pm$22\\\\\n\\hline\nE331 ~\\cite{E331_1}&p+C&20.6&278$\\pm$32.8\\\\\n\\hline\nE444 ~\\cite{E444}&p+C&20.6&176.5$\\pm$23.3\\\\\n\\hline\nE705 ~\\cite{E705}&p+Li&23.8&271.51$\\pm$29.84\\\\\n\\hline\nUA6 ~\\cite{UA6}&p+p&24.3&171.42$\\pm$22.21\\\\\n\\hline\nE288 ~\\cite{E288}&p+Be&27.4&294.12$\\pm$73.53\\\\\n\\hline\nE595 ~\\cite{E595}&p+Fe&27.4&264$\\pm$56\\\\\n\\hline\nNA38\/51 ~\\cite{NA38, NA51}&p+A&29.1&229.5$\\pm$34.4\\\\\n\\hline\nNA50 ~\\cite{alpha_na50}&p+A&29.1&250.7$\\pm$37.6\\\\\n\\hline\nE672\/706 ~\\cite{E672}&pBe&31.6&343.07$\\pm$75.12\\\\\n\\hline\nE771 ~\\cite{E771}&p+Si&38.8&359.1$\\pm$34.2\\\\\n\\hline\nE789 ~\\cite{E789}&p+Au&38.8&415.04$\\pm$100\\\\\n\\hline\nISR ~\\cite{ISR52}&p+p&52&716$\\pm$303\\\\\n\\hline\nPHENIX ~\\cite{PHENIX200}&p+p&200&4000$\\pm$938\\\\\n\\hline\nCDF ~\\cite{CDF1960}&p+$\\bar{p}$&1960&22560$\\pm$3384\\\\\n\\hline\nALICE ~\\cite{ALICE2760}&p+p&2760&29912.6$\\pm$5384.3\\\\\n\\hline\nALICE ~\\cite{ALICE7000}&p+p&7000&54449.4$\\pm$8494\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\caption{(color online) Updated total ($\\sigma_{J\/\\psi}$) production cross sections in proton-induced interactions.}\n\\label{table1}\n\\end{table*} \n\\section{Results}\n\\renewcommand{\\floatpagefraction}{0.75}\n\\begin{figure}[htbp]\n\\begin{center}\n\\includegraphics[keepaspectratio,width=0.45\\textwidth]{crosssectionfit.pdf}\n\\caption{(color online) Energy dependence of inclusive $J\/\\psi$ prodcution cross section. The open circle is the fit from CEM shape.The solid line is a function fit as discuss in the text.}\n\\label{figure2}\n\\end{center}\n\\end{figure}\nThe energy evolution of the total inclusive $J\/\\psi$ production cross section in proton induced interactions is shown in Fig.~\\ref{figure2}. The first approach is to use the predicted shape in the Colour Evaporation Model at Next to Leading Order (NLO) ~\\cite{CEM} to describe the energy dependence of $J\/\\psi$ cross section. The central CT10 parton density set ~\\cite{PDF_CT10} and $\\{m,\\mu_{F}\/m,\\mu_{R}\/m\\}=\\{1.27 (GeV), 2.10, 1.60\\}$ set is utilized in the predicted shape, where m is the charm quark mass, $\\mu_{F}$ is the factorization scale, $\\mu_{R}$ is the renormalization scale. The fit is defined such that the normalization of the NLO CEM calculation is left as a free parameter ($\\alpha$): $\\sigma=\\alpha \\times \\sigma_{CEM}$. The second approach is to use a functional form to describe the cross section energy evolution: $f(\\sqrt{s})=a \\times y_{max}^{d}\\times e^{\\frac{-b}{y_{max}+c}}$, where $y_{max} = ln(\\frac{\\sqrt{s}}{m_{J\/\\psi}})$, a, b, c and d are free parameters. As shown in Fig.~\\ref{figure2}, both approaches can describe the energy evolution trend of $J\/\\psi$ cross section. The $\\chi^{2}\/NDF$ for CEM and functional fit are 90.5\/22 and 76.7\/20, respectively. The large $\\chi^{2}$ mainly comes from three experimental points which contradict with the common trend (E331 and E444 measurements at 20.6 GeV, E705 measurement at 23.8 GeV). If we exclude these three data points and refit the results, the  $\\chi^{2}\/NDF$ for CEM and functional fit are 41.1\/19 and 16.7\/16, respectively. The values extrapolated (without the three bad experimental points) for the $J\/\\psi$ cross sections at $\\sqrt{s} = $ 39 and 62.4 GeV, utilizing the functional form and the NLO CEM based fit are listed in Table~\\ref{table2}.\n\\renewcommand{\\floatpagefraction}{0.75}\n\\begin{table}[htbp]\n\\newcommand{\\tabincell}\n\\centering\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline\n\\multirow{2}{*}{Fit} & \\multicolumn{2}{|c|}{cross section (nb\/nucleon)}\\\\\\cline{2-3}&$\\sqrt{s} = $39 GeV &$\\sqrt{s} = $62.4 GeV\\\\\n\\hline\nNLO CEM& 425$\\pm$20&941$\\pm$42\\\\\n\\hline\nfunction&445$\\pm$30&995$\\pm$66\\\\\n\\hline\nevaluated results&445$\\pm$30$\\pm$20&995$\\pm$66$\\pm$54\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\caption{Extrapolated values of the $J\/\\psi$ production cross section at $\\sqrt{s} =$ 39 and 62.4 GeV. The difference between CEM and function fit has been taken as the systematic uncertainties of the extrapolation.}\n\\label{table2}\n\\end{table} \n\n\\renewcommand{\\floatpagefraction}{0.75}\n\\begin{figure}[htbp]\n\\begin{center}\n\\includegraphics[keepaspectratio,width=0.45\\textwidth]{drawfity.pdf}\n\\caption{(color online) Normalized $J\/\\psi$ production cross section as a function of $y\/y_{max}$. Two function fits are shown: one is Gaussian function, the other one is $\\frac{a}{1-(y\/y_{max})^{2}}e^{-b(ln(\\frac{1+y\/y_{max}}{1-y\/y_{max}}))^{2}}$. The difference between these two curves has been considered as systematic errors.}\n\\label{figure3}\n\\end{center}\n\\end{figure}\n\nThe knowledge of the rapidity dependence of $J\/\\psi$ production at different cms-energies is crucial to obtain a reference for the measurements at mid-rapidity from RHIC. Based on a universal energy scaling behavior in the rapidity distribution obtained at different cms-energies, we explore approaches to the extrapolation of the rapidity distribution. As shown in Fig.~\\ref{figure3}, the y-differential cross sections at different cms-energies have been normalized by the total cross section, and the normalized values are plotted verse $y\/y_{max}$, where $y_{max}$ has been previously defined. Despite of huge cms-energy difference, the treated RHIC ~\\cite{PHENIX200} and LHC ~\\cite{ALICE2760, ALICE7000, LHCb7000} experimental distributions fall into a universal trend, which allows us to perform global fits to all the experimental results with suitable functions. Two functional forms are chosen to do the fits: one is Gaussian function, the other one is  $\\frac{a}{1-(y\/y_{max})^{2}}e^{-b(ln(\\frac{1+y\/y_{max}}{1-y\/y_{max}}))^{2}}$, where a and b are free parameters. Both of them can describe the global distribution very well($\\chi^{2}\/NDF = 10.1\/27$ for gaussian fit, $\\chi^{2}\/NDF = 11.2\/27$ for the other fit). With the extrapolated $J\/\\psi$ cross sections and rapidity distributions, the predicted $J\/\\psi$ cross section times branching ratio at $\\sqrt{s} =$ 39 and 62.4 GeV in mid-rapidity are $Br(e^{+}e^{-})d\\sigma\/dy|_{|y|<1.0} = 9.04 \\pm 0.69$ and $17.74 \\pm 1.06$ nb, respectively.  The uncertainties include statistical and systematic uncertainties. These values are highly consistent with the estimations from CEM model ($8.7 \\pm 4.5$ nb for 39 GeV, $17.4 \\pm 8.0$ for 62.4 GeV).\n\n\\renewcommand{\\floatpagefraction}{0.75}\n\\begin{figure}[htbp]\n\\begin{center}\n\\includegraphics[keepaspectratio,width=0.45\\textwidth]{1.pdf}\n\\caption{(color online) $J\/\\psi$ $z_{T}$ distributions  for available experimental results  from $\\sqrt{s} =$ 10 to 7000 GeV. The solid line is a function fit as discussed in the text.}\n\\label{figure4}\n\\end{center}\n\\end{figure}\n\nThe energy evolution of $J\/\\psi$ transverse momentum distribution are also studied via available experimental measurements from $\\sqrt{s} = $ 10 - 7000 GeV ~\\cite{alpha_na3, E288, E672, E331_1,PHENIX200, ALICE7000, CDF1960, ISR53}. We use part of the world-wide fixed-target data (with only  p, Be, Li, and C respectively) measured with incident protons. In this way, we avoid uncertainties due to ignoring any cold nuclear matter effects on the $J\/\\psi$ transverse momentum distributions. To compare the different experimental measurements at different energies and rapidity domains, as shown in Fig.~\\ref{figure4}, the transverse momentum distributions are normalized by their $p_{T}$-integrated cross sections and plotted verse the $z_{T}$ variable, which is defined as $z_{T} = p_{T}\/<p_{T}>$.  The treated distributions follow a universal trend despite of the different cms-energies and rapidity domains. We can describe the global distributions very well by the following function: $\\frac{1}{d\\sigma\/dy}\\frac{d^{2}\\sigma}{z_{T}dz_{T}dy} =a \\times \\frac{1}{(1+b^{2}z_{T}^{2})^{n}}$ ~\\cite{function}, where $a=2b^{2}(n-1)$, $b=\\Gamma(3\/2)\\Gamma(n-3\/2)\/\\Gamma(n-1)$, and n is the only free parameter.  From the fit, we obtain $n=3.93 \\pm 0.03$ with $\\chi^{2}\/NDF = 143.9\/162$. \n\n\\renewcommand{\\floatpagefraction}{0.75}\n\\begin{figure}[htbp]\n\\begin{center}\n\\includegraphics[keepaspectratio,width=0.45\\textwidth]{ptaverage.pdf}\n\\caption{(color online) $J\/\\psi$ $<p_{T}>$ at mid-rapidity as a function of cms-energy  from $\\sqrt{s} =$ 10 to 7000 GeV. The solid line is a function fit as discussed in the text.}\n\\label{figure5}\n\\end{center}\n\\end{figure}\nWith the universal shape and $<p_{T}>$ information at certain energy and rapidity domain (we focus on mid-rapidity), we can extrapolate the transverse momentum distribution at any cms-energy. Thus the next step is to evaluate the energy evolution of $<p_{T}>$. The $<p_{T}>$ at mid-rapidity as a function of cms-energy from world-wide experiments ~\\cite{alpha_na3, E288, E672, E331_1,PHENIX200, ALICE7000, CDF1960, ISR53, ISR30, ISR52}  is shown in Fig.~\\ref{figure5}. Also, only part of the world-wide fixed-target data (with p, Be, Li, and C respectively) are used to reduce the cold nuclear matter effects. The $<p_{T}>$ versus energy can be fitted by the function form: $f(\\sqrt{s}) = p + q ln\\sqrt{s}$, where p, q are free parameters. The fit parameters are $p=0.0023 \\pm 0.0182$, $q = 0.329 \\pm 0.031$ with $\\chi^{2}\/NDF = 41.1\/15$.  The estimated $<p_{T}>$ from the fit function at $\\sqrt{s} =$ 39 and 62.4 GeV are $1.21 \\pm 0.04$ and $1.36 \\pm 0.04$ GeV\/c, respectively. With these inputs, the transverse momentum distribution at these two cms-energies can be completely determined.  \n\n\\renewcommand{\\floatpagefraction}{0.75}\n\\begin{figure}[htbp]\n\\begin{center}\n\\includegraphics[keepaspectratio,width=0.45\\textwidth]{crosscheck1.pdf}\n\\caption{(color online) The ratios of  $J\/\\psi$ $\\sigma|_{|y|<1.0}$ to $\\sigma_{total}$ as a function of  cms-energy. The open points are the estimations using the two fit functions in Fig.~\\ref{figure3}.}\n\\label{figure6}\n\\end{center}\n\\end{figure}\n\nThere are rare  rapidity distribution measurements in p$+$A collisions at $\\sqrt{s} < 200$. Therefore, the universal energy scaling parameters of rapidity distributions are determined by the measurements at $\\sqrt{s} \\geq 200$ GeV.  Its validity at low energy ($<$200 GeV) range still need to be further investigated. But we do have various  $x_{F}$ distribution measurements of  $J\/\\psi$ in fix-target experiments ~\\cite{IHEP, E331_1, E444, E595, E705, E672, E771, E789}. \nCooperated with the $\\alpha$ verse $x_{F}$ curve in Fig.~\\ref{figure1} and the transverse momentum distributions obtained using the strategy described in the above section, we can evaluate the rapidity distributions via the $x_{F}$ distributions measurements in the fix-target experiments to check the validity of the rapidity interpolation method.  The ratios of  $J\/\\psi$ $\\sigma|_{|y|<1.0}$ to $\\sigma_{total}$, which are calculated utilizing the evaluated rapidity distributions in fix-target experiments, verse cms-energy are shown in Fig.~\\ref{figure6}. The open points plotted in the figure are the estimations using the two fit functions in Fig.~\\ref{figure3}.  In this figure, we can see that our extrapolation strategy also works at low cms-energy range. \n\\section{summary} \nWe study the world-wide data of $J\/\\psi$ production and kinematics  at  $\\sqrt{s} = 6.8-7000$ GeV. We have developed a strategy to interpolate the $J\/\\psi$ cross section, rapidity distribution, and transverse momentum distribution at any cms-energy in  $\\sqrt{s} = 6.8-7000$ GeV. The rapidity and transverse momentum distributions measured in different energies have a universal energy scaling behavior. With this strategy, we predicted that the $J\/\\psi$ cross section times branching ratio at $\\sqrt{s} =$ 39 and 62.4 GeV in mid-rapidity are $Br(e^{+}e^{-})d\\sigma\/dy|_{|y|<1.0} = 9.04 \\pm 0.69$, $17.74 \\pm 1.06$ nb, respectively.\n\n\\section{Acknowledgments}\nWe express our gratitude to the STAR Collaboration and the RCF at BNL for their support. This work was supported in part by the U.S. DOE Office of Science under the contract No. DE-SC0012704; authors Wangmei Zha and Chi Yang are supported in part by the National Natural Science Foundation of China under Grant Nos 11005103 and 11005104, China Postdoctoral Science Foundation funded project, and the Fundamental Research Funds for the Central Universities.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
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+{"text":"\\section{Introduction}\n\n\n\n\n\n\n\n\nFinancial systems consist of many units influencing each other through interactions of different nature and scale, thereby exhibiting rather complex dynamics. The time series of the system observables, which capture these dynamics, are functions with pronounced random components. Hence, one requires convenient statistical tools to infer both the behavior of individual units and the overall performance of the financial system. In this aspect, a lot of effort has been put into developing tools for studying the pairwise relationships between assets as they provide direct estimate for the intensity of the mutual interactions. Besides this, the pairwise relationships also have particular practical relevance in construction of optimal portfolios and efficient asset allocations. As a result, various statistical approaches have been applied to plethora of financial markets, among which, equity prices at stock markets~\\cite{plerou1999universal, mantegna1999hierarchical}, currencies at foreign exchanges~\\cite{mizuno2006correlation, naylor2007topology} and even market indexes~\\cite{eryiugit2009network}.\n\nThe majority of these studies mainly focus on relationships based on \\textit{simultaneous} observations of the logarithmic returns of the examined assets. The results obtained from such studies are able to explain the mutual interactions only when the time needed for spreading of the news across the financial market is negligible in comparison to the period of calculation of log returns. The relevance of the results obtained in such situations is backed by the efficient market hypothesis. The hypothesis states that the current price of any asset traded in the market incorporates all relevant information and no  prediction regarding the future evolution would be profitable without taking additional risks~\\cite{malkiel1970efficient}. Numerous studies confirm that in practice this usually holds when one considers log returns on daily or longer time scale. When shorter time scales are considered, such as one-minute log returns, one might expect significant delay effects. To address this issue, one usually resorts to the usage of \\textit{lagged} approaches. These approaches give estimates for the relationship between the observations of the two quantities of interest which are apart from each other for certain period ~\\cite{kawaller1987temporal,lo1990contrarian}. The variable whose values are delayed is called the \\textit{lagger}, whereas the other one is the \\textit{leader}. \n\n\nResearch on these lead-lag relationships predominantly focuses on correlation analyses of dynamics of stock prices or market indexes~\\cite{huth2014high,xia2018emergence,valeyre2019emergence}\\footnote{We note that the ordinary correlations are special case of the lagged ones, and are called zero-lagged or contemporary correlations in order to distinguish them from the latter.}. To the best of our knowledge, the examination of the lead-lag relationships in a foreign exchange market remains largely unexplored. To bridge this gap, here we study the relationships between one-minute log returns on exchange rates with a lag of one minute. We focus on returns lagged for one minute due to three reasons. First, even though past research suggests that the lead-lag relationships can be felt in the price of the lagger even up to 45 minutes later, as trading becomes more and more automatic, the lagging period has decreased dramatically to typical value measured in seconds~\\cite{huth2014high}, or even milliseconds~\\cite{dao2018ultra}. Second, the foreign exchange is known to be a very liquid one, with most of the transactions being ordered automatically and one can not expect significant lags that span longer than one minute. This reasoning was supported by studying lagged effects with two-minute lags. In this case, we found that although such lagged relationships might appear sporadically, the pattern is not persistent as it is when one-minute lags are considered.\n\nWe consider three different approaches to estimate the lead-lag relationships: i) lagged correlations, ii) lagged partial correlations and iii) Granger causality. The lagged correlations provide a direct estimate for the intensity of linear lead-lag relationship between two exchange rates. The lagged partial correlations extend this approach by eliminating the possible serial autocorrelation of the lagger and the contemporaneous correlation of both rates under study. Finally, the Granger causality~\\cite{granger1969investigating} statistically tests for possible causal relationship between two exchange rates by considering the predictive potential by using past returns. We find that, with few exceptions, the lagged correlations between exchange rate pairs which relate currencies do not pass tests of statistical significance, which is in accordance with the efficient market hypothesis. However, there are many statistically significant lagged correlations, particularly when one considers rates which involve stock market indexes. In these correlation coefficients, the stock market indexes, which are known to have slower dynamics than the currency exchange raters, appear as leaders. Interestingly, this is opposite to previous findings which suggest that assets with faster dynamics behave as leaders \\cite{kawaller1987temporal, lo1990contrarian, toth2006increasing}. The partial correlation analysis further confirmed our findings. The Granger causality analysis, in addition to providing a test for the findings in the correlation analysis, revealed that the leaders in the lead-lag relationships also increase the predictive ability for the determination of future returns of the lagger. Based on these observations one could believe that the information from the leader towards the lagger does not transfer simultaneously, but it can be seen as a process that stretches for a certain period. \n\n\nOut of the statistically significant pairwise correlations and causality relationships we obtained matrices, which can be regarded as directed networks that describe the effect of one asset towards another. To infer the most influential leaders, in the spirit of~\\cite{brin1998anatomy}, we apply the PageRank algorithm. PageRank is a widely used procedure that has been applied in original or modified form to various domains \\cite{ white2003algorithms, ma2008bringing, falagas2008comparison, radicchi2011best}. The resulting ranking allows us to infer the major sources of information spillover in the studied financial network.\n\n\n\nThe outline of the paper is as follows. In Section 2 we introduce the methods applied for the estimation of the lagged correlations, lagged partial correlations and causality, as well as the generation of the resulting networks. Section 3 presents the empirical results. The last section summarizes our findings and provides directions for future research.\n\n\n\n\n\n\n\n\n\n\\section{\\label{sec:methods}Methods}\n\n\\subsection{Lagged correlations\\label{Lagged_corr_theory}}\n\nThe dynamics of the prices of financial assets are known to be non-stationary. Hence, one can not simply use them to examine the relationship between different assets. Nevertheless, the logarithmic return,\n\\begin{equation}\n    r_n = \\log p(t_{n+1}) - \\log p (t_{n}),\n    \\label{eq:log_ret_def}\n\\end{equation}\nwhere the price $p$ is assumed to be observed at discrete moments $t_n$, is usually assumed to be weakly stationary~\\cite{fan2017elements}. This property of log returns makes them more appropriate quantities for uncovering statistical relationships between assets.\n\nAssuming that we have observations of the log returns $r_i$ and $r_j$ of two prices at the series of discrete moments $t_n$, the $\\tau$-lagged covariance between them is given by\n\\begin{equation}\nC_{i,j}(\\tau) = \\langle \\left[r_i\\left(t_n\\right) -  \\langle r_i \\rangle \\right] \\left[r_j\\left(t_n + \\tau \\right) -  \\langle r_j \\rangle \\right] \\rangle,\n\\label{eq:lag_cov_def}\n\\end{equation}\nwhere the angular brackets denote averaging. We emphasize that one should keep the order of indices since in this notation the first index is the leader, while the second denotes the lagger. In general, the lagged covariances are not commutative $C_{i,j}(\\tau) \\neq C_{j,i}(\\tau)$, in contrast to the ordinary, zero-lag covariances. Since the log return of one price might typically deviate more than that of the other one, a more appropriate quantity is the correlation coefficient\n\\begin{equation}\n\\rho_{i,j}(\\tau) = \\frac{C_{i,j}(\\tau)}{\\sqrt{C_{i,i}(0) C_{j,j}(0)}} = \\frac{C_{i,j}(\\tau)}{\\sigma_{i} \\sigma_{j}}.\n\\end{equation}\nIn the last expression the notation is simplified by using the standard deviation $\\sigma_i = \\sqrt{C_{i,i}}$.\n\n\n\\subsection{Lagged partial correlations \\label{Lagged_partial_theory}}\n\nIn reality, the existence of lagged correlation can be due to one exchange rate being the driving force of the other, or due to the combination of mutual contemporaneous correlation and lagged autocorrelation. In order to isolate this potential effect, we calculate the partial correlation coefficient. For three random variables $X$, $Y$, and $Z$ with respective pairwise correlations $\\rho(X,Y)$, $\\rho(Y,Z)$, and $\\rho(X,Z)$, the partial correlation between $X$ and $Y$ with $Z$ considered known, is defined as\n\\begin{equation}\n    \\rho(X,Y|Z) = \\frac{\\rho(X,Y) - \\rho(X,Z)\\rho(Y,Z)}{\\sqrt{[1-\\rho^2(X,Z)][1-\\rho^2(Y,Z)]}}.\n\\end{equation}\nTherefore, when the current return of the lagger $j$ has the role of known variable, the correlation between its next value and current return on the leader $i$ is\n\\begin{equation}\n    \\rho_{i,j}^P(\\tau) = \\frac{\\rho_{i,j}(\\tau) - \\rho_{i,j}(0)\\rho_{j,j}(\\tau)}{\\sqrt{[1-\\rho_{i,j}^2(0)][1-\\rho_{j,j}^2(\\tau)]}}.\n\\end{equation}\nThe last expression is useful when one has calculated already the values of the ordinary correlations and thus would immediately obtain the partial one. Another approach for calculation of the partial correlation is based on linear regression~\\cite{baba2004partial}. It can be described as follows. Let $Z$ be the variable whose influence has to be removed, the two other variables being $X$ and $Y$, and their best estimates by observing $Z$ being  $\\hat{X}_Z$ and $\\hat{Y}_Z$ respectively. The respective partial correlation is then the ordinary correlation between the residuals $r_X = X-\\hat{X}_Z$ and $r_Y = Y-\\hat{Y}_Z$, given by\n\\begin{equation}\n    \\rho(X,Y|Z) = \\rho(X-\\hat{X}_Z, Y-\\hat{Y}_Z).\n\\end{equation}\nThis approach allows for easier calculation of the statistical significance of the estimated partial correlation, and as such has been widely applied in studies of relationships between currencies and stocks \\cite{kenett2010dominating, kenett2015partial, mai2018currency}.\n\n\n\\subsection{Lagged correlation networks \\label{Lagged_net_theory}}\n\n\nAs the lagged correlations are not commutative (in contrast to the contemporaneous correlations), the resulting network is directed. In order to keep the strength of influence we create a weighted network where the direction is from the lagger towards the leader with weight that is equal to the absolute value of the lagged correlation coefficient $w_{j,i} = |\\rho_{j,i}|$. We consider absolute values since the sign of the correlation coefficient denotes only the direction of change of the exchange rate. Typically, extraction of the core of financial correlation networks is performed with the Minimal Spanning Tree (MST) sub-graph procedure~\\cite{mantegna1999hierarchical} or the Planar Maximally Filtered Graph (PMFG)~\\cite{kenett2010dominating, tumminello2005tool}. Because the obtained statistically validated lagged correlation networks are rather sparse, we may instead use the PageRank algorithm in order to determine the most influential leaders~\\cite{brin1998anatomy}. The PageRank algorithm was originally used to rank web pages, by assuming that pages with more incoming links from others are more important. A particular feature which favors PageRank above other ranking procedures is that it intrinsically assigns higher weights to links that originate from important nodes. \n\nThe application of PageRank first involves creating a row stochastic matrix from the weighted network with elements\n\\begin{equation}\n    a_{j,i} = \\frac{w_{j,i}}{\\sum_k w_{j,k}}.\n\\end{equation}\nThe last matrix can be seen as a Markov chain transition matrix. In terms of Markov chain theory, the element $a_{j,i}$ corresponds to the probability of jumping from state $j$ to $i$. For such matrices arising from correlation networks, the bigger values within $j$-th row correspond to the columns $i$ associated with rates from which $j$ obtains larger impact. As such, the resulting rankings should provide information regarding the market news spreading among the the exchange rates included in the analysis. Higher ranking should correspond to exchange rates whose changes in returns will also have a higher overall impact in the overall system dynamics.\n\n\n\\subsection{Granger causality \\label{Granger_theory}}\n\n\n\n\n\nThe potential influence of the return on certain exchange rate on future returns on other exchange rates can be assessed by applying the causality analysis in the sense of Granger~\\cite{granger1969investigating}. WIthin this framework, cause and effect relationship between a pair of two dynamical variables exists if knowledge of past values of one of them improves the prediction of the future of the other.\nGranger causality is estimated as follows. Consider the linear regression of the nearest future value of some variable $x$ from its past $p$ terms\n\\begin{equation}\n    x_{n+1} = \\sum_{k=0}^{p-1} \\alpha_k x_{n-k} + \\varepsilon_n,\n    \\label{eq:self_regression}\n\\end{equation}\nwhere $\\varepsilon_n$ is the regression residual. The weights $\\alpha_k$ are such that the residual variance $\\sigma_{\\varepsilon}^2$ is minimal, so the linear regression is optimal. Now, make an optimal combined regression by using $q$ past values of the variable $y$ as well\n\\begin{equation}\n    x_{n+1} = \\sum_{k=0}^{p-1} \\alpha_k x_{n-l} + \\sum_{l=0}^{q-1} \\beta_l y_{n-l} + \\eta_n.\n\\end{equation}\nIf some of the parameters $\\beta_l$ are nonzero with certain statistical significance, which in turn leads to reduced variance $\\sigma_{\\eta}^2 < \\sigma_{\\varepsilon}^2$, then it is said that $y$ Granger causes $x$. If $x$ also Granger causes $y$ than one has a feedback system. The regression depth $q$ (and $p$ as well) depends on the problem at hand. We consider only one past step, as it has been observed that in foreign exchange markets the serial autocorrelation quickly vanishes.\nAnother reason for this choice is that, as it will be seen in the Data Section, due to the presence of gaps and periods of repeating identical values in the studied time series, there is a much smaller number of consecutive nonzero returns than the one required for a meaningful regression with more explanatory variables.\nTherefore, our Granger causality setting for the effect of exchange rate $i$ on exchange rate $j$ is described as\n\\begin{equation}\n    r_j(t_{n+1}) = \\alpha_{i,j} r_j(t_n) + \\beta_{i,j} r_i(t_n) + \\gamma_{i,j} + \\eta_{i,j,n}.\n    \\label{eq:regression_def}\n\\end{equation}\nIn the last equation $\\alpha_{i,j}$ estimates the self driving force, $\\beta_{i,j}$ measures the influence of the return of exchange rate $r_i$, $\\gamma_{i,j}$ accounts for possible nonzero mean return of the rate $r_j$, and $\\eta_{i,j,n}$ is the noise term. When $\\beta_{i,j}$ is zero, then $r_j$ is not caused by $r_i$, otherwise there is causal relationship from returns on rate $i$ to $j$. \n\n\n\nThe quality of a regression model is usually estimated in terms of the mean of the squared residuals. Concretely, let us denote with $S_0$ the variance of the dependent variable. Correspondingly, let $S$ be the mean of the square of the residuals obtained from regression of the kinds of Eqs. (\\ref{eq:self_regression}) or (\\ref{eq:regression_def}). The estimate of the quality of the model is then given by the coefficient of determination \n\\begin{equation}\n    R^2 = 1 - \\frac{S}{S_0}.\n\\end{equation}\nWhen one compares two regression models, nested into each other, one needs a way to compare them. Because the one with more parameters is expected to have better performance than the other, one needs to know whether it significantly outperforms the simpler peer. The respective tool for such estimates is the $F$-test. Consider a simpler regression model with $p_1$ parameters which result in residual sum of squares $S_1$, and its bigger alternative with $p_2$ parameters and residual sum of squares $S_2$ , applied on the same $N$ data items. Then, if both have the same quality in the null hypothesis, the respective $F$-test statistic\n\\begin{equation}\n    F = \\frac{\\frac{S_1-S_2}{p_2-p_1}}{\\frac{S_2}{N-p_2}},\n\\end{equation}\nhas $F$ distribution with $(p_2-p_1,N-p_2)$ degrees of freedom.\n\nWe note that a more general approach can be obtained with the vector autoregression model (VAR)~\\cite{lutkepohl2005new}. VAR is a generalization of the previously explained procedure, where the log return $r_j (t_{n+1})$ is regressed with more than one, or even all other returns. Unfortunately, we cannot apply this procedure on the data under study, because many exchange rates have either zero return, or missing values at different moments, and the regression would then be meaningless.\n\n\n\n\n\n\n\n\n\n\n\n\\section{Data}\n\n\n\\subsection{Data source}\n\n\n\n\n\n\n\nWe use data gathered from \\url{www.histdata.com}\\footnote{All studied data is made freely available by its publisher.}. The dataset contains highly frequent one-minute exchange rate values only on the bid quotes, which is a slight drawback since generally as price of an asset is considered the mean of the respective bid and ask values. Even though the bid is not simply a drifted version of the mean price, it can serve in the analysis as an estimate for the value from the point of view of the brokers.\n\n\nWe extract exchange rate data for 66 pairs among 33 assets consisting of 19 currencies, 10 indexes of major stock markets, 2 oil types, and gold and silver. The list of assets together with their abbreviations is given in Table~\\ref{tab:Abbreviations}.\n\n\n\n\n\\begin{table}[h!]\n  \\begin{center}\n    \\caption{List of studied assets}\n   \\label{tab:Abbreviations}\n    \\begin{tabular}{l|l}\n    \\textbf{Currencies} \\\\\n      \\hline      \n     AUD -- Australian Dollar & MXN -- Mexican Peso\\\\\n     CAD -- Canadian Dollar & NOK -- Norwegian Krone\\\\\n     CHF -- Swiss Franc & NZD -- New Zealand Dollar\\\\\n     CZK -- Czech Koruna & PLN -- Polish Zloty\\\\\n     DKK -- Danish Krone & SEK -- Swedish Krona\\\\\n     EUR -- EURO & SGD -- Singapore Dollar\\\\\n     GBP -- British Pound & TRY -- Turkish Lira\\\\\n     HKD -- Hong Kong Dollar & USD -- US Dollar\\\\\n     HUF -- Hungarian Forint & ZAR -- South African Rand\\\\\n     JPY Japanese Yen \\\\\n     \\hline      \n     \\textbf{Indexes} \\\\\n     \\hline      \n     AUX -- ASX 200 & JPX -- Nikkei Index 400 \\\\\n     ETX -- EUROSTOXX 50 & NSX -- NASDAQ 100 \\\\\n     FRX -- CAC 40 & SPX -- S\\&P 500 \\\\\n     GRX -- DAX 30 & UDX -- Dollar Index \\\\\n     HKX -- HAN SENG & UKX -- FTSE 100 \\\\\n     \\hline      \n     \\textbf{Commodities} \\\\\n     \\hline      \n\t BCO -- Brent Crude Oil & XAG -- Silver \\\\\n     WTI -- West Texas Intermediate & XAU -- Gold \\\\\n     \\hline\n  \n    \\end{tabular}\n  \\end{center}\n\\end{table}\n\n\n\n\n\n\n \n\n\\subsection{\\label{sec:dataProc}Data preprocessing}\n\nIn spite of the foreign exchange market being highly dynamic, the data which we study includes several cases where a rate has the same value in few consecutive minutes. This means that the respective one-minute returns are zero. In addition, there are gaps with missing data in the time series. We filter out the data from such situations and examine four different lead-lag scenarios, as illustrated in Fig.~\\ref{fig:case-studies}\n One can think of the correlations and causal relationships studied in these scenarios as conditional ones, because the calculations are conditioned on the presence of nonzero return on certain variables. In the first scenario, only the leader is restricted to have nonzero return, while the lagger is allowed to be dormant in the following minute. In this aspect, we calculate the lagged correlation only from pairs in which the exchange rate which precedes has only nonzero returns. If in such case one obtains statistically significant correlation, it should mean that, although sometimes the lagger might retain its value in the following minute, when it modifies, the change would likely have the same sign and similar size as the leader had in the past minute. We argue that this is due to market information flowing from the leader towards the lagger. In addition, the statistically significant correlation might represent a \\textit{potential statistical arbitrage}, since after observing the return of the leader, fast-profit seekers could take the appropriate position on the lagger. We consider this as potential arbitrage, because even though the lagger's exchange rate would more likely have the right direction of change, the expectation of the profit might not compensate the transaction costs. Obviously, a detailed study involving also data on the transaction costs and ask quotes could reveal whether these lead-lag relationships are indeed profitable. \n\n\\begin{figure*}[t!]\n\\begin{adjustwidth}{0in}{0in}\n\\includegraphics[width=12.7cm]{lagged_correlations_fig.eps}\n\\caption{Visual representation of the four scenarios of restrictions on the values of the log returns and in which calculations are they used (bottom lines). In all four cases the left square denotes the leader, while the right one(s) correspond to the lagger. Full square denotes that only observations with nonzero value is considered, while empty one means that the log return which is used might have zero value as well.\n\\label{fig:case-studies}}\n\\end{adjustwidth}\n\\end{figure*}\n\nThe second case corresponds to the correlations obtained from the observations of simultaneous nonzero returns on the leader and the lagger in the next minute. Under such circumstances, one has an estimate on how much of the change of the price of the lagger, which certainly occurred, is possibly influenced by the previous return on the leader. \n\nIn order to calculate the partial correlation, in the third scenario we further specify the lagger to have nonzero return at the same minute as the leader. Such restriction is necessary for removal of the correlation between simultaneous returns of the leader and the lagger and the lagged autocorrelation of the latter, as potential contributors. This scenario was also used for determination of causal relationships.\n\nIn the last case we use observations of nonzero returns on the leader and lagger at the same minute, and apply it solely for identifying Granger causality. Under this scenario, one checks for predictability potential based on linear regression when one has two signals -- simultaneous observations of nonzero values of the two relevant returns.\n\nThe collected data spans from January 2016 until December 2018. For computational reasons we calculated the quantities of interest for each of the 36 months separately. In representing the rankings, the averages of the monthly results are given. \n\n\n Moreover, we point out that even though log returns are usually assumed to be weakly stationary, the empirical data may not exhibit such properties. This might be especially true for foreign exchange markets where the assets display extremely high dynamics and volatility. To statistically test whether the data used here is appropriate for studying lead-lag relationships that we are interested in, we utilize the Dickey-Fuller test~\\cite{dickey1979distribution}. This is a standard test used in time series analysis for examining the weak stationarity of a series. Under the null hypothesis, the test assumes that the time series under study has unit root. More precisely, we have applied augmented version of the test \\cite{wooldridge2015introductory}, where the difference of consecutive returns $\\Delta r_i(t_n) = r_i(t_n) - r_i(t_{n-1})$ is regressed with the past return $r_i(t_{n-1})$, and the previous difference $\\Delta r_i(t_{n-1})$. We could not examine lags of the difference of log returns of higher order because the presence of gaps in the data would decrease the number of samples where chains of consecutive differences are available. Correspondingly, this would weaken the statistical power of the test. Also, possible presence of time trend in the series was accounted for. To sum up, we have considered the following regression model\n \\begin{equation}\n     \\Delta r_i(t_n) = \\alpha + \\delta t_n + \\theta r_i(t_{n-1}) + \\gamma_1 \\Delta r_i(t_{n-1}) + \\epsilon_n,\n \\end{equation}\nwhere $\\alpha$, $\\delta$, $\\theta$, and $\\gamma_1$ are coefficients, and $\\epsilon_n$ is the error term. Under the null hypothesis, $\\theta=0$ suggests presence of unit root.\n \n The Dickey Fuller test statistic calculated for each month in 2016 separately, and for all exchange rates is reported in the Table \\ref{tab:DFTestStat}. Because the critical value of the test statistic for level 0.01 is -3.96 \\cite{fuller2009introduction}, one can observe that in each case the null hypothesis of presence of unit root can be rejected with high confidence. Accordingly, one can consider that the time series of log returns are weakly stationary.\n \n \n \\begin{table}[h!]\n\\begin{minipage}{\\textwidth}\n  \\begin{center}\n    \\caption{Dickey-Fuller test  statistic (DFTS) for studied exchange rates in 2016}\n    \n   \\label{tab:DFTestStat}\n    \\begin{tabular}{|l|r||l|r||l|r|}\n          \\hline      \n    \\textbf{Rate} & \\textbf{DFTS} & \\textbf{Rate} & \\textbf{DFTS} & \\textbf{Rate} & \\textbf{DFTS}\\\\\n      \\hline      \n     AUD\/CAD & -125.6 & EUR\/SEK & -113.8 & USD\/CAD & -121.8 \\\\ \n     \\hline\nAUD\/CHF & -122.1 & EUR\/TRY & -117.0 & USD\/CHF & -122.5 \\\\ \n     \\hline\nAUD\/JPY & -121.4 & EUR\/USD & -131.0 & USD\/CZK & -118.8 \\\\ \n     \\hline\nAUD\/NZD & -126.3 & FRX\/EUR & -89.9 & USD\/DKK & -122.1 \\\\ \n     \\hline\nAUD\/USD & -122.0 & GBP\/AUD & -123.8 & USD\/HKD & -49.2 \\\\ \n     \\hline\nAUX\/AUD & -79.8 & GBP\/CAD & -123.7 & USD\/HUF & -111.1 \\\\ \n     \\hline\nBCO\/USD & -96.4 & GBP\/CHF & -123.5 & USD\/JPY & -117.4 \\\\ \n     \\hline\nCAD\/CHF & -122.6 & GBP\/JPY & -118.7 & USD\/MXN & -113.2 \\\\ \n     \\hline\nCAD\/JPY & -120.4 & GBP\/NZD & -123.2 & USD\/NOK & -118.3 \\\\ \n     \\hline\nCHF\/JPY & -118.5 & GBP\/USD & -120.5 & USD\/PLN & -116.3 \\\\ \n     \\hline\nETX\/EUR & -54.7 & GRX\/EUR & -92.5 & USD\/SEK & -125.5 \\\\ \n     \\hline\nEUR\/AUD & -119.0 & HKX\/HKD & -83.8 & USD\/SGD & -116.4 \\\\ \n     \\hline\nEUR\/CAD & -122.0 & JPX\/JPY & -68.9 & USD\/TRY & -103.1 \\\\ \n     \\hline\nEUR\/CHF & -121.4 & NSX\/USD & -105.4 & USD\/ZAR & -111.4 \\\\ \n     \\hline\nEUR\/CZK & -39.6 & NZD\/CAD & -123.7 & WTI\/USD & -98.4 \\\\ \n     \\hline\nEUR\/DKK & -28.1 & NZD\/CHF & -122.6 & XAG\/USD & -108.9 \\\\ \n     \\hline\nEUR\/GBP & -122.6 & NZD\/JPY & -121.1 & XAU\/AUD & -117.4 \\\\ \n     \\hline\nEUR\/HUF & -91.2 & NZD\/USD & -121.0 & XAU\/CHF & -118.9 \\\\ \n     \\hline\nEUR\/JPY & -117.7 & SGD\/JPY & -118.8 & XAU\/EUR & -118.7 \\\\ \n     \\hline\nEUR\/NOK & -121.7 & SPX\/USD & -75.7 & XAU\/GBP & -102.1 \\\\ \n     \\hline\nEUR\/NZD & -122.1 & UDX\/USD & -105.9 & XAU\/USD & -117.4 \\\\ \n     \\hline\nEUR\/PLN & -101.8 & UKX\/GBP & -89.9 & ZAR\/JPY & -110.2 \\\\ \n     \\hline\n    \\end{tabular}\n  \\end{center}\n  \\end{minipage}\n\\end{table}\n\n \n \n\n\nFinally, we point that here we have considered exchange rates as assets, instead of using values of currencies or commodities. To obtain the value of a currency one should quote it in terms of another one, taken as base, by using the appropriate exchange rate~\\cite{basnarkov2019correlation}. However, one does not always have a direct exchange rate between the appropriate base and any other currency in this market. In such cases two or more exchange rates might be needed for determination of the value of the asset. When many gaps in the data are present, or when some returns are inactive for certain period, getting such values can be problematic. Besides this, it has been found that the choice of basic currency can result in nontrivial difference in the obtained correlations~\\cite{keskin2011topology, basnarkov2019correlation}. \n\n\n\n\n\\section{\\label{sec:results}Results and discussion}\n\n\\subsection{Statistical significance of results}\n\n\nTo determine statistical significance of the results, we applied the Bonferroni threshold correction. The Bonferroni correction is standardly used for handling situations when one makes multiple tests simultaneously, as is the case with the overall significance of the correlation matrix~\\cite{tumminello2011statistically, curme2015emergence}. For correlations between each of the $N$ assets the Bonferroni correction is $N \\cdot N$. Thus, the appropriate threshold for $p$ value at level $0.01$, which is widely applied in the literature~\\cite{curme2015emergence}, is $0.01 \/ (66 \\cdot 66)$. This threshold was applied for the two types of lagged correlations and for the Granger causality relationships.\n\n\n\n\\subsection{Lagged correlations}\n\nAs it was elaborated in Section~\\ref{Lagged_corr_theory}, the lagged correlations quantify the relationship between series of one-minute log returns of two exchange rates with one of them trailing the other for a unit period. The existence of statistically significant correlation implies that the one with preceding returns presumably influences the other. We calculated such lagged correlations for all pairs in the dataset and summarized them in the respective $66\\times 66$ correlation matrix. Due to the very intensive trading of the currencies, and highly dynamical nature of their values, most of the lagged correlations between exchange rates involving currencies do not pass the statistical significance tests. However, there are many nonzero terms in the lagged correlation matrix, notably those involving stock market indexes. \nAs expected, the correlation matrix is asymmetrical because the influence is not identical in both directions. Out of this lagged correlation matrix we create a directed network where a link from node $j$ to $i$ exists if the rate $i$ has statistically significant correlation with $j$, and where $i$ is the leader.\n\n In the second, third and fourth columns of Table~\\ref{tab:Ranking} we present the ten most influential exchange rates on average, according to the PageRank for the three years under consideration and the three lagged correlation scenarios respectively. The results appear rather surprising, since market indexes with slower dynamics are put on top. This is opposite to previous findings where it was discovered that the more liquid assets lead the others~\\cite{kawaller1987temporal, lo1990contrarian, toth2006increasing}.  In particular, the first four entries, all corresponding to such market indexes, appear rather high on the rank list nearly every month. The following ones, such as WTI oil exhibit varying influence in the lagged correlation matrix and are ranked rather differently in different months. The reason that the market indexes are most influential could be the fact that their price dynamics is slower and every change of their value incorporates some market news.\n\n\\begin{sidewaystable}[h!]\n  \\begin{center}\n    \\caption{Top ten most influential exchange rates in five cases: LC1, LC2 and LC3 -- lagged correlations in scenarios 1, 2, and 3 respectively; LPC -- most influential rates in lagged partial correlations; C1 and C2 -- ranking of Granger causality significance in scenarios 3 and 4 respectively.}\n   \\label{tab:Ranking}\n    \\begin{tabular}{c|c|c|c|c|c|c}\n    \\textbf{Rank} & \\textbf{LC1} & \\textbf{LC2} & \\textbf{LC3} & \\textbf{LPC} & \\textbf{C1} & \\textbf{C2}\\\\\n      \\hline      \n     1 & ETX\/EUR & ETX\/EUR & ETX\/EUR & ETX\/EUR & ETX\/EUR & ETX\/EUR\\\\\n     2 & JPX\/JPY & JPX\/JPY & JPX\/JPY & JPX\/JPY & JPX\/JPY & JPX\/JPY\\\\\n     3 & AUX\/AUD & AUX\/AUD & AUX\/AUD & SPX\/USD & SPX\/USD & SPX\/USD\\\\\n     4 & SPX\/USD & SPX\/USD & SPX\/USD & AUX\/AUD & AUX\/AUD & AUX\/AUD\\\\\n     5 & USD\/CZK & USD\/CZK & USD\/CZK & WTI\/USD & USD\/CZK & USD\/CZK\\\\\n     6 & WTI\/USD & WTI\/USD & WTI\/USD & USD\/CZK & WTI\/USD & WTI\/USD\\\\\n     7 & EUR\/USD & USD\/HUF & USD\/HUF & NZD\/USD & AUD\/USD & AUD\/USD\\\\\n     8 & USD\/HUF & ZAR\/JPY & ZAR\/JPY & AUD\/USD & NZD\/USD & UDX\/USD\\\\\n     9 & ZAR\/JPY & EUR\/USD & AUD\/USD & USD\/DKK & UDX\/USD & NZD\/USD\\\\\n     10 & UDX\/USD & UDX\/USD & EUR\/USD & BCO\/USD & BCO\/USD & USD\/DKK\\\\\n     \n      \\hline\n    \\end{tabular}\n  \\end{center}\n\\end{sidewaystable}\n\n\n\n\n\n\n\n\nTo validate whether some correlations are not a random result, but simply correspond to low influence, we also look at the results without the Bonferroni correction. The results for the statistically significant lagged correlations, which pass the threshold $p=0.01$ in each of the studied 36 months are displayed in Table~\\ref{tab:PersistentCorr}. These results correspond to the first three scenarios. One can note that mostly the same correlations are present in the three situations. Only in few cases some additional correlation pairs appear when either the return in the leader is nonzero, or both the leader and the lagger in the next minute have nonzero returns. Although accidental emergence of correlation among $N$ uncorrelated time series with such significance threshold would not be a surprise, its appearance in 36 months consecutively suggests that some relationships between all such pairs really exist. From the same table one can notice some interesting patterns. First, dominant leaders are the same four stock market indexes AUX, ETX, JPX, and SPX, that appear as top sources of information spillover as detected with the PageRank. They influence the other indexes FRX, GRX, HKX, NSX, UKX and UDX. It is interesting that the other US-based index NSX is not as influential as the SPX. In addition, one can note that as laggers appear many exchange rates involving the Japanese Yen. When the above mentioned leading market indexes gain value, the Yen seems to react by weakening with respect to other assets. Another intriguing observation is the lowering of the value of gold ounce, XAU, quoted in AUD, when these indexes rise. One can also note that rise or fall of the MXN with respect to the US dollar, is followed by similar behavior of the TRY. These two minor currencies have been also found to be mutually related in a previous study \\cite{basnarkov2019correlation}. Finally, it is interesting that the fall of the MXN with respect to the USD, is followed by similar behavior of the ZAR with respect to the JPY.\n\n\n\n\n\\begin{table}[h!]\n\\begin{minipage}{\\textwidth}\n  \\begin{center}\n    \\caption{Persistent statistically significant correlations.}\n   \\label{tab:PersistentCorr}\n    \\begin{tabular}{l|l}\n    \\textbf{Leader} & \\textbf{Positively correlated lagger} \\\\\n      \\hline      \n     AUX\/AUD & AUD\/JPY, CAD\/CHF, CAD\/JPY, FRX\/EUR, \\\\ & GRX\/EUR, HKX\/HKD, NSX\/USD, NDZ\/JPY, \\\\ & SGD\/JPY, SPX\/USD\\footnote{\\label{ftnt:L_or_LF}Persistent correlation when either the leader, or both the leader and the lagger have nonzero returns (scenarios 1 and 2).}, UDX\/USD, UKX\/GBP,\\\\ & USD\/JPY\\\\\n     \\hline    \n     ETX\/EUR & AUD\/JPY, CAD\/JPY, FRX\/EUR, GBP\/JPY, \\\\ & GRX\/EUR, HKX\/HKD, NSX\/USD, NDZ\/JPY,\\\\ \n     & SGD\/JPY, SPX\/USD, UDX\/USD, UKX\/GBP,\\\\ & USD\/JPY\\\\\n     \\hline    \n     JPX\/JPY & AUD\/JPY, CAD\/CHF, CAD\/JPY, CHF\/JPY\\footref{ftnt:L_or_LF}, \\\\ & \n     EUR\/JPY, FRX\/EUR, GBP\/JPY, GRX\/EUR,\\\\ & HKX\/HKD, NSX\/USD, NDZ\/JPY, SGD\/JPY, \\\\ & SPX\/USD\\footref{ftnt:L_or_LF}, UDX\/USD, UKX\/GBP, USD\/JPY\\\\\n     \\hline    \n     SPX\/USD & AUD\/JPY, CAD\/JPY, SGD\/JPY\\footref{ftnt:L_or_LF}\\\\\n     \\hline\n     USD\/MXN & USD\/TRY\\\\\n     \\hline\n\\textbf{Leader} & \\textbf{Negatively correlated lagger}\\\\\n      \\hline\n     AUD\/USD & USD\/TRY \\footnote{Persistent correlation when only the leader has nonzero return (scenario 1). \\label{ftnt:L}}\\\\\n      \\hline\n     ETX\/EUR & XAU\/AUD\\\\\n     \\hline\n     JPX\/JPY & XAU\/AUD\\\\\n     \\hline\n     SPX\/USD & XAU\/AUD\\\\\n     \\hline\n     USD\/MXN & ZAR\/JPY\\footref{ftnt:L}\\\\\n     \\hline\n    \\end{tabular}\n  \\end{center}\n  \\end{minipage}\n\\end{table}\n\n\n\n\n\\subsection{Lagged partial correlations}\n\nWe quantify the importance of the exchange rates as determined from the lagged partial correlations through the PageRank algorithm, as well. In the fifth column of Table~\\ref{tab:Ranking}, we show the ranking of the most influential exchange rates. The same four major market indexes, as in the lagged correlation case, appear at the top of the rankings. When applying the ordinary critical value of $0.01$ instead of the Bonferroni correction\nwe find similar results as in the previous section. These results are provided in Table~\\ref{tab:PersPartCorrAndCaus}.\nHowever, these results also suggest why at the top is the European stock market index ETX.\nNamely, the log returns on it, lead the returns of all market indexes AUX, FRX, GRX, HKX, JPX, NSX, SPX, and UKX. It is influenced by the FRX and GRX, which is a feedback relationship, something that was not present in the ordinary correlations. This influence is not symmetrical and is more pronounced from the ETX towards FRX and GRX, than in the opposite direction.\n\nWe find that other bidirectional partial correlations are those between the two oil brands, and between TRY and ZAR when quoted in US dollars. We remark that in the ordinary case, these currencies did not possess any mutual lagged correlation. Moreover, our results show that the value of TRY and ZAR in US dollars seems to be also similar in their trailing of the dynamics of the two Oceanic currencies AUD and NZD as quoted in the USD. The returns on AUD\/USD also show sign of having some influence on those on SGD\/USD. Particularly important is the fact that the return on the silver in USD, precedes similar behavior of the gold in the next minute. In a related observation involving precious metals, it appears that the CHF adjusts its value in terms of gold, after the neighboring EUR has done it one minute before. When any of the MXN, TRY, or ZAR gains its value in USD,  ZAR is induced to behave similarly with respect ot the JPY. Also, it is likely that the MXN has some influence on the ZAR which was not observed from the ordinary lagged correlations. Finally, interesting observations are those involving currencies from the Eurozone. The value of PLN in USD seems to influence the HUF quoted in the same currency base. It is also peculiar that the value of the minor currency CZK given in terms of US dollars, influences the major EUR, but not the opposite.  \n\n\n\n\\subsection{Granger causality}\n\nThe tests for presence of Granger causality were performed under scenarios 3 and 4, where both the leader and lagger must have nonzero returns simultaneously, while in scenario 3 additionally the lagger also needs to have non-vanishing returns in two consecutive periods.\nThe statistically significant causal relationships were presented in a directed network and the importance of exchange rates was again determined with the PageRank algorithm. We note that the networks which we have considered for depicting the causal relationships are not weighted, which means that a link between two pairs exists only if the source node is influenced by the target node, and the weight of each such link is one. As expected, the rates involving market indexes appear at the top of the list. The rankings of ten rates with strongest causal influence are provided in the last two columns in table~\\ref{tab:Ranking}, where similar ordering with the other two measures (lagged correlations and lagged partial correlations) is observed. Clearly, it can be argued that the lagged correlations, both partial and ordinary, suggest that a causal relationship is present between a leader and its lagger. By lowering the threshold for statistical significance to $0.01$, as in previous cases, we obtain almost the same pairs of exchange rates as in the case of partial correlations. The only exception is the existence of statistically significant partial lagged correlation between the JPX\/JPY as leader and the CHF\/JPY. The causality relationships under both scenarios between the same pair does not pass the threshold for only one month, December in 2017. This might be result of statistical nature and one could speculate that both scenarios produce the same results.\n\nWe state that one might be suspicious in the predictability under scenario 3, where we determine causality when the lagger is constrained to have nonzero return in the next minute. However, in the weaker case, when non-vanishing returns of the leader and the lagger are observed simultaneously, one can use them as signals, and make a regression on the future value of the return on the lagger.\n\n\\begin{table}[h!]\n  \\begin{center}\n    \\caption{Persistent statistically significant partial correlations and causality relationships.}\n   \\label{tab:PersPartCorrAndCaus}\n    \\begin{tabular}{l|l}\n    \\textbf{Leader} & \\textbf{Same direction} \\\\\n      \\hline      \n     AUX\/AUD & AUD\/JPY, CAD\/CHF, CAD\/JPY, FRX\/EUR, \\\\ & GBP\/JPY, GRX\/EUR, HKX\/HKD, NSX\/USD, \\\\ & NDZ\/JPY, SGD\/JPY, SPX\/USD, UDX\/USD, \\\\ & UKX\/GBP, USD\/JPY, ZAR\/JPY\\\\\n     \\hline    \n     BCO\/USD & WTI\/USD \\\\\n     \\hline\n     ETX\/EUR & AUD\/JPY, AUX\/AUD, CAD\/CHF, CAD\/JPY, \\\\ & FRX\/EUR, GBP\/JPY, GRX\/EUR, HKX\/HKD, \\\\ & JPX\/JPY, NSX\/USD, NDZ\/JPY, SGD\/JPY, \\\\ & SPX\/USD, UDX\/USD, UKX\/GBP, USD\/JPY\\\\\n     \\hline \n     FRX\/EUR & ETX\/EUR, GRX\/EUR \\\\\n     \\hline\n     GRX\/EUR & ETX\/EUR\\\\\n     \\hline\n     JPX\/JPY & AUD\/JPY, CAD\/CHF, CAD\/JPY, CHF\/JPY \\footnote{Only the partial lagged correlation is persistent in the considered 36 months.\\label{ftnt:Part_Corr}}, \\\\ & EUR\/JPY, FRX\/EUR, GBP\/JPY, GRX\/EUR,\\\\ & HKX\/HKD, NSX\/USD, NDZ\/JPY, SGD\/JPY, \\\\ & SPX\/USD, UDX\/USD, UKX\/GBP, USD\/JPY\\\\\n     \\hline    \n     SPX\/USD & AUD\/JPY, CAD\/JPY, GRX\/EUR, NSX\/USD, \\\\ & NZD\/JPY, SGD\/JPY, UDX\/USD\\\\\n     \\hline\n     USD\/CAD & USD\/ZAR \\\\\n     \\hline\n     USD\/MXN & EUR\/TRY, USD\/TRY, USD\/ZAR\\\\\n     \\hline\n     USD\/PLN & USD\/HUF \\\\\n     \\hline\n     USD\/TRY & USD\/ZAR \\\\\n     \\hline\n     USD\/ZAR & EUR\/TRY, USD\/TRY\\\\\n     \\hline\n     WTI\/USD & BCO\/USD \\\\\n     \\hline\n     XAG\/USD & XAU\/USD \\\\\n     \\hline\n     XAU\/EUR & XAU\/CHF \\\\\n     \\hline\n     ZAR\/JPY & SGD\/JPY \\\\\n     \\hline\n\\textbf{Leader} & \\textbf{Opposite direction}\\\\\n      \\hline\n     AUD\/USD & USD\/SGD, USD\/TRY, USD\/ZAR\\\\\n     \\hline\n     AUX\/AUD & XAU\/AUD\\\\\n      \\hline\n     ETX\/EUR & XAU\/AUD\\\\\n     \\hline\n     JPX\/JPY & XAU\/AUD\\\\\n     \\hline\n     NZD\/USD & USD\/TRY, USD\/ZAR\\\\\n     \\hline\n     SPX\/USD & XAU\/AUD\\\\\n     \\hline\n     USD\/CZK & EUR\/USD \\\\\n     \\hline\n     USD\/MXN & ZAR\/JPY\\\\\n     \\hline\n     USD\/TRY & ZAR\/JPY\\\\\n     \\hline\n     USD\/ZAR & ZAR\/JPY\\\\\n     \\hline\n     ZAR\/JPY & EUR\/TRY\\\\\n     \\hline\n    \\end{tabular}\n  \\end{center}\n\\end{table}\n\nSince the foreign exchange is known to be very liquid, one can not expect significant lags that span longer than one minute. To empirically check this hypothesis we also made an analysis where we examine whether these lagged relationships persist for longer periods. For this purpose we re-estimated our metrics for lead-lag relationships by taking into account for lagger returns that trail two minutes. We found that there are some pairs of exchange rates that pass the significance threshold of 0.01. However, they are not consistent. In particular, no such pair passed the test for all months in 2016. This is a further indication that the relevant lagging time scale is of order of one minute. Due to spatial constraints, we do not show these results, but make them available upon request.\n\n\n\\section{\\label{sec:conclusions}Conclusions}\n\nTo conclude, here we studied the relations between pairs of exchange rates where one exchange rate lags the other for one minute, and considered three different approaches. The first one considers lagged correlations which quantify similarity of log returns between lead and lagged exchange rate. The second approach restricts the lagged correlations to partial, in order to account for the potential autocorrelation. Finally, the last approach tries to uncover the causal relationships in the foreign exchange market in the sense of Granger. \n\nThe existence of statistically significant lagged correlations shows that, even though, the foreign exchange market is known to have very fast dynamics, information spreading is not instantaneous. We discovered that the rates which cause others to follow their dynamics are mostly those which involve stock market indexes. Observing changes in the value of an index, implies that certain currencies, or market indexes would more likely gain, while others would loose value. This was further confirmed by the calculation of the lagged partial correlation between the leader and the lagger exchange rate. By applying the PageRank algorithm on the statistically significant correlations in both cases we found that the most influential rates are indeed those involving market indexes. The same conclusions hold even when we estimated the Granger causality between pairs of exchange rates. When lagging period is two minutes, these lead-lag effects disappear, which suggests that the typical lagging time is of the order of one minute.\n\nIn spite of the fact that the existence of lagged correlations and causality challenges the efficient market hypothesis in foreign exchange markets, we are still uncertain of the existence of arbitrage. In order for this phenomenon to be proven, one should verify whether the potential statistical-arbitrage-based profit \ncan overcome the transaction costs. Investigating the presence of arbitrage should be a topic of future research which, besides the bid quotes, requires additional information such as ask price, transaction costs and time needed to complete the transaction.\n\n\n\nAs a final remark, we state that here we did not investigate the temporal dynamics of the discovered correlation patterns. A more detailed study which captures the dependencies among these temporal correlations could reveal novel insights for the nature of the lead-lag relationships in foreign exchange markets.\n\n\n\n\\section{Acknowledgement}\n\nWe are grateful to \\url{histdata.com} for freely sharing their data. This research was partially supported by the Faculty of Computer Science and Engineering at ``SS. Cyril and Methodius'' University in Skopje, Macedonia and by DFG through grant ``Random search processes, L\\'evy flights, and random walks on complex networks''.\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\n\nModeling and analyzing the dynamics of social networks allows scientists to understand the impact of social interactions on areas as diverse as politics (opinion formation, spread of (dis)information), economic development, and health (spread of diseases, update of vaccines)~\\cite{read2008dynamic,baumann2020modeling,DBLP:journals\/tcss\/BolzernCN20}. \n  %\nMuch of the more foundational literature approach social network analysis from a perspective informed by statistical physics~\\cite{newman2008physics}\nusing a combination of mathematical models (differential equations) and programmed simulation, both derived from an intuitive understanding of the operation of the network. This works well for static networks, where the structure is fixed and changes are to node or link attributes only, but in complex adaptive networks~\\cite{Gross2008} the interconnectedness of structure and data evolution poses additional challenges.\n\nStochastic typed attributed graph transformation~\\cite{HLM06FI} is an obvious choice to formalize and analyze complex adaptive networks. The formalism provides both tool support for simulation and analysis and an established theory to derive mathematical models from the same rule-based descriptions, thus replacing the informal, and sometimes vague, descriptions in natural language. A case in point are the various voter models~\\cite{Durrett2012,zschaler2012early,klamser2017zealotry}\nwhich describe opinion formation in a network of agents. The operations, as described in~\\cite{Durrett2012} seem clear enough. \n\n\\begin{quotation}\n\\dots we consider two opinions (called 0 and 1) \\dots; and on each step, we pick a discordant edge $(x,y)$ at random \\dots. With probability $1 - \\alpha$, the voter at $x$ adopts the opinion of the voter at $y$. Otherwise (i.e., with probability $\\alpha$), $x$ breaks its connection to $y$ and makes a new connection to a voter chosen at random from those that share its opinion. The process continues until there are no edges connecting voters that disagree.\n\\end{quotation}\n\nIntuitively, this is a graph transformation system of four rules over undirected graphs whose nodes are attributed by 0 or 1, shown below using $\\circ$ and $\\bullet$, respectively. \nReferring to~\\cite{bp2019-ext,nbSqPO2019,behrCRRC,BK2020} for further details, we utilise a ``right-to-left'' convention for rewriting rules in order to accommodate a natural order of composition of the rule algebra representations.%\n\n\\[\n\\begin{matrix}\\bullet \\hphantom {-}\\circ \\\\[-0.675em] \\!\\!\\!\\!\\!\\!\\backslash \\\\[-0.675em]\\bullet \\end{matrix}\\;\\leftharpoonup \\;\\begin{matrix}\\bullet \\!\\!-\\!\\!\\circ \\\\[-0.25em]\\bullet \\end{matrix}\n\\qquad\n\\begin{matrix}\\bullet \\hphantom {-}\\circ \\\\[-0.675em] \\;\\;\\;\/ \\\\[-0.675em]\\circ \\end{matrix}\\;\\leftharpoonup \\;\n\\begin{matrix}\\bullet \\!\\!-\\!\\!\\circ \\\\[-0.25em]\\circ \\end{matrix}\n\\qquad\n\\bullet \\!\\!-\\!\\!\\bullet \\;\\leftharpoonup \\;\\bullet \\!\\!-\\!\\!\\circ\n\\qquad\n\\circ \\!\\!-\\!\\!\\circ \\;\\leftharpoonup \\;\\bullet \\!\\!-\\!\\!\\circ\n\\]\n\nThe first pair of rules models \\emph{rewiring} where an agents disconnects from another one with a different opinion to form a connection with a third agent of the same opinion. In the second pair of rules, an agent connected to one with a different opinion \\emph{adopts} the opinion of the other. \nWe could now associate rates with these rules, resulting in a stochastic graph transformation system that allows simulation using the SimSG tool~\\cite{DBLP:journals\/jot\/EhmesFS19} and the derivation of differential equations using the rule algebra approach~\\cite{bp2019-ext,nbSqPO2019, behrCRRC,BK2020}.\n\nHowever, on closer inspection we discover a number of discrepancies. First, the model in~\\cite{Durrett2012} and related papers is probabilistic, but without time. This is an abstraction of real-world behavior in social networks, where time is not discrete and actions not round-based. Arguably, a continuous-time model is a better representation of this behavior. Semantically, a stochastic graph transformation system induces a continuous-time Markov Chain (CTMC) --- an established model with clear links to logics, model checking and simulation techniques, while the operational model behind \\cite{Durrett2012} and others is left informal, but could be formalized as a discrete-time Markov chain (DTMC) or decision process (MDP)~\\cite{bdg2016, bdg2019,bp2019-ext,BK2020}. %\n\nMore specifically, looking at the description of the operation, this is a two- or three-step process, where first a conflict edge is selected at random, then a decision made based on the fixed probability $\\alpha$ between adopting another opinion, and rewiring which requires another random selection of a node with the same opinion. That means, in the rewiring case, the combined behavior of the operation is not reflected directly by the rewiring rules above, which choose all three nodes first. Also, the race between the rewiring and adopt rules in a stochastic graph transformation system depends on the number of available matches (the candidates for the 3rd agent to link) while the probability is fixed in the original formulation. Stochastic graph transformation realizes a mass action semantics which reflects the behavior of physical, chemical and  biological processes where the frequency of actions (formally the jump rate of the CTMC) depends on both a rate constant and the concentration or amount available of the input materials required for the action. \n\nIn our view, the informal description of operations, lack of continuous time, and non-standard selection and execution procedure all represent weaknesses in the formulation which inhibit a natural mathematical interpretation of the operational behavior of the model and consequently a formal and systematic connection of this operational description with the simulation and equational model. \n\nOther authors have studied algorithmic problems in social networks, such as what subset of actors to target with interventions (e.g., in marketing or public health campaigns) so as to maximise the impact of the campaign on the network as a whole~\\cite{DBLP:journals\/toc\/KempeKT15,DBLP:journals\/kbs\/LiuYWLLT16}. Such research is based on models of opinion formation and the spread of information in networks, typically divided into \\emph{cascading} and \\emph{threshold models}. In a cascading model, an actor is activated by a single message or activation from a peer. The behavior outlined above, where a discordant edge represents an activation, falls into this category. Instead, in a threshold model, an actor becomes active once a certain number of its peers are activated. \n\nDifferent models give rise to different centrality measure for actors~\\cite{DBLP:journals\/kbs\/RiquelmeCMS18} and hence to different algorithmic solutions for discovering the most influential set of actors to target. These models assume static networks, but one could ask the question of centrality of actors for a dynamic network model given by a stochastic graph transformation system incorporating both the spread of information and the change of topology. \n\nIn this paper, we present an approach addressing weaknesses in dynamic social network modelling by starting from a formal graph transformation model as operational description. We investigate the links to the existing voter models both analytically, using the rule algebra framework to establish how to translate operations and parameters to stochastic graph transformation, and experimentally trying to recreate the observed emergent behavior in the literature. Apart from making a convincing claim for the superiority of our methodological approach, this will allow us in the future to both compare new analysis results to existing ones in the literature.\n\nWe start by introducing the model as a stochastic graph transformation system in the format accepted by our simulation tool, then study the theory of relating the different CTMC and DTMC semantics to support different possible conversions between models before reporting on the experimental validation of the resulting models through simulation.  \n\n\n\\section{Voter Models as Stochastic Typed Attributed Graph Rewrite Systems}\\label{sec:voter-models}\n\nWe model voter networks as instances of the type graph below (Figure~\\ref{fig:voter-model-tg}), where \\emph{Group} nodes represent undirected links connecting \\emph{Agent} nodes. This means that two agents are linked if they are  members of the same group. For now, the cardinality of each group is exactly 2, so these groups are indeed a model of undirected edges between agents (and  we are planning to generalize to groups with several members later).\n\\begin{figure}[h]\n\t\\centering\n\t\\includegraphics[width=0.50\\textwidth]{graphics\/TypeGraph.pdf}\n\t\\caption{Type graph of the basic voter model}\\label{fig:voter-model-tg}\t\n\\end{figure}\nWe see the voter network as an undirected multi graph, i.e., parallel links between two voters $v1$ and $v2$ are permitted. \nThat means, in our representation, $v1, v2$ can jointly make up one group $g1$ as well as another group $g2$. \nIt is worth noting that the multi-graph interpretation is never explicitly stated in~\\cite{Durrett2012} nor the literature building on it. \nHowever it is the only interpretation consistent with the usual assumptions made, in particular that rewiring is always possible after the selection of the 3rd node, which may or may not be connected to the first node $v1$ already, and that the total number of edges in the graph is constant, so we have to create a new edge on rewiring even if $v1$ and $v2$ are already connected.\n\\begin{figure}[h]\n\t\\centering\n\t\\includegraphics[width=0.80\\textwidth]{graphics\/AdoptRules.pdf}\n\t\\includegraphics[width=0.80\\textwidth]{graphics\/Rewire1Rule.pdf}\n\t\\includegraphics[width=0.80\\textwidth]{graphics\/Rewire2Rule.pdf}\n\t\\caption{Rules of the basic voter model}\\label{fig:voter-model-rules}\n\\end{figure}\n\nIn this paper we use SimSG \\cite{DBLP:journals\/jot\/EhmesFS19} to simulate rule-based models, such as the basic voter model, for a given start graph and rates according to the semantics of stochastic graph transformations~\\cite{HLM06FI}.\nSimSG implements its own version of Gillespie's well-known algorithm~\\cite{Gillespie1977} which describes the behavior of stochastic systems over time using a continuous-time Markov Chain with exponentially distributed transition delays.\nSimSG is build upon the graph transformation rule interpreter eMoflon \\cite{eMoflon}, which provides the means to define and execute rules. For example, there are four rules in the basic voter model, two dual variants each of the \\emph{adopt} and \\emph{rewire} operations. \nThe graphs in Figure~\\ref{fig:voter-model-rules} show a visual representation of these four rules as defined in the eMoflon::IBeX-GT\\footnote{eMoflon::IBeX-GT: \\url{https:\/\/emoflon.org\/\\#emoflonIbex}} syntax.\nIn these rules, black and red elements (\\texttt{--}) specify context elements that need to be present in an instance graph, while green elements (\\texttt{++}) will be created.\nA pattern matcher will search for matches in an instance graph that fit these requirements.\nAs shown in Figure~\\ref{fig:voter-model-rules}, in addition to structural constraints, eMoflon allows the specification of attribute conditions.\nIf a match is found, the rule can be applied by deleting all graph elements matching red elements in the rule, and creating new instances of all green elements.  \nIn addition to the structural constraints and attribute conditions shown in the example, eMoflon-GT also allows the definition of more complex conditions, such as negative application conditions that filter out matches connected to prohibited graph structures. \nBeyond the specification of rules, SimSG allows for the annotation of rules with rates, either through value literals or statically evaluated arithmetic expressions.\nMost importantly, eMoflon provides SimSG with an interface to its underlying incremental graph pattern matching engines, such as Viatra\\cite{VIATRA}, Democles\\cite{DEMOCLES} or the recently developed HiPE\\footnote{HiPE: \\url{https:\/\/github.com\/HiPE-DevOps\/HiPE-Updatesite}}, all of which can be used to find matches for rules and track observable patterns during simulations.\nDuring each simulation, SimSG tracks occurrence counts of these patterns and provide the user with the option to plot these counts over the simulation time or save them to a file.\n \n\n\n\n\\section{Theory: CTMCs and DTMCs via Rule-algebraic Methods}\\label{sec:theory}\n\n\nApproaches to social network modeling can be broadly classified by their underlying semantics. In this paper, we consider the two major classes consisting of \\emph{discrete-time Markov chains (DTMCs)} and \\emph{continuous-time Markov Chains (CTMCs)} (leaving for future work the class of Markov decision processes). We will utilize the \\emph{rule algebra formalism}~\\cite{bp2019-ext,nbSqPO2019, behrCRRC,BK2020} as our central technical tool, with CTMCs in so-called mass-action semantics implemented via the \\emph{stochastic mechanics framework}~\\cite{bdg2016, bdg2019,bp2019-ext, BK2020}. Here, the firing rate of a given rule for a system state at some time $t\\geq 0$ is proportional to a \\emph{base rate} (i.e., a positive real parameter) times the number of admissible matches of the rule into the system state.\nNote however that even in the CTMC setting, this semantics is only one of several conceivable variants, and indeed we will study in this paper also a variation of rule-based CTMC semantics wherein rule activities in infinitesimal jumps are not weighted by their numbers of matches. In order to faithfully implement rule-based DTMCs, we will adopt the approach of~\\cite{Behr2021}.\n\n\n\\subsection{Preliminaries: ``compositional'' rewriting theory}\n\nWe will focus throughout this paper on the case\\footnote{Since the rules in our concrete models are \\emph{linear} and will not involve vertex deletions nor creations, we could have equivalently opted for DPO- or SPO-semantics, which are well-known to coincide with SqPO-semantics in this special situation.} of Sesqui-Pushout (SqPO) semantics~\\cite{Corradini2006}, which under certain conditions on the underlying base categories furnishes a ``compositional'' rewriting semantics~\\cite{nbSqPO2019}, i.e., supports the requisite construction of rule algebras. Since the main theme of this paper is to advocate rewriting-based methods for implementing models, we discuss here the recent extension of the SqPO-formalism to include rules with conditions and under the influence of constraints~\\cite{behrCRRC,BK2020}. We refer the interested readers to~\\cite{BK2020} for the analogous formalism in the Double Pushout (DPO) setting.\n\nConsider thus a \\emph{base category} $\\bfC$ that is \\emph{$\\cM$-adhesive} (for some class $\\cM$ of monomorphisms), \\emph{finitary}, possesses an $\\cM$-initial object, $\\cM$-effective unions and an epi-$\\cM$-factorization, and such that all final pullback complements (FPCs) along composable pairs of $\\cM$-morphisms exist (compare~\\cite{BK2020}). Throughout this paper, we will consider the particular example of the category $\\mathbf{uGraph}\/T$ (for some $T\\in \\obj{\\mathbf{uGraph}}$) of \\emph{typed undirected multigraphs}, which according to~\\cite{BK2020} satisfies all of the aforementioned requirements.\n\nLet us briefly recall the salient points of SqPO-type ``compositional'' rewriting theory:\n\n\\begin{definition}[Rules]\nDenote by $\\LinAc{\\bfC}$ the set of equivalence classes of linear rules with conditions,\n\\begin{equation}\n\\LinAc{\\bfC}:= \\{ R=(O\\xleftarrow{o}K\\xrightarrow{i}I,\\ac{c}_I)\\vert i,o\\in \\cM, \\ac{c}_I\\in \\cond{\\bfC}\\}\\diagup_{\\sim}\\,,\n\\end{equation}\nwhere $R\\sim R'$ if and only if $\\ac{c}_I\\dot{\\equiv}\\ac{c}_I'$ (i.e., if the conditions are equivalent for all matches of the rules) and the rules are isomorphic. The latter entails the existence of isomorphisms $\\omega:O\\xrightarrow{\\cong} O'$, $\\kappa:K\\xrightarrow{\\cong} K'$ and $\\iota:I\\xrightarrow{\\cong} I'$ such that the obvious diagram commutes. We will adopt the convention to speak of ``a'' rule $R\\in \\LinAc{\\bfC}$ to mean an equivalence class of rules.\n\\end{definition}\n\n\\begin{definition}\nGiven a rule $R\\in \\LinAc{\\bfC}$ and an object $X\\in \\obj{\\bfC}$, an \\emph{SqPO-admissible match} $m\\in \\RMatchGT{}{R}{X}$ is an $\\cM$-morphism $m:I\\rightarrow X$ that satisfies the application condition $\\ac{c}_I$. Then an \\emph{SqPO-type direct derivation} of $X$ along $R$ with a match $m\\in \\RMatchGT{}{R}{X}$ is defined via a commutative diagram of the form\n\\begin{equation}\n\\ti{dd}\n\\end{equation}\nwhere the object $R_m(X)$ is defined up to the universal isomorphisms of FPCs and pushouts (POs).\n\\end{definition}\nNote that in all of our applications, we will only consider objects up to isomorphisms, so we will in a slight abuse of notations speak of taking direct derivations of iso-classes $X\\in \\obj{\\bfC}_{\\cong}$ along (equivalence classes of) rules, understood as a mapping from iso-classes to iso-classes. With the focus of the present paper upon implementation strategies, we forgo here a complete review of the concepts of compositional rewriting theory (see e.g.\\ \\cite{behrCRRC,BK2020}), and limit ourselves to the following salient points. From hereon, $\\bfC$ will always denote a category suitable for SqPO-type transformation.\n\n\\begin{definition}\nLet $\\cR_{\\bfC}$ denote the \\emph{$\\bR$-vector space ``over rules''} spanned by basis vectors $\\delta(R)$, where $\\delta:\\LinAc{\\bfC}\\xrightarrow{\\cong} \\mathsf{basis}(\\cR_{\\bfC})$ is an isomorphism. Let $\\hat{\\bfC}$ denote the \\emph{$\\bR$-vector space ``over states''}, which is defined via the isomorphism $\\ket{.}:\\obj{\\bfC}_{\\cong}\\rightarrow \\mathsf{basis}(\\hat{\\bfC})$ from isomorphism-classes of objects to basis vectors of $\\hat{\\bfC}$. We introduce the notation $End_{\\bR}(\\hat{\\bfC})$ to denote the space of \\emph{endomorphisms} on $\\hat{\\bfC}$ (i.e., of linear operators from $\\hat{\\bfC}$ to itself). Then we denote by $\\rho_{\\bfC}:\\cR_{\\bfC}\\rightarrow End_{\\bR}(\\hat{\\bfC})$ the morphism defined via\n\\begin{equation}\\label{eq:defCanRep}\n\\forall R\\in \\LinAc{\\bfC}, X\\in \\obj{\\bfC}_{\\cong}:\\quad\n\\rho_{\\bfC}(\\delta(R))\\ket{X} := \\sum_{m\\in \\RMatchGT{}{R}{X}} \\ket{R_m(X)}\\,.\n\\end{equation}\nThe above definition extends to arbitrary elements of $\\cR_{\\bfC}$ and $\\hat{\\bfC}$ by \\emph{linearity}, i.e., for $A=\\sum_{j=1}^M \\alpha_j\\delta(R_j)$ and $\\ket{\\Psi}:=\\sum_{X}\\psi_X\\ket{X}$, we define $\\rho_{\\bfC}(A)\\ket{X}:= \\sum_{j=1}^M\\alpha_j\\sum_{X} \\psi_X \\,\\rho_{\\bfC}(\\delta(R_j))\\ket{X}$.\n\\end{definition}\n\nIntuitively, $\\rho_{\\bfC}$ takes a rule vector in $\\cR_{\\bfC}$ and delivers a transformation between state vectors, applying the rules to the input states, and ``weighing'' the resulting states according to the coefficients in the rule vector. This concept is useful in particular in order to formalize the jumps of a CTMC (see Section~\\ref{sec:CTMC}).\n\n\\begin{theorem}[Cf.\\ \\cite{BK2020}]\n\\begin{itemize}\n\\item[(i)] The \\emph{trivial rule} $R_{\\mathop{\\varnothing}}:=[(\\mathop{\\varnothing}\\leftarrow\\mathop{\\varnothing}\\rightarrow\\mathop{\\varnothing},\\ac{true})]_{\\sim}\\in \\LinAc{\\bfC}$ satisfies\n\\begin{equation}\n\\rho_{\\bfC}(\\delta(R_{\\mathop{\\varnothing}}))=Id_{End_{\\bR}(\\hat{\\bfC})}\\,.\n\\end{equation}\n\\item[(ii)] Denote by $\\bra{}:\\hat{\\bfC}\\rightarrow \\bR$ the so-called \\emph{(dual) projection vector}, defined via $\\braket{}{X}:=1_{\\bR}$ for all $X\\in \\obj{\\bfC}_{\\cong}$. Extending this definition by linearity, $\\bra{}$ thus implements the operation of \\emph{summing coefficients}, i.e., for $\\ket{\\Psi}=\\sum_{X}\\psi_X\\ket{X}$, we define $\\braket{}{\\Psi}:=\\sum_X \\psi_X\\braket{}{X}=\\sum_X\\psi_X$. Then $\\rho_{\\bfC}$ satisfies the so-called \\textbf{SqPO-type jump-closure property}:\n\\begin{equation}\\label{eq:jc}\n\\forall R\\in \\LinAc{\\bfC}:\\quad \\bra{}\\rho_{\\bfC}(\\delta(R))\n=\\bra{}\\jcOp{\\delta(R)}\\,,\\quad  \\jcOp{\\delta(R)}:=\\rho_{\\bfC}(\\delta([I\\leftarrow I\\rightarrow I,\\ac{c}_I]_{\\sim}))\\,.\n\\end{equation}\n\\end{itemize}\n\\end{theorem}\nThe last point of the above theorem alludes to the important special case of rule-based linear operators that are \\emph{diagonal} in the basis of $\\hat{\\bfC}$, since these implement operations of \\emph{counting patterns}. In the particular case at hand, we may combine the definition of $\\rho_{\\bfC}$ in~\\eqref{eq:defCanRep} with~\\eqref{eq:jc} in order to obtain\n\\begin{equation}\\label{ed:obs}\n\\bra{}\\jcOp{\\delta(R)}\\ket{X}=\\bra{}\\rho_{\\bfC}(\\delta(R))\\ket{X}=\\sum_{m\\in \\RMatchGT{}{R}{X}}\\braket{}{R_m(X)} =\n\\sum_{m\\in \\RMatchGT{}{R}{X}} 1_{\\bR}= \\vert \\RMatchGT{}{R}{X}\\vert\\,.\n\\end{equation}\nIn this sense, $\\jcOp{\\delta(R)}$ as defined in~\\eqref{eq:jc} ``counts'' the numbers of admissible matches of $R$ into objects. \n\n\n\\subsection{Rule-based CTMCs}\\label{sec:CTMC}\n\nTraditionally, CTMCs based upon transformation rules have been defined in so-called \\emph{mass-action semantics}. In the rule algebra formalism, such types of CTMCs are compactly expressed as follows (with $\\rho\\equiv \\rho_{\\bfC}$):\n\n\\begin{theorem}[Mass-action semantics for CTMCs]\\label{def:masCTMC}\nLet $\\cT:=\\{(\\kappa_j,R_j)\\}_{j=1}^N$ denote a (finite) set of pairs of \\emph{base rates} $\\kappa_{j}\\in \\bR_{>0}$ and rules $R_j\\in \\LinAc{\\bfC}$ (for $j=1,\\dotsc,N$) over some category $\\bfC$. Denote by $\\mathsf{Prob}(\\hat{\\bfC})$ the space of (sub-)probability distributions over the state-space $\\hat{\\bfC}$, and choose an \\emph{initial state} $\\ket{\\Psi_0}:=\\sum_X \\psi_X^{(0)}\\ket{X}\\in \\mathsf{Prob}(\\hat{\\bfC})$. Then the data $(\\cT,\\ket{\\Psi_0})$ defines a \\textbf{SqPO-type rule-based CTMC} via the following \\textbf{evolution equation} for the \\textbf{system state} $\\ket{\\Psi(t)}:=\\sum_X \\psi_X(t)\\ket{X}$ at time $t\\geq0$:\n\\begin{equation}\n\\tfrac{d}{dt}\\ket{\\Psi(t)}=H\\ket{\\Psi(t)}\\,,\\quad \\ket{\\Psi(0)}=\\ket{\\Psi_0}\\,,\\quad H:=\\rho(h)-\\jcOp{h}\\,,\\quad h:=\\sum_{j=1}^N \\kappa_j\\delta(R_j)\n\\end{equation}\nHere, we used linearity to extend the definition of the jump-closure operator $\\jcOp{.}$ of~\\eqref{eq:jc} to arbitrary elements of $\\cR_{\\bfC}$, i.e., $\\jcOp{h}:=\\sum_{j=1}^N \\kappa_j\\jcOp{\\delta(R_j)}$.\n\\end{theorem}\n\nHowever, while mass-action semantics is of key importance in the modeling of chemical reaction systems, it is of course not the only conceivable semantics. In particular, as we shall demonstrate in the later part of this paper, for certain applications it will prove useful to utilize alternative adjustments of the ``firing rates'' of individual rules other than the one fixed in mass-action semantics.\n\n\\begin{definition}[Generalized rule-based CTMC semantics]\\label{def:gsCTMC}\nFor a suitable base category $\\bfC$, let $\\cT:=\\{(\\gamma_j, R_j, W_j)\\}_{j=1}^N$ be a set of triples of \\emph{base rates} $\\gamma_j\\in \\bR_{>0}$, \\emph{rules} $R_j\\in \\LinAc{\\bfC}$ and \\emph{(inverse) weight functions} $W_j\\in End(\\hat{\\bfC})_{diag}$ ($j=1,\\dotsc,N$). Here, $End(\\hat{\\bfC})_{diag}$ denotes the space of \\emph{diagonal operators} (with respect to the basis of $\\hat{\\bfC}$). Together with a choice of \\emph{initial state} $\\ket{\\Psi_0}\\in \\mathsf{Prob}(\\hat{\\bfC})$, this data defines a \\emph{rule-based SqPO-type CTMC} via the \\emph{evolution equation}\n\\begin{equation}\n\\begin{aligned}\n&\\tfrac{d}{dt}\\ket{\\Psi(t)}=H_{\\vec{W}}\\ket{\\Psi(t)}\\,,\\quad\n\\ket{\\Psi(0)}=\\ket{\\Psi_0}\\,,\\quad\nH_{\\vec{W}}:= \\sum_{j=1}^N \\gamma_j\\left(\n\\rho(\\delta(R)_j)-\\jcOp{\\delta(R_j)}\n\\right)\\frac{1}{W_j^{*}}\\\\\n&\\forall F\\in End(\\hat{\\bfC})_{diag},\\ket{X}\\in \\hat{\\bfC}:\\quad \\frac{1}{F^{*}}\\ket{X}:=\\begin{cases}\n\\ket{X} \\quad&\\text{if }F\\ket{X}=0_{\\bR}\\\\\n\\frac{1}{\\bra{}F\\ket{X}}\\ket{X} &\\text{otherwise.}\n\\end{cases}\n\\end{aligned}\n\\end{equation}\n\\end{definition}\n\n\\begin{example}\nGiven a set of pairs of base rates and rules $\\cT=\\{(\\kappa_j,R_j)\\}_{j=1}^N$ for a  rule-based CTMC with mass-action semantics as in Definition~\\ref{def:masCTMC}, one may define from this transition set in particular a \\emph{uniformed} CTMC with infinitesimal generator $H_U$ defined as follows (with $\\rho\\equiv \\rho_{\\bfC}$):\n\\begin{equation}\nH_U:=-Id_{End(\\hat{\\bfC})}+\\sum_{j=1}^N p_j \\cdot\\rho(\\delta(R_j))\\frac{1}{\\jcOp{\\delta(R_j)}^{*}}\\,,\\quad p_j:=\\frac{\\kappa_j}{\\sum_{j=1}^N \\kappa_j}\\,.\n\\end{equation}\nNote in particular that since all base rates $\\kappa_j$ are positive real numbers, the parameters $p_j$ are \\emph{probabilities}. Moreover, applying $H_U$ to an arbitrary basis state $\\ket{X}$, one finds that the overall jump rate (i.e., minus the coefficient of the diagonal part of $H_U$) is precisely equal to $1$, so that the $p_j$ in the non-diagonal part of $H_U$ encodes in fact the probability for the ``firing'' of rule $R_j$, regardless of the numbers of admissible matches of $R_j$ into the given state $\\ket{X}$. Finally, under the assumption that both the mass-action and the uniformed CTMC admit a \\emph{steady state}, we find by construction that\n\\begin{equation}\n\\lim\\limits_{t\\to\\infty}\\tfrac{d}{dt}\\ket{\\Psi(t)}=0\\quad \\Leftrightarrow \\quad\\lim\\limits_{t\\to\\infty}H\\ket{\\Psi(t)}=0\\quad \n\\Leftrightarrow \\quad \\lim\\limits_{t\\to\\infty}\nH_U\\left(\\jcOp{h}\\cdot \\ket{\\Psi(t)}\\right)=0\\,.\n\\end{equation}\nLetting $\\ket{\\Psi_U(t)}$ denote the system state at time $t$ of the ``uniformed'' CTMC with generator $H_U$, and assuming $\\ket{\\Psi(0)}=\\ket{\\Psi_U(0)}$, the above entails in particular that $\\ket{\\Psi_U(t\\to\\infty)}= (\\jcOp{h}^{*})^{-1}\\cdot\\ket{\\Psi(t\\to\\infty)}$, i.e., the steady state of the CTMC generated by $H_U$ and the one of the CTMC generated by $H$ are related by an operator-valued rescaling (via the operator $(\\jcOp{h}^{*})^{-1}$, and thus in general in non-constant fashion). A similar construction will play a key role when studying rule-based discrete-time Markov chains.\n\\end{example}\n\nAnother interesting class of examples is motivated via the ``Potsdam approach'' to probabilistic graph transformation systems as advocated in~\\cite{giese2012}. \n\n\\begin{example}[LCM-construction]\\label{ex:LCM}\nGiven a generalized CTMC with infinitesimal generator $H_{\\vec{W}}$ specified as in Definition~\\ref{def:gsCTMC}, construct the least common multiple (LCM) $L$ of the inverse weight functions:\n\\begin{equation}\nL:= LCM(W_1,\\dotsc,W_N)\\,.\n\\end{equation}\nThen we define the \\emph{LCM-variant} of the CTMC as\n\\begin{equation}\nH_{LCM}:=H_{\\vec{W}}\\cdot L\\,.\n\\end{equation}\nBy construction, $H_{LCM}$ does not contain any operator-valued inverse weights (in contrast to the original $H_{\\vec{W}}$). Moreover, for certain choices of (inverse) weight functions $W_1, \\dotsc, W_N$, the LCM-construction results in an infinitesimal generator $H_{LCM}$ in which all contributing rules have the same input motif $I$, thus making contact with the methodology of~\\cite{giese2012}. \n\\end{example}\n\n\\subsection{Rule-based DTMCs}\\label{sec:dtmc}\n\nDespite their numerous applications in many different research fields, to date discrete-time Markov chains (DTMCs) that are based upon notions of probabilistic transformation systems have not been considered in quite a comparable detail as the CTMC constructions. Following~\\cite{Behr2021}, we present here a possible general construction of rule-based DTMC via a rule-algebraic approach:\n\n\\begin{definition}\\label{def:DTMC}\nFor a suitable category $\\bfC$, let $\\cT=\\{(\\gamma_j,R_j,W_j)\\}_{j=1}^N$ be a (finite) set of triples of positive coefficients $\\gamma_j\\in \\bR_{>0}$, transformation rules $R_j\\in \\LinAc{\\bfC}$ and (inverse) weight functions $W_j\\in End(\\hat{\\bfC})_{diag}$ ($j=1,\\dotsc,N$), with the additional constraint that\n\\begin{equation}\n\\sum_{j=1}^{N} \\gamma_j\\jcOp{\\delta(R_j)}\\cdot\\frac{1}{W_j^{*}} = Id_{End(\\hat{\\bfC})}\\,.\n\\end{equation}\nThen together with an initial state $\\ket{\\Phi_0}\\in \\mathsf{Prob}(\\hat{\\bfC})$, this data defines a \\emph{SqPO-type rule-based discrete-time Markov chain (DTMC)}, whose $n$-th state  (for non-negative integer values of $n$) is given by\n\\begin{equation}\n\\ket{\\Phi_n}:=D^n \\ket{\\Phi_0}\\,,\\quad D:=\\sum_{j=1}^N\\gamma_j\\rho(\\delta(R_j))\\cdot\\frac{1}{W_j^{*}}\\qquad (\\rho\\equiv\\rho_{\\bfC})\\,.\n\\end{equation}\n\\end{definition}\n\n\\begin{figure}\n\\centering\n\\[\n\\ti{AVM}\n\\]\n\\caption{Specification of the adaptive voter model (AVM) according to~\\cite{Durrett2012} via a probabilistic decision tree (black arrows), and as combined one-step probabilistic transitions ({\\color{qOrange}orange arrows}).}\\label{fig:AVM}\n\\end{figure}\n\n\\begin{example}[Adaptive Voter Model] As a typical example of a social network model, consider the specification of the \\emph{adaptive voter model (AVM)} in the variant according to Durrett et al. [ref], which has as its \\emph{input parameters} an \\emph{initial graph state} $\\ket{\\Phi_0}=\\ket{X_0}$ (with $N^{(0)}_{\\bullet}$ and $N^{(0)}_{\\circ}$ vertices of types $\\bullet$ and $\\circ$, respectively, and with $N_E$ undirected edges) and a \\emph{probability} $0\\leq \\alpha\\leq1$, and whose transitions as depicted in Figure~\\ref{fig:AVM} are given via a form of a probabilistic decision procedure in several steps (black arrows): in each round of the AVM, an edge is chosen at random; if the edge is linking two nodes of different kind, with probability $p$, one of the rewiring rules is ``fired'', or with probability $(1-p)$ one of the adopt rules, respectively; otherwise, i.e., if the chosen edge is linking two vertices of the same kind, no action is performed. As annotated in {\\color{darkblue}dark blue}, each phase of this probabilistic decision procedure is dressed with a probability (and so that all probabilities for a given phase sum to $1$). These probabilities in turn depend upon constant parameters (here, $p$ and $N_E$), as well as on \\emph{pattern counts} $N_{\\bullet}$, $N_{\\circ}$, $N_{\\bullet\\!-\\!\\bullet}$, $N_{\\bullet\\!-\\!\\circ}$ and $N_{\\circ\\!-\\!\\circ}$ that dynamically depend on the current system state. Note that $N_V:=N_{\\bullet}+N_{\\circ}$ and $N_E=N_{\\bullet\\!-\\!\\bullet}+N_{\\bullet\\!-\\!\\circ}+N_{\\circ\\!-\\!\\circ}$ are \\emph{conserved quantities} in this model, since none of the transitions create or delete vertices, but at most exchange vertex types\\footnote{Strictly speaking, we implement the two vertex types $\\bullet$ and $\\circ$ as attributes in our \\texttt{SimSG} implementation, which in the theoretical setting can be emulated via using self-loops of two different types; evidently, this amounts merely to a slight modification of the type graph plus the enforcement of some structural constraints (compare~\\cite{BK2020}), thus for notational simplicity, we do not make this technical detail explicit in our diagrams.}, and since the transitions manifestly preserve the overall number of edges.\n\nUpon closer inspection, the transition probabilities may be written in a form that permits to compare the ``firing'' semantics to the mass-action and to the generalized semantics used in rule-based CTMCs. According to~\\eqref{ed:obs}, we may implement the operation of counting patterns via linear operators based upon ``identity rules'', since for arbitrary graph patterns $P$ and graph states $\\ket{X}$,\n\\begin{equation}\nN_P(X) = \\bra{}\\hat{O}_P\\ket{X}\\,,\\quad \\hat{O}_P:=\\rho(\\delta([P\\leftarrow P\\rightarrow P,\\ac{true}]_{\\sim}))\\,.\n\\end{equation}\nSince rule algebra theory is not the main topic of the present paper, we provide below some operator relations without derivation\\footnote{In fact, for the simple case at hand, one may derive the relations heuristically, noting that applying $\\hat{O}_{\\bullet\\!-\\!\\circ}\\hat{O}_{x}$ to some graph state amounts to first counting all vertices of type $x$ (for $x\\in \\{\\bullet,\\circ\\}$), followed by counting all $\\bullet\\!\\!-\\!\\!\\circ$ edges; performing this operation in one step, this amounts to either counting the $x$-type vertices separately (i.e., counting the pattern $\\bullet\\!\\!-\\!\\!\\circ\\; x$), or counting the $x$-type vertices on the same location as counting the $\\bullet\\!\\!-\\!\\!\\circ$ patterns, thus explaining the two contributions in~\\eqref{eq:auxObsAVM}.}, noting that they may be computed utilizing the fact that $\\rho$ is a so-called representation of the SqPO-type rule algebra (cf.\\ \\cite[Thm.~3]{BK2020}):\n\\begin{equation}\\label{eq:auxObsAVM}\n\\hat{O}_{\\bullet\\!-\\!\\circ}\\hat{O}_{x}=\\hat{O}_{\\bullet\\!-\\!\\circ\\;x}+\\hat{O}_{\\bullet\\!-\\!\\circ} \\quad \\Leftrightarrow\\quad \n\\hat{O}_{\\bullet\\!-\\!\\circ\\;x}=\\hat{O}_{\\bullet\\!-\\!\\circ}(\\hat{O}_{x}-1)\\qquad (x\\in \\{\\bullet,\\circ\\})\\,,\n\\end{equation}\nwhich permit us to interpret the AVM model in the following way as a rule-based DTMC: starting by computing the overall one-step transitions and their respective probabilities ({\\color{qOrange}orange arrows} in Figure~\\ref{fig:AVM}), and using the above operator relations, we  find the rule-based DTMC generator\n\\begin{subequations}\n\\begin{align}\nD_{AVM}&={\\color{qOrange}\\frac{\\alpha}{2N_E}}\n\\rho\\left(\\delta\\left(\\begin{matrix}\\bullet \\hphantom {-}\\circ \\\\[-0.675em] \\!\\!\\!\\!\\!\\!\\backslash \\\\[-0.675em]\\bullet \\end{matrix}\\;\\leftharpoonup \\;\\begin{matrix}\\bullet \\!\\!-\\!\\!\\circ \\\\[-0.25em]\\bullet \\end{matrix}\\right)\\right){\\color{qOrange}\\frac{1}{(\\hat{O}_{\\bullet}-1)^{*}}}\n+{\\color{qOrange}\\frac{\\alpha}{2N_E}}\\rho\\left(\\delta\\left(\\begin{matrix}\\bullet \\hphantom {-}\\circ \\\\[-0.675em] \\;\\;\\;\/ \\\\[-0.675em]\\circ \\end{matrix}\\;\\leftharpoonup \\;\\begin{matrix}\\bullet \\!\\!-\\!\\!\\circ \\\\[-0.25em]\\circ \\end{matrix}\\right)\\right){\\color{qOrange}\\frac{1}{(\\hat{O}_{\\circ}-1)^{*}}}\\label{eq:D-AVM-rewire}\\\\\n&\\quad+{\\color{qOrange}\\frac{(1-\\alpha)}{2N_E}}\\rho\\left(\\delta\\left(\n\\bullet \\!\\!-\\!\\!\\bullet \\;\\leftharpoonup \\;\\bullet \\!\\!-\\!\\!\\circ\n\\right)\\right)+{\\color{qOrange}\\frac{(1-\\alpha)}{2N_E}}\\rho\\left(\\delta\\left(\n\\circ \\!\\!-\\!\\!\\circ \\;\\leftharpoonup \\;\\bullet \\!\\!-\\!\\!\\circ\n\\right)\\right) \\label{eq:D-AVM-adopt}\\\\\n&\\quad+{\\color{qOrange}\\frac{1}{N_E}}\\rho\\left(\\delta\\left(\n\\bullet \\!\\!-\\!\\!\\bullet \\;\\leftharpoonup \\;\\bullet \\!\\!-\\!\\!\\bullet\n\\right)\\right)+{\\color{qOrange}\\frac{1}{N_E}}\\rho\\left(\\delta\\left(\n\\circ \\!\\!-\\!\\!\\circ \\;\\leftharpoonup \\;\\circ \\!\\!-\\!\\!\\circ\n\\right)\\right) \\label{eq:D-AVM-inactive}\\,.\n\\end{align}\n\\end{subequations}\nInterestingly, the particular semantics for the ``firing'' of transitions as encoding in this DTMC generator is neither a variant of mass-action semantics (wherein each rule would fire with a rate dependent on its number of matches, and so that the overall firing rate of all rules would be utilized to normalize all state-dependent firing rates to probabilities as described in Definition~\\ref{def:DTMC}), nor do all transitions have state-independent, i.e., constant rates. Instead, the \\emph{rewiring rules}~\\eqref{eq:D-AVM-rewire} have rates proportional to $N_{\\bullet\\!-\\!\\circ}$; according to~\\eqref{eq:auxObsAVM}, we have that $N_{\\bullet\\!-\\!\\circ}=N_{\\bullet\\!-\\!\\circ\\;x}\/(N_X-1)^{*}$ (for $x\\in \\{\\bullet,\\circ\\}$), whence the firing rates of the rewiring transitions of the AVM model are found to be proportional to a state-dependent fraction of their mass-action rates! In contrast, the \\emph{adoption} transitions~\\eqref{eq:D-AVM-adopt} as well as the \\emph{inactive} transitions~\\eqref{eq:D-AVM-inactive} are found to follow standard mass-action semantics, which might raise the question of whether the overall ``mixed'' semantics chosen for the AVM model indeed reflect the intended intuitions and empirical findings.\n\nFinally, in view of simulation experiments, we would like to advocate the use of dedicated and high-performance Gillespie-style stochastic graph transformation software such as in particular \\texttt{SimSG}~\\cite{DBLP:journals\/jot\/EhmesFS19} (cf.\\ Section~\\ref{sec:simulations}). More concretely, one may take advantage of the rule-algebraic formulation of DTMCs and CTMCs to identify for a given DTMC with generator $D$ a particular CTMC based upon the \\emph{uniform} infinitesimal generator $H_U:=D-Id_{End(\\hat{\\bfC})}$, so that (if both limits exist) the two alternative probabilistic systems have the same limit distribution (i.e., $\\ket{\\Phi_{\\infty}}=\\lim\\limits_{t\\to\\infty}\\ket{\\Psi(t)}$):\n\\begin{equation}\nD\\ket{\\Phi_{\\infty}}=\\ket{\\Phi_{\\infty}}\\quad \\Leftrightarrow\\quad\n(D-Id_{End(\\hat{\\bfC})})\\ket{\\Phi_{\\infty}}=0\\quad\\leftrightarrow\\quad\n\\left(\\tfrac{d}{dt}\\ket{\\Psi(t)}\\right)\\big\\vert_{t\\to\\infty}\n=\\left(H_U\\ket{\\Psi(t)}\\right)\\big\\vert_{t\\to\\infty}=0\n\\end{equation}\nHowever, CTMC simulations for rules that are not following mass-action semantics are non-standard to date, which is why it is also of interest to consider two particular mass-action type alternative CTMC models that are motivated by the original AVM model:\n\\begin{itemize}\n\\item A ``standard'' \\emph{mass-action semantics (MAS)} CTMC, where the transformation rules in $D_{AVM}$ are defined to act in mass-action semantics (with the base rates ${\\color{qOrange}\\kappa_{\\bullet}}, {\\color{qOrange}\\kappa_{\\circ}},{\\color{qOrange}\\alpha_{\\bullet}},{\\color{qOrange}\\alpha_{\\circ}}\\in \\bR_{>0}$ however not fixed in any evident way from the original AVM model interpretation):\n\\begin{subequations}\n\\begin{align}\nH_{MAS}&={\\color{qOrange}\\kappa_{\\bullet}}\\cdot\n\\rho\\left(\\delta\\left(\\begin{matrix}\\bullet \\hphantom {-}\\circ \\\\[-0.675em] \\!\\!\\!\\!\\!\\!\\backslash \\\\[-0.675em]\\bullet \\end{matrix}\\;\\leftharpoonup \\;\\begin{matrix}\\bullet \\!\\!-\\!\\!\\circ \\\\[-0.25em]\\bullet \\end{matrix}\\right)\\right)\n+{\\color{qOrange}\\kappa_{\\circ}}\\cdot\\rho\\left(\\delta\\left(\n\\begin{matrix}\\bullet \\hphantom {-}\\circ  \\\\[-0.675em] \\;\\;\\;\/\\\\[-0.675em]\\circ \\end{matrix}\\;\\leftharpoonup \\;\\begin{matrix}\\bullet \\!\\!-\\!\\!\\circ \\\\[-0.25em]\\circ \\end{matrix}\\right)\\right)\\label{eq:AVM-H-MAS-rewire}\\\\\n&\\quad+{\\color{qOrange}\\alpha_{\\bullet}}\\cdot\\rho\\left(\\delta\\left(\n\\bullet \\!\\!-\\!\\!\\bullet \\;\\leftharpoonup \\;\\bullet \\!\\!-\\!\\!\\circ\n\\right)\\right)\n+{\\color{qOrange}\\alpha_{\\circ}}\\cdot\\rho\\left(\\delta\\left(\n\\circ \\!\\!-\\!\\!\\circ \\;\\leftharpoonup \\;\\bullet \\!\\!-\\!\\!\\circ\n\\right)\\right) \\label{eq:AVM-H-MAS-adopt}\\\\\n&\\quad-\\hat{O}_{\\bullet\\!-\\!\\circ}({\\color{qOrange}\\kappa_{\\bullet}}(\\hat{O}_{\\bullet}-1)+{\\color{qOrange}\\kappa_{\\circ}}(\\hat{O}_{\\circ}-1)+{\\color{qOrange}\\alpha_{\\bullet}}+{\\color{qOrange}\\alpha_{\\circ}})\\label{eq:AVM-H-MAS-diag}\\,.\n\\end{align}\n\\end{subequations}\nNote that if we let $\\rho(h_{MAS}):=\\eqref{eq:AVM-H-MAS-rewire}+\\eqref{eq:AVM-H-MAS-adopt}$, then the terms in~\\eqref{eq:AVM-H-MAS-diag} are indeed found to be equal to $-\\jcOp{h_{AVM}}$ (utilizing~\\eqref{eq:auxObsAVM} to simplify terms) as required by Theorem~\\ref{def:masCTMC}.\n\\item A \\emph{least-common-multiple (LCM)} variant which is computable from $D_{AVM}$ via the method presented in Example~\\ref{ex:LCM} (with constant and operator-valued contributions to firing rates in {\\color{qOrange}orange}):\n\\begin{subequations}\n\\begin{align}\nH_{LCM}&=\n{\\color{qOrange}\\frac{\\alpha}{2N_E}}\n\\rho\\left(\\delta\\left(\\begin{matrix}\\bullet \\hphantom {-}\\circ \\\\[-0.675em] \\!\\!\\!\\!\\!\\!\\backslash \\\\[-0.675em]\\bullet \\end{matrix}\\;\\leftharpoonup \\;\\begin{matrix}\\bullet \\!\\!-\\!\\!\\circ \\\\[-0.25em]\\bullet \\end{matrix}\\right)\\right){\\color{qOrange}(\\hat{O}_{\\circ}-1)}\n+{\\color{qOrange}\\frac{\\alpha}{2N_E}}\\rho\\left(\\delta\\left(\\begin{matrix}\\bullet \\hphantom {-}\\circ  \\\\[-0.675em] \\;\\;\\;\/\\\\[-0.675em]\\circ \\end{matrix}\\;\\leftharpoonup \\;\\begin{matrix}\\bullet \\!\\!-\\!\\!\\circ \\\\[-0.25em]\\circ \\end{matrix}\\right)\\right){\\color{qOrange}(\\hat{O}_{\\bullet}-1)}\\label{eq:H-AVM-LCM-rewire}\\\\\n&\\begin{aligned}\n&\\quad+{\\color{qOrange}\\frac{(1-\\alpha)}{2N_E}}\\rho\\left(\\delta\\left(\n\\bullet \\!\\!-\\!\\!\\bullet \\;\\leftharpoonup \\;\\bullet \\!\\!-\\!\\!\\circ\n\\right)\\right){\\color{qOrange}(\\hat{O}_{\\bullet}-1)(\\hat{O}_{\\circ}-1)}\\\\\n&\\quad+{\\color{qOrange}\\frac{(1-\\alpha)}{2N_E}}\\rho\\left(\\delta\\left(\n\\circ \\!\\!-\\!\\!\\circ \\;\\leftharpoonup \\;\\bullet \\!\\!-\\!\\!\\circ\n\\right)\\right){\\color{qOrange}(\\hat{O}_{\\bullet}-1)(\\hat{O}_{\\circ}-1)}\\end{aligned} \\label{eq:H-AVM-LCM-adopt}\\\\\n&\\quad-{\\color{qOrange}\\frac{1}{N_E}\\hat{O}_{\\bullet\\!-\\!\\circ}{\\color{qOrange}(\\hat{O}_{\\bullet}-1)(\\hat{O}_{\\circ}-1)}} \\label{eq:H-AVM-LCM-diag}\\,.\n\\end{align}\n\\end{subequations}\nExpanding terms in $H_{LCM}$ via utilizing once again the representation property of $\\rho$ (not presented here for brevity; cf.\\ \\cite[Thm.~3]{BK2020} for the details), we may write $H_{LCM}$ in the equivalent form below, which exhibits this CTMC model as a particular instance of a model for which all rules have the same input motif (and thus as a model in the spirit of the ``Potsdam approach'' as in~\\cite{giese2012}):\n\\begin{subequations}\\label{eq:potsdam-rules}\n\\begin{align} \nH_{LCM}&={\\color{qOrange}\\frac{\\alpha}{2N_E}}\\rho\\left(\\delta\\left(\n\\begin{matrix}\n\\bullet \\hphantom {-}\\circ\\\\[-0.65em]\n| \\hphantom{-\\circ}\\\\[-0.65em]\n\\bullet \\hphantom {-}\\circ\n\\end{matrix}\\;\\leftharpoonup\\;\n\\begin{matrix}\n\\bullet \\!\\!-\\!\\!\\circ\\\\[-0.65em]\n\\hphantom{-\\circ}\\\\[-0.65em]\n\\bullet \\hphantom {-}\\circ\n\\end{matrix}\n\\right)\\right)\n+{\\color{qOrange}\\frac{\\alpha}{2N_E}}\\rho\\left(\\delta\\left(\n\\begin{matrix}\n\\bullet \\hphantom {-}\\circ\\\\[-0.65em]\n\\hphantom{\\bullet-}|\\\\[-0.65em]\n\\bullet \\hphantom {-}\\circ\n\\end{matrix}\\;\\leftharpoonup\\;\n\\begin{matrix}\n\\bullet \\!\\!-\\!\\!\\circ\\\\[-0.65em]\n\\hphantom{-\\circ}\\\\[-0.65em]\n\\bullet \\hphantom {-}\\circ\n\\end{matrix}\n\\right)\\right)\\label{eq:H-AVM-LCM-alt-rewire}\\\\\n&\\quad+{\\color{qOrange}\\frac{1-\\alpha}{2N_E}}\\rho\\left(\\delta\\left(\n\\begin{matrix}\n\\bullet \\!\\!-\\!\\!\\bullet\\\\[-0.65em]\n\\hphantom{-\\circ}\\\\[-0.65em]\n\\bullet \\hphantom {-}\\circ\n\\end{matrix}\\;\\leftharpoonup\\;\n\\begin{matrix}\n\\bullet \\!\\!-\\!\\!\\circ\\\\[-0.65em]\n\\hphantom{-\\circ}\\\\[-0.65em]\n\\bullet \\hphantom {-}\\circ\n\\end{matrix}\n\\right)\\right)\n+{\\color{qOrange}\\frac{1-\\alpha}{2N_E}}\\rho\\left(\\delta\\left(\n\\begin{matrix}\n\\circ \\!\\!-\\!\\!\\circ\\\\[-0.65em]\n\\hphantom{-\\circ}\\\\[-0.65em]\n\\bullet \\hphantom {-}\\circ\n\\end{matrix}\\;\\leftharpoonup\\;\n\\begin{matrix}\n\\bullet \\!\\!-\\!\\!\\circ\\\\[-0.65em]\n\\hphantom{-\\circ}\\\\[-0.65em]\n\\bullet \\hphantom {-}\\circ\n\\end{matrix}\n\\right)\\right)\\label{eq:H-AVM-LCM-alt-adapt}\\\\\n&\\quad -{\\color{qOrange}\\frac{1}{N_E}\\hat{O}_{\\text{\\tiny{$\\begin{matrix}\n\\bullet \\!\\!-\\!\\!\\circ\\\\[-0.65em]\n\\hphantom{-\\circ}\\\\[-0.65em]\n\\bullet \\hphantom {-}\\circ\n\\end{matrix}$}}}}\\label{eq:H-AVM-LCM-alt-diag}\n\\end{align}\n\\end{subequations}\n\\end{itemize}\n\\end{example}\n\n\n\n\n\n\\section{Simulating the Models}\\label{sec:simulations}\n\n\nIn Section~\\ref{sec:dtmc} we presented several ways of converting a DTMC-based model into a CTMC-based one. The first (M1) is based on introducing weight factors correcting for the deviation of the probabilistic view of the DTMC from the CTMC mass action semantics. This allows us to use a modified stochastic simulation algorithm to recover the behavior of the DTMC. Then we have the mass action stochastic graph transformation system (M2) as introduced in Section~\\ref{sec:voter-models}, in our view the most natural and closest to reality due to its use of continuous time, but in order to relate to the original probabilistic formulation we have to sample rate constants experimentally until the behavior matches that observed in the given model. Finally we consider a model (M3) obtained by mutually extending the rules of the system to the same left-hand side. Then all rules have the same number of matches and hence rates directly reflect probabilities. \n\nIn this section we simulate these models with the CTMC-based SimSG tool~\\cite{DBLP:journals\/jot\/EhmesFS19} to see how, with suitably chosen parameters, their behavior matches that of the original formulation~\\cite{Durrett2012}. In particular, we want to answer the following questions.\n\\begin{description}\n\\item[RQ1:] Can we reproduce the results of~\\cite{Durrett2012} by simulating (M1) in SimSG?\n\\item[RQ2:] What rates do we have to use to reproduce the behavior of~\\cite{Durrett2012} in (M2)?\n\\item[RQ3:] Does (M3) with rates reflecting the probabilities of~\\cite{Durrett2012} lead to the same overall behavior?\n\\end{description}\nNote that in (M1)  and (M2) rates are derived analytically based on the theory in Section~\\ref{sec:dtmc} while they are determined experimentally for (M3). \n\\begin{figure}[h] \n\t\\centering\n\t\\subfigure[Initial graph (u=0.5)]{\\includegraphics[width=0.31\\textwidth]{graphics\/initialGraph.PNG}}\n\t\\hfill\n\t\\subfigure[Giant component]{\\includegraphics[width=0.31\\textwidth]{graphics\/giantComponentGraph.PNG}}\n\t\\hfill\n\t\\subfigure[Fragmented graph]{\\includegraphics[width=0.31\\textwidth]{graphics\/segmentedGraph.PNG}}\n\t\\caption{Graphs before and after simulation}\\label{fig:instance-graphs}\n\\end{figure}\nAs in~\\cite{Durrett2012} initial graphs are generated randomly based on a fraction $u$ of agents voting 0 (where $u = 0.5$ gives a 50\/50 split between opinions) by deciding for each pair of nodes with probability $v$ if they should be linked. This means that, with 100 voters and $v = 0.04$, we create an Erd{\\\"o}s-R{\\'en}yi graph with 400 links and average degree 8.\nAccording to~\\cite{Durrett2012} we expect to see one of two behaviors, depending on the probability $\\alpha$ of rewiring (vs. $1 - \\alpha$ for adoption) for a given discordant link. With $\\alpha > 0.43$ rewiring causes a fragmentation of the graph into homogeneous connected components; otherwise adoption leads to the dominance of a single opinion (usually the initial majority) in a giant component.  \nVisually we indicate opinion 1 in green and opinion 0 in red. Homogeneous components are highlighted in their respective color, whereas heterogeneous components are shown in gray. For example, Figure~\\ref{fig:instance-graphs}(a) shows the initial graph. In the limit, if the rates favor the adopt rules we obtain a graph as in Figure~\\ref{fig:instance-graphs}(b), while Figure~\\ref{fig:instance-graphs}(c) shows a possible result of dominant rewiring where the graph has split split into two components, one for each opinion.\n\\begin{figure}[h] \n\t\\centering\n\t\\subfigure[DTMC Version of the Voter Model]{\\includegraphics[width=0.48\\textwidth]{graphics\/ResultsDiscrete.pdf}}\n\t\\hfill\n\t\\subfigure[CTMC Version of the Voter Model]{\\includegraphics[width=0.48\\textwidth]{graphics\/ResultsMassAction.pdf}}\n\t\\caption{Simulation results}\\label{fig:sim-results}\n\\end{figure}\n\nTo answer RQ1 we use the rules as presented in Section~\\ref{sec:voter-models}, but modify the simulation algorithm by the weight factors derived in Section~\\ref{sec:dtmc}. This produces a simulation matching that of a discrete time Markov chain. While  fixing the model size, we perform a nested parameter sweep over $\\alpha$, the static probability of rewiring, and over the fraction $u$ of agents voting $0$.\nThe results are shown in Figure~\\ref{fig:sim-results}(a). On the $y$-axis we plot the fraction of voters with the minority opinion in the final graph, while the $x$-axis shows the \\(\\alpha\\) value for each simulation. Furthermore, each set of symbols in the figure represents a different opinion ratio $u$ in the initial graph. As we can see, independently of the $u$ there is a clear point after which an increase in $\\alpha$ leads to a separation of voters by opinion, which implies a segmentation of the graph. In turn, if $\\alpha$ is low, the minority opinion disappears. Thus, Figure~\\ref{fig:sim-results}(a) reflects very closely the findings of~\\cite{Durrett2012}, with only a minor deviation of the value of $\\alpha$ separating the two outcomes.\t\n\t\t\nFor RQ2, we execute the same rules with our standard implementation simulation algorithm reflecting mass action CTMC semantics. While fixing the rate of the adopt rules as 1, we perform a nested parameter sweep over $\\alpha$, in this case denoting the rate of the rewiring rules, and the minority fraction $u$. \nThe results are shown in Figure~\\ref{fig:sim-results}(b), again with the $y$-axis showing the fractions of voters in the minority in each final graph and the $x$-axis tracking the $\\alpha$ values. As before, each set of symbols represents a different initial fraction $u$. In contrast to Figure~\\ref{fig:sim-results}(a), here the threshold of $\\alpha$ at which the final graph becomes segmented is orders of magnitudes smaller. This is a result of the CTMC-based simulation algorithm, that obtains the rule application probability by multiplying a rule's match count with its static rate. Intuitively, the set of matches for each of the adopt rules consists of all connected pairs of voters $v1, v2$ of different opinion. Instead, the set of matches of the rewire rules is made up by the Cartesian product of this first set with the set of voters sharing the opinion of $v1$.  To find the same balancing point as in the probabilistic model, this ``unfair advantage\" of the rewire rules is compensated for by a very low rate.\n\n\n\\begin{figure}[h] \n\t\\centering\n\t\\includegraphics[width=0.48\\textwidth]{graphics\/ResultsPotsdam.pdf}\n\t\\caption{Simulation results of the alternative CTMC Version described by the rules in equation (\\ref{eq:potsdam-rules})}\\label{fig:sim-results2}\n\\end{figure}\n\nFinally, to address RQ3 we perform simulations using adopt and rewire rules extended to a common left-hand side consisting of two connected voters $v1,v2$ of conflicting opinions plus one extra voter each of opinion $0$ and $1$. By the same argument as above this leads to a large increase in the number of matches and hence poses scalability challenges to the simulation. To address this we used a smaller initial graph of 50 Voters and 200 groups and executed only 10 simulation runs per parameter configuration rather than 40 as in the other two models. (In each case, configurations range across 3 values for $u$ and 7 values for $\\alpha$ totaling 21 parameter configurations for each model.) The results are shown in Figure~\\ref{fig:sim-results2} using the same layout as before.  \nIt is interesting that, despite the high degree of activity in this model due to the very large match count, it displays almost the same behavior as the DTMC version (M1), even down to the $\\alpha$ threshold. \n\nThe limited scalability of this approach is in part due to the global nature of the requirement that all rules share the same left-hand side. In the MDP-based approach of~\\cite{giese2012} this applies only to the subsets of rules defining the same action. One could then consider the  four alternatives of rewire and adopt as cases of the same action of resolving a conflict edge, leading to a probabilistic graph transformation system with one rule. An analysis of the relation of mass-action CTMC with MDP-based semantics, however, is beyond the scope of this paper.\n\nSocial network analysis of the voter model and its variants is limited to a theoretical level, exploring mechanisms resulting in certain emergent phenomena that are observable in real-life networks, but are not quantified using real data. For a deeper quantitative analysis of phenomena such as the spread of opinions or the fragmentation of networks, the parameters of our rule-based models need to be matched to real social network data where such is available. This means, in particular, to determine the rates of the rules, e.g., from observations of pattern frequencies.\n \nSuch approaches are well established in chemical and biological modeling where statistical methods are used to derive rates of reaction rules from concentrations, i.e., relative pattern frequencies describing the ratios of the different types molecules~\\cite{ Klinke2014InSM, Eydgahi2013MSB}. Instead, the derivation of an equational model from the operational rule-based description based on the rule algebra approach described in this paper could allow for an analytical approach where rates are determined by solving a system of equations. The precise conditions under which this is possible are a subject of future research.\n\n\n\\section{Conclusion}\n\n\nIn this paper we analyzed the non-standard semantics behind the formulation of adaptive system models in the literature. \nFor a simple but prototypical example, we focused specifically on the voter models of opinion formation in social networks. We analyzed the non-standard semantics behind these models and established that they can be seen as Discrete-Time Markov Chains (DTMCs). In order to start the study of such models using the concepts, theories and tools of stochastic graph transformations (SGTS), we formalized the semantic relation between the rule-based specification by SGTS of mass-action Continuous-Time Markov Chains (CTMCs) with the DTMC-based semantics, identifying two systematic ways by which an SGTS can be derived from a DTMC-based model while preserving the behavior in the limit. \n\nIn the first derivation, this leads to a generalized notion of SGTS with weight factors correcting for the mass-action component represented by the dependency of the jump rate on the number of matches for each rule. This new type of SGTS is supported by a generalized simulation algorithm supporting the analysis of DTMC-based probabilistic graph transformation systems which, to our knowledge, is original. The second derivation converts the rules of the system by extending them to the same left-hand sides, producing a model resembling Markov-Decision Process (MDP)-based probabilistic graph transformation rules. \n\nApart from the theoretical analysis, we validate both resulting systems through simulations, establishing that they reproduce the expected behavior of the model. We also create a direct model of the same system as an SGTS with standard mass-action CTMC semantics and succeed in determining its parameters experimentally to match the expected behavior. We conclude that we can use standard mass-action stochastic GTS to model the phenomena expressed by the voter models in the literature, providing a starting point for further more elaborate modeling and analyses. \n\nIn future work we want to study more complex adaptive networks, including variations on the voter model with groups of more than two members, opinion profiles for a set of topics instead of a single opinion per voter, and including concepts such as influencers (who actively try to link to and persuade others), or zealots (who do not change their opinions). We are also planning to study how to match models to  social network data.\nOn the foundational side, we are planning optimizations to the simulation algorithm and a study of the relation between mass-action CTMC and MDP semantics of probabilistic graph transformations. We can also derive and study differential equations (ODEs) from our SGTS using the rule-algebra formalism. This provides a more scalable solution to analyzing their behavior complementing the simulation-based approach.   \n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nDespite the efforts made to understand and constrain the first stars and the process of element formation connected to them, we are after several decades still left with many unanswered questions. How massive were the first stars, and how were the heavy elements we detect in old metal-poor stars created? One way of answering these questions is to study old metal-poor stars. From these stars we can derive accurate stellar abundances, allowing us to trace the progenitor stars that yielded the gas the later stellar generations were made from. It is therefore important to understand if this gas was pure, or mixed with other gases in the interstellar medium.\nMost old dwarf stars of spectral type F and G preserve the original gas composition in their outer atmospheres. This allows us to study pristine gases of elements between lithium and uranium. The lighter elements (Z $< 26$) provide information on the characteristics of the supernova that created them during the explosion. The heavy elements (Z $> 38$) are formed by neutron-capture (n-capture) processes. We have detailed information for some n-capture processes while others remain poorly constrained. By studying abundances of elements that we can tie to the different processes, we can learn about their similarities and differences, which will bring us closer to understanding the formation processes as well as the supernovae (SNe) that host them. \n \n\\section{Data, Sample and Method}\nThe data cover 73 stars in total, two RR lyrae, 29 giants and 42 dwarfs. The high-resolution spectra have been obtained with UVES\/VLT \\cite{dekker} and Hires\/Keck \\cite{vogt94}. The data reduction and stellar parameter determination is described in \\cite{CJHag}.\nTo derive the abundances we used the 1D local thermodynamic equilibrium (1D LTE) spectral synthesis code MOOG \\cite{snedenphd} and MARCS model atmospheres \\cite{Gus08}.\n\n\\section{Tracing the first supernovae with RR Lyrae stars}\nSeveral studies have shown that very evolved stars, such as RR lyrae stars, can be used as chemical tracers \\cite{taut,hansenRR,for} as they preserve the gases of elements heavier than lithium in their surfaces.\nBy comparing the derived stellar abundances to a variety of SN yields we can extract information about the early (first?) SN such as mass, energy and electron fractions ($Y_e$). This may provide insight into the nature of the first stars. We compare to yield predictions from \\cite{lim,koba,tom,Izu} covering a mass range of 13-40$M_{\\odot}$, and an energy range of 1-10 foe, with or without jets\/asymmetric explosions (see Fig. \\ref{SN}).\n\\begin{figure}\n  \\includegraphics[height=.45\\textheight]{SNy_proceednew_lte.eps}\n  \\caption{Stellar abundances derived for the two RR lyrae stars are compared to the SN yield predictions (references are listed in the legend).\\label{SN}}\n\\end{figure}\nThe odd-even effect help to constrain the SN progenitor mass, the iron-peak elements are connected to the peak temperature of the explosion, while e.g. Sc provides information on the explosion energy and $Y_e$. The comparison in Fig. \\ref{SN} points towards an early generation of SN, which existed well below [Fe\/H]=$-3.3$ with a progenitor mass of around 40$M_{\\odot}$ and high explosion energy. However, several quantities such as the estimated SN mass will be lowered if non-LTE effects are considered. These SN could be the objects that created the very heavy elements during their explosion. \n\n\\begin{figure}\n  \\includegraphics[height=.28\\textheight]{AgSrSrH_DGfit_astPH.ps}\n\\end{figure}\n\\vspace{-19mm}\n\\begin{figure}\n  \\includegraphics[height=.28\\textheight]{AgPdPdH_DGfit_astPH.ps}\n\\end{figure}\n\\vspace{-9mm}\n\\begin{figure}\n  \\includegraphics[height=.32\\textheight]{AgEuEuH_DGfit_astPH_new.ps}\n  \\caption{Silver compared to Sr, Pd, and Eu in the giant and dwarf stars from our sample.\\label{SrAgEu}}\n\\end{figure}\n\\clearpage\n\n\n\\section{The evolution of heavy elements}\nThe majority of the heavy elements are produced in neutron-rich, very energetic environments.\nThere are two main channels through which the heavy elements can be made: a secondary slow n-capture (s-)process and a primary rapid n-capture (r-)process. Each of these production channels seem to branch into two (weak and main) n-capture processes. Here an observational study is presented attempting to map the features of the weak r-process.\n\n\nThe elements that were targeted for this study are: Sr, Y, Zr, Pd, Ag, Ba, and Eu. Pd and Ag are assumed to be created by the weak r-process, whereas e.g. Sr is created by a weak s-process \\cite{heil} (or charged particle process at low metallicity) and Eu is formed by a main r-process \\cite{arland} at all metallicities. In order to understand the weak r-process better we compare Ag to Sr and Pd to see how their formation processes differ. If the two elements are formed by the same process this will be seen as a flat (horizontal) trend in the abundance plots, otherwise the trend will be a line with a negative slope.\nFigure \\ref{SrAgEu} shows that Pd and Ag share a formation process, which is very different from the weak s-process\/charged particle process and the main r-process. This weak r-process is also very different from the main s-process responsible for creating Ba (cf. \\cite{CJHag}).\nTo understand the characteristics and environment of the weak r-process, the observationally derived abundances are compared to self-consistent faint O-Ne-Mg electron-capture SN 2D models \\cite{wan11} as well as the high-entropy wind (HEW) \\cite{farou} parameter studies.    \n\n\n\nThe right-hand plots in Fig. \\ref{model} shows the abundances compared to the HEW model predictions, and the left-hand plots illustrates the O-Ne-Mg SN yields. In general Sr-Ag can in all stars and both models be produced by one model\/one set of parameters, while Ba and Eu require very different parameters\/features in the formation processes. The elements lighter than Ag can be correctly predicted either by an entropy $125 \\leq S \\leq 175 k_B\/baryon$ or an $Y_e \\geq 0.25$, while Ba and Eu generally need $S > 225$ and $Y_e < 0.2$. This is also true for stars with pure r-process abundance patterns ([Ba\/Eu]$<-0.74$), which confirms the r-process nature. These results apply to both r-poor and r-rich stars. It is evident from the comparison to the two models that r-poor and r-rich stars cannot be produced at the same site. The faint O-Ne-Mg SN seems to be a promising site for the weak r-process, and the HEW models yield a pattern that fits those of the r-rich stars well. \n\n\n\\section{Summary}\nThe abundances derived under non-LTE, compared to those derived under the LTE assumption, will provide e.g. a different mass and energy of the SN we are trying to trace. Hence it is central to understand the abundances and stellar parameters when these are derived including non-LTE and 3D effects.\n\n\\begin{figure}[!h]\n  \\includegraphics[height=.25\\textheight]{AllYeBD+42621_wanfewy_astPH.ps}\n  \\includegraphics[height=.24\\textheight]{BD+42621comp_ye045hewless_astPH.eps}\n\\end{figure}\n\\begin{figure}[!h]\n  \\includegraphics[height=.25\\textheight]{AllYeHD115444_wanfewy_astPH.ps}\n  \\includegraphics[height=.24\\textheight]{HD115444comp_ye045hewless_astPH.eps}\n\\end{figure}\n\\begin{figure}[!h]\n  \\includegraphics[height=.25\\textheight]{AllYeHD122563_wanfewy_astPH.ps}\n  \\includegraphics[height=.24\\textheight]{HD122563comp_ye045hewless_astPH.eps}\n  \\caption{Abundances of all seven elements compared to model yield predictions. Three stars have been selected, one that shows a pure r-process pattern, one with an r-poor, and one with an r-rich abundance pattern. The stars are compared to O-Ne-Mg SN [16] on the left-hand side and to the HEW predictions on the right-hand side.\\label{model}}\n\\end{figure}\n\n\nTo explain Pd and Ag abundances we need a weak r-process, which so far seems to differ strongly from the weak\/main s-process as well as the main r-process. The weak r-process is efficiently yielding Pd and Ag at metallicities below [Fe\/H]$=-3.3$. This weak r-process needs lower neutron densities as well as entropies compared to what the main r-process needs, but higher such values than the s-process requires. We need 3D self-consistent SN models and optimised networks to understand quantities such as entropy and electron fractions before we can constrain this weak r-process.   \n\n\n\\begin{theacknowledgments}\n  This work was supported by Sonderforschungsbereich SFB 881 'The Milky Way System' (subproject A5) of the German Research Foundation (DFG). CJH is grateful to F. Primas, H. Hartman, K.-L. Kratz, S. Wanajo, B. Leibundgut, K. Farouqi, N. Christlieb, B. Nordstr\\\"om, P. Bonifacio, M. Spite, J. Andersen, and the First Stars IV organizers.\n\\end{theacknowledgments}\n\n\n\n\\bibliographystyle{aipproc}  \n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nDiffraction puts a limit on the the resolution of optical devices. According to the Rayleigh criterion \\cite{rayleigh,goodman}, the ability to resolve two point sources is limited by the wavelength of the light. The Rayleigh or diffraction limit is not an absolute limit and proposals to exceed it have been known for a long time\n\\cite{goodman}. Recently, new proposals to improve resolution beyond the Rayleigh limit have been made based on the use of entangled sources and new measurement techniques. Improving the resolving power of optical systems beyond the diffraction limit not only is of interest to the fundamental research, but also holds promise applications in remote sensing and quantum sensors.\n\nClassical imaging can be thought of as a single photon process in the sense that the light detected is composed of photons each of which illuminates the object, consequently, the image can be constructed one photon at time. What we mean by referring to this as classical is that the source of the light may be described by a density matrix with a\npositive P-function \\cite{pos1,pos2}. In this sense the Rayleigh limit may be thought of as a single photon limit. Recall that ideal imaging is a process in which there is a point-to-point mapping of the object to a unique image plane. Diffraction causes each point of the object to be mapped onto a disk, the Airy disk, in the image plane.\n\nOne of the new approaches to improving resolution is based on using non-classical light sources. Quantum ghost imaging\n\\cite{todd,streklov,rubin,imaging,shih,milenaL} is a process that uses two-photon entanglement. The unique features of this process are that entanglement allows only one photon to illuminate the object while the second photon does not. All the photons that illuminates the object are detected in a single (bucket) detector that does not resolve the image. The point detectors that detect the second photon must lie in a specific plane. This plane is called the image plane\nalthough there is no image in that plane; the image is formed in the correlation measurement of entangled photons. The image is constructed one pair at a time. The resolution of this system has recently been discussed \\cite{rubin2008,milena}. Losses in this system affect the counting rate but not the quality of the image.\n\nA second approach using non-classical source is based on entangled photon-number states \\cite{dowling}, e.g., N00N state. When the number of entangled photons exceeds two there are many possible imaging schemes that can be envisioned and so the analysis of these cases is still being carried out. This interferometric approach achieves a sub-wavelength spatial resolution by a factor $N$ and requires an $N$-photon absorption process. Another quantum source used to study imaging is to generate squeezed states \\cite{squeezed}. The image can be reconstructed through the homodyne detection \\cite{homodyne}. However, both of these techniques are severely limited by the loss of photons.\n\nA second class of approaches to improving resolution uses classical light sources. One method uses classical light with measurements based on correlations similar to ghost imaging and the Hanbury-Brown and Twiss experiment \\cite{h-t,texts}. This method has the advantage of being more robust with respect to losses \\cite{thermal,thermal2}. Another approach is to build an interferometric lithography with use of classical coherent state \\cite{coherent,coherent2}, which has similar setup to the case using entangled photon-number states.\n\nIn this paper we will consider improving spatial resolution beyond the Rayleigh diffraction limit using quantum imaging with an entangled photon-number state $|1,N\\rangle$. In our imaging scheme by sending the $N$ degenerate photons to the object while keeping the non-degenerate photon and imaging lens in the laboratory, a factor of $N$ improvement can be achieved in spatial resolution enhancement compared to classical optics. The assumptions required for the enhancement by a factor of $N$ are that the $N$ photons sent to the object scatter off the same point and are detected by either an $N$-photon number detector or a bucket detector. This sub-Rayleigh imaging resolution may have important applications in such as improving sensitivities of classical sensors and remote sensing. We emphasize that it is the quantum nature of the state that offers such sub-wavelength resolving power with high visibility. However, the system is very sensitive to loss. While we give general results, our main concern will be with the case in which the object is far from the source and the detectors and optics are close to the source. A different but related approach to the one discussed here is given in \\cite{giovannetti}.\n\nWe organize the paper as follows. We will discuss our imaging scheme with entangled photon-number state $|1,2\\rangle$ in some detail in Sec.~II. In previous work \\cite{wen1,wen2} we have shown that imaging occurs in correlation measurement, as in the ghost imaging case. Here we will show that under certain stringent conditions, the resolution\ncan be improved by a factor of $2$ compared to classical optics. In Sec.~III we generalize the scheme to the\n$|1,N\\rangle$ case and show that resolution improvement by a factor of $N$ can be obtained. In Sec.~IV some discussions will be addressed on other experimental configurations. Finally we will draw our conclusions in Sec.~V.  In an appendix we discuss the meaning of the approximation that the $N$ photons illuminate the same point on the object.\n\n\\section{Three-Photon Optics}\nWe start with three photons because this is the easiest case to investigate the various configurations. Throughout the paper we shall assume that the source of the three photons is a pure state and that the three-photon counting rate for three point detectors is give by\n\\begin{equation}\nR_{cc}=\\frac{1}{T^2}\\int_{0}^{T}dt_1\\int_{0}^{T}dt_2\\int_{0}^{T}dt_3|\\Psi(1,2,3)|^{2},\\label{eq:Coin}\n\\end{equation}\nwhere the three-photon amplitude is determined by matrix element between the vacuum state and the three-photon state\n$|\\psi\\rangle$\n\\begin{equation}\n\\Psi(1,2,3)=\\langle0|E^{(+)}_1E^{(+)}_2E^{(+)}_3|\\psi\\rangle,\\label{eq:Ampl}\n\\end{equation}\nand\n\\begin{equation}\nE^{(+)}_j(\\vec{\\rho}_j,z_j,t_j)=\\int{d}\\omega_j\\int{d^{2}}\\alpha_jE_jf_j(\\omega_j)e^{-i\\omega_jt_j}g_j(\\vec{\\alpha}_j,\n\\omega_j;\\vec{\\rho}_j,z_j)a(\\vec{\\alpha}_j,\\omega_j),\\label{eq:freefield}\n\\end{equation}\nwhere $E_j=\\sqrt{\\hbar\\omega_{j}\/2 \\epsilon_{0}}$, $\\vec{\\alpha}_j$ is the transverse wave vector, and\n$a(\\vec{\\alpha}_j,\\omega_j)$ is a photon annihilation operator at the output surface of the source,\n\\begin{equation}\n[a(\\vec{\\alpha},\\omega),a^{\\dagger}(\\vec{\\alpha}\\prime,\\omega\\prime)]=\\delta(\\vec{\\alpha}-\\vec{\\alpha}\\prime)\n\\delta(\\omega-\\omega\\prime).\\label{eq:commutation rel}\n\\end{equation}\nThe function $f_{j}(\\omega)$ is a narrow bandwidth filter function which is assumed to be peaked at $\\Omega_j$. The function $g_j$ is the Green's function \\cite{goodman,rubin} that describes the propagation of each mode from the output surface of the source to the $j$th detector at the transverse coordinate $\\vec{\\rho}_j$, at the distance from the\noutput surface of the crystal to the plane of the detector, $z_j$. $\\Psi$ is referred to as the \\textit{three-photon amplitude} (or three-photon wavefunction).\n\nWe start with the case in which the source produces three-photon entangled states with a pair of degenerate photons, that is $\\psi\\rightarrow\\psi_{{1,2}}$\n\\begin{equation}\n|\\psi_{1,2}\\rangle=\\int{d}\\omega_1{d}\\omega_2\\int{d^{2 }}\\alpha_1d^2 \\alpha_2\\delta(2\\omega_1+\\omega_2-\\Omega)\\delta(\n2\\vec{\\alpha}_1+\\vec{\\alpha}_2)a^{\\dagger}(\\vec{\\alpha}_2,\\omega_{2})\\big[a^{\\dagger}(\\vec{\\alpha}_1,\\omega_{1})\\big]^2\n|0\\rangle,\\label{eq:state1}\n\\end{equation}\nwhere $\\Omega$ is a constant, $\\omega_{1,2}$ and $\\vec{\\alpha}_{1,2}$ are the frequencies and transverse wave vectors of the degenerate and non-degenerate photons, respectively. The $\\delta$-functions indicate that the source is assumed to produce three-photon states with perfect phase matching. We assume the paraxial approximation holds and that the temporal and transverse behavior of the waves factor. The frequency correlation determines the three-photon temporal\nproperties. The transverse momentum correlation determines the spatial properties of entangled photons. It is this wave-vector correlation that we are going to concentrate on. As discussed in \\cite{wen1}, several imaging schemes can be implemented with this three-photon source. To demonstrate spatial resolution enhancement beyond the Rayleigh diffraction limit, consider the experimental setup shown in Fig.~\\ref{fig:2photon}. It will be shown that for this configuration the spatial resolving power is improved by a factor of 2, provided the degenerate photons\nilluminate the same point on the object and are detected by a two photon detector.\n\\begin{figure}[tbp]\n\\includegraphics[scale=0.6]{2photon.pdf}\n\\caption{(color online) Schematic of quantum imaging with a three-photon entangled state $|1,2\\rangle$. $d_1$ is the distance from the output surface of the source to the object. $L_1$ is the distance from the object to a 2-photon detector, D$_1$. $d_2$ is the distance from the output surface of the source to the imaging lens with focal length $f$ and $L_2$ is the length from the imaging lens to a single-photon detector D$_2$, which scans coming signal photons in its transverse plane. ``C.C.\" represents the joint-detection measurement.}\\label{fig:2photon}\n\\end{figure}\n\nAs depicted in Fig.~\\ref{fig:2photon}, two degenerate photons with wavelength $\\lambda_1$ are sent to a two-photon detector (D$_1$) after illuminating an object, and the non-degenerate photon with wavelength $\\lambda_2$ propagates to a single-photon detector (D$_2$) after an imaging lens with focal length $f$. The three-photon amplitude\n(\\ref{eq:Ampl}) for detectors D$_1$ and D$_2$, located at $(z_1,\\vec{\\rho}_1)$ and $(z_2,\\vec{\\rho}_2)$, now is\n\\begin{equation}\n\\Psi\\rightarrow\\Psi_{1,2}=\\langle0|E^{(+)}_2(\\vec{\\rho}_2,z_2,t_2)\\big[E^{(+)}_1(\\vec{\\rho}_1,z_1,t_1)\\big]^2|\\psi_{1,2}\n\\rangle, \\label{eq:coincidence}\n\\end{equation}\nFollowing the treatments in \\cite{rubin,goodman,wen1}, we evaluate the Green's functions\n$g_1(\\vec{\\alpha}_1,\\omega_2;\\vec{\\rho}_1,z_1)$ and $g_2(\\vec{\\alpha}_2,\\omega_2;\\vec{\\rho}_2,z_2)$ for the experimental setup of Fig.~\\ref{fig:2photon} assuming that the narrow bandwidth filter allows us to make the assumption that $\\omega_{j}=\\Omega_j+\\nu_j$ where $|\\nu_j|\\ll\\Omega_j$ and $2\\Omega_1+\\Omega_2=\\Omega$.\n\nIn the paraxial approximation it is convenient to write\n\\begin{equation}\ng_j(\\vec{\\alpha}_j,\\omega_j;\\vec{\\rho}_j,z_j)=\\frac{\\omega_je^{i\\omega_jz_j \/c}}{i 2\\pi cL_jd_j}\n\\chi_j(\\vec{\\alpha}_{j},\\omega_{j};\\vec{\\rho}_{j},z_{j}),\\label{eq:chi}\n\\end{equation}\nthen\n\\begin{eqnarray}\n\\chi_1(\\vec{\\alpha}_1,\\Omega_1;\\vec{\\rho}_1,z_1)&=&e^{-i\\frac{d_1|\\vec{\\alpha}_1|^2}{2K _1}}\\int{d^{2}}\\rho_o\nA(\\vec{\\rho}_o)e^{i\\frac{K_1|\\vec{\\rho}_o|^2}{2L_1}}e^{-i\\frac{K_1\\vec{\\rho}_1\\cdot\\vec{\\rho}_o}{L_1}}\ne^{i\\vec{\\alpha}_1\\cdot\\vec{\\rho}_o},\\label{eq:g1}\\\\\n\\chi_2(\\vec{\\alpha}_2,\\Omega_2;\\vec{\\rho}_2,z_2)&=&e^{-i\\frac{d_2|\\vec{\\alpha}_2|^2}{2K_2}}\\int{d^{2}}\\rho_l\ne^{i\\frac{K_2|\\vec{\\rho}_l|^2}{2}(\\frac{1}{L_2}-\\frac{1}{f})}e^{i(\\vec{\\alpha}_2-\\frac{K_2}{L_2}\\vec{\\rho}_2)\\cdot\n\\vec{\\rho}_l},\\label{eq:g2}\n\\end{eqnarray}\nwhere we replace $\\omega_j$ by $\\Omega_j$ in $\\chi_j$, $K_j=\\Omega_j \/c=2\\pi\/\\lambda_j$, $z_1=d_1+L_1$, and $z_2=d_2+L_2$, respectively. In Eqs.~(\\ref{eq:g1}) and (\\ref{eq:g2}), $A(\\vec{\\rho}_o)$ is the aperture function of the object, and $\\vec{\\rho}_o$ and $\\vec{\\rho}_l$ are two-dimensional vectors defined, respectively, on the object and the imaging lens planes. With use of Eqs.~(\\ref{eq:freefield}) and (\\ref{eq:state1}), the three-photon amplitude (\\ref{eq:coincidence}) becomes\n\\begin{equation}\n\\Psi_{1,2}=e^{i(2\\Omega_1\\tau_1+\\Omega_2\\tau_2)}\\Phi_{1,2},\\label{Phi12}\n\\end{equation}\nwhere $\\tau_j=t_j-z_j\/c$ and\n\\begin{eqnarray}\n\\Phi_{1,2}=\\int{d}\\nu_1d\\nu_2\\delta(2\\nu_1+\\nu_2)e^{i(2\\nu_1 \\tau_1+\\nu_2\\tau_2)}f_1(\\Omega_1+\\nu_1)^2f_2 (\\Omega_2+\\nu_2)B_{1,2}.\\label{eq:Psi1}\n\\end{eqnarray}\nwhere\n\\begin{eqnarray}\nB_{1,2}&=&B_{0}\\int{d^{2}}\\rho_oA(\\vec{\\rho}_o)e^{i\\frac{K_1|\\vec{\\rho}_o|^2}{2L_1}}e^{-i\\frac{K_1\\vec{\n\\rho}_1\\cdot\\vec{\\rho}_o}{L_1}}\\int{d^{2}}\\rho'_oA(\\vec{\\rho}'_o)e^{i\\frac{K_1|\\vec{\\rho}'_o|^2}{2L_1}}e^{-i\n\\frac{K_1\\vec{\\rho}_1\\cdot\\vec{\\rho}'_o}{L_1}}\\int{d^{2}}\\rho_le^{i\\frac{K_2|\\vec{\\rho}_l|^2}{2}(\\frac{1}{\nL_2}-\\frac{1}{f})}e^{-i\\frac{K_2}{L_2}\\vec{\\rho}_2\\cdot\\vec{\\rho}_l}\\nonumber\\\\\n&&\\times\\int{d^{2 }}\\alpha_1e^{-i|\\vec{\\alpha}_1|^2(\\frac{d_1}{K_1}+\\frac{2d_2}{K_2})}e^{-i\\vec{\\alpha}_1\n\\cdot(2\\vec{\\rho}_l-\\vec{\\rho}_o-\\vec{\\rho}'_o)},\\label{eq:psiapproximation}\n\\end{eqnarray}\nwhere we collect all the slowly varying quantities into the constant $B_{0}$. To proceed the discussion, in the following we will consider two different detection schemes. One uses a point two-photon detector for two degenerate photons after the object and the other has a two-photon bucket detector.\n\n\\subsection{Point Two-Photon Detector Scheme}\nIn this detection scheme, a point two-photon detector is necessary to retrieve the information of degenerate photons scattered off the same point in the object. We therefore make the key assumption that the detector D$_1$ is only sensitive to the signals from the same point in the object, i.e., $\\delta(\\vec{\\rho}_o-\\vec{\\rho}'_o)$ [The validity of this assumption is addressed in the Appendix]. With this assumption, Eq.~(\\ref{eq:psiapproximation}) becomes\n\\begin{eqnarray}\nB_{1,2}&=&B_{0}\\int{d^{2}}\\rho_oA^2(\\vec{\\rho}_o)e^{i\\frac{K_1|\\vec{\\rho}_o|^2}{L_1}}e^{-i\\frac{2K_1\\vec{\n\\rho}_1\\cdot\\vec{\\rho}_o}{L_1}}\\int{d^{2}}\\rho_le^{i\\frac{K_2|\\vec{\\rho}_l|^2}{2}(\\frac{1}{L_2}-\\frac{1}{f})}\ne^{-i\\frac{K_2}{L_2}\\vec{\\rho}_2\\cdot\\vec{\\rho}_l}\\nonumber\\\\\n&&\\times \\int{d^{2 }}\\alpha_1e^{-i|\\vec{\\alpha}_1|^2(\\frac{d_1}{K_1}\n+\\frac{2d_1}{K_2})}e^{-2i\\vec{\\alpha}_1\\cdot(\\vec{\\rho}_l-\\vec{\\rho}_o)}.\\label{eq:Psiassumption}\n\\end{eqnarray}\nCompleting the integration on the transverse mode $\\vec{\\alpha}_1$ in Eq.~(\\ref{eq:Psiassumption}) gives\n\\begin{eqnarray}\nB_{1,2}&=& B_{0}\\int{d^{2}}\\rho_oA^2(\\vec{\\rho}_o)e^{iK_1|\\vec{\\rho}_o|^2\n[\\frac{1}{L_1}+\\frac{1}{d_1+(2\\lambda_2\/\\lambda_1)d_2}]}e^{-i\\frac{2K_1\\vec{\\rho}_1\\cdot\\vec{\\rho}_o}{L_1}}\\nonumber\\\\\n&&\\times\\int{d^{2}}\\rho_le^{i\\frac{K_2|\\vec{\\rho}_l|^2}{2}[\\frac{1}{L_2}+\\frac{1}{d_2+(\\lambda_1\/2\\lambda_2)d_1\n}-\\frac{1}{f}]}e^{-iK_2\\vec{\\rho}_l\\cdot[\\frac{\\vec{\\rho}_2}{L_2}+\\frac{\\vec{\\rho}_o}{d_2+(\\lambda_1\/2\n\\lambda_2)d_1}]}.\\label{eq:psiassumption2}\n\\end{eqnarray}\nBy imposing the Gaussian thin-lens imaging condition in Eq.~(\\ref{eq:psiassumption2})\n\\begin{eqnarray}\n\\frac{1}{f}=\\frac{1}{L_2}+\\frac{1}{d_2+(\\lambda_1\/2\\lambda_2)d_1},\\label{eq:GTLE1}\n\\end{eqnarray}\nthe transverse part of the three-photon amplitude reduces to\n\\begin{eqnarray}\nB_{1,2}&=&B_{0}\\int{d^{2}}\\rho_oA^2(\\vec{\\rho}_o)e^{iK_1|\\vec{\\rho}_o|^2[\\frac{1}{L_1}+\\frac{1}{d_1\n+(2\\lambda_2\/\\lambda_1)d_2}]}e^{-i\\frac{2K_1\\vec{\\rho}_1\\cdot\\vec{\\rho}_o}{L_1}}\\mathbf{somb}\\bigg(\\frac{2\\pi{R}}{\n\\lambda_2[d_2+(\\lambda_1\/2\\lambda_2)d_1]}\\bigg|\\vec{\\rho}_o+\\frac{\\vec{\\rho}_2}{m}\\bigg|\\bigg),\\label{eq:psif}\n\\end{eqnarray}\nwhere $R$ is the radius of the imaging lens, $R\/[d_2+(\\lambda_1\/2\\lambda_2)d_1]$ may be thought of as the numerical aperture of the imaging system, and $m=L_2\/[d_2+(\\lambda_1\/2\\lambda_2)d_1]$ is the magnification factor. In Eq.~(\\ref{eq:psif}) the Airy disk is determined, as usual, by $\\mathbf{somb}(x)=2J_1(x)\/x$, where $J_1(x)$ is the first-order Bessel function.\n\nBefore proceeding with the discussion of resolution, let us look at the physics behind Eqs.~(\\ref{eq:GTLE1}) and (\\ref{eq:psif}). Equation (\\ref{eq:GTLE1}) defines the image plane where the ideal the point-to-point mapping of the\nobject plane occurs. The unique point-to-point correlation between the object and the imaging planes is the result\nof the transverse wavenumber correlation and the fact that we have assumed that the degenerate photons illuminate the same object point. Let us make a comparison with the two-photon and three-photon geometrical optics\n\\cite{rubin,wen1,rubin2008}. In the Gauss thin lens equation the distance between the imaging lens and the object planes, $d_2+(\\lambda_1\/2\\lambda_2)d_1$ is similar to the form that appears in the non-degenerate two-photon case except for the factor of 2. This factor 2 comes from the degeneracy of the pair of photons that illuminate the object. As we will show below, this factor of 2 is the source of the improved spatial resolution. Equation (\\ref{eq:psif}) implies that a coherent and inverted image magnified by a factor of m is produced in the plane of $D_{2}$. Of course, there really is no such image and the true image is \\textit{nonlocal}. The point-spread function in Eq.~(\\ref{eq:psif}) is generally determined by both wavelengths of the degenerate and non-degenerate photons.\n\nTo examine the resolution using the Rayleigh criterion, we consider an object consisting of two point scatters, one located at the origin and the other at the point $\\vec{a}$ in the object plane,\n\\begin{equation}\nA(\\vec{\\rho}_o)^2=A_0^2\\delta(\\vec{\\rho}_o)+A_{\\vec{a}}^2\\delta(\\vec{\\rho}_o-\\vec{a}).\\label{eq:object}\n\\end{equation}\nBy substituting Eq.~(\\ref{eq:object}) into (\\ref{eq:psif}) we obtain\n\\begin{eqnarray}\nB_{1,2}=B_{0}\\bigg({A}^2_0 \\mathbf{somb}\\bigg(\\frac{2\\pi{R}}{\\lambda_2}\\bigg|\\frac{\\vec{\\rho}_2}{L_2}\\bigg|\\bigg)+e^{i\n\\varphi_2}A_{\\vec{a}}^2\\mathbf{somb}\\bigg[\\frac{2\\pi{R}}{\\lambda_2}\\bigg|\\frac{\\vec{\\rho}_2}{L_2}+\\frac{\\vec{a}}{d_2+(\n\\lambda_1\/2\\lambda_2)d_1}\\bigg|\\bigg]\\bigg),\\label{eq:Psirayleigh}\n\\end{eqnarray}\nwhere the phase\n\\begin{equation}\n\\varphi_2=K_1\\bigg[|\\vec{a}|^2\\bigg(\\frac{1}{L_1}+\\frac{1}{d_1+d_2(2\\lambda_2\/\\lambda_1)}\\bigg)-\\frac{\\vec{a}\n\\cdot(\\vec{\\rho}_1+\\vec{\\rho}'_1)}{L_1}\\bigg]\\label{eq:phase2}\n\\end{equation}\nindicates that the image is coherent. For a point $2$-photon detector, we require $\\vec{\\rho}_1=\\vec{\\rho}'_1$ in Eq.~(\\ref{eq:phase2}). As is well-known \\cite{goodman} for coherent imaging the Rayleigh criterion is not the best choice for characterizing the resolution, however, it is indicative of the resolution that can be attained and it is convenient. For a circular aperture, the radius of the Airy disk, $\\xi$, is determined by the point-spread function, which is\n\\begin{equation}\n\\xi=0.61\\frac{\\lambda_2L_2}{R}.\\label{eq:airydisk1}\n\\end{equation}\nNote that the radius of the Airy disk is proportional to the wavelength of the non-degenerate photon. This is the standard result as obtained in classical optics. Using the Rayleigh criterion, the image of the second term in Eq.~(\\ref{eq:Psirayleigh}) is taken to lie on the edge of the Airy disk of the first term, therefore,\n\\begin{equation}\na_{\\mathrm{m}}=0.61\\frac{\\lambda_2}{R}\\bigg(d_2+\\frac{\\lambda_1}{2\\lambda_2}d_1\\bigg).\\label{eq:resolution1}\n\\end{equation}\nWe see from Eq.~(\\ref{eq:resolution1}) that the resolution depends on the wavelengths of the degenerate and the non-degenerate photons. In the case that $d_1\\gg{d}_2$, so that $d_2+(\\lambda_1\/2\\lambda_2)d_1$, is approximately  $(\\lambda_1\/2\\lambda_2)d_1$. In this case Eq.~(\\ref{eq:GTLE1}) implies that $L_2\\approx f$ and the radius of the Airy disk approaches to $1.22\\lambda_2f\/R$, and\n\\begin{equation}\na_{\\mathrm{m}}=0.61\\frac{\\lambda_1d_1\/2}{R}.\\label{eq:resolution2}\n\\end{equation}\nEquation~(\\ref{eq:resolution2}) shows a gain in spatial resolution of a factor of 2 compared to classical optics.\nFurthermore, there is no background term which is characteristic of the quantum case.\n\n\\subsection{Bucket Detector Scheme}\nIf the two-photon detector is replaced by a bucket detector and  the two degenerate photons are collected by two single-photon detection events, located at $(L_1,\\vec{\\rho}_1)$ and $(L_1,\\vec{\\rho}'_1)$, in the bucket, Eq.~(\\ref{eq:psiapproximation}) becomes\n\\begin{eqnarray}\nB_{1,2}&=&B_{0}\\int{d^{2}}\\rho_oA(\\vec{\\rho}_o)e^{i\\frac{K_1|\\vec{\\rho}_o|^2}{2L_1}}e^{-i\\frac{K_1\\vec{\n\\rho}_1\\cdot\\vec{\\rho}_o}{L_1}}\\int{d^{2}}\\rho'_oA(\\vec{\\rho}'_o)e^{i\\frac{K_1|\\vec{\\rho}'_o|^2}{2L_1}}e^{-i\n\\frac{K_1\\vec{\\rho}'_1\\cdot\\vec{\\rho}'_o}{L_1}}\\int{d^{2}}\\rho_le^{i\\frac{K_2|\\vec{\\rho}_l|^2}{2}(\\frac{1}{\nL_2}-\\frac{1}{f})}e^{i\\frac{K_2}{L_2}\\vec{\\rho}_2\\cdot\\vec{\\rho}_l}\\nonumber\\\\\n&&\\times\\int{d^{2 }}\\alpha_1e^{-i|\\vec{\\alpha}_1|^2(\\frac{d_1}{K_1}+\\frac{2d_2}{K_2})}e^{-i\\vec{\\alpha}_1\n\\cdot(2\\vec{\\rho}_l-\\vec{\\rho}_o-\\vec{\\rho}'_o)}.\\label{eq:bucketdetector}\n\\end{eqnarray}\nUnder the assumption that the  two degenerate photons are scattered off the same point in the object, Eq.~(\\ref{eq:bucketdetector}) takes the similar form as Eq.~(\\ref{eq:Psiassumption}), except that the second phase term in the first integrand of (\\ref{eq:Psiassumption}) is replaced by $\\mathrm{exp}\\big[-i\\frac{K_1(\\vec{\\rho}_1+\\vec{\\rho}'_1)\\cdot\\vec{\\rho}_o}{L_1}\\big]$.\nIt is easy to show that the Gaussian thin-lens equation takes the same form as Eq.~(\\ref{eq:GTLE1}). By performing the same analysis as done in Sec.~IIA on the resolving two spatially close point scatters, the three-photon amplitude (\\ref{eq:Psirayleigh}) now is\n\\begin{eqnarray}\nB_{1,2}=B_{0}\\bigg(A_0^2\\mathbf{somb}\\bigg(\\frac{2\\pi{R}}{\\lambda_2}\\bigg|\\frac{\\vec{\\rho}_2}{L_2}\\bigg|\\bigg)+e^{i\n\\varphi_2}A_{\\vec{a}}^2\\mathbf{somb}\\bigg[\\frac{2\\pi{R}}{\\lambda_2}\\bigg|\\frac{\\vec{\\rho}_2}{L_2}+\\frac{\\vec{a}}{d_2+(\n\\lambda_1\/2\\lambda_2)d_1}\\bigg|\\bigg]\\bigg).\\label{eq:Psirayleighbucket}\n\\end{eqnarray}\nSince the bucket detector gives no position information, we must square the amplitude and integrating over the bucket detector,\n\\begin{equation}\nI=\\int{d^{2}}\\rho_{1}  \\int{d^{2}}\\rho_{1}'  |B_{1,2}|^{2}=s_{b}^2|B_{0}|^{2}\\bigg(|A_0|^4 \\mathbf{somb}^{2}\\bigg(\\frac{2\\pi{R}}{\\lambda_2}\\bigg|\\frac{\\vec{\\rho}_2}{L_2}\\bigg|\\bigg)+\n|A_{\\vec{a}}|^{4} \\mathbf{somb}^2\\bigg[\\frac{2\\pi{R}}{\\lambda_2}\\bigg|\\frac{\\vec{\\rho}_2}{L_2}+\\frac{\\vec{a}}{d_2+(\n\\lambda_1\/2\\lambda_2)d_1}\\bigg|\\bigg]\\bigg)\\label{eq:bucket}\n\\end{equation}\nwhere $s_b$ is the area of the bucket detector.  It is easy to see that the spatial resolution improvement is the same as in Sec.~IIA, the difference is that now we get an incoherent image.  The advantage is that a two photon bucket detector should be easier to construct than a point two photon detector.\n\n\\section{$N+1$ Photon Optics}\n\\begin{figure}[tbp]\n\\includegraphics[scale=0.6]{Nphoton.pdf}\n\\caption{(color online) Generalization of quantum imaging with $N+1$ entangled photons in state $|1,N\\rangle$. For notations please refer to Fig.~\\ref{fig:2photon} except that here D$_1$ is an $N$-photon detector. The image is formed in the coincidence measurement and is not localized at either detector.}\\label{fig:Nphoton}\n\\end{figure}\nIn Sec.~II, we have shown that with the entangled photon-number state $|1,2\\rangle$, the ability to resolve two point sources in the object can be improved by a factor of 2 by sending two degenerate photons to the object while keeping the non-degenerate photon and imaging lens in the laboratory. In this section, we are going to generalize the experimental configuration (Fig.~\\ref{fig:2photon}) with use of the entangled state of $|1,N\\rangle$, as described in Fig.~\\ref{fig:Nphoton}. For simplicity, we first address the case shown in Fig.~\\ref{fig:Nphoton} where the $N$ degenerate photons traverse to the $N$-photon detector, D$_1$, after the object and the non-degenerate photon propagates to the single-photon detector, D$_2$. The assumption required for the enhancement by a factor of $N$ are that the $N$ photons sent to the object scatter off the same point and are detected by the $N$-photon detector, D$_1$.\n\nThe $N+1$ photons are assumed to be in a non-normalized pure state\n\\begin{eqnarray}\n|\\psi_{1,N}\\rangle=\\int{d}\\omega_1{d}\\omega_2\\int{d^{2 }}\\alpha_1d^2\\alpha_2\\delta(N\\omega_1+\\omega_2-\\Omega)\\delta\n(N\\vec{\\alpha}_1+\\vec{\\alpha}_2)a^{\\dagger}_{\\vec{k}_2}\\big(a^{\\dagger}_{\\vec{k}_1}\\big)^N|0\\rangle.\\label{eq:state2}\n\\end{eqnarray}\nAgain the $\\delta$-functions in Eq.~(\\ref{eq:state2}) indicate perfect phase matching. The $N+1$-photon coincidence counting rate is defined as\n\\begin{eqnarray}\nR_{cc}=\\frac{1}{T}\\int^T_0dt_1\\int^T_0dt_2\\cdots\\int^T_0dt_{N+1}|\\Psi_{1,N}(1,2,\\cdots,N+1)|^2,\\label{eq:coincidence2}\n\\end{eqnarray}\nwhere $\\Psi_{1,N}$ is referred to as the \\textit{$N+1$-photon amplitude}. That is\n\\begin{eqnarray}\n\\Psi_{1,N}(1,2,\\cdots,N+1)&=&\\langle0|E^{(+)}_1E^{(+)}_2\\cdots{E}^{(+)}_{N+1}|\\psi_{1,N}\\rangle\\nonumber\\\\\n&=&\\langle0|E^{(+)}_2(\\vec{\\rho}_2,z_2,t_2)[E^{(+)}_1(\\vec{\\rho}_1,z_1,t_1)]^N|\\psi_{1,N}\\rangle.\\label{eq:ampN}\n\\end{eqnarray}\n\nFollowing the procedure done for the $|1,2\\rangle$ case, we calculate the transverse part of the $N+1$-photon amplitude $\\Psi_{1,N}$ (\\ref{eq:ampN}) as\n\\begin{eqnarray}\n\\Psi_{1,N}&=&e^{i(N\\Omega_1\\tau_1+\\Omega_2\\tau_2)}\\Phi_{1,N}(\\tau_1,\\tau_2)B_{1,N}\\nonumber\\\\\nB_{1,N}&=&B_0\\underbrace{\\int{d^{2}}\\rho_oA(\\vec{\\rho}_o)e^{i\\frac{K_1|\\vec{\\rho}_o|^2}{2L_1}}e^{-i\\frac{\nK_1\\vec{\\rho}_1\\cdot\\vec{\\rho}_o}{L_1}}\\cdots\\int{d^{2}}\\rho'_oA(\\vec{\\rho}'_o)e^{i\\frac{K_1|\\vec{\\rho}'_o|\n^2}{2L_1}}e^{-i\\frac{K_1\\vec{\\rho}_1\\cdot\\vec{\\rho}'_o}{L_1}}}_{\\mathrm{N\\;fold}}\\int{d^{2}}\\rho_le^{i\\frac{\nK_2|\\vec{\\rho}_l|^2}{2}(\\frac{1}{L_2}-\\frac{1}{f})}e^{-i\\frac{K_2}{L_2}\\vec{\\rho}_2\\cdot\\vec{\\rho}_l}\\nonumber\\\\\n&&\\times\\int{d^{2}}\\alpha_1e^{-i\\frac{N^2|\\vec{\\alpha}_1|^2}{2}(\\frac{d_1}{NK_1}+\\frac{d_2}{K_2})}e^{-i\\vec{\\alpha}_1\n\\cdot(N\\vec{\\rho}_l-\\underbrace{\\vec{\\rho}_o-\\cdots-\\vec{\\rho}'_o}_{\\mathrm{N}})}.\\label{eq:psiapproximation2}\n\\end{eqnarray}\nHere $\\Phi_{1,N}(\\tau_1,\\tau_2)$ describes the temporal behavior of entangled three photons. By applying the same argument that the $N$-photon detector D$_1$ only receives the signals from the same spatial point in the object, Eq.~(\\ref{eq:psiapproximation2}) can be further simplified as\n\\begin{eqnarray}\nB_{1,N}&=&B_0\\int{d^{2}}\\rho_oA^N(\\vec{\\rho}_o)e^{i\\frac{NK_1|\\vec{\\rho}_o|^2}{2L_1}}e^{-i\\frac{N K_1\n\\vec{\\rho}_1\\cdot\\vec{\\rho}_o}{L_1}}\\int{d^{2}}\\rho_le^{i\\frac{K_2|\\vec{\\rho}_l|^2}{2}(\\frac{1}{L_2}-\\frac{1}{\nf})}e^{-i\\frac{K_2}{L_2}\\vec{\\rho}_2\\cdot\\vec{\\rho}_l}\\nonumber\\\\\n&&\\times \\int{d^{2}}\\alpha_1e^{-i\\frac{N^2|\\vec{\\alpha}_1|^2}{2}(\\frac{d_1}{N\nK_1}+\\frac{d_2}{K_2})}e^{-Ni\\vec{\\alpha}_1\\cdot(\\vec{\\rho}_l-\\vec{\\rho}_o)}.\\label{eq:Psiassumption2}\n\\end{eqnarray}\nPerforming the integration on the transverse mode $\\vec{\\alpha}_1$ in Eq.~(\\ref{eq:Psiassumption2}) gives\n\\begin{eqnarray}\nB_{1,N}&=&B_0\\int{d^{2}}\\rho_oA^N(\\vec{\\rho}_o)e^{i\\frac{NK_1|\\vec{\\rho}_o|^2}{2}[\\frac{1}{L_1}+\\frac{1}{d_1+(N\n\\lambda_2\/\\lambda_1)d_2}]}e^{-i\\frac{NK_1\\vec{\\rho}_1\\cdot\\vec{\\rho}_o}{L_1}}\\nonumber\\\\\n&&\\times\\int{d^{2}}\\rho_le^{i\\frac{K_2|\\vec{\\rho}_l|^2}{2}[\\frac{1}{L_2}+\\frac{1}{d_2+(\\lambda_1\/N\\lambda_2)d_1\n}-\\frac{1}{f}]}e^{-iK_2\\vec{\\rho}_l\\cdot[\\frac{\\vec{\\rho}_2}{L_2}+\\frac{\\vec{\\rho}_o}{d_2+(\\lambda_1\/N\\lambda_2)d_1}\n]},\\label{eq:psiassumptionn}\n\\end{eqnarray}\nwhere, again, we have assumed multimode generation in the process. Applying the Gaussian thin-lens imaging condition\n\\begin{eqnarray}\n\\frac{1}{f}=\\frac{1}{L_2}+\\frac{1}{d_2+(\\lambda_1\/N\\lambda_2)d_1},\\label{eq:GTLEn}\n\\end{eqnarray}\nthe transverse part of the $N+1$-photon amplitude (\\ref{eq:psiassumptionn}) between detectors D$_1$ and D$_2$ now\nbecomes\n\\begin{eqnarray}\nB_{1,N}&=&B_0\\int{d^{2}}\\rho_oA^N(\\vec{\\rho}_o)e^{i\\frac{NK_1|\\vec{\\rho}_o|^2}{2}[\\frac{1}{L_1}+\\frac{1}{d_1+(N\\lambda\n_2\/\\lambda_1)d_2}]}e^{-i\\frac{NK_1\\vec{\\rho}_1\\cdot\\vec{\\rho}_o}{L_1}}\\mathbf{somb}\\bigg[\\frac{2\\pi{R}}{\\lambda_2}\\bigg|\n\\frac{\\vec{\\rho}_2}{L_2}+\\frac{\\vec{\\rho}_o}{d_2+(\\lambda_1\/N\\lambda_2)d_1}\\bigg|\\bigg].\n\\label{eq:psin}\n\\end{eqnarray}\nAs expected, Eqs.~(\\ref{eq:GTLEn}) and (\\ref{eq:psin}) have the similar forms as Eqs.~(\\ref{eq:GTLE1}) and (\\ref{eq:psif}) for the $|1,2\\rangle$ case. The unique point-to-point relationship between the object and the imaging planes is enforced by the Gaussian thin-lens equation (\\ref{eq:GTLEn}). The coherent and inverted image is demagnified by a factor of $L_2\/[d_2+d_1(\\lambda_1\/N\\lambda_2)]$. The spatial resolution is determined by the width of the point-spread function in Eq.~(\\ref{eq:psin}). Note that a factor of $N$ appears in the distance between the imaging lens and the object planes, $d_2+d_1(\\lambda_1\/N\\lambda_2)$. We emphasize again that the image is nonlocal and exists in the coincidence events.\n\nTo study the spatial resolution, we again consider the object represented by Eq.~(\\ref{eq:object}). Plugging Eq.~(\\ref{eq:object}) into (\\ref{eq:psin}) yields\n\\begin{eqnarray}\nB_{1,N}=B_0\\bigg(A_{0}^N\\mathbf{somb}\\bigg(\\frac{2\\pi{R}}{\\lambda_2}\\bigg|\\frac{\\vec{\\rho}_2}{L_2}\\bigg|\\bigg)+e^{i\n\\varphi_{N}}A_{\\vec{a}}^N\\mathbf{somb}\\bigg[\\frac{2\\pi{R}}{\\lambda_2}\\bigg|\\frac{\\vec{\\rho}_2}{L_2}+\\frac{\\vec{a}}{d_2+\n(\\lambda_1\/N\\lambda_2)d_1}\\bigg|\\bigg]\\bigg).\\label{eq:Psinrayleigh}\n\\end{eqnarray}\nFor $N$ single photon detectors located at $\\vec{\\rho}_{1}^{(1)},\\cdots,\\vec{\\rho}_1^{(N)}$ the phase is given by\n\\begin{equation}\n\\varphi_N=K_1\\bigg[\\frac{N|\\vec{a}|^2}{2}\\bigg(\\frac{1}{L_1}+\\frac{1}{d_1+d_2(N\\lambda_2\/\\lambda_1)}\\bigg)-\\frac{\n\\vec{a}\\cdot(\\overbrace{\\vec{\\rho}_{1}^{(1)}+\\vec{\\rho}^{(2)}_{1}+\\cdots}^{\\mathrm{N}})}{L_1}\\bigg]\\label{eq:phaseN}\n\\end{equation}\nFor a point $N$-photon number detector, we require $\\vec{\\rho}_{1}^{(1)}=\\vec{\\rho}^{(2)}_{1}=\\cdots$ and a coherent imaging is achievable in this case. The first term on the right-hand side in Eq.~(\\ref{eq:Psirayleigh}) gives the radius of the Airy disk, which is the same as the $|1,2\\rangle$ case, see Eq.~(\\ref{eq:airydisk1}). Applying the Rayleigh criterion, the minimum resolvable distance between two points in the transverse plane now is\n\\begin{eqnarray}\na_{\\mathrm{m}}=0.61\\frac{\\lambda_2}{R}\\bigg(d_2+\\frac{\\lambda_1}{N\\lambda_2}d_1\\bigg).\\label{eq:resolutionn}\n\\end{eqnarray}\nFor the case of $N=2$, Eq.~(\\ref{eq:resolutionn}) reduces to Eq.~(\\ref{eq:resolution1}). In the case that $d_1\\gg{d_2}$, this becomes\n\\begin{eqnarray}\na_{\\mathrm{m}}=0.61\\frac{\\lambda_1d_1}{NR}.\\label{eq:resolutionf}\n\\end{eqnarray}\nAs expected, Eq.~(\\ref{eq:resolutionf}) shows a gain in sub-Rayleigh resolution by a factor of $N$ with respect to what one would obtain in classical optics. We therefore conclude that in the proposed imaging protocol, the spatial resolving power can be improved by a factor of $N$ with use of the entangled photon-number state $|1,N\\rangle$. Furthermore, because we are using an entangled state with a specific type of detector, the image has high contrast because of the lack of background noise.\n\nBy following the analysis in Sec.~IIB, we can show that by replacing the $N$-photon detector with an $N$-photon bucket detector, we get an incoherent image but the sub-Rayleigh imaging process is not changed.\n\n\\section{Discussions and other Configurations}\nIn the previous two sections, we have analyzed a novel ghost imaging by sending $N$ degenerate photons to the object while keeping the non-degenerate photon and imaging lens in the lab. We find that if the distance between the object plane and the output surface of the source is much greater than the distance between the imaging lens and the single-photon detector planes, we can gain spatial resolution improvement in the object by a factor of $N$ compared to classical optics. In the cases that we have discussed in this paper, this enhancement beyond the Rayleigh criterion is due to the quantum nature of the entangled photon-number state. The assumptions required for such an enhancement are that the $N$ degenerate photons sent to the object scatter off the same point and are detected by either an $N$-photon number detector or a bucket detector. An $N$-photon bucket detector is much easier to realize than an $N$-photon point detector. Such a bucket detector could be an array of single photon point detectors which only sent a signal to the coincidence circuit if exactly $N$ of them fired.\n\n\\begin{figure}[tbp]\n\\includegraphics[scale=0.6]{otherconfigurations.pdf}\n\\caption{(color online) Other schematics of quantum ghost imaging with three entangled photons in state $|1,2\\rangle$. (a) Both the imaging lens and the object are inserted in the non-degenerate photon channel. (b) The imaging lens is placed in the degenerate photon pathway while the object is in the non-degenerate optical pathway.}\n\\label{fig:otherconfigurations}\n\\end{figure}\nBesides the favorable configuration discussed above, one may wonder what happens if we switch the $N$ degenerate photons to detector $D_1$ and the non-degenerate photon to $D_2$ after an imaging lens and an object? Do we gain any spatial resolution improvement? To answer the questions, let us look at the $|1,2\\rangle$ case as illustrated in Fig.~\\ref{fig:otherconfigurations}(a). Following the treatments in Sec.~IIA, after some algebra we find that the transverse part of the three-photon amplitude (\\ref{eq:coincidence}) is\n\\begin{eqnarray}\nB_{1,2}&=&B_0 \\int{d^{2}}\\rho_oA(\\vec{\\rho}_o)e^{i\\frac{K_2|\\vec{\\rho}_o|^2}{2}(\\frac{1}{L_2}+\\frac{1}{d'_2})}\ne^{-i\\frac{K_2\\vec{\\rho}_2\\cdot\\vec{\\rho}_o}{L_2}}\\nonumber\\\\\n&&\\times\\int{d^{2}}\\rho_le^{i\\frac{K_2|\\vec{\\rho}_l|^2}{2}[\\frac{1}{d'_2}+\\frac{1}{d_2+(\\lambda_1\/2\\lambda_2)L_1}-\n\\frac{1}{f}]}e^{-iK_2\\vec{\\rho}_l\\cdot[\\frac{\\vec{\\rho}\n_o}{d'_2}+\\frac{\\vec{\\rho}_1}{d_2+(\\lambda_1\/2\\lambda_2)L_1}]}.\\label{eq:Psi22}\n\\end{eqnarray}\nIn the derivation of Eq.~(\\ref{eq:Psi22}), the Green's functions associated with each beam give\n\\begin{eqnarray}\n\\chi_1(\\vec{\\alpha}_1,\\Omega_1;\\vec{\\rho}_1,L_1)&=&e^{-i\\frac{L_1|\\vec{\\alpha}_1|^2}{2K_1}}e^{i\\vec{\\rho}_1\\cdot\n\\vec{\\alpha}_1},\\label{eq:g12}\\nonumber\\\\\n\\chi_2(\\vec{\\alpha}_2,\\Omega_2;\\vec{\\rho}_2,z_2)&=&e^{-i\\frac{d_2|\\vec{\\alpha}_2|^2}{2K_2}}\\int{d^{2}}\\rho_oA(\n\\vec{\\rho}_o)e^{i\\frac{K_2|\\vec{\\rho}_o|^2}{2}(\\frac{1}{L_2}+\\frac{1}{d'_2})}e^{-i\\frac{K_2\\vec{\\rho}_2\\cdot\n\\vec{\\rho}_o}{L_2}}\\int{d^{2}}\\rho_le^{i\\frac{K_2|\\vec{\\rho}_l|^2}{2}(\\frac{1}{d'_2}-\\frac{1}{f})}e^{i\\vec{\\rho}\n_l\\cdot(\\vec{\\alpha}_2-\\frac{K_2\\vec{\\rho}_o}{d'_2})}.\\nonumber\n\\end{eqnarray}\nApplying the Gaussian thin-lens imaging condition\n\\begin{eqnarray}\n\\frac{1}{d'_2}+\\frac{1}{d_2+(\\lambda_1\/2\\lambda_2)L_1}=\\frac{1}{f},\\label{eq:GTLE2}\n\\end{eqnarray}\nthe transverse spatial part of the three-photon amplitude (\\ref{eq:Psi22}) reduces to\n\\begin{eqnarray}\nB_{1,2}=B_0\\int{d^{2}}\\rho_oA(\\vec{\\rho}_o)e^{i\\frac{K_2|\\vec{\\rho}_o|^2}{2}(\\frac{1}{L_2}+\\frac{1}{d'_2})}\ne^{-i\\frac{K_2\\vec{\\rho}_2\\cdot\\vec{\\rho}_o}{L_2}}\\mathbf{somb}\\bigg(\\frac{2\\pi{R}}{\\lambda_2}\\bigg|\\frac{\\vec{\n\\rho}_o}{d'_2}+\\frac{\\vec{\\rho}_1}{d_2+(\\lambda_1\/2\\lambda_2)L_1}\\bigg|\\bigg).\\label{eq:Psi222}\n\\end{eqnarray}\nFrom this we see that the magnification is $m=[d_2+(\\lambda_1\/2\\lambda_2)L_1]\/d'_2$.  Comparing Eqs.~(\\ref{eq:GTLE2}) and (\\ref{eq:Psi222}) with Eqs.~(\\ref{eq:GTLE1}) and (\\ref{eq:psif}), we see that the distances between the object and the thin lens and between the thin lens and the imaging plane are interchanged. Since the degenerate photons are measured at the imaging plane in the setup of Fig.~\\ref{fig:otherconfigurations}(a), the requirement of a point $N$-photon detector cannot be relaxed.\n\nComputing the spatial resolution as in Sec. II we have\n\\begin{eqnarray}\nB_{1,2}=B_0\\bigg[A_{0}\\mathbf{somb}\\bigg(\\frac{2\\pi{R}}{\\lambda_2}\\bigg|\\frac{\\vec{\\rho}_1}{d_2+(\\lambda_1\/2\n\\lambda_2)L_1}\\bigg|\\bigg)+e^{i\\varphi'} A_{\\vec{a}}\\mathbf{somb}\\bigg(\\frac{2\\pi{R}}{\\lambda_2}\\bigg|\\frac{\\vec{a}}\n{d'_2}+\\frac{\\vec{\\rho}_1}{d_2+(\\lambda_1\/2\\lambda_2)L_1}\\bigg|\\bigg)\\bigg],\\label{eq:Psi22f}\n\\end{eqnarray}\nwhere $\\varphi'=K_2\\big[\\frac{|\\vec{a}|^2}{2}((\\frac{1}{L_2}+\\frac{1}{d'_2})-\\frac{\\vec{\\rho}_2\\cdot\\vec{a}}{L_2}\\big].$\nThe radius of the Airy disk is\n\\begin{eqnarray}\n\\xi=0.61\\frac{\\lambda_2}{R}\\bigg(\\frac{\\lambda_1}{2\\lambda_2}L_1+d_2\\bigg).\\label{eq:diskrudius2}\n\\end{eqnarray}\nIf $L_1\\gg{d_2}$, $\\xi\\rightarrow\\frac{0.61L_1}{R}(\\frac{\\lambda_1}{2})$, so that the width of the point-spread function shrinks to one half its value compared to the classical cases.  Applying the Rayleigh criterion to see the minimum resolvable distance between two point sources in the object. From the second term of Eq.~(\\ref{eq:Psi22f}) the minimum distance turns out to be\n\\begin{eqnarray}\na_{\\mathrm{min}}=0.61\\frac{d'_2\\lambda_2}{R},\\label{eq:arayleigh2}\n\\end{eqnarray}\nwhich only is a function of the wavelength of the non-degenerate photon; therefore, no spatial resolution improvement can be achieved compared to classical optics.\n\nFinally, we consider the configuration shown in Fig.~\\ref{fig:otherconfigurations}(b) which was analyzed in \\cite{wen1} where it was shown that no well-defined images could be obtained.\n\nIt is straightforward to generalize the above two configurations with use of the $|1,N\\rangle$ state. By replacing the source state by the state $|1,N\\rangle$ in Fig.~\\ref{fig:otherconfigurations}(a), it can be shown that the radius of the Airy disk becomes\n\\begin{eqnarray}\n\\xi=0.61\\frac{\\lambda_2}{R}\\bigg(\\frac{\\lambda_1}{N\\lambda_2}L_1+d_2\\bigg).\\label{eq:diskrudiusN}\n\\end{eqnarray}\nIf $L_1\\gg{d_2}$, $\\xi\\rightarrow\\frac{0.61L_1}{R}(\\frac{\\lambda_1}{N})$, so the Airy disk shrinks to one $N$th of its radius compared to classical optics. However, if $L_1\\ll{d_2}$, Eq.~(\\ref{eq:diskrudiusN}) gives the same result as in\nclassical optics. Replacing the source with photon state $|1,N\\rangle$ in Fig.~\\ref{fig:otherconfigurations}(b), the above conclusion is still valid. The analysis has been presented in \\cite{wen2} and we will not repeat here.\n\n\\section{Conclusions}\nIn summary, we have proposed a quantum-imaging scheme to improve the spatial resolution in the object beyond the Rayleigh diffraction limit by using an entangled photon-number state $|1,N\\rangle$. We have shown that by sending the $N$ degenerate photons to the object, keeping the non-degenerate photon and imaging lens in the lab, and using a resolving $N$-photon detector or a bucket detector, a factor of $N$ can be achieved in spatial resolution enhancement using the Rayleigh criterion. The image is nonlocal and the quantum nature of the state leads to the sub-Rayleigh imaging resolution with high contrast. We have also shown that by sending the $N$ degenerate photons freely to a point $N$-photon detector while propagating the non-degenerate photon through the imaging lens and the object, the Airy disk in the imaging can be shrunk by a factor of $N$ under certain conditions. However, it may be possible to show that a similar effect can occur using non-entangled sources. In the language of quantum information, the non-degenerate photon may be thought of as an ancilla onto which the information about the object is transferred for measurement. Our imaging protocol may be of importance in many applications such as imaging, sensors, and telescopy.\n\n\\section{Acknowledgement}\nThis work was supported in part by U.S. ARO MURI Grant W911NF-05-1-0197 and by Northrop Grumman Corporation through the Air Force Research Laboratory under contract FA8750-07-C-0201 as part of DARPA's Quantum Sensors Program.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction} \\label{sec:Introduction}\nIn the era of big data, effective management of extensive feature spaces represents a genuine hurdle for scientists and practitioners. Only some features have significant relevance in real-world data, while the redundancy of the remaining ones actively inflates data-driven models' complexity. The search for always new and increasingly performing dimensionality reduction algorithms is hence justified by four primary needs: (i) reduce data maintenance costs; (ii) reduce the impact of the `curse of dimensionality' on data-driven models; (iii) increase data-driven models' interpretability; (iv) reduce energy costs for model training. Reducing data maintenance costs involves an articulate corpus of engineering applications including, but not limited to, the effective management of storage space \\cite{siddiqa2017big, katal2013big, padgavankar2014big, strohbach2016big}, continuous databases maintenance \\cite{madden2012databases}, design and implementation of cost-effectively data pipelines \\cite{eichelberger2017experiences, wu2016building}. These challenges are particularly evident in a heterogeneous range of application domains such as bioinformatics \\cite{mak2006solution, sen2005gini, antoniadis2003effective}, healthcare \\cite{patorno2013propensity, berisha2021digital, jiwani2021novel}, robotics \\cite{da2019combining, li2016utilizing}, object and speech recognition tasks \\cite{stommel2009binarising, lotfi2014neural, estellers2011multipose}, sentiment analysis \\cite{singh2020sentiment, skowron2016fusing} and finance \\cite{verleysen2005curse, wang2007brownian, gueant2019deep}. These disciplines historically represented the testing ground for data models suffering the `curse of dimensionality' \\cite{bellman1959mathematical}. In the literature, the `curse of dimensionality' refers to the difficulty in effectively modelling high-dimensional data due to the exponential increase in the number of samples required to cover the input space as the number of dimensions increases \\cite{donoho2000high, poggio2017and}. This phenomenon is even riskier in critical applicative domains like medicine \\cite{holzinger2017we, singh2020explainable}, physics \\cite{lai2022explainable}, communication technologies \\cite{guo2020explainable}, and automated trading \\cite{leal2020learning, briola2020deep, briola2021deep, nagy2023asynchronous, zhang2019deeplob}, where, in addition to generalisation power, models' interpretability represents an essential requirement. Thanks to remarkable advancements in hardware technology and neural networks training methodologies, in recent years, some of these last drawbacks have been partially addressed. This has paved the way for developing a new breed of large-scale models trained on expansive datasets, leading to notable improvements across a range of tasks. However, it is worth noting that these models come at a substantial cost in terms of finances and environmental impact. The financial costs associated with electricity consumption are significant, and the carbon footprint generated by the energy-intensive modern tensor processing hardware represents a growing environmental concern \\cite{strubell2019energy, patterson2021carbon}.\n\nDimensionality reduction addresses all these problems by decreasing the complexity of the feature space while minimally affecting information loss \\cite{miner2012practical}. Such a field can be further specified into two macro areas: (i) feature extraction and (ii) feature selection. Feature extraction techniques originate new features by transforming the original ones into a space with a different dimensionality and then choosing linear or non-linear combinations of them. They are mainly used in the presence of a limited understanding of raw data. On the other hand, feature selection techniques directly choose a subset of features from the original set while maintaining their physical meaning. Usually, they are a 'block' of a more complex pipeline including also a classification (or regression) step. The level of contamination among 'blocks' is more or less evident depending on the nature of the feature selection algorithm. Indeed, feature selection techniques are classified as (i) supervised \\cite{huang2015supervised}; (ii) unsupervised \\cite{solorio2020review}: and (iii) semi-supervised \\cite{sheikhpour2017survey}. In the supervised case, features' relevance is usually assessed via their correlation degree with class labels or regression targets. These models take advantage of the learning performance of the classification (or regression) algorithm to refine the choice of the meaningful subset of features while maintaining, at the same time, 'block' independence from it. This loop interaction is convenient only in scenarios where retrieving labels and executing classification (or regression) tasks is computationally efficient. On the contrary, unsupervised feature selection is applied in scenarios where retrieving labels is costly. These algorithms select relevant features based on specific data properties (e.g. variance maximisation). Different classes of unsupervised feature selection approaches exist: (i) filters; (ii) wrappers; (iii) embedded methods. In filter-based methods, the feature selection stage is entirely independent from the classification (or regression) algorithm; in wrapper-based methods, the feature selection process takes advantage of classification (or regression) performance to improve its performance; in embedded methods, the feature selection step is embedded into the classification algorithm in a way that the two 'blocks' take advantage from each other. \\\\\nLastly, semi-supervised feature selection represents a hybrid approach with the highest potential applicability in real-world problems. Indeed, labels are often only partially provided, and semi-supervised learning techniques are specifically designed to learn from a reduced number of labelled data, efficiently handling, at the same time, a large number of unlabeled samples.\n\nIn its general formulation, given a starting set of features $F = \\{f_1, \\dots, f_n\\}$, where $n \\gg 1$ is the cardinality, dimensionality reduction is an \\textit{NP-hard} problem \\cite{guyon2008feature, roffo2015infinite} where the goal is selecting the optimal subset of features with cardinality $m \\ll n$, among the ${n \\choose m}$ possible combinations. Due to the exponentially increased time required to find the globally optimal solution, existing feature selection algorithms employ heuristic rules to find dataset-dependent sub-optimal solutions \\cite{ge2016mctwo}. In this paper, we propose a novel unsupervised, graph-based filter algorithm for feature selection which (i) builds a topologically constrained network representation of raw features' dependency structure and (ii) exploits their relative position into the graph to reduce the input's dimensionality, minimising the information loss. \n\nA network (or graph) represents components of a system as nodes (or vertices) and interactions among them as links (or edges). The number of nodes defines the size of the network, and the number of links establishes the network's sparsity (or, conversely, density). Reversible interactions between components are represented through undirected links, while non-reversible interactions are represented as direct links \\cite{briola2022dependency}. Topologically constrained networks, also known as information filtering networks (IFNs), constitute a family of graphs built imposing topological constraints (such as being a tree or a planar graph) while optimising global properties (such as the likelihood) \\cite{mantegna1999hierarchical, tumminello2005tool, serin2016learning, marti2021review}. In this paper, starting from the raw set of features $F$, we exploit the power of a specific class of IFNs, namely the Triangulated Maximally Filtered Graph (TMFG), to capture a meaningful and intuitive description of dependency structures among features in an unsupervised manner (i.e. without exploring their relationships with labels or regression targets). Consequently, we study the relative position of elements inside the network to maximise the likelihood of features' relevance while minimising information loss. Based on this construction schema, we name our approach 'Topological Feature Selection' (TFS).\n\nTo prove the effectiveness of the proposed methodology, we test it against what is currently considered the state-of-the-art counterpart in unsupervised, graph-based filter feature selection approaches, i.e. Infinite Feature Selection ($\\textrm{Inf-FS}_U$) \\cite{roffo2015infinite}. The two feature selection algorithms are tested on $16$ benchmark datasets from different application domains. The proposed training\/test pipeline and the statistical validation one are designed to handle dataset imbalance and evaluate results based on fair performance metrics. The results are clear-cut. In most cases, TFS outperforms or equalises its alternative, redefining or teeing state-of-the-art performances. Our contribution to the existing literature is relevant since we propose an extraordinarily flexible, computationally cheap and remarkably intuitive (compared to its alternative) unsupervised, graph-based filter algorithm for feature selection guaranteeing complete control of the dimensionality reduction process by considering only the relative position of features inside well-known graph structures.\n\nThe rest of the paper is organised as follows. In Section \\ref{sec:Data}, we describe the datasets used to prove the effectiveness of the TFS algorithm. In Section \\ref{sec:Information_Filtering_Networks}, we review the theoretical foundations of IFNs and present the TMFG algorithm. In Section \\ref{sec:Topologically_Constrained_Feature_Selection}, we describe in a detailed manner the TFS methodology. In Section \\ref{sec:Experiments}, we describe the experimental protocols, while obtained results are presented in Section \\ref{sec:Results}. Finally, in Section \\ref{sec:Conclusions}, we discuss the meaning of our results and future research lines in this area.\n\n\\section{Data and Methods}\\label{sec:Data_and_Methods}\n\n\\subsection{Data} \\label{sec:Data}\nIn order to prove TFS' effectiveness, we extensively test it on $16$ benchmark datasets (all in a tabular format) belonging to different application domains. For each dataset, Table \\ref{tab:Datasets_Description} reports, respectively, the name, the application domain, the reference paper (or website), the downloading source, the number of features, the number of samples, the number of classes and the split dynamics.\n\n\\begin{table}[H]\n\\centering\n\\caption{Benchmark datasets used to compare feature selection algorithms considered in the current work. The order of appearance is inherited from \\cite{ASUDatasets}.}\n\\label{tab:Datasets_Description}\n\\resizebox{\\columnwidth}{!}{%\n\\begin{tabular}{@{}cccccccc@{}}\n\\toprule\n\\textbf{Name} &\n  \\textbf{Category} &\n  \\textbf{Reference} &\n  \\textbf{Source} &\n  \\textbf{\\# Features} &\n  \\textbf{\\# Samples} &\n  \\textbf{Classes} &\n  \\textbf{Split Provided} \\\\ \\midrule\nPCMAC       & Text Data              & \\cite{lang1995newsweeder}   & \\cite{ASUDatasets} & 3289 & 1943 & binary      & false \\\\\nRELATHE     & Text Data              & \\cite{lang1995newsweeder}   & \\cite{ASUDatasets} & 4322 & 1427 & binary      & false \\\\\nCOIL20      & Face Images Data         & \\cite{nene1996columbia}     & \\cite{ASUDatasets} & 1024 & 1440 & multi-class & false \\\\\nORL &\n  Face Images Data &\n  \\cite{samaria1994parameterisation} &\n  \\cite{ASUDatasets} &\n  1024 &\n  400 &\n  multi-class &\n  false \\\\\nwarpAR10P   & Face Images Data        & \\cite{li2018feature}        & \\cite{ASUDatasets} & 2400 & 130  & multi-class & false \\\\\nwarpPIE10P  & Face Images Data       & \\cite{sim2002cmu}           & \\cite{ASUDatasets} & 2420 & 210  & multi-class & false \\\\\nYale &\n  Face Images Data &\n  \\cite{belhumeur1997eigenfaces} &\n  \\cite{ASUDatasets} &\n  1024 &\n  165 &\n  multi-class &\n  false \\\\\nUSPS        & Hand Written Images Data & \\cite{hull1994database}     & \\cite{GitHubIFS}     & 256  & 9298 & multi-class & false \\\\\ncolon       & Biological Data         & \\cite{alon1999broad}        & \\cite{GitHubIFS}     & 2000 & 62   & binary      & false \\\\\nGLIOMA      & Biological Data         & \\cite{li2018feature}        & \\cite{ASUDatasets} & 4434 & 50   & multi-class & false \\\\\nlung        & Biological Data        & \\cite{GitHubIFS}            & \\cite{GitHubIFS}     & 3312 & 203  & multi-class & false \\\\\nlung\\_small & Biological Data        & \\cite{GitHubIFS}            & \\cite{GitHubIFS}     & 325  & 73   & multi-class & false \\\\\nlymphoma    & Biological Data        & \\cite{golub1999molecular}   & \\cite{ASUDatasets} & 4026 & 96   & multi-class & false \\\\\nGISETTE     & Digits Data  & \\cite{guyon2007competitive} & \\cite{Dua:2019}      & 5000 & 7000 & binary      & true  \\\\\nIsolet &\n  Spoken Letters Data &\n  \\cite{li2018feature} &\n  \\cite{ASUDatasets} &\n  617 &\n  1560 &\n  multi-class &\n  false \\\\\nMADELON     & Artificial Data         & \\cite{guyon2007competitive} & \\cite{Dua:2019}      & 500  & 2600 & binary      & true  \\\\ \\bottomrule\n\\end{tabular}%\n}\n\\end{table}\n\nWe distinguish among $7$ different application domains (i.e. text data, face images data, hand written images data, biological data, digits data, spoken letters data and artificial data). Categories follow the taxonomy in \\cite{li2018feature}. The average number of features is $2248$. The dataset with the lowest number of features is 'USPS' (i.e. $256$). The dataset with the largest number of features is 'GISETTE' (i.e. $5000$). The average number of samples is $1666$. The dataset with the lowest number of samples is 'GLIOMA' (i.e. $50$), while the one with the largest number of samples is 'USPS' (i.e. $9298$). $5$ of the considered datasets are binary, while $11$ are multi-class. Depending on the source, training\/test split could be provided or not. The two datasets 'GISETTE' and 'MADELON' come with a provided training\/validation\/test split. In both cases, the data source (i.e. \\cite{Dua:2019}) does not provide test labels. Because of this, we use the validation set for testing. For all the other datasets, $70\\%$ of the raw dataset is used as a training set, while $30\\%$ is used as a test set. We use a stratified splitting procedure to ensure that each set contains, for each target class, approximately the same percentage of samples as per in the raw dataset.\n\n\\begin{comment}\n\\begin{figure}[H]\n    \\centering\n    \\includegraphics[scale=0.25]{images\/Data_Pipeline.png}\n    \\caption{The data preprocessing pipeline consists of $4$ different steps: (i) data reading and format unification, (ii) training\/test splitting, (iii) constant features pruning and (iv) metadata production.}\n    \\label{fig:Data_Pipeline}\n\\end{figure}\n\nFigure \\ref{fig:Data_Pipeline} reports a pictorial schema of the data pre-processing pipeline. We distinguish 4 different steps: (i) data reading and format unification, (ii) training\/test splitting, (iii) constant features pruning and (iv) metadata production. The first step allows to read  data and unify formats coming from different sources. The second step consists of the train\/test splitting and has been presented early in this section. In the third step, non-informative, constant covariates are detected on the training set and permanently removed from training, validation and test set. The fourth step allows to produce useful metadata that highly facilitate data management.\n\\end{comment}\n\nWe design the data pre-processing pipeline as consisting of $3$ different steps: (i) data reading and format unification; (ii) training\/test splitting; (iii) constant features pruning. The first step allows us to read data and unify formats coming from different sources. The second step consists of the train\/test splitting and has been presented early in this section. In the third step, non-informative, constant covariates are detected on the training set and permanently removed from the training, validation and test set. \n\nTable \\ref{tab:Pre_Processed_Data} reports datasets' specifics after the preprocessing step. Looking at it, we remark that most considered datasets are not affected by the constant features filtering step. The only $4$ datasets which are reduced in the number of covariates are 'PCMAC' (with a reduction of $0.07\\%$), 'RELATHE' (with a reduction of $0.03\\%$), 'GLIOMA' (with a reduction of $0.03\\%$) and 'GISETTE' (with a reduction of $0.9\\%$). Table \\ref{tab:Pre_Processed_Data} also reports the training and test dataset's labels' distributions. Datasets are generally balanced; the main exceptions are:\n\n\\begin{itemize}\n    \\item 'USPS': classes 1 and 2 are over-represented compared to the other classes.\n    \\item 'colon': class 1 is under-represented compared to the other class.\n    \\item 'GLIOMA': class 2 is under-represented compared to other classes.\n    \\item 'lung': class 1 is over-represented compared to the other classes.\n    \\item 'lung\\_small': classes 1, 2, 3 and 5 are under-represented compared to the other classes.\n    \\item 'lymphoma': class 1 is over-represented compared to the other classes.\n\\end{itemize}\n\n\\begin{table}[H]\n\\caption{Datasets' specifics after the preprocessing step. For each benchmark dataset, we report the number of features, the number of samples and the labels' distribution for training and test data. The labels' distribution entry consists of a tuple for each class. The first element of the tuple represents the class itself, while the second represents the number of samples with that label.}\n\\label{tab:Pre_Processed_Data}\n\\resizebox{\\columnwidth}{!}{%\n\\begin{tabular}{|c|ccc|ccc|}\n\\hline\n\\textbf{Dataset} &\n  \\multicolumn{3}{c|}{\\textbf{Training}} &\n  \\multicolumn{3}{c|}{\\textbf{Test}} \\\\ \\hline\n &\n  \\multicolumn{1}{c|}{\\textbf{\\# Features}} &\n  \\multicolumn{1}{c|}{\\textbf{\\# Samples}} &\n  \\textbf{Labels' Distribution} &\n  \\multicolumn{1}{c|}{\\textbf{\\# Features}} &\n  \\multicolumn{1}{c|}{\\textbf{\\# Samples}} &\n  \\textbf{Labels' Distribution} \\\\ \\hline\nPCMAC &\n  \\multicolumn{1}{c|}{3287} &\n  \\multicolumn{1}{c|}{1360} &\n  (1, 687), (2, 673) &\n  \\multicolumn{1}{c|}{3287} &\n  \\multicolumn{1}{c|}{583} &\n  (1, 295), (2, 288) \\\\ \\hline\nRELATHE &\n  \\multicolumn{1}{c|}{4321} &\n  \\multicolumn{1}{c|}{998} &\n  (1, 545), (2, 453) &\n  \\multicolumn{1}{c|}{4321} &\n  \\multicolumn{1}{c|}{429} &\n  (1, 234), (2, 195) \\\\ \\hline\nCOIL20 &\n  \\multicolumn{1}{c|}{1024} &\n  \\multicolumn{1}{c|}{1008} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 50), (2, 51), (3, 50), (4, 50), \\\\ (5, 50), (6, 50), (7, 51), (8, 50), \\\\ (9, 51),  (10, 50), (11, 51), (12, 50), \\\\ (13, 50),  (14, 51), (15, 50), (16, 50), \\\\ (17, 50),  (18, 51), (19, 51), (20, 51)\\end{tabular} &\n  \\multicolumn{1}{c|}{1024} &\n  \\multicolumn{1}{c|}{432} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 22), (2, 21), (3, 22), (4, 22), \\\\ (5, 22), (6, 22), (7, 21), (8, 22), \\\\ (9, 21), (10, 22), (11, 21), (12, 22), \\\\ (13, 22), (14, 21), (15, 22), (16, 22), \\\\ (17, 22), (18, 21), (19, 21), (20, 21)\\end{tabular} \\\\ \\hline\nORL &\n  \\multicolumn{1}{c|}{1024} &\n  \\multicolumn{1}{c|}{280} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 7), (2, 7), (3, 7), (4, 7), (5, 7), \\\\ (6, 7), (7, 7), (8, 7), (9, 7), (10, 7),\\\\  (11, 7), (12, 7), (13, 7), (14, 7), (15, 7), \\\\ (16, 7), (17, 7), (18, 7), (19, 7), (20, 7), \\\\ (21, 7), (22, 7), (23, 7), (24, 7), (25, 7), \\\\ (26, 7), (27, 7), (28, 7), (29, 7), (30, 7), \\\\ (31, 7), (32, 7), (33, 7), (34, 7), (35, 7), \\\\ (36, 7), (37, 7), (38, 7), (39, 7), (40, 7)\\end{tabular} &\n  \\multicolumn{1}{c|}{1024} &\n  \\multicolumn{1}{c|}{120} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 3), (2, 3), (3, 3), (4, 3), (5, 3),\\\\  (6, 3), (7, 3), (8, 3), (9, 3), (10, 3), \\\\ (11, 3), (12, 3), (13, 3), (14, 3), (15, 3),\\\\  (16, 3), (17, 3), (18, 3), (19, 3), (20, 3), \\\\ (21, 3), (22, 3), (23, 3), (24, 3), (25, 3), \\\\ (26, 3), (27, 3), (28, 3), (29, 3), (30, 3), \\\\ (31, 3), (32, 3), (33, 3), (34, 3), (35, 3), \\\\ (36, 3), (37, 3), (38, 3), (39, 3), (40, 3)\\end{tabular} \\\\ \\hline\nwarpAR10P &\n  \\multicolumn{1}{c|}{2400} &\n  \\multicolumn{1}{c|}{91} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 9), (2, 9), (3, 10), (4, 9), (5, 9), \\\\ (6, 9), (7, 9), (8, 9), (9, 9), (10, 9)\\end{tabular} &\n  \\multicolumn{1}{c|}{2400} &\n  \\multicolumn{1}{c|}{39} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 4), (2, 4), (3, 3), (4, 4), (5, 4), \\\\ (6, 4), (7, 4), (8, 4), (9, 4), (10, 4)\\end{tabular} \\\\ \\hline\nwarpPIE10P &\n  \\multicolumn{1}{c|}{2420} &\n  \\multicolumn{1}{c|}{147} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 14), (2, 15), (3, 15), (4, 14), (5, 15),\\\\ (6, 14), (7, 15), (8, 15), (9, 15), (10, 15)\\end{tabular} &\n  \\multicolumn{1}{c|}{2420} &\n  \\multicolumn{1}{c|}{63} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 7), (2, 6), (3, 6), (4, 7), (5, 6), \\\\ (6, 7), (7, 6), (8, 6), (9, 6), (10, 6)\\end{tabular} \\\\ \\hline\nYale &\n  \\multicolumn{1}{c|}{1024} &\n  \\multicolumn{1}{c|}{115} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 7), (2, 8), (3, 8), (4, 7), (5, 8), \\\\ (6, 7), (7, 8), (8, 8), (9, 8), (10, 8), \\\\ (11, 8), (12, 7), (13, 7), (14, 8), (15, 8)\\end{tabular} &\n  \\multicolumn{1}{c|}{1024} &\n  \\multicolumn{1}{c|}{50} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 4), (2, 3), (3, 3), (4, 4), (5, 3), \\\\ (6, 4), (7, 3), (8, 3), (9, 3), (10, 3), \\\\ (11, 3), (12, 4), (13, 4), (14, 3), (15, 3)\\end{tabular} \\\\ \\hline\nUSPS &\n  \\multicolumn{1}{c|}{256} &\n  \\multicolumn{1}{c|}{6508} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 1087), (2, 888), (3, 650), (4, 577), (5, 596), \\\\ (6, 501), (7, 584), (8, 554), (9, 496), (10, 575)\\end{tabular} &\n  \\multicolumn{1}{c|}{256} &\n  \\multicolumn{1}{c|}{2790} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 466), (2, 381), (3, 279), (4, 247), (5, 256), \\\\ (6, 215), (7, 250), (8, 238), (9, 212), (10, 246)\\end{tabular} \\\\ \\hline\ncolon &\n  \\multicolumn{1}{c|}{2000} &\n  \\multicolumn{1}{c|}{43} &\n  (-1, 28), (1, 15) &\n  \\multicolumn{1}{c|}{2000} &\n  \\multicolumn{1}{c|}{19} &\n  (-1, 12), (1, 7) \\\\ \\hline\nGLIOMA &\n  \\multicolumn{1}{c|}{4433} &\n  \\multicolumn{1}{c|}{35} &\n  (1, 10), (2, 5), (3, 10), (4, 10) &\n  \\multicolumn{1}{c|}{4433} &\n  \\multicolumn{1}{c|}{15} &\n  (1, 4), (2, 2), (3, 4), (4, 5) \\\\ \\hline\nlung &\n  \\multicolumn{1}{c|}{3312} &\n  \\multicolumn{1}{c|}{142} &\n  (1, 97), (2, 12), (3, 15), (4, 14), (5, 4) &\n  \\multicolumn{1}{c|}{3312} &\n  \\multicolumn{1}{c|}{61} &\n  (1, 42), (2, 5), (3, 6), (4, 6), (5, 2) \\\\ \\hline\nlung\\_small &\n  \\multicolumn{1}{c|}{325} &\n  \\multicolumn{1}{c|}{51} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 4), (2, 3), (3, 4), (4, 11), \\\\ (5, 5), (6, 9), (7, 15)\\end{tabular} &\n  \\multicolumn{1}{c|}{325} &\n  \\multicolumn{1}{c|}{22} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 2), (2, 2), (3, 1), (4, 5), \\\\ (5, 2), (6, 4), (7, 6)\\end{tabular} \\\\ \\hline\nlymphoma &\n  \\multicolumn{1}{c|}{4026} &\n  \\multicolumn{1}{c|}{67} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 32), (2, 7), (3, 6), (4, 8), (5, 4), \\\\ (6, 4), (7, 3), (8, 1), (9, 2)\\end{tabular} &\n  \\multicolumn{1}{c|}{4026} &\n  \\multicolumn{1}{c|}{29} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 14), (2, 3), (3, 3), (4, 3), (5, 2), \\\\ (6, 2), (7, 1), (8, 1)\\end{tabular} \\\\ \\hline\nGISETTE &\n  \\multicolumn{1}{c|}{4955} &\n  \\multicolumn{1}{c|}{6000} &\n  (-1.0, 3000), (1.0, 3000) &\n  \\multicolumn{1}{c|}{4955} &\n  \\multicolumn{1}{c|}{1000} &\n  (-1.0, 500), (1.0, 500) \\\\ \\hline\nIsolet &\n  \\multicolumn{1}{c|}{617} &\n  \\multicolumn{1}{c|}{1092} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 42), (2, 42), (3, 42), (4, 42), (5, 42), \\\\ (6, 42), (7, 42), (8, 42), (9, 42), (10, 42), \\\\ (11, 42), (12, 42), (13, 42), (14, 42), (15, 42), \\\\ (16, 42), (17, 42), (18, 42), (19, 42), (20, 42), \\\\ (21, 42), (22, 42), (23, 42), (24, 42), (25, 42), (26, 42)\\end{tabular} &\n  \\multicolumn{1}{c|}{617} &\n  \\multicolumn{1}{c|}{468} &\n  \\begin{tabular}[c]{@{}c@{}}(1, 18), (2, 18), (3, 18), (4, 18), (5, 18), \\\\ (6, 18), (7, 18), (8, 18), (9, 18), (10, 18), \\\\ (11, 18), (12, 18), (13, 18), (14, 18), (15, 18), \\\\ (16, 18), (17, 18), (18, 18), (19, 18), (20, 18), \\\\ (21, 18), (22, 18), (23, 18), (24, 18), (25, 18), (26, 18)\\end{tabular} \\\\ \\hline\nMADELON &\n  \\multicolumn{1}{c|}{500} &\n  \\multicolumn{1}{c|}{2000} &\n  (-1.0, 1000), (1.0, 1000) &\n  \\multicolumn{1}{c|}{500} &\n  \\multicolumn{1}{c|}{600} &\n  (-1.0, 300), (1.0, 300) \\\\ \\hline\n\\end{tabular}%\n}\n\\end{table}\n\nThanks to the stratification technique discussed earlier in this Section, the same conclusions on labels balancing can be applied both to the training and the test datasets.\n\n\\subsection{Information Filtering Networks} \\label{sec:Information_Filtering_Networks}\nInformation Filtering Networks (IFNs) \\cite{mantegna1999hierarchical, aste2005complex, barfuss2016parsimonious, massara2017network, tumminello2005tool} are an effective tool to represent and model dependency structures among variables characterising complex systems. They have been extensively applied to a vast range of systems, including finance \\cite{procacci2022portfolio, briola2022anatomy, wang2022dynamic, seabrook2022quantifying, wang2022sparsification}, psychology \\cite{christensen2018network, christensen2018networktoolbox}, medicine \\cite{hutter2019multi, danoff2021genetic} and biology \\cite{song2008correlation, song2012hierarchical}. Sometimes IFNs are also referred to as Correlation Networks (CNs). Such an association is, however, inaccurate. Indeed, the two methodologies slightly differ, with CNs being normally obtained by applying a threshold that retains only the largest correlations among variables of the system, while IFNs being instead constructed imposing topological constraints (e.g. being a tree or a planar graph) and optimising specific global properties (e.g. the likelihood) \\cite{aste2022topological}. Both methodologies end in the determination of a sparse adjacency matrix, \\textbf{\\textit{A}}, representing relations among variables in the system with the fundamental difference that the former approach generates a disconnected graph, while the latter guarantees the connectedness. Based on the nature of the relationships to be modelled (i.e. linear, non-linear), one can choose different metrics to build the adjacency matrix \\textbf{\\textit{A}}. In most cases, \\textbf{\\textit{A}} is built on an arbitrary similarity matrix $\\hat{\\textbf{C}}$, which often corresponds to a correlation matrix. From a network science perspective, $\\hat{\\textbf{C}}$ can be considered as a fully connected graph where each variable of the system is represented as a node, and each pair of variables is joined by a weighted and undirected edge representing their similarity. Historically, the main IFNs were the Minimum Spanning Tree (MST) \\cite{papadimitriou1998combinatorial, mantegna1999hierarchical} and the Planar Maximally Filtered Graph (PMFG) \\cite{tumminello2005tool}. MSTs are a class of networks connecting all the vertices without forming cycles (i.e. closed paths of at least three nodes) while retaining the network's representation as simple as possible (i.e. representing only relevant relations among variables characterising the system under analysis) \\cite{briola2022dependency}. Prim's algorithm for MST construction sorts all edges' weights (i.e. similarities) in descending order and adds the largest possible edge weight among two nodes in an iterative way. The resulting network has $n-1$ edges and retains only the most significant connections, assuring, at the same time, that connectedness' property is fulfilled \\cite{christensen2018network}. For a complete pedagogical exposition of the determination of the MST, the interested reader is referred to the works by \\cite{mantegna1999hierarchical, briola2022dependency}. Despite being a powerful method to capture meaningful relationships in network structures describing complex systems, MST presents some aspects that can be unsatisfactory. Paradoxically, the main limit is represented by its tree structure (i.e. it cannot contain cycles) which does not allow to represent direct relationships among more than two variables showing strong similarity. The introduction of the Planar Maximally Filtered Graph (PMFG) \\cite{tumminello2005tool} overcomes such a shortcoming. Similarly to MST, also the PMFG algorithm sorts edge weights in descending order, incrementally adding the largest ones while imposing planarity \\cite{christensen2018network}. A graph is planar if it can be embedded in a sphere without edges crossing. Thanks to this, the same powerful filtering properties of the MST are maintained, and, at the same time, extra links, cycles and cliques (i.e. complete subgraphs) are added in a controlled manner. The resulting network has $3n-6$ edges and is composed of three- and four-nodes cliques. A nested hierarchy emerges from these cliques \\cite{song2011nested}: dimensionality is reduced in a deterministic manner while local information and the global hierarchical structure of the original network are retained. For a complete pedagogical exposition of the determination of the PMFG and a detailed analysis of its properties, the interested reader is referred to the works by \\cite{aste2005complex, tumminello2005tool, briola2022dependency}. The PMFG represents a substantial step forward compared to the MST. However, it still presents two limits: (i) it is computationally costly and (ii) it is a non-chordal graph. A graph is said to be chordal if all cycles made of four or more vertices have a chord, reducing the cycle to a set of triangles. A chord is defined as an edge that is not part of the cycle but connects two vertices of the cycle itself. The advantage of chordal graphs is that they fulfill the independence assumptions of Markov (i.e., bidirectional or undirected relations) and Bayesian (i.e., directional relations) networks \\cite{koller2009probabilistic, christensen2018network}. The Triangulated Maximally Filtered Graph (TMFG) \\cite{massara2017network} has been explicitly designed to be a chordal graph while retaining the strengths of PMFG.\n\n\\begin{algorithm}\n    \\caption{TMFG built on the similarity matrix $\\hat{\\textbf{C}}$ to maximise the likelihood of features' relevance.}\\label{alg:TMFG_Algo}\n    \\textbf{Input} Similarity matrix $\\hat{\\textbf{C}}$ $\\in \\mathbb{R}^{n, n}$ from a set of observations $\\{x_{1, 1}, \\dots, x_{s, 1}\\}, \\{x_{1, 2}, \\dots, x_{s, 2}\\} \\dots \\{x_{1, n}, \\dots, x_{s, n}\\}$.\\\\\n    \\textbf{Output} Sparse adjacency matrix \\textbf{\\textit{A}} describing the TMFG. \n\n    \\vspace{0.05cm}\n    \n    \\begin{algorithmic}[1]\n\n        \\Function{MaximumGain}{$\\hat{\\textbf{C}}$, $\\mathcal{V}$, $t$}\\funclabel{alg:MaximumGain}\n            \\State Initialize a vector of zeros $g \\in \\mathbb{R}^{1 \\times n}$;\n            \\For{$j \\in 0, \\dots n$}\n                \\For{$v \\notin \\mathcal{V}$}\n                    \\State $\\hat{\\textbf{C}}_{v,j} = 0$\n                \\EndFor\n                \n                \\State $g = g \\oplus \\hat{\\textbf{C}}_{v,j}$\n            \\EndFor\n            \n            \\State \\Return $\\max{\\{g\\}}$.\n        \\EndFunction\n\n        \\Statex\n\n        \\State Initialize four empty sets: $\\mathcal{C}$ (cliques), $\\mathcal{T}$ (triangles), $\\mathcal{S}$ (separators) and $\\mathcal{V}$ (vertices);\n        \\State Initialize an adjacency matrix $\\textbf{\\textit{A}} \\in \\mathbb{R}^{n, n}$ with all zeros;\n        \\State $\\mathcal{C}_1 \\leftarrow$ tetrahedron, $\\{v_1, v_2, v_3, v_4\\}$, obtained choosing the $4$ entries of $\\hat{\\textbf{C}}$ maximising the similarity among features;\n        \\State $\\mathcal{T} \\leftarrow$ the four triangular faces in $\\mathcal{C}_1: \\{v_1, v_2, v_3\\}, \\{v_1, v_2, v_4\\}, \\{v_1, v_3, v_4\\}, \\{v_2, v_3, v_4\\}$;\n        \\State $\\mathcal{V} \\leftarrow$ Assign to $\\mathcal{V}$ the remaining $n-4$ vertices not in $\\mathcal{C}_1$;\n\n        \\While{$\\mathcal{V}$ is not empty}\n            \\State Find the combination of $\\{v_a, v_b, v_c\\} \\in \\mathcal{T}$ (i.e. $t$) and $v_d \\in \\mathcal{V}$ which maximises \\Call{MaximumGain}{$\\hat{\\textbf{C}}$, $\\mathcal{V}$, $t$}; \n            \\State \\parbox[t]{\\dimexpr\\linewidth-\\algorithmicindent}{%\n            \/* $\\{v_a, v_b, v_c, v_d\\}$ is a new 4-clique $\\mathcal{C}$, $\\{v_a, v_b, v_c\\}$ becomes a separator $\\mathcal{S}$, three new triangular faces, $\\{v_a, v_b, v_d\\}$, $\\{v_a, v_c, v_d\\}$ and $\\{v_b, v_c, v_d\\}$ are created *\/.\n            }\n            \\State Remove $v_d$ from $\\mathcal{V}$;\n            \\State Remove $\\{v_a, v_b, v_c\\}$ from $\\mathcal{T}$;\n            \\State Add $\\{v_a, v_b, v_d\\}$, $\\{v_a, v_c, v_d\\}$ and $\\{v_b, v_c, v_d\\}$ to $\\mathcal{T}$;\n        \\EndWhile\n\n        \\State For each pair of nodes $i, j$ in $\\mathcal{C}$, set $\\textbf{\\textit{A}}_{i,j} = 1$;\n        \\State \\Return $\\textbf{\\textit{A}}$.\n    \\end{algorithmic}\n\\end{algorithm}\n\nThe building process of TMFG (see Algorithm \\ref{alg:TMFG_Algo}) is based on a simple topological move that preserves planarity: it adds one node to the centre of three-nodes cliques by using a score function that maximises the sum of the weights of the three edges connecting the existing veritces. This addition transforms three-nodes cliques (i.e. triangles) into four-nodes cliques (i.e. tetrahedrons) characterised by a chord that is not part of the clique but connects two nodes in the clique, forming two triangles and generating a chordal network \\cite{christensen2018network}. Also, in this case, the resulting network has $3n-6$ edges and is composed of three- and four-nodes cliques. TMFG has two main advantages compared to PMFG: (i) it can be used to generate sparse probabilistic models as a form of topological regularization \\cite{aste2022topological} and (ii) it is computationally efficient. On the other hand, the two main limitations of chordal networks are that (i) they may add unnecessary edges to satisfy the property of chordality and (ii) their building cost can vary based on the chosen optimization function. For a complete pedagogical exposition of the determination of the TMFG and a detailed analysis of its properties, the interested reader is referred to the works by \\cite{massara2017network, briola2022dependency}.\n\n\\subsection{Topological Feature Selection} \n\\label{sec:Topologically_Constrained_Feature_Selection}\nTopological Feature Selection (TFS) algorithm is a graph-based filter method to perform feature selection in an unsupervised manner. Given a set of features $F = \\{f_1, \\dots, f_n\\}$, where $n \\gg 1$ is the cardinality, we build the adjacency matrix \\textbf{\\textit{A}} of the corresponding TMFG based on one of the following three metrics: (i) the Pearson's estimator of the correlation coefficient, (ii) the Spearman's rank correlation coefficient and (iii) the Energy coefficient (i.e. the weighted combination of two pairwise measures described later in this Section). Depending on the metric's formulation, it is possible to capture different kinds of interactions among covariates (e.g. linear or non-linear interactions).\n\nThe Person's estimator of the correlation coefficient for the two covariates $f_i$ and $f_j$, is defined as:\n\n\\begin{equation}\n    r_{f_i, f_j} = \\frac{\\sum_{s=1}^S ({f_{i,s}} - \\hat{\\mu}_{f_i}) ({f_{j,s}} - \\hat{\\mu}_{f_j})}{\\hat{\\sigma}_{f_i}\\hat{\\sigma}_{f_j}}\n\\end{equation}\n\nwhere $S$ is the sample size, $f_{i,s}$ and $f_{j, s}$ are two sample points indexed with $s$, $\\hat{\\mu}$ is the sample mean and $\\hat{\\sigma}$ is the sample standard deviation. By definition, $r_{f_i, f_j}$ has values between $-1$ (meaning that the two features are completely, linearly anti-correlated), and $+1$ (meaning that the two features are completely, linearly correlated). When $r_{f_i, f_j} = 0$, the two covariates are said to be uncorrelated. The Person's estimator of the correlation coefficient heavily depends on the distribution of the underlying data and may be influenced by outliers. In addition to this, it only captures linear dependence among variables, restricting its applicability to real-world problems where non-linear interactions are often relevant \\cite{shirokikh2013computational}. \n\nThe Spearman's rank correlation coefficient is based on the concept of `variables ranking'. Ranking a variable means mapping its realizations to an integer number that describes their positions in an ordered set. Considering a variable with cardinality $|s|$, this means assigning 1 to the realization with the highest value and $|s|$ to the realization with the lowest value.\n\nThe Spearman's rank correlation coefficient for the two covariates $f_i$ and $f_j$, is defined as the Parson's correlation between the ranks of the variables:\n\n\\begin{equation}\n    r_{s_{f_i, f_j}} = \\frac{\\sum_{s=1}^S (R_{f_{i, s}} - \\hat{\\mu}_{R_{f_i}})(R_{f_{j, s}} - \\hat{\\mu}_{R_{f_j}})}{\\hat{\\sigma}_{R_{f_i}}\\hat{\\sigma}_{R_{f_j}}}\n\\end{equation}\n\nwhere $S$ is the sample size, $R_{f_{i, s}}$ and $R_{f_{j, s}}$ are the ranks of the two sample points indexed with $s$, $\\hat{\\mu}$ is the sample mean for $R_{f_i}$ and $R_{f_j}$ and $\\hat{\\sigma}$ is the sample standard deviation for $R_{f_i}$ and $R_{f_j}$. If there are no repeated data samples, a perfect Spearman's rank correlation (i.e. $r_{s_{f_i, f_j}} = 1$ or $r_{s_{f_i, f_j}} = -1$ occurs when each of the features is a perfect monotone function of the other). Spearman's rank correlation technique is distribution-free and allows to capture monotonic, but not necessarily linear, relationships among variables \\cite{shirokikh2013computational}. \n\nThe Energy coefficient is a metric introduced by \\cite{roffo2015infinite} and, in this paper, it is used as the primary benchmark for comparison between our method and the current state-of-the-art. It is a weighted combination of two different pairwise measures defined as follows:\n\n\\begin{equation} \\label{eq:Energy_Coefficient}\n    \\phi_{f_i, f_j} = \\alpha E_{f_i,f_j} + (1-\\alpha) \\rho_{f_i,f_j}\n\\end{equation}\n\nwhere $E_{f_i,f_j} = \\max(\\hat{\\sigma}_{f_i}, \\hat{\\sigma}_{f_j})$, with $\\hat{\\sigma}$ being the sample standard deviation computed on features $f_i$ and $f_j$ normalized to the range $[0,1]$, $\\rho_{f_i,f_j} = 1 - |r_{s_{f_i, f_j}}|$ and $\\alpha$ is a threshold value with a value $\\in [0, 1]$. $\\phi_{f_i, f_j} \\in [0, 1]$ analyses two features distributions (i.e. $f_i$ and $f_j$) taking into account both their maximal dispersion (i.e. standard deviation) and their level of uncorrelation. Computing $\\phi_{f_i, f_j}$ for all the features in $F$ in a pairwise manner, one can define a matrix which is $n \\times n$ symmetric and completely characterized by $n(n-1)\/2$ coefficients. For simplicity, we refer to this matrix as $\\hat{\\textbf{C}}$ too.\n\nOnce one of the above mentioned metrics is chosen and $\\hat{\\textbf{C}}$ is computed, TFS applies the standard TMFG algorithm defined in Section \\ref{sec:Information_Filtering_Networks} on the corresponding fully connected graph, creating a sparse chordal network which is able to retain useful relationships among features, pruning the weakest ones. The last step toward the selection of the most relevant features, is represented by the choice of the right nodes inside the TMFG. In this sense, multiple approaches of increasing complexity can be formulated. In this paper, which is a foundational one, we study the relative position of the nodes in the network computing their degree centrality. Degree centrality is the simplest and least computationally intensive measure of centrality. Typically, all the other centrality measures are strictly related \\cite{valente2008correlated, lee2006correlations}.\n\nGiven the sparse adjacency matrix \\textbf{\\textit{A}} representing the TMFG, degree centrality of a node $v$ is denoted as $\\deg(v)$ and represents the number of neighbours (i.e. how many edges a node has) of $v$ as follows:\n\n\\begin{equation}\n    \\deg(v) = \\sum_{w=1}^n A_{f_v,f_w}\n\\end{equation}\n\nwhere $n$ is the cardinality of $F$ and $f_v$ and $f_w$ are two features $\\in F$. Although its simplicity, degree centrality can be very illuminating and can be considered a crude measure of whether a node is influential or not in the TMFG. Once obtained $\\deg(v) \\; \\forall v \\in \\textrm{TMFG}$, we rank these values in a descending order and we take the top $k$ central nodes, where $k$ is the cardinality of the features' subset we want to consider. \n\n\\begin{figure}[H]\n    \\centering\n    \\includegraphics[scale=0.24]{images\/TMFG_FS_Pipeline.png}\n    \\caption{TFS algorithm's working schema consists of three different steps: (i) construction of a fully connected graph based on a similarity metric (e.g. $r_{f_i, f_j}$ or $r_{s_{f_i, f_j}}$ or $\\phi_{f_i, f_j}$), (ii) TMFG-based filtering of weakest relationships between nodes and (iii) selection of relevant features based on a centrality measure (e.g. degree centrality).}\n    \\label{fig:TMFG_FS_Pipeline}\n\\end{figure}\n\n\\subsection{Benchmark method: Infinite Feature Selection ($\\textrm{Inf-FS}_U$)} \nTo prove the effectiveness of the proposed methodology, we test the TFS algorithm against one of the state-of-the-art counterparts in unsupervised, graph-based filter feature selection techniques, i.e. Infinite Feature Selection ($\\textrm{Inf-FS}_U$) \\footnote{The Python implementation of $\\textrm{Inf-FS}_U$ algorithm used in this paper can be reached at \\url{https:\/\/github.com\/fullyz\/Infinite-Feature-Selection}.} \\cite{roffo2015infinite}. $\\textrm{Inf-FS}_U$ represents features as nodes of a graph and relationships among them as weighted edges. Weights are computed as per in Equation \\ref{eq:Energy_Coefficient}. Each path of a given length over the network is seen as a potential set of relevant features. Therefore, varying paths and letting them tend to an infinite number permits the investigation of the importance of each possible subset of features. Based on this, assigning a score to each feature and ranking them in descendant order allows us to perform feature selection effectively. It is worth noting that $\\textrm{Inf-FS}_U$ has a computational complexity equal to $\\approx \\mathcal{O}(n^3)$. In contrast, TFS has a computational complexity equal to $\\approx \\mathcal{O}(n^2)$, with $n$ being the number of the features.\n\n\\section{Experiments} \\label{sec:Experiments}\nFigure \\ref{fig:Train_Test_Pipeline} reports a pictorial representation of training\/validation\/test pipeline adopted to evaluate and compare the performances of TFS and $\\textrm{Inf-FS}_U$ algorithms. \n\n\\begin{figure}[h]\n    \\centering\n    \\includegraphics[scale=0.25]{images\/Train_Test_Pipeline.png}\n    \\caption{Pictorial representation of the training\/validation\/test pipeline. We distinguish $3$ main stages: (i) $\\textrm{Inf-FS}_U$- or TFS-based feature selection; (ii) features' standardisation (see Appendix \\ref{Appendix_B} and classifier's training; (iii) model's evaluation on out-of-sample data (i.e. validation or test set). Hyper-parameters optimization is performed using a parallel grid search approach and raw dataset's labels distribution is kept intact adopting a stratified \\textit{k}-fold cross validation approach.}\n    \\label{fig:Train_Test_Pipeline}\n\\end{figure}\n\nModel hyper-parameters (see Table \\ref{tab:Hyperparameters_Table}) are optimised adopting a parallel grid search approach. For $\\textrm{Inf-FS}_U$, the first hyper-parameter to be optimised is $\\alpha$, which can take values between $0$ and $1$. To tune this parameter, we use a range of equally spaced realisations between $0.1$ and $1.0$, all at a distance of $0.1$. The second hyper-parameter to be optimised is $\\theta$ and represents a regularisation factor which, in the original paper \\cite{roffo2015infinite}, has a fixed value equal to $0.9$. Here, instead, we tune this parameter in the same way as $\\alpha$. In the case of TFS, the first hyper-parameter to be optimised is the metric to be used in the building process of the initial fully connected graph (see Figure \\ref{fig:TMFG_FS_Pipeline}). As reported in Section \\ref{sec:Topologically_Constrained_Feature_Selection}, we test three different metrics: (i) the Pearson's estimator of the correlation coefficient, (ii) the Spearman's rank correlation coefficient and  (iii) the Energy coefficient. The second hyper-parameter to be tuned is a boolean value which regulates the possibility to use the coefficients mentioned above in a squared form. It is worth mentioning that, if the Energy metric is chosen, the corresponding $\\hat{\\textbf{C}}$ is never squared ($\\hat{\\textbf{C}}$ already contains only positive values). The last hyper-parameter to be optimised is $\\alpha$, and it should be considered only when the Energy coefficient is chosen as a metric. The meaning of this hyper-parameter is the same as its homologous in the $\\textrm{Inf-FS}_U$ model. All the models are finally evaluated on feature subsets with cardinalities $\\in [10, 50, 100, 150, 200]$.\n\n\\begin{table}[H]\n\\centering\n\\caption{Model dependent hyper-parameters search spaces. In the case of the TFS algorithm, the $\\dagger$ symbol indicates that, if the Energy metric is chosen, the corresponding $\\hat{\\textbf{C}}$ is never squared ($\\hat{\\textbf{C}}$ already contains only positive values). The $\\ddagger$ symbol, on the other hand, indicates that $\\alpha$ parameter should be considered only when the Energy coefficient is chosen as a metric.}\n\\label{tab:Hyperparameters_Table}\n\\begin{tabular}{@{}cc@{}}\n\\toprule\n\\textbf{Model} & \\textbf{Hyper-parameters}                                      \\\\ \\midrule\n$\\textrm{Inf-FS}_U$   & \\begin{tabular}[c]{@{}c@{}}$\\alpha$: {[}0.1: 0.1: 1.0{]}\\\\ $\\theta$: {[}0.1: 0.1: 1.0{]}\\end{tabular}                                              \\\\ \\midrule\nTFS & \\begin{tabular}[c]{@{}c@{}}metric: {[}Pearson, Spearman, Energy{]}\\\\ square$^\\dagger$: {[}True, False{]}\\\\ $\\alpha^\\ddagger$: {[}0.1: 0.1: 1.0{]}\\end{tabular} \\\\ \\bottomrule\n\\end{tabular}\n\\end{table}\n\nFor each hyper-parameter combination, a stratified $k$-fold cross-validation with $k=3$ is performed on the training set. The value of $k$ is chosen to take into account labels' distributions reported in Table \\ref{tab:Datasets_Description}. Results' reproducibility and a fair comparison between models are guaranteed by fixing the random seed for each step of the training\/validation\/test pipeline. \n\nThe meaningfulness of each subset of features chosen by the two algorithms is evaluated based on the classification performance achieved by three classification algorithms: (i) Linear Support Vector Classifier (LinearSVM); (ii) \\textit{k}-Nearest Neighbors Classifier (KNN); (iii) Decision Tree Classifier (Decision Tree). LinearSVM is a sparse kernel-based method designed to convert non-linearly separable problems in the low-dimensional space, into linearly separable problems in the higher-dimensional space, thereby achieving classification \\cite{han2022data}. KNN is a lazy learning algorithm, which classifies test instances evaluating their distance from the nearest \\textit{k} training samples stored in an \\textit{n}-dimensional space (where \\textit{n} is the number of dataset's covariates) \\cite{han2022data}. Finally, Decision Tree is a flowchart-like tree structure computed on training instances which classifies test samples tracing a path from the root to a leaf node holding the class prediction \\cite{han2022data}. The inherently different nature of the three classifiers prevents from obtaining biased results for the two feature selection approaches. More details about chosen classifiers and their implementations are reported in Appendix \\ref{Appendix_A}.\n\nResults obtained in the current paper are evaluated using three different performance metrics: (i) the Balanced Accuracy score (BA) \\cite{mosley2013balanced, kelleher2020fundamentals}; (ii) the F1 score (F1); (iii) the Matthews Correlation Coefficient (MCC) \\cite{baldi2000assessing, gorodkin2004comparing, jurman2012comparison}. We use the BA score for the hyper-parameters optimization process and as the reference metric to present results in Section \\ref{sec:Results}. The BA score for the multi-class case is defined as:\n\n\\begin{equation} \\label{eq:BA_multi}\n    BA = \\frac{1}{|Z|} \\left(  \\sum_{z \\in Z} \\frac{\\textrm{TP}_z}{\\textrm{TP}_z+\\textrm{FN}_z} + \\frac{\\textrm{TN}_z}{\\textrm{TN}_z+\\textrm{FP}_z}   \\right).\n\\end{equation}\n\n$\\textrm{TP}$ is the number of outcomes where the model correctly classifies a sample as belonging to a positive class (or detects an event of interest), when in fact it does belong to that class (or the event is present). $\\textrm{TN}$ is the number of outcomes where the model correctly classifies a sample as belonging to a negative class (or fails to detect an event of interest), when in fact it does not belong to that class (or the event is not present). $\\textrm{FP}$ is the number of outcomes where the model incorrectly classifies a sample as belonging to a positive class (or detects an event of interest), when in fact it does not belong to that class (or the event is not present). $\\textrm{FN}$ is the number of outcomes where the model incorrectly classifies a sample as belonging to a negative class (or fails to detect an event of interest), when in fact it belongs to a positive class (or the event of interest is present).  $|Z|$ indicates the cardinality of the set of different classes.\n\nGiven Equation \\ref{eq:BA_multi}, it is easy for the interested reader to reconstruct the formulation for the binary case. General formulations for the F1 score, and the MCC are reported in Appendix \\ref{Appendix_C} together with an extended version of results described later in this Section.\n\nFor each model and for each subset cardinality, hyper-parameters configuration which maximises the BA score while minimising the number of parameters is applied to test datasets. In order to assess the robustness of results, we test if the results achieved by the two feature selection approaches are statistically different. For this we use an improved version of the classic $5\\times2$ cv paired \\textit{t}-test\\footnote{The Python implementation of the original $5\\times2$ cv paired \\textit{t} test can be reached at \\url{http:\/\/rasbt.github.io\/mlxtend\/user_guide\/evaluate\/paired_ttest_5x2c}.} \\cite{dietterich1998approximate}. The test is constructed as follows. Given two classifiers $A$ and $B$ and a dataset $D$, $D$ is first randomly split into two balanced subsets $D_1$, $D_2$ (one for training and one for test). Both $A$ and $B$ are then estimated on $D_1$ and evaluated on $D_2$ obtaining performance measures $a_1, b_1$. The roles of the datasets are then switched by estimating $A$ and $B$ on $D_2$ and evaluating on $D_1$ which results in further performance measures $a_2, b_2$. The random division of $D$ is performed for a total of $5$ times, obtaining the matched performance evaluations $\\{a_1, b_1\\}, \\{a_2, b_2\\} \\dots, \\{a_{10}, b_{10}\\}$. The test statistic \\textit{t} is then computed as follows:\n\n\\begin{equation}\n    t = \\frac{\\sqrt{10} \\bar d}{\\hat{\\sigma}},\n\\end{equation}\n\nwhere $d_h=a_h-b_h$ for $ h=1,\\dots, 10$, is the difference between the matched performances metrics of the two classifiers, $\\bar d = \\frac{1}{10}\\sum_{h=1}^{10} d_h$ and $\\hat{\\sigma}^2 = \\frac{1}{10} \\sum_{h=1}^{10}(d_h - \\bar d)^2$. \\textit{t} follows a \\textit{t}-distribution with $9$ degrees of freedom and the null hypothesis is that \\textit{the two classifiers $A$ and $B$ are not statistically different in their performances}. Starting from this basic formulation of the $5\\times2$ cv paired \\textit{t}-test, we simply increased the number of iterations, making it a $15\\times2$ cv paired \\textit{t}-test, in order to increase the statistical robustness of the achieved results. Also in this case, results reproducibility is guaranteed through a strict control of random seeds.\n\n\\section{Results} \\label{sec:Results}\n\nFor both $\\textrm{Inf-FS}_U$ and TFS, for each one of the three considered classifiers and for each feature subset cardinality $\\in [10, 50, 100, 150, 200]$, results obtained running the hyper-parameter optimisation pipeline described in Section \\ref{sec:Experiments} are reported in Appendix \\ref{Appendix_B}.\n\nTables \\ref{tab:local_bests_LinearSVM}, \\ref{tab:local_bests_KNN} and \\ref{tab:local_bests_Decision_Tree} report out-of-sample Balanced Accuracy scores obtained using subset's cardinality-dependent optimal hyper-parameter configurations for LinearSVM, KNN and Decision Tree classifier respectively. For each dataset, we highlight in bold the best achieved result. If one classifier performs equally across multiple subsets' cardinalities, the winning configuration is the one which minimises the subset's cardinality itself. If one classifier performs equally under the two feature selection schema, the winning feature selection approach is the one which minimises the computational complexity (i.e. TFS). \n\nTo compare $\\textrm{Inf-FS}_U$ and TFS, we consider three different measures: (i) the number of times a classifier achieves optimal results under each feature selection schema; (ii) the cross-datasets average balanced accuracy score; (iii) the cross-datasets average maximum drawdown ratio (i.e. the difference between the highest and the lowest achieved result).\n\n\\begin{table}[H]\n\\centering\n\\caption{Subset size-dependent, out-of-sample Balanced Accuracy scores using a LinearSVM classifier. For each dataset, we boldly highlight the combination between feature selection schema and classifier producing the best out-of-sample result. For each subset size, we report, in the last row, the number of times a feature selection approach outperforms the other across datasets.}\n\\label{tab:local_bests_LinearSVM}\n\\scalebox{0.85}{\n\\begin{tabular}{c|cccccccccc}\n\\hline\n &\n  \\multicolumn{10}{c}{\\textbf{LinearSVM}} \\\\ \\hline\n &\n  \\multicolumn{2}{c|}{\\textbf{10}} &\n  \\multicolumn{2}{c|}{\\textbf{50}} &\n  \\multicolumn{2}{c|}{\\textbf{100}} &\n  \\multicolumn{2}{c|}{\\textbf{150}} &\n  \\multicolumn{2}{c}{\\textbf{200}} \\\\ \\cline{2-11} \n &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\multicolumn{1}{c|}{\\textbf{TFS}} &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\multicolumn{1}{c|}{\\textbf{TFS}} &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\multicolumn{1}{c|}{\\textbf{TFS}} &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\multicolumn{1}{c|}{\\textbf{TFS}} &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\textbf{TFS} \\\\ \\hline\nPCMAC &\n  0.52 &\n  \\multicolumn{1}{c|}{0.50} &\n  0.57 &\n  \\multicolumn{1}{c|}{0.67} &\n  0.59 &\n  \\multicolumn{1}{c|}{0.70} &\n  0.61 &\n  \\multicolumn{1}{c|}{\\textbf{0.71}} &\n  0.62 &\n  0.69 \\\\\nRELATHE &\n  0.47 &\n  \\multicolumn{1}{c|}{0.49} &\n  0.43 &\n  \\multicolumn{1}{c|}{\\textbf{0.53}} &\n  0.51 &\n  \\multicolumn{1}{c|}{0.53} &\n  0.44 &\n  \\multicolumn{1}{c|}{0.49} &\n  0.53 &\n  0.53 \\\\\nCOIL20 &\n  0.52 &\n  \\multicolumn{1}{c|}{0.63} &\n  0.77 &\n  \\multicolumn{1}{c|}{0.90} &\n  0.84 &\n  \\multicolumn{1}{c|}{0.92} &\n  0.90 &\n  \\multicolumn{1}{c|}{0.94} &\n  0.94 &\n  \\textbf{0.96} \\\\\nORL &\n  0.40 &\n  \\multicolumn{1}{c|}{0.44} &\n  0.63 &\n  \\multicolumn{1}{c|}{0.88} &\n  0.72 &\n  \\multicolumn{1}{c|}{0.89} &\n  0.86 &\n  \\multicolumn{1}{c|}{0.93} &\n  0.84 &\n  \\textbf{0.94} \\\\\nwarpAR10P &\n  0.33 &\n  \\multicolumn{1}{c|}{0.44} &\n  0.56 &\n  \\multicolumn{1}{c|}{0.78} &\n  0.72 &\n  \\multicolumn{1}{c|}{0.85} &\n  0.70 &\n  \\multicolumn{1}{c|}{\\textbf{0.95}} &\n  0.75 &\n  0.85 \\\\\nwarpPIE10P &\n  0.85 &\n  \\multicolumn{1}{c|}{0.89} &\n  0.95 &\n  \\multicolumn{1}{c|}{\\textbf{1.00}} &\n  0.98 &\n  \\multicolumn{1}{c|}{1.00} &\n  1.00 &\n  \\multicolumn{1}{c|}{1.00} &\n  1.00 &\n  1.00 \\\\\nYale &\n  0.14 &\n  \\multicolumn{1}{c|}{0.33} &\n  0.25 &\n  \\multicolumn{1}{c|}{0.50} &\n  0.39 &\n  \\multicolumn{1}{c|}{0.67} &\n  0.37 &\n  \\multicolumn{1}{c|}{0.69} &\n  0.53 &\n  \\textbf{0.70} \\\\\nUSPS &\n  0.72 &\n  \\multicolumn{1}{c|}{0.65} &\n  0.90 &\n  \\multicolumn{1}{c|}{0.90} &\n  0.91 &\n  \\multicolumn{1}{c|}{0.92} &\n  0.92 &\n  \\multicolumn{1}{c|}{\\textbf{0.93}} &\n  0.92 &\n  0.93 \\\\\ncolon &\n  0.70 &\n  \\multicolumn{1}{c|}{0.69} &\n  0.69 &\n  \\multicolumn{1}{c|}{0.66} &\n  \\textbf{0.92} &\n  \\multicolumn{1}{c|}{0.82} &\n  0.85 &\n  \\multicolumn{1}{c|}{0.74} &\n  0.85 &\n  0.88 \\\\\nGLIOMA &\n  \\textbf{0.61} &\n  \\multicolumn{1}{c|}{0.25} &\n  0.30 &\n  \\multicolumn{1}{c|}{0.30} &\n  0.30 &\n  \\multicolumn{1}{c|}{0.38} &\n  0.60 &\n  \\multicolumn{1}{c|}{0.41} &\n  0.59 &\n  0.25 \\\\\nlung &\n  0.39 &\n  \\multicolumn{1}{c|}{0.47} &\n  0.67 &\n  \\multicolumn{1}{c|}{0.89} &\n  0.81 &\n  \\multicolumn{1}{c|}{\\textbf{0.95}} &\n  0.71 &\n  \\multicolumn{1}{c|}{0.87} &\n  0.90 &\n  0.81 \\\\\nlung\\_small &\n  0.49 &\n  \\multicolumn{1}{c|}{0.57} &\n  0.76 &\n  \\multicolumn{1}{c|}{0.79} &\n  0.82 &\n  \\multicolumn{1}{c|}{0.68} &\n  0.79 &\n  \\multicolumn{1}{c|}{0.75} &\n  0.82 &\n  \\textbf{0.93} \\\\\nlymphoma &\n  0.22 &\n  \\multicolumn{1}{c|}{0.50} &\n  0.58 &\n  \\multicolumn{1}{c|}{0.96} &\n  0.78 &\n  \\multicolumn{1}{c|}{0.87} &\n  0.90 &\n  \\multicolumn{1}{c|}{0.82} &\n  0.81 &\n  \\textbf{0.98} \\\\\nGISETTE &\n  0.50 &\n  \\multicolumn{1}{c|}{0.49} &\n  0.48 &\n  \\multicolumn{1}{c|}{0.47} &\n  0.51 &\n  \\multicolumn{1}{c|}{\\textbf{0.52}} &\n  0.47 &\n  \\multicolumn{1}{c|}{0.50} &\n  0.49 &\n  0.50 \\\\\nIsolet &\n  0.32 &\n  \\multicolumn{1}{c|}{0.51} &\n  0.74 &\n  \\multicolumn{1}{c|}{0.78} &\n  0.81 &\n  \\multicolumn{1}{c|}{0.82} &\n  0.88 &\n  \\multicolumn{1}{c|}{0.83} &\n  0.89 &\n  \\textbf{0.89} \\\\\nMADELON &\n  0.59 &\n  \\multicolumn{1}{c|}{\\textbf{0.59}} &\n  0.58 &\n  \\multicolumn{1}{c|}{0.56} &\n  0.55 &\n  \\multicolumn{1}{c|}{0.57} &\n  0.54 &\n  \\multicolumn{1}{c|}{0.57} &\n  0.57 &\n  0.57 \\\\ \\hline\\hline\n  \\# bests&\n  5 &\n  \\multicolumn{1}{c|}{11} &\n  3 &\n  \\multicolumn{1}{c|}{13} &\n  2 &\n  \\multicolumn{1}{c|}{14} &\n  5 &\n  \\multicolumn{1}{c|}{11} &\n  2 &\n  14 \\\\ \\hline\n\\end{tabular}\n}\n\\end{table}\n\nLooking at Table \\ref{tab:local_bests_LinearSVM}, we notice that TFS combined with LinearSVM classifier produces higher Balanced Accuracy scores in $14$ out of $16$ datasets (i.e. $87.5\\%$ of cases), while $\\textrm{Inf-FS}_U$ combined with the same classifier has a higher Balanced Accuracy scores only in $2$ out of $16$ datasets (i.e. $12.5\\%$ of cases). Considering only the scenarios where TFS is the winning feature selection schema, we notice that in $1$ case, the optimal cardinality is equal to $10$, in $2$ cases, the optimal cardinality is equal to $50$ and $100$, in three cases the optimal cardinality is equal to $150$, and in $6$ cases the optimal cardinality is equal to $200$. When the $\\textrm{Inf-FS}_U$ is used as feature selection algorithm and LinearSVM as classifier, the cross-datasets average Balanced Accuracy score grows from a value equal to $0.49$ at cardinality $10$ to a value of $0.75$ at cardinality $200$ with an increase of $26\\%$. When the TFS is used as feature selection algorithm and LinearSVM as classifier, cross-datasets average Balanced Accuracy score grows from a value equal to $0.52$ at cardinality $10$ to a value of $0.78$ at cardinality $200$ with an increase of $26\\%$. Finally, we notice that when the $\\textrm{Inf-FS}_U$ is used as feature selection algorithm and LinearSVM as classifier, the average maximum drawdown ratio is equal to $31\\%$. Using TFS as feature selection algorithm, instead, the average maximum drawdown ratio is equal to $28\\%$.\n\n\\begin{table}[H]\n\\centering\n\\caption{Subset size-dependent, out-of-sample balanced accuracy scores using a KNN classifier. For each dataset, we boldly highlight the combination between feature selection schema and classifier producing the best out-of-sample result. For each subset size, we report, in the last row, the number of times a feature selection approach outperforms the other across datasets.}\n\\label{tab:local_bests_KNN}\n\\scalebox{0.85}{\n\\begin{tabular}{c|cccccccccc}\n\\hline\n &\n  \\multicolumn{10}{c}{\\textbf{KNN}} \\\\ \\hline\n &\n  \\multicolumn{2}{c|}{\\textbf{10}} &\n  \\multicolumn{2}{c|}{\\textbf{50}} &\n  \\multicolumn{2}{c|}{\\textbf{100}} &\n  \\multicolumn{2}{c|}{\\textbf{150}} &\n  \\multicolumn{2}{c}{\\textbf{200}} \\\\ \\cline{2-11} \n &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\multicolumn{1}{c|}{\\textbf{TFS}} &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\multicolumn{1}{c|}{\\textbf{TFS}} &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\multicolumn{1}{c|}{\\textbf{TFS}} &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\multicolumn{1}{c|}{\\textbf{TFS}} &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\textbf{TFS} \\\\ \\hline\nPCMAC &\n  0.52 &\n  \\multicolumn{1}{c|}{0.53} &\n  0.57 &\n  \\multicolumn{1}{c|}{0.61} &\n  0.61 &\n  \\multicolumn{1}{c|}{0.62} &\n  0.59 &\n  \\multicolumn{1}{c|}{\\textbf{0.63}} &\n  0.60 &\n  0.62 \\\\\nRELATHE &\n  0.46 &\n  \\multicolumn{1}{c|}{0.46} &\n  0.50 &\n  \\multicolumn{1}{c|}{\\textbf{0.57}} &\n  0.48 &\n  \\multicolumn{1}{c|}{0.49} &\n  0.46 &\n  \\multicolumn{1}{c|}{0.45} &\n  0.48 &\n  0.48 \\\\\nCOIL20 &\n  0.70 &\n  \\multicolumn{1}{c|}{0.82} &\n  0.86 &\n  \\multicolumn{1}{c|}{0.93} &\n  0.93 &\n  \\multicolumn{1}{c|}{0.93} &\n  0.96 &\n  \\multicolumn{1}{c|}{0.94} &\n  \\textbf{0.97} &\n  0.93 \\\\\nORL &\n  0.38 &\n  \\multicolumn{1}{c|}{0.52} &\n  0.52 &\n  \\multicolumn{1}{c|}{\\textbf{0.77}} &\n  0.62 &\n  \\multicolumn{1}{c|}{0.70} &\n  0.73 &\n  \\multicolumn{1}{c|}{0.71} &\n  0.72 &\n  0.77 \\\\\nwarpAR10P &\n  0.36 &\n  \\multicolumn{1}{c|}{0.30} &\n  0.36 &\n  \\multicolumn{1}{c|}{\\textbf{0.51}} &\n  0.43 &\n  \\multicolumn{1}{c|}{0.46} &\n  0.32 &\n  \\multicolumn{1}{c|}{0.38} &\n  0.42 &\n  0.48 \\\\\nwarpPIE10P &\n  0.83 &\n  \\multicolumn{1}{c|}{0.72} &\n  0.86 &\n  \\multicolumn{1}{c|}{0.91} &\n  0.92 &\n  \\multicolumn{1}{c|}{\\textbf{0.97}} &\n  0.89 &\n  \\multicolumn{1}{c|}{0.92} &\n  0.89 &\n  0.95 \\\\\nYale &\n  0.14 &\n  \\multicolumn{1}{c|}{0.42} &\n  0.28 &\n  \\multicolumn{1}{c|}{0.41} &\n  0.26 &\n  \\multicolumn{1}{c|}{0.42} &\n  0.43 &\n  \\multicolumn{1}{c|}{0.38} &\n  0.35 &\n  \\textbf{0.49} \\\\\nUSPS &\n  0.78 &\n  \\multicolumn{1}{c|}{0.77} &\n  0.94 &\n  \\multicolumn{1}{c|}{0.94} &\n  \\textbf{0.96} &\n  \\multicolumn{1}{c|}{0.95} &\n  0.96 &\n  \\multicolumn{1}{c|}{0.95} &\n  0.95 &\n  0.95 \\\\\ncolon &\n  0.77 &\n  \\multicolumn{1}{c|}{0.82} &\n  0.89 &\n  \\multicolumn{1}{c|}{0.77} &\n  0.89 &\n  \\multicolumn{1}{c|}{0.85} &\n  \\textbf{1.00} &\n  \\multicolumn{1}{c|}{0.70} &\n  0.85 &\n  0.77 \\\\\nGLIOMA &\n  0.24 &\n  \\multicolumn{1}{c|}{0.10} &\n  0.40 &\n  \\multicolumn{1}{c|}{0.40} &\n  0.42 &\n  \\multicolumn{1}{c|}{\\textbf{0.62}} &\n  0.52 &\n  \\multicolumn{1}{c|}{0.62} &\n  0.52 &\n  0.62 \\\\\nlung &\n  0.33 &\n  \\multicolumn{1}{c|}{0.51} &\n  0.65 &\n  \\multicolumn{1}{c|}{\\textbf{0.79}} &\n  0.71 &\n  \\multicolumn{1}{c|}{0.65} &\n  0.72 &\n  \\multicolumn{1}{c|}{0.68} &\n  0.78 &\n  0.79 \\\\\nlung\\_small &\n  0.57 &\n  \\multicolumn{1}{c|}{0.61} &\n  0.80 &\n  \\multicolumn{1}{c|}{0.87} &\n  0.82 &\n  \\multicolumn{1}{c|}{0.90} &\n  \\textbf{0.93} &\n  \\multicolumn{1}{c|}{0.90} &\n  0.90 &\n  0.76 \\\\\nlymphoma &\n  0.44 &\n  \\multicolumn{1}{c|}{0.50} &\n  0.60 &\n  \\multicolumn{1}{c|}{0.74} &\n  0.69 &\n  \\multicolumn{1}{c|}{0.69} &\n  \\textbf{0.76} &\n  \\multicolumn{1}{c|}{0.75} &\n  0.69 &\n  0.74 \\\\\nGISETTE &\n  0.49 &\n  \\multicolumn{1}{c|}{0.51} &\n  0.52 &\n  \\multicolumn{1}{c|}{\\textbf{0.54}} &\n  0.50 &\n  \\multicolumn{1}{c|}{0.51} &\n  0.50 &\n  \\multicolumn{1}{c|}{0.53} &\n  0.50 &\n  0.49 \\\\\nIsolet &\n  0.32 &\n  \\multicolumn{1}{c|}{0.49} &\n  0.72 &\n  \\multicolumn{1}{c|}{0.73} &\n  0.78 &\n  \\multicolumn{1}{c|}{0.78} &\n  \\textbf{0.83} &\n  \\multicolumn{1}{c|}{0.81} &\n  0.82 &\n  0.83 \\\\\nMADELON &\n  0.61 &\n  \\multicolumn{1}{c|}{\\textbf{0.78}} &\n  0.58 &\n  \\multicolumn{1}{c|}{0.74} &\n  0.64 &\n  \\multicolumn{1}{c|}{0.66} &\n  0.62 &\n  \\multicolumn{1}{c|}{0.64} &\n  0.57 &\n  0.63 \\\\ \\hline\\hline\n  \\# bests &\n  4 &\n  \\multicolumn{1}{c|}{12} &\n  1 &\n  \\multicolumn{1}{c|}{15} &\n  3 &\n  \\multicolumn{1}{c|}{13} &\n  10 &\n  \\multicolumn{1}{c|}{6} &\n  4 &\n  12 \\\\ \\hline\n\\end{tabular}\n}\n\\end{table}\n\nLooking at Table \\ref{tab:local_bests_KNN}, we notice that TFS combined with KNN classifier produces higher Balanced Accuracy scores in $10$ out of $16$ datasets (i.e. $62.5\\%$ of cases), while $\\textrm{Inf-FS}_U$ combined with the same classifier has higher Balanced Accuracy scores in $6$ out of $16$ datasets (i.e. $37.5\\%$ of cases). Considering only the scenarios where TFS is the winning feature selection schema, we notice that in $1$ case, the optimal cardinality is equal to $10$, $150$ and $200$, in $5$ cases, the optimal cardinality is equal to $50$, in two cases the optimal cardinality is equal to $100$. When the $\\textrm{Inf-FS}_U$ is used as feature selection algorithm and KNN as classifier, the cross-datasets average Balanced Accuracy score grows from a value equal to $0.46$ at cardinality $10$ to a value of $0.69$ at cardinality $200$ with an increase of $23\\%$. When TFS is used as feature selection algorithm and KNN as classifier, the cross-datasets average Balanced Accuracy score grows from a value equal to $0.55$ at cardinality $10$ to a value of $0.71$ at cardinality $200$ with an increase of $16\\%$. Finally, we notice that when $\\textrm{Inf-FS}_U$ is used as feature selection algorithm and KNN as classifier, the average maximum drawdown ratio is equal to $23\\%$. Using TFS as feature selection algorithm, instead, the average maximum drawdown ratio is equal to $21\\%$.\n\n\\begin{table}[H]\n\\centering\n\\caption{Subset size-dependent, out-of-sample balanced accuracy scores using a Decision Tree classifier. For each dataset, we boldly highlight the combination between feature selection schema and classifier producing the best out-of-sample result. For each subset size, we report, in the last row, the number of times a feature selection approach outperforms the other across datasets.}\n\\label{tab:local_bests_Decision_Tree}\n\\scalebox{0.85}{\n\\begin{tabular}{c|cccccccccc}\n\\hline\n &\n  \\multicolumn{10}{c}{\\textbf{Decision Tree}} \\\\ \\hline\n &\n  \\multicolumn{2}{c|}{\\textbf{10}} &\n  \\multicolumn{2}{c|}{\\textbf{50}} &\n  \\multicolumn{2}{c|}{\\textbf{100}} &\n  \\multicolumn{2}{c|}{\\textbf{150}} &\n  \\multicolumn{2}{c}{\\textbf{200}} \\\\ \\cline{2-11} \n &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\multicolumn{1}{c|}{\\textbf{TFS}} &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\multicolumn{1}{c|}{\\textbf{TFS}} &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\multicolumn{1}{c|}{\\textbf{TFS}} &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\multicolumn{1}{c|}{\\textbf{TFS}} &\n  \\textbf{$\\textrm{Inf-FS}_U$} &\n  \\textbf{TFS} \\\\ \\hline\nPCMAC &\n  0.53 &\n  \\multicolumn{1}{c|}{0.50} &\n  0.56 &\n  \\multicolumn{1}{c|}{0.69} &\n  0.58 &\n  \\multicolumn{1}{c|}{0.71} &\n  0.57 &\n  \\multicolumn{1}{c|}{0.68} &\n  0.60 &\n  \\textbf{0.73} \\\\\nRELATHE &\n  0.49 &\n  \\multicolumn{1}{c|}{0.50} &\n  0.51 &\n  \\multicolumn{1}{c|}{\\textbf{0.51}} &\n  0.49 &\n  \\multicolumn{1}{c|}{0.42} &\n  0.48 &\n  \\multicolumn{1}{c|}{0.51} &\n  0.48 &\n  0.51 \\\\\nCOIL20 &\n  0.68 &\n  \\multicolumn{1}{c|}{0.81} &\n  0.83 &\n  \\multicolumn{1}{c|}{0.89} &\n  0.85 &\n  \\multicolumn{1}{c|}{\\textbf{0.90}} &\n  0.89 &\n  \\multicolumn{1}{c|}{0.90} &\n  0.90 &\n  0.90 \\\\\nORL &\n  0.36 &\n  \\multicolumn{1}{c|}{0.39} &\n  0.42 &\n  \\multicolumn{1}{c|}{0.48} &\n  0.49 &\n  \\multicolumn{1}{c|}{0.54} &\n  0.59 &\n  \\multicolumn{1}{c|}{0.61} &\n  0.49 &\n  \\textbf{0.62} \\\\\nwarpAR10P &\n  0.37 &\n  \\multicolumn{1}{c|}{0.33} &\n  0.46 &\n  \\multicolumn{1}{c|}{0.59} &\n  0.55 &\n  \\multicolumn{1}{c|}{0.59} &\n  0.41 &\n  \\multicolumn{1}{c|}{0.64} &\n  0.68 &\n  \\textbf{0.80} \\\\\nwarpPIE10P &\n  0.74 &\n  \\multicolumn{1}{c|}{0.74} &\n  0.80 &\n  \\multicolumn{1}{c|}{0.73} &\n  0.77 &\n  \\multicolumn{1}{c|}{0.85} &\n  0.76 &\n  \\multicolumn{1}{c|}{\\textbf{0.87}} &\n  0.76 &\n  0.81 \\\\\nYale &\n  0.17 &\n  \\multicolumn{1}{c|}{0.31} &\n  0.26 &\n  \\multicolumn{1}{c|}{0.34} &\n  0.39 &\n  \\multicolumn{1}{c|}{0.42} &\n  0.50 &\n  \\multicolumn{1}{c|}{0.43} &\n  0.43 &\n  \\textbf{0.52} \\\\\nUSPS &\n  0.73 &\n  \\multicolumn{1}{c|}{0.72} &\n  0.84 &\n  \\multicolumn{1}{c|}{0.85} &\n  0.85 &\n  \\multicolumn{1}{c|}{0.86} &\n  0.86 &\n  \\multicolumn{1}{c|}{0.86} &\n  \\textbf{0.88} &\n  0.87 \\\\\ncolon &\n  0.61 &\n  \\multicolumn{1}{c|}{0.64} &\n  0.82 &\n  \\multicolumn{1}{c|}{0.74} &\n  0.76 &\n  \\multicolumn{1}{c|}{\\textbf{0.92}} &\n  0.89 &\n  \\multicolumn{1}{c|}{0.83} &\n  0.85 &\n  0.83 \\\\\nGLIOMA &\n  0.34 &\n  \\multicolumn{1}{c|}{\\textbf{0.61}} &\n  0.36 &\n  \\multicolumn{1}{c|}{0.31} &\n  0.35 &\n  \\multicolumn{1}{c|}{0.44} &\n  0.38 &\n  \\multicolumn{1}{c|}{0.31} &\n  0.31 &\n  0.44 \\\\\nlung &\n  0.44 &\n  \\multicolumn{1}{c|}{0.70} &\n  0.75 &\n  \\multicolumn{1}{c|}{0.71} &\n  0.87 &\n  \\multicolumn{1}{c|}{0.70} &\n  \\textbf{0.90} &\n  \\multicolumn{1}{c|}{0.73} &\n  0.71 &\n  0.79 \\\\\nlung\\_small &\n  0.46 &\n  \\multicolumn{1}{c|}{0.42} &\n  0.58 &\n  \\multicolumn{1}{c|}{\\textbf{0.63}} &\n  0.47 &\n  \\multicolumn{1}{c|}{0.57} &\n  0.52 &\n  \\multicolumn{1}{c|}{0.63} &\n  0.52 &\n  0.49 \\\\\nlymphoma &\n  0.20 &\n  \\multicolumn{1}{c|}{\\textbf{0.69}} &\n  0.45 &\n  \\multicolumn{1}{c|}{0.55} &\n  0.45 &\n  \\multicolumn{1}{c|}{0.44} &\n  0.63 &\n  \\multicolumn{1}{c|}{0.60} &\n  0.51 &\n  0.62 \\\\\nGISETTE &\n  0.52 &\n  \\multicolumn{1}{c|}{0.50} &\n  0.44 &\n  \\multicolumn{1}{c|}{\\textbf{0.52}} &\n  0.48 &\n  \\multicolumn{1}{c|}{0.47} &\n  0.50 &\n  \\multicolumn{1}{c|}{0.49} &\n  0.49 &\n  0.48 \\\\\nIsolet &\n  0.27 &\n  \\multicolumn{1}{c|}{0.43} &\n  0.69 &\n  \\multicolumn{1}{c|}{0.67} &\n  0.73 &\n  \\multicolumn{1}{c|}{0.71} &\n  0.74 &\n  \\multicolumn{1}{c|}{0.73} &\n  \\textbf{0.78} &\n  0.73 \\\\\nMADELON &\n  0.58 &\n  \\multicolumn{1}{c|}{0.66} &\n  0.70 &\n  \\multicolumn{1}{c|}{\\textbf{0.81}} &\n  0.78 &\n  \\multicolumn{1}{c|}{0.79} &\n  0.75 &\n  \\multicolumn{1}{c|}{0.77} &\n  0.74 &\n  0.77 \\\\ \\hline\\hline\n  \\# bests &\n  6 &\n  \\multicolumn{1}{c|}{10} &\n  5 &\n  \\multicolumn{1}{c|}{11} &\n  5 &\n  \\multicolumn{1}{c|}{11} &\n  7 &\n  \\multicolumn{1}{c|}{9} &\n  5 &\n  11 \\\\ \\hline\n\\end{tabular}\n}\n\\end{table}\n\nLooking at Table \\ref{tab:local_bests_Decision_Tree}, we notice that TFS combined with Decision Tree classifier produces higher Balanced Accuracy scores in $13$ out of $16$ datasets (i.e. $81.25\\%$ of cases), while $\\textrm{Inf-FS}_U$ combined with the same classifier produces higher Balanced Accuracy scores in $3$ out of $16$ datasets (i.e. $18.75\\%$ of cases). Considering only the scenarios where TFS is the winning feature selection schema, we notice that in $2$ cases, the optimal cardinality is equal to $10$ and $100$, in $4$ cases, the optimal cardinality is equal to $50$ and $200$, in only one case the optimal cardinality is equal to $150$.  When the $\\textrm{Inf-FS}_U$ is used as feature selection algorithm and Decision Tree as classifier, the cross-datasets average Balanced Accuracy score grows from a value equal to $0.47$ at cardinality $10$, to a value of $0.63$ at cardinality $200$ with an increase of $16\\%$. When TFS is used as feature selection algorithm and Decision Tree as classifier, the cross-datasets average Balanced Accuracy score grows from a value equals to $0.56$ at cardinality $10$, to a value of $0.68$ at cardinality $200$ with an increase of $12\\%$. Finally, we notice that, when $\\textrm{Inf-FS}_U$ is used as feature selection algorithm and Decision Tree as classifier, the average maximum drawdown ratio is equal to $22\\%$. Using TFS as feature selection algorithm, instead, the average maximum drawdown ratio is equal to $20\\%$.\n\nConsidering the cross-datasets average Balanced Accuracy scores discussed earlier in this Section, we conclude that, independently from the chosen classifier, TFS always allows to select more informative features, guaranteeing higher classification performances. Both the  cross-datasets average Balanced Accuracy score percentage increase and the cross-datasets average maximum drawdown ratio are lower when TFS is chosen as feature selection schema, further certifying an higher stability and an ability to choose higher quality features.\n\n\\begin{table}[h]\n\\centering\n\\caption{Out-of-sample Balanced Accuracy scores obtained by LinearSVM, KNN and Decision Tree classifier on the raw datasets (i.e. the datasets containing all the original features). We boldly highlight the entries where a TFS improves the classifier's performance. We do not highlight the entries where a classifier performs better on the raw dataset (i.e. where feature selection algorithms $\\textrm{Inf-FS}_U$ and TFS are not effective). The $^*$ symbol highlights the scenarios where the optimal feature selection schema is $\\textrm{Inf-FS}_U$ but TFS, in combination with the classifier, still outperforms the classifier on the raw dataset. The $^\\dagger$ symbol highlights the scenarios where the optimal feature selection schema is $\\textrm{Inf-FS}_U$ while TFS, in combination with the classifier, cannot outperform the classifier on the raw dataset.}\n\\label{tab:Full_dataset_results}\n\\scalebox{0.85}{%\n\\begin{tabular}{c|c|c|c}\n\\hline\n            & \\textbf{LinearSVM} & \\textbf{KNN}  & \\textbf{Decision Tree}   \\\\ \\hline\nPCMAC       & 0.83     & 0.71 & 0.90  \\\\\nRELATHE     & 0.84     & 0.77 & 0.85 \\\\\nCOIL20      & 0.97      & \\;0.96$^\\dagger$          & \\textbf{0.87}          \\\\\nORL         & 0.97      & 0.82 & 0.68 \\\\\nwarpAR10P   & 1.00      & 0.53 & \\textbf{0.66}          \\\\\nwarpPIE10P  & \\textbf{1.00}               & \\textbf{0.84}          & \\textbf{0.84}          \\\\\nYale        & 0.82               & \\textbf{0.46}          & \\textbf{0.44}          \\\\\nUSPS        & \\textbf{0.93}               & \\;0.95$^*$          & \\;0.87$^*$          \\\\\ncolon       & \\;0.80$^*$               & \\;0.73$^*$          & \\textbf{0.80}           \\\\\nGLIOMA      & \\;0.56$^\\dagger$               & 0.78 & \\textbf{0.44}          \\\\\nlung        & \\textbf{0.93}               & \\textbf{0.76}          & \\;0.66$^*$          \\\\\nlung\\_small & \\textbf{0.79}               & \\;0.76$^*$          & \\textbf{0.63}          \\\\\nlymphoma    & \\textbf{0.93}               & \\;0.69$^*$          & \\textbf{0.61}          \\\\\nGISETTE     & 0.98     & 0.96 & 0.92 \\\\\nIsolet      & 0.93     & 0.84 & 0.79 \\\\\nMADELON     & \\textbf{0.58}               & \\textbf{0.51}          & \\textbf{0.74}          \\\\ \\hline\n\\end{tabular}%\n}\n\\end{table}\n\nThe power of TFS can be further investigated by comparing results obtained by applying the three classification algorithms on the raw datasets (i.e. the datasets containing all the original features) against the best ones obtained by applying the same classifiers combined with the novel feature classification technique presented in this paper. Results are reported in Table \\ref{tab:Full_dataset_results}. When LinearSVM is chosen as a classifier, feature selection turns out to be beneficial on $9$ out of $16$ datasets (i.e. $56.25\\%$ of cases). In $7$ cases, TFS is the optimal feature classification approach; in the case of the \"colon\" dataset, even if $\\textrm{Inf-FS}_U$ is the optimal feature selection approach, results achieved using TFS are still better than the ones obtained on the raw dataset; in the case of \"GLIOMA\" dataset, $\\textrm{Inf-FS}_U$ is the optimal feature selection approach and results achieved using TFS are lower than the ones obtained on the raw dataset. When KNN is chosen as a classifier, feature selection is beneficial on $9$ out of $16$ datasets (i.e. $56.25\\%$ of cases). In $4$ cases, TFS is the optimal feature classification approach; in the case of \"USPS\", \"colon\", \"lung\\_small\" and \"lymphoma\" dataset, even if $\\textrm{Inf-FS}_U$ is the optimal feature selection approach, results achieved using TFS are still better than the ones obtained on the raw dataset; in the case of \"COIL20\" dataset, $\\textrm{Inf-FS}_U$ is the optimal feature selection approach and results achieved using TFS are lower than the ones obtained on the raw dataset. Finally, when Decision Tree is chosen as a classifier, feature selection is beneficial on $11$ out of $16$ datasets (i.e. $68.75\\%$ of cases). In $9$ cases, TFS is the optimal feature classification approach; in the case of \"USPS\" and \"colon\" dataset, even if $\\textrm{Inf-FS}_U$ is the optimal feature selection approach, results achieved using TFS are still better than the ones obtained on the raw dataset. \\\\\nLooking at the results reported above, we notice that the application domains where TFS is more compelling are the ones where the tabular format is the natural data format (i.e. biological data and artificial data). This finding is not unexpected. Application domains such as text, face images and spoken letters data would require a more complex data pre-processing pipeline (e.g. encoding) and specific deep learning-based classification algorithms (e.g. convolutional and recurrent neural networks). A deeper analysis of this aspect is left for the upcoming TFS-centered research.\n\n\\begin{table}[H]\n\\centering\n\\caption{Comparison between $\\textrm{Inf-FS}_U$' and TFS' \\textit{p}-values obtained performing a $15 \\times 2$ cv paired \\textit{t}-test. \\textit{p}-values $> 0.1$ are reported in their numerical form, \\textit{p}-values $\\leq 0.1$ and $> 0.05$ are marked as $^{*}$, \\textit{p}-values $\\leq 0.05$ and $> 0.01$ are marked as $^{**}$, \\textit{p}-values $\\leq 0.01$ and $> 0.001$ are marked as $^{***}$ and \\textit{p}-values $\\leq 0.001$ are marked as $^{****}$. $(\\vee)$ and $(\\wedge)$ symbols indicate that, when the two feature selection schemes combined with the same classifier, produce statistically robust different results, TFS performs, respectively, better or worse than $\\textrm{Inf-FS}_U$ according to results reported in Tables \\ref{tab:local_bests_LinearSVM}, \\ref{tab:local_bests_KNN} and \\ref{tab:local_bests_Decision_Tree}.}\n\\label{tab:StatTests}\n\\resizebox{\\columnwidth}{!}{%\n\\begin{tabular}{c|ccccc|ccccc|ccccc}\n\\hline\n            & \\multicolumn{5}{c|}{\\textbf{LinearSVM}} & \\multicolumn{5}{c|}{\\textbf{KNN}} & \\multicolumn{5}{c}{\\textbf{DT}}  \\\\ \\cline{2-16} \n &\n  \\textbf{10} &\n  \\textbf{50} &\n  \\textbf{100} &\n  \\textbf{150} &\n  \\textbf{200} &\n  \\textbf{10} &\n  \\textbf{50} &\n  \\textbf{100} &\n  \\textbf{150} &\n  \\textbf{200} &\n  \\textbf{10} &\n  \\textbf{50} &\n  \\textbf{100} &\n  \\textbf{150} &\n  \\textbf{200} \\\\ \\hline\nPCMAC       & *$^{(\\wedge)}$ & 0.50   & 0.79  & 0.80  & 0.49  & 0.19  & 0.37 & 0.90 & 0.81 & 0.94 & *$^{(\\wedge)}$   & 0.69 & 0.93 & 0.75 & 0.73 \\\\\nRELATHE     & 0.87   & **$^{(\\vee)}$     & ****$^{(\\vee)}$  & ***$^{(\\vee)}$   & **$^{(\\vee)}$ & 0.61  & 0.17 & ****$^{(\\vee)}$ & *$^{(\\wedge)}$ & 0.14 & 0.90 & ***$^{(\\vee)}$ & 0.58 & *$^{(\\vee)}$ & 0.47 \\\\\nCOIL20      & ***$^{(\\vee)}$    & ****$^{(\\vee)}$   & ****$^{(\\vee)}$  & ***$^{(\\vee)}$   & **$^{(\\vee)}$    & **$^{(\\vee)}$    & **$^{(\\vee)}$   & **$^{(\\vee)}$   & 0.39 & 0.40 & *$^{(\\vee)}$    & **$^{(\\vee)}$   & ***$^{(\\vee)}$  & ***$^{(\\vee)}$  & **$^{(\\vee)}$   \\\\\nORL         & 0.14   & ***$^{(\\vee)}$    & 0.22  & **$^{(\\vee)}$    & ***$^{(\\vee)}$   & **$^{(\\vee)}$    & ***$^{(\\vee)}$  & 0.72 & 0.44 & 0.51 & 0.88 & 0.49 & 0.67 & **$^{(\\vee)}$   & 0.93 \\\\\nwarpAR10P   & 0.23   & ***$^{(\\vee)}$    & 0.38  & 0.23  & 0.20  & **$^{(\\wedge)}$    & **$^{(\\vee)}$   & **$^{(\\vee)}$   & 0.48 & 0.69 & 0.77 & ***$^{(\\vee)}$  & 0.32 & 0.16 & 0.39 \\\\\nwarpPIE10P  & 0.98   & 0.52   & 0.67  & 0.39  & 1.00  & 0.50  & 0.93 & 0.17 & 1.00 & 0.51 & 0.41 & 1.00 & 0.65 & 0.39 & 0.68 \\\\\nYale        & ***$^{(\\vee)}$    & **$^{(\\vee)}$     & 0.17  & 0.19  & 0.64  & 0.81  & **$^{(\\vee)}$   & 0.28 & 0.78 & 0.10 & 0.60 & **$^{(\\vee)}$   & 0.90 & 0.45 & 0.23 \\\\\nUSPS        & 0.89   & 0.38   & 0.29  & ***$^{(\\vee)}$   & *$^{(\\vee)}$     & 0.69  & 0.19 & ***$^{(\\wedge)}$  & *$^{(\\wedge)}$    & 0.26 & *$^{(\\wedge)}$    & 0.74 & 0.71 & 0.62 & 0.95 \\\\\ncolon       & 0.15   & 0.42   & 0.19  & 0.37  & 0.53  & 0.92  & 0.48 & 0.63 & 1.00 & 0.18 & 0.89 & 0.35 & 0.15 & 0.59 & 0.50 \\\\\nGLIOMA      & 0.54   & 0.63   & 0.45  & *$^{(\\wedge)}$     & 0.74  & 0.68  & 0.73 & 0.25 & 0.65 & 0.91 & **$^{(\\vee)}$   & 0.52 & *$^{(\\vee)}$    & *$^{(\\wedge)}$    & *$^{(\\vee)}$    \\\\\nlung        & ***$^{(\\vee)}$    & 0.12   & ***$^{(\\vee)}$   & **$^{(\\vee)}$    & 0.19  & ***$^{(\\vee)}$   & 0.46 & 0.61 & 0.84 & 0.58 & ***$^{(\\vee)}$  & 0.11 & 0.28 & 0.47 & 0.86 \\\\\nlung\\_small & 0.72   & 0.83   & **$^{(\\wedge)}$    & 0.54  & 0.32  & 0.38  & 0.77 & 0.32 & 0.82 & 0.72 & 0.73 & 0.99 & 0.53 & *$^{(\\vee)}$    & 0.63 \\\\\nlymphoma    & 0.56   & 0.26   & 0.37  & 0.74  & 0.92  & 1.00  & 0.69 & 0.41 & 0.25 & 0.86 & 0.35 & 0.58 & 0.32 & 0.45 & 0.85 \\\\\nGISETTE     & ****$^{(\\wedge)}$   & ***$^{(\\wedge)}$    & ***$^{(\\vee)}$   & ***$^{(\\vee)}$   & **$^{(\\vee)}$    & ****$^{(\\vee)}$  & ****$^{(\\vee)}$ & ****$^{(\\vee)}$ & ****$^{(\\vee)}$ & ****$^{(\\wedge)}$ & ****$^{(\\wedge)}$ & ***$^{(\\vee)}$  & ***$^{(\\wedge)}$  & **$^{(\\wedge)}$   & *$^{(\\vee)}$    \\\\\nIsolet      & ****$^{(\\vee)}$   & ***$^{(\\vee)}$    & 0.15  & 0.15  & **$^{(\\vee)}$    & ****$^{(\\vee)}$  & 1.00 & 0.28 & 0.38 & 0.88 & **$^{(\\vee)}$   & 0.81 & 0.61 & *$^{(\\wedge)}$    & 0.39 \\\\\nMADELON     & *$^{(\\vee)}$      & 0.75   & 0.93  & 0.19  & 0.15  & 0.91  & 0.69 & 0.22 & 0.65 & 0.49 & 0.32 & 0.65 & 0.57 & 0.69 & 0.59 \\\\ \\hline\n\\end{tabular}%\n}\n\\end{table}\n\nThe statistical significance of results discussed earlier in this Section is assessed in Table \\ref{tab:StatTests}. Here we report the \\textit{p}-values obtained performing a $15 \\times 2$cv \\textit{t}-test as described in Section \\ref{sec:Experiments}. Specifically, \\textit{p}-values $> 0.1$ are reported in their numerical form, \\textit{p}-values $\\leq 0.1$ and $> 0.05$ are marked as $^{*}$, \\textit{p}-values $\\leq 0.05$ and $> 0.01$ are marked as $^{**}$, \\textit{p}-values $\\leq 0.01$ and $> 0.001$ are marked as $^{***}$ and \\textit{p}-values $\\leq 0.001$ are marked as $^{****}$. Looking at the entries of Tables \\ref{tab:local_bests_LinearSVM}, \\ref{tab:local_bests_KNN}, \\ref{tab:local_bests_Decision_Tree} where TFS defines a new state-of-the-art, we notice that (i) when LinearSVM is used as classifier, TFS is statistically different from $\\textrm{Inf-FS}_U$ in $8$ out of $14$ cases ($57\\%$); (ii) when KNN is used as classifier, TFS is statistically different from $\\textrm{Inf-FS}_U$ in $3$ out of $10$ cases ($30\\%$); (iii) when Decision Tree is used as classifier, TFS is statistically different from $\\textrm{Inf-FS}_U$ in $4$ out of $13$ cases ($31\\%$). There is only one dataset (i.e. 'GISETTE') where TFS is statistically different from $\\textrm{Inf-FS}_U$ independently from the classifier: in all the other cases, results are dependent on the choice of the classifier.\n\n\\section{Conclusions} \\label{sec:Conclusions}\nIn this work, we combine the power of state-of-the-art IFNs, and instruments from network science in order to develop a novel unsupervised, graph-based filter method for feature selection. Features are represented as nodes in a TMFG, and their relevance is assessed by studying their relative position inside the network. Exploiting topological properties of the network used to represent meaningful interactions among features, we propose a physics-informed feature selection model that is highly flexible, computationally cheap, fully explainable and remarkably intuitive. To prove the effectiveness of the proposed methodology, we test it against the state-of-the-art counterpart (i.e. $\\textrm{Inf-FS}_U$) on $16$ benchmark datasets belonging to different applicative domains. Employing a Linear Support Vector classifier, a k-Nearest Neighbors classifier and a Decision Tree classifier, we show how our algorithm achieves top performances on most benchmark datasets, redefining the current state-of-the-art on a significant number of them. The proposed methodology demonstrates effectiveness in conditions where the amount of training data largely varies. Compared to its main alternative, TFS has a lower computational complexity and provides a much more intuitive overview of the feature selection process. Thanks to the possibility of studying the relative position of nodes in the network in many different ways (i.e. choosing different centrality measures or defining new ones), TFS is highly versatile and fully adaptable to input data. This research work is also relevant since it underlines some criticalities in the way that the effectiveness of the feature selection methods is evaluated and proposes a rigorous pipeline to compare models and assess the statistical significance of achieved results. It is worth noting that the current work is a foundational one. It presents three aspects that are unsatisfactory and we plan to cover in the future: (i) the need to explicitly specify the cardinality of the subset of relevant features is limiting and requires an a priori knowledge of the applicative domain or, at least, an extended search for the optimal realization of this hyper-parameter; (ii) the usage of classic correlation measures in the TMFG's building process prevents from the possibility to handle problems with mixed type of features (continuous-categorical, categorical-categorical); (iii) TMFG is non-differentiable and this prevents from a direct integration with advanced Deep Learning-based architectures. More generally, this study points to many future directions spanning from the development of data-centred measures to assess features relevance, to the possibility of replicating the potential of this method and inferring them through automated learning techniques. The first steps have been taken in the latter research direction by introducing a new and potentially groundbreaking type of neural networks called Homological Neural Networks. \n\n\\section*{Acknowledgments} \\label{sec:Aknowledgments}\nThe author, T.A, acknowledges the financial support from ESRC (ES\/K002309\/1), EPSRC (EP\/P031730\/1) and EC (H2020-ICT-2018-2 825215). Both the authors acknowledge Agne Scalchi, Silvia Bartolucci and Paolo Barucca for for the fruitful discussions on foundational topics related to this work.\n\n\\bibliographystyle{unsrt}  \n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
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+{"text":"\\section{Introduction}\n\nThe study of electronic transport in quantum confined model systems like \nquantum rings, quantum dots, arrays of quantum dots, quantum dots embedded \nin a quantum ring, etc., has become one of the most fascinating branch of\nnanoscience and technology. With the aid of present nanotechnological\nprogress~\\cite{nanofab1,nanofab2}, these simple looking quantum confined \nsystems can be used to design nanodevices especially in electronic as \nwell as spintronic engineering. The key idea of \nmanufacturing nanodevices is based on the concept of quantum \ninterference effect~\\cite{imry1,imry2,gefen1}, and it is generally \npreserved throughout the sample having dimension smaller or comparable \nto the phase coherence length. Therefore, ring type conductors or two \npath devices are ideal candidates to exploit the effect of quantum \ninterference~\\cite{bohm}. In a ring shaped geometry, quantum \ninterference effect can be controlled by several ways, and most \nprobably, the effect can be regulated significantly by tuning the \nmagnetic flux, the so-called Aharonov-Bohm (AB) flux~\\cite{chang,\nhan,he,wel}, that threads the ring. This key feature motivates us to \nwidely use quantum interference devices in mesoscopic solid-state \nelectronic circuits~\\cite{roh}. Using a mesoscopic ring we can \nconstruct a quantum interferometer, and here we will show that the \ninterferometer \nexhibits several exotic features of electron transport which can be \nutilized in designing nanoelectronic circuits. To reveal the phenomena, \nwe make a bridge system, by inserting the interferometer between two \nelectrodes (source and drain), the so-called source-interferometer-drain \nbridge. Following the pioneering work of Aviram and Ratner~\\cite{aviram},\ntheoretical description of electron transport in a bridge system has got \nmuch progress. Later, many excellent experiments~\\cite{holl,\nkob,kob1,ji,yac,reed1,reed2} have been done in several bridge systems \nto understand the basic mechanisms underlying the electron transport. \nThough extensive studies on electron transport have already been done \nboth theoretically~\\cite{chang,han,he,wel,orella1,orella2,nitzan1,\nnitzan2,bai,muj1,muj2,cui,baer2,baer3,tagami,walc1,baer1,maiti1,\nmaiti2,maiti3,walc2,gefen,kubo,naka,aharony,konig,ern2} as well as \nexperimentally~\\cite{holl,kob,kob1,ji,yac,reed1,reed2}, yet lot of \ncontroversies are still present between the theory and experiment, and \nthe complete description of the conduction mechanism in this scale is \nnot very well defined even today. Several controlling \nfactors are there which can significantly regulate electron transport in \na conducting bridge, and all these factors have to be taken into account \nproperly to understand the transport mechanism. For our illustrative \npurposes, here we mention some of these issues.\n\\begin{enumerate}\n\\item The quantum interference effect~\\cite{baer2,baer3,tagami,walc1,\nbaer1,maiti1,maiti2} of electronic waves passing through different \narms of the bridging material becomes the most significant issue. \n\\item The coupling of the bridging material to the electrodes significantly\ncontrols the current amplitude across any bridge system~\\cite{baer1}. \n\\item Dynamical fluctuation in small-scale devices is another important \nfactor which plays an active role and can be manifested through the \nmeasurement of {\\em shot noise}~\\cite{walc2}, a direct consequence of \nthe quantization of charge.\n\\item Geometry of the conducting material between the two electrodes\nitself is an important issue to control electron transmission which\nhas been described quite elaborately by Ernzerhof \n{\\em et al.}~\\cite{ern2} through some model calculations. \n\\end{enumerate}\n\nAddition to these, several other factors of the tight-binding \nHamiltonian that describe a system also provide important effects in \nthe determination of current across a bridge system.\n\nIn this presentation we explore electron transport properties of a \nquantum interferometer based on the single particle Green's function \nformalism. The interferometer is sandwiched between two semi-infinite\none-dimensional ($1$D) metallic electrodes, viz, source and drain, and, \ntwo sub-rings of the interferometer are subject to the Aharonov-Bohm (AB) \nfluxes $\\phi_1$ and $\\phi_2$, respectively. The schematic view of the\nbridge system is depicted in Fig.~\\ref{ring}. A simple tight-binding model \nis used to describe the system and all the calculations are done \nnumerically, which illustrate conductance-energy and current-voltage \ncharacteristics as functions of the interferometer-to-electrode coupling \nstrength, magnetic fluxes and the difference of these two fluxes. \nSeveral exotic features are observed from this study. These are: (i) \nsemiconducting or metallic nature depending on the coupling strength of \nthe interferometer to the side attached electrodes, (ii) appearance of \nanti-resonant states~\\cite{chang,han,he} and (iii) unconventional \nperiodic behavior of typical conductance\/current as a function of \nthe difference of two AB fluxes.\n\nThe scheme of the paper is as follows. Following the introduction (Section \n$1$), in Section $2$, we describe the model and theoretical formulation \nfor the calculation. Section $3$ explores the results, and finally, we \nconclude our study in Section $4$.\n\n\\section{Model and synopsis of the theoretical background}\n\nLet us begin with the model presented in Fig.~\\ref{ring}. A quantum\ninterferometer with four atomic sites ($N=4$, where $N$ gives the total\nnumber of atomic sites in the interferometer) is attached symmetrically \nto two semi-infinite one-dimensional ($1$D) metallic electrodes, namely,\nsource and drain. The atomic sites $2$ and $3$ of the interferometer are \ndirectly coupled to each other, and accordingly, two sub-rings, left and \nright, are formed. These two sub-rings are subject to the AB fluxes \n$\\phi_1$ and $\\phi_2$, respectively.\n\nConsidering linear transport regime, conductance $g$ of the interferometer \ncan be obtained using the Landauer conductance formula~\\cite{land1,land2,\nland3,datta,marc},\n\\begin{equation}\ng=\\frac{2e^2}{h} T\n\\label{equ1}\n\\end{equation}\nwhere, $T$ becomes the transmission probability of an electron across \nthe interferometer. It $(T)$ can be expressed in terms of the Green's \nfunction of the interferometer and its coupling to the side-attached \nelectrodes by the relation~\\cite{datta,marc},\n\\begin{equation}\nT={\\mbox{Tr}}\\left[\\Gamma_S G_{I}^r \\Gamma_D G_{I}^a\\right]\n\\label{equ2}\n\\end{equation}\nwhere, $G_{I}^r$ and $G_{I}^a$ are respectively the retarded and advanced \nGreen's functions of the interferometer including the effects of the \nelectrodes. Here $\\Gamma_S$ and $\\Gamma_D$ describe the coupling of the \n\\begin{figure}[ht]\n{\\centering \\resizebox*{6.5cm}{3.5cm}{\\includegraphics{ring.eps}}\\par}\n\\caption{(Color online). Schematic view of a quantum interferometer\nwith four atomic sites ($N=4$) attached to two semi-infinite \none-dimensional metallic electrodes.}\n\\label{ring}\n\\end{figure}\ninterferometer to the source and drain, respectively. For the complete \nsystem i.e., the interferometer, source and drain, Green's function \nis defined as,\n\\begin{equation}\nG=\\left(E-H\\right)^{-1}\n\\label{equ3}\n\\end{equation}\nwhere, $E$ is the injecting energy of the source electron. To Evaluate\nthis Green's function, inversion of an infinite matrix is needed since\nthe complete system consists of the finite size interferometer and \ntwo semi-infinite electrodes. However, the entire system can be \npartitioned into sub-matrices corresponding to the individual sub-systems \nand the Green's function for the interferometer can be effectively \nwritten as,\n\\begin{equation}\nG_{I}=\\left(E-H_{I}-\\Sigma_S-\\Sigma_D\\right)^{-1}\n\\label{equ4}\n\\end{equation}\nwhere, $H_{I}$ is the Hamiltonian of the interferometer that can be \nexpressed within the non-interacting picture like,\n\\begin{equation}\nH_{I} = \\sum_i \\epsilon_i c_i^{\\dagger} c_i + \\sum_{<ij>} t_{ij} \n\\left(c_i^{\\dagger} c_j e^{i\\theta_{ij}}+ c_j^{\\dagger} c_i \ne^{-i\\theta_{ij}}\\right)\n\\label{equ5}\n\\end{equation}\nIn this Hamiltonian $\\epsilon_i$ gives the on-site energy for the atomic \nsite $i$, where $i$ runs from $1$ to $4$, $c_i^{\\dagger}$ ($c_i$) is the \ncreation (annihilation) operator of an electron at the site $i$ and \n$t_{ij}$ is the hopping integral between the nearest-neighbor sites \n$i$ and $j$. For the sake of simplicity, we assume that the magnitudes of\nall hopping integrals ($t_{ij}$) are identical to $t$. The phase factor \n$\\theta_{ij}$, associated with the hopping integral $t_{ij}$, comes due to \nthe fluxes $\\phi_1$ and $\\phi_2$ in the two sub-rings. The phase factors \n($\\theta_{ij}$) are chosen as, $\\theta_{12}=\\theta_{23} =\\theta_{34}=\n\\theta_{41}=2\\pi\\phi\/4\\phi_0$, $\\theta_{24}=2\\pi \\Delta \\phi\/2 \\phi_0$, \nwhere $\\phi=\\phi_1+\\phi_2$, $\\Delta \\phi=\\phi_1-\\phi_2$ and $\\phi_0=ch\/e$ \nis the elementary flux-quantum. Accordingly, a minus sign is used for \nthe phases when the electron hops in the reverse direction. For the two \n$1$D electrodes, a similar kind of tight-binding Hamiltonian is also used, \nexcept any phase factor, where the Hamiltonian is parametrized by constant \non-site potential $\\epsilon_0$ and nearest-neighbor hopping integral $t_0$. \nThe hopping integral between the source and interferometer is $\\tau_S$, \nwhile it is $\\tau_D$ between the interferometer and drain. The parameters \n$\\Sigma_S$ and $\\Sigma_D$ in Eq.~(\\ref{equ4}) represent the self-energies \ndue to the coupling of the interferometer to the source and drain, \nrespectively, where all the information of this coupling are included into \nthese self-energies~\\cite{datta}.\n\nThe current passing through the interferometer is depicted as a \nsingle-electron scattering process between the two reservoirs of charge \ncarriers. The current $I$ can be computed as a function of the applied \nbias voltage $V$ by the expression~\\cite{datta},\n\\begin{equation}\nI(V)=\\frac{e}{\\pi \\hbar}\\int \\limits_{E_F-eV\/2}^{E_F+eV\/2} T(E)~ dE\n\\label{equ8}\n\\end{equation}\nwhere $E_F$ is the equilibrium Fermi energy. Here we assume that the \nentire voltage is dropped across the interferometer-electrode interfaces, \nand it is examined that under such an assumption the $I$-$V$ characteristics \ndo not change their qualitative features. \n\nAll the results in this communication are determined at absolute zero \ntemperature, but they should valid even for some finite (low) temperatures, \nsince the broadening of the energy levels of the interferometer due to \nits coupling to the electrodes becomes much larger than that of the thermal \nbroadening~\\cite{datta}. On the other hand, at high temperature limit, all \nthese phenomena completely disappear. This is due to the fact that the \nphase coherence length decreases significantly with the rise of temperature \nwhere the contribution comes mainly from the scattering on phonons, and \naccordingly, the quantum interference effect vanishes. Our unit system\nis simplified by choosing $c=e=h=1$. \n\n\\section{Numerical results and discussion}\n\nBefore going into the discussion, let us first assign the values of\ndifferent parameters those are used for our numerical calculation. The \non-site energy $\\epsilon_i$ of the interferometer is taken as $0$ for \nall the four sites $i$, and the nearest-neighbor hopping strength $t$ \nis set to $3$. On the other hand, for two side attached $1$D electrodes \nthe on-site energy ($\\epsilon_0$) and nearest-neighbor hopping strength \n($t_0$) are fixed to $0$ and $4$, respectively. The equilibrium Fermi \nenergy $E_F$ is set to $0$. \n\nThroughout the analysis we present the basic features of electron\ntransport for two distinct regimes of electrode-to-interferometer \ncoupling.\n\n\\noindent\n\\underline{Case 1:} Weak-coupling limit\n\\vskip 0.1cm\n\\noindent\nThis limit is set by the criterion $\\tau_{S(D)} << t$. In this case,\nwe choose the values as $\\tau_S=\\tau_D=0.5$.\n\n\\noindent\n\\underline{Case 2:} Strong-coupling limit\n\\vskip 0.1cm\n\\noindent\nThis limit is described by the condition $\\tau_{S(D)} \\sim t$. In this\nregime we choose the values of hopping strengths as $\\tau_S=\\tau_D=2.5$.\n\n\\subsection{Interferometric geometry with $4$ atomic ($N=4$) sites}\n\n\\subsubsection{Conductance-energy characteristics}\n\nIn Fig.~\\ref{cond}, we plot conductance $g$ as a function of the \ninjecting electron energy $E$ for the interferometer considering $\\phi=1$, \nwhere (a), (b), (c) and (d) correspond to $\\Delta \\phi=0.2$, $0.4$, $0.6$ \n\\begin{figure}[ht]\n{\\centering \\resizebox*{8cm}{12cm}{\\includegraphics{cond.eps}}\\par}\n\\caption{(Color online). $g$-$E$ curves in the weak- (black) and\nstrong-coupling (red) limits for the interferometer with four\natomic sites ($N=4$) considering $\\phi=1$. (a) $\\Delta \\phi=0.2$, \n(b) $\\Delta \\phi=0.4$, (c) $\\Delta \\phi=0.6$ and (d) $\\Delta \\phi=0.8$.}\n\\label{cond}\n\\end{figure}\nand $0.8$, respectively. The black curves represent the results for the \nweak-coupling limit, while the results for the strong-coupling limit are \nshown by the red curves. In the limit of weak-coupling, conductance shows \nfine resonant peaks for some particular energies, while it ($g$) drops to\nzero almost for all other energies. At these resonances, conductance \nreaches the value $2$, and therefore, the transmission probability $T$ \nbecomes unity, since the relation $g=2T$ is satisfied from the Landauer \nconductance formula (see Eq.~(\\ref{equ1}) with $e=h=1$). The transmission \nprobability of getting an electron across the interferometer significantly \ndepends on the quantum interference of electronic waves passing \nthrough the different arms of the interferometer, and accordingly, the\nprobability amplitude becomes strengthened or weakened. Now all the\nresonant peaks in the conductance spectra are associated with the \nenergy eigenvalues of the interferometer, and thus it is emphasized \nthat the conductance spectrum reveals itself the electronic structure of \nthe interferometer. The situation becomes quite interesting as long as \nthe coupling strength of the interferometer to the electrodes is\nincreased from the weak regime to the strong one. In the strong-coupling\nlimit, all the resonances get substantial widths compared to the \nweak-coupling limit. The contribution for the broadening of the resonant \npeaks in this strong-coupling limit appears from the imaginary parts of \nthe self-energies $\\Sigma_S$ and $\\Sigma_D$, respectively~\\cite{datta}. \nHence, by tuning the coupling strength from the weak to strong regime,\nelectronic transmission across the interferometer can be obtained for\nthe wider range of energies, while a fine scan in the energy scale is\nneeded to get the electron conduction across the bridge in the limit\nof weak-coupling. These results provide an important signature in the \nstudy of current-voltage ($I$-$V$) characteristics. Another interesting\nfeature observed from the conductance spectra is the existence of the\nanti-resonant states. The positions of the anti-resonance states can be\nclearly noticed from the red curves, compared to the black curves since\nthe widths of these curves are too small, where they sharply drop to zero \nfor the respective energy values associated with the different values of \n$\\Delta \\phi$ (see Figs.~\\ref{cond}(a)-(d)). Such anti-resonant states \nare specific to the interferometric nature of the scattering and do not \noccur in conventional one-dimensional scattering problems of potential \nbarriers~\\cite{chang,han,he}. A clear investigation shows that the \npositions of the anti-resonances on the energy scale are independent \nof the interferometer-to-electrode coupling strength. Since the width \nof these anti-resonance states are too small, they do not provide any \nsignificant contribution in the current-voltage ($I$-$V$) characteristics. \n\n\\subsubsection{Typical conductance $g_{typ}$ as a function of \n$\\Delta \\phi$}\n\nThe effect of $\\Delta \\phi$, the difference between two AB fluxes $\\phi_1$\n\\begin{figure}[ht]\n{\\centering \\resizebox*{8cm}{11cm}{\\includegraphics{cond1.eps}}\\par}\n\\caption{(Color online). $g_{typ}$-$\\Delta \\phi$ curves in the\nstrong-coupling limit for the interferometer with four atomic sites\n($N=4$), where (a) $\\phi=0.2$, (b) $\\phi=0.4$, (c) $\\phi=0.6$ and \n(d) $\\phi=0.8$. The typical conductances are calculated at the energy \n$E=5$.}\n\\label{cond1}\n\\end{figure}\nand $\\phi_2$, on the electron transport through the interferometer is\nalso an important issue in the present context. To visualize it, in\nFig.~\\ref{cond1}, we display the variation of the typical conductance\n($g_{typ}$) as a function of $\\Delta \\phi$ for the interferometer in\nthe limit of strong-coupling. Figures~\\ref{cond1}(a), (b), (c) and (d) \ncorrespond to the results for $\\phi=0.2$, $0.4$, $0.6$ and $0.8$, \nrespectively. The typical conductances are calculated for the fixed\nenergy $E=5$. Very interestingly we observe that, for a fixed value of\n$\\phi$, typical conductance varies periodically with $\\Delta \\phi$\nshowing $2\\phi_0$ ($=2$, since $\\phi_0=1$ in our chosen unit) \nflux-quantum periodicity, associated with the number of atomic sites ($2$) \nin the vertical line connecting two sub-rings of the quantum interferometer. \nThis period doubling behavior is completely different from the traditional \nperiodic nature, since in conventional geometries we get simple $\\phi_0$ \nflux-quantum periodicity. In the limit of weak-coupling we will also get \nthe similar behavior of periodicity ($2\\phi_0$) for the typical \nconductance with $\\Delta \\phi$, and due to the obvious reason we do not \nplot the results for this coupling limit once gain. \n\n\\subsubsection{Current-voltage characteristics}\n\nAll these features of electron transfer become much more clearly visible\nby studying the current-voltage ($I$-$V$) characteristics. The current \n$I$ passing through the interferometer is computed from the integration \nprocedure of the transmission function $T$ as prescribed in \nEq.~(\\ref{equ8}) which is not restricted in the linear response regime,\nbut it is of great significance in determining the shape of the full\ncurrent-voltage characteristics. As illustrative examples, in \nFig.~\\ref{current}, we plot the current-voltage characteristics of \nthe interferometer for the three different values of $\\phi_2$, keeping \nthe flux $\\phi_1$ in the left sub-ring to a fixed value $0.2$. The red, \nblue and black\ncurves correspond to $\\phi_2=0$, $0.1$ and $0.4$, respectively. In the\nlimit of weak-coupling (see Fig.~\\ref{current}(a)), it is observed that\nthe current exhibits staircase-like structure with fine steps as a\nfunction of the applied bias voltage $V$. This is due to the existence of\nthe sharp resonant peaks in the conductance spectrum in this coupling\nlimit, since the current is computed by the integration method of the\ntransmission function $T$. With the increase of the bias voltage $V$,\nthe electrochemical potentials on the electrodes are shifted gradually,\nand finally cross one of the quantized energy levels of the interferometer.\nAccordingly, a current channel is opened up which provides a jump in the \n\\begin{figure}[ht]\n{\\centering \\resizebox*{8cm}{10cm}{\\includegraphics{current.eps}}\\par}\n\\caption{(Color online). $I$-$V$ characteristics of the interferometer\nwith four atomic sites ($N=4$) for a fixed value of $\\phi_1=0.2$, where \nthe red, blue and black curves correspond to $\\phi_2=0$, $0.1$ and $0.4$,\nrespectively. (a) Weak-coupling limit and (b) strong-coupling limit.}\n\\label{current}\n\\end{figure}\n$I$-$V$ characteristic curve. The most important feature observed from \nthe $I$-$V$ curves for this weak-coupling limit is that, the non-zero\nvalue of the current appears beyond a finite bias voltage, the so-called\nthreshold voltage $V_{th}$. This is quite analogous to the \nsemiconducting nature of a material. Most interestingly, the results \npredict that the threshold bias voltage of electron conduction can be \ncontrolled very nicely by tuning the AB flux $\\phi_2$. The situation \nbecomes much different for the strong-coupling case. The results are \ngiven in Fig.~\\ref{current}(b). In this limit, the current varies almost \ncontinuously with the applied bias voltage and achieves much larger \namplitude than the weak-coupling case. The reason is that, in the limit \nof strong-coupling all the energy levels get broadened which provide \nlarger current in the integration procedure of the transmission function \n$T$. Thus by tuning the strength of the interferometer-to-electrode \ncoupling, we can achieve very large, even an order of magnitude, current \namplitude from the very low one for the same bias voltage $V$, which\nprovides an important signature in designing nanoelectronic devices.\nIn contrary to the weak-coupling limit, here the electron starts to\nconduct as long as the bias voltage is given i.e., $V_{th}\\rightarrow 0$,\nwhich reveals the metallic nature. Thus it can be emphasized that the\ninterferometer-to-electrode coupling is a key parameter which controls \nthe electron transport in a meaningful way. Additionally, the existence \nof the semiconducting or the metallic behavior of the interferometer \nalso significantly depends on the AB fluxes $\\phi_1$ and $\\phi_2$. The \nnature of all these $I$-$V$ curves, presented in Fig.~\\ref{current}, will \nbe exactly similar if we plot the results for the different values of \n$\\phi_1$, keeping $\\phi_2$ as a constant. \n\n\\subsubsection{Typical current amplitude $I_{typ}$ as a function of\n$\\phi_2$}\n\nNow, we draw our attention on the variation of the typical current\namplitude with anyone of these two fluxes, when the other one is fixed. \nTo explore it, in Fig.~\\ref{typcurr}, we show the variation of the typical \ncurrent amplitude ($I_{typ}$) with $\\phi_2$, considering $\\phi_1$ as a \nconstant, where (a) and (b) correspond to $\\phi_1=0$ and $0.3$, respectively. \nThe black and red lines represent the results for the weak- and \nstrong-coupling limits, respectively. The typical current amplitudes are\ncalculated for the fixed bias voltage $V=1.02$. Both for these two limiting \ncases, the typical current amplitude varies periodically with $\\phi_2$, \nexhibiting $\\phi_0$ flux-quantum periodicity, as expected. Similar feature \nis also observed for the $I_{typ}$ vs $\\phi_1$ curves, when $\\phi_2$ becomes \nconstant. Here it is also important to note that the variation of $I_{typ}$\nwith $\\Delta \\phi$ is quite similar to that as presented in Fig.~\\ref{cond1}.\nThe typical current amplitude varies periodically with $\\Delta \\phi$\n\\begin{figure}[ht]\n{\\centering \\resizebox*{8cm}{10cm}{\\includegraphics{typcurr.eps}}\\par}\n\\caption{(Color online). $I_{typ}$-$\\phi_2$ curves in the weak- (black)\nand strong-coupling (red) limits for the interferometer with four\natomic sites ($N=4$), where (a) $\\phi_1=0$ and (b) $\\phi_1=0.3$. The \ntypical current amplitudes are calculated at the bias voltage $V=1.02$.}\n\\label{typcurr}\n\\end{figure}\nshowing $2\\phi_0$ flux-quantum periodicity, following the \n$g_{typ}$-$\\Delta \\phi$ characteristics.\n\nWith the above description of electron transport for a $4$-site ($N=4$)\nquantum interferometer, now we can extend our discussion for an\ninterferometer with higher number of atomic sites i.e., $N>4$.\n\n\\subsection{Interferometric geometry with $N$ atomic ($N>4$) sites}\n\nTo get an experimentally realizable system, here we \nconsider a quantum interferometer with large number of atomic sites \ncompared to our presented mathematical model with $4$ atomic sites.\nThe schematic view of such a quantum interferometer is given in \nFig.~\\ref{ring1}, where we set $N=15$.\nThe vertical line connecting left and right sub-rings contains $5$\n\\begin{figure}[ht]\n{\\centering \\resizebox*{8cm}{3.75cm}{\\includegraphics{ring1.eps}}\\par}\n\\caption{(Color online). Schematic view of a quantum interferometer \nwith $15$ atomic sites ($N=15$) attached to two semi-infinite \none-dimensional metallic electrodes.}\n\\label{ring1}\n\\end{figure}\natomic sites, where the individual sub-rings are penetrated by AB\nfluxes $\\phi_1$ and $\\phi_2$, respectively. In this interferometric \ngeometry, the phase factors ($\\theta_{ij}$'s) are chosen according\n\\begin{figure}[ht]\n{\\centering \\resizebox*{8cm}{10cm}{\\includegraphics{cond2.eps}}\\par}\n\\caption{(Color online). $g_{typ}$-$\\Delta \\phi$ curves in the \nstrong-coupling limit for the interferometer with $15$ atomic sites\n($N=15$), where (a) $\\phi=0.4$ and (b) $\\phi=0.8$. The typical \nconductances are calculated at the energy $E=1.5$.}\n\\label{cond2}\n\\end{figure}\nto our earlier prescription. Along the circumference of the ring\n$\\theta_{ij}=2\\pi \\phi\/12 \\phi_0$ and along the vertical line\n$\\theta_{ij}=2\\pi\\Delta \\phi\/5\\phi_0$, where $\\phi$ and $\\Delta \\phi$\ncorrespond to the identical meaning as before.\n\nFor this bigger quantum interferometer ($N=15$), exactly \nsimilar features of conductance-energy and current-voltage characteristics \nare observed as we see in the case of a $4$-site interferometer. Also, \ntypical current amplitude $I_{typ}$ shows identical variation with \n$\\phi_2$ to our previous study. Only the typical conductance $g_{typ}$ \nvaries in a different way as a function of $\\Delta \\phi$. As illustrative \nexamples in Fig.~\\ref{cond2} we plot $g_{typ}$-$\\Delta \\phi$ \ncharacteristics for the quantum interferometer with $N=15$ in the limit \nof strong-coupling, where (a) and (b) correspond to $\\phi=0.4$ and $0.8$, \nrespectively. The typical conductances are determined at the energy \n$E=1.5$. From the spectra we notice that for a fixed value of $\\phi$,\ntypical conductance oscillates as a function of $\\Delta \\phi$ exhibiting\n$5 \\phi_0$ flux-quantum periodicity. This phenomenon is completely \ndifferent from the traditional periodic nature. Comparing the results\npresented in Figs.~\\ref{cond1} and \\ref{cond2} it is manifested that\nthe periodicity of $g_{typ}$-$\\Delta \\phi$ curves depends on the total\nnumber of atomic sites in the vertical line connecting left and right \nsub-rings of a quantum interferometer. Therefore, changing the length\nof the vertical line, periodicity can be changed accordingly.\n\n\\section{Closing remarks}\n\nTo summarize, we have explored electron transport properties through a \nquantum interferometer using the single particle Green's function \nformalism. We have adopted a simple tight-binding framework to illustrate \nthe bridge system, where the interferometer is sandwiched between two\nelectrodes, viz, source and drain. We have done exact numerical calculation \nto study conductance-energy and current-voltage characteristics as functions \nof the interferometer-to-electrode coupling strength, magnetic fluxes \n$\\phi_1$ and $\\phi_2$ penetrated by left and right sub-rings of the \ninterferometer and the difference of these two fluxes. Several key features \nof electron transport have been observed those may be useful in \nmanufacturing nanoelectronic devices. The most exotic features are: (i) \nexistence of semiconducting or metallic behavior, depending on the \ninterferometer-to-electrode coupling strength, (ii) appearance of the \nanti-resonant states and (iii) unconventional periodic behavior of the \ntypical conductance\/current as a function of the difference of two AB \nfluxes.\n\nThroughout our work, we have addressed the essential \nfeatures of electron transport through a quantum interferometer with \ntotal number of atomic sites $N=4$. Next, we have extended our discussion\nfor an interferometer with higher number of atomic sites where we set \n$N=15$ to achieve an experimentally realizable system. In our model \ncalculations, these typical numbers ($N=4$ and $15$) are chosen only \nfor the sake of simplicity. Though the results presented here change \nnumerically with ring size ($N$), but all the basic features remain \nexactly invariant. To be more specific, it is important to note that, \nin real situation experimentally achievable rings have typical diameters \nwithin the range $0.4$-$0.6$ $\\mu$m. In such a small ring, very high \nmagnetic fields are required to produce a quantum flux. To overcome \nthis situation, Hod {\\em et al.} have studied extensively and proposed \nhow to construct nanometer scale devices, based on Aharonov-Bohm \ninterferometry, those can be operated in moderate magnetic \nfields~\\cite{hod1,hod2,hod3,hod4,hod5}.\n\nThis is our first step to describe the electron transport in a quantum\ninterferometer. Here we have made several realistic approximations by\nignoring the effects of electron-electron correlation, electron-phonon \ninteraction, disorder, temperature, etc. Over the last few many years \npeople have studied a lot to incorporate the effect of electron-electron \ncorrelation in the study of electron transport, yet no such proper theory \nhas been well established. Thus the inclusion of electron-electron \ncorrelation in the present model is a major challenge to us. The presence \nof electron-phonon interaction in\nAharonov-Bohm interferometers provides phase shifts of the conducting\nelectrons and due to this dephasing process electron transport through an \nAB interferometer becomes highly sensitive to the AB flux $\\phi$ with the \nincrease of electron-phonon coupling strength~\\cite{hod6}. In the present \nwork, we have addressed our results considering the site energies of all \nthe atomic sites of the interferometer are identical i.e., we have treated \nthe ordered system. But in real case, the presence of impurities will \naffect the electronic structure and hence the transport properties.\nThe effect of the temperature has already been pointed out earlier, and, \nit has been examined that the presented results will not change \nsignificantly even at finite temperature, since the broadening of the \nenergy levels of the interferometer due to its coupling to the electrodes \nwill be much larger than that of the thermal broadening~\\cite{datta}.\nAt the end, we would like to mention that we need further study in such \nsystems by incorporating all these effects.\n\nThe importance of this article is mainly concerned with (i) the simplicity \nof the geometry and (ii) the smallness of the size, and our exact analysis\nmay be utilized to study electron transport in Aharonov-Bohm geometries.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\n\n\n\\chapter{Higher-order thinking in network analysis}\n\\label{ch:intro}\n\n\\newcommand*{introduction}{introduction}\n\nA network is a model for a system of connections between things.  The core of a\nnetwork model is a graph, a mathematical object consisting of nodes (modeling\nthe things) and edges (modeling the connections between things).  This\nthesis provides new graph theoretic methods to analyze datasets associated with\nnetwork models.  Such network datasets show up in a wide variety of scientific\ndisciplines, and this thesis alone analyzes networks from the following domains.\n\n\\begin{itemize}\n\\item \\emph{Ecological systems --} Nodes are species and edges are who-eats-whom\n  relationships in food web models.  (Here, the edges are \\emph{directed} to\n  represent asymmetry---sharks regularly consume sardines, but sharks are not a\n  part of a sardine's diet!)  We examine the graph structure behind aquatic\n  layers in a food web of Florida Bay.\n  \n\\item \\emph{Human communication systems --} Nodes are people and edges are\n  messages between people.  Again, there is a natural direction to the edges.\n  Our network datasets also have temporal information associated with the graph\n  to denote when messages are sent.  We analyze the differences between communication\n  behaviors in e-mail, SMS texting, and phone call networks.\n  \n\\item \\emph{Neural systems --} Nodes are neurons and edges are synapses.  We\n  examine the patterns of connections in the complete neural network of the\n  nematode worm \\emph{C.~elegans}.\n  \n\\item \\emph{Payment systems --} Nodes are people, businesses, or accounts and\n  edges are payments between them.  We analyze transactions between addresses on\n  Bitcoin.  We again have temporal information corresponding to when payments\n  are made.\n  \n\\item \\emph{Transcription regulation networks --} Nodes are groups of genes and\n  edges represent which groups of genes regulate genetic transcription in which\n  other groups of genes.  The edges in the network data also carry information\n  about whether the regulation type is activation or suppression (in this case,\n  we say that the edges are \\emph{signed}).  We analyze the transcription regulation network\n  of the yeast \\emph{S.~cerevisiae}.\n  \n\\item \\emph{Transportation systems --} Nodes are locations and edges represent\n  connectivity.  We analyze an air travel reachability network, where nodes are\n  cities and edges represent how long it takes to travel from one city to\n  another using commercial airline flights.  Our analysis also incorporates\n  additional geographical data available for the nodes.\n    \n\\item \\emph{Scientific collaborations --} Nodes are scientists and there is an\n  edge between two scientists if they have co-authored a paper.  We look at\n  collaboration patterns between physicists.\n\n\\item \\emph{Social networks --} Nodes are people and edges are social\n  relationships.  We examine Facebook friendships, Twitter followers, and Stack\n  Overflow question-and-answer interactions.\n\n\\item \\emph{The World Wide Web --} Nodes are web pages and edges are hyperlinks.\n  We analyze the structure of the Stanford web graph and Wikipedia.\n\\end{itemize}\n\nThe above descriptions illustrate how graphs, which consist of nodes and edges,\nare a natural mathematical structure for network models.  The graph is the\nbackbone of the network datasets, even though we may have additional information\nsuch as timestamps, signed edges, geographical data, etc.  Consequently, we often frame our\nanalysis of and questions about networks in terms of nodes and edges.  For\nexample, we might be interested in the number of edges that a node is in (how\nmany different species does the shark consume in the food web?), the number of\nedges between subsets of the nodes (how many Facebook friendships are there\nbetween Stanford students?), or whether or not there exists a sequence of edges\nto traverse to go from one node to another (can I get from Palo Alto to Berkeley\non public transit?).\n\n\\input{CH1-FIG-intro-ffl}\n\nWhile analysis in terms of nodes and edges is natural, there is substantial\nevidence that \\emph{higher-order structures}, or small subgraph patterns between\na few nodes (\\cref{fig:intro_ffl}), are essential to the behavior of many\ncomplex systems modeled by\nnetworks~\\cite{milo2002network,yaverouglu2014revealing}.  This idea has a long\nhistory in sociology.  In the early 1900s, Simmel theorized that triangles (a\ncomplete graph on three nodes) form in social networks because two friends of\nthe same individual get opportunities to meet and become friends\nthemselves~\\cite{simmel1908sociology}, an idea later popularized by\n\\citet{granovetter1973strength} as \\emph{triadic closure}.\n\\Citet{bavelas1950communication} surveyed several studies that examined how\nsmall communication patterns used between individuals in a group affects their\nability to jointly perform tasks, and \\citet{davis1971structure} found that\ncertain directed triads were less common than predicted by a null model,\nproviding numerical evidence for the ranked groups social network theory of\n\\citet{homans1950human}.  In more recent work, \\citet{ugander2013subgraph} use\nsmall subgraph frequencies within induced Facebook friendship subgraphs to\nidentify social processes.\n\nIn network analysis more broadly, higher-order structure is often described\nthrough the idea of a \\emph{network motif}.  \\Citet{shen2002network}\nintroduced the term when they analyzed the frequency of higher-order\ninteractions through subgraph patterns, which they called network motifs, in\nthe transcription regulation network of \\emph{E. coli}.\\footnote{\\Citet{shen2002network} borrowed the phrase motif from gene\n  sequence analysis, where motifs are ``short, recurring patterns in DNA that\n  are presumed to have a biological function''~\\cite{d2006dna}.}  This style of\nanalysis was popularized in a landmark paper of \\citet{milo2002network}\n(published in \\emph{Science} the same year), where they dubbed network motifs the\n``building blocks of complex networks'' and identified motifs common in gene\nregulation networks, food webs, and electronic circuits.  In follow-up work,\n\\citet{milo2004superfamilies} showed that the profile of z-scores (with\nrespect to samples of a configuration model with the same degree distribution)\nfor the frequencies of the 13 connected, 3-node directed subgraphs were\nsufficient to distinguish biological, neurological, social, and linguistic\nnetworks.  In subsequent research, important motifs have been identified in a\nvariety of domains, including brain science~\\cite{sporns2004motifs},\necology~\\cite{camacho2007quantitative}, biology~\\cite{wuchty2003evolutionary},\nand social network analysis~\\cite{leskovec2010signed}.\n\n\\Citet{milo2002network} defined network motifs as ``patterns of interconnections\noccurring in complex networks at numbers that are significantly higher than\nthose in randomized networks.''  The ``significant'' qualifier in this\ndefinition has caused some confusion around the terminology.  Some take the\nqualifier to heart and use the term \\emph{graphlet} to specify any small network\npattern and reserve the motif designation for graphlets that occur significantly\nmore frequently with respect to some null model and some measure of statistical\nsignificance~\\cite{prvzulj2004modeling}.\\footnote{Presumably, the term graphlets\n  is a play on wavelets, which are used in signal processing to localize time\n  and frequency, but I have not found this explicitly mentioned in the\n  literature.}  However, one could just as well call a graphlet a small\nsubgraph, and indeed, many\ndo~\\cite{ugander2013subgraph,demeyer2013index,lahiri2007structure,pinar2017escape}.\nUsually, there is an implicit assumption that motifs and graphlets are\n\\emph{connected} patterns, whereas general subgraphs do not carry this\nassumption.  In this thesis, we just use ``motifs'' to specify patterns in\nnetworks and sometimes use the term subgraph when discussing the more\nmathematical points.  In \\cref{ch:honc}, we also add to the vernacular by\ndefining an ``anchored motif'', which provides a formalism for specifying a\nsubset of the nodes in a motif relevant to certain computations.  We also use\n``higher-order structures'' as a catch-all phrase.\n\nOperating under the assumption that higher-order structures are important to\nnetworks, the algorithmic data mining community has developed a litany of\nmethods for efficiently finding and counting them.  These include, to name a\nfew, algorithms for enumerating triangles that perform especially well given the\npower-law degree distributions typical of many real-world\nnetworks~\\cite{schank2005finding,latapy2008main,berry2014why}, fast algorithms\nfor enumerating general motifs via principled\nheuristics~\\cite{wernicke2006fanmod,demeyer2013index,houbraken2014index,ahmed2015efficient},\nalgorithms that approximate the total number of\ntriangles~\\cite{tsourakakis2009doulion,seshadhri2014wedge,lim2015mascot,de2016triest},\nand algorithms that approximate the total number of motifs composed of 4 or more\nnodes~\\cite{jha2015path,bressan2017counting,wang2014efficiently,slota2013fast}.\nFor the computations in this thesis, we only need the method of \\citet[Algorithm 1]{schank2005finding}\nfor enumerating triangles and the method of\n\\citet{chiba1985arboricity} for enumerating cliques.  We use these algorithms\nbecause they are straightforward to implement and are fast for the datasets\nthat we analyze.\n\nWe summarize the setup---networks consisting of nodes and edges model a broad\nrange of systems, higher-order interactions (patterns between a small number of\nnodes) are important to many networks, and we have algorithms adept at finding\nand counting these higher-order structures.  However, higher-order structures\nhave not been well integrated into the analyses, models, and algorithms that we\nactually use to study the structure of complex networks.  This thesis develops\nnew methods, or \\emph{tools}, for analyzing network data based on higher-order\nstructures, i.e., \\emph{for higher-order network analysis}.  Consequently, the\nnetwork analyst is able to examine data in terms of\nthe higher-order interactions that are important to him or her.\n\nWe demonstrate how our tools use higher-order interactions as a primitive in order\nto gain new insights into complex systems.  For example, our analysis of the neural\nnetwork for the nematode worm \\emph{C. elegans} in \\cref{sec:honc_celegans}\nfinds a cluster of 20 neurons in the frontal section of the worm that is a\nplausible control of nictation, a type of worm movement.  We discover this group\nthrough a new algorithm that looks for subsets of the graph in which a certain\n4-node ``bi-fan'' motif is contained.  The higher-order structure is key to the\ndiscovery---we need to optimize an objective function for sets of nodes that\nmodels the bi-fan motif---and \\emph{not} simply edges, as is typically done---in\norder to find this group.  Later, in \\cref{sec:ccfs_empirical}, we find that\nunder a generalized ``closure'' model for the presence of edges in the network,\n3-cliques (triangles) in \\emph{C. elegans} are more common than expected, while\n4-cliques are less common than expected, which challenges a longstanding view of\nhow edges tend to cluster together in network models of complex\nsystems~\\cite{watts1998collective}.  In this case, the consideration of\nhigher-order structure at the level of 4-cliques was necessary for the finding.\n\nHigher-order analysis is a small part of network science, but\nhigher-order thinking has still shown up in several contexts.  For example, motifs\nhave been used to generate features for both prediction\nproblems~\\cite{milenkovic2008uncovering,bonato2014dimensionality,ugander2013subgraph,chakraborty2014automatic}\nand unsupervised learning\ntasks~\\cite{yaverouglu2014revealing,henderson2012rolx}, motif frequencies are\nused to fit parameters of random graph\nmodels~\\cite{gleich2012moment,benson2014learning,bickel2011method,wasserman1996logit},\nand motif modeling is used to improve network alignment\nalgorithms~\\cite{milenkovic2010optimal,mohammadi2016triangular}.  In addition,\nthere are several higher-order approaches that do not necessarily use motif\nstructure but are similar in spirit.  Examples include ``meta paths'' to\nrepresent multi-relational networked data~\\cite{zhang2014meta,sun2011pathsim},\nhigher-order and variable-order Markov chain\nmodels~\\cite{rosvall2014memory,chierichetti2012web,benson2017spacey,wu2016general}, and\n``higher-order network'' models for aggregating temporal paths in networks where\nedges have\ntimestamps~\\cite{scholtes2014causality,scholtes2017network,scholtes2016higher}.\n\nThe new ideas in \\cref{ch:honc,ch:hoccfs} also align with recent higher-order\nnetwork analyses that directly generalize classical ideas to account for\nhigher-order structures in the network.  For example, \\citet{tsourakakis2015k}\ngeneralized the (edge) densest subgraph problem to the $k$-clique densest\nsubgraph problem, \\citet{zhang2012extracting} generalized (edge-based) $k$-cores\nto triangle-based $k$-cores, and \\citet{sariyuce2015finding} generalized\n$k$-core and $k$-truss decompositions to account for clique containment with the\nnucleus decomposition.  We describe our contributions in more detail in the\nfollowing section.\n\n\\section{Contributions}\n\nThe core contributions of this thesis are three new tools for higher-order\nnetwork analysis.  We contextualize and summarize them in\n\\cref{tab:contributions}.\n\\input{CH1-TAB-contributions}\n\nIn addition to developing the tools, we make a concerted effort to use the tools\nto gain new insights into a variety of network datasets.  Thus, there is a\nconsiderable data mining component to the chapters ahead, which are also\nmeaningful contributions.  The next few subsections provide additional details\non the tools and the insights that they provide.\n\n\\subsection{\\cref{ch:honc} -- Higher-order network clustering}\n\nThe first tool is a framework for graph clustering based on motifs.  Graph\nclustering is a broad research problem that assigns nodes in a graph to\nclusters, where the clusters are meant to represent some module in the network.\nTypically, the objective function modeling what it means to have good clusters\ninvolves a combination of the number of \\emph{edges} contained within the\nclusters and the number of \\emph{edges} that go between clusters.  We re-define\nwhat it means to be a good cluster with an objective function that considers the\nnumber of \\emph{motifs} contained within the clusters and the number of\n\\emph{motifs} that go between clusters.  Thus, if a particular motif is\nimportant for some domain, we can run an algorithm to optimize an objective\nfunction that accounts for that motif.\n\nOur main theoretical contributions include (i) defining the new objective\nfunction, \\emph{motif conductance}, which is a generalization of the classical\nconductance measure of cluster quality; and (ii) a spectral algorithm for\nfinding sets with small motif conductance.  The algorithm is accompanied by an\napproximation guarantee on the quality of the output clusters in terms of motif\nconductance.  The algorithm and quality guarantee are generalizations of the\nFiedler partition or sweep cut procedure and the Cheeger inequality.\n\nUsing this framework we show that\n\\begin{itemize}\n\\item a particular directed triangular motif reveals aquatic layers in a food\n  web;\n\\item in the \\emph{C. elegans} neural system, a cluster we find based\n  on a previously studied 4-node motif (the ``bi-fan'')\n  is a plausible control mechanism for nictation, a type of movement in the worm;\n\\item clustering with length-2 paths automatically reveals the hub structure and\n  geography of an air travel transportation reachability network;\n\\item clustering with the feedforward loop (\\cref{fig:intro_fflC}) reveals known\n  modules in transcription regulation networks with higher accuracy than\n  edge-based methods; and\n\\item clustering with particular directed triangular motifs reveal anomalous clusters in\n  the English Wikipedia web graph and the Twitter follower network.\n\\end{itemize}\n\nWe then extend the algorithm to handle the problem of \\emph{localized\n  clustering} or \\emph{targeted clustering}, where the goal is to find a (small) cluster\nof nodes containing a given seed node.  Again, existing approaches optimize the\nclassical conductance, and we instead optimize motif conductance.  Our\napproach is a generalization of the approximate Personalized PageRank\nmethod~\\cite{andersen2006local}.\n\nThe algorithmic framework and applications appeared as a publication in\n\\emph{Science}~\\cite{benson2016higher},\\footnote{See the accompanying\n  perspective piece by \\citet{prvzulj2016network} for a broader context for this\n  work.} which was joint work with David Gleich and Jure Leskovec.  The\nextension to localized clustering will appear in a paper in the proceedings of\nthe 2017 KDD conference~\\cite{yin2017local}, which was joint work with Hao Yin,\nDavid, and Jure.  Hao implemented the localized algorithm, ran the experiments for the\nresults in \\cref{sec:local}, and came up with the idea to look at recovery in the\nplanted partition model (\\cref{sec:local_synth}).\n\n\\subsection{\\cref{ch:hoccfs} -- Higher-order clustering coefficients}\n\nThe second tool is a measurement for the extent to which nodes in a network\ncluster together.  This is a generalization of the classical clustering\ncoefficient that measures the fraction of length-2 paths that induce a triangle.\nWe reinterpret the clustering coefficient as a clique expansion and closure\nprocess---a 2-clique (an edge) \\emph{expands} with an adjacent edge and we check\nif this structure \\emph{closes} by forming a 3-clique (a triangle).  We\ngeneralize this by considering an $\\ell$-clique that expands with an adjacent\nedge and checking if this structure closes by forming an $(\\ell + 1)$-clique.\nWe call the fraction of ($\\ell$-clique, adjacent edge) pairs that induce an\n$(\\ell + 1)$-clique the $\\ell$th-order clustering coefficient.\n\nWe theoretically analyze the higher-order clustering coefficient in the\nErd\\H{o}s-R\\'enyi and small-world random graph models and empirically analyze\nthe higher-order clustering coefficient on three real-world networks.  We find that\nalthough the \\emph{C. elegans} neural network has high clustering in the\ntraditional sense, it does not have high third-order clustering (3-cliques tend\nnot to expand into 4-cliques).  This could arise from the fact that 4-cliques represent\nredundant processing units and their absence leads to a more efficient neural\narchitecture.\n\nWe also make a connection between higher-order clustering coefficients and motif\nconductance.  We show that if a network has a large $\\ell$th-order clustering\ncoefficient, then there is a node whose 1-hop neighborhood subgraph has small motif\nconductance for the $\\ell$-clique motif.  This is a generalization of the $\\ell = 2$\ncase studied by \\citet{gleich2012vertex}.  In fact, I came up with the\ndefinition for the higher-order clustering coefficient when I was trying to\ngeneralize a lemma from \\citet{gleich2012vertex} to the $\\ell = 3$ case (for\ntriangle conductance).\n\nThe definitions and analysis of the higher-order clustering coefficient is based\non a paper with Hao Yin and Jure Leskovec that has been submitted for\npublication and is currently on arXiv~\\cite{yin2017higher}.  The connection to\nmotif conductance is based on part of a paper with Hao, Jure, and\nDavid Gleich that will appear in the proceedings of the 2017 KDD\nconference~\\cite{yin2017local}.  Hao helped a substantial amount on the proofs\nof \\cref{prop:ccf_er,prop:ccf_sw,thm:nbrhd_main}.\n\n\\subsection{\\cref{ch:tm} -- Motifs in temporal networks}\n\nThe third tool is a definition of motifs in temporal networks along with\nalgorithms for efficiently counting them.  The goal of the research in\n\\cref{ch:tm} is to provide the foundations of higher-order network analysis---a\ndefinition for higher-order structures and efficient algorithms for finding\nthem---for a broader class of network datasets, i.e., those that contain temporal\ninformation.  We consider a temporal network to be a collection of $(u, v, t)$\ntuples (temporal edges), where $u$ and $v$ are elements of a node set $V$ and $t\n\\in \\mathbb{R}_{+}$ is a timestamp.  We define a temporal motif by a multigraph,\nan ordering on the edges in the multigraph, and a time window $\\delta$, and we\ndefine an instance of the temporal motif in a temporal network to be a subset of\nthe temporal edges that match the edge pattern of the multigraph, appear in the\nspecified order, and all occur within $\\delta$ time units of each other.  We\nprovide a general algorithm for efficiently counting the number of instances of\ntemporal motifs in a given temporal network along with specialized fast\nalgorithms for certain classes of motifs.  We also show some basic higher-order\nanalyses on several temporal network datasets.\n\n\\Cref{ch:tm} is based on a paper with Ashwin Paranjape and Jure Leskovec that\nappeared in the proceedings of the 2017 WSDM\nconference~\\cite{paranjape2017motifs}.  Ashwin helped with the design,\nimplementation, and analysis of the algorithms and executed the experiments in\n\\cref{sec:tm_empirical}.\n\n\\subsection{Additional artifacts and impact}\n\nIn addition to the content of this thesis and the associated publications, other\nartifacts of this research include the following.\n\n\\begin{itemize}\n\\item Implementations of the motif-based spectral clustering algorithm\n \\begin{itemize}\n \\item for the SNAP software library, which is available at\\\\\n   \\url{https:\/\/github.com\/snap-stanford\/snap};\n \\item in Julia, which is available at\\\\\n   \\url{https:\/\/github.com\/arbenson\/higher-order-organization-julia}; and\n \\item in MATLAB, which is available at\\\\\n   \\url{https:\/\/github.com\/arbenson\/higher-order-organization-matlab}.\n \\end{itemize}\n\\item Implementations of the temporal motif counting algorithms for the\n  SNAP software library, which is available at\\\\\n  \\url{https:\/\/github.com\/snap-stanford\/snap}. \n \\item Julia notebooks to reproduce the results in the main text of\n   \\citet{benson2016higher}, which are available at\\\\\n   \\url{https:\/\/github.com\/arbenson\/higher-order-organization-julia}.\n\\item Metadata for the nodes in the transportation reachability network of\n  \\citet{frey2007clustering} (city latitudes, longitudes, and metropolitan\n  populations), which is available at\\\\\n  \\url{http:\/\/snap.stanford.edu\/data\/reachability.html}.\n\\item Metadata for the nodes in the Florida Bay food web\n  \\citet{frey2007clustering} (group classification), which is available at\\\\\n  \\url{http:\/\/snap.stanford.edu\/data\/Florida-bay.html}.  \n\\item The $\\dataset{email-Eu-core}$ network dataset with department\nlabels for all of the nodes, which is available at\\\\\n  \\url{http:\/\/snap.stanford.edu\/data\/email-Eu-core.html}.  \n\\item The $\\dataset{wiki-cats}$ network dataset with article names and category\n  classifications for all of the nodes, which is available at\\\\\n  \\url{http:\/\/snap.stanford.edu\/data\/wiki-topcats.html}.  \n\\item The $\\dataset{StackOverflow}$ temporal network dataset, which is available at\\\\\n  \\url{http:\/\/snap.stanford.edu\/data\/sx-stackoverflow.html}.\n\\item The $\\dataset{MathOverflow}$ temporal network dataset, which is available at\\\\\n  \\url{http:\/\/snap.stanford.edu\/data\/sx-mathoverflow.html}.\n\\item The $\\dataset{SuperUser}$ temporal network dataset, which is available at\\\\\n  \\url{http:\/\/snap.stanford.edu\/data\/sx-superuser.html}.\n\\item The $\\dataset{AskUbuntu}$ temporal network dataset, which is available at\\\\\n  \\url{http:\/\/snap.stanford.edu\/data\/sx-askubuntu.html}.\n\\item The $\\dataset{email-Eu}$ temporal network dataset and 4 department-level\n  subnetworks, which are available at\\\\\n  \\url{http:\/\/snap.stanford.edu\/data\/email-Eu-core-temporal.html}.\n\\item The $\\dataset{WikiTalk}$ temporal network dataset, which is available at\\\\\n  \\url{http:\/\/snap.stanford.edu\/data\/wiki-talk-temporal.html}.\n\\end{itemize}\n\nFurthermore, the ideas of this thesis have already had impact on the broader\nresearch community.  As an example, \\citet{meier2016motif} used the motif-based\nclustering algorithm in functional connectivity networks of brains and found\nsymmetry patterns between the hemispheres of the brain.\nIn their article ``Network analytics in the age of big data''\npublished in \\emph{Science}, \\citet{prvzulj2016network} contextualize the\nframework of \\cref{ch:honc} as an important step towards understanding\nthe large-scale datasets coming from a ``complex world of interconnected\nentities.''  As discussed at the beginning of this introduction, network models\nand analysis are fundamental because of their wide applicability, and\n\\Citet{prvzulj2016network} emphasize this point when (generously) discussing our work:\n``The importance of this result lies in its applicability to a broad range of\nnetworked data that we must understand to answer fundamental questions facing\nhumanity today, from climate change and impacts of genetically modified\norganisms, to the environment, to food security, human migrations, economic and\nsocietal crises, understanding diseases, aging, and personalizing medical\ntreatments.''\nIndeed, I hope that the ideas that follow are a step towards tackling these problems.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\subsection{Alternative clustering algorithms for evaluation}\n\\input{CH2-TXT-alternatives}\n\n\\subsection{Comparing motif conductance and edge conductance}\n\\label{sec:comparing_cond}\n\\input{CH2-TXT-comparing-conductance}\n\n\\subsection{Motif $M_{6}$ in the Florida Bay food web}\n\\label{sec:honc_foodweb}\n\\input{CH2-TXT-foodweb}\n\n\\subsection{Coherent feedforward loops in the \\emph{S.~cerevisiae} transcriptional regulation network}\n\\label{sec:honc_yeast}\n\\input{CH2-TXT-yeast}\n\n\\subsection{Bi-directed length-2 paths in a transportation reachability network}\n\\label{sec:honc_airports}\n\\input{CH2-TXT-airports}\n\n\\subsection{The bi-fan motif in the \\emph{C.~elegans} neuronal network}\n\\label{sec:honc_celegans}\n\\input{CH2-TXT-celegans}\n\n\\subsection{Motif $M_{6}$ in the English Wikipedia article network}\n\\label{sec:honc_enwiki}\n\\input{CH2-TXT-enwiki}\n\n\\subsection{Motif $M_{6}$ in the Twitter follower network}\n\\label{sec:honc_twitter}\n\\input{CH2-TXT-twitter}\n\n\\subsection{Motif $M_{7}$ in the Stanford web graph}\n\\label{sec:honc_stanford}\n\\input{CH2-TXT-stanford}\n\n\\subsection{Semi-cliques in collaboration networks}\n\\label{sec:honc_collaboration}\n\\input{CH2-TXT-collaboration}\n\n\n\n\n\n\n\n\n\n\n\n\\chapter{Higher-order network clustering}\n\\label{ch:honc}\n\n\\section{Organization via higher-order structures}\n\\input{CH2-TXT-intro}\n\n\\section{The motif-based spectral clustering algorithm}\n\\label{sec:honc_derivation}\n\\input{CH2-TXT-theory}\n\n\\section{Case studies}\n\\input{CH2-TXT-case-studies}\n\n\\section{Scalability experiments}\n\\label{sec:honc_scalability}\n\\input{CH2-TXT-scalability}\n\n\\section{An extension to local higher-order clustering}\n\\label{sec:local}\n\\input{CH2-TXT-local}\n\n\\section{Related work and discussion}\n\\label{sec:honc_discussion}\n\\input{CH2-TXT-discussion}\n\n\n\n\n\n\\subsection{Overview}\n\\input{CH2-TXT-local-overview}\n\n\\subsection{Motif-based personalized PageRank}\n\\input{CH2-TXT-motifppr}\n\n\\subsection{Experiments on synthetic networks}\n\\label{sec:local_synth}\n\\input{CH2-TXT-local-synthetic-exps}\n\n\\subsection{Experiments on real-world networks}\n\\label{sec:local_real}\n\\input{CH2-TXT-local-real-exps}\n\n\n\n\n\n\n\n\n\\subsection{Triangular motifs}\n\\label{sec:scalability}\n\nIn this section, we demonstrate that our method scales to real-world networks\nwith billions of edges.  We tested the scalability of our method on 16 large\ndirected graphs from a variety of real-world applications.  These networks range\nfrom a couple hundred thousand to two billion edges and from 10 thousand to over\n50 million nodes.  We briefly describe the networks here and provide some\nsummary statistics in \\Cref{tab:networks_description}.\n\\begin{itemize}\n\\item \\dataset{wiki-RfA} represents which users voted for which other users for\n  adminship rights on Wikipedia~\\cite{west2014exploiting}.\n\\item \\dataset{email-EuAll} represents who emailed whom at a European research\n  institution~\\cite{leskovec2005graphs}.\n\\item \\dataset{cit-HepPh} represents citations between papers in the ``High\n  Energy Physics -- Phenomenology'' category on\n  arXiv~\\cite{gehrke2003overview}.\n\\item \\dataset{web-NotreDame} is the hyperlink structure of web pages in the\n  \\texttt{nd.edu} domain~\\cite{albert1999internet}.\n\\item \\dataset{amazon0601} consists of connections between frequently\n  co-purchased products on Amazon~\\cite{leskovec2007dynamics}.\n\\item \\dataset{wiki-Talk} represents which users wrote on which other users' talk page\n  on Wikipedia~\\cite{leskovec2010governance}.\n\\item \\dataset{ego-Gplus} is a collection of egonetworks (1-hop neighborhoods)\n  on the online social network Google+~\\cite{leskovec2012learning}.\n\\item \\dataset{uk-2014-tpd} is the hyperlink structure of top private domain\n  links in the \\texttt{.uk}\n  domain~\\cite{boldi2004webgraph,boldi2011layered,boldi2014bubing}.\n\\item \\dataset{soc-Pokec} consists of the friendship relationships on the online\n  social network Pokec~\\cite{takac2012data}.\n\\item \\dataset{uk-2014-host} is the hyperlink structure of host links on the\n  \\texttt{.uk} domain~\\cite{boldi2004webgraph,boldi2011layered,boldi2014bubing}.\n\\item \\dataset{soc-LiveJournal1} consists of the friendships on the online\n  social network LiveJournal~\\cite{backstrom2006group}.\n\\item \\dataset{enwiki-2013} is the hyperlink structure of articles on English\n  Wikipedia~\\cite{boldi2004webgraph,boldi2004ubicrawler,boldi2011layered}\n\\item \\dataset{uk-2002} is the hyperlink structure of web pages in the\n  \\texttt{.uk}\n  domain~\\cite{boldi2004webgraph,boldi2004ubicrawler,boldi2011layered}.\n\\item \\dataset{arabic-2005} is the hyperlink structure of arabic-language web\n  pages~\\cite{boldi2004webgraph,boldi2004ubicrawler,boldi2011layered}.\n\\item \\dataset{twitter-2010} represents the followers of users on the online\n  social network\n  Twitter in 2010~\\cite{boldi2004webgraph,boldi2011layered,kwak2010twitter}.\n\\item \\dataset{sk-2005} is the hyperlink structure of web pages in the\n  \\texttt{.sk}\n  domain~\\cite{boldi2004webgraph,boldi2004ubicrawler,boldi2011layered}.\n\\end{itemize}\n\n\\input{CH2-TAB-networks-description}\n\\clearpage\n\nRecall that \\Cref{alg:motif_fiedler} consists of two major computational components:\n\\begin{enumerate}\n\\item Form the weighted graph $W_M$.\n\\item Compute the eigenvector $z$ of second smallest eigenvalue of $N_M$.\n\\end{enumerate}\nAfter computing the eigenvector, we sort the vertices and loop over prefix sets\nto find the lowest motif conductance set.  We consider these final steps as part\nof the eigenvector computation for our performance experiments.\n\nFor each network in \\cref{tab:networks_description}, we ran the method for all\ndirected triangular motifs ($M_1$--$M_7$).  To compute $W_M$, we used a standard\nalgorithm that meets the $O(m^{3\/2})$\nbound~\\cite{schank2005finding,latapy2008main} with some additional\npre-processing based on the motif.  Conceptually, the algorithm is as follows:\n\n\\begin{enumerate}\n\\item Take motif type $M$ and graph $G$ as input.\n\n\\item (Pre-processing)  If $M$ is $M_1$ or $M_5$, ignore all bidirectional\n  edges in $G$ as these motifs only contain unidirectional edges.  If $M$ is\n  $M_4$, ignore all unidirectional edges in $G$ as this motif only contains\n  bidirectional edges.\n  \n\\item Form the undirected graph $G_{\\textnormal{undir}}$ by removing the\n  direction of all edges in $G$.\n  \n\\item Let $d_u$ be the degree of node $u$ in $G_{\\textnormal{undir}}$.  Order\n  the nodes in $G_{\\textnormal{undir}}$ by increasing degree, breaking ties\n  arbitrarily.  Denote this ordering by $\\psi$.\n  \n\\item For every edge undirected edge $\\{u, v\\}$ in $G_{\\textnormal{undir}}$, if\n  $\\psi_u < \\psi_v$, add directed edge $(u, v)$ to $G_{\\textnormal{dir}}$;\n  otherwise, add directed edge $(v, u)$ to $G_{\\textnormal{dir}}$.\n  \n\\item For every node in $u$ in $G_{\\textnormal{dir}}$ and every pair of directed\n  edges $(u, v)$ and $(u, w)$, check to see if edge $(v, w)$ or $(w, v)$ is in\n  $G_{\\textnormal{dir}}$.  If so, check if these three nodes form motif $M$ in\n  $G$.  If they do, increment the weights of edges $(W_M)_{uv}$,\n  $(W_M)_{uw}$, and $(W_M)_{vw}$ by $1$.\n  \n\\item Return $W_M + W_M^T$ as the motif weighted adjacency matrix.  \n\\end{enumerate}\n\nThe algorithm runs in time $O(m^{3\/2})$ time and is also\nknown as an effective heuristic for real-world\nnetworks~\\cite{berry2014why,latapy2008main}.  After, we find the largest\nconnected component of the graph corresponding to the motif adjacency matrix\n$W_M$, form the motif normalized Laplacian $N_M$ of the largest\ncomponent, and compute the eigenvector of second smallest eigenvalue of\n$N_M$.  To compute the eigenvector, we use MATLAB's \\texttt{eigs}\nroutine with tolerance 1e-4 and the ``smallest algebraic'' option for the\neigenvalue type.\n\n\\Cref{tab:scalability_results} lists the time to compute $W_M$ and the time to\ncompute the eigenvector for each network.  We omit the time to read the graph\nfrom disk because this time strongly depends on how the graph is compressed.\nAll experiments ran on a 40-core server with four 2.4 GHz Intel Xeon E7-4870\nprocessors.  All computations of $W_M$ were in serial and the computations of\nthe eigenvectors were done in parallel (as defaulted to by MATLAB).\n\nOver all networks and all motifs, the longest computation of $W_M$ (including\npre-processing time) was for $M_2$ on \\dataset{sk-2005} and took roughly 52.8\nhours.  The longest eigenvector computation was for $M_6$ on \\dataset{sk-2005}\nand took about 1.62 hours. We note that $W_M$ only needs to be computed once per\nnetwork, regardless of the eventual number of clusters that are extracted.\nAlso, the computation of $W_M$ can easily be accelerated by parallel computing\n(the enumeration of motifs can be done in parallel over nodes, for example) or\nby more sophisticated algorithms~\\cite{berry2014why}.  In this work, we perform\nthe computation of $W_M$ in serial in order to better understand the\nscalability.  Our results serve only as a rough baseline.\n\n\\input{CH2-TAB-scalability-results}\n\\clearpage\n\n\nIn theory, the worst-case time for triangle enumeration scales as $m^{1.5}$.\nWe fit a linear regression of the log of the computation time of the last step of the\nenumeration algorithm to the regressor $\\log(m)$ and a constant term:\n\\begin{equation}\\label{eqn:regression}\n\\log(\\text{time}) \\sim a\\log(m) + b\n\\end{equation}\nIf the computations truly took $cm^{1.5}$ for some constant $c$, then the\nregression coefficient for $\\log(m)$ would be $1.5$.  Because of the\npre-processing of the algorithm, the number of edges $m$ depends on the motif.\nFor example, with motifs $M_1$ and $M_5$, we only count the number of\nunidirectional edges.  The pre-processing time, which is linear in the total\nnumber of edges, is not included in the time.  The regression coefficient for\n$\\log(m)$ (the variable $a$ in \\cref{eqn:regression}) is smaller than $1.5$ for\neach motif (\\cref{tab:scale_conf}).  The largest regression coefficient is\n$1.31$ for $M_3$ (with 95\\% confidence interval $1.31 \\pm 0.19$).  The\nregression coefficient over the aggregation of data points (the ``combined''\ncolumn in \\cref{tab:scale_conf}) is $1.17$ (with 95\\% confidence interval $1.17\n\\pm 0.09$).  We conclude that on real-world datasets, the algorithm for\ncomputing $W_M$ performs much better than the worst-case guarantees.\n\n\\input{CH2-TAB-scalability-regression}\n\\clearpage\n\n\\subsection{Larger $k$-clique motifs}\n\nOn smaller graphs, we can compute larger motifs.  To demonstrate this point, we\nform the motif adjacency matrix $W_M$ based on the $k$-cliques motif for $k = 4,\n\\dots, 9$ using the algorithm of \\citet{chiba1985arboricity} with the additional\npre-processing of computing the ($k-1$)-core of the graph.  (This pre-processing\nimproves the running time in practice but does not affect the asymptotic\ncomplexity.)  The motif adjacency matrices for $k$-cliques are sparser than the\nadjacency matrix of the original graph, so we do not worry about spatial\ncomplexity for these motifs.\n\nWe evaluate this procedure on nine real-world networks, ranging from roughly\nfour thousand nodes and 88 thousand edges to over two million nodes and around\nfive million edges.  We briefly describe the networks here and list summary\nstatistics in \\cref{tab:cliques_perf}.\n\\begin{itemize}\n\\item \\dataset{ego-Facebook} is the union of ego networks from the user\n  friendship graph of the online social network\n  Facebook~\\cite{leskovec2012learning}.\n\n\\item \\dataset{ca-AstroPh} represents scientists who have co-authored a paper\n  listed on the AstroPhysics category on\n  arXiv~\\cite{leskovec2005graphs}.\n\n\\item \\dataset{soc-Slashdot0811} represents who tagged whom during an event on\n  the online social network Slashdot~\\cite{leskovec2009community}.  The\n  original network data is directed and signed, and we ignore both of these\n  properties here.\n\n\\item \\dataset{com-DBLP} represents scientists who have co-authored a paper\n  listed on DBLP~\\cite{yang2012defining}.\n\n\\item \\dataset{com-Youtube} consists of friendships on the online social network\n  YouTube~\\cite{mislove2007measurement}.\n\\end{itemize}\nWe also use the \\dataset{wiki-RfA}, \\dataset{email-EuAll}, \\dataset{cit-HepPh},\nand \\dataset{wiki-Talk} datasets described earlier, although we now consider the\ngraphs to be undirected.\n\nEach network contains at least one $9$-clique and hence at least one $k$-clique\nfor $k < 9$.  All computations ran on the same server as for the triangular\nmotifs and again there was no parallelism.  We terminated computations after two\nhours.  For five of the nine networks, it takes less than two hours to compute\n$W_M$ for any $k$-clique motif, $k = 4, \\ldots, 9$ (\\cref{tab:cliques_perf}).\nFurthermore, on all of these networks, the computation takes less than two hours\nfor $k = 4, 5, 6$.  The smallest network (in terms of number of nodes and number\nof edges) is \\dataset{ego-Facebook}, where it took just under two hours to\ncomptue $W_M$ for the $6$-clique motif and over two hours for the $7$-clique\nmotif.  This network has around 80,000 edges.  On the other hand, for\n$\\dataset{com-Youtube}$, which contains nearly 3 million edges, we can compute $W_M$ for the\n$9$-clique motif in under a minute.  We conclude that it is possible to use our\nframework with motifs much larger than the three-node motifs on which we\nperformed many of our experiments.  However, the number of edges is not a\ngood predictor of the running time to compute $W_M$.  This makes sense because the\ncomplexity of the algorithm of \\citet{chiba1985arboricity} is $O(a^{k-2}m)$,\nwhere $a$ is the arboricity of the graph.  Hence, the dependence on the number\nof edges is always linear, and the arboricity drives the running time.\n\n\\input{CH2-TAB-clique-performance}\n\\clearpage\n\n\n\\subsection{Review of cuts, volumes, conductance and the graph Laplacian for weighted, undirected graphs}\n\\input{CH2-TXT-review}\n\n\\subsection{Definition of network motifs}\n\\label{sec:motif_def}\n\\input{CH2-TXT-motif-definitions}\n\n\\subsection{Motif conductance}\n\\label{sec:motif_cond}\n\\input{CH2-TXT-motif-conductance}\n\n\\subsection{The motif adjacency matrix and the motif Laplacian}\n\\label{sec:motif_adjacency}\n\\input{CH2-TXT-motif-adjacency}\n\n\\subsection{The spectral algorithm for finding a single cluster}\n\\label{sec:honc_alg}\n\\input{CH2-TXT-algorithm}\n\n\\subsection{Interlude for matrix computations}\n\\label{sec:honc_matrix}\n\\input{CH2-TXT-matrix}\n\n\\subsection{Motif Cheeger inequality for network motifs with three nodes}\n\\label{sec:motif_cheeger}\n\\input{CH2-TXT-cheeger-3}\n\n\\subsection{Motif Cheeger inequality for network motifs with four or more nodes}\n\\label{sec:fournode}\n\\input{CH2-TXT-cheeger-4}\n\n\\subsection{Analysis of computational complexity}\n\\label{sec:honc_basic_complexity}\n\\input{CH2-TXT-complexity}\n\n\\subsection{Methods for simultaneously finding multiple clusters}\n\\label{sec:honc_multiple_clusters}\n\\input{CH2-TXT-multiple-clusters}\n\n\\subsection{Extensions for multiple motifs, weighted motifs, and weighted, signed, and colored networks}\n\\label{sec:honc_extensions}\n\\input{CH2-TXT-extensions}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\chapter{Higher-order clustering coefficients}\n\\label{ch:hoccfs}\n\n\\section{The clustering coefficient and closure probabilities}\n\\input{CH3-TXT-intro}\n\n\\section{Definitions of higher-order clustering coefficients}\n\\input{CH3-TXT-definitions}\n\n\\section{Theoretical Analysis}\n\\input{CH3-TXT-theory}\n\n\\section{Empircal Analysis}\n\\label{sec:ccfs_empirical}\n\\input{CH3-TXT-empirical}\n\n\\section{Relating higher-order clustering coefficients to motif conductance through 1-hop neighborhoods}\n\\label{sec:nbrhood_cond}\n\\input{CH3-TXT-neighborhoods}\n\n\\section{Related work and discussion}\n\\input{CH3-TXT-discussion}\n\n\n\n\n\n\n\n\n\\subsection{A formal relationship between 1-hop neighborhoods and motif conductance}\n\\sectionmark{1-hop neighborhoods and motif conductance}\n\\label{sec:nbrhd_thy}\n\\input{CH3-TXT-neighborhoods_theory}\n\n\\subsection{Experiments}\n\\label{sec:nbrhd_exps}\n\\input{CH3-TXT-neighborhoods_experiments}\n\n\n\n\n\\subsection{A method to compute higher-order clustering coefficients}\n\\input{CH3-TXT-complexity}\n\n\\subsection{Probabilistic interpretations}\n\\input{CH3-TXT-probabilistic}\n\n\\subsection{Bounds on higher-order clustering coefficients}\n\\input{CH3-TXT-bounds}\n\n\\subsection{Analysis for the $G_{n, p}$ model}\n\\input{CH3-TXT-er_analysis}\n\n\\subsection{Analysis for the small-world model}\n\\input{CH3-TXT-sw_analysis}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\subsection{General counting framework}\\label{sec:tm_general_framework}\n\nWe begin with a general framework for counting the number of instances of a of a\ntemporal motif $M = (K, \\sigma, \\delta)$.  To start, consider $H$ to\nbe the static directed graph induced by $K$ (i.e., $H$ consists of all\nunique edges in $K$).  A sequence of temporal edges is an instance\nof $M$ if and only if\n\\begin{enumerate}\n\\item the static subgraph induced by the edges in the sequence is isomorphic to $H$\n\\item the ordering of the edges in the sequence matches $\\sigma$,\n\\item all the edges in the sequence span a time window of at most $\\delta$ time units.\n\\end{enumerate}\nThis leads to the following general algorithm for counting instances of $M$ in a\ntemporal graph $T$:\n\\begin{enumerate}\n\\item\nIdentify all instances $H'$ of the static motif $H$ within the static graph $G$\ninduced by the temporal graph $T$.  For example, there are three instances of\n$H$ induced in \\cref{fig:intro1} ($\\{(a, b), (a, c), (c, a)\\}$, $\\{(a, d), (a, c), (c, a)\\}$, and\n$\\{(c, d), (c, a), (a, c)\\}$).\n\\item\nFor each static motif instance $H'$, gather all temporal edges between pairs of\nnodes forming an edge in $H'$ into an ordered sequence $S =$ $(u_1, v_1, t_1)$,\n$\\ldots$, $(u_L, v_L, t_L)$.\n\\item\nCount the number of (potentially non-contiguous) subsequences of edges in $S$\noccurring within $\\delta$ time units that match $(K, \\sigma)$.\n\\end{enumerate}\n\nThe first step can use known algorithms for enumerating motifs in static graphs\nsuch as those by \\citet{wernicke2006fanmod}, and the second step is a simple\nmatter of fetching the appropriate temporal edges.  To perform the third step\nefficiently, we develop a dynamic programming approach for counting the number\nof subsequences (instances of motif $M$) that match a particular pattern within\na larger sequence ($S$).  The key idea is that, as we stream through an input\nsequence of edges, the count of a given length-$l$ pattern (i.e., motif) with a\ngiven final edge is computed from the current count of the length-($l-1$) prefix\nof the pattern.  Inductively, we maintain auxiliary counters of all of the\nprefixes of the pattern (motif).  Second, we also require that all edges in the\nmotif be at most $\\delta$ time apart.  Thus, we use the notion of a moving time\nwindow such that any two edges in the time window are at most $\\delta$ time\napart.  The auxiliary counters now keep track of only the subsequences occurring\nwithin the current time window.  Last, it is important to note that the\nalgorithm only \\emph{counts} the number of instances of motifs rather\nthan \\emph{enumerating} them.  This is critical to making the algorithm fast.\n\n\\input{CH4-ALG-general}\n\nFor simplicity of presentation, \\cref{alg:general} counts \\emph{all} possible\n$l$-edge motifs that occur in a given sequence of edges.  The data structure\n$\\textnormal{counts}[\\cdot]$ maintains auxiliary counts of all (ordered) patterns of length\nat most $l$. Specifically, $\\textnormal{counts}[e_1\\cdots e_r]$ is the number of times the\nsubsequence $[e_1\\cdots e_r]$ occurs in the current time window (if $r < l$) or\nthe number of times the subsequence has occurred within all time windows of\nlength $\\delta$ (if $r = l$).  Crucially, we also assume the keys of $\\textnormal{counts}[\\cdot]$ are\naccessed in order of length.  Moving the time window forward by adding a new\nedge into the window, all edges $(e = (u, v), t)$ farther than $\\delta$ time\nfrom the new edge are removed from the window and the appropriate counts are\ndecremented (the \\emph{DecrementCounts()} method)---first, the single edge\ncounts ($[e]$) are updated. Based on these updates, length-$2$ subsequences\nformed with $e$ as its first edge are updated and so on, up through\nlength-($l-1$) subsequences. On the other hand, when an edge $e$ is added to the\nwindow, similar updates take place, but in reverse order, from longest to\nshortest subsequences, in order to increment counts in subsequences where $e$ is\nthe last edge (the \\emph{IncrementCounts()} method). Importantly, length-$l$\nsubsequence counts are incremented in this step but never decremented.  As the\ntime window moves from the beginning to the end of the sequence of edges, the\nalgorithm accumulates counts of all length-$l$ subsequences in all possible time\nwindows of length $\\delta$.\n\n\\input{CH4-TAB-general-algorithm-example}\n\nWhile \\cref{alg:general} maintains counts for all $l$-edge motifs, we could\nsimply maintain the $\\textnormal{counts}[\\cdot]$ data structure for the contiguous prefixes\nof the motif $M$.  As an example, \\cref{tab:general_alg_example} shows the\nexecution of \\cref{alg:general} for a particular sequence of edges and a particular\nmotif, where counts of only the necessary contiguous subsequences of the motif are maintained.\nIn general, there are $O(l^2)$ contiguous subsequences of an $l$-edge motif $M$,\nand there are $O(\\lvert H \\rvert^l)$ total keys in $\\textnormal{counts}[\\cdot]$, where\n$\\lvert H \\rvert$ is the number of edges in the static subgraph $H$ induced by\n$M$, in order to count all $l$-edge motifs in the sequence (i.e., not just motif\n$M$).\n\nWe now analyze the complexity of the overall 3-step algorithm.  We assume that\nthe temporal graph $T$ has edges sorted by timestamps, which is reasonable if\nedges are logged in their order of occurrence, and we also assume that we have pre-processed\n$T$ so that we can access the sorted list of all edges between $u$ and $v$ in\n$O(1)$ time.  Given an instance $H'$ of $H$, constructing the time-sorted\nsequence $S$ in step 2 of the algorithm then takes\n$O(\\log({\\lvert H \\rvert}) {\\lvert S \\rvert})$\ntime (by merging sorted lists).  Each edge inputted to\n\\cref{alg:general} is processed exactly twice: once to increment counts when\nit enters the time window and once to decrement counts when it exits the time\nwindow.  As presented in \\cref{alg:general}, each update changes $O(\\vert H \\vert^l)$\ncounters resulting in an overall complexity of $O(\\vert H \\vert^l {\\lvert S \\rvert})$.\nHowever, one could modify \\cref{alg:general} to only update counts for\ncontiguous subsequences of the sequence $M$, which would change $O(l^2)$\ncounters and have overall complexity $O(l^2 {\\lvert S \\rvert})$.  We are typically only\ninterested in small constant values of $\\vert H \\rvert$ and $l$ (for our\nexperiments in \\cref{sec:tm_experiments}, $\\lvert H \\rvert \\le 3$ and $l = 3$),\nin which case the running time of \\cref{alg:general} \nis linear in the size of the input to the algorithm, i.e., $O({\\lvert S \\rvert})$.\nWhat remains is to identify all instances $H'$ of $H$.  Of course, this depends\non the structure of $H$.  For example, if $H$ is an edge, this can be done in\nlinear time.  If $H$ is a triangle, this can be done in $O(a \\lvert G \\rvert)$ time,\nwhere $\\lvert G \\rvert$ is the number of edges in the static graph $G$ induced\nby $T$ and $a$ is the arboricity of $G$~\\cite{chiba1985arboricity}.\n\nIn the remainder of this section we analyze our 3-step algorithm with respect to\ndifferent types of motifs (2-node, stars, and triangles) and argue benefits and\ndeficiencies of the proposed framework.  We show that for $2$-node motifs, our\ngeneral counting framework takes time linear in the total number of edges $m$.\nSince all the input data needs to be examined for computing exact counts, this\nmeans the algorithm is optimal for $2$-node motifs. However, we also show that\nfor star and triangle motifs the algorithm is not optimal, which then motivates\nus to design faster algorithms in \\cref{sec:tm_faster_algs}.\n\n\\xhdr{General algorithm for 2-node motifs}\nWe first show how to map $2$-node motifs to the framework described above.  Any\ninduced graph $H$ of a $2$-node $\\delta$-temporal motif is either a single or a\nbidirectional edge.  In either case, it is straightforward to enumerate over all\ninstances of $H$ in the induced static graph.  This leads to the following procedure.\nFor each pair of nodes $u$ and $v$ for which there is at least one edge,\ngather and sort the edges in either direction between $u$ and $v$\nand call \\cref{alg:general} with these edges.  To obtain the total motif count,\nwe simply need to sum the results from each call to \\cref{alg:general}.\n\nWe only need to input each edge to \\cref{alg:general} once, and\nunder the assumption that we can\naccess the sorted directed edges from one node to another in $O(1)$ time, the\nmerging of edges into sorted order takes linear time (merging 2 sorted lists).\nTherefore, the total running time is $O(l^2m)$, where $l$ is the number\nof edges in the motif, which is linear in the number of temporal edges $m$.  \nWe are mostly interested in small patterns, i.e., cases\nwhen $l$ is a small constant.  Thus, this methodology is optimal (linear in the\ninput size, $m$) for counting $2$-node $\\delta$-temporal motif instances.\n\n\\xhdr{General algorithm for star motifs}\nNext, we consider $k$-node, $l$-edge star motifs $M$, whose induced static graph\n$H$ consists of a center node and $k-1$ neighbors, where edges may occur in\neither direction between the center node and a neighbor node.  For example, in\nthe top left corner of \\cref{fig:three_edge_motifs}, $M_{1,1}$ is a star motif\nwith all edges pointing toward the center node (the orange node).  In such\nmotifs, the induced static graph $H$ contains at most $2(k - 1) = 2k - 2$ static\nedges---one incoming and outgoing edge from the center node to each neighbor\nnode.  We have the following method for counting the number of instances of\n$k$-node, $l$-edge star motifs. For each node $u$ in the static graph and for\neach unique set of $k - 1$ neighbors, gather and sort the edges in either\ndirection between $u$ and the neighbors.  Then, count the number of instances of\n$M$ using \\cref{alg:general}.  The counts from each call to \\cref{alg:general}\nare summed over all center nodes and sets of $k - 1$ neighbors.\n\nThe major drawback of this approach is that we have to loop over each\nsize-$(k-1)$ neighbor set.  This can be prohibitively expensive even when $k =\n3$ if the center node has large degree.  In \\cref{sec:tm_faster_algs}, we will\ndesign an algorithm that avoids this issue for the case when the star motif has\n$k = 3$ nodes and $l = 3$ edges.\n\n\\input{CH4-FIG-three-edge-motifs.tex}\n\\clearpage\n\n\\xhdr{General algorithm for triangle motifs}\nWith triangle motifs, the induced graph $H$ consists of 3 nodes and at least one\ndirected edge between any pair of nodes (see \\cref{fig:three_edge_motifs}\nfor all eight of the $3$-edge triangle motifs).  The induced static graph $H$ of $M$\ncontains at least three and at most six static edges.  A straightforward\nalgorithm for counting $l$-edge triangle motifs in a temporal graph $T$ is:\n\\begin{enumerate}\n\\item Use a fast static graph triangle enumeration algorithm to find all\n  triangles in the static graph $G$ induced by $T$ (using, e.g.,\n  one of the methods analyzed by \\citet{latapy2008main}).\n\\item For each triangle, merge all temporal edges from each pair of nodes to\n  get a time-sorted list of edges.  Use \\cref{alg:general} to count the\n  number of instances of $M$.\n\\end{enumerate}\nThis approach is problematic as the edges between a pair of nodes may\nparticipate in many triangles. \\Cref{fig:worstcase} shows a worst-case example\nfor the motif $M = (w, u), (w, v), (u, v)$ with $\\delta = \\infty$.\nIn the figure, the timestamps are ordered by their index. There are\n$m-2n$ edges between $u$ and $v$, and each of these edges forms an instance of\n$M$ with every $w_i$. Thus, the overall worst-case running time of the algorithm\nis $O(\\Delta_{\\textnormal{enum}} + \\min(m\\tau, mn))$, where $\\Delta_{\\textnormal{enum}}$ is the time to enumerate\nthe number of triangles $\\tau$ in the static graph.  (The $mn$ running time comes\nfrom the case that each edge can participate in at most $n$ triangles).\nIn the following section, we devise an algorithm that significantly reduces the dependency on $\\tau$ from\nlinear to sub-linear (specifically, to $O(\\Delta_{\\textnormal{enum}} + \\min(m\\sqrt{\\tau}, mn)$)\nwhen there are $l = 3$ edges.\n\n\\input{CH4-FIG-worstcase}\n\n\n\\subsection{Faster algorithms}\\label{sec:tm_faster_algs}\n\nThe general counting algorithm from the previous section counts the number of\ninstances of any $k$-node, $l$-edge $\\delta$-temporal motif, and is also optimal\nfor $2$-node motifs.  However, the computational cost may be expensive for other\nmotifs such as stars and triangles.  We now develop specialized algorithms that\ncount certain motif classes faster.  Specifically, we design faster algorithms\nfor counting all 3-node, 3-edge star and 3-node, 3-edge triangle motifs\n(\\cref{fig:three_edge_motifs} illustrates these motifs).  Our algorithm for\nstars is linear in the input size, so it is optimal up to constant factors.\n\n\n\n\\xhdr{Fast algorithm for 3-node, 3-edge stars}\nWith $3$-node, $3$-edge star motifs, the drawback of the previous algorithmic\napproach is the need to loop over all pairs of neighbors given a center node.\nInstead, we will count all instances of star motifs for a given center node in\njust a single pass over the edges adjacent to the center node.\n\n\\input{CH4-FIG-star-classes}\n\nWe use a dynamic programming approach for counting star motifs.  First, note\nthat every temporal edge in a star with center $u$ is defined by\n\\begin{enumerate} \n\\item a neighbor node,\n\\item a direction of the edge (outward from or inward toward $u$), and\n\\item the timestamp.\n\\end{enumerate}\nWith this characterization, there are 3 classes of star motifs with 3 nodes and 3 edges\n(illustrated in \\cref{fig:star_classes}).\n\\begin{enumerate}\n\\item ``pre'' -- the first two edges contain node $u$ and neighbor $v$, and the third\nedge contains node $u$ and a different neighbor $w$.\n\\item ``post'' -- the last two edges contain node $u$ and neighbor $w$, and the first\nedge contains node $u$ and a different neighbor $v$.\n\\item ``peri'' -- the first and third edges contain node $u$ and neighbor $v$, and the second\nedge contains node $u$ and a different neighbor $w$.\n\\end{enumerate}\nEach class consists of $2^3 = 8$ motifs corresponding to the different combinations\nof the direction of the edges from $u$ to the neighbors (see \\cref{fig:three_edge_motifs}, which shows all of the $3 \\cdot 8 = 24$ 3-node, 3-edge stars).\n\nNow, suppose we process the time-ordered sequence of all edges containing the center\nnode $u$.  We maintain the following counters when processing an edge with\ntimestamp $t_j$:\n\\begin{itemize}\n\\item $\\textnormal{pre\\_sum}[\\dir1, \\dir2]$ is the number of sequentially ordered pairs of\n  edges in $[t_j - \\delta, t_j)$ where the first edge points in direction\n    $\\dir1$ and the second edge points in direction $\\dir2$.  We can think of a\n    direction as being outward from $u$ or inward toward $u$.\n    \n\\item $\\textnormal{post\\_sum}[\\dir1, \\dir2]$ is the number of sequentially ordered\npairs of edges in $(t_j, t _j + \\delta]$ where the first edge points in\ndirection $\\dir1$ and the second edge points in direction $\\dir2$.\n\n\\item $\\textnormal{peri\\_sum}[\\dir1, \\dir2]$ is the number of pairs of edges where the first\n  edge is in direction $\\dir1$ and occurred at time $t < t_j$, the second edge\n  is in direction $\\dir2$ and occurred at time $t' > t_j$, and $t' - t \\le \\delta$.\n  \n\\end{itemize}\n\nIf we are currently processing an edge, the ``pre'' class gets\n$\\textnormal{pre\\_sum}[\\dir1, \\dir2]$ new motif instances for any choice of directions $\\dir1$\nand $\\dir2$ (specifying the first two edge directions) and the current edge\nserves as the third edge in the motif (hence specifying the third edge\ndirection).  Similar updates are made with the $\\textnormal{post\\_sum}[\\cdot,\\cdot]$ and\n$\\textnormal{peri\\_sum}[\\cdot,\\cdot]$ counters, where the current edge serves as the first\nor second edge in the motif, respectively.\n\nIn order for our algorithm to be fast, we must be able to efficiently update\nthese counters when processing edges.  To aid in this, we introduce two\nadditional counters:\n\\begin{itemize}\n\\item $\\textnormal{pre\\_nodes}[\\textnormal{dir}, v_i]$ is the number of times node $v_i$ has appeared\n  in an edge with $u$ with direction $\\textnormal{dir}$ in the time window $[t_j - \\delta, t_j)$.\n  We can think of the direction as being outward from $u$ to $v_i$ or\n  inward from $v_i$ toward $u$.\n  \n\\item $\\textnormal{post\\_nodes}[\\textnormal{dir}, v_i]$ is the number of times node $v_i$ has appeared\n  in an edge with $u$ with direction $\\textnormal{dir}$ in the time window $(t_j, t_j + \\delta]$.\n\\end{itemize}\n\nFollowing the ideas of \\cref{alg:general}, it is easy to update these counters\nwhen we process a new edge.  Consequently, $\\textnormal{pre\\_sum}[\\cdot,\\cdot]$,\n$\\textnormal{post\\_sum}[\\cdot,\\cdot]$, and $\\textnormal{peri\\_sum}[\\cdot,\\cdot]$ can be maintained when\nprocessing an edge with just a few simple primitives:\n\\begin{itemize}\n\\item\n  \\emph{Push()} and \\emph{Pop()} update the counts for\n  $\\textnormal{pre\\_nodes}[\\cdot,\\cdot]$, $\\textnormal{post\\_nodes}[\\cdot,\\cdot]$,\n  $\\textnormal{pre\\_sum}[\\cdot,\\cdot]$ and $\\textnormal{post\\_sum}[\\cdot,\\cdot]$ when edges enter and leave\n  the time windows $[t_j - \\delta, t_j)$ and $(t_j, t_j + \\delta]$.\n\\item\n  \\emph{ProcessCurrent()} updates motif counts involving the current edge and\n  updates the counter $\\textnormal{peri\\_sum}[\\cdot,\\cdot]$.\n\\end{itemize}\n\nWe describe the general procedure in \\cref{alg:fast_framework}, which calls the\nsubroutines \\emph{Push()}, \\emph{Pop()}, and\n\\emph{ProcessCurrent()}, and \\cref{alg:fast_wedges} implements\nthese subroutines.  The $\\textnormal{pre\\_count}[\\cdot,\\cdot,\\cdot]$,\n$\\textnormal{post\\_count}[\\cdot,\\cdot,\\cdot]$, and $\\textnormal{peri\\_count}[\\cdot,\\cdot,\\cdot]$ counters\nin \\cref{alg:fast_wedges} maintain the counts of the three different classes of\nstars described above.  The edges input to each call of \\cref{alg:fast_wedges}\nassumes that an edge consists of the following two pieces of information:\n\\begin{enumerate}\n \\item the neighbor node $\\textnormal{nbr}$ of $u$ and\n \\item the direction $\\textnormal{dir}$ of the edge.\n\\end{enumerate}\nThe timestamps are all handled in \\cref{alg:fast_framework}.\n\nWe have intentionally separated the logic of\nthe \\emph{Push()}, \\emph{Pop()}, and \\emph{ProcessCurrent()}\nfrom \\cref{alg:fast_framework}.  The reason for this is that our fast $3$-node,\n$3$-edge triangle counting procedure follows the same logic\nof \\cref{alg:fast_framework}, only with different implementations of these\nsubroutines.  We will get to this idea shortly.\n\nFinally, we note that our counting scheme incorrectly includes instances of\n$2$-node motifs such as $M = (u, v_i)$, $(u, v_i)$, $(u, v_i)$, but we can use\nour fast $2$-node motif counting algorithm to account for this.  Putting\neverything together, we have the following procedure:\n\\begin{enumerate}\n\\item For each node $u$ in the temporal graph $T$, get a time-ordered\n  list of all edges containing $u$.\n  \n\\item Use \\cref{alg:fast_framework,alg:fast_wedges} to count\n  star motif instances.\n  \n\\item For each neighbor $v$ of a star center $u$, subtract the 2-node motif\n  counts using \\cref{alg:general}.\n\\end{enumerate}\n\nIf the $m$ temporal edges of $T$ are time-sorted, the first step takes linear\ntime.  The second and third steps also run in linear time in the input size.\nEach edge is used in steps (ii) and (iii) exactly twice: once for each end point\nas the center node.  Thus, the overall complexity of the algorithm is $O(m)$.\nThis is optimal (linear in the size of the dataset).  We also need $O(n)$\nmemory (in addition to storing the graph) to maintain the counters in \\cref{alg:fast_framework}.\n\n\\input{CH4-ALG-fast_framework}\n\n\\input{CH4-ALG-wedges}\n\\clearpage\n\n\\xhdr{Fast algorithm for 3-edge triangle motifs}\nWhile our fast 3-node, 3-edge star counting routine relied on counting motif instances for all\nedges adjacent to a given \\emph{node}, our fast triangle algorithm is based on\ncounting instances for all edges adjacent to a given \\emph{pair of nodes}.\nSpecifically, given a pair of nodes $u$ and $v$ and a list of common neighbors\n$w_1, \\ldots, w_d$, we count the number of motif instances for triangles $(w_i, u, v)$,\n$i = 1, \\ldots, d$.  Given all of the temporal edges in these $d$ static triangles,\nthe counting procedures are nearly identical to the case of stars.\nWe use the same general counting method (\\cref{alg:fast_framework}), but the behavior of the\nsubroutines \\emph{Push()}, \\emph{Pop()}, and \\emph{ProcessCurrent()} depends on\nwhether or not the edge is between $u$ and $v$.\n\n\\input{CH4-ALG-triad_subroutine}\n\nThese methods are implemented in \\cref{alg:fast_triangles}.  The input\nis a list of edges adjacent to a given pair of neighbors $u$ and $v$, where each\nedge consists of three pieces of information:\n\\begin{enumerate}\n \\item a neighbor node $\\textnormal{nbr}$,\n \\item an indicator of whether or not the node $\\textnormal{nbr}$ connects to node $u$ or node $v$, and\n \\item the direction $\\textnormal{dir}$ of the edge.\n\\end{enumerate}\n\nThe node counters ($\\textnormal{pre\\_nodes}[\\cdot,\\cdot,\\cdot]$ and\n$\\textnormal{post\\_nodes}[\\cdot,\\cdot,\\cdot]$) in \\cref{alg:fast_triangles} have an extra\ndimension compared to \\cref{alg:fast_wedges} to indicate whether the counts\ncorrespond to edges containing node $u$ or node $v$ (denoted by ``$\\textnormal{u\\_or\\_v}$'').\nFor example, $\\textnormal{pre\\_nodes}[u, \\textnormal{dir}, w_i]$ is the number of times node $w_i$ has\nappeared in an edge with $u$ with directed $\\textnormal{dir}$ (incoming to $u$ or outgoing\nfrom $u$) in the time window $[t_j - \\delta, t_j)$.  Similarly, the sum counters\n($\\textnormal{pre\\_sum}[\\cdot,\\cdot,\\cdot]$, $\\textnormal{peri\\_sum}[\\cdot,\\cdot,\\cdot]$ and\n$\\textnormal{post\\_sum}[\\cdot,\\cdot,\\cdot]$) have an extra dimension to denote if the first\nedge is incident on node $u$ or node $v$.  For example,\n$\\textnormal{pre\\_sum}[u, \\dir1, \\dir2]$ is the number of sequentially ordered pairs of edges\ncontaining some node $w_i$ in the time window $[t_j - \\delta, t_j)$, where the\nfirst edge is adjacent to $u$ in direction $\\dir1$ and the second edge is\nadjacent to $v$ in direction $\\dir2$.\n\n\\input{CH4-ALG-triad_main}\n\\clearpage\n\nRecall that the problem with counting triangle motifs by the general framework\nin \\cref{alg:general} is that a pair of nodes with many edges might have to be\ncounted for many triangles in the graph.  However, with\n\\cref{alg:fast_triangles}, we can simultaneously count all triangles\nadjacent to a given pair of nodes.  What remains is that we must assign each\ntriangle in the static graph to a pair of nodes.  Here, we propose to assign\neach triangle to the pair of nodes in that triangle containing the largest\nnumber of edges (this is sketched in \\cref{alg:triangle}).  The core\nidea of this assignment procedure is that we should simultaneously\nprocess as many triangles as possible for pairs of nodes with many\nedges. The following theorem says that this is faster than simply counting for\neach triangle (described in \\cref{sec:tm_general_framework}).  Specifically, we\nreduce $O(\\Delta_{\\textnormal{enum}} + \\min(m\\tau, mn))$ complexity to $O(\\Delta_{\\textnormal{enum}} + \\min(m\\sqrt{\\tau}, mn))$, where\n$\\tau$ is the number of triangles in the graph.\n\n\\begin{theorem}\\label{thm:fast_triangles}\nIn the worse case, \\cref{alg:triangle} runs in time\n$O(\\Delta_{\\textnormal{enum}} + \\min(m\\sqrt{\\tau}, mn))$\nwhere $\\Delta_{\\textnormal{enum}}$ is the time to enumerate all triangles in the static graph\n$G$, $m$ is the total number of temporal edges, $n$ is the number of nodes, and\n$\\tau$ is the number of static triangles in $G$.\n\\end{theorem}\n\\begin{proof}\n\nLet $\\rho_e$ be the number of temporal edges along the static edge $e$, and\nlet $z_e \\ge 1$ be the number of times that timestamps along this static edge\nare used in a call to \\cref{alg:fast_triangles} by\n\\cref{alg:triangle}.  Since \\cref{alg:fast_triangles} runs in\nlinear time in the number of edges in its input, the total running time is on\nthe order of $\\sum_{e}\\rho_ez_e$.  Each static edge appears in at\nmost $n$ triangles and has at most $m$ temporal edges, so $\\sum_{e}\\rho_ez_e \\le mn$.\nWe now consider the case when $\\sqrt{\\tau} \\le n$.\n\nThe $\\rho_e$ are fixed, and we wish to find the values of $z_e$ that maximize\nthe summation.  Without loss of generality, write $\\{\\rho_e\\}$ by\n$\\rho_1 \\ge \\rho_2 \\ge \\ldots \\ge \\rho_r$, where $r$ is the number of\nstatic edges in the static graph induced by the temporal graph.  Consequently,\n$z_i \\le i$, $i = 1, \\ldots, r$.  There are $\\tau$ static triangles,\nso \\cref{alg:fast_triangles} will look at the timestamps along $3\\tau$ static\nedges.  Thus, $\\sum_{i}z_i \\le 3\\tau$.  The summation\n$\\sum_{i=1}^{r}\\rho_iz_i$ is maximized when $z_1 = 1$, $z_2 = 2$, and so on up\nto some index $J = O(\\sqrt{\\tau})$ for which\n$\\sum_{i=1}^{J}z_i = \\sum_{i=1}^{J}i = 3\\tau$.\nNow given that the $z_i$ are fixed and the $\\rho_i$\nare ordered, the summation is maximized when\n$\\rho_1 = \\rho_2 = \\ldots = \\rho_j = m \/ j$.\nIn this case,\n\\[\n\\sum_{i}\\rho_iz_i \n= \\sum_{i=1}^{J}\\frac{m}{J} \\cdot i \n= \\frac{m}{J}\\sum_{i=1}^{J} \n= O\\left(\\frac{m}{J} \\cdot J^2\\right) \n= O(m\\sqrt{\\tau}).\n\\]\n\\end{proof}\n\n\\input{CH4-FIG-fast-worstcase}\n\nWe now show a worst-case example for the algorithm, which\nis illustrated in \\cref{fig:fast_worstcase}.\nThe graph consists of $k + 1$ nodes $u$, $v_1$, $\\ldots$, $v_k$, and the\nstatic edges are $(v_i, v_j)$, $1 \\le i < j \\le k$, and $(v_r, u)$, $1 \\le r \\le k$.\nEach edge $(v_i, v_j)$ has a single temporal timestamp, and each edge $(v_i, u)$\nhas an equal number of timestamps.  Without loss of generality, the first\n$k$ edges in the ordering of the static edges is $\\rho_1 = (v_1, u)$, $\\rho_2 = (v_2, u)$,\n$\\ldots$, $\\rho_k = (v_k, u)$ (the remainder of the ordering is arbitrary).\nFinally, suppose that we are counting the motif $M = (a, b), (a, c), (b, c)$.  \n\nIn this case, the call to the \\cref{alg:fast_triangles} subroutine for edge $(v_r, u)$ ($1 \\le r \\le k$)\nin \\cref{alg:triangle} processes temporal edges along $(v_r, v_2)$, $\\ldots$, $(v_r, v_k)$\nand $(v_r, u)$, $\\ldots$, $(v_k, u)$.  Each temporal edge along $(v_i, v_j)$ is processed\nonly once, and the temporal edges along $(v_r, u)$ are processed $r$ times.  Thus, the\ntotal number of temporal edges processed is\n\\begin{align*}\n{k \\choose 2} + \\sum_{r = 1}^{k}r\\frac{m - {k \\choose 2}}{k}\n= O(k^2) + O(mk)\n= O(\\tau + m\\sqrt{\\tau}).\n\\end{align*}\n\nIn this case, \\cref{alg:general} has the same asymptotic running time.  Each of\nthe $O(k^2)$ static triangles contains $O(m \/ k)$ temporal edges.\n\nFinally, we emphasize that, if we ignore the pre-processing time in \\cref{alg:fast_triangles},\nthe amount of computation in \\cref{alg:fast_triangles}\nis always less than the computation done by \\cref{alg:general}\nfor counting triangles.  Thus, regardless of the asymptotics,\n\\cref{alg:fast_triangles} is still a strict improvement over the general algorithm.\n\n\n\\subsection{Data}\\label{sec:tm_data}\n\n\\input{CH4-TAB-network-descriptions}\n\nWe gathered a variety of datasets in order to study the patterns of\n$\\delta$-temporal motifs in several domains.  The datasets are described below\nand summary statistics are in \\cref{tab:datasets}.  The time resolution of the\nedges in all datasets is one second.\n\n\\begin{itemize}\n\\item $\\dataset{email-Eu}$\\footnote{This is the same network as $\\dataset{email-Eu-core}$\nin \\cref{sec:local_real}, but we are now using the temporal information.}\nis a collection of emails between members of a European\nresearch institution~\\cite{leskovec2007graph}.  An edge $(u, v, t)$ signifies\nthat person $u$ sent person $v$ an email at time $t$.\n\n\\item $\\dataset{Phonecall-Eu}$ was constructed from telephone call records for a major European\nservice provider.  An edge $(u, v, t)$ signifies that person $u$ called person\n$v$ starting at time $t$.\n\n\\item $\\dataset{SMS-A}$ is a collection of short messaging service (SMS) texting\nrecords from a company charging account~\\cite{wu2010evidence}.\nIn this dataset, an edge $(u, v, t)$ means that person $u$ sent\nan SMS message to person $v$ at time $t$.\n\n\\item $\\dataset{CollegeMsg}$ is comprised of private messages sent on an online social network\nat the University of California, Irvine~\\cite{panzarasa2009patterns}.  Users\ncould search the network for others and then initiate conversation based on\nprofile information.  An edge $(u, v, t)$ means that user $u$ sent a private\nmessage to user $v$ at time $t$.\n\n\\item $\\dataset{StackOverflow}$ is constructed from communication on Stack Overflow.\nOn stack exchange web sites, users post questions and receive answers from other\nusers, and users may comment on both questions and answers.  We derive a\ntemporal network by creating an edge $(u, v, t)$ if, at time $t$, user $u$: (1)\nposts an answer to user $v$'s question, (2) comments on user $v$'s question, or\n(3) comments on user $v$'s answer.  We formed the temporal network from the\nentirety of Stack Overflow's history up to March 6, 2016.\n\n\\item $\\dataset{Bitcoin}$ consists of all payments made with the decentralized\ndigital currency and payment system Bitcoin up to October 19, 2014~\\cite{kondor2014rich}.\nNodes in the network correspond to Bitcoin addresses, and an individual may have\nseveral addresses.  An edge $(u, v, t)$ signifies that bitcoin was transferred\nfrom address $u$ to address $v$ at time $t$.  \n\n\\item $\\dataset{FBWall}$ consists of wall posts between users on the social network\nFacebook located in the New Orleans region~\\cite{viswanath2009evolution}.  Any friend of\na given user can see all posts on that user's wall, so communication is public\namong friends.  An edge $(u, v, t)$ means that user $u$ posted on user $v$'s\nwall at time $t$.\n\n\\item $\\dataset{WikiTalk}$ represents edits on user talk pages on\nWikipedia~\\cite{leskovec2010governance}.  An edge $(u, v, t)$ means that\nuser $u$ edited user $v$'s talk page at time $t$.\n\n\\item $\\dataset{Phonecall-ME}$ is constructed from phone call records of a large\ntelecommunications service provider in the Middle East.  An edge $(u, v, t)$ \nmeans that user $u$ initiated a call to user $v$ at time $t$.\n\n\\item $\\dataset{SMS-ME}$ is constructed from SMS texting records from the same\ntelecommunications service provider in the Middle East.\nAn edge $(u, v, t)$ means that user $u$ sent an\nSMS message to user $v$ at time $t$.\n\\end{itemize}\n\n\\subsection{Empirical observations of motif counts}\\label{sec:tm_empirical}\n\nWe first examine the distribution of 2- and 3-node, 3-edge motif instance counts\nfrom 8 of the datasets described in \\cref{sec:tm_data} with $\\delta = 1$ hour\n(\\cref{fig:raw_counts}).  We choose 1 hour for the time window as this is close\nto the median time for a node to take part in three edges in most of our\ndatasets. We make a few empirical observations uniquely available due to\ntemporal motifs and provide possible explanations for these observations.\n\n\\input{CH4-FIG-raw-counts}\n\\clearpage\n\n\n\\input{CH4-FIG-blocking}\n\\xhdr{Blocking communication}\nIf an individual typically waits for a reply from one individual before\nproceeding to communicate with another individual, we consider it a\n\\emph{blocking} form of communication. A typical conversation between two\nindividuals characterized by fast exchanges happening back and forth is blocking\nas it requires complete attention of both individuals. We capture this\nbehavior in the ``blocking motifs'' $M_{5,1}$, $M_{5,2}$ and $M_{6,2}$, which\ncontain 3 edges between two nodes with at least one edge in either direction\n(\\cref{fig:blocking}, left).  However, if the reply doesn't arrive soon,\nwe might expect the individual to communicate with others without waiting for a\nreply from the first individual. This is a non-blocking form of communication\nand is captured by the ``non-blocking motifs'' $M_{4,1}$, $M_{4,3}$ and $M_{6,3}$\nhaving edges originating from the same source but directed to different\ndestinations (\\cref{fig:blocking}, right)\n\nThe fractions of counts corresponding to the blocking and non-blocking motifs\nout of the counts for all 36 motifs in \\cref{fig:three_edge_motifs}\nuncover several interesting characteristics in communication networks ($\\delta =\n1$ hour; see \\cref{fig:blocking}). In $\\dataset{FBWall}$ and $\\dataset{SMS-A}$, blocking\ncommunication is vastly more common, while in $\\dataset{email-Eu}$ non-blocking\ncommunication is prevalent.  Email is not a dynamic method of\ncommunication and replies within an hour are rare.  Thus, we would expect\nnon-blocking behavior.  Interestingly, the $\\dataset{CollegeMsg}$ dataset shows both\nbehaviors as we might expect individuals to engage in multiple conversations\nsimultaneously.  In complete contrast, the $\\dataset{Phonecall-Eu}$ dataset shows neither\nbehavior.  A simple explanation is that that a single edge (a phone call)\ncaptures an entire conversation and hence blocking behavior does not emerge.\n\n\\input{CH4-FIG-switching}\n\\xhdr{Cost of switching}\nAmongst the non-blocking motifs discussed above, $M_{4,1}$ captures two\nconsecutive ``switches'' between pairs of nodes whereas $M_{4,3}$ and $M_{6,3}$ each\nhave a single switch (\\cref{fig:switching}, right). In communication networks, a switch\ncorresponds to a change in message destination for a node $u$.  Prevalence of\n$M_{4,1}$ indicates a lower cost of switching targets, whereas prevalence of the\nother two motifs are indicative of a higher cost.  We observe in\n\\cref{fig:switching} that the ratio of 2-switch to 1-switch motif counts\nis the least in $\\dataset{StackOverflow}$, followed by $\\dataset{WikiTalk}$, $\\dataset{CollegeMsg}$ and then\n$\\dataset{email-Eu}$. On Stack Overflow and Wikipedia talk pages, there is a high\ncost to switch targets because of peer engagement and depth of discussion.  On the other\nhand, in the $\\dataset{CollegeMsg}$ dataset there is less cost to switch because it\nlacks depth of discussion within the time frame of $\\delta = $ 1 hour.\nIn $\\dataset{email-Eu}$, there is almost no peer engagement, and cost of switching is\nnegligible.\n\n\\input{CH4-FIG-cycles}\n\\xhdr{Cycles in $\\dataset{Bitcoin}$}\nOf the eight $3$-edge triangle motifs, $M_{2,4}$ and $M_{3,5}$ are cyclic, i.e.,\nthe target of each edge serves as the source of another edge.\\footnote{By ``cyclic''\nwe do not mean that the temporal edges must form a cycle.  Rather, the multigraph\n$K$ in the formal motif definition is a cycle.}  We observe in\n\\cref{fig:cycles} that the fraction of triangles that are cyclic is much higher in\n$\\dataset{Bitcoin}$ compared to any other dataset.\nThis can be attributed to the transactional nature of $\\dataset{Bitcoin}$ where\nthe total amount of bitcoin is limited. Since remittance (outgoing edges) is typically associated\nwith earnings (incoming edges), we should expect cyclic behavior.\n\n\n\n\\input{CH4-FIG-stackoverflow-time}\n\\xhdr{Motif counts at varying time scales}\nWe now explore how motif counts change at different time scales.  For the\n$\\dataset{StackOverflow}$ dataset we counted the number of instances of $2$- and\n$3$-node, $3$-edge $\\delta$-temporal motifs for $\\delta = $ 60, 300, 1800, and\n3600 seconds (\\cref{fig:so_counts_over_time}).  These counts determine the\nnumber of motifs that completed in the intervals\n[0, 60], (60, 300], (300, 1800s], and (1800, 3600] seconds\n(e.g., subtracting 60 second counts from 300 second counts gives the interval (60, 300]).\nObservations at smaller timescales reveal phenomenon which start to get eclipsed\nat larger timescales.  For instance, on short time scales, motif $M_{1,1}$\n(\\cref{fig:so_counts_over_time}, top-left corner) is quite common.  We\nsuspect this arises from multiple, quick comments on the original question, so\nthe original poster receives many incoming edges.  At larger time scales, this\nbehavior is still frequent but relatively less so.  Now let us compare counts\nfor $M_{1,5}$, $M_{1,6}$, $M_{2,5}$, $M_{2,6}$ (the four in the top right\ncorner) with counts for $M_{3,3}$, $M_{3,4}$, $M_{4,3}$, $M_{4,4}$ (the four in\nthe center). The former counts likely correspond to conversations with the\noriginal poster while the latter are constructed by the same user interacting with\nmultiple questions.  Between 300 and 1800 seconds (5 to 30 minutes),\nthe former counts are relatively more common while the latter counts only become\nmore common after 1800 seconds. A possible explanation is that the typical\nlength of discussions on a post is about 30 minutes, and later on, users answer\nother questions.\n\n\\input{CH4-FIG-collegemsg}\n\nNext, we examine messaging behavior in the $\\dataset{CollegeMsg}$ dataset at fine-grained\ntime intervals.  We counted the number of motifs consisting of a single node\nsending three outgoing messages to one or two neighbors (motifs $M_{6,1}$,\n$M_{6,3}$, $M_{4,1}$, and $M_{4,3}$) in the time bins $[10(i-1), 10i)$ seconds,\n$i = 1, \\ldots, 500$ (\\cref{fig:IM_over_time}).  We first notice that at\nsmall time scales, the motif consisting of three edges to a single neighbor\n($M_{6,1}$) occurs frequently.  This pattern could emerge from a succession of\nquick introductory messages.  Overall, motif counts increase from roughly 1\nminute to 20 minutes and then decline.  After 5 minutes, counts\nfor the three motifs with one switch in the target ($M_{6,1}$, $M_{6,3}$, and\n$M_{4,3}$) grow at a faster rate than the counts for the motif with two switches\n($M_{4,1}$).  As mentioned above, this pattern could emerge from a tendency to\nsend several messages in one conversation before switching to a conversation\nwith another friend.\n\n\\subsection{Algorithm scalability}\\label{sec:tm_scalability}\n  \nFinally, we performed scalability experiments of our algorithms.  All algorithms\nwere implemented in C++, and all experiments ran using a single thread of a\n2.4GHz Intel Xeon E7-4870 processor.  We did not measure the time to load\ndatasets into memory, but our timings include all pre-processing time needed by\nthe algorithms (e.g., the triangle counting algorithms first find triangles in\nthe static graph).  We emphasize that our implementation is single threaded, and\nthere is ample room for parallelism in our algorithms.\n\n\\input{CH4-TAB-triangle-speedups}\n\nFirst, we used both the general counting method (\\cref{alg:general}) and the\nfast counting method (\\cref{alg:triangle}) to count the number of all eight\n3-edge $\\delta$-temporal triangle motifs in our datasets ($\\delta =$ 1 hour).\n\\Cref{tab:scalability} reports the running times of the algorithms for all\ndatasets with at least one million triangles in the static graph. For all of\nthese datasets, our fast temporal triangle counting algorithm provides\nsignificant performance gains over the general counting method, ranging between\na 1.29x and a 56.5x speedup.  The gains of the fast algorithm are the largest\nfor $\\dataset{Bitcoin}$, which is due to some pairs of nodes having many edges between\nthem and also participating in many triangles.\n\n\\input{CH4-FIG-scalability}\n\nSecond, we measured the time to count various $3$-edge $\\delta$-temporal motifs\nin our largest dataset, $\\dataset{Phonecall-ME}$.  Specifically, we measured the time to\ncompute (1) $2$-node motifs, (2) $3$-node stars, and (3) triangles on the first\n$k$ million edges in the dataset for $k = 250, 500, \\ldots, 2000$\n(\\cref{fig:scalability}).  The time to compute the $2$-node, $3$-edge motifs and\nthe $3$-node, $3$-edge stars scales linearly, as expected from our complexity\nanalysis.  The time to count triangle motifs grows superlinearly and becomes the\ndominant cost when there is a large number of edges.  For practical purposes,\nthe running times are quite modest.  With two billion edges, our methods take\nless than 3.5 hours to complete (executing sequentially).\n\n\n\n\n\\chapter{Motifs in temporal networks}\n\\label{ch:tm}\n\\chaptermark{Motifs in temporal networks}\n\n\\section{Analyzing network data with timestamped edges}\n\\label{sec:tm_introduction}\n\\input{CH4-TXT-introduction}\n\n\\section{Definitions of temporal networks and temporal motifs}\n\\label{sec:tm_preliminaries}\n\\input{CH4-TXT-preliminaries}\n\n\\section{Counting algorithms}\n\\label{sec:tm_algorithms}\n\\input{CH4-TXT-algorithms}\n\n\\section{Experiments}\n\\label{sec:tm_experiments}\n\\input{CH4-TXT-experiments}\n\n\\section{Prior definitions of temporal motifs and other related work}\n\\sectionmark{Prior definitions and related work}\n\\label{sec:tm_related}\n\\input{CH4-TXT-related}\n\n\\section{Discussion}\n\\label{sec:tm_discussion}\n\\input{CH4-TXT-discussion}\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{\\bf Introduction }\n\\label{sec:introduction}\nIn recent years, random graph theory has been applied to model many complex real-world phenomena. A basic random graph used to model complex networks is the \\gls{ER} graph \\cite{erdos1959random}, where edges between the nodes appear with equal probabilities.  In \\cite{gilbert1961random}, the author introduces another random graph called \\gls{RGG} where nodes have some random position in a metric space and the edges are determined by the position of these nodes.  Since then, \\gls{RGG}  properties have been widely studied \\cite{penrose2003random}.\n\n \\glspl{RGG} are very useful to model problems in which the geographical distance is a critical factor.  For example, {\\glspl{RGG}} have been applied to wireless communication network \\cite{bettstetter2002minimum}, sensor network \\cite{yick2008wireless} and to study the dynamics of a viral spreading in a specific network of interactions  \\cite{preciado2009spectral}, \\cite{ganesh2005effect}.  Another motivation for \\glspl{RGG} in arbitrary dimensions is multivariate statistics of high-dimensional data. In this case, the coordinates of the nodes can represent the attributes of the data. Then, the metric imposed by the \\gls{RGG} depicts the similarity between the data.\n\nIn this work,  the \\gls{RGG} is constructed by considering a finite set $\\mathcal{X}_{n}$ of $n$ nodes, $x_{1},...,x_{n},$ distributed uniformly and independently on the $d$-dimensional torus $\\mathbb{T}^d \\equiv [0, 1]^d$. We choose a torus instead of a cube in order to avoid boundary effects. Given a geographical distance, $r_{n} >0 $, we form a graph by connecting two nodes $x_{i}, x_{j} \\in \\mathcal{X}_{n}$  if their $\\ell_{p}$-distance, $p \\in [1, \\infty]$ is at most $r_{n}$, i.e., $\\|x_{i}-x_{j} \\|_{p} \\leq r_{n}$, where $\\|.\\|_{p}$ is the $\\ell_{p}$-metric defined as\n\\begin{equation*}\n\\small\n\\label{eqq1}\n\\| x_{i}- x_{j} \\|_{p} =\\left\\{\n\\begin{array}{ll}\n \\left(  \\sum_{k=1}^d \\vert x_{i}^{(k)}-x_{j}^{(k)}\\vert^p \\right)^{1\/p} &   p \\in [1, \\infty),\\\\ \n \\max\\lbrace \\vert x_{i}^{(k)}-x_{j}^{(k)}\\vert, \\ k \\in [1, d]  \\rbrace & p=\\infty.\n    \\end{array}\n\\right. \n\\end{equation*}\n\nThe \\gls{RGG} is denoted by $G(\\mathcal{X}_{n}, r_{n})$.  Note that for the case $p=2$ we obtain the Euclidean metric on $\\mathbb{R}^d$.   Typically, the function $r_{n}$ is chosen such that $r_{n}\\rightarrow 0$ when $n \\rightarrow \\infty$. \n\n\nThe degree of a vertex in $G(\\mathcal{X}_{n}, r_{n})$ is the number of edges connected to it.  The average vertex degree in $G(\\mathcal{X}_{n}, r_{n})$ is given by \\cite{penrose2003random}\n\\begin{equation*}\na_{n} = \\theta^{(d)} nr_{n}^d,\n\\end{equation*} \nwhere $\\theta^{(d)}=\\pi^{d\/2}\/\\Gamma(d\/2+1)$ denotes the volume of the $d$-dimensional unit hypersphere in $\\mathbb{T}^d$ and $\\Gamma(.)$ is the Gamma function. \n\nDifferent values of $r_{n}$, or equivalently $a_{n}$, lead to different geometric structures in \\glspl{RGG}. In \\cite{penrose2003random}, different interesting regimes are introduced: the \\textit{connectivity regime} in which $a_{n}$ scales as $\\log(n)$ or faster, i.e., $\\Omega(\\log(n))$\\footnote{The notation $f(n) =\\Omega(g(n))$ indicates that $f(n)$ is bounded below by $g(n)$ asymptotically, i.e., $\\exists K>0$ and $ n_{o} \\in \\mathbb{N}$ such that $\\forall n > n_{0}$ $f(n) \\geq K g(n)$.},  the  \\textit{thermodynamic regime} in which $a_{n}\\equiv \\gamma$, for $\\gamma >0$ and the \\textit{dense regime}, i.e., $a_{n}\\equiv \\Theta(n).$ \n\n\n\\glspl{RGG} can be described by a variety of random matrices such as adjacency matrices, transition probability matrices and normalized Laplacian. The spectral properties of those random matrices are powerful tools to predict and analyze complex networks behavior.  In this work, we  give a special attention to the \\gls{test} of the adjacency matrix of \\glspl{RGG}  in the connectivity regime.\n\n\nSome works analyzed the spectral properties of \\glspl{RGG} in different regimes. In particular, in the thermodynamic regime, the authors in \\cite{bordenave2008eigenvalues}, \\cite{blackwell2007spectra} show that the spectral measure of the adjacency matrix of \\glspl{RGG} has a limit as $n \\to \\infty$. However, due to the difficulty to compute exactly this spectral measure,  Bordenave in \\cite{bordenave2008eigenvalues} proposes an approximation for it as $\\gamma \\rightarrow \\infty$.\n\n In the connectivity regime, the work in \\cite{preciado2009spectral} provides a closed form expression for the asymptotic spectral moments of the adjacency matrix of $G(\\mathcal{X}_{n}, r_{n})$. Additionnaly,  Bordenave in \\cite{bordenave2008eigenvalues} characterizes the spectral measure of the adjacency matrix normalized by $n$ in the dense regime. However, in the connectivity regime and as $n\\rightarrow \\infty$,  the normalization factor $n$ puts to zero all the eigenvalues of the adjacency matrix that are finite and only the infinite eigenvalues in the adjacency matrix are nonzero in the normalized adjacency matrix. Motivated by this results, in this work we analyze the behavior of the eigenvalues of the adjacency matrix  without normalization in the connectivity regime and in a wider range of the connectivity regime.\n\n\nFirst, we propose an approximation for the actual \\gls{test} of the \\gls{RGG}. Then, we provide a bound on the Levy distance between this approximation and the actual distribution. More precisely, for $\\epsilon>0$ we show that the \\glspl{test} of the adjacency matrices of the \\gls{RGG} and the \\gls{DGG} with nodes in a grid converge to the same limit when $a_{n}$ scales as $\\Omega (\\log^{\\epsilon}(n)\\sqrt{n})$ for $d=1$ and as $\\Omega (\\log^{2}(n))$ for $d\\geq 2$. \nThen, under the $\\ell_{\\infty}$-metric we provide an analytical approximation for the eigenvalues of the adjacency matrix of \\glspl{RGG} by taking the $d$-dimensional discrete Fourier transform (DFT) of an $n=\\mathrm{N}^{d}$ tensor of rank $d$ obtained from the first block row of the adjacency matrix of the \\gls{DGG}.\n\nThe rest of this paper is organized as follows.  In Section \\ref{sec:systemmodel} we describe the model, then we present our main results on the concentration of the \\gls{test} of large \\glspl{RGG} in  the connectivity  regime.  Numerical results are given in Section \\ref{sec:results} to validate the theoretical results. Finally, conclusions are given in Section \\ref{sec:conclusion}.\n\\begin{comment}\n\\begin{figure*}[!t]\n\\centering\n\\subfloat[Thermodynamic regime]{\\includegraphics[width=2.1in]{thermodynamic}%\n\\label{fig_first_case}}\n\\hfil\n\\subfloat[Connectivity regime]{\\includegraphics[width=2.1in]{connected}%\n\\label{fig_second_case}}\n\\caption{An illustration of an \\gls{RGG} on a torus with $n=200$ nodes with a connection radius $r_{n}$= $0.02$ in (a) and $r_{n}$= $0.1$ in (b). }\n\\label{fig_RGG1}\n\\end{figure*}\n\n\\end{comment}\n\\section{\\bf\\bf Spectral Analysis of \\glspl{RGG}}\n\\label{sec:systemmodel} \nTo study the spectrum of $G(\\mathcal{X}_{n}, r_{n})$ we introduce an auxiliary graph called the \\gls{DGG}. The \\gls{DGG} denoted by $G(\\mathcal{D}_{n}, r_{n})$ is formed by letting $\\mathcal{D}_{n}$ be the set of $n$ grid points that are at the intersections of axes parallel hyperplanes with separation $n^{-1\/d}$, and connecting two points $x'_{i}$, $x'_{j}$ $\\in \\mathcal{D}_{n}$ if $\\|x'_{i}-x'_{j} \\|_{p} \\leq r_{n}$ with $p\\in [1, \\infty]$. Given two nodes, we assume that there is always at most one edge between them. There is no edge from a vertex to itself. Moreover,  we assume that the edges are not directed. \n \n  Let $\\mathbf{A}(\\mathcal{X}_{n})$  be the  adjacency matrix of $G(\\mathcal{X}_{n}, r_{n})$, with entries \n\\begin{equation*}\n\\mathbf{A}(\\mathcal{X}_{n})_{i j}=\\chi [x_{i} \\sim x_{j}],\n\\label{RW}\n\\end{equation*}\nwhere the term $\\chi[x_{i}\\thicksim x_{j}] $ takes the value 1 when there is a connection between nodes $x_{i}$ and $x_{j}$ in $G(\\mathcal{X}_{n}, r_{n})$ and zero otherwise, represented as\n\\begin{equation*}\n\\label{eqq1}\n\\chi[x_{i}\\thicksim x_{j}] =\\left\\{\n    \\begin{array}{ll}\n        1, &  \\| x_{i} - x_{j}\\|_{p} \\leq r_{n}, \\ \\ i \\neq j,  \\ \\ p \\in [1, \\infty]\\\\\n       0, & \\mathrm{otherwise}.\n    \\end{array}\n\\right.\n\\end{equation*}\n\nA similar definition holds for $\\mathbf{A}(\\mathcal{D}_{n})$ defined over $G(\\mathcal{D}_{n}, r_{n})$. The matrices $\\mathbf{A}({\\mathcal{X}_{n}})$  and $\\mathbf{A}({\\mathcal{D}_{n}})$ are symmetric and their spectrum consists of real eigenvalues. We denote by $\\lbrace \\lambda_{i}, i=1,..,n \\rbrace$ and $\\lbrace \\mu_{i}, i=1,..,n \\rbrace$ the sets of all real eigenvalues of the real symmetric square matrices $\\mathbf{A}({\\mathcal{D}_{n}})$  and $\\mathbf{A}({\\mathcal{X}_{n}})$ of order $n$, respectively.\nThe empirical spectral distribution functions $v_{n}(x)$ and $v'_{n}(x)$ of the adjacency matrices of an \\gls{RGG} and a \\gls{DGG}, respectively  are defined as\n\\begin{equation*}\nv_{n}(x)=\\dfrac{1}{n} \\sum\\limits_{i=1}^n \\mathrm{I}\\lbrace \\mu_{i} \\leq x\\rbrace \\ \\ \\mathrm{and }\\  \\ \\ v'_{n}(x)=\\dfrac{1}{n} \\sum\\limits_{i=1}^n \\mathrm{I}\\lbrace \\lambda_{i}\\leq  x\\rbrace,\n\\end{equation*}\nwhere $\\mathrm{I}\\lbrace \\mathrm{B} \\rbrace$ denotes the indicator of an event $\\mathrm{B}$.\n\nLet $a'_{n}$ be the degree of the nodes in $G(\\mathcal{D}_{n}, r_{n})$. In the following Lemma \\ref{bound}  we provide an upper bound for $a'_{n}$ under any $\\ell_{p}$-metric.\n\n\\begin{lemma}\n\\label{bound}\n For any chosen $\\ell_{p}$-metric with $p \\in [1,\\infty]$ and $d\\geq1$, we have\n\\begin{equation*}\na'_{n} \\leq d^{\\frac{1}{p}}2^{d}a_{n}  \\left( 1+\\frac{1}{2a_{n}^{1\/d}}\\right)^d.\n\\end{equation*}\n\\end{lemma}\n\\begin{proof}\nSee Appendix \\ref{app:bound}\n\\end{proof}\n\nTo prove our result on the concentration of the \\gls{test} of \\glspl{RGG} and investigate its relationship with the \\gls{test} of \\glspl{DGG} under any $\\ell_{p}$-metric, we use the Levy distance between two distribution functions defined as follows.\n \n\\begin{definition}(\\cite{taylor2012introduction}, page 257)\nLet $v_{n}^A$ and $v_{n}^B$ be two distribution functions on $\\mathbb{R}$. The Levy distance $L(v_{n}^A, v_{n}^B)$ between them is the infimum of all positive $\\epsilon$ such that, for all $x \\in \\mathbb{R}$ \n\\begin{equation*}\nv_{n}^A(x-\\epsilon) -\\epsilon \\leq v_{n}^B(x)\\leq v_{n}^A(x+\\epsilon)+\\epsilon.\n\\end{equation*}\n\\end{definition}\n\n\\begin{lemma}(\\cite{bai2008methodologies}, page 614)\n\\label{Difference Inequality}\nLet A and B be two $n$ $\\times$ $n$ Hermitian matrices with eigenvalues $\\lambda_{1},...,\\lambda_{n}$ and $\\mu_{1},...,\\mu_{n}$, respectively. Then\n\\begin{equation*}\nL^{3}(v_{n}^A, v_{n}^B) \\leqslant \\dfrac{1}{n}tr(A-B)^2,\n\\end{equation*}\nwhere $L(v_{n}^{A},v_{n}^{B})$ denotes the Levy distance between the empirical distribution functions $v_{n}^{A}$ and $v_{n}^{B}$ of the eigenvalues of $A$ and $B$, respectively.\n\\end{lemma}\n\n\nLet $\\mathrm{M}_{n}$ be the minimum bottleneck matching distance corresponding to the minimum length such that there exists a perfect matching of the random nodes to the grid points for which the distance between every pair of matched points is at most $\\mathrm{M}_{n}$.\n\nSharp bounds for $\\mathrm{M}_{n}$ are given in \\cite{shor1991minimax}\\cite{leighton1986tight}\\cite{goel2004sharp}. We repeat them in the following lemma for convenience.\n\\begin{lemma}\nUnder any $\\ell_{p}$-norm, the bottleneck matching is \n \\begin{itemize}\n \\item $\\mathrm{M}_{n} = O \\left( \\left( \\dfrac{\\log n}{n}\\right)^{1\/d}\\right),$ \\ \\ when $d \\geq 3$ \\cite{shor1991minimax}.\n \\vspace{0.1cm}\n \n  \\item $\\mathrm{M}_{n} = O \\left(\\left(\\dfrac{\\log^{3\/2} n}{n}\\right)^{1\/2} \\right),$ \\ \\ when $d= 2$ \\cite{leighton1986tight}.\n   \\vspace{0.1cm}\n  \n    \\item $\\mathrm{M}_{n} = O \\left(\\sqrt{\\dfrac{\\log \\epsilon^{-1}}{n}}\\right),$ with prob. $\\geq 1-\\epsilon$,\\ $d= 1$  \\cite{goel2004sharp}.\n \\end{itemize}\n\\end{lemma}\n\nUnder the condition $\\mathrm{M}_{n}= o(r_{n})$, we provide an upper bound for the Levy distance between $v_{n}$ and $v'_{n}$ in the following lemma.\n\n\\begin{lemma}\n\\label{lemafirst}\nFor $d \\geq 1$, $p \\in [1, \\infty]$ and $\\mathrm{M}_{n}= o(r_{n})$, the Levy distance between $v_{n}$ and $v'_{n}$ is upper bounded as\n\\begin{equation}\n\\begin{aligned}\n\\label{equation0}\n& L^{3} \\left( v_{n}, v'_{n} \\right)  \\leq d^{\\frac{1}{p}}  2^{d+1} \\left|  \\frac{1}{n}\\sum\\limits_{\\substack{ i}}^{} \\mathbf{N}(x_{i}) - a_{n} \\right|  \\\\\n &+d^{\\frac{1}{p}} 2^{d+1}  \\left| a_{n} -\\frac{2}{n}  \\sum\\limits_{\\substack{ i}}^{} \\mathrm{L}_{i} \\right| +a'_{n},\n\\end{aligned}\n\\end{equation}\nwhere,  $\\mathbf{N}(x_{i})$ denotes the degree of $x_{i}$ in $G(\\mathcal{X}_{n}, r_{n})$ and $\\mathrm{L}_{i} \\sim \\mathrm{Bin}\\left(n, \\theta^{(d)}\\left( r_{n}-2\\mathrm{M}_{n}\\right) \\right)$. \\comment{Due to space constraints we omit the details of the proof}. \n\\end{lemma}\n\\begin{proof}\nSee Appendix  \\ref{app:lemmafirst}.\n\\end{proof}\n\nThe condition enforced on $r_{n}$, i.e., $\\mathrm{M}_{n}= o(r_{n})$ implies that for $\\epsilon >0$, (\\ref{equation0}) holds when $a_{n}$ scales as $\\Omega (\\log^{\\epsilon}(n)\\sqrt{n})$ for $d=1$, as $\\Omega (\\log^{\\frac{3}{2}+\\epsilon}(n))$ for $d= 2$ and as $\\Omega (\\log^{1+\\epsilon}(n))$ for $d\\geq 3$.\n\nIn what follows, we show that the \\gls{test} of the adjacency matrix of $G(\\mathcal{X}_{n}, r_{n})$ concentrate around the \\gls{test} of the adjacency matrix of $G(\\mathcal{D}_{n}, r_{n})$ in the connectivity regime in the sense of convergence in probability.\n\nNotice that the term $ \\sum\\limits_{\\substack{ i}}^{} \\mathbf{N}(x_{i}) \/ 2$  in Lemma \\ref{lemafirst} counts the number of edges in $G(\\mathcal{X}_{n}, r_{n})$. For convenience, we denote $ \\sum\\limits_{\\substack{ i}}^{} \\mathbf{N}(x_{i}) \/ 2$ as $\\xi_{n}$.  To show our main result we apply the Chebyshev inequality given in Lemma \\ref{Chebyschev-inequality} on the random variable $\\xi_{n}$. For that, we need to determine $\\mathrm{Var}(\\xi_{n})$\n\n\\begin{lemma}(Chebyshev Inequality)\n\\label{Chebyschev-inequality}\nLet $\\mathrm{X}$ be a random variable with an expected value $\\mathbb{E}\\mathrm{X}$ and a variance $\\mathrm{Var}\\left(\\mathrm{X}\\right)$. Then, for any $t>0$\n\\begin{equation*}\n\\mathbb{P}  \\lbrace \\vert \\mathrm{X}-\\mathbb{E}\\mathrm{\\mathrm{X}} \\vert  \\geq t \\rbrace \\leq \\dfrac{\\mathrm{Var}(\\mathrm{X})}{t^2}.\n\\end{equation*}\n\\end{lemma}\n\n\\begin{lemma}\n\\label{variance-edges}\nWhen $x_{1},...,x_{n}$ are i.i.d. uniformly distributed in the $d$-dimensional unit torus $\\mathbb{T}^{d}=[0, 1]$\n\\begin{equation*}\n\\mathrm{Var} \\left(\\xi_{n}\\right) \\leq [\\theta^{(d)}+2\\theta^{(d)} a_{n} ].\n\\end{equation*}\n\\end{lemma}\n\\begin{proof}\nThe proof follows along the same lines of Proposition A.1 in \\cite{muller2008two} when extended to a unit torus and applied to i.i.d. and uniformly distributed nodes.\n\\end{proof}\n\n\n\n\\begin{comment}\n Let us consider a $d$-dimensional {\\gls{DGG}} with $n= \\mathrm{N}^d$ nodes and assume the use of the $\\ell_{\\infty}$-metric. Then, the  degree of a vertex in $G(\\mathcal{D}_{n}, r_{n})$ is given as {\\cite{nyberg2014laplacian}}\n\\begin{equation*}\na'_{n}=(2k_{n}+1)^d-1, \\ \\ \\ \\mathrm{ with} \\ \\ k_{n}= \\left\\lfloor \\mathrm{N}r_{n} \\right\\rfloor,\n\\label{eq:degree}\n\\end{equation*}\nwhere $ \\left\\lfloor x \\right\\rfloor$ is the integer part, i.e.,  the greatest integer less than or equal to $x$. Note that when $d=1$, the Chebyshev distance and the Euclidean distance are the same.  In the following lemma, we provide an upper bound on the degree of the each node $a'_{n}$ in $G(\\mathcal{D}_{n}, r_{n})$ for any $\\ell_{p}$-norm\n\\end{comment}\n\nWe can now state the main theorem on the concentration of the adjacency matrix of $G(\\mathcal{X}_{n}, r_{n})$.\n \n\\begin{theorem}\n\\label{theorem-connectivity} \nFor  $d \\geq 1$, $p\\in[1, \\infty]$, $a \\geq 1$, $\\mathrm{M}_{n}= o(r_{n})$ and  $t >0$,  we have\n\\begin{equation*}\n\\mathbb{P} \\lbrace L^{3} \\left( v_{n}, v'_{n} \\right) >t\\rbrace  \\leq   2n \\exp\\left( \\dfrac{-a_{n}\\varepsilon^2}{3} \\left(1-\\dfrac{2\\mathrm{M}_{n}}{r_{n}}\\right)   \\right)\n\\end{equation*}\n\\begin{equation*}\n + \\frac{n \\left[\\theta^{(d)}(r_{n}-2\\mathrm{M}_{n})(a-1)+1\\right]^n}{a^{\\left(\\frac{t}{d^{\\frac{1}{p}}2^{d+3}}+\\frac{a_{n}(2-c)}{4}\\right)}}\n\\end{equation*}\n\\begin{equation}\n\\ \\ \\ \\ +\\frac{d^{\\frac{2}{p}} 2^{2d+6}\\left[ \\theta^{(d)}+2\\theta^{(d)} a_{n} \\right]}{n^2t^2},\n\\end{equation}\nwhere $\\varepsilon= \\left( \\frac{t}{d^{\\frac{1}{p}}2^{d+2}a_{n}}+\\dfrac{(2-c)}{4}- \\frac{2\\mathrm{M}_{n}}{r_{n}} \\right)$ and $c=\\left(1+\\frac{1}{2a_{n}^{1\/d}} \\right)^d$.\n\\\\\n\nIn particular,  for every $t>0$, $a \\geq 2$, $\\epsilon>0$ and $a_{n}$ that scales as $\\Omega (\\log^{\\epsilon}(n)\\sqrt{n})$ when $d=1$, as $\\Omega (\\log^{2}(n))$ when $d\\geq 2$, we have\n\n\\begin{equation*}\n\\lim_{n \\to\\infty} \\mathbb{P} \\left\\lbrace L^{3} \\left( v_{n}, v'_{n} \\right) >t  \\right\\rbrace  = 0.\n\\end{equation*}\n\\end{theorem}\n\\begin{proof}\n  See Appendix \\ref{app:theorem-connectivity}.\n\\end{proof}\nThis result is shown in the sense of convergence in probability by a straightforward application of Lemma  \\ref{Chernoff} and \\ref{Chernof-binomial} on the random variable $\\mathrm{L}_{i}$, then by applying Lemma \\ref{Chebyschev-inequality} and \\ref{variance-edges} to $\\xi_{n}.$\n\nIn what follows, we provide the eigenvalues of $\\mathbf{A}(\\mathcal{D}_{n})$ which approximates the eigenvalues of $\\mathbf{A}(\\mathcal{X}_{n})$ for $n$ sufficiently large.\n\n\\begin{lemma}\n\\label{corollary1:density}\n For $d \\geq 1$ and using the $\\ell_{\\infty}$-metric, the eigenvalues of $\\mathbf{A}(\\mathcal{D}_{n})$ are given by\n \\begin{equation}\n \\label{equation5}\n\\lambda_{m_{1},...,m_{d}}= \\prod_{s=1}^d  \\dfrac{\\sin(\\frac{m_{s} \\pi}{\\mathrm{N}}(a'_{n}+1)^{1\/d})}{\\sin(\\frac{m_{s} \\pi}{\\mathrm{N}})}  -1,\n \\end{equation}\nwhere,  $m_{1},...,m_{d}$ $\\in$ $\\lbrace 0,...\\mathrm{N}-1 \\rbrace$, $a'_{n}=(2k_{n}+1)^d-1, k_{n}= \\left\\lfloor \\mathrm{N}r_{n} \\right\\rfloor \\ \\ \\mathrm{and} \\ \\ n=\\mathrm{N}^{d}.$ The term $ \\left\\lfloor x \\right\\rfloor$ is the integer part, i.e.,  the greatest integer less than or equal to $x$.\n\\end{lemma}\n\\begin{proof}\n See Appendix  \\ref{app:lemma3}. \n\\end{proof}\nThe proof utilizes the result in \\cite{nyberg2014laplacian} which shows that the eigenvalues of the adjacency matrix of a \\gls{DGG} in $\\mathbb{T}^d$ are found by taking the $d$-dimensional DFT of an $\\mathrm{N}^{d}$ tensor of rank $d$ obtained from the first block row of $\\mathbf{A}(\\mathcal{D}_{n})$.\n\nFor $\\epsilon >0$, Theorem \\ref{theorem-connectivity} shows that when $a_{n}$ scales as $\\Omega (\\log^{\\epsilon}(n)\\sqrt{n})$ for $d=1$ and  as $\\Omega (\\log^{2}(n))$ when $d\\geq 2$, the \\gls{test} of the adjacency matrix of an \\gls{RGG} concentrate around the \\gls{test} of the adjacency matrix of a \\gls{DGG} as $n \\rightarrow \\infty$.   Therefore, for $n$ sufficiently large, the eigenvalues of the \\gls{DGG} given in (\\ref{equation5}) approximate very well the eigenvalues of the \\gls{DGG}.\n\n\n\n\\section{\\bf  Numerical Results}\n\\label{sec:results}\nWe present simulations to validate the results obtained in Section \\ref{sec:systemmodel}. More specifically, we corroborate our results on the spectrum of the adjacency matrix of \\glspl{RGG} in the connectivity regime by comparing the simulated and the analytical results.\n\nFig. \\ref{figg}(a) shows the cumulative distribution functions of the eigenvalues of the adjacency matrix of an \\gls{RGG} realization and the analytical spectral distribution in the connectivity regime. We notice that  for the chosen average vertex degree $a_{n}= \\log(n)\\sqrt{n}$ and $d=1$, the curves corresponding to the eigenvalues of the \\gls{RGG} and the \\gls{DGG} fit very well for a large value of $n$.\n\n\\captionsetup[figure]{labelfont={bf},labelformat={default},labelsep=period,name={Fig.}}\n\\begin{figure}\n\\begin{minipage}[b]{0.45\\textwidth}\n\\begin{subfigure}[b]{\\linewidth}\n\\includegraphics[width=\\linewidth]{RGG}\n\\caption{Connectivity regime, $r_{n}=\\frac{\\log(n)}{\\sqrt{n}}$, $n=2000$.}\n\\end{subfigure}\n\n\\end{minipage}\n\\caption{An illustration of the cumulative distribution function of the eigenvalues of an \\gls{RGG}. }\n\\label{figg}\n\\end{figure}\n\n\\section{\\bf Conclusion}\n\\label{sec:conclusion}\nIn this work, we study the spectrum of the adjacency matrix of \\glspl{RGG} in the connectivity regime.  Under some conditions on the average vertex degree $a_{n}$, we show that the \\glspl{test} of the adjacency matrices of an \\gls{RGG} and a \\gls{DGG} converge to the same limit as $n \\rightarrow \\infty$. Then,  based on the regular structure of the \\gls{DGG}, we approximate the  eigenvalues of $\\mathbf{A}(\\mathcal{X}_{n})$ by the eigenvalues of $\\mathbf{A}(\\mathcal{D}_{n})$ by taking the $d$-dimensional DFT of an $\\mathrm{N}^{d}$ tensor of rank $d$ obtained from the first block row of $\\mathbf{A}(\\mathcal{D}_{n})$.\n\n\\section{\\bf Acknowledgement}\nThis research was funded by the French Government through the Investments for\nthe Future Program with Reference: Labex UCN@Sophia-UDCBWN.\n\n\n\\bibliographystyle{IEEEtran}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\\label{sec:introduction}\n\\setcounter{equation}{0}\n\nOne of the fundamental question in physics is to\nunderstand the properties of matter at extreme density and temperature in\nthe first few microseconds after the big bang. Such a state of matter is\nknown as Quark-Gluon-Plasma (QGP) state where the quarks and the gluons are\nin deconfined state. A lot of progress has been made in undertanding the\nproperties and various aspects of the evolution of the strongly coupled QGP\nthrough the heavy-ion collision experiments at RHIC \n\\cite{Shuryak:2005, Kolb:2003KH} (see also \\cite{Tannenbaum:2006}) as well\nas in LHC (see \\cite{Florkowski:2017} for a comprehensive review).\nHydrodynamics plays an important role after the system undergoes a rapid \nthermalization and local thermal equilibrium is reached. Since it \nis difficult to solve the strongly coupled QCD, the qualitative \nfeatures of the hydrodynamics regime in the evolution of QGP has been \nextensively studied by using AdS\/CFT duality. This has provided \nan important framework for studying\nthe strongly coupled dynamics in a class of superconformal field theories,\nin particular, ${\\cal N} = 4$  super Yang-Mills theory\nand the corresponding gravity dual description in AdS space-time\n\\cite{Malda:1998, WittenGubser:1998}. In the context of heavy ion\ncollisions, AdS\/CFT correspondence has led to interesting results\nlike computation of shear viscosity of\nfinite temperature ${\\cal N} = 4$ Supersymmetric Yang-Mills theory\n\\cite{Policastro:2001}, viscosity from gravity dual description involving\nblack holes in AdS space  \\cite{Kovtun:2005} etc.\nAs we know, perfect local equilibrium system is described by ideal\nfluid dynamics. For small departures from equilibrium, the system is\ndescribed by dissipative fluid dynamics. The nonrelativistic \nlimit of hydrodynamics can be described by \nNavier-Stokes equations involving the energy density, pressure of the fluid \nas well as the shear and bulk viscosities. These equations are relevant \nfor describing the fluid at low energy.\nHowever, in the context of \nultrarelativistic heavy-ion collisions at RHIC and LHC, one needs \nto use relativistic hydrodynamics to study the evolution and properties \nof QGP describing fluid at high energy. \n\nThe microscopic dynamics describing \nprocesses characterized by $kl_{mfp}$ ($k$ being the momentum scale \nand $l_{mfp}$ is the mean free path of the system) has been studied \nin great detail using the relativistic hydrodynamics setup. \nIn the framework of gradient expansion in relativistic dissipative \nhydrodynamics, \nthe zeroth order theory is described by ideal hydrodynamics. \nFirst order theory is described by relativisitc Navier-Stokes \nequations. In first order hydrodynamics, due to the \nlack of an initial value formulation, \nsignals can be transmitted with arbitrarily high speed thereby violating \ncausality. The system in this case is described by parabolic equations. \nThe first order theory has\nbeen extended by M\\\"uller \\cite{Muller:67} and independently \nby Israel and Stewart(IS)\n\\cite{Israel:197679IS} by including the second order gradient terms thereby\npreserving causality in the resulting relativistic hydrodynamics equations.\nThe set of transport coefficients are extended in the second order\nhydrodynamics and the resulting equations become hyperbolic. However, the  \nM\\\"uller-Israel-Stewart theory does not contain all the corrections \nto second order in gradient. Subsequently, \nthe authors in refs \n\\cite{Baier:2007BRSSS, Sayantani:2007BHMR} obtained additional terms in \nthe stress-energy tensor by \nutilising the conformal symmetries of the theory and the new transport \ncoefficients were explicitly determined. The relaxation time \n(a transport coefficient \nin second order viscous hydrodynamics) has also been computed from the \nanalysis of the regularity of the dual geometry \\cite{Heller:2007HJ}. \n\nIn the second order Israel-Stewart (IS) theory, the equations in relativistic \ndissipative fluid dynamics have been obtained using the second \nmoment of Boltzmann equation in the kinetic theory description and \nGrad's 14-moment expansion \\cite{Grad} for the phase-space distribution \nfunction. \nHowever, 14-moment approximation used in IS theory does not provide\na unique theory as it leads to multiple fluid dynamical equations\nwith similar general structure but different transport coefficients\n\\cite{Denicol:2010xn, Denicol:2012}. For one dimensional Bjorken \nexpansion \\cite{Bjorken:1983}, it has been discussed  \nthat the second order \nIS theory has also some unphysical features like reheating of the \nexpanding medium \\cite{Muronga:2003ta}, negative pressure \n\\cite{Martinez:2009mf} for large viscosity and small initial expansion time; \nlarge ratio of shear viscosity to entropy \ndensity \n\\cite{El:2008yy} etc.\nIn order to address these problems with IS theory, higher order \ncorrections in the dissipative hydrodynamics were considered to study \ntheir effects \\cite{El:2009vj}.\nThough the resulting evolution equation \ndid not contain all possible terms in the second order dissipative \nhydrodynamics, the solutions with higher order correction indicated better\nagreement with the results from kinetic transport theory.   \n\nSecond-order dissipative equations have been \nderived from relativistic Boltzmann equation (BE)  \nusing gradient expansion of the distribution function thereby including\nnonlocal effects in the collision term \\cite{Jaiswal:2012qm}. In the above \nsetup, while deriving the evolution equations, the authors use the \ndefinition of dissipative current directly instead of \nusing the second moment of BE and it is important \nto note that the evolution equations included all possible second \norder terms allowed by the symmetry. Subsequently considering the nonlocal \ncollision term, the relativistic \nthird order dissipative evolution equation for the shear stress tensor has \nbeen derived from kinetic theory without using Grad's \n14-moment approximation and second moment of BE \\cite{AJ}. \nIn the above formalism, BE has been solved \niteratively in the relaxation \ntime approximation (RTA) for the collision term \nand the nonequilibrium phase space distribution function has been obtained\n(see also \\cite{Jaiswal:2013npa} for the discussion in\nthe context of first order and second order evolution equations).\nThe formulation of RTA for the collision term was proposed in a very \ninteresting paper by Anderson and Witting \\cite{Anderson-Witting} \nfor solving the relativistic BE as a power series in the relaxation \ntime and the transport coefficients \nfor a single component gas were obtained and compared with the relativistic \nGrad's moment method. \nIterative solution method has also been useful in obtaining \nhigher order corrections to entropy four current \\cite{CJPR:2014}.\nHydrodynamics gradient expansion in higher orders has been discussed \nin ref.\\cite{Grozdanov:2015}, where, third order corrections in conformal as \nwell as nonconformal hydrodynamics of neutral fluids have been investigated. \nIn the case of nonrelativistic systems, \nhigher order constitutive equations from kinetic theory have been discussed \nearlier in ref.\\cite{Cha}. \nThere has been progress in hydrodynamical \nformulations from various other approaches \n\\cite{Manes:2022, Cantarutti:2020, Jaiswal-rev:2021}.\nIn this work, we consider a generalization of Bjorken's one dimensional \nexpansion to three dimensional anisotropic expansion of the relativistic \nfluid, where the local rest frame (LRF) of the \nanisotropically expanding fluid is described by time \ndependent Kasner space-time. \nFor time dependent AdS\/CFT correspondence, Kasner \nspace-time has been studied earlier in the \ncontext of anisotropic expansion of the RHIC and LHC fireball, where \nexplicit expressions for the hydrodynamic quantities have been obtained \nin first and second order relativistic viscous hydrodynamics \nand gravity dual description has been studied \n\\cite{Nakamura:2006SNK, ppsm:2020}. Collisionless Boltzmann \nequation in Kasner space-time and its relation to \nanisotropic hydrodynamics has been discussed in ref.\\cite{Jaiswal:2017}.\nThough Kasner space-time is a curved space-time, Sin {\\it et al} \n\\cite{Nakamura:2006SNK} have shown that under a well controlled \napproximation, it can be considered as the LRF of the anisotropically \nexpanding fluid on Minkowski space-time. \nHere, we study the relativistic BE in RTA for the collision term. \nWe extend the results of \nref. \\cite{AJ} to three dimensional expansion case. Using the \niterative solution of BE for the nonequilibrium distribution function,\nwe obtain the dissipative evolution equations for the shear stress tensor \nand energy density to second and third order in gradients from kinetic \ntheory in Kasner space-time. These expressions have not \nbeen obtained before. We show that our results reduce to that of one\ndimensional expansion case under suitable conditions for the Kasner \nparameters. \n\nThe paper is organized as follows: Section 1 contains the introduction \nand motivation for the present study. Section 2 deals with the basic \nformalism for solving the relativistic BE \niteratively in RTA for the collision term. \nWe discuss the basic set-up in Minkowski space-time.  \nIn section 3, we generalize the \none dimensional Bjorken expansion to three dimensional anisotropic \nexpansion by considering Kasner space-time. Using the iterative \nsolutions of the Boltzmann equation for the nonequilibrium distribution\nfunction, we obtain the second and third order evolution equations \nfor the shear stress tensor ind energy density in terms of Kasner \nparameters. We also show that our evolution equations  \nagree with the one dimensional Bjorken expansion case \nin the appropriate limit of the Kasner parameters. We summarise \nand discuss the future perspective in section 4. \n\n\n\\section{Kinetic theory and iterative solution of relativistic \nBoltzmann equation}\n\\label{sec:Iterative solution}\n\\setcounter{equation}{0}\n\nAs we know, the macroscopic state of a system in relativistics \nfluid dynamics is described by the energy-momentum tensor and \nthe corresponding conservation law plays an important role in \nthe hydrodynamic evolution of a system. The conserved energy-momentum \ntensor $T^{\\mu\\nu}$ can be decomposed as, \n\\begin{eqnarray}\n\\label{NTD}\nT^{\\mu\\nu} = \\epsilon u^{\\mu} u^{\\nu} - P \\Delta^{\\mu\\nu} + \\pi^{\\mu\\nu},\n\\end{eqnarray}\nwhere, $\\epsilon$, $P$ and $\\pi^{\\mu\\nu}$ represent the energy density, \npressure and shear stress tensor respectively. The bulk viscosity \nvanishes for a system of massless particles and the corresponding \ntheory is conformal. We work in the Landau frame.  \nThe projection operator $\\Delta^{\\mu\\nu}$ defined on the space \northogonal to the fluid velocity is given by: \n$\\Delta^{\\mu\\nu} = g^{\\mu\\nu}-u^{\\mu} u^{\\nu}$, where the metric \ntensor $g^{\\mu\\nu} = diag (+, -, -, -)$ and $u^{\\mu}$ is the \nfluid 4-velocity. $u^{\\mu}$ is an eigen vector of the energy-momentum \ntensor ($T^{\\mu\\nu} u_{\\nu} = \\epsilon u^{\\mu}$) and it satisfies the \nfollowing properties: $\\Delta^{\\mu\\nu} u_{\\mu} = 0 = \\Delta^{\\mu\\nu} u_{\\nu}; \n\\,\\, \\Delta^{\\mu\\nu} \\Delta^{\\alpha}_{\\nu} = \\Delta^{\\mu\\alpha}$. \nIn the local rest frame of the fluid, the 4-velocity is given by \n$u^{\\mu} = (1, 0, 0, 0)$. \nProjecting the energy-momentum tensor conservation equation  \nin the direction parallel and perpendicular \nto the fluid 4-velocity results in the following fundamental \nequations for a relativistic viscous fluid: \n\n\\begin{eqnarray}\\label{evol}\n\\dot\\epsilon + (\\epsilon+P)\\theta - \\pi^{\\mu\\nu} \\sigma_{\\mu\\nu} &=0,\\nonumber\\\\\n(\\epsilon+P)\\dot u^\\alpha - \\nabla^\\alpha P + \\Delta^\\alpha_\\mu \\partial_\\nu\n\\pi^{\\mu\\nu} &= 0.\n\\end{eqnarray}\nWe use the notations of ref.\\cite{AJ}. Here\n$\\dot \\epsilon = u^\\mu\\partial_\\mu \\epsilon $ denotes the comoving\nderivative of the energy density, $\\theta \n\\equiv \\nabla_\\mu u^\\mu$ is the expansion\nscalar, $\\nabla^\\alpha\\equiv \\Delta^{\\mu\\alpha}\\partial_\\mu$ denotes \nthe space-like derivative and $\\sigma^{\\mu\\nu} \\equiv \n\\Delta^{\\langle\\mu}u^{\\nu\\rangle} = \n\\Delta^{\\mu\\nu}_{\\alpha\\beta} \\nabla^{\\alpha} u^{\\beta}$. \nSymmetrization is defined by $A^{(\\mu}B^{\\nu )}\n\\equiv \\frac{1}{2} (A^\\mu B^\\nu + A^\\nu B^\\mu)$. \n\n\nRelativistic hydrodynamics can be derived from kinetic theory where \nthe fundamental equation is Boltzmann equation. \nRelativistic BE in kinetic theory is given by\n\\cite{deGroot}, \n\\begin{equation}\\label{BE}\np^{\\mu} \\partial_{\\mu} f(x, p) =  {\\cal C}[f](x, p)\n\\end{equation}\nwhere $p^{\\mu}$ is the particle 4-momentum, $p^{\\mu} = \n(p^0, {\\bf p}$) with $p^0 = {\\sqrt {{\\bf p}^2 + m^2}}$, $f(x, p)$ is the \none particle phase space distribution function and \n${\\cal C}[f](x, p)$ is the collision term. \nRight hand side of the \nabove equation becomes zero if the collision between particles is neglected. \nIn the kinetic theory, the energy-momentum tensor is expressed in terms\nof the distribution function $f(x, p)$ and particle 4-momentum $p^{\\mu}$:\n\n\\begin{eqnarray}\\label{NTD}\nT^{\\mu\\nu} &= \\!\\int\\! dp \\ p^\\mu p^\\nu\\, f(x,p)\n\\end{eqnarray}\nwhere $dp\\equiv g d{\\bf p}\/[(2 \\pi)^3|\\bf p|]$ and g is the number of\ninternal degrees of freedom and we are considering a system of massless\nparticles.\n\nIn the RTA, the collision term is given by\n\\cite{Anderson-Witting}, \n\\begin{equation}\\label{collision}\n{\\cal C}[f](x, p) = \\frac{u \\cdot p}{\\tau_R} (f(x,p) - f_{eq}(x,p))\n\\end{equation}\nwhere, $u\\cdot p = u_{\\mu} p^{\\mu}$, $\\tau_R$ is the relaxation time, \n$f_{eq}(x, p)$ is the equilibrium distribution function and \nthe deviation $\\delta f$ from the equilibrium value is assumed to be \nsmall. We write,\n\\begin{equation}\\label{deviation} \nf(x, p) = f_{eq} (x, p) +  \\delta f(x, p)\n\\end{equation}\n\nThe shear stress tensor $\\pi^{\\mu\\nu}$ in the decomposition of $T^{\\mu\\nu}$ \ncan be calculated in terms of $\\delta f$ which is the deviation from \nthe equilibrium distribution function. \n$\\pi^{\\mu\\nu}$ can be written as, \n\\begin{eqnarray}\\label{FSE}\n\\pi^{\\mu\\nu} &= \\Delta^{\\mu\\nu}_{\\alpha\\beta} \\int dp \\, p^\\alpha p^\\beta\\, \n\\delta f,\n\\end{eqnarray}\n\nwhere,\n\\begin{equation}\\label{sym-proj-op}\n\\Delta^{\\mu\\nu}_{\\alpha\\beta}\\equiv \n\\frac{1}{2}(\\Delta^{\\mu}_{\\alpha}\\Delta^{\\nu}_{\\beta} + \n\t\\Delta^{\\mu}_{\\beta}\\Delta^{\\nu}_{\\alpha} - \n\t\\frac{2}{3}\\Delta^{\\mu\\nu}\\Delta_{\\alpha\\beta}) \n\\end{equation}\nis a traceless symmetric projection operator orthogonal to \n$u^\\mu$ and it satisfies the following properties: \n$\\Delta^{\\mu\\nu}_{\\alpha\\beta} \\Delta_{\\mu\\nu} = 0 = \n\\Delta^{\\mu\\nu}_{\\alpha\\beta} \\Delta^{\\alpha\\beta}$, \n$\\Delta^{\\mu\\nu}_{\\rho\\sigma}\\Delta^{\\rho\\sigma}_{\\alpha\\beta} \n= \\Delta^{\\mu\\nu}_{\\alpha\\beta}$.\n\nIn order to obtain the expression for the nonequilibrium part  $\\delta f$ \nappearing above in the expression for $\\pi^{\\mu\\nu}$, one solves \nthe BE iteratively in RTA \\cite{Jaiswal:2013npa}.  \nIn this formalism, one writes the deviation $\\delta f$ in a gradient \nexpansion \\cite{Chapman}:\n$\\delta f = \\delta f^{(1)} + \\delta f^{(2)} + \\delta f^{(3)} + \\cdots $,\nwhere $\\delta f^{(1)}$ is first order in gradient, $\\delta f^{(2)}$, \n$\\delta f^{(3)}$ are second and third order in gradients respectively. \n\nUsing the expression for the collision functional in the RTA \n\\cite{Anderson-Witting},\n\\begin{eqnarray}\\label{collision-RTA}\n{\\cal C}[f] = -u\\!\\cdot\\! p\\frac{\\delta f}{\\tau_R},\n\\end{eqnarray}\nthe relativistic BE has been solved iteratively \n\\cite{Jaiswal:2013npa}, where,   \n\\begin{eqnarray}\\label{F1F2}\nf_1 &= f_{eq} -\\frac{\\tau_R}{u\\!\\cdot\\! p} \\, p^\\mu \\partial_\\mu f_0, \\quad \n\\nonumber \\\\\nf_2 &= f_{eq} -\\frac{\\tau_R}{u\\!\\cdot\\! p} \\, p^\\mu \\partial_\\mu f_1, \n~~\\, \\cdots\n\\end{eqnarray}\nwith the notation $f_n = f_{eq} + \\delta f^{(1)} + \n\\delta f^{(2)} + \\cdot + \\delta f^{(n)}$.\nFrom here, one obtains the expressions for the deviation $\\delta f$ \nin an gradient expansion as \\cite{AJ}: \n\\begin{eqnarray}\n\\delta f^{(1)} &= -\\frac{\\tau_R}{u\\!\\cdot\\! p} \\, p^\\mu \\partial_\\mu f_{eq} \n\\label{FOC} \\\\\n\\delta f^{(2)} &= \\frac{\\tau_R}{u\\!\\cdot\\! p}p^\\mu p^\\nu\n\\partial_\\mu\\Big(\\frac{\\tau_R}{u\\!\\cdot\\! p} \n\\partial_\\nu f_{eq}\\Big). \\label{SOC}\n\\end{eqnarray}\nThe shear stress tensor to first order in gradients can be calculated \nby using the expression for $\\delta f^{(1)}$ given above \n[eqn.(\\ref{FOC})] in eqn.(\\ref{FSE}) resulting  \n$\\pi^{\\mu\\nu} = 2\\tau_R\\beta_\\pi\\sigma^{\\mu\\nu}, \n\\quad\\beta_\\pi = \\frac{4}{5}P$.  \nUsing the above results, one can obtain the expressions \nfor the shear stress tensor and its evolution to higher orders \nin derivatives.   \n\nThe above hydrodynamics set up has been dicussed in \nMinkowski space-time.\nIn the next section, we shall discuss the anisotropic expansion \nof the fluid, in which, Kasner space-time has been considered as the \nlocal rest frame of the fluid.  \nIt is important to note that though Kasner space-time is a curved \nspace-time, Sin {\\it et al} \\cite{Nakamura:2006SNK} have shown that \nunder a well controlled\napproximation, it can be considered as the LRF of the anisotropically\nexpanding fluid on Minkowski space-time. The classical Boltzmann equation in\ncurved space-time involves the Christoffel symbol, which is given by,\n\\begin{equation}\n\t(p^{\\mu} \\partial_{\\mu}-\n\\Gamma^{\\lambda}_{\\mu \\nu} \n\tp^{\\mu} p^{\\nu} \\partial_{\\lambda}) f(p,x)= {\\mathcal C} [f]\n\\end{equation}\nThe stress energy tensor is defined as, \n\\begin{equation}\nT^{\\mu\\nu} = \\int {\\sqrt{-g}}\\frac{d^3p}{p^0} p^{\\mu}p^{\\nu} f(x, p)\n\\end{equation}\nwhere, $g$ is the determinant of the metric tensor $g_{\\mu\\nu}$. \nOne obtains the hydrodynamic equations by taking the moments {\\it w.r.t.}\nto the particle momentum.  \nBaier {\\it et al} have discussed the set up in curved background in \nref.\\cite{Baier:2007BRSSS}. Hence instead of repeating, \nWe refer to the readers ref. \\cite{Baier:2007BRSSS} \nfor the discussion in a general curved background.\nIn the present framework, the effect of a general background \nspace-time \ncan be accounted for by replacing the partial derivative \n$\\partial_\\mu$ with the covariant derivative $D_\\mu$ throughout. \nFor example, we have, \n$\\dot u^{\\alpha} = u^{\\mu} D_{\\mu} u^{\\alpha}$ and  \nthe covariant derivative of a vector is given by ,\n\\begin{eqnarray}\\label{covariant-d}\nD_{\\mu} A^{\\nu} = \\partial_\\mu A^{\\nu} + \\Gamma^{\\nu}_{\\mu\\rho} A^{\\rho}; \n\\,\\,\\,\nD_{\\mu} A_{\\nu} = \\partial_\\mu A_{\\nu} - \\Gamma^{\\rho}_{\\mu\\nu} A_{\\rho}\n\\end{eqnarray} \nIn the next section, we use the covariant derivative for \ncomputing various expressions where \nwe consider Kasner space-time as the local rest frame \n(LRF) of the fluid.\n\\section{Evolution equations for shear stress tensor and Kasner space-time}\n\nIn order to obtain the evolution equation for the shear stress tensor\nto higher orders, \none needs to compute the comoving derivative of $\\delta f$ \n(which is the deviation from the equilibrium distribution function) \nexpanded in powers of space-time derivatives. In particular, one has,   \n\\begin{equation}\n\\dot\\pi^{\\langle\\mu\\nu\\rangle} = \\Delta^{\\mu\\nu}_{\\alpha\\beta} \n\\int dp\\, p^\\alpha p^\\beta\\, \\delta\\dot f, \\label{SSE}\n\\end{equation}\nwhere we have used the standard notation $A^{\\langle\\mu\\nu\\rangle}\\equiv \n\\Delta^{\\mu\\nu}_{\\alpha\\beta}A^{\\alpha\\beta}$. To second order in \ngradients, the evolution equation for the shear tensor is given by \n\\cite{Jaiswal:2013npa}, \n\\begin{equation}\\label{SOSHEAR}\n\\dot{\\pi}^{\\langle\\mu\\nu\\rangle} \\!+ \\frac{\\pi^{\\mu\\nu}}{\\tau_\\pi}\\!= \n2\\beta_{\\pi}\\sigma^{\\mu\\nu}\n\\!+2\\pi_\\gamma^{\\langle\\mu}\\omega^{\\nu\\rangle\\gamma}\n\\!-\\frac{10}{7}\\pi_\\gamma^{\\langle\\mu}\\sigma^{\\nu\\rangle\\gamma} \n\\!-\\frac{4}{3}\\pi^{\\mu\\nu}\\theta,\n\\end{equation}\nwhere $\\omega^{\\mu\\nu}\\equiv \\frac{1}{2}(\\nabla^\\mu u^\\nu-\\nabla^\\nu u^\\mu)$\nis the fluid vorticity.\nIn the derivation of this equation, one uses the expression for \n$\\delta f^{(1)}$ in the expansion of the particle distribution \nfunction $f$ and keeps terms upto quadratic in the gradient \nexpansion. In the above, the Boltzmann relaxation time $\\tau_R$ has \nbeen replaced by the shear relaxation time $\\tau_{\\pi}$ which is \na second order transport coefficient and can be expressed as \n$\\tau_{\\pi} = \\frac{\\eta}{\\beta_{\\pi}}$ where $\\eta$ is the first order \ntransport coefficient and $\\beta_{\\pi}$ is related to the pressure \n$P$ of the fluid. \n\nSimilarly, using the expressions for $\\delta f^{(1)}$ (eqn.\\ref{FOC}), \n$\\delta f^{(2)}$ (eqn.\\ref{SOC}), computing their comoving derivatives \nand keeping terms upto cubic order in derivatives, the \nthird order evolution equation for $\\pi^{\\mu\\nu}$ has \nbeen obtained by Jaiswal \\cite{AJ}:\n\n\\begin{eqnarray}\\label{TOSHEAR}\n\\dot{\\pi}^{\\langle\\mu\\nu\\rangle} =& -\\frac{\\pi^{\\mu\\nu}}{\\tau_\\pi}\n+2\\beta_\\pi\\sigma^{\\mu\\nu}\n+2\\pi_{\\gamma}^{\\langle\\mu}\\omega^{\\nu\\rangle\\gamma}\n-\\frac{10}{7}\\pi_\\gamma^{\\langle\\mu}\\sigma^{\\nu\\rangle\\gamma}  \n-\\frac{4}{3}\\pi^{\\mu\\nu}\\theta\n+\\frac{25}{7\\beta_\\pi}\\pi^{\\rho\\langle\\mu}\\omega^{\\nu\\rangle\\gamma}\\pi_{\\rho\\gamma}\n-\\frac{1}{3\\beta_\\pi}\\pi_\\gamma^{\\langle\\mu}\\pi^{\\nu\\rangle\\gamma}\\theta \\nonumber \\\\\n&-\\frac{38}{245\\beta_\\pi}\\pi^{\\mu\\nu}\\pi^{\\rho\\gamma}\\sigma_{\\rho\\gamma}\n-\\frac{22}{49\\beta_\\pi}\\pi^{\\rho\\langle\\mu}\\pi^{\\nu\\rangle\\gamma}\\sigma_{\\rho\\gamma} \n-\\frac{24}{35}\\nabla^{\\langle\\mu}\\left(\\pi^{\\nu\\rangle\\gamma}\\dot u_\\gamma\\tau_\\pi\\right)\n+\\frac{4}{35}\\nabla^{\\langle\\mu}\\left(\\tau_\\pi\\nabla_\\gamma\\pi^{\\nu\\rangle\\gamma}\\right) \\nonumber \\\\\n&-\\frac{2}{7}\\nabla_{\\gamma}\\left(\\tau_\\pi\\nabla^{\\langle\\mu}\\pi^{\\nu\\rangle\\gamma}\\right)\n+\\frac{12}{7}\\nabla_{\\gamma}\\left(\\tau_\\pi\\dot u^{\\langle\\mu}\\pi^{\\nu\\rangle\\gamma}\\right) \n-\\frac{1}{7}\\nabla_{\\gamma}\\left(\\tau_\\pi\\nabla^{\\gamma}\\pi^{\\langle\\mu\\nu\\rangle}\\right)\n+\\frac{6}{7}\\nabla_{\\gamma}\\left(\\tau_\\pi\\dot u^{\\gamma}\\pi^{\\langle\\mu\\nu\\rangle}\\right) \\nonumber \\\\\n&-\\frac{2}{7}\\tau_\\pi\\omega^{\\rho\\langle\\mu}\\omega^{\\nu\\rangle\\gamma}\\pi_{\\rho\\gamma}\n-\\frac{2}{7}\\tau_\\pi\\pi^{\\rho\\langle\\mu}\\omega^{\\nu\\rangle\\gamma}\\omega_{\\rho\\gamma} \n-\\frac{10}{63}\\tau_\\pi\\pi^{\\mu\\nu}\\theta^2\n+\\frac{26}{21}\\tau_\\pi\\pi_\\gamma^{\\langle\\mu}\\omega^{\\nu\\rangle\\gamma}\\theta.\n\\end{eqnarray}\n\nNote that the above equation was formulated within the \nframework of kinetic theory for a system of massless particles which has \nconformal symmetry. For such a system, dissipation due to bulk viscosity \nand heat current can be neglected.\nUsing entropy current and \nsecond law of thermodynamics, El {\\it etal} (ref.\\cite{El:2009vj})\nhave obtained the evolution equation before. However, in the context \nof one dimensional Bjorken expansion, the evolution equation \nobtained there misses out many more terms. \nNext, we study the evolution equation to second \nand third order for the shear stress tensor and energy density \nin the context of three dimensional anisotropic\nexpansion of the conformal fluid. \nWe consider the generalisation of Bjorken's 1-dimensional expansion to \n3-dimensional expansion of the fluid in order to \nconnect to the realistic description of the RHIC and LHC fireball and  \nfor this, we consider Kasner space-time as the LRF of the fluid\n\\cite{Nakamura:2006SNK, ppsm:2020, Jaiswal:2017}.\nThe metric is \\cite{Kasner:1921}: \n\\begin{eqnarray}\\label{Kasner}\nds^{2} = (d \\tau)^{2} - \\tau^{2a}(dx_{1})^{2} - \\tau^{2b}(dx_{2})^{2}\n- \\tau^{2c}(dx_{3})^{2}\n\\end{eqnarray}\n\nHere $x_1, x_2, x_3$ are the comoving coordinates, $\\tau$ is \nthe proper time and $a, b, c$ are constants known as Kasner parameters. \nThe Kasner parameters satisfy\nthe conditions,\n\\begin{eqnarray}\\label{Kasner-condn}\na + b + c = 1, \\hspace{20pt}a^2 + b^2 + c^2 = 1 \n\\end{eqnarray}\nThe above metric is an exact solution of vacuum Einstein's\nequation and it describes a homogeneous and anisotropic\nexpansion of the Universe. The physical quantities are assumed to \ndepend only on proper time $\\tau$.\nThe nonzero components of the affine connection \nfor the Kasner metric are given by, \n\\begin{eqnarray}\\label{affine}\n\\Gamma^{\\tau}_{x_1 x_1} = a \\tau^{2 a -1},\\, \\Gamma^{\\tau}_{x_2 x_2}\n= b \\tau^{2 b -1},\\, \\Gamma^{\\tau}_{x_3 x_3} = c \\tau^{2 c -1},\\nonumber \\\\ \n\\Gamma^{x_1}_{x_1 \\tau} = \\frac{a}{\\tau}, \\,\n\\Gamma^{x_2}_{x_2 \\tau} = \\frac{b}{\\tau}, \\,\\Gamma^{x_3}_{x_3 \\tau} = \n\\frac{c}{\\tau}\n\\end{eqnarray}\n\nThe Ricci tensor turns out\nto be zero upon using Kasner conditions $a + b + c =1$; $a^2 + b^2 + c^2 =1$.\nRicci tensor for Kasner space-time is give by,\n\\begin{eqnarray}\nR_{00} & = & \\frac{1}{\\tau^2} [ (a + b + c) - (a^2 + b^2 + c^2)] \\\\ \\nonumber\nR_{11} & = & a [(a + b + c) - 1] \\tau^{2a-2} \\\\ \\nonumber\nR_{22} & = & b [(a + b + c) - 1] \\tau^{2b-2} \\\\ \\nonumber\nR_{33} & = & c [(a + b + c) - 1] \\tau^{2c-2} \n\\end{eqnarray}\nwhere, $1, 2, 3$ corresponds to $x_1, x_2, x_3$ coordinates, and\n$0$ corresponds to $\\tau$ coordinate. As one can see, the components\nvanish upon using Kasner conditions. The nonzero components of Riemann tensor\nare given by,\n\\begin{eqnarray}        \nR_{0101} &=& (1-a)a \\tau^{2a-2}, \\, R_{0202} = (1-b) b\\tau^{2b-2} \n        \\\\ \\nonumber \n        R_{0303} &=& (1-c) c \\tau^{2c-2}, \\,\n        R_{1212} = a b \\tau^{2a+2b-2} \\\\ \\nonumber\n        R_{1313} &=& a c \\tau^{2a + 2c-2} , \\, R_{2323} = \n        b c \\tau^{2b + 2c -2} \n\\end{eqnarray}\nThese expressions become zero for the Bjorken case corresponding to\n$a=1, b=0, c=0$. So the terms involving $R^{\\mu\\nu\\rho\\sigma}$\ncould contribute to the shear tensor $\\pi^{\\mu\\nu}$ with a coefficient\n$\\kappa$ (we refer to eqn. 3.12 in ref. \\cite{Baier:2007BRSSS}).\nHowever, the general expression for the shear stress tensor $\\pi^{\\mu\\nu}$\nwhen derived from kinetic theory does not contain the $\\kappa$ term which\nwould have involved the Riemann tensor (we refer to eqn. 5.23 of\nthe above reference \\cite {Baier:2007BRSSS} and subsequent discussion). \nBoltzmann equation does not contain the term involving $\\kappa$. \nHence, there is no inconsistency in the order of the derivative expansion.\n\nWe compute various quantities appearing in the second and third order \nevolution equations for the shear stress tensor. \nAs mentioned in the previous section, here\nwe use the notations involving covariant \nderivative $D_{\\mu}$ (as defined in eqn. (\\ref {covariant-d})) instead \nof partial \nderivative $\\partial_{\\mu}$.\nWe have, \n\\begin{eqnarray}\n\\nabla_{\\mu}u_{\\nu} = \\Delta^{\\rho}_{\\mu} D_{\\rho}u_{\\nu},\n\\nonumber \\\\\n\\sigma^{\\mu\\nu}  = \\Delta^{\\mu\\nu}_{\\alpha\\beta} \\nabla^{\\alpha} u^{\\beta}=\n\\Delta^{\\mu\\nu}_{\\alpha\\beta} \\Delta^{\\alpha\\rho} D_{\\rho}u^{\\beta}\n\\end{eqnarray}\n\nWe obtain the \ncomponents of the projection operator as,\n\\begin{equation}\\label{projector}\t\n\\Delta ^{\\mu \\nu}\\equiv\\mathrm{diag}(0, \n\t- \\frac{1}{\\tau^{2a}},\n\t- \\frac{1}{\\tau^{2b}}, - \\frac{1}{\\tau^{2c}})\n\\end{equation}\nComponents of the shear tensor are obtained as,  \n\n\\begin{eqnarray}\\label{secondterm}\n\\sigma^{\\tau\\tau} = 0,\\,\n\\sigma^{x_1 x_1} = \\frac{-2a+b+c}{3}\\tau^{-2a-1},\\,\\nonumber\\\\\n\\sigma^{x_2 x_2} = \\frac{a-2b+c}{3}\\tau^{-2b-1},\\,\\nonumber\\\\\n\\sigma^{x_3 x_3} = \\frac{a+b-2c}{3}\\tau^{-2c-1}\n\\end{eqnarray}\nwhere we have used Kasner conditions and,\n\n\\begin{equation}\\label{theta}\n\\theta\\equiv \\nabla_\\mu u^\\mu = \\Delta^{\\nu}_{\\mu}D_{\\nu}u^{\\mu} \n=\\frac{a+b+c}{\\tau}.\n\\end{equation}\n\nUpon using Kasner condition, $\\theta$ becomes $\\frac{1}{\\tau}$ \nwhich is the same as in one dimensional Bjorken expansion case. \nThe shear stress tensor is diagonal. \nWe assume that it can be \ncharacterized by a function $\\pi$ and the  Kasner parameters in the \nfollowing form:   \n$\\pi^{\\mu\\nu}\\equiv\\mathrm{diag}(0,-\\pi\\tau^{-2a},\n\\frac{\\pi}{2}\\tau^{-2b},\\frac{\\pi}{2}\\tau^{-2c})$. One can check \nthat $\\pi^{\\mu\\nu}$ is traceless \nas we are considering a conformal fluid. \n\nThe components of $\\dot{\\pi}^{\\langle \\mu\\nu \\rangle}$ are given by, \n\\begin{eqnarray}{\\label{zeroterm}}\n\\dot{\\pi}^{\\langle \\tau\\tau \\rangle}= 0, \\,\n\\dot{\\pi}^{\\langle x_1x_1 \\rangle}=\\frac{-1}{\\tau^{2a}}\\frac{d\\pi}{d\\tau}, \\,\\nonumber\\\\\n\\dot{\\pi}^{\\langle x_2x_2 \\rangle}=\\frac{1}{2\\tau^{2b}}\\frac{d\\pi}{d\\tau}, \\,\n\\dot{\\pi}^{\\langle x_3x_3 \\rangle}=\\frac{1}{2\\tau^{2c}}\\frac{d\\pi}{d\\tau}\n\\end{eqnarray}\n\nComponents of other terms appearing in the second order \nevolution equation are obtained as,\n\\begin{eqnarray}{\\label{fourthterm}}\n\\pi_\\gamma^{\\langle \\tau}\\sigma^{\\tau\\rangle\\gamma}=0,\n\\pi_\\gamma^{\\langle x_1}\\sigma^{x_1\\rangle\\gamma}=\\frac{\\pi(b+c-2a)}\n{6 \\tau^{2a+1}},\\nonumber\\\\\n\\pi_\\gamma^{\\langle x_2}\\sigma^{x_2 \\rangle\\gamma}=\n\\frac{\\pi(a+b-2c)}{6 \\tau^{2b+1}},\\nonumber\\\\\n\\pi_\\gamma^{\\langle x_3}\\sigma^{x_3 \\rangle\\gamma}=\\frac{\\pi(a+c-2b)}\n{6 \\tau^{2c+1}}\n\\end{eqnarray}\nSubstituing the above expressions, the second order evolution equations\nare given by\n\\begin{eqnarray}\n\\frac{d\\epsilon}{d\\tau} &= -\\frac{1}{\\tau}\\left(\\epsilon + P \\right)  \n-\\frac{\\pi(b+c-2a)}{2\\tau} \\label{BED1}, \\\\\n\\frac{d\\pi}{d\\tau} &= - \\frac{\\pi}{\\tau_\\pi} - \n\\frac{2\\beta_\\pi (-2a+b+c)}{3\\tau} - \\frac{\\pi(38a+23b+23c)}{21\\tau}, \n\\label{Bshear1}\n\\end{eqnarray}\nNote that, adding the three equations for the nonzero components of\n$\\dot{\\pi}^{\\langle \\mu\\nu \\rangle}$, we get only one independent \nequation as given above in eqn.(\\ref{Bshear1}). \nIt is important to note that the Kasner metric in the limit of \n$a=1, b=0, c=0$ reduces to that of the Minkowski metric in \nMilne coordinates. In this limit, the above second order evolution \nequations reduce to the evolution equations in the one dimensional \nBjorken expansion case \\cite{AJ}:\n\\begin{eqnarray}\n\\frac{d\\epsilon}{d\\tau} &= -\\frac{1}{\\tau}\\left(\\epsilon + P \\right)  \n+\\frac{\\pi}{\\tau} \\label{BED2} \\\\\n\\frac{d\\pi}{d\\tau} &= - \\frac{\\pi}{\\tau_\\pi} + \\frac{4\\beta_{\\pi}}{3\\tau} \n- \\frac{38\\pi}{21\\tau}  \\label{Bshear2}\n\\end{eqnarray}\n\nNext, we compute the other terms appearing in the third order \nevolution equation of $\\pi^{\\mu\\nu}$ and give the explicit expressions \nfor the various terms. Components of $\\pi_\\gamma^{\\langle \\tau}\\pi^{\\tau \n\\rangle\\gamma}\\theta$ are given by, \n\n\\begin{eqnarray}{\\label{seventhterm}}\n\\pi_\\gamma^{\\langle \\tau}\\pi^{\\tau \\rangle\\gamma}\\theta=0,\n\\pi_\\gamma^{\\langle x_1}\\pi^{x_1 \\rangle\\gamma}\\theta=\n\\frac{\\pi^{2}(a+b+c)}{2\\tau^{2a+1}},\\nonumber\\\\\n\\pi_\\gamma^{\\langle x_2}\\pi^{x_2 \\rangle\\gamma}\\theta=\n\\frac{\\pi^{2}(a+b+c)}{4\\tau^{2b+1}}\\nonumber\\\\\n\\pi_\\gamma^{\\langle x_3}\\pi^{x_3 \\rangle\\gamma}\\theta=\n\\frac{\\pi^{2}(a+b+c)}{4\\tau^{2c+1}}\n\\end{eqnarray}\n\nComponents of $\\pi^{\\mu\\nu}\\pi^{\\rho\\gamma}\\sigma_{\\rho\\gamma}$ are : \n\\begin{eqnarray}{\\label{eightterm}}\n\\pi^{\\tau\\tau}\\pi^{\\rho\\gamma}\\sigma_{\\rho\\gamma}=0,\\nonumber\\\\\n\\pi^{x_1x_1}\\pi^{\\rho\\gamma}\\sigma_{\\rho\\gamma}=\n\\frac{-\\pi^{2}(2a-b-c)}{2\\tau^{2a+1}},\\nonumber\\\\\n\\pi^{x_2x_2}\\pi^{\\rho\\gamma}\\sigma_{\\rho\\gamma}=\n\\frac{\\pi^{2}(2a-b-c)}{4\\tau^{2b+1}}\\nonumber\\\\\n\\pi^{x_3x_3}\\pi^{\\rho\\gamma}\\sigma_{\\rho\\gamma}=\n\\frac{\\pi^{2}(2a-b-c)}{4\\tau^{2c+1}}\n\\end{eqnarray}\n\nComponents of $\\pi^{\\rho\\langle \\mu}\\pi^{\\nu \\rangle\\gamma}\\sigma_{\\rho\\gamma}$\nare given by, \n\\begin{eqnarray}{\\label{ninethterm}}\n\\pi^{\\rho\\langle \\tau}\\pi^{\\tau \\rangle\\gamma}\\sigma_{\\rho\\gamma}=0,\\nonumber\\\\\n\\pi^{\\rho\\langle x_1}\\pi^{x_1\\rangle\\gamma}\\sigma_{\\rho\\gamma}=\n\\frac{\\pi^{2}(-2a+b+c)}{4\\tau^{2a+1}},\\nonumber\\\\\n\\pi^{\\rho\\langle x_2}\\pi^{x_2 \\rangle\\gamma}\\sigma_{\\rho\\gamma}=\n\\frac{\\pi^{2}(a-b)}{4\\tau^{2b+1}}\\nonumber\\\\\n\\pi^{\\rho\\langle x_3}\\pi^{x_3 \\rangle\\gamma}\\sigma_{\\rho\\gamma}=\n\\frac{\\pi^{2}(a-c)}{4\\tau^{2c+1}}\n\\end{eqnarray}\n\nFor $\\nabla^{\\langle \\mu}\\left(\\nabla_\\gamma\\pi^{\\nu \\rangle\\gamma}\\right)$\nwe have, \n\\begin{eqnarray}{\\label{eleventhterm}}\n\\nabla^{\\langle \\tau}\\left(\\nabla_\\gamma\\pi^{\\tau \\rangle\\gamma}\\right)=0\\nonumber\\\\\n\\nabla^{\\langle x_1}\\left(\\nabla_\\gamma\\pi^{x_1 \\rangle\\gamma}\\right) =\\frac{\\pi}{6\\tau^{2a+2}}(8a^{2}+2b^{2}+2c^{2}\n-4ab+2bc-4ac)\\nonumber\\\\\n\\nabla^{\\langle x_2}\\left(\\nabla_\\gamma\\pi^{x_2\\rangle\\gamma}\\right) =\n\\frac{\\pi}{6\\tau^{2b+2}}(-4a^{2}-4b^{2}+2c^{2}\n+5ab-bc-ac)\\nonumber\\\\\n\\nabla^{\\langle x_3}\\left(\\nabla_\\gamma\\pi^{x_3\\rangle\\gamma}\\right) =\n\\frac{\\pi}{6\\tau^{2c+2}}(-4a^{2}+2b^{2}-4c^{2}\n-ab-bc+5ac)\n\\end{eqnarray}\n\nFor $\\nabla_{\\gamma}\\left(\\nabla^{\\langle \\mu}\\pi^{\\nu \\rangle\\gamma}\\right)$,\nwe get, \n\\begin{eqnarray}{\\label{twelveterm}}\n\\nabla_{\\gamma}\\left(\\nabla^{\\langle \\tau}\\pi^{\\tau \\rangle\\gamma}\\right)=0\\nonumber\\\\\n\\nabla_{\\gamma}\\left(\\nabla^{\\langle x_1}\\pi^{x_1\\rangle\\gamma}\\right) =\n\\frac{\\pi}{6\\tau^{2a+2}}(8a^{2}+2b^{2}+2c^{2}\n+5ab+2bc+5ac)\\nonumber\\\\\n\\nabla_{\\gamma}\\left(\\nabla^{\\langle x_2}\\pi^{x_2 \\rangle\\gamma}\\right) =\n\\frac{\\pi}{6\\tau^{2b+2}}(-4a^{2}-4b^{2}+2c^{2}\n-4ab-bc-ac)\\nonumber\\\\\n\\nabla_{\\gamma}\\left(\\nabla^{\\langle x_3}\\pi^{x_3 \\rangle\\gamma}\\right) =\n\\frac{\\pi}{6\\tau^{2c+2}}(-4a^{2}+2b^{2}-4c^{2}\n-ab-bc-4ac)\n\\end{eqnarray}\n\nComponents of $\\pi^{\\mu\\nu}\\theta^2$ are given by, \n\\begin{eqnarray}{\\label{eighteenterm}}\n\\pi^{\\tau \\tau}\\theta^2=0,\n\\pi^{x_1x_1}\\theta^2=\\frac{-\\pi}{\\tau^{2a}}\\left(\\frac{a+b+c}{\\tau}\\right)^{2} \\nonumber\\\\\n\\pi^{x_2x_2}\\theta^2=\\frac{\\pi}{2\\tau^{2b}}\\left(\\frac{a+b+c}{\\tau}\\right)^{2}\n\\nonumber\\\\\n\\pi^{x_3x_3}\\theta^2=\\frac{\\pi}{2\\tau^{2c}}\\left(\\frac{a+b+c}{\\tau}\\right)^{2}\n\\end{eqnarray}\n\nFor $\\nabla_{\\gamma}\\left(\\tau_\\pi\\nabla^{\\gamma}\\pi^{\\langle \\mu\\nu \\rangle}\n\\right)$, we obtain, \n\\begin{eqnarray}{\\label{fourteenterm}}\n\\nabla_{\\gamma}\\left(\\tau_\\pi\\nabla^{\\gamma}\\pi^{\\langle \\tau\\tau \\rangle}\n\\right)=0,\\nonumber\\\\\n\\nabla_{\\gamma}\\left(\\tau_\\pi\\nabla^{\\gamma}\\pi^{\\langle x_1x_1 \\rangle}\\right)\n=\\frac{\\pi(4a^{2}+b^{2}+c^{2})}{3\\tau^{2a+2}},\\nonumber\\\\\n\\nabla_{\\gamma}\\left(\\tau_\\pi\\nabla^{\\gamma}\\pi^{\\langle x_2x_2 \\rangle}\\right)\n=\\frac{\\pi(-2a^{2}-2b^{2}+c^{2})}{3\\tau^{2b+2}}\\nonumber\\\\\n\\nabla_{\\gamma}\\left(\\tau_\\pi\\nabla^{\\gamma}\\pi^{\\langle x_3x_3 \\rangle}\\right)\n=\\frac{\\pi(-2a^{2}+b^{2}-2c^{2})}{3\\tau^{2c+2}}\n\\end{eqnarray}\n\nAll these expressions can be simplified further by using Kasner \nconditions. Here we have \n$\\omega^{\\mu\\nu} = \\dot {u}^{\\mu} = \\nabla^{\\mu} \\tau_{\\pi} = 0$.\nThe other terms in the evolution equations as given below become zero, namely, \n\\begin{eqnarray}{\\label{zero-terms}}\n\\pi_{\\gamma}^{\\langle\\mu}\\omega^{\\nu\\rangle\\gamma} & =0 \\\\ \n\\nonumber\n\\pi^{\\rho\\langle\\mu}\\omega^{\\nu\\rangle\\gamma}\\pi_{\\rho\\gamma} & =0 \\\\\n\\nonumber\n\\nabla^{\\langle\\mu}\\left(\\pi^{\\nu\\rangle\\gamma}\\dot u_\\gamma\\tau_\\pi\\right) \n&=0 \\\\\n\\nonumber\n\\nabla_{\\gamma}\\left(\\tau_\\pi\\dot u^{\\langle\\mu}\\pi^{\\nu\\rangle\\gamma}\\right)\n& =0 \\\\\n\\nonumber\n\\nabla_{\\gamma}\\left(\\tau_\\pi\\dot u^{\\gamma}\\pi^{\\langle\\mu\\nu\\rangle}\\right)\n&=0 \\\\\n\\nonumber\n\\tau_\\pi\\omega^{\\rho\\langle\\mu}\\omega^{\\nu\\rangle\\gamma}\\pi_{\\rho\\gamma}&=0 \\\\\n\\nonumber\n\\tau_\\pi\\pi^{\\rho\\langle\\mu}\\omega^{\\nu\\rangle\\gamma}\\omega_{\\rho\\gamma} &=0 \\\\\n\\nonumber\n\\tau_\\pi\\pi_\\gamma^{\\langle\\mu}\\omega^{\\nu\\rangle\\gamma}\\theta &=0 \n\\end{eqnarray}\n\nSubstituting the expressions for the above nonzero terms, the third order \nevolution equations for $x_1x_1$, $x_2x_2$, $x_3x_3$ components of the \nshear stress tensor are obtained as,  \n\\begin{eqnarray}{\\label{x-x term}}\n\\frac{d\\pi}{d\\tau} &=-\\frac{\\pi}{\\tau_\\pi}-2\\beta_\\pi\\frac{(-2a+b+c)}{3\\tau}+\\frac{\\pi(-38a-23b-23c)}{21\\tau}\n+\\frac{\\pi^{2}(-803a+34b+34c)}{1470\\beta_{\\pi}\\tau}\\nonumber\\\\\n&+\\frac{\\pi^{2}(106a^{2}-11b^{2}-11c^{2}-13ab-13ac-76bc)}{420\\beta_{\\pi}\\tau}  \n\\end{eqnarray}\n\\begin{eqnarray}{\\label{y-y term}}\n\\frac{d\\pi}{d\\tau} &= - \\frac{\\pi}{\\tau_\\pi} + 4\\beta_\\pi\\frac{(a-2b+c)}{3\\tau}+\\frac{\\pi(-38a-38b-8c)}{21\\tau}\n+\\frac{\\pi^{2}(-803a+199b-131c)}{1470\\beta_{\\pi}\\tau}\\nonumber\\\\\n&+\\frac{\\pi^{2}(53a^{2}+53b^{2}-64c^{2}+25ab-38ac-38bc)}{210\\beta_{\\pi}\\tau}  \n\\end{eqnarray}\n\\begin{eqnarray}{\\label{z-z term}}\n\\frac{d\\pi}{d\\tau} &= - \\frac{\\pi}{\\tau_\\pi} + 4\\beta_\\pi\\frac{(a+b-2c)}{3\\tau}+\\frac{\\pi(-38a-8b-38c)}{21\\tau}\n+\\frac{\\pi^{2}(-803a-131b+199c)}{1470\\beta_{\\pi}\\tau}\\nonumber\\\\\n&+\\frac{\\pi^{2}(53a^{2}-64b^{2}+53c^{2}+25ac-38ab-38bc)}{210\\beta_{\\pi}\\tau}  \n\\end{eqnarray}\n\nThese equations can be further simplified by using Kasner conditions.  \nOne can check that adding the equations for the $x_1x_1$, \n$x_2x_2$ and $x_3x_3$ components, \none gets only one independent equation, which is eq.(\\ref{x-x term}). \nThe evolution equation for the energy density $\\epsilon$ is obtained as, \n\\begin{eqnarray}\\label{epsilon}\n\\frac{d\\epsilon}{d\\tau} = -\\frac{1}{\\tau} (\\epsilon + P){\\tau} \n- \\frac{\\pi (b + c -2a)}{2\\tau}\n\\end{eqnarray}\n\nIn the limit $a=1, b=0, c=0$ for the Kasner parameters, \nthe evolution equation for the energy density reduces\nto that of the one dimensional Bjorken expansion case \\cite{AJ}, \n\\begin{eqnarray}\\label{epsilon-1}\n\\frac{d\\epsilon}{d\\tau} &= -\\frac{1}{\\tau} (\\epsilon + P -\\pi)\n\\end{eqnarray}\nand the third order evolution equation for the shear stress tensor \n$\\pi^{\\mu\\nu}$ reduces to \nthat of the equation for the Bjorken's one dimensional \nexpansion case, namely, \n\\begin{eqnarray}\n\\frac{d\\pi}{d\\tau} &= - \\frac{\\pi}{\\tau_\\pi} + \n\\frac{4 \\beta_\\pi}{3\\tau} - \n\\frac{38}{21}\\frac{\\pi}{\\tau} - \\frac{72}{245}\\frac{\\pi^2}{\\beta_\\pi\\tau}. \n\\end{eqnarray}\nBy comparing the above equation with the third order evolution equation \nin the one dimensional expansion case \\cite{AJ}\n\\begin{eqnarray}\n\\frac{d\\pi}{d\\tau} &= - \\frac{\\pi}{\\tau_\\pi} +\n\\frac{4 \\beta_\\pi}{3\\tau} -\n\\lambda \\frac{\\pi}{\\tau} - \\chi \\frac{\\pi^2}{\\beta_\\pi\\tau},\n\\end{eqnarray}\nthe transport coefficients are given by, \n\\begin{equation}\\label{BTC}\n\\tau_\\pi = \\frac{\\eta}{\\beta_\\pi}, \\quad \\beta_\\pi = \\frac{4P}{5}, \n\\quad \\lambda = \\frac{38}{21}, \\quad \\chi = \\frac{72}{245}.\n\\end{equation}\nwhich matches with the results in the one dimensional expansion case. \n\nHere we would like to point out that one could have \nintroduced three \nindependent fields $\\pi_i (i=1, 2, 3)$ for the shear stress tensor \n$\\pi^{\\mu\\nu}$ instead of a\nsingle function $\\pi$, as has been introduced in the above discussion \nto charataterize $\\pi^{\\mu\\nu}$. We have\nexplicitly checked that by making a general ansatz\nfor the shear stress tensor $\\pi^{\\mu\\nu} = diag (0, \\pi_1 \\tau^{-2a},\n\\pi_2 \\tau^{-2b}, \\pi_3 \\tau^{-2c})$ by introducing three independent\nfunctions $\\pi_1, \\pi_2, \\pi_3$, we get three independent third order\nevolution equations (also second order) for the components of the shear \nstress tensor \ninvolving $\\pi_1, \\pi_2$ and $\\pi_3$. These are given by, \n\\begin{eqnarray}\n\\frac{d\\pi_{1}}{d\\tau} &= - \\frac{\\pi_{1}}{\\tau_\\pi}+\n2\\beta_\\pi\\frac{(-2a+b+c)}{3\\tau}+\\frac{\\pi_{1}(-124a-64b-64c)}{63\\tau}\n+\\frac{\\pi_{2}(-10a+20b-10c)}{63\\tau}+\n\\frac{\\pi_{3}(-10a-10b+20c)}{63\\tau}\\nonumber\\\\\n&-\\frac{1}{735\\beta_{\\pi}\\tau}[\\pi_{1}^{2}(-386a-52b-52c)\n+\\pi_{2}^{2}(45a+155b+45c)+\\pi_{3}^{2}(45a+45b+155c)\\nonumber\\\\\n&+\\pi_{1}\\pi_{2}(38a-76b+38c)+\\pi_{1}\\pi_{3}(38a+38b-76c)]\\nonumber\\\\\n&+\\frac{\\tau_{\\pi}}{630 \\tau^{2}}[\\pi_{1}(212a^{2}-100b^{2}-100c^{2}-68ab-68ac\\nonumber\\\\\n&-200bc)+\\pi_{2}(-156b^{2}-84ab-48bc)\n+\\pi_{3}(-156c^{2}-84ac-48bc)]\n\\end{eqnarray}\n\\begin{eqnarray}\n\\frac{d\\pi_{2}}{d\\tau} &=-\\frac{\\pi_{2}}{\\tau_\\pi}+\n2\\beta_\\pi\\frac{(a-2b+c)}{3\\tau}+\\frac{\\pi_{1}(20a-10b-10c)}{63\\tau}\n+\\frac{\\pi_{2}(-64a-124b-64c)}{63\\tau}+\\frac{\\pi_{3}(-10a-10b+20c)}{63\\tau}\\nonumber\\\\\n&-\\frac{1}{735\\beta_{\\pi}\\tau}[\\pi_{1}^{2}(155a+45b+45c)\n+\\pi_{2}^{2}(-52a-386b-52c)+\\pi_{3}^{2}(45a+45b+155c)\\nonumber\\\\\n&+\\pi_{1}\\pi_{2}(-76a+38b+38c)+\\pi_{2}\\pi_{3}(38a+38b-76c)]\\nonumber\\\\\n&+\\frac{\\tau_{\\pi}}{315\\tau^{2}}[\\pi_{1}(-78a^{2}-42ab-24ac)+\\pi_{2}(-50a^{2}+106b^{2}\\nonumber\\\\\n&-50c^{2}-34ab-34bc\n-100ac)+\\pi_{3}(-78c^{2}-24ac-42bc)]\n\\end{eqnarray}\n\\begin{eqnarray}\n\\frac{d\\pi_{3}}{d\\tau} &=-\\frac{\\pi_{3}}{\\tau_\\pi} +\n2\\beta_\\pi\\frac{(a+b-2c)}{3\\tau}+\\frac{\\pi_{1}(20a-10b-10c)}{63\\tau}\n+\\frac{\\pi_{2}(-10a+20b-10c)}{63\\tau}+\\frac{\\pi_{3}(-64a-64b-124c)}{63\\tau}\\nonumber\\\\\n&-\\frac{1}{735\\beta_{\\pi}\\tau}[\\pi_{1}^{2}(155a+45b+45c)\n+\\pi_{2}^{2}(45a+155b+45c)+\\pi_{3}^{2}(-52a-52b-386c)\\nonumber\\\\\n&+\\pi_{1}\\pi_{3}(-76a+38b+38c)+\\pi_{2}\\pi_{3}(38a-76b+38c)]\\nonumber\\\\\n&+\\frac{\\tau_{\\pi}}{315\\tau^{2}}[\\pi_{1}(-78a^{2}-24ab-42ac)\n+\\pi_{2}(-78b^{2}-24ab-42bc)+\\pi_{3}(-50a^{2}-50b^{2}\\nonumber\\\\\n&+106c^{2}-34ac-34bc-100ab)]\n\\end{eqnarray}\nSince $\\pi^{\\mu\\nu}$ is traceless, for the Kasner metric $g_{\\mu\\nu}$, \nwe get the condition\n\\begin{equation}\n\\pi_1 + \\pi_2 + \\pi_3 = 0\n\\end{equation}\nUsing this tracelessness condition, we find\nthat adding the equations for $\\pi_2$ and $\\pi_3$, we get precisely the\nequation for $\\pi_1$ (where, $\\dot\\pi^{\\langle 1 1 \\rangle} = \n\\frac{-1}{\\tau^{2 a}} \\frac{d\\pi_1} {d\\tau}$). Below we show this \nexplicitly. For making this check, \nwe have also computed all the relevant terms appearing in the third order\nevolution equations in term of $\\pi_1, \\pi_2, \\pi_3$ (we give these \nexpressions in the appendix).  \nAdding the equations for $\\frac{d\\pi_{2}}{d\\tau}$ and $\\frac{d\\pi_{3}}{d\\tau}$,\nand using $\\pi_2 + \\pi_3 = -\\pi_1$, we obtain,\n\\begin{eqnarray}{\\label{11-final-term}}\n\\frac{d\\pi_{1}}{d\\tau} &= - \\frac{\\pi_{1}}{\\tau_\\pi}+ 2\\beta_\\pi\\frac{(-2a+b+c)}{3\\tau}+\\frac{\\pi_{1}(-40a+20b+20c)}{63\\tau}\n+\\frac{\\pi_{2}(74a+104b+74c)}{63\\tau}+\\frac{\\pi_{3}(74a+74b+104c)}{63\\tau}\\nonumber\\\\\n&-\\frac{1}{735\\beta_{\\pi}\\tau}[\\pi_{1}^{2}(-310a-90b-90c)\n+\\pi_{2}^{2}(7a+231b+7c)+\\pi_{3}^{2}(7a+7b+231c)\\nonumber\\\\\n&+\\pi_{1}\\pi_{2}(76a-38b-38c)+\\pi_{1}\\pi_{3}(76a-38b-38c)\\nonumber\\\\\n&+\\pi_{2}\\pi_{3}(-76a+38b+38c)]\n+\\frac{\\tau_{\\pi}}{315 \\tau^{2}} [\\pi_{1}(156 a^{2} +\n66 ab + 66ac) + \\pi_2 (50 a^2 -28 b^2 \\nonumber\\\\\n&+ 50c^2+58ab + 76 bc + 100 ac)+\\pi_3 (50 a^2\\nonumber\\\\\n& + 50 b^2 -28 c^2 + 76 bc + 58 ac + 100ab)]\n\\end{eqnarray}\nThis can be simplified to,\n\\begin{eqnarray}{\\label{eta-eta term}}\n\\frac{d\\pi_{1}}{d\\tau} &= - \\frac{\\pi_{1}}{\\tau_\\pi}+ 2\\beta_\\pi\\frac{(-2a+b+c)}{3\\tau}+\\frac{\\pi_{1}(-124a-64b-64c)}{63\\tau}\n+\\frac{\\pi_{2}(-10a+20b-10c)}{63\\tau}\n+\\frac{\\pi_{3}(-10a-10b+20c)}{63\\tau}\\nonumber\\\\\n&-\\frac{1}{735\\beta_{\\pi}\\tau}[\\pi_{1}^{2}(-386a-52b-52c)\n+\\pi_{2}^{2}(45a+155b+45c)+\\pi_{3}^{2}(45a+45b+155c)\\nonumber\\\\\n&+\\pi_{1}\\pi_{2}(38a-76b+38c)+\\pi_{1}\\pi_{3}(38a+38b-76c)]\\nonumber\\\\\n&+\\frac{\\tau_{\\pi}}{630 \\tau^{2}}[\\pi_{1}(212a^{2}-100b^{2}-100c^{2}-68ab-68ac-200bc)+\\pi_{2}(-156b^{2}\n\\nonumber\\\\\n&-84ab-48bc)+\\pi_{3}(-156c^{2}\n-84ac-48bc)]+\\frac{(\\pi_{1}+\\pi_{2}+\\pi_{3})(84a+84b+84c)}{63\\tau} \\nonumber\\\\\n&+ \\frac{1}{735\\beta_{\\pi}\\tau}[(-38a-38b-38c)\n(\\pi_1+\\pi_2+\\pi_3)^2 \n+ 114 (a \\pi_1 + b \\pi_{2} + c \\pi_{3})(\\pi_{1}+\\pi_{2}+\\pi_{3})] \\nonumber\\\\\n&+\\frac{\\tau_{\\pi}}{630 \\tau^{2}}\n(\\pi_{1}+\\pi_{2}+\\pi_{3})(100a^2 + 100b^2+100c^2\n+200ab+200bc+200ac)\n\\end{eqnarray}\nwhere the last three terms are zero as $\\pi_1 + \\pi_2 + \\pi_3 = 0$.\nRest of\nthe terms are precisely the expression for the $\\frac{d\\pi_1}{d\\tau}$\nequation. Hence there is no inconsistency and there is only one\nindependent ordinary differential equation (ODE).\nHence, for simplicity, we have made the assumption that\n$\\pi_{\\mu\\nu}$\ncould be characterized by a single function $\\pi$ and the three ODEs\ninvolving $x_1x_1, x_2x_2, x_3x_3$ components of the shear tensor \nare not totally\nindependent, rather adding the $x_2x_2$ and $x_3x_3$ equations ,\nit reduces to the equation for the $x_1x_1$ component. This we have \nalready discussed with reference to equations (40), (41) and (42) \nin this section. We have shown above \nthat this is also the case for the general ansatz in terms\nof $\\pi_1, \\pi_2$ and $\\pi_3$. We have also checked that putting\n$\\pi_1 = - \\pi, \\pi_2 = \\frac{\\pi}{2}, \\pi_3 = \\frac{\\pi}{2}$ in the\nODEs, we get back the earlier equations in terms of $\\pi$, namely, \nequations (40), (41) and (42) (where we have used the first order \nrelation $\\pi = \\frac{4\\beta_{\\pi}\\tau_{\\pi}}{3 \\tau}$ for rewriting \nthe last term in terms of the coefficient $\\frac{\\pi^2}{\\beta_{\\pi}\\tau}$. \nAll these expressions also reduce to the\nBjorken case for $a=1, b=0=c$.\nHence the ansatz is consistent. This is also true for the second\norder evolution equation.  \n\n\n\\section{Summary and discussion}\n\\label{sec:Summary}\n\\setcounter{equation}{0}\n\nIn this work, we have studied relativistic viscous hydrodynamics \nfrom kinetic theory to second and third order in gradient expansion. \nWe have considered Kasner space-time as the LRF\nof the three dimensional anisotropic expansion of a conformal fluid \nand have obtained the second and \nthird order evolution equations for the shear stress tensor and energy \ndensity. \nWe have used the iterative solutions of the Boltzmann \nequation for the nonequilibrium distribution function in RTA. \nWe have shown that our \nresults for the three dimensional expansion agree with the one dimensional \nBjorken expansion case in appropriate limit of the anisotropy parameters. \nFor a general \nfluid in Kasner space-time, the system may not be conformal, in which \ncase the stress energy tensor will not be traceless. It is a challenging \ntopic to study the evolution of the shear stress tensor for a nonconformal \nsystem with nonzero bulk viscosity in a general curved background. \nNonconformal fluid models contain a much larger number of transport \ncoefficients. There has been some progress in related aspects from various \napproaches (see for example, \n\\cite{Romatschke:2009, Denicol:2014, Finazzo:2014}).\nIt will be certainly interesting to explore the dissipative evolution \nequations in a higher order gradient expansion involving nonconformal \nfluid in Kasner space-time.\nOne can also work out the higher order corrections to entropy four current \nin our setup of anisotropic expansion. It will be interesting to \nrelate our results for anisotropic \nspace-time to anisotropic hydrodynamics \n(see ref.\\cite{Strickland:2014} for a review on anisotropic hydrodynamics). \nIt will be worth exploring higher order dissipative hydrodynamics for \nGubser flow \\cite{Chandrodoy:2018} and relate it to anisotropic hydrodynamics \nin the present scenario. \nIn the context of anisotropic expansion of the fluid, it will also be\ninteresting to study the higher order corrections in relativistic \nhydrodynamics in extended relaxation time approximation \n\\cite{Rocha-etal:2021, Jaiswal-etal:2021}, where the \nrelaxation time depends on particle energy. We hope to report \non these issues in future. \n\n\\vskip 10pt\n\\noindent\n{\\bf Acknowledgements} \\\\\nWe would like to thank Amaresh Jaiswal for helpful discussions.\n\\vskip 10pt\n\n\\section{Appendix}\n\\label{sec:Appendix}\n\\setcounter{equation}{0}\nWe assume that the shear stress tensor is diagonal and \nis characterized \nby three functions $\\pi_1, \\pi_2$ and $\\pi_3$, namely,  \n$\\pi^{\\mu\\nu}\\equiv\\mathrm{diag}(0,\\pi_{1}\\tau^{-2a},\n\\pi_{2}{\\tau^{-2b}},\\pi_{3}{\\tau^{-2c}})$.\nThe components of $\\dot{\\pi}^{\\langle \\mu\\nu \\rangle}$ are \ngiven by, \n\\begin{eqnarray}{\\label{zeroterm}}\n\\dot{\\pi}^{\\langle \\tau\\tau \\rangle}= 0, \\,\n\\dot{\\pi}^{\\langle x_1x_1 \\rangle}=\\frac{1}{\\tau^{2a}}\\frac{d\\pi_1}{d\\tau}, \\,\n\\nonumber\\\\\n\\dot{\\pi}^{\\langle x_2x_2 \\rangle}=\\frac{1}{\\tau^{2b}}\\frac{d\\pi_2}{d\\tau}, \\,\n\\dot{\\pi}^{\\langle x_3x_3 \\rangle}=\\frac{1}{\\tau^{2c}}\\frac{d\\pi_3}{d\\tau}\n\\end{eqnarray}\n\nComponents of other terms appearing in the third order \nevolution equation are obtained as,\n\\begin{eqnarray}{\\label{fourthterm}}\n\\pi_\\gamma^{\\langle \\tau}\\sigma^{\\tau\\rangle\\gamma}= 0\\nonumber\\\\\n\\pi_\\gamma^{\\langle x_{1}}\\sigma^{x_{1}\\rangle\\gamma}=\\frac{1}\n{9 \\tau^{2a+1}}(-2\\pi_{1}(-2a+b+c)\\nonumber\\\\\n+\\pi_{2}(a-2b+c)+\\pi_{3}(a+b-2c)\\nonumber\\\\\n\\pi_\\gamma^{\\langle x_{2}}\\sigma^{x_{2} \\rangle\\gamma}=\n\\frac{1}{9 \\tau^{2b+1}}(\\pi_{1}(-2a+b+c)\\nonumber\\\\\n-2\\pi_{2}(a-2b+c)+\\pi_{3}(a+b-2c)\\nonumber\\\\\n\\pi_\\gamma^{\\langle x_{3}}\\sigma^{x_{3} \\rangle\\gamma}=\\frac{1}\n{9 \\tau^{2c+1}}(\\pi_{1}(-2a+b+c)\\nonumber\\\\\n+\\pi_{2}(a-2b+c)-2\\pi_{3}(a+b-2c)\n\\end{eqnarray}\n\nComponents of $\\pi_\\gamma^{\\langle \\tau}\\pi^{\\tau \n\\rangle\\gamma}\\theta$ are given by, \n\\begin{eqnarray}{\\label{seventhterm}}\n\\pi_\\gamma^{\\langle \\tau}\\pi^{\\tau \\rangle\\gamma}\\theta=0\\nonumber\\\\\n\\pi_\\gamma^{\\langle x_{1}}\\pi^{x_{1} \\rangle\\gamma}\\theta=\n\\frac{(-2\\pi_{1}^{2}+\\pi_{2}^{2}+\\pi_{3}^{2})(a+b+c)}{3\\tau^{2a+1}}\\nonumber\\\\\n\\pi_\\gamma^{\\langle x_{2}}\\pi^{x_{2} \\rangle\\gamma}\\theta=\\frac{(\\pi_{1}^{2}-\n2\\pi_{2}^{2}+\\pi_{3}^{2})(a+b+c)}{3\\tau^{2b+1}}\\nonumber\\\\\n\\pi_\\gamma^{\\langle x_{3}}\\pi^{x_{3} \\rangle\\gamma}\\theta=\\frac{(\\pi_{1}^{2}+\n\\pi_{2}^{2}-2\\pi_{3}^{2})(a+b+c)}{3\\tau^{2c+1}}\n\\end{eqnarray}\n\nComponents of $\\pi^{\\mu\\nu}\\pi^{\\rho\\gamma}\n\\sigma_{\\rho\\gamma}$ are : \n\\begin{eqnarray}{\\label{eightterm}}\n\\pi^{\\tau\\tau}\\pi^{\\rho\\gamma}\\sigma_{\\rho\\gamma}=0\\nonumber\\\\\n\\pi^{x_{1}x_{1}}\\pi^{\\rho\\gamma}\\sigma_{\\rho\\gamma}=\\frac{\\pi_{1}}{3\\tau^{2a+1}}[(\\pi_{1}(-2a+b+c)\\nonumber\\\\\n+\\pi_{2}(a-2b+c)+\\pi_{3}(a+b-2c)]\\nonumber\\\\\n\\pi^{x_{2}x_{2}}\\pi^{\\rho\\gamma}\\sigma_{\\rho\\gamma}=\\frac{\\pi_{2}}{3\\tau^{2b+1}}[(\\pi_{1}(-2a+b+c)\\nonumber\\\\\n+\\pi_{2}(a-2b+c)+\\pi_{3}(a+b-2c)]\\nonumber\\\\\n\\pi^{x_{3}x_{3}}\\pi^{\\rho\\gamma}\\sigma_{\\rho\\gamma}=\\frac{\\pi_{3}}{3\\tau^{2c+1}}[(\\pi_{1}(-2a+b+c)\\nonumber\\\\\n+\\pi_{2}(a-2b+c)+\\pi_{3}(a+b-2c)]\n\\end{eqnarray}\n\nComponents of $\\pi^{\\rho\\langle \\mu}\\pi^{\\nu \\rangle\\gamma}\n\\sigma_{\\rho\\gamma}$ are given by, \n\\begin{eqnarray}{\\label{ninethterm}}\n\\pi^{\\rho\\langle \\tau}\\pi^{\\tau \\rangle\\gamma}\\sigma_{\\rho\\gamma}=0\\nonumber\\\\\n\\pi^{\\rho\\langle x_{1}}\\pi^{x_{1}\\rangle\\gamma}\\sigma_{\\rho\\gamma}=\n\\frac{1}{9\\tau^{2a+1}}[(2\\pi_{1}^{2}(-2a+b+c)\\nonumber\\\\\n-\\pi_{2}^{2}(a-2b+c)-\\pi_{3}^{2}(a+b-2c)]\\nonumber\\\\\n\\pi^{\\rho\\langle x_{2}}\\pi^{x_{2} \\rangle\\gamma}\\sigma_{\\rho\\gamma}=\n\\frac{1}{9\\tau^{2b+1}}[-\\pi_{1}^{2}(-2a+b+c)\\nonumber\\\\\n+2\\pi_{2}^{2}(a-2b+c)-\\pi_{3}^{2}(a+b-2c)]\\nonumber\\\\\n\\pi^{\\rho\\langle x_{3}}\\pi^{x_{3} \\rangle\\gamma}\\sigma_{\\rho\\gamma}=\n\\frac{1}{9\\tau^{2c+1}}[-\\pi_{1}^{2}(-2a+b+c)\\nonumber\\\\\n-\\pi_{2}^{2}(a-2b+c)+2\\pi_{3}^{2}(a+b-2c)]\n\\end{eqnarray}\n\nFor $\\nabla^{\\langle \\mu}\\left(\\nabla_\\gamma\\pi^{\\nu \n\\rangle\\gamma}\\right)$ we have, \n\\begin{eqnarray}{\\label{eleventhterm}}\n\\nabla^{\\langle \\tau}\\left(\\nabla_\\gamma\\pi^{\\tau \\rangle\\gamma}\\right)=0\n\\nonumber\\\\\n\\nabla^{\\langle x_{1}}\\left(\\nabla_\\gamma\\pi^{x_{1} \\rangle\\gamma}\\right)=\n\\frac{1}{3\\tau^{2a+2}}(\\pi_{1}(-4a^{2}+ab+ac)\\nonumber\\\\\n+\\pi_{2}(2b^{2}-2ab+bc)+\\pi_{3}(2c^{2}+bc-2ac))\\nonumber\\\\\n\\nabla^{\\langle x_{2}}\\left(\\nabla_\\gamma\\pi^{x_{2} \\rangle\\gamma}\\right)=\n\\frac{1}{3\\tau^{2b+2}}(\\pi_{1}(2a^{2}-2ab+ac)\\nonumber\\\\+\\pi_{2}(-4b^{2}+ab+bc)+\\pi_{3}(2c^{2}-2bc+ac))\\nonumber\\\\\n\\nabla^{\\langle x_{3}}\\left(\\nabla_\\gamma\\pi^{x_{3} \\rangle\\gamma}\\right)=\n\\frac{1}{3\\tau^{2c+2}}(\\pi_{1}(2a^{2}+ab-2ac)\\nonumber\\\\+\\pi_{2}(2b^{2}+ab-2bc)\n+\\pi_{3}(-4c^{2}+bc+ac))\n\\end{eqnarray}\n\nFor $\\nabla_{\\gamma}\\left(\\nabla^{\\langle \\mu}\\pi^{\\nu \n\\rangle\\gamma}\\right)$, we get, \n\\begin{eqnarray}{\\label{twelveterm}}\n\\nabla_{\\gamma}\\left(\\nabla^{\\langle \\tau}\\pi^{\\tau \\rangle\\gamma}\\right)=0\n\\nonumber\\\\\n\\nabla_{\\gamma}\\left(\\nabla^{\\langle x_{1}}\\pi^{x_{1} \\rangle\\gamma}\\right)=\n\\frac{1}{3\\tau^{2a+2}}(\\pi_{1}(-4a^{2}-2ab-2ac)\\nonumber\\\\\n+ \\pi_{2}(2b^{2}+ab+bc)+\\pi_{3}(2c^{2}+bc+ac))\\nonumber\\\\\n\\nabla_{\\gamma}\\left(\\nabla^{\\langle x_{2}}\\pi^{x_{2} \\rangle\\gamma}\\right)=\n\\frac{1}{3\\tau^{2b+2}}(\\pi_{1}(2a^{2}+ab+ac)\\nonumber\\\\\n+\\pi_{2}(-4b^{2}-2ab-2bc)+\\pi_{3}(2c^{2}+bc+ac))\\nonumber\\\\\n\\nabla_{\\gamma}\\left(\\nabla^{\\langle x_{3}}\\pi^{x_{3} \\rangle\\gamma}\\right)=\n\\frac{1}{3\\tau^{2c+2}}(\\pi_{1}(2a^{2}+ab+ac)\\nonumber\\\\\n+\\pi_{2}(2b^{2}+ab+bc)+\\pi_{3}(-4c^{2}-2bc-2ac))\n\\end{eqnarray}\n\nFor $\\nabla_{\\gamma}\\left(\\tau_\\pi\\nabla^{\\gamma}\n\\pi^{\\langle \\mu\\nu \\rangle} \\right)$, we obtain, \n\\begin{eqnarray}{\\label{fourteenterm}}\n\\nabla_{\\gamma}\\left(\\tau_\\pi\\nabla^{\\gamma}\\pi^{\\langle \\tau\\tau \\rangle}\n\\right)=0\\nonumber\\\\\n\\nabla_{\\gamma}\\left(\\tau_\\pi\\nabla^{\\gamma}\\pi^{\\langle x_{1}x_{1} \\rangle}\n\\right)=\\frac{2\\tau_\\pi(-2a^{2}\\pi_{1}+b^{2}\\pi_{2}+c^{2}\\pi_{3})}{3\\tau^{2a+2}}\\nonumber\\\\\n\\nabla_{\\gamma}\\left(\\tau_\\pi\\nabla^{\\gamma}\\pi^{\\langle x_{2}x_{2} \\rangle}\n\\right)=\\frac{2\\tau_\\pi(a^{2}\\pi_{1}-2b^{2}\\pi_{2}+c^{2}\\pi_{3})}{3\\tau^{2b+2}}\n\\nonumber\\\\\n\\nabla_{\\gamma}\\left(\\tau_\\pi\\nabla^{\\gamma}\\pi^{\\langle x_{3}x_{3} \\rangle}\n\\right)=\\frac{2\\tau_\\pi(a^{2}\\pi_{1}+b^{2}\\pi_{2}-2c^{2}\\pi_{3})}{3\\tau^{2c+2}}\n\\end{eqnarray}\n\nComponents of $\\pi^{\\mu\\nu}\\theta^2$ are given by, \n\\begin{eqnarray}{\\label{eighteenterm}}\n\\pi^{\\tau \\tau}\\theta^2=0\\nonumber\\\\\n\\pi^{x_{1}x_{1}}\\theta^2=\\frac{\\pi_{1}}{\\tau^{2a}}\\left(\\frac{a+b+c}{\\tau}\n\\right)^{2}\\nonumber\\\\\n\\pi^{x_{2}x_{2}}\\theta^2=\\frac{\\pi_{2}}{\\tau^{2b}}\\left(\\frac{a+b+c}{\\tau}\n\\right)^{2}\\nonumber\\\\\n\\pi^{x_{3}x_{3}}\\theta^2=\\frac{\\pi_{3}}{\\tau^{2c}}\\left(\\frac{a+b+c}{\\tau}\n\\right)^{2}\n\\end{eqnarray}\nThese expressions have beeen used to obtain the differential equations \nfor the components of $\\pi^{\\mu\\nu}$ in terms of \n$\\pi_1, \\pi_2, \\pi_3$. All these expressions reduce to our earlier \nresults where we have considered a single function $\\pi$ to characterize\nthe shear stress tensor $\\pi^{\\mu\\nu}$.  \n\n\\providecommand{\\href}[2]{#2}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nThe cyclic sieving phenomenon for rectangular standard tableaux was first\nproved in \\cite{Rhoades2010}. This proof used the Khazdhan-Lusztig\nbasis of the Hecke algebras. This result has been reproved in \\cite{Purbhoo2013} using the geometry of the Wronksian and has been generalised in using \\cite{Fontaine2014} using the geometry\nof the affine Grassmannian and in \\cite{Westbury2016} using Lusztig's\nbased modules. Here we give a new proof which is relatively self-contained\nusing the action of the cactus groups in the seminormal bases for the\nirreducible representations of the Hecke algebras.\n\nOur main theorem has a straightforward statement.\nLet $\\lambda$ be a partition of size $r$ and let $U_\\lambda$ be the\nassociated irreducible representation of the symmetric group, $\\mathfrak{S}_r$,\nover the rational field, $\\mathbb{Q}$. Let $c_1$ be the matrix representing the\nlong cycle with respect to a chosen basis.\nLet $c_0$ be the permutation matrix of the jeu-de-taquin promotion acting\non the set of standard tableaux of shape $\\lambda$.\nThen our main theorem is:\n\\begin{thm}\\label{thm:main} If the partition $\\lambda$ has rectangular shape then the matrices $c_1$ and $c_0$ are conjugate.\n\\end{thm}\n\nThe method of proof is to construct an interpolating matrix. This is a matrix, $c_q$, with entries in the field of rational functions, $\\mathbb{Q}(q)$, with\nthe properties:\n\\begin{itemize}\n\t\\item The evaluation of $c_q$ at $q=1$ is defined and gives $c_1$\n\t\\item The evaluation of $c_q$ at $q=0$ is defined and gives $c_0$\n\t\\item $c_q^r=1$\n\\end{itemize}\n\nThis proves Theorem~\\ref{thm:main} since $c_q$ is semisimple, the eigenvalues\nare $r$-th roots of unity and the eigenvalues are analytic functions of $q$.\nHence the eigenvalues and their multiplicities are independent of $q$.\n\n\\begin{ex}\nThe rotation matrix and its inverse are\n\\begin{equation*}\n\\left(\\begin{array}{rrrrr}\n\\frac{1}{3} & \\frac{4}{9} & 0 & \\frac{2}{3} & 0 \\\\\n\\frac{1}{2} & -\\frac{1}{12} & \\frac{3}{8} & -\\frac{1}{8} & \\frac{9}{16} \\\\\n1 & -\\frac{1}{6} & -\\frac{1}{4} & -\\frac{1}{4} & -\\frac{3}{8} \\\\\n0 & \\frac{1}{2} & \\frac{3}{4} & -\\frac{1}{4} & -\\frac{3}{8} \\\\\n0 & 1 & -\\frac{1}{2} & -\\frac{1}{2} & \\frac{1}{4}\n\\end{array}\\right)\n\\qquad\n\\left(\\begin{array}{rrrrr}\n\\frac{1}{3} & \\frac{4}{9} & \\frac{2}{3} & 0 & 0 \\\\\n\\frac{1}{2} & -\\frac{1}{12} & -\\frac{1}{8} & \\frac{3}{8} & \\frac{9}{16} \\\\\n0 & \\frac{1}{2} & -\\frac{1}{4} & \\frac{3}{4} & -\\frac{3}{8} \\\\\n1 & -\\frac{1}{6} & -\\frac{1}{4} & -\\frac{1}{4} & -\\frac{3}{8} \\\\\n0 & 1 & -\\frac{1}{2} & -\\frac{1}{2} & \\frac{1}{4}\n\\end{array}\\right)\n\\end{equation*}\n\nThe promotion matrix and its inverse are\n\\begin{equation*}\n\\left(\\begin{array}{rrrrr}\n0 & 0 & 0 & 1 & 0 \\\\\n0 & 0 & 0 & 0 & 1 \\\\\n1 & 0 & 0 & 0 & 0 \\\\\n0 & 0 & 1 & 0 & 0 \\\\\n0 & 1 & 0 & 0 & 0\n\\end{array}\\right)\n\\qquad\n\\left(\\begin{array}{rrrrr}\n0 & 0 & 1 & 0 & 0 \\\\\n0 & 0 & 0 & 0 & 1 \\\\\n0 & 0 & 0 & 1 & 0 \\\\\n1 & 0 & 0 & 0 & 0 \\\\\n0 & 1 & 0 & 0 & 0\n\\end{array}\\right)\n\\end{equation*}\n\nThe matrix which interpolates between promotion and rotation and its inverse are\n\\begin{equation*}\n\\left(\\begin{array}{rrrrr}\n\\frac{1}{[3]} & \\frac{[4]}{[3]^2} & 0 & \\frac{[4]}{[2][3]} & 0 \\\\\n\\frac{1}{[2]} & \\frac{-1}{[3][2]^2} & \\frac{[3]}{[2]^3} & \\frac{-1}{[2]^3} & \\frac{[3]^2}{[2]^4} \\\\\n1 & \\frac{-1}{[2][3]} & \\frac{-1}{[2]^2} & \\frac{-1}{[2]^2} & \\frac{-[3]}{[2]^3} \\\\\n0 & \\frac{1}{[2]} & \\frac{[3]}{[2]^2} & \\frac{-1}{[2]^2} & \\frac{-[3]}{[2]^3} \\\\\n0 & 1 & \\frac{-1}{[2]} & \\frac{-1}{[2]} & \\frac{1}{[2]^2}\n\\end{array}\\right)\n\\qquad\n\\left(\\begin{array}{rrrrr}\n\\frac{1}{[3]} & \\frac{[4]}{[3]^2} & \\frac{[2]}{[3]} & 0 & 0 \\\\\n\\frac{1}{[2]} & -\\frac{1}{[2]^2[3]} & -\\frac{1}{[2]^3} & \\frac{[3]}{[2]^3} & \\frac{[3]^2}{[2]^4} \\\\\n0 & \\frac{1}{[2]} & -\\frac{1}{[2]^2} & \\frac{[3]}{[2]^2} & -\\frac{[3]}{[2]^3} \\\\\n1 & -\\frac{1}{[2][3]} & -\\frac{1}{[2]^2} & -\\frac{1}{[2]^2} & -\\frac{[3]}{[2]^3} \\\\\n0 & 1 & -\\frac{1}{[2]} & -\\frac{1}{[2]} & \\frac{1}{[2]^2}\n\\end{array}\\right)\n\\end{equation*}\n\nIn this example the matrix which intertwines promotion and rotation can be given explicitly.\nThis matrix and its inverse are:\n\\begin{equation*}\n\\left(\\begin{array}{rrrrr}\n1 & -\\frac{[2]}{[3]} & 0 & 0 & -\\frac 1{[2]} \\\\\n0 & 1 & -\\frac 1{[2]} & -\\frac 1{[2]} & \\frac 1{[2]^2} \\\\ \n0 & 0 & 1 & 0 & -\\frac 1{[2]} \\\\\n0 & 0 & 0 & 1 & -\\frac 1{[2]} \\\\\n0 & 0 & 0 & 0 & 1\n\\end{array}\\right)\n\\qquad\n\\left(\\begin{array}{rrrrr}\n1 & \\frac{[2]}{[3]} & \\frac 1{[3]} & \\frac 1{[3]} & \\frac {[2]}{[3]} \\\\\n0 & 1 & \\frac 1{[2]} & \\frac 1{[2]} & \\frac 1{[2]^2} \\\\\n0 & 0 & 1 & 0 & \\frac 1{[2]} \\\\\n0 & 0 & 0 & 1 & \\frac 1{[2]} \\\\\n0 & 0 & 0 & 0 & 1\n\\end{array}\\right)\n\\end{equation*}\n\\end{ex}\n\nOur construction of the interpolating matrix uses the cactus group $\\mathfrak{C}_r$.\nThis group acts on the set of standard tableaux of shape $\\lambda$. This\naction is given explicitly in \\cite{Kirillov1995} (where the cactus groups are\nimplicit) and implicitly in \\cite{Henriques2006d} (where the cactus groups are\nexplicit). The relationship between these two papers was established in\n\\cite{Chmutov2016}.\n\nThe Hecke algebra, $H_r$, is a $q$-analogue of the symmetric group algebra $\\mathbb{Q}\\,\\mathfrak{S}_r$. As a $\\mathbb{Q}(q)$-algebra it is split semisimple and each \n$U_\\lambda$ has a $q$-analogue which is also absolutely irreducible.\nOur main technical tool is that, for $r>1$, there is a homomorphism\n$\\mathfrak{C}_r\\to H_r$. This homomorphism is constructed implictly using \nquantum Schur-Weyl duality and the result that the category of type I\nfinite dimensional representations of a quantised enveloping algebra is a\ncoboundary category; this is part of the construction in \\cite{Drinfelprimed1989}.\nThis implies that, for each $\\lambda\\vdash r$, there\nis an action of $\\mathfrak{C}_r$ on $U_\\lambda$.\nThis action was made explicit in \\cite{Westbury2018} in that the matrices\nrepresenting a set of generators with respect to the seminormal basis\nof $U_\\lambda$ are given explicitly. Here we make use of these matrices.\n\nThe contents of the sections are:\n\\begin{description}\n\t\\item[Cyclic sieving phenomenon] In this section we give the background\non the cyclic sieving phenomenon and deduce the cyclic sieving phenomenon\nfrom Theorem~\\ref{thm:main}.\n\\item[Cactus groups] In this section we define the cactus groups by\nfinite presentations and give the results that are needed in the proof of\nTheorem~\\ref{thm:main}.\n\\item[Hecke algebras] In this section we recall the construction of\nthe representations of the Hecke algebra in the seminormal basis and\nprove Theorem~\\ref{thm:main}.\n\\item[Conclusion] In this section we put the statement and method of proof\nof Theorem~\\ref{thm:main} in the context of the representation theory\nof quantised enveloping algebras and discuss the main difficulty in\ngeneralising Theorem~\\ref{thm:main} to this context.\n\\end{description}\n\n\\section{Cyclic sieving phenomenon}\nIn this section we explain how Theorem~\\ref{thm:main} gives the\ncyclic sieving phenomenon in \\cite{Rhoades2010}.\n\nLet $r>1$ and $\\omega$ be a primitive $r$-th root of unity. Recall the\ndefinition of the cyclic sieving phenomenon from \\cite{Reiner2004}.\n\\begin{defn}\nLet $X$ be a finite set and $c\\colon X\\to X$ a bijection that satisfies\n$c^r=1$. If the polynomial $P\\in \\mathbb{Z}[q]$ \\footnote{Note that the $q$ in this section is not the $q$ used in other sections.} satisfies\n\\begin{equation*}\n\tP(\\omega^k) = |\\Fix(c^k)|\n\\end{equation*}\nfor all $k$ where $\\Fix$ is the set of fixed points then the triple $(X,c,P)$\nexhibits the \\Dfn{cyclic sieving phenomenon}.\n\\end{defn}\nLet $\\lambda\\vdash r$ be a rectangular shape and let $X$ be the set of\nstandard tableaux of shape $\\lambda$. Denote the promotion operator\non $X$ by $p$. The problem is to determine a polynomial $P$ such that\n$(X,p,P)$ exhibits the cyclic sieving phenomenon.\n\nThe linear version of the cyclic sieving phenomenon is:\n\\begin{defn}\nLet $U$ be a finite dimensional vector space over $\\mathbb{Q}$ and $\\rho\\colon U\\to U$ an isomorphism that satisfies $\\rho^r=1$. A \\Dfn{character polynomial} is a \npolynomial $P\\in \\mathbb{Q}[q]$ that satisfies\n\\begin{equation*}\n\tP(\\omega^k) = \\tr(\\rho^k)\n\\end{equation*}\nfor all $k$.\n\\end{defn}\n\nThe two basic properties of the character polynomial are:\n\\begin{itemize}\n\\item If $\\rho$ is the permutation matrix of a bijection $c$ then $(X,c,P)$\nsatisfies the cyclic sieving phenomenon if and only if $P$ is a\ncharacter polynomial of $\\rho$.\n\n\\item Given $\\rho\\colon U\\to U$ with character polynomial $P$ and\n$\\rho'\\colon U'\\to U'$ with character polynomial $P'$ then \n$(U,\\rho)$ and $(U',\\rho')$ are isomorphic if and only if $P=P'$.\n\\end{itemize}\nIt then follows from Theorem~\\ref{thm:main} that $(X,p,P)$ exhibits the cyclic sieving phenomenon if and only if $P$ is a character polynomial for the\naction of the long cycle on $U_\\lambda$.\n\nThis character polynomial can be determined using:\n\\begin{prop}\\label{prop:fr} Let $U$ be a representation of $\\mathfrak{S}_r$. Then the principal specialisation of the Frobenius character of $U$ is a character polynomial for the action of the long cycle.\n\\end{prop}\n\n\\begin{lemma} Let $\\lambda\\vdash r$. Take $P$ to be the $q$-analogue of the hook-length formula\n\t\\begin{equation*}\n\t\t\\frac{[n]!}{\\prod_{(i,j)\\in \\lambda} [h(i,j)]}\n\t\\end{equation*}\n\twhere $h(i,j)$ is the hook length of the cell $(i,j)$ and $[n]$ is given by\n\t\\begin{equation*}\n\t\t[n] = \\frac{1-q^n}{1-q}\n\t\\end{equation*}\nThen $P$ is a character polynomial for the action of the long cycle on $U_\\lambda$.\n\\end{lemma}\n\n\\begin{proof} This is an application of Proposition~\\ref{prop:fr}.\nThe Frobenius character of $U_\\lambda$ is the Schur function $s_\\lambda$;\nand the principal specialisation of $s_\\lambda$ is given by\nthe $q$-analogue of the hook-length formula.\n\\end{proof}\n\nOther interpretations of this polynomial are available. For example,\nthis polynomial is the generating function for the statistic major index\non the set of standard tableaux of shape $\\lambda$.\n\nThe conclusion is that if $P$ is the $q$-analogue of the hook-length formula\nthen $(X,p,P)$ exhibits the cyclic sieving phenomenon. This is the main\ntheorem of \\cite{Rhoades2010}.\n\n\\section{Cactus group}\\label{sec:cactus}\nThe finite presentations of the cactus groups are:\n\\begin{defn}\\label{defn:cactus} The \\Dfn{$r$-fruit cactus group}, $\\mathfrak{C}_r$, has generators $s_{p,\\,q}$ for $1\\le p<q\\le r$ and defining relations\n\\begin{itemize}\n\t\\item $s_{p,\\,q}^2=1$\n\t\\item $s_{p,\\,q}\\, s_{k,\\,l}=s_{k,\\,l}\\, s_{p,\\,q}$ if $\\os{p,q}\\cap\\os{k,l}=\\emptyset$\n\t\\item $s_{p,\\,q}\\, s_{k,\\,l}=s_{p+q-l,\\,p+q-k}\\, s_{p,\\,q}$ if $\\os{k,l}\\subseteq\\os{p,q}$\n\\end{itemize}\n\\end{defn}\n\nLet $\\mathfrak{S}_r$ be the symmetric group on $r$ letters.\nThere is a homomorphism $\\mathfrak{C}_r\\rightarrow \\mathfrak{S}_r$ defined by $s_{p,\\,q}\\mapsto \\widehat{s}_{p,\\,q}$ where $\\widehat{s}_{p,\\,q}$ is the permutation\n\\begin{equation}\\label{eq:hom}\n\\widehat{s}_{p,\\,q}(i)=\\begin{cases}\np+q-i & \\text{if $p\\le i\\le q$} \\\\\ni & \\text{otherwise}\n\\end{cases}\n\\end{equation}\n\nNote that $\\mathfrak{C}_r$ is generated by $s_{1,q}$ for $2\\le q\\le r$, since\n\\begin{equation}\\label{eqn:gen}\ns_{p,\\,q}=s_{1,\\,q}s_{1,\\,q-p}s_{1,\\,q}\n\\end{equation}\n\nNext we introduce several sets of generators for the cactus groups,\nfollowing \\cite{Kirillov2001}.\n\nThe first set is $q_i=s_{1,\\,i}$ for $1\\leqslant i\\leqslant n$.\nThese are generators, as noted in \\eqref{eqn:gen}.\nThe second set of generators\nare $p_i$ given by the relations\n\\begin{equation*}\np_i=\\begin{cases}\nq_1 & \\text{if $i=1$}\\\\\nq_{i-1}\\,q_i & \\text{if $i>1$}\n\\end{cases} \\qquad\nq_i = p_1\\,p_2\\dotsb p_i\n\\end{equation*}\nThe third set of generators are $t_i$ given by\n\\begin{equation*}\nt_i=\\begin{cases}\np_1 & \\text{if $i=1$}\\\\\np_i\\,p_{i-1}^{-1} & \\text{if $i>1$}\n\\end{cases} \\qquad\np_i = t_i\\,t_{i-1}\\dotsb t_1\n\\end{equation*}\n\nThen we also have\n\\begin{equation*}\nt_i=\\begin{cases}\nq_1 & \\text{if $i=1$}\\\\\nq_1\\,q_2\\,q_1 & \\text{if $i=2$}\\\\\nq_{i-1}\\,q_i\\,q_{i-1}\\,q_{i-2} & \\text{if $i>2$}\n\\end{cases}\n\\end{equation*}\n\nThe images of these three sets of generators under the homomorphism to $\\mathfrak{S}_r$ are:\n\\begin{itemize}\n\\item the image of $t_i$ is the transposition $(i,i+1)$\n\\item the image of $p_i$ is the cycle $(i,1,2,\\dotsc,i-1)$\n\\item the image of $q_i$ is the involution\n\\begin{equation*}\nq_i(j)=\\begin{cases}\ni-j+1  & \\text{if $1\\leqslant j\\leqslant i$}\\\\\nj & \\text{if $j>i$}\n\\end{cases}\n\\end{equation*}\nIn particular, the image of $p_{r-1}\\in\\mathfrak{S}_r$ is the long cycle and\nthe image of $q_r\\in\\mathfrak{S}_r$ is the longest element.\n\\end{itemize}\n\nThere is a dual version of these generators.\n\\begin{align*}\n\tv_i &= t_i\\,t_{i+1}\\dotsc t_{r-1}\\\\\n\tw_i &= v_{r-1}\\,v_{r-2}\\dotsc v_{r-i}\n\\end{align*}\n\nThe following is \\cite[Proposition~1.4]{Kirillov1995} and is also clear from\nthe growth diagram.\n\\begin{lemma}\\label{lem:cyclic} For $r>1$,\n\t\\begin{equation*}\n\tp_{r-1}^r=w_{r-1}\\,q_{r-1}\n\t\\end{equation*}\n\\end{lemma}\n\nFor a standard tableau, $T$, let $s_iT$ be the\ntableau obtained from $T$ by interchanging $i$ and $i+1$.\nDefine an involution $t_i$ on standard tableaux by\n\\begin{equation*}\n\tt_i(T) = \\begin{cases}\n\t\ts_iT & \\text{if $s_iT$ is standard} \\\\\n\t\tT & \\text{otherwise}\n\t\\end{cases}\n\\end{equation*}\n\nThen these involutions generate an action of the cactus group $\\mathfrak{C}_r$\non standard tableaux of size $r$. The action of the element $p_{r-1}\\in\\mathfrak{C}_r$\nis the same as jeu-de-taquin promotion.\n\n\\begin{prop}\\label{prop:order} The operator $p_{r-1}$ acting on rectangular tableaux of size $r$\n\tsatisfies\n\t$$p_{r-1}^r=1$$\n\\end{prop}\n\n\\begin{proof}\n\tBy Lemma~\\ref{lem:cyclic} it is sufficient to show $w_{n-1} = q_{n-1}$.\n\tThis follows from two observations on the reverse-complement.\n\tRecall that reverse-complement is the involution given by rotating a rectangular shape\n\tstandard tableaux through a half-turn and reversing the numbering.\n\t\n\tThe first observation is that conjugating by reverse-complement interchanges the two actions of the cactus groups. In particular, $w_{r-1}$ is the conjugate of $q_{n-1}$.\n\tThe second observation is that $q_{r-1}$ commutes with reverse-complement.\n\\end{proof}\n\n\\section{Hecke algebras}\\label{sec:hecke}\nLet $\\mathbb{Q}(q)$ be the field of rational functions in an indeterminate $q$.\nThe quantum integers $[n]\\in \\mathbb{Q}(q)$ are defined by\n\\begin{equation*}\n[n] = \\frac{q^n-q^{-n}}{q-q^{-1}}\n\\end{equation*}\n\n\n\\begin{defn}\n\tThe Hecke algebra $H_r(q)$ is generated by $u_i$ for $1\\le i\\le r-1$\n\tand the defining relations are\n\t\\begin{align*}\n\tu_i^2 &= -[2]\\, u_i \\\\\n\tu_i\\,u_{i+1}\\,u_i-u_i&=u_{i+1}\\,u_i\\,u_{i+1}-u_{i+1} \\\\\n\tu_i\\,u_j&=u_j\\,u_i\\qquad\\text{for $|i-j|>1$}\n\t\\end{align*}\n\\end{defn}\n\nLet $\\sigma_i$ be the standard generators of the braid group, $B_r$.\nThen we have a homomorphism $B_r\\to H_r(q)$ given by\n\\begin{equation*}\n\t\\sigma_i^{\\pm 1} \\mapsto q^{\\pm1}  + u_i\n\\end{equation*}\nThe image of $\\sigma_i$ then satisfies\n\\begin{equation*}\n\t\\sigma_i-\\sigma_i^{-1} = q - q^{-1}\n\\end{equation*}\nYoung's seminormal forms are representations of the symmetric groups.\nThese were introduced in \\cite[Theorem~IV]{Young1932}. Here we give\nthe analogous construction for the Hecke algebras.\n\nFix a shape $\\lambda$ of size $r$. Then we construct a \nrepresentation of $H_r(q)$ on the vector space with basis the set\nof standard tableaux of shape $\\lambda$.\n\nThe \\Dfn{content vector} of a standard tableau $T$ of size $n$ is a function\n$\\mathbf{ct}_T\\colon [1,2,\\dotsc ,n]\\to\\mathbb{Z}$. The entry\n$\\mathbf{ct}_T(k)\\in\\mathbb{Z}$ is given by $\\mathbf{ct}_T(k)=j-i$ if $k$ is in box $(i,j)$ in $T$.\nThe content vector of $T$ determines $T$. The \\Dfn{axial distance}\nis $a_T(i) = \\mathbf{ct}_{T}(i+1)-\\mathbf{ct}_{T}(i)$.\n\nDefine a linear operator $\\overline{s}_i$ by\n\\begin{equation*}\n\t\\overline{s}_i(T) = \\begin{cases}\n\t\ts_iT & \\text{if $s_iT$ is standard} \\\\\n\t\t0 & \\text{otherwise}\n\t\\end{cases}\n\\end{equation*}\n\nThe following is \\cite[Theorem~3.22]{Ram2003}. The seminormal representations of\n$H_r(q)$ are defined by giving the matrices representing the generators.\n\\begin{prop}\n\tThe action of $u_i$ is given by\n\t\\begin{equation*} u_i\\:T = \n\t\\begin{cases}\n\t-\\frac{[a-1]}{[a]}\\:T + \\frac{[a-1]}{[a]}\\:\\overline{s}_iT &\\text{if $\\mathbf{ct}_T(i+1)>\\mathbf{ct}_T(i)$}\\\\\n\t-\\frac{[a-1]}{[a]}\\:T + \\frac{[a+1]}{[a]}\\:\\overline{s}_iT &\\text{if $\\mathbf{ct}_T(i)>\\mathbf{ct}_T(i+1)$}\t\n\t\\end{cases}\n\t\\end{equation*}\nwhere $a$ is the axial distance $a_T(i)$.\n\\end{prop}\n\nAssume $T$ and $s_iT$ are standard and $a_T(i)>1$. Then on the subspace\nwith ordered basis $(T,s_iT)$.\n\\begin{equation*}\nu_i =\t\\left[ \\begin {array}{cc} -\\frac {[a-1]}{ [a]  }& \\frac{[a-1]}{[a]}\n\\\\ \\noalign{\\medskip}{\\frac {[a+1]  }{\n\t\t[a]}}&-\\frac {[a+1]}{ [a]  }\\end {array} \\right]\n\t\\qquad\n\\sigma_i=\\left[ \\begin {array}{cc} \\frac {q^a}{ [a]  }&\\frac{[a-1]}{[a]}\\:\n\\\\ \\noalign{\\medskip}{\\frac {[a+1]  }{\n\t\t[a]}}&\\frac {-q^{-a}}{ [a]  }\\end {array} \\right]\n\\end{equation*}\n\nThe action of $\\mathfrak{C}_r$ is defined by giving the matrices representing the generators\n$\\{t_i\\}$. The following is \\cite[Theorem~4.8]{Westbury2018}.\n\\begin{thm} The action of $t^{(q)}_i$ is given by\n\t\\begin{equation*} t^{(q)}_i (T) = \n\t\\begin{cases}\n\t-\\frac{1}{[a]}\\:T + \\frac{[a-1]}{[a]}\\:s_iT &\\text{if $\\mathbf{ct}_T(i+1)>\\mathbf{ct}_T(i)$}\\\\\n\t-\\frac{1}{[a]}\\:T + \\frac{[a+1]}{[a]}\\:s_iT &\\text{if $\\mathbf{ct}_T(i)>\\mathbf{ct}_T(i+1)$}\t\n\t\\end{cases}\n\t\\end{equation*}\n\\end{thm}\n\nAssume $T$ and $s_iT$ are standard and $a_T(i)>1$. Then on the subspace\nwith ordered basis $(T,s_iT)$.\n\\begin{equation*}\nt^{(q)}_i=\\left[ \\begin {array}{cc} \\frac {1}{ [a]  }&\\frac{[a-1]}{[a]}\n\\\\ \\noalign{\\medskip}{\\frac {[a+1]  }{\n\t\t[a]}}&-\\frac {1}{ [a]  }\\end {array} \\right]\n\\end{equation*}\n\nLet $p^{(q)}_{r-1}$ be the matrix representing $p_{r-1}\\in\\mathfrak{C}_r$. Then we prove\nTheorem~\\ref{thm:main} by showing that a modification of $p^{(q)}_{r-1}$\nis an interpolating matrix.\n\n\\begin{prop} The operator $p^{(q)}_{r-1}$ acting on rectangular tableaux of size $r$\n\tsatisfies\n\t$$(p^{(q)}_{r-1})^r=1$$\n\\end{prop}\n\n\\begin{proof} The proof is the same as the proof of Proposition~\\ref{prop:order}.\n\\end{proof}\n\n\\begin{lemma} The evaluation of $p^{(q)}_{r-1}$ at $q=1$ is defined and gives the action of the long cycle. \n\\end{lemma}\n\n\\begin{proof} The action of $\\mathfrak{C}_r$ on $U_\\lambda$ can be evaluated at $q=1$.\nThis action factors through the homomorphism in \\eqref{eq:hom} to give the\nstandard action of $\\mathfrak{S}_r$ in the seminormal basis. In particular,\nthe homomorphism in \\eqref{eq:hom} maps $p^{(q)}_{r-1}$ to the long cycle in\n$\\mathfrak{S}_r$.\n\\end{proof}\n\nThe matrix $t^{(q)}_i$ is not regular at $q=0$ as $\\frac{[a+1]}{[a]}$ has a\nsimple pole at $q=0$. Let $D$ be the diagonal matrix whose diagonal entry\ncorresponding to $T$ is $q^{\\mathrm{inv}(T)}$ where $\\mathrm{inv}(T)$ is the\ninversion number of $T$. Let $\\widehat{t}^{(q)}_i$ be $t^{(q)}_i$ conjugated by $D$.\n\n\\begin{lemma}\nThe matrix $\\widehat{t}^{(q)}_i$ is regular at $q=0$ and the evaluation at $q=0$ is the matrix of the involution $t_i$.\n\\end{lemma}\n\\begin{proof} By inspection.\n\\end{proof}\n\nFor any $\\lambda\\vdash r$, the matrices $\\widehat{t}^{(q)}_i$ generate an action of $\\mathfrak{C}_r$ and the matrix\nof any element is regular at $q=0$. Let $\\widehat{p}^{(q)}_{r-1}$ be the matrix\nof $p_{r-1}\\in\\mathfrak{C}_r$. Then we have shown that if $\\lambda$ has rectangular shape then $\\widehat{p}^{(q)}_{r-1}$\nis an interpolating matrix and so have proved Theorem~\\ref{thm:main}.\n\n\\section{Conclusion}\nIn conclusion we put this result in the context of the representation theory\nof quantum groups and discuss the generalisation of the statement and method of proof of Theorem~\\ref{thm:main} in this context.\n\nLet $\\mathsf{C}$ be a finite type Cartan matrix and $U_q(\\mathsf{C})$ the associated\nquantised enveloping algebra. Let $\\varpi$ be a dominant weight in the\nweight lattice of $\\mathsf{C}$. Let $V_q(\\varpi)$ be the type I highest weight\nrepresentation of $U_q(\\mathsf{C})$ and let $C(\\varpi)$ be the crystal of $V_q(\\varpi)$.\n\nThe cactus group $\\mathfrak{C}_r$ acts on the crystal $\\otimes^r C(\\varpi)$.\nThis implies that $\\mathfrak{C}_r$ acts on the set of highest weight words\nin $\\otimes^r C(\\varpi)$, preserving the weight. \nIn particular $\\mathfrak{C}_r$ acts on $\\Inv_r(C(\\varpi))$, the set of highest weight\nwords of weight 0. Let $c_0$ be the permutation matrix of the action of\n$p_{r-1}\\in\\mathfrak{C}_r$.\n\nLet $L(\\mathsf{C})$ be the semisimple Lie algebra of $\\mathsf{C}$. Let $V(\\varpi)$ be the\nhighest weight representation of $L(\\mathsf{C})$. The symmetric group $\\mathfrak{S}_r$\nacts on the representation $\\otimes^r V(\\varpi)$. \nThis implies that $\\mathfrak{S}_r$ acts on the space of highest weight tensors\nin $\\otimes^r V(\\varpi)$, preserving the weight. \nIn particular $\\mathfrak{S}_r$ acts on $\\Inv_r(V(\\varpi))$, the space of invariant tensors.\nLet $c_1$ be the matrix representing the long cycle with respect to a\nchosen basis.\n\nThe generalisation of Theorem~\\ref{thm:main} is that the matrices\n$c_0$ and $c_1$ are conjugate. Theorem~\\ref{thm:main} is the case $\\mathsf{C}$\nhas type $A$ and $\\varpi$ is the first fundamental weight; so \n$L(\\mathsf{C})$ is $\\mathfrak{sl}(n)$ for some $n$ and $V(\\varpi)$ is the vector representation.\n\nNow we attempt to generalise the proof of Theorem~\\ref{thm:main}.\nThe cactus group $\\mathfrak{C}_r$ acts on the representation $\\otimes^r V_q(\\varpi)$.\nThis implies that $\\mathfrak{C}_r$ acts on the set of highest weight tensors\nin $\\otimes^r V_q(\\varpi)$, preserving the weight. \nIn particular $\\mathfrak{C}_r$ acts on $\\Inv_r(V_q(\\varpi))$, the space of invariant tensors. Let $c_q$ be the matrix representing $p_{r-1}\\in\\mathfrak{C}_r$. with respect to a\nchosen basis.\n\nThen $c_q$ has the following two of the three properties of an interpolating\nmatrix. These properties are independent of the choice of basis of\n$\\Inv_r(V_q(\\varpi))$.\n\\begin{itemize}\n\t\\item If the evaluation of $c_q$ at $q=1$ is defined then this gives the action of the long cycle.\n\t\\item $c_q^r=1$.\n\\end{itemize}\n\nHence to show that $c_q$ is an interpolating matrix it remains to show\nthat there exists a basis of $\\Inv_r(V_q(\\varpi))$ such that $c_q$ is\nregular at $q=0$ and the evaluation at $q=0$ is $c_0$. If\n$V(\\varpi)$ admits an invariant symplectic form then there are sign issues.\nThese sign issues can be dealt with by taking $V(\\varpi)$ to be an odd super vector\nspace so that the symplectic form becomes a symmetric inner product.\nThis is proved in \\cite{Westbury2016} using the theory of based modules\nin \\cite{Lusztig1993}.\nIt would be preferable to have a self-contained proof.\n\nIn the proof of Theorem~\\ref{thm:main} we showed that a modification of the seminormal basis has the desired property. The seminormal basis\nof $\\Inv_r(V_q(\\varpi))$ is defined for any $\\varpi$ such that all nonzero\nweight spaces of $V(\\varpi)$ are one dimensional. Examples are,\n\\begin{itemize}\n\t\\item All minuscule representations.\n\t\\item The symmetric powers of the vector representation of $\\mathfrak{sl}(n)$.\n\t\\item The fundamental representation of $G_2$.\n\\end{itemize}\nThis raises the question of whether a modification of the seminormal basis\nhas the desired property.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
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+{"text":"\\section{Introduction}\\setcounter{equation}{0}\\label{S1}\n\nDirected hypergraphs are the generalization of digraphs and  have been widely  used  in  \ndiscrete mathematics and computer science, see e.g. \\cite{Sur}, \\cite{Berge},  \\cite{mor},  and \\cite{Gallo}. \nIn particular,  the  directed hypergraphs  give effective  tools  for the investigation of databases and \nstructures on complicated  discrete  objects. \n\nRecently, the topological properties of digraphs, hypergraphs, multigraphs, and \nquivers have been studied using various (co)homologies theories, consult e.g. \\cite{Embed}, \n\\cite{Graham}, \\cite{Betti}, \\cite{Parks}, \\cite{Mi3}, \\cite{Forum}, \\cite{Hyper}, \\cite{Pcomplex}. \n\n In this paper,  we  construct  several functorial and homotopy invariant homology theories on \n the category of directed hypergraphs  using the  path homology theory introduced in \\cite{Mi4},  \\cite{Hyper},   \\cite{Mi2}, \\cite{Pcomplex}, and \n\\cite{Forum}. \n\n A rich structure of a directed hypergraph gives a number of opportunities  to define \n functorially a path complex for   the category of hypergraphs which we construct in the paper. \n We describe these  constructions in Section \\ref{S3}.   We  introduce also a notion of a homotopy in the category of directed hypergraphs  and describe  functorial relations  between homotopy categories of directed hypergraphs,  digraphs,   and path complexes.  \n  \nThe essential difference from the situation of the category of digraphs is \nthe  existence of the notion of the density of the path complex that we introduce for the two  of the introduced path complexes of directed hypergraphs. This notion \ngives an opportunity to define a filtration on the corresponding path complex and hence a filtration on\nits path homology groups.  We consider all homology groups with  coefficients in a unitary   commutative ring $R$.\n\nIn Section  \\ref{S2},   we  define a category  of directed hypergraphs  and introduce the notion of homotopy in this category. \n\nIn  Section \\ref{S3}, we  construct several path homology theories on the category of directed  hypergraphs.\n\n\n \\section{Path complexes and homotopy of directed hypergraphs}\\label{S2}\n\\setcounter{equation}{0}\n\nLet $\\Pi=(V,P)$ be a path complex with $V=\\{0,\\dots, n\\}$ and $J=\\{0,1\\}$ be a set, see \\cite{Hyper}, \\cite{Pcomplex}. \nDefine a path complex $\\Pi^{\\prime}=(V^{\\prime}, P^{\\prime})$ where $V^{\\prime}=\\{0^{\\prime}, \\dots, n^{\\prime}\\}$ and  \n$p^{\\prime}=(i_0^{\\prime}\\dots i_n^{\\prime})\\in P^{\\prime}$ iff $p=(i_0\\dots i_n)\\in P$. We  identify \n$V\\times J=V\\times\\{0\\}\\amalg V\\times\\{1\\}$ with  $V\\amalg V^{\\prime}$. Define  a path complex $\\Pi^{\\uparrow}=(V\\times J, P^{\\uparrow})$  where  \n\\begin{equation*}\\label{2.1}\n\\begin{matrix}\nP^{\\uparrow}=P\\cup P^{\\prime}\\cup P^{\\#}, \\\\\n{P^\\#}=\\{ q^\\#_k=(i_0\\dots i_ki_k^{\\prime}i^{\\prime}_{k+1}\\dots i_n^{\\prime})|q=(i_0\\dots i_ki_{k+1}\\dots i_n)\\in P \\}.\\\\\n\\end{matrix}\n\\end{equation*}\nWe have   morphisms \n$\ni_{\\bullet}\\colon \\Pi \\to \\Pi^{\\uparrow}\n$\nand $j_{\\bullet}\\colon \\Pi \\to \\Pi^{\\uparrow}$\nthat are  induced by the natural inclusion $V$ onto $V\\times \\{0\\}$ and  onto   $V\\times\\{1\\}$, respectively.\n \n\\begin{definition} \\label{d2.1}\\rm   (i) A  \\emph{ hypergraph} is a pair $G=(V,E)$  consisting of  a non-empty   \n\tset  $V$ and  a  set  $E=\\{\\bold e_1,\\dots, \\bold e_n\\}$  of    distinct and non-ordered subsets of $V$ such that \n\t$\n\t\\bigcup_{i=1}^n \\bold  e_i=V\n\t$ and every $\\mathbf e_i$ contains strictly more than one element. \n\tThe elements of $V$ are called \\emph{vertices} and the elements of  $E$ are called \\emph{edges}.\n\n\n\t\n\t\n\t(ii) A \\emph{directed hypergraph} $G$  is a pair $(V,E)$ consisting of a  set $V$   and a   set \n\t$E=\\{\\bold e_1,\\dots , \\bold e_n\\}$   where $\\bold e_i\\in E$    is an ordered pair $(A_i,B_i)$  of disjoint non-empty subsets  of the set $V$  such that \n\t$V=\\bigcup_{\\bold e_i\\in  E} (A_i\\cup B_i)$. The elements of $V$ are called \\emph{vertices} and   the elements of $E$  are called \\emph{arrows}.  \n\tThe set $A=\\mbox{orig }(A\\rightarrow B)$ is called \n\tthe \\emph{origin of the arrow} and the set  $B=\\mbox{end}(A\\rightarrow B)$\n\tis called the \\emph{end of the arrow}. The elements of $A$ are called \n\tthe \\emph{initial vertices} of $A\\to B$ and  the elements of $B$ are called its \\emph{terminal vertices}.  \n\n\\end{definition}\n\n \nFor a finite set  $X$  let ${\\mathbf{P}}(X)$ denote as usual the power set. \nWe define  a set \n$\n\\mathbb P(X)\\colon =  \\{{\\mathbf{P}}(X)\\setminus \\emptyset\\}\\times  \n\\{{\\mathbf{P}}(X)\\setminus \\emptyset\\}\n$\nconsisting  of ordered pairs of non-empty subsets of $X$.   \nEvery  map of finite sets $f\\colon V\\to W$ induces a map $\\mathbb P(f)\\colon\\mathbb P(V)\\to \\mathbb P(W)$. \nFor a directed hypergraph $G=(V,E)$,   by Definition \\ref{d2.1}, we have the natural map  $\\varphi_G\\colon E\\to \\mathbb P(V)$ defined by  $\\varphi_G(A\\to B)\\colon =(A,B)$. \n\n\\begin{definition}\\label{d2.2} \\rm   Let $G=(V_G,E_G)$  and\n$H=(V_H,E_H)$  be two  directed hypergraphs. A  \\emph{morphism} $f\\colon G\\to H$  is given by a pair of maps  $f_V\\colon V_G\\to V_H$ \nand $f_E\\colon E_G\\to E_H$ \n such that  the following diagram \n$$\n\\begin{matrix}\nE_G&\\overset{\\varphi_G}\\longrightarrow &\\mathbb P(V_G)\\\\\n\\ \\ \\downarrow f_E&&\\ \\  \\downarrow \\mathbb P(f_V)\\\\\nE_H&\\overset{\\varphi_H}\\longrightarrow &\\mathbb P(V_H)\\\\\n\\end{matrix}\n$$\nis commutative. \n\\end{definition}\n\nLet us denote by  $\\mathcal{DH}$  the category whose objects are directed  hypergraphs and whose morphisms are morphisms of  directed hypergraphs. \n\n For a directed hypergraph $G=(V_G,E_G)$, we  can  consider \nsubsets \n${\\mathbf{P}}_0(G)\\subset  {\\mathbf{P}}(V_G)\\setminus \\emptyset$,  \n${\\mathbf{P}}_1(G)\\subset  {\\mathbf{P}}(V_G)\\setminus \\emptyset$ and \n${\\mathbf{P}}_{01}(G)={\\mathbf{P}}_{0}(G)\\cup {\\mathbf{P}}_{1}(G)$\nby setting\n\\begin{equation*}\\label{2.1}\n\\begin{matrix}\n{\\mathbf{P}}_0(G)=\\{A\\in  {\\mathbf{P}}(V_G)\\setminus \\emptyset| \\exists \nB\\in  {\\mathbf{P}}(V_G)\\setminus \\emptyset:  \\ A\\to B\\in E_G\\}, \\\\\n{\\mathbf{P}}_1(G)=\\{B\\in  {\\mathbf{P}}(V_G)\\setminus \\emptyset| \\exists \nA\\in  {\\mathbf{P}}(V_G)\\setminus \\emptyset: \\ A\\to B\\in E_G\\}. \\\\\n\\end{matrix}\n\\end{equation*} \n\n\\begin{definition}\\label{d2.3}\\rm  Let $G=(V_G,E_G)$ and $H=(V_H, E_H)$ be  directed hypergraphs. \nWe define the \\emph{box product} $G\\Box H$ as a directed hypergraph \nwith the set of vertices $V_{G\\Box H}=V_{G}\\times V_{H}$ and the set of  arrows  \n$E_{G\\Box H}$ consisting of the union of  arrows \n$\n\\{A\\times C\\to  B\\times C\\}\n$\nwith $(A\\to B)\\in E_G$,   $C\\in {\\mathbf{P}}_{01}(H)$ and \n$ \\{A\\times C\\to  A\\times D\\}$\nwith \n$ (C\\to D)\\in E_H$,  $A\\in \n{\\mathbf{P}}_{01}(G)$.\n\\end{definition}\n Every connected digraph $H=(V_H, E_H)$ can be considered as a  directed  hypergraph \n with the same set of vertices and  of  a set of arrows of the form $\\{v\\}\\to \\{w\\}$  whith  $(v\\to w)\\in E_H$.  \n Hence,  Definition \\ref{d2.3} gives naturally \na box product   $G\\Box H$  of a directed hypergraph $G$ and a connected digraph $H$.  \nNote that a line digraph $I_n$ defined for example in \\cite[Sec. 3.1]{MiHomotopy} is connected and  that we have two digraphs $I_1$, namely $0\\to 1$ and $1\\to 0$.  \n\n\n\\begin{definition}\\label{d2.4} \\rm i) Two  morphisms  $f_0, f_1\\colon G\\rightarrow H$ of directed hypergraphs  \n\tare called \\emph{one-step homotopic} if there exists a line digraph $I_1$  and  a morphism  \n\t$F\\colon G\\Box I_1\\rightarrow H$,  such that \n\\begin{equation*}\nF|_{G\\Box \\{0\\}}=f_0\\colon G\\Box \\{0\\}\\rightarrow H,\\ \\ F|_{G\\Box\n\\{1\\}}=f_1\\colon G\\Box \\{1\\}\\rightarrow H.\n\\end{equation*}\nIf the appropriate morphism $F$ called a one-step homotopy exists, we write  $f_0\\simeq_1 f_1$.\n \n\nii) Two  morphisms  $ f,g\\colon G \\to  H$  of directed hypergraphs are called  \\emph{homotopic},  which we denote   $ f\\simeq  g$ if there exists a sequence \nof morphisms \n$\nf_i\\colon G\\to H$ for   $i=0,\\dots,  n$  such that \n $ f=f_0\\simeq_1  f_1\\simeq_1 \\dots \\simeq_1  f_n =g$.\n\niii) Two  directed hypergraphs   $G$ and $H$ are \\emph{homotopy equivalent} if there\nexist  morphisms \n$\nf\\colon G\\to H$ and $g\\colon H\\to G$\nsuch that \n$ fg \\simeq  { \\operatorname{Id}_{H}}$ and \n$ gf\\simeq {\\operatorname{Id}_G}\n$. \n  In such a case,  we write $G\\simeq H$ and  call the  morphisms  $f$, $g$ \\emph{homotopy inverses } of each other.\n\\end{definition}\n\n\\begin{proposition}\\label{p2.5} Two  morphisms  $ f,g\\colon G \\to  H$  of directed hypergraphs \n\tare homotopic if and only if there is a line digraph $I_n$ with $n\\geq 0$ and a morphism  \n\t$F\\colon G\\Box I_n\\rightarrow H$   such that \n$\nF|_{G\\Box \\{0\\}}=f_0\\colon G\\Box \\{0\\}\\rightarrow H,\\ \\ F|_{G\\Box\n\\{n\\}}=g\\colon G\\Box \\{n\\}\\rightarrow H. \\ \\  \\ \n$  $\\blacksquare$\n\\end{proposition}\n\nThe relation \"to be homotopic\"  is  an equivalence relation on the set of morphisms between  two directed  \nhypergraphs, and homotopy equivalence  is an equivalence relation on the set of directed hypergraphs. \nThus, we can consider  a category \n${h} \\mathcal{ DH}$ whose objects are directed hypergraphs and morphisms are the classes of homotopic morphisms. \nWe shall call the category ${h} \\mathcal{DH}$  by \n\\emph{homotopy category of directed hypergraphs}.\n\n\n\\section{Path homology of directed hypergraphs}\\setcounter{equation}{0}\\label{S3}\n\n\\subsection{k-connective  path homology}\\label{S31}\n\n For a  directed hypergraph   $G= (V, E)$ and $c=1,2,3, \\dots $\ndefine a path complex  \\cite[S3.1]{Pcomplex}  $\\mathfrak C^c(G)=(V^c, P_G^c)$   where  \n$V^c=V$ and  a path $(i_0\\dots i_n)\\in P_{V}$ lies in $P_G^c$  iff \nfor any pair of consequent vertices $(i_{k}, i_{k+1})$  of the path, we have $i_{k}=i_{k+1}$ or\nthere are at least $c$  different edges $\\bold e_1=(A_1\\to B_1), \\dots , \\bold e_c=(A_c\\to B_c)$ such that \nthe vertex $i_k$ is the initial vertex and the vertex $i_{k+1}$ is the terminal vertex of  every edge $\\bold e_i$. \nThe number  $c$ is called the \\emph{density} of the path complex $\\mathfrak C^c(G)$. It is clear that we have \na filtration \n\\begin{equation}\\label{3.1}\n\\mathfrak C(G)= \\mathfrak C^{1}(G)\\supset \\mathfrak C^{2}(G)\\supset \\mathfrak C^{3}(G)\\supset \\dots\n\\end{equation}\n  \n\n\\begin{proposition}\\label{p3.1}\n For every morphism of directed hypergraphs $f\\colon G\\to H$  define a  morphism  \n$$\n\\mathfrak C(f)=(f_V^1, f_p^1)\\colon \\mathfrak C(G)\\to \\mathfrak C(H)\n$$ \nof path complexes putting $f_V^1\\colon =f_V$ and    \n$f_p^1\\colon=f_p|_{P^1_G}  \\colon P^1_G\\to  P^1_H$ where     $f_p$ is defined \nby  $f_p(i_0\\dots i_n)= \\left(f(i_0)\\dots f(i_n)\\right)$. Then \n we have the functor $\\mathfrak C$  from the category $\\mathcal{DH}$ of directed hypergraphs to the category  $\\mathcal P$ of path complexes.\n \\quad $ \\blacksquare$\n\\end{proposition}\n\n The functor   $\\mathfrak C$ \n provides the functorial  path homology theory on the category  $\\mathcal{DH}$\nof directed hypergraphs. For any  directed hypergraph $G$ and $k\\in \\mathbb N$, we set\n $\n H_*^{\\bold {c}( k)}(G)\\colon = H_*(\\mathfrak C^k(G))$  as \\emph{regular path homology groups} \nof  path complex\n$\\mathfrak C^k(G)$, see  \\cite[S2]{Hyper}. We denote $H_*^{\\bold c}(G)\\colon =H_n^{\\bold {c}(1)}(G)$.  \n\nWe  call these homology groups  \\emph{the connective path homology groups} \nand for $k\\geq 2$ \\emph{the $k$-connective path homology groups} of the\n directed  hypergraph $G$, respectively.  The connective path homology theory is\n functorial  by Proposition \\ref{p3.1}.  However\nthe $k$-connective homology theory $H_n^{\\bold{c}( k)}(G)$ is not functorial for \n$k\\geq 2$ as it follows from Example \\ref{e3.2} below.  For any directed hypergraph\n $G$  the filtration in\n (\\ref{3.1}) induces homomorphisms \n\\begin{equation*}\nH_n^{\\bold c}(G)=H_n^{\\bold {c}( 1)}(G)\\longleftarrow  H_n^{\\bold{c}( 2)}G)\\longleftarrow H_n^{\\bold{c}( 3)}(G)\\longleftarrow \\dots \\ \\ .\n\\end{equation*}\n\n Let $\\mathcal D$  be a category of  digraphs without loops \n\\cite[S2]{MiHomotopy}. A category $\\mathcal G$ of graphs  is defined similarly \n\\cite[S6]{MiHomotopy}. \n\nLet $G=(V, E)$ be a directed hypergraph. Define a digraph \n$\\mathfrak G(G)=\\left(V^d_G, E^d_G\\right)$ where $V_G^d=V$ and   an arrow $v\\to w$ lies in $E^d_G$ iff \nthere is a hyperedge  $(A\\to B)\\in E$ such that $v\\in A, w\\in B$. \n\n\\begin{example}\\label{e3.2} \\rm   i) Let $G=(V,E)$ be a directed hypergraph  such that \n$V$ is the union $A\\cup B$ of two  non-empty sets  with empty intersection and  the set $E$ consists \nof one element $\\bold e=(A\\to B)$. Then $\\mathfrak G(G)$ is a  complete bipartite\n digraph with arrows  \nfrom  vertices lying  in $A$ to vertices lying in $B$. \n\nii) Let $G=(V_G, E_G)$ and $H=(V_H, E_H)$ be two directed hypergraphs with \n$V_G=\\{1,2,3,4\\}, E_G=\\{\\mathbf e_1=(\\{1\\}\\to \\{2,3\\}), \\mathbf e_2=(\\{1\\}\\to \\{2.4\\})\\}$, \n$V_H=\\{a,b,c\\}, E_H=\\{\\mathbf e_1^{\\prime}=(\\{a\\}\\to \\{b,c\\})\\}$. The map $f_V\\colon V_G\\to V_H$,  \ngiven by $f_V(1)=a, f_V(2)=b, f_V(3)=f_V(4)=c$,  induces a morphism $f$ of directed hypergraphs.  \nHowever the map $f$ does not induce a morphism from $\\mathfrak C^2(G)$ to $\\mathfrak C^2(H)$. \n\\end{example}\n\n For every morphism  $f=(f_V,f_E)\\colon G\\to H$ of directed hypergraphs, define a  map  \n$\n\\mathfrak G(f)\\colon V^d_G \\to V^d_H \\ \\ \\text{by}\\  \\mathfrak G(f)=f_V.\n$\nFor any arrow  $(v\\to w)\\in E^d_G$,  we have  $(f_V(v)\\to f_V(w))\\in E^d_H$   and  the morphism  \n$ \\mathfrak G(f)$ of digraphs is well defined.   Thus we have  a functor \n$\\mathfrak G$   from the category $\\mathcal{DH}$ of directed hypergraphs to the category  $\\mathcal D$ of digraphs.\n\\emph{Regular path homology of digraphs} was constructed in \\cite{Axioms}, \\cite{Mi3}. \nIt is based on the natural functor  $\\mathfrak D$  from the category $\\mathcal D$ of \ndigraphs to the category  $\\mathcal P$ of path complexes.\n\n\\begin{theorem}\\label{t3.3} For every directed hypergraph $G$ there is an\nisomorphism \n$\nH^{\\mathbf c}_*(G)\\cong H_*(\\mathfrak{D}\\circ\\mathfrak{G}(G))\n$\n of path homology groups.\n\\end{theorem}\n\\begin{proof} The path complexes $\\mathfrak C(G)$ and $\\mathfrak  D\\circ \\mathfrak G(G)$ coincide.   \n\\end{proof}\n\n\n\\begin{example}\\label{e3.4}   \\rm  The following example  illustrates the technique of computations of the connective path homology groups  $H_*^{\\bold c(k)}(G)$.  \nFor \n$k\\geq 3$ in the presented case, there \nis \nnothing to compute. Let $R=\\mathbb R$ be the ring of coefficients. Consider a hypergraph $G=(V_G,E_G)$ for which \n   $\nV_G=\\{1,2, 3, 4\\}, \\ \\ E_G=\\{\\bold e_1,\\bold  e_2,\\bold  e_3, \\bold e_4, \\bold e_5, \\bold e_6\\},\n$\n $\n\\bold e_1=(\\{1\\}\\to \\{2\\}), \\bold e_2=(\\{2\\}\\to \\{3, 4\\}), \\bold e_3=(\\{4\\}\\to \\{1\\}), \n$\n$\n\\bold e_4=(\\{1\\}\\to \\{2,3\\}), \\bold e_5=(\\{2\\}\\to \\{3\\}), \\bold e_6=(\\{2\\}\\to \\{4\\})$.\n  \nWe compute homology of the path complex $\\mathfrak C^c(G)=(V^c, P_G^c)$ as in \\cite{Hyper}. We have \n$\n\\mathcal{R}_0^{reg}=\\left<1, 2, 3, 4\\right>=\\Omega_0\n$, \n$\n\\mathcal {R}_1^{reg}=\\left<e_{12}, e_{13}, e_{23}, e_{24}, e_{41}\\right>\n$.\nWe get $\\partial(e_{ij})\\in \\mathcal{R}_0^{reg}$ for all basic elements  $e_{ij}\\in \\mathcal{R}_1^{reg}$,  so \n$\n\\Omega_1=\\mathcal{R}_1^{reg}\n$.\nThus, $\\Omega_1$ is generated by all directed edges of  the digraph $\\mathfrak G(G)$ presented below\n$$\n\\begin{matrix}\n&  & \\underset{3}\\bullet &&&&\\\\\n &\\nearrow  &&\\nwarrow&&&\\\\\n\\overset{1}\\bullet &              &\\to                          &  &\\overset{2}\\bullet& &\\\\\n                           &\\nwarrow  &&\\swarrow&&&\\\\\n&  & \\underset{4}\\bullet &&&&\\\\\n\\end{matrix}\n$$\nFrom the definition  of  $\\mathfrak G(G)$, it follows that $\\Omega_i=0$\nfor $i\\geq 2$ and the homology of the chain complex $\\Omega_*$ coincides with the regular path homology $\\mathfrak G(G)$. \nHence\n $\nH_0^{\\bold c(1)}(G)= H_1^{\\bold c(1)}(G)=\\mathbb R$ and $H_i^{\\bold c(1)}(G)=0$ for $i\\geq 2$. \n\n For \n$H_i^{\\bold c(2)}(G)$,   we have    \n$\\Omega_0=\\left<1, 2, 3, 4\\right>$ and by definition\n$\n\\Omega_1=\\left<e_{12},  e_{23}, e_{24}\\right>\n$.\nMoreover, $\\Omega_i=0$\nfor $i\\geq 2$.  Thus,  homology groups $H_i^{\\bold c(2)}(G)$ coincide with the homology groups \nof the digraph  which has the  set of vertices $V_{\\mathfrak G(G)}$ and the set of arrows  obtained \nfrom $E_{\\mathfrak G(G)}$ by deleting  arrows $(1\\to 3)$ and \n$(4\\to 1)$. Hence,   $\nH_0^{\\bold c(2)}(G)=\\mathbb R$ and $H_i^{\\bold c(2)}(G)=0$ for $i\\geq 1$. \nFor $k\\geq 3$ we have \n $\nH_0^{\\bold c(k)}=\\mathbb R^4$ and $H_i^{\\bold c(k)}(G)=0$ for $i\\geq 1$.\n\\end{example}  \n\n\\begin{lemma}\\label{l3.5} Let $G=(V,E)$ be a directed hypergraph and \n$I_1=(0\\to 1)$. We have a natural isomorphism\n$\\mathfrak{C}(G\\Box I_1)\\cong[\\mathfrak{C}(G)]^{\\uparrow}$\nof \npath complexes.\n\\end{lemma}\n\\begin{proof} By Definition \\ref{d2.3} a directed hypergraph $G\\Box I_1=(V_{G\\Box I_1},E_{G\\Box I_1}) $ \nhas the set of vertices $V_{G\\Box I_1}= V\\times J=V\\times \\{0,1\\}$ which we \nidentify  with $V\\cup V^{\\prime}$,  where $V=\\{0,\\dots, n\\}, \\ V^{\\prime}=\\{0^{\\prime}, \\dots, n^{\\prime}\\}$ and  the set of edges  $E_{G\\Box I_1}$ is the union  $E^0\\cup E^1\\cup  E^{01}$\nof sets \n$E^i=\\{A\\times\\{i\\}\\to B\\times\\{i\\}\\}$ with  $(A\\to B)\\in E_G$ for  $i=0,1$ \nand  $E^{01}=\\{C\\times\\{0\\}\\to C\\times\\{1\\}\\}$ with  $C\\in \\mathbb{S}_{01}(G)$. Let \n$q=\\left(i_0\\dots i_n\\right)$ be a path lying in $\\mathfrak{C}(G\\Box I_1)$. It follows from definition, that there are only three possibilities, namely\n\n(1)  all the vertices $i_j\\in V\\times \\{0\\}$ and, hence, $q$ determines  the unique path in \nin $\\mathfrak{C}(G)$, \n\n(2) all the vertices $i_j\\in V\\times \\{1\\}$ and, hence, $q$ determines the unique path in \nin $[\\mathfrak{C}(G)]^{\\prime}$, \n\n(3) there exists exactly one pair $(i_k,i_{k+1})$ of consequent vertices  in $q$ such that  $i_k\\in C\\times \\{0\\}, \ni_{k+1}\\in C\\times  \\{1\\}$ for $C\\in \\mathbb{S}_{01}(G)$. \n\nThus, the union of paths  from (1)-(3) on the set  of vertices \n$V\\times J$  defines the path complex $[\\mathfrak{C}(G)]^{\\uparrow}$ and vice versa. \n\\end{proof}\n\n\\begin{theorem}\\label{t3.6} For a directed hypergraph $G$,   the connective path homology groups $H^{\\bold c}(G)$\nare homotopy invariant.\n\\end{theorem}\n\\begin{proof} By Definition \\ref{d2.4}, it is sufficient to prove \n homotopy invariance for a one-step homotopy. Then the result follows from Lemma \\ref{l3.5} and  \\cite[Th. 3.4]{Hyper}.\n\\end{proof}\n\n\\subsection{Bold path homology}\\label{S32}\n\nLet  $p=\\left(i_0\\dots i_n\\right)$ and $q=\\left(j_0\\dots j_m\\right)$ be two paths of a  path complex \n$\\Pi$   with $i_n=j_0$. The \\emph{concatenation}  $p\\vee q$  of these paths  is  a path  given by \n$\np\\vee q=\\left(i_0\\dots i_nj_1\\dots j_m\\right)\n$. \nThe concatenation is well defined only if\n $i_n=j_0$.\n\nFor a  directed hypergraph   $G= (V, E)$, \ndefine a path complex  $\\mathfrak B(G)=(V^b_G, P_G^b)$   where $V^b_G=V$ and  \na path $q=(i_0\\dots i_n)\\in P_{V}$ lies in $P_G^b$  iff  there is a sequence of \n hyperedges $(A_0\\to B_0), \\dots, (A_r\\to B_r)$  in $E$ such that   \n $B_i\\cap A_{i+1}\\ne \\emptyset$ for $0\\leq i\\leq r-1$ and  the path $q$ has the \n  presentation \n\\begin{equation}\\label{3.2}\n\\left(p_0\\vee v_0w_0 \\vee p_1  \\vee v_1w_1\\vee p_2\\vee \\dots  \\vee p_{r}\\vee  v_r w_r\\vee p_{r+1}\\right)\n\\end{equation}\nwhere $p_0\\in P_{A_0}$,  $p_{r+1}\\in P_{B_r}$,  $v_i\\in A_i$, $w_i\\in B_i$, $p_i\\in P_{B_{i-1}}\\cap  P_{A_{i}}$  \nfor  $1\\leq i\\leq r$  and all concatenations in (\\ref{3.2}) are well defined.  Note, that in the case of empty \nsequence of edges $A_i\\to B_i$ every  path  $q\\in P_A$ and every path $q\\in P_B$ for an edge $A\\to B$ lies\nin $P^b_G$. \n\n \\begin{proposition}\\label{p3.7} Let  $f\\colon G=(V_G, E_G)\\to H=(V_H,E_H)$ be a  morphism of directed hypergraphs. \nDefine a morphism  of path complexes\n$$\n\\mathfrak B(f)=(f^b_V, f_p^b) \\colon (V_G^b,P^b_G)\\to (V_H^b, P^b_H)\n$$ \nby  $f^b_V=f\\colon V_G^b= V_G\\to V_H=V_H^b$ and $f_p^b=f_p|{_{P^b_G}}$,  where \n$f_p$ is defined as in Proposition \\ref{p3.1}.\n Thus,    we obtain  a functor $\\mathfrak B$  from the category $\\mathcal{DH}$ of directed hypergraphs to the category  $\\mathcal P$ of path complexes.  \\quad $ \\blacksquare$\n\\end{proposition}\n\n \n Let us define  \\emph{the bold path homology groups}  of  directed  hypergraph \n $G$ by \n$\nH_*^{\\bold b}(G)\\colon = H_*(\\mathfrak B(G))\n$.\nBy \nProposition \\ref{p3.7},  we  obtain a  functorial \n path homology  theory on the category $\\mathcal{DH}$ of directed hypergraphs. \n\n\\begin{example}\\label{e3.8} \\rm   Let $G=(V, E)$ be a directed \n hypergraph such that for  every edge $\\bold e=(A\\to B)\\in E$ the sets $A$ and $B$ \nare one-vertex sets, \n$A=\\{v\\}, B=\\{w\\}, v,w\\in V$. \n We can consider the hypergraph $G$ as a digraph and\n  $H^{\\bold c}_*(G)\\cong H^{\\bold b}_*(G)$.\nOn the category of connected digraphs that can be considered as the\n subcategory of directed hypergraphs,   the bold path homology groups are \n naturally isomorphic to the connective path homology groups and to the regular path\n  homology groups  $H_*(G)$ defined in  \\cite{Axioms}. \n\\end{example} \n\n\\begin{example}\\label{e3.9} \\rm Now we compute  the bold path homology groups \n\t$H^{\\bold b}_*(G)$ of  the directed hypergraph $G$  from  Example \\ref{e3.4} in  dimensions 0,1,2 for $R=\\mathbb R$. \n First,  we describe the modules $\\mathcal R_n^{reg}(\\mathfrak B(G))$  for $0\\leq n\\leq 4$.  We have \n$$\n\\mathcal R_0^{reg}=\\langle e_1,e_2,e_3,e_4\\rangle, \\ \\\n\\mathcal R_1^{reg}=\\langle e_{12}, e_{13},\ne_{23},e_{24},\ne_{32}, e_{34}, \ne_{43},e_{41}\\rangle,\n $$\n$$\n\\mathcal R_2^{reg}=\\langle e_{123},e_{124},\n e_{132},\n e_{232}, e_{234}, \ne_{241}, e_{243},\ne_{323},\n e_{343},\n e_{434},\ne_{412}, e_{413}\\rangle,\n $$\n$$\n\\begin{matrix}\n\\mathcal R_3^{reg}=\\langle e_{1232},e_{1234}, \ne_{1241},   e_{1243},\ne_{1323},\ne_{2323},   \ne_{2343},\\\\\ne_{2412}, e_{2413},\ne_{2434},\ne_{3232},\ne_{3434}, \ne_{4343},\ne_{4123}, e_{4124},\ne_{4132}\n\\rangle,\n\\end{matrix}\n $$\n$$\n\\begin{matrix}\n\\mathcal R_4^{reg}=\n\\langle e_{12323},\ne_{12343}, \ne_{12412},  e_{12413}, \n e_{12434},\ne_{13232},\ne_{23232},   \ne_{23434},\\\\\ne_{24123},\n e_{24132},\ne_{24343},\ne_{32323},\ne_{34343}, \ne_{43434},\ne_{41232},e_{41234},\n e_{41243},\ne_{41323}\n\\rangle.\n\\end{matrix}\n $$\n$$\n \\Omega_n=\\mathcal{R}_n^{reg} \\ \\ \\text{for} \\ \\ n=0,1.\n$$\nThus $\\Omega_0$ is generated by all the vertices and $\\Omega_1$ is generated \nby all directed edges of  the digraph $H$ on Fig. 1.  \n\n\\begin{figure}[th]\\label{fig1}\n\\centering\n\\begin{tikzpicture}\n\\node (1) at (4,3) {$1$};\n\\node (2) at (8,3) {$2$};\n\\node (3) at (6,5) {$3$};\n\\node (4) at (6,2) {$4$};\n\\draw (1) edge[ thick, ->] (3);\n\\draw (4) edge[ thick, ->] (1);\n\\draw (2) edge[thick, ->] (4);\n\\draw (3) edge[bend right=12, thick, ->]  node [left]{} (2);\n\\draw (2) edge[bend right=15, thick, ->] node [right]{} (3);\n\\draw (1) edge[bend right=90,  thick, ->] node [right]{} (2);\n\\draw (3) edge[bend right=15,  thick, ->] node [right]{} (4);\n\\draw (4) edge[bend right=15,  thick, ->] node [right]{} (3);\n\\end{tikzpicture}\n\\caption{The digraph $H$.}\n\\end{figure}\nAs it follows from the path homology theory of digraphs, the rank \nof the image \n$\\partial\\colon   \\Omega_1\\to \\Omega_0$ is equal to 3, \nthe rank \nof the kernel $\\partial$ is equal to 5,  \nand hence  $H^{\\bold b}_0(G)=\\mathbb R$.\n  \nBy the direct computation $\\Omega_2$ is the vector space with the following basis:\n$\n\\{\ne_{123},\ne_{132},\ne_{232}, \ne_{234},\n e_{243},\ne_{323}, \ne_{343},\ne_{434},\ne_{413}\n\\}\n $.\nIn this basis the matrix of homomorphism $\\partial \\colon \\Omega_2\\to \\Omega_1$ has the form:\n$$\n\\left(\\begin{matrix}\n            &e_{12}&e_{13}&e_{23}&e_{24}&e_{32}&e_{34}&e_{43}&e_{41}\\\\\ne_{123}&1         &-1       &1        &0         &0        &0        &0        &0        \\\\\ne_{132}&-1         &1       &0        &0         &1        &0        &0        &0        \\\\\ne_{232}&0        &0       &1        &0         &1       &0        &0        &0        \\\\\ne_{234}&0        &0      &1        &-1        &0        &1       &0        &0        \\\\\ne_{243}&0        & 0     &-1        &1       &0        &0        &1        &0        \\\\\ne_{323}& 0       &0      &1        &0         &1      &0        &0        &0        \\\\\ne_{343}&0        &0       &0        &0         &0        &1       &1        &0        \\\\\ne_{434}&0        &0       &0        &0         &0        &1       &1        &0        \\\\\ne_{413}&0        &1      &0        &0         &0        &0       &-1      &1        \\\\\n\\end{matrix}\\right).\n$$\nIts rank is equal to 5. \nHence the rank \nof the image of\n$\\partial$ is equal to 5, \nthe rank \nof the kernel $\\partial$ is equal to 4,  \nand hence  $H^{\\bold b}_1(G)=0$.  \n\nWe have \n$\n\\begin{matrix}\n\\Omega_3=\\langle e_{1232},\ne_{1323},\ne_{2323},   \ne_{2343},\ne_{2434},\ne_{3232},\ne_{3434}, \ne_{4343}\n\\rangle.\\\\\n\\end{matrix}\n $\nSimilar to the previous calculation,  the rank \nof the image \n$\\partial\\colon   \\Omega_3\\to \\Omega_2$ is equal to 4, \nthe rank \nof the kernel $\\partial$ is  equal to 4,  \nand hence  $H^{\\bold b}_2(G)=0$.  \n\nWe have \n$\\Omega_4=\\langle e_{12323}, e_{13232}, e_{23232}, \ne_{23434}, \ne_{24343}, e_{32323}, e_{34343}, e_{43434}\\rangle \n $ \n and, similar to the previous calculation, the  rank \nof the image \n$\\partial\\colon   \\Omega_4\\to \\Omega_3$ is equal to 4, \nthe rank \nof the kernel $\\partial$ is equal to 4.\nHence  $H^{\\bold b}_3(G)=0$.  \n\\end{example} \n\n\\begin{lemma}\\label{l3.10}  Let $G=(V,E)$ be a directed hypergraph and \n$I_1=(0\\to 1)$  the digraph. There is an inclusion \n$\\lambda\\colon [\\mathfrak{B}(G)]^{\\uparrow}\\to \\mathfrak{B}(G\\Box I_1)$\nof path complexes. The restrictions of \n$\\lambda$ to the  images of the morphisms $i_{\\bullet}$ and $j_{\\bullet}$,   defined in Section \\ref{S2}, \nare the natural identifications. \n\\end{lemma}\n\\begin{proof} By definition in Section \\ref{S2}, \n  we have\n$\n[\\mathfrak{B}(G)]^{\\uparrow}=(V\\times J, [P^b_G]^{\\uparrow}))$, \nwhere $[P^b_G]^{\\uparrow}=P^b_G\\cup [P^b_G]^{\\prime}\\cup [P^b_G]^{\\#} $.  \nWe have  $V_{G\\Box I_1}= V\\times J=V\\times \\{0,1\\}=V\\cup V^{\\prime}$ with\n$V=\\{0,\\dots, n\\}, \\ V^{\\prime}=\\{0^{\\prime}, \\dots, n^{\\prime}\\}$ and   \n$E_{G\\Box I_1}$ is  the union  of sets $E^0\\cup E^1\\cup  E^{01}$,  where\n$\nE^i=\\{A\\times\\{i\\}\\to B\\times\\{i\\} \\, | \\, (A\\to B)\\in E_G\\}\n$\n for  $i=0,1$ and \n$\nE^{01}=\\{C\\times\\{0\\}\\to C\\times\\{1\\} \\, | \\, C\\in {\\mathbf{P}}_{01}(G))\\}\n$.  \nNow it follows\nthat \n$\n\\mathfrak{B}(G)=\\mathfrak{B}(G\\Box\\{0\\}), \\mathfrak{B}(G)^{\\prime}=\\mathfrak{B}(G\\Box\\{1\\})\n$, \nwhere $\\mathfrak{B}(G\\Box\\{0\\}),\\mathfrak{B}(G\\Box\\{1\\})\\subset \\mathfrak{B}(G\\Box I_1)$.\nLet $q=(i_0\\dots i_n)$ be $n$-path in $\\mathfrak{B}(G)=\\mathfrak{B}(G\\Box\\{0\\})$. Consider  \nits presentation in the form (\\ref{3.2}) and let   $A_i, B_i$ be the corresponding sets \nof vertices. \n For   $0\\leq k \\leq n$,  consider a path \n $q_k^{\\#}=\\left(i_0\\dots i_ki_k^{\\prime}i^{\\prime}_{k+1}\\dots i_n^{\\prime}\\right)\\in [P^b_G]^{\\#}$.  \n  We will prove now that this path  in \n$P^b_{G\\Box I_1}$. There are  following possibilities for the path $q$.\n\n(1) Vertices\n$i_k, i_{k+1}\\in p_s$  for $1\\leq s\\leq r+1$ in presentation (\\ref{3.2}). \nThen we  \nwrite  path $q_k^{\\#}$ in the form \n\\begin{equation}\\label{3.3}\nq_k^{\\#}=\\left(p_0^{\\#}\\vee v_0^{\\#}w_0^{\\#} \\vee p_1^{\\#} \\vee  \\dots  \\vee \np_{r+1}^{\\#}\\vee  v_{r+1}^{\\#} w_{r+1}^{\\#}\\vee\n p_{r+2}^{\\#}\\right)\n\\end{equation}\n  putting \n$$\nA_i^{\\#}=\\begin{cases}  A_i\\times\\{0\\} & \\text{for} \\ i\\leq s-1\\\\\n B_{s-1}\\times\\{0\\} & \\text{for} \\ i=s\\\\\nA_{s-1}\\times\\{1\\} & \\text{for} \\ i\\geq s+1, \\\\\n\\end{cases}\\ \\ \\\nB_i^{\\#}=\\begin{cases}  B_i\\times\\{0\\} & \\text{for} \\ i\\leq s-1\\\\\nB_{s-1}\\times\\{1\\} & \\text{for} \\ i\\geq s. \\\\\n\\end{cases}\n$$\nWe have the following arrows  in  $E_{G\\Box I_1}$:\n$$\n(A_i^{\\#}\\to B_i^{\\#})= \n(A_i\\times \\{0\\}\\to  B_i\\times\\{0\\}) \\ \\ \\text{for} \\  0\\leq i\\leq s-1, \n$$\n$$\n(A_s^{\\#}\\to B_s^{\\#})= \n(B_{s-1}\\times \\{0\\}\\to  B_{s-1}\\times \\{1\\}), \n$$\n$$\n(A_i^{\\#}\\to B_i^{\\#})= \n(A_{i-1}\\times \\{1\\}\\to  B_{i-1}\\times\\{1\\}) \\ \\ \\text{for} \\  s+1\\leq i\\leq r+2. \n$$\n Using identifications \n$\n\\mathfrak{B}(G)=\\mathfrak{B}(G\\Box\\{0\\}), \\mathfrak{B}(G)^{\\prime}=\\mathfrak{B}(G\\Box\\{1\\})\n$,  \nwe obtain\n\\begin{equation}\\label{3.4}\np_i^{\\#}= \\begin{cases}p_i& \\text{for}  \\  i\\leq s-1\\\\\np_i^{\\prime}& \\text{for}  \\  s+2\\leq i\\leq r+2\\\\\n(w_{s-1}\\dots i_s) &\\text{for}  \\  i=s\\\\\n(i_{s}^{\\prime}i_{s+1}^{\\prime} \\dots v_s^{\\prime})&\\text{for}  \\  i=s+1\\\\\n\\end{cases}\n\\end{equation}\nwhere \n$\n(w_{s-1}\\dots i_s)\\in P_{B_{s-1}^{\\#}\\cap A_s^{\\#}}=\nP_{B_{s-1}\\times\\{0\\}}\n$, \n$\n\\left(i_{s}^{\\prime}i_{s+1}^{\\prime} \\dots v_s^{\\prime}\\right)\n\\in P_{B_{s}^{\\#}\\cap A_{s+1}^{\\#}}=\nP_{(B_{s-1}\\times\\{1\\})\\cap (A_{s}\\times\\{1\\})}\n$.\nPaths $p_i^{\\#}$ in (\\ref{3.4}) \n define  vertices \n$v_i^{\\#}, w_{i}^{\\#}$ in (\\ref{3.3}). \nHence,   (\\ref{3.3}) gives a presentation of $q_k^{\\#}$ in the form (\\ref{3.2}) \nfor the hypergraph $G\\Box I_1$  and  $q_k^{\\#}\\in P_{G\\Box I_1}^b$ in the considered case. \n\n(2)  \nVertices  $i_k,i_{k+1}\\in p_0$ in presentation (\\ref{3.2}).  Then we  \nwrite  \npath $p_k^{\\#}$ in the form  \n(\\ref{3.3})  putting \n$$\nA_i^{\\#}=\\begin{cases}  A_0\\times\\{0\\} & \\text{for} \\ i=0\\\\\n A_{i-1}\\times\\{1\\} & \\text{for} \\ 1\\leq  i\\leq r+2, \\\\\n\\end{cases} \n$$\n$$\nB_i^{\\#}=\\begin{cases}  A_0\\times\\{1\\} & \\text{for} \\ i=1\\\\\nB_{i-1}\\times\\{1\\} & \\text{for} \\ 2\\leq  i\\leq r+2 \\\\\n\\end{cases}\n$$\nand  \n$$\np_i^{\\#}= \\begin{cases}(i_0\\dots i_k)& \\text{for}  \\  i=0\\\\\n\\left(i_k^{\\prime}\\dots v_0^{\\prime}\\right)& \\text{for}  \\  i=1\\\\\np_{i-1}^{\\prime} &\\text{for}  \\ 2\\leq i \\leq r+2\\\\\n\\end{cases}\n$$\nwhere \n$(i_0\\dots i_k)\\in P_{A_0^{\\#}}$,  $\\left(i_k^{\\prime}\\dots v_0^{\\prime}\\right)\\in \nP_{B_0^{\\#}\\cap  A_1^{\\#}}=P_{A_{0}\\times\\{1\\}}$\nHence,   (\\ref{3.3}) gives a presentation of $q_k^{\\#}$ in the form (\\ref{3.2})\nin the hypergraph $G\\Box I_1$  and  $q_k^{\\#}\\in P_{G\\Box I_1}^b$ in the considered case.\n\n(3) Let $i_k=v_s, i_{k+1}=w_s$  for $0\\leq s\\leq r$ in the presentation (\\ref{3.2}). \n Then we   \n write   \n path $q_k^{\\#}$ in the form  \n(\\ref{3.3})  putting \n$$\nA_i^{\\#}=\\begin{cases}  A_i\\times\\{0\\} & \\text{for} \\ i\\leq s\\\\\n A_{s+1}\\times\\{1\\} & \\text{for} \\ i=s+1\\\\\nA_{s-1}\\times\\{1\\} & \\text{for} \\ i\\geq s+2, \\\\\n\\end{cases}\\ \nB_i^{\\#}=\\begin{cases}  B_i\\times\\{0\\} & \\text{for} \\ i\\leq s-1\\\\\nA_s\\times\\{1\\} & \\text{for} \\ i=s\\\\\nB_{s-1}\\times\\{1\\} & \\text{for} \\ i\\geq s+1. \\\\\n\\end{cases}\n$$\nWe have the following arrows  in $E_{G\\Box I_1}$:\n$$\n(A_i^{\\#}\\to B_i^{\\#})= \n(A_i\\times \\{0\\}\\to  B_i\\times\\{0\\}) \\ \\ \\text{for} \\  0\\leq i\\leq s-1, \n$$\n$$\n(A_s^{\\#}\\to B_s^{\\#})= \n(A_{s}\\times \\{0\\}\\to  A_{s}\\times \\{1\\}), \n$$\n$$\n(A_i^{\\#}\\to B_i^{\\#} )= \n(A_{i-1}\\times \\{1\\}\\to  B_{i-1}\\times\\{1\\}) \\ \\ \\text{for} \\  s+1\\leq i\\leq r+2. \n$$\nSimilarly to  case (1),  we have  \n$$\np_i^{\\#}= \\begin{cases}p_i& \\text{for}  \\  i\\leq s\\\\\n(v_s^{\\prime})& \\text{for}  \\  i=s+1\\\\\np_{i-1}^{\\prime} &\\text{for}  \\ s+2\\leq i \\leq r+2,\\\\\n\\end{cases}\n$$\nwhere \n$\nw_{s}^{\\#}=v_s, v_{s}^{\\#}=v_s^{\\prime}, \nw_{s+1}^{\\#}=v_s^{\\prime}$.\nHence,   (\\ref{3.3}) gives a presentation of $q_k^{\\#}$ in the form (\\ref{3.2})\nin  the hypergraph $G\\Box I_1$  and  $q_k^{\\#}\\in P^b_{G\\Box I_1}$ in the considered case.  \n\\end{proof}\n\n\\begin{theorem}\\label{t3.11}  Let $G$ be a directed hypergraph. The bold  path homology groups $H^{\\bold b}_*(G)$\nare homotopy invariant.\n\\end{theorem}\n\\begin{proof} By Definition \\ref{d2.4}, it is sufficient to prove \n homotopy invariance for  the one-step homotopy.  Let $f_0, \\, f_1\\colon G\\to H$ be \n  one-step homotopic morphisms of directed hypergraphs with  homotopy \n$F\\colon G\\Box I_1\\to H$,  where $I_1=(0\\to 1)$. \nSince $\\mathfrak B$ is a functor,  we obtain\nmorphisms of path complexes\n$\n\\mathfrak B(f_0), \\, \\mathfrak B(f_1)\\colon \\mathfrak B(G)\\to \\mathfrak B(H)$\nand $\\mathfrak B(F)\\colon \\mathfrak B(G\\Box I_1)\\to \\mathfrak B(H)$. Consider the composition \n$\n[\\mathfrak{B}(G)]^{\\uparrow}\\overset{\\lambda}{\\longrightarrow} \\mathfrak{B}(G\\Box I_1)\\overset{\\mathfrak B(F)}{\\longrightarrow}\n\\mathfrak B(H)\n$\nwhich gives a homotopy between morphisms \n$\\mathfrak B(f_0)$ and $\\mathfrak B(f_1)$ of\npath complexes by using identifications of the top and the bottom \nof $[\\mathfrak{B}(G)]^{\\uparrow}$\ndescribed in Lemma \\ref{l3.10}.\nNow the result follows from \n\\cite[Th. 3.4]{Hyper}.\n\\end{proof}\n\n\n\\subsection{Non-directed path homology}\\label{S33}\n\nIn this subsection, we describe several path  homology theories on the category of directed  hypergraphs  \n$\\mathcal{DH}$ that are based on    functorial relations between  hypergraphs and directed  hypergraphs. \n\n For  a hypergraph $G=(V_G,E_G)$,  we have  a natural map   \n $\\phi_G\\colon  E_G \\to  {\\mathbf{P}}(V_G)\\setminus \\emptyset$.\n A  \\emph{morphism} of hypergraphs $f\\colon G\\to H=(V_H,E_H)$   \n is given by the pair of maps  $f_V\\colon V_G\\to V_H$ \nand $f_E\\colon E_G\\to E_H$ \n such that  ${\\mathbf{P}}(f_V)\\circ \\phi_G=\\phi_H\\circ f_E$,  \nwhere \n${\\mathbf{P}}(f_V)\\colon{\\mathbf{P}}(V_G)\\setminus \\emptyset \\to {\\mathbf{P}}(V_H)\\setminus \\emptyset$ \nis the map induced by $f_V$. So  we may turn to \nthe category   of hypergraphs  $\\mathcal H$ in \\cite{Hyper}. \n\n\nFirst,  define  a functor from  category $\\mathcal{DH}$\n to category $\\mathcal H$. For a finite set $X$, define  a map $\\sigma_X\\colon \\mathbb P(X)\\to {\\mathbf{P}}(X)$ by setting $\\sigma_X(A,B)=A\\cup B$.   \n Let $G=(V, E)$ be a directed hypergraph. \nDefine a hypergraph $\\mathfrak E(G)=(V^e, E^e)$ where  $V^e=V$ and \n\\begin{equation}\\label{3.5}\nE^{e}=\\{C\\in {\\mathbf{P}}(V)\\setminus \\emptyset \\, | \\, C=A\\cup B, (A\\to B)\\in E\\}.\n\\end{equation}\nRecall that in Section \\ref{S2},  for a directed hypergraph $G=(V,E)$ we defined a map $\\varphi_G\\colon E\\to \\mathbb P(V)$ by $\\varphi_G(A\\to B)=\n(A,B)$. \n\n\n \\begin{proposition}\\label{p3.12} Let  $f=(f_V, f_E)\\colon G=(V_G, E_G)\\to H=(V_H,E_H)$ be a  morphism of directed hypergraphs. \nDefine a map $f_E^e\\colon  E^e_G\\to {\\mathbf{P}}(V_H)$ \nputting \n$\nf_E^e(C)=[{\\mathbf{P}}(f_V)](C)\n$\nfor every  $C=A\\cup B\\in E^e_G$. \nThen the map $f_E^e$ is a well defined map \n$  E^e_G\\to  E^e_H$  and the pair \n$\n(f_{V}^e, f_{E}^e)$ with $f_{V}^e=f_V$\ndefines  a morphism \n$\n\\mathfrak E(f) \\colon  (V_G^e,E^e_G)\\to (V_H^e, E^e_H)\n$\n of hypergraphs.  Thus,    we obtain  a functor $\\mathfrak E$  from  the category \n $\\mathcal{DH}$ of directed hypergraphs to the category  $\\mathcal H$ of hypergraphs. \n\\end{proposition}\n\\begin{proof} The map $f_E^e$ is \n\twell defined. Now we prove that its image lies in $E^e_H$. \nLet  $C\\in E^e_G$,  $C=\\sigma_{V_G}\\circ \\varphi_G(A\\to B)=A\\cup B$ and \n$f_{E_G}(A\\to B)=(A^{\\prime}\\to B^{\\prime})\\in E_H$. Then,  by Definition \\ref{d2.2}, \n$[\\mathbb{P}(f_{V_G})](A,B)= (A^{\\prime},  B^{\\prime})\\in\\mathbb{P}(V_G))$ and, hence, \n$A^{\\prime}=[{\\mathbf{P}}(f_V)](A), B^{\\prime}=[{\\mathbf{P}}(f_V)](B)$. \nWe have \n$$\n[{\\mathbf{P}}(f_V)](C)= [{\\mathbf{P}}(f_V)](A\\cup B)=\\{ [{\\mathbf{P}}(f_V)](A)\\}\\cup \n\\{ [{\\mathbf{P}}(f_V)](B)\\}=A^{\\prime}\\cup B^{\\prime}. \n$$\nHowever, \n$\nA^{\\prime}\\cup B^{\\prime}=\\sigma_{V_H}\\circ \\varphi_H(A^{\\prime}\\to B^{\\prime})\\in E^e_H\n$\nand the claim  that morphism $f^e_E$ is well defined is proved. \nThe \nfunctoriality is evident.\n\\end{proof} \n\nFor a hypergraph   $G= (V, E)$, \ndefine a path complex  $\\mathfrak H^{q}(G)=(V^{q}, P_G^{ q})$ of \\emph{density} $q\\geq 1$\n where $V^{ q}=V$ and   a path $(i_0\\dots i_n)\\in P_{V}$ lies $\\in P_G^{ q}$  \n iff  every $q$  consequent vertices of this path\nlie in a  hyperedge $\\mathbf e$, see \\cite{Hyper}. \nThus,  we obtain a collection of functors $\\mathfrak H^{ q}$  from  the category $\\mathcal H$ to  the category  $\\mathcal P$.  \nComposition  $\\mathfrak H^{ q}\\circ \\mathfrak E$ gives collection of functors   \nfrom category $\\mathcal{DH}$  to category  $\\mathcal P$.\n For a  directed hypergraph $G$ define \n\\begin{equation*}\nH_*^{\\bold e(q)}(G)\\colon = H_*(\\mathfrak H^{q}\\circ \\mathfrak E(G))\n\\ \\text{for} \\ \\ q=1,2,\\dots \\ \\ .\n\\end{equation*}\nWe  call these groups by  the \\emph{non-directed path homology groups of density \n\t$q$}  of a directed  hypergraph $G$. We \ndenote $H_*^{\\bold e}(G)\\colon =H_*^{\\bold e(1)}(G)$.\n\n\\begin{proposition}\\label{p3.13} Let $G=(V,E)$ be a directed hypergraph and \n\t$\\Pi_V$ be a path complex of all paths on the set $V$. Then  \n\t$H_*^{\\bold e}(G)=H_*(\\Pi_V)$.\n\\end{proposition}\n\\begin{proof} By Definition \\ref{d2.1}, $V=\\cup_{\\bold e_i\\in E} (A_i\\cup B_i)$ \n\tand every vertex $v\\in V^e=V$ lies in an edge $e\\in E^e$. So path complexes \n$\\Pi_V$ and $\\mathfrak H^{1}\\circ \\mathfrak E(G)$ coincide.\n\\end{proof}\n\\begin{example}\\label{e3.14} \\rm  Now we compute   path homology groups \n$H^{\\bold e(q)}_*(G)$ of density  $q=1,2,3$ with coefficients in $\\mathbb R$ of the  \n directed hypergraph $G$ with \n   $\nV_G=\\{1,2, 3, 4,5,6\\}, \\ \\ E_G=\\{\\bold e_1,\\bold  e_2,\\bold  e_3, \\bold e_4, \\bold e_5\\},\n$\n where \n $\n\\bold e_1=(\\{1\\}\\to \\{2\\}), \\bold e_2=(\\{1\\}\\to \\{3\\}), \\bold e_3=(\\{2\\}\\to \\{4,6\\}), \n\\bold e_4=(\\{3\\}\\to \\{5\\}), \\bold e_5=(\\{4\\}\\to \\{5,6\\})\n$.\nThen  the hypergraph $\\mathfrak E(G)$ has the set of vertices\n$V_G^e=\\{1,2, 3, 4,5,6\\}$ and the set of hyperedges \n$$\nE_G^e=\\left\\{ \n\\bold e_1^{\\prime}=\\{1,2\\}, \n\\bold e_2^{\\prime}=\\{1, 3\\}, \n\\bold e_3^{\\prime}=\\{2,4,6\\}, \n\\bold e_4^{\\prime}=\\{3, 5\\},\n \\bold e_5^{\\prime}=\\{4,5,6\\}\\right\\}.\n$$ \nIn the case of $q=1$, the homology groups $H_*^{\\mathbf e}(G)$ \ncoincide with the path homology group of the complete  digraph \n$D=(V_D, E_D)$ which has six vertices and for every two vertices \n$v,w\\in V_D$  there are two arrows $(v\\to w), (w\\to v)\\in E_D$. \nThis digraph is contractible, and hence, see  \\cite[S3.3]{MiHomotopy}, \n$\nH_0^{\\bold e}(G)= \\mathbb R$ and groups $H_i^{\\bold e}(G)$ are trivial for $i\\geq 1$.\n\\begin{figure}[th]\\label{fig2}\n\\centering\n\\begin{tikzpicture}\n\\node (1) at (5,3) {$1$};\n\\node (3) at (7,3) {$3$};\n\\node (5) at (9,3) {$5$};\n\\draw (1) edge[ thick, ->] (3)\n(3) edge[ thick, ->] (1)\n (3) edge[ thick, ->] (5)\n(5) edge[ thick, ->] (3);\n\\node (2) at (5,5) {$2$};\n\\node (4) at (7,5) {$4$};\n\\node (6) at (9,5) {$6$};\n\\draw  (4) edge[ thick, ->] (6);\n\\draw  (6) edge[ thick, ->] (4)\n(2) edge[ thick, ->] (4)\n(4) edge[ thick, ->] (2)\n(5) edge[ thick, ->] (4)\n(4) edge[ thick, ->] (5)\n (1) edge[ thick, ->] (2)\n (2) edge[ thick, ->] (1)\n (5) edge[ thick, ->] (6) \n (6) edge[ thick, ->] (5) \n(2) edge[bend left,  thick, ->] node [right]{} (6) \n(6) edge[bend right,  thick, ->] node [right]{} (2);\n\\end{tikzpicture}\n\\caption{The digraph $D_2$ for $q=2$.}\n\\end{figure}\n\n\\noindent\nIf $q=2$,  homology groups $H_*^{\\mathbf e(2)}(G)$ \ncoincide with path homology group of the  digraph $D_2$ on Fig. 2,  where  two-sided arrow   \n$a\\longleftrightarrow b$ means that there are arrows \n$a\\to b$ and $b\\to a$.  The digraph $D$ is homotopy equivalent to the induced \nsub-digraph $D_2^{\\prime}\\subset D_2$ with the set of vertices $\\{1,2,3,4,5\\}$. \n We  compute directly the path homology of \n$D_2^{\\prime}$ and we obtain  \n$ \nH_0^{\\bold e(2)}(G)=H_1^{\\bold e(2)}(G)=\\mathbb R$ and  trivial groups \n$H_i^{\\bold e}(G)$  for $i\\geq 2$.\n\nNow we consider the case of $\\mathbf e(3)$.\nWe have  $\\Omega^{\\mathbf e(3)}_n=\\Omega^{\\mathbf e(2)}_n$  for $n=0,1$ and \nthis equality is also true  for all $n\\geq 0$.  We have \n$$\n {\\mathcal{R}_2^{\\mathbf e(3)}}^{reg}= A \\oplus A_{246}\\oplus A_{456},\n $$\nwhere $A=\\langle e_{121}, \ne_{212}, e_{131}, e_{313}, e_{353},e_{535}\\rangle$ and\n$A_{abc}$ is  the module generated by all regular paths with three vertices  \nin the full digraph with vertices $a,b,c$.\nHence $\\Omega_2^{\\mathbf e(3)}={\\mathcal{R}_2^{\\mathbf e(3)}}^{reg}$.  \nConsidering  the digraph $D_2$, \nwe obtain that  $\\Omega_2^{\\mathbf e(3)}= \n\\Omega_2^{\\mathbf e(2)}$. The cases with \n$n\\geq 4$ are similar and  $\\Omega_n^{\\mathbf e(3)}= \n\\Omega_n^{\\mathbf e(2)}$ for $n\\geq 4$.  Hence,  \n$ \nH_n^{\\bold e(2)}(G)=H_n^{\\bold e(3)}(G)$ for $n\\geq 0$. \n\\end{example}\n\\begin{proposition}\\label{p3.15} Let $G=(V,E)$ be a directed hypergraph, \n$I_1=(0\\to 1)$,\nand $ I=(V_I, E_I)$ be the hypergraph  \nwith the set of vertices $V_I=\\{0,1\\}$ and the set of edges  \n$ E_I=\\{ \\bold e_0^{\\prime}=\\{0\\}, \\bold e_1^{\\prime}=\\{1\\}, \\bold e_2^{\\prime}=\\{0,1\\}\\}$. \nThere is a natural inclusion  of path complexes\n\\begin{equation}\\label{3.6}\n\\mathfrak H^{ q}[\\mathfrak{E}(G\\Box I_1)] \\subset \\mathfrak H^{ q}[\\mathfrak{E}(G)\\times I]\n\\end{equation}\nfor $q\\geq 2$. Moreover,  in general case  complexes in (\\ref{3.6}) are not equal. \n\\end{proposition}\n\\begin{proof} Recall that the product $\"\\times\"$ of hypergraphs is defined in \\cite{mor}, \\cite{Hyper}. \nThe directed hypergraph  \n $G\\Box I_1=(V_{G\\Box I_1}, E_{G\\Box I_1}) $ has the set of vertices  \n $V_{G\\Box I_1}=V\\times \\{0,1\\}$ and the set of edges that can be presented as the  union  \n $E_0\\cup E_1\\cup E_{01}$ of three pairwise disjoint sets \n\\begin{equation*}\n\\begin{matrix}\nE_0=\\{(C\\times \\{0\\}\\to  D\\times \\{0\\})| (C\\to D)\\in E\\},\n\\\\\nE_1=\\{(C\\times \\{1\\}\\to  D\\times \\{1\\})| (C\\to D)\\in E\\},\n\\\\\nE_{01}=\\{A\\times\\{0\\}\\to A\\times\\{1\\}| A\\subset {\\mathbf{P}}_{01}(G) \\}.\\ \\ \\ \\  \\\\\n\\end{matrix}\n\\end{equation*}\nHence,  the hypergraph \n$\n\\mathfrak E(G\\Box I_1)=\\left( V_{\\mathfrak E(G\\Box I_1)}, E_{\\mathfrak E(G\\Box I_1)}  \\right)\n$\nhas the set of vertices  $V_{\\mathfrak E(G\\Box I_1)}=  V_{G\\Box I_1}=V\\times \\{0,1\\}$ and the set of edges  \nthat can be presented as a union of three pairwise disjoint sets $E_0^{\\prime}\\cup E_1^{\\prime}\\cup E_{01}^{\\prime}$ where\n\\begin{equation}\\label{3.7}\n\\begin{matrix}\nE_0^{\\prime}=\\{(C\\times \\{0\\})\\cup (D\\times \\{0\\})| (C\\to D)\\in E\\},\n\\\\\nE_1^{\\prime}=\\{(C\\times \\{1\\})\\cup  (D\\times \\{1\\})| (C\\to D)\\in E\\},\n\\\\\nE_{01}^{\\prime}=\\{(A\\times\\{0\\})\\cup( A\\times\\{1\\})| A\\subset {\\mathbf{P}}_{01}(G) \\}.\n\\ \\     \\\\\n\\end{matrix}\n\\end{equation}\nBy definition of a hypergraph  $\\mathfrak{E}(G)=(V^e, E^e)$,   we obtain that the hypergraph \n $\\mathfrak{E}(G)\\times I=(V_{\\mathfrak{E}(G)\\times I}, E_{\\mathfrak{E}(G)\\times I}) $ has the set of vertices \n$V_{\\mathfrak{E}(G)\\times I}=V\\times \\{0,1\\}$ and the set of edges that can be presented as  \na union of three pairwise disjoint sets \n$E_0^{\\prime\\prime}\\cup E_1^{\\prime\\prime}\\cup E_{01}^{\\prime\\prime}$ where\n\\begin{equation}\\label{3.8}\n\\begin{matrix}\nE_0^{\\prime\\prime}=\\{(C\\cup D) \\times \\{0\\}, C\\cup D, \\{0\\})\\, | \\,(C\\to D)\\in E\\},\\\\\nE_1^{\\prime\\prime}=\\{(C\\cup D) \\times \\{1\\}, C\\cup D, \\{0\\})\\, |\\,  (C\\to D)\\in E\\},\\\\\nE_{01}^{\\prime\\prime}=\\{(A, C\\cup D, \\{0,1\\})\\, | \\, (C\\to D)\\in E, A\\subset (C\\cup D) \\times \\{0,1\\} \\}.\\\\\n\\end{matrix}\n\\end{equation}\nLet $p_1\\colon V\\times \\{0,1\\}\\to V,  \\,\np_2\\colon V\\times \\{0,1\\}\\to \\{0,1\\}$ be natural projections. \nThen  $p_1(A)=C\\cup D$ and  $p_2(A)=\\{0,1\\}$ by definition of the product of hypergraphs.  \nThus,  path complexes $\\mathfrak H^{q}\\left[\\mathfrak E(\\Box I_1)\\right]$  and  \n$\\mathfrak H^{ q}\\left[\\mathfrak E(G)\\times  I\\right]$ have the same vertex set   and,  by  (\\ref{3.7})  and (\\ref{3.8}), \n$\nE_0^{\\prime}=E_0^{\\prime\\prime},\\ \n E_1^{\\prime}= E_1^{\\prime\\prime}, \\ E_{01}^{\\prime}\\subset E_{01}^{\\prime\\prime}\n$\nand (\\ref{3.6}) follows. \n\nNow we prove that in general case  of (\\ref{3.6}) there is no equality. \nLet $(C\\to  D)\\in E$ be a directed edge \nand $v\\in C, w\\in D$ be such vertices that the pair $(v,w)$ does not lie in a set $A\\in {\\mathbf{P}}_{01}(G)$. \nThen  the two vertex  path $(v\\times\\{0\\}), \n(w\\times\\{1\\})\\in\\mathfrak H^{q}\\left[\\mathfrak E(G)\\times  I\\right]$  for $ q=2$ lies in\n$E_{01}^{\\prime\\prime}$ and does not lie in  $E_0^{\\prime}\\cup\n E_1^{\\prime}\\cup E_{01}^{\\prime}$.\n\n\\end{proof}\n\\begin{lemma}\\label{l3.16}  Let $G=(V,E)$ be a directed hypergraph,\n$I_1=(0\\to 1)$.\nThere is the  inclusion \n$\n\\mu\\colon [\\mathfrak H^{ 2}\\circ\\mathfrak{E}(G)]^{\\uparrow}\\to \n\\mathfrak{H}^{2}\\circ \\mathfrak E(G\\Box I_1)\n$\nof path complexes. \n\\end{lemma}\n\\begin{proof} By definition of the hypergraph  $\\mathfrak{E}(G)=(V^e, E^e)$ and  the functor $\\mathfrak H^2$,   \n\twe obtain that the set  $P_{\\mathfrak{E}(G)}^2$ of $\\mathfrak H^{ 2}\\circ\\mathfrak{E}(G)$ consists \nof  paths $p=(i_0\\dots i_n)$ on the set $V$ such that every two \nconsequent vertices $i_s,i_{s+1}\\in p$ lie in a set \n$\\{C\\cup D\\, | \\, (C\\to D)\\in E\\}$. By definition,  the set of paths of  the path\ncomplex  $[\\mathfrak H^{ 2}\\circ\\mathfrak{E}(G)]^{\\uparrow}$\nis a union of paths \n\\begin{equation}\\label{3.9}\nP_{\\mathfrak{E}(G)}^2\\cup [P_{\\mathfrak{E}(G)}^2]^{\\prime}\\cup {[P_{\\mathfrak{E}(G)}^2]}^{\\#}\n\\end{equation}\non the set $V\\times\\{0,1\\}=V\\cup V^{\\prime}$. \nA path $p=(i_0\\dots i_n)$ on the set $V\\times \\{0,1\\}$ lies in  \n$P_{\\mathfrak E(G\\Box I_1)}^2$ if any two consequent vertices lie in the exactly one of the sets \n$\nE_0^{\\prime}, E_1^{\\prime}, E_{01}^{\\prime}\n$\n defined in (\\ref{3.7}).  From definition of the functor $\\mathfrak{E}$, we conclude that  in (\\ref{3.9}) \n any pair of consequent vertices of a path  from $P_{\\mathfrak{E}(G)}^2$ lies in an  edge from $E_0^{\\prime}$, \nany pair of consequent vertices of a path from $[P_{\\mathfrak{E}(G)}^2]^{\\prime}$ lies in an  edge from \n$E_1^{\\prime}$, and any pair of consequent vertices of a path from \n${[P_{\\mathfrak{E}(G)}^2]}^{\\#}$  lies in an  edge from $E_0^{\\prime}\\cup  E_1^{\\prime}\\cup E_{01}^{\\prime}$.  \n\\end{proof} \n\\begin{theorem}\\label{t3.17}  For a directed hypergraph $G$,  \nthe non-directed  path homology groups $H^{\\bold e(2)}_*(G) $\n  of density two  are homotopy invariant.\n\\end{theorem}\n\\begin{proof} It is sufficient to prove \n homotopy invariance for the  one-step homotopy. \nLet $f_0, \\, f_1\\colon G\\to H$ be  one-step homotopic morphisms of directed hypergraphs with a homotopy \n$F\\colon G\\Box I_1\\to H$.  Since $\\mathfrak H^{2}\\circ \\mathfrak E$ is a functor,  we obtain\nmorphisms of path complexes\n$\n\\mathfrak H^{2}\\circ \\mathfrak E(f_0), \\, \n\\mathfrak H^{2}\\circ \\mathfrak E(f_1)\\colon\n \\mathfrak H^{2}\\circ \\mathfrak E(G)\\to \\mathfrak H^{2}\\circ \\mathfrak E(H), \n$\nand \n$\n\\mathfrak H^{2}\\circ \\mathfrak E(F)\\colon\n\\mathfrak H^{2}\\circ \\mathfrak E(G\\Box I_1)\\to \n\\mathfrak H^{2}\\circ \\mathfrak E(H)\n$.\n Using Lemma \\ref{l3.16},  we can consider the composition \n$$\n[\\mathfrak H^{2}\\circ \\mathfrak E(G)]^{\\uparrow}\\overset{\\mu}\n{\\longrightarrow} \\mathfrak H^{2}\\circ \\mathfrak E(G\\Box I_1)\\overset{\\mathfrak H^{2}\\circ \\mathfrak E(F)}{\\longrightarrow}\n\\mathfrak H^{2}\\circ \\mathfrak E(H)\n$$\nwhich gives a homotopy between morphisms \n$ \\mathfrak H^{2}\\circ \\mathfrak E(f_0)$ and \n$\n\\mathfrak H^{2}\\circ \\mathfrak E(f_1)$.\nNow the result follows from \n\\cite[Th. 3.4]{Hyper}.\n\\end{proof}\n\n\\subsection{Natural path homology}\\label{S34}\n\nLet $G=(V,E)$ be a directed hypergraph.\n Define a digraph \n$\n\\mathfrak N(G)= (V^n_G, E^n_G)\n$\nwhere  \n$\nV^n_G=\\{ C\\in {\\mathbf{P}}(V)\\setminus \\emptyset | C\\in {\\mathbf{P}}_{01}(G)\\}\n$\n  and   \n$\nE^n_G=\\{A\\to B| (A\\to B)\\in E\\}.\n$\n Thus a set  $X\\in  {\\mathbf{P}}(V)\\setminus \\emptyset $ is a  vertex of  the digraph  \n $\\mathfrak N(G)$ iff  $X$  is an  origin or an end  of an arrow $\\mathbf e\\in E$.\nAny arrow $\\bold e=(A\\to B)\\in E$  gives\nan  arrow $(A\\to B)\\in E^n$.\n\n\n \\begin{proposition}\\label{p3.18} Every morphism of directed hypergraphs $f\\colon G\\to H$ \ndefines a morphism  of digraphs \n$\n[\\mathfrak N(f)]=(f_{V}^n, f_{E}^n) \\colon (V_G^n,E^n_G)\\to (V_H^n, E^n_H)\n$ \nby\n $\nf^n_V(C) \\colon =[{\\mathbf{P}}(f)]\\circ \\phi_G(C)\n$\nand \n$\nf_E^n(A\\to B) =(f_V(A)\\to f_V(B))\\in E^n_H\n$. Moreover,     $\\mathfrak N$ is a functor  from  the category $\\mathcal{DH}$ \nto the  category  $\\mathcal D$  of  digraphs. \\ \\ \\  $\\blacksquare$\n\\end{proposition}\nThe composition $\\mathfrak D\\circ \\mathfrak N$  gives a functor from  \n $\\mathcal{DH}$  to the category of path complexes.   \nFor a  directed hypergraph $G$,  we set \n$\nH_*^{\\bold n}(G)\\colon = H_*(\\mathfrak D\\circ \\mathfrak N(G))\n$.\nThese homology groups   will be called the \\emph{natural path homology groups}  \nof   $G$.  \n\\begin{example}\\label{e3.19} \n\\rm  Now we compute  \n$H^{\\bold{n}}_*(G)$ with  coefficients in $\\mathbb R$  of   directed hypergraph  $G=(V_G,E_G)$:\n   $$\nV_G=\\{1,2, 3, 4,5,6,7,8\\}, \\ \\ E_G=\\{\\bold e_1,\\bold  e_2,\\bold  e_3, \\bold e_4, \\bold e_5, \\bold e_6,\\bold e_7, \\bold e_8, \\bold e_9\\},\n$$\n $$\n\\bold e_1=(\\{1\\}\\to \\{3,4\\}), \\bold e_2=(\\{1\\}\\to \\{5, 6\\}), \\bold e_3=(\\{1\\}\\to \\{7,8\\}), \n$$\n$$\n\\bold e_4=(\\{2\\}\\to \\{3,4\\}), \\bold e_5=(\\{2\\}\\to \\{5,6\\}), \\bold e_6=(\\{2\\}\\to \\{7,8\\}), \n$$ \n$$\n\\bold e_7=(\\{3,4\\}\\to \\{5,6\\}), \\bold e_8=(\\{5,6\\}\\to \\{7,8\\}), \\bold e_9=(\\{7,8\\}\\to \\{3,4\\}).\n$$\nThe groups $H_*^{\\bold n}(G)$ coincide\nwith the regular path  homology groups of the digraph \ngiven on  Fig. 3. \n\n\\begin{figure}[h]\\label{fig3}\n\\setlength{\\unitlength}{0.14in} \\centering\n\\begin{picture}(16,18)(2,2)\n\\centering\n\\thicklines\n \\put(5,12){\\vector(1,0){7.2}}\n\\put(4.2,11.8){$\\bullet$}\n\\put(12.1,11.7){$\\bullet$}\n\\put(12.4,12){\\vector(1,1){3.2}}\n\\put(15,15.3){\\vector(-3,-1){9.6}}\n\\put(8.3, 19.7){$\\bullet$}\n \\put(15.6,15.1){$\\bullet$}\n\\put(8.6, 19.4){\\vector(-1,-2){3.7}}\n\\put(8.6, 19.6){\\vector(1,-2){3.6}}\n\\put(8.9, 19.5){\\vector(3,-2){6.4}}\n\\put(15.3, 4.4){$\\bullet$}\n\\put(15.6, 5.1){\\vector(-1,2){3.4}}\n\\put(15.3, 5){\\vector(-3,2){10.1}}\n\\put(15.6, 5.2){\\vector(0,1){10}}\n\\end{picture}\n\\caption{The digraph of Example 3.19.}\n\\end{figure}\n\\noindent \nComputation gives: \n$\nH_0^{\\mathbf n}(G)=H_2^{\\mathbf n}(G)=\\mathbb R$ and \n$H_i^{\\mathbf n}(G)=0$ for other $i$.\n\\end{example}\n\\begin{lemma}\\label{l3.20}  Let $G=(V,E)$ be a directed hypergraph and \n$I_1=(0\\to 1)$. \nThere is  an equality   \n$\n\\mathfrak N(G)\\Box I_1=\n\\mathfrak{N}(G\\Box I_1)\n$\nof digraphs.\n\\end{lemma}\n\\begin{proof}  The digraph \n$\\mathfrak N(G)\\Box I_1$  has \n$\nV_{\\mathfrak N(G)\\Box I_1}=\\left\\{C\\times \\{0, 1\\}|\\, C\\in {\\mathbf{P}}_{01}(G)\\right\\}\n$\nand  $E_{\\mathfrak N(G)\\Box I_1}=E_{0,1}\\cup E_{0\\to 1}$ where \n$\nE_{0,1}=\\{A\\times \\{i\\}\\to B\\times\\{i\\}|\n\\, A\\to B\\in E; i=0,1\\}$, \n$E_{0\\to 1}=\\left\\{C\\times\\{0\\}\\to C\\times\\{1\\}|\\, C\\in {\\mathbf{P}}_{01}(G)\\right\\}$. \nThe digraph \n$\\mathfrak N(G\\Box I_1)$  has the set of vertices \n$\nV_{\\mathfrak N(G\\Box I_1)}=\\left\\{C\\times \\{0, 1\\}|\\, C\\in {\\mathbf{P}}_{01}(G)\\right\\}\n$\nwhich  coincides with $V_{\\mathfrak N(G)\\Box I_1}$\nand the set of edges $E_{\\mathfrak N(G\\Box I_1)}=E_{0,1}\\cup E_{0\\to 1}$ which  coincides with $E_{\\mathfrak N(G)\\Box I_1}$. \n\\end{proof}\n\n\\begin{theorem}\\label{t3.21} For a directed hypergraph $G$,  the natural path \n\thomology groups $H^{\\bold n}_*(G)$ are  homotopy invariant.\n\\end{theorem}\n\\begin{proof} The path homology groups defined on the category of digraphs are homotopy \n\tinvariant \\cite{Hyper},\\cite{MiHomotopy} and thus,  the result follows from Lemma \\ref{l3.20}. \n\\end{proof}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{\\label{sec:Introduction} Introduction}\nOriginally suggested~\\cite{old} as descriptive of adsorption of molecules on a substrate (a motivation that has been renewed in recent experiments~\\cite{Blunt}), dimer models have attracted the interest of researchers in various branches of physics, ranging from statistical and condensed matter physics to high-energy physics~\\cite{string}. Their distinctive properties essentially result from the close-packing condition, which imposes that on a lattice, each site should be part of one and only one dimer. This strict condition generates strong correlations between degrees of freedom, even when interactions are absent from the system. \n\nClassical dimer models have been originally studied in statistical mechanics, with the famous result that non-interacting dimer models on planar graphs can be solved exactly using Pfaffians~\\cite{60a,60b}. On the square lattice for instance, it was shown using subsequent techniques that dimer correlation functions decay algebraically with distance~\\cite{60c}. It was latter shown that dimer models can also be viewed as dual versions of Ising models~\\cite{60b} and generate the ground-state manifolds of fully frustrated Ising models~\\cite{FF}. For bipartite lattices in three dimensions, dimers can be represented by an effective magnetic field living on the bonds of the lattice. The close-packing condition for the dimers encodes a Gauss law for the magnetic field~\\cite{Huse}. Postulating a quadratic dependence on this field of the effective entropic action suggests the existence of {\\it dipolar} dimer-dimer correlations. Monte Carlo simulations~\\cite{Huse} indeed confirm this picture with a great accuracy, and the corresponding phase of dimers on 3d bipartite lattice is often referred to as a Coulomb phase~\\cite{HenleyCoulomb} with this electromagnetic analogy in mind.\n\nIn some sense, dimer models form the ``Ising model\" of  local constraint, spelling out  their ubiquity in physics. In condensed-matter, dimer models emerged as classical counterparts of quantum dimer models~\\cite{QDM} (which properties for particular values of parameters are determined by those of the classical problem), as well as effective models for magnetization plateaus in frustrated magnets~\\cite{plateaus}. Dimer models show also close similarities with spin-ice systems~\\cite{Isakov} which can also host a Coulomb phase. There the close-packing condition translates into the ``ice rule''.\n\nIntriguing physics take place in classical dimer models when interactions are present. The perhaps simplest case to study is to add local interactions which favor parallel alignment of dimers on a plaquette of the lattice. In two dimensions on bipartite lattices, the system undergoes a phase transition from a columnar phase at low temperature to a disordered critical phase at high temperature~\\cite{Alet2d}. The transition is of the Kosterlitz-Thouless type. It is possible to obtain a field theoretical description of the transition in terms of an height model which predicts accurately the behavior of the correlation functions of different observables~\\cite{Alet2d,Papanikolaou,Castelnovo}. The situation is much less clear in three dimensions. At high temperature on the cubic lattice, the system is located in the Coulomb phase which is destabilized as the temperature is lowered towards a columnar order of dimers.  Quite surprisingly, the transition between the critical Coulomb phase and the ordered phase is \\textit{continuous}~\\cite{Alet3d}. Critical exponents estimated from the numerical simulations do not appear to be those of a known ``simple'' universality class, although being very close to those of a tricritical theory.\n\n A field theoretical description of the transition observed in the $3d$ classical dimer model is not easy. In particular, it cannot be properly addressed in the traditional Ginzburg-Landau formalism since the correlations between degrees of freedom in the disordered phase decay algebraically and not exponentially. Different attempts to provide for a field theoretical description of the critical point have led to a representation in the continuum in terms of two complex matter fields coupled to a non compact $U(1)$ gauge field~\\cite{Chalker,Charrier, Chen}, a theory known as the non compact $CP^1$ ($NCCP^1$) theory. The problem is that it is not clear at present if this theory possesses in fact an infra-red fixed point. Efforts to simulate lattice versions of the $NCCP^1$ model either lead to a weakly first-order transition~\\cite{Kuklov1}, or to a continuous transition with unconventional critical exponents~\\cite{Charrier,Motrunich}. Of course, it is possible that the $NCCP^1$ theory possesses a tricritical point and that the different simulated microscopic models all correspond to the same theory  but flow in the continuum toward different parameter regimes.  \n \n Another possibility is that the microscopic dimer model of Ref.~\\onlinecite{Alet3d} sits at a tricritical point, which would be the essentially unique way of reconciling the observed continuous transition with a Ginzburg-Landau approach based on symmetry-breaking. Note that the value of the critical exponents $\\alpha \\simeq 0.5$, $\\nu \\simeq 0.5$ and $\\eta \\simeq 0$~\\cite{Alet3d} are suggestive of this scenario as they are close to the ones of a $O(N)$ tricritical theory. This putative tricritical point could be the one of the $NCCP^1$ theory, or of another field theory yet to be specified. It is however unclear why the dimer model should be precisely located at a tricritical point: this usually requires a fine-tuning of parameters, and there is no other parameter than temperature in the original microscopic model~\\cite{Alet3d}. \\\\\n \n In this paper, we step aside from field theoretical considerations and instead provide new valuable data regarding the critical behavior of 3d classical dimer models. We have carried an extensive Monte Carlo (MC) simulation of a dimer model consisting of a four-dimers interaction on a cubic lattice, in addition to the usual attractive two-dimers plaquette interactions. The cubic interaction corresponds to a coupling between four parallel dimers sitting on the edges of a cube which can be attractive (non frustrated regime) or repulsive (frustrated regime). The system is studied with a worm MC algorithm which allows us to sample  systems of linear size up to $L = 180$. Our results suggest that the phase transition between Coulomb and columnar phases is first order almost everywhere in the non frustrated regime, and second order in the frustrated side - forcing the existence of a tricritical point in between these two regimes. Moreover, we find that the critical exponents in the strongly frustrated regime are different from the ones measured in the absence of the cubic interaction, with $\\eta \\sim 0.2$ and $\\nu \\sim 0.6$. In order to rule out  a very weak first order transition for all the range of parameters (which is always possible), we performed a flowgram analysis  which clearly indicates two collapses above and below the tricritical point. Finally, at very low temperature in the strongly frustrated regime, we observe a new crystalline phase resulting from the destabilization of the columnar phase. This phase has a degeneracy growing extensively with the linear system size and is separated from the columnar phase by a first order transition. The final phase diagram that we obtain is presented in Fig.~\\ref{fig:phasediag}. We note that similar results were recently obtained by Papanikolaou and Betouras~\\cite{Papanikolaou2} in a different deformation of the dimer model. A comparison between the two works will be made in Sec.~\\ref{sec:conclusion}.\\\\\n \n The plan of the paper is the following. In Sec.~\\ref{sec:def}, we describe the model, the algorithm and the relevant observables for its study. In Sec.~\\ref{sec:nonfrustrated}, we present our results in the non frustrated regime, when both interactions are attractive. In Sec.~\\ref{sec:frustated}, we analyze the frustrated regime where the plaquette interaction is attractive but the cubic interaction is repulsive. The final form of the phase diagram is obtained with a flowgram analysis, which we present in Sec.~\\ref{sec:flow}. We finally discuss the implications of our results in Sec.~\\ref{sec:conclusion}.\n \n   \n \\begin{figure}[h]\n \\begin{center}\n\\includegraphics*[width=8.5cm]{Figures\/phasediagram.png}\n\\caption{Phase diagram of the attractive dimer model with cubic interactions. Dots indicate values of interactions where simulations were performed. Dashed lines and green dots represent second order transitions. Solid lines and red dotes correspond to first order transitions. The white dot represents a point where the nature of the transition is still unclear.}\n\\label{fig:phasediag}\n\\end{center}\n\\end{figure}\n  \n\n \\section{Definitions}\n \\label{sec:def}\n \\subsection{System}\n The system we consider is a cube of linear dimension $L$ (total number of sites $N=L^3$) covered by hard-core dimers. Only dimer configurations $\\mathcal{C}$ obeying the close-packing condition contribute to the partition function. The partition function reads:\n\\begin{equation}\nZ = \\sum_{\\mathcal{C}} \\exp(-\\beta E_\\mathcal{C}),\n\\end{equation}\nand the energy of an allowed configuration $\\mathcal{C}$ is given by:\n \\begin{equation}\n \\label{eq:model}\n E_\\mathcal{C} = v_2( N_{||} + N_{=} +N_{\/\/})+v_4 N_{\\rm cubes},\n \\end{equation} \nwhere the first term is proportional to the number of plaquettes in the configuration containing two parallel dimers (referred in the following as ``parallel plaquettes'') and the second counts the number of unit cubes sustaining four parallel dimers (see Fig.~\\ref{fig:cubes}). Both occurences of terms in a given dimer configuration are illustrated in Fig.~\\ref{fig:3d}. In the remainder of this study, we will restrict ourselves  to the case of attractive plaquette interactions $v_2 < 0$ while cubic interaction $v_4$ can be attractive or repulsive. We investigate the properties of the system as a function of the ratio $x = v_4\/v_2$ and temperature $T = 1\/\\beta$. When $x > 0$, both interactions have the same sign and the system will be said to be non frustrated, as both interactions favor the same columnar ground-states. On the opposite, when $x<0$, the system will be in a frustrated regime ($v_2$ and $v_4$ terms compete). In general, we take $v_2  = -1$ and vary $v_4$. The only exception is the two limits $x \\rightarrow \\pm \\infty$ where we consider the system in absence of plaquette interactions ($v_2 = 0^-$) and take $v_4 = \\pm 1$.  \n\n\n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics*[width=\\columnwidth]{Figures\/mini_dimer.pdf}\n\\caption{The three different possibilities with four parallel dimers parallel on a unit cube. Each pattern contributes $v_4$ to the energy $E_{\\mathcal{C}}$ in Eq.~\\ref{eq:model}.}\n\\label{fig:cubes}\n\\end{center}\n\\end{figure} \n\n\\begin{figure}[h]\n\\begin{center}\n\\includegraphics*[width= \\columnwidth]{Figures\/model3d.pdf}\n\\includegraphics*[width=\\columnwidth]{Figures\/model3dcubic.pdf}\n\\caption{Illustration of occurences of the $v_2$ (top) and $v_4$ (bottom) terms of the model defined in Eq.~\\ref{eq:model} : interacting plaquettes (top) and cube (bottom) are represented with shaded surfaces. }\n\\label{fig:3d}\n\\end{center}\n\\end{figure} \n\nWe simulate the dimer model by means of a worm Monte Carlo algorithm with a local heat-bath detailed balance condition~\\cite{SandvikMoessner}. Compared to a local Metropolis algorithm, autocorrelation times are drastically reduced with a worm algorithm due to the use of non-local moves, which allows us to reach systems of linear size up to $L = 180$.  As we will see in the next section, the ability to simulate very large system sizes is of crucial importance to distinguish between continuous and weakly first-order transitions. We would indeed like to emphasize that for systems like dimer models, or others which contain \\textit{a priori} long-range correlations, one should be particularly cautious regarding the issue of finite-size scaling. Here, for the largest system sizes, up to $5. 10^6$ sweeps have been carried (we define one sweep by performing enough worm moves such that on average every site of the lattice is visited). The convergence of simulations is checked by looking at autocorrelation times of the various observables, as obtained from a binning analysis.  \n \n \\subsection{Observables}\n \\label{sec:observables}\nThe observables in our system are of three kinds: a first group is made of the thermodynamic quantities such as the average energy, a second type of observables is related to the columnar ordering, and the third type is related to the stiffness of the system (fluctuations of dimer fluxes).\n\n \\subsubsection{Thermodynamic quantities}\n\nA phase transition can generally be detected by monitoring the probability distribution of the energy of the system. For a first order transition, the average energy $\\langle E \\rangle$ is discontinuous and exhibits a latent heat when the temperature is lowered. For a second order transition, the average energy is continuous but its first derivative, the specific heat per site $C_v\/N$, obeys the scaling law:\n\\begin{equation}\n\\frac{C_v}{N} = \\frac{1}{N}\\frac{d\\langle E \\rangle}{dT}=\\frac{\\langle E^2\\rangle-\\langle E\\rangle ^2}{T^2 L^3} \\simeq C_v^{\\rm reg} + A L^{\\alpha\/\\nu}.\n\\end{equation}\nThe first term $C_v^{\\rm reg}$, corresponding to the regular part of the specific heat at criticality, is often forgotten in fits of numerical data as the divergence of the second term usually dominates (for $\\alpha>0$). However, at several points of the phase diagram, we find that this term cannot be neglected as the divergence of the specific heat can turn quite slow. In this situation, one can take $C_v^{\\rm reg}$ as either a new fitting parameter or as given by results obtained on small systems where the second term is negligible. In these cases, we take a conservative approach for the error bar on $\\alpha \/ \\nu$ and quote a result which encloses all possibilities.\n\nIn comparison, for a first order transition, the specific heat diverges like the volume: $C_v\/N \\propto L^3$. Finally, another mean to distinguish between first and second order transitions is to consider the whole histogram of energy at the transition temperature, as obtained in the Monte Carlo simulation. We expect for a first order phase transition the appearance of double peaks, centered at the average energy of the two co-existing phases. These peaks will appear only for samples with size above (or close  to) the correlation lenght at the transition, and should keep being separated when increasing system size. For a second order phase transition, the histogram should contain a unique peak. \n\n\\subsubsection{Columnar order parameter}\nThe local columnar order parameter $\\mathbf{m}(\\mathbf{r})$ is defined with respect to the dimer occupation number at each site $\\mathbf{n}(\\mathbf{r})$:\n\\begin{equation}\n\\mathbf{m}(\\mathbf{r}) = (-1)^\\mathbf{r} \\mathbf{n}(\\mathbf{r}).\n\\end{equation}\nThe global order parameter reads $\\mathbf{C} = \\frac{2}{L^3} \\sum_\\mathbf{r} \\mathbf{m}(\\mathbf{r}) $ and is normalized such that the six columnar states correspond to: $\\mathbf{C} = \\{ \\pm 1, 0,0 \\} , \\{ 0 , \\pm 1, 0 \\} , \\{ 0,0,\\pm 1 \\}$ and $C = \\langle | \\mathbf{C} | \\rangle = 1$. One also considers the corresponding susceptibility $\\chi$. In particular, for a second order transition:\n\\begin{equation}\n\\chi\/N = \\frac{\\langle \\mathbf{C}^2\\rangle - \\langle |\\mathbf{C}|\\rangle^2}{L^3} \\propto L^{2-\\eta},\n\\end{equation}\nwhile for a first order transition $\\chi\/N \\propto L^3$. Finally, the Binder cumulant:\n\\begin{equation}\nB = \\frac{\\langle \\mathbf{C}^4\\rangle}{\\langle \\mathbf{C}^2\\rangle^2}.\n\\end{equation}\nis a scale-invariant quantity in the case of a continuous transition, and should thus exhibit a crossing point at criticality as a function of the system size. Moreover, the finite size-scaling (FSS) of its derivative with respect to the temperature: \n\\begin{equation}\n\\frac{\\textrm{d} B}{\\textrm{d} T} \\propto L^{1\/\\nu},\n\\end{equation}\ngives a direct access to the critical exponent $\\nu$.\n \\subsubsection{Stiffness}\nThe (inverse) stiffness encodes fluctuations of dimer fluxes across a plane~\\cite{Huse,Alet3d}:\n\\begin{equation}\nK^{-1} = \\sum_{\\alpha = x,y,z} \\frac{\\langle \\phi_\\alpha^2\\rangle}{3L}\n\\end{equation}\nwhere the flux $\\phi_\\alpha$ is the algebraic number of dimers crossing a plane\nperpendicular to the unit vector $\\hat{\\alpha}$ . Given a lattice direction, the contribution to the flux is $+1$ for a dimer going\nfrom one sublattice to the other and $-1$ for the reverse situation. The stiffness is finite in the Coulomb phase, reflecting the presence of dipolar correlations between dimers. On the other hand, the columnar phase is robust to insertion of fluxes and $K^{-1}$ vanishes exponentially with system size. At a second order phase transition, the quantity $L K^{-1}$ should be scale invariant~\\cite{Alet3d} and the scaling of its derivative:\n\\begin{equation}\nL.\\frac{ dK^{-1}}{dT} \\propto L^{1\/\\nu}\n\\end{equation}\nprovides another access from the high temperature side to the exponent $\\nu$. In general, the error bars that we quote on exponents include at the same time errors due to the fitting procedure (which we measure by considering stability of fits with exclusion of a few data points), errors from the determination of critical temperature as well as statistical errors.\n\n\\section{Non frustrated side: $v_2 < 0$, $v_4 < 0$.}\n\\label{sec:nonfrustrated}\nWe start the discussions of our numerical results on the non-frustrated side $v_4 < 0$ and $v_2 < 0$ of the phase diagram. When both interactions are attractive, we expect to find the same phases as in the simple attractive plaquette model: a six-fold degenerate columnar phase at low temperature and a Coulomb phase with dipolar correlations at high temperature. \n\nAt first, let us consider the extreme case where only attractive cubic interactions are present ($v_2=0$ or $\\tanh (v_4\/v_2 ) = 1$ in the phase diagram of Fig.~\\ref{fig:phasediag}). The evolution of the energy, columnar order parameter $C$ and inverse stiffness $K^{-1}$ for small system sizes is presented on Figure \\ref{fig:extremeNF}. As expected, the columnar order is non-zero only at low temperature where the inverse stiffness vanishes. But in constrast with the attractive plaquette model, both quantities exhibit a strong discontinuity at the transition temperature $T_c \\sim 1.1$. In fact, the energy also displays such a jump, characteristic of a latent heat. This shows undoubtedly a first order transition.   \n\n \\begin{figure}[h]\n \\begin{center}\n\\includegraphics*[width=7cm]{Figures\/orders.pdf}\n\\caption{Left: Evolution of the columnar order parameter $C$ and inverse stiffness $K^{-1}$ as a function of temperature for $v_2=0$ and $v_4=-1$. Right: Temperature dependence of the average energy per site $\\langle E \\rangle\/N$. Here L = 16.}\n\\label{fig:extremeNF}\n\\end{center}\n\\end{figure}\n\nTo settle definitively the nature of the transition as well as to benchmark the method, we also study the histogram of energy observed during the simulation, which corresponds to the probability distribution of the energy $P(E)$. The appearance of a double peak distribution at the critical temperature is a typical sign of a first order transition. For $v_4\/v_2 = \\infty$, we can easily detect this double peak for system sizes as small as $L = 8$ (see Fig.~\\ref{fig:histos}). \n\nWe now introduce a small attractive plaquette interaction $v_2$ and repeat the procedure by tracking the temperature at which columnar order sets in and inverse stiffness vanishes. We observe that the nature of the transition remains discontinuous but that the correlation length grows as the ratio $v_4\/v_2$ is decreased: for $v_4\/v_2 = 0.8$ we find double peaks only at sizes $L \\geq 16$, for $v_4\/v_2 = 0.6$ at sizes $L \\geq 32$ and for $v_4\/v_2 = 0.4$ at $ L \\geq 80$ (see Fig.~\\ref{fig:histos}). Finally, for systems close to the pure plaquette model $v_4\/v_2 = 0$, it becomes extremely difficult to distinguish double peaks in the energy distribution. In fact, the histogram for $v_4\/v_2 = 0.2$ shows a slightly deformed single peak for $L = 140$. We were not able to see any sign of double peaks for $v4\/v2 = 0.1$ up to $L=140$.  \n\n \\begin{figure}[h]\n \\begin{center}\n\\includegraphics*[width=8cm]{Figures\/histo.pdf}\n\\caption{Energy per site probability $P(e)$ as a function  of energy per site $e=E\/N$, for different ratios $v_4\/v_2>0$ at the critical temperature separating columnar and Coulomb phases. The size $L$ corresponds to the minimal length for which the histograms start to display a double peak distribution. For $v_4\/v_2 = 0.2$, a deformed single peak is observed in the distribution for $L = 140$, the maximal sample size simulated for this parameter.}\n\\label{fig:histos}\n\\end{center}\n\\end{figure}\n \nAnother possibility to discern a discontinuous transition is to measure the critical scaling of the maximum of the susceptibility and the specific heat per site. At a first order transition, both quantities should diverge like the volume $L^3$. In terms of the critical exponents introduced in section \\ref{sec:observables}, this would correspond to effective critical exponents $\\left.\\frac{\\alpha}{\\nu}\\right|_{\\rm eff}= 3$ and $\\eta_{\\rm eff} = -1$. We have determined the scaling laws of these two quantities for several values of the ratio $v_4\/v_2$ (see table \\ref{tab:tableau1}) and find that when $v_4\/v_2$ is large, the exponents agrees with the first order values. As we approach $v_4\/v_2 = 0$, the scalings of $C_v$ and $\\chi$ get smoother and the exponents closer to the values of Ref.~\\onlinecite{Alet3d} $\\left.\\frac{\\alpha}{\\nu}\\right|_{\\rm eff} \\sim 1$ and $\\eta_{\\rm eff} \\sim 0$. At this point, it is not possible to conclude on the order of the transition at $v_4\/v_2 = 0.1$. The transition can be either continuous or very weakly first order. \n\n\\begin{center}\n\\begin{table}[h]\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline \n$v_4\/v_2$ & $T_c$ &$ L_{\\rm min}$ & $ L_{\\rm max}$ &$\\left.\\frac{\\alpha}{\\nu}\\right|_{\\rm eff}$ & $\\eta_{\\rm eff}$ \\\\\n\\hline \n0.6 & $2.225$&$ 16 $& $32$ &$ 3 $ & $-1.00$\\\\\n\\hline\n0.4 & $2.033$&$ 56 $ & $80$ & $ 2.9$& $ -0.90$ \\\\\n\\hline\n0.2 & $1.851$&$ 64$ & $140$ & $2$ &$-0.40$ \\\\\n\\hline\n0.1 & $ 1.7625 $ &$64 $&$140$&$1.4$& $-0.25$ \\\\\n\\hline\n0 & $ 1.765$&$56 $ & $96$&$ 1.11(5)$ & $ -0.02(5) $ \\\\\n\\hline\n\\end{tabular}\n\\caption{Critical temperature and effective critical exponents for different non frustrating coupling ratios. For each ratio, the exponents have been measured by a FSS analysis using $L_{\\rm min}$ as the minimal size. The values at $v_4\/v_2=0$ are taken from Ref.~\\onlinecite{Alet3d}.}\n\\label{tab:tableau1} \n\\end{table}\n\\end{center}\n\n\\section{Frustrated side: $v_2 < 0$ $v_4 > 0$}\n \\label{sec:frustated}\n \n We now turn to the analysis of the system where plaquette interactions are attractive but cubic interactions are repulsive. As the two interactions compete with each other, we can expect, at least at low temperature and in the regime $v_4\/v_2 \\ll -1$, that new phases may appear. \n\nLet us again first discuss the extremal case where only cubic interactions are present ($v_2 = 0$). We observe that the columnar order parameter vanishes for all temperature while the inverse stiffness $K^{-1}$ remains always non-zero and finite (see Fig.~\\ref{fig:extremeF} left). Moreover, although the specific heat displays a maximum (see Fig.~\\ref{fig:extremeF} right), it does not display any dependence on the size of the system and cannot be related to a critical phenomena. Thus, we obtain the surprising result that the system is always disordered when $v_4 > 0$ and $v_2 = 0$. In other words, the Coulomb phase can accomodate for having no cubes occupied by four dimers (as in Fig.~\\ref{fig:cubes}), even down to very low temperatures.  Even more, the Coulomb phase appears to be strenghten in this situation as the inverse stiffness increases slightly as temperature is lowered. \n   \n \\begin{figure}[h]\n \\begin{center}\n\\includegraphics*[width=7cm]{Figures\/ordersINF.pdf}\n\\caption{For $v_4 = 1$ and $v_2 = 0$. Left: Evolution of the stifness $K^{-1}$ and columnar order $C$ as a function of temperature for $L=16$. The non-zero value reached by $C$ is due to the finite size of the sample. Right: The height of the peak of the specific heat per site does not display any dependence on system size.}\n\\label{fig:extremeF}\n\\end{center}\n\\end{figure}\n\nAs soon as a finite attractive coupling $v_2$ is introduced, we find that the specific heat per site displays two peaks as a function of temperature: one at a lower temperature $T_{c_1}$ which is strongly diverging with the system size and another at an upper temperature $T_{c_2}$ which diverges very slowly. Fig~\\ref{fig:result1} and its insets display results at $v_4\/v_2=-1$, which are typical of what we observe in the frustrated regime. The first peak of the specific heat is associated with the freezing of the columnar order parameter to a value smaller than $1$ at $T < T_{c_1}$ , the second to the appearance of the Coulomb phase for $T>T_{c_2}$ (see upper inset of figure \\ref{fig:result1}). In the next two sections, we will detail the nature of these two phase transitions and of the phase separating them. We note that as the ratio $v_4\/v_2 \\rightarrow - \\infty$, the two critical temperatures get closer such that it becomes more difficult to detect the peak at $T_{c2}$. \n\n\\begin{figure}[h]\n \\begin{center}\n\\includegraphics*[width=8cm]{Figures\/results1.pdf}\n\\caption{Evolution of the specific heat per site as a function of temperature for $v_4 \/v_2= -1$. The first peak at $T_{c_1} \\sim 0.5$ is associated with the crystallisation of the system in an ordered phase different from the columnar phase, which can be readily seen by the evolution of the columnar order parameter (see upper inset). The second peak, at $T_{c_2} \\sim 0.95$, delimitates a region with non-zero columnar order from  a region with non-zero inverse stiffness. Upper inset: evolution of the inverse stiffness $K^{-1}$ and of the columnar order parameter $C$ for $L = 16$. Lower inset: zoom of the specific heat close to $ T_{c_2}$ . }\n\\label{fig:result1}\n\\end{center}\n\\end{figure}\n    \n \\subsection{Low temperature phase transition $T_{c_1}$}\n \n We now discuss the nature of the phase below the lower transition by first considering the evolution of the $T=0$ ground-states as a function of the frustration ratio $v_4\/v_2$. For large positive values of $v_4$ (but still with $v_2=-1$), we expect the columnar ground-states to become unstable as they maximize the number of parallel cubes. In this limit, we must find dimer configurations which have exactly zero parallel cubes but that can nonetheless support a maximal number of parallel plaquettes. We find that there are several configurations  (in fact an exponential number) that satisfy this frustrating condition. For instance, we present in Fig.~\\ref{fig:packing} on the example of a $L=6$ cube three configurations satisfying these two constraints. Configuration $A$ is made of a unit pattern consisting of two planes repeating each other. The unit pattern of configurations $B$ and $B'$ posseses three planes. Configurations $B$ and $B'$ are simply related by a unit translation of the two bottom planes. If we now consider larger systems, it is easy to see that we can use the same plane patterns at will, by randomly choosing $B$ or $B'$ every three planes and this, without creating parallel cubes. Therefore the degeneracy of the ground-state is at least growing like $2^{L\/3}$, that is exponentially with the linear system size. It is possible that by forming other cost-free defects within a plane, the degeneracy is even higher $\\propto e^{a L^2}$, but we have not made any further investigations in this direction.\n \n \\begin{figure}[h]\n \\begin{center}\n\\includegraphics*[width=8cm]{Figures\/packing.pdf}\n\\vspace{-4cm}\n\\caption{Three configurations on the $L=6$ cube which maximize the number of parallel plaquettes without having any parallel cubes. Configuration $A$ is built out of a unit pattern containing two planes which repeats itself three times. This unit pattern possesses $42$ parallel plaquettes, leading to a number of $7\/12$ parallel plaquettes per unit site.  Configurations $B$ and $B'$ both consist of a unit pattern of three planes repeating itself twice. The unit pattern possesses $63$ parallel plaquettes, leading also to a number of $7\/12$ parallel plaquettes per unit site. Configuration $B'$ is obtained from configuration $B$ by shifting the dimer pattern on the two lowest planes by one unit cell on the right direction. Mixing $B$ and $B'$ patterns, one can create several dimer configurations having the same energy.}\n\\label{fig:packing}\n\\end{center}\n\\end{figure}\n\nFor what thermodynamics is concerned, it is easy to check that all such configurations with no parallel cubes have on average $7\/36$ plaquettes that are parallel. We refer to the corresponding phase as Crystal II. While it may be possible to define correctly an order parameter for this crystal (and this in spite of the high ground-state degeneracy), we simply concentrate on a simple comparison between the energy of the Crystal II ground-states with those of the columnar phase. A columnar ground-state satisfies $1\/3$ of the possible parallel plaquettes, and one parallel cube out of two. Since the number of plaquettes (cubes) is three times (equal to) the number of lattice sites, we obtain:\n\\begin{eqnarray}\nE_{\\rm Crystal \\, II} \/ L^3 &=& E_{\\rm columnar} \/ L^3\\nonumber \\\\\n\\Leftrightarrow \\frac{7}{12} v_2 &=& v_2 - \\frac{v_4}{2} \\\\\n\\Leftrightarrow \\frac{v_4}{v_2} &=& -\\frac{10}{12}. \\nonumber \n\\end{eqnarray}\nThat is, the Crystal II phase should be favored as soon as $v_4\/v_2 < -10\/12\\simeq 0.833$. We now compare this simple estimate with numerical simulations. Considering the evolution of the columnar order parameter as a function of $T$ for different ratios $v_4\/v_2$, we find that $C$ converges to $1$ at very low temperature for $v_4\/v_2 > -0.8$, while for $v_4\/v_2 \\leq -0.8$ it converges towards a smaller value (see Fig.~\\ref{fig:crystal} top). This indicates that the lowest energy configurations are no longer the columnar ones. A further indication of the Crystal II phase is given by the average number per site of parallel cubes $\\langle N_{\\rm cube} \\rangle\/L^3$ and parallel plaquettes $\\langle N_{\\rm plaquette}\\rangle\/L^3$. As expected, we find (see Fig.~\\ref{fig:crystal} bottom) that $\\langle N_{\\rm cube} \\rangle\/L^3$  decreases from $1\/2$ to $0$ and  $\\langle N_{\\rm plaquette}\\rangle \/L^3$ from $1$ to $7\/12$ quite abruptly as soon as $v_4\/v_2 \\lesssim -0.8$. Note that the estimate $\\left.v_4\/v_2\\right|_c \\simeq -0.8$ that we obtain is quite rough as it is affected by the chosen grid in $v_4\/v_2$, the moderate size of the sample ($L=32$) and the finite temperature used in our simulations. Given this, it can be considered as in good agreement with the exact value $-10\/12$.\n\nThe abrupt behaviour observed in Fig.~\\ref{fig:crystal} tends to indicate a first order transition between the Crystal II and columnar phases. This is confirmed by the strong divergence of the specific heat  (Fig.~\\ref{fig:result1}), but also by the apparition of a latent heat (see Fig.~\\ref{fig:crystal} top). We find that in the full phase diagram, the transition at $T_{c_1}$ is always of first-order nature. When $v_4\/v_2 \\gtrsim -0.8$, the Crystal II phase and the low-$T$ phase transition disappear. \n  \n \\begin{figure}[h]\n \\begin{center}\n\\includegraphics*[width=7cm]{Figures\/ColumnarT.pdf}\n\\includegraphics*[width=6.5cm]{Figures\/phasev2.pdf}\n\\caption{Top: Evolution as a function of temperature of the columnar order parameter $C$ for different ratios $v_4\/v_2$ at $L = 32$. For $v_4\/v_2 < -0.8$, $C$ does not converge towards $1$ at $T=0$. Inset: Evolution of the average energy per site. A discontinuity corresponding to the phase transition can easily be deteted. Bottom: Evolution of $C$, $\\langle N_{\\rm plaquette} \\rangle\/N$ and $\\langle N_{\\rm cube} \\rangle\/N$ as a function of $v_4\/v_2$ for $T = 0.3$ and $L = 32$.}\n\\label{fig:crystal}\n\\end{center}\n\\end{figure}\n    \n\n\\subsection{High temperature phase transition $T_{c_2}$} \n\nThe high temperature phase transition corresponds to the simultaneous emergence of dipolar correlations at high temperature and disappearance of the columnar order. \nBefore performing a detailed scaling analysis, we already make an important statement : in all simulations for $v_4>0$, we found {\\it no evidence} for a first-order phase transition at $T_{c_2}$ between the columnar and the Coulomb phases. This has been checked in all observables at hand (thermodynamics, related to columnar order or the Coulomb phase), including energy histograms at the transition. We will come back to this issue at the end of this section, and in Sec.~\\ref{sec:flow}.\n\n\\subsubsection{Strongly frustrated regime}\n\nIn order not to be influenced by any crossover effect, we first concentrate on the transition at $T_{c_2}$ far away from the putative tricritical point at $v_4 = 0$. For $v_4\/v_2 = -10$, we performed large scale simulations and applied the FSS analysis to calculate the critical exponents. Our set of data is presented in Fig.~\\ref{fig:results10}. Let us first concentrate on the specific heat per site (see Fig.~\\ref{fig:results10} top). At the transition, it exhibits a very slow growth with system size, suggestive of a continuous transition. In fact, the divergence is so small that the regular part $C_v^{\\rm reg}$ of the specific heat contributes the most even for $L = 140$. The best fit we obtained for system sizes ranging from $L = 32$ to $L=140$ gives an estimate of $\\alpha\/\\nu \\sim 0.4$ (Fig.~\\ref{fig:results10} top inset). Unfortunately, this estimate varies a lot when considering another subset of system sizes. For instance, discarding the point at $L = 140$ leads to an estimate $\\alpha\/\\nu = 0.6$ and discarding the two points $L=120$ and $L=140$ leads to $\\alpha\/\\nu \\sim 0.8$. Thus, while we cannot conclude on the precise value of $\\alpha$ at this point, it seems at least to be quite small. The evolution of the Binder cumulant and of the product $K^{-1} . L$ is presented in the middle panel of Fig.~\\ref{fig:results10}. For both quantities, we observe a crossing point, in agreement with a second order transition. The two crossing points temperatures are very close: $T_{\\rm Binder} = 0.672$ and $T_{\\rm Stiffness} = 0.6715$. The thermodynamic measurements of the derivative quantities $dB\/dT$ and $L dK^{-1}\/dT$, shown in the insets, allows us to have access to two independent estimates of the exponent $\\nu$. We find $\\nu_{\\rm Binder} = \\nu_{\\rm Stiffness} =  0.63(4)$. These exponents are compatible with the Ising and XY universality classes in $3d$. Moreover, this is consistent with a small value of $\\alpha$ assuming hyperscaling $\\alpha = 2 - d\\nu$. The value of the Binder cumulant and the stiffness at the critical point, $B_c$ and $(K^{-1} \\cdot L)_c$, also furnish valuable information, because these quantities are also universal. Checking the crossings of the three largest system sizes of our system, we find $1.28 \\leq B_c \\leq 1.30$ and $ 0.16 \\leq (K^{-1} \\cdot L)_c \\leq 0.20$. While the value of $B_c$ is consistent with the result obtained for the pure plaquette model $B_c(v_4\/v_2 = 0) = 1.27(1)$, the value at criticality for the stiffness is rather smaller $(K^{-1}\\cdot L)_c(v_4\/v_2 = 0) =0.28(2)$. Finally, we discuss the scaling of the columnar susceptibility (see Fig.~\\ref{fig:results10} bottom), obtaining $\\eta = 0.25(3)$. The fact that $\\eta$ is large and positive for the strongly frustrated system is an unambiguous result of our study, as it is robust for instance on the set of sizes chosen to perform the FSS analysis. Such a strong $\\eta$ rules out the possibility of a simple transition such as the Ising or XY universality class. Finally, we note that all the exponents differ considerably from those measured in Ref.~\\onlinecite{Alet3d}, implying a different type of transition. This can be already be seen at the qualitative level as  the specific heat does not display any (strong) divergence.\n\n\\begin{figure}[h]\n \\begin{center}\n\\includegraphics*[width=7cm]{Figures\/Cv.pdf}\n\\includegraphics*[width=7cm]{Figures\/Crossings.pdf}\n\\includegraphics*[width=7cm]{Figures\/Sc.pdf}\n\\caption{ As a function of temperature,  for $v_4\/v_2 = -10$ . Top: Specific heat per site $C_v\/N$. The dashed line represents a linear interpolation of the regular part of the specific heat. Inset: Maximum of $C_v\/N$ as a function of system size.  Middle: Binder cumulant and inverse stiffness  crossings. Insets : Binder cumulant derivative (at $T=0.672$) and derivative $L.dK^{-1}\/dT$ (at $T = 0.6715$) as a function of system size (log-log scale). Bottom: Columnar susceptibility $\\chi$ per site. Inset: Maximum of $\\chi$ as a function of system size (log-log scale). All lines in insets denote power-law fits of critical exponents (see text for details).}\n\\label{fig:results10}\n\\end{center}\n\\end{figure}\n\n\\begin{center}\n\\begin{table*}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|}\n\\hline \n$v_4\/v_2$ & $T_c$ & $\\alpha\/\\nu$ & $\\nu_{\\rm Binder}$ & $\\nu_{\\rm Stiffness}$ &$\\eta$&$B_c$&$(K^{-1}\\cdot L)_c $\\\\\n\\hline \n-10 & $ 0.672(1) $&$0.4^*$& $0.63(4)$ & $0.63(4)$ & $0.25(3)$ & $1.28 - 1.30$ & $0.16 - 0.20$\\\\\n\\hline\n-1 & $ 0.953(1) $ &$0.35(10)$& $ 0.60(4) $& $ 0.61(4) $& $0.16(6)$ & $1.27 - 1.29$& $0.18 - 0.22$\\\\\n\\hline\n-0.2 & $ 1.508(1) $ &$0.80(15)$&$0.50(3)$ &$ 0.58(4)$ & $ -0.02(5)$&$1.26 - 1.28$&$0.23 - 0.27 $\\\\\n\\hline\n0 & $ 1.675(1) $&$1.11(15) $ & $0.51(3) $& $0.50(4)$ & $-0.02(5) $ & $ 1.26 - 1.28 $ & $0.26-0.29$ \\\\\n\\hline\n\\end{tabular}\n\\caption{Critical exponents for different frustrating coupling ratios. For the ratio $\\alpha\/\\nu$, the exponents have been measured by a FSS analysis using sizes comprised between $L_{\\rm min} = 32$ and $L_{\\rm max} = 140$. For the other exponents, we can limit ourselves to larger system sizes between $L_{\\rm min} = 80$ and $L_{\\rm max} = 140$. In the last row, we remind the results for the pure plaquette model (taken from Ref.~\\onlinecite{Alet3d}). The symbol $^*$ denotes one case where the determination of $\\alpha\/\\nu$ is impossible due to the strong contribution of the regular part of the specific heat (see Sec.~\\ref{sec:def}).}\n\\label{tab:tableau2} \n\\end{table*}\n\\end{center}\n\n\\subsubsection{Medium and weakly frustrated regime}\n\nWe repeated the same analysis for different values of $v_4\/v_2$ on the frustrated side, measuring the exponents $\\alpha$, $\\nu$ and $\\eta$. In particular, we carried out extensive simulations at $v_4\/v_2 = -1$ and $v_4\/v_2 = -0.2$. Results are summarized in Tab.~\\ref{tab:tableau2}. For $v_4\/v_2 = -1$, the exponent $\\nu$ is compatible with the one obtained for $v_4\/v_2 = -10$, and while estimations of $\\eta$ are slightly different, the anomalous dimension is clearly non-zero in both cases. The ratio of exponents $\\alpha\/\\nu$ is again the hardest to determine reliably due to the important contribution of the regular part in the specific heat.  For $v_4\/v_2 = -1$, $C_v\/N$ has however a clear diverging tendency and it is then easier to extract $\\alpha\/\\nu$ (see figure.~\\ref{fig:Cv1.0}). We find $\\alpha\/\\nu \\sim 0.35$, a value in accordance with the rough estimate at $v4\/v2 = -10$ and with the hyper-scaling relation: $\\alpha = 2 -d\\nu$. \nIn any case, the set of exponents we obtain for $v_4\/v_2 = -10$ and $v_4\/v_2 = -1$ are clearly different from the one obtained for the model with no cubic term. For $v_4\/v_2 = -0.2$, the values are on the contrary compatible with the ones obtained from Ref.~\\onlinecite{Alet3d}: $\\alpha \\simeq 0.5$ and $\\eta \\simeq 0$. Interestingly, we find two non overlapping estimates of $\\nu$ from the Binder cumulant and the stiffness derivatives. That may indicate a possible crossover. As a further information, we also give the values of Binder cumulant and stiffness at criticality. \n\n\\begin{figure}[h]\n \\begin{center}\n\\includegraphics*[width=7cm]{Figures\/Cv-1.pdf}\n\\caption{ Specific heat per site $C_v\/N$ at $v_4\/v_2 = -1.0$. The dashed line represents a linear interpolation of the regular part of the specific heat. Inset: Maximum of $C_v\/N$ as a function of system size. }\n\\label{fig:Cv1.0}\n\\end{center}\n\\end{figure}\n\nThe results on the frustrated regime bring some interrogations. Our results suggest that there are two different sets of critical exponents (and therefore universality classes) for the Coulomb-columnar phase transition in the extended dimer model: one for the highly frustrated regime with $\\alpha \\sim 0.2$, $\\nu \\simeq 0.63$ and $\\eta \\sim 0.2$ and one close to the point $v_4 = 0$ where the exponents are close to those of the $O(N)$ tricriticality class. Moreover, in the non frustrated regime, we have seen in section \\ref{sec:nonfrustrated} that the transition between Coulomb and columnar phases is clearly first order, at least when $v_4\/v_2 > 0.4$. A natural interpretation of these data is that there is a tricritical point for a value $v_4^*$ in the vicinity of $v_4 = 0$, separating a continuous transition in the frustrated case to a discontinuous one in the non-frustrated case. The presence of a tricritical point can influence the effective critical exponents measured for values of $v_4\/v_2$ in the vicinity of ${v_4^*\/v_2}$. Despite the large samples used in our simulations, we are not able to precise the exact location of this tricritical point. In particular, there is no formal reason to believe that the tricritical point is located exactly at $v_4 = 0$. In the next section, we will show that the tricritical point should at least be located on the non frustrated side, that is ${v_4^*\/v_2} \\geq 0$. \n\nAnother possible explanation that we cannot exclude {\\it a priori} is that the transition is always first order. In fact, by looking at the evolution of the different exponents from the non frustrated to the frustrated side, one can perfectly imagine that the correlation length grows continuously but remains \\textit{finite} at any $v_4\/v_2$. That would mean in particular, that the exponents found in Ref.~\\onlinecite{Alet3d} for the pure plaquette model are artifacts caused by a very weakly first order transition. There are several examples of models where reports of unconventional continuous phase transitions have been made and which were finally found to be weakly first order. In order to rule out this scenario, we present in the next section a flowgram analysis combined with a study of histograms at very large system sizes. \n\n\\section{Flowgram analysis}\n \\label{sec:flow}\n\nThe flowgram method is an advanced version of the FSS analysis which was proposed by Kuklov and coauthors~\\cite{Kuklov2}. Consider two points located on the critical line separating the Coulomb and columnar phases in Fig.~\\ref{fig:phasediag}. The method relies on the demonstration that the large scale behavior for one given point is identical to that of the second point where the nature of the transition can be easily determined. If this is true, then the two points are in the same critical regime and the nature of the transition remains unchanged all between the two points. On the contrary, a change in the nature of the transition must occur if this is not true. \n\nThe key elements of the method are to {\\it (i)} introduce a definition of the critical point for finite-size systems consistent with the thermodynamic limit and which is insensitive to the transition order and {\\it (ii)}  compute a quantity $Q$ which is scale invariant at criticality, vanishes in one phase and diverges in the other. To define the operational critical temperature, we assume a finite probability of having a non-zero flux at criticality~\\cite{Kuklov1}:\n\\begin{equation}\n\\frac{P(\\mathbf{\\phi} = {\\bf 0})}{1- P(\\mathbf{\\phi} = {\\bf 0})} = A,\n\\end{equation}\nwhere $A$ is some constant which exact value is not relevant for the rest of the method. In practice, we chose A in such a way that it is close to typical values found at the transition for a large system size for $v_4\/v_2=-0.2$. We then consider $Q=L.K^{-1}$, as this product is indeed scale invariant for a second order transition, vanishes in the columnar phase (as we expect $K^{-1}$ to vanish exponentally with system size) there and diverges in the Coulomb phase (as $K^{-1}$ is a constant). \n\nThe flows $Q_{v_4\/v_2}(L)$ for several values of $v_4\/v_2$ in the interval $[-0.6,0.7]$ are presented on Fig.~\\ref{fig:flowgram} top. The flows can be roughly divided into two groups: for $v_4\/v_2 < 0.2$, the flows show a very slow divergence with the system size. For $v_4\/v_2 > 0.2$, the flows are strongly diverging. The second group of flows is thus associated with the strongly discontinuous transition. At this stage we cannot draw any conclusion about the first group of curves since it might be that all curves diverge and are actually connected by a scaling transformation. By this, we mean that we need to check if there exists no renormalization fonction $g(v_4\/v_2)$ such that plotted as a function of the renormalized length:\n\\begin{equation}\nL_{\\rm eff} = g(v_4\/v_2) L,\n\\end{equation}\nall the different flows collapse into a single master curve:\n\\begin{equation}\nQ_{v_4\/v_2=a}(L_{\\rm eff}) = Q_{v_4\/v_2=b}(L_{\\rm eff}) \\; \\; \\forall \\; (a,b).\n\\end{equation}\n To search for such a transformation, we first try to collapse the flows two by two, starting from the largest positive values of $v_4\/v_2$. Fixing $g(v_4\/v_2 = 0.7) = 1$, we find the best numerical value for $g(v_4\/v_2 = 0.65)$ such that the corresponding flows collapse as a function of $L_{\\rm eff}$. We then proceed successively with the next two consecutive values of $v_4\/v_2$ and find the best factor for $g(v_4\/v_2 = 0.6)$. In this manner, we go through all the parameter space, trying to collapse the curves two by two and finding the corresponding $g(v_4\/v_2)$, down to $v_4\/v_2 = -0.6$. If such an action is possible, and if the estimated function $g$  varies monotonically as a function of $v_4\/v_2$, then all the critical points in the interval $[-0.6,0.7]$  should refer to the same critical behavior. \n \n We have searched for such a scaling function $g$ and we have arrived to the unambiguous conclusion that it is \\textit{not possible} to perform a global collapse of the flows. In particular, the slow divergence of the flow for $v_4\/v_2 = -0.02$ is not compatible with the strong growth shown by the flows around $v_4\/v_2 = 0.6$. This is because the flows between these two intervals can hardly be collapsed with their neighbors (meaning that for any pair of consecutive flows in the interval $0 < v_4\/v_2 < 0.4$, we could not find a rescaling factor such that the two flows are superimposed). On the contrary, we have succeeded in performing two local collapses: one for the region $-0.6 \\leq v_4\/v_2 \\leq 0.02$, and the other for the region $ 0.4 \\leq v_4\/v_2 \\leq 0.7$ (see Fig.~\\ref{fig:flowgram} bottom). This is a clear indication of the presence of two different critical behaviors in the phase diagram. Because the collapse for positive $v_4\/v_2>0$ is strongly diverging, we naturally associate it with a first order transition. The collapse in the negative range of $v_4\/v_2$ describes most probably a second order regime. One can see that this collapse has  actually not converged, as it should for a continuous transition. This is partly due to our original choice of the constant $A$ which made our operational critical temperature slightly above the real $T_c$. A small amount of non-zero stiffness remains present in the system and perturbs the convergence towards the fixed point behavior.\n\t  \n\\begin{figure}[h]\n \\begin{center}\n\\includegraphics*[width=7cm]{Figures\/flowgram.pdf}\n\\includegraphics*[width=7cm]{Figures\/collapse1.pdf}\n\\caption{Flowgram (top) and performed collapses (bottom) for the extended dimer model. See text for details of the flowgram procedure.}\n\\label{fig:flowgram}\n\\end{center}\n\\end{figure}\n \n To further confirm our conclusion on the flowgram, we have performed the following check. Suppose that the points $v_4\/v_2 = -0.02$ and $v_4\/v_2 = 0.6$ refer nevertheless to the same critical regime. Then, there should exist a scaling function connecting the flows at $v_4 = -0.02$ and $v_4 = 0.6$. It is in fact possible to connect \\textit{very roughly} the two flows by renormalizing the length $L$ for $v_4\/v_2 = 0.6$ by a factor $g(0.6) = 8$ while leaving the flow for $v_4\/v_2 = -0.02$ unchanged (see Fig.~\\ref{fig:histo180} left)).  If this rescaling is really a physical renormalization transformation, then the properties of the system at $v_4\/v_2 = -0.02$ and $L = 160$ should correspond to those at $v_4\/v_2 = 0.6$ and $L = 32$. For this latest value, we know in particular that the transition is first order since the energy histogram displays a double peak (see Fig.~\\ref{fig:histos}). If the critical point $v_4=0$ is indeed in the same regime as the critical point at $v_4\/v_2=0.6$, we should expect to see a double-peak also for samples of sizes $L\\geq 160$ at $v_4=0$. We have therefore carried a simulation at $v_4 = 0$ with $L = 180$ and have then measured the histogram of energy at the maximum of the specific heat. The histogram displays a unique and well-defined peak (see Fig.~\\ref{fig:histo180} bottom right), which confirms that the transition at $v_4=0$ is continuous. Moreover, the value of the specific heat maximum is perfectly compatible with the exponents measured previously at $v_4 = 0$ (see Fig.~\\ref{fig:histo180} top right), confirming the validity of the exponent $\\alpha \/ \\nu \\simeq 1.11(15)$ found in Ref.~\\onlinecite{Alet3d}.\n \n \\begin{figure}[h]\n \\begin{center}\n\\includegraphics*[width=8cm]{Figures\/HistoL180.pdf}\n\\caption{Left: Flows at $v_4\/v_2 = -0.02$ and $v_4\/v_2 = 0.6$ at the rescaled length $L_{\\rm eff}$. Top right: Maximum of the specific heat for $v_4 = 0$ as a function of the system size. Data are taken from Ref.~\\onlinecite{Alet3d} except for the value at $L = 180$. The solid line is the power-law fit, giving rise to the estimate $\\alpha\/\\nu=1.15(15)$ compatible with the result of Ref.~\\onlinecite{Alet3d} {\\it without} the knowledge of the L=180 point. Bottom right: Probability of energy per site at $v_4 = 0$ and $L = 180$.}\n\\label{fig:histo180}\n\\end{center}\n\\end{figure}   \n\nTo conclude on this part, not only can we drive out the possibility that the regimes $v_4\/v_2 < 0$ and $v_4\/v_2 > 0$ are connected but we can also state that the tricritical point is necessarily located at a value $v_4^*\/v_2 \\geq 0$. \n   \n\\section{Discussion}   \n \\label{sec:conclusion}\n In this study, we presented an extended version of the classical dimer model with  plaquettes  and cubic interactions. Our simulations indicate that depending on the sign of the interactions, the nature of the critical phase transition between the Coulomb and columnar phases changes. Compared to the pure plaquette model ($v_4\/v_2 = 0$), a cubic interaction which reinforces the alinement of dimers ($v_4\/v_2 > 0$) leads to a first order transition, identified by a double peak distribution of the energy and a strong divergence in thermodynamic quantities. Whether an infinitesimal positive cubic coupling is enough to alter the nature of the transition is not certain, as we lack any theoretical argument to support this, but simulations tend to indicate that this change should occur very close to $v_4 = 0$. On the other side, when both interactions compete ($v_4\/v_2 < 0$), finite size scaling analysis of thermodynamic quantities shows no sign of any discontinuity at the transition. When the cubic interaction is largely dominant ($v_4\/v_2 = -10$), the critical exponents deviate significantly from those measured in the pure plaquette model, with $\\alpha \\sim 0.2$, $\\nu \\sim 0.6$ and $\\eta \\sim 0.2$ in the first case and $\\alpha \\sim 0.5$, $\\nu \\simeq 0.5$ and $\\eta \\simeq 0$ in the latter. In the interval $-1 \\leq v_4\/v_2 \\leq 0$, we find exponents in between these two cases, probably due to a cross-over effect. To discharge the possibility of a weak first order transition on the frustrated side, we carried out a flowgram analysis in the vicinity of $v_4 = 0$. The flowgram clearly demonstrates the presence of two groups of flows, one corresponding to positive values of $v_4\/v_2$ and the other to negative values. This rules out the possibility of a connection between the two parts of the phase diagram, and thus reveal the presence of a tricritical point~\\cite{Kuklov2}. Finally, we also detected the presence of a new crystalline phase at low temperature, deep in the frustrated regime. This phase is characterized by a degeneracy growing with the system size. \n \nIn a parallel work, Papanikolaou and Betouras recently studied another extension of the dimer model that slightly differs from ours but which leads to similar conclusions~\\cite{Papanikolaou2}. To perturb the pure plaquette model, these authors introduce further neighbor interactions between dimers which preserve the cubic symmetry. They find that when the extra couplings favor the columnar alinement, the transition becomes first order. On the opposite, a frustrating coupling maintains the continuity of the transition. The critical exponents they measure are in agreement with ours in the limit of large frustration. Our study has the advantage of using much larger samples (the maximum system size used in Ref.~\\onlinecite{Papanikolaou2} is $L=32$), giving more confidence  on the values of exponents. Furthermore, the use of the flowgram analysis provides an explicit evidence for tricriticality. In another related work, Chen {\\it et al.}~\\cite{Chen} find that by favoring one particular subset of the 6 columnar orderings at low temperature, the transition between the Coulomb and columnar phases becomes either first order or in the $3d$ $XY$ universality class. \n \n While not entirely interpretive, it is tempting to compare the exponents on the frustrated side of the dimer model to other models which also display unconventional phase transitions. In Ref.~\\onlinecite{Charrier}, a lattice gauge theory representing a coarse-grained version of the dimer model was simulated by Monte Carlo. There, the exponents were found to be very close to the $3d$ $XY$ universality class and thus differ from those presented here. Another source of information is given by the study of the $NCCP^1$ field theory. There exists several indications that the exponent $\\eta$ in the $NCCP^1$ theory should be large and positive~\\cite{Senthil}. For instance, the transition observed in the ring-exchange models studied in Ref.~\\onlinecite{JQ} provide an estimate of $\\eta \\sim 0.2 - 0.35$ (depending on which correlation function is looked at) and $\\nu \\sim 0.68(1)$. These values are not far from those we observed in the strong frustration regime. On the other hand, direct simulations of lattice versions of the $NCCP^1$ all exhibit a first order transition~\\cite{Kuklov1}. This possibility is ruled out in the dimer model, thanks to our results obtained with the flowgram analysis. \\\\\n \n\\section{Acknowledgments}   \nWe gratefully thank L. Marty for her active participation at an early stage of this work. We also thank S. Trebst for useful discussions. This work was performed using HPC resources from GENCI-CCRT\/IDRIS (Grant 2009-100225). We also thank CALMIP for allocation of CPU time. We use the ALPS libraries~\\cite{ALPS} for the Monte Carlo simulations.\n   \n   \n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Conclusion}\\label{conclusion}\nA data fusion framework for detecting false command and measurement injections due to cyber intrusion is presented in this paper. To design an IDS that uses cyber and physical features, we aggregate features from cyber and physical sensors and align the data, then perform preprocessing techniques, followed by inter-domain fusion. \n\nOur results find that classifier performance improves on an average of 15- 20\\% (based on F1-score) when cyber physical features are considered instead of pure cyber features. Results also show that the performance improved on an average of 10-20\\% (based on F1-score) when labels from Snort are replaced by the labels considered based on intrusion timestamps.  From our evaluations of the IDS, we also find that scenarios with balanced and larger records result in better performance.  Additionally,  co-training based semi-supervised learning technique, which is realistic for a real-world scenario, is found to perform similar to supervised techniques and even better by 2-5\\% (based on F1-score) using some classifiers. Among the unsupervised learning techniques, k-mean clustering technique is found to be more robust and accurate. Moreover, training the classifier with the embeddings from manifold learning didn't improve the accuracy. Hence, manifold learning should only be considered for visualization rather than rely on accuracy.\n\nWe believe our fused dataset and results provide one of the first publicly available studies with cyber and physical features, particularly for power systems, where the experimental data is collected from a testbed that contains both cyber and physical emulation. This benefits research in multi-disciplinary areas such as cyber physical security and data science. \n\n\\section{Introduction}\nMulti-sensor data fusion is a widely-known research area adopted in many areas including military, medical science, and finance as well as in the energy sector. Recently, automatic driving systems widely use data fusion to fuse images and videos from similar or disparate sensor types~\\cite{auto_vehicle}. In power systems, most fusion applications are currently intradomain and consider only physical data. Examples include fault detection~\\cite{pure_phy} and intrusion detection using Principal Component Analysis (PCA)~\\cite{pure_phy2}. Similarly, for network protection in industrial control systems (ICS), intrusion detection systems (IDS) such as Snort, BRO, Suricatta, etc., are increasingly used. These offer a pure cyber-centric approach that results in high false alarms~\\cite{false_alarms} Combining the benefits of visibility of both cyber and physical, cross-domain data fusion has the potential to help methodically and accurately detect mis-operations and measurement tampering in power systems caused by cyber intrusions.\n\nIn power system operations, the telemetry used for collecting wide area measurements may have errors due to sensor damage or cyber-induced compromise; if undetected, applications that rely on these data can become unreliable and\/or untrustworthy. Sensor verification based on multi-source multi-domain measurement collection and fusion can be performed to solve such problems, and it is a valuable mechanism for detection and detailed forensics of cyber intrusions targeting physical impact.  While offering numerous potential benefits, fusion for attack detection in real-world utility-scale power systems presents challenges that hinder adoption including the creation, storage, processing, and analysis of the associated large datasets. Fortunately, with the proliferation of affordable computing capability for processing high-dimensional data, it is becoming more feasible to deploy fusion techniques for accurately detecting intrusions.  Thus, research is needed to take advantage of these data and computing capabilities and create fusion-based detection techniques that solve this problem.\n\nCyberattacks often progress in multiple stages, e.g., initiating with a reconaissance phase, executing intrusions and vulnerability exploitations, and culminating in actions targeting the physical system such as manipulating measurements and commands. \nThe events that comprise these incidents and provide forensics about what occurred are not reflected using only coarse cyber-side features.\nAdditionally, the system dynamics in both cyber and physical space vary considerably; this causes challenges in merging data. For example, an intruder may take months in the reconaissance phase, but during this period, none of the physical side features reflect any abnormality. Similarly, later when an intruder is injecting false commands or tampering measurements, most of the cyber side features do not reflect any abnormality, assuming the adversary is stealthy.\n\nSensor time resolution varies across domains and within domains, which causes challenges when merging the data. The resolution of physical measurements depends on polling rates as well as the specifications of the device. For example, phasor measurement units (PMUs) provide GPS synchronized data at subsecond data rates, supervisory data acquisition and control (SCADA) systems provide data on the seconds to minutes time frame, and smart meters deployed residentially may have hourly resolution~\\cite{pmustandard}. Relays monitoring system transients have resolution on the order of milliseconds. Similarly, network logs and IDS such as Snort have resolution of milliseconds. Data fusion solutions for cyber-physical power systems must be able to effectively handle the range of time scales.\n\nThe use of machine learning (ML) and deep learning (DL) for intrusion detection faces the problem that the trained model's effectiveness depends on the data collected; it is a challenge to obtain a realistic baseline and to use realistic data to validate the solution for a real-time cyber-physical system. Detection is affected by the choice of data processing techniques applied (e.g., balancing, scaling, encoding). The impact of such factors on detection accuracy must therefore be quantified before the techniques can be trusted for use in securing critical infrastructure.\n\nThe hypothesis of this work is that the use of fused data from cyber and physical domains can enable better attack detection performance than either domain separately, if the challenges above are addressed. Hence, we present a heterogeneous-source platform that fuses data and detects cyber intrusions. First, we provide interfaces for collecting data sources from cyber and physical side emulators. Then, we use these interfaces to collect real-time data from cyber, physical, and security domains; finally, we fuse the datasets and detect cyber intrusions. We aggregate and merge real-time sensor data from multiple sources including Elasticsearch\\cite{elasticsearch}, TShark\\cite{tshark}, raw packet captures with DNP3 traffic, and Snort logs \\cite{snort_cookbook} that are created during emulation of Man-in-the-Middle attacks on a synthetic electric grid, modeled in the Resilient Energy Systems Laboratory (RESLab) testbed \\cite{Sahu2020}.\nFig. \\ref{fig:flowchart} gives an overview of the multi-source data fusion presented.  The major contributions of this paper are as follows: \n\n\\begin{figure}\n    \n\\smartdiagramset{text width=4.5cm,\n}\n\\begin{center}\n\\smartdiagramset{module shape=rectangle,\nuniform arrow color=true,\narrow color=gray!50!black,\nback arrow disabled=true,\n}\n\\smartdiagramset{\nuniform color list=white!90!black for 6 items}\n\\smartdiagram[flow diagram]{Set up testbed architecture in RESLab,MiTM attacks in synthetic electric grid in RESLab,{Collect sensor data from multiple sources}, Integration of data aggregator for merging real-time data,Data pre-processing techniques,\nCompare performance of models from fused dataset with other IDS models}\n\\end{center}\n\\caption{Multi-source data fusion steps}\\label{fig:flowchart}\n\\end{figure}\n\n\n\\begin{enumerate}\n    \\item To present the aggregation and merging of real-time sensor data from multiple sources for cyberattack detection in a cyber-physical testbed emulation of a synthetic electric grid.\n    \\item To quantify the value of different data pre-processing techniques such as balancing, normalization, encoding, imputation, feature reduction, and correlation before training the machine learning models.\n    \\item To demonstrate the improved detection capability of models built from fused dataset performance by comparing with pure cyber and physical feature based intrusion detection models. \n    \\item To evaluate the performance of the supervised, unsupervised and semi-supervised learning based intrusion detection for use cases explored in the MiTM attacks.\n\\end{enumerate}\n\n\nThe paper proceeds as follows. Section~\\ref{background} provides background on data fusion techniques incorporated in areas such as military, healthcare, software firms, security, and cyber-physical systems. In Section~\\ref{architecture}, we discuss the RESLab architecture, the attack types considered, and the data fusion procedure. The details on the data sources, the data fusion types, and the dataset transformations used in this work are presented in Sections~\\ref{dataset}, \\ref{data_transformation}, and \\ref{fusion_types} respectively.\nFinally, intrusion detection based on unsupervised, supervised, and semi-supervised learning methods is presented in Section~\\ref{ids}.\nExperiments are performed for four use cases, and results are analyzed in Section~\\ref{results} and finally concluding the paper in Section~\\ref{conclusion}.\n\\section{Data Fusion Background}\\label{background}\n\\subsection{Multi-Sensor Data Fusion}\nThe goal of multi-sensor data fusion is to make better inferences than those that could be accrued from a single source or sensor.  According to \\textit{Mathematical Techniques in Multisensor Data Fusion}~\\cite{hall_book}, multi-sensor data fusion is defined as \\textit{``a technique concerned with the problem of how to combine data from multiple (and possibly diverse) sensors in order to make inferences about a physical event, activity, or situation.''} A data fusion process is modeled in three ways: a) functional, b) architectural, and c) mathematical~\\cite{hall_book}. A functional model illustrates the primary functions, relevant databases, and inter-connectivity to perform fusion. It involves primarily filtering, database creation, and pre-processing such as scaling and encoding, etc. An architectural model specifies hardware and software components, associated data flows, and external interfaces~\\cite{extra_fusion_ref}. For example, it models the location of the fusion tool in a testbed. The fusion architecture can be three types: centralized, autonomous, and hybrid~\\cite{hall_book}. In centralized architectures, either raw or derived data from multiple sensors are fused before they are fed into a classifier or state estimator.  In autonomous architectures, the features extracted are fed to the classifiers or estimators for decision making before they are fused. The fusion techniques used in the second case involve techniques including Bayesian~\\cite{intro1} and Dempster Shafer inference~\\cite{zadeh}, because these fusion algorithms are fed with the probability distributions computed from the classifiers or the estimators. The hybrid type mixes both centralized and autonomous architectures. The mathematical model describes the algorithms and logical processes.\n\n\\begin{figure*} [!htb]\n    \\centering\n    \\vspace{-0.2cm}\n    \\includegraphics[width=0.8\\linewidth]{Figures\/fusion_architecture_v2.JPG}\n    \\vspace{-0.35cm}\n    \\caption{Centralized fusion architecture. In the autonomous architecture the Fusion and Learning blocks will be interchanged with an addition of another Learning block post fusion. \n    }\n    \\label{fig:architecture_types}\n\\end{figure*}\n\nA holistic data fusion method must consist of all three: functional, architectural, and mathematical models.  The functional model defines the objective of the fusion. Since the goal of this work is to detect intrusions, we must determine which data are due to cyber compromise. Functional goals may also include estimating the position of the intruder in the system or estimating the state of an electric grid, where the preprocessing techniques to use vary based on the goal.  The architecture model defines the sequence of operations. Our fusion follows the centralized architecture. Finally, the mathematical model defines how these features are processed and merged. Section \\ref{dataset} details our fusion models. \n\n\n\\subsection{Multi-Sensor Fusion Applications}\nRecently, work on multi-sensor fusion has been adopted in the areas of computer vision, automatic vehicle communication, and it is entering into the areas of power systems. The authors in ~\\cite{ref3} review multi-sensor data fusion technology, including benefits and challenges of different methods. The challenges are related to data imperfection, outliers, modality, correlation, dimensionality, operational timing, inconsistencies, etc. For example, different time resolutions of sensors result in under-sampling or over-sampling data in some sensors. The response time of certain sensors also vary depending on the sensor age and type.  Data received from multiple sensors must be transformed to a common spatial and temporal reference frame~\\cite{hall_book}. Imperfection is dealt using fuzzy set theory, rough set theory, Dempster Shafer theory, etc. \n\nMulti-sensor data fusion is used in military applications for automated target recognition, battle-field surveillance, and guidance and control of autonomous vehicles~\\cite{hall}. Further, the idea has been expanded to non-defense areas such as medical diagnosis, smart buildings, and automatic vehicular communications ~\\cite{multi2}. Authors in~\\cite{ref4} explore techniques in multi-sensor satellite image fusion to obtain better inferences regarding weather and pollution. Data fusion has also been proposed to accurately detect energy theft from multiple sensors in advanced metering infrastructure (AMI) in power distribution systems~\\cite{multi}.\n\nData fusion is expanded in ~\\cite{ref1} from cyber-physical systems (CPSs) to cyber-physical-social systems (CPSSs) with the use of tensors. Algorithms proposed for mining heterogeneous information networks cannot be directly applied to cross-domain data fusion problems; fusion of the knowledge extracted from each dataset gives better results ~\\cite{cross_fusion}.\n\n\n\\subsection{Data Fusion in Power Systems}\nThe data from diverse domains play a major role in power system operation and control. Weather data is vital for forecasting, e.g., for solar, wind, and load, to schedule generation. Data in cyberspace include data that provide for automation in power system ICS and play a crucial role in wide area control and operation in the electric grid. However, to proceed with multi-domain fusion, the following question must first be answered: To what measurable quantities do \\textit{cyber data} and \\textit{physical data} refer? \n\nA simple example of \\textit{cyber data} in ICS is a spool log of a network printer in the control network.  It is crucial to question, could we have prevented the attack on the centrifuge in the Natanz Uranium Enrichment plant, if we had a logger to record the events of a machine with shared printer, so as to prevent the exploitation of remote code execution on this machine? The answer is \\textit{no}, because there were many other vulnerabilities such as WinCC DB exploit, network share, and server service vulnerability, in parallel to print server vulnerability that compromised the Web Navigation Server which was connected to the Engineering Station that configured the S7-315 PLCs which over-speeded the centrifuge~\\cite{stuxnet}. Hence, the deployment of cyber telemetry in every computing node in an ICS network is a solution which seems attractive but results in numerous false alarms. Then, the question arises, can we reduce such alerts by amalgamating such data with data from physical sensors? \n\nData fusion proposed in the areas of power systems are mainly intra-domain. Existing works do not consider fusion of cyber and physical attributes for intrusion detection together. A probabilistic graphic model based power systems data fusion is proposed in~\\cite{pure_phy3}, where the state variables are estimated based on the measurements from heterogeneous sources by belief propagation using factor graphs. These probabilistic models require the knowledge of the priors of the state variables and also assume the measurements to be trustworthy. Hence, such solutions cannot detect cyber induced stealth false data injection attacks. Several works on false data injection detection are based on machine learning~\\cite{ml_power_1,ml_power_2,ml_power_3,ml_power_4} and deep learning~\\cite{dl_power_1,dl_power_2,dl_power_3,arnav_rnn_lstm,a3d,paved} techniques. The authors in~\\cite{pure_phy4} address stealthy attacks using multi-dimensional data fusion by collecting information from power consumption of physical devices, control operation and system states feed to the cascade detection algorithm to identify stealthy attack using Long Short Term Memory (LSTM).   Machine learning techniques including clustering are used in power system security for grouping similar operating states (emergency, alert, normal, etc.) to automatically identify the subset of attributes relevant for prediction of the security class. A decision tree based transient stability assessment of the Hydro-Quebec system is presented in~\\cite{ml_power_sys}. Techniques of fusion for fault detection~\\cite{pure_phy} and real-time intrusion detection using Principal Component Analysis (PCA)  (PCA)~\\cite{pure_phy2} are specific to the physical domain. Design of such models require data fusion and must consider impending system instabilities that can be caused by cyber intrusions.\n\nCymbiote~\\cite{cymbiote} multi-source sensor fusion platform is one of the work, equivalent to ours, that have leveraged fusion from multiple cyber and physical streams and trained with only supervised learning based IDS. Moreover, their work doesnt clearly describes the features extracted from different sources.\n\n\\subsection{Multi-Domain Fusion Techniques}\n\nTechniques such as co-training, multiple kernel learning, and subspace learning are used for data fusion problems. Co-training based algorithms~\\cite{co_training} maximizes the mutual agreement between two distinct views of the data. This technique is used in fault detection and classification in transmission and distribution systems~\\cite{cotrain_1} as well as in network traffic classification~\\cite{cotrain_2}.  \nTo improve learning accuracy, Multiple kernel learning algorithms~\\cite{mkl} are also considered, which utilize kernels that implicitly represent different views and combines them linearly or non-\nlinearly . Subspace learning algorithms~\\cite{subspace_learning} aim to obtain a latent subspace shared\nby multiple views, assuming that the input views are generated from this latent subspace.\nDISMUTE~\\cite{dismute} performs feature selection for multi-view cross-domain learning. Multi-view discriminant transfer (MDT)~\\cite{mv_transfer_learning} learns discriminant weight vectors for each view to minimize the domain\ndiscrepancy and the view disagreement simultaneously. These techniques can be used for cross-domain data fusion. \n\nCoupled matrix factorization and manifold alignment methods are used for similarity based data fusion~\\cite{cross_fusion}. These methods can be implemented intra-domain with multiple data sources. Manifold alignment is another technique that generate projections between disparate data sources, but assumes the generating process shares a common manifold. \nSince the primary goal in this work is to fuse datasets from inter-domain such methods may not be effective enough. Still we have explored manifold learning for the purpose of feature reduction to train the supervised learning based classifier.\n\nTo the best of our knowledge, co-training has not yet been implemented in an intrusion detection system that uses inter-domain fusion. Hence, in this work, we perform co-training in inter-domain fused datasets by splitting the dataset into cyber and physical views.  \n\n\n\\subsection{Data Creation, Storage, and Retrieval}\n\nThe storage and retrieval of multi-sensor data play a major role in fusion and learning. A relational database management system (DBMS) is predominantly used in traditional EMS applications. For example, B.C. Hydro proposes a data exchange interface in a legacy EMS and populates a relational database with the schematic of the Common Information Model (CIM) defined in IEC 61970~\\cite{rdbms}. With the proliferation of multiple protocols and data from diverse sources, it is difficult to construct the Entity Relationship model of a relational database management system (RDBMS), since the schema cannot be fixed. Since NoSQL stores unstructured or semi-structured data, usually in the key-value pairs or JSON  documents,  NoSQL is  highly  encouraged  to make use of database such as Elasticsearch~\\cite{elasticsearch}, MongoDB~\\cite{mongodb}, Cassandra~\\cite{cassandra}, etc., for multi-sensor fusion with heterogeneous sources.\n\nCreation of multi-domain datasets to advance the research is a challenging task, since it requires development of a cyber-physical testbed that processes real-time traffic from different simulators, emulators, hardware, and software. Currently, few datasets are publicly available that provide features from diverse domains and sources. Most of the datasets are simulator-specific, which restricts the domain to either pure physical or cyber. The widely-known KDD \\cite{kdd} and CIDDS\\cite{cidds} datasets used in developing ML-based IDS for bad traffic detection and attack classification are centric to features in the cyber domain~\\cite{ieee_cqr}. Tools such as MATPOWER \\cite{matpower} and pandapower \\cite{pandapower} provide datasets for physical-side bad data detection. Datasets that include measurements related to electric transmission systems including normal, disturbance, control, and cyberattack behaviors are presented in~\\cite{dataset0,dataset1,dataset2,dataset3}. The datasets contain phasor measurement unit (PMU) measurements, data logs from Snort, and also data from a gas pipeline and water storage tank plant. The features in these datasets lack fine-grained details in the cyber, relay, and control spaces, as all the features are binary in nature. A cyber-physical dataset is presented in~\\cite{dataset4} for a subsystem consisting of liquid containers for fuel or water, with its automated control and data acquisition infrastructure showing 15 real-world scenarios; while it presents a useful way of framing the data fusion problem and approaches for cyber-physical systems (CPS), it is not power system specific.     \n\nA problem in training machine learning (ML) or deep learning (DL) models for intrusion detection through classification, clustering, and fine-tuning hyper-parameters is that its effectiveness depends on the data collected. That is, a practical challenge is to obtain a baseline which needs to come from realistic data. Emulation is preferred to simulation for CPS networks since a simulator demonstrates a network's behavior while an emulator functionally replicates its behavior and produces real data. Using real data is important to validate that ML or DL solutions address the actual challenges faced in the data from a real-time cyber-physical system. \n\nThe performance of ML and DL models is impacted by the choice of data processing techniques applied to the inputs such as balancing, scaling, or encoding before training the models. The effect of these preprocessing techniques needs to be quantified on the outputs of such ML models before they can be trusted for use in industry.\n\n\n\\section{Data Fusion Architecture}\\label{architecture}\nBefore discussing the data fusion procedures, it is essential to understand the architecture of the RESLab testbed that is producing the data during emulation of the system under study. \n\n\\subsection{Testbed Architecture}\n\nThe RESLab testbed consists of a network emulator, a power system emulator, an OpenDNP3 master and a RTAC based master, an intrusion detection system, and data storage, fusion and visualization software. A brief overview of each component is given below. The detailed explanation of RESLab including its architecture and use cases is provided in ~\\cite{Sahu2020}.\n\\begin{itemize}\n\n  \\item \\emph{Network Emulator} - Common Open Research Emulator (CORE) is used to emulate the communication network that consists of routers, linux servers, switches, firewalls, IDSes and bridges with other components emulated with other virtual machines (VMs) in vSphere environment. \n  \n  \\item \\emph{Power Emulator} - Power World Dynamic Studio (PWDS) is a real-time simulation engine for operating the simulated power system case in real-time as a DS server~\\cite{powerworld}. It is used to simulate the substations in the Texas 2000 case as DNP3 outstations. \\cite{synthetic_comm}.\n\n  \\item \\emph{DNP3 Master} - DNP3 Masters are incorporated using an open DNP3 based application (both GUI and console based) and a SEL-3530 Real-Time Automation Controller (RTAC) that polls measurements and operates outstations, sending its traffic through CORE to the emulated outstations in PowerWorld DS.  \n\n  \\item \\emph{Intrusion Detection System} - Snort is used in the testbed as the rule-based, open-source intrusion detection system (IDS). It is configured to generate alerts for Denial of Service (DoS), MiTM, and ARP cache poisoning based attacks. Currently Snort is running as a network IDS in the router in the substation network.\n  \n  \\item \\emph{Storage and Visualization} - The Elasticsearch, Logstash, and Kibana (ELK) stack is used to probe and store all virtual and physical network interface traffic. In addition to storing all Snort alerts generated during each use case, this data is able to be queried using Lucene queries to perform in depth visualization and cyber data correlation.\n  \n  \\item \\emph{Data Fusion } - A different VM is dedicated to operate the fusion engine that collects network logs and Snort alerts from ELK stack using an Elasticsearch client and raw packet captures from CORE using pyshark. This engine constructs cyber and physical features and merges them using the time stamps from different sources to ensure correct alignment of information. Further it pre-processes them using imputation, scaling and encoding before training them for intrusion detection using supervised, unsupervised and semi-supervised learning techniques.  This VM is equipped with resources to utilize ML and DL based library such as scikit, Tensorflow and Keras to train the engine for classification, clustering and inference problem. \n  \n\\end{itemize}\n\n\n\n\n\n\n\n\n\n\\begin{figure} [h]\n    \\centering\n    \\vspace{-0.2cm}\n    \\includegraphics[width=1.0\\linewidth]{Figures\/testbed_architecture_fusion.JPG}\n    \\vspace{-0.35cm}\n    \\caption{Testbed architecture with data fusion}\n    \\label{fig:architecture}\n\\end{figure}\n\nThere can be considered three broad kinds of IDS for ICS: protocol analysis based IDS, traffic mining based IDS, control process based IDS~\\cite{pure_cy_pure_phy}. The fusion engine in RESLab combines all these types. It performs protocol specific feature extraction from data link, network, transport layers alongwith DNP3 layer, control and measurement specific information through DNP3 payload and headers, traffic mining by extracting network logs from multiple sources.\n\n\n\\subsection{Attack Experiments}\n\nNow that we have discussed the architecture of the testbed, we delve further into how this testbed is utilized to demonstrate a few cyber attacks targeting the grid operation. The threat model we consider is based on emulating multi-stage attacks in a large-scale power system communication network. In the initial stage, the adversary gains access to the substation LAN through Secure Shell (SSH) access, further performing DoS and ARP cache poisoning based MiTM attack to cause False Data injections (FDI) and False Command injections (FCI).\n\n\n\n\n\nIn Man-in-the-Middle attacks, usually the adversary secretly observes the communication between sender and receiver and sometimes manipulates the traffic between both ends. There are different ways to perform MitM such as IP spoofing, ARP spoofing, DNS spoofing, HTTPS spoofing, SSL hijacking, stealing browser cookies, etc. In this current work, we focus on MitM using ARP spoofing. ARP spoofing or poisoning is a type of attack in which an adversary sends false ARP messages over a local network (LAN). This results in the linking of an adversary's MAC address with the IP address of a legitimate machine on the network (in our case, the outstation VM). This attack enables the adversary to receive packets from the master as an impersonator for the outstation and modify commands and forward them to the outstation. In this way, the adversary can cause contingencies such as misoperation of the breakers. The attack is not only to modify but also to sniff the current state of the system since it can receive the outstation response to the master. \n\nThe MiTM attacks are performed considering the four use cases targeting different part of the Texas synthetic grid following different strategies presented in detail in ~\\cite{Sahu2020}. The use cases are combinations of FDI and FCI attacks performed with different polling rates from the DNP3 Master and the number of master application considered. In our previous work, we demonstrated Snort IDS based detection which resulted in many false positives. In this work, we employ fusion techniques, along with machine learning techniques, to enhance the accuracy of detection by evaluating them using F1-scores, Recall, and Precision values.\n\n\n\n\n\\subsection{Data Fusion Procedure}\nThe steps followed in the data fusion engine, from extracting the features from different sources, with their merge of pyshark, snort, packetbeat, raw packet capture to form cyber table, and the final fusion of cyber and physical table, with the steps of imputation, encoding and visualization is presented in Alg.~\\ref{alg:data_fusion}. The details of the sensor sources and the data processing will be discussed in details in the next sections.\n\n\\begin{algorithm}[h]\n\\begin{small}\n  \\caption{Data Fusion Procedure}\\label{alg:data_fusion}\n\t\\begin{algorithmic}\n\t\\State{1. Load json from raw pcaps.}\n\t\\State{2. Extract cyber features: network, transport, datalink layer information and store as raw cyber data.}\n\t\\State{3. Extract features using pyshark.}\n\t\\State{4. Merge pyshark to the raw cyber data.}\n\t\\State{5. Extract snort alert.}\n\t\\State{6. Merge snort to the raw cyber data.}\n\t\\State{7. Extract features from packetbeat index in elasticsearch.}\n\t\\State{8. Merge packetbeat features to raw cyber data.}\n\t\\State{9. Extract DNP3 features (DNP3 points and headers) from raw packet capture.}\n\t\\State{10. Fuse cyber data with physical data.}\n\t\\State{11. Imputate missing values.}\n\t\\State{12. Encode categorical features.}\n\t\\State{13. Visualize the merged table.}\n  \\end{algorithmic}\n  \\end{small}\n\\end{algorithm}\n\n\\subsection{Fusion Challenges}\nThe most challenging task in fusion is to\nperform merge operations, because of the different time stamps generated at\ndifferent sensors. An event will trigger the time stamped measurements at the sensors. Hence, each\nsensor's location impacts the time at which the event is recorded. Domain knowledge\nhas been used to write the algorithm to merge different sources meticulously. For\nexample, Elasticsearch's Packetbeat index stores each record that reflects the\ntraffic between a given small time interval. Each record has an event start and end\ntime. While merging Elasticsearch features, such as flow count attribute, we have to\ncompare the raw packet timestamp and event start and end time of Elasticsearch to\ncalculate the flow counts.\nMoreover, the number of records in the power system side will be less than the\ncyber side, as events in power system side are triggered based on the polling\nfrequency as well as on the time at which an operator performs a control operation.\nHence we remove missing data for the records that do not have any physical side\ntraffic.\n\n\\section{Multi Sensor Data}\\label{dataset}\nA sensor's data is the output or readings of a device that detects and responds to changes in the physical environment. Every sensor has a unique purpose that helps create crucial features that can assist in intrusion detection. In RESLab, the cyber sensors are deployed as Wireshark instances at different locations in the network for raw packet capture. Additionally, monitoring tool such as Packetbeat are integrated for extracting network flow-based information. For security sensors, Snort IDS logs and alerts are considered.  Since the physical system is emulated with PWDS acting as a collection of DNP3 outstations, the real-time readings provided by physical sensors are extracted from the observed measurements at the DNP3 master, from the application layer of the raw packet captured at the DNP3 master. The extractions of these multiple sensors are explained in detail:\n\n\\subsection{Raw pcaps from json}\nThe packet captures from Wireshark are packet dissected and saved in the json format, which are loaded using the panda data frame. Further, from the json, around 12 features from physical, datalink, network, and transport layer of OSI stack are extracted, as shown in Table~\\ref{table:fusion_features}. The features primarily consist of the source and destination IP and MAC addresses, along with the port numbers, flags, and lengths in these layers. \n\n\\subsection{Elasticsearch}\nReal-time traffic collection is performed from network interfaces in CORE, using the Packetbeat plugin in the ELK stack. The Packetbeat plugin helps us extract the flow-based information such as \\textit{Flow Count}, \\textit{Flow Count Final}, \\textit{Packets} shown in Table~\\ref{table:fusion_features}.\nElasticsearch queries are based on Lucene, the search library from Apache. Kibana is used to visualize the graphs and real time data visualization for packetbeat index. An example query is shown below:\n\\begin{lstlisting}[language=json,numbers=none]\n\"query\": {\n    \"bool\": {\n      \"must\": [\n          { \"range\": {\n            \"event.end\": {\n            \"gte\": \"2020-01-22T00:00:00.000Z\",\n            \"lte\": \"2020-01-26T00:00:00.000Z\"}}\n          },\n          {\"range\": {\n           \"event.duration\": {\n            \"gte\": 0,\n            \"lte\": 3000000}}\n          },\n          {\"bool\": \n          {\"should\": [\n          {\"match\": {\n            \"destination.port\": \"20000\"}},\n          {\"match\": {\n            \"source.port\": \"20000\"}}\n              ]\n          }\n          },\n          {\"match\":\n            {\"flow.final\": \"true\"}\n          }    \n            ]}}\n\\end{lstlisting}\n\nThe above query returns the records with event start time $2020-01-22T00:00:00.000Z$ and end time $2020-01-26T00:00:00.000Z$, and the event duration is within $0-300000$ ms, and the source or destination port is $20000$ (port number associated with DNP3), and the flow is a $final$ flow. Keyword $must$ designates an $AND$ operation, $should$ is an $OR$ operation, and $match$ is an $equals\\: to$ operation.\nA logstash index is also created in Elasticsearch to store the logs of Snort alerts, which is also extracted along with the packetbeat index.\n\nThere are two operations on the response from Elasticsearch: a) $Extraction$ of essential features b) $Merge$ of features to the existing cyber features data frame $cb\\_table$ from raw packet captures. \nEach record in the packetbeat index is stored in the form of an event with start and end times. In the extraction phase, we extract the $source.packets$, $flow.id$, $flow.final$, $event.end$, $event.start$, $flow.duration$ features and store them in a new data frame $pb\\_table$.\nThe merge operation of $pb\\_table$ into the existing cyber features is non-trivial due to different timestamps in existing features and features from packetbeat. We compute the features in Table~\\ref{table:fusion_features} $flow.count$, $flow.final\\_count$, and $packets$ using the features of $event.end (end)$, $event.start (start)$ in $pb\\_table$ and $Time$ in the $cb\\_table$ based on the logical OR of three conditions:\n\\begin{enumerate}\n    \\item $Condition\\:1:$ add counters if the event start is within the range of current and next records in the $cyber\\_table$\n    \\begin{equation}\n        cb\\_table[i][t] \\leq start \\land cb\\_table[i+1][t] \\geq start\n    \\end{equation}\n    \\item $Condition\\:2:$ if the event end is within the range of current and next records in the $cyber\\_table$.\n    \\begin{equation}\n        cb\\_table[i][t] \\leq end \\land cb\\_table[i+1][t] \\geq end\n    \\end{equation}\n    \\item $Condition\\:3:$ if the event start is less than the current record and event end is greater than the next record in the $cyber\\_table$.\n    \\begin{equation}\n        cb\\_table[i][t] \\geq start \\land cb\\_table[i+1][t] \\leq end\n    \\end{equation}\n\\end{enumerate}\n\n\n\nThe $\\lor$ and $\\land$ are the logical $or$ and $and$ operators respectively.\nIn this manner, we merge the three features from $pb\\_table$ to the $cb\\_table$. \n\n\n\\subsection{Pyshark}\nPyshark is a Python wrapper for tshark, allowing python packet parsing using Wireshark dissectors.\nUsing $Pyshark$ features such as $Retransmissions$ and $Round Trip Time (RTT)$ are obtained. The RTT is the time duration for a signal or message to be sent plus the time it takes for the acknowledgment of that signal to be received. It has been observed that if congestion is created in any location in between the source and destination such as router or switch, the RTT increases. It also increases due to DoS attacks on the servers or any intermediery nodes in the path between source and destination. The $TCP$ based packet follows different retransmission policies based on the TCP congestion control flavour. Hence, the number of $retransmission$ packets observed within a given time frame is an indicator of loss of communication or increased delay. Usually, a sender retransmits a request if it did not receive an acknowledgment after some multiples of a $RTT$, whose multiplicity is dependent on the TCP flavour. The $retransmission$ and $RTT$ features are selected, as features are correlated and directly related to attacks targeting availability and integrity.\n\n\n\n\\subsection{Snort}\nThe router inside the CORE emulator runs the Snort daemon based on the specific rules, pre-processors, and decoders enabled in the configuration file to create logs. \nSnort operates in three modes: packet sniffer, packet logger, and intrusion detection system (IDS) modes. We run the snort in the IDS mode.\nThe alerts generated at the router in the substation network is continuously probed during the simulation. The alerts are recorded in the form of the $unified2$ format as well as pushed to the Logstash index created in Elasticsearch.\nUnified2 works in three modes, packet logging, alert logging, and true unified logging. We run Snort in alert logging mode to capture the alerts, timestamped with alert time. Further, the $idstools$ python package is utilized to extract these $unified2$ formatted logs. The Snort configuration determines which rules and preprocessor are enabled. The features extracted are the $alert$,$alert\\_type$, and $timestamp$. The merge into the $cb\\_table$ is performed based on the $timestamp$ of each Snort record. The record is inserted based on the condition:\n\\begin{equation}\n    cb\\_table[i][t] \\geq timestamp \\leq cb\\_table[i+1][t]\n\\end{equation}\n\n\n\n\\subsection{Physical Features from DNP3}\n\n    The Distributed Network Protocol version 3 (DNP3) is widely used in SCADA systems for monitoring and control. This protocol has been upgraded to use TCP\/IP in its transport and network layer. It is based on the master\/outstation architecture, where field devices are at outstations and the monitoring and control is done by the master. DNP3 has its own three layers: a) Data Link Layer, to ensure reliability of physical link by detecting and correcting errors and duplicate frames, b) Transport Layer, to support fragmentation and reassembly of large application payload, and c) Application Layer, to interface with the DNP3 user software that monitors and controls the field devices. Every outstation consists of a collection of measurements such as breaker status, real power output, etc., which are associated with a DNP3 point and classified under one of the five groups: binary inputs (BI), binary outputs (BO), analog inputs (AI), analog outputs (AO), and counter input. The physical features consist of the information carried in the headers in the three layers of DNP3, along with the values carried by the DNP3 points in the application layer payload. Every DNP3 payload's purpose is indicated by a header in the application layer called function code (FC). In our simulations, we extract the features with FCs: 1(READ), 5(DIRECT OPERATE), 20 (ENABLE spontaneous message), 21(Disable spontaneous message), and 129 (DNP3 RESPONSE). The details of the features are in Table~\\ref{table:fusion_features}.   \n\n\n\n\\begin{table}[]\n\\caption{Description of the features used in data fusion.}\n\\begin{tabular}{|p{0.8cm}|m{6.5cm}|m{0.4cm}|}\n\\cline{1-3}\n Features & Description & Def   \\\\ \\cline{1-3}\n \nFrame Len  &  Length of the frame after network, transport and application header and payload are added and fragmented based on the channel type. For ethernet, the frame length can be max. 1518 bytes, which varies for wireless channels. & 0\\\\ \\cline{1-3}\n\nFrame Prot. & Determines the list of protocols in the layers above link layer encapsulated in the frame. & Nan \\\\\\cline{1-3}\n\nEth Src &   Unique source MAC address. Crucial for detection in ARP spoof attacks. & 0\\\\\\cline{1-3}\n\nEth Dst &  Unique destination MAC address. Crucial for detection in ARP spoof attacks. & 0\\\\\\cline{1-3}\n\nIP Src &  Unique source IP address. & 0\\\\ \\cline{1-3}\n\nIP Dst &  Unique destination IP address. & 0\\\\\\cline{1-3}\n\nIP Len &  Stores the length of the header and payload in a IP-based packet. This correlates well with the DNP3 payload size. & 0\\\\ \\cline{1-3}\n\nIP Flags & Indicator of fragmentation caused due to link or router congestion in the intermediary nodes. & 0x00\\\\ \\cline{1-3}\n\nSrc Port &  Indicates the port number used by the source application using TCP in transport layer. Ex: if the source is the DNP3 outstation, default port is 20000. & 0\\\\ \\cline{1-3}\n\nDest Port &   Indicates the port number used by the destination application using TCP in transport layer. & 0\\\\\\cline{1-3}\n\nTCP Len &  Stores the length of the header and payload in a TCP-based segment. This correlates well with the DNP3 payload size. & 0\\\\ \\cline{1-3}\n\nTCP Flags &   Flags are used to indicate a particular state of connection such as SYN, ACK, etc. & 0x00\\\\ \\cline{1-3}\n\nRetrans.  &  Indicates if the current record is from a retransmitted packet, caused due to attack or network congestion.& 0\\\\\\cline{1-3}\n\nRTT & Indicator of propagation and processing delay. High RTT can be caused due to MiTM attack.& -1\\\\\\cline{1-3}\n\nFlow Cnt &  Indicates the number of TCP flows in a specific time interval. Indicates the connected and disconnected DNP3 masters. Flow is collection of packets. & -1 \\\\\\cline{1-3}\n\nFlow Fin Cnt &  Indicates if the current flow carries the final packet. & -1\\\\\\cline{1-3}\n\nPackets & Number of packets transmitted in a specific time interval. & -1\\\\ \\cline{1-3}\n\nSnort Alert &  Boolean indicating an alert from snort. & 0\\\\\\cline{1-3}\n\nAlert Type  &  Indicates the alert type such as DNP3, ARP spoof, ICMP flood or any other types. & Nan\\\\\\cline{1-3}\n\nLL Src & Source id of the DNP3 master or outstation. Indicator of which outstation communicates with the master in that specific record. & -1 \\\\ \\cline{1-3}\n\nLL Dest &  Destination id of the DNP3 master or outstation. Indicator of which outstation communicates with the master in that specific record. & -1\\\\ \\cline{1-3}\n\nLL Len  &  Indicator of the DNP3 payload size as well as the function type. Usually the response carries DNP3 point information, hence this length correlates with the function code as well as the outstation currently communicating. & 0\\\\\\cline{1-3}\n\nLL Ctrl & This indicates the initiator of the communication. Determines the primary\/secondary server. & 0x00\\\\\\cline{1-3}\n\nTL Ctrl &  Indicates the FIN\/FIR\/Sequence number for determining if the DNP3 payload is the first or final segment. & 0x00  \\\\\\cline{1-3}\n\nFunc. code &  Indicates the function code: either READ, WRITE, OPERATE, DIRECT OPERATE, etc. & -1\\\\\\cline{1-3}\n\nAL Ctrl & Indicates the FIN\/FIR\/Seq\/Confirm and Unsolicited flags. This indicates if there are unsolicited, first, final from application layer standpoint.\n& 0x00\\\\\\cline{1-3}\n\nObj count &  This count determines the number of BI, BO, AI, AO points associated with a substation.& 0\\\\\\cline{1-3}\n         \nAL Payload &  Contains the DNP3 points used to extract the physical features such as branch status, real power flows and injections in branch and buses for a substation. & Nan\\\\\\cline{1-3}\n\n\\end{tabular}\n\\label{table:fusion_features}\n\\vspace{-0.5cm}\n\\end{table}\n\n\\section{Data Transformation}\\label{data_transformation}\nReal-time testbed data is usually insufficient, conflicting, diverse format and at times lack in certain pattern or trends. Hence, data pre-processing is essential in transforming raw data into an understandable format. The raw data extracted from multiple-sensors are processed through three steps: a) data imputation, b) data encoding, c) data scaling, and d) feature reduction.\n\n\\subsection{Data Imputation}\n\nImputation is a statistical method of replacing the missing data with substituted values. Substitution of a data point is unit imputation, and substituting a component is item imputation. Imputation tries to preserves all the records in the data table by replacing missing data with an estimated value based on other available information or feeds from domain experts.  There are other forms of imputation such as mean, stochastic, regression imputation etc. Imputation can introduce a substantial amount of bias and can also impact efficiency. In this work, we have not tried to address such discrepancies of bias introduced due to imputation.\nSince we merge data from different sources with unique features, the chances of missing data are high. Hence, we perform unit imputation in our dataset based on the default values in the $Def$ column of the Table~\\ref{table:fusion_features}.\n\n\\subsection{Data Encoding}\nThere are numerous features in the fused dataset which are categorical. These categorical features are encoded using the preprocessing libraries in scikit learn, so that the predictive model can better understand the data. There are different types of encoders such as an ordinal encoder, label encoder, one hot encoder, etc. In this work, we use label encoding. Label encoding is preferred over one hot encoding when the cardinality of the categories in the categorical feature is quite large as it results in the issue of high dimensions. \nWe also do not consider an ordinal encoder, as it is processed on the 2D dataset ($samples$*$features$). Since we process cross domain features, we perform encoding on individual features separately using label encoding. \n\n\\subsection{Scaling and Normalization}\nScaling and normalizing the feature is essential for various ML and DL techniques such as Principal Component Analysis (PCA), Multi-Layer Perceptrons (MLPs), Support Vector Machines (SVMs),  etc. Though certain techniques such as Decision Trees or Random Forest, are scale-invariant, it is still essential to normalize and train. Before performing normalization, we perform log transformation and categorical encoding for the features with high variance and varied range of values, respectively. Hence, \nwe evaluate both log transformation as well as scaling. Additionally, we considered \\textit{Min-Max scaling} as performed in our prior works on intrusion detection on KDD and CIDDS datasets~\\cite{ieee_cqr}.\n\n\\subsection{Feature Reduction}\nOnce the features from multiple sensors are merged, dimension reduction (inter-feature correlation) is performed to remove the trivial features using Principal Component Analysis (PCA). PCA is a linear dimensionality reduction method that uses Singular Value Decomposition (SVD) on the data to project it to a lower dimensional space \\cite{wold1987PCA}. The inter-feature correlation for our fused dataset from RESLab is based on the Pearson Coefficient \\cite{pearson}, shown in as shown in Fig.~\\ref{fig:feature_correlation}, where it can be observed that intra-domain features have higher correlation amongst each other. There is also some correlation observed across the cyber and physical features. Features with higher correlation are more linearly dependent and thus have a similar effect on dependent variables. For example, if two features have high correlation, one of the two features can be eliminated.\n\n\\begin{figure} [h]\n    \\centering\n    \\vspace{-0.2cm}\n    \\includegraphics[width=1.0\\linewidth]{Figures\/inter_feature_correlation.png}\n    \\vspace{-0.35cm}\n    \\caption{Inter-feature correlation based on Pearson Coefficient}\n    \\label{fig:feature_correlation}\n\\end{figure}\n\\section{Fusion}\\label{fusion_types}\nAs presented in Fig.~\\ref{fig:architecture_types}, the \\textit{Fusion} block involves different types of fusion. Intra-domain and inter-domain are considered for training the IDS using supervised and unsupervised learning techniques. We also explore location-based fusion and visualization for causal inference of the impact of the intrusion in different locations of the network. Finally, co-training with feature split is used to train the IDS using semi-supervised learning with labeled and unlabeled data.\n\n\\subsection{Intra-Domain and Inter-Domain Fusion}\nFusion of cyber sensor information from different sources is homogeneous source fusion. For example, the operation of fusing Elasticsearch logs with pyshark or raw packet capture to form the $cyber\\_table$ is intra-domain fusion.\n\nFusion of cyber and physical sensor information from different sources is heterogeneous source fusion. For example, the operation of fusing $cyber\\_table$ with $physical\\_table$ is inter-domain fusion.  \n\n\\subsection{Location-Based Fusion}\nIn multi-sensor data fusion, sensor location plays a major role. For example, the military uses location-based multi-sensor fusion to estimate the location of enemy troops by amalgamating sensor information from multiple radars and submarines. The challenges associated with different locations stem from time differences in event recognition. A radar can pick up a signal with a different latency than a submarine due to the difference in communication medium as well as its location relative to the enemy troop. Similarly, our sensors such as IDS, firewall alerts, and network logs are positioned at different locations in the network. It is essential to correlate events among different locations before merging them for inferring any attacks.\n\\begin{figure*} [!htb]\n    \\centering\n    \\vspace{-0.2cm}\n    \\includegraphics[width=1.0\\linewidth]{Figures\/location_based_fusion.jpg}\n    \\vspace{-0.35cm}\n    \\caption{Location based fusion from the master, outstation, and substation router. The high density traffic observed in the places marked with red rectangles is an indicator of DoS attack. This fusion assists in causal analysis for determining the initial victim of the DoS intrusion as well as inferring the pattern of impact across other devices in the network.}\n    \\label{fig:location_fusion}\n\\end{figure*}\n\n\\subsection{Co-Training Based Split and Fusion}\nThere exist scenarios where labels cannot be captured.  \nThe co-training algorithm~\\cite{co_training} uses feature split when learning from a dataset containing a mix of labeled and unlabeled data. This algorithm is usually preferred for datasets that have a natural separation of features into disjoint sets~\\cite{cotraining2}. Since the cyber and physical features are disjoint, we adopt feature split based co-training. \nThe approach is to incrementally build classifiers over each of the split feature sets. In our case, we split the fused features into cyber and physical features. Each classifier, $cy\\_cfr$ (first 17 features in Table~\\ref{table:fusion_features}) and $phy\\_cfr$(last 9 features in Table~\\ref{table:fusion_features}), is initialized using a few labeled records. At every loop of co-training, each classifier chooses one unlabeled record per class to add to the labeled set. The record is selected based on the highest classification confidence, as provided by the underlying classifier.  Further, each classifier rebuilds from the augmented labeled set, and the process repeats. Finally, the two classifiers $cy\\_cfr$ and  $phy\\_cfr$ obtained from the co-training algorithm gives probability score against the classes for each record, which is added and normalized to determine the final class of the record~\\cite{cotraining2}. The classifiers selected in our experiments are Linear Support Vector Machine (SVM), Logistic Regression, Decision Tree, Random Forest, Naive Bayes, and Multi-Layer Perceptron. \n\n\\begin{figure} [h]\n    \\centering\n    \\vspace{-0.2cm}\n    \\includegraphics[width=1.0\\linewidth]{Figures\/CoTraining_CP.JPG}\n    \\vspace{-0.35cm}\n    \\caption{Co-training based fusion for  labeled and unlabeled datasets. The fused dataset is split into cyber and physical views and trained in the cyber and physical classifiers separately, finally fusing and normalizing the probability scores for final classification.}\n    \\label{fig:cotraining}\n\\end{figure}\n\\section{Intrusion Detection Post Fusion}\\label{ids}\nAfter the features are extracted, merged, and pre-processed we design IDS using different ML techniques. We have con- sidered manifold learning and clustering as the unsupervised learning techniques, a few linear and non-linear supervised learning techniques, and co-training based semi-supervised learning methods for training the IDS. In this section, we briefly explain the ML techniques we use. \n\n\\subsection{Manifold Learning}\nPCA for feature reduction does not perform well when there are nonlinear relationships within the features. Manifold learning is adopted in the scenarios where the projected data in the low dimensional planar surface is not well represented and needs more complex surfaces. Multi-featured data are described as a function of a few underlying latent parameters. Hence the data points can be assumed to be samples from a low-dimensional manifold embedded in a high-dimensional space. These algorithms tries to decipher these latent parameters for low-dimensional representation of the data. There are a lot of approaches to solve this problem such as  Locally Linear Embedding, Spectral Embedding, Multi Dimensional Scaling, IsoMap etc. \n\n\\subsubsection{Locally Linear Embedding (LLE)}\nLLE computes the lower-dimensional projection of the high dimensional data by preserving distances within local neighborhoods. It is equivalent to a series of local PCA which are globally compared to obtain the best non-linear embedding~\\cite{scikit_manifold}. The LLE algorithm consists of 3 steps~\\cite{lle}: a) Compute k-nearest neighbor for a data point. b) Construct a weight matrix associated with the neighborhood of each data point. Obtains the weights \nthat best reconstruct each data from its neighbors, minimizing the cost.\nc) Compute the transformed data point $Y$ best reconstructed by the weights, minimizing the quadratic form.\n\n\n\n\\subsubsection{Spectral Embedding}\nSpectral embedding builds a graph incorporating neighborhood information. Considering the Laplacian of the graph, it computes a low dimensional representation of the data set that optimally preserves local neighborhood information~\\cite{se}. Minimization of a cost function, based on the graph ensures that points closer on the manifold are mapped closer in the low dimensional space, preserving local distances~\\cite{scikit_manifold}. \nThe Spectral Embedding algorithm consists of 3 steps: a) Weighted Graph Construction in which raw data are input into a graph representation using an adjacency matrix. b) Construction of unnormalized and a normalzied graph Laplacians as $L = D- A$ and $L = D^{-0.5}(D-A)D^{-0.5}$, respectively. c) Finally, partial eigenvalue decomposition is done on the graph Laplacian.\n\n\\subsubsection{Multi Dimensional Scaling (MDS)}\nMDS performs projection to lower dimension to improve interpretability while preserving `dissimilarity' between the samples. It preserves the dissimilarity by minimizing the square difference of the pairwise distances between all the training data between the projected, lower dimensional and the original higher dimensional space, \n\\begin{equation}\n    \\operatorname{Diff}_{P}\\left(X_{1}, \\ldots, X_{n}\\right)=\\left(\\sum_{i=1}^{n} \\sum_{j=1 \\mid i \\neq j}^{n}\\left(\\left\\|x_{i}-x_{j}\\right\\|-\\delta_{i, j}\\right)^{2}\\right)^{1 \/ 2}\n\\end{equation}\n\n\\noindent where $\\delta_{i,j}$ is the general dissimilarity metric in the original higher dimensional space and $\\left\\|x_{i}-x_{j}\\right\\|$ is the projected\/lower dimensional dissimilarity pairwise between training samples $i$ and $j$. The model can be finally validated by a scatter plot of pairwise distance in projected and original space. There are two types of MDS: Metric and Non-Metric based.  In Metric MDS, the distances between the two points in projection are set to be as close as possible to the dissimilarity (or distance) in original space. Non-metric MDS tries to preserve the order of the distances, and hence seeks a monotonic relationship between the distances in the embedded  and original space.\n\n\n\n\n\n\\subsubsection{t-SNE Visualization}\nThe manifold learning technique called t-distributed Stochastic Neighbor Embedding is useful to visualize high-dimensional data, as it reduces the tendency of points to crowd together at the center. This technique converts similarities between data records to joint probabilities and then tries to minimize the Kullback-Leibler divergence (technique used to compare two probability distributions) between the joint probabilities of the low-dimensional embedding and the high-dimensional data using gradient descent. The only issue with the use of this technique is that it is computationally expensive and is limited by two or three embeddings in some methods. In our intrusion detection methods, our purpose is to evaluate if in the low-dimensional embedding we can find some correlation of the data points with the labels.\n\n\\subsubsection{IsoMap Embedding}\nIsomap stands for isometric mapping and is an extension to the MDS technique discussed earlier. It uses geodesic\npaths instead of eucledian distance for nonlinear dimensionality reduction. Since MDS tries to preserve large pairwise distance over the small pairwise distance, Isomap first determine a neighborhood graph by finding the k nearest neighbor of each point, further connecting this points in the graph and assigns weights. Then it computes the shortest geodesic path between all pairs of point in the graph, to use this distance measure between connected points as weights to apply MDS to the shortest-path distance matrix~\\cite{extra_fusion_ref1}. \n\n\\subsection{Clustering}\nOne of the fundamental problems in multi-sensor data fusion is \\textit{data association}, where different observations in the dataset are grouped into clusters~\\cite{hall_book}. Hence, various clustering techniques are explored for data association.  \n\\subsubsection{K-means Clustering}\nThe k-means algorithm clusters data by separating samples in $n$ groups of equal variance, minimizing a criterion known as the inertia. The algorithm starts with a group of randomly selected centroids, which are used as the beginning points for every cluster, then performs iterative calculations to optimize the positions of the centroids by minimizing inertia. The process stops when either \nthe centroids have stabilized or the number of iterations has been achieved.\n\n\n\n\n\n\\subsubsection{Spectral Clustering}\nThe main concept behind spectral clustering is the graph Laplacian matrix. The algorithm takes the following steps~\\cite{spectral_clustering}:\n\\begin{enumerate}\n    \\item Construct a similarity graph either based on an $\\epsilon$-neighborhood graph, a $k-nearest$ neighbor graph, or a fully connected graph.\n    \\item Compute the normalized Laplacian $L$.\n    \\item Compute the first $k$ eigen-vectors $u_{1},u_{2}...,u_{k}$ of $L$. The first eigen-vectors are related to the $k$ smallest eigen values of $L$.\n    \\item Let $U \\in R^{n*k}$ be the matrix containing the vectors $u_{1},u_{2}...,u_{k}$ as columns.\n    \\item For $i=1,,,,n$, let $y_{i} \\in R^{k}$ be the vector corresponding to the $i^{th}$ row of $U$.\n    \\item Cluster points $(y_{i})$ in $R^{k}$ with k-means algorithm into clusters $C_{1},...C_{k}$.\n\\end{enumerate}\n\n\n\\subsubsection{Agglomerative Clustering}\nAgglomerative clustering in a bottom-up manner, where at the beginning, where each object belongs to one single-element cluster, which are the leaf clusters of a dendogram. At each step of the algorithm, the two clusters that are most similar (based on a similarity metric such as distance) are combined into a larger cluster. The procedure is followed until all points are members of a single big cluster. The steps form a hierarchical tree, where a distance threshold is used considered to cut the tree to partition the data into clusters. As per scikit, this algorithm recursively merges the pair of clusters that minimally increases a given linkage distance~\\cite{scikit_clustering}. The parameter \\textit{distance\\_threshold} in the scikit-learn implementation is used to cut the dendogram.\n\n\\subsubsection{Birch Clustering}\nThe Balanced Iterative Reducing and Clustering Using Hierarchies (BIRCH) \\cite{zhang1996birch} algorithm is more suitable for the cases where the amount of data is large and the number of categories K is also relatively large. It runs very fast, and it only needs a single pass to scan the data set for clustering.\n\n\n\n\\subsection{Supervised Learning}\nThough manifold learning and clustering techniques helps visualize and cluster the data samples in the intrusion time-interval from the non-intrusion ones, still the results of these techniques are hard to validate without any labels, hence various supervised learning techniques are also considered in designing the anomaly based IDS.\n\n\n\\subsubsection{Support Vector Classifier (SVC)}\n Support vector machine builds an hyperplane or set of hyperplanes in a higher dimensional space which are further used as a decision surface for classification or outlier detection. It is a supervised learning based classifier  which performs better even for scenarios with higher feature size than sample size. The decision function, or support vectors, defined using the  kernel type such as sigmoid, polynomial, linear or radial basis function plays a major impact on the classifier performance. Different variants of SVCs have been predominantly proposed in intrusion detection solutions~\\cite{svm1,svm2}.\n\n\n\\subsubsection{Logistic Regression (LR) Classifier}\nLR is a classification algorithm, used mainly for discrete set of classes. It is a probability-based classification technique which minimizes the error cost using the logistic sigmoid function. It uses the gradient descent technique to reduce the error cost function. Industries make a wide use of it, since it is very efficient and highly interpretable\\cite{lr}.\n\n\n\\subsubsection{Naive Bayes (NB) Classifier}\nNB is a supervised learning technique based on the Bayes Theorem, with the naive assumption of independent features, conditioned on the class. Based on the feature likelihood distribution, they posses different forms: Gaussian, Bernoulli, Categorical, Complement, etc. Though it is computationally efficient, the selection of feature likelihood may alter results. Spam filtering, text classification, and also in network intrusion detection it is used profusely~\\cite{nb1}. A naive-bayes based solution was proposed for IDS in a smart meter network~\\cite{sahu_naive_bayes}.\n\n\\subsubsection{Decision Tree (DT) Classifier}\nThe advantage of using DT is that it requires the least data transformation. Fundamentally it creates internally, models that predicts the target class by learning decision rules inferred from the features. \nThis technique sometimes meet with over-fitting issues while learning complex trees that are hard to generalize. Hence, it adopts pruning techniques such as reducing the tree max-depth to deal with over-fitting. If data in the samples are biased it may highly likely create biased trees. The computation cost of using this classifier is logarithmic in the number of data records. It has been used in protocol classification problem~\\cite{dt3,dt4} for classifying anomalous packets.\n\n\n\n\\subsubsection{Random Forest (RF) Classifier}\nBasically, RF creates decision trees on randomly picked data samples, further computes prediction from each tree and selects the best solution through voting. More trees results in a more robust forest. It is an ensemble based classifier in which a diverse collection of classifiers (decision trees) are constructed by incorporating randomness in tree construction.\nRandomness decreases the variance to address the overfit issues prevailing in DT. While comparing with SVMs, RF is fast and works well with a mixture of numerical and categorical features.\nIt has a variety of applications, such as recommendation engines, image classification and feature selection.\nDue to its variance reduction feature and least need of data pre-processing, it is also preferred in the cyber security area~\\cite{rf1,rf2}.\n\n\\subsubsection{Neural Network (NN) Classifier}\nNeural networks is effective in the case of complex non-linear models. In our IDS classification problem, we make use of multi-layer perceptron (MLP) as the supervised learning algorithm. It learns a non-linear function approximator whose inputs are the features for a record and outputs the class. Unlike a logistic regressor, it comprises of multiple hidden layers. A major issue with NN models is it large set of hyper tuning parameter such as number of hidden neurons, layers, iterations, dropouts, etc., that can affect the hyper-parameter tuning process for improving accuracy. Additionally, it is quite sensitive to feature scaling. \nFollowing Occam's razor, security professionals tend to avoid \nneural networks in intrusion detection, wherever possible. Still NN can be explored to capture temporal pattern with the use of Recurrent Neural Networks (RNN) and spatial pattern using Graph Neural Networks (GNN). \n\n\n\n\n\\section{Results and Analysis}\\label{results}\n\n\nIn this section, we study the improvement of the detection performance of IDS, when a fused dataset is considered in comparison to the use of only cyber or physical features. We design the IDS as a classifier when training with supervised and semi-supervised based ML techniques. We analyze the IDS performance based on the different types of MiTM attack carried out in the RESLab testbed. For supervised learning techniques, we analyse the impact of labeling as well as feature reduction on the detection accuracy. For unsupervised learning techniques, we compare the performance of the clustering techniques based on different metrics. In most of the experiments, we expect to receive highest scores for \neither 2 or 3 clusters, since we want to cluster attacked traffic from non-attacked. The third cluster can be an undetermined cluster. We also utilize and test a co-training based semi-supervised learning technique by assuming loss of labels for some experiments and compare them with supervised learning techniques. \n\n\n\n\\subsection{Supervised Technique Intrusion Detection with Snort Alert as Label}\n\n\\subsubsection{Metrics for evaluation}\nThe IDS performance is evaluated by classifier's accuracy computed using metrics such as \\textit{Recall}, \\textit{Precision}, and \\textit{F1-score}. Recall is the ratio of the true positives to the sum of true positives and false negatives. Precision is the ratio of the true positives to the sum of true positives and false positives.\nHigh precision is ensured by a low false positive rate. High recall is an indication of low false negative rate. \nFalse negatives are highly unwanted in security, since an undetected attack may result in more privilege escalations and can impact a larger part of network. False positives is expensive as time and money is invested for security professionals to investigate a non-critical alert.\nHence, harmonic mean of recall and precision, called F1-score, is a preferred metric for a balanced evaluation.\n\n\n\\subsubsection{Labels Evaluation}\nThe performances are compared, considering labels from Snort alerts and labels based on the intruders' attack windows, to train the supervised learning based IDS classifiers. The intruders' attack window is the difference between the attack script end and start time. We label every record in this window belonging to the compromised class. It is interesting to observe from Table~\\ref{tab:label_comparison} that the classifier trained using the attack window label performed better than the Snort labels, based on the average F1-score, Recall, and Precision. \nThese metrics are computed by taking the average of all the metrics from different use cases. This analysis indicates that training a model from well-known IDS may not act as an ideal classifier for intrusion detection. Hence, for our further studies, we train the classifier using the attack window based label. \n\n\\begin{table}[h]\n    \\centering\n    \\begin{tabular}{|l|l|l|l|l|l|l|}\n     \\hline\nClassifier & \\multicolumn{3}{|c|}{Snort Label} & \\multicolumn{3}{|c|}{Label from Attack Window}\\\\\n\n    \\hline\n        Avg. & F1 score & Rec. & Prec. & F1 score & Rec. & Prec.\\\\ \\hline\n        SVC & .566 & .69 & .496 & .752 & .776 & .799 \\\\ \\hline\n        DT & .738 & .73 & .757 & .909 & .909 & .92 \\\\ \\hline\n        RF & .764 & .789 & .776 & .891 & .896 & .903 \\\\ \\hline\n        GNB & .598 & .574 & .745 & .724 & .729 & .748 \\\\ \\hline\n        BNB & .57 & .589 & .621 & .634 & .655 & .676 \\\\ \\hline\n        MLP & .561 & .671 & .491 & .621 & .695 & .604 \\\\ \\hline\n    \\end{tabular}\n    \\caption{Comparison of the labels using different classifier based on the evaluation metrics.}\n    \\label{tab:label_comparison}\n    \\vspace{-0.2 cm}\n\\end{table}\n\n\n\n\n\n\n\n\n\n\\subsubsection{Use Case Specific Evaluation} \nWe analyze the dataset constructed from four use cases based on different strategies of FDI and FCI attacks (measurement and control, respectively). These cases use different polling rates and DNP3 masters on the synthetic 2000-bus grid case illustrated in the RESLab paper~\\cite{Sahu2020}. Use Case 1 and 2 are FCI attacks on binary and mixed binary\/analog commands from the control center to some selected outstations, selected from our prior work on graph-based contingency discovery~\\cite{n_x}. Use Case 3 and 4 are a mix of FCI and FDI attacks. These use cases differ based on the type and sequence of modifications done by the intruder as shown in Table~\\ref{tab:uc_table}.\n\n\n\\begin{table*}[t]\n    \\centering\n    \\begin{tabular}{|l|l|l|l|}\n     \\hline\n \\multicolumn{2}{|c|}{FCI} & \\multicolumn{2}{|c|}{FCI with FDI}\\\\\n\n    \\hline\n         UC1 & UC2 & UC3 & UC4\\\\ \\hline\n        Binary Commands & Analog, Binary Commands & Measurements=$>$Commands & Measurements=$>$ Commands=$>$Measurements \\\\ \\hline\n    \\end{tabular}\n    \\caption{Use cases based on the type and sequence of modifications.}\n    \\label{tab:uc_table}\n    \\vspace{-0.2 cm}\n\\end{table*}\n\nDue to the variation of attempts an intruder needs to take to implement the use cases, the number of samples collected for every scenario differs. \nIn the MLP based classifier, the number of samples plays a vital role; hence, MLP performs better for scenarios with the number of DNP3 masters equal to 10 versus 5 and with a DNP3 polling interval of 30 s versus 60 s. The DT and RF classifiers outperform the other classifiers in almost all the scenarios. The NB classifiers, both Gaussian and Bernoulli, need the features to be independent for optimal performance. Since most of the features are strongly correlated based on Fig.~\\ref{fig:feature_correlation}, the performance of NB is relatively weak compared to other classifiers. Usually, Gaussian Naive Bayes (GNB) is considered for features that are continuous and Bernoulli Naive Bayes (BNB) for discrete features. In our fused dataset, since we have both types of features, we consider both techniques for evaluation. In majority of the scenarios, GNB performed better than BNB, indicating the physical features have more impact on the detection compared to categorical cyber features. Table~\\ref{tab:uc_comparison} shows the comparison of classifiers for different use cases, and Table~\\ref{tab:uc_comparison_gridsearch} shows the comparison using grid search cross validation based tuning of hyper-parameters for each classifier.\n\n\\begin{table}[!h]\n   \n    \\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}\n     \\cline{1-9}\n\\multicolumn{3}{|c|}{Scenarios} & \\multicolumn{6}{|c|}{Classifiers}\\\\\n    \\cline{1-9}\n    uc & masters & PI & SVC & DT & RF & GNB & BNB & MLP\\\\\n    \\cline{1-9}\n        \\multirow{2}{*}{\\textbf{UC1}}  & 10 & 30 & .70 & .74 & .75 & .59 & .70 & .70\\\\ \\cline{2-9}\n        & 10 & 60 & .78 & .87 & .81 & .75 & .49 & .58\\\\ \\cline{1-9}\n        \\multirow{4}{*}{\\textbf{UC2}}  & 5 & 30 & .88 & .76 & .92 & .73 & .52 & .86\\\\ \\cline{2-9}\n       & 5 & 60 & .88 & .89 & 1.0 & .94 & .89 & .66\\\\ \\cline{2-9}\n        & 10 & 30 & .84 & .93 & .93 & .73 & .59 & .77\\\\ \\cline{2-9}\n       & 10 & 60 & .64 & .97 & .88 & .33 & .58 & .52\\\\ \\cline{1-9}\n       \\multirow{4}{*}{\\textbf{UC3}}  & 5 & 30 & .95 & .98 & .93 & .93 & .57 & .72\\\\ \\cline{2-9}\n       & 5 & 60 & .50 & 1.0 & .88 & .72 & .33 & .40\\\\ \\cline{2-9}\n       & 10 & 30 & .85 & 1.0 & .97 & .83 & .66 & .86\\\\ \\cline{2-9}\n       & 10 & 60 & .89 & .98 & .91 & .84 & .73 & .91\\\\ \\cline{1-9}\n       \\multirow{4}{*}{\\textbf{UC4}}  & 5 & 30 & .59 & .86 & .88 & .56 & .54 & .39\\\\ \\cline{2-9}\n       & 5 & 60 & .63 & .81 & .77 & .74 & .77 & .31\\\\ \\cline{2-9}\n       & 10 & 30 & .65 & .96 & .97 & .63 & .78 & .57\\\\ \\cline{2-9}\n       & 10 & 60 & .75 & .98 & .88 & .83 & .80 & .50\\\\ \\cline{1-9}\n       \\hline\n    \\end{tabular}\n    \\caption{Comparison of the classifier based on the scenarios i.e. use cases, number of masters and the polling interval (PI) in sec. }\n    \\label{tab:uc_comparison}\n    \\vspace{-0.2 cm}\n\\end{table}\n\n\n\\begin{table}[!h]\n   \n    \\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}\n     \\cline{1-9}\n\\multicolumn{3}{|c|}{Scenarios} & \\multicolumn{6}{|c|}{Classifiers}\\\\\n    \\cline{1-9}\n    uc & masters & PI & SVC & DT & RF & GNB & BNB & MLP\\\\\n    \\cline{1-9}\n        \\multirow{2}{*}{\\textbf{UC1}}  & 10 & 30 & .70 & .78 & .75 & .70 & .69 & .70\\\\ \\cline{2-9}\n        & 10 & 60 & .54 & .87 & .81 & .78 & .52 & .7\\\\ \\cline{1-9}\n        \\multirow{4}{*}{\\textbf{UC2}}  & 5 & 30 & .51 & .88 & .84 & .72 & .51 & .67\\\\ \\cline{2-9}\n       & 5 & 60 & .66 & 1.0 & 1.0 & .83 & .89 & .62\\\\ \\cline{2-9}\n        & 10 & 30 & .45 & .94 & .89 & .81 & .44 & .86\\\\ \\cline{2-9}\n       & 10 & 60 & .52 & .97 & .85 & .75 & .61 & .58\\\\ \\cline{1-9}\n       \\multirow{4}{*}{\\textbf{UC3}}  & 5 & 30 & .36 & .98 & .93 & .93 & .50 & .91\\\\ \\cline{2-9}\n       & 5 & 60 & .40 & 1.0 & .96 & .88 & .26 & .44\\\\ \\cline{2-9}\n       & 10 & 30 & .41 & 1.0 & .99 & .84 & .63 & .69\\\\ \\cline{2-9}\n       & 10 & 60 & .40 & .93 & .88 & .89 & .76 & .82\\\\ \\cline{1-9}\n       \\multirow{4}{*}{\\textbf{UC4}}  & 5 & 30 & .39 & .97 & .93 & .57 & .56 & .61\\\\ \\cline{2-9}\n       & 5 & 60 & .31 & .63 & .68 & .65 & .77 & .68\\\\ \\cline{2-9}\n       & 10 & 30 & .44 & .96 & .95 & .65 & .78 & .65\\\\ \\cline{2-9}\n       & 10 & 60 & .50 & .88 & .85 & .80 & .80 & .50\\\\ \\cline{1-9}\n       \\hline\n    \\end{tabular}\n    \\caption{\\textbf{Optimal HyperParameter with GridSearch} Comparison of the classifier based on the scenarios i.e. use cases, number of masters and the polling interval (PI) in sec. }\n    \\label{tab:uc_comparison_gridsearch}\n    \\vspace{-0.2 cm}\n\\end{table}\n\n\\subsubsection{Impact of Fusion}\nWe evaluate the performance of the classifier by considering pure physical and pure cyber based intra-domain fusion as well as cyber-physical inter-domain fusion. The pure physical and cyber physical based fusion outperforms pure-cyber based fusion for all the classifiers shown in Table~\\ref{tab:fusion_type_comparison}. Hence, it indicates that introduction of physical side features can improve the accuracy of conventional IDS that only considers network logs in communication domain. The pure physical features relatively performed better than cyber physical because in the testbed, only few features (i.e. measurements for the impacted substation) are considered for extraction. If we consider all the measurements from the grid simulation, the detection accuracy will decrease due to feature explosion. Feature reduction techniques  such as PCA for the physical features  may not be an ideal solution for a huge synthetic grid. \n\n\\begin{table}[!h]\n    \\centering\n    \\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}\n     \\hline\nClfr & \\multicolumn{3}{|c|}{Pure Cyber} & \\multicolumn{3}{|c|}{Pure Physical} & \\multicolumn{3}{|c|}{Cyber Physical}\\\\\n\n    \\hline\n         Avg. & F1 & Rec. & Pre. & F1 & Rec. & Pre. & F1  & Rec. & Pre.\\\\ \\hline\n        SVC & .62 & .68 & .59 & .75 & .77 & .80 & .75 & .77 & .80\\\\ \\hline\n        DT & .77 & .77 & .77 & .93 & .93 & .94 & .91 & .91 & .92\\\\ \\hline\n        RF & .69 & .69 & .68 & .92 & .92 & .93 & .89 & .90 & .90\\\\ \\hline\n        GNB & .58 & .57 & .59 & .78 & .77 & .81 & .72 & .73 & .75\\\\ \\hline\n        BNB & .52 & .56 & .55 & .65 & .68 & .66 & .63 & .66 & .68\\\\ \\hline\n        MLP & .56 & .66 & .53 & .72 & .76 & .77 & .62 & .70 & .61\\\\ \\hline\n    \\end{tabular}\n    \\caption{Comparison of the classifier with pure cyber fusion, pure physical fusion, and cyber-physical fusion features }\n    \\label{tab:fusion_type_comparison}\n    \\vspace{-0.2 cm}\n\\end{table}\n\n\\subsubsection{Impact of Feature Reduction}\nIn this subsection, we analyze feature reduction techniques such as PCA  and Shapiro ranking for feature reduction and feature filtering to evaluate the performance of the IDS. Table~\\ref{tab:feature_selection_comparison} illustrates the performance scores for different classifiers with PCA transformed features and shapiro features selected for scores more than 0.7.   It can be observed that except for the DT and RF, other classifier's performance improved by both operation. DT and RF behaves the best when most of the features are kept intact. In most of the case selection of features based on Shapiro features performed better than PCA transformation. Still the total variance threshold taken may impact the number of principal components considered, which can affect the results.\n\n\n\\begin{figure} [!h]\n    \\centering\n    \\vspace{-0.2cm}\n    \\includegraphics[width=1.0\\linewidth]{Figures\/shapiro_feature_ranks.png}\n    \\vspace{-0.35cm}\n    \\caption{Ranking feature importance for extracting features. Of all the features, scores above 0.7 is selected for training.}\n    \\label{fig:shapiro_ranking}\n\\end{figure}\n\n\\begin{table}[h]\n    \\centering\n    \\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}\n     \\hline\nClfr & \\multicolumn{3}{|c|}{All Features} & \\multicolumn{3}{|c|}{PCA} & \\multicolumn{3}{|c|}{Shapiro Ftrs $\\ge$ 0.7}\\\\\\hline\n         Avg. & F1 & Rec. & Pre. & F1 & Rec. & Pre. & F1  & Rec. & Pre.\\\\ \\hline\n        SVC & .75 & .77 & .80 & .77 & .80 & .81 & .77 & .78 & .79\\\\ \\hline\n        DT & .91 & .91 & .92 & .82 & .82 & .83 & .89 & .89 & .91\\\\ \\hline\n        RF & .89 & .90 & .90 & .86 & .86 & .87 & .84 & .84 & .84\\\\ \\hline\n        GNB & .72 & .73 & .75 & .77 & .78 & .78 & .83 & .84 & .87\\\\ \\hline\n        BNB & .63 & .66 & .68 & .74 & .76 & .76 & .80 & .82 & .86\\\\ \\hline\n        MLP & .62 & .70 & .61 & .61 & .68 & .64 & .50 & .64 & .41\\\\ \\hline\n    \\end{tabular}\n    \\caption{Comparison of the classifier with all features, reduced feature with PCA transformation, and feature selection based on shapiro ranking }\n    \\label{tab:feature_selection_comparison}\n    \\vspace{-0.2 cm}\n\\end{table}\n\n\n\n\n\\subsection{Unsupervised Learning Techniques}\n\n\\subsubsection{Metrics for evaluation}\nFor evaluating the performance of the clustering techniques, the Silhoutte scores, Calinski Harabasz score, Adjusted Rand score, and Davies Bouldin scores are considered. The \\textit{Silhoutte score} (S) is the mean Silhouette Coefficient of all samples. The Silhouette Coefficient is calculated using the mean intra-cluster distance (a) and the mean nearest-cluster distance (b) for each sample, using $\\frac{b - a} {max(a, b)}$. The \\textit{Calinski Harabasz score} (CH) is computed based on~\\cite{ch_score}. It is the ratio between the within-cluster dispersion and the between-cluster dispersion. The \\textit{Rand Index} computes a similarity measure between two clusterings by considering all pairs of samples and counting pairs that are assigned in the same or different clusters in the predicted and true clusterings. This index is further adjusted to be called the Adjusted Rand Index (AR). The \\textit{Davies Bouldin score} (DB) is defined as the average similarity measure of each cluster with its most similar cluster, where similarity is the ratio of within-cluster distances to between-cluster distances~\\cite{db_score}. Thus, clusters which are farther apart and less dispersed will result in a better score.\n\n\n\\subsubsection{Clustering}\nPrior to the clustering techniques, we scaled and normalized the dataset using scaler  and normalize functions since otherwise there will be feature-based bias. We implement four types of clustering techniques: Agglomerative, k-means, Spectral and Birch clustering, to evaluate the optimal number of clusters based on the S, CH, AR, and DB scores. For determining the clusters, we merged the samples from all the use cases to form a larger dataset and then trained the clustering methods by tuning the number of clusters hyper-parameter ($N_c$) from 2 to 10. Fig 8 (a-e)\nshow the clustered plots using Agglomerative clustering with different number of clusters.\nThe number of clusters, or centroids, are selected for hyper-parameter tuning since it is found to be the most important factor for success of the algorithm~\\cite{clus_ref}.\nIdeally, there need to be 3 clusters for un-attacked, attacked with DNP3 alerts, and attacked with ARP alerts, but the distance metric considered results in a greater number of clusters in some methods. Among all the clustering techniques presented in the previous section, the affinity propagation technique does not converge to obtain the exemplars with default paramaters ($damping$ =50, $convergence\\_iter$ =200). Hence, the damping and maximum convergence iteration parameters are increased to 0.95 and 2000 respectively, resulting in 34 clusters. The S, CH, DB, and AR scores obtained are 0.605, 3658.1, 0.736, and 0.00085 respectively. \n\n\n\\begin{table}[h]\n    \\centering\n    \\begin{tabular}{|l|l|l|l|l|}\n\n    \\hline\n         Clustering Algo & S & CH & AR & DB\\\\ \\hline\n        Agglomerative & 3 & 3 & 2 & 6\\\\ \\hline\n        K-means & 3 & 5 & 2 &  6\\\\ \\hline\n        Spectral & 3 & 5 & 2 & 6 \\\\ \\hline\n        Birch & 3 & 3 & 3 & 2\n        \\\\ \\hline\n    \\end{tabular}\n    \\caption{Optimal clusters (Opt $N_c$) using different algorithm obtained using four different evaluation metric}\n    \\label{tab:unsup_cluster_comparison}\n    \\vspace{-0.2 cm}\n\\end{table}\n\n\\begin{figure*}[!htb]\n  \\centering\n  \\subfigure[]{\\includegraphics[height=1.3 in,width=1.37 in]{Figures\/Agglomerative\/ac2.jpg}\\label{ac2}}\n  \\subfigure[]{\\includegraphics[height=1.3 in,width=1.37 in]{Figures\/Agglomerative\/ac3.jpg}\\label{ac3}}\n  \\subfigure[]{\\includegraphics[height=1.3 in,width=1.37 in]{Figures\/Agglomerative\/ac4.jpg}\\label{ac4}}\n  \\subfigure[]{\\includegraphics[height=1.3 in,width=1.37 in]{Figures\/Agglomerative\/ac5.jpg}\\label{ac5}}\n  \\subfigure[]{\\includegraphics[height=1.3 in,width=1.37 in]{Figures\/Agglomerative\/ac6.jpg}\\label{ac6}}\n  \\caption{Agglomerative clustering with different number of clusters. Clustering with size 2 and 3 outperforms others, validating the detection accuracy of a attacked traffic from a non-attacked one.}\n\\end{figure*}\n\n\n\n\\subsubsection{Impact of Fusion}\nConsidering only physical side fea- tures, most of the evaluation metrics computed very low or negative (in the case of Adjusted Rand index) values, indicating inefficient clusters. The scores of the optimal clusters with combined cyber-physical features had an AR score of more than 0.8, but its maximum is 0.01 for 6 clusters with only physical features. The pure cyber features performed similar to the cyber physical case, but the scores are less compared to the merged features. Hence, it is essential to fuse cyber and physical features prior to perform clustering based unsupervised learning.\n\\begin{table}[h]\n    \\centering\n    \\begin{tabular}{|l|l|l|l|l|l|l|l|l|}\n\n    \\hline\n    & \\multicolumn{4}{|c|}{Pure Cyber} & \\multicolumn{4}{|c|}{Pure Physical}\\\\ \\hline\n         Clustering  & S & CH & AR & DB& S & CH & AR & DB\\\\ \\hline\n        Agglo. & 3 & 5 & 2 & 6 & 2 & 6 & 6 (neg) & 2\\\\ \\hline\n        K-means & 3 & 6 & 2 &  5 & 3 & 6 & 6 (neg) & 2\\\\ \\hline\n        Spectral & 3 & 5 & 2 & 6 & 3 & 3 & 6 (neg) & 2 \\\\ \\hline\n        Birch & 3 & 3 & 2 & 2 & same & 3 & 3 (neg) & 2\n        \\\\ \\hline\n    \\end{tabular}\n    \\caption{Comparison of Optimal clusters (Opt $N_c$) using different algorithm considering pure cyber and physical features}\n    \\label{tab:unsup_cluster_cyphy_comparison}\n    \\vspace{-0.2 cm}\n\\end{table}\n\n\\subsubsection{Robustness}\nThe robustness of the clustering techniques can be evaluated based on the variance of these evaluation metrics with respect to a) hyper-parameter tuning and b) dataset alterations. In the first case, the mean, variance, and normalized variance ($NVar$ = $\\frac{sd}{mean}$) of the evaluation metric $S$, $CH$, $AR$, and $DB$ are computed by altering $N_c$ from 2 to 10 and using the complete dataset extracted for all the use cases. In the second case, similar statistics are computed by keeping the number of clusters fixed at $N_c=3$ and altering the dataset i.e. by using different use cases. A clustering technique that has a lower normalized variance is more robust, and a better mean score is more accurate. Based on the silhoutte scores ($S$) from Table~\\ref{tab:clustering_robustness}, k-mean based clustering is found to be more robust to varying data source and has a better mean score, but a main limitation of k-means is its strong dependence on $N_c$. Still, k-means is used in many practical situations such as anomaly detection~\\cite{kmean} due to its low computation cost.    \n\n\\begin{table}[h]\n   \n    \\begin{tabular}{|l|l|l|l|l|l|l|l|}\n     \\cline{1-8}\n\\multicolumn{2}{|c|}{Scenarios} & \\multicolumn{3}{|c|}{Effect of Parameters}& \\multicolumn{3}{|c|}{Effect of Data Alt.}\\\\\n    \\cline{1-8}\n    Met & Algo & Mean & Var & NVar & Mean & Var & NVar\\\\\n    \\cline{1-8}\n        \\multirow{4}{*}{\\textbf{S}} \n        & Agg & .52 & .0175 & .254 & .609 & .01 & .164\\\\ \\cline{2-8}\n        & K-m & .54 & .013 & .212 & \\fontseries{b}\\selectfont .615 & .008 & \\fontseries{b}\\selectfont .145\\\\ \\cline{2-8}\n        & Spec & .504 & .021 & .287 & .581 & .015 & .213 \\\\ \\cline{2-8}\n         & Bir & \\fontseries{b}\\selectfont .74 & .011 & \\fontseries{b}\\selectfont .146 & .599 & .010 & .172 \\\\ \\cline{1-8}\n        \\multirow{4}{*}{\\textbf{CH}}  \n       & Agg & 9965 & \\num[round-precision=2,round-mode=figures,\n     scientific-notation=true]{5516755} & \\fontseries{b}\\selectfont .235 & 337 & 36880 & .569\\\\ \\cline{2-8}\n        & K-m & \\fontseries{b}\\selectfont 10822 & \\num[round-precision=2,round-mode=figures,\n     scientific-notation=true]{66329012} & .237 & \\fontseries{b}\\selectfont 346 & 35690 & .545\\\\ \\cline{2-8}\n        & Spec & 8765 & \\num[round-precision=2,round-mode=figures,\n     scientific-notation=true]{10066904} & .362 & 311 & 34047 & .592 \\\\ \\cline{2-8}\n         & Bir & 10484 & \\num[round-precision=2,round-mode=figures,\n     scientific-notation=true]{13395600} & .349 & 331 & 35637 & .57 \\\\ \\cline{1-8}\n       \\multirow{4}{*}{\\textbf{AR}}  \n       & Agg & .703 & .035 & .266 & .534 & .029 & .319\\\\ \\cline{2-8}\n        & K-m & .672 & .027 & \\fontseries{b}\\selectfont .248 & .529 & .022 & \\fontseries{b}\\selectfont .281\\\\ \\cline{2-8}\n        & Spec & \\fontseries{b}\\selectfont .714 & .039 & .278 & \\fontseries{b}\\selectfont .638 & .049 & .349 \\\\ \\cline{2-8}\n         & Bir & .342 & .014 & .35 & .589 & .047 & .368 \\\\ \\cline{1-8}\n       \\multirow{4}{*}{\\textbf{DB}} \n      & Agg & .026 & 0.0 & \\fontseries{b}\\selectfont .32 & .053 & .003 & 1.038\\\\ \\cline{2-8}\n        & K-m & .54 & 0.0 & .322 & .063 & .003 & .925\\\\ \\cline{2-8}\n        & Spec & .504 & 0.0  & .559 & .058 & .003 & 1.037\\\\ \\cline{2-8}\n         & Bir & \\fontseries{b}\\selectfont .74 & 0.0  & 1.344 & \\fontseries{b}\\selectfont .065 & .003 & \\fontseries{b}\\selectfont .895\\\\ \\cline{1-8}\n       \\hline\n    \\end{tabular}\n    \\caption{Evaluation of the Robustness of the Clustering Algorithm by varying hyper-parameters and data source.}\n    \\label{tab:clustering_robustness}\n    \\vspace{-0.2 cm}\n\\end{table}\n\n\n\n\\subsubsection{Manifold Learning}\nManifold learning is adopted for the purpose of visualization. \nFor quantitative comparisons, we need to employ classification techniques on the features projected in the lower dimensions using these embeddings.  We evaluate the performance of manifold learning methods by testing them with the classifiers presented in the previous subsection.  Table~\\ref{tab:manifold_learning_comparison} presents the comparison of the LLE, MDS, spectral, t-SNE, and IsoMap \\cite{tenenbaum2000isomap} embeddings considered for classification using SVC, k-NN, DT, RF, GNB, BNB and MLP. Inter-domain fusion doesnt gain much from manifold learning, but an interesting observation is made on the decrease in the difference of F1-scores among the high performing DT and RF classifiers, with the low performing SVC and k-NN classifiers. Hence, we conclude that it is unadvisable to perform manifold learning for our datasets, if training using Decision Tree or Random Forest. The IsoMap embedding that preserves local features of the data by first determining neighbor-hood graph and uses MDS in its last stage performs better than MDS for all the classifier only with the exception of SVC.\n\n\\begin{table}[h]\n    \\centering\n    \\begin{tabular}{|l|l|l|l|l|l|l|l|}\n     \\hline\n        Clfr$\\rightarrow$ & SVC & k-NN & DT & RF & GNB & BNB & MLP\\\\\\hline\n        Manifold $\\downarrow$ & \\multicolumn{7}{|c|}{F1 scores}\\\\\\hline\n        LLE & .66 & .74 & .66 & .64 & .38 & .39 & .49\\\\ \\hline\n        MDS & .65 & .78 & .77 & .80 & .54 & .48 & .55\\\\ \\hline\n        Spectral & .61 & .75 & .73 & .75 & .61 & .62 & .54\\\\ \\hline\n        t-SNE & .64 & .74 & .73 & .76 & .63 & .57 & .63\\\\ \\hline\n        IsoMap & .65 & .78 & .77 & .79 & .54 & .48 & .55\\\\ \\hline\n    \\end{tabular}\n    \\caption{Comparison of the different manifold learning embeddings considered with different classifiers.}\n    \\label{tab:manifold_learning_comparison}\n    \\vspace{-0.2 cm}\n\\end{table}\n\n\\subsection{Semi-Supervised Learning}\n\n\n\\subsubsection{Co-Training}\nFor co-training, we first split the dataset into labeled and unlabeled sets randomly in the ratio of 1:2. In the real world, this randomness may be caused due to accidental cessation of the Snort application or if a network security expert cannot make an inference of intrusion. Further both the labeled and unlabeled data are split into cyber and physical views consisting of respective features. In these experiments, we compare the supervised learning techniques on the labeled dataset with the co-training technique which uses supervised learning cyber and physical classifiers as shown in Fig.~\\ref{fig:cotraining}. It is expected to have a reduction in performance from supervised learning techniques, due to lack of labels for some samples, but it can be observed from Table~\\ref{tab:cotrain_comparison}, that the co-training based classification outperforms supervised for some classifiers such as $LR$,$GNB$,$BNB$,$MLP$ and performs at par with other classifiers with a difference of a mere 8 percent in the case of $RF$. The probable reason for improvement in performance using co-training may be due to the training of two different classifiers using intra-domain features.\n\n\\begin{table}[h]\n    \\centering\n    \\begin{tabular}{|l|l|l|l|l|l|l|}\n\n    \\hline\n    Classifier & \\multicolumn{3}{|c|}{Supervised} & \\multicolumn{3}{|c|}{Co-Training}\\\\ \\hline\n          & F1-score & Rec.& Prec.& F1-score & Rec.& Prec.\\\\ \\hline\n        LR & .63 & .67 & .64 & .64 & .73 & .58\\\\ \\hline\n        SVC & .63 & .67 & .64 & .59 & .70 & .52\\\\ \\hline\n        DT & .69 & .71 & .69 & .64 & .71 & .65 \\\\ \\hline\n        RF & .73 & .77 & .72 & .65 & .72 & .72\\\\ \\hline\n         GNB & .28 & .33 & .66 & .30 & .32 & .56\\\\ \\hline\n        BNB & .53 & .51 & .67 & .58 & .66 & .52\\\\ \\hline\n        MLP  & .59 & .71 & .51 & .61 & .71 & .55\\\\ \\hline\n    \\end{tabular}\n    \\caption{Comparison of the classifier using supervised and co-training based unsupervised learning.}\n    \\label{tab:cotrain_comparison}\n    \\vspace{-0.2 cm}\n\\end{table}\n\n\n\\section{Discussion}\\label{challenges}\n\\textcolor{red}{temp; MOVE TO FUTURE WORK: Knowledge extraction prior to fusion is currently not incorporated in this work but can be easily leveraged since we perform sequential merge of features.}\n\n\\textcolor{red}{temp; MOVE TO discussion: Supervised, semi-supervised, and un-supervised techniques all need to be explored since each can be more appropriate in different scenarios.  \nOther work fails to consider packet header details in creating feature space.  Our previous work \\cite{} included evaluation of cyber-side features like retransmission, round trip time (RTT), and flow counts; this motivates the need of extraction of measurements from packet capture. \nDeploying the data to a datasource such as Elasticsearch makes data aggregation, filtering, visualization convenient.  \n}\n\n\n\\textcolor{red}{temp;Move to DISCUSSION ?:\nA challenge with power system data fusion is the location of the fusion engine. If the fusion and inference engine are located outside the control network, security to pull out the data is an issue. In the real world, it is important to consider how the physical data will be available to a fusion engine, the size of the database, and whether anonymization techniques may be applied to preserve privacy.   If such challenges are overcome, multi-sensor fusion enable stakeholders to classify data to identify and localize mis-operations due to system faults as well as intruder-instigated failure.}\n\n\n\\textcolor{red}{[like in paper 1, you don't really need a future work section in a journal paper, but a discussion section (or could be a final subsection of previous section) instead, so I suggest turning this section into that instead, but of course keeping our list of next-steps for ourselves. Discussing the \"current challenges\" in the discussion section is still a good idea and it can also still mention next steps\/future work, but you really want to capture\/highlight the main aspects and key results of the paper in this discussion section.  You could check different papers to get examples of how this might be done well. There are likely a variety of different good ways. ]} Data Fusion is a prior step followed before\nstate estimation. Hence, in our current work we have used fusion to infer an attack\nand the time when the attack was performed. In our future work we will explore, if\nsuch inference can improve the cyber physical state estimation. Also in the current\nwork, we are using decimal to compress the information of the binary array, which is\nonly efficient in storage and neither interpretable nor comparable. Our next step is\ncoming up with a method to better map a variant-length of data (BI, BO, AI, AO) to a\nfixed-dimension space where the mapped data will have the following properties,\nwhich enable us to easily find anomaly event chronologically and spatially:\n\\begin{enumerate}\n    \\item Reconstructed data will be the same if their original data are the same\n    \\item Reconstructed data will be close if their original data are similar\n    \\item Reconstructed data will be an outlier if the original data has values that is out of\nnormal range\n\\end{enumerate}\n\\section*{Acknowledgment}\nThis research is supported by the US Department of Energy's (DoE) Cybersecurity for Energy Delivery Systems program under award DE-OE0000895.\n\n\n\n\\bibliographystyle{IEEEtran}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{INTRODUCTION}\n\\label{sec:intro}\nIn Self-induced transparency (SIT), an optical pulse propagates resonantly through the two-level absorbing medium without any loss and distortion. This pioneering work was carried out by McCall and Hahn \\cite{McHa1, McHa2}. SIT originates from the generated coherence of a strongly coupled light-medium interaction. Therefore for observing SIT, the incident pulse should be short compared to the various relaxation times present in the system, such that the coherence will not vanish during the pulse propagation. Further, the pulse should also be strong enough to excite the atom from the ground state.  \n One of the best theoretical estimations of the input pulse was reported in the ``area theorem\" \\cite{McHa2}. This theorem dictates that a 2$\\pi$ secant pulse can propagate through the medium without any loss and distortion in the pulse shape. In general, for an initial pulse area $\\theta_{0}$ obeying the condition $(n+1)\\pi >\\theta_{0}>n\\pi$, evolves the area towards $(n+1)\\pi$ or $n\\pi$ depending on whether $n$ is odd or even. Therefore input pulse with a larger area of $2n\\pi$, breaks up into $n$ number of $2\\pi$ pulses with different propagation velocities. These effects have been observed experimentally in atomic rubidium medium by Slusher and Gibbs \\cite{SluGib1}. In particular, they have found excellent agreement between numerical simulations and experimental results. These fundamental properties of the SIT were investigated several times, both theoretically and experimentally \\cite{Allen1, Lamb1, Eilbeck1}.\n\nHowever, in atomic medium, the preparation and trapping of atomic gas required a vast and sophisticated setup. Moreover, due to the gaseous nature of the medium, the different velocity of the atom shows Dopler broadening in output result.\nFor the last two decades, solid-state semiconductor mediums have emerged as a potential candidate for optical applications, particularly for scalable on-chip quantum technology. Earlier, the resonant coherent pulse propagation in bulk and quantum-well semiconductors behaves differently compared to a two-level atomic medium. The discrepancy mentioned above occurs due to the many-body Coulomb interaction of the different momentum states present in a bulk medium\\cite{SWKoch1, HG1, ASch1}. This problem has been overcome in three-dimensionally confined excitons in quantum dots (QD's). The quantum dots can easily be engineered to get the desired transition frequency to avoid the problem of laser availability. The scalability and fabrication technology make the semiconductor QDs suitable for modern quantum optics experiments. There have been some interesting theoretical proposals about the possibility of observing SIT in self-organized InGaAs QDs\\cite{Gpan1}. Excitonic transition in InGaAs QDs have large transition dipole moments and long dephasing time in the range of nanoseconds at cryogenic temperatures \\cite{PBor1} and are, therefore a promising candidate for SIT.\n\nThough the QD medium is a potential candidate for observing SIT, it has a few drawbacks also. All the QDs inside the medium are not identical, so an inhomogeneous level broadening is always present in the system. In semiconductors,  longitudinal acoustic phonon interaction is vital because of the environment temperature. Interactions between phonon and exciton lead to dephasing in coupled dynamics of exciton-photon interaction\\cite{DPHZ1,DPHZ2}. Several theoretical models and experiments have recently explained SIT in the semiconductor QD medium \\cite{QDSIT1, QDSIT2, QDSIT3}. Few of them consider the effect of the phonon environment on the system dynamics in the context of group velocity dispersion\\cite{Phonon1}. Another recent experimental work showed the SIT mode-locking and area theorem for semiconductor QD medium, and rubidium atom \\cite{MODELOCK1, MODELOCK2}.\n\nIn this paper, we discuss the possibility of SIT in a semiconductor QD medium incorporating the effect of phonon bath in our model. We utilize the recently developed polaron transformed master equation keeping all orders of exciton-phonon interaction \\cite{POLARON1, POLARON2, POLARON3}. Our model's pulse propagation dynamics depend on system and bath parameters. Hence, the propagation dynamics become more transparent by knowing both the system and the bath's contribution.The motivation behind this work is to find long-distance optical communication without loss of generality in an array of QD. Due to strong confinement of electron hole pairs, QDs have discrete energy levels thus QD arrays mimic atomic medium with the added advantage of scalability and controllability with advanced semiconductor technology. It is also possible to create QD fibers which can be used for quantum communication channels \\cite{QDFIBER,QCOM}. Motivated by this work, we theoretically investigate the self-induced transparency effect in a semiconductor QD medium.\n\nOur paper is organized as follows. Sec.\\ \\ref{sec:intro} contains a brief introduction of the SIT in a QD medium and its application.\nIn Sec.\\ \\ref{sec:model}, we present our considered model system along with the theoretical formalism of the polaron master equation. In Sec.\\ \\ref{sec:result} we discuss the result after numerically solving the relevant system equations. Finally, we draw a conclusion in Sec.\\ \\ref{sec:conclud}.   \n\n\n\\section{MODEL SYSTEM}\n\\label{sec:model}\n\nThe phonon contribution to QD dynamics at low temperature is mandatory. We assume the propagation of an optical pulse along the $z$-direction. Accordingly, we define the electric field of the incident optical pulse as\n\\begin{equation}\n\\vec{E}(z,t) = \\hat{e}\\mathcal{E}(z,t)e^{i(kz-\\omega t)} + c.c ,\n\\end{equation}\nwhere $\\mathcal{E}(z,t)$ is the slowly varying envelop of the field. The bulk QD medium comprises multiple alternating InGaAs\/GaAs QD deposition layers. Every QD inside the medium strongly interacts with the electric field due to the significant dipole moment. The QD can be modelled as a two-level system with exciton state $\\vert 1\\rangle$, and ground state $\\vert 2\\rangle$ with energy gap $\\hbar\\omega_{12}$ by taking proper choice of biexciton binding energy and polarisation as shown in the Fig.\\ref{Fig.1}. The raising and lowering operator for the QD can be written as $\\sigma^{+} = \\vert 1\\rangle\\langle 2\\vert$ and $\\sigma^{-} = \\vert 2\\rangle\\langle 1\\vert$. In case of semiconductor QD's, the optical properties get modified due to the lattice mode of vibration \\textit{i.e.}, the acoustic phonon. Hence, QD exciton transition coupled to an acoustic phonon bath model mimics the desired interaction. The phonon bath consists of a large number of closely spaced harmonic oscillator modes. Therefore, we introduce the annihilation and creation operators associated with $k^{th}$ phonon mode having frequency $\\omega_{k}$ as $b_{k}$ and $b_{k}^{\\dagger}$. The mode frequency can be expressed as $\\omega_{k} = c_{s}k$ where $k$ and $c_{s}$ are the wave vector and velocity of sound. The Hamiltonian for the described model system after making dipole and rotating wave approximation is given by\n\\begin{figure}[t]\n   \\includegraphics[scale=0.4]{fig_1}\n    \\caption{A Schematic diagram of the QD level system with ground state $\\vert 2 \\rangle$ and exciton state $\\vert 1 \\rangle$ driven by the optical pulse with effective coupling $\\langle B\\rangle\\Omega$(blue line). The spontaneous decay from the exciton state to the ground state is shown using a curly red line. The parallel violet lines represent the phonon modes interacting with the exciton state. The red and blue dashed lines represent the phonon-induced decay and pumping rate respectively.}\n    \\label{Fig.1}\n\\end{figure}\n\\begin{equation}\n\\begin{split}\nH &= - \\hbar\\delta\\sigma^{+}\\sigma^{-} + \\frac{1}{2}\\hbar\\Bigl( \\Omega(z,t)\\sigma^{+} + \\Omega^{*}(z,t)\\sigma^{-} \\Bigr) \\\\\n  &+\\hbar\\sum\\limits_k\\omega_kb_k^{\\dag}b_k + \\hbar\\sigma^{+}\\sigma^{-}\\sum\\limits_{k}\\lambda_{k}\\left(b_k+b_k^{\\dag}\\right),\n\\end{split}\n\\end{equation}\nwhere $\\lambda_{k}$ is the exciton phonon mode coupling constant and $\\Omega(z,t) = - 2 \\vec{d}_{12}\\cdot\\hat{e}\\mathcal{E}(z,t)\/\\hbar$ is the Rabi frequency with transition dipole moment vector $\\vec{d}_{12}$. The detuning of the optical field with QD transition is defined as $\\delta = \\omega - \\omega_{12}$. We notice that the Hamiltonian contains an infinite sum over phonon modes. Keeping all order of exciton phonon interaction, we made a transformation in the polaron frame. The transformation rule for modified Hamiltonian is given by  $H^{'} = e^{P} H e^{-P}$ where the operator P = $\\sigma^{+}\\sigma^{-}\\sum_{k}\\lambda_{k}( b_{k}^{\\dagger} - b_{k})\/\\omega_{k}$. This transformation also helps us to separate the system Hamiltonian from the total Hamiltonian which is our primary interest. The transformed Hamiltonian is divided into system, bath and interaction part, which can be decompsed as $H^{\\prime}=H_s+H_b+H_{I}$, where\n\\begin{eqnarray}\nH_{s} &=& - \\hbar\\Delta\\sigma^{+}\\sigma^{-} + \\langle B\\rangle X_{g},\\\\\nH_b &=& \\hbar\\sum_k\\omega_k b_k^{\\dag}b_k,\\\\\n H_{I} &=& \\xi_gX_g+\\xi_uX_u,\n\\end{eqnarray}\n and $\\Delta$ is the redefined detuning by considering the polaron shift $\\sum_k\\lambda_{k}^2\/\\omega_k$.\nThe definition of phonon-modified system operators is given by \n\\begin{eqnarray}\nX_{g} &=& \\frac{\\hbar}{2}\\left(\\Omega(z,t)\\sigma^{+} + \\Omega^{*}(z,t)\\sigma^{-} \\right),\\\\\nX_{u} &=& \\frac{i\\hbar}{2}\\left(\\Omega(z,t)\\sigma^{+} - \\Omega^{*}(z,t)\\sigma^{-} \\right).\n\\end{eqnarray}\nThe phonon bath fluctuation operators are\n\\begin{eqnarray}\n \\xi_{g} &=& \\frac{1}{2}\\left( B_{+} + B_{-} -2\\langle B\\rangle  \\right),\\\\\n \\xi_{u} &=& \\frac{1}{2i}\\left( B_{+} - B_{-} \\right),\n \\end{eqnarray}\n\nwhere $B_{+}$ and $B_{-}$ are the coherent-state phonon  displacement operators. Explicitly, the phonon displacement operators in terms of the phonon mode operators can be written as\n\\begin{equation}\nB_{\\pm} =  \\exp\\left[{\\pm \\sum_{k} \\frac{\\lambda_{k}}{\\omega_{k}}\\left( b_{k}^{\\dagger} - b_{k}\\right)}\\right].\\nonumber \n\\end{equation}\nFrom this expression, it is clear that the exponential of the phonon operator takes care of all the higher order phonon processes.\nTherefore, the phonon displacement operator averaged over all closely spaced phonon modes at a temperature T, obeys the relation $\\langle B_{+}\\rangle =\\langle B_{-}\\rangle = \\langle B\\rangle$ where\n\\begin{equation}\n\\langle B\\rangle= \\text{exp}\\left[-\\frac{1}{2}\\int_0^{\\infty}d\\omega\\frac{J(\\omega)}{\\omega^2}\n\\coth\\left(\\frac{\\hbar\\omega}{2K_{B}T}\\right)\\right],\n\\end{equation}\nand $K_{B}$ is the Boltzman constant.\nThe phonon spectral density function $J(\\omega)= \\alpha_{p}\\omega^3\\exp[-\\omega^2\/2\\omega_b^2]$  describes longitudinal acoustic(LA) phonon coupling via a deformation potential \\cite{SPECT} for QD system, where the parameters $\\alpha_p$ and $\\omega_b$ are the electron-phonon coupling and cutoff frequency, respectively.\n\nNext we use the master equation(ME) approach to solve the polaron-transformed system Hamiltonian dynamics by considering the phonon bath as a perturbation. The Born-Markov approximation can be performed with respect to the polaron-transformed perturbation in the case of nonlinear excitation. Hence, the density matrix equation for the reduced system under Born-Markov approximation can be written as\n\\begin{equation}\n\\dot{\\rho} = \\frac{1}{i\\hbar}[H_s,\\rho]+{\\cal L}_{ph}\\rho\n+\\frac{\\gamma}{2}{\\cal L}[\\sigma^{-}]\\rho\n +\\frac{\\gamma_d}{2}{\\cal L}[\\sigma^{+}\\sigma^{-}]\\rho\\label{meq},\n\\end{equation}\nwhere $\\gamma$ is the spontaneous decay rate of the exciton state. \nIn addition, we incorporate the pure-dephasing process phenomenologically in ME with a decay rate $\\gamma_d$. This additional dephasing term explains the broadening of the zero-phonon line (ZPL) in QD with increasing temperatures \\cite{ZPL1,ZPL2}. The Lindblad superoperator $\\cal L$ is expressed as  ${\\cal L}[\\cal O]\\rho = \\text{2} {\\cal O} \\rho {\\cal} O^{\\dagger} - {\\cal O}^{\\dagger}{\\cal O} \\rho - \\rho \\cal O^{\\dagger}\\cal O $, under the operation of $\\cal O$ operator. The term ${\\cal L}_{ph}$ represents the effect of phonon bath on the system dynamics. Therefore the explicit form of ${\\cal L}_{ph}\\rho$ in terms of previously defined  system operators can be expressed as\n\\begin{eqnarray}\n{\\cal L}_{ph}\\rho &=& -\\frac{1}{\\hbar^2}\\int_0^{\\infty}d\\tau\\sum_{j=g,u}G_j(\\tau)[X_j(z,t),X_j(z,t,\\tau)\\rho(t)]~\\nonumber\\\\\n &+& H.c.,\n\\end{eqnarray}\nwhere $X_j(z,t,\\tau)=e^{-iH_s\\tau\/\\hbar}X_j(z,t)e^{iH_s\\tau\/\\hbar}$, and the polaron Green's functions are $G_g(\\tau)=\\langle B\\rangle^2\\{\\cosh\\left[\\phi(\\tau)\\right]-1\\}$ and $G_u(\\tau)=\\langle B\\rangle^2\\sinh[\\phi(\\tau)]$. \nThe phonon Green's functions depend on phonon correlation function given below \n\\begin{equation}\n\\phi(\\tau)=\\int_0^{\\infty}d\\omega\\frac{J(\\omega)}{\\omega^2}\n\\left[\\coth\\left(\\frac{\\hbar\\omega}{2K_{B}T}\\right)\\cos(\\omega\\tau)-i\\sin(\\omega\\tau)\\right].\\label{phi}\n\\end{equation}\nThe polaron ME formalism is not generally valid for arbitrary excitation strength and exciton phonon coupling. The validity of polaron ME is stated as \\cite{POLARON1}\n\\begin{equation}\n      \\left( \\frac{\\Omega}{\\omega_{b}} \\right)^{2} \\left(1 - \\langle B\\rangle^{4}\\right) \\ll 1 .\\label{valid}\n\\end{equation}\nIt is clear from the above equation that, at low temperatures $\\langle B\\rangle \\approx 1$ and $\\Omega\/\\omega_{b} < 1$ fulfil the above criteria. Hence, we restrict our calculation in the weak field regime satisfying $\\Omega\/\\omega_{b} < 1$   at a low phonon bath temperature.\\\\\n\nThe full polaron ME (\\ref{meq}) contains multiple commutator brackets and complex operator exponents, which require involved numerical treatment for studying time dynamics. We make some simplifications of the full ME by using various useful identities.  These reduce ME  into a simple analytical form with decay rates corresponding to the various phonon-induced processes. Though we have not made any approximation, simplified ME scales down the numerical computation efforts and gives better insight into the physical process. By expanding all the commutators in Eq.(\\ref{meq}) and rearranging using fermion operator identities, we get the simplified ME as\n\\begin{equation}\n\\begin{split}\n\\dot{\\rho} &= \\frac{1}{i\\hbar}[H_s,\\rho]+\\frac{\\gamma}{2}{\\cal L}[\\sigma^{-}]\\rho +\\frac{\\gamma_d}{2}{\\cal L}[\\sigma^{+}\\sigma^{-}]\\rho +\\frac{\\Gamma^{\\sigma^{+}}}{2}{\\cal L}[\\sigma^{+}]\\rho \\\\\n&+\\frac{\\Gamma^{\\sigma^{-}}}{2}{\\cal L}[\\sigma^{-}]\\rho -\\Gamma^{cd}(\\sigma^{+}\\rho\\sigma^{+} + \\sigma^{-}\\rho\\sigma^{-})\\\\\n&- i\\Gamma^{sd}(\\sigma^{+}\\rho\\sigma^{+} - \\sigma^{-}\\rho\\sigma^{-}) + i\\Delta^{\\sigma^{+}\\sigma^{-}}[\\sigma^{+}\\sigma^{-},\\rho]\\\\\n&-[i\\Gamma^{gu+}(\\sigma^{+}\\sigma^{-}\\rho\\sigma^{+} + \\sigma^{-}\\rho - \\sigma^{+}\\sigma^{-}\\rho\\sigma^{-})+H.c.]\\\\\n&-[\\Gamma^{gu-}(\\sigma^{+}\\sigma^{-}\\rho\\sigma^{+} - \\sigma^{-}\\rho + \\sigma^{+}\\sigma^{-}\\rho\\sigma^{-})+H.c.]\\label{smeq}.\n\\end{split}\n\\end{equation}\nThe phonon-induced decay rates are given by \n\\begin{comment}\n\\begin{align}\n\\Gamma^{\\sigma^{+} \/ \\sigma^{-}} &= \\frac{\\Omega_R(z,t)^2}{2}\\int_{0}^{\\infty}\\Bigg(\\operatorname{Re}\\bigg\\{(\\cosh(\\phi(\\tau))-1)f(z,t,\\tau) \\nonumber\\\\\n&+ \\sinh(\\phi(\\tau))\\cos(\\eta(z,t)\\tau)\\bigg\\} \\nonumber\\\\\n&\\mp \\operatorname{Im}\\left\\{(e^{\\phi(\\tau)}-1)\\frac{\\Delta\\sin(\\eta(z,t)\\tau)}{\\eta(z,t)}\\right\\}\\Bigg)\\,d\\tau, \\label{phdrate1}\\\\\n\\Gamma^\\mathrm{cd} &= \\frac{1}{2}\\int_{0}^{\\infty} \\operatorname{Re}\\bigg\\{\\Omega_{S}(z,t)\\sinh(\\phi(\\tau))\\cos(\\eta(z,t)\\tau) \\nonumber\\\\\n& - \\Omega_{S}(z,t)(\\cosh(\\phi(\\tau))-1) f(z,t,\\tau) \\nonumber\\\\\n& + \\Omega_{T}(z,t)(e^{-\\phi(\\tau)}-1) \\frac{\\Delta\\sin(\\eta(z,t)\\tau)}{\\eta(z,t)}\\bigg\\} d\\tau, \\label{gmcd}\\\\\n\\Gamma^\\mathrm{sd} &= \\frac{1}{2}\\int_{0}^{\\infty} \\operatorname{Re}\\bigg\\{\\Omega_{T}(z,t)\\sinh(\\phi(\\tau))\\cos(\\eta(z,t)\\tau)\\nonumber \\\\\n& - \\Omega_{T}(z,t)(\\cosh(\\phi(\\tau))-1) f(z,t,\\tau) \\nonumber\\\\\n& - \\Omega_{S}(z,t)(e^{-\\phi(\\tau)} - 1) \\frac{\\Delta\\sin(\\eta(z,t)\\tau)}{\\eta(z,t)}\\bigg\\} d\\tau, \\\\\n\\Delta^{\\sigma^{+}\\sigma^{-}} &= \\frac{\\Omega_R(z,t)^2}{2}\\int_{0}^{\\infty} \\operatorname{Re}\\bigg\\{(e^{\\phi(\\tau)} - 1) \\frac{\\Delta\\sin(\\eta(z,t)\\tau)}{\\eta(z,t)}\\bigg\\} d\\tau,\\label{delpm}\\\\\n\\Gamma^{\\mathrm{gu+}} &= \\frac{\\Omega_R(z,t)^2}{2}\\int_{0}^{\\infty}\\bigg\\{(\\cosh(\\phi(\\tau))-1)\\operatorname{Im}[\\langle B\\rangle\\Omega]h(z,t,\\tau) \\nonumber\\\\\n&+ \\sinh(\\phi(\\tau))\\frac{\\operatorname{Re}[\\langle B\\rangle\\Omega]\\sin(\\eta(z,t)\\tau)}{\\eta(z,t)}\\bigg\\}\\,d\\tau, \\\\\n\\Gamma^{\\mathrm{gu-}} &= \\frac{\\Omega_R(z,t)^2}{2}\\int_{0}^{\\infty}\\bigg\\{(\\cosh(\\phi(\\tau))-1)\\operatorname{Re}[\\langle B\\rangle\\Omega]h(z,t,\\tau) \\nonumber\\\\\n&- \\sinh(\\phi(\\tau))\\frac{\\operatorname{Im}[\\langle B\\rangle\\Omega]\\sin(\\eta(z,t)\\tau)}{\\eta(z,t)}\\bigg\\}\\,d\\tau,\\ \\label{phdrate2}\n\\end{align}\n\\end{comment}\n\n\\begin{align}\n\\Gamma^{\\sigma^{+} \/ \\sigma^{-}} &= \\frac{\\Omega_R(z,t)^2}{2}\\int_{0}^{\\infty}\\Bigg(\\operatorname{Re}\\bigg\\{(\\cosh(\\phi(\\tau))-1)f(z,t,\\tau) \\nonumber\\\\\n&+ \\sinh(\\phi(\\tau))\\cos(\\eta(z,t)\\tau)\\bigg\\} \\nonumber\\\\\n&\\mp \\operatorname{Im}\\left\\{(e^{\\phi(\\tau)}-1)\\frac{\\Delta\\sin(\\eta(z,t)\\tau)}{\\eta(z,t)}\\right\\}\\Bigg)\\,d\\tau, \\label{phdrate1}\\\\\n\\Gamma^\\mathrm{cd} &= \\frac{1}{2}\\int_{0}^{\\infty} \\operatorname{Re}\\bigg\\{\\Omega_{S}(z,t)\\sinh(\\phi(\\tau))\\cos(\\eta(z,t)\\tau) \\nonumber\\\\\n& - \\Omega_{S}(z,t)(\\cosh(\\phi(\\tau))-1) f(z,t,\\tau) \\nonumber\\\\\n& + \\Omega_{T}(z,t)(e^{-\\phi(\\tau)}-1) \\frac{\\Delta\\sin(\\eta(z,t)\\tau)}{\\eta(z,t)}\\bigg\\} d\\tau, \\label{gmcd}\\\\\n\\Gamma^\\mathrm{sd} &= \\frac{1}{2}\\int_{0}^{\\infty} \\operatorname{Re}\\bigg\\{\\Omega_{T}(z,t)\\sinh(\\phi(\\tau))\\cos(\\eta(z,t)\\tau)\\nonumber \\\\\n& - \\Omega_{T}(z,t)(\\cosh(\\phi(\\tau))-1) f(z,t,\\tau) \\nonumber\\\\\n& - \\Omega_{S}(z,t)(e^{-\\phi(\\tau)} - 1) \\frac{\\Delta\\sin(\\eta(z,t)\\tau)}{\\eta(z,t)}\\bigg\\} d\\tau,\n\\end{align}\n\\begin{align}\n\\Delta^{\\sigma^{+}\\sigma^{-}} &= \\frac{\\Omega_R(z,t)^2}{2}\\int_{0}^{\\infty} \\operatorname{Re}\\bigg\\{(e^{\\phi(\\tau)} - 1) \\frac{\\Delta\\sin(\\eta(z,t)\\tau)}{\\eta(z,t)}\\bigg\\} d\\tau,\\label{delpm}\\\\\n\\Gamma^{\\mathrm{gu+}} &= \\frac{\\Omega_R(z,t)^2}{2}\\int_{0}^{\\infty}\\bigg\\{(\\cosh(\\phi(\\tau))-1)\\operatorname{Im}[\\langle B\\rangle\\Omega]h(z,t,\\tau) \\nonumber\\\\\n&+ \\sinh(\\phi(\\tau))\\frac{\\operatorname{Re}[\\langle B\\rangle\\Omega]\\sin(\\eta(z,t)\\tau)}{\\eta(z,t)}\\bigg\\}\\,d\\tau, \\\\\n\\Gamma^{\\mathrm{gu-}} &= \\frac{\\Omega_R(z,t)^2}{2}\\int_{0}^{\\infty}\\bigg\\{(\\cosh(\\phi(\\tau))-1)\\operatorname{Re}[\\langle B\\rangle\\Omega]h(z,t,\\tau) \\nonumber\\\\\n&- \\sinh(\\phi(\\tau))\\frac{\\operatorname{Im}[\\langle B\\rangle\\Omega]\\sin(\\eta(z,t)\\tau)}{\\eta(z,t)}\\bigg\\}\\,d\\tau,\\ \\label{phdrate2}\n\\end{align}\n\n\n\n\\noindent where $f(z,t,\\tau) = (\\Delta^2\\cos(\\eta(z,t)\\tau)+\\Omega_R(z,t)^2)\/\\eta(z,t)^2$, $h(z,t,\\tau) = \\Delta(1 - \\cos(\\eta(z,t)\\tau))\/\\eta^{2}(z,t)$ and $\\eta(z,t) = \\sqrt{\\Omega_R(z,t)^2 + \\Delta^2}$ with the polaron-shifted Rabi frequency, $\\Omega_R(z,t) = \\langle B\\rangle\\vert\\Omega(z,t)\\vert$, $ \\Omega_{S}(z,t)=\\operatorname{Re}[\\langle B\\rangle\\Omega(z,t)]^{2}-\\operatorname{Im}[\\langle B\\rangle\\Omega(z,t)]^{2}$, $ \\Omega_{T}(z,t)= 2\\operatorname{Re}[\\langle B\\rangle\\Omega(z,t)]\\operatorname{Im}[\\langle B\\rangle\\Omega(z,t)]$.\n\nNext, we use Maxwell wave equation to describe the propagation dynamics of the electromagnetic field inside the QD medium\n\\begin{equation}\n\\bigg(\\nabla^{2} - \\frac{1}{c^{2}}\\frac{\\partial^{2}}{\\partial t^{2}}\\bigg)\\vec{E}(z,t) = \\mu_{0} \\frac{\\partial^{2}}{\\partial t^{2}} \\vec{P}(z,t)\\label{wave_eq}\n\\end{equation}\nwhere $\\mu_{0}$ is the permeability of free space. The induced polarisation $\\vec{P}(z,t)$ originates from the alignment of  the medium dipole in the presence of an applied field. The induced macroscopic polarisation can be written in terms of the density matrix element as \n\\begin{equation}\n\\vec{P}(z,t) = N \\int_{-\\infty}^{\\infty}\\left(\\vec{d}_{12}\\rho_{12}(\\Delta,z,t)e^{i(kz-\\omega t)} + c.c.\\right) g(\\Delta)d\\Delta,\n\\end{equation}\nwhere $N$ is the QD volume number density and $\\rho_{12}$ is induced coherence. The inhomogeneous level broadening function in the frequency domain is defined by $g(\\Delta)$.\nIn our calculation, the form of $g(\\Delta)$ is\n\\begin{equation}\ng(\\Delta) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{(\\Delta -\\Delta_{c})^{2}}{2\\sigma^{2}}},\n\\end{equation}\nwhere the standard deviation is $\\sigma$. The detuning between the applied field and the QD's central frequency is represented by $\\Delta_{c}$.\nBy applying slowly varying envelop approximation, one can cast inhomogeneous second order partial differential Eq.(\\ref{wave_eq})  to first order differential equation  as\n\\begin{equation}\n\\bigg(\\frac{\\partial}{\\partial z} + \\frac{1}{c}\\frac{\\partial}{\\partial t} \\bigg) \\Omega(z,t) = i\\hspace{1pt}\\eta \\int_{-\\infty}^{\\infty}\\rho_{12}(\\Delta,z,t)g(\\Delta)d\\Delta, \\label{prop_eq}\n\\end{equation}\nwhere the coupling constant $\\eta$ is defined by \n\\begin{equation}\n\\eta = - 3N\\lambda^{2}\\gamma\/4\\pi\n\\end{equation}\nand $\\lambda$ is the carrier wavelength of the QD transition. The self consistent solution of Eq.($\\ref{smeq}$) and ($\\ref{prop_eq}$) with proper initial conditions can display the spatiotemporal  evolution of the field inside the medium. Moreover the analytical solution of the coupled partial differential equation is known only for some special conditions, hence we adopted numerical integration of Eq.($\\ref{smeq}$) and ($\\ref{prop_eq}$) to depict the results. For numerical computation, a useful frame transformation $\\tau = t - z\/c$ and $\\zeta = z$ is needed which removes the explicit time variable from Eq.($\\ref{prop_eq}$), which now only depends on the one variable $\\zeta$.\n\n\n\\section{NUMERICAL RESULT}\n\\label{sec:result}\n\n\\subsection{Phonon-induced scattering rates}\n\nFirst we discuss various decay rates for the QD system with experimentally available parameter regions \\cite{PARA1,PARA2}.\nThe medium comprises InGaAs\/GaAs QDs with volume density $N = 5\\times 10^{20} \\text{m}^{-3}$ and a length of 1\\ mm. The central QD excitation energy is $\\hbar \\omega_{12}$ =1.3 eV with a Gaussian spectral distribution having FWHM of 23.5 meV. The QD is driven by the optical pulse at $\\zeta$ = 0 with a hyperbolic secant profile\n\\begin{equation}\n\\vert\\Omega(0,\\tau)\\vert = \\Omega_{0}\\hspace{1pt}\\text{sech}\\left(\\frac{\\tau-\\tau_{c}}{\\tau_{0}}\\right)\\label{rabi}\n\\end{equation}\nwhere $\\tau_{0}$, and $\\tau_{c}$ defines the width, and center of the pulse, respectively. For numerical computation, the amplitude and width of the pulse are taken to be $\\Omega_{0}$ = 0.2 meV and $\\tau_{0}$ = 6.373 ps.\nThe phonon bath temperature  T = 4.2 K gives $\\langle B \\rangle = 0.95 $. Other parameters are $\\alpha_{p} = 0.03\\ \\text{ps}^{2}$, $\\omega_{b} = 1\\ \\text{meV}$. The system under consideration has a relaxation rate $\\gamma =\\gamma_{d} = 2\\ \\mu\\text{eV}$(2 ns). In order to normalize all the system parameters to a dimensionless quantity we have chosen normalization frequency to be $\\gamma_{n}$ = 1 rad\/ps.\n\nIn Fig.(\\ref{Fig.2}), the color bar represents the variation of various phonon-induced scattering rates as a function of  detuning and time, both at normalised units along the $x$- and $y$-axis respectively. In the QD system, various phonon processes are connected with exciton transitions. In the case of ground state to exciton transition, phonon absorption occurs while in the opposite process, phonon emission occurs.\n\\begin{figure}[h]\n   \\includegraphics[scale=0.4]{fig_2} \n    \\caption{The variation of phonon-induced scattering rates with detuning and time of a QD at $\\zeta$ = 0 for the applied secant pulse in Eq.(\\ref{rabi}). a) Phonon-induced pumping rate $\\Gamma^{\\sigma^{+}}$[Eq.(\\ref{phdrate1})] b) Phonon-induced decay rate $\\Gamma^{\\sigma^{-}}$[Eq.(\\ref{phdrate1})] c) Phonon induced dephasing $\\Gamma^\\mathrm{cd}$[Eq.(\\ref{gmcd})] d) Phonon induced detuning $\\Delta^{\\sigma^{+}\\sigma^{-}}$[Eq.(\\ref{delpm})] for peak Rabi frequency $\\Omega_{0}$ = 0.2 meV, pulse width $\\tau_{0}$ = 6.373 ps and pulse center $\\gamma_{n}\\tau_{c} = 40$. The phonon bath temperature T = 4.2 K corresponds to $\\langle B \\rangle = 0.95 $ with spectral density function parameters $\\alpha_{p} = 0.03\\ \\text{ps}^{2}$, $\\omega_{b} = 1\\ \\text{meV}$.}\n   \\label{Fig.2}\n\\end{figure}\nNow we discuss the physical process associated with the phonon scattering rates $\\Gamma^{\\sigma^{+}}$ and $\\Gamma^{\\sigma^{-}}$. For positive detuning, the applied field frequency is larger than the QD transition frequency. Subsequently a  phonon generates with $\\Delta$ frequency in order to make a resonant QD transition. These emitted phonons develop an incoherent excitation in the system referred by the $\\Gamma^{\\sigma^{+}}$. Oppositely for negative detuning, the applied field frequency is smaller than the QD transition frequency,  and a resonant QD transition is possible only  when some phonon of frequency $\\Delta$ will be absorbed from the bath. With this mechanism, QD exciton to ground state decay enhances the radiation which is represented by the $\\Gamma^{\\sigma^{-}}$. This low-temperature asymmetry is clearly visible in Fig.$\\ref{Fig.2}$(a) and $\\ref{Fig.2}$(b). At higher temperatures, this  asymmetry gets destroyed, and  both rates overlap and are centered at $\\Delta$ = 0. Fig.$\\ref{Fig.2}$(c) shows the variation of $\\Gamma^{cd}$ which is only present in the off-diagonal density matrix element and responsible for the additional dephasing in the system dynamics. The additional detuning $\\Delta^{\\sigma^{+}\\sigma^{-}}$ from the simplified master equation plotted in Fig.$\\ref{Fig.2}$(d), shows a very tiny value compared to the system detuning $\\Delta$. We also notice that the sign of $\\Delta^{\\sigma^{+}\\sigma^{-}}$ changes according to the system detuning $\\Delta$. It is important to keep in mind that we display the variation along the $y$-axis around $\\gamma_{n}\\tau$ =40, which is the centre of the pulse with the secant profile.\n\n\\subsection{Pulse area theorem}\nIt is well know from Beer's law,  that a weak pulse gets absorbed inside the medium due to the presence of opacity at the resonance condition. However, McCall and Hahn showed that some specific envelope pulse shape remains intact for a long distance without absorption, even at resonance\\cite{McHa1, McHa2}. Inspired of  this phenomena, we have taken into account of a time-varying pulse whose envelope shape is stated in the Eq.(\\ref{rabi}). The area $\\Theta(z)$ enclosed by its hyperbolic envelope shape is defined as\n\\begin{equation}\n\\Theta(z) = \\int_{-\\infty}^{+\\infty}\\Omega(z,t^{'})dt^{'}.\n\\end{equation}\nTo see the spatial variation of the pulse area, we integrate over time and detuning in Eq.($\\ref{prop_eq}$).  \nThe evolution of the pulse area $\\Theta(z)$ during its propagation in a two-level absorbing QD medium is given by\n\\begin{equation}\n\\frac{d\\Theta(z)}{dz} = -\\frac{\\alpha}{2} \\sin\\Theta(z)\\label{paeq}\n\\end{equation}\nwhere $\\alpha$ is the optical extinction per unit length. The optical extinction depends on the various system parameters as $\\alpha = 2\\pi\\eta g(0)$.  The solution of the Eq.(\\ref{paeq}) is\n\\begin{equation}\n \\tan \\frac{\\Theta(z)}{2} = \\tan \\frac{\\Theta(0)}{2} e^{-\\alpha z\/2},\\label{pasol}\n\\end{equation}\n where $\\Theta(0)$ is the pulse area at $z$ =0. From the above expression, we find that $\\Theta(z) = 2n\\pi$ is the stable solution, whereas $\\Theta(z) = (2n+1)\\pi$ is the unstable. The pulse area of the given envelope as stated in Eq.(\\ref{rabi}) is $\\Theta(0) = \\pi\\Omega_{0}\\tau_{0}$. Thus, the envelope with amplitude $\\Omega_{0} = 2\/\\tau_{0}$ gives  2$\\pi$ area pulse. This envelope shape remains preserve for the long propagation distance even though it interacts resonantly  with the medium.\n\\begin{figure}[h]\n   \\includegraphics[scale=0.4]{fig_3}\n    \\caption{Evolution of the pulse area($\\Theta$) as a function of propagation distance $\\zeta$ started with $2\\pi$ sech-type pulse for different temperatures. The applied pulse has a width of $\\tau_{0}$ = 6.373 ps and centered at $\\gamma_{n}\\tau_{c} = 40$. The system under consideration without phonon bath(black) and with phonon bath maintaining temperature T = 4.2K(red), 10K(blue), 20K(green) with electron phonon coupling $\\alpha_{p} = 0.03\\ \\text{ps}^{2}$ and cut off frequency $\\omega_{b} = 1\\ \\text{meV}$.The central QD detuning $\\Delta_{c}$ = 0 with spontaneous decay and the pure dephasing rate $\\gamma =\\gamma_{d} = 2\\ \\mu\\text{eV}$(2 ns).The optical extinction per unit length $\\alpha$ = 10 mm$^{-1}$. The inset figure shows the stability of the pulse area higher than $2\\pi$ for different phonon bath temperatures.}\n    \\label{Fig.3}\n\\end{figure}\nFig.(\\ref{Fig.3}) exhibits the variation of pulse area with the propagation distance inside the QD medium. It is evident from this figure that the propagation dynamics of 2$\\pi$ area pulse through the medium of length $L$ has negligible loss in pulse area. In the absence of phonon(black line) interaction, the system behaves identical to the atomic system and hence follows $\\Theta \\approx 2\\pi(1 - \\tau_{0}\/T_{2}^{'})$ reported earlier by McCall and Hahn \\cite{McHa2}. The loss in pulse area comes from the finite lifetime $T_{2}^{'}$ of the QD which is inversely proportional to $\\gamma_{d}$. Ideally, the pulse will retain initial pulse area for an arbitrary distance in absence of decay and decoherence. However, in presence of phonon contribution, we have noticed the pulse area gets enhanced by a small amount. The amount of raise in the  pulse area linearly depends on the bath temperature as indicated in Fig.($\\ref{Fig.3}$).  This effect can be explained by carefully examing the definition of an effective Rabi frequency $\\Omega_R(z,t) = \\langle B\\rangle\\vert\\Omega(z,t)\\vert$ where $\\langle B\\rangle$ is dependent on the bath temperatures. The inset of Fig.(\\ref{Fig.3}) illustrate the convergence of the pulse area shifted from the $2\\pi$ value at different temperatures.\n\\begin{figure}[h]\n   \\includegraphics[scale=0.4]{fig_4}\n    \\caption{The real(black) and imaginary(red) part of the coherence $\\rho_{12}$ of a single QD at different times for a $2\\pi$ sech-type short pulse with pulse center at $\\gamma_{n}\\tau_{c}$ = 40 as a function of detuning. The pulse has a width $\\tau_{0}$ = 6.373 ps. Corresponding phonon bath parameters are T = 4.2K, $\\alpha_{p} = 0.03\\ \\text{ps}^{2}$, $\\omega_{b} = 1\\ \\text{meV}$. Considered QD relaxation rates are $\\gamma =\\gamma_{d} = 2\\ \\mu\\text{eV}$(2 ns). }\n    \\label{Fig.4}\n\\end{figure}\nTo explain the behavior of Fig.(\\ref{Fig.3}), we study the absorption and dispersion properties of the medium as a function of detuning at various time intervals of the pulse. Fig.(\\ref{Fig.4}) delineates the physical process behind the dispersion and absorption. We assume all the population in the ground state, before the leading edge of the pulse reaches the medium. The peak of incident pulse enters inside the medium at $\\gamma_{n}\\tau_{c}$ = 40. It is clear from Fig.\\ref{Fig.4}(a) that most of the leading edge pulse energy gets absorbed by the ground state population and the population goes to the excited state. Hence the medium shows maximum absorption at $\\gamma_{n}\\tau$ = 30, hence elucidating the absorption phenomenon at resonance. Simultaneously, the nature of the dispersion curve is anomalous as previously reported \\cite{BOYD}. The anomalous dispersion accompanied fast velocity is completely prohibited due to huge absorption at the resonance condition. The medium becomes saturated as the centre of the pulse enters the medium; consequently, the medium turns less absorbent to the pulse.  Nonetheless, a tiny absorption peak still exists at the resonance condition due to the presence of various decay processes of the medium as indicated by Fig.\\ref{Fig.4}(b).  Therefore, the excited state gets populated during the passage of the leading edge pulse. This population can leave the excited state and return to the ground by stimulated emission in the presence of the trailing edge of the pulse. As a results, a gain can be experienced by the incident pulse at $\\gamma_{n}\\tau$ = 50 as revealed in Fig.\\ref{Fig.4}(c). From these three panels, we can conclude that the leading edge of the pulse gets absorbed by the medium, while the tailing edge of the pulse experiences gain. Towards the trailing end of the pulse, the dispersive nature of the medium changes from anomalous to normal, as shown in Fig.\\ref{Fig.4}(d). The positive slope of the dispersion curve lead to slow group velocity that started at $\\gamma_{n}\\tau$ = 60 shown in Fig.\\ref{Fig.4}(d). Fig.\\ref{Fig.4}(d)  to Fig.\\ref{Fig.4}(f) indicate that the optical pulse regeneration process is completed due to the medium-assisted gain; hence, the pulse shape remains preserved. This is the explanation of the underpinning mechanism behind SIT.\n\\begin{figure}[h]\n   \\includegraphics[scale=0.4]{fig_5}\n    \\caption{The variation of excited state population with input pulse area at resonance condition $\\Delta_{c}$ = 0. The system and bath parameters are $\\tau_{0}$ = 6.373 ps, $\\gamma_{n}\\tau_{c}$ = 40, T = 4.2K, $\\alpha_{p} = 0.03\\ \\text{ps}^{2}$, $\\omega_{b} = 1\\ \\text{meV}$, $\\gamma =\\gamma_{d} = 2\\ \\mu\\text{eV}$(2 ns).}\n    \\label{Fig.5}\n\\end{figure}\nThe claim of the above physical mechanism can be supported by studying population dynamics at the excited state. For this purpose, we have plotted the excited state population as a function of the pulse area in Fig.(\\ref{Fig.5}). A noticeable population redistribution among the levels is feasible within few widths of incident pulse wherein intensity is appreciable. As soon as the pulse intensity diminishes at the trailing end, spontaneous emission takes care of depletion of the excited state population. This leads to vanishing population at the excited state after a sufficiently long time from the pulse centre. As a consequence, it is crucial to decide the observation time of the QD population. Hence, we display the exciton population at just the end of the pulse $\\gamma_{n}\\tau = 60$, to capture the outcome of the pulse. It is clear from Fig.(\\ref{Fig.5}) that the excited state population shows a decaying Rabi oscillation kind of behaviour. It is also confirmed that the population never fully transferred to the excited state or fully returned to the ground state for any pulse area, indicating to non-constant phonon induced decay and gain process involved in the system. The decaying features of the local population maximum can be justified by the examining the photon and phonon induced decay rates. The various phonon decay  rates are given in Eq.(\\ref{phdrate1})-(\\ref{phdrate2}) where increasing incident pulse amplitude $\\Omega(z,t)$ results in the enhancement of these decay rates.  This field amplitude dependent phonon decay together with constant photon decay can explain the gradual decay of the population local maxima. On the contrary, the dip of local minima increases due to the presence of phonon induced gain processes $\\Gamma^{\\sigma+}$ as suggested in Eq.(\\ref{phdrate1}).  The local maximum and minimum of the exciton population are located respectively near odd and even integer multiples of $\\pi$ pulse area. The maxima signifies the pulse absorption by the medium, resulting in population inversion. Similarly, minima manifests the transparency of the medium. Thus, the leading edge of the pulse excite the population whereas the tailing edge assists in stimulated emission leaving the population in the ground state of the medium. It is evident that only even integer multiples of $\\pi$ pulse can propagate through the medium without absorption that is consistent with the pulse area theorem. That the local maxima and minima of exciton population never match exactly with the integer value can be figured out later by investigating pulse propagation dynamics. Previously, we found the stable pulse area is higher than $2\\pi$ as shown in Fig.($\\ref{Fig.3}$) which also agrees with the above observation.  Therefore, the analysis of coherence and population ensures us that SIT phenomena can be accomplished in the QD medium.\n\\begin{figure}[h]\n   \\includegraphics[scale=0.4]{fig_6}\n    \\caption{The Rabi frequency normalized with the input peak value is  plotted against retarded time at different propagation distances inside the medium at resonance condition $\\Delta_{c}$ = 0. The input pulse has the following parameters $\\Theta(0) = 2\\pi$, $\\tau_{0}$ = 6.373 ps, $\\gamma_{n}\\tau_{c}$ = 40. Other parameters are T = 4.2K, $\\alpha_{p} = 0.03\\ \\text{ps}^{2}$, $\\omega_{b} = 1\\ \\text{meV}$, $\\gamma =\\gamma_{d} = 2\\ \\mu\\text{eV}$(2 ns).}\n    \\label{Fig.7}\n \\end{figure}   \n\\subsection{Self Induced Transparency}\nA homogenous QD medium with length $1$\\ mm is taken into account for studying spatio-temporal evolution of hyperbolic secant optical pulse. To achieve a stable pulse propagation, we have chosen the initial pulse area to be 2$\\pi$. Fig.$\\ref{Fig.7}$ confirms the area theorem by showing a stable optical pulse propagation for a longer distance. However, the pulse shape at larger distances has noticed some distortion and absorption.\nFig.$\\ref{Fig.7}$ also indicates that the pulse's peak value gradually decreases by increasing the propagation distance. This suggests a finite absorption in the QD medium that prohibited complete transparency in the system.  In particular, the statement agrees well  with the small absorption peak at resonance in the absorption profile shown in Fig.$\\ref{Fig.4}$b.\n\\begin{figure}[h]\n   \\includegraphics[scale=0.4]{fig_7}\n    \\caption{The Rabi frequency normalized with the individual peak value is  plotted against retarded time at different propagation distances inside the medium at resonance condition $\\Delta_{c}$ = 0. All the other parameters are the same as Fig.(\\ref{Fig.7}).}\n    \\label{Fig.8}\n\\end{figure}\nFigure \\ref{Fig.8} displays the individually normalized pulse for different propagation distances. Inspection says that the input pulse experiences delay and a little broadening during the propagation through the medium. The sole reason behind the pulse broadening is the dispersive nature of the system. In the frequency domain, a temporal pulse can be treated as a linear superposition of many travelling plane waves with different frequencies. These individual frequency waves gather different phases and move with varying velocities during the pulse propagation in a dispersive medium. Therefore the pulse gets broader as the leading part(low frequency) moves faster, and the tailing end(high frequency) goes slower. In the QD system, the pure dephasing rate is also responsible for this broadening as it destroys the coherence.\nFrom Fig.$\\ref{Fig.8}$, a distinct peak shift is observed while optical pulse propagating through the medium. This peak shift arises because of normal dispersive medium that induced slow group velocity of the optical pulse inside the medium.\nWe adopt the analytical expression of time delay in the ideal case by considering $\\sigma \\gg 1\/\\tau_{0}$ reported earlier\\cite{RAHMAN}. The  analytical expression for time delay found to be $\\gamma_{n}\\tau_{d} = \\alpha L \\gamma_{n}\\tau_{0}\/4$. Here the absorption coefficient $\\alpha$ is approximately 10 mm$^{-1}$ calculated from the chosen parameters. Therefore the calculated  analytical time delay $\\gamma_{n}\\tau_{d}\\approx$ 15 shows excellent agreement with the numerical result. Recalling the pulse area theorem again, we observe that the pulse area is almost constant throughout the propagation near $2\\pi$. The result is consistent because as the pulse amplitude decreases, the pulse width increases, maintaining the constant area under the curve. Therefore an absorbing QD medium can exhibit the SIT phenomena at low temperatures.\n\\subsection{Phonon bath parameter dependence on SIT }\nIn the simplified master equation ($\\ref{smeq}$), various phonon-induced scattering rates depend on both the system and bath parameters. Hence it is crucial to study the effect of phonon bath on the SIT dynamics. The phonon contribution comes to the picture in two ways; one from the reduced Rabi frequency, which depends on the $\\langle B \\rangle$ and the other is the phonon-induced scattering rates connected with the phonon spectral density function.\n\\begin{figure}[h]\n   \\includegraphics[scale=0.4]{fig_8}\n    \\caption{The plot of Rabi frequency envelope with time at a propagation distance $\\zeta\\eta\/\\gamma_{n}$ = 50 for different phonon bath temperatures at resonance condition $\\Delta_{c}$ = 0. The common parameters are  $\\Theta(0) = 2\\pi$, $\\tau_{0}$ = 6.373 ps, $\\gamma_{n}\\tau_{c}$ = 40, $\\alpha_{p} = 0.03\\ \\text{ps}^{2}$, $\\omega_{b} = 1\\ \\text{meV}$, $\\gamma =\\gamma_{d} = 2\\ \\mu\\text{eV}$(2 ns). The figure display four different configurations, system without a phonon bath (black) and with a phonon bath at a temperature T = 4.2K(red), 10K(blue), 20K(green).}\n    \\label{Fig.9}\n\\end{figure}\nTherefore increasing phonon bath temperatures reduces the value of $\\langle B \\rangle$ and $\\hbar\\omega\/2K_{b}T$ present in the expression of $\\phi(\\tau)$ given in the Eq.($\\ref{phi}$). Consequently, effective coupling between QD and applied field gets reduced, but the phonon-induced decay rates get enhanced. From Fig.($\\ref{Fig.9}$), we notice that the final pulse shape experiences more deformation for higher temperatures. The peak of the output pulse is also very much reduced for the higher temperature T =20 K. Therefore, the bath temperature should be minimised to see the SIT in the QD medium.\n\\begin{figure}[h]\n   \\includegraphics[scale=0.4]{fig_9}\n    \\caption{The Rabi frequency envelop with time at a propagation distance $\\zeta\\eta\/\\gamma_{n}$ = 50 for different electron-phonon coupling strength $\\alpha_{p}$ at resonance condition $\\Delta_{c}$ = 0. All the parameters are same as Fig.(\\ref{Fig.9}) except T = 4.2K and various electron-phonon coupling $\\alpha_{p} = 0.03\\ \\text{ps}^{2}$(red), 0.06\\ $\\text{ps}^{2}$(blue), 0.12\\ $\\text{ps}^{2}$(green).}\n    \\label{Fig.10}\n\\end{figure}\nAnother controlling factor of the SIT is the interaction strength between the QD and the phonon bath. So the increment of system-bath coupling leads to the reduction of the coherence in the system. This statement is understandable by looking at the phonon correlation function shown in Eq.($\\ref{phi}$). Thus the final pulse shape for the equal propagation distances is significantly modified by the electron-phonon coupling constant, as shown in Fig.($\\ref{Fig.10}$). Therefore we also have to ensure that the QD bath interacts weakly to get SIT phenomena in the QD medium.\n\\subsection{Higher pulse area and pulse breakup}\nFinally, we discuss the behaviour of a pulse propagating through the absorbing QD medium with a higher pulse area than $2\\pi$. Therefore we consider the next stable pulse area solution 4$\\pi$ for further investigation. The numerical result of the pulse propagation in both space and time is shown in Fig.($\\ref{Fig.11}$). Unlike the 2$\\pi$ pulse case, here, the initial pulse breaks into two pulses as it travels through the medium. This phenomenon is also well explained by the pulse area theorem where $2n\\pi$ pulse is split into $n$ number of 2$\\pi$ pulses. Surprisingly, the initial pulse breakup into two pulses is not identical in shape. One pulse gets sharper, and the other gets broader in the time domain and adjusts the peak value such that the area under the curve is 2$\\pi$. The broader pulse component shows a prominent time delay, whereas the sharper pulse component propagates with a tiny time delay. As a result, total pulse area is constant throughout the propagation distance near 4$\\pi$.\n\\begin{figure}[h]\n   \\includegraphics[scale=0.4]{fig_10}\n    \\caption{The propagation dynamics of a 4$\\pi$ area pulse in an absorbing QD medium as a function of both space and time at resonance condition $\\Delta_{c} = 0$. All other parameters are same as Fig.(\\ref{Fig.7}).}\n    \\label{Fig.11}\n\\end{figure}\n\\section{CONCLUSIONS}\n\\label{sec:conclud}\nWe have investigated the SIT phenomena in an inhomogeneously broadened semiconductor QD medium. In our model, we have included the effect of phonon in the total Hamiltonian to describe the modified optical properties of QD in the presence of a thermal environment. We then adopted the polaron ME formalism to analytically derive the simplified ME with various phonon-induced decay rates. These phonon-induced scattering rates are plotted against detuning and time, which verify the presence of low-temperature asymmetry of phonon-induced pumping and decay in our system. We solve numerically the density matrix equation and Maxwell equation selfconsistently with suitable parameters. We observe that stable pulse propagation is possible in the QD medium with pulse area slightly higher  than 2$\\pi$, depending on the phonon bath temperature. The physical mechanism of the SIT is clearly understood by analyzing the absorption and dispersion of the medium. The leading edge of the pulse gets absorbed by the medium, whereas the tailing edge of the pulse experience gain, hence the pulse shape remains intact and propagate through  medium with short length. However, for longer propagation distances, we find that even though the pulse propagation through the medium is possible, the propagating pulse gets absorbed and broadened. The final pulse shape is preserved on exiting the medium. Increasing the phonon bath temperature and coupling produce more deformation in the final pulse shape, as it destroys the coherence in the system. Finally, we explore the propagation of a 4$\\pi$ pulse in the QD medium, which shows prominent pulse breakup phenomena reported earlier in the literature.\nTherefore our investigation ensures that a short pulse can propagate through the considered QD medium with a tiny change in shape. Hence, this work may have potential applications in quantum communication, quantum information, and mode-locking.\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{RED by PGD attack: Performing PGD back to the true class} \\label{sec:naive_red}\n\nA naive approach to reverse engineer the adversarial perturbation is using the target PGD attack to revert the label back to the groundtruth. However, this requires additional assumptions. \nFirst, since PGD is a test-time deterministic optimization approach for perturbation generation, its targeted implementation requires the true class of the adversarial example, which could be unknown at testing time. What is more, one has to pre-define the perturbation budget $\\epsilon$ for PGD. This value is also unknown. \nSecond, performing PGD back to the true class might not exactly recover the ground-truth adversarial perturbations. By contrast, its RED counterpart could be over-perturbed. To make it more convincing, we applied the target $l_\\infty$ PGD attack method to adversarial examples generated by PGD (assuming true class, victim model, and attack budget are known). We tried various PGD settings ($\\text{PGD10}_{\\epsilon=10\/255}$ refers to PGD attack using 10 steps and $\\epsilon=10\/255$). Eventually, we compare these results to our CDD-RED method in Table \\ref{table:PGD_back}. \n\n\nGiven that the average reconstruction error between $\\mathbf x$ and $\\mathbf x'$ is 20.60, we can see from Table \\ref{table:PGD_back} that PGD attacks further enlarge the distortion from the clean data. Although PGD attacks can achieve high accuracy after reverting the adversarial data back to their true labels, the resulting perturbation estimate is far from the ground-truth in terms of their prediction alignment. We can tell from the low $\\text{PA}_{\\text{adv}}$  by PGD methods that $\\mathbf x_{\\mathrm {RED}}'$ does not align with the input $\\mathbf x'$ at all.\n\n\n\\begin{table}[H]\n\\begin{center}\n\\caption{The performance comparison among DO, DS, and {\\text{CDD-RED}} on the CIDAR-10 dataset.} \\label{table:PGD_back}\n{\n\\begin{tabular}{ccccc}\n\\toprule\\hline\n                                       & PGD10{$\\epsilon_{20\/255}$} & PGD10{$\\epsilon_{10\/255}$}            & PGD20{$\\epsilon_{20\/255}$}            & CDD-RED                                                \\\\ \\hline\n$d(\\mathbf x, \\mathbf x_\\mathrm{RED})$ & 27.63                                     & 22.67                                                 & 27.53                                                 & \\textbf{11.73}                                                  \\\\ \\hline\n$\\text{\\text{PA}}_{\\mathrm{benign}}$         & 96.20\\%                                & 82.60\\%                                               & \\textbf{99.80\\%}                                               & 83.20\\%                                                \\\\ \\hline\n$\\text{\\text{PA}}_{\\mathrm{adv}}$            & 6.20\\%                                    & 7.20\\% &  4.80\\% & \\textbf{97.40\\%}\\\\ \\hline\\bottomrule\n\\end{tabular}}\n\\end{center}\n\\end{table}\n\n\\section{Dataset Details.} \\label{sec:dataset_details}\n\nThe training and testing dataset is composed of three attack methods including  PGD \\cite{madry2017towards}, FGSM  \\cite{Goodfellow2015explaining}, and CW attack \\cite{carlini2017towards}, applied to \\textbf{5 models} including pre-trained ResNet18 (Res18), Resnet50 (Res50) \\cite{DBLP:journals\/corr\/HeZRS15}, VGG16, VGG19, and InceptionV3 (IncV3) \\cite{DBLP:journals\/corr\/SzegedyVISW15}. By default, PGD attack and FGSM attack are bounded by $\\ell_\\infty$-norm constraint and CW attack is bounded by $\\ell_2$-norm. The range of the perturbation strength $\\epsilon$ for PGD attack and FGSM attack are $[1\/255,40\/255)$ and $[1\/255,20\/255)$, respectively. As for CW attack, the adversary's confidence parameter $k$ is uniformly sampled from from $[1,20]$.\nOne attack method is applied to one victim model to obtain \\textbf{3K successfully attacked images}. As a consequence, 45K ($3\\times5\\times3$K) adversarial images are generated in total: 37.5K for training and 7.5K for validating. \nThe testing set contains 28K adversarial images generated with the same attack method \\& victim model.\n\n\\section{performance on more   attack types} \\label{sec:appendix_unseen}\n\n{We show more evaluations of the RED approaches on unforeseen attacks during training. The denoisers are all trained on the training dataset containing adversarial examples generated on the ImageNet dataset, as in Appendix \\ref{sec:dataset_details}. The test data includes adversarial examples generated on the CIFAR-10 dataset in \\ref{sec:cifar10}, Wasserstein minimized attackers in \\ref{sec:W_attack}, and attacks on smoothed classifiers in \\ref{sec:attack_against_smoothed_classifiers}.}\n\n\\subsection{{Performance on CIFAR-10 dataset}} \\label{sec:cifar10}\n\n{\nWe further evaluate the performance of the RED approaches on the adversarial examples generated on the CIFAR-10 dataset. As the denoiser is input agnostic, we directly test the denoiser trained on adversarial examples generated on the ImageNet dataset. Here we consider the $10$-step PGD-$l_{\\inf}$ attack generation method with the perturbation radius $\\epsilon = 8\/255$. And these examples are not seen during our training. As shown in the Table \\ref{table:cifar10_result}, the proposed {\\text{CDD-RED}} method provides the best $\\text{PA}_{\\text{clean}}$ and $\\text{PA}_{\\text{adv}}$ with a slightly larger $d(\\mathbf x, \\mathbf x_\\mathrm{RED})$ than DO. This is not surprising as DO focuses only on the pixel-level denoising error metric. However, as illustrated in Sec.\\,\\ref{sec:evaluation_metric}, the other metric like PA also plays a key role in evaluating the RED performance.\n}\n\n\\begin{table}[H]\n\\begin{center}\n\\caption{{The performance comparison among DO, DS, and {\\text{CDD-RED}} on the CIDAR-10 dataset.}} \\label{table:cifar10_result}\n{\n\\begin{tabular}{c|c|c|c}\n\\toprule\\hline\n                                       & DO      & DS      & \\text{CDD-RED} \\\\ \\hline\n$d(\\mathbf x, \\mathbf x_\\mathrm{RED})$ & \\textbf{0.94}    & 4.50   & 1.52                 \\\\ \\hline\n$\\text{\\text{PA}}_{\\mathrm{benign}}$         & 9.90\\% & 71.75\\% & \\textbf{71.80\\%}               \\\\ \\hline\n$\\text{\\text{PA}}_{\\mathrm{adv}}$            & 92.55\\% & 89.70\\% & \\textbf{99.55\\%}               \\\\ \\hline\\bottomrule\n\\end{tabular}}\n\\end{center}\n\\end{table}\n\n\\subsection{{Performance on Wasserstein minimized attackers}} \\label{sec:W_attack}\n\n\n{\nWe further show the performance on Wasserstein minimized attackers, which is an unseen attack type during training. The adversarial examples are generated on the ImageNet sub-dataset using Wasserstein ball. \nWe follow the same setting from  \\cite{wong2019wasserstein}, where the attack radius $\\epsilon$ is 0.1 and the maximum iteration is 400 under $l_\\infty$ norm inside Wasserstein ball. \nThe results are shown in Table \\ref{table:w_attack}.\nAs we can see, Wasserstein attack is a more challenging attack type for RED than the $l_p$ attack types considered in the paper, justified by the lower prediction alignement $\\text{PA}_\\text{benign}$ across all methods. \nThis implies a possible limitation of supervised training over ($l_2$ or $l_\\infty$) attacks. One simple solution is to expand the training dataset using more diversified attacks (including Wasserstein attacks). However, we believe that the further improvement of the generalization ability of RED deserves a more careful study in the future, e.g., an extension from the supervised learning paradigm to the (self-supervised) pre-training and finetuning paradigm.\n}\n\n\n\\begin{table}[H]\n\\begin{center}\n\\caption{{The performance comparison among DO, DS, and {\\text{CDD-RED}} on  Wasserstein minimized attackers.}} \\label{table:w_attack}\n{\n\\begin{tabular}{c|c|c|c}\n\\toprule\\hline\n                                       & DO      & DS      & \\text{CDD-RED} \\\\ \\hline\n$d(\\mathbf x, \\mathbf x_\\mathrm{RED})$ & \\textbf{9.79}    & 17.38   & 11.66                 \\\\ \\hline\n$\\text{\\text{PA}}_{\\mathrm{benign}}$         & 92.50\\%\t\t & 96.20\\% & \\textbf{97.50\\%}               \\\\ \\hline\n$\\text{\\text{PA}}_{\\mathrm{adv}}$            & 35.00\\% & \t37.10\\%\t& \\textbf{37.50\\%}                \\\\ \\hline\\bottomrule\n\\end{tabular}}\n\\end{center}\n\\end{table}\n\n\n\\subsection{{Performance on attacks against smoothed classifiers}} \\label{sec:attack_against_smoothed_classifiers}\n\n\n{\nWe further show the performance on the attack against smoothed classifiers, which is an unseen attack type during training. A smoothed classifier predicts any input $x$ using the majority vote based on   randomly perturbed inputs $\\mathcal{N}(x,\\sigma^2I)$   \\cite{cohen2019certified}. Here we consider the 10-step PGD-$\\ell_\\infty$ attack generation method with the perturbation radius $\\epsilon=20\/255$, and $\\sigma=0.25$ for smoothing. As shown in Table \\ref{table:attack_smoothed_clf}, the proposed CDD-RED method provides the best $\\text{PA}_\\text{clean}$ and $\\text{PA}_\\text{adv}$ with a slightly larger $d(\\mathbf x, \\mathbf x_\\mathrm{RED})$ than DO. \n}\n\n\\begin{table}[H]\n\\begin{center}\n\\caption{{The performance comparison among DO, DS, and {\\text{CDD-RED}} on the PGD attack against smoothed classifiers.}} \\label{table:attack_smoothed_clf}\n{\n\\begin{tabular}{c|c|c|c}\n\\toprule\\hline\n                                       & DO      & DS      & \\text{CDD-RED} \\\\ \\hline\n$d(\\mathbf x, \\mathbf x_\\mathrm{RED})$ & \\textbf{15.53}\t&22.42&\t15.89                   \\\\ \\hline\n$\\text{\\text{PA}}_{\\mathrm{benign}}$         & 68.13\\%&\t70.88\\%\t& \\textbf{76.10\\%}               \\\\ \\hline\n$\\text{\\text{PA}}_{\\mathrm{adv}}$            & 58.24\\%&\t58.79\\%\t& \\textbf{61.54\\%}               \\\\ \\hline\\bottomrule\n\\end{tabular}}\n\\end{center}\n\\end{table}\n\n\\section{{Computation cost of RED}} \\label{sec:cost}\n{We measure the computation cost on a single RTX Titan GPU. The inference time for DO, DS, and {\\text{CDD-RED}} is similar as they use the same denoiser architecture. For the training cost, the maximum training epoch for each method is set as 300. The average GPU time (in seconds) of one epoch for DO, DS, and {\\text{CDD-RED}} is 850, 1180, and 2098, respectively. It is not surprising that {\\text{CDD-RED}} is conducted over a more complex RED objective. Yet, the denoiser only needs to be trained once to reverse-engineer a wide variety of adversarial perturbations, including those unseen attacks during the training.}\n\n\\section{{Ablation Studies on {\\text{CDD-RED}}}} \\label{sec:ablation}\n\n{In this section, we present additional experiment results using the proposed {\\text{CDD-RED}} method for reverse engineering of deception (RED). We will study the effect of the following model\/parameter choice on the performance of {\\text{CDD-RED}}: 1) pretrained classifier $\\hat{f}$ for PA regularization, 2) data augmentation strategy  $\\check{\\mathcal T}$     for PA regularization, and 3) regularization parameter $\\lambda$ that strikes a balance between the pixel-level reconstruction error and PA in \\eqref{eq: overall_DeRED}.\nRecall that the {\\text{CDD-RED}} method  in the main paper sets $\\hat{f}$ as VGG19, $\\check{\\mathcal T} = \\{ t \\in \\mathcal T\\,| \\,  \\hat{F}(t(\\mathbf{x})) = \\hat{F}(\\mathbf{x}),  \\hat{F}(t(\\mathbf{x}^{\\prime})) = \\hat{F}(\\mathbf{x}^{\\prime}) \\ \\}$, and $\\lambda=0.025$. }\n\n\n\\subsection{{Pretrained classifier  \\texorpdfstring{$\\hat f$}{}.}}\n\n\\begin{table}[htb]\n\\begin{center}\n\\caption{{The performance of {\\text{CDD-RED}}   using a different   pretrained classifier $\\hat{f}$ (either Res50 or R-Res50)  compared with the default setting $\\hat{f}=$VGG19.} }\\label{table:surrogate_model}\n\\begin{threeparttable}\n{\n\\begin{tabular}{c|c|c}\n\\toprule\n\\hline\n & $\\hat{f}$=Res50 & $\\hat{f}$=R-Res50\\\\ \\hline\n\\begin{tabular}[c]{@{}c@{}}$d(\\mathbf x, \\mathbf x_\\mathrm{RED})$\\\\ (\\textcolor{red}{$\\downarrow$} is better)\\end{tabular} & 12.84 (\\textcolor{red}{$\\downarrow$ 0.20}) & 10.09 (\\textcolor{red}{$\\downarrow$ 2.95}) \\\\ \\hline\n\\begin{tabular}[c]{@{}c@{}}$\\text{\\text{PA}}_{\\mathrm{benign}}$\\\\ (\\textcolor{red}{$\\uparrow$} is better)\\end{tabular} & 84.33\\% ({$\\downarrow$1.38\\%}) & 57.88\\% ($\\downarrow$ 27.83\\%) \\\\ \\hline\n\\begin{tabular}[c]{@{}c@{}}$\\text{\\text{PA}}_{\\mathrm{adv}}$\\\\ (\\textcolor{red}{$\\uparrow$} is better)\\end{tabular} & 79.94\\% ($\\downarrow$ 0.49\\%) & 71.02\\% ($\\downarrow$ 9.40\\%) \\\\ \\hline\\bottomrule\n\\end{tabular}}\n\\end{threeparttable}\n\\end{center}\n\\end{table}\n\n\n{Besides setting $\\hat f$ as VGG19, Table \\ref{table:surrogate_model} shows the RED performance using  the other pretrained models, {\\it i.e.}, Res50 and R-Res50. As we can see, the use of  Res50 yields the similar performance as VGG19. Although some minor improvements are observed in terms of \npixel level reconstruction error,  the PA performance suffers a larger degradation.\nCompared to  Res50, \nthe use of an adversarially robust model \nR-Res50 significantly hampers the RED performance. \nThat is because the adversarially robust model typically lowers the prediction accuracy, it is not able to ensure the class-discriminative ability in the non-adversarial context, namely, the {\\text{PA}} regularization performance. }\n\n\\subsection{{Data selection for {\\text{PA}} regularization.}}\n\n\\begin{table}[htb]\n\\begin{center}\n\\caption{{Ablation study on the selection of $\\check{\\mathcal T}$ ($\\check{\\mathcal T}=\\mathcal{T}$ and without (w\/o) $\\check{\\mathcal T}$)) for training {\\text{CDD-RED}}, compared with $ \\check{\\mathcal T} = \\{ t \\in \\mathcal T\\,| \\,  \\hat{F}(t(\\mathbf{x})) = \\hat{F}(\\mathbf{x}),  \\hat{F}(t(\\mathbf{x}^{\\prime})) = \\hat{F}(\\mathbf{x}^{\\prime}). \\ \\}$}} \\label{table:ablation_data}\n\\begin{threeparttable}\n{\n\\begin{tabular}{c|c|c}\n\\toprule\n\\hline\n & $\\check{\\mathcal T}=\\mathcal{T}$ & w\/o $\\check{\\mathcal T}$ \\\\ \\hline\n\\begin{tabular}[c]{@{}c@{}}$d(\\mathbf x, \\mathbf x_\\mathrm{RED})$\\\\ (\\textcolor{red}{$\\downarrow$} is better)\\end{tabular} & 15.52 ($\\uparrow$ 2.48)  & 13.50 ($\\uparrow$ 0.46)  \\\\ \\hline\n\\begin{tabular}[c]{@{}c@{}}$\\text{\\text{PA}}_{\\mathrm{benign}}$\\\\ (\\textcolor{red}{$\\uparrow$} is better)\\end{tabular} & 83.64\\% ($\\downarrow$ 2.07\\%) &  84.04\\% ({$\\downarrow$1.67\\%}) \\\\ \\hline\n\\begin{tabular}[c]{@{}c@{}}$\\text{\\text{PA}}_{\\mathrm{adv}}$\\\\ (\\textcolor{red}{$\\uparrow$} is better)\\end{tabular} & 75.92\\% ($\\downarrow$ 4.51\\%) & 79.99\\% ($\\downarrow$ 0.44\\%)  \\\\ \\hline\\bottomrule\n\\end{tabular}}\n\\end{threeparttable}\n\\end{center}\n\\end{table}\n\n{As data augmentation might alter the classifier's original decision in \\eqref{eq: overall_DeRED},  we study how $\\check{\\mathcal T}$ affects the RED performance by setting   $\\check{\\mathcal T}$ as the original data, i.e., without data augmentation, and all data, i.e., $\\check{\\mathcal T} = \\mathcal{T}$. Table \\ref{table:ablation_data} shows the performance of different $\\check{\\mathcal T}$ configurations, compared with the default setting.\nThe performance is measured on the testing dataset. As we can see, using all data or original data cannot provide an overall better performance than {\\text{CDD-RED}}. That is because the former might cause over-transformation, and the latter lacks generalization ability. }\n\n\n\\subsection{{Regularization parameter  \\texorpdfstring{$\\lambda$}{}.}}\n\n\n\\begin{table}[htb]\n\\begin{center}\n\\caption{{Ablation study on the regularization parameter $\\lambda$ (0, 0.0125, and 0.05) for {\\text{CDD-RED}} training, compared with $\\lambda$=0.025. }} \\label{table:ablation_lambda}\n\\begin{threeparttable}\n{\n\\begin{tabular}{c|c|c|c}\n\\toprule\\hline\n & $\\lambda$=0 & $\\lambda$=0.0125 & $\\lambda$=0.05 \\\\ \\hline\n\\begin{tabular}[c]{@{}c@{}}$d(\\mathbf x, \\mathbf x_\\mathrm{RED})$\\\\ (\\textcolor{red}{$\\downarrow$} is better)\\end{tabular} & 8.92 (\\textcolor{red}{$\\downarrow$ 4.12}) & 12.79 (\\textcolor{red}{$\\downarrow$ 0.25}) & 14.85 ($\\uparrow$ 2.13) \\\\ \\hline\n\\begin{tabular}[c]{@{}c@{}}$\\text{\\text{PA}}_{\\mathrm{benign}}$\\\\ (\\textcolor{red}{$\\uparrow$} is better)\\end{tabular} & 47.61\\% ({$\\downarrow$38.10\\%}) & 81.00\\% ({$\\downarrow$4.71\\%}) & 85.56\\% ({$\\downarrow$ 0.15\\%)} \\\\ \\hline\n\\begin{tabular}[c]{@{}c@{}}$\\text{\\text{PA}}_{\\mathrm{adv}}$\\\\ (\\textcolor{red}{$\\uparrow$} is better)\\end{tabular} & 73.37\\% ({$\\downarrow$7.06\\%}) & 78.25\\% ($\\downarrow$ 2.18\\%) & 79.94\\% ($\\downarrow$ 0.49\\%) \\\\ \\hline\\bottomrule\n\\end{tabular}}\n\\end{threeparttable}\n\\end{center}\n\\end{table}\n\n{The overall training objective of {\\text{CDD-RED}} is (\\ref{eq: overall_DeRED}), which is the weighted sum of the reconstruction error and PA  with a regularization parameter $\\lambda$. We further study the sensitivity of {\\text{CDD-RED}} to the choice of \n$\\lambda$, which is set by  $0, 0.0125$, and $0.05$. Table \\ref{table:ablation_lambda} shows the RED performance of using different $\\lambda$ values, compared with the default setting $\\lambda=0.025$. We report the average performance on the testing dataset. As we can see, the use of $\\lambda=0$, which corresponds to training the denoiser without PA regularization, achieves a lower pixel-level reconstruction error $d(\\mathbf x, \\mathbf x_\\mathrm{RED})$, but   degrades the prediction-level performance, especially $\\text{\\text{PA}}_{\\mathrm{benign}}$ greatly. In the same time, $\\lambda=0$ provides a smaller pixel-level reconstruction error with a better PA performance than DO, which indicates the importance of using proper augmentations. We also observe that keep increasing  $\\lambda$ to $0.05$ is not able to provide a better PA.} \n\n\\section{{Ablation study of different attack hyperparameter settings}}\n\\label{sec:diff_attack_hyper}\n\n\n\n{We test on PGD attacks generated with different step sizes, including $4\/255$ and $6\/255$, and with and without random initialization (RI). Other hyperparameters are kept the same. The adversarial examples are generated by the same set of images w.r.t. the same classifier ResNet-50. The results are shown in Table \\ref{table:diff_pgd_hyper}. As we can see, the RED performance is quite robust against the varying hyperparameters of PGD attacks. Compared with DO, CDD-RED greatly improves $\\text{PA}_{\\text{benign}}$ and achieves higher $\\text{PA}_{\\text{adv}}$ with a slightly larger $d(\\mathbf x, \\mathbf x_\\mathrm{RED})$. Compared to DS, {\\text{CDD-RED}} achieves slightly better PA but with a much smaller reconstruction error $d(\\mathbf x, \\mathbf x_\\mathrm{RED})$.} \n\\begin{table}[H]\n    \\centering\n        \\caption{{RED performance for PGD with different hyperparameter settings, including stepsize as $4\/255$ and $6\/255$, and with and without RI.}}\n    \\label{table:diff_pgd_hyper}\n    \\begin{tabular}{cc}\n \\begin{tabular}{c|c|c|c|c}\n\\toprule\\hline\nWithout RI \/ With RI                                     & Stepsize & DO                                                             & DS                                                             & CDD-RED                                                        \\\\ \\hline\n                                                         & 4\/255    & \\textbf{5.94\/5.96}                                                      & 16.56\/16.57                                                    & 8.91\/8.94                                                      \\\\ \\cline{2-5} \n\\multirow{-2}{*}{$d(\\mathbf x, \\mathbf x_\\mathrm{RED})$} & 6\/255    & \\textbf{5.99\/5.98}                                                      & 16.52\/16.50                                                    & 8.97\/8.94                                                      \\\\ \\hline\n                                                         & 4\/255    & 40.00\\%\/47.00\\%                                                & 91.00\\%\/91.00\\%                                                &\\textbf{ 94.00\\%\/93.00\\%  }                                              \\\\ \\cline{2-5} \n\\multirow{-2}{*}{$\\text{\\text{PA}}_{\\mathrm{benign}}$}         & 6\/255    & 51.00\\%\/61.00\\%                                                & 94.00\\%\/93.00\\%                                                & \\textbf{95.00\\%\/94.50\\%}                                                \\\\ \\hline\n                                                         & 4\/255    &  97.50\\%\/97.50\\% &  97.50\\%\/97.50\\% & \\textbf{ 99.50\\%\/99.50\\%} \\\\ \\cline{2-5} \n\\multirow{-2}{*}{$\\text{\\text{PA}}_{\\mathrm{adv}}$}            & 6\/255    & 96.50\\%\/96.50\\% &  95.50\\%\/95.50\\% & \\textbf{98.50\\%\/99.50\\%} \\\\ \\hline\\bottomrule\n\\end{tabular}\n    \\end{tabular}\n\\end{table}\n\n\n\\section{{Performance without adversarial detection assumption}} \\label{sec:mixture}\n\n {The focus of RED is to demonstrate the feasibility of recovering the adversarial perturbations from an adversarial example. However, in order to show the RED performance  on the global setting, we experiment with a mixture of 1) adversarial images, 2) images with Gaussian noise (images with random perturbations), and 3) clean images on the ImageNet dataset. The standard deviation of the Gaussian noise is set as 0.05. Each type of data accounts for \\textbf{1\/3} of the total data. The images are shuffled to mimic the live data case. The overall accuracy before denoising is 63.08\\%. After denoising, the overall accuracy obtained by DO, DS, and CDD-RED is 72.45\\%, 88.26\\%, and \\textbf{89.11\\%}, respectively. During the training of the denoisers, random noise is not added to the input. }\n \n \n\n\n\n\n\n\\section{{Transferability of reconstructed adversarial estimate}} \\label{sec:tranferability}\n\n{We further examine the transferability of RED-synthesized perturbations. In the experiment, RED-synthesized perturbations are generated from PGD attacks using ResNet-50. We then evaluate the attack success rate (ASR) of the resulting perturbations transferred to the victim models ResNet-18, VGG16, VGG19, and Inception-V3. The results are shown in Table \\ref{table:transferability}. As we can see, the perturbation estimates obtained via our {\\text{CDD-RED}} yield better attack transferability than DO and DS. Therefore, such RED-synthesized perturbations can be regarded as an efficient transfer attack method.}\n\n\\begin{table}[H]\n\\begin{center}\n\\caption{{The tranferability of RED-synthesized perturbations.}} \\label{table:transferability}\n{\n\\begin{tabular}{c|c|c|c}\n\\toprule\\hline\n                                       & DO      & DS      & \\text{CDD-RED} \\\\ \\hline\nResNet-18 & 66.50\\%\t& 70.50\\% &\t \\textbf{77.50\\%}               \\\\ \\hline\nVGG16        & 71.50\\%\t& 74.00\\% &\t\\textbf{81.00\\%}              \\\\ \\hline\nVGG19        & 71.50\\%\t& 70.00\\%\t& \\textbf{80.00\\%}               \\\\ \\hline\nInception-V3            & 86.00\\% &\t85.50\\%\t& \\textbf{ 90.00\\%}               \\\\ \\hline\\bottomrule\n\\end{tabular}}\n\\end{center}\n\\end{table}\n\n\\section{{potential applications of RED}} \\label{section:potential_app}\n\n{In this paper, we focus on recovering attack perturbation details from adversarial examples. But in the same time, the proposed RED can be leveraged for various potential interesting  applications. In this section, we delve into three applications, including RED for adversarial detection in \\ref{sec:detection}, inferring the attack identity in \\ref{sec:identity}, and provable defense in \\ref{sec:provable}. }\n\n\\subsection{{RED for adversarial detection }} \\label{sec:detection}\n {The outputs of RED can be looped back to help the design of adversarial detectors. Recall that our proposed RED method (CDD-RED) can deliver an attribution alignment test, which reflects the sensitivity of input attribution scores to the pre-RED and post-RED operations. Thus, if an input is an adversarial example, then it will cause a high attribution dissimilarity (i.e., misalignment) between the pre-RED input and the post-RED input, i.e., $I(x, f(x))$ vs. $I(D(x), f(D(x)))$ following the notations in Section \\ref{sec:evaluation_metric}. In this sense, attribution alignment built upon $I(x, f(x))$ and $I(D(x), f(D(x)))$ can be used as an adversarial detector. Along this direction, we conducted some preliminary results on RED-assisted adversarial detection, and compared the ROC performance of the detector using CDD-RED and that using denoised smoothing (DS).  In Figure \\ref{fig:RoC}, we observe that the CDD-RED based detector yields a superior detection performance, justified by its large area under the curve. Here the detection evaluation dataset is consistent with the test dataset in the evaluation section of the paper.}\n \n \\begin{figure}[H]\n    \\centering\n    \\includegraphics[width=0.5 \\columnwidth]{Figs\/detection.png}\n    \\caption{{RoC of detecting adversarial examples.}}\n    \\label{fig:RoC}\n\\end{figure}\n\n\\subsection{{RED for attack identity inference}}\\label{sec:identity}\n\n{We consider another application to infer the attack identity using the reverse-engineered adversarial perturbations. Similar to the setup of Figure \\ref{fig:correlationmatrix}, we achieve the above goal using the correlation screening between the new attack and the existing attack type library. Let $z^\\prime$  (e.g., PGD attack generated under the unseen AlexNet victim model) be the new attack. We can then adopt  the RED model $D(\\cdot)$ to estimate the perturbations $\\delta_{new} = z^\\prime - D(z^\\prime)$. And let $x^\\prime_{Atk_i}$ denote the generated attack over the estimated benign data $D(z^\\prime)$ but using the existing attack type i. Similarly, we can obtain the RED-generated perturbations $\\delta_{i} = x^\\prime_{Atk_i} - D(x^\\prime_{Atk_i})$. With the aid of $\\delta_{new}$ and $\\delta_{i}$ for all $i$, we infer the most similar attack type by maximizing the cosine similarity: $i^* = \\text{argmax}_{i} ~ cos(\\delta_{new},\\delta_{i})$. Figure \\ref{fig:identity} shows an example to link the new AlexNet-generated PGD attack with the existing VGG19-generated PGD attack. The reason is elaborated on below. (1) Both attacks are drawn from the PGD attack family. And (2) in the existing victim model library (including ResNet, VGG, and InceptionV3), VGG19 has the most similar architecture as AlexNet, both of which share a pipeline composed of convolutional layers following fully connected layers without residual connections.}\n\n\\begin{figure}[H]\n    \\centering\n    \\includegraphics[width=1 \\columnwidth]{Figs\/RED_corr_alex.pdf}\n    \\caption{{Similarity between AlexNet-generated PGD vs. existing attacks in the library.}}\n    \\label{fig:identity}\n\\end{figure}\n \n\\subsection{{RED for provable defense}} \\label{sec:provable}\n\n\n\n{We train the RED models to construct smooth classifiers, the resulting certified accuracy is shown in Figure \\ref{fig:certified}. Here the certified accuracy is defined by the ratio of correctly-predicted images whose certified perturbation radius is less than the $\\ell_2$ perturbation radius shown in the x-axis.}\n\n\\begin{figure}[H]\n    \\centering\n    \\includegraphics[width=0.6\\columnwidth]{Figs\/CAbyVariousMethods.png}\n    \\caption{{Certified Robustness by different methods.}}\n    \\label{fig:certified}\n\\end{figure}\n\n\\section{#1} \\vspace{-2mm}}\n\\newcommand{\\SubSection}[1]{\\vspace{-2mm} \\subsection{#1} \\vspace{-2mm}}\n\\newcommand{\\SubSubSection}[1]{\\vspace{-1mm} \\subsubsection{#1} \\vspace{-1mm}}\n\n\\newcommand{\\Paragraph}[1]{\\vspace{1mm} \\noindent \\textbf{#1} \\hspace{0mm}}\n\n\\newcommand{\\text{AD}}{\\text{AD}}\n\\newcommand{\\text{AT}}{\\text{AT}}\n\\newcommand{\\text{IAA}}{\\text{IAA}}\n\n\n\n\n\n\n\\title\nReverse Engineering of Imperceptible   Adversarial Image Perturbations}\n\n\\author{%\n  Yifan Gong$^1$\\thanks{Equal contributions.}, Yuguang Yao$^{2*}$, Yize Li$^{1}$, Yimeng Zhang$^{2}$, Xiaoming Liu$^{2}$, Xue Lin$^{1}$, Sijia Liu$^{2,3}$\n \\\\\n  $^{1}$ Northeastern University, $^{2}$ Michigan State University, $^{3}$ MIT-IBM Watson AI Lab, IBM Research\n\\\\\n  \\texttt{\\{gong.yifa, li.yize, xue.lin\\}@northeastern.edu}, \\\\\n  \\texttt{\\{yaoyugua, zhan1853, liusiji5\\}@msu.edu, liuxm@cse.msu.edu}}\n\n\n\\newcommand{\\marginpar{FIX}}{\\marginpar{FIX}}\n\\newcommand{\\marginpar{NEW}}{\\marginpar{NEW}}\n\n\\iclrfinalcopy\n\\begin{document}\n\n\n\\maketitle\n\n\\begin{abstract}\nIt has been well recognized that neural network based image classifiers are easily fooled by images with tiny perturbations crafted by an adversary. There has been a vast volume of research to generate and defend such adversarial attacks. However, the following problem is left unexplored: \\textit{How to reverse-engineer adversarial perturbations from an adversarial image?}\nThis leads to a new adversarial learning paradigm---Reverse Engineering of Deceptions (RED). \nIf successful, RED allows us to estimate adversarial perturbations and recover the original images. \nHowever, carefully crafted, tiny adversarial perturbations are difficult to recover by optimizing a unilateral RED objective. For example, the pure image denoising method may overfit to minimizing the reconstruction error but hardly preserves the classification properties of the true adversarial perturbations. \nTo tackle this challenge, we formalize the RED problem and identify a set of principles crucial to the RED approach design. \nParticularly, we find that prediction alignment and proper data augmentation (in terms of spatial transformations) are two criteria to achieve a generalizable  RED approach. \nBy integrating these RED principles with image denoising, we propose a new \\underline{C}lass-\\underline{D}iscriminative \\underline{D}enoising based \\underline{RED} framework, termed {{\\text{CDD-RED}}}.\nExtensive experiments demonstrate the effectiveness of {\\text{CDD-RED}} under different evaluation metrics (ranging from the pixel-level,   prediction-level to the attribution-level alignment) and a variety of attack generation methods ({\\it e.g.}, FGSM, PGD, CW,  AutoAttack, and adaptive attacks). Codes are available at \\href{https:\/\/github.com\/Yifanfanfanfan\/Reverse-Engineering-of-Imperceptible-Adversarial-Image-Perturbations}{\\texttt{link}}. \n\\end{abstract}\n\n\\vspace{-3mm}\n\\section{Introduction}\n\n\nDeep neural networks (DNNs) are susceptible\nto adversarially-crafted tiny input perturbations during inference.\nSuch imperceptible   perturbations, {\\it a.k.a.}~adversarial attacks, could cause  DNNs to draw manifestly wrong conclusions. \nThe existence of adversarial attacks was first uncovered in the domain of image classification \\citep{Goodfellow2015explaining,carlini2017towards,papernot2016limitations}, and was then rapidly extended to  the other domains, such as object detection \\citep{xie2017adversarial,serban2020adversarial}, language modeling \\citep{cheng2020seq2sick,srikant2021generating}, and medical machine learning \\citep{finlayson2019adversarial,antun2020instabilities}. Despite different applications, the underlying attack  formulations and generation methods commonly obey the ones used in image classification.\n\n\nA vast volume of existing works have been devoted to designing defenses against such attacks, mostly focusing on either detecting adversarial examples \\citep{grosse2017statistical,yang2020ml,metzen2017detecting,meng2017magnet,wojcik2020adversarial} or acquiring  adversarially robust DNNs \\citep{madry2017towards,zhang2019theoretically,wong2017provable,salman2020denoised,wong2020fast,carmon2019unlabeled,shafahi2019adversarial}.\nDespite the plethora of prior work on adversarial defenses, it seems impossible to achieve `perfect'    robustness.\nGiven the fact that adversarial attacks are inevitable~\\citep{shafahi_are_2020}, we ask whether  or not an adversarial  attack can be  reverse-engineered so that one can estimate the  adversary's  information ({\\it e.g.}, adversarial perturbations) behind the attack instances.\nThe above problem is referred to as \\textit{Reverse Engineering of Deceptions (RED)}, fostering  a new adversarial learning regime. \nThe development of RED technologies will also\nenable the adversarial situation awareness in high-stake applications.\n\nTo the best of our knowledge, few work studied the RED problem. The most relevant one  that we are aware of is \\citep{pang_advmind_2020}, which proposed the so-called query of interest (QOI) estimation model to  \n infer the   adversary's   target class by model queries.\n However, the work \\citep{pang_advmind_2020} was restricted to the black-box attack scenario and thus lacks a general formulation of RED. Furthermore, it has  not    built\n  a complete RED pipeline, which  should not only provide a solution to estimating the adversarial example but also  formalizing  evaluation metrics to comprehensively measure the  performance of RED.\n    In this paper, we aim to take a solid step towards addressing the RED problem.\n\n\n\n\n\n\n\n\\iffalse\nDeep Neural Networks (DNNs) are inherently susceptible to adversarial\nattacks even under black-box settings, in which the adversary\nonly has query access to the target models. In practice, while it\nmay be possible to effectively detect such attacks ({\\it e.g.}, observing\nmassive similar but non-identical queries), it is often challenging to\nexactly infer the adversary intent ({\\it e.g.}, the target class of the adversarial\nexample the adversary attempts to craft) especially during\nearly stages of the attacks, which is crucial for performing effective\ndeterrence and remediation of the threats in many scenarios.\nIn this paper, we present AdvMind, a new class of estimation\nmodels that infer the adversary intent of black-box adversarial attacks\nin a robust and prompt manner. Specifically,\n\\fi\n\n\\iffalse\nDenoising-based strategies for detection:\nMagNet:\nThe detector\nnetworks learn to differentiate between normal and adversarial examples\nby approximating the manifold of normal examples.\nAnother work: Adversarial Examples Detection and Analysis with\nLayer-wise Autoencoders\n\\fi \n\n\\iffalse\nARE ADVERSARIAL EXAMPLES INEVITABLE?\nExistence of adversarial examples.\n\\fi \n\n\\SubSection{Contributions}\nThe main contributions of our work is listed below. \n\n\\noindent $\\bullet$ \nWe formulate the Reverse Engineering of Deceptions (RED) problem that is able to estimate adversarial perturbations and \nprovides the feasibility of inferring the intention of an adversary, {\\it e.g.}, `adversary saliency regions' of an adversarial image.\n\n\\noindent $\\bullet$ \nWe identify a series of RED principles to  \neffectively estimate the adversarially-crafted tiny perturbations.\nWe find that the class-discriminative ability is crucial to evaluate the RED performance.\nWe also find that \ndata augmentation, \\textit{e.g.}, spatial transformations, is another key to  improve the RED result.\n Furthermore, we integrate the developed RED principles into \nimage denoising  and \npropose a denoiser-assisted RED approach.\n\n\n\\noindent $\\bullet$ \nWe  \nbuild a comprehensive evaluation pipeline to quantify the RED performance from different perspectives, such as pixel-level reconstruction error, prediction-level alignment, and attribution-level adversary saliency region recovery. \nWith an extensive experimental study,\n we show that, \n compared to image denoising baselines,\n\n\n our proposal\n yields a consistent   improvement across diverse RED evaluation metrics and attack generation methods, {\\it e.g.},  FGSM \\citep{Goodfellow2015explaining}, CW \\citep{carlini2017towards}, PGD \\citep{madry2017towards} and AutoAttack \\citep{croce2020reliable}. \n \n\n\n\n\n\n\n\\SubSection{Related work}\n\n\\paragraph{Adversarial attacks.}\nDifferent types of adversarial attacks have been proposed, ranging from digital attacks   \\citep{Goodfellow2015explaining,carlini2017towards,madry2017towards,croce2020reliable,xu2019structured,chen2017ead,xiao2018spatially}\n to physical attacks \\citep{eykholt2018robust,li2019adversarial,athalye18b,chen2018shapeshifter,xu2019evading}. The former  \ngives the most fundamental threat model that\ncommonly deceives DNN models during inference by crafting imperceptible adversarial perturbations.\nThe latter extends the former to fool the victim models in the physical environment. Compared to digital attacks, physical attacks require  much larger perturbation strengths to enhance the adversary's resilience to various physical conditions such as lightness and object   deformation \\citep{athalye18b,xu2019evading}.\n\nIn this paper, we focus on $\\ell_p$-norm ball constrained   attacks, {\\it a.k.a.}~$\\ell_p$ attacks, for $p \\in \\{ 1,2,\\infty\\}$, most widely-used in digital attacks. \nExamples  include FGSM \\citep{Goodfellow2015explaining}, PGD \\citep{madry2017towards}, CW \\citep{carlini2017towards}, and the recently-released attack benchmark AutoAttack \\citep{croce2020reliable}. \nBased on the adversary's intent, $\\ell_p$ attacks are further divided into untargeted attacks and targeted attacks, where in contrast to the former, the latter designates the (incorrect) prediction label of a victim model.\nWhen an adversary has no access to victim models' detailed information (such as architectures and model weights), $\\ell_p$ attacks can   be further generalized to   black-box attacks  by leveraging either surrogate victim models \\citep{papernot_practical_2017,papernot_transferability_2016,dong_evading_2019,liu_delving_2017} or  input-output queries from   the original black-box models \\citep{chen2017zoo,liu2018signsgd,cheng2019sign}. \n\n\\paragraph{Adversarial defenses.}\nTo improve the robustness of DNNs, a variety of approaches have been proposed\nto defend against   $\\ell_p$ attacks.\nOne line of research focuses on enhancing the robustness of DNNs during training, {\\it e.g.},\nadversarial training \\citep{madry2017towards}, TRADES \\citep{zhang2019theoretically}, randomized smoothing \\citep{wong2017provable}, and their variants \\citep{salman2020denoised,wong2020fast,carmon2019unlabeled,shafahi2019adversarial,uesato2019labels,chenliu2020cvpr}.\nAnother line of research is to detect adversarial attacks without altering the victim model or the training process. \nThe key  technique is to differentiate between benign and adversarial examples by measuring their `distance.'\nSuch a distance measure has been defined in the input space via pixel-level reconstruction error~\\citep{meng2017magnet,liao_defense_2018}, in the intermediate layers via neuron activation anomalies \\citep{xu2019interpreting}, and in the  logit space by tracking the sensitivity of deep feature attributions to input perturbations \\citep{yang2020ml}. \n\nIn contrast to RED, \\textit{adversarial detection is a relatively simpler problem} as a roughly approximated distance possesses detection-ability \\citep{meng2017magnet,luo2015foveation}. \n \n \n  Among the existing adversarial defense techniques, the recently-proposed Denoised Smoothing (DS) method \\citep{salman2020denoised} is more related to ours.  In \\citep{salman2020denoised}, an image denoising network   is  prepended to  an existing victim model so that the augmented   system can be performed as a smoothed image classifier with certified robustness.  \n  Although DS is not designed for RED, its denoised output can be regarded as a benign example estimate.\n  The promotion of classification stability in DS also motivates us to design the RED methods with class-discriminative ability. \n  Thus, DS will be  a main baseline approach for comparison.   Similar to our RED setting, the concurrent work \\citep{souri2021identification} also identified the feasibility of estimating adversarial perturbations from adversarial examples.\n  \n  \n\n  \n \n \n  \n  \n  \n  \n\n\\vspace{-3mm}\n\\section{Reverse Engineering of Deceptions: Formulation and Challenges} \\label{sec:red_formulation_challenges}\n\n\n\\vspace{-2mm}\nIn this section, we first introduce the threat model of our interest: adversarial attacks on images. \nBased on that, we formalize the Reverse Engineering of Deceptions (RED) problem and demonstrate its challenges through some `warm-up' examples.\n\\vspace{-2mm}\n\\paragraph{Preliminaries on threat model.}\nWe focus on $\\ell_p$ attacks, where the \\textit{adversary's goal} is to generate imperceptible input perturbations to fool a well-trained image classifier.\nFormally, let $\\mathbf x$ denote a benign image, and $\\boldsymbol \\delta$ an additive   perturbation variable. Given a victim classifier $f$ and a perturbation strength tolerance $\\epsilon$ (in terms of, {\\it e.g.}, $\\ell_\\infty$-norm constraint  $ \\| \\boldsymbol{\\delta} \\|_\\infty  \\leq   \n\\epsilon$), the desired \\textit{attack generation algorithm} $\\mathcal A$    then seeks the optimal   $\\boldsymbol \\delta$ subject to the perturbation constraints. Such an attack generation process is   denoted by \n$\\boldsymbol \\delta = \\mathcal A (\\mathbf x, f, \\epsilon)$, resulting in an adversarial example   $\\mathbf x^{\\prime} = \\mathbf x + \\boldsymbol \\delta$.\n{Here $\\mathcal A$ can be fulfilled by different attack methods, e.g., FGSM~\\citep{Goodfellow2015explaining}, CW~\\citep{carlini2017towards}, PGD~\\citep{madry2017towards}, and AutoAttack \\citep{croce2020reliable}.}\n\\vspace{-2mm}\n\\paragraph{Problem formulation of RED.}\nDifferent from conventional defenses to detect or reject   adversarial instances \\citep{pang_advmind_2020,liao_defense_2018,shafahi_are_2020,niu_limitations_2020}, RED aims to address the following question.\n\\begin{center}\n\t\\vspace{-2mm}\n\t\\setlength\\fboxrule{0.0pt}\n\t\\noindent\\fcolorbox{black}[rgb]{0.95,0.95,0.95}{\\begin{minipage}{0.98\\columnwidth}\n\t\t\n\t\t\t\t\\vspace{-0.07cm}\n\t\t\t\t{\\bf (RED problem)}  Given an adversarial instance, can we reverse-engineer the adversarial perturbations $\\boldsymbol \\delta$, and infer    the adversary's objective and knowledge, {\\it e.g.}, true image class behind deception and adversary saliency image region? \n\t\t\t\t\\vspace{-0.07cm}\n\t\n\t\\end{minipage}}\n\t\\vspace{-2mm}\n\\end{center}\n\n \nFormally,\nwe aim to recover  $\\boldsymbol \\delta$  from an adversarial example $\\mathbf x^{\\prime}$\nunder the prior knowledge   \nof the  victim model $f$ or its substitute  $\\hat{f}$ if the former is a black box.\nWe denote the RED operation as $\\boldsymbol \\delta = \\mathcal R(\\mathbf x^{\\prime}, \\hat {f})$, \nwhich covers the white-box   scenario ($\\hat {f} = f$) as a special case. \nWe   propose to learn a\nparametric model $\\mathcal D_{\\boldsymbol \\theta}$ ({\\it e.g.}, a denoising  neural network that we will focus on)\nas an approximation of $\\mathcal R$ through\n  a  training\ndataset of adversary-benignity pairs $ \\Omega = \\{ (\\mathbf x^{\\prime}, \\mathbf x) \\}$. \n Through $\\mathcal D_{\\boldsymbol \\theta}$, \nRED will provide   a \\textbf{benign example estimate} $\\mathbf x_{\\mathrm{RED}}$ and a   \\textbf{adversarial example estimate} $\\mathbf x_{\\mathrm{RED}}^\\prime$ as below:\n\n\n{\n\\vspace*{-6mm}\n\\small{\n\\begin{align}\\label{eq: RED_results}\n    \\mathbf x_{\\mathrm{RED}} = \\mathcal D_{\\boldsymbol{\\theta}} (\\mathbf x^{\\prime}), \\quad \\mathbf x_{\\mathrm{RED}}^\\prime = \\underbrace{ \\mathbf x^{\\prime} -\\mathbf x_{\\mathrm{RED}} }_\\text{perturbation estimate} + \\mathbf x,\n\\end{align}\n}}%\n\nwhere a   \\textbf{perturbation estimate} is given by subtracting the RED's output with its input, \n$ \\mathbf x^{\\prime} - \\mathcal D_{\\boldsymbol \\theta}(\\mathbf x^{\\prime})$.\n\n\n\n\\begin{wrapfigure}{r}{60mm}\n\\vspace{-5mm}\n\\centering{\n\\begin{tabular}{c}\n\\hspace*{-3mm}\n\\includegraphics[width=0.4\\textwidth]{Figs\/RED_figure.png}\n\\end{tabular}\n}\n\\vspace{-5mm}\n\\caption{\\footnotesize{Overview of {RED} versus {\\text{AD}}.\n}}\n\\vspace{-4mm}\n\\label{fig: REDvsAD}\n\\end{wrapfigure}\nWe \\textbf{highlight} that RED yields a new  defensive approach aiming to `diagnose' the perturbation details of an existing adversarial example in a post-hoc, forensic manner. \nThis is different from   {adversarial detection ({\\text{AD}})}. Fig.\\ref{fig: REDvsAD} provides a visual comparison of {RED} with {\\text{AD}}.\n Although {\\text{AD}} is  also   designed in a post-hoc manner, it  aims  to determine whether  an input is an adversarial example for a victim model based on certain statistics on  model features or logits. Besides, \n{\\text{AD}} might    be used as a pre-processing step of {RED}, where the former provides `detected' adversarial examples for  fine-level RED diagnosis.\n{In our experiments, we will also show that the outputs of RED can be   leveraged to guide the design of adversarial detection. In this sense, {RED} and {\\text{AD}}  are  complementary building blocks within a closed loop.}\n\n\n\n\n\\paragraph{Challenges of RED}\nIn this work, we  will specify the   RED model $\\mathcal D_{\\boldsymbol{\\theta}}$  as a {denoising network}. However,\nit is highly non-trivial to design a proper  denoiser for RED. \nSpeaking at a high level, \nthere exist two {main challenges}. \nFirst, unlike \nthe conventional image denoising strategies~\\citep{DNCNN_denoiser},\nthe design of an RED-aware denoiser needs to take into account the effects of    victim models    and   data properties of  adversary-benignity pairs. \nSecond,  it might be insufficient to merely minimize the reconstruction error as the adversarial perturbation is  \nfinely-crafted~\\citep{niu_limitations_2020}. Therefore, either under- or over-denoising   will lead to poor RED performance.\n \n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\\section{{RED Evaluation Metrics and   Denoising-Only Baseline}} \\label{sec:evaluation_metric}\n\nSince RED  is different from existing defensive approaches, we first develop new performance metrics of RED, ranging from\npixel-level reconstruction error to attribution-level adversary saliency region. \nWe next leverage the proposed performance metrics to  demonstrate why a pure image denoiser is incapable of fulfilling RED. \n\n\\paragraph{RED evaluation metrics.}\n  \n   Given a learned RED model $\\mathcal D_{\\boldsymbol{\\theta}}$, the RED performance will be evaluated over a testing dataset $(\\mathbf x^{\\prime}, \\mathbf x)  \\in \\mathcal D_{\\mathrm{test}}$; see implementation details in Sec.\\,\\ref{sec: exp}. Here, $\\mathbf x^{\\prime}$ is used as the testing  input of the RED model, \n   and $\\mathbf x$ is the associated ground-truth benign example for comparison.  The benign example estimate $\\mathbf x_{\\mathrm{RED}}$ and adversarial example estimate  $\\mathbf x_{\\mathrm{RED}}^\\prime$ are obtained following \\eqref{eq: RED_results}. \n  \n   RED evaluation pipeline is conducted from  the following aspects: \\ding{172} pixel-level reconstruction error, \\ding{173} prediction-level inference  alignment, and \\ding{174} attribution-level adversary saliency region.\n    \n    \n\\noindent \\ding{226}    \\ding{172} \\textbf{Pixel-level}: Reconstruction error given by\n $d(\\mathbf x, \\mathbf x_\\mathrm{RED})=\n\\mathbb E_{(\\mathbf x^\\prime, \\mathbf x) \\in \\mathcal D_{\\mathrm{test}}} [\\| \\mathbf x_{\\mathrm{RED}} - \\mathbf x \\|_2 ]$.  \n\n\n\n\\noindent \\ding{226} \\ding{173} \\textbf{Prediction-level}:\nPrediction alignment (\\text{PA}) between the pair of \\textit{benign} example and  its estimate $(\\mathbf x_{\\mathrm{RED}}, \\mathbf x)$ and {\\text{PA}} between the pair of \\textit{adversarial} example and its estimate $(\\mathbf x_{\\mathrm{RED}}^\\prime, \\mathbf x^\\prime)$, given by\n\n{\n\\small{\n\\vspace*{-5mm}\n\\begin{align}\n\\text{\\text{PA}}_{\\mathrm{benign}} =  \\frac{ \\mathrm{card}( \\{ (\\mathbf x_{\\mathrm{RED}}, \\mathbf x) \\, | \\,F(\\mathbf x_{\\mathrm{RED} } ) = F(\\mathbf x  ) \\} ) }{\\mathrm{card}(\\mathcal D_{\\mathrm{test}})},~\n\\text{\\text{PA}}_{\\mathrm{adv}}=  \\frac{ \\mathrm{card}( \\{ (\\mathbf x_{\\mathrm{RED}}^\\prime, \\mathbf x^\\prime) \\, | \\, F(\\mathbf x_{\\mathrm{RED} }^\\prime ) = F(\\mathbf x^\\prime  ) \\} ) }{\\mathrm{card}(\\mathcal D_{\\mathrm{test}})} \\nonumber \n\\end{align}\n}}%\nwhere $\\mathrm{card}(\\cdot)$ denotes a cardinality function of a set and $F$ refers to the prediction label provided by the victim model $f$. \n\n\n\\noindent \\ding{226}    \\ding{174} \\textbf{Attribution-level}:\nInput attribution alignment ({\\text{IAA}}) between  the benign pair $(\\mathbf x_{\\mathrm{RED}}, \\mathbf x)$ and   between the adversarial pair   $(\\mathbf x_{\\mathrm{RED}}^\\prime, \\mathbf x^\\prime)$. In this work, we adopt \nGradCAM \\citep{selvaraju_grad-cam_2020} to attribute the predictions of classes back to input \nsaliency regions.\nThe rationale behind {\\text{IAA}} is that the unnoticeable adversarial perturbations (in the pixel space) can introduce  an evident input attribution   discrepancy with respect to (w.r.t.) the true label $y$ and the adversary's target label $y^\\prime$ \\citep{boopathy2020proper,xu2019structured}. Thus, an accurate RED should be able to\nerase the adversarial attribution effect through $\\mathbf x_{\\mathrm{RED}}$, and   \nestimate the adversarial intent through the saliency region of $\\mathbf x_{\\mathrm{RED}}^\\prime$ (see Fig.\\,\\ref{fig: REDvsAD} for   illustration).\n\n\n\n\n\n\n\\mycomment{\nAs a complement of quantitative RED metrics \\ding{172}-\\ding{173}, \nwe next introduce \\textbf{RED triangle}, a visualization tool for adversarial diagnosis. The {RED triangle} is defined with three vertices representing $\\mathbf x^\\prime$, $\\mathbf x$, and $\\mathbf{x}_{\\mathrm{RED}}$. It lies in a Cartesian coordinate system that represents the pixel space or the \nlogit space of the victim model, \\textit{i.e.}, the output by the victim model before the softmax layer, noted by   $f(\\mathbf x)$.\nTherefore, a necessary condition for an ideal $\\mathbf{x}_{\\mathrm{RED}}$ is that it should lie on the arc centered at \n$\\mathbf x^\\prime$ with radius equal to $\\|\\mathbf x^\\prime - \\mathbf x  \\|_2$, {\\it i.e.}, the dashed arc in Fig.\\,\\ref{fig: warm_up}.  This implies an exact recovery of the perturbation norm.\nMeanwhile, an accurate estimate  $\\mathbf{x}_{\\mathrm{RED}}$ is expected to\nhave a smaller angle\nbetween the directional vector $(\\mathbf{x}_{\\mathrm{RED}} - \\mathbf x^\\prime)$ and $(\\mathbf{x} - \\mathbf x^\\prime)$, noted by $\\angle{\\mathbf x'}$, \n\\textit{i.e.}, the `Optimal Direction' toward $\\mathbf x$ in Fig.\\,\\ref{fig: warm_up}.\nIdeally,\nthe perfect estimation is $\\mathbf{x}_{\\mathrm{RED}} = \\mathbf x$. \n}\n\n\n\\paragraph{Denoising-Only (DO) baseline.}\n\\begin{wrapfigure}{r}{70mm}\n  \\vspace{-10mm}\n  \\centering\n  \\begin{adjustbox}{max width=0.5\\textwidth }\n  \\begin{tabular}{@{\\hskip 0.00in}c @{\\hskip 0.00in}c | @{\\hskip 0.00in} @{\\hskip 0.02in} c @{\\hskip 0.02in} | @{\\hskip 0.02in} c @{\\hskip 0.02in} |@{\\hskip 0.02in} c @{\\hskip 0.02in} |@{\\hskip 0.02in} c @{\\hskip 0.02in} \n  }\n& \n\\colorbox{lightgray}{ \\textbf{Input image}}\n&\n\\colorbox{lightgray}{ \\textbf{DO}} \n&\n\\colorbox{lightgray}{  \\textbf{Groundtruth}}\n\n\\\\\n \\begin{tabular}{@{}c@{}}  \n\n\\rotatebox{90}{\\parbox{10em}{\\centering  \\textbf{\\large{Benign example $\\mathbf x$\/$\\mathbf x_{\\mathrm{RED}}$}}}}\n \\\\\n\n\\rotatebox{90}{\\parbox{10em}{\\centering  \\textbf{\\large{Adv. example $\\mathbf x^\\prime$\/$\\mathbf x_{\\mathrm{RED}}^\\prime$} \n}}}\n\n\\end{tabular} \n& \n\\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}}\n\n\\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/clean.jpg}\n\n }  \n\\end{tabular}\n \\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}}\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/adv.jpg}}  \n\\end{tabular}\n\\end{tabular}\n&\n\\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}}\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n      \\begin{tabular}{@{\\hskip 0.00in}c@{\\hskip 0.00in}}\n     \\parbox{10em}{\\centering   $I(\\cdot, y)$}  \n    \\end{tabular} \n     &  \n      \\begin{tabular}{@{\\hskip 0.00in}c@{\\hskip 0.00in}}\n       \\parbox{10em}{\\centering   $I(\\cdot, y^\\prime )$} \n    \\end{tabular} \n\\end{tabular}\\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DOcc.jpg}\n\n } &    \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DOct.jpg}} \n\\end{tabular}\n \\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DOac.jpg}} &    \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DOat.jpg}} \\\\\n\\end{tabular}\n\\end{tabular}\n&\n\\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}}\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n      \\begin{tabular}{@{\\hskip 0.00in}c@{\\hskip 0.00in}}\n     \\parbox{10em}{\\centering   $I(\\cdot, y)$}  \n    \\end{tabular} \n     &  \n      \\begin{tabular}{@{\\hskip 0.00in}c@{\\hskip 0.00in}}\n       \\parbox{10em}{\\centering   $I(\\cdot, y^\\prime )$} \n    \\end{tabular} \n\\end{tabular}\\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/cc_gt.jpg}} &    \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/ct_gt.jpg}} \n\\end{tabular}\n \\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/ac_gt.jpg}} &    \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/at_gt.jpg}} \n \\\\\n\\end{tabular}\n\\end{tabular}\n\\end{tabular}\n  \\end{adjustbox}\n  \\vspace*{-3mm}\n\\caption{\\footnotesize{\nIAA  of DO compared with ground-truth.\n}}\n\\label{fig: DOIAA}\n\n\\end{wrapfigure}\nWe further show that how a pure image denoiser, a `must-try' baseline, is insufficient of  \ntackling the RED problem.\nThis failure case drive us to rethink the denoising strategy through the lens of RED. \nFirst, we obtain the denoising network by minimizing the reconstruction error:\n\n{\\small\n\\vspace*{-2.5mm}\n\\begin{align}\n    \\begin{array}{ll}\n\\displaystyle \\minimize_{\\boldsymbol{\\theta}}         & \\ell_{\\mathrm{denoise}}(\\boldsymbol{\\theta}; \\Omega) \\Def \\mathbb E_{(\\mathbf x^{\\prime}, \\mathbf x) \\in \\Omega }\\|  \\mathcal D_{\\boldsymbol{\\theta}} (\\mathbf x^{\\prime}) - \\mathbf x \\|_1,\n     \n    \\end{array}\n    \\label{eq: MAE_only}\n\\end{align}\n}%\nwhere a Mean Absolute Error (MAE)-type loss is used for denoising \\citep{liao_defense_2018}, and the creation of training dataset $\\Omega$ is illustrated in Sec.\\,\\ref{sec: exp_setup}.\nLet us then evaluate the performance of {DO} through the non-adversarial prediction alignment $\\mathrm{PA}_\\mathrm{benign}$ and {\\text{IAA}}. We find that\n$\\mathrm{PA}_\\mathrm{benign} = 42.8\\%$ for DO. And\n Fig.\\,\\ref{fig: DOIAA} shows  the {{\\text{IAA}}} performance   of DO w.r.t. an input example. As we can see,  DO is not capable of exactly recovering the adversarial saliency regions compared to the ground-truth adversarial perturbations.\n These suggest that\n DO-based RED lacks\n the reconstruction ability at the prediction and the attribution levels. {Another naive approach is performing adversarial attack back to $x'$, yet it requires additional assumptions and might not precisely recover the ground-truth perturbations. The detailed limitations are discussed in Appendix \\ref{sec:naive_red}.}\n\n\n\n\n \n\\iffalse\nFirst, \n the denoising-only criterion is insufficient to warrant RED. This can be observed from  a significant degradation of IA, i.e., lower prediction accuracy of  $\\mathbf x_{\\mathrm{RED}} $ and lower attack success rate (ASR) of $\\mathbf x_{\\mathrm{RED}}^{\\prime} $ than the original data \n$\\mathbf x$ and $\\mathbf x^{\\prime}$. This implies that both the benign example estimate $\\mathbf x_{\\mathrm{RED}} $  and adversarial example estimate $\\mathbf x_{\\mathrm{RED}}^{\\prime} $ lose the \\textit{class-discriminative ability} of the original benign and adversarial examples.\nSecond, although\nthe reconstruction error    is minimized during training, \nthe denoising ability fails to generalize to  adversarial examples during inference. This can be seen from   a fairly large RMSE  $\\|\n \\mathbf x_{\\mathrm{RED}} - \\mathbf x\n\\|_2$ vs. the ground-truth perturbation error $\\|\n \\mathbf x^{\\prime} - \\mathbf x\n\\|_2$.  \nBased on the insight from the denoising-only baseline, in the next section we will propose an RED-aware denoiser that yields improved    \\textit{class-discriminative ability} and \\textit{generalization ability}.\n\\fi \n \n\n\n \n\n\n\n\n\n\n\n\\section{{Class-Discriminative Denoising for RED}}\n\\label{sec: approach}\n\n\\begin{wrapfigure}{r}{70mm}\n    \\vspace*{-5mm}\n\\centerline{\n\\includegraphics[width=.46\\textwidth,height=!]{Figs\/RED_figure_overview.png}\n}\n\\vspace*{-5mm}\n\\caption{\\footnotesize{\n{\\text{CDD-RED}} overview.  \n}}\n  \\label{fig: overview}\n  \\vspace*{-5mm}\n\\end{wrapfigure}\n\nIn this section, we propose a novel \n\\underline{C}lass-\\underline{D}iscriminative \n\\underline{D}enoising based \\underline{RED} approach termed {{\\text{CDD-RED}}}; see Fig.\\,\\ref{fig: overview} for an overview.\n{{\\text{CDD-RED}}} contains two key  components. First, we propose a \n{\\text{PA}}\nregularization   to enforce the prediction-level stabilities of both estimated benign example  $\\mathbf x_{\\mathrm{RED}}$ and adversarial example  $\\mathbf x_{\\mathrm{RED}}^\\prime$ with respect to their true counterparts $\\mathbf x$ and $\\mathbf x^\\prime$, respectively. \nSecond, \nwe propose a data augmentation strategy\nto improve the  {{RED}}'s generalization  without losing  its class-discriminative ability. \n\n\n\n\\paragraph{Benign and adversarial prediction alignment.}\nTo accurately estimate the adversarial perturbation from an adversarial instance, the lessons from the DO approach suggest to preserve the class-discriminative ability of   RED estimates to align with the original predictions, given by $\\mathbf x_{\\mathrm{RED}}$ vs. $\\mathbf x$, and $\\mathbf x_{\\mathrm{RED}}^\\prime$ vs. $\\mathbf x^\\prime$.\nSpurred by that, \nthe training objective  \nof {\\text{CDD-RED}} is required \n   not only to  minimize the reconstruction error like \\eqref{eq: MAE_only} but also to maximize  {{\\text{PA}}}, namely,\n`clone' the class-discriminative ability of original data. \nTo achieve this goal,  we augment the  denoiser  $\\mathcal D_{\\boldsymbol{\\theta}}$ with a known classifier $\\hat{f}$ to generate predictions of \nestimated  benign and adversarial examples (see Fig.\\,\\ref{fig: overview}), \\textit{i.e.}, $\\mathbf x_{\\mathrm{RED}}$ and $\\mathbf x_{\\mathrm{RED}}^{\\prime}$ defined in \\eqref{eq: RED_results}. \nBy contrasting $\\hat {f} (\\mathbf x_{\\mathrm{RED}})$ with \n$\\hat{f}(\\mathbf x) $, and  $\\hat {f} (\\mathbf x_{\\mathrm{RED}}^\\prime)$ with \n$\\hat{f}(\\mathbf x^{\\prime}) $, we can promote {\\text{PA}} by minimizing  the prediction gap between true examples and estimated ones:\n\n{\\vspace*{-3.5mm}\n\\small\\begin{align}\\label{eq: IA}\n    \\ell_{\\text{\\text{PA}}} ( \\boldsymbol{\\theta}; \\Omega) =  \n   \\mathbb E_{(\\mathbf x^\\prime, \\mathbf x) \\in \\Omega } [ \\ell_{\\text{\\text{PA}}} ( \\boldsymbol{\\theta}; \\mathbf x^\\prime, \\mathbf x) ], ~ \n    \\ell_{\\text{\\text{PA}}} ( \\boldsymbol{\\theta}; \\mathbf x^\\prime, \\mathbf x) \\Def    \\underbrace{ {\\mathrm{CE}}( \\hat {f} (\\mathbf x_{\\mathrm{RED}}), \\hat{f}(\\mathbf x)) }_\\text{{\\text{PA}} for benign prediction} + \\underbrace{  {\\mathrm{CE}}( \\hat {f} (\\mathbf x_{\\mathrm{RED}}^{\\prime}), \\hat{f}(\\mathbf x^{\\prime})) }_\\text{{\\text{PA}} for adversarial prediction}, \n\\end{align}}%\nwhere CE denotes the cross-entropy loss.\nTo enhance the class-discriminative ability, it is desirable to\nintegrate  the denoising loss \\eqref{eq: MAE_only} with the PA regularization \\eqref{eq: IA}, leading to $\\ell_{\\mathrm{denoise}} + \\lambda  \\ell_{\\text{\\text{PA}}}$, where $\\lambda > 0$ is a regularization parameter. \n\n \n\nTo address this issue,  we will further propose a data augmentation method to improve the denoising ability  without losing the advantage of {\\text{PA}} regularization.\n\n\\paragraph{Proper data augmentation improves RED.}\n\n\\begin{wrapfigure}{r}{70mm}\n\\vspace*{-5mm}\n\\centering{\n\\begin{tabular}{c}\n\\hspace*{-3mm}\n\\includegraphics[width=0.48\\textwidth]{Figs\/aug_fig.pdf}\n\\end{tabular}\n}\n\\vspace*{-6mm}\n\\caption{\\footnotesize{The influence of different data augmentations. `Base' refers to the base training without   augmentation.\n}}\n\\vspace*{-5mm}\n\\label{fig: aug_study}\n\\end{wrapfigure}\n\nThe rationale behind \n incorporating image transformations  into  {\\text{CDD-RED}} lies in two aspects.\nFirst, data transformation  can\nmake RED foveated to the most informative attack artifacts since   an adversarial instance could be {sensitive} to  input transformations \\citep{luo2015foveation,athalye18b,xie2019improving,li2020practical, fan2021does}.\nSecond,  the identification of  \n  transformation-resilient benign\/adversarial instances may enhance the capabilities of {\\text{PA}}  and {\\text{IAA}}.\n  \n  However, it is highly non-trivial to determine the most appropriate   data augmentation operations. For example, a pixel-sensitive data transformation, e.g., Gaussian blurring and colorization, would hamper the reconstruction-ability of the original \n   adversary-benignity pair $(\\mathbf x^\\prime, \\mathbf x)$. Therefore, we focus on spatial image transformations, including rotation, translation,  cropping \\& padding, cutout, and CutMix \\citep{yun2019cutmix}, which keep the original perturbation in a linear way. \n In Fig.\\ref{fig: aug_study}, we evaluate the RED performance, in terms of pixel-level reconstruction error  and  prediction-level alignment accuracy, for different kinds of spatial image transformations. As we can see, CutMix and  cropping \\& padding can increase the both performance simultaneously, considered as the appropriate augmentation to boost the RED. Furthermore, we empirically find that combining the two transformations can further  improve the performance.\n   \n\n  \n  Let $\\mathcal T$ denote a transformation set, including cropping \\& padding and CutMix operations. \n  With the aid of the denoising loss  \\eqref{eq: MAE_only}, {\\text{PA}} regularization \\eqref{eq: IA}, and data transformations $\\mathcal T$,  we then cast\n the overall training objective of {\\text{CDD-RED}} as  \n\n\n {\\small\n \\vspace*{-3.5mm}\n \\begin{align}\n  \\hspace*{-5mm}  \\begin{array}{ll}\n\\displaystyle \\minimize_{\\boldsymbol{\\theta}}         & \n\\underbrace{ \\mathbb E_{(\\mathbf x^{\\prime}, \\mathbf x) \\in \\Omega , t \\sim   \\mathcal T }\\|  \\mathcal D_{\\boldsymbol{\\theta}} (t(\\mathbf x^{\\prime})) - t(\\mathbf x) \\|_1 }_\\text{$\\ell_{\\mathrm{denoise}}$ \\eqref{eq: MAE_only} with data augmentations}   + \\underbrace{  \\lambda\n\\mathbb E_{(\\mathbf x^\\prime, \\mathbf x) \\in \\Omega, t \\sim \\check {\\mathcal T} } [  \n\\ell_{\\text{\\text{PA}}} ( \\boldsymbol{\\theta}; t(\\mathbf x^\\prime), t(\\mathbf x))\n] }_\\text{$\\ell_{\\text{\\text{PA}}}$ \\eqref{eq: IA} with data augmentation via $\\check{\\mathcal T}$},\n    \\end{array}\n\\hspace*{-5mm}    \\label{eq: overall_DeRED}\n\\end{align}}%\nwhere \n$\\check{\\mathcal T}$ denotes a properly-selected subset of \n$\\mathcal T$, and $\\lambda > 0$  is a regularization parameter. \nIn the {\\text{PA}} regularizer  \\eqref{eq: overall_DeRED}, we need to avoid the scenario of\n    over-transformation   where  data augmentation alters the classifier's original decision. \nThis suggests  \n$ \\check{\\mathcal T} = \\{ t \\in \\mathcal T\\,| \\,  \\hat{F}(t(\\mathbf{x})) = \\hat{F}(\\mathbf{x}),  \\hat{F}(t(\\mathbf{x}^{\\prime})) = \\hat{F}(\\mathbf{x}^{\\prime}) \\ \\}$, where $\\hat{F}$ represents the prediction label of the pre-trained classifier $\\hat f$, \\textit{i.e.}, $\\hat{F}(\\cdot)=\\mathrm{argmax}(\\hat f(\\cdot))$.\n \n \n \n \n \n\n  \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\\section{Experiments}\n\\label{sec: exp}\nWe show the effectiveness of our proposed method in {$5$ aspects}: \\textbf{a)} reconstruction error of adversarial perturbation inversion, \\textit{i.e.,} $d(\\mathbf x, \\mathbf x_\\mathrm{RED})$,\n\\textbf{b)} class-discriminative ability of the benign and adversarial example estimate, \\textit{i.e.},\n$\\text{\\text{PA}}_{\\mathrm{benign}}$ and $\\text{\\text{PA}}_{\\mathrm{adv}}$ by victim models,\n\\textbf{c)} adversary saliency region recovery, \\textit{i.e.}, attribution alignment, and \n\\textbf{d)} RED evaluation over unseen attack types and adaptive attacks.\n\n\\SubSection{Experiment setup}\n\\label{sec: exp_setup}\n\n\n\n\n\\paragraph{Attack datasets.} \n\n\nTo train and test RED models, we generate adversarial examples on the ImageNet dataset \\citep{deng2009imagenet}.\nWe consider \\textbf{$3$ attack methods} including PGD \\citep{madry2017towards}, FGSM  \\citep{Goodfellow2015explaining}, and CW attack \\citep{carlini2017towards}, applied to \\textbf{$5$ models} including pre-trained ResNet18 (Res18), Resnet50 (Res50) \\citep{DBLP:journals\/corr\/HeZRS15}, VGG16, VGG19, and InceptionV3 (IncV3) \\citep{DBLP:journals\/corr\/SzegedyVISW15}.  \n{The detailed parameter settings can be found in Appendix \\ref{sec:dataset_details}.} Furthermore, to evaluate the RED performance on unseen perturbation types during training, additional 2K adversarial examples generated by  \\textbf{AutoAttack} \\citep{croce2020reliable} and 1K adversarial examples generated by \\textbf{Feature Attack} \\citep{sabour2015adversarial}  are included as the unseen testing dataset. AutoAttack is applied on VGG19, Res50 and \\textbf{two new victim models}, i.e., Alexet and Robust Resnet50 (R-Res50), via fast adversarial training \\citep{wong2020fast} while Feature Attack is applied on VGG19 and Alexnet. The rational behind considering Feature Attack is that feature adversary has been recognized as an effective way to circumvent adversarial detection \\citep{tramer2020adaptive}. Thus, it provides a supplement on detection-aware attacks. \n\n\n\\paragraph{RED model configuration, training and evaluation.} During the training of the RED denoisers, VGG19 \\citep{vgg19} is chosen as the pretrained classifier $\\hat{f}$ for {\\text{PA}} regularization. Although different victim models were used for generating adversarial examples, we will show that the inference guided by VGG19 is able to accurately estimate the true image class and the intent of the adversary. In terms of the  architecture of $\\mathcal D_{\\boldsymbol{\\theta}}$, DnCNN \\citep{DNCNN_denoiser} is adopted. \nThe RED problem is solved using an Adam optimizer \\citep{KingmaB2015adam} with the initial learning rate of $10^{-4}$, which decays $10$ times for every $140$ training epochs. In \\eqref{eq: overall_DeRED}, the regularization parameter $\\lambda$ is set as $0.025$. The transformations for data augmentation include CutMix and cropping \\& padding. The maximum number of training epochs  is set as $300$. \n{The computation cost and ablation study of {\\text{CDD-RED}} are in Appendix \\ref{sec:cost} and \\ref{sec:ablation}, respectively.}\n\n\n\\paragraph{Baselines.}\nWe compare {\\text{CDD-RED}} with two baseline approaches: \\textbf{a)} the conventional denoising-only (DO) approach with the objective function \\eqref{eq: MAE_only}; \\textbf{b)} The state-of-the-art Denoised Smoothing (DS) \\citep{salman2020denoised} approach that considers both the reconstruction error and the {\\text{PA}} for benign examples in the objective function.\nBoth methods are tuned to their best configurations.\n\n\\subsection{Main  results}\n\n\\paragraph{Reconstruction error {$d(\\mathbf x, \\mathbf x_\\mathrm{RED})$} and {\\text{PA}}.}\nTable  \\ref{table:RMSE_IA_comparison} presents the comparison of {\\text{CDD-RED}} with the baseline denoising approaches in terms of $d(\\mathbf x, \\mathbf x_\\mathrm{RED})$, $d(f(\\mathbf x), f(\\mathbf x_\\mathrm{RED}))$, $d(f(\\mathbf x'), f(\\mathbf x'_\\mathrm{RED}))$, $\\text{\\text{PA}}_{\\mathrm{benign}}$, and $\\text{\\text{PA}}_{\\mathrm{adv}}$ on the testing dataset. As we can see, our approach ({\\text{CDD-RED}}) improves the class-discriminative ability from benign perspective by 42.91\\% and adversarial perspective by 8.46\\% with a slightly larger reconstruction error compared with the DO approach.\n\\begin{wraptable}{r}{58mm}\n\\begin{center}\n\\vspace*{-6mm}\n\\caption{\\footnotesize{The performance comparison among DO, DS and {\\text{CDD-RED}} on the testing dataset.}} \\label{table:RMSE_IA_comparison}\n\\begin{threeparttable}\n\\resizebox{0.4\\textwidth}{!}{\n\\begin{tabular}{c|c|c|c}\n\\toprule\\hline\n                                       & DO      & DS      & \\text{CDD-RED} \\\\ \\hline\n$d(\\mathbf x, \\mathbf x_\\mathrm{RED})$ & 9.32    & 19.19   & 13.04                 \\\\ \\hline\n$d(f(\\mathbf x), f(\\mathbf x_\\mathrm{RED}))$ & 47.81   & 37.21   & 37.07                 \\\\ \\hline\n$d(f(\\mathbf x'), f(\\mathbf x'_\\mathrm{RED}))$ & 115.09    &  150.02  &      78.21          \\\\ \\hline\n$\\text{\\text{PA}}_{\\mathrm{benign}}$         & 42.80\\% & 86.64\\% & 85.71\\%               \\\\ \\hline\n$\\text{\\text{PA}}_{\\mathrm{adv}}$            & 71.97\\% & 72.47\\% & 80.43\\%               \\\\ \\hline\\bottomrule\n\\end{tabular}}\n\\end{threeparttable}\n\\end{center}\n\\vspace*{-7mm}\n\\end{wraptable}\nIn contrast to DS, \n{\\text{CDD-RED}} achieves similar $\\text{\\text{PA}}_{\\mathrm{benign}}$ \nbut improved pixel-level   denoising error and $\\text{\\text{PA}}_{\\mathrm{adv}}$. Furthermore, {\\text{CDD-RED}}  achieves the best logit-level reconstruction error for both $f(\\mathbf x_\\mathrm{RED})$ and $f(\\mathbf x'_\\mathrm{RED})$ among the three approaches. This implies that $\\mathbf{x}_\\mathrm{RED}$ rendered by {\\text{CDD-RED}} can achieve highly similar prediction to the true benign example $\\mathbf x$, and the perturbation estimate ${\\mathbf x^{\\prime} -\\mathbf x_{\\mathrm{RED}}}$ yields a similar misclassification effect to the ground-truth perturbation. \n{Besides, {\\text{CDD-RED}} is robust against attacks with different hyperparameters settings, details can be found in Appendix \\ref{sec:diff_attack_hyper}.}\n\n\n\n\n\n\n\n\n\n \\begin{figure*}[htb]\n  \\centering\n  \\begin{adjustbox}{max width=1\\textwidth }\n  \\begin{tabular}{@{\\hskip 0.00in}c @{\\hskip 0.00in}c | @{\\hskip 0.00in} @{\\hskip 0.02in} c @{\\hskip 0.02in} | @{\\hskip 0.02in} c @{\\hskip 0.02in} |@{\\hskip 0.02in} c @{\\hskip 0.02in} |@{\\hskip 0.02in} c @{\\hskip 0.02in} \n  }\n& \n\\colorbox{lightgray}{ \\textbf{Input image}}\n&\n\\colorbox{lightgray}{ \\textbf{DO}} \n&  \n\\colorbox{lightgray}{ \\textbf{DS}} \n&\n\\colorbox{lightgray}{  \\textbf{{\\text{CDD-RED}} (ours)}}\n&\n\\colorbox{lightgray}{  \\textbf{Groundtruth}}\n\n\\\\\n \\begin{tabular}{@{}c@{}}  \n\n\\rotatebox{90}{\\parbox{10em}{\\centering  \\textbf{\\large{Benign example $\\mathbf x$\/$\\mathbf x_{\\mathrm{RED}}$}}}}\n \\\\\n\n\\rotatebox{90}{\\parbox{10em}{\\centering  \\textbf{\\large{Adv. example $\\mathbf x^\\prime$\/$\\mathbf x_{\\mathrm{RED}}^\\prime$} \n}}}\n\n\\end{tabular} \n& \n\\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}}\n\n\\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/clean.jpg}\n\n }  \n\\end{tabular}\n \\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}}\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/adv.jpg}}  \n\\end{tabular}\n\\end{tabular}\n&\n\\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}}\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n      \\begin{tabular}{@{\\hskip 0.00in}c@{\\hskip 0.00in}}\n     \\parbox{10em}{\\centering   $I(\\cdot, y)$}  \n    \\end{tabular} \n     &  \n      \\begin{tabular}{@{\\hskip 0.00in}c@{\\hskip 0.00in}}\n       \\parbox{10em}{\\centering   $I(\\cdot, y^\\prime )$} \n    \\end{tabular} \n\\end{tabular}\\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DOcc.jpg}\n\n } &    \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DOct.jpg}} \n\\end{tabular}\n \\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DOac.jpg}} &    \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DOat.jpg}} \\\\\n\\end{tabular}\n\\end{tabular}\n&\n\\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}}\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n      \\begin{tabular}{@{\\hskip 0.00in}c@{\\hskip 0.00in}}\n     \\parbox{10em}{\\centering   $I(\\cdot, y)$}  \n    \\end{tabular} \n     &  \n      \\begin{tabular}{@{\\hskip 0.00in}c@{\\hskip 0.00in}}\n       \\parbox{10em}{\\centering   $I(\\cdot, y^\\prime )$} \n    \\end{tabular} \n\\end{tabular}\\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DScc.jpg}} &    \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DSct.jpg}} \n\\end{tabular}\n \\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DSac.jpg}} &    \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DSat.jpg}} \n \\\\\n\\end{tabular}\n\\end{tabular}\n&\n\\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}}\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n      \\begin{tabular}{@{\\hskip 0.00in}c@{\\hskip 0.00in}}\n     \\parbox{10em}{\\centering   $I(\\cdot, y)$}  \n    \\end{tabular} \n     &  \n      \\begin{tabular}{@{\\hskip 0.00in}c@{\\hskip 0.00in}}\n       \\parbox{10em}{\\centering   $I(\\cdot, y^\\prime )$} \n    \\end{tabular} \n\\end{tabular}\\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DeREDcc.jpg}} &    \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DeREDct.jpg}} \n\\end{tabular}\n \\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DeREDac.jpg}} &    \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/DeREDat.jpg}} \n \\\\\n\\end{tabular}\n\\end{tabular}\n&\n\\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}}\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n      \\begin{tabular}{@{\\hskip 0.00in}c@{\\hskip 0.00in}}\n     \\parbox{10em}{\\centering   $I(\\cdot, y)$}  \n    \\end{tabular} \n     &  \n      \\begin{tabular}{@{\\hskip 0.00in}c@{\\hskip 0.00in}}\n       \\parbox{10em}{\\centering   $I(\\cdot, y^\\prime )$} \n    \\end{tabular} \n\\end{tabular}\\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/cc_gt.jpg}} &    \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/ct_gt.jpg}} \n\\end{tabular}\n \\\\\n \\begin{tabular}{@{\\hskip 0.02in}c@{\\hskip 0.02in}c@{\\hskip 0.02in} }\n \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/ac_gt.jpg}} &    \\parbox[c]{10em}{\\includegraphics[width=10em]{Figs\/piggybank\/at_gt.jpg}} \n \\\\\n\\end{tabular}\n\\end{tabular}\n\n\\end{tabular}\n  \\end{adjustbox}\n\\caption{\\footnotesize{\nInterpretation  ($I$) of benign  ($\\mathbf x$\/$\\mathbf x_{\\mathrm{RED}}$) and adversarial ($\\mathbf x^\\prime$\/$\\mathbf x_{\\mathrm{RED}}^\\prime$)    image w.r.t. the true label {$y$=`ptarmigan'} and the adversary targeted label {$y^\\prime$=`shower curtain'}.\nWe compare three methods of RED training,  DO, DS, and {\\text{CDD-RED}} as our method, to the ground-truth interpretation.  Given an RED method,  the first column is  $I(\\mathbf x_{\\mathrm{RED}}, y)$ versus $I(\\mathbf x_{\\mathrm{RED}}^\\prime , y)$,   the second column is $I(\\mathbf x_{\\mathrm{RED}}, y^\\prime)$ versus $I(\\mathbf x_{\\mathrm{RED}}^\\prime , y^\\prime)$, and  all maps under each RED method are normalized w.r.t. their largest value. For the ground-truth, the first column is  $I(\\mathbf x, y)$ versus $I(\\mathbf x^\\prime , y)$,   the second column is $I(\\mathbf x, y^\\prime)$ versus $I(\\mathbf x^\\prime , y^\\prime)$.\n}}\n\\label{fig: attribution}\n\n\\end{figure*}\n\n\n\n\n\\paragraph{Attribution alignment.}\nIn addition to pixel-level alignment and prediction-level alignment to evaluate the RED performance, attribution alignment is examined in what follows. \nFig.\\,\\ref{fig: attribution} presents attribution maps generated by GradCAM \n{in terms of $ I(\\mathbf x, y)$, $ I(\\mathbf x^\\prime, y)$, $I(\\mathbf x, y^\\prime)$, and $ I(\\mathbf x^\\prime, y^\\prime)$, where  $\\mathbf x^\\prime$ denotes the perturbed version of $\\mathbf x$, and $y^\\prime$ is the adversarially targeted label}. From left to right is the attribution map over DO, DS, {\\text{CDD-RED}} (our method), and the ground-truth. \nCompared with DO and DS, {\\text{CDD-RED}} yields \na closer attribution alignment with the ground-truth especially when making a comparison between $I(\\mathbf x_{\\mathrm{RED}}, y)$ and $I(\\mathbf x, y)$.\nAt the dataset level, \nFig.\\,\\ref{fig: IoU} shows the distribution of attribution IoU scores. It is observed that the IoU distribution of {\\text{CDD-RED}}, compared with DO and DS, has a denser concentration over the high-value area, corresponding to closer alignment with the attribution map by the adversary. {This feature indicates an interesting application of the proposed RED approach, which is to achieve the recovery of adversary's saliency region, in terms of the class-discriminative image regions that the adversary focused on.}\n\n\n\n\\begin{figure}[htb]\n\\centering\n\\subfigure\n[Denoising Only] \n{\\includegraphics[width=12em]{Figs\/IoU_DO.png}} \n\\subfigure[Denoised Smoothing]{\\includegraphics[width=12em]{Figs\/IoU_DS.png}}\n\\subfigure[{\\text{CDD-RED}} (ours)]{\\includegraphics[width=12em]{Figs\/IoU_DeRED.png}}\n\\caption{\\footnotesize{IoU distributions of the attribution alignment by three RED methods. Higher IoU is better. For each subfigure, the four IoU scores standing for $\\mathrm{IoU}( \\mathbf x_{\\mathrm{RED}}, \\mathbf x, y )$,\n$\\mathrm{IoU}( \\mathbf x_{\\mathrm{RED}}, \\mathbf x, y^\\prime )$,\n$\\mathrm{IoU}( \\mathbf x_{\\mathrm{RED}}^\\prime, \\mathbf x^\\prime, y )$,\nand\n$\\mathrm{IoU}( \\mathbf x_{\\mathrm{RED}}^\\prime, \\mathbf x^\\prime, y^\\prime )$.} }\n\\label{fig: IoU} \n\\vspace*{-3mm}\n\\end{figure}\n\n\n\n\n\n\\vspace{-2mm}\n\\paragraph{RED vs. unforeseen attack types.}\n\n\\begin{figure}[htb]\n\\centering\n\\subfigure\n[Accuracy of $\\mathbf{x}^{\\prime p}_{\\mathrm{RED}}$] \n{\\includegraphics[width=0.33\\linewidth]{Figs\/perturbation_portion\/denoise_pertubation_portion_acc.pdf}} \n\\subfigure[Success rate of $\\mathbf{x}^{\\prime p}_{\\mathrm{RED}}$]{\\includegraphics[width=0.33\\linewidth]{Figs\/perturbation_portion\/denoise_pertubation_portion_suc_rate.pdf}}\n\\subfigure[$d(f(\\mathbf{x}'^{p}_{\\mathrm{RED}}),f(\\mathbf{x}))$]{\\includegraphics[width=0.332\\linewidth]{Figs\/perturbation_portion\/denoise_pertubation_portion_logit.pdf}}\n\\subfigure[$d(\\mathbf{x}'^{p}_{\\mathrm{RED}},\\mathbf{x})$]{\\includegraphics[width=0.33\\linewidth]{Figs\/perturbation_portion\/denoise_pertubation_portion_mse.pdf}}\n\\vspace{-5mm}\n\\caption{\\footnotesize{Reverse engineer partially-perturbed data under different interpolation portion $p$.} }\n\\vspace{-7mm}\n  \\label{fig:interpolation}  \n\\end{figure}\n\nThe experiments on the recovery of unforeseen attack types  are composed of two parts: \\textbf{a)} partially-perturbed data via linear interpolation, and \\textbf{b)} the unseen attack type,  AutoAttack, Feature Attack, and Adaptive Attack. \n{More   attack results including adversarial attacks on CIFAR-10 dataset, Wasserstein minimized attacks, and attacks on smoothed classifiers can be found in Appendix \\ref{sec:appendix_unseen}.}\n\nFirst, we construct  partially-perturbed   data by adding a portion $p \\in \\{0\\%, 20\\%, \\cdots, 100\\%\\}$ of the perturbation $\\mathbf{x}^{\\prime}-\\mathbf{x}$ to the true benign example $\\mathbf{x}$, namely, $\\mathbf{x}^{\\prime p} = \\mathbf{x} + p(\\mathbf{x}^{\\prime}-\\mathbf{x})$. The interpolated $\\mathbf{x}^{\\prime p}$ is then used as the input to an RED model. We aim to investigate whether or not the proposed RED method can recover partial perturbations (even not successful attacks). \n\nFig.\\,\\ref{fig:interpolation} (a) and (b) show the the prediction alignment with $y$ and $y^\\prime$, of the adversarial example estimate $\\mathbf{x}^{\\prime p}_{\\mathrm{RED}}=\\mathbf{x}^{\\prime p}-\\mathcal D_{\\boldsymbol{\\theta}}(\\mathbf{x}^{\\prime p})+\\mathbf{x}$ by different RED models. Fig.\\,\\ref{fig:interpolation} (c) shows the logit distance between the prediction of the partially-perturbed adversarial example estimate and the prediction of the benign example while Fig.\\,\\ref{fig:interpolation} (d) demonstrates the pixel distance between $\\mathbf{x}^{\\prime p}_{\\mathrm{RED}}$ and the benign example. \n\nFirst, a smaller gap between the ground-truth curve (in red) and the adversarial example estimate $\\mathbf{x}^{\\prime p}_{\\mathrm{red}}$ curve indicates a better performance. \nFig.\\,\\ref{fig:interpolation} (a) and (b) show that {\\text{CDD-RED}} estimates the closest adversary's performance to the ground truth in terms of the prediction accuracy and attack success rate. This is also verified by the distance of prediction logits in Fig.\\,\\ref{fig:interpolation} (c). Fig.\\,\\ref{fig:interpolation} (d) \nshows that DS largely over-estimates the additive perturbation, while {\\text{CDD-RED}} maintains the perturbation estimation performance closest to the ground truth. {Though DO is closer to the ground-truth than {\\text{CDD-RED}} at p < 40\\%, DO is not able to recover a more precise adversarial perturbation in terms of other performance metrics. For example, in Fig.\\,\\ref{fig:interpolation} (b) at p = 0.2, $\\mathbf{x}^{\\prime p}_{\\mathrm{RED}}$ by DO achieves a lower successful attack rate compared to CDD-RED and the ground-truth.}\n\n\n\\begin{wraptable}{r}{80mm}\n\\begin{center}\n\\vspace*{-8mm}\n\\caption{\\footnotesize{The $d(\\mathbf x, \\mathbf x_\\mathrm{RED})$, $\\text{\\text{PA}}_{\\mathrm{benign}}$, and $\\text{\\text{PA}}_{\\mathrm{adv}}$ performance of the denoisers on the unforeseen perturbation type AutoAttack, Feature Attack, and Adaptive Attack.\n}}\n\\label{table:unforeseen_results}\n\\begin{threeparttable}\n\\resizebox{0.57\\textwidth}{!}{\n\\begin{tabular}{c|c|c|c|c}\n\\toprule\\hline\n\\multicolumn{2}{c|}{}                                                    & DO      & DS      & \\text{CDD-RED} \\\\ \\hline\n\\multirow{3}{*}{$d(\\mathbf x, \\mathbf x_\\mathrm{RED})$} & AutoAttack    & 6.41    & 16.64   & 8.81                  \\\\ \\cline{2-5} \n                                                        & Feature Attack & 5.51    & 16.14   & 7.99                  \\\\ \\cline{2-5} \n                                                        & Adaptive Attack& 9.76    & 16.21   & 12.24                 \\\\ \\hline         \n\\multirow{3}{*}{$\\text{\\text{PA}}_{\\mathrm{benign}}$}         & AutoAttack    & 84.69\\% & 92.64\\% & 94.58\\%               \\\\ \\cline{2-5} \n                                                        & Feature Attack & 82.90\\% & 90.75\\% & 93.25\\%               \\\\ \\cline{2-5} \n                                                        & Adaptive Attack& 33.20\\% & 27.27\\% & 36.29\\%               \\\\ \\hline\n\\multirow{3}{*}{$\\text{\\text{PA}}_{\\mathrm{adv}}$}            & AutoAttack    & 85.53\\% & 83.30\\% & 88.39\\%               \\\\ \\cline{2-5} \n                                                        & Feature Attack & 26.97\\% & 35.84\\% & 63.48\\%               \\\\ \\cline{2-5} \n                                                        & Adaptive Attack& 51.21\\% & 55.41\\% & 57.11\\%               \\\\ \\hline\\bottomrule\n\\end{tabular}}\n\\end{threeparttable}\n\\end{center}\n\\vspace{-5mm}\n\\end{wraptable}\nMoreover, as for benign examples with $p=0\\%$ perturbations, though the RED denoiser does not see benign example pair ($\\mathbf x$, $\\mathbf x$) during training, it keeps the performance of the benign example recovery. {\\text{CDD-RED}} can handle the case with a mixture of adversarial and benign examples. That is to say, even if a benign example, detected as adversarial, is wrongly fed into the RED framework, our method can recover the original perturbation close to the ground truth. {See Appendix \\ref{sec:mixture} for details.} \n\nTable\\,\\ref{table:unforeseen_results} shows the RED performance  on the unseen attack type,  AutoAttack, Feature Attack, and Adaptive Attack.  For AutoAttack and Feature Attack, {\\text{CDD-RED}} outperforms both DO and DS in terms of PA from both benign and adversarial perspectives. Specifically, {\\text{CDD-RED}} increases the $\\text{\\text{PA}}_{\\mathrm{adv}}$ for Feature Attack by 36.51\\% and 27.64\\% compared to DO and DS, respectively. \n\nAs for the adaptive attack {\\citep{tramer2020adaptive}}, we assume that the attacker has access to the knowledge of the RED model, \\textit{i.e.}, $D_{\\boldsymbol{\\theta}}$. It can then perform the PGD attack method to generate successful prediction-evasion attacks even after taking the RED operation.\n\n\nWe use PGD methods to generate such  attacks  within the $\\ell_\\infty$-ball of \nperturbation radius \n$\\epsilon=20\/255$. Table\\,\\ref{table:unforeseen_results} shows that Adaptive Attack is much stronger than Feature Attack and AutoAttack, leading to larger reconstruction error and lower PA. However,  {\\text{CDD-RED}} still outperforms DO and DS in    $\\text{\\text{PA}}_{\\mathrm{benign}}$ and $\\text{\\text{PA}}_{\\mathrm{adv}}$. Compared to DS, it achieves a better trade-off with denoising error $d(\\mathbf x, \\mathbf x_\\mathrm{RED})$.\n\n\n\n\n \n\n\n\n\n\nIn general, {\\text{CDD-RED}} can achieve high PA even for unseen attacks, indicating the generalization-ability of our method to estimate not only new adversarial examples (generated from the same attack method), but also new attack types.\n\\vspace{-3mm}\n\\paragraph{RED to infer correlation between adversaries.}\n\nIn what follows, we investigate whether the RED model guided by the single classifier (VGG19) enables to identify different adversary classes, given by combinations of attack types (FGSM, PGD, CW) and   victim model types (Res18, Res50, VGG16, VGG19, IncV3). \n\n\\begin{wrapfigure}{r}{100mm}\n\\vspace{-10mm}\n\\centering\n\\subfigure\n[Groundtruth]   \n{\\includegraphics[width=14em]{Figs\/heatmap_gt.png}} \n\\subfigure[{\\text{CDD-RED}} (ours)]{\\includegraphics[width=14em]{Figs\/heatmap_CDDRED.png}}\n\\vspace*{-5mm}\n\\caption{\\footnotesize{Correlation matrices between different adversaries. For each correlation matrix, rows and columns represent adversarial example estimate $\\mathbf x_{\\mathrm{RED}}^\\prime$ and true adversarial example $\\mathbf x^\\prime$ (For the ground-truth correlation matrix,   $\\mathbf x_{\\mathrm{RED}}^\\prime = \\mathbf x^\\prime $). Each entry represents the average Spearman rank correlation between the logits of two adversary settings $\\in$ \\{(victim model, attack type)\\}.\n}}\n\\vspace*{-3mm}\n\\label{fig:correlationmatrix} \n\\end{wrapfigure}\nFig.\\,\\ref{fig:correlationmatrix} presents \nthe correlation between every two adversary classes in the logit space.  \nFig.\\,\\ref{fig:correlationmatrix} (a) shows the ground-truth correlation map. \nFig.\\,\\ref{fig:correlationmatrix} (b) shows correlations  between logits of  $\\mathbf x_{\\mathrm{RED}}^\\prime$ estimated by our RED  method ({\\text{CDD-RED}})\nand logits of the true $\\mathbf x^\\prime$. \nAlong the diagonal of each correlation matrix, the darker implies the better RED estimation under the same adversary class. \nBy peering into off-diagonal entries, \nwe find that   FGSM attacks\nare more resilient to the choice of a victim model (see the cluster of high correlation values  at the top left corner of Fig.\\,\\ref{fig:correlationmatrix}).\nMeanwhile, the proposed {\\text{CDD-RED}} precisely  recovers the correlation behavior of the true adversaries. Such a correlation matrix can help explain the similarities between different attacks' properties. Given an inventory of existing attack types, if a new attack appears, then one can resort to RED to estimate the correlations between the new attack type and the existing attack types. {Based on the correlation screening, it can infer the properties of the new attack type based on its most similar counterpart in the existing attack library; see Appendix \\ref{sec:identity}. Inspired by the correlation, RED-synthesized perturbations can also be used as a transfer attack as well; see Appendix \\ref{sec:tranferability}.} \n\\vspace{-3mm}\n\\paragraph{Other applications of RED.}\n{In Appendix \\ref{section:potential_app}, we also empirically show that  the proposed RED approach can be applied  to adversarial detection, attack identity inference, and adversarial defense.}\n\n\n \\iffalse\nFig.\\,\\ref{fig:correlationmatrix}(a) presents the correlation matrix between the logits of $\\mathbf x^\\prime$ by different adversaries. For each entry, 100 benign images are utilized to generate their adversarial counterparts respectively by two adversaries from 15 settings and got their logits by corresponding victim models. Then the average Spearman correlation score is calculated over these 100 pairs of adversarial images.  Fig.\\,\\ref{fig:correlationmatrix}(b) and (c) present correlation matrices between logits of $\\mathbf x_{\\mathrm{RED}}^\\prime$ estimated by the RED model and $\\mathbf x^\\prime$. Along the diagonal of each correlation matrix, the darker means the better estimation. For other entries in Fig.\\,\\ref{fig:correlationmatrix}(a), they reflect the correlation between different adversaries. It is worth noting that CW attacks targeting different victim models have similar logit outputs. Comparing Fig.\\,\\ref{fig:correlationmatrix}(b) and (c), our {\\text{CDD-RED}} method results in a more similar correlation matrix to the ground-truth than the denoised smoothing method, especially for the high values along the diagonal. Our proposed {\\text{CDD-RED}} can not only recover the inference alignment of the same adversary but also keep the inference discrepancy between different adversarial settings. \n\\fi\n\n\\mycomment{\n\\paragraph{Ablation study.}\nIn    the Supplementary Material, we conduct additional experiments to demonstrate  the effect of the selection of a pretrained classifier $\\hat f$ and  the selection of a subset  $\\check{\\mathcal T}$ on RED. \nWe find that the RED performance is not sensitive to the choice of   $\\hat f$.\nFurthermore, we find that \nthe absence of $\\check{T}$ (\\textit{i.e.}, without data augmentation) hampers the RED performance. Meanwhile, the use of all data transformations (\\textit{i.e.}, $\\check{T} = \\mathcal T$) will also cause a degradation of PA.}\n\n\n\n\n\\vspace*{-4mm}\n\\section{Conclusion}\\label{ref:conclusion}\n\\vspace*{-3mm}\nIn this paper, we study the problem of Reverse Engineering of Deceptions (RED), to recover the attack signatures (\\textit{e.g.} adversarial perturbations and adversary saliency regions) from an adversarial instance.  \nTo the best of our knowledge, RED has not been well studied. \nOur work makes a solid step towards formalizing the RED problem and developing a systematic pipeline, covering not only a solution but also a complete set of evaluation metrics. \nWe have identified a series of RED principles, ranging from the pixel level to the attribution level, desired to reverse-engineer adversarial attacks. \nWe have developed  an effective denoiser-assisted RED approach by integrating class-discrimination   and   data augmentation into an image denoising network. \nWith extensive experiments, our approach outperforms the existing baseline methods and generalizes well to unseen attack types.\n\n\\section*{Acknowledgment}\n\nThe work is supported by the DARPA RED program. \nWe also thank the MIT-IBM Watson AI Lab, IBM Research for supporting us with GPU computing resources.\n\n\n\n{{\n\\bibliographystyle{iclr2022_conference}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
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+{"text":"\\section{Introduction}\n\nThe search for the Flavor Changing Neutral Current (FCNC) processes, has\nbeen one of the leading tools to test\nthe Standard Model (SM), in an attempt of either discovering or putting\nstringent limits on new physics\nscenarios. The discovery of the Higgs boson at the LHC, has lead the way to\na comprehensive program of measuring of \nits properties and branching ratios, in order to look for deviations\nfrom the SM predicted Higgs. Within the SM, there are no FCNC transitions at tree level\nmediated by the Higgs boson, due to the the presence of only one \nHiggs doublet and at the one-loop level these FCNC interactions are extremely small.  There are  however many extensions of the SM\nwhere the suppression of the neutral flavor changing transitions due to the\nGlashow-Iliopoulos-Maiani (GIM) mechanism \ncan be relaxed, with the presence of additional scalar doublets or through\nthe additional contributions of new particles in the loop diagrams. \nIn the presence of two or more scalar doublets, these FCNC interactions will be generated at tree level and can be very large unless some ad-hoc discrete symmetry is imposed.\n \nMotivated by the nature of the standard Yukawa coupling scheme \nthe authors of~\\cite{Cheng:1987rs} observed that the new FCNC couplings in the general two-Higgs doublet model  naturally follow the hierarchical structure of the quark masses and therefore \nany $\\bar{q}q' H$ coupling should experience the following structure \n\\begin{equation}\ng_{qq'H} \\sim \\sqrt{m_q m_q'},\n\\end{equation} \nindicating that the larger couplings can be expected in the FCNC interactions of a top-quark with the Higgs field.\nThe large production rate of the top quarks at the LHC allows one to look for a transition of the top quark to a quark of a different flavor but same charge, $t\\rightarrow cH$ (and $t\\rightarrow uH$),\nas no symmetry prohibits this decay. The SM branching ratio of this process is extremely small, of the order BR($t\\rightarrow cH)_{{\\rm SM}} \\approx 10^{-15}$~\\cite{Mele:1998ag,AguilarSaavedra:2004wm}, \nwhich is many orders of magnitude smaller than the value to be measured\nat the LHC at 14 TeV. Therefore an affirmative observation of the process $t\\rightarrow qH$, well above the SM rate,\nwill be a conclusive indication of new physics beyond the SM. \n\nThe probing of FCNC couplings in the quark sector, can be performed either at\na high energy collider or indirect limits can be obtained from neutral meson \noscillations ($K^0-\\bar{K}^0$, $B^0-\\bar{B}^0$ \nand $D^0-\\bar{D}^0$)~\\cite{Bona:2007vi, Blankenburg:2012ex, Aranda:2009cd}. \nThe $tqH$ coupling also affects the $Z\\rightarrow c\\bar{c}$ decay at the loop\nlevel and is therefore constrained by the electroweak precision observables\nof the $Z$ boson~\\cite{Larios:2004mx}. \nThe ATLAS and the CMS collaborations have \nset upper limits on the flavor changing neutral currents in the top sector  \nthrough the top pair production, with one top decaying to $Wb$ and the other \ntop assumed to decay to $qH$. The leptonic decay mode of the $W$ is considered\nand the different Higgs decay channels are analyzed,  \nwith the Higgs decaying either to two photons~\\cite{Aad:2014dya,CMS:2014qxa} \nor to $b\\bar{b}$~\\cite{Aad:2015pja,CMS:2015qhe}.\nCombining the analysis of the different Higgs decay channels,\nbased at $\\sqrt{s}$ = 8 TeV and \nan integrated luminosity of 20.3 (19.7) fb$^{-1}$, the 95\\% CL upper limits\nobtained by ATLAS (CMS)~\\cite{Aad:2015pja,Khachatryan:2016atv} are\nBr$(t\\rightarrow cH) \\leq 4.6 (4.0) \\times 10^{-3}$ \nand Br$(t\\rightarrow uH) \\leq 4.5 (5.5) \\times 10^{-3} $.  On the phenomenological \nside the sensitivity of LHC measurements to these non-standard flavor violating couplings in \nthe top sector has been explored in great details, considering ($a$) the \ntop quark pair production~\\cite{AguilarSaavedra:2000aj, Atwood:2013ica, Kobakhidze:2014gqa, Wu:2014dba}, \n($b$) the single top $+$ Higgs production~\\cite{AguilarSaavedra:2004wm, Greljo:2014dka}\n and ($c$) single top $+$ W production~\\cite{Liu:2016dag}. \n\nThe analysis of the $tqH$ coupling has also been carried out in the context \nof the next generation $e^-e^+$ linear colliders, the International Linear Collider (ILC)\nand the Compact Linear Collider (CLIC)~\\cite{Behnke:2013xla, Aicheler:2012bya}. \nThese planned high energy $e^-e^+$ colliders are expected to perform \nprecision measurements of the top-quark and the Higgs boson.\nThey will be able to scrutinize the couplings\nin the top-Higgs sector to the extreme precision, making them suitable for the sensitive tests of physics beyond the SM. \nThe baseline machine design for both colliders allows for up to\n$\\pm 80 \\%$ electron polarization, while provisions have been made to allow positron polarization of $\\pm 30 \\%$ as \nan upgrade option. Both these machines are designed to operate at centre of mass energies of 350, 500 \nand 1000 GeV, with the possibility of CLIC to be also adapted for the 3 TeV operation. Several studies have been carried out in the context of zero beam polarization at the ILC~\\cite{Han:2001ap, Hesari:2015oya} in an attempt\nto constrain the $tqH$ vertex. \n \nThe Higgs boson within the SM couples similarly to \n$\\bar{q}_Lq_R$ and $\\bar{q}_Rq_L$, i.e. $y_{LR}=y_{RL}$. Most of the studies \nin the context of the FCNC in the Higgs sector takes into effect this \nconsideration and assumes the similarity between the chiral \ncouplings.  In this work we have focussed on the chiral nature of the FCNC \ncouplings and have shown how the inequality of chiral couplings leads to distinct behaviour \nin the distributions of final states at linear colliders. \nWe work in the context of initial beam polarization for both the electron and the positron, \nusing the advantages of their adjustment for enhancing the sensitivities of the measured branching ratios and \nthe asymmetries on the FCNC parameters. We also present the results in the case of transverse polarized beams. \n\n\nIt is a well known fact that by a detailed study of the top (antitop)\ndecay products one can obtain valuable information about the top spin\nobservables and then use them for the detailed exploration of the top quark\npair production or decay \ndynamics to distinguish among different models of new physics ~(\\cite{KamenikMelic} and references therein). In order to maximize the top spin effects it is advisable to \nchoose a proper spin quantization axis. \nAt the Tevatron, where the top quark pair production was\ndominated by the quark-antiquark annihilation a special off-diagonal axis was shown to exist~\\cite{Parke:1996pr},\nmaking top spins $100\\%$ correlated. On the other hand, at the LHC \nthe top quark pair production is dominated by the gluon-gluon fusion and \nthere is no such optimal axis for this process\\footnote{At \nlow $m_{t\\bar t}$ the top quark pair production via gluon-gluon fusion is \ndominated by like-helicity gluons. Consequently, spin correlations are \nmaximal in the helicity basis~\\cite{Mahlon:2010gw}.}. The $t\\bar{t}$ \nproduction through the electron-positron annihilation at the linear \ncolliders will be similar to the Tevatron production, therefore\nthe top quark spins will also be maximally correlated in the off-diagonal basis. \nThe $t$, $\\bar{t}$ spin effects, can be analyzed in the lepton-lepton \nor lepton+jets final states through a number of angular distributions and \ncorrelations. The spin information is proportional\nto the spin analyzing power of the decay products of the top and will\ntherefore differ from the SM one in the case of FCNC top-Higgs decay.\nWe therefore also carry out a detailed study of the FCNC $t\\to qH$ decay \nwith different spin observables, and in different top-spin polarization basis, \nusing both unpolarized and longitudinally polarized beams. \n\nThe outlay of the paper is as follows. We discuss in Sec.~\\ref{sec:FCNC}, \nthe most general FCNC lagrangian considered for our analysis.\nWe give a brief review of the effects of initial beam polarizations in the $t\\bar{t}$ production at the linear \ncollider in Sec.~\\ref{sec:beam_pol}. The detailed analysis of the $tqH$\nfinal state is performed in Sec.~\\ref{sec:cmframe} and constraints are \nobtained from angular asymmetries. The top spin observables in the context of \ndifferent spin bases are discussed in Sec.~\\ref{sec:spintop}. A thorough numerical\nstudy of the process $e^-e^+\\rightarrow t\\bar{t}\\rightarrow qHW^-\\bar{b}\\rightarrow \nqb\\bar{b}l^-\\bar{\\nu}_l\\bar{b}$ including top FCNC coupling is performed in \nSec.~\\ref{sec:numericalstudy}, and finally we conclude in Sec.~\\ref{sec:conclusion}.\nThe analytical form of the different production and decay matrices, along with the expressions for the \ntop spin observables used for our analysis are listed in Appendix~\\ref{sec:All_appen}\nand \\ref{sec:appen_spin}.\n\n\n\\section{The flavor changing top quark coupling}\\label{sec:FCNC}\n\nWe concentrate on the most general FCNC $tqH$ Lagrangian of the form \n\\begin{eqnarray}\\label{eq:tqhA}\n{\\cal L}^{tqH} &=& g_{tu} \\bar{t}_R u_L H + g_{ut} \\bar{u}_R t_L H +  g_{tc} \\bar{t}_R c_L H \n+ g_{ct} \\bar{c}_R t_L H +  h.c \\nonumber \\\\\n&=& \\bar{t} (g_{tq} P_L + g_{qt}^\\ast P_R ) q H  + \\bar{q} (g_{qt} P_L + g_{tq}^\\ast P_R ) t H.\n\\end{eqnarray}   \nThis Lagrangian gives rise to the tree-level FCNC decays $t \\to H q,(q=u,c)$ with the partial decay width given as \n\\begin{eqnarray}\\label{eq:top_TDW}\n\\Gamma_{t\\rightarrow q H}&=&\\frac{1}{32 \\pi m_t^3}\\sqrt{m_t^2-(m_q-m_H)^2}\n\\sqrt{m_t^2-(m_q+m_H)^2}\\left[(\\mid g_{tq}\\mid^2 + \\mid g_{qt}\\mid^2)(m_t^2+m_q^2-m_H^2) \\right. \\nonumber \\\\\n&& \\left. +4 m_t m_q \n\\left(g_{tq}^\\ast g_{qt} + g_{qt}^\\ast g_{tq}\\right)\\right].\n\\end{eqnarray}\nThe SM top-quark decay is dominated by $t\\rightarrow b W^+$ and it is given by\n\\begin{equation}\\label{eq:tWb}\n \\Gamma_{t\\rightarrow b W^+} = \\frac{G_F}{8 \\sqrt{2} \\pi m_t^3}(m_t^2-m_W^2)^2(m_t^2+2 m_W^2) \\,.\n\\end{equation}\nWe neglect the mass of the emitted quark $m_q$, in our \nanalysis. The branching ratios of the top decaying in the presence of these \nflavor violating Yukawa couplings is then given by\n\\begin{eqnarray}\\label{eq_BR}\n {\\rm BR}(t\\rightarrow q H) &=& \\frac{1}{2\\sqrt{2}G_F}\\frac{(m_t^2-m_H^2)^2}{(m_t^2-m_W^2)^2 (m_t^2+2 m_W^2)}\n (\\mid g_{tq}\\mid^2 + \\mid g_{qt}\\mid^2) \\alpha_{QCD},\n    \\end{eqnarray}\nwhere the NLO QCD corrections to the SM decay width \\cite{Li:1990qf} and the $t \\to c H$ \ndecay \\cite{Zhang:2013xya} are included in the factor $\\alpha_{QCD} = 1+0.97 \\alpha_s = 1.10$ \\cite{Greljo:2014dka}. \nThe total decay width of the top in the presence of these FCNC couplings is then \n\\begin{eqnarray}\n \\Gamma_t &=& \\Gamma_t^{SM} + \\Gamma_{t\\rightarrow q_H} \n  \\approx \\Gamma_t^{SM} + 0.155 (\\mid g_{tq}\\mid^2 + \\mid g_{qt}\\mid^2) \\,.\n\\end{eqnarray}\nWe have $\\Gamma_{t}^{SM} = \\Gamma_{t\\rightarrow W^+ b}$ = 1.35 GeV  \nfor $m_t$ = 173.3 GeV at NLO, while the experimentally observed value of the total \ntop-quark  width is, $\\Gamma_t = 1.41^{+0.19}_{-0.15}$ GeV~\\cite{Agashe:2014kda}.\nThe additional FCNC decay processes give positive contributions to $\\Gamma_t$, proportional to \n$(\\mid g_{tq}\\mid^2 + \\mid g_{qt}\\mid^2)$ and from the experimentally observed \n$\\Gamma_t$ an upper bound on $\\sqrt{\\mid g_{tq}\\mid^2 + \\mid g_{qt}\\mid^2}$ \ncan be obtained. \nThese  flavor changing couplings can also lead to the \nthree body decay $h\\rightarrow t^\\ast (\\to  W^+ b)\\bar{q}$, where top is\nproduced off-shell and $q=u,~c$. Then total width of the Higgs gets\nmodified and the couplings  $g_{tq},~g_{qt}$ can be \nindependently constrained from the measurement of the Higgs \ndecay width at the LHC~\\cite{Atwood:2013ica}.\n \n\\section{Polarized beams in $t\\bar{t}$ production at the $e^- e^+$ linear collider}\\label{sec:beam_pol}\n\nThe most general formula for the matrix element square $|T_{e^-e^+}|^2$ for arbitrary polarized $e^-e^+$ beams producing a $t\\bar{t}$ pair \nis given in Refs.~\\cite{Kleiss:1986ct, Hikasa:1985qi}. However for the annihilation process \nwith massless electron and  positron, the helicity of the electron has to be opposite to \nthat of the positron, and the final formula is reduced to the form,\n\\begin{eqnarray}\n |T|^2 &=&  \\frac{1}{4}\\left\\lbrace(1-P^L_{e^-})(1+P^L_{e^+}) |T_{e^-_L e^+_R}|^2 + \n (1+P^L_{e^-})(1-P^L_{e^+}) |T_{e^-_R e^+_L}|^2 \\right. \\nonumber \\\\\n && \\hspace*{0.5cm}\\left. + P^T_{e^-} P^T_{e^+} {\\rm Re} \\left[  e^{-i(\\alpha_- + \\alpha_+)} \n T_{e^-_R e^+_L} T_{e^-_L e^+_R}^{\\ast}+ e^{i(\\alpha_- + \\alpha_+)}T_{e^-_L e^+_R} T_{e^-_R e^+_L}^{\\ast}\\right ]\n \\right\\rbrace,\n \\label{eq:fin2a}\n\\end{eqnarray}\nwhere $T_{e^-_{\\lambda_1} e^+_{\\lambda_2}}$ is the helicity amplitude for the process under\nconsideration, and $\\lambda_1,~\\lambda_2$ are the helicities of the electron and the positron,\nrespectively. $P^L_{e^\\mp}$ is the degree of the longitudinal polarization and $P^T_{e^\\mp}$ \nis the transversal polarization for the electrons and positrons. \nThe $\\alpha_{\\mp}$ refers to the angle of polarization of the electron and the positron, \nrespectively.  The polarizations of the electron and the positron at the linear colliders\nare independent and can be arbitrarily changed. The proposed linear colliders (ILC and CLIC)\nassume that the following polarizations can be achieved\\footnote{It is important to note \nthe role of the beam polarization in the $t\\bar{t}$ production. For the $-80\\%$ of the electron\npolarization and $+30\\%$ of the positron polarization the initial stated will be dominantly \npolarized as $e^-_L e^+_R$, giving in the SM\na constructive interference of the $\\gamma$ and $Z$ amplitudes\nfor the production of $t_L\\bar{t}_R$ pair, and a destructive interference for the \nproduction of $t_R \\bar{t}_L$, which then leads to a large positive forward-backward asymmetry. \n} \n\\begin{eqnarray}\nP^{L,T}_{e^-} = \\pm 80\\% \\;, P^{L,T}_{e^+} = \\pm 30\\% \\,.\n\\end{eqnarray}\nAs it was shown in Ref.~\\cite{Hikasa:1985qi}, if one is interested in the $\\phi_t$ (azimuthal angle of \nthe top quark) dependence of the cross section,  instead of discussing $\\phi_t$ dependence directly, \nit is simpler to study $\\alpha_{\\mp}$ dependence, since the latter is explicit in above. It can be shown that \n\\begin{eqnarray}\n | \\langle f(\\phi_t,...) | T | e^-(\\alpha_-) e^+ (\\alpha_+) \\rangle |^2 = | \\langle f(\\phi_t = 0,...) | T |\n e^-(\\alpha_- - \\phi_t) e^+ (\\alpha_+ - \\phi_t) \\rangle |^2 \\,,\n\\end{eqnarray}\nfrom the rotational invariance with respect to the beam direction, i.e. the rotation of the final state \nby $\\phi_t$ is equivalent to the rotation of the initial state by $-\\phi_t$.\nWith this assumption Eq.~(\\ref{eq:fin2a}) becomes \n\\begin{eqnarray}\n |T|^2 &=&  \\frac{1}{4}\\left\\lbrace(1-P^L_{e^-})(1+P^L_{e^+}) |T_{e^-_L e^+_R}|^2 + \n (1+P^L_{e^-})(1-P^L_{e^+}) |T_{e^-_R e^+_L}|^2 \\right. \\nonumber \\\\\n && \\hspace*{0.5cm}\\left. -2 P^T_{e^-} P^T_{e^+} \n\\rm{Re}~e^{i(\\eta-2\\phi_t)} T^{\\ast}_{e^-_R e^+_L} T_{e^-_L e^+_R}\n \\right\\rbrace,\n \\label{eq:fin2}\n\\end{eqnarray}\nwhere $\\eta = \\alpha_-+\\alpha_+$.\nThe effects of various beam polarizations in above will be discussed in the following.  \n \n\\section{Analysis of the $tqH$ final state at the $e^- e^+$ linear collider}\\label{sec:cmframe}\n\nWe study the $t\\bar{t}$ production in the context of\nthe $e^-e^+$ linear collider, where one of the top decays to $Wb$, and the \nother decays to $q(u,c)H$ and the leptonic decay mode of \nthe $W$ boson is considered:\n\\begin{eqnarray}\n&&  e^-(p_1) + e^+(p_2)\\rightarrow t(q_1)+\\bar{t}(q_2), \\nonumber \\\\\n&&  \\hspace*{3cm} t(q_1) \\rightarrow q (p_{q})+ H,  \\qquad \n\\bar{t}(q_2) \\rightarrow \\bar{b} (p_b)+ l^+(p_l)+ \\nu(p_\\nu).\n\\end{eqnarray}\nWe first consider the leading order spin dependent differential cross-section of the top pair production\nin a generic basis. The total phase space is split into the product of the differential cross-section for \nthe $t\\bar{t}$ production, the three-particle decay of the antitop quark  and the two-particle decay \nof the top quark, with the Higgs decaying to $b\\bar{b}$. We first do the analysis considering the decay of $t$ to $qH$ and the inclusive decay of $\\bar{t}$. In an attempt to make a comparative study, we also consider the $t\\bar{t}$ production, with the SM decay of top to $W^+b$,\nand the inclusive decay of $\\bar{t}$. This SM process will be a background for the $tqH$ final state, with the $H$ \nand the $W$ decaying hadronically. \nSince the analysis is being similar for both, the considered signal and the SM \nbackground, we only discuss the calculation of the signal in details.\nThe differential cross section in the centre of mass frame becomes\n\\begin{eqnarray}\\label{df_cs1}\nd\\sigma &=& \\frac{1}{2s} \\int \\frac{ds_1}{2\\pi} \\frac{1}{((s_1-m_t^2)^2+\\Gamma_t^2m_t^2)}\n \\times \\mid \\bar{\\mathcal{M}}^2 \\mid \\nonumber \\\\\n&\\times&  (2 \\pi)^4 \\delta^4 (q_1+q_2-p_1-p_2) \\frac{d^3q_1}{(2\\pi^3) 2E_1} \\frac{d^3q_2}{(2\\pi^3) 2E_2}~~~~~\n[\\rm{production~of}~ t\\bar{t}] \\nonumber \\\\\n&\\times&  (2\\pi)^4 \\delta^4(p_q+p_H-q_1) \\frac{d^3p_q}{(2\\pi^3) 2E_q} \\frac{d^3p_H}{(2\\pi^3) 2E_H} \n~~~~~[\\rm{decay~ of}~ t]\\,,\n\\end{eqnarray}\nwhere $\\sqrt{s}$ is the centre of mass energy and $s_1 = (p_q+p_H)^2$. The energies of the produced top and the antitop are given by \n$E_1,~E_2$, whereas the energies of the decay products are denoted by $E_q$ and $E_H$. \nFor these decays, in the center of mass frame and in the narrow width approximation, we can express the elements of the phase space in (\\ref{df_cs1}) as\n\\begin{eqnarray}\n&&\\int \\frac{ds_1}{2\\pi} \\frac{1}{((s_1-m_t^2)^2+\\Gamma_t^2m_t^2)}\n = \\int \\frac{ds_1}{2\\pi} \\frac{\\pi}{m_t \\Gamma_t} \\delta(s_1-m_t^2)\n =\\frac{1}{2 m_t \\Gamma_t} \\,,\\label{t_prop} \\\\ \n&&\\int \\frac{1}{2s} (2 \\pi)^4 \\delta^4 (q_1+q_2-p_1-p_2) \\frac{d^3q_1}{(2\\pi^3) 2E_1} \\frac{d^3q_2}{(2\\pi^3) 2E_2}\n = \\frac{3\\beta}{64 \\pi^2 s} d\\cos\\theta_t d\\phi_t  \\,, \\label{prod_tt} \\\\\n&&\\int (2\\pi)^4 \\delta^4(p_q+p_H-q_1) \\frac{d^3p_q}{(2\\pi^3) 2E_q} \\frac{d^3p_H}{(2\\pi^3) 2E_H}=\\frac{1}{2(2\\pi)^2}\n\\int d\\Omega_q \\frac{\\mid p_q \\mid^2}{(m_t^2-m_H^2)} \\,. \n\\label{t_decay}\n\\end{eqnarray}\nThe total matrix element squared $\\mid \\bar{\\mathcal{M}}^2 \\mid $ in Eq.~(\\ref{df_cs1}), \nis defined as\n\\begin{eqnarray}\n\\mid \\bar{\\mathcal{M}}^2 \\mid&=& \\sum_{L,R}\\sum_{(\\lambda_t\\lambda_t'=\\pm)}\\rho^{P(t\\bar{t})}_{LR,\\lambda_t\\lambda_t'}\\rho^{D(t)}_{\\lambda_t\\lambda_t'} = \\sum_{L,R}\\sum_{(\\lambda_t\\lambda_t'=\\pm)}\n \\mathcal{M}^{L,R}_{\\lambda_t}\\mathcal{M}^{*L,R}_{\\lambda_t'}\n \\rho^{D(t)}_{\\lambda_t\\lambda_t'},\n\\end{eqnarray}\nwhere $ \\mathcal{M}^{L,R}_{\\lambda_t}$ is the production helicity amplitude of the top with a given helicity \n$\\lambda_t$. The helicities of the antitop are summed over. The production helicity amplitudes are listed\nin Eqs.(\\ref{va_hel}) of Appendix \\ref{sec:Appendix1}. \nThe decay matrix of the top quark is defined as $\\rho^{D(t)}_{\\lambda_t\\lambda_t'}=\\mathcal{M}(\\lambda_t)\n\\mathcal{M}^*(\\lambda_t')$ and for $t \\to q H$ the explicit expressions in the rest frame of the top,  as well as in the centre of mass frame are given in Appendix \\ref{sec:appen_decaytcH}. For the top decaying to $W^+b$ the spin density matrix \n$\\rho^{D(t)}_{\\lambda_t\\lambda_t'}$, is given in Appendix~\\ref{sec:appen_decaytWb}, \nfor both the top rest frame and the centre of mass frame. \n\nWe have performed our calculations, in the frame where the electron beam direction  \nis in the positive $z$ direction, with the top emitted at a polar angle \n$\\theta_t$ and the quark emitted in the top decay makes a polar $\\theta_q$ angle with\nthe electron beam, as \nshown in Fig.~\\ref{fig:eett_2nd_frame}. \n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=10cm, height=6.5cm]{eett_3frames.eps}\n\\caption{The coordinate system in the colliding $e^-e^+$ centre of mass \nframe. The $y$-axis is chosen along the $p_1 (e^-) \\times q_1 (t)$ direction and is pointing towards\nthe observer. The coordinate systems in the $t$ and $\\bar{t}$ rest frames are obtained from it by rotation \nalong the $x$ axis and then boost along the $y$ axis.}\n\\label{fig:eett_2nd_frame}\n\\end{figure}\nThe four-vector in the rest frame of the top are related to the c.m. frame by the following \nboost and the rotation matrices (the boost matrix is along the $z$ direction, whereas the \nrotation matrix is applied along the $y$ axis):\n\\begin{eqnarray}\n q_1&=&\\begin{pmatrix}\n          1&0&0&0 \\\\ 0&\\cos\\theta_t&0&\\sin\\theta_t \\\\ 0&0&1&0 \\\\ 0&-\\sin\\theta_t &0&\\cos\\theta_t\n         \\end{pmatrix} \\begin{pmatrix} \n                \\gamma &0&0&\\gamma\\beta \\\\ 0&1&0&0 \\\\0&0&1&0 \\\\ \\gamma\\beta &0&0&\\gamma            \n            \\end{pmatrix} q_1^{top}   \\,,   \n\\end{eqnarray}\nwhere $q_1^{top}$ is defined in the rest frame of the top. \nThe momentum four-vectors in the c.m frame are given by\n\\begin{eqnarray}\np_1 &=& \\frac{\\sqrt{s}}{2}(1,0,0,1),~~~~p_2 = \\frac{\\sqrt{s}}{2}(1,0,0,-1) \\nonumber \\\\\nq_1&=& \\frac{\\sqrt{s}}{2}(1,\\beta \\sin\\theta_t,0,\\beta\\cos\\theta_t),~~~~\nq_2= \\frac{\\sqrt{s}}{2}(1,-\\beta \\sin\\theta_t,0,-\\beta\\cos\\theta_t)  \\nonumber \\\\\np_{q}&=&(E_{q}, E_{q}\\sin\\theta_{q} \\cos\\phi_{q}, E_{q}\\sin\\theta_{q}\\sin\\phi_{q}, E_{q}\\cos\\theta_{q})\n\\end{eqnarray}\nThe momentum of the emitted light quark $\\mid p_q \\mid$ is equal to its energy \n$E_{q}$\nand in the c.m frame the following relations are obtained: \n\\begin{eqnarray} \\label{eq:cosTHtq}\n\\mid p_q \\mid &=& E_{q} = \\frac{(m_t^2-m_H^2)}{\\sqrt{s} (1-\\beta \\cos\\theta_{tq})}, \\nonumber \\\\\n\\cos \\theta_{tq} &=& \\cos\\theta_t \\cos \\theta_q +\\sin\\theta_t \\sin \\theta_q \\cos \\phi_q \\,. \n\\end{eqnarray}\nwhere $\\cos \\theta_{tq}$ is the angle between the top and the emitted light quark in the c.m. frame.\n\nCombining the production and the density matrices in the narrow width approximation for $t$, we get the \npolar distribution of the emitted quark $q$, in the presence of the beam polarization\nafter integrating over $\\phi_q,\\theta_t$, to be \n\\begin{eqnarray}\n \\frac{d\\sigma}{ds~d\\cos\\theta_q~d\\phi_t} &=& |T|^2\n\\end{eqnarray}\nwhere $|T|^2$ is of the form given in Eq.~(\\ref{eq:fin2}). We compute $|T_{e^-_L e^+_R}|^2$, $|T_{e^-_R e^+_L}|^2$\nfor the considered process, and present them in the most general form:\n\\begin{eqnarray}\n |T_{e^{\\mp}_L e^{\\pm}_R}|^2 &=& (|g_{tq}|^2+|g_{qt}|^2) \\left(a_0 + a_1 \\cos\\theta_q  + a_2 \\cos^2\\theta_q \\right) \\nonumber \\\\ \n&& \\pm(|g_{tq}|^2-|g_{qt}|^2) \\left(b_0+ b_1 \\cos\\theta_q + b_2 \\cos^2\\theta_q \\right) \\,.\n\\end{eqnarray}\nThe coefficients $a_{i},b_{i}$ \ncan be deduced from the following expressions: \n\\begin{align}\\label{eq:Long_mp}\n |T_{e^-_L e^+_R}|^2 &= (m_t^2-m_H^2) \\frac{\\pi s}{\\beta} \\left \\lbrace \\frac{|g_{tq}|^2+|g_{qt}|^2}{\\beta^2-1}\n \\left[-4 A_L B_L \\cos\\theta_q \\left ( \\beta +(\\beta^2-1)\\tanh^{-1}\\beta\\right)  \\right. \\right. \\nonumber \\\\\n & \\left. \\left.+ (A_L^2+B_L^2) \\cos^2\\theta_q \\left (\\beta(2\\beta^2-3)-3(\\beta^2-1)\\tanh^{-1} \\beta\\right )\n  \\right. \\right. \\nonumber \\\\\n & \\left. \\left. +\\left(-\\beta +(\\beta^2-1)\\tanh^{-1}\\beta\\right)(A_L^2+B_L^2) -2\\beta(\\beta^2-1)B_L^2 \\right]\n \\right.  \\nonumber \\\\\n & \\left. + 2(|g_{tq}|^2-|g_{qt}|^2)\\left[\\cos\\theta_q \\left((A_L^2+B_L^2)\\tanh^{-1} \\beta -\\beta B_L^2 \\right)\n \\right. \\right. \\nonumber \\\\ \n& \\left. \\left. \n+A_L B_L \n \\left(1-3 \\cos^2\\theta_q\\right) (\\beta-\\tanh^{-1} \\beta) \\right] \\right\\rbrace, \\\\\n |T_{e^-_R e^+_L}|^2 &= (m_t^2-m_H^2) \\frac{\\pi s}{\\beta} \\left \\lbrace \\frac{|g_{tq}|^2+|g_{qt}|^2}{\\beta^2-1}\n \\left[-4 A_R B_R \\cos\\theta_q \\left ( \\beta +(\\beta^2-1)\\tanh^{-1}\\beta\\right )  \\right. \\right. \\nonumber \\\\\n & \\left. \\left.+ (A_R^2+B_R^2)\\cos^2\\theta_q \\left ( \n \\beta(2\\beta^2-3)-3(\\beta^2-1)\\tanh^{-1} \\beta\\right )\n  \\right. \\right. \\nonumber \\\\\n & \\left. \\left. +\\left(-\\beta +(\\beta^2-1)\\tanh^{-1}\\beta\\right)(A_R^2+B_R^2) -2\\beta(\\beta^2-1)B_R^2 \\right]\n \\right.  \\nonumber \\\\\n & \\left. - 2(|g_{tq}|^2-|g_{qt}|^2)\\left[\\cos\\theta_q \\left((A_R^2+B_R^2)\\tanh^{-1} \\beta -\\beta B_R^2 \\right)\n \\right. \\right. \\nonumber \\\\ \n& \\left. \\left. +A_R B_R \n \\left(1-3 \\cos^2\\theta_q\\right) (\\beta-\\tanh^{-1} \\beta) \\right] \\right\\rbrace,\\label{eq:Long_pm}\n\\end{align}\nand \n\\begin{align}\\label{eq:Trans}\n T^{\\ast}_{e^-_R e^+_L} T_{e^-_L e^+_R} &=  \\frac{\\pi s}{\\beta}\n(m_t^2-m_H^2) (\\beta-\\tanh^{-1} \\beta) (3\\cos^2\\theta_q-1) \\cos (\\eta-2\\phi_t) \\nonumber \\\\\n&\\left\\lbrace  (|g_{tq}|^2+|g_{qt}|^2)(A_L A_R-B_L B_R)\n+(|g_{tq}|^2-|g_{qt}|^2)(A_L B_R -A_R B_L)\\right\\rbrace,\n \\end{align}\nwhere $A_{L,R}$ and $B_{L,R}$ are combinations of the standard SM $\\gamma$ \nand $Z$ couplings with the top and the leptons in the $t\\bar{t}$ production given \nin the Eq.~(\\ref{eq:albl}). The Yukawa chiral couplings, as seen from \nEqs.~(\\ref{eq:Long_mp}),~(\\ref{eq:Long_pm}) are both proportional \nto the polar angle of the emitted light quark, $\\cos\\theta_q, \\cos^2\\theta_q$, but \nhave different dependencies. The coefficients of the coupling $|g_{tq}|^2$, which \nmeasures the coupling strength of $t_L$ with $q_R$ and the Higgs, are summed \nin Eq.~(\\ref{eq:Long_mp}), whereas the coefficients of the other chiral coupling\n$|g_{qt}|^2$ do not add up, but cancel each other partially. This is the case \nwhen the electron beam is left polarized and the positron is right polarized. \nThis behaviour of $|g_{tq}|^2$ and $|g_{qt}|^2$ is reversed \nwith the right polarized electrons and the left polarized positrons, as can be noticed from Eq.~(\\ref{eq:Long_pm}), where the coefficients of $|g_{qt}|^2$ add up. Therefore, \nit will be possible to control the influence of particular chiral couplings with a\nsuitable choice of beam polarization. The case of transverse polarization is also \nconsidered, although both $|g_{tq}|^2,~|g_{qt}|^2$ involve same angular dependencies in \nEq.~(\\ref{eq:Trans}) and therefore cannot be used for the analysis of the chirality of the FCNC couplings. \nIt is clear from Eqs.~(\\ref{eq:Long_mp}),~(\\ref{eq:Long_pm}),~(\\ref{eq:Trans}), that $|g_{tq}|^2$ and $|g_{qt}|^2$ cannot be isolated separately, but \ntheir effects can be individually controlled with suitable choice of beam \npolarization. We next study different distributions in the presence of the \nchiral FCNC couplings and accordingly construct asymmetries to set limits on them.\n\n\\subsection{Constraints on the chiral FCNC couplings by angular asymmetries}\\label{sec:cmf_asymmetries}\n\nNext, we perform a detailed analysis of the signal FCNC process considered, along with the standard SM background ($t\\bar{t}, t\\rightarrow Wb$, W decaying hadronically) and construct different asymmetries for obtaining limits on the couplings. \n\nThe total cross section for both the signal and\nthe background, in case of the longitudinal beam polarization is \n\\begin{eqnarray}\n\\sigma_{Signal} &=& \\frac{(m_t^2-m_H^2)^2}{4 s \\Gamma_t m_t}\\frac{1}{1-\\beta^2}(|g_{tq}|^2+|g_{qt}|^2)\\left((1-P^L_{e^-})(1+P^L_{e^+})\n\\left(s \\beta^2  B_L^2 + (2 m_t^2+s) A_L^2\\right)  \\right. \\nonumber \\\\\n&& \\left. + (1+P^L_{e^-})(1-P^L_{e^+}) \\left(s \\beta^2 B_R^2  + (2 m_t^2+s) A_R^2  \\right) \\right)\\,, \\\\\n\\sigma_{Bkg} &=&\\frac{g^2 m_t}{2 s^2 \\Gamma_t m_W^2}\\frac{1}{(1-\\beta^2)^2} (m_t^2-m_W^2)^2(m_t^2+2m_W^2)\n\\left((1-P^L_{e^-})(1+P^L_{e^+})\n\\left(s \\beta^2  B_L^2 \\right. \\right. \\nonumber \\\\ \n&& \\left. \\left. + (2 m_t^2+s) A_L^2\\right)  \n + (1+P^L_{e^-})(1-P^L_{e^+}) \\left(s \\beta^2 B_R^2  + (2 m_t^2+s) A_R^2  \\right) \\right)\\,, \n\\end{eqnarray}\nwhere again $A_{L,R}$ and $B_{L,R}$ are combinations of the SM $\\gamma$ and $Z$ couplings with\nthe quarks in the $t\\bar{t}$ production given in Appendix~\\ref{sec:All_appen}.  \n\n\nWe have performed our analysis considering $\\sqrt{|g_{tq}|^2+|g_{qt}|^2}$ = 0.16,\nin accordance with the latest LHC bounds~\\cite{Greljo:2014dka}.\nThe background i.e. the SM $\\bar{t}Wb$ contribution is scaled down, to be  \ncompared with the signal. We are currently not applying any cuts on the \nfinal state, but a detailed analysis using all the experimental cuts will be\nperformed in Sec.~\\ref{sec:numericalstudy}.\n\nThe polar angle distribution of the \nemitted quark is plotted in Fig.~\\ref{fig:dist_pol} for both, the signal and \nthe background, for \n($a$) $P^L_{e^-} = P^L_{e^+} = 0$, ($b$) $P^L_{e^-} = -0.8,~P^L_{e^+} = 0.3$ \nand $c$) $P^L_{e^-} = 0.8,~P^L_{e^+} = -0.3$. The polar \nangle distribution will be  sensitive to the chirality of the Yukawa couplings and \ntherefore we present our results for three different cases:\n\\begin{itemize}\n \\item Case 1 : $\\sqrt{|g_{tq}|^2+|g_{qt}|^2}$ = 0.16\\,,\n \\item Case 2 : $\\sqrt{|g_{tq}|^2+|g_{qt}|^2}$ = 0.16, with $|g_{qt}|^2$ = 0 \\,,\n \\item Case 3 : $\\sqrt{|g_{tq}|^2+|g_{qt}|^2}$ = 0.16, with $|g_{tq}|^2$ = 0 \\,.\n\\end{itemize}\n\\begin{figure}[htb]\n  \\begin{subfigure}{0.45\\linewidth}\n  \\centering\n    \\includegraphics[width=6.5cm, height=5cm]{Pol_dist_up.eps}\n\\caption{}\n\\label{fig:upa}\n  \\end{subfigure}\n   \\hspace{1.0cm}\n  \\begin{subfigure}{0.45\\linewidth}\n  \\centering\n    \\includegraphics[width=6.5cm, height=5cm]{Pol_dist_eLpR.eps}\n\\caption{}\n\\label{fig:plr}\n  \\end{subfigure}\\\\[1ex]\n  \\begin{subfigure}{\\linewidth}\n    \\hspace{3.5cm}\n  \\includegraphics[width=6.5cm, height=5cm]{Pol_dist_eRpL.eps}\n\\caption{}\n\\label{fig:prl}\n  \\end{subfigure}\n   \\caption{The polar angle distribution of the quark at $\\sqrt{s}= 500$ GeV,\nfor ($a$) $P^L_{e^-} = P^L_{e^+} = 0$, ($b$) $P^L_{e^-} = -0.8,~P^L_{e^+} = 0.3$ and \n($c$) $P^L_{e^-} = 0.8,~P^L_{e^+} = -0.3$. The different Cases\nare discussed in the text.}\n\\label{fig:dist_pol}\n\\end{figure}\nIt can be clearly seen from Fig:~\\ref{fig:dist_pol}, that $|g_{tq}|^2$ \nand $|g_{qt}|^2$ are sensitive to the beam polarization. The different Cases\nbehave similar in the unpolarized case, Fig.~\\ref{fig:upa}.\nCase 2 is most prominent when the electron beam is left polarized and \nthe positron is right polarized, Fig.~\\ref{fig:plr}, whereas Case 3 is distinct for \nthe scenario with right polarized electrons and \nleft polarized positrons, Fig.~\\ref{fig:prl}. Therefore the manifestation of the \ndominance of one of the coupling, if present, will be prominent using the \nsuitable initial beam polarization.  \n\nUsing the above fact that the couplings are sensitive to the polar \nangle distributions of the quark, we next consider \ndifferent asymmetries to give simultaneous limits to both of the \ncouplings. The $|g_{tq}|^2$ and $|g_{qt}|^2$ terms are accompanied by $\\cos\\theta_q$,~ $\\cos(\\eta-2\\phi)$ and $\\cos(\\eta-2\\phi) \\cos^2\\theta_q$ angular \ndependence. The asymmetries which will isolate these terms are the forward-backward asymmetry \nand the azimuthal asymmetry defined as \n\\begin{eqnarray}\nA_{fb}(\\cos\\theta_0)&=& \\frac{1}{d\\sigma\/ds}\n\\left(\\int^1_{\\cos\\theta_0} d\\cos\\theta_q -  \\int^{\\cos\\theta_0}_{-1} d\\cos\\theta_q \\right)\n\\frac{d\\sigma}{ds~d\\cos\\theta_q} \\,,\\label{eq:fb}\\\\\nA_{\\phi}(\\cos\\theta_0) &=& \\frac{1}{d\\sigma\/ds}\\left(\\int^{\\cos\\theta_0}_{-\\cos\\theta_0} d\\cos\\theta_q\n\\int_0^{2\\pi} d \\phi_t~sgn(\\cos(\\eta - 2\\phi_t))\\right) \\frac{d\\sigma}{ds~d\\Omega} \\,,\n\\label{eq:trans_asym} \n\\end{eqnarray}\nwhere $\\theta_0$ is the experimental polar-angle cut \\cite{Grzadkowski:2000nx,Rindani:2003av}\nand $\\Omega = d\\cos\\theta_q~d\\phi_t$. \nThe forward-backward asymmetry will isolate the terms proportional to $\\cos\\theta_q$ in Eqs.(\\ref{eq:Long_mp})\nand (\\ref{eq:Long_pm}). We plot in Fig.~\\ref{fig:FB}, the forward backward asymmetry as a function of \nthe cut-off angle $\\cos\\theta_0$. The dip in the plot is where the value of \n$A_{fb}(\\cos\\theta_0)$ is zero. \nIn the presence of $|g_{tq}|^2~(|g_{qt}|^2 = 0)$, i.e Case 2, with left polarized electrons \nand right polarized positrons, the quarks are emitted in the forward direction with the dip \nof $A_{fb}$ to be greater than zero, Fig.~\\ref{fig:fb_lr},  \nwhereas the other Cases almost follow the SM distribution.  \nSimilarly, with the opposite choice of beam polarization, the \n$|g_{qt}|^2~(|g_{tq}|^2 = 0)$ coupling leads to the quarks being emitted in the forward direction, \nresulting in the dip of $A_{fb}$ to be greater than zero for Case 3 in Fig.~\\ref{fig:fb_rl}.  \n\\begin{figure}[htb]\n  \\begin{subfigure}{0.45\\linewidth}\n  \\centering\n    \\includegraphics[width=6.5cm, height=5cm]{FB_unpol.eps}\n\\caption{}\n\\label{fig:fb_up}\n  \\end{subfigure}\n   \\hspace{1.0cm}\n  \\begin{subfigure}{0.45\\linewidth}\n  \\centering\n    \\includegraphics[width=6.5cm, height=5cm]{FB_eLpR.eps}\n\\caption{}\n\\label{fig:fb_lr}\n  \\end{subfigure}\\\\[1ex]\n  \\begin{subfigure}{\\linewidth}\n    \\hspace{3.5cm}\n  \\includegraphics[width=6.5cm, height=5cm]{FB_eRpL.eps}\n\\caption{}\n\\label{fig:fb_rl}\n  \\end{subfigure}\n\\caption{The forward backward asymmetry as a function of the cut-off angle \n$\\cos\\theta_0$ Eq.~(\\ref{eq:fb}) at $\\sqrt{s}= 500$ GeV, for ($a$) $P^L_{e^-} = P^L_{e^+} = 0$,\n($b$)$P^L_{e^-} = -0.8,~P^L_{e^+} = 0.3$ and ($c$) $P^L_{e^-} = 0.8,~P^L_{e^+} = -0.3$. The different Cases are discussed in the text.}\n\\label{fig:FB}\n\\end{figure}\n\nNext, we plot the azimuthal asymmetry $A_{\\phi}(\\cos\\theta_0)$ as a function \nof $\\cos\\theta_0$ in Fig.~\\ref{fig:azimuthal}. The terms proportional \nto $\\cos(\\eta-2\\phi_t)$ in Eq.~(\\ref{eq:Trans}) survive. We have considered\n$\\eta$ = 0 for our analysis and $P^T_{e^-} = 0.8$ and $P^T_{e^+} =$ 0.3. The \ndistribution is similar for the signal and the background, therefore this \nwill not be an useful observable\\footnote{ \nHowever once the FCNC coupling is discovered, this asymmetry can\nbe used as an additional observable to give limits to the couplings.}.\n\\begin{figure}[htb]\n\\centering\n\\includegraphics[width=6.9cm, height=4.9cm]{Azimuth.eps}\n\\caption{The azimuthal asymmetry $A_{\\phi}(\\theta_0)$ as a function of\n$\\cos\\theta_0$  Eq.~(\\ref{eq:trans_asym}) at $\\sqrt{s}= 500$ GeV, for the transversal polarizations \n$P^T_{e^-} =0.8$ and $P^T_{e^+} =$ 0.6. The different Cases are discussed in\nthe text.}\n\\label{fig:azimuthal}\n\\end{figure}\n\nWe compute the limits on the FCNC couplings from the measurement of the forward-backward asymmetry, \nof $e^-e^+ \\rightarrow t\\bar{t}, t\\rightarrow b W^+$ in the SM.\nThe statistical fluctuation in the asymmetry ($A$), for a given luminosity $\\mathcal{L}$ \nand fractional systematic error $\\epsilon$, is given as\n\\begin{eqnarray}\n\\Delta A^2 &=&\\frac{1-A^2}{\\sigma \\mathcal{L}}+\\frac{\\epsilon^2}{2}(1-A^2)^2,\n\\end{eqnarray}\nwhere $\\sigma$ and $A$ are the values of the cross section and the asymmetry. The value\nof $\\epsilon$ is set to zero for our analysis. \nWe define the statistical significance of an asymmetry prediction for the new physics,\n$A_{FCNC}$, as the number of standard deviations that it lies away from the SM result $A_{SM}$, \n\\begin{equation}\n s=\\frac{|A_{FCNC}-A_{SM}|}{\\Delta A_{SM}}\\,,\n\\end{equation}\nwhere $A_{FCNC}$ is the asymmetry calculated for the process $e^-e^+ \\rightarrow t(\\to c H) \\bar{t}$. \n\\begin{figure}[h]\n  \\begin{subfigure}{0.45\\linewidth}\n  \\centering\n    \\includegraphics[width=7cm, height=5cm]{Contours_unpolLR.eps}\n\\caption{}\n\\label{fig:contour1}\n  \\end{subfigure}\n   \\hspace{1.0cm}\n  \\begin{subfigure}{0.45\\linewidth}\n  \\centering\n    \\includegraphics[width=7cm, height=5cm]{Contours_LRRL.eps}\n\\caption{}\n\\label{fig:contour2}\n  \\end{subfigure}\\\\[1ex]\n\\caption{Contour plots of 3$\\sigma$ and 5$\\sigma$ statistical significance \nin the $|g_{tq}|^2-|g_{qt}|^2|$ region from $A_{fb}$ for $\\theta_0$ = 0, Eq.~(\\ref{eq:fb})\nat $\\sqrt{s}$ = 500 GeV and ${\\cal L}$ = 500 fb$^{-1}$. \nThe solid lines are for the unpolarized case, the dashed lines are for a beam polarization of\n($a$) $P^L_{e^-}$ = -0.8, $P^L_{e^+}$ = 0.3 ($b$)  $P^L_{e^-}$ = 0.8, \n$P^L_{e^+}$ = -0.3. Region in blue will be probed at 5$\\sigma$ and the green+blue area will be explored at 3$\\sigma$\nwith unpolarized beams. The inclusion of the beam polarization probes yellow+green+blue area \nat 5$\\sigma$ and pink+yellow+green+blue at 3$\\sigma$. The region which can not be probed\nby ILC with this choice of beam polarization is shown in grey.}\n\\label{fig:contourall}\n\\end{figure}\nWe show in Fig.~\\ref{fig:contourall} the $|g_{tq}|^2-|g_{qt}|^2$ region, which can be probed \nat a statistical significance of 3$\\sigma$ and 5$\\sigma$, with both unpolarized and \npolarized beams. The outside area surrounding solid lines can be probed with unpolarized\nbeams and the outside area surrounding dashed lines can be probed with a beam\npolarization of $P_{e^-}^L = -0.8,~P_{e^+}^L = 0.3$ (Fig.~\\ref{fig:contour1}),\n$P_{e^-}^L = 0.8,~P_{e^+}^L = -0.3$ (Fig.~\\ref{fig:contour2}). Obviously, the inclusion of the beam \npolarization can probe a greater region of the $|g_{tq}|^2-|g_{qt}|^2$\nparameter space. The $\\cos\\theta_q$ terms \nin Eqs.~(\\ref{eq:Long_mp}-\\ref{eq:Long_pm}) \ncancel each other in case of unpolarized beams.\nThe region in grey is the one, which cannot be explored by ILC with this choice of\nthe beam polarization.\n\nNow we turn to the discussion of  different top spin observables which can be used to study the FCNC couplings. \n\n\\section{Top spin observables at the ILC}\\label{sec:spintop}\n\nWe investigate in this section the top spin polarization in the context of the linear collider, \nas the spin information of the decaying top is not diluted by hadronization. In an attempt\nto understand the top spin correlations, we work in the zero momentum frame ($t\\bar{t}$-ZMF)\n\\cite{Bernreuther:2004jv} of the $t\\bar{t}$ quarks, which is \n\\begin{eqnarray}\n (q_1+q_2)^\\mu =\\left(\\sqrt{(q_1+q_2)^2},0,0,0\\right).\n\\end{eqnarray}\nThe $t$ and the $\\bar{t}$ rest frames are then obtained, by boosting (no rotation is involved) into the $t\\bar{t}$-ZMF. This is\ndifferent from the laboratory frame considered before in Sec.~\\ref{sec:cmframe},\nwhere the electron beam is chosen along the $z$ axis, and the $t$ and the $\\bar{t}$ rest\nframes were constructed by boosting from the lab frame along with a suitable Wigner rotation.\n\nThe top quark pair production at $O(\\alpha_{\\rm em})$ is given by\na direct production with the $\\gamma$ and $Z$ exchange: \n\\begin{eqnarray}\ne^-(p_1,\\lambda_1) e^+(p_2,\\lambda_2) \\overset{\\gamma,Z}{\\to} t(q_1,s_t) \\bar{t}(q_2,s_{\\bar{t}})\\,.\n\\label{eq:prod} \n\\end{eqnarray} \nThe spin four-vectors of the top, $s_t$ and the antitop, $s_{\\bar{t}}$ satisfy the usual relations\n\\begin{equation}\ns_t^2 = s_{\\bar{t}}^2 = -1\\,, \\quad\\quad  k_1 \\cdot s_t = k_2 \\cdot s_{\\bar{t}} = 0 \\,.\n\\end{equation}\nThe leading order differential cross section for the $t\\bar{t}$ production,\nin the presence of longitudinal polarization Eq.~(\\ref{eq:fin2}), has the phase space factor\nEq.~(\\ref{prod_tt}) and can be written in the spin density matrix representation as\n\\begin{eqnarray}\n&& d\\sigma (\\lambda_1,\\lambda_2,s_t,s_{\\bar{t}}) = \\frac{3 \\beta}{32 \\pi s} |\\mathcal T|^2 \\,,\n\\nonumber \\\\\n&& \n|\\mathcal T|^2 =  \\frac{1}{4}{\\rm Tr} \\left [ \\rho \\cdot ({\\bf 1} + {\\bf\\hat{s}}_t \n\\cdot {\\bf\\sigma})\\otimes ({\\bf 1} + {\\bf\\hat{s}}_{\\bar{t}} \\cdot {\\bf\\sigma}) \\right ]\\,.\n\\end{eqnarray}\nIn the above equation, $\\rho = \\rho^{P(t\\bar{t})}$ is the corresponding production spin density matrix \ndescribing the production of (on-shell) top quark pairs in a specific spin configuration,\nwhile $\\mathbf{\\hat{s}}_t$ ($\\mathbf{\\hat{s}}_{\\overline{t}}$) is the unit polarization \nvector of the top (antitop) quark in its rest frame and \n$\\boldsymbol\\sigma = (\\sigma_1,\\sigma_2,\\sigma_3)^T$ is a vector of Pauli matrices.\nConveniently, the most general decomposition of the spin density matrix $\\rho$ for the $t\\bar{t}$ \nproduction is of the form\n\\begin{eqnarray}\n\\rho = A\\, {\\bf 1} \\otimes  {\\bf 1} + B_i^{t} \\, \\sigma_i  \\otimes {\\bf 1} +  B_i^{\\overline{t}} \\, {\\bf 1} \\otimes \\sigma_i + C_{ij} \\, \\sigma_i \\otimes \\sigma_j \\, , \n\\label{eq:rho}\n\\end{eqnarray}\nwhere the functions $A$, ${B}_i^t$ (${B}_i^{\\overline{t}}$) and $C_{ij}$ describe the spin-averaged production\ncross section, polarization of top (antitop) quark and the top-antitop spin-spin correlations, respectively.\nUsing the spin four-vectors defined as\n\\begin{eqnarray}\ns_t^{\\mu} &=&  \\left ( \\frac{ \\mathbf{q}_1 \\cdot \\mathbf {\\hat{s}}_t}{m_t}, \\mathbf {\\hat{s}}_t + \\frac{ \\mathbf{q}_1 (\\mathbf{q}_1 \\cdot \\hat{\\mathbf s}_t)}{ m_t (E_t + m_t)} \\right )\\,,\n\\nonumber \\\\\ns_{\\overline{t}}^{\\mu} &=&  \\left (  \\frac{ \\mathbf{q}_2\\cdot \\mathbf{\\hat{s}}_{\\overline{t}}}{m_t}, \\mathbf{\\hat{s}}_{\\overline{t}} + \\frac{ \\mathbf{q}_2 (\\mathbf{q}_2 \\cdot \\mathbf{\\hat{s}}_{\\overline{t}})}{ m_t (E_{\\bar t} + m_t)} \\right )\\,,\n\\end{eqnarray}\nthe decomposition of the squared scattering amplitude $|\\mathcal T|^2$ can be written as\n\\begin{eqnarray}\n|\\mathcal T|^2 = a + b^{t}_\\mu s_t^{\\mu} + b^{\\overline{t}}_\\mu s_{\\overline{t}}^{\\mu} + c_{\\mu\\nu} s_t^{\\mu} s_{\\overline{t}}^{\\nu}\\,,\n\\label{eq:M2}\n\\end{eqnarray}\nand by comparing expressions \\eqref{eq:rho} and \\eqref{eq:M2} one can extract the functions $A$, ${B}_i^t$ (${B}_i^{\\overline{t}}$) and $C_{ij}$.\nThe functions $B_i^t (B_i^{\\bar t})$ and $C_{ij}$ can be further decomposed as \n\\begin{eqnarray}\nB_i^t &=& b_p^t \\hat{p}_i + b_q^t \\hat{q}_i \\,,\\nonumber \\\\\nC_{ij} &=& c_o \\delta_{ij} + c_4 \\hat{p}_i\\hat{p}_j +  c_5 \\hat{q}_i\\hat{q}_j + c_6 \n(\\hat{p}_i\\hat{q}_j +  \\hat{q}_i\\hat{p}_j)\\,,\n\\end{eqnarray}\nwhere $\\hat{k}$ denotes the unit vector, and we have kept only nonvanishing terms for our case \n\\footnote{In the SM the top-quark spin polarization in the normal direction to the production \nplane only exists if one considers QCD radiative corrections or absorptive part of the \n$Z$-propagator. However, since these contributions for the $t\\bar{t}$ production at \nlinear colliders are extremely small~\\cite{GK1,GK2,Groote:2010zf,KornerNEW}\n(apart from the threshold region) we do not consider them here.}.\n\nThe various top spin observables $\\langle {\\cal O}_i \\rangle$ can then be calculated as\n\\begin{eqnarray}\n \\langle {\\cal O}_i (\\mathbf{{S}}_t, \\mathbf{{S}}_{\\overline{t}})\\rangle\n = \\frac{1}{\\sigma} \\int d\\Phi_{t\\bar t} { {\\rm Tr} [ \\rho \\cdot {\\cal O}_i (\\mathbf{{S}}_t, \n \\mathbf{{S}}_{\\overline{t}} ) ]} \\,,\n \\end{eqnarray}\nwhere $\\sigma = \\int d\\Phi_{t\\bar t} {\\rm Tr}[\\rho]$ is the unpolarized production cross-section,\n$d\\Phi_{t\\bar{t}}$ is the phase space differential and  \n$\\mathbf{{S}}_t = \\boldsymbol{\\sigma}\/2 \\otimes {\\bf 1} \\, \n( \\mathbf{{S}}_{\\overline{t}} = {\\bf 1} \\otimes \\boldsymbol{\\sigma}\/2)$ is the top (antitop) spin operator.  \nWe consider the following spin observables\n\\begin{eqnarray}\\label{eq:observables}\n{\\cal O}_1 &=&  \\frac{4}{3} \\mathbf{{S}}_t \\cdot \\mathbf{S}_{\\overline{t}} \\,,\n\\nonumber \\\\\n{\\cal O}_2 &=&  \\mathbf{{S}}_t \\cdot \\mathbf{\\hat{a}},~~~~~\\bar{\\cal O}_2 = \\mathbf{{S}}_{\\bar t} \\cdot \\mathbf{\\hat{b}} \\,,\n\\nonumber \\\\\n{\\cal O}_3 &=& 4 ( \\mathbf{{S}}_t \\cdot \\mathbf{\\hat{a}} ) ( \\mathbf{S}_{\\overline{t}} \\cdot \\mathbf{\\hat{b}} ),\\nonumber \\\\\n{\\cal O}_4 &=& 4 \\left ( (\\mathbf{{S}}_t \\cdot \\mathbf{\\hat{p}} ) \n( \\mathbf{S}_{\\overline{t}} \\cdot \\mathbf{\\hat{q}}) + (\\mathbf{{S}}_t \\cdot \\mathbf{\\hat{q}} )\n( \\mathbf{S}_{\\overline{t}} \\cdot \\mathbf{\\hat{p}} ) \\right ),\n\\end{eqnarray}\ngiving the net spin polarization of the top-antitop system (${\\cal O}_1$), polarization of the top (antitop)\nquark (${\\cal O}_2 (\\bar{{\\cal O}}_2)$), the top-antitop spin correlation (${\\cal O}_3$), with respect to spin quantization axes $\\mathbf{\\hat a}$ \nand $\\mathbf{\\hat b}$. The observable ${\\cal O}_4$ is an additional top-antitop \nspin correlation with respect to the momentum of the incoming and\nthe outgoing particles~\\cite{BrandUwer}. \n\nThe observable ${\\cal O}_1$ can be probed using the opening angle distribution \n($\\varphi$), i.e. the angle between the direction of flight of the two (top and antitop) spin analyzers (which are the final particles produced in the top and antitop decays)  \ndefined in the $t$ and $\\bar{t}$ frames, \nrespectively, i.e ${\\bf\\hat{p}}_q \\cdot {\\bf\\hat{p}}_l = \\cos\\varphi$, \n\\begin{eqnarray}\\label{eq:dobservable}\n\\frac{1}{\\sigma} \\frac{d \\sigma}{d \\cos \\varphi} &=& \\frac{1}{2} \\left (  1 - D  \\cos\\varphi \\right ),\n\\end{eqnarray}\nand\n\\begin{equation}\nD = \\braket{\\mathcal O_1} \\kappa_f \\kappa_{\\bar{f}} \n\\end{equation}\nwhere $\\kappa_f(\\kappa_{\\bar{f}})$ are the top, antitop spin analyzers considered here. The spin analyzer \nfor the FCNC top-Higgs decays can be either a direct $t$-quark daughter, i.e. $H$ or $c\/u$-quark, \nor $H$ decay products like $b$ or $\\bar{b}$ in $b\\bar{b}$ decay, or $\\tau^+(\\tau^-)$ in $H \\to \\tau^+\\tau^-$ decay, or jets. On the other hand, \nthe spin analyzer for $\\bar{t}$ are $W^-$ or $\\bar{b}$, or a $W^-$ decay products $l^-, \\bar \\nu$ or jets. \nWe consider the $q=c\/u$ quark from the top and the $l^-$ from the antitop as spin analyzers in this work.\nThe spin analyzers are calculated from the one-particle decay density matrices given as \n\\begin{eqnarray}\n\\rho^{t \\to f(\\bar{t} \\to \\bar{f})}_{\\alpha\\alpha'} &=& \\Gamma^{t \\to f(\\bar{t} \\to \\bar{f})}\n\\left[\\frac{1}{2} \\left({\\bf 1} + \\kappa_{f(\\bar{f})} \n{\\bf\\hat{p}}_{f(\\bar{f})}\\cdot \\bf{\\sigma} \\right)\\right]_{\\alpha\\alpha'}. \n\\end{eqnarray}\nwhere $\\alpha,\\alpha'$ denote the $t$-quark spin orientations, ${\\bf\\hat{p}}_{f}$ and ${\\bf\\hat{p}}_{\\bar{f}}$ are the directions of flight \nof the final particles $f$ and $\\bar {f}$ in the rest frame of the top and the antitop quarks respectively. \nThe values of various $\\kappa_{f(\\bar f)}$ for SM top (antitop) decays are presently known at NLO in QCD\nand can be found in~\\cite{Brandenburg:2002xr}. The top quark polarization matrix can be also written as \n \\begin{equation}\n\\rho^{t \\to f}_{\\alpha\\alpha'} = \\frac{1}{2} \n\\begin{pmatrix}\n1 + \\kappa_f \\cos\\theta^{top}_f  & \\kappa_f \\sin \\theta^{top}_f e^{i \\phi^{top}_f} \\\\\n\\kappa_f \\sin \\theta^{top}_f e^{-i \\phi^{top}_f}  &1 - \\kappa_f \\cos\\theta^{top}_f \n                                               \\end{pmatrix}_{\\alpha\\alpha'},\n \\end{equation}\n and similarly for the antitop spin matrix $\\rho^{\\bar{t} \\to \\bar{f}}$.\nThe top spin analyzing power of $q$ ($\\kappa_{q}$) from the $t \\to H q$ decay\ncan be calculated from Eq.~(\\ref{eq_me_topch_rest}), in Appendix~\\ref{sec:appen_decaytcH}, \n\\begin{eqnarray}\n\\kappa_q &=& \\frac{|g_{qt}|^2-|g_{tq}|^2}{|g_{qt}|^2+|g_{tq}|^2} \\,.\\label{eq:kappa1}\n\\end{eqnarray}\n Similarly, \nthe spin analyzing power for the $b$ quark ($\\kappa_b$), from the top decay to $W^+b$  can be obtained from \nEqs.~(\\ref{eq_me_topWB_rest}), in Appendix~\\ref{sec:appen_decaytWb}, \n\\begin{eqnarray}\n \\kappa_b &=& \\frac{m_t^2-2m_W^2}{m_t^2+2m_W^2} \\,. \\label{eq:kappa2}\n\\end{eqnarray}\nLeptons emitted from the antitop decay, due to the $V-A$ interactions\nare the perfect top spin analyzers (Eqs.~(\\ref{eq_me_top}), in Appendix~\\ref{sec:appen_decaytWb}) with \n\\begin{equation}\n\\kappa_{\\bar{f}} = \\kappa_l =1,\n\\end{equation} \nat LO QCD ($\\alpha_s$ corrections are negligible \\cite{Brandenburg:2002xr}),   \nwith their flight directions being 100\\% correlated with the directions of the top spin.\nIt is clear from Eq.~(\\ref{eq:kappa1}) that with $|g_{qt}|^2 \\simeq |g_{tq}|^2$, the spin information of the top is lost ($\\kappa_q \\approx$ 0). However in the presence or dominance of only one of the coupling,\nthe emitted quark acts as a perfect spin analyzer ($\\kappa_q \\approx 1$).  \n\nThe top (antitop)-quark polarization and spin-spin correlations can be measured using the double differential \nangular distribution of the top and antitop quark decay products:\n\\begin{eqnarray}\n\\frac{1}{\\sigma} \\frac{d^2 \\sigma}{d \\cos\\theta_f d\\cos\\theta_{\\bar f}} = \\frac{1}{4} \\left ( 1 + B_t \n \\cos\\theta_f + B_{\\bar{t}}  \\cos\\theta_{\\bar f} - C \\cos\\theta_f \\cos\\theta_{\\bar f} \\right )\\,,\n\\label{eq:diffsigma}\n\\end{eqnarray}\nwhere $\\theta_f (\\theta_{\\bar f})$ is the angle between the direction of the top (antitop) \nspin analyzer $f,\\,(\\bar f)$ in the $t$ $(\\bar{t})$ rest frame and the \n$\\hat{\\bf a}$ ($\\hat{\\bf  b}$) direction in the $t\\bar{t}$-ZMF, c.f.~\\cite{Bernreuther:2004jv}.  \nComparing Eq.~(\\ref{eq:diffsigma}), with Eq.~(\\ref{eq:observables}), we have\n\\begin{eqnarray}\nB_t  &=& \\braket{\\mathcal O_2} \\kappa_{f} \\,,\\quad \n\\quad B_{\\bar t}  = \\braket{\\bar {\\mathcal O}_2} \\kappa_{\\bar f}\\,,\n\\nonumber \\\\\nC  &=& \\braket{\\mathcal O_3} \\kappa_{f} \\kappa_{\\bar f}\\,.\n\\end{eqnarray}\nwhere ${\\cal O}_2$ and $\\bar{\\cal O}_2$ are related to the top, antitop spin polarization \ncoefficients $B_t$ and $B_{\\bar t}$. Since there is no CP violation in our case, we consider\n$B \\equiv B_t = \\mp B_{\\bar t}$ for $\\hat{\\bf a} = \\pm \\hat{\\bf b}$ . \nThis limit is a good approximation for the charged leptons \nfrom $W$ decays~\\cite{Brandenburg:2002xr}. \nThe spin observable ${\\cal O}_3$ is also related to the spin correlation function $C_{ij}$ \nin Eq.~(\\ref{eq:rho}), \n\\begin{eqnarray}\n\\braket{ {\\cal O}_3 } = \\frac{ \\sigma_{t \\bar{t}} (\\uparrow \\uparrow) + \\sigma_{t \\bar{t}} (\\downarrow \\downarrow) - \\sigma_{t \\bar{t}} (\\uparrow \\downarrow)- \n\\sigma_{t \\bar{t}} (\\downarrow \\uparrow)}\n{\\sigma_{t \\bar{t}} (\\uparrow \\uparrow) + \\sigma_{t \\bar{t}} (\\downarrow \\downarrow) + \\sigma_{t \\bar{t}} (\\uparrow \\downarrow)+ \\sigma_{t \\bar{t}} (\\downarrow \\uparrow)}\\,,\n\\end{eqnarray}\nwhere the arrows refer to the up and down spin orientations of the top and the antitop \nquark with  respect to the $\\mathbf{\\hat a}$ and $\\mathbf{\\hat b}$ quantization axes,\nrespectively. \n\\\\\nAlso ${\\cal O}_4$ gets corrected by $\\kappa_{f} \\kappa_{\\bar f}$ depending on the final particles measured from the $t$ and $\\bar{t}$ decays. \n\nThe arbitrary unit vectors $\\bf{\\hat a}$ and $\\bf{\\hat b}$ specify different\nspin quantization axes which can be chosen to maximize\/minimize the desired polarization \nand the correlation effects. We work with the following choices:\n\\begin{align}\n\\hat{\\bf a} &= - \\hat{\\bf b} = \\hat{\\bf q}\\,,  && ({\\rm ``helicity\" \\; basis})\\,,&&\n\\nonumber \\\\\n\\hat{\\bf a} &= \\hat{\\bf b} = \\hat{\\bf p}\\,,  && ({\\rm ``beamline\" \\; basis})\\,,&&\n\\nonumber \\\\\n\\hat{\\bf a} &= \\hat{\\bf b} = \\hat{\\bf d}_{\\bf X}\\,,  && ({\\rm ``off-diagonal\" \\; basis\\, (specific \\, for\\,some \\,model\\, X)})\\,,&&\n\\nonumber \\\\\n\\hat{\\bf a} &= \\hat{\\bf b} = \\hat{\\bf e}_{\\bf X}  &&({\\rm ``minimal\" \\; basis\\, (specific \\, for\\,some \\,model\\, X)})\n\\label{eq:axes}\n\\end{align}\nwhere $\\hat{\\bf p}$ is the direction of the incoming beam and $\\hat{\\bf q} = \\hat{\\bf q}_1$ is\nthe direction of the outgoing top quark, both in the $t\\bar t$ center of mass frame. The \noff-diagonal basis \\cite{Parke:1996pr} is the one, where the top spins are $100\\%$ correlated and\nis given by quantizing the spins along the axis $ \\hat {\\bf d}_{\\rm SM}$ determined as\n\\begin{eqnarray}\n\\hat{\\bf d}_{\\rm SM} = \\hat{\\bf d}_{\\rm SM}^{\\rm max} =\n\\frac{ - \\hat{\\bf p}  + ( 1 - \\gamma) z \\; \\hat{\\bf q}_1}{\\sqrt{ 1 - (1 - \\gamma^2) z^2}}\\,,\n\\label{eq:dSM}\n\\end{eqnarray}\nwhere $z = \\hat{\\bf p} \\cdot \\hat{\\bf q}_1 = \\cos \\theta$ and \n$\\gamma = E_t\/m_t = 1\/\\sqrt{1 - \\beta^2}$ and which interpolates between the beamline \nbasis at the threshold ($\\gamma \\to 1$) and the helicity basis for\nultrarelativistic energies ($\\gamma \\to \\infty$). We would like to point out here that this\noff-diagonal basis $\\hat{\\bf d}_{\\rm SM}$ is specific to the SM $t\\bar{t}$ production, but a\ngeneral procedure for finding such an off-diagonal basis is given \nin~\\cite{Mahlon:1997uc, Uwer:2004vp}. The idea is to determine the maximal eigenvalue\nof the matrix function $C_{ij}$ in Eq.~(\\ref{eq:rho}) and the corresponding eigenvector,\nwhich provides the off-diagonal quantization axis $\\hat {\\bf d}_X$, for any model X \n\\cite{KamenikMelic}.\n\nHere we introduce the complementary basis to the ``off-diagonal'' one, $\\bf{\\hat{e}}_{\\rm SM}$, \nwhere the eigenvector corresponds to the minimal eigenvalue of $C_{ij}$  in the\nSM quark-antiquark production. The correlation of the top-antitop spins\nin this basis is minimal. This axis could be useful in the \nnew model searches since the minimization of the top-antitop correlations in the SM \ncan, in principle, enhance the non-SM physics. The `minimal basis' is defined by the axis  \n\\begin{eqnarray}\n{\\bf\\hat{e}}_{\\rm SM} = \\hat{\\bf e}_{\\rm SM}^{\\rm min} = \n\\frac{ - \\gamma z  {\\bf\\hat{p}}  +  (1 - ( 1 - \\gamma^2) z^2 )\\; \n{\\bf\\hat{q}_1}}{\\sqrt{ (1 - z^2) (1 - (1 - \\gamma^2) z^2)}}.\n\\label{eq:eSM}\n\\end{eqnarray}\n\\begin{figure}\n\\hspace{3.5cm}\n\\includegraphics[width=6cm, height=4.5cm]{spin_top.eps}\n\\caption{The top quark spin vector $s_t$ in the $t\\bar{t}$ production in $t$ rest frame, with\nthe direction of $s_t$ given by an angle $\\xi$. The angle $\\xi$ is measured in the \nclockwise direction from the $\\bar{t}$ momenta.}\n\\label{fig:spin}\n\\end{figure}\nThe `off-diagonal' and the `minimal' basis define the angle $\\xi$ between the top-quark\nspin vector and the antitop direction in the top-quark rest frame~\\cite{Mahlon:2010gw}, \nshown in Fig.~\\ref{fig:spin}, \n\\begin{eqnarray}\n\\tan \\xi^{\\rm off(=max)} &=& \\frac{\\tan \\theta_t }{\\gamma} \\,, \\quad\n\\tan \\xi^{\\rm min} = \\frac{\\gamma }{\\tan \\theta_t} \\,,\n\\end{eqnarray}\nor \n\\begin{eqnarray}\n \\cos^2 \\xi^{\\rm min} + \\cos^2 \\xi^{\\rm off(=max)} = 1 \\,,\n\\end{eqnarray} \nas expected. As already stated, such axes which minimize or maximize spin correlations can be constructed for any model. \n\nThe analytical form of the observables defined in Eq.~(\\ref{eq:observables}), \nis listed in appendix~\\ref{sec:appen_spin} for the SM $t\\bar{t}$ production in the presence\nof longitudinal polarization. The observables ${\\cal O}_i$, ($i$ = 1,2,3,4) are then \nmultiplied with the appropriate $\\kappa$ factors. The QCD radiative corrections for all \nthe top spin observables considered here are calculated in \\cite{BrandUwer} and it is shown \nto be small. Also recently it has been shown that the $O(\\alpha_S)$ corrections to the \nmaximal spin-spin correlations in the off-diagonal basis are negligible \\cite{KornerNEW}. \nTherefore we neglect them all in our calculations. \n\nNext, we present the results for spin correlations\nand top (antitop)-quark polarizations in the helicity basis ($C_{\\rm hel}$, $B_{\\rm hel}$),\nbeamline basis ($C_{\\rm beam}$, $B_{\\rm beam}$), off-diagonal ($C_{\\rm off}$, $B_{\\rm off}$)\nand the minimally polarized basis ($C_{\\rm min}$, $B_{\\rm min}$), as \ndefined by Eqs.~\\eqref{eq:axes}, \\eqref{eq:dSM} and~\\eqref{eq:eSM} respectively, and check\nfor their sensitivity to the initial beam polarization. These results are presented in the \nabsence of cuts, realistic cuts severely distort the non-zero coefficients of \nEq.~(\\ref{eq:dobservable}) and Eq.~(\\ref{eq:diffsigma}). The observable ${\\cal O}_1$ as seen\nfrom Eq.~(\\ref{eq:O1}), is equal to 1 and is therefore independent of beam polarization. \nHowever, it is dependent on the value of $\\kappa_f$. \n\nIn Table~\\ref{tab:O1-4} we present the values of the different spin observables\nin the different spin basis considered here, in the presence of beam polarizations. We have\nconsidered the case, when the antitop is decaying to lepton ($\\kappa_{\\bar{f}}$ =1), \n$\\kappa_f = \\kappa_q$, Eq.~(\\ref{eq:kappa1}) for the  \nFCNC top decay, and $\\kappa_f = \\kappa_b$, Eq.~(\\ref{eq:kappa2}) for the top decaying to $W^+b$.\n\\begin{table}[htb]\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|} \\hline\nObservables &Basis &$P^L_{e^-} = 0, P^L_{e^+} = 0$ &$P^L_{e^-} = 0.8, P^L_{e^+} = -0.3$\n&$P^L_{e^-} = -0.8, P^L_{e^+} =0.3$ \\\\ \\hline\n${\\cal O}_1$ &      &0.333$\\kappa_f$  &0.333$\\kappa_f$  &0.333$\\kappa_f$    \\\\ \\hline\n          &hel    &$-$0.076$\\kappa_f$  & 0.247$\\kappa_f$  &$-$0.239$\\kappa_f$    \\\\ \n          &beam    &$-$0.174$\\kappa_f$  & 0.344$\\kappa_f$  &$-$0.436$\\kappa_f$    \\\\ \n${\\cal O}_2$ &off   &0.176$\\kappa_f$  &$-$0.351$\\kappa_f$  & 0.443$\\kappa_f$    \\\\ \n          &min    & 0.04$\\kappa_f$  &$-$0.131$\\kappa_f$  & 0.127$\\kappa_f$    \\\\ \\hline\n          &hel    & $-$0.654$\\kappa_f$  & $-$0.666$\\kappa_f$  & $-$0.648$\\kappa_f$    \\\\ \n          &beam    & 0.881$\\kappa_f$  &0.852 $\\kappa_f$  &0.897$\\kappa_f$    \\\\ \n${\\cal O}_3$ &off   &0.911$\\kappa_f$  & 0.886$\\kappa_f$  &0.924$\\kappa_f$    \\\\ \n          &min    & 0.224$\\kappa_f$  &0.229 $\\kappa_f$  &0.222$\\kappa_f$    \\\\ \\hline                                     \n${\\cal O}_4$ &      & 0.546$\\kappa_f$  & 0.612$\\kappa_f$  &0.512$\\kappa_f$    \\\\ \\hline                                    \n\\end{tabular}\n\\caption{The value of the spin observables in different bases, with different choices  of initial beam polarization. $\\kappa_f = \\kappa_q$ for FCNC $t$-decays and $\\kappa_f = \\kappa_b$ for $t \\to W^+ b$.}\n\\label{tab:O1-4}\n\\end{center}\n\\end{table} \nWe note that the top (antitop) spin polarizations are quite sensitive to the beam polarization, while \nthis is not the case for the spin-spin correlations ${\\cal O}_3,{\\cal O}_4$ where the influence of the beam \npolarizations gets diluted, see Eqs.~(\\ref{eq:O3h}-\\ref{eq:O4}). \nAlso note that all observables are proportional to $\\kappa_f = \\kappa_q$ and  will be equal to zero if $g_{tq}$ and $g_{qt}$ are equal. \n\\section{Numerical analysis of the FCNC $g_{tq},~g_{qt}$ couplings at the ILC}\\label{sec:numericalstudy}\n\nIn this section we perform a detailed numerical simulation of the FCNC interactions in the $t \\to qH$ \ndecay at the ILC. As before, the process we consider is the top pair production, \nwith the top decaying to $qH$, the antitop decaying to $W^-\\bar{b}$ with the $W^-$ decaying\nleptonically and subsequently the Higgs decaying to a $b\\bar{b}$ pair.\nThe main background for the process under study comes from the $t\\bar{t}$ pair production, with \none of the top decaying hadronically and the other decaying to a lepton, $\\nu$ and a $b$ quark.\nWe have performed our calculations, by first generating the Universal Feynrules Output (UFO) model \nfile using FeynRules 2.3~\\cite{Alloul:2013bka}, including\nthe effective interaction, defined in Eq.~(\\ref{eq:tqhA}). The UFO file is then implemented in\nMadGraph 5 v2.4.2~\\cite{Alwall:2011uj}, for Monte Carlo simulation. We also employ\nPythia 8~\\cite{Sjostrand:2014zea} for parton showering and hadronization along with \nFastjet-3.2.0~\\cite{Cacciari:2011ma} for the jet formation.\nThe cross section of the signal and the background, at $\\sqrt{s}$ = 500 GeV, before the\napplication of the event selection criteria is listed in Table~\\ref{tab:allowedcs}. \n\\begin{table}[htb]\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|} \\hline\n&$\\sigma$(fb)&$\\sigma$(fb)&$\\sigma$(fb) \\\\\n$e^-e^+\\rightarrow t\\bar{t}$ &$P^L_{e^-} = 0, P^L_{e^+} = 0$  & $P^L_{e^-} = -0.8, P^L_{e^+} = 0.3$ \n& $P^L_{e^-} = 0.8, P^L_{e^+} = -0.3$  \\\\ \n \\hline\n{\\rm signal:}&&& \\\\$t\\rightarrow q b\\bar{b},\n\\bar{t}\\rightarrow  l^- \\bar{\\nu}_l \\bar{b}$ &$73.4(|g_{tq}|^2+|g_{qt}|^2)$ \n&$120.5(|g_{tq}|^2+|g_{qt}|^2)$ &$62(|g_{tq}|^2+|g_{qt}|^2)$  \\\\ \\hline\n{\\rm background:}&&&\\\\\n$t\\rightarrow q_1 q_2 b,\n\\bar{t}\\rightarrow  l^- \\bar{\\nu}_l \\bar{b}$  &74.5 &124.7 &58.9 \\\\ \\hline\n\\end{tabular}\n\\caption{The production cross section of the signal and the background at $\\sqrt{s}$ = 500 GeV. The results\nare presented for both the polarized and the unpolarized beams.}\n\\label{tab:allowedcs}\n\\end{center}\n\\end{table}\n\nWe now describe in details \nthe different cuts and conditions considered for our analysis. Since the top\nfrom the $tqH$ final state decays to $Wb$, the lepton from the $W$, tends to be energetic\nand isolated. Therefore firstly the events \nwith one isolated lepton are selected, through the lepton isolation cut. An isolated lepton is identified, \nby demanding that the scalar sum of the energy of all the stable\nparticles within the cone of $\\Delta R = \\sqrt{\\Delta \\eta^2 +\\Delta\\phi^2}\\leq 0.2$ about \nthe lepton is less than  $\\sqrt{6(E_l-15)}$~\\cite{Yonamine:2011jg}, where\n$E_l$ is the energy of the lepton. Furthermore, the transverse momenta of the \nleptons are assumed as $p_T>$10 GeV. The events with more than one isolated lepton are discarded.\nThe remaining stable visible particles of the event, are then clustered into four jets using the \ninbuilt $k_t$ algorithm in FastJet for $e^-e^+$ collisions, which is similar to the Durham algorithm.\nThe reconstructed jets and the isolated lepton are combined to form the intermediate heavy states. \nThe three jets with the highest $b$ tagging probability are considered as the $b$ jets. A jet \nis tagged as a $b$ jet if it has a $b$ parton within a cone of $\\Delta R <$ 0.4 with the jet axis.\nA tagging efficiency of 80\\%~\\cite{Asner:2013psa} is further incorporated. The jets are checked \nfor isolation and are expected to have $p_T>$ 20 GeV.\nThe momentum of the neutrino is calculated by summing over all the visible momenta\nand the energy of the neutrino is assigned the magnitude of its momenta vector. The isolated lepton and the neutrino reconstructs the leptonically decaying $W$ boson. \n\nThere will be three $b$ tagged jets and a non $b$ jet in the final state and therefore\nthree possible combinations to reconstruct the Higgs mass from the $b$ tagged jets. Additionally\none of this pair of $b$ jets reconstructing the Higgs mass, along with the the non $b$ jet should\ngive an invariant mass close to $m_t$. We choose the combination of the jets,\nwhich minimizes the quantity $|m_{b_ib_j}-m_H|^2 +|m_{b_ib_jQ}-m_t|^2$, with \n$i,j$ taking values for various combinations of the $b$ jets and $Q$ is the non-$b$ jet. \nThe reconstructed Higgs mass is given by $m_{b_ib_j}$, and the reconstructed top\nmass is denoted by $m_{b_ib_jQ}$. In order to account for the detector resolution, \nwe have smeared the leptons and the jets using the following parametrization. The\njet energies are smeared~\\cite{BrauJames:2007aa} with the different \ncontributions being added in quadrature,\n\\begin{eqnarray}\n \\frac{\\sigma(E_{jet})}{E_{jet}}&=& \\frac{0.4}{\\sqrt{E_{jet}}} \\oplus 2.5\\% \\,.\n\\end{eqnarray}\nThe momentum of the lepton is smeared as a function of the momentum and the angle $\\cos\\theta$ \nof the emitted leptons~\\cite{Li:2010ww}\n\\begin{eqnarray}\n \\frac{\\sigma(P_l)}{P_l^2} =\\left(\\begin{array}{cc}a_1\\oplus\\frac{b_1}{P_l},&|\\cos\\theta_l|< 0.78 \\\\\n                \\left(a_2 \\oplus \\frac{b_2}{P_l}\\right)  \\left(\\frac{1}{\\sin(1-|\\cos\\theta_l|)}\n                \\right) & |\\cos\\theta_l|> 0.78 \n               \\end{array}\\right) \\,,\n\\end{eqnarray}\nwith\n\\begin{eqnarray}\n(a_1,~b_1) &=& 2.08\\times10^{-5}~({\\rm{1\/GeV}}),~~8.86\\times10^{-4}, \\nonumber \\\\\n(a_2,~b_2) &=& 3.16\\times10^{-6}~({\\rm{1\/GeV}}),~~2.45\\times10^{-4}. \n\\end{eqnarray}\n\nWe plot in Fig.~\\ref{fig:m_recons}, the reconstructed Higgs, $t$ and the $\\bar{t}$ masses. The \nHiggs mass is reconstructed as $m_H^2 = (p_b +p_{\\bar{b}})^2$, whereas the top \nthe antitop masses are calculated as \n$m_t^2 = (p_b + p_{\\bar{b}} + p_{non-b})^2$, \n$m_{\\bar{t}}^2 = (p_{l^-}+ p_{\\bar{\\nu}}+ p_{\\bar{b}})^2$. \nThe plots for the signal are constructed \ntaking into account the current stringent LHC constraint on the FCNC couplings, $\\sqrt{|g_{tq}|^2+|g_{qt}|^2}$ = 0.16. We have shown the results for Case 1, discussed\nin Sec.~\\ref{sec:cmf_asymmetries}, as the reconstructed mass will be the same for all three cases.\n\\begin{figure}[htb]\n\\vspace{1cm}\n$\\begin{array}{ccc}\n \\includegraphics[width=5 cm, height= 6cm]{mHiggs.eps} &\n  \\includegraphics[width=5 cm, height= 6cm]{mass_t.eps} &\n    \\includegraphics[width=5 cm, height= 6cm]{mass_tbar.eps}\n    \\end{array}$\n \\caption{The reconstructed masses of the Higgs, $t$-quark and $\\bar{t}$, for the signal \nand the $t\\bar{t}$ background, at $\\sqrt{s}$ =  500 GeV, with ${\\cal L}$ = 500 fb$^{-1}$\nand unpolarized beams. For the \nsignal we have considered Case 1 from Sec.~\\ref{sec:cmf_asymmetries}  with $\\sqrt{|g_{tq}|^2+|g_{qt}|^2}$ = 0.16.}\n  \\label{fig:m_recons}\n\\end{figure}\nWe note that since we have not done a real detector analysis, the mass reconstruction of the $W$ boson is poor\nin our case, due to the presence of missing energy. Therefore a loose cut on $m_W$ is applied for our analysis.\nIt is clear from Fig.~\\ref{fig:m_recons}, that the cut imposed on the reconstructed $m_t$ and \n$m_{\\bar{t}}$ should be different. The reconstructed mass of $\\bar{t}$ is broad, due\nto the presence of the missing energy from the $W$ decay.  We have applied the same kinematic cut to the mass\nof the top and the antitop for the sake of simplicity. The implementation of these cuts, eliminates the \n$Wb\\bar{b}jj$ and $Zb\\bar{b}jj$ backgrounds.\nThe kinematical cuts, which are imposed on the various reconstructed masses are summarized below:\n\\begin{itemize}\n\\item 115 $\\leq m_H$ (GeV) $\\leq$ 135,~~~~160 $\\leq m_t$ (GeV) $\\leq$ 188~~~~30 $\\leq m_W$ (GeV) $\\leq$ 100\n\\end{itemize}\nAdditional cuts can be applied, on the energy of the emitted quark in the top rest frame~\\cite{Han:2001ap}, so as \nto increase the signal to background ratio. The energy of the emitted quark, as a result of the\ntwo body decay of the top is \n\\begin{equation}\n E_{q}^{top}=\\frac{m_t}{2}\\left(1-\\frac{m_H^2}{m_t^2}\\right),\n\\end{equation}\nand is peaked around 42 GeV, for a Higgs mass of 125 GeV. The jet from the background, which will fake the $q$\njet, will have a more spread out energy. We do not apply this cut, as the application of the above cuts \nalready lead to a much reduced background. The energy distribution of both the signal and the background\nare shown in Fig.~\\ref{fig:energy_rf}.\n\\begin{figure}\n\\centering\n\\begin{minipage}{0.45\\textwidth}\n\\centering\n\\includegraphics[width=6.5cm, height=6cm]{energy_top_rf.eps}\n\\caption{The energy distribution of the non-$b$ jet ($t\\rightarrow qH$) in the rest frame of the top, \nat $\\sqrt{s}$ = 500 GeV, with unpolarized beams and ${\\cal L}$ = 500 fb$^{-1}$.}\n\\label{fig:energy_rf}\n\\end{minipage}\n\\hspace{0.5cm}\n\\begin{minipage}{0.45\\textwidth}\n\\centering\n\\includegraphics[width=6.5cm, height=6cm]{lep_jet.eps}\n\\caption{The opening angle distribution, Eq.~(\\ref{eq:dobservable}) between the\ndirection of the lepton (from $\\bar{t}\\rightarrow l^-\\bar{\\nu} \\bar{b}$)  and the non-$b$ jet (from $t\\rightarrow qH$), in the $t$ and $\\bar{t}$ rest frame. }\n\\label{fig:lepjet}\n\\end{minipage}\n\\end{figure}\n\nFurther on, we concentrate on the observables which will be sensitive to the chiral nature of the FCNC interactions. \nOne of them is the polar angle distribution of the non-$b$ jet, which was earlier shown in Fig.~\\ref{fig:dist_pol}.\nThe effect of the individual chiral couplings is more evident with a suitable choice of initial \nlongitudinal beam polarization.  The various distributions which we consider here \nare all calculated\nin the $t\\bar{t}-$ZMF. The decay products, which act as spin analyzers for our case are \nthe non-$b$ jet ($q$) from the decay $t\\rightarrow q H$ and the lepton ($l^-$)from the decay \n$\\bar{t} \\rightarrow l^-\\bar{\\nu} \\bar{b}$. All the distribution plots are given with the \nnumber of surviving events, for $\\mathcal{L}$ = 500 fb$^{-1}$.\nWe plot the opening angle distribution $1\/\\sigma (d\\sigma\/d\\cos\\varphi)$ (Eq.~(\\ref{eq:dobservable}))\nin Fig.~\\ref{fig:lepjet}, which is\nsensitive to the top and the antitop spin analyzers.  The distribution is\nflat for Case 1, when $|g_{tq}|^2 = |g_{qt}|^2$, leading \nto $\\kappa_q = 0$. It peaks in the forward direction in the presence of $|g_{tq}|^2$, and in the backward\ndirection for $|g_{qt}|^2$ (clearly seen in the inset of Fig.~\\ref{fig:lepjet}). \nThe top spin\nis considered\nin the normalized distribution $1\/\\sigma (d\\sigma\/d\\cos\\theta_{qs_t})$, where \n$\\theta_{qs_t}$ is the angle between the direction of the top spin analyzer (non-$b$ jet) \nin the top rest frame and the top spin quantization axis ($s_t$) in the \n$t\\bar{t}$-ZMF. The angle $\\cos\\theta_{qs_t}$ is the angle $\\cos\\theta_f$ defined\nin Eq.~(\\ref{eq:diffsigma}). The spin of the top can be chosen in the direction\nof any of the spin quantization axes as defined in Sec.~\\ref{sec:spintop}. \nThis distribution is sensitive to the polarization of the top and we show in \nFig.~\\ref{fig:basis} the distribution calculated in the different bases. As \nexpected, the `beamline' basis and the `off-diagonal' basis are most sensitive \nto the top polarization and therefore also to the decay dynamics of the top.\nThe chiral nature of the FCNC coupling will be more clearly visible in these \ntwo basis, with a flat distribution in case of the equality of the two chiral \ncoupling. The `helicity' and the `minimal' basis will not be effective in \ndiscriminating the chirality and they are shown just for the illustration. \nThe effect is further enhanced with the  \nbeam polarizations of $P^L_{e^-} = -0.8$ and $P^L_{e^+} = 0.3$,\nin all the spin bases considered here. We show the distribution in the `off-diagonal' basis \nin Fig.~\\ref{fig:offDB}, as it is most sensitive to the beam polarization.\n\\begin{figure}[htb]\n\\vspace{0.4cm}\n  \\begin{subfigure}{0.45\\linewidth}\n  \\centering\n    \\includegraphics[width=7cm, height=6cm]{jettop_hb.eps}\n     \\caption{}\n    \\label{fig:hb}\n  \\end{subfigure}\n   \\hspace{1.0cm}\n  \\begin{subfigure}{0.45\\linewidth}\n  \\centering\n    \\includegraphics[width=7cm, height=6cm]{jettop_bb.eps}\n     \\caption{}\n    \\label{fig:bb}\n  \\end{subfigure}\n    \\begin{subfigure}{0.45\\linewidth}\n\\centering\n\\vspace{0.6cm}\n  \\includegraphics[width=7cm, height=6cm]{jettop_odb.eps}\n     \\caption{}\n    \\label{fig:odb}\n  \\end{subfigure}\n  \\hspace{1.3cm}\n  \\begin{subfigure}{0.45\\linewidth}\n  \\vspace{0.6cm}\n\\centering  \n    \\includegraphics[width=7cm, height=6cm]{jettop_mb.eps}\n     \\caption{}\n    \\label{fig:mb}\n  \\end{subfigure}\n  \\caption{The distribution $1\/\\sigma (d\\sigma\/d\\cos\\theta_{qs_t})$, with unpolarized beams\n  at $\\sqrt{s}$ = 500 GeV and $\\cal L$ = 500 fb$^{-1}$, where $\\theta_{qs_t}$ is the \nangle between the direction of the top spin analyzer (non-$b$ jet from $t\\rightarrow q H$) in \n$t$ rest frame and the spin quantization axis of\nthe top ($s_t$) in the $t\\bar{t}$-ZMF. The different spin quantization axes considered are discussed\nin Eq.~(\\ref{eq:axes}).}\n\\label{fig:basis}\n\\end{figure}\n\nThe double differential angular distribution of the top and the antitop\ndefined in Eq.~(\\ref{eq:diffsigma}) provides a measurement of the spin-spin \ncorrelations. It was shown in Ref.~\\cite{Bernreuther:2013aga} that, for the  \nexperimental analysis, it is more suitable to use the one-dimensional \ndistribution of the product of the cosines, ${\\cal O}_{s_t,s_{\\bar{t}}} =\n\\cos \\theta_f \\cos \\theta_{\\bar{f}}$, rather than analyzing \nEq.~(\\ref{eq:diffsigma}). We define $\\cos \\theta_f \\cos \\theta_{\\bar{f}}$ \nas $\\cos\\theta_{qs_t} \\cos\\theta_{ls_{\\bar{t}}}$ for our analysis. The \n$1\/\\sigma (d\\sigma\/d{\\cal O}_{s_t,s_{\\bar{t}}})$ distribution is shown \nin Fig.~\\ref{fig:coscos}, using the `off-diagonal' basis and a longitudinal\nbeam polarization of  $P^L_{e^-} = -0.8$ and $P^L_{e^+} = 0.3$ . \nThe asymmetry of the plot around $\\cos\\theta_{qs_t} \\cos\\theta_{ls_{\\bar{t}}}$ = 0, \nsignals for the spin-spin correlation. The plot for Case 2 ($|g_{qt}|^2$ = 0) shows more events for \npositive values for $\\cos\\theta_{qs_t} \\cos\\theta_{ls_{\\bar{t}}}$, \nwhereas for Case 3 ($|g_{tq}|^2$ = 0)\none gets more events for negative values of $\\cos\\theta_{qs_t} \\cos\\theta_{ls_{\\bar{t}}}$. \n\\begin{figure}\n\\centering\n\\begin{minipage}{0.45\\textwidth}\n\\centering\n\\includegraphics[width=6.5cm, height=6cm]{odb_polarized.eps}\n\\caption{The normalized $1\/\\sigma (d\\sigma\/d\\cos\\theta_{qs_t})$ distribution\n(the definitions are same as in Fig.~\\ref{fig:basis}) at $\\sqrt{s}$ = 500 GeV,\nwith polarized beams and ${\\cal L}$ = 500 fb$^{-1}$.}\n\\label{fig:offDB}\n\\end{minipage}\n\\hspace{0.5cm}\n\\begin{minipage}{0.45\\textwidth}\n\\centering\n\\includegraphics[width=6.5cm, height=6cm]{cosfcosfbar.eps}\n\\caption{The normalized distribution of the product \n$\\cos\\theta_{qs_t} \\cos\\theta_{ls_{\\bar{t}}}$ , \n($\\theta_{qs_t} = \\angle (\\hat{\\bf p}_q,\\hat{\\bf a}), \n\\theta_{qs_{\\bar{t}}} = \\angle (\\hat{\\bf p}_l,\\hat{\\bf b})$),\nusing the off-diagonal basis, at $\\sqrt{s}$ = 500 GeV, with \npolarized beams and ${\\cal L}$ = 500 fb$^{-1}$. }\n\\label{fig:coscos}\n\\end{minipage}\n\\end{figure}\n\nWe next estimate the sensitivity that can be obtained for the FCNC $tqH$ couplings, \ngiven by the efficient signal identification and the significant background suppression\nwhich can be achieved at the linear collider. We adopt the following formula for \nthe significance measurement~\\cite{Cowan:2010js},\n\\begin{equation}\n S = \\sqrt{2\\left[\\left(N_S+N_B\\right) {\\rm ln}\\left(1+\\frac{N_S}{N_B}\\right)-N_S\\right]},\n\\end{equation}\nwith $N_S$ and $N_B$ being the number of signal and background events. \nIn Fig.~\\ref{fig:sig1} we present the contours of 3$\\sigma$ and 5$\\sigma$ significance\nfor our process in the $|g_{tq}|^2-|g_{qt}|^2$ plane. The sensitivity of the linear \ncollider will increase with the implementation of beam polarization with left polarized \nelectrons and right polarized positrons. Since the total cross section is  proportional\nto $|g_{tq}|^2+|g_{qt}|^2$, the contours are symmetric in that plane. \nThe sensitivity to the coupling $\\sqrt{|g_{tq}|^2+|g_{qt}|^2}$, as a function of the \nintegrated luminosity for $\\sqrt{s}$ = 500 GeV is shown Fig.~\\ref{fig:sig2}. \nOne can see that at 3$\\sigma$ statistical sensitivity and \n${\\cal L}$ = 500 fb$^{-1}$, $\\sqrt{|g_{tq}|^2+|g_{qt}|^2}$\ncan be probed to 0.063 (0.056) with unpolarized (polarized) beams. The limits obtained from the asymmetries, specially \n$A_{fb}$ from Sec.~\\ref{sec:cmf_asymmetries} will be more stronger\nand will not be symmetric in the $|g_{tq}|^2-|g_{qt}|^2$ plane.\n\\begin{figure}\n\\centering\n\\begin{minipage}{0.45\\textwidth}\n\\centering\n\\includegraphics[width=7cm, height=6cm]{Significance1.eps}\n\\caption{Contour plots in the $|g_{tq}|^2-|g_{qt}|^2$ plane, for the statistical significance \n$S$, from the production cross section, at $\\sqrt{s}$ = 500 GeV and a luminosity of 500 fb$^{-1}$, with\nunpolarized beams [black] and a beam polarization of $P^L_{e^-}$ = -0.8 and $P^L_{e^+}$ = 0.3 [red-dashed].}\n\\label{fig:sig1}\n\\end{minipage}\n\\hspace{0.2cm}\n\\begin{minipage}{0.45\\textwidth}\n\\centering\n\\includegraphics[width=7cm, height=6cm]{Significance2.eps}\n\\caption{The sensitivity of 3$\\sigma$ and 5$\\sigma$ to the FCNC coupling $\\sqrt{|g_{tq}|^2 +|g_{qt}|^2}$\nat $\\sqrt{s}$ = 500 GeV, as a function of integrated luminosity. The black solid line is for unpolarized beams,\nand the red-dashed line is for a beam polarization of $P^L_{e^-}$ = -0.8 and $P^L_{e^+}$ = 0.3. }\n\\label{fig:sig2}\n\\end{minipage}\n\\end{figure}\nWe find the following upper bounds as listed in Table~\\ref{tab:limits} at the 2$\\sigma$, \n3$\\sigma$ and the 5$\\sigma$ level from the total cross section, in the case of the \npolarized and the unpolarized beams.\n\\begin{table}[htb]\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|} \\hline\n &\\multicolumn{2}{|c|}{$P^L_{e^-} = 0, P^L_{e^+} = 0$}&\\multicolumn{2}{|c|}{$P^L_{e^-} = -0.8, P^L_{e^+} = 0.3$} \\\\ \\hline\n &&&& \\\\\nSignificance &$\\sqrt{|g_{tq}|^2+|g_{qt}|^2}$ &BR($t\\rightarrow qH$)\n&$\\sqrt{|g_{tq}|^2+|g_{qt}|^2}$ &BR($t\\rightarrow qH$) \\\\ \\hline\n2$\\sigma$ &0.052                &7.61$\\times 10^{-4}$               &0.046                &5.96$\\times 10^{-4}$  \\\\ \\hline\n3$\\sigma$ &0.063                &1.19$\\times 10^{-3}$                &0.056               &8.84$\\times 10^{-4}$   \\\\ \\hline\n5$\\sigma$ &0.085                &2.04$\\times 10^{-3}$                &0.074               &1.54$\\times 10^{-3}$   \\\\ \\hline\n\\end{tabular}\n\\caption{Upper bounds on $\\sqrt{|g_{tq}|^2+|g_{qt}|^2}$ and the respective branching ratios,\nthat can be obtained in the ILC, at $\\sqrt{s}$ = 500 GeV, with a luminosity of 500 fb$^{-1}$.\nThe results are presented for both, the polarized and the unpolarized case.}\n\\label{tab:limits}\n\\end{center}\n\\end{table}\n\n\\section{Conclusion}\\label{sec:conclusion}\n\nWe have studied the flavor violating top-Higgs interactions, \nat the $e^-e^+$ linear colliders using different beam polarizations.  There are \nseveral works exhibiting the prospects of the LHC to constrain or discover \nthese couplings, by considering several signatures of the flavor violating interactions.\nThe LHC experiments have also looked into these couplings and have obtained bounds on the branching ratio\nof the process $t\\rightarrow q H$. These flavor violating interactions can have a chiral structure with the top coupling differently to the left handed and the right handed fermions. \nSince the branching ratio of the top to $qH$, as well as, the total \nproduction cross section is being proportional to $|g_{tq}|^2+|g_{qt}|^2$, the chiral\nnature won't be evident from these measurements.\n\nTherefore, we have looked in the context of the linear collider into various observables  \nwhich will highlight this aspect of the couplings. The polar angle distribution\nof the quark emitted from the $t\\rightarrow cH$ decay, will exhibit a behaviour\nsensitive to the nature of the coupling. This will change with\nthe change of the beam polarization.  The distribution will be flat for all the \npolarization combinations if $|g_{tq}|^2 = |g_{qt}|^2$. The presence of only\none of the coupling ($|g_{tq}|^2$) leads to a forward peak for $e^-_L e^+_R$ polarization\nand will be unchanged for the $e^-_R e^+_L$ polarization. The opposite behaviour is observed for \n$|g_{qt}|^2$. Next, the forward-backward asymmetry $A_{fb}$ is used in order\nto constrain the $|g_{tq}|^2-|g_{qt}|^2$ parameter space. \n\nThe spins of the tops are correlated in the top pair production and the decay products of the \ntops are correlated with the spins, therefore the decay products of the top and the antitop\nare correlated. \nThe presence of new physics in the top decay will therefore, lead to a change in \nthe correlation coefficient in the angular distribution of the top decay products. A right \nchoice of spin basis of the top quark pair\nis also important in enhancing the correlation. We consider different \nobservables in Sec.~\\ref{sec:spintop}, which are sensitive to the spin analyzing power\n($\\kappa$) of the top decay product. The quark emitted\nfrom the top FCNC decay, will be a perfect spin analyzer ($\\kappa_q =1$)\nin the presence of a single chiral coupling. The $\\kappa_q$ of the emitted quark \nwill be zero when $|g_{tq}|^2 = |g_{qt}|^2$ and the correlation will be lost. \nWe have performed an analysis applying\nall the cuts at the linear collider in Sec.~\\ref{sec:numericalstudy}, and have studied the spin observables\nin the context of different spin bases. We find that the off-diagonal basis along with \nthe beamline basis are the most sensitive to the chirality of the couplings. The  effect is even more enhanced by polarizing \nthe initial beams of left handed electrons and right handed positrons.\n\nFinally, we have obtained a limit on the couplings from the total cross section and find \nthat BR($t\\rightarrow qH$) can be probed to $5.59 \\times 10^{-3}(8.84 \\times 10^{-4})$\nat 3$\\sigma$ level at the ILC, with $\\sqrt{s} =$ 500 GeV, $\\cal L$ = 500 fb$^{-1}$ and \na beam polarization of $P^L_{e^-} = 0 (-0.8), P^L_{e^+} = 0 (0.3)$ , which hopefully will be observed \nat the future linear colliders. \n\n\\section*{Acknowledgments}\nWe would like to thank Juan Antonio Aguilar Saavedra for very useful discussions. \nThis work is supported by the Croatian Science Foundation (HRZZ) project PhySMaB,\n``Physics of Standard Model and Beyond\" as well as by the H2020 Twinning\nproject No. 692194, ``RBI-T-WINNING''.\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\\label{sec:intro}\n\nThe dynamics of a finite quantum system, i.e., one with a finite number\nof degrees of freedom described by a Hilbert space ${\\mathcal H}$, is given by the \nSchr\\\"odinger equation. The Hamiltonian $H$ is a densely \ndefined self-adjoint operator on ${\\mathcal H}$, and for a vector $\\psi(t)$ in\nthe domain of $H$  the state at time $t$ satisfies\n\\begin{equation}\ni\\partial_t \\psi(t) = H\\psi(t) \\, .\n\\label{se}\\end{equation}\nFor all initial conditions $\\psi(0)\\in{\\mathcal H}$, the unique solution is given by\n$$\n\\psi(t)=e^{-itH}\\psi(0), \\mbox{ for all } t\\in\\bR.\n$$\nDue to Stone's Theorem $e^{-itH}$ is a strongly continuous one-parameter group of\nunitary operators on ${\\mathcal H}$, and the self-adjointness of $H$ is the necessary and sufficient\ncondition for the existence of a unique continuous solution for all times.\n\nAn alternative description of this dynamics is the so-called Heisenberg picture\nin which the time evolution is defined on the algebra of observables instead\nof the Hilbert space of states. The corresponding Heisenberg equation is\n\\begin{equation}\n\\partial_t A(t)=i[H,A(t)]\\, ,\n\\label{he}\\end{equation}\nwhere, for each $t\\in \\bR$, $A(t)\\in{\\mathcal B}({\\mathcal H})$ is a bounded linear operator\non ${\\mathcal H}$. Its solutions are given by a one-parameter group of $*$-automorphisms,\n$\\tau_t$, of ${\\mathcal B}({\\mathcal H})$:\n$$\nA(t)=\\tau_t(A(0)).\n$$\n\nFor the description of physical systems we expect the Hamiltonian, $H$,\nto have some additional properties. E.g., for finite systems such as atoms or\nmolecules, stability of the system requires that $H$ is bounded from below.\nIn this case, the infimum of the spectrum is expected to be an eigenvalue and\nis called the ground state energy. When the model Hamiltonian, $H$, is describing \nbulk matter rather than finite systems, we expect some additional properties. \nE.g., the stability of matter requires that the ground state energy has a lower bound\nproportional to $N$, where $N$ is the number of degree of freedom. Much progress\non this stability property has been made in the last several decades \n\\cite{lieb_selecta_stability,lieb-seiringer}.\nWe also expect that the dynamics of local observables of bulk matter, or large\nsystems in general, depends only on the local environment. Mathematically this \nis best expressed by the existence of the dynamics in the thermodynamic limit,\ni.e., in infinite volume. This is the question we address in this paper.\n\nThere are two settings that allow one to prove a rich set of important physical\nproperties of quantum dynamical systems, including infinite ones: the $C^*$ \ndynamical systems and the $W^*$ dynamical systems \\cite{bratteli1987}. In both cases, the \nalgebra of observables can be thought of a norm-closed $*$-subalgebra ${\\mathcal A}$ of some algebra\nof the form ${\\mathcal B}({\\mathcal H})$, but in the case of the $W^*$-dynamical systems we additionally\nrequire that the algebra is closed for the weak operator topology, which makes it a \nvon Neumann algebra.  For a $C^*$-dynamical  system the group of automorphisms \n$\\tau_t$ is assumed to be strongly continuous, i.e., for all $A\\in{\\mathcal A}$, the map \n$t\\mapsto \\tau_t(A)$ is continuous in $t$ for the operator norm ($C^*-$norm) on ${\\mathcal A}$. \nIn a $W^*$-dynamical system the continuity  is with respect to the weak topology.\n\nIn the case of lattice systems with a finite-dimensional Hilbert space\nof states associated with each lattice sites, such as quantum spin-lattice systems \nand lattice fermions, it has been known for a long time that under rather\ngeneral conditions the dynamics can be described by a $C^*$ dynamical\nsystem, including in the thermodynamic limit \\cite{bratteli1997}.  When the Hilbert \nspace at each site is infinite-dimensonal and the finite-system Hamiltonians are \nunbounded, this is no longer possible and the {\\em weak continuity} becomes a natural \nassumption.\n\nThe class of systems we will primarily focus on here are lattices of quantum oscillators but\nthe underlying lattice structure is not essential for our method. Systems defined on \nsuitable graphs, such as the systems considered in \\cite{eisert2005,eisert2008} can\nalso be analyzed with the same methods. In a recent preprint \\cite{amour2009}, it was shown \nthat convergence of the dynamics in the thermodynamic limit can be obtained for a modified \ntopology. Here, we follow a somewhat different approach. The main difference is that we study\nthe thermodynamic limit of anharmonic perturbations of an {\\em infinite} harmonic lattice\nsystem described by an explicit $W^*$-dynamical system. The more traditional way\nis to first define the dynamics of anharmonic systems in finite volume (which can be done \nby standard means \\cite{reed-simon}), and then to study the limit in which the volume \ntends to infinity.  This is what is done in \\cite{amour2009}, but it appears that controlling \nthe continuity of the limiting dynamics is more straightforward \nin our approach. In fact, we are able to show that the resulting dynamics for the class of \nanharmonic lattices we study is indeed weakly continuous, and we obtain a \n$W^*$-dynamical system for the infinite system. The $W^*$-dynamical setting is \nobtained by considering the GNS representation of a ground state or thermal \nequilibrium state of the harmonic system. The ground states and thermal states \nare quasi-free states in the sense of \\cite{robinson1965}, or convex mixtures\nof quasi-free states. In the ground state case the GNS representations are the well-known\nFock reprensentations. For the thermal states the GNS representations have been constructed \nby Araki and Woods \\cite{araki1963}.\n\nCommon to both approaches, ours and the one of \\cite{amour2009}, is the crucial role\nplayed by an estimate of the speed of propagation of perturbations in the system, commonly\nreferred to as Lieb-Robinson bounds \\cite{hast2006,lieb1972,nach12006,nach22006,nach2007}.\nBriefly, if $A$ and $B$ are two \nobservables of a spatially extended system, localized in regions $X$ and $Y$ of our graph,\nrespectively, and $\\tau_t$ denotes the time evolution of the system then, a Lieb-Robinson\nbound is an estimate of the form\n$$\n\\Vert [\\tau_t (A), B]\\Vert\\leq C e^{-a(d(X,Y)-v\\vert t\\vert)}\\, ,\n$$\nwhere $C, a$, and $v$ are positive constants and $d(X,Y)$ denotes the distance\nbetween $X$ and $Y$. Lieb-Robinson bounds for anharmonic \nlattice systems were recently proved in \\cite{nachtergaele2009}, and this work builds on the\nresults obtained there. Our results are mainly limited to short-range interactions that are either \nbounded or unbounded perturbations of the harmonic interaction (linear springs).\n\nTo conclude the introduction, let us mention that the same questions, the existence of the\ndynamics for infinite oscillator lattices, can and has been asked for classical systems. Two\nclassic papers are \\cite{lanford1977,marchioro1978}. Many properties of this classical infinite\nvolume harmonic dynamics have been studied in detail e.g. \\cite{Spohn77, vanhem} and \nsome recent progress on locality estimates for anharmonic systems is reported in \n\\cite{butta2007,raz2009}.\n\nThe paper is organized as follows. We begin with a section discussing bounded interactions.\nIn this case, the existence of the dynamics follows by mimicking the proof valid in the \ncontext of quantum spins systems. Section 3 describes the infinite volume harmonic dynamics on\ngeneral graphs. It is motivated by an explicit example on $\\mathbb{Z}^d$. Next, in Section 4, we \ndiscuss finite volume perturbations of the infinite volume harmonic dynamics and prove that\nsuch systems satisfy a Lieb-Robinson bound. In Section 5 we demonstrate that the existence\nof the dynamics and its continuity follow from the Lieb-Robinson estimates established in \nthe previous section.\n\n\n\n\\section{Bounded Interactions} \\label{sec:bdints}\n\nThe goal of this section is to prove the existence of the dynamics for oscillator systems\nwith bounded interactions. Since oscillator systems with bounded interactions can be treated \nas a special case of more general models with bounded interactions, we will use \na slightly more general setup in this section, which we now introduce.\n\nWe will denote by $\\Gamma$ the underlying structure on which our models will be defined.\nHere $\\Gamma$ will be an arbitrary set of sites equipped with a metric $d$.\nFor $\\Gamma$ with countably infinite cardinality, we will need to assume that there exists a\nnon-increasing function $F: [0, \\infty) \\to (0, \\infty)$ for which:\n\n\\noindent i) $F$ is uniformly integrable over $\\Gamma$, i.e.,\n\\begin{equation} \\label{eq:fint}\n\\| \\, F \\, \\| \\, := \\, \\sup_{x \\in \\Gamma} \\sum_{y \\in \\Gamma}\nF(d(x,y)) \\, < \\, \\infty,\n\\end{equation}\n\n\\noindent and\n\n\\vspace{.3cm}\n\n\\noindent ii) $F$ satisfies\n\\begin{equation} \\label{eq:intlat}\nC \\, := \\, \\sup_{x,y \\in \\Gamma} \\sum_{z \\in \\Gamma}\n\\frac{F \\left( d(x,z) \\right) \\, F \\left( d(z,y)\n\\right)}{F \\left( d(x,y) \\right)} \\, < \\, \\infty.\n\\end{equation}\n\nGiven such a set $\\Gamma$ and a function $F$, by the triangle inequality,\nfor any $a \\geq 0$ the function\n\\begin{equation*}\nF_a(x) = e^{-ax} \\, F(x),\n\\end{equation*}\nalso satisfies i) and ii) above with $\\| F_a \\| \\leq \\| F \\|$ and $C_a \\leq C$.\n\nIn typical examples, one has that $\\Gamma  \\subset \\mathbb{Z}^{d}$ for\nsome integer $d \\geq 1$, and the metric is\njust given by $d(x,y) = |x -  y|=\\sum_{j=1}^{d} |x_j - y_j|$.\nIn this case, the function $F$ can be\nchosen as $F(|x|) = (1 + |x|)^{- d - \\epsilon}$ for any $\\epsilon >0$.\n\n\nTo each $x \\in \\Gamma$, we will associate a Hilbert space $\\mathcal{H}_x$.\nIn many relevant systems, one considers\n$\\mathcal{H}_x = L^2( \\mathbb{R}, {\\rm d} q_x)$, but this is not essential.\nWith any finite subset $\\Lambda \\subset \\Gamma$,\nthe Hilbert space of states over $\\Lambda$ is given by\n\\begin{equation*}\n\\mathcal{H}_{\\Lambda} \\, = \\, \\bigotimes_{x \\in \\Lambda} \\mathcal{H}_x,\n\\end{equation*}\nand the local algebra of observables over $\\Lambda$ is then defined to be\n\\[\n\\mathcal{A}_{\\Lambda} = \\bigotimes_{x \\in \\Lambda} {\\mathcal B} ({\\mathcal H}_x),\n\\]\nwhere ${\\mathcal B} ({\\mathcal H}_x)$ denotes the algebra of bounded linear operators on ${\\mathcal H}_x$.\n\nIf $\\Lambda_1 \\subset \\Lambda_2$, then there is a natural way of identifying\n$\\mathcal{A}_{\\Lambda_1} \\subset \\mathcal{A}_{\\Lambda_2}$, and we may thereby\ndefine the algebra of quasi-local observables by the inductive limit\n\\begin{equation*}\n\\mathcal{A}_{\\Gamma} \\, = \\, \\bigcup_{\\Lambda \\subset \\Gamma} \\mathcal{A}_{\\Lambda},\n\\end{equation*}\nwhere the union is over all finite subsets $\\Lambda \\subset \\Gamma$; see\n\\cite{bratteli1987,bratteli1997} for a discussion of these issues in general.\n\nThe result discussed in this section corresponds to bounded perturbations of\nlocal self-adjoint Hamiltonians. We fix a collection of on-site local operators\n$H^{\\rm loc} = \\{ H_x \\}_{x \\in \\Gamma}$ where each $H_x$ is a self-adjoint\noperator over $\\mathcal{H}_x$. In addition, we will consider a general class of bounded perturbations.\nThese are defined in terms of an interaction $\\Phi$, which is a map from the\nset of subsets of $\\Gamma$ to $\\mathcal{A}_{\\Gamma}$ with the property that\nfor each finite set $X \\subset \\Gamma$, $\\Phi(X) \\in \\mathcal{A}_X$ and\n$\\Phi(X) ^*= \\Phi(X)$. As with the Lieb-Robinson bound proven in \\cite{nachtergaele2009}, \nwe will need a growth condition on the set of interactions $\\Phi$ for which we can prove\nthe existence of the dynamics in the thermodynamic limit.\nThis condition is expressed in terms of the following norm. \nFor any $a \\geq 0$, denote by $\\mathcal{B}_a(\\Gamma)$ the set of interactions\nfor which\n\\begin{equation} \\label{eq:defphia}\n\\| \\Phi \\|_a \\, := \\, \\sup_{x,y \\in \\Gamma}  \\frac{1}{F_a (d(x,y))} \\,\n\\sum_{X \\ni x,y} \\| \\Phi(X) \\| \\, < \\, \\infty.\n\\end{equation}\n\nNow, for a fixed sequence of local Hamiltonians $H^{\\rm loc} = \\{H_x \\}_{x\\in\\Gamma}$, as\ndescribed above, an interaction $\\Phi \\in \\mathcal{B}_a(\\Gamma)$, and a finite subset\n$\\Lambda \\subset \\Gamma$, we will consider self-adjoint Hamiltonians of the form\n\\begin{equation} \\label{eq:localham}\nH_{\\Lambda} \\, = \\, H^{\\rm loc}_{\\Lambda} \\, + \\, H^{\\Phi}_{\\Lambda} \\, = \\, \\sum_{x \\in \\Lambda} H_x \\, + \\, \\sum_{X \\subset \\Lambda} \\Phi(X),\n\\end{equation}\nacting on $\\mathcal{H}_{\\Lambda}$ (with domain given by $\\bigotimes_{x \\in \\Lambda} D(H_x)$ where $D(H_x) \\subset {\\mathcal H}_x$ denotes the domain of $H_x$). As these operators are self-adjoint, they generate a dynamics, or time evolution, $\\{ \\tau_t^{\\Lambda} \\}$,\nwhich is the one parameter group of automorphisms defined by\n\\begin{equation*}\n\\tau_t^{\\Lambda}(A) \\, = \\, e^{it H_{\\Lambda}} \\, A \\, e^{-itH_{\\Lambda}} \\quad \\mbox{for any} \\quad A \\in \\mathcal{A}_{\\Lambda}.\n\\end{equation*}\n\n\\begin{thm}\nUnder the conditions stated above, for all $t \\in {\\mathbb R}$, $A \\in \\mathcal{A}_{\\Gamma}$, \nthe norm limit \n\\begin{equation}\\label{eq:claim} \n\\lim_{\\Lambda \\to \\Gamma} \\, \\tau_t^{\\Lambda} (A) = \\tau_t(A)\n\\end{equation} exists in the sense of non-decreasing exhaustive sequences of finite\nvolumes $\\Lambda$ and defines a group of $*-$automorphisms $\\tau_t$ on the completion of\n$\\mathcal{A}_\\Gamma$. The convergence is uniform for $t$ in a compact set.\n\\end{thm}\n\n\n\\begin{proof} \nLet $\\Lambda \\subset \\Gamma$ be a finite set. Consider the unitary propagator\n\\begin{equation} \\label{eq:intuni}\n {\\mathcal U}_{\\Lambda} (t,s) = e^{i t H_{\\Lambda}^{\\text{loc}} } \\, e^{-i (t-s) H_{\\Lambda}} \\, e^{-is H_{\\Lambda}^{\\text{loc}}} \n\\end{equation}\nand its associated {\\it interaction-picture} evolution defined by\n\\begin{equation} \\label{eq:intpic}\n\\tau^{\\Lambda}_{t, \\text{int}} (A) = {\\mathcal U}_{\\Lambda} (0,t) \\, A \\; {\\mathcal U}_{\\Lambda} (t,0) \\quad \\mbox{for all } A \\in \\mathcal{A}_{\\Gamma} \\, .\n\\end{equation} \nClearly, $\\mathcal{U}_{\\Lambda}(t,t) = \\idty$ for all $t \\in \\mathbb{R}$, and it is also easy to check \nthat \n\\begin{equation*}\ni \\frac{{\\rm d}}{{\\rm d} t} \\, {\\mathcal U}_{\\Lambda} (t,s) =  H_{\\Lambda}^{\\text{int}} (t) \\, {\\mathcal U}_{\\Lambda} (t,s)  \\quad \\mbox{and} \\quad\n- i \\frac{{\\rm d}}{{\\rm d} s} \\, {\\mathcal U}_{\\Lambda} (t,s) =  {\\mathcal U}_{\\Lambda} (t,s) \\, H_{\\Lambda}^{\\text{int}} (s) \n\\end{equation*}\nwith the time-dependent generator \n\\begin{equation} \\label{eq:gen}\nH^{\\text{int}}_{\\Lambda} (t) = e^{i H_{\\Lambda}^{\\text{loc}} t} H_{\\Lambda}^{\\Phi} e^{-i H^{\\text{loc}}_{\\Lambda} t} = \\sum_{Z \\subset \\Lambda} e^{i H_{\\Lambda}^{\\text{loc}} t} \\, \\Phi (Z)  \\, e^{-i H^{\\text{loc}}_{\\Lambda} t} \\, . \n\\end{equation}\n\nFix $T>0$ and $X \\subset \\Gamma$ finite. For any $A \\in \\mathcal{A}_X$, we will show that \nfor any non-decreasing, exhausting sequence $\\{ \\Lambda_n \\}$ of $\\Gamma$, the sequence\n$\\{ \\tau_{t, \\text{int}}^{\\Lambda_n}(A) \\}$ is Cauchy in norm, uniformly for $t \\in [-T,T]$.\nMoreover, the bounds establishing the Cauchy property depend on $A$ only through $X$ and $\\|A\\|$.\nSince\n\\begin{equation*}\n\\tau_t^{\\Lambda} (A) = \\tau_{t,\\text{int}}^{\\Lambda} \\left(e^{itH_{\\Lambda}^{\\text{loc}}} \\, A \\,  e^{-it H_{\\Lambda}^{\\text{loc}}} \\right) = \n\\tau_{t,\\text{int}}^{\\Lambda} \\left(e^{it \\sum_{x \\in X}H_x} \\, A \\, e^{-i t \\sum_{x \\in X} H_x} \\right) \\, ,\n\\end{equation*}\nan analogous statement then immediately follows for $\\{ \\tau_t^{\\Lambda_n}(A) \\}$, since they\nare all also localized in $X$ and have the same norm as $\\|A\\|$.\n\nTake $n \\leq m$ with $X \\subset \\Lambda_n \\subset \\Lambda_m$ and calculate\n\\begin{equation} \\label{eq:diff}\n\\tau_{t,\\text{int}}^{\\Lambda_m} (A) - \\tau_{t,\\text{int}}^{\\Lambda_n} (A) = \\int_0^t \\frac{{\\rm d}}{{\\rm d} s} \\left\\{ {\\mathcal U}_{\\Lambda_m} (0,s) \\, {\\mathcal U}_{\\Lambda_n} (s,t) \\, A \\, {\\mathcal U}_{\\Lambda_n} (t,s) \\, {\\mathcal U}_{\\Lambda_m} (s,0) \\right\\} \\, ds \\, .\n\\end{equation}\nA short calculation shows that\n\\begin{equation}\n\\begin{split}\n\\frac{{\\rm d}}{{\\rm d} s} {\\mathcal U}_{\\Lambda_m} (0,s) & \\, {\\mathcal U}_{\\Lambda_n} (s,t) \\, A \\, {\\mathcal U}_{\\Lambda_n} (t,s) \\, {\\mathcal U}_{\\Lambda_m} (s,0) \\\\\n& = \\, i \\mathcal{U}_{\\Lambda_m}(0,s) \\left[ \\left( H^{\\text{int}}_{\\Lambda_m}(s) - H^{\\text{int}}_{\\Lambda_n}(s) \\right), \\mathcal{U}_{\\Lambda_n}(s,t) \\, A \\, \\mathcal{U}_{\\Lambda_n}(t,s) \\right] \\mathcal{U}_{\\Lambda_m}(s,0) \\\\\n& = \\, i \\mathcal{U}_{\\Lambda_m}(0,s) e^{is H_{\\Lambda_n}^{\\text{loc}}} \\left[ \\tilde{B}(s), \\tau_{s-t}^{\\Lambda_n} \\left( \\tilde{A}(t) \\right) \\right] e^{-is H_{\\Lambda_n}^{\\text{loc}}} \\mathcal{U}_{\\Lambda_m}(s,0) \\, ,\n\\end{split}\n\\end{equation}\nwhere\n\\begin{equation} \\label{eq:tat}\n\\tilde{A}(t) = e^{-it H_{\\Lambda_n}^{\\text{loc}}} A \\, e^{it H_{\\Lambda_n}^{\\text{loc}}} = e^{-it H_{X}^{\\text{loc}}} A \\, e^{it H_{X}^{\\text{loc}}} \n\\end{equation}\nand\n\\begin{eqnarray} \\label{eq:tbs}\n\\tilde{B}(s) & = & e^{-is H_{\\Lambda_n}^{\\text{loc}}}\\left( H^{\\text{int}}_{\\Lambda_m}(s) - H^{\\text{int}}_{\\Lambda_n}(s) \\right) e^{is H_{\\Lambda_n}^{\\text{loc}}} \\nonumber \\\\\n& = & \\sum_{Z \\subset \\Lambda_m} e^{is H_{\\Lambda_m \\setminus \\Lambda_n}^{\\text{loc}}} \\Phi(Z)  e^{-is H_{\\Lambda_m \\setminus \\Lambda_n}^{\\text{loc}}} - \\sum_{Z \\subset \\Lambda_n} \\Phi(Z) \\nonumber \\\\\n& = & \\sum_{\\stackrel{Z \\subset \\Lambda_m:}{ Z \\cap \\Lambda_m \\setminus \\Lambda_n \\neq \\emptyset}} e^{is H_{\\Lambda_m \\setminus \\Lambda_n}^{\\text{loc}}} \\Phi(Z)  e^{-is H_{\\Lambda_m \\setminus \\Lambda_n}^{\\text{loc}}} \n\\end{eqnarray}\nCombining the results of (\\ref{eq:diff}) -(\\ref{eq:tbs}), and using unitarity, we find that\n\\begin{equation}\n\\left\\| \\tau_{t,\\text{int}}^{\\Lambda_m} (A) - \\tau_{t,\\text{int}}^{\\Lambda_n} (A)  \\right\\| \\leq \\int_0^t \\left\\| \\left[ \\tau_{s-t}^{\\Lambda_n} \\left( \\tilde{A}(t) \\right), \\tilde{B}(s)  \\right] \\right\\| \\, ds \\,\n\\end{equation}\nand by the Lieb-Robinson bound proven in \\cite{nachtergaele2009}, it is clear that\n\\begin{eqnarray}\n&&\\left\\| \\left[ \\tau_{s-t}^{\\Lambda_n} \\left( \\tilde{A}(t) \\right), \\tilde{B}(s)  \\right] \n\\right\\|\\\\\n& \\leq &  \\sum_{\\stackrel{Z \\subset \\Lambda_m:}{ Z \\cap \\Lambda_m \\setminus \n\\Lambda_n \\neq \\emptyset}} \n\\left\\| \\left[ \\tau_{s-t}^{\\Lambda_n} \\left( \\tilde{A}(t) \\right),  \ne^{is H_{\\Lambda_m \\setminus \\Lambda_n}^{\\text{loc}}} \\Phi(Z)  \ne^{-is H_{\\Lambda_m \\setminus \\Lambda_n}^{\\text{loc}}}  \\right] \\right\\| \\nonumber \\\\\n& \\leq & \\frac{2 \\| A \\|}{C_a} \\left( e^{2 \\| \\Phi \\|_a C_a |t-s|} - 1 \\right)  \\sum_{y \\in \\Lambda_m \\setminus \\Lambda_n} \\sum_{\\stackrel{Z \\subset \\Lambda_m:}{ y \\in Z }}  \\| \\Phi(Z) \\| \\sum_{x \\in X} \\sum_{z \\in Z} F_a( d(x,z)) \\nonumber \\\\ & \\leq &  \\frac{2 \\| A \\|}{C_a} \\left( e^{2 \\| \\Phi \\|_a C_a |t-s|} - 1 \\right)  \\sum_{y \\in \\Lambda_m \\setminus \\Lambda_n} \\sum_{z \\in \\Lambda_m} \\sum_{\\stackrel{Z \\subset \\Lambda_m:}{ y, z \\in Z }}  \\| \\Phi(Z) \\| \\sum_{x \\in X}  F_a( d(x,z)) \\nonumber \\\\\n& \\leq & \\frac{2 \\| A \\| \\| \\Phi \\|_a}{C_a} \\left( e^{2 \\| \\Phi \\|_a C_a |t-s|} - 1 \\right)  \\sum_{y \\in \\Lambda_m \\setminus \\Lambda_n}  \\sum_{x \\in X}  \\sum_{z \\in \\Lambda_m}  F_a( d(x,z)) F_a(d(z,y)) \\nonumber \\\\\n& \\leq & 2 \\| A \\| \\| \\Phi \\|_a \\left( e^{2 \\| \\Phi \\|_a C_a |t-s|} - 1 \\right)  \\sum_{y \\in \\Lambda_m \\setminus \\Lambda_n}  \\sum_{x \\in X} F_a( d(x,y)) \\, .\\nonumber\n\\end{eqnarray}\nWith the estimate above and the properties of the function $F_a$, it is clear that\n\\begin{equation}\n\\sup_{t \\in [-T,T]} \\left\\| \\tau_{t,\\text{int}}^{\\Lambda_m} (A) - \\tau_{t,\\text{int}}^{\\Lambda_n} (A)  \\right\\| \\to 0 \\quad \\mbox{ as } n, m \\to \\infty \\, ,\n\\end{equation}\nand the rate of convergence only depends on the norm $\\| A \\|$ and the set $X$ where $A$ is\nsupported. This proves the claim.\n\\end{proof}\n\nIf all\nlocal Hamiltonians $H_x$ are bounded, $\\{\\tau_t\\}$ is strongly continuous. \nIf the $H_x$ are allowed to be densely defined unbounded self-adjoint operators, \nwe only have weak continuity and the dynamics is more naturally defined on a\nvon Neumann algebra. This can be done when we have a suffiently nice invariant\nstate for the model with only the on-site Hamiltonians. E.g., suppose that\nfor each $x\\in \\Gamma$, we have a normalized eigenvector $\\phi_x$ of $H_x$.\nThen, for all $A\\in\\mathcal{A}_\\Lambda$, for any finite $\\Lambda\\subset \\Gamma$,\ndefine\n\\begin{equation}\n\\rho(A)=\\langle \\bigotimes_{x\\in\\Lambda}\\phi_x, A \\bigotimes_{x\\in\\Lambda}\\phi_x\\rangle\\, .\n\\end{equation}\n$\\rho$ can be regarded as a state of the infinite system defined on the norm completion \nof $\\mathcal{A}_\\Gamma$. The GNS Hilbert space $\\mathcal{H}_\\rho$\nof $\\rho$ can be constructed as the closure of \n$\\mathcal{A}_\\Gamma \\bigotimes_{x\\in\\Gamma}\\phi_x$. \nLet $\\psi\\in \\mathcal{A}_\\Gamma \\bigotimes_{x\\in\\Gamma}\\phi_x$.\nThen \n\\begin{equation}\n\\begin{split}\n\\left\\| \\left( \\tau_t(A) - \\tau_{t_0}(A) \\right)  \\psi \\right\\| \\leq & \\left\\| \n\\left( \\tau_t(A) - \\tau_t^{(\\Lambda_n)}(A) \\right)  \\psi \\right\\| \\\\\n+ & \\left\\| \\left( \\tau_t^{(\\Lambda_n)}(A) - \\tau_{t_0}^{(\\Lambda_n)}(A) \\right)  \n\\psi \\right\\| +\n\\left\\| \\left( \\tau_{t_0}^{(\\Lambda_n)}(A) - \\tau_{t_0}(A) \\right)  \\psi \\right\\| \\, ,\n\\end{split}\n\\end{equation}\nFor sufficiently large $\\Lambda_n$, the $\\lim_{t\\to t_0}$ of middle term vanishes \nby Stone's theorem. The two other terms are handled by \\ref{eq:claim}. It is clear\nhow to extend the continuity to $\\psi\\in\\mathcal{H}_\\rho$.\n \nWe will discuss this type of situation in more detail in the next three sections\nwhere we consider models that include quadratic (unbounded) interactions as well.\n\n\n\n\\section{The Harmonic Lattice}\\label{sec:harm}\n\nAs noted in the introduction, we will consider anharmonic perturbations of infinite\nharmonic lattices. In this section we discuss the properties\nof the harmonic systems that we need to assume in general in order\nto study the perturbations in the thermodynamic limit. We will also\nshow in detail that a standard harmonic lattice model posesses all the\nrequired properties.\n\n\\subsection{The CCR algebra of observables}\n\nWe begin by introducing the CCR algebra on which the harmonic dynamics will be\ndefined. Following \\cite{manuceau1973}, one can define the CCR algebra over any \nreal linear space\n$\\mathcal{D}$ equipped with a non-degenerate, symplectic bilinear form $\\sigma$, i.e.\n$\\sigma : \\mathcal{D} \\times \\mathcal{D} \\to \\mathbb{R}$ with the property that\nif $\\sigma(f,g) = 0$ for all $f \\in \\mathcal{D}$, then $g = 0$, and \n\\begin{equation} \\label{eq:symp}\n\\sigma(f,g) = - \\sigma(g,f) \\quad \\mbox{for all } f, g \\in \\mathcal{D} .\n\\end{equation}\nIn typical examples, $\\mathcal{D}$ will be a complex inner product space associated \nwith $\\Gamma$, e.g.\n$\\mathcal{D} = \\ell^2( \\Gamma)$ or a subspace thereof such as $\\mathcal{D} = \\ell^1( \\Gamma)$, \nor $\\ell^2(\\Gamma_0)$, with $\\Gamma_0\\subset\\Gamma$, and\n\\begin{equation}\n\\sigma(f,g) = \\mbox{Im} \\left[ \\langle f, g \\rangle \\right] \\, .\n\\end{equation}\nThe Weyl operators over $\\mathcal{D}$ are defined by associating non-zero elements\n$W(f)$ to each $f \\in \\mathcal{D}$ which satisfy\n\\begin{equation} \\label{eq:invo}\nW(f)^* = W(-f) \\quad \\mbox{for each } f \\in \\mathcal{D} \\, ,\n\\end{equation}\nand\n\\begin{equation} \\label{eq:weylrel}\nW(f) W(g) = e^{-i \\sigma(f,g)\/2} W(f+g) \\quad \\mbox{for all } f, g \\in \\mathcal{D} \\, .\n\\end{equation}\nIt is well-known that there is a unique, up to $*$-isomorphism, $C^*$-algebra generated\nby these Weyl operators with the property that $W(0) = \\idty$, $W(f)$ is unitary\nfor all $f \\in \\mathcal{D}$, and $\\| W(f) - \\idty \\| = 2$ for all $ f \\in \\mathcal{D} \\setminus \\{0 \\}$, \nsee e.g. Theorem 5.2.8 \\cite{bratteli1997}. This algebra, commonly known as the CCR algebra, or Weyl algebra, over\n$\\mathcal{D}$, we will denote by $\\mathcal{W} = \\mathcal{W}( \\mathcal{D})$.\n\n\\subsection{Quasi-free dynamics}\nThe anharmonic dynamics we study in this paper will be defined as\nperturbations of harmonic, technically {\\em quasi-free}, dynamics.\nA quasi-free dynamics on $\\mathcal{W}(\\mathcal{D})$ is a one-parameter\ngroup of *-automorphisms $\\tau_t$ of the form\n\\begin{equation}\n\\tau_t(W(f))=W(T_t f), \\quad f\\in \\mathcal{D}\n\\end{equation}\nwhere $T_t:\\mathcal{D}\\to\\mathcal{D}$ is a group of real-linear, symplectic\ntransformations, i.e., \n\\begin{equation} \\label{eq:sympT}\n\\sigma(T_t f, T_t g)= \\sigma(f,g)\\, .\n\\end{equation}\nAs $\\| W(f) - W(g) \\| = 2$ for all $ f\\neq g \\in \\mathcal{D}$, one should not\nexpect $\\tau_t$ to be strongly continuous; only a weaker form of\ncontinuity is present. This means that $\\tau_t$ does {\\em not}\ndefine a $C^*$-dynamical system on $\\mathcal{W}$, and thus we \nlook for a $W^*$-dynamical setting in which the weaker form of\ncontinuity is naturally expressed. \n\nIn the present context, it suffices to regard a {\\it $W^*$-dynamical system} as a pair $\\{ \\mathcal{M}, \\alpha_t \\}$\nwhere $\\mathcal{M}$ is a von Neumann algebra and $\\alpha_t$ is a weakly continuous, \none parameter group of $*$-automorphisms of $\\mathcal{M}$. For the harmonic systems we are \nconsidering, a specific  $W^*$-dynamical system arises as follows. Let $\\rho$ be a \nstate on $\\mathcal{W}$ and denote by $\\left( \\mathcal{H}_{\\rho}, \\pi_{\\rho}, \n\\Omega_{\\rho} \\right)$ the corresponding GNS representation. We will assume\nthat $\\rho$ is both regular and $\\tau_t$-invariant. Recall that $\\rho$ is \nregular if and only if $t \\mapsto \\rho( W(tf) )$ is continuous \nfor all $f \\in \\mathcal{D}$, and $\\tau_t$-invariance means\n\\begin{equation}\n\\rho( \\tau_t(A) ) = \\rho(A) \\quad \\mbox{for all } A \\in \\mathcal{W}.\n\\end{equation}\nFor the von Neumann \nalgebra $\\mathcal{M}$, take the weak-closure of $\\pi_{\\rho}( \\mathcal{W})$ in $\\mathcal{L}\n( \\mathcal{H}_{\\rho})$ and let $\\alpha_t$ be the weakly continuous, \none parameter group of $*$-automorphisms of $\\mathcal{M}$ obtained by lifting $\\tau_t$ to \n$\\mathcal{M}$. The latter step is possible since $\\rho$ is $\\tau_t$-invariant, see e.g. Corollary 2.3.17 \\cite{bratteli1987}.\n\n\\subsection{Lieb-Robinson bounds for harmonic lattices}\nTo prove the existence of the dynamics for anharmonic models, we use that the unperturbed harmonic\nsystem satisfies a Lieb-Robinson bound. Such an estimate depends directly on\nproperties of $\\sigma$ and\n$T_t$. In fact, it is easy to calculate that\n\\begin{eqnarray}\n\\left[ \\tau_t(W(f)), W(g) \\right]  & = & \\left\\{ W( T_t f) - W(g) W( T_tf) W(-g) \\right\\} W(g)  \\nonumber \\\\\n& = & \\left\\{ 1 - e^{i \\sigma( T_tf, g)} \\right\\} W( T_tf) W(g) \\, ,\n\\end{eqnarray}\nusing the Weyl relations (\\ref{eq:weylrel}).  For the examples we consider below, one can prove that\nfor every $a>0$, there exists positive numbers $c_a$ and $v_a$ for which \n\\begin{equation} \\label{eq:dynestex}\n\\left| \\sigma( T_t f, g ) \\right| \\leq c_a e^{ v_a |t|} \\sum_{x, y \\in \\mathbb{Z}^d} |f(x)| \\, |g(y)| \\frac{e^{-a|x-y|}}{(1+|x-y|)^{d+1}}\n\\end{equation}\nholds for all $t \\in \\mathbb{R}$ and all $f, g \\in \\ell^2( \\mathbb{Z}^d)$. In general, we will assume that\nthe harmonic dynamics satisfies an estimate of this type. Namely, we suppose that there exists a number\n$a_0 >0$ for which given $0<a \\leq a_0$, there are numbers $c_a$ and $v_a$ for which \n\\begin{equation} \\label{eq:dynest2}\n\\left| 1 - e^{i\\sigma( T_t f, g )} \\right| \\leq c_a e^{ v_a |t|} \\sum_{x, y \\in \\Gamma} |f(x)| \\, |g(y)| F_a \\left( d(x,y) \\right) \n\\end{equation}\nholds for all $t \\in \\mathbb{R}$ and all $f, g \\in \\ell^2( \\Gamma)$. Here we describe the spatial decay in $\\Gamma$\nthrough the functions $F_a$ as introduced in Section~\\ref{sec:bdints}.  Since the Weyl operators are unitary, the norm estimate\n\\begin{equation}  \\label{eq:freest}\n\\left\\| \\left[ \\tau_t(W(f)), W(g) \\right]  \\right\\| \\leq  c_a e^{v_a |t| } \\sum_{x, y} |f(x)| \\, |g(y)| \\, F_a \\left( d(x,y) \\right) \\, ,\n\\end{equation}\nreadily follows.\n\n\\subsection{An important example}\n\nUsing the example given below, we illustrate the general discussion above in terms of \na standard harmonic model defined over $\\Gamma = \\mathbb{Z}^d$.\nWe begin with a description of some well known calculations that are valid\nfor these models when restricted to a finite volume. This analysis motivates\nthe definition of the harmonic dynamics in the infinite volume. We then \ndemonstrate that this infinite volume dynamics satisfies a Lieb-Robinson bound. \nBy representing this dynamics in a suitable state, the relevant weak-continuity \nis readily verified. Interestingly, our analysis also applies to the massless case\nof $\\omega =0$, see below, and we discuss this briefly. We end this subsection\nwith some final comments.\n\n\\subsubsection{Finite volume analysis} We consider a system of coupled harmonic oscillators restricted to a finite volume. \nSpecifically on cubic subsets $\\Lambda_L \\, = \\, \\left( -L, L \\right]^d  \\subset \\mathbb{Z}^d$,\nwe analyze Hamiltonians of the form\n\\begin{equation} \\label{eq:harham}\nH_L^{h} \\, = \\,  \\sum_{ x \\in \\Lambda_L} p_{ x }^2 \\, +\\, \\omega^2 \\, q_{ x}^2 \\, + \\,\n\\sum_{j = 1}^{d}  \\lambda_j \\, (q_{ x } - q_{ x + e_j})^2\n\\end{equation}\nacting in the Hilbert space\n\\begin{equation} \\label{eq:hspace}\n\\mathcal{H}_{\\Lambda_L} = \\bigotimes_{x \\in \\Lambda_L} L^2(\\mathbb{R}, dq_x).\n\\end{equation}\nHere the quantities $p_x$ and $q_x$, which appear in (\\ref{eq:harham}) above, are the \nsingle site momentum and position operators regarded as operators on the full Hilbert space $\\mathcal{H}_{\\Lambda_L}$\nby setting \n\\begin{equation} \\label{eq:pandq}\np_x = \\idty \\otimes \\cdots \\otimes \\idty\n\\otimes -i \\frac{d}{dq} \\otimes \\idty \\cdots \\otimes \\idty \\quad\n\\mbox{ and } \\quad q_x = \\idty \\otimes \\cdots \\otimes \\idty \\otimes q \\otimes \\idty\n\\cdots \\otimes \\idty,\n\\end{equation}\ni.e., these operators act non-trivially only in the $x$-th factor of $\\mathcal{H}_{\\Lambda_L}$. These operators satisfy the canonical commutation relations\n\\begin{equation} \\label{eq:comm}\n[p_x, p_y] \\, = \\, [q_x, q_y] \\, = \\, 0 \\quad \\mbox{ and } \\quad\n[q_x, p_y] \\, = \\, i \\delta_{x,y},\n\\end{equation}\nvalid for all $x, y \\in \\Lambda_L$.  In addition,  $\\{ e_j \\}_{j=1}^{d}$ are the canonical basis vectors in $\\mathbb{Z}^{d}$, the numbers\n$\\lambda_j \\geq 0$ and $\\omega \\geq 0$ are the parameters of the system, and the Hamiltonian\nis assumed to have periodic boundary conditions, in the sense that $q_{x+e_j} = q_{x-(2L-1)e_j}$ \nif $x \\in \\Lambda_L$ but $x+ e_j \\not\\in \\Lambda_L$. It is well-known that Hamiltonians \nof this form can be diagonalized in Fourier space. We review this quickly to establish some notation and\nrefer the interested reader to \\cite{nachtergaele2009} for more details.\n \nIntroducing the operators\n\\begin{equation} \\label{eq:Q+Pk}\nQ_k \\, = \\, \\frac{1}{ \\sqrt{ | \\Lambda_L |}} \\sum_{x \\in \\Lambda_L} e^{- i k \\cdot x} q_x \\quad \\mbox{and} \\quad\nP_k \\, = \\, \\frac{1}{ \\sqrt{ | \\Lambda_L |}} \\sum_{x \\in \\Lambda_L} e^{- i k \\cdot x} p_x \\, ,\n\\end{equation}\ndefined for each $k \\in \\Lambda_L^* \\, = \\, \\left\\{ \\, \\frac{x \\pi}{L} \\, : \\, x \\in \\Lambda_L \\, \\right\\} $,\nand setting \n\\begin{equation} \\label{eq:defgamma}\n\\gamma(k) \\, = \\,  \\sqrt{ \\omega^2 \\, + \\, 4 \\sum_{j=1}^{d} \\lambda_j \\, \\sin^2(k_j\/2) },\n\\end{equation}\none finds that \n\\begin{equation} \\label{eq:diagham}\nH_L^h \\, = \\, \\sum_{k \\in \\Lambda_L^*} \\, \\gamma(k) \\, \\left( \\, 2 \\, b_k^*\\,  b_k \\, + \\, 1 \\, \\right) \\, \n\\end{equation}\nwhere the operators $b_k$ and $b_k^*$ satisfy\n\\begin{equation} \\label{eq:beqns}\nb_k \\, = \\, \\frac{1}{ \\sqrt{2 \\gamma(k)}} \\, P_k - i \\sqrt{ \\frac{\\gamma(k)}{2}} \\, Q_k \\quad {\\rm and} \\quad\nb_k^* \\, = \\, \\frac{1}{ \\sqrt{2 \\gamma(k)}} \\, P_{-k} + i \\sqrt{ \\frac{\\gamma(k)}{2}} \\, Q_{-k} \\, .\n\\end{equation}\nIn this sense, we regard the Hamiltonian $H_L^h$ as diagonalizable.\n\nUsing the above diagonalization, one can determine the action of the dynamics corresponding to \n$H_L^h$ on the Weyl algebra $\\mathcal{W}( \\ell^2( \\Lambda_L) )$. In fact, by setting\n\\begin{equation}\nW(f) = \\mbox{exp} \\left[ i \\sum_{x \\in \\Lambda_L} \\mbox{Re}[f(x)] q_x + \\mbox{Im}[f(x)] p_x \\right] \\, ,\n\\end{equation}\nfor each $f \\in \\ell^2( \\Lambda_L)$, it is easy to verify that (\\ref{eq:invo}) and (\\ref{eq:weylrel}) hold with\n$\\sigma(f,g) = \\mbox{Im}[ \\langle f, g \\rangle]$.\nIt is convenient to express these Weyl operators in terms of annihilation and creation operators, i.e.,\n\\begin{equation} \\label{eq:anncre}\na_x \\, = \\, \\frac{1}{\\sqrt{2}} \\left( q_x \\, + \\, i p_x \\right) \\quad \\mbox{and} \\quad a^*_x \\, = \\, \\frac{1}{\\sqrt{2}} \\left( q_x \\, - \\, i p_x \\right),\n\\end{equation}\nwhich satisfy \n\\begin{equation} \\label{eq:comrela}\n[a_x, a_y] = [a_x^*, a_y^*] = 0 \\quad \\mbox{and} \\quad [a_x, a_y^*] = \\delta_{x,y} \\quad \\mbox{for all } x,y \\in \\Lambda_L \\, .\n\\end{equation}\nOne finds that\n\\begin{equation} \\label{eq:weyla}\nW(f)  =  \\mbox{exp} \\left[ \\frac{i}{\\sqrt{2}} \\left( a(f) \\, + \\, a^*(f) \\right) \\right] \\, ,\n\\end{equation}\nwhere, for each $f \\in \\ell^2(\\Lambda_L)$, we have set\n\\begin{equation} \\label{eq:defafa*f}\na(f) \\, = \\, \\sum_{x \\in \\Lambda_L} \\overline{f(x)} \\, a_x,  \\quad a^*(f) \\, = \\, \\sum_{x \\in \\Lambda_L} f(x) \\, a_x^*\\, .\n\\end{equation}\n\nNow, the dynamics corresponding to $H_L^h$, which we denote by $\\tau_t^{L}$, is trivial with \nrespect to the diagonalizing variables, i.e., \n\\begin{equation}\n\\tau_t^{L}(b_k) = e^{-2i \\gamma(k) t} b_k \\quad \\mbox{and} \\quad \\tau_t^{L}(b_k^*) = e^{2i \\gamma(k) t} b_k^* \\, , \n\\end{equation}\nwhere $b_k$ and $b_k^*$ are as defined in (\\ref{eq:beqns}). \nHence, if we further introduce\n\\begin{equation} \\label{eq:defb}\nb_x = \\frac{1}{ \\sqrt{| \\Lambda_L|}} \\sum_{k \\in \\Lambda_L^*} e^{ikx} b_k \\quad \\mbox{and} \\quad \nb_x^* = \\frac{1}{ \\sqrt{| \\Lambda_L|}} \\sum_{k \\in \\Lambda_L^*} e^{ikx} b_k^*, \n\\end{equation}\nfor each $x \\in \\Lambda_L$ and, analogously to (\\ref{eq:defafa*f}), define\n\\begin{equation} \\label{eq:defbfb*f}\nb(f) \\, = \\, \\sum_{x \\in \\Lambda_L} \\overline{f(x)} \\, b_x,  \\quad b^*(f) \\, = \\, \\sum_{x \\in \\Lambda_L} f(x) \\, b_x^*,\n\\end{equation}\nfor each $f \\in \\ell^2( \\Lambda_L)$, then one has that\n\\begin{equation} \\label{eq:taub}\n\\tau_t^L \\left( b(f) \\right) = b \\left( [\\mathcal{F}^{-1} M_t \\mathcal{F}] f \\right) \\, , \n\\end{equation}\nwhere $\\mathcal{F}$ is the unitary Fourier transform on $\\ell^2(\\Lambda_L)$ and $M_t$ is the \noperator of multiplication by $e^{2i \\gamma(k) t}$ in Fourier space with $\\gamma(k)$ as in (\\ref{eq:defgamma}). We need only determine\nthe relation between the $a$'s and the $b$'s.\n\nA short calculation shows that there exists a linear mapping $U: \\ell^2( \\Lambda_L) \\to \\ell^2( \\Lambda_L)$\nand an anti-linear mapping $V: \\ell^2( \\Lambda_L) \\to \\ell^2( \\Lambda_L)$ for which\n\\begin{equation} \\label{eq:b=a}\nb(f) = a(Uf) + a^*(Vf) \\, ,\n\\end{equation}\na relation know in the literature as a Bogoliubov transformation \\cite{manuceau1968}.\nIn fact, one has that\n\\begin{equation} \\label{eq:defU+V}\nU = \\frac{i}{2} \\mathcal{F}^{-1} M_{\\Gamma_+} \\mathcal{F} \\quad \\mbox{ and } \\quad V = \\frac{i}{2} \\mathcal{F}^{-1} M_{\\Gamma_-} \\mathcal{F} J\n\\end{equation}\nwhere $J$ is complex conjugation and $M_{\\Gamma_{\\pm}}$ is the operator of multiplication\nby\n\\begin{equation} \\label{eq:multg}\n\\Gamma_{\\pm}(k) = \\frac{1}{\\sqrt{ \\gamma(k)}} \\pm \\sqrt{ \\gamma(k)} \\, ,\n\\end{equation}\nwith $\\gamma(k)$ as in (\\ref{eq:defgamma}).\nUsing the fact that $\\Gamma_{\\pm}$ is real valued and even, it is easy to check that\n\\begin{equation} \\label{eq:bog1}\nU^* U - V^* V = \\idty = U U^* - V V^*\n\\end{equation}\nand\n\\begin{equation} \\label{eq:bog2}\nV^* U - U^* V = 0 =  V U^* - UV^* \\,\n\\end{equation}\nwhere we stress that $V^*$ is the adjoint of the {\\it anti-linear} mapping $V$. The relation (\\ref{eq:b=a}) is invertible, in fact,\n\\begin{equation}\na(f) = b(U^*f) - b^*(V^*f) \\, ,\n\\end{equation}\nand therefore\n\\begin{equation}\nW(f) = \\mbox{exp} \\left[  \\frac{i}{ \\sqrt{2}} \\left( b((U^*-V^*)f) + b^*((U^*-V^*)f) \\right) \\right] \\, .\n\\end{equation}\nClearly then,\n\\begin{equation}\n\\tau_t(W(f)) = W( T_t f) \\, ,\n\\end{equation}\nwhere the mapping $T_t$ is given by\n\\begin{equation}\nT_t = (U+V) \\mathcal{F}^{-1} M_t \\mathcal{F} (U^*-V^*) \\, ,\n\\end{equation}\nand we have used (\\ref{eq:taub}).\n\n\\subsubsection{Infinite volume dynamics} It is now clear how to define the infinite volume harmonic dynamics.\nConsider a subspace $\\mathcal{D} \\subset \\ell^2( \\mathbb{Z}^d)$ and define\n$\\mathcal{W}( \\mathcal{D})$ as above with $\\sigma(f,g) = \\mbox{Im}[ \\langle f, g \\rangle ]$.\nFirst assume $\\omega >0$, take $\\gamma : [- \\pi, \\pi)^d \\to \\mathbb{R}$ as in \n(\\ref{eq:defgamma}), and\nset $U$ and $V$ as in (\\ref{eq:defU+V}) with (\\ref{eq:multg}). If $\\omega >0$, both \n$U$ and $V$ are bounded transformations on $\\ell^2( \\mathbb{Z}^d)$. We will treat \nthe case $\\omega =0$ by a limiting argument. The mapping $T_t$ defined by setting\n\\begin{equation} \\label{eq:deftt}\nT_t = (U+V) \\mathcal{F}^{-1} M_t \\mathcal{F} (U^*-V^*) \\, ,\n\\end{equation}\nis well-defined on $\\ell^2( \\mathbb{Z}^d)$. To define the dynamics on $\\mathcal{W}(\\mathcal{D})$\nwe will need to choose subspaces $\\mathcal{D}$ that are $T_t$ invariant. \nOn such $\\mathcal{D}$, $T_t$ is clearly real-linear. With (\\ref{eq:bog1}) \nand (\\ref{eq:bog2}), one\ncan easily verify the group properties $T_0 = \\idty$, $T_{s+t} = T_s \\circ T_t$, and\n\\begin{equation}\n\\mbox{Im} \\left[ \\langle T_t f, T_t g \\rangle \\right] = \\mbox{Im} \\left[ \\langle f,g \\rangle \\right] \\, ,\n\\end{equation}\ni.e. $T_t$ is sympletic in the sense of (\\ref{eq:sympT}). Using Theorem 5.2.8 of \\cite{bratteli1997}, \nthere is a unique \none parameter group of $*$-automorphisms on $\\mathcal{W}( \\mathcal{D})$, which we will denote\nby $\\tau_t$, that satisfies\n\\begin{equation}\n\\tau_t(W(f)) = W(T_tf) \\quad \\mbox{for all } f \\in \\mathcal{D} \\, .\n\\end{equation}\nThis defines the harmonic dynamics on $\\mathcal{W}( \\mathcal{D})$.\n\nHere it is important that $T_t : \\mathcal{D} \\to \\mathcal{D}$. As we demonstrated in \\cite{nachtergaele2009},\nthe mapping $T_t$ can be expressed as a convolution. In fact, \n\\begin{equation} \\label{eq:defft}\nT_tf = f * \\overline{ \\left(H_t^{(0)} + \\frac{i}{2}(H_t^{(-1)} + H_t^{(1)}) \\right)} + \\overline{f}*\\left( \\frac{i}{2}(H_t^{(1)} - H_t^{(-1)}) \\right).\n\\end{equation}\nwhere\n\\begin{equation}\\label{eq:h}\n\\begin{split}\nH^{(-1)}_t(x) &= \\frac{1}{(2 \\pi)^d} {\\rm Im} \\left[ \\int \\frac{1}{ \\gamma(k)} e^{i(k \\cdot x-2\\gamma(k)t)} \\, d k \\right],\n\\\\\nH^{(0)}_t(x) &= \\frac{1}{(2 \\pi)^d}  {\\rm Re} \\left[ \\int e^{i(k \\cdot x - 2\\gamma(k)t)} \\, dk \\right],\n\\\\\nH^{(1)}_t(x) &=  \\frac{1}{(2 \\pi)^d} {\\rm Im} \\left[ \\int \\gamma(k) \\, e^{i(k \\cdot x-2\\gamma(k)t)} \\, dk \\right] .\n\\end{split}\n\\end{equation}\nUsing analysis similar to what is proven in \\cite{nachtergaele2009}, the following result holds.\n\\begin{lem}\\label{lem:htx}\nConsider the functions defined in (\\ref{eq:h}). For $\\omega\\geq 0, \\lambda_1,\n\\ldots,\\lambda_d\\geq 0$, but such that  \n$c_{\\omega,\\lambda} = (\\omega^2 + 4 \\sum_{j=1}^d \\lambda_j )^{1\/2} >0$, \nand any $\\mu >0$, the bounds\n\\begin{equation}\n\\begin{split}\n\\left| H_t^{(0)}(x) \\right| &\\leq  e^{-\\mu \\left( |x| - c_{\\omega,\\lambda} \\max \\left( \\frac{2}{\\mu} \\, , \\, e^{(\\mu\/2)+1}\\right) |t| \\right)}\n\\\\\n\\left| H_t^{(-1)}(x) \\right| &\\le  c^{-1}_{\\omega,\\lambda}e^{-\\mu \\left( |x| - c_{\\omega,\\lambda} \\max \\left( \\frac{2}{\\mu} \\, , \\, e^{(\\mu\/2)+1}\\right) |t| \\right)}\n\\\\\n\\left| H_t^{(1)}(x) \\right| &\\le c_{\\omega,\\lambda}e^{\\mu\/2}e^{-\\mu \\left( |x| - c_{\\omega,\\lambda} \\max \\left( \\frac{2}{\\mu} \\, , \\, e^{(\\mu\/2)+1}\\right) |t| \\right)}\n\\end{split}\n\\end{equation}\nhold for all $t \\in \\mathbb{R}$ and $x \\in \\mathbb{Z}^d$. Here  $|x| = \\sum_{j=1}^{d} |x_i|$.\n\\end{lem}\n\nGiven the estimates in Lemma~\\ref{lem:htx}, equation (\\ref{eq:defft}) and \nYoung's inequality imply that $T_t$ can be defined as\na transformation of $\\ell^p(\\mathbb{Z}^d)$, for $p\\geq 1$. However,\nthe symplectic form limits us to consider $\\mathcal{D}=\\ell^p(\\mathbb{Z}^d)$\nwith $1\\leq p\\leq 2$.\n\nThe following bound now readily follows:\n\\begin{equation}\n\\begin{split}\n\\vert \\mbox{Im} \\langle T_t f, g\\rangle\\vert \\leq & \\left(1+2 e^{\\mu\/2}c_{\\omega,\\lambda} + 2 c_{\\omega,\\lambda}^{-1}\\right) \\times \\\\\n& \\quad \\times \\sum_{x,y} \\vert f(x)\\vert\\, \\vert g(y)\\vert \ne^{-\\mu \\left( |x| - c_{\\omega,\\lambda} \\max \\left( \\frac{2}{\\mu} \\, , \\, e^{(\\mu\/2)+1}\\right) |t| \\right)}\n\\end{split}\n\\end{equation}\nThis implies an estimate of the form (\\ref{eq:dynestex}), and hence a Lieb-Robinson bound as in (\\ref{eq:freest}).\n\nA simple corollary of Lemma~\\ref{lem:htx} follows.\n\n\\begin{cor} \\label{cor:hest} Consider the functions defined in (\\ref{eq:h}). For $\\omega\\geq 0, \\lambda_1,\n\\ldots,\\lambda_d\\geq 0$, but with \n$c_{\\omega,\\lambda} = (\\omega^2 + 4 \\sum_{j=1}^d \\lambda_j )^{1\/2} >0$.\nTake $\\| \\cdot \\|_1$ to be the $\\ell^1$-norm. One has that \n\\begin{equation}\n\\| H_t^{(0)} - \\delta_0 \\|_1 \\to 0  \\quad \\mbox{as} \\quad t \\to 0,\n\\end{equation}\nand\n\\begin{equation}\n\\| H_t^{(m)}  \\|_1 \\to 0  \\quad \\mbox{as} \\quad t \\to 0, \\quad \\mbox{for } m \\in \\{ -1, 1\\}.\n\\end{equation}\n\\end{cor} \n\\begin{proof}\nThe estimates in Lemma~\\ref{lem:htx} imply that the functions $H_t^{(m)}$ are bounded by exponentially decaying functions (in $|x|$).\nThese estimates are uniform for $t$ in compact sets, e.g. $t \\in [-1,1]$, and therefore dominated convergence applies. It is clear that\n$H_0^{(0)}(x) = \\delta_0(x)$ while $H_0^{(m)}(x) = 0$ for $m \\in \\{-1,1\\}$. This proves the corollary.\n\\end{proof}\n\n\\subsubsection{Representing the dynamics} The infinite-volume ground state of the model (\\ref{eq:harham}) is the vacuum\nstate for the $b-$operators, as can be seen from (\\ref{eq:diagham}). This state\nis defined on $\\mathcal{W}(\\mathcal{D})$ by\n\\begin{equation}\\label{eq:state}\n\\rho(W(f))=e^{-\\frac{1}{4}\\Vert (U^*-V^*)f\\Vert^2}\n\\end{equation}\nBy standard arguments this defines a state on $\\mathcal{W}(\\mathcal{D})$\n\\cite{bratteli1997}. Using (\\ref{eq:deftt}), (\\ref{eq:bog1}) and (\\ref{eq:bog2}) one \nreadily verifies that $\\rho$ is $\\tau_t$-invariant. $\\rho$ is regular\nby observation. The weak continuity of the dynamics in the GNS-representation\nof $\\rho$ will follow from the continuity of the functions of the form\n\\begin{equation}\\label{eq:weakcont}\nt\\mapsto \\rho(W(g_1)W(T_t f)W(g_2)), \\mbox{ for}\\ g_1, g_2, f\\in \\mathcal{D}.\n\\end{equation}\nWhen $\\omega>0$, this continuity can be easily observed from the\nfollowing expresion:\n\\begin{equation} \\label{eq:defstate}\n\\begin{split}\n\\rho(W(g_1)W(T_t f)W(g_2)) = & e^{i\\sigma(g_1, g_2)\/2}\ne^{i\\sigma(T_t f, g_2 - g_1)\/2} \\times \\\\\n&\\times  e^{-\\Vert(U^*-V^*)(g_1+g_2+T_t f)\\Vert^2\/4}\n\\end{split}\n\\end{equation}\nNote that $T_t$ is differentiable with bounded derivative and that both $U$ and $V$ \nare bounded. This establishes the continuity in the case that $\\omega>0$. \n\nAs discussed in the introduction of the section, the $W^*$-dynamical system\nis now defined by considering the GNS representation $\\pi_\\rho$\nof $\\rho$. This yields a von Neumann algebra \n$\\mathcal{M}=\\overline{\\pi_\\rho(\\mathcal{W}(\\mathcal{D}))}$. The invariance of\n$\\rho$ implies that the dynamics is implementable by unitaries $U_t$, i.e.,\n\\begin{equation}\n\\pi_\\rho(\\tau_t(W(f)))=U_t^* \\pi_\\rho(W(f)) U_t\\, .\n\\end{equation}\nUsing $U_t$, the dynamics can be extended to $\\mathcal{M}$. As a consequence of\n(\\ref{eq:weakcont}), this extended dynamics is weakly continuous.\n\n\\subsubsection{The case of $\\omega=0$} We now discuss the case $\\omega =0$. Here, the maps $T_t$ are defined\nusing the convolution formula (\\ref{eq:defft}). By Lemma \\ref{lem:htx},\n$T_t$ is well-defined as a transformation of $\\ell^p(\\mathbb{Z}^d)$, for\n$1\\leq p\\leq 2$. Both the group property of $T_t$ and the invariance of \nthe symplectic form $\\sigma$ follow in the limit $\\omega\\to 0$ by\ndominated congervence which is justified by Lemma \\ref{lem:htx}.\nThis demonstrates that the dynamics is well defined.\n\nWe represent the dynamics in a state $\\rho$ is defined by (\\ref{eq:state}), but with the understanding\nthat $\\Vert (U^*- V^*)f\\Vert$ may take on the value $+\\infty$, in which case\n$\\rho(W(f))=0$. $\\rho$ is still clearly regular. It remains to show that the\ndynamics is weakly continuous.\n\nObserve that\n\\begin{equation}\n\\begin{split}\nT_t f - f =  f * \\left(H_t^{(0)} - \\delta_0 \\right) & - f* \\left( \\frac{i}{2}(H_t^{(-1)} + H_t^{(1)}) \\right) \\\\\n& \\quad + \\overline{f}*\\left( \\frac{i}{2}(H_t^{(1)} - H_t^{(-1)}) \\right),\n\\end{split}\n\\end{equation}\nfollows from (\\ref{eq:defft}). Using Young's inequality and Corollary~\\ref{cor:hest}, it is clear that $\\| T_t f - f \\| \\to 0$ as \n$t \\to 0$ for any $f \\in \\ell^p( \\mathbb{Z}^d)$ with $1 \\leq p \\leq 2$. A calculation shows that\n\\begin{equation}\n(U^*-V^*)(T_t f - f) = F_1 *  \\left(H_t^{(0)} - \\delta_0 \\right) - F_2 * H_t^{(-1)}  - i F_3 *H_t^{(1)} \\, ,\n\\end{equation}\nwhere\n\\begin{equation}\n\\begin{split}\n& \\quad \\quad F_1 =   \\, \\mathcal{F}^{-1} M_{\\sqrt{ \\gamma}} \\mathcal{F} \\mbox{Im}[f] \n - i \\mathcal{F}^{-1} M_{ \\gamma^{-1\/2}} \\mathcal{F} \\mbox{Re}[f] \\, , \\\\\n & F_2 =  \\mathcal{F}^{-1} M_{\\sqrt{ \\gamma}} \\mathcal{F} \\mbox{Re}[f] \\, , \\quad \\mbox{and} \\quad\n F_3 = \\mathcal{F}^{-1} M_{\\gamma^{-1\/2}} \\mathcal{F} \\mbox{Im}[f] \\, . \n\\end{split}\n\\end{equation}\nA similar argument to what is given above now implies that \n$\\| (U^*-V^*)(T_tf-f) \\| \\to 0$ as $t \\to 0$, for any $f \\in \\mathcal{D}_0$, \nwhere\n\\begin{equation}\n\\mathcal{D}_0 = \\left\\{ f \\in \\ell^2( \\mathbb{Z}^d) : \\mathcal{F}^{-1} M_{\\gamma^{-1\/2}} \\mathcal{F} \\mbox{Re}[f] \\in \\ell^2( \\mathbb{Z}^d) \\right\\} \\, .\n\\end{equation}\nNo additional assumption on $\\mbox{Im}[f]$ is necessary since $F_3$ is\nconvolved with $H_t^{(1)}$. Given the form of (\\ref{eq:defstate}), this suffices to prove weak continuity.\nIn fact, one can check that $T_t$ leaves $\\mathcal{D}_0$ invariant and that if $f \\in \\mathcal{D}_0$, then  \n$(U^*-V^*)T_t f \\in \\ell^2( \\mathbb{Z}^d)$ for all $t \\in \\mathbb{R}$. \nThis establishes weak continuity of the dynamics, defined on $\\mathcal{W}( \\mathcal{D}_0)$.\n\n\n\\begin{rem}  We observe that, when $\\omega=0$, the finite volume Hamiltonian $H_L^h$ (\\ref{eq:harham}) is translation invariant and commutes with the total momentum operator $P_0$ (see (\\ref{eq:Q+Pk})). In fact, $H_L^h$ can be written as \n\\[ \\begin{split} H_L^h &= P_0^2 + \\sum_{k \\in \\Lambda_L^* \\backslash \\{ 0 \\}} P_k^* P_k + \\gamma^2 (k) Q_k^* Q_k \\\\ &= P_0^2 + \\sum_{k \\in \\Lambda_L^* \\backslash \\{ 0 \\}} \\gamma(k) (2 b_k^* b_k + 1) \\end{split} \\] where we used the notation (\\ref{eq:Q+Pk}) and, for $k \\not = 0$, we introduced the operators $b_k, b_k^*$ as in (\\ref{eq:beqns}). \nIn this case, the operator $H_L^h$ does not have eigenvectors; its spectrum is purely continuous. By a unitary transformation, the Hilbert space ${\\mathcal H}_{\\Lambda_L}$ (see (\\ref{eq:hspace})) can be mapped into the space $L^2 ({\\mathbb R}, {\\rm d} P_0 ; {\\mathcal H}_b)$ of square integrable functions of $P_0 \\in {\\mathbb R}$, with values in ${\\mathcal H}_b$. Here, ${\\mathcal H}_b$ denotes the Fock space generated by all creation and annihilation operators $b_k^*, b_k$ with $k \\not = 0$. It is then easy to construct vectors which minimize the energy by a given distribution of the total momentum; for an arbitrary (complex valued) $f \\in L^2 ({\\mathbb R})$ with $\\| f \\|=1$, we define $\\psi_f \\in L^2 ({\\mathbb R}, {\\rm d} P_0 ; {\\mathcal H}_b)$ by setting $\\psi_f (P_0) = f (P_0) \\Omega$ (where $\\Omega$ is the Fock vacuum in ${\\mathcal H}_b$). These vectors are not invariant with respect to the time evolution. It is simple to check that the Schr\\\"odinger evolution of $\\psi_f$ is given by $e^{-iH_{L}^h t} \\psi_f = \\psi_{f_t}$ with $f_t (P_0) = e^{-it P_0^2} f (P_0)$ is the free evolution of $f$. In particular, for $\\omega =0$, $H_L^h$ does not have a ground state in the traditional sense of an eigenvector. \nFor this reason, when $\\omega =0$, it is not a priori clear what the natural choice of state should be. As is discussed above, one possibility is to consider first $\\omega \\not = 0$ and then take the limit $\\omega \\to 0$. This yields a ground state for the infinite system \nwith vanishing center of mass momentum of the oscillators. By considering non-zero values\nfor the center of mass momentum, one can also define other states with similar properties.\n\\end{rem}\n\n\\subsubsection{Some final comments} The analysis in the following sections and our main result is not limited\nto the class of examples we discussed above. E.g., harmonic systems defined on \nmore general graphs, such as the ones considered in \\cite{eisert2005,eisert2008} \ncan also be treated. Also note that our choice of time-invariant\nstate, while natural, is by no means the only possible. Instead of the\nvacuum state defined in (\\ref{eq:state}), equilibrium states at positive temperatures could be used in exactly the same way. It would also make\nsense to study the convergence of the equilibrium or ground states\nfor the perturbed dynamics and to consider the dynamics in the representation of the limiting infinite-system state, but we have\nnot studied this situation and will not discuss it in this paper.\n\n\n\\section{Perturbing the Harmonic Dynamics}\n\nIn this section, we will discuss finite volume perturbations of the infinite volume \nharmonic dynamics which we defined in Section~\\ref{sec:harm}. To begin, we recall a\nfundamental result about perturbations of quantum dynamics defined by adding a bounded term\nto the generator. This is a version of what is usually known as the Dyson or Duhamel \nexpansion. The following statement summarizes Proposition 5.4.1 of \\cite{bratteli1997}.\n\\begin{prop} \\label{prop:perdyn} Let $\\{ \\mathcal{M}, \\alpha_t \\}$ be a $W^*$-dynamical system and let $\\delta$ denote the\ninfinitesimal generator of $\\alpha_t$. Given any $P = P^* \\in \\mathcal{M}$, set $\\delta_P$ to be the bounded \nderivation with domain $D( \\delta_P) = \\mathcal{M}$ satisfying $\\delta_P(A) = i [P, A]$ for all $A \\in \\mathcal{M}$.\nIt follows that $\\delta + \\delta_P$ generates a one-parameter group of $*$-automorphisms $\\alpha^P$ of $\\mathcal{M}$\nwhich is the unique solution of the integral equation\n\\begin{equation} \\label{eq:defpdyn}\n\\alpha_t^P(A) = \\alpha_t(A) + i \\int_0^t \\alpha_s^P \\left( \\left[ P, \\alpha_{t-s}(A) \\right] \\right) \\, ds \\, . \n\\end{equation}\nIn addition, the estimate\n\\begin{equation} \\label{eq:dynestpert}\n\\left\\| \\alpha_t^P(A) - \\alpha_t(A)  \\right\\| \\leq \\left( e^{|t| \\| P \\|} - 1 \\right) \\, \\| A \\| \\, \n\\end{equation}\nholds for all $t \\in \\mathbb{R}$ and $A \\in \\mathcal{M}$.\n\\end{prop}\n\nSince the initial dynamics $\\alpha_t$ is assumed weakly continuous, the norm estimate (\\ref{eq:dynestpert}) can be used to\nshow that the perturbed dynamics is also weakly continuous. Hence, for each $P = P^* \\in \\mathcal{M}$ the pair \n$\\{ \\mathcal{M}, \\alpha_t^P \\}$ is also a $W^*$-dynamical system. Thus, if $P_i=P_i^* \\in \\mathcal{M}$ \nfor $i=1,2$, then one can define $\\alpha_t^{P_1+P_2}$ iteratively.\n\n\n\\subsection{A Lieb-Robinson bound for on-site perturbations} \\label{subsec:onsite}\n\nIn this section we will consider perturbations of the harmonic dynamics \ndefined in Section~\\ref{sec:harm}. Recall that our general assumptions for the harmonic\ndynamics on $\\Gamma$ are as follows.\n\nWe assume that the harmonic dynamics, $\\tau^0_t$, is defined on a Weyl algebra\n$\\mathcal{W}( \\mathcal{D})$ where $\\mathcal{D}$ is a subspace of $\\ell^2(\\Gamma)$.\nIn fact, we assume there exists a group $T_t$ of real-linear\ntransformations which leave $\\mathcal{D}$ invariant and satisfy\n\\begin{equation}\n\\tau_t^0(W(f)) = W(T_tf) \\quad \\mbox{for all } f \\in \\mathcal{D} \\, .\n\\end{equation}\nIn addition, we assume that this harmonic dynamics satisfies a Lieb-Robinson \nbound. Specifically, we suppose that there exists a number $a_0 >0$ for which\ngiven any $0<a \\leq a_0$, there are positive numbers $c_a$ and $v_a$ for which\n\\begin{equation} \\label{eq:prelrb}\n\\left| 1 - e^{ i \\sigma(T_tf, g)} \\right| \\leq c_a e^{v_a|t|} \\sum_{x,y \\in \\Gamma} |f(x)| \\, |g(y)| \\, F_a \\left( d(x,y) \\right) \\,\n\\end{equation}\nhere the spatial decay in $\\Gamma$ is described by the function $F_a$ as introduced in\nSection~\\ref{sec:bdints}. As we discussed in Section~\\ref{sec:harm}, the estimate (\\ref{eq:prelrb})\nimmediately implies the Lieb-Robinson bound\n\\begin{equation} \\label{eq:freelrb}\n\\left\\| \\left[ \\tau_t^0 \\left( W(f) \\right), W(g) \\right] \\right\\| \\leq c_a e^{v_a|t|} \\sum_{x,y \\in \\Gamma} |f(x)| \\, |g(y)| \\, F_a \\left( d(x,y) \\right) \\, .\n\\end{equation}\nFinally, we assume that we have represented this harmonic dynamics in a regular and\n$\\tau_t^0$-invariant state $\\rho$ for which the pair $\\{ \\mathcal{M}, \\tau_t^0 \\}$, with\n$\\mathcal{M} = \\overline{\\pi_{\\rho}(\\mathcal{W}( \\mathcal{D}))}$, is a $W^*$-dynamical system.\n\nOur first estimate involves perturbations defined as finite sums of on-site terms.\nMore specifically, the perturbations we consider are defined as follows.\n\nTo each site $x \\in \\Gamma$, we will associate a finite measure $\\mu_x$ on $\\mathbb{C}$, and\nan element $P_x \\in \\mathcal{W}(\\mathcal{D})$ which has the form\n\\begin{equation} \\label{eq:defpx}\nP_x = \\int_{\\mathbb{C}} W(z \\delta_x) \\mu_x(dz) \\, .\n\\end{equation}\nWe require that each $\\mu_x$ is even, i.e. invariant under $z \\mapsto -z$, to ensure \nself-adjointness, i.e. $P_x^* = P_x$. Our Lieb-Robinson bounds hold \nunder the additional assumption that the second moment\nis uniformly bounded, i.e. \n\\begin{equation} \\label{eq:totbd}\n\\sup_{x \\in \\Gamma} \\int_{\\mathbb{C}} |z|^2 \\, | \\mu_x |( dz ) < \\infty \\, .\n\\end{equation}\n\nWe use Proposition~\\ref{prop:perdyn} to define the perturbed dynamics.\nFix a finite set $\\Lambda \\subset \\Gamma$. Set\n\\begin{equation} \\label{eq:defpl}\nP^{\\Lambda} = \\sum_{x \\in \\Lambda} P_x \\, ,\n\\end{equation}\nand note that $(P^{\\Lambda})^* = P^{\\Lambda} \\in \\mathcal{W}(\\mathcal{D})$. \nWe will denote by $\\tau_t^{(\\Lambda)}$ the dynamics that results from \napplying Proposition~\\ref{prop:perdyn} to the $W^*$-dynamical system $\\{ \\mathcal{M}, \\tau_t^0 \\}$\nand $P^{\\Lambda}$.\n\nBefore we begin the proof of our estimate, we discuss two examples.\n\\begin{ex} 1) Let $\\mu_x$ be supported on $[- \\pi, \\pi)$ and absolutely \ncontinuous with respect to Lebesgue measure, i.e. \n$\\mu_x(dz) = v_x(z) dz$. If $v_x$ is in $L^2([-\\pi,\\pi))$, then $P_x$ is proportional to an operator of multiplication by the \ninverse Fourier transform of $v_x$. Moreover, since the support of $\\mu_x$ is real, $P_x$ corresponds to \nmultiplication by a function depending only on $q_x$.\n\\end{ex}\n\\begin{ex}\n2) Let $\\mu_x$ have finite support, e.g., take $\\mbox{supp}( \\mu_x) = \\{ z, -z \\}$ for some number\n$z = \\alpha +  i \\beta \\in \\mathbb{C}$. Then\n\\begin{equation}\nP_x = W( z \\delta_x) + W(- z \\delta_x) = 2 \\cos( \\alpha q_x + \\beta p_x) \\, .\n\\end{equation}\n\\end{ex}\n\nWe now state our first result.\n\n\\begin{thm} \\label{thm:ahlrb}\nLet $\\tau_t^0$ be a harmonic dynamics defined on $\\Gamma$ as described above. Suppose that\n\\begin{equation}\n\\kappa = \\sup_{x \\in \\Gamma} \\int_{\\mathbb{C}} |z|^2 | \\mu_x| (d z) < \\infty \\, ,\n\\end{equation}\nand define the perturbed dynamics $\\tau_t^{(\\Lambda)}$ as indicated above.\nFor every $0<a \\leq a_0$, there exist positive numbers $c_a$ and $v_a$ for which\nthe estimate\n\\begin{equation} \\label{eq:anharmbd}\n\\left\\| \\left[ \\tau_t^{(\\Lambda)} \\left( W(f) \\right), W(g) \\right] \\right\\| \\leq c_a e^{ (v_a + c_a \\kappa C_a ) |t|} \\sum_{x, y} |f(x)| \\, |g(y)| F_a \\left( d(x,y) \\right)\n\\end{equation}\nholds for all $t \\in \\mathbb{R}$ and for any functions $f, g \\in \\mathcal{D}$. \n\\end{thm}\n\nHere the numbers $c_a$ and $v_a$ are as in (\\ref{eq:prelrb}), whereas $C_a$ is the convolution constant\nas defined in (\\ref{eq:intlat}) with respect to the function $F_a$.\n\\begin{proof}\nFix $t >0$ and define the function $\\Psi_t : [0,t] \\to \\mathcal{W}(\\mathcal{D})$ by setting\n\\begin{equation} \\label{eq:defpsit}\n\\Psi_t(s) = \\left[  \\tau_s^{(\\Lambda)} \\left( \\tau_{t-s}^0(W(f)) \\right), W(g) \\right] \\, .\n\\end{equation}\nIt is clear that $\\Psi_t$ interpolates between the commutator associated with the original harmonic dynamics, $\\tau_t^0$ at $s=0$, \nand that of the perturbed dynamics, $\\tau_t^{(\\Lambda)}$ at $s=t$. A calculation shows that\n\\begin{equation} \\label{eq:dpsit}\n\\frac{d}{ds} \\Psi_t(s) = i \\sum_{x \\in \\Lambda} \\left[ \\, \\tau_s^{(\\Lambda)} \\left( \\left[ P_x, W ( T_{t-s}f) \\right] \\right) , W(g) \\right] \\, ,\n\\end{equation}\nwhere differentiability is guaranteed by the results of Proposition~\\ref{prop:perdyn}.\nThe inner commutator can be expressed as\n\\begin{eqnarray}\n \\left[ P_x, W ( T_{t-s}f) \\right] & = & \\int_{\\mathbb{C}} \\left[ W(z \\delta_x), W( T_{t-s}f) \\right] \\mu_x( dz) \\nonumber \\\\\n & = & W( T_{t-s}f) \\mathcal{L}_{t-s;x}(f)  \\, .\n\\end{eqnarray}\nwhere\n\\begin{equation} \\label{eq:defLx}\n\\mathcal{L}^*_{t-s;x}(f) = \\mathcal{L}_{t-s;x}(f) =  \\int_{\\mathbb{C}} W(z \\delta_x) \\left\\{e^{i \\sigma( T_{t-s}f, z \\delta_x)} -1 \\right\\} \\mu_x(dz) \\, \\in \\mathcal{W}(\\mathcal{D}) \\, .\n\\end{equation}\nThus $\\Psi_t$ satisfies\n\\begin{equation}\n\\begin{split}\n\\frac{d}{ds} \\Psi_t(s) =   i \\sum_{x \\in \\Lambda} & \\Psi_t(s)  \\tau_s^{(\\Lambda)} \\left( \\mathcal{L}_{t-s;x}(f) \\right)  \\\\ \n+ & i \\sum_{x \\in \\Lambda} \\tau_s^{(\\Lambda)} \\left( W( T_{t-s}f) \\right) \\, \\left[ \\tau_s^{(\\Lambda)} \\left( \\mathcal{L}_{t-s;x}(f) \\right), W(g) \\right]  \\, .\n\\end{split}\n\\end{equation}\nThe first term above is norm preserving. In fact, define a unitary evolution $U_t(\\cdot)$ by setting\n\\begin{equation}\n\\frac{d}{ds}U_t(s) = - i \\sum_{x \\in \\Lambda} \\tau_s^{(\\Lambda)} \\left( \\mathcal{L}_{t-s;x}(f) \\right) U_t(s) \\quad \\mbox{with } U_t(0) = \\idty \\, .\n\\end{equation}\nIt is easy to see that\n\\begin{equation}\n\\frac{d}{ds} \\left( \\Psi_t(s) U_t(s) \\right) =  i \\sum_{x \\in \\Lambda} \\tau_s^{(\\Lambda)} \\left( W( T_{t-s}f) \\right) \\, \\left[ \\tau_s^{(\\Lambda)} \\left( \\mathcal{L}_{t-s;x}(f) \\right), W(g) \\right] U_t(s) \\, ,\n\\end{equation}\nand therefore,\n\\begin{equation}\n\\Psi_t(t) U_t(t) = \\Psi_t(0) + i \\sum_{x \\in \\Lambda} \\int_0^t  \\tau_s^{(\\Lambda)} \\left( W( T_{t-s}f) \\right) \\, \\left[ \\tau_s^{(\\Lambda)} \\left( \\mathcal{L}_{t-s;x}(f) \\right), W(g) \\right] U_t(s) \\, ds \\, .\n\\end{equation}\nEstimating in norm, we find that\n\\begin{equation} \\label{eq:norm1}\n\\begin{split}\n\\Big\\| \\Big[ \\tau_t^{(\\Lambda)} \\left(W (f)\\right)  , W(g) \\Big] \\Big\\|  \\leq &  \\Big\\| \\Big[ \\tau_t^0 \\left(W (f)\\right) , W(g) \\Big] \\Big\\| \\\\\n& +  \\sum_{x \\in \\Lambda} \\int_0^t  \\Big\\| \\left[  \\tau_s^{(\\Lambda)} \\left( \\mathcal{L}_{t-s;x}(f) \\right) , W(g) \\right] \\Big\\| \\, ds \\, .\n\\end{split}\n\\end{equation}\nMoreover, using (\\ref{eq:defLx}) and the bound (\\ref{eq:prelrb}), it is clear that\n\\begin{equation} \\label{eq:norm2}\n\\begin{split}\n \\Big\\| \\left[  \\tau_s^{(\\Lambda)} \\left( \\mathcal{L}_{t-s;x}(f) \\right) , W(g) \\right] \\Big\\| \\leq & \\, c_a e^{v_a(t-s)} \\sum_{x' \\in \\Gamma} |f(x')| F_a \\left( d(x,x') \\right) \\times \\\\\n& \\quad \\times \\int_{\\mathbb{C}} |z|  \\, \\Big\\| \\left[  \\tau_s^{(\\Lambda)} \\left( W(z \\delta_x) \\right) , W(g) \\right] \\Big\\| \\, |\\mu_x|(dz)\n\\end{split}\n\\end{equation}\nholds. Combining (\\ref{eq:norm2}), (\\ref{eq:norm1}), and (\\ref{eq:freelrb}), we have proven that\n\\begin{equation}\\label{eq:norm3}\n\\begin{split}\n\\Big\\| \\Big[ \\tau_t^{(\\Lambda)} \\left(W (f)\\right)  , W(g) \\Big] \\Big\\| \\leq \\; & c_a e^{v_a t} \\sum_{x, y} |f(x)| \\, |g(y)| \\, F_a \\left( d(x,y) \\right) \\\\ \n&+ c_a \\sum_{x' \\in \\Gamma} |f(x')| \\sum_{x \\in \\Lambda} F_a \\left( d(x,x') \\right) \\int_0^t  e^{v_a (t-s)}  \\times \\\\\n&\\quad  \\times \\int_{\\mathbb{C}} |z| \\, \\Big\\| \\left[  \\tau_s^{(\\Lambda)} \\left( W(z \\delta_x) \\right) , W(g) \\right] \\Big\\| \\, |\\mu_x|(dz) \\, ds \\,.\n\\end{split}\n\\end{equation}\nFollowing the iteration scheme applied in \\cite{nachtergaele2009}, one arrives at (\\ref{eq:anharmbd}) as claimed.\n\\end{proof}\n\n\n\n\n\\subsection{Multiple Site Anharmonicities} \\label{subsec:anharmms}\n\nIn this section, we will prove that Lieb-Robinson bounds, similar to those in\nTheorem~\\ref{thm:ahlrb}, also hold for perturbations involving short range interations.\nWe introduce these as follows.\n\nFor each finite subset $X \\subset \\Gamma$, we associate a finite measure $\\mu_X$ on\n$\\mathbb{C}^X$ and an element $P_X \\in \\mathcal{W}(\\mathcal{D})$ with the form\n\\begin{equation} \\label{eq:PX}\nP_X = \\int_{\\mathbb{C}^X} W( z \\cdot \\delta_X) \\, \\mu_X(d z) \\, ,\n\\end{equation}\nwhere, for each $z \\in \\mathbb{C}^X$, the function $z \\cdot \\delta_X : \\Gamma \\to \\mathbb{C}$ is\ngiven by\n\\begin{equation}\n(z \\cdot \\delta_X)(x)  = \\sum_{x' \\in X} z_{x'} \\delta_{x'}(x) = \\left\\{ \\begin{array}{cc} z_x & \\mbox{if } x \\in X , \\\\ 0 & \\mbox{otherwise.} \\end{array} \\right.\n\\end{equation}\nWe will again require that $\\mu_X$ is invariant with respect to $z \\mapsto -z$, and hence, $P_X$ is\nself-adjoint. In analogy to (\\ref{eq:defpl}), for any finite subset $\\Lambda \\subset \\Gamma$, we will set\n\\begin{equation} \\label{eq:defpl2}\nP^{\\Lambda} = \\sum_{X \\subset \\Lambda} P_X\\, ,\n\\end{equation}\nwhere the sum is over all subsets of $\\Lambda$.\nHere we will again let $\\tau^{(\\Lambda)}_t$ denote the dynamics resulting from Proposition~\\ref{prop:perdyn}\napplied to the $W^*$-dynamical system $\\{ \\mathcal{M}, \\tau_t^0 \\}$ and the perturbation $P^{\\Lambda}$ defined by (\\ref{eq:defpl2}). \n\nThe main assumption on these multi-site perturbations follows.\nThere exists a number $a_1 >0$ such that for all $0< a \\leq a_1$, there is a number $\\kappa_a >0$ for which\ngiven any pair $x_1, x_2 \\in \\Gamma$, \n\\begin{equation} \\label{eq:pertbd}\n\\sum_{\\stackrel{X \\subset \\Gamma:}{x_1, x_2 \\in X}} \\int_{\\mathbb{C}^X} |z_{x_1}| | z_{x_2}| \\big| \\mu_X \\big|(dz) \\leq \\kappa_a F_a \\left( d(x_1,x_2) \\right) \\, .\n\\end{equation} \n\n\\begin{thm} \\label{thm:ahlrbms} Let $\\tau_t^0$ be a harmonic dynamics defined on $\\Gamma$.\nAssmue that (\\ref{eq:pertbd}) holds, and that $\\tau_t^{(\\Lambda)}$ denotes the corresponding\nperturbed dynamics. For every $0< a \\leq \\min(a_0, a_1)$, there exist positive numbers $c_a$ and $v_a$ for which\nthe estimate\n\\begin{equation} \\label{eq:anharmbdms}\n\\left\\| \\left[ \\tau_t^{(\\Lambda)} \\left( W(f) \\right), W(g) \\right] \\right\\| \\leq c_a e^{ (v_a +  c_a \\kappa_a C_a^2 ) |t|} \\sum_{x, y} |f(x)| \\, |g(y)| F_a \\left( d(x,y) \\right)\n\\end{equation}\nholds for all $t \\in \\mathbb{R}$ and for any functions $f, g \\in \\mathcal{D}$. \n\\end{thm}\nThe proof of this result closely follows that of Theorem~\\ref{thm:ahlrb}, and so we only comment on\nthe differences.\n\\begin{proof}\nFor $f,g \\in \\mathcal{D}$ and $t >0$, define $\\Psi_t :[0,t] \\to \\mathcal{W}(\\mathcal{D})$ as in (\\ref{eq:defpsit}).\nThe derivative calculation beginning with (\\ref{eq:dpsit}) proceeds as before. Here\n\\begin{equation} \\label{eq:deflzms}\n\\mathcal{L}_{t-s;X}(f) = \\int_{\\mathbb{C}^X} W( z \\cdot \\delta_X) \\left\\{ e^{i \\sigma(T_{t-s}f, z \\cdot \\delta_X) } - 1 \\right\\} \\, \\mu_X( d z) \\, ,\n\\end{equation}\nis also self-adjoint. The norm estimate\n\\begin{equation} \\label{eq:norm1ms}\n\\begin{split}\n\\Big\\| \\Big[ \\tau_t^{(\\Lambda)} \\left(W (f)\\right)  , W(g) \\Big] \\Big\\|  \\leq  & \\Big\\| \\Big[ \\tau_t^0 \\left(W (f)\\right) , W(g) \\Big] \\Big\\| \\\\ & +  \\sum_{X \\subset \\Lambda} \\int_0^t  \\Big\\| \\left[  \\tau_s^{(\\Lambda)} \\left( \\mathcal{L}_{t-s;X}(f) \\right) , W(g) \\right] \\Big\\| \\, ds \\, ,\n\\end{split}\n\\end{equation}\nholds similarly. With (\\ref{eq:deflzms}), it is easy to see that the integrand in (\\ref{eq:norm1ms}) is bounded by\n\\begin{equation} \nc_a e^{v_a(t-s)} \\sum_{x\\in \\Gamma} \\, |f(x)| \\, \\sum_{x' \\in X} F_a \\left( d(x,x') \\right) \\int_{\\mathbb{C}^X}  | z_{x'}|  \\,  \\, \\Big\\| \\left[  \\tau_s^{(\\Lambda)} \\left( W(z \\cdot \\delta_X) \\right) , W(g) \\right] \\Big\\| \\, |\\mu_X|(dz) \\, ,\n\\end{equation}\nthe analogue of (\\ref{eq:norm2}), for $0<a \\leq a_0$. Moreover, if $0<a \\leq \\min(a_0,a_1)$, then \n\\begin{equation}\\label{eq:norm4}\n\\begin{split}\n\\Big\\| \\Big[ \\tau_t^{(\\Lambda)} \\left(W (f)\\right)  , W(g) \\Big] \\Big\\| \\leq \\; &  c_a e^{v_a t} \\sum_{x, y \\in \\Gamma} |f(x)| \\, |g(y)| \\, F_a \\left( d(x,y) \\right) \\\\ &+ c_a \\sum_{x \\in \\Gamma} |f(x)| \\sum_{X \\subset \\Lambda} \\sum_{x' \\in X} F_a \\left( d(x,x') \\right) \\times \\\\\n& \\quad \\times \\int_0^t  e^{v_a (t-s)}  \n\\int_{\\mathbb{C}^X} |z_{x'}| \\, \\Big\\| \\left[  \\tau_s^{(\\Lambda)} \\left( W(z \\cdot \\delta_X) \\right) , W(g) \\right] \\Big\\| \\, |\\mu_X|(dz) \\, ds \\, .\n\\end{split}\n\\end{equation}\nThe estimate claimed in (\\ref{eq:anharmbdms}) follows by iteration. In fact, the first term in the iteration is bounded by\n\\begin{equation}\n\\begin{split}\nc_a \\sum_x |f(x)| \\sum_{X \\subset \\Lambda} \\sum_{x_1 \\in X} & F_a \\left( d(x,x_1) \\right) \\int_0^t  e^{v_a (t-s)}  \\\\  \n& \\times \\int_{\\mathbb{C}^X} |z_{x_1}| \\, \\Big( c_a e^{v_a s} \\sum_{x_2 \\in X} \\sum_y |z_{x_2}| \\, |g(y)| \\, F_a \\left( d(x_2,y) \\right) \\Big) \\, |\\mu_X|(dz) \\, ds \\, \\\\\n\\leq  c_a  t \\cdot c_a e^{v_a t}  \\sum_{x,y} & |f(x)| |g(y)|  \\sum_{x_1, x_2 \\in \\Gamma} F_a \\left( d(x,x_1) \\right)  F_a \\left( d(x_2,y) \\right) \\sum_{\\stackrel{X \\subset \\Gamma:}{x_1,x_2 \\in X}} \\int_{\\mathbb{C}^X} | z_{x_1}| |z_{x_2}| | \\mu_{X}|(dz) \\, \\\\\n\\leq   \\kappa_a c_a t  \\cdot  c_a e^{v_a t} \\sum_{x,y} & |f(x)| |g(y)|  \\sum_{x_1, x_2 \\in \\Gamma} F_a \\left( d(x,x_1) \\right) F_{a} \\left( d(x_1, x_2) \\right)  F_a \\left( d(x_2,y) \\right) \\\\\n\\leq  \\kappa_a C_{a}^2 c_{a} t  \\cdot  c_a e^{v_a t} \\sum_{x,y} & |f(x)| |g(y)| F_a \\left( d(x,y) \\right) \\, .\n\\end{split}\n\\end{equation}\nThe higher order iterates are treated similarly.\n\\end{proof}\n\n\n\n\\section{Existence of the Dynamics}\nIn this section, we demonstrate that the finite volume dynamics analyzed in the previous section\nconverge to a limiting dynamics as the volume $\\Lambda$ on which the perturbation is defined\ntends to $\\Gamma$. We state this as Theorem~\\ref{thm:exist} below.\n\n\\begin{thm} \\label{thm:exist}\nLet $\\tau_t^0$ be a harmonic dynamics defined on $\\mathcal{W}( \\ell^1( \\Gamma) )$ as described in Section~\\ref{subsec:onsite}.\nLet $\\{ \\Lambda_n \\}$ denote a non-decreasing, exhaustive sequence of finite subsets of $\\Gamma$. \nConsider a family of perturbations $P^{\\Lambda_n}$ as defined in (\\ref{eq:defpl2}) and (\\ref{eq:PX}) which satisfy\n(\\ref{eq:pertbd}). Suppose in addition that\n\\begin{equation} \\label{eq:1mom}\nM = \\sup_{x \\in \\Gamma} \\sum_{\\stackrel{X \\subset \\Gamma:}{x \\in X}} \\int_{\\mathbb{C}^X} |z_x| | \\mu_X|(dz) < \\infty \\, .\n\\end{equation}\nThen, for each $f \\in \\ell^1( \\Gamma)$ and $t \\in \\mathbb{R}$ fixed, the limit\n\\begin{equation} \\label{eq:lim}\n\\lim_{n \\to \\infty} \\tau_t^{(\\Lambda_n)} \\left( W(f) \\right) \\, \n\\end{equation}\nexists in norm. The limiting dynamics, which we denote by $\\tau_t$, is weakly continuous.\n\\end{thm}\n\nIt is important to note that since the estimates in Theorem~\\ref{thm:ahlrbms} are independent of $\\Lambda$,\nthe limiting dynamics also satisfies a Lieb-Robinson bound as in (\\ref{eq:anharmbdms}). We now\nprove Theorem~\\ref{thm:exist}.\n\n\\begin{proof}\nFix a Weyl operator $W(f)$ with $f \\in \\ell^1(\\Gamma)$. \nLet $T>0$ and take $m \\leq n$. Iteratively applying Proposition~\\ref{prop:perdyn}, we have that\n\\begin{equation} \\label{eq:dyn3}\n\\tau_t^{(\\Lambda_n)}(W(f)) = \\tau_t^{(\\Lambda_m)}(W(f)) + i \\int_0^t \\tau_s^{(\\Lambda_n)} \\left( \\left[ P^{\\Lambda_n \\setminus \\Lambda_m}, \\tau_{t-s}^{(\\Lambda_m)}(W(f)) \\right] \\right) \\, ds \\, ,\n\\end{equation}\nfor all $-T \\leq t \\leq T$. The bound\n\\begin{eqnarray}\n&&\\left\\| \\left[ P^{\\Lambda_n \\setminus \\Lambda_m}, \\tau_{t-s}^{(\\Lambda_m)}(W(f)) \\right] \\right\\|\\\\\n & \\leq & \\sum_{\\stackrel{X \\subset \\Lambda_n:}{ X \\cap \\Lambda_n \\setminus \\Lambda_m \\neq \\emptyset}} \\int_{\\mathbb{C}^X}\n\\left\\| \\left[ W(z \\cdot \\delta_X) , \\tau_{t-s}^{(\\Lambda_m)}(W(f)) \\right] \\right\\| \\, | \\mu_X| ( dz) \\nonumber \\\\\n& \\leq & c_a e^{(v_a +c_a \\kappa_a C_a^2)(t-s)} \\sum_{x \\in \\Gamma} |f(x)| \\sum_{\\stackrel{X \\subset \\Lambda_n:}{ X \\cap \\Lambda_n \\setminus \\Lambda_m \\neq \\emptyset}} \\sum_{y \\in X} F_a \\left( d(x,y) \\right) \\int_{\\mathbb{C}^X} |z_y| \\, | \\mu_X| (dz) \\nonumber \\\\ & \\leq & c_a e^{(v_a +c_a \\kappa_a C_a^2)(t-s)} \\sum_{x \\in \\Gamma} |f(x)| \\sum_{y \\in \\Lambda_n \\setminus \\Lambda_m }   F_a \\left( d(x,y) \\right) \\sum_{\\stackrel{X \\subset \\Gamma:}{ y \\in X}}   \\int_{\\mathbb{C}^X} |z_y| \\, | \\mu_X| (dz) \\nonumber \\\\ & \\leq & M c_a e^{(v_a +c_a \\kappa_a C_a^2)(t-s)} \\sum_{x \\in \\Gamma} |f(x)| \\sum_{y \\in \\Lambda_n \\setminus \\Lambda_m }   F_a \\left( d(x,y) \\right) \\nonumber\n\\end{eqnarray}\nfollows readily from Theorem~\\ref{thm:ahlrbms} and assumption (\\ref{eq:1mom}).\nFor $f \\in \\ell^1( \\Gamma)$ and fixed $t$, the upper estimate above goes to zero as\n$n,m \\to \\infty$. In fact, the convergence is uniform for $t \\in [-T,T]$. \nThis proves (\\ref{eq:lim}).\n\nBy an $\\epsilon\/3$ argument, similar to what is done at the end of Section~\\ref{sec:bdints}, weak continuity follows since we know it holds for the \nfinite volume dynamics.\nThis completes the proof of Theorem~\\ref{thm:exist}.\n\\end{proof}\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{KG-agnostic Entity Linkers}\n\\label{sec:appendix}\n\nAGDISTIS~\\cite{DBLP:conf\/ecai\/UsbeckNRGCAB14} is an EL approach expecting already marked entity mentions. It expects a KG dump available in the Turtle format~\\cite{beckett2014rdf}. For candidate generation, first, an index is created which contains all available entities and their labels. They are extracted from the available Turtle dump. The input entity mention is first normalized by reducing plural and genitive forms and removing common affixes. Furthermore, if an entity mention consists of a substring of a preceding entity mention, the succeeding one is directly mapped to the preceding one. Additionally, the space of possible candidates can be limited by configuration. Usually, the candidate space is reduced to organizations, persons and locations. The candidates are then searched for over the index by comparing the reduced entity mention with the labels in the index using trigram similarity. No candidates are included, which contain time information inside the label.\nAfter gathering all candidates of all entity mentions in the utterance, the candidates are ranked by building a temporary graph. Starting with the candidates as the initial nodes, the graph is expanded breadth-first by adding the adjacent nodes and the edges in-between. It is done to some previously set depth. This results in a partly connected graph containing all candidates. \nThen the HITS-algorithm~\\cite{Kleinberg1999} is run and the most authoritative candidate nodes are chosen per entity mention. Thus, the approach is performing a global entity coherence optimization. \nThe approach uses label and alias information for building the index. Type information can be used to restrict the candidate space and the KG structure is utilized during the candidate ranking. \n\n\\paragraph{MAG.} MAG~\\cite{Moussallem2017} is a multilingual extension of AGDISTIS. Again, no ER is performed. The same label index as used in AGDISTIS is employed. Besides that, the following additional indices were created: \n\\begin{itemize}\n    \\item A person index, containing the person names and the variations in different languages\n    \\item A rare references index containing textual descriptions of entities\n    \\item An acronym index based on the commercial STANDS4~\\footnote{\\label{footnote1}\\url{http:\/\/www.abbreviations.com\/}} data\n    \\item A context index containing semantic embeddings of Concise Bounded Description~\\footnote{\\url{https:\/\/www.w3.org\/Submission\/CBD\/}}\n\\end{itemize} \nDuring candidate generation, it is first checked if the entity mention corresponds to an acronym. If it is one, no further preprocessing is done. If not, the entity mention is normalized by removing special characters, changing the casing and splitting camel-cased words. After preprocessing, the candidates are searched by first checking for exact matches, then searching via trigram similarity. If this still did not produce any candidates, the entity mention is stemmed and the search is repeated. If a mention is an acronym, the candidate list is expanded with the corresponding entities.\nThen, more candidates are searched by taking an entity mention and the set of all entity mentions in the utterance. Those are used to build a tf-idf search query over the context index. All returned candidates are then first filtered by trigram similarity between entity mention and candidate. A second filtering is applied by counting the number of direct connections between the remaining candidates and the candidates of the other entity mentions. The candidates with too few links are pruned away. All the candidates of the entity mention are then sorted by their popularity (calculated via PageRank~\\cite{page1999pagerank}) and the top 100 are returned.\nThen, the entities are disambiguated in nearly the same way as done by AGDISTIS. The only difference is the option to use PageRank instead of HITS to rank the final candidates. \nAdditionally to the properties already used by AGDISTIS, item descriptions are incorporated via the context index.\n\nDoSeR~\\cite{DBLP:conf\/esws\/ZwicklbauerSG16} also expects already marked entity mentions. The linker focuses being to link to multiple knowledge graphs simultaneously. Here, they support RDF-based KGs and entity-annotated document (EAD) KGs (e.g., Wikipedia). The KGs are split into core and optional KGs. Core KGs contain the entities to which one wants to link. Optional KGs complement the core KGs with additional data.\nFirst, an index is created which includes the entities of all core KGs. In the index, the labels or surface forms, a semantic embedding, and each entity's prior popularity are stored. \nThe semantic embeddings are computed by using Word2Vec. For EAD-KGs, the different documents are taken and all words, which are not pointing to entities, are removed. All remaining words are replaced with the corresponding entity identifier. These sequences are then used to train the embeddings. For RDF-KGs, a Random Walk is performed over the graph and the resulting sequences are used to train the embeddings. The succeeding node is chosen with a probability corresponding to the reciprocal of the number of edges it got. The same probability is used to sometimes jump to another arbitrary node in the graph. \nThe prior probability is calculated by either using the number of incoming\/outgoing edges in the RDF-KG or the number of annotations that point to the entity in the EAD KG. If type information is available, the entity space can be limited here too. \nFirst, candidates are generated by searching for exact matches and then the AGDISTIS candidate generation is used to find more candidates. \nThe candidates are disambiguated, similar to the way AGDISTIS and MAG are doing it. First, a graph is built though not a complete graph but a $K$-partite graph where $K$ is the number of all entity mentions. Edges exist only between candidates of different entities. Using the complete graph resulted in a loss of performance. After the graph is created, PageRank is done to score the different entities coherently. The edge weights correspond to the (normalized) cosine similarity of the semantic embeddings of the two connected entities. Additionally, at any point during PageRank computation, it is possible to jump to an arbitrary node with a certain probability. This probability depends on the prior popularity of the entity.\nIt uses label information, the knowledge graph structure and type information (if desired). \n\\begin{table*}[tbh!]\n    \\centering\n     \\begin{tabularx}{\\textwidth}{p{3cm}YYYYYY}\n        \\toprule\n         \\textbf{Approach}&\\textbf{Labels\/\\allowbreak Aliases} & \\textbf{Descriptions}& \\textbf{Knowledge graph structure} & \\textbf{Hyper-relational structure} & \\textbf{Types} & \\textbf{Additional Information} \\\\ \\midrule\n         AGDISTIS~\\cite{DBLP:conf\/ecai\/UsbeckNRGCAB14} & \\cmark & \\xmark & \\cmark & \\xmark & \\cmark & \\\\\n         MAG~\\cite{Moussallem2017} & \\cmark & \\cmark & \\cmark & \\xmark & \\cmark & STANDS4~\\ref{footnote1} \\\\\n         DoSeR~\\cite{DBLP:conf\/esws\/ZwicklbauerSG16} & \\cmark & \\xmark & \\cmark & \\xmark & \\cmark & \\\\\n        \\bottomrule\n    \\end{tabularx}\n    \\caption{Comparison between the utilized Wikidata characteristics of each KG-agnostic approach.}\n    \\label{tab:comparison_KG_agnostic_approaches_wikidata}\n\\end{table*}\n\n\n\n\\section{EL-only results and discussion}\n\n\\begin{table*}\n    \\centering\n    \\begin{threeparttable}\n        \\begin{tabular}{cccP{3cm}c}\n                \\toprule\n               \n                &\\rotatebox[origin=c]{-66}{Mulang et al.~\\cite{DBLP:journals\/corr\/abs-2008-05190}}\n                &\\rotatebox[origin=c]{-66}{LSH-ELMo model~\\cite{perkins2020separating}}\n                &\\rotatebox[origin=c]{-66}{\\parbox{3cm}{NED using DL on Graphs~\\cite{DBLP:journals\/corr\/abs-1810-09164}~\\tnotex{tn:elonly1}}} &\\rotatebox[origin=c]{-66}{Botha et al.~\\cite{Botha2020}}\\\\\n                \\midrule\n                AIDA-CoNLL~\\cite{hoffart-etal-2011-robust}&0.9494~\\cite{DBLP:journals\/corr\/abs-2008-05190}~\\tnotex{tn:elonly6}~\\tnote{,}~\\tnotex{tn:elonly3}&0.73~\\cite{perkins2020separating}&-&-\\\\\n                ISTEX-1000~\\cite{DBLP:journals\/corr\/abs-1904-09131}&0.9261~\\cite{DBLP:journals\/corr\/abs-2008-05190}~\\tnotex{tn:elonly4}&-&-&-\\\\\n                Wikidata-Disamb~\\cite{DBLP:journals\/corr\/abs-1810-09164}&0.9235~\\cite{DBLP:journals\/corr\/abs-2008-05190}~\\tnotex{tn:elonly5}&-&0.916~\\cite{DBLP:journals\/corr\/abs-1810-09164}&-\\\\\n                Mewsli-9~\\cite{Botha2020}  & - & - & - & 0.91~\\cite{Botha2020}~\\tnotex{tn:elonly7} \\\\\n               \n                \\bottomrule\n        \\end{tabular}\n        \\begin{tablenotes}\n            \\setlength{\\columnsep}{0.8cm}\n            \\setlength{\\multicolsep}{0cm}\n            \\begin{multicols}{3}\n                \\small\n                \\item[1] \\label{tn:elonly1} Model with best result\n                \\item[2] \\label{tn:elonly6} Accuracy instead of $F_1$\n                \\item[3] \\label{tn:elonly3} DCA-SL used\n                \\item[4] \\label{tn:elonly4} XLNet used\n                \\item[5] \\label{tn:elonly5} Roberta used\n                \\item[6] \\label{tn:elonly7} Recall instead of $F_1$\n            \\end{multicols}\n        \\end{tablenotes}\n    \\end{threeparttable}\n    \\caption{Results: EL-only.}\n    \\label{tab:dataset_results_el_only}\n\\end{table*}\n\nThe results for EL-only approaches can be found in Table~\\ref{tab:dataset_results_el_only}.\nAIDA-CoNLL results are available for three of the four approaches, but the results for one is the accuracy instead of the $F_1$-measures. \nThe available labels for each item and property make language-model-based approaches possible that perform quite well~\\cite{DBLP:journals\/corr\/abs-2008-05190}. No approaches are available to compare to the one by Botha et al.~\\cite{Botha2020}, but the result demonstrates the promising performance of multilingual EL with Wikidata as the target KG.\n\n\n\\begin{table*}[]\n    \\centering\n    \\begin{tabular}{ll}\n    \\toprule\n        Dataset & Links \\\\\n         \\midrule\n         T-REx~\\cite{elsahar2019t} & \\url{https:\/\/hadyelsahar.github.io\/t-rex} \\\\ \n         NYT2018~\\cite{DBLP:journals\/pvldb\/LinLXLC20, DBLP:conf\/icde\/LinC19} & not found \\\\\n         ISTEX-1000~\\cite{DBLP:journals\/corr\/abs-1904-09131} & \\url{https:\/\/github.com\/wetneb\/opentapioca\/blob\/master\/data} \\\\\n         LC-QuAD 2.0~\\cite{dubey2019lc} &  \\url{https:\/\/github.com\/AskNowQA\/LC-QuAD2.0\/tree\/master\/dataset}\\\\\n         Knowledge Net~\\cite{mesquita2019knowledgenet} & \\url{https:\/\/github.com\/diffbot\/knowledge-net\/tree\/master\/dataset}\n         \\\\\n         KORE50DYWC~\\cite{noullet2020kore} & \\url{https:\/\/www.aifb.kit.edu\/web\/KORE_5\n         Kensho Derived Wikimedia Dataset~\\cite{KenshoRD} &  \\url{https:\/\/www.kaggle.com\/kenshoresearch\/kensho-derived-wikimedia-data} \\\\\n         CLEF HIPE 2020~\\cite{Ehrmann2020} & \\url{https:\/\/github.com\/impresso\/CLEF-HIPE-2020\/tree\/master\/data}   \\\\\n         Mewsli-9~\\cite{Botha2020} & \\url{https:\/\/metatext.io\/datasets\/mewsli-9-}  \\\\\n         TweekiData~\\cite{tweeki:wnut20} & \\url{https:\/\/github.com\/ucinlp\/tweeki\/tree\/main\/data\/Tweeki_data} \\\\\n         TweekiGold~\\cite{tweeki:wnut20}& \\url{https:\/\/github.com\/ucinlp\/tweeki\/tree\/main\/data\/Tweeki_gold}\\\\\n         \\bottomrule\n    \\end{tabular}\n    \\caption{Links to datasets}\n    \\label{tab:dataset_links}\n\\end{table*}\n\n\\end{appendix}\n\\section{Discussion} \\label{sec:discussion}\n\\subsection{Current Approaches, Datasets and their Drawbacks}\n\\paragraph{Approaches.}\nThe number of algorithms using Wikidata is small; the number of algorithms using Wikidata solely is even smaller. Most algorithms employ labels and alias information contained in Wikidata. Some deep learning-based algorithms leverage the underlying graph structure, but the inclusion of that information is often superficial. The same information is also available in other KGs. Additional statement-specific information like qualifiers is used by only one algorithm (OpenTapioca), and even then, it only interprets qualifiers as extra edges to the item. Thus, there is no inclusion of the actual structure of a hyper-relation. Information like the descriptions of items that are providing valuable context information is also rarely used. Wikidata includes type information, but almost none of the existing algorithms utilize it to do more than to filter out entities that are not desired to link in general. An exception is perhaps Tweeki, though it only uses types during ER.\n\nIt seems that most of the authors developed approaches for Wikidata due to it being popular and up-to-date while not specifically utilizing its structure. With small adjustments, many would also work on any other KG. \nBesides the less-dedicated utilization of specific characteristics of Wikidata, it is also notable that there is no clear focus on one of the essential characteristics of Wikidata, continual growth. Many approaches use static graph embeddings, which need to be retrained if the KG changes. EL algorithms working on Wikidata, which are not usable on future versions, seem unintuitive. But there also exist some approaches which can handle change. They often rely on more extensive textual information, which is again challenging due to the limited amount of such data in Wikidata. Wikidata descriptions do exist, but only short paragraphs are provided, in general, insufficient to train a language model. To compensate, Wikipedia is included, which provides this textual information. It seems like Wikidata as the target KG with its language-agnostic identifiers and the easily connectable Wikipedia with its multilingual textual information are a great pair. But surprisingly, most methods do use either Wikipedia or Wikidata. A combination happens rarely but seems very fruitful, as can be seen via the performance of the multilingual EL by Botha et al.~\\cite{Botha2020}. Though even this approach still uses Wikidata only sparsely.  \n\nNone of the investigated approaches' authors tried to examine the performance between different versions of Wikidata. Since continuous evolution is a central characteristic of Wikidata, a temporal analysis would be reasonable. \nAs we are confronted with a fast-growing ocean of knowledge, taking into account the change of Wikidata and hence developing approaches that are robust against that change will undoubtedly be useful for numerous applications and their users. \n\nThis survey aimed to identify the extent to which the current state of the art in Wikidata EL is utilizing the characteristics of Wikidata. As only a few are using more information than on other established KGs, there is still much potential for future research. \n\n\\paragraph{Datasets.} Only a limited number of datasets were created entirely with Wikidata in mind exist. Many datasets used are still only mapped versions of datasets created for other knowledge graphs. Multilingualism is present so far that some datasets contain documents in different languages. However, only different documents for different languages are available. Having the same documents in multiple languages would be more helpful for an evaluation of multilingual Entity Linkers.  The fact that the Wikidata is ever-changing is also not genuinely considered in any datasets. Always providing the dump version on which the dataset was created is advisable. A big advantage for the community  is that datasets from very different domains like news, forums, research, tweets exist. The utterances can also vary from shorter texts with only a few entities to large documents with many entities.\nThe difficulty of the datasets significantly differs in the ambiguity of the entity mentions. \nThe datasets also differ in quality. Some were automatically created and others annotated manually by experts.\nThere are no unanimously agreed-upon datasets used for Wikidata EL.\nOf course, a single dataset can not exist as different domains and text types make different approaches, and hence datasets necessary.\n\n\\subsection{Future Research Avenues}\n\\label{subsec:future}\n\nIn general, Wikidata EL could be improved by including the following aspects:\n\n\\paragraph{Hyper-relational statements.}\nThe qualifier and rank information of Wikidata could be suitable to do EL on time-sensitive utterances~\\cite{DBLP:conf\/acl\/AgarwalSCHW18}. The problem revolves around utterances that talk about entities from different time points and spans and thus, the referred entity can significantly diverge.\nThe usefulness of other characteristics of Wikidata, e.g., references, may be limited but could make EL more challenging due to the inclusion of contradictory information. Therefore, research into the consequences and solutions of conflicting information would be advisable.\nAnother possibility would be to directly include the qualifier information via the KG embeddings. For example, the StarE~\\cite{Galkin2020} embedding includes qualifiers directly during training. It performs superior over regular embeddings on the task of link prediction if enough statements have qualifiers assigned. This is promising but whether this directly applies to EL approaches, which use such embeddings, has to be evaluated.\n\n\\paragraph{More extensive type information.}\nWhile type information is incorporated by some linkers, it is generally done to simply limit the candidate space to the three main types: location, organization and person. But Raiman and Raiman~\\cite{DBLP:conf\/aaai\/RaimanR18} showed that a more extensive system of types proves very effective on the task of EL. If an adequate typing system is chosen and the correct type of an entity mention is available, an entity linker can achieve a near-perfect performance. Especially as Wikidata has a much more fine-grained and noisy type system than other KGs, evaluating the performance of entity linkers, which incorporate types, is of interest. \nWhile most approaches use types directly to limit the candidate space, incorporating them indirectly via type-aware ~\\cite{Zhang2020} or hierarchy-sensitive embeddings~\\cite{Chami2020, Nayyeri2021, DBLP:conf\/nips\/BalazevicAH19} might also prove useful for EL.\nBut note that the incorporation of type information heavily depends on the performance of the type classifier, and the difficulty of the type classification task again depends on the type system. Nevertheless, an improved type classification would directly benefit type-utilizing entity linkers. \n\n\\paragraph{Inductive or efficiently trainable knowledge graph embeddings.}\nTo reiterate, due to the fast rate of change of Wikidata, approaches are necessary, which are more robust to such a dynamic KG. Continuously retraining transductive embeddings is intractable, so more sophisticated methods like inductive or efficiently retrievable graph embeddings are a necessity~\\cite{Wang2019, Wang2019a, Teru2020,Baek2020,Albooyeh2020,Hamaguchi2017,Wu2019a, galkin2021nodepiece, Daruna2021}.\nFor example, the embedding by Albooyeh et al.~\\cite{Albooyeh2020} can be employed, which can handle out-of-sample entities. These are entities, which were not available at training time, but are connected to entities, which were existing.\nTo go even further, NodePiece~\\cite{galkin2021nodepiece}, the KG-embedding counterpart of sub-word embeddings like BERT, works by relying on only a small subset of anchor nodes and all relations in the KG. While it uses a fraction of all nodes, it still is able to achieve performance competitive with transductive embeddings on the task of link prediction. By being independent of most nodes in a KG, one can include new entities (in the form of nodes) without having to retrain.  As an alternative, standard continual learning approaches could be employed to learn new data while being robust against catastrophic forgetting. An examination of the performance of popular techniques in the context of KG embeddings can be found in the paper by Daruna et al.~\\cite{Daruna2021}.\n\n\\paragraph{Item label and description information in multiple languages for multilingual EL.}\nMultilingual or cross-lingual EL is already tackled with Wikidata but currently mainly by depending on Wikipedia. Using the available multilingual label\/description information in a structured form together with the rich textual information in Wikipedia could move the field forward. The approach by Botha et al.~\\cite{Botha2020}, which could be seen as an extension of BLINK~\\cite{Wu2019}, performs very well on the task of cross- and multilingual EL. \nFor example, the approach by Mulang et al.~\\cite{DBLP:journals\/corr\/abs-2008-05190}, which fully relies on label information, could be extended in a similar way as BLINK was extended. Instead of only using labels (of items and properties) in the English language, training the model directly in multiple languages could prove effective. Additionally, multilingual description information might be used too. We are convinced that also investigations into the linking of long-tail entities are needed.\n\nIt seems like there exist no commonly agreed-on Wikidata EL datasets, as shown by a large number of different datasets the approaches were tested on. Such datasets should try to represent the challenges of Wikidata like the time-variance, contradictory triple information, noisy labels, and multilingualism.\n\n\n\\section*{Acknowledgments}\nWe acknowledge the support of the EU project TAILOR (GA 952215), the Federal Ministry for Economic Affairs and Energy (BMWi) project SPEAKER (FKZ 01MK20011A), the German Federal Ministry of Education and Research (BMBF) projects and excellence clusters ML2R (FKZ 01 15 18038 A\/B\/C), MLwin (01S18050 D\/F), ScaDS.AI (01\/S18026A) as well as the Fraunhofer Zukunftsstiftung project JOSEPH. The authors also acknowledge the financial support by the Federal Ministry for Economic Affairs and Energy of Germany in the project CoyPu (project number 01MK21007G).\n\\section{Datasets}\n\\label{sec:datasets}\n\\subsection{Overview}\nThis section is concerned with analyzing the different datasets which are used for Wikidata EL. A comparison can be found in Table~\\ref{tab:datasets}. \n\\begin{table*}[ptb!]\n    \\small\n    \\centering\n    \\rotatebox{-90}{\n    \\begin{threeparttable}\n    \\begin{tabularx}{0.95\\textheight}{p{4cm}p{3cm}XXp{2.8cm}P{1.5cm}p{3cm}}\n         \\toprule\n         \\textbf{Dataset} & \\textbf{Domain} & \\textbf{Year} & \\textbf{Annotation process} & \\textbf{Purpose} &  \\textbf{Spans given} & \\textbf{Identifiers} \\\\ \\midrule\n         T-REx~\\cite{elsahar2019t} & Wikipedia abstracts  & 2015& automatic & Knowledge Base Population (KBP), Relation Extraction (RE), Natural Language Generation (NLG) &\\cmark& Wikidata \\\\ \n         NYT2018~\\cite{DBLP:journals\/pvldb\/LinLXLC20, DBLP:conf\/icde\/LinC19} & News & 2018& manually & EL &\\cmark & Wikidata, DBpedia \\\\\n         ISTEX-1000~\\cite{DBLP:journals\/corr\/abs-1904-09131} & Research articles& 2019 & manually&EL & \\cmark& Wikidata \\\\\n         LC-QuAD 2.0~\\cite{dubey2019lc} & General  complex questions (Wikidata) & 2019& semi-automatic &Question Answering (QA) &\\xmark& DBpedia, Wikidata \\\\\n         Knowledge Net~\\cite{mesquita2019knowledgenet} & Wikipedia abstracts, biographical texts & 2019& manually & KBP  &\\cmark& Wikidata\n         \\\\\n         KORE50DYWC~\\cite{noullet2020kore} & News & 2019& manually & EL & \\cmark& Wikidata, DBpedia, YAGO, Crunchbase \\\\\n         Kensho Derived Wikimedia Dataset~\\cite{KenshoRD} & Wikipedia & 2020& automatic & Natural Language Processing (NLP) &\\cmark & Wikidata, Wikipedia  \\\\\n         CLEF HIPE 2020~\\cite{Ehrmann2020} & Historical newspapers & 2020& manually & ER, EL & \\cmark &Wikidata  \\\\\n         Mewsli-9~\\cite{Botha2020} & News in multiple languages & 2020& automatic & Multilingual EL & \\cmark & Wikidata  \\\\\n         TweekiData~\\cite{tweeki:wnut20} & Tweets&2020& automatic&EL&\\cmark & Wikidata \\\\\n         TweekiGold~\\cite{tweeki:wnut20}&Tweets&2020& manually&EL&\\cmark& Wikidata\\\\\n         \\bottomrule\n    \\end{tabularx}\n    \\begin{tablenotes}\n        \\setlength{\\columnsep}{0.8cm}\n        \\setlength{\\multicolsep}{0cm}\n        \\begin{multicols}{2}\n            \\item[1] \\label{datasets:tnote1} data from 2010\n            \\item[2] \\label{datasets:tnote2} Original dataset on Wikipedia\n        \\end{multicols}\n    \\end{tablenotes}\n    \\end{threeparttable}\n    }\n    \\caption{Comparison of used datasets.}\n    \\label{tab:datasets}\n\\end{table*}\nThe majority of datasets on which existing Entity linkers were evaluated,  were originally constructed for KGs different from Wikidata. Such a mapping can be problematic as some entities labeled for other KGs could be missing in Wikidata. Or some NIL entities that do not exist in other KGs could exist in Wikidata.\nEleven datasets~\\cite{DBLP:journals\/corr\/abs-1904-09131,DBLP:journals\/pvldb\/LinLXLC20,dubey2019lc, elsahar2019t, noullet2020kore, mesquita2019knowledgenet, KenshoRD, Ehrmann2020, Botha2020, tweeki:wnut20} were found for which Wikidata identifiers were available from the start. \nIn the following the datasets are separated by their domain. A list of all examined datasets - including links where available - can be found in the Appendix in \\Cref{tab:dataset_links}.\n\n\\subsubsection{Encyclopedic datasets}\nLC-QuAD 2.0~\\cite{dubey2019lc} is a semi-automatically created dataset  for  Questions Answering providing complex natural language questions. For each question, Wikidata and DBpedia identifiers are provided. The questions are generated from subgraphs of the Wikidata KG and then manually checked. The dataset does not provide annotated mentions.\n\nT-REx~\\cite{elsahar2019t} was constructed automatically over Wiki\\-pedia abstracts. Its main purpose is Knowledge Base Population (KBP). According to Mulang et al.~\\cite{mulang2020encoding}, this dataset describes the challenges of Wikidata, at least in the form of long, noisy labels, the best. \n\nThe Kensho Derived Wikimedia Dataset~\\cite{KenshoRD} is an automatically created condensed subset of Wikimedia data. It consists of three levels: Wikipedia text, annotations with Wikipedia pages and links to Wikidata items. Thus, mentions in Wikipedia articles are annotated with Wikidata items. However, as some Wikidata items do not have a corresponding Wikipedia page, the annotation is not exhaustive. It was constructed for NLP in general. \n\n\\subsubsection{Research-focused datasets}\nISTEX-1000~\\cite{DBLP:journals\/corr\/abs-1904-09131} is a research-focused dataset containing 1000 author affiliation strings. It was manually annotated to evaluate the OpenTapioca~\\cite{DBLP:journals\/corr\/abs-1904-09131} entity linker. \n\n\\subsubsection{Biographical datasets}\nKnowledgeNet~\\cite{mesquita2019knowledgenet} is a Knowledge Base Population dataset with 9073 manually annotated sentences. The text was extracted from biographical documents from the web or Wikipedia articles.\n\n\\subsubsection{News datasets}\nNYT2018~\\cite{DBLP:journals\/pvldb\/LinLXLC20, DBLP:conf\/icde\/LinC19} consists of 30 news documents that were manually annotated on Wikidata and DBpedia. It was constructed for KBPearl~\\cite{DBLP:journals\/pvldb\/LinLXLC20}, so its main focus is also KBP which is a downstream task of EL.\n\nOne dataset, KORE50DYWC~\\cite{noullet2020kore}, was found, which was not used by any of the approach papers. \nIt is an annotated EL dataset based on the KORE50 dataset, a manually annotated subset of the AIDA-CoNLL corpus. The original KORE50 dataset focused on highly ambiguous sentences. All sentences were reannotated with DBpedia, Yago, Wikidata and Crunchbase entities.\n\n\n\n\nCLEF HIPE 2020~\\cite{Ehrmann2020} is a dataset based on historical newspapers in English, French and German. Only the English dataset will be analyzed in the following. This dataset is of great difficulty due to many errors in the text, which originate from the OCR method used to parse the scanned newspapers. For the English language, only a development and test set exist. In the other two languages, a training set is also available. It was manually annotated.\n\nMewsli-9~\\cite{Botha2020} is a multilingual dataset automatically constructed from WikiNews. It includes nine different languages. A high percentage of entity mentions in the dataset do not have corresponding English Wikipedia pages, and thus, cross-lingual linking is necessary. Again, only the English part is included during analysis.\n\n\\subsubsection{Twitter datasets}\nTweekiData and TweekiGold~\\cite{tweeki:wnut20} are an automatically annotated corpus and a manually annotated dataset for EL over tweets. TweekiData was created by using other existing tweet-based datasets and linking them to Wikidata data via the Tweeki EL. TweekiGold was created by an expert, manually annotating tweets from another dataset with Wikidata identifiers and Wikipedia page-titles. \n\n\\subsection{Analysis} \n\\begin{table*}[ptb!]\n    \\centering\n    \\rotatebox{-90}{\n    \\begin{threeparttable}\n        \\begin{tabularx}{0.95\\textheight}{p{5cm}p{2cm}p{2cm}XXXX}\n            \\toprule\n             \\textbf{Dataset}& \\# \\textbf{documents} & \\# \\textbf{mentions} & \\textbf{NIL entities} & \\textbf{Wikidata entities} & \\textbf{Unique Wikidata entities} & \\textbf{Mentions per document} \\\\ \\midrule\n             T-REx~\\cite{elsahar2019t} & \\num{4650000} & \\num{51297484}&0\\% &100\\% & 9.1\\% & 11.03\\\\\n             NYT2018~\\cite{DBLP:journals\/pvldb\/LinLXLC20, DBLP:conf\/icde\/LinC19}~\\tnotex{tn:tabced1} & \\num{30}\n             &- &-& - & - & -\\\\\n             ISTEX-1000~\\cite{DBLP:journals\/corr\/abs-1904-09131} (train) & \\num{750}& 2073& 0\\%&100\\%& 53.7\\%& 2.76\\\\\n             ISTEX-1000~\\cite{DBLP:journals\/corr\/abs-1904-09131} (test) & 250 & 670 & 0\\%&100\\%& 65.8\\%&2.68\\\\\n             LC-QuAD 2.0~\\cite{dubey2019lc} & \\num{6046} & \\num{44529} & 0\\%& 100\\%& 51.2\\% & 1.47\\\\\n             Knowledge Net~\\cite{mesquita2019knowledgenet} (train) & \\num{3977} & \\num{13039}& 0\\%&100\\%& 30\\% &3.28\\\\\n             Knowledge Net~\\cite{mesquita2019knowledgenet} (test)~\\tnotex{tn:tabced2} & \\num{1014} & -& -&-& - &-\\\\\n             KORE50DYWC~\\cite{noullet2020kore} & \\num{50} & \\num{307}& 0\\%&100\\%  & 72.0\\%  & 6.14 \\\\\n             Kensho Derived Wikimedia Dataset~\\cite{KenshoRD} & \\num{14255258} &\\num{121835453}&0\\% &100\\%&3.7\\%& 8.55\\\\\n             CLEF HIPE 2020 (en, dev)~\\cite{Ehrmann2020} & 80& 470& 46.4\\%&53.6\\%& 31.9\\%& 5.88\\\\\n             CLEF HIPE 2020 (en, test)~\\cite{Ehrmann2020} & 46&134& 33.6\\%&66.4\\%& 42.5\\% & 2.91\\\\\n             Mewsli-9 (en)~\\cite{Botha2020} & \\num{12679}  \n             &\\num{80242} &0\\% & 100\\% & 48.2\\% &6.33\\\\\n             TweekiData~\\cite{tweeki:wnut20}&\\num{5000000}&\\num{5038870}& 61.2\\%& 38.8\\%&5.4\\% &1.01\\\\\n             TweekiGold~\\cite{tweeki:wnut20}&500&\\num{958}&11.1\\%&88.9\\%&66.6\\%&1.92\\\\\n             \\bottomrule\n        \\end{tabularx}\n        \\begin{tablenotes}\n            \\item[1] \\label{tn:tabced1} Information gathered from accompanying paper as dataset was not available \n            \\item[2] \\label{tn:tabced2} Available dataset did not contain mention\/entity information\n        \\end{tablenotes}\n        \\end{threeparttable}\n    }\n    \\caption{Comparison of the datasets with focus on the number of documents and Wikidata entities.}\n    \\label{tab:comp_entities_datasets}\n\\end{table*}\nTable~\\ref{tab:comp_entities_datasets} shows the number of documents, the number of mentions, NIL entities and unique entities, and the mentioned ratio. What classifies as a document in a dataset depends on the dataset itself. For example, for T-REx, a document is a whole paragraph of a Wikipedia article, while for LC-QuAD 2.0, a document is just a single question. Due to this, the average number of entities in a document also varies, e.g., LC-QuAD 2.0 with $1.47$ entities per document and T-REx with $11.03$. If a dataset was not available, information from the original paper was included. If dataset splits were available, the statistics are also shown separately. The majority of datasets do not contain NIL entities. For the Tweeki datasets, it is not mentioned which Wikidata dump was used to annotate. For a dataset that contains NIL entities, this is problematic. On the other hand, the dump is specified for the CLEF HIPE 2020 dataset, making it possible to work on the Wikidata version with the correct entities missing.\n\n\\begin{highlightbox}{\\hyperlink{rq1}{Research Question 1}}{Which Wikidata EL datasets exist, how widely used are they and how are they constructed?}\nThe preceding paragraphs answer the following two aspects of the first research question. First, we provided descriptions and an overview of all datasets created for Wikidata, including statistics on their structure. This answers which datasets exist. Furthermore, for each dataset it is stated how they were constructed, whether automatically, semi-automatically or manually. Thus information on the quality and construction process of the datasets is given.\nTo answer the last part of the question, how widely are the datasets in use, Table~\\ref{tab:dataset_usage} shows how many times each Wikidata dataset was used in Wikidata EL approaches during training or evaluation. As one can see, there exists no single dataset used in all research of EL. This is understandable as different datasets focus on different document types and domains as shown in Table~\\ref{tab:datasets}, what again results in different approaches. \n\\end{highlightbox}\n\n\\begin{table*}[htb!]\n    \\centering\n    \\begin{threeparttable}\n        \\begin{tabular}{lc}\n        \\toprule\n        \\textbf{Dataset} & \\textbf{Number of usages in Wikidata EL approach papers} \\\\\n        \\midrule\n        T-REx~\\cite{elsahar2019t} & 2~\\cite{mulang2020encoding, DBLP:journals\/pvldb\/LinLXLC20} \\\\\n        NYT2018~\\cite{DBLP:journals\/pvldb\/LinLXLC20, DBLP:conf\/icde\/LinC19} & 1~\\cite{DBLP:journals\/pvldb\/LinLXLC20}\n        \\\\\n        ISTEX-1000~\\cite{DBLP:journals\/corr\/abs-1904-09131} & 2~\\cite{DBLP:journals\/corr\/abs-2008-05190, DBLP:journals\/corr\/abs-1904-09131} \\\\\n        LC-QuAD 2.0~\\cite{dubey2019lc} & 2~\\cite{DBLP:journals\/corr\/abs-1912-11270, Banerjee2020} \\\\\n        Knowledge Net~\\cite{mesquita2019knowledgenet} & 1~\\cite{DBLP:journals\/pvldb\/LinLXLC20}\n        \\\\\n        KORE50DYWC~\\cite{noullet2020kore} & 0 \\\\\n        Kensho Derived Wikimedia Dataset~\\cite{KenshoRD} & 1~\\cite{perkins2020separating} \\\\\n        CLEF HIPE 2020~\\cite{Ehrmann2020} & 3~\\cite{borosrobust, Labusch2020, Provatorova2020}  \\\\\n        Mewsli-9~\\cite{Botha2020} & 1~\\cite{Botha2020}  \\\\\n        TweekiData~\\cite{tweeki:wnut20} & 1~\\cite{tweeki:wnut20} \\\\\n        TweekiGold~\\cite{tweeki:wnut20}& 1~\\cite{tweeki:wnut20}\\\\\n        \\bottomrule\n    \\end{tabular}\n    \\caption{Usage of datasets for training or evaluation.}\n    \\label{tab:dataset_usage}\n    \\end{threeparttable}\n\\end{table*}\n\n\\begin{table*}[htb!]\n    \\centering\n    \\begin{tabularx}{\\textwidth}{p{5cm}XXXX}\n     \\toprule\n     \\textbf{Dataset} & \\textbf{Average number of matches} & \\textbf{No match} & \\textbf{Exact match} & \\textbf{More than one match} \\\\ \\midrule\n     T-REx & 4.79 & 31.36\\% & 32.98\\% & 35.65\\% \\\\\n     ISTEX-1000 (train) & 23.23 & 8.06\\%& 26.34\\% & 65.61\\%\\\\\n     ISTEX-1000 (test) & 25.85 & 10.30\\% & 23.88\\% & 65.82\\%\\\\\n     Knowledge Net (train) & 21.90 & 10.41\\% & 22.29\\% & 67.3\\% \\\\\n     KORE50DYWC & 28.31 & 3.93\\% & 7.49\\% & 88.60\\%  \\\\\n     Kensho Derived Wikimedia Dataset & 8.16 & 35.18\\% & 30.94\\% & 33.88\\% \\\\\n     CLEF HIPE 2020 (en, dev) & 24.02 & 35.71\\% & 11.51\\% & 52.78\\% \\\\\n     CLEF HIPE 2020 (en, test) & 17.78 & 43.82\\% & 6.74\\% & 49.44\\% \\\\\n     Mewsli-9 (en) &11.09&16.80\\%&34.90\\%&47.30\\% \\\\\n     TweekiData &19.61&19.98\\%&12.01\\%&68.01\\% \\\\\n     TweekiGold &16.02&7.41\\%&20.25\\%&72.34\\% \\\\\n     \\bottomrule\n    \\end{tabularx}\n    \\caption{Ambiguity of mentions (existence of a match does not correspond to a correct match), NYT2018 dataset was not available and LC-QuAD 2.0 is not annotated.}\n    \\label{tab:ambiguity_mentions}\n\\end{table*}\n\\begin{table}[htb!]\n    \\centering\n    \\begin{tabularx}{\\linewidth}{p{4cm}cc}\n     \\toprule\n     \\textbf{Dataset} & \\textbf{Acc.} & \\textbf{Acc. filtered} \\\\ \\midrule\n     ISTEX-1000 (train) & 0.744 &0.716\\\\\n     ISTEX-1000 (test) & 0.716&0.678\\\\\n     Knowledge Net (train) &  0.371&0.285 \\\\\n     KORE50DYWC & 0.225& 0.187\\\\\n     CLEF HIPE 2020 (en, dev) & 0.333&0.287 \\\\\n     CLEF HIPE 2020 (en, test) & 0.258& 0.241\\\\\n     TweekiGold & 0.565 & 0.520\\\\\n     Mewsli-9 (en) & 0.602&0.490\\\\\n     \\bottomrule\n    \\end{tabularx}\n    \\caption{EL accuracy - Kensho Derived Wikimedia Dataset, T-REx and TweekiData are not included due to size, \\textbf{Acc. filtered} has all exact matches removed, NYT2018 dataset was not available and LC-QuAD 2.0 is not annotated.}\n    \\label{tab:es}\n\\end{table}\nThe difficulty of the different datasets was measured by the accuracy of a simple EL method (Table~\\ref{tab:es}) and the ambiguity of mentions (Table~\\ref{tab:ambiguity_mentions}). \nThe simple EL method searches for entity candidates via an ElasticSearch index, including all English labels and aliases. It then disambiguates by taking the one with the largest tf-idf-based BM25 similarity measure score and the lowest Q-identifier number resembling the popularity. Nothing was done to handle inflections.\\footnote{All source code, plots and results can be found on \\url{https:\/\/github.com\/semantic-systems\/ELEnglishWD}}\nOnly accessible datasets were included. As one can see, the accuracy is positively correlated with the number of exact matches. The more ambiguous the underlying entity mentions are, the more inaccurate a simple similarity measure between label and mention becomes. In this case, more context information is necessary. The simple Entity Linker was only applied to datasets that were feasible to disambiguate in that way. T-REx and the Kensho Derived Wikimedia Dataset were too large in terms of the number of documents to run the linker on commodity hardware. \nAccording to the EL performance, ISTEX-1000 is the easiest dataset. Many of the ambiguous mentions reference the most popular one, while also many exact unique matches exist.\nT-REx, the Kensho Derived Wikimedia Dataset and the Mewsli-9 training dataset have the largest percentage of exact matches for labels.\nWhile TweekiGold is quite ambiguous, deciding on the most prominent entity appears to produce good EL results.\nThe most ambiguous dataset is KORE50DYWC. Additionally, just choosing the most popular entity of the exact matches results in worse performs than for example on TweekiGold which is also very ambiguous.  This is due to the fact that the original KORE50 dataset focuses on difficult ambiguous entities which are not necessarily popular. The CLEF HIPE 2020 dataset also has a low EL accuracy but not due to ambiguity but many mentions with no exact match.  The reason for that is the noise created by OCR. \n\nThe second column of Table~\\ref{tab:es} specifies the accuracy with all unique exact matches removed. This is based on the intuition that exact matches without any competitors are usually correct. \n\nAs seen in the \\Cref{tab:datasets,tab:ambiguity_mentions,tab:comp_entities_datasets,tab:es}, there exists a very diverse set of datasets for EL on Wikidata, differing in the domain, document type, ambiguity and difficulty. \n\\begin{highlightbox}{\\hyperlink{rq2}{Research Question 2}}{Do the characteristics of Wikidata matter for the design of EL datasets and if so, how?}\nExcept the Mewsli-9~\\cite{Botha2020} and CLEF HIPE 2020~\\cite{Ehrmann2020} datasets, none of the others take any specific characteristics of Wikidata into account. \nThe two exceptions focus on multilinguality and rely therefore directly on the language-agnostic nature of Wikidata.\nThe CLEF HIPE 2020 dataset is designed for Wikidata and has documents for  English, French and German, but each language has a different corpus of documents. The same is the case for the Mewsli-9 dataset, while here, documents in nine languages are available.\nIn the future, a dataset similar to VoxEL~\\cite{rosales2018voxel}, which is defined for Wikipedia, would be helpful. Here, each utterance is translated into multiple languages, which eases the comparison of the multilingual EL performance. Having the same corpus of documents in different languages would allow a better comparison of a method's performance in various languages. Of course, such translations will never be perfectly comparable. \n\\end{highlightbox}\n\n\nBesides that, we identified one additional characteristic which might be of relevance to Wikidata EL datasets.\nIt is the large rate of change of Wikidata.\nDue to that, it would be advisable that the datasets specify the Wikidata dumps they were created on, similar to Petroni et al.~\\cite{petroni2020kilt}. Many of the existing datasets do that, yet not all. In current dumps, entities, which were available while the dataset was created, could have been removed. It is even more probable that NIL entities could now have a corresponding entity in an updated Wikidata dump version. If the EL approach now would detect it as a NIL entity, it is evaluated as correct, but in reality, this is false and vice versa. \nOf course, this is not a problem unique to Wikidata. Anytime, the dump is not given for an EL dataset, similar uncertainties will occur. But due to the fast growth of Wikidata (see Figure~\\ref{fig:wikidata_items}), this problem is more pronounced.\n\nConcerning \\textit{emerging entities}, another variant of an EL dataset could be useful too. Two Wikidata dumps from different time points could be used to label the utterances. Such a dataset would be valuable in the context of an EL approach supporting emerging entities (e.g., the approach by Hoffart et al.~\\cite{DBLP:conf\/www\/HoffartAW14}). With the true entities available, one could measure the quality of the created emerging entities. That is, multiple mentions assigned to the same emerging entity should also point to a single entity in the more recent KG. \nAlso, constraining that the method needs to perform well on both KG dumps would force EL approaches to be less reliant on a fixed graph structure.\n\n\n\n\n\n\\section{Introduction}\n\\subsection{Motivation}\n\\begin{figure}\n    \\centering\n    \\includegraphics[width=\\linewidth, trim={0 2cm 0 0},clip]{Images\/EntityLinkingExample.pdf}\n    \\caption{Entity Linking - Mentions in the text are linked to the corresponding entities (color-coded) in a knowledge graph (here: Wikidata).}\n    \\label{fig:ELExample}\n\\end{figure}\nEntity Linking (EL) is the task of connecting already marked mentions in an utterance to their corresponding entities in a knowledge graph (KG), see Figure~\\ref{fig:ELExample}. In the past, this task was tackled by using popular knowledge bases such as DBpedia~\\cite{DBLP:journals\/semweb\/LehmannIJJKMHMK15}, Freebase~\\cite{DBLP:conf\/sigmod\/BollackerEPST08} or Wikipedia. While the popularity of those is still imminent, another alternative, named Wikidata~\\cite{DBLP:journals\/cacm\/VrandecicK14}, appeared. \n\nWikidata follows a similar philosophy as Wikipedia as it is curated by a continuously increasing community, see Figure~\\ref{fig:editors}. However, Wikidata differs in the way knowledge is stored -  information is stored in a structured format via a knowledge graph (KG). \nAn important characteristic of Wikidata is its inherent multilingualism. While Wikipedia articles exist in multiple languages, Wikidata information are stored using language-agnostic identifiers. This is of advantage for multilingual entity linking. \nDBpedia, Freebase or Yago4~\\cite{Tanon2020} are KGs too which can become outdated over time~\\cite{Ringler2017}. They rely on information extracted from other sources in contrast to the Wikidata knowledge which is inserted by a community. \nGiven an active community, this leads to Wikidata being frequently and timely updated - another characteristic.\nNote that DBpedia also stays up-to-date but has a delay of a month\\footnote{\\url{https:\/\/release-dashboard.dbpedia.org\/}} while Wikidata dumps are updated multiple times a month.\nThere are up-to-date services to access knowledge for both KGs, Wikidata and DBpedia (cf. DBpedia Live~~\\footnote{\\url{https:\/\/wiki.dbpedia.org\/online-access\/DBpediaLive}}), but full dumps are preferred as else the FAIR replication~\\cite{wilkinson2016fair} of research results based on the KG is hindered. \nAnother Wikidata characteristic interesting for Entity Linkers, are hyper-relations (see Figure~\\ref{fig:wikidata_subgraph} for an example graph), which might affect their abilities and performance. \n\nTherefore, it is of interest how existing approaches incorporate these characteristics.\nHowever, existing literature lacks an exhaustive analysis which examines Entity Linking approaches in the context of Wikidata.\n\n\\begin{figure}[htb!]\n    \\centering\n    \\includegraphics[width=\\linewidth]{Images\/active_editors.pdf}\n    \\caption{Active editors in Wikidata~\\cite{Foundation2020}.}\n    \\label{fig:editors}\n\\end{figure}\n\nUltimately, this survey strives to expose the benefits and associated challenges which arise from the use of Wikidata as the target KG for EL. \nAdditionally, the survey provides a concise overview of existing EL approaches, which is essential to (1) avoid duplicated research in the future and (2) enable a smoother entry into the field of Wikidata EL. \nSimilarly, we structure the dataset landscape which helps researchers find the correct dataset for their EL problem.\n\n\\begin{figure}[htb!]\n    \\centering\n    \\includegraphics[width=\\linewidth]{Images\/papers_timeline.pdf}\n    \\caption{Publishing years of included Wikidata EL papers (Table~\\ref{tab:comparison_approaches_wikidata}).}\n    \\label{fig:papers}\n\\end{figure}\n\n\nThe focus of this survey lies on EL approaches, which operate on already marked mentions of entities, as the task of Entity Recognition~(ER) is much less dependent on the characteristics of a KG. However, due to the recent uptake of research on EL on Wikidata, there is only a low number of EL-only publications. To broaden the survey's scope, we also consider methods that include the task of ER. We do not restrict ourselves regarding the type of models used by the entity linkers. \n\nThis survey limits itself to all EL approaches supporting the English language as most frequent language, and thus, a better comparison of the approaches and datasets is possible. We also include approaches that support multiple languages. The existence of such approaches for Wikidata is not surprising as an important characteristic of Wikidata is the support of a multitude of languages. \n\n\n\\begin{figure}[htb!]\n    \\centering\n    \\includegraphics[width=\\linewidth]{Images\/KGExample.pdf}\n    \\caption{Wikidata subgraph - Dashed rectangle represents a claim with attached qualifiers.}\n    \\label{fig:wikidata_subgraph}\n\\end{figure}\n\n\n\n\\subsection{Research Questions and Contributions}\nFirst, we want to develop an overview of datasets for EL on Wikidata. Our survey analyses datasets and whether they are designed with Wikidata in mind and if so, in what way?\nThus, we post the following two research questions:\n\\begin{quote}\n    \\hypertarget{rq1}{\\textbf{RQ 1}: Which Wikidata EL datasets exist, how widely used are they and how are they constructed?} \n\\end{quote}\n\\begin{quote}\n    \\hypertarget{rq2}{\\textbf{RQ 2}: Do the characteristics of Wikidata matter for the design of EL datasets and if so, how?}\n\\end{quote}\nTo answer those two research questions, an overview of the structure of Wikidata and the amount of information it contains (see Section~\\ref{sec:wikidata}) is given. All current Wikidata-specific EL datasets are gathered and analyzed with the research questions in mind. Furthermore, we discuss how the characteristics of Wikidata might affect the design of datasets (see Section~\\ref{sec:datasets}).\n\nEL approaches use many kinds of information like labels, popularity measures, graph structures, and more. This multitude of possible signals raises the question of how the characteristics of Wikidata are used by the current state of the art of EL on Wikidata. Thus, the third research question is:\n\\begin{quote}\n    \\hypertarget{rq3}{\\textbf{RQ 3}: How do current Entity Linking approaches exploit the specific characteristics of Wikidata?}\n\\end{quote}\nIn particular, which Wikidata-specific characteristics contribute to the solution? Wikidata-specific characteristics mean characteristics that are part of Wikidata but not necessarily only occurring in Wikidata.\n\nLastly, we identify what kind of characteristics of Wikidata are of importance for EL but are insufficiently considered. \nThis raises the last research question:\n\\begin{quote}\n    \\hypertarget{rq4}{\\textbf{RQ 4}: Which Wikidata characteristics are unexploited by existing Entity Linking approaches?}\n\\end{quote}\nThe last two questions are answered by gathering all existing approaches working on Wikidata systematically, analyzing them, and discussing the potential and challenges of Wikidata for EL (see Section~\\ref{sec:approaches}).\n\nThis survey makes the following contributions:\n\\begin{itemize}\n    \\item An overview of all currently available EL datasets focusing on Wikidata\n    \\item An overview of all currently available EL approaches linking on Wikidata \n    \\item An analysis of the approaches and datasets with a focus on Wikidata characteristics\n    \\item A concise list of future research avenues\n\\end{itemize}\n\n\n\\section{Approaches}\n\\label{sec:approaches}\nCurrently, the number of methods intended to work explicitly on Wikidata is still relatively small, while the amount of the ones utilizing the characteristics of Wikidata is even smaller. \n\nThere exist several KG-agnostic EL approaches~\\cite{Moussallem2017,DBLP:conf\/ecai\/UsbeckNRGCAB14,DBLP:conf\/esws\/ZwicklbauerSG16}. However, they were omitted as their focus is being independent of the KG. While they are able to use Wikidata characteristics like labels or descriptions, there is no explicit usage of those. They are available in most other KGs. None of the found KG-agnostic EL papers even mentioned Wikidata. Though we recognize that KG-agnostic approaches are very useful in the case that a KG becomes obsolete and has to be replaced or a non-public KG needs to be used, such approaches are not included in this section. However, Table~\\ref{tab:comparison_KG_agnostic_approaches_wikidata} in the Appendix provides an overview of the used Wikidata characteristics of the three approaches. \n\nDeepType~\\cite{DBLP:conf\/aaai\/RaimanR18} is an entity linking approach relying on the fine-grained type system of Wikidata and the categories of Wikipedia. As type information is not evolving as fast as novel entities appear, it is relatively robust against a changing knowledge base. While it uses Wikidata, it is not specified in the paper whether it links to Wikipedia or Wikidata. Even the examination of the available code did not result in an answer as it seems that the entity linking component is missing. While DeepType showed that the inclusion of Wikidata type information is very beneficial in entity linking, we did not include it in this survey due to the aforementioned reasons.\nAs Wikidata contains many more types ($\\approx$\\num{2400000}) than other KGs, e.g., DBpedia ($\\approx$\\num{484000})~\\cite{Tanon2020}~\\footnote{if all rdf:type objects are considered, else $\\approx$ 768 (gathered via https:\/\/dbpedia.org\/sparql\/) if only considering types of the DBpedia ontology}), it seems to be more suitable for this fine-grained type classification. Yet, not only the number of types plays a role but also how many types are assigned per entity. In this regard, Wikipedia provides much more type information per entity than Wikidata~\\cite{Weikum2020}. That is probably the reason why both Wikipedia categories and Wikidata types are used together. As Wikidata is growing every minute, it may also be challenging to keep the type system up to date. \n\nTools without accompanying publications are not considered due to the lack of information about the approach and its performance. Hence, for instance, the Entity Linker in the \nDeepPavlov~\\cite{burtsev2018deeppavlov} \nframework is not included, although it targets Wikidata and appears to use label and description information successfully to link entities.\n\nWhile the approach by Zhou et al.~\\cite{DBLP:journals\/tacl\/ZhouRWCN20} does utilize Wikidata aliases in the candidate generation process, the target KB is Wikipedia and was therefore excluded.\n\nThe vast majority of methods is using machine learning to solve the EL task~\\cite{DBLP:journals\/corr\/abs-1810-09164,mulang2020encoding,DBLP:conf\/lrec\/KlangN20,DBLP:conf\/starsem\/SorokinG18, Banerjee2020, huangentity, perkins2020separating, DBLP:journals\/corr\/abs-2008-05190, borosrobust, Provatorova2020, Labusch2020, Botha2020, DBLP:journals\/corr\/abs-1904-09131}. Some of those approaches solve the ER and EL jointly as an end-to-end task.  Besides that, there exist two rule-based approaches\n~\\cite{DBLP:journals\/corr\/abs-1912-11270, tweeki:wnut20} and two based on graph optimization~\\cite{DBLP:conf\/lrec\/KlangN20, DBLP:journals\/pvldb\/LinLXLC20}.\n\nThe approaches mentioned above solve the EL problem as specified in Section~\\ref{sec:problem}. That is, other EL methods with a different problem definition also exist. For example, Almeida et al.~\\cite{almeida2016streets} try to link street names to entities in Wikidata by using additional location information and limiting the entities only to locations. As it uses additional information about the true entity via the location, it is less comparable to the other approaches and, thus, was excluded from this survey.  Thawani et al.~\\cite{DBLP:conf\/semweb\/ThawaniHHZDSQSP19} link entities only over columns of tables. The approach is not comparable since it does not use natural language utterances. \nThe approach by Klie et al.~\\cite{DBLP:conf\/acl\/KlieCG20} is concerned with Human-In-The-Loop EL. While its target KB is Wikidata, the focus on the inclusion of a human in EL process makes it incomparable to the other approaches.\nEL methods exclusively working on languages other than English~\\cite{ElVaigh2020,Ellgren2020, Klang2014, Veen2016, Ehrmann2020a} were not considered but also did not use any novel characteristics of Wikidata.\nIn connection to the CLEF HIPE 2020 challenge~\\cite{Ehrmann2020a}, multiple Entity Linkers working on Wikidata were built. While short descriptions of the approaches are available in the challenge-accompanying paper, only approaches described in an own published paper were included in this survey. The approach by Kristanti and Romary~\\cite{Kristanti2020} was not included as it used pre-existing tools for EL over Wikidata, for which no sufficient documentation was available. \n\nDue to the limited number of methods, we also evaluated methods that are not solely using Wikidata but also additional information from a separate KG or Wikipedia. This is mentioned accordingly. Approaches linking to knowledge graphs different from Wikidata, but for which a mapping between the knowledge graphs and Wikidata exists, are also not included. Such methods would not use the Wikidata characteristics at all, and their performance depends on the quality of the other KG and the mapping.\n\nIn the following, the different approaches are described and examined according to the used characteristics of Wikidata. An overview can be found in \\Cref{tab:comparison_approaches_wikidata}.\nWe split the approaches into two categories, the ones doing only EL and the ones doing ER and EL.\nFurthermore, to provide a better overview of the existing approaches, they are categorized by notable differences in their architecture or used features. This categorization focuses on the EL aspect of the approaches. \n\nFor each approach, it is mentioned what datasets were used in the corresponding paper. Only a subset of the datasets was directly annotated with Wikidata identifiers. Hence, datasets are mentioned, which do not occur in \\Cref{sec:datasets}.\n\n\\begin{table*}[tbh!]\n    \\centering\n    \\begin{threeparttable}\n         \\begin{tabularx}{\\textwidth}{p{3cm}YYYYYY}\n            \\toprule\n             \\textbf{Approach}&\\textbf{Labels\/\\allowbreak Aliases} & \\textbf{Descriptions}& \\textbf{Knowledge graph structure} & \\textbf{Hyper-relational structure} & \\textbf{Types} & \\textbf{Additional Information} \\\\ \\midrule\n            OpenTapioca~\\cite{DBLP:journals\/corr\/abs-1904-09131} & \\cmark & \\xmark & \\cmark & \\cmark & \\cmark & \\xmark  \\\\\n            Falcon 2.0~\\cite{DBLP:journals\/corr\/abs-1912-11270}&\\cmark&\\xmark&\\cmark\\tnotex{tn:tabcwc3}&\\xmark &\\xmark & \\xmark\\\\\n            Arjun~\\cite{mulang2020encoding}&\\cmark&\\xmark&\\xmark &\\xmark& \\xmark & \\xmark\\\\\n            VCG~\\cite{DBLP:conf\/starsem\/SorokinG18}&\\cmark&\\xmark& \\cmark& \\xmark & \\xmark & \\xmark \\\\\n            KBPearl~\\cite{DBLP:journals\/pvldb\/LinLXLC20} & \\cmark & \\xmark& \\cmark & \\xmark & \\xmark & \\xmark \\\\\n            PNEL~\\cite{Banerjee2020} & \\cmark & \\cmark& \\cmark & \\xmark & \\xmark & \\xmark\n            \\\\\n            Mulang et al.~\\cite{DBLP:journals\/corr\/abs-2008-05190} & \\cmark & \\cmark~\\tnotex{tn:tabcwc2}& \\cmark & \\xmark & \\xmark & \\xmark\n            \\\\\n            Perkins~\\cite{perkins2020separating} & \\cmark & \\xmark& \\cmark & \\xmark & \\xmark & \\xmark \\\\\n            NED using DL on Graphs~\\cite{DBLP:journals\/corr\/abs-1810-09164}&\\cmark&\\xmark&\\cmark&\\xmark & \\xmark & \\xmark\\\\\n            Huang et al.~\\cite{huangentity} & \\cmark & \\cmark& \\cmark & \\xmark & \\xmark & Wikipedia \\\\\n            Boros et al.~\\cite{borosrobust} & \\xmark & \\xmark & \\xmark & \\xmark & \\cmark & Wikipedia, DBpedia \\\\\n            Provatorov et al.~\\cite{Provatorova2020} & \\cmark & \\cmark & \\xmark & \\xmark & \\xmark & Wikipedia \\\\ \n            Labusch and Neudecker~\\cite{Labusch2020} & \\xmark & \\xmark & \\xmark & \\xmark & \\xmark & Wikipedia \\\\\n            Botha et al.~\\cite{Botha2020} & \\xmark & \\xmark & \\xmark& \\xmark & \\xmark & Wikipedia \\\\\n            Hedwig~\\cite{DBLP:conf\/lrec\/KlangN20}&\\cmark&\\cmark& \\cmark& \\xmark & \\xmark & Wikipedia\\\\\n            Tweeki~\\cite{tweeki:wnut20} & \\cmark & \\xmark & \\xmark & \\xmark & \\cmark & Wikipedia \\\\\n            \\bottomrule\n        \\end{tabularx}\n        \\begin{tablenotes}\n            \\setlength{\\columnsep}{0.8cm}\n            \\setlength{\\multicolsep}{0cm}\n            \\begin{multicols}{2}\n                \\small\n                \\item[2] \\label{tn:tabcwc2} Appears in the set of triples used for disambiguation\n                \\item[1] \\label{tn:tabcwc3} Only querying the existence of triples\n            \\end{multicols}\n        \\end{tablenotes}\n    \\end{threeparttable}\n    \\caption{Comparison between the utilized Wikidata characteristics of each approach.}\n    \\label{tab:comparison_approaches_wikidata}\n\\end{table*}\n\n\\subsection{Entity Linking} \n\\label{subsec:el}\n\\subsubsection{Language model-based approaches}\nThe approach by Mulang et al.~\\cite{DBLP:journals\/corr\/abs-2008-05190} is tackling the EL problem with transformer models~\\cite{Vaswani2017}. It is assumed that the candidate entities are given. For each entity, the labels of 1-hop and 2-hop triples are extracted. Those are then concatenated together with the utterance and the entity mention. The concatenation is the input of a pre-trained transformer model. With a fully connected layer on top, it is then optimized according to a binary cross-entropy loss. This architecture results in a similarity measure between the entity and the entity mention.\nThe examined models are the transformer models Roberta~\\cite{DBLP:journals\/corr\/abs-1907-11692}, XLNet~\\cite{DBLP:conf\/nips\/YangDYCSL19} and the DCA-SL model~\\cite{DBLP:conf\/emnlp\/YangGLTZWCHR19}.\nThe approach was evaluated on three datasets with no focus on certain documents or domains: ISTEX-1000~\\cite{DBLP:journals\/corr\/abs-1904-09131}, Wikidata-Disamb~\\cite{DBLP:journals\/corr\/abs-1810-09164} and AIDA-CoNLL~\\cite{hoffart-etal-2011-robust}. AIDA-CoNLL is a popular dataset for evaluating EL but has Wikipedia as the target. ISTEX-1000 focuses on research documents, and Wikidata-Disamb is an open-domain dataset.\nThere is no global coherence technique applied.\nOverall, up to 2-hop triples of any kind are used. For example, labels, aliases, descriptions, or general relations to other entities are all incorporated. It is not mentioned if the hyper-relational structure in the form of qualifiers was used.\nOn the one hand, the purely language-based EL results in less need for retraining if the KG changes as shown by other approaches~\\cite{Botha2020, Wu2019}. This is the case due to the reliance on sub-word embeddings and pre-training via the chosen transformer models. If full word-embeddings were used, the inclusion of new words would make retraining necessary. \nStill, an evaluation of the model on the zero-shot EL task is missing and has to be done in the future.\nThe reliance on the triple information might be problematic for long-tail entities which are rarely referred to and are part of fewer triples. Nevertheless, a lack of available context information is challenging for any EL approach relying on it.\n\n\nThe approach designed by Botha et al.~\\cite{Botha2020} tackles multilingual EL. It is also crosslingual. That means it can link entity mentions to entities in a knowledge graph in a language different from the utterance one. The idea is to train one model to link entities in utterances of 100+ different languages to a KG containing not necessarily textual information in the language of the utterance. While the target KG is Wikidata, they mainly use Wikipedia descriptions as input. This is the case as extensive textual information is not available in Wikidata. \nThe approach resembles the Wikification method by Wu et al.~\\cite{Wu2019} but extends the training process to be multilingual and targets Wikidata.\nCandidate generation is done via a dual-encoder architecture. Here, two BERT-based transformer models~\\cite{Devlin2019} encode both the context-sensitive mentions and the entities to the same vector space.\nThe mentions are encoded using local context, the mention and surrounding words, and global context, the document title. Entities are encoded by using the Wikipedia article description available in different languages. In both cases, the encoded CLS-token are projected to the desired encoding dimension. The goal is to embed mentions and entities in such a way that the embeddings are similar.\nThe model is trained over Wikipedia by using the anchors in the text as entity mentions. There exists no limitation that the used Wikipedia articles have to be available in all supported languages. If an article is missing in the English Wikipedia but available in the German one, it is still included.\nNow, after the model is trained, all entities are embedded. The candidates are generated by embedding the mention and searching for the nearest neighbors.\nA cross-encoder is employed to rank the entity candidates, which cross-encodes entity description and mention text together by concatenating and feeding them into a BERT model. Final scores are obtained, and the entity mention is linked.\nThe model was evaluated on the cross-lingual EL dataset TR2016\\textsuperscript{hard}~\\cite{Tsai2016} and the multilingual EL dataset Mewsli-9~\\cite{Botha2020}. Furthermore, it was tested how well it performs on an English-only dataset called WikiNews-2018~\\cite{Gillick2019}.\nWikidata information is only used to gather all the Wikipedia descriptions in the different languages for all entities. \nThe approach was tested on zero- and few-shot settings showing that the model can handle an evolving knowledge graph with newly added entities that were never seen before. This is also more easily achievable due to its missing reliance on the graph structure of Wikidata or the structure of Wikipedia. It is the case that some Wikidata entities do not appear in Wikipedia and are therefore invisible to the approach. \nBut as the model is trained on descriptions of entities in multiple languages, it has access to many more entities than only the ones available in the English Wikipedia. \n\n\\subsubsection{Language model and graph embeddings-based approaches}\nThe master thesis by Perkins~\\cite{perkins2020separating} is performing candidate generation by using anchor link probability over Wikipedia and locality-sensitive hashing (LSH)~\\cite{Gionis1999}  over labels and mention bi-grams. Contextual word embeddings of the utterance (ELMo~\\cite{DBLP:conf\/naacl\/PetersNIGCLZ18}) are used together with KG embeddings (TransE~\\cite{DBLP:conf\/nips\/BordesUGWY13}), calculated over Wikipedia and Wikidata, respectively.\nThe context embeddings are sent through a recurrent neural network. The output is concatenated with the KG embedding and then fed into a feed-forward neural network resulting in a similarity measure between the KG embedding of the entity candidate and the utterance.\nIt was evaluated on the AIDA-CoNLL~\\cite{hoffart-etal-2011-robust} dataset. \nWikidata is used in the form of the calculated TransE embeddings. Hyper-relational structures like qualifiers are not mentioned in the thesis and are not considered by the TransE embedding algorithm and, thus, probably not included. \nThe used KG embeddings make it necessary to retrain when the Wikidata KG changes as they are not dynamic. \n\n\\subsubsection{Word and graph embeddings-based approaches}\nIn 2018, Cetoli et al.~\\cite{DBLP:journals\/corr\/abs-1810-09164} evaluated how different types of basic neural networks perform solely over Wikidata. Notably, they compared the different ways to encode the graph context via neural methods, especially the usefulness of including topological information via GNNs~\\cite{Sperduti1997, wu2020comprehensive} and RNNs~\\cite{Hochreiter1997}. \nThere is no candidate generation as it was assumed that the candidates are available.\nThe process consists of combining text and graph embeddings. The text embedding is calculated by applying a Bi-LSTM over the Glove Embeddings of all words in an utterance. The resulting hidden states are then masked by the position of the entity mention in the text and averaged. A graph embedding is calculated in parallel via different methods utilizing GNNs or RNNs. The end score is the output of one feed-forward layer having the concatenation of the graph and text embedding as its input. It represents if the graph embedding is consistent with the text embedding. \nWikidata-Disamb30~\\cite{DBLP:journals\/corr\/abs-1810-09164} was used for evaluating the approach. Each example in the dataset also contains an ambiguous negative entity, which is used during training to be robust against ambiguity.\nOne crucial problem is that those methods only work for a single entity in the text. Thus, it has to be applied multiple times, and there will be no information exchange between the entities.  While the examined algorithms do utilize the underlying graph of Wikidata, the hyper-relational structure is not taken into account. The paper is more concerned with comparing how basic neural networks work on the triples of Wikidata. Due to the pure analytical nature of the paper, the usefulness of the designed approaches to a real-world setting is limited. The reliance on graph embeddings makes it susceptible to change in the Wikidata KG.\n\n\\subsection{Entity Recognition and Entity Linking}\n\\label{subsec:erel}\nThe following methods all include ER in their EL process. \n\n\\subsubsection{Language model-based approaches}\nIn connection to the \\emph{CLEF 2020 HIPE challenge}~\\cite{Ehrmann2020a}, multiple approaches~\\cite{borosrobust, Labusch2020, Provatorova2020} for ER and EL of historical newspapers on Wikidata were developed. Documents were available in English, French and German. Three approaches with a focus on the English language are described in the following. Differences in the usage of Wikidata between the languages did not exist. Yet, the approaches were not multilingual as different models were used and\/or retraining was necessary for different languages. \n\n\nBoros et al.~\\cite{borosrobust} tackled ER by using a BERT model with a CRF layer on top, which recognizes the entity mentions and classifies the type. During the training, the regular sentences are enriched with misspelled words to make the model robust against noise.\nFor EL, a knowledge graph is built from Wikipedia, containing Wikipedia titles, page ids, disambiguation pages, redirects and link probabilities between mentions and Wikipedia pages are calculated. The link probability between anchors and Wikipedia pages is used to gather entity candidates for a mention. \nThe disambiguation approach follows an already existing method~\\cite{Kolitsas2018}. Here, the utterance tokens are embedded via a Bi-LSTM. The token embeddings of a single mention are combined. Then similarity scores between the resulting mention embedding and the entity embeddings of the candidates are calculated. The entity embeddings are computed according to Ganea and Hofmann~\\cite{Ganea2017}. These similarity scores are combined with the link probability and long-range context attention, calculated by taking the inner product between an additional context-sensitive mention embedding and an entity candidate embedding. The resulting score is a local ranking measure and is again combined with a global ranking measure considering all other entity mentions in the text.\nIn the end, additional filtering is applied by comparing the DBpedia types of the entities to the ones classified during the ER. If the type does not match or other inconsistencies apply, the entity candidate gets a lower rank. Here, they also experimented with Wikidata types, but this resulted in a performance decrease.\nAs can be seen, technically, no Wikidata information besides the unsuccessful type inclusion is used. Thus, the approach resembles more of a Wikification algorithm. Yet, they do link to Wikidata as the HIPE task dictates it, and therefore, the approach was included in the survey. New Wikipedia entity embeddings can be easily added~\\cite{Ganea2017} which is an advantage when Wikipedia changes. Also, its robustness against erroneous texts makes it ideal for real-world use. \nThis approach reached SOTA performance on the CLEF 2020 HIPE challenge.\n\nLabusch and Neudecker~\\cite{Labusch2020} also applied a BERT model for ER. For EL, they used mostly Wikipedia, similar to Boros et al.~\\cite{borosrobust}. They built a knowledge graph containing all person, location and organization entities from the German Wikipedia. Then it was converted to an English knowledge graph by mapping from the German Wikipedia Pages via Wikidata to the English ones. This mapping process resulted in the loss of numerous entities. The candidate generation is done by embedding all Wikipedia page titles in an Approximative Nearest Neighbour index via BERT. Using this index, the neighboring entities to the mention embedding are found and used as candidates. For ranking, anchor-contexts of Wikipedia pages are embedded and fed into a classifier together with the embedded mention-context, which outputs whether both belong to the same entity. This is done for each candidate for around 50 different anchor contexts. Then, multiple statistics on those similarity scores and candidates are calculated, which are used in a Random Forest model to compute the final ranks. \nSimilar to the previous approach, Wikidata was only used as the target knowledge graph, while information from Wikipedia was used for all the EL work. Thus, no special characteristics of Wikidata were used. The approach is less affected by a change of Wikidata due to similar reasons as the previous approach. This approach lacks performance compared to the state of the art in the HIPE task. The knowledge graph creation process produces a disadvantageous loss of entities, but this might be easily changed.\n\nProvatorov et al.~\\cite{Provatorova2020} used an ensemble of fine-tuned BERT models for ER. The ensemble is used to compensate for the noise of the OCR procedure. The candidates were generated by using an ElasticSearch index filled with Wikidata labels. The candidate's final rank is calculated by taking the search score, increasing it if a perfect match applies and finally taking the candidate with the lowest Wikidata identifier number (indicating a high popularity score). They also created three other methods of the EL approach: (1) The ranking was done by calculating cosine similarity between the embedding of the utterance and the embedding of the same utterance with the mention replaced by the Wikidata description. Furthermore, the score is increased by the Levenshtein distance between the entity label and the mention. (2) A variant was used where the candidate generation is enriched with historical spellings of Wikidata entities. (3) The last variant used an existing tool~\\cite{Hulst2020}, which included contextual similarity and co-occurrence probabilities of mentions and Wikipedia articles. In the tool, the final disambiguation is based on the ment-norm method by Le and Titov~\\cite{Le2018} .\nThe approach uses Wikidata labels and descriptions in one variant of candidate ranking. Beyond that, no other characteristics specific to Wikidata were considered. Overall, the approach is very basic and uses mostly pre-existing tools to solve the task. The approach is not susceptible to a change of Wikidata as it is mainly based on language and does not need retraining. \n\nThe approach designed by Huang et al.~\\cite{huangentity} is specialized in short texts, mainly questions.\nThe ER is performed via a pre-trained BERT model \\cite{Devlin2019} with a single classification layer on top, determining if a token belongs to an entity mention.\nThe candidate search is done via an ElasticSearch\\footnote{\\url{https:\/\/www.elastic.co\/elasticsearch\/}} index, comparing the entity mention to labels and aliases by exact match and Levenshtein distance.\nThe candidate ranking uses three similarity measures to calculate the final rank. A CNN is used to compute a character-based similarity between entity mention and candidate label. This results in a similarity matrix whose entries are calculated by the cosine similarity between each character embedding of both strings. \nThe context is included in two ways. First, between the utterance and the entity description, by embedding the tokens of each sequence through a BERT model. Again, a similarity matrix is built by calculating the cosine similarity between each token embedding of both utterance and description. The KG is also considered by including the triples containing the candidate as a subject. For each such triple, a similarity matrix is calculated between the label concatenation of the triple and the utterance. The most representative features are then extracted out of the matrices via max-pooling, concatenated and fed into a two-layer perceptron.\nThe approach was evaluated on the WebQSP~\\cite{DBLP:conf\/starsem\/SorokinG18} dataset, which is composed of short questions from web search logs.\nWikidata labels, aliases and descriptions are utilized. Additionally, the KG structure is incorporated through the labels of candidate-related triples. This is similar to the approach by Mulang et al.~\\cite{DBLP:journals\/corr\/abs-2008-05190}, but only 1-hop triples are used. There is also no hyper-relational information considered.\nDue to its reliance on text alone and using a pre-trained language model with sub-word embeddings, it is less susceptible to changes of Wikidata. While the approach was not empirically evaluated on the zero-shot EL task, other approaches using language models (LM)~\\cite{Logeswaran2019,Botha2020, Wu2019} were and indicate a good performance. \n\n\\subsubsection{Word embedding-based approaches}\n\\emph{Arjun}~\\cite{mulang2020encoding} tries to tackle specific challenges of Wikidata like long entity labels and implicit entities. Published in 2020, Arjun is an end-to-end approach utilizing the same model for ER and EL. It is based on an Encoder-Decoder-Attention model. First, the entities are detected via feeding Glove~\\cite{Pennington2014} embedded tokens of the utterance into the model and classifying each token as being an entity or not. Afterward, candidates are generated in the same way as in Falcon 2.0~\\cite{DBLP:journals\/corr\/abs-1912-11270} (see \\Cref{subsubsec:rule}). The candidates are then ranked by feeding the mention, the entity label, and its aliases into the model and calculating the score. The model resembles a similarity measure between the mention and the entity labels. \nArjun was trained and evaluated on the T-REx~\\cite{elsahar2019t} dataset consisting of extracts out of various Wikipedia articles. \nIt does not use any global ranking. Wikidata information is used in the form of labels and aliases in the candidate generation and candidate ranking. The model was trained and evaluated using GloVe embeddings, for which new words are not easily addable. New entities are therefore not easily supported. However, the authors claim that one can replace them with other embeddings like BERT-based ones.  While those proved to perform quite well in zero-shot EL~\\cite{Botha2020, Wu2019}, this was usually done with more context information besides labels. Therefore it remains questionable if using those would adapt the approach for zero-shot EL.   \n\n\n\n\\subsubsection{Word and graph embeddings-based approaches}\nIn 2018, Sorokin and Gurevych~\\cite{DBLP:conf\/starsem\/SorokinG18} were doing joint end-to-end ER and EL on short texts. The algorithm tries to incorporate multiple context embeddings into a mention score, signaling if a word is a mention, and a ranking score, signaling the candidate's correctness. First, it generates several different tokenizations of the same utterance. For each token, a search is conducted over all labels in the KG to gather candidate entities. If the token is a substring of a label, the entity is added.\nEach token sequence gets then a score assigned. The scoring is tackled from two sides. On the utterance side, a token-level context embedding and a character-level context embedding (based on the mention) are computed. The calculation is handled via dilated convolutional networks (DCNN) \\cite{Yu2016}. On the KG side, one includes the labels of the candidate entity, the labels of relations connected to a candidate entity, the embedding of the candidate entity itself, and embeddings of the entities and relations related to the candidate entity. This is again done by DCNNs and, additionally, by fully connected layers. The best solution is then found by calculating a ranking and mention score for each token for each possible tokenization of the utterance. All those scores are then summed up into a global score. The global assignment with the highest score is then used to select the entity mentions and entity candidates. \nThe question-based EL datasets WebQSP~\\cite{DBLP:conf\/starsem\/SorokinG18} and GraphQuestions~\\cite{su2016generating} were used for evaluation. GraphQuestions contains multiple paraphrases of the same questions and is used to test the performance on different wordings.\nThe approach uses the underlying graph, label and alias information of Wikidata. Graph information is used via connected entities and relations. They also use TransE embeddings, and therefore no hyper-relational structure. Due to the usage of static graph embeddings, retraining will be necessary if Wikidata changes.\n\n\\emph{PNEL}~\\cite{Banerjee2020} is an end-to-end (E2E) model jointly solving ER and EL focused on short texts. PNEL employs a Pointer network~\\cite{DBLP:conf\/nips\/VinyalsFJ15} working on a set of different features. An utterance is tokenized into multiple different combinations. Each token is extended into the (1) token itself, (2) the token and the predecessor, (3) the token and the successor, and (4) the token with both predecessor and successor. For each token combination, candidates are searched for by using the BM25 similarity measure. Fifty candidates are used per tokenization combination. Therefore, 200 candidates (not necessarily 200 distinct candidates) are found per token. For each candidate, features are extracted. Those range from the simple length of a token to the graph embeddings of the candidate entity.\nAll features are concatenated to a large feature vector. \nTherefore, per token, a sequence of 200 such features vectors exists.\nFinally, the concatenation of those sequences of each token in the sentence is then fed into a Pointer network. At each iteration of the Pointer network, it points to one distinct candidate in the network or an \\texttt{END} token marking no choice. Pointing is done by computing a softmax distribution and choosing the candidate with the highest probability. Note that the model points to a distinct candidate, but this distinct candidate can occur multiple times. Thus, the model does not necessarily point to only a single candidate of the 200 ones.\nPNEL was evaluated on several QA datasets, namely WebQSP~\\cite{DBLP:conf\/starsem\/SorokinG18}, SimpleQuestions~\\cite{bordes2015large} and LC-QuAD 2.0~\\cite{dubey2019lc}. SimpleQuestions focuses, as the name implies, on simple questions containing only very few entities. LC-QuAD 2.0, on the other hand, contains both, simple and more complex, longer questions including multiple entities.\nThe entity descriptions, labels and aliases are all used. Additionally, the graph structure is included by TransE graph embeddings, but no hyper-relational information was incorporated.\nE2E models can often improve the performance of the ER. Most EL algorithms employed in the industry often use older ER methods decoupled from the EL process. Thus, such an E2E EL approach can be of use. Nevertheless, due to its reliance on static graph embeddings, complete retraining will be necessary if Wikidata changes. \n\n\\subsubsection{Non-NN ML-based approaches}\n\\emph{OpenTapioca}~\\cite{DBLP:journals\/corr\/abs-1904-09131} is a mainly statistical EL approach published in 2019. \nWhile the paper never mentions ER, the approach was evaluated with it. In the code, one can see that the ER is done by a SolrTextTagger analyzer of the Solr search platform\\footnote{\\url{https:\/\/lucene.apache.org\/solr\/}}.  \nThe candidates are generated by looking up if the mention corresponds to an entity label or alias in Wikidata stored in a Solr collection. Entities are filtered out which do not correspond to the type person, location or organization.\nOpenTapioca is based on two main features, which are local compatibility and semantic similarity. First, local compatibility is calculated via a popularity measure and a unigram similarity measure between entity label and mention. The popularity measure is based on the number of sitelinks, PageRank scores, and the number of statements. Second, the semantic similarity strives to include context information in the decision process. All entity candidates are included in a graph and are connected via weighted edges. Those weights are calculated via a statistical similarity measure. This measure includes how likely it is to jump from one entity candidate to another while discounting it by the distance between the corresponding mentions in the utterance. The resulting adjacency matrix is then normalized to a stochastic matrix that defines a Markov Chain. One now propagates the local compatibility using this Markov Chain. Several iterations are then taken, and a final score is inferred via a Support Vector Machine. It supports multiple entities per utterance.\nOpenTapioca is evaluated on AIDA-CoNLL~\\cite{hoffart-etal-2011-robust}, Microposts 2016~\\cite{Rizzo}, ISTEX-1000~\\cite{DBLP:journals\/corr\/abs-1904-09131} and RSS-500~\\cite{roder2014n3}. RSS-500 consists of news-based examples and Microposts 2016 focuses on shorter documents like tweets. OpenTapioca was therefore evaluated on many different types of documents.\nThe approach is only trained on and evaluated for three types of entities: locations, persons, and organizations. \nIt facilitates Wikidata-specific labels, aliases, and sitelinks information. More importantly, it also uses qualifiers of statements in the calculation of the PageRank scores. But the qualifiers are only seen as additional edges to the entity.\nThe usage in special domains is limited due to its restriction to only three types of entities, but this is just an artificial restriction. It is easily updatable if the Wikidata graph changes as no immediate retraining is necessary.\n\n\\subsubsection{Graph optimization-based approaches}\n\\emph{Hedwig}~\\cite{DBLP:conf\/lrec\/KlangN20} is a multilingual entity linker specialized on the TAC 2017~\\cite{Ji2017} task but published in 2020. Another entity linker~\\cite{DBLP:journals\/corr\/abs-1903-05498}, developed by the same authors, is not included in this survey as Hedwig is partly an evolution of it. The entities to be linked are limited to only a subset of all possible entity classes. Hedwig employs Wikidata and Wikipedia at the same time. The Entity Recognition uses word2vec embeddings~\\cite{Mikolov2013}, character embeddings, and dictionary features where  the character embeddings are calculated via a Bi-LSTM. The dictionary features are class-dependent, but this is not defined in more detail. Those embeddings and features are computed and concatenated for each token.  Afterward, the whole sequence of token features is fed into a Bi-LSTM with a linear chain Conditional Random Field (CRF) layer at the end to recognize the entities. The candidates for each detected entity mention are then generated by using a mention dictionary. The dictionary is created from Wikidata and Wikipedia information, utilizing labels, aliases, titles or anchor texts. The candidates are disambiguated by constructing a graph consisting of all candidate entities, mentions, and occurring words in the utterance. The edges between entities and other entities, words, or mentions have the normalized pointwise mutual information (NPMI) assigned as their weights. The NPMI specifies how frequently two entities, an entity and a mention or an entity and a word, occur together. Those scores are calculated over a Wikipedia dump. Finally, the PageRank of each node in the graph is calculated via power iteration, and the highest-scoring candidates are chosen. \n \nThe type classification is used to determine the types of entities, not mentions. As this is only relevant for the TAC 2017 task, the classifier can be ignored. \nThe approach was evaluated on the TAC 2017~\\cite{Ji2017} dataset, which  focuses on entities of type person, organization, location, geopolitics and facilities. The documents originate from discussion forums and newswire texts.\nLabels and aliases from multiple languages are used. It also uses sitelinks to connect the Wikidata identifiers and Wikipedia articles. The paper also claims to use descriptions but does not describe anywhere in what way. No hyper-relational or graph features are used. As it employs class-dependent features, it is limited to the entities of classes specified in the TAC 2017 task. The NPMI weights have to be updated with the addition of new elements in Wikidata and Wikipedia.  \n\n\\emph{KBPearl}~\\cite{DBLP:journals\/pvldb\/LinLXLC20}, published in 2020, utilizes EL to populate incomplete KGs using documents. First, a document is preprocessed via Tokenization, POS tagging, NER, noun-phrase chunking, and time tagging. Also, an existing Information Extraction tool is used to extract open triples from the document. They experimented with four different tools (ReVerb~\\cite{Fader2011}, MinIE~\\cite{Gashteovski2017}, ClausIE~\\cite{Corro2013} and Stanford Open IE Tool~\\cite{Angeli2015}), Open triples are non-linked triples extracted via an open information extraction tool. The triples consist of a subject, predicate and object in unstructured text. For example, the open triple \\texttt{<Ennio Morricone, composed, soundtrack of The Hateful Eight>} can be extracted from \"Ennio Morricone, known for numerous famous soundtracks of the Spaghetti Western era, composed the soundtrack of the movie The Hateful Eight.\". The triples are processed further by filtering invalid tokens and doing canonicalization. Then, a graph of entities, predicates, noun phrases, and relation phrases is constructed. The candidates are generated by comparing the noun\/relation phrases to the labels and aliases of the entities\/predicates. The edges between the entities\/relations and between entities and relations are weighted by the number of intersecting one-hop statements. The next step is the computation of a maximum dense subgraph. Density is defined by the minimum weighted degree of all nodes \\cite{hoffart-etal-2011-robust}. As this problem is NP-hard, a greedy algorithm is used for optimization. New entities relevant for the task of Knowledge Graph Population are identified by thresholding the weighted sum of an entity's incident edges.\nLike used here, global coherence can perform sub-optimally since not all entities\/relations in a document are related. Thus, two variants of the algorithm are proposed. First, a pipeline version that separates the full document into sentences. Second, a near neighbor mode, limiting the interaction of the nodes in the graph by the distances of the corresponding noun-phrases and relation-phrases.\nKBPearl was evaluated on many different datasets: ReVerb38~\\cite{DBLP:journals\/pvldb\/LinLXLC20}, NYT2018~\\cite{DBLP:journals\/pvldb\/LinLXLC20, DBLP:conf\/icde\/LinC19}, LC-QuAD 2.0~\\cite{dubey2019lc}, QALD-7-WIKI~\\cite{usbeck20177th}, T-REx~\\cite{elsahar2019t}, Knowledge Net~\\cite{mesquita2019knowledgenet} and CC-DBP~\\cite{glass2018dataset}. These datasets encompass news articles, questions, and general open-domain documents.\nThe approach includes label and alias information of entities and predicates. Additionally, one-hop statement information is used, but hyper-relational features are not mentioned. However, the paper does not claim that its focus is entirely on Wikidata. Thus, the weak specialization is understandable. While it utilizes EL, the focus of the approach is still on knowledge base population.\nNo training is necessary, which makes the approach suitable for a dynamic graph like Wikidata.\n\n\\subsubsection{Rule-based approaches}\n\\label{subsubsec:rule}\n\\emph{Falcon 2.0}~\\cite{DBLP:journals\/corr\/abs-1912-11270} is a fully linguistic approach and a transformation of Falcon 1.0~\\cite{DBLP:conf\/naacl\/SakorMSSV0A19} to Wikidata. Falcon 2.0 was published in 2019, and its focus lies on short texts, especially questions. It links entities and relations jointly. Falcon 2.0 uses entity and relation labels as well as the triples themselves. The relations and entities are recognized by applying linguistic principles. The candidates are then generated by comparing mentions to the labels using the Levenshtein distance. The ranking of the entities and relations is done by creating triples between the relations and entities and checking if the query is successful. The more successful the queries, the higher the candidate will be ranked. If no query is successful, the algorithm returns to the ER phase and splits some of the recognized entities again. As Falcon 2.0 is an extension of Falcon 1.0 from DBpedia to Wikidata, the usage of specific Wikidata characteristics is limited. Falcon 2.0 is tuned for EL on questions and short texts, as well as the English language and it was evaluated on the two QA datasets LC-QuAD 2.0~\\cite{dubey2019lc} and SimpleQuestions~\\cite{bordes2015large}.\nIt is not generalizable to longer, more noisy, non-question texts. The used rules follow the structure of short questions. Hence, longer texts consisting of multiple sentences or non-questions are not supported. If the text is grammatically incorrect, the linguistic rules used to parse the utterance would fail. For example, linking Tweets would then be infeasible. \nAs it is only based on rules, it is clearly independent of changes in the KG.\n\n\\emph{Tweeki}~\\cite{tweeki:wnut20} is an approach focusing on unsupervised EL over tweets. The ER is done by a pre-existing Entity Recognizer~\\cite{Gardner2018} which also tags the mentions. The candidates are generated by first calculating the link probability between Wikidata aliases over Wikipedia and then searching for the aliases in a dictionary. \nThe ranking is done using the link probabilities while pruning all candidates that do not belong to the type provided by the Entity Recognizer. \nTweeki was evaluated on the accompanied dataset TweekiGold, consisting of random annotated tweets. Additionally, it was tested on the Microposts 2016~\\cite{Rizzo} dataset and the datasets by Derczynski~\\cite{Derczynski2015} which both also focus on shorter, noisy texts like tweets.\nThe approach does not need to be trained, making it very suitable for linking entities in tweets. In this document type, often novel entities with minimal context exist.\nRegarding features of Wikidata, it uses label, alias and type information. Due to it being unsupervised, changes to the KG do not affect it.\n\n\\subsection{Analysis}\n\\label{sec:approaches_evaluation}\n\nMany approaches include some form of language model or word embedding. This is expected as a large factor of entity linking encompasses the comparison of word-based information. And in that regard, language models like BERT~\\cite{Devlin2019} proved very performant in the last years. Furthermore, various language models rely on sub-word or character embeddings which also work on out-of-dictionary words. This is in contrast to regular word-embeddings, which can not cope with words never seen before.\nIf graph information is part of the approach, the approaches either used graph embeddings, included some coherence score as a feature or created a neighborhood graph on the fly and optimized over it. Some approaches like OpenTapioca, Falcon 2.0 or Tweeki utilized more old-fashioned methods. They either employed classic ML together with some basic features or worked entirely rule-based. \n\n\\subsubsection{Performance}\nTable~\\ref{tab:dataset_results_el_er} gives an overview of all available results for the approaches performing ER and EL. While results for the EL-only approaches exist, the used measures vary widely. Thus, it is very difficult to compare the approaches. To not withhold the results, they can still be found in the appendix in Table~\\ref{tab:dataset_results_el_only} with an accompanying discussion. We aim to fully recover this table and also extend Table~\\ref{tab:dataset_results_el_er} in future work.\n \nThe micro $F_1$ scores are given:\n\\begin{equation*}\n    F_1 = 2 \\cdot \\frac{p \\cdot r}{p +r}\n\\end{equation*}\nwhere p is the precision $p=\\frac{\\mathit{tp}}{\\mathit{tp} + \\mathit{fp}}$ and r is the recall $r=\\frac{\\mathit{tp}}{\\mathit{tp} + \\mathit{fn}}$. Here, $\\mathit{tp}$ is the number of true positives, $\\mathit{fp}$ is the number of false positives and $\\mathit{fn}$ is the number of false negatives over a ground truth. Micro $F_1$ means that the scores are calculated over all linked entity mentions and not separately for each document and then averaged. True positives are the correctly linked entity mentions, false positives incorrectly linked entities that do not occur in the set of valid entities and false negatives entities that occur  in the set of valid entities but are not linked to~\\cite{Cornolti2013}. \nThe approaches were evaluated on many different datasets, which makes comparison very difficult. Additionally, many approaches are evaluated on datasets designed for knowledge graphs different from Wikidata and then mapped. \nOften, the approaches are evaluated on the same dataset but over different subsets, which complicates a comparison even more.\nThe method by Perkins~\\cite{perkins2020separating} was also evaluated on the Kensho Derived Wikimedia Dataset~\\cite{KenshoRD}, but it was only used to compare different variants of the designed approach and focused on different amounts of training data. Thus, inclusion in the evaluation table is not reasonable. \n\n\\begin{table*}\n    \\centering\n    \\rotatebox{-90}{\n    \\resizebox{0.95\\textheight}{!}{\n    \\begin{threeparttable}\n        \\begin{tabular}{ccccccccccccc}\n            \\toprule\n            &\\rotatebox[origin=c]{-66}{OpenTapioca~\\cite{DBLP:journals\/corr\/abs-1904-09131}} & \n            \\rotatebox[origin=c]{-66}{Falcon 2.0~\\cite{DBLP:journals\/corr\/abs-1912-11270}} &\n            \\rotatebox[origin=c]{-66}{Arjun~\\cite{mulang2020encoding}} & \n            \\rotatebox[origin=c]{-66}{VCG~\\cite{DBLP:conf\/starsem\/SorokinG18}} &\n            \\rotatebox[origin=c]{-66}{KBPearl~\\cite{DBLP:journals\/pvldb\/LinLXLC20}~\\tnotex{tn:erel2}} &\n            \\rotatebox[origin=c]{-66}{PNEL~\\cite{Banerjee2020}}&\n            \\rotatebox[origin=c]{-66}{Huang et al.~\\cite{huangentity}} &\n            \\rotatebox[origin=c]{-66}{Boros et al.~\\cite{borosrobust}} &\n            \\rotatebox[origin=c]{-66}{Provatorov et al.~\\cite{Provatorova2020}} &\n            \\rotatebox[origin=c]{-66}{\\parbox{2cm}{Labusch \\& Neudecker~\\cite{Labusch2020}}} &\n            \\rotatebox[origin=c]{-66}{Hedwig~\\cite{DBLP:conf\/lrec\/KlangN20}} &\n            \\rotatebox[origin=c]{-66}{Tweeki~\\cite{tweeki:wnut20}}\\\\\n            \\toprule \n            AIDA-CoNLL~\\cite{hoffart-etal-2011-robust} &0.482~\\cite{DBLP:journals\/corr\/abs-1904-09131}&-&-&-&-&-&-&-&-&-&-&-\\\\\n            Microposts 2016~\\cite{Rizzo}&0.087~\\cite{DBLP:journals\/corr\/abs-1904-09131}, 0.148~\\cite{tweeki:wnut20}&-&-&-&-&-&-&-&-&-&-&0.248~\\cite{tweeki:wnut20} \\\\\n            ISTEX-1000~\\cite{DBLP:journals\/corr\/abs-1904-09131}&0.87~\\cite{DBLP:journals\/corr\/abs-1904-09131}&-&-&-&-&-&-&-&-&-&-&- \\\\\n            RSS-500~\\cite{roder2014n3} & 0.335~\\cite{DBLP:journals\/corr\/abs-1904-09131}&-&-&-&-&-&-&-&-&-&-&-\\\\\n            LC-QuAD 2.0~\\cite{dubey2019lc}&0.301~\\cite{Banerjee2020} & 0.445~\\cite{Banerjee2020}&-&\n            0.47~\\cite{Banerjee2020}&-&0.589~\\cite{Banerjee2020}~\\tnotex{tn:erel3}&-&-&-&-&-&-\n            \\\\\n            LC-QuAD 2.0~\\cite{dubey2019lc}~\\tnotex{tn:erel8}&0.25~\\cite{DBLP:journals\/corr\/abs-1912-11270} & 0.68~\\cite{DBLP:journals\/corr\/abs-1912-11270}&-&\n            &-&-&-&-&-&-&-&-\n            \\\\\n            LC-QuAD 2.0~\\cite{dubey2019lc}~\\tnotex{tn:erel1}&-& 0.320~\\cite{Banerjee2020}&-&-&-&0.629~\\cite{Banerjee2020}~\\tnotex{tn:erel3}&-&-&-&-&-&-\n            \\\\\n            Simple-Question&0.20~\\cite{Banerjee2020}& 0.41~\\cite{Banerjee2020}&-&-&-&0.68~\\cite{Banerjee2020}~\\tnotex{tn:erel4}&-&-&-&-&-&-\\\\\n            Simple-Question~\\cite{bordes2015large}~\\tnotex{tn:erel9}&-& 0.63~\\cite{DBLP:journals\/corr\/abs-1912-11270}&-&-&-&-&-&-&-&-&-&-\\\\\n            T-REx~\\cite{elsahar2019t}& 0.579~\\cite{mulang2020encoding}&-&0.713~\\cite{mulang2020encoding}&-&-&-&-&-&-&-&-&-\\\\\n            T-REx~\\cite{elsahar2019t}~\\tnotex{tn:erel7}& -&-&-&-&0.421~\\cite{DBLP:journals\/pvldb\/LinLXLC20}&-&-&-&-&-&-&-\\\\\n            WebQSP~\\cite{yih2016value}&-&-&0.730~\\cite{Banerjee2020,DBLP:conf\/starsem\/SorokinG18}&-&-&0.712~\\cite{Banerjee2020}~\\tnotex{tn:erel5}&0.780~\\cite{huangentity}&-&-&-&-&-\\\\\n            CLEF HIPE 2020~\\cite{Ehrmann2020}&-&-&-&-&-&-&-&0.531~\\cite{Ehrmann2020a}~\\tnotex{tn:erel6}&0.300~\\cite{Ehrmann2020a}~\\tnotex{tn:erel6}&0.141~\\cite{Ehrmann2020a}~\\tnotex{tn:erel6}&-&-\\\\\n            TAC2017~\\cite{Ji2017}&-&-&-&-&-&-&-&-&-&-&0.582~\\cite{DBLP:conf\/lrec\/KlangN20}\\\\\n            Graph-Questions~\\cite{su2016generating}&-&-&0.442~\\cite{DBLP:conf\/starsem\/SorokinG18}&-&-&-&-&-&-&-&-&-\\\\\n            QALD-7-WIKI~\\cite{usbeck20177th}&-&-&-&-&0.679~\\cite{DBLP:journals\/pvldb\/LinLXLC20}&-&-&-&-&-&-&-\\\\\n            NYT2018~\\cite{DBLP:journals\/pvldb\/LinLXLC20, DBLP:conf\/icde\/LinC19}&-&-&-&-&0.575~\\cite{DBLP:journals\/pvldb\/LinLXLC20}&-&-&-&-&-&-&-\\\\\n            ReVerb38~\\cite{DBLP:journals\/pvldb\/LinLXLC20}&-&-&-&-&0.653~\\cite{DBLP:journals\/pvldb\/LinLXLC20}&-&-&-&-&-&-&-\\\\\n            Knowledge Net~\\cite{mesquita2019knowledgenet}&-&-&-&-&0.384~\\cite{DBLP:journals\/pvldb\/LinLXLC20}&-&-&-&-&-&-&-\\\\\n            CC-DBP~\\cite{glass2018dataset}&-&-&-&-&0.499~\\cite{DBLP:journals\/pvldb\/LinLXLC20}&-&-&-&-&-&-&-\\\\\n            TweekiGold~\\cite{tweeki:wnut20}&0.291~\\cite{tweeki:wnut20}&-&-&-&-&-&-&-&-&-&-&0.65~\\cite{tweeki:wnut20}\\\\\n            Derczynski~\\cite{Derczynski2015}&0.14~\\cite{tweeki:wnut20}&-&-&-&-&-&-&-&-&-&-&0.371~\\cite{tweeki:wnut20}\\\\\n            \\bottomrule\n        \\end{tabular}\n        \\begin{tablenotes}\n            \\setlength{\\columnsep}{0.8cm}\n            \\setlength{\\multicolsep}{0cm}\n            \\begin{multicols}{3}\n                \\small\n                \\item[1] \\label{tn:erel2} NN model\n                \\item[2] \\label{tn:erel3} L model\n                \\item[3] \\label{tn:erel8} 1000 sampled questions from LC-QuAD 2.0\n                \\item[4] \\label{tn:erel1} LC-QuAD 2.0 test set used in KBPearl paper\n                \\item[5] \\label{tn:erel4} S model\n                \\item[6] \\label{tn:erel9} Probably evaluated on train and test set\n                \\item[7] \\label{tn:erel7} Evaluation on subset of T-REx data different to the subset used in Arjun paper\n                \\item[8] \\label{tn:erel5} W model\n                \\item[9] \\label{tn:erel6} Strict mention matching\n            \\end{multicols}\n        \\end{tablenotes}\n    \\end{threeparttable}\n    }}\n    \\caption{Results: ER + EL.}\n    \\label{tab:dataset_results_el_er}\n\\end{table*}\n\nInferring the utility of a Wikidata characteristic from the different approaches' $F_1$-measures is inconclusive due to the sparsity of results.\nFor ER + EL approaches, most results were available for LC-QuAD 2.0. Yet, no conclusion can be drawn as many approaches were evaluated on different subsets of the dataset. Falcon 2.0 performs well, but it does not substantially rely on Wikidata characteristics. The performance is good as it is designed for simple questions that follow its rules very closely. Arjun performs well on T-REx by mainly using label information, but the number of methods tested on the T-REx dataset is too low to be conclusive. Besides that, PNEL and the approach by Huang et al. also achieve good results; both include a broader scope of Wikidata information in the form of labels, descriptions and graph structure. As HIPE challenge approaches are using Wikidata only marginally and the difference in performance depends more on the robustness against the OCR-introduced noise, comparing them is not providing information on the relevance of Wikidata characteristics.\n\n\\subsubsection{Utilization of Wikidata characteristics}\nWhile some algorithms~\\cite{mulang2020encoding} do try to examine the challenges of Wikidata, like more noisy long entity labels, many fail to use most of the advantages of Wikidata's characteristics. If the approaches are using even more information than just the labels of entities and relations, they mostly only include simple n-hop triple information. Hyper-relational information like qualifiers is only used by OpenTapioca but still in a simple manner. This is surprising, as they can provide valuable additional information. As one can see in Figure~\\ref{fig:qualifiers_bars}, around half of the statements on entities occurring in the LC-QuAD 2.0 dataset have one or more qualifiers. These percentages differ from the ones in all of Wikidata, but when entities are considered, appearing in realistic use cases like QA, qualifiers are much more abundant.   Thus, dismissing the qualifier information might be critical. The inclusion of hyper-relational graph embeddings could improve the performance of many approaches already using non-hyper-relational ones.\nRank information of statements might be useful to consider, but choosing the best one will probably often suffice. \n\n\\begin{figure}[hbt!]\n    \\centering\n    \\includegraphics[width=\\linewidth]{Images\/statement_qualifiers_bar_both.pdf}\n    \\caption{Percentage of statements having the specified number of qualifiers for all LC-QuAD 2.0 and Wikidata entities.}\n    \\label{fig:qualifiers_bars}\n\\end{figure}\n\nOf all approaches, only two algorithms~\\cite{huangentity, Banerjee2020} use descriptions explicitly. Others incorporate them through triples too, but more on the side~\\cite{DBLP:journals\/corr\/abs-2008-05190}. Descriptions can provide valuable context information and many items do have them; see Figure~\\ref{fig:wikidata_descriptions}. Hedwig~\\cite{DBLP:conf\/lrec\/KlangN20} claims to use descriptions but fails to describe how.  \n\nTwo approaches~\\cite{DBLP:conf\/lrec\/KlangN20, Botha2020} demonstrated the usefulness of the inherent multilingualism of Wikidata, notably in combination with Wikipedia. \n\n\\begin{table}[htb!]\n    \\centering\n    \\begin{tabularx}{\\linewidth}{Xcc}\n        \\toprule\n         \\textbf{Approach} & \\textbf{Code} & \\textbf{Web API} \\\\ \\midrule\n         OpenTapioca~\\cite{DBLP:journals\/corr\/abs-1904-09131} & \\cmark & \\cmark \\\\\n        Falcon 2.0~\\cite{DBLP:journals\/corr\/abs-1912-11270}&\\cmark&\\cmark\\\\\n        Arjun~\\cite{mulang2020encoding}&\\cmark&\\xmark\\\\\n        VCG~\\cite{DBLP:conf\/starsem\/SorokinG18}&\\cmark&\\xmark \\\\\n        KBPearl~\\cite{DBLP:journals\/pvldb\/LinLXLC20} & \\xmark & \\xmark \\\\\n        PNEL~\\cite{Banerjee2020} & \\cmark & \\xmark \\\\\n        Mulang et al.~\\cite{DBLP:journals\/corr\/abs-2008-05190} & \\cmark & \\xmark\\\\\n        Perkins~\\cite{perkins2020separating} & \\xmark & \\xmark\\\\\n        NED using DL on Graphs~\\cite{DBLP:journals\/corr\/abs-1810-09164}&\\cmark&\\xmark\\\\\n        Huang et al.~\\cite{huangentity} & \\xmark & \\xmark\\\\ \n        Boros et al.~\\cite{borosrobust} & \\xmark & \\xmark \\\\\n        Provatorov et al.~\\cite{Provatorova2020} & \\xmark & \\xmark \\\\\n        Labusch and Neudecker~\\cite{Labusch2020} & \\cmark & \\xmark \\\\\n        Botha et al.~\\cite{Botha2020} & \\xmark & \\xmark \\\\\n        Hedwig~\\cite{DBLP:conf\/lrec\/KlangN20}&\\xmark&\\xmark \\\\\n        Tweeki~\\cite{tweeki:wnut20} & \\xmark & \\xmark\\\\\n        \\bottomrule\n    \\end{tabularx}\n    \\caption{Availability of approaches.}\n    \\label{tab:availability}\n\\end{table}\n\nAs Wikidata is always changing, approaches robust against change are preferred. A reliance on transductive graph embeddings~\\cite{DBLP:conf\/starsem\/SorokinG18,Banerjee2020, DBLP:journals\/corr\/abs-1810-09164, perkins2020separating}, which need to have all entities available during training, makes repeated training necessary. Alternatively, the used embeddings would need to be replaced with graph embeddings, which are efficiently updatable or inductive~\\cite{Wang2019, Wang2019a, Teru2020,Baek2020,Albooyeh2020,Hamaguchi2017,Wu2019a, galkin2021nodepiece, Daruna2021}.\nThe rule-based approach Falcon 2.0~\\cite{DBLP:journals\/corr\/abs-1912-11270} is not affected by a developing knowledge graph but only usable for correctly-stated questions. \nMethods only working on text information~\\cite{mulang2020encoding, Provatorova2020, huangentity, Botha2020, DBLP:journals\/corr\/abs-2008-05190} like labels, descriptions or aliases do not need to be updated if Wikidata changes, only if the text type or the language itself does. This is demonstrated by the approach by Botha et al.~\\cite{Botha2020} and the Wikification EL BLINK~\\cite{Wu2019}, which mainly use the BERT model and are able to link to entities never seen during training. If word-embeddings instead of sub-word embeddings are used, for example, GloVe~\\cite{Pennington2014} or word2vec~\\cite{Mikolov2013}, this advantage diminishes as new never-seen labels could not be interpreted. Nevertheless, the ability to support totally unseen new entities was only demonstrated for the approach by Botha et al~\\cite{Botha2020}. The other approaches still need to be evaluated on the zero-shot EL task to be certain. \nFor approaches~\\cite{DBLP:conf\/lrec\/KlangN20, huangentity, tweeki:wnut20} that rely on statistics over Wikipedia, new entities in Wikidata may sometimes not exist in Wikipedia to a satisfying degree.\nAs a consequence, only a subset of all entities in Wikidata is supported. This also applies to the approaches by Boros et al.~\\cite{borosrobust}, and Labusch and Neudecker~\\cite{Labusch2020} which are mostly using Wikipedia information. Additionally, they are susceptible to changes in Wikipedia, especially specific statistics calculated over Wikipedia pages which have to be updated any time a new entity is added.\nBotha et al.~\\cite{Botha2020} also mainly depend on Wikipedia and thus on the availability of the desired Wikidata entities in Wikipedia itself. Since the approach uses Wikipedia articles in multiple languages, it encompasses many more entities than the previous approaches that focus on Wikipedia. Botha et al.'s~\\cite{Botha2020} approach was designed for the zero- and few-shot setting, it is quite robust against changes in the underlying knowledge graph.\n\n\\begin{table*}[hb!]\n    \\centering\n    \\begin{tabularx}{0.99\\linewidth}{lcccc}\n        \\toprule\n         \\textbf{Survey} & \\textbf{\\# Approaches} & \\textbf{\\# Wikidata Approaches} & \\textbf{\\# Datasets} & \\textbf{\\# Wikidata Datasets}    \\\\ \\midrule\n         Sevgili et al.~\\cite{DBLP:journals\/corr\/abs-2006-00575} & 30 & 0 & 9 & 0 \\\\\n         Al-Moslmi et al.~\\cite{al2020named} & 39 & 0 & 17 & 0\\\\ \n         Oliveira et al.~\\cite{oliveira2020towards}  & 36 & 0 & 32 & 0 \\\\\n         This survey & 16 & 16 & 21 & 11 \\\\\n         \\bottomrule\n    \\end{tabularx}\n    \\caption{Survey Comparison}\n    \\label{tab:survey_comparison}\n\\end{table*}\n\nApproaches relying on statistics~\\cite{DBLP:journals\/pvldb\/LinLXLC20, DBLP:journals\/corr\/abs-1904-09131} need to update them regularly, but this might be efficiently doable.\nOverall, the robustness against change might be negatively affected by static\/transductive graph embeddings.\n\n\\begin{highlightbox}{\\hyperlink{rq3}{Research Question 3}}{How do current Entity Linking approaches exploit the specific characteristics of Wikidata?}\nThe preceding summary and evaluation of the existing Wikidata Entity Linkers, together with \\Cref{tab:comparison_approaches_wikidata} and the descriptions in \\Cref{subsec:el,subsec:erel}, provide an overview of all approaches with a focus on the incorporated Wikidata-characteristics.\n\\end{highlightbox}\n\\begin{highlightbox}{\\hyperlink{rq4}{Research Question 4}}{Which Wikidata characteristics are unexploited by existing Entity Linking approaches?}\nThe most unexploited characteristics are the descriptions, the hyper-relational structure and the type information, as can be seen in \\Cref{tab:comparison_approaches_wikidata}.\nNearly none of the found approaches exploited hyper-relational information in the form of qualifiers. And the one (i.e. OpenTapioca) using them did that in a simple way. As it is confirmed by the benchmarks that the inclusion of those can improve the performance of link prediction~\\cite{Galkin2020}, this might also be the case for the task of EL. \nFurthermore, description information is still greatly underutilized. It can be a valuable piece of context information of an entity. Of course, it is not ideal as often the description can be short, especially for long-tail entities. \nA possible way to circumvent this challenge is the recent development of \\textbf{Abstract Wikipedia\n}~\\cite{DBLP:journals\/cacm\/Vrandecic21}, which will support the multilingual generation of descriptions in the future. \nWhile some approaches utilize type information, most use them to limit the set of valid entity candidates to instances of only a small subset of all types, namely person, organization and location. This is surprising as the non-included paper by Raiman and Raiman~\\cite{DBLP:conf\/aaai\/RaimanR18} shows that a fine-grained type system can heavily improve the entity linking performance.\nAs mentioned in \\Cref{sec:wikidata}, rank information might also be used by not only including statements of the best rank but also of others. For example, in the case that statements exist which were valid at different points of time, including all could prove useful when linking documents of different ages. But such a special use case is not considered by any existing Wikidata EL approach.\nFor some more ideas on how to include those characteristics in the future, please refer to \\cref{subsec:future}.\n\\end{highlightbox}\n\n\n\n\n\\subsection{Reproducibility}\nNot all approaches are available as a Web API or even as source code. An overview can be found in Table~\\ref{tab:availability}. \nThe number of approaches for Wikidata having an accessible Web API is meager. While the code for some methods exists, this is the case for only half of them. The effort to set up different approaches also varies significantly due to missing instructions or data. \nThus, we refrained from evaluating and filling the missing results for all the datasets in Tables~\\ref{tab:dataset_results_el_only} and~\\ref{tab:dataset_results_el_er}. However, we seek to extend both tables in future work.\n\n\n\n\\section{Problem Definition}\n\\label{sec:problem}\nEL is the task of linking an entity mention in unstructured or semi-structured data to the correct entity in a KG. The focus of this survey lies in unstructured data, namely, natural language utterances.\n\n\\subsection{General terms}\n\\paragraph{Utterance.}\nAn utterance $u$ is defined as a sequence of $n$ words $w$.\n\\begin{equation*}\n    u = (w_0, w_1, ... w_{n-1})\n\\end{equation*}\n\n\\paragraph{Entity.}\nThere exists no universally agreed-on definition of an entity in the context of EL~\\cite{rosales2020fine}. \nAccording to the Oxford Dictionary, an entity is:\n\\begin{quote}\n    \"something that exists separately from other things and has its own identity\"~\\cite{oxford_entity}\n\\end{quote}\nWhat elements of a KG correspond to entities depends on the KG itself. \nIn the case of Wikidata, we define it as follows:\n\\begin{quote}\n    Any Wikidata item is an entity. \n\\end{quote}\nIn Section~\\ref{sec:wikidata}, we further define Wikidata items.\nMany EL approaches limit the space of valid entities. Usually, named entities like a specific person (e.g. \\texttt{Barack Obama}), an organization (e.g. \\texttt{NASA}) or a movie (e.g. \\texttt{The Hateful Eight}) are desirable to link. In general, any entity which can be denoted with a proper noun is a named entity. But sometimes, also common entities like concepts (e.g. \\texttt{dog} or \\texttt{theater}) are included. What exactly is linked depends on the use case~\\cite{rosales2020fine}. \n\n\n\\paragraph{Knowledge Graph.}\nWhile the term knowledge graph was already used before, the popularity increased drastically after Google introduced the \\texttt{Knowledge Graph} in 2012~\\cite{singhal2012introducing, Ehrlinger2016}.  \nHowever, similar to an entity, there exists no unanimous definition of a KG~\\cite{Ehrlinger2016, hogan2020knowledge}.  \nFor example, F\u00e4rber et al. define a KG as an RDF graph~\\cite{DBLP:journals\/semweb\/FarberBMR18}.\nHowever, a KG being an RDF graph is a strict assumption. While the Wikidata graph is available in the RDF format, the main output format is JSON. Freebase, often called a KG, did not provide the RDF format until a year after its launch~\\cite{freebase_rdf}. \nPaulheim defines it less formal as: \n\\begin{quote}\n    \"A knowledge graph (i) mainly describes real world entities and their interrelations, organized in a graph, (ii) defines possible classes and relations of entities in a schema, (iii) allows for potentially interrelating arbitrary entities with each other and (iv) covers various topical domains.\"~\\cite{Paulheim2017}\n\\end{quote}\nBut constraint (iv) of Paulheims definition alienates commercial KGs, focusing on a single domain, such as a financial, medical, or geographical one. \nAs no unanimously agreed definition exists, we define a knowledge graph very broadly in the following and the Wikidata KG more concrete in Section~\\ref{sec:wikidata}.\nThe term KG is often used as a synonym for the term knowledge base~(KB), but they are not the same~\\cite{jarke1989kbms}. No single definition for a KB exists either. Jarke et al. define it as \"a representation of heuristic and factual information, often in the form of facts, assertions and deduction rules\"~\\cite{jarke1989kbms}. The term is often loosely used to describe a system that is able to store knowledge in the form of structured or unstructured information. While any KG is a KB, not any KB is a KG. The main difference is that a KB does not have to be graph-structured.\n\nIn this survey, a knowledge graph is defined as a directed graph $G=(V,E, \\mathcal{R})$ consisting of vertices $V$, edges $E$ and relations $\\mathcal{R}$. A subset of the vertices corresponds to entities $\\mathcal{E}$ or literals $\\mathcal{L}$. A literal is a concrete value of information like the height or a name of an entity. A literal vertex has incoming edges but no outgoing ones. Other types of vertices might exist depending on the KG.\n$E$ is a set $\\{e_1, \\dots, e_{|E|}\\}$ of edges with $e_j \\in V \\times \\mathcal{R} \\times V$ where relations $\\mathcal{R}$ assign a certain meaning to the connection between entities. Such edges are also called triples. \nThere are special subtypes of KGs, e.g., hyper-relational graphs such as Wikidata.\n\n\\paragraph{Hyper-Relational Knowledge Graphs. \\label{par:hyper}} In a hyper-relational knowledge graph,  statements can be specified by more information than a single relation. Multiple relations are, therefore, part of a statement.\nIn case of a hyper-relatio\\-nal graph $\\mathcal{G} = (V, E, \\mathcal{R})$, $E$ is a list $(e_1, \\dots, e_n)$ of edges with $e_j \\in V \\times \\mathcal{R} \\times V \\times \\mathcal{P}(\\mathcal{R} \\times V)$ for $1\\le j \\le n$, where $\\mathcal{P}$ denotes the power set. A hyper-relational fact $e_j \\in E$ is usually written as a tuple $ (s,r,o,\\mathcal{Q})$, where $\\mathcal{Q}$ is the set of \\emph{qualifier pairs} $\\{(qr_{i},qv_{i}) \\}$ with \\emph{qualifier relations} $qr_{i} \\in \\mathcal{R}$ and \\emph{qualifier values} $qv_{i} \\in V$. The triple $(s,r,o)$ is referred to as the \\emph{main triple} of the fact. $Q_j$ denotes the qualifier pairs \nof $e_j$~\\cite{Galkin2020}. \nFor example, the \\texttt{nominated for}~edge in Fig.~\\ref{fig:wikidata_subgraph} has two additional qualifier relations and would be represented as \\nohyphens{\\texttt{(Ennio Morricone, nominated for,  Academy Award for Best Original Score, \\{( for work, The Hateful Eight ), (statement is subject of, 88th A-cademy Awards)\\})}}. \n\n\\subsection{Tasks}\nSince not only approaches that solely do EL were included in the survey, Entity Recognition will also be defined. \n\n\\paragraph{Entity Recognition.} ER is the task of identifying the mention span $$m = (w_i, ..., w_k) | 0 \\leq i \\leq k \\leq n-1$$ of all entities in an utterance $u$. Each such span is called an entity mention $m$. The word or word sequence referring to an entity is also known as the surface form of an entity.\n An utterance can contain more than one entity, often also consisting of more than one word. Sometimes, a broad type of an entity is classified too. Usually, those are \\texttt{person}, \\texttt{location} and \\texttt{organization}. Some of the considered approaches do such a classification task and also use it to improve the EL.\n \n It is also up to debate what an entity mention is. In general, a literal reference to an entity is considered a mention. But whether to include pronouns or how to handle overlapping mentions depends on the use case. \n\n\\paragraph{Entity Linking.} \nThe goal of EL is to find a mapping function that maps all found mentions to the correct KG entities and also to identify if an entity mention does not exist in the KG. \n\nIn general, EL takes the utterance $u$ and all $k$ identified entity mentions $M=(m_1, ... m_k)$ in the utterance and links each of them to an element of the set $(\\mathcal{E}\\cup \\{\\mathit{NIL}\\})$. The $\\mathit{NIL}$ element is added to the set of vertices to be able to signalize that the entity, that the mention is referring to, is not known to the KG. Such a $\\mathit{NIL}$ entity is also called an out-of-KG entity. Another way to handle such unknown entities is to create emerging entities~\\cite{DBLP:conf\/www\/HoffartAW14}. In that case, the entity is still unknown to the KG, but after encountering it, it is separately stored using information like the provided entity mentions. Now no single $\\mathit{NIL}$ entity, but a growing set of emerging entities exists. EL is then done using the entities in the KG and all already encountered emerging entities. While all KG-unknown entities point to the same single $\\mathit{NIL}$ entity, they might point to different emerging entities. \n\n\n\nEL is often split into two subtasks. First, potential candidates for an entity are retrieved from a KG. This is necessary as doing EL over the whole set of entities is often intractable. This \\emph{Candidate generation} is usually performed via efficient metrics measuring the similarities between mentions in the utterance and entities in the KG. The result is a set of candidates $C=\\{c_0, \\cdots, c_l\\}$ for each entity mention $m$ in the utterance. \nAfter limiting the space of possible entities, one of the available candidates is chosen for each entity. This is done via a \\emph{candidate ranking} algorithm, which assigns a rank to each candidate.\nThe assignment is done by computing a score for each candidate signalizing how likely it is the correct entity. The candidate with the highest score is chosen as the correct entity for the mention.\n\nThere are two different categories of reranking methods are called \\emph{local} or \\emph{global}~\\cite{DBLP:conf\/acl\/RatinovRDA11}.  \n\\begin{align*}\n \\mathit{score_{\\mathit{local}}}: C \\times M &\\to \\mathbb{R}\\\\ \n \\text{ given by } (c,m) &\\mapsto \\mathit{score_{\\mathit{local}}}(c, m)\n\\end{align*}\nwhere $\\mathit{score_{\\mathit{local}}}$ is a local scoring function of a candidate. The goal is then to optimize the objective function:\n\\begin{equation*}\n    A^* = \\argmax_A \\sum_{i=1}^k \\mathit{score_{\\mathit{local}}}(a_i, m_i) | a_i \\in C_i\n\\end{equation*}\nwhere $A = \\{a_1, ... , a_k\\} \\in \\mathcal{P}(\\mathcal{E})$ is an assignment of one candidate to each entity mention $m_i$. $\\mathcal{P}(*)$ is the power set operator.\n\nThe rank assignment and score calculation of the candidates of one entity is often not independent of the other entities' candidates. In this case, the ranking will be done by including the whole assignment via a global scoring function:\n\\begin{equation*}\n \\mathit{score_{\\mathit{global}}}: \\mathcal{P}(\\mathcal{E}) \\to \\mathbb{R} \\text{ given by }A \\mapsto \\mathit{score_{\\mathit{global}}}(A)\n\\end{equation*}\nThe objective function is then:\n\\begin{align*}\n    A^* &= \\argmax_A \\left[\\sum_{i=1}^k \\mathit{score_{\\mathit{local}}}(a_i, m_i)\\right] \\\\ \n    &+ \\mathit{score_{\\mathit{global}}}(A) \\ | \\ a_i \\in C_i\n\\end{align*}\n \n\nNote, there also exists some ambiguity in the objective of linking itself. For example, there exists a Wikidata entity \\texttt{2014 FIFA World Cup} and an entity \\texttt{FIFA World Cup}. There is no unanimous solution on how to link the entity mention in the utterance \\texttt{In 2014, Germany won the \\underline{FIFA World Cup}}.\n\nSometimes EL is also called Entity Disambiguation, which we see more as part of EL, namely where entities are disambiguated via the candidate ranking.\n\nThere exist multiple special cases of EL.\n\\textit{Multilingual EL} tries to link entity mentions occurring in utterances of different languages to one shared KG, for example, English, Spanish or Chinese utterances to one language-agnostic KG. \nFormally, an entity mention $m$ in some utterance $u$ of some context language $l_c$ has to be linked to a language-agnostic KG which includes information in multiple languages $L_{KG}=\\{l_1,...,l_k\\}$ where $l_c$ can but has not to be an element of $L_{KG}$~\\cite{Botha2020}.\n\n\\textit{Cross-lingual EL} tries to link entity mentions in utterances in different languages to a KG in one dedicated language, for example, Spanish and German utterances to an English KG~\\cite{Rijhwani2019}. In that case, the multilingual EL problem gets constrained to $L_{KG}=\\{l_{KG}\\}$ where $l_c \\neq l_{KG}$.\n\nIn \\textit{zero-shot EL}, the entities during test time $\\mathcal{E}_{\\mathit{test}}$ are not available at training time $\\mathcal{E}_{\\mathit{train}}$. \n$$\n\\mathcal{E}_{\\mathit{test}} \\cap \\mathcal{E}_{\\mathit{train}} = \\emptyset~\\text{where}~\\mathcal{E}_{\\mathit{test}} \\subset \\mathcal{E},~\\mathcal{E}_{\\mathit{train}} \\subset \\mathcal{E}\n$$\nThus, the entity linker must be able to handle unseen entities. \nThe term was coined by Logeswaran et al.~\\cite{Logeswaran2019}, but they limited the task to only have descriptions available while our definition does not include such a limitation. \n\n\\textit{KB\/KG-agnostic EL} approaches are able to support different KBs respectively KGs, often multiple in parallel. \nFor example, a KG must be available in RDF format. We refer the interested reader to central works~\\cite{DBLP:conf\/ecai\/UsbeckNRGCAB14, Moussallem2017, DBLP:conf\/esws\/ZwicklbauerSG16} or our Appendix.\n\\section{Related work}\n\\label{sec:related-work}\n\nWhile there are multiple recent surveys on EL, none of those are specialized in analyzing EL on Wikidata.\n\nThe extensive survey by Sevgili et al.~\\cite{DBLP:journals\/corr\/abs-2006-00575} is giving an overview of all neural approaches from 2015 to 2020. It compares 30 different approaches on nine different datasets. \nAccording to our criteria, none of the included approaches focuses on Wikidata. The survey also discusses the current state of the art of domain-independent and multi-lingual neural EL approaches. However, the influence of the underlying KG was not of concern to the authors. It is not described in detail how they found the considered approaches.\n\nIn the survey by Al-Moslmi et al.~\\cite{al2020named}, the focus lies on ER and EL approaches over KGs in general. It considers approaches from 2014 to 2019.  It gives an overview of the different approaches of ER, Entity Disambiguation, and EL. A distinction between Entity Disambiguation and EL is made, while our survey sees Entity Disambiguation as a part of EL. The roles of different domains, text types, or languages are discussed.  The authors considered 89 different approaches and tools. \nMost approaches were designed for DBpedia or Wikipedia, some for Freebase or YAGO, and some to be KG-agnostic. Again, none focused on Wikidata. $F_1$ scores were gathered on 17 different datasets.\nFifteen algorithms, for which an implementation or a WebAPI was available, were evaluated using GERBIL~\\cite{Roeder2018}.\n\nAnother survey~\\cite{oliveira2020towards} examines recent approaches, which employ holistic strategies. Holism in the context of EL is defined as the usage of domain-specific inputs and metadata, joint ER-EL approaches, and collective disambiguation methods. Thirty-six research articles were found which had any holistic aspect - none of the designed approaches linked explicitly to Wikidata.\n\nA comparison of the number of approaches and datasets included in the different surveys can be found in Table~\\ref{tab:survey_comparison}. \n\nIf we go further into the past, the existing surveys~\\cite{shen2014entity, DBLP:journals\/tacl\/LingSW15} are not considering Wikidata at all or only in a small amount as it is still a rather recent KG in comparison to the other established ones like DBpedia, Freebase or YAGO. For an overview of different KGs on the web, we refer the interested reader to the paper by Heist et al.~\\cite{DBLP:series\/ssw\/HeistHRP20}.\n\nNo found survey focused on the differences of EL over different knowledge graphs, respectively, on the particularities of EL over Wikidata. \n\\section{Survey Methodology}\nThere exist several different ways in which a survey can contribute to the research field~\\cite{Kitchenham2004}:\n\\begin{enumerate}\n    \\item \\label{cont_1} Providing an overview of current prominent areas of research in a field\n    \\item \\label{cont_2} Identification of open problems\n    \\item \\label{cont_3} Providing a novel approach tackling the extracted open problems (in combination with the identification of open problems)\n\\end{enumerate}\nWe analyse different recent and older surveys on EL and highlight specific areas which are not covered as well as our survey's novelties (see also Section~\\ref{sec:discussion}). While some very recent surveys exist~\\cite{al2020named, oliveira2020towards, DBLP:journals\/corr\/abs-2006-00575}, they do not consider the different underlying Knowledge Graphs as a significant factor affecting the performance of EL approaches. Furthermore, barely any approaches included in other surveys are working on Wikidata and take the particular characteristics of Wikidata into account (see Section~\\ref{sec:related-work}). \nOur survey fills these gaps by contributing according to \\Cref{cont_1,cont_2}.\n\n\\begin{table*}[htb!]\n    \\centering\n    \\begin{tabularx}{.78\\textwidth}{Y Y}\n        \\toprule\n        \\multicolumn{2}{c}{\\textbf{Criteria}} \\\\ \\midrule\n         \\textbf{Must satisfy all} & \\textbf{Must not satisfy any} \\\\ \n         \\midrule\n         \\begin{itemize}\n             \\item Approaches that consider the problem of unstructured EL over Knowledge Graphs \n             \\item Approaches where the target Knowledge Graph is Wikidata \n         \\end{itemize}\n         &\n         \\begin{itemize}\n             \\item Approaches conducting Semi-structured EL\n             \\item Approaches not doing EL in the English language\n         \\end{itemize} \\\\\n         \\bottomrule\n    \\end{tabularx}\n    \\caption{Qualifying and disqualifying criteria for approaches. \"Semi-structured\" in this table means that the entity mentions do not occur in natural language utterances but in more structured documents such as tables.}\n    \\label{tab:qual_disqual}\n\\end{table*}\n\n\\begin{table*}[htb!]\n    \\centering\n    \\begin{tabularx}{.78\\textwidth}{YY}\n        \\toprule\n        \\multicolumn{2}{c}{\\textbf{Criteria}} \\\\ \\midrule\n         \\textbf{Must satisfy all} & \\textbf{Must not satisfy any} \\\\ \\midrule\n         \\begin{itemize}\n             \\item Datasets that are designed for EL or are used for evaluation of Wikidata EL\n             \\item Datasets must include Wikidata identifiers from the start; an existing dataset later mapped to Wikidata is not permitted\n         \\end{itemize} &\n         \\begin{itemize}\n             \\item Datasets without English utterances\n         \\end{itemize} \\\\\n         \\bottomrule\n    \\end{tabularx}\n    \\caption{Qualifying and disqualifying criteria for the dataset search.}\n    \\label{tab:qual_disqual_datasets}\n\\end{table*}\n\nUntil December 18, 2020, we continuously searched for existing and newly released scientific work suitable for the survey.\nNote, this survey includes only scientific articles that were accessible to the authors.\\footnote{\\url{https:\/\/www.projekt-deal.de\/about-deal\/}}\n\n\\subsection{Approaches}\nOur selection of approaches stems from a search over the following search engines:\n\\begin{itemize}\n    \\item Google Scholar\n    \\item Springer Link\n    \\item Science Direct \n    \\item IEEE Xplore Digital Library\n    \\item ACM Digital Library\n\\end{itemize}\n\nTo gather a wide choice of approaches, the following steps were applied.\n\\texttt{Entity Linking}, \\texttt{Entity Disambiguation} or variations of the phrases~\\footnote{Google Scholar search query: \\texttt{(intitle:\"entity\" OR intitle:\"entities\") AND (intitle:\"link\" OR intitle:\"linking\" OR intitle:\"disambiguate\" OR entitle:\"disambiguation\") AND intext:\"Wikidata\"}} had to occur in the title of the paper. The publishing year was not a criterion due to the small number of valid papers and the relatively recent existence of Wikidata. Any approach where \\texttt{Wikidata} was not occurring once in the full text was not considered.  \nThe systematic search process resulted in exactly 150 papers and theses (including duplicates). \n\nFollowing this search, the resulting papers were filtered again using the qualifying and disqualifying criteria which can be found in Table~\\ref{tab:qual_disqual}. This resulted in 15 papers and one master thesis in the end.\n \nThe search resulted in papers in the period from 2018 to 2020. While there exist EL approaches from 2016~\\cite{spitz2016so, almeida2016streets} working on Wikidata, they did not qualify according to the criteria above. \n\n\\subsection{Datasets}\n\nThe dataset search was conducted in two ways. \nFirst, a search for potential datasets was performed via the same search engines as used for the approaches.\nSecond, all datasets occurring in the system papers were considered if they fulfilled the criteria.\nThe criteria for the inclusion of a dataset can be found in Table~\\ref{tab:qual_disqual_datasets}. \n\nWe filtered the dataset papers in the following way. First, in the title, \\texttt{Entity Linking} or \\texttt{Entity Disambiguation} or variations thereof had to occur, similar to the search for the Entity Linking approaches. Additionally, \\texttt{dataset}, \\texttt{data}, \\texttt{corpus} or \\texttt{benchmark} had to occur once in title~\\footnote{Google Scholar Search Query: \\texttt{intext:\"Wikidata\" AND (intitle:dataset OR intitle:data OR intitle:benchmark OR intitle:corpus) AND (intitle:entity OR intitle:entities) AND (intitle:link OR intitle:linking OR intitle:disambiguate OR intitle:disambiguation)}} must occur in the title and \\texttt{Wikidata} has to appear at least once in the full text. Due to those keywords, other datasets suitable for EL, but constructed for a different purpose like KG population, were not included. This resulted in 26 papers (including duplicates). Of those, only two included Wikidata identifiers and focused on English.\n\nEighteen datasets were accompanying the different approaches. Many of those did not include Wikidata identifiers from the start. This made them less optimal for the examination of the influence of Wikidata on the design of datasets. They were included in the section about the approaches but not in the section about the Wikidata datasets.\n\nAfter the removal of duplicates, 11 Wikidata datasets were included in the end.\n\n\\section{Wikidata}\n\\label{sec:wikidata}\nWikidata is a community-driven knowledge graph edited by humans and machines. \nThe Wikidata community can enrich the content of Wikidata by, for example, adding\/changing\/removing entities, statements about them, and even the underlying ontology information.\nAs of July 2020, it contained around 87 million items of structured data about various domains. Seventy-three  million items can be interpreted as entities due to the existence of an \\texttt{is instance} property. As a comparison, DBpedia contains around 5 million entities~\\cite{Tanon2020}. Note that the \\texttt{is instance} property includes a much broader scope of entities than the ones interpreted as entities for DBpedia.\nIn comparison to other similar KGs, the Wikidata dumps are updated most frequently~(\\Cref{tab:kg_statistics}). But note that this only applies to the dumps, if one considers direct access via the Website or a SPARQL endpoint, both, Wikidata~\\footnote{https:\/\/www.wikidata.org\/}\\footnote{https:\/\/query.wikidata.org} and DBpedia~\\footnote{https:\/\/www.dbpedia.org\/resources\/live\/}\\footnote{https:\/\/www.dbpedia.org\/resources\/live\/dbpedia-live-sync\/} provide continuously updated knowledge.\n\n\\begin{table*}[htb!]\n    \\centering\n    \\begin{tabular}{l c  c c}\n    \\toprule\n        \\textbf{KG}& \\textbf{\\#Entities in million} & \\textbf{\\#Labels\/Aliases in million} &\\textbf{last updated} \\\\ \\midrule\n         Wikidata   & 78 & 442 & up to 4 times a month~\\footnote{https:\/\/dumps.wikimedia.org\/wikidatawiki\/entities\/} \\\\\n         DBpedia    & 5 & 22 & monthly\\\\\n         Yago4      & 67 & 371 & November 2019\\\\\n         \\bottomrule\n    \\end{tabular}\n    \\caption{KG statistics by~\\cite{Tanon2020}.}\n    \\label{tab:kg_statistics}\n\\end{table*}\n\n\\subsection{Definition}\nWikidata is a collection of \\emph{entities} where each such entity has a page on Wikidata. An entity can be either an \\textit{item} or a \\textit{property}. Note, an entity in the sense of Wikidata is generally not the same as an entity one links to via EL. For example, Wikidata entities are also properties that describe relations between different items. Linking to such relations is closer to Relation Extraction~\\cite{Sorokin2017,Lin2017,Bastos2020}. Furthermore, many items are more abstract classes, which are usually not considered as entities linked to in EL.\nNote that if not mentioned otherwise, if we speak about entities, entities in the context of EL are meant.\n \n\\paragraph{Item.} Topics, classes, or objects are defined as items. An item is enriched with more information using statements about the item itself. In general, items consist of one label, one description, and aliases in different languages. An unique and language-agnostic identifier identifies items in the form \\texttt{Q[0-9]+}. An example of an item can be found in Figure~\\ref{fig:item_example}.\n\nFor example, the item with the identifier \\texttt{Q23848} has the label \\texttt{Ennio~Morricone}, two aliases, \\texttt{Dan Savio} and \\texttt{Leo Nichols}, and \\texttt{Italian composer, orchestrator and conductor \\\\ (1928-2020)} as description at the point of writing. The corresponding Wikidata page can also be seen in Figure~\\ref{fig:item_example}. \n\\begin{figure}[hb!]\n    \\includegraphics[width=\\linewidth]{Images\/WD_Ennio.png}\n    \\caption{Example of an item in Wikidata.}\n    \\label{fig:item_example}\n\\end{figure}\n\n\\paragraph{Property.} A property specifies a relation between items or literals. Each property also has an identifier similar to an item, specified by \\texttt{P[0-9]+}.  For instance, a property \\texttt{P19} specifies the place of birth \\texttt{Rome} for \\texttt{Ennio~Morricone}. In NLP, the term \\texttt{relation} is commonly used to refer to a connection between entities.  A property in the sense of Wikidata is a type of relation. To not break with the terminology used in the examined papers, when we talk about relations, we always mean Wikidata properties if not mentioned otherwise. \n\n\\paragraph{Statement.} A statement introduces information by giving structure to the data in the graph. It is specified by a \\emph{claim}, and \\emph{references}, \\emph{qualifiers} and \\emph{ranks} related to the claim. Statements are assigned to items in Wikidata.\nA claim is defined as a pair of property and some value. A value can be another item or some literal. Multiple values are possible for a property. Even an \\texttt{unknown value} and a \\texttt{no value} exists. \n\n\\emph{References} point to sources making the claims inside the statements verifiable. In general, they consist of the source and date of retrieval of the claim. \n\n\\emph{Qualifiers} define the value of a claim further by contextual information. For example, a qualifier could specify for how long one person was the spouse of another person. Qualifiers enable Wikidata to be hyper-relational (see \\Cref{par:hyper}). Structures similar to qualifiers also exist in some other knowledge graphs, such as the inactive Freebase in the form of Compound Value Types~\\cite{DBLP:conf\/sigmod\/BollackerEPST08}. \n\n\\emph{Ranks} are used if multiple values are valid in a statement. If the population of a country is specified in a statement, it might also be useful to have the populations of past years available. The most up-to-date population information usually has then the highest rank and is thus usually the most desirable claim to use. \n\nStatements can be also seen in Figure~\\ref{fig:item_example} at the bottom. For example, it is defined that \\texttt{Ennio~Morricone} is an \\texttt{instance of} the class \\texttt{human}. This is also an example for the different types of items. While \\texttt{Ennio~Morricone} is an entity in our sense, \\texttt{human} is a class. \n\n\\begin{figure*}[htb!]\n    \\begin{subfigure}{0.45\\linewidth}\n    \\centering\n    \\includegraphics[width= \\linewidth]{Images\/items_wikidata.pdf}\n    \\caption{Number of items of Wikidata since launch~\\cite{Manske2020}.}\n    \\label{fig:wikidata_items}\n    \\end{subfigure}\\qquad\n    \\begin{subfigure}{0.45\\linewidth}\n      \\centering\n      \\includegraphics[width=\\linewidth]{Images\/labels_per_item.pdf}  \n      \\caption{Average number of labels (+ aliases) per item~\\cite{Manske2020}.}\n      \\label{fig:sub_item_labels}\n    \\end{subfigure}\n    \n    \\begin{subfigure}{0.45\\linewidth}\n      \\centering\n      \\includegraphics[width=\\linewidth]{Images\/percentage_items_without_aliases.pdf}  \n      \\caption{Percentage of items without any aliases~\\cite{Manske2020}.}\n      \\label{fig:item_labels_no_aliases}\n    \\end{subfigure}\\qquad\n    \\begin{subfigure}{0.45\\linewidth}\n    \\centering\n    \\includegraphics[width= \\linewidth]{Images\/percentage_items_without_description.pdf}\n    \\caption{Percentage of items without a description~\\cite{Manske2020}.}\n    \\label{fig:wikidata_descriptions}\n     \\end{subfigure}\n    \\caption{Statistics on Wikidata based on~\\cite{Manske2020}.}\n\\end{figure*}\n\n\\paragraph{Other structural elements.}\nThe aforementioned elements are essential for Wikidata, but more do exist. For example, there are entities (in the sense of Wikidata) corresponding to Lexemes, Forms, Senses or Schemas. Lexemes, Forms and Senses are concerned with lexicographical information, hence words, phrases and sentences themselves. This is in contrast to Wikidata items and properties, which are directly concerned with things, concepts and ideas. Schemas formally subscribe to subsets of Wikidata entities. For example, any Wikidata item which has \\texttt{actor} as its \\texttt{occupation} is an \\texttt{instance of} the class \\texttt{human}. Both, lexicographical and schema information, are usually not directly of relevance for EL. Therefore, we refrain from introducing them in more detail.\n\nFor more information on Wikidata, see the paper by Denny Vrande{\\v{c}}i{\\'c} and Markus Kr{\\\"{o}}tzsch~\\cite{DBLP:journals\/cacm\/VrandecicK14}.\n\n\\paragraph{Differences in structure to other knowledge graphs}\nDBpedia extracts its information from Wikipedia and Wikidata. It maps the information to its own ontology.\nDBpedia's statements consist of only single triples (\\texttt{<subject, predicate, object>}) since it follows the RDF specification~\\cite{DBLP:journals\/semweb\/LehmannIJJKMHMK15}. Additional information like qualifiers, references or ranks do not exist. But it can be modeled via additional triples. As it is no inherent feature of DBpedia, it is harder to use as there a no strict conventions. Entities in DBpedia have human-readable identifiers, and there exist entities per language~\\cite{DBLP:journals\/semweb\/LehmannIJJKMHMK15} with partly differing information. Hence, for a single concept or thing, multiple DBpedia entities might exist. For example, the English entity of the city Munich\\footnote{https:\/\/dbpedia.org\/page\/Munich} has 25 entities as \\texttt{dbo:administrativeDistrict} assigned. The German entity\\footnote{http:\/\/de.dbpedia.org\/page\/M\u00fcnchen} only a single one. It seems that this originates from a different interpretation of the predicate \\texttt{dbo:administrativeDistrict}. \n\nYago4 extracts all its knowledge from Wikidata but filters out information it deems inadequate. For example, if a property is used too seldom, it is removed. If a Wikidata entity does not have a class that exists in Schema.org\\footnote{https:\/\/schema.org}, it is removed. The RDF specification format is used. Qualifier information is included indirectly via separate triples. Rank information and references of statements do not exist. The identifiers follow either a human-readable form if available via Wikipedia or Wikidata or use the Wikidata QID. However, in contrast to DBpedia, only one entity exists per thing or concept~\\cite{Tanon2020}.\n\nFor a thorough comparison of Wikidata and other KGs (in respect to Linked Data Quality~\\cite{zaveri2016quality}), please refer to the paper by F\u00e4rber et al.~\\cite{DBLP:journals\/semweb\/FarberBMR18}.\n\\subsection{Discussion}\n\\paragraph{Novelties.} A useful characteristic of Wikidata is that the community can openly edit it. Another novelty is that there can be a plurality of facts, as contradictory facts based on different sources are allowed. Similarly, time-sensitive data can also be included by qualifiers and ranks. The population of a country, for example, changes from year to year, which can be represented easily in Wikidata. Lastly, due to their language-agnostic identifiers, Wikidata is inherently multilingual. Language only starts playing a role in the labels and descriptions of an item.\n\n\\paragraph{Strengths.} Due to the inclusion of information by the community, recent events will likely be included. The knowledge graph is thus much more up-to-date than most other KGs. Freebase is unsupported for years now, and DBpedia updates its dumps only every month. Note, the novel DBpedia live 2.0\\footnote{\\url{https:\/\/forum.dbpedia.org\/t\/differences-in-results-on-dbpedia-live-and-http-dbpedia-org-sparql-endpoint\/888\/2}} is updated when changes to a Wikipedia page occur, but, as discussed, makes research harder to replicate. Thus, Wikidata is much more suitable and useful for industry applications such as smart assistants since it is the most complete open-accessible data source to date. In Figure~\\ref{fig:wikidata_items}, one can see that number of items in Wikidata is increasing steadily. The existence of labels and additional aliases (see Figure~\\ref{fig:sub_item_labels}) helps EL as a too-small number of possible surface forms often lead to a failure in the candidate generation. DBpedia does, for example, not include aliases, only a single exact label~\\footnote{There exist some predicates (e.g., \\texttt{foaf:name},  \n\\texttt{dbp:commonName} or \\texttt{dbp:conventionalLongName}) that might point to aliases but they are often either not used or specify already stated aliases.}; to compensate, additional resources like Wikipedia are often used to extract a label dictionary of adequate size~\\cite{Moussallem2017}. Even each property in Wikidata has a label~\\cite{DBLP:journals\/cacm\/VrandecicK14}. Fully language model-based approaches are therefore more naturally usable~\\cite{mulang2020encoding}.\nAlso, nearly all items have a description, see Figure~\\ref{fig:wikidata_descriptions}. This short natural language phrase can be used for context similarity measures with the utterance. \nThe inherent multilingual structure is intuitively useful for multilingual Entity Linking. \nTable~\\ref{tab:statistics_languages} shows information about the use of different languages in Wikidata. As can be seen, item labels\/aliases are available in up to 457 languages. But not all items have labels in all languages. On average, labels, aliases and descriptions are available in 29.04 different languages. However, the median is only 6 languages. Many entities will, therefore, certainly not have information in many languages. The most dominant language is English, but not all elements have label\/alias\/description information in English. For less dominant languages, this is even more severe. German labels exist, for example, only for 14 \\%, and Samoan labels for 0.3 \\%. \nContext information in the form of descriptions is also given in multiple languages. Still, many languages are again not covered for each entity (as can be seen by a median of only 4 descriptions per element). \nWhile the multilingual label and description information of items might be useful for language model-based variants, the same information for properties enables multilingual language models. Because, on average, 21.18 different languages are available per property for labels, one could train multilingual models on the concatenations of the labels of triples to include context information. But of course, there are again many properties with a lower number of languages, as the median is also only 6 languages. Cross-lingual EL is therefore certainly necessary to use language model-based EL in multiple languages.\n\n\\begin{table*}[htb!]\n    \\centering\n    \\begin{tabularx}{\\linewidth}{p{10cm}XX}\n         \\toprule\n         & \\textbf{Items} & \\textbf{Properties} \\\\\n         \\midrule\n         \\textbf{Number of languages} & 457 & 427\\\\\n         \\textbf{(average, median) of \\# languages per element (labels +  descriptions)}&29.04, 6 &21.24, 13 \\\\\n         \\textbf{(average, median) of \\# languages per element (labels)}&5.59 , 4 &21.18, 6 \\\\\n         \\textbf{(average, median) of \\# languages per element (descriptions)}&26.10, 4&9.77, 6 \\\\\n         \\textbf{\\% elements without English labels}&15.41\\% & 0\\% \\\\\n         \\textbf{\\% elements without English descriptions}&26.23\\%&1.08\\% \\\\\n         \\bottomrule\n    \\end{tabularx}\n    \\caption{Statistics - Languages Wikidata (Extracted from dump~\\cite{Foundation2020a}).}\n    \\label{tab:statistics_languages}\n\\end{table*}\nBy using the qualifiers of hyper-relational statements, more detailed information is available, useful not only for Entity Linking but also for other problems like Question Answering. The inclusion of hyper-relational statements is also more challenging. Novel graph embeddings have to be developed and utilized, which can represent the structure of a claim enriched with qualifiers~\\cite{DBLP:conf\/www\/RossoYC20, Galkin2020}.  \n\nRanks are of use for EL in the following way. Imagine a person had multiple spouses throughout his\/her life. In Wikidata, all those relationships are assigned to the person via statements of different ranks. If now an utterance is encountered containing information on the person and her\/his spouse, one can utilize the Wikidata statements for comparison. Depending on the time point of the utterance, different statements apply. One could, for example, weigh the relevance of statements according to their rank. If now a KG (for example Yago4~\\cite{Tanon2020}) includes only the most valid statement, the current spouse, utterances containing past spouses are harder to link. \n\nFor references, up to now, no found approach did utilize them for EL. One use case might be to filter statements by reference if one knows the source's credibility, but this is more a measure to cope with the uncertainty of statements in Wikidata and not directly related to EL.\n\n\\begin{table*}[htb!]\n    \\centering\n        \\begin{tabular}{lccccc}\n              \\toprule\n        \\textbf{\\# Labels\/aliases}& \\num{70124438} & \\num{2041651} & \\num{828471} & \\num{89210} & \\num{3329} \\\\\n         \\textbf{\\# Items per label\/alias}&$1$ & $2$  & $3-10$ & $11 - 100$ & $< 100$ \\\\ \n             \\bottomrule\n        \\end{tabular}\n    \\caption{Number of English labels\/aliases pointing to a certain number of items in Wikidata (Extracted from dump~\\cite{Foundation2020a}).}\n    \\label{tab:mention_items}\n\\end{table*}\n\n\\paragraph{Weaknesses.} However, this community-driven approach also introduces challenges. For example, the list of labels of an item will not be exhaustive, as shown in Figures~\\ref{fig:sub_item_labels} and ~\\ref{fig:item_labels_no_aliases}. The graphs consider labels and aliases of all languages. While the median of labels and aliases is around 4 per element, not all are useful for Entity Linking. \\texttt{Ennio Morricone} does not have an alias solely consisting of \\texttt{Ennio} while he will certainly sometimes be referenced by that. Thus, one can not rely on the exact labels alone. But interestingly, Wikidata has properties for the fore- and surname alone, just not as a label or alias. A close examination of what information to use is essential. \n\nThis is also a problem in other KGs.  Also, Wikidata often has items with very long, noisy, error-prone labels, which can be a challenge to link to~\\cite{mulang2020encoding}. Nearly 20 percent of labels have a length larger than 100 letters, see Figure~\\ref{fig:wikidata_label_lengths}. Due to the community-driven approach, false statements also occur due to errors or vandalism~\\cite{Heindorf2016}.\n\n\\begin{figure}[htb!]\n    \\centering\n    \\includegraphics[width=\\linewidth]{Images\/wikidata_length_percentiles.pdf}\n    \\caption{Percentiles of English label lengths (Extracted from dump~\\cite{Foundation2020a}).}\n    \\label{fig:wikidata_label_lengths}\n\\end{figure}\nAnother problem is that entities lack of facts (here defined as statements not being labels, descriptions, or aliases). According to Tanon et al.~\\cite{Tanon2020}, in March 2020, DBpedia had, on average, $26$ facts per entity while Wikidata had only $12.5$. This is still more than YAGO4 with $5.1$. \nTo tackle such long-tail entities, different approaches are necessary.\nThe lack of descriptions can also be a problem. Currently, around 10\\% of all items do not have a description, as shown in Figure~\\ref{fig:wikidata_descriptions}. Luckily, the situation is increasingly improving. \n\nA general problem of Entity Linking is that a label or alias can reference multiple entities, see Table~\\ref{tab:mention_items}. While around 70 million mentions point each to a unique item, 2.9 million do not. Not all of those are entities by our definition but, e.g., also classes or topics. In addition, longer labels or aliases often correspond to non-entity items. Thus, the percentage of entities with overlapping labels or aliases is certainly larger than for all items. To use Wikidata as a Knowledge Graph, one needs to be cautious of the items one will include as entities. For example, there exist \\texttt{Wikimedia disambiguation page} items that often have the same label as an entity in the classic sense. Both \\texttt{Q76} and \\texttt{Q61909968} have \\texttt{Barack Obama} as the label. Including those will make disambiguation more difficult.\nAlso, the possibility of contradictory facts will make EL over Wikidata harder. \n\nIn Wikification, also known as EL on Wikipedia, large text documents for each entity exist in the knowledge graph, enabling text-heavy methods~\\cite{Wu2019}. Such large textual contexts (besides the descriptions and the labels of triples itself) do not exist in Wikidata, requiring other methods or the inclusion of Wikipedia. However, as Wikidata is closely related to Wikipedia, an inclusion is easily doable. Every Wikipedia article is connected to a Wikidata item. The Wikipedia article belonging to a Wikidata item can be, for example, extracted via a SPARQL~\\footnote{https:\/\/www.w3.org\/TR\/rdf-sparql-query\/} query to the Wikidata Query Service~\\footnote{https:\/\/query.wikidata.org} using the \\texttt{http:\/\/schema.org\/about} predicate. The Wikidata item of a Wikipedia article can be simply found on the article page itself or by using the Wikipedia API~\\footnote{https:\/\/en.wikipedia.org\/w\/api.php}. \n\nOne can conclude that the characteristics of Wikidata, like being up to date, multilingual and hyper-relational, introduce new possibilities. At the same time, the existence of long-tail entities, noise or contradictory facts poses a challenge.\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\nThe rapid development of experimental techniques in cold-atom systems\\cite{Bloch_2005, giorgini_theory_2008, Strinati_2018} gave rise to a revival of interest in unconventional fermionic superfluids exhibiting pairing at finite center of mass momentum, the so called Fulde-Ferrell-Larkin-Ovchinnikov states.\\cite{fulde_superconductivity_1964, larkin_nonuniform_1965, Agterberg_2020} Such phases were since long discussed in solid-state physics contexts, but more recently were also predicted to arise in Fermi mixtures of ultracold atoms involving a population (and\/or mass) imbalance between the two particle species forming the Cooper pairs. Due to the high level of controllability, this class of systems constitutes an interesting and promising platform for exploiting exotic superfluid phases including those of the FFLO type. \n\n In a cold, two-component Fermi mixture increasing the concentration imbalance may serve to gradually mismatch the Fermi surfaces of the two atomic species, which suppresses pairing and ultimately drives the system to the normal, polarized metallic phase. The modulated FFLO-type superfluid was predicted to occur as an intermediate phase constituting an energetic compromise between the uniform, BCS-type superfluid and the polarized Fermi liquid. Extensive studies spread over years (see e.g. Refs. \\onlinecite{He_2006,   Gubbels_2009, Baarsma_2010, radzihovsky_imbalanced_2010, Cai_2011, Baarsma_2013, Rosher_2015, Karmakar_2016, Kinnunen_2018, Pini_2021_2, Rammelmuller_2021}) addressed the energetic aspects of the problem, in particular the competition between the different candidate modulated ground states. The emergent consensus is that (at mean field level) a superfluid pair-density-wave (FFLO) phase is rather robustly stable, albeit in a relatively narrow region of the phase diagram. \n\nSomewhat surprisingly, fluctuation effects occurring in the FFLO phases were addressed much less comprehensively and rather coherently pointed towards instability of these long-range-ordered pair-density-wave states to thermal order-parameter fluctuations.\\cite{Shimahara_1998, Samokhin_2010, Radzihovsky_2009, Radzihovsky_2011, Yin_2014, Jakubczyk_2017, Wang_2018} The mechanism destabilizing the FFLO states is  somewhat akin to that prohibiting the long-range order in  $XY$ or Heisenberg ferromagnets in dimensionality $d\\leq 2$. However, in contrast to the conventional  magnets, the FFLO phases involve not only rotational (superfluid) symmetry breaking, but also breaking of translational symmetry, leading to a significantly softer Goldstone fluctuation spectrum in the (putative) ordered phases. In consequence, the possibilities of realizing such symmetry-breaking states at $T>0$ is severely restricted also in $d=3$.  \n\nThe previous studies of Refs. \\onlinecite{Shimahara_1998, Samokhin_2010, Radzihovsky_2009, Radzihovsky_2011, Yin_2014, Jakubczyk_2017, Wang_2018} departed from a (putative) FFLO type state and investigated the low-energy fluctuations around it. In other words, they addressed the question of stability of the modulated phase without recourse to global features of the phase diagram. \nIn contrast, our present approach implements a different logical line  invoking the properties of the mean-field (MF) phase diagram, which, by necessity involves the presence of both uniform and nonuniform phases leading to the emergence of  a thermal Lifshitz point where the normal (Fermi liquid like), the modulated (FFLO), and the uniform superfluid (BCS-like) phases all coexist. We point out that the stability conditions for the Lifshitz point at $T>0$ to fluctuations are significantly stronger as compared to those of the FFLO phase alone. For the isotropic systems we demonstrate the instability of the Lifshitz point to order-parameter fluctuations in $T>0$ at any dimensionality $d<4$, which should in consequence lead to a complete suppression of the pair-density wave phase at any $T>0$. \nOur conclusion is therefore stronger than those reached in the previous studies. Moreover, our reasoning does not require any detailed knowledge concerning the FFLO-type state and the associated excitation spectrum above it. We argue on the other hand that the FFLO-type states of the uniaxial type, such as coupled arrays of atomic tubes considered e.g. in Refs.~\\onlinecite{Lutchyn_2011, Revelle_2016, Sundar_2020} are stable in dimensionality $d=3$ (but not in $d=2$) and present themselves as plausible candidates for hosting the FFLO phases. \n\nWe also point out that the situation at $T=0$ is entirely different.\nWe predict that the FFLO state may well be a stable ground state in a range of values of the imbalance parameters, squashed (at $T=0$) between the BCS-type superfluid and normal metallic phases.  The emergent structure of the phase diagram at $T\\geq 0$ implies the generic existence of a point located at $T=0$, where the three phases meet (i.e. the quantum Lifshitz point). Notably, such a quantum Lifshitz point\\cite{Zdybel_2020} should occur as a fluctuation-driven entity without any need for fine-tuning of the system parameters.      \n\nThe outline of this paper is as follows:  In Sec.~II we summarize the standard model to describe Fermi mixtures with population\/mass imbalance (applicable in both the solid-state and cold-atom contexts) and give an overview of the features of the corresponding mean-field phase diagram. We in particular point out the generic occurrence of a thermal Lifshitz point located at a temperature $T_L>0$. We subsequently elucidate the structure of the effective action to describe the system in the vicinity of the Lifshitz point. In Sec.~III we discuss the stability of the Lifshitz point to order parameter fluctuations at Gaussian level depending on the system dimensionality $d$ and the anisotropy index $m$. In Sec.~IV we provide an estimate of the Lifshitz critical exponents from a truncation of functional renormalization group for general $d$, $m$ and number of order parameter components $N$. We in particular confirm the picture derived in Sec.~III and point out that the anomalous dimension associated with a class of spatial directions is negative. We summarize the paper in Sec.~V.                   \n\n\\section{Summary of the model and mean-field results}\nThe common point of departure for theoretical studies of imbalanced Fermi mixtures (applicable also to electronic systems) is provided by the grand canonical Hamiltonian \n\\begin{equation} \n\\mathcal{H} = \\sum_{\\vec{k}, \\sigma} \\xi_{\\vec{k}, \\sigma} c^\\dagger_{\\vec{k}, \\sigma} c_{\\vec{k}, \\sigma} + \\frac{g}{V}\\sum_{\\vec{k}, \\vec{k}', \\vec{q}} c^\\dagger_{\\vec{k}+\\frac{\\vec{q}}{2}, \\uparrow} c^\\dagger_{-\\vec{k}+\\frac{\\vec{q}}{2}, \\downarrow} c_{\\vec{k}'+\\frac{\\vec{q}}{2}, \\downarrow} c_{-\\vec{k}'+\\frac{\\vec{q}}{2}, \\uparrow} \n\\label{Ham}\n\\end{equation} \ninvolving the kinetic energy term with species-dependent dispersion relation and chemical potential \n\\begin{equation} \n\\xi_{\\vec{k}, \\sigma} =\\epsilon_{\\vec{k}, \\sigma}-\\mu_\\sigma \n\\end{equation} \n as well as  an attractive two-body interaction potential  driving $s$-waver pairing. For convenience the latter is taken in the form of a point-like interaction with $g<0$.  For the isotropic cold-atomic gases the dispersion reads $\\epsilon_{\\vec{k}, \\sigma}=\\frac{\\vec{k}^2}{2 \\mathcal{M}_\\sigma}$, where the masses $\\mathcal{M}_\\sigma$ of the two fermionic species may in general be different. As we argue below, anisotropic kinetic terms allow for stabilizing the FFLO phases. This conclusion actually seems in line with experimental findings, since the most convincing evidence for FFLO-like features was reported for highly anisotropic situations both in the solid state\\cite{Uji_2012, Uji_2013, Tsuchiya_2015, Koutroulakis_2016, Cho_2021} and ultracold gases contexts. We therefore do not restrict to any specific form of the dispersion. We nonetheless have in mind the setup, where $\\tilde{m}$ out of the $d$ spatial directions are distinct from the remaining $d-\\tilde{m}$.\n As an experimentally relevant case one may, for example, invoke the following dispersion\n \\begin{equation} \n \\epsilon_{\\vec{k},\\sigma}=    \\sum_{i=1}^{\\tilde{m}}  \\frac{{k_i}^2}{2 \\mathcal{M}_\\sigma}  - 2 t_\\perp \\sum_{i=\\tilde{m}+1}^d \\cos k_i\\;. \n\n \\label{Anizo_disp}\n \\end{equation}      \nIn particular, for $d=2$ and $\\tilde{m}=1$ this dispersion\nwas implemented to describe coupled atomic tubes\\cite{Lutchyn_2011} in the cold-atom context as well as specific organic superconductors.\\cite{Mayaffre_2014, Piazza_2016} Note that the corresponding Fermi surfaces exhibit a considerable degree of nesting, favoring finite-momentum pairing. Clearly, for $\\tilde{m}=d$ we recover from Eq.~(\\ref{Anizo_disp}) the standard continuum gas, while $\\tilde{m}=0$ yields the hipercubic lattice dispersion. One virtue of the parametrization is that both $d$ and $\\tilde{m}$ ($\\tilde{m}\\leq d$) may formally be treated as real parameters, providing a way of continuously interpolating between different physically relevant cases (e.g. $\\tilde{m}=0$ and $\\tilde{m}=1$), see Sec.~III and IV.   \n\\begin{figure}[ht] \n\\begin{center}\n\\includegraphics[width=9cm]{Phase_diag}\n\\caption{(Color online) Left panel: schematic mean-field phase diagram of a system described by the Hamiltonian of Eq.~(\\ref{Ham}). Increasing the imbalance parameter $h=(\\mu_\\uparrow -\\mu_\\downarrow)\/2$ suppresses pairing. The pair density wave (FFLO)  phase is energetically favored in a (typically tiny) region between the uniform superfluid (BCS) and Fermi-liquid (FL) states. The Lifshitz point where these three phases coexist, is inevitably present at $T>0$ and constitutes the bottleneck for stability of the phase diagram with respect to fluctuations. Right panel: The anticipated renormalized phase diagram of an isotropic system, where the FFLO phase survives only at $T=0$ and a quantum Lifshitz point occurs (see the main text). }\n\\label{Phase_diag}\n\\end{center} \n\\end{figure} \n\\subsection{Pairing susceptibility}\nWe will now approach the pairing instability from the symmetric (Fermi-liquid) phase (compare Fig.~1) corresponding to sufficiently large imbalance parameter $h=(\\mu_\\uparrow - \\mu_\\downarrow)\/2$ and\/or temperature $T$. \nThe effective (Landau-Ginzburg) order-parameter action for the model given by Eq.~(\\ref{Ham}) can be constructed by a standard procedure described in literature (see e.g. Refs.~\\onlinecite{Strack_2014, Piazza_2016, Zdybel_2018, Zdybel_2019}) analogous to the one developed long ago for magnetic transitions.\\cite{Nagaosa_book} Up to terms quadratic in the pairing field $\\phi$, the effective action reads\n\\begin{equation}\n\\mathcal{S}_{eff}^{(2)} = \\sum_{\\vec{q}, i\\omega_n} \\phi^*_{\\vec{q}, i\\omega_n} \\left[ -1\/g - \\chi_0 (\\vec{q}, i\\omega_n) \\right] \\phi_{\\vec{q}, i\\omega_n}\\;. \n\\label{action}\n\\end{equation} \nHere $\\phi_{\\vec{q}, i\\omega_n}$ is the (scalar) complex $s$-wave pairing field written in the momentum-frequency representation, while $\\chi_0 (\\vec{q}, i\\omega_n)$ involves the particle-particle bubble and may be expressed as\n\\begin{equation}\n\\chi_0 (\\vec{q}, i\\omega_n) = T\\int_{\\vec{k}}\\frac{1-f\\left(\\xi_{\\vec{k}, \\downarrow}\\right)-f\\left(\\xi_{\\vec{k}+\\vec{q}, \\uparrow}\\right)}{\\xi_{\\vec{k}+\\vec{q}, \\uparrow}+\\xi_{\\vec{k}, \\downarrow}-i\\omega_n}\\;,\n\\end{equation}\nwhere  $f(X)=(e^{X\/T}+1)^{-1}$ is the Fermi-Dirac distribution and $\\int_{\\vec{k}}=\\int\\frac{d\\vec{k}}{(2\\pi)^d}$.\n\n At mean-field level an instability towards superfluidity occurs once the Landau coefficient $a_2 =\\left[ -1\/g - \\chi_0 (\\vec{q}, 0) \\right] $ in Eq.~(\\ref{action}) becomes negative for some value of $\\vec{q}$ (hereafter denoted as $\\vec{Q}$). A nonzero ordering wavevector $\\vec{Q}$ marks an FFLO-type instability. Note that $\\chi_0 (\\vec{q}, i\\omega_n)$ involves no dependence on $g$. In consequence, once a set of parameters for which $\\chi_0 (\\vec{q}, 0)$ features a maximum at $\\vec{q} = \\vec{Q}\\neq 0$  is identified, the (mean-field) transition between the normal and FFLO phases can be conveniently tuned by modifying $g$ alone.\n\\begin{figure}[ht] \n\\begin{center}\n\\includegraphics[width=9cm]{chi_0_anizot_gray.png}\n\\caption{Evolution of the pairing susceptibility $\\chi_0 (\\vec{q}, 0)$ upon varying $h$ for the dispersion given by Eq.~(\\ref{Anizo_disp}) and $(d,\\tilde{m})=(2,1)$. The sharp peak located for $h=0$ at $\\vec{q}=(0,0)$ broadens and for $h=h_c\\approx 0.03$ continuously splits. At $h=h_c$ and $q$ small, the  pairing field propagator is quadratic in momentum in the $q_y$ direction, but quartic along $q_x$. The degenerate maxima of $\\chi_0 (\\vec{q}, 0)$ are located at the $q_x$ axis and remain well separated from zero for $h>h_c$. For a projection on the $q_x$ axis, compare Fig.~\\ref{chi_projection}. The plot parameters are $t_\\perp=\\frac{1}{2}$, $\\mu_\\uparrow+\\mu_\\downarrow=6.6$, $\\mathcal{M}_\\downarrow\/\\mathcal{M}_{\\uparrow}=1.0$, $T=10^{-2}$.}\n\\label{chi}\n\\end{center} \n\\end{figure} \n\\begin{figure}[ht] \n\\begin{center}\n\\includegraphics[width=9cm]{chi_0_anizot_rzut.png}\n\\caption{Projection of the pairing susceptibility $\\chi_0 (\\vec{q}, 0)$ plotted in Fig.~\\ref{chi} on $\\vec{q}=(q_x,0)$.  }\n\\label{chi_projection}\n\\end{center} \n\\end{figure} \n\\begin{figure}[ht] \n\\begin{center}\n\\includegraphics[width=9cm]{chi_0_uniform_r403_gray_v2.png}\n\\caption{Evolution of the pairing susceptibility $\\chi_0 (\\vec{q}, 0)$ upon varying $h$ for the dispersion given by Eq.~(\\ref{Anizo_disp}) and $(d,\\tilde{m})=(3,0)$ [i.e. for an isotropic continuum system of atomic particles]. The sharp peak located for $h$ sufficiently small at $\\vec{q}=(0,0)$ broadens upon increasing $h$ and for $h=h_c\\approx 0.62$ becomes degenerate on a two-dimensional sphere. At $h=h_c$ the pairing field propagator is quartic in momentum $\\vec{q}$. We put $q_z=0$ in the plot.  A projection on the $q_x$ (or any other) axis, yields a picture qualitatively equivalent to the one presented in Fig.~\\ref{chi_projection} for the anisotropic situation. The plot parameters are: $\\mu_{\\downarrow} +\\mu_{\\uparrow}=1$, $\\mathcal{M}_{\\downarrow}\/\\mathcal{M}_{\\uparrow}=4.03$, $T=10^{-3}$ and were chosen to mimic the experimentally relevant $^{161}Dy$-$^{40}K$ mixture.\\cite{Ravensbergen_2020}  }\n\\label{chi_iso}\n\\end{center} \n\\end{figure} \n The point $(\\vec{Q}, 0)$ serves as a reference for the momentum\/frequency expansion of the vertex functions in the Landau-Ginzburg action. In particular, the order parameter mass is given by \n\\begin{equation} \nr = [-1\/g -\\chi_0(\\vec{Q}, 0)]\\;. \n\\end{equation}\nAs already remarked, $\\chi_0 (\\vec{q}, 0)$ does not depend on $g$, which may therefore always be adjusted to obtain $r=0$. In Figs.~\\ref{chi} and \\ref{chi_iso} we plot $\\chi_0 (\\vec{q}, 0)$ for two situations corresponding to the uniaxial and isotropic cases. By varying $h$ or $T$ the position of the maximum (i.e. the ordering wavevector $\\vec{Q}$) may be continuously shifted towards zero, where the superfluid phase becomes uniform [see Fig.~(\\ref{Phase_diag})]. For clarity, in Fig.~\\ref{chi_projection} we also expose the projection of $\\chi_0 (\\vec{q}, 0)$ plotted in Fig.~\\ref{chi} on the $q_x$ axis.\n\nIn addition to the quadratic term given by Eq.~(\\ref{action}) the effective action $\\mathcal{S}_{eff}[\\phi]$ involves order parameter self-interaction terms of order higher than two in the field $\\phi$. \n\nConsider now the structure of the effective action approaching the Lifshitz point along the superfluid phase transition line (given by $r=0$) from above (compare Fig.~1). Upon crossing the Lifshitz point the ordering wavevector $\\vec{Q}$ is continuously shifted away from zero and becomes degenerate. The degeneracy level is determined by the symmetry of the Fermi surface. For the isotropic case (see Fig.~\\ref{chi_iso}) $\\vec{Q}$ picks up any direction in the $(d-1)$-dimensional space. In the immediate vicinity of the Lifshitz point one may expand $\\chi_0$ in momentum $\\vec{q}$ around zero (retaining  terms up to quartic order). Right at the Lifshitz point the coefficients of at least some of the $q^2$ terms vanish and become negative below the Lifshitz point. Stability of the system is then retained due to the terms quartic in momentum. \n\n\n\n\\section{The Lifshitz point stability}\nWe now analyze the structure of the effective action for the order parameter $\\phi$. \nFrom the expansion described above in Sec.~II A we obtain at the Lifshitz point an effective Landau-Ginzburg action which, when expressed in position representation, reads: \n\\begin{equation} \n\\mathcal{S}_{eff} =\\int d^d x \\left[U(|\\phi|^2) +\\frac{1}{2}Z_\\perp \\left(\\nabla_\\perp\\phi\\right)^2 +\\frac{1}{2} Z_{||} \\left(\\Delta_{||} \\phi\\right)^2  \\right]\\;, \n\\label{Seff}\n\\end{equation} \nwhere $U(|\\phi|^2)$ denotes the effective potential, which may be expanded to yield a polynomial in $|\\phi|^2$\n\\begin{equation} \nU(|\\phi|^2) = r |\\phi|^2 + u |\\phi|^4 +\\dots \\,.\n\\end{equation}\nThe $\\sim|\\phi|^2$ term coefficient, resulting from Eq~(\\ref{action})  vanishes at the entire phase transition line, including the Lifshitz point. The coefficients of the higher-order terms of $U(|\\phi|^2)$ may be expressed by the fermionic loops evaluated at external momenta $\\vec{q}=0$. The energy cost of creating order-parameter nonuniformities is governed by the laplacian terms in $m$ spatial directions and gradient terms in the remaining $d-m$ directions. Explicitly:  \n\\begin{equation}\n \\left(\\Delta_{||} \\phi\\right)^2 = \\sum_{i=1}^2\\sum_{\\alpha,\\,\\beta =1}^m  \\frac{\\partial^2 \\phi_i}{\\partial x_\\alpha \\partial x_\\beta}\\frac{\\partial^2 \\phi_i}{\\partial x_\\alpha\\partial x_\\beta}\n\\end{equation} \nand\n \\begin{equation}\n\\left(\\nabla_\\perp\\phi\\right)^2 = \\sum_{i=1}^2\\sum_{\\alpha =m+1}^d \\frac{\\partial \\phi_i}{\\partial x_\\alpha}\\frac{\\partial \\phi_i}{\\partial x_\\alpha}\\;,\n\\end{equation}\nwhere the $i$ summation runs over the two  components of the pairing field $\\phi$. For symmetry reasons the number $m$ of 'soft' directions in the action of Eq.~(\\ref{Seff}) must either coincide with the anisotropy index $\\tilde{m}$ of Eq.~\\ref{Anizo_disp} or be equal $d-\\tilde{m}$. \nSince, for the time being, we are interested in the thermal phase transition, we dropped the contributions from quantum fluctuations in Eq.~(\\ref{Seff}).\nIn the above form $\\mathcal{S}_{eff}$ accounts for a generic anisotropic situation, where the dispersion is quartic in $m$ ($m\\leq d$) spatial directions and quadratic in the remaining ones (compare Sec.~II A). The isotropic case  corresponds to $m=d$. The above effective action describes the $m$-axial Lifshitz point, analogous to those studied previously in the contexts of anisotropic magnets \n\\cite{Grest_1978, Selke_1988, Diehl_2002, Butera_2008} and liquid crystals.\\cite{Chaikin_book, Singh_2000} One may now adopt the standard Gaussian level arguments \\cite{Goldenfeld_book} to argue for the instability of the Lifshitz point with respect to order parameter fluctuations at sufficiently low dimensionality. Considering that the (putative) homogeneous ordered phase supports a massless transverse mode, from the structure of the effective action of Eq.~(\\ref{Seff}) it follows that (in Fourier space) the (transverse) 2-point correlation function in the immediate vicinity of the Lifshitz point reads:\n\\begin{equation} \nG(\\vec{q})=G(\\vec{q}_\\perp, \\vec{q}_{||})=\\frac{1}{Z_\\perp \\vec{q}_\\perp^2 +Z_{||}(\\vec{q}_{||}^2)^2}\\;,\n\\end{equation}\nwhile in real space \n\\begin{equation}\nG(\\vec{x}_\\perp, \\vec{x}_{||}) \\sim \\int d^d q G(\\vec{q})e^{i(\\vec{q}_\\perp \\vec{x}_\\perp + \\vec{q}_{||} \\vec{x}_{||})}=\\int d^d q\\frac{e^{i(\\vec{q}_\\perp \\vec{x}_\\perp + \\vec{q}_{||} \\vec{x}_{||})}}{Z_\\perp \\vec{q}_\\perp^2 +Z_{||}(\\vec{q}_{||}^2)^2}\\,.\n\\end{equation}\nBy substituting $(\\vec{q}_{||}^2)=\\tilde{q}_{||}$, expanding the exponential occurring in the numerator, passing to spherical coordinates in each of the two subspaces and integrating over the angular coordinates, one arrives at the following expression: \n\\begin{equation} \n\\mathcal{C}\\int_0^{\\Lambda_\\perp} dq_\\perp \\int_0^{\\Lambda_{||}^2}d\\tilde{q}_{||} \\frac{\\tilde{q}_{||}^{\\frac{m}{2}-1} q_\\perp^{d-m-1}}{Z_\\perp \\vec{q}_\\perp^2 + Z_{||}\\tilde{q}_{||}^2}\n\\end{equation}\nwith $\\mathcal{C}$ constant and $\\Lambda_\\perp$, $\\Lambda_{||}$ being microscopic (momentum) cutoffs. Transformation to polar coordinates: $\\sqrt{Z_{||}}\\tilde{q}_{||} = r\\cos\\phi$, $\\sqrt{Z_\\perp}q_\\perp = r \\sin{\\phi}$ leads to an integral of the form \n\\begin{equation}\nG(\\vec{x}_\\perp, \\vec{x}_{||})\\sim\\int_0^\\Lambda dr r^{d-\\frac{m}{2}-3}\\;,\n\\end{equation}\ndivergent for $d\\leq 2+\\frac{m}{2}$. This implies instability of the Lifshitz point with respect to order parameter fluctuations for $d$ below $2+\\frac{m}{2}$. The above treatment is analogous to a Gaussian level demonstration of the Mermin-Wagner theorem in the standard isotropic situations.\\cite{Goldenfeld_book} \nThe obtained condition coincides with those previously recognized for Lifshitz points for magnets and liquid crystals and may be cast in the form: \n\\begin{equation}\nd_L = 2+\\frac{m}{2} \\;,\n\\label{dL}\n\\end{equation}  \nwhere $d_L$ is the lower critical dimension for occurrence of an $m$-axial Lifshitz point where the normal, homogeneous superfluid and FFLO phases would coexist. Note that for $m=0$ we recover $d_L=2$ in line with the Mermin-Wagner theorem,  while for the isotropic case ($m=d$) Eq.~(\\ref{dL}) leads to $d_L=4$, which in dimensionality $d=3$ and $d=2$ prohibits the occurrence of the isotropic Lifshitz point, and in consequence also the FFLO phase squashed between the BCS-like and Fermi liquid phases according to the mean-field predictions. \n\nThe expression of Eq.~(\\ref{dL}) is not new and was first derived in the context of magnetic systems long ago by Grest and Sak\\cite{Grest_1978} within the $2+\\epsilon$ expansion of the nonlinear sigma model. It is expected to be valid for situations characterized by the number of order parameter components $N\\geq 2$. Analysis of the Ginzburg criterion for the Lifshitz point\\cite{Diehl_2002} indicates a similar effect on the upper critical dimension $d_u$, such that $d_u=4+\\frac{m}{2}$.\n\nAs concerns the stability of the FFLO states, we emphasize the difference between the above arguments and those presented in earlier literature. While the previous studies addressed stability of different putative ground states of the FFLO type to Goldstone fluctuations, the present analysis invokes the envisaged presence of the thermal Lifshitz point in the phase diagram and inspects its stability to critical order parameter fluctuations. This yields in the isotropic situation a condition by far more restrictive. The absence of a thermodynamically stable long-range ordered FFLO phase certainly does not contradict the presence of regions of the phase diagram exhibiting enhanced FFLO pairing fluctuations (see Ref.~\\onlinecite{Pini_2021} for a recent discussion) which may well be detected in experiments on various systems. On the other hand, our argument offers an explanation of why convincing experimental evidence for FFLO states was reported only for strongly anisotropic situations and demonstrates that the occurrence of a true long-range ordered FFLO thermodynamic phase in isotropic three-dimensional systems is in fact completely excluded. Also note that the FFLO phase may well remain stable at $T=0$ (compare Fig.~\\ref{Phase_diag}) which implies the presence of a quantum Lifshitz point in addition to the FFLO quantum critical point\\cite{Piazza_2016, Pimenov_2018} in the phase diagram.  \n\nWe also make the  observation that the condition for stability of the Lifshitz point is significantly weaker in the anisotropic case ($m<d$). For the most relevant uniaxial case $m=1$ one obtains $d_L=5\/2$, which indicates a stable Lifshitz point in $d=3$, but not $d=2$. In this situation the stability restrictions for the FFLO phase with respect to Goldstone fluctuations (the spectrum of which depends on the details of the ground state)  are in fact more demanding,\\cite{Radzihovsky_2011} implying in $d=3$ that the FFLO state may presumably appear as a quasi-long-range ordered phase.   \n\nIn the next section we provide further evidence, based on nonperturbative RG, which supports the above picture, and, in addition, yields estimates of the critical exponents at the Lifshitz point.  \n\n\\section{Lifshitz critical behavior} \nIn this section we extend and deepen the above argumentation by analyzing the critical behavior at thermal $m$-axial Lifshitz points in $d$ dimensions beyond the Gaussian level. We generalize out  calculation by allowing for an arbitrary number of order parameter components $N$. It is worth emphasizing that a description of this class of critical phenomena by the tools of perturbative renormalization group (RG) is, as compared to the standard $O(N)$-symmetric case, way more demanding,\\cite{Shpot_2001, Shpot_2005, Shpot_2008, Burgsmuller_2010, Shpot_2012}  and has up to now been carried out only up to two loop level. In the present chapter we implement a nonperturbative RG approach based on a truncation of the Wetterich equation. We begin by discussing the leading order of the derivative expansion, the so-called local potential approximation (LPA), which allows us to build a mapping between the Lifshitz and standard $O(N)$-symmetric critical behaviors. The discussed connection is exact at the LPA  level, but becomes violated after accounting for the anomalous dimensions, i.e. going to higher orders in the derivative expansion. This is here achieved with the simplest truncation in the spirit of the so-called LPA'. \n The Lifshitz critical behavior was previously addressed with slightly different nonperturbative RG truncations in Ref.~\\onlinecite{Essafi_2012} for the unaxial Heisenberg case in three dimensions $(d,N,m)=(3,3,1)$ and in Refs.~\\onlinecite{Zappala_2017, Zappala_2018} for the isotropic case in $d\\geq 4$. See also Ref.~\\onlinecite{Defenu_2021} for an interesting connection between the isotropic Lifshitz point in $d=4$ and the Kosterlitz-Thouless transition. Our major current aim is to strengthen  the argumentation leading to the conclusion of Sec.~III and  build up a connection to the standard isotropic $O(N)$-symmetric models. We shall therefore consider $m$ varying continuously between zero and $d$. As a byproduct we provide estimates of the critical indices of the Lifshitz point characterized by general $(d,N,m)$ as obtained within our present relatively simple approach.   \n\\subsection{Wetterich equation and the derivative expansion} \nThe Wetterich approach\\cite{Wetterich_1993} constitutes a nonperturbative implementation of Wilsonian renormalization group. It relies on the exact RG flow equation\n\\begin{align}\n\\partial_k\\Gamma_k[\\phi] = \\frac{1}{2}\\textrm{Tr}\\left\\{\\partial_k R_k \\left[\\Gamma_k^{(2)}[\\phi] +R_k\\right]^{-1}\\right\\}\\;,\n\\label{Wetterich}\n\\end{align}\nwhich evolves the effective average action $\\Gamma_k[\\phi]$ between the microscopic action $\\mathcal{S}[\\phi]$ and the thermodynamic free energy $\\mathcal{F}[\\phi]$ upon varying the infrared (momentum) cutoff parameter $k$ from the microscopic scale $k=\\Lambda$ towards zero. Specifically: $\\Gamma_{k\\to\\Lambda}[\\phi]\\to \\mathcal{S}[\\phi]$ and $\\Gamma_{k\\to 0}[\\phi]\\to \\mathcal{F}[\\phi]$. The infrared cutoff is implemented by adding a momentum-dependent function $R_k=R_k(\\vec{q})$ to the inverse propagator, thus effectively damping  modes with momentum $q<k$, leaving the modes with $q>k$ untouched. The trace in Eq.~(\\ref{Wetterich}) encompasses in the present context summation over momentum as well as components of the order-parameter field $\\phi$, while $\\Gamma_k^{(2)}[\\phi] $ denotes the second functional derivative of $\\Gamma_k[\\phi]$. The framework resting upon Eq.~(\\ref{Wetterich}) was over the last years fruitfully applied in a broad range of contexts (for reviews see for example Refs.~\\onlinecite{Berges_2002, Pawlowski_2007, Kopietz_book, RG_book, Metzner_2012, Dupuis_2021}). \n\nOne successful approximation scheme to integrate the Wetterich equation is recognized as the derivative expansion (DE). It amounts to classifying the symmetry-allowed terms occurring in $\\Gamma_k[\\phi]$  according to the number of field derivatives and truncating terms of order higher than a given value. This projects the functional differential equation Eq.~(\\ref{Wetterich}) onto a finite, numerically manageable set of partial (integro-)differential flow equations. Only very recently was this framework systematically applied\\cite{Polsi_2020}  to the case of $O(N)$-symmetric models at order $\\partial^4$ (and  $\\partial^6$ for the Ising universality class\\cite{Balog_2019}) in dimensionality $d=3$. These computations led to estimates of the critical exponents of accuracy comparable to those delivered by the best Monte Carlo simulations and perturbation theory calculations. It will become clear that the case of the Lifshitz point constitutes a significantly more demanding challenge for the treatment based on the Wetterich approach. The reason for this is at least two-fold: (i) terms quartic in momentum appear in the inverse propagator even at the bare level and are crucial for capturing the relevant physics; (ii) the anisotropic nature of the problem complicates the loop integrals. Despite these, as we demonstrate below,  the Wetterich approach captures a substantial amount of physics and delivers estimates of the critical exponents even at the lowest orders of the DE.     \n\\subsection{Local potential approximation}\nWe now consider the leading (zeroth order) truncation of the derivative expansion, where the effective potential is a flowing (scale dependent) function, but the momentum dependencies in the propagator are not renormalized. This is known commonly as the local potential approximation (LPA) and, for the present problem, amounts to parametrizing $\\Gamma_k[\\phi]$ via the following form    \n\\begin{equation} \n \\Gamma_k[\\phi]=\\int d^d x \\left[U_k(\\rho) +\\frac{1}{2}Z_\\perp \\left(\\nabla_\\perp\\phi\\right)^2 +\\frac{1}{2} Z_{||} \\left(\\Delta_{||} \\phi\\right)^2  \\right]\\;, \n\\label{LPA}\n\\end{equation} \nwhere we introduced $\\rho =\\frac{1}{2}|\\phi|^2$. At this approximation level the gradient coefficients $Z_\\perp$ and $ Z_{||}$ are scale independent (in consequence the anomalous dimensions are neglected), while there is no  preimposed parametrization of the flowing effective potential $U_k(\\rho)$. Crucially, a term $\\sim \\left(\\nabla_{||}\\phi\\right)^2$ is absent in Eq.~(\\ref{LPA}). In a higher order calculation involving the flow of momentum dependencies of the propagator,  this term is present and should scale to zero at the Lifshitz point only for vanishing $k$. \n\n\n   By plugging Eq.~(\\ref{LPA}) into Eq.~(\\ref{Wetterich}) we obtain a closed flow equation for $U_k(\\rho)$ of the form     \n\\begin{equation}\n\\partial_k U_k(\\rho) = \\frac{1}{2}\\int_q \\partial_k R_k (\\vec{q})\\left[G_\\sigma(\\vec{q},\\rho, m) + (N-1)G_\\pi(\\vec{q},\\rho, m)\\right]\\;,\n\\label{LPA_eq}\n\\end{equation}\nwhere \n\\begin{align}\nG_\\sigma^{-1}(\\vec{q},\\rho, m)&= Z_{||}(\\vec{q}_{||}^2)^2 + Z_\\perp \\vec{q}_\\perp^2 + U_k'(\\rho)+2\\rho U_k''(\\rho)+R_k(\\vec{q}) \\nonumber \\\\\nG_\\pi^{-1} (\\vec{q},\\rho, m)&= Z_{||}(\\vec{q}_{||}^2)^2 + Z_\\perp \\vec{q}_\\perp^2 + U_k'(\\rho)+R_k(\\vec{q}) \n\\label{Gs}\n\\end{align}\nare the regularized inverse propagators for the longitudinal ($\\sigma$) and transverse ($\\pi$) modes. The integral $\\int_q = \\int\\frac{d^m q_{||}}{(2\\pi)^m}\\int \\frac{d^{d-m} q_{\\perp}}{(2\\pi)^{d-m}}$ in Eq.~(\\ref{LPA_eq}) encompasses the two subspaces characterized by distinct behavior of the dispersion. For $m=0$ we recover the standard LPA equation well studied for the $O(N)$-symmetric models, while for $m=d$ the $\\vec{q}_{\\perp}$-space is 0-dimensional which corresponds to the isotropic Lifshitz point. \n\nWe now implement the following rescaling \n\\begin{align}\n\\vec{q}_\\perp = k \\tilde{\\vec{q}}_\\perp\\;,\\; \\vec{q}_{||}=(Z_\\perp\/Z_{\\parallel})^{1\/4} k^{1\/2}\\tilde{\\vec{q}}_{||} \\nonumber \\\\\n\\rho = Z_\\perp^{\\frac{m}{4}-1} Z_{\\parallel}^{-\\frac{m}{4}}k^{d-\\frac{m}{2}-2}\\tilde{\\rho}\\;,\\; U_k(\\tilde{\\rho})=Z_\\perp^{\\frac{m}{4}} Z_{\\parallel}^{-\\frac{m}{4}}k^{d-\\frac{m}{2}}\\tilde{u}_k(\\tilde{\\rho})\n\\end{align} \nand consider the cutoff of the form \n\\begin{equation}\nR_k(\\vec{q})=Z_{\\perp}k^2 r\\left(\\tilde{\\vec{q}}_\\perp^2+(\\tilde{\\vec{q}}_{||}^2)^2\\right)\\;.\n\\end{equation}\nThis allows us to cast the LPA flow equation in a  scale invariant form:\n\\begin{align}\n&\\partial_t \\tu_k = - \\left(d-\\frac{m}{2}\\right)\\tilde{u}_k - \\left(2+\\frac{m}{2}-d\\right)\\trho \\tu_k'+\\nonumber \\\\ \n&\\frac{1}{2}\\int_{\\tilde q}\\left[\\frac{1}{y+\\tu_k'+2\\trho\\tu_k''+r(y)} +\\frac{N-1}{y+\\tu_k' +r(y)} \\right]\\left[2r(y)-2yr'(y)\\right]\\;,\n\\end{align}\nwhere we introduced $y=\\tilde q_\\perp^2 +\\tilde q_{||}^4$ and $t=\\log(k\/\\Lambda)$. In each of the two subspaces corresponding to $\\tilde q_\\perp$ and $\\tilde q_{||}$ we now pass to the (hyper)spherical coordinates and perform the angular integrations. Subsequently the change of variables $\\tilde q_\\perp =\\zeta \\cos\\theta$, $\\tilde q_{||}^2=\\zeta\\sin\\theta$ (with $\\zeta=\\sqrt{y}$) and integration over $\\theta$ leads to the following form of the flow equation: \n\\begin{align}\n\\partial_t \\tu_k =& - \\left(d-\\frac{m}{2}\\right)\\tilde{u}_k- \\left(2+\\frac{m}{2}-d\\right)\\trho \\tu_k'+\\nonumber \\\\\n&\\mathcal{V}_{d,m}\\int_0^\\infty dy y^{\\frac{d}{2}-\\frac{m}{4}-1}\\times\\nonumber \\\\ \n&\\left[2r(y)-2yr'(y)\\right] \\left[\\frac{1}{y+\\tu_k'+2\\trho\\tu_k''+r(y)} +\\frac{N-1}{y+\\tu_k' +r(y)} \\right]\\;, \n\\label{LPA_resc}\n\\end{align}\nwith\n\\begin{equation}\n\\mathcal{V}_{d,m}=\\frac{\\mathcal{S}^{d-m-1}\\mathcal{S}^{m-1}}{16(2\\pi)^d}\\mathcal{B}\\left(\\frac{d-m}{2},\\frac{m}{4}\\right)\\;,\n\\end{equation} \nwhere in turn $\\mathcal{S}^{n-1}=\\frac{2\\pi^{n\/2}}{\\Gamma(n\/2)}$ is the surface area of the $(n-1)$-dimensional unit sphere, and $\\mathcal{B}(x,y)$ denotes the Euler beta function.  \n\nWe now observe that by substituting $(d-\\frac{m}{2})\\rightarrow d_{eff}$ and $\\mathcal{V}_{d,m}\\rightarrow v_d= [2^{d+1}\\pi^{d\/2}\\Gamma (d\/2)]^{-1} $ in Eq.~(\\ref{LPA_resc}) we recover the LPA equation for the standard $O(N)$-symmetric case in dimensionality $d_{eff}$. It follows that, at the LPA level of approximation, the RG equation for the $m$-axial Lifshitz point in $d$ dimensions differs from the corresponding flow equation for the $O(N)$ model in dimensionality $d_{eff}=d+\\frac{m}{2}$ exclusively by the $m$-dependent constant multiplying the integral. The quantity $\\mathcal{V}_{d,m}$ (and $v_d$ alike) is however redundant as it can be absorbed by the transformation \n\\begin{equation}\nu_k =   \\mathcal{V}_{d,m} w_k \\;,\\;\\;\\;\\; \\tilde{\\rho}=\\mathcal{V}_{d,m}\\tilde{\\gamma}\\;,\n\\end{equation}\nwhich casts the LPA equation in the form \n\\begin{align}\n\\partial_t \\tilde{w}_k =& - \\left(d-\\frac{m}{2}\\right)\\tilde{w}_k- \\left(2+\\frac{m}{2}-d\\right)\\tilde{\\gamma} \\tilde{w}_k'+\\nonumber \\\\\n&\\int_0^\\infty dy y^{\\frac{d}{2}-\\frac{m}{4}}\\times\\nonumber \\\\ \n&\\left[2r(y)-2yr'(y)\\right] \\left[\\frac{1}{y+\\tilde{w}_k'+2\\tilde{\\gamma}\\tilde{w}_k''+r(y)} +\\frac{N-1}{y+\\tilde{w}_k' +r(y)} \\right]\\;, \n\\label{LPA_resc_2}\n\\end{align}\nwhere $\\tilde{w}_k=\\tilde{w}_k(\\tilde{\\gamma})$ and prime now denotes differentiation with respect to $\\tilde{\\gamma}$. It follows that the critical behavior at the $m$-axial Lifshitz point is fully equivalent to the one at the $O(N)$-symmetric critical point at dimensionality reduced by $\\frac{m}{2}$. This fact was previously recognized at the mean-field and Gaussian level as well as in the limit  $1\/N\\to 0$.\\cite{Diehl_2002, Shpot_2008, Burgsmuller_2010, Shpot_2012, Jakubczyk_2018, Lebek_2020, Lebek_2021} The above reasoning indicates that the correspondence remains valid within the LPA approximation, and in fact should remain correct as long as the anomalous dimensions are neglected. \nIn particular the lower (as well as the upper) critical dimension describing these two situations are then shifted by $m\/2$ in agreement with the Gaussian argument presented in Sec.~III. In view of the above, the critical exponents for the Lifshitz point may be extracted using the routines previously developed for the $O(N)$ models. Here we focus on the $\\nu_\\perp$ exponent describing the decay of the correlation function $G(\\vec{x}_\\perp, \\vec{x}_{||}=0)$. The analogous exponent $\\nu_{||}$ controlling $G(\\vec{x}_\\perp=0, \\vec{x}_{||})$ is related to $\\nu_\\perp$ via the scaling relation\\cite{Diehl_2002} \n\\begin{equation}\n\\nu_{||}=\\frac{2-\\eta_\\perp}{4-\\eta_{||}}\\nu_\\perp\\;.\n\\end{equation} \nIn the absence of anomalous dimensions we find $\\nu_{||} =\\frac{1}{2}\\nu_\\perp$. Other critical exponents are then also recovered via scaling relations.\\cite{Diehl_2002}\n\n    The quantity $\\nu_\\perp^{-1}$ may  be identified as the leading eigenvalue of the RG transformation of Eq.~(\\ref{LPA_resc}) [or Eq.~(\\ref{LPA_resc_2})] linearized around the fixed point. Technically, we first discretize Eq.~(\\ref{LPA_resc}) on the $\\trho$-grid (typically involving $\\approx 60$ points) and solve for the fixed point $u^*(\\trho)$. The RG equation Eq.~(\\ref{LPA_resc}) is then linearized around $u^*(\\trho)$ and its diagonalization yields the spectrum, which contains a single positive eigenvalue $\\lambda_\\nu$, which we identify with $\\nu_\\perp^{-1}$. For details on the numerical procedure, see Ref.~\\onlinecite{Chlebicki_2021}. For $m\\to 0$ we obviously recover the value pertinent to the standard $O(N)$ model. In the practical calculation we consider two families of cutoff functions: \n \\begin{align}\n r(y)= (1-y)\\theta (1-y)\\;\\;\\;\\; &\\textrm{(Litim cutoff)}  \\\\ \n r(y)= \\alpha \\frac{y}{e^y-1} \\;\\;\\;\\; &\\textrm{(Wetterich cutoff)}\\;, \n \\label{cutoffs}\n \\end{align}\n the latter one involving a variable parameter $\\alpha$. The obtained value of $\\nu_\\perp^{-1}$ carries a weak dependence on $\\alpha$. In accord with the principle of minimal sensitivity\\cite{Canet_2003_2, Balog_2020} (PMS) one chooses $\\alpha$ so that $\\nu_\\perp^{-1}$ is locally stationary with respect to variation of $\\alpha$. Our results for $\\nu_\\perp$ depending on $N$, $d$ and $m$ are presented in Figs.~5-7 and compared with those obtained within the $\\epsilon=4+\\frac{m}{2}-d$ expansion and $\\frac{1}{N}$ expansion. The differences between the values obtained using the different cutoff functions are relatively small and here we present the results obtained using the Litim cutoff. \n\\begin{figure}[ht] \n\\begin{center}\n\\includegraphics[width=9cm]{LPA_vs_eps.png}\n\\caption{The correlation length exponent $\\nu_\\perp$ for the uniaxial ($m=1$) Lifshitz point for $N=2$ plotted as a function of dimensionality $d$. The results obtained within the LPA approximation are superimposed with those resulting from the $\\epsilon=4\\frac{1}{2}-d$ expansion in Ref.~(\\onlinecite{Shpot_2001}) up to order $\\epsilon^2$. The two sets of points coincide in the vicinity of the upper critical dimension $d_u=4\\frac{1}{2}$, above which we recover the mean-field result $\\nu_\\perp=\\frac{1}{2}$. An increase of $\\nu_\\perp$ upon lowering $d$, indicating the expected divergence at the lower critical dimension $d_L=2\\frac{1}{2}$ is clearly visible in the LPA data. }\n\\label{LPA_vs_eps}\n\\end{center} \n\\end{figure} \n\\begin{figure}[ht] \n\\begin{center}\n\\includegraphics[width=9cm]{d_dep.png}\n\\caption{The correlation length exponent $\\nu_\\perp$ for the $m$-axial Lifshitz point for $N=2$ plotted as a function of dimensionality $d$ for a sequence of values  of $m$. The plot demonstrates the shift of the upper critical dimension $d_u$ as well as the growing degree of divergence occurring upon increasing $m$. The curves are all related by translations in the horizontal direction (see the main text).  }\n\\label{d_dep}\n\\end{center} \n\\end{figure} \n\\begin{figure}[ht] \n\\begin{center}\n\\includegraphics[width=9cm]{N_infty.png}\n\\caption{The (inverse) correlation length exponent $\\lambda_{\\nu}=\\nu_{\\perp}^{-1}$ obtained within the LPA approximation plotted as a function of $m$ for $d=3$ and a sequence of values of $N$. The plot demonstrates in particular the convergence of the results towards the (exact) limit $\\nu_{\\perp}^{-1}\\to d-2-\\frac{m}{2}$ for $N\\to\\infty$. Interestingly, our results indicate significantly faster convergence for $m$ large.  }\n\\label{N_infty}\n\\end{center} \n\\end{figure} \n\nOur approach correctly reproduces the $1\/N\\to 0$ as well as $\\epsilon\\to 0$ limits and is applicable to a broad range of parameters in the $(d,m,N)$ space. At the present truncation level it is however not sufficient to correctly address the limit of dimensionality $d$ approaching $d_L$, which is dominated by the neglected anomalous dimensions (see Sec.~IVC for an extension in this direction). Nonetheless our LPA data indicates a rapid growth of $\\nu_\\perp$ upon lowering $d$ towards $d_L$ (see e.g. Fig.~\\ref{LPA_vs_eps}). \n\n\\subsection{Constrained LPA' and the anomalous dimensions}\nWe now extend the truncation described in Sec.~IVB to account for the anomalous dimensions in the simplest conceivable way. This amounts to treating the quantities $Z_{\\perp}$ and $Z_{||}$ in Eq.~(\\ref{Gs}) as scale-dependent (but not field-dependent) quantities, while disregarding the term $\\sim (\\nabla_{||}\\phi )^2$ (alike at the LPA level). The latter constitutes here an additional approximation. An analogous procedure for the case of isotropic $O(N)$ models is recognized as  ''LPA' '' and yields, for the $d=3$ XY or Heisenberg universality classes a somewhat overestimated value of the anomalous dimension $\\eta$. For the present anisotropic situation (characterized by the effective dimensionality below 3) we may expect only a qualitative estimate of the values of  $\\eta_\\perp$ and $\\eta_{||}$. Interestingly, we find nonetheless that the degree of violation of the correspondence discussed in Sec.~IVB upon including the anomalous dimensions is in fact very low in the physically interesting situations.\nAnother interesting point concerns the sign of $\\eta_{||}$. In this respect, for example in  $(d,m,N)=(3,1,3)$ the $1\/N$ expansion (up to terms $\\sim 1\/N$) predicts\\cite{Shpot_2005, Shpot_2012} a positive value in contrast to the $\\epsilon$-expansion\\cite{Shpot_2001} as well as the nonperturbative RG study of Ref.~(\\onlinecite{Essafi_2012}). \n\nThe running anomalous dimensions are related to the flowing $Z$-factors via\\cite{Essafi_2012} $\\eta_{\\perp}=-\\frac{1}{Z_\\perp}\\partial_t Z_{\\perp}$ and $\\eta_{||}=-\\frac{1}{\\theta Z_{||}}\\partial_t Z_{||}$ with $\\theta = \\frac{2-\\eta_{\\perp}}{4-\\eta_{||}}$ being the anisotropy exponent. The flow of the effective potential is derived along the line of Sec.~IVB. We obtain: \n\\begin{align}\n\\partial_t \\tu_k =& - \\left(d-\\frac{m}{2}-\\frac{m}{4}(\\eta_\\perp-\\eta_{||}) \\right)\\tilde{u}_k \\nonumber \\\\ \n&-\\left(2+\\frac{m}{2}-d-\\eta_\\perp (1-\\frac{m}{4})-\\eta_{||}\\frac{m}{4} \\right)\\trho \\tu_k' \\nonumber \\\\\n&+\\mathcal{V}_{d,m}\\int_0^\\infty dy y^{\\frac{d}{2}-\\frac{m}{4}-1}\\times\\nonumber \\\\ \n&\\left[(2-\\eta_\\perp)r(y)-2yr'(y)\\right] \\left[\\frac{1}{y+\\tu_k'+2\\trho\\tu_k''+r(y)} +\\frac{N-1}{y+\\tu_k' +r(y)} \\right] \\nonumber \\\\\n&+\\mathcal{W}_{d,m}\\int_0^\\infty dy y^{\\frac{d}{2}-\\frac{m}{4}}\\times\\nonumber \\\\ \n&\\left[\\eta_\\perp -\\eta_{||}\\right]r'(y) \\left[\\frac{1}{y+\\tu_k'+2\\trho\\tu_k''+r(y)} +\\frac{N-1}{y+\\tu_k' +r(y)} \\right]\\;,\n\\label{LPA_prime_resc}\n\\end{align}\nwhere \n\\begin{equation}\n\\mathcal{W}_{d,m} =\\frac{\\mathcal{S}^{d-m-1}\\mathcal{S}^{m-1}}{16(2\\pi)^d}\\mathcal{B}\\left(\\frac{d-m}{2},\\frac{m}{4}+1\\right)\\;.\n\\end{equation}\nThe above flow equation for $u_k$ must be supplemented by the expressions for the running anomalous dimensions $\\eta_\\perp$ and $\\eta_{||}$. These are evaluated along the line well described in literature (see e.g. Ref.~\\onlinecite{Dupuis_2021}). By differentiating the Wetterich equation Eq.~(\\ref{Wetterich}) twice, we obtain the flow of the two-point function $\\Gamma^{(2)}$. Subsequently, by taking the second derivative with respect to momentum in the $\\perp$ direction and the fourth derivative with respect to momentum in the $||$ direction evaluated at vanishing momentum, we extract the flow of $Z_\\perp$ and $Z_{||}$, from which $\\eta_\\perp$ and $\\eta_{||}$ follow. The resulting expressions (especially for $\\eta_{||}$)  are very lengthy and we refrain from quoting them here.  \nThe physical anomalous scaling dimensions correspond to the fixed-point values of $\\eta_\\perp$ and $\\eta_{||}$, which we extract numerically. The data presented below corresponds to results obtained with the PMS-optimized Wetterich cutoff. We note that for a range of $d$ and $m$ corresponding to low effective dimensionalities we were not able ot obtain a PMS value of $\\alpha$, in which case we chose a value of $\\alpha$ corresponding to a global extremum over a range of considered values. As representative results, in Figs.~\\ref{eta_1} and \\ref{eta_2}  we plot the obtained dependencies of $\\eta_\\perp$ and $\\eta_{||}$ with fixed $N=1$, varying $d$ and $m$. Our numerical values are larger as compared to those resulting from the $\\epsilon$ expansion which is probably due to both our truncation errors and the low order of the implemented $\\epsilon$ expansion.  We point out that the sign of $\\eta_{||}$ is negative in the entire region of parameters considered by us. As concerns the limit $m\\to 0$, we observe  convergence of both $\\eta_\\perp$ and $\\nu_\\perp$ to the anticipated values corresponding to the standard $O(N)$ models. The quantity $\\eta_{||}$ becomes a meaningless (redundant) parameter but does not vanish for $m\\to 0$.      \n\\begin{figure}[ht] \n\\begin{center}\n\\includegraphics[width=9cm]{eta_1_d.png}\n\\caption{The anomalous scaling dimension $\\eta_\\perp$ as function of $d$ for a sequence of values of $m$ and $N=1$. }\n\\label{eta_1}\n\\end{center} \n\\end{figure} \n\\begin{figure}[ht] \n\\begin{center}\n\\includegraphics[width=9cm]{eta_2_d.png}\n\\caption{ The anomalous scaling dimension $\\eta_{||}$ as function of $d$ for a sequence of values of $m$ and $N=1$.}\n\\label{eta_2}\n\\end{center} \n\\end{figure} \n\nWe now investigate to which extent the relation between the Lifshitz point in $d$ dimensions and the $O(N)$ critical point in dimensionality $d_{eff}$ explored in Sec.~IVB becomes violated in presence of the anomalous dimensions. For this aim we plot the critical exponents as function of the effective dimensionality in Figs.~\\ref{eta_1_coll} and ~\\ref{eta_2_coll}. The collapse of the curves indicates a high level of  agreement with the picture demonstrated IVB at the LPA level for all of the critical exponents (including the anomalous dimensions).   \n\\begin{figure}[ht] \n\\begin{center}\n\\includegraphics[width=9cm]{eta_1_d_collapse.png}\n\\caption{The anomalous scaling dimension $\\eta_\\perp$ as function of $d_{eff}$ for a sequence of values of $m$ and $N=1$. The collapse of the curves indicates approximate fulfillment of the correspondence between the Lifshitz and $O(N)$-symmetric critical behavior also in presence of the anomalous dimensions.}\n\\label{eta_1_coll}\n\\end{center} \n\\end{figure} \n\\begin{figure}[ht] \n\\begin{center}\n\\includegraphics[width=9cm]{eta_2_d_collapse.png}\n\\caption{ The anomalous scaling dimension $\\eta_{||}$ as function of $d_{eff}$ for a sequence of values of $m$ and $N=1$. The collapse of the curves indicates approximate fulfillment of the correspondence between the Lifshitz and $O(N)$-symmetric critical behavior also in presence of the anomalous dimensions.}\n\\label{eta_2_coll}\n\\end{center} \n\\end{figure} \nWe by no means expect this equivalence to remain exact beyond the LPA approximation, however the level of numerical agreement is striking. \n\nWe finally point out that the present LPA' level of approximation is the lowest possible allowing for capturing the anomalous dimensions. It would be very interesting to extend the present analysis by including $\\rho$-dependencies as well as accounting for the  neglected $\\sim (\\nabla_{||}\\phi )^2$ term. We relegate this to future studies.\n\n\\section{Summary}\nIn this paper we addressed the restrictions on the stability of the long-range ordered pair density wave (FFLO superfluid) states arising due to the presence of a thermal Lifshitz point as predicted by the mean-field theory. We pointed out that the occurrence of these phases in isotropic systems (such as ultracold atoms in continuum) is in fact completely excluded both in dimensionality $d=2$ and $d=3$, except for zero temperature. In consequence, the corresponding phase diagram should generically host a quantum Lifshitz point. This is no longer the case in systems exhibiting a unidirectional anisotropy, where a Lifshitz point at $T>0$ may be stable in $d=3$ (but not in $d=2$).   \n\nThe study of the FFLO superfluid Lifshitz point prompted us to readdress the Lifshitz critical behavior with arbitrary $d$, $m$ and $N$ from the point of view of functional renormalization group. We have found that at the approximation level of the local potential approximation (LPA), which amounts to disregarding the anomalous dimensions, the $m$-axial Lifshitz critical behavior is \\emph{exactly} equivalent to that describing the standard $O(N)$-symmetric critical point in effective dimensionality $d_{eff}=d-m\/2$. Our numerical analysis going beyond LPA level and accounting for $\\eta_\\perp$ and $\\eta_{||}$ indicates that this relation is only mildly violated also in this case. In particular, we have found that the anomalous dimension $\\eta_\\perp$ with a high level of accuracy coincides with the value of the $\\eta$ exponent of the corresponding $O(N)$ model in dimensionality reduced by $m\/2$. We obtained negative values of $\\eta_{||}$ for the entire range or scanned values of $(d, m, N)$. \n\nOur work opens avenues for future studies in at least two separate directions. On one hand, it would be interesting to explore thermodynamic and transport properties accompanying the vicinity of the fluctuation induced quantum Lifshitz point approaching it from finite $T$, in particular exploiting the interplay of order parameter and fermionic fluctuations. On the other hand, it might appear very fruitful to employ more sophisticated truncations of the Wetterich equation to further clarify the nature of the thermal Lifshitz points.      \n\n\\begin{acknowledgments}\nWe are grateful to Hans Werner Diehl, Dominique Mouhanna, Pierbiagio Pieri, and Mykola Shpot for useful correspondence and remarks on the content of the manuscript. P. J. thanks  Hiroyuki Yamase for numerous discussions on closely related topics. We acknowledge support from the Polish National Science Center via 2017\/26\/E\/ST3\/00211. \n\\end{acknowledgments}\n\n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction} \\label{sec:Introduction}\n\n\n\nRecent years have seen a number of efforts to apply photon pixel count statistics to gamma-ray data, in order to characterize populations of point sources (PSs) too faint to be individually detected at high significance (e.g. \\cite{Malyshev:2011zi, Lee:2014mza,Lee:2015fea, Linden:2016rcf, Lisanti:2016jub, Zechlin:2015wdz, Zechlin:2017wsy,Zechlin:2017uzo, Daylan:2016tia, Portillo_2017, Collin:2021ufc}). The general idea of these methods is to exploit the fact that an unmodeled PS population gives rise to non-Poissonian fluctuations in the number of photons per pixel, with ``hot spots'' corresponding to the locations of sources. Even if no individual hot spot is significant enough to be established as a PS with high probability, the distribution of fluctuations can be used to infer the properties of the population. These methods have been applied to characterize contributions to the extragalactic gamma-ray background (e.g.~\\cite{Lisanti:2016jub, Zechlin:2017wsy, Zechlin:2017uzo}) and to study inner Galaxy PS populations (e.g.~\\cite{Lee:2015fea, Linden:2016rcf, Calore:2021bty}); they have also been applied to other datasets, e.g. crowded optical fields \\cite{Portillo_2017} and high-energy neutrinos \\cite{IceCube:2019xiu}. \n\nInitially these methods focused on the case of isotropic PS populations, which is likely to be a good approximation for all-sky background radiation generated by a large ensemble of faint extragalactic sources. However, subsequent studies \\cite{Lee:2015fea, Daylan:2016tia, Collin:2021ufc}  extended this approach to the case of source populations with an arbitrary spatial distribution.\n\nIn this work we focus on one such method, {\\it Non-Poissonian Template Fitting} (NPTF) \\cite{Lee:2014mza, Lee:2015fea,Mishra-Sharma:2016gis}, which has been applied in a range of contexts but particularly to study the Galactic Center Excess (GCE) in public data from the {\\it Fermi} Gamma-Ray Space Telescope (hereafter {\\it Fermi}). The GCE is an extended and roughly spherical (not disk-like) source of GeV-scale gamma rays filling the region within $1.5 \\text{ kpc}$ of the Galactic Center (GC) \\cite{Goodenough:2009gk,Hooper:2010mq, Hooper:2011ti,Hooper:2013rwa,Daylan:2014rsa,Calore:2014xka,TheFermi-LAT:2015kwa}. \n\nThe origin of the GCE has been the subject of active controversy for the past decade, with two explanations receiving the most attention. One possibility is that the GCE originates from diffuse particle dark matter (DM) undergoing annihilation (e.g. \\cite{Goodenough:2009gk,dan_foreman_mackey_2016_53155,Daylan:2014rsa,Karwin:2016tsw}), as the flux, energy spectrum, and spatial morphology of the GCE appear broadly consistent with a DM origin. If this hypothesis were confirmed, it would be a discovery of profound importance, representing the first evidence of non-gravitational interactions between DM and visible particles. However, the energy spectrum of the GCE also closely resembles that of gamma-ray pulsars observed by {\\it Fermi}, and a number of studies have found that the spatial morphology of the GCE is a closer match to the stellar bulge than to a DM annihilation signal \\cite{Macias:2016nev, Bartels:2017vsx, Macias:2019omb, Pohl:2022nnd}.\\footnote{However, other recent studies \\cite{DiMauro:2021raz,Cholis:2021rpp} have found the opposite preference; the result appears to be sensitive to how the Galactic background emission is modeled.} For these reasons, it seems plausible that the GCE represents the detection of a pulsar population in the Galactic bulge (e.g.  \\cite{Abazajian:2012pn,Abazajian:2014fta,Hooper:2013nhl,Mirabal:2013rba,Calore:2014oga,Cholis:2014lta,Yuan:2014yda,OLeary:2015qpx,Ploeg:2017vai,Hooper:2018fih,Bartels:2018xom,Bartels:2018eyb}). If this population includes sources with brightness approaching the {\\it Fermi} sensitivity threshold, then NPTF methods have the potential to characterize at least the bright end of this new population, and provide strong evidence against the DM hypothesis.\n\nPrevious NPTF studies have claimed evidence for a GCE source population comprised of relatively bright and rare PSs \\cite{Lee:2015fea}, but recent studies have found that those claims may have been premature due to unaccounted-for systematic errors \\cite{Leane:2019xiy,Chang:2019ars,Buschmann:2020adf,Leane:2020nmi,Leane:2020pfc}. Other analyses have found a preference for a significant diffuse emission component \\cite{List:2020mzd, Calore:2021bty}, although this does not exclude the pulsar hypothesis, since the sources might simply be too faint to detect with current methods. At the same time, work on modeling the  pulsar population in the bulge has suggested that plausible pulsar luminosity functions could generate very few {\\it Fermi} detected sources, while yielding an appreciable number of sources in the flux range potentially detectable by NPTF methods \\cite{Ploeg:2020jeh, Gautam:2021wqn, Dinsmore:2021nip} or related approaches using machine learning \\cite{List:2021aer,Mishra-Sharma:2021oxe}.\n\nGiven this uncertain situation, it is timely to understand how well NPTF can be expected to perform in detecting faint PS populations, and how this performance can be optimized by analysis choices. For example, many previous studies have chosen {\\it Fermi} event selections to optimize angular resolution, at the cost of exposure. While several studies have explored the effect on their results of varying the event selection (e.g. \\cite{Lisanti:2016jub, Leane:2020nmi, Leane:2020pfc}), this has not yet been done in a systematic way.\n\nIn this work, we systematically explore the ability of the public \\texttt{NPTFit} algorithm (as described in Ref.~\\cite{Mishra-Sharma:2016gis}) to reconstruct faint sources in simulated data, as a function of the instrument capabilities and analysis choices. We focus primarily on the analysis of the inner Milky Way, as relevant for the GCE, but also provide results for the simpler case where signal and background are both isotropic.\n\n\n\nWe begin in Sec.~\\ref{sec:analyticforms} by discussing how we expect the likelihood ratio in favor of a point-source population to behave, in a simplified approximate context that can be treated analytically, by approximating some or all of the relevant Poisson distributions as Gaussian. This approximation is not expected to hold in detail in the cases of greatest interest to us, but it is helpful for building intuition.\n\nIn Sec.~\\ref{sec:Methodology}, we then move on to our numerical study, starting by discussing the procedure by which we perform fits to the real {\\it Fermi} data to derive reasonable baseline estimates for the properties of the background model and PSs. We use these results to generate simulated data that is similar to the true gamma-ray sky as observed by {\\it Fermi}, using the public code \\texttt{NPTFit-Sim}, a package designed to simulate populations of unresolved PSs.\\footnote{\\url{https:\/\/github.com\/nickrodd\/NPTFit-Sim}} In this section we also discuss our methodology for fitting to simulated data, and the test statistic we will use to describe the sensitivity of NPTF methods to faint sources.\n\nIn Sec.~\\ref{sec:varyingdiffparams} we lay out the parameters we will vary in our simulations: exposure, angular resolution, energy window, pixel size, and source brightness. We describe the procedure for varying each of these parameters using \\texttt{NPTFit} and \\texttt{NPTFit-Sim}, including any associated modifications to the prior ranges.\n\nIn Sec.~\\ref{sec:isotropic} we perform an initial analysis and comparison between simulated data and our analytic approximations, in the simplified scenario where the PS and smooth contributions to the gamma-ray sky are both isotropic.\n\nWe then move on to a full realistic inner Galaxy analysis; conduct variations of the various analysis parameters, singly and in combination; and present the (numerical) results in Sec.~\\ref{sec:results}. In particular, we explore the individual effects of varying the exposure level and the point spread function (PSF), and map out the tradeoff when exposure level is increased (reduced) with the effect of worsening (improving) angular resolution, using the specific examples of {\\it Fermi} event classes sorted by angular resolution. Modifying the energy window varies the effective exposure, the PSF, and also (in real data) the relative amplitude of the various background and signal components; we explore these effects independently. We then demonstrate the effect of varying the brightness of the PSs while keeping the total flux of the population constant (as appropriate for hypothetical source populations that explain the bulk of the GCE). Finally, we examine the question of the optimal pixel size for NPTF analyses, exploring both the sensitivity to faint PSs and accuracy of the parameter reconstruction. \n\nIn Sec.~\\ref{sec:conclusion} we summarize our results and discuss some implications for NPTF analyses of {\\it Fermi} gamma-ray data in the inner Galaxy.\n\n\nIn Appendix~\\ref{app:detailedmethodology} we present further details of our simulation parameters and fitting methodology; in Appendix~\\ref{app:sharpSCF} we discuss the degree to which our source count functions model a single-brightness PS population;\nin Appendix~\\ref{app:isotropic} we show additional results for the simpler case where both signal and background are isotropic; and in Appendix~\\ref{app:modela} we show the results of using an alternative Galactic diffuse model as the basis for our simulations.\n\n\n\n\\section{Analytic approximations for non-Poissonian template fitting}\n\\label{sec:analyticforms}\n\nLet us begin by building some intuition for how the detectability of PSs is likely to scale in a NPTF-like setup. We will initially follow the approach of Ref.~\\cite{Leane:2020pfc}, essentially replacing the Poisson distributions with Gaussians; this will be a good approximation when the number of sources per pixel and number of counts\/source are both large, and can more generally provide qualitative insights into how various inputs affect the PS sensitivity.\n\nHere we will compute likelihoods and likelihood ratios as a measure of sensitivity, whereas in the numerical analysis of later sections we will perform a Bayesian analysis and evaluate Bayes factors. The Bayesian evidence is an integral of the likelihood weighted by the priors, and so loosely speaking we expect them to have qualitatively similar properties under variations of the source brightness, exposure, etc. However, our expressions for the likelihood ratios should not a priori be expected to accurately approximate the Bayes factors, since Bayes factors incorporate information from the priors (including the number of free parameters in the model), and the likelihood ratios do not.\\footnote{However, in practice, we will find that for our default choice of priors, the differences between the likelihood ratios and Bayes factors are small compared with other differences between the analytic and numerical results.}\n\\subsection{Pixel likelihood to observe $N$ photons} \\label{subsubsec:settingupanalytic}\n\nLet us first review some relevant results from Ref.~\\cite{Leane:2020pfc}. Consider a simplified scenario where our PS population model predicts $n_0$ sources per pixel, and all sources are identical, with an expected number of photons per source of $s$. For the moment, we will ignore leakage out of the pixel due to the non-trivial angular resolution, but as a first approximation the effect of such leakage would be to reduce $s$. We are interested in calculating the probability to observe $N$ photons in a pixel. \n\nIf we fix the number of observed sources (in a given pixel) to be $n$, then the total number of photons in the pixel will follow a Poisson distribution with mean $n s$. For $n s \\gg 1$, we can approximate this distribution as a Gaussian with a mean and variance of $n s$, via the Central Limit Theorem. Then the probability to observe $N$ photons is given approximately by:\n\\begin{equation}\n    P(N|\\{n, s \\}) = \\frac{1}{\\sqrt{2 \\pi n s}} e^{-(N-n s)^{2}\/(2 n s)}\n    \\label{eqn:p(n|nchis)}\n\\end{equation}\nAs a note, this expression can be thought of as a continuous probability density function (PDF), but also as a measure of the finite probability to observe $N$ photons by integrating the PDF over a bin of width $dN=1$ (i.e. the difference between adjacent values of $N$). Provided the PDF does not vary rapidly over the bin, this integral can simply be approximated by the value of the PDF at the center of the bin. We will use both interpretations of $P(N|\\{n,s\\})$ and similar quantities in the following calculations.\n\n\n\nThis distribution function is convolved with $P(n|n_{0})$, a distribution that describes the probability of drawing $n$ sources given that the expected number of sources is $n_{0}$. The resulting function, which we denote $P(N|{n_0, s})$, describes the likelihood of obtaining $N$ photons given that the number of sources is described by a Poisson distribution with an expectation value of $n_{0}$. If the number of sources is large, we can also approximate the distribution that describes the number of sources with a Gaussian with mean and variance $n_{0}$. Furthermore, the integrand is dominated by the region where $n s \\approx N$, so we can set $n s \\approx N$ except where $N- n s$ appears in an exponent. \n\nThese approximations yield the following equation for the probability to observe $N$ photons given $n_0$ and $s$:\n\n\\begin{align}\n    P(N|\\{n_{0},s \\}) &= \\int dn P(N |\\{n, s\\}) P(n|n_{0}) \\nonumber \\\\\n    &\\approx \\int dn \\frac{1}{\\sqrt{2 \\pi N}} e^{-(n s -N)^{2}\/(2N)} \\nonumber \\\\ & \\times \\frac{1}{\\sqrt{2 \\pi  n_{0}}}e^{-(n_{0}-n)^2\/(2 n_{0})}\n    \\label{eqn:convolution}\n\\end{align}\n\nThe integral over $n$ can be performed analytically and takes a simple form, if we assume the peak in the integrand is sufficiently far away from the limits of integration that we can take those limits to $\\pm \\infty$ without affecting the result. Furthermore, around the peak of the probability distribution we have $N \\approx n_{0} s$, so we can approximate $N\\approx n_0 s$ except when $N - n_0 s$ appears in an exponent. These approximations yield:\n\\begin{equation}\n\\begin{split}\n    P(N|\\{n_{0},s \\}) &\\approx \\frac{1}{\\sqrt{2 \\pi (N+n_{0} (s)^{2})}} e^{\\frac{-(N-n_{0} s)^{2}}{2(N+n_{0} s^{2})}}\\\\\n    &\\approx \\frac{1}{\\sqrt{2 \\pi n_{0}  s(1+ s)}} e^{\\frac{-(N-n_{0}  s)^{2}}{2 n_{0} s (1+ s)}}\n\\end{split}\n\\label{eqn:integraresult}\n\\end{equation}\n\n\n\nThat is, under these approximations the probability of observing $N$ photons takes a Gaussian form (at least near the peak of the distribution), but with an inflated variance of $n_0 s (1 + s)$, a factor of $(1+s)$ greater than the expectation value of $n_0 s$.\n\n\n\nIf $s \\ll 1$, our model corresponds to a very faint source population that should be indistinguishable from diffuse emission. In this case, we recover the standard Gaussian approximation to the Poisson distribution, with equal mean and variance of $n_0 s$, \n\n\\begin{equation}\n    P(N|\\{n_{0}, s \\}) \\approx \\frac{1}{\\sqrt{2 \\pi n_{0}  s}} e^{\\frac{-(N-n_{0} s)^{2}}{2 n_{0}  s }}\n\\label{eqn:poissondistribution}\n\\end{equation}\n\nThus the characteristic feature of a PS population (within these approximations) is an enhanced variance, by a factor of $1+s$. \n\nIn the event that the number of counts per source satisfies $s \\gg 1$ but the number of sources per pixel $n_0 \\lesssim 1$, a more refined approximation for the distribution may be useful (going beyond the results of Ref.~\\cite{Leane:2020pfc}). If $i$ sources are drawn in a given pixel ($i$ being an integer), the number of counts from those sources will be Poisson-distributed with expectation $s i$; for $s\\gg 1$ and $i > 0$, we can approximate each of these individual distributions as a Gaussian with mean and variance $s i$, so overall we have:\n\\begin{equation}\n    P(N|\\{n_{0}, s \\}) \\approx p_0(n_0) \\delta_{N,0} + \\sum_{i=1}^\\infty p_i(n_0) \\frac{1}{\\sqrt{2 \\pi s i}} e^{\\frac{-(N- s i)^{2}}{2 s i}},\n\\label{eqn:doublepoissondistribution}\n\\end{equation}\nwhere $p_i(n_0)$ is the Poisson probability of drawing $i$ sources when $n_0$ are expected.\n\n\n\\subsection{Likelihood ratio between models (Gaussian approximation)}\nNow suppose the true underlying model for a given pixel yields a Gaussian distribution for $N$ with mean $X$ and variance $\\sigma^2$. We wish to evaluate the expected log likelihood ratio between the correct model and an alternative model that predicts mean $Y$ and variance $\\tau^2$. We will denote these models respectively as $(X,\\sigma^2)$ and $(Y,\\tau^2)$. This result has been computed previously in Ref.~\\cite{Leane:2020pfc}; we review it here.\n\nFor context, the correct model might represent a linear combination of a PS population and a diffuse signal, while the alternative model allows only for a diffuse signal; the expected log likelihood ratio in this case then gives a measure of how well we will be able to exclude the all-diffuse model and thus detect the PS population. We will work out the case for general $(X,Y,\\sigma^2,\\tau^2)$ first, under the approximation where all the relevant probability distributions are Gaussian, and then apply this general result to several scenarios in which we might wish to detect PS populations. \n\n\n\nFor a single pixel, the probability of finding $N$ photons predicted by the model $(Y,\\tau^2)$) is:\n\\begin{equation}\n    \\mathcal{L} = P(N|\\{Y,\\tau^2 \\}) = e^{[-(N-Y)^{2}]\/(2 \\tau^{2})}\/\\sqrt{2 \\pi \\tau^{2}}\n    \\label{eqn:likelihoodeqn}\n\\end{equation}\ncorresponding to a log likelihood of $\\ln{\\mathcal{L}} = -\\frac{(N-Y)^2}{2\\tau^2} - \\frac{1}{2} \\ln{2\\pi \\tau^2}$. To get the expected value of the log likelihood, we can integrate against the true distribution of $N$, i.e. $P(N|\\{X,\\sigma^2\\})$. This yields \\cite{Leane:2020pfc}:\n\\begin{equation}\n    \\left \\langle \\ln{\\mathcal{L}}(Y,\\tau^2) \\right \\rangle = -\\frac{\\left[(X-Y)^2 + \\sigma^2\\right]}{2\\tau^2} - \\frac{1}{2} \\ln(2\\pi\\tau^2)\n \\end{equation}\n\n\n\nNow we diverge from Ref.~\\cite{Leane:2020pfc}, which focused on determining the best-fit choice for $\\tau^2$ given a discrepancy between $X$ and $Y$. Let us instead simply examine the expected $\\Delta \\ln\\mathcal{L}$ between the fitted model $(Y,\\tau^2)$ and the best-fit model $(X,\\sigma^2)$, which is given by:\n\\begin{align}\n    \\left \\langle \\Delta \\ln{\\mathcal{L}} \\right \\rangle & \\equiv\n     \\left \\langle \\ln{\\mathcal{L}}(X,\\sigma^2) - \\ln{\\mathcal{L}}(Y,\\tau^2)  \\right \\rangle \\nonumber \\\\\n     & =\\frac{\\left[(X-Y)^2 + \\sigma^2\\right]}{2\\tau^2} + \\frac{1}{2} \\ln(2\\pi\\tau^2) - \\frac{1}{2} - \\frac{1}{2} \\ln(2\\pi\\sigma^2) \\nonumber \\\\\n    & = \\frac{\\left[(X-Y)^2 + \\sigma^2\\right]}{2\\tau^2} - \\frac{1}{2} \\left[1 +  \\ln\\left(\\frac{\\sigma^2}{\\tau^2}\\right) \\right]\n \\end{align}\n \n If both models produce a very similar expected number of  photons, i.e. $X\\approx Y$, and differ only in their variances, then this result can be simplified to:\n \\begin{align}\n    \\left \\langle \\Delta \\ln{\\mathcal{L}} \\right \\rangle \n    & = \\frac{\\sigma^2}{2\\tau^2} - \\frac{1}{2} \\left[1 +  \\ln\\left(\\frac{\\sigma^2}{\\tau^2}\\right) \\right] \\label{eqn:bayesfactor}\n \\end{align}\n \n Note however that if $Y$ and $\\tau^2$ are allowed to vary within certain limits or while satisfying certain conditions, then it is not guaranteed that the best-fit point lies at $Y=X$; if the global likelihood maximum (at $Y=X$, $\\tau^2=\\sigma^2$) cannot be attained, then the best-fit value of $Y$ will depend on the value of $\\tau^2$ (and vice versa). Most simply, this can occur when the model is Poissonian, in which case $\\tau^2$ is fixed to $Y$, but the data has non-Poissonian components and so $\\sigma^2$ differs from $X$ in the true underlying model. A related scenario, studied in Refs.~\\cite{Leane:2020nmi, Leane:2020pfc}, occurs when the model requires the same value of $Y$ in multiple pixels but the true underlying model varies across those pixels; this leads to a best-fit model variance $\\tau^2$ that differs from the true underlying variance $\\sigma^2$ (possibly leading to misattribution of the enhanced variance to a PS population).\n\n\n\n\n\\subsection{Variance between realizations (Gaussian approximation)}\n\nIn addition to working out the expected log likelihood ratio as a measure of sensitivity to incorrect modeling (such as attempting to describe PSs with a Poissonian template), it is helpful to understand the expected variability in this ratio between different realizations. In the limit where the number of pixels is large, the total $\\Delta \\ln\\mathcal{L}$ for the image is the sum of many independent random variables ($\\Delta \\ln\\mathcal{L}$ for each pixel), and so is expected to follow a Gaussian probability distribution by the Central Limit Theorem (even if the probability distribution for $\\Delta \\ln\\mathcal{L}$ in a single pixel is highly non-Gaussian). Consequently, in this limit, we expect the distribution of the total $\\Delta \\ln\\mathcal{L}$ (summed over pixels) to be well-characterized by its expectation value and variance.\n\nAs in the previous subsection, we will work out the result initially for general choices of the PDF parameters for the true and alternative hypotheses, $(X,Y,\\sigma^2,\\tau^2)$. We will then apply these results to specific scenarios, in particular where the true model (described by $(X,\\sigma^2)$) includes a PS component but the alternative model (described by $(Y,\\tau^2)$) does not.\n\n\nWe can estimate the variance of $\\Delta \\ln \\mathcal{L}$ by evaluating $\\text{Var}(\\Delta\\ln \\mathcal{L}) \\equiv \\langle (\\Delta \\ln\\mathcal{L})^2 \\rangle - \\langle \\Delta \\ln\\mathcal{L} \\rangle^2$. Let us first focus on the case  where $\\sigma \\gg \\tau$ and $\\left \\langle \\Delta \\ln{\\mathcal{L}} \\right \\rangle \\gg 1$ and so the first term dominates in Eq.~\\ref{eqn:bayesfactor}. This can occur, for example, where there is a bright PS population inducing a large variance $\\sigma^2 \\gg X$, which cannot be replicated by an alternative model based solely on diffuse emission with Poissonian statistics; in that sense this is a high-detectability limit.\n\n\nThen using the estimates above and again taking $X\\approx Y$, we find that:\n\\begin{align} \\langle (\\Delta \\ln\\mathcal{L})^2 \\rangle &\\approx \\int dN \\left[-\\frac{(N-X)^2}{2\\tau^2} + \\frac{(N-X)^2}{2\\sigma^2}\\right]^2 \\nonumber \\\\\n& \\times P(N|\\{X,\\sigma^2\\}) \\nonumber \\\\\n& \\approx \\frac{3}{4} \\left(\\frac{\\sigma}{\\tau}\\right)^4,\\end{align}\nand thus:\n\\begin{align} \\text{Var}(\\Delta\\ln \\mathcal{L}) & \\approx \\frac{3}{4} \\left(\\frac{\\sigma}{\\tau}\\right)^4 - \\frac{1}{4} \\left(\\frac{\\sigma}{\\tau}\\right)^2 \\nonumber \\\\\n& = \\frac{1}{2} \\left(\\frac{\\sigma}{\\tau}\\right)^4.\\end{align}\nThus we expect the standard deviation in this regime to be:\n\\begin{align}\\text{std}(\\Delta\\ln \\mathcal{L}) & \\approx \\frac{1}{\\sqrt{2}}\\frac{\\sigma^2}{\\tau^2} \\nonumber \\\\\n&\\approx \\sqrt{2} \\langle \\Delta \\ln \\mathcal{L}\\rangle.\\end{align}\nWe see that we generically expect the scatter in $ \\Delta \\ln\\mathcal{L}$ (from a single pixel) to be of the same order as its expected value. When combining $n_\\text{pix}$ pixels, the expectation value and variance are both enhanced by a factor of $n_\\text{pix}$, so the standard deviation should be suppressed relative to the expectation value by a factor of $1\/\\sqrt{n_\\text{pix}}$.\n\nIn this high-detectability, purely Gaussian case, there is actually a simple analytic expression for the full PDF of $\\Delta \\ln \\mathcal{L}$,\n\\begin{equation} P(\\Delta \\ln \\mathcal{L} = x) = \\frac{1}{\\sqrt{\\pi x \\delta}} e^{-x\/\\delta}, \\, x \\ge 0, \\end{equation}\nwhere $\\delta \\equiv (\\sigma^2\/\\tau^2) - 1$. It can be readily checked that this distribution reproduces the expectation value and variance given above for $\\delta \\gg 1$. Note that this distribution is not at all Gaussian; however, as discussed above, combining a large number of pixels and summing their $\\Delta \\ln \\mathcal{L}$ contributions is expected to give an approximately Gaussian PDF by the Central Limit Theorem.\n\nIf we instead consider the low-detectability case where $\\tau^2 \\approx \\sigma^2$, i.e. $\\delta = (\\sigma^2\/\\tau^2) -1 \\ll 1$, then we instead obtain:\n\\begin{align} \\langle (\\Delta \\ln\\mathcal{L})^2 \\rangle & \\approx \\int dN \\left[-\\frac{(N-X)^2}{2\\tau^2} + \\frac{(N-X)^2}{2\\sigma^2}\\right.\\nonumber \\\\\n& \\left. - \\frac{1}{2}\\ln \\frac{\\tau^2}{\\sigma^2} \\right]^2 P(N|\\{X,\\sigma^2\\}) \\nonumber \\\\\n& \\approx \\delta^2 \\int dN  \\left[- \\frac{(N-X)^2}{2\\sigma^2} + \\frac{1}{2} \\right]^2 P(N|\\{X,\\sigma^2\\}) \\nonumber \\\\\n& \\approx \\delta^2\/2.\\end{align}\nIn the same limit, \n\\begin{align} \\langle \\Delta \\ln\\mathcal{L} \\rangle &\\approx \\delta^2\/4.\\end{align}\nThus for $\\delta \\ll 1$, the first term dominates the variance and we have:\n\\begin{align} \\text{Var}(\\Delta\\ln \\mathcal{L}) & \\approx \\delta^2\/2 \\approx 2 \\langle \\Delta \\ln\\mathcal{L} \\rangle.\\end{align}\nThus in this case the square root of the variance is parametrically enhanced (by a factor of $1\/\\delta$) relative to the expectation value. The variance and expectation value are parametrically similar and will both be enhanced by a factor of $n_\\text{pix}$ when multiple pixels are combined, and so in this regime the standard deviation (square root of the variance) should be of the same order as the square root of the expectation value.\n\nNow we will apply these results to estimate the expected log likelihood ratio between a model containing PSs and one that omits them, when a real population of PSs is present in the data. This $\\Delta \\ln \\mathcal{L}$ will tell us the confidence level with which we expect to be able to exclude the model with no PSs, and hence the confidence level for PS detection. It is similar to the metric we will use for sensitivity to a PS population in our numerical studies.\n\n\\subsection{Single component (100 \\% PS emission)} \\label{subsubsec:case1analytic}\n\nLet us begin by assuming that the data is completely described by a PS population (of identical sources, as described above) without any contribution from a smooth background source. The PS emission has a mean and variance approximated by $(X,\\sigma^{2}) = (N, N (1+s))$, where $s$ is the number of photons per source and $N$ the total number of photons. \n\nLet us consider the expected $\\Delta \\ln \\mathcal{L}$ between the correct PS-based model, and a model that includes only smooth emission, but which correctly predicts the expected number of photons $N$. Such a smooth model must have equal mean and variance, so we must have $(Y,\\tau^{2}) = (N,N)$.\n\n\n\nUsing Eq.~\\ref{eqn:bayesfactor}, we plug in these parameters and obtain:\n\n\\begin{equation}\n   \\langle \\Delta \\ln{\\mathcal{L}}\\rangle \\approx \\frac{1}{2} \\left[s - \\ln\\left(1+ s\\right) \\right]\n    \\label{eqn:case1naturallogbf}\n\\end{equation}\nNote that {\\it all} dependence on the total number of photons $N$ has canceled out; only the number of photons per source is relevant. In particular, this property ensures the likelihood ratio will go to 1 when $s \\ll 1$ as required (since this corresponds to the limit of many very faint sources, at which point the smooth model is perfectly adequate), even if the number of sources is very large. Specifically, at small $s$ we have $\\langle \\Delta \\ln{\\mathcal{L}}\\rangle \\approx (s\/2)^2$.\n\nHowever, this behavior also has the perhaps-surprising implication that having {\\it more} sources (and hence more photons) of fixed brightness in a single pixel neither increases nor decreases the PS sensitivity based on the pixel likelihood, at least once the numbers are large enough that the relevant likelihoods can be approximated as Gaussian. \n\nThe leading order behavior of this function at large $s$ is $\\langle \\Delta \\ln{\\mathcal{L}}\\rangle \\approx s\/2$, i.e. the log likelihood in favor of PSs grows linearly with the brightness of the sources. Since the number of photons seen from a given source is directly proportional to the exposure (i.e. time viewing the source multiplied by the effective area of the instrument), we expect that (at least in this background-free case) $\\langle \\Delta \\ln{\\mathcal{L}}\\rangle$ will also grow linearly with exposure. The normalization factor here is also familiar. $2\\Delta \\ln\\mathcal{L} \\approx s$ is often used as a test statistic, whose square root translates to the significance in sigma; thus roughly speaking, we expect the detection significance of the PS population (measured in sigma) from a given pixel to approach $\\sqrt{s}$ for large $s$.\n\n\n\nIf we do not impose the condition that the expected number of photons is $N$, we can maximize the likelihood for this model under the condition $Y=\\tau^2$, obtaining:\n\\begin{equation}Y_\\text{optimal} = \\frac{1}{2} \\left(\\sqrt{4 X^2 + 4\\sigma^2 + 1} -1\\right).\\end{equation}\nFor the case at hand, this yields $Y_\\text{optimal} = \\frac{1}{2} \\left(\\sqrt{4 N^2 + 4 N(1+s) + 1} -1\\right)$. If $N \\gg s$, $N \\gg 1$ (i.e. the number of both sources and photons is large, consistent with our Gaussian approximations), then to a good approximation $Y_\\text{optimal} \\approx N$ and the estimates above should be reasonable. It is also true in practice, in NPTF analyses of the GCE, that the total photon flux associated with the best-fit GCE model is typically very similar when comparing the fits with and without a model for GCE PSs (e.g. \\cite{Lee:2015fea}).\n\n\\subsection{Generalization to arbitrary ratio of PS and smooth emission}\n\nNow let us consider the scenario in which a fraction $k$ of the emission is associated with PSs and the remainder with smooth emission. We seek to evaluate $\\langle \\Delta \\ln{\\mathcal{L}}\\rangle$ between the best-fit model (corresponding to the truth) and the model with only smooth emission.\n\nThe total number of predicted photons is the sum of the predicted photons associated with each component. The sum of two Gaussian-distributed random variables is also Gaussian-distributed, with mean (variance) given by the sum of the means (variances) for the individual distributions. Thus within our approximations, the best-fit model (matching the truth) has a Gaussian probability distribution for the number of photons $N$ with parameters $(X,\\sigma^{2})=(kN+(1-k)N,kN(1+ s)+(1-k)N)$. \n\nThe model with only smooth components that matches the total number of photons has (as in our previous example) $(Y,\\tau^{2}) = (N,N)$. \n\nUsing Eq.~\\ref{eqn:bayesfactor}, we obtain:\n\n\\begin{equation}\n   \\langle \\Delta\\ln \\mathcal{L}\\rangle \\approx \\frac{k}{2} s  +\\ln{\\left(\\frac{1}{\\sqrt{1+k s}}\\right)}\n    \\label{eqn:lnBFcase2}\n\\end{equation}\n\nThus the effect of a non-zero background fraction on the sensitivity is equivalent to rescaling the photon flux of individual sources. In this case, the change in scaling behavior from $\\langle \\Delta\\ln \\mathcal{L}\\rangle \\propto s^2$ to $\\langle \\Delta\\ln \\mathcal{L}\\rangle \\propto s$ will occur parametrically around $k s \\sim 1$. It is worth noting that if there are a large number of pixels, a significant detection may be consistent with $k s \\ll 1$ from every individual pixel, and in this case we should expect a faster-than-linear scaling of the log likelihood ratio with increasing $s$ (or $k$).\n\n\\subsection{A more accurate probability distribution: accounting for rare sources}\n\nWe can also compute the expected value of the likelihood ratio and its variance, between two Gaussian models, if the underlying ``true'' probability distribution is given by Eq.~\\ref{eqn:doublepoissondistribution}, for the case $n_0 \\lesssim 1$ where the Gaussian approximations break down. For a Gaussian distribution with mean $X$ and variance $\\sigma^2$, we find:\n\n\\begin{align} \\langle \\ln \\mathcal{L}\\rangle & = \\int dN \\left[-\\frac{(N-X)^2}{2\\sigma^2} - \\frac{1}{2} \\ln(2\\pi\\sigma^2)\\right] P(N|n_0, s) \\nonumber \\\\\n& = p_0(n_0) \\left[-\\frac{X^2}{2\\sigma^2} - \\frac{1}{2} \\ln(2\\pi\\sigma^2)\\right] \\nonumber \\\\\n& + \\sum_{i=1}^\\infty p_i(n_0) \\int dN \\left[-\\frac{(N-X)^2}{2\\sigma^2} - \\frac{1}{2} \\ln(2\\pi\\sigma^2)\\right] \\nonumber \\\\\n&\\times \\frac{1}{\\sqrt{2\\pi i s}} e^{-(N - i s)^2\/2 i s} \\nonumber \\\\\n& = -\\frac{1}{2} \\sum_{i=0}^\\infty p_i(n_0) \\left[\\frac{(i s -X)^2+ i s}{\\sigma^2} + \\ln(2\\pi\\sigma^2)\\right], \\end{align}\nwhere again we have made the approximation of taking the limits of integration to $\\pm \\infty$, relying on $i s \\gg 1$ for $i \\ge 1$ (so that the Gaussians are centered well away from the limits of integration). Now the infinite sums over $i$ can be computed by using the fact that the Poisson probabilities $p_i(n_0) = n_0^i e^{-n_0}\/i!$ satisfy $\\sum_{i=0}^\\infty p_i(n_0) = 1$. In particular, by relabeling dummy indices the following identities can easily be proved:\n\\begin{align} \\sum_{k=0}^\\infty k p_k(n_0) & = n_0,\\nonumber \\\\\n\\sum_{k=0}^\\infty k^2 p_k(n_0) & = n_0 (n_0 + 1). \\nonumber \\\\\n\\sum_{k=0}^\\infty k^3 p_k(n_0) & = n_0^3 +3 n_0^2 + n_0, \\nonumber \\\\\n \\sum_{k=0}^\\infty k^4 p_k(n_0) & = n_0^4 + 6 n_0^3 + 7 n_0^2 + n_0. \\label{eqn:poissonidentities}\n\\end{align}\n\nApplying these results we find:\n\\begin{align} \\langle \\ln \\mathcal{L}\\rangle & = - \\frac{1}{2} \\left[\\ln(2\\pi \\sigma^2) + \\frac{X^2 + s^2 n_0 (n_0 + 1) + s n_0 (1 - 2 X)}{\\sigma^2}\\right] \\end{align}\n\nIn particular, if we hold the variance constant then the likelihood is maximized for $X=n_0 s$, and if we set $X=n_0 s$ (i.e. the model matches the expected total number of photons), then we obtain:\n\\begin{align} \\langle \\ln \\mathcal{L}\\rangle & = - \\frac{1}{2} \\left[\\ln(2\\pi \\sigma^2) + \\frac{n_0 s(1+s)}{\\sigma^2}\\right] \\end{align}\nThe likelihood is then maximized for $\\sigma^2 = n_0 s (1+s)$, which is the same variance we found when we directly approximated the probability distribution for the point-source population as Gaussian.\n\nIf we examine the expected $\\Delta \\ln \\mathcal{L}$ between this best-fit Gaussian model and a Gaussian model with $\\sigma^2 = X = n_0 s$ (representing a purely diffuse signal), we find:\n\\begin{align} \\langle \\Delta \\ln \\mathcal{L}\\rangle & = - \\frac{1}{2} \\left[\\ln(1+s) + \\frac{n_0 s(1+s)}{n_0 s(1+s)} - \\frac{n_0 s(1+s)}{n_0 s}\\right] \\nonumber \\\\\n& = \\frac{1}{2} \\left[s - \\ln(1+s)\\right]  \\end{align}\nRemarkably, this is exactly the same result we found under the Gaussian approximation for the underlying probability distribution (Eq.~\\ref{eqn:case1naturallogbf}), suggesting that this result is quite robust even when the assumptions needed to justify the Gaussian approximation break down.\n\nAs previously, we can generalize to the case where PSs constitute a fraction $k$ of the total emission, so the total expected photon count is $n_0 s\/k$ with an expected number of $(1-k) n_0 s\/k$ photons originating from diffuse emission. In this case the probability distribution for $N$ given in Eq.~\\ref{eqn:doublepoissondistribution} must be updated accordingly. As previously, we approximate the probability distribution for the number of photons from diffuse emission as a Gaussian with mean and variance $(1-k) n_0 s\/k$; for each choice $i$ for the number of sources drawn, the emission from sources (mean and variance $s i$) can be added to that from diffuse emission by the usual prescription for the sum of normally-distributed random variables (i.e. the means and variances add). Thus the overall distribution becomes:\n\\begin{align} & P(N|n_0, s, k) \\approx \\nonumber \\\\\n& \\sum_{i=0}^\\infty p_i(n_0) \\frac{e^{-(N- s (i + n_0(1\/k- 1)))^2\/2 s (i + n_0(1\/k- 1))}}{\\sqrt{2 \\pi s (i + n_0(1\/k- 1))}}, \\label{eqn:doublepoissonmixed}\\end{align}\nwhere as previously $p_i(n_0)$ is the Poisson probability of drawing $i$ sources when $n_0$ are expected.\n\nUnder this distribution, if we compute the expected likelihood of a Gaussian model with mean $X$ and variance $\\sigma^2$, we find (by the same methods as previously):\n\\begin{align} \\langle \\ln \\mathcal{L}\\rangle  \n& =  - \\frac{1}{2} \\left[ \\frac{1}{\\sigma^2} \\left(X^2 - \\frac{2 X n_0 s}{k} \\right. \\right. \\nonumber \\\\\n& \\left. \\left. + \\frac{n_0 s(k + s (k^2 + n_0))}{k^2}  \\right) + \\ln(2\\pi \\sigma^2) \\right]  \\end{align}\nFor fixed $\\sigma^2$, this is maximized for $X=n_0 s\/k$ (as expected, when the model matches the total number of counts); if we fix $X=n_0 s\/k$, then we obtain:\n\\begin{align} \\langle \\ln \\mathcal{L}\\rangle = - \\frac{1}{2} \\left[ \\frac{1}{\\sigma^2} \\left(\\frac{n_0 s (ks + 1)}{k}  \\right) + \\ln(2\\pi \\sigma^2 ) \\right].  \\end{align}\nThe expected log likelihood difference between the purely diffuse Gaussian model with $\\sigma^2=X= n_0 s$ and the Gaussian model with $\\sigma^2=(n_0 s \/ k) (k s + 1)$ (matching our previous prescription in the case of mixed PS and smooth emission) is then given by,\n\\begin{align} \\langle \\Delta \\ln \\mathcal{L} \\rangle = \\frac{1}{2} \\left[k s + \\ln \\frac{1}{1+k s} \\right], \\end{align}\nexactly as previously.\n\nHowever, while the expected log likelihood is unchanged by shifting to this modified probability distribution, the variance differs. Working in the limit where the log terms in the delta log likelihood can be ignored, let us examine the variance of the delta log likelihood between the Gaussian models with  $\\sigma^2= n_0 s$ and $\\sigma^2=(n_0 s \/ k) (k s + 1)$. In both cases we take $X=n_0 s\/k$. Then using the identities in Eq.~\\ref{eqn:poissonidentities}, we obtain:\n\\begin{align}\n\\text{Var}(\\Delta \\ln \\mathcal{L}) & =  \\langle (\\Delta \\ln \\mathcal{L})^2 \\rangle - \\langle \\Delta \\ln \\mathcal{L} \\rangle^2 \\nonumber \\\\\n & \\approx k^2 \\frac{s(s+6) + 3}{4 n_0} \\left( \\frac{ks}{k s + 1}\\right)^2 + \\frac{1}{2} (k s)^2 \\nonumber \\\\\n & \\rightarrow \\langle \\Delta \\ln \\mathcal{L}\\rangle^2 \\left(\\frac{1}{n_0} + 2 \\right), \\quad k s \\gg 1 .  \\end{align}\n\nIn particular, we observe that there is now an additional term in the variance which scales as $1\/n_0$. Consistently with our previous calculation, this term will be negligible when $n_0 \\gg 1$ and our original Gaussian approximation holds, but it can lead to a significant enhancement to the variance when $n_0\\ll 1$. In particular, for $k s \\gg 1$ and $n_0 \\ll 1$, we expect that the variance over the full dataset can be approximated as:\n\\begin{align}\\text{Var}(\\Delta \\ln \\mathcal{L}) & \\approx n_\\text{pix} \\langle \\Delta \\ln \\mathcal{L}\\rangle^2_\\text{per pixel} \/n_0 \\nonumber \\\\\n& \\approx \\langle \\Delta \\ln \\mathcal{L}\\rangle^2_\\text{overall} \/n_0 n_\\text{pix}, \\nonumber \\\\\n\\Rightarrow \\text{std}(\\Delta \\ln \\mathcal{L}) & \\approx \\frac{\\langle \\Delta \\ln \\mathcal{L}\\rangle_\\text{overall}}{\\sqrt{n_0 n_\\text{pix}}}.\\end{align}\nThus we see that in this case, rather than the suppression of $1\/\\sqrt{n_\\text{pix}}$ that we found earlier (for the high-$k s$ case), instead the suppression is only $1\/\\sqrt{n_\\text{tot}}$, where $n_\\text{tot}=n_0 n_\\text{pix}$ is the total number of PSs in the image.\n\nBroadly speaking, the standard deviation in $\\Delta \\ln\\mathcal{L}$ is always related to $\\langle \\Delta \\ln \\mathcal{L}\\rangle$ by a factor of $1\/\\sqrt{A}$, but $A$ can be either the number of pixels, the number of PSs (when the number of sources per pixel is small), or the test statistic $\\langle \\Delta \\ln \\mathcal{L}\\rangle$ itself (when the contribution to the test statistic per pixel is small). In the examples we have checked, it is always the smallest of these three parameters that dominates the variance, which is intuitively sensible. \n\nNote that in particular this means the variance can be much larger than one might naively estimate from the square root of the test statistic; if the number of sources is only $\\mathcal{O}(100)$, then the variance in the test statistic will be consistently at the $\\mathcal{O}(10\\%)$ level even if the sources are bright and the significance of detection is very high. Furthermore, we have so far neglected contributions to the variance from the width of the source count function (which will modify the effective $s$ entering these calculations from realization to realization, and hence increase the variance), the presence of a non-zero point spread function (likewise), and cross-talk and degeneracies with other background components.  \n\n\\subsection{Implications for analysis choices}\n\nIf the overall number of photon counts increases, due to increased exposure (i.e. increased observation time or effective area), the signal fraction $k$ remains constant while $s$ varies linearly. Consequently, we expect $\\langle \\Delta \\ln \\mathcal{L}\\rangle$ to depend linearly on exposure for sufficiently large $s$, with the transition from quadratic to linear scaling beginning around $s \\sim 1\/k$.\n\nSuppose a non-zero angular resolution for the instrument causes the expected number of photons from a single source in a pixel to be reduced, due to leakage into neighboring pixels. Then $\\langle \\Delta \\ln \\mathcal{L}\\rangle$ will be reduced by the same factor, in the regime where the delta log likelihood scales linearly with $s$. The signal fraction $k$ should not be affected by this leakage unless the overall distribution of either the signal or background varies rapidly relative to the angular resolution scale; if there is such a rapid variation, there may also be a correction corresponding to the change in $k$. \n\nThe fact that the sensitivity depends only on $ks$ suggests that it is generally more important to have a low background fraction (high $k$) than a high density of sources (since the latter has no effect on the expected sensitivity in the regimes of validity of our analytic approximations). This suggests that the sensitivity is likely to be dominated by pixels where the expected PS signal is brightest as a fraction of all diffuse backgrounds (which may not be the pixels with the largest number of sources).\n\n\nWe have derived these results for the contribution to $\\langle \\Delta \\ln \\mathcal{L}\\rangle$ from a single pixel, but the overall log likelihood is simply the sum of the results for the individual pixels. We can thus apply these results even to the realistic case where the background and signal models can have quite different spatial distributions: we simply calculate the appropriate $k$-value in each pixel and estimate the contribution to $\\langle \\Delta \\ln \\mathcal{L}\\rangle$ accordingly. Also note that the smooth model can be arbitrarily complicated; the only information we have used is that it has Poissonian statistics.\n\n\n\\section{Inputs and methodology for numerical calculations} \\label{sec:Methodology}\n\\subsection{Data selection} \\label{subsec:DataSelection}\nTo calibrate our simulations to the real gamma-ray sky, we employ eleven years of the Pass 8 public \\textit{Fermi} data. The data were collected over 573 weeks from August 4, 2008 to June 19, 2019. To employ the most stringent cosmic-ray rejection criteria, we restrict our selection to the ULTRACLEANVETO event class. For most tests, except those that varied energy range, we limited the energy range to $2 - 20$ GeV, following the default in \\texttt{NPTFit} and previous NPTF analyses. We restrict ourselves to an analysis of the top three quartiles of the data graded by angular resolution, as this provides enough range in angular resolution to explore the tradeoff with exposure, and the angular resolution degrades significantly in the bottom quartile.\n\n\\subsection{\\texttt{NPTFit} scan setup} \\label{subsec:NPTFit}\n\nWe employ \\texttt{v.0.2} of \\texttt{NPTFit}, together with \\texttt{MultiNest}, a Bayesian inference tool \\cite{Mishra-Sharma:2016gis,Feroz:2008xx}. For fits of the simulated data, the number of live points is described within the individual procedure sections; when not otherwise specified we used nlive=100. (We have checked that the effect on $\\langle \\ln \\text{BF}\\rangle$ of increasing nlive beyond 100 was consistently very small.)\n\n\nWhen fitting to simulated data, our region of interest (ROI) is centered on the GC and has a radius of $15^{\\circ}$. We exclude the band with galactic latitude $|b| < 2^{\\circ}$. This ROI is chosen for computational efficiency and to minimize contamination from background emissions, while preserving sensitivity to the GCE, motivated by a recent study finding that sensitivity to GCE PSs plateaus for ROIs with radii between $15^{\\circ}$ and $20^{\\circ}$ \\cite{Buschmann:2020adf}. Our expectation is that shifting to a modestly different ROI would not significantly affect the scaling with exposure, angular resolution, etc, that we study in this work, although the overall sensitivity would change and so should not be compared directly between analyses with different ROIs.\n\nDuring \\texttt{NPTFit} scans, the non-Poissonian components of the sky maps must be exposure corrected at each pixel (a computationally-costly process) since the exposure map (a map that reflects the duration of observation and the stringency of data selection) is non-uniform \\cite{Mishra-Sharma:2016gis,Feroz:2008xx}. In order to optimize computational efficiency (and consistent with the recommendations in \\texttt{NPTFit}), we set $\\text{nexp} = 5$ to divide the ROI into $5$ distinct regions within which the exposure is treated as uniform. \n\n\\subsection{Modeling the gamma-ray sky}\n\nWe conducted a Bayesian \\texttt{NPTFit} analysis of the (real data) \\textit{Fermi} sky map at nlive = 500, modeling the sky as a linear combination of spatial templates characterized by parameters and prior distributions that are described in Appendix~\\ref{app:detailedmethodology}. For this analysis, and subsequent fits to real data (which were used only to choose parameters for the subsequent simulations), we extended the radius of the ROI from $15^\\circ$ to $30^\\circ$, but retained the mask of the Galactic plane (consistent with defaults in \\texttt{NPTFit}). Smooth\/diffuse templates were included for the \\textit{Fermi} Bubbles (``Bub\"), smooth isotropic emission (``Iso\"), smooth GCE (``GCE\"), and Galactic diffuse emission (``Dif\"). Templates were included for PS populations associated with the GCE (``GCE PS\"), isotropic \/ extragalactic sources (``Iso PS\"), and the Galactic disk (``Disk PS\"). Smooth\/diffuse templates each have one associated parameter, $A_{\\text{smooth}}$, controlling their overall normalization in the model; PS population templates (hereafter ``PS templates'') are associated with an overall normalization parameter $A_{\\text{PS}}$ which controls the number of sources, and with a source count function (SCF) which describes the number of sources as a function of their flux. We use a singly-broken power law model for the SCF, as is the default in \\texttt{NPTFit}:\n\\begin{equation}\n    \\frac{dN}{dS} = A_{\\text{PS}} T_{\\text{PS}}\n    \\begin{cases}\n    \\left ( \\frac{S}{S_{b}} \\right )^{-n_{1}}  & S \\geq S_{b} \\\\\n    \\left ( \\frac{S}{S_{b}} \\right )^{-n_{2}} & S \\le S_{b}\n    \\end{cases},\n    \\label{eqn:scf}\n\\end{equation}\nwhere $A_{\\text{PS}}$ is an overall normalization factor, and $T_{\\text{PS}}$ is the position-dependent template with the fixed normalization given in the \\texttt{NPTFit} code (see Appendix \\ref{app:detailedmethodology} for details). Note the parameter $S_b$ controls the expected number of photon counts per source at the position of the break in the power law. The total number of sources in a given pixel is then set by:\n\\begin{equation} N_\\text{tot} = A_{\\text{PS}} T_{\\text{PS}} S_b \\left(\\frac{1}{n_1 - 1} + \\frac{1}{1 - n_2}\\right)\\label{eq:nsource} \\end{equation}\nwhereas the total number of photons is set by:\n\\begin{equation} S_\\text{tot} = A_{\\text{PS}} T_{\\text{PS}} S_b^2 \\left(\\frac{1}{n_1 - 2} + \\frac{1}{2 - n_2}\\right). \\label{eq:nphotons} \\end{equation}\n\nNote that in the main text of the paper we employ the default Galactic diffuse emission model from \\texttt{NPTFit}, constructed from the {\\it Fermi} Collaboration's \\texttt{p6v11} diffuse model. This model is known to have features that can bias the results \\cite{Buschmann:2020adf} when it is used directly to reconstruct PS populations from the real data; however, it should provide a reasonable description of the data when we are only interested in constructing and analyzing simulations (where the model is correct by construction). To check this assertion, in Appendix~\\ref{app:modela} we recalculate our results with a different Galactic diffuse emission model and comment on the differences. Either of these Galactic diffuse emission models reconstruct the GCE as being $100\\%$ PSs, with the smooth GCE component being negligible: consequently, our simulations will generally explore the sensitivity of NPTF methods to a PS population bright enough to explain the full GCE.\n\nAfter performing this fit, we extracted the posterior median parameters associated with each template, which were then used as the baseline inputs to  simulations for the rest of the paper. These simulation parameters are displayed in Table \\ref{tab:fitparam} in Appendix~\\ref{app:detailedmethodology}. Note in particular that (consistent with previous NPTF studies) the inferred shape of the SCF for the GCE PS is quite sharply peaked around $S_b$, so we will generally be simulating GCE PS populations where the PSs all have roughly the same brightness as observed at Earth (fixed by $S_b$). This is likely {\\it not} a realistic luminosity function, but serves as a convenient basis for understanding the sensitivity of NPTF methods. We discuss the sharpness of the SCF peak further in Appendix~\\ref{app:sharpSCF}.\n\n\\subsection{Producing simulated sky maps}\n\\label{subsec:skymapsimulations}\n\nFor each template, we generated realizations based on the posterior median parameters from the real data. For the smooth\/diffuse emission components, we performed a Poisson draw from the associated template (with normalization given by the simulation parameters taken from the fit to real data).  To obtain realizations of PS populations, we employed \\texttt{NPTFit-Sim}.\n\nTo obtain the full skymaps, the individual components were summed. All skymaps were binned using \\texttt{HEALPix}, a package designed to allow equal-area pixelization of the sky \\cite{Gorski:2004by}. The nside value controls the pixel size, with the sky having a total of $12\\times \\text{nside}^2$ equal-area pixels. By default we set nside to 128, which is also the \\texttt{NPTFit} default, and corresponds to roughly a $~0.5^{\\circ}$ mean spacing between individual pixel centers in the region toward the GC. For nside=128, there are 2808 pixels within our ROI.\n\n\\subsection{Sensitivity figure of merit} \\label{subsec:sensitivity}\n\n\nA \\texttt{NPTFit} analysis returns posterior probability distributions for each of the parameters, and an estimate of the overall Bayesian evidence for the model. Comparing two \\texttt{NPTFit} analyses, with different template choices, allows us to evaluate the Bayes factor (BF) between the two scenarios, as the ratio of their evidences. In particular, we can define the sensitivity to a GCE PS population in terms of the BF in favor of a model that contains the complete set of templates (Dif, Bub, Iso, GCE, GCE PS, Disk PS, Iso PS) compared with a model that excludes the GCE PS template. A high value of this BF corresponds to a high-significance detection of the GCE PS template, over and above the smooth GCE template. For convenience, we will generally work with $\\ln{\\text{BF}}$ rather than the BF itself. Where $\\text{BF} \\lesssim 1$ and so $\\ln\\text{BF}$ is negative, there is no detection of GCE PSs. \n\nThe BF directly gives the ratio of Bayesian probabilities that the model with the GCE PS template is correct, compared to the model without that contribution. For those more accustomed to frequentist statistics, it may be helpful to think of the BF as comparable to a likelihood ratio $\\mathcal{L}_1\/\\mathcal{L}_2$, with additional terms that penalize models with more degrees of freedom. In this sense $2 \\ln{\\text{BF}}$ is broadly analogous to the commonly-used test statistic $2 \\Delta \\ln{\\mathcal{L}}$, which for a likelihood that is Gaussian near its maximum ($\\mathcal{L}(x) \\propto e^{-x^2\/(2\\sigma^2)}$) can be written as $2 \\Delta \\ln{\\mathcal{L}} \\approx (x\/\\sigma)^2$, and thus can be thought of as the ``number of sigma'' squared associated with the deviation from the best-fit point.\n\nThe $\\ln \\text{BF}$ in favor of a GCE PS population can vary widely between realizations. For our main figure of merit for sensitivity, we will use the expected value of $\\ln \\text{BF}$ obtained by taking the average across realizations, $\\langle \\ln \\text{BF} \\rangle$, although we will also show the scatter between realizations. \n\n\\section{Procedures for parameter variation}\n\\label{sec:varyingdiffparams}\n\nWithin each subsection below, we describe the general procedure for varying different inputs: exposure, angular resolution, source brightness, and pixel size. We describe the method for adjusting parameters in the simulation of skymaps as well as how to account for these variations through the priors when analyzing the skymaps using \\texttt{NPTFit}. If the test involves combinations of these variations, then the priors must be modified by simultaneously implementing the adjustment factors to the priors for each alteration performed. \n\n\\subsection{Exposure}\n\\label{subsec:varyingexposue}\n\nAlthough \\textit{Fermi} is a space-based telescope, it does not observe every part of the sky simultaneously. As a result, an exposure map is needed to keep track of how long \\textit{Fermi} observed a particular region of the sky and with what effective area. The exposure map provided by the \\textit{Fermi}-LAT Collaboration and implemented in \\texttt{NPTFit} has units of $\\text{cm}^{2}\\text{s}$ \\cite{Mishra-Sharma:2016gis}.\n\nIncreasing the amplitude of the exposure map could describe longer observations with \\textit{Fermi} or less stringent cuts on photons as part of the data selection. We define an exposure rescaling factor $\\chi$, which allows us to vary the intensity of the exposure map through a scalar multiplicative factor, hence rescaling the expected number of photons present in simulated data. In our baseline case, $\\chi=1$. In general, the exposure rescaling could be position-dependent (e.g. corresponding to longer observations of only part of the ROI). However, we expect such position-dependent variations to be modest for the inner Galaxy region, as the size of our ROI is smaller than the field of view of {\\it Fermi}.\n\nWe implemented the variation of exposure in the simulated data by modifying the template parameters as follows. For smooth\/diffuse templates, the template normalization $A_{\\text{smooth}}$ is multiplied by the rescaling factor $\\chi$, since $A_{\\text{smooth}}$ determines the mean photon counts within each pixel. For non-Poissonian templates, when the other parameters are held fixed, $A_{\\text{PS}}$ determines how {\\it many} sources are present, which is not a function of exposure. Therefore, we instead multiply the counts break $S_b$ by $\\chi$, as $S_{b}$ controls the expected number of photons emitted by a source lying at the break in the SCF; as discussed previously, for the fits we perform, $S_b$ corresponds to the typical number of photons per source. To ensure that the total number of sources does not change, we divide $A_{\\text{PS}}$ by $\\chi$ following Eq.~\\ref{eq:nphotons}. \n\nWhen performing \\texttt{NPTFit} analyses on these modified skymaps, the input exposure map must be multiplied by $\\chi$. Furthermore, we adjust the range of priors governing $A_{\\text{smooth}}$ for Poissonian sources and $A_{\\text{PS}}$ and $S_{b}$ for non-Poissonian sources, so that they correspond to the same underlying physical emission parameters as in the original $\\chi=1$ analysis. For example, the boundaries of a log prior on $\\log A_{\\text{smooth}}$ are shifted by $+\\log\\chi$; the boundaries of a log prior on $\\log A_{\\text{PS}}$ are shifted by $-\\log\\chi$; and the boundaries of the linear prior on $S_b$ are multiplied by $\\chi$. (The original values of all priors are displayed in Table~\\ref{tab:priors} in Appendix~\\ref{app:detailedmethodology}.) For simulated data, the number of live points we utilized in the scans is nlive=300. We checked that the relative changes in the recovered evidences (under variations to nlive) are negligible for all individual realizations.\n\n\\subsection{Angular resolution}\n\\label{subsec:methodangularresolution}\n\nAngular resolution, characterized by the Point Spread Function (PSF), represents how well a telescope such as \\textit{Fermi} is able to reconstruct the original direction of a detected photon.  A non-delta-function PSF represents an uncertainty in the direction of a photon's origin. As a result, the image produced of a photon source is ``smeared\" across one or more pixels. Since the \\texttt{NPTFit} implementation does not account for correlations between neighboring pixels (see e.g. \\cite{Collin:2021ufc} for a discussion), this smearing has the potential to bias the recovered SCF. \n\nModifications to the photon direction reconstruction, or construction of future gamma-ray telescopes, may allow for better angular resolution (equivalently, a narrower PSF) than {\\it Fermi} can currently achieve. However, even within the {\\it Fermi} dataset photons can be separated by the quality of their directional reconstruction, allowing us to improve angular resolution at the cost of exposure. Specifically, {\\it Fermi} photons are divided into four quartiles ranked by angular resolution, and separate PSF estimates are provided for each of the quartiles. Furthermore, lower-energy photons have intrinsically worse angular resolution, so a cut on photon energy has the effect (among others) of modifying the effective PSF. \n\n\\textit{Fermi}'s PSF is modeled by a pair of King functions (defined in Eq.~\\ref{eqn:kingfunction}) and is characterized by a set of several parameters. The PSF is approximately Gaussian near the core, with larger non-Gaussian tails. Eq.~\\ref{eqn:fermipsf} displays the full functional form of  \\textit{Fermi}'s PSF. \\footnote{\\url{https:\/\/fermi.gsfc.nasa.gov\/ssc\/data\/analysis\/documentation\/Cicerone\/Cicerone_LAT_IRFs\/IRF_PSF.html}} \n\n\\begin{equation}\n    P(x,\\vec{\\alpha_{P}})=f_{\\text{core}}K(x,\\sigma_{\\text{core}},\\gamma_{\\text{core}})+(1-f_{\\text{core}})K(x,\\sigma_{\\text{tail}},\\gamma_{\\text{tail}})\n    \\label{eqn:fermipsf}\n\\end{equation}\n\\begin{equation}\n    K(x,\\sigma,\\gamma) = \\frac{1}{2 \\pi \\sigma ^{2}} \\left (1 - \\frac{1}{\\gamma}\\right) \\left [1+\\frac{x^{2}}{2 \\gamma \\sigma^{2}} \\right ]^{-\\gamma}\n    \\label{eqn:kingfunction}\n\\end{equation}\nHere $x$ is a rescaled distance from the center of the source, with an energy-dependent scale factor $S_p(E)$: \n\\begin{align}\n    x & = \\frac{\\delta p}{S_{p}(E)} \\nonumber \\\\\n    \\delta p & = 2 \\sin^{-1} \\left(\\frac{|\\hat{p}^\\prime - \\hat{p}|}{2}\\right),\n    \\label{eqn:xspepsf}\n\\end{align}\nwhere $\\hat{p}$ and $\\hat{p}^\\prime$ are the unit vectors corresponding respectively to the true and reconstructed directions of the photon. The parameters that define the PSF ($S_p(E)$, $f_\\text{core}$, and $\\gamma$ and $\\sigma$ for the two King functions in Eq.~\\ref{eqn:fermipsf}) are provided with the \\textit{Fermi} dataset as functions of energy and event selection. \n\nNote that because of the rather complex form of the {\\it Fermi} PSF, different event selections may have PSFs that are not related simply by an overall shift in scale (e.g. by a modification to $S_p(E)$), but are different in shape. To maximize the practical applicability of our work, rather than simply rescaling the PSF, we test the effect of using the true PSFs for different quartiles of the {\\it Fermi} data ranked by PSF, and for different energy ranges. However, we will show that within the range of event selections we study, the effect on sensitivity of changing the PSF can be quite well described by the variation of a summary parameter such as the $68\\%$ containment angle, suggesting that the detailed form of the {\\it Fermi} PSF is not a crucial ingredient.\n\nWe divide the dataset into 40 log-spaced energy bins spanning the range from 0.2 GeV to 2000 GeV (i.e. 10 bins per decade). For each quartile and energy bin, we re-simulate the data with the same underlying model parameters but different PSF parameters. We stack these simulations together where appropriate (e.g. when testing multiple quartiles simultaneously, or when considering a broad energy range). When we analyze the simulated data, we use the worst PSF for any subset of the simulated data, which is consistent with what has been done in previous studies on the real data \\cite{Lee:2015fea, Leane:2020pfc}. For example, if the simulated data involved photons from the top three PSF quartiles and a range of energies from $E_\\text{min}$ to $E_\\text{max}$, the PSF parameters used will correspond to the third-best PSF quartile and the energy $E_\\text{min}$ (since the angular resolution of {\\it Fermi} improves monotonically with increasing energy). For tests that varied angular resolution, the number of live points we utilized in the scans is nlive=100. To check that this value of nlive was adequate, we randomly selected a subset of the realizations at given angular resolution and performed a cross-check at nlive=500. We found that the differences in the recovered evidences were negligible in all cases. Hence, it is reasonable to assume that the scans across all realizations are well-converged with respect to nlive variations.\n\n\\subsection{Energy range}\n\nVarying the energy range of the data selection has multiple effects. Including a wider range of energies effectively increases the exposure; including lower-energy photons worsens the angular resolution. As mentioned above, we use the real PSF of {\\it Fermi} for different energy ranges as one way to probe the effects of varying angular resolution. However, changing the energy range has additional effects that are not reducible to changes to angular resolution and exposure: low-energy photons are more abundant than high-energy ones in general, but also the spectra of the various emission components are different. Consequently, changing the energy range will modify the flux fraction associated with the GCE (and all other components). The choice of energy range thus needs to be optimized depending on the signal of interest.\n\nTo address the specific question of the optimal energy range for GCE studies, we change our energy cut on the real data and then repeat the analysis described in Sec.~\\ref{sec:Methodology}. That is, we re-fit the templates to the real data with the new energy range, simulate the data based on these new template parameters, and determine the sensitivity to PSs as a function of energy range.\n\nFor all simulations involved in the variation of energy range, the number of live points we used to scan the data was set to nlive=100. To check that this value of nlive was adequate, we randomly selected a subset of the realizations at each energy range, and performed a cross-check at nlive=300. We found that the differences in the recovered evidences were negligible in all cases. Hence, it is reasonable to assume that the scans across all realizations are well-converged with respect to nlive variations.\n\n\\subsection{Pixel size}\n\\label{subsec:pixelsizevarmethod}\n\nAnother somewhat ad-hoc choice in the standard NPTF analysis is the choice of spatial binning for the photons, i.e. the size of the equal-area \\texttt{HEALPix} pixels (or equivalently, their number). Following previous studies such as \\cite{Lee:2015fea,Mishra-Sharma:2016gis,Leane:2019xiy}, we utilized $\\text{nside}=128$ for the majority of our analysis. The reason for this choice is the similarity between the $\\text{nside}=128$ pixel radius and \\textit{Fermi}'s angular resolution in the energy range of interest. \n\nIf the pixel size chosen is substantially smaller than the angular resolution, PSs will always occupy multiple pixels, and the fact that \\texttt{NPTFit} does not model correlations between neighboring pixels could lead to a loss of sensitivity. In the extreme limit of small pixel size, where all pixels contain either 0 or 1 photons, all sensitivity to PS populations would be lost. On the other hand, pixels much larger than the angular resolution increase the background from diffuse signals in any given pixel, and again this might be expected to reduce the sensitivity to PSs.\n\nTo examine these effects in detail, we use the same template parameters derived from the data for $\\text{nside}=128$ (without any adjustment of parameters or priors) but simulate skymaps at $\\text{nside} = 512$ using the procedure described in Sec.~\\ref{sec:Methodology}.\nAfter generating simulated skymaps at this higher resolution, we can increase the pixel size for each realization as desired, using a HEALPix package that combines ``children\" pixels to create a superpixel, while accounting for proper normalization of photon counts \\cite{Gorski:2004by}. This preserves the distribution of sources in the individual realizations as we explore different pixel sizes.\n\nFor variations in pixel size, priors do not need to be adjusted. Instead, the templates must be properly normalized within the ROI to ensure accurate scaling during parameter retrieval (see Appendix \\ref{app:detailedmethodology}). \n\nFor all simulations involved in the variation of pixel size, the number of live points we used to scan the data was set to nlive=100. To check that this value of nlive was adequate, we randomly selected a subset of the realizations at each pixel size and performed a cross-check at nlive=500. We found that the differences in the recovered evidences were negligible in all cases. Hence, it is reasonable to assume that the scans across all realizations are well-converged with respect to nlive variations.\n\n\\subsection{Source brightness}\n\nThe previously-discussed parameters describe instrumental properties and analysis choices. In this section, we discuss how the template model parameters are adjusted to describe a genuinely different source population. In analyses of sensitivity as a function of source brightness, our goal is to understand the potential of the \\texttt{NPTFit} algorithm to detect faint sub-threshold sources.\n\nThe brightness of PSs can be varied by adjusting the $S_{b}$ and $A_{\\text{PS}}$ parameters of the SCF (Eq.~\\ref{eqn:scf}). We tested the effect of varying the brightness of individual PSs while keeping the total flux in the PS population fixed (as appropriate for a PS population making up most or all of the GCE). Using Eq.~\\ref{eq:nphotons}, this requirement can be satisfied by simultaneously varying $S_b$ and $A_{\\text{PS}}$ as follows:\n\\begin{equation}\n    S_{b} \\to n S_{b}, A_{\\text{PS}} \\to \\frac{1}{n^{2}} A_{\\text{PS}}\n    \\label{eqn:countsbrightness}\n\\end{equation}\nFor example, if $n = 1\/2$, the number of photons each source emits is reduced by half, however, the number of sources increases by a factor of 2 to compensate. This equates to a factor of 4 increase in the template normalization factor $A_{\\text{PS}}$, since the number of sources scales as $A_{\\text{PS}} S_b$.\n\nAs for the exposure tests, when we rescale the simulated parameters we also rescale the priors in the fit to simulated data. For example, if $S_b \\to n S_b$ and there was initially a linear prior on $S_b$ in the range $[0.05,80]$, the new prior is linear with range $[0.05n, 80n]$. If the prior on $\\log_{10} A_{\\text{PS}}$ is initially $[-6, 1]$, it is adjusted to $[-6- 2\\log_{10}{n},1 - 2 \\log_{10}{n}]$. We also checked the effect of keeping the priors fixed; except in situations where the true parameters approached the edge of the prior (or fell outside it), the effect was minimal.\n\nFor all simulations involved in the variation of source brightness, the number of live points we used to scan the data was set to nlive=100 for computational efficiency.\n\n\\section{A simplified isotropic scenario}\n\\label{sec:isotropic}\n\nBefore analyzing the results with all templates, we perform a simplified analysis including only isotropic components in our simulations, and approximating the exposure map as uniform. This analysis serves as a test of our analytic predictions. We describe some additional studies under this simplified scenario in Appendix \\ref{app:isotropic}.\n\nIn this case, our normalization convention for the emission templates requires that the templates $T$ and $T_\\text{PS}$ are both 1 in all pixels within the ROI. The normalization of the simulated signals was determined by matching the parameters for the PS component ($A_\\text{PS}$, $n_1$, $n_2$ and $S_b$) to the isotropic PS component extracted from the real {\\it Fermi} data.\nFor our baseline analyses, the smooth component normalization was chosen such that the total flux contributions of the smooth isotropic and PS components are equal. Explicitly, given our normalization convention for the templates $T$ and $T_\\text{PS}$, this means that $A(\\theta)_\\text{smooth}$ is given by:\n\\begin{equation}\n    A(\\theta)_\\text{smooth}=A(\\theta)_{\\text{PS}}S_{b}^{2} \\left [\\frac{(n_{1}-n_{2})}{(n_{1}-2)(2-n_{2})} \\right ]\n    \\label{eqn:normalization}\n\\end{equation}\nwhere (as previously) $A(\\theta)_{\\text{PS}}$ is the template normalization for the emission associated with the isotropic PS population, $S_b$ is the break of the source-count function, \nand $n_1, n_2$ are the slope of the source count functions defined by a singly-broken power law.\n\nAs previously, we use \\texttt{NPTFit-Sim} to simulate PSs and a Poisson draw to simulate the smooth component. The priors on the various parameters are set as discussed in Sec.~\\ref{sec:varyingdiffparams} and Appendix \\ref{app:detailedmethodology}. (Note that if the simulated value of $A_\\text{smooth}$ was outside the prior range on $A_\\text{iso}$ in the main analysis, we would need to adopt different priors for this isotropic study, but in fact it lies well within the prior range so this is not a problem.)\n\n\\subsection{Variation of exposure (narrow PSF)}\n\\label{subsec:isotropicpsf}\n\n\\begin{figure*}[ht]\n    \\centering\n    \\includegraphics[width=0.49\\linewidth]{lowexpisoanalyticpsf.pdf}\n    \\hspace{0.4em}\n    \\includegraphics[width=0.49\\linewidth]{highexpisoanalyticpsf.pdf}\n    \\caption{$\\ln{\\text{BF}}$ and $\\langle \\ln{\\text{BF}} \\rangle $ (magenta) across 10 realizations at varying $\\chi$ values for isotropic emission, simulated and scanned using a narrow Gaussian PSF. The dashed line denotes the modified power law fit defined in Eq.~\\ref{eqn:powerlawshift}. The dotted line denotes the first term of the analytic form Eq.~\\ref{eqn:lnBFcase2}, while the dash-dot line denotes the full analytic solution described in Eq.~\\ref{eqn:lnBFcase2}.  }\n    \\label{fig:analyticcase2comparisonpsf}\n\\end{figure*}\n\n\\begin{figure*}[ht]\n    \\centering\n    \\includegraphics[width=0.49\\linewidth]{lowexpisoanalytic.pdf}\n    \\hspace{0.4em}\n    \\includegraphics[width=0.49\\linewidth]{highexpisoanalytic.pdf}\n    \\caption{$\\ln{\\text{BF}}$ and $\\langle \\ln{\\text{BF}} \\rangle $ (magenta) across 10 realizations at varying $\\chi$ values for isotropic emission, simulated and scanned using a realistic PSF model. The dashed line denotes the modified power law fit defined in Eq.~\\ref{eqn:powerlawshift}. The dotted line denotes the first (linear) term of the analytic form in Eq.~\\ref{eqn:lnBFcase2}, while the blue dash-dot line denotes the full analytic solution from the same equation with $s \\rightarrow S_b$. The green dash-dot line shows the analytic solution with $s \\rightarrow S_b\/3$.}\n    \\label{fig:analyticcase2comparison}\n\\end{figure*}\n\nThe analytic solutions we derived in Sec.~\\ref{sec:analyticforms} assumed that the PSs were not smeared by the PSF. Thus as a cross-check of the scaling behavior estimated from our analytic results, we performed an initial set of simulations where the PSF was taken to be extremely narrow (i.e. the angular reconstruction was effectively perfect), covering a range of exposure levels $\\chi$. Specifically, we sampled exposure rescaling factors $\\chi$ between $10^{-2}$ and $10$ (recall $\\chi=1$ corresponds to the baseline exposure), and for each case generated and scanned skymaps that employed a Gaussian PSF with a tiny variance $10^{-20}$. For each choice of $\\chi$ we ran the analysis for 10 simulated realizations, and for each realization evaluated the $\\ln{\\text{BF}}$ between models with and without isotropically distributed PSs (both models allow for an isotropically distributed smooth component).\n\nFig.~\\ref{fig:analyticcase2comparisonpsf} plots the Bayes factor preference in favor of PSs as a function of exposure, together with the analytic solution for the likelihood ratio in the case where PSs and background are equally bright (Eq.~\\ref{eqn:lnBFcase2} with $k=1\/2$ and $s= S_b$). We also show the result of including only the linear $ks\/2$ term in the analytic estimate of Eq.~\\ref{eqn:lnBFcase2}. \n\nFor each choice of exposure, we evaluate $\\langle \\ln \\text{BF}\\rangle(\\chi)$ by taking the average of $\\ln\\text{BF}$ across realizations at each exposure level; we also compute the standard error of the mean across the realizations for this quantity at each $\\chi$ value (indicated by magenta vertical bars in Fig.~\\ref{fig:analyticcase2comparisonpsf}).\n\nWe work by default (here and in the remainder of this work) with the log of the Bayes factor between models, rather than the likelihood ratio; however, in this specific example we also evaluated the log likelihood ratio and found that it was generically quite close to the log Bayes factor (and in particular the difference between the two was not responsible for the difference between the numerical results and the analytic approximation for $\\langle \\Delta \\ln \\mathcal{L}\\rangle$). Thus we treat our analytic approximation as a rough estimate for $\\langle \\ln \\text{BF}\\rangle$.\n\nFor these parameter choices, we observe that the analytic form mildly overestimates the sensitivity, by a factor of roughly 20-30\\% in $\\langle \\ln \\text{BF}\\rangle$ at high exposure, but accurately captures the fall-off of the detection sensitivity at low exposure, and the scaling at high exposure. The remaining discrepancy is likely due to the approximations we have made in deriving our analytic results (e.g. relating to the shape of the probability distribution, and assuming we can treat all integrals as having limits $\\pm \\infty$, as well as approximating the SCF as a delta-function).\n\nWe observe a consistent scatter at the $\\mathcal{O}(10\\%)$ level in $\\langle \\ln \\text{BF}\\rangle$ between different realizations, which does not obviously decrease at large $\\chi$. (Note that here we are discussing the standard deviation across realizations, not the standard error of the mean; the latter is smaller.) This can be understood in terms of our variance calculations in Sec.~\\ref{sec:analyticforms}. The parameters we have simulated correspond to $5.61\\chi$ photons\/source, 2808 pixels, and an average of $0.11$ sources\/pixel; thus we expect a total number of sources in the ROI around $280$, and a standard deviation in the log likelihood ratio that is of order $\\langle \\ln \\text{BF}\\rangle\/\\sqrt{280} \\sim 0.06 \\langle \\ln \\text{BF}\\rangle$ or $\\sqrt{\\langle \\ln \\text{BF}\\rangle}$, whichever is larger. This is consistent with the $\\mathcal{O}(10\\%)$ scatter we observe at high exposure.\n\nIn addition to the comparison to the analytic prediction, we can parameterize the scaling of the sensitivity with $\\chi$ as a power law and fit for the parameters (although power-law behavior should be expected to break down at sufficiently small $\\chi$, where $\\ln \\text{BF}$ can attain negative values). The fitting function we use is:\n\\begin{equation} \\langle \\ln \\text{BF}\\rangle(\\chi) = \\alpha \\chi^{\\beta} + \\gamma,\n    \\label{eqn:powerlawshift}\\end{equation}\nwhere the offset parameter $\\gamma$ serves to correct the behavior at small $\\chi$ where there is not enough data to detect a significant signal. For each value of $\\chi$ we took the central value of $\\langle \\ln \\text{BF}\\rangle(\\chi)$ to be the average over realizations, with an error bar determined by the standard error of the mean, and performed a least-squares fit. The resulting best-fit model is also plotted in Fig.~\\ref{fig:analyticcase2comparisonpsf}.\n\n\n\n\\subsection{Variation of exposure (realistic PSF)}\n\nIn a realistic scenario, we will always have to deal with a PSF that is not arbitrarily narrow. We repeat the simulation and analysis described above using the full PSF appropriate to the real  {\\it Fermi} dataset (for the top PSF quartile), and show results in Fig.~\\ref{fig:analyticcase2comparison}. We compare these results to the same analytic solution (i.e. with no allowance for the PSF) as in the previous analysis, and again perform a least-squares fit to a simple power law fitting function.\n\nWe observe that the analytic solution still describes the shape of $\\langle \\ln \\text{BF}\\rangle$ as a function of $\\chi$ quite well, but now the discrepancy in our sensitivity metric is more pronounced (a factor of a few at high $\\chi$). At least qualitatively, this discrepancy can be largely absorbed by taking $s\/S_b$ to be a constant other than unity; Fig.~\\ref{fig:analyticcase2comparison} shows the effect of using the analytic approximation with $s$ replaced by $ S_b\/3$. The variance remains $\\mathcal{O}(10\\%)$ at high $\\chi$, which can be understood as discussed above.\n\nIn this more realistic case, we thus recommend using the analytic estimate only to understand scaling behavior rather than as a quantitative estimate of the expected sensitivity, although a reasonably good description can be obtained by fitting a constant rescaling factor to be applied to $s$.\n\n\\subsection{Variation of relative flux contributions}\n\\label{app:subdominantcomp}\n\nWe can also test the effects of varying the relative flux contributions of the smooth and PS components while allowing the total flux to remain constant. \nFig.~\\ref{fig:isotropicfluxfrac} demonstrates how the sensitivity changes as the PS flux fraction is varied, for both the narrow PSF and realistic PSF (top quartile) cases. For comparison, we also overlay the predictions given by our analytic solutions, Eq.~\\ref{eqn:lnBFcase2}, with $s \\rightarrow S_b$ and $s\\rightarrow S_b\/3$. We find that as the relative contribution of the PS component increases, the sensitivity of \\texttt{NPTFit} to PSs naturally increases with a shape consistent with the analytic prediction provided by Eq.~\\ref{eqn:lnBFcase2}, and in the narrow-PSF case the $s\\rightarrow S_b$ substitution provides quantitatively accurate results. Although the case where the map is simply produced with a smooth component is not shown in the figure due to the log-scaling, the result averages to $-0.54 \\pm 0.067$ in the realistic-PSF case and $-0.56 \\pm 0.14$ in the narrow-PSF case, both of which are small, as expected.\n\n\n\\begin{figure}[ht]\n    \\centering\n    \\includegraphics[width=0.98\\linewidth]{isotropicfluxfrac_narrowpsf.pdf}\n    \\caption{$\\ln{\\text{BF}}$ and $\\langle \\ln{\\text{BF}}\\rangle $, as the relative contributions between a smooth and PS component within an isotropic map are varied, for realistic and narrow PSF prescriptions. Dashed lines indicate the analytic prescription of Eq.~\\ref{eqn:lnBFcase2} with the replacements $s\\rightarrow S_b$ (black) and $s\\rightarrow S_b\/3$ (red).}\n    \\label{fig:isotropicfluxfrac}\n\\end{figure}\n\n\\section{Results of simulated parameter variations in the full inner Galaxy analysis}\n\\label{sec:results}\n\nIn this section we now proceed to a numerical analysis using simulated {\\it Fermi} data for the inner Galaxy, employing the complete set of templates discussed in Sec.~\\ref{sec:Methodology}. The results of this section can thus be used directly to optimize \\texttt{NPTFit}-based approaches to studies of the inner Galaxy and GCE.\n\n\\subsection{Varying the exposure}\n\\label{sec:exposuretest}\n\nAs in the isotropic case, we sampled exposure rescaling factors $\\chi$ between $10^{-2}$ and $10$. For each choice of $\\chi$ we ran the analysis for 20 simulated realizations, and for each realization evaluated the $\\ln{\\text{BF}}$ between models with and without the GCE PS template. \n\nFig.~\\ref{fig:exposuretest} shows the resulting values of $\\ln\\text{BF}$ for each exposure level. We evaluate $\\langle \\ln \\text{BF}\\rangle(\\chi)$ by taking the average of $\\ln\\text{BF}$ across realizations at each exposure level (indicated by magenta vertical bars in the figure along with errorbars that denote the $1\\sigma$ standard error of the mean across all the realizations within a particular case). \n\nAs discussed in Sec.~\\ref{sec:isotropic}, we fit a power-law function (Eq.~\\ref{eqn:powerlawshift}) to the data for $\\langle \\ln \\text{BF}\\rangle(\\chi)$. The resulting best-fit parameters are given in Table \\ref{tab:exposurefit}, and the best-fit model is plotted in Fig.~\\ref{fig:exposuretest} (solid blue line). We find approximately that $\\langle \\ln \\text{BF} \\rangle \\propto \\chi^{0.8}$ at large BF. This is broadly consistent with our expectation from the analytic estimate in Sec.~\\ref{sec:analyticforms} that $\\langle \\ln \\text{BF} \\rangle$ should scale $\\sim$linearly in $\\chi$.\n\n\\begin{figure*}\n    \\centering\n    \\includegraphics[width=0.49\\linewidth]{lowexposurevarp6v11.pdf}\n    \\hspace{0.4em}\n    \\includegraphics[width=0.49\\linewidth]{highexposurevarp6v11.pdf}\n    \\caption{$\\ln{\\text{BF}}$ and $\\langle \\ln{\\text{BF}}\\rangle$ (magenta) across 20 realizations sampled at various levels of exposure. \\textit{Left}: realizations with $\\chi<1$. \\textit{Right}: realizations with $\\chi \\geq 1$. The best-fit line is a standard power law with an additive shift defined in Eq.~\\ref{eqn:powerlawshift}.}\n    \\label{fig:exposuretest}\n\\end{figure*}\n\n\\begin{table}[H]\n\\centering\n\\begin{tabular}{r r r }\n\\hline\nRecovered Parameters & \\texttt{p6v11}\\\\\n\\hline\n$\\alpha$ (coefficient) & $11.30 \\pm 0.69$ \\\\\n$\\beta$ (power) & $0.76 \\pm 0.04$  & \\\\\n$\\gamma$ (shift) & $-0.62 \\pm 0.20$  & \\\\\n\\botrule\n\\end{tabular}\n\\caption{Best-fit parameters obtained using least-squares regression method along with the $1\\sigma$ error for the power law fit of $\\langle \\ln{\\text{BF}}\\rangle$ to $\\chi$, as defined in Eq.~\\ref{eqn:powerlawshift}.}\n\\label{tab:exposurefit}\n\\end{table}\n\n\\subsection{Varying the angular resolution}\n\\label{sec:varyingangexp}\n\n\\subsubsection{PSF models for different quartiles} \\label{subsec:varyingpsf}\n\nWe begin by examining how the sensitivity of \\texttt{NPTFit} varies when the top three quartiles of data by PSF are analyzed separately, keeping the energy range fixed at its default value of $2-20 \\text{ GeV}$. Quartiles are labeled in order of decreasing angular resolution (so e.g. ``PSF 01'' represents the best quartile). \n\nWithin each quartile, we simulated and analyzed 20 realizations. All simulations are generated at a rescaling factor of $\\chi = 1$.  Fig.~\\ref{fig:psfquartiletest} shows a striking decline in sensitivity in the quartiles with worse angular resolution. As previously, we display both the scatter between realizations and the average $\\langle \\ln \\text{BF}\\rangle$ across realizations for a given quartile.\n\n\\begin{figure}\n    \\centering\n    \\includegraphics[width=0.98\\linewidth]{psfvarp6v11.pdf}\n    \\caption{$\\ln{\\text{BF}}$  and  $\\langle \\ln{\\text{BF}}\\rangle$ (magenta) values across 20 realizations at each PSF quartile.}\n    \\label{fig:psfquartiletest}\n\\end{figure}\n\\begin{figure*}\n    \\centering\n    \\includegraphics[width=0.98\\linewidth]{containmentangle.pdf}\n    \\caption{$\\ln{\\text{BF}}$ and $\\braket{\\ln{\\text{BF}}}$ (magenta) from 20 realization at each energy range parameterized by the absolute value of $68 \\%$ containment angle of the PSF. For the baseline $2-20$\\,GeV range, we test each of the top three quartiles individually. The best-fit line (black) is the power-law fit to the $\\langle \\ln{\\text{BF}}\\rangle$ obtained using least-squares. The baseline case (blue vertical line) denotes the baseline case 2-20\\,GeV at quartile 1, typically used in previous \\textit{Fermi} analyses. }\n    \\label{fig:containmentanglep6v11}\n\\end{figure*}\n\\subsubsection{PSF models for different energies} \\label{subsec:varyingpsfenergy}\n\nAnother practical way to vary the angular resolution in {\\it Fermi} data is to modify the energy window. We first examined the (theoretical) case where the angular resolution is varied while keeping all other parameters constant. We re-simulated the data with the original exposure map ($\\chi=1$) but with PSF corresponding to the appropriate {\\it Fermi} PSF for energies between 0.6 GeV and 3.2 GeV (recall that the baseline analysis uses the {\\it Fermi} PSF at 2 GeV), in the top PSF quartile. In each case we performed 20 realizations.\n\nIn Fig.~\\ref{fig:containmentanglep6v11} we plot the resulting values of $\\ln\\text{BF}$, against the value of the $68 \\%$ containment angle associated with each PSF model (in degrees), which we denote $\\eta$. We also include the results for the 2 GeV PSF in all three quartiles (discussed above).\n\nTo summarize the results, we fit the data with a power law, $\\langle \\ln \\text{BF}\\rangle(\\eta) = a \\eta^{b}$, using the same least-squares analysis as described above for the case of $\\langle \\ln \\text{BF}\\rangle(\\chi)$.\nTab.~\\ref{tab:containmentanglefit} displays the resulting best-fit parameters. We find that $\\langle \\ln \\text{BF}\\rangle(\\eta) \\propto \\eta^{-1}$, i.e. the sensitivity appears to scale approximately inversely with the containment radius, at least while holding the pixel size constant at $\\text{nside}=128$.\n\n\n\n\\begin{table}[H]\n\\centering\n\\begin{tabular}{r r c}\n\\hline\n\nParameter & \\texttt{p6v11} \\\\\n\\hline\n$a$ (coefficient) & $2.5 \\pm 0.6$ \\\\\n$b$ (power) & $-1.0 \\pm 0.2$  & \\\\\n\n\\botrule\n\\end{tabular}\n\\caption{Recovered parameters and the $1\\sigma$ error for the power-law fit to $\\langle \\ln \\text{BF}\\rangle$ as a function of $68\\%$ containment angle.}\n\\vspace{-10pt}\n\\label{tab:containmentanglefit}\n\\end{table}\n\nThus as a rule of thumb, we expect an increase in the exposure by a factor of $n$ to be approximately compensated by an increase in the containment radius (not the containment area) by a factor of $n$; if the exposure can be more than doubled while worsening the containment angle by less than a factor of two, this will generally be a beneficial tradeoff. \n\n\\begin{figure*}\n    \\centering\n    \\includegraphics[width=0.49\\linewidth]{lowtradeoffp6v11.pdf}\n    \\hspace{0.4em}\n    \\includegraphics[width=0.49\\linewidth]{hightradeoffp6v11.pdf}\n    \\caption{$\\langle \\ln{\\text{BF}}\\rangle$ and the $1\n    \\sigma$ standard error of the mean across 20 realizations for the top three quartiles graded in angular resolution sampling different values of $\\chi$. \\textit{Left}: realizations with $\\chi<1$. \\textit{Right}: realizations with $\\chi \\geq 1$. The best-fit lines show the Eq.~\\ref{eqn:powerlawshift} fit to the data.}\n    \\label{fig:angularexp1sb}\n\\end{figure*}\n\n\nNote that our choice of $\\text{nside}=128$ corresponds to a mean pixel spacing ($0.46^\\circ$) that exceeds or is comparable to the $68\\%$ containment angle for all but the widest energy range (0.6-20 GeV) that we consider. We will show in Sec.~\\ref{sec:pixelsizevar} that decreasing the pixel size below the PSF does not appear to have large effects on the expected sensitivity (although it can increase the variance), but studies focusing on a broader energy range might still wish to test smaller nside values to reduce leakage of PSs into neighboring pixels.\n\n\n\n\\subsubsection{Simultaneous variation of exposure and angular resolution} \n\\label{subsec:tradeoffs}\nTo check the stability of the scaling rules we have found so far and the validity of this simple estimate, we now explicitly test the effect of simultaneously varying the angular resolution and the exposure. In many realistic situations, and in particular for \\textit{Fermi} data, relaxing cuts on photon quality will simultaneously increase the effective exposure and worsen angular resolution.\n\n\nWe repeat the analysis described in Sec.~\\ref{sec:exposuretest} for simulated data using the appropriate PSF model for PSF quartiles 2 and 3, with 20 realizations for each combination of $\\chi$ and quartile. We scanned the realizations at nlive = 300. Our results for $\\langle \\ln \\text{BF} \\rangle(\\chi)$ for each quartile are summarized in Fig.~\\ref{fig:angularexp1sb}. As in Eq.~\\ref{eqn:powerlawshift}, we fit the data for each quartile with a power law with a constant offset, and provide the best-fit parameters in Tab.~\\ref{tab:tradeoffp6v11}.\n\nIn general we observe that the slope appears to become steeper (more rapid increase in sensitivity with exposure) in quartiles with worse angular resolution. This reflects that significant detection of PSs requires a higher $\\chi$ value when the angular resolution is worse, but for sufficiently large $\\chi$ factors, the significance becomes almost independent of angular resolution. This may be related to the pixels surrounding a PS becoming bright enough to be individually detected as significant PSs.\n\n\nWe can also test the effect of stacking together the simulated data corresponding to the different quartiles, which has the effect of increasing the effective exposure $\\chi_{\\textrm{eff}} >\\chi$ relative to the one-quartile case. The sum of the first and second quartile has $\\chi_{\\text{eff}} = 2$, and the combined top three quartiles have $\\chi_{\\textrm{eff}} = 3$. \n\n\n Fig.~\\ref{fig:multiquartilesuperposed} shows the sensitivity based on 20 realizations for each of these three cases scanned at nlive=300. We find that to quite a good approximation, the increased number of photons simply cancels out the effects of worsening the angular resolution on average. As a simple estimate we calculated the combined effects of the predictions of varying the exposure and angular resolution. To do so, we define a rescaling factor $r=r_{\\text{exposure}}(\\chi)r_{\\text{PSF}}(\\text{Quartile})$, where $r_{\\text{exposure}}(\\chi)$ is the ratio of the expected log BF at exposure $\\chi$, denoted $\\langle\\ln{\\text{BF}}\\rangle(\\chi)$, to the baseline expected log BF $\\langle\\ln{\\text{BF}}\\rangle(\\chi=1)$, as obtained from Eq.~\\ref{eqn:powerlawshift} and Table~\\ref{tab:exposurefit}. Thus $r_\\text{exposure}(\\chi)$ characterizes the increase in sensitivity with enhanced exposure. $r_{\\text{PSF}}(\\text{Quartile})$ is the ratio of the expected log BF for a specified single quartile, denoted $\\langle\\ln{\\text{BF}}\\rangle(\\text{Quartile})$, to the baseline expected log BF $\\langle\\ln{\\text{BF}}\\rangle(\\text{Quartile}=1)$, obtained from Fig.~\\ref{fig:psfquartiletest}. Thus $r_\\text{PSF}(\\text{Quartile})$ characterizes the decline of sensitivity with worsening angular resolution. $\\langle\\ln{\\text{BF}}\\rangle(\\chi)$ and $\\langle\\ln{\\text{BF}}\\rangle(\\text{Quartile})$ are denoted as blue stars and orange pentagons on Fig.~\\ref{fig:multiquartilesuperposed}, respectively. To obtain the combined estimate denoted by the black filled ``X\", we multiplied the calculated $r$ factor with the baseline value $\\langle \\ln{\\text{BF}}\\rangle(\\text{Quartile 1})$ obtained from the realizations for the baseline case in Fig.~\\ref{fig:multiquartilesuperposed}. We find that this estimate agrees with the simulation results that on average adding quartiles with worse angular resolutions to gain exposure does not yield large increases (or decreases) in the average sensitivity to PSs.\n \n Quantitatively, Q3 has a containment angle slightly more than twice that of Q1 (see Fig.~\\ref{fig:containmentanglep6v11}), while including Q2 and Q3 triples the exposure. The scaling of the sensitivity with exposure is slightly sublinear whereas for containment angle it is linear to a good approximation, and in practice we find that these two effects almost completely cancel out. Thus the overall sensitivity is (perhaps surprisingly, and somewhat coincidentally) insensitive to the inclusion of additional quartiles.\n \n We might wonder if by approximating the PSF in the stacked dataset as the PSF of the worst quartile, we introduce biases in the recovered parameters. We checked this explicitly over our sample of 20 realizations. On average, we find that the median parameter deviations were rather small, mostly at $<1\\sigma$ level, with some exceptions for components such as the isotropic emission. However, we also checked cases where we stacked different realizations of the same quartile, so that the PSF was the same between different subpopulations and was thus modeled in the same way for the simulated data and the fit. We found, on average, that the biases were similar in these cases; they were not obviously worsened by stacking maps with different PSFs, while modeling with the worst PSF. Thus, the mis-reconstruction cannot be attributed to mismodeling of the PSF in a subset of the data. \n \n\\begin{figure}\n    \\centering\n    \\includegraphics[width=0.98\\linewidth]{multqmapp6v11.pdf}\n    \\caption{$\\ln{\\text{BF}}$ and $\\langle \\ln{\\text{BF}}\\rangle$ (magenta) across 10 realizations that stacked skymaps generated with different angular resolutions (PSF quartiles). The scans assumed the worst angular resolutions. The blue stars indicate the increased sensitivity as predicted by varying the exposure, while the orange pentagons indicate the worsening of sensitivity due to angular resolution degradation. As a estimate, the black filled \"X\" symbols display the combined estimate from varying the two parameters.}\n    \\label{fig:multiquartilesuperposed}\n\\end{figure}\n\n\\subsubsection{Varying the energy range} \\label{subsec:energyrangeevenquartile}\n\nWhile we have previously explored the effect of changing the PSF to one appropriate for other energy ranges, we now  explore the effect of changing the energy range itself. We kept the upper limit of the energy range fixed at 20 GeV, since high-energy photons are rare and their inclusion\/exclusion is unlikely to qualitatively change the results. We varied the low-energy limit of the energy range between 0.6-3.2 GeV, spanning the peak of the GCE, by including or excluding low-energy bins. As discussed previously, the bin boundaries are log-spaced in energy, with 10 bins per decade, starting at 0.2 GeV.\n\n\nAs a first test, we sought to understand how the sensitivity could be expected to vary just as a result of the modified angular resolution combined with the larger number of photons in low-energy bins. To explore this question, we held the underlying physical model fixed, and treated the enhanced number of photons as an effective exposure factor $\\chi_{\\text{eff}}$, while using the appropriate PSF for the lowest-energy photons in the analysis. Specifically, we took $\\chi_\\text{eff}$ to be the ratio of the total number of photons in the real data (over the whole sky) in the modified energy range, to the total number of photons in the original energy range.\n\n\\begin{figure}\n    \\centering\n    \\includegraphics[width=0.98\\linewidth]{energyrangetype1.pdf}\n    \\caption{$\\ln{\\text{BF}}$ and $\\braket{\\ln{\\text{BF}}}$ (magenta) resulting from simulations that varied energy while allowing parameters to remain constant. The increase in photon counts is folded through the effective exposure factor $\\chi_{\\text{eff}}$. The red stars display the predictions resulting from the tests that varied exposure, while the orange diamonds are predictions provided by the containment angle. As an estimate, the black squares represent the combined effects of varying exposure and containment angle.}\n    \\label{fig:energyrangevaryparamconst}\n\\end{figure}\n\nFig.~\\ref{fig:energyrangevaryparamconst} shows the results of this test. The results indicate that due to the worse angular resolution obtained by including data from lower energy ranges, we expect at best a mild increase in the (expected) sensitivity, compared with a substantial increase in the case where only the exposure is varied. As a first-order comparison to our simulated results, we analyzed the combination of the effects of varying the exposure and PSF as discussed in Sec.~\\ref{subsec:varyingexposue}, \\ref{subsec:varyingpsf}. Similar to Sec.~\\ref{subsec:energyrangeevenquartile}, we define a rescaling factor $r=r_{\\text{exposure}}(\\chi)r_{\\text{PSF}}(\\eta)$, where $r_{\\text{exposure}}(\\chi)$ is the ratio of $\\langle\\ln{\\text{BF}}\\rangle(\\chi)$ to $\\langle\\ln{\\text{BF}}\\rangle(\\chi=1)$, obtained from Eq.~\\ref{eqn:powerlawshift} and Table~\\ref{tab:exposurefit}. $r_{\\text{PSF}}(\\eta)$ is the ratio of $\\langle\\ln{\\text{BF}}\\rangle(\\eta)$ to $\\langle\\ln{\\text{BF}}\\rangle(\\eta[2-20\\,\\text{GeV}])$ (baseline case), obtained from Fig.~\\ref{fig:containmentanglep6v11}. $\\langle\\ln{\\text{BF}}\\rangle(\\chi)$ and $\\langle\\ln{\\text{BF}}\\rangle(\\eta)$ are denoted as red stars and orange diamonds on Fig.~\\ref{fig:energyrangevaryparamconst}, respectively. To obtain the combined estimate denoted by the black filled ``X\", we multiplied the calculated $r$ to the $\\langle \\ln{\\text{BF}}\\rangle [2-20\\,\\text{GeV}]$ obtained from the simulations in Fig.~\\ref{fig:energyrangevaryparamconst}. The estimates indicate a fairly flat scaling behavior of sensitivity across different energy ranges. This suggests that the beneficial effects of increasing sensitivity are canceled out by the worsening of angular resolution at lower energy ranges. \n\nAs an example, consider varying the minimum energy of the event selection from 2.0 to 1.0 GeV. The $68 \\%$ containment angle of the PSF increases from the baseline $~0.23^{\\circ}$ to $~0.40^{\\circ}$. As shown in Fig.~ \\ref{fig:containmentanglep6v11}, this change in PSF induces a decrease in $\\braket{\\ln{\\text{BF}}}$ by a factor of $0.58$. However, the larger number of photon counts with a minimum energy of 1.0 GeV corresponds to an effective rescaling factor of $\\chi_{\\text{eff}} =2.75$ relative to the case with minimum energy 2.0 GeV (ignoring differences in the spectrum between the different components). Therefore, based on Tab. \\ref{tab:exposurefit}, the value of $\\ln{\\text{BF}}$ should increase by a factor of $\\sim 2.10$, if this exposure change were the only factor. The combined effect would correspond to only a $\\sim 22\\%$ increase in $\\ln{\\text{BF}}$. Thus in this case, we would expect the increase in sensitivity from additional photons to come close to offsetting the loss of angular resolution, leading to very little net change in sensitivity (with perhaps a slight advantage for a 1.0 GeV minimum energy). This resembles the roughly flat behavior with energy we actually observe in Fig.~\\ref{fig:energyrangevaryparamconst}.\n\nThis is how the sensitivity would behave if the signal and backgrounds had identical spectra, but of course this is not the case for the GCE. For a specific signal, such as the GCE in this case, we need to either input a theoretical spectrum for each component, or re-fit the model parameters from the real data in each energy band. We take the latter approach here, and then repeat the sensitivity analysis on data simulated using these updated, energy-dependent parameters.\n\\begin{figure}\n    \\centering\n    \\includegraphics[width=0.98\\linewidth]{energyrangetype2.pdf}\n    \\caption{$\\ln{\\text{BF}}$ and $\\braket{\\ln{\\text{BF}}}$ (magenta) at different energy ranges while varying the template parameters to match the posterior median parameters from fits to the real data.} \n    \\label{fig:energyvariationrefit}\n\\end{figure}\n\nFig.~\\ref{fig:energyvariationrefit} shows the result of these simulations and analyses. If only photon number and angular resolution were relevant, there would be a strong argument for extending the energy range for the analysis all the way down to 0.6 MeV (or lower), but for the actual GCE spectrum we observe that the highest expected sensitivity is obtained for a minimum energy of 1.0 or 1.6 GeV. This energy scale roughly coincides with the peak of the GCE distribution. \n\nOne might ask if features in Fig.~\\ref{fig:energyvariationrefit} simply reflect fluctuations in the total GCE flux inferred from the real data in different energy ranges (used to fix the simulation parameters). We checked this explicitly and found no evidence of such an association; the parameters controlling the simulated GCE PS flux vary smoothly over the relevant range of threshold energies, and the fluctuations in Fig.~\\ref{fig:energyvariationrefit} are thus likely to be statistical.\n\n\n\\subsection{Pixel size variation} \\label{sec:pixelsizevar}\nWe examined a wide range of pixel size to determine an optimal value for analysis. We started at an nside value of 512 and downgraded to nside values of 256, 128, 64, 32. At each pixel level, we computed $\\ln{\\text{BF}}$ across 20 realizations.\n\n\\begin{figure}\n    \\centering\n    \\includegraphics[width=0.98\\linewidth]{nsidep6v11.pdf}\n    \\caption{$\\ln{\\text{BF}}$ and $\\braket{\\ln{\\text{BF}}}$ (magenta) at each realization across five pixel sizes, where the pixel size decreases as nside correspondingly increases.}\n    \\label{fig:pixelvar}\n\\end{figure}\n\nFig. \\ref{fig:pixelvar} shows the recovered sensitivity as a function of nside. \nWe find that there is a slight increase in the sensitivity to a population of PSs as resolution is improved. However, the scatter between individual realization is also increased. It is plausible that this occurs because with small pixel sizes there is a greater risk that a relatively-bright source happens to land near a pixel boundary and consequently loses significance. In realizations where this behavior happens to be rare, the significance is naturally higher than for smaller nside (as the likelihood contributions from a larger number of pixels are summed), but in other realizations this effective dimming of the sources will markedly decrease the inferred significance of the population. (An alternative way to think about this is that pixels much smaller than the PSF are not independent data points, and so by treating them as independent we may artificially enhance the apparent significance of the result \\cite{Collin:2021ufc},\\footnote{We thank Nicholas Rodd for pointing out this effect.} but may also miss correlations that could reveal a signal.) In the regime where the pixel size is significantly larger than the PSF, we expect the significance to be reduced because we have reduced the number of independent data points (pixels), discarding information in the process.\n\nIt appears that nside 128 and 256 are likely the optimal values: nside 256 has a slightly higher average sensitivity but with considerably more scatter between realizations. The relative insensitivity of NPTF methods to pixel size, in a simpler context, was previously studied in Ref.~\\cite{Malyshev:2011zi}.\n\n\\begin{figure*}\n    \\centering\n    \\includegraphics[width=0.49\\linewidth]{normalfluxfracp6v11.pdf}\n    \\includegraphics[width=0.49\\linewidth]{fluxfracdegeneracyp6v11.pdf}\n    \\caption{\\textit{Left}: Flux fraction plot at the common pixel size employed in previous analyses (nside = 128) of certain emissions: \\textit{Fermi} bubbles (purple), diffuse emission (red), GCE PS (blue), disk PS (orange). \\textit{Right}: Flux fraction plot demonstrating mis-reconstruction of the diffuse (red) and disk PS (orange) components at a low nside value (nside = 32). The recovered flux fraction are obtained from 20 simulations.  The vertical dashed lines denote the flux fraction injected into the simulations.}\n    \\label{fig:pixelvarintensityp6v11}\n\\end{figure*}\n\nOn the other end of the spectrum, low nside values cause severe discrepancies in the recovered flux fraction for Galactic diffuse emission and PS populations associated with the Galactic disk (Disk PS). At an nside value of 32, for example, a significant portion of the injected Galactic diffuse emission is absorbed into the Disk PS template. In contrast, at the standard choices of pixel size (such as nside = 128), the recovered flux fractions are fairly consistent with the injection values. The left panel of Fig.~\\ref{fig:pixelvarintensityp6v11} shows the recovered flux fractions and the injected values (dashed lines) for nside = 128 for the \\textit{Fermi} bubbles, diffuse, GCE PS, and disk PS contributions. The right panel of Fig.~\\ref{fig:pixelvarintensityp6v11} displays the mis-reconstruction of the diffuse and disk PS emissions due to a large pixel size (nside = 32). The recovered flux fractions are systematically biased across all realizations, even in this case where the model is correct by construction. Thus low-nside analyses should be treated with considerable caution, in addition to their lack of sensitivity.\n\n\n\\subsection{Source brightness} \\label{subsec:nptfitdetectionlimit}\n\\begin{table*}\n\\centering\n\\begin{tabular}{l r r r r  }\n\\hline\n &  $n=1\/4$ & $n = 1\/2$ & $n=1$ & \\\\\n\\hline\n\\textit{Quartile} 1\\\\\n\\hline\n$\\alpha$ (coefficient) & $3.18 \\pm 0.70$ & $7.35 \\pm 0.49$ & $11.30 \\pm 0.69$ \\\\\n$\\beta$ (power) & $1.43 \\pm 0.13$  & $0.97 \\pm 0.05$ & $0.76 \\pm 0.04$ \\\\\n$\\gamma$ (shift) & $0.0003 \\pm 0.31$ & $-0.40 \\pm 0.14$& $-0.62 \\pm 0.20$\\\\\n\\hline\n\\textit{Quartile} 2\\\\\n\\hline\n$\\alpha$ (coefficient) & $0.48 \\pm 0.18$ & $3.97 \\pm 0.48$& $6.14 \\pm 0.78$  \\\\\n$\\beta$ (power) & $2.24 \\pm 0.20$  & $1.22 \\pm 0.07$& $1.01 \\pm 0.08$ \\\\\n$\\gamma$ (shift) & $0.11 \\pm 0.26$  & $-0.34\\pm 0.18$& $-0.002 \\pm 0.37$ \\\\\n\\hline\n\\textit{Quartile} 3\\\\\n\\hline\n$\\alpha$ (coefficient) & $0.02 \\pm 0.02$ & $0.88 \\pm 0.39$ & $2.44 \\pm 0.96$ \\\\\n$\\beta$ (power) & $3.67 \\pm 0.40$  & $ 2.01 \\pm 0.22$& $1.50 \\pm 0.21$ \\\\\n$\\gamma$ (shift) & $0.18 \\pm 0.30$  & $-0.23 \\pm 0.19 $& $0.30 \\pm 0.37$ \\\\\n\\hline\n\\botrule\n\\end{tabular}\n\\caption{Best-fit parameters obtained using least-squares regression method for the power law fit to the $\\ln{\\text{BF}}$ values as we varied the source brightness of the GCE PS component in \\texttt{p6v11}. Note that $n=1$ is the result from averaging across 20 realizations, while $n=1\/2,1\/4$ result from 20 realizations.}\n\\label{tab:tradeoffp6v11}\n\\end{table*}\n\nFinally, we would like to understand how sensitivity scales with the brightness of the sources. This is important both for understanding the prospects for future detection of a bulge PS population with {\\it Fermi}, and in understanding the likely sensitivity of future telescopes with different exposure and angular resolution.\n\n\\begin{figure}\n    \\centering\n    \\includegraphics[width=0.98\\linewidth]{sensitivitydiffbrightness.pdf}\n    \\caption{$\\langle \\ln{\\text{BF}}\\rangle$ and the $1\\sigma$ standard error of the mean (obtained from 20 realizations at each point) across the top three quartiles at varying brightness level for the full \\textit{Fermi} case, with the baseline exposure. The best-fit $S_b$ in the real data is 17.11; we test the effect of reducing $S_b$ by a factor of 2 or 4. The baseline case was scanned using nlive=300, while the other cases were performed using nlive=100 for computational efficiency.\n    }\n    \\label{fig:sensitivitychi1}\n\\end{figure}\n\nWe perform the same test as described in Sec.~\\ref{subsec:tradeoffs}, where now the source brightness parameter $S_b$ is multiplied by a factor of $n=1\/2$ or $1\/4$ (and the number of sources is modified to keep the total flux constant). Fig.~\\ref{fig:angexp0.5sb} shows the results, while Table~\\ref{tab:tradeoffp6v11} shows the corresponding best-fit parameters and uncertainties obtained from the power-law fit in Eq.~\\ref{eqn:powerlawshift}, using the least-squares method.\n\n\\begin{figure*}\n    \\centering\n    \\includegraphics[width=0.49\\linewidth]{lowtradeoffp6v110.5s.pdf}\n    \\hspace{0.4em}\n    \\includegraphics[width=0.49\\linewidth]{hightradeoffp6v110.5s.pdf} \\\\\n    \\includegraphics[width=0.49\\linewidth]{lowtradeoffp6v110.25s.pdf}\n     \\hspace{0.4em}\n     \\includegraphics[width=0.49\\linewidth]{hightradeoffp6v110.25s.pdf}\n    \\caption{$\\langle \\ln{\\text{BF}}\\rangle$ and the $1\\sigma$ standard error of the mean across 20 realizations at different $\\chi$ values for the top three quartiles graded by angular resolution. \\textit{Left}: realizations with $\\chi<1$. \\textit{Right}: realizations with $\\chi \\geq 1$. In the \\textit{upper panels} we simulated the sources at half of the baseline brightness ($S_{b}=17.11$ from Table~\\ref{tab:fitparam}), but doubled the number of sources, in accordance with Eq.~\\ref{eq:nphotons}; in the \\textit{lower panels} we simulated the sources at $1\/4$ of the baseline brightness but quadrupled the number of sources. The dashed, dotted, and dash-dotted lines correspond to the shifted power law (Eq.~\\ref{eqn:powerlawshift} for quartiles 1, 2, and 3, respectively.}\n    \\label{fig:angexp0.5sb}\n\\end{figure*}\n\n\nOur results indicate that the parameter (of the power-law fit) $\\alpha$ increases at higher values of $n$. Since $\\alpha$ corresponds to the sensitivity at $\\chi=1$, it is expected to observe an increase as the brightness of the sources increase. On the other hand, $\\beta$ decreases modestly as $n$ increases. Assuming that $\\braket{\\ln{\\text{BF}}}$ has the same functional behavior as $\\braket{\\Delta\\ln{\\mathcal{L}}}$, our expectation from the analytic results is $\\beta\\approx 1$, at least if the fit is dominated by the region where the expected number of counts\/source and hence $\\braket{\\ln{\\text{BF}}}$ is large. However, at low brightness levels, as predicted by the analytic equations, we expect a quadratic scaling, $\\beta\\approx 2$. Thus it is reasonable to see a stronger scaling for smaller values of $n$, where the quadratic behavior is relevant for a larger range of $\\chi$. In other words, increased exposure is more important for fainter sources.\n\nTo clearly demonstrate the effect of varying the source brightness on the overall sensitivity, we plotted  $\\langle \\ln{\\text{BF}}\\rangle(\\chi=1)$ across 20 realizations as a function of $S_{b}$, for the top three PSF quartiles, in Fig.~\\ref{fig:sensitivitychi1}. The baseline case corresponds to $S_{b}=17.11$. As expected, we find that, on average, sensitivity increases as the PS population brightens.\n\nApproximating the sensitivity-exposure relation by the power law with an additive shift as in Eq.~\\ref{eqn:powerlawshift}, we can estimate the $\\chi$ value that corresponds to  $\\ln{\\text{BF}} \\geq 1$ for Quartile 1, as a function of the brightness of the source population (indicating some sensitivity to the sources; we could increase this threshold to require a more significant detection). Using the best-fit parameters in Table~\\ref{tab:tradeoffp6v11}, we find that for $n=1$, this threshold corresponds to $\\chi \\geq 0.08$; for $n=1\/2$, to $\\chi \\geq 0.18$; and for $n=1\/4$, to $\\chi \\geq 0.45$. As expected, a higher level of exposure is required to detect fainter populations of PSs. \n\n\\section{Conclusions} \\label{sec:conclusion}\n\nWe have investigated the statistical behavior of non-Poissonian template fitting, as implemented in the \\texttt{NPTFit} public code, when characterizing unresolved point sources. In particular we have explored the sensitivity to point sources both analytically and numerically, in a simplified isotropic-emission scenario and a realistic scenario relevant to gamma rays from the inner Galaxy. We define the sensitivity to point sources (or detectability of point sources) as the ratio of the maximum likelihood (analytic case) or Bayesian evidence (numerical case) between the true underlying model versus a model that excludes point sources associated with the signal component. \nWe first derived analytic estimates of the sensitivity for point sources with a delta-function source count function, where all sources have the same expected number of photons per source $s$. We found that the expected contribution to the log likelihood ratio from a given pixel is a function only of $ks$, where $k$ is the fraction of the emission that is attributed to point sources; the scaling of the log likelihood with $k s$ is linear for $k s \\gg 1$ and quadratic for $k s \\ll 1$. We also examined the variance in this sensitivity, reflecting the expected scatter between realizations. By exploring a range of scenarios, we found that the standard deviation of our sensitivity metric was generically smaller than the expectation value by a factor of $\\sqrt{A}$, where $A$ can be the total number of sources in the ROI, the total number of pixels in the ROI, or the log likelihood ratio itself; in general, whichever parameter is smallest dominates the variance. This behavior can lead to a relatively large scatter between the sensitivity inferred from different simulations, which we indeed observe in the numerical data. We tested our analytic predictions using numerical simulations in a simplified case where both point sources and smooth emission are isotropic (detailed in Sec.~\\ref{sec:isotropic} and Appendix \\ref{app:isotropic}), and found that the analytic results were quantitatively quite accurate in the case where the PSF is very narrow, and provide a good description of various scaling relations even with a more realistic PSF. The analytic and isotropic results may be relevant to other analyses employing non-Poissonian template fitting, e.g. the analysis of the neutrino background presented in \\cite{Aartsen:2019mbc}.  \n\nWe then numerically investigated the role of several key parameters in the \\texttt{NPTFit} analysis of a population of point sources associated with the \\textit{Fermi} gamma-ray skymap. The parameters we tested included exposure, angular resolution, source brightness and pixel size. This analysis was performed within the full \\textit{Fermi} scenario using both \\texttt{p6v11} templates and Model A templates for the Galactic diffuse emission (detailed in Appendix \\ref{app:modela}). The results we quote below are based on simulations with the default \\texttt{p6v11} template from the public \\texttt{NPTFit} code, but we found consistent results using an alternative background model denoted Model A. \n\nFor the cases we tested, we found the following general relationships between exposure, angular resolution, and sensitivity: \n\\begin{itemize}\n\\item Gaining exposure alone induces an increase in sensitivity that is roughly linear for the exposure range and analysis choices we focused on. The analytic approximation predicts a scaling between linear and quadratic; our results are broadly consistent with this expectation, but in complex\/realistic sky models involving multiple templates with different morphologies, we have observed both slightly sub-linear scaling and stronger-than-quadratic scaling, the latter in quartiles with poor angular resolution.  \n\\item Worse angular resolution results in lower sensitivity (as expected) such that the third-highest-quality angular resolution quartile has average sensitivity approximately $60\\%$ lower than of the highest quality quartile (although the degree of degradation can vary depending on the exposure level and the brightness of the sources, with the loss of sensitivity being more pronounced for fainter sources and lower exposure).\n\\item As a simplified parametrization of the angular resolution (which varies according to quartile selection and included energy range), we examined how the sensitivity varies according to the $68\\%$ containment angle radius $\\eta$, and found that sensitivity has an approximate inverse proportionality relation to $\\eta$. \n\\item With these results, we tested the effects of increasing exposure at the expense of angular resolution in practical situations relevant to {\\it Fermi} data, by varying the quartile selection and energy range. We find, on average, that the increase in sensitivity from a larger exposure is offset by the degraded angular resolution to a good approximation. \n\\item Hence, this tradeoff only produces a small net change in sensitivity; there is a broad range of possible analysis choices that yield similar expected sensitivity. The large scatter in sensitivity between realizations means that some caution is needed when interpreting changes in the Bayes factor in real data upon addition of extra quartiles, energy bins, ROI, etc; it appears possible for changes in the analysis choice that modify the dataset to have a large apparent effect on the Bayes factor purely due to this scatter.\n\\end{itemize}\n\nWe also examined the role of source brightness to the sensitivity of \\texttt{NPTFit} to point sources to understand how the sensitivity falls off as the source brightness declines. For sufficiently faint point sources, as expected, \\texttt{NPTFit} is unable to distinguish point sources from background smooth emission. More specifically, in the top graded quartile for angular resolution, the minimum exposure (in relation to the baseline exposure) required to achieve any hint of detection (defined somewhat arbitrarily as an average Bayes factor $\\ln{\\text{BF}}\\geq 1$) scales as $O(S_{b}^{-1.28})$, where $S_{b}$ is the peak number of photons per Galactic Center Excess point source.\n\nWe explored simulations with different pixel sizes, and found that pixel size was not a crucial factor in determining the sensitivity of \\texttt{NPTFit}, except in the case of extremely large or small pixel sizes. Very large pixel sizes induced inaccurate recovery of the various physical emission components; small pixel sizes led to higher variance across realizations.\n\nThese results serve as a systematic demonstration of the behavior of \\texttt{NPTFit} under a range of conditions relevant to analyses of {\\it Fermi} data from the inner Galaxy (and potentially more broadly).\n\n\\section*{Acknowledgements}\n\nThe authors thank Siddharth Mishra-Sharma and Nicholas Rodd for helpful feedback and suggestions. TRS was supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics of U.S. Department of Energy under grant Contract Number DE-SC0012567 through the Center for Theoretical Physics at MIT, and the National Science Foundation under Cooperative Agreement PHY-2019786 (The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, \\url{http:\/\/iaifi.org\/}). The work of LGCB was funded by the Massachusetts Institute of Technology Undergraduate Research Opportunities Program (UROP) office. \n\n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
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+{"text":" \nBooks by V. M. Burns\n\nMystery Bookshop Mysteries   \nTHE PLOT IS MURDER   \nREAD HERRING HUNT   \nTHE NOVEL ART OF MURDER   \nWED, READ & DEAD   \nBOOKMARKED FOR MURDER\n\nDog Club Mysteries   \nIN THE DOG HOUSE   \nTHE PUPPY WHO KNEW TOO MUCH   \nBARK IF IT'S MURDER\n\nPublished by Kensington Publishing Corporation\nBookmarked for Murder\n\nV. M. BURNS\n\nKENSINGTON BOOKS   \nwww.kensingtonbooks.com\n\nAll copyrighted material within is Attributor Protected.\nTable of Contents\n\nAlso by  \nTitle Page  \nCopyright Page  \nAcknowledgments  \nChapter 1  \nChapter 2  \nChapter 3  \nChapter 4  \nChapter 5  \nChapter 6  \nChapter 7  \nChapter 8  \nChapter 9  \nChapter 10  \nChapter 11  \nChapter 12  \nChapter 13  \nChapter 14  \nChapter 15  \nChapter 16  \nChapter 17  \nChapter 18  \nChapter 19  \nChapter 20  \nChapter 21\n\nThis book is a work of fiction. Names, characters, places, and incidents either are products of the author's imagination or are used fictitiously. Any resemblance to actual persons, living or dead, events, or locales is entirely coincidental.\n\nKENSINGTON BOOKS are published by\n\nKensington Publishing Corp.   \n119 West 40th Street   \nNew York, NY 10018\n\nCopyright \u00a9 2019 by Valerie Burns\n\nAll rights reserved. No part of this book may be reproduced in any form or by any means without the prior written consent of the Publisher, excepting brief quotes used in reviews.\n\nKensington and the K logo Reg. U.S. Pat. & TM Off.\n\nISBN-13: 978-1-4967-1832-7 (ebook)   \nISBN-10: 1-4967-1832-1 (ebook)   \nFirst Kensington Electronic Edition: December 2019\n\nISBN: 978-1-4967-1831-0\n\nAcknowledgments\n\nAs always, I want to thank my agent Dawn Dowdle at Blue Ridge Literary and the wonderful people at Kensington who help make my dreams a reality, John, Paula, Michelle, Lauren, and all the folks who do so much behind the scenes.\n\nI am blessed to have a broad network of friends who support me in so many ways, including Patricia Lillie and my fellow Seton Hill University tribe. Thanks to the Barnyardians, Tim, Chuck, Lindsey, Jill, and our fearless leader, Sandy, for all the support and shameless promotional plugs. Thanks to my official team, Amber, Derrick, Eric, Jennifer, Jonathan, and Robin. I also have to thank my unofficial team, Deborah, Grace, Jamie, and Tena. Once a trainer . . .\n\nThanks to Trooper Tony for the technical assistance with police and TBI policy and Abby Vandiver for the legal insights. Thanks to Alexia Gordon for assistance with medical questions and for the unicorn support from both you and Kellye Garrett and the Crime Writers of Color. I appreciate the Cozy Mystery Crew, SinC, and Guppies. Thanks to Dru Ann Love, Karen Owen, Colleen Finn, Jerri Cachero, Lisa A. Kelley, Karen Kenyon, and Lori Caswell for the support, encouragement, and for all you do to help authors.\n\nThanks to my family, Ben Burns, Jackie Rucker, Christopher (Carson) and Crosby Rucker, Jillian (Drew) and Marcella Merkel. Special thanks to my friends Sophia and Shelitha for always having my back.\n\nLastly, thanks to Linda Herold for coming up with the title.\nChapter 1\n\n\"Samantha Marie Washington!\"\n\nIt was never good when my grandmother included my middle name. Mid-thirties and I still cringed as much as I did as a kid. I snapped the book I was perusing closed and looked up. \"What?\"\n\n\"You own a mystery bookshop where you spend 99 percent of your life. It's our last day in the Windy City, and you want to spend the time we have left before our bus leaves in a mystery bookshop?\" She straightened her nearly five-foot-ten frame to its fullest extent and looked down her nose at me.\n\n\"It's research.\" I glanced around the room to make sure the owner who greeted us when we came in wasn't within hearing distance. Thankfully, the owner, Linda Herold, was occupied with another customer. Linda was a stunning woman with a statuesque frame and immaculate hair, nails, and clothes. She looked as though she'd just stepped off the cover of Vogue rather than out of the back of a storage room. I stared down at my blue jeans and tried not to slump at the realization I looked more like a country hick than an aspiring author and mystery bookshop owner. I leaned closer to Nana Jo and whispered, \"Keep your voice down.\"\n\n\"If you don't put that book back on the shelf and get your hiney out of this store at once, so help me God, I'm going to take you over my knee.\" She turned to march out of the store, but something caught her attention and she stopped. \"Isn't that the man Irma picked up at the bar the other night?\"\n\n\"Are you joking? Irma Starczewski picks up at least two men every day of the week. I don't even try to keep track.\" I followed Nana Jo's gaze.\n\nShe was looking at a secluded area in the back of Murder Between the Pages. The bookstore wasn't large, but it took advantage of the vertical space. There were tall bookshelves along the walls and narrow rows with five-foot bookshelves. In the back corner, there was a spiral staircase that led to a loft area that was dark and filled with books. An older man wearing a hat and heavy coat was upstairs arguing with someone I thought to be a woman.\n\n\"I can't see his face.\"\n\n\"Stand over here.\" She stepped aside and pulled me closer. \"His face looks familiar, but, for the life of me, I can't remember where I've seen him before.\" Nana Jo stared.\n\n\"I know what you mean, but maybe he just has one of those faces . . . Maybe he just seems familiar because he was wrapped around Irma at the House of Blues.\" I laughed.\n\n\"Shhhh.\" Nana Jo inclined her head toward a big man wearing tight jeans, a tight leather jacket, a baseball cap, and sunglasses standing nearby. \"Check out Mr. Big.\"\n\nNana Jo leaned close to me and whispered, \"Even if he wasn't wearing sunglasses inside a store, he'd stand out like a stripper at a Baptist camp meeting.\"\n\nNana Jo's metaphor might not have been politically correct, but I couldn't argue with her logic. \"Mr. Big\" definitely stood out. Wearing mirrored sunglasses inside was only part of his disguise fail. Add to that, the extra tight leather jacket, which rode up in the back and exposed part of the butt of a gun in the back waistband of his jeans, and he might have had a neon sign over his head that read \"Security.\"\n\n\"Yeah. He's holding that book upside down,\" I joked.\n\nNana Jo stared at me. I smirked and she flashed a brief smile and then narrowed her eyes. \"Don't try to get on my good side, Samantha Marie. I want you outside in two minutes.\" She turned and walked out.\n\nMore than the use of my middle name, I recognized the tone. I sighed and returned the book to the shelf. I took one last look at \"Mr. Big\" and then hurried outside. I could always come back to Chicago another time and check out the store, preferably without my pushy grandmother in tow.\n\nOutside, Nana Jo impatiently tapped her foot, one hand on her hip, and had a look I knew could silence a classroom of rambunctious teens from her days as a high school math teacher.\n\nI slunk up to my Nana Jo and gave her a kiss on the cheek. \"I'm sorry.\"\n\nThe corners of her lips twitched. All was forgiven.\n\n\"Where are the girls?\"\n\nNana Jo pointed to a line of people that wrapped around the corner. \"They refused to leave the city without popcorn.\"\n\nWhen we agreed to take the Shady Acres four-day shopping excursion to Chicago, we knew time was limited. The trip fee was extremely reasonable and had included four days and three nights at a four-star hotel in the theatre district, tickets to a play, and one meal in the hotel dining room. The theatre district was close to the large Macy's and a short cab or elevated train ride from Michigan Avenue shopping. There was so much to do in the limited time we were there, each of the five of us identified one thing we wanted to do while in the city. Dorothy Clark wanted to shop, so we spent several enjoyable hours walking the Magnificent Mile and admiring the lights and seasonal atmosphere. The week between Christmas and New Year's wasn't the best time for outdoor excursions in Chicago. The wind from Lake Michigan could be bitterly cold, even in warmer months. However, we all dressed warmly and the wind was bearable. Excursions into Water Tower Place, Nordstrom, and Bloomingdale's provided warmth and major hits to a few credit cards but was well worth the journey. Nana Jo chose a matinee performance of the Nutcracker ballet with live music by the Chicago Philharmonic as her one must-see event, and the performance was spectacular. Irma Starczewski, true to her nature, wanted to dance and pick up men, so she chose a night at the Chicago House of Blues. I chose tea at one of the fancy hotels downtown. We'd all managed to fit in everything, except Ruby Mae Stevenson's wish. All Ruby Mae wanted was to get popcorn from a well-known Chicago attraction, Garrett's Popcorn.\n\nThe tiny popcorn shop wasn't much bigger than a telephone booth, but each time we walked by, the line of people was outside and wrapped around the building. We promised to try again every day in hopes of finding a time when the line wasn't so bad, but here it was our last day and we still hadn't found that moment.\n\n\"I'm glad Ruby Mae is getting her popcorn. Maybe I should go and take her place in the line.\" I started to walk toward the line.\n\nNana Jo nudged my arm. \"No need. Here they come.\"\n\nI looked up and Ruby Mae, Irma, Dorothy, and a tall good-looking gentleman followed with two large shopping bags in each hand.\n\nThe group approached and Ruby Mae broke into a big grin. \"Sam, I want you to meet my cousin Arnold's boy, Terrence.\"\n\nTerrence was a dark-skinned young man with a bright smile. He nodded politely.\n\n\"We better hurry if we're going to get back to the hotel in time to catch our bus.\" Nana Jo glanced down the street, lifted her arm, and let out a whistle that would have rivaled those produced by most trains.\n\nA yellow taxi skidded to a stop at the curb and the five of us piled inside while Terrence and the taxi driver crammed our shopping bags in the trunk.\n\nNot surprisingly, the traffic in Chicago was bumper to bumper. The trip, although relatively short, was an adventure. Our driver jammed on his brakes at least four times on the short five-block journey to our hotel, which would have sent us through the front windshield if we hadn't been crammed inside like sardines. He screamed what I could only assume were obscenities in a foreign language at least twice at his fellow motorists. When he pulled up to the curb in front of our hotel, we pried ourselves out of the car, and I overcame a burning desire to drop to my knees and kiss the ground.\n\n\"That was certainly an adventure.\" Nana Jo fanned herself as she straightened up slowly. \"I think he just took five years off my life.\"\n\nRuby Mae patted Nana Jo on the shoulder. \"He certainly has improved my prayer life. I don't think I've prayed that earnestly in quite some time.\"\n\nDorothy staggered out of the front seat. Her purse was clutched to her chest. \"I thought the taxi drivers in New York were bad, but they're tame compared to Mario Andretti back there.\" She pointed at our driver.\n\nWe stared as the taxi sped away from the curb so quickly he left skid marks in the street and a barrage of horn blasts in his wake.\n\n\"Come on, Josephine. Don't just stand there gawking, get a move on.\" Irma prodded Nana Jo in the back. \"I see Max getting on the bus and I need to get up there and secure my seat before that hussy Velma Levington gets it.\"\n\nIrma's back was to Nana Jo, so she missed seeing her raise her purse like a bat. Fortunately, I grabbed her arm and stopped her before she could club Irma.\n\n\"I'm going to brain that dingbat one of these days,\" Nana Jo said through clenched teeth.\n\nIrma ran to the bus in the six-inch heels Nana Jo called hooker heels, and I marveled at her balance.\n\nIrma Starczewski was a petite woman, barely reaching five feet, even in her hooker heels. In her mid-eighties, she was the oldest of Nana Jo's friends. Years of heavy chain-smoking had left their marks and she spoke with a raspy voice and had a persistent cough, which was either a result of the smoking or the alcohol she kept in a flask in her purse. She swore like a sailor and flirted with every man she met. Irma also had a big heart, and I knew Nana Jo loved her like a sister.\n\nWe'd checked out of our rooms earlier and left our luggage with the bellmen, so there wasn't much for us to do except get onboard the charter bus and sit for the two-hour drive back to North Harbor, Michigan.\n\nThe bus driver, a tall man who looked to be in his thirties, stood at the door and offered a hand to each of us as we loaded onto the bus.\n\nNana Jo was in front of me. \"You're new. What happened to Earl?\"\n\nFrom the angle where she stood, Nana Jo probably wasn't able to see the man's face, but a bright red patch spread from his neck. However, it was quickly gone.\n\nThe man smiled. \"Earl had an emergency and had to leave. However, I promise to take real good care of you.\" He smiled again, but there was something behind his eyes that sent a shiver up my spine.\n\nI forced myself not to wrench my hand away as the driver assisted me into the bus, but I couldn't help wiping my hand on my jeans once I was inside and safely out of sight.\n\nNana Jo scooted over so I could sit next to her. \"Something clammy about that one, isn't there?\" She inclined her head in the direction of the driver. \"I wonder what really happened to Earl.\"\n\n\"I'm sure it's just like he said. Earl probably had something come up and had to go home.\"\n\n\"Hmm . . .\" She tilted her head to the side and stared at me.\n\n\"What?\"\n\n\"You look like my granddaughter, but she's smart enough to recognize cow dung when someone shovels it out.\"\n\n\"She's also smart enough to know when something is none of her business, and she knows how to keep her nose out of trouble.\"\n\nShe raised an eyebrow but said nothing.\n\nIrma had outrun Velma Levington. She cozied up next to Max Franck, a short, bald man with glasses and an air of something European. Irma met Max at the House of Blues a couple of nights ago. Apart from being able to hold his own with Irma when it came to shots, Max was also an enthusiastic dancer. He and Irma hit it off and spent the entire night drinking, dancing, drinking, and then drinking. Not unlike many residents of large cities like Chicago, Max didn't drive and was surprisingly enthusiastic when Irma told him about the bus trip to North Harbor. At the time, I wondered why anyone from Chicago would want to go to North Harbor, Michigan. However, the look in Max's eyes led me to believe his interest had less to do with the location and more to do with Irma.\n\nThey were so close at the House of Blues, I felt sure Irma would take him back to her hotel room. However, she was disappointed when he begged off, saying he had business he had to take care of but promised to join her today. Irma had been looking forward to his visit to Shady Acres and barely spoke of anything else. The bus wasn't full, and the activities manager permitted Max to join the trip for the ride home for free since he hadn't stayed at the hotel, eaten any meals, or taken part in any of the other activities. Besides, two residents had paid for seats on the trip but had been unable to attend at the last minute due to medical reasons. Max wasn't the only new addition to the bus. There was another woman I hadn't recognized from the first trip. She stood out because she didn't seem like one of the seniors, although it was hard to tell. She had on a large hat, which hid part of her face. She walked down the aisle. As she passed by Max and Irma, I thought I noticed a glint of recognition in Max's eyes.\n\nNana Jo leaned close. \"I wonder who that is.\"\n\nI shrugged. \"Probably someone's daughter or granddaughter getting a free ride to North Harbor.\"\n\nNana Jo nudged me. \"Look, it's Mr. Big.\"\n\nI stared after the man in question. He was the big, stocky man from the bookstore we'd seen earlier, with tight jeans and mirrored sunglasses.\n\n\"I wonder if he still has that gun in his pants?\"\n\nNana Jo patted her purse. \"Well, if he does, I've got my peacemaker with me and I'll drop him like a Thanksgiving turkey if he so much as reaches a finger toward his waistband.\"\n\nHe sidled down the aisle with a duffle bag. He took a seat directly across from Irma and Max. I could have sworn a look of recognition passed across Max's face, but with sunglasses, it was hard to tell if Mr. Big had the same reaction and the recognition was mutual.\n\nWhen Velma boarded, she glanced toward Max and Irma. For a brief second, she hesitated. That momentary hesitation brought a look in Irma's face which could only be described as gloating. Velma glared. However, she quickly plastered on a fake smile and glanced around for a seat. Velma was about the same height and weight as Irma, but she lacked Irma's outgoing personality. She had long white hair, which she usually wore in a tight bun. Velma's most distinct feature was her eyes. They were blue, a cold, steely blue like Lake Michigan in the winter when the ice covered the water. Velma turned toward the seat next to Mr. Big but was thwarted when the stranger picked up his duffle bag from the floor and placed it in the empty seat.\n\n\"Well, I never.\" Velma stomped down the aisle in search of another seat.\n\nIf Mr. Big took note of Velma's ire, it was well hidden behind his sunglasses. He slouched in his seat and pulled his cap down so most of his face was hidden. Arms folded across his chest, he presented a stony barrier that screamed, \"Do Not Disturb,\" louder than any placard on a hotel room.\n\nIf the smile on Irma's face and her body language were any indication, Irma reveled in her victory over Velma, whom Irma viewed as competition. Velma hadn't been at Shady Acres long, but, in just a few short months, she and Irma had become bitter rivals in practically every area. This round was definitely scored in Irma's favor.\n\nMax, on the other hand, seemed agitated and distracted. He was definitely not as attentive to Irma as he'd been in the bar. Whether due to the light of day, lack of alcohol, or improved judgment, which often occurred outside of bars, Max wasn't nearly as flirtatious and enamored with Irma as he'd been in the House of Blues.\n\nThe bus filled up and, once the new activities director made sure everyone was present and accounted for, we were off. At the House of Blues, Max was jovial and charming. However, on this return trip, his disposition appeared to be quiet and taciturn. However, I grew tired of people-watching and pulled out a book I'd picked up at Murder Between the Pages by Ellery Adams, The Secret, Book & Scone Society, and buried my head in murder, mystery, and intrigue set in a bookshop.\n\n* * *\n\nI went to college in the Chicago suburbs many moons ago. However, after more than a decade, the one thing that hadn't changed much was the traffic. Traffic in Chicago was a nightmare, especially on weekdays. I knew many natives who owned cars but left them at home and used public transportation, especially the elevated trains, known locally as \"the EL,\" to avoid the rush hour. There was even a commuter train that ran between River Bend, Indiana, and Chicago, which was popular with commuters and anyone who wanted to take advantage of the theatre, shopping, or sports events without the hassle of sitting on the interstate for what felt like eons. Charter bus trips, like the one Shady Acres provided, were very popular as a way to enjoy the sites of the city without the hassle of driving or dealing with parking.\n\nNormally, the interstates were less busy on weekends. However, the holidays were on the weekend this year, which would have meant several of the places we wanted to visit would be unavailable. So, this trip was Monday through Thursday. I had hoped the holidays would mean less people on the interstate and, hopefully, less traffic congestion. However, road construction on the toll road had diverted a lot of traffic onto the expressway, and we spent several hours inching our way eastward. What should have been two hours and twenty minutes turned into four hours and we'd barely crossed over into the state of Indiana.\n\nOnce we finally began to move, I noticed a rumble coming from the crowd. I lifted my head when I heard Nana Jo shout. \"Hey, driver. We're going to need to stop at a rest area.\"\n\nI looked up and saw the driver glance in the mirror, but he neither slowed his pace nor acknowledged the request as he sped past several exits.\n\n\"There's a toilet in the back.\" Our driver glanced into the rearview mirror and gave a halfhearted smile to soften the words.\n\n\"It's broken,\" someone yelled from the back. I didn't recognize the voice, but I definitely recognized the tone.\n\nOur driver passed two more exits with no signs of slowing down. That was when the buzz got louder and less polite.\n\n\"We've been on this missile for four hours. You've got old people with small bladders,\" Nana Jo yelled. \"Listen, Bub, I suggest you pull this tank over or you're going to have a lot of clean up.\"\n\nWhether it was Nana Jo's tone or the look in the eyes of some of the other prisoners, her message finally came through.\n\nThe activities director, Caroline Fenton, leaned forward and whispered something to the driver, who then pulled off the interstate into a rest area.\n\nNana Jo was one of the first people at the door. When the driver assisted her down, I heard him whisper, \"My name is Bob, not Bub.\"\n\nNana Jo hurried off, but I could tell by the set of her shoulders and her ramrod straight back, she'd heard him.\n\nThere was a mass exodus to get off the bus. I was half the age of most of the people on the bus, so I stayed in my seat to allow the others to leave first.\n\n\"Come on, Max. Let's take a walk.\" Irma stood up.\n\n\"No. I think I'll just wait here.\" Max looked around. \"You go on.\" He smiled and stood up to allow Irma to slide past him into the aisle before he returned to his seat.\n\nIf the call of nature hadn't been so strong, I suspect Irma might have spent more time cajoling Max to join her. Instead, she hurried down the aisle and off the bus.\n\nI stood and stretched. Velma looked to be asleep in the back of the bus. Mr. Big with the mirrored glasses remained in his seat. Max and the activities director were the only other ones left as I got off the bus.\n\nPublic restrooms, especially at rest stops, are often a place I avoided whenever possible. However, while I was fine while sitting, gravity wasn't my friend. Once I stood, the urge to go increased. So, I took a few deep breaths and did what I had to do.\n\nNana Jo waited for me near the vending machines. She juggled chips, bottled water, candy bars, and donuts.\n\n\"You can't possibly be planning to eat all of that.\"\n\nShe never took her gaze from the vending machine. \"You got any ones?\"\n\n\"I'm not hungry.\"\n\n\"You will be before we get home.\"\n\nI stared at her. \"We're through the worst of the traffic now. We should be home in less than an hour.\"\n\nShe smirked. \"What do you think the likelihood is our prison guard is going to stop for food?\"\n\nI stared at her for several seconds and then reached in my purse and pulled out my wallet. \"Good point. Maybe you should get some of those beef jerky things and cheese crackers.\"\n\nOnce our bags were full of snacks, we headed back to the bus. The driver was nowhere to be found and the doors of the bus were locked. Several of the others stood outside waiting.\n\nCaroline Fenton, the activities director, hurried to the front of the line. \"What's wrong? We should get back on the road.\"\n\n\"The door's locked.\" I pointed to the door.\n\nShe smiled. \"That's impossible.\" She shook the door and realized what we already knew, and the smile left her face. She looked around like a frantic rabbit. \"Where's Bob?\"\n\nWe shrugged and looked around.\n\n\"I assume he went to the bathroom,\" Nana Jo said what we all thought must have been obvious.\n\nAt that point, Bob hurried to the front.\n\n\"Sorry.\" He pulled keys out of his pocket and unlocked the doors and climbed into the bus.\n\nHe helped each of us onto the bus, same as before. Sarah Howard was the first person on the bus. The only person onboard was Max, who hadn't left his seat. We each returned to our seats. Irma was one of the last to board. When she got to her seat, she waited for Max to stand and allow her to return to her seat. However, he didn't move.\n\nShe gave him a playful shake. \"Maxie, wake up. I need to get by.\" When Max didn't respond, she shook him harder. \"Max, come on.\"\n\nPeople huffed with impatience, as did the bus driver.\n\nMiss Fenton stood and looked back. \"If everyone would take their seats, we'll be able to leave.\"\n\nIrma shook Max harder. This time, Max slumped over in his seat and slowly slid to the floor. Irma stood in shock for what felt like a full minute. Then she let out a bloodcurdling scream and fainted.\nChapter 2\n\nThe rest stop on the Indiana toll road wasn't exactly the most restful place I'd ever been. I'd been to rest areas with restaurants, gas stations, and even showers for truckers. This wasn't one of those. The building was a basic concrete block. There were restrooms for men and women, vending machines, and a display stand with brochures and maps. Outside, there were picnic tables and an area for dogs to play and relieve themselves, complete with trash receptacles and plastic bags for the waste. It was much too cold outside to sit at the picnic tables, and the public restrooms didn't lend themselves to long stays. The state police wouldn't allow us back onto the bus until the forensics team finished. So, a busload of seniors and about four people who had yet to make it to the half-century mark were all huddled inside the concrete building. The vending machine looked as though it had been raided by locusts. The only things left in the machine were a pack of chewing gum and a Milky Way that had gotten twisted and was impaled on the spiral coil used to push it forward.\n\n\"Hand me a piece of that shoe leather.\" Nana Jo reached out her hand.\n\nI gave her one of the pieces of beef jerky I had left.\n\n\"My teeth aren't what they used to be, but I'm starving.\"\n\nDorothy stared at the flat stick. \"Josephine, you must be pretty desperate to even consider eating that.\" She frowned. \"I don't think my teeth could take it.\"\n\n\"I'm desperate. It's either the shoe leather or I'm going to pass out.\" She bit into the jerky and tugged. Unfortunately, it had been in the machine quite a while and was tougher than rubber.\n\nRuby Mae scowled. \"If we could get to our luggage, I could get my popcorn.\"\n\nThe police had taped off the area around the bus and, unfortunately, our luggage was within the boundary and therefore, off-limits.\n\n\"Well, I can't eat this.\" Nana Jo tossed the beef jerky stick into a nearby trash can. \"Where are we?\"\n\nDorothy pulled out her cell phone. \"Hey, Siri.\"\n\n\"How can I serve you today, my queen,\" Siri responded.\n\nDorothy didn't bat an eyelash. \"Where am I?\"\n\nAfter a few moments, the phone responded with an address.\n\n\"Ask her to order ten large pepperoni pizzas and have them delivered.\" Nana Jo turned around to face the majority of the crowd. \"We're ordering pizza. Who wants in?\"\n\nEvery hand raised and Nana Jo took a quick count. \"Better add five cheese to the order.\"\n\nDorothy promptly updated her request to her cellular servant.\n\n\"I wonder how Irma's doing?\" Ruby Mae craned her neck to look around the crowd toward a small maintenance closet where Irma had been carried after she fainted.\n\n\"No idea, but she's surrounded by men, so I'd say she's in hog heaven,\" Nana Jo said.\n\nIt took less than thirty minutes for a Volkswagen Beetle that was probably older than me, with a black roof, baby-blue body, one green door, and one orange door to arrive at our rest area. The myriad of police cars had cordoned off the area by the bus, but the car chugged its way to the front. The driver pulled up front. He left the car running, hopped out, and looked around. Nana Jo and I went outside.\n\n\"You ordered fifteen pizzas?\" A freckle-faced kid, who looked about twelve, with curly red hair, ripped jeans, a red hoodie with a Star Trek insignia, and red Converse All-Stars, held up a smartphone that looked as though it cost more than the car.\n\n\"Nice shoes.\" Nana Jo scribbled her name with her finger.\n\n\"Thanks. All the old ladies usually like them.\" He reached inside his car and handed out the pizzas. \"What happened over there?\" He inclined his head toward the bus.\n\nThe coroner was removing the body from the bus.\n\n\"That's what's left of the last person who called me an old lady. Remember, on Star Trek, the red shirts always die first.\" Nana Jo handed me half of the pizzas, turned, and walked toward the building.\n\nThe driver stood there staring for a half minute and then laughed.\n\nI hurried to catch up to my grandmother. \"What's that mean, 'the red shirts always die first'?\"\n\nNana Jo smirked. \"And I thought you were a trekkie.\"\n\nI thought about her comment and that was when the lightbulb went on and I chuckled.\n\nAs we were about to enter the building, everyone started to come outside.\n\n\"What's going on?\" I juggled my pizza boxes to alleviate some of the heat and grease coming through the boxes.\n\nCaroline Fenton pointed to the back. \"The replacement charter bus finally arrived.\" She reached for some of the boxes. \"Let me help you.\"\n\n\"Great. Maybe we can get home soon,\" Nana Jo said.\n\n\"Unfortunately, we can't leave until the police finish questioning everyone, but at least we can sit down.\" She followed the herd of seniors heading to the bus.\n\nLike lemmings, we marched to the bus. Once onboard, everyone dug into the pizza and found seats. The new bus driver had come prepared with a cooler full of bottled water and everyone was grateful.\n\nEveryone wanted to give Nana Jo something for the pizza, but she declined. Caroline Fenton said Shady Acres would reimburse her for the costs.\n\nFed and finally able to sit, I hoped we would be able to leave soon. My brother-in-law, Tony Rutherford, had been looking after my dogs, Snickers and Oreo, so I knew they were in good hands. However, my sister, Jenna, wasn't a big fan and the medicine Snickers had to take for her heart disease was causing her kidneys to fail. Combined with the fact she was fourteen, she had the occasional accident. Too many accidents and Jenna would blow a gasket. I'd called earlier to let them know what happened, but they weren't home.\n\n\"Boy, that hit the spot.\" Nana Jo wiped her mouth with a napkin. \"I was so hungry I was getting hangry.\"\n\n\"How can you tell the difference?\" Dorothy leaned over the seat.\n\nNana Jo swiped at her friend. \"Very funny.\"\n\n\"I wonder what happened to the cop.\"\n\nI looked back at her. \"What cop?\"\n\nRuby Mae Stevenson sat next to Dorothy in the seat behind Nana Jo and me. She pulled out her knitting from a bag, which she always carried with her, and started knitting what appeared to be a baby hat. She knitted a few more stitches. \"The one that was sitting across from Irma and Max.\"\n\n\"How do you know he was a cop?\" I asked the question but something in my mind knew she was right.\n\nShe looked up over her glasses. \"The mirrored sunglasses, the gun he had in the back of his pants, the policeman-military haircut under the baseball cap.\" She shrugged. \"It all adds up. He's either a cop or he's a former policeman. Plus, there's just something about police.\" She stopped for a moment. After a few seconds, she shook her head and continued knitting. \"They always have an air of authority about them.\" She shrugged again. \"Besides, he and Irma are the only ones allowed to walk around.\"\n\nI thought about what she said and realized I hadn't seen Mr. Big since we were ushered off the bus and told to wait. I should have recognized that, but, seeing him at the mystery bookstore, I suspected something sinister from him. \"I wonder why he was following Max.\"\n\nWe shared what we'd seen at the bookstore, but no one had answers.\n\nNana Jo stretched. \"I'm tired. I think I'll take a nap.\"\n\nShe pulled her coat close and snuggled down in her seat.\n\nDorothy pulled a book out of her purse and Ruby Mae continued knitting.\n\nI sighed. I wasn't in the mood for my book. Suddenly, my reality was much more interesting than my book. I pulled a notebook out of my purse that I had taken to keeping with me all the time. I flipped to a blank page.\n\n\"I'm shattered.\" Lady Penelope flopped onto a chair in an unladylike manner.\n\nLady Elizabeth Marsh looked intently at her niece. \"I hope you haven't overdone it. Boxing Day shopping at Harrods is a lot, especially for someone in your condition should\u2014\"\n\n\"Don't you start too.\" Lady Penelope stared at her aunt, but, after a few seconds, her eyes and voice softened. \"I'm sorry. I know you mean well, but I've had enough babying from Victor.\" She reached across the table and patted her aunt's hand. \"I don't mean to be cross, but I'm fine. Dr. Haygood says I'm as strong as an ox and the baby is doing just fine.\" She patted her stomach. \"Besides, we've got a long way to go.\"\n\n\"How's the morning sickness?\"\n\n\"I'm much better. Mrs. McDuffie suggested tea and soda crackers first thing and amazingly, it's done the trick.\" She smiled. \"Victor brings them religiously every morning and won't let me move until I've eaten them.\"\n\n\"Good.\" Lady Elizabeth relaxed and smiled at her niece. \"I suppose hitting the Boxing Day sales is enough to wear anyone out.\" She sighed. \"I'm fairly shattered myself.\"\n\nA very prim and proper waitress placed a pot of tea on the table in the department store dining room along with a triple-tiered plate stand, which was piled high with scones, sandwiches, and tarts.\n\n\"That looks scrumptious.\" Lady Penelope helped herself to a scone and slathered a generous helping of clotted cream and strawberry preserves over the top. She took a bite.\n\nLady Elizabeth's niece closed her eyes and moaned. When Lady Penelope opened her eyes, her aunt was staring at her and both ladies laughed.\n\n\"I just needed a little nourishment and then I intend to get back into the fray. There are some sheets I want to get for the nursery.\" Lady Penelope washed her scone down with tea and then tackled a cucumber sandwich.\n\nLady Elizabeth sipped her tea and listened as her niece talked about her plans for decorating the nursery and the preparations she and her husband, Victor Carlston, were making for their first child. She smiled as she listened to her niece's enthusiastic plans. Lady Elizabeth shared her excitement at finding the perfect fabric for curtains for the bedroom at Wickfield Lodge, which was being shared by Josiah and Johan, the two Jewish boys the Marshes were keeping from the Kindertransport. Lady Elizabeth feared the nursery where the young boys stayed, along with their younger sister, Rivka, was too frilly for two rambunctious boys. Not having any children of their own, Lady Elizabeth and Lord William Marsh had only experienced girls, having raised their nieces, Lady Daphne and Lady Penelope, after their parents were killed in an automobile accident. Lady Elizabeth knew the children wouldn't be staying with them long, but she was determined to make what time the children did stay as pleasant as possible. It was clear these Polish refugees had witnessed not only the death of their parents but had seen atrocities that could scar them for life. Lady Elizabeth knew curtains, a few toys, and warm clothes couldn't wipe away the horror, but she hoped she could help to create an environment of safety and love where they would now see there were people who cared.\n\n\"Penny for your thoughts,\" Lady Penelope joked.\n\n\"I'm sorry, dear. I was woolgathering.\" Lady Elizabeth smiled. She reached into one of her bags and pulled out a lovely Chinese silk pillowcase. \"I found these wonderful silk pillowcases for the boys' rooms. I have no idea what these markings mean, but the color was perfect. What do you think?\"\n\nLady Penelope admired the pillowcases and nodded her agreement about the color.\n\nLady Elizabeth glanced up and noticed an elderly woman staring at her. When the woman made eye contact, she smiled broadly and hurried to the table.\n\n\"Hello, I thought that was you. It's been such a long time.\" She glanced around nervously.\n\n\"Hello,\" Lady Elizabeth said hesitantly. She put the pillowcases back into the bag.\n\n\"I saw your lovely Chinese pillowcases.\" She reached out a hand. \"May I?\"\n\nLady Elizabeth passed the woman the pillowcases.\n\nShe examined them and smiled. \"Beautiful embroidery.\" She glanced at Lady Elizabeth. \"Do you know what it says?\"\n\nLady Elizabeth shook her head.\n\n\"It's the English equivalent to Sweet Dreams.\" She smiled. \"My husband and I lived in China for many years. It's not easy learning the language, but I was determined to master it and I found an excellent teacher.\" She sighed and reluctantly passed the items back.\n\n\"That's wonderful. Thank you. They were the perfect color and I got an excellent price, so I bought them, but then I wondered if I should have. I had just asked my niece about the markings.\"\n\nThe woman looked as though she was remembering something extremely pleasant. \"I loved China. My husband and I were missionaries.\" She sighed. \"I love puzzles and China and all things Chinese, especially my Chinese puzzle boxes.\" She looked at Lady Elizabeth. \"You don't remember me, but then why should you. It's been such a long time since we've seen each other. It's me, Eleanor . . . Eleanor Forsythe.\" She looked around nervously, then turned back to Lady Elizabeth. \"Do you mind if I sit for a moment? I'm a bit tired.\"\n\nLady Elizabeth clearly didn't remember, but good breeding took over. \"Of course. Forgive my manners. Please, won't you join us?\"\n\nThe lady eagerly sat down.\n\nThe waitress had been hovering nearby and hurried over to the table with an extra cup and plate setting for the new arrival. She'd barely finished filling the woman's cup, before the woman whisked it to her mouth and drank as though she was parched.\n\nLady Elizabeth requested more sandwiches and the waitress hurried to fulfill the order.\n\nEleanor Forsythe was a thin woman with wispy white hair, which was a bit wild. Her hat and coat were of a good quality, but they were old and outdated. Her hat was slightly askew and sat at a rakish angle. She hungrily ate the sandwiches and scones that the waitress brought and drank several cups of tea, all the while maintaining a steady stream of conversation. \"How is his lordship?\"\n\n\"He's well. He's been plagued by gout. I think he outdid it at the wedding.\"\n\n\"Wedding? Don't tell me I missed a wedding?\" She turned to Lady Penelope.\n\n\"Not Penelope. No, it was my other niece, Lady Daphne, who married Lord Browning, the Duke of Kingfordshire.\"\n\nEleanor smiled. \"How wonderful. I positively love weddings. I love puzzles and I love weddings. I'm sorry to have missed it.\" She looked around nervously. \"I don't get out much anymore. My cousin Desmond, and his wife, Constance, have moved into my home at Battersley Manor.\" Eleanor leaned forward as she spoke and stared into Lady Elizabeth's eyes and reached out and clutched her hand. \"They are so careful about me getting out . . . afraid I'll catch a cold or take a fall. They do worry so.\"\n\nLady Elizabeth stared back. \"Yes, one can never be too careful.\"\n\nEleanor Forsythe's eyes darted around. \"No, indeed, especially as I've aged. I have gotten so forgetful. Only last week when my nephew was out of town, I slipped on a bar of soap. I would have broken an arm or a leg if my maid, Dora, hadn't come to fill my hot water bottle.\" She gazed at Lady Elizabeth. \"I don't even remember taking a bath, but Constance, that's Desmond's wife, says I did. I'm so forgetful these days.\"\n\n\"Gracious. You are so fortunate to have Dora,\" Lady Penelope said slowly.\n\nEleanor nodded. \"Yes, it was fortunate, indeed. Although, my cousin says the taxes are so bad and my investments aren't doing well. He doesn't know how much longer I will be able to afford to keep her, but Dora is wonderful. She appreciates my treasures. She's the only one who does.\"\n\n\"I see.\" Lady Elizabeth's gaze never wavered from Eleanor. After a moment, she looked around. \"How did you manage to get out today?\"\n\n\"Constance and Desmond went out of town for Christmas. They left the new housekeeper, Mrs. Sanderson, in charge. Actually, Muriel is a distant cousin of my late husband, but I managed to get out.\" She looked around. \"I don't have much time.\"\n\nA large, barrel-shaped woman rushed into the dining room like a blustery wind. She looked around the room with a frantic gaze.\n\n\"Is Mrs. Sanderson a large woman with a rather equine-shaped face and a no-nonsense way about her?\" Lady Penelope cast a sidewise glance toward the front of the dining room.\n\nMrs. Forsythe nodded.\n\n\"I think she may be looking for you.\" Lady Penelope inclined her head toward the front of the dining room.\n\nMrs. Forsythe glanced over her shoulder and her eyes took on a frightened expression, like a deer caught in the headlamps of a car. She turned toward Lady Elizabeth and clasped her hand tighter. \"I don't have much time. Please, they're trying to kill me and take my treasures. Please, I\u2014\"\n\n\"There you are. I've been looking all over for you. I just called your cousin Desmond. I was so frightened.\" Mrs. Sanderson rushed to the table.\n\nShe looked quickly at Lady Elizabeth, and something in her manner changed. Lady Elizabeth was accustomed to the change. She'd experienced it many times before. In the woman's voice and in her bearing, something changed. She'd assessed Lady Elizabeth Marsh and knew she was a well-bred woman of status. Whether due to the cut of her simple, but well-made clothing, her expensive coat with its luxurious fur collar, or perhaps due to the intelligent expression on her face, Lady Elizabeth Marsh was a woman of prominence and Mrs. Sanderson's attitude and mannerisms adjusted accordingly.\n\n\"I'm so sorry if she's been bothering you. I'm afraid the poor dear is easily confused.\" She smiled.\n\n\"Not in the least. Eleanor and I are old friends.\" Lady Elizabeth smiled and patted the older woman's hand. \"We were just enjoying a chat.\"\n\nThe waitress returned. \"Would your ladyship care for anything else?\"\n\n\"Your ladyship?\" Mrs. Sanderson muttered.\n\nLady Elizabeth turned to the gaping woman. \"Would you care to join us for tea?\"\n\nMrs. Sanderson's face grew red and she shook her head. \"No . . . no thank you.\"\n\nLady Elizabeth turned to the waitress and indicated she was done and would like her bill.\n\nThe young girl bobbed a curtsey and then hurried away.\n\n\"Excuse me, but . . . your ladyship?\" Mrs. Sanderson said.\n\nLady Elizabeth smiled. \"I'm sorry. I didn't introduce myself. I'm Lady Elizabeth Marsh and this is my niece, Lady Penelope Carlston.\"\n\nThe housekeeper's already red face grew redder. \"Your ladyship.\" She made a slight curtsy. She nervously glanced from her charge to Lady Elizabeth. \"Did you say, you and Mrs. Forsythe are friends?\"\n\nLady Elizabeth waved her hand. \"Yes. Eleanor and I go way back. It's shameful how people lose touch these days, but I intend to rectify that.\" She turned to Mrs. Forsythe. \"I was just saying, we'll have to come by Battersley Manor soon, and, of course, Eleanor has an open invitation to visit us at Wickfield Lodge. I know Lord William will love to see you.\"\n\nMrs. Sanderson's face registered surprise, but she quickly tried to hide it. \"Well, of course, your ladyship is welcome any time, but Mrs. Forsythe isn't well and can't get out like she used to.\" She collected the woman's purse and helped her up from her chair. \"In fact, I'm afraid this excursion may have been too much. She's looking rather flushed.\" She glanced from Mrs. Forsythe to Lady Elizabeth. \"I'd better get the old dear home before . . . well, before she gets worse. Plus, I need to call Mrs. Tarkington and let her know you're safe. She was so concerned about you. She was actually going to come and help me look for you.\"\n\nMrs. Forsythe, who moments earlier was alert and talkative, was suddenly quiet and withdrawn.\n\nThe housekeeper hustled the older woman away, leaving Lady Elizabeth and Lady Penelope staring at their hasty retreat.\n\n\"Now, that was odd,\" Lady Penelope said. \"Do you believe her? Do you really believe her family is trying to kill her?\"\n\nLady Elizabeth stared after the retreating ladies. \"I don't know. There's definitely something suspicious going on, and it's clear Eleanor believes it.\"\n\n\"What are you going to do?\"\n\nLady Elizabeth was silent for a moment. \"There's not much I can do about it today.\" She smiled at her niece. \"Now, that I've regained my energy, I'm going to fight my way through the crowd and get the rest of the things on my list. I'll tackle the problem of Eleanor Forsythe tomorrow.\"\n\nLady Elizabeth achieved success and acquired everything on her list. Laden down with packages, she and Lady Penelope hurried to the Knightsbridge station to catch the train which would take them home. The ladies were jostled along by the crowds who'd packed the station. The station bustled with activity as people anxiously awaited the approaching train.\n\nJust as the ladies left the ticket hall with their first-class tickets and hurried to catch their train, they heard the rumble of the train as it pulled into the station. The ground vibrated and the engines roared.\n\nThey queued up to get on the escalator to descend to the platform. The impatient crowds pushed, shoved, and jostled their way onto the metal stairs of the escalators and were carried underground.\n\nLady Elizabeth felt a tug on her sleeve and turned as a woman screamed and then fell headlong down the metal stairs onto the concrete platform below.\n\nLady Elizabeth gasped but then quickly collected herself and hurried down to the platform.\n\nSprawled on the ground lay the body of Eleanor Forsythe. Her eyes glanced up at Lady Elizabeth, who quickly knelt down and attempted to assess the lady's injuries. \"Someone get a doctor,\" Lady Elizabeth ordered. However, it was obvious from the unnatural angle in which she lay, that her injuries were severe. She felt a tug on her arm.\n\nMrs. Forsythe's lips moved, but she was unable to speak loudly. Lady Elizabeth bent close to the woman's face and Mrs. Forsythe whispered into her ear.\n\nAfter a few moments, Mrs. Forsythe's lips stopped and she lay very still.\n\nMrs. Sanderson suddenly appeared and stared at Lady Elizabeth. \"Gracious me. The poor woman must have lost her footing. What did she say?\"\n\nLady Elizabeth stood. \" 'Murder.' She said, 'I was murdered.' \"\n\nChapter 3\n\n\"Sam, pay attention.\" Nana Jo followed up the request with a sharp jab to my side.\n\nI looked up from my writing. \"What?\"\n\nShe pointed toward the front of the bus, where a large man with a potbelly that overflowed the top of his pants and a head full of thick, curly hair stood.\n\n\"Ladies and gentlemen, my name is Sergeant Dominic Davis. I'm sorry for the long wait, but we'll get to all of you as quickly as possible.\"\n\n\"Too late,\" Nana Jo yelled.\n\n\"Shhush.\" This time it was my turn to nudge her, but my elbows weren't as pointy and she simply ignored me.\n\n\"We've been on this bus for hours. We're cold and ready to go home,\" Nana Jo said.\n\nThere were a lot of shouts of agreement from everyone on the bus.\n\nSergeant Davis held up his hands to quiet the rowdy crowd. \"I'm sure you're all very anxious to get home. However, we need to get statements from everyone. As soon as we finish, you'll be on your way.\" He stared at Nana Jo. \"Why don't we start with you?\"\n\nNana Jo climbed over me to get out of her seat. \"Gladly. I'll do anything to get this over with. I need a shower, a stiff drink, and the comfort of my own bed, and not necessarily in that order.\"\n\nThe process for taking statements was slow and methodical. There were four policemen assigned to take statements, of which Sergeant Davis was one. It took two hours to get all the statements. I felt like a youngster compared to some of the other people on the bus, and I was exhausted. Even though most of the residents of Shady Acres Retirement Village were more active than me and enjoyed activities like surfing, martial arts, and their newest obsession, Hip Hop Dancing, I felt guilty about going in front of people who were my elders, at least in years, so I waited until most of the others had gone before I left to give my statement.\n\nWhen it was my turn, I was directed by a rather good-looking policeman to a makeshift office area with a folding chair in the utility closet of the rest area. Sergeant Luis Alvarez was young, probably late twenties, with a clean-cut face, olive complexion, and dark hair, which was shorter on the sides and curly on top. He had blue eyes the color of Lake Michigan in the summer and the whitest teeth I'd ever seen. When he smiled, I was dazzled and found myself staring at him and giggling like a teenager.\n\n\"May I see your driver's license?\"\n\nI stared for a few seconds. He had a very nice accent, which took several seconds for my brain to decipher. I watched his lips moving but wasn't exactly focused on the words coming out of his mouth. When I finally realized he was waiting for a response, heat rushed up my neck and I fumbled in my purse for my wallet. \"Sorry.\"\n\nHe smiled again and I giggled. I needed to pull myself together. This was embarrassing. I took a bottle of water from my purse and concentrated way too much effort into opening the top.\n\n\"Mrs. Washington, did you know the deceased?\" He had a deep voice that was soft and smooth and very sexy. \"Mrs. Washington?\"\n\nUnfortunately, I squeezed the bottle too tightly and when the top came off, water overflowed all over my lap. \"I'm sorry.\"\n\nHe handed me a few napkins he found nearby.\n\n\"What was the question?\"\n\n\"I asked if you knew the victim?\"\n\nI took a deep breath and tried to focus on the dead body and ignore the water seeping down my pants or Sergeant Alvarez's super white teeth, smooth voice, or . . . darn it. This wasn't working. I dug my fingernails into my palm and looked straight at Sergeant Handsome. \"I met him for the first time about two nights ago at the Chicago House of Blues. He was . . . interested in my grandmother's friend, Irma Starczewski.\"\n\n\"You'd never seen him before?\" He asked the question as though he found the fact hard to believe.\n\nI shook my head. \"Noooo. I'm pretty sure I haven't.\"\n\nHe looked at his notes. \"Your grandmother, Josephine Thomas, says you own a mystery bookshop in . . . North Harbor, Michigan.\"\n\nI eased up on the nails in my palm. \"I do. I used to be an English teacher but after my husband, Leon, died, I retired and opened Market Street Mysteries.\" I was rambling, but I didn't know what owning a mystery bookshop had to do with Irma's dead boyfriend.\n\n\"You read a lot of mysteries?\"\n\n\"I used to, although I don't have as much time to read now.\"\n\nHe leaned back and tapped his pen on his thigh. I tried not to look, but I knew my gaze kept going to his thighs. He had very nice thighs.\n\n\"Umm, excuse me. Did you say something?\" I went back to the nails in my palm. Darn. This was a lot harder than talking to Detective Stinky Pitt in North Harbor.\n\n\"I asked about the type of books you read.\"\n\n\"I read a lot of cozy mysteries mostly.\"\n\nHe scowled. \"What's a cozy mystery?\"\n\nNow I was on comfortable footing. I could talk about cozy mysteries for hours. \"Cozy mysteries are mysteries with an amateur sleuth, usually female. There's no sex, violence, or bad language in cozies. Have you ever seen Murder, She Wrote?\"\n\nHe nodded.\n\n\"That's a cozy mystery. The point is to find the clues and figure out whodunit.\"\n\nHe nodded and something in his eyes told me he knew exactly what a cozy mystery was. The thought crossed my mind that I needed to be on my guard, but I had no idea why. So, I sat quietly and waited.\n\n\"Do you read any other types of mysteries?\"\n\n\"Sometimes, but I don't like books with lots of violence, so I usually stick to cozies.\"\n\n\"Are cozy mysteries the only types of books you sell in your store?\"\n\n\"Of course not. Just because I read cozies doesn't mean everyone does. I sell all types of mysteries.\"\n\nHe extended a hand to indicate I should elaborate.\n\n\"I sell cozies, police procedurals, soft- and hard-boiled private detective books, true crime . . . pretty much anything mystery or crime related.\"\n\nApparently, I'd said what he wanted to hear.\n\nSergeant Sparkling Teeth smiled and leaned forward. \"So, you sell true crime books.\"\n\nConsidering I'd just said that, I became instantly suspicious. My left eyebrow lifted on its own. \"Why is it important what types of mysteries I sell in my mystery bookshop? I sell pretty much all types of mysteries and true crime books.\"\n\nHe tapped his pen on his thigh, but I was no longer focused on his thighs . . . well, not much anyway. \"Would you consider yourself an expert?\"\n\n\"On what? Mysteries?\"\n\n\"Your grandmother said you not only read mysteries and sell mysteries, but you write them too.\"\n\nMy grandmother had a big mouth. \"I write cozy mysteries, but I'm not published yet.\"\n\n\"You must do a lot of research for your books.\"\n\n\"That's true. I write cozy mysteries that are set in England in 1938. I do a lot of research, especially on the time period. You have to make sure the details are as accurate as possible.\"\n\n\"What type of research do you do? I mean do you look up weapons?\"\n\n\"I research weapons, but not a lot. Cozy mysteries don't have a lot of violence, so I don't spend much time on weapons.\"\n\nHe chuckled. \"You write murder mysteries. Unless you're an expert on weapons, wouldn't you have to research different types of weapons and wounds?\"\n\n\"In cozies, typically the murder isn't graphic. These books aren't really about the act of murder. Like I said before, it's about the clues and figuring out whodunit.\"\n\nHe looked puzzled.\n\n\"It's like story problems when you were in school. It's a story. The author is writing a story and hopefully, the reader is enjoying the story. The author drops clues in the story. Does the fact that the butler had mud on his shoes mean something? Or is it a red herring, a false clue. The author's job is to weave the clues into the story and hope the reader figures out whodunit at the same time as the detective. That's the best case.\" I shook my head. \"The actual weapon used to murder the victim isn't really that important, unless it's some specialized weapon that only one or two people knew how to use.\" I paused and thought. \"Like a bow and arrow or some rare poison only found in the rain forests of South America.\"\n\nHe nodded and tapped his pen. However, now the pen tapping didn't interest me in the least. \"I just wonder how you read true crime books and you sell true crime books, and yet you say you didn't know Max Franck.\"\n\n\"Who is Max Franck? Was he an author?\"\n\nSergeant Alvarez spread his hands wide.\n\n\"What did he write?\"\n\nHe grinned. \"You've never heard of him?\"\n\n\"Sergeant, mystery is one of the most popular genres of fiction, surpassed only by romance. There are millions of mystery and suspense novels published every year. I'm guessing by your response that Max Franck must have been some type of writer.\" I was frustrated and Sergeant Alvarez's appeal had diminished considerably.\n\n\"Are you saying you've never heard of him?\"\n\n\"I'm saying, I've heard of and read a lot of books. If I have read anything he wrote, I don't remember it at this moment.\"\n\nHe stared.\n\nHowever, my days as a high school English teacher had taught me the value of silence and given me the patience of Job. I waited patiently and quietly, volunteering nothing. We sat in silence for nearly a minute.\n\nIf this was a game of chicken, he blinked first and I could tell by his body language, he wasn't happy about it. \"Max Franck was a writer, like yourself. He wrote true crime.\"\n\n\"Then he was not like me. I don't write true crime.\"\n\nHe waved away the differences. \"He was a Pulitzer Prizewinning journalist.\"\n\nDespite my resolve to remain disinterested, I was very interested in the fact that Irma had picked up such a distinguished date. \"What did he win the Pulitzer Prize for?\"\n\n\"You really have no idea?\"\n\nI shook my head. \"I really have no idea.\"\n\nHe sighed and looked at his notes. \"He earned the Pulitzer Prize for an expos\u00e9 on government corruption, but he was best known for his work on the Kennedy assassination.\"\n\nThat was when the lightbulb went off. I sat up straighter in my seat. \"I remember him now. He's supposed to be writing another book.\" I snapped my fingers, trying to remember. \"There was something in the paper recently, wasn't there?\"\n\nHe nodded. \"Yeah. He was writing another book.\"\n\n\"That's it. He wrote books about JFK's assassination and was about to publish a new book about the assassination of Robert Kennedy. That's Max Franck? That's the man who picked up Irma at the House of Blues?\"\n\nHe nodded. \"And you didn't know any of this?\"\n\n\"Well, obviously I knew it. It must have been buried in my head, but I didn't remember until you brought it up. He certainly didn't talk about it . . . Well, he didn't really talk to me much, anyway.\"\n\n\"He never mentioned his books?\"\n\nI shook my head. \"He barely said anything to me. He spent his time drinking, dancing, and, as my grandmother would say, 'feeling up' Irma.\"\n\nHe chuckled. \"Yeah, I think those were your grandmother's exact words.\"\n\nI nodded. \"Wow. So, Max Franck was a writer.\" I sighed. \"I wish I'd known that. I would have liked to have talked to him about it. His life must have been fascinating.\"\n\nSomething about Sergeant Alvarez's demeanor shifted. His shoulders relaxed and his face muscles were much smoother. He was back to being the charming policeman I'd first thought him. \"Tell me all you know about Max Franck, even if it seems irrelevant.\"\n\nI took a moment to collect my thoughts and told him everything I knew, which really wasn't much. \"He and Irma met at the House of Blues. They flirted and danced and drank and flirted and well, when they were done flirting, they flirted more.\" I told him how he and Irma planned a romantic tryst at Shady Acres and how he ended up on the bus.\n\nHe scribbled in his notebook. When I stopped, he looked up. \"Is that all?\"\n\n\"Well, I don't think it means anything, but we saw him earlier today.\" I described what we saw at Murder Between the Pages.\n\nHe asked quite a few questions about the lady we saw arguing with Max Franck, but, unfortunately, I couldn't provide a lot of information. I described her, but the angle of the loft meant that I couldn't see her face. Surprisingly, he didn't seem nearly as excited about Mr. Big with the mirrored sunglasses and the gun in his waistband as I would have expected. In fact, he didn't seem to be taking notes.\n\n\"Aren't you going to write this down?\"\n\nHe shook his head. \"We've already cleared Mr. Sherman.\"\n\n\"Sherman? Is that his name?\"\n\nHe nodded. \"Sidney Sherman isn't a person of interest in this investigation.\"\n\n\"I don't know why not? He was obviously following Max Franck. Plus, he had a gun.\"\n\nSergeant Alvarez sighed. \"If you don't have any other useful information, I think we're done. I have your address and telephone number. If we have any more questions, we'll get in touch.\" He handed me his business card.\n\nHe stood and ushered me out of the utility closet. Outside, I glanced around the corner and noticed Mr. Big, aka Sidney Sherman, standing around with some of the other policemen, drinking coffee. They looked pretty chummy.\n\nI was one of the last people interviewed, so when I got on the bus, I heard Nana Jo say, \"Thank God. I thought they'd never finish. Maybe we can leave now.\"\n\nSergeant Davis had accompanied me onto the bus. \"Ladies and gentlemen, we appreciate your cooperation. We have all your contact information. If you think of anything else, please feel free to call us.\"\n\nIrma was the last person to board. Irma was the oldest of Nana Jo's friends. She was also the vainest. She dressed and acted years younger and took pride in still being able to attract men of all ages. However, the woman who climbed aboard the bus looked and acted decades older. She looked tired and, while she was already a petite woman, she seemed to have shrunk in the past few hours.\n\nIrma walked toward the same seat she'd had previously. Even though this was a different bus, she stopped just short of her seat, and the color left her face.\n\nI stood up and moved into the aisle, using my body to block the seat that mirrored the one Max had died in earlier.\n\n\"Irma, come over here.\" Nana Jo stood and placed an arm around her shoulders.\n\nIrma allowed herself to be led into the seat I'd just abandoned next to Nana Jo, and I took the seat across the aisle.\n\nI settled into my seat, but I zoned out on the last bits of Sergeant Davis's spiel. Mr. Big had followed me onto the bus. He sat in his seat, mirrored glasses and aloof attitude both securely in place. The glance I had of him with the other policemen told me he wasn't one of us. The question I wanted answered was, who was he?\nChapter 4\n\nThe remainder of the ride home was, thankfully, uneventful. Less than one hour after we pulled out of the rest area, the driver pulled up through the gates of Shady Acres Retirement Village.\n\nThe passengers left the bus quickly, stretching and complaining.\n\nNana Jo stood her nearly six-foot frame and stretched. \"Now I know what Gilligan must have felt like.\"\n\nI grabbed my book and other belongings. \"What do you mean? You feel like a castaway?\"\n\n\"No. What was supposed to have been a three-hour tour turned into three years on that blasted island. The drive from Chicago should have taken two hours. It's been twelve since we left.\"\n\nRuby Mae followed. \"I'm going to bed. What time are we meeting?\"\n\nI stared at her. \"Meeting for what?\"\n\nNana Jo, Dorothy, and Ruby Mae all stared at me as if I'd suddenly lost my mind.\n\n\"What time are we meeting to figure out who killed Max?\" Irma said softly. \"You have to figure out who killed Max.\" She swallowed hard. \"We owe him that much.\"\n\n\"The police are going to find his killer. That Sergeant Alvarez is a lot smarter than Detective Pitt. I'm sure he'll be able to catch Max's killer without our intervention. Besides, do we even know he was killed?\" I looked at their faces. \"Maybe it was natural causes?\"\n\nNana Jo scoffed. \"You've got to be joking. Of course he was murdered.\"\n\n\"Maybe he was. Regardless, it doesn't have anything to do with us.\"\n\nIrma's eyes filled with tears. \"Please, Sam. You don't understand.\"\n\nI stared from her to Nana Jo and the others, looking for help. However, their faces clearly said they were aligned with Irma on this one.\n\n\"Nana Jo?\" I looked at my grandmother.\n\nShe looked at me. \"I'm sorry, Sam. I know you don't like getting involved, but we need you, this time more than ever.\"\n\n\"I don't understand. Why is this time more important?\" I was tired and my voice sounded more whiney than ever. \"I don't think any of those detectives believe you killed Max,\" I pleaded with Irma. \"There's no need for us to get involved this time.\"\n\nRuby Mae supplied the answer. \"Because this time, it's one of us.\"\n\n\"What?\" I stared at her.\n\nNana Jo shook me by the shoulders. \"Sam, I know you're tired, but you have to see this. Max Franck was alive when he boarded that bus. Someone on that bus killed him.\"\n\nRuby Mae nodded. \"It had to be one of us.\"\n\n\"There's a murderer at Shady Acres, and we need to find out who it is,\" Dorothy said.\n\n\"This time the murder is too close for comfort. We need you to help us catch a murderer, Sam.\"\nChapter 5\n\nIt was the early hours of the morning and I was exhausted. I wanted nothing more than to sleep through the remaining three days and into the new year. My loft over my bookshop would be quiet, especially without my dogs, Snickers and Oreo, to help welcome me home. Nana Jo stayed in my guest bedroom most weekdays, but then went to her villa at Shady Acres on the weekends and spent time with her boyfriend. She offered to come back with me, but I knew she was concerned about Irma, so I declined.\n\nWhen my husband, Leon, died, I sold the home we shared and took the proceeds and the insurance money and followed our dream and opened a mystery bookshop. That was over a year ago, and I had no regrets. The building we'd walked by for years and dreamed about \"one day,\" \"when our ship comes in,\" was now the home of Market Street Mysteries and the upstairs was my new home.\n\nI pulled into my garage and noticed the apartment above my garage was dark and uninviting. Not only were my grandmother and my poodles gone, but my tenant, Dawson Alexander, was gone too. Dawson left earlier today with the Michigan Southwest University Tigers, MISU to the locals, football team. MISU had gone undefeated this season and were going to be playing in their first bowl game in over a decade. Dawson was the quarterback as well as my part-time assistant and master baker.\n\nAs I climbed the stairs to my loft, the dark, empty space weighed on me more than ever before. Normally, I relished being alone and wasn't one of those people who needed to be surrounded by people to feel comfortable. However, tonight was different. Tonight, I felt not only alone, but lonely.\n\nThe hours on the bus left me exhausted. It took everything in me to drag my body up the flight of stairs to my loft. I didn't have the energy to drag my suitcase too, so I left it at the bottom of the stairs. I'd get one of my nephews or Frank to help me haul it up the stairs later. Frank Patterson was my not-quite-a-boyfriend-but-more-than-a-friend and I smiled at the thought of him. He was a good man, and I was fortunate to have him in my life. I marveled at the fact I was feeling more comfortable with him. Initially, I'd felt like I was cheating on my husband, even though he was dead. However, I knew in my heart Leon wouldn't want me to be alone and that helped.\n\nUpstairs, I showered and prepared for bed. However, the events of the past few hours had my mind racing in a hundred different directions. My body was fatigued, but my mind refused to shut down. I tossed and turned but couldn't stop thinking about Max Franck. After an hour of restlessness, I gave up and flipped on the lights. Maybe the physical action of flipping on the lamp in my bedroom flipped on the lightbulb in my head. I tossed the covers off, grabbed my robe and slippers, and hurried downstairs.\n\n\"You're right, Sergeant Alvarez. I own a freakin' mystery bookshop.\"\n\nOnce downstairs, I disengaged the alarm system and hurried to fire up my point-of-sale system. It didn't take long to find Max Franck. As luck would have it, I owned one of his books and went in search of it. When I opened the bookstore, I debated how to shelve the books. Should I shelve them by genre and subgenre or by author? In the early hours of the morning, I was extremely thankful I had shelved the books alphabetical by author. The only exceptions were a cozy section that showcased my personal favorites and a newly added children's section.\n\nI hurried to the Fs and grabbed Max Franck's book, The Kennedy Conspiracy. According to the medallion on the cover, the book was a New York Times Best Seller, an Edgar Award winner, and a Booker Prize finalist. Normally, a true crime book with the word \"conspiracy\" in the title, wasn't anything that would grab my attention. However, award-winning books sold well.\n\nI grabbed my book, reset the alarm, and hurried back upstairs. I debated whether I should have coffee while I read. The last thing I wanted in the wee hours of the morning was anything that would keep me awake, but there was something about drinking a warm beverage when I read that always made me feel warm and cozy. I was more than a little curious about Max Franck, but the last thing I wanted was to be awake all night. I compromised. Instead of coffee, I made a cup of Earl Grey, grabbed a blanket, and curled up on my sofa. Best-case scenario, I would learn who wanted to kill Max without leaving my living room. Worst-case scenario, The Kennedy Conspiracy would put me to sleep. Either way, I won.\n\nSeveral hours later I heard the alarm being disengaged. I looked at the time on my cell phone. I had been reading all night or rather, all morning. As was often the case, neither the best-case, nor the worst-case scenario had occurred. Reality had been somewhere in the middle. I hadn't fallen asleep reading nor did I know who killed Max Franck. However, I had spent the night reading a well-written, thoughtful, and extremely well-researched book about the murder of President John F. Kennedy.\n\nI heard the eager clicking of nails on hardwood floors, which let me know Snickers and Oreo were on their way. Knowing they would smell my presence before they saw me, I braced myself.\n\nAt twelve, Oreo was the younger of my two chocolate toy poodles. Despite his age, he was more like a rambunctious toddler than the old dog the charts at my vet's office stated he was. He flew at me like a torpedo, tail wagging and body in constant motion. Snickers, on the other hand, was a distinguished female of advanced years. Nevertheless, she too leapt onto my lap. Oreo's constant movement and eagerness always made me laugh. He had such a zest for life. However, laughing was a mistake I should have been prepared for. Snickers stood on my lap on her hind legs and the moment my mouth opened, she licked.\n\n\"Blaagh. Ack!\" I turned my head and used the blanket to wipe my mouth.\n\n\"Hey, Aunt Sammy. Welcome back.\"\n\nMy nephew Zaq followed the dogs upstairs. He was a twin and I heard footsteps that indicated his brother, Christopher, was on his way. \"Hey.\"\n\nChristopher followed and placed my suitcase in the living room. \"Welcome home.\"\n\n\"Thank you.\"\n\nMy nephews were juniors at Jesus and Mary University (JAMU) and were much more literate than their dialogue demonstrated.\n\n\"Good morning. Thank you both for taking care of the store and please thank your dad for taking care of Snickers and Oreo.\"\n\nSnickers was lying on her back, using her paw to guide my hand while I scratched her tummy with one hand. My other hand was occupied scratching the spot behind Oreo's ear, which made his eyes roll back in his head and always caused his leg to twitch.\n\nThe twins laughed. They were both tall and thin, just like their dad. Even though they were identical twins, their personalities made it very easy to tell them apart.\n\n\"Hey, you're paying us.\" Christopher shrugged. He was the more serious of the two. He liked to dress in what would have been described as \"preppy\" in my day but which he called \"snappy casual.\" Christopher was a marketing major and was great at helping with my displays and promotional campaigns.\n\nZaq punched his brother in the arm. \"He's joking. We'd help even if you weren't paying us.\" Zaq was the technology geek. He loved computers and was a whiz at managing my point-of-sale system and had created an amazing website for the bookstore and was just about done with one for my author platform as well.\n\nThey grinned. I knew their playful banter well after more than twenty years.\n\n\"Dad said someone died.\" Zaq sat on the sofa and Oreo moved from my lap to his.\n\nI told them what I knew, which really wasn't much. \"You going to solve another murder, Aunt Sammy?\" Christopher asked.\n\n\"Of course she is.\"\n\nI was so engrossed in recounting the story to my nephews, I hadn't heard Nana Jo come in.\n\nThe boys got up and gave their great-grandmother a kiss.\n\n\"Now, it's almost time to open up. You two better get downstairs.\" She went to the kitchen and made a cup of coffee in my single-cup coffee maker. \"You planning to lounge around all day or are you planning to do any sleuthing?\"\n\nI wanted to go to sleep, but that ship had sailed. Instead, I took a long, hot shower and got dressed. I got a whiff of two of my favorite things, bacon and coffee, and followed my nose into the kitchen.\n\n\"I knew that would get your attention.\" Nana Jo slid a cup of coffee to me and then handed me the bottle of sweet creamer from the refrigerator.\n\nI climbed onto a barstool and Nana Jo handed me a plate with bacon, eggs, and toast.\n\nNana Jo allowed me to eat and drink my coffee in peace until the moment the last bite of toast and eggs hit my lips. \"I told the girls to meet us at Frank's place for lunch.\"\n\nI didn't respond.\n\n\"Sam, I know you don't want to get involved solving a murder, but we need you. You've got a knack for this stuff.\" She paused. \"I'm not a young woman, and most of the time I'm doing good to remember where I left my keys.\"\n\n\"Don't give me that old, pathetic, woe-is-me song and dance. There's nothing wrong with your little gray cells. You're physically fit and mentally sharp as a knife.\"\n\nShe chuckled. \"True, but everyone has their strengths. I excel as the sidekick. I'm great at coordinating the team, doing the legwork, and acting as a sounding board for you to bounce ideas off. Plus, I'm your muscle.\" She stretched, tilted her head from side to side, and cracked her knuckles like a prize fighter getting prepared to go into the ring.\n\nI laughed and nearly spit out my coffee.\n\nShe smiled. \"Seriously, I'm not the master sleuth. Putting all of the clues together and figuring out how everything fits together, that's what you're good at.\"\n\nI sighed. \"I didn't say I wouldn't help. I was just hoping to relax a bit. We just got through the entire nightmare with Mom's wedding and Lydia Lighthouse.\" I sighed again.\n\n\"Two sighs in less than a minute means there's more going on here. What's wrong?\" She leaned against the counter and waited.\n\nI sat for a few moments and tried to gather my thoughts. \"I miss Lexi and Angelo.\"\n\nNana Jo reached across and drew me into a hug. I placed my head on my grandmother's shoulder and cried.\n\n\"I know you thought the bus trip would help me get my mind off the fact they were leaving, and I know I only had them here for a short time, but . . .\"\n\n\"It's okay to miss them. I miss them too.\"\n\nI looked up. \"You do?\"\n\n\"Of course I do. The twins are grown men now, and it's been a long time since there have been any children around.\"\n\nLexi and Angelo were two orphans Frank found asleep in the back of his restaurant a few weeks ago. They had run away from their foster family in Chicago and made their way to North Harbor. The bruises on their bodies told a tale that I shuddered to think about. However, Lexi and Angelo had family in Italy who had been looking for them. When Frank Patterson found their family, they rushed to the United States for a reunion.\n\n\"It's only been a few days and they need time with their family.\"\n\nI sniffed. \"I know.\"\n\n\"Besides, their grandparents promised to bring them back to say goodbye before they left the country.\"\n\n\"I know.\"\n\nShe held me at arm's length and looked into my eyes. \"Then, what's the real problem?\"\n\nI shook my head. \"I don't know. I just feel in a bit of a funk. Maybe it's the holidays or maybe it's another senseless murder.\" I took several deep breaths. \"I mean, what is wrong with people? Why do people think it's okay to kill each other?\" I shrugged. \"I feel like, what's the point. There's no value for human life anymore.\"\n\nNana Jo looked at me. \"That's why we need you.\"\n\nI looked up at her. \"What do you mean?\"\n\n\"Someone has to care. Look, someone killed that poor man. Too many people don't want to get involved. They go about their lives and try to stay out of trouble. They work and go home. The reason people abuse children, rape, steal, and kill is because they think they'll get away with it. There used to be a time when people looked out for each other.\" She shook her head. \"Now, it's mind your own business or I'm not my brother's keeper. Your fellow man is your business. It's all of our business and, unless more people get involved and become their 'brother's keeper,' nothing changes.\" She paused, taking several deep breaths. \"I'm sorry, honey. I don't mean to preach. It just burns my butt to think about Irma crying her eyes out and this . . . Max Franck getting killed on that bus.\" She shivered. \"The same bus we were on.\"\n\nI stared at her. \"You think the murder was random? That the killer meant to kill someone else?\"\n\nShe paced. \"I don't know what I mean.\" She stopped, turned, and looked at me. \"No, I don't think it was random or that the killer meant to kill someone else.\" She shook her head. \"The killer took a big chance. I find it hard to believe anyone would take that kind of risk unless they were very angry or . . .\"\n\n\"Or very desperate.\"\n\nShe nodded. \"Look, if you really don't want to get involved, then I'll understand. You've got a lot on your plate with the bookstore and your book, and you're entitled to a little romance.\" Nana Jo forced a smile that didn't reach her eyes. \"I'll call the girls and let them know we're leaving this one up to the police. That Sergeant Alvarez was a hottie, but I think he has brains too, at least a lot more than Stinky Pitt. Maybe he'll nab the killer before the new year.\" She reached into her bag and pulled out her cell phone.\n\n\"Wait.\"\n\nShe looked up.\n\nI took a deep breath. \"You're right. More people do need to get involved.\" I sighed. \"I'll help.\"\n\n\"Are you sure?\" She stared into my eyes.\n\n\"Yes. I'm sure.\" I nodded.\n\nShe smacked her hand on the breakfast bar. \"Hot diggity!\"\n\n* * *\n\nShowered, dressed, fed, and caffeinated, I still couldn't sleep. I finished Max Franck's book and spent a little time on Google, trying to find out as much as I could about him. The Internet was an amazing source of information, even though everything on the Internet wasn't true. Nevertheless, there were links to books and articles at the library and other sources I knew were trustworthy. I marveled at all the information available online. No wonder people were paranoid about \"Big Brother.\" It wasn't long after I started surfing for information about Max Franck that I started getting items in my news feed about the Kennedys and conspiracy theories. Following the threads led me from one rabbit hole to another, with tons of information. I found a lot of fascinating information about some of the lesser-known Kennedys. A couple of hours later, I emerged from the last rabbit hole I'd tumbled down. Since sleep remained elusive and I still had time before lunch, I might as well be productive and write.\n\nLady Elizabeth Marsh sat in the first-class compartment of the train that would take her from the lights and the bustling streets of London home to the peace and quiet of Wickfield Lodge in the English countryside. In spite of the darkness, she gazed out of the window as the train raced through the night. Despite the lateness of the hour and the traumatic events she'd witnessed, she sat straight with her back and head held high. The casual observer would never guess the path her thoughts had taken. Like cream rising to the top, breeding and manners always showed through. Only those on the most intimate terms would notice the lines between her normally smooth brow and the firm set of her mouth, usually quick to smile and welcome, but now with a distinct downward curve.\n\n\"Aunt Elizabeth,\" Lady Penelope spoke loudly.\n\nLady Elizabeth shook herself and forced a smile. \"I'm so sorry, dear. I'm afraid I was distracted.\" She turned her gaze toward her niece and waited expectantly.\n\nLady Penelope smiled. \"I shouldn't have roused you, but I suddenly felt in need of conversation.\" She shook herself. \"I don't know. I just felt cold. I can't seem to get that poor woman out of my mind.\"\n\nLady Elizabeth reached across and patted her niece's hand. \"I've been thinking about Mrs. Forsythe too.\"\n\nDespite the fact that they were alone, Lady Penelope looked around as though to make certain they wouldn't be overheard. Then she leaned forward to her aunt, who sat across from her in the compartment, and whispered, \"You don't really believe she was murdered, do you?\" Her eyes searched her aunt's face for the truth. \"You don't honestly believe someone pushed her.\"\n\nLady Elizabeth thought for a moment. \"Actually, I very much believe she was pushed.\"\n\nLady Penelope shivered. \"I suppose it was rather an odd coincidence that not only was Mrs. Sanderson there, but her cousin Desmond, and his wife, Constance, just happened to be in the tube station at the exact time Eleanor tumbled down those stairs.\"\n\n\"That's too many coincidences for me to accept.\"\n\n\"What are you going to do?\" Lady Penelope stared at her aunt.\n\nLady Elizabeth was silent for a long moment. \"I didn't know Eleanor Forsythe. She might just be a balmy old dear.\" She sighed. \"I will admit, for a moment, I was tempted to do nothing. It's none of my business if an old woman I just met falls down an escalator. If there was something sinister going on, then it's up to the police to find the truth.\"\n\n\"I sense a 'but' coming.\" Lady Penelope smiled kindly at her aunt.\n\n\"But, she was a human being. I think our world has far too many people who don't value lives.\" She bowed her head for a moment. \"I keep thinking about Johan, Josiah, and poor little Rivka.\" She swallowed hard. \"Someone needs to care. Bad things are happening to human beings, and it's our duty to do something.\" She paused. \"Besides, I had tea with her.\" She shook herself. \"I think she chose to come to my table because she thought she could trust me, and I'm determined to see that her trust wasn't misplaced.\" She sighed. \"Whatever the situation, she deserved better. I'm going to find out the truth. If she was murdered, then I intend to find the person who murdered her and see that justice is served.\" She looked out the window into the darkness and spoke quietly. \"It's the least I can do.\"\n\n\"Samantha!\" Nana Jo yelled.\n\n\"I'm sorry. I was lost in my writing.\"\n\n\"I could tell that. It's time we leave to meet the girls.\"\n\nI looked at my watch. \"It's noon already?\" My stomach growled. I'd been surfing the Internet and writing for close to four hours. \"Let me grab my coat and I'll meet you downstairs.\"\n\nThe poodles had curled up together in the dog bed I kept under my desk. Nana Jo's entrance had roused them from their slumbers. They stretched several times as though they had been the ones who were awake for more than twenty-four hours instead of me.\n\n\"Come on.\" Nana Jo patted her leg. \"Let's go get a treat.\"\n\nNana Jo knew the magic word that was capable of rousing the poodles from a dead sleep, \"treat.\" I'd always heard that poodles were smart, which was why they were often used in circuses, because they were easy to train. However, it wasn't until I discovered exactly how smart they were that I was able to truly appreciate them. When I looked into their eyes and saw the lightbulb of recognition at the word \"treat,\" that's when I realized these creatures were intelligent beings.\n\nThe poodles followed Nana Jo downstairs, fully aware that a biscuit awaited them if they simply went potty outside rather than inside. It was definitely a cushy life.\n\nOnce the poodles were tended to, Nana Jo and I bundled up and walked down the street to North Harbor Caf\u00e9, the restaurant owned by my friend, Frank Patterson. We promised to bring lunch back for my nephews too.\n\nWhen we walked in the door, I immediately looked toward the bar. Frank was behind the counter. He smiled. He was tall with salt-and-pepper hair, which he wore cut short. Even though he was wearing jeans and a polo shirt, there was something about him that screamed I used to be in the military. I thought it was the haircut that former military and policemen often continued long after they left the service. However, as I stared at him, I wondered if it was something in his bearing. He was lean and fit with a straight posture and confident stride.\n\n\"You gonna stand there gawking all day?\" Nana Jo jostled me, and I realized I was standing in the middle of the floor staring.\n\nI hurried to the tables the staff had pushed together for our group. Ruby Mae, Dorothy, and Irma were already there.\n\nNana Jo and I sat at the two empty seats and removed our coats and hats.\n\nFrank brought a large pitcher of water with lemons in it to the table and placed it in front of me. He greeted everyone and leaned down and whispered in my ear, \"Welcome home. I missed you.\"\n\nThe warmth of his breath tickled my neck and my breathing increased as his lips lightly touched my ear.\n\n\"I missed you too.\" I'd kept him in the loop through a series of texts and phone messages over the past day. Had it really only been one day since Max Franck was killed? It certainly felt like a lot more time had passed.\n\n\"I'm looking forward to hearing all about it tonight. Are we still on for dinner?\"\n\nI'd forgotten we'd arranged to have dinner tonight. \"Definitely.\" I worked to avoid a yawn.\n\nHe stared. \"You look tired.\"\n\nI smiled. \"Thanks. That's just what every woman wants to hear.\"\n\nHe placed a hand over his heart. \"My apologies. Please forgive me.\"\n\nI smiled. \"You're going to need to do better than that.\"\n\n\"Maybe I can make it up to you,\" he whispered, and his lips brushed my ear and sent a shiver up my spine.\n\n\"Ahemm.\" Nana Jo cleared her throat. \"Normally, I would never dream of interrupting my granddaughter's flirtations, but we have a mystery to solve.\"\n\nFrank bowed to Nana Jo, turned, and winked at me.\n\nNana Jo yelled, \"And you're looking rather tired yourself, Frank. You need to hire an assistant.\"\n\nFrank raised an eyebrow and smiled and then hurried back to work.\n\nI could still feel the effects of the gentle caress of his lips and the heat rose up my neck. I took a sip of water and tried to focus my attention on something other than Frank Patterson. My husband, Leon, and I had been married for a long time and after his death, I was out of practice when it came to flirting. However, practice made perfect, so I was just practicing. At least that was what I told myself.\n\n\"Earth to Sam.\"\n\nNana Jo's prompting, and the laughter I heard from the others, forced me to drag my mind back to the task at hand.\n\n\"Sorry.\"\n\nWe gave our orders to the waitress, and I watched my grandmother, determined not to allow my thoughts to drift into dangerous waters.\n\n\"Now, who wants to go first.\" Nana Jo pulled her iPad out of her large purse and prepared to take notes.\n\nIrma raised a hand. \"I think I should go first since I knew him better than the rest of you.\"\n\nWe all nodded.\n\nIrma coughed. \"I didn't know Max long, and, to be completely honest, we didn't spend much time talking.\" She cast her gaze downward and took a deep breath. \"I knew he used to be married. Although, he's been divorced for decades and his ex-wife is deceased. They had one child, a daughter.\" She paused and looked up as though trying to remember. \"I think he said her name is . . . Rosemary.\" Irma paused.\n\n\"Is she married?\" Nana Jo asked. \"Is her last name Franck?\"\n\n\"I don't . . . wait, yes. I think he said she's married and has a daughter.\" Irma paused again. \"I don't think they had a very good relationship. He was a journalist and traveled a lot. I think he and his daughter were estranged, but . . .\"\n\n\"What? Anything he said might prove important,\" Dorothy encouraged her friend and reached across the table and squeezed her hand.\n\nIrma nodded. \"I got the impression that he had seen her recently and wanted to make things right between them, but . . . I don't think it was going well.\" She looked up. \"At least, I got that impression.\"\n\nNana Jo looked at her friend with more compassion than usual. \"That's great, Irma. You've given us a lot to go on.\"\n\nIrma smiled.\n\n\"Now, who's next?\"\n\nI raised my hand. \"Something Sergeant Alvarez said made me think Max Franck was an author, so when\u2014\"\n\nNana Jo smacked her hand against her forehead. \"That's where I knew him.\" She glanced around the table. \"I read in one of those publishing newsletters you subscribe to about a new book deal he had.\" She looked at me. \"I'm sorry, dear. I didn't mean to interrupt.\"\n\nI shook my head. \"It's okay.\" I pulled the book I'd shoved in my bag onto the table. \"Apparently, Max Franck was an investigative journalist.\" I read the back cover of his book, which listed the many awards he'd won. Then I told them about his book about the conspiracy he believed surrounded the assassination of Robert Kennedy.\n\nThe others listened silently. The waitress brought our food and we paused for a few moments to allow her to distribute it.\n\n\"That's fascinating, and I'd love to read the book.\" Dorothy wiped her mouth. \"I just don't see what that could possibly have to do with his murder?\"\n\n\"I don't know that it does. It's just background information more than anything.\" I chewed my BLT, minus the T. \"I think it speaks to the type of person he was . . . his character, more than anything.\"\n\n\"Anything else?\" Nana Jo's voice held a nervous excitement that told me she was eager to share.\n\nI shook my head. \"Not really.\"\n\n\"If no one minds, I'll go next.\" She gave a courtesy glance around the table, but no one objected.\n\n\"I was a little bummed because I didn't have much to talk about, but after hearing Sam's information, I remembered something important. In fact, I may know why Max Franck was killed.\"\n\nAfter dropping that bombshell, Nana Jo, the ultimate performer, waited until surprise showed on everyone's face. \"Like I said, I read one of those publishing newsletters Sam has and I remembered reading about Max Franck.\" She looked around. \"I knew his name sounded familiar, but I couldn't figure out why. There was no picture in the newsletter, so I think I buried the information in the back of my head.\"\n\nDorothy Clark leaned forward. \"Josephine, if you don't hurry up and get to the point, I'm going to brain you. You're starting to sound like Irma.\" She leaned toward Irma. \"No offense.\"\n\nIrma waved away any offense.\n\n\"Well, Max Franck's agent announced that, after years of hiding, Max Franck had written a new book, which would blow the lid off all other books dealing with the assassination of Robert Kennedy.\" She glanced around. \"According to this agent, the book that would name names, answer questions, and forever close the door on all speculation about the assassination of Robert Kennedy had been sold for a six-figure amount.\"\n\nWe gasped and demonstrated the appropriate amount of surprise to satisfy my grandmother, who sat looking as pleased as a cat who'd caught a mouse.\n\nI pondered that information. \"You think he was murdered because he was about to release a book that would identify a murderer?\"\n\nNana Jo shrugged. \"I don't know, but I do know I don't believe in coincidences. I think the moment that announcement about the book was posted, Max Franck was a marked man. That book marked him for murder.\"\nChapter 6\n\nNeither Ruby Mae nor Dorothy had anything to contribute, although Ruby Mae had a third cousin who used to work for the Chicago Sun-Times. She contacted him and was waiting for information about Max Franck.\n\n\"I'm not sure where to start with this one.\" Dorothy gave Irma a sympathetic look.\n\nAll faces turned toward me.\n\nI struggled to find the right words, which must have been evident on my face.\n\n\"Spit it out, Sam. No point in trying to sugarcoat anything,\" Nana Jo said.\n\n\"I think we need to look at everyone on the bus.\" I looked around the table. \"Present company excluded.\"\n\nIrma reached into her purse, which wasn't unusual. However, when she pulled out a sheet of paper rather than her flask, that shocked all of us. \"I thought you might want something like that.\" She unfolded the sheet. \"I wrote down the names of everyone on the bus. Counting the five of us, there were twenty-five.\" She looked up. \"If we divide the names, we could each take four.\" She looked at me. \"If that's okay with you, Sam.\"\n\n\"Of course. It's perfect.\" I was shocked and tried to shake it off. Normally, Irma was much more interested in flirting and having a good time. This murder must have really left her rattled.\n\nThe girls divided the names on the list, and I noticed my names included Mr. Big, whom Irma described as the large hunk with the mirrored sunglasses. I took a pen and wrote Sidney Sherman next to his name so I wouldn't forget.\n\nThe meeting ended with Nana Jo promising to get what she could from her boyfriend, Freddie, who was a retired policeman and whose son was a state policeman.\n\nNana Jo and I walked back to my building after the meeting. I was tired but still not sleepy. I helped out in the bookstore for a couple of hours to allow the twins to eat their lunches, but the traffic after Christmas wasn't nearly as much as it had been prior to the holiday. I puttered around for a while but eventually gave up and went upstairs.\n\n\"Are you still stressing about this murder?\" Nana Jo asked.\n\n\"I don't know.\" I paced. \"I just realized I won't have Stinky Pitt to help with this one.\"\n\nNana Jo snorted. \"I never thought I'd hear the day when you'd be missing Stinky Pitt.\"\n\nDetective Pitt, Stinky Pitt, as he'd been labeled as a child, was a detective with the North Harbor Police and we'd crossed paths several times in the past. Normally, he wasn't a fan of what he referred to as \"nosy amateurs\" meddling in police investigations. However, Detective Pitt, as Nana Jo often said, wasn't the sharpest knife in the drawer and we'd helped him out several times. Our help hadn't exactly endeared us, but it had forced him to tolerate us.\n\n\"It's not that I miss him, exactly. It's more that I'm missing the access to the police and coroner's report.\"\n\n\"Hmmm. You might have a point.\" Nana Jo poured herself a cup of tea. \"Maybe that sexy Sergeant Alvarez will share his . . .\"\n\nI was shaking my head before the words left her mouth. \"Sergeant Alvarez isn't a small-town policeman who doesn't know how to investigate a murder.\" I followed Nana Jo into the kitchen and poured a cup of tea for myself. \"He doesn't need our help and he's not likely to share any information with us.\" I took a sip. \"In fact, he probably still suspects us of the murder.\"\n\n\"You're probably right.\" She smiled. \"However, you have to admit, he was definitely a hunk.\" She started to walk away but stopped abruptly. \"Are you done with that book?\"\n\nI gave Nana Jo Max Franck's book from my purse.\n\nShe settled onto the sofa with the book and her tea and, within a few moments, was engrossed.\n\nI paced around my bedroom for a few moments, trying to decide what to do. I felt anxious, probably from my lack of sleep. After a few moments, I grabbed my coat and headed out. \"I'll be back.\"\n\nNana Jo grunted an acknowledgment.\n\nI got in my car and drove, something I often did to clear my mind. Despite the cold weather and the snow on the ground, the streets were clear. North Harbor was an economically depressed city situated on prime real estate alongside the Lake Michigan shoreline. The city was separated from its twin city of South Harbor by the St. Thomas River, which flowed out into the Great Lake. In contrast, South Harbor was a prosperous, quaint town of cobblestoned streets, lighthouses, and thriving shops.\n\nPractically on autopilot, I pulled into the lot for the North Harbor Police Department, which was attached to the county courthouse. Memories of an unpleasant experience where an overzealous police officer mistook Nana Jo's iPad for a weapon reminded me to double-check my purse before I got out of the car.\n\nInside, I walked through the metal detectors without incident and breathed a sigh of relief.\n\nI recognized the policeman behind the desk, although I didn't know his name. Apparently, he recognized me too because when he looked up from his computer, he said, \"You here for Detective Pitt?\"\n\nI nodded and he picked up the phone and dialed.\n\nIt didn't take long for Detective Pitt to come up for me. The scowl on his face told me he was as happy to see me as I knew he would be.\n\n\"Whaddaya want?\"\n\nI smiled. \"I'm glad to see you too, Detective Pitt. I'd like a word with you in private, if you can spare the time.\"\n\nHe narrowed his eyes and stared for several seconds. Eventually, he sighed. \"Might as well come on.\" He turned and walked down the hall to the closet he had transformed into an office.\n\nI followed Detective Pitt down the hall, but after many trips to the North Harbor Police Department, I knew my way by heart.\n\nThe office had, indeed, once been a closet, and he had to suck in his stomach and turn sideways to get through the doorway if anyone was sitting in the guest chair. Once inside, he flopped down onto his chair and turned to face me. \"No one's died in the past week, so what brings you out.\"\n\nDetective Pitt was short, fat, and balding. He chose to take the few remaining hairs that still clung to the edges of his head and comb them over the rather large dome on top. The task of covering his egg-shaped skull was too much for the strands that remained and many of them refused to lie quietly and instead stood at various angles as though looking for an escape route. His fondness for polyester was evident from the too-tight polyester pants and shirt he wore to the polyester jacket that he had draped over the back of his chair. His office reeked from the cheap cologne he wore and the half-consumed liverwurst sandwich that lay on his desk.\n\n\"Did I interrupt your lunch?\"\n\n\"Never mind that. Whaddaya want? No one's died. No reason for you and those batty old broads to interfere.\"\n\nI took a deep breath and reminded myself I was asking for a favor and would need to stay on the detective's good side. I forced myself to remain serious and not think of how Nana Jo would react if she heard him refer to her as a \"batty old broad.\" \"Actually, that's not entirely true.\" I took a deep breath.\n\n\"What's not entirely true?\"\n\n\"That one part.\"\n\nHe leaned forward. \"What part?\"\n\n\"The part about no one having died in the past week . . . That's not exactly, ah . . . true.\"\n\nNow I had his complete attention. He smacked his hand on the desk. \"What? Who's dead? Nobody told me!\"\n\nThe flash of anger he'd exhibited moments earlier instantly vanished. Instead, the spark was replaced with a wariness that caused his gaze to dart around the small room. He leaned across and whispered, \"Who was assigned the case?\" He leaned forward. \"It's Wilson, that brownnoser, isn't it?\" He muttered. \"Backstabbing traitor.\"\n\n\"No. It's not Wilson. It's not a local murder.\"\n\nHe stared. \"Whaddaya mean?\"\n\nThe English teacher in me cringed every time he mushed his words together and slurred them into some mutation that barely resembled the English language, but I screwed my smile on tighter. \"The murder happened on a bus trip from Chicago.\"\n\nI could tell by the way he relaxed and leaned back he was about to dismiss me. \"Not my jurisdiction.\" He picked up his sandwich and took a bite. \"Amateurs don't know how these things work.\" He forced the words around his food as he chewed, giving me a good glance of his teeth in action.\n\n\"I understand the murder took place in another state, but the victim was on a Michigan bus, in fact Shady Acres chartered the bus. So, nearly all the passengers were locals. Plus, the bus was en route to Shady Acres. So, it really gives you a better chance of solving the murder since you're already more familiar with the people involved than some out-of-town Chicago policeman coming on your turf and trying to make a name for himself by solving a high-profile murder.\"\n\nHe sat up in his chair. \"High profile?\"\n\nMy bait had worked. I'd hooked my fish. Now, if I could just reel him in. I nodded, took a deep breath, leaned close, and whispered, \"Yes. The victim was a well-known author\u2014a Pulitzer Prize\u2013winning, bestselling author.\"\n\n\"You don't say.\" He rubbed his chin.\n\nI wiped the tears from my eyes. His cologne, combined with the liverwurst, which was obviously covered in onions, and the closeness of the space was overwhelming.\n\nHe reached in a pocket and pulled out a lime-green polyester handkerchief. \"Did you know the victim well?\"\n\nI shook my head. \"Not at all. It's just the thought that Detective Alvarez will come over here and solve a murder and will probably make a name for himself and end up in the newspaper and on television when . . . well, it could be someone local.\" I gave him a pointed stare and blinked to get the tears out of my eyes.\n\nHe leaned back. \"You say the victim won awards?\"\n\nI nodded. \"A Pulitzer. Plus, he was about to publish another book, some big expos\u00e9 about the murder of Robert Kennedy. You know something like that always generates tons of media attention.\"\n\nHe sat up. \"The Robert Kennedy? As in brother to the late president of the United States?\"\n\nI nodded.\n\nDetective Pitt looked up and smiled. After a few minutes he looked at me. \"I'll bet you have some angle on this case.\"\n\n\"Same deal as last time. If you help me get the forensic information and police reports, then when we solve the case, you get all of the credit.\"\n\nHe was silent for a moment. \"It may not be easy to get the forensic information on this one. The Chicago Police Department isn't just going to turn that stuff over to me.\"\n\n\"I was thinking maybe you could ask to be added to the case as a local consultant or something. I mean, I can't believe the Chicago Police Department has the money or the resources to stay in North Harbor. Couldn't you do some of the local . . . legwork or whatever it's called?\"\n\n\"Maybe . . . it's the holidays and most police departments are short staffed around this time of year, including us.\"\n\n\"I'm sure they'd be happy to have your help.\" I hesitated. \"That is, unless you're super busy.\"\n\nDetective Pitt's desk always looked as though a tornado had passed over the papers. However, the magazines he'd tried to conceal under the files told a different story.\n\n\"We're at rather a slow time right now. Most of the college students from MISU are gone for Christmas break, and we don't get many tourists during the winter. So, things are slower than normal at the moment. Just a few domestic disputes and bar fights, but nothing to really sink your teeth into.\" He leaned back. \"I might be able to manage a few hours. You better give me the specifics and I'll see what I can do.\"\n\n\"Great.\" I smiled.\n\nIt took thirty minutes to fill Detective Pitt in on what I'd learned about Max Franck. He surprised me by asking quite a few questions about Sergeants Alvarez and Davis. However, I felt the more information he had, the better, so I told him all I knew.\n\nI drove home and went back upstairs. Nana Jo was in the exact same spot where I'd left her with her nose glued to the book. I smiled and headed to my bedroom. I still wasn't sleepy, so I decided to take a trip to the British countryside.\n\nLord William Marsh sat in the library of Wickfield Lodge and watched. He was accustomed to his wife, Lady Elizabeth, sitting quietly while she knitted. However, there was something different about her silence tonight. He puffed on his pipe and watched through the haze of smoke. Eventually, the silence grew too much for him. \"All right, let's have it.\"\n\nLady Elizabeth looked up. \"What do you mean?\"\n\nHe puffed. \"What's wrong?\"\n\nLady Elizabeth opened her mouth to speak, but Lord William interceded. \"And, don't tell me there's nothing wrong.\" He tapped the ashes from his pipe onto an ashtray the butler, Thompkins, had placed nearby. \"I know when something's wrong. Now, you just tell me. It has to do with that woman . . . Forsythe or some such name. Something about that has you bothered.\"\n\nLord William was a kind, portly older man, a blustery English gentleman who enjoyed his pipe, rich foods, wine, and family. His fondness for rich food and wine had led to a bit of overindulgence during his niece's wedding and the holiday meal that followed and the kindly man was paying for his intemperance with an attack of gout. He sat with one leg wrapped heavily and propped on a cushioned footstool.\n\nLady Elizabeth finished the row she was knitting. \"I don't know what's wrong. I just know something isn't right.\"\n\nLord William took several puffs on his pipe. \"People do fall.\" He tilted his head and stared at his wife. \"You said it was crowded. Isn't it possible she lost her footing and fell?\"\n\nLady Elizabeth knitted. After a few moments, she stopped and looked up. \"It's possible. In fact, it's highly probable.\" She stared at her husband. \"That's what's so darned difficult. It's the type of accident that happens every day. An elderly lady loses her footing on the escalator of a busy tube station and falls to her death.\" She knitted. \"It's on the back page of the paper and no one thinks twice about it.\"\n\n\"Then what's the problem?\"\n\nShe knitted. \"If I hadn't met her earlier. If I hadn't talked to her . . . shared tea and scones with her, I would write her off as some batty old dear who wasn't quite right in the head, but . . .\"\n\nLord William waited. \"But?\"\n\n\"I don't know. She wasn't batty. She was intelligent and she made complete sense. She was scared and she honestly believed someone was trying to kill her.\"\n\nLord William leaned forward and winced. He took a deep breath and patted his leg. \"Isn't that what batty old dears do? They may be normal in every other respect, but they get some bit of nonsense fixed in their heads and they can't let go.\" He sat back. \"Like that chap over in Kent who believed he was a Chinese emperor or that fellow in . . . where was it . . . Torquay who believed he was Napoleon.\" He shook his head. \"Normal in every other respect, except no one could convince him he wasn't Napoleon Bonaparte.\" He shook his head.\n\nLady Elizabeth smiled. \"I understand what you're saying and, in my head, I know you're absolutely right. After all, I'd only known the woman a short time and she may very well have been exactly as you say.\"\n\n\"But, you don't believe it.\"\n\nShe shook her head. \"No. I don't.\"\n\nLord William nodded. \"Well, what are you going to do about it?\"\n\n\"I thought I'd call our friend Detective Inspector Covington at Scotland Yard and invite him down for a few days.\"\n\nLord William smiled. \"Ah . . . I see.\"\n\nLady Elizabeth glanced over at her husband. \"What do you see? He's always been so helpful before when we've had problems. I just wondered if he could find out some information about Mrs. Forsythe and a few of the people in her household.\"\n\n\"Hmmm.\" Lord William smiled and puffed on his pipe.\n\n\"I hope you're not implying there's more to my desire to invite the detective inspector down than my desire to get his help.\"\n\nThe corners of his lips twitched as he tried to conceal a smile. \"Of course, dear.\" He took several puffs on his pipe. There was a long pause. \"I'm sure your invitation has nothing at all to do with the fact you've received a request from your cousin Mildred to put up her daughter, Clara, for a few weeks.\" His lips twitched with the effort to keep from smiling. \"Clara just happens to be about the same age as Detective Inspector Covington, isn't she?\"\n\nLady Elizabeth glanced at her husband for several seconds and then smiled. \"She is indeed.\"\n\nBefore Lord William could respond, Thompkins, the Marsh family butler, quietly entered the room. He stood tall and erect and gave a discrete cough. \"I beg your pardon, but there's a phone call for your ladyship.\"\n\nDespite the fact that the Marshes' prim and proper servant rarely displayed emotions, he was able to convey his displeasure quite well.\n\n\"Who the dickens would be calling at this time?\" Lord William pulled out his pocket watch and frowned when he saw the lateness of the hour.\n\nLady Elizabeth looked concerned as she glanced at the clock over the mantle. \"I hope everything is okay with Daphne and James.\" She clutched at the pearls around her neck.\n\n\"I'm sorry, m'lady. I didn't mean to distress you. It's a person named Desmond Tarkington.\" Thompkins hurried on. \"I asked if there was a message I could convey and have your ladyship return the call tomorrow, but he was insistent.\"\n\nLady Elizabeth breathed a sigh of relief. \"Thank goodness.\" She stood. \"It's . . . okay, Thompkins. I'll take the call.\"\n\nThe butler bowed stiffly.\n\n\"Who in the blazes is Desmond Tarkington?\" Lord William asked.\n\n\"That's the cousin of Mrs. Eleanor Forsythe, the woman who died today.\"\n\nLord William was momentarily stunned. \"What could he possibly want at this hour?\"\n\nLady Elizabeth shook her head. \"I have no idea.\" She turned to walk out of the door. \"However, I intend to find out.\"\n\n\"Snickers. Oreo. Wanna treat?\" My nephew Zaq called from the living room and my two companions, who were just, moments earlier, sound asleep in a dog bed, hopped up and ran barking into the living room.\n\nI glanced at the clock on my computer and realized it was later than I thought. Frank and I had a date and I needed to get dressed.\n\nI stretched and tried to figure out the answer to Lord William's question. What could Desmond Tarkington possibly want? Nothing came to mind, so I tucked the question back into the recesses of my brain and focused on a more important question. What was I going to wear for my date?\n\nDespite a warm, invigorating shower, the best my brain, and my limited closet selection, could come up with was a black dress and black boots. I stared at my reflection in the mirror and knew this wasn't my best effort. My dark hair was curly and today was one of the days it decided to rebel. Instead of laying down when I combed it, the static electricity gave it a life of its own and it stuck out like Albert Einstein's. I grabbed a can of what I thought was hair spray but, after a few spritzes, I realized was starch, which made my hair stiff and sticky. The comb was barely able to make it through the strands. As the starch dried, it acted like glue. My comb was now glued to my hair. I gave it a yank and it broke off. I'd need to go get scissors and cut it out. This wasn't going well. I took another look at my drab reflection in the mirror and grabbed a colorful scarf Lexie and Angelo gave me for Christmas, to keep from looking as though I was going to a funeral. The lack of sleep had finally caught up with me and, as much as I wanted to see Frank and spend time with him, I couldn't muster up the energy to make a greater effort at looking date worthy. Tonight, I was a dating fail. My boots weren't even the high-heeled fashion boots I'd bought in Chicago. One glance at the snow outside confirmed if I tried to walk in those boots, I'd end up flat on my backside before I made it to his car. Besides, those boots cost a small fortune and as a native Michigander, I knew very well the effect snow and salt had on leather boots. My feet would be wet and the boots would be ruined from the white salt residue, and I'd have a broken ankle from the attempt. Nope, those babies would get worn indoors or only when the weather was dry and boots were a fashion accessory rather than a mobility requirement.\n\nI went to the main living area to wait. Nana Jo was still reading on the sofa. She looked up from her book at my entrance and I gleaned her appraisal of my ensemble in her silence and a single raised eyebrow.\n\n\"Don't start.\" I flopped down on the sofa next to her.\n\n\"I didn't say a word.\"\n\n\"No, but your eyebrow spoke volumes.\"\n\nShe flipped the page of her book. \"Going to a funeral?\"\n\n\"I haven't slept in twenty-four hours and I'm dead on my feet. It's going to take all the energy I can muster to eat, make polite conversation, and keep from dozing off during the soup course.\"\n\nShe patted my leg. \"I'm sure Frank will understand if you postpone your date. You're beat.\"\n\nI picked up one of the magazines on my coffee table and flipped to a survey. \"Are you pushing your man into the arms of another woman?\" I waved the magazine at her. \"According to this magazine, I'm a pathetic excuse for a date. I fail in practically every category except keeping date night.\"\n\nNana Jo took the magazine and glanced at the survey. \"This is rubbish and if you weren't so tired, you'd realize it too. Any man would be lucky to have you and if Frank Patterson doesn't recognize what a prize you are, then he doesn't deserve you.\"\n\nI smiled and leaned over and kissed my grandmother. \"Thank you. You're sweet, although you may be slightly biased.\"\n\n\"I'm more than slightly biased. However, it's true, regardless. Frank Patterson, or any man, will be lucky to have you . . . although.\"\n\nI waited for the other shoe to drop. \"Although?\"\n\n\"You should probably take the comb out of the back of your hair.\"\n\nI felt the back of my hair and realized that I'd forgotten the comb glued and tangled in my hair. I forgot the scissors. I fiddled with it but only got it more entangled.\n\nNana Jo reached over. \"Here, let me help you.\" She grabbed at the plastic comb and gave it a hard yank. \"What's in your hair, glue?\" She pulled the plastic out and handed it to me.\n\nI wiped the tears from my face and tried not to notice the strands of hair fused to the comb. \"I mistook the starch for hair spray.\"\n\nNana Jo stuck her head behind her book to hide her face, but the laughter rang out anyway. She gave up trying to conceal the fact she was laughing at me and put down her book and laughed heartily until she had to wipe tears from her eyes.\n\n\"I'm glad one of us is able to enjoy themselves at my expense.\"\n\n\"Sam, I'm sorry, but you're exhausted. I don't care what that magazine says. Canceling a date when you haven't slept in over twenty-four hours isn't a dating fail. It's common sense and Frank will understand.\"\n\n\"Understand what?\" Frank walked up the stairs.\n\nI hopped up and grabbed my coat. \"Nothing. I didn't hear you come in.\"\n\n\"One of the twins let me in.\" He came up and gave me a kiss. \"You look . . . nice.\" He lied and I appreciated him for that. Although, his eyes kept staring at my hair.\n\n\"What's wrong? Don't tell me there's more of that blasted comb in there?\"\n\nHe shook his head. \"No, but your hair just looks different tonight.\"\n\n\"She's trying a new product . . . sizing.\" Nana Jo laughed.\n\nFrank frowned. \"Starch?\"\n\nI handed him my coat so he could focus on something other than the fact that my grandmother was intent on sharing my humiliation. \"Yeah, well, we'll see you later.\"\n\nI hurried downstairs before Nana Jo could respond and felt Frank's presence behind me. He was a gentleman who liked to open doors and I knew he wouldn't linger once I started. Thankfully, I was right. At the bottom of the stairs, he turned me toward him and looked into my eyes. \"You okay?\"\n\nI stifled a yawn. \"Of course.\"\n\nHe hesitated but gave up and opened the door for me. The bookstore was a brownstone in downtown North Harbor. The front of the building was on Market Street. Like most of the buildings on Market, the building backed up to an alley. Unlike the other buildings, this building wasn't as deep as the others and occupied a corner lot. The previous owner had built a garage at the back of the property and enclosed the lot with a fence, which created a courtyard. So, I was able to drive through the alley and enter the garage. There was a door that led to the back courtyard from the building and a side door that led out to a parking lot, which separated my building from the others on the street on one side. Technically, I owned the parking lot, but when I purchased the building, I continued the \"gentlemen's agreement\" the previous owner had and shared the parking lot with the church, which worked out well since the church mostly used the lot on Sundays.\n\nFrank had parked his Porsche Cayenne in the parking lot near the side door. He went out and pulled the car as close as possible to the side door and kept the engine running so I only had a few steps on concrete before getting into the warm interior.\n\nI slid onto the soft, supple leather seat and ran my hand across the leather, always amazed at the softness.\n\nFrank came around the back of the car and got in. \"Any place in particular you want to go?\"\n\nI shook my head. \"No, I'm game for whatever.\"\n\n\"Great. There's a great little Greek restaurant in South Haven I've been dying to try.\" He glanced at me. \"Are you up for the ride?\"\n\nI nodded. \"Sounds great.\"\n\nHe pulled out of the parking lot and I prepared to enjoy the ride.\n\nFrank's car was luxurious in every respect, and the smooth ride felt like you were floating on clouds. The seats were warm, and I adjusted the thermostat so I was warm and toasty. He had satellite radio and smooth jazz played through the speakers as we drove through the dark.\n\nI leaned my head back onto the headrest and thought about Max Franck. There were no easily identifiable signs to indicate the method of his death. As far as I could tell, there were no gunshots, at least not visible. There hadn't been a lot of blood that would indicate a stab wound. He could have been poisoned, but I didn't recall seeing him eat or drink anything on the bus. Although, it could have been administered while we were at the rest area. Someone could have come back onboard and given him something laced with poison and then removed the evidence afterward. It was clear the timeline would be critical. We'd need to find out where everyone was and verify.\n\n\"Sam.\" Frank shook my shoulder.\n\nI opened my eyes. For a split second, I had no idea where I was. I looked around and saw Frank staring at me.\n\n\"I'm sorry. I must have dozed off.\" I reached down to remove my seat belt.\n\nFrank reached his hand over and clasped my hand. \"We don't have to do this\u2014\"\n\n\"I want to . . . I'm sorry about falling asleep, but your car is so comfortable and\u2014\"\n\n\"And you haven't slept in more than twenty-four hours.\" He smiled. \"I should have realized you were exhausted.\" He leaned over and kissed me. \"I'm sorry. Let's do this another time.\"\n\nI started to protest but realized opening my eyes had been a huge struggle. I glanced over at Frank, who had backed the car out of the restaurant parking lot and was turning around. \"I'm sorry. I didn't want to disappoint you.\"\n\n\"You could never disappoint me.\"\n\nI could tell by his voice he was smiling, even though it was dark in the car and I couldn't see his face. \"Are you sure?\"\n\n\"Of course. We can go another night.\"\n\n\"I'll make it up to you.\"\n\nHe stopped at a stoplight, leaned over, and kissed me. \"Now that sounds promising.\"\n\nI managed to stay awake for the ride home, but I was grateful when we arrived. He pulled up to the side door and hurried around the car to open my door. I unlocked the building and turned off the security system. I turned to Frank and we made our good night brief.\n\nInside, I rearmed the security system, called on the last dregs of energy, and climbed the stairs. Nana Jo must have finished the book because she had vacated the sofa and her bedroom door was closed.\n\nSnickers and Oreo were asleep in my bedroom. I should have taken them downstairs to take care of their business, but I knew there was no way I'd be able to tackle those stairs again. I didn't even have the energy to undress. Instead, I flopped down on the bed, boots and all, and fell fast asleep.\n\nI woke up once during the night with a ten-pound weight of a poodle on my chest. I opened my eyes and Snickers was staring into my eyes. I rolled over onto my side, forcing her off. \"You're just going to have to go potty in the house. I'll clean it up later.\"\n\nShe marched around for a few more moments but eventually must have decided she could hold it. She walked in circles a couple of times and then curled into a ball near my chest. Within moments, I heard a gentle snore coming from her.\n\nOreo was in his crate near the foot of my bed. The only sound from him was a soft, \"woof.\"\n\nI wasn't sure if he was dreaming about chasing squirrels or ripping the stuffing out of his stuffed toys. Whatever the source of his dreams, he was a happy dog. My last thought was of Oreo running free in a field with his ears flapping in the wind and it made me smile. I snuggled close to Snickers and fell back asleep.\n\nThe next time Snickers woke me up, she not only walked on my chest, but this time, she followed it up with a lick to my nose.\n\n\"All right. I'm getting up.\" I stretched.\n\nSnickers jumped off the bed and ran to the door. Oreo was sitting up in his crate.\n\nI was still wearing the clothes I'd worn last night, boots and all. So, I opened the bedroom door and hurried the poodles downstairs to take care of their business.\n\nBoth dogs were anxious to go and barely made it over the threshold.\n\nI appreciated the fact that they hadn't gone in the house and planned to reward them with extra treats when we got back upstairs.\n\nIt snowed overnight and the ground was covered by another blanket of snow. Snickers wasn't a fan of the cold Michigan winters. She hurriedly took care of the call of nature and was back inside before her paws got too cold. Oreo, on the other hand, liked to run and play in the new snow and was halfway across the small yard before his under belly registered the cold. Then he quickly ran to the door, expecting entr\u00e9. However, I'd learned from experience to watch and make sure he had not just peed but had also pooped before letting him back inside.\n\nHe stood at the door and looked at me with sad eyes that seemed to ask, aren't you going to let me inside too?\n\nI steeled my heart and kept the door closed and waited. Eventually, he wandered to the side and pooped. This time, I had the door open wide to welcome him.\n\nHe shook, and snow flew everywhere. I grabbed the towel I kept at the back door and wiped as much of the excess snow from his underbelly and paws as possible for both of our comfort and well-being. Snow beaded up on his belly, which I was sure was cold. When the snow melted, it left trails across the floor, which I stepped in whenever I walked around without shoes. Snickers rarely ventured too far away from the shoveled path and rarely needed the towel. Instead, she stood by and watched while I dried off Oreo, and looked at me with an expression that said, he's not the brightest dog in this pack, is he?\n\nI ignored her.\n\nUpstairs, I stripped off the clothes I'd slept in, showered, and allowed the warm water to pelt my skin. I washed the starch out of my hair, which took longer than I'd expected. However, perseverance and a lot of shampoo did the trick. When I finally emerged, dressed and thoroughly refreshed, I sniffed the air. Coffee, sausage, and something cinnamony drew me to the kitchen.\n\n\"Hmmm. What is that wonderful smell?\"\n\nNana Jo smiled. \"Dawson left us a gift.\" She placed a bubbling cheesy dish on the counter beside a plate of warm cinnamon rolls.\n\n\"How? He's in Florida getting ready for his bowl game.\"\n\nShe took two plates from a cabinet and placed them on the counter. \"He called when you were in the shower and said he made us a breakfast casserole and put it in the back of the refrigerator. He also made homemade cinnamon rolls.\"\n\nI breathed in the delicious aroma and my stomach growled in response.\n\n\"It's supposed to sit for ten minutes, but I can't wait.\" Nana Jo grabbed a spatula and cut into the casserole, which sizzled and bubbled. She scooped out servings for each of us. I burned my fingers grabbing a cinnamon roll with hot icing, but it was well worth it.\n\nWe both tucked into our breakfast and didn't speak for several moments.\n\n\"That's so good.\" I sloshed down some hot coffee.\n\n\"How was your date last night? You were back pretty early.\"\n\nI was tempted to fib and tell her the restaurant was closed and we decided to make an early night of it, but I was a horrible liar. When I finished explaining that I fell asleep in the car and Frank brought me home, she laughed, making me wish I were better at lying. At least she refrained from saying, \"I told you so.\" However, the smug look she cast over her coffee cup said what her mouth didn't.\n\nWe sat in blessed silence for several moments.\n\n\"What are your plans today?\" she asked.\n\n\"I think I'll go to Shady Acres and tackle the people on my list.\"\n\n\"Great idea. I'll go with you and work on mine.\" She walked over to her purse and pulled her iPad out and brought it back to the kitchen. She swiped a few times and then asked, \"Who do you have?\"\n\nI unfolded the paper I'd stuck into my pocket before coming out for breakfast. I glanced over the list. \"I've got the activities director, Caroline Fenton, Sidney Sherman\u2014\"\n\nNana Jo frowned. \"Who on earth is Sidney Sherman?\"\n\n\"Mr. Big.\"\n\nShe nodded. \"Aww. Okay.\"\n\n\"Lady in the big floppy hat, Bob the bus driver, and Sara Jane Howard.\" I paused. \"Why does that name sound familiar?\"\n\nNana Jo smiled. \"Because Sara Jane Howard is the nosiest woman in Michigan.\"\n\nI tilted my head back and smacked my leg. \"I remember now. When we were investigating the murder of Maria\u2014\"\n\n\"Yeah, that's her.\" Nana Jo had a lot of bad memories about Maria Romanov's murder, especially since the police thought she'd had a good reason for wanting her dead. Sara Jane Howard hadn't helped matters. \"Looks like Irma gave you the people she doesn't know well and the ones she doesn't like.\"\n\n\"I was thinking the same thing, although, maybe that's good. If it's someone she knows, it'll be easier for her to talk to them. Plus, if she leaves the ones she doesn't like to someone else, then it should help eliminate any biases.\"\n\n\"Good point.\"\n\n\"Who do you have?\"\n\nNana Jo read off her list of bus patrons. Most were names I'd heard mentioned but weren't people Nana Jo or the girls had mentioned a lot. The only person who would prove interesting was Velma Levington.\n\nWe finished eating just as my nephews arrived. They finished off the rest of the cinnamon rolls and began working on the breakfast casserole like locusts.\n\n* * *\n\nThe drive to Shady Acres was short and uneventful. I made a detour on the way and stopped at one of my favorite bakeries and picked up a few pastries. There was nothing like fruit tarts from A Taste of Switzerland Bakery to help put people in the mood to chat.\n\nWe pulled through the gates into the parking lot of Shady Acres Retirement Village. The development sat on the Lake Michigan shoreline and contained single-family detached homes, referred to as villas, that were painted pastel colors and sat with views of the lake. There was also a large building that housed condos that could be purchased or rented. Nana Jo bought into the village in the early stages and had a great villa with lake views. Dorothy, Irma, and Ruby Mae all lived in condos. Dorothy owned her unit, while Irma and Ruby Mae rented. Although, now that Ruby Mae had moved into one of the larger apartments, she was contemplating purchasing too. The village was restricted to people sixty and over and the wait list was always very long.\n\nI let Nana Jo out at the main building. She took the large boxes of pastries inside while I found a parking space.\n\nOnce inside, I looked around. There was a guard at the front desk, Larry Barlow, who was a friend of Nana Jo's boyfriend, Freddie. They'd been on the police force together. He was eating a pecan roll and talking to Nana Jo. I decided not to disturb them.\n\nI walked into the main public living space, which was comfortable with a large fireplace and comfortable chairs and sofas placed to provide conversational areas. Ruby Mae sat on the sofa with her knitting and was talking to another woman. She nodded when she saw me, but I could tell she was engrossed in conversation and didn't want to stem the flow of information.\n\nBack in the lobby, Nana Jo had finished talking to Larry and motioned for me to join her. \"I've got good news and bad news. Which one do you want?\"\n\n\"I need some good news.\"\n\n\"You're in luck. Larry said Earl is still here.\"\n\nI scoured my brain, but eventually gave up. \"Who's Earl?\"\n\n\"Earl was our original bus driver. I was afraid he'd have hightailed it back to Chicago.\"\n\n\"So was I.\" I pondered for a moment. \"I wonder why he's still here.\"\n\n\"According to Larry, he's staying for a few days.\" She raised an eyebrow and gave me a look that suggested she questioned Earl's intentions for staying on.\n\nI ignored her look. \"What's the bad news?\"\n\n\"Mr. Big went back to Chicago last night.\"\n\n\"Darn it.\"\n\n\"No need crying over spilled whiskey. Let's just be thankful for what we have and we'll figure out the rest later.\" Nana Jo looked at her watch. \"Jujitsu starts in ten minutes. If I hurry, I can get changed and join in.\"\n\n\"Aren't you supposed to be investigating, not practicing your martial arts?\"\n\n\"Velma Levington has a green belt in jujitsu. I'll bet my vintage Colt .45 she's in that class.\"\n\n\"I'm sure cornering Velma Levington is your only motivation for getting to jujitsu class and has nothing to do with the fact you're hoping to go for your brown belt next month?\"\n\nShe winked. \"Two birds, one stone. Don't knock it.\"\n\nNana Jo hurried to the jujitsu class and I followed the signs that directed me to the office of the activities director.\n\nCaroline Fenton's office door was open. She was pacing in her office. She was a husky woman with dark hair, which she wore cropped at her shoulders, brown eyes, and bushy eyebrows.\n\nI rapped on the door.\n\nShe turned around. \"Come in.\"\n\nI extended my box of goodies. \"Hello, I hate to bother you, but I was hoping you had time for a coffee break.\"\n\nShe craned her neck. \"Are those from A Taste of Switzerland?\"\n\nI nodded.\n\nShe closed her eyes momentarily and her face took on a look I'd seen many times from people who thought they could resist the pastries. However, resistance was futile and she opened her eyes and nodded vigorously.\n\nI should have felt bad for tempting her, but all was fair in love, war, and coercing people to talk and give up information when you had no legal authority. So, I did what I had to do.\n\nIn her office, she had a small personal coffeemaker. She grabbed two individual coffee pods and two coffee cups and made coffee for both of us. Once the coffee was made, she settled behind her desk and stretched her neck to look over the options in my glorious white box. Her eyes lit up when she saw the lemon tarts. She reached for one and stopped and looked up at me.\n\n\"Go ahead. It's all yours.\"\n\nShe reached over and grabbed the tart. She bit into it and moaned as the gooey yellow filling squirted out the sides of her mouth.\n\nI was tempted to hand her a napkin, but experience had told me she'd rather use her tongue than waste any of the lemony goodness.\n\nI knew I was right when I saw her lick the powdered sugar and lemon filling from the sides of her mouth and her fingers.\n\nShe glanced at me once, but, at the time, I was having a spiritual moment of my own with a caramel apple tart.\n\nWe sat and ate in silence for several moments. When we finished, we both sat back and drank our coffees. I suspected she was doing the same thing as me, swishing the liquid around in her mouth to get the crumbs, but I couldn't be sure.\n\n\"Okay, you've tamed the savage beast.\" She smiled. \"What can I do for you?\"\n\nI'd thought a lot about how to approach her on my drive to Shady Acres. \"Irma was really upset about the sudden death of her friend the other night. I know he wasn't a resident at Shady Acres, but I wondered if anyone was planning a memorial or any type of funeral services?\"\n\nShe sighed. \"I hadn't really thought about a memorial since he didn't live here.\" Her gaze darted around the room and she reluctantly put down her cup and picked up a pen and started to make notes.\n\n\"I really want to help. I know you're busy and I'm sure there have to be a hundred things on your to-do list. Would it be okay if I helped? I'm more than willing to organize it.\"\n\n\"That would be great. There are a lot of things to do and I'm a bit short staffed at the moment with . . . well, you know, they haven't replaced Denise Bennett, the administrator.\" She blushed. \"You know what happened to her.\"\n\n\"Yes, I definitely remember her.\"\n\nShe cleared her throat. \"Anyway, I'm doing both jobs at the moment.\"\n\nI scooted to the edge of my seat. \"I'd love to help.\"\n\nShe smiled. \"Great.\"\n\n\"Would we be able to have the memorial observance here?\"\n\nShe nodded and pulled a calendar up on her computer. \"I'm sure we can arrange that. The only events we've got planned for the next week are the New Year's Eve Dance and a tailgate party to watch the MISU bowl game and cheer the Tigers on to victory.\" She smiled at me.\n\n\"I don't think we'll need much. Do you think Gaston could provide a few . . . snacks?\"\n\nShe nodded. \"I'm sure that won't be a problem.\"\n\n\"Then the only other thing I need would be a few names.\"\n\nShe tilted her head. \"Names?\"\n\n\"For the invitations.\"\n\n\"I have a mailing list for the residents, I can\u2014\"\n\n\"I'm not concerned about the residents, actually. I'm sure between my grandmother and her friends, they can get the word out to those who live here. I was thinking about some of the people who were on the bus who don't live here.\"\n\nShe leaned back. \"Most of those people probably didn't really know Mr. Franck. I can't believe they'd want to come back to Shady Acres to attend a memorial service for a complete stranger.\"\n\n\"You may be right, but well . . . we spent several long hours together at that rest area and developed a bit of a bond. Plus, being on the bus when someone dies is a traumatic event. It might actually provide closure for some of them . . . us.\" I didn't want to lay it on too thick, but I needed to make it personal.\n\nShe reached across the desk and patted my hand. \"I'm very sorry. I didn't really think about it from that angle.\"\n\nI sniffed and bit the inside of my cheek to bring a tear to my eyes. It worked.\n\nShe opened a drawer and pulled out a box of tissue and slid the box toward me.\n\nI pulled two tissues from the box and dabbed at my eyes. \"Thank you.\"\n\n\"I guess there's no harm in giving you the names and contact information for the people who were on the bus.\" She tapped the keys of her computer.\n\nAfter a few seconds, the printer on the file cabinet behind her came alive and spit out several sheets of paper.\n\nWhen it finished, she reached around and collected the sheets. She glanced at them and then folded them and handed them to me.\n\n\"Thank you.\"\n\n\"No, thank you for thinking of this. I'm afraid I've only been thinking about the paperwork from our corporate office and filling out the insurance paperwork. I hadn't really thought about it from the people side.\" She shook her head. \"I'm sure Mrs. Starczewski must be really upset.\"\n\n\"She is. Irma really liked Max Franck a lot.\"\n\nShe scooted her chair back in preparation of rising. \"I wish I'd gotten to know him better.\"\n\n\"Did you?\"\n\nShe looked puzzled.\n\n\"Did you know him?\"\n\nShe shook her head. \"No, not really. I only met him that day on the bus for the first time.\"\n\nSomething about the way she avoided eye contact made me think there might be more to it than Caroline Fenton was letting on. I waited, allowing the silence to work its magic. Eventually, she gave in to the pressure of silence.\n\n\"Well, I wouldn't say I knew him. I knew of him, of course. I was born and raised in Chicago.\" She picked at an invisible piece of lint on her sleeve. \"You couldn't grow up in Chicago without hearing of the great, renowned Max Franck.\" Her tone implied she thought Max Franck anything but great.\n\nI waited silently and worked to make my face appear as sympathetic as possible, but the inside of my cheek was pretty sore and I wasn't sure the expression was working. What I hoped was a sympathetic smile felt like a lopsided grimace. Nevertheless, she must have felt some type of compassion because she caved in.\n\n\"I don't know why I'm hesitating.\" She sighed. \"It'll probably come out anyway.\" She looked at me. \"I didn't know Max Franck, not personally, but I knew who he was.\" She swiveled around in her chair so she could look out of the window, which had a view of Lake Michigan. \"Max Franck was a mean, vicious, cruel man\u2014a crusader.\"\n\n\"That's different from what I've read about him.\" I tried to hide the shock on my face. \"Everything I've read indicated he was a highly thought of journalist who dedicated his life to exposing government corruption.\"\n\nShe snorted. \"That's what the newspapers said. The great Max Franck, investigative journalist intent on uncovering corruption at all costs.\" She took a deep breath. \"Even if it cost a man's life.\"\n\n\"What man?\"\n\n\"My father. Max Franck killed him. He killed my father.\"\nChapter 7\n\nI was dazed by her response and sat gaping for several seconds. I pulled myself together and asked, \"How? What?\"\n\nShe sat still for so long, I thought she wouldn't answer the question. However, eventually, she took a deep breath and gazed out the window as though watching a movie. \"My father was a good man. He was kind and gentle and loved his family.\" She swallowed hard and paused. \"He worked hard . . . so hard. He was a cop. He worked the southside of town. He was loyal and he never took a bribe. He believed in doing everything by the book.\" Tears streamed down her face.\n\n\"So, what happened?\" I asked softly.\n\nShe swiveled her chair around and pulled tissues from the box she'd offered me earlier. \"Twenty-two years on the force and he never had one black mark against him. His one fault was his loyalty. His boss, Chief Roland Waters . . . Uncle Rolly, I called him.\" She scoffed. \"Chief Waters was on the take. When Max Franck's story first broke, my dad wouldn't believe it . . . he couldn't believe it. He'd known Roland Waters for years. They started on the force together.\" She returned her gaze to the window. \"Uncle Rolly's career skyrocketed and he was promoted rapidly. My dad wasn't jealous.\" She looked earnestly at me. \"He was glad, happy for his friend. He believed him to be a good man and Chief Waters promised to always take care of my dad.\" She snorted. \"He looked out for him all right.\"\n\n\"What happened?\"\n\n\"Max Franck went undercover. He found the information he needed and he approached my dad for corroboration, but my dad refused.\" She turned and held her hands out. \"How could he corroborate? He hadn't known. He believed his friend was honorable, but Max Franck wouldn't believe him. When the story broke, he painted my dad and anyone who supported the chief with the same brush of corruption.\" She bowed her head. \"It crushed my dad. He was investigated by internal affairs and cleared of any wrongdoing, but the court of public opinion wasn't so forgiving. People who had been his friend and looked up to him, treated him like dirt and it broke my dad.\" She cried in silence for several moments. Eventually, she wiped her eyes and pulled herself together. \"Something died in him after that. So, when the doctors diagnosed him with cancer, he just gave up. He refused treatment and refused to fight. He died within six months of the diagnosis. My mom died a month later.\" She sniffed. \"So, Max Franck took both of my parents from me.\"\n\n\"Your father died of cancer,\" I said softly. \"Surely, you can't\u2014\"\n\n\"I can't what? Blame Max Franck? But I do. I do blame him. My dad used to be strong. He was a fighter. The cancer wasn't advanced. It hadn't spread. With surgery and chemo, he could have beaten it, but he didn't have the will to fight after Max Franck destroyed his life. I had to move to this two-bit town to escape the scandal while the mighty Max Franck was exalted as a champion of justice . . . a man of the people.\" She pushed her chair back, hopped up, and paced around her small office like a tiger in a cage.\n\n\"Did you confront him?\"\n\nShe took several short trips back and forth across the room before she stopped and folded her arms across her chest. \"I waited for everyone to leave the bus. Velma Levington was asleep in the back, as was that woman . . . Rosemary.\"\n\n\"Rosemary?\"\n\nShe waved her hand. \"The woman in the floppy hat.\"\n\nI nodded and made a mental note to write Rosemary beside the floppy-hatted woman on my list. \"Were those the only two people who stayed on the bus?\"\n\nShe paused in her pacing. Then she shrugged. \"I think so. Those two and his bodyguard.\"\n\n\"Bodyguard?\"\n\nShe sighed. \"The big guy with the sunglasses. You couldn't miss him.\"\n\nI nodded. So, Sidney Sherman was Max Franck's bodyguard. Another mental note to see what I could find out about him.\n\nCaroline Fenton seemed anxious to finish her tale now that she'd started. \"He finally got off the bus to smoke a cigarette.\" She laughed. \"A cigarette, can you believe it? My dad died of lung cancer and this idiot was smoking a cigarette with no ill-effects.\" She shook her head at the irony. \"Anyway, he got off and lit his cigarette. That's when I confronted him. I told him exactly what I thought of him and how I held him personally responsible for the death of my parents.\"\n\n\"What did he say?\"\n\nShe huffed. \"Nothing. The cretin just stood there puffing on his cigarette. When I was done, he flicked his cigarette away and turned and got back on the bus.\" She was breathing heavily with anger. \"Can you believe it? He just turned his back on me as though none of it mattered.\" She paced, her steps filled with anger. \"I was furious.\"\n\n\"What did you do?\"\n\n\"Do? I didn't do anything. I was too angry to do anything.\" She looked away. \"I walked around the parking lot to give myself time to cool off.\" Her eyes blazed and she snarled. \"But I wish I'd been the one to kill him. I wish I'd had a gun and could have shot him dead right there.\" She stopped and turned away toward the window. \"I'd have slept well knowing I'd performed that community service.\"\n\nI left Caroline Fenton steaming in her office and went in search of my grandmother. One glance at my watch told me Nana Jo's jujitsu class was over. I found her, Ruby Mae, Dorothy, and Irma waiting for me in the living room.\n\n\"There you are, Sam. We were just talking about whether we should stay here for lunch or go out.\" Nana Jo tilted her head. \"Are you okay?\"\n\n\"Sure. I'm thinking maybe we should stay here for lunch and talk to a few more people.\" I looked around at the girls. \"Unless you're all finished?\"\n\n\"Lawd, no. I still have a few more people on my list,\" Ruby Mae said.\n\nThe others nodded.\n\n\"Good. I need to talk to Gaston about catering the memorial too, so maybe we should eat here and push our meeting back to dinner.\"\n\nEveryone agreed.\n\n\"Great.\" Nana Jo fanned herself. \"I, for one, need a shower. That jujitsu class wore me out.\"\n\n\"I know a better way to work up a sweat.\" Irma glanced at a white-haired gentleman who walked down the hall. \"I'm going to track down Melvin Cooper. That man has buns of steel. You could bounce a penny off his a\u2014\"\n\n\"Irma!\" we all shouted.\n\nIrma burst into a coughing fit. \"Sorry.\" She fumbled in her purse for her flask and took a swig and returned the flask to her bag. She made a few adjustments to her blouse, patted her beehive hairpiece into place, plastered a smile on her face, and then waved. \"Melvin.\" She stood up and pushed her chest out and glided in the direction of her prey, like a lioness about to pounce on a gazelle.\n\n\"Looks like Irma's back to normal.\" Dorothy smiled.\n\n\"Heaven help us,\" Nana Jo said.\n\nNana Jo went to her villa to shower. Dorothy and Ruby Mae spotted others on their lists to question and managed a seemingly random encounter.\n\nI headed in the direction of the dining room in search of Gaston Renoir, Shady Acres' chef. A graduate of France's Le Cordon Bleu, he relocated to Michigan and found his way to the kitchens of Shady Acres. His love of cooking prevented him from merely sitting back and enjoying retirement. Instead, he had negotiated a reduced rate for staying at the retirement village in exchange for the opportunity to do what he enjoyed most, sharing his love of food and cooking skills with the residents. Prior to Gaston's arrival, the meals provided at Shady Acres were okay, but they were certainly nothing to write home about. Since his arrival, his wonderful meals were the subject of conversations not only with Shady Acres but in the surrounding community. He'd won an award in a local competition, and I knew, from my connections with Frank, he'd been approached by local restaurants seeking to coerce him out of retirement.\n\nFinding the chef proved relatively easy. I merely followed my nose to the kitchen where the smell of a lemon garlic roasted chicken was making my stomach growl and my mouth salivate.\n\nThe kitchen at Shady Acres was an industrial space with lots of stainless steel. It was busy but exceptionally clean. Several young people manned various workstations and Gaston moved effortlessly from one station to the other, tasting, stirring, chopping, and throwing out instructions.\n\n\"Ah . . . the beautiful Samantha.\" Gaston hurried to my side and kissed both of my cheeks. \"What an honor it is to see you. What can I do for you?\" He smiled broadly.\n\nGaston Renoir was a man who was happy, confident, and flirtatious. \"Aw . . . where is that nice man of yours? If I were a couple of years younger, I might try to steal you away from him.\"\n\nI giggled. \"You're a terrible flirt, you know that.\"\n\n\"What is the fun in life if a man cannot eat what he wants, drink wine, and flirt with a beautiful woman.\" He shook his head. \"He might as well be dead.\" He laughed.\n\n\"You have a lot more people working back here now.\" I looked at the younger people who rushed around the kitchen.\n\n\"Oui. I am now an instructor.\" He puffed out his chest. \"You must call me Professor Gaston now.\" He laughed. \"The Hospitality Program at MISU, they contact me. They ask if I will consider teaching at the school.\"\n\n\"Wow. That's impressive.\"\n\nHe smiled. \"I say, NO. I can't possibly leave my kitchen here. But, if you want to send your students to me, then I will teach them here.\" He spread his arms out wide. \"And, what do you think? They say yes. So, now I have students who come here to learn from me.\" He proudly patted himself on the chest. Then he turned to me. \"But you did not come here to listen to me talk. No, you come here to eat, yes?\"\n\nI laughed. \"No. I came to ask a favor.\"\n\nHe hurried to the stove and dipped a spoon into a sauce one of the students was stirring. He rushed over to me and held it out. \"You taste and give me your opinion.\"\n\nI tasted the sauce, which was creamy and delicious. \"Hmm that's yummy. What is it?\"\n\n\"Ah . . . that I cannot tell. It is a secret. I don't even tell my students all of my secrets.\" He laughed. \"However, you will have it tonight if you dine here.\"\n\n\"I'm definitely planning to dine here.\"\n\nHe clapped his hands. \"Magnifique.\" He leaned close and smiled. \"Now, what favor do you need? If it is at all in my power, you will have.\"\n\nI smiled. \"I think this will be an easy one.\" I explained about the memorial service for Max Franck.\n\n\"Ah. I heard of the death. Although I did not go on the trip to Chicago, I heard of this. I will be honored to cook.\"\n\nWe discussed a few simple foods, which he assured me he would be happy to provide. I promised to confirm once I'd checked with Caroline Fenton and left.\n\nAs luck would have it, when I left the kitchen, I spotted another one of my assignments sitting in the dining room looking out of the window, Sarah Jane Howard.\n\nSarah Jane Howard was a big woman. She wasn't fat but was what my mom called, \"big boned.\" Her features were big and whenever I saw her, I was reminded of the lines from Little Red Riding Hood when Red says, \"Oh, Grandmother, what big ears . . . eyes . . . hands . . . and teeth you have.\" Sarah Jane Howard was big and when she smiled, I knew what poor little Red must have felt when faced by the talking wolf dressed up to look like her grandmother. Nevertheless, there was a murder to solve, so I took a deep breath, stood tall, and prepared myself.\n\n\"Samantha, what a pleasure to see you.\" She smiled big and flashed her large teeth at me.\n\n\"Hello, Mrs. Howard.\"\n\n\"Why don't you call me Sarah Jane. Everyone else does.\" She smiled again. I tried to focus on some part of her face that wasn't big and didn't remind me of a wolf ready to pounce, but her nose was also big and rather bulbous on the end. I focused instead on the mole on her chin. It was big too but didn't seem the least bit threatening.\n\n\"How are you today?\" I sat down across from her and smiled.\n\n\"I'm doing rather poorly today, I'm afraid.\" She preceded to tell me about her racing pulse, blood pressure, heart fluctuations, and bowel disorder that completely turned my stomach.\n\n\"I'm sorry to hear you're unwell.\"\n\n\"Thank you, dear, but I suppose every day above ground is a blessing.\"\n\nI nodded to the mole. \"You're right. Things could always be worse, like that poor man who died on the bus.\"\n\nThat intro was all it took to divert her attention away from her personal maladies so she could talk about Max Franck.\n\n\"Dear me. I was so shocked to have something like that happen and see that poor man dead on the bus. It practically rattled my insides and, I tell you, my digestion hasn't been the same since.\"\n\nClearly, I was wrong about diverting Sarah Jane Howard away from her digestive issues and was forced to listen to several more minutes of the complaints that occurred because of the death. When she slowed talking long enough for me to interject, I tried again. \"The death was definitely a distressing ordeal. Did you by any chance know Max Franck?\"\n\nShe reluctantly shook her head. \"No. I'd never met him before. But I had heard he was famous.\"\n\n\"He was a famous journalist and author.\"\n\nShe shook her head. \"I wish I'd had time to talk to him.\"\n\n\"I don't suppose you noticed anyone who did talk to him?\"\n\n\"Well, funny you should mention that.\" She leaned closer and smiled her big smile. \"I returned to the bus a little early because I'd forgotten my gloves and it was bitterly cold outside and those winds are terrible for my rheumatism.\"\n\nI prayed silently the story of her rheumatism was a short one. Thankfully, she merely spent two minutes describing the pain.\n\n\"Now, where was I?\"\n\n\"You returned early to the bus.\"\n\n\"Yes, that's right. As I got there, I saw that man . . . Max . . . arguing with a woman.\"\n\nMy heart sank and I tried not to let my disappointment show. \"That must have been Caroline Fenton. She had words with\u2014\"\n\n\"No, dear, not Caroline. I know her. It was another woman.\"\n\nI stared. \"Do you remember who?\"\n\n\"I didn't recognize the woman. She had a large floppy hat on, and I couldn't see her face.\" She shook her head in disappointment. \"I don't think I knew her anyway. She wasn't from the Harbor.\" She sniffed.\n\nI sat up eagerly. \"I don't suppose you remember what they were arguing about?\"\n\nSarah Jane Howard smiled slyly. \"Well, I'm not one to eavesdrop on conversations that don't concern me, mind you.\" She looked at me with the most serious expression.\n\nI stifled a desire to laugh. \"No, of course not.\"\n\n\"However, they were arguing and I just thought it was unseemly and perhaps I should stand nearby in case the gentleman got rough and the lady might need assistance.\" She opened her big eyes even larger.\n\n\"What a wonderful idea.\" I made a mental note to add lying through my teeth to the list of things I needed to seek forgiveness for when I said my nightly prayers. \"You never can tell these days.\"\n\n\"My thoughts exactly.\" She leaned even closer. \"That woman called him a good many names that nearly curled my hair, I can tell you.\"\n\nI'll bet they did. \"Shocking.\"\n\n\"It was indeed. I'm a woman of a delicate constitution, and I wasn't raised to use such language.\" She fanned herself. \"Then she said she'd never asked him for anything in her whole life and wouldn't be asking now if it wasn't a matter of life and death, but there was nothing she wouldn't do for Isabelle.\"\n\n\"Really?\"\n\nShe nodded vigorously.\n\n\"What happened next?\"\n\nHer expression changed to one of disappointment. \"That's when the man, Max, noticed me standing near the bus and called me a busy old broad and accused me of deliberately listening in on his conversation.\"\n\n\"The nerve of the man.\" I managed to avoid laughing by digging my nails into my palms.\n\nShe nodded. \"My thoughts exactly. Why, I was just minding my own business and they were the ones fighting in the streets like common hooligans.\"\n\nI nodded my agreement.\n\n\"Did you tell the police about this?\"\n\nSarah Jane Howard looked as though I had slapped her. \"Of course not. I'm not one to gossip and I certainly was never raised to have dealings with the police, especially after the last time when that man was murdered here. Why, I had people call me a nosy busybody.\" She bristled. \"I can tell you, I made up my mind then and there, that I would never get involved with the police again.\"\n\nApparently, Max had waved her off and she hadn't even been able to get on the bus and get her gloves, which she attributed to her current arthritic distress. She didn't have anything else of value to add and I managed to slip away with the excuse I needed to find my grandmother.\n\nI walked away to find a quiet place to think. All the time, I wondered who the lady in the floppy hat really was and who was Isabelle? Could the floppy hat lady have actually threatened to kill Max Franck? Was it his death she was talking about? Or, was someone else in danger?\nChapter 8\n\nMy mind was reeling with all of the information I'd found and I needed to think. I sent Nana Jo a text message and learned she had just tracked down Velma Levington and would \"corner her,\" her words, not mine, to get what she could out of her.\n\nI walked the short distance to Nana Jo's villa and let myself inside. As much as I enjoyed Gaston's food, I needed a little quiet to sift through everything I'd heard.\n\nAt Nana Jo's, I found a can of vegetable soup in the cabinet. I heated it and made myself a peanut butter and jelly sandwich. Nana Jo's beverage selection was limited to alcohol, coffee, and Coke, but I found a shriveled-up lemon and made a glass of lemon ice water. One of the best features of Nana Jo's house was the unobstructed view she had of Lake Michigan. I put my food on a tray and sat in the sunroom at the back of the house where I could curl up on the window seat and eat and enjoy the view and think.\n\nBefore I could take my first spoonful of soup, my phone rang. When I glanced at the picture that popped up, I smiled. Lexi and Angelo stared back at me.\n\nI quietly swiped the phone and smiled. \"Hello, how are you doing?\"\n\nLexi and Angelo were both excited and talked quickly and simultaneously, so it was hard to distinguish what they were saying, but it didn't really matter. The sound of their voices was far more important to me than the actual words being spoken. Both were happy and that was the important thing.\n\n\"You've met your cousins, already?\"\n\nLexi and Angelo were orphaned when their parents were killed several years ago in a car accident while on a trip from New York to Chicago. Unfortunately, their relatives in Italy had no idea where the children were. Both were too young to remember their family roots extended to Italy, although they both spoke Italian. When the pair landed in Frank's restaurant, he'd used his connections to discover the history none of the governmental agencies had been able to find. The grandparents had been so excited when they learned the children were alive and well. They had immediately flown to the States. The plan was the grandparents would spend the week in the States getting reacquainted with them before taking them back to Italy after the new year. However, it appeared, the grandparents weren't the only ones who'd traveled to the United States. If Angelo was to be believed, he had lots of cousins who had flown over, and he was enjoying playing with them and teaching them English.\n\n\"That's great. I'm so excited for you both.\" I tried to keep the sadness out of my voice. It really was a wonderful thing that the pair would be reunited with family. Their foster family in Chicago had been horrible and I didn't relish the idea that they would ever have to see that couple again.\n\nOur call was short. Both children merely wanted to say hello and it warmed my heart to hear their voices.\n\nWhen we disconnected, I cried a bit and then pulled myself together and reheated my soup in the microwave.\n\nAfter I ate, I sat on the window seat, looking out the window, and pulled my notepad out of my purse. I jotted down notes from my conversations with Caroline Fenton and Sarah Jane Howard, while they were still fresh in my mind. I tried to make sense of what I'd learned, but, after about twenty minutes of doodling, I gave up and decided to do something else to help organize my thoughts.\n\nWriting British historic cozy mysteries had been a dream of mine for a long time. After my husband's death, I realized life was too short to keep dreams bottled up and had pursued not only our shared dream of opening a mystery bookstore but my dream of being a published author. Nana Jo was the one who first helped me realize that writing allowed my subconscious mind to sort through the details of what I was dealing with in real life. So, I decided a little writing might help me make sense of things.\n\nLady Elizabeth Marsh picked up the receiver of the telephone and had barely finished with her greeting before Desmond Tarkington interrupted.\n\n\"Lady Elizabeth, I hate to bother you at this late hour, but as you can imagine, the tragic accident that has led to the death of my beloved cousin has left me bereft.\"\n\nLady Elizabeth struggled to keep the irritation out of her voice. \"I'm very sorry to hear that, but I hardly see how I\u2014\"\n\n\"I've heard from Mrs. Sanderson, how incredibly helpful your ladyship was during the last hours of her life. I was hoping you might be able to provide some comfort during our time of mourning and would consider a trip to Battersley Manor.\" He paused briefly before hurrying on. \"Or I would be more than happy to make a trip to Wickfield Lodge, if that would be more convenient.\"\n\nShe was silent for several moments. \"Actually, I promised Eleanor I'd stop by Battersley, and I like to keep my word. So, if it's convenient, I'd prefer to come there.\"\n\nDesmond Tarkington was ecstatic to entertain her ladyship and spent several minutes thanking her for her kindness, generosity, and compassion to condescend to visit his humble abode.\n\nLady Elizabeth confirmed the plan to visit Battersley Manor the next day and hung up the phone. She paused for a brief moment before entering the library. She searched for a few moments until she found the book she wanted and then pulled it down from the shelf. It was a favorite by Jane Austen, Pride and Prejudice. Lady Elizabeth flipped through the pages of the much-read novel until she found the passage she wanted. She smiled to herself while she read.\n\nLord William watched his wife in silence. When she was done, he asked, \"What could that Desmond Tarkington fellow possibly want at this time of night that would draw you to Jane Austen?\"\n\nLady Elizabeth returned to her seat and picked up her knitting. \"He called to invite me to Battersley Manor.\"\n\nLord William stared at his wife in shocked silence for a moment before blustering. \"You can't be serious. What nerve. I hope you sent him away with a flea in his ear.\"\n\nLady Elizabeth smiled. \"Actually, I accepted his invitation.\"\n\nShocked speechless, Lord William stared at his wife in disbelief. \"You can't go . . . why . . . this is ridiculous. I won't stand for it.\" He slapped his leg, which was propped on the footstool, causing the duke to clench his jaw in pain.\n\n\"I'll be fine, dear. No need to worry. I shan't go alone, and I certainly won't be staying in that house. I looked up Battersley Manor, and it's very close to Dinsmore.\" She stared at her husband. \"You remember Dinsmore is where Lady Alistair goes to take the waters. I think I'll ask her to accompany me.\" She stopped knitting and thought for a moment. \"Maybe I'll even take Clara with me.\"\n\n\"Disgusting odor.\" He frowned.\n\n\"I know the mineral baths do have a rather potent odor, but many people swear by them.\"\n\nLord William was familiar enough with his wife to realize when she'd made up her mind. \"Well, it's clear you can't go unaccompanied. I'll just have to go with you.\"\n\nLady Elizabeth smiled fondly at her husband. \"Don't be ridiculous, dear. You can't possibly travel with your gout.\"\n\n\"Maybe I'll take the waters,\" he blustered.\n\n\"Excellent idea. We can ask Thompkins to come and bring a chair to wheel you to the baths.\" She smiled at her husband.\n\nLord William muttered and folded his arms.\n\nLady Elizabeth smiled fondly at her husband. She knew her husband would rather have his leg amputated before he would allow himself to be wheeled around.\n\nLord William started to protest but was stopped when Lady Elizabeth said, \"However, I may ask Detective Inspector Covington to join us. I'm sure even policemen must be able to take a holiday sometimes.\" She knitted while smiling.\n\n\"If you're going to do this, maybe you can at least humor me and tell me what that young man could possibly have said to you that caused you to consult Pride and Prejudice?\"\n\nLady Elizabeth smiled. \"Nothing, really. I just thought I recognized some of the flowery language used by Desmond Tarkington as belonging to Mr. Collins.\"\n\nLord William gaped at his wife. \"Mr. Collins?\"\n\nLady Elizabeth nodded. \"Yes, I think Mr. Desmond Tarkington must be, like Mr. Collins, one of the stupidest men in England.\"\n\nChapter 9\n\n\"Sam,\" Nana Jo yelled in my ear.\n\nI nearly jumped out of my skin. \"My God.\" I placed my hand over my heart in an attempt to slow its rapid pace. \"I didn't hear you come in.\"\n\n\"I gathered as much.\" Nana Jo smiled. \"Especially since I've been calling you for a good five minutes.\"\n\nI felt confident Nana Jo was exaggerating, but I was still unnerved from the scare she'd given me, so I didn't take the time to argue.\n\n\"We're picking up the girls in front of the main building in fifteen minutes.\" She stood over me. \"You better shake a leg.\"\n\nI took my dirty dishes into the kitchen and prepared to wash them when Nana Jo stood over my shoulder. \"What're you doing?\"\n\nI wondered if this was a trick question. \"I'm washing my dishes.\"\n\n\"I know that.\" She swatted my arm. \"Why are you washing dishes when I have a machine built for that exact task.\" She waved a Vanna White hand in front of the dishwasher and then opened the door.\n\n\"It's just a couple of things. It hardly seems worth it to run a full load and waste water for these few items.\"\n\nNana Jo grabbed the items and loaded them into the dishwasher. \"I don't have to waste water. I just load the dishes and when the dishwasher is full, I turn it on.\"\n\nThere were already a few items in the dishwasher, so I shrugged and packed up my notebook.\n\nI walked to the car and drove to the front and picked up the others, who were waiting in the lobby.\n\n\"Where to?\" I glanced in the rearview mirror as I pulled away from the building and headed toward the gate.\n\n\"I've got a taste for seafood. Let's go to The Catch,\" Nana Jo said.\n\nThere were no disagreements, so I headed toward downtown. The Daily Catch was the restaurant's real name, but locals always shortened it to \"The Catch.\" It had good food and a 1970s-themed d\u00e9cor, which was somewhat off-putting to tourists until they tasted the food. It was located on the inlet where the St. Thomas River met Lake Michigan. Inside, if you looked in one direction, you saw the boats docked on the river. If you looked in the other direction, you had an excellent view of the beach and the Lake Michigan shoreline. The restaurant needed an update. However, every time I went, I was glad it hadn't been done. I loved the retro style.\n\nI let my passengers out at the door and parked. Timing was everything, and I lucked into a parking space near the door. Inside, I saw Nana Jo and the girls seated near the window that faced the river. The booths were large, with high-backed wooden seats that resembled church pews. The seat backs were so tall, it was impossible to see people behind you, but conversations could easily be overheard if you weren't careful. During my last visit, I left with bruises from banging my head and elbow on the wood benches while trying to eavesdrop on someone I suspected might have been a murderer.\n\nOne of The Catch's signature attractions was their handmade onion rings, which they brought out on a large spindle. Nana Jo usually ordered two spindles whenever we came. So, when the waiter came, I just ordered an ice water with lemon.\n\nOnce I was settled, Nana Jo pulled out her iPad. \"Now, I know we all collected a lot of information so we better get started.\"\n\nI raised my hand and relayed the information I learned from Caroline Fenton, along with the information from Sarah Jane Howard.\n\nNana Jo took notes. \"Do you think the woman Sarah Jane saw arguing with Max was the same woman we saw him arguing with in the bookstore?\"\n\nI shrugged. \"I have no idea. Part of me thinks it has to be the same woman. How many different women could he have ticked off in one day?\"\n\nNana Jo smiled. \"At this rate, that list could be fairly long.\"\n\nRuby Mae raised her hand to go next. \"I didn't learn much from any of the people from Shady Acres who were on my list.\" She pulled out the knitting she was rarely without. Tonight, she was knitting a pink baby blanket for one of her countless relatives. Ruby Mae Stevenson was my favorite of all of Nana Jo's friends. In her mid-sixties, she was also one of the youngest. Ruby Mae was an African American woman with dark skin that reminded me of coffee with a touch of cream. She had salt-and-pepper hair that she wore pulled back at the nape of her neck in a bun. Nana Jo said when she let her hair down, it reached down so far, she could sit on it, but I'd never seen it down. Ruby Mae was born in Alabama and had a soft Southern accent. Her story was an interesting one. She moved to Chicago in the early sixties to live with her older sister when both of her parents were killed in one of the civil rights marches. She had just graduated from high school. She met and married a plumber who walked out and left her to raise their nine children single-handed. Ruby Mae cleaned houses to feed, clothe, and educate her children. She was proud of the fact that all nine of them had graduated from college and were very successful. While I knew she was proud of all of them, I suspected her youngest daughter held a special place in her heart as she had started her own cleaning business. Ruby Mae was retired, but she had a host of grandchildren, nieces, nephews, and friends who always stopped to talk to her wherever we went. Tonight was no different. One of the cooks came over to the table and gave Ruby Mae a big hug. They chatted for a few minutes and Ruby Mae introduced him as her cousin's boy Carl. Carl greeted us and quickly hurried off to continue working. However, when several plates of appetizers showed up, which we didn't order, we knew Carl had been busy.\n\nThere were so many appetizers that we didn't bother to order entrees. Instead, we munched on seafood tacos, onion rings, crab cakes, crab stuffed mushrooms, calamari, and a few other items that looked and smelled delicious, but I was too full to try.\n\nRuby Mae put away her knitting while she ate, but when she was full, she wiped her hands and pulled out her knitting, which I suspected helped her think. She picked up the conversation right where she left off. \"Like I said, I didn't get much out of the people on my list from Shady Acres. None of them saw or heard anything. But remember I told you my third cousin Darius worked at the Chicago Sun-Times.\" She knitted a row and updated the row counter on the end of her needles. \"Darius knew exactly who Max Franck was. Apparently, the man was a legend around Chicago. We've already found out most of what Darius told me. He won a lot of awards and had written several books. But Darius found someone who knew Max personally and he found out he had a tumultuous relationship with his ex-wife and his daughter, Rosemary.\"\n\n\"Great. I sure hope he gave you a description of the girl.\"\n\nShe shook her head. \"No, but he's going to email me some articles from the newspaper, so if there's a description or picture of her in any of them, I'll send them to everyone.\"\n\nWe nodded.\n\n\"Apparently, Max Franck was so obsessed with his career, he neglected his family. His wife divorced him and moved out with their daughter.\" She looked over her glasses at us. \"According to Darius, it took Max about six months before he even noticed.\"\n\n\"That's horrible,\" Irma said. \"That dirty piece of sh\u2014\"\n\n\"Irma!\" we all said.\n\nIrma coughed.\n\nWhen the commotion died down, Ruby Mae continued, \"Well, recently, Rosemary reached out to someone at the newspaper, asking if they knew where her father was.\"\n\n\"How sad she had to ask someone,\" Dorothy said.\n\nRuby Mae nodded. \"They didn't know but, apparently, she said her daughter has some rare disease and needs a bone marrow donation. Neither she nor her husband are matches.\"\n\n\"The poor little girl. Where's the mother, Max's ex-wife?\" Nana Jo asked.\n\n\"Dead.\" Ruby Mae shook her head. \"So, out of desperation, she was trying to track down her father to see if he would consent to be a donor.\" She pursed her lips. \"Although, he seemed like the type who was too wrapped up in his own career to think about anyone else. The poor child.\" Ruby Mae shook her head.\n\nWe sat in stunned silence for several moments.\n\n\"Well, on that sad note, I might as well go next,\" Dorothy said. \"I didn't have a lot of luck with my Shady Acres list either. However, I did get one bit of information from Earl.\"\n\nRuby Mae frowned. \"Who's Earl?\"\n\n\"Earl, the bus driver who drove us to Chicago.\" Dorothy fidgeted with her napkin.\n\n\"And how did you happen to run into Earl?\" Nana Jo asked.\n\nDorothy blushed. \"Well, Earl and I spent some quality time together one night in Chicago.\"\n\nNana Jo clucked her tongue but said nothing else.\n\n\"Anyway, I was curious what happened to him. He did have a family emergency. His brother's appendix burst and he had to be rushed to the hospital.\"\n\n\"Is he okay?\" I asked.\n\n\"Fortunately, he is.\" Dorothy released a sigh of relief. \"Anyway, he was in a real pickle about driving us home. So, they had to get someone at the last minute to fill in.\" She paused.\n\n\"Well, what's wrong with that?\" Nana Jo looked up.\n\nDorothy smiled. \"The problem was, they didn't have time to go through all of the new procedures the board put in place after the debacle with the former administrator, Denise Bennett. She hired him, but no one double-checked his background until after he got back. Turns out Bob, our replacement driver, is an ex-con.\"\n\n\"Good Lord. Did Denise Bennett hire anyone who wasn't a criminal?\"\n\nWe all shrugged.\n\n\"What was he in jail for?\" I asked.\n\nDorothy leaned forward. \"Armed robbery and murder.\"\nChapter 10\n\nDorothy dropped that bombshell and everyone immediately started firing questions at her. She held up her hands to fend off the onslaught. \"Hold on.\" She turned to each person and responded to the questions she'd heard asked. \"I don't know who he murdered. I don't know how long he was in prison. Nor do I know why Shady Acres would hire a murderer to drive our bus.\" She took a deep breath and turned to Nana Jo. \"I was hoping Josephine could get Freddie to look it up.\"\n\nNana Jo, normally anxious to volunteer Freddie to use his influence or his son's to get information, was abnormally quiet. \"I'll try, but his son, Mark, had to take the family to his in-law's in upstate New York for the holidays.\"\n\nI raised my hand. \"I might be able to help.\"\n\nEveryone turned to me.\n\n\"I forgot to mention it, but I stopped by the police station and talked to Detective Pitt.\"\n\n\"What's Stinky Pitt been up to?\" Nana Jo asked.\n\n\"I think he's a bit bored.\" I told them about my conversation and our deal.\n\n\"Why, the lazy parasite,\" Nana Jo said. \"He's going to sit back and let you solve another murder for him while he takes all of the credit.\"\n\nI could feel my grandmother's blood pressure rising. \"Hold on. Let's be fair. Technically, this isn't his murder. It didn't even happen in the state of Michigan.\"\n\nNana Jo reluctantly agreed.\n\n\"Plus, he's going to be providing us with information we probably couldn't get anywhere else.\" I stared at her. \"Besides, the last thing I want is 'credit' for solving anything.\"\n\n\"Well, okay, if you're going to put it like that, then I take back what I said.\" Nana Jo huffed.\n\nI pulled out my notepad and made a note to ask Detective Pitt about Bob the bus driver.\n\nNana Jo was the last to report. \"I didn't find out a lot of information. Most of the people on my list were too busy answering the call of nature and didn't go near the bus until it was time to board.\" She looked disgusted.\n\n\"Well, you can't blame them for that,\" I said.\n\n\"Pshaw.\" She snorted. \"I certainly do blame them. People should be more interested in their surroundings and their fellow man.\"\n\nI took a sip to avoid laughing.\n\n\"I didn't get much from Velma.\" Nana Jo sighed. \"Actually, I didn't get anything from Velma.\"\n\nIrma snorted.\n\n\"Did you say something?\" Nana Jo turned to Irma.\n\nIrma muttered something that sounded like \"cheap man-stealing witch,\" but she broke out in a coughing fit and I didn't want to aggravate her throat unnecessarily by asking her to repeat herself.\n\n\"I thought you went to the jujitsu class specifically so you could talk to her?\" I asked.\n\n\"I did.\" Nana Jo raised her hands.\n\n\"Well, what happened?\" I asked.\n\nShe shrugged. \"I tried several times to partner with her, but she always had another partner before I could get to her. Then, when we had our break, I made sure I was right beside her and I tried to strike up a conversation, but the woman is deaf as a doormat. She couldn't hear one single word I said. When class ended, she rushed out of that room so fast, I nearly got whiplash from watching her.\"\n\n\"Harrumph.\" Irma grunted. \"There's nothing wrong with that woman's hearing. She's got ears like a bat.\"\n\nNana Jo looked skeptical.\n\n\"I'll bet if a single man whispered his telephone number in the middle of gale force winds, she'd catch every digit.\" Irma folded her arms and glared.\n\nRuby Mae grinned.\n\n\"Sounds like someone else we know,\" Dorothy joked.\n\nNana Jo narrowed her eyes and stared at Irma. \"Are you sure?\"\n\nIrma nodded. \"I promise you. There's nothing wrong with Velma's hearing.\" She used her finger to cross her heart and then confirmed her pledge by holding up three fingers in the Girl Scouts' salute.\n\n\"I guess I'm going to have to work harder to corner Velma.\" Nana Jo looked thoughtful.\n\nI recognized that look and felt a momentary pang of pity for Velma. My grandmother was taking this as a challenge and Josephine Thomas was a competitive woman who didn't like losing; even if the loss was only in her mind. I suspected Nana Jo's next encounter would end very differently than the last one.\n\n* * *\n\nWe chatted a bit, and then I drove back to Shady Acres. Irma wanted to go to a bar to have a drink to memorialize Max, or so she said, but I suspected that was merely an excuse to party a bit. However, maybe I was being uncharitable. We vetoed Irma's request and I drove them back to Shady Acres.\n\nI pulled up to the main building as usual and let the girls out, which was expected, but my surprise came when Nana Jo got out.\n\n\"Are you staying at your place tonight?\"\n\n\"I'm going to corner that Velma Levington if it kills me.\" She stared at me. \"Do you need my help at the bookstore?\"\n\nI shook my head. \"No. Zaq and Christopher have everything under control.\"\n\nShe nodded, then looked closely into my eyes. \"Are you sure you don't need my help?\"\n\n\"I'll be fine. I'll probably talk to Stinky Pitt and see what I can find out. I'll see you at the meeting tomorrow night.\"\n\nWe had agreed to skip our noon meeting and meet for dinner instead. Shady Acres was preparing for the big New Year's Eve party and everyone was signed up to help. They were going to use that as another opportunity to collect information.\n\nNana Jo accepted my response, and we parted with me promising to call if I needed her.\n\nAs I pulled away, I got a call from Frank. One of the things I loved about my new-to-me Ford Escape was Bluetooth, which enabled me to talk without holding my phone.\n\n\"Hey, beautiful.\"\n\nI smiled even though he couldn't see me. \"Hey, yourself.\"\n\n\"I'm thinking about taking a day off tomorrow and wondered if I could cash in that rain check you gave me.\"\n\n\"Time off during the day? I don't think you've done that since I met you.\" I laughed.\n\n\"I think I'm getting burned out working such long hours. I took Nana Jo's advice and hired an assistant.\"\n\nI laughed. \"Nana Jo was joking, but I think it's great. I knew you were looking for someone, but I didn't know you'd finally found someone you could trust.\"\n\n\"It wasn't easy, but actually, an old buddy of mine from my military days reached out and mentioned he was looking for a new start. He's a Catholic priest but needs a break, so . . . he's looking for someplace quiet where he can think.\"\n\nFrank didn't talk much about his time in the military, and I knew better than to ask too many questions. However, I hoped I'd have an opportunity to meet his friend. \"So, you're starting him tomorrow?\"\n\nHe laughed. \"No. I wouldn't do that to him. The mornings are pretty light, so I hoped I could spend a little time with you and then I'd work the evening shift. He'll be at the restaurant tomorrow, but just as an observer.\"\n\n\"Sounds great.\" I got an idea. \"Hey, how do you feel about a quick trip to Chicago? There are a few people I need to talk to.\"\n\n\"I can't believe it. You're finally going to let me go sleuthing with you?\" he joked.\n\n\"Well, usually I have Nana Jo with me, so you'll have some big shoes to fill.\"\n\n\"I'll do my best to live up to the high standard your grandmother has set.\" He laughed. \"Actually, if you don't mind making a few extra stops, that would work out great. There's a restaurant distributor in Chicago and I could pick up a few things.\" He hesitated. \"That is, if it's okay with you?\"\n\n\"Of course.\"\n\nWe talked a bit more about tomorrow. By the time we hung up, I had made it home.\n\nI took care of Snickers's and Oreo's immediate needs, which included a potty break and treats, and then I went upstairs.\n\nI checked my email and was pleasantly surprised and a bit terrified to see an email from my agent, Pamela Porter, at Big Apple Literary Agency. For some reason, whenever I opened emails from her, my heart raced. I took a deep breath and clicked open.\n\nThe email was an update letting me know she'd just heard from one of the editors she'd sent a query about my manuscript. He requested a full. I met my agent briefly when I was in New York after Thanksgiving and received a crash course in the lingo. She'd explained a query was a high-level pitch about my book. If an editor was interested, they might request to read a partial, a specific number of pages or chapters, or a full, which was a request to read the entire manuscript. She cautioned me that this was a good thing but not to get too excited. He may still reject the manuscript and the timing was horrible because most of the publishers were closed for the holidays. However, she told me to remain \"cautiously optimistic.\"\n\n\"Cautiously optimistic?\" I picked up Snickers. \"She has got to be joking.\" I spun around in a circle and did a happy dance. Oreo pawed at my leg, but he wasn't nearly as good a dancer as Snickers. Nevertheless, I picked him up and did a two-dog happy dance. As soon as I stopped, he leapt out of my arms and gave himself a shake.\n\nSnickers clung to my shirt for dear life. When she was sure I'd stopped spinning, she gave my face a lick.\n\nI put her down and went back to my laptop. \"My first full.\" I couldn't stop smiling, and knew I was too excited to sleep now. I said a silent prayer he, whoever he was, would like my manuscript and decided to spend a few hours in the British countryside. Maybe a few hours with Lady Elizabeth Marsh would help me make sense of Max Franck's murder.\n\n\"Aunt Elizabeth!\" Lady Clara Trewellen-Harper ran to her cousin and engulfed her in a warm embrace.\n\nLady Clara was tall, slim, and stately. She had light brown curly hair, intelligent eyes, and a quick smile.\n\nLady Elizabeth smiled. Her cousin Mildred's daughter had always called Lady Elizabeth, Aunt Elizabeth. She'd grown up with Daphne and Penelope and picked up the habit from them. Lady Elizabeth hadn't minded and the familiar moniker had continued into adulthood.\n\nShe embraced her cousin warmly. \"Hello, Clara. I'm so glad you were able to come.\"\n\n\"Wild horses couldn't have prevented me from joining in on the fun.\"\n\nLady Elizabeth withdrew from her young cousin and smiled broadly. \"Detective Inspector Covington. Thank you so much for coming.\"\n\nThe detective inspector stepped forward and tipped his hat. \"I had holiday time to use by year's end, so it worked out well.\" He smiled. \"Plus, I like to keep an eye on things.\"\n\nLady Elizabeth turned to her cousin. \"Clara, dear. I want you to meet a good friend of mine.\" She smiled warmly. \"This is Detective Inspector Covington.\" She turned to the detective. \"This is my cousin Lady Clara Trewellan-Harper.\"\n\nLady Clara's eyes widened and she smiled warmly at the detective. \"A real policeman. How delicious.\"\n\nDetective Inspector Covington smiled, tipped his hat, and bowed slightly. A careful observer would note the detective's eyes held a sparkle and a slight blush rose up his neck.\n\nLady Elizabeth was just such a careful observer.\n\n\"Please call me Clara.\" Lady Clara extended her hand to the detective.\n\nThe detective inspector shook her hand but said nothing.\n\nAfter an awkward moment of silence, Lady Elizabeth turned to her cousin. \"Do you have luggage?\"\n\nLady Clara turned and noted a porter struggling with several large pieces of luggage. \"There's the porter now.\"\n\nLady Elizabeth smiled and led the small party through the small Dinsmore rail station and outside to the curb, where a car waited. Standing stiffly beside a Rolls-Royce Wraith was Thompkins, the Marsh family butler. He opened the rear car door.\n\nLady Clara smiled at the butler as she folded herself into the back. \"Thompkins, I didn't know you were coming on this adventure too.\"\n\nThe butler bowed. \"Lady Clara.\"\n\nLady Elizabeth instructed the porter to load the luggage into the boot of the car. She then turned to the detective inspector. \"You're able to drive this beast, right?\" She extended a set of keys.\n\nDetective Inspector Covington looked stunned but nodded as he tossed his small duffle next to the driver's seat and accepted the keys. \"Yes, m'lady.\"\n\n\"Thank heavens. I don't think Thompkins's nerves can handle much more of my driving.\" She scooted into the back seat next to her cousin.\n\nOnce all the luggage was loaded, Thompkins tipped the porter and got into the front passenger seat of the car.\n\nDetective Inspector Covington started the car and took one moment to caress the wood dashboard, then he turned to the back. \"Where to?\"\n\nLady Elizabeth pulled a notepad out of her purse and read. \"I intended to stay at Dinsmore Inn, but as it turns out, Lady Alistair keeps a cottage here.\" She glanced at the notes. \"Hapsmere Grange.\" She looked up. \"She's graciously invited us to stay with her.\" She passed the directions up to the detective, who read them, put the car in gear, and pulled away from the curb.\n\nThe drive to Lady Alistair's cottage was short, only two miles from the train station. Despite the diminutive name of \"cottage,\" Hapsmere Grange was a seven-bedroom, three-storied mansion spanning over ten thousand square feet on fifty acres of land.\n\nWhen the car pulled up to the front, Lady Alistair Browning opened the front door and came outside to greet her guests.\n\nLady Alistair Browning was a tall, slender woman with piercing blue eyes and unnaturally blonde hair. She was always fastidiously dressed. Today she wore an elegant, and undoubtedly expensive, navy-blue, fur-trimmed suit with a matching cloche hat. The outfit was tubular with a drop waist. By her side was her companion, a Chihuahua named Bitsy.\n\nThompkins hopped out of the car as soon as the motor stopped and opened the back door to assist Lady Elizabeth and Lady Clara out of the car.\n\nDetective Inspector Covington stared at the large estate and whistled.\n\nThe women embraced and headed toward the door. Lady Alistair turned to Detective Inspector Covington. \"Nice to see you again, Detective Inspector.\"\n\nDetective Inspector Covington tipped his hat. \"Lady Alistair.\" He followed slowly behind, allowing Bakerton, Lady Alistair's stately but elderly butler to take his bag.\n\nLady Clara walked slowly behind the older ladies, allowing Detective Inspector Covington to catch up to her. \"I do hope you're going to be reasonable and at least talk to me.\"\n\nDetective Inspector Covington blushed. \"Of course, your ladyship. What would you like to talk about?\"\n\nLady Clara giggled. \"Why murder. What else?\" She stopped and grabbed the detective inspector by the arm. \"I intend to be a world-famous writer some day and this could be just the thing for me to write about. Everyone loves a good murder.\"\n\nDetective Inspector Covington smiled. \"Hardly a proper topic for a lady to write about.\"\n\nShe huffed. \"I can see you're going to be tiresome about that title.\" She dropped his arm and hurried ahead.\n\nStanding at the top of the steps, talking, were Lady Elizabeth and Lady Alistair. They chatted while inconspicuously glancing at the younger people.\n\nLady Clara flounced through the door. Moments later, Detective Inspector Covington followed, nodding to the ladies as he entered the house.\n\nHelene, Lady Alistair Browning, was the mother of James FitzAndrew Browning, the 15th duke of Kingfordshire and recently married husband of Lady Elizabeth's niece, Daphne. The women had known each other a long time, but the courtship and wedding had reconnected the women. Lady Alistair gave her friend a meaningful look.\n\nLady Elizabeth smiled. \"Give them time.\"\n\nChapter 11\n\nI woke up next morning with my head lying on my keyboard. I panicked for a moment, afraid I'd lost my manuscript. Thankfully, the document was still there, but there were 819 pages of gibberish where my chin rested on the keyboard. I deleted the excess pages and saved again to be safe.\n\nI looked at the time. I had about thirty minutes until the time Frank and I had arranged to meet. Strapped for time, I hurried the poodles downstairs and put them out. It was chilly, but they were wearing sweaters and I knew Christopher and Zaq would be here shortly. So, I left them out while I showered. By the time I was out of the shower, I heard them barking and knew the twins had let them inside.\n\nI still felt guilty about falling asleep on our date and considered putting on a skirt until I checked the weather app and saw it was eight degrees in Chicago. Instead, I put on jeans and a warm sweater. I took extra care with my hair and makeup. You could catch pneumonia trying to look cute in the winter in the Midwest.\n\nWhen I emerged from my bedroom, Frank was having coffee with Nana Jo at the breakfast bar.\n\nHe winked. \"Good morning, gorgeous.\"\n\n\"Good morning, handsome.\"\n\nNana Jo rolled her eyes. \"Good grief. Let's not start that again.\" She sipped her coffee. \"I can feel my blood sugar rising.\"\n\n\"Speaking of sugar.\" I turned to Frank. \"Did you remember to bring the cake?\"\n\nFrank helped me on with my coat. \"Yes. It's in the car.\"\n\n\"Cake?\" Nana Jo looked up with a hopeful expression.\n\n\"Sorry. It's spoken for, but Dawson left some cookie dough in the freezer.\" I turned to leave.\n\n\"Wait.\" I turned back around at the stairs. \"What are you doing here? I thought you were staying at Shady Acres to talk to suspects?\"\n\nShe sipped her coffee. \"When I got home, I remembered I had arranged to meet Elliott this morning. Your place is closer to MISU's library.\"\n\nElliott was a research librarian and one of Nana Jo's old beaus. He still held a torch for her, even though Nana Jo had moved on.\n\nI wished her well and hurried downstairs.\n\n* * *\n\nFrank navigated the Chicago traffic like a pro. About halfway there he asked, \"Where to first?\"\n\n\"Well, there's this mystery bookstore I'd love to visit. Then we can hit the restaurant supply store.\"\n\nFrank smiled. \"Let me guess. It's the mystery bookstore your grandmother pulled you out of the last time you were here.\"\n\nI smiled. \"Right the first time.\"\n\nFrank navigated city traffic much easier than our taxi driver and dropped me off around the corner from the Murder Between the Pages bookstore. He drove around in search of a parking space.\n\nInside, the building was warm and the smell of books and freshly brewed coffee greeted me like an old friend. I stopped and inhaled the familiar aroma as my gaze traveled around the store. The mystery lover in me admired the colorful stocked shelves and something deep inside my soul rejoiced at seeing the shelves full of tales of mayhem and suspense. I smiled. The bookstore owner inside me couldn't stop myself from looking critically at the dusty shelves, dimmed lighting, and water-stained roof. However, the allure of books overpowered the bookstore owner and I got lost.\n\n\"Can I help you find anything?\"\n\nI nearly jumped out of my skin. \"Dear God, you scared me.\" I was miles away in an Irish cottage following Alexia Gordon's enchanting sleuth, Gethsemane Brown, through the twists and turns of solving a murder.\n\n\"I didn't mean to frighten you.\" Linda Herald, the bookstore owner I met on my first visit, apologized.\n\nWhen my heart stopped racing, I smiled and reassured her I was fine.\n\n\"Samantha, right?\"\n\n\"You have a great memory.\"\n\n\"Not really. It's just that I don't meet many mystery bookstore owners.\" She smiled. \"Anything in particular you're looking for?\"\n\nI shrugged. \"I'm just browsing.\" I looked around. \"You have a lovely shop and I may steal some of your ideas.\"\n\nShe laughed. \"Feel free. I've probably stolen them from someone else.\"\n\n\"Do you remember a man and a woman having an argument in your loft the last time I was here? They got quite heated.\"\n\n\"Pity. That must have been Max Franck and his daughter, Rosemary.\"\n\n\"You know them?\" I tried to hide my surprise.\n\nShe nodded. \"Max Franck is a bestselling crime writer. He's done several book signings here.\"\n\nI leaned closer. \"You know he was killed?\"\n\nShe nodded. \"I saw it in the newspaper. I think he expected something like that. Well, maybe not murder, but he must have expected some type of trouble.\"\n\n\"What makes you say that?\"\n\n\"Why else would he have hired a bodyguard?\" She shrugged. \"You must have seen him. He was here at the same time Max and Rosemary were arguing. The big guy with the mirror sunglasses.\"\n\n\"I saw him. He was pretty hard to miss.\"\n\nShe gave a half shrug and adjusted some books on a nearby shelf. \"Actually, I think his agent or editor hired him, but I thought it was all just a big hoax.\"\n\nI must have looked as puzzled as I felt because she colored slightly and shrugged. \"Max was here for his last book signing about a week ago. His editor made a big deal about Max's next book. She stuck out her chest and puffed up her cheeks. 'This next book is going to blow the lid off the theories about who killed Robert Kennedy.' \" Linda tilted her head and gave a cocky chuckle. \" 'Max is in so much danger. I'm concerned for his safety. I've gone so far as to hire a professional bodyguard to protect him.' \"\n\nI stared for a few seconds and then realized my mouth was open and closed it.\n\nShe nodded. \"That's the same expression I had.\"\n\n\"You didn't believe him?\"\n\nShe thought for a moment and then shook her head. \"Honestly, I didn't believe him. At the time, I remember thinking it was a gimmick to get publicity and increase book sales.\" She sighed. \"I mean, if you wanted to hire a bodyguard, why hire someone so . . . I don't know . . . so . . .\"\n\n\"Obvious,\" I volunteered.\n\n\"Exactly. I mean, he was so big and those mirrored sunglasses were over the top.\" She paused. \"I guess maybe he was right. Maybe it wasn't just hype.\"\n\n\"Max was here a week ago?\"\n\n\"Christmas Eve.\" She hurried to the counter and came back with a brochure. \"This is the brochure advertising the book signing.\"\n\nI quickly read over the brochure. \"May I keep this?\"\n\n\"Of course. They'll just go in the trash now.\"\n\n\"So, if Max was here Christmas Eve, why was he back the day I saw him here?\"\n\n\"He said he forgot something,\" she said hesitantly.\n\n\"He said? You didn't find anything?\"\n\nShe shrugged. \"Only the brochures. I offered to mail whatever it was to him, but he wanted to get it himself.\"\n\n\"Did he say what it was?\"\n\nShe shook her head. \"No, but when he came in, he went up to the loft area.\" She pointed to the area where I'd seen Max on the day he died.\"\n\n\"Why was he arguing with his daughter? Rosemary is his daughter, isn't she?\"\n\nShe nodded.\n\nSomeone entered the store and she excused herself to go and check on her customer. However, they must not have needed assistance because she returned quickly. \"Sorry about that.\"\n\n\"No need to apologize. Customers come first.\"\n\n\"Where were we?\" She was silent for a moment. \"Rosemary. I think he must have arranged to meet her here because she came not long after he arrived.\"\n\n\"Do you know why they were arguing?\"\n\nShe shook her head. \"Honestly, I wasn't paying attention.\"\n\nWe chatted a little longer, but her customer selected a book and was waiting at the counter.\n\nFrank had entered the store while Linda and I were talking but had maintained a discrete distance. I found him glancing through a thriller near the back of the store.\n\n\"Find something you like?\"\n\nHe grinned and the look he gave me made the heat come up my neck.\n\nI giggled. \"I'm talking about the book.\"\n\nHe returned it to the shelf. \"I like to patronize my local mystery bookstore.\" He leaned close and whispered, \"I'm kind of sweet on the owner.\"\n\nI grinned. \"I hear she's kind of sweet on you too.\"\n\nI waved at Linda Herald as we left the store.\n\nFrank had found a great parking space a block away and we were quickly on our way to the restaurant supply store.\n\nSimilar to the way I could spend hours in a bookstore, Frank could spend hours looking at ginormous pots, pans, and commercial bakeware. I wandered around while he picked out the items he wanted. Surprisingly, we were on our way in less than an hour.\n\nBack hatch fully loaded, Frank got into the car and turned to me. \"Where to now?\"\n\nI pulled out the list Caroline Fenton gave me with the names and addresses of the bus passengers. I looked for Rosemary Lindley's name and saw she lived in Lake Forest. I went to college in Evanston, Illinois, so I was familiar with many of the suburbs and recognized the city as one of the more exclusive areas where a lot of professional athletes bought large homes. \"Rosemary Lindley is Max Franck's daughter.\" I glanced down the sheet.\n\n\"How are you going to question her?\"\n\nI smiled. \"That's why I asked you to bring your delicious sour cream cake.\"\n\nHe chuckled. \"I should have known you weren't planning snacks for us to enjoy.\"\n\n\"If we run into traffic like we did the last time I left Chicago, we might have to dig into that cake and pick up some flowers for the grieving daughter,\" I joked.\n\nTraffic cooperated and we made it to Rosemary Lindley's home midmorning.\n\nAs I suspected, the suburb was north of Chicago, not far from the northern border of the state. The street was called Lake Road, and we got a glimpse of Lake Michigan through the trees as we drove.\n\nFrank pulled his car in front of the address his GPS indicated was our final destination, and we sat outside and admired the architecture. Rosemary Lindley lived in what I could only describe as a large brick mansion. The homes on this street were all massive and set on enormous lots well away from the street. Mature trees shaded the yards and, combined with the lush landscaping, created an atmosphere that screamed wealth. Unlike Chicago and the immediate suburbs, where houses were conjoined to each other or so close together you could stand between them, extend your arms and touch them, these homes were much farther apart. The lawns were vast and landscaped to provide maximum privacy from prying eyes, while providing the owners with plenty of elbow room.\n\nRosemary Lindley's house had a semicircular drive with brick pavers that looked wider than the interstate we'd just exited. The front fa\u00e7ade had three arches, which welcomed invited guests and intimidated the uninvited.\n\nI wasn't easily awed by ostentatious demonstrations of wealth, but this house was impressive. I was grateful Frank drove. His Porsche fit perfectly with the neighborhood whereas my Ford Escape would have been a red flag to the neighbors that we didn't belong and to call the police.\n\nHe whistled. \"Looks like Max Franck's daughter did pretty well for herself.\"\n\nI stared at the brick and stone mansion for a few seconds and then took a deep breath and opened my door. \"Let's do this before I lose my nerve.\" For a half second, I wondered about the many ways money could intimidate but decided it would only work if I allowed it to.\n\nWe got out of the car and Frank handed me the cake he had brought. Together, we walked through the middle archway to the large, double front door. Once there, I quickly rang the doorbell before my nerves came back.\n\nI expected a butler or maid to answer but was pleasantly surprised when a woman, who was obviously the homeowner, answered.\n\n\"May I help you?\"\n\n\"My name's Samantha Washington and this\"\u2014I pointed to Frank\u2014\"is Frank Patterson. We were acquainted with your father and\u2014\"\n\n\"If you're friends of my father, you can just go to hades, where I'm sure you'll no doubt run into him.\" She stepped back and prepared to push the door closed but was halted as Frank put out a hand and stopped the door.\n\nShe flushed from her angry outburst and, like the steam in a teakettle, looked as though she was revved up for an explosion.\n\nI quickly collected my wits. \"Mrs. Lindley, I didn't say I was friends with your father. In fact, I barely knew him. However, I was acquainted with him and I wanted to provide my condolences to you and your family.\" I extended my peace offering. \"I hope you'll accept this cake.\" I turned to Frank. \"Frank Patterson is an excellent chef and owns a small restaurant in North Harbor, Michigan.\" I thrust the cake into her hands. \"Or, if you prefer not to eat it, maybe you would give it to someone else at a hospital or nursing home rather than let it go to waste.\" I nodded to Frank and turned to leave.\n\nWe were down the stairs before she spoke.\n\n\"Wait. Please. I'm so sorry.\"\n\nWe turned around.\n\n\"Please, I'm sorry. Won't you come inside?\"\n\nFrank looked at me. I shrugged and we returned to the door.\n\nShe stepped aside and we entered.\n\nIf I thought the house was impressive on the outside, the inside was even more so. We entered the two-story foyer with black and white marble tile floors and a chandelier overhead. There was an elegant curved staircase that led upstairs and, to the right, a curved doorway led to a wood-paneled room that looked like a study. I would have loved to explore the library but followed my host to the left to a formal living room.\n\nThe first home that Leon and I bought would have fit in that one room. The room was furnished with traditional sofas, chairs, and dark wood tables. A marble fireplace was centered in the middle of one of the walls, with doorways on either side. The back end of the room had a curved window and built-in window seat that looked out onto the backyard, pool, and, through the distance, the faint blue of Lake Michigan.\n\nAs we were about to sit, a faint voice called, \"Mom.\"\n\nMrs. Lindley paused. For a split second, she hesitated, but only for a split second. Her loyalties were clear. She handed me back my cake. \"Excuse me.\" She hurried out of the back of the room.\n\nFrank and I glanced at each other.\n\n\"I'm going after her.\" I passed the cake to him and hurried after Mrs. Lindley, straining my ears to hear conversation. The house was so large; I was afraid I'd get lost. I went through a massive kitchen, which would have made Frank drool with envy, before I heard two voices.\n\nI peeked into a long, narrow sunroom on the back of the house. The room had one wall of windows and French doors that led outside. The floor was blue and white tile, and the d\u00e9cor continued the theme with blue-and-white striped sofas and comfortable chairs. Sitting on one of the sofas, covered in blankets, was a small, thin little waif of a girl with large, dark eyes. She looked very pale and frail.\n\nThe girl was connected to several machines. One provided a drip that went into her arm. Oxygen tubes went into her nose.\n\nMrs. Lindley adjusted one of the machines, which was beeping, and had her back to me.\n\nThe girl looked up and caught sight of me. I backed up and turned to leave.\n\n\"No, please.\"\n\nI turned and saw the girl smiling at me.\n\n\"Please. I don't get much company.\"\n\nI smiled and took a few steps into the room. I hesitated and looked to Mrs. Lindley. \"I'm sorry. I didn't mean to intrude. I . . . I was just really curious about your beautiful house and I let my curiosity take control over my manners.\"\n\nMrs. Lindley shrugged. \"It's okay.\"\n\nI decided to take that as an invitation to stay and walked over toward the girl and smiled. \"Hello. My name is Samantha but everyone calls me Sam.\"\n\nShe smiled. \"I like that. My name's Isabelle, but everyone calls me Isabelle.\" She giggled. \"I wish I had a nickname.\" She glanced at Mrs. Lindley, who was replacing one of the fluid bags. \"Why don't I have a nickname, Mom?\"\n\nMrs. Lindley glanced lovingly at the girl. \"Don't you like your name? Isabelle was your grandmother's name.\" She placed the bag onto the hook and stood. \"Every time I say your name, it reminds me of her.\" She gently caressed the young girl's cheek.\n\n\"That's okay, then. I don't mind not having a nickname.\" She leaned back against her cushions. \"Can you stay a bit and talk to me?\"\n\n\"I'd love to.\" I looked at Mrs. Lindley.\n\nShe nodded.\n\nI smiled and moved to one of the comfortable chairs and sat down. \"Great.\" I looked at Isabelle and, for a moment, I was unable to think of anything to say. After spending more than two decades as a high school English teacher, I usually felt very comfortable talking to young people. However, this little girl with the big eyes had me dumbstruck.\n\nShe smiled at me again. \"Are you friends with my mom? Have we met before?\"\n\n\"No. Actually, I've just met your mom.\" I started to tell her I came to give my condolences but didn't know if hearing her grandfather was dead would upset her. I hurriedly shut my mouth.\n\nMrs. Lindley must have sensed what I was thinking because she relieved my mind by stating, \"Samantha came to tell me how sorry she was about your grandfather.\" She swallowed hard. \"She even brought a yummy cake.\"\n\nIsabelle's eyes got even larger and a huge smile illuminated her face. \"CAKE.\" She clapped her hands.\n\nFrank stuck his head around the corner. \"Did I hear someone say cake?\" He held up his cake.\n\nI looked to Mrs. Lindley, and she smiled and nodded.\n\n\"Why don't I take that and bring us some tea.\" She reached out her hands and Frank handed over the cake.\n\n\"This is my . . . friend Frank.\"\n\nFrank smiled and bowed to Isabelle.\n\nShe giggled.\n\nHe looked around and noticed a chessboard in the corner. \"Do you play chess?\"\n\nIsabelle nodded vigorously. \"I love chess, but my mom doesn't play and my dad isn't here.\" She looked sadly at the chessboard. \"My granddad played, but he's in heaven with my grandmother now. So, I don't have anyone to play with.\"\n\nFrank smiled and went to the corner, picked up the chessboard, and brought it to the table next to Isabelle. \"Well, you do now.\" He sat down and smiled. \"Black or white?\"\n\n\"White.\"\n\nHe spun the board around so the black pieces were in front of him. Then he removed his jacket.\n\nThe two of them talked quietly and were quickly engulfed in a game I never learned to appreciate. After watching for a few moments, I removed my jacket and went in search of our somewhat-reluctant hostess.\n\nI followed the clinking of dishes and the familiar sounds of water filling a teakettle back to the kitchen.\n\nMrs. Lindley opened multiple cabinets as she searched for the items she needed to fill the large tea cart on the granite counter.\n\nThe kitchen would have made a commercial chef like Frank extremely happy. While I was no expert, I recognized the distinctive red knobs that adorned the massive eight-burner stainless steel gas stoves. There were two of them. Glancing around the kitchen, I noticed there were also two refrigerators and an incredible amount of cabinets.\n\nA large island was situated in the center of the space, and I pulled out a barstool and perched on one of the stools. \"Your house is beautiful, Mrs. Lindley.\"\n\nShe continued collecting coffee mugs. \"Please, call me Rosemary.\"\n\n\"Thank you, Rosemary. I hope you'll call me Sam.\"\n\nShe put the kettle on the stove and turned to face me. \"I'm very sorry for the way I behaved earlier.\" She leaned against the cabinet. \"My father and I didn't have a very good relationship, but that's no reason for me to take out my anger on you.\"\n\n\"No apologies necessary.\" I thought for a brief moment. \"I didn't know your father. I only met him a few days before he died. However, he was very friendly with one of my grandmother's friends . . . with my friend Irma.\" I smiled. \"She was the reason he was on the bus to North Harbor. They were going to . . . spend some time together.\"\n\nRosemary laughed. \"You don't have to sugarcoat it. I know my dad fancied himself as a Don Juan. It's the reason he and my mother divorced.\" She smiled. \"My mom called him a tomcat.\"\n\nI smiled. \"My students would have called him a playah.\"\n\nShe laughed for a long time. \"I haven't laughed in a very long time.\" She sighed. \"I find it hard to think of my dad as anything as hip as that, but I suppose the label fits.\"\n\nThe kettle whistled and she turned off the stove and filled a teapot. \"Would you or . . . Frank, prefer coffee?\"\n\nI shook my head. \"Tea's fine.\" I hesitated. \"We're planning a bit of a memorial for your dad at Shady Acres. We're hoping it will help Irma and some of the other people who were on the bus get some closure.\" I took a deep breath. \"I was hoping you might have seen or heard something that might help.\"\n\nShe tilted her head and stared. \"Help how?\"\n\n\"Help figure out who might have wanted to murder your dad.\"\n\nShe laughed. \"That list would be way too long.\"\n\nI was silent for a moment. \"Well, maybe you noticed something that seemed . . . odd. It might be able to lead the police to the killer.\"\n\nShe turned away and fidgeted with the cups on the tray. She took the kettle from the stove and started to fill the cups.\n\nOn a whim, I asked, \"Why were you arguing with your dad at Murder Between the Pages, and why were you on the bus?\"\n\nHer hand pouring the water into the teapot faltered and she spilled water onto the counter, but she quickly recovered.\n\nI hopped off the barstool and got a paper towel and helped to clean up.\n\n\"How did you know about the bookstore?\"\n\n\"My grandmother and I were there.\"\n\nShe sighed. \"I called him to talk . . . about Isabelle.\" She swallowed hard and paused. \"He said he couldn't meet me because he was going out of town on this bus trip and needed to pick up something from the bookstore. I thought I could talk to him . . . reason with him.\" She stopped. \"Plead with him, but it didn't do any good.\"\n\n\"Why did you need to plead with him?\"\n\n\"Isabelle is sick. She has aplastic anemia.\"\n\nI must have looked puzzled because she sighed. \"I recognize that look. Most people have never heard of it. Basically, her body doesn't produce enough red blood cells.\" She paused. \"She needs a bone marrow transplant.\" She looked at me. \"That's why I was arguing with my dad. Neither my husband nor I are matches. I pleaded with him to get tested.\" She sniffed. \"For Isabelle's sake.\"\n\n\"He wouldn't?\"\n\nShe shook her head. \"At first he said he would, but he never did.\" She rolled her eyes and slammed the kettle on the stove. \"He was too busy. Too busy? Can you imagine? He was too busy to take a quick test that might possibly save his granddaughter's life.\" She cried.\n\nFor a brief moment, I looked on in disbelief. Then, I collected my wits, walked over, and hugged Rosemary Lindley. Initially, she stood very stiffly, but, after a few seconds, her shoulders shook and she sobbed. We stood that way for several minutes while she cried. Eventually, she pushed away.\n\nShe walked to the sink, turned on the faucet, and splashed water on her face.\n\nWhen she turned the water off, I handed her a paper towel.\n\n\"Thank you.\" She wiped her face. \"I'm sorry. It's been a while since I've cried like that. I didn't think I had any tears left.\"\n\nWe heard laughter from the sunroom and she smiled. \"We better get this tea into our chess masters before it gets cold.\"\n\nShe picked up the tray and carried it through the entry toward the sunroom at the back of the house, and I followed.\n\nAt the entry to the sunroom, Rosemary paused. We stood for a moment and listened. Isabelle was laughing.\n\n\"Wait. How did you do that?\" Frank asked.\n\nIsabelle laughed. \"It's called winning.\"\n\nThe two laughed.\n\n\"It's been a long time since I've heard her laugh like that,\" Rosemary whispered.\n\n\"It's not too much excitement for her, is it? Maybe we should go.\"\n\nShe shook her head. \"No. It's not too much.\" She whispered, \" 'A merry heart doeth good like a medicine.' \"\n\n\"Proverbs, seventeenth chapter, twenty-second verse.\" I released a heavy sigh. \"That was one of my husband's favorite scriptures.\"\n\nShe tilted her head toward the sunroom.\n\nI shook my head. \"No, my husband, Leon, died of cancer.\" I pointed toward the sunroom. \"Frank is a new . . . friend.\" I smiled.\n\nShe nodded knowingly. \"You're a lucky woman.\" She walked into the sunroom.\n\nI thought for a few moments and smiled. It was true. I was a lucky woman. I followed her into the room.\n\nWe stayed another hour talking, eating cake, and laughing. Frank requested and was granted a replay, which he also lost.\n\nIsabelle yawned and we made our exit.\n\nRosemary walked us to the door, where she thanked us, profusely. \"It's been a long time since I've seen Isabelle that happy. Thank you.\"\n\nFrank looked confused. \"No thanks necessary. I enjoyed myself.\"\n\nRosemary's eyes and her body language reflected an internal conflict. One second, she looked as though she wanted to talk, but then a few seconds later, like she had changed her mind. I was curious how the battle would end. Eventually, she took a deep breath and blurted out, \"You asked if I saw anything unusual on the bus.\"\n\n\"Yes.\" I didn't want to seem too eager, but I sure hoped she was going to tell me she saw someone murdering her father.\n\n\"I did notice something.\"\n\n\"Anything that seemed odd to you might be important.\" I gave her my most encouraging smile.\n\n\"It's just that when I walked down the aisle to my seat, I noticed his face and something struck me as odd.\" She pondered for a moment and eventually shook her head. \"It was an impression more than anything. I felt like he saw someone he recognized.\"\n\nI waited, but that was all she said. She shrugged and shook her head. \"I know it's probably nothing, and I almost\u2014\"\n\n\"No, I'm glad you mentioned it.\"\n\nShe sighed. \"It was probably me.\" She laughed. \"I thought I was so clever in that floppy hat with the big glasses, but I guess he saw right through me.\"\n\nShe was probably right, but I didn't want to discourage her. \"Well, if you remember anything else, please call me.\" I gave her one of the business cards my nephew Christopher had created for Market Street Mysteries, and we made our exit.\n\nIt didn't take long to get back on the interstate. We drove a few miles in silence before Frank added, \"That little girl is a chess shark.\"\n\nI laughed. \"You're going to have to learn to lose gracefully.\"\n\nHe grumbled, \"Easy for you to say.\"\n\nOur last stop was to the address listed for Sidney Sherman. When Frank pulled up to the address, it was a small commercial storefront on the south side of town. The lights were out and the building had bars across the windows and doors. It was obvious it was closed, so we quickly moved on.\n\nI filled Frank in on my conversation with Rosemary Lindley. He listened quietly.\n\n\"Sounds like Max Franck was a real piece of work.\"\n\nI was glad he'd come to the same conclusion I had. \"I know. It seems so bizarre. I mean, I didn't know him long, but he didn't seem like a jerk.\"\n\nHe smiled. \"Sometimes it's not easy to tell how big of a jerk someone is until they say or do something . . . or, in this case, fail to do something important.\"\n\nDespite the cake and tea we'd eaten, we were both hungry and decided to stop for a late lunch in Michigan City, Indiana.\n\nSenior Kelly's was a Mexican\/Irish pub. Neither ethnic group was authentic, but the margaritas were large and the atmosphere was always festive. Just as we finished eating, I got a call from Nana Jo.\n\n\"Sam, you better get back here.\"\n\n\"What's happened?\"\n\n\"Someone just tried to kill Irma.\"\nChapter 12\n\nA few probing questions revealed that Irma had taken a tumble down a flight of steps. I tactfully questioned whether Irma's tumble down the stairs could have been an accident. After all, she did wear six-inch hooker heels on a daily basis, and it was possible she merely tripped.\n\nNana Jo's response was that Irma'd been wearing stilettos for more years than I'd been alive and she would fill me in more when I got back.\n\nI relayed the conversation to Frank and we quickly left and headed back. During the short ride from Michigan City, Indiana, to North Harbor, Michigan, we discussed the latest developments.\n\n\"Do you think someone really tried to kill Irma?\" he asked.\n\n\"I don't know why they would. It seems so far-fetched.\" I shook my head. \"If anyone other than Nana Jo told me someone tried to kill Irma, I wouldn't have believed it, but . . .\"\n\n\"Your grandmother is usually a very reliable source.\" Frank turned into Shady Acres.\n\nOne glance at the parking lot sent my heart racing. There were at least four fire trucks, two police cars, and several ambulances. I gasped.\n\nFrank reached over and gave my hand a squeeze. Then he navigated around the vehicles and pulled up as close to the curb near the door to the lobby as he could and let me out.\n\nI hurried inside. The scene in the lobby was pure chaos. Irma was strapped onto a gurney in the lobby. Dorothy and Ruby Mae were shouting orders at the emergency technicians. Caroline Fenton looked as though she'd been crying. If she'd had a run-in with my grandmother, then she probably had. There was a crowd of residents gawking nearby. I recognized Sarah Jane Howard, who seemed as though she was trying desperately to get Nana Jo's attention. However, Nana Jo and Velma Levington had Bob the bus driver in a choke hold. Sidney Sherman was arguing with Detective Pitt, and the decibel level was unreal. Everyone was shouting.\n\nI stood for a few seconds and watched in openmouthed wonder.\n\nFrank whispered in my ear, \"What's going on here?\"\n\nI shook my head. \"I have no idea, but I'm going to find out.\" I reached into my purse and pulled out a whistle Nana Jo had given me when we went to New York for Thanksgiving. My grandmother was amazed to learn I had never learned to whistle, so she'd picked up a police whistle to help me hail a taxi.\n\nI gave the whistle a long blow, which produced an eardrum-bursting sound that stunned the crowds into silence and had the desired effect of stopping the commotion.\n\n\"What on earth is going on here?\" I asked.\n\nUnfortunately, everyone started talking at once and I was forced to give the whistle another toot. \"One at a time.\"\n\nNana Jo started. \"Velma and I caught the murderer when he tried to kill Irma.\"\n\n\"I didn't kill anyone,\" Bob croaked, and squirmed under the pressure applied around his neck by the two women.\n\nIrma moaned from the gurney. \"Someone pushed me.\" She pointed her finger at Bob. \"Why'd you do it? Why'd you kill poor Max?\" She burst into tears, and Ruby Mae handed her a handkerchief.\n\nFrank walked over to the EMTs and had a quick word and then they moved forward and wheeled Irma out of the building.\n\nDorothy and Ruby Mae followed hot on their tails. \"We're going too.\"\n\nI turned to Detective Pitt.\n\nHe stared at me. \"Don't look at me. I just got here.\"\n\nI tilted my head and narrowed my eyes and gave him a look that said, aren't you going to take control?\n\nA tall, handsome African American man dressed in full firefighter gear came up and whispered something to Detective Pitt.\n\nI recognized the man as the North Harbor Fire Chief. Something in the way he glanced around the lobby made me wonder if he was another of Ruby Mae's relatives. After a few moments, he motioned for the other firefighters to leave and gave the all-clear for the residents to go back to their rooms.\n\nLarry Barlow, the security guard, helped usher the residents, many of whom were wearing lightweight clothing and slippers, which explained a bit of the chaos. It was too cold to go outside without proper winter wear, and, from my days dealing with fire drills as a teacher in the public schools, I was aware the firemen weren't going to allow anyone to return to their rooms for appropriate clothing.\n\nApparently, even Detective Pitt was constrained by the fire department. Only after the whispered conversation from the fire chief did he act. \"All right, everyone is clear to return to your rooms. Clear the lobby.\" He glanced at Bob, still under the control of Nana Jo and Velma Levington. \"Everyone except you.\" He motioned for one of the uniformed officers to take control of their prisoner. Then he looked around. His gaze landed on Caroline Fenton.\n\nCaroline Fenton's eyes looked wild. She looked on the verge of collapse, and I hurried to her side just in time. She collapsed and would have crumpled to the ground if Frank hadn't been there.\n\nFrank scooped the woman up and looked around for a place to take her.\n\n\"In here.\" I led him to her office.\n\nHe placed her on the small sofa.\n\nNana Jo and Velma followed us into the room.\n\nVelma announced she'd been medically trained in the military and immediately sat down and checked her pupils. \"She fainted.\" She turned to Frank. \"Get a cold compress and a glass of water.\" She grabbed a pillow and propped it under her legs to elevate them.\n\nFrank hurried out of the room. He was back so quickly with the items requested, I knew someone must have anticipated the orders and had them already prepared.\n\nVelma put the compress on Caroline's forehead and gave her cheeks a light tap.\n\nCaroline's eyes fluttered.\n\nI glanced around at Nana Jo as she breathed a sigh of relief.\n\n\"Drink this.\" Velma reached behind her neck to help Caroline lift up enough to drink the water.\n\nAfter a few sips, Caroline Fenton laid her head back against the cushions. \"I'm sorry. It's just been such a crazy day, and I don't even remember if I ate anything.\"\n\n\"Well, that's the first thing we need to take care of.\" Nana Jo turned to Frank. \"Would you ask Gaston to prepare some scrambled eggs and toast?\"\n\nFrank nodded and hurried out of the room.\n\nI glanced at Detective Pitt, who looked a bit pale. I remembered how he panicked the last time a woman fainted and had to turn away to keep him from seeing the twitch of my lips as I struggled to keep from smiling. Once I had control of my face, I turned back around. \"Detective Pitt, is it true that he tried to kill Irma.\" I pointed at Bob, who was handcuffed.\n\nThe prisoner struggled. \"I didn't try to kill anyone.\"\n\nNana Jo looked as though she would wring the bus driver's neck. She took a step in his direction. \"Maybe I should have walloped you a bit harder to help jar your memory.\"\n\nI stepped in front of my grandmother.\n\n\"That's enough of that.\" Detective Pitt pulled a notepad out of his pocket. \"The district attorney frowns on prisoners coming in bruised.\"\n\nI detected the first glimpse of humor in the detective's eyes.\n\nHe sat behind the desk and looked from the handcuffed man to Nana Jo and then to Velma Levington. \"Now, does someone want to tell me what happened?\"\n\nNana Jo opened her mouth, but Velma Levington beat her to it. \"He pushed her. I saw it.\"\n\nDetective Pitt held up his hands to stop the flood of words. When he had quiet, he turned to Nana Jo. \"Perhaps Mrs. Thomas can explain what happened.\"\n\nNana Jo nodded. \"We were upstairs. I was . . . hoping to talk to Velma about what she saw on the bus.\" Nana Jo blushed and I knew there was more behind her words, but I'd ask her about it later. \"I had just approached her when we heard Irma scream. Her apartment is down the hall from Velma's.\"\n\n\"Was that when he pushed her?\" Detective Pitt asked.\n\n\"I never pushed anyone. I swear, I\u2014\"\n\nDetective Pitt held up a hand. \"Allegedly pushed.\"\n\n\"No. Actually, that happened later. I rushed down the hall when I heard Irma scream.\" Nana Jo scowled at Bob. \"Someone had broken into her room and ransacked it.\"\n\n\"What?\" Detective Pitt stood up. \"No one mentioned there had been a break-in.\"\n\n\"In all of the commotion, we forgot,\" Nana Jo said.\n\nDetective Pitt walked over to the door and yanked it open. \"Cooper.\"\n\nThe uniformed policeman who'd handcuffed Bob hurried to the door. Detective Pitt whispered something to him and he nodded and hurried off.\n\nDetective Pitt closed the door and returned to his seat. \"You amateurs have probably trampled all over the evidence,\" he mumbled.\n\nNana Jo narrowed her eyes. \"We didn't touch anything.\" She took a deep breath. \"Every dodo knows better than to interfere with a crime scene.\"\n\nDetective Pitt muttered, \"Dodo is about right.\"\n\nThe look in Nana Jo's eyes made me reach out a hand to prevent my grandmother from throttling a policeman.\n\nDetective Pitt must have sensed his life was in danger because he thankfully stopped the insults. \"Now, anything else important you want to tell me.\"\n\nNana Jo cleared her throat. \"As I was saying, Irma's apartment had been ransacked. Just as we were about to enter, the fire alarm went off.\"\n\n\"The fire department should be able to tell us which alarm was pulled,\" Detective Pitt said.\n\n\"Yes, they can do that,\" Caroline Fenton mumbled from the sofa. \"Plus, Larry can check the security cameras.\"\n\nDetective Pitt made notes. \"I'll get Cooper on that as soon as he finishes with the break-in.\"\n\nBob started to speak and Detective Pitt added, \"Alleged break-in.\" He looked at Nana Jo.\n\n\"When did the attempted murder occur?\"\n\nShe sighed. \"A crowd gathered in the hallway after Irma screamed. So, it was a bit chaotic. When we heard the alarm, we all headed for the stairs.\" She glanced at Caroline Fenton. \"The elevators don't work when the fire alarm goes off.\"\n\n\"It's the law,\" Caroline Fenton said.\n\nThere was a knock at the door.\n\nDetective Pitt tapped his pen in frustration. \"Enter.\"\n\nFrank returned with a Styrofoam container, which smelled delicious. He walked over to Caroline Fenton, who was sitting up on the sofa now.\n\nShe thanked him and took the container. She opened the lid. Gaston had outdone himself. Inside was an omelet, toast, and a few slices of fruit. She tucked into the food.\n\nDetective Pitt glanced in her direction with a bit of envy. Perhaps he was remembering the delicious breakfast he'd had when he investigated a murder here previously. However, he sighed and quickly returned to the task at hand. \"What happened after the alarm went off?\"\n\nNana Jo shrugged. \"We all hurried to the stairs. We were just headed down the stairwell when Irma went careening down the stairs.\" She glared at Bob.\n\n\"Did you see him push her?\" Detective Pitt asked.\n\nNana Jo paused. \"No, but Velma did.\" She turned to Velma Levington, who was standing quietly in a corner.\n\n\"That's right. I was standing very close to Irma and I saw his hand extended toward her back. That's when I reached out and grabbed his arm,\" Velma Levington said.\n\n\"I reached out to catch her. I saw the lady flying down the stairs, and I reached out my hand to catch her. That's when these crazy old bats tackled me.\" Bob tilted his head to indicate Nana Jo and Velma.\n\nDetective Pitt wrote in his notepad. \"So, you saw him actually reach out his hand and push Mrs. Starczewski down the steps?\"\n\n\"Well . . .\" Nana Jo stammered. \"I didn't see it, but Velma did. She was a lot closer to Irma than I was.\"\n\n\"Yes. I saw him. He reached out his arm and shoved her in the back,\" Velma Levington said with confidence. \"And furthermore, I'm sure he must have been the one who killed Max Franck. I fell asleep on the bus and was one of the last ones to get off when we stopped. When I did, I saw him standing over Max Franck. He jumped when he saw me.\"\n\n\"You're crazy.\" Bob tried to stand. \"It's a setup. I didn't kill anyone.\"\n\n\"Well, we know that's not true,\" Nana Jo said. \"You went to jail for murder.\"\n\n\"WHAT?\" Detective Pitt smacked his notepad down on the desk.\n\nI explained what Dorothy had found out from her friend Earl.\n\nDetective Pitt looked from me to Nana Jo to Caroline Fenton. \"Why didn't someone tell us sooner?\"\n\n\"I didn't hire him.\" Caroline Fenton swallowed hard. \"That was my predecessor's doing, Denise Bennett.\"\n\nDetective Pitt groaned. \"Not her again.\"\n\n\"I was going to tell you when we met,\" I whispered.\n\nHe scowled at me and then turned to Bob.\n\nThe blood drained from Bob's face, and he sat still for a second. \"I was set up before and now it's happening all over again.\"\n\n\"It's always a setup with you people.\" Detective Pitt leaned across the desk. \"Everyone is innocent. You never killed anyone.\"\n\n\"Wait.\" Bob shook his head. \"It's not like that.\" He scooted to the edge of his seat. \"I was young and stupid. I fell in with the wrong crowd and when they suggested we rob a bank, I agreed.\" His voice shook. He paused for a moment. \"No one was supposed to get hurt. We were just going to take the money and get out.\"\n\n\"But, that's not what happened, is it?\" Detective Pitt added sarcastically.\n\nBob shook his head. \"No. There were four of us. Lenny drove the get-away car. Jack and Carl were brothers.\" He shook his head. \"Carl was the brains. He planned the entire thing.\" He sighed. \"Carl and I were supposed to burst in and wave our guns around. Jack was supposed to get the money.\"\n\nI looked at the pitiful creature in the chair. His eyes filled with tears. \"One of the tellers pushed the silent alarm, and Jack flew into a rage. He pistol-whipped her.\" He looked at me. \"He hit an old woman.\" He swallowed hard. \"I was in shock. I couldn't move. That's when Carl started yelling. 'Get out! We gotta get outta here,' but I couldn't move. The security guard reached for his gun and Jack raised his arm. He pointed his weapon. He was gonna shoot him.\"\n\n\"What did you do?\" I asked.\n\nHe shook his head. \"I couldn't let him shoot that man. I saw the look in his eyes, and I knew he was going to shoot.\" He lowered his head. \"I don't even remember raising my gun. I just remember the sound it made.\"\n\n\"You shot your partner?\" Detective Pitt asked.\n\nHe nodded. The tears flowed down his face. \"He was a hothead. He had a record and had been in and out of jail. He said he'd never go back inside. So, that's how I knew he'd kill them rather than go back to prison.\"\n\n\"You killed him?\" I asked.\n\nHe nodded. \"Carl and Lenny got away, but I just stood there. I couldn't move.\"\n\n\"So, you went to jail for murder?\" Nana Jo asked.\n\nHe nodded.\n\n\"Doesn't sound like an innocent person getting set up to me. It sounds like cold-blooded murder.\" Detective Pitt scowled.\n\nBob sat in the chair and cried.\n\nDetective Pitt closed his notebook. \"I've heard enough.\" He walked over to the crying man. \"Come on. I'm arresting you for the attempted murder of Irma Starczewski and suspicion of the murder of Max Franck.\" He grabbed him by the arm. \"Let's go.\"\n\nBob's gaze traveled around the room like a trapped animal. \"Please, I swear I didn't do it. Please.\" He gazed into my eyes. \"Please. You have to believe me.\"\n\nDetective Pitt led him out of the room, none too gently.\n\nFor a few moments, we all looked on in shock.\n\nAfter a few seconds, Velma walked toward the door. \"I'm glad they were able to catch that dangerous killer before he killed anyone else.\" She grabbed the doorknob and then walked out of the room.\n\nCaroline Fenton swiveled her legs off the sofa and stood. \"I've got a ton of paperwork to fill out. Today has been one crazy day, and we have that memorial service tomorrow.\" She moved over to her desk, and we all took the message and made our way out of her office.\n\nOutside, Nana Jo turned to me. \"What are you thinking?\"\n\n\"I'm thinking something doesn't feel right.\"\n\nShe nodded. \"I'm thinking the same thing.\"\n\nFrank shook his head. \"You two just feel sorry for him because he seemed remorseful, but Detective Pitt had no choice. There's a lot of evidence against him.\"\n\n\"What evidence?\" Nana Jo asked.\n\nFrank ticked off the answers. \"He was seen on the bus standing over Max Franck. He was on the stairs when Irma fell. He was seen with his arm outstretched toward her just as she tumbled down the stairs.\"\n\n\"Circumstantial evidence,\" Nana Jo added.\n\nFrank shrugged. \"It may be circumstantial, but it may be enough to convict him.\" He paused. \"Plus, he's a convicted murderer.\" He looked from me to Nana Jo. \"He may just be a great actor. He may have turned on the tears to make himself seem innocent.\" He reached out a hand and rubbed my arm. \"He might be playing on your emotions.\"\n\nNana Jo looked at me. \"What do you think?\"\n\nI thought for a moment. \"I think I believe him.\" Frank started to speak, and I hurriedly continued, \"Look, I may be wrong. He may be a cold-blooded murderer, but something about this whole thing doesn't feel right.\"\n\nFrank smiled. \"Then let's get to work.\"\nChapter 13\n\nIrma's tumble down the stairs wasn't nearly as bad as it could have been. Thankfully, she only had some bumps and bruises and a badly sprained ankle. However, the hospital decided to keep her overnight for observation.\n\nFrank dropped Nana Jo at the hospital and then took me home. We were gone a lot longer than we originally planned. There was still a couple of hours before the bookstore closed, but traffic was light. I needed to distract my mind and had been missing time in the bookstore, so I let my nephews leave early and took over. It was wonderful to get back into the swing of things. I loved walking around my bookstore and helping customers, especially new customers, find just the right book, which I hoped would open their minds to the genre I loved.\n\nDuring a lag in customer traffic, I reshelved books and couldn't help thinking about how much my life had changed since I opened Market Street Mysteries.\n\n\"Mrs. Washington.\"\n\nI jumped at the unexpected intrusion into my dream world. \"My goodness. You scared me.\" I turned around and saw a familiar face. \"Taylor?\"\n\n\"I can't believe you remembered my name.\" Taylor smiled.\n\n\"You're hard to forget.\" I smiled. \"You have such a beautiful face.\"\n\nShe blushed.\n\nI looked at the Goth goddess dressed in black from head to toe, with black lipstick, black fingernails, and hair dyed so deeply it looked purple under the lights. \"Come for more Charlaine Harris?\"\n\nTaylor was a student at MISU and a member of a book club started by a couple of students, Jillian Clark, who was Dorothy's granddaughter and was dating my assistant Dawson, and Emma Lee, who was dating my nephew Zaq.\n\n\"I can always use more Charlaine Harris.\" She laughed. \"But the main reason I came was to thank you.\"\n\nI had just reached up to get the latest book in the Harper Connelly Mystery series, which had enough paranormal activity that I knew Taylor would love it, when her words sunk in. \"Thank me? For what?\"\n\nShe smiled. \"You suggested I talk to my guidance counselor about combining my love of writing and video games with my dad's desire for me to become a computer programmer.\" She grinned so large and rocked on the balls of her feet.\n\n\"And?\"\n\nShe squealed. \"It's so awesome. There's this special course I can take and get a certificate and my guidance counselor actually knows one of the founders of Vamps.\" She waited expectantly, as though the name would mean something.\n\nI shook my head. \"Sorry. I've never heard of Vamps.\"\n\nShe jumped up and down. \"Ohmygodohmygod. Vamps is the number one gaming company. They have the best graphics. I absolutely love their games.\" She took a deep breath and steadied herself. \"It's just too amazing for words.\"\n\nShe was so excited; I was afraid she'd pass out. There'd been enough of that for one day, so, I suggested we go to the back of the store and sit down.\n\nThe store traffic was virtually nonexistent, and I knew the seat that would give me a clear view of anyone entering or leaving. We went to the back and I brought two cups of tea to a small bistro table. Dawson had prepared a host of goodies to keep the store stocked before he left. Today, my nephews had defrosted the dough for peanut butter cookies, Zaq's favorite. A few cookies had escaped the twins' notice, and I brought them over to the table.\n\nBy the time I sat down, Taylor had calmed down enough to tell me her news.\n\n\"My guidance counselor, Mr. Leonard, knows one of the guys who started Vamps. So, when he found out what I wanted to do, he called him.\" She started breathing heavily again.\n\nI reached out a hand. \"Breathe.\"\n\nShe stopped and took a deep breath. \"Bottom line, he's going to give me a summer internship with the company.\"\n\n\"That's fantastic. How did your dad take it?\"\n\nShe smiled. \"At first, he thought I was crazy. He said, 'It's just a fad and it'll die out like the' \"\u2014she used air quotes\u2014\" 'dot com bubble.' \" She puffed up her chest and tilted her head in a cocky manner. Then she laughed. \"That was until he heard how much money I'm going to be making.\"\n\n\"I'm really happy for you, Taylor. I hope you have a great internship.\"\n\nShe spent a few minutes gushing about Vamps and how jealous her boyfriend was when he heard where she was going to be working.\n\nWhen she finished, we chatted about books for a bit and then she selected and paid for some and left.\n\nI couldn't help smiling as I closed the shop and tidied up. Taylor was a smart young girl, and I was glad she was having an opportunity to pursue her dream. Working with kids and seeing them achieve things they never knew they could was one of the things I missed about teaching. Seeing the excitement on Taylor's face filled a void I didn't know I had.\n\nChristopher and Zaq had let the poodles outside before they left, but I took them down again. Snickers was old and took advantage of the opportunity to go potty every time it presented itself. Oreo took the opportunity to play in the snow until his underbelly and paws were cold. Then he tried to get back inside. However, I had learned to harden my heart against his sad poodle eyes and stood firm behind the closed door until he gave up, went to a nearby bush, and hiked his leg.\n\nMission accomplished, I opened the door and wiped the excess snow from him. Thankfully, Oreo didn't hold a grudge and gave my hand a lick.\n\nUpstairs, I wasn't hungry. The events from earlier today were tumbling around in my mind, and I needed a way to sort through everything.\n\nSo, I sat down and fired up my laptop.\n\nDespite the massive size of the house, the drawing room of Hapsmere Grange was small. There was an oversized marble fireplace on one wall and a crystal chandelier that hung from the center of the coffered ceiling. There was also a large overstuffed sofa and several cushioned chairs\u2014too many chairs.\n\nBakerton, the ancient butler who'd served the duke's family for decades, opened the double doors that led into the room and Thompkins pushed in a tea cart laden full of cakes, pastries, sandwiches, and tea.\n\nOnce the items were distributed, Bakerton and Thompkins turned to leave.\n\n\"Thompkins, I would appreciate it if you'd stay,\" Lady Elizabeth said.\n\nBakerton bowed and left while Thompkins, who was accustomed to her ladyship's odd requests, walked over to a corner and stood stiffly.\n\nLady Elizabeth knew Thompkins well enough to know he would never sit in her presence, so she smiled and hurried on. \"Now, I think we all know why we're here.\" She looked around.\n\nEveryone nodded, although Detective Inspector Covington frowned. The tall, gangly man looked puzzled. \"Well, your ladyship. To be completely honest, I know why I'm here.\" He looked around. \"You think Mrs. Forsythe's death may have been murder rather than an accident.\"\n\nLady Elizabeth nodded.\n\n\"I'm a policeman, so it makes sense for me to be here. I get paid to investigate things like this.\" He leaned forward and scratched the back of his neck. \"What doesn't make sense to me is why the rest of you are here.\"\n\nLady Clara huffed and made a very unladylike snort. \"It's rather obvious why we're here.\" She leaned toward the detective inspector and glared. \"We're here because your bloody lot didn't believe Aunt Elizabeth when she said she thought poor Mrs. Forsythe had been murdered. Now, she's here to find the evidence to prove that she was. She's doing the job you should have done in the first place.\"\n\nBlood rushed to Detective Inspector Covington's cheeks and he looked like a teakettle about to blow.\n\nLady Elizabeth raised her hands and halted the storm, which looked about to explode in the Hapsmere Grange drawing room. \"That's not entirely true, dear.\" She turned to her cousin. \"The police at the tube station were very kind and attentive; however, they have to work with facts.\"\n\nLady Clara snorted.\n\n\"Scotland Yard does a wonderful job and we've had the pleasure of working with Detective Inspector Covington several times in the past. He's always been very good about listening to our ideas.\" She turned to the young man. \"There's absolutely no evidence that Mrs. Forsythe was murdered. Nothing, but a . . . feeling.\"\n\nLady Alistair reached across and squeezed her friend's hand. \"Your feelings have been pretty accurate.\"\n\nDetective Inspector Covington gave Lady Elizabeth a sheepish look. \"Your feelings have been pretty bang on, and I'm sorry.\"\n\nShe smiled. \"Thank you, Detective Inspector. That means a great deal coming from you.\" She paused for a moment. \"However, the truth of the matter is, we don't have any proof whatsoever that Mrs. Forsythe didn't have an accident.\" She put down her teacup and picked up the knitting bag she'd set by her side. She took out a ball of pale yellow wool and a pair of knitting needles. \"Mrs. Forsythe might be exactly what Mrs. Sanderson accused her of being, a batty old dear.\"\n\n\"You don't believe that.\" Lady Clara stared at her cousin.\n\nLady Elizabeth knitted a few stiches and then smiled. \"No. There was something about her that didn't seem like she'd lost her wits. No. In fact, I think she was quite clever.\" She knitted a few more stiches. \"The way she managed to sneak away from the house when her cousin and his wife were out and how she slipped away from Mrs. Sanderson. That took some cunning.\"\n\n\"Okay, what do you want us to do?\" Lady Clara asked eagerly.\n\nLady Elizabeth knitted. \"We don't have much time. The cousin wants something.\" She paused. \"I don't know what, but I intend to find out.\"\n\n\"What do you want the rest of us to do?\" Lady Alistair asked.\n\n\"Well, I was hoping we could divide and conquer.\" She smiled. \"I couldn't help but notice Mrs. Sanderson seemed a bit . . . awed by my title.\" She glanced at Lady Alistair. \"I was hoping we could both tackle her.\"\n\nLady Alistair took a bite from her scone. \"Shall I pull out one of my tiaras for the occasion?\"\n\nLady Elizabeth smiled. \"I don't think we'll need to go to that extreme, but if you have your chauffeur, I think we could definitely borrow him.\" She looked from Detective Inspector Covington to her cousin. \"Now, I have noticed that men are often more receptive to a pretty woman.\" She turned to Detective Inspector Covington. \"While women are often more responsive to a handsome young man. I was hoping that you\"\u2014she looked at her cousin\u2014\"if the opportunity presented itself, could talk to Desmond Tarkington alone.\" She turned to the Scotland Yard detective. \"While you could have a talk, informally of course, with his wife, Constance.\"\n\nDetective Inspector Covington frowned. \"I've noticed that murderers aren't usually very forthcoming with information when they find out I'm with Scotland Yard.\"\n\nLady Elizabeth smiled. \"Exactly. Which is why I was hoping we could introduce you as a friend of the family.\" She looked slyly at her young cousin. \"I hoped we could explain your presence as a close friend of Lady Clara.\"\n\nThe two young people glanced at each other and color rose up both of their necks. However, neither objected.\n\nLady Elizabeth turned to the butler. \"Thompkins, I was hoping you might see what you could find out about Mrs. Forsythe's maid, Dora.\"\n\nThompkins bowed.\n\nShe smiled. \"Mrs. Forsythe mentioned they'd had to cut back on expenses. I gathered they may not have many servants, so I was hopeful that tomorrow you would accompany us and . . . well, perhaps you could help find out what's going on below stairs.\"\n\nThompkins nodded stiffly.\n\nLady Elizabeth knitted. \"I want to caution everyone to be very careful. If I'm right and Mrs. Forsythe was murdered, then someone believes they got away with murder. If they think there's someone nosing around who suspects the truth, well . . . he or she could prove very dangerous.\" She paused and gazed into the fireplace. \"Yes. It could prove very dangerous indeed.\"\n\nChapter 14\n\nOften, writing provides clarity and helps me put things into perspective. Tonight's writing didn't accomplish this task. In fact, if anything, I felt more confused. However, I had learned to try not to force things. Instead of staying up worrying, I went to bed and surprised myself by sleeping through the night. It was only when Snickers pounced on my chest, causing momentary panic and temporary loss of breath, that I woke up.\n\nI rolled over, forcing the poodle off my chest, remembering to keep my mouth closed to prevent her attempts to lick my teeth.\n\nI took care of my call of nature first and then quickly took the poodles downstairs to allow them to answer theirs.\n\nSnickers stepped over the threshold and executed a circus-worthy maneuver where she balanced all of her weight on her back right leg, enabling her to keep three paws off the ground while she took care of her business.\n\nYet again, Oreo jumped around in the snow for several moments and spent extra time playing before he remembered why he was there and went over and hiked his leg.\n\nInside, I cleaned the excess snow off his belly and looked him in the eyes. \"You might want to skip your romps through the snow and follow your sister's lead.\"\n\nHe gave my hand another lick, similar to the previous night, and I couldn't help but laugh. \"You have such a zest for life, don't you, boy.\" I dried him and scratched that place behind his ear that made his eyes roll back into his head and caused his leg to jiggle.\n\nEventually, Snickers had had enough of me playing with the boy dog and gave my legs a scratch.\n\nI hadn't bothered to put on pants, so it was a painful lesson to learn. Don't keep the girl poodle waiting while I played with the boy poodle. \"Message received.\" I put the dogs down and hurried upstairs, making a mental note to take them to get their nails trimmed.\n\nI showered, dressed, and cooked breakfast. By the time I finished, I heard Christopher and Zaq coming upstairs.\n\n\"Hey, Aunt Sammy,\" Zaq said.\n\n\"You boys want some bacon?\" I asked the question even though I already knew the answer. It wouldn't matter how many times or how much my nephews ate, the answer was always going to be yes when the question involved bacon. Nana Jo said we had a bacon gene.\n\nI took three pieces of bacon and left the rest for the twins. They each grabbed bread and stacked it with the remaining bacon. Mouths full, they descended the stairs, mumbling, \"Thanks.\"\n\nI was just about to load the dishwasher when I heard my nephew's call. \"Aunt Sammy!\"\n\nOne glance at my watch showed me the store wasn't opened yet, and I gave a silent prayer of thanks that my nephews hadn't yelled for me with a store full of customers. Rather than yelling back, I went downstairs.\n\n\"You yelled?\" I joked as I walked around the corner. I stopped with the smile frozen on my face when I saw Detective Pitt. Based on the scowl on his face, and the pacing he was doing around the small bistro tables in the back of my bookstore, he wasn't happy.\n\n\"Detective Pitt, I wasn't expecting\u2014\"\n\nHe marched to within inches of me and pointed his finger in my face. \"You're behind all of this. What have you gotten me involved in?\"\n\nI was shocked into silence for several seconds. Detective Pitt and I hadn't always gotten on like best friends, but he'd never taken such a hostile attitude toward me. From behind the steaming detective, I saw my nephews watching. Both were over six feet and, based on their stances and the frowns on their faces, they were prepared to protect me. It was clear to me that this situation was about to get out of hand quickly.\n\nI channeled my school teacher attitude and stood tall and straight. \"Detective Pitt, stop shaking your finger at me and sit down.\"\n\nThe detective dropped his hand instantly. He took a deep breath and pulled out a chair and flopped down.\n\nMy nephews' shoulders relaxed, although their eyes indicated they were still on high alert.\n\n\"It's okay, boys. I'm fine. Detective Pitt and I are going to have a friendly conversation. You both can get back to work.\"\n\nThe boys hesitated for a moment. Zaq nodded and turned and walked away first.\n\nChristopher stayed a few seconds longer. \"We'll be right up front if you need us.\"\n\nI nodded. When they were both up front, I turned my attention to the detective. I glared at him. \"Now, it's obvious you're upset and your mind isn't functioning properly or you would never have marched in here and yelled at me like that.\" I took a deep breath. \"I know you've got better manners than that, so I'm going to excuse your behavior.\"\n\nA flush rose up his neck, and his eyes flashed. However, the spark quickly vanished and the detective took a deep breath. \"I'm sorry.\"\n\nI pulled out the chair across from the detective and sat. \"Would you like a coffee?\"\n\nHe shook his head. \"No . . . thank you.\" He ran his fingers over his head. Unfortunately, this action served to dislodge the hairs he'd combed over his bald spot and now, rather than bending over his dome, they stood straight up.\n\nI tried not to stare, but the hairs were so rigid, it took a lot of control not to stare. \"What can I do for you?\"\n\nHe leaned forward. \"You got me involved in this murder business and now, I've got Sergeant Alvarez, the district attorney, and the Justice Department asking questions.\n\nI raised an eyebrow. \"Really? Why so much interest?\"\n\nHe banged his hand on the table. \"You tell me.\"\n\n\"Well, I told you it would be a high-profile case, but\u2014\"\n\n\"High profile is one thing, but the bleeding Justice Department is another thing altogether.\"\n\nI stared across the table. \"What's the real problem?\" Detective Pitt glanced at me but then reached inside his coat and pulled out a folder. He slid the folder across the table while looking over his shoulder. \"That's the coroner's report about Max Franck, and getting a copy of that nearly cost me my job.\"\n\nI suspected the detective was exaggerating. His job had been in jeopardy for quite some time, if my sister, Jenna's, sources were to believed. I scanned the file. However, Detective Pitt leaned across the table and stared the entire time. I found myself distracted not only by his eyes but the strands of hair, which seemed to stand at attention, atop his head, as well as the scrambled eggs that he'd dropped on his shirt. \"Look, I can't read this if you're going to stare at me. Why don't you get yourself a cup of coffee and a cookie?\" I pointed to the counter.\n\nDetective Pitt walked over to the counter, giving me a little breathing room.\n\nI sighed and read through the report as quickly as possible. Max Franck had been killed by a thin knife to the kidneys. I reread that several times to make sure I understood.\n\n\"What's got you so engrossed?\" Detective Pitt said around a mouthful of chocolate chip cookies and dropped crumbs on my shoulder.\n\n\"The murder was caused by a thin stiletto-type knife wound to the kidneys.\" I flicked the crumbs off my shoulder and the table. \"Would that cause a lot of blood?\"\n\nHe shrugged. \"Beats me.\"\n\nI sighed. \"Does this mean they're going to let you work the case?\"\n\nHe flopped back down in his seat and leaned close. \"That Alvarez wants to take me prisoner. He's madder than a wet cat.\" He grunted. \"I'd be fine if it was just a matter of Alvarez, but the Justice Department is an entirely different matter. I've got a meeting with my chief in\"\u2014he pulled up his sleeve and glanced at his watch\u2014\"in an hour.\" He looked at me. \"What am I supposed to say? Did this bus driver . . . Bob Marcus . . . did he kill Franck? If so, why?\"\n\nI thought for a few minutes. \"I don't think he did kill Max Franck. I'm not even convinced he pushed Irma down a flight of stairs.\" Detective Pitt started to talk and I held up a hand to stop him. \"Look, I don't think Sergeant Alvarez has anything connecting Bob Marcus to Max Frank's murder. If he did, he would have arrested him at the rest stop.\"\n\nHe rubbed his chin. \"Yeah, that's a good point.\"\n\nI nodded. \"Look, if it were me, I'd go into this meeting and say you were just responding to a call for an attempted murder. If Sergeant Alvarez believes the attempt on Irma's life is connected, then it makes sense for you to investigate. It's your territory, after all.\"\n\nHe nodded. \"Yeah, you're right.\"\n\nIt took a little more pumping up, but, by the time I finished, Detective Pitt was chomping at the bit and ready to take on Sergeant Alvarez and the entire United States Justice Department.\n\nI, on the other hand, felt drained. Something about the coroner's report bothered me, but I couldn't figure out what it was. I sat for a few moments, but customers started to come in.\n\nI helped my nephews for a few hours. When it was close to lunchtime, I went upstairs and put on my winter gear and then walked down the street to Frank's restaurant to pick up lunch for my nephews.\n\nWhen I walked into Frank's place, he was behind the bar. He smiled and I walked over and hopped onto a barstool.\n\nHe finished providing beverages for one of his waitresses. There was another man behind the counter who came over. However, before he could ask for my drink order, Frank sidled up next to him. \"Sorry, Benny, I've got this one.\" He leaned across and kissed me on the cheek.\n\nBenny grinned. \"I'm sorry. I get it.\" He held up both hands. \"Off limits. I got it.\" He winked at me.\n\nFrank laughed. \"Exactly.\"\n\nHeat rose up my neck, but I smiled and extended my hand. \"Hello, Father. I'm Samantha, but everyone calls me Sam.\"\n\nHe looked at Frank. \"Is it okay if I shake?\"\n\nFrank gave him a playful punch.\n\nBenny wiped his hands on a towel and then shook my extended hand. \"Hello, Sam. I'm Bernard Lewis. You can drop the 'Father.' Just call me Benny.\"\n\n\"Nice to meet you, Benny.\"\n\nHe smiled and then walked a discrete distance away.\n\nFrank poured me a glass of lemon water. \"Are you here for lunch?\"\n\n\"Yes, and I need lunch for my nephews too.\"\n\nHe nodded and took our orders. Once he placed those, he leaned across the counter and smiled. \"It's great to see you.\"\n\nI smiled. \"It's great to see you too, but . . .\"\n\nHe stood up. \"You've got that look in your eyes.\"\n\nI tilted my head. \"What look?\"\n\nHe leaned closer. \"The look that says you're investigating and need information.\" He whispered, \"When I was hoping you just wanted me for my body.\"\n\nI had just taken a drink of my water and spit it out as I laughed.\n\nFrank laughed and grabbed a towel and wiped up the water I'd spewed across the counter. \"What can I do for you?\"\n\nOnce I was able to talk again, I looked around. Thankfully, the restaurant wasn't very crowded and we had a bit of privacy. \"I just saw the coroner's report on Max Franck.\" I quickly explained the little bit of information I'd gleaned from the file. \"I remember you mentioning once that the best way to kill someone quietly was a knife to the kidneys.\"\n\nHe nodded. \"It's a technique that was used by military during World War II.\"\n\n\"Is that something that's common knowledge? Or is it specialized.\" I noted the confused look in his eyes and tried to explain. \"I guess what I'm asking is, whether this is something you'd have to be in the police or military to know? Or, is that something that anyone could know?\"\n\nHe stood still for a moment and then shrugged. \"Honestly, in this day and age, anyone with access to the Internet could figure it out. Heck, there's probably a video demonstrating the technique if you look long enough.\"\n\nI sighed. \"Well, that's a bummer.\"\n\nFrank's brow was furrowed.\n\n\"What?\"\n\nHe took a deep breath. \"It's just that most of the people on that bus trip were seniors. Many of them may have been in World War II or Korea, Vietnam . . . anything. Men and women all served and were trained to kill silently. Between that and the Internet, your killer could have been just about anyone.\"\n\nI sighed. \"That's what I was afraid of.\"\n\nWe chatted until my order arrived.\n\n\"Will I see you tonight?\" He smiled. \"You still owe me dinner.\"\n\n\"I'm going to the memorial service for Max Franck. Wanna come?\"\n\nHe grinned. \"Not exactly the romantic evening I was thinking about.\"\n\n\"Well, we're still on for New Year's Eve, right?\"\n\nHe nodded. \"Definitely.\"\n\n* * *\n\nI worked in the bookstore while my nephews ate lunch, although there weren't very many people. Afterward, I went upstairs and ate my lunch while I sat at my laptop.\n\nI tried to make sense of the information, but nothing made sense. It would be so easy if Bob was the murderer, but no matter how much I wanted it to be over, I knew in my heart he wasn't the murderer. He wasn't cold and calculating enough to have stabbed Max Franck in the kidneys. If he was the killer, that would eliminate Rosemary as a suspect. She'd fought with her father twice and seemed like a really good suspect, but she was in Chicago when the attempt was made on Irma. Although, I had to wonder, why try to kill Irma? Was it attempted murder? Or did she simply lose her balance and stumble? I really wanted to believe Irma tripped and the entire thing was merely an accident. Because if it wasn't an accident, if someone really had tried to kill Irma, then the killer must believe she knew something, and her life was in danger.\nChapter 15\n\nI couldn't stop thinking about Irma. Was she really in danger? Why was her room searched? I never asked if anything was stolen or not. Why Irma's room? I made a mental note to ask Nana Jo if any other rooms were broken in to. As I thought about my grandmother, my cell phone rang and her picture appeared on the screen.\n\n\"Sam, I'm at the hospital. They're releasing Irma in a couple of hours.\"\n\n\"Would you like a lift?\"\n\nNana Jo released a breath and I could hear the smile through the phone. \"That's what I was hoping you'd say.\"\n\nShe promised to text when it was time to go and then said she needed to go stop Irma from flirting with the medical students making rounds with the doctor and hung up.\n\nI took out a notepad and wrote down what I remembered from the coroner's report so I could fill Nana Jo and the girls in when I saw them later. I also jotted down a few questions that kept running through my mind. Was the break-in at Irma's apartment a coincidence? If not, what was the killer looking for? Was she pushed? Or, did she trip? If she was pushed, why? What does the killer think Irma knows?\n\nI looked over my notes. \"Those are good questions. I wish I had the answers.\"\n\nOreo barely glanced up from his nap. Snickers yawned, stood, turned around in a circle, and lay down with her back to me. I guess my talking was disturbing her nap. Perhaps a little writing would help.\n\nBattersley Manor was a large home but looked quite demure when compared to Hapsmere Grange. The house sat back from the road, and Lady Alistair's chauffeur pulled the Rolls up to the front steps. Before he could get out, Thompkins, who was on the front seat, promptly hopped out and opened the doors for Lady Alistair and Lady Elizabeth.\n\nDetective Inspector Covington pulled up behind. Lady Elizabeth felt it would be better if the two younger people arrived together.\n\nThe front door of the manor was opened, and Mrs. Sanderson hurried down the steps to greet the guests.\n\n\"Your ladyship.\" She curtsied and nervously bounced around as though unsure if she should walk in front, behind, or simply stand silently.\n\nLady Elizabeth smiled fondly and offered her hand. \"Mrs. Sanderson, let me introduce you to my dear friend, Lady Alistair Browning.\"\n\nMrs. Sanderson bobbed and smiled. \"Your ladyship.\"\n\nLady Alistair smiled. \"I was so sorry to hear of the death of Mrs. Forsythe. Please accept my sincere condolences.\"\n\nMrs. Sanderson blushed and nervously turned from one woman to the other.\n\nDetective Inspector Covington and Lady Clara approached the small party.\n\n\"This is my cous . . . ah, niece, Lady Clara Trewellen-Harper and her friend, Peter Covington.\" Lady Elizabeth hoped her faux pas went unnoticed. They'd agreed previously it would be easier to introduce Lady Clara as her niece, especially since Lady Clara had the habit of calling her \"aunt\" anyway. They'd also agreed to say as little as possible about the detective inspector. He was a close friend of Lady Clara's, spending his holiday with them.\n\nMrs. Sanderson seemed overwhelmed by the number of visitors but bobbed to Lady Clara and the detective inspector.\n\nWhen it seemed Mrs. Sanderson had met everyone, she looked up and noticed Thompkins.\n\n\"This is my butler, Thompkins,\" Lady Elizabeth announced.\n\nAnother decision made previously was to say as little as possible about Thompkins' presence. The butler had, in fact, suggested people might not question his presence. He reminded them it had been quite common in the past for aristocrats to travel with maids, valets, and butlers.\n\nApparently, the butler had been correct because Mrs. Sanderson merely nodded to the butler and asked no other questions.\n\nA dark-haired woman with a birdlike face stood in the doorway. \"Sanderson, don't leave our guests waiting outside in the cold.\"\n\nEveryone followed Mrs. Sanderson up the stairs. At the door, the introductions were made again.\n\nThe woman introduced herself as Constance Tarkington. She was a large-boned woman with an athletic build. She looked to be the type who spent a great deal of time outdoors and was more comfortable in the company of horses than people.\n\nOn the outside, Battersley Manor was a classic English Edwardian manor house. The inside was a completely different matter. Once you stepped over the threshold, you stepped into the Orient. From the large Oriental rugs that covered the floors to the silk screen, blue and white vases, and silk draperies. There were large collections of swords, teacups, and even what appeared to be a collection of Buddhas, which varied in size from tiny miniatures to a massive one near the front door.\n\nConstance led the group into a dark, dusty sitting room, where they were joined by her husband, Desmond Tarkington. Desmond was a dark-haired man with a weak chin. He had dark eyes and a theatrical air. He wore a smoking jacket and cravat and carried a pipe, although it wasn't lit and was clearly for effect.\n\nDesmond struck a thoughtful pose and leaned against the fireplace. \"Welcome to Battersley Manor.\" He nodded.\n\nLady Elizabeth smiled. \"Thank you, Mr. Tarkington. I'm so glad you were able to accept a visit during your time of mourning.\"\n\nDesmond looked confused for a few seconds but quickly regained his composure. \"Yes. Yes, well, the old dear was rather old and we knew it was coming.\"\n\n\"You knew she'd fall down the stairs?\" Detective Inspector Covington asked innocently.\n\n\"Well, no, of course we didn't know that.\" He waved away the comment. \"However, she'd been sick and she was subject to . . . well . . . to . . . accidents,\" he said casually. \"These things happen when people get old, don't they?\"\n\nConstance Tarkington frowned at her husband but soon turned back to her guests. \"Did you know Eleanor long? We never heard her mention you.\"\n\nLady Elizabeth sat very straight and forced a smile. \"Your cousin was a very old and dear friend.\" She paused as though trying to remember but, after a few seconds, she simply shook her head. \"It's no use. I can't recall the last time we saw each other.\"\n\nConstance smiled. \"What a coincidence you two running into each other that way.\"\n\n\"A coincidence?\" Lady Elizabeth asked.\n\n\"Of all the days of the year, what are the chances that two old friends who haven't seen each other in . . . a long time would both be at Harrods having tea at the same time.\"\n\nLady Elizabeth smiled. \"I don't know that it's too much of a coincidence. Not really.\" She smiled. \"After all, who wants to miss a Boxing Day sale at Harrods?\" She laughed.\n\nLady Alistair smiled. \"I intended to go myself, but, at the last minute, something came up.\"\n\nThere was an awkward silence for several seconds. Lady Clara stared at Desmond Tarkington and then scooted to the edge of her seat. \"Haven't I seen you someplace before?\"\n\nDesmond Tarkington hemmed and blustered for a few moments. \"I've had the great pleasure to be featured in several . . . small roles on the stage.\"\n\n\"That's it. I knew your face looked familiar.\" She smiled. \"How exciting to meet a real-life actor in the flesh.\"\n\nDesmond puffed out his chest.\n\nConstance rolled her eyes.\n\nLady Clara stood. \"Would it be possible for me to get your autograph?\"\n\nDesmond smiled. \"Of course, my dear girl.\" He turned to leave. \"If you'll accompany me to my office, I'm sure I have a photograph that I'll be more than happy to sign to you.\"\n\nLady Clara gushed and followed Desmond out of the room.\n\nTaking his cue, Detective Inspector Covington turned his attention to Constance Tarkington. \"I couldn't help but notice your stables when we drove up. Do you ride?\"\n\nConstance Tarkington gave the first real smile since their arrival. \"We do have some rather fine horses. Would you care to . . . ?\"\n\nDetective Inspector Covington nearly leapt from his chair. \"I'd love to see them.\"\n\nConstance headed out of the room but turned back to her guests. \"If you'll excuse us, we're just going to run down to the stables unless. . .\"\n\n\"Don't mind us. We'll be perfectly fine here talking to Mrs. Sanderson.\" Lady Elizabeth smiled.\n\n\"Yes. Please take your time,\" Lady Alistair said.\n\nConstance Tarkington and Detective Inspector Covington left, and Mrs. Sanderson looked nervous and picked imaginary pieces of lint from her skirt.\n\nLady Elizabeth smiled at the woman. \"Now we can have a nice chat.\"\n\nIn the kitchen, Thompkins met Dora, the maid. She was a plump, freckled girl. She wasn't attractive, but she had an honest face.\n\nThompkins stood stiffly in the kitchen and watched as the girl worked. She appeared to be cooking over an ancient wood-burning stove while tending to a kettle. \"Are you the only servant?\"\n\nDora chopped vegetables. \"Yaw.\"\n\nThe butler removed his jacket and rolled up his sleeves. He reached out and removed the knife from the young girl's hand. \"Let me.\"\n\nDora stood back in shocked silence. She watched as the butler expertly peeled and then chopped the carrots.\n\nAfter a few seconds, she nodded her approval and went over to the pot simmering on the stove. \"Well, I thank you for that.\" She stirred.\n\n\"Don't tell me they expect you to cook and clean.\"\n\nShe nodded. \"Plus, I tended to Mrs. Forsythe when she was alive. May she rest in peace.\" She stirred. \"But I didn't mind because the mistress was a wonderful woman. Always saying please and thank you.\" She snorted. \"Not like that other one.\"\n\nThompkins glanced back at the maid. \"Mrs. Sanderson?\"\n\n\"Pshaw. Good Lawd, no. That other one. Mrs. High and Mighty Tarkington.\"\n\n\"Not a very good mistress?\"\n\n\"Naw, and I won't be staying much longer now that Mrs. Forsythe is gone. I won't be staying to work for that stingy cow.\"\n\nThompkins continued peeling and cutting. \"Tell me about your mistress.\"\n\nDora's face lit up as she talked about Mrs. Forsythe's kindnesses to her, which included a lot more than just saying please and thank you. Apparently, Mrs. Forsythe was generous and sent old clothes to Dora's ailing mother and often paid her younger brother to do odd jobs around the house. \"But, when Mr. Desmond came, he put a stop to that.\" She stirred the pot and then set a tray with cups for tea. \"Fired all of the other servants. We used to keep a cook and manservant and then there was Mrs. Bolton, who came in twice a week to do the washing.\"\n\n\"Don't tell me they expect you to do that too?\"\n\nShe nodded.\n\n\"What about Mrs. Sanderson. Doesn't she help?\"\n\nDora laughed. \"That one? She couldn't tell a chicken from an egg unless someone gave her instructions.\" She shook her head. \"She wasn't hired to help with the work. She was hired to keep an eye on the mistress. She's some distant cousin or something.\" She shook her head. \"No, she's just one more mouth to feed as far as I'm concerned.\"\n\nThompkins stared. \"But why would you put up with that? Why stay?\"\n\nShe sighed. \"I stayed for her . . . for Mrs. Forsythe. I could see clear enough they wanted to get rid of me too, but that was where the mistress put her foot down. 'No,' she said. She wouldn't allow them to fire me.\" She smiled. \"So, they went about trying to force me to quit. More and more work they piled up on me, but I did it.\" She sighed. \"But, now that the mistress is gone, well, I don't have to put up with the likes of them no more.\" She took a kettle of boiling water off the stove and filled the teapot. \"I've given my notice and I'll stay my thirty days so she can't try to send me off without a notice.\"\n\nThompkins finished the chopping. He watched while the maid prepared the tea tray and transferred the vegetables to the pot. \"Was Mrs. Forsythe . . . a bit addled?\"\n\nDora slammed the teakettle onto the table, spilling hot water onto the table. \"No, she was not and don't you dare say she was.\"\n\nThompkins stepped back. \"I didn't mean any offense. It's just I heard my lady say someone told her that she was.\"\n\nDora wiped up the water she spilled. \"Well, whoever said the mistress was daft musta been daft themselves, that's what. Mind, she was a bit queer about her Oriental treasures.\" She smiled. \"That's what she called them, her treasures, but that don't mean she was balmy. It's just that China was where she and her husband were happy.\"\n\n\"They weren't happy here?\"\n\nDora sighed. \"I don't think so. Not like they was in China. Missionaries they was.\" She paused for a few moments. \"But I think it was more about being free. They didn't have nobody telling them what to do and which way to go when they was in China, but then Mr. Forsythe's father got sick and they had to come back.\" She shook her head. \"I don't think they was ever really happy again, not really. But if you asked me, wasn't nothing wrong with her, except too much money and too many relatives.\"\n\n\"Was Mrs. Forsythe wealthy?\"\n\n\"She wasn't as wealthy as your ladyship out there, with her fancy car and that fur coat and all them jewels.\" Dora tilted her head toward the sitting room. \"But her husband left her real comfortable and she was generous, but she wasn't wasteful. She was always careful with her money.\" She smiled. \" 'Dora,' she used to say to me. 'One day, I'm gonna take care of you because you've done such a good job taking care of me.'\" Dora sniffed. \"But that was before Mr. Desmond arrived.\"\n\n\"Maybe she left you something . . . a legacy in her will.\"\n\nDora sniffed. \"That's just the thing. She didn't leave a will.\"\n\n\"No will? Surely her solicitors . . . have a copy.\"\n\nDora shook her head. \"You better believe Mr. Desmond called the very day she died. But Mr. Danvers, that was her family solicitor, he said she didn't leave a will with him.\" She paused. \"Which is really odd considering her husband used to be a solicitor. You'd have thought she would have been sure to make a will.\"\n\n\"Her husband was a solicitor?\"\n\nDora nodded. \"When he come back from China, his mother talked him into doing something 'sensible.' Well, I ask you, what could be more sensible than helping heathens in foreign parts?\"\n\nThompkins shrugged.\n\nDora nodded. \"Anyways, he studied to become a solicitor and they became sensible about everything, except their Oriental treasures. Crazy about their Oriental knickknacks and furniture they was.\" She shook her head. \"Mr. Forsythe goes into business with his friend. It used to be called Forsythe and Danvers, but after Mr. Forsythe died, he chucked the Forsythe and shortened it to Danvers.\"\n\n\"What happens to her money without a will?\"\n\nDora shrugged. \"I don't know. I guess Mr. Desmond gets it. The house is . . . some funny name . . . like fairy tales.\"\n\n\"You mean entailed?\"\n\n\"Yaw, that's it.\" She stared. \"That means Mr. Desmond gets it?\"\n\n\"It means, the house goes to a particular relative, usually a male.\"\n\nShe nodded. \"I thought so. More's the pity.\" She shook her head. \"That's the last person she would have wanted to have it. 'Dora,' she says to me. 'I think I'd rather burn my money in a bonfire than see Desmond and his greedy wife get it.' \"\n\n\"What makes you think they're greedy? I mean, if Mrs. Forsythe was family, then it would make sense for the money to stay in the family.\"\n\nDora snorted. \"I ain't saying that's not true, but that Mrs. Tarkington was always trying to get Mrs. Forsythe to spend money on them horses and redo the stables and such. One day I admired a pretty red box with one of those dragons on it that Mrs. Forsythe had. She collected the boxes . . . Chinese puzzle boxes they was. Well, Mrs. Forsythe gives it to me. Says she wants me to have it. I was showing it to Cook before they let her go and Mrs. Busybody comes in and accuses me of stealing and gives me the sack.\" She huffed. \"Well, I tells her Mrs. Forsythe gave me that box. I ain't never stole nothing in my life.\" She took several deep breaths to steady her nerves. \"Well, just then, Mrs. Forsythe come down the stairs and tells her she did give me the box and she didn't have the authority to fire me, not so long as she was alive.\" Dora smiled at the memory.\n\n\"I'll bet that didn't sit very well with Mrs. Tarkington.\"\n\nDora laughed. \"You got that right. She was furious. Stomped out of the room. Well, the next thing you know, that box comes up missing. Well, I didn't think too much about it, but then later that night, in waltzes Mrs. Tarkington smiling like the cat that got the last of the cream. She plops that box on the table and says she took it into town to a friend of hers. Says it's just a cheap piece of junk and not worth more than two quid.\" She stared at the butler. \"I tells her plain as day, I don't care if it wasn't worth but two pence, it was a gift and she didn't have no right to take it.\"\n\n\"What did she do then?\"\n\n\"She just laughed and waltzed out.\" She shook her head. \"The house was entailed and he gets that regardless, but the money doesn't go with the house. It was Mrs. Forsythe's money, not her husband's.\" She shrugged. \"Well, I guess Mr. Desmond and that woman is gonna get Mrs. Forsythe's money regardless of what she wanted.\" She sighed. \"It's a pure shame too, but I guess if she didn't want him to get the money, then she shoulda made a will.\"\n\nThompkins watched the maid finish the tea and wondered. That was very odd indeed.\n\nChapter 16\n\nNana Jo texted that Irma had been discharged and I needed to get my butt to the hospital before she ended up committed to the psychiatric ward for being a nymphomaniac. I grabbed my notebook and hurried downstairs.\n\nMy nephews had things well under control and promised to lock up and take care of the poodles before they left.\n\nWhen I arrived, Nana Jo, Irma, Dorothy, and Ruby Mae were waiting in the lobby. Irma was in a wheelchair, being pushed by a small, dark-skinned woman with a short afro. She was petite with smooth skin and had a big smile.\n\nRuby Mae got in the car. \"Sam, this is my granddaughter Francesca. She's a medical student at JAMU.\"\n\nI smiled. Ruby Mae had nine children and her extended family was larger than the population of North Harbor.\n\nThe ride to Shady Acres was uneventful, apart from the bickering between Nana Jo, Irma, and Dorothy.\n\nI pulled up to the front of the main building and let everyone out and then parked and went inside to check on the arrangements.\n\nA memorial service was a fairly simple affair to arrange. Gaston was providing some appetizers and light refreshments. Most of the residents weren't familiar with Max Franck, but they would attend for the refreshments, if nothing else.\n\nCaroline Fenton had reserved the main living room area and several people were already there. Irma had a compression boot on her left foot, which was only slightly shorter than her hooker heels. She had one arm in a sling. Other than that, she looked pretty much the same. However, she walked up to the first man she saw and stared up with large doe eyes and milked her injuries for all she was worth.\n\n\"Gerald, would you help me to the sofa, please. I'm not used to this boot, and I need a strong man to hold on to.\" Irma grabbed hold of Gerald's arm.\n\n\"That poor man should have run. With one good leg and an arm in a sling, she could still calf wrestle a grown man to the ground in less than five seconds,\" Nana Jo said.\n\nThere were a couple of lovely floral arrangements near the picture of Max at the front of the room.\n\n\"Who sent flowers?\" I asked.\n\n\"My sister's art gallery is next to that florist shop, so I ordered one arrangement, but I have no idea who the other one is from.\" She walked over to the flowers and looked at the card. When she returned, she said, \"Rosemary Lindley.\"\n\nI hadn't had an opportunity to fill them all in on everything I'd learned in Chicago, but we planned to get together for drinks following the memorial.\n\nThe girls split up and mingled. One thing I'd learned from these ladies was that the best way to get information was to divide and conquer. Ruby Mae took her knitting and sat down on the sofa. It wasn't long before someone came and sat down next to her. She had one of those faces that people felt comfortable confiding in. Irma was flirting with Gerald on the sofa at the other end of the room. Irma was the world's biggest flirt, but she wouldn't forget to pump Gerald for information. Dorothy was also a flirt, but she was subtler than Irma, which wasn't saying a lot. At close to six feet, Dorothy managed to attract men of all ages.\n\nNana Jo had a steady boyfriend, Freddie, but he was nowhere to be found. She headed toward Velma Levington. \"I never did get a chance to question Velma.\"\n\nThat left me standing alone. I was probably the most awkward of the bunch. I smiled as I remembered the first time I went with my grandmother to a reception after a funeral and drank several glasses of champagne on an empty stomach and ended up puking and humiliating myself. I bypassed the glasses of white wine and grabbed a small plate of appetizers. I spotted Sidney Sherman standing nearby and casually walked over so I was standing next to him. \"I remember you from the bus. You were the bodyguard.\"\n\nSidney Sherman stood in his tight jeans and leather jacket. Although he wasn't wearing the mirrored sunglasses, he might as well have been. His face and his eyes were stone and gave away nothing of his thoughts or feelings.\n\n\"Perhaps I should introduce myself.\" I wiped my hand on my napkin and extended it. \"I'm Samantha Washington.\"\n\nSidney Sherman barley glanced at my hand.\n\nAfter a few moments, I dropped it. \"If you weren't going to talk and just wanted to stand around and be rude, why did you bother to come?\"\n\nHe barely moved, but a muscle at the corner of his jaw pulsed.\n\n\"Surely now that the person you were guarding is dead, your assignment is over.\"\n\nThe jaw clenched and a slight flush of color rose up the side of his neck.\n\n\"Unless, of course, you're the one who killed him.\"\n\nThe blood from his neck hit his ears and he turned to face me. His eyes were slits and the muscle on the side of his face was pulsing like crazy. He pushed a finger in my face and glared. \"Are you accusing me of murdering my client?\"\n\nNana Jo walked up beside the bodyguard. She was taller than him and she looked like a mother bear protecting a cub. \"I've got a .38 pointed at your side, and I'm a darned good shot. Now, you've got three seconds to get your finger out of my granddaughter's face before I redecorate this room with your guts.\" She pushed the barrel of the gun into his side. \"And, just in case you're wondering, I wasn't making a pass. I removed your gun from your waistband.\" She smiled and passed me her purse and another gun, which I assumed from the look in Sidney Sherman's eyes, he recognized.\n\nSidney Sherman lowered his fingers from my face. He gritted his teeth. \"What do you want?\"\n\n\"My granddaughter wants to ask you a few questions. So, we're going to sit down in these chairs, nice and friendly, like human beings. She's going to talk and you're going to answer.\" Nana Jo inclined her head toward several Queen Anne chairs in a quiet corner of the room.\n\nWe walked over slowly, smiling the entire time. Nana Jo walked next to Sidney Sherman with her gun in his side. She used her body to conceal the weapon from view.\n\nSarah Jane Howard approached us, but Nana Jo turned. \"Not now, Sarah.\"\n\n\"I really need to talk to you, Josephine.\"\n\n\"Sure. I just need to talk to this gentleman first. Why don't you wait for me over there?\" She inclined her head to the lobby. \"I'll be there in just a minute.\"\n\nSarah Jane Howard looked reluctant but eventually left.\n\nOnce we were seated, she glanced at me. \"Now, Sam, why don't you ask your questions?\"\n\nI took a deep breath. \"Who hired you to guard Max Franck?\"\n\nSidney Sherman clamped his jaws closed, but, after a few seconds, he said, \"I was hired by Mr. Franck's agent, John Goldberg.\"\n\n\"Why?\" I asked.\n\nHe sighed. \"Obviously, he believed he was in danger. Why else would he hire a bodyguard?\"\n\n\"In danger from whom?\"\n\nHe was silent but eventually shrugged. \"I don't know.\"\n\nNana Jo's eye narrowed. \"Now, why do I get the impression you didn't take this threat seriously?\"\n\nHe shrugged. \"I dunno what you're talking about.\"\n\n\"Look, you were hired to protect Max Franck and someone killed him. That can't be good for business,\" Nana Jo said.\n\nHe huffed. \"Okay. You're right. I didn't believe he was in danger.\" He paused but rushed on. \"I thought it was a publicity stunt.\" He adopted an attitude. \" 'Mr. Franck's next book is going to rock the world. It's so dangerous I'm hiring a bodyguard to protect him.' \" He shook his head. \"He was just trying to sell more books.\"\n\n\"Well, obviously, not, since the man is dead,\" Nana Jo said.\n\nSidney Sherman turned and Nana Jo leveled her gun.\n\nSherman stopped and raised his hands. \"All right. Could you drop the gun? I'm talking. I'm answering her questions. I don't want you getting nervous and that thing going off and killing someone.\"\n\nNana Jo smiled. \"Look, I'm not suffering from the palsy and my hands are still steady. So, as long as you don't make any sudden movements, you'll be safe.\"\n\nHe sighed.\n\n\"Why do you think hiring you was merely a publicity stunt?\" I asked.\n\n\"Because he told me it was. He said I just needed to look the part and stay close to him for a couple of days.\"\n\n\"Why didn't you?\" I asked.\n\n\"Why didn't I what?\"\n\n\"Stay close to him? What happened?\"\n\nHe sighed. \"When everyone got off the bus, he said he wanted to stretch and take a leak. When I got up to go with him, he said he didn't need help.\" He sighed. \"He got off the bus. There was one old lady asleep in the back and then he got into an argument with his daughter. I hung around for a bit, but I could see she wasn't a threat.\" He paused for a few minutes. \"So, I went to the bathroom and, by the time I got back . . . well, you know.\"\n\nI couldn't think of anything else to ask. I turned to Nana Jo.\n\n\"Why are you here now?\" she asked.\n\nHe sighed. \"I wanted to pay my respects.\" He looked down. \"I thought maybe I could remember something that would help the police.\"\n\n\"Did you?\" I asked.\n\nHe shook his head. \"Nothing.\"\n\nNana Jo looked at him for several seconds. Then she lowered her gun. \"Sam, you can return his gun.\"\n\nI made sure no one was watching and then slid the gun across.\n\nHe took it and slipped it inside his jacket. \"Are we done?\"\n\nI nodded.\n\nHe stood. He glared at Nana Jo and then turned and walked out.\n\nA few seconds later, we heard a scream.\n\n\"That sounded like Irma.\" Nana Jo stared at me.\n\nWe rushed toward the direction of the scream. In a corridor off the lobby near the elevators, lying in a heap, was the body of Sarah Jane Howard.\n\nIrma screamed once more and then fell down in a dead faint.\nChapter 17\n\nIf I thought the murder of Max Franck on a chartered bus between North Harbor, Michigan, and Chicago, Illinois, was chaos, I was wrong. Between the police and the ambulance and Irma's hysterics, this was an absolute circus.\n\nDetective Pitt marched through the lobby and glared at me as though I was responsible for murdering Sarah Jane Howard. He glowered. \"Come with me.\"\n\nHe marched off in the direction of Caroline Fenton's office.\n\nI looked around for Nana Jo but remembered she was comforting or threatening Irma, depending on what the situation called for. After a brief moment's hesitation, I decided to suck it up and followed Detective Pitt to the office.\n\nIn Caroline Fenton's office, he paced. \"Shut the door.\"\n\nI closed the door behind me and stepped up to the desk. \"Detective Pitt, you seem to be angry, but, for the life of me, I can't\u2014\"\n\nHe halted. \"Angry? Angry? You think I'm angry?\" He glared. \"I haven't even begun to get angry. What the\u2014\"\n\nI held up a hand. \"I didn't kill her. For some reason, you seem to believe this is all somehow my fault, but you're wrong. All I did was arrange a memorial for Max Franck.\"\n\nHe paced, but I could tell he'd lost some of his steam. \"I don't know how, but I'm sure you or your nutcase of a grandmother are somehow responsible for this mess.\" He paced a bit more and then flung himself into a chair. He leaned back and then made a sweeping gesture indicating I should sit.\n\nI sat down on the guest chair across the desk from the detective.\n\n\"Now, will you tell me what's going on?\"\n\nI took a deep breath and recounted what I knew of the events.\n\nDetective Pitt watched me but said nothing until I was done. \"That's it? That's all you've got?\"\n\nI nodded. \"That's all I've got.\"\n\nHe rubbed his hand through his comb-over. Just like before, the few strands stood at attention as though electrified. \"Well, I'm going to need something to go on. When the chief heard there was another murder here, he went crazy. He insisted I call in Sergeant Alvarez.\"\n\n\"Why? I thought Sergeant Alvarez thought Bob Marcus was responsible for Max's death? Since you have him in custody, it can't be him and that blows his theory out of the water.\" I smiled. However, I should have known better than to get excited too early. One look at Detective Pitt's face told me my assumptions were wrong.\n\nDetective Pitt shook his head. \"Had to let him go.\"\n\nI dropped my head. \"You let him go? Why?\"\n\n\"He made bail.\"\n\nI stared openmouthed. \"Does Sergeant Alvarez . . .\"\n\nHe was nodding before the words left my mouth.\n\n\"Well, fiddle sticks.\"\n\nDetective Pitt smiled. \"You better be careful. Your grandmother might just wash your mouth out with soap.\"\n\nI tried to smile at the detective's joke, but my heart wasn't in it. \"If Bob left jail and came here, I haven't seen him.\" I thought for a moment. \"Are you sure it was murder?\"\n\nHe nodded. \"We'll have to wait to hear from the coroner, but she's got the same type of wound.\"\n\n\"That wound seems rather specialized, don't you think?\"\n\nHe shrugged. \"A sharp object to the kidneys is pretty effective.\" He looked hopeful. \"Are you asking if the murderer would have had medical training?\"\n\nI told Detective Pitt what I'd learned from Frank about quiet kills.\n\nA flash of what I would call respect crossed his face but was quickly replaced by the anxious expression he'd started this round of conversations with. \"So, basically anyone with any type of medical or military experience or anyone who has access to the Internet would have known how to kill quietly.\"\n\n\"True, but . . . why would they?\"\n\nHe stared. \"What do you mean?\"\n\n\"Okay, so maybe Max Franck knew something. Maybe during the course of researching his next book, he stumbled across something that made him dangerous to someone. Or maybe he made his daughter angry for not getting tested or maybe he was just a plain jerk who was responsible for someone committing suicide. Whatever the killer's motive for killing Max Franck, why kill Sarah Jane Howard?\" I paused.\n\n\"I remember her from that other murder, when that Romanov woman was murdered.\" He colored slightly.\n\nI guessed he was remembering how he nearly arrested my grandmother for that one but chose to remain silent.\n\nHe hurried on. \"That Sarah Jane Howard was a nosy old busybody.\"\n\n\"Exactly.\"\n\nHe looked surprised. \"What?\"\n\n\"She was nosy. Nana Jo said Sarah Jane Howard was the nosiest person she'd ever met.\" I thought back for a moment. \"I remember Ruby Mae saying she used to sit at her window with binoculars and spy on people.\" I paused, but Detective Pitt didn't seem to be catching on.\n\n\"What are you saying?\"\n\nI sighed. \"I'm saying, maybe Sarah Jane Howard was being her normal, nosy self. And, what if she saw something she wasn't supposed to see?\"\n\nHe shook his head. \"Naw, that's no good.\"\n\nI was crestfallen. \"Why not?\"\n\n\"Because busybodies like that Howard woman are all the same. What's the good of knowing something if no one knows you know it?\" He gave me a knowing look.\n\nI thought about what he was saying.\n\nHe leaned across the desk. \"Trust me. If that woman knew something, or even if she thought she might possibly know something, she would have told someone. She would have reported it.\"\n\nI scooted to the edge of my seat in excitement. \"What if she didn't know she knew something?\"\n\nHe rubbed his forehead. \"You're making my head hurt.\"\n\n\"Stay with me. What if she didn't realize what she saw until later?\" I gasped in excitement. \"Or, what if she didn't know anything about Max Franck's murder, but what if what she knew was related to the attempt on Irma's life?\"\n\n\"I thought you didn't believe Irma was pushed?\"\n\nI thought about it. \"I don't believe Bob pushed Irma. But what if it wasn't Bob? What if she saw the person who really did push Irma?\"\n\nHe shook his head. \"She still would have wanted someone to know. She would have told someone.\"\n\nI nodded. \"What if the person she told was the real killer?\"\nChapter 18\n\nDetective Pitt didn't look convinced, but he shrugged. \"Okay, I'll bite. Who did she talk to?\"\n\nHeat rose up my neck. \"I don't know that she actually talked to anyone.\"\n\nHe squinted. \"Who did she attempt to talk to?\"\n\nI squirmed in my seat. \"I don't know who she talked to, but I do know she wanted to talk to Nana Jo.\"\n\nLuckily, Nana Jo had an ironclad alibi for the time of the murder. Although she wasn't thrilled when Detective Pitt pulled her into the tiny office to ask her about her movements.\n\n\"Listen here, I was too busy putting the drop on that Sidney Sherman character and preventing him from getting violent with my granddaughter to be going around killing Sarah Howard,\" Nana Jo exaggerated.\n\nAfter a good fifteen minutes of yelling, Nana Jo made her point and stomped out of the office.\n\nDetective Pitt looked as though he'd been working out. He had beads of sweat on his forehead and, unfortunately, under the pits of his arms.\n\nIt was several hours later before we were released to leave. By the time I got home, I was exhausted. It wasn't until I made my way upstairs that I realized part of my problem was that the only thing I'd had to eat was appetizers.\n\nI looked in my refrigerator and smiled when I saw a pint of Frank's taco soup. He must have dropped it off earlier. I smiled as I put a generous serving into a bowl and heated it in the microwave while I changed into yoga pants and a warm sweater. By the time I was comfy, my food was ready.\n\nI crushed several saltines and dumped them into the soup. While I sat at the breakfast bar and ate, I marveled at the wonders of technology, which allowed me to heat dishes in seconds and send text messages of gratitude, which I knew would be received almost instantly. Technology was a wonderful thing. At least it was when it worked. Unfortunately, the cameras in the stairwell at Shady Acres hadn't been working. Although, it wasn't necessarily that the cameras weren't working but that they weren't pointed in the direction to capture Sarah Jane Howard's murder. Which I found interesting. Either the killer knew the exact location where he or she could murder someone without being caught on camera or our murderer was extremely lucky. The truth was probably a combination of both.\n\nAfter dinner, I let the poodles outside and decided to spend some time writing in the hopes that I could collect my thoughts.\n\nDetective Inspector Covington traipsed through the cold, damp ground to the stables and tried to smile and not think of his wet shoes, although the squishing he heard each time his foot hit the ground made it extremely difficult to think of anything else. In the stables, he was assaulted by the stench of damp horse flesh and manure. He tried not to think of Lady Clara sitting in the office with smiling Desmond Tarkington or even Lady Elizabeth sitting in front of a warm fireplace sipping tea.\n\nConstance Tarkington walked up to a tall beast of a horse that seemed taller than any horse he'd seen. Although, granted, growing up in the streets of London meant he hadn't seen many. Not up close and personal, anyway. He forced a smile and took several deep breaths to steady his nerves. He'd always heard animals could sense fear.\n\n\"What a magnificent animal,\" he said with what he hoped was the right amount of enthusiasm in his voice.\n\nConstance opened the stall door and led the beast out.\n\n\"What's his name?\" He asked more for something to say rather than a desire to know. He had no intention of addressing the creature.\n\n\"Satan.\"\n\n\"Excuse me?\"\n\nConstance laughed. \"His name is Satan.\" She caressed the animal's back. \"My husband's idea of a joke.\"\n\nThe animal stomped his feet and snorted in a manner that indicated the name might not have been a joke after all.\n\n\"I know what you want.\" She reached into her coat pocket and held up a carrot, which the beast quickly chomped. When he finished, he used his head to push her forward. She would have fallen had Covington not reached out to catch her.\n\nHe helped to right Constance, who clutched his arms, forcing him to hold her closer and longer than necessary. When he looked at the woman, he recognized a hungry look in her eyes.\n\nThe detective forced himself to smile and hoped the smile extended to his eyes. \"Mrs. Tarkington.\"\n\n\"Constance.\"\n\nHe looked around. \"You have very nice stables . . . Constance . . . but I don't see any helpers. Surely your husband doesn't do all of the work himself.\"\n\nShe snorted. \"Him? You must be joking. Desmond isn't into horses or riding or anything fun.\" She released the detective's shoulders and walked around the stables. \"This is all mine.\" She raised her hands to encompass the entire stables.\n\n\"But surely it's too much for one woman . . . even a woman such as yourself.\"\n\nShe smiled, accepting the comment as a compliment. \"My husband doesn't believe in 'wasting money.'\" She used air quotes. \"At least not on anything that interests me. However, he can waste plenty of money on plays.\"\n\nThe detective tsked. \"Surely your husband's cousin could afford to pay for someone to run your stables.\"\n\n\"Eleanor wasn't fond of horses either.\" She sighed. \"More's the pity.\"\n\nThe detective inspector chuckled. \"Well, now that she's gone . . .\"\n\nConstance smiled. \"Yes, now that she's gone, we shall be able to afford some improvements.\"\n\nConstance Tarkington glowed. She spent the next five minutes telling the detective inspector exactly what improvements she planned for the stables. Even to someone unfamiliar with animals or construction, the plans sounded expensive. Clearly, Constance Tarkington had put a lot of thought into how she would spend Eleanor Forsythe's money. The question that crossed the young detective's mind was how long she'd been making plans.\n\nLady Clara Trewellen-Harper sat in Desmond Tarkington's study. The conceited old bore had been talking for what felt like hours about his roles in various theatrical performances. Fortunately, Desmond Tarkington, like many men, didn't really need or expect much from her, other than the occasional coos of awe and \"Oh my, aren't you amazing,\" and \"How fascinating.\" Recalling her days in finishing school, she was highly skilled at small talk and pretending to listen to conversations she knew nothing about.\n\nLady Clara glanced out the window and wondered what Detective Inspector Covington was talking about with Constance Tarkington.\n\n\"Is anything wrong?\"\n\n\"No, why do you ask?\"\n\n\"You were frowning and I wondered if I'd said something to offend you.\"\n\nLady Clara laughed. \"I'm sorry. I was just thinking about your wonderful career. I find it so fascinating, and I was thinking how wonderful that you can live in such a grand home and go on the stage and meet fascinating people.\"\n\nDesmond Tarkington chuckled. \"Well, I suppose it is fascinating to an outsider.\"\n\nLady Clara nodded. \"Indeed, I mean, if I lived in a beautiful house like this, I don't think I would ever want to leave.\"\n\nThe frown on Desmond Tarkington's face indicated that wasn't exactly the direction he expected the conversation to go. \"Yes, well, the house is rather nice, I suppose. Although, it's not really my taste.\"\n\n\"I suppose a famous actor like you would rather be in a modern house in London or . . . Hollywood,\" she whispered with enthusiasm.\n\nHe sat straighter in his seat. \"I suppose so . . . One of these days I'll make a film or two, but I have to say, I prefer the stage. There's nothing like a live audience to bring out the best in an actor's performance.\" He stuck his prop pipe in his mouth and put his other hand inside the front of his smoking jacket.\n\nLady Clara thought he looked like Napoleon and found it rather difficult to take him seriously. But she'd been entrusted with the task of getting Desmond Tarkington to talk and she refused to go back and have that arrogant Scotland Yard detective providing clues and solving the murder while she sat listening to dreary Desmond Tarkington talk about his glory days on the stage. \"I suppose now that your cousin has died, you'll be famous and rich.\"\n\nDesmond Tarkington frowned. \"Well, I hardly think that's a proper conversation to have.\" He looked at Lady Clara but eventually smiled. \"However, I suppose it's true that I'll inherit. My cousin was very wealthy, and I am her closest relative.\" He bit the end of his pipe. \"We were very close.\" He smiled but quickly looked away and frowned.\n\nLady Clara batted her eyelashes. \"Why, Mr. Tarkington, is there anything wrong?\"\n\nAt first, Desmond Tarkington denied anything was wrong, but with just the slightest bit of prodding from Lady Clara, he admitted something was bothering him.\n\n\"Desmond . . . you don't mind if I call you Desmond?\" She smiled.\n\nDesmond smiled in a way that indicated he didn't mind the least bit that Lady Clara called him by his first name. \"Well, there's nothing wrong . . . not really. I've just been concerned about my cousin's will.\"\n\n\"Her will? You don't mean to tell me she's done something silly and left all of her money to a cat or something?\"\n\nDesmond chuckled. \"No. Nothing like that. It's just that she indicated she had a will but no one can seem to find it. In fact, I rather hoped she might have said something to your aunt, Lady Elizabeth, when they were in London.\"\n\nSuddenly, all was clear to Lady Clara. \"Did you indeed?\"\n\nLady Elizabeth and Lady Alistair sat in the sitting room with Mrs. Muriel Sanderson. The woman had barely said anything and spent the majority of the time gaping at Lady Alistair's jewels and the fox stole she wore around her neck.\n\n\"How long have you been with Eleanor?\" Lady Alistair asked.\n\n\"About two months.\"\n\n\"What brought you here?\" Lady Alistair smiled at the tedious manner they were having to pull information out of the frightened woman.\n\n\"Eleanor was my cousin,\" the woman mumbled. \"A distant cousin, but . . . family.\"\n\n\"So nice to have family.\" Lady Elizabeth, who was highly skilled at small talk, smiled and took a sip of the tea Thompkins had brought them. \"Now that Eleanor is gone, will you stay on here?\"\n\nMuriel Sanderson dropped her spoon. She reached down and picked it up. \"I . . . don't . . . I suppose . . .\" She dropped her napkin. \"It depends on the . . . I mean . . . I'm sure they wouldn't . . .\" She choked back a cry and pulled a handkerchief from the sleeve of her dress and dabbed at her eyes.\n\nLady Alistair and Lady Elizabeth exchanged glances.\n\n\"Surely Eleanor provided for you? Some type of . . . legacy perhaps?\" Lady Elizabeth asked.\n\nMuriel Sanderson choked back tears. \"I don't know. I just don't know. I assumed there would be something, but with no will . . .\"\n\n\"No will?\" Lady Alistair asked. \"You don't mean to say she died without making arrangements for her family and the servants?\"\n\nMuriel nodded. \"Nothing. If she had a will, no one knows where it is. There's only one servant, Dora, and she's going to give her notice.\"\n\n\"I suppose you've tried her solicitor?\" Lady Elizabeth asked.\n\nMuriel nodded. \"Desmond called him first thing.\"\n\n\"How odd.\" Lady Alistair sipped her tea.\n\n\"We wondered if maybe she hid it somewhere or . . .\" She stared at Lady Elizabeth. \"Or perhaps, she gave it to someone close to her.\"\n\nLady Elizabeth sipped her tea. \"I wonder the same thing.\"\n\nChapter 19\n\nAt some point during the night, I stopped writing and got in bed. Although, I couldn't remember actually going through the motions. I knew it must have happened since I was in bed. I received a jolt when I recognized the noise that woke me was the sound of snoring in my ear. I sat up straight in my bed, wide-awake. When I realized the snoring was coming from Snickers, who was curled up asleep on my pillow, I relaxed. Apart from Snickers' snoring, which was amazingly loud for a ten-pound poodle, the house was quiet. Nana Jo had wanted to keep Irma company, so she spent the night at Shady Acres. Regardless of whether I believed Irma was pushed down a flight of stairs or tripped, she had found two dead bodies, sprained an ankle, and fainted twice. That was a lot for anyone.\n\nA hot shower provided some time for me to think through recent events. I kept going back to my conversation with Detective Pitt and asking, why would someone want to kill Sarah Jane Howard? It seemed obvious that the murder was connected to Max Franck's murder in some way. The method used to kill both people was too similar for the two deaths not to be connected. By the time I finished my shower, dressed, and took the dogs downstairs to take care of their business, I still didn't have any answers.\n\nI wasn't in the mood to cook today, so when my nephews arrived, I sent a message to my sister, Jenna, asking if she wanted to meet me for breakfast. I even offered to treat. Being the trusting soul that she was, her reply was, What do you want?\n\nI took her snarkiness as acceptance and typed the location of her favorite breakfast spot.\n\nAs usual, I arrived before my sister, who was known for always being ten minutes late, and she didn't disappoint.\n\nJenna and her husband, Tony, were both attorneys, although Jenna was a criminal attorney and Tony practiced corporate law. Roughly the same height as me, Jenna was four years older, although you couldn't tell by looking at her. She was also known within law enforcement circles as \"The Pit Bull,\" a label she embraced.\n\nJenna flew into the restaurant wearing her lucky suit, which indicated she would be heading to court when she left the restaurant. She sat down and the waitress immediately brought her a cup of hot tea. \"Can I have a butter croissant to go and a take-out cup, please? I won't be staying long.\"\n\nThe waitress smiled. \"You just enjoy that one and I'll bring you a fresh tea in a to-go cup. Same kind as usual?\"\n\nJenna nodded. \"Yes, English Breakfast.\"\n\nThe waitress nodded and hurried to take care of Jenna's order.\n\nMy sister sipped her tea and looked at me. \"What's up?\"\n\n\"Nice to see you too.\"\n\nShe looked at her watch. \"I have to be in court in thirty minutes. Make it quick.\"\n\n\"I'm offended that you think the only reason I would call you is because I want something. I've left you alone because I know you've been busy, but maybe I just missed spending time with my older, wiser big sis.\"\n\nJenna glanced over her cup. \"My clock is ticking. In ten minutes, I'm going to be walking out so I can get to work. If you want something, you better make it quick.\"\n\n\"All right.\" I knew my sister and she'd walk out in ten minutes regardless of what I said. I quickly told her about Bob Marcus.\n\nThe waitress brought Jenna's croissant in a bag along with another tea, this time in a paper cup.\n\nJenna stood. \"What do you want me to do?\"\n\n\"I don't think Bob killed Sarah Jane Howard, and whoever killed Sarah Jane Howard more than likely is responsible for killing Max Franck. Sergeant Alvarez wants to wrap this thing up, and I'm afraid he's going to arrest Bob and charge him with both murders. He'll take him to Chicago and no one will do anything, and an innocent man will spend more time in jail.\"\n\nShe glared. \"So, how does this affect me?\"\n\n\"You're a lawyer . . . a pit bull. Don't let them railroad an innocent man. At the least, don't let them take him to Chicago until we can find the real killer.\"\n\nJenna stared for several seconds and then lifted her cup. \"I've gotta go. Thanks for breakfast.\" She held up her cup and the bag with the croissant, turned, and walked out.\n\nMy sister got into her car and I wondered why I had bothered. Obviously, I didn't know my sister as well as I thought. I slumped down in my seat but nearly jumped when my phone vibrated, indicating I'd gotten a text message. I lifted my head and pulled my cell phone out of my pocket.\n\nThe text was from Jenna. Text me Bob's full name. No promises.\n\nA smile spread across my face as I replied. Maybe I knew my sister after all. The waitress returned and I smiled. \"I'm ready to order.\"\n\nAfter I left the restaurant, I went back to the bookstore. Today was New Year's Eve, and I planned to close the store early. The twins would be going out to celebrate later, so I thanked them for helping out, paid them, so they'd have plenty of spending money, and let them go. Traffic in the store was light, and I was well able to handle things myself until noon, when I closed down.\n\nI got a text message from Nana Jo instructing me to meet at her house for a noon meeting. Her message was immediately followed by a message from Frank saying Nana Jo had ordered lunch and told him I'd bring it with me. Unlike the mystery-book shoppers, his customers were there in droves. He didn't have a lot of time, but if I pulled up to the back of his restaurant, he would load the food into my truck. He was a good man.\n\nI went upstairs and noticed Snickers and Oreo asleep in their beds. My poodles were getting older. Their muzzles were filled with white and their once-dark chocolate coats were now more caf\u00e9 au lait than espresso. I also noted they spent a lot more time sleeping and wondered how many more years I'd get to spend with them.\n\nThose dark thoughts made me sad, and I picked up Snickers and gave her a tight squeeze. She was the older of the two and held a special place in my heart. \"I need to spend more time with you, girl, don't I?\"\n\nShe yawned and then licked my nose.\n\nNana Jo and the girls would want to ring in the new year with drinks, dancing, and fun, which meant a late night for me. \"Wanna go to Nana Jo's house?\"\n\nShe yawned again. Obviously, she'd had a busy day.\n\nOreo scratched at my legs. I'd neglected to make their grooming appointment.\n\nI grabbed my coat and purse and a handful of dog biscuits. \"Come on.\" I needn't have bothered speaking. The treats were enough to get them to follow me. Outside, I waited while they took care of business. Today was one of those days where I was grateful for automatic start. I used it to make sure the car and the seats were nice and warm by the time the poodles finished and we were ready to leave. I might not have a luxury vehicle like Frank, but I was definitely fond of my Ford Escape with its bells and whistles.\n\nI loaded up the poodles and sent Frank a text before I pulled out of the garage, letting him know I was on my way.\n\nIt was a short drive to his restaurant, and he was waiting as soon as I pulled up, which let me know he had been looking out for me.\n\nOne button on the dashboard opened my back hatch and I didn't even have to get out of my car. Frank had a large cardboard box, which he quickly loaded into the rear, and then pressed the button to close the hatch.\n\nI pushed the button that rolled down the window when he hurried toward my window. \"Thank you, but you'll catch a cold out here with no coat.\"\n\nHe stuck his head inside and kissed me. After a few seconds, when he pulled away, I felt a bit dizzy.\n\nHe smiled. \"I'm warm enough now.\"\n\nI grinned like a silly schoolgirl. \"I wish you didn't have to work tonight, but I understand.\" We'd talked about not being able to ring in the new year together.\n\nFrank released a heavy breath. \"I know it's our first New Year's Eve, but I don't want to leave Benny here alone or\u2014\"\n\nI held up a hand to stem the explanation. \"I know. It's okay. I absolutely understand and it's okay.\"\n\nHe gazed into my eyes with intensity. \"Are you sure?\"\n\nI smiled and nodded. \"I'm very sure.\"\n\nBenny came to the back door of the restaurant. \"Frank, we have a problem.\"\n\n\"You better get back to work.\" I crooked a finger and beckoned for him to lean close. When he did, I kissed him again. \"Thank you.\"\n\nHe fanned himself. \"You're welcome.\"\n\nI smiled most of the way to Nana Jo's. In fact, I was so distracted by Frank Patterson, I nearly forgot that Snickers and Oreo were in the car until I glanced in the rearview mirror and saw them cuddled up together in their dog bed on the back seat of the car.\n\nAt Nana Jo's I pulled into her driveway and blew the horn. After a few seconds, the door lifted and I pulled into the garage.\n\nNana Jo helped me bring the food from the back of the car into the house, where the others were waiting. Snickers and Oreo trotted in like they owned the place. Of course, everyone petted them, so they were very happy. Eventually, Nana Jo found the extra food dishes that we kept at her house and the poodles were distracted by food.\n\nWe took thirty minutes and ate lunch without talking about murders or crime. However, when everyone had finished eating, Nana Jo picked up her iPad, which signaled it was time for business.\n\nI got up and let the dogs out to take care of business and quickly came back inside and got them settled down by my feet.\n\n\"Okay, who wants to go first?\" Nana Jo looked around and her gaze landed on Irma. \"Irma, maybe you should go first. I think you should tell us everything that happened.\"\n\nIrma was wearing a lot more makeup than usual, which was saying a lot. \"I told Gerald I wanted a throw and he'd gone to get one.\" She smiled demurely. \"He's such a thoughtful man.\"\n\nNana Jo squinted and looked as though she would strangle Irma.\n\n\"Actually, I'd like you to go back to the other day, when your room was searched and you fell down the stairs,\" I said.\n\nIrma nodded. \"Of course. I forgot you weren't there when the killer made the first attempt on my life.\"\n\nNano Jo rolled her eyes at Irma's first attempt.\n\nIrma recapped the incident from the other night, which was very similar to what Nana Jo had said.\n\n\"Who was in the stairway?\" I asked.\n\nEveryone exchanged glances. Irma shrugged. Nana Jo frowned for several seconds as she tried to remember. \"Sam, honey, everyone was in the stairwell. The fire alarm was blaring and flashing like a strobe light at a disco.\" She paused. \"I know all of us were there. I'd just been trying to track down Velma Levington.\" She shook her head. \"That is one woman who's hard to reach. I spotted her down the hall and headed that way, and that's when I got distracted because Irma screamed.\" Nana Jo frowned at Irma. \"You've been doing a lot of screaming lately.\"\n\nIrma sniffed. \"The next time you find two dead bodies and someone tries to kill you, we'll see if you scream.\"\n\n\"Don't get your panties twisted in a wad.\" Nana Jo tapped her stylus on the table for several seconds but eventually gave up and shook her head. \"I'm sorry, but I can't remember who was in the stairwell.\"\n\n\"Where was Bob?\" I looked around. \"Was he near Irma's room?\"\n\nEveryone looked around. Eventually, Dorothy shook her head. \"No, I don't think he was.\"\n\nRuby Mae looked up from the knitting she had just taken out of her bag. \"I know he wasn't because Bob came upstairs with me.\"\n\nEveryone turned to Ruby Mae and started hurling questions at her. \"Are you sure?\" \"How do you know?\" \"Why didn't you say something sooner?\"\n\nShe huffed. \"Now, y'all are gonna need to stop firing questions at me and let me tell you.\" Ruby Mae took a few deep breaths. \"I had been downstairs talking to Melvin.\"\n\n\"Melvin Cooper?\" Irma asked. \"He's so handsome. I didn't know you were interested in Melvin.\"\n\nRuby Mae looked at Irma out of the side of her eyes. \"Honey, I ain't interested in no pretty boys like Melvin Cooper. Ain't no way a man that good looking is going to be satisfied with one woman, and I don't believe in sharing.\" Ruby Mae looked down her nose at Irma. \"I was talking to Melvin Cooper to see if he had any information about Max's murder.\" She glanced at Irma again. \"You remember him. Max, the man you were gushing over just a few days ago.\"\n\nIrma stuck out her tongue but started coughing. She reached into her purse. Usually, she pulled out a flask, but she felt around and didn't seem to find one. Eventually, she dumped the contents of her purse on the table and started sorting through them.\n\nRuby Mae continued, \"We were in the elevator together. We had just gotten off the elevator when we heard Irma scream and we rushed to your room to see what had happened.\" She turned to me. \"Does that help?\"\n\nI thought for a moment. \"Not really. Unless Bob was with you the entire time, it doesn't mean he couldn't have ransacked Irma's apartment earlier.\"\n\n\"What's this?\" Irma held up a key.\n\n\"I know you pretend to be a ditz sometimes, but now isn't the time.\" Nana Jo turned away from Irma.\n\n\"I know it's a key,\" she said sharply. \"I mean why is it in my purse?\"\n\nI stared at Irma. \"Isn't it yours?\"\n\nShe shook her head. \"I've never seen it before.\"\n\nI held out my hand and Irma gave me the key. I turned it around. \"It looks like a key to a locker.\" The key had a cheap circular tab with a number written on it. \"Eight one nine.\"\n\nNana Jo leaned across the table. Then she looked at me. \"You don't suppose Max put it in her purse.\"\n\nI shrugged. \"Who had access to your purse?\"\n\nIrma thought for several seconds but then shook her head. \"Beats me.\"\n\n\"Did you leave it on the bus when we stopped at the rest area?\" I asked.\n\nIrma's eyes grew larger and she nodded. \"I left it on the bus because Max said he wasn't going and I knew it would be safe\"\n\nThe excitement grew as we examined the key.\n\n\"Anything else in there?\" I asked.\n\nIrma sifted through the items scattered across the table.\n\nMy gaze landed on a picture. I pointed. \"What's that?\"\n\nIrma leaned across. She picked it up and stared. \"It looks like a picture of Robert Kennedy.\"\n\nThat got our attention. We all crowded around Irma and stared at the picture for several seconds.\n\n\"Who's that with him?\" Ruby Mae asked.\n\nWe stared harder. It was an old black-and-white Polaroid photo that had seen better days. The photo was approximately three and a half inches by four. There was a white border around the outside. One corner was missing, and the photo had a bend that went straight across. However, the image showed Robert Kennedy lying on the floor of the kitchen in the Ambassador Hotel in California where he had been shot. I had seen a similar photo in textbooks. However, something was different about this photo. I couldn't figure out what. It appeared to have been taken immediately after he was shot, which would have been in June 1968. Crouched beside the body was the busboy who had been shaking Kennedy's hand when he was shot. However, this photo showed several people standing nearby.\n\nWe passed around the photo, but no one recognized anything particular about the photo.\n\nNana Jo stared at the photo for a very long time. \"Something seems familiar about this, but I just can't put my finger on it.\"\n\n\"Are photos like this rare?\" I asked.\n\n\"I can ask my sister. She'd know.\" Dorothy shrugged. Her sister owned a gallery in downtown South Harbor and she'd been instrumental in finding information previously.\n\nI sighed. \"Most likely he had it for research for his book. He was writing a book about Robert Kennedy's assassination.\"\n\n\"What do you think we should do with it?\" Ruby Mae asked.\n\nI looked around the table. \"As much as I hate to say it, I think we need to give the key and the photograph to Sergeant Alvarez or at least Detective Pitt.\"\n\nEveryone started talking at once, which made it hard to understand.\n\n\"I don't see why we have to turn this stuff over to the police,\" Irma said. \"It was in my purse.\"\n\n\"Besides, we don't know for certain Max is the one who put those items in Irma's bag,\" Nana Jo argued.\n\n\"Right. I mean, she's had that bag in a lot of places. Anyone could have put that stuff in there,\" Dorothy said.\n\n\"We don't even know what the key opens,\" Ruby Mae said.\n\nI scowled. \"You've got to be joking. Who else would put a picture of Robert Kennedy on the day he was assassinated in Irma's purse, along with a locker key, except the man who was writing a book about the subject?\"\n\nI looked from one of them to the other. \"Look, you may be right. Maybe it is some grand coincidence. Maybe the key fell into her purse and it has absolutely nothing to do with his murder, but if it is important, then it's against the law to withhold evidence to a crime.\"\n\n\"But we don't know it's evidence. So, if you don't know it's evidence, then you can't be held accountable.\"\n\nSomething about the way Nana Jo looked when she said that made me wonder if she was serious. I stared at her. \"Are you making that up?\"\n\nShe hesitated for a few seconds but eventually shrugged. \"I'm sure I saw it on Law and Order or maybe it was Perry Mason.\"\n\nI sighed. \"I tell you what, I'll run it by Jenna and see what she says.\" I glanced around the table.\n\nThey weren't happy, but eventually everyone agreed.\n\nI held out my hand and Irma turned over the key and the picture.\n\nThe rest of the meeting was relatively uneventful. I updated everyone on my conversation with Detective Pitt and my conversation with Jenna.\n\nNana Jo filled the group in on our conversation with Sidney Sherman.\n\n\"Do you think he's telling the truth?\" Ruby Mae asked.\n\nI glanced at Nana Jo, and we both shrugged. After a few minutes, though, I added, \"I think he was telling the truth. I mean, if he was going to lie, he would have tried to make himself look better, don't you think?\" I glanced around.\n\n\"Well, he sure didn't help his reputation as a bodyguard to admit he permitted his client to get murdered while under his protection, did he?\" Nana Jo tapped her stylus.\n\nIrma turned to me. \"You do believe the two murders are connected, don't you?\"\n\nI nodded. \"I do. I can't see why anyone would kill Sarah Jane Howard unless she knew something about the first murder.\"\n\n\"Well, heck, I can think of a lot of people who would want to murder that nosy busybody,\" Nana Jo said.\n\n\"Me too,\" everyone added.\n\n\"She was a nosy busybody, that's true, but she's been at Shady Acres for how long?\" I glanced around.\n\n\"Ten years?\" Nana Jo looked at the others, who nodded.\n\n\"Well, I think that means you all found a way to either ignore her or shun her, but, in the past ten years, no one has killed her.\"\n\n\"I sure wanted to,\" Nana Jo mumbled.\n\n\"Especially after the way she tried to cast suspicion on you after Maria Romanov's murder,\" Dorothy said.\n\n\"That's all true, but you didn't murder her.\" I looked at Nana Jo.\n\nShe sighed. \"I get what you're saying.\"\n\n\"Good. So, back to Irma's original question. Do I believe the two murders are connected?\" I looked around. \"My answer is yes. I do.\"\n\nNana Jo read back through her notes from the conversation I'd had with Sarah Jane. \"What about the argument she overheard between Rosemary and Max?\" She looked up. \"I mean, the woman was furious about him not at least getting tested to see if he could donate bone marrow. I know I would have killed someone if I thought it would help my daughter.\"\n\nI looked at my grandmother, who had the mother bear look in her eyes again. \"I know that just sounds so coldhearted. Christopher and Zaq aren't my children, but I think I could easily kill if it meant saving their lives.\" A chill ran down my spine, and I shuddered.\n\nEveryone agreed, although Ruby Mae seemed distracted.\n\n\"Ruby Mae?\"\n\nShe knitted a few more stitches before she looked up. \"I agree with what everyone said. Y'all know I have nine children and I would do whatever I have to do to make sure my children are safe. I was just wondering . . . is this Rosemary a smart woman?\"\n\nI squinted and stared at Ruby Mae. \"Yes. She seemed like a very intelligent woman.\"\n\nShe nodded. \"I thought so too. I can't see her killing him and not getting the bone marrow.\" She glanced around. \"I mean, if you're going to kill him, at least make sure you take his body to the hospital and get what you need.\"\n\n\"I'm not sure you can take someone's bone marrow without their permission. Even if they're dead,\" I said.\n\n\"I know that.\" Ruby Mae knitted a few stitches. \"But, if it were me, I'd make sure there was a note or something that gave me permission to take the bone marrow.\"\n\nI thought about it. \"I think you're right.\"\n\nThe only new information anyone had learned was that Caroline Fenton had submitted her resignation and was planning to leave Shady Acres. Rumor had it, she said her nerves were shot after all of the murders, but no one knew for sure.\n\n\"I don't think Caroline Fenton's the only person who thinks Shady Acres is dangerous. I've heard several people are planning to leave.\" Ruby Mae knitted.\n\n\"Anyone we care about?\" Nana Jo asked.\n\nRuby Mae glanced at Irma. \"I've heard Melvin Cooper is one.\"\n\nIrma gasped. \"Why that dirty son of a\u2014\"\n\n\"Irma!\" everyone yelled.\n\nIrma coughed and began looking for her flask in the dumped contents of her purse. She sifted through all of the items on the table. When she found it, she took a swig.\n\n\"I heard Velma Levington was another one,\" Dorothy said.\n\nNow it was Nana Jo's turn to look surprised. \"Velma Levington? That is one busy woman. Every time I try to get close to the woman to talk to her, something happens. Either fire alarms go off or people are murdered.\"\n\n\"Maybe you need to stop trying to talk to her.\" Ruby Mae shuddered. \"I can't handle no more murders right now.\" She looked down her nose at Nana Jo. \"I know that isn't grammatically correct, but you know what I mean.\"\n\nWe chatted a bit longer, and then Irma said, \"It's New Year's Eve and I want to go party.\"\n\n\"I thought Shady Acres was having a New Year's Eve party?\" I asked.\n\n\"Caroline Fenton canceled it,\" Dorothy said.\n\nI must have looked puzzled because Nana Jo added, \"She said, with Sarah Jane's murder and the police crawling around everywhere looking for clues, it was irreverent and too much of a hassle.\"\n\nI blinked to try to clear my confusion. \"But today is New Year's Eve. How can she wait 'til the last minute to cancel your party?\"\n\nEveryone shrugged.\n\n\"Let's go to the casino,\" Irma suggested.\n\nI wasn't ecstatic about a trip to the casino. My hair and clothes always reeked of cigarette smoke afterward, however, the idea of sitting home and watching the ball drop on Times Square wasn't appealing this year either, especially alone.\n\nI nodded and the girls packed up their belongings.\n\nIt had been quite a while since the poodles had stayed at Nana Jo's, but, in addition to extra food and water dishes and dog food, she also kept an extra crate and dog bed for what she referred to as her \"great-grand poodles.\" So, we made another trip outside. When they were done, I cut a piece of string cheese into small toy poodle-sized pieces and put them in one of Nana Jo's spare bedrooms. I turned on the radio and gave them the treats. Then I quickly left and closed the door, a habit I'd developed since they were puppies. If they had an accident in the house, at least it would be contained. Thankfully, Nana Jo didn't stress about the dogs the way Jenna did. She had a host of rules, which included no poodles on the furniture, no accidents in the house, and no table food for the dogs. I suspected between Jenna's husband, Tony, and the twins, they'd broken nearly every rule. However, at least at Nana Jo's, I knew I wouldn't hear about it.\n\nOnce the poodles were taken care of, I found Nana Jo and the girls waiting for me in the car.\n\nThe drive to the Four Feathers Casino wasn't far. The casino was located in a small nearby town, with a population less than two thousand five hundred people. For a small town, the Four Feathers Casino and Resort, owned by the Pontolo-mas, a recently recognized Native American Tribe, was surprisingly grand. Just off Interstate 94, the uninformed traveler might have passed by the casino without giving it a second look. It appeared to be in the middle of nowhere. A winding road snaked around a picturesque woodland environment, which was the home to many deer and other animals that drivers learned to watch for as they traveled the winding road. There was a man-made lake and the drive was designed to showcase the natural landscape. At the end of the drive, there was a massive pillared entrance that led to the 150,000-square-foot casino and 500-room luxury hotel and resort. Inside, the casino had three bars, seven restaurants, retail shops, and an event center that drew big-name entertainers from all over the world.\n\nNormally, I parked in the attached parking garage. However, I was concerned the crowds would be large and parking might be challenging. Instead, I pulled up to the valet parking lane and let the casino deal with parking.\n\nOnce we were inside, we had a set routine that involved eating at the buffet and then splitting up for a few hours of gambling. Ruby Mae's expansive family generally meant we didn't have to pay for our meals. Tonight was no different. Ruby Mae had sent a text message to a niece, great-niece, cousin, or some other relation while we were traveling. So, when we arrived and approached the hostess station, our names mysteriously had already been added to the list and our table was ready and waiting for us.\n\nI didn't glance at the crowds of people standing waiting for tables.\n\nOnce we were seated in a prime location, close to Ruby Mae's favorite buffet table, I leaned across the table and whispered, \"Don't you feel bad about getting in front of all of those people?\"\n\nAll of the girls looked at me with the same, \"you must be joking\" expression and said in unison, \"No.\"\n\nI'd eaten a big lunch just a couple of hours ago, so I wasn't starving, but I did enjoy the casino's fried chicken and the smell enticed me to load up my plate. I also loved the casino's dessert bar. They had lime tarts that were amazing.\n\nWhen we were done, the hostess told us they had some bags for us that we could pick up when we were ready to leave. Normally, I would haul everyone's boxes to the car. However, Ruby Mae must have sent a message to her grandson, third cousin twice removed, or nephew-in-law, letting them know I valet parked. For that, I was grateful.\n\nThe casino was elaborately decorated, and I marveled at the hours and manpower it must have taken to transform the space into what appeared to be a mystical wonderland.\n\nNana Jo enjoyed playing poker and headed to find a game. Dorothy, who was wealthier than the rest of us, liked to play blackjack or high-limit slots. She went in search of a blackjack seat. Irma, as usual, went to the bar to pick up men. Ruby Mae, who was rarely without her knitting bag, ran into someone she knew as we were leaving the buffet and they went off to catch up on old times.\n\nI wandered around the penny slots, looking for an interesting game with an empty seat. I wouldn't call myself a big gambler; although, since I'd started hanging out with my grandmother and her friends, I'd certainly gambled a lot more than I had before. I found a seat near a game I recognized, with cute panda bears, and sat down and put twenty dollars in the machine. I could bet a minimum of fifty cents, and that was just about my limit. I set a maximum of fifty dollars and, at fifty cents per spin, I could play for quite some time.\n\nIn addition to the New Year's Eve festivities, the Four Feathers was also giving away a thousand dollars every hour, and, at the end of the night, they would give away two sports cars parked in the lobby. This meant there was a lot more noise and excitement as the announcer randomly selected names of people who had their Four Feathers's Rewards cards in the machines. Names were called and people were given five minutes to make their way to one of the stations to claim their prize. Failure to claim your prize in the allotted time meant another name would be selected.\n\nYou didn't have to be a statistician to realize you stood a better chance of getting struck by lightning than having your name called. So, I tuned out the buzz and enjoyed the monotony of pushing the button. Honestly, playing the slot machine required very little brain power since the machine did all of the work. If I went into a bonus, the machine told me. After a while, I was lost in the spin of the wheels and the routine of pushing the button. There was something therapeutic about watching the wheels spin, and I allowed my mind to wander. I thought about Max Franck and Sarah Jane Howard. Solving one murder was challenging. Solving two murders should be more challenging. However, part of me felt the second murder helped to narrow things down. Instead of just figuring out who murdered Max Franck, I could eliminate people who wouldn't or couldn't have also murdered Sarah Jane Howard. I thought through the list of suspects.\n\nI thought about Bob Marcus, the bus driver. Technically, he could have killed Max and since he'd been released from jail, he could have also killed Sarah Jane Howard. I made a mental note to check with Jenna on his alibi for the second murder. He didn't really have a reason that we knew of for killing Max. Just because he'd killed before didn't automatically mean he'd kill again. Besides, deep inside, I didn't believe he killed Max and, try as I might, I couldn't picture him killing an old woman.\n\nSidney Sherman was next. Him, I could imagine killing both Max and Sarah Jane Howard, but I couldn't believe he'd be so sloppy as to do it when he knew it would reflect negatively upon him. Sidney Sherman seemed like the type of man who would always look out for number one. Besides, I didn't see a motive.\n\nCaroline Fenton was a tough one. She definitely had a strong motive and desire for killing Max Franck. She believed him responsible for her father's downfall and death. She admitted she hated the man. But, could she kill him? Could she kill Sarah Jane Howard? I thought and thought about that one through multiple spins and several bonus games. Still, in my mind, the answer was no. Although, I couldn't deny the fact she was leaving was suspicious. Something flashed across my mind and, for an instant, I felt a jolt like lightning. However, just as quickly as the jolt appeared, it vanished. Try as I might, I couldn't get whatever thought had appeared to reappear. I knew better than to keep trying. I pushed the button for my slot machine and nothing happened. When I checked my balance, I realized there was nothing left. No need putting more money into a losing machine. So, I got up and wandered around. The next machine that caught my eye advertised X-Men. I sat down and inserted twenty dollars. I'd never played the game before, but, again, it wasn't rocket science and the machine did all of the work. I was intrigued by the graphics and thought briefly about Taylor, the MISU student who'd be working for the video game company, Vamps. I shook my head.\n\n\"Did you say something?\" the lady sitting next to me asked.\n\n\"No. I'm sorry. I was just trying to figure out how this machine works,\" I lied.\n\nShe smiled. \"It's very simple. If you get three Xs, then you get into the Free Spin bonus.\"\n\n\"Thank you.\"\n\nI pushed the button and watched reels of X-Men characters like Magneto, Charles Xavier, Wolverine, and Storm appear. After a few spins, I was able to allow my mind to wander again.\n\nRosemary Lindley was harder for me. She had the best motive for wanting to kill Max Franck. But I couldn't see her killing Sarah Jane Howard. Plus, Ruby Mae was right when she said Rosemary would have made sure, if she did kill her father, she could have gotten his bone marrow.\n\nWho was left? I pushed the button and three Xs appeared on the screen.\n\n\"You've gotten into the bonus now. It'll keep giving you free spins, but if you get a wild on the middle reel, then it switches in between heroes and villains,\" my helpful neighbor explained.\n\nI stared at the Xs and again felt that jolt of lightning through my mind. X . . . who was X? Could there be another person, someone else on the bus that we just hadn't found yet? I pushed the start button and watched the reels roll by. Who were we missing? Nana Jo and the girls had interviewed everyone. Well, everyone except Velma Levington. Nana Jo had yet to corner her. We'd have to make sure we questioned her. My phone vibrated. I had a text from Frank.\n\nWhere are you?\n\nFour Feathers Casino.\n\nI miss you.\n\nDitto.\n\nI waited, but there wasn't another text. So, I put my phone back in my pocket. I had won two hundred fifty dollars in my bonus spin, and that was good enough for me. I cashed out and took my ticket, indicating I'd won.\n\n\"You're smart to leave while you're ahead,\" my helpful neighbor said.\n\nI smiled. \"I think this noise has given me a headache. I'm going to find a quiet place to sit and think.\"\n\nI passed one of the waitresses dressed like a stereotypical Hollywood rendition of an Indian squaw in a short brown dress and got a Diet Coke. Then I walked to the hotel section of the resort, which I knew from past experience was quieter and a lot less smoky.\n\nI found a comfortable seat and sat down. After a few seconds, I pulled out my notepad and a pen and started to write.\n\nLady Elizabeth sat on the sofa in the drawing room at Hapsmere Grange. Lady Alistair sat next to her. Detective Inspector Covington warmed his hands in front of the fireplace. Lady Clara stood nearby.\n\n\"You look dreadful,\" Lady Clara declared. \"Your face is flushed and\u2014\"\n\nDetective Inspector Covington sneezed. \"Thank you, Lady Clara. I get the picture.\"\n\n\"I was only trying to be helpful. You shouldn't have gone traipsing through those fields out to the stables with Mrs. Tarkington without wellies.\" Lady Clara glanced at the detective's feet. \"Your shoes are ruined, and your feet must be soaked.\"\n\nThe detective inspector sneezed again. \"Yes, I have realized that, but I didn't know I'd have to walk through wet grass when I agreed to holiday here, so I didn't pack my Wellingtons.\"\n\nLady Clara pushed the bell, which summoned Bakerton. When the butler arrived, she gave an order. \"Please bring a large tub of hot water, towels, a warm blanket, and a huge pot of hot tea and lemon.\"\n\nBakerton bowed. \"Yes, m'lady.\"\n\n\"Look, I'll be\u2014\" Detective Inspector Covington sneezed again.\n\nLady Clara pulled a handkerchief from her sleeve and handed it to the detective inspector.\n\nHe took the dainty handkerchief and promptly put it to use. When he was done, he looked sheepish. \"Thank you.\"\n\nLady Clara pushed a chair behind his knees. \"Now, sit down and take off those wet shoes and socks and put your feet in front of the fire.\"\n\nThe detective gave Lady Elizabeth an alarmed look that begged for assistance.\n\nHowever, Lady Elizabeth merely shook her head. \"I think you'd better do as you're told. You'll catch your death of cold and I'll never forgive myself.\"\n\nLady Clara gave the detective inspector a stern look, and he sneezed three times in succession and then sat down and did as he was told.\n\nLady Elizabeth and Lady Alistair exchanged a triumphant glance.\n\nThompkins opened the doors and entered, carrying towels and a blanket. He glanced at Lady Elizabeth, who gave a slight nod in the direction of Lady Clara, who promptly took the blanket and ordered Thompkins to assist the detective inspector.\n\nThompkins placed the wet shoes and socks in front of the fireplace to dry and put the towels down near the hearth. By the time they were done, Bakerton entered with a large plastic tub filled with steaming water. He and Thompkins placed the tub in front of the detective.\n\nThe embarrassed detective attempted to get up. \"Maybe I should take the train back to London. I don't want to inconvenience anyone. I'm\u2014\"\n\nLady Clara glared. \"Sit!\" She pointed to the chair.\n\nThe detective inspector sat.\n\n\"Now, put your feet in that water, or so help me, I'll have Thompkins tie you to that chair.\"\n\nLady Elizabeth nearly burst out laughing at the look on the detective inspector's face but covered it by coughing.\n\nThe defeated Scotland Yard detective did as he was told.\n\nBakerton turned to Lady Alistair. \"Tea for everyone?\"\n\nLady Alistair nodded. \"Yes, that would be nice.\"\n\nBakerton left.\n\nThompkins turned to go but was halted when Lady Elizabeth said, \"Thompkins, I'd like for you to stay.\"\n\nThe butler bowed. \"Yes, m'lady.\"\n\nBakerton brought the tea and left, closing the doors behind him.\n\nLady Alistair poured and Thompkins assisted in distributing the tea. When everyone was served, the butler stood quietly near the wall.\n\n\"Now, who would like to go first?\" Lady Elizabeth asked.\n\nDetective Inspector Covington sneezed twice and then pulled out his notepad. \"Maybe I should go before I'm sent to my bed like a child.\" He glanced at Lady Clara, who merely raised an eyebrow but remained silent.\n\nHe told them about the conversation he'd had with Constance Tarkington and her desires to expand the stables.\n\nLady Clara picked at an imaginary piece of lint on her skirt. \"Is that all that you two talked about?\"\n\nIf Detective Inspector Covington hadn't been ill, he might have noticed that Lady Clara avoided making eye contact and had a very pretty flush in her cheeks. However, the detective didn't seem as observant as usual. Instead, he merely said, \"Pretty much. The woman is obsessed with horses and riding. She hardly talked of anything else.\" He shivered. \"She's got some beast of a horse named Satan, who she's particularly attached to.\" He muttered silently, \"Which seems fitting.\"\n\nLady Clara smiled and glanced at the detective. \"Well . . . that's . . . why that's splendid,\" she said a bit breathy.\n\nDetective Inspector Covington sneezed again. \"What did you find out from Desmond?\"\n\nLady Clara sighed. \"Not much. He's such a bore. I sat there for what felt like hours while he nattered on about himself and his career on the stage. No one understands him. His wife doesn't appreciate him. His cousin didn't understand the artistry involved in going onstage and wouldn't shell out money to put on productions, which would guarantee him good roles and gain him the recognition he deserved.\" She recited. \"However, he has high hopes that things will change now that Mrs. Forsythe is dead.\"\n\n\"Did he say that?\" Lady Alistair paused with her cup midway to her mouth.\n\nLady Clara shook her head. \"No. He was careful.\" She bit her lip. \"But he does seem concerned about the fact that no one can find Mrs. Forsythe's will. He thought she might have given it to you.\" She turned to Lady Elizabeth.\n\n\"Does he indeed?\" Lady Elizabeth knitted.\n\nLady Elizabeth shared the information she and Lady Alistair heard from Mrs. Sanderson.\n\nLady Clara paced. \"What do you suppose it means? I mean, why would they kill the old lady if they didn't know for certain they'd get the money? I wonder where she hid the will.\"\n\nThompkins coughed discretely. \"M'lady, I think I might be able to shed some light.\" He recounted what he'd learned from the maid and told them about the red lacquered box.\n\nLady Elizabeth sat up straighter in her chair. \"That's very interesting. Those boxes often have multiple hiding places.\" Lady Elizabeth stared into space for several moments.\n\nDetective Inspector Covington stared at Lady Elizabeth. \"You're concerned about something. What is it?\"\n\nShe sighed. \"To be completely honest, I'm worried. I'm very worried about that maid, but as long as none of the others realize that the lacquered box could have multiple hiding places, she should be safe.\"\n\nLady Clara gasped and covered her mouth with her hand.\n\n\"What is it, dear?\" Lady Elizabeth asked.\n\n\"When I was in the study with Desmond, I noticed the collection of Chinese boxes.\" She paused and her eyes went from one person to the other. \"I went to a lecture about Chinese artifacts at the National Museum, and I mentioned about the different hiding places.\" She stared like a deer caught in headlights at Lady Elizabeth.\n\nLady Elizabeth turned to Detective Inspector Covington. \"We need to get to Battersley Manor at once.\"\n\nThe Scotland Yard detective stood up. \"You believe the maid's in danger?\"\n\n\"I'm afraid I do. I believe she may be in a great amount of danger.\"\n\nThe detective dried off his feet and grabbed his socks from the mantle.\n\n\"I believe if we don't act quickly, that poor girl will be murdered,\" Lady Elizabeth said.\n\nLady Clara looked stricken but stared at Detective Inspector Covington. \"You can't possibly put those wet things back on.\"\n\n\"If you think I'm staying here\"\u2014he sneezed\u2014\"while you all go after a murderer, then you're batty.\"\n\nThompkins walked over. \"Perhaps you would permit me.\" He handed the detective a pair of clean, but more importantly, dry socks. \"I believe I can find you a pair of dry boots, but, if you will permit, I have a bit of information to report.\" He turned and left.\n\nThompkins returned with the boots and the detective donned them. He sneezed several more times. Thompkins also reached inside his jacket and pulled out a red lacquered box with a gold filigree dragon on top.\n\nLady Elizabeth took the box the butler extended to her. \"How did you get this?\"\n\nThompkins coughed. \"When Dora mentioned the box, I wondered if there might be more to it and asked if she would permit me to borrow it for a short time.\"\n\nLady Elizabeth stared at the butler with wide eyes filled with admiration. \"Thompkins, you're wonderful.\"\n\nThe door to the drawing room opened and Bakerton entered slowly. The butler seemed stiffer than normal. He stood silently for several seconds.\n\nLady Alistair looked with confusion. \"Bakerton?\"\n\nThe door opened wider to reveal Constance Tarkington with a gun pointed at Bakerton's back. \"You can hand over that box.\"\n\nLady Elizabeth stood very still. \"Where's Dora?\"\n\nConstance Tarkington gave a mad laugh. \"Sleeping, very soundly at the moment, thanks to a double dose of sleeping draught.\"\n\nDetective Inspector Covington moved toward Constance Tarkington, who pushed the gun into Bakerton's back. \"Keep moving and I'll be forced to use this relic as a shield.\"\n\n\"Please, don't,\" Lady Alistair pleaded.\n\n\"Then give me what I want and no one will get hurt.\" She extended her hand to Lady Elizabeth.\n\n\"I don't believe that,\" Lady Elizabeth said. \"You pushed Eleanor Forsythe down a flight of stairs. Why should we believe you won't kill us too?\"\n\nConstance Tarkington sneered. \"That old woman had it coming. Her and all her blasted Chinese vases and boxes. She didn't care about anything except her Oriental treasures. The bloody cow didn't give two pence for me and my comfort. I asked . . . no, begged her to upgrade the stables, but no. She wouldn't and Desmond doesn't care about anything but the theatre and trying to pursue a career on the stage.\" She turned to Lady Elizabeth. \"Do you know that sniveling idiot had the nerve to tell me he plans to sell the house as soon as he can.\" She took a step into the room toward Lady Elizabeth. \"After all the years I've put up with his droning on and on about the stage . . . I've put up with living in that damp, dark mausoleum and all I asked was for a little money to go into the stables and the horses.\" She was now standing directly in front of Lady Elizabeth.\n\n\"Surely, you didn't have to kill her,\" Lady Alistair said.\n\nConstance Tarkington shrugged. \"I'd waited long enough and I'm done waiting.\" She leveled her gun at Lady Elizabeth. \"Now, give me that box.\"\n\nDetective Inspector Covington inched closer to Constance. One of the floorboards squeaked and Constance Tarkington turned her gaze to the side.\n\nLady Elizabeth tossed the red box across the room to Lady Clara, who reached up and caught it.\n\nConstance Tarkington turned toward Lady Clara just as Detective Inspector Covington leapt across the room. He wrestled the gun away from Constance Tarkington, who wiggled and squirmed. Eventually, the detective inspector managed to wrap both arms around the woman and hold her until she stilled.\n\nLady Elizabeth turned to Thompkins. \"Please call the police to come pick up Mrs. Tarkington and send the doctor to Battersley Manor to check on Dora.\"\n\n\"Yes, m'lady.\" Thompkins turned to leave.\n\nBakerton, who was visibly shaking, did the first unprofessional thing in his entire career. He sat down in the presence of his mistress.\n\nChapter 20\n\nMy phone vibrated and brought me away from 1938 England. I glanced down and saw a message from Frank. What are you doing?\n\nSitting in the hotel lobby, writing.\n\nI waited, but there was no response. I stretched and glanced down at the time. We always met in the lobby, but tonight, we would wait until after the New Year's festivities. I yawned.\n\n\"Tired?\"\n\nI looked up. \"Frank? What are you doing here?\" I stared in shocked surprise.\n\n\"I really wanted to ring in the New Year with you. So, I left Benny in charge and drove here.\" He stared into my face. \"Is that okay?\"\n\nI sprang from my seat, threw my arms around his neck, and squeezed him.\n\nHe nuzzled my neck. \"I'll take that as a yes.\"\n\nI responded with a passionate kiss.\n\nFrank pulled away. \"Wow.\" He tugged at his shirt collar. \"Is it just me or did it suddenly get warm in here?\"\n\nI laughed. I reached down and grabbed my purse and notebook. \"How about I buy you a drink with my winnings?\"\n\nHe raised an eyebrow. \"If you think you can ply me with liquor and then have your way with me, then I just have one thing to say.\"\n\nI waited. \"Well?\"\n\n\"Don't waste your money on the liquor.\"\n\nWe laughed and walked hand in hand.\n\nThe Four Feathers had recently added a piano bar to the hotel area of the resort. This allowed those staying at the hotel, who wanted a drink in a slightly quieter locale, to relax. We headed there in the hopes that it would be a little less congested.\n\nAt the bar, we found Irma leaning against the bar with men on either side of her. Dorothy was perched atop a baby grand piano belting out a song while a middle-aged man with vibrant red hair and a beard, who was dressed in a tuxedo, accompanied her.\n\nFrank paused for a moment when he recognized Dorothy. He stopped and looked at me.\n\nI shrugged and hurried toward a small table I spotted in the corner.\n\nSeated, he leaned over. \"I knew you said your grandmother's friends were a bit . . . uninhibited, but I didn't expect . . . I mean, are they like this all the time?\"\n\nI shook my head. \"No. They aren't like this all the time, but you should see them when they really get revved up.\"\n\nHis eyes widened, but he merely smiled.\n\nDorothy was a surprisingly good singer. She had a deep, throaty voice, and her style matched the bar's atmosphere. When she finished, everyone applauded.\n\nIt looked as though Dorothy was going to slide down off the piano, but her audience was having none of it. The small crowd applauded and yelled and cajoled until she agreed to sing more. Her response was met with enthusiastic applause. Dorothy and the pianist consulted for a few seconds and then decided on their next song, which was Nat King Cole's \"Unforgettable .\"\n\nWe sat in silence for a few seconds and listened along with everyone else. Then our waiter broke the spell by asking what we wanted to drink.\n\nFrank ordered a bottle of champagne, which I recognized as being expensive. Our waiter smiled and left to get the order with a bit more pep in his step than when he'd first come to our table, perhaps sensing the expensive bottle of champagne meant a higher tip.\n\nI raised an eyebrow, but Frank merely shrugged. \"You only live once. This is our first New Year's together, I thought it should be special.\"\n\nI smiled at the thoughtfulness and wished I'd taken more care in my attire. However, I decided to let those thoughts of insecurity stay in the past and focus on the moment and the future.\n\nThe waiter returned quickly with our champagne, a bucket of ice, and two glasses. He popped the cork, which made a momentary interruption to Dorothy's song, and then quickly filled our glasses with the bubbling elixir before rushing away.\n\nWe toasted to the future and then sipped our champagne.\n\nWe talked about nothing important, drank champagne, held hands, and enjoyed each other's company until the announcer announced five minutes until the new year. Frank quickly paid the bill, poured the remaining champagne into our glasses, and indicated we should leave.\n\nI grabbed ahold of his arm and followed. I was surprised when he led me outside. It was December in Michigan, which meant cold, but I followed.\n\nOutside of the main doors was a covered porch with large overhead heat lamps. He guided me there, then passed me the glasses. He took off his jacket and put it around my shoulders and held me close and rubbed my arms to keep my blood circulating. He leaned down and whispered in my ear, \"You okay? If you're freezing, we can go back inside, but I love to watch the stars every New Year's Eve.\"\n\nI smiled. \"Actually, I feel rather warm.\"\n\nI felt his laughter and he held me tightly to his chest with his arms around me.\n\nWe heard the announcer and everyone in the casino begin the countdown. When they got to five, I handed Frank a glass of champagne.\n\nI looked at the night sky and marveled at the vastness of space. The countdown continued. When they reached one, there was an uproar of cheers, noisemakers, and what sounded like fireworks. I looked at Frank, prepared to toast, but the look in his eyes indicated he had other ideas. He bent down and kissed me. When he pulled away, he smiled. \"I hope we can spend every New Year's Eve this way.\"\n\nI nodded. \"Me too.\"\n\nWe toasted the new year and watched the stars a bit longer until some of the casino patrons started to wander outside, breaking the lovely mood.\n\nWe finished our champagne and then went back inside.\n\nRuby Mae was sitting by one of the enormous fireplaces that flanked either side of the casino lobby. She was surrounded by several people, who I assumed were relatives. We decided not to disturb them and waited near the other fireplace.\n\nEventually, Nana Jo made her way to the lobby. She was wearing a paper hat and had a noisemaker. She smiled when she saw Frank. \"Glad you made it.\" She looked around. \"Where are Irma and Dorothy?\"\n\nI told her we left them in the piano bar and she left to go get them.\n\nFrank looked concerned. \"Maybe I should go give her a hand. I don't think Irma and Dorothy may be too anxious to leave.\"\n\nI smiled. \"Trust me, Nana Jo will drag them out if she has to.\"\n\nAbout five minutes later, Nana Jo returned. She and Dorothy were on either side of Irma, who was quite tipsy.\n\nFrank took Nana Jo's place as Irma's prop while Nana Jo took our tickets to the cash machine to cash out. Irma flirted with Frank, who looked uncomfortable but endured.\n\nWhen Nana Jo returned, she divided up the winnings, which amounted to five hundred dollars each. I gasped at the money when she handed it to me.\n\n\"Somebody won big tonight. I only contributed two hundred and fifty to the pot.\"\n\nWe always pooled our winnings at the end of the night and divided them. That way, everyone usually left with something. If one person lost, someone else usually won. Rarely had we ever left with nothing.\n\n\"I had a great night on the poker table and Dorothy hit it big on the blackjack table.\"\n\nSince I valet parked, I gave the parking ticket to the attendant so they would bring my car around.\n\nRuby Mae's family had made sure our to-go bags were brought to the front and before long, we loaded up and prepared to go.\n\nFrank saw us all into the car. He bent down and kissed me. \"Are you okay to drive home?\"\n\nI smiled. \"Absolutely.\"\n\n\"Maybe I should follow you.\"\n\nI shook my head. \"That's sweet but completely unnecessary. I'm fine.\"\n\nThe drive back to Shady Acres was uneventful. Irma slept the entire way. The others were tired and talked about the fun they'd all had at the casino. When I complimented Dorothy on her singing voice, she explained she used to sing at nightclubs on the weekends while she was in college to earn extra spending money.\n\n\"I guess that's where Jillian gets her talent.\" I glanced in the rearview mirror and was rewarded by Dorothy's smile.\n\nI went inside Nana Jo's to collect my poodles, who were fast asleep in the guest room. In fact, turning on the lights didn't even wake them. I had to shake them.\n\nSnickers looked around as though confused and yawned.\n\n\"Some watchdog. I could have been a robber and neither of you bothered to bark,\" I joked.\n\nSnickers stretched several more times and yawned.\n\nOreo stretched and pranced around as though to say, I wasn't sleeping.\n\nI let them outside to potty and went back in to say goodbye to my grandmother.\n\n\"It's almost two in the morning. Why don't you all just sleep here tonight. You can go home later.\" She yawned.\n\nI thought about it but decided I'd rather sleep in my own bed. I was grateful I'd made that decision when, just a few seconds later, we heard a key in the lock.\n\nFreddie, Nana Jo's boyfriend, walked in. \"Is everything okay? I saw the light on.\"\n\n\"When did you get back?\" Nana Jo asked.\n\nHe released a deep breath. \"Just now. I'm worn out.\" He glanced over at me. \"Hi, Sam.\" There was a moment of indecision when he looked as though he was going to leave.\n\nI smiled. \"Hello. I'm glad you're back. I was just leaving.\" I turned and gave my grandmother a kiss. \"Happy New Year.\"\n\n\"Happy New Year.\"\n\nThe poodles and I drove home. When we left the garage, I couldn't help pausing to look at the stars. I smiled as I remembered the moment outside of the casino, looking up into that same night sky with Frank. It was a lovely memory. Snickers took advantage of being outside to answer the call of nature, while Oreo sniffed and played in the snow.\n\nInside, I dried off the poodles and we hurried upstairs.\n\nI was exhausted and got ready for bed. However, something kept tickling the back of my mind. Just as I dozed off to sleep, I remembered what it was. I picked up my phone and dialed my sister. The phone rang several times before she answered.\n\n\"Are you in jail?\"\n\nI paused. \"No.\"\n\n\"The hospital?\"\n\n\"No.\"\n\nShe sighed. \"Then you better have a really good reason for calling at this time of the morning.\"\n\nI glanced at the clock. \"Sorry.\"\n\nShe grunted. \"What do you want?\"\n\nI quickly explained about finding the photograph and the key.\n\nShe was silent for a long time and I was afraid she'd fallen asleep.\n\n\"Jenna?\" I whispered. \"Are you still there?\"\n\n\"Yes. It's evidence and you need to turn it over to the police.\"\n\n\"Okay, but we were hoping maybe we could . . . Jenna?\" I glanced down. The phone was black. She'd hung up. \"Happy New Year.\"\n\nI called Nana Jo. I knew she'd be awake. She picked up after just a couple of rings.\n\n\"Did you ever get a chance to interview Velma Levington?\"\n\n\"Not yet, but I plan to tackle her first thing.\"\n\n\"Well, maybe you should get to it. Remember what Ruby Mae said.\" I paused. \"Or was it Dorothy? Well, one of them mentioned that several people were planning to leave Shady Acres.\"\n\n\"You think she knows something?\"\n\nI paused. \"I'm working on an idea . . . it's a crazy idea, so I want to think it through a bit more.\"\n\nI heard Freddie ask a question and Nana Jo whispered a response, which reminded me of the time.\n\n\"Look, I want to mull this idea over a bit more. In fact, I might bounce it off Detective Pitt first. I'll call you in a few hours and let you know.\"\n\nI needed to make one more call, but Chicago was an hour behind and decided I had better wait. I put my cell phone down and thought over what I knew of Max Franck and the other suspects. I thought I was right, but how to prove it?\n\nAs tired as I was just a short time ago, there was no chance of sleep now. I was wired. I tossed and turned for close to an hour before I gave up on sleep and went to my computer to write.\n\nDetective Inspector Covington kept a firm hand on his captive, but Constance Tarkington had spent all of her energy and sat quietly in the chair.\n\nWhen Thompkins returned, he brought a tea cart.\n\nLady Elizabeth smiled. \"I think Bakerton might need something a little stronger than tea.\" She turned to Lady Alistair, who nodded. \"In fact, I think we might all do with something a bit stronger.\"\n\nThompkins nodded. He left the room and returned with a bottle of brandy and several glasses. He poured a bit of the amber liquid into the glasses and turned to leave.\n\n\"I think you should stay, Thompkins.\" Lady Elizabeth sipped the liquid. \"After all, if it weren't for your quick thinking, Constance Tarkington might have gotten away with this.\"\n\nThe butler bowed stiffly and stood silently in the corner.\n\n\"Nice catch, by the way.\" Lady Elizabeth smiled at Lady Clara. \"Do you think you can open the box?\"\n\nConstance Tarkington looked up but said nothing.\n\nLady Clara turned the box around in her hands while she talked. \"Well, I've been looking at this dragon on top and I think if you . . .\" She put the box onto a table and pushed down on both of the eyes of the dragon and a panel opened. She looked inside, frowned, and continued to stare at the box. After a few seconds, she slid the dragon's tail and another panel flipped down.\n\nConstance Tarkington gulped.\n\nLady Clara examined the opening. After a few seconds, she reached in and pulled out a folded sheet of paper. She passed the paper to Lady Elizabeth.\n\nLady Elizabeth unfolded the paper and read it. \"Eleanor Forsythe's will.\" She perused the document. \"Desmond Tarkington gets the house, but that's it. She left her favorite red lacquered Chinese puzzle box and a small legacy to her maid, Dora . . . Bakerton.\" She turned to the butler.\n\n\"Dora's my granddaughter,\" he said with a quiver in his voice. \"I nearly passed out when she said she'd put her to sleep.\"\n\nThere was a timid knock on the door and a maid stuck her head inside. \"Constable Redmond.\" She stepped back and the door opened to a constable, who looked around nervously. He spotted Detective Inspector Covington and walked over to him. He whispered something to the Scotland Yard detective.\n\nDetective Inspector Covington smiled. \"The maid is okay. The doctor said she'll be fine.\"\n\nBakerton put his face in his hands and wept.\n\nThe Scotland Yard detective handed Constance Tarkington over to the constable and announced, \"I'm going into the village with Constable Redmond.\" He glanced around the room, but his gaze lingered longest on Lady Clara. Then, the two policemen left with their prisoner.\n\nAfter a few minutes, Bakerton pulled himself together and stood. \"I'm terribly sorry.\"\n\n\"No apologies necessary,\" Lady Alistair reassured the butler. \"Thompkins, perhaps you could\u2014\"\n\n\"Of course, your ladyship.\" Thompkins bowed and then assisted the older butler out of the room.\n\nLady Clara continued to examine the red lacquered box.\n\nLady Alistair sipped her brandy. \"That was certainly astonishing.\" She turned to her friend. \"What on earth put you on to her?\"\n\nLady Elizabeth took a sip of her brandy and then placed her glass on a nearby table and picked up her knitting. \"Several things, actually. First, I thought it was suspicious that Constance just happened to be in the subway at the same time when Eleanor Forsythe had a fatal fall. Mrs. Sanderson mentioned she'd called them, but it bothered me she had the fall after she'd talked to me. I also thought it odd Mrs. Forsythe mentioned she'd had an accident with the soap. She might have fallen, if it hadn't been for Dora. At the time, I didn't put together the fact that Desmond had been gone.\" She pursed her lips. \"Maybe, if I'd been quicker . . .\"\n\nLady Alistair reached across and squeezed her friend's hand. \"You can't blame yourself.\"\n\nLady Elizabeth sighed and smiled weakly. \"I know you're right, but . . .\" She shuddered.\n\n\"Is that all?\" Lady Clara asked while she continued to examine the lacquered box.\n\nLady Elizabeth knitted. \"I remembered Eleanor Forsythe mentioned how much she loved puzzles and Chinese artifacts.\" She paused and thought for a few moments. \"She kept saying how she loved puzzles when we were at tea. Then, when Thompkins mentioned how Constance Tarkington always seemed to be listening, well . . . I just felt it had to be her. Desmond seemed too timid to have killed his cousin.\" She glanced over at Lady Clara. \"Clara, you seem absolutely intrigued by that box.\"\n\nLady Clara picked up the box and stared at it. \"There's a very strange symbol on the corner that really seems out of place.\" She reached out a finger and pressed. \"I just wonder if we've uncovered all of the box's secrets.\"\n\nA very small drawer popped open and Lady Clara gave a small cry of surprise. Her eyes grew wide and she tilted the box and out came several brightly colored stones. \"My goodness.\"\n\nLady Elizabeth nodded. \"If I'm not mistaken, that's the real treasure Eleanor Forsythe and her husband had. She couldn't leave the house to Dora because it was entailed to Desmond. However, if you recall what Dora said to Thompkins, Eleanor Forsythe and her husband loved China, but his family wanted him to be sensible.\" She smiled. \"This was their way of rebelling. They took their money and put it into gems and hid them in that box, which she knew neither Desmond nor Constance would appreciate.\"\n\n\"Goodness gracious.\" Lady Clara held up one of the stones. \"This appears to be jade.\"\n\nLady Alistair said, \"Do you think Dora will get to keep them?\"\n\nLady Elizabeth nodded. \"I believe that's what Eleanor intended.\" She nodded. \"I think Dora will be an excellent steward.\"\n\nChapter 21\n\nAs soon as the clock hit a decent hour, I called Detective Pitt. There was so much to go over, I asked if he would come to the store so I could fill him in. My second call was to Rosemary Lindley. I had two pressing questions. The first one was easy. Did she know if her father had a gym membership or if he had a locker anyplace?\n\nSurprisingly, she didn't ask why I wanted to know. The idea of her father working out made her laugh, but eventually she sobered up and thought for a few minutes.\n\n\"When I was small, he used to like to box. If he went anywhere, it would have been the gym. There used to be one near the newspaper where he worked. It was a terrible neighborhood, but he loved it.\"\n\n\"Great.\" My second question was a little harder. I filled her in on the events that happened at her father's memorial. I asked if she would call and ask Caroline Fenton if she would be willing to try again, this afternoon, with a brief Mass. Even her silence sounded reluctant, but I'd had hours to work up a counter. \"I know it's a holiday and last minute. However, I think it's important. In fact, I think it would be really awesome if you could come too.\"\n\n\"It's New Year's Day. Can't this wait until tomorrow?\"\n\n\"Actually, there are several people who I know are planning to leave and won't be here tomorrow. I know it's a huge inconvenience, but I wouldn't ask if it wasn't important.\" I waited.\n\nShe was silent for so long I actually looked at my cell to make sure she hadn't hung up, but the call was still engaged. Eventually, she said, \"Yes. I'll do it.\" She released a heavy sigh. \"But you need to know something. I'm not doing it for him or for me. I'm doing it for Isabelle. I think she needs this. She needs to say goodbye.\"\n\nI said a silent prayer of thanks and worked to keep the glee from my voice. \"Great. Leave the details to me. I'll take care of it, but I need you to call Caroline Fenton to get permission. It'll hold more weight coming from you.\"\n\nWhile I was on a roll, I called Frank. \"Happy New Year. Can I borrow Benny for a few hours today?\"\n\n\"Happy New Year to you.\" I could hear the laughter in his voice. \"If I didn't know you better, I might be worried about that request.\"\n\n\"Don't be silly. I just need a priest to do a Mass at the last minute, and he's the only one I know.\"\n\n\"Should I ask why?\"\n\n\"You probably don't want to know. Can you check and text me and let me know?\"\n\nWe chatted for a few minutes about nothing, but my cheeks got warm and I remembered I needed to get showered before Detective Pitt arrived.\n\nI hung up with Frank and showered, dressed, and grabbed a cup of coffee and some scones from the freezer and headed downstairs. The poodles trotted along beside me and, by the time Detective Pitt arrived, we were all set.\n\nFrank sent a text message while I was walking downstairs that Benny agreed. So, I gave him the time I'd worked out with Rebecca Lindley for the Mass and told him I'd meet him there.\n\nWhen I opened the door, Detective Pitt growled, \"This better be good.\"\n\n\"Happy New Year.\"\n\nHe grunted and walked to the back of the store.\n\nSince we were officially closed, I locked the door and followed him to the back.\n\n\"Coffee?\"\n\nHe grunted again.\n\nI took that grunt to mean yes and handed him a mug of coffee and a scone.\n\nI waited for him to sit before I started.\n\n\"I think I know who killed Max Franck and Sarah Jane Howard, but I'm going to need your help to prove it.\"\n\nHe glared over the top of his coffee mug but said nothing.\n\nHe was definitely grumpy in the morning.\n\n\"What I'd like to do is have a big reveal, like in Hercule Poirot books, where you bring all of the suspects together and then the sleuth\"\u2014I pointed to him\u2014\"can reveal whodunit.\"\n\nThe glare he gave me earlier became a scowl. \"Why don't you tell me whodunit and I'll go arrest them and we can skip this 'big reveal.'\"\n\nI was afraid he'd go there. \"Because I don't really have any proof.\"\n\n\"What good is bringing people together and accusing someone with no proof?\"\n\nI took a deep breath. \"Well, I'm hoping someone will remember something or say something to help. Or maybe the killer will say or do something to give themselves away.\"\n\nHe laughed. \"Are you joking? This isn't television. Real killers don't crack under the pressure of hearing the evidence against them. Real killers laugh in the face of overwhelming mountains of evidence and deny to their dying day that they're guilty.\"\n\n\"If that's the case, then I doubt you'll ever be able to arrest the killer.\"\n\nThe scowl came back. \"Who's the murderer?\"\n\nI hesitated. \"Before I tell you that, I need to give you something.\" I reached in my pocket and handed over the locker key and the photograph.\n\n\"What's this?\"\n\n\"Irma found them in her purse.\"\n\nLike a pot that bubbled up on the stove, I could see the steam bubbling up inside. His face grew red. His eyes were huge, and his nostrils flared.\n\nBefore he blew a gasket, I held up a hand. \"Look, we weren't withholding evidence in a murder investigation. She just found these items last night.\"\n\nHe huffed. \"How is it possible she had these items in her purse for an entire week and just now noticed them?\"\n\n\"Have you seen the inside of her purse? Nana Jo says it's where sick elephants go to die. Honestly, you're lucky she found them at all.\"\n\nHe took several deep breaths. \"Okay,\" he said slowly. \"What are they?\"\n\nI reminded Detective Pitt that Max Franck was a writer. \"I suspect the photograph was research for his book.\"\n\nHe picked up the photo and stared at it for several seconds and then put it down and picked up the key. \"And this?\"\n\nI shrugged. \"I called Rosemary Lindley this morning and she said her dad used to have a locker at the gym near his newspaper.\" I gave him the address I'd googled after talking to Rosemary. \"I don't know if he still has a locker there or if this key is even Max Franck's key.\" I stared at him. \"However, I think someone\"\u2014I looked pointedly at Detective Pitt\u2014\"should go and check the locker.\"\n\n\"It's New Year's Day. Can't this wait until tomorrow? I have plans.\"\n\n\"We don't have time to wait. Caroline Fenton is leaving and so is Velma Levington. Sergeant Alvarez is trying to extradite Bob Marcus to Chicago, and Sidney Sherman could be in Timbuktu in a couple of days.\"\n\nDetective Pitt stared at me and then ran his hand over his head and ruined his comb-over. \"Fine.\" He took the key and put it in his pocket, finished his coffee, and shoved the last bits of scone into his mouth. Then he got up and walked out.\n\nI called Nana Jo and gave her instructions and then hurried upstairs. I was antsy and nervous. I'd never tried anything like this before, and it could end up being a big mess. However, no matter how I played things in my mind, I couldn't think of any other way to prevent the killer from getting out of town without at least trying.\n\nI let the poodles outside and gave them treats when they came in. I then grabbed my purse and left. I stopped at the grocery store and picked up the food I'd ordered for the MISU football tailgate party we'd planned for Nana Jo's. There was plenty of food, and I was able to buy extra chicken wings, dip, and chips. The food would have to do double duty\u2014tailgate\/memorial Mass.\n\nCaroline Fenton was clearly not happy about the last-minute Mass for Max Franck and Sarah Jane Howard. However, rejecting the request of a bereaved daughter would have reflected very poorly not only on Caroline Fenton but Shady Acres. Regardless of her feelings about the man, Sarah Jane Howard was a resident of Shady Acres. She deserved to be remembered. Plus, I was providing the food and the drinks, and I was even providing my own priest. How could she say no.\n\nNana Jo and the girls were there, and they'd enlisted the help of several others to unload everything from my car.\n\nGaston stopped me and gave me a pouty look. \"Store-bought chicken wings? Samantha, you have wounded my soul. You know I can provide herb marinated chicken wings with a scallion goat cheese dip that would make your soul sing.\"\n\nI laughed. \"I know you're an excellent chef, but this was rather last minute.\"\n\nHe shook his head. \"I forgive you this time, but next time, you call me.\"\n\nI promised him I would.\n\nThe lounge was decorated in MISU colors, with streamers hanging from the ceiling, in preparation for the tailgate party, but we would have to ignore that.\n\nFrank and Benny arrived shortly afterward. This time, Benny looked very clerical with his black shirt and white cleric collar. He had a beautiful embroidered stole, which he wore around his neck.\n\n\"Thank you so much for agreeing to do this, especially last minute.\" I shook his hand.\n\nBenny smiled, but the smile didn't reach his eyes. \"Anything for Frank. I owe him so much.\"\n\nI felt horrible using my relationship with Frank, but I didn't have much time to dwell on my feelings. People were starting to fill the lounge.\n\nRosemary Lindley arrived with Isabelle in a wheelchair. The fragile girl looked tired, but her eyes were bright.\n\n\"Thank you so much for coming.\" I looked at Isabelle. \"Both of you.\"\n\nShe smiled. \"It's a sad occasion, but I'm glad Mom let me come.\"\n\nRosemary wheeled her daughter into the lounge.\n\nI glanced at my watch. Detective Pitt had yet to arrive, but I didn't think we could wait any longer.\n\nTen minutes after the appointed time, I gave Benny a nod to get things started and went into the lounge for the Mass.\n\nI wasn't Catholic, so I hadn't attended very many Masses, but the ones I had attended always impressed me. I remember wondering how the congregation knew how to respond and when. \"Peace be with you. And also with you,\" threw me for a loop the first time I attended Mass. The service was short, but Benny made it very meaningful.\n\n\"Are you sure this is going to work?\" Nana Jo asked.\n\n\"No.\"\n\n\"Well, okay.\"\n\n\"How did you get Velma Levington to agree to stay?\"\n\n\"I did what you suggested. I told her we might need her help with security. Since she was so skilled in aikido, I asked her to be part of the security team.\" She chuckled. \"Don't worry. Dorothy and I will be nearby.\"\n\nI nodded. I looked around and was relieved when Detective Pitt arrived with Bob Marcus in tow. That had been the trickiest part of the entire plan, but Detective Pitt came through.\n\nBob sat near the door. Detective Pitt walked up to me and handed me a large envelope.\n\nInside the envelope were articles and notes, receipts, and even napkins with information scribbled on them. There was an envelope addressed to Rosemary and a flash drive. I wished I'd had time to check the drive, but instead, I quickly flipped through the notes.\n\nThe stage was set.\n\nWhen Benny finished the Mass, he asked if anyone had anything to say. That was Detective Pitt's cue. He walked to the front of the room and looked around at everyone.\n\n\"Hello . . . I'm . . . um . . . I'm . . . my . . . ah . . . name,\" he stammered and stumbled.\n\n\"Dear God, the man's afraid of public speaking,\" Nana Jo whispered.\n\nThe crowd's energy and interest began to waver and the impact of the detective's performance was lost.\n\n\"Do something,\" Nana Jo said.\n\nI sighed. \"Detective Pitt has been battling a bit of a cold, and I think he could use some water.\" I grabbed a bottle of water and walked to the front. I handed the bottle to the detective, who immediately feigned a coughing fit and stepped back to allow me to talk.\n\n\"I think Detective Pitt wanted to thank all of you for coming out to honor and remember Max Franck and Sarah Jane Howard.\" I looked up and saw that Velma Levington, Dorothy, and Nana Jo had moved closer to Bob.\n\nI took a deep breath. \"Many of us didn't know Max Franck long. In fact, many of you may not have known Max Franck had been an investigative reporter for many years. He won many prizes over the course of his long career.\"\n\nCaroline Fenton snorted.\n\nI ignored her outburst. \"He was a published author. In fact, he was in the process of writing another book.\" I held up the envelope Detective Pitt gave me. \"He had information that would send a murderer who has gone unpunished for decades to prison.\" I took a deep breath. \"That's why he was killed, to prevent him from revealing the truth.\"\n\nDetective Pitt stepped forward and whispered in my ear. \"What are you doing? This wasn't part of the script. The murderer's going to think . . .\"\n\nI nodded. \"Yes, exactly.\"\n\n\"But you're making yourself a target.\"\n\n\"It's the only way.\"\n\nI stepped forward and announced loudly, \"Sarah Jane Howard knew who murdered Max Franck, and that's why she was killed. Once the police get a chance to look through this evidence, they'll know what I do.\" I took a deep breath. \"But, we're here to honor Max Franck and Sarah Jane Howard. So, please bow your heads for a moment of silence.\"\n\nEveryone looked stunned, but they bowed their heads. I waited several seconds and then said. \"Amen. Now, please help yourself to refreshments.\"\n\nI walked toward the back of the room. Frank was beside me by the time I got to the lobby. \"Just what do you think you're doing?\"\n\nI looked at him. \"I need you to trust me.\"\n\nHe stared at me as though I'd lost my mind. \"This isn't about trust. This is about your safety.\"\n\n\"I need you to trust me. Please?\"\n\nI could see the internal struggle, but, after a few seconds, he let go of my arm and allowed me to walk out alone.\n\nI walked to the back of the building and stood near the door and waited. It didn't take long. I heard a crunch of a foot in the snow.\n\n\"You're one gutsy broad.\" Velma Levington slipped around the corner of the building. She had a large gun leveled at me.\n\nVelma Levington laughed. \"How did you know it was me?\"\n\n\"It was something Sarah Jane Howard said. She noticed everyone and she mentioned that you stayed on the bus, supposedly asleep. She also said she was the first one back on the bus and you were already there. Several people said you were on the bus . . . asleep. No one saw you get off. I found it hard to believe you could have slept through a man getting stabbed in the kidneys.\"\n\nShe frowned. \"That's it?\"\n\n\"Then you said Bob stabbed Max and Sarah Jane, but the police hadn't released the cause of death. There's no way you could have known that, unless you were the one who stabbed them. You were the only one who said you saw Bob standing over Max's body. You were the one who saw Bob push Irma.\" I tried to regulate my breathing so I didn't sound as nervous as I felt. \"Then, when Caroline Fenton fainted, you said you had medical training from when you were in the military.\" I took a deep breath. \"Is that where you learned how to kill silently with a knife to the kidneys?\"\n\nShe nodded. \"I saw plenty of silent kills in my time. After a while, you get desensitized to it.\"\n\nI saw a slight movement in the distance but tried not to focus on it and focused on keeping Velma talking. \"How'd you get into killing for money?\"\n\nShe laughed. \"When I left the military, I was broke. I had no money. No job. Nothing. The war was supposed to make things better, but it wasn't long before I realized nothing had changed.\" She sneered. \"Well, nothing outside had changed, but I had. I was different. I wasn't the same bright-eyed, na\u00efve girl who had gone into the military. I'd seen too much.\" She shrugged. \"Done too much. Then, I met a man who asked if I wanted to make a lot of money.\" She paused. \"Give me the envelope.\"\n\nI clutched it to my chest. \"If I give you the envelope, you're going to shoot me.\"\n\nShe nodded. \"You're right.\"\n\n\"Why don't I leave the envelope on the ground.\" I bent down. \"I'll step away and you can take it and get away.\"\n\nShe shook her head. \"I can't do that. I don't believe in loose ends. That's why I had to kill Sarah Jane. Sooner or later, I knew she would remember something that could lead the police to me. She was a loose end.\"\n\n\"And, Irma?\" I whispered.\n\n\"She's a dingbat, but I couldn't take a chance that she'd have an epiphany and realize it wasn't Bob who pushed her.\" She shrugged. \"She was another loose end. You'd be another one.\" She held out her hand. \"Give me the envelope.\"\n\nI shook my head. My throat was too dry to talk.\n\nShe leveled her gun. \"Have it your way. I'll have to shoot you first and then take the envelope.\"\n\nNana Jo moved out from the shadows. She had a gun pointed at Velma Levington, and her eyes looked like black ice cubes.\n\n\"Josephine, I wouldn't if I were you. I've got this gun pointed straight at your granddaughter. I'm just as good of a shot as you are and I suspect I've got less of a conscience about killing people than you.\"\n\n\"I wouldn't be so sure about that,\" Nana Jo growled. \"I don't think I'd lose much sleep about taking you out.\"\n\nVelma Levington laughed. \"Maybe, but, either way, your granddaughter will be dead.\"\n\nThere was a noise from behind and, in the split second that Velma Levington's eyes moved to see what was behind her, Nana Jo fired.\n\nVelma Levington's gun flew out of her hand.\n\nStrong arms grabbed me and pushed me behind what felt like a solid wall but was actually, Father Benny.\n\nNana Jo spun around and drop-kicked Velma Levington and then Irma pounced on Velma's chest and started to pummel her with her fist.\n\nFrank picked up Velma's gun and pointed it at her head.\n\nIt took both Ruby Mae and Dorothy to pull Irma off of Velma, all the while, Frank kept the gun pointed at her head. His confident stance, the way he held the gun, and the steely look in his eyes told me this wasn't the first time he'd been in this position.\n\nEventually, Detective Pitt came around the corner. It wasn't until Velma was handcuffed and lying on the ground that I breathed.\n\n\"You okay?\" Frank asked.\n\nI nodded. The words wouldn't come.\n\nHe turned Velma's gun over to Detective Pitt and then walked over and grabbed me by the shoulders. \"That was the craziest thing you have ever done and if you do anything like that again, I'll . . .\" His voice shook. He pulled me to his chest and held me tightly. His body shook, and I felt guilty for the scare I'd given him.\n\nMy legs were jelly, so I was grateful for Frank's strength. He led me inside to the lounge.\n\nMost of the residents weren't sure what had happened, but word spread quickly and the room was abuzz.\n\nDetective Pitt took statements and arranged for his prisoner to be picked up.\n\nRosemary Lindley thanked me. \"I still don't understand what happened. Why did she kill my father?\"\n\n\"While researching his book about the assassination of Robert Kennedy, your father recognized Velma in a photo and discovered she was a contract killer.\"\n\nShe looked surprised. \"But I thought that man . . . Sirhan killed Robert Kennedy.\"\n\nI nodded. \"There have been a lot of theories.\" I smiled. \"I wasn't even aware of them until I read your father's book. He found a photo of a woman he recognized. After some digging, he believed the woman was a paid assassin responsible for killing some politicians in Chicago.\"\n\nShe folded her arms across her chest. \"It just seems so cold.\"\n\n\"She was cold.\" I handed her an envelope.\n\n\"What's this?\" She looked puzzled.\n\n\"Detective Pitt said it was okay for you to read this. It was in your father's locker.\"\n\nRosemary Lindley looked puzzled but opened the envelope and took out the paper. She started to read, and I saw a wave of emotions cross her face. Plus, surprise at seeing her father's words. That was followed by shock and disbelief. Then tears of joy flooded her eyes. She looked at me. \"He was tested.\" She covered her mouth and cried silently. When she was able to talk, she said, \"He found out, not only wasn't he a match for Isabelle, he wasn't my father.\"\n\nI hadn't expected that and watched her closely to see if I could sort through all of her emotions. \"Are you okay?\"\n\nShe nodded. \"Yes. I don't care about that.\" She took several breaths. \"He got tested. I have had so much hatred in my heart when I thought he wouldn't even get tested when he knew it could save Isabelle.\" She glanced around at her daughter, who was chatting with Frank and Melvin. \"That was so . . . cold. But now I know he did care. He got tested. I can accept that he wasn't my biological father. I couldn't accept that he wouldn't at least try.\" She cried, but there was joy and relief in her tears. She hugged me. \"Thank you.\"\n\nWe both cried for several moments. Eventually, she pulled away and wiped her face with the sleeve of her coat. \"I better get Isabelle home.\" She looked at her daughter, who appeared to be having a serious game of chess with Melvin, Irma's new friend.\n\nWe said our goodbyes.\n\n\"You ready to go home?\" Frank whispered.\n\n\"I'm not going home. We have a tailgate party.\"\n\nHe stared at me as though he didn't recognize me. \"You're joking. After everything you've been through?\" He felt my forehead. \"Maybe you're sick. You could be suffering from shock.\"\n\nI shook my head. \"I'm not suffering from shock. I'm fine.\" I struggled to find the right words. I looked around. Nana Jo and Freddie were arguing over the remote control. Irma had recovered from her hysterics earlier and was flirting with Melvin while he played chess. Ruby Mae had her knitting out and was sitting on the sofa, and Dorothy was engrossed in conversation with Benny. \"These people have become my family, just as much as Jenna, Tony, the twins, and my mom. When Leon died, I thought my life was going to be so empty without him. He'd been such a big part of me, but now I've got you and all of them.\" I waved my arm around. \"I've got Dawson and so many people in my life. I want to start this new year surrounded by the people I care about.\"\n\nHe pulled me close and I smiled at him. \"There's only one thing that could make this day more special.\"\n\nHe raised an eyebrow. \"What?\"\n\n\"If the MISU Tigers win the Appliance Bowl.\"\n\nHe smiled. \"Go, Tigers!\"\n\n# Contents\n\n  1. Also by\n  2. Title Page\n  3. Table of Contents\n  4. Copyright Page\n  5. Acknowledgments\n  6. Chapter 1\n  7. Chapter 2\n  8. Chapter 3\n  9. Chapter 4\n  10. Chapter 5\n  11. Chapter 6\n  12. Chapter 7\n  13. Chapter 8\n  14. Chapter 9\n  15. Chapter 10\n  16. Chapter 11\n  17. Chapter 12\n  18. Chapter 13\n  19. Chapter 14\n  20. Chapter 15\n  21. Chapter 16\n  22. Chapter 17\n  23. Chapter 18\n  24. Chapter 19\n  25. Chapter 20\n  26. Chapter 21\n\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":" \nALSO BY **MARSHALL DE BRUHL**\n\n_Sword of Jacinto: A Life of Sam Houston_\n\nCopyright \u00a9 2006 by Marshall De Bruhl\n\nAll rights reserved.\n\nPublished in the United States by Random House, an imprint of The Random House Publishing Group, a division of Random House, Inc., New York.\n\nRANDOM HOUSE and colophon are registered trademarks of Random House, Inc.\n\nAll photographs, with the exception of the image of the reconstructed Frauenkirche, are from the collection of the S\u00e4chsische Landesbibliothek-Staats-und Univerit\u00e4tsbibliothek Dresden\/Abt. Deutsche Fotothek. Photographers are listed with their individual works.\n\nLIBRARY OF CONGRESS CATALO GING-IN-PUBLICATION DATA\n\nDe Bruhl, Marshall.  \nFirestorm: Allied airpower and the destruction of Dresden\/by Marshall De Bruhl.  \np. cm.  \neISBN: 978-0-307-76961-9  \n1. Dresden (Germany)\u2014History\u2014Bombardment, 1945.  \nI. Title.  \nD757.9.D7D4 2006 940.54'2132142\u2014dc22 2006041059\n\nwww.atrandom.com\n\n_Title-page photograph, Mathildenstrasse, by Paul Winkler, Stadtmuseum, Dresden, 1945_\n\nv3.1\nFOR BARBARA\n\n# PREFACE\n\nD **uring a visit to the coast of France in the summer of 1984** , I found myself standing on a platform at the top of a stairway that led down to a beach. It was a beautiful day, warm and sunny. From far below I could hear the squeals of children splashing in the mild surf, young men shouting to one another as they kicked a soccer ball around, and, occasionally, music being borne along on the slight breeze.\n\nIt was a very different scene from that of four decades earlier, when the sounds coming from the beach below were those of one of the most desperate struggles of modern times. For this was Normandy and that place was Omaha Beach.\n\nI was on my own pilgrimage, just a few days after thousands of veterans and world leaders had come to this site for the fortieth-anniversary celebrations of the Allied invasion. I was just a boy in a small town in North Carolina when the Allies landed here to free Europe from the Nazis, but I vividly remember how my family gathered around the radio in our living room and listened to the live broadcasts from the landing sites.\n\nMy thoughts that morning in June 1984 were of the cousins and uncles who had been with the invasion force. One of them, an infantry officer, saw his promising professional baseball career ended by a German bullet in the left lung. Another, the executive officer of a paratroop unit, was killed just a few days after landing behind the beaches\u2014coincidentally, not far from where his father was killed in World War I.\n\nMy sad but proud reflections were interrupted by the laughter of a young woman and two young men who were making their way up the long stairway from the beach. As they reached the landing where I stood, the girl suddenly exclaimed, \"My God. What is this place?\" The three of them fell silent.\n\nSpread out before them in perfectly ordered rows were the 9,387 marble Christian crosses and Stars of David of the United States Military Cemetery at Colleville-sur-Mer. Most of the men buried there were about the ages of these young people when they died on the beach below, or fighting their way up the very same steep bluff, or during the bloody advance inland after D-day.\n\nThose young people had come to spend a few hours at the beach, not to visit a battlefield or a war memorial, but they listened attentively to my brief but emotional account of the Normandy invasion, of which they knew nothing. It was as distant to them as the wars of ancient Greece. They then quietly took their leave to wander among the graves.\n\nThe ravages of the Second World War are hardly to be seen today as one travels through the cities and countryside of Europe. There are war memorials to be sure\u2014obelisks, vast monuments to the dead, eternal flames, and in some cities the hulk of a burned-out building left untouched as a reminder to the passersby that something terrible happened here over a half century ago.\n\nMost Americans, however, are so inured to seeing cities being torn down and rebuilt that they are like those carefree students on their holiday. They seem not to be aware, or much care, that the lovely beaches, the beautiful orchards and vineyards, and the rolling fields of France and Belgium and Germany were once soaked with the blood of hundreds of thousands of young men.\n\nFor a truer picture of the carnage of World War II, one must look to the cities, not the battle sites, which, often as not, now resemble well-tended parks. The healing power of nature is evident in the countryside. Vines, wildflowers, and grasses cover the shell holes and bomb craters. Bones of unknown war dead still work their way to the surface or are accidentally turned up by plows and spades, and hapless farmers still occasionally fall victim to the random unexploded shell or land mine long buried in the soil. But instead of ravaged farmlands and the lanes and byways ripped up by the passage of thousands of tanks and trucks and armored vehicles, the fields are much as they were before total war came to these bucolic regions.\n\nMan-made structures can be restored and reconstituted only by other men, however, not by nature. And it was the urban environment\u2014with its villas, houses and palaces, apartment blocks, factories, government buildings, churches and cathedrals, schools, and shops\u2014that was the scene of the greatest devastation. This sort of destruction could never be imagined until the twentieth century and the birth and development of a new form of warfare.\n\nThis new war bypassed the armies clashing in the field. It was waged hundreds, often thousands, of miles from any battlefront. This campaign was against the civilian population, which, as war has become more brutal, has increasingly become the target and borne the brunt of military operations.\n\nIn the great cities of Germany, visitors are largely oblivious to what predated the ubiquitous glass towers, the pedestrians-only shopping areas, and the almost too wide streets and expressways. To be sure, many historic structures, indeed whole areas of cities, have been reconstructed exactly as they were. But prewar urban Germany\u2014that congested, vibrant, thousand-year-old architectural museum\u2014was washed away in a rain of bombs and could never be wholly reclaimed.\n\nFor some cities, such as Berlin, the rain of fire was constant, day after day, night after night. But for one city, there had been only two raids in the more than five years that Germany had been at war. Both had been relatively minor attacks, so the people of Dresden were lulled into that false security that is often a prelude to a great disaster. When their storm came, it was a firestorm, and the destruction and death were on a scale not hitherto imagined in warfare.\n\nThe Dresden raid, on 13\u201314 February 1945, by an Anglo-American force of over a thousand planes, has been a source of controversy, debate, and denial for six decades. It is one of the most famous incidents of the war, yet one of the least understood. It has led to rumors and conspiracy theories, to wrecked reputations, and to charges of war crimes. And it is another reason for the question that has been asked millions of times after the battlefields have been cleared, the wounded gathered up, the dead buried, and the monuments raised. It is a simple question: Why?\n\nThe Dresden story is one with particular relevance to our own era. The moral issues presented by war and, especially, aerial bombardment are timeless. The efficacy of bombing continues to be an article of faith among not only leaders of armies but leaders of nations\u2014even though noncombatants, people far from the lines of combat, are most often the victims. In Germany, hundreds of thousands of civilians\u2014mostly women, children, and old men\u2014died as the cities were blasted away.\n\nSince the advent of airpower in World War I, the bombardment of civilians has been decried but never stopped. Indeed, as historian Michael Sherry has put it, \"Limited or ambitious men, both in and out of the military, often sanctioned a kind of casual brutality.\" For almost a century, military planners and political leaders have been beguiled by this particular form of warfare\u2014believing that it holds the promise of a quick and speedy end to hostilities.\n\nThe lessons of Guernica, London, Rotterdam, Coventry, Hamburg, Berlin, Tokyo, Hiroshima, Nanking, Nagasaki, and Shanghai are consistently ignored. More recently, the massive bombardments during the Vietnam War and the reprisal bombing in Cambodia, the destruction of Afghanistan, the bombing of Iraq in the two gulf wars, and the devastation of the cities and villages of the former Yugoslavia remind us that airpower still reigns supreme among the planners.\n\nHowever, there have been raids so controversial as to raise serious doubts about the usefulness and certainly the morality of the bombing of cities. Since 1945, the debate has centered for the most part on the atomic bombing of two Japanese cities\u2014Hiroshima and Nagasaki. The horror of those two events has overshadowed the destruction of dozens of other cities by more conventional means. Nagasaki and Hiroshima served for the last half of the twentieth century as the greatest symbols of the horrors of nuclear warfare, and the result has been rather a tolerance of bombing as long as it is not nuclear. However, the great air raid and firestorm that consumed Dresden, Germany, was as awesome and dreadful as any raid of the war. Both the physical destruction and the casualties were truly horrific.\n\n**I first became interested** in the Dresden raid in the summer of 1965, when I made a trip to Coventry to see the new St. Michael's Cathedral, designed by Sir Basil Spence. The medieval church was destroyed in the famous raid by the German Luftwaffe in November 1940. Early on, it had been decided to leave the ruins and tower of the old church as a memorial and build a new, modern St. Michael's immediately adjacent.\n\nDuring my tour through the church much was made of the comparison between the bombing of Coventry and the raid on Dresden four years later. And in spite of the fact that we were then in the midst of the Cold War and Dresden lay in one of the most extreme of the Soviet satellites, a certain understanding had developed between the two cities. The new cathedral, in fact, featured a cross made from melted and twisted metal from the ruins of Dresden.\n\nThe next summer I went to Dresden. Even after two decades, signs of the war were still evident everywhere. What had once been one of the busiest thoroughfares in the world\u2014the Pragerstrasse, which ran from the central train station to the city center\u2014was still a vast open field, through which one walked to the rebuilt Zwinger, that rococo exuberance that houses one of the world's greatest art collections. The museum had been faithfully restored and reopened as both a symbol of civic pride and propaganda for the Communist regime.\n\nRuins can inform, and it was not too difficult to reconstruct, in the mind's eye at least, the grandeur that was Dresden. And, of course, to mourn its loss. The blackened ruins of the royal palace, the opera house, the theater, the Albertinum museum, the great cathedral, or Hofkirche, along with dozens of other ruined buildings lay behind chain link and board fences, where they awaited a promised restoration\u2014which, in some cases, would not be done for decades. Indeed, the restoration still continues, most recently with the reconstruction of the symbol of Dresden, the Frauenkirche. The ruins of the Church of Our Lady\u2014a vast pile of rubble in the Neumarkt\u2014served for fifty years as a war memorial and the center of the annual commemoration of the bombing.\n\nThe questions that have since 1945 swirled around the great raid that destroyed what was arguably the most beautiful city in Germany and for many the most beautiful in Europe have never been satisfactorily answered.\n\nI can only hope, as all chroniclers of history must hope, that my work contributes to a better understanding of those times when no weapon was considered inappropriate and all targets\u2014whether persons or places\u2014were considered appropriate.\n\n# CONTENTS\n\n_Cover_\n\n_Other Books by This Author_\n\n_Title Page_\n\n_Copyright_\n\n_Dedication_\n\nPREFACE\n\nPROLOGUE\n\nCHAPTER ONE \" **THE BOMBER WILL ALWAYS GET THROUGH\": Aerial Bombardment: Theory and History**\n\nCHAPTER TWO **THE ARCHITECTS OF DESTRUCTION** **The Bomber Barons and Total Air War**\n\nCHAPTER THREE **WEAPONS FOR THE NEW AGE** **OF WARFARE: The Race for** **Aerial Superiority**\n\nCHAPTER FOUR **THE FATAL ESCALATION** **Air War Against Civilians**\n\nCHAPTER FIVE **_VERGELTUNGSWAFFEN_** **The V-Weapons**\n\nCHAPTER SIX **OPERATION THUNDERCLAP** **Run-up to the Inferno**\n\nCHAPTER SEVEN **THE TARGET** **Florence on the Elbe**\n\nCHAPTER EIGHT **SHROVE TUESDAY, 1945 Dresden on the Eve of the Apocalypse**\n\nCHAPTER NINE **PILLAR OF FIRE BY NIGHT Bomber Command Takes the Lead**\n\nCHAPTER TEN **A COLUMN OF SMOKE BY DAY** **The American Third Wave**\n\nCHAPTER ELEVEN **ASH WEDNESDAY, 1945** **A City Laid Waste**\n\nCHAPTER TWELVE \" **MR. PRIME MINISTER?\"** **Questions in Parliament and** **World Opinion**\n\nCHAPTER THIRTEEN **FROM THE ASHES** **Dresden Is Reborn**\n\nEPILOGUE\n\nACKNOWLEDGMENTS\n\nNOTES\n\nBIBLIOGRAPHY\n\n# PROLOGUE\n\n**\"A sh Wednesday and St. Valentine's Day, an inharmonious combination**,\" confided Prime Minister Winston Churchill's private secretary to his diary on 14 February 1945. A thirty-year-old former diplomat\u2014he had been transferred from the Foreign Office to Downing Street in 1939\u2014John Colville wrote those words from the relative comfort of London. He had not been included in the British delegation to the Yalta Conference, which had ended, for better or worse, three days before.\n\nChurchill himself was now en route home from the Crimea, and on this \"inharmonious\" day he was in Athens. As his motorcade made its way through the streets of that ancient city, he gloried in the adulation of hundreds of thousands of Greeks, who hailed him not only as their liberator from the hated Germans but also as a bulwark against a Communist takeover of the country.\n\nIt was one of Churchill's greatest public triumphs, and there had been many. \"Were you there, Charles?\" he said to his physician, Lord Moran, after the group reached the British embassy. \"I have never seen a greater or more demonstrative crowd.\"\n\nTwelve hundred miles away, in the streets of another city, the sounds were not those of a cheering throng but the insistent klaxons of fire engines and ambulances, the crash of collapsing buildings, and the screams of the wounded and the dying. The sun had risen on this combined Ash Wednesday and St. Valentine's Day in Dresden, Germany, to reveal a city laid waste.\n\nBaroque bell towers stood silently over smoking and burned-out shells of eighteenth-century churches that just hours before had seemed to owe more to the art of the confectioner than to that of the architect. The Altmarkt and the Neumarkt, the ancient city squares, were now surrounded by roofless, gutted buildings and littered with the burned, twisted, melted-down hulks of cars, trucks, and streetcars.\n\nThe Br\u00fchl Terrace\u2014the so-called balcony of Europe, that great esplanade overlooking the river Elbe\u2014had been turned into jagged bits of masonry and broken statuary. The adjoining avenues and boulevards were obliterated. Only charred stumps marked the location of century-old plane and linden trees. The narrow streets of the Altstadt, the Old City, had simply disappeared. Palaces, museums, and galleries were now unidentifiable heaps of smoking rubble.\n\nIn the great public park called the Grosser Garten, high-explosive bombs had plowed up the ground and created hundreds of deep craters. The ancient trees were leveled or splintered. And everywhere in the park lay thousands more of the dead and dying\u2014refugees from the east who had sheltered there in their flight to the west, as well as native Dresdeners who had fled to this oasis to escape the bombs and the flames. For two centuries people had found refuge here amidst nature. This time, they had met their end.\n\nThe monuments and statues in every square and park in the city had been replaced by mounds of corpses. Thousands and thousands of the dead were carried out of the ruined buildings, to any available open space. There the survivors attempted the impossible task of identification. But when entire families, entire neighborhoods have died, who remains to identify the dead?\n\nTwo waves of bombers from British Bomber Command had attacked the unsuspecting and undefended city\u2014the first at just past ten o'clock on the eve of St. Valentine's Day and the second a little after one o'clock the following morning. The initial raid created the firestorm, and the second, as designed, helped spread the conflagration that destroyed everything in its path.\n\nAt midday, as Churchill was being hailed in Athens, a third wave of planes, from the U.S. Eighth Air Force, appeared over the stricken capital of Saxony. The American raid, which lasted just ten minutes, has been called the most cruel element of the triple blow against Dresden. Such a series of closely spaced and coordinated raids against a major German city\u2014code-named Operation Thunderclap\u2014had first been promulgated by air planners in the summer of 1944. And the results of the raids of 13\u201314 February against Dresden were precisely as envisioned by the planners of Thunderclap.\n\nThe two nighttime British raids had been spaced so as to cause maximum damage and chaos and create the unusual but longed-for phenomenon of a firestorm. Now the bombs from the American B-17s fell on emergency workers and rescuers as they struggled to put out the fires and extricate victims from the rubble.\n\nWhen this third wave departed, the great city that was known as \"the Florence on the Elbe\" was already only a memory. In less than fourteen hours the work of centuries had been undone.\n\n# CHAPTER ONE\n\n**\"THE BOMBER WILL ALWAYS GET THROUGH\"**\n\nAerial Bombardment: Theory and History\n\n**W ar, despicable and despised, has nevertheless been one of** mankind's most widespread and popular activities. \"Human history is in essence a history of ideas,\" said H. G. Wells, a noble idea in itself. However, human history is more realistically described as a history of warfare. The chronicles and annals, century after century, millennium after millennium, are dominated by war.\n\nMercifully, there have been periods of peace; but, for the most part, they have been brief. The era beginning with the end of the Napoleonic Wars in 1815 to the outbreak of World War I in 1914 was relatively calm. To be sure, there were smaller wars aplenty\u2014the Mexican War, the Franco-Prussian War, the Sino-Japanese War, the Boer War, and the Spanish-American War\u2014and one large one, indeed: the American Civil War.\n\nHowever, for a full century there was no great multinational conflagration such as the Seven Years' War or the Napoleonic Wars. Then came a period of hitherto unimaginable ferocity. The three decades from 1914 to 1945 might well be regarded as a modern Thirty Years' War, interrupted by a turbulent recess before the principals returned to the battlefield and even greater bloodletting.\n\n**The frightful and bloody** battles of World War I remained fresh in the minds of both victor and vanquished throughout the 1920s and 1930s. Time did nothing to erase the memories. The contests for small patches of ground in France and Flanders and the Eastern Front had resulted in millions of dead and maimed. Families around the world grieved for their dead sons, brothers, and fathers and recoiled at the idea of another such conflict. It was inconceivable to most civilized people that the world would ever again witness such carnage.\n\nBattle deaths among the Central Powers (Germany, Austria-Hungary, Bulgaria, and the Ottoman Empire) were 3,500,000. Among the Allies, who lost 5,100,000 soldiers, the French nation was scarred like no other. Most of the Western Front was on French soil, and over 1,380,000 Frenchmen died on the battlefield or from war wounds, almost 3.5 percent of the entire population of the country. Twenty-five percent of all Frenchmen between the ages of eighteen and thirty died in World War I.\n\nThe other Allies suffered great casualties as well. Britain, with 743,000 deaths, and the commonwealth, with another 192,000, were particularly stunned by the losses, as was Italy, with 615,000 dead.\n\nUnited States battle-related deaths were nowhere near those of most of the other belligerents. Just 48,000 Americans died in battle in World War I. Disease caused the greatest number of deaths; more than 62,000 Americans were carried off by the great influenza epidemic of 1918.\n\nWhile America has honored its war dead\u2014indeed, the Tomb of the Unknown Soldier and the Vietnam Veterans Memorial in Washington are major tourist attractions\u2014its wars have generally faded from memory. The simpler monuments in the cities, towns, and villages of America have become a familiar part of the background of everyday life and eventually are barely noticed as people go about their daily tasks. Memorial Day is now more than likely a day devoted to pleasure than to remembering the dead or decorating their graves. As each generation of veterans dies out, their contributions slip into history.\n\nThis has been so from the American Revolution to the First Gulf War. Each war and the reasons for fighting it become hazy with time. For decades after the Civil War, veterans' reunions, stirring speeches, and grand parades kept the memories and the sacrifices fresh in both the North and the South. Today, few people notice the bronze or granite Union or Confederate soldier who keeps watch over countless village greens and courthouse squares.\n\nIn Europe, which has suffered the devastations of centuries of warfare, memory has not been so quick to fade. War memorials and burial grounds have not been allowed to disappear into the background. This is especially true in France and Belgium, the scene of so much carnage. One cannot ignore the perfectly maintained burial grounds that dot the landscape and that reflect the nationalities of the dead interred there. There are the somber Germanic memorials, the rather more nationalistic American tributes, the sad formalism of the French, and the tranquillity of the English cemeteries. In the latter, the flower of an entire generation lies at peace in gardens much like those in Kent or Surrey or the Cotswolds.\n\nThe Great War stayed fresh in the memory of the survivors, and in the interwar years thousands of people from both sides made pilgrimages to decorate the graves of the dead in France and Belgium. The senseless battles, the mindless charges and assaults, and the mountains of dead hovered over every postwar conference, every planning session, every strategic discussion. Diplomacy, however misguided, had as its end the avoidance of any repetition of the Great War.\n\nThe memories of World War I did not serve just to underscore the need for a permanent peace. In the defeated countries, memory also fostered revanchist emotions, a desire for revenge. \"The world must be made safe for democracy,\" the American president had said in his message asking Congress to declare war on Germany in 1917. No sooner had the war ended than Wilson's words began to echo with a hollow sound. Absolutism rose instead: Communism in Russia, Nazism in Germany, Fascism in Italy, and a virulent militarism and expansionism in Japan.\n\nAnother war seemed inevitable to many, and when it came it would prove to be the most devastating conflict in the history of mankind. And there was one great difference between World War II and any preceding war. Because of a new method of warfare, with its more powerful weapons, great numbers of the dead would be noncombatants, far from the front lines.\n\nAmong less traditional military planners of the major powers, this new weapon was of particular interest in that it was potentially capable of such power and destruction that it might ensure permanent peace. The airplane might well prove to be the weapon that would put an end to warfare itself.\n\n**In 1914, when** World War I began, powered flight was still in its infancy. The Wright brothers' first flight had been just a little more than a decade before, in December 1903. The infant was a robust one, however, and grew so quickly that there seemed to be some new breakthrough almost daily.\n\nIn 1908, the Wrights shipped one of their aircraft to France, where Wilbur flew a series of demonstrations of the plane at the racetrack at Le Mans. In the delirious crowd was Louis Bl\u00e9riot, a French aviation visionary who would make history himself in less than a year. On 25 July 1909, Bl\u00e9riot flew the English Channel from Calais to Dover. The flight was short, only thirty minutes, but it was a powerful portent.\n\nGovernments immediately began buying aircraft for their militaries. By the beginning of World War I, the French air force comprised 1,000 planes. The British had an equal number, and the Germans 1,200.\n\nBut the birthplace of aviation lagged far behind the European countries' exploitation of aircraft for their militaries. The isolation from Europe and its gathering problems was a strong argument against increased spending for any arms, least of all aircraft, and the American isolationist politicians were aided and abetted by the military traditionalists. Many of the ranking generals were veterans of the Indian wars of the 1880s and were blind to the importance of the airplane; and the admirals, naturally, were wedded to the doctrine of invincible sea power and its most visible component, the battleship. Consequently, when war came, the U.S. Army Air Service had less than 250 aircraft, few of them combat-worthy.\n\nEven in those nations with a relatively advanced air force, airplanes initially were used almost exclusively for reconnaissance over enemy lines. In short order, however, other, more aggressive uses recommended themselves. The first recorded aerial bombardment occurred as early as 1911. In the Italo-Turkish War, Italian pilots dropped small bombs on Turkish troops in Tripoli. The next year, in the First Balkan War, two Bulgarian airmen leaned out of their cockpit and dropped thirty bombs, weighing just a few pounds each, on Edirne, Turkey.\n\nThese two minor engagements, with just a handful of bombs and only minor damage, did little to advance the cause of aerial bombardment, and little more was thought about it by most military planners.\n\nThere were a few isolated bombing incidents at the beginning of the war\u2014all but two on the Continent\u2014but they were little more than calling cards. Then, on 19 January 1915, the first fatalities occurred. A German dirigible raid, the first of fifty-two in World War I, killed four people in England. In the next three years, another 556 people were killed from bombs dropped from German zeppelins. The first raid on London was on 31 May 1915.\n\nThe zeppelin raids were by no means a strategic threat to England, and the casualties were minuscule, at least compared to what was occurring across the Channel. It was not lost on the populace and the politicians, however, that 90 percent of the casualties were civilians.\n\nTwo years after the commencement of the dirigible raids, the Germans increased the pressure on English civilians. Gotha bombers began dropping 1,000-pound bomb loads on the British Isles. The first raid, on 25 May 1917, killed 95 people, 80 percent of them civilians. On 13 June the bombers attacked London. Not surprisingly, the attacks on the congested British capital caused a far greater number of deaths and injuries than other German air raids, and as would be the case in World War II, the attacks caused a great public outcry.\n\nThere were other parallels with the great conflict that was to come. British defensive measures forced the Germans to give up daylight bombing by August 1917, and the following May they ended their aerial bombardment of England. While they were active in the skies over England, the German raids totaled just 27. There were 836 deaths, however, and 72 percent of them were civilians.\n\nThe British also were active in aerial bombardment in World War I, and they had the honor of staging the very first long-range air raid. Three two-seater Avro 504s bombed the zeppelin sheds at Friedrichshafen on 21 November 1914. The raid accomplished little\u2014one of the planes was shot down and the pilot almost murdered by an enraged mob\u2014but it proved that long-distance aerial bombardment was not just theoretical. It was practicable.\n\nTotal civilian and military deaths in the three years of dirigible and bomber attacks on Great Britain were, according to historian John Terraine, \"less than those sometimes suffered by a single division of the citizen army on the Western Front in _one day.\"_\n\nThe effect of the German bombing cannot be measured in lives lost or property destroyed. Neither of those measures was of much consequence. The aerial bombings ushered in a whole new way of looking at war. By May 1918 it was clear that morale bombing would henceforth be a powerful force in military planning. Aerial theorists soon appeared to codify and give philosophical weight to the arguments of the men in the field.\n\n**The first great proponent** of airpower, the preeminent theorist, was Giulio Douhet, an Italian general and aviator. Douhet was no stranger to controversy. In World War I, he was court-martialed\u2014and imprisoned\u2014for exposing the weakness of Italy's air force. Vindicated when the Italians were defeated at Caporetto, he subsequently became head of the Italian army aviation service. In 1921, Douhet published _II dominio dell'aria_ (The Command of the Air), which soon became the bible of airpower apostles, priests, and converts. Early in his work, in a few well-chosen words, Douhet laid out the essential elements of his thesis.\n\n\"As long as man remained tied to the surface of the earth, his activities had to be adapted to the conditions imposed by that surface,\" said Douhet. \"Since war had to be fought on the surface of the earth, it could be waged only in movements and clashes of forces along lines drawn on its surface.\" Far removed from these lines of combat, civilian populations had good reason to feel distant from the battlefield. \"The majority went on working in safety and comparative peace to furnish the minority with the sinews of war,\" he said.\n\nThis state of affairs arose from the fact that _it was impossible_ to invade the enemy's territory without first breaking through his defensive lines.\n\nBut that situation is a thing of the past; for now _it is possible_ to go far behind the fortified lines of defense without first breaking through them. It is airpower which makes this possible.\n\nThe airplane has complete freedom of action and direction; it can fly to and from any point of the compass in the shortest time\u2014in a straight line\u2014by any route deemed expedient. Nothing man can do on the surface of the earth can interfere with a plane in flight, moving freely in the third dimension. All the influences which have conditioned and characterized warfare from the beginning are powerless to affect aerial action.\n\nBy virtue of this new weapon, the repercussions of war are no longer limited by the farthest artillery range of surface guns, but can be directly felt for hundreds and hundreds of miles over all the lands and seas of nations at war. No longer can areas exist in which life can be lived in safety and tranquility, nor can the battlefield any longer be limited to actual combatants. On the contrary, the battlefield will be limited only by the boundaries of the nations at war, and all of their citizens will become combatants, since all of them will be exposed to the aerial offensives of the enemy. There will be no distinction any longer between soldiers and civilians.\n\nIn yet another bold break with tradition, Douhet also called for separate, autonomous air forces. These independent air arms might coordinate their activities with the army and the navy, which might, indeed, have their own planes; but they would in no sense be subordinate.\n\nSoon, the English military historian and theorist B. H. Liddell Hart provided powerful support for the Douhet doctrine. Great destruction could be visited on urban areas and the civilian population if the bombs and the means of delivering them were developed. There would be no front lines, with great armies throwing themselves against each other. Instead, said Liddell Hart, fleets of bombers would \"jump over the army which shields the enemy government, industry, and the people and so strike direct and immediately at the seat of the opposing will and policy.\"\n\nHowever, the theorists surmised, these new weapons would never actually be used. They were to be deterrents to war. Indeed, the very threat of such terror would lead to the quick end of any war\u2014if, indeed, diplomacy between potential adversaries had allowed the situation to deteriorate to that point. But if war did come, said Liddell Hart, and cities such as London were bombed, \"Would not the general will to resist vanish...?\"\n\nAnother airway theoretician, J. F. C. Fuller, was more quantitative, assigning an acceptable number of dead that might be necessary to achieve a greater goal. \"If a future war can be won at the cost of two or three thousand of the enemy's men, women and children killed... then surely an aerial attack is a more humane method than the existing traditional one.\"\n\nThe men who flew in the fledgling air forces of World War I quickly embraced the new theories. Douhet was hailed as one of the great military thinkers, for he had given airmen a philosophical underpinning\u2014as, in the nineteenth century, Alfred Thayer Mahan had done for the admirals and Carl von Clausewitz for the generals. It is not such a large step from theory to dogma; early on, minds were set in a strategy that would govern thinking about aerial warfare.\n\nA new era in warfare thus began. The unthinkable would prevent the unimaginable. In the event, warfare did not change, of course. The weapons being extolled by Douhet and Liddell Hart not only did not prevent another world war but would themselves cause even more destruction and death\u2014particularly among the noncombatants. Even greater armies contested the field, and those bombers that were supposed to have deterred the war or to bring it to an early end instead flew over them night after night, day after day, year after year, taking the war, as predicted, to the ground combatants' homes, far from the battlefield.\n\n**Few branches of** the military forged such close bonds as the flying corps. The other services had distinguished themselves in World War I and served just as heroically, but the pilots were different. They were an elite group, few in number, better paid, and isolated by their mastery of a still unusual, even unique skill. In addition, they benefited from their messianic zeal. For them, airpower had become a new religion.\n\nThe bonds formed by these pioneers would be lasting and help them build a devastating war-making machine in the decades ahead. Much has been said in condemnation of so-called old-boy networks, but such networks went far in defeating Axis tyranny.\n\nHowever, upstarts too can soon become the old guard, with an entrenched doctrine and calcified thinking. When the admirals and generals insisted that the airplane was just another weapon, not a revolutionary method of waging war, the airpower enthusiasts were quick to circle the wagons. And just as quickly they began to overstate the effectiveness of their new weapon and create inter- and intraservice rivalries that would last for decades.\n\nGeneral Jan Christian Smuts and Major General Hugh Trenchard were among the chief proselytizers in the United Kingdom. As Smuts wrote to Prime Minister Lloyd George on 17 August 1917:\n\nAir power can be used as an independent means of war operations.... Nobody that witnessed the attack on London on 7th July, 1917, could have any doubt on that point. Unlike artillery an air fleet can conduct extensive operations far from and independently of both Army and Navy. As far as can at present be foreseen there is absolutely no limit to the scale of its future independent war use. And the day may not be far off when aerial operations with their devastation of enemy lands and destruction of industrial and populous centres on a vast scale may become the principal operations of war, to which older forms of military operations may become secondary and subordinate.\n\nOn 1 April 1918, these two visionaries saw their dream realized. The Royal Air Force, the RAF, was founded, with Trenchard himself as chief of the air staff.\n\nThe views of Trenchard, Smuts, and the other early apostles of airpower and their glowing predictions of the future of airpower continued to rankle the old-line admirals and generals in both England and America who saw the airplane as little more than a toy and pilots as a brash group of show-offs. In 1919, the American secretary of war, Newton D. Baker, reflected this mind-set. Of aviation, he said, \"the art itself is so new and so fascinating, and the men in it have so taken on the character of supermen, that is difficult to reason coldly.\"\n\n**Oddly, it was** an advocate of disarmament who gave the pro-bomber proponents their most potent axiom. On 10 November 1931, Prime Minister Stanley Baldwin said in the House of Commons, \"I think it is well also for the man in the street to realize that there is no power on earth that can prevent him from being bombed. Whatever people may tell him, the bomber will always get through. The only defence is offence, which means you have to kill more women and children more quickly than the enemy if you want to save yourselves.\"\n\nBaldwin was, of course, denouncing aerial bombardment and what he perceived, correctly, as its inevitable escalation. But in one of those not unusual twists that result in a speaker's words being used in a way he never intended, the prime minister's statement was taken up by the proponents of the invincible, self-defending heavy bomber. \"The bomber,\" they cried, \"will always get through.\"\n\nThe opposing group was equally mistaken in their expropriation of the prime minister's remarks, although they at least were in philosophical agreement. The fear of aerial bombardment led many in his and later governments, as well as the public, to attempt to placate Hitler and then to acquiesce in his designs on neighboring states.\n\n**Wise military leaders** learn from their mistakes and are quick to embrace new weaponry and technology. They always seek to devise more effective methods for fighting the next round of engagements. Not for them the adage that military men always seem prepared to fight the last war. Prescience is not without its price, however.\n\nThe military landscape is littered with the wrecked careers of revolutionaries who ran afoul of the system when they tried to institute new and untried tactics or weapons of warfare. Billy Mitchell, that brilliant but impolitic apostle of airpower, is perhaps the twentieth century's most resonant example.\n\nGeneral Mitchell, who had learned firsthand the effect of airpower as head of the American air service in France in 1917\u201318, was the most visible and voluble of the alleged air supermen, and he carried on a ceaseless and often intemperate campaign for airpower and an air service. In this he was supported by other zealots, several of whom, in the next two decades, would carry Mitchell's plans to fruition. They included Henry (Hap) Arnold, Carl Spaatz, and Ira C. Eaker, among others.\n\nMitchell's ideas were anathema to the traditionalists in the army and the navy, who were quick to protect their territories, but it was the latter service that was his particular target, and eventually the navy rose to his challenge that airplanes could sink capital ships.\n\nA demonstration was set up off the Virginia Capes in July 1921. As Mitchell predicted, air service planes sank a captured German destroyer, a cruiser, and, to everyone's consternation, the battleship _Ostfriesland_.\n\nTo further drive home his point and to prove that the first engagement was not just a fluke, Mitchell repeated the lesson in September. Army planes bombed and sank the decommissioned battleship _Alabama_.\n\nEven so there were still doubters, and in September 1923, Mitchell sought to convert them as well. He arranged for the destruction of two more old battleships\u2014the _Virginia_ and the _New Jersey_.\n\nBut the bombs that sank obsolete warships were not the only ones dropped by Billy Mitchell. In a series of articles for the _Saturday Evening Post_ , he went all out in his advocacy of airpower and his criticism of those who could not see that it was the future of warfare. He accused the military's top brass of muzzling their subordinates and preventing them from telling the truth.\n\nMitchell had crossed the line between advocacy and insubordination. He was demoted to colonel and transferred to a remote base in Texas. He had, of course, become the darling of the press, and before his departure he pulled off another coup\u2014or stunt. He took arguably the most popular and widely read American of his time, Will Rogers, for a much reported first airplane ride.\n\nBut Mitchell was not just a publicity hound. He was genuinely concerned with aviation and was determined to overcome the American reluctance to build an air force. Even from his exile in the outback he would not be silenced, particularly when he was given two spectacular disasters as a springboard.\n\nOn a misconceived public relations mission to Hawaii, a navy flying boat, the PN-9 No. 1, ran out of fuel and ditched at sea. The crew was rescued after ten days adrift in their plane, but the navy was accused of dereliction. Worse was the destruction of the dirigible _Shenandoah_ , which went down while the search for the missing flying boat was still going on. The aircraft had been ordered to fly into a severe thunderstorm to maintain its schedule of public appearances in the Midwest.\n\nMitchell's response was immediate and scathing. He charged that the loss of the _Shenandoah_ was \"the result of incompetency, criminal negligence, and the almost treasonable negligence of our national defense by the War and Navy departments.\"\n\nIronically, the flying boat and the dirigible had both been dispatched in order to gain publicity for navy air and as an effort to counter Mitchell's charges that the air arm was being ignored.\n\nThe Coolidge administration and the military could not ignore such a broadside from a military officer, and their response was swift. Mitchell was court-martialed.\n\nBoth Carl Spaatz and Hap Arnold testified for the defense, which the country knew was a defense of airpower as well. Though Mitchell's point was made, his career was over. He was given a five-year suspension, but he chose to resign from the army and continue his crusade as a civilian.\n\nForty years later, Spaatz made it clear that his testimony at the trial had to do with advocating airpower. Mitchell's insubordination was, indeed, actionable by a military court. Spaatz said that he and Arnold and Mitchell's other friends \"had no quarrel with the administration of military justice as it applied to him.... He brought it upon himself and I think he did it deliberately.\"\n\nMitchell is mostly remembered for his advocacy of aerial bombardment, and bombers were, to be sure, the mainstay of his envisioned air force. But he also believed in fighter planes. Indeed, he felt that 60 percent of any air force should be pursuit planes\u2014small defensive fighters that would be employed to destroy an enemy's air force.\n\nClaire Chennault was another advocate of fighter planes. His public stance also angered his superiors, but he left the army quietly in 1937 for medical reasons. The next day, however, he traveled to China, where he organized and trained the Chinese air force.\n\nWork on fighter planes had been effectively halted, and the United States aircraft industry did not develop a first-rate fighter, either for escort or pursuit, until 1940\u2014for the British Royal Air Force.\n\nSome good did come from the Mitchell scandal. Both the public and Congress benefited from the discussion, and at least one important step was taken in regard to airpower. The Morrow Board, an investigative body appointed by Calvin Coolidge, recommended the creation of the Army Air Corps, and Congress passed the Air Corps Act of 1926. For airpower advocates it was only half a loaf\u2014there would be no separate and autonomous air force\u2014but it was clearly better than none.\n\nThe chief objection to building up this new force was in no small degree a moral one in the eyes of many congressmen and the public. Building more planes and a greater air force directly contravened the recently negotiated naval treaties. What use was it, detractors argued, to limit the tonnage of capital ships and go all out in building planes and an air force?\n\nMilitary opponents of the Army Air Corps were, of course, willing to embrace any argument to limit its growth, and thus the new aviation branch of the army remained a stepchild\u2014underfunded, understaffed, and shunted aside by the traditional services.\n\nAccording to the findings of the Morrow Board, \"The next war may well start in the air, but in all probability it will wind up, as the last one did, in the mud.\" Events justified this statement, at least in Europe. Adolf Hitler began with air attacks, but the war ended with ground troops fighting street by street in Berlin. In the Pacific it was otherwise. The Japanese began their expansion with air attacks\u2014the raid on Pearl Harbor, while certainly the most well known, was just one of many\u2014and the war was brought to a rapid conclusion by the Americans with the most famous air raids in history, Hiroshima and Nagasaki.\n\n**The Morrow Board notwithstanding** , aviation could not be ignored. The thought of flight has always engaged the imagination of mankind, and in 1927 Charles Lindbergh's solo flight across the Atlantic galvanized the world. While the civilian population was celebrating Lindbergh's singular accomplishment and was set to dreaming of a new age of travel and communication, the more prescient of the military establishment saw his flight as further proof of a theorem.\n\nTo be sure, other pilots had flown long distances before Lindbergh\u2014as early as 1919 a U.S. Navy crew had flown a seaplane across the Atlantic\u2014but his nonstop, solo feat brought hitherto unimagined interest in the possibility of flights across oceans and continents.\n\nAnd clearly long-distance planes could be used for something far more sinister than aerial stunts. They were obvious vehicles for the delivery of weapons of destruction. Bombers were the ideal machines for terrorizing the civilian population and destroying the manufacturing centers of an enemy nation. Theory could indeed be joined with practice. Wars could be fought and won without the use of invading armies.\n\nTradition dies hard, and nowhere does it take as long or succumb as slowly as in the military. In Germany, also, the old-line generals and admirals were just as suspicious of and patronizing toward this new form of warfare as their French, British, and American counterparts. But if airpower was indeed to prove to be the weapon of the future, they were just as determined to control its growth and its deployment, and until Hitler came to power they did just that.\n\nDictators do not suffer the constraints of a congress or a parliament, and they can also overrule objections from the general staff. Hitler saw the terroristic advantages of bombing or the threat of bombing, and the buildup of the German air force, the Luftwaffe, was given high priority in his plans to rearm Germany. By 1937\u201338, almost 40 percent of the German defense budget was allocated to the Luftwaffe.\n\nJoseph Goebbels, the propaganda minister, began to trumpet the legend of the invincible Luftwaffe, and his half-truths and outright lies went unquestioned by foreign air ministries and visiting dignitaries who were beguiled by the Nazi regime and who swallowed whole the propaganda.\n\nNone of the visitors to Nazi Germany was as credulous or as influential as that quintessential American hero Charles Lindbergh, who on his return to America after visiting Nazi Germany naively extolled the myth of German airpower. In 1939, the Lone Eagle made two radio addresses and wrote an article for _Reader's Digest_ , in which he cautioned his fellow Americans against involvement in any European war and reminded them of the special obligation that Anglo-Saxons owed to one another.\n\nLittle wonder that Roosevelt responded with hostility to such rhetoric, which gave the isolationists a powerful weapon. \"I am absolutely convinced that Lindbergh is a Nazi,\" he said to his secretary of the treasury, Henry Morgenthau.\n\nLindbergh was wrong in other ways as well. His projections of the Luftwaffe's strength and aircraft production were incredibly wide of the mark. However, unlike his political pronouncements, they had a salutary effect. They spurred the administration to action.\n\nThe myths of the German war machine and German technological superiority were strong, and remain so still. They are not easily dispelled. Perhaps it would be wise to heed historian A. J. P. Taylor: \"The decisive difference between the British and the Germans is the British... knew what they were doing and the Germans did not.\"\n\nHowever, in the 1930s the threat of the German air force was very real to the more immediately endangered Czechs, Poles, French, and British, who would have to bear the first onslaught of any German moves east or west. Most Americans were content to go about their business, protected by the great moat of the Atlantic Ocean.\n\nThe isolationist sentiments that prevented America from joining the League of Nations had grown stronger. If Americans needed proof that the United States should stick to the affairs of the Western Hemisphere, what better examples were there than the rise of Hitler, Mussolini, and the Japanese warlords?\n\nAmerican involvement in World War I had come to be seen by millions of Americans as a futile exercise. Indeed, the American public had begun to question the aims and the results of World War I as soon as it ended. Now the general feeling seemed to be \"We bailed them out, and here they are\u2014at it again.\"\n\nIn just fifteen years the war clouds that had been dispersed in 1918 began to gather again, but the new storm threatened to be much more violent. However, none of the American armed services was preparing itself for a modern war. Tactics were still based on those of World War I. The navy paid little attention to the U-boat threat, the army was deficient in knowledge and training in the new mechanized warfare, and the air corps, in spite of its gains in acceptability, still was mired in the strategy of another era. This was to be expected; after all, their equipment was of an earlier era.\n\n**Events, however, soon began** to dictate strategy. By the fall of 1938 only the most obtuse could not, or would not, admit to the evil designs of the National Socialists in Germany and the inevitability of a new, or resumed, world war. Franklin Roosevelt certainly was under no illusions about the nature of Hitler's government. On 14 November 1938, in response to the Nazi pogrom against the Jews known as Kristallnacht, or the Night of Broken Glass, he recalled the American ambassador from Berlin. There was no break in diplomatic relations, however, and much to the dismay of his admirers and future chroniclers, there the matter rested.\n\nAs historian and Roosevelt biographer Kenneth S. Davis stated, \"He was determined to conserve every bit of his depleted political capital for expenditure on matters he deemed of supreme importance, and the Jewish refugee crisis was not one of these.... National defense on the other hand was paramount.\"\n\nThat same day, Roosevelt assembled a group of close advisers at the White House to discuss his plans for expanding the American air force. Among them was the new chief of the U.S. Army Air Corps, Hap Arnold, who was now a major general. The president immediately made known his concern about the woeful state of the air corps. The total number of operational planes was about 1,600, and fewer than 90 were being built each month. Roosevelt wanted an air force of 20,000 planes and a production capacity of 2,000 planes a month.\n\nThe American president, like the German F\u00fchrer, believed in the power of numbers. He seemed not to have concerned himself with the equally important training and operations of an expanded air corps. When he was challenged on this he bristled that he \"had sought $500,000,000 worth of airplanes, and he was being offered everything except airplanes.\"\n\nRoosevelt did listen to the objections, especially those of General George Marshall, who, as usual, was able to rise above the army's natural but parochial opposition to the huge new expenditure for a competing military arm and support the plan\u2014if it included training and operations. Otherwise, America, too, would have only a \"shop-window\" air force. The president acquiesced, but he made it clear that any such additions to the program would have to come from the original appropriation.\n\nThe American public had bought the argument that warplanes represented real power to a potential enemy. Had not Hitler proved that at Munich? Even fervid isolationists might endorse the buildup of an air force\u2014as a deterrent. And if deterrence failed and war did come, then the planes could be used as offensive weapons. But the battle would be far from America's shores.\n\nAs Michael Sherry has said, the new aerial policy put forth by Roosevelt \"squared with the dominant prejudices and priorities of Americans: alarm over fascist aggression, aversion to military expeditions abroad, desire to preserve American isolation, and faith in aviation as a benign technology.\"\n\nEven though a public opinion poll in 1938 showed that 90 percent of Americans thought there should be a larger air force\u2014in almost the same numbers the public felt that there should be a larger army and navy, as well\u2014Roosevelt knew that he could not hope to have a force anywhere near the scale he envisioned. His plans were just too ambitious for the new Congress and the country. The president scaled back his request to a total of 10,000 planes and a monthly production of fewer than 1,000.\n\nHap Arnold moved immediately to bring in his old friend to help him implement the new presidential directive. Carl Spaatz was transferred to Washington in late November 1938, on temporary assignment from nearby Langley Field, in Virginia. Early in the new year the job became a permanent one. He was now chief of planning of the office of the chief of the air corps.\n\nSpaatz soon learned the vast distance between the president's wishes, no matter how urgent and well-founded, and the Congress, which had to grant the wishes. Even in times of international crisis, the adage still applies: \"The president proposes, but Congress disposes.\" And Congress was still not in an internationalist mood.\n\nThe final air corps plan was nowhere near what the president had in mind, but at least it was a start. Congress appropriated $180 million with a ceiling of 5,500 planes.\n\nEven this modest number of aircraft was not practicable. Foreign governments were desperately seeking to build up their own air forces, which they could do only with the aid of the American aircraft industry. The Americans clearly could not supply both the army air corps and the Allies.\n\nTo Arnold's chagrin, Roosevelt came down on the side of those most directly threatened by a rearmed and aggressive Germany. The American military had to give its place in line to England and France. And, perhaps even more galling, a hundred scarce fighter planes were earmarked for Claire Chennault's Chinese operations, the famous Flying Tigers.\n\nMany have argued that Roosevelt's plan all along was not to build up the American air forces\u2014which would account for his disregard for support and training facilities\u2014but to manufacture airplanes for the Allies.\n\nIn spite of the clear threat posed by a rearmed and aggressive Germany, the war in Europe still did not engage the attention of the American military, which continued to deal primarily with hemisphere defense. Indeed, at a 1940 conference that discussed the various options that the U.S. military might face in the foreseeable future, an offensive war in Europe was ranked fifth.\n\nThere was, however, real fear that Germany and Italy might establish bases in South America, not a far-fetched idea at all since both countries already had commercial air service to Latin America. The tiny American bomber fleet had the range to reach South America, but no fighter plane had anywhere near that range, which made little difference to the planners. Fighters were still considered as interceptors only, not escorts. Self-defending bombers were still an article of faith among air planners.\n\nIn a 31 October 1939 memo to Ira Eaker, H. S. Hansell said that \"long range bombers must rely on their own defensive power to get them out of trouble.\" Hansell's view was not particular to him. At the time he was assistant executive officer for public relations for Hap Arnold.\n\nThis particular orthodoxy of the airpower enthusiasts\u2014that bomber formations, with their multiple guns covering every part of the sky, were therefore invincible\u2014went down in flames over the North Sea in just a few weeks, but it took years for the lesson to be fully absorbed.\n\nThe question as to why American or British fighters could shoot down German bombers over Great Britain but German fighters would presumably be ineffective over the Reich, or at least enough so that Allied bombers would get through, was never seriously raised. But startling proof came that the theory was false came on 14 December 1939.\n\nFive of twelve Wellington bombers were shot down by Luftwaffe fighters off Wilhemshaven, the great German naval base. Bomber Command maintained that it was flak that did the damage, and therefore in a follow-up raid on 18 December the twenty-four Wellingtons dispatched were ordered to maintain an altitude of 10,000 feet. Two of the planes turned back, but out of the twenty-two effectives, twelve were shot down by German fighters. And worse, all of the action was miles out to sea. No plane had reached Germany itself.\n\nTheorists and supporters of the self-defending bomber formation immediately searched for reasons for the disaster that would not call into question the underlying strategy. The major cause of the catastrophe, stated a report, was poor leadership. The pilots had not maintained the tight formation necessary for mutual defense.\n\nTwo other contributing factors, both technological, were admitted to and would be addressed. The fuel tanks were not self-sealing, and the gun turrets on the Wellington had a field of fire of only eighty degrees. New fuel tanks were ordered and waist guns installed. But the strategy of the self-defending bomber fleet remained unquestioned\u2014until 12 April 1940.\n\nOn that day, disaster struck again. Nine out of eighty-three aircraft were shot down in a daylight raid on Stavanger, Norway. However, only sixty had been attacked by the German fighters, which elevated the loss rate considerably\u2014from an unacceptable 11 percent to a catastrophic 15 percent.\n\nPlanners began to entertain the possibility that perhaps the bomber would not always get through\u2014at least not in daylight. There now occurred what RAF historians Martin Middlebrook and Chris Everitt have called \"undoubtedly the most important turning-point in Bomber Command's war.\" Henceforth, the Wellingtons and Hampdens and their four-engine successors would fly only at night.\n\n**In America, meanwhile** , the master politician Franklin Roosevelt kept his eye on the voters. Given public opinion and political opposition, Roosevelt could never have placed the country on a war footing. He could, however, maneuver to place the country in a position to aid its allies, particularly Britain.\n\nRoosevelt met with Winston Churchill on 9\u201312 August 1941 at the Atlantic Conference in Newfoundland. They were attended by high-ranking officers from all of the services and the heads of the civilian planning agencies. As Wesley Frank Craven and James Lea Cate observed, it was \"obvious to any literate citizen that those officers had not boarded the _Prince of Wales_ [Churchill's flagship] to discuss the Four Freedoms.\"\n\nThe two leaders did release a manifesto called the Atlantic Charter, which called for the renunciation of territorial expansion or territorial changes not sanctioned by the people affected. In the postwar world, people would be guaranteed self-determination, equal access to trade and raw materials, international economic cooperation, improved labor standards and social security, freedom from fear, freedom from want, freedom of the seas. Further, aggressor nations would be disarmed.\n\nThe charter would later serve as the basis for the United Nations, but, as Craven and Cate rightly said, Roosevelt and Churchill had more immediate concerns on their minds in Newfoundland. Their main purpose was to move neutral America closer to war with Germany, which Roosevelt correctly perceived to be an immediate threat to the United States.\n\nIndeed, a month earlier Roosevelt had requested the secretary of war to provide him with \"the overall production requirements required to defeat our potential enemies.\" The air corps estimates were assigned to the new Air War Plans Division. In early August, Lieutenant Colonel Harold George, Major Kenneth Walker, Major H. S. Hansell Jr., and Major Laurence Kuter produced the famous document AWPD-1, which set forth the initial air force policy for the bombing of Nazi Germany\u2014four months before the United States was at war with the Third Reich.\n\nThe priority targets for a bombing campaign as set out in AWPD-1, after the destruction of the German Luftwaffe, were (1) the electric power grid, (2) the transportation system, and (3) the oil supply and production facilities. The fourth item on the list was, most tellingly, the civilian population.\n\nJust after Pearl Harbor a new directive was issued, AWPD-4, which stated clearly that \"a powerful air force, waging a sustained air offensive against carefully selected targets, may destroy the sources of military power.\" Not only were the authors saying that airpower alone could bring about the end of the war; AWPD-4 was also seen by the other services as a call for a larger slice of the appropriation pie by the air commanders and, of course, a separate and equal United States Air Force.\n\nA year later, in December 1942, Hap Arnold ordered a review of the bombing plan by a group of civilian analysts and intelligence personnel. In the new directive, AWPD-42, the pro-air rhetoric was toned down a bit. Further, in a classic example of the ongoing conflict between civilian and military planners that can bedevil any defense establishment, the Committee of Operations Analysts (COA) determined that the operations recommended by the drafters of AWPD-1 were in some cases not feasible.\n\nIn their revised list of priorities, after the destruction of the German air force, the electric power system, the power grid, was now third in order of priority. As the war progressed, target priorities were changed several times\u2014oil, for example, went to the top of the list\u2014but the electric power system of the Third Reich was never reassigned primacy.\n\nHansell, in 1972, said this decision was \"one of the tragic mistakes of the war.\" And there is more than a little justification for his opinion. In a modern industrial society, which Germany certainly was in 1941, everything comes to a halt when the power goes off. This was made startlingly clear in the United States, beginning in the mid-1960s, when a series of blackouts brought great sections of the country to a complete halt. In each of those cases, the causes were fairly simple\u2014defective switches combined with human error. No structural damage had occurred in the system. The total destruction of power plants, transmission lines, and substations would have caused a long-term or complete breakdown in the Third Reich.\n\n**Capital ships and tanks** , to use Craven and Cate's felicitous phrase, \"carried with them the reassuring weight of military tradition.\" Strategic bombers were new and exotic and unproved weapons. Hap Arnold and Carl Spaatz had to show that they could win a war.\n\nThey were fully aware of the setbacks at British Bomber Command and the now-proscribed daylight operations. But the strategy was not at fault, they reasoned. The primary strategy was sound. The necessary element for its successful prosecution was the proper weapon, which the British did not possess. A four-engine, heavily armed daylight bomber would prove the point, and such a plane was becoming operational in the United States. The B-17, the legendary Flying Fortress, properly deployed and manned, would be able to look after itself in any situation.\n\nSince offensive war was anathema and Americans recoiled at the thought of bombing civilians, the military couched its plans, as it always does, in palatable, defensive terms. Thus until bombers became a retaliatory force and began to visit death and destruction on the cities of Europe, they continued to be touted as deterrents to aggression. The purpose of bombers was to prevent war, not make war. The public accepted this line of reasoning, even though events in Europe should have made it clear to them that the opposite was true.\n\nThe American president had responded to the invasion of Poland two years earlier by imploring the European belligerents to renounce the bombing of cities and the civilian populace. Roosevelt's call for restraint was heeded, more or less, for a few months.\n\nPurely military installations and naval vessels remained the primary targets until 14 May 1940, when the Dutch port city of Rotterdam was devastated by the Luftwaffe. It was now clear that civilians would not be spared in any all-out bombardment by either side.\n\nAmericans, meanwhile, in spite of Roosevelt's sympathies, were still in no mood to involve themselves in a new European war. Their fears were embodied in such organizations as the ultraisolationist America First Committee.\n\nThe committee's chief spokesman was Charles Lindbergh, who in a radio address in late May 1940, while the British and French were facing annihilation at Dunkirk, dismissed the president's plan for thousands of warplanes as \"hysterical chatter.\"\n\nBut the public sensed that perhaps the airplane might be the weapon that would keep the country safely removed from involving itself in Europe's headlong rush into disaster. Polls showed that while support for a larger air force had fallen, it was still at 73 percent. Americans clearly felt that if war should come, the airplane was the best way of keeping it a very long arm's length from the United States.\n\n# CHAPTER TWO\n\n**THE ARCHITECTS OF DESTRUCTION**\n\nThe Bomber Barons and Total Air War\n\n**M ost of the men who ran the air war in World War II began their** careers as airmen in the same patches of sky over the battlefields of the Western Front in World War I\u2014the first air war. They were part of that small cadre of brash young men who, in their primitive biplanes and triplanes, helped usher in the age of aerial warfare. While still in their early twenties all of them became heroes, veterans of the dogfights and seat-of-the-pants flying that characterized combat above the trenches of the Western Front.\n\nThey were young and often reckless, but they knew instinctively that their aircraft were not the \"toys\" derided by more conventional military men, and they would live to see the Spads, Sopwiths, and Fokkers of their youth evolve into the Mustangs, Hurricanes, Messerschmitts, Flying Fortresses, Junkerses, Halifaxes\u2014and even jet planes and rockets\u2014that would redefine military strategy. In a little over two decades, the small bombs they casually tossed from their open cockpits, like so many firecrackers, would give way to the incendiaries, the massive blockbusters, and even the atomic bomb itself.\n\nBut the development of airpower by no means proceeded in anything resembling an orderly progression. The road to a coherent and practicable air policy was filled with twists, turns, cutoffs, and detours. The rights-of-way were littered with discredited strategies, failed weapons, and not a few damaged reputations and wrecked careers.\n\nHowever, by the late 1930s, the theorists and philosophers of airpower had carried the day. There was a U.S. Army Air Corps, a Royal Air Force, and a Luftwaffe. Of the three, Germany and Great Britain had made their air arms autonomous, separate institutions\u2014Britain at the end of World War I and Germany after the accession of Adolf Hitler. Interservice rivalries and politics forestalled such a move in the United States, where the air force, which had been created as a branch of the army, would remain so until after World War II.\n\nBut theories had to be put into practice. It was now the turn of the men of action, pragmatic men who could take the directives of a prime minister or a president or a f\u00fchrer and get the planes built and the men trained to fly them.\n\nHowever, just as the stubborn orthodoxy of the army and navy had been overcome, the airmen also espoused and defended policies and strategies long after they had been proved wrong. The almost blind adherence to the doctrine of the self-defending bomber was as misguided as had been the insistence on the invulnerability of the battleship.\n\nTechnology was promoted extravagantly only to be summarily cast aside for newer, even more ambitious schemes. Aircraft manufacturers and arms makers had a more than patriotic interest in promoting their own hardware. The profits to be made were enormous. And, of course, the generals and admirals, even as they prepared for and fought a war, kept a wary eye on the rival services.\n\n**Billy Mitchell's contemporaries** , both in the United States and abroad, fared somewhat better than he had done with their crusades to promote airpower. They too had learned from the grand rehearsal of World War I, and they were equally zealous; but they knew how to proselytize without being impaled on their own swords. Indeed, they would be rewarded with the highest honors and military rank.\n\nHugh Trenchard, an early and lifelong advocate of the power of bombardment from aircraft, had said in 1923, \"It is on the bomber that we must rely for defence. It is on the destruction of enemy industries and, above all, on the lowering of morale... caused by bombing that ultimate victory rests.\"\n\nTrenchard never lost his enthusiasm for airpower or his zeal for aerial bombardment, and even after the \"father of the RAF\" retired from the military and was raised to the peerage, he continued his proselytizing. The enemy, he always maintained, could be defeated by taking the war directly to its homeland, and he never retreated from his early pronouncement that \"the moral effect of bombing stands to the material in a proportion of 20 to 1.\"\n\nIn 1942, on the eve of the battle of El Alamein, Lord Trenchard said to Churchill's physician, Lord Moran, \"We must avoid the stupendous drain on manpower of an attempt to win victory by land warfare. You must get this into the Prime Minister's head. If he puts his faith in bombers, it will save millions of lives.\" As we will see, this view was echoed by almost every air commander until the end of World War II.\n\nThe first commander in chief of Bomber Command, Sir Edgar Ludlow-Hewitt, was one of the few who disagreed. He argued that longrange bombing was going to have to be conducted at night and with fighter escorts. If England engaged in a sustained campaign against Germany, he warned, the bomber fleets would be completely wiped out in just a few weeks. But his heresies did not stop there.\n\nLudlow-Hewitt also began to insist that a major component of any buildup had to be operational training units. Otherwise the RAF, and by extension Bomber Command, would be just a so-called shop-window air force. So much for twenty years of RAF orthodoxy. Ludlow-Hewitt paid for his outspokenness. He was relieved as head of Bomber Command in April 1940.\n\nBomber Command then went through a rough patch for almost two years, until it found its proper strategic role in the prosecution of the war. Some of the problems were administrative, some were due to a lack of proper bombing platforms\u2014the available planes simply could not do the job required\u2014but most were due to a lack of judgment as to how the bombing should be carried out.\n\nAir Marshal Sir Charles Portal, a fervent disciple of Hugh Trenchard's, was appointed to succeed Ludlow-Hewitt, but in just six months he moved up to the post of chief of the air staff.\n\nFrom this powerful position\u2014he attended every major planning session and was part of the British delegation at conferences in Casablanca, Washington, Tehran, and Yalta\u2014Portal played a crucial role in developing the doctrine of the massive bombing of German cities.\n\nHis November 1942 plan called for completely destroying, through the use of heavy bombers, not only Germany's industrial capacity but also 6 million German dwellings. Not only would the proposed joint Anglo-American campaign \"dehouse\" 25 million people, it was estimated that there would be 900,000 civilians killed and another 1 million seriously injured. The plan was approved by the Chiefs of Staff on 31 December 1942.\n\nPortal then flew with Churchill in the prime minister's plane to the Casablanca Conference, which began on 14 January 1943. There it was officially decided that through round-the-clock bombing Germany's military, industrial, and economic systems were to be systematically destroyed. In addition, although it was not publicly stated, attacks would also be directed so as to destroy the will of the people to resist. In other words, morale bombing was to be official policy.\n\n**When Air Marshal Portal** left Bomber Command, he was succeeded by Air Marshal Sir Richard E. C. Peirse. As a young naval aviator in World War I, Peirse had distinguished himself, and after he transferred to the RAF his rise was rapid. He was commander of the British forces in Palestine, and by 1936 he was an air vice marshal and then director of operations and intelligence at the Air Ministry. When he came to Bomber Command in October 1940, he was vice chief of the air staff, and with his impeccable background and knowledge it seemed that any problems with the command would soon be set right.\n\nIt was not to be. During Peirse's tenure at High Wycombe, Bomber Command began to suffer disastrous and unsustainable losses of planes in raids over the Continent. Worse, the revelation that the British bombing had been nowhere near as accurate as reported caused an uproar. Thus, in December 1941 it was clear that drastic measures had to be taken. Peirse was relieved.\n\nHis replacement would become more famous\u2014some would say more infamous\u2014than any of the men, both civilian and military, who were responsible for the bombing campaigns of World War II. Indeed, he has come to symbolize the power or weakness, failure or success, effectiveness or folly of aerial bombardment of civilian populations.\n\nUnlike his less colorful associates, the new head of Bomber Command was known by a variety of nicknames. He was affectionately called \"Bert\" or \"Bud\" by his friends, the \"Chief Bomber\" by Winston Churchill, and \"Butch\" by his \"bomber boys.\"\n\n\"Butcher\" was the term favored by his detractors, who included Joseph Goebbels, an expert in such things. He said of Harris, \"You have only to look into his eyes to know what to expect from such a man. He has the icy-cold eyes of a born murderer.\"\n\nHowever, it is as \"Bomber Harris,\" the name bestowed by an admiring public, that he is best known. But whatever the sobriquet, Air Marshal Sir Arthur Travers Harris would, over time, stand as the prototypical airman of World War II.\n\n**Harris was born on** 13 April 1892, while his parents were on home leave from India, where his father was a civil servant. The family soon returned to the subcontinent, where the boy lived until he was five, when he was sent back to England for schooling.\n\nHarris therefore saw almost nothing of his parents in his formative years. In that way, his childhood was strikingly similar to that of another controversial British military hero and a colleague of his in the British army, Bernard Law Montgomery, as well as Winston Churchill's.\n\nAnd Harris responded in much the same way as did those two worthies. He became independent, strong-willed, and supremely self-confident and self-sufficient. Perhaps because of the enforced solitude of his youth, Harris was also attuned to the loneliness of a soldier's life and sympathetic to the needs of his men, qualities that would later endear him to his subordinates.\n\nAt age eighteen\u2014he said he was fed up with the snobbery of England\u2014Harris fled to Rhodesia, where he took up farming. That British colony was not beyond the reach of world events, and in August 1914, with the outbreak of war, Harris joined the army. He fought in the successful campaign against the Germans in southwest Africa, and with the German surrender there in July 1915, his war was ostensibly over. The real war, in Europe, was only beginning, however, and by that autumn Harris was back in England, where he was accepted for pilot's training with the Royal Flying Corps at Brooklands.\n\nAside from riding as a passenger in a Maurice Farman Longhorn and a BE2c, Harris's pilot training comprised less than half an hour of dual instruction. He then took a plane up by himself. Thus between 7 October 1915, when he arrived back in London, and 6 November, Harris went from the infantry to pilot's training to being an officer in the Royal Flying Corps.\n\nHarris was then assigned to the Central Flying School at Upavon, which was only marginally more rigid than the one at Brooklands. As Harris said, \"I completed the long course.... The Long Course, ye Gods!...I suppose it must have been about ten hours.\"\n\nHis first active-duty station was at Northolt, in Middlesex. When his new commander asked the young pilot if he could fly in the dark, Harris replied, \"I can't fly in the daylight, so maybe I can fly in the dark.\"\n\nThe remark was not atypical. Harris was famous for the barbed comment, but he was also a man of dry wit and droll humor. He liked to drive fast and was once stopped for speeding near an air base. \"You might have killed someone, sir,\" said the policeman in an attempt to chastise the air marshal. \"I kill thousands of people every night,\" replied the head of Bomber Command.\n\nHarris's squadron was put on antizeppelin duty, charged with intercepting and destroying the airships that Germany was using to bomb London at night. Harris literally had to teach himself night flying. It was dangerous work and many men were killed, but the experience taught him that thorough training was the essential element for an air force. Of equal importance, here was the beginning of his theories about the use of planes at night to bomb enemy cities. Later, when he was head of Bomber Command, these two ideas would reach full fruition.\n\nHarris recalled his later combat duty in France\u2014flying the Morane Parasol, the Morane Bullet, the Sopwith 1\u00bd Strutter, and finally the legendary Sopwith Camel\u2014in his usual style, which was a combination of the testy, the arrogant, and the self-deprecating.\n\nHe seemed to have come out of the war more bemused than enlightened. \"We just flew about,\" he said. \"There didn't seem to be any plan.\"\n\nHarris, his offhanded comments aside, gained valuable ideas from his derring-do over Flanders' fields. The military planners and the public would in time learn the value of the airplane as a strategic and tactical weapon. Harris never doubted the airplane's future. It was to be his crusade to turn this potent new weapon, this \"toy,\" into the primary means of attacking the enemy. He was given the opportunity to do so when he was asked to stay on in what was now the Royal Air Force.\n\nHugh Trenchard, the first chief of the new RAF and chief of the air staff from 1919 to 1929, managed to hold off the skeptics who had not let up in their efforts to undermine the RAF and keep them at bay. He thus kept the RAF alive, but it was barely breathing.\n\nHarris, in _Bomber Offensive_ , his postwar memoir, wrote scathingly of the campaigns against the air services by the old guard during the inter-war period. \"Thereafter for nearly twenty years,\" he said, \"I watched the army and navy, both singly and in concert, engineer one deliberate attempt after another to destroy the Royal Air Force. Time after time they were within a hairbreadth of success; time after time Trenchard, and Trenchard alone, saved us. If they had succeeded they would have abolished our air power as they succeeded in abolishing our tank power, while retaining the Camberley drag hunt.\"\n\nRegarding the vaunted battleship, Harris said that their \"bones now lie where air power so easily consigned them, littering the floors of the ocean or obstructing the harbours of the world.\"\n\nAs an acolyte of Trenchard's, Harris had paid close attention to his new ideas, and Smuts's manifesto would become his credo when he became head of Bomber Command. Harris early on saw the power of bombs as a deterrent when he was stationed in India in 1921. One twenty-pound bomb dropped onto the grounds of the palace of the emir of Afghanistan, who had launched an insurgency against Great Britain, had been enough to convince that worthy to negotiate.\n\nAfter his tour in India, Harris was sent to Iraq, where the RAF was charged with subduing another restive, even rebellious populace. Between 1922 and 1924, the RAF heavy bombers destroyed villages and killed or injured thousands of the rebels before calm was restored.\n\nBut the lessons of India and Iraq, while instructive, were improper for the wars of the 1930s and 1940s. The intimidation of petty tribal chieftains, illiterate villagers and nomads, or eastern potentates, who had never seen an airplane, was a far easier task than cowing the populace of a major industrial power ruled by a fanatic.\n\nAfter his service in India and the Middle East, Harris returned to England and began his unremarkable but steady rise through the officer ranks of the Royal Air Force, eventually joining the Air Ministry, where he became deputy director of operations and intelligence, and then, within a year, head of the Planning Department.\n\nHarris and others in the military in England were successful in their efforts to counteract those who scoffed at the idea that German bombers might be able to so immobilize Britain that it would be isolated. Further, their argument that in the event of such a disaster only a bomber force could continue to wage offensive war against Hitler began to be taken seriously. But, as in America, the pacifists and the isolationists wielded enormous power and used it either to block or to much reduce military spending.\n\nNowhere was this shortsightedness more evident than in the decision not to fund an RAF entry in the Schneider Trophy high-speed flying contest in 1931. The Labour undersecretary of state for air saw no reason for the government to fund a \"sporting event.\"\n\nLady Lucy Houston immediately agreed to donate \u00a3100,000, a plane was built, and the RAF won the race. But the trophy symbolized something far more important. The research and development that produced the winning plane and its engine were crucial to the design and manufacture of the Rolls-Royce engines used in the famous Spitfire fighter and the Lancaster bomber. Later, Harris credited this eccentric widow of Sir Robert Patterson Houston, along with Fighter Command, of winning the Battle of Britain.\n\nWhen Adolf Hitler came to power in 1933 and began to rearm Germany, the RAF had only 850 first-line aircraft. By 1935, the F\u00fchrer could brag to a British delegation headed by Foreign Secretary Sir John Simon that the Luftwaffe already had that many planes and would soon have 2,000.\n\nHitler's boast, which was intended to intimidate any potential enemies, spurred advocates of British rearmament to action\u2014in particular, Winston Churchill, who in dozens of speeches and articles called for a much enlarged Royal Air Force to counteract what he saw as the coming German threat. Although Churchill was mocked by the opposition and ignored by many in his own party, he did have some success with his campaign.\n\nWhen faced with the incontrovertible fact of German rearmament, the British government approved plans to produce 816 new bombers by 1937. This number was increased to 990 in February 1936. In addition, production of new fighter planes was to begin.\n\nHarris was troubled by the air staff's plan, which included light bombers, medium bombers, and fighter-bombers\u2014any one of which, he said, would be obsolete by its delivery date. He called instead for a plane with a range of one thousand miles and a top speed of 250 miles per hour\u2014in other words, a heavy bomber.\n\nHe was able to influence strategic planning as one of three authors of a 1936 report entitled \"Appreciation of the Situation in the Event of War Against Germany in 1939.\" Few military documents have proved to be so prophetic. Harris and his coauthors, Forbes Adams and Tom Phillips, predicted exactly the German war aims and strategies and the only possible defense for Great Britain.\n\nA quick advance by Germany into France and the Low Countries would give the Germans the air bases from which to make concentrated attacks on the United Kingdom, which was clearly vulnerable to such assaults. Germany would then, they warned, do everything to guarantee a quick end so that Britain would not have time to mobilize for war.\n\nIn other words, the only course for the next two to three years was to prepare the country for defense against the coming German air raids. Harris was sure that the RAF could hold off the Germans with the fighter force that was in the works, and England could thus hold out until the offensive bomber force was in place. But the medium bombers could not be ready until 1940 at the earliest, and the heavies not until 1942.\n\nThe three authors also offered the opinion that any war with Germany would ultimately be decided on land. Harris would, of course, totally abandon this theory. He came to believe strongly that bombers alone could end the war.\n\nBecause even the thought of bombing cities and towns was still anathema, the three RAF officers were careful not to dwell on the fact that a bomber offensive would kill and maim thousands of enemy civilians. They had, however, made it clear that perhaps as many as 150,000 Englishmen would be killed or injured by German bombardment.\n\nNow came the job of mobilizing industry to build a war machine. The RAF comprised just 1,000 first-line aircraft in 1936. Great Britain ranked fifth among the world's air powers. Harris wanted to have at least 2,000 first-line planes by 1939 with a reserve force of 200 percent.\n\nBritish intelligence that the Luftwaffe would produce 2,500 first-line planes by that date and its reserve would be 100 percent was right on the mark. Production for the Luftwaffe in 1939 was 2,518 planes. However, in 1940 German production rose to 10,247.\n\n**In 1937 it appeared** to the advocates of aerial bombardment that they had won their campaign for increased aircraft production and procurement, and Harris happily accepted his promotion to air commodore and the command of a bomber group. But the triumph over the admirals and generals and the pacifist politicians was short-lived.\n\nIn an almost exact replication of what was happening in Germany and the United States, the decision was made to concentrate on medium bombers instead of the more expensive heavies. Almost as serious were the cuts in the reserve forces.\n\nHowever, much good also came out of this reordering of priorities, which concentrated on defensive aircraft. The Hurricane and Spitfire fighter planes, which won the Battle of Britain, are the most resonant examples.\n\nThe British realized early on that their aircraft industry could not meet even reduced goals in any reasonable time, and the RAF had to turn to the United States. Harris was part of a British mission that arrived in Washington in April 1938 to negotiate with the Americans for planes and equipment.\n\nHe was singularly impressed with American efficiency and enthusiasm, particularly the executives and engineers at the Lockheed Aircraft Corporation. The British ordered \"batches of Hudsons and Harvards.\" As Harris wrote after the war, \"The Hudsons beyond doubt pulled us out of the soup when we used them for anti-submarine patrols... and the Harvards broke the back of our problem in finding training aircraft.\"\n\nBut his praise extended only to the civilian sector. As for the U.S. Army Air Corps, \"I am at a loss to understand where the myth of American air power and efficiency arose,\" he reported back to England.\n\nHarris acidly observed that the Americans \"have one or two 'stunt' units which can, and occasionally do, put up 'stunt' performances.\" In short, said Harris, the Americans had only \"an elaborate and expensive piece of window dressing, which comes perilously near to being little more than a jest when judged by the standards of any first class air power.... Their major obsession,\" said Harris, \"is that all their geese are swans, and that everybody else's are, at the best, ducks.\"\n\nIt is clear, using Harris's standards, that no country, in 1938, was a first-class air power. Certainly Great Britain was not, and in the not too distant future, events would prove how ineffective Germany's \"shopwindow\" Luftwaffe actually was.\n\nHarris did praise the American advances in navigation and recommended that Britain should order navigation and communications equipment from the United States. However, the item that the British were most anxious to learn about was off-limits. Harris ran into a stone wall when it came to the Norden bombsight. No information was available.\n\nGiven his scornful dismissal of the American air force, it is surprising that he became friends with the commander, Hap Arnold, and his deputy, Ira Eaker.\n\nHarris's reputation for speaking his mind made it unlikely that the American commanders did not hear of his remarks, but they refrained from responding to the testy Briton, who was doubtless venting some of his rage against the shortsighted bureaucrats at home. It cannot have been pleasant for this proud and touchy man to have gone hat in hand to the Americans.\n\nBy 1939, the situation began to change. Hap Arnold and Carl Spaatz, who were charged with a quantum expansion of the U.S. Army Air Corps, now ran head-on into balancing their needs with the needs of the RAF. Spaatz was flatly opposed to sending planes abroad when the American air force, if one could even call it that, was so deficient. No doubt Harris became aware of Spaatz's opposition, which may have colored his somewhat negative view of the American airman when they had to work together so closely later in the war.\n\nJust before Harris's mission to Washington in 1938, the forty-five-year-old bachelor officer had become engaged to twenty-year-old Therese Hearne. When he returned from the United States, they were married and soon afterward Harris began a second tour in the Middle East as air officer commanding Palestine and Transjordan.\n\nThe British attempt to adjudicate the troubles between the Jewish settlers and the Arabs often led to armed clashes, assassinations, and open revolt. Harris applied the techniques developed ten years earlier in India and Afghanistan, and once again airpower proved to be a useful tool of intimidation.\n\nHe returned to England in midsummer 1939, just after his promotion to air vice marshal, and when the war began he became head of 5 Group, one of the five bomber groups that made up Bomber Command, with headquarters at Grantham, an ancient and historic town on the Witham, in Lincolnshire.\n\nThe winter dragged on, and Hitler still did not press his presumed advantage after the invasion of Poland by moving west. This period, the so-called Phony War, which lasted from October 1939 until April 1940, was a time of waiting and watching, and for Harris it was a particularly dispiriting period.\n\n\"I have in the course of my lifetime rarely been so depressed,\" he said. His surroundings did little to lift his gloom. Grantham had once been the haunt of King John and Richard III, but Harris's troubles were of more recent vintage. He felt he was in a backwater and saddled with equipment that in his opinion was useless.\n\nHarris, in his pursuit of his military ideals, spared no one throughout his career in his relentless advocacy of better training, planes, and weaponry. When he saw the prototype of the twin-engine Avro Manchester in September 1940, he said that the only use for the plane as presently configured was for \"throwing away crews.\"\n\nHe was particularly derisive concerning the small escape hatches on the Avro Manchester. Someone at the Air Ministry should realize that if a man has to jump out of an airplane he should be able to take his parachute, Harris sarcastically observed.\n\nDespite Harris's criticisms, some two hundred Avro Manchesters were built and delivered to the RAF; but, as he predicted, they were a failure and were withdrawn from service in less than two years. The plane did serve a useful purpose, however. It would be the basis for the aircraft that became the backbone of the bomber fleet, the Lancaster.\n\nIn the same memo addressing the shortcomings of the Manchester, Harris's credo regarding aerial bombardment was simple. Heavy bombers should be used only for nighttime operations. Daylight bombing had been proved to be a \"busted flush.\" As he put it, this was a \"childishly obvious fact.\"\n\nArthur Harris's first concern was always the welfare and safety of his crews, which endeared him to the rank and file of the RAF. He was particularly distressed by what he saw as foolhardy actions by pilots to save a plane or avoid civilian casualties on the ground if a plane crashed. Trained pilots and crew, he said, were far more important than either a plane or any unfortunate civilian who happened to be in the way.\n\nPlanes and crew, as vital as they were, existed for only one reason, to rain destruction on the enemy, and Harris early on pressed for the development of more powerful bombs. The Germans had by the winter of 1940 demonstrated the destruction that could be caused by large highexplosive bombs, and intelligence indicated that the Nazis were developing a 4,000-pound version.\n\nHarris was quick to trade on the German advances and to adopt the Luftwaffe's bombing policies. It mattered not at all to him where ideas came from. Effectiveness was the only criterion. In a memorandum he laid out the two principal bombing methods as he saw it.\n\nThe first was so-called precision bombing, wherein factories, communications centers, and other industrial sites were hit directly, or nearly so, by heavy fragmentation bombs.\n\nThe other method was the Luftwaffe's. Light-case bombs with huge amounts of explosives were dropped with little regard for accuracy. Damage was more widespread; it interrupted all essential services and so damaged buildings that production would be halted. The effect could be increased exponentially if the high explosives were accompanied by incendiaries. This plan would evolve into the system that would become standard bombing procedure. Incendiaries were used to set the fires and the high explosives\u20142,000-pound, 4,000-pound, and even larger bombs\u2014would crash through, destroying roads, water mains, and the electrical supply.\n\nThus, in late 1940, Bomber Command, as Harris had always argued it would, became the only British means of engaging the Germans directly on the Continent.\n\nIn June 1941, Harris returned to the United States as head of a delegation charged with expediting the purchase and delivery of American war mat\u00e9riel. Harris had not tempered his view of America\u2014the only thing worse than going there, he said, was staying at the Air Ministry\u2014but only someone of his rank and experience could deal with the American officers on equal terms, so he accepted the assignment.\n\nHarris particularly disliked Washington, though he managed to hide his disdain. And he was wise enough to realize that there were many in the Roosevelt administration who were sincerely trying to help his beleaguered country.\n\nHe reached out to them, and to one in particular: a man who was singled out and praised unstintingly by both Harris and Churchill\u2014Harry Hopkins. The mild-mannered midwesterner was a strong interventionist, and he now became Harris's personal conduit to his boss, the president, who already was bending every effort, and not a few laws, to overcome the ingrained opposition to foreign involvement by powerful leaders in the Congress and the majority of his countrymen.\n\nHarris toured the country, visiting aircraft factories and training fields and forging firm alliances with other military men with whom he would work closely in the coming months and years. He also came to admire George Marshall\u2014whom Churchill called \"the noblest Roman of them all\"\u2014and he developed strong relationships with Robert Lovett and Averell Harriman, two other influential figures in the Roosevelt administration and strong anglophiles.\n\nOn 22 June 1941, just days after Harris arrived in Washington, Germany invaded the Soviet Union. The opening of this second front, in the east, with the diversion of much of the Third Reich's war-making potential, relieved a great deal of the immediate pressure on Great Britain; but Harris and his countrymen's most fervent prayers had yet to be answered.\n\nThey had not long to wait. On 8 December, the day after the attack on Pearl Harbor, Roosevelt went before the Congress and asked for a declaration of war against Japan. And on 11 December, in what historian Martin Gilbert has called \"perhaps the greatest error, and certainly the single most decisive act, of the Second World War,\" Hitler declared war on the United States.\n\nAmerica was now firmly and officially allied with Britain in the war, but, paradoxically, Harris's job did not become easier. The equipment he had obtained with such difficulty was now needed by Britain's new ally.\n\nThere was also the question of which theater of operations the United States would consider the more important. In order to ensure that it would be Europe, Churchill left England the day after Hitler's declaration of war, bound for Washington and his second meeting with Roosevelt in ten months. In the delegation was Air Chief Marshal Sir Charles Portal, chief of the air staff.\n\nAfter the first meeting of Roosevelt and Churchill with the Combined Chiefs of Staff, Portal pulled Harris aside and informed him that he was going to recommend to the prime minister his appointment as head of Bomber Command. The next day Harris was told that Churchill, who was impressed by the close relationship that Harris had developed with Roosevelt and Hopkins, had agreed.\n\nHarris may have ingratiated himself with the president and his trusted adviser or, more likely, they with him, but their goodwill seems not to have tempered his view of things American. Roosevelt's boast to Harris that the average American could quickly learn to fly a plane\u2014\"because you see our boys are all used to mechanical things\u2014they can drive a car long before they are legally allowed to\"\u2014was swallowed at the time by the air marshal.\n\nIn his postwar memoirs, however, he let fly. \"Well,\" he said, \"the answer to that sort of statement is that any moron can drive a motor car and it is generally the moron who takes most delight in doing so.\"\n\nOn 10 February 1942, Harris sailed from Boston for home, aboard HMS _Alcantara_ , a passenger liner that had been converted into an armed merchant cruiser. While he was at sea, the famous area-bombing directive was sent to Bomber Command. Along with the decision to fly only at night because of the enormous losses, it had become clear that precision bombing, with the equipment then at hand, was also not possible. The only appreciable damage that could be meted out to the enemy was to bomb the cities. After all, as Harris had observed more than once, that is where the industry was. And while the area-bombing directive was drafted while he was in the United States, its contents could hardly have come as a surprise. In any event, he embraced it wholeheartedly.\n\nHarris also maintained, somewhat disingenuously, that while morale bombing of Germany was high on others' lists of priorities, it was never a major priority of Bomber Command. As he said, \"The idea that the main object of bombing German industrial cities was to break the enemy's morale proved to be wholly unsound.\" His argument had to do not with morality, however, but with practicality.\n\nHow could it have been effective, he argued, when in the brutal police state that was Nazi Germany there was never a possibility that the people could successfully rebel against the regime? As Harris said, the Gestapo was firmly in control and the leaders of the Reich made a clear distinction between the morale of the people and their conduct. The people suffered terribly from the raids, but they still reported for work. He might also have added that millions of workers in the Reich and the occupied territories were slave laborers.\n\nHarris, ever the advocate of airpower, did not rule out morale bombing. \"I do not, of course, suggest that bombing is not a useful weapon against morale,\" he wrote, citing the successes of the Luftwaffe in 1939 and 1940 in Poland and Holland. But, he added, the German \"attempts to break the morale of Britain by bombing altogether failed.\"\n\nHere one encounters again the oft-stated, contradictory arguments for morale bombing of civilians. On the one hand, it might work if one's own planes are doing the bombing. On the other hand, it is not effective if the enemy is dropping the bombs.\n\nA letter written by a survivor of the Dresden raids and firestorm is instructive on this point. \"The damage surpasses all one could imagine.... But we must not give up. Somehow we have to get through it all as it seems to be our duty.\"\n\nOn 23 February 1942, Harris assumed his new post, commander in chief, Bomber Command. He quickly settled in at the headquarters five miles from High Wycombe, in Buckinghamshire, and at once began to develop and refine the bombing practices that in the next three years would blast Germany's cities into heaps of rubble. Also buried in the dust of the cities of the Reich was the fine distinction between morale and area bombing.\n\n**The Billy Mitchell episode** had served to put the issue of American airpower front and center, where it belonged, but it did nothing to tamp down interservice rivalries. The American military was not completely blind to the potential of airpower, but the American generals and admirals saw the airplane only in terms of tactical support for ground troops and naval vessels. And they certainly did not want any air arm to be on a par with the U.S. Army and the U.S. Navy\u2014not in congressional appropriations, not in strength, and certainly not in influence.\n\nThere were minor but encouraging advances, however. The National Defense Act of 1920 established the U.S. Army Air Service, within the U.S. Army and equal to the infantry and the cavalry\u2014at least in theory. The reality was otherwise. The act required that 90 percent of the officers in the air service be rated fliers. In addition, anyone transferring into the air service had to pass the stringent physical requirements. For senior military officers, this was, by and large, not possible. They were too old. The air service was therefore staffed with junior men in the military hierarchy.\n\nIn July 1923, the future head of the U.S. Army Air Forces, thirty-seven-year-old Henry Harley (Hap) Arnold, and the future head of the Eighth Air Force, thirty-two-year-old Carl Spaatz, held only the rank of major. Clearly, this lack of seniority hampered any serious buildup of the air service, whose officers did not have the clout in the army to advance their views\u2014much less impose their will.\n\nAs sometimes happens, this detriment turned out to be an asset. These relatively young men were obliged to perform the tasks of men much older and much more senior in the regular army. And, of course, among themselves they were not bound by the archaic rules and attitudes of the traditional services.\n\nHap Arnold was a true aviation pioneer. Anxious to get out of the infantry, he'd applied in 1909 for a transfer to the Aeronautical Division of the Signal Corps. His application was approved in 1911, when the War Department contracted with the Wright Brothers to buy three airplanes. The transaction included pilot training at the Wright Brothers Flying School outside Dayton, Ohio, for Arnold and a fellow officer, Thomas DeWitt Milling.\n\nAlthough Arnold worked closely with both Wright brothers at the school and factory, he never flew with either of them. The Wrights concentrated on the mechanics of aircraft with the students. An assistant took them up in the planes.\n\nAfter total air time of about six and a half hours, Hap Arnold found himself a licensed pilot, one of the first in the United States. He and Milling were the only two pilots in the United States Army.\n\nArnold's early flying career was distinguished by his winning the Mackay Trophy for an outstanding military flight, but it was also marred by one crash and one near crash, which he admitted so unnerved him that he voluntarily removed himself from active flying duty in 1912. His subsequent marriage reinforced his decision to stay on the ground. But after unrewarding tours back in the infantry, he once again felt the pull of aviation, and in November 1916, at age thirty, he returned to the air.\n\nWhen America entered the war in 1917, Arnold, in the belief that any future promotions would depend on frontline experience, applied several times for postings to Europe. His superiors felt he was needed in Washington, so his requests were denied until November 1918. He finally made it to the war, but just barely. He arrived in France on 4 November, just a week before the Armistice. Thus, to his everlasting regret, his illustrious career lacked one important element: actual aerial combat.\n\nBut the War Department experience would prove just as valuable in more important ways in the years to come. During his time in Washington he had seen firsthand the problems that would bedevil the buildup of a proper air force\u2014research and development, aircraft manufacturing, the training of pilots, and the building of the infrastructure necessary for a proper air arm. It would take years to solve the problems\u2014if indeed they were ever solved to Arnold's satisfaction\u2014but this hands-on experience in Washington laid the foundation.\n\nArnold's World War I tour in Washington also involved the development of an experimental aircraft that in retrospect was more prescient than its designers imagined. The Liberty Eagle, or \"Bug,\" as the plane was called, was an unmanned biplane loaded with explosives. It employed a rudimentary form of the system used to launch and guide the V-1, or Buzz Bomb, the weapon developed by the Germans and used with deadly effect against the cities of England in 1944\u201345.\n\nThe Bug never flew successfully, and the project was abandoned and forgotten by the military. It was thus consigned to the same shelf as two other revolutionary ideas that were conceived early on by the Americans but never developed until years later: midair refueling and wing tanks.\n\nThe interwar years were difficult for a career officer in any branch of the military. Wartime promotions were revoked, and Arnold briefly found himself reduced in rank from colonel to captain before it was settled that he would have the permanent rank of major\u2014a bitter pill for a thirty-four-year-old. He also (at least he so believed) suffered from his defense of Billy Mitchell. Beginning in 1926, he was \"exiled,\" as he put it, to a string of air fields in the Midwest for five years.\n\nMeanwhile, other airmen found themselves in a similar situation, existing on the fringes of the American military establishment. Among them were James Doolittle, Carl Spaatz, and Ira Eaker, with whom Arnold forged strong ties and who in two decades would help him transform the United States into the greatest air power in the world.\n\nIn 1931, Arnold's career began to look up, with his promotion to lieutenant colonel and his appointment as commanding officer of March Field, in California. And in 1934, he was awarded a Distinguished Flying Cross and another Mackay Trophy for his command of a group of ten Martin B-10 bombers on a round-trip flight from Washington, D.C., to Fairbanks, Alaska.\n\nThe following year, Arnold was promoted to brigadier general, temporary, and in January 1936, he was posted back to Washington as assistant chief of the U.S. Army Air Corps.\n\nArnold's military credentials were certainly impeccable, but he had also cultivated powerful friends in the Roosevelt administration, in particular the president's closest confidant (some would say alter ego), the redoubtable Harry Hopkins. Through Hopkins he gained the respect and confidence of the president himself, and on 21 September 1938, Arnold was given the top Army Air Corps job, chief of the air force, and a second general's star. Henceforth the president relied on Arnold for advice on all matters concerning airpower, and Arnold's was a major voice at the Big Power conferences.\n\nIn June 1941, the U.S. Army Air Forces was created and Arnold's title became chief of the army air forces, part of the promotion being so that there would be an American equivalent of the British air marshals at the upcoming Atlantic Conference in Newfoundland being arranged secretly by Hopkins.\n\nArnold also attended the conferences, at Quebec, Cairo, and Potsdam; but it was at Casablanca in January 1943 that he did perhaps his most important and, some would say, controversial work. There he helped craft the bombing directive for the massive Allied air campaign against the Third Reich.\n\nArnold, to his chagrin, realized soon after arriving in Casablanca that the British air staff had convinced Churchill that only night bombing could succeed. After all, daylight raids had been a disaster for the RAF and had been abandoned. This was no small matter, since the Americans had been trained only for daylight operations.\n\nThe American commander wisely left it to his more experienced and knowledgeable subordinates\u2014in particular Eaker, who at the time was head of the Eighth Air Force in England\u2014to make the case for daylight raids. Thus the policy of round-the-clock bombing of the Third Reich\u2014the Americans by day and the British by night\u2014was born.\n\nThere was no argument about the ultimate purpose of the combined bomber offensive, which was to bring about \"the progressive destruction and dislocation of the German military, industrial and economic system.\" But there was a secret directive as well: \"the undermining of the morale of the German people to a point where their capacity for armed resistance is fatally weakened.\"\n\nDuring the war and after, the Americans insisted that their unchanging and official policy throughout was always the precision bombing of military targets, and that civilians were never purposely targeted. It is clear, however, from the Casablanca directive that terror bombing of civilians was an official, albeit unannounced, policy of both the RAF and the Eighth Air Force. And Hap Arnold, as the ranking American airman present, doubtless played a major role in formulating the policy that by war's end had caused the death of an estimated 600,000 German civilians.\n\n**If Arthur Harris is** indeed the archetype of the World War II airman, the man responsible for the rebirth, expansion, and subsequent policies of the German air force was an archetype of a very different sort. Harris and the other bomber barons are now known chiefly by students of the period, but as so often happens with history's true scoundrels, Hermann G\u00f6ring's fame is widespread and enduring.\n\nBut G\u00f6ring's place in history comes from his politics, not his military prowess. He was part of Adolf Hitler's innermost circle and was one of the most notorious criminals of the Nazi era.\n\nG\u00f6ring's position in the Third Reich, in that it was both military and political, was much higher than that of any of his opposite numbers among the Allies, but his direct control of the Luftwaffe put him in a rather similar operational position. And he is, of course, irrevocably tied to his conquerors, although, unlike them, he left no aviation legacy.\n\nThe virulently anti-Semitic G\u00f6ring was the namesake and godson of Hermann von Eppenstein, an Austrian-born Jew who had converted to Catholicism. Eppenstein was not only the godfather of Hermann and his siblings, he was also the lover of G\u00f6ring's mother for fifteen years.\n\nEppenstein had been ennobled, and in keeping with his position he maintained two castles\u2014Schloss Veldenstein, at Neuhaus an der Pegnitz, near Nuremberg, and Schloss Mauterndorf, at Salzburg, where the G\u00f6ring family lived after the father retired from the diplomatic service. It was among the medieval towers and battlements of the castles that young Hermann discovered his love for the Germany of myth and legend. He also developed a taste for opulence and grandeur.\n\nYoung Hermann had an illustrious career in the German air force, downing twenty-two enemy planes, for which he received Germany's highest military decoration, the Pour le M\u00e9rite. When Manfred von Richthofen, the legendary Red Baron, was killed, G\u00f6ring became commander of his squadron.\n\nLike millions of his countrymen, G\u00f6ring left the military a bitter and resentful man. In Munich, where he had gone to study at the university, he met the man who would harness his nation's resentments and ride them to power.\n\nAdolf Hitler and his fledgling National Socialist Party, the Nazis, promised to right the wrongs visited on Germany. What did the methods matter if the F\u00fchrer could reverse the decline of Germany, abrogate the hated Versailles Treaty, and restore the Fatherland to its rightful place in the world? Hitler's rage and anger were focused on two groups in particular. The chief authors of German defeat and humiliation, he said, were the Bolsheviks and the Jews.\n\nAdolf Hitler's message was easily assimilated by the twenty-nine-year-old war veteran, and he was welcomed into the Nazi Party in October 1922. Two months later, Hermann G\u00f6ring, godson and prot\u00e9g\u00e9 of an Austrian Jew, was head of the SA, the Sturmabteilung, or Storm Troopers, Hitler's elite guard.\n\nThe bond between the two men was further strengthened when G\u00f6ring was wounded in the Beer Hall Putsch in 1923. He fled Germany to avoid imprisonment and spent the next four years in exile. He returned to Germany in 1927 and renewed his relationship with Hitler. When the Nazis won twelve seats in the Reichstag in the 1928 elections G\u00f6ring took one of them, alongside Joseph Goebbels.\n\nBy 1932, the Nazis were strong enough that they were able to force the election of G\u00f6ring as president of the Reichstag. By the time of Hitler's triumph\u2014the accession to the chancellorship in 1933\u2014Hermann G\u00f6ring's future was assured.\n\nThe old loyalist was given three cabinet posts. He was made minister without portfolio, which meant, to use his own word, he was the F\u00fchrer's \"paladin.\" As minister of the interior for Prussia, which included the capital, he had control of the police of the most powerful state in Germany.\n\nHe soon made known his intentions, bragging that he alone would be in charge in Prussia. Thus was born an organization whose name would become synonymous with torture, murder, and suppression of all dissent\u2014the _Geheime Staatspolizei_ , or Gestapo.\n\nIn the dog-eat-dog world of Nazi politics, G\u00f6ring's power always depended on the will or whim of the F\u00fchrer, who encouraged infighting among his subordinates. It was, after all, a basic Nazi belief that the most worthy man would triumph and come out on top. And if he did so, was he not, according to the doctrine of the survival of the fittest, ipso facto the best man for the job, whatever that job may be? Thus, in a series of intrigues, G\u00f6ring lost control of the Gestapo to Heinrich Himmler, and also lost the interior ministry for Prussia.\n\nHowever, there remained the seemingly innocuous third cabinet post, air traffic minister. That one would prove to be the most important, at least as concerns the military, of G\u00f6ring's government assignments. He at once began to combine the civilian air clubs and aviation organizations into the German Air Club and German Air Sport Union.\n\nGoebbels immediately began to beat his propaganda drums. He warned the German people in the most strident terms of the nation's vulnerability to air attack and the need to build up a defense. A National Flying Day was held at Berlin's Tempelhof Airport on 15 June 1933, and a week later the Goebbels-controlled press fired the first shot in the air war: \"Red Plague over Berlin: Foreign Planes of an Unknown Type Escaped Unrecognized; Defenseless Germany.\"\n\nThe 1926 Pact of Paris allowed Germany air police protection, and G\u00f6ring moved immediately to take advantage of this clause and exploit the scare invented by the propaganda minister. He successfully negotiated with Sir John Siddeley, the British aircraft manufacturer, to provide aircraft to Germany.\n\nFormer wartime comrades of G\u00f6ring's\u2014in particular, Karl Bodenschatz, Erhard Milch, Bruno Loerzer, and Ernst Udet\u2014were only too anxious to join him in building the German air force, but the emphasis was placed on training younger men for a modern air force. One of the first to be enlisted was twenty-one-year-old Adolf Galland, the future head of the Luftwaffe fighter command.\n\nThe putative Lufthansa trainee, along with several other young men, was sent for secret training as a fighter pilot with the Italian air force. Within the year, as Hitler became bolder, Galland and other of the Italian-trained pilots were transferred to the military and commissioned as officers.\n\nIn fairness\u2014if such a word can be used in such a context as Hitler's Germany\u2014no man could have fulfilled all the duties that were assigned to Hermann G\u00f6ring. Not only was he to oversee the buildup of the German air force, but he was also in charge of overseeing the economic plans of the Reich and then of the conquered territories. It would be as if in America one person were placed in charge of the Federal Bureau of Investigation, the Treasury and Commerce departments, the Office of Management and Budget, and the air force. Failure was inevitable.\n\nBefore the collapse, however, there were years of stunning successes, or so it seemed to the outside world. In the early years of the Reich, G\u00f6ring was by no means a hands-on manager of the Luftwaffe. He attended few staff meetings and was seldom seen in his office at the Air Ministry. His chief role was ensuring that funds were available for the vast buildup envisioned by a capable group of subordinates\u2014Walther Wever, Helmut Wilberg, and Robert Knauss.\n\nThese three men were fervid believers in the philosophy of Giulio Douhet and advocated early on the building of a large bomber fleet to deter any aggression from Germany's enemies and to take the war to the enemy homeland if necessary. Their philosophy was embodied in \"Luftwaffe Regulation 16: The Conduct of the Aerial War.\"\n\nAlthough the regulation stressed that the purpose of an air war was to destroy the enemy's military forces\u2014\"The will of the nation finds its greatest embodiment in its armed forces\"\u2014there was no doubt in its supporting arguments that any segment supporting the military was a fit target for attack: factories, rail lines, administrative centers, power plants, and so on. In other words, the civilian population would not be spared in the event of a war.\n\nIn June 1936, the hitherto relatively smoothly functioning bureaucracy of the Luftwaffe received a blow from which it never recovered. Lieutenant General Walter Wever, the chief of staff, was killed in an air crash in Dresden.\n\nForthwith, G\u00f6ring began to take a more active role in Luftwaffe planning and policies, and he appointed his old friend Ernst Udet chief of aircraft production. Udet, who was little more than a glorified test pilot, had no knowledge of aeronautics or airplane design.\n\nBy this time, although the resurgence of the German military machine was a reality, much of the power attributed to it was a bluff. However, when visitors from abroad were shown the new planes and the factories and introduced to the dashing young Teutonic pilots, they spread the word of the powerful armada that Germany was building and could launch against any potential enemies.\n\nGeneral Joseph Vuillemin, a French air commander, was led to believe\u2014and did believe\u2014that the test-model Heinkel bomber that roared overhead during his visit to a Luftwaffe airfield was in full production. Heinkel was said to be producing seventy He 111s a month.\n\nIn addition, it was said that the Messerschmitt Me 109 fighter was also being turned out in vast numbers, and the French delegation was treated to an awesome display of firepower from a jacked-up Me 110\u2014 again, only a prototype passed off as being in full production.\n\nBut the Luftwaffe was, in reality, as historian Michael Sherry has pointed out, a \"shop-window\" air force. It was \"designed to intimidate or to demonstrate resolve,\" but it had very little to back it up. In no area was it as it was presented. Not only were the planes for show but command structure was weak, as were logistics, training, and reserves.\n\nIn Poland, in September 1939, the weaknesses were quickly made manifest to the knowing, but they were concealed by the rapidity of the assault and conquest of the country. Newsreel pictures of the Stuka dive-bomber attacking men on horseback reinforced the image of a technologically superior nation. The reality was otherwise. The Luftwaffe lost 285 planes and 734 men in the four-week campaign.\n\nHitler himself was taken in by the propaganda extolling the invincible Luftwaffe, and the F\u00fchrer was lavish with honors and high position for the man he saw as its progenitor. It would take him years to realize that his trust in G\u00f6ring was misplaced, but by then the war was lost.\n\nG\u00f6ring's great failing was that he did not use his influence and proximity to educate Hitler on the importance of strategic airpower and to institute a rational plan for research, development, and production of aircraft. In this he was, of course, like most yes-men. Whatever the F\u00fchrer said was correct.\n\nOtto Dietrich, Hitler's chief of press relations from 1933 until 1935, offered interesting insights into Hitler's attitude toward airpower. According to Dietrich, the F\u00fchrer had no feeling for airplanes. In fact, he did not like to fly himself, although he had used an aircraft to telling effect while campaigning for office.\n\nThe F\u00fchrer, however, never hesitated to interfere in design or production, and thus designers and builders were allowed to develop whatever struck their and the F\u00fchrer's fancy at the moment rather than concentrating on proven aircraft.\n\nG\u00f6ring has often been painted as something of a buffoon, a beer hall glad-hander, an incompetent who succeeded to his positions of power through his doglike devotion to Adolf Hitler. And, indeed, there is truth to these assessments. There is also the fact it was his devotion and loyalty and proximity to the F\u00fchrer that were integral to the founding and early growth of the Luftwaffe.\n\nFor all his failings, G\u00f6ring turned out to have been a realist about German power in 1939 and the consequent ability of the Reich to wage war. The vaunted air force was something of a sham, and he knew it. But he said nothing, and it would be a year before the truth became obvious.\n\nGerman medium bombers might be able to carry a thousand pounds of bombs to England, but they would have to do so without anywhere near effective fighter escorts. Therefore, it was essential to knock out the British fighter squadrons if the bombers were to get through. Thus when G\u00f6ring laid down the priorities and the strategy for the Luftwaffe in January 1940, he made it clear that the aircraft industry and the RAF establishments were far and away the most important targets.\n\nBut there was the added danger that such precision required. The Luftwaffe would have to operate in daylight or when there was a full moon. Otherwise, said G\u00f6ring, many of the raids on aircraft factories would have to be undertaken by single aircraft or small groups of planes to ensure surprise.\n\nAlthough he would have to revise his thinking in the light of the harsh realities, in January 1940 Hermann G\u00f6ring characterized night raids as merely \"nuisance raids,\" which would be carried out only to keep the British on edge. As for the bombing of cities, he said, \"An endeavor will be made to avoid for the time being considerable casualties among the civilian population.\"\n\nOn 7 September 1940, when it seemed that success in the Battle of Britain was within reach, G\u00f6ring reversed this policy. It was the greatest strategic blunder of the many that the head of the Luftwaffe made. The bombers were redirected to the cities of Britain, particularly London, and when the Blitz ended in November, Germany had lost hundreds of planes and men and Hitler and G\u00f6ring's grand plan to conquer Britain was finished. But neither man was ever able to reconcile the fact that it was their strategy that was at fault and not the men charged with carrying it out.\n\nIndeed, when apprised that RAF fighters were appearing in ever-increasing numbers to shoot down his bombers, G\u00f6ring exulted, \"That's just what we want! If they come at us in droves, we can shoot them down in droves.\"\n\n\"In the face of such arguments no fruitful discussion was possible,\" wrote German historian Cajus Bekker. \"The Luftwaffe's supreme commander had lost touch, to a disturbing degree, with operational problems. He dwelt in a world of illusions.\"\n\n# CHAPTER THREE\n\n**WEAPONS FOR THE NEW AGE OF WARFARE**\n\nThe Race for Aerial Superiority\n\n**A merica, Germany, and Britain produced a remarkable array of** aircraft as they prepared for and fought World War II. In the race to win defense contracts and reap the immense sums allocated for building up air forces, competition was fierce and was not limited to the industrial sector. Politics, both civilian and military, played a role as well.\n\nAs in America, where there were ruthless interservice rivalries and each branch had its own sometimes peculiar demands for aircraft, so was it in Great Britain. The Germans had a somewhat different problem, in that the byzantine workings of Hitler's inner circle and the underlings who aspired to be part of it often led to procurement decisions that had little to do with offensive or defensive needs.\n\nWhether in democratic or totalitarian societies, technological breakthroughs ran up against an almost willful blindness by military leaders and politicians, who, in pursuit of their own agendas, could be oblivious to what was needed by the men who had to fly or defend against the fighters and bombers in combat.\n\nIn Great Britain the first bombers put into service, the twin-engine Wellingtons, Hampdens, Whitleys, Manchesters, and Blenheims\u2014which bore the brunt of the aerial offensive from 1939 until 1942\u2014were all deficient, often in many important ways. But each had its partisans, and crucial time was lost before it was clear that twin-engine aircraft, even in great numbers, would never be equal to the task set for Bomber Command: the obliteration of Germany.\n\nThe first of the four-engine heavy bombers to see action with the RAF was the Short Stirling. The initial order was delivered to the RAF in August 1940. The Handley Page Halifax followed in November of the same year. The Avro Lancaster lagged somewhat behind these first two heavy bombers. Production did not begin until early in 1942. But massive production of the heavy bombers would not really get under way until even later, when much of it was farmed out to countries in the commonwealth.\n\nIndeed, when Arthur Harris assumed command in late February 1942, the total operational night-bomber strength of Bomber Command was only 469 aircraft, of which just 53 were the new four-engine bombers. There were an additional 78 day bombers, all of them twin-engined.\n\nAmerican aircraft manufacturers were just as anxious to gain as large a piece of the armaments pie as their British and German counterparts, and they too trotted out various designs and prototypes that they promoted as the bombing platform that would guarantee U.S. superiority. By the time the American aircraft industry finally geared up, the country was on a war footing. There was little time to try many different aircraft and then pick the one that worked best, but a plethora of manufacturers, contractors, and subcontractors turned out dozens of mock-ups and prototypes of bombers, fighters, and transports.\n\nWhen the dust settled, however, just three twin-engine medium bombers, two four-engine heavy bombers, and three fighters carried the brunt of the American campaign in Europe. The largest bomber of all, the B-29 Superfortress, was not deployed until mid-1944 and only in the Far East.\n\nThe Douglas Boston medium bomber was first produced for the French air force, but with the fall of France in 1940 the planes were diverted to Britain, where they were instrumental in whatever early successes Bomber Command had.\n\nThe Martin B-26 Marauder was a versatile tactical bomber that was used with great success by America and the Allies. It became fully operational in the summer of 1941, and some 5,000 saw action during the war.\n\nThe best-known of the American twin-engine bombers was the North American B-25 Mitchell, which first flew in January 1939 and was in full production by February 1941. This plane, of which some 10,000 were built, gave the Allies a much-needed psychological lift on 18 April 1942 when General James H. Doolittle led a group of sixteen B-25s from the aircraft carrier _Hornet_ in the western Pacific and successfully raided Tokyo. The raid was little more than a calling card, but it served notice that the Japanese home islands were in striking distance of a determined enemy.\n\nArguably the best-known American heavy bomber of World War II was the Boeing B-17, the legendary Flying Fortress. Its predecessors were the 1931 twin-engine Boeing B-9, the first single-wing, all-metal bomber, and the 1933 Martin B-10.\n\nIt was clear soon after its introduction that the B-9 was more useful as a model for the nascent airline industry than for the air corps, and by 1934 Boeing was already at work on a successor. In July 1935, the XB-17, as it was called, was introduced at the Boeing plant in Seattle. The prototype flew on 28 July, and the following month the plane flew nonstop to Dayton, Ohio. A new era in aerial bombardment had clearly begun. The air corps ordered sixty-five of the new bombers. The euphoria was brief. In October, the XB-17 crashed on takeoff.\n\nThe cause was pilot error, but the accident served as ammunition for jittery congressmen who were not unlike their counterparts in Britain and Germany. Could you not, they asked, have many more twin-engine bombers for the same amount of money? The B-17 program was kept alive, but barely; the order was reduced to just thirteen planes.\n\nThe first operational B-17 was delivered to 2nd Wing, GHQ Air Force, in January 1937. The remaining twelve planes on order from Boeing trickled in over the next two and a half years, until the thirteen-plane order had been fulfilled. The 2nd Wing thus had the only operational squadron of four-engine heavy bombers\u2014which was the American bomber force\u2014in September 1939, when Hitler invaded Poland and World War II began.\n\nThe B-17 was the plane that the theorists had long called for. It so bristled with armaments that it surely justified its name, Flying Fortress. No attacking fighter force would be a match or be a danger. This bomber would always get through.\n\nThis unshakable faith in the plane's invincibility created a dangerous situation in the air force that would take years to rectify. The development of new fighter planes ceased to have any priority. They weren't needed by a self-defending bomber fleet, said the advocates of bombardment.\n\nThis universal blindness to the need for development of a powerful single-engine interceptor or escort is well illustrated by an October 1934 visit to a BMW plant in Germany by the vice president of Wright Aeronautics. The BMW director sent along the American's remarks to Ernst Udet, head of aircraft production for the Luftwaffe, who forwarded them to Erhard Milch, secretary of state for air.\n\n\"According to the American habit [he] spoke quite frankly and we thereby received very valuable information,\" said the BMW director. The single-seat fighter \"had played out its part.\" Only a twin-engine plane could ever hope to catch one of the new bombers, of which, he said, the best was the new Curtiss A-18, a twin-engine bomber with 850-horsepower engines.\n\nBecause the Allies had delayed the full-scale peacetime development of a long-range, heavy bomber force, the planes perforce had to be put into service before many of the operational problems were even recognized, much less corrected. Sometimes fatal design flaws thus came to light under the grueling and dangerous conditions of actual combat.\n\nThe first sale of heavy bombers to Great Britain comprised twenty of the new B-17Cs, and Bomber Command crews came to America to train in the planes at McChord Field, near Tacoma, Washington, in January 1941. This group of RAF Flying Fortresses began to be ferried across the Atlantic in April.\n\nAdditional training was necessary in Britain, but by summer all seemed ready for the new American bomber's combat debut. On 8 July 1941, three B-17s were dispatched to raid Wilhemshaven in daylight. Two of the planes successfully bombed the docks, and all three planes returned to their home base. It was a reasonably auspicious beginning but by no means a true test.\n\nHarris's withering assessment of the Americans and their equipment would prove to be on target. American Anglophobia and British smugness aside, the criticisms seemed justified. The subsequent performance of the U.S. plane was disappointing.\n\nIn fifty-one sorties, eight of the aircraft were lost either in combat or to accidents, and only 2,240 pounds of bombs could definitely be said to have fallen on the assigned targets. No enemy fighters were shot down. Harris ordered a halt in their use in operations on the Continent.\n\nWas this record the fault of the plane or the way in which it was deployed by the RAF? There were design problems to be sure, but the problems were exacerbated by Bomber Command policy. The B-17 was slow and was designed to operate in daylight, and the British were wedded to high-altitude nighttime operations. Since many of the planes were delivered with no heating system, the B-17s' guns froze, their windshields frosted over, and their engines did not operate efficiently. Worse, since the engines had no flare dampers, the exhaust flames could be seen for thirty miles, which made the planes an easy target for enemy interceptors and antiaircraft batteries.\n\nAnd the RAF never used more than four of the aircraft at a time, thus ensuring that there could be no proper bomb pattern. As far as the British pilots were concerned, Hermann G\u00f6ring's taunt that the B-17 was a \"flying coffin\" was all too accurate. The British B-17 operational difficulties might very well have been the result of not using the plane properly, but when the Americans arrived in force, they too had serious problems with the plane.\n\nOn one U.S. raid, when the thirty-eight B-17s were en route back to their home base in England they were suddenly attacked by German fighters. But only two of the Fortresses could return fire because the windows had frosted up. Fortunately for the helpless crews, the enemy interceptors were at the limit of their range and had to turn back.\n\nMost of the problems with the Flying Fortress were ironed out over time, and slowly the fleet was built up so that by the end of November 1944 there were over 1,300 operational B-17s with the Eighth Air Force.\n\nThe problems with another American plane, the B-24 Liberator, were more substantial and were the results of basic design flaws. This plane was designed to carry four tons of bombs\u2014one ton more than the B-17\u2014and was supposed to fly at greater speeds and higher altitudes.\n\nHowever, the plane's armament proved so deficient in combat that it immediately had to be increased. The added weight increased fuel consumption and lowered both the speed and the operational altitude. To compensate, the bomb load was reduced by a ton and half\u2014from 8,000 pounds to 5,000 pounds. And, of course, the range of the plane was also substantially reduced.\n\nThe B-24 had other problems as well, which gave it a reputation as a hard plane to fly and a poor bombing platform. The normal upward angle of the nose of the plane in flight was made even more pronounced once the speed was reduced. This change in the plane's attitude further reduced the visibility for the pilot, the navigator, and the bombardier, who sat in the nose turret. It took a crew of great skill to man the plane and overcome General Doolittle's complaint that 75 percent of mission failures were caused by poor navigation. Doolittle's low estimate of the plane's operational abilities could not be raised by increasing the crew's navigational skills, however.\n\nAs late as 25 January 1945, he wrote to Lieutenant General Barney M. Giles, chief of the air staff, \"It is my studied opinion that no minor modifications will make the B-24 a satisfactory airplane for this theater.\" This, after the plane had been in service for five years and undergone countless modifications. Giles replied on 10 February that the staff was about at \"the end of their rope\" as far as the B-24 was concerned. Arnold really blew his stack when he learned during an inspection trip that some five hundred modifications were then being done on the plane.\n\nHowever, one Liberator did prove to be particularly airworthy. The pilot and crew managed to bring the critically damaged plane back to England, but it was clear that they were not going to be able to land it safely. They headed the aircraft out to sea, set the autopilot, and then bailed out. But the plane turned around at the coast and for ten minutes flew around the airfield at Woodbridge until the tail fell off and the plane \"landed\" on the runway.\n\nAnd the sad honor of being the last American bomber on a combat mission to be shot down over Germany in World War II fell to a B-24. On 21 April 1945, the _Black Cat_ fell victim to antiaircraft fire at Regensburg.\n\nOfficial assessments of the B-24 were not much shared by the pilots who flew the plane, it seems, although their copilots were not so enthusiastic. Seventy-nine percent of the pilots who were surveyed felt that the B-24 was the best plane for the job. Only 58 percent of copilots agreed. Figures for the B-17 were much higher: 92 percent and 88 percent, respectively.\n\n**The bombing campaign** against Germany would never have achieved the success it did without the development of a long-range fighter that could escort the bombers all the way into the Reich and back. Otherwise, as Bomber Harris said repeatedly, daylight bombing was a \"busted flush.\"\n\nChief among these planes was the North American P-51 Mustang, the greatest fighter plane of World War II. Like virtually all new planes, the Mustang had a rocky beginning. (The de Havilland Mosquito was the single exception; it was a success from the start.) Originally built to British specifications, the P-51 made its first test flight in November 1940, an amazing one hundred days from the first design, and the initial British order began arriving in Great Britain just a year later, in November 1941.\n\nIt was immediately obvious to the British that the new plane, with its American-built Allison engines, was underpowered and was not effective at higher altitudes. It was thus used only as a low-altitude reconnaissance fighter. There was also another drawback. In a masterpiece of British understatement, one analyst said, \"The only criticism of the P-51 is the shedding of wings.\"\n\nThe structural problems were soon solved, but not until the British installed a Rolls-Royce Merlin engine and changed the propeller to a four-bladed airscrew did the Mustang begin to come into its own. Eventually, with more modifications, the P-51 could fly at 437 miles per hour and climb to 20,000 feet in seven minutes; it had a range of 2,300 miles.\n\nThe British improvements in the plane were immediately undertaken by North American Aviation during manufacture of new planes in the States, most notably the installation of a Packard-built Merlin engine, instead of the General Motors Allison. By the end of World War II, over 15,000 P-51 Mustangs had been built.\n\nTwo other major American fighters played an important role in the air campaign in northern Europe: the P-47 Thunderbolt, from Republic Aviation, and the Lockheed P-38 Lightning. Along with the P-51, these fighters also had the capability of flying deep into Germany, and after their introduction the air war took a dramatic turn.\n\nRepublic began work on the Thunderbolt a month before the first design for the Mustang. Unlike the short gestation of that plane, the prototype of the P-47 took somewhat longer. There were many design problems, and the plane did not fly until 6 May 1941. The first production model did not come off the assembly line until March 1942, but by 1944 more than 10,000 of the fighters had seen service.\n\nIt was the largest of the American single-engine fighters\u2014empty, the Thunderbolt weighed more than five tons\u2014but its great size was for many its primary asset. Many pilots who otherwise would have died in less rugged planes managed to bring a shot-up Thunderbolt back to England.\n\nSmall numbers of the planes began to arrive in Great Britain in November 1942, and twenty-three P-47s flew their first Eighth Air Force operation, a high-altitude sweep over Holland, on 8 April 1943.\n\nThe most glamorous of the three American fighters, both to the men who flew them and to little boys who built and collected model airplanes in the 1940s, was the Lockheed P-38 Lightning. It had two engines, twin tails, and a cockpit suspended in the middle; no aircraft of World War II was so instantly recognizable.\n\nWork began on the P-38 as early as 1936, when twin-engine aircraft were still considered the best alternative, but the first versions of the plane were dogged by design flaws and accidents. A prototype flew in January 1939, and all seemed well until, after a record-breaking coast-to-coast dash, the plane crashed on a golf course on Long Island. The pilot survived the crash, but it set back production by a good two years.\n\nHowever, many modifications and versions later, production began. In 1943 the P-38 was the first fighter to be ferried across the Atlantic to England, where it became one of the big three fighters with the Eighth Air Force. Later models of the P-38 had an operating range of 2,300 miles and could stay aloft for ten hours. They could also carry two 2,000-pound bombs. This was remarkable in a fighter, since it was not so much less than the bomb load of a B-17.\n\nBut the plane's high rate of engine failure\u2014many pilots blamed the low-grade British aircraft fuel, the British weather, or both\u2014put it at a decided disadvantage next to the more reliable Mustangs and Thunderbolts, which also could penetrate deep into Germany. But in spite of the problems with the plane, over 10,000 of them were built.\n\nIts speed and maneuverability made the P-38 a superb plane for photo reconnaissance and for Pathfinder duty, but its career in Europe was a brief one. It is last mentioned in the _Mighty Eighth War Diary_ on 15 October 1944. Two P-38s were in charge of control and operation of two explosive-laden, unmanned B-17s on a mission to Heligoland. Sixteen P-51s provided the escort cover.\n\nBy late 1944, the P-47 was also all but phased out for support on deep penetration raids. For example, all of the escort fighters that were dispatched to support the American raid on Dresden on 14 February 1945 were P-51s.\n\n**Harris and his American** counterparts notwithstanding, a twin-engine bomber was not a completely retrograde idea in the 1930s. Nor was the idea of using the same material that the Wright Brothers had used in their first plane as far-fetched as it first seemed. Indeed, one of the most successful warplanes ever built had two engines and was made almost entirely of wood. The legendary Mosquito\u2014the \"Mossie,\" the \"Wooden Wonder,\" or \"Freeman's Folly\"\u2014was first proposed in 1938, and a prototype appeared in 1939. Fifty were ordered, but the minister for aircraft production, Lord Beaverbrook, canceled the order. Only the perseverance of the plane's advocates\u2014in particular Air Chief Marshal Sir Wilfred Freeman; hence the less kind label attached to the plane\u2014kept the program alive. With the flight of the first Mosquito in November 1940, its backers' faith was borne out. Its great potential was immediately apparent. In November 1941 the plane became operational.\n\nWith its light wooden frame, two powerful Rolls-Royce Merlin engines, and no defensive armor to add to its weight, the Mosquito depended on speed and maneuverability for defense. With a crew of two, pilot and navigator-bombardier, the plane cruised at over 300 miles per hour and could reach maximum speeds of over 400 miles per hour with a 2,000-pound bomb load. It operated at a ceiling of 36,000 feet and had a range of 1,500 miles. It was not only the fastest piston-engine bomber in World War II, it was one of the fastest and most effective combat aircraft of any kind.\n\nThe Wooden Wonder went through various metamorphoses, including the installation of armaments on many models, which enabled it to be used in a multitude of ways by the RAF: bomb marker, night fighter, pure bomber, ground attacker, and photo reconnaissance plane. The bomb capacity eventually hit 4,000 pounds on some versions, but even then the plane had no trouble reaching Berlin and even beyond.\n\nThe Mosquito flew so many missions over the German capital that it is difficult, if not impossible, to document them all. Goebbels railed against it in entry after entry of his diaries. \"In the evening we again had the regulation Mosquito raids on Berlin,\" he wrote. \"The population of the capital is gradually becoming habituated to the necessity of spending one or two hours every evening in the air-raid shelters.\"\n\nIn addition to its spectacular record as a pure combat aircraft\u2014pilots of Mossies shot down 600 German aircraft and as many V-1 flying bombs\u2014the Mosquito was, of course, the mainstay of the Pathfinders and the bombing-marker groups.\n\n**As with the Eighth** Air Force B-17 Flying Fortress and the B-24 Liberator, two British heavy bombers were the workhorses of Bomber Command: the Avro Lancaster and the Handley Page Halifax.\n\nHarris's condemnation of the 1939 Manchester twin-engine bomber did not halt production of the aircraft, but when it entered service its failings were quickly apparent. The Rolls-Royce Vulture engines could not power it enough to climb rapidly, and the maximum ceiling was much less than expected.\n\nThe virtues of the basic design were recognized, however, and if the plane could be reconfigured to accept four Rolls-Royce Merlin engines, it might just be able to do the job. This was done, and by early 1942 the new bomber, rechristened the Lancaster, began to come off the production lines. With a crew of seven and a standard bomb load of 18,000 pounds, the Lancaster had a top speed of 275 miles per hour and a range of 3,000 miles.\n\nBy 1 March 1942, only four of the aircraft were on active duty, but their numbers would increase rapidly. By war's end Lancasters would account for 60 percent of the bombs dropped on Europe by Bomber Command\u2014everything from the small incendiaries to the 22,000-pound Earthquake.\n\nThe Handley Page Halifax also grew out of an aborted two-engine medium bomber, which was also to be equipped with the inadequate Rolls-Royce Vulture engines. The decision to replace the Vultures with Merlins was taken more quickly, however, and the prototype Halifax flew in October 1939. The first planes went to service with Bomber Command in March 1941.\n\nThe Halifax and the Lancaster were roughly equal in number of crew, speed, and basic flight range, but the Halifax's range was less than the Lancaster when carrying a full bomb load of 14,500 pounds.\n\n**G\u00f6ring's plans for** the expansion of the Luftwaffe were predicated on a war beginning no earlier than the mid-1940s, by which time, he felt, Germany would be invincible. Until that time expansion should come about through annexation, as in Austria, or through the threat of war, as in Czechoslovakia.\n\nBut even in his pursuit of offensive weapons for the German air force, the F\u00fchrer was equally blind to the possibilities. In 1934 development had begun of a four-engine aircraft purported to be for the civil airline, Lufthansa. This so-called airliner flew nonstop to New York in 1937, earning much publicity for the Reich and causing apprehension in London and Washington. The plane eventually metamorphosed into a heavy bomber, the Focke-Wulf Fw 200 Condor.\n\nTwo other four-engine bombers were also in development by the Nazis. Junkers was at work on the Ju 89, which was nicknamed the Ural Bomber since its chief function was to strike deep into the Soviet Union when the time came. Dornier was also developing a heavy bomber, the Do 19.\n\nIn 1937 the decision was made to abandon research on these promising four-engine aircraft and concentrate on producing two-engine planes, which could be manufactured more quickly and, of course, more cheaply.\n\nAlthough a four-engine bomber was officially proscribed, aircraft designer Willy Messerschmitt was never one to take no for an answer. He had continued to work on such a plane, and a prototype was flown in December 1942. The Me 264, christened by the optimists the Amerika Bomber and the New York Bomber, was designed to carry a bomb load to North America and return. The reality was somewhat different. It was soon clear that the bomber could do no such thing. Late in the war, it was even suggested that perhaps Me 264s could raid the East Coast cities of the United States and then ditch in the Atlantic, where the crews could be rescued by U-boats.\n\nThe lag time between prototype and production of aircraft was just too great, and thus it is unlikely that the Me 264 could have ever seen active service, particularly so in the light of the demands on the airplane industry at that stage of the war. Then too, as Armaments Minister Albert Speer said in his memoirs, explosives were in too short supply to make the heavy bombs for such a plane. Only three Me 264s were ever built.\n\nThe decision by Hitler and G\u00f6ring to concentrate on twin-engine bombers was not completely to the detriment of Junkers. Although it had to scrap its four-engine plane, the firm built more than 15,000 twin-engine Ju 88 bombers in various models and configurations, some of which, in versatility and usefulness, resembled the British twin-engine Mosquito. The Ju 88 was used as a bomber, a reconnaissance aircraft, and as a night fighter. In the latter role it was particularly deadly against the British bomber fleets\n\nHeinkel and Dornier were also the beneficiaries of the twin-engine bomber diktat. The Heinkel He 111, which first flew in 1936, was the chief Luftwaffe bomber during the Battle of Britain, and by war's end over 7,000 of the various models of this plane had been built.\n\nThe Dornier Do 217 series of twin-engine bombers also served somewhat successfully in many capacities\u2014bomber, night fighter, and reconnaissance\u2014and was a major component of the Luftwaffe during the Blitz. But like the other German twin-engine medium bombers, with their limited ceiling, short range, and slow speed, it too came to grief in the skies over Great Britain in 1940. The Heinkels, Dorniers, and Junkerses and their fighter escorts, which were operating at the outer limits of their range, were no match for the British fighters.\n\nG\u00f6ring's prot\u00e9g\u00e9 Udet was only too happy to comply with the twin-engine bomber directive. Udet had pulled off something of a coup when just a few months after Hitler became chancellor in 1933 he had gone to the United States and arranged to buy two Curtiss XP-17 Hawk aircraft and spirited them out of the country aboard a German merchant ship.\n\nIn December 1933, Udet put on a spectacular display of the diving capabilities of the Hawk, which was instrumental in the development of the Ju 87\u2014the famous _Sturzkampfflugzeug_ , an unwieldy German term for dive-bomber that would become familiar to the world in its abbreviated form, _Stuka_.\n\nUdet became blinded by the publicity surrounding the early but misleading successes of his brainchild and was so besotted with the Stuka concept that he was oblivious to the aircraft's shortcomings. For example, no version of the plane, and there were many, was ever to fly faster than 250 miles per hour.\n\nHe therefore saw no reason why all new planes could not be redesigned as dive-bombers, even the four-engine Heinkel He 177. Although it had the potential of being the German equivalent of any of the Allied heavy bombers, the He 177 was never put into active production and was eventually scrapped.\n\nUdet's obstinacy proved nearly fatal for the development of aircraft in Germany, which went to war with a plane that was already obsolete. Indeed, it had already been decided to halt production of the Ju 87 by the time Germany invaded Poland in 1939. However, G\u00f6ring knew that Germany was not armed for a long war, so every type of plane that had had any success was kept in service. Therefore, not only was the Ju 87 retained but its production was increased.\n\nGeneral Herhudt von Rohden, in a report after the war, stated what the planners were up against. \"We [Germany] were prepared for a short war and could not keep pace with the production of the Allies; consequently, there was on hand a too large number of obsolete aircraft, which were suitable only for the Russian front.\"\n\nAlthough G\u00f6ring initially supported a heavy bomber for the Luftwaffe, he quickly divined that Hitler opposed it, and as always, he deferred to the F\u00fchrer. As he said, Hitler was interested not in the size of the Luftwaffe bombers but in how many there were.\n\nJust as in America and Great Britain in the mid-1930s, the materials necessary for manufacturing four-engine bombers were diverted to turn out many more twin-engine planes. But the Allies were quick to see the advantage of a heavy bomber and reversed course.\n\nStill, G\u00f6ring never completely abandoned the idea of a heavy bomber, and somewhat quixotically thought that one might be in full production by the mid-1940s. But the decision made in 1937 meant that years of necessary research and development were lost.\n\nMeanwhile, a version of the Condor was developed for the Japanese, and a modified version of the plane was the one used in the campaign against the Allied convoys in the North Atlantic. But this bomber, the Fw 200C Condor, was an unstable aircraft, given to breaking up in the air or during the stress of landing, and only 278 were ever built.\n\nThe decision to halt research and development of a four-engine bomber came back to haunt Erhard Milch. In a surprisingly frank speech in 1943, the field marshal and secretary of state for air was openly critical of his fellow Nazis and obliquely praised the British effort.\n\nMilch, of course, had kept his mouth shut when it would have mattered. General von Rohden was especially critical of Milch and all those other colleagues who, he said, \"tried to assume as little responsibility as possible in order to be able to prove that they were not responsible personally.\" In the general's opinion, \"The unmaneuverable and unwieldy four-engine bomber was the decisive weapon of World War II.\"\n\nErhard Milch's belated outspokenness about the shortsightedness of the leadership cost him. He became increasingly isolated within the Nazi hierarchy, and by 1944 he had been forced to give up his posts in the government. Milch may have been marginalized but he was still a true believer in National Socialism. He was found guilty of war crimes at Nuremberg and served seven years in prison.\n\nUdet came to an earlier and equally ignominious end, although it was hidden from the public. G\u00f6ring's decision in 1940 to halt further research and development of new aircraft and to build only planes with a proven record in order to try to end the war quickly led Udet to brag, \"The war is over! To hell with all our aircraft projects\u2014they'll no longer be needed!\"\n\nThe Battle of Britain exposed the fallacy. Udet realized that the Luftwaffe was not going to save Germany and that his own decisions had contributed to the coming calamity. He began to be slowly stripped of his duties by G\u00f6ring and pushed aside. Seeing enemies on every side, on 17 November 1941 he wrote a note on his office wall, saying that he had been sacrificed by G\u00f6ring to the Jews in the Air Ministry, and committed suicide.\n\nUdet's suicide note presumably referred to Milch, who in spite of his rabid Nazism was himself half Jewish, and Lieutenant General Helmut Wilberg, who was also legally a Jew since his mother was Jewish. These two high-ranking generals were among the hundreds of thousands of so-called _Mischlinge_ , literally \"half-breeds,\" according to the Nazi racial laws.\n\nBut through influence, favoritism, or the whim of the F\u00fchrer, a successful applicant received a paper certifying that he was of German blood and could henceforth be so described in all official documents. Hitler took a keen interest in the issue and personally decided on all of the applications. Thousands of these _Mischlinge_ , ranging from privates and seamen to generals and admirals, were granted the _Deutschbl\u00fctigkeitserkl\u00e4rung_ , an official \"declaration of German blood.\"\n\nThe sycophancy and infighting that prevented the development of a heavy bomber were replicated in the procurement processes for a singleseat, single-engine fighter that could challenge the best of the British and American planes.\n\nHere, again, that poisonous mixture of politics, intrigue, and Darwinian struggle that characterized Hitler's court came into play. Loyalty to the F\u00fchrer and the Nazi Party permeated every aspect of German life and nowhere more so than in the military, where a major component of personnel evaluations was the adherence to National Socialist ideals.\n\nIn the early days of World War II, the Messerschmitt Me 109 had a great success, but when it went up against the British in the Battle of Britain its flaws became apparent. The plane's limited range, just a little over 400 miles, meant that it could stay over England for just a few minutes before having to head back to bases in France. Many Me 109s had to ditch in the Channel.\n\nSubsequent versions of the plane went through many alterations, but its range never exceeded 600 miles, and in no way was it ever the equivalent of the British or American single-engine fighters that escorted the Allied bomber fleets over the Continent.\n\nAlthough the Messerschmitt remained the fighter of choice\u2014more than 30,000 of the various models were built\u2014another fighter, the Focke-Wulfe Fw 190, had its partisans because of its greater speed. But even this plane had a limited range and under the best conditions could stay aloft only three hours from takeoff to landing.\n\nIn spite of their shortcomings, the German fighters were able to inflict massive damage on their bomber fleets until the long-range Allied support fighters began their deep penetration of the Reich in early 1944. It is still a matter of great speculation as to how the air war would have evolved if the Germans had early on pushed ahead with the development of a revolutionary aircraft, in a field in which they had a commanding, if not insurmountable, lead at the end of the war.\n\nWilly Messerschmitt had been working on a successor to the famous Me 109 and Me 110 for years, but the aircraft visionary had quite a different sort of fighter in mind to supersede those redoubtable aircraft.\n\nAn experimental jet plane flew as early as 1939, and if Hitler and G\u00f6ring had been more farsighted and Milch and Udet not so hesitant, jet fighters could have been flying in great numbers by 1942. The 540-mile-per-hour Me 262s would have eliminated the much slower Allied fighter escorts, and once the P-51s were out of the way the Allied bombers would have been easy prey for the more conventional Me 109s and Fw 190s.\n\nMesserschmitt was considered something of a serial liar by people who had to deal with him. No matter what he was asked, he always painted a rosy picture. Planes were on schedule. The planes could carry impossible bomb loads. Everything was in order.\n\nMesserschmitt may have had personality flaws, but he did know something about airplanes. The Me 262, the world's first operational jet, made its maiden flight on 18 April 1941. The first turbojet engines were problematical, but many of the obstacles were overcome by July 1942, when it looked as if the Luftwaffe would have a plane that was superior to any fighter in the world and could defend the homeland against any bomber attacks. There the matter rested.\n\nHitler was still obsessed with the idea of light bombers, and further development of the new fighter was scaled back. It was no longer a priority item. However, when the Me 262 was shown to him at a Potemkin-like display of aircraft at Insterburg on 26 November 1943\u2014the planes were still prototypes and nowhere near production\u2014the F\u00fchrer seemed to soften his views somewhat. But there was a catch. Hitler wanted the Me 262 to be redesigned as a high-speed bomber even though both he and G\u00f6ring were made well aware that no bombsight was suitable for the plane and that the maximum bomb load would be just two 250-kilogram bombs. There was still no rush to fully develop the plane.\n\nMesserschmitt may have been a liar, an optimist, and a dissembler, but he was correct in saying that turning the Me 262 into a dive-bomber would make it just another airplane\u2014one that would be ineffective in opposing the now daily onslaught of Allied fighters and bombers.\n\nIt was not until there was real fear that the Allies were themselves developing jet aircraft that Hitler began to come around, or so it seemed. In January 1944, a London newspaper reported considerable advances by the British in jet-propulsion technology. Hitler, who was kept apprised of reports in the foreign press and often reacted to them, reinstated full production of the advanced plane\u2014but, he decreed, as a bomber.\n\nThe Allies had learned of the German advances in the new technology in March 1944. Intercepted messages to Tokyo from the Japanese military attach\u00e9 in Berlin revealed that the Germans would have an operational jet-propelled aircraft in 1944 or early 1945.\n\nTwo months later, in May 1944, in a stormy session at Berchtesgaden, Hitler discovered that the Me 262 had not been redesigned as a highspeed bomber and was still classified as a fighter. He pressed for his original orders to be carried out, and G\u00f6ring complied.\n\nThe Luftwaffe thus had two versions of the plane, a single-seat fighter and a two-seat fighter-bomber. Several of the bomber version of the aircraft were available in August 1944, but they had little success in stopping the breakout from the Normandy beachhead. The single-seat fighters met with more success against the bomber fleets. But once again it was too little too late, although the possibilities of the Luftwaffe's new defensive weapon caused great apprehension among the Allied commanders.\n\nSources differ on how many jet aircraft Germany actually produced. The figure of 1,294 given by Cajus Bekker in _The Luftwaffe War Diaries_ seems a reasonable number. Most of these were built in March and April of 1945. However, not more than 300 jets ever saw combat, and never more than three or four at a time were sent against the thousands of bombers and fighters that now ranged at will over the Third Reich.\n\nAnd, of course, there was another problem, as serious as the tardy development and introduction of the Me 262: the severe shortage of trained pilots, without whom there could be no widespread deployment.\n\nThe German jets may have been few in number, but their actions served as a telling reminder of what might have been if Messerschmitt had been heeded two years before. In October 1944, according to Bekker, a jet _Gruppe_ shot down twenty-two Allied planes. It is easily imagined what the carnage would have been if the planes could have been flown in force instead of in the pitifully small numbers that were deployed, especially once the Me 262 was equipped in early 1945 with a new form of rocket that could be fitted beneath the wings. On 10 April 1945, Luftwaffe jet aircraft shot down ten American bombers over the Berlin area.\n\nMuch has been written about oil shortages and lack of fuel for airplanes in the waning days of the Third Reich. This did not present a great problem for the jet plane, which ran on low-grade fuels such as kerosene. However, the planes used such vast quantities that they could stay aloft for only a short time. The Me 262 used forty liters of jet fuel per minute to taxi to its takeoff position. To conserve fuel and allow the plane to extend its flight time, the Me 262 was often towed to its takeoff position by oxen.\n\nThe problem of unsupportable fuel consumption was also shared by another Messerschmitt aircraft, the single-seat, rocket-propelled Me 163. Its great speed and rate of climb enabled the pilot to reach operational altitudes in just two minutes, but it could stay airborne for a maximum of only ten minutes, which could be lengthened by the risky expedient of cutting the engine and gliding. This aircraft was, as a consequence, never a serious threat to the Allies.\n\n**Late in 1944** a delusory chapter in jet aircraft development in Germany began to unfold, around the Volksj\u00e4ger, or \"People's Fighter.\" The He 162 was designed to be built by semiskilled workers, using as few strategic materials as possible, which meant that the chief structural material in the plane was wood.\n\nIn the twelve-year Reich, probably no other decision was taken with such little regard to reality as the Volksj\u00e4ger. The director of the project, a rabid Nazi, fervently believed that the new plane could be flown by even teenage boys and could take off and land on any meadow or highway.\n\nIn the furtherance of this scheme, Hitler Youth were given a quick course in piloting gliders and then immediately set to learning to fly a jet plane. Predictably, the results were disastrous. The plane never saw action and only 116 of them were ever completed, even though thousands were in some stage of production when the war ended.\n\nThe Volksj\u00e4ger was not the only fantastic scheme concocted as the Third Reich crumbled. Several flying bombs were reequipped to carry a pilot who was to bail out after directing the bomb into an Allied bomber. Several volunteers were killed while testing the idea, and the plan was shelved.\n\nAnother bizarre plan was hatched by a fanatical woman aviator Hanna Reitsch. She suggested replicating in Germany the Japanese kamikazes, and in the desperate last month of the war pure suicide missions, under the code name Werewolf, were carried out. Some 130 pilots died crashing their planes into bridges and enemy bombers. In a tortured parody of a Wagnerian immolation, they went to their own fiery deaths accompanied by marches and the national anthem, all broadcast over the radio.\n\n**All war planes** had but one overriding purpose, which was destruction. They were designed to shoot down enemy aircraft; reduce enemy cities to rubble; destroy factories, refineries, and communications systems; and kill and demoralize the civilian population.\n\nThe Allied offensive was spectacularly successful in attaining all the goals except the last. Just as the German bombing of Britain, had, if anything, stiffened British will to resist, so did the bombing campaign have the same effect on the German civilian population.\n\nAlthough Goebbels himself fretted that the German people might succumb to the terror of aerial bombardment, German civilians showed no slackening of morale when the bombing campaign against them was escalated to staggering proportions. In spite of the psychological toll and the sleeplessness, the inhabitants of Berlin went about their business\u2014that is, those who were still in the capital. Many thousands of Berliners, like the citizens of all other sizable German cities, had long since been evacuated. But those who remained cheered the propaganda chief when he toured bombed-out cities. Large crowds, predominantly female, hailed him wherever he went.\n\nThe Germans were thus like their British counterparts, who did not succumb in the face of terror from the skies\u2014be it the bombers of the Blitz and the Baedeker raids or the V-1s and V-2s. British civilians cheered the prime minister and the royal family whenever they toured the bombed cities.\n\nAs Molly Painter-Downs reported in her \"Letter from London\" in the _New Yorker_ magazine, \"London has accepted its sirens with the usual exciting British display of complete impassiveness.... People have queued up for the public shelters as quietly as if waiting to see a motion picture.\" Indeed, the chief question seemed to be where the best place to seek shelter was, with Harrods being a clear favorite of shoppers because it provided comfortable chairs and first-aid workers. One of the chief complaints was that there was no smoking allowed in the air-raid shelters.\n\nThe situation was much the same in Berlin and the other cities of the Reich. People went about their daily business whatever the thinking of the military commanders of both sides, who continued to believe that carrying the war to the civilian populace was the way to victory.\n\nAnd just as commanders believe their armies are invincible, so did they believe in the invincibility of their people. The obvious paradox seemed never to be addressed: Why would one nationality succumb to terror bombing and not another?\n\nAt the Casablanca Conference in January 1943, the bombing strategy of the Allies was codified, and Trenchard and his disciples remained persuaded until the end that if the bombing of Germany was intensive and massive enough, it would have the desired effect. The Germans had failed in 1940 and 1941 only because they had not carried their campaign to the necessary extreme.\n\nCarl Spaatz was one of those who fully endorsed Trenchard's view that airpower could win the war, and on 8 May 1943, just before Churchill and Roosevelt met again in Washington at the Trident Conference, Spaatz wrote to Lyle G. Wilson, \"We have ample evidence to clearly indicate they [B-17s] can blast their way through any defenses and destroy the will to fight in any nation which may oppose us.\"\n\nAnd on 24 May 1943 he wrote to Arnold, \"In our day to day operations at the present time, we feel any area can be completely neutralized, even blown into oblivion, by high altitude attacks, without incurring any serious losses on our part.\"\n\nSpaatz went even further in November 1943. He told Harry Hopkins, who stopped over with Roosevelt in North Africa, where Spaatz was overseeing operations in the Mediterranean, that Operation Overlord, the planned invasion of Europe, was not going to be necessary. Beginning in April or May 1944, raids from both England and Italy would bring Germany to its knees in three months. If Spaatz was correct, the war would end in August or September 1944, and no Allied troops would be needed in northern Europe except as an occupying army.\n\nRound-the-clock bombing had already begun, in February 1943, but it was a modest effort compared to the vast air fleets that would be launched against the Third Reich by the Allies later in the war. Nevertheless the effect for the first year and a half was not anywhere near what the air planners had hoped, and there were disturbing portents.\n\nAt the Octagon Conference in Quebec in September 1944, the Combined Intelligence Committee reported that the German people still strongly supported the war effort and this was unlikely to change unless there was a \"military debacle.\" As for a surrender by Hitler and his government, the intelligence experts said flatly that neither the present government nor any Nazi successor was likely to surrender.\n\nThe commanders in the field held the key to the end of the Reich, said the intelligence experts. Once they saw the hopelessness of their situation they would begin to surrender, albeit in piecemeal fashion.\n\n**At the end of 1944** , the United States had 2,970 heavy bombers with the Eighth Air Force in the United Kingdom and another 1,512 with the Fifteenth in the Mediterranean area. Of these, 2,980 were operational, and each aircraft had two crews and thus could be used every day.\n\nSpaatz, the commander designate of the United States Strategic Air Forces in Europe, would formally assume his new post on 1 January 1944. He would soon learn that conditions over northern Europe and the Reich, in particular, were much different from the relatively undefended sunny skies of the Mediterranean. The lessons of the previous three months were there for anyone who cared to learn and profit from them. But orthodoxy was still the order of the day.\n\nOn 17 August 1943, it became clear that bombers in daylight raids, no matter how strongly self-defended, were extremely vulnerable to the German fighter squadrons. Two Eighth Air Force missions that day, in the morning to Regensburg and in the afternoon to Schweinfurt, were among the costliest of the war.\n\nOf the 376 B-17s dispatched on the two raids, 345 were effective, that is, reached the targeted cities. The bombers were escorted, but only in the first stage of the mission, by 240 P-47s. In August 1943, the P-47 Thunderbolt, even with an extra 108-gallon gas tank underneath the belly, had a maximum escort range of only about 375 miles. The \"little friends\" thus had to turn back near the German-Belgian border. After that the bombers were on their own.\n\nAs soon as their escorts peeled off and headed back to England, the B-17s immediately came under attack by swarms of waiting German fighters. There was also intense antiaircraft fire from the ground. Before the day ended there was a trail of wrecked American Flying Fortresses extending from the Low Countries, across Germany, and south to the Mediterranean. The terminus for the Regensburg raid was North Africa, where the Allies had several air bases.\n\nSixty planes were lost and 168 damaged. No air force could sustain such losses, but the catastrophe that was the Schweinfurt-Regensburg raid was not immediately evident\u2014certainly not to the true believers. The next day General Harold L. George sent a euphoric \"Secret: Eyes Only\" message to Arnold.\n\nToday I saw air power used in manner which if continued will without slightest doubt accomplish collapse of Nazi economic structure by Christmas. With this statement Harris agrees. Today's operation must have struck shattering blow at the very foundation of Nazi morale for Nazi air force as well as those in high command. Saw it demonstrated that American bombardment aviation can penetrate in daylight to very vitals of Germany against most powerful air defenses in the world, fighting its way against concentrated enemy pursuit for two hours and then perform superb precision bombing. That this is kind of lesson Nazi command can understand. They cannot help but realize the hopelessness of their resistance.\n\nWhile losses were heavy the history of war cannot show where equal expenditure of efforts were so productive in depriving an enemy of those things he needs to continue the fight. Preliminary reports indicate that Messerschmitt plant at Regensburg completely destroyed. Damage at Schweinfurt uncertain due to heavy smoke over area which precluded definite photo reconnaissance but destruction appears to be extensive....\n\nMy reason for sending this message is because I realize some folks without knowledge of the facts might think the price paid for such air operations is too great. If they understand these facts then this day's operations will go down in history as a glorious achievement of American air power....\n\nWith double the bomber force the losses today would have been no greater but percentage would have been so reduced that continuous operations would be assured. Vital objective now is unquestionably the destruction of Nazi fighter force. With this accomplished the rest of the job is in the bag.\n\nGeneral George, who had helped draft AWPD-1, was clearly still in the grip of air force orthodoxy, but his almost giddy message to Hap Arnold could not and did not disguise the catastrophe. The Schweinfurt-Regensburg losses could not be ignored by even the most zealous advocates of the self-defending bomber fleet. The Eighth shifted its attention to close-by targets in western Europe, well within fighter-escort range of bases in England. American bombers did not return to Germany until 6 September. Again, the raid\u2014Stuttgart and various targets of opportunity\u2014was a disaster. Of the 338 planes, only 262 were counted effective. Of these, 45 were lost and another 116 damaged. Casualties\u2014killed, wounded, or missing in action\u2014totaled 362.\n\nDuring the rest of the month the only large raids in Germany were attacks on the port cities of Emden and Bremen. But these targets were relatively near, and the bombers had fighter escort out and back. During this time, small numbers of B-17s flew night missions with the RAF, with little success. Otherwise the Eighth restricted its activity to France and the Low Countries.\n\nFinally, on 10 October 1943, the Eighth returned in force to Germany. Out of 313 bombers dispatched to M\u00fcnster, only 236 were effective. Again, the losses were horrendous\u201430 planes down and 102 damaged. One bomber group, the 100th, lost 12 out of 14 bombers.\n\nThere was worse to come. Just four days later, on 14 October, a bomber force of 320 B-17s and 29 B-24s returned to Schweinfurt. The B-24s were part of a force of 60 planes, but the others were unable to rendezvous because of bad weather. Even those that had successfully formed up failed to join the bomber stream because of the weather. Instead, they flew a diversionary mission to Emden. They were fortunate.\n\nThe carnage of this second Schweinfurt raid caused a major reassessment. Another 60 bombers were lost out of the 229 effectives, a staggering 26 percent. The casualties totaled 639, most of them killed.\n\nThe Schweinfurt raids were a perfect example of orthodoxy triumphing over common sense. The primary targets were the factories manufacturing ball bearings, without which, it was reasoned, the Germans would not be able to produce aircraft, rolling stock, or almost anything else that moved. This line of reasoning, a variation on the theme \"For want of a nail...,\" can be traced back to at least one prewar incident related by H. S. Hansell.\n\n\"We discovered one day,\" said Hansell, \"that we were taking delivery on new airplanes, flying them to their points of reception, removing the propellers back to the factories and ferrying out additional airplanes. The delivery of controllable pitch propellers had fallen down. Inquiries showed that the propeller manufacturer was not behind schedule. Actually, it was a relatively simple, but highly specialized spring that was lacking, and we found that all the springs made for all the controllable pitch propellers of that variety in the U.S. came from one plant and that that plant in Pittsburgh had suffered from a flood.\"\n\nAs historian Steven A. Parker observed, \"This observation led Hansell and the other planners to conclude that the loss of one specialized item, such as the spring, could have a tremendous effect on industrial output in time of war and could ground airplanes just as effectively as if enemy forces had shot them up or if enemy bombs had destroyed the factories.\"\n\nGeorge was right that Arthur Harris agreed that Germany could be destroyed by Christmas 1943 through massive bombing. Harris made such projections himself. But he disagreed vehemently with the Americans as to whether daylight raids were the proper method.\n\nAs for the Schweinfurt raids, his view was that such raids were futile\u2014the Germans had plenty of ball bearings in reserve until they could repair the plants or disperse them elsewhere\u2014and the Americans seemed to agree, judging by their subsequent actions. There were no more deep penetrations into German airspace by American bombers until early 1944.\n\nAlthough the myth of the self-defending bomber force had exploded over the skies of Germany along with dozens of American bombers, myths die hard. Spaatz himself did not begin to cast aside orthodoxy until he assumed, or reassumed, command in Great Britain, where he soon realized that fighter escorts were the key to success.\n\nUnlike Ira Eaker, the unfortunate interim commander who had run the air war from Great Britain while Spaatz was in the Mediterranean, Spaatz was able to call on vast numbers of the new long-range fighters. Within a month of his taking command of the Eighth Air Force, hundreds of bombers and their fighter escorts began to reappear over Germany almost daily. The command of the air would never again be in doubt.\n\n# CHAPTER FOUR\n\n**THE FATAL ESCALATION**\n\nAir War Against Civilians\n\n**I n turbulent times a few outsized figures arise and often become** the personification of the national will. Sometimes these individuals are not just responding to the turbulence but are the authors of it\u2014Adolf Hitler is a resonant example.\n\nOther twentieth-century figures who for good or ill became the embodiment of their nations were Franklin Roosevelt in the United States, Joseph Stalin in the Soviet Union, Mao Tse-tung in China, Mahatma Gandhi in India, and Charles de Gaulle in France. Great social or political movements were set in motion by these men and became inseparable from them\u2014the New Deal, Stalinism, Maoism, nonviolence in the pursuit of independence, and Gaullism.\n\nThe argument is endless over whether the times make the man or the other way around, but Winston Churchill's life and career does provide much fodder for those who share his view that men make the times\u2014no matter that most of his actions were reactions to events set in motion by a counterpart across the Channel in Germany.\n\nIndeed, Adolf Hitler is a compelling argument that men do make the times. The founder of the Nazi Party, Hitler was a charismatic figure who became the very embodiment of his nation. He was the face, voice, and driving force of the Third Reich. Without the F\u00fchrer, that dismal period in German history could not have come about.\n\nChurchill was able, through oratory and an almost mystical belief in his mission, to rally the British people in the darkest period of his country's long history. Not so incidentally, he was busily fashioning his own myth as well.\n\nAfter the fall of France in June 1940, England was alone and dangerously vulnerable to Adolf Hitler's threatened cross-Channel invasion. The F\u00fchrer's Operation Sea Lion called for creating a corridor between two massive minefields backed up by U-boats and protected by airpower. Hundreds of thousands of German soldiers would then traverse this corridor in barges and ships to invade the British Isles.\n\nChurchill, much after the fact, in his memoirs, maintained that no such scheme could ever have succeeded. Germany, he said, never had the resources, particularly the ships and crews, for such an operation. More important, according to the prime minister, who never missed an opportunity to stress the singularity of the English people, the Germans never understood what he called \"the sea affair.\"\n\nSaid Churchill, \"For centuries, it has been in our blood, and its traditions stir not only our sailors but the whole race. It was this above all things which enabled us to regard the menace of invasion with a steady gaze.\"\n\nChurchill's postwar retrospective somewhat downplayed the greatest danger to England since the Spanish Armada in 1588. In 1940, an invasion seemed real enough, particularly to the Royal Navy and the RAF, which bore first responsibility for turning back or destroying a Nazi onslaught. Churchill himself fretted a great deal about it to his aides and the War Cabinet. His secretary John Colville recorded in his diary on 21 September: \"The PM seems rather more apprehensive than I had realized about the possibility of invasion in the immediate future and he keeps ringing up the Admiralty and asking about the weather in the Channel.\"\n\nThe next day, 22 September, General Frederick Pile, head of the Antiaircraft Command, was at Chequers, the prime minister's country residence, for lunch. Churchill told the general that he had a \"hot tip\" that the invasion was to be at three o'clock that afternoon. \"However, I stayed to tea,\" said the general, \"and no invasion took place.\"\n\nThe \"hot tip\" had come from the Americans, who had intercepted a message relaying the information that the Japanese were to invade French Indo-China on 22 September at 1500 hours. Somewhere between the translation of the original message and its retransmission from Roosevelt to Churchill, England had been substituted for the French colony in Southeast Asia.\n\nOn 15 October, Churchill's comments to the War Cabinet showed how anxious he had been all along about the invasion threat: \"Should October pass without invasion, which cannot yet be assumed, we should begin the reinforcement of the Middle East.\"\n\nPublicly, however, the prime minister was sanguine. He never faltered, whether delivering a radio address, responding to questions in Parliament, or meeting with a head of state. And no one dwelt much on the successful cross-Channel invasions in English history\u2014the early Saxons, the Vikings, the Roman legions, and, of course, the Normans under William the Conqueror in 1066.\n\nA more recent invasion had been unopposed, that of William of Orange and his army in 1688. Churchill's great ancestor John Churchill was commander of the defending forces and was thus at least supposed to be nominally loyal to his king and patron, James II. Instead he went over to the side of the usurper William. He was rewarded with the earldom of Marlborough.\n\nBut Britain was now to be tested as never before. It was clear to the admirals and generals that an invasion could be successful only if the RAF failed to beat back an attempt by the Luftwaffe to destroy the British air force and thereby establish German air superiority over England and the Channel. Hitler and his generals knew that Sea Lion depended completely on invincible air cover. Thus began the greatest air battle in history, the Battle of Britain.\n\n**The Luftwaffe offensive** divided into three discrete but overlapping phases. In mid-July 1940, massive bombing of naval convoys in the Channel and the southern port cities began. A month later the Luftwaffe began to concentrate on the destruction of British airfields, supply depots, and aircraft factories. The last, desperate phase, the indiscriminate bombing of British cities, particularly London, was initiated in early September.\n\nAt the beginning of hostilities, Franklin Roosevelt had asked all sides to desist from bombing undefended towns and cities and the civilian populace. The moratorium was observed for several reasons, not all of them moral. Great Britain was particularly happy to comply since Bomber Command did not want to send its relatively few bombers against the German fighter defenses.\n\nEveryone, of course, knew that the restriction on the bombing of cities could not hold forever. Air raids on civilians by all the belligerents were inevitable. In that event, said G\u00f6ring, much of the German fighter fleet would eventually have to be used to protect the homeland. To that end, the Reichsmarschall disclosed plans to construct coastal defenses as far as Biarritz, near the Spanish border. This formidable defensive perimeter would require vast numbers of fighter planes and men.\n\nBomber Command introduced a small cloud in G\u00f6ring's rosy picture on the first day of the war. Britain declared war at 1100 hours on 3 September 1939, and by early afternoon a Blenheim reconnaissance bomber appeared over the German coast. This was more bluff than substance, of course. Britain was in no position as yet to do much more. Nevertheless, it was a portent of the future.\n\nG\u00f6ring estimated that it would take three days for his Luftwaffe to destroy the RAF fighter defenses. After that, the German bombers would be able to roam at will over the British Isles. His enthusiasm for the air campaign was based on some truths. The Luftwaffe pilots were better trained, and many of them had become seasoned in the Spanish Civil War, the invasion of Poland, and the campaigns in the Low Countries and France.\n\nHowever, G\u00f6ring made a mistake that no military commander ever should but many often do. He underestimated the strength and determination of his opponent. The British had, contrary to the accepted view, rough parity in numbers of first-line fighter planes. Only about 700 Me 109s were available for the Battle of Britain, and the Germans had no long-range single-engine fighter. Worse, replacement planes only trickled to the front. In the four months of the campaign, just 775 Me 109s were produced. The British produced twice as many fighters in the same period so they could fill the gaps in the first line.\n\nMore important, the British pilots, in their Supermarine Spitfires and Hawker Hurricanes, proved more than a match for the Germans and their Messerschmitts. As one Luftwaffe fighter pilot said, \"The Spitfires showed themselves wonderfully manoeuvrable. Their aerobatics display\u2014looping and rolling, opening fire in a climbing roll\u2014filled us with amazement.\"\n\nThen, too, the British had the advantage of operating close to their own bases. They could land, refuel, and rejoin the battle in a very short time. London was at the outer limit of the range of the Me 109, and the German fighter pilots, no matter how the battle was going, had no choice but to head back to France when their fuel ran low.\n\nAnother surprise for Reichsmarschall G\u00f6ring was the discovery that the British were far ahead in the development of an early-warning system called RDF, radio direction finding, which would become better known as radar. The device was so classified that not even the Americans were told of it.\n\nThe Germans had a form of radar, but they were by no means as far along in deployment as the British, who by late 1938 had in place along the Channel coast facing Europe a chain of early-warning stations. The Germans had exactly two radar installations in the summer of 1940\u2014 one in the Ruhr and a portable one on the French coast to track enemy convoys.\n\nThere was also another top secret enterprise of inestimable importance in the Battle of Britain and, indeed, for the entire Allied war effort. At Bletchley Park, the headquarters of the British intelligence codebreaking operation called Ultra, cryptographers had succeeded in cracking the German Enigma code. Even with the key to the German ciphers, it was still no quick and easy job to decrypt messages; it was with some pride that veterans of the effort told of delivering decoded messages to headquarters in times as brief as two and a half hours after they were intercepted.\n\nThis was still a considerable delay, considering the proximity of the Luftwaffe airfields in France, but it was possible to anticipate and act on any plans involving missions only a few hours in the future. These developments\u2014early warning and decryption\u2014were important elements in the RAF triumph in the Battle of Britain, but Churchill, as was his wont, credited a less quantifiable element for the success of his countrymen. The British pilots, said Churchill, \"had supreme confidence in themselves as individuals and that determination which the British race displays in fullest measure when in supreme adversity.\"\n\nAnother factor that bedeviled both the Allies and the Germans\u2014one that is frequently mentioned but never emphasized enough\u2014was the weather. The weather in northern Europe\u2014English weather, in particular\u2014was and is extremely variable and difficult to forecast with any degree of accuracy. Aircraft formations were easily dispersed in the dense cloud cover or fog that swept in without warning, targets were hard to find, and the bomber groups were often fatally separated from their fighter escorts.\n\nAn unresolved source of contention concerning the weather was the understandable reluctance of the U.S. and Royal navies to provide hourly weather reports from the convoy escorts in the Atlantic. Such information would have been of immeasurable help to the forecasters, but it would have also given away the position of the ships to the roaming U-boat wolf packs.\n\nWhatever the reasons for the final British victory\u2014men, machines, meteorology, or mistakes by the enemy\u2014it was very nearly a British defeat. The Germans came perilously close to realizing their goal of destroying British airpower. The RAF fighter pilots might have had the edge over their Luftwaffe counterparts, but attrition took its toll. Although reserves were dangerously thin, the planes could be replaced; the men to fly them could not. Between 24 August and 6 September, 103 pilots were killed and another 128 severely wounded. Twenty-five percent of the British fighters had been destroyed as well.\n\nLuftwaffe losses in men and planes were even more staggering. However, by early September 1940, German air force pilots began to report a decline in the intensity of the British fighter defense. The success of G\u00f6ring's strategy to control the skies over Great Britain seemed to be in the offing, but then Adolf Hitler ordered a sudden and disastrous reallocation of Luftwaffe resources.\n\nAs he had already shown, the F\u00fchrer had no qualms about bombing the citizens of any city if it suited his purposes. London, however, was still marked as a prohibited area on all Luftwaffe charts at the beginning of the Battle of Britain.\n\nBut two incidents had already occurred, the repercussions of which hastened the change in tactics. On 15 August, Luftwaffe pilots mistook the civil airport at Croydon for their assigned targets, the RAF stations at Kenley and Biggin Hill. Croydon, less than ten miles from central London, was well within the forbidden zone decreed by Hitler, and an enraged G\u00f6ring ordered that the pilots who committed the blunder be court-martialed. The order was never carried out, since none of the offenders made it home from the raid. They were either dead or prisoners of war.\n\nA more serious incident occurred on the night of 24\u201325 August. The assigned targets were the aircraft factories at Rochester and oil storage tanks on the Thames. But a navigational error led two pilots astray, and they dropped their bombs directly on London.\n\nThe day after the London raid, the Reichsmarschall, who was following the air war not from the front lines or Luftwaffe headquarters but from his vast estate, Carinhall, fired off another angry message to the Luftwaffe airfields. He reserved \"to himself personal punishment of the commanders concerned by mustering them to the infantry,\" he said. G\u00f6ring's responses back up the German arguments that the first bombings of London and Croydon were the result of pilot error.\n\nA month before, Churchill had written to Archibald Sinclair, secretary of state for air, \"In case there is a raid on the centre of Government in London, it seems very important to be able to return the compliment the next day upon Berlin.\" Sinclair assured the prime minister that by 1 September the RAF could mount such a raid.\n\nThe morning after those few bombs fell on London, Churchill called on Sinclair to keep his promise. That night, 25\u201326 August, about fifty Hampdens and Wellingtons bombed Berlin. The raid was more symbolic than destructive. Visibility was limited, and only a few bombs fell within the city limits. A summerhouse was destroyed and two people injured in a Berlin suburb, but most of the bombs fell well outside the city on farmland, which prompted the Berliners to joke, \"Now they are trying to starve us out.\"\n\nNo German commander disputed that London was to become a target eventually. As their campaign proceeded, the city would have to be bombed as a way of forcing the remaining planes in Fighter Command to take to the air to defend the capital. The British, the argument went, would throw everything into the fight to save London.\n\nChurchill was passionately attached to London, but he was more passionately attached to democracy and destroying totalitarianism. Cities can be reconstructed; the destruction of democracy creates less tractable problems. Unlike P\u00e9tain, who saw the destruction of Paris as a desecration, Churchill would have sacrificed London without hesitation in order to fight on against the Nazis.\n\nNo doubt to the dismay of at least some of the members, he told the House of Commons during the Blitz that \"the law of diminishing returns operates in the case of the demolition of large cities. Soon many of the bombs would only fall upon houses already ruined and only make the rubble jump.\"\n\nIn September 1940 Churchill was concerned chiefly with the protection and continued operation of RAF Fighter Command and its airfields. \"Far more important to us than the protection of London from terror bombing,\" he said after the war, \"was the functioning and articulation of these airfields and the squadrons working from them.... We never thought of the struggle in terms of the defence of London or any other place, but only who won in the air.\"\n\nThe Luftwaffe raids, accidental or not, and the British retaliatory raid quickly changed the thinking on both sides. Escalation of the air war had come. The British returned to Berlin on 28\u201329 August and again on 31 August\u20131 September.\n\nOn 3 September, G\u00f6ring left the safety of Carinhall and traveled to The Hague to meet with his top air commanders. They were informed that henceforth the Luftwaffe was to concentrate on London instead of continuing the attacks on the RAF airfields, aircraft factories, and shipping. The strategy recommended itself for two reasons. First of all, German bombers over the British capital would bring up the rest of the RAF fighters, which would easily be destroyed by the Luftwaffe. Second\u2014for some this was even more important\u2014such raids would pay back the British for the raids on Berlin.\n\nThat night (3\u20134 September) and the next (4\u20135 September), Bomber Command again raided Berlin. On the night of 5\u20136 September, the Luftwaffe responded. Sixty-eight bombers dropped 60 tons of bombs on the London docks. The Blitz had begun.\n\nTwo days later G\u00f6ring watched from the French coast as the first massive fleet of German aircraft headed for London. Over 1,200 planes attacked the city in the late afternoon and evening. The armada was almost evenly divided between fighters and bombers, many of which carried a new 3,600-pound bomb.\n\nChurchill was correct that the Blitz was not just an act of inhumanity. It was also an enormous strategic blunder, a view borne out by German accounts as well. Fighter Command was reeling from its losses, and the Luftwaffe's diversion to bombing London was, said Churchill, \"a breathing space of which we had the utmost need.\" The German attacks had damaged not only the airfields and planes; the communications and organizational structure had also suffered extensively. A few more such raids and Fighter Command might have collapsed completely.\n\n\"G\u00f6ring should certainly have persevered,\" said Churchill. \"By departing from the classical principles of war, as well as from the hitherto accepted dictates of humanity, he made a foolish mistake.\"\n\nG\u00f6ring would later blame everyone but himself for the disintegrating air war in the west. In the meantime, it was clearly necessary to shift completely to night bombing, and for fifty-seven consecutive nights as many as 200 German bombers a night raided London. The damage was enormous, but, as Churchill put it, \"London was like some huge prehistoric animal, capable of enduring terrible injuries, mangled and bleeding from many wounds, and yet preserving its life and movement.\"\n\nStill, Churchill wondered after the war what the reaction of Londoners would have been if they had been subjected to the heavy bombers and high explosives that were available to the Allies after 1943\u2014 weaponry \"which might have pulverised all human organisation.\" No one, he said, \"has a right to say that London, which was certainly unconquered, was not also unconquerable.\"\n\nFighter Command rose to the battle with stunning success. Evading or ignoring the roving German fighters, the RAF attacked the bombers directly. On a memorable day\u201415 September 1940, celebrated as Battle of Britain Day\u2014the Luftwaffe lost 56 planes, 34 of them bombers. Other planes were so damaged that many had to be scrapped. Such losses, some 25 percent of the entire bomber force, were insupportable.\n\nThe British capital held out, and finally, on the night of 3 November, Londoners had their first night of unbroken sleep in two months. No sirens sounded and no bombs fell. The Battle of Britain was over. The Germans had lost 1,389 aircraft and the British 790. The defeat forced Hitler to do more than just postpone Operation Sea Lion; henceforth, it played no part in German strategic planning.\n\nBesides, Hitler's attention was now fully focused on a plan that had long been gestating: Operation Barbarossa, the invasion and subjugation of the Soviet Union. Afterward, said Hitler, he would revisit the Western Front.\n\nThe bombing continued, of course\u2014England could not be allowed to rebuild and expand its armed forces and plan a return to the Continent unchallenged\u2014but it became more diffuse. The raids also served to distract attention from the buildup in the east. However, there was yet another change in Luftwaffe strategy by G\u00f6ring. Henceforth the chief targets were to be the industrial towns and cities of Great Britain.\n\nThe new policy was announced with an attack that decisively turned the British public toward thoughts of total war and retribution. The Coventry raid, on the night of 14\u201315 November 1940, provided the British with a propaganda windfall.\n\nMany so-called historical truths begin life in a propaganda ministry or a press department, and in World War II not a few of these involved the air war. Two well-known and much-discussed \"facts\" have thus come to dominate any discussion of Coventry. The first is that the city was leveled and thousands of people were killed, with additional thousands injured. The second is that Churchill and the British high command knew well in advance that the city was targeted but declined to warn the populace so as not to reveal to the Germans that British intelligence had broken their top secret codes.\n\nThe first point is easily corrected, but even there the correctors are often at odds. All agree, however, that the death toll was wildly exaggerated for propaganda purposes. The most reasonable and probably most accurate figures are from the weekly r\u00e9sum\u00e9 of military activity given to the War Cabinet and the prime minister the week of the raid which states that some 380 people were killed and 800 injured. In London that same week, deaths totaled 484 and injuries 1,080.\n\nThe physical destruction in Coventry was indeed horrific, but it was limited to the city center. The important Coventry factories, the ostensible reason for the raid, were located out of the main blast areas and were back in business in fairly short order, as were transportation and essential services.\n\nThe area of devastation\u2014some one hundred acres\u2014was, however, of historical and architectural importance and included the fourteenth-century St. Michael's Cathedral, only the 295-foot spire of which survived. Photographs of the burned-out church and the visit by King George VI were sent around the world. Coventry became a symbol of Nazi barbarity, alongside another notorious raid earlier that year, the bombing of Rotterdam on 14 May 1940.\n\nWhile certainly horrible, the Rotterdam raid was nowhere near the tragedy trumpeted by Allied propaganda. Some 800 people died, not the 25,000 or 30,000 alleged to have been killed by the German bombers. But the Allies skillfully exploited the raid to firmly fix the Nazis in the world's mind as a nation of barbarians who wantonly bombed the peaceful and civilized Netherlands, the land of tulips and silver skates.\n\nThe rumors of a conspiracy to conceal the fact that the British had broken the German code are less easy to refute. Conspiracy theories take on a life of their own and are generally impervious to refutation, no matter how strong the evidence to the contrary. They will always have their adherents. However, this much seems clear: the British did know by 11 November 1940, via the Ultra decryptions, that an operation called Moonlight Sonata, in which one of four possible targets was to be attacked, would take place at the next full moon\u2014around the fifteenth of the month.\n\nDuring the afternoon of 14 November, British radio operators began to pick up powerful concentrated radio beams from the Continent. These were the signals from the German system called _X-Ger\u00e4t_ , or X-Device, which was used by the Luftwaffe to triangulate a target. One beam, the direction beam, was the main flight path. As long as there was a buzzing sound in the pilot's earphones, his plane was on course. Dots and dashes signaled if he veered to port or starboard.\n\nThe pilot maintained his course while the aircraft's radio operator listened for a second signal, which crossed the aircraft's path and indicated that it was thirty miles from the target area. A timer was then set that ran until a third signal indicated that the bomber was nine miles from the target. The timer was reset, and the release of the bombs was automatic when it registered zero.\n\nChurchill attended Neville Chamberlain's funeral at Westminster Abbey at noon on Friday, 14 November, then returned to the Annexe, his quarters in the Board of Trade Building, where he had moved on 16 September after a particularly heavy raid had damaged 10 Downing Street. He and his wife lived at the Annexe until the war ended.\n\nDownstairs from their living quarters were the famous War Rooms, where most of the decisions pertaining to the war were made and seen through. This warren of rooms was deep belowground, and the prime minister was carried down the stairs and back up in a chair by three Royal Marines.\n\nAt the Annexe on this afternoon, he prepared to leave for a weekend at Ditchley Park, an estate northwest of Oxford, which had been placed at his disposal. Ditchley was much more secure than the official country residence, Chequers, which was just thirty miles from London and well known to the Germans.\n\nChequers was especially vulnerable during the full moon, when the long drive, which somewhat resembled an arrow pointed directly at the house, was easily seen from the air. And this weekend there was to be a full moon.\n\nAs he stepped into his car, Churchill was handed a message. His secretary recalled that the car had reached Kensington Gardens when the prime minister ordered the driver to turn around and return to the Annexe. According to the message, the German radio beams converged over London, and Churchill refused to travel to the country if there was to be a raid on the capital.\n\nBy 1500 hours it was clear that the beams converged instead over Coventry. The RAF was alerted, and antiaircraft batteries were readied and fighter planes put on alert. However, no warning was passed to the civil authorities. But there was a good reason for this.\n\nThe British had developed a system, called Cold Water, designed to jam or divert the _X-Ger\u00e4t_ transmissions and cause the German planes to drop their bombs well outside any populated areas.\n\nThe first German bombers cleared the Channel coast just after 1800 hours, and the RAF unit assigned the electronic countermeasures went into action. Unfortunately, Cold Water failed. Coventry was attacked an hour later. The 449 bombers dropped 500 tons of high explosives and 30 tons of incendiaries on the city center.\n\nSince the final determination that Coventry was the target came through conventional radio signal intercepts, there was no risk in issuing a warning. Ultra would not have been compromised. But myths die hard, especially when conspiracy theories have arisen.\n\nAdding to the controversy was the dismal fact that even though the RAF dispatched 200 fighter planes and there was an antiaircraft barrage, only one German bomber was shot down. Questions were asked in Parliament, and there were demands for retribution.\n\nIf there was a bright side to the Coventry raid, it was that the German air force did not follow up with another raid while the city was reeling from the disaster. In this the Germans were not unlike their British and American counterparts. The Germans had bombed London night after night, but the aim there was to bring up the defenders so that the Luftwaffe could destroy the fighter screen and then bomb with impunity and make way for an invasion.\n\nNeither side seemed to grasp the importance of the double or even the triple blow from the air, which, theoretically at least, could prevent a city from recovering for many months, if ever. Neither side seemed to grasp how important this was until late in the game. Two important factors must be considered, however, before one blames either the Allies or the Germans for lack of imagination or planning. While the Allies had more resources available to them in terms of planes and weaponry, the lack of trained air crews often did not allow a follow-up raid. And both sides were subject to the whims of the weather. There were seldom consecutive clear nights over England or the Continent.\n\nChurchill and his War Cabinet ordered Bomber Command to bomb the center of a German city in retaliation for the Coventry raid. Mannheim was the chosen target, but the raid had to await the next full moon. Finally, on the night of 16\u201317 December 1940, the largest raid of the war up to that time\u2014and perhaps the first instance of pure morale bombing\u2014was launched.\n\nThe \"fire raisers,\" the precursors of the Pathfinders, whose job it was to set fires to mark the target, missed the center of the city, and therefore most of the damage was in residential areas. Thus from a military point of view the raid was a failure. But it marked a turning point in the thinking of many in the British high command. Morale bombing was elevated to strategy. If pursued relentlessly, senior officers argued, it could bring Germany to its knees without a single Allied soldier ever setting foot on the Continent.\n\nLater, in defense of the British area bombing of cities, as opposed to the American bombing of precise targets, one document stated, \"While the success of [the Americans'] attacks against the aircraft and ball-bearing industries must have undermined the confidence of the German High Command, the civilian population was little affected. Only the RAF bomber command component of the offensive could have been expected to evoke any considerable reaction from the civilian population.\"\n\nFor this to happen, area bombing had to be employed, although the drafters of the report continued to maintain that \"the object of the RAF attacks was the destruction of industrial areas. For this purpose the incendiary bombs pay far higher dividend.\"\n\nFurther, they said, \"The risk of death from incendiary attacks is comparatively small, save in exceptional cases, such as Hamburg, when enormous conflagrations are set up. In the majority of our attacks the concentrations achieved were not such as to produce those conditions.\"\n\nThe incendiary bomb was a small, rather insignificant-looking device\u2014most of those dropped on Dresden weighed just four pounds\u2014that fire wardens advised they could be extinguished with nothing more than a bucket of sand if an individual reacted quickly. And there were incidences where they were picked up and tossed out a window before they ignited. Such actions were rare in actuality, since incendiaries were dropped by the hundreds of thousands.\n\nIn the early bombs, phosphorus was used, but as the war progressed other materials were soon found to be more effective and lethal. Thermite, a mixture of aluminum powder and iron oxide, set alight with a magnesium fuse, could generate temperatures well over twelve hundred degrees Fahrenheit. Such high temperatures coupled with the vast quantities of the weapons dropped on an urban area ensured that firefighters and rescue workers would be overwhelmed.\n\nAfter Coventry and until the invasion of the Soviet Union, the Luftwaffe repeatedly bombed Manchester, Plymouth, Southampton, and Liverpool-Birkenhead. And London was revisited several times as well. The raid on 29 December 1940 was particularly damaging. Churchill called it \"an incendiary classic.\"\n\nThe Luftwaffe first dropped high explosives to sever the water mains, followed by incendiaries, which set more than fifteen hundred fires. This was the raid that destroyed eight Wren churches and the Guildhall and almost incinerated St. Paul's Cathedral. It was also a powerful demonstration of the proper bombing of highly flammable old cities, a lesson duly noted by Arthur Harris and other advocates of area bombing.\n\nAs the winter wore on, the Luftwaffe raids decreased in size and ferocity. There were fewer sorties and a dramatic decrease in the bomb tonnage. However, with the coming of better weather in March and April 1941, there was an upsurge. On 16\u201317 April and 19\u201320 April, London was hit by the heaviest raids in the long Luftwaffe campaign against the city, which doubtless gave the advocates of morale bombing renewed vigor.\n\nThe majority opinion that Bomber Command's resources would be better spent bombing the German synthetic oil plants still held, but the seeds for massive area bombing had been planted. In any event, the oil campaign was thwarted in early 1941. Clear weather and a full moon were the necessary elements for the night raids on these difficult-to-find targets, and the weather was particularly foul in February and March 1941. Fog, wind, rain, and snow, not enemy action, caused the loss of seventy RAF planes in one thirty-day period.\n\nBy early March, however, the target priorities had been changed. The German navy threatened to succeed where the Luftwaffe had failed. Between June 1940 and March 1941, U-boats, battle cruisers, and pocket battleships, aided by Focke-Wulf Condor long-range maritime bombers, sank almost 900 merchant ships carrying supplies for the relief of England. From then until the middle of the summer, Bomber Command was ordered to concentrate on the U-boat bases and shipyards, the factories that made submarine components, and the Condor airfields.\n\nThere was much carping within Bomber Command about this change of targets, but Sir Charles Portal, chief of the air staff, saw it as an opportunity. He was fully aware that Bomber Command's claims of success in bombing the oil targets were greatly exaggerated. He was only too happy to divert the planes to these easier-to-find and thus more vulnerable targets. He made no effort to have the order reversed.\n\nThe 9 March 1941 directive ordering Bomber Command to concentrate on the U-boat menace had a qualifier: \"Priority of selection should be given to those [targets] in Germany which lie in congested areas where the greatest moral [sic] effect is likely to result.\" On 18 March, Arthur Harris, then deputy chief of the air staff, referring to Mannheim and Stuttgart, said, \"Both are suitable as area objectives and their attack should have high morale value.\"\n\nAny talk about the relative merits or morality of area bombing versus precision bombing was just that in the early years of Bomber Command\u2014talk. At most there were only nine nights a month\u2014the time of the full moon\u2014when there was any chance of what was called accurate bombing. And even then the weather had to cooperate. Rivers, coastlines, and other prominent geographical features were useful reference points\u2014when they could be seen. The port cities of Germany, the Netherlands, and France and the industrial cities on the Rhine, the Weser, and the Elbe were therefore bombed consistently.\n\nA method resembling the German system of triangulation of radio beams was being worked out by British scientists but would not become available to Bomber Command until 1942. The major method of navigation remained dead reckoning, that combination of compass course, air speed, and wind velocity and drift which, theoretically, gave the navigator his position. The system was so dependent upon factors that were little more than guesswork, however, that a pilot was fortunate if he was over the right city; it was folly to hope to hit a small target within that city. Until the introduction of advanced navigational aids in 1943, nighttime precision bombing was only a strategic concept. Therefore, \" 'area bombing' against German cities with a view to breaking German civilian morale was the most useful means of employing the bomber force.\"\n\nA fairly simple pattern thus developed. A part of the bomber force was directed at a major industrial or port facility in the target city. Other planes were directed to bomb the city itself, in order to cause maximum disruption among the civilian population. It was area bombing, not precision bombing, although the target was \"nominally industrial.\"\n\nThe optimistic predictions of victory through aerial bombardment of Germany and the occupied countries came back to haunt Bomber Command in August 1941 when D. M. Butt, of the War Cabinet secretariat, issued his report on bombing accuracy. Just one-third of the pilots who had said they had successfully attacked the assigned target had come within five miles of it, said Butt. Two-thirds were within five miles of targets on the more visible and closer French coast, but in the industrial and smoggy Ruhr the figure fell to one-tenth. On the nights of a bomber's moon, the optimum condition, only two-fifths of the bombers dropped their loads within five miles of the target, and on moonless nights the figure fell to one-fifteenth.\n\nWhen two-thirds of the bomber force dropped their bombs five miles or more from the designated targets, the obvious question was how many bombs were actually hitting a worthwhile target. And the person who was asking and answering this question was Winston Churchill himself. Did not this report give the lie to his 1940 prediction that British bombers would bring Germany to its knees?\n\nChurchill's disillusionment was not long in manifesting itself. In response to Portal's plan to \"Coventryize\" forty-five German cities, the prime minister said, \"It is very debatable whether bombing by itself will be a decisive factor in the present war.\" He cited the British people, who, he said, had been \"stimulated and strengthened\" by the German raids. \"The most we can say,\" Churchill acerbically remarked, \"is that [bombing] will be a heavy and I trust seriously increasing annoyance.\"\n\nPortal did not let this go unanswered, and as RAF historian Denis Richards said, he \"spiked Churchill's guns.\" Who was to carry the war to Germany if not Bomber Command? Portal forthrightly asked the prime minister. Portal admitted that ground forces would eventually have to be used, but it would be 1943 before any such offensive was possible on the Continent. In the meantime, he said, \"The only plan is to persevere.\" In other words, Bomber Command must continue the attacks on German manufacturing and morale. Otherwise there would be no Allied offensive operation in western Europe until an invasion could be launched across the Channel. Churchill acquiesced.\n\nAs for the success of the RAF campaign against the submarine pens, those in Holland were active until February 1945. The ones in France also went relatively unscathed until late in the war. As Admiral Karl D\u00f6nitz said, \"No dog nor cat is left in these towns. Nothing but the submarine shelters remain.\"\n\nPortal's contretemps with Churchill resulted in a reprieve for Bomber Command and its head, Air Marshal Sir Richard Peirse, who had succeeded to the post when Portal had been promoted to chief of the air staff. Bomber Command was allowed to resume its attacks on Germany and the occupied countries. The reprieve was a brief one and ended the night of 7\u20138 November 1941, when 37 planes, out of 392 dispatched, were lost\u20149.4 percent, which was double the loss rate of any previous night operation.\n\nThe raids included Berlin, Cologne, Mannheim, and a few minor targets, but it was the operation against Berlin that caused a storm of criticism. Out of 169 aircraft sent to the German capital, only 148 returned \u2014a staggering loss of 12.4 percent. There were no losses over Cologne, but there was also little damage\u2014even less damage than in Berlin, where it was negligible. Mannheim reported no damage at all. Bomber Command would not return to Berlin in force until January 1943.\n\nThe day after the debacle at Berlin, Sir Richard Peirse was driven down to Chequers to meet with an angry prime minister. A week later, Churchill ordered a reduction in Bomber Command operations until new and more effective policies could be developed.\n\nThe first order of business was the removal of Peirse himself, which was accomplished on 8 January 1942. There was also to be a new bombing policy\u2014the direct response to the Butt Report, which had been so critical of the so-called precision bombing.\n\n\"It has been decided,\" wrote Air Vice Marshal Norman Bottomley, \"that the primary objective of your operations should now be focussed on the morale of the enemy civil population and in particular of the industrial workers.\" The date of this area bombing, or morale bombing, directive was prophetic: 14 February.\n\nFinally, on 22 February 1942, the third and arguably the most important component was put in place. Air Chief Marshal Sir Arthur Harris assumed his new post: commander in chief, Bomber Command.\n\nOfficially, Harris did not have a hand in drafting the morale-bombing directive. He was en route home from Washington when the directive was issued. But he wholeheartedly endorsed it and proceeded at once to implement it, although he chose his words carefully when describing what Bomber Command policy actually was. \"Area bombing\" became the preferred formulation.\n\nDuring the three months while Bomber Command was effectively \"standing down\" on the Continent, the British were being battered elsewhere. General Erwin Rommel and his Afrika Korps successfully counterattacked in North Africa, Singapore was lost, and HMS _Prince of Wales_ and HMS _Repulse_ were sunk by the Japanese. However, Hitler had already committed the great follies that would bring him and the Third Reich to total destruction. He had drawn both Russia and America into the war on the side of England.\n\nOn the night of 28\u201329 March 1942, Arthur Harris put the new policy into effect and Bomber Command had its first great success of the war. More than 200 bombers attacked L\u00fcbeck. Although the city was famous worldwide for its picturesque architecture and as the setting for Thomas Mann's novel _Buddenbrooks_ , it was, and is, the most important German port on the Baltic. But Harris was not primarily interested in destroying the docks and piers.\n\nThe medieval Altstadt was the target. \"L\u00fcbeck,\" said Harris, \"was more like a fire-lighter than a human habitation,\" and with this raid he spectacularly demonstrated his theory of \"concentrated incendiarism.\" As historian Max Hastings wrote, \"L\u00fcbeck, then, did not attract the attention of the bombers because it was important, but became important because it could be bombed.\"\n\nThe German high command was stunned by the ferocity of the attack. More than a quarter of the medieval heart of the city went up in flames. And Goebbels was quick to bemoan the loss of the great artistic monuments to the \"British craze for destruction.\"\n\n**While the debate** over morale bombing versus precision bombing continued among the Allied commanders, there was no debate among the enemy about a policy that was being implemented with increasing ferocity. At five o'clock in the afternoon before the L\u00fcbeck raid, Special Train 767 left the Paris suburb of Drancy, where the Germans, aided by French collaborators, had begun to intern Jews in 1941. Aboard were 1,113 foreign-born Jews, mostly Poles. The train arrived at the concentration-camp complex near the Polish town of Oswiecim in Galicia three days later, after a stopover at the concentration camp at Compi\u00e8gne.\n\nThis camp complex, better known by its German name, Auschwitz, would in time become the very symbol of Nazi depravity. Construction at Auschwitz was authorized by Heinrich Himmler in April 1940, and the first, experimental gassings took place in September 1941.\n\nBy early 1942, more than 700,000 Jews had already been murdered as the Nazis moved eastward. Word of these atrocities, particularly in Poland and the Soviet Union, had long since reached the West, but there was no acknowledgment by either London or Washington of the crimes being committed.\n\nNow, as the gas chambers at Auschwitz became fully operational, the Nazis were prepared for murder on a truly industrial scale. The men, women, and children on this first French deportation train were among the early victims.\n\n**For the citizens** of the cities of both sides, the air war gained in intensity in 1942. Hitler ordered \"terror attacks of a retaliatory nature\" against Britain for the L\u00fcbeck raid. Beginning on the night of 23 April, the Luftwaffe responded with a series of raids on the British equivalents of L\u00fcbeck: Bath, Exeter, Norwich, Canterbury, and York. These were the notorious \"Baedeker raids.\" The term was coined by Baron Braun von Stumm in the press department of the German Foreign Ministry. For compiling a list of Britain's historic cities, what better source was there than the authoritative and complete Baedeker guide to Great Britain?\n\nGoebbels was quick to see that the term was causing revulsion in the world. \"I censured this in the sharpest terms and took measures for preventing the repetition of such folly,\" he recorded in his diary. Only the unfortunate choice of words used to denote the operation upset him. He heartily approved of the raids themselves. \"There is talk about scenes like those in Coventry,\" he said. \"That's the sort of music we like to hear.\"\n\nThe RAF, meanwhile, did not hold back from destroying another historic German city, although Rostock was also an important Baltic port and home to the Heinkel aircraft factory. On four consecutive nights in late April, a total of 520 bombers attacked Rostock, destroying 60 percent of the city center. A new term began to appear in the German reports of the Rostock raids\u2014 _Terrorangriff_ (\"terror raid\")\u2014and clearly terror bombing was a tool to be used as any other weapon would be to carry the fight to the enemy.\n\nNew names began to be added to the growing list of wrecked cities in England and Germany, bombed-out symbols of the new warfare conducted by both the Luftwaffe and the RAF. Rotterdam, Coventry, and the Baedeker raids are the most often cited atrocities against non-combatants by the Luftwaffe, but another, much more horrifying example is little known or remarked on. On 6 April 1941 the German air force killed some 17,000 civilians in a raid on the Yugoslav capital of Belgrade.\n\nAs for the British, there seemed no strategic justification for the bombing of L\u00fcbeck\u2014the target was the center of the medieval and highly incendiary Altstadt, after all\u2014but it did serve to demonstrate the effectiveness of the fire-raising strategy. Indeed, for the rest of the war, L\u00fcbeck suffered no further concentrated attacks by the RAF. The International Red Cross persuaded Britain to spare the city so the port could be used for the shipment of Red Cross supplies.\n\nThe fire raids on the two old Hanseatic League cities of Rostock and L\u00fcbeck were more than just revenge for the depredations of the Luftwaffe, of course. Harris needed to demonstrate to Churchill and the air command that his bombers could do what he said they could do: take the war to the enemy and cause massive destruction, with minimum, or at least acceptable, losses.\n\nAfter the L\u00fcbeck raid there was a considerable bump in the road. Harris had come in for severe criticism for a low-level, daylight raid on Augsburg on 17 April, which, while partially successful in bombing, resulted in a loss of seven out of twelve Lancasters. Rostock partially redeemed the error. But Harris was more than thin-skinned; he often seemed to have no skin at all. He brooked no criticism, not even from Churchill. His correspondence with the prime minister is peppered with defensive, self-serving comments.\n\nIn a memorandum of 2 May 1942, he dismissed the suggestion of his chief critic, the minister of economic warfare, that the target should have been Stuttgart and not Augsburg as \"Plain Suicide\" and \"just silly.\" As for the implied criticism that Bomber Command did not cooperate with other departments, he said he would do so if possible. However, he added, \"I could not in any circumstances agree to discuss projected attacks outside my Headquarters with other Departments. I do not even tell my crews, to whom security is a matter of life and death, where they are going until the last moment before briefing.\"\n\nFor the next full moon, Harris put into effect a plan that was to profoundly alter the future of aerial bombardment. On the night of 30\u201331 May 1942, he dispatched 1,047 Wellingtons, Stirlings, Halifaxes, Whitleys, Manchesters, and Hampdens\u2014every plane that he could beg, borrow, or steal\u2014on the first thousand-bomber raid. The target was the Rhineland city of Cologne.\n\nNot all the planes reached the target; only 868 did. But two-thirds of the 1,455 tons of bombs dropped were incendiaries, and their effect was devastating. Thousands of buildings were destroyed, 45,000 people were bombed out of their homes, and at least a third of the population fled the city.\n\nAlbert Speer was visiting G\u00f6ring at Schloss Veldenstein on the day after the raid and listened while the Reichsmarschall talked by telephone with Joseph Groh\u00e9, gauleiter of Cologne. G\u00f6ring adamantly refused to believe that so many planes could be put in the air and so many tons of bombs dropped in one raid. He ordered the gauleiter to revise his reports to the F\u00fchrer to reflect lower figures.\n\nA few days later at the Wolfsschanze (Wolf's Lair), Hitler's headquarters near Rastenburg, in East Prussia, Speer discussed the incident with the F\u00fchrer. Hitler had already discounted G\u00f6ring's estimates and chose to rely instead on his own reports, which were based largely on accounts in the foreign press, no doubt provided by Goebbels. G\u00f6ring suffered no diminution in status, however, much to the chagrin of Speer and the disgust of Goebbels, who despised him. G\u00f6ring, he said, \"has as much to do with the [Nazi] Party as a cow with radiology.\"\n\nThe propaganda minister stayed remarkably well informed about what was happening in the field and in the world's capitals. His interpretations of the intelligence that he received and conclusions that he reached were quite something else. His diaries are filled with keen insights that are immediately rendered worthless when they are refracted through his ideological lens.\n\nFor example, he and Churchill were as one in their fear and certainty of Stalin's designs on eastern Europe. The Nazis, after all, had used the issue of Communist expansion and domination in their rise to power. Goebbels, however, saw Communism purely as part of a Bolshevik-Jewish conspiracy to take over the world.\n\nGoebbels was sometimes fairly clear-eyed about the prospects for the war. As early as 8 May 1943, he confided in his diary, \"The end is in sight in Africa.... In the end the Axis is to be thrown out of Africa entirely. There is tremendous confidence of victory in London, and rightly so. I see hardly any chance for us.\" The following day he described the debacle in North Africa as a \"sort of second Stalingrad.\"\n\nBut Goebbels was also one of the first practitioners, some would say the inventor, of what in years to come would be called \"spin.\" His justification of the African adventure is a masterpiece of the genre. While the struggle went on in the deserts of North Africa, he said, there could be no invasion of Europe proper. Therefore the defenses in western Europe, the so-called Atlantic Wall, could be constructed relatively unimpeded.\n\nGoebbels's ability to rally the German people through propaganda was tested further in the disastrous month of July 1943. The deposition and arrest of Mussolini and the ascension of Marshal Pietro Badoglio\u2014precursors to the end of Fascism in Italy and that country's surrender\u2014was called \"the greatest example of perfidy in modern history\" by the propaganda minister. His remarks rather oddly echoed Franklin Roosevelt's more famous indictment of Italy in 1940 when Mussolini declared war on France: \"On this tenth day of June 1940, the hand that held the dagger has struck it into the back of its neighbor.\"\n\nGoebbels's ruminations on Italian treachery were interrupted by news that was beginning to come in concerning a disturbing new Allied air offensive. The RAF and the U.S. Eighth Air Force had launched the Battle of Hamburg, a series of raids on Germany's major seaport and one of the Reich's most important industrial centers. Bomber Command led off on the night of 24\u201325 July 1943. A force of 728 aircraft out of 791 dispatched dropped 2,284 tons of bombs in fifty minutes. The bombs fell over a wide area, some six miles long, but caused considerable damage and 1,500 deaths.\n\nThe Americans followed up in daylight raids on Sunday, 25 July, and Monday, 26 July. Dense smoke from the fires caused by the massive British bombardment, combined with cloud cover, made visual targeting nearly impossible. Indeed, only 100 of the 182 U.S. B-17s dropped their bombs, just 195 tons, on the city. The next day the Americans fared even worse. Only 54 bombers out of 121 dispatched were effective, dropping 126 tons of bombs. As the historians Middlebrook and Everitt said in their _Bomber Command War Diaries_ , \"The Americans quickly withdrew from the Battle of Hamburg and were not keen to follow immediately on the heels of R.A.F. raids, in future, because of the smoke problem.\"\n\nOn the night of 27\u201328 July 1943, however, the British returned. Seven hundred and twenty-nine bombers dropped 2,326 tons of bombs on the city center in a relatively concentrated pattern. The city was still reeling from three raids in seventy-two hours, and its rescue and fire-fighting services were overwhelmed. Temperature and humidity were also in perfect alignment to create a cataclysm.\n\nAs the fires that raged throughout the city spread and joined together, air from outside the fire zones was sucked in, creating hurricane-force winds, which further fed the flames. The air war's first recorded firestorm was born. Contrary to popular belief, the Hamburg firestorm was not the result of advance planning. It was the result of powerful and unexpected forces, which in the future seldom came together in such a way that it was replicated, although it became a much desired goal of Bomber Command.\n\nIndeed, there were only a handful of true firestorms created during the long Allied bombardment of Germany. But the lessons learned from these incendiary attacks on Germany would prove valuable later in the American bombing campaign against Japan. In the most devastating air raid of the war using conventional weapons, the raid on Tokyo on 9 March 1945, between 90,000 and 100,000 people were killed and half the city was destroyed.\n\nBut that lay far into the future. For now, Germany was the primary target, and the night after the firestorm, Bomber Command raided Hamburg again. Another 729 aircraft dropped an additional 2,326 tons of bombs on the crippled city. A severe thunderstorm prevented a third raid, comprising 740 bombers, from reaching Hamburg on the night of 2\u20133 August. No matter. Much of the city lay in ruins, and two-thirds of the population, some 1.2 million people, had fled to other cities, towns, or the countryside.\n\nMost of Germany's cities now began to witness firsthand the destructive might of Allied airpower. The British by night and the Americans by day. No city was safe from the destruction and death raining from the skies.\n\nNot all successful raids involved massive fleets of bombers. Nor were they all recognized as a great success. On the night of 18\u201319 November 1943, ten Mosquitoes attacked Essen in a raid characterized as a \"minor operation\" by Middlebrook and Everitt. _The Goebbels Diaries_ , however, reports a different result. The propaganda minister lamented that the Krupp steel works was 100 percent closed down by the Mosquito raid.\n\nWhile it may not have been the most strategically important of the German cities\u2014in terms of weapons plants, military bases, or oil refineries\u2014the destruction of Berlin carried incalculable psychological weight. Therefore, a devastating series of sixteen raids by Bomber Command began on the night of 18\u201319 November 1943 and continued for two and a half months. The second raid, on 22\u201323 November, caused more damage than any other raid in Bomber Command's long campaign against the German capital. Cloud cover kept the Luftwaffe on the ground, setting off a renewed round of criticism of G\u00f6ring and his pilots.\n\nThe poor visibility also meant that the raid was pure blind bombing. But the bombs found the target, falling in a swath some twelve miles wide across the city. Among the destroyed buildings was the Kaiser Wilhelm Church, the blackened ruins of which would become a stark reminder in postwar Berlin of the carnage of war. The ruins were incorporated into a new war memorial church in 1959.\n\nGoebbels admitted, but only in the private confines of his diary, the destructive effect of the Allied bombing. Time and again he lamented the inability of the Luftwaffe to stop the Allied planes, which were destroying one city after another. And while the bombing was nowhere near as precise as advertised by the Allies, it did succeed in bringing the war home to the enemy and causing great disruption.\n\nOf the more than a million residents who fled Hamburg, most filtered back into the city during the next months and tried to resume their lives. The Reich, however, had to divert staggering amounts of supplies, thousands of men, and great effort to protect, house, and feed the beleaguered civilian populace. The effort was a tremendous drain on the German war effort. In Berlin alone, after the great raid of 22\u201323 November, two and a half divisions, 50,000 Wehrmacht troops, were called in to clear the streets and restore services.\n\nIn spite of the destruction and the horror of the raids, Goebbels averred that Germany and the Germans remained unbowed. A diary entry of 25 November 1943 is a fair example of the Nazi mind-set. \"Of what avail are all sorrow and pain? They won't change conditions. This war must be seen through. It is better that our workers crawl into cellars than that they be sent to Siberia as slave labor. Every decent German realizes this.\"\n\nAnd, in spite of the carnage from the skies, Germany did manage to rally, through the use of a seemingly inexhaustible source of labor. Slaves from the east, prisoners of war, political prisoners, and, of course, hundreds of thousands of Jews from the concentration camps worked around the clock in the factories, mines, and refineries, and in rebuilding the wrecked highways, railroads, and buildings. Historian Daniel Goldhagen has estimated that there were at least 10,000 concentration camps and ghettos in Germany and the occupied territories. In Berlin alone there were no fewer than 645 forced-labor camps.\n\nWith such a huge labor force available, it is little wonder that in Hamburg, five months after the raids, industry had recovered 80 percent of its preraid capacity. But no nation could constantly rebuild itself from within, produce arms and armaments for a vast army, and fight a two-front war. The bombing campaign would ensure the ultimate collapse of the Third Reich.\n\nGoebbels and others in the Nazi hierarchy, in spite of some pessimism and barely concealed anger at G\u00f6ring and his inability to fight back against the British and American bombers, still looked for a miracle in the form of new weaponry, which would not only stem the tide but bring them victory.\n\nSpeer was not so sanguine. He doubted that either new weapons or reprisals against Britain would provide the key to victory. In any event, no such weapon could possibly be deployed until March 1944, at the earliest. Thus the Germans could only watch helplessly as their leaders led them further down the road to ruin and the deaths of hundreds of thousands of civilians in the air war, which would increase in ferocity, not lessen, as the Allies closed in on the Third Reich.\n\n# CHAPTER FIVE\n\n**_VERGELTUNGSWAFFEN_**\n\nThe V-Weapons\n\n**L ess than a week had passed since the successful landings in** Normandy when there came a sobering reminder that the final collapse of the Third Reich might not be as close as it had seemed. But the feared Nazi counterattack came not against the Allied forces moving inland from the beaches of France; it was directed against the civilian population in England.\n\nOn the night of 12\u201313 June 1944, thousands of people from the Channel coast to London were roused from sleep by a high-pitched, pulsating sound from the sky\u2014a strange noise that would become all too familiar in the months ahead. A new weapon, a pilotless \"flying bomb,\" had made its debut.\n\nThe official German designation was FZG-76. The Allied military called it the V-1. Civilians, however, ignored both designations. To them the new terror weapon was simply the \"buzz bomb\" or \"doodlebug\"\u2014a twenty-five-foot-long unmanned aircraft with a wingspan of seventeen and a half feet that carried an 1,870-pound explosive warhead and was powered by a pulse-jet engine that gave it a distinctive sound.\n\nThe V-1 was an ingenious device, not only cheap to build\u2014it was made of low-carbon steel and wood\u2014but also easily transported and launched, and its preset course ensured that the weapon was secure against electronic countermeasures such as jamming or interference.\n\nA small propeller in the missile's nose was set to rotate a certain number of times, each revolution representing a fraction of the distance from the launch site to the target. When the proper number of revolutions was reached a signal cut off the pulse-jet engine and the flying bomb dropped like a stone.\n\nIt was calculated that some 80 percent of the V-1s would land within a target circle eight miles in diameter, a rather rough target area at best. But its slow speed (a maximum velocity of 350 miles per hour) and low cruising altitude (3,500 to 4,000 feet) made the V-1 vulnerable to both fighter planes and antiaircraft fire. Thus the weapon never approached the 80 percent accuracy figure.\n\nMuch of the V-1's effectiveness, however, was psychological. It was a fiendish device that announced its own coming. The throbbing engine sound was immediately identifiable, and as long as one could hear the V-1 engine, one was safe. But when the engine cut out, there was a brief silence followed by a piercing whine as the projectile, with nearly a ton of high explosives, hurtled to earth. To a person on the ground the weapon always seemed to be coming from directly overhead.\n\nOn 13 June, at the meeting of the War Cabinet, Churchill was advised of the \"attack by pilotless aircraft.\" The number of the flying bombs was given as twenty-seven. There had actually been only eleven, and the damage was slight. It was therefore decided that there would be no official acknowledgment of this new threat.\n\nOn 15 June the danger became much clearer. At least 50 people died that night and 400 were injured. By the end of the week, the death toll had risen to 526 and 5,000 people had been injured, 2,200 seriously. It was obvious to the British public that something new had been introduced, and equally obvious that the government must acknowledge the threat.\n\nChurchill rose to the occasion. In announcing the new German aerial offensive, he praised the people at home and exhorted them to be brave in the face of the attacks. Like the brilliant commander he was, he managed to convince the British public that they should accept this latest outrage with the same stoic courage they had displayed during the Battle of Britain, the Blitz, and the Baedeker raids.\n\nIn addition, he said, the people at home should welcome the opportunity to share in the battle with their troops on the Continent and in Asia. He also pointed out that the German attacks on the British homeland drew resources from the battlefield, which saved Allied lives and would hasten the end of the war.\n\nIn Berlin, Joseph Goebbels lost no time in trumpeting the power and destructiveness of the new weapon. He broadcast a recording of the launch of a V-1 from the Channel coast with an eyewitness account. There followed lurid descriptions of the carnage in London and the south of England. \"England is trembling\u2014London is ablaze,\" intoned the announcer.\n\nBut while the British were struggling with how to deal with the buzz bombs and their destructiveness, at Hitler's headquarters the reaction was quite different. The F\u00fchrer's military commanders predicted no miracles from its deployment and did not hesitate to say so, even to the F\u00fchrer. Indeed, Albert Speer reported that Hitler was so disappointed at the initial performance of the V-1 that he was on the point of canceling the program altogether.\n\nThen, almost as if it were a theatrical production, the reviews from London came in. The press chief handed Hitler the vivid accounts from the British newspapers about the flying bombs and their effect on the capital. His mood changed at once. He ordered the escalation of the V-1 campaign. The wily Goebbels had once again trumped his opposition.\n\nDuring the week ending 29 June, 650 tons of high explosives were dropped on London, not much less than the 770 tons that fell on the city during the worst fortnight of the Blitz in 1940. Total casualties to date from the flying bombs were 17,328. More disturbing was the report that although the number of dead was about 2,000, the number of killed and seriously injured was 7,403\u2014compared with 16,456 for the whole month of September 1940.\n\nThe figures were not released, however, and the government's silence, which was designed to deny the Germans valuable information on the efficacy of their weapons, only added to the public's fear. After all, the physical damage could not be concealed. Some 500 houses were being destroyed each day and 21,000 damaged. Thousands of civilians were made homeless. But, again, these figures, along with the number of casualties, were kept secret.\n\nWhile no one believed that the flying bomb was the rumored secret weapon that would turn the tide for Hitler\u2014the kill rate for the V-1 was a low one fatality per bomb, with three more persons injured\u2014both politicians and military strategists had to take any new weapons as a serious threat. It was not known how much more intense the attacks might become or what deadlier weapons might be in the offing. Nothing, it seemed, was too outlandish to contemplate. There was even talk of a mysterious \"death ray.\"\n\nThe War Cabinet was also faced with the question of whether to provide misinformation to Germany about where the flying bombs were actually falling. The designated ground zero was clearly Charing Cross, and it was argued that if the enemy could be convinced that they were overshooting the mark, they might adjust their aiming so that many of the bombs would fall in the open country. Opponents of misinformation argued that it could backfire. The Germans might very quickly ascertain that they were being fed false data and correct their aim so that even more bombs might fall on central London. More to the point, no one, civilian or military, wanted to take responsibility for redirecting the German fire from one area of England to another.\n\nTherefore Churchill and the War Cabinet stayed with the devil they knew, and there was no doubt by now that it was, indeed, Satan they were dealing with. By 1 August, 3,407 of the flying bombs had appeared over England, and 1,594 had landed on London\u2014killing 4,175 people and injuring 12,284. By the end of September, a total of 5,890 of the weapons had eluded flak and Fighter Command to kill 5,835 people and injure 16,762 others, almost all of them in London or its suburbs.\n\nAfter the war, it would be revealed that there had been at least one source feeding misinformation to Berlin about the accuracy of the V-1 weapons. Eddie Chapman, a British safecracker, went to work for the Germans when they captured the Isle of Jersey, where he was imprisoned. In June 1944, he parachuted into England to report to his supposed new masters on the flying bombs. Chapman, whose code name was Zig-Zag, was loyal to his country, however. He immediately volunteered his services to British intelligence and became a double agent. His false reports resulted in many of the buzz bombs landing harmlessly in the countryside.\n\n**The V-1 was** by no means a surprise to Churchill and the War Cabinet. British intelligence had first become aware of the development of the vengeance weapons in January 1943. During an interrogation, a German Luftwaffe captain shot down in Africa revealed that he had once landed at a place called Peenem\u00fcnde. The report was forwarded to England and the intelligence service at once turned its attention to the site, which lay at the tip of an isolated peninsula on the island of Usedom, just off the Baltic coast.\n\nIn the spring of 1943, the RAF began a two-month series of reconnaissance flights over Peenem\u00fcnde. The aerial photographs revealed what was clearly a manufacturing and test facility, and the product was all too visible as well\u2014rockets and a rather strange-looking smaller craft with short wings. One of the test vehicles had crashed on the Danish island of Bornholm, and a sketch, which resembled those spotted in the reconnaissance photos of Peenem\u00fcnde, was smuggled out to British intelligence.\n\nThe RAF was ordered to destroy the base, but Bomber Command had to await a full moon. Finally, on the bright night of 17\u201318 August 1943, Peenem\u00fcnde was attacked by nearly 600 planes from Bomber Command. The crews were not told what the target was, only that it was important. Nearly 1,800 tons of bombs were dropped, 85 percent of them high explosives.\n\nAlso in the summer of 1943 Allied reconnaissance flights revealed suspicious construction sites in the Pas-de-Calais and the Cherbourg Peninsula. A French agent, Michel Hollard, enlisted a workman at the installation at Bois Carr\u00e9 who was able to obtain drawings of one of the buildings. Intelligence experts realized these strange ski-shaped structures must be the launch platforms for the flying bombs.\n\nIn December 1943 aerial bombardment of the French sites began, and by the time of Overlord, 103 of the 140 identified sites had been destroyed. While this campaign, labeled Crossbow, delayed the launching of the V-1s, it by no means eliminated them as a threat. The Germans simply changed their tactics. Instead of building large, easily spotted concrete ramps for the launching of the missile, they made the launch sites smaller and thus more easily camouflaged.\n\nFew weapons of war have had such a powerful effect, out of all proportion to their real toll in terms of physical destruction, deaths, and injuries. The Germans miscalculated, however. The vengeance weapons' greatest effect was to raise the stakes in the retaliatory war against civilians. Residents of the cities of the Reich would soon be targeted as never before. But first it was felt that a massive aerial campaign\u2014Crossbow redux, as it were\u2014had to be launched to neutralize the V-1 launch sites.\n\nJust four days after the first V-1 landed in London, Churchill dispatched 405 aircraft of Bomber Command to attack the flying-bomb sites in the Pas-de-Calais. This raid, on 16\u201317 June 1944, was the beginning of a massive three-month bombing campaign, which Churchill urged on Bomber Command and the U.S. Army Air Forces.\n\nOver the objections of those military advisers who saw the V-1 as a deadly nuisance but not one that could affect the outcome of the war, Churchill appealed to Supreme Commander Dwight Eisenhower to give top priority to destroying the launch sites, which\u2014on paper, at least\u2014seemed to be a simple matter. The range of the flying bomb was only 130 miles, which put the launch sites in easy target range of planes based in England.\n\nCarl Spaatz, especially, objected to the bombing campaign against the V-weapon sites. He said that the long summer days\u2014over sixteen hours of daylight in midsummer\u2014should be used to maximize the American daylight bombing of strategic targets, such as the synthetic oil plants.\n\nSpaatz argued that while the H2X radar then in use enabled bomber crews to locate cities, it was of little use in finding these all-important targets, which had been built away from the cities. These plants had to be located and bombed visually.\n\nSpaatz was overruled, but it became clear after the war that his so-called oil plan was more strategically sound than any other. Chief among the critics of the Allies' not pursuing the systematic destruction of the Nazi's oil supply was none other than Albert Speer, the Nazi armaments czar.\n\nAccording to Speer, a great turning point in the war occurred on 12 May 1944. \"On that day,\" wrote Speer, \"the technological war was decided.\" Even as the Allied air forces were preparing to support the invasion of the Continent, the Eighth Air Force, in a massive raid, attacked fuel plants in eastern and central Germany. Daily production was immediately reduced by 20 percent. Two weeks later other devastating American raids, which included attacks on the oil fields at Ploesti, Romania, resulted in a loss for the month of 50 percent of production capacity. And in the summer of 1944, when both the Eighth Air Force and Bomber Command were allowed to return to their preinvasion strategies, a series of crippling blows was launched against the German oil fields, refineries, and storage facilities.\n\nHowever, in his diaries Speer repeatedly returned to what he called the Allies' \"lack of consistency.\" Why, he wondered, did the RAF and the USAAF switch target priorities instead of following up immediately on these successful raids?\n\nInstead, in a reprise of the Luftwaffe's actions during the summer of 1940, the Allied command did not immediately revisit the sites of raids that had seriously damaged critical industries. Speer maintained that they could have put the sites permanently out of commission by a second or perhaps a third raid. If they had done so, he said, the Allies could have completely halted German war production. Instead, both the RAF and the USAAF often diverted their forces to less worthwhile targets.\n\nIn late July 1944, for example, according to Speer, a series of massive raids knocked out 98 percent of the aircraft fuel plants. But almost immediately the bombers were diverted to Crossbow targets, tactical support of troops, and the area bombing of cities. Speer was quick to take advantage of the lull. By November 1944 production had risen to 28 percent of the July levels.\n\nThe repair and rebuilding of the production facilities, bridges, rail lines, and highways was not the miracle of Nazi organization and the Aryan work ethic trumpeted by Goebbels and the other Nazis, including the armaments minister himself. There was a darker explanation. The German war machine had a workforce that made no demands as to food, housing, or wages. Millions of slave laborers worked around the clock to meet the goals set by Speer.\n\n**The V-1, as British** intelligence had warned, was the forerunner of a much more dangerous weapon. Two months after the first buzz bombs hit London, word came from the Continent that the Germans had launched another, very different form of missile. Two of these had been fired against Paris on 6 September, and although both had exploded in midflight the new threat was clear.\n\nAt the noon meeting of the War Cabinet on 9 September, it was announced that two of the new weapons, \"of the type expected,\" had landed the evening before, one in Chiswick, at 1843 hours, and one near Epping just a few seconds later.\n\nSome knowledge of the V-1 had been gleaned from the sketches of the downed test vehicle made by the Danish underground, but British intelligence knew a great deal more about this new weapon, which was dubbed the V-2. The Polish underground had been able to recover a test vehicle that had failed to explode, and an RAF Dakota was dispatched to Poland to bring the pieces of the rocket to England, where it was reassembled.\n\nBut the knowledge was of little use in defending against the weapon. The rocket traveled at supersonic speed, more than a mile per second, and thus there was no radar trace and no advance warning.\n\nThree more of the rockets fell over the weekend, but again there were few casualties and little damage. Indeed, for the entire week only five people were killed in all of England from enemy action. However, the next week was a frightening one: 56 people died in rocket attacks, another 13 from flying bombs, and 22 in the coastal areas from longrange shelling from the French coast.\n\nChurchill decided not to go public with this second new German weapon. He saw no reason to alarm the people further, and besides, he reasoned, why do anything that could buttress morale in the Reich? Also, to the mystification of the War Cabinet, the Germans themselves were not trumpeting this latest achievement and would not do so until the first week of November, when Goebbels broke his silence. The earlier campaign, he said, \"has now been intensified by the employment of another and far more effective explosive.\"\n\nThree weeks later the propaganda chief's threat was borne out by a particularly appalling incident. On Saturday, 25 November 1944, a V-2 ripped into a Woolworth store in Deptford, killing 157 people and injuring 178.\n\n**The launch of the** V-weapons, the feverish preparations for repelling the Allied landings in France in 1944, and the fearsome efforts against the Soviet armies in the east in no way interfered with another vast Nazi program, which continued apace.\n\nNothing was to be allowed to halt or interfere with the cornerstone of Nazi ideology and strategic planning: the total eradication of European Jewry. Indeed, the threats from without accelerated the program. Incredibly, on 15 May 1944, the greatest single deportation of the war began.\n\nMost of the 750,000 Jews of Hungary had been rounded up and interned, but the Hungarian leader, Admiral Miklos Horthy, refused repeated requests, at least one delivered in a stormy meeting by Hitler himself, to turn them over for deportation to the labor or death camps.\n\nWhen the Germans, who had become increasingly unsure of their putative allies, took matters into their own hands and occupied Hungary, the long-sought deportations finally began, supervised by Adolf Eichmann, who had set up headquarters in Budapest. By mid-July, more than 435,000 Hungarian Jews had been crammed aboard trains, a hundred to a boxcar, and shipped to Auschwitz, where all but a handful were murdered.\n\nHorthy, invoking the international outcry from the International Red Cross, the Vatican, and others, was able to stop the deportations, but it was not because the Germans had had a change of heart. Trading Jews for military equipment was one of the odious parts of the bargain that was struck.\n\nIn any event, the reprieve was temporary. Horthy was forcibly removed by the Nazis and imprisoned in Bavaria, and most of the 300,000 Hungarian Jews who were still alive were now conscripted as slave laborers. They were worked to death in mines and factories in the Reich proper or were murdered by Hungarian Fascist collaborators, who regularly assaulted them in the ghetto in Budapest. It was estimated that when the Red Army entered the city in February 1945, the bodies of 10,000 murdered Jews lay unburied.\n\n**In July and August 1944** , one-fourth of the total bombs dropped by the U.S. Army Air Forces were directed to eliminating the V-weapons sites. Whether they hit their targets became a much-debated and much-disputed point. What was not disputed was the fact that the V-1 attacks continued unabated.\n\nIndeed, there was no appreciable letup until ground forces began to overrun the launch sites in the Cherbourg Peninsula and the Pas-de-Calais, which led to an announcement in early September that the V-1 campaign had been defeated.\n\nThe announcement was premature. The Germans still had V-1 launch sites in Belgium and the Netherlands, and the Luftwaffe had developed the capability to launch the flying bombs from Heinkel bombers. Eleven V-1s hit London during the week of 18 September.\n\nAs we have seen, the damage done by the V-1s was relatively minor and the casualties relatively light, but there was no convincing the British public that this was so. The _V_ was shorthand, after all, for _Vergeltungswaffe_ , \"vengeance weapon.\"\n\nVengeance was in the air, and while in less turbulent times revenge might be a dish best eaten cold, no such sentiment intruded on Churchill and the Chiefs of Staff. There would be increasing numbers of reprisal raids against the German civilian population.\n\nRetribution as a weapon was not a novel idea or a new option. It was always part of the arsenal of war for Winston Churchill. Two years earlier, in June 1942, in response to the Nazi massacre and destruction of the Czech village of Lidice\u2014itself an act of retribution for the assassination by Czech partisans of Reinhard Heydrich, SS Deputy Reich Protector of Bohemia and Moravia\u2014the prime minister had instructed Arthur Harris to launch Operation Retribution. Bomber Command was ordered to obliterate three German villages comparable in size and population to Lidice.\n\nHarris responded that it would take a force of 100 bombers for each village, attacking low and dropping two-thirds incendiaries and one-third high explosives to do the job. Since the targets were small and not easily distinguishable, a full moon was necessary.\n\nHarris, a loyal soldier who had the confidence of the prime minister, pointed out to Churchill that the \"justification of giving up one of our rare fine moonlight nights to this task can only be judged on political factors.\" It is clear from the memorandum that it was not retribution that bothered Harris; his concern was that the operation would take Bomber Command away from bigger and more important game. Churchill acquiesced to the air marshal's argument, and Operation Retribution never came off.\n\nWhat was left unsaid in the Harris memo was that in 1942 such precise bombing was beyond the scope of Bomber Command. Indeed, such a surgical strike was probably beyond the scope of Bomber Command or the Americans throughout the war.\n\n**The thirteen-month** Crossbow campaign, which began with the August 1943 raid on Peenem\u00fcnde, was, from its inception, the subject of intense debate, and the argument continued long after the war. The _United States Strategic Bombing Survey_ , for example, concluded that the Peenem\u00fcnde raid had little or no effect on development or production of the V-weapons.\n\nThere was also the question of the cost in men and planes of the Peenem\u00fcnde raid. Bomber Command lost 40 aircraft\u201423 Lancasters, 15 Halifaxes, and 2 Stirlings\u2014and 243 airmen. Since most of the losses were in the last wave of the attacking aircraft\u2014which fell victim to the late-arriving German night fighters\u2014the total losses were judged to be an acceptable 6.7 percent. In this last wave were the Canadian 6 Group, which lost 12 out of 57 planes, or 21 percent, and the British 5 Group, which lost 17 out of 109 planes, or 15.6 percent. Such losses as these were staggering.\n\nBomber Harris and RAF historian Denis Richards reached a very different conclusion from the American postwar investigators. They defended the raid and the losses at Peenem\u00fcnde, claiming that the action cost the Germans an estimated two months in lost manufacturing and deployment time\u2014two months that proved crucial in the summer of 1944. They had an unlikely ally in Joseph Goebbels, who recorded in his diary that the raids on Peenem\u00fcnde and the launch sites in the Pas-de-Calais \"have thrown our preparations back four and even eight weeks.\"\n\nAnd the director of the rocket base, Walter Dornberger, in his self-serving memoir, titled _V-2_ , said that although the damage was nowhere as great as the British believed, the first RAF raid caused a delay of four to six weeks in the development program, which was passed on to the production stage. Four weeks off the schedule meant that the V-1s were not ready until mid-June 1944 instead of mid-May\u2014when the invasion fleets were being readied in the Channel ports\u2014and the V-2s not until September.\n\nThus it is clear that the Crossbow raids did have an important effect. If the V-weapons had been operational in the months preceding Overlord, they might well have caused it to fail, as the supreme commander himself, Dwight Eisenhower, said.\n\n**The raid on** Peenem\u00fcnde had other ramifications besides the destruction of the physical plant. Several of the key scientists who had developed the rocket program were killed. And on the very day of the raid by Bomber Command, Dornberger had reassured his restive staff that the rocket program now had the highest priority in Berlin. \"Personnel is streaming in,\" he recalled telling them. \"In the last fortnight over twelve hundred men have arrived.\" In his memoirs he was still employing the circumlocutions and euphemisms of the Third Reich. The \"personnel\" that were \"streaming in\" were slave laborers.\n\n\"Losses were particularly heavy among foreign construction workers at Trasenheide camp,\" said Dornberger matter-of-factly. Between five and six hundred of the dead\u2014about 75 percent of the total\u2014were these slave laborers, another sobering reminder that even the victims of the Nazis were as likely to be killed in air raids as their tormenters.\n\nThe raid also served notice that the site was in reach of Allied heavy bombers, which forced the Germans to move production to vast underground factories that were carved out in the Harz Mountains near Nordhausen. The excavation was done by slave laborers from concentration camps, and when the factories were completed still others worked around the clock under the most barbaric conditions to produce the V-weapons.\n\nThe testing of the V-weapons was transferred to southeast Poland, deep in the forests of the triangle formed by the Vistula and San Rivers. Thousands of Poles were forcibly removed from the villages in the area to make way for the vast test site, which was served by the rail line that ran through Dresden. And there would be no shortage of labor. In addition to the Poles, who could be pressed into service, the Auschwitz-Birkenau and Majdanek camps lay in close proximity.\n\nIn one of the most tragic incidents of the war, Bomber Command attacked the Nordhausen camp on 3 and 4 April 1945, believing that the buildings in the aerial photographs were military barracks. Hundreds, or perhaps thousands, of the inmates were killed.\n\n**As the Germans** continued their retreat back into the Reich, they threw everything they had left into the V-weapons arsenal against England. The first week in March 1945, 68 V-2s hit England, 41 landing in London. It was the worst bombardment since the campaign began. Three hundred and four people died that week. The next week saw some drop-off in the casualties, but for a jittery populace it was only marginally better; 200 people were killed, 125 in one incident.\n\nBy the third week of March, the V-weapon campaign was nearing its end, although twenty V-2s and two V-1s hit the capital. Finally, on 29 March 1945, what would be the last of the flying bombs, eleven in all, were launched from the Continent. Only five got through. There were no deaths, and just five people were wounded. But earlier in the week, seven V-2s had hit London and four had landed in Essex, killing a total of 137 people, bringing the toll for the month to almost 600.\n\nAlong with the V-1 and V-2 attacks, the Luftwaffe also managed to stage a few last-ditch bombing raids. One such raid, on 17\u201318 March, killed twelve people in Hull. Three nights later, Norfolk was bombed.\n\nBut at last the ten-month _Vergeltungswaffen_ campaign was over. The V-2s had killed 2,754 people and seriously injured 6,523. Flying bombs had killed 6,184 and seriously injured 17,981.\n\nHowever, it was not until 26 April 1945, just eleven days before the surrender of Germany, that Winston Churchill reported to the House of Commons, with relative certainty, that the V-weapon attacks against England had ended. But Churchill knew too much of his military history not to hedge his bets. More than 30,000 Londoners had died as a result of Luftwaffe raids, flying bombs, and rockets, and more than 130,000 had been injured.\n\n\"It is my duty,\" he said, \"to record facts rather than indulge in prophecy, but I have recorded certain facts with a very considerable air of optimism which I trust will not be brought into mockery by events.\"\n\nAs for who should be credited with stopping the attacks, the prime minister was willing to congratulate the RAF and the antiaircraft gunners, but, he said, \"[We] should not forget it was the British Army that took the sites.\"\n\n**Another campaign** , indeed the longest German campaign against the British civilian population, was one that has received relatively little attention: the artillery bombardment of the English Channel ports. The first shells from the German batteries on the French coast fell on Folkestone in August 1940 and the last on Dover on 26 September 1944. It took only a minute for a shell to cross the twenty-two-mile strait that separates England from the Continent. Therefore, when the Germans opened fire, sirens warned the people that they had sixty seconds to find cover. Thousands hid in the caves and tunnels that honeycombed the famous chalk.\n\nThe bombardment was sporadic\u20142,226 shells landed on Dover, killing 109 people in four years\u2014but it was a siege nevertheless, one that lasted longer than Stalingrad. Some 17,000 homes were damaged or destroyed. At the end of the siege, the Germans, anticipating the immediate capture of the coastal batteries\u2014Calais surrendered to Canadian troops on 1 October 1944\u2014began to fire everything in their arsenal at the British coast, including 16-inch armor-piercing shells. That last day 63 shells (50 in one hour) hit Dover.\n\n**The V-2 has enjoyed** great fame, but it was one of the most inefficient weapons ever devised. Each rocket carried less than a ton of explosives, and every launch was a one-way trip. Therefore, if every V-2 built had landed on London, the total amount of high explosives delivered would have been less than 10,000 tons. By way of comparison, in just one raid on Cologne, on the night of 30\u201331 October 1944, Bomber Command dropped 4,000 tons of high explosives and incendiaries on the city.\n\nPerhaps a more resonant indictment of the wasteful V-2 program is the contrast between it and the development of the Mosquito bomber by the British. Each of these 400-mile-per-hour planes was capable of carrying a 2,000-pound bomb, which was the rough equivalent of the pay-load of a V-2 rocket. And every Mozzie could make flight after flight over Germany, practically at will, returning to its home base to rearm and fly again.\n\nBut in reality the Allied response to the V-weapons was almost as misguided as the development of the weapons themselves by the Germans. Operation Crossbow is a textbook example of the danger of political solutions being given priority over military matters in wartime\u2014thus extending the hostilities. Thousands of sorties were flown against the V-weapons sites\u2014one Bomber Command raid comprised 1,114 planes\u2014instead of the more important targets in Germany and eastern Europe espoused by Carl Spaatz: the oil fields and refineries.\n\nIn spite of its failure, the German rocket program has since its inception engaged the imagination of the public. Much of its fame, of course, is tied to its role as the precursor of the intercontinental ballistic missile and the giant rockets of space exploration. However, it was the less glamorous but far more deadly weaponry of the Allies that decided the issue and destroyed the Axis powers.\n\nAs Bomber Harris observed, Germany put its faith in the weaponry of the First World War\u2014the U-boat\u2014and the unproved and ultimately futile weaponry of the next war\u2014the rocket program. To quote A. J. P. Taylor again: \"The decisive difference between the British and the Germans is the British... knew what they were doing and the Germans did not.\"\n\nAlbert Speer might have agreed. The Allied bombers were effectively doing the job of pulverizing Germany, which, Speer maintained, could have been halted if there had not been the lamentable waste of men and mat\u00e9riel in developing the V-weapons. But Hitler, enraged by the increased bombing of German cities, chose to concentrate on terror weapons.\n\nThe chief losers in this misallocation of resources were the _Wasserfall_ (Waterfall), a large surface-to-air missile, which was developed as early as 1942, and the new jet plane, which was in production but too late to make a difference. Speer was confident that these weapons could have beaten back the Allied air offensive against German industry in 1944 if development had been started earlier.\n\nThe Waterfall was guided by remote control to its target and was capable of destroying bombers at altitudes as high as 50,000 feet. The ground controller had to see the plane, however, which meant that the rocket could not be used in heavy cloud cover or at night; but this problem could have been solved in perhaps eighteen months. Only about 220 scientists were assigned to work on the Waterfall, as opposed to the more than 2,000 who were involved in the development of the V-weapons.\n\nInstead of focusing on the Waterfall, the F\u00fchrer ordered Speer to in crease V-2 rocket production to 900 per month. Speer later derisively pointed out that this would have been thirty rockets a day, which, assuming they all reached their targets, meant delivering a payload of just twenty-four tons of high explosives, the equivalent of the bomb load of twelve B-17s. As he said, it would have taken 66,000 rockets\u2014more than six years' production\u2014to match the explosives dropped by the Allies on just one city, Berlin.\n\nSpeer ruefully recalled that he had ignored an urgent appeal from Professor C. Krauch, the commissioner for chemical production, to concentrate on the antiaircraft missile. In a memorandum to the armaments minister, Krauch condemned those who argued that terror must be answered with terror.\n\nThe only sensible course, Krauch argued, was to develop the Waterfall surface-to-air missile. Speer, who differed from the other Nazi satraps in that he at least sometimes went his own way, this time followed his F\u00fchrer. He ignored Krauch's appeal, and the Allied bombers continued to devastate the cities of Germany and terrorize its citizens.\n\nProfessor Krauch was correct. The chief effect of the rocket and flying-bomb attacks against Great Britain was to still the minor but vocal segment of the British population that had begun to question the bombing of civilian populations and to strengthen the position of the advocates of the terror bombing of German cities.\n\n# CHAPTER SIX\n\n**OPERATION THUNDERCLAP**\n\nRun-up to the Inferno\n\n**N o politician can ignore the rumblings of a beleaguered citizenry**, and Winston Churchill was a master at judging public opinion and the psychology of the people. Once, in response to praise for his oratory from his personal physician, Lord Moran, Churchill said, \"I don't know about oratory, but I do know what's in people's minds and how to speak to them.\" Lord Moran offered the explanation that the war and the threat to the nation had given Churchill this insight.\n\nWinston Churchill, the son of Lord Randolph Churchill and the grandson of the 7th Duke of Marlborough, knew nothing of the lives of common people, but beginning in May 1940 he became their voice. He wonderfully articulated the hopes and dreams of the entire British people, a remarkable achievement for a man who had never ridden a public bus and whose one excursion on the London Underground, during the General Strike in 1926, ended with his getting lost and having to be rescued by friends.\n\nChurchill's reading of the popular will told him, correctly, that foremost in the thoughts of the British people in the summer of 1944 was revenge. Although accepting of their role of \"frontline soldiers\" in the V-weapons attacks, Englishmen believed that equal punishment should be meted out to enemy civilians. There was thus much agitation for the reprisal bombing of German cities\u2014no matter that most of the larger German cities had already been destroyed.\n\nThe call for vengeance knew no class boundaries. Most of the residents of South London had probably never heard of either Vita Sackville-West, the writer, or Knole, the great house in Kent where she grew up. Sackville-West, like Churchill a member of the upper reaches of British society, reacted in precisely the same way as bombed-out tenement dwellers when she heard that her ancestral home had been hit.\n\nIn an angry letter to her husband, Harold Nicolson, Sackville-West spoke for most of her countrymen. \"Those filthy Germans!\" she cried. \"Let us level every town in Germany to the ground! I shan't care.\"\n\nChurchill, whose own grand boyhood home, Blenheim Palace, was also damaged by bombs, doubtless agreed with the formidable Vita, and he had both the authority and the will to \"level every town in Germany.\"\n\nHe also had the means at hand. The prime minister was as much soldier as politician. He was a graduate of Sandhurst and had served with some distinction in India and Egypt as a young man. And he also knew something of airplanes.\n\nWhile he was first lord of the Admiralty, he had become so enamored with flying that in 1913 he began lessons at the Eastchurch naval air station on the Isle of Sheppey, flying as many as ten times in one day. He was thus an early and enthusiastic proponent of airpower; it may be apocryphal or not\u2014his biographer Martin Gilbert says not\u2014that he coined the term \"seaplane.\"\n\nOnly the entreaties of his wife and friends and the deaths of two of his instructors, one in a plane in which Churchill had just flown, convinced him to give up flying. But soldiering was never very far beneath the surface. At the age of forty-one, he went back into the British army, serving in France from November 1915 until May 1916.\n\nNow, his natural reaction was a military one: strike back. On 1 July 1944, after two weeks of flying-bomb attacks, the prime minister asked the Chiefs of Staff to restudy the question of reprisal raids. As for himself, Churchill had already made up his mind. The Germans would pay heavily for this latest outrage.\n\nHowever, during all the carrying on about vengeance weapons and London, Chief of Air Staff Charles Portal observed, rightly, that the city was a legitimate military target. It was not only the seat of the British government but an important center of war production and communications.\n\nChurchill was adamant. There must be reprisals. The people would accept no less, he argued. In the War Cabinet meeting on 3 July, he reported receiving a large number of letters from the general public urging him to take strong countermeasures against Germany for what he termed an \"indiscriminate form of attack.\" Terror bombing was at last on the table.\n\nIn calling for reprisals, Churchill first suggested that the Germans be warned that if they did not halt the V-1 attacks, Bomber Command would systematically raze smaller German cities in retaliation. General Walter Bedell Smith, Eisenhower's chief of staff, supported the prime minister. It is therefore reasonable to assume that both Eisenhower and Roosevelt did, or would, as well.\n\nHis plan called for the systematic destruction of small towns of populations of 20,000 people or so. To destroy such small targets, it would be necessary to drop 600 tons of bombs on each target in daylight, which meant that the Americans would have to do it. The planners admitted that somewhere on the order of 900 tons would actually be necessary to ensure a raid's success.\n\nIt was estimated that five such towns could be destroyed in one good-weather operation. Since there were only three or four days a month when weather conditions, less than 2\/10 to 3\/10 cloud cover (20 to 30 percent), were favorable for such an operation, the Americans could be expected to destroy fifteen to twenty small towns per month.\n\nWhile the destruction of small towns would no doubt have serious effects on morale, such a campaign could not be planned in advance to produce the desired devastating effect. News of the bombings could be controlled locally, for one thing, and the weather could never be relied upon. Besides, said the planners, even if a hundred towns of 20,000 people were destroyed, only 3 percent of the population of Germany would be affected.\n\nActing Major General L. C. Hollis, senior assistant secretary, Office of the War Cabinet, wrote to Churchill that for the Germans to change their policies in the light of such a threat would be militarily foolish. What, after all, were a few small towns to the German high command when weighed against the success of the flying-bomb campaign against England, which was not only slowing production owing to a jittery populace but also tying up 50 percent of Bomber Command in Operation Crossbow?\n\nThe first sea lord, Sir Andrew Cunningham, took the opposite view. He felt that such a threat might well have the desired demoralizing effect on the people and that the Nazi military leaders might well call off the V-weapons attacks.\n\nCharles Portal and Air Chief Marshal and Deputy Supreme Allied Commander Arthur Tedder opposed any plan that would divert Bomber Command from what it saw as its primary mission. Oil and communications should remain the primary targets for Bomber Command. Besides, Hitler cared nothing for the cities of Germany, large or small\u2014he never toured a bombed-out city\u2014and would willingly sacrifice any or all of them. Indeed, he remarked more than once that the Allied air raids actually made his dream of building a new Germany that much easier by destroying the old.\n\nAnother form of attack that was discussed was the widespread strafing of civilians by fighters, although everyone knew that this action could not be done on the scale that would produce a widespread catastrophe.\n\nEverything, it seems, was on the table for discussion, including the use of poison gas, not only against the Crossbow installations but also in Germany itself. Other actions against civilians included the proposal that Germany be warned that from a certain date all movement by road or rail was forbidden and subject to attack.\n\nThe use of poison gas was eliminated as an option, even though Churchill argued strongly for it, and wholesale bombing and strafing of all occupied Europe was impossible. There were nowhere near enough men or planes available to carry out such an ambitious plan.\n\nChurchill clearly had come some distance in the four years since he had sent a memorandum to Alfred Duff Cooper, minister of information, on how to handle the reporting of air raids on England. \"Press and broadcast should be asked to handle air raids in a cool way and on a diminishing tone of public interest,\" he wrote. \"The facts should be chronicled without undue prominence or headlines. The people should be accustomed to treat air raids as a matter of ordinary routine.... It must be remembered that the vast majority of people are not at all affected by any single air raid, and would hardly sustain any evil impression if it were not thrust before them. Everyone should learn to take air raids and air raid alarms as if they were no more than thunderstorms.\"\n\nThis rather Olympian pronouncement could well have been issued by leaders of any of the Axis powers or their propaganda ministers. But statistical analysis was certainly on Churchill's side. The odds of being killed by a flying bomb were only one in thirty thousand.\n\nOn 5 July 1944, the Chiefs of Staff met to discuss Churchill's call for reprisal raids against Germany for the V-1 attacks. Afterward they reported \"that the time might well come in the not too distant future when an all-out attack by every means at our disposal on German civilian morale might be decisive.\" Further, the Chiefs of Staff recommended to Churchill that \"the method by which such an attack would be carried out should be examined and all possible preparations made.\"\n\nThus began intensive planning sessions by a committee that included not only representatives from the American and British air staffs but also the British Foreign Office and the Ministry of Economic Warfare. The representatives from these various groups began to develop a new policy with a new name. Henceforth the planners would talk of \"morale bombing.\"\n\nAccording to the committee's top secret report, entitled \"Attack on German Civilian Morale,\" Berlin was to be the target of a four-day, three-night round-the-clock bombardment by Bomber Command and the Eighth Air Force. During the raids, 20,000 tons of bombs would be dropped. Many things recommended the German capital as the target, not the least of which was its vast size. Even in bad weather it could be found.\n\nBerlin was also the premier population and administrative center of the Reich, as well as a vital industrial and communications center. And, of course, the most important Nazis, including the F\u00fchrer himself, were in residence. In these particulars, Berlin differed not at all from London\u2014although not even Portal offered this analogy publicly.\n\nSince a daylight raid on Berlin would produce the greatest number of casualties because of the population density during working hours, the specialists in daylight bombing, the Eighth Air Force, would have to lead the way. Under visual conditions, 2,000 American bombers would drop 5,000 tons of bombs on a 2.5-square-mile area of central Berlin. At that time of day, the area, which would absorb a bomb density of 2,000 tons of bombs per square mile, was estimated to contain some 375,000 people.\n\nThe effectiveness of the initial raid would be compounded by an \"all-incendiary attack by Bomber Command, on the heaviest scale, on the remainder of the city.\" Bomber Command, in a departure from standard operating procedure, would attack in daylight, which would necessitate the Americans' providing a large force of escort fighters. If necessary, Bomber Command would follow up that night with another incendiary attack.\n\nNot so incidentally, such a raid would have postwar ramifications as well. Churchill always viewed the Soviet allies with suspicion and had few illusions about the extent to which they could be expected to cooperate after the defeat of Germany.\n\n\"The total devastation of the centre of Berlin would, moreover, offer incontrovertible proof of the power of a modern bomber force; it would convince our Russian allies and representatives of other countries visiting Berlin of the effectiveness of Anglo-American air power,\" said the drafters of the report. Further: \"A spectacular and final object lesson to the German people on the consequences of universal aggression would be of continuing value in the post-war period and would appreciably ease the task of policing the occupied areas by means of air forces.\"\n\nOfficially, RAF policy was to destroy industrial areas, which, as Harris often observed, were located in the cities of the Reich. So, naturally, his bombers attacked cities. And for his purposes, incendiaries were more effective and paid a larger dividend than high explosives. So the ratio of incendiary bombs to heavy bombs was very large. It was also argued, somewhat disingenuously, that incendiaries caused fewer casualties among civilians than did high explosives.\n\nFurther, the British pointed out, the RAF raids had caused much greater disruption among the civilian populace than did the American raids, which were ostensibly against precise targets\u2014oil refineries, aircraft plants, railroad yards, and the like. Since these targets were in outlying areas, civilians were little affected, or so it was officially stated. In reality, the truth was otherwise.\n\nIn chilling detail, the report reveals how far planners on both sides had descended after five years of warfare. There would be, it was projected, approximately 275,000 casualties\u2014137,500 dead and 137,500 seriously injured. The name chosen for this massive raid connoted both its suddenness and its deadliness: Operation Thunderclap.\n\nAs the report stated, \"The main purpose of [Thunderclap], which may be carried out in the closing stages of the war, is to precipitate the capitulation of the German High Command. If the operation should succeed in curtailing the duration of the war by even a few weeks it would save many thousands of Allied casualties and would justify itself many times over.\" The memorandum also said forthrightly, \"The operation would not, necessarily, cause any sudden breakdown in German administration.\" After all, most of the government had already left town or was dispersed. The postal system, for example, was being administered from Dresden.\n\nBut the destruction of the administrative apparatus was not the goal of Thunderclap. As the drafters of the plan said, \"The essential purpose of the attack however is to deliver an overwhelming blow to German national morale.... The whole population of Berlin would be spectators of the catastrophe, and, in the state of war, which has been postulated, the effect might well be decisive.\"\n\nOn 13 August, John Strachey, director of bomber operations, received a memorandum advocating the Thunderclap plan. \"I still feel there is a strong case,\" wrote the unidentified correspondent, \"after the virtual collapse of the [German] Army in Normandy, for laying on a 'Rotterdam' on the centre of the Capital.\" The terror bombing of Berlin and killing or injuring of hundreds of thousands of civilians would cause a national panic that \"at the best may prove the last straw.\"\n\nThe air staff had consulted with the Foreign Office, the Ministry of Economic Warfare, and an \"unofficial representative\" from General Spaatz's headquarters. There was general consensus about Thunderclap, but there were still deep divisions among the principals about diverting men and mat\u00e9riel from destroying the German armed forces and bombing strategic supplies, particularly oil. But everyone regretted that Thunderclap had not been in place to take advantage of the attempt on Hitler's life on 20 July 1944.\n\nAfter all suggestions were discussed and most eliminated, one target still recommended itself for a Thunderclap-type raid: Berlin. A genuine crisis could be effected by destroying the government communications and public services of the center of Nazi power. Although some two million people, half the city, had been evacuated, there were as many people, some 3 percent of the population of Germany, still living in Berlin. A catastrophic raid on the capital would thus have the greatest possible effect on the civilian population of Germany, since no attack of such magnitude could be covered up or disguised.\n\nHarris and Spaatz were in agreement that their two commands would be able to drop a total 20,000 tons of bombs on Berlin over a period of four days and three nights. With that added to the 48,000 tons of bombs that had already been dropped on the German capital, the estimate of destruction and death seems accurate enough.\n\nA first draft of the report went so far as to suggest that a large raid might even trigger revolt in Berlin, which had, it was said, \"some traditions of anti-Nazi activity.\" This last projection was a bit too roseate. It was dropped from the final version.\n\nIn the final report, issued on 22 August, under the heading \"Other Large Towns,\" the planners discussed the alternatives to Berlin. \"In the main the tactical factors governing the attack on other large towns such as Hamburg, Cologne, Frankfurt or Munich, are similar to those of attack on Berlin.\"\n\nWhile Allied losses would be less since at least three of these targets were near the German border and thus the penetration would be not as deep as with Berlin, they were also harder to find in bad weather. But, more important, there would be less destruction in each of these cities per ton of bombs dropped. The original report thus clearly and unmistakably called for the Thunderclap target to be Berlin.\n\nThe report acknowledged that \"immense devastation could be produced if the entire attack was concentrated on a single big town other than Berlin and the effect would be especially great if the town was one hitherto relatively undamaged.\" This is the sentence often cited in reference to the Dresden raid as evidence that the planners had Dresden or a similar city in mind in 1944. Not so, it seems. The very next sentence reads, \"The political effect would however be less than that of comparable devastation in Berlin.\" For the planners, Thunderclap meant the bombing of Berlin, which was not only \"unmissable,\" even in the worst weather, but would also allow for a \"banquet raid,\" offering something for everyone and every taste.\n\nThe main impetus or ingredient necessary for launching Thunderclap was less easily defined or recognized. What would be the actual flash point, the crisis that when fully and quickly exploited by a devastating raid could bring down the Reich? No one was certain, but until then, said the report, \"it is essential that we should devote our maximum effort to attacks on the German war economy and on the German army and its essential supplies.\"\n\nThe planners\u2014whose report was, after all, for Winston Churchill, who was calling for vengeance for the V-weapons\u2014left themselves an out. \"There may, however, be a moment,\" they wrote, \"at which the balance can be tipped by an attack directed against the morale of the High Command, the army and the civilian population rather than against objectives immediately related to the battle.\"\n\nIn other words, Bomber Command and the U.S. Army Air Forces would together so devastate the Reich and terrorize the populace that Hitler and his cohorts would either capitulate or be overthrown. There were three main factors to be considered:\n\n1. The morale of the political and military leaders could be affected by heavy attacks on government and military centers and by \"well judged propaganda.\"\n\n2. The morale of the armed forces could be affected by conditions in the field, by interdiction of supplies and weapons, and by the conditions at home.\n\n3. While admitting that riots, strikes, uncontrolled looting, or other civil disorder might occur in \"an extreme case,\" the report concluded that \"this is not in any circumstance a probable contingency except among foreign workers.\"\n\nThere was, however, some chance of absenteeism, shirking off at work, and general hostility toward government and administration if civilian morale deteriorated\u2014a very big \"if.\" But, the report continued, an attack on morale \"may force the authorities to divert increasing resources to the maintenance of morale at the expense of other vital commitments.\" In other words, thousands of field guns would have to be used to defend cities from air attack instead of being deployed as artillery at the front. Civil defense measures would cause additional diversion of large numbers of men and huge amounts of mat\u00e9riel to aid the civilian populace. In particular, hundreds of thousands of people made homeless by the raids would have to be cared for, causing further disruption.\n\nIf anyone still had doubts that the chief target in any civilian bombing campaign would be women and children, this report resolved those doubts. \"It must be remembered that there are few able-bodied male Germans between 17 and 45 left in Germany outside the Army and the Police.\" As for foreign workers, they might be more sensitive to air attack, but the report admitted that they were subject to total police control. These workers were, after all, mainly slave laborers. The report continued:\n\nIn this situation it is unlikely that fluctuations in civilian morale will have any decisive influence upon the High Command until its authority has already been greatly weakened by other causes and the machinery of repression has begun to break down. The occasion for an attack on civilian morale as such will not arise until it is generally believed even in Germany that the Nazi system is collapsing and that total defeat is imminent. This opportunity to enforce surrender may be a fleeting one; if it is not seized either the extremist elements may succeed in rallying the army for a further stand or the collapse may spread so rapidly that central government ceases to exist.\n\nIt is generally agreed that the greatest effect on morale will be produced if a new blow of catastrophic force can be struck at a time when the situation already appears desperate. The blow should be such that it cannot be concealed or minimised, and it should if possible imply a threat that it will be continued and intensified if surrender does not follow. The German attack on Rotterdam in May 1940 was made in somewhat analogous conditions, and illustrates the effect which may be produced. Carefully coordinated propaganda is of course essential.\n\nThe report admitted that the \"available evidence suggests that German civilian morale is at present negative rather than positively good or bad.\" The average person was concerned only with getting by from one day to the next and was under no illusion that resistance to authority or protest against the war would improve his or her lot.\n\nThe hopeful but guarded note that foreign workers might become restive reflected the view of Goebbels himself. As early as April 1942 he wrote in his diary, \"It is now also becoming evident that the great successes of the English with their air raids are due to sabotage on the part of foreign workers.\" British intelligence was doubtless made aware of the Nazi chiefs' fear of the foreign workers in their midst and the police investigations of their alleged sabotage and aid to the enemy. In reality, of course, there was little to hope for among the British and little to fear from the foreigners on the part of the Germans. The slaves remained quiescent.\n\nClearly, in a short time, British and American planners had learned the craft and the importance of propaganda. Joseph Goebbels himself could not have phrased it better.\n\nNeither Arthur Harris nor Carl Spaatz sat in on the sessions that devised the Thunderclap plan. Although the American commander was in agreement with the final draft, he asked that no mention be made in the report of \"the concurrence of his unofficial representative at the Meeting.\"\n\nAs for Harris, it can be surmised that he had no qualms about such a massive raid on Berlin since he had planned a similar Anglo-American operation against the German capital for 21 June 1944 in retaliation for the flying-bomb attacks.\n\nAccording to Harris, Doolittle, the Eighth Air Force commander, came to Bomber Command headquarters the day before to confer with the British staffs and go over the final plans. The discussions were proceeding amicably and the operation seemed feasible to everyone until Harris asked about the long-range American fighter support necessary to protect the British bombers. Not only would it be an unusually deep penetration into the Third Reich, but the British would be raiding in daylight, an unusual move for them. Bomber Command would thus require an extraordinarily large number of fighter escorts.\n\nNeither Doolittle nor his boss, Carl Spaatz, commanding general of the U.S. Strategic Air Forces, was anxious to deploy the American fighter squadrons over such a vast area. The bomber stream would run some sixty miles in length. When they told Harris that he could have nowhere near the number of fighter planes that he demanded, he withdrew from the plan forthwith.\n\nHarris, in his memoirs, maintained that his withdrawal forced the cancellation of the entire operation, which was not so. A thousand American B-17s and B-24s did raid Berlin on 21 June 1944, dropping almost 1,400 tons of bombs on the German capital and its environs.\n\nSpaatz was very much troubled by the bombing of civilians as outlined in the Thunderclap plan. He wrote to Eisenhower on 24 August that the Eighth would participate in the raid against Berlin, but the American goal would remain attacking targets of military importance. \"U.S. bombing policy, as you know,\" he reminded Ike, \"has been directed against precision military objectives, and not morale.\" Eisenhower reassured Spaatz, telling him, \"We will continue precision bombing and not be deflected to morale bombing.\"\n\n**The V-1 terror attacks** on the British cities, the calls for reprisals, and the drafting of the Thunderclap plan were part of the backdrop of the Octagon Conference in Quebec on 12\u201316 September 1944. At the conference, Churchill and Roosevelt provided a resonant example of the odium in which Germany was held and the desire for revenge that permeated the thinking of otherwise rational beings. The two leaders approved and initialed the Morgenthau Plan, a scheme concocted by Roosevelt's secretary of the treasury, Henry Morgenthau.\n\nThe Morgenthau Plan called for the elimination of Germany as an industrial power. Any successor state to the Third Reich was to be reduced to an agricultural and pastoral society. British Foreign Secretary Anthony Eden and U.S. Secretary of State Cordell Hull were appalled at the idea that postwar Germany would be so crippled and prevailed on Churchill and Roosevelt to disavow their actions. The plan was scrapped.\n\n**Concurrent with Thunderclap** , it was also proposed that bombers attack SS and Gestapo headquarters and, in an effort to stop the murder of the remaining Jews of Europe, the concentration camps themselves. However, in a tacit admission that bombing was not all that accurate, the planners had to reject these addenda.\n\nThe headquarters were too scattered throughout urban areas to be bombed effectively. As for the concentration camps, by far the largest number of deaths would be among the inmates\u2014a supposition that was borne out by the raids on Peenem\u00fcnde and Nordhausen, in which great numbers of slave laborers and very few Nazis were killed.\n\nThis last decision would later fuel charges that in spite of knowing of the persecution and murder of the Jews, Churchill, Roosevelt, and their military advisers passed up opportunities to save them by destroying the rail lines leading to the death camps.\n\nAn examination of the map of the largest camp, Auschwitz-Birkenau, clearly points up the difficulty of accurately bombing an area approximately two by five miles in area, when it was considered good bombing if the bombs fell within half a mile of the target. The factories that were staffed with slave labor, the barracks for the inmates, and the grisly machinery of extermination were in such close proximity that bombs would have killed many thousands of the people that any such raids were supposed to save. As for the rail lines\u2014there were four serving the camp\u2014the Germans had millions of slave laborers, and until the very end of the war they were quickly able to repair damaged rail lines, often within hours of their being bombed.\n\nSince at least August 1941, it had been known what was happening in the Nazi-occupied areas in eastern Europe. Neutral governments, intelligence sources, and \u00e9migr\u00e9s were reporting the German atrocities in frightening detail. A week after returning from the meeting with Roosevelt in Newfoundland, Churchill declared in a broadcast speech, \"Since the Mongol invasion of Europe... there has never been methodical, merciless butchery on such a scale, or approaching such a scale.... We are in the presence of a crime without a name.\"\n\nChurchill had spoken out even earlier, on 21 December 1937, against Hitler's persecution of the Jews. During a debate in the Commons over Lord Halifax's visit to Hitler in Berlin, Churchill described the visit as appeasement of the F\u00fchrer and tacit approval of his racial policies.\n\nDebate has long centered on whether in his \"crime without a name\" speech Churchill was referring to what became known as the Holocaust or calling the world's attention to the murder of Russian noncombatants. Certainly, it was known that Jews were being rounded up, interned, and deported. After all, Churchill received weekly reports on German police activities.\n\nMany explanations have been put forth as to why these facts were not made more of by the British government. The press was certainly reporting the atrocities. One construction is that old standby: to have done so would have compromised the Ultra program. Historian Richard Breitman takes a different view. He cites a July 1941 Ministry of Information caveat that propaganda must be handled very carefully so as not to seem too extreme. If filled with seemingly fantastical reports of atrocities, instead of rousing the British people to action it might have the opposite effect.\n\nEven allowing for a half century of retrospection, reading the now declassified reports and memoranda one is sometimes almost overcome by whiffs of the unmistakable anti-Semitism of the British Foreign Office and Ministry of Information in the 1930s and 1940s. What else can one make of a memorandum that says that information and propaganda \"must deal always with treatment of indisputably innocent people. Not with violent political opponents. And not with Jews\"?\n\nHarold Nicolson, that pillar of the diplomatic establishment, confided to his diary in June 1945, well after the Nazi genocidal policies and atrocities had been publicized around the world, \"The Jewish capacity for destruction is illimitable. And although I loathe anti-Semitism, I do dislike Jews.\"\n\nBy the time of Churchill's speech, hundreds of thousands of Jews were already dead\u2014starved to death or victims of disease in the concentration camps that had sprung up all over Europe; beaten or shot to death by camp guards; or murdered by the Einsatzgruppen, the killing squads that followed the troops and executed the civilian populace as the Wehrmacht moved across eastern Europe and into the Soviet Union. In the first three weeks of Barbarossa, some 50,000 Jews were murdered by the Einsatzgruppen.\n\nPoland, with the largest concentration of Jews in the world, some three million, had already been under the Nazi terror for almost two years. The Warsaw Ghetto was home to over 400,000 people, each of whom had a food allotment of 183 calories per day, about the number of calories in two slices of bread. By the end of 1942 most of Poland's Jews had been liquidated.\n\nThe program of transporting the Jews to the east and certain death was highly classified, and the operation was carried out in all of Europe by relatively few people, considering its vast scope. As Hitler had fore- told in _Mein Kampf_ , \"If propaganda has imbued a whole people with an idea, the organization can draw the consequences with a handful of men.\" The German people had for over a decade been barraged with the anti-Semitic propaganda of the Nazis and had become inured to the suffering of their neighbors and fellow citizens.\n\nThe term _Sonderbehandlung_ (\"special treatment\") was devised by Himmler and his staff to describe the deportations and killing. Even this euphemism became troublesome, so by April 1942 the program was changed to \"Transportation of the Jews to the Russian East.\"\n\n_Sonderbehandlung_ was applied to other groups as well. Hundreds of thousands of non-Jews\u2014Catholic priests and nuns, Communists, Polish prisoners of war, homosexuals, and Gypsies\u2014were rounded up and sent to the camps or murdered where they were found. By the end of the war three million non-Jewish Poles had also been killed.\n\nJewish leaders in Britain and America repeatedly tried to apprise the world of the enormity of the Nazi crimes against their coreligionists. Influential newspapers, in particular the _New York Times_ , joined in the chorus of horror. In England, the archbishop of Canterbury wrote a letter to the _Times_ of London. Finally, on 17 December 1942, an Allied declaration condemning the systematic murder of European Jewry was issued; but, significantly, it offered no plan for saving those millions still alive.\n\nThe official line was that victory over the Germans was the first order of business and everything else must be subordinate. There were many underlying issues as well. One was the fear of a massive influx of Jewish refugees, which was of especial importance to those such as Anthony Eden. Another concern was the reaction of the Arab world. How would the inevitable introduction of huge numbers of Jews into their ancient homeland in Palestine affect relations with the Arabs, who controlled much of the world's oil supply?\n\nIn late 1942 and early 1943, however, there were no Allied ground forces in Europe except the Russians, who were fighting a purely defensive war for their very existence. The only way to take the war to the Germans was by air; but the RAF was still hesitant to venture too deeply into Germany because of the unacceptable losses over the heavily defended Fatherland, and the U.S. Army Air Forces was still feeling its way. Its operations were more or less restricted to bombing French and German ports.\n\nThe campaign to save the Jews was thus limited to a war of propaganda, although it was not a war of lies and deceptions. All of the horrors were true. And it may have resulted in the saving of some of the persecuted by lending encouragement to the brave souls who hid their unfortunate countrymen and by convincing those Jews who could still do so to go into hiding or to flee.\n\nNothing can spare those civilian and religious and military leaders from the judgment of history that they did not at the very least speak out against the atrocities being perpetrated against the Jews. At the same time, credit must be given the military for moving as rapidly as possible to destroy the Nazis and bring down the system responsible for the atrocities.\n\nAs for precision bombing of the camps or the rail lines leading to them: that was never a real option. The technology that could ensure the pinpoint bombing of such small targets was never available. It is estimated that anywhere from 50 to 75 percent of the bombs being dropped by Bomber Command were not even hitting the cities they were intended to, which were large targets indeed. And when the American bombers entered the war in force in 1943, they quickly learned that their bombing tactics and accuracy were also sadly deficient. In the first half of 1943, they managed to drop only 14 percent of their bombs within 1,000 feet of the target. By the end of the war the figure had improved considerably but was still just 44 percent. Some 73 percent still fell within only 2,000 feet of the target\u2014nearly half a mile. As for the rail lines, the Germans demonstrated again and again that they could repair bombed rail lines in just a few hours.\n\nHitler's victims were locked up in a vast Continental prison or death camp. In 1942, moral suasion was the only weapon the Allies had against an enemy without morals. Therefore, the world watched helplessly, and for the most part silently, as the remaining Jews of Europe were slaughtered.\n\nFor Hitler, G\u00f6ring, Goebbels, Himmler, and the other top Nazis, there was no turning back from the course they had set. They would fight on no matter what. They knew full well that a German defeat and surrender meant a hangman's rope for them. Each of them might say, with Shakespeare's Macbeth, \"I am in blood \/ Stept in so far that, should I wade no more, \/ Returning were as tedious as go o'er.\"\n\n**In Washington, the Thunderclap** report and its clear endorsement of terror bombing was greeted with some alarm by many members of the air force staff, in particular Major General Laurence S. Kuter, assistant chief of staff for plans.\n\nKuter was one of Hap Arnold's so-called boy generals. This characterization was not always applied kindly, at least by the senior officers in the other services and, indeed, in the U.S. Army itself. The public and press delighted in the appellation, however. In any event, the classification was born of necessity. The army air chief had had no choice but to promote a group of young officers to senior rank. The air services were so new that there weren't enough old-timers to fill the slots. Arnold never had any cause to regret raising relatively youthful men to positions of prominence. Many of them went on to positions of great power in the military and defense establishment.\n\nThe dashingly handsome Kuter was both an articulate spokesman for the military and a man of strong convictions. \"It is contrary to our national ideals,\" he wrote, \"to wage war against civilians.\" Kuter doubtless believed this, but as Spaatz biographer Richard C. Davis points out, it was directly counter to what he had written three years earlier when he helped draft AWPD-1. That directive promoted morale bombing as a viable policy. However, AWPD-1 also warned that bombing of civilians might very well have the opposite effect. It could stiffen the people's will to resist\u2014a point no doubt much influenced by the example of the British during the recent Blitz.\n\nThe 1941 directive also specified that there must be definite signs that the enemy's morale and will to fight on had declined and, further, that there must be signs that the people were losing faith in the military. In addition, all psychological conditions for such a campaign must be in place\u2014a very big caveat. Now, three years later, Kuter was clearly disturbed by what he saw as a strategic wrong turn. \"Our entire target policy,\" he said, \"has been founded on the fact that it was uneconomical to bomb any except military objectives and the German productive capacity.\"\n\nKuter identified a simple fact that was invariably overlooked or ignored by the advocates of morale bombing. \"The bombing of civilian targets in Germany cannot be expected to have similar effects to those which can be expected in a democratic country where the people are still able to influence national will,\" he said. The objects of civilian terror bombing had no way to communicate their misery, fear, and anger to the government in power. And even if they did, their protests would be ignored or stamped out. Only Hitler himself decided the course of action.\n\nHis compunctions about morale bombing notwithstanding, Kuter was compelled by duty to draw up a plan for the bombing of population centers. His suggestion in some ways paralleled or supplemented Thunderclap, but it had one significant difference. Why not, Kuter said, concentrate on a smaller city, one that was \"ancient, compact, historic\" but also had \"as much industrial importance as possible.\"\n\nA dozen such cities should be chosen and announced to the Germans. However, to cause maximum chaos, the Germans should be warned that just one of the designated targets would bear the brunt of the massive attack by a thousand or more bombers. After that, if necessary, another city would be targeted, until all twelve were obliterated.\n\nKuter's \"death by a thousand cuts\" had little chance of causing the collapse of the Third Reich for the very reasons he had put forth himself. The people's misery would not sway the Nazis, who ruled their lives. As the war came closer to home, the vise of the police state closed ever tighter. Then, too, the German people were clearly in no mood to capitulate. Consider the adulation of Goebbels when he toured bombed-out cities: he was cheered as a hero by the survivors.\n\nHap Arnold proposed yet another plan. The air force chief suggested a full week of round-the-clock bombing throughout the Third Reich by all available fighters and bombers. No area was to be spared. Arnold's plan was the least viable and must have disappointed his many admirers. There were nowhere near enough crews, planes, or escorts to implement such a mission. As the top-ranking airman, Arnold should have known this.\n\nEarly in 1944, the American ambassador in London, John G. Winant, had written to Roosevelt objecting to the bombing of civilians. As Winant pointed out to the president, it was understandable that the British might be justified in their nighttime raids on populated areas because the Germans had done the same thing to them. The American reluctance to bomb civilians was therefore understandable, since no Americans cities had been bombed. But, Winant told the president frankly, many of the target selections made by the British and then passed on to the Americans for execution were political judgments and not based on military needs.\n\n\"In the European area I believe that British political considerations are integrated in military decisions and that they do not conform necessarily with United States long term interests,\" said Winant. The Americans should concentrate on aircraft factories, ball-bearing plants, and other such targets, he argued.\n\nThe ambassador was particularly disturbed by the American attacks on Budapest, Bucharest, and Sofia, which theoretically were supposed to destroy the railway marshaling yards but were also directed at the morale of the civilians. He said such raids were ineffective since railroads could be repaired very quickly but the political ramifications would be severe. The Soviets had not bombed the cities, but the Americans had. Winant was no doubt looking to the future and the by then clear Soviet role in the makeup of postwar Europe.\n\nThe State Department also weighed in, saying that the bombing of civilians was causing diplomatic problems. The Joint Chiefs replied that only military targets had been bombed and that, besides, the targets had been picked not by Washington but by the chief of the air staff of the Royal Air Force.\n\n**In spite of** the lip service being paid to precision bombing, everyone knew that the almost constant cloud cover over Europe ensured that targets were obscured most of the time. Civilian deaths were inevitable. But the euphemistic \"precision bombing\" at least provided some sort of moral fig leaf.\n\nWhile Eisenhower promised to respect Spaatz's scruples about morale bombing, he clearly left himself a way out. The agreed-upon bombing priorities would be observed, he told Spaatz, \"unless in my opinion an opportunity arises where a sudden and devastating blow may have an incalculable result.\" The supreme commander soon seemed ready to invoke his proviso. On 9 September 1944, he notified Spaatz that he should be ready to launch Thunderclap at any time. Spaatz accordingly instructed Doolittle to be prepared to reorder the bombing priorities. The Eighth must be ready to bomb Berlin \"indiscriminately.\"\n\nSpaatz's biographer Davis speculates that Eisenhower's order perhaps was prompted by the upcoming Operation Market Garden, which was designed to capture bridgeheads on the Lower Rhine in the Netherlands and open the way for a rapid advance into the Reich itself. The crossing by Allied troops of the great river, with its mythic connection to the German people\u2014it flows through the nation's psyche\u2014combined with a devastating air raid on the capital might be the one-two punch so long sought by the Allies.\n\nMarket Garden (17\u201325 September 1944) was a disaster, a stunning reversal for the Allies. Not only were the Rhine bridges not captured, but troops that should have been used to clear the Scheldt Estuary and open the port of Antwerp had been diverted to Holland. Antwerp, although it was in Allied hands, was not opened to traffic until the end of November.\n\nThunderclap was thus delayed, but only temporarily, and it stayed in the forefront of the strategic bombing plans. In a matter of just a few weeks the \"crisis\" necessary\u2014the imminent collapse of the Third Reich\u2014seemed at hand.\n\n**The Germans staged** one more massive ground offensive: the attempted breakout in the Ardennes on 16 December. The Battle of the Bulge, which was designed to split the Allied armies and recapture the port of Antwerp, was a sobering warning to the Allies, but the 27 December 1944 War Cabinet Joint Intelligence Sub-Committee Report, \"German Ability to Maintain the Present Counter-Offensive,\" was right on target with its assessment of the German breakout. It could not be sustained since Germany could not move the substantial numbers of reinforcements needed into the Ardennes because of the expected massive Soviet push in the east.\n\nAs predicted, the German counterattack was short-lived, and the Wehrmacht retreat into the Reich resumed. Eisenhower, however, never underestimated the enemy, a sound rule for all commanders. In a dispatch dated 7 January 1945 he said, \"There seems to be a kind of fanaticism or 'German Fury' behind the present operations and I have no doubt but that the Germans are making a supreme and all-out effort to achieve victory in the West in the shortest possible time. The Ardennes battle is in my opinion only one episode and we must expect attempts in other areas.\"\n\nThere would be no other major German land offensive, but Eisenhower would have been most unwise not to have considered the possibility and planned accordingly. His assessment was made even more difficult because of the reticence of the Soviets to show their hand or confide in their British and American allies.\n\nThe supreme commander and his colleagues had long chafed at the lack of information about Soviet movements in the east and the Russians' almost paranoid hesitance to put anything important in writing. Someone always had to be dispatched to Moscow to deal with them directly. Winston Churchill, Anthony Eden, Harry Hopkins, and Cordell Hull, among others, had all made the pilgrimage, some more than once.\n\nNow, as the war seemed to be heading into its final stages, some news from the Russians about an offensive would be welcome. In turn, Eisenhower would be glad to exchange information with his Soviet counterparts. It would thus be necessary for another face-to-face meeting to work out a more coherent strategy between the two uneasy Allies.\n\nOn 14 December, American ambassador Averell Harriman met with Stalin to assure him that Eisenhower \"was very anxious to operate in concert with the Russians and to help the Russian armies whenever such support might be needed.\"\n\nEisenhower, naturally, had to remain at his headquarters in France, but on 23 December 1944, Roosevelt cabled Stalin that Eisenhower would be sending a representative to the Soviet Union \"to discuss with you the situation in the West and its relation to the Russian front in order that information essential to our efforts may be available to all of us.\" Eisenhower's choice was Air Marshal Sir Arthur Tedder, deputy supreme Allied commander and head of all Allied air operations.\n\nOn 15 January 1945 Tedder met with the Soviet premier. The wily Stalin said that even though there was no Soviet-Allied treaty it was in the self-interest of the Allies to ensure that the Soviet Union was not annihilated by the Nazis, just as it was in the self-interest of the Soviet Union to ensure the survival of the West in the struggle against Nazism.\n\nStalin was particularly concerned that the German communications system was such that it was an easy matter to move troops between the two fronts. Even now, Stalin said, the Germans must be moving forces from the west to the east, and although there was no specific mention of Dresden, it was clear to all that Wehrmacht men and mat\u00e9riel would have to pass through the Saxon city to reach the Eastern Front.\n\nAccording to the Air Force Historical Office, \"Tedder outlined to Stalin the 'application of the Allied air effort with particular reference to strategic bombing of communications as represented by oil targets, railroads and waterways.' There was also specific discussion of the problem that would face the Russians if the Germans attempted to shift forces from the West to the East and of the necessity of preventing this possibility.\"\n\n**The bad weather of** January and February 1945 kept many of Bomber Command's planes grounded, but any break in the weather was seized upon by Harris, who had already begun to look farther east for targets.\n\nBomber Command had made several deep penetration raids, one as early as October 1940. The first was an unsuccessful effort to bomb the \u0160koda arms works at Pilsen, in Czechoslovakia. Other small raids followed, but they were chiefly calling cards, part of the plan to force the Germans to scatter their antiaircraft defenses all over Europe. In April 1943 another attempt was made to destroy the \u0160koda works, but the bombers mistakenly bombed an asylum seven miles from the target. Other raids on the \u0160koda factory were equally unsuccessful.\n\nBomber Command had also ranged as far as Italy in 1943, bombing both Turin and Milan. These major northern Italian industrial cities were legitimate targets, but the most notable casualty of the raids was the famous Milanese opera house La Scala\u2014not the primary target, the Fiat factories.\n\nTo the end, Harris believed wholeheartedly that his avowed plan to destroy all of the cities of the Reich was the surest way to end the war. But he now had to give way to Portal, who directly ordered him to commence attacks on the oil targets, raids that Speer would characterize as fatal blows to the German war machine.\n\nThe first Bomber Command raid on a major eastern German oil facility was at 'Leuna, near Leipzig, on 6\u20137 December 1944. This RAF raid was seven months after the first American raids on oil facilities in eastern Germany\u2014the series of raids on 12 May that Speer said had decided the technological war.\n\nBut there were no further major British raid on oil targets until 14\u201315 January 1945, when Bomber Command returned to Leuna. This was partly because of the foul weather and partly because planes were diverted to pound the Germans who had broken out in the Ardennes.\n\nHowever, directives from Portal or no, Bomber Harris never lost sight of his chief goal, as his detractors point out. On the night of 2\u20133 January he staged one of the great area raids of the war. Nuremberg\u2014the city of the Meistersingers, with its two thousand medieval houses\u2014was obliterated by over 500 Lancasters.\n\nHarris was careful to satisfy Portal's demands, however, and the RAF resumed deep penetration raids into eastern Germany and western Czechoslovakia in search of oil targets. P\u00f6litz, near Stettin, and Zeitz, near Leipzig, and Br\u00fcx, fifty-five miles from Prague, were all heavily bombed and largely destroyed. If there was any possibility of flying, Harris launched his bombers. But after the P\u00f6litz raid on the night of 8\u20139 February, the weather was again uncooperative. Bomber Command mounted no more serious offensives until Dresden.\n\n**The debate as to** which policy was more effective\u2014more-or-less blind bombing as practiced by the RAF or the much touted precision bombing of the Eighth Air Force\u2014has raged since the bombing campaigns began. The British, under Bomber Harris, felt no reason to explain or apologize for their form of aerial warfare. The Americans, while taking the moral high ground (or so it seemed to many of their colleagues in the RAF), never returned with their bomb loads if they could not find the designated target. They simply bombed what they could find. If it was a city, so be it.\n\nGreat claims for American precision bombing were made during World War II. \"Our bombers can drop a bomb in a pickle barrel!\" trumpeted the Americans. \"Of course we can,\" one airman wryly observed. \"We just have to find the barrel.\"\n\nHere was the crux of the problem: how to find the target and bomb it when the pilot and the bombardier could not see it. Neither the Americans nor the British ever came close to achieving pinpoint or precision bombing. Even the Norden bombsight, which has been much celebrated as having ushered in a new and more effective bombing policy, was accurate only in direct proportion to the visibility of the target on the ground.\n\nThus began the search for navigational systems that would provide a solution to the problem, and as each new one was unveiled it was hailed as the answer. But their drawbacks became apparent almost as soon as they were deployed.\n\nThe first was the system called Gee. Using this system the navigator relied on radio signals transmitted from a master station and two slave stations to plot his course. Theoretically, the plane's position was at the intersection of the lines on a special Gee chart. It was hoped that the device would be able to direct the planes to within a mile or so of the city to be bombed. Heretofore, only one in ten Bomber Command planes had bombed within five miles of the target.\n\nThe major drawback to Gee was that its range was only 350 to 400 miles. Further, once the frequencies had been worked out by the Germans it could be easily jammed. The limited range still put the cities of the Ruhr in reach, as well as many cities beyond. Although the Germans could devise jamming techniques\u2014after all, they had used similar systems to bomb England\u2014there would be at least a five-month window of opportunity.\n\nGee did not prove to be as effective as predicted. There were glitches in the transmission of the radio signals, and visual landmarks still were necessary to guide the bombers after Gee had brought them to the supposed target.\n\nBut the system was helpful in other ways. With the aid of Gee it was easier to concentrate the bomber streams, making them more defensible against night fighters. Even more important, the return flight home was no longer a nightmare that could end in fiery death or in the freezing waters of the English Channel or the North Sea, as these flights often did. The signals became stronger as the planes neared their home bases, making the landing fields easier to locate.\n\nAs predicted, by August 1942 the Germans were jamming the Gee frequencies, shortening its effective range by at least a hundred miles. But something new was already waiting in the wings: again, a device not unlike the system used so successfully by the Germans during the Blitz. This was Oboe, which sent radar signals from two ground stations to an aircraft and thus plotted its course and position. When the aircraft reached a preset position, the target, a signal was sent for it to unload the bombs.\n\nThe drawbacks of the Oboe system were obvious. Like Gee, the range was fairly short because of the curvature of the earth. And the bombers had to fly a steady course, with little or no deviation, which made it impossible for them to take evasive action when attacked by the German fighters or when they ran into heavy antiaircraft fire.\n\nAs Arthur Harris observed in his memoirs, the limitations of both Gee and Oboe necessitated yet another change in strategy. Instead of hundreds of bombers finding the target individually, a few planes\u2014Halifaxes, Lancasters, and, best of all, the new high-speed Mosquitoes\u2014equipped with the latest navigation systems could lay out a path to the target, dropping aerial route-marker flares to guide the way. Once the target was located, marker aircraft dropped massive incendiary bombs, which showed the bomber fleets where to release their ordnance.\n\nThis elite group that was formed to lead the way was christened the Pathfinder Force, and if it was not quite the longed-for turning point for Bomber Command, its actions did indeed improve the accuracy of aerial bombardment and herald the imminent destruction of most of Germany's cities.\n\nBy early 1945 a yet more advanced navigation system, loran (longrange navigation), was made available to Bomber Command. The navigator was able to determine his position by locating the point where a ground wave and a sky wave intersected. The sky wave was not dependent on the curvature of the earth, since it was bounced off the ionosphere, and the ground wave had a much longer range than other systems, 600 to 900 miles. The loran system was employed by the Pathfinder Lancasters and the marker Mosquitoes for the first time on the Dresden raid.\n\nAnother step forward in actual bombing practice came with the introduction of H2S (called H2X by the Americans), a self-contained radar navigation system that could project an image of the ground below on a cathode-ray tube in the plane itself. It was, admittedly, a rough image of the terrain, but H2S did afford a view of the proposed target\u2014assuming, of course, that the bomber stream was over the designated target.\n\n**By the end** of January 1945, with the Russians advancing rapidly in the east, the time seemed ripe for the revival of the plan known as Operation Thunderclap\u2014a massive raid on Berlin. Bomber Command had not staged a major raid on the German capital since the disaster of 24\u201325 March 1944, when 72 bombers were lost, 8.9 percent of the total force.\n\nThe British Mosquito bombers had continued to take the war to the citizens of the German capital, and during one period, they attacked Berlin on thirty-six consecutive nights. These were not solely harassing raids. The plane, which could carry a 4,000-pound bomb, was capable of doing real damage, and one measure of its effectiveness is a telling entry in Joseph Goebbels's diary. \"In the evening we have the regulation Mosquito raid on Berlin,\" he wrote. \"During the night the cursed Englishmen return to Berlin with their Mosquitoes and deprive one of the few hours' sleep which one needs more than ever these days.\"\n\nLarge-scale bombardment of Berlin had been delegated to the Americans, who averaged one major daylight raid a month. No city was as well protected and thus more feared than the city known to the bomber crews as \"the Big B.\" On 29 April 1944, the Americans lost 63 planes and another 432 were damaged out of a total effective force of 618 aircraft.\n\nAs the Germans withdrew from the west, the removal to the Fatherland of antiaircraft batteries was one of their highest priorities. The major cities were ringed with more and more of these deadly weapons. Thus the cities of Germany, in particular Berlin, became more, rather than less, dangerous as the Western Front contracted. In a series of raids throughout northern Germany on 6 August 1944, for example, 531 out of 929 effectives were damaged by enemy fighters or flak. In raids on 7 October 1944, over half of an effective force of 1,400 bombers was damaged and 40 were shot down.\n\n**Ten days after** Tedder's meeting with Stalin, on 25 January 1945, the Joint Intelligence Sub-Committee of the War Cabinet had ready a proposal for closer Soviet-Allied cooperation on the Eastern Front. Entitled \"Strategic Bombing in Relation to the Present Russian Offensive,\" the report recommended a four-day raid on Berlin in which 25,000 tons of bombs would be dropped on the German capital.\n\nNo one thought that this new version of Thunderclap would lead directly to surrender, but it was expected to generate such numbers of refugees fleeing from Berlin along with the millions fleeing the Russians that it would \"create great confusion, interfere with the orderly movement of troops to the front, and hamper the German military and administrative machine.\" Further, the raid would \"materially assist the Russians in the all important battle now raging on the Eastern Front and would justify temporary diversion from attacks against communications or indeed any targets other than oil plants or tank factories.\"\n\nChurchill, in a 25 January meeting with Sir Archibald Sinclair, secretary of state for air, asked during a general discussion of the RAF what the plans were for \"basting the Germans in their retreat from Breslau.\" The prime minister was concerned about the upcoming Yalta Conference, at which an important issue would be how the British and American air forces were planning to support the now-rapid Russian advance into the Third Reich.\n\nThe next day Portal told Sinclair that oil was still the number one priority. After that the RAF could assist in harassing the retreating German troops. This would move such actions up the list, above the previously decided targets, the jet-engine factories and the submarine yards.\n\nAfter meeting with Portal, Sinclair replied to the prime minister. He recommended that the tactical air forces and not the heavy bombers be used to attack the Germans retreating from Breslau.\n\nSinclair felt that the heavy bombers should continue the attacks on the German oil industry. Such attacks, he pointed out, would benefit all the Allies, including the Russians. However, since attacking small targets depends very much on good weather and attacking large targets does not, he advocated the bombing of Berlin and other large east German cities such as Leipzig, Dresden, and Chemnitz.\n\nAll of these cities, Sinclair pointed out, were not just administrative centers but also the centers of vital rail and highway networks through which most of the enemy's men and mat\u00e9riel had to pass.\n\nChurchill's response was immediate and Churchillian. \"I did not ask you last night about plans for harrying the German retreat from Breslau,\" he testily wrote to Sinclair. \"On the contrary, I asked whether Berlin, and no doubt other large cities in East Germany, should not now be considered especially attractive targets. I am glad that this is 'under consideration.' Pray report to me tomorrow what is going to be done.\"\n\nSinclair immediately called Bottomley about the matter, and the next day, 27 January, Bottomley wrote to Arthur Harris about Bomber Command attacking Berlin, Dresden, Chemnitz, and Leipzig.\n\nHarris's biographer Dudley Saward was hardly a disinterested party\u2014he worked closely with Harris throughout the war\u2014but he is certainly right that the Dresden decision did not originate with Harris but at the highest levels of command, and Harris was provided with a paper trail to explain his actions, particularly in the final paragraph of Bottomley's message: The chief priority remained German oil production, but next in order came attacks on Berlin, Leipzig, and Dresden, designed to create chaos among the refugees that had flooded into those cities and to disrupt troop movements and reinforcements to, or retreat from, the Russian front.\n\nBottomley enclosed a copy of the 25 January Joint Intelligence Sub-Committee report, which he said had not yet been considered by the Chiefs of Staff. In his note, he said that while Portal did not feel that Thunderclap would be effective in Berlin, subject to the \"overriding claims of oil and the other approved target systems, there should be one large attack on Berlin and related attacks on Dresden, Leipzig, Chemnitz, or any other cities where a severe blitz will not only cause confusion in the evacuation from the East but will also hamper the movement of troops from the West.\"\n\nWhile the priorities (oil and other approved target systems) were to be observed, enough leeway was built in to satisfy everyone, and on 27 January Sinclair wrote reassuringly to Churchill. While oil would remain the chief priority, the Air Staff had put into effect plans to bomb Berlin, Dresden, Chemnitz, and Leipzig and other cities in the east where massive air raids would destroy roads and railways and thus disrupt or halt both the massive movements of civilians and any reinforcements from the Western front.\n\nThe next day, 28 January, Churchill acknowledged without comment the receipt of Sinclair's memorandum. That same day Portal, who was to accompany Churchill to Yalta, met with Bottomley and Spaatz to discuss the plans.\n\nEverything was now in place for Thunderclap. When Churchill left for Yalta, via Malta, on 29 January, he was assured that his call for \"basting the Germans in their retreat from Breslau\" had been heeded by the air barons, and on 31 January, Bottomley sent a cable to Portal, in Malta, outlining for Churchill the \"order of priorities for Strategic Air Forces.\"\n\nThe chief targets remained the synthetic oil plants. Next in order came the attacks on Berlin, Leipzig, and Dresden, designed to disrupt civilian evacuation and hamper all troop movement. Attacks on communications\u2014rail lines, marshaling yards, highways, bridges, and the like\u2014were third in importance.\n\nThe new jet planes were causing increasing anxiety in Bomber Command, and thus attacks on jet-aircraft plants and airfields and communications in southern Germany were added to the list.\n\nOther targets (tank factories, submarine yards) were to be considered marginal, although these might be \"substantial\" since they constituted convenient tactical \"filler\" targets in those areas of priority oil targets when the primary target could not be attacked.\n\nThe report also included a directive that would turn out, in the event, to be used as evidence to support the accusations of Allied barbarity during the Dresden raid. The escort fighters were to attack all rail movement after their primary task of escorting the bombers had been carried out.\n\nThere was nothing unusual in this further assignment for the fighters, if it can be called an additional duty. A primary function of fighter planes was and remains the strafing of enemy troops and rail and road traffic. And since all rail lines in and out of Dresden paralleled streets and roads and ran through heavily built up areas, it was to be expected that civilians would be exposed to the fire from the American fighters.\n\nWith an eye toward Yalta, Bottomley concluded by pointing out that the Russians \"may wish to know our intentions\" concerning the targets as outlined and which lay just a few miles to the west of their lines.\n\nMeanwhile, discussions continued between the Americans and the British about how best to support the Soviets. On 1 February 1945, \"Strategic Bombing in Relation to the Present Russian Offensive\" was promulgated by Air Marshal Sir Douglas Evill, vice chief of the air staff. Of particular interest was the following:\n\nEvacuees from German and German-Occupied Provinces to the East of Berlin are streaming westward though Berlin itself and through Leipzig, Dresden and other cities in the East of Germany. The administrative problems involved in receiving the refugees and redistributing them are likely to be immense. The strain on the administration and upon communications must be considerably increased by the need for handling military reinforcements on their way to the Eastern Front. A series of heavy attacks by day and night upon these administrative and control centres is like to create considerable delays in the deployment of troops at the Front, and may well result in establishing a state of chaos in some or all of these centres. It is for these reasons that instructions have been issued for heavy scale attacks to be delivered on these centres at the earliest possible moment, in priority immediately after that of the important oil producers. The justification for the continuance of such attacks would be largely reduced if the enemy succeeded in stabilising his Eastern Front. Successful attacks of this nature delivered at once, however, my well prevent him from achieving this aim.\n\nIn other words, with the Russians moving rapidly westward, everything that could be done by Allied airpower to prevent reinforcements from the west must be done. Events were rapidly overtaking the planners. Something approaching a total breakdown might be brought about by day and night bombing of the eastern German cities that were already overwhelmed by the hundreds of thousands of refugees fleeing the Russian advance.\n\nOn this same day, 1 February, the Russians were only fifty miles from Berlin and the capital was declared a fortress city. It was to be defended to the death.\n\nThis air staff note, code-named Fleece 75, was sent out to the Chiefs of Staff at Malta on 2 February. This message was to be used to coordinate the Allied air offensive with the Russian ground offensive on the Eastern Front. The bombing priorities were listed as follows:\n\n1. Oil\n\n2. Communications\u2014particularly \"focal points of communication in the evacuation areas behind the Eastern Front, namely Berlin, Leipzig, Dresden, and Chemnitz or similar areas\"\n\n3. Tank factories\n\n4. Jet fighter production\n\n5. U-boat construction and assembly\n\nKuter, who in spite of his two-star rank and relative youth had been deputized by Arnold to represent him at Malta and Yalta, had already cabled acting air force commander Barney Giles from Malta, listing the targets in order of priority as agreed to by Portal, Bottomley, and Spaatz. The second component of the target list was described a bit more fully, however: \"Attack of Berlin, Leipzig, Dresden and associated cities where heavy attack will cause great confusion in civil population from East and hamper movement of reinforcements from other fronts will be next in order of priority for air forces operating from the United Kingdom.\"\n\nAlso on 2 February, in a message to Spaatz marked \"Top Secret\u2014Personal,\" Major General F. L. Anderson, Spaatz's personal representative at Malta, told his boss that General Marshall wanted to be sure that no Russians were inadvertently attacked by American bombers on the missions to eastern Europe. In addition, said Anderson, Marshall had suggested that \"in conjunction with our attacks on Berlin and associated cities attacks on Munich would probably be of great benefit because it would show the people that are being evacuated to Munich that there is no hope. Perhaps the Fifteenth Air Force could take this on in conjunction with the Eighth's attacks on Berlin.\"\n\nSpaatz immediately sent a message to Generals Twining and Eaker of the Fifteenth Air Force, informing them that the British were continuing their nightly Mosquito raids on Berlin and that Bomber Command planned to attack Leipzig and Dresden. The Eighth would attack Berlin when weather permitted. The Fifteenth, meanwhile, was \"to attack [Munich] when tactical and other conditions are appropriate and within your transportation priority.\"\n\nThis promised massive strike against Berlin was scheduled by the Eighth Air Force for the afternoon of 2 February, but it was scrubbed because of the weather. If the weather had been clear some 120 miles to the southeast in Saxony, the entire Dresden controversy would perhaps have never engaged the attention of military historians to quite the degree it has. For Dresden was an alternate target of the planned thousand-bomber raid by the Eighth Air Force on 2 February. There would have been massive destruction to be sure, but the city would have been spared the firestorm.\n\nThe next day, 3 February, the weather was more cooperative, and Carl Spaatz, who had for the most part stuck to the policy of bombing oil targets and military installations, did Bomber Harris one better in the category of area bombing. Although the target was officially categorized as \"marshalling yards,\" the purpose of the raid was to create maximum chaos in Berlin, which was overrun with refugees from the east. More than 1,000 B-17s, with 600 P-51 escorts, dropped 2,267 tons of bombs on the center of the city.\n\n**The thousand-bomber** American raid on Berlin was the heaviest raid of the war on the German capital by either the RAF or the U.S. Army Air Force. A vast swath of the city was destroyed, including Hitler's headquarters.\n\nBut oil-production facilities were not forgotten on this day by the Americans. Another 434 B-24s were sent against the oil refineries at Magdeburg. Two-thirds of the planes failed to find the oil targets, but with the aid of H2X radar they located the city and emptied their bomb loads blindly through the cloud cover.\n\nOn 5 February, Spaatz cabled Kuter in Yalta: \"All out effort will be placed against targets mentioned whenever weather conditions permit. Necessity for liaison party with various Russian Armies becomes increasingly apparent. On recent attack in Berlin our fighters were practically over Russian lines and destroyed a number of German airplanes taking off from an airdrome east of Berlin.\"\n\nThe Eighth returned to its appointed rounds, the oil plan, on 6 February, with a massive raid directed at production facilities at L\u00fctzkendorf, B\u00f6hlen, and Magdeburg. The expected good weather did not materialize, and the bombers were unable to find the primary targets. The secondary targets and targets of opportunity were obscured as well, and the raids were conducted using H2X. Hardest hit were Chemnitz and Magdeburg.\n\nAlthough the Yalta Conference was being convened to plan for a postwar Europe, the date of the end of the war was by no means certain. Indeed, Spaatz wrote to Arnold on 7 January, \"Our estimate of the situation concerning the whole German war proposition does not lead up to the conclusion that German strength will crack in the near future.\"\n\nThe Germans had pulled one great surprise with the Ardennes offensive; and Allied leaders, with good reason, were much concerned about two new German weapons: the snorkel U-boat and the jet fighter.\n\nThe snorkel device allowed the submarine to bring in and exhaust air without surfacing, which made it far less vulnerable to detection and greatly increased its range. The new U-boats were also faster and could be turned out relatively quickly. If sufficient quantities could be produced, the transatlantic shipping lanes would again be at risk and the end of the war delayed by many months.\n\nThe Me 262 jet fighters were appearing in increasing numbers and were having some success against Eighth Air Force bombers. They were clearly a formidable weapon. Moreover, unlike the Fw 190s and the Me 109, which required high-grade aviation fuel, the Me 262 burned low-grade fuels such as kerosene, which was in ample supply.\n\nTherefore, Spaatz began to argue in January 1945 that the heavy bombers should return to their primary role of strategic bombing and that the bombing of jet-aircraft production facilities be accorded as much importance as other targets\u2014in particular, oil. Eisenhower, who still very much had the German breakout in the Ardennes on his mind, felt that the bombers should continue to support the ground troops at this time. Spaatz, with the help of Doolittle and Bedell Smith, had his way, and Eisenhower reluctantly agreed.\n\n**At Malta, there** surfaced one of those plans that are the bane of serious military strategists. Although unlikely to work, they take up much energy and time but must be attended to for political reasons. This one, however, was first proposed by Carl Spaatz, a serious military strategist indeed.\n\nThe Americans floated the idea of flying radio-controlled, unmanned \"war-weary\" bombers loaded with 20,000 pounds of high explosives into industrial targets (that is, cities) in Germany. This was actually a dustedoff plan, called Aphrodite or Weary Willie, that Spaatz had devised in June 1944 as part of the Crossbow campaign against the V-1 and V-2 sites.\n\nAt one test of such a weapon, at Shoeburyness, a pilotless B-17 carrying 20,000 pounds of Minol-2, or Torpex, was crashed. It showed that a B-17 so loaded with high explosives could do nine to twelve and a half times the damage of a 4,000-pound bomb. If it was crashed into a built-up location, the damage would be catastrophic, destroying everything within a radius of 145 yards\u2014a total area of 66,000 square yards, or more than 13.5 acres.\n\nBoth the air force and the U.S. Navy had been involved in testing and launching several missions against various sites on the Continent, using worn-out B-17s and B-24s. A pilot and copilot would get the plane airborne, set the remote controls, and bail out. Escort aircraft would then guide the plane by remote control to the target.\n\nA half dozen or so Aphrodite missions using war-weary planes took place in 1944, but none was successful and several of the pilots were killed, most notably a navy lieutenant named Joseph P. Kennedy Jr., the son of the former ambassador and the older brother of the future president. He took off in a navy B-24 loaded with 21,000 pounds of high explosives on 12 August 1944. Before he and his copilot could turn the plane over to the two control planes that would guide it to the target, a V-2 launch site in France, and bail out, the bomber exploded.\n\nAt Malta, Aphrodite was scuttled by the British, who were still being bombarded by the V-weapons and who worried that the Weary Willies might embolden the Germans to use their own war-weary bombers to stage reprisal raids against British cities, particularly London.\n\nThe plan would not die, however, and its most important advocate turned out to be the American commander in chief himself, Franklin Roosevelt. On 29 March, the president cabled Churchill that his Chiefs of Staff had assured him that technological advances in remote control would make the planes more accurate, thus presumably sparing civilians.\n\nFurther, said the president, \"many lucrative targets in the industrial areas in Germany can be leveled and the German war effort correspondingly weakened.\" The Germans, said Roosevelt, did not need the impetus of drone bombers filled with high explosives to attack England. \"In addition,\" he mused, \"combat experience with this type of weapon on the Continent will make possible the most effective use of this type of weapon in the battle against the highly concentrated areas of the Japanese homeland.\"\n\nChurchill felt he had to refer Roosevelt's cable to the British Chiefs of Staff for a decision, or so he said. He did not respond until 14 April 1945, by which time Roosevelt, who had died suddenly, had been succeeded by Harry S. Truman. The message is pure Winston Churchill.\n\n\"If the United States military authorities really consider this practice necessary to bring about the end of the German war we will not dissent,\" he said. However, he pointed out that the war situation had turned decidedly in favor of the Allies and \"these great explosions in German cities\" no longer had their former importance.\n\nAnd the retaliatory argument was still strong with the British. As the prime minister said, if the Germans also had a number of \"war-weary bombers that could make the distance, London is the obvious and indeed the only target, and even a few very big explosions in London would be a very great disappointment to the people.\"\n\nHe reminded Truman that so far 1 in 131 Londoners had already died in air attacks, a figure higher than that of any other locality on the Allied side. Presumably, he was not counting the Soviet Union.\n\nChurchill closed by saying, \"Having put the facts before you I leave the decisions entirely in the hands of your military advisers, and we shall make no complaint if misfortune comes to us in consequence.\"\n\nThe Weary Willie concept compared favorably, if one can use that word, with a brainstorm of Lord Selbourne, of the Ministry of Economic Warfare. On 28 July 1944 he bypassed all chains of command and wrote directly to Eisenhower. He recommended that fifty Lancasters be sent to the Ruhr that week to drop a half million incendiary devices known as the Braddock. This was an extremely small bomb attached to a card that served as a parachute. Printed on the card were directions in eleven languages as to how to use it. All the finder had to do was plant the bomb in some flammable place and press a red button. The would-be saboteur then had half an hour to escape before the bomb went off and everything went up in flames. The idea was that slave laborers and left-wing opponents of the Nazi regime, as well as hundreds of thousands of ordinary Germans who were disillusioned by the Nazis and the Reich's declining military fortunes, would use the small firebombs to commit wholesale sabotage and help bring down the regime.\n\nEisenhower preferred to drop real bombs rather than Braddocks and turned down the idea, but the supreme commander did leave the door open if the time ever became ripe.\n\nSelbourne tartly commented, \"This is again 'jam tomorrow.' \" He also made no attempt to hide his scorn for \"certain distinguished officers who have never concealed their disbelief in 'BRADDOCK.' \"\n\nBut in February 1945, the Braddock plan was dusted off and given a try. There were no reports of arson or sabotage, although the police chief of Mannheim did note that some of the incendiaries had been dropped in his area and warned about their danger to \"children at play.\" He also said that anyone who let one fall into the hands of foreigners or did not report it to the police would be punished.\n\n**At Yalta, General Aleksei I. Antonov** , chief of staff of the Soviet army, briefed the American president, the British prime minister, and their staffs on the situation on the Eastern Front and the Russian operational plans for the succeeding months.\n\nAfter a long and discursive account of the ground campaign, Antonov turned to the question of the air war in the east and how the Allies could best support the advancing Soviet armies. He asked the British and Americans \"in particular to paralyze the junctions of Berlin and Leipzig.\"\n\nThe Russians were naturally keen to have Allied air support, but they were equally anxious to avoid friendly fire as their troops moved westward into Germany. While the accuracy of the bombers had marginally increased, no one believed that lines of troops 25,000 feet below heavy cloud cover were not in great danger of being wiped out unless protected by a fairly wide safety zone.\n\nNow, with the Soviet troops so close to the target cities, a so-called bomb line would have to be created to protect Antonov's troops from being killed by errant bombs from the British and American planes, which could in just a matter of minutes stray over the Soviet advance lines.\n\nThe Americans, British, and Soviets agreed on the bomb line, and the operational date set for it to go into effect was 8 February. This limit line or prohibition zone would run from Stettin to Berlin to Dresden and on to Pardubitce, Brno, Vienna, Maribor, and Zagreb. All of these points were to be \"inclusive to the Allied Strategic Air Forces.\" The line also extended to Sarajevo, P\u00e9cs, the eastern border of Albania, and the southern border of Bulgaria.\n\n\"Inclusive\" meant, of course, that all of these cities were to be considered suitable bomb targets. The line was to be adjusted as the Soviets moved west, and the Allies could bomb in the east in exceptional circumstances\u2014but with not less than twenty-four hours' notice to the Soviets. The zone as refined was to be sixty kilometers in advance of the forward troops of the Soviet army, about thirty-five miles.\n\nThe limit-line agreement was signed by Sir Charles Portal, marshal of the Royal Air Force, S. A. Khudyakov, marshal of aviation of the Red Army, and Laurence S. Kuter, major general of the U.S. Army Air Forces. The two-star was not only very young, but he was outranked by three full grades by most of the men he had to deal with it at Malta and Yalta, and he was made painfully aware of it. \"Without you,\" he wrote to Hap Arnold, \"we are just tolerated from bottom to _top.\"_\n\nBut he rose to the occasion. He did, after all, have the backing of Arnold, a five-star general who could hold his own with any military grandee from Great Britain or the Soviet Union. Then, too, there was the overwhelming might of the American air arm behind Kuter. Thus he did not hesitate to speak his mind.\n\nOn 8 February, Khudyakov sent along the agreement to Kuter \"as confirmed by the Soviet High Command.\" Kuter quickly realized that there were changes \"concerning the announcement of the limiting line, and the agreement required to operations by the British and U.S. Army Air Forces to the east of the designated line.\" He rejected the changes and informed Marshal Khudyakov that \"the U.S. Air Forces will continue to operate under the arrangements in effect prior to the 6th of February 1945.\" He pointedly concluded, \"This represents the views of the United States Chiefs of Staff.\"\n\nAlso on 8 February, Major General S. P. Spalding, acting chief of the U.S. military mission in Moscow, sent to Major General H. V. Slavin, assistant chief of staff of the Red Army, \"a list of strategic targets subject to bombardment by the 8th Air Force.\"\n\nOil still headed the list, but the communications targets were second. Of these, Berlin was first, Leipzig was second, and Dresden was third. It thus seems clear that Dresden was considered to be if not the equal of Berlin and Leipzig, an important, even vital, military target. The only remaining question was how soon Thunderclap or some variant could be put into effect. In the event, it was only a matter of a few days.\n\nAs the earlier Thunderclap report put it, \"Immense devastation could be produced if the entire attack was concentrated on single big town other than Berlin and the effect would be especially great if the town was one hitherto relatively undamaged.\"\n\nHeavy cloud cover, snow, and winter storms hampered both the British and the Americans for the ten days after the large American raid on Berlin on 3 February, although both Bomber Command and the Eighth Air Force had two notable successes. The Americans staged a massive raid on Chemnitz, just forty-five miles from Dresden, and the British put the synthetic oil plant at P\u00f6litz, near Hamburg, permanently out of commission.\n\nThen the weather picture changed. Meteorologists reported that favorable conditions beginning on 13 February might finally ensure that the long-planned triple blow against a large German city\u2014Thunderclap\u2014might be possible at last.\n\nSpaatz had already notified the American military mission in Moscow that Berlin, Leipzig, Chemnitz, and Dresden were on the priority list of communications targets. Berlin had already been devastated by the Eighth Air Force on 3 February and would not be bombed again by the Americans until two weeks after Spaatz cabled the Russians his intentions. Leipzig had also suffered heavy raids and was bombed hardly at all for the remainder of the war by either the Eighth Air Force or Bomber Command. And Bomber Command would not revisit Chemnitz, albeit with a massive raid, until early March 1945.\n\nOf the cities mentioned by Spaatz, only Dresden would appear to be a serious target in mid-February 1945. Therefore, on 12 February, he cabled the American military mission that \"weather permitting, Eighth Air Force will attack Dresden Marshalling Yard on 13 February with a force of 1,200 to 1,400 bomber planes.\" The Americans would lead off with a massive daylight raid at midday and the British would follow it up that night with two more assaults, about three hours apart. The message was passed on to the Russians.\n\n**The picture-book** capital of Saxony, which was relatively untouched by the ravages of a war that was now in its sixth year, would now join its sister cities of the Third Reich as a prime target of Allied airpower. The narrow streets, the flammable ancient buildings, and the enormous congestion caused by half a million refugees had created a potential bonfire on the Elbe that was waiting to be lit.\n\n_Visitors to prewar Dresden often referred to the city as \"the Florence on the Elbe. \" The Zwinger Complex, the cathedral, Theaterplatz, the royal palace, and the Semper Opera House, built over three centuries in styles ranging from Renaissance to Baroque to rococo to neoclassical, constituted one of the most beautiful and harmonious architectural assemblages in the world_.  \nWALTER HAHN\n\n_The twentieth century revealed a darker side of Saxon society. Dresdeners were early and enthusiastic supporters of the Nazi party and German expansionism_. TOP: _The Sturmabteilung, the SA, parades in honor of Hindenburg and Hitler on February 1, 1933_.\n\nBOTTOM: _With Germany triumphant in Europe, Dresdeners turned out in August 1940 to salute the military at a parade through the Schlossplatz_. WALTER HAHN (TOP); HEROLD (BOTTOM)\n\n_The Altmarkt, the great square in the Altstadt, was for centuries the epicenter of Dresden commercial life_. TOP: _The square as it appeared in 1943_.\n\nBOTTOM: _The Altmarkt with the tower of the Kreuzkirche, the oldest church in Dresden (right); the Rathaus, or town hall (left); and the statue of Germania, the symbol of German pride and nationhood_.  \nWALTER HAHN (TOP)\n\n_Reconstruction of the Altmarkt into a semblance of its prewar aspect took almost twenty years after its destruction on the night of February 13\u201314, 1945. The square as it appeared in 1956 (top), in 1951 (left), and in the 1960s (above, right)_.  \nw. M\u00d6BIUS (LEFT)\n\n_The wreckage of the Grosse Meissner-Strasse, on the right bank of the Elbe in Dresden Neustat, graphically illustrates the vast area covered by the firestorm_.  \nW. PETER SENIOR\n\n_The Wallpavillion, or Rampart Pavillion, the most beautiful of the three great Baroque entrances to the courtyard of the Zwinger, Augustus's pleasure palace and museum. The Zwinger was completely destroyed in the three-part raid.  \n_ W. M\u00f6bius (top);\n\nR. PETER SENIOR (BOTTOM)\n\n_The Frauenkirche, built 1726\u20131734 by Protestant Dresdeners in part to protest the conversion to Catholicism of the Augustuses, became the symbol of the city for over two hundred years. It withstood the bombing of February 13\u201314, but collapsed February 15 when the intense heat melted its sandstone supports_.\n\n_The extent of the devastation caused by the firestorm as seen from the tower of the Rathaus in the Altstadt_.\n\n_The firestorm temperatures ranged as high as 1,500 degrees centigrade, which twisted steel girders and melted street lamps_.  \nR. PETER SENIOR\n\n_Nothing could survive in the inferno that swept across Dresden during the night of the raid. These two incinerated, shrunken corpses were found in the ruins_. R. PETER SENIOR\n\n_Overwhelmed by the number of unburied bodies and faced with the threat of a catastrophic outbreak of disease, the authorities were forced to burn the victims instead of transporting them out of the city for burial in a mass grave. A giant pyre was erected in the Altmarkt, and the burning of the corpses began on February 25, 1945_. WALTER HAHN\n\n_Bodies were brought by wagon to the Altmarkt, where they were stacked, doused with gasoline, and set afire in the very shadow of the statue of Germania_. WALTER HAHN\n\n_The ruins of Frauenkirche, seen here, in the winter of 1965, served for half a century as a reminder of the horrors of war and the suffering of the people of Dresden_. R. PETER SENIOR\n\n_In February 1990, just four months after the fall of the Berlin Wall and the first moves toward German reunification, a worldwide campaign and appeal for funds was launched to rebuild the Frauenkirche. Work began in 1993, and in October 2005 the reconstructed church, incorporating thousands of blackened stones from the original structure, was finished_. MARSHALL DE BRUHL\n\n# CHAPTER SEVEN\n\n**THE TARGET**\n\nFlorence on the Elbe\n\n**O ne of Germany's grandest cities had the most humble of beginnings**. Dresden began life in the Middle Ages as a Slav fishing settlement. The fishermen founded their little village, originally known as Drezdany\u2014meaning \"forest dwellers on the plain\"\u2014on the left bank of the Elbe at a natural crossing of the river.\n\nThe first historical mention of Dresden is in a document dated 31 March 1206, signed by Heinrich, margrave of Meissen. Another document, dating from 1216, refers to Dresden as a _civitas_ , a town.\n\nOn the right bank, or the north shore, of the Elbe another settlement was founded. It became somewhat confusingly known as Altendresden, perhaps signifying that it was even older. A wooden bridge was soon built across the river to link the two settlements, but in 1287 it was replaced with a stone bridge, which became something of a medieval tourist attraction.\n\nAltendresden, which did not receive a charter until 1403, burned to the ground in 1491, and the newly built town became known as the Neustadt. The original settlement across the river then became known as the Altstadt. The two separate towns became one in the sixteenth century.\n\nDresden was ruled not by kings but by electors\u2014so called because they were one of the seven rulers entitled to elect the Holy Roman Emperor. Two of the electors, through treaties, war, and outright bribery, served simultaneously as elector of Saxony and king of Poland. The electors were, in the main, devoted to the arts and sciences, and through their patronage Dresden became a city unrivaled for art and culture in Germany and, indeed, throughout much of Europe.\n\nElector Friedrich the Wise, who ruled from 1486 until 1525, was a true Renaissance man. Not only did he found the University of Wittenberg, he earned everlasting fame as the protector and patron of Martin Luther. Many of Friedrich's successors continued the Saxon tradition of humanism and support for the arts.\n\nMoritz, called the savior of Protestantism, was also a great patron of the arts. His lasting contribution was the founding, in 1547, of the court orchestra that is today the world-renowned Dresden Staatskapelle.\n\nAugust, who became elector in 1553, was the first of the electors to begin to amass the collections that would make the city a cultural mecca. He began the great collection of books and manuscripts that in time would become the S\u00e4chsiche Landesbibliothek, the Saxon State Library.\n\nBut August had other interests as well. He collected lavish examples of the jeweler's, goldsmith's, and silversmith's art. This collection eventually grew so large that it was necessary to house it in a series of vaulted rooms in the _Schloss_ , the royal residence. In time, the collection became world famous as the Gr\u00fcnes Gew\u00f6lbe, the Green Vault. August also started the royal picture collection. Thus, by the end of the sixteenth century, Dresden was already the envy of Europe for its collections of books, paintings, manuscripts, and decorative objects.\n\nSucceeding electors added to their patrimony, but it was Augustus II, called Augustus the Strong (1670\u20131733), who ushered in what became known as Dresden's Augustan age. Although it spanned less than a hundred years, it imparted to Dresden the look and reputation that has endured to the present day.\n\nFor centuries, Germany was ridden with princes who vied with one another to have a personal Versailles, complete with ballet, theater, and even the occasional harem. These petty princes ruled supreme in their small worlds, with little regard for the common people. As historian Robert B. Asprey so aptly put it, Europe \"belonged largely to emperors, kings, nobles, and priests. They made war as they made love: Scarcely one affair ended before another began.\"\n\nAugustus resembled his fellow nobles in many respects. German historian Leopold von Ranke, in his _Memoirs of the House of Brandenburg and History of Prussia_ , said that Augustus went \"from pleasure to pleasure, without the least regard to duty or to dignity.\" The king, said von Ranke, \"delighted in a mixture of power and licentiousness.\" Dresden was a \"voluptuous court in which the relations of the sexes were emancipated from all restraint and decorum.\"\n\nAugustus was, indeed, a man of great appetites. He allegedly fathered three hundred children, one of whom, by one of his mistresses, Aurora von K\u00f6nigsmark, was the celebrated French soldier the mar\u00e9chal de Saxe.\n\nHe was not, however, just a voluptuary. His many additions to the royal picture collection were of the finest quality, as were his acquisitions of sculptures, porcelains, books, and manuscripts. Augustus was also a patron of music and theater. Under this elector of Saxony and king of Poland, Dresden was the most glittering court in Germany, and in Europe second only to Versailles.\n\nAugustus the Strong also saw one of his passions\u2014the collection of porcelains\u2014translate into an economic boon for his kingdom. The process for making porcelain had been known in China for over a thousand years, but no one in the West had been able to unravel the secret of its manufacture.\n\nThe mystery was solved in 1708 by the Dresden alchemist Johann Friedrich B\u00f6ttger. The technique for making porcelain was soon wedded to the Saxon penchant for the fanciful, and one of the major industries of Saxony, indeed of Germany, was born. Figurines, dinner services, vases, and all sorts of decorative pieces in the most ornate and whimsical shapes began to appear from the royal porcelain works.\n\nAlthough porcelain and fine china are inextricably linked in the popular mind with Dresden, in 1710 the Royal Saxon Porcelain Manufactory was moved nine miles down the Elbe, to the Albrechtsburg, the medieval fortress castle overlooking Meissen.\n\nAugustus the Strong died in 1733. \"I have not at present strength to name my many and great sins,\" he told his confessor.\n\nAugustus's son and heir, Augustus III (1696\u20131763), who was also King Frederick-Augustus II of Poland, spent his thirty-year reign in Dresden, content to let Count Heinrich von Br\u00fchl, the prime minister who had served his father, run the affairs of state. The elector's interests lay elsewhere.\n\nIn January 1742, Frederick the Great came to Dresden to persuade Augustus to join him against Austria during the First Silesian War. Augustus did not join the meeting until it was well under way and, according to Frederick \"answered yes to everything with an air of conviction mixed with a look of boredom.\"\n\nDiplomacy was not on Augustus's mind. The Saxon was anxious to get to the opera, and the overture was about to begin. Frederick was also a music lover, but war was an even greater passion. \"Ten kingdoms to conquer would not keep the King of Poland one minute longer,\" sniffed the Prussian.\n\nAugustus III may have slighted politics and diplomacy, but such cannot be said about his artistic endeavors. Under his aegis, the royal picture collection grew into that assemblage of paintings, drawings, and sculpture that ranks among the finest in the world and is the reason that Dresden became a primary destination for art lovers.\n\nThe centerpiece of the collection, _The Sistine Madonna_ , Raphael's most famous work, was acquired by Augustus in 1754. In addition, there were many of the greatest paintings of the greatest masters: Titian, Correggio, Veronese, Giorgione, Tintoretto, Poussin, Watteau, Lorrain, Carracci, Rubens, Van Dyck, Vermeer, Botticelli, Caravaggio, Tiepolo, Vel\u00e1zquez, Zurbar\u00e1n, Murillo, D\u00fcrer, Holbein the Younger, Cranach the Elder, van Eyck, and Rembrandt. Augustus III appointed Bernardo Bellotto the court painter in 1747. This nephew and student of Canaletto's produced many fine views of the city in the style of his famous uncle, and fourteen of them were installed in the Gem\u00e4ldegalerie at the Zwinger.\n\nCount von Br\u00fchl's diplomacy and Augustus's lack of interest in diplomatic affairs eventually brought great suffering and destruction to Dresden. In the Seven Years' War, Saxony allied itself with the wrong side, and its erstwhile ally Frederick was merciless.\n\nAugustus III and Br\u00fchl fled to Warsaw after the defeat of the Saxon army at Pirna in 1756. When they returned to Dresden after the cessation of hostilities in February 1763, two-thirds of their city lay in ruins. The Prussian cannons had done their work well, and what was left of the fortifications was dismantled.\n\nThe king and his minister were both broken by the defeat of Saxony and the humiliations they suffered at the hands of Frederick, and they died within weeks of each other in October 1763. The brief but glittering Augustan age was at an end, and Dresden was no longer the capital of an important German political entity. Prussia was now the great German power and would remain so.\n\nDresden did regain its importance as a cultural and artistic center, however. Subsequent rulers repaired the ravages of warfare, and once again Dresden beguiled the visitor with its dazzling assemblage of the baroque, rococo, neoclassical, and German Renaissance, which blended into a startingly beautiful cityscape and served as architectural stage set before which all civic activities were played out.\n\nThe Br\u00fchlsche Terrasse, the esplanade above the Elbe in the Altstadt, had been a special place for Dresdeners since 1738, when it was laid out along the former ramparts in front of his palace by Br\u00fchl, then at the height of his powers as prime minister. Celebrated as the \"balcony of Europe,\" it afforded a sweeping view of the river and the grand buildings on the opposite shore, the most impressive and recognizable being the Japanisches Palais, so called because of its upturned roof corners, reminiscent of Japanese temple architecture.\n\nBuilt in 1715 to house the royal porcelain collection, the Japanese Palace became, in 1786, the Royal Library, the repository for hundreds of rare medieval illuminated manuscripts: the works of Martin Luther (including his German translation of the Bible), illustrated works by Albrecht D\u00fcrer and Lucas Cranach, Persian and Chinese illuminations, a thirteenth-century Jewish holy day prayer book, and, of course, the Dresden Codex, one of only three extant Mayan manuscripts. Other treasures included two sections of Johann Sebastian Bach's great Mass in B Minor, the Kyrie, and Gloria. Bach enclosed the music in a letter of 27 July 1733 to Augustus III that was a petition for the position of court composer. He was turned down because he was a Protestant.\n\nNear the Japanese Palace stood a more utilitarian circular building just as dear to the fun-loving Saxons as its more imposing cousin. This was the Zirkusgeb\u00e4ude, the amphitheater on the Carolaplatz that was the home of a Dresden institution, the Sarrasani Circus.\n\nNot far away, also in the Neustadt but visible from the Altstadt, across the river, stood, as it had since 1736, the _Goldener Reiter_ , the gilded equestrian statue of Augustus the Strong\u2014Dresden's greatest ruler.\n\n**Behind the Br\u00fchlsche Terrasse lay the Altstadt** , or the Old City, that assemblage of baroque and German Renaissance buildings and parks that had so impressed visitors for over two hundred years.\n\nAmong these buildings, the most immediately recognizable was the Frauenkirche, the Church of Our Lady. Dresden was overwhelmingly Lutheran, and although the Dresdeners were always loyal to the electors, they had never accepted the Augustuses' conversion to Roman Catholicism, which they had done in order to gain the Polish throne. The church, it was said, was erected by the Dresden town council only three hundred meters from the Royal Palace as a monumental Lutheran rebuke.\n\nConstruction of the Frauenkirche began in August 1726 and the church was dedicated in 1734, although it was not finally completed until 1743, five years after the death of its architect, the German baroque master Georg B\u00e4hr. On 1 December 1736, Bach gave a two-hour organ recital there with much of the royal court in attendance.\n\nThe Frauenkirche at once became the most famous building in the city and arguably the most important example of eighteenth-century Protestant ecclesiastical architecture in the world. Its height was 312 feet from the base to the top of the lantern, and some four thousand worshippers could gather inside what became known as the \"Stone Bell\" because of its distinctive shape.\n\nAugustus III, to appease his Catholic subjects, rose to the Protestant challenge of the Frauenkirche. In 1738 he commissioned the Italian Gaetano Chiaveri to build the enormous Katholische Hofkirche, the largest Catholic cathedral in Saxony, on a site adjacent to the Royal Palace.\n\nDresden's oldest church, the Kreuzkirche, just a few streets farther on, was founded about 1200. It became a Lutheran church during the Reformation and the official church of the court when the electors embraced Protestantism. In 1760, during the Seven Years' War, it was destroyed by Frederick the Great's artillery and was rebuilt in the baroque style.\n\nThe fourth of the great churches of Dresden was the Sophienkirche, which also adjoined the Royal Palace. Like the Kreuzkirche it was originally a medieval Roman Catholic church, but with the Reformation it too became a Lutheran church. Johann Sebastian Bach's eldest son, Wilhelm Friedmann Bach, was the organist at the Sophienkirche, and his father gave a concert at the church on 14 September 1731. As a Dresden periodical reported, the great master performed \"in the presence of all the Court musicians and virtuosos.\"\n\nThe Royal Palace, or _Schloss_ , in its various forms, was home to the rulers of Saxony from the Middle Ages until 1918. Immediately adjacent to the _Schloss_ and connected by a covered passage, Augustus the Strong built the luxurious Taschenberg Palace for his mistress Constantia, the Countess Cosel.\n\nThe Royal Palace faced one of the most beautiful urban complexes in the world: the Theaterplatz. Around this massive square were arranged not only the Royal Palace and the cathedral but also the Semper Opera House, the luxurious Hotel Bellevue and its gardens on the Elbe, and the great museum complex called the Zwinger. Particularly at night, the Theaterplatz presented a glittering array of water, light, and architectural exuberance unmatched anywhere.\n\nFew places bear a name that so belies their purpose and splendor as the Zwinger. The vast ornate complex is so called because it was built on the outer court of the medieval fortress that had stood on the site and also was the site of the royal kennels. Matth\u00e4us Daniel P\u00f6ppelmann was commissioned by Augustus II to build an orangery, which would wrap around a racecourse and festival site for the court. But the brilliant architect soon won over the king to a more ambitious design. Between 1711 and 1722 P\u00f6ppelmann, who was heavily influenced by his travels in Italy, translated his designs into one of the greatest examples of the German baroque.\n\nHe enclosed an immense courtyard with carved stone-and-glass one-story galleries and two-story pavilions of the most exquisite refinement. Every cornice, pilaster, and column was covered with nymphs, cherubim, seashells, and flowers. Hundreds of statues from the studio of the Bavarian master Balthasar Permoser adorned the ramparts, stairways, and columns.\n\nIn this splendid group of buildings, which Sir Nikolaus Pevsner called \"the product of an inexhaustible creative power,\" Augustus installed his collection of paintings.\n\nThe architect most associated with Dresden, not excluding those masters of the baroque P\u00f6ppelmann and B\u00e4hr, is Gottfried Semper, who was a professor of architecture at Dresden and the court architect from 1843 until 1849. It was Semper who completed P\u00f6ppelmann's grand design for the Zwinger. The northeast side of the compound remained open to the Theaterplatz and the riverfront until it was enclosed by Semper's Renaissance-style picture gallery.\n\nBut neither the Hofkirche nor the Zwinger dominates the Theaterplatz. That honor goes to the monumental Semper Oper, the home of the S\u00e4chsische Staatsoper. Semper's first opera house burned in 1869, but his son Manfred, who was designated to rebuild it, used plans drawn by his father for the new building. The rebuilt house, a grand neo-Renaissance structure, opened in 1878.\n\nThe Semper Opera House, in its several incarnations, played host to some of the world's greatest composers and artists\u2014many of whom were resident in Dresden. The post of _Hofkappelmeister_ , or conductor, which entailed oversight of both the opera and the orchestra, the Staatskapelle, was held at various times by Heinrich Sch\u00fctz, Carl Maria von Weber, and Richard Wagner. In addition, Hans von B\u00fclow, Johannes Brahms, and Richard Strauss had close associations with the Semper.\n\nAlthough Johann Sebastian Bach did not get the longed-for post, he gave numerous recitals in the Saxon capital, and one of his most celebrated works, _The Goldberg Variations_ , was commissioned by the Russian ambassador to the Saxon court, Count Keyserlingk, and first performed at the Russian embassy in Dresden.\n\nBach's great contemporary Antonio Vivaldi also spent time in Dresden, where he produced several works for patrons. Bach, an admirer of the Italian virtuoso, transposed for other instruments some of the Vivaldi concertos.\n\nWagner's _Rienzi, The Flying Dutchman_ , and _Tannh\u00e4user_ had their world premieres at the Semper. His next work, _Lohengrin_ , was written in Dresden but did not premiere there because of the Revolution of 1849. Dresden also was the birthplace of _Der Ring des Nibelungen_ and _Die Meistersinger von N\u00fcrnberg_. Wagner began to sketch out the great tetralogy as well as his comic masterpiece while he was in residence in the city, and the composer conducted the premiere of his _Love Feast of the Apostles_ at the Frauenkirche in July 1843.\n\nRobert Schumann did not fare as well in the city as his counterparts. The mentally troubled composer eked out a living as a poorly paid choir director. He did record an interesting historical footnote for posterity. While composing the song \"Des Sennen Abschied\" (\"The Cowherd's Farewell\"), he was interrupted by the beginning of the Revolution of 1849. The manuscript of the piece, which is in the Dresden State Library, has the notation \"interrupted by the alarm bells on May 3, 1849.\"\n\n_A German Requiem_ , which established Brahms as a great new voice in music, was first presented in Dresden in 1868. And an acolyte of Brahms's\u2014Richard Strauss\u2014would become the leading German composer of the twentieth century.\n\nStrauss had a lifelong affection for Dresden, and the premieres of nine of his operas were held at the State Opera, beginning with _Salome_ in 1905 and ending with _Capriccio_ in 1942. During rehearsals he shuttled back and forth across the Theaterplatz between the Semper Oper and the Hotel Bellevue, where he lived during rehearsals.\n\nOther great composers who lived and worked for a time in Dresden were Sergei Rachmaninoff, Paul Hindemith, and Ferruccio Busoni.\n\nHindemith's _M\u00f6rder, Hoffnung der Frauen, Das Nusch-Nuschi_ , and _Cardillac_ and Busoni's _Doktor Faust_ were all staged first at the Semper.\n\n**The two giants of** German literature, Friedrich Schiller and Johann Wolfgang von Goethe, were frequent visitors to Dresden. It was Goethe's close friend and mentor, the philosopher-theologian Johann Gottfried von Herder, who first compared Dresden to Florence. His appellation \"Florence on the Elbe\" was happily expropriated, with some justification, by the Dresdeners. Schiller wrote much of _Don Carlos_ in the summerhouse of the villa of friends in Loschwitz.\n\nHeinrich von Kleist lived in Dresden from 1807 to 1809, and novelist and critic Ludwig Tieck lived there twice, the second time from 1819 to 1841. And the greatest musical romantic of the nineteenth century, Fr\u00e9d\u00e9ric Chopin, lived in a flat on the Seestrasse in 1835.\n\nBut perhaps the works that most evoke the Romantic era in Dresden are the lush, moody, darkly mysterious paintings of Carl Gustav Carus, Caspar David Friedrich, Johan Christian Dahl, and Adrian Ludwig Richter. Friedrich's _Two Men Contemplating the Moon_ and Richter's _The Crossing of the Elbe at the Schreckenstein_ are the visual definition of the term and the era.\n\nAs the Romantics rebelled against eighteenth-century classicism, so did the movement called Die Br\u00fccke rebel against nineteenth-century forms. This short-lived advance guard of German Expressionism, which was born in Dresden in 1905, drew its name from the Augustusbr\u00fccke, the bridge that spans the Elbe near the Academy of Fine Arts, where many of its practitioners either studied or taught.\n\nTheir works featured deformed nature, landscapes, and figures; and their brilliant, even garish colors created a sensation. The group eventually comprised Ernst Ludwig Kirchner, Karl Schmidt-Rottluff, Erich Heckel, Emil Nolde, and Max Pechstein. Die Br\u00fccke lasted only until 1913, but its influence was felt throughout the twentieth century.\n\nThe Expressionist Oskar Kokoschka taught at the academy from 1919 to 1924, and Otto Dix, a leading figure in the Neue Sachlichkeit movement, was a student there and later a teacher.\n\n**Dresden, of course** , was not alone among German cities as a bastion of civilization and high culture. It was not alone when, like other areas during the turmoil of the Weimar Republic, it embraced National Socialism and its promise of social order and German rebirth. Nor was it alone in ignoring the dark side of the Nazi movement. Indeed, Dresden firmly embraced National Socialism, and Hitler, whenever he visited the city, was received rapturously by the populace.\n\nThe Dresdeners, like most of their countrymen, endorsed the restrictive laws and the curbs on their own liberties, and many of them also endorsed the racial laws that curtailed the rights of the Jews.\n\n**Jews are first recorded** in Dresden in the early fourteenth century, and their history was a replication of that of all the Jews of Europe and England. The Dresden Jewish community was destroyed during the Black Death persecutions of 1349. But by 1375, Jews were again resident in Dresden, and they had even built a synagogue. This community lasted only until 1430, however; it fell victim to another pogrom and was expelled.\n\nThere is no further mention of Jews in Dresden until the 1690s, when Augustus the Strong's lust for the Polish crown and the money needed to fulfill his dream overrode any religious prejudice. Had he not himself cast aside Protestantism for Catholicism to gain the crown?\n\nHe turned to Jewish bankers, who were eager to help the elector. Augustus, partially out of gratitude but mainly because he had further need of their favors, allowed a small group of Jews to settle in Dresden in 1708\u2014about a hundred in all.\n\nIn Bismarck's empire, Jews were allowed to attend the German universities and live in previously forbidden areas, and this emancipation led to more rapid growth in the Jewish population and to assimilation, although there were still only 23,000 Jews in all of Saxony in 1925\u2014less than one-half of 1 percent of the total population. Indeed the number of Jews in all of Germany was never more than 1 percent of the population.\n\nWhen Adolf Hitler came to power on 30 January 1933, he immediately moved to put into place the racial program he had expounded since he'd founded the Nazi Party and had so forcefully advocated during his rise to power.\n\nThe burning of the Reichstag building by a young Communist on 27 February was used as a pretext for a decree for the \"Protection of the People and the State,\" which suspended all civil rights. On 24 March the Reichstag voted in the Enabling Act, which turned over all legislative functions to Hitler and his ministers. Within a week, the Law for the Reestablishment of the Professional Civil Service was passed. It eliminated all non-Aryans\u2014anyone with a Jewish parent or grandparent\u2014from the civil service.\n\nFurther restrictions followed with sickening regularity. On 25 April 1933 came the Law Against Overcrowding of German Schools, which limited the number of Jews admitted to 1.5 percent.\n\nIt was soon forbidden for anyone with Jewish blood to pursue a profession that had any influence on the German _Volk_. This, in effect, put all Jews out of work except those who dealt only with their coreligionists.\n\nAs Hitler and his cohorts tightened their grip on the nation, more decrees against the Jews were issued. They were forbidden to farm land. The German citizenship of Jewish immigrants was revoked, which meant expulsion. Jews were forbidden to serve in the military.\n\nAt Nuremberg on 15 September 1935, the Reichstag met and endorsed a series of decrees\u2014the Nuremberg Laws\u2014that further codified the status of German Jews. They were stripped of their citizenship and their rights. Marriage between Jews and Aryans was forbidden, and existing marriages were ruled invalid. Extramarital intercourse between Jews and Aryans was a criminal act. Anyone who had one Jewish grandparent was considered a Jew, as were offspring of any liaison between Jews and Aryans and anyone married to a Jew. No one of German or kindred blood under forty-five years of age could be employed by Jews as a domestic. Jews were no longer allowed to drive automobiles. And Jews, who had already been forbidden to borrow books from libraries, were now barred from the buildings altogether.\n\nA visitor to prewar Dresden might have asked what the ruins were just to the east of the Br\u00fchl Terrace\u2014just steps from the Frauenkirche, the Academy of Fine Arts, and the Albertinum Museum. These fire-blackened stones were the remains of another Gottfried Semper building, the nineteenth-century Romanesque-style Jewish synagogue. On 9 November 1938, during the Nazi rampage called Kristallnacht, the building was burnt to the ground and dozens of Dresden's Jews were assaulted and arrested.\n\nThe traveler to Dresden in 1939 would have looked in vain for another famous site in the city center\u2014the ancient Judenhof, or Jews' Courtyard. The name had survived even though the synagogue that had stood there had been destroyed in the pogrom of 1430. But in 1936 the Judenhof disappeared from guidebooks and city maps\u2014another victim of the Nazi purge of all things Jewish in the Third Reich. The space officially became an extension of the adjoining square, the Neumarkt.\n\n**The official RAF** target description of Dresden, which was first drawn up in 1942, made no mention of china, porcelain figurines, or great works of art. There was a passing reference to the city's medieval origins. But the emphasis was, rightly, on the fact that Dresden was at the center of a vital transportation network. While the individual defense establishments were not the equal of the vast armaments factories in such areas as the Ruhr, in the aggregate they were important indeed.\n\nDRESDEN is the historical capital of Saxony and an administrative centre of considerable importance. It is the eight[h] largest town in Germany but at the same time has a very low overall density of population. Apart from the central area, which has narrow streets and many ancient domestic and public buildings, the town is mainly modern, with a preponderance of large single villas with spacious gardens.\n\nThere are a large number of industries, and collectively these are of considerable importance, but individually none are of outstanding value. The principal industrial activities are repairs to rolling stock, aircraft and aero-engines, and the manufacture of machine tools, small arms, optical instruments, medicinal preparations and poison gas.\n\n_Transportation:_ DRESDEN is the centre of an extensive railway system and main lines radiate from here in all directions.\n\nThere were nineteen priority targets listed for Dresden, including the Zeiss-lkon optical factory, power stations, water- and gasworks, a gun factory, and small electrical shops. Strategically, however, the important targets were the Friedrichstadt and the Pieschen railway marshaling yards and repair shops. The four railway stations\u2014the Central Station, Dresden-Neustadt, Wettinerstrasse, and Friedrichstadt\u2014were but a short distance from the marshaling yards.\n\nThe target map also indicated that most of the ancient heart of Dresden, the Altstadt, was well within the second of the concentric circles drawn at one-mile intervals from the central aiming point, the Friedrichstadt train yards. All the major museums, monuments, churches, and historic buildings were thus within the acceptable target zone.\n\nFrom the photographs and the briefing it was clear that Dresden would be easy to find, nestled as it was within the serpentine curves of the Elbe. The image on the H2S radar screen should easily match up with the photographic maps and charts. The rail lines snaking out from the passenger and freight stations and marshaling yards stood out boldly.\n\nHospitals were denoted by red crosses, and at the top of the map was the enjoinder that hospitals were clearly marked and \"must be avoided.\" Hospitals, of course, were as vulnerable as any other structure to the vagaries of visibility, wind, airspeed, and bomb drift. Three hospitals were within a mile of the designated central aiming point. The red crosses and warnings on the maps were designed chiefly to pacify international relief agencies and organizations. No one familiar with bombing practices could guarantee that they could be heeded by air crews flying at 25,000 feet in 10\/10, or total, cloud cover or at night.\n\nAnother Dresden landmark, but of quite another variety, was also within the inner aiming circle. Immediately north of the Friedrichstadt yards, in a bend of the Elbe in the Grosses Ostragehege, lay the municipal slaughterhouses. These _Schlachthoffen_ housed Allied prisoners of war in 1945. In _Schlachthof_ No. 5, an American soldier listened as Allied bombers destroyed the city outside the protective walls of his prison. Kurt Vonnegut would later transmute the experience into art in his famous novel _Slaughterhouse-Five_.\n\nLeipzig was the major manufacturing city in all of Saxony, but in February 1945 Dresden had at least 110 factories and industrial enterprises that employed 50,000 workers in turning out arms and other military equipment. Scattered around the city were aircraft-components factories, a poison-gas factory, an antiaircraft and field gun factory, and other factories for producing small arms, X-ray equipment, electrical apparatus, gauges, and gears and differentials. The plants and the number of workers involved constituted a considerable defense industry, which, transportation and communication aside, would have made the city a legitimate military target.\n\nFor example, before the war Seidel & Naumann, AG, manufactured typewriters, sewing machines, and bicycles. The company was converted to the manufacture of high-precision testing equipment. A Herr W., in an interview long after the war, said, \"Only a few knew what the finished product would look like and what it was to be used for. It was important enough, however, that it had repeatedly protected me from being drafted into the Armed Forces.\"\n\n_Bomber's Baedeker: Guide to the Economic Importance of German Towns and Cities_ gave the population of Dresden in 1944 as 640,000 and reported that in peacetime the production of tobacco products, chocolate, and confectionaries were a large component of the city's industrial activity. With the coming of war, small factories and light engineering had become important, particularly of electric motors and precision and optical instruments.\n\nNorth of the river and the Neustadt, there was a large military complex containing barracks, an old arsenal, and a museum. Immediately to the east lay a vast natural preserve, the Dresdner Heide, or heath, where it was reported the Germans were storing large quantities of munitions. In fact, the arsenal had been converted into munitions workshops, and these and other industrial sites abutted the railway that ran northeast to G\u00f6rlitz on the Polish border and on the Eastern Front.\n\nThe stations and marshaling yards in Dresden were vital components of the rail system connecting northern and central Germany to Poland, Czechoslovakia, Bavaria, and Austria. As such, Dresden was a major transport center for moving supplies and reinforcements to the east. It would also be integral for the transfer of men, and particularly panzer divisions, from the collapsing Western Front to the east.\n\nConversely, when the Eastern Front finally collapsed, which was imminent, Dresden would be a major center on the line of retreat for the Wehrmacht back into Germany. The city was an important strategic target, the crippling of which would help support the Russian offensive; and the Russian front line was less than two hours away, by rail or road.\n\nAn examination of contemporary railway maps clearly shows that Dresden was an integral junction of three of the most important longdistance routes of the German railway system: Berlin\u2014Prague\u2014Vienna; Munich\u2014Breslau; and Hamburg\u2014Leipzig\u2014Prague. The railway system in Saxony, while seventh in mileage in the Third Reich, was third in the amount of tonnage carried. The Dresden stations and marshaling yards were vital components of this system. The Dresden-Friedrichstadt marshaling yards had \"a maximum capacity of 4,000 trucks per 24 hours.\"\n\nThese rail lines had become even more important to the German war effort as the industrial regions in the west were being destroyed by the Allied raids. Meissen, Radebeul, Coswig, and Freital, with its steel mills and lubricating oil plant, were all nearby, and as the 1942 targeting report made clear, \"Dresden is one of the few direct links through the Erz-Gebirge, between Czecho-Slovakia and Germany. In view of the exploitation of Czech industry, damage to the railway here would cause considerable confusion to rail transit.\" In 1945, Germany relied heavily on Czech industry, which was still churning out war mat\u00e9rial.\n\nIn addition to its importance as a rail center, Dresden was an important river port and the center of freight traffic on the Elbe, which was still, as it had been for centuries, one of the major waterways of Europe.\n\nWorthy as all these targets were, in February 1945 the Soviets were more concerned with interdicting troop movements and reinforcements from the west to the east and disrupting any streams of retreating troops from the east to the west.\n\nAnd there was yet another reason for destroying Dresden as a rail center\u2014one that strongly recommended itself to the Allied high command. If the Germans were planning a last stand in a redoubt in the Bavarian Alps, as was strongly believed by Eisenhower and other Allied leaders, Dresden lay on the direct line to Bavaria from Berlin. Men and mat\u00e9rial would have to pass through the city to either establish or reinforce such a stronghold in southern Germany.\n\nThe alpine redoubt was as chimerical as the death ray and other schemes that were supposedly being concocted by the leaders of the collapsing Third Reich. But military planners must take into account the many possibilities open to a determined and fanatical enemy, no matter how far-fetched they might seem.\n\nAnd as for any future reaction to the destruction of one more German city, no matter how beautiful and culturally important, that did not loom large among the air barons and their nominal civilian masters in February 1945.\n\n# CHAPTER EIGHT\n\n**SHROVE TUESDAY, 1945**\n\nDresden on the Eve of the Apocalypse\n\n**B y the evening of 12 February, meteorological data indicated** that the major air operations in eastern Germany that Spaatz had cabled Moscow would take place the next day would not be possible. The cloud cover that had obscured the Continent for most of the past week had once again moved in, and snow was falling on the Saxon capital. The daylight raid, the massive American first strike, was called off. The Americans would not be going to Dresden on Shrove Tuesday, 13 February. The Eighth Air Force bomber crews and fighter pilots were ordered to stand down.\n\nThe Russians were notified of the cancellation, but they also were put on notice that if the weather cooperated, the Americans would go the following day, 14 February. Presumably, in line with the agreement concerning bomb lines and prior notification, the British were also keeping the Russians abreast of their own preparations.\n\nAt 0900 the next morning, 13 February, the weather scouts, the aircraft that penetrated far into Europe and relayed meteorological data back to the weather centers in the United Kingdom, reported that the weather had changed for the better over central Europe. The three-part mission was back on, but it would be in reverse order. Bomber Command would lead off that night with the first two waves and the Americans would follow the next day. Harris gave the order to proceed.\n\nBy that afternoon, at the 1600 weather conference, the meteorologists at High Wycombe were forecasting even more improvement in the weather conditions over Europe for the next twenty-four hours. There would be approximately four to five hours of clear weather over Dresden beginning at about 2200 hours, which would guarantee the success of a double blow. Further, by delaying the forces for just an hour, it was predicted, the Allies could further increase the possibility of visual sightings.\n\nThere was other welcome news from the weather forecasters. Conditions would be favorable over the United Kingdom for the return of the British planes during the early-morning hours of 14 February and for the launch of the American third wave.\n\n**In Saxony** , six hundred miles from Bomber Command headquarters, Dresdeners had awakened to a cold and overcast day. All of central Europe was covered by a thick layer of clouds on this Shrove Tuesday morning. The snow that had fallen in the night had given the buildings and monuments of the Augustuses a light frosting, which further softened their baroque and rococo embellishments and gave them an even more fanciful air.\n\nA disheveled figure shuffled through the quiet, confectionary streets of the city on this chill morning. The man bore little resemblance to the esteemed professor of French literature at the Dresden Technical University that he had once been. After fifteen years in his post, Professor Victor Klemperer had been dismissed in 1935. The distinguished scholar was now dressed in a tattered and patched coat emblazoned with a yellow Star of David and the word _Jude_ , which marked him as a pariah in the Third Reich.\n\nLike many assimilated Jews, Klemperer saw himself as completely German. Indeed, he was so far removed from the faith of his birth that he was fifty-nine years old when he attended his first Orthodox funeral and set foot in a Jewish cemetery, although his father had been a rabbi, first in Landsberg on the Warthe, in Brandenburg, then at the Reform synagogue in Berlin. But Victor and his brothers had abandoned Judaism for Christianity, and he had married Eva Schlemmer, a German Protestant.\n\nKlemperer's view of religion is summed up in a remark he made in 1937: \"Pity that I have one screw too few or too many to be a good Catholic.\" For him Zionism was as threatening to assimilated Jews as Nazism, a distorted idea that was as fallacious as his belief that his Protestantism, his marriage, and his heroic service in World War I set him apart from his former coreligionists. His folly was not an unusual one, although the fate of most of Europe's Jews was slower in overtaking him.\n\nHis errand today was not unlike many other rounds he had made, delivering announcements from the authorities to Dresden's 198 surviving Jews.\n\nThe Jewish community in Dresden had never been a large one, as in Berlin, and when emigration was halted in late 1941 there were just 1,265 left in the city, most of them in the protected category. These were men and women of Jewish birth who were married to Aryans or were the children of mixed marriages. But protection was capricious and arrest was an ever-present danger.\n\nLike all their compatriots who had remained in the Reich, the Dresden Jews were the victims of a relentless campaign whose end was their destruction. Many had been murdered by the Gestapo in the grim cells of the headquarters on Schiessgasse, their deaths listed as suicides. Hundreds had been deported, either directly to the labor or extermination camps or to Theresienstadt, some sixty miles up the Elbe in Czechoslovakia.\n\nTheresienstadt, or Terez\u00edn in Czech, was set up by the Nazis in 1941 as a showcase concentration camp and did serve for a while to hide the enormity of their crimes from the world. The small town and fortress, which was famous as the prison of Gavrilo Princip, the assassin of Archduke Francis Ferdinand in 1914, was not an extermination center but a way station for some 120,000 Jews. Nevertheless, more than 30,000 internees died there while awaiting deportation to the labor or death camps, mainly to Auschwitz-Birkenau.\n\n**The circulars distributed** by Klemperer this cold morning stated that the recipient or recipients were to gather at the Jewish Center, at 3 Zeughausstrasse, in three days' time, on Friday, 16 February. They were to wear work clothes and bring hand luggage\u2014which, the notice advised, would have to be carried for a considerable distance\u2014and enough provisions for a journey of two or three days.\n\nKlemperer had no illusions about the messages he carried, even though the wording was rather benign. \"On this occasion,\" he wrote in his diary, \"there is to be no confiscation of property, furniture, etc.; the whole thing is explicitly no more than outside work duty\u2014but without exception is regarded as a death march.\" His own name was not on the list, but he had little doubt that he too would soon be following the others.\n\nAge, physical condition, and marriage to non-Jews all meant nothing. There were to be no exceptions to the order. Mixed marriages no longer were to be tolerated. \"The most cruel separations are taking place,\" wrote Klemperer. The Aryan half of a couple was to stay behind, but the Jewish partner and any children, since they were considered Jewish, were to be deported.\n\nJews had long since been forbidden to move about the city unless they were on prescribed missions, and then they were allowed only on narrowly defined routes. Star-wearing Jews were further prohibited from walking along or entering the B\u00fcrgerwiese, the long narrow park adjoining the Grosser Garten. Jews were allowed to cross the park only by way of the L\u00fcttichstrasse, a detour so circuitous that it effectively ruled out doing so. Therefore Klemperer's melancholy task took him until well after dark.\n\nAs Klemperer called at the private houses or tenements that had been set aside as residences for Jews\u2014the so-called Jews' houses, some of them in sections of the city that he had not visited in years because of the restrictions\u2014to a person, the people on his list knew that they were being summoned to their deaths.\n\nAt each house, the reaction was despair, but he was particularly moved by a young woman, a Frau Bitterwolf, who lived in the Struvestrasse.\n\n\"Again a shabby house,\" he wrote. \"I was vainly studying the list of names in the entrance hall when a blond, snub-nosed young woman with a pretty, well-looked-after little girl, perhaps four years old, appeared. Did a Frau Bitterwolf live here? She was Frau Bitterwolf. I had to give her an unpleasant message. She read the letter, several times, said quite helplessly: 'What is to become of the child?' then signed silently with a pencil. Meanwhile the child pressed up against me, held out her teddy bear, and, radiantly cheerful, declared: 'My teddy, my teddy, look!' The woman then went silently up the stairs with the child. Immediately afterward I heard her weeping loudly. The weeping did not stop.\"\n\nAt another of the Jews' houses lived a Frau Koch and her mother. The older woman was on the list of deportees, but the daughter had received a postcard to report to the employment office for a medical examination to determine if she should be sent along on the work detail as well. The daughter later related, \"Now we were examined and, of course, we were all fit to work.... So my mother had her deportation order and I was given a slip of paper that I had to show up for work away from the city, also on the 16th of February.\"\n\nThere were other Jews in Dresden on this day as well. But these unfortunates had already felt the full impact of the Nazi deportation and extermination program. They were slave laborers sent to Dresden from concentration camps to work in the various electronics, optical, aircraft parts, or munitions plants scattered throughout the city.\n\nOne group, Jewish women from the camp at Ravensbr\u00fcck, had been roused from its makeshift barracks well before dawn and was at work assembling precision instruments at the Zeiss-Ikon factory in Striesen. Zeiss was the largest employer in Dresden. Some fourteen thousand people, which included thousands of laborers from the occupied countries and Jews from the concentration camps, worked in its factories.\n\n**The non-Jewish Dresdeners** , in spite of the usual deprivations of war, had suffered far fewer hardships than the citizens of other cities of the Third Reich or in many cities of the occupied territories. Their city had seen no great physical damage in almost six years of war. Indeed, the eighteenth-century court painter Bernardo Bellotto would have had no trouble recognizing the subjects of his many paintings of Dresden. The city was as before. No exploding bombs had marred the famous prospect from the Br\u00fchl Terrace along the Elbe. No fires had blackened the churches, the museums, or the other great monuments of the rococo.\n\nDresden had been designed by the Augustuses as a stage set for the court and for their entertainments, and while the sets were physically intact, no Dresdener could pretend that the city reflected much of its glittering prewar image as a great cultural center. Bellotto's paintings had long since been removed, along with the porcelains, the statuary, the bejeweled objects in the Gr\u00fcnes Gew\u00f6lbe, and the works of the old masters, to safer locales. The art treasures were stacked in cellars below medieval castles or deep in salt mines.\n\nFor the ordinary Dresdener, there were still some amenities, and life, although difficult, continued in many ways as before. There were caf\u00e9s and coffeehouses; mail was delivered; the trains and streetcars, although delayed, operated. The telephone system worked.\n\nThe Semper Opera was dark, but another famous Dresden attraction was open for business. At the Zirkusgeb\u00e4ude, the amphitheater on the Carolaplatz in the Neustadt, the Sarrasani Circus, in the best tradition of that ancient form of entertainment, was continuing with performances. Indeed, there would be one that evening.\n\nEven the animal keepers at the Dresden Zoo in the Grosser Garten had managed to keep their charges relatively healthy. Their task cannot have been a simple one, with the human population suffering such shortages of food. Although butchers were selling sausages made of cabbage, somehow food was found for these wild animals, no matter how exotic or in need of pampering. In Berlin one of the animal keepers kept his charges, some flamingos, alive in the tub in his bathroom.\n\nBesides the removal of art treasures, few other wartime precautions had been taken, and the habitual confidence of the Dresdeners was undiminished. Strict blackout procedures were enforced, but unlike in other Reich cities, there was no ring of antiaircraft batteries. The 88- millimeter antiaircraft guns had been removed to where they could be of greater use\u2014as artillery pieces and antitank weapons on the Eastern Front, against the advancing Red Army.\n\nDresdeners were not unaware of air raids, although they had no experience of prolonged aerial bombardment. They had spent hours and sometimes entire nights in cellars and air-raid shelters since the British had begun the bombing of Germany.\n\nIn his diary, Victor Klemperer reports hearing explosions and antiaircraft fire as early as 20 November 1940. On that night the RAF raided the \u0160koda arms works in Pilsen, Czechoslovakia, and five targets in Germany. Dresden, where the air-raid sirens went off at 0200, was not targeted, but since only seventeen of the sixty-three Bomber Command aircraft dispatched found the primary target, perhaps some of the planes jettisoned their bombs near the city.\n\nThe city had been the target of two raids within the last four months, but they had gone largely unnoticed by the general populace. On 7 October 1944, 333 American B-17s of the First Bomb Division were dispatched to attach the oil installations at Ruhland. Only 59 of the 318 aircraft found the primary target. The remaining 259 headed for targets of opportunity, one of which was Dresden.\n\nAt about 1140 a preliminary air-raid warning was issued when planes were detected heading toward the city. Twenty minutes later, at noon, a full-scale air-raid alarm was sounded.\n\nThirty B-17s dropped 72.5 tons of bombs on the area around the Friedrichstadt station and marshaling yards. At 1330, when the all clear sounded, people began to emerge from the shelters. The physical destruction was minimal, but 435 people had been killed. The raid itself was such a rarity that people actually went to look at the damage.\n\nOn 16 January 1945, 364 B-24s from the Second Air Division took off from England to raid the oil installations at Magdeburg and Ruhland. The bad weather played havoc with the mission, and on the return 70 B-24s had to land in France because of the fog in England. But 138 of the B-24s bombed Dresden, a secondary target, beginning at around 1200. Again the marshaling yards were hit, this time with 341.8 tons of bombs, and another 376 people were killed.\n\nStill, the Dresdeners saw the second raid as an anomaly as well. A young woman who lived with her newborn baby in a fourth-floor apartment on the Weisseritzstrasse reported that a crowd of people had come to see the damaged Wettinerstrasse Bahnhof after the October raid. Pieces of the station roof lay in the yard of her building; the blast had blown out the windows of her apartment, and the glass shards had cut her new draperies. Otherwise, she paid little attention to the uproar.\n\nBut the war seemed very far away on this February day, and the Dresdeners, in spite of the menacing signs, continued to trust in their good fortune. The two air raids, even with over 800 deaths, were minor incursions compared to what had befallen Berlin, Hamburg, Munich, Essen, Stuttgart\u2014indeed, every other major city of Germany, with their hundreds of thousands of dead, injured, and homeless.\n\nThe militarily sophisticated of the city's inhabitants speculated, correctly, that in the October and January raids their city had really been the secondary target. It had been attacked only because the Allied bombers had failed to locate or reach their primary targets\u2014the oil refineries or one of the important industrial cities of eastern Europe. They had released their bombs almost by accident, or so it was argued.\n\nIn any event, this was the day before the beginning of Lent, and many Dresdeners, in spite of the exigencies imposed by war, looked forward to celebrating the Teutonic version of the rowdy and raucous Mardi Gras. Since 1933 and the rise of the Nazis, extreme forms of behavior had disappeared from the celebration, but it was still popular, particularly with children, who looked forward to the games, costumes, and masks.\n\nThe Dresdeners did not have a compelling reason to celebrate this year\u2014too many of the men of Dresden would never return to the city\u2014but they could be grateful that their elegant city, with its terraces, palaces, art museums, and parks, had been spared.\n\nIn the west, the Allied ground forces were moving slowly but inexorably toward the Rhine. In the east, in three short weeks, the Russian army had advanced across Poland and had reached the east bank of the Oder\u2014only seventy-five miles from Dresden and just thirty-five miles from Berlin. And night after night, day after day, hundreds of British and American bombers systematically went about their task of reducing the Third Reich to rubble.\n\nBut in Dresden, the old Germany was still alive. The Frauenkirche, the Semper Opera House, the cathedral, and the great public buildings still rose majestically into the Saxon sky. And the continued, almost undamaged existence of their beautiful city imparted a confidence to the populace.\n\nHowever, Dresden's miraculous survival also spawned and fed dozens of rumors. Two of the more common were that a relative of Winston Churchill's lived in the city or that the Allies had agreed among themselves to spare Dresden so that it could serve as the capital of a new Germany. This latter rumor was bruited about carefully. To talk of a new Germany was to talk of defeat, and defeatism was a capital offense.\n\nWhile Dresden had suffered few of the physical effects of war, other damage was evident. Like all German cities in early 1945, Dresden was a city of women, children, and old men. Any young men there were attached to the police and civil defense or were disabled veterans. In addition, there were thousands of forced civilian laborers from western Europe, along with American, British, French, and Russian prisoners of war. There were also scattered all over Germany many thousands of men from the occupied countries who had volunteered for work in Germany.\n\nA small monument on the Hamburgerstrasse honors six Belgian and two French workers who were killed in the October raid. Were they unfortunate foreigners who had been transported to Germany as slave laborers? Or were they workers who had willingly taken up the Nazis' offer of jobs and high wages in the Third Reich?\n\nThere was also another group of young German men\u2014hidden, furtive, living on the edges of society. These were the military deserters who were becoming a commonplace in the cities of the Reich. As the Allies tightened the vise, their numbers soared. Men on leave simply did not return to the front.\n\nJoseph Goebbels estimated that there were tens of thousands of such fugitives hiding out in Germany. He therefore forbade civilians to give food or lodging to soldiers, any one of whom could be a deserter. He had nothing but praise for Colonel General Ferdinand Sch\u00f6rner, an ardent Nazi who was a commander in the east. Sch\u00f6rner employed the most brutal methods to deter desertions, malingering, and absenteeism.\n\n\"Sch\u00f6rner is decidedly a personality as a commander,\" Goebbels wrote. \"The details he gave me about the methods he uses to raise morale were first-rate and demonstrate not only his talents as a commander in the field but also his superb political insight. He is using quite novel modern methods.\" A particularly effective method devised by Sch\u00f6rner was to hang miscreants \"on the nearest tree with a placard announcing: 'I am a deserter and have declined to defend German women and children.' \"\n\nGoebbels made no distinction between military and civilian duty. Later in the war, when bread riots erupted in the Rahnsdorf area of Berlin, the ringleaders, two women and a man, were arrested after they helped loot a bakery. Goebbels pardoned one woman, but, as he wrote in his diary, \"the other two who were condemned to death I shall have beheaded during the night.\" Their grisly deaths were announced on placards placed throughout Rahnsdorf and broadcast over the radio to the city at large.\n\nThere are no reliable estimates of the number of soldiers who joined up with the refugee columns headed west or who were hiding out in the crowded city, but the Reichsminister's fulminations indicate that the problem was a serious one. Hundreds of deserters were picked up by patrols in Dresden alone.\n\nAbove all, there was one compelling and unmistakable sign that the war was going badly, a sign that could not be hidden from the public or disguised by the propaganda from Berlin\u2014the vast influx of refugees from the east. The stream swelled from the hundreds to the thousands to the millions. Every road, highway, and railway from the east was clogged with humanity, trying to escape being caught between the Soviet and Nazi forces clashing on the constantly contracting Eastern Front. A more compelling reason for the exodus was the fear of being left behind to suffer the barbarities of the advancing Soviets.\n\nMillions of ethnic Germans from East Prussia and Silesia were fleeing before the advancing Red Army, and their flight to the west was already causing enormous disruption on the rail lines and highways. Almost the entire population of East Prussia fled to the Baltic Coast for transport to the Reich proper. Over 450,000 refugees were evacuated from Pillau in January alone. In the harbor at Kiel, the _Wilhelm Gustloff_ , arriving with 8,000 soldiers and civilians, was torpedoed by a Soviet submarine. More than 6,000 of the passengers drowned in the icy waters.\n\nWith such suffering, it is easy to understand the public's outrage over an act of G\u00f6ring's that Joseph Goebbels called a Marie-Antoinette gesture. When a column of refugees from the east passed by on the road near his vast estate northeast of Berlin, the Reichsmarschall shot a bison from his herd and gave them the meat. G\u00f6ring was crucified in the press for the incident, and Hitler was furious. The uncontrite air marshal soon abandoned Prussia altogether. In March, he commandeered two trains to transport his artworks and left for the relative safety of the Obersalzburg.\n\nOthers had no way to escape except on foot. Nearly a million people walked to Danzig in the bitter cold. The same sad tale was playing itself out farther south as well. Hundreds of thousands of refugees passed through or around Dresden. Thousands of German soldiers willingly turned from their primary duties to aid the refugees, who could have been their own wives, parents, or children. They often exhibited great bravery and ingenuity in protecting the civilians from certain murder by the Russians who, as they overtook the refugee columns, did not hesitate to gun them down.\n\nAs historian John Keegan said, \"The flight of January 1945 was an episode of human suffering almost without parallel in the Second World War\u2014outside the concentration camps.\" The Germans themselves created the climate of revenge. During their advance in the opposite direction, toward Moscow, Stalingrad, and Leningrad, beginning in the summer of 1941, they committed unspeakable atrocities. It made no difference who did the killing\u2014Gestapo, SS, or ordinary Wehrmacht soldiers. Millions of Russian civilians were slaughtered as the Germans made their way across the Soviet Union.\n\n**The crumbling Western** and Eastern Fronts, the destruction of their cities, and the desperate measures necessary to rescue their own people from the bombers and invaders did not deter the Nazis from continuing to pursue one of the primary aims of National Socialism: the destruction of the Jews. In the vast catalog of Nazi horrors, these last acts of barbarism are perhaps the most appalling.\n\nAs the Soviets advanced in the east, the Nazis murdered the concentration-camp inmates who were too ill or too weak to move. They then began the transfer of the surviving prisoners to the west. Vehicles, ships, and trains were diverted from transporting troops and ammunition to transporting Jews back into the Reich. Many thousands of the evacuees traveled on foot, however, and on these death marches few of the Jews survived.\n\nOf the 29,000 Jews in the Stutthof camp, near Danzig, only 3,000 survived the transfer by ship to Stettin and then on by train to Ravens-br\u00fcck and Sachsenhausen. In a satellite camp farther east of Danzig, 3,700 Jewish slave laborers in K\u00f6nigsberg were marched to the Baltic coast, where they were told they would board ships bound for Germany. Seven hundred were killed on the march; no ships awaited the others. Instead, the 3,000 survivors were gunned down by their guards when they reached the sea. Almost all of these wretched victims were women.\n\nAt Neusalz on the Oder, another thousand Jewish women were marched from the camp to Flossenburg, near Marienbad\u2014a distance of almost two hundred miles. Eight hundred died or were murdered en route. The remaining 200 were then shipped to Bergen-Belsen by train. More died inside the closed boxcars as the train traveled north in the dead of winter.\n\nThese scenes of sadism and murder were played out all over the Reich and the occupied territories as the Allies closed in. The argument that the Nazis needed the slave labor in the Reich itself and were therefore willing to divert much-needed transport to move them there is destroyed by cold-blooded fact. The contrary seems to be the case. The few who had managed to survive the beatings, the starvation, and the disease in the camps were now systematically slaughtered as they were transported, often on foot, on their hopeless journeys.\n\nWhile the inmates of the camps in Upper Silesia were being evacuated, time had also run out for the hundreds of German Jews who had escaped deportation and certain death because they had Aryan husbands or wives. Hence the deportation orders being delivered by Victor Klemperer on 13 February.\n\n**Dresden did its best** to cope with the influx of refugees from the east, but the city had become so overtaxed that police checkpoints were set up at the eastern approaches to encourage the refugees to bypass Dresden and proceed directly to the west. There was no room for any more of them in the already dangerously overcrowded city. As these legions of the dispossessed made their way across the bridges of the Elbe, the view south made them forget, temporarily, their own sorry plight and that of their country, which was in its death throes. Dresden had survived. Perhaps, they dared to hope, other cities had as well.\n\nThe refugees' respite was brief. They could not tarry. Not even the most fervid and ardent supporters of Adolf Hitler and National Socialism could pretend that the war was just going badly. It was lost. The Saxon capital might be intact, but they must move on. The police at the barricades politely but firmly showed them the way west.\n\nAs Victor Klemperer made his rounds of the Jews' houses, Sybil Schneider, a Silesian farm girl, and her family were approaching the city in a horse-drawn wagon. The Schneiders' wagon was piled high with the few possessions that they had hurriedly packed when they'd fled their farm home before the advancing Soviet army.\n\nThe girl was excited about seeing the Saxon capital and perhaps resting there. Also, the weather had cleared, as the meteorologists with the RAF had predicted. It was now a sunny, perfect spring day in Saxony.\n\nBut Sybil's father had other ideas. He was only too glad to move on when directed by the police. While Dresden had not been bombed, he said, no city was safe. They would camp on the other side of the city, out in the open countryside.\n\nEven had Herr Schneider chosen to remain in the city, he would have found it difficult to find a place to spend the night. Nearly every apartment and house was crammed with relatives or friends from the east; many other residents had been ordered to take in strangers. There were makeshift campsites everywhere. Some 200,000 Silesians and East Prussians were living in tents or shacks in the Grosser Garten. The city's population was more than double its prewar size. Some estimates have put the number as high as 1.4 million.\n\nUnlike other major German cities, Dresden had an exceptionally low population density, due to the large proportion of single houses surrounded by gardens. Even the built-up areas did not have the congestion of Berlin and Munich. However, in February 1945, the open spaces, gardens, and parks were filled with people.\n\nThe Reich provided rail transport from the east for hundreds of thousands of the fleeing easterners, but the last train out of the city had run on 12 February. Transport farther west was scheduled to resume in a few days; until then, the refugees were stranded in the Saxon capital.\n\nHerr Schneider had no intention of waiting for a train. His horse and wagon would do. He proceeded with his family slowly around the darkening city and on to the low hills to the west.\n\n**Eight days earlier** a rather more distinguished refugee had arrived from the east. On the morning of 5 February, the very day that Spaatz cabled Kuter in Yalta that Dresden and other targets in the east would be bombed as weather permitted, an unusual car\u2014a steam car fueled by wood\u2014arrived at Villa Wiesenstein in the mountain village of Agnetendorf, in Upper Silesia. For four decades, the villa had been the retreat of novelist, poet, playwright, and Nobel laureate Gerhart Hauptmann, now eighty-three years old.\n\nNo bombs had fallen and no invading armies had appeared in the Riesengebirge, the mountain range between Silesia and Bohemia, and the birthplace of the Elbe. But the war was coming ever closer each day as the Red Army continued its advance to the west.\n\nFor the past two years, so many thousands of Germans fleeing the Soviet troops in the east and the air raids in the west had flocked to the area that it had become known as Germany's air-raid shelter. No one, no matter how privileged, was exempt from housing refugees, who numbered in the thousands, and the Hauptmanns had had to take in two women and seven children.\n\nHis solitude shattered, Hauptmann, after much reflection and anguish, decided to remove himself to Dresden, where so often in the past he had gone to refresh his spirits. Then, too, Margarete Hauptmann was ailing. The car had been dispatched by Weidner's Sanatorium, in the Dresden suburb of Oberloschwitz, to fetch the couple and Anni, their servant and secretary. Weidner's had agreed to admit Frau Hauptmann for treatment, and her husband, in the solitude of a cottage on the grounds of the famous hospital, might also find a degree of serenity.\n\nAfter the Hauptmann's arrival, the physicians at Weidner's determined that Margarete Hauptmann needed more intensive care than could be provided by a sanatorium, and she was transferred to a hospital in Dresden proper. The old man stayed up on the heights and on his walks in the garden reflected on his ties to this magical city. He could see the tower of the Johanneskirche, where he had married his first wife, and the Royal Academy on the Br\u00fchl Terrace, where he had studied art. Down there were the theaters where his plays had been produced, and spread out along the Elbe was the Hotel Bellevue and its gardens. For years the hotel had, in the German style, treated the visiting writer like royalty. \"Really, one is compelled to love it, my jewel, my Dresden,\" Hauptmann remarked to a companion on one of his strolls. \"May it never share the fate of other cities!\"\n\nSoon Margarete Hauptmann returned to the cottage at Weidner's. The hospital in Dresden had determined that she was not as ill as first diagnosed, but there was another, darker reason for her quick return. Anni had brought her the disturbing news that Hauptmann was drinking heavily and quickly declining.\n\nAfter her return to the sanatorium, Frau Hauptmann soon had the situation in hand, and under her ministrations or, more probably, her proscriptions, Gerhart Hauptmann sobered up. On 13 February he was so much improved in body and spirit that he was able to write a new poem, \"Zauberblume\" (\"Magic Flower\").\n\nThe rest of the day was whiled away with friends at a luncheon, followed by a nap, then afternoon tea, during which the faithful Anni read aloud. Later, Hauptmann shared a quiet dinner with his wife. There was talk of leaving the cottage at Weidner's for the more congenial atmosphere of the Hotel Bellevue, and then Hauptmann went to bed.\n\n# CHAPTER NINE\n\n**A PILLAR OF FIRE BY NIGHT**\n\nBomber Command Takes the Lead\n\n**The sun had long since set when the first of the Lancasters of** 5 Group, the Pathfinders, or flare force, of 83 and 97 Squadrons, lifted off and headed for Germany. It was approximately 1720 hours on 13 February 1945.\n\nIn an age of satellites and global positioning systems, navigation in February 1945 seems primitive indeed. Often the finding of a target was little more than sophisticated guesswork, although the newest system, called loran, which was used on this raid for the first time, was far ahead of any previous device. But mistakes were still not uncommon. As has been observed, bombing a city was the least of it. Finding the city was the problem.\n\nFlying just minutes ahead of the main bomber fleet, the Pathfinders had a single objective: to find Dresden and drop parachute flares, which would illuminate an area one to two miles square.\n\nWhen the ground below was lit up as if by daylight, the second phase of the raid would begin. The faster and more agile Mosquito marker planes, which would not take off for almost two and a half hours after the Lancasters were airborne, would now have to identify the central aiming point and then drop their 1,000-pound Tls, the target indicators. The bombardiers in the main bomber fleet, which was to approach from the northwest, were then to center their bomb patterns on the brilliant red glow from the target indicator bombs. These intricate maneuvers were, at least in theory, guided by a master bomber who circled the city in another Mosquito and conducted the raid as if he were the leader of a great orchestra.\n\nThe metaphor is an apt one. As in a symphony, everything must come together in a well-defined sequence and time frame\u2014twenty to twenty-five minutes\u2014from the illuminator flares from the Pathfinders, to the target indicators from the Mosquito marker bombers, to the rain of high explosives and incendiaries from the main bomber force.\n\nSome ten minutes after the Pathfinders were airborne and en route to Saxony, the main bomber force, code-named \"Plate-Rack,\" began taxiing into position for takeoff. Within a half hour, 254 Lancasters, all from 5 Group, Harris's old command at Grantham, with their cargo of almost 900 tons of high explosives and incendiaries, were en route to the assembly point at Reading and thence to the Channel and on to the Continent.\n\nThis night every crewman on any plane that was to come anywhere close to the Eastern Front carried something new: a Union Jack embossed with the words, in Russian, \"I am an Englishman.\" It was hoped that this might save the life of anyone who had to parachute behind the Russian lines, but no one much counted on it.\n\nThe weather that had caused the scrubbing of the daylight American raid was even more dangerous for the night operations of the British. Navigation was more complicated, and the return in the dark and the fog to the home bases was often a nightmarish experience. However, unlike the Eighth Air Force, which had been called on to bomb the rail centers and marshaling yards, \"precision targets,\" the RAF had a more broadly defined assignment. Their target was simply the \"town area.\" Visibility was less important.\n\nTonight's raid would become the prime example of the Bomber Command theory of the double blow, an air attack in which a second wave of bombers would arrive just as the firefighters and rescue teams below were fully occupied in battling the fires caused by the earlier raid and attempting to bring out survivors.\n\nOnly a handful of raids ever actually conformed to this double-strike model, which was a supposed cornerstone of Bomber Command policy. Those that did were cataclysmic, and thus the question is why the method was not used more than it was. The reason or reasons are rather simple: bad weather and the lack of men and machines for a double or triple blow.\n\nThe Dresden raid now began to unfold. In its execution, it was theory put into flawless practice: two waves of bombers, three hours apart, followed the next day by a massive daylight raid by more bombers and escort fighters with the additional task of strafing rail and road traffic.\n\nOther raids planned for that night were designed to keep the German defenses in the dark as to the RAF's true intentions toward Dresden. Mosquitoes attacked Magdeburg, Bonn, Misburg, and Nuremberg, and another 360 Lancasters and Halifaxes\u2014a larger force than that headed for Dresden\u2014were dispatched to bomb the synthetic oil plant at B\u00f6hlen, just south of Leipzig and less than sixty miles from Dresden.\n\n**The two bomber streams** followed more or less parallel courses for the journey out. They crossed the Channel and entered French airspace near the Somme. Their route was thus far a relatively safe one, since the Allied lines lay far to the east at this stage of the war. Window, aluminum foil strips that jammed German radar, was liberally scattered along a broad north-south front west of Duisburg, to west of Mannheim, a 120-mile screen behind which the bombers advanced into the Reich.\n\nWhen they emerged from behind the screen of Window, the German trackers could see that there were clearly two distinct bomber streams. The Plate-Rack bomber fleet crossed the Rhine just north of Cologne. The force bound for B\u00f6hlen crossed farther south, just north of Koblenz.\n\nBut any number of possible targets lay in their paths as they pressed on, and the German radar operators and air defense teams now had to make agonizing projections as to where they might actually be heading. The standard operating procedure was for the tracking data to be refined and a series of preliminary warnings issued.\n\nOn the night of 13 February 1945, the system seems to have failed. There was no preliminary warning even when it was obvious that the planes were heading for Saxony, and it was not until the bombers were almost over the city that the air observers realized that Dresden was the intended target. Thus when the _Fliegeralarm_ , the actual air-raid alarm, did sound, Dresdeners had just a few minutes to find cover.\n\nMeanwhile, the two bomber forces maintained their parallel course until just before 2200 hours, when the planes on the more southerly route peeled off toward B\u00f6hlen. At about the same time the northern wave of planes, all Lancasters, made a turn to the southeast, a heading that would bring them to the Elbe and then, just a few minutes later, to Dresden.\n\nOf the original 254 Lancasters designated for Dresden, ten were now out of action for one reason or another, a not unusual number. The attacking force thus comprised 244 Lancasters, carrying over 500 tons of high-explosive bombs and more than 375 tons of incendiaries.\n\n**As the British** air fleet lumbered toward Saxony, Winston Churchill and the British delegation were comfortably ensconced aboard SS _Franconia_ in the harbor at Sevastopol. The Yalta Conference had ended two days earlier, but the British united front that had been so evident when important issues were at stake had disappeared.\n\nTo the dismay of their aides, Eden and Churchill were arguing over the next stop, Athens. Churchill kept everyone on edge with his to-ing and fro-ing. He would go to Athens. He would not go to Athens. Each time he decided in favor of the trip Eden became more annoyed. The foreign secretary did not want to be upstaged in the Greek capital by the prime minister. An exasperated Alexander Cadogan said to Lord Moran, \"I never bargained to take Tetrazzini and Melba round the world together in one party.\"\n\nBy the next morning the little contretemps was settled\u2014everyone would go to Athens\u2014and the British party was driven from Sevastopol to the airfield at Saki for the flight to the Greek capital. En route, Churchill, again displaying that touch that distinguished him from lesser beings, had the pilot circle the island of Skyros and the tomb of Rupert Brooke.\n\n**Just before 2000 hours** , the eight Mosquitoes that were to drop the target indicators on the central aiming point and thus lay out the bombing path for the heavies took off from their base at Woodhall Spa.\n\nA few minutes later, the master bomber, Wing Commander Maurice Smith, and his navigator, Pilot Officer Leslie Page, climbed into their Mosquito at Coningsby. The fast Mosquitoes would reach Dresden, if all went according to plan, just behind the Pathfinders and just ahead of the Plate-Rack force.\n\nThe Mosquito was designed to fly at high altitudes to avoid flak and at great speed to elude interceptors, but the nine planes on this mission would be operating at the outer limits of their capabilities. They were thus obliged to take an almost direct route from their bases to the Saxon capital.\n\nTheir route took them out across the North Sea to Holland and then directly southeast. They would approach the target from the southwest, swooping down from 20,000 feet at Chemnitz to well below 1,000 feet at Dresden.\n\n**While Gerhart Hauptmann** , his wife, and his secretary were making do in reduced but still comfortable circumstances in Oberloschwitz, overlooking Dresden, the Silesian farmer Herr Schneider was settling his family for the night at their camp in the hills on the western side of the city. A few minutes before ten o'clock, they heard the sound of airplane engines. As they looked apprehensively for the source of the noise, the night sky over the city to the east was turned to day by white and green flares.\n\nThe flares were eerily beautiful on this winter evening, reminiscent of prewar _Feuerwerk_ along the Elbe. But these were not civic fireworks to celebrate Shrove Tuesday. Lancaster Pathfinders from 83 Squadron, 5 Group, of the RAF had released green primaries and white illuminator magnesium flares to light the way for the target indicator Mosquitoes that were racing toward Dresden.\n\nThe Pathfinders had picked out the unmistakable S-curve of the Elbe that identified the target as Dresden. The first flares, the primary greens, fell directly in the bend of the river. Using the primary greens as a marker, the other Pathfinder aircraft began to unload their brilliant whites. The distant spires of the city stood out in sharp relief in the glow.\n\nAs the flares floated slowly to earth, almost at once there was another roar of planes. The nine Mosquito bombers, eight marker planes and the master bomber, had begun their run. As they made their vertiginous descent toward the city, they passed over the refugee camps. The Schneider family had good reason to be grateful that the father had insisted that they move on rather than rest in the city. The attack he feared had begun.\n\nThe timing of the Mosquitoes was perfect, and from the refugee camp there could be seen the reddish glow that had begun to replace the brilliant whites and greens. The Mosquitoes had begun to drop the target indicators.\n\n**The nine Mosquitoes had** descended from almost 20,000 feet in just five minutes in order to fulfill their mission. In just a few more minutes the main bomber fleet would arrive, and they needed the target indicators to be afire to guide them to the bombing zones. The master bomber now broke radio silence. He called out, \"Controller to Marker Leader. How do you hear me? Over.\" The marker leader, Flight Lieutenant William Topper, who would drop the first target-indicator bomb, replied that Wing Commander Smith was coming in loud and clear.\n\nTopper was now just 2,000 feet above the city, which was brilliantly illuminated by the marker flares. He could make out many of the landmarks, which he had seen on the briefing photographs and target maps.\n\nThe Hauptbahnhof, the main railway station, with its glass roof, was easily identified, as were the tracks snaking out from it, which would lead him to the central aiming point, a sports stadium close by the railroad bridge that crossed the Elbe beside it. The stadium had been chosen because of its unmistakable oval shape and its proximity to the river.\n\nShouting, \"Marker Leader: Tally-ho!\" to signal that he was going in and that all other marker Mosquitoes should hold back, Topper roared down to 800 feet and released his 1,000-pound target-indicator bomb. Below him the stadium was lit up by a burst of red fire. The TI had landed within a hundred yards of it, an almost perfect drop. In quick succession, more Mosquitoes began to drop their red TIs into the stadium, but since the preliminary marking had been so accurate the master bomber decided to hold a few in reserve, in case they were needed for further marking.\n\nHigh above the Mosquitoes, a Lancaster bomber circled the city to act as radio relay for the marker bombers, the master bomber, and the home base if necessary. The pilot reported that he could see the red TIs burning 18,000 feet below, through the thin cloud cover. All was in readiness for the fast-approaching Plate-Rack force, which would clearly have no trouble finding the target.\n\nThe plan of attack called for the first wave of Lancasters to cross the city from the northwest to the southeast. The central aiming point, the stadium, was approximately a mile from the Friedrichstadt marshaling yards, but this important target was on the approach path. Unless the bombing backed up on the aiming point it would be passed over.\n\nBut the elements that were to enable the RAF to raise a firestorm lay directly ahead of the central aiming point: the Altstadt. Congested old Dresden, with its medieval street plan, highly combustible ancient buildings, and several hundred thousand people, lay entirely within the bombing path of the first wave of planes.\n\nWith frightening precision, the first raid in the Bomber Command and Eighth Air Force plan to completely destroy a large city with a triple blow of air strikes began to unfold. The 244 Lancasters of 5 Group fanned out from the aiming point, the sports stadium by the Elbe, and prepared to release their cargo, 875 tons of high-explosive bombs and incendiaries. At 2210 the first bombs began to fall.\n\nThe heavy bombs and thousands of smaller incendiaries that rained down on the city in the first wave would, Arthur Harris had long theorized, set so many hundreds of small fires that no matter how well organized or well equipped a firefighting service might be it could not hope to cope with all of them. Further, the firefighting efforts would be hampered, if not halted, by the huge blasts caused by 2,000-pound, 4,000-pound, or even more powerful high-explosive bombs. As Harris said in his memoirs, if \"a rain of incendiaries is mixed with high explosive bombs there is an irresistible temptation for the fireman to keep his head down.\"\n\nThe first wave of planes from Bomber Command had, as it turned out, the relatively simple task of raising a fire by igniting the combustible Altstadt of Dresden. The resulting beacon would light the way for the larger second wave, scheduled to arrive three hours later.\n\nThe second wave would appear over Dresden at the very time that the optimum number of fire brigades and rescue teams were in the streets of the burning city. The high explosives of the first wave would have destroyed most of the water mains, and the collapsed buildings would have rendered the streets impassable. The second wave would compound the earlier destruction many times and, by design, kill the firemen and rescue workers so the destruction could rage on unchecked.\n\nIt was soon apparent to the master bomber that there was no high-altitude flak and he could bring the Plate-Rack force down to just 8,000 feet, the upper limit of the range of the few 20-millimeter guns that were throwing up flak. At that altitude, the entire city was visible to the bombardiers.\n\nIn his Mosquito, master bomber Maurice Smith, like the maestro he was, exhorted the bombardiers, praising their accuracy and correcting the tempo as necessary. \"Good shot!\" \"Back up!\" \"Back up!\" Everywhere below him fires were breaking out as over 200,000 incendiaries crashed through the roofs of apartment houses, museums, churches, palaces, theaters, and government buildings.\n\nThe high-explosive ordnance, bombs ranging in weight from 500 pounds to over 4,000 pounds\u2014two-ton \"cookies\"\u2014did their assigned tasks well, rupturing water mains and interdicting emergency workers' access. They also carried out an even more deadly mission. The enormous pressure waves created by the cookies blew out doors and windows, thereby increasing the effectiveness of the incendiary bombs, the weapon that was designed to do the most damage. Buildings were turned into vast flues as air was drawn through blasted-out doors and windows to feed the already fiercely burning incendiaries. Firefighters, both professional and amateur, would soon be overwhelmed.\n\nIn just twenty minutes the mission of the aircrews of 5 Group had been completed and they had turned back toward England. Wing Commander Smith turned his Mosquito as well. He had been over the city for less than half an hour. As the Plate-Rack force began the long return flight, behind them the plane crews could see thousands of small fires burning.\n\n**By the time Victor Klemperer** had finished his mournful errands late on 13 February and returned to his crowded quarters at the Jews' house at 1 Zeughausstrasse, the wintry day had become \"perfect spring weather,\" as he recorded later in his diary.\n\nAround 2130 that evening he sat down to have coffee with his wife. A few minutes before 2200 the _Fliegeralarm_ , a full-scale air-raid alarm, sounded. The Klemperers and the other residents of the Jews' house rushed down to the air-raid shelter that had been set aside for Jews in the building next door, 3 Zeughausstrasse. Upstairs was the headquarters for the now tiny Dresden Jewish community, as well as the assembly point for the work details and deportations.\n\nIn the darkened shelter, the Klemperers trembled at the sound of airplanes and the crash of bombs. There was fear, he said, but no panic, and when the all clear sounded at 2330 they left the cellar and returned to their rooms.\n\nThey could see from the smoke and the flames that a major raid had occurred, but their building was intact and Klemperer, who was exhausted from his day walking the streets of Dresden, thought only of sleep. He and Eva went back to bed.\n\n**While the Klemperers slept** , the small fires set by the thousands of incendiaries from the first wave of British planes began to spread and intensify. One of the few civil defense measures made available to the citizens of Dresden\u2014buckets of sand\u2014proved useless in fighting the fires that suddenly seemed to be everywhere.\n\nThe flames raced from room to room, from floor to floor, and from building to building, joining forces and growing ever larger and stronger, leaping across courtyards, alleys, and the narrow streets of the Altstadt.\n\nThe process was repeated on an ever-increasing scale as houses ignited and burned, then entire blocks went up, until whole sections of the city were afire. Streets and alleys became rivulets of fire that coalesced into rivers of fire that converged until they formed an ocean of fire that covered Dresden.\n\nAs the storm grew, air from outlying areas was sucked into the center to feed the flames, creating huge backdrafts, then gales, and finally winds of hurricane force, which swept everything into the fiery maelstrom that was consuming the city center. Trees were uprooted. Trams, trucks, even railroad engines were overturned and thrown about.\n\nTemperatures soared to a thousand, fifteen hundred, two thousand degrees. Lampposts, street signs, and even the bricks themselves disintegrated. The open streets became death traps as the asphalt melted in the terrible heat and the fleeing refugees found themselves unable to move. After terrible struggles to free themselves, they collapsed and died, falling into the burning tar, where they were incinerated.\n\nPeople who were blocks from the flames and thought themselves safe were suddenly picked up by the hurricane-force winds and pulled into the inferno, where their bodies ignited and their corpses were reduced to ash. In the makeshift air-raid shelters, thousands suffocated as the superheated air pulled cooler, breathable air from the basements where they had sought shelter. Instead, these havens from the death and destruction above became death traps filled with overheated and poisonous gases. Thousands of others died when their internal organs were ripped apart by the tremendous concussions caused by the high-explosive bombs.\n\nAs the wooden beams and trusses and supports gave way, floors and roofs collapsed, burying the thousands huddled in the cellars below. Entire blocks of buildings with nothing to support them buckled and fell into the streets. Firefighters, ambulance drivers, and rescue teams found their way blocked by giant mounds of burning rubble in every avenue and street. Instead of fighting the fires and extricating the injured, they soon would be looking for ways out of the conflagration themselves.\n\n**At 0105 air-raid alarms** again sounded, but since the electrical system had been largely destroyed in the earlier raid, these were hand-cranked devices limited to small areas of perhaps a block or so. Bomber Harris's second wave\u2014529 Lancasters from 1, 3, 6, and 8 Groups\u2014had arrived punctually at the appointed hour.\n\nTheir route into the Reich had been somewhat farther to the south than that of 5 Group, and they approached the city from almost due west. Pathfinders from 8 Group were the designated markers. They had no trouble finding the target. The red glow from the burning city was visible on the horizon from more than sixty miles out.\n\nThe weather had cleared further, as predicted, and as they neared Dresden, the Pathfinders in the second wave could see that the only visual impediment was the thick smoke from the fires. Although they were superfluous, at 0123 hours away went the marker flares, which had been designed to light up a target that now needed no illumination. The city below was completely in flames, engulfed in a firestorm.\n\nWhen the master bomber, Squadron Leader C. P. C. de Wesslow, and his deputy, Wing Commander H. J. F. Le Good, arrived just minutes later they were faced with a quandary. The first wave was such a success, with the entire city on fire, that to proceed with the prearranged bombing plan was no longer the most effective use of their own high explosives and incendiaries. Dresden was, in actuality, already one giant target indicator.\n\nThe decision was quickly made to mark areas outside the firestorm and drop the bombs accordingly, thus expanding the area of destruction. Le Good, who went in first, dropped his target indicators to one side of the fires, and the other markers followed suit, first to one side of the firestorm and then to the other, to lay out the path for the bombing fleet.\n\nBombs now began to rain down on the Hauptbahnhof, the Central Station, which had escaped relatively untouched in the first raid since it lay outside the direct bombing path. Hundreds of refugees had taken shelter in the tunnels underneath the station, and the trains had been shunted out of the station three hours earlier. But in the belief that it was now safe to do so, the trains had been brought back into the station to reload their passengers.\n\nAs the high explosives and incendiaries tore through the immense glass cover over the train shed, thousands of shards rained down on the people crowded onto the platforms below. Those who were not killed or critically injured by the falling glass were blown apart by the explosions or burned to death by the incendiaries. The hundreds of refugees who were huddled in the darkness of the tunnels met a similar fate as the bombs ripped through the ceilings and created an underground inferno.\n\nThe master bomber was somewhat baffled by a large black area abutting the city center, which strangely showed no sign of fire. He ordered it bombed. This last place was the Grosser Garten, and now the great public park also became a scene of fire and devastation as incendiaries and high explosives ripped up the earth, flattened the trees, and tore into the vast refugee camp set up there, to which many other thousands had fled to escape the firestorm in the nearby neighborhoods.\n\nVictor and Eva Klemperer, asleep and unaware that the city outside the Jews' house was completely on fire, were roused by the handheld air-raid sirens being sounded in the street outside. As they raced back to the Jews' house cellar bombs were already falling everywhere around them.\n\nThey remained in the cellar until the all clear was sounded at 0215, but when they emerged, Eva Klemperer realized that their world had changed forever. The air raids might have destroyed her city and killed thousands of people, but they had also provided a long-hoped-for but unexpected lifeline for her husband and herself. She immediately determined to take advantage of the ensuing confusion.\n\nShe removed the yellow star from Victor Klemperer's coat, and with little more than the clothes on their backs they joined the great stream of refugees beginning the trek south toward Bavaria. For the few weeks remaining until the fall of the Reich, they managed to blend in with the thousands of other displaced persons moving about the countryside, and thus they survived the Holocaust.\n\n**By 0155 on the morning** of 14 February, the last British bomber was en route home to England. The double blow had turned out to be one of the most successful operations in Bomber Command history and one of the safest. Only six aircraft had been lost, just one to enemy fire, the victim of one of the two German fighters that had come up to defend the city.\n\nAltogether, in a total of about forty-five minutes, more than 650,000 small incendiaries and hundreds of high-explosive bombs ranging in weight from 500 to 8,000 pounds had rained down on Dresden.\n\nThe British bombers had turned the city into a vast sea of flame, a firestorm that would not burn itself out for days. But it was left to the Americans, who had been slated to strike the first blow, to deliver the coup de gr\u00e2ce to the mortally wounded Florence of the Elbe.\n\n# CHAPTER TEN\n\n**A COLUMN OF SMOKE BY DAY**\n\nThe American Third Wave\n\n**A t 0300 on 14 February, thousands of airmen were roused from** sleep at the American bomber and fighter bases scattered across England. With less than ten hours of daylight at this time of year, every minute was precious. Daylight helped to ensure not just the success of the bombing run but also the return trip home. The Allied advance had made available many emergency landing fields in France and hundreds of aircraft had made use of them, but there was still the risk of bringing a badly shot-up bomber home in the dark or, worse, ditching in the English Channel.\n\nCarl Spaatz and his deputies in the Eighth Air Force were determined to take advantage of the promised break in the weather, and on this day they would launch almost 1,400 heavy bombers and nearly 1,000 fighter escorts against targets in Germany.\n\nThe reversal of the bombing order of the original Thunderclap plan had also resulted in a change in Spaatz's promise of sending a 1,400-bomber armada against one target. The American force was now to be split into three main components. Some 461 bombers were assigned to Dresden, 457 to Chemnitz, and 375 to Magdeburg. A smaller force of 84 planes would bomb Wesel.\n\nThe airmen slated for a mission were served a serious breakfast, which featured real eggs with Spam, and at about 0440 they crowded into the briefing huts for the general briefing. The men of the First Air Division learned that their mission was a deep penetration into eastern Germany, to the Saxon capital of Dresden, a round-trip of some fifteen hundred miles.\n\nThe 461 B-17s assigned to Dresden would first head across the North Sea to the Dutch coast, where they would be joined by their escort of 316 P-51s, many of them from newly established fighter bases on the Continent. The bomber crews would thus have no worries about adequate fighter protection as they made their way deep into Germany.\n\nAfter the rendezvous with their \"little friends,\" the fighters, the B-17s of the First Air Division would proceed to Quakenbr\u00fcck, fifty-five miles southwest of Bremen, and from there they would head directly across Germany to the initial point, Torgau, sixty miles northwest of Dresden, on the Elbe.\n\nFlying up the river from Torgau, it should have been a simple matter to find the target, either visually or using H2X radar. Dresden should have been unmistakable, lying as it did in the bend of the Elbe. But for some of the navigators it turned out not to be so.\n\nIn the event of a sudden change in the weather, the alternate target for the First Air Division was Kassel. Some ninety miles west of Dresden, Kassel had been bombed by the Eighth Air Force many times since mid-1943, most recently just two weeks before. Many of these crews thus had some experience with flying deep into Germany.\n\nAfter the general briefing, there was a specialized briefing for each crew position, and then the men went to the personal-effects hut to turn in any items or papers that in the event of capture might be of use to the Germans in determining where an air crewman was stationed and where the planes were based. The only identifying documents allowed were military-issue dog tags.\n\nHidden on their persons, however, were religious artifacts, pictures of sweethearts, wives, or mothers, and good-luck charms of every description\u2014a rabbit's foot, a battered cap, a lucky scarf. Many airmen purposely left their beds unmade, a superstition that supposedly guaranteed a safe return. The combinations to guard against harm were countless.\n\n**The next stop was** to pick up their flight equipment, and then the crews boarded trucks to be driven out to the waiting planes to begin the preparation for takeoff. It took nearly an hour to go through the long checklist. Each item was called out and verified by the pilot and copilot. Every switch, gauge, and valve had to be double-checked. The procedure was replicated aboard each Flying Fortress and Liberator before the great planes with their combined crews of over 10,000 American airmen took to the skies and headed for the Continent and the day's work.\n\nThe powerful engines came to life and the planes began to move. Between 0700 and 0800, the aircraft began to lift off and make for the assembly areas. The predawn warm-up of over 6,000 engines and the takeoff of nearly 2,500 bombers and fighters shattered the quiet of the English countryside. Thus, almost every day, did the Eighth Air Force test the patience and patriotism of the residents of the towns and villages that very often lay directly in the flight paths or just outside the sprawling bases.\n\nHundreds of planes roared overhead on their way to the assembly points where the bomber streams formed up and headed for Saxony and, unknown to them, its already destroyed capital.\n\nIn a much-disputed and much-denied directive, even though it was by no means a deviation from standard operating procedure, the P-51 fighter pilots were also instructed after the bomb run to range afield and strafe \"targets of opportunity\"\u2014columns of troops, convoys of trucks, and railroad trains. In short, anything that moved was an acceptable target, even people in the streets, as eyewitnesses alleged for many years afterward. This further \"atrocity\" has become part of the Dresden legend.\n\nThe strafing policy had begun early in 1944 in order to maximize the use of the fighter squadrons. When there were no large missions scheduled, fighter groups were often sent out independently on strafing and bombing missions.\n\nIndeed, it was on one such mission over Normandy, on 17 July 1944, that a British fighter pilot strafed the staff car of Erwin Rommel near Livarot. The field marshal was injured so seriously that he was taken to Germany for treatment and convalescence. He never returned to the front. When it was discovered that he was deeply implicated in the 20 July plot against the F\u00fchrer, he was forced to commit suicide.\n\n**At Podington Air Base** , some fifteen miles east of Northampton, Second Lieutenant Walter S. Kelly; his copilot, Second Lieutenant Alexander M. Ellett Jr.; the navigator, Flight Officer Walter S. Sierzant Jr.; and the bombardier, Staff Sergeant Roman Pasinski entered the briefing room.\n\nComic strips were a favorite source for names of aircraft in World War II, and their B-17, the _Flat Top_ , carried on its nose a picture of the eponymous character from the comic strip _Dick Tracy_.\n\nA native of Repton, Alabama, Kelly was a senior at Auburn University when he enlisted in the army in February 1943. After twelve days of basic training he was sent for what he called \"pre-pre-flight training\" at Centre College in Danville, Kentucky, where he sang in the choir of the Methodist church and where he met and fell in love with a high school senior named Margaret Armstrong. Kelly went on to train at various bases around the country and finally, in May 1944, he was commissioned as a second lieutenant and earned his pilot's wings.\n\nMargaret Armstrong, who had completed her freshman year at Randolph-Macon College, in Virginia, traveled to the base where he was stationed in Stuttgart, Arkansas. They were together on D-day and read about the invasion in the newspaper. Later, they walked the streets of the small town, looking in shopwindows, and then sat on the fire escape of Margaret's hotel, \"feeling a little unsettled,\" as she recalled many years later.\n\nIn December 1944, Kelly was ordered overseas to England, and Margaret, now wearing his pilot's wings, was in her sophomore year at Randolph-Macon. In one of those coincidences that often define a life, on the campus one day she struck up a conversation with another girl who was wearing gunner's wings. It turned out that the wings had been given to her by William Balentine, of Greenville, South Carolina, a member of Walter Kelly's flight crew.\n\nMeanwhile, Second Lieutenant Kelly and the crew of the _Flat Top_ were getting their first taste of aerial warfare over Germany. On 15 January 1945, they were dispatched to Freiburg. Two days later they bombed the rail yards at Paderborn. On 28 January the target was Cologne and on 1 February the _Flat Top_ bombed Ludwigshafen.\n\nKelly's next flight was in many ways the supreme test for all bomber pilots: Berlin. An amalgam of the military, the psychological, and the political, Berlin was the heart of the Reich, and as such it carried a symbolism like that of no other German city. It was both hated as an enemy and desired as a target by all bomber crews. Its formidable antiaircraft defenses also instilled much fear in them, especially the more experienced airmen.\n\nOn 3 February 1945, the _Flat Top_ was part of the massive American thousand-bomber raid on Berlin. Although the Luftwaffe fighter forces were much weakened by early 1945, they still presented a threat, and the antiaircraft defenses were more powerful than ever. The retreat of the Wehrmacht back into the Reich had made more of the 88-millimeter guns available for air defense around key targets, and the flak, always a serious problem over the capital, was particularly heavy on this day. Twenty-three planes were lost, 339 damaged, and the casualties (dead, wounded, and missing) totaled 218.\n\nKelly and the crew of the _Flat Top_ fared reasonably well. They returned to Podington with just two holes in the aircraft. All were aware, however, that a few more inches in either direction could have brought them the fate of their colleagues who had gone down over Germany.\n\nSo by 14 February 1945, Walter Kelly and all his crew\u2014save one, the radioman, for whom this was the first combat mission\u2014were seasoned veterans of the air war over Germany. They had five successful missions under their belt, including the Big B itself.\n\n**Ten miles to the east** of Podington, at Kimbolton, the crew of another B-17, the _Miss Conduct_ , were performing an identical ritual. The crew, under the pilot, Second Lieutenant Stanley W. Cebuhar of Albia, Iowa, was part of the 527th Bomb Squadron of the 379th Bombardment Group. They had been together for most of the plane's missions, but there was a relative newcomer, the navigator, a twenty-year-old from Minnesota, Second Lieutenant Raymond G. Engstrand.\n\nIn June 1943, Engstrand had enlisted in the army and begun five weeks of basic training as his first step toward duty in the army air forces. Since he had entered the military directly from high school, Engstrand was first sent to a small college in Nashville, Tennessee, as preparation for further training and an officer's commission.\n\nSix months later, in early 1944, Engstrand began preflight training, which led, however, not to flight school but to training as a bombardier, which included a stretch at gunnery school. Engstrand and several of his fellow trainees at the base in Kingman, Arizona, were quarantined by an outbreak of scarlet fever, but the delay was temporary and by August 1944 Engstrand was training with a full crew\u2014flying B-24 Liberators in the sunny skies over the Southwest.\n\nOn 11 December, his training completed, Second Lieutenant Engstrand shipped out aboard the converted cruise liner _Manhattan_ from Boston, bound for Liverpool. Nine days later, with some relief, he arrived in England. There had been widespread speculation aboard the ship that they were going to proceed directly to the Continent as reinforcement ground troops in the Battle of the Bulge. Like most shipboard scuttlebutt, the rumor was false, and in a few days Engstrand was checking into the American base at Kimbolton, in Cambridgeshire.\n\nA few days later, on Christmas Eve, a sickening event in the English Channel underscored the still deadly might of the Nazi war machine. A German submarine torpedoed a Belgian troopship, the SS _Leopoldville_ , carrying 2,235 American troops; 763 infantrymen drowned.\n\nThe English weather was as predicted, with a fog so thick that the men had to be led to their billets. And when the fog burned off there was a surprise: there was not a B-24 in sight. Engstrand and his Liberator-trained colleagues were going to fly in B-17s with the 527th Bomb Squadron of the 379th Bombardment Group.\n\nThe transition was a relatively easy one, and although the die-hard B-24 men loyally entered into their shotgun marriage with the B-17, the Liberator remained their true love. This flexibility was characteristic of the Allied war effort. Men were assigned where they were needed and they did their duty.\n\nHowever, the new arrivals in England faced a different air campaign than that of their predecessors. The raids in late 1944 bore little resemblance to those staged by the first American pilots deployed to England. Greater range, fighter protection, and a large swath of friendly territory on the Continent increased the chances of survival.\n\nPilots struggled to get a damaged plane back over friendly territory, where they could bail out. At least one pilot turned his B-17 back toward enemy territory and put it on automatic pilot before bailing out, turning the plane into an improvised flying bomb.\n\nAnother very large difference was that crews no longer functioned as a complete unit, one that was assigned to a single aircraft. Rotation, death, and injury ensured that no group of men stayed together for any length of time. It was not unusual for an airman's first mission to be with men he hardly knew. The same was true of the planes. Bombers were designed to be interchangeable, and crews quickly adjusted. They flew what was available.\n\nIn addition, in August 1944 a new rotation policy had been instituted. Formerly, Eighth Air Force combat personnel were sent home for a thirty-day leave, but then they had to return to active duty in Europe. Knowing that they would return to the cause of their anxieties effectively canceled the benefits of rest and relaxation in the States.\n\nFrom now on, when a man's tour was over, he was sent back to the States for reassignment elsewhere. The effects of the new policy were dramatic. Cases of chronic and acute combat fatigue dropped by more than 50 percent. The less severe anxiety reactions dropped by 90 percent.\n\nBy late 1944, flak, not enemy fighters, posed the greatest danger. Consequently, two waist gunners were seen as superfluous, and thus many B-17s now flew with a nine-man crew instead of the original complement of ten. But the _Flat Top_ had a full crew: pilot, copilot, bombardier, navigator, top turret gunner\/flight engineer, radioman, right waist gunner, left waist gunner, ball turret gunner, and tail gunner.\n\nThere were other operational changes as well. Early on, the bombardier in effect flew the plane while on the bomb run. This approach was both inaccurate and wasteful. Greater concentration could be attained if the bombardier in the lead aircraft targeted the central aiming point and the other planes in the bomber stream coordinated their bomb release with him.\n\nThus came into being the \"togalier\"\u2014a combination of bombardier and nose gunner\u2014whose job was to \"toggle,\" or release the bombs by hitting a toggle switch on the signal of the bombardier in the lead plane. During the few minutes of the bomb run the togalier sat in the Plexiglas nose of the B-17. Otherwise he manned a machine gun in the chin turret of the plane.\n\nA further refinement in bombing tactics was the placement of a flight officer in the tail gunner position of the lead aircraft. From that vantage point he had a clear view of the bomber stream to the rear and was better able to keep the lead pilot apprised of the action.\n\nThe four ranking officers on the _Miss Conduct_ crowded into the smoky briefing room to receive their orders for the day. The other six crew members\u2014Technical Sergeant Lester F. Higginbotham of Frankfurt, Indiana; Staff Sergeant Waldon R. Hardy of Seattle, Washington; Staff Sergeant George R. Byers of Stockton, California; Sergeant Francis E. Beam of Galion, Ohio; Sergeant John P. Dillon of Asheville, North Carolina; and Staff Sergeant Lloyd H. Gates Jr. of Jackson, Mississippi\u2014would have to wait until they were briefed by the senior men before learning when and where they were going that day.\n\nBehind the briefing officer was the familiar map of northern Europe. However, the mention of the Saxon capital signaled even to the veterans, many of whom were near the twenty-five-mission limit, that something different was in the offing. Such a raid called for a deep penetration into Germany, almost seven hundred miles, and might run as long as eleven hours, with six hours on oxygen. Everyone would be taxed to the limit.\n\nThe intense cold, the constant vibration and noise, and the ever-present threat of a violent and horrible death tested even the strongest men. Ironically, only one of the four men who were directly briefed played an offensive role in the mission: the bombardier. The pilot, copilot, and navigator were concerned only with keeping the plane on course and in formation\u2014no small task.\n\nThe other crewmen who were directly engaged with the enemy were the gunners. For them the long flights were particularly arduous. In the early bombing campaign, waist gunners spent almost the entire flight directly exposed to the elements. Unlike the positions in the top turret, the ball turret, the tail, or the nose, there was no Plexiglas surrounding their guns. Freezing wind, rain, sleet, and snow swept into the fuselage. The temperature was often as low as minus sixty degrees. In 1943, 38 percent of Eighth Air Force casualties were caused by frostbite. The waist gun positions remained exposed until the end of 1943, when Plexiglas windows were installed. Fleece-lined flight suits and electrically heated boots also helped lower the rate to .5 percent in 1944, but the danger of frostbite was ever present.\n\nIn his isolation in the extreme rear of the aircraft, the tail gunner lay in a prone position and constantly scanned the sky to the rear for enemy fighters. The ball turret gunner flew doubled up in a Plexiglas bubble that was suspended below the B-17 and could be rotated a full 360 degrees. Except for takeoff and landing, he passed the entire flight alone in his cocoon.\n\nFor the _Flat Top_ 's radioman, Sergeant Ernest Robertson, a young airman from Acworth, Georgia, this was to be his first taste of combat. The long mission to Dresden would be a baptismal rite. His many months of training were over. In a few hours, he would be a combat veteran. Duty such as this demanded courage, skill, physical strength, and quick reflexes\u2014and not a little bravado and optimism. It is little wonder then that the bomber crews were composed of exceptionally young men, many of them barely out of their teens.\n\n\"I was the old man in the crew,\" recalled Colonel Robert Morgan, the captain of the legendary _Memphis Belle_. Morgan was all of twenty-three years old when he became the first B-17 pilot to complete twenty-five missions\u2014with a raid on the submarine pens at Lorient on 17 May 1943.\n\nThe swagger of young World War II airmen was not the usual teenage or post-teenage machismo. It was, considering the statistical certainty that on any given day some would die, be wounded, or end their war staring through the barbed wire of a German prisoner of war camp, a necessity.\n\nAs predicted, the weather high over Europe was clear, with a brilliant blue sky, but 27,000 feet below the bombers the ground was obscured by 10\/10 cloud cover. However, as the planes went deeper into Germany, some of the cloud cover broke and, as Engstrand recalled years later, Chemnitz could be glimpsed through broken clouds far off to the starboard side of the plane.\n\nThe break in the clouds was brief, however, and it was obvious that the ground would not be visible until the planes were near Dresden, if at all. The bombing would be by H2X. As the bomber fleet roared up the Elbe, it soon became apparent that finding Dresden was not to be a problem. Dead ahead was an unmistakable target marker. A column of smoke rose to at least 15,000 feet through the cloud cover. It was the burning city.\n\nAs the American B-17s began the bomb run a few minutes past noon, there were occasional glimpses of the ground below, although the mixture of clouds and smoke had created 7\/10 cloud cover. Some crew members recalled that they had even seen patches of snow.\n\nThe aiming point was the Friedrichstadt marshaling yards, but because of the cloud cover bombing was basically blind and the bombing pattern was spread out. Other parts of the city were hit as well, in particular parts of the Neustadt, north of the river and directly ahead of the aiming point.\n\n**Just as earthquakes are** remembered long after as having lasted an eternity, so it was with the air raids of World War II. For the victims of a raid the aftermath was, of course, a long-term, often harrowing experience. For the bomber crews, the raids were brief affairs, and this third, American, raid on Dresden was brief indeed. Between the moment the first bombs fell and the order for the withdrawal of the B-17s, the elapsed time was just a little more than ten minutes.\n\nBut in this fraction of an hour, another 771 tons of bombs fell on the burning and wrecked Saxon capital\u2014475 of the 500-pound highexplosive bombs and over 136,000 of the small but deadly incendiaries.\n\nThe American raid was judged as having produced only \"fair results,\" but the psychological damage to the people who had survived the first two waves of bombers was incalculable. The daylight raid came as thousands of rescue workers were pouring into the city, trying to extinguish the fires and to extricate the injured and dying from the air-raid shelters, cellars, and wreckage.\n\nThe U.S. raid also gave rise to charges of a further atrocity against the civilian population of Dresden. Reports, neither substantiated nor refuted in the sixty years since the raid, immediately began to circulate about the American fighter escorts. It was charged that while looking for so-called targets of opportunity, which was part of their orders, the P-51 fighter escorts indiscriminately strafed survivors in the streets and the refugees who had fled to the parks and to the meadows along the banks of the Elbe.\n\n**Of the 461 American** First Air Division B-17s scheduled to bomb Dresden, just 311 were effective. They were protected by 281 of the originally assigned 316 P-51 fighter escorts. But where were the other 150 American bombers that had been dispatched to bomb Dresden on 14 February with their load of over 300 tons of high explosives and incendiaries?\n\nBad weather combined with poor navigation had begun to dog the planes as soon as they entered European airspace. Eighty-eight of the bombers were forced to drop their bomb loads, some 150 tons, on Br\u00fcx, Pilsen, and assorted other targets of opportunity. The remaining sixty-two B-17s, in a celebrated miscalculation, underscored how problematical the so-called precision bombing actually was, even this late in the war.\n\nThe bombardiers on these planes saw on their screens the perfect image of a large city in the bend of a river, which dovetailed perfectly with the pictures and maps of Dresden. It was not Dresden. That city was half an hour behind them. The B-17s had strayed into Czechoslovakia, and the city below was Prague. More than 150 tons of bombs were dropped on the Czech capital.\n\n**After the bomb run** over Dresden, the American fleet turned to the west and began the arduous and dangerous journey back to England\u2014six hours and almost seven hundred miles away. Once again there was 10\/10 cloud cover until they reached Frankfurt. They crossed the Rhine south of Koblenz. The Mosel was visible off to the left of the aircraft.\n\nThere was light flak, but the Allied lines lay just a few miles away. All seemed to be going well when, in the tail of the _Miss Conduct_ , Sergeant Dillon felt a bump above him. He looked up to see that a large chunk was missing from the stabilizer above his head. His frantic message to the pilot that they had been hit was immediately echoed by Sergeant Beam. Another shell had hit the waist of the plane. Almost immediately copilot Reopelle shouted that another burst had hit the right wing and they were on fire. Lieutenant Cebuhar ordered everyone out of the plane.\n\nIn the tail, Dillon prematurely opened the escape hatch before attaching his parachute, and it was swept away in the slipstream of the plane. He desperately began the long crawl forward to find another chute.\n\nEngstrand opened the forward escape hatch, glanced apprehensively at the propellers, and dropped out of the plane. He could see that the ball turret guns were pointing straight down, and he hoped that this was a sign that Sergeant Byers had managed to extricate himself. Then the plane blew up. \"It was like metal confetti all around me,\" recalled Engstrand.\n\nHe landed on a hill to the east of the Our River, the border between Germany and Luxembourg, and he soon realized that he was between the two battle lines. Artillery shells were roaring overhead. He also could see another member of the crew floating to earth; the man landed about a half mile away. Suddenly the deafening roar of airplane engines shook the ground. Two American P-51s were buzzing him and the other downed flier. It was an encouraging but futile show of support.\n\nEngstrand ducked inside a small farm shack and took stock of his situation. Clearly he was at least within artillery range of the Allied lines, but how to get there? The sound of someone shouting in German put an end to his speculation. Cautiously he opened the door and stepped outside. After no more than five steps rifle fire froze him in his tracks. When he attempted to raise his hands he found that his shoulders had been dislocated in his escape from the plane. He made no further moves but stood silently as the German patrol advanced with their rifles pointed at him. Engstrand then heard the most chilling greeting of his life: \"For you the war is over.\"\n\nHe was marched away to a building where the crewman he had seen earlier was being held. \"Hi! My name is Ray Engstrand,\" he said to the other airman. \"What's yours?\" The Germans, of course, knew that they were from the same crew. As Engstrand later said, \"We were all the same age, and I think they were as nervous as we were.\"\n\nThe two young Americans were taken to a nearby interrogation center; on the way they passed the wreckage of the tail of the _Miss Conduct_. Engstrand later speculated that the other part of the plane had landed behind the Allied lines, with the bodies of the radioman and the ball turret gunner.\n\nThe interrogations were the beginning of a six-week ordeal as a prisoner of war. Engstrand was beaten and threatened with execution when he would not talk. He was able to make it because, as he said, \"I was young and strong and knew I could take whatever they dished out.\"\n\nThe prisoners, among whom were three other crew members, Cebuhar, Beam, and Dillon, who had managed to find another parachute on the crippled plane, were taken to Bonn, mainly on foot. At one point they traveled briefly on a truck captured from the U.S. 106th Infantry Division. There was no water and only a small piece of bread.\n\nFrom Bonn they were transferred to a camp near Cologne, where they were loaded into a boxcar. Five days later they were in Stalag 11-B at Fallingbostel, about forty miles north of Hannover. On a phonograph, one of the guards played a song Engstrand had never heard before, \"September Song.\"\n\nOn 21 March the prisoners were taken to Hannover and loaded on a train to Frankfurt. The Americans were already across the Rhine, and as the Germans retreated back into the Fatherland they marched the prisoners ahead of them. On 28 March, as the exhausted men struggled along a road, a group of P-47s swept low and wagged their wings. The Americans were at hand. The prisoners must hold on.\n\nThe next day, the prisoners were halted by an SS tank unit. Only the intervention of a Luftwaffe major prevented a massacre. On 30 March at about 1600 an American tank unit began to fire on the town where they had taken shelter, and when the Germans threw away their weapons and ran off, Engstrand came out of the cellar where he was hiding and grabbed a German pistol as a souvenir of the war. His fellow prisoners were certain he would be shot, but the commander of the American unit blithely said they were never in real danger because he had known all along who they were.\n\nTheir German guards who had stayed behind now found themselves in the same predicament that the Allied prisoners had been in just a day or two before. Only the intervention of one of the British prisoners, a major, prevented their being gunned down by the Americans. These are good Germans, he told the tank commander, noting in particular the Luftwaffe officer who had saved them from the SS.\n\n**Like the crews** of the other American planes, the men aboard the _Flat Top_ had also been surprised but relieved by the ease of the mission. There was neither flak nor fighter interception over Dresden.\n\nVisibility was another issue altogether. Cloud cover ranged from 7\/10 to 10\/10, much of it caused by the dense smoke from the fires that were still burning throughout the city. At an altitude of between 27,000 and 28,000 feet, the city was well nigh invisible therefore, and the bombing was done by H2S.\n\nThe _Flat Top_ 's bomb run had gone without incident, and Kelly turned the plane from its north-northeast heading and began the return flight to England and their home base. He and his crew remained wary and on the alert. There were many well-defended cities beneath them on the return flight path before they crossed into friendly territory. But the Western Front now reached almost to the Rhine, and once they were over the Allied lines, they could relax somewhat and settle in for the long flight to Podington.\n\n**A few days later** , Margaret Armstrong looked up to see the fianc\u00e9e of Sergeant Balentine standing in the door of her room in the dormitory at Randolph-Macon College. The young woman was crying. Her mother had just telephoned with the news that the _Flat Top_ was missing in action.\n\nMargaret Armstrong, the young girl from South Carolina, and the families of the crew of the _Flat Top_ spent the next eight months in a state of uncertainty and dread. At last, in the autumn, their vigil of hope ended. On 15 October, Hap Arnold wrote to the families of the crew that the men \"previously reported missing on February 14, 1945, died in action on that date over France.\" Like many deaths in wartime, their end had come suddenly and from an unexpected quarter.\n\nAfter capturing Dunkirk in June 1940, Germany quickly moved to reinforce that important port city, which had become such a galling symbol of defeat to both the British and the French. To the Germans, of course, it was a symbol of the superiority of German arms and the strategy known as _Blitzkrieg_ and would remain so to the very end of the war.\n\nThe Germans constructed a vast underground garrison, protected from bombardment from the sea and air by yards of concrete and earth and camouflage. The city was circled by gun emplacements, which held massive coastal and land artillery batteries designed to repel attack from every direction. Central to the defense as well was a string of antiaircraft batteries and a force of 12,000 men. The overall commander of the garrison, port, and submarine pens was Vice Admiral Friedrich Frisius.\n\nJust outside the fortress city, its German occupiers maintained four large farms to supply the garrison with beef, dairy products, vegetables, and fodder for the nearly one thousand horses used for transport. The bulk of the foodstuffs was produced by slave labor or commandeered from the local populace. Admiral Frisius kept a six-month reserve of supplies inside Dunkirk in case it was cut off completely.\n\nAt about 1500 hours on 14 February 1945, the crew of an antiaircraft battery at Couderkerque, on the outskirts of Dunkirk, heard the now familiar droning of an approaching American four-engine bomber. They watched in disbelief as the plane came in low from the east. The identifying markings of the B-17, which had to be returning from a raid on the Fatherland, were easily discerned by the gunners. In a matter of minutes, the plane would be over the English Channel and safely out of the range of their 88-millimeter antiaircraft guns.\n\nAt that moment aboard the plane, there was no thought of danger from the ground. Every effort was being directed to keep the plane in the air for the remaining minutes until it reached the safety of the coast of England. The _Flat Top_ was dangerously low on fuel, and Kelly was struggling to reach one of the emergency landing fields just across the Channel.\n\nThe antiaircraft gunners opened up on the bomber. The first two bursts were wide of the target, but the third caught the plane squarely in the port wing. The great plane shuddered as it was hit, and a shout went up from the gun crew.\n\nSergeant Robertson, seated at his radio, heard a loud crunch as the shell exploded and he felt the plane lurch. He looked out the window and saw the port wing of the bomber beginning to buckle. Unstrapping himself from his seat, he ran back to the midsection of the plane, shouting to the two waist gunners that they had to get out. The plane was going down. Neither of them moved or responded. \"They just sat there,\" he recalled later. \"They just froze.\"\n\nAlmost immediately, a large crack opened in the fuselage beside him. Robertson did not hesitate. He dived through the opening. He was outside the plane and hurtling toward the earth. He jerked the rip cord on the parachute and in an instant felt a violent tug as his parachute opened. Robertson began the floating descent down toward what just minutes before he and his fellow airmen had thought was friendly territory.\n\nHe was completely alone. There were no other parachutes. The Fortress had disappeared. Below him lay what seemed to be a large lake\u2014the Germans had flooded the fields near Dunkirk\u2014and, as the sergeant hit the cold but shallow water, the parachute acted as a sail and began to drag him along toward dry land. Robertson disentangled himself from the shrouds and limped out onto a dirt road.\n\nHe had landed on one of the German farms. There was no one in sight. He soon realized, however, that he was not going to get very far. His ankle was broken, and he was wearing only the electrically heated inner boots. The sturdier outer flight boots had been ripped from his feet by the force of the parachute opening.\n\nA German patrol soon found Robertson hobbling down the road. He was taken to the Dunkirk city jail, where he joined other prisoners from Canada and the United States.\n\nThere then occurred one of those coincidences that sometimes create a bond between even the bitterest enemies. When the German officer in charge learned during the interrogation that Robertson was from Georgia, his demeanor softened somewhat. He had run the high hurdles on the German team at the 1936 Olympics in Berlin, and he had become friendly with an American hurdler from Robertson's home state.\n\nThe Wehrmacht officer ensured that the sergeant's ankle was cared for and that he was well treated during the sixty-three days he was a prisoner of war. In April, Robertson was repatriated in an exchange of prisoners of war negotiated by the International Red Cross.\n\nThe _Flat Top_ had crashed on land just a few miles short of the Channel. The bodies of Kelly and the seven other men who had gone down with the plane were recovered from the wreckage and buried by the Germans outside Dunkirk. They were not officially declared dead until the following October, when the graves were examined by the Americans. Kelly's body was shipped home on an army transport and buried in his hometown. He was awarded the Purple Heart and the Air Medal.\n\nDunkirk, like several other isolated German-occupied garrisons scattered along the French coast, held out until the very end of the war. This small French coastal town, which had become so famous at the beginning of the war as a symbol of military folly, British resolve, or both, was among the very last Nazi strongholds to fall to the Allies. Dunkirk did not surrender until 9 May 1945.\n\nSergeant Robertson's war injury continued to vex him more than fifty years later. From a veteran's nursing home in Decatur, Georgia, he castigated Montgomery for the loss of the _Flat Top_ and the deaths of his companions. The victor of El Alamein, said Robertson, bore responsibility because he had failed in his assignment to clear the remaining Nazis out of the French coastal areas and adjoining Belgium and Holland.\n\nMargaret Armstrong traveled to Alabama for her fianc\u00e9's funeral. Eventually she married and had children and grandchildren. But she retained her memories of Walter Kelly. \"I can still remember his accent,\" she recalled a half century later.\n\n# CHAPTER ELEVEN\n\n**ASH WEDNESDAY, 1945**\n\nA City Laid Waste\n\n**W hen he emerged from the air-raid shelter at Weidner's Sanato**rium at dawn on Ash Wednesday, Gerhart Hauptmann caught his breath. The evening before he had beheld from the heights of Oberloschwitz a city still celebrated for its grace and beauty. This morning the fabled spires and towers rose from a sea of flame and smoke. Sections of Dresden would become visible as the firestorm swept away the smoke, like a curtain being pulled back, revealing a city in its death throes. Almost at once the curtain would fall again, but the fiery hurricane would sweep away the pall covering another part of the city and the poet would be given a glimpse of yet more horror. Hauptmann at once began an elegy to the city he called \"my jewel.\"\n\n\"A person who has forgotten how to weep,\" he wrote, \"learns how once more at the sight of the destruction of Dresden. Till now, this clear morning star of my youth has illumined the world. I know that there are quite a few good people in England and America, to whom the divine light of the Sistine Madonna was not unknown, and who now weep, profoundly and grievously affected by the extinguishing of this star....\n\n\"From Dresden, from its wonderfully sustained nurturing of the fine arts, literature, and music, glorious streams have flowed throughout all the world, and England and America have also drunk from them thirstily. Have they forgotten that?\n\n\"I am nearly eighty-three years old and stand before God with a last request, which is unfortunately without force and comes only from the heart: it is the prayer that God should love and purify and refine mankind more than heretofore\u2014for their own salvation.\"\n\n**A young Dresden historian** , Matthias Neutzner, began a systematic study of the Dresden raids in the 1980s. His landmark work, collected in two books\u2014 _Angriff: Martha Heinrich Acht\u2014Leben im Bombenkrieg, Dresden, 1944\/45_ and _Lebenszeichen: Dresden im Luftkrieg, 1944\/1945\u2014_ provides invaluable first-person accounts by survivors of the firestorm.\n\nA woman identified as Nora L., the daughter of a laborer, recalled her own family's ordeal the night of 13\u201314 February. She was then thirteen years old and lived with her family at 50 Holbeinstrasse, in Johannstadt, which lay in the direct line of attack of the first wave of bombers.\n\nDuring this raid, Nora, her parents, and her two brothers, aged fifteen and five, huddled in the basement, listening to the roar of the British aircraft and the crash of bombs. They had brought with them the always-packed emergency suitcase and their identity papers.\n\nNora said she was trembling so badly that people sitting with them became alarmed and entreated her mother, who was holding the youngest child on her lap, to attend to her. But, said Nora, \"She could not, she was like a piece of stone.\"\n\nAs terrible as the ordeal in the cellar was, the girl was relatively safe there. It was when they emerged from the shelter that their nightmare began. The parents were determined to save what they could from their burning apartment building, and they left the girl and her little brother in the nearby D\u00fcrerplatz. It was a large square with grass and trees, and the parents felt that the children would be safe there from the burning debris, which had begun to fly through the air as the flames grew.\n\nWhen her parents did not return and the flames became more threatening, a young neighbor from their apartment building, who had also taken refuge in the comparative safety of the D\u00fcrerplatz with her baby, took charge of Nora and her little brother. They set off for the open spaces along the Elbe, just a few blocks away, as Nora recalled.\n\n\"I took my brother by the hand and we left. We tried to get through in the direction of the Elbe. The woman carried her baby. I had the suitcase and two blankets. It was a lot to carry. Some items I carried on my back, some stuff under my arm and I dragged my little brother behind me.\n\n\"We tried D\u00fcrerstrasse, but that was no longer possible because the burning houses collapsed. We kept in the middle of the street to avoid the stuff that came flying\u2014bricks, window frames, and whatever. It was a firestorm like a tornado. We imagined it to be simple. And it was not really far, only twenty-two meters to F\u00fcrstenstrasse. But we could not get through. The woman with the baby kept urging me on and I tried to hide my fear. But there was no alternative and then we decided to enter a house and wait in the cellar till morning. And there we witnessed the second raid and that was even worse. The first time my parents had been around me and now I was alone with the little one.\"\n\nThe girl and her brother and their unnamed but heroic guardian had fortunately sheltered in a large house in a row of houses with connecting basements. One of the few air-raid precautions taken in the city was to replace the thick cellar walls between adjoining houses with thin partitions. As one basement filled with smoke or the house above collapsed, the inhabitants would then be able to knock out the thin brick or plaster partition and flee into the next house. And thus, by fleeing from house to house the people would, theoretically, be able to reach safe ground.\n\nIn actuality the system often doomed more people than it saved. In a firestorm, the fire was all around. A group fleeing one burning building might very well run directly into a group fleeing from the opposite direction. And when the fires had died down, thousands of bodies were found in the end houses of city blocks, where the people fleeing the flames and smoke had found themselves with no more walls to tear down. The system had created hundreds of fatal cul-de-sacs.\n\nOther precautions also turned out to be a cause of death rather than a preventive. Gigantic open rectangular water tanks were erected in several of the squares, the one in the Altmarkt being particularly large. Ostensibly for use by the fire brigades after the water mains were destroyed, these uncovered reservoirs turned into death traps.\n\nIn a desperate attempt to escape the flames, hundreds of people scaled the walls of the tanks and jumped into the water. Inside, they soon realized their mistake. Unable to scale the walls and get out of the tanks, they either drowned or were boiled alive in the superheated water.\n\nWhen the second raid collapsed the house above them, Nora and her brother began the trek through the subterranean passages from house to house in the block where they had sought refuge. \"We passed from one cellar to the next. First I passed through our bags, my brother and so on.... But we finally got out and I don't remember how. I could do it only because the woman with the baby kept urging me on.\"\n\nShe was fortunate. They were able to exit onto the wide F\u00fcrsten-strasse, where it was possible to breathe, and with breath came some hope, even though most of the neighborhood of Johannstadt was a burning wreck. The hospital at the end of the F\u00fcrstenstrasse, near the Elbe, had survived the raid, and there the children stayed until dawn, when they headed for the safety of the river.\n\n\"Then we went to the Elbe,\" she said. \"It was a gruesome picture. Corpses lying about, sometimes only a head or leg. And I trudged along with little brother. I had lost the woman in the crowds. Large numbers of people were at the Elbe. Those who had lived nearby had things they saved from the houses and put them down at the bank. Many had fled to the Elbe after the first raid and had died there.\"\n\nNora led her brother around the pitiful piles of shattered possessions and the mutilated corpses and crossed the river via the Albertbr\u00fccke, which had a large hole from a high-explosive bomb.\n\n\"My parents had told us that when something goes wrong\u2014and one had to expect that it would, there were rumors\u2014we will meet in Wilschdorf, where the family had a garden. So we made for Wilschdorf and it took a long time. Progress was slow, we had not slept and were exhausted. But we were in the Neustadt. There were houses standing and we felt a little safer.\"\n\nThe safety, however, was illusory. At midday, the third raid, this time by the U.S. Eighth Air Force, began. Nora and her brother had taken shelter at a hospital at the intersection of Liststrasse and Grossenhainerstrasse, and she vividly remembered hearing the detonations of the bombs from the American B-17s.\n\nAt this hospital shelter, three other children, also refugees from 50 Holbeinstrasse, were overjoyed to see Nora and her brother. \"So now we were five on the way to Wilschdorf,\" she related.\n\nThe other children, who were even younger, soon tired and said they could not go on, but Nora managed to get them to the next reception center, where they were able to spend the night. The next morning, since the children were still too exhausted to resume the trek, she decided to go on to Wilschdorf alone, get a cart, and return for them.\n\n\"My brother of course did not want to be separated from me, so we followed Moritzburger Chaussee toward Wilschdorf. Trucks loaded high with corpses passed us going to the Heidefriedhof [the central cemetery]. That was on 15 February.\"\n\nAfter almost two days on foot, the heroic thirteen-year-old girl and her little brother covered the twelve miles from their home on the Holbeinstrasse to the family garden plot in the suburb of Wilschdorf. Her parents' joy was matched only by that of a neighbor who also had found her way to Wilschdorf but was grieving for her lost children.\n\n\"I could tell her that they had also been saved,\" said Nora. \"So we went and got them right away.\"\n\n**The great decision facing** every survivor after the initial bombardments was whether to remain in the relative safety of the shelters or leave them for the dangers in the streets. Typical was the woman who stayed in a shelter throughout the two raids but then decided to take her chances aboveground. She emerged from the basement into the heart of the firestorm. She later recalled the experience:\n\n\"In the street all hell had broken loose and I became suddenly aware of the violent storm from which we had been protected in the basement. It blew like a hurricane from the direction of Borsbergstrasse. Of some houses, only the roofs were in flames, others spewed flames from the first floor apartments. The heat was so great that I was not conscious at that time of my burns....\n\n\"Parts of roofs fell from some houses into the street or the burned floors within the buildings came down making an enormous noise and released giant clouds of sparks moving through the street. When the stones gave way, they and the roof tiles crashed on the granite tiles of the sidewalk and broke apart. The air was filled with the stench of burning material and biting smoke and clouds of sparks came at us from all sides. These obstacles delayed our flight. We did not see any others, who should have also been fleeing at this time. Our residential area appeared to have turned into a fiery hell devoid of people.\"\n\n**A Dresdener who directed** a Red Cross camp in Meissen mourned for her bombed city, and her cries might have been those of millions of other Germans: \"I don't understand anything anymore. It always sounded different when they spoke of other cities. But perhaps it was never the same as here.\" In the same mournful letter written to her daughters on 15 February 1945, she mentions that while the raid was in progress she \"stood in our small yard and guarded my Polish women, because they keep running from the shelter and out in the street.\"\n\nThe Polish women at the Red Cross camp were part of the more than eight million \"foreign workers\" in the Third Reich. Whether these women were there willingly is not clear. One recoils at the thought of the German Red Cross using slave labor. Then again, many military prisoners of war wound up in slave-labor camps.\n\nDetermined to find her children, whom she had left at their home in Dresden, the Red Cross worker started out on the morning of 14 February to look for them. Her moving account of the search for her children could be that of any desperate mother, whether a citizen of London, Coventry, Rotterdam, or Hamburg. Ideology and politics become distant concerns when one's children are in danger.\n\nAt the Meissen station, she was told that trains were running as far as Radebeul, about halfway to Dresden, but at K\u00f6tzschenbroda everyone was obliged to leave the train since the tracks ahead were destroyed. The trams, however, were operating as far as the terminal at Radebeul, after which the woman had no choice but to proceed on foot.\n\nIt was by then noon and the third wave of planes, the American Eighth Air Force, appeared over the city. \"The bombs fell, they were shooting from the planes and everyone ran to the next bomb shelter,\" she said.\n\nAfter the all clear, the woman was able to flag down a car bearing a red cross. Since she was in uniform the driver agreed to let her ride as far as the Neustadt, but after just a short distance the car could go no farther. The road was impassable.\n\n\"The car stopped below an underpass and we saw the first corpses,\" she related. \"So I got out and planned to walk to the Marienbr\u00fccke, because the Augustusbr\u00fccke was said to be destroyed. People coming from there told me it was impossible because of the thick smoke and I knew they were right. The whole city was behind a thick black layer of smoke. So I went through the park toward the Neust\u00e4dter Markt. There I met fire brigades from Meissen and other places, but they did nothing, although houses were burning all along the Elbe, although there should have been enough water. They told me that it was impossible to enter into the city without a gas mask or goggles and all of them had red, inflamed eyes, same as I today.\n\n\"Twenty paces away from me fell the burning roof of the Japanese Palace on the street. I ran to Meissener Gasse, which burned bright. Detoured through another street that was not so totally bad and reached the Neust\u00e4dter Markt, where many houses were burning or had collapsed. The base of the memorial [the equestrian statue of Augustus the Strong] stood and the steeple of the Martin Luther Church could be seen.\n\n\"But fear for my children drove me on and I chanced along onto the [Augustus] bridge, while the men stayed back. The driving surface had large holes, handrails torn off, stones broken, but I did not care, all I wanted was to get across and I made it. On the Schloss-platz were two units with shovels but they just stood there. I did not see anybody moving a hand or dig as long as I was in Dresden. Could not pass through the Schloss-strasse, which was blocked by mountains of debris. So also the Augustus-strasse. The St\u00e4ndehaus was aflame. The [Br\u00fchl] Terrace, I think, was still there and of the Schloss, the lower part. I could not see and remember everything. And the thick smoke and rain of sparks from the burning houses, because on top of everything, a strong wind came up.\n\n\"At where the Neumarkt starts, I passed burning streetcars and debris several meters high. But it was not possible to cross. Debris covered all to a height of several meters.\"\n\nShe returned the way she had come, and at the Georgentor, the great neo-Renaissance gate leading into the Royal Palace, a rider on a motorcycle stopped her and asked if he could get through to the police headquarters on the Schiessgasse. Learning that the way was blocked, he decided that he would detour around the ruins by way of the Elbe and the Carolabr\u00fccke.\n\n\"I said I wanted to go with him,\" she recalled, \"climbed on the passenger seat and we proceeded over burning stuff, wood, etc., to where the Ringstrasse begins and where I got off. The police station was gone.\"\n\nBy this time she had crossed most of Dresden, from the outskirts of the Neustadt, across the river, and through the Altstadt. The piles of rubble that she was forced to negotiate or detour around had been, just a few hours before, some of the most beautiful buildings in the world.\n\nShe had passed the ruins of the cathedral, the broken and burned-out Zwinger, the wreckage of the _Schloss_ , the collapsed and burning opera house, the ruins of the Albertinum, and the blackened but miraculously still-standing Frauenkirche.\n\nIn an ordinary time, she would have been able to reach her neighbor-hood\u2014the area around Sidonienstrasse, L\u00fcttichaustrasse, and Beuststrasse, not far from the central train station, the Hauptbahnhof\u2014in fairly short order. The walk from the Neustadt is not a long one. But this day she had already been en route for hours.\n\nNow she began to see the human toll from the carnage. There were, she said, \"corpses everywhere... a gruesome picture, one next to the other, one on top of the other, naked, burned and totally carbonized... shrunken clumps that used to be humans.... L\u00fcttichaustrasse was totally blocked by ruins. I tried to walk hand in hand with a man since by oneself it was not possible anywhere because of the constant sliding. I had to give up before I got to Moltkeplatz.\n\n\"I thought that along a residential street with detached houses that were not built so close to the street I might be able to pass and so went to Beuststrasse. Here again, every house was destroyed, no tree left, debris in the street. But crawling under or over downed trees and the wreckage of houses I made it. Then Sidonienstrasse. Mountains of debris and not one house that was not burning as everywhere else in the inner city. I met a gentleman and hand in hand we climbed over the ruins.\n\n\"With great effort, scraped shoes and burning eyes we arrived among burning houses, chunks of which fell into the street without pause, over stones, debris, and burning wood to our corner.\"\n\nShe soon discovered that it was impossible to get near her house because of the debris and the flames, but she did not despair, holding out hope that the children had somehow managed to reach a shelter and perhaps were now already out of the city.\n\nIf she had truly believed that they were buried, she said, \"I would, in that case, have had to try all by myself to dig a way to the air-raid shelter and to remove every single stone.\"\n\nUnlike thousands of survivors, this desperate mother found her perseverance rewarded. Her children and an aunt had managed to reach the air-raid shelters and then afterward make their way to the refugee center at Possendorf.\n\nOthers would never know what had happened to their friends and relatives. Were they entombed beneath mountains of rubble? Had they been burned alive or suffocated in the cellars as the firestorm swept over them? Had their bodies been put to the torch in the great funeral pyres in the pubic squares? Or did they lie with thousands of others, unidentified, in the huge communal graves dug outside the city? For many months the ruins of Dresden were covered with notices, often containing photographs, tacked up by survivors desperately looking for the missing.\n\n**In spite of the raids** , the German postal system continued to function, albeit sporadically, and many of the letters and cards from the bombed-out Dresdeners have survived. In addition to longer letters, there were brief notes\u2014senders were limited to just ten words\u2014on red-bordered postcards, which had been issued by the authorities for use in emergencies.\n\nTypical of the letters describing the raid was one from a woman who had found refuge in a school at Reichstadt. She and two other women and an infant had escaped with just a few clothes from Dresden's Altstadt.\n\n\"After the first raid, we had to get out of the cellar without knowing how and when. Everything thickly covered with smoke. No passage open. We sat there for a long time. Then passed through Viktoriastrasse into a sea of flames. By myself I would probably not have found the courage and strength to pass through fire and tons of debris. We just wanted to find an open area. Everything in flames. Turned the corner toward main station. Train station still stood and we went upstairs to the guard room. Fearful masses of debris. We thought ourselves saved. After a few minutes of silence the 2nd air raid alert sounded. 1\u00bd hours at train station in basement.... The basement ceiling held, but we did not believe we could get out and lay down to die. At about 0500 came word that a passage was open. So we took backpack and suitcase and all and clambered out with great effort. Again a gigantic fire. So we sat in the street for a few hours.\n\n\"Now we are in a school in Reichstadt. It is more than primitive. Toelschen, see if you can send us something. I own what I am wearing, nightgown, panties, sweat pants, pullover, jacket, coat, torn shoes and stockings. Not even a belt. It is awful, I cannot yet comprehend fully and could weep all the time.\"\n\nThis woman and her companions were fortunate to escape from the Hauptbahnhof. Hundreds of other refugees and Dresdeners who had fled to the Central Station perished when the superheated air and poisonous gases swept through the maze of underground tunnels and passages where they had sought refuge.\n\n**Hans-Joachim D. was fifteen years old** in February 1945. He lived with his widowed mother, two-year-old-brother, and some relatives who had fled Silesia in an apartment on the Wiener Platz at the Pragerstrasse, directly across from the Central Station.\n\nThe family realized that something was amiss when they turned on their radio shortly before 2200 hours and there was no music. Suddenly, they heard an announcement that large bomber formations were approaching the city and there was a \"Maximum Threat for Dresden.\"\n\nThe announcement, he recalled, was almost immediately followed by the roar of airplane engines. From the garden, the boy watched as the \"Christmas trees\" and marker flares lit up the night sky, but he quickly retreated into the cellar, a public air-raid shelter designed for sixty that was soon packed with over a hundred people.\n\n\"The first night raid seemed endless. It was horrible in the tightly packed cellar. The many people, the unending thunder of falling bombs, nearby explosions and pressure waves, which tore even the strong metal doors off their hinges. At the door a wave of fire rolled into the shelter and the whole stairwell was in flames. A glance through the cellar window showed that the path through the garden was also blocked.\n\n\"Finally we found a passage through a first floor apartment and through a wall of flames to Wiener Platz.... Around us screaming, despairing people. Refugees with their last belongings. We looked along Pragerstrasse, formerly so splendid and elegant, where the 19th-century building of the Kaiser Wilhelm Caf\u00e9 was hidden by flames. Flames shot everywhere from shop windows. It looked like a painting of hell. Further away, resembling a torch, the tower of City Hall. Flames came out of its roof below the Golden Man.\"\n\nThis last is a reference to the gigantic gilded statue of Hercules that stood atop the tower of the Rathaus, or City Hall. The tower with its golden statue miraculously survived and once again crowns the rebuilt Dresden City Hall.\n\nLike many of his fellow citizens, the young man attempted to return to the family apartment to salvage something before the building was totally consumed. He left his mother and brother in a house behind the Hauptbahnhof and returned to Wiener Platz, where with the aid of fellow tenants, some French workers, he carried suitcases, dishes, and food into the square. He hoped the pitiful pile of belongings would be safe there until they could be gathered up the next day. But now the second wave of bombers appeared.\n\n\"Suddenly we heard the whine of a siren again, very weak. It was not the large ones on the rooftops, which had all been destroyed. This thin whine came from a portable hand-operated siren. They come again! Passed on from mouth to mouth. Again the bombs crashed down and the bombers roared through the sky. We ran for our lives and reached the house where I knew my mother and brother would be. It was a miracle I found them again in the crowd that ran to the shelters. This was also a public shelter. So many came in that the stairway was full of people and the steel door could hardly be closed. Several steel lockers stood in the shelter corridor in a row. We found space between two of them and this turned out later to be what saved us.\n\n\"We lay on the floor, mouths open\u2014as we had learned to do because of the explosion pressure\u2014when the terror began again. We felt that the bombs were concentrated on the rail station and buildings near it. A full hit during the first few minutes destroyed the adjoining house down to the cellar. A cellar wall broke open and a flood of fire reached the people standing and sitting in our cellar. Women, children, and men fell over each other in a panic. The screams of the wounded mixed with the roaring of the explosions above us.\n\n\"Then followed a tremendous boom that lifted us off the floor. A pressure wave raced along the cellar corridor. Then it was still. This pressure wave had torn the lungs of almost everyone in the cellar corridor. Only the few of us who had lain between the steel lockers survived.\"\n\nThe boy, his mother, and his little brother did survive, and after several hours in the pitch-blackness of the cellar, among the piles of corpses, they were rescued when a hole was opened through a wall into Winckelmannstrasse by a rescue team that had heard them knocking on the wall.\n\n\"Outside we encountered the indescribable firestorm,\" he said. \"In front and behind us, the roofs of two houses fell down. For some minutes, my mother and brother had disappeared in a cloud of sparks. Then I heard a voice from the other side of the street, 'Over here!' Holding onto each other, our clothes on fire, we jumped across the already burning asphalt and reached a house that had little damage.\n\n\"This single villa on Winckelmannstrasse survived all air raids and is now the Hotel Classic. There, our saviors threw wet blankets over us, took us into the cellar and so let us survive the night a second time.\"\n\nThe boy, his mother, and his little brother set out in the morning for his grandparents' house in the suburb of Kemnitz. Their circuitous route led them over piles of smoking rubble many meters high, and everywhere were corpses, many of them carbonized. A few days later, he and his grandfather, pulling a wooden handcart, returned to the Wiener Platz to look for the household goods.\n\n\"How I wish we had not done so,\" he recalled. \"Everything was actually there on Wiener Platz, where we had dumped the things after the first raid. But everything had melted: glass, flatware, porcelain. Behind the train station, under the track overpass, were stacked hundreds of dead and more were being added all the time from the station and nearby cellars. A wave of bad-smelling heat from the cellar where we had barely escaped hit us in the face. Of our house, only a piece of wall and a mountain of debris lay on Wiener Platz.\n\n\"As was the routine, we wrote our address on a wall: 'We are alive, live in Kemnitz, Flensburgerstrasse 16.'\n\n\"This scrawl remained there for a long time. Today, the tunnel on the train station side passes through what was our cellar.\"\n\n**In the early evening** of 13 February, fourteen-year-old Renate Heilfort was standing in the ticket line at the cinema on the Postplatz. The line was long, and when it was announced that there would be no more tickets available until the nine o'clock showing the young girl decided not to wait but to take the tram home to the suburb of Zschachwitz, a distance of about five kilometers. This decision would save her life. Not long after she reached home the first bombs began to fall on the Postplatz, which was at the center of the firestorm. The theater and all the surrounding buildings were obliterated.\n\n**Gerhart Sommer, who was** eight years old in 1945, lived with his mother, his little sister, and his thirteen-year-old brother, who was an assistant on an ambulance, in the suburb of Reick, just southeast of the Grosser Garten. His father was with the Wehrmacht in Hungary.\n\nOne is struck time and again, in the wrenching stories of the survivors, by the central role played by women and children, who were, of course, the main component of the civilian urban population.\n\nGerhart's mother herded the two smaller children into the basement of the house when the alarm sounded. His brother was on duty in the town center. First, however, she checked to make sure that each had a handkerchief. This was not just a typical mother's admonition. A handkerchief soaked in one's own urine could serve as a makeshift gas mask and save one's life in the dense smoke in the streets or in a cellar suddenly filled with smoke and carbon monoxide.\n\nAs they fled into the basement shelter, the \"Christmas trees\" had started to fall and the city was lit up like daylight. It was eerily beautiful, recalled Gerhart, but the mother did not allow them to tarry.\n\nWithin minutes the bombs began to fall, and although Reick was well out of the central targeting area, several high-explosive bombs fell within a hundred meters of the house. The concussion was so great that even at that distance the family was lifted into the air and flung against the far wall of the cellar. Doors buckled, and every window was blown out.\n\nThe family was fortunate to have survived the blasts from the highexplosive bombs, which were designed not only to blow up buildings but to create shock waves of such power that all the internal organs that were filled with air\u2014the lungs, the stomach, and the intestines\u2014exploded. Thus many corpses had no external wounds or damage.\n\nOne witness reported seeing a tram filled with passengers, all of them dead, killed instantly by the concussion wave from a highexplosive bomb, which had destroyed their hearts and lungs. Not one had an external wound. The windows had exploded outward, so that none of the glass had pierced their bodies. There they sat, he recalled, appearing as if they had just fallen asleep.\n\nThe Sommer family stayed in their shelter until daylight, when Gerhart and a friend named Peter, a child of the same age who lived next door, went out to investigate. Even small children had been taught how to deal with unexploded ordnance, in particular the small incendiary bombs, and the two little boys set off several that they found in the street by poking them with a piece of lumber.\n\nJust before noon, Gerhart's brother arrived home. His ambulance, which had been transporting wounded to the Elbe Meadows, had been hit and destroyed by machine-gun fire from an American fighter plane. The mother then loaded up a four-wheeled cart with household goods and with her three children began the trek to relatives in the countryside, where they would live until the end of April.\n\nIn May, the entire family was reunited when the father returned home from the east. He and a group of comrades had commandeered a locomotive and had managed to get as far as Pirna, just a few miles from Dresden, before the engine gave out. They had walked the rest of the way home.\n\n**All the stories told** by survivors heartbreakingly underscore the true cost of air war against civilians, but that of Mrs. S., who lived at 19 Webergasse, just a block from the Altmarkt and thus at the epicenter of the firestorm, is particularly wrenching.\n\n\"Then came the second raid and we went down into the basement again,\" she recalled. \"I carried my son and placed a wet cloth over his face because of the smoke.... I do not know at what time my child was dead, or my mother. I fainted. When I came to, the corpses were lying on top of me.\n\n\"I pulled myself out from under to see if there was a way out. But my legs would not support me because of a torn ligament and so I could only crawl on my knees. But I could not see an exit.\"\n\nMrs. S. lay there until Thursday with the bodies of her son and her mother. When they were finally dug out, she was told she was one of six survivors out of ninety-five people who had sought refuge in the cellar. \"You cannot imagine how they were stacked on top of each other,\" she said. \"Eighty-nine corpses.\"\n\nMore than thirty years later she still carried the photographs and the death certificates of her son and mother. \"This was the little one,\" she said, showing her interviewer the picture of her dead son. \"He was seventeen months old.\"\n\n**As these tragedies and** dramas were playing out in the streets of Dresden, the aerial bombardment continued. The American air force, which had completed the triple blow on 14 February, was back the next day. On 15 February 1945, another 211 B-17s from the Eighth Air Force dropped another 464 tons of bombs on the crippled city. The primary targets that day were the oil refineries at B\u00f6hlen and Ruhland, but when the weather closed in over those targets, the pilots had to opt for the secondary target, Dresden.\n\nBombing was done by H2X, and though it was scattered and by no means as effective as during the three previous raids, it was devastating to the stunned survivors below, who were struggling desperately, searching for victims while trying to extinguish the hundreds of fires that were still burning.\n\nAnd on this day, perhaps the most crushing psychological blow of all was delivered to the Dresdeners. The Frauenkirche, the Church of Our Lady, the dominant feature of the townscape, miraculously still stood after three devastating waves of Allied bombers had destroyed everything around it.\n\nBut the sandstone foundation and supports were fatally weakened by the flames that had roared around the great church since the first British planes had appeared two nights before. At 1015 on 15 February, the dome of the church, more than a hundred meters high, began to buckle. In just a few seconds the proud symbol of the Florence on the Elbe since 1734 was a pile of smoking rubble. The last vestige of old Dresden was gone.\n\n**Later that same day** , at 1530, another plane appeared over Dresden, but this one was hardly noticed by the dazed survivors, if they even bothered to register its presence. This plane from 542 Squadron of the RAF had a benign mission: to photograph the carnage below. The quality of the prints is poor because of the smoke from the fires, but it is clear that the raids had their intended effect.\n\nThe areas most affected were south of the Elbe\u2014the city center, or Altstadt, and the adjoining areas of Johannstadt and S\u00fcduorstadt\u2014which were effectively 100 percent destroyed. Houses were destroyed or damaged as far as the suburb of Loschwitz. The Neustadt, north of the river, was less severely damaged, but the sectors near the river were essentially flattened and burned out. The Carola Bridge was judged out of service, and while the Augustus Bridge was heavily damaged it was probably usable. The railway bridge was seriously damaged as well.\n\nPut simply, the destroyed area contained all the important cultural, religious, and civic buildings of Dresden. These included the Zwinger, the Albertinum, the Academy of Art, the Japanese Palace, the state archives; the museums of antiquities, of the army, of folklore, of history, and of prehistory; the Hofkirche, the Kreuzkirche, the Sophienkirche, and the Frauenkirche; the Semper Oper and the Schauspielhaus; the Royal Palace and the adjoining Taschenbergpalais; the Rathaus; the Zoological Garden; the Grosser Garten; the train stations; and the majority of the hospitals.\n\nBut as vast as the destruction of the cultural treasures was, the destruction of thousands of private homes and apartments, the electrical-generating system, the food-distribution system, and the sewage and water systems were the more immediate calamity. And everywhere there were the bodies of the dead, whose decomposing corpses portended a health crisis of terrible proportions.\n\nWhat was to be done with the thousands of corpses being carried out of the basements or still lying in the streets? Day after day, bodies were loaded onto the only available transport, horse-drawn wagons, and taken away to be buried in vast mass graves at the Heidefriedhof, on the Dresdner Heide, the heath northeast of the city.\n\nBy the end of February, it was realized that this system could not cope with the rising health emergency. The city center was sealed off and giant grills made of girders and metal shutters from a nearby department store were erected in the Altmarkt. The horse-drawn carts with their cargoes of corpses were then diverted to the ancient square. There the bodies were stacked on the grills like cordwood, five hundred at a time, doused with gasoline, and set ablaze. Almost ten thousand of the dead were disposed of in this way, and the stench of burning flesh hung in the air for weeks.\n\nFor some of the survivors it was the smell in the streets\u2014a sickening mixture of high explosives, phosphorous, ash, smoke, and, above all, burning flesh\u2014that they would never forget. A woman who survived the firestorm and later immigrated to America recounted that on a visit to Dresden fifty years later she could still smell the burning corpses and was nearly overcome when she stepped out of a car at the Altmarkt.\n\n**In 1975, a gravedigger** at the Heidefriedhof unearthed an urn while opening a new grave. The urn contained a report written by a young soldier identified only as Gottfried, and dated 12 March 1945.\n\n\"On 13 February we heard the early warning. Mother got ready and kept her good humor, while father was seriously concerned as he always is when danger threatens from the air. Christa [the soldier's wife] wrapped up her little Mike and we went to the air raid shelter under the house in front of ours. Everything was as usual and we hoped to be able to return soon upstairs. This was Shrove Tuesday (Mardi Gras)! But it was not long before [a neighbor] brought us the report: 'Fighter units en route to city.' A few minutes later we no longer needed an air situation report to know that this time we were it.\n\n\"The enemy planes dropped flares and the well-known 'Christmas trees' over the whole area of the city. The first detonator bombs fell. Outside the wild dance of the man-made elements of destruction. The raid lasted an eternity, finally, 'All Clear.'\n\n\"My father and I immediately went upstairs to see what had become of the house.... All doors and windows were torn to pieces. Both houses, front and back plus those on both sides looked awful. On the top floor of the building in back I extinguished two incendiary bombs.... The building along the side was already burning and a blast of wind threatened our building in the back. The wind soon turned into a storm and tore up everything inside, because there were no more doors. The house across the street was also in flames. I stood on the roof garden surrounded by a firestorm that kept getting worse. Before long, all buildings in this area were on fire. Timed explosives kept going off.\"\n\nWhen the second raid came, the soldier, his wife, and their infant son took refuge in the basement of an already burning house, where they remained, surrounded by fire, until 0930 on the morning of 14 February. When they emerged, on the Grosse Plauensche Strasse, they could see that his parents' house had taken a direct hit and was just a smoking ruin. The entire area around the Central Station, he said, \"was nothing but debris and ashes as far as the eye could see.\"\n\n\"Total destruction. Lunacy.... Only a few survivors came crawling out of their basements, no air raid wardens, no help, just nothing. We had to get the child out of this hellish smoke. I carried the boy over mountains of debris, between burning and collapsing buildings, past the dead and dying.\n\n\"Six days later I went to the wrecked house. The debris was still so hot that one could not step on it without burning the soles of one's shoes. Then I heard that the recovered bodies were being taken to the Altmarkt to be burned with flame throwers. I wanted to spare our relatives this fate.\"\n\nWith the help of a corporal from his unit and six prisoners of war, the young man started digging into the shelter beneath his parents' house. Even then, a week after the raid, the heat was still so intense in the cellar that they could remain there for only a few minutes. But despite the poor light, he said, \"I saw the most painful scene ever.... Several persons were near the entrance, others at the flight of steps and many others further back in the cellar. The shapes suggested human corpses. The body structure was recognizable and the shape of the skulls, but they had no clothes. Eyes and hair carbonized but not shrunk. When touched, they disintegrated into ashes, totally, no skeleton or separate bones.\n\n\"I recognized a male corpse as that of my father. His arm had been jammed between two stones, where shreds of his grey suit remained. What sat not far from him was no doubt mother. The slim build and shape of the head left no doubt. I found a tin and put their ashes in it. Never had I been so sad, so alone and full of despair. Carrying my treasure and crying I left the gruesome scene. I was trembling all over and my heart threatened to burst. My helpers stood there, mute under the impact.\n\n\"What else is there to write? There are three copies, one I put in the urn.\"\n\n**Variations on this melancholy** theme were played out for decades after the war. For years the skeletons of victims were discovered in the ruins of Dresden as rubble was removed or foundations for new buildings were erected.\n\nOne particularly poignant discovery was made when the ruins adjacent to the Altmarkt were being excavated in the 1990s. The workmen found the skeletons of a dozen young women who had been recruited from the countryside to come into Dresden and help run the trams during the war. They had taken shelter from the rain of bombs in an ancient vaulted subbasement, where their remains lay undisturbed for almost fifty years.\n\n# CHAPTER TWELVE\n\n**\"MR. PRIME MINISTER?\"**\n\nQuestions in Parliament and World Opinion\n\n**A t the Allied Air Commanders Conference two weeks after the** Dresden firestorm, there seemed to be no particular concern with public opinion. And the outcry over Dresden had caused no change in Bomber Command's policies. On the night of 23\u201324 February, ten days after the triple blow on Dresden, some areas of which were still smoldering, Pforzheim had been subjected to one of the most devastating raids of the war. The area of destruction comprised 83 percent of the town, and 17,600 people died.\n\nThe Pforzheim attack, according to the minutes of the meeting, \"had been what was popularly known as a terror attack.\" Harris knew that in certain quarters the value of these area attacks was disputed, but the town contained innumerable small workshops for the manufacture of precision instruments, and he said that the attack must have destroyed the \"home-work\" of the population and their equipment, since 25 percent of the population was now dead. Given the percentage of the population killed, the Pforzheim raid was probably the most deadly raid of the war. Bomber Command had now destroyed sixty-three German towns in this fashion.\n\nWhile Spaatz and Doolittle kept silent at this meeting, they made clear elsewhere and with some frequency their opposition to morale bombing. But they had also called for widespread attacks across Germany, which, combined with heavy attacks against places like Berlin, would have had \"a more decisive effect upon morale.\" Spaatz had, five days earlier, been singled out in a broadcast by the turncoat commentator Donald Day on the Nazi English-language radio station, who'd declared,\n\nThe Wehrmacht has decided to confer a special decoration upon Gen. Spaatz, the commander of the US bombing forces in England. This special decoration is the Order of the White Feather. The Wehrmacht thinks that Gen. Spaatz earned this decoration when he sent over a fleet of nearly 1,000 US bombers to lay a carpet of bombs across Berlin. Gen. Spaatz and the Americans commanded by him knew that Berlin was crowded with hundreds of thousands of refugees, principally women and children, who had fled before the organized savagery and terrorism of the Bolshevik Communist Red Army.\n\nDay was referring to the thousand-bomber raid of 3 February. Berlin, he said, was already taxed to the limit housing and feeding refugees, and the planes that should have protected the city were in the east, helping the German army fend off the common foe of Bolshevism, which threatened not just Germany but all of Europe.\n\nOn the day of this broadcast, 17 February, while Day was warning of the horrors of Bolshevism, thousands of Jews were being herded along roads and highways like so many cattle, forced to make their way westward on foot in the bitter cold of an eastern European winter. These were the pitiful remnants, the last few survivors of the concentration camps in the east, which lay in the path of the Soviet advance.\n\nWhile Day was ranting about American atrocities and the dangers of Bolshevism, the forced march of a thousand Jewish women from the camp at Neusalz on the Oder had reached the Neisse River\u2014at least for those who were still alive. The survivors\u2014there would be only two hundred at the end of the ordeal\u2014would not reach the camp at Flossenburg for another three weeks.\n\nThe day after Day's broadcast, 18 February, the last of the few hundred protected Jews in the German homeland were ordered to collection points for deportation to Theresienstadt. There were to be no exceptions. Marriage to an Aryan no longer could save them.\n\nDay, of course, did not mention that the American bombs also dispensed a rough justice at the court building in Berlin where the trials of the conspirators in the 20 July bomb plot against the F\u00fchrer were going on. Thousands of accused conspirators had already been tried in show trials and executed.\n\nThe president of the People's Court was the rabid Nazi Roland Freisler, who did not so much preside as perform. His hysterical diatribes were cunningly devised to humiliate the defendants, cow the onlookers, and, not so incidentally, curry favor with Hitler, who viewed the news-reels of the trials.\n\nFreisler was crushed to death as the court building collapsed around him during the raid. The trials were suspended and several of the defendants were saved by the raid and survived the war. Other plotters, such as Admiral Wilhelm Canaris, chief of the Abwehr, military intelligence, were not so fortunate. He was executed by the Gestapo on 9 April, just a month before the German surrender.\n\n**Bomber Harris somewhat peevishly** complained to his colleagues at the Allied Air Commanders Conference that although Bomber Command had been fighting Germany for five years, their role in the destruction of Germany was not being properly appreciated by the ground forces, which were just entering Germany. In response, it was suggested that perhaps air crews should visit the infantry and tank divisions and that ground forces could profit from visits to airfields.\n\nDoolittle, mindful of the criticism of the friendly-fire disasters caused by bad navigation during close air support of ground troops, was not optimistic about such a public relations campaign. \"Eighth Air Force Crews would have to be careful not to visit an outfit that they had bombed,\" he wryly remarked.\n\nInterestingly, Harris had been with Churchill at Chequers the evening of the Pforzheim attack. Churchill had returned just four days before from the Yalta Conference. When Bomber Command had finished with its task, the prime minister mused aloud over dinner, \"What will lie between the white snows of Russia and the White Cliffs of Dover?\" Churchill's remark to Harris can be read in several ways, but it is clear that he recognized the awful power of aerial bombardment.\n\nHe added that if he lived he would concentrate on one thing: the building and maintenance of a powerful air force. No doubt Britain, in the postwar world, would have to carve out a new niche for itself, caught as it was between the \"huge Russian bear and a great American elephant.\"\n\nHarris, surprisingly, demurred. He saw more promise in the German V-2 rockets. Although they were no match at that stage for the devastating power of his bomber fleets, they were clearly a portent of the future. \"The bomber is a passing phase and, like the battleship, it has nearly passed,\" he said to the prime minister.\n\nEarlier, as the guests had gathered in the great hall of Chequers, waiting to go into dinner, John Colville, Churchill's secretary, had asked Harris what the effect of the raid on Dresden had been. \"Dresden? There is no such place as Dresden,\" Harris had replied.\n\nColville also records that during this same evening Churchill remarked that Carl Spaatz was \"a man of limited intelligence,\" to which Harris replied, \"You pay him too high a compliment.\"\n\nIf his book _Bomber Offensive_ is any guide, Harris seemingly never changed his opinion of his American counterpart. He mentions Spaatz only once, in passing. As for Eaker, Anderson, and Doolittle, Harris wrote, \"We could have no better brothers in arms... and the Americans could have had no better commanders than these three. I was, and am, privileged to count all three of them as the closest of friends.\" Harris wrote these words in 1947, when Spaatz had not only succeeded Hap Arnold but had been made head of the new and separate United States Air Force.\n\nChurchill, when he made his disparaging remark about Spaatz, no doubt knew of the American's upcoming promotion to four-star general, which came on 11 March. Spaatz himself was informed of the promotion during a poker game. His response was in character. He ordered champagne for everyone and then returned to the business at hand. \"Come on and deal,\" he said.\n\nCarl Spaatz was now one of the highest-ranking men in the American military, but the European operations that he oversaw were already being relegated to second place by Washington. By late March, Spaatz let his anger at the new policies, particularly the diversion of mat\u00e9rial to the Far East, spew forth.\n\n\"It seems,\" he said, \"unjustified that so great and expensive a Military Organization as the Air Force should have its potentialities limited to such serious extent by failure to set up adequate bomb production facilities.\"\n\nSpaatz's cable raised hackles at the Pentagon, but no increases were forthcoming. Lieutenant General Barney M. Giles wrote to his friend that \"it is most improbable that your ultimate desired requirements can ever be met.\"\n\nAttention was shifting to the Pacific theater, where in a short time Spaatz himself would be running the air war. Such are the fortunes of war.\n\n**Goebbels, when he heard** the news of Dresden, wept openly and called on Hitler\u2014who, according to his personal physician was thrown into a black depression\u2014to repudiate the Geneva Convention and start shooting captured pilots and parachutists.\n\nThe propaganda minister issued Gerhart Hauptmann's elegy to the dead city to the press and radio. Hauptmann's work, which Goebbels extolled as exemplifying the work of Germany's most famous poet, was soon broadcast and printed around the world via the neutral countries.\n\nAs for Hitler, he quickly rallied and threatened to heed Goebbels's advice. \"This constant sniveling about humanity will cost us the war,\" he said. A few days later, when he deigned to look at photographs of the thousands of dead Dresdeners, the F\u00fchrer lapsed again into a despairing mood, but it was brief and had no effect on his resolve to fight on.\n\nHitler's quick recovery from his brief and uncharacteristic shock at the destruction of Dresden mirrored his attitude toward the destroyed cities of the Reich. Cities can be rebuilt, he had said more than once in response to the Allied raids. Besides, it had always been his plan to rebuild the cities according to National Socialist ideals, and he had often remarked to Albert Speer that the raids would make the rebuilding easier.\n\nSpeer was an unknown architect in 1933 when he was brought into Hitler's circle to help the F\u00fchrer realize his grandiose schemes, in particular his dream of transforming Berlin into Germania, the new capital of the Thousand-Year Reich. And even though he was raised to the position of armaments minister in 1941, he continued working up plans for this vast transformation. Even as Soviet troops were on the outskirts of Berlin he and Hitler would study the architectural models.\n\nOther high-ranking Nazis were just as zealous as Hitler in their desire to forge a Germany completely based on National Socialist ideals. If the cities and monuments of Germany were destroyed, so be it.\n\nWhen Robert Ley, the German Labor Front leader, heard of the destruction of Dresden, he was exultant. Germany, he said, could \"almost draw a sigh of relief. It is over now. In focusing on our struggle and victory we are now no longer distracted by concerns for the monuments of German culture.\" For Ley these monuments were \"superfluous ballast,\" just so much \"heavy spiritual and material bourgeois baggage.\"\n\nEarly on the evening of 14 February, Goebbels met again with Hitler in the _F\u00fchrerbunker_. Dresden was still aflame. Goebbels denounced G\u00f6ring to the F\u00fchrer and called for his trial and certain execution by hanging or a firing squad for dereliction of duty, citing in particular the miserable showing of the Luftwaffe during the three-part Dresden raid. Hitler put him off.\n\nThree days later, Goebbels resurrected his scheme to execute one Allied prisoner of war for each air-raid victim. Hitler approved, and Goebbels produced a plan justifying this abrogation of the Geneva Convention. This vengeful barbarism came to nothing when Hitler again changed his mind. Several of his henchmen took credit for the plan's demise, particularly those later arrested and tried at Nuremberg.\n\nDwight Eisenhower might have had something to do with the reversal as well. The supreme allied commander warned the Nazis and the German people themselves, in a widely disseminated announcement, that they would be held fully accountable for such actions.\n\n**The Dresden raids** and firestorm immediately became the symbol to many of the horror of a war waged against civilian populations, and for a while in the spring of 1945 there was something of a firestorm as well in the press, the Parliament, the highest reaches of government, and military headquarters. Everyone, it seemed, now had questions about Allied bombing policy in general and the raid on Dresden in particular.\n\nThe brouhaha began just a day or two after the raid when Air Commodore A. M. Grierson briefed reporters at the Supreme Headquarters Allied Expeditionary Force (SHAEF) on the continuing air campaign. Grierson then offered to take questions from the reporters, and the very first had to do with the attacks on Dresden and other points just ahead of the advancing Red Army. As Grierson explained it, the attacks were the result of recommendations made by the combined strategic targets committee and had three purposes.\n\nDresden and other eastern targets were evacuation centers, and bombing such crowded places would materially disrupt the German war effort. The Wehrmacht had to reassign entire divisions to help out after the raids, and vast amounts of food, fuel, and other mat\u00e9riel had to be diverted to aid the refugees.\n\nDresden and other such cities in the east were also important communications centers, through which passed reinforcements to the Russian front, in particular troops and armaments being withdrawn from the Western Front and transferred to the east.\n\nFinally, by heavily bombing targets so close to the Eastern Front, the Anglo-American air forces were substantially aiding the Soviet advance into the Reich. Russian troops had already crossed the Oder and were threatening Berlin.\n\nGrierson also revealed that there were no Russians on the targets committee; it was purely an Anglo-American body. In answer to a reporter's question, he said that there had been no Russian pressure to bomb Dresden and other eastern cities, that there was no prior consultation, and that thus far the Russians had not commented on the RAF-USAAF offensive.\n\nIndeed, according to Grierson, there was \"no definite arrangement made with [the Russians] for planning beforehand or discussion afterwards at the moment.\" And in response to a question as to what other cities might be on the list of targets, he responded that he couldn't answer offhand but any city that lay on the east-west or north-south communications lines, any city that was a center for evacuation, and any city that had stores of emergency food supplies might be a likely target.\n\nAs for Dresden itself, while the primary goal was to blast communications carrying military supplies, there was another goal, said Grierson: \"to stop movement in all directions if possible\u2014movement of everything.\"\n\nGrierson's frank and, to many of those present, disturbing comments were meant as background, but among the reporters was Howard Cowan of the Associated Press. It is little wonder that Cowan drew the obvious conclusion that bombing policy had, indeed, changed\u2014not so much that of Bomber Command, which had called for bombing German population centers for years, but that of the American Eighth Air Force.\n\nCowan used the briefing as the basis for a story that ran on page one in the _Washington Star_ on 18 February 1945. The article, which inexplicably passed the SHAEF censors without comment, created its own firestorm. At the Pentagon, an outraged and angry Hap Arnold fired off a cable to Spaatz, in which he quoted Cowan's piece in its entirety.\n\nThe Allied Air Commanders have made the long awaited decision to adopt deliberate terror bombing of the great German population centers as a ruthless expedient to hasten Hitler's doom.\n\nMore raids such as the British and American heavy bombers carried out recently on the residential sections of Berlin, Dresden, Chemnitz, and Cottbus are in store for the Reich, and their avowed purpose will be creating more confusion in the German traffic tangle and sapping German morale.\n\nThe all out air war in Germany became obvious with the unprecedented daylight assault on the refugee-crowded capital two weeks ago and subsequent attacks on other cities jammed with civilians fleeing from the Russian advance in the East.\n\nThe Allied view is that bombardment of large German cities creates immediate need for relief. This is moved into the bombed areas both by rail and road and not only creates a traffic problem but draws transport away from the battlefront. Evacuation of the homeless has the same result.\n\nReconnaissance has shown that the best way to create road bottlenecks through key cities is to topple buildings into the streets. One spot on the Western Front recently was made impassable for nine days by such tactics. The effect on morale both at home and at the front is quite obvious.\n\nThe decision may revive protests from some Allied quarters against \"uncivilized warfare,\" but they are likely to be balanced by satisfaction in those sections of Europe where the German Air Force and the Nazi V-weapons have been responsible for the indiscriminate slaughter of tens of thousands.\n\nThe reaction of the Germans, who still are bombing England blindly with long-range rockets, is expected to be a new outburst of violent words, but there is little more the Nazi propagandists can say\u2014all the previous Allied air raids on the Reich have been described by Berlin as \"Terror Attacks.\"\n\nArnold complained that he was already getting calls from influential radio and newspaper commentators asking who had ordered the change in bombing policy from the often-stated goal of precision bombing to area bombing. \"What do we say?\" he asked Spaatz plaintively.\n\nSpaatz, who was in the Mediterranean, ordered his staff back in England to put out the fires, or at least bring them under control. On 19 February, Major General F. L. Anderson, deputy commander for operations, cabled Arnold an explanation of the public relations fiasco. Anderson quoted the \"pertinent portions\" of Grierson's press conference\u2014which, he somewhat surprisingly enjoined Arnold, who knew a thing or two about security, \"are not repeat not for publication.\"\n\nTo start with the Heavies, the overall communications plan is going ahead and in communications I include oil. I understand you have already heard something about the oil plan and the oil war generally, but the situation now is such that we might expect very big results from the bombing of the oil refineries and production plants. The bombing of communications centers and railways is having an increasingly serious effect on the German economy generally and with the loss of Silesia the importance of the communications out of the Ruhr has become emphasized more than ever. I think if you will notice from now on, the sort of targets being chosen for attack by the Heavies, and for that matter the Mediums as well, you will see the sort of general results of the planning which has been going on in the last fortnight.\n\nAnother matter, which has been given a lot of thought and which required a lot of careful consideration, is the employment of the Heavies against the centres of population. The effect of the Heavy raids on population centres has always been first of all to cause the Germans to bring in train loads of supplies of extra comforts and to take away the population which have been rendered homeless. Now that form of relief relies very, very much to a pretty great extent on rapid and sound communications between the big cities and the whole of the interior of Germany itself, so that the destruction not only of communications centres, but also of the towns where the relief comes from and where the refugees go to, are very definitely operations which contribute greatly towards the break up of the German economic system.\n\nAlthough Anderson maintained that Cowan had exaggerated Grierson's views, he admitted in the cable that \"Grierson did imply that attacks were to be directed against civilian populations.\" However, he emphasized, \"We have not, or do not, intend to change the basic policy which has governed the direction of effort of the United States Strategic Air Force in Europe from the first time they started operations in this Theater. Our attacks have been directed in all cases against military objectives.\"\n\nWhile Arnold was no doubt relieved to hear that the chief targets of American bombers were and remained oil and communications, he cannot have failed to understand what all military commanders understand. No operation in wartime, let alone bombers operating at 30,000 feet, can guarantee that there will be no collateral damage. Oil refineries and marshaling yards are inevitably near or adjoin major civilian population centers. But Anderson (and Spaatz) insisted there was no change in policy. \"There has been,\" the cable said, \"only a change of emphasis in locale.\"\n\nAs promised to Arnold, Anderson met that same day with Eisenhower to draft an official and public response to the changes of terror bombing. Eisenhower's headquarters issued a denial that terror bombing was official policy and explained that Dresden was a viable military target.\n\nSecretary of War Henry L. Stimson echoed Eisenhower's denial of a change in U.S. policy, and the _Washington Star_ , which had set off the furor in the first place with Cowan's article, accepted his explanation. Cowan had simply been guilty of \"an excusable but incorrect interpretation\" of Grierson's remarks. This was, says historian Tami Davis Biddle, a \"1940s version of spin control.\"\n\nStimson, however, began to have second thoughts about the matter and reopened the question of the Dresden raid. Arnold was having none of it. \"We must not get soft,\" he fumed. \"War must be destructive and to a certain extent inhuman and ruthless.\"\n\n_The New York Times_ was hardly less forthright. The day after the American raid, on 15 February, the paper had editorialized that if a great German city and its cultural treasures were obliterated, the Germans had only themselves and their F\u00fchrer to blame.\n\nOthers were not so accommodating. On 26 February 1945, _Newsweek_ , in an article headlined \"Now Terror, Truly,\" reported the Dresden inferno and a new military policy. \"Allied air chiefs have decided to adopt deliberate terror bombing of German population centers as a military means of hastening the Reich's surrender by snarling up communications and sapping morale,\" said the magazine.\n\nJournalists resident in Germany from such neutral countries as Switzerland and Sweden had more or less parroted the Goebbels line that the raid had been an atrocity, and their dispatches had also begun to find their way into the Allied press. The notorious press conference at SHAEF headquarters had only added further fuel.\n\nIn Great Britain two of the most influential prewar advocates of aerial bombardment had already recanted and had written scathing denunciations of the Bomber Command policy of systematic destruction of German cities and the killing of noncombatants.\n\nIn 1943, J. F. C. Fuller said that next to Bomber Command's actions \"the worst devastations of the Goths, Vandals, Huns, Seljuks, and Mongols pale into insignificance.\" B. H. Liddell Hart was hardly less censorious. In 1942, he wrote that the Luftwaffe and Bomber Command were now engaged in a \"mad competition in mutual devastation.\"\n\nFinally, the controversy spread to the House of Commons. On 6 March, a firebrand Labour MP from Ipswich, Richard Stokes, took to the floor to question the entire bombing policy of Bomber Command, in particular the Dresden raid and in general the laying waste of the cities of Germany.\n\nStokes's speech was brief, but it ignited a controversy\u2014particularly his charge that history would record the raids as \"a blot on our escutcheon.\" As the story continued to unfold, the blot threatened to tarnish the escutcheon of the prime minister himself. On 28 March he began to distance himself from his earlier policies.\n\nEver mindful of public opinion, of his place in history, and that his government was a coalition, the prime minister ordered a reassessment of the policies that he had set in motion. In a letter to General H. L. Ismay, his chief of staff, Churchill said, \"It seems to me that the moment has come when the question of bombing of German cities simply for the sake of increasing the terror, though under other pretexts, should be reviewed.\"\n\nThe prime minister's reasons were not altruistic. He went on to complain that if Germany were \"utterly ruined,\" German resources that could be used to rebuild Great Britain would instead have to be used in Germany to provide housing for the defeated enemy. But he quickly returned to questioning the policies of Bomber Command and the Eighth Air Force.\n\n\"The destruction of Dresden remains a serious query against the conduct of Allied bombing,\" said Churchill. \"I am of the opinion that military objectives must henceforward be more strictly studied in our own interests rather than that of the enemy.... The Foreign Secretary has spoken to me on this subject, and I feel the need for more precise concentration upon military objectives, such as oil and communications behind the immediate battle-zone, rather than on mere acts of terror and wanton destruction, however impressive.\"\n\nThe record is clear on Churchill's role in developing the bombing policies of Bomber Command, so it must have been with some dismay that Ismay, Portal, Bottomley, and Harris himself were now hearing that the prime minister was not only disavowing a program that had his fingerprints all over it but also saying that it might have been a mistake.\n\nHad not the prime minister, at the summit meeting with Joseph Stalin in August 1942, drawn a picture of a crocodile to represent Europe and then delighted Stalin by ripping at its belly and hitting it on the snout at the same time? The dictator saw at once the strategic value of attacking the \"soft underbelly of Europe\" and gaining a beachhead on the Continent from that direction.\n\nAnd the Soviet leader was also delighted, according to both the British and the American ambassadors, Archibald Clark Kerr and Averell Harriman, who were present, when Churchill explained the RAF bombing policy put into effect the previous February: the morale bombing of the German cities. Stalin at once began to list the most important urban targets, urging Churchill to spare no one, to bomb homes as well as factories. Churchill, responding to his host's enthusiasm, promised the Soviet leader that the RAF would be \"ruthless.\" Between them, said Harriman, \"they soon had destroyed most of the important industrial cities of Germany.\"\n\nThe list of actual cities is not given in the accounts of the meeting, but it seems unlikely that Germany's seventh-largest city and the one closest to the Eastern Front would not have been included.\n\nSo as early as August 1942, the British prime minister had pledged to the Russians that the RAF would wage total aerial war against the cities of Germany. Civilians were not to be spared.\n\n**Ismay was not the** only recipient of the Churchill memorandum. Portal received a copy, and he passed it on to Bottomley, who was instructed to get Bomber Harris's response to Churchill's allegations. But Harris was not to be shown the full text. He was to be apprised of only the prime minister's main points.\n\nHarris realized soon enough what was afoot, and in just one day he had his reply ready. \"To suggest that we have bombed German cities 'simply for the sake of increasing the terror though under other pretexts' and to speak of our offensive as including 'mere acts of terror and wanton destruction' is an insult both to the bombing policy of the Air Ministry and to the manner in which that policy has been executed by Bomber Command,\" he fumed. \"This sort of thing if it deserves an answer will certainly receive none from me, after three years of implementing official policy.\"\n\nHarris, of course, went on for several pages, explaining and justifying in increasingly outraged tones Bomber Command policy, which had been official policy since before he had assumed command, but made no apologies for carrying out his duties. \"I have always held and still maintain,\" said Harris, \"that my Directive, which you quote, the progressive destruction and dislocation of the German military, industrial and economic systems, could be carried out only by the elimination of German industrial cities and not merely by attacks on individual factories however important these might be in themselves.\"\n\nHarris forcefully argued that the policies that he had pursued for three years had fatally weakened the German war effort and at that very time were enabling Allied troops to advance into Germany with \"negligible casualties.\" Harris was, of course, referring to the more recent weeks. January and February 1945 were two of the bloodiest months of the war in Europe. Casualties on the Western Front totaled over 136,000, with a third of them occurring in the week immediately preceding and the week following the Dresden raid.\n\nBomber Harris was in no mood to either defend or apologize for his actions. Instead he warmed to his task of explaining to the air minister and even the prime minister what the campaign had been about and what they could expect from him for the duration of the war\u2014and while he was at it, he gave them some advice.\n\n\"I therefore assume that the view under consideration is something like this: no doubt in the past we were justified in attacking German cities. But to do so was always repugnant and now that the Germans are beaten anyway we can properly abstain from proceeding with these attacks. This is a doctrine to which I could never subscribe. Attacks on cities like any other act of war are intolerable unless they are strategically justified. But they are strategically justified in so far as they tend to shorten the war and so preserve the lives of Allied soldiers. To my mind we have absolutely no right to give them up unless it is certain they will not have this effect. I do not personally regard the whole of the remaining cities of Germany as worth the bones of one British Grenadier,\" said Bomber Harris.\n\nIf one is looking for a succinct justification or rationale for Harris's actions in World II, there it is. He went on to argue that the only choice was to continue as before or \"very largely stand down altogether.\" That would be fine with him, he said. \"I take little delight in the work and none whatever in risking my crews avoidably.\" And what of the future? he asked.\n\n\"Japan remains,\" said the flinty air chief. \"Are we going to bomb their cities flat\u2014as in Germany\u2014and give the Armies a walk over\u2014as in France and Germany\u2014or are we going to bomb only the outlying factories, largely underground by the time we get going, and subsequently invade at the cost of 3 to 6 million casualties? We should be careful of precedents.\"\n\nThis was not only an apologia. It was also a gauntlet thrown down in front of Churchill, Portal, and Bottomley, and their opposite numbers at American headquarters and in Washington. And it had its effect.\n\nChurchill's original memorandum was immediately revised, with the offensive wording removed\u2014Harris had called it an insult\u2014and in a directive issued on 4 April 1945, it was announced that Bomber Command would continue as before.\n\nBut in the event there was little left to destroy. To be sure, during April there were massive raids on Hamburg, Kiel, Potsdam, Heligoland, and Wangerooge, as well as one abortive raid on Bremen. There were smaller raids as well, and the Mosquitoes kept up the pressure on Berlin, but the great campaign was winding down.\n\n**The angry exchange among** Churchill, Portal, Bottomley, and Harris in March 1945 was not the first time they had crossed swords in their battle of wills. In a particularly spirited exchange of letters with Portal, from early November 1944 through mid-January 1945, the head of Bomber Command had defended his position that although the oil plan was a chimera, Bomber Command was doing its part to seek out and destroy the refineries. Portal was not convinced and even went so far as to suggest that perhaps Harris's views were filtering down through Bomber Command and creating opposition to the oil plan.\n\nHarris was quick to respond. \"I do not give my staff views,\" he said. \"I give them orders.\"\n\nThe exchange between the two airmen degenerated further and became so heated that Portal finally aroused Harris to very real anger, a not too difficult task. The chief of Bomber Command, referring to what he called \"an intolerable situation,\" by which, of course, he meant anyone presuming to meddle in how he ran his command, wrote to Portal, \"I therefore ask you to consider whether it is best for the prosecution of the war and the success of our arms, which alone matters, that I should remain in this situation....\"\n\nHarris's resignation would have caused another kind of firestorm, this one from the British public, and Portal damped the fires immediately. Harris responded in kind. He would follow orders and implement the oil plan, although he remained convinced to the end that it was not the most effective use of men and machines. In any event, simultaneously with the promised implementation of the oil plan, Bomber Command continued to level German cities and towns.\n\nUnknown to Harris, Portal was in possession of information from the codebreakers at Bletchley Park that the oil plan was having a devastating effect on the Reich. This was information that one would have thought would have been disseminated as a matter of course to someone of Harris's stature and rank; but it was not, at least not sufficiently enough to convince the head of Bomber Command that his superiors in the military and the political spheres were pursuing the best policies.\n\n**The principals settled their** problems and their infighting with letters and memorandums and directives, in the interest of successfully bringing to an end the war against the Nazis in 1945. However, in the postwar period both Churchill and Harris seemed to have had bouts of selective forgetting. They were more than disingenuous in their recollections of the Dresden raid and its aftermath and their own roles in the controversy.\n\nSir Arthur Harris, \"Bomber Harris,\" the erstwhile hero, had become something of an embarrassment in peacetime England, and he disposed of the issue of Dresden in less than a page in his 1947 memoirs. The former head of Bomber Command said only that \"the attack on Dresden was at the time considered a military necessity by much more important people than myself.\"\n\nAs we have seen, one of these \"much more important people\" was Winston Churchill, who in his multivolume history of World War II was even more succinct, disposing of the issue in one sentence. \"Throughout January and February our bombers continued to attack, and we made a heavy raid in the latter month on Dresden, then a centre of communications of Germany's Eastern Front,\" said the former prime minister. And once, when asked about it directly, he allegedly replied to his questioner that he would have to ask the Americans about that, since it was their show.\n\nAll efforts to ignore or paper over the Dresden raid would of course fail. It continued to fester among the victors as well as the vanquished, and in the early 1950s, the first books on the Dresden firestorm began appearing in Germany.\n\nSensationalist in tone and often lurid in detail, some of them became best sellers, either in spite of or because of their historical inaccuracies. First off the mark, in 1952, was Axel Rodenberger with _Der Tod von Dresden_ (The Death of Dresden).\n\nRodenberger's book was notable for lending a false legitimacy to a clearly erroneous casualty figure and for perpetuating one of those legends that with repetition becomes a truism. He put the number of dead at between 350,000 and 400,000, a figure whose wide acceptance was in direct proportion to its inaccuracy.\n\nRodenberger also helped perpetuate the myth, almost certainly invented by the Goebbels propaganda machine immediately after the raid, that American fighter pilots had indiscriminately strafed crowds of fleeing refugees on the streets and in the parks of Dresden, most particularly the thousands who had sought refuge from the firestorm in the Elbe Meadows and the Grosser Garten.\n\nHowever, the mythology surrounding the destruction of Dresden reached full flower in 1963, and became firmly implanted in the world's consciousness, with the publication of David Irving's _The Destruction of Dresden_.\n\nIrving's documentation seemed exemplary, the book was well written, and it was well received. Almost at once the author became a celebrity historian, and in the next three decades he produced a series of books that were praised by such estimable figures as Hugh Trevor-Roper, A. J. P. Taylor, and John Keegan. The latter called Irving's _Hitler's War_ \"one of the half dozen most important books about the war,\" and the _Times_ of London said, \"Irving is in the first rank of Britain's historical chroniclers.\"\n\nIn 1993, however, a dissenting voice was raised by an American historian, Deborah Lipstadt. In her book _Denying the Holocaust_ , Lipstadt charged that Irving had not only twisted historical data to conform to his preconceived ideas about Hitler and the Third Reich but had also in many instances distorted data to prove his points. David Irving had, she said, not only falsified the historical record but also provided ammunition for those who denied that there had been any such thing as the Holocaust. In fact, she charged, David Irving was himself a Holocaust denier.\n\nIn what would turn out to be not only an ill-advised action but a disastrous one, Irving brought suit for libel against Lipstadt and her publisher, Penguin Books. Penguin engaged Richard J. Evans, professor of modern history at Cambridge University, to help prepare the case for the defense. Evans and a team of researchers began at once to comb through Irving's entire body of work.\n\nDuring the course of the trial, which began in London on 11 January 2000, Evans presented example after example of precisely what Lipstadt had accused Irving of doing, citing in particular his most famous work, _The Destruction of Dresden_. Irving had alleged that the city was of no military importance and that 135,000 people, mostly women, children, and old men, had died during the air raids and firestorm of 13\u201314 February 1945.\n\nIrving's casualty figures proved to be wildly off the mark. According to evidence introduced at the trial, even though he was aware that the figure compiled by the Dresden authorities was probably closer to 35,000, Irving had knowingly published the higher figure. His reason for doing so, he argued in the book, was that the East German authorities had probably struck out the first digit in the number, changing 135,000 to 35,000, to satisfy their Soviet postwar masters. At the time of publication of the book, no one had bothered to point out the obvious flaw in Irving's argument: the Soviets had not bombed Dresden, and therefore none of the onus of the raid was attached to them.\n\nAt the trial it was revealed that Irving's original publisher, William Kember, had accused the author of \"falsifications of the historical facts\" and warned him that the book \"could be interpreted as the work of a propagandist for Nazism who had not scrupled to distort many facts and omit numerous others in order to vilify the British War Government and in particular Winston Churchill.\"\n\nKember and his staff then set about to modify, edit, and in many cases simply omit what they saw as the more egregious examples. But the casualty figures and the overall conclusion of the book stood, and in at least two subsequent editions of _The Destruction of Dresden_ Irving raised the number of casualties to 250,000.\n\nHe based the new figures on a German document, _Tagesbefehl_ 47 (Order of the Day, No. 47), which had purportedly been drawn up in March 1945 by the head of the Dresden police. Irving had first been made aware of TB 47 in 1963, but he had dismissed it then as a forgery. In the interim, he had purportedly seen what he said were convincing copies of the original and he was now prepared to vouch for TB 47's authenticity.\n\nIn reality, he had seen no such thing. Irving had seen what Evans described as a \"typed-up transcript at least several removes from the original.\" TB 47, it turned out, was indeed a forgery, concocted by Goebbels's Propaganda Ministry and first published in the Nazi weekly _Das Reich_.\n\nIrving himself had long known of the doubtful provenance of TB 47 and had admitted as much, but the spurious data had nevertheless continued to appear in editions of the book, as did the story of the omitted digit in the casualty figure.\n\nEven when a 1995 revision of the work appeared, retitled _Apocalypse 1945: The Destruction of Dresden_ , Irving was still unwilling or unable to accept what by then had become the accepted death toll, around 35,000. Instead, he wrote, the number of dead was \"sixty thousand or more; perhaps a hundred thousand\u2014certainly the largest single air raid massacre of the War in Europe.\" And in his 1996 biography of Joseph Goebbels, Irving repeated his death toll of 65,000\u2013100,000.\n\nThe minds of millions of people have remained unchanged as well, bearing out the view of L. A. Jackman, a chief historian of the Air Ministry, who wrote, \"It is practically impossible to kill a myth of this kind once it has become widespread and perhaps reprinted in other books all over the world.\"\n\nTo a large extent this is the view of the larger public as well. In spite of the trial and the damaging revelations, Irving's 1963 descriptions\u2014and his numbers\u2014have remained firmly fixed in the popular imagination. A city of no appreciable importance to the Nazi war effort, filled with innocent people, mostly women and children and hundreds of thousands of refugees, was obliterated for no discernible reason with the end of the war just weeks away.\n\nIf further proof is needed of Jackman's sad assessment of the power of historical revisionism, one need look no further than a speech that David Irving gave in South Africa in 1986. \"Of course now everybody talks about Dresden in the same breath as they talk about Auschwitz and Hiroshima,\" said Irving. \"That's my achievement, ladies and gentlemen. I'm a little bit proud when I look at the newspapers every 13th and 14th of February, when the anniversary comes and they mention Dresden, because until my book was published on that subject the outside world had never heard of what happened in Dresden when 100,000 people were killed in one night by an RAF and American air force raid on one undefended German town at the end of the war.\"\n\nWhen the libel trial ended in April 2000, David Irving's reputation as a historian was in tatters. In addition to having been exposed as a manipulator of historical data, he was also labeled by the court as a racist, an anti-Semite, and a neo-Fascist.\n\nDeborah Lipstadt was vindicated, but the issue did not die. What she referred to in a 2005 interview as David Irving's \"immoral equivalency\"\u2014the Dresden raid was as bad as the war crimes that the Nazis had committed\u2014has been embraced and is fervently believed by many thousands of people.\n\nIrving, meanwhile, soldiered on. In a 12 March 2002 posting on his Web site, he wrote the following comparison of the attack on the New York World Trade Center and the Dresden firestorm: \"Thousands of victims were cremated in the Altmarkt square on makeshift funeral pyres of five hundred civilians at a time. (Rather more than the WTC's three thousand died in that inferno: about thirty times that number, I still aver.)\"\n\nIn November 2005, Irving was arrested by Austrian authorities when he made a clandestine trip to Vienna to address a student group. He had been barred from Austria since 1989 for his views, which allegedly violated the Austrian law forbidding denial of the crimes of the Nazi years or historical revisionism that seeks to cast a favorable light on the Third Reich. He was jailed and denied bail. In February 2006, Irving was sentenced to three years in prison.\n\nAuthor Kurt Vonnegut shares with David Irving the distinction of being one of the two best-known sources of information about the destruction of Dresden. Indeed, Vonnegut pays homage to Irving, of a sort, by quoting from _The Destruction of Dresden_ in his satirical novel _Slaughterhouse-Five_ , in which the Dresden raid is the defining event.\n\nThe principal character, Billy Pilgrim, is an American prisoner of war who is caught in the city when the bombers come. Vonnegut, who was a prisoner of war in Dresden in February 1945, was interned in the eponymous slaughterhouse of the title and witnessed the raid firsthand.\n\nAlthough the novel is heavily science fiction, Vonnegut's view of the raid is never in doubt. He maintains that it was unnecessary, another slaughter of the innocents\u2014a view that has been absorbed by countless undergraduates for whom the book has been received wisdom since its publication in 1969.\n\nBoth books appeared in the tumultuous 1960s, during the debate over the war in Southeast Asia in which thousands of civilians were dying in air attacks. It was, the historian Charles C. Gillispie remarked, a time of \"romantic resentment,\" when it seemed appropriate to reexamine all wartime policies, both past and present.\n\nIn Great Britain, the Royal Air Force was especially sensitive to what it saw as revisionism and even the repudiation of its own noble role in the victory over Fascism in World War II. Much was made in magazine articles and reviews of Irving's book about the misgivings of the aircrews before this raid. Efforts immediately began to shore up the Bomber Command position and refute the critics. The task fell to the Air Historical Branch.\n\nThe AHB began by examining the operational record books of Bomber Command, the bomber groups, and the fifty-five squadrons that took part in the raid. There was no justification, said the reporting officer, for any of the statements that the Bomber Command crews were uneasy about the operation because of moral scruples.\n\nOne's overall impression from scrutiny of these contemporary accounts is that to the aircrew involved it was very little different from other raids, except for the distance, the fact that Dresden had not been attacked before by Bomber Command and the raid's spectacular success.\n\nTheir reaction on their return was one of jubilation the raid had been so successful, tempered by the fatigue consequent on a round trip that had lasted for some ten hours, after which many had to be prepared at short notice for another flight to Chemnitz in the same area.\n\nThere were well over 5,000 aircrew involved in the Dresden raid and it was the prerogative of all airmen, aircrew or not, to indulge in \"binding.\" Among these men it is possible that there were individuals who may have had doubts about this raid, bearing in mind the fact that by February, 1945 there was a certain war weariness and the raid was certainly a test of endurance, but none of this is reflected in the O.R.B.s. Certainly, there is nothing to justify a general statement of this nature, as though there was a widespread mood of criticism of the raid on moral grounds. There is a possibility that after 18 years and with knowledge of the destruction and casualties inflicted some of these aircrew may have rationalized their feelings at the time and expressed doubts, but none of this is expressed in these contemporary accounts. Indeed, the comments reveal that they returned remarkably well pleased with the success of the operation.\n\nThe report includes excerpts from a cross-section of the squadron operational record books, which, critics naturally enough point out, support the conclusions already laid out as the official RAF view. But these are statements from debriefings that were made just hours after the two raids were completed, not reassessments ten, fifteen, or twenty years later. They thus carry considerable historical weight.\n\n**12 SQUADRON** Bomber Command made the inevitable assault on Dresden. Thousands of incendiaries rained down on Germany's 7th. largest city. This is considered a really first-class attack. The route was satisfactory but too long.\n\n**431 (R.C.A.F)** Really pranged the target. Head wind on return kept aircraft airborne for over 10 hours, so it was a very weary group that piled into bed for only, as it turned out, a few hours' sleep at the most. Only the long time in the air marred a pleasant ride.\n\n**467 (R.A.A.F)** Everyone had been hoping for a \"support of the army\" target for some time. to-day was the day but it was the wrong way. Another full petrol load and the target is Dresden if Joe Stalin isn't there beforehand. Trip well planned and a big success for the Command.\n\n**90 SQUADRON** Best attack seen so far.\n\n**434 (R.C.A.F.)** Briefing lasted longer than usual for this long trip. A very good concentrated attack.\n\n**3 GROUP** Attack carried out in direct support of the Russian offensive. Crews were enthusiastic. The first night on which Dresden has been attacked in force by Bomber Command.\n\n**166 SQUADRON** For the first time the Squadron was ordered to take part in an attack on Dresden, a flight involved one of the deepest penetrations into enemy territory yet made. Altogether a highly satisfactory night's work.\n\n**514 SQUADRON** Whole area reported as one mass of smoke and flames. Crews highly delighted.\n\n**433 (R.A.A.F.)** It is understood that this raid was one of the first fruits of combined planning from the Yalta Conference thus beginning the ensuing 7,000 aircraft support to the Eastern front.\n\nTen years earlier an American report classified as \"Top Secret Security Information\" had been circulated to a small number of people. Entitled \"Historical Analysis of the 14\u201315 February 1945 Bombing of Dresden,\" the report was prepared by the USAF Historical Division. Its subsequent declassification and availability has changed few minds on either side of the bombing question, particularly those whose natural propensity it is to distrust all government documents, but in spite of its provenance the report is a valuable contribution to the debate and its arguments are sound.\n\nThe impetus for the study was the increasing use of the Dresden raid by the Soviet Union and its client state East Germany to demonize the Western democracies. This is clear from the introduction, which states, \"From time to time there appears in letters of inquiry to the United States Air Force evidence that American nationals are themselves being taken in by the Communist propaganda line concerning the February 1945 bombings of Dresden.\"\n\nThe United States at the time was involved in the Korean War, and the nation was also transfixed by the revelation of so-called security threats and the fulminations and denunciations of fervent anti-Communist politicians, most notably Senator Joseph McCarthy. Perhaps that is why the language of the report is remarkably free of the overheated rhetoric of the period.\n\nAfter laying out a series of questions, beginning with \"Was Dresden a legitimate military target?,\" the air force historians addressed the conventional belief that the 13\u201314 February bombing of Dresden, the famous triple blow, was a one-time, isolated event. Not so, said the drafters of the report.\n\nBefore 13\u201314 February 1945, Dresden had already been bombed twice, and while these first two raids were, admittedly, minor operations they served notice that the city was not off-limits to Bomber Command or the Eighth Air Force. After 13\u201314 February, Dresden was bombed four more times, with raids on 15 February and 2 March and two raids on 17 April. Also, as we have seen, Dresden was the alternate target for the thousand-bomber American raid against Berlin that was scheduled for 2 February 1945 but was canceled because of bad weather.\n\nDuring the seven months that Dresden was a target of Allied air operations (October 1944\u2014April 1945), some 2,448 bombers dropped a total of 7,100.5 tons of bombs\u20145,278 tons of high explosives and 1,822.5 tons of incendiaries.\n\nThe 2 March raid was particularly heavy. Of the 450 B-17s of the American Third Air Division, which had been dispatched to bomb oil targets at Ruhland, 406 were unable to find the primary target and dropped 1,080.8 tons of bombs on the ruins of Dresden, including 140.5 tons of incendiaries. In this raid, the last of the major Dresden landmarks was destroyed\u2014the Japanese Palace, which housed the Dresden State Library.\n\nThe two final raids, both on 17 April, by 580 bombers from the Eighth Air Force, saw more heavy explosives dropped on the city\u20141,554.4 tons\u2014than any previous raid, plus an additional 164.5 tons of incendiaries. Thus the outcry over the firebombing of 13\u201314 February did nothing to halt the continued bombing, at least by the Americans\u2014Bomber Command did not return to Dresden\u2014of what was still considered to be an important military target.\n\nBut was Dresden a legitimate target? This question has persisted for the sixty years since the firebombing and has been kept alive by both democratic and totalitarian regimes, advocates from the far left and the far right, militarists and pacifists.\n\nComparison with other military targets is thus not only useful but imperative. When World War II began, Dresden was the seventh-largest city in Germany, with a population of 642,143. Only Berlin, Hamburg, Munich, Cologne, Leipzig, and Essen were larger. While the size of a city does not necessarily make it a prime military target, the activities out of which large cities evolve and around which they revolve often do. Dresden was a major commercial and transportation center and the capital of the state of Saxony.\n\nThe city had since medieval times lain athwart two primary military routes: the east-west route of the valley and gorge of the Elbe River between Germany and Czechoslovakia and the east-west land route along the central European uplands.\n\nThree great trunk routes of the German railway system converged at Dresden: Berlin\u2013Prague\u2013Vienna; Munich\u2013Breslau; and Hamburg\u2013Leipzig\u2013Prague. Two main lines connected Dresden with Leipzig and Berlin. In fact, the first railroad line in Germany ran between Dresden and Leipzig.\n\nIt is rail traffic that is the best indicator, however, and by any measure Dresden was an important rail hub, destination, and transfer point. The Dresden-Saxony railway system ranked seventh in the country in mileage, but it was third in total tonnage carried.\n\nThe final issue\u2014were the factories, machine shops, and industrial sites important enough to justify the wholesale destruction of the city in order to guarantee their incapacitation?\u2014has been more problematical for historians since the raids of 13\u201314 February 1945. It need not have been. According to the American air force, there were 110 such sites\u2014all legitimate military targets\u2014employing 50,000 workers.\n\nThese installations included dispersed aircraft factories; a poison-gas factory (Chemische Fabric Goye); an antiaircraft and field gun factory (Lehman); and Germany's most famous optical instruments firm (Zeiss-Ikon). There were also manufacturers of electrical products and X-ray apparatus (Kock and Starzel); small arms (Seidel and Naumann); molds and metal packings (Anton Reich); gears and differentials (Saxonizwerke); and electric gauges (Gebruder Bessler).\n\nTypical was the J. C. M\u00fcller Universelle-Werke, which had been founded to make machinery for the manufacture of cigarettes. In the First World War, the company had gone into armaments, but afterward, with such activity forbidden by treaty, it went back to making cigarette machinery. Under Adolf Hitler the company grew exponentially, and by the time of the raid 4,000 workers, which included slave laborers and Jews from concentration camps, were turning out a plethora of military equipment\u2014including machine guns and aircraft parts.\n\nEarly in the war, the Nazis had begun to transport Jews to Dresden to work in the factories. For most of them, it was only a brief stopover before they were sent on to the death camps. Later, as labor shortages became more critical, some of them avoided the further deportation to the east and even survived until the end of the war.\n\nNot mentioned by the air force was another vital service that was centered in Dresden. The city had become a key link in the German postal and telegraph system. The central offices, in which hundreds of German civilians and British prisoners of war worked, were located on the Postplatz, in the very center of the Altstadt. Berlin had moved other important services to Dresden as well, including the Berlin Grossbank.\n\nDresden was also a favored haven for refugees from the capital and other bombed-out cities of the Reich, and it still was a favorite retreat of the Nazis. Frau Goebbels herself spent much time at one of the Dresden sanatoriums, and Hitler's half sister, Angela, was married to Martin Hammitzsch, the director of the State School of Building Construction in Dresden.\n\nAs for military installations, the report did err in its estimation of the air defenses in the city. While there was a fighter squadron based nearby, the other air defenses were minimal. As we have seen, the antiaircraft guns had been moved to the east to be used as antitank weapons in the attempt to hold back the Russian advance.\n\nThere were also an ammunition storage depot and a new SS headquarters, but they were unlikely to be destroyed in any raid on the city. They were miles from the central area and far belowground.\n\nAnother continuing point of controversy has been the argument that the Russians requested specifically that Dresden be bombed. The 1953 air force report also errs in stating that it was not until early 1943 that the Allies and Russians began high-level consultations to coordinate their military efforts against Germany. Such plans began to be laid soon after America entered the war in 1941 and were discussed in earnest at the highest levels in August 1942, more than a year before the Tehran Conference of the Big Three. Stalin, up to and during the Yalta Conference in February 1945, had been repeatedly reassured by visiting emissaries and by both Churchill and Roosevelt personally that Allied bombers could be counted on to support the Russian offensive in the east when the time came.\n\nThe air force report, which dutifully laid out the facts of the Dresden raid of 13\u201314 February 1945, could have gone a long way to lay the controversy to rest if it had been released in 1953. But it was not declassified for public dissemination for another twenty-five years. Thus the questions were resolved only to the satisfaction of the limited number of military and Defense Department officials who were allowed to read it.\n\nTherefore, the books and articles that condemned the raid as unnecessary\u2014even a war crime\u2014ensured that the Dresden controversy would not only take on a new life and interest but would grow in the intervening years. The failed U.S. intervention in Vietnam, various other American adventures abroad, and the worldwide peace movement guaranteed a continuing interest. Dresden's place on the lists of bombing atrocities, alongside Coventry, Rotterdam, Guernica, and, of course, Hiroshima and Nagasaki, was assured.\n\n**Every book, article, and documentary** concerning the Dresden firestorm rightly has extolled the city of the Augustuses as an architectural and cultural marvel, which it certainly was; but also, with a few notable exceptions, all have decried the raid as unnecessary and an act of unparalleled barbarity.\n\nIn addition, was not the war at an end? After all, the Eastern and Western Fronts were rapidly contracting, with the last vestiges of Nazi Germany being squeezed tight in the vise created by the Allied forces. Indeed, with the Soviet forces just a few miles from Dresden in mid-February 1945, was not the final collapse only days or, at most, a few weeks away?\n\nHarry Truman's memoirs cast a revealing light on this argument. On 13 April 1945\u2014his first full day as president and exactly two months after the Dresden raid and just three weeks before the unconditional surrender of Nazi Germany\u2014Truman was told in a meeting with his top military advisers and the secretary of war that the assessment by intelligence sources presented to Roosevelt and Churchill at the Octagon Conference in Quebec in September 1944 still held. Germany would not be defeated for at least six months and Japan for a year and a half.\n\nIn other words, Secretary of War Henry L. Stimson, Secretary of the Navy James V. Forrestal, Army Chief of Staff George C. Marshall, Chief of Naval Operations Ernest J. King, Lieutenant General Barney M. Giles, representing the air force, and White House Chief of Staff Admiral William D. Leahy all assured Truman that Germany would not fall before October 1945, at the earliest, and Japan not before October 1946.\n\nWhen Truman assumed the presidency on 12 April 1945, he was completely in the dark about the development of the atomic bomb. After a hastily convened cabinet meeting immediately after he was sworn in, Stimson stayed behind to tell the new president of \"the development of a new explosive of almost unbelievable destructive power.\" Amazingly, that was all the secretary of war felt free to confide to his boss, the president of the United States.\n\nThe next day, James F. Byrnes, who had been director of war mobilization, came to see Truman. While he allowed that the new weapon was \"great enough to destroy the whole world,\" he provided no further details.\n\nThe commander in chief, who, as he admitted in his memoirs, was \"puzzled,\" did not press his subordinates for more information. Perhaps he was being deferential. While the new president was being briefed, his predecessor's funeral train was still en route from Warm Springs, Georgia, to Washington.\n\nIt was not until the next day that Truman was told of the atomic bomb by Vannevar Bush, the head of the Office of Scientific Research and Development. He also learned from Bush the startling news that the new weapon was almost ready to be tested.\n\nAdmiral William Leahy, Roosevelt's, and now Truman's, chief of staff, sat in on the scientific briefing. The admiral, who just hours earlier had concurred with his colleagues on the end dates for the war in Europe and the Pacific, now volunteered an even less prescient prediction. \"That is the biggest fool thing we have ever done,\" he said. \"The bomb will never go off, and I speak as an expert in explosives.\"\n\n**Dresden, the seventh-largest city** in Germany, with its prewar light industries retooled and revamped to provide vital military goods and services, and with its vast network of railroads, highways, and river traffic, was clearly a viable military target. No responsible military planner could ignore it. The city was an important component of the Nazi war machine.\n\nWhen the bombers had departed, much of this manufacturing capability had been destroyed or seriously crippled\u2014though more of it would have been devastated if the massive British raids had concentrated on the industrial areas just outside the city instead of the Altstadt. Dresden would not regain the major role as a producer of armaments that it had enjoyed prior to 13 February. Too many workers were dead. Too much of the infrastructure had been destroyed. And the ensuing American follow-up raids were designed to ensure that this would remain the case.\n\nBomber Harris summed it up in his acerbic response to Churchill's questioning of the necessity of the destruction of Dresden. \"The feeling, such as there is, over Dresden could be easily explained by any psychiatrist,\" said Harris. \"It is connected with German bands and Dresden shepherdesses. Actually Dresden was a mass of munitions works, an intact government centre, and a key transportation point to the East. It is now none of these things.\"\n\nHarris might also have pointed out that the week of the Dresden raid the Germans launched the greatest number of rockets against England of any week since the beginning of the vengeance-weapons campaign.\n\n# CHAPTER THIRTEEN\n\n**FROM THE ASHES**\n\nDresden Is Reborn\n\n**F ew cities in the world had such a concentration of cultural trea**sures as Dresden in 1945. All of the city's major architectural sites and art collections were in walking distance of one another and all were located within the area of total devastation\u2014some sixteen hundred acres, two and a half square miles. Comparisons with other cities whose cultural riches lie in similar proximity provide some perspective on the loss.\n\nParisians would be devastated by the loss of the Louvre, the Palais-Royal, the Jeu de Paume, the Invalides, the Tuileries, the Champs-\u00c9lys\u00e9es, the Arc de Triomphe, Sainte-Chapelle, the Eiffel Tower, Notre-Dame and the \u00cele de la Cit\u00e9, the Op\u00e9ra, Saint-Sulpice, and the Sorbonne. In a firestorm like the Dresden raid, all of these monuments of French culture and their surrounding neighborhoods would be gutted by fire and reduced to mounds of rubble.\n\nLondoners\u2014whose city, of course, did suffer; many landmarks were wrecked or seriously damaged, in particular the Houses of Parliament and dozens of historic churches\u2014might think differently about the bombing of other cities if Covent Garden, Westminster Abbey, St. Paul's, the National Gallery, the Victoria and Albert Museum, Buckingham Palace, the West End, the Strand, and all of Mayfair and Belgravia and their environs were leveled.\n\nAmericans, as well, might benefit from the cautionary tale presented by the destruction of Dresden. Imagine if, in Washington, D.C., all of the public buildings, national monuments, and museums, from the Capitol to the Lincoln Memorial and beyond, were destroyed in one great cataclysm.\n\nThe National Gallery, the White House, the Capitol, the Washington Monument, the Lincoln and Jefferson Memorials, the Kennedy Center, the Smithsonian Institution, and much of Capitol Hill and Georgetown lie well within the parameters of a raid the size of the Dresden firestorm. All would have been obliterated or reduced to smoking ruins.\n\nIn New York, a similar series of raids would lay waste a great swath of Manhattan if the central aiming point were Fourteenth Street. Everything between the East River and the Hudson River and well into Central Park would be razed. The Metropolitan Museum of Art, the American Museum of Natural History, St. Patrick's Cathedral, the Museum of Modern Art, Central Park, Times Square and the Theater District, and thousands of office and apartment buildings would be gone.\n\nPerhaps another comparison is in order as well. The area destroyed by the 2001 attack on the World Trade Center in New York, which caused such devastation and grief, was some twenty-five acres, about 1.5 percent of the area of the firestorm in Dresden.\n\n**February in Saxony is rainy** and chilly, but there are sunny days with blue, cloudless skies. Like everywhere in midwinter, when the trees are bare and the vines leafless, the skeleton of Dresden can be seen, the underlying landscape visible. But in this old city other outlines are visible as well. When one masters the clues, one can find the scars from the firestorm more than sixty years ago.\n\nThe great open spaces, some of them still punctuated by the foundations of the buildings that once occupied the sites, are the products of explosions and fires, not the wrecker's ball. From time to time one comes upon fenced-in enclosures containing bits and pieces of statuary, broken masonry and marble, plinths and columns, architraves and garlands, and assorted other architectural elements. The shards and pieces were carefully numbered and cataloged long ago and now wait to be attached to, or perhaps reintegrated into, reconstructed buildings.\n\nWithout the softening effects of summer greenery, the ugliness of the Communist-era buildings are magnified many times. What the _Great Soviet Encyclopedia_ called the \"socialist reconstruction of Dresden\" is epitomized on the northern side of the Altmarkt, the ancient square at the heart of Dresden. There stands the Stalinist Kulturpalast, the perfect example\u2014or nadir\u2014of Socialist building in Saxony. One guidebook extols this uneasy alliance as a marriage of modern urbanism with an ancient heritage. It's a shotgun marriage at best.\n\nThe new buildings combine the worst aspects of Socialist cookiecutter architecture and the dehumanizing elements of modernism gone awry or misunderstood. And nowhere else in the world is the contrast between the beauty and the exuberance of the baroque, the rococo, and the neoclassical and the blandness of the modern more apparent than in Dresden.\n\nIn much of old Dresden, however, the eye is still beguiled and the mind stimulated by the beauty of the surviving or reconstructed buildings ordered up by the Augustuses and their successors. For while the Communist rulers of the former East Germany can be faulted for erecting buildings of a transcendent ugliness, they must also be credited with saving and rebuilding many of the major monuments.\n\nThis strange dichotomy of preserving the cultural heritage while destroying the aristocracy and the class system that created it prevailed in all the satellite states. It followed the example of the Soviet Union, which after 1917 ruthlessly liquidated the nobility but kept their palaces.\n\nHistorical preservation was not universal. Many monuments that survived the destruction of the World War II were toppled by the tribunes of the people. Statues of kings and statesmen of the ancien r\u00e9gime were often dismantled or melted down. In the Altmarkt, the statue of Germania was considered too representative of a militant and Fascist Germany, so it was taken away after the war. The statue of the Iron Chancellor, Bismarck, at the upper end of the Pragerstrasse; Augustus the Strong at the entrance to the Neustadt; and Martin Luther in the Neumarkt by the Frauenkirche also survived, although Luther and Augustus were severely damaged. All three were put in storage, but in a stunning example of political inconsistency, Luther and Augustus were repaired and restored to their pedestals in the 1950s. Bismarck and Germania remain exiles.\n\nRestoration has been slow and even after six decades is not complete. The first task of the new postwar regime in East Germany was not historical preservation. The overriding priority, after clearing the hundreds of thousands of tons of rubble, was to build housing for millions of homeless and displaced people. So one is forced to understand, if not forgive, the blocks of utilitarian apartment buildings that today coexist uneasily with their exuberant baroque distant cousins.\n\nWhile the aesthetics of the Communist-era public housing blocks might have been the subject of debate, their monetary value to the city after German reunification was clear. In a stunning example of the triumph of capitalism, the mayor of Dresden agreed in March 2006 to sell all of the city-owned apartments, a total of 48,000 units, to an American investment firm for $1.2 billion. The move completely retired the massive municipal debt.\n\nThe Communist regime of the GDR, like many governments in the eastern bloc, was not oblivious to the past. Employing the same arguments that were made in the Soviet Union for restoring the palaces and resorts of the czars\u2014that princely art and architecture were the patrimony of all the people\u2014the leaders of the GDR began to rebuild Dresden in the 1950s. What the postwar buildings lacked in architectural interest was more than offset by the German craftsmen and artisans who set to work to re-create their lost heritage with great fidelity and not a little love.\n\nFirst and foremost was, of course, the Zwinger, the world-famous museum and crown jewel of the city. The Soviets, who had taken the collections away for \"safekeeping\" at the end of the war, heeded their fellow Communists' call to return the looted art in 1955, and the great collection of the electors was reinstalled in the meticulously restored museum.\n\nThe reconstruction efforts were by no means characterized by system or logic. Opposite the Zwinger lay another ruin, the Sophienkirche, which could easily have been reconstructed\u2014much of the original building survived the raid\u2014but, over much protest, the site was leveled. And across the Theaterplatz, near the Semper Opera House, the site of another famous Dresden landmark, the Hotel Bellevue\u2014that bastion of privilege\u2014was also completely cleared. Eventually a new Bellevue was built, by an international hotel chain, but on the other side of the river.\n\nThe oldest church in Dresden, the Kreuzkirche, which was built in the Gothic style in the thirteenth century, was destroyed by Prussian artillery in 1760. The rebuilt baroque church was destroyed by fire in 1897 but was restored. The tower and the facade survived the firestorm more or less intact, although the interior was completely gutted.\n\nNo attempt was made during the restoration of the church to replicate the fanciful baroque decorative features. Instead the church walls and vaulting were covered with a rough, concrete-like plaster, with the occasional fragment of a cherubim or angel, recovered from the ruins of the old church, embedded in the surface. The effect is restrained, reverential, and ultimately very moving, especially during musical performances of the Dresden Kreuzchor, the boys' choir that has performed in the church for almost eight centuries.\n\nThe residential neighborhood that the desperate Red Cross worker was trying to reach was totally destroyed in the raid; the ruins were leveled, and the debris carted away. Much of the neighborhood is again residential, but the prewar villas and small apartment buildings had to give way to large apartment buildings for the masses during the postwar housing crisis.\n\nThe Hauptbahnhof is the only recognizable prewar building in the immediate area, but as in the old days the Central Station, which faces onto the Pragerstrasse, functions as the major entrance to the city.\n\nThe Pragerstrasse was not rebuilt until the late 1960s, and it in no way today physically resembles the fashionable prewar avenue that connected the Altstadt and the Hauptbahnhof. The street is now a rather ordinary pedestrians-only mall, lined with shops and midpriced hotels, but whatever its architectural shortcomings, it has been reborn as a vibrant center of Dresden commercial life.\n\nAfter the war, other buildings in various stages of ruin and disrepair remained boarded up, and their rebuilding and restoration proceeded at a glacial pace for the next decades. The Hofkirche was rebuilt fairly early on, but the Semper Opera House did not reopen until 13 February 1985, exactly forty years after it had been destroyed by bombs, with a performance of Weber's _Der Freisch\u00fctz_.\n\nAlthough the Dresden Staatskapelle had to wait forty years for the restoration of its permanent home at the Semper, the world-renowned orchestra continued to perform regularly in other venues in Dresden and to make regular concert appearances abroad.\n\nAfter the reunification of East and West Germany in 1990, reconstruction and preservation became issues of national, not just Saxon, pride. East Berlin, Leipzig, and Dresden, even under the Communists, had never lost their image as powerful symbols of the great contributions to Western civilization made by German writers, philosophers, and musicians. Indeed, these cities had for centuries been the cultural patrimony of all Germans. Billions of deutschmarks became available for historic reconstruction, and of course the newly introduced capitalism spurred many projects.\n\nThe long-delayed rebuilding of the Royal Palace could now finally be undertaken. However, progress was slow, and it was not until 2005 that the work had advanced to the point that the extraordinary collection of jewels and decorative objects known as the Gr\u00fcnes Gew\u00f6lbe could be moved from the temporary home in the Albertinum back into the building. The completely restored building was opened to the public in 2006.\n\nNext to the Royal Palace is the restored Taschenberg Palace. The original was built by Augustus the Strong for one of his many favorites, Constantia, the Countess Cosel. Augustus had an enclosed bridge built between the Royal Palace and the Taschenberg, much like the bridge that connected the palace with the Hofkirche. But the bridge to the Taschenberg had a more secular purpose than the one to the cathedral. It ensured the king's privacy when he visited his mistress. The \"Saxon Pompadour\" reigned supreme in Augustus's affections for nine years until palace intrigues, some of them her own, led to her banishment to Burg Stolpen, where she spent the last twenty-one years of her life under house arrest. Her palace has a new life as the Grand Hotel Taschenberg Palais Kempinski.\n\nForeign largesse has been important as well in the reconstruction of what is arguably Dresden's most famous building. An international campaign was launched in 1992 to raise money for the rebuilding of the Frauenkirche. The reconstruction project attracted donations from nearly every country in the world, and the restoration of the symbol of Dresden began the following year.\n\nDuring the forty-five years of Communist rule, the sad pile of rubble of the once-great church lay at the very heart of the city, in the Neumarkt. It not only served as a reminder of the horrors of warfare; it was, not so incidentally, a rebuke to the West. On 13 February each year, thousands of Dresdeners, carrying candles, gathered at the ruins and sang old songs and hymns, falling silent as every bell in the city began to toll at 1010, the precise time that the first bombs began to fall on the city on that terrible night in February 1945.\n\nWorkers began sifting through the vast pile of fire-blackened stones of the original Frauenkirche in 1993, carefully marking each stone that was still usable and could be incorporated into the fabric of the new church. In June, the badly damaged but intact pinnacle cross and its boss were uncovered, a happy omen.\n\nIn May 1994, the first of the new foundation stones was laid. The original foundation stone, which was laid on 26 August 1726, was still in place in the choir. The reborn Frauenkirche now began to rise from the blackened eighteenth-century foundation. In ten years, the outer construction was complete, and once again the great stone bell that defined Dresden soared over the skyline. A new gold pinnacle cross, an exact replica of the original, financed by British donations and made by British artisans, was set in place and crowned the church.\n\nWithin, master plasterers, painters, and artists, working from old photographs and using the latest computer technology, painstakingly restored the grand rococo interior. To the dismay of many purists, reproducing a facsimile of the original organ of Gottfried Silbermann was deemed not feasible, and a modern organ, with a baroque outer covering, was installed in the church.\n\nAnother building that has played a central role in the Dresden drama lies just behind the Frauenkirche, and every regime for the past hundred years has made use of the massive structure. In this brooding pile of a building, \"enemies of the state\"\u2014common criminals, political dissidents, Jews, and homosexuals\u2014were questioned, detained, and tortured by the Gestapo or shipped on to concentration camps. In 1938, the Gestapo and the Dresden police had an unobstructed view of the burning synagogue, situated only a block away, during the outrage called Kristallnacht.\n\nThe police building was one of the first to be restored and operating again after the war, and here the notorious Stasi, the East German secret police, intimidated and terrorized the populace, from the same offices used earlier by Himmler's henchmen. In the mid-1980s a young Soviet agent named Vladimir Putin, who would go on to greater fame as president of Russia, was a KGB operative in Dresden, where he worked hand in hand with the Stasi.\n\n\"We started the fire, and it came back and consumed us,\" said the mayor of Dresden on the fiftieth anniversary of the firestorm, 14 February 1995. A group of leftists disrupted the memorial service in the Hofkirche. They charged that it was unseemly to commemorate the Dresden dead when so many innocents, in particular the Jews, suffered at the hands of the Germans. \"Germans were the criminals, not the victims,\" they shouted at the startled audience, which included Chancellor Helmut Kohl. In their view the Dresden dead were victims of the evil Nazis, not of the Allied bombers.\n\nThese young people were viewed by many as representative of a healthy German democracy that tolerated dissent. Others were not so forbearing. The German political scene is both fractured and fractious. There are leftists, rightists, centrists, old-line Communists, and a small but increasingly vocal ultra-right-wing element, neo-Nazis in all but name.\n\nAn incident on a research trip to Dresden is informative. In a caf\u00e9 near my hotel on the Pragerstrasse, I watched as the barman became more and more agitated over the presence of three men sitting at a table. There was nothing remarkable about either their looks or their behavior, but he identified them as Turks. Finally, after much muttering, he stormed over to their table and ordered them out of the caf\u00e9. When they protested, he threatened to call the police. They left.\n\nAs it turned out, he would not have had to go very far for the police. After further conversation with the gentleman on my right, I found out that he was a high-ranking police official whose job it was to ferret out former Stasi agents in the new Saxon police force. He had watched the expulsion of the foreign \"guest workers\" with studied detachment.\n\nOn the sixtieth anniversary of the bombing, five thousand of that barman's fellow travelers from the far-right, anti-immigrant National Democratic Party marched through the streets of Dresden. In a more hopeful sign, an opposition group of nearly equal strength also took to the streets to protest against the rightists.\n\nPerhaps more representative was a group of German students I encountered on a Danube steamer. They were outraged that the captain who was pointing out the attractions along each side of the river had neglected to tell the passengers that we were passing near the site of one of the most infamous of the Nazi concentration camps, Mauthausen. A petition was circulated, most of the passengers signed it, and the matter was put right on the public address system, which was an encouraging sign indeed.\n\n**Even if rare, any** antipathy toward outsiders or lack of tolerance for liberal views is a source of worry in a country with such a violent past as Germany. So the small but active Jewish congregation in Dresden is a hopeful portent. Like all religions, Judaism was discouraged under the Communist regime, but within five years of the end of World War II a small group of Jews was worshipping again in Dresden.\n\nIn the Neustadt, the resurgent Jewish community founded the Center for Jewish History and Culture in Saxony, in a building facing the eighteenth-century Jewish Cemetery, which miraculously survived the Nazi era. The old cemetery draws throngs of the faithful, the merely curious, and sometimes the obtuse or unreconstructed.\n\nIn order to enter the site, men are obliged to don one of the yarmulkes provided by the guides, but on the day I was there, a German tourist refused to do so. He was quietly asked to wait outside while his embarrassed wife stayed on for the tour. It is devoutly to be wished that she, and not the recalcitrant husband, is the true face of the new Germany.\n\nOur guide stressed that the unofficial name for the Jewish Center in the Neustadt is Hatikva, \"hope\" in Hebrew, and hope is certainly the proper word to describe the Jewish community in Dresden, which by 2005 had grown to about 250, helped along by emigration from Russia.\n\nMore important than the size of the congregation is that the Jews of Dresden now have a synagogue, the first to be built in eastern Germany since the 1920s. Their new building sits on the site of the original synagogue built by Gottfried Semper in the nineteenth century. The dedication took place on 9 November 2001, the sixty-third anniversary of Kristallnacht, the night that the old building was burned to the ground by the Nazis.\n\nA relic of Semper's original synagogue, a Star of David, has been incorporated into the ultramodern twenty-first-century building. A local firefighter, Alfred Neugebauer, salvaged the Jewish symbol from the wreckage on the night of the Nazi rampage and, at the risk of imprisonment or death, hid it in his home. The star is now enshrined above the entrance of the new synagogue.\n\n# EPILOGUE\n\n**W inston Churchill, celebrated by many as the greatest wartime** civilian leader in history, was not so fortunate in peacetime. The great threat to England's very existence had brought Churchill to power, but now domestic issues, which had been relegated to the wings during the effort to win the war, were suddenly front and center. The quotidian, the mundane, were of little interest to the prime minister, and he made plain his annoyance with having to deal with them.\n\nInstead of planning grand strategy involving thousands of warplanes, hundreds of ships, and hundreds of thousands of men, he was now badgered by politicians concerned by such issues as the postwar use of the soon-to-be-abandoned airfields scattered across England. Would they be available as sites for commercial aviation?\n\nAs Lord Moran recorded in his diaries, even though Churchill spent many hours with the reform-minded American president, he did not share Roosevelt's \"preoccupation with social problems and the rights of the common man.\" The presidential concerns \"struck no sparks in Winston's mind,\" he observed. The war was their only common interest.\n\nWithin just a little over two weeks after the German surrender, it was clear that the national government that Churchill had put together in 1940, with members of the Labour, Conservative, and Liberal Parties in prominent posts, was finished. The Labourites sensed that they were now in the ascendant and would finally be able to enact many of their long-delayed populist ideas and reforms into law. They withdrew from the coalition. Churchill had no choice but to tender his resignation, but the king immediately asked him to form a \"caretaker\" government until elections could be held to settle the matter as to who would govern postwar Britain.\n\nBritish public opinion was not congruent with that of the larger world, which viewed Churchill as a towering figure, an indispensable man. On 25 July 1945, in a stunning reversal of fortune, Labour was triumphant, and Winston Churchill became a private citizen. Clement Attlee was now prime minister.\n\nArthur Harris, like his old boss, also found himself, at the end of World War II, not a nationally celebrated hero. Instead he became almost a forgotten man. Churchill had raised him from the rank of knight commander to knight grand cross of the Order of the Bath and had also offered him the post of governor general of Bermuda.\n\nThe new prime minister agreed to the appointment, and he invited Harris and his wife to Chequers by way of further congratulations. Attlee's colleagues in the new Labour government turned out to be more chary. He rescinded the offer of the Bermuda post within days.\n\nHarris was also left out of the Victory Honours List, which was bad enough in itself, but the insult was compounded by the elevation to the peerage or a baronetcy of the other wartime military leaders. The calculated slight caused a furor in England. Many theories were put forward for the affront: the newly rediscovered pacifism of the Labourites; the settling of old scores by the many enemies Harris had made; even the embarrassment, in the postwar atmosphere, of what had been done to Germany by \"Bomber\" Harris.\n\nHarris and his many supporters, for good reason, placed the blame on the machinations of John Strachey, an old adversary who had become undersecretary for air in the Attlee government. During the war, Harris had never hidden his disdain for and distrust of Strachey, whose politics had careered from the extreme right to the extreme left.\n\nBut Harris's ire had extended to everyone. Whether the supposed malefactor was an undersecretary, a member of the Cabinet, or even the prime minister, he'd cared not at all. In one particularly abusive memo to Strachey's predecessor, he had excoriated the defense establishment for not producing a workable cluster of incendiary bombs. The letter is studded with such expressions as \"gross incompetence,\" \"hopeless,\" \"poor,\" \"misplaced energy... being put into petty and useless improvements,\" and \"deplorable.\" Amazingly, this letter was written ten days _after_ incendiaries had devastated Dresden.\n\nIn January 1946, preparatory to his retirement from the RAF, Harris was promoted from air chief marshal to marshal of the Royal Air Force, the highest rank attainable in the RAF. And there the matter rested. There were no further official honors for the man who had taken the war to the enemy for five years.\n\nForeign governments were not so stingy with accolades for the leader of Bomber Command, in particular the United States. At a special service at the Pentagon in September 1946, Eisenhower himself presented Harris with the Distinguished Service Medal on behalf of President Truman and the American people.\n\nBy this time, Harris's connections, in particular his acquaintance with Averell Harriman, had led to his becoming managing director of the South African Marine Corporation, Ltd., a shipping line with offices in New York and Cape Town. He and Lady Harris maintained homes in both cities.\n\nOne of the advantages of a society with free elections is that wrongs are sometimes righted when the outs become the ins. Such was the case when Churchill was returned to power as prime minister of Great Britain on 26 October 1951, a month shy of his seventy-seventh birthday. The following April, he offered Harris the long-overdue peerage.\n\nHarris's departure from England six years earlier had come amid much speculation that he had abandoned his homeland because of the shoddy treatment he had received at the hands of an ungrateful Labour government. He felt that once he accepted this honor from the new Tory government, perhaps these rumors, which were not completely unjustified, might at least be put to rest.\n\nBut he refused the highest honor. To be called \"Lord Harris\" just would not do in South Africa. As he put it, it would be \"as out of place [there] as a hippopotamus in Trafalgar Square.\"\n\nOpposition to honoring Harris was still strong, and according to Churchill's private secretary John Colville, there was \"consternation\" at the meeting of the Honours Committee when Churchill proposed Harris's name.\n\nThe tenacious Churchill would not be denied, however, and the following New Year's Day, 1953, Harris's name appeared on the Honours List. He was to become a baronet, a title he'd chosen since he would not have to change the way he was addressed. But the overriding reason he allowed such an honor was that it would also recognize the thousands of men who had served and died under him in the war against the Axis\u2014his \"bomber boys.\" Not so incidentally, it would also be \"a thistle for Strachey.\"\n\nSir Arthur Harris, Bt, GCB, OBE, AFC, LLD, eventually resettled in England in the Oxfordshire village of Goring-on-Thames, the name of which no doubt amused him greatly. There he lived quietly, receiving old friends and maintaining his contacts with former comrades in arms.\n\nOn 5 June 1964, the day before the twentieth anniversary of D-day, Harris received a particularly welcome message. \"Dear Bert,\" wrote his old comrade in arms, \"To you, one of my close associates in OVERLORD, I am impelled to send, once more, a special word of thanks... no historian could possibly be aware of the depth of my obligation to you.\" The cable was signed simply \"Ike.\"\n\nOn Arthur Harris's ninetieth birthday, in 1982, part of the celebration included a flyover by a Lancaster bomber. At noon, the old man was asked to come outside. As he stood in his garden the great plane roared in low over the town. The air marshal looked at his watch. \"Late, as always,\" he said.\n\nThe controversy that swirled around Arthur Harris and Bomber Command continues to crop up as new revelations come to light and World War II strategy is rethought, reinterpreted, and in many cases condemned anew. The announcement that at long last a memorial to the men of Bomber Command, with a statue of the air marshal, was to be erected in front of St. Clement Danes, the RAF church, in the Strand, elicited protests from around the world, including the _Times_ of London and the mayor of Dresden.\n\nOpposition was effectively damped down, or at least muted, when one of the RAF's staunchest wartime sponsors announced that not only would she attend the ceremony but would unveil the statue to Bomber Harris herself. On 31 May 1992, Elizabeth, the ninety-two-year-old Queen Mother, proudly took her place beside the old airmen at the dedication, many of whom she had met when she'd tirelessly toured the RAF bases a half century earlier.\n\n**With the Russian soldiers** only a few streets away, Adolf Hitler killed himself in the _F\u00fchrerbunker_. Joseph Goebbels and his wife, Magda\u2014after dispatching their six sleeping children by forcing cyanide capsules into their mouths\u2014chose to die upstairs, outside the chancellery. Heinrich Himmler was captured by the British, but he too chose death, by biting down on a cyanide capsule while being examined by a doctor. Hermann G\u00f6ring, therefore, was the only one of the four highest-ranking Nazis to stand trial.\n\nSoon after his arrest by American troops, G\u00f6ring held a press conference, where he drank champagne while holding forth for reporters and photographers. The subsequent picture spread in _Life_ magazine created the predictable storm, and the Reichsmarschall disappeared from sight until he testified in his own defense at his trial before the War Crimes Tribunal at Nuremberg. Rudolf Hess, Jaochim von Ribbentrop, Speer, Karl D\u00f6nitz, and other Nazi leaders shared the dock with him, but, as always, attention was squarely on G\u00f6ring, who was unrepentant to the end.\n\nBy most accounts, G\u00f6ring gave as good as he got in dealing with his prosecutors and inquisitors. The sly Reichsmarschall was a master showman, but his fluency of speech and brilliance in retort could not mask his crimes and his role as one of the architects of the Nazi campaign of conquest, terror, and murder. He was sentenced to die by hanging. G\u00f6ring protested that he should be given a soldier's death in front of a firing squad.\n\nWhether the promise of a more dignified exit than death at the end of a rope would have deterred him from his final act is open to question. The night before his scheduled execution, G\u00f6ring bit down on a cyanide capsule in his cell at Nuremberg and died within minutes. The provenance of the poison has never been satisfactorily determined.\n\nG\u00f6ring had been searched regularly to avoid just such an occurrence and nothing had been found on his person, so the theory that it was smuggled into him by one of his last visitors, a sympathetic American guard or doctor\u2014he had made friends with several\u2014has never been disproved.\n\n**Carl Spaatz was at** the schoolhouse in Rheims on 7 May when Germany surrendered unconditionally. Two days later he flew to Berlin for the formal surrender of the German general staff at the headquarters of the Soviet commander, Marshal Georgi K. Zhukov.\n\nCarl Spaatz was also the only top-ranking American officer to meet one of the Nazi chieftains. Eisenhower refused to meet or greet any of his erstwhile enemies. Spaatz and Hoyt Vandenberg met G\u00f6ring face-to-face on 10 May 1945, at Augsburg. Spaatz stirred up a controversy by returning G\u00f6ring's salute, which he denied was inappropriate. Indeed, he defended it as the right and proper action from one officer to another.\n\nThe fallen Reichsmarschall told his conqueror that he had not wanted to fight the Battle of Britain because he knew that the Luftwaffe was not ready. He further admitted that his only effective bomber, the Junkers 88, was slow, had limited firepower, and needed a tight fighter escort. In that he was correct, but the Ju 88 was nevertheless an effective bomber in that it carried a sizable bomb load and was operating well within its range. With properly deployed fighter escorts\u2014which, of course, it did not have\u2014it could have been a formidable weapon.\n\nG\u00f6ring also insisted to Spaatz that if Germany could have held out for four or five more months, enough jet planes would have been available and enough fuel produced to turn the tide. He even maintained that there were enough trained pilots to do the job. This was clearly as unrealistic an appraisal of Luftwaffe capabilities in mid-1945, as so many of his prewar predictions had been.\n\nIn the postwar years, both Carl Spaatz and Dwight Eisenhower continued in military posts of great prominence, in Eisenhower's case to the highest civil office as well, the presidency.\n\nSpaatz, when his task in Europe ended, was appointed air force commander in the Far East, where he helped bring a quick end to the war against the Japanese. Some of the old team was reassembled when the Eighth Air Force, still under Doolittle, was transferred to the Pacific war and was based on Okinawa. Carl Spaatz thus found himself a witness to yet more of the great events of the twentieth century.\n\nAs air force commander, he was directly responsible for implementing the order to drop the atomic bombs on Hiroshima and Nagasaki. Indeed, he met the _Enola Gay_ when it returned from Hiroshima and pinned the Distinguished Flying Cross on the pilot, Paul W. Tibbets.\n\nOn 1 September 1945, Spaatz watched as the Japanese delegation was brought aboard the USS _Missouri_ in Tokyo Bay for the surrender ceremony. He was thus the only officer to be present at each of the three surrender ceremonies that ended World War II: Rheims, Berlin, and Tokyo.\n\nCarl Spaatz's central role in the defeat of the Axis was honor enough for any soldier, but perhaps his enduring monument is the separate and independent United States Air Force, which, in 1947, was finally freed of its subservience to the United States Army. In 1946, Spaatz had succeeded Hap Arnold, and he therefore had the distinction of being the last head of the U.S. Army Air Forces and the first chief of staff of the new United States Air Force.\n\nThe air force could not be truly independent, he argued, without an academy, which would be the equal of West Point and Annapolis. An air force academy was authorized by Congress in 1954, and construction began not long after near Colorado Springs, Colorado, on a site that Spaatz helped select and where, fittingly, he is buried.\n\nThe man immediately responsible for the three most controversial air raids of World War II\u2014Dresden, Hiroshima, and Nagasaki\u2014gave little thought to them afterward. And if he ever regretted any of his actions, he certainly never said so. On the contrary.\n\n\"Well, I had no difficulty in that,\" he said about ordering the raid on Hiroshima. \"I ordered the drop. That was purely a political decision, wasn't a military decision. The military man carries out the orders of his political bosses.\"\n\nAs for precision bombing, the general admitted that so much of the bombing was inaccurate that the \"general effect was the same as area bombing.\"\n\nAnd when asked about the sometimes critical _United States Strategic Bombing Survey_ , the man who directed the strategic bombing of Germany replied, \"I've never been interested enough to read it... the successful conclusion of the war was enough to justify what we had done. If we had lost, then the survey might have meant something.\"\n\n**People can evolve, cities** can be rebuilt, and even disgraced nations can rejoin the world community. The firestorm that destroyed the dense urban mix that was prewar Dresden on the night of 13\u201314 February 1945 was not unlike the purifying fire that brings to a close Wagner's epic _Ring of the Nibelung_.\n\nJust as that great conflagration consumes Valhalla and its corrupt gods and heralds redemption for mankind, so the fires of World War II were necessary in order to destroy an evil society and portend a new beginning for Germany.\n\nBut much of the new Germany found itself trapped in yet another totalitarian state. The eastern half, christened the German Democratic Republic, in many ways resembled the old police state of the Hitler years, except that the oppression of the Nazis had been replaced by that of the Communist Party.\n\nHowever, an increasingly restive population eventually joined with the political liberalization movements sweeping the Soviet satellite countries in 1989 and deposed the ruling party. Within a year East and West Germany were reunited. The Dresdeners, who had known nothing but one-party, despotic rule since 1933, were now part of a freely elected, democratic republic.\n\nThe ghosts of despots are hard to exorcise\u2014particularly for the victims. The crimes of the Third Reich have rightly been called crimes against humanity and must never be allowed to be forgotten. Nor should the small but increasingly vocal neo-Nazi movement that has arisen in Germany be dismissed as the ravings of a small minority. German history teaches us that to ignore any movement that appears to exist only on the margins of civilized society is to do so at great peril.\n\nThe reconstruction and revival of the city of Dresden from the ruins that served for decades as the perfect symbol of the universal barbarity of war offers more than a ray of hope for Germany and the world. Nowhere is this reconciliation more manifest than in the reconsecrated Frauenkirche, the great church that has been resurrected from the broken and charred pile of rubble that for half a century lay at the very heart of Dresden.\n\nIt is cause for rejoicing, not only for Germans but for everyone, that the Frauenkirche once again resounds with the music of Johann Sebastian Bach, the exemplar of all that was and is great in the German people.\n\n# ACKNOWLEDGMENTS\n\n**M any institutions and individuals provided encouragement and** support during the research and writing of this book.\n\nIn the United Kingdom I am particularly indebted to the Public Record Office, Kew; the Imperial War Museum, Lambeth; the Bomber Command Association, Hendon, in particular Douglas Radcliffe; the British Library; the Royal Air Force Museum, Hendon; and the Air Force Museum, Duxford.\n\nIn Germany, Matthias Neutzner made available his wide knowledge and extensive research on the Dresden raids. The Stadtmuseum Dresden and the Deutsches Fotothek, at the S\u00e4chsische Landesbibliothek, in particular Bettina Erlenkamp, were most accommodating. Lutz Werner, at the Neue Synagoge, provided valuable information on the Jewish community in Dresden.\n\nIn America, I am grateful for the assistance rendered by staff at the Library of Congress; the United States Air Force Historical Research Center, Maxwell Air Force Base, Ala.; the library at the United States Air Force Academy; the library at the United States Military Academy; the Daniel Library at the Citadel; the New York Public Library; the Ramsay Library at the University of North Carolina at Asheville; the Mighty Eighth Air Force Museum and Library, Pooler, Ga.; and the Pack Memorial Library, Asheville, N.C.\n\nThe Wurlitzer Foundation, Taos, N.M., provided much needed solitude at a critical time in this book's genesis, and I was able to work in other special places through the generosity of Eleanor Crook, John Ehle, Rosemary Harris, and Fredda Culbreth.\n\nThe Experimental Aircraft Association, Oshkosh, Wisc., afforded me an indelible research experience\u2014the opportunity to be co-pilot, navigator, waist gunner, and bombardier on a B-17 Flying Fortress, the _Aluminum Overcast_ , and then take the controls of the great plane and fly it for a few unforgettable minutes over my hometown.\n\nVivian Dillingham was a stalwart throughout the long process, and others to whom I am especially grateful are David Phillips, Phillip Earnshaw, Arthur Humphrey, Carlos S\u00e1nchez, the late Gloria Jones, Enid Hardwicke, John R. Hearst, Budd Levinson, Ruben Johnson, Adolf Kremel, Kathy Taylor, Les Doss, Patrick Read, Liz Carpenter, Malcolm Goldstein, Dr. William R. McKenna, Dr. Snehal Vyas, and Tom McLellan.\n\nCarole Gardiner was particularly generous with her support and offered much wise counsel.\n\nKate Davison was my skillful translator, and Carolyn Blakemore and the late Joel Honig provided useful editorial advice at an early stage.\n\nHowever, it is Robert Loomis of Random House, that nonpareil of editors, to whom I am most indebted. He kept the faith, overlooked the missed deadlines, and urged me to press on. I owe him much.\n\nMarshall De Bruhl  \nAsheville, N.C.   \nJune 2006 \n\n# **NOTES**\n\n## **PREFACE**\n\n _\"Limited or ambitious men\":_ Michael S. Sherry, _The Rise of American Air Power_ , p. xi.\n\n## **PROLOGUE**\n\n _\"Ash Wednesday and St. Valentine's Day\":_ John Colville, _The Fringes of Power_ , p. 559.\n\n _\"Were you there, Charles?\":_ Lord Moran, _Churchill_ , p. 256.\n\n## **CHAPTER ONE: \"THE BOMBER WILL ALWAYS GET THROUGH \"**\n\n _\"less than those sometimes suffered\":_ John Terraine, _A Time for Courage_ , p. 10.\n\n _\"As long as man remained tied to the surface of the earth\":_ Giulio Douhet, _Il dominio dell'aria_ , pp. 7\u201310. 10\n\n _\"jump over the army\":_ Charles Messenger, _Bomber Harris and the Strategic Bombing Offensive_ , p. 18.\n\n _\"If a future war can be won\":_ Charles Messenger, _Bomber Harris and the Strategic Bombing Offensive_ , p. 18.\n\n _\"Air power can be used as an independent means\":_ Max Hastings, _Bomber Command_ , p. 38.\n\n _\"I think it is well also for the man in the street\":_ John Terraine, _A Time for Courage_ , p. 13.\n\n _\"the result of incompetency\":_ C. V. Glines, \"Air Power Visionary Billy Mitchell,\" _Aviation History Magazine_ , Sept. 1997, vol. 8.\n\n _\"had no quarrel with the administration\":_ U.S. Air Force Historical Division, Oral History K105.5\u201335.\n\n _By 1937\u201338, almost 40 percent:_ Richard Overy, _Goering_ , p. 38. _\"I am absolutely convinced\":_ Kenneth S. Davis, _FDR_ , p. 504.\n\n _\"The decisive difference\":_ A. J. P. Taylor quoted in Len Deighton, _Fighter_ , p. xviii.\n\n _\"He was determined\":_ Kenneth S. Davis, _FDR_ , p. 372.\n\n _When he was challenged:_ Michael S. Sherry, _The Rise of American Air Power_ , p. 86.\n\n _\"squared with the dominant prejudices and priorities\":_ Michael S. Sherry, _The Rise of American Air Power_ , p. 82.\n\n _The final Air Corps plan:_ Michael S. Sherry, _The Rise of American Air Power_ , p. 86.\n\n _\"long range bombers must rely\":_ Papers of Ira C. Eaker, Library of Congress.\n\n _\"undoubtedly the most important turning-point\":_ Martin Middlebrook and Chris Everitt, _Bomber Command War Diaries_ , p. 31.\n\n _\"obvious to any literate citizen\":_ Wesley Frank Craven and James Lea Cate, _The Army Air Forces in World War II_ , vol. 1, p. 142.\n\n _In their revised list of priorities:_ AWPD-42 Target Priorities Table, reproduced in James R. Cody, _AWPD-42 to Instant Thunder_ , Maxwell Air Force Base, Alabama: Air University Press, 1996.\n\n _\"one of the tragic mistakes of the war\":_ Steven A. Parker, United States Air Force Academy, \"AWPD-1: Targeting for Victory,\" _Aerospace Power Journal_ , Summer 1989.\n\n _\"carried with them the reassuring weight\":_ Wesley Frank Craven and James Lea Cate, _The Army Air Forces in World War II_ , vol. 1, p. 667.\n\n _\"hysterical chatter\":_ Kenneth S. Davis, _FDR_ , p. 549. _it was still at 73 percent:_ Michael S. Sherry, _The Rise of American Air Power_ , p. 82.\n\n## CHAPTER TWO: THE ARCHITECTS OF DESTRUCTION\n\n _\"It is on the bomber that we must rely\":_ Charles Messenger, _\"Bomber\" Harris and the Strategic Bombing Offensive_ , p. 17.\n\n _\"the moral effect of bombing\":_ John Terraine, _A Time for Courage_ , p. 9.\n\n _\"We must avoid the stupendous drain\":_ Lord Moran, _Churchill_ , p. 81.\n\n _His November 1942:_ Max Hastings, _Bomber Command_ , p. 180.\n\n _In addition, although it was not publicly stated:_ Martin Gilbert, _The Second World War_ , p. 393.\n\n _\"You have only to look\":_ Dudley Saward, _\"Bomber\" Harris_ , p. 1.\n\n _\"I completed the long course\":_ Dudley Saward, _\"Bomber\" Harris_ , p. 13.\n\n _\"I can't fly\":_ Dudley Saward, _\"Bomber\" Harris_ , p. 13.\n\n _\"We just flew about\":_ Dudley Saward, _\"Bomber\" Harris_ , p. 16.\n\n _\"Thereafter for nearly twenty years\":_ Sir Arthur Harris, _Bomber Offensive_ , p. 277.\n\n _\"bones now lie\":_ Sir Arthur Harris, _Bomber Offensive_ , p. 277.\n\n _Harris early on saw the power:_ Sir Arthur Harris, _Bomber Offensive_ , p. 19.\n\n _Later, Harris credited:_ Dudley Saward, _\"Bomber\" Harris_ , p. 45.\n\n _A quick advance by Germany:_ Dudley Saward, _\"Bomber\" Harris_ , p. 52.\n\n _British intelligence that the Luftwaffe:_ Cajus Bekker, _The Luftwaffe War Diaries_ , p. 377.\n\n _\"batches of Hudsons and Harvards\":_ Sir Arthur Harris, _Bomber Offensive_ , p. 27.\n\n _\"I am at a loss\":_ Dudley Saward, _\"Bomber\" Harris_ , p. 60.\n\n _Harris acidly observed:_ Dudley Saward, _\"Bomber\" Harris_ , p. 61.\n\n _\"Their major obsession\":_ Dudley Saward, _\"Bomber\" Harris_ , p. 61.\n\n _\"I have in the course of my lifetime\":_ Sir Arthur Harris, _Bomber Offensive_ , p. 33.\n\n _Someone at the Air Ministry:_ Dudley Saward, _\"Bomber\" Harris_ , p. 82. 39 _Harris's credo:_ Dudley Saward, _\"Bomber\" Harris_ , p. 83.\n\n _\"perhaps the greatest error\":_ Martin Gilbert, _The Second World War_ , p. 277.\n\n _\"because you see\":_ Sir Arthur Harris, _Bomber Offensive_ , p. 64.\n\n _\"The idea that the main object of bombing\":_ Sir Arthur Harris, _Bomber Offensive_ , p. 78.\n\n _\"I do not, of course, suggest that bombing\":_ Sir Arthur Harris, _Bomber Offensive_ , p. 79.\n\n _\"The damage surpasses all one could imagine\":_ Matthias Neutzner, _Angriff: Martha Heinrich Acht_ , letter of 21 February 1945, p. 106.\n\n _There was no argument about the ultimate purpose:_ Martin Gilbert, _The Second World War_ , p. 393.\n\n _\"Red Plague over Berlin\":_ Roger Manvell and Heinrich Fraenkel, _Goering_ , p. 116.\n\n _only a prototype passed off as being in full production:_ David Irving, _G\u00f6ring_ , p. 224.\n\n _\"designed to intimidate\":_ Michael S. Sherry, _The Rise of American Air Power_ , p. 359.\n\n _\"An endeavor will be made\":_ \"Preliminary Tactical Guiding Principles for the Employment of Luftwaffe Units Against England,\" 10 January 1940, Maxwell Air Force Base, microfilm.\n\n _\"That's just what we want!\":_ Cajus Bekker, _The Luftwaffe War Diaries_ , p. 126.\n\n _\"In the face of such arguments\":_ Cajus Bekker, _The Luftwaffe War Diaries_ , p. 176.\n\n## CHAPTER THREE: WEAPONS FOR THE NEW AGE OF WARFARE\n\n _Indeed, when Arthur Harris assumed command:_ Martin Middlebrook and Chris Everitt, _The Bomber Command War Diaries_ , p. 241.\n\n _\"According to the American habit\":_ Air University Library, Maxwell Air Force Base, Microfilm K2625.\n\n _As late as 25 January 1945:_ Spaatz Papers, Library of Congress.\n\n _\"In the evening we again\":_ Joseph Goebbels, _Final Entries, 1945_ , p. 35.\n\n _Udet had pulled off something of a coup:_ Air University Library, Maxwell Air Force Base, Microfilm K2625.\n\n _\"We [Germany] were prepared for a short war\":_ \"The Development of Ground Attack Aviation,\" Air University Library, Maxwell Air Force Base, No. 4376\u2013584.\n\n _In a surprisingly frank speech:_ Dudley Saward, _\"Bomber\" Harris_ , p. 54.\n\n _\"tried to assume as little\":_ \"The Development of Jet and Rocket Airplanes in Germany, 1938\u20131945,\" Air University Library, Maxwell Air Force Base, Microfilm K2625.\n\n _\"The war is over!\":_ Cajus Bekker, _The Luftwaffe War Diaries_ , p. 230.\n\n _Seeing enemies on every side:_ Richard Overy, _Goering_ , p. 155.\n\n _Thousands of these_ Mischlinge: Bryan Mark Riggs, _Hitler's Jewish Soldiers_ , p. 29.\n\n _Hitler, who was kept apprised:_ Albert Speer, _Inside the Third Reich_ , pp. 362\u201363.\n\n _However, not more than 300 jets:_ Cajus Bekker, _The Luftwaffe War Diaries_ , p. 356.\n\n _In October 1944, according to Bekker:_ Cajus Bekker, _The Luftwaffe War Diaries_ , p. 356.\n\n _On 10 April 1945, Luftwaffe jet aircraft:_ Richard G. Davis, _Carl A. Spaatz and the Air War in Europe_ , p. 584.\n\n _As Molly Painter-Downs reported: The New Yorker Book of War Pieces_ , pp. 56\u201357.\n\n _\"We have ample evidence\":_ Richard G. Davis, _Carl A. Spaatz and the Air War in Europe_ , p. 261.\n\n _And on 24 May 1943 he wrote to Arnold:_ Richard G. Davis, _Carl A. Spaatz and the Air War in Europe_ , p. 200.\n\n _\"Today I saw air power\":_ \"8th Air Force Miscellaneous Correspondence, 1942\u20131945.\" 6 vols. USAF HRA\/ISR. Air Force Historical Research Agency, Maxwell Air Force Base, Alabama, File 520.161.\n\n _\"We discovered one day\":_ Steven A. Parker, United States Air Force Academy, \"AWPD-1: Targeting for Victory.\" _Aerospace Power Journal_ , Summer 1989.\n\n## CHAPTER FOUR:THE FATAL ESCALATION\n\n _\"For centuries, it has been in our blood\":_ Winston Churchill, _Memoirs of the Second World War_ , p. 354.\n\n _\"The PM seems rather more apprehensive\":_ John Colville, _The Fringes of Power_ , p. 245.\n\n _Churchill told the general:_ Martin Gilbert, ed., _The Churchill War Papers_ , vol. 2, p. 852.\n\n _Somewhere between the translation:_ Warren F. Kimball, _Forged in War_ , p. 65.\n\n _\"Should October pass\":_ Public Record Office (Kew), CAB 66\/13 WP (40) 421.\n\n _As one Luftwaffe fighter pilot said:_ Cajus Bekker, _The Luftwaffe War Diaries_ , p. 169.\n\n _The British pilots, said Churchill:_ Winston Churchill, _Memoirs of the Second World War_ , p. 358.\n\n _He reserved \"to himself personal punishment\":_ Cajus Bekker, _The Luftwaffe War Diaries_ , p. 172.\n\n _A month before, Churchill had written:_ Martin Gilbert, ed., _The Churchill War Papers_ , vol. 2, p. 555.\n\n _\"Now they are trying to starve us out\":_ Martin Middlebrook and Chris Everitt, _The Bomber Command War Diaries_ , p. 77.\n\n _\"the law of diminishing returns\":_ Winston Churchill, _Memoirs of the Second World War_ , p. 372.\n\n _\"Far more important to us\":_ Winston Churchill, _Memoirs of the Second World War_ , p. 361.\n\n _\"a breathing space of which we had the utmost need\":_ Winston Churchill, _Memoirs of the Second World War_ , p. 361.\n\n _\"G\u00f6ring should certainly have persevered\":_ Winston Churchill, _Memoirs of the Second World War_ , p. 361.\n\n _\"London was like some huge prehistoric animal\":_ Winston Churchill, _Memoirs of the Second World War_ , p. 377.\n\n _Still, Churchill wondered:_ Winston Churchill, _Memoirs of the Second World War_ , p. 375.\n\n _Some 380 people were killed:_ Public Record Office (Kew), CAB 66\/13 WP (40) 457.\n\n _But myths die hard:_ Allan W. Kurki, _Operation Moonlight Sonata_.\n\n _\"While the success of [the Americans'] attacks\":_ Public Record Office (Kew), AIR 20\/4826.\n\n _\"The risk of death from incendiary attacks\":_ Public Record Office (Kew). AIR 20\/4826.\n\n _\"Priority of selection\":_ Martin Middlebrook and Chris Everitt, _The Bomber Command War Diaries_ , p. 132.\n\n _\"Both are suitable as area objectives\":_ Martin Middlebrook and Chris Everitt, _The Bomber Command War Diaries_ , p. 132.\n\n _\" 'area bombing' against German cities\":_ Martin Middlebrook and Chris Everitt, _The Bomber Command War Diaries_ , p. 132.\n\n _Just one-third:_ Denis Richards, _The Hardest Victory_ , p. 96.\n\n _Did not this report give the lie:_ Denis Richards, _The Hardest Victory_ , p. 97.\n\n _\"It is very debatable\":_ Denis Richards, _The Hardest Victory_ , p. 97.\n\n _\"spiked Churchill's guns\":_ Denis Richards, _The Hardest Victory_ , p. 97.\n\n _As for the success of the RAF campaign:_ Public Record Office (Kew), \"Weekly R\u00e9sum\u00e9 (no. 286) of the Naval, Military and Air Situation from 0700 15th February to 0700 22nd February, 1945,\" War Cabinet Files, Public Record Office (Kew), W.P. (45) 106, 22 Feb. 1945.\n\n _\"No dog nor cat is left\":_ Michael S. Sherry, _The Rise of American Air Power_ , p. 150.\n\n _\"It has been decided\":_ Martin Middlebrook and Chris Everitt, _The Bomber Command War Diaries_ , p. 240.\n\n _\"L\u00fcbeck,\" said Harris:_ Max Hastings, _Bomber Command_ , pp. 147\u201348.\n\n _\"I censured this\":_ Joseph Goebbels, _The Goebbels Diaries, 1942\u20131943_ , p. 200.\n\n _\"There is talk about scenes\":_ Joseph Goebbels, _The Goebbels Diaries, 1942\u20131943_ , p. 201.\n\n _On 6 April 1941:_ Martin Gilbert, _The Second World War_ , p. 170.\n\n _In a memorandum of 2 May 1942:_ Public Record Office (Kew), AIR 14\/3507.\n\n _He ordered the gauleiter:_ Albert Speer, _Inside the Third Reich_ , pp. 279\u201380.\n\n _\"The end is in sight in Africa\":_ Joseph Goebbels, _The Goebbels Diaries, 1942\u20131943_ , p. 353.\n\n _\"the greatest example of perfidy in modern history\":_ Joseph Goebbels, _The Goebbels Diaries, 1942\u20131943_ , p. 410.\n\n _The bombs fell:_ Martin Middlebrook and Chris Everitt, _The Bomber Command War Diaries_ , p. 411.\n\n _The Americans followed up:_ Roger A. Freeman, Alan Crouchman, and Vic Maslen, _The Mighty Eighth War Diary_ , pp. 78\u201379.\n\n _\"The Americans quickly withdrew\":_ Martin Middlebrook and Chris Everitt, _The Bomber Command War Diaries_ , p. 410.\n\n _Historian Daniel Goldhagen has estimated:_ Daniel Jonah Goldhagen, _Hitler's Willing Executioners_ , p. 171.\n\n## CHAPTER FIVE: _VERGELTUNGSWAFFEN_\n\n _\"attack by pilotless aircraft\":_ Public Record Office (Kew), CAB 65\/42.\n\n _\"England is trembling\": New York Times_ , 18 June 1944.\n\n _He ordered the escalation:_ Albert Speer, _Inside the Third Reich_ , p. 356.\n\n _More disturbing was the report:_ Public Record Office (Kew), CAB 65\/43.\n\n _He immediately volunteered:_ Chapman obituary, _New York Times_ , 20 December 1997.\n\n _During an interrogation:_ Kenneth Grubb, \"How We Make Captured Luftwaffe Crews Talk.\"\n\n _103 of the 140 identified sites:_ Denis Richards, _The Hardest Victory_ , p. 225.\n\n _Just four days after the first V-1:_ Martin Middlebrook and Chris Everitt, _The Bomber Command War Diaries_ , 16\u201317 June 1944.\n\n _\"On that day\":_ Albert Speer, _Inside the Third Reich_ , p. 346.\n\n _By November 1944:_ Albert Speer, _Inside the Third Reich_ , pp. 346\u201350.\n\n _The Polish underground:_ Martin Gilbert, _The Second World War_ , p. 561.\n\n _\"has now been intensified\":_ Public Record Office (Kew), CAB 65\/44, p. 213.\n\n _It was estimated:_ Ian Kershaw, _Hitler: 1936\u20131945: Nemesis_ , p. 736.\n\n _\"justification of giving up\":_ Public Record Office (Kew), AIR 14\/3507.\n\n _\"have thrown our preparations\":_ Joseph Goebbels, _The Goebbels Diaries, 1942\u20131943_ , p. 435.\n\n _\"Losses were particularly heavy\":_ Walter Dornberger, _V-2_ , p. 105.\n\n _The next week saw some drop-off:_ Public Record Office (Kew), \"Weekly R\u00e9sum\u00e9 (no. 291) of the Naval, Military and Air Situation from 0700 22nd March to 0700 29th March, 1945,\" W.P. (45) 201.\n\n _But at last the ten-month:_ Public Record Office (Kew), CAB 65\/50.\n\n _\"It is my duty\":_ Public Record Office (Kew), 410 H.C. DEB. 5s, col. 985.\n\n _As for who should be credited:_ Public Record Office (Kew), 410 H.C. DEB. 5s, col. 985.\n\n _\"The decisive difference\":_ A. J. P. Taylor quoted in Len Deighton, _Fighter_ , p. xviii.\n\n _Speer later derisively pointed out:_ Albert Speer, _Inside the Third Reich_ , p. 365.\n\n## **CHAPTER SIX: OPERATION THUNDERCLAP**\n\n _\"I don't know about oratory\":_ Lord Moran, _Churchill_ , p. 13.\n\n _\"Those filthy Germans!\":_ Harold Nicolson, _Diaries and Letters_ , vol. 2, _The War Years_ , 16 February 1944.\n\n _The use of poison gas:_ Martin Gilbert, _Winston S. Churchill, 1942\u20131945: Road to Victory_ , p. 840.\n\n _\"Press and broadcast should be asked\":_ Martin Gilbert, _The Churchill War Papers_ , Vol. 2, _Never Surrender_ , p. 423.\n\n _The odds of being killed:_ Public Record Office (Kew), AIR 20\/4826.\n\n _\"that the time might well come\":_ Public Record Office (Kew), AIR 20\/3227; Public Record Office (Kew), AIR 20\/4831.\n\n _\"Attack on German Civilian Morale\":_ Public Record Office (Kew), AIR 20\/3227.\n\n _\"A spectacular and final object lesson\":_ Public Record Office (Kew), AIR 20\/3227.\n\n _\"The main purpose of [Thunderclap]\":_ Public Record Office (Kew), Air 20\/4826.\n\n _\"The essential purpose of the attack\":_ Public Record Office (Kew), Air 20\/4826.\n\n _\"at the best may prove the last straw\":_ Public Record Office (Kew), Air 20\/4831.\n\n _\"In this situation it is unlikely\":_ Public Record Office (Kew), Air 20\/4826.\n\n _Neither Arthur Harris nor Carl Spaatz:_ Richard G. Davis, _Carl A. Spaatz and the Air War in Europe_ , p. 436.\n\n _As for Harris:_ Sir Arthur Harris, _Bomber Offensive_ , p. 245.\n\n _When they told Harris:_ Richard G. Davis, _Carl A. Spaatz and the Air War in Europe_ , pp. 432\u201333.\n\n _A thousand American B-17s:_ Roger A. Freeman, Alan Crouchman, and Vic Maslen, _The Mighty Eighth War Diary_ , p. 273.\n\n _\"U.S. bombing policy, as you know\":_ Spaatz Papers, Library of Congress.\n\n _\"We will continue precision bombing\":_ Richard G. Davis, _Carl A. Spaatz and the Air War in Europe_ , p. 434.\n\n _The plan was scrapped:_ Martin Gilbert, _The Second World War_ , p. 592.\n\n _\"Since the Mongol invasion\":_ Richard Breitman, _Official Secrets_ , p. 93.\n\n _\"And not with Jews\":_ Richard Breitman, _Official Secrets_ , p. 102.\n\n _\"The Jewish capacity for destruction\":_ Harold Nicolson, _Diaries and Letters_ , vol. 2, _The War Years_ , 13 June 1945.\n\n _\"If propaganda has imbued a whole people\":_ Adolf Hitler, _Mein Kampf_ , p. 582.\n\n _And when the American bombers entered the war:_ Conrad C. Crane, _Bombs, Cities, and Civilians_ , p. 64.\n\n _\"It is contrary to our national ideals\":_ Richard G. Davis, _Carl A. Spaatz and the Air War in Europe_ , p. 435.\n\n _\"Our entire target policy\":_ Richard G. Davis, _Carl A. Spaatz and the Air War in Europe_ , p. 435.\n\n _\"The bombing of civilian targets\":_ Richard G. Davis, _Carl A. Spaatz and the Air War in Europe_ , p. 435.\n\n _\"ancient, compact, historic\":_ Richard G. Davis, _Carl A. Spaatz and the Air War in Europe_ , p. 436.\n\n _\"In the European area\":_ Winant to FDR, 23 April 1944. National Archives; photocopy on file in David Irving Archives.\n\n _\"There seems to be a kind of fanaticism\":_ National Archives; photocopy on file in David Irving Archives.\n\n _\"was very anxious to operate\": Historical Analysis of the 14\u201315 February 1945 Bombing of Dresden_ , p. 4.\n\n _\"to discuss with you the situation\": Historical Analysis of the 14\u201315 February 1945 Bombing of Dresden_ , p. 4.\n\n _\"Tedder outlined to Stalin\": Historical Analysis of the 14\u201315 February 1945 Bombing of Dresden_, p. 4.\n\n _But he now had to give way:_ Martin Middlebrook and Chris Everitt, _The Bomber Command War Diaries_ , p. 661.\n\n _In the evening:_ Joseph Goebbels, _Final Entries, 1945_ , p. 3.\n\n _On 29 April 1944:_ Roger A. Freeman, Alan Crouchman, and Vic Maslen, _The Mighty Eighth War Diary_ , p. 232.\n\n _In a series of raids:_ Roger A. Freeman, Alan Crouchman, and Vic Maslen, _The Mighty Eighth War Diary_ , p. 316.\n\n _In raids on 7 October:_ Roger A. Freeman, Alan Crouchman, and Vic Maslen, _The Mighty Eighth War Diary_ , p. 360.\n\n _Entitled \"Strategic Bombing\":_ Public Record Office (Kew), AIR 8\/1745.\n\n _\"basting the Germans\":_ Max Hastings, _Bomber Command_ , p. 341.\n\n _The Prime Minister was concerned:_ Dudley Saward, _\"Bomber\" Harris_ , p. 282.\n\n _Sinclair felt:_ Dudley Saward, _\"Bomber\" Harris_ , p. 283.\n\n _\"I did not ask you last night\":_ Max Hastings, _Bomber Command_ , p. 341.\n\n _The chief priority:_ Dudley Saward, _\"Bomber\" Harris_ , p. 284.\n\n _While oil would remain:_ Dudley Saward, _\"Bomber\" Harris_ , p. 284.\n\n _Bottomley sent a cable:_ Dudley Saward, _\"Bomber\" Harris_ , p. 285.\n\n _\"Evacuees from German and German-Occupied\":_ Public Record Office (Kew), AIR 8\/1745.\n\n _\"Attack of Berlin, Leipzig, Dresden\":_ Maxwell Air Force Base, Microfilm K2625, 2078.\n\n _\"in conjunction with our attacks on Berlin\":_ Maxwell Air Force Base, Microfilm K2625, 2078.\n\n _\"to attack [Munich]\":_ Maxwell Air Force Base, Microfilm K2625, 2078.\n\n _For Dresden was an alternate target:_ Melden E. Smith Jr., \"The Bombing of Dresden Reconsidered,\" p. 230.\n\n _\"All out effort will be placed\":_ Maxwell Air Force Base, Microfilm K2625, 2078.\n\n _\"Our estimate of the situation\":_ Richard G. Davis, _Carl A. Spaatz and the Air War in Europe_ , p. 541.\n\n _Eisenhower reluctantly agreed:_ Richard G. Davis, _Carl A. Spaatz and the Air War in Europe_ , p. 541.\n\n _Further, said the president:_ Warren F. Kimball, ed., _Churchill and Roosevelt: The Complete Correspondence_ , vol. 3, p. 592.\n\n _\"If the United States\":_ National Archives; photocopy on file in David Irving Archives.\n\n _\"This is again 'jam tomorrow' \":_ National Archives; photocopy in David Irving Archives.\n\n _He asked the British and Americans: Historical Analysis of the 14\u201315 February 1945 Bombing of Dresden_.\n\n _The limit-line agreement:_ \"Agreement for the Establishment of Limit Line (Prohibited Zone) for Operations of Allied Strategic Air Forces on the Front of Soviet Troops,\" 6 February 1945, Maxwell Air Force Base, Microfilm K2625, 2078.\n\n _\"Without you\":_ Richard G. Davis, _Carl A. Spaatz and the Air War in Europe_ , p. 547.\n\n _Kuter quickly realized:_ Maxwell Air Force Base, Microfilm K2625, 2078.\n\n _Therefore, on 12 February:_ Melden E. Smith Jr., \"The Bombing of Dresden Reconsidered,\" p. 234.\n\n## **CHAPTER SEVEN: THE TARGET**\n\n _\"belonged largely to emperors\":_ Robert B. Asprey, _Frederick the Great_ , p. xiii.\n\n _\"from pleasure to pleasure\":_ Leopold von Ranke, _Memoirs of the House of Brandenburg and History of Prussia_ , vol. 1, pp 343\u201344.\n\n _\"I have not at present\":_ Thomas Carlyle, _History of Frederick II of Prussia_. vol. 3, p. 135.\n\n _\"answered yes to everything\":_ Robert B. Asprey, _Frederick the Great_ , p. 234. 175 _\"in the presence of all\":_ Hans T. David and Arthur Mendel, _The Bach Reader_ , p. 226.\n\n _\"DRESDEN is the historical capital of Saxony\":_ Public Record Office (Kew), AIR 14\/3682.\n\n _\"Hospitals were denoted by\":_ Targeting information, Dresden, 27 February 1942, Public Record Office (Kew), AIR 40\/1680.\n\n _\"Only a few knew what the finished product\":_ Matthias Neutzner, _Lebenszeichen_ , p. 67.\n\n _\"a maximum capacity\":_ Targeting information, Dresden, 27 February 1942, Public Record Office (Kew), AIR 40\/1680.\n\n _\"Dresden is one of the few direct links\":_ Targeting information, Dresden, 27 February 1942, Public Record Office (Kew), AIR 40\/1680.\n\n## **CHAPTER EIGHT: SHROVE TUESDAY , 1945**\n\n _\"Pity that I have one screw too few\":_ Victor Klemperer, _I Will Bear Witness: A Diary of the Nazi Years, 1933\u20131941_ , p. 236.\n\n _Nevertheless, more than 30,000 internees:_ Martin Gilbert, _The First World War_ , p. 539.\n\n _\"On this occasion\":_ Victor Klemperer, _I Will Bear Witness: A Diary of the Nazi Years, 1942\u20131945_ , p. 404.\n\n _\"The most cruel separations\":_ Victor Klemperer, _I Will Bear Witness: A Diary of the Nazi Years, 1942\u20131945_ , p. 404.\n\n _\"Again a shabby house\":_ Victor Klemperer, _I Will Bear Witness: A Diary of the Nazi Years, 1942\u20131945_ , p. 405.\n\n _\"Now we were examined\":_ Matthias Neutzner, _Lebenszeichen_ , pp. 21\u201322.\n\n _\"Sch\u00f6rner is decidedly a personality\":_ Joseph Goebbels, _Final Entries, 1945_ , p. 80.\n\n _\"the other two who were condemned\":_ Joseph Goebbels, _Final Entries, 1945_ , p. 317.\n\n _\"The flight of January 1945\":_ John Keegan, _The Second World War_ , p. 592.\n\n _\"Really, one is compelled\":_ Gerhart Pohl, _Gerhart Hauptmann and Silesia_ , p. 5.\n\n## CHAPTER NINE: A PILLAR OF FIRE BY NIGHT\n\n _The attacking force:_ Public Record Office (Kew), AIR 14\/3713, \"Daily Attack Book.\"\n\n _\"I never bargained to take Tetrazzini\":_ Lord Moran, _Churchill_ , p. 255.\n\n _En route, Churchill:_ Winston Churchill, _Memoirs of the Second World War_ , p. 929.\n\n _The attack he feared had begun:_ Author's interview with family member.\n\n _The master bomber now broke radio silence:_ David Irving, _Apocalypse 1945_ , p. 134.\n\n _The stadium had been chosen:_ Target map of Dresden, Public Record Office (Kew), AIR 14\/3682.\n\n _Shouting, \"Marker Leader: Tally-ho!\":_ David Irving, _Apocalypse 1945_ , p. 135.\n\n _\"a rain of incendiaries\":_ Sir Arthur Harris, _Bomber Offensive_ , p. 83.\n\n _By the time Victor Klemperer:_ Victor Klemperer, _I Will Bear Witness: A Diary of the Nazi Years, 1942\u20131945_ , p. 404.\n\n _Only six aircraft:_ Royal Air Force Operations Record Book, Feb. 1945. Public Record Office (Kew), AIR 24\/307, AIR 24\/309.\n\n## CHAPTER TEN: A COLUMN OF SMOKE BY DAY\n\n _Some 461 bombers:_ Roger A. Freeman, Alan Crouchman, and Vic Maslen, _The Mighty Eighth War Diary_ , p. 439.\n\n _a high school senior:_ Author's interview with Margaret Armstrong Campbell.\n\n _Twenty-three planes were lost:_ Roger A. Freeman, Alan Crouchman, and Vic Maslen, _The Mighty Eighth War Diary_ , p. 432.\n\n _there was a relative newcomer:_ Author's interview with Raymond G. Engstrand.\n\n _The long mission to Dresden:_ Author's interview with Ernest Robertson.\n\n _\"I was the old man in the crew\":_ Roger A. Freeman, Alan Crouchman, and Vic Maslen, _The Mighty Eighth War Diary_ , p. 60. Colonel Morgan, in an interview with the author, recalled that it was St. Nazaire.\n\n _The B-17s had strayed into Czechoslovakia:_ In Roger A. Freeman, Alan Crouchman, and Vic Maslen, _The Mighty Eighth War Diary_ , p. 439, Prague is denoted as a \"target of opportunity.\"\n\n _There was light flak:_ Author's interview with Raymond G. Engstrand.\n\n _On 15 October, Hap Arnold:_ Letter to Joseph E. Kelly, Kelly family records, Repton, Alabama.\n\n _At that moment aboard:_ Author's interview with Ernest Robertson.\n\n _He was awarded the Purple Heart:_ Kelly family records, Repton, Alabama.\n\n## **CHAPTER ELEVEN: ASH WEDNESDAY , 1945**\n\n _\"A person who has forgotten how to weep\":_ Gerhart Pohl, _Gerhart Hauptmann and Silesia_ , p. 8.\n\n _A woman identified as Nora L.:_ Matthias Neutzner, _Angriff: Martha Heinrich Acht_ , pp. 130\u201334.\n\n _\"In the street all hell had broken loose\":_ Matthias Neutzner, _Lebenszeichen_ , pp. 94\u201395.\n\n _A Dresdener who directed a Red Cross camp:_ Matthias Neutzner, _Lebenszeichen_ , pp. 25\u201329.\n\n _\"After the first raid\":_ Matthias Neutzner, _Angriff: Martha Heinrich Acht_ , pp. 103\u201304.\n\n _Hans-Joachim D.:_ Matthias Neutzner, _Angriff: Martha Heinrich Acht_ , pp. 194\u201396.\n\n _Gerhart Sommer, who was eight years old:_ Author's interview with Sommer, 6 June 2005.\n\n _\"Then came the second raid\":_ Matthias Neutzner, _Lebenszeichen_ , pp. 19\u201321.\n\n _\"On 13 February we heard the early warning\":_ Matthias Neutzner, _Lebenszeichen_ , pp. 16\u201318.\n\n## **CHAPTER TWELVE: \"MR. PRIME MINISTER?\"**\n\n _The Pforzheim attack:_ Allied Air Commanders Conference, 1 March 1945, Minutes.\n\n _\"The Wehrmacht has decided to confer\":_ Spaatz Papers, Library of Congress.\n\n _\"Eighth Air Force Crews\":_ Allied Air Commanders Conference, 1 March 1945, Minutes.\n\n _\"What will lie\":_ John Colville, _The Fringes of Power_ , p. 563.\n\n _\"The bomber is a passing phase\":_ John Colville, _The Fringes of Power_ , p. 564.\n\n _\"Dresden? There is no such place\":_ John Colville, _The Fringes of Power_ , p. 562.\n\n _\"a man of limited intelligence\":_ John Colville, _The Fringes of Power_ , p. 563.\n\n _\"We could have no better brothers\":_ Sir Arthur Harris, _Bomber Offensive_ , p. 246.\n\n _\"Come on and deal\":_ Captain Harry C. Butcher, _My Three Years with Eisenhower_ , p. 770.\n\n _\"It seems,\" he said:_ Spaatz Papers, Library of Congress.\n\n _\"it is most improbable\":_ Spaatz Papers, Library of Congress.\n\n _\"This constant sniveling\":_ David Irving, _Hitler's War_ , p. 739.\n\n _\"almost draw a sigh of relief\":_ Joachim Fest, _Speer_ , p. 194.\n\n _\"The Allied Air Commanders\":_ Arnold to Spaatz, 18 February 1945, Maxwell Air Force Base, microfilm K2625, 2078.\n\n _\"To start with the Heavies\":_ Spaatz Papers, Library of Congress.\n\n _\"We must not get soft\":_ Tami Davis Biddle. \"Sifting Dresden's Ashes,\" p. 75.\n\n _\"the worst devastations\":_ Max Hastings, _Bomber Command_ , p. 176.\n\n _\"a blot on our escutcheon\": Hansard_ , Fifth Series, vol. 408, col. 1901.\n\n _\"It seems to me\":_ Public Record Office (Kew), CAB 120\/303.\n\n _Between them, said Harriman:_ Richard Overy, _Why the Allies Won_ , p. 102; Lord Moran, _Churchill_ , p. 61; Winston Churchill, _Memoirs of the Second World War_ , p. 623.\n\n _\"To suggest that we have\":_ Public Record Office (Kew), AIR 20\/3218.\n\n _The exchange between:_ Max Hastings, _Bomber Command_ , pp. 332\u201335.\n\n _\"the attack on Dresden was at the time\":_ Sir Arthur Harris, _Bomber Offensive_ , p. 242.\n\n _\"Throughout January and February\":_ Winston Churchill, _The Second World War: Triumph and Tragedy_ , pp. 540\u201341. In the single-volume abridgement of the work, there is no mention of the Dresden raid.\n\n _In her book:_ Deborah Lipstadt, _Denying the Holocaust_ , passim.\n\n _\"falsifications of the historical facts\":_ Richard J. Evans, _Lying About Hitler_ , pp. 177\u201378.\n\n _In reality, he had seen:_ Richard J. Evans, _Lying About Hitler_ , p. 156.\n\n _Instead, he wrote:_ David Irving, _Apocalypse 1945_ , p. 245.\n\n _And in his 1996 biography:_ David Irving, _Goebbels_ , p. 501.\n\n _\"It is practically impossible to kill a myth\":_ Richard J. Evans, _Lying About Hitler_ , p. 169.\n\n _\"Of course now everybody talks\":_ Richard J. Evans, _Lying About Hitler_ , p. 181.\n\n _When the libel trial ended:_ D. D. Guttenplan, _The Holocaust on Trial_ , pp. 281\u201383.\n\n _What she referred to in a 2005 interview:_ Australian Radio National, \"Saturday Breakfast with Geraldine Doogue,\" 21 May 2005.\n\n _\"One's overall impression\":_ Public Record Office (Kew), AIR 19\/1028.\n\n _Under Adolf Hitler:_ Frederick Taylor, _Dresden: Tuesday, February 13, 1945_ (New York, 2004), p. 150.\n\n _Every book, article, and documentary:_ A notable exception is historian Frederick Taylor, _Dresden_.\n\n _Germany would not be defeated:_ Harry S. Truman, _Memoirs_ , vol. 1, _Year of Decisions_ , p. 17.\n\n _\"the development of a new explosive\":_ Harry S. Truman, _Memoirs_ , vol. 1, _Year of Decisions_ , p. 10.\n\n _\"That is the biggest fool thing\":_ Harry S. Truman, _Memoirs_ , vol. 1, _Year of Decisions_ , p. 11.\n\n _\"The feeling, such as there is\":_ Public Record Office (Kew), AIR 20\/3218. 285 _Harris might also have pointed out:_ Public Record Office (Kew), \"Weekly R\u00e9sum\u00e9 (no. 285) of the Naval, Military and Air Situation from 0700 8th February to 0700 15th February, 1945,\" War Cabinet Files, W.P. (45) 98, 15 February 1945.\n\n## EPILOGUE\n\n _\"preoccupation with social problems\":_ Lord Moran, _Churchill_ , p. 322.\n\n _The letter is studded:_ Public Record Office (Kew), AIR 24\/309, 24 February 1945.\n\n _To be called \"Lord Harris\":_ Dudley Saward, _\"Bomber\" Harris_ , p. 331. _Opposition to honoring Harris:_ John Colville, _The Fringes of Power_ , p. 644.\n\n _\"a thistle for Strachey\":_ Letter from Viscount Bracken to Harris, quoted in Dudley Saward, _\"Bomber\" Harris_ , p. 332.\n\n _\"To you, one of my close associates\":_ Dudley Saward, _\"Bomber\" Harris_ , p. 334.\n\n _\"Well, I had no difficulty\":_ U.S. Air Force Historical Division, Oral History K105.5\u201335.\n\n# BIBLIOGRAPHY\n\nAmbrose, Stephen E. _Eisenhower: Soldier, General of the Army, President-Elect, 1890\u20131952_. New York, 1983.\n\nAsprey, Robert B. _Frederick the Great: The Magnificent Enigma_. New York, 1986.\n\nBauer, Yehuda. _A History of the Holocaust_. 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File 248.532. 4 May 1945.\n\nMartin, Albert. \"Airborne Radar: Operational Results in the Combat Zones.\" Special Intelligence Report. August 1944. Air Force Historical Research Agency, Maxwell Air Force Base, Alabama. File 248.532\u201359.\n\nMassie, Robert K. _Peter the Great: His Life and World_. New York, 1980. McArthur, Charles W. _Operations Analysis in the U.S. Army Eighth Air Force in_ _World War II_. London Mathematical Society and American Mathematical Society, N.D.\n\nMessenger, Charles. _\"Bomber\" Harris and the Strategic Bombing Offensive, 1939\u20131945_. London, 1984.\n\nMichie, Allan A. _The Air Offensive Against Germany_. New York, 1943.\n\nMiddlebrook, Martin, and Chris Everitt. _The Bomber Command War Diaries: An Operational Reference Book, 1939\u20131945_. Harmondsworth, 1985.\n\nMitford, Nancy. _Frederick the Great_. New York, 1970.\n\nMontgomery, Colonel H.G., Jr. \"Night Air Attack of Tactical Objectives.\" January 1945. 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London, 1967.\n\n\"Organization of the Eighth Air Force.\" Air Force Historical Research Agency, Maxwell Air Force Base, Alabama. File 520.201\u20131. 28 May 1943.\n\nOsmont, Marie-Louise. _The Normandy Diary of Marie-Louise Osmont, 1940\u20131944_. Translated by George L. Newman. New York, 1994.\n\nOvery, Richard. _Goering: The Iron Man_. London, 1984.\n\n_______. _Why the Allies Won_. New York, 1995.\n\nOvery, Richard, and Andrew Wheatcroft. _The Road to War: The Origins of World War II_. London, 1989.\n\nPapen, Franz von. _Memoirs_. Translated by Brian Connell. New York, 1953.\n\n_Parliamentary Debates_. (Hansard) Fifth Series, vol. 408. House of Commons. 6 March 1945.\n\nPatton, George S., Jr. _War as I Knew It_. Boston, 1947.\n\nPeyser, Joan, ed. _The Orchestra: Origins and Transformations_. New York, 1986.\n\nPogue, Forrest C. _George C. Marshall: Organizer of Victory, 1943\u20131945_. New York, 1973.\n\nPohl, Gerhart. _Gerhart Hauptmann and Silesia_. Grand Forks, N.D., 1962.\n\nPrice, G. Ward. _I Know These Dictators_. New York, 1938.\n\nRanke, Leopold von. _Memoirs of the House of Brandenburg and History of Prussia, During the Seventeenth and Eighteenth Centuries_. 3 vols. Translated by Sir Alexander and Lady Duff-Gordon. London, 1849. Reprint, New York, 1969.\n\nRector, Frank. _The Nazi Extermination of Homosexuals_. New York, 1981.\n\nRhodes, Richard. _The Making of the Atomic Bomb_. New York, 1986.\n\nRigg, Bryan Mark. _Hitler's Jewish Soldiers_. Lawrence, Kans., 2000.\n\nRichards, Denis. _The Hardest Victory: RAF Bomber Command in the Second World War_. London, 1994.\n\nRichards, J. M., ed. _The Bombed Buildings of Britain_. London, 1942.\n\nRichardson, John, and Eric Zafran. _Master Paintings from the Hermitage and the_ _State Russian Museum: Leningrad_. New York, 1975.\n\nRiefenstahl, Leni. _Leni Riefenstahl: A Memoir_. New York, 1993.\n\nRodenberger, Axel. _Der Tod von Dresden_. Dortmund, 1953.\n\nRommel, Field-Marshal Erwin. _The Rommel Papers_. Edited by B. H. Liddell Hart. Translated by Paul Findlay. New York, 1953.\n\nRose, Norman. _Churchill: An Unruly Life_. London, 1994.\n\nRothnie, Niall. _The Baedeker Blitz: Hitler's Attack on Britain's Historic Cities_. Shepperton, 1992.\n\nRowe, Group Captain H. C. \"Recent RAF Tactics and Late Information from the European War Theater.\" Air Force Historical Research Agency, Maxwell Air Force Base, Alabama. File 248.532.60. 28 July 1944.\n\nRyan, Cornelius. _The Last Battle_. New York, 1966.\n\nSaward, Dudley. _\"Bomber\" Harris: The Authorised Biography_. London, 1984.\n\nSchaarschuch, Kurt. _Bilddokument Dresden, 1933\u20131945_. Dresden, n.d.\n\nSchreiber, Hermann. _Teuton and Slav: The Struggle for Central Europe_. Translated by James Cleugh. New York, 1965.\n\nSereny, Gitta. _Albert Speer: His Battle with the Truth_. New York, 1995.\n\nSherry, Michael S. _The Rise of American Air Power: The Creation of Armageddon_. New Haven, 1987.\n\nShirer, William L. _The Rise and Fall of the Third Reich: A History of Nazi Germany_. New York, 1959.\n\nShoemaker, Major Davis W. \"Recent Observations from Europe: Intelligence Observations in the European Theater.\" 21 Feb. 1945. Air Force Historical Research Agency, Maxwell Air Force Base, Alabama. File 248.532\u201382A.\n\nSimon, Edith. _The Making of Frederick the Great_. Boston, 1963.\n\nSington, Derrick, and Arthur Weidenfeld. _The Goebbels Experiment: A Study of the Nazi Propaganda Machine_. New Haven, 1943.\n\nSmith, Melden E., Jr. \"The Bombing of Dresden Reconsidered: A Study in Wartime Decision-Making.\" Doctoral diss., Boston University, 1971.\n\nSpaatz, Carl A. Papers of Carl A. Spaatz. Library of Congress, Manuscript Division.\n\n_______. U.S. Air Force Academy. Oral History Interview. No. 186.27. September 1968.\n\n_______. U.S. Air Force Historical Division. Oral History Interview. No. K105.5\u201335.\n\nSpaatz, Ruth. U.S. Air Force Academy. Oral History Interview. 3 March 1981. No. K239.0512\u20131266.\n\nSpeer, Albert. _Inside the Third Reich: Memoirs_. Translated by Richard and Clara Winston. New York, 1970.\n\n_______. _Spandau: The Secret Diaries_. Translated by Richard and Clara Winston. New York, 1976.\n\nSpencer, Andrew John. \"Of Literature and Legend: German Writers and the\n\nBombing of Dresden.\" Doctoral diss., Ohio State University, 1992.\n\nSteinbeck, John. _Bombs Away_. New York, 1942.\n\nSterling, Charles. _Great French Paintings in the Hermitage_. New York, 1958.\n\nStern, Fritz. _Gold and Iron. Bismarck, Bleichr\u00f6der, and the Building of the_ _German Empire_. New York, 1977.\n\nStone, Norman. _Hitler_. London, 1980.\n\nStrawson, John. _Hitler's Battles for Europe_. New York, 1971.\n\n_Summary of Operations 8th Air Force_. Air Force Historical Research Agency, Maxwell Air Force Base, Alabama. File 519.308\u20134. Jan.\u2013Jun. 1945.\n\nTerraine, John. _A Time for Courage: The Royal Air Force in the European War, 1939\u20131945_. New York, 1985.\n\nThurlow, Richard. _Fascism in Britain: A History, 1918\u20131985_. London, 1987.\n\nToland, John. _Hitler_. New York, 1976.\n\n_______. _Hitler: The Pictorial Documentary of His Life_. New York, 1980.\n\nTruman, Harry S. _Memoirs by Harry S. Truman_. Vol. 1, _Year of Decisions_. New York, 1955.\n\nTurner, Henry Ashby, Jr. _German Big Business and the Rise of Hitler_. New York, 1985.\n\nValentin, Veit. _The German People: Their History and Civilization from the Holy_ _Roman Empire to the Third Reich_. New York, 1949.\n\nVerrier, Anthony. _The Bomber Offensive_. New York, 1969.\n\nVonnegut, Kurt, Jr. _Slaughterhouse-Five_. New York, 1969.\n\nWagner, Richard. _Selected Letters of Richard Wagner_. Translated and edited by Stewart Spencer and Barry Millington. New York, 1988.\n\nWebster, Sir Charles, and Noble Franklin. _The Strategic Air Offensive Against Germany, 1939\u20131945_. 4 vols. London, 1977.\n\nWeekly R\u00e9sum\u00e9(s) of the Naval, Military and Air Situation. Nos. 288\u2013293. PRO W.P. (45). 166, 186, 201, 217, 243.\n\nWeidauer, Walter. _Inferno Dresden_. Berlin, 1990.\n\nWinterbotham, F. W. _The Ultra Secret_. New York, 1974.\n\nWohlfarth, Hannsdieter. _Johann Sebastian Bach_. Philadelphia, 1985.\n\nWoolner, David B., ed. _The Second Quebec Conference Revisited_. New York, 1998.\n\nWoolnough, John H. _Eighth Air Force Album_. Hollywood, Fla., 1980.\n\nZweig, Stefan. _Erasmus of Rotterdam_. Translated by Eden Paul and Cedar Paul. New York, 1934, 1956.\n\n**LIBRARIES, MUSEUMS, AND RESEARCH CENTERS**\n\n## **UNITED KINGDOM**\n\nImperial War Museum, Lambeth\n\nRoyal Air Force Museum, Hendon\n\nBomber Command Association, Hendon\n\nPublic Record Office, Kew\n\nImperial War Museum, Duxford\n\nBritish Library\n\n## **UNITED STATES**\n\nLibrary of Congress\n\nUnited States Air Force Historical Research Center, Maxwell Air Force, Alabama\n\nUnited States Air Force Academy, Colorado Springs\n\nNew York Public Library\n\nUnited States Military Academy, West Point\n\nDaniel Library, The Citadel, Charleston, South Carolina\n\nMighty Eighth Air Force Museum and Library, Pooler, Georgia\n\nRamsay Library, University of North Carolina at Asheville\n\nPack Memorial Library, Asheville, North Carolina\n\nEAA Aviation Foundation, Oshkosh, Wisconsin\n\n## **GERMANY**\n\nDeutsche Fotothek: S\u00e4chsische Landesbibliothek, Dresden\n\nStadtmuseum Dresden\n\n## **FRANCE**\n\nMemorial Museum of the Battle of Normandy, Bayeux\n\nUtah Beach Landing Museum, Sainte-Marie-du-Mont\n\nThe Airborne Museum, Sainte-M\u00e8re-Eglise\n\nMemorial Museum, Caen\n\nAmerican Cemetery, Colleville-sur-Mer\n\n# ABOUT THE AUTHOR\n\nMARSHALL DE BRUHL was for many years an executive and editor with several major American publishing houses, specializing in history and biography, most notably as editor of, and contributor to, the _Dictionary of American History_ and the _Dictionary of American Biography_. He is the author of _Sword of San Jacinto: A Life of Sam Houston_ and the co-compiler of _The International Thesaurus of Quotations_. He lives in Asheville, North Carolina.\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":" \nReordering the World\n\nReordering the World\n\nESSAYS ON LIBERALISM AND EMPIRE\n\nDuncan Bell\n\nPRINCETON UNIVERSITY PRESS\n\n_Princeton and Oxford_\nCopyright \u00a9 2016 by Princeton University Press\n\nPublished by Princeton University Press, 41 William Street,\n\nPrinceton, New Jersey 08540\n\nIn the United Kingdom: Princeton University Press, 6 Oxford Street,\n\nWoodstock, Oxfordshire OX20 1TW\n\npress.princeton.edu\n\n_Jacket art_ : Coiling the Atlantic Telegraph cable in one of the tanks on board the _Great Eastern_ (engraving). \u00a9 Look and Learn \/ Illustrated Papers Collection \/ Bridgeman Images\n\nAll Rights Reserved\n\nLibrary of Congress Cataloging-in-Publication Data\n\nBell, Duncan, 1976\u2013 author.\n\nReordering the world : essays on liberalism and empire \/ Duncan Bell.\n\npages cm\n\nIncludes bibliographical references and index.\n\n9780691138787 (hardcover : alk. paper)\n\nl. Liberalism\u2014Great Britain\u2014History. 2. Imperialism\u2014History. 3. Great Britain\u2014Colonies\u2014History.\n\nJC574.2.G(Great Britain) 2015027893\n\nBritish Library Cataloging-in-Publication Data is available\n\nThis book has been composed in Garamond Pro and Ideal Sans\n\nPrinted on acid-free paper. \u221e\n\nPrinted in the United States of America\n\n1 3 5 7 9 10 8 6 4 2\nFOR DOROTHY, WITH LOVE AND THANKS\nCONTENTS\n\n  | _Acknowledgments_ | xi\n\n---|---|---\n\n 1. | Introduction: Reordering the World |\n\n|\n\nPolitical Thought and Empire |\n\n|\n\nStructure of the Book |\n\n|\n\nPart I: Frames\n\n|\n\n 2. | The Dream Machine: On Liberalism and Empire |\n\n|\n\nLanguages of Empire |\n\n|\n\nIntertextual Empire: Writing Liberal Imperialism |\n\n|\n\nOn Settler Colonialism |\n\n|\n\nThe Tyranny of the Canon |\n\n 3. | What Is Liberalism? |\n\n|\n\nConstructing Liberalism: Scholarly Purposes and Interpretive Protocols |\n\n|\n\nA Summative Conception |\n\n|\n\nLiberalism before Locke |\n\n|\n\nWars of Position: Consolidating Liberalism |\n\n|\n\nConclusion: Conscripts of Liberalism |\n\n 4. | Ideologies of Empire |\n\n|\n\nImperial Imaginaries |\n\n|\n\nIdeologies of Justification |\n\n|\n\nIdeologies of Governance |\n\n|\n\nIdeologies of Resistance |\n\n|\n\nConclusions |\n\n|\n\nPart II: Themes\n\n|\n\n 5. | Escape Velocity: Ancient History and the Empire of Time |\n\n|\n\nThe Time of Empire: Narratives of Decline and Fall |\n\n|\n\nHarnessing the Time Spirit: On Imperial Progress |\n\n|\n\nThe Transfiguration of Empire |\n\n 6. | The Idea of a Patriot Queen? The Monarchy, the Constitution, and the Iconographic Order of Greater Britain, 1860\u20131900 |\n\n|\n\nConstitutional Patriotism and the Monarchy |\n\n|\n\nCivic Republicanism and the Colonial Order |\n\n|\n\nConclusions |\n\n 7. | Imagined Spaces: Nation, State, and Territory in the British Colonial Empire, 1860\u20131914 |\n\n|\n\nSalvaging Empire |\n\n|\n\nRemaking the People |\n\n|\n\nTranslocalism: Expanding the Public |\n\n|\n\nConclusions |\n\n 8. | The Project for a New Anglo Century: Race, Space, and Global Order |\n\n|\n\nEmpire, Nation, State: On Greater Britain |\n\n|\n\nThe Reunion of the Race: On Anglo-America |\n\n|\n\nAfterlives of Empire: Anglo-America and Global Governance |\n\n|\n\nMillennial Dreams, or, Back to the Future |\n\n|\n\nPart III: Thinkers\n\n|\n\n 9. | John Stuart Mill on Colonies |\n\n|\n\nOn Systematic Colonization: From Domestic to Global |\n\n|\n\nColonial Autonomy, Character, and Civilization |\n\n|\n\nMelancholic Colonialism and the Pathos of Distance |\n\n|\n\nConclusions |\n\n10. | International Society in Victorian Political Thought: T. H. Green, Herbert Spencer, and Henry Sidgwick _With Casper Sylvest_ |\n\n|\n\nProgress, Justice, and Order: On Liberal Internationalism |\n\n|\n\nInternational Society: Green, Spencer, Sidgwick |\n\n|\n\nCivilization, Empire, and the Limits of International Morality |\n\n|\n\nConclusions |\n\n11. | John Robert Seeley and the Political Theology of Empire |\n\n|\n\nEnthusiasm for Humanity |\n\n|\n\nOn Nationalist Cosmopolitanism |\n\n|\n\nExpanding England: Democracy, Federalism, and the World-State |\n\n|\n\nEmpire as Polychronicon: India and Ireland |\n\n12. | Republican Imperialism: J. A. Froude and the Virtue of Empire |\n\n|\n\nJohn Stuart Mill and Liberal Civilizing Imperialism |\n\n|\n\nRepublican Themes in Victorian Political Thought |\n\n|\n\nJ. A. Froude and the Pathologies of the Moderns |\n\n|\n\nDreaming of Rome: The Uses of History and the Future of \"Oceana\" |\n\n|\n\nConclusions |\n\n13. | Alter Orbis: E. A. Freeman on Empire and Racial Destiny |\n\n|\n\nPalimpsest: A World of Worlds |\n\n|\n\nThe \"Dark Abyss\": Freeman on Imperial Federation |\n\n|\n\nOn Racial Solidarity |\n\n14. | Democracy and Empire: J. A. Hobson, L. T. Hobhouse, and the Crisis of Liberalism |\n\n|\n\nConfronting Modernity |\n\n|\n\nHobhouse and the Ironies of Liberal History |\n\n|\n\nHobson and the Crisis of Liberalism |\n\n|\n\nConclusions |\n\n15. | Coda: (De)Colonizing Liberalism |\n\n|\n\n_Bibliography_ |\n\n|\n\n_Index_ | \nACKNOWLEDGMENTS\n\nThe essays collected in this volume were written over a period of more than a decade, and along the way I have accumulated numerous personal and intellectual debts. I'd like to thank the following for their generous support and penetrating discussions about political theory and imperial history: David Armitage, Peter Cain, Michael Freeden, Ian Hall, Zaheer Kazmi, Karuna Mantena, Jeanne Morefield, Isaac Nakhimovsky, and Richard Tuck. In Cambridge, Joel Isaac, Duncan Kelly, and Peter Mandler are ideal interlocutors. The great Istvan Hont provided intellectual encouragement and friendship over many years. I miss him greatly. Casper Sylvest has commented incisively on just about everything I've written, and for that act of supererogatory endurance, and much else besides, I'm deeply grateful to him. Moreover, I thank him for allowing me to reprint our jointly authored essay as chapter 10 of this volume. The following all commented on one or more of the chapters: Robert Adcock, Jens Bartelson, Mark Bevir, Alex Bremner, Chris Brooke, David Cannadine, Greg Claeys, Linda Colley, David Craig, Mary Dietz, Saul Dubow, Daniel Deudney, Mark Goldie, John Gunnell, Ian Hunter, Ben Jackson, Charles Jones, Stuart Jones, Peter Katzenstein, Ira Katznelson, Daniel O'Neill, Martti Koskenniemi, Ron Krebs, Chandran Kukuthas, Anthony Lang, Michael Ledger-Lomas, Joanna Lewis, Patchen Markell, Mark Mazower, Iain McDaniel, Jennifer Mitzen, Robert Nichols, Jon Parry, Nicholas Phillipson, Quentin Skinner, Katherine Smits, Tim Stanton, Gareth Stedman Jones, Anders Stephanson, Miles Taylor, Colin Tyler, Cheryl Welch, Brian Young, and Bernardo Zacka. Caroline Ashcroft and Eliza Garnsey did stellar work helping to prepare the manuscript. Kathleen Cioffi has been an exemplary production editor. Ben Tate has been a marvelously positive and sympathetic editor. Above all, Sarah Fine has been a constant source of inspiration, as have our daughters, Juliet and Alice. Thanks to one and all.\n\nA number of institutions have provided essential practical and financial support. The Centre of International Studies, and now the Department of Politics and International Studies, both at the University of Cambridge, have been admirably collegial environments in which to pursue serious scholarly work at the intersection of political theory, history, and international relations. The same is true of Christ's College, Cambridge. The Minda de Gunzburg Center for European Studies at Harvard hosted me for a productive period of sabbatical leave. The Leverhulme Trust has been a magnificent sponsor of the humanities and social sciences in the United Kingdom, and I have benefitted greatly from their largesse, first with the award of an Early Career Fellowship, and more recently, with a Philip Leverhulme Prize. These have given me invaluable time to conduct research for some of the chapters in this book.\n\nFinally, I am grateful to the editors and publishers for permission to reprint the following material:\n\nChapter 3: \"What Is Liberalism?,\" _Political Theory_ , 42\/6 (2014), doi: 10.1177\/0090591714535103, ptx.sagepub.com\n\nChapter 4: \"Ideologies of Empire,\" in _The Oxford Handbook of Political Ideologies_ , ed. Michael Freeden, Marc Stears, and Lyman Tower Sargent (2013), reproduced by permission of Oxford University Press, global.oup.com\n\nChapter 5: \"Empire,\" in _Historicism in the Victorian Human Sciences_ , ed. Mark Bevir (Cambridge: Cambridge University Press, forthcoming). Reprinted with permission\n\nChapter 6: \"The Idea of a Patriot Queen? The Monarchy, the Constitution, and the Iconographic Order of Greater Britain, 1860\u20131900,\" _Journal of Imperial and Commonwealth History_ , 34\/1 (2006), 3\u201322, www.tandfonline.com\n\nChapter 7: \"Imagined Spaces: Nation, State, and Territory in the British Colonial Empire, 1860\u20131914,\" in _The Primacy of Foreign Policy in British History_ , ed. William Mulligan and Brendan Simms (Basingstoke: Palgrave, 2010), reproduced with permission of Palgrave Macmillan\n\nChapter 8: \"The Project for a New Anglo Century: Race, Space, and Global Order,\" in _Anglo-America and Its Discontents: Civilizational Politics Beyond East and West_ , ed. Peter Katzenstein (London: Routledge, 2012)\n\nChapter 9: \"John Stuart Mill on Colonies,\" _Political Theory_ , 38\/1 (2010), doi: 10.1177\/0090591709348186, ptx.sagepub.com\n\nChapter 10: \"International Society and Victorian Political Thought: Herbert Spencer, T. H. Green, and Henry Sidgwick,\" with Casper Sylvest, _Modern Intellectual History_ , 3\/2 (2006) \u00a9 Cambridge University Press. Reprinted with permission\n\nChapter 12: \"Republican Imperialism: J. A. Froude and the Virtue of Empire,\" _History of Political Thought_ , 30\/1 (2009), reproduced courtesy of Imprint Academic\n\nChapter 13: \"Alter Orbis: E. A. Freeman on Empire and Racial Destiny,\" in _Making History: Edward Augustus Freeman and Victorian Cultural Politics_ , ed. G. A. Bremner and Jonathan Conlin (2015), reproduced by permission of Oxford University Press, global.oup.com\n\nChapter 14: \"Democracy and Empire: Hobson, Hobhouse, and the Crisis of Liberalism,\" in _British International Thought from Hobbes to Namier_ , ed. Ian Hall and Lisa Hill (Basingstoke: Palgrave, 2009), reproduced with permission of Palgrave Macmillan\n\nThis book is dedicated to my wonderful mother, Dorothy.\nReordering the World\n\nCHAPTER 1\n\nIntroduction\n\nReordering the World\n\n[C]entral to the lives of all empires have been the ways in which they have been constituted through language and their own self-representations: the discourses that have arisen to describe, defend, and criticize them, and the historical narratives that have been invoked to make sense of them.1\n\n\u2014JENNIFER PITTS\n\nFrom the earliest articulations of political thinking in the European tradition to its most recent iterations, the nature, justification, and criticism of foreign conquest and rule has been a staple theme of debate. Empires, after all, have been among the most common and the most durable political formations in world history. However, it was only during the long nineteenth century that the European empire-states developed sufficient technological superiority over the peoples of Africa, the Americas, and Asia to make occupation and governance on a planetary scale seem both feasible and desirable, even if the reality usually fell far short of the fantasy. As J\u00fcrgen Osterhammel reminds us, the nineteenth century was \"much more an age of empire than... an age of nations and nation-states.\"2 The largest of those empires was governed from London.\n\nEven the most abstract works of political theory, Quentin Skinner argues, \"are never above the battle; they are always part of the battle itself.\"3 The ideological conflict I chart in the following pages was one fought over the bitterly contested terrain of empire. The main, though not the only, combatants I survey are British liberal political thinkers\u2014philosophers, historians, politicians, imperial administrators, political economists, journalists, even an occasional novelist or poet. Multifaceted and constantly mutating, liberalism was chiefly a product of the revolutionary ferment of the late eighteenth century, of the complex dialectic between existing patterns of thought and the new egalitarian and democratic visions pulsating through the Euro-Atlantic world. A squabbling family of philosophical doctrines, a popular creed, a resonant moral ideal, the creature of a party machine, a comprehensive economic system, a form of life: liberalism was all of these and more. Intellectuals were central to the propagation and renewal of this expansive ideology, though they were far from the only agents involved. From Bentham to Hobson, from Macaulay to Mill, from Spencer to Sidgwick, a long parade of thinkers helped sculpt the contours of the evolving tradition, elaborating influential accounts of individual freedom, moral psychology, social justice, economic theory, and constitutional design. Liberal thinkers wrote extensively about the pathologies and potentialities of empire, developing both ingenious defenses and biting critiques of assorted imperial projects. The conjunction of a vibrant intellectual culture and a massive and expanding imperial system makes nineteenth-century Britain a vital site for exploring the connections between political thought and empire in general, and liberal visions of empire in particular. The vast expanses of the British empire provided both a practical laboratory and a space of desire for liberal attempts to reorder the world.\n\n_Reordering the World_ collects together a selection of essays that I have written over the last decade. Some explore the ways in which prominent thinkers tackled the legitimacy of conquest and imperial rule, while others dissect themes that pervaded imperial discourse or address theoretical and historiographical puzzles about liberalism and empire. They are united by an ambition to probe the intellectual justifications of empire during a key period in modern history. The materials I analyze are the product of elite metropolitan culture, including works of technical philosophy and recondite history, but also pamphlets, speeches, editorials, periodical articles, and personal correspondence. Such sources helped constitute the intellectual lifeblood of Victorian political discourse, feeding into the creation of a distinctive \"imperial commons,\" a globe-spanning though heavily stratified public constituted in part through the production and circulation of books, periodicals, and newspapers.4 The bulk of the volume focuses on the late Victorian and Edwardian eras, the years that Eric Hobsbawm once characterized as the \"age of empire.\"5 During that period the empire assumed a newfound significance in political argument, looming large over debates on a plethora of issues from social policy to geopolitical strategy and beyond. However, I also explore earlier currents of political thinking, and trace some of the echoes of nineteenth-century ideologies across the twentieth century and into the present.\n\nPolitical Thought and Empire\n\nAs late as 2006 Anthony Pagden could write that the study of empire had until recently been \"relegated to the wastelands of the academy.\"6 It was dragged in from the cold during the 1980s as postcolonial scholarship percolated through the humanities (and more unevenly across the social sciences). Imperial history was rejuvenated, moving swiftly from the periphery to the center of historical research, where it remains ensconced to this day.7 Political theory, like political science more broadly, has proven rather more resistant to the imperial turn. During the postwar years the field was characterized by a revealing silence about both the history of empire and the wave of decolonization then overturning many of the governing norms and institutions that had shaped the architecture of world order for five centuries.8 Adam Smith remarked in the _Wealth of Nations_ that the \"discovery\" of the Americas was one of the \"most important events recorded in the history of mankind,\" and he and his contemporaries, as well as many of their nineteenth-century heirs, wrestled incessantly with its meaning and consequences.9 Political theorists barely registered its passing.10 Mainstream approaches to the subject, at least in the Anglo-American tradition, continue to argue about the nature of justice, democracy, and rights, while ignoring the ways in which many of the ideas and institutions of contemporary politics have been (de)formed or inflected by centuries of Western imperialism\u2014\"this half millennium of tyranny against diverse civilisational forms of self-reliance and association\"11\u2014and the deep complicity in this enterprise of the canon from which they draw inspiration, concepts, arguments, and authority. While a persistent tattoo of criticism has been maintained by dissident scholars, it has made little impact on the core concerns or theoretical approaches of the field.12\n\nHistorians of political thought have been more willing to take empire and its multifarious legacies seriously, tracing the ways in which European thinkers grappled with projects of imperial conquest and governance.13 One of the guiding themes of this scholarship\u2014sometimes rendered explicit, sometimes lurking in the wings\u2014has been a concern with the relationship between liberal political thought and empire, between the dominant ideology of the contemporary Western world and some of the darkest, most consequential entanglements of its past.14 Both the political context for this scholarly reorientation and the stakes involved in it are clear. Against a backdrop of numerous \"humanitarian intervention\" operations, blood-letting in Iraq, Afghanistan and beyond, the forever war against terror, challenges from competing theocratic fundamentalisms, the specter of neoliberal globalization, and a burgeoning interest in questions of global poverty and inequality, the ethico-political status of liberalism has been put in question. Is it necessarily an imperial doctrine or a welcome antidote to imperial ambition? Perhaps liberals should face up to their imperial obligations rather than ducking them? \"Nobody likes empires,\" Michael Ignatieff argues, \"but there are some problems for which there are only imperial solutions.\"15 If so, what are they? Alternatively, is it possible to foster anti-imperial forms of politics, liberal or otherwise, in an increasingly interdependent world? Such concerns permeate the febrile debate. In chapter 2 I discuss some of the main trends in the scholarship, as well as identifying some of its weaknesses\n\nThroughout the book I treat liberalism chiefly as an actor's category, a term to encompass thinkers, ideas, and movements that were regarded as liberal at the time. (In chapter 3, I discuss the origins and development of liberal discourse in Britain and the United States.) Nineteenth-century British liberalism drew on multiple sources and was splintered into a kaleidoscope of ideological positions, some of which overlapped considerably, while others pulled in different directions. Indeed one of the main purposes of _Reordering the World_ is to highlight the ideological complexity and internal variability of liberalism, and in doing so to call into question sweeping generalizations about it. Benthamite utilitarianism, classical political economy, the historical sociology of the Scottish Enlightenment, Comtean positivism, partially digested German, French, and Greek philosophy, an emergent socialist tradition, the expansive legacies of republicanism, assorted forms of political theology, miscellaneous evolutionary theories, the democratic ethos inherited from the revolutionary era, the comforting embrace of Burkean organicism: all (and more) fed the cacophony. They cross-fertilised to spawn various identifiable articulations of liberal thinking, several of which are discussed in the following chapters. These include liberal Whig ideology (Macaulay, for example), forms of radical liberalism (including, in their different ways, Richard Cobden, John Stuart Mill, and Herbert Spencer), and late Victorian \"new liberalism\" (most notably J. A. Hobson and L. T. Hobhouse).16 This list is far from exhaustive, of course, and the period was also populated by multiple ideological hybrids, idiosyncratic figures whose ideas are hard to categorize, and less conspicuous or long-lived threads of political thinking. While they differed in many respects, including the philosophical foundations of their ideas and the public policies they endorsed, all shared a commitment to individual liberty, constitutional government, the rule of law, the ethical significance of nationality, a capitalist political economy, and belief in the possibility of moral and political progress.17 But the ways in which they interpreted, combined, and lexically ordered these abstract ideas, as well as the range of institutions they prescribed as necessary for their realization, varied greatly. So too did their attitudes to empire, though few rejected all its forms, and most (as I will argue) endorsed the formation of settler colonies.\n\nBritish imperial expansion was never motivated by a single coherent ideology or a consistent strategic vision. This was the grain of truth in the historian J. R. Seeley's famous quip that the empire seemed to have been \"acquired in a fit of absence of mind.\"18 Characterized by instability, chronically uncoordinated, and plagued by tensions between and within its widely dispersed elements, it was \"unfinished, untidy, a mass of contradictions, aspirations and anomalies.\"19 Yet despite this, or perhaps because of it, the empire was a subject of constant deliberation, celebration, denunciation, and anxiety.20 It was, as Jennifer Pitts notes in the epigraph, partly constituted (and contested) through language and legitimating representations. One of the main goals of imperial ideologists was to impose order on the untidy mass, to construct a coherent view of the past, present, and future that served to justify the existence of the empire, while their critics repeatedly stressed the manifest dangers of embarking on foreign conquest and rule. Imperial themes were woven through the fabric of nineteenth-century British political thinking, from the abstract proclamations of philosophers to the vernacular of parliamentary debate through to quotidian expressions of popular culture. Conceptions of liberty, nationality, gender, and race, assumptions about moral equality and political rationality, debates over the scope and value of democracy, analyses of political economy, the prospects of \"civilization\" itself: all were inflected to varying degrees with imperial concerns, explicit or otherwise.\n\nWhile each chapter can be read as a self-contained study of a particular topic, two general themes run through the book. The first is the pivotal importance of _settler colonialism_. As I argue in greater detail in chapter 2, the welcome revival of imperial history in the 1980s produced its own lapses and silences, one of the most significant of which was the sidelining of settler colonialism\u2014or \"colonization\" as it was called at the time\u2014in accounts of the long nineteenth century. There is a considerable historical irony involved in this redistribution of attention, given that the sub-discipline of imperial history was created at the turn of the twentieth century as part of a conscious effort to proselytize the superiority of the settler empire over other imperial spaces, above all India.21 While (what became) Australia, Canada, New Zealand, and South Africa were far less heavily populated than India, they nevertheless played a crucial role in the liberal imperial imagination, especially during the \"age of empire.\" In recent years the imbalance has been corrected and settler colonialism is once again a lively source of historical debate.22 Replicating the earlier pattern of omission, however, much of the literature on nineteenth-century British imperial political thought has consistently underplayed the significance of the colonies. Among other things, this has led to a skewed understanding of liberal accounts of empire. As I hope to demonstrate, acknowledging the importance of settler colonialism in nineteenth-century political thought unsettles some of the main ways in which scholars have interpreted the nature of \"imperial\" and \"anti-imperial\" arguments since the late eighteenth century.\n\nThe second recurrent theme is the multivalent role that historical consciousness performed in shaping visions of empire. While it is certainly arguable that political economists were the most influential imperial ideologists in the first half of the century, historians assumed this mantle in the second half. From James Mill and Macaulay to Froude and Seeley, historians were among the most prominent imperial thinkers, writing and rewriting the history of empire to bolster specific political projects.23 Their messages resonated in a culture obsessed with the past and the lessons it purportedly encoded.24 The \"English,\" Seeley observed in 1880, \"guide ourselves in the great political questions by great historical precedents.\"25 Historical-mindedness, as it was often called, structured political argument, rendering some lines of reasoning more intelligible, more perspicacious, and more plausible, than others. Precedent, tradition, organic development: all were invoked _ad infinitum_. It was this obsession with history that prompted A. V. Dicey to complain that it was better to be found guilty of \"petty larceny\" than to admit to skepticism about the universal validity of the historical method or to remain unconvinced by the patent superiority of \"historical-mindedness.\"26 Three of my chapters are thus dedicated to the imperial thought of renowned late Victorian historians. But the imaginative significance of history was not confined to the writings of professional scholars. Rather, a sense of the importance of historical time\u2014of the legitimating functions of precedent and tradition, of appeals to ancient authorities and the rhetoric of longevity, of the temporal logic of decline and fall, of the uses and abuses of historical analogies and metaphors, of the political possibilities inherent in the technological \"annihilation\" of time and space\u2014helped animate and condition imperial discourse.\n\nStructure of the Book\n\nOffered as an invitation for further reflection rather than an exhaustive account of the topic, _Reordering the World_ seeks to illuminate significant aspects of imperial debate and potentially open up new lines of inquiry. The book is divided into three parts. The first, \"Frames,\" contains three essays that probe the diverse meanings of liberalism and empire. Part II, \"Themes,\" comprises four historical essays that examine some salient topics in Victorian imperial thought (and beyond). The six chapters in the third part, \"Thinkers,\" dissect the imperial political thought of influential philosophers and historians, focusing in particular (though not exclusively) on their accounts of settler colonialism. Chapter 2 was written especially for this volume, while chapter 11 combines new research with some previously published materials.27 The remaining chapters were originally published in edited volumes and academic journals spanning the fields of political theory, history, and international relations. I have made only minor changes to them, occasionally excising some of the original text to avoid undue repetition, correcting stylistic infelicities where possible, and identifying connections and disjunctions between the chapters where appropriate.\n\nChapter 2 opens with a discussion of the mutable vocabulary of empire and liberalism, before analyzing some of the most important recent scholarship on the subject. I argue that despite the excellence of much of this work, it exhibits two recurrent flaws. First, it tends to overlook the significance of settler colonialism in the political imagination of the Victorians and their successors. In particular, many British liberals regarded settler colonialism as a preferable model of empire to the conquest and alien rule associated with India, and they invested their hopes in assorted projects of colonial reform. The colonies, they argued, were spaces of political freedom for their (white, \"civilized\") inhabitants, and as such they were not burdened by the moral and political dangers associated with the despotic rule prevalent throughout the rest of the empire. This made them ideal communities for the articulation of liberal ideas and institutions. Second, I argue that much work on political theory and empire is constrained by \"canonical\" approaches to intellectual history. Focusing on a narrow range of \"major\" thinkers can be illuminating\u2014I do so myself in several chapters\u2014but it can also lead to oversights and omissions, especially when trying to capture broad patterns of thinking. In particular, attempts to divine a connection between the inner essence of liberalism and imperialism efface the complexity and messiness of the historical record. To investigate imperial discourse it is necessary to dig deeper into the imperial commons, incorporating an extensive archive of intellectual production.\n\nThe following two chapters explore each side of the \"liberal empire\" compound. Isaiah Berlin once described freedom as \"a term whose meaning is so porous that there is little interpretation that it seems able to resist.\"28 Something similar could be said about liberalism. Challenging conventional understandings of the liberal tradition, chapter 3 presents both a theoretical argument and a historical interpretation. Theoretically, I propose that liberalism can be characterized as the sum of the arguments that have been classified as liberal, and recognized as such by other self-proclaimed liberals, over time and space. The historical argument suggests that between 1850 and 1950 the meaning of liberalism was transformed in the Anglo-American world. For most of the nineteenth century, liberalism was commonly viewed as a product of late eighteenth-century revolutionary turmoil, but it was reimagined during the opening decades of the twentieth century, its origins pushed further back in time and its scope expanded massively, such that it came to be seen as the overarching ideology of Western modernity. This transmutation was profoundly influenced by the wars fought against \"totalitarianism,\" both hot and cold. I illustrate this example of ideological shape-shifting by tracing how John Locke came to be conscripted as a paradigmatic liberal during that period. Demonstrating the instability of \"liberalism\" as a category, this analysis challenges the unreflective manner in which the term is employed in contemporary scholarly inquiry\u2014including (but not only) in debates over liberalism and empire. The final chapter in the section anatomizes different types of argument made about empire, especially during the last couple of hundred years. I distinguish between political ideologies, theories, and imaginaries, before sketching an ideal-typical account of ideologies of justification, governance, and resistance. Throughout, I emphasize the variety of arguments available to both advocates and critics of empire and colonialism, the patchwork forms they often assumed in political disputation, and some of their contemporary legacies.\n\nChapter 5 examines how historical time was conceptualized in imperial debate, focusing in particular on the diverse invocations of classical models of empire. Contrary to most scholarship on the subject, I argue that Victorian imperialists were often keen to escape the gravitational pull of the ancients, because the resonant lesson they drew from the Romans and the Greeks was that empires were self-dissolving, that they were fragile and temporary forms of political order rather than the basis for permanence and stability. Roman experience taught that empires eventually collapsed in ruins, Greek experience that settler colonies only thrived when formally independent of the \"mother country.\" Neither vision appealed to those aiming to create a resilient imperial formation, and so they borrowed selectively from the hallowed past, arguing that unlike its predecessors and potential competitors the British empire was not condemned to repeat the ostensible pattern of all human history. I demarcate two popular argumentative strategies. One attempted to reconcile progress and empire by insisting that the British were unique in some important respect\u2014usually their self-proclaimed ability to harmoniously combine \"libertas et imperium\" in a manner appropriate for an industrial, democratic age.29 The other was to argue that Greater Britain\u2014the settler colonies plus the \"mother country\"\u2014constituted a radically new type of political association. According to such accounts, empire was transfigured into something else: a federation, a transcontinental state, a multinational commonwealth. It had transcended its originary form. This novel type of polity was not subject to traditional anxieties about dissolution, corruption, or overextension, but was instead a pioneering manifestation of political trends reshaping world order at the time. It heralded the future rather than embodying the past.\n\nChapters 6 and  analyze aspects of the debate over Greater Britain that I didn't cover in my earlier book on the subject.30 The first discusses how the monarchy was figured in arguments about imperial federation. Queen Victoria was assigned two main functions. First, it was argued that the august institution of the monarchy could act as a marker of stability and constitutional fidelity in a globe-spanning imperial polity, thus reassuring skeptics that a strong thread of historical continuity ran through proposals for uniting Britain and the settler colonies. The British political tradition would be reinforced, rather than undermined, by the creation of an imperial federal structure. This line of argument formed the basis for an audacious account of constitutional patriotism. Secondly, an idealized representation of Victoria served as an anchor for national identity across vast geographical distances, her popularity binding the far-flung peoples of her realm in close communion. Or so it was claimed. I also contend that the way in which she was often represented in imperial debate echoed an older civic humanist language of \"patriot kingship,\" a fantasy vision of the monarch as the enemy of corruption, the protector of the people, and the strong but benevolent leader of a dynamic commercial people. Chapter 7, meanwhile, argues that the purported scope of the \"people\" and the \"public\" was transformed in debates over colonial unification. Both were conceptually decoupled from the state and imaginatively extended to encompass the geographically fragmented settler empire. As innovative communications technologies revolutionized understandings of time and space, so thinkers began to envision new forms of political and cultural solidarity on a global scale.31 Greater Britain was conceptualized as a discrete political space populated by a unified \"people\"\u2014coded typically as either a superior \"race\" or \"nation\"\u2014and governed by a constitutional monarchy sensitive to the preferences of an emergent transoceanic public. This spatial extension prefigures recent debates about the possibility of creating a global public sphere.\n\nThe final chapter in the section steps back from the patterns of Victorian political argument, and seeks to locate the intellectual history of the British empire in a wider frame. It reads the debates over Greater Britain as a formative moment in what I term the \"project for a new Anglo century\"\u2014the repeated attempt to create the political and social conditions necessary to secure the global domination of the \"Anglo-Saxon\" or \"English-speaking\" people. These were variations on the theme of white supremacism, a racial vision of global governance that frequently served as both a grounding assumption and a prescriptive conclusion throughout the nineteenth and much of the twentieth century. Towards the close of Victoria's reign Gilbert Murray, leading classicist and liberal political thinker, voiced a widely shared supposition.\n\nThere is in the world a hierarchy of races. The bounds of it are not, of course, absolute and rigid... but on the whole, it seems that those nations which eat more, claim more, and get higher wages, will direct and rule the others, and the lower work of the world will tend in the long-run to be done by the lower breeds of men. This much we of the ruling colour will no doubt accept as obvious.32\n\nWhile the specific theoretical frameworks and vocabularies used to justify this \"hierarchy of races\" mutated over time, it was nevertheless usually accepted as \"obvious,\" the commonsense of the geopolitical imagination. After outlining the overlapping debates about Greater Britain and the possibilities of an Anglo-American (re)union, I follow these ideas through the twentieth century and into our own world. I delineate four models that drew inspiration (and sometimes personnel) from the earlier Victorian debates: Anglo-American, imperial-commonwealth, democratic unionist, and world federalist. I conclude by discussing recent accounts of Anglo-world supremacy, suggesting that they should be interpreted as the latest iterations of a long-standing racialized vision of world order.\n\nSection III examines the political thinking of some key Victorian public intellectuals, chiefly historians and philosophers. I start with a reading of John Stuart Mill. Recent scholarship on Mill has greatly improved understanding of his arguments about the ethical defensibility of imperial rule, and in particular his account of India, but it has tended to ignore or downplay his extensive writings on colonization. Yet this was a subject that Mill returned to frequently throughout his long and illustrious career. While initially he regarded colonization as a solution to the \"social problem\" in Britain, he came to believe that its legitimacy resided primarily in the universal benefits\u2014civilization, peace, and prosperity\u2014that it generated for humanity as a whole. In the final years of his life Mill seemed to lose faith in the project. Confronted with the political intransigence and violence of the settlers, yet refusing to give up on the settler empire altogether, his colonial romance gave way to a form of melancholic resignation.\n\nChapter 10\u2014which was co-authored by Casper Sylvest\u2014discusses the content and boundaries of liberal internationalism. An ideology that imagined a world of self-determining nation-states gradually socialized into cooperative interaction through international commerce, law, and incremental democratization, it was typically predicated on a distinction between \"civilized\" and \"uncivilized\" peoples, applying one set of arguments to those within the privileged circle and another to those who fell outside it. Many (but not all) of its fundamental assumptions about the nature and direction of progress in the international system were shared by large swathes of the Victorian and Edwardian intellectual elites. It remains a potent force to this day, the dominant internationalist ideology of the modern West.33 The chapter examines how the very different philosophical systems crafted by T. H. Green, Henry Sidgwick, and Herbert Spencer issued in similar prescriptions for the international system.34 They diverged, though, over the legitimacy of empire, with Sidgwick adumbrating a fairly conventional liberal civilizational imperialism, Green largely silent on the issue, and Spencer a fierce critic.\n\nThen it is the turn of the historians. In an account of Edward Freeman's lifework, J. A. Doyle observed that it was \"scarcely possible\" to avoid comparisons between Froude, Freeman, and Seeley. All three scaled the heights of the blossoming professional discipline in Britain. Seeley was Regius Professor of Modern History at Cambridge from 1869\u20131895, Freeman held the equivalent chair in Oxford from 1884\u20131892, whereupon he was succeeded (albeit briefly) by Froude. All three were leading public moralists, contributing to debates on a plethora of issues beyond their putative historical expertise.35 Despite their many and varied differences, there was one \"point of community\" that united them. \"To each of them history was something more than an inspiring and impressive drama. Each fully acknowledged the truth... that the things of history happened for an example; that it is only by a knowledge of history that the citizen can attain a clear understanding of the duties and responsibilities which lie about him.\" Yet this similarity, Doyle continued, produced divergent conclusions: \"[I]t would be hard to imagine political ideas or conceptions of national life differing more widely than did those held by Freeman and those of his two contemporaries.\"36 So it appeared to each of them and many of their readers.\n\nIt was a late Victorian platitude that Seeley's _The Expansion of England_ (1883) and Froude's _Oceana_ (1886) played a pivotal role in reorienting British attitudes to the settler colonies and stoking the fire of popular imperialism. \"The work of Seeley and Froude in one sphere of literary activity, of Kipling in another, and the strong personality of Mr. Chamberlain... combined to draw the outposts of the realm into a closer union,\" wrote one informed observer.37 Half a century later Hannah Arendt underlined their significance in her discussion of imperialism in _The Origins of Totalitarianism_.38 Disagreeing fundamentally over the appropriate way to study and write history\u2014Froude harking back to the narrative mode of Macaulay, Seeley impressed by the rigorous historical positivism imported from Germany\u2014they were nevertheless both ardent imperial federalists, keen to formally unite the scattered elements of the British colonial system. C. A. Bayly has argued that the decades prior to the outbreak of war in 1914 can be seen as an \"idealist\" age, with both nationalism and empire \"tinctured with religion.\"39 In chapter 11 I argue that Seeley's political thought, including his wildly popular account of empire, was structured by concepts\u2014nation, history, state, civilization\u2014that he interpreted in theological terms. I read his vision of world order as an idiosyncratic expression of \"cosmopolitan nationalism,\" an attempt to reconcile human universality with national particularity. Moreover, I contend that although he never outlined his plans for Greater Britain in any detail, he was committed to the creation of a federal nation-state encompassing Britain and its settler colonies. Chapter 12 engages Froude's elusive political thought. I start by distinguishing two modes of justifying imperialism, a \"liberal civilizational\" model (as articulated by John Stuart Mill) that did so principally in terms of the benefits that it bestowed on subject populations, and a \"republican\" model that focused instead on a specific set of benefits\u2014glory, honor, virtue\u2014that accrued to the imperial state. The remainder of the chapter offers a \"republican\" interpretation of Froude's writings on settler colonialism, arguing that both his diagnosis of the problems besetting modern Britain and his prescribed solutions were derived in part from his reading of the fate of the Roman Republic.\n\nFreeman pursued a relentless intellectual vendetta against Froude, frequently challenging his credentials as a serious historian.40 Freeman and Seeley had more in common: both were fairly conventional liberals, albeit of different stripes, and both concurred on the intimate connection between history and politics. But Freeman scorned the vision of empire articulated by Seeley and Froude. Chapter 13 unpacks the intellectual sources of his skepticism. Drawing in particular on the history of federalism\u2014a subject on which he was the recognized authority\u2014he argued that plans for uniting the colonies were absurd, based on a flagrant misunderstanding of both the federal idea and the true meaning of empire. Properly understood, the history of empire instilled the need for colonial independence, not unification. But it would be a mistake to exaggerate Freeman's anti-imperial credentials, or characterize him (following Doyle) as the antithesis of Seeley and Froude, because he shared with them a belief in the unity and superiority of the \"English-speaking race.\" His preferred political vehicle for this racial vision of world order was an alliance, cemented by common citizenship, between Britain and the United States, countries that were ordained to lead and police the world.41 Like many critics of formal empire during the period, Freeman was nevertheless committed to a hierarchical conception of global politics predicated on white racial supremacy.\n\nThe final full chapter analyzes two renowned \"new liberal\" thinkers, J. A. Hobson and L. T. Hobhouse, focusing in particular on how they conceived of the relationship between democracy, empire, and international politics between the late 1890s and the First World War. I start by highlighting how they positioned themselves in relation to the past and present of the mutating liberal tradition, before turning to examine their writings on settler colonialism, showing how they both supported projects for the unification of Greater Britain, albeit in a qualified manner. Posterity has been kind to Hobson, who is usually remembered as one of the major anti-imperial thinkers of the twentieth century (not least because of his influence on Lenin).42 Yet his writings present a rather more complicated picture, for he was not opposed to empire in all its forms, only to what he saw as pathological variants of it, and he was a keen advocate of settler colonialism. Hobhouse, meanwhile, sketched an idealized account of the colonial empire. He argued that if transmuted into a federal institution it would be compatible with democracy, in a manner that traditional forms of empire were not, and as such it could serve as a privileged agent of progress, fermenting the democratization of the international system and acting as a template for a future \"international state.\" Like many liberal thinkers, both Hobson and Hobhouse invested far more political hope in settler colonialism that in other modes of empire-building.\n\nIn the brief coda, I revisit some of the main lines of argument developed in the preceding chapters. Reiterating the centrality of historical-mindedness and settler colonialism in nineteenth-century visions of empire, I finish with some tentative suggestions about the need to \"de-colonize\" liberalism, to seek ways to acknowledge and transcend the legacies of colonial occupation and rule, rather than either ignoring this tainted history or rejecting liberalism altogether.\n\n1 Pitts, \"Political Theory of Empire and Imperialism,\" _Annual Review of Political Science_ , 13 (2010), 226.\n\n2 Osterhammel, _The Transformation of the World_ , trans. Patrick Camiller (Princeton, 2014), 392. On the nineteenth-century imperial order, see also C. A. Bayly, _The Birth of the Modern World, 1780\u20131914_ (Oxford, 2004); Jane Burbank and Frederick Cooper, _Empires in World History_ (Princeton, 2010), chs. 10\u201311. On some of the distinctive features of Victorian imperialism, see Duncan Bell, \"Victorian Visions of Global Order,\" in _Victorian Visions of Global Order_ , ed. Bell (Cambridge, 2007), 1\u201325.\n\n3 Skinner, _Hobbes and Republican Liberty_ (Cambridge, 2008), xvi.\n\n4 See Antoinette Burton and Isabel Hofmeyr, \"The Spine of Empire?,\" in _Ten Books That Shaped the British Empire_ , ed. Burton and Hofmeyr (Durham, NC, 2014), 1\u201328. Later, of course, radio, cinema, and television added new dimensions to the imperial commons.\n\n5 Hobsbawm, _The Age of Empire, 1875\u20131914_ (London, 1987).\n\n6 Pagden, \"The Empire's New Clothes,\" _Common Knowledge_ , 12\/1 (2006), 36.\n\n7 For accounts of the revival, see Linda Colley, \"What Is Imperial History Now?,\" in _What Is History Now?_ , ed. David Cannadine (Basingstoke, 2002); John Mackenzie, \"The British Empire,\" _Journal of Imperial and Commonwealth History_ , 43\/1 (2015), 99\u2013124; Dane Kennedy, \"The Imperial History Wars,\" _Journal of British Studies_ , 54\/1 (2015), 1\u201322.\n\n8 For exceptions that prove the rule, see Hannah Arendt, _The Origins of Totalitarianism_ [1951] (New York, 1985), pt. 2; John Plamenatz, _On Alien Rule and Self-Government_ (London, 1960); Louis Hartz, ed., _The Founding of New Societies_ (New York, 1964). Yet imperial questions often intruded in unexpected places; see, for example, James Tully's analysis of the subtle imperial entailments of Isaiah Berlin's seminal essay on liberty. Tully, \"'Two Concepts of Liberty' in Context,\" in _Isaiah Berlin and the Politics of Freedom_ , ed. Bruce Baum and Robert Nichols (Abingdon, 2013), 23\u201352.\n\n9 Smith, _An Inquiry into the Nature and Causes of the Wealth of Nations_ [1776], ed. R. H. Campbell, Andrew S. Skinner, and W. B. Todd (Oxford, 1976), bk. 4, ch. 7, p. 166. The only other event of equal significance, he wrote, was the opening of \"a passage to the East Indies by the Cape of Good Hope.\" For a brilliant account of Smith and his context, see Istvan Hont, _Jealousy of Trade_ (Cambridge, MA, 2005); Hont, _The Politics of Commercial Society_ , ed. B\u00e9la Kapossy and Michael Sonenscher (Cambridge, MA, 2015).\n\n10 The same was true of much postwar social science. For conflicting interpretations of the role of empire and decolonization in International Relations, the scholarly field dedicated to the analysis of world politics, see Nicolas Guilhot, \"Imperial Realism,\" _International History Review_ , 36\/4 (2014), 698\u2013720; Robert Vitalis, _White World Order, Black Power Politics_ (Ithaca, 2015). See also John Hobson, _The Eurocentric Conception of World Politics_ (Cambridge, 2012), chs. 8\u201313.\n\n11 James Tully, \"Lineages of Informal Imperialism,\" in _Lineages of Empire_ , ed. Duncan Kelly (Oxford, 2009), 29.\n\n12 For acute criticisms of this tendency, see Charles Mills, \"Decolonizing Western Political Philosophy,\" _New Political Science_ , 37\/1 (2015), 1\u201324. The partial exception to this claim is the literature on historical injustice.\n\n13 For influential examples, see Richard Tuck, _The Rights of War and Peace_ (Oxford, 1999); Anthony Pagden, _Lords of All the World_ (London, 1995); David Armitage, _The Ideological Origins of the British Empire_ (Cambridge, 2000). The literature is discussed in Pitts, \"Political Theory of Empire\"; David Armitage, _Foundations of Modern International Thought_ (Cambridge, 2013), pt. 1.\n\n14 Valuable earlier accounts include Bernard Semmel, _Imperialism and Social Reform_ (Cambridge, MA, 1960); Semmel, _The Rise of Free Trade Imperialism_ (Cambridge, 1970); Eric Stokes, _The English Utilitarians and India_ (Oxford, 1959); A. P. Thonton, _The Imperial Idea and Its Enemies_ (London, 1959); Donald Winch, _Classical Political Economy and Colonies_ (Cambridge, 1965).\n\n15 Ignatieff, _Empire Lite_ (London, 2003), 11.\n\n16 For different perspectives on Victorian liberalism, see Richard Bellamy, _Liberalism and Modern Society_ (Cambridge, 1992); Bellamy, ed., _Victorian Liberalism_ (Abingdon, 1990); John Burrow, _Whigs and Liberals_ (Oxford, 1988); Stefan Collini, _Public Moralists_ (Oxford, 1991); Michael Freeden, _The New Liberalism_ (Oxford, 1978); Elaine Hadley, _Living Liberalism_ (Chicago, 2010); Simon Gunn and James Vernon, eds., _The Peculiarities of Liberal Modernity in Imperial Britain_ (Berkeley, 2011); Peter Mandler, ed., _Liberty and Authority in Victorian Britain_ (Oxford, 2006); J. P. Parry, _The Politics of Patriotism_ (Cambridge, 2009).\n\n17 Note that this is an empirical claim about the ideological commitments of Victorian liberalism, not a conceptual or normative evaluation of the necessary or sufficient elements of liberal political thinking in general. For further discussion on this methodological issue, see chapter 3.\n\n18 Seeley, _The Expansion of England_ (London, 1883), 8.\n\n19 John Darwin, _The Empire Project_ (Cambridge, 2011), xi. Darwin's work offers a powerful structural account of the empire as a fragile, fragmented system, the fate of which was ultimately dependent on wider geopolitical currents largely outside British control. For some brief reflections on his work, see Duncan Bell, \"Desolation Goes before Us,\" _Journal of British Studies_ , 54\/4 (2015), 987\u201393.\n\n20 My understanding of ideology has been influenced by the work of Michael Freeden and Quentin Skinner. See, for example, Freeden, _Ideologies and Political Theory_ (Oxford, 1998); Freeden, _The Political Theory of Political Thinking_ (Oxford, 2013); Skinner, _Visions of Politics_ , vol. 1 (Cambridge, 2002). See also the discussion in chapter 4, section 2.\n\n21 See, in particular, Amanda Behm, \"The Bisected Roots of Imperial History,\" _Recherches Britanniques_ , 1\/1 (2011), 54\u201377. For the educational networks binding Greater Britain, see Tamsin Pietsch, _Empire of Scholars_ (Manchester, 2013).\n\n22 See the references in chapter 2, section 3.\n\n23 On James Mill, see Javeed Majeed, _Ungoverned Imaginings_ (Oxford, 1992); on Macaulay, see Catherine Hall, _Macaulay and Son_ (London, 2012); on Seeley, see chapter 11. Tadhg Foley argues that from the 1830s onwards, colonization was \"theorized and justified by the hired-prize fighters of empire totally in economic terms.\" Foley, \"'An Unknown and Feeble Body,'\" in _Studies in Settler Colonialism_ , ed. Fiona Bateman and Lionel Pilkington (Basingstoke, 2011), 10. However, this sweeping contention is implausible, especially when directed at the second half of the nineteenth century.\n\n24 For an insightful recent analysis, see Theodore Koditschek, _Liberalism, Imperialism, and the Historical Imagination_ (Cambridge, 2011).\n\n25 Seeley, \"Political Somnambulism,\" _Macmillan's Magazine_ , 43 (1880), 32.\n\n26 Dicey, _Introduction to the Study of the Law of the Constitution_ , 4th ed. (London, 1893), 14. On the ubiquity of \"historical mindedness\" in Victorian culture, see also Lord Acton, \"Inaugural Lecture on the Study of History,\" in _Lectures on Modern History_ , ed. J. N. Figgis and R. V. Laurence (London, 1906), 22. On the role of historical imagination in Victorian political thinking, see especially John Burrow, _Whigs and Liberals_ (Oxford, 1988); Stefan Collini, Donald Winch, and John Burrow, _That Noble Science of Politics_ , (Cambridge, 1983), chs. 6\u20137.\n\n27 As well as including a considerable amount of new research, chapter 11 synthesizes material from several chapters of Bell, _The Idea of Greater Britain_ (Princeton, 2007); as well as Bell, \"Unity and Difference,\" _Review of International Studies_ , 31\/3 (2005), 559\u201379.\n\n28 Berlin, \"Two Concepts of Liberty\" [1958], in _Liberty_ , ed. David Miller (Oxford, 1991), 168.\n\n29 The problematic of liberty and empire ran through modern European political thought. For the period until the end of the eighteenth century, see David Armitage, \"Empire and Liberty,\" in _Republicanism_ , vol. 2, ed. Martin van Gelderen and Quentin Skinner (Cambridge, 2002), 29\u201347.\n\n30 Bell, _The Idea of Greater Britain_.\n\n31 For more on the transformation of conceptions of time and space, see Duncan Bell, \"Dissolving Distance,\" _Journal of Modern History_ , 77\/3 (2005), 523\u201362; Bell, _The Idea of Greater Britain_ , ch. 3.\n\n32 Murray, \"The Exploitation of Inferior Races in Ancient and Modern Times,\" in _Liberalism and the Empire_ , by F. W. Hirst, Gilbert Murray, and J. L. Hammond (London, 1899), 156. On Murray's theoretical account of empire and international politics, see Christopher Stray, ed., _Gilbert Murray Reassessed_ (Oxford, 2007), chs. 11\u201312; Jeanne Morefield, _Covenants without Swords_ (Princeton, 2004).\n\n33 For a recent critical analysis, see Beate Jahn, _Liberal Internationalism_ (London, 2013). For a more positive account, see John Ikenberry, \"Liberal Internationalism 3.0,\" _Perspectives on Politics_ , 7\/1 (2009), 71\u201387. See also the essays in Tim Dunne and Trine Flockhart, eds., _Liberal World Orders_ (Oxford, 2013).\n\n34 For a more detailed analysis, covering the work of historians and lawyers as well as philosophers, see Casper Sylvest, _British Liberal Internationalism, 1880\u20131930_ (Manchester, 2009). For a general history, see Mark Mazower, _Governing the World_ (London, 2012), pt. 1.\n\n35 Doyle, \"Freeman, Froude, Seeley,\" _Quarterly Review_ , 182\/364 (1895), 296. Doyle was a Fellow of All Souls, Oxford, best known for his multivolume history of the British colonization of North America. Doyle, _The English in America_ , 5 vols. (London, 1882\u20131907). For the institutional and cultural context of this professionalization, see Reba Soffer, _Discipline and Power_ (Stanford, 1994); Philippa Levine, _The Amateur and the Professional_ (Cambridge, 1986); Peter Slee, _Learning and a Liberal Education_ (Manchester, 1986). Their intellectual and social milieu is brilliantly evoked in Collini, _Public Moralists_.\n\n36 Doyle, \"Freeman, Froude, Seeley,\" 296.\n\n37 W. Alleyne Ireland, \"The Victorian Era of British Expansion,\" _North American Review_ , 172\/533 (1901), 563. See also Ireland, \"The Growth of the British Colonial Conception,\" _Atlantic Monthly_ , April 1899, 488\u201398; J. H. Muirhead, \"What Imperialism Means\" [1900], in _The British Idealists_ , ed. David Boucher (Cambridge, 1997), 244.\n\n38 Arendt, _The Origins of Totalitarianism_ , 181\u201382. For Arendt on empire, see Richard King and Dan Stone, eds., _Hannah Arendt and the Uses of History_ (Oxford, 2007), pt. 1; A. Dirk Moses, \"Das r\u00f6mische Gespr\u00e4ch in a New Key,\" _Journal of Modern History_ , 85\/4 (2013), 867\u2013913.\n\n39 Bayly, \"Michael Mann and Modern World History,\" _Historical Journal_ , 58\/1 (2015), 334.\n\n40 On Freeman's campaign against Froude, see Ian Hesketh, \"Diagnosing Froude's Disease,\" _History and Theory_ , 47\/3 (2008), 373\u201395.\n\n41 For more on the late Victorian interest in cooperation (even union) with the United States, including visions of \"isopolitan citizenship,\" see Duncan Bell, \"Before the Democratic Peace,\" _European Journal of International Relations_ , 20\/3 (2014), 647\u201370; Bell, \"Beyond the Sovereign State,\" _Political Studies_ , 62\/2 (2014), 418\u201334. I address the topic in a forthcoming book, _Dreamworlds of Empire_.\n\n42 Lenin, _Imperialism_ [1917], in _Selected Works_ (Moscow, 1963), 1:667\u2013766.\nPART I\n\nFrames\nCHAPTER 2\n\nThe Dream Machine\n\nOn Liberalism and Empire\n\nIn the empire, one might say, liberalism had found the concrete place of its dreams.1\n\n\u2014UDAY SINGH MEHTA\n\nThe relationship between liberalism and empire has been a recurrent topic of debate among political theorists and intellectual historians during the last two decades. The timing is no coincidence. In the \"new world order\" purportedly hatched by the dissolution of Cold War certainties, liberals and their critics sought to diagnose the virtues and vices of the triumphant ideology.2 Evaluating the present triggered an urgent turn to history, as the record of liberal engagement with empire was scoured for lessons, precedents, and forecasts. As old arguments have been reanimated and mobilized, so political thought has been articulated in the register of historical investigation. In this chapter I survey the scholarly field, concentrating in particular on work that emphasizes the centrality of British imperial ideology in the long nineteenth century, from the turmoil of the American and French Revolutions to the onset of the First World War.3 During that extraordinary period Britain was both the crucible of liberal political thinking and the most extensive imperial formation in history.\n\nLiberalism was a protean phenomenon, a shape-shifting amalgam of philosophical arguments and political-economic practices encompassing diverse views on the self, society, economy, and government. Its ideological reach and complexity grew steadily as the century unfolded. By 1860 liberals of different stripes were beginning to converge on a relatively stable \"internationalist\" doctrine that championed the benefits of conjoining international commerce and international law, but such arguments applied only (or primarily) to relations between purportedly \"civilized\" states.4 Then, as now, liberals remained divided over the question of empire. Most supported it, but then so too did most non-liberals, and liberal imperialists differed over the forms of empire they defended, the intensity of support they offered, and perhaps most significantly, the justificatory arguments that they articulated. There were also assorted liberal critics of empire, though they were always in a minority. Reductive generalizations about \"liberalism and empire,\" whether directed at the heyday of the British empire or the contemporary world, are usually more misleading than illuminating.\n\nTwo main weaknesses run through scholarly commentary on liberalism and empire: a tendency to overlook the significance of _settler colonialism_ and an over-reliance on _canonical_ interpretations of liberalism. I address both in this chapter. Settler colonialism played a crucial role in nineteenth-century imperial thought, and liberalism in particular, yet it has largely been ignored in the burst of writing about the intellectual foundations of the Victorian empire. Utilizing canonical interpretations of liberalism, meanwhile, has generated some skewed claims about the historical connections between liberal political thought and empire.\n\nLanguages of Empire\n\nThe study of liberal attitudes to empire is beset with conceptual, historical, and semantic difficulties. To say something perspicacious about the relationship between X and Y, it is vital to have a clear sense of their meaning, but \"liberalism\" and \"empire\" both rank among the most polysemous concepts in the modern political lexicon, and as a result debates about their relationship are often characterized by confusion. Since there is no settled agreement on their meaning, the selection of definitions\u2014and thus the determination of conclusions\u2014is the product of an opaque combination of scholarly sensibility, disciplinary socialization, and political commitments. The bulk of the literature produced by political theorists employs a plausible but relatively narrow understanding of empire\u2014chiefly what John Plamenatz termed \"alien rule,\" the conquest and governance of distant populations and territories.5 This definitional preference conditions a particular range of questions and answers.\n\nScholarship on liberal political theory and empire is divided by three main issues. First, there is profound disagreement over whether the relationship is _rejectionist, necessary_ , or _contingent_. The _rejection thesis_ posits that liberalism and imperialism are mutually exclusive, that authentic liberals cannot be imperialists. In contrast, the _necessity thesis_ asserts that imperialism is an integral feature of liberal political thought\u2014that to be a proper liberal is to be committed to the legitimacy of (liberal) empire. Those espousing the _contingency thesis_ argue that liberal normative commitments do not necessarily entail support for empire. Instead, the imperialism of liberal writers, past and present, can be explained either through reference to superseded historical conditions or by disaggregating discrete strands of liberalism, some of which are more susceptible to imperial temptation than others. The political and theoretical repercussions of this disagreement are palpable, not least because it raises the question of whether forms of non-imperial liberalism are even possible.\n\nThe second line of divergence concerns the extent to which the history of liberalism contaminates its contemporary expressions. While overlapping with the first point, this is nevertheless a distinct issue. Even if one denies the necessity thesis, it might still be argued that liberal assumptions, categories, and institutions cannot escape their original imperial entanglements\u2014that the history of Western conquest is so deeply implicated in shaping the present order that it permeates liberal political thinking and practice, as well as the ways in which it is perceived in places with long experience of European intervention. Such an argument is normatively indeterminate. One version embraces the continuities, viewing the history of empire as a fertile resource for contemporary projects of imperial world ordering.6 Another, less celebratory, response acknowledges the deep historical roots of contemporary liberal political ideas, but suggests that this historical lineage does not in itself invalidate them. Their \"genealogy,\" Anthony Pagden argues, should not be \"counted as grounds for dismissing them.\"7 To do so, proponents of this line charge, would be to commit the genetic fallacy, the mistake of evaluating something solely in terms of its origins. But the most common line of argument maintains that liberals can and should escape the burdens of imperial history; that the liberalism of today is (or can be) radically different from that which went before. The third main source of disagreement concerns the historical trajectory of liberalism. This dispute is often tied up with the long-standing historical debate about the origins of liberalism, with some tracing the ideology to early modern Europe, and in particular the seventeenth century, while other scholars (myself included) claim that it is best seen as a product of the late eighteenth century. One line of argument posits that the history of liberal political thought has always been thoroughly imperial (whether through conceptual necessity or otherwise), another that it is marked by significant ideological variability and ruptures. The most common line, which I return to later in this chapter, suggests that the late eighteenth century witnessed a major transition in liberal visions of empire, an ideological break that allows us to draw a firm line between the epochs. Others, though, propose different historical chronologies, identify alternative discursive shifts, or place greater emphasis on long-run continuities in liberal thinking.\n\nWhile pure examples of the rejection and necessity theses are (and always have been) rare, liberals have developed a range of argumentative strategies that articulate weak forms of the rejectionist line. In the late nineteenth century, for example, it was common to distinguish between _imperialism_ (an unjustified form of aggressive expansionism) and _empire_ (a potentially legitimate form of political order). This distinction was central to Gladstone's fierce critique of Disraeli's romantic defense of imperialism.8 \"Liberalism and Imperialism,\" the historian J. L Hammond wrote at the turn of the twentieth century, \"differ in their morals, their manners and their ideals.\" Whereas the former (represented by Cobden, Bright, and Spencer) was pacific in intent, the latter was militaristic, and whereas liberals affirmed the value of nationality, imperialists rejoiced in the \"funerals of other nationalities.\"9 Yet empire was legitimate if it was motivated by broadly liberal ambitions and functioned according to broadly liberal norms. Thus Hammond could argue that even as they firmly rejected imperialism, true liberals recognized that the possession of empire imposed a \"special obligation to act with self-control and moderation.\"10 Dismissive of imperialism, he praised the value of settler colonialism. L. T. Hobhouse adopted a similar argument, insisting that the \"central principle\" of liberalism was self-government, whereas imperialists hymned the \"subordination of self-government to Empire,\" and that as such they were antithetical ideological positions. Like Hammond, though, he nevertheless suggested that if understood properly\u2014in his case as \"a great aggregation of territories enjoying internal independence while united by some common bond\"\u2014the pursuit of empire was compatible with liberalism.11\n\nEchoing this distinction, liberal internationalists today often scramble to differentiate \"hegemony\" from \"empire,\" with the former typically construed as normatively desirable and the latter as both obsolete and objectionable. Thus John Ikenberry celebrates American global leadership in the post-1945 era as a victory of liberal hegemony, while castigating the imperial depredations of the George W. Bush administration. This argument presupposes a restrictive definition. \"If empire has any meaning,\" he maintains, \"it refers to political control by a dominant state of the domestic and foreign policy of weaker countries.\"12 Hegemony is different. In an empire, \"the lead state operates unilaterally and outside the order, whereas in a hegemonic order, the lead establishes multilateral rules and institutions that it itself operates within.\" As with the late Victorian attempt to separate empire from imperialism, the line between empire and hegemony is often hard to sustain. Ikenberry, for example, anoints Victorian Britain and the postwar United States as the two \"great historical cases of liberal hegemony,\" but since Britain was an empire-state the historical (as opposed to ideological) value of the distinction he draws is unclear.13 Not everyone is convinced by such acts of semantic jujitsu. Niall Ferguson, a proud liberal imperialist, is right to observe that \"hegemony\" is \"really just a way to avoid talking about empire,\" and that it is only convincing if one assumes an implausibly narrow definition of the latter.14 Indeed it can be seen as a rhetorical move within imperial ideology rather than a disinterested description of an alternative political formation. The history of imperial ideology is in part a story of contestation over the vocabulary of domination.\n\nAnother mode of argument maintains that the spread of capitalism will ultimately render imperialism obsolete. The most influential twentieth-century version was developed by Joseph Schumpeter, who equated liberalism with _laissez-faire_ capitalism and declared that in its purest form it was hostile to imperialism. \"[W]here free trade prevails,\" he predicted, \"no class has an interest in forcible expansion as such.\"15 Imperialism was an atavistic throw-back to a feudal age. Such arguments temporalize liberal anti-imperialism, implying that at some (indefinite) point in the future an authentic post-imperial liberal political order will emerge. Schumpeter inherited a long-standing line of reasoning about the emergent conditions and likely consequences of commercial society. Benjamin Constant's assault on the \"spirit of conquest,\" Herbert Spencer's historical sociology of industrial society, Richard Cobden's relentless promotion of free trade, Hobson's critique of the financial \"taproot\" of imperialism, Norman Angell's account of the irrationality of war in an economically interdependent world: all posited that the development of capitalism would lead eventually to the supersession of the will-to-empire.16 Yet none of them rejected empire in all its forms, and nor did they think that capitalism was always and everywhere opposed to imperialism. Indeed specific instantiations of capitalism were key to their respective explanations for the persistence of imperialism in the industrial age. Only in the long run would the perfection of the liberal capitalist order consign imperialism to the proverbial dustbin of history. Lineal descendants of this argument can be found in Panglossian cheerleading for neoliberal globalization.\n\nJames Tully's work illustrates the political and theoretical stakes involved in defining empire. Rejecting a narrow conception of empire-as-alien-rule, and of imperialism as the policy dedicated to the creation of such an empire, he adopts a much broader interpretation in order to critique the manifold continuities between the past and present. He contends that Western political thought has long articulated the right (even duty) of purportedly \"advanced\" states to remake the world in their own image, a self-defined mission that has been undertaken in the name of various related ideals: \"to improve, to civilise, develop, modernise, constitutionalise, democratise, and bring good governance and freedom.\"17 From this perspective, virtually all extant liberal political thought has been corrupted by its entanglement with empire. Tully also delineates various modalities of imperial rule. The subtlest is _informal imperialism_ , under which there is no need to govern populations and territories through formal-legal means because the most powerful states \"induce local rulers to keep their resources, labour, and markets open to free trade dominated by western corporations and global markets, thereby combining 'empire and liberty.'\"18 This account dissolves the distinction between hegemony and empire. In the nineteenth century, \"free trade imperialism\" was one of the main instruments through which Britain integrated much of Latin America into the global capitalist system. During the twentieth century, and especially after the defeat of Nazi and Soviet alternatives, it emerged as the preferred mode of domination by the leading powers, chiefly the United States. On this account, modernization, development, and globalization are best characterized as \"the continuation of Western imperialism by informal means and through institutions of global governance.\"19 The domain of empire, then, extends far beyond alien rule. Yet although Tully presents one of the most sweeping accounts of the imperial legacy of Western thought, he stops short of endorsing the necessity thesis. In Wittgensteinian terms, he argues that imperialism is only a contingent feature of dominant theoretical languages and practices, and that as such it does not exhaust them. The imperial dimensions of liberalism can thus be transcended or eliminated, at least in principle. A similar line is adopted by Charles Mills, who argues that despite its deep historical complicity in racism and imperialism, liberalism\u2014albeit of a radically transformed kind\u2014can be salvaged.20 Both argue that liberal political thinking is capable of redemption.\n\nWriting against the grain, some liberals acknowledge an intrinsic connection, with Ignatieff and Ferguson perhaps the best-known examples.21 According to Alan Ryan, liberal imperialism is the doctrine that \"a state with the capacity to force liberal political institutions and social aspirations upon nonliberal states and societies is justified in so doing,\" and in light of this he argues both that \"liberalism _is_ intrinsically imperialist\" and that we should \"understand the attractions of liberal imperialism and not flinch,\" before immediately warning against \"succumbing to that attraction,\" chiefly on the pragmatic grounds that imperialism usually doesn't work in practice. The implication, of course, is that if it did work liberal imperialism would be legitimate in a wide range of cases.22 While the vast majority of contemporary liberals would reject Ryan's framing of the issue, insisting that there is a fundamental difference between humanitarian intervention and imperialism, that difference is rarely spelt out, and when it is the reasoning is usually based on a very narrow conception of empire and imperialism. Once again, it is the choice of definitions (and the interpretation of polyvalent political terms) that shapes the parameters of the theoretical debate, as well as its political complexion.\n\nThe bulk of the recent literature on liberalism and empire employs variations on the theme of historical contingency. Scholars differ chiefly over where they place the emphases and on how much continuity and change they discern in the historical development of liberal ideology. In the following section, I outline some of the key contributions to this debate.\n\nIntertextual Empire: Writing Liberal Imperialism\n\nUday Singh Mehta's _Liberalism and Empire_ , published in 1999, set the terms for much of the recent scholarship.23 His sophisticated analysis is as much epistemological as ethical. Drawing principally on John Locke and John Stuart Mill, he contends that liberalism encodes a particular vision of historical development and a preordained response to it. Incapable of respecting the \"unfamiliar,\" defined in terms of radical difference, liberal thought is marked by a \"singularly impoverished understanding of experience.\"24 When liberals confronted alterity they (almost) invariably judged it through reference to an antecedently fixed standard of evaluation, rooted in Eurocentric conceptions of what it means to be fully human and\/or a legitimate society. While liberalism claimed the mantle of universalism\u2014the \"cosmopolitanism of reason\"\u2014it was deeply parochial, seeking \"relentlessly\" to \"align or educate the regnant forms of the unfamiliar with its own expectations.\"25 Indians were thus portrayed as backward due to their failure to conform to purported universal norms of rational conduct. On this account, the liberal dream of disembodied reason is a cognitive technology for imaginatively assimilating the unfamiliar to a pre-given local structure of rationality. Liberal empire is the product of a loaded encounter between abstract universalism and the concrete lifeworlds of other peoples.\n\nAccording to Mehta, the nineteenth century witnessed the climacteric of the liberal \"urge\" to empire, as liberals grafted a heavily over-determined vision of civilization and historical progress onto a Lockean account of rationality. The result was a developmental picture that bifurcated the world into those (coded as \"adults\") who possessed reason and were thus capable of self-government and those (coded as \"children\") who required tutelage to bring them up to the required standard. Liberals, in other words, were committed to what Dipesh Chakrabarty famously termed the \"waiting room\" view of history, a view that \"came to non-European peoples in the nineteenth century as somebody's way of saying 'not yet' to somebody else.\"26 The \"standard of civilization\" stratified human reason as well as geographical space, identifying a differential capacity for \"improvement\" among assorted human groups. Underpinning Mehta's theoretical argument is a sweeping historical claim: liberalism has been an imperial ideology from its inception in seventeenth-century Europe. Its two leading figures\u2014Locke and Mill\u2014provide the intellectual scaffolding for enduring liberal justifications of empire.\n\nWhile Mehta's argument is theoretically powerful, its scope and thus its ultimate force are obscure. He oscillates between a weak and a strong thesis. The anthropomorphic language of \"urge\" and \"impulse\"\u2014as if liberalism was a self-realizing ideological formation\u2014might be read as endorsing the necessity thesis. Thus he insists that the imperial urge is \"integral\" to the \"political vision\" of liberalism.27 This is how his argument has often been interpreted. But elsewhere Mehta qualifies the contention. \"Urges can of course be resisted, and liberals offer ample evidence of this ability, which is why I do not claim that liberalism _must be_ imperialistic, only that the urge is _internal_ to it.\"28 This is equivocal. If by \"urge\" Mehta means that liberal thought contains theoretical resources that can be employed to justify empire, then few would dissent, but if he means either that authentic liberals must always support empire or alternatively that a special act of will or theoretical circumspection is required to stop liberals becoming imperialists\u2014as the main thrust of the book seems to suggest\u2014then this position is hard to sustain, not least because the concept of \"urge\" is too vague and indeterminate to do the explanatory work required. After all, liberalism contains plenty of other \"urges,\" some of which can underpin the critique of empire, including a concern with the dangers of state coercion, individual freedom, toleration, collective self-government, and universal moral equality. Hence Frederick Cooper's riposte that the \"urge\" to anti-imperialism is also \"internal to it.\"29 What matters is the lexical ordering or conceptual configuration of such \"urges\" in any given context, and Mehta fails to establish that the urge to empire is uniformly prioritized either across the history of liberalism or within the catholic expanses of Victorian liberal thought. Finally, it isn't clear where Mehta draws the discursive boundaries of liberalism. He suggests, for example, that anti-imperial forms of liberalism coexisted with the civilizing vision, and to make this case he counterposes the \"cosmopolitanism of sentiment\" articulated by Hume and especially Burke to the \"cosmopolitanism of reason,\" defining it as part of an \"other liberal tradition,\" though to muddy the waters further he also labels Burke a conservative.30 If we acknowledge this other tradition, however, the ostensible \"urge\" to empire is not internal to liberalism, but rather to specific articulations of it. On either the weak or the strong reading, though, Mehta suggests that only through misunderstanding or suppressing some of their own basic theoretical commitments can (most) liberals avoid becoming imperialists.\n\nThree prominent analyses\u2014by Sankar Muthu, Jennifer Pitts, and Karuna Mantena\u2014offer alternative accounts of the connections between universalism and the project of empire.31 In _Enlightenment against Empire_ Muthu targets the pervasive claim that late eighteenth-century intellectual life in Europe was shaped by a monolithic \"Enlightenment project\" complicit in imperial expansion. Despite their manifest differences, he argues that Kant, Diderot, and Herder shared philosophical commitments that underpinned a thoroughgoing critique of European conquest. The condition of possibility for anti-imperialism was a radical transformation in understanding what it meant to be human, a shift that facilitated three other philosophical claims. First, and most fundamentally, it grounded an account of basic moral equality, the view that all humans \"deserve some modicum of moral and political respect\" in virtue of their shared humanity. This was combined with an argument that humans were \"fundamentally cultural beings,\" immersed in a complex web of attachments, the spatio-temporal variation of which produces difference. Finally, Muthu contends that Enlightenment anti-imperialism was premised on a robust account of \"moral incommensurability and relativity,\" meaning that individuals and communities could not be judged according to a single scale of value.32 In a retort to Mehta's starkly drawn contrast between the (abstract) universal and the (concrete) particular, Muthu suggests that when tempered by recognition of cultural agency universalism offers a potent resource for anti-imperialism. \"[A]n increasingly acute awareness of the _irreducible plurality_ and _partial incommensurability_ of social forms, moral values, and political institutions engendered a historically uncommon, inclusive moral _universalism_.\"33 His acute philosophical analysis is tethered to a historical argument. Contra Mehta, Burke was no \"lone voice in the wilderness\" but rather one among a constellation of brilliant thinkers who assailed the injustices of European conquest during the second half of the eighteenth century. This moment, though, was an \"historical anomaly,\" for European thought had previously been dominated by fantasies of the \"noble savage,\" which denied basic moral equality, while the period that followed it was defined by the victory of aggressive imperial ideologies. \"By the mid-nineteenth century, anti-imperialist political thinking was virtually absent from Western European intellectual debates, surfacing only rarely by way of _philosophically obscure and politically marginal figures_.\"34 I return to this bold historical claim later in the chapter.\n\nJennifer Pitts pushes the analysis deep into the nineteenth century. She offers a convincing corrective to Mehta, suggesting that liberalism is best understood as a \"complex ideology whose exemplars share family resemblances rather than any strict doctrine.\"35 It contains resources to both combat and justify empire. She too identifies a resplendent period of enlightenment anti-imperialism followed by a pronounced \"turn to empire,\" though unlike Muthu she explicitly narrates this as part of the history of liberalism, refiguring it as an ideology born in a dazzling moment of imperial critique. Rather than its besetting original sin, exemplified by Locke's complicity in the colonization of the Carolinas, empire is posited as a tragic betrayal of its early promise. She casts Burke, Bentham, and Adam Smith in the anti-imperial role and tracks the emergence of \"imperial liberalism\" through James Mill's writings, before pinpointing its full realization in the work of Alexis de Tocqueville and John Stuart Mill. Pitts presents her argument as (among other things) a rejoinder to Mehta's overly reductive account of liberalism, although given Mehta's ambiguity it can also be read as a subtle fleshing out of the underdeveloped \"weak thesis\" hinted at in _Liberalism and Empire_ : the recognition of an alternative liberal tradition containing a battery of arguments to level against empire. With admirable dialectical skill, Pitts demonstrates how her catalog of anti-imperial liberals rejected European expansion and displayed considerable respect for societies at different stages of socioeconomic development. Thus while Smith deployed a stadial theory to explain the emergence of commercial society, he accounted for differential patterns of growth in terms of serendipitous historical circumstances rather than the intrinsic faults of other peoples. A \"theory of progress,\" Pitts argues, \"need not imply a pejorative assessment of less 'advanced' peoples or support for European colonial expansion.\"36 However, she continues, the empathetic subtlety that characterized late eighteenth-century political thought was supplanted during the course of the nineteenth century by a crude binary division of the world into civilized\/barbarian. In this narrative John Stuart Mill is presented as the apotheosis of imperial liberalism. Her historical timeline matches that of Muthu. By the mid-nineteenth century, \"we find _no prominent political thinkers in Europe_ questioning the justice of European empires.\"37\n\nKaruna Mantena argues for an alternative chronology, maintaining that liberal \"ethical\" visions flared only for a brief moment, before being superseded with a different form of imperial justification during the second half of the nineteenth century. \"Late imperial ideologies and discourses of justification were grounded in a common, conservative _opposition to the liberal project_.\"38 On this account, liberal confidence in imperial progress\u2014predicated on \"the language of a civilizing rule and the goal of self-government\"\u2014was corroded by the Sepoy Rebellion of 1857 and subsequent episodes of resistance.39 Under the influence of Henry Maine, an eminent scholar of comparative jurisprudence, imperial ideologists adopted a \"culturalist\" narrative, which emphasized the Sisyphean difficulty of transforming colonized spaces in the image of liberal modernity.40 Thus from the 1860s onwards we see a \"decisive turning away\" from liberal arguments to a view that emphasized the protection of (newly conceptualized) \"native communities.\"41 Social theory rather than political philosophy provided a novel intellectual foundation for imperial ideology.42 Maine and his followers argued for the prolongation of empire on the grounds that intervention had so weakened traditional communities that retreat would herald disaster. \"Native society here functioned both as a pretext and solution, as an _alibi_ for the fait accompli of empire.\"43 Mantena reimagines the lineage between Burke and Mill, viewing them less as antipodes than as avatars of a tradition of \"ethical\" imperialism. Mill is presented as a \"crucial transitional figure,\" a bridge between the exuberant optimism of the 1830s and 1840s and the later period of disenchantment, rather than the assured culmination of liberal imperial ideology.44 The shift to alibis had important practical effects, shaping the policy of \"indirect rule\" that was enacted by British imperial administrators, including Lugard in Africa and Cromer in Egypt. Furthermore, it established the intellectual groundwork for the League of Nations mandate system (itself a model for UN practices in the 1990s and beyond).45\n\nEven as Mehta's account comes closest to the necessity thesis, he ultimately pulls back from endorsing it, and in so doing weakens the general thrust of his argument, leaving its theoretical and political implications unclear. Muthu and Pitts advocate variations on the theme of contingency, with both postulating a late eighteenth-century moment of anti-imperialism supplanted by an overwhelming turn to empire. The contemporary lesson is clear: while liberalism is not intrinsically imperial, liberals must avoid replicating the corrupted position adopted by their nineteenth-century predecessors. Mantena, meanwhile, complicates this narrative arc by stepping outside the canon and rerouting the historical trajectory, suggesting that liberal imperial optimism was neither inscribed in the ideology from its very inception, as with Mehta, nor was it as pervasive in the nineteenth century as Muthu and Pitts imply. It was instead a brief, anomalous episode tied to specific developments in the empire in India. Diverging over the three issues I outlined earlier in the chapter\u2014conceptual architecture, contemporary legacy, and historical narrative\u2014these bold lines of argument have helped to set the coordinates for debate over liberal visions of empire during the long nineteenth century.\n\nOn Settler Colonialism\n\nDuring the 1980s and 1990s the field of imperial history was revivified by an infusion of new theoretical approaches, the most influential of which was postcolonialism.46 This intervention served both to illuminate and obscure. One significant consequence was a narrowing of geographical focus, with India looming so large that it sometimes performed a metonymic function, standing for empire as a whole and nearly exhausting the space of argument and interpretation.47 As a sympathetic observer noted in 1998, \"[p]ostcolonial commentary in the nineties has been remarkable in the degree of its engrossment with India.\"48 The settler empire was relegated to the margins of debate, despite its historical importance. Scholars of nineteenth-century political thought have tended to follow this general trend.\n\nThe distorting effects of this gaze assume different forms. Witness, for example, the attention lavished on Edmund Burke. While Pitts offers a qualified view of his enlightened credentials, Mehta, Muthu, and Frederick Whelan celebrate him as a coruscating scourge of European imperialism.49 Yet Burke's newfound status as a progressive hero is a product of selection bias, based on emphasizing his commentary on India while downplaying his views on other imperial spaces. India was the exception not the rule in Burke's sympathies\u2014and even then the extent of his \"anti-imperialism\" is open to serious question.50 A very different picture emerges if we turn to his writings on North America and the Caribbean. Committed to a civilizing vision of history, he promoted a reformed slave trade and denied what Muthu would call \"cultural agency\" to \"savage\" populations. Until the eve of the American Revolution he \"heartily endorsed British imperial aggrandizement and colonialism, and defended at length the subjugation of Native Americans and Africans alike to that end.\"51 Burke argued that British domination helped civilize those benighted souls, chiefly through prolonged exposure to commerce and Christianity.\n\nHowever, the main lacuna created by focusing relentlessly on India is the downplaying (even absence) of settler colonialism in accounts of liberalism and empire. During the nineteenth and twentieth centuries the settler empire played a fundamental role in British imperial ideology, and it was central to liberal visions of world order. Indeed British liberals often privileged the settler colonies over the imperial territories in Africa, Asia, and the Caribbean, viewing them as both more legitimate and more durable. To ignore this is to miss much of what constituted the relationship between liberal political thought and empire in the nineteenth century (and beyond). It was in the settler colonies, not India, that many liberals found the concrete place of their dreams.\n\nOne possible rejoinder to this line of argument is that even if the nineteenth century has been overlooked, settler colonialism has played a formative role in elucidating the connections between liberalism and empire due to the prominence of John Locke in recent scholarship.52 Forty years ago John Dunn observed that Locke had \"worn many faces\": \"only begetter of the Enlightenment, self-conscious and dedicated ideologist of the rising bourgeoisie, greatest of the exponents of English liberal constitutionalism... majoritarian populist, most shifty and esoteric of the treasonous clerks.\"53 Now add to that another face: progenitor of liberal empire. Since Locke was involved in the project to legitimate colonization in North America, and since he is now regarded as one of the founding fathers of liberalism, the inference is clear: \"T]he liberal involvement with the British empire,\" Mehta declares, was \"largely coeval with liberalism itself.\"54 On this account, liberalism was born imperial, the complicity of Locke setting a pattern that was to be repeated down the centuries and into the present. However, I am not persuaded that we can learn much about liberal accounts of empire (in general) by studying Locke. As I show in [chapter 3, Locke was not widely regarded as a liberal until the twentieth century; his conscription to the canon occurred a century after liberalism emerged as an explicit body of political thinking. We would do well to remember Quentin Skinner's warning about the dangers of the \"mythology of prolepsis,\" a mythology in which the attribution of retrospective significance to an event, thinker, or text clouds understanding of their meaning to historical actors. Indeed Skinner identifies Locke's supposed paternity of liberalism as a paradigmatic example, noting that while it might be plausible to describe Locke as a founding figure of liberal political thought, insofar as that is how he came to be seen, it would be a mistake to call Locke himself a liberal.55 Moreover, the study of Locke sheds little light on imperial ideology during the nineteenth century, for he was rarely invoked by Victorian imperialists or their successors, and their justificatory claims seldom drew on Lockean theoretical machinery.56 Moreover, Lockean arguments could just as easily be employed for anti-imperial ends, as when they were utilized to defend the rights of native property ownership in Bengal.57 Locke's relative insignificance at the time should induce skepticism about the general salience of his views on empire (important as they are to understanding the character of his own political thinking). Liberal attitudes to empire are illuminated more clearly by turning attention to the nineteenth century, the era of liberal ascendency and the apogee of Western imperial ambition.\n\nOther chapters in this book explore the justificatory arguments offered in support of the settler colonies. Here it is simply worth noting that they were many and varied, spanning economic, geopolitical, social, and racial claims. It is possible, though, to trace a general shift in the representation of the settler empire, from a time when it barely registered in metropolitan consciousness to its elevation to the very heart of political debate. During the 1830s and 1840s a group of \"colonial reformers\" set out to overturn the economic orthodoxy that colonies were drains on the \"mother country\" and colonists disreputable emigrants\u2014or worse, criminals banished beyond the horizon\u2014worthy of little attention and even less support. The discourse of political economy was central to the revolt, as thinkers grappled with the urgent \"social question.\" In the late eighteenth and early nineteenth centuries, colonies had often been thought of, if at all, as dumping grounds for excess population. As Charles Buller explained, emigration policy was seen as \"little more than shoveling out your paupers to where they might die, without shocking their betters with the sight and sound of their last agony.\"58 The colonial reformers, though, sought a more far-reaching reappraisal of British political economy. Challenging Ricardian orthodoxy, they diagnosed the stagnation of the British economy as a product of excess domestic capital and labor supply, which depressed wages and profits. Their prescribed solution was \"systematic colonization,\" which would allow for the productive export of capital and labor.59 Looking back on the early years of the reform movement from the vantage point of 1864, the political economist J. E. Cairnes praised this collection of \"visionaries\" for elaborating \"[f]or the first time something like a sound and complete theory of colonization.\" It posited that colonization \"confers a double benefit: it relieves the old country from the pressure of its superabundant population, and gives a field for its unemployed capital; while, at the same time, by opening up new lands and placing their resources at her disposal, it widens indefinitely the limits which restrain her future growth.\"60\n\nWhile Nassau Senior, Robert Torrens, and Herman Merivale all played important roles in proselytizing the colonial reform vision, the most significant figure was the mercurial E. G. Wakefield, who developed an ambitious scheme predicated on the role of government in regulating the distribution of colonial land. He argued that if land prices were set artificially high, profits could be utilized for supporting further emigration, towns would grow as centers of civilization, and British class hierarchies could be replicated.61 Moreover, he insisted that contrary to existing practice, colonists should be selected for their suitability as pioneers. Above all, he and the other reformers stressed the importance of granting the new colonies a significant degree of self-government.62 Under the degraded, haphazard old system, \"colonies and colonists are in fact, as well as in the estimation of the British gentry, inferior, low, unworthy of much respect, properly disliked and despised by people of honour here, who happen to be acquainted with the state of society in the colonies.\"63 He believed that applying the lessons of political economy would transform the image and the reality of colonization, at once remaking them as economically productive and socially respectable. This argument exerted an abiding influence on John Stuart Mill, among many others, and it is little wonder that Marx's critique of colonialism in _Capital_ focused almost exclusively on Wakefield's work.64\n\nThe reform movement, then, reimagined the colonies as productive spaces for economic growth, outlets for helping to defuse combustible domestic social conditions, fecund territories for the reproduction of civilized societies, and as nodes in a globe-spanning imperial security apparatus. From then on, and especially following the midcentury grant of significant constitutional autonomy to the colonies in Canada and Australia, the settler empire assumed a privileged role in the political visions of many British thinkers, including\u2014and perhaps especially\u2014liberals. The transformation of the colonial empire threatened its ultimate dissolution. Granting self-government to the colonies, under the rubric of \"responsible government,\" led to a widespread sense that they were inevitably bound for independence. This line was articulated most forcefully by Goldwin Smith.65 In a similar vein, Cairnes argued that the colonial empire had \"reached its natural goal.\" But all was not lost, and like Smith he argued that what remained would fulfill the admirable role of the ancient Greek colonies. \"Instead of a great political, we shall be a great moral, unity; bound together no longer indeed by Imperial ligaments supplied from the Colonial Office, but by the stronger bonds of blood, language, and religion\u2014by the common inheritance of laws fitted for free men, and of a literature rich in all that can keep alive the associations of our common glory in the past.\"66 It was this sense of inevitability that John Stuart Mill challenged in the _Considerations on Representative Government_ , arguing that although the colonies were free to seek independence it was in both their interest and that of the \"mother country\" to remain united. Anxiety about the political status of the settler colonies catalyzed a major debate over the future of the empire in the closing decades of the century.67\n\nBetween 1870 and the outbreak of the First World War, the settler empire assumed an unprecedented role in British political discourse. It was widely acknowledged that the colonies were vitally important elements of the imperial system, and that unless something was done, and done soon, the logic of self-government identified by Smith and Cairnes, as well as the embryonic development of settler nationalisms, would eventually lead to independence. Advocates of \"imperial federation\" sought to establish permanent bonds between Britain and its settler colonies, creating a vast racial polity\u2014even a global federal state\u2014spanning oceans and continents. Many of the leading ideologues of the movement were liberals, including Seeley, its most influential cheerleader, and numerous liberal politicians were only too happy to lend their support, including W. E. Forster and Lord Rosebery.68 I have explored this topic at length in _The Idea of Greater Britain_ , and I address it in several chapters in this book. Those opposed to such grandiose institutional plans, such as Freeman and Goldwin Smith, still tended to emphasize the importance of settler colonies, whether they remained politically bound to the \"mother country\" or secured independence. All thought it a topic of great significance. The historian W.E.H. Lecky was far from alone in his belief that it was \"unspeakably important\" to the \"future of the world that the English race, through the ages that are to come, should cling as closely as possible together.\"69 Indeed it was a commonplace. The colonial unification discourse blurred into another set of arguments, popular during the 1890s in particular, that demanded the \"reunion\" of Britain and the United States, the two great \"Anglo-Saxon\" powers ordained to reorder the world. As with imperial federation, plans for transatlantic reunion stretched from the moderate to the radical, from closer friendship to full federal union, and once again liberals were among the most vociferous exponents. Andrew Carnegie, James Bryce, A. V. Dicey, and W. T. Stead all advocated transatlantic (racial) union of one kind or another.70 In chapter 8, I track some of the descendants of these arguments across the arc of the twentieth century.\n\nAccording to the conventional Victorian understanding of the term, \"colonies\" were territories claimed by emigrants from the \"mother country\" with the intention of founding permanent communities that replicated key aspects of the original society. This was an act\u2014or at least a fantasy\u2014of mimetic transfer. The aim of colonization, Gladstone proclaimed in 1858, \"was to reproduce the likeness of England, as they were doing in Australia, New Zealand, North America, and the Cape, thereby contributing to the general happiness of mankind.\"71 This kind of argument was predicated on an imagined isomorphism between mother country and colony. The colonies were populated, as one scholar put it, by people \"predominantly blood of our blood, bone of our bone, with our language, our laws (in the main), and our manners.\"72 This meant, chiefly, what we might call the _second settler empire_ : the colonies in Canada, Australia, New Zealand, and (more ambiguously) South Africa. From the mid-nineteenth century onwards, the normative and legal distinction between settler colonies and the rest of the empire was inscribed evermore deeply into the elite British political imagination. Presented as radically different from\u2014and often superior to\u2014other imperial spaces, they were the subject of different ideologies of justification and governance.73 For Seeley, \"[t]he colonies and India are in opposite extremes. Whatever political maxims are most applicable to one, are most inapplicable to the other.\"74 The liberal historian G. P. Gooch likewise emphasized the \"vital distinction\" between empire and colony. \"In passing from Colonies to dependencies we enter a different world, to which different principles must be applied.\"\n\nIndeed the very circumstances that call forth the enthusiasm in the one case compel us, in some degree, to withhold it in the other. Where our flag flies over willing subjects and the institutions of self-government our rule may count on great reserves of moral and material strength; where it does not, our material strength may be great, but the moral basis is either weak or totally lacking.75\n\nOn this account, the empire was imaginatively bifurcated, with the self-governing colonies assigned to a completely separate category of rule and ethico-political judgment.\n\nTwo key thematics underpinned the demarcation between the settler empire and other kinds of foreign rule: _racial identity_ and _self-government_. Colonists were figured as always already civilized, and as carrying with them a bundle of rights and obligations that marked them indelibly as both facsimiles (or not-quite-facsimiles) of those inhabiting the mother country and radically different from (and superior to) other peoples they encountered\u2014and especially those they invaded and dispossessed. This set of assumptions underwrote the argument for self-government. As another liberal historian, C. P. Lucas, once put it, \"[t]he ground of self-government is, that those who are in the colony are on the same level in physique and intelligence with those who are in the mother country, and that, being on the spot, they are best able to take care of themselves.\"76 The original inhabitants were in turn pictured as incapable, as immature, lacking in both rationality and competence, and thus as unworthy of political or social equality. The logic of settler colonialism, then, was a powerful mix of intraracial egalitarianism and interracial exclusion. The British settler empire enacted a version of what Charles Mills terms the _racial contract_ : a vision of the just polity predicated on the ascription of political equality to whites and its concurrent denial to nonwhites. It thus expressed a form of _Herrenvolk_ ethics, a normative system intended to structure settler societies as racially exclusive communities.77 Indigenous peoples continue to suffer its pernicious effects.\n\nSettler colonialism is a distinct modality of imperial governance, and one that until recently was too often conflated with, or subsumed under, more general models of domination.78 It is a process comprising a four-dimensional interaction between the metropole from which the settlers departed, the settler colonial community, the indigenous populations whose lands and lifeworlds were transformed or occupied by the settlers, and those non-indigenous non-settlers living within or moving through the settler colonial space.79 The intricate and shifting relations between these various elements shape the history\u2014and the present\u2014of the settler colonial condition. It was typically manifested in the instantiation of a highly ambivalent form of sovereignty, a claim that settlers exerted over the indigenous populations inhabiting the land they invaded, which served as a source of friction and constant negotiation with the government of the metropolitan center.80\n\nModern settler colonialism, British or otherwise, almost invariably relies on violence against indigenous peoples and everyday forms of humiliation, exclusion, and racial segregation, some informal, some sanctioned by law. As Patrick Wolfe argues, it is an \"inclusive, land-centred project that coordinates a comprehensive range of agencies, from the metropolitan centre to the frontier encampment, with a view to _eliminating_ Indigenous societies.\"81 Colonial eliminativism encompasses assorted practices, including assimilation, displacement, legal domination, intimidation, and the use of lethal violence, even genocide.82 The purpose is to secure territory while destroying the sense of peoplehood of those supplanted by the settler community. This is not to suggest that all settlers, politicians, colonial advocates, and London-based officials necessarily thought of it in those terms, or that practices of colonialism were everywhere and always the same\u2014far from it.83 But that was what it usually entailed.84 Even the most purportedly \"benign\" forms of erasure resulted in destruction. \"Here, in essence, is assimilation's Faustian bargain\u2014have our settler world, but lose your Indigenous soul. Beyond any doubt, this is a kind of death.\"85 Moreover, settlement is not an autochthonous founding moment superseded by postcolonial state formation, but rather a process of domination with effects that continue to shape the lifeworlds of indigenous populations long after the formal age of empire. Invasion is a \"structure not an event.\"86 Indeed settler colonialism has generated some of the most challenging problems in the contemporary world, from the desperate plight of the Palestinian people to pressing questions about the rights of indigenous peoples within purportedly liberal democratic polities.87 Political theory has barely begun to confront its implications.\n\nThe settler project incited much debate. Some celebrated the cleansing violence of its professed \"civilizing\" mission, while others damned it. The violence of founding was often naturalized, imagined as an inevitable fate for \"savages\" who came into contact with superior peoples\u2014a sad but necessary feature of historical progress.88 Aboriginal protection societies sprang up, and colonial officials tried to rein in the worst excesses, though such campaigns rarely managed to stop the attempted extirpation of existing communities. \"[I]n spite of their human likeness,\" the Tasmanians, H. G. Wells wrote in _The War of the Worlds_ (1898), \"were entirely swept out of existence in a war of extermination waged by European immigrants in the space of fifty years.\"89 Over half a century earlier, the political economist Herman Merivale was equally clear about the consequences of settler colonialism. \"Desolation goes before us,\" he lamented, \"and civilisation lags slowly and lamely behind.\" South Africa, Van Diemen's land, Newfoundland, the interior of the United States, New Zealand: all were marked by the \"ferocity and treachery\" of \"civilised\" men and governments.90 In an intriguing twist on normative arguments about the rectification of historical injustice, the recognition of colonial ultra-violence could even be invoked to legitimate empire. The Cambridge theologian and philosopher Alfred Caldecott argued that as a consequence of their despicable treatment of the Australian \"nature people,\" the British had a moral obligation to continue the educative mission of empire: in India, \"we may redeem the past.\"91 Gilbert Murray outlined a similar argument. \"If ever in the lifetime of the world a duty has been laid upon a nation,\" he wrote, \"a great and manifest obligation lies on us towards our subject peoples, the duty of endeavoring by strenuous and honest sympathy, justice, and even magnanimity, to obliterate our cruel conquests, and justify our world-wide usurpation.\"92 Only future empire could erase the moral stains of past empire. Merivale was optimistic that the \"ferocity and treachery\" in the colonies could be ameliorated. \"Our errors are not of conception so much as of execution.\"93 By locating (or deflecting) responsibility in this manner, such arguments denied the systemic character of the violence, reducing it to the excessive, localized behavior of a few rogue settlers.\n\nMost accounts of settler colonialism were marked by an ideological aporia. Colonial identities are shaped by settler _mythscapes_ , evocative narratives that embody claims about the origins, the legitimacy, and the destiny of the enterprise.94 The founding moment is typically figured as heroic, the epic fabrication of new \"civilized\" communities in the wilderness. Legitimacy is usually grounded in a dual claim: of the civilizational superiority of the settler over the indigenous and of the productive recuperation of under-utilized or vacant land. Plotting colonial destiny was more contested, oscillating (in the British case at least) between dreams of future political independence and of assuming a vanguard role within an expansive imperial formation, a better (global) Britain. Settler mythscapes were invariably marked by a constitutive forgetting of the claims of indigenous populations.\n\nThe play of similarity and difference was central to British representations of both the colonies and India. Early in the nineteenth century, British imperial ideologues often sought out points of similitude between the conquered and the conquerors in India, though as the century wore on the call of radical difference came to predominate.95 But expressions of similarity can assume contrasting forms. In the Indian case, what was (occasionally) imagined was similarity despite apparent difference, a basic uniformity grounded either in professed essential human characteristics or (more frequently) a shared \"Aryan\" heritage, traceable to an ancient ur-race.96 Similarity was thus embedded in a deep history of human evolutionary development that both explained its uneven progress over the preceding centuries and legitimated the hierarchical ordering of the contemporary world. It could only be rendered intelligible by ignoring surface phenomena and physical appearance. Settler colonialism was predicated on a different logic of identity. Colonists were seen as reproductions of the basic metropolitan archetype, as passing the minimum threshold of civilized life even as they often failed to live up to its very highest standards. The variation was reflected in subtly contrasting metaphors of maturity. While Chakrabarty and Mehta correctly highlight the authoritative role played by the trope of childhood in legitimating British rule in India, the rhetorical strategy was ubiquitous and assumed different forms across the space of empire.97 Liberals routinely applied it to the settler colonies, but they did so in a way that goes to the heart of the contrasting ideological justifications of colonialism and imperialism. Whereas in India (for example) the language of childhood was applied to the individual subjects of empire, connoting a deficit of rationality and a lack of capacity for individual autonomy and collective self-government, it was applied to the colonies as a whole, not to the individual settlers. It was the political institutions and socioeconomic systems of the nascent communities that were coded as immature and in need of (some) guidance. While settlers were frequently the butt of metropolitan condescension, they were accepted as fully rational autonomous agents and granted civilizational standing. Instead, the individuated language of childhood was often displaced onto indigenous populations.\n\nDespite general agreement on the distinctiveness of settler colonialism, there were some conceptual disputes over its exact meaning. In an influential text published in 1841, the liberal politician and writer George Cornewall Lewis defined a colony as \"a body of persons belonging to one country and political community, who, having abandoned that country and community, form a new and separate society, independent or dependent, in some district which is wholly or nearly uninhabited, or from which they expel the ancient inhabitants.\"98 \"Of colonization,\" wrote Wakefield, \"the principal elements are emigration and the permanent settlement of the emigrants on unoccupied land.\"99 He then distinguished between two classes of colony, the _dependent_ , which was still subject to a political connection, and the _independent_ , which was not. The status of colony, then, was derived from the initial practice of colonizing rather than from any enduring formal political relationship between the founding and the founded communities. Writing half a century later, the historian Hugh Egerton instead accentuated the necessity of a _continuing_ political tie. A colony, he maintained, was \"a community, politically dependent in some shape or form, the majority, or dominant portion, of whose members belong by birth or origin to the Mother country, such persons having no intention to return to the Mother country, or to seek a permanent home elsewhere than in the colony.\"100 These accounts differ over the kind of connection thought necessary to classify a political community as a colony. This disagreement had some substantive implications. For example, it generated divergent classifications of states that had once been formal colonies but were now independent, a question relevant for thinking about both the ontological status of the United States and the future unity of the British settler empire. On the former account, for instance, the United States was still a colony of Britain, albeit an autonomous one. \"To my view,\" Wakefield argued, \"the United States of America, formed by emigration from this country, and still receiving a large increase of people by emigration from this country, are still colonies of England.\"101 On the latter account, it ceased to be a colony the moment it gained political independence. This was the most common position. Seeley evaded this thorny conceptual issue altogether in _The Expansion of England_ by stipulating that the United States \"are to us almost as good as a colony,\" since \"our people can emigrate there without sacrificing their language or chief institutions or habits.\"102 On this more ambiguous account, the United States was once a _de jure_ colony but was now best understood as a (quasi) _de facto_ one.\n\nOnce we expand the interpretive aperture to encompass settler colonialism, the \"anti-imperialism\" of the Enlightenment begins to look rather less clear-cut. As Muthu concedes, Diderot affirmed the value of colonies, while Burke was a zealous proponent of settler colonialism in North America.103 Nor was Bentham immune. At the turn of the century he commended the socioeconomic benefits of settler colonization, and towards the end of his life he produced an unpublished plan for a new colony in South Australia.104 Moreover, some of the most acerbic nineteenth-century \"anti-imperialists\" endorsed settler colonialism. In _Imperialism_ , J. A. Hobson distinguished between \"genuine colonialism\" and \"Imperialism.\" Whereas colonialism represented the progressive spread of civilization through settlement, imperialism meant the \"expansion of autocracy.\" As I discuss in chapter 14, he also argued that one of the problems with the \"new imperialism\" of the 1880s and 1890s was that it undermined the chances of securing the unification of the British state and its settler colonies.105 Like that of many self-professed anti-imperialists, his target was a particular species of empire, not all forms of Western control or expansion. Paying attention to settler colonialism, then, reconfigures the way in which we understand \"imperialist\" and \"anti-imperial\" arguments since the late eighteenth century.\n\nMehta briefly acknowledges the discrepancy between nineteenth-century justifications of empire and settler colonialism, but he draws the line in a misleading fashion. He regards the former as \"crucially predicated\" on notions of tutelage and kinship, while the latter involved the peopling of distant territories where there \"was often an ideology and practice of exterminating aboriginal populations.\" Since liberals did not countenance extermination, he concludes that the topic can be left aside.106 There are three problems with this brief account. First, as we shall see, liberal justifications of empire were not exhausted by tutelary arguments. Second, arguments for settler colonialism, liberal or otherwise, usually did not explicitly invoke extermination (though they often entailed elimination). Finally, and conversely, some liberals (including Spencer) did discuss the eventual extinction of indigenous populations, albeit as an inevitable function of historical progress rather than a policy to be actively pursued.107\n\nArguing that colonialism was compatible with (or an expression of) basic liberal normative commitments, liberal thinkers often claimed the settler world as their own progeny. It was liberals, they boasted, who brought self-government to the colonies, thus rescuing the empire from potential dissolution and laying the foundation for future British greatness. According to Hammond, \"[a]ll that has made this Commonwealth great and strong is the work of Liberalism.\"108 Hobhouse agreed: \"The Colonial Empire as it stands today is in substance the creation of the older Liberalism.\"109 This was not simply a claim about intellectual patrimony, for it was conjoined with an argument that the settler colonies were both more important and more legitimate than the dependent empire. Their high degree of internal self-government placed them on sound moral and political foundations. \"Where is it that, after all, the great strength of the Empire resides,\" asked one liberal imperialist. \"Not in the great military dependencies of India, Egypt and the Far East. No! It is in the free communities which have sprung from these shores and which have carried to the ends of the earth the name and fame of Britain and the strength of British character.\" This was \"true Imperialism.\"110 John Morley, esteemed historian and prominent liberal politician, adopted a similar line.\n\nBy Imperialism the better men of the school understood a free and informal union with the Colonies, combined with a conscientious and tolerant government of tropical dependencies. This was in essence the conception of the Empire bequeathed by the older generation of Liberals, and precisely the antithesis of present-day Imperialism, the operative principle of which is the forcible establishment and maintenance of racial ascendency.111\n\nMorley thus espoused a variation of the common distinction drawn between empire and imperialism, contrasting _old_ (reputable, liberal) against _new_ (degraded, aggressive) forms of imperialism.\n\nAlterity, then, acted as a repellent not a magnet. An empire encompassing radically different institutions and populations was both fundamentally unstable and incapable of serving as a platform for further political integration. While few liberals advocated immediate withdrawal from India, or denied that Britain had a \"duty\" to help improve its subjects, they recognized that it was, and would always remain, alien, exotic, different\u2014even if it was \"civilized\" to the point where it was ready for self-government. It was precisely because of its alien character that it was impossible to regard as a site for realizing the true destiny of the English people. After stressing the importance of permanent unity between the settler colonies and the metropole, the novelist and liberal social reformer Walter Besant observed that India, despite its undoubted value, \"cannot be integrated\" and that \"our occupation... must remain, as it is, a strong, just hand, restraining and leading, but the hand of a foreigner.\" The future greatness of Britain resided instead in the \"Anglo-Saxon\" settler colonies.112 This was one of the central claims of Seeley's influential analysis in _The Expansion of England_. \"When we inquire into the Greater Britain of the future,\" he announced, \"we ought to think much more about our colonial than our Indian empire.\"113 Racial or cultural or national similarity\u2014the three interwoven in Victorian political consciousness\u2014exerted the greatest imaginative pull on liberal thinkers. The extended racial Self was accorded normative primacy over the alien Other.\n\nDue to their considerable political autonomy, some liberals argued that the settler colonies were not, strictly speaking, \"imperial\" spaces, and that as such they no longer formed part of the British empire. As Goldwin Smith put it in 1890: \"Over the colonies England has resigned all real power: they are substantially so many independent nations. The only empire, properly so called, which she now has is India.\"114 Empire, the authors of _Liberalism and the Empire_ wrote, was the rule of one nation over another, and the term was thus applicable to India but not to \"free\" Canada and Australia, which were \"grander evidences of England's greatness and solider elements in her strength than all those tropical provinces which she has won as a conqueror and holds as a foreign despot.\"115 Seeley argued that the British settler empire constituted a \"world-state\" rather than an empire, and that the latter designation was only appropriate for India. Empire, he counseled, \"seems too military and despotic to suit the relation of mother-country to colonies.\"116 Hammond reiterated the point: \"The name 'Empire' is charged with associations for which Liberals have little liking, and they would prefer to apply the term 'Commonwealth' to the confederacy of states which make up the dominions of the Crown.\"117 From this perspective, settler colonialism represented a different, perhaps nobler, kind of civilizing mission, defined by the construction of exemplary new political communities embodying the virtues of British freedom and law. Rather than civilizing backward native populations through direct tutelage, it instead helped to civilize humanity as a whole by simultaneously exporting the institutions and values of Britain to \"fresh\" territories, thus providing a shining model of how best to organize sociopolitical life. Combining \"imperium\" with \"libertas\" this type of empire had the potential to escape the historical fate of all previous instances, the inevitability of decline and fall (a topic I address in chapter 5). It would long outlast the transient occupation of India, Egypt, and even the Caribbean. Indeed some liberals regarded it as an embryonic form of cosmopolitical order, the herald of a future form of world government. Hence Hobhouse saw the colonial empire as a \"natural outgrowth of a common sentiment,\" and as \"one of the steps towards a wider unity which involves no backstroke against the ideal of self-government.\" Scanning the horizon, he offered it as a \"model\" of the coming \"International State.\"118\n\nA comprehensive understanding of liberal attitudes to empire, then, must pay more attention to settler colonialism than is usually the case. Settler colonies offered liberals a way of celebrating expansion and rule cleansed of traditional anxieties about foreign conquest\u2014the perennial corrupting dynamics of empire. Instead, they were premised on a comforting fantasy about the occupation of new lands, free of established institutions and settled communities. The result was both the founding of dynamic communities and a legacy of expropriation and horrific violence. This is a bequest that \"liberal democracies\" face (or refuse to face) to this day.\n\nThe Tyranny of the Canon\n\nIn chapter 3 I discuss various \"interpretive protocols\" that scholars employ to demarcate liberalism (and other politico-intellectual traditions). The most common protocol, the _canonical_ , constructs liberalism through analyzing one or more exemplary figures who are taken, whether implicitly or explicitly, to stand in for the whole. John Locke and John Stuart Mill often perform this role in the literature on liberal empire.119 While canonical approaches have their uses, they are incapable of generating satisfactory accounts of multifaceted political ideologies. Relying on an overly narrow evidentiary base, they cannot support felicitous generalizations about continuities and change in patterns of political thinking.\n\nMehta, Muthu, and Pitts all make bold historical claims based chiefly on interpretations of canonical thinkers. Whereas Mehta argues for a strong line of ideological continuity from Locke onwards, Muthu and Pitts identify a radical break at the end of the eighteenth century. However, the historical arcs that they carve through the long nineteenth century are in part artifacts of the canon of European political theory, a canon largely constructed during the twentieth century.120 If we expand the range of sources analyzed, a rather different picture emerges. In contrast to the narratives of the nineteenth century presented in their work, I would argue that the liberalism of the time was just as diverse, and contained just as much critical energy, as the intellectual world of the late eighteenth century. Leading politicians and thinkers expressed disdain for territorial expansion. Auguste Comte, for one, railed against the injustice of empire, focusing his attention on the French occupation of Algeria and the British in India.121 Cobden, to give an especially prominent British example, was both one of the most significant liberal politicians and ideologues of the age and a fierce (albeit somewhat inconsistent) critic of imperialism.122 He believed that the spread of free trade would corrode patriotism, eradicate the feudal scourge of war, and undermine the rationale for empire. In 1850 he wrote to John Bright that the world had \"never yet beheld such a compound of jobbing, swindling, hypocrisy, and slaughter, as goes to make up the gigantic scheme of villainy called the 'British rule in India.'\"123 Three years later he warned of \"our insatiable love of territorial aggrandizement,\" and lamented the \"deeds of violence and injustice which have marked every step of our progress in India.\"124 Lauded as one of the greatest philosophers alive, and certainly one of the most influential, Herbert Spencer was a vitriolic critic of empire from the 1840s until his death in 1902. In an emblematic British radical idiom he decried imperialism as the preserve of the governing elite, the aristocrats, military, clergy, and politicians.125 Recoding the common trope of \"civilisation versus barbarism,\" he argued that the pursuit of empire threatened the \"re-barbarization\" of Britain.126 But as with the Enlightenment anti-imperialists there were limits to his critique, for he endorsed a \"natural system\" of settler colonization through which people emigrated to create new communities, as long as this was the result of private initiative not state action.127 Libertarian settler colonialism was legitimate. Imperial ideology was marked more by continuity than rupture across the late eighteenth and nineteenth centuries. While the critique of alien rule was a recurrent (albeit minority) phenomenon from the Enlightenment to the era of decolonization, it was often conjoined with support for settler colonization.\n\nCritical of British belligerence and worried about aristocratic privilege and the threat to domestic liberty, Cobden and Spencer epitomize an important strand in nineteenth-century liberal international thought. But the staunchest anti-imperialists in Victorian Britain were the Comtean positivists, prophets of the \"religion of humanity,\" many of whom were proud liberals.128 Assailing British occupation in India, Ireland, and Egypt, positivists including Edward Beesly, Richard Congreve, and Frederic Harrison argued that the pursuit of empire unjustly prevented national cultures from flourishing as part of a wider universal humanity. A radical liberal and leading intellectual, Harrison offered a sustained critique of the British empire, which he once described as a \"huge crime against mankind\" and the result of a \"career of evil.\"129 He gave a distinctive Comtean twist to the conventional radical critique. \"In the religion of Humanity,\" he asserted, \"there are no distinctions of skin, or race, of sect or creed; all are our brothers and fellow-citizens of the world\u2014children of the same great kith and kin.\"130 Attacking the \"military and commercial aristocracy\" for morally degrading the country through their egotistical quest for domination, he maintained that an \"empire of subjects trains up the imperial race to every injustice and deadens them to any form of selfishness.\"131 While many critics of empire focused almost exclusively on the baneful consequences for the imperial power, Harrison also attended to those denied the possibility of self-determination. Taking a swipe at fellow liberals, he observed that \"[w]e do not pick and choose our oppressed nationalities to be favoured with the blessings of self-government,\" and he insisted that the positivists were \"against all oppression of conquered by their conquerors; we look for the dissolution of these empires of conquest; we desire decentralisation of vast political communities, and not a never-ending system of annexations; and, above all, we protest against military government in every form.\"132 Harrison never demanded immediate withdrawal from India, reasoning that it would be disastrous for the Indians, and he concluded that until self-government was viable, it \"must be governed in the sole interest of the countless millions who compose it; and not only in their interest, but in their spirit, until the time shall arrive when, part by part, it may be developed into normal and national life of its own.\" But this concession should not blind us to the important difference between Harrison's Comtist liberalism and the Millian vision. They diverged fundamentally on the question of imperial legitimacy and Britain's role in the world. \"We can accept neither the selfish plea of national glory, nor the specious plea of a civilising mission.\"133\n\nNot only did the Victorians produce a considerable body of writing deeply critical of empire\u2014or at least a body as critical as that found in the previous century\u2014they also justified empire with a wider variety of arguments than is often acknowledged. In chapter 4 I demarcate five ideal-typical justificatory strategies: realist-geopolitical; commercial-exploitative; civilizing; republican; and martialist. The first four studded nineteenth-century liberal accounts of empire.134 In public intellectual discourse liberal-civilizational arguments predominated, while republican themes often coexisted with them, occasionally moving to the foreground. The civilizational model can be understood as a species of the doctrine that liberal states can justifiably employ force to realize liberal ends. Its exponents assert that empire is legitimate if (and only if) it is primarily intended to benefit the populations subjected to it. Premised on a hierarchal conception of global politics, only some polities are regarded as displaying sufficient competence for self-government. It comes in weak and strong forms.135 The former diagnoses incompetent or malign _government_ as the main cause of incapacity. The remedy is the amputation of the government, by force if necessary, emancipating the subjugated people and putting them in a position to achieve self-rule. Justified under the rubric of \"humanitarian intervention,\" this is the most common contemporary iteration of the idea. The strong version regards the people as the problem, imagining them as incapable of creating or maintaining a stable and progressive political order. The prescribed solution is cognitive, affective, and behavioral transformation through expert liberal tutelage. During the nineteenth century this was most commonly articulated in terms of the propensity for civilization\u2014itself a vague and elusive category.136 In both cases, sovereignty is regarded as a privilege not a right: only those governments and\/or peoples that have displayed the appropriate political qualities are candidates for self-government and equal recognition. While liberals often claimed that the ultimate goal of tutelage was the inculcation of a capacity for national self-determination, I would argue that this is not a _necessary_ feature of liberal civilizing rule.137 Rather, such rule is constituted by two central claims: that imperial tutelage can only be justified in terms of the benefits it brings to the governed and that civilizing rule involves the transformation of existing societies into liberal ones (broadly-defined). It thus encompasses the rule of law, the upholding of contracts, the development of representative institutions, the grant of a range of civil and political liberties, and the introduction of a capitalist political economy. This menu of liberal reform does not automatically entail national self-determination\u2014at least in the foreseeable future\u2014though liberals often gestured vaguely in that direction.\n\nSuch \"altruistic\" justificatory arguments were usually bolstered by a claim that what liberal imperialists were advocating was radically new, something that both distinguished them from and elevated them above all previous empires. Joseph Chamberlain, leading radical politician and arch-imperialist, argued that a palpable change could be discerned in justifications of empire, writing in 1897 that \"[w]e feel now that our rule over their territories can only be justified if we can show that it adds to the happiness and prospects of the people.\"138 The American historian and political theorist William Dunning neatly summarized and dissected this line of reasoning. Supporters of the \"new imperialism\" that dominated the closing years of the nineteenth century liked to claim that the \"modern movement is essentially altruistic\u2014that it is founded upon duty to others rather than satisfaction of our own desires.\" Underlying the daunting complexity of imperial policy lay a single overarching principle, a \"philosophic theory,\" namely that \"the nation... must break the bonds of ethnic and geographic homogeneity and project its beneficent influence into the world at large.\" The modern democratic empire must, that is, act as a beacon for civilization and order in a turbulent age. Yet the professed principles and the grubby reality were very different, and Dunning argued that imperial expansion was driven principally by the insatiable desire for new markets. He looked on in horror, complaining that there was no longer \"one first-class nation whose conscious aim is internal perfection rather than external dominion\u2014not one that does not see in dependencies the indispensable proof of political competence. Constitutionalism and Nationalism have been superseded as controlling dogmas in the world's politics.\"139 Moreover, there was little new under the sun, for such self-aggrandizing claims had permeated the imperial ideologies of Greece, Rome, and many others since. The new imperialism, he concluded wryly, \"can hardly be said to have manifested thus far any characteristics that distinguish it from the movements in which throughout all history the powerful governments of the earth have extended their sway over the weak and incapable.\"140 Its proponents were deluded in thinking otherwise.\n\nThis is correct as far as it goes. Advocates of empire have almost always boasted that they were spreading civilization to those subjected to their rule. This was an animating feature of Roman imperial ideology. Writing a thousand years after the fall of the Western Roman Empire, near the dawn of the European conquest of the earth, Francisco de Vitoria claimed that while the subjection of \"barbarians\" was justified, it was nevertheless subject to a \"limitation\": that \"everything be done for the benefit and good of the barbarians, and not merely for the profit of the Spaniards.\"141 Three centuries later, James Mill too was keen to stress the altruism of empire, this time of the British in India. \"If we wish for the prolongation of an English government in India, which we do most sincerely, it is for the sake of the natives, not of England. India has never been anything but a burden; and anything but a burden, we are afraid, it cannot be rendered. But this English government in India, with all its vices, is a blessing of unspeakable magnitude to the population of Hindostan.\"142 Here, though, we see a subtle shift, and one unique to the nineteenth century\u2014the idea that not only was empire intended to benefit those subjected to it, but that this was its primary, overarching justification. What had changed over time, then, was not the basic _form_ of the justificatory argument but rather the professed _content_ of civilization and the _priority_ accorded to it. The export of civilization had been elevated from one among several goals (or consequences) of imperial expansion to the overriding one, and at the same time it had been reimagined such that civilization now encompassed a wide variety of values compatible with liberalism, though not exclusive to it.\n\nRepublican justifications, in contrast, are primarily motivated by a concern with the character of the imperial power, legitimating empire in terms of a particular class of benefits that it generates for the state. Its proponents seek to foster individual and collective virtue in their compatriots, while encouraging the pursuit of national honor and glory. This kind of argument also has deep roots in Western political thought, traceable to Rome. Machiavelli presented one of its most powerful modern statements, combining an account of liberty at home with imperial expansion abroad.143 Its echoes can be discerned in assorted nineteenth-century arguments. As Pitts makes clear, for example, Tocqueville advocated empire principally in terms of the reanimating effects of colonialism on French society.144 Republican justifications were woven through nineteenth-century British defenses of empire. In chapter 12 I explore how the historian J. A. Froude offered one of the clearest expressions of it.\n\nIt is important to remember, though, that these categories are analytical abstractions, and they neither fully capture the idiosyncrasies of flesh-and-blood thinkers nor exhaust the range of imperial justifications circulating at the time. James Fitzjames Stephen presents an interesting case in point. A judge and jurisprudence scholar who served as Legal Member of the Viceroy's Council in India (1868\u201372), Stephen defended a hard-edged utilitarian liberalism that would govern with a \"liberal imperial spirit.\"145 He plays an important but contested function in scholarship on the intellectual foundations of the Victorian empire. Stephen stands at the center of the narrative in Eric Stokes's classic _The English Utilitarians and India_.146 Mehta contends that Stephen's defense of empire was illiberal, but rather than inferring from this that liberals could justify empire in a variety of ways, he resolves the interpretive conundrum by denying that Stephen was an authentic liberal. He had absorbed too much Hobbes and not enough Locke, \"the true progenitor and enduring mentor of liberalism.\" Pitts reads him as offering a \"moral\" justification of empire despite his anti-democratic posturing, whereas Mantena reads Stephen's \"imperial authoritarianism\" as exemplifying a \"distinct break\" from liberal \"ethical\" justifications.147\n\nRather than seeing Stephen's authoritarian construal of imperial legitimacy as the culmination of an internal tendency in utilitarian thinking, indicative of a fracture in late imperial ideology, or as a quixotic antiliberal justificatory strategy, I suggest that it is better to view his work as indexing one possible liberal utilitarian pathway among many.148 While numerous utilitarians supported the empire, there was no necessary connection between the philosophy and the political project. After all, both Bentham and Spencer were fierce critics of the empire in India. Nor did utilitarian defenses of empire follow a clear unilinear historical chronology. Writing _after_ Stephen's main interventions, Henry Sidgwick, the most sophisticated nineteenth-century utilitarian, proselytized a fairly conventional liberal civilizing view, counseling that the \"business\" of civilized nations was to \"educate and absorb\" savage peoples, and he expressed admiration for the \"justifiable pride\" that the \"cultivated members of a civilized community feel in the beneficent exercise of dominion, and in the performance by their nation of the noble task of spreading the highest kind of civilisation.\"149 The \"gruffian,\" as Stephen was known, was right to protest that his views ran counter to the dominant intellectual trends of the time.\n\nFor Stephen, liberalism was an expression of a patriotic sense of English preeminence, while the empire was an integral element of the moral and political grandeur of the country. Since the conquest and rule of India was the \"greatest achievement of the race,\" threats to imperial supremacy presented an existential challenge.150 This anxiety of loss underpinned both his support for revenge against the Sepoy rebels of 1857 and his hatred of the \"Manchester School\" of political economists.151 As he argued in _Liberty, Equality, Fraternity_ , a patriotic citizenry should bask in the glory of military victories in India.152 Rejecting Bright's argument that the British had an obligation to the Indians to make amends for the original crime of conquest, he demanded that the empire be venerated. \"I deny that ambition and conquest are crimes; I say that ambition is the great incentive to every manly virtue, and conquest is the process by which every great state in the world... has been built up.\" Empire elevated the moral and material condition of its subjects, serving as a \"vast bridge\" from a moribund violent past to a stable and orderly future. This task, if accomplished, would constitute \"the greatest feat of strength, skill and courage in the whole history of the world.\"153 Here his argument came close to the republican line endorsed by his friend Froude.154\n\nYet Stephen was also committed to a version of the civilizing mission. British dominion offered an unparalleled opportunity to enact a \"true liberalism\" by fulfilling an obligation to rule justly.155 The \"great and characteristic task\" of the British in India was to spread European civilization. They were embarked on \"one of the most extensive and far-reaching revolutions recorded in history,\" involving the \"radical change\" of the institutions and ideas of countless people.156 The \"essential parts\" of that civilization included peace, order, the supremacy of law, the prevention of crime, the redress of wrong, the enforcement of contracts, and the use of taxation revenue for the public good. It was thus necessary to base the law and institutions of the country \"on European secular morality, on European views of political economy, and on the principle that men ought to be enabled by law, irrespective of religion, race, caste, and similar considerations, to enjoy securely whatever property they have, to get rich if they can by legal means, and to be protected in doing as they please, so long as they do not hurt others.\"157 Here he sounded like Mill. This was, he concluded, the near unanimous view of the Europeans who governed India. Insofar as Stephen diverged from them, it was chiefly over the _telos_ of empire. Critical of the \"Divine Right of Representative Institutions,\" the view that the \"exercise of absolute power can never be justified except as a temporary expedient used for the purpose of superseding itself,\" Stephen advised that representative institutions were not always and everywhere appropriate (chiefly because they came into conflict with more fundamental liberal utilitarian commitments).158 India was an unsuitable candidate. But this says as much about his hostility to democracy as a form of government as it does about his conception of India. Deeply critical of democratic institutions in British life, he grudgingly accepted that there was no point in fighting against them since they were an achieved fact. India, though, could still be saved from the blight. While he was more explicit than most other liberals about the coercive foundations of empire, and while he was skeptical about the goal of Indian self-government, he nevertheless argued that British rule was only legitimate insofar as it brought civilizational benefits to the governed. His justificatory argument, then, was an awkward fusion of liberal civilizing and republican themes, with a distinctive authoritarian flavor. Stephens's heterodox political thought highlights the internal variety of Victorian liberal ideology.\n\nThe historical narrative embedded in Mantena's powerful account of liberal supersession is also open to challenge. Recall her argument about the impact of 1857: liberal justifications \"were dramatically eclipsed\" and the period witnessed \"a more general waning of ethical arguments and moral justifications of empire.\"159 The evidence she adduces for this _general transformation_ of metropolitan British liberalism is chiefly drawn from her superb interpretation of Maine's personal intellectual trajectory combined with the shift in policy enforced by the British administration in India.160 Mantena thus sets up an equivalence, implying that British liberal ideology and Indian imperial policy developed together, from ethics to alibis of empire. Maine, Seeley, and Stephen are read as representative of a ubiquitous disillusionment with democracy that reshaped imperial ideology. Hence her claim that \"a growing illiberal or antiliberal consensus\" was \"fuelled by domestic fears about the growth of mass democracy.\"161 However, this is an overly homogenous view of British elite political culture. While there was a fairly widespread sense that the onset of democracy posed a threat to Britain and its empire, it was far from universal. It was not the only\u2014indeed not the dominant\u2014strand of liberal thinking.162 Intellectual currents in Britain and India were not closely aligned. As Jon Wilson puts it, \"British political thought and administrative practice marched to a different beat in the colonial context.\"163\n\nThe closing three decades of the century witnessed a remarkable burst of innovation in British political thinking. While the Liberal Party split over Home Rule, and even as some older liberals (including Maine) lamented the direction of popular government, other thinkers and movements were emerging or gaining ground. New conceptions of the state, of the individual, and of community flourished. More important than the pained ripostes to democracy was the emergence of collectivist forms of liberalism, challenging both older _laissez-faire_ articulations and conservative critics. At a fundamental philosophical level, Sidgwick revived a tired utilitarianism in _The Methods of Ethics_ , while the final third of the century witnessed an efflorescence of idealist philosophy, drawing on both ancient Greek and modern German influences. T. H. Green, Bernard Bosanquet, and J. H. Muirhead, among others, all sought to craft idealist liberal political theories.164 In the 1890s and beyond a group of \"new liberal\" thinkers began to self-consciously develop a more egalitarian form of liberalism.165 Drawing on the German historian Otto von Gierke, pluralists, including Maitland, Neville Figgis, and G.D.H. Cole, challenged the normative and ontological centrality of the sovereign state, seeking answers to political challenges in a plethora of civil society associations and overlapping sources of political authority.166 The idealists and new liberals helped to lay the intellectual foundations for the nascent welfare state.167 Horrified at this development, Spencer and his followers restated the case for a libertarian vision. In short, this was a period of great intellectual ferment. Liberalism was reworked for an emerging democratic age.\n\nMoreover, and just as importantly, the liberal civilizing mission remained a central feature of imperial ideology deep into the twentieth century. Stephen's complaint about his contemporaries had been correct. In one of the most significant early twentieth-century accounts of liberalism, Herbert Samuel asserted that the \"foundation of Liberalism is the moral law that the State has the duty of advancing the welfare both of its own members and of all whom it can influence.\" But the form of this duty varied according to the level of sociopolitical development found in communities around the world. For those in which people were both free and civilized, liberal states should adopt a stance of noninterference, interacting with them harmoniously and seeking influence, if at all, through diplomatic engagement. If a people was \"civilized\" but living under the iron rule of a foreign despot, liberals had a duty to offer moral, and sometimes material, support. Finally, if they were \"savage or semi-civilized,\" liberalism directed that the state \"may itself undertake their government and help their progress by the gift of good laws and good administration.\"168 Empire was thus a moral agent, a \"civilizing and pacifying force, helpful to the progress of mankind.\"169 In Millian vein, he stressed the enduring relevance of the civilizing mission.\n\nIndependence, however valuable to a people, is not their highest good. Liberals hold that the ultimate purpose of politics is nothing narrower than to help men to advance towards the best type. No people can reach the goal, indeed, unless they have liberty; but there may be stages in the march when unrestrained liberty is rather a hindrance to them than a help. A barbarian race may prosper best if for a period, even for a long period, it surrenders the right of self-government in exchange for the teachings of civilization.\n\nHe concluded that \"England is honestly seeking to teach her native subjects to be self-dependent, and in place of the barbaric license of which they are deprived, to give them in the fullness of time, and under the aegis of her own flag, a new and a better freedom.\"170 This was a paradigmatic expression of the ethical justification of imperial intervention. That the empire was a virtuous engine of civilization remained a metropolitan platitude deep into the twentieth century\u2014and beyond.\n\nOthers went further still in their encomiums for a moralized vision of imperial rule. In his textbook on the subject, Caldecott even claimed that India, under British guidance, had partially realized \"Plato's conception of the good state,\" shorn of its \"extremes\": a wise governing cadre, a courageous intermediary administrative class, a temperate mass of people, all working together in harmony. But whereas Plato thought that such a state would inevitably foster debilitating corruption, the \"virtues of the Indian state are preparing for consolidation and progress.\"171 Another textbook, written after the war in South Africa, hymned the empire as an \"agent making for the advance of civilisation.\" Invoking the spirit of Tennyson, the author decreed that it was the primary instrument of global progress, and thus essential for the future development of humanity.\n\nWorking for the gradual elimination of discord and war and for the foundation of a system of universal freedom and justice leading up to that perfectibility of which poets dream, a federation of mankind speaking a common language and governed by a common law, the British Empire could scarcely be supplanted by any other aggregation of kindred peoples. Thus the extinction of the empire would mean a distinct, and so far as one can see, an irreparable, check to the progress of the world.172\n\nEdwin Arnold, a leading poet and journalist, likewise evoked the world-historical mission of the British, contrasting a Hobbesian global state of nature with the reforming cosmopolitical ambitions of the empire.\n\nThe loss of India to England would mean the breaking up and decay of our ancient empire; the eventual spread of Slavonic and Mongolian hordes all over the vacant places and open markets of the world; the world's peace gone; again, as in the days of Belisarius, the march of sciences, arts, religions, arrested as when Omar burned the Alexandrian library; and history once more put back to the beginning of a new effort, under novel and gloomy auspices, to effect that which is the perpetual object of its course and its combinations\u2014the final amalgamation of all the people of the globe under one law and one common faith and culture.173\n\nMoreover, criticizing the coercive imposition of uniform standards of British \"civilization\" on India did not lead invariably to the kind of \"conservatism\" advocated by Maine. Ramsay MacDonald, one of the founders of the Labour Party and later Prime Minister, commenced his analysis of British imperialism from a position similar to Maine\u2014indeed he went further in stressing the need to protect Indian communities from the corrosive power of imperial capitalism. \"Our fundamental mistake in native policy is that we regard the native as a Briton in the making,\" he warned, and \"the less we interfere with native administration the better.\"174 The answer, though, was a democratized civilizing vision. The imperialism of a future Labour government, he stated, \"does not believe in the subjugation of other nationalists; it takes no pride in the 'government' of other peoples. To its subject races it desires to occupy the position of a friend; to its self-governing imperial States it seeks to be an equal; to the world it asks to be regarded as a neighbour.\"175 The aim of empire in India was ultimately the creation of a self-governing nation-state. In short, while Mantena does an admirable job of anatomizing an important and novel form of imperial ideology, she exaggerates both the homogeneity of British liberal thought at the time and the decline of liberal civilizing accounts of imperial rule.\n\nEuropean and American political thinking in the nineteenth century was typically predicated on a vision of the world as a space divided between competing civilizations, each at a different level of socioeconomic, political, and moral development, each populated by members of distinct races, each subject to contrasting forms of evaluation and judgment. Assumed or endorsed by British liberals and their critics, and by imperialists and those who rejected empire, few completely escaped the ideological shadow of this imagined geography. Its legacy continues to shape visions of world order.\n\n1 Mehta, _Liberalism and Empire_ (Chicago, 1999), 37.\n\n2 For a challenge to such certainties, see Duncan Bell and Joel Isaac, eds., _Uncertain Empire_ (Oxford, 2012).\n\n3 For global accounts of the period, see Chris Bayly, _The Birth of the Modern World, 1780\u20131914_ (Oxford, 2004); Barry Buzan and George Lawson, _The Global Transformation_ (Cambridge, 2015); J\u00fcrgen Osterhammel, _The Transformation of the World_ (Princeton, 2014).\n\n4 For a detailed exposition, see Casper Sylvest, _British Liberal Internationalism, 1880\u20131930_ (Manchester, 2009). See also the discussion in chapter 10. For further comments on the nature of liberalism, and for bibliographical references on the topic, see chapters 1 and .\n\n5 Plamenatz, On _Alien Rule and Self-Government_ (London, 1960). This was one of only a handful of books written by a political theorist during the Cold War that addressed the question of empire. For an attempt to resuscitate it, see Brian Barry, \"On Self-Government,\" in _The Nature of Political Theory_ , ed. David Miller and Larry Siedentop (London, 1983), 121\u201354. For a recent defense of \"alien rule\" (understood in broader terms), see Michael Hechter, _Alien Rule_ (Cambridge, 2013).\n\n6 For a prominent example, see Niall Ferguson, _Empire_ (London, 2003).\n\n7 Anthony Pagden, _The Burdens of Empire_ (Cambridge, 2015), 37. For a more detailed account, see Pagden, \"Human Rights, Natural Rights, and Europe's Imperial Legacy,\" _Political Theory_ , 31 (2003), 171\u201399. This essay is reprinted in _Burdens_ , on pages 243\u201363.\n\n8 Peter Cain, \"Radicalism, Gladstone, and the Liberal Critique of Disraelian 'Imperialism,'\" in _Victorian Visions of Global Order_ , ed. Duncan Bell (Cambridge, 2007), 215\u201339. For the liberal critique of \"imperialism,\" see also Miles Taylor, \"Imperium et Libertas?,\" _Journal of Imperial and Commonwealth History_ , 19 (1991), 1\u201323.\n\n9 Hammond, \"Colonial and Foreign Policy,\" in _Liberalism and the Empire_ , by Hammond, Hirst, and Murray (London, 1899), 196.\n\n10 Ibid., 171.\n\n11 Hobhouse, _Democracy and Reaction_ 1904], ed. Peter Clarke (Brighton, 1972), 48, 154; Hobhouse once defined imperialism as \"the doctrine of racial ascendency and territorial aggression.\" Hobhouse, \"The Growth of Imperialism,\" _Speaker_ (January 25, 1902), 474. I examine his views in [chapter 14.\n\n12 Ikenberry, \"Liberalism and Empire,\" _Review of International Studies_ , 30 (2004), 619. If, on the other hand, \"empire is defined more loosely as a hierarchical system of political relationships in which the most powerful state exercises decisive influence, the postwar American system indeed qualifies\" (619).\n\n13 Ikenberry, \"Liberalism and Empire,\" 615, 616. For more on liberal hegemony, see Ikenberry, _Liberal Order and Imperial Ambition_ (London, 2006).\n\n14 Ferguson, \"Hegemony or Empire?,\" _Foreign Affairs_ , 82\/5 (2003), 160.\n\n15 Schumpeter, _Imperialism and Social Classes_ (New York, 1955), 75. See also Bernard Semmel, _The Liberal Ideal and the Demons of Empire_ (Baltimore, 1993), 167\u201376.\n\n16 Constant, \"The Spirit of Conquest\" [1814], in _Political Writings_ , ed. Biancamaria Fontana (Cambridge, 1988), 51\u201381; Angell, _The Great Illusion_ (London, 1910). See also Peter Cain, \"Capitalism, Aristocracy and Empire,\" _Journal of Imperial and Commonwealth History_ , 35\/1 (2007), 25\u201347.\n\n17 Tully, \"Lineages of Contemporary Imperialism,\" in _Lineages of Empire_ , ed. Duncan Kelly (Oxford, 2009), 11. On Tully's vision, see Duncan Bell, \"To Act Otherwise,\" in _On Global Citizenship_ , ed. David Owen (London, 2014), 181\u2013207.\n\n18 Tully, \"Lineages of Contemporary Imperialism,\" 13. Here he draws on a seminal article, Ronald Robinson and John Gallagher, \"The Imperialism of Free Trade,\" _Economic History Review_ , 6 (1953), 1\u201315.\n\n19 Tully, _Public Philosophy in a New Key_ (Cambridge, 2008), 2:7.\n\n20 Tully, _Strange Multiplicity_ (Cambridge, 1995); Mills, \"Occupy Liberalism!,\" _Radical Philosophy Review_ , 15\/2 (2012), 305\u201323.\n\n21 For a powerful critique of their uses of history, and much else besides, see Jeanne Morefield, _Empires without Imperialism_ (Oxford, 2014).\n\n22 Ryan, \"Liberal Imperialism\" [2004], in _The Making of Modern Liberalism_ (Princeton, 2012), 107, 122. For a sophisticated liberal account of the practical difficulties of humanitarian intervention, and the normative implications to be drawn from this, see Michael Doyle, _The Question of Intervention_ (New Haven, 2015). Doyle, though, exaggerates the differences between past modes of imperialism and current ideas and practices.\n\n23 Mehta's timing was exemplary. In April that year, British Prime Minister Tony Blair gave a speech in Chicago presenting the case for \"humanitarian\" intervention in Kosovo, invoking the \"doctrine of the international community.\" It synthesised many of the liberal arguments that had been percolating around Western politics elites and academic discourse during the preceding few years. Subsequently, this line of thinking was formalised into the doctrine of \"Responsibility to Protect.\" For supportive accounts, see Alex Bellamy, _Responsibility to Protect_ (Oxford, 2014); Luke Glanville, _Sovereignty and the Responsibility to Protect_ (Chicago, 2014). For a critique, see Philip Cunliffe, ed., _Critical Perspectives on the Responsibility to Protect_ (London, 2011).\n\n24 Mehta, _Liberalism and Empire_ , 11, 23. Mehta is clear he is not concerned here with authorial intent, but with \"foundational commitments\" (47, 1n).\n\n25 Ibid., 18. Intriguingly, this argument was itself employed by liberal defenders of empire. Hammond, for example, admonished \"imperialists\" for \"that intolerance which regards every diversity of religion, of polity, as an eyesore, which sees a moribund civilization in every civilization not immediately intelligible or sympathetic to our own... and takes pride in its rigid Procrustean measurements of every nation by our own standard\" (\"Colonial and Foreign Policy,\" 199).\n\n26 Chakrabarty, _Provincializing Europe_ (Princeton, 2000), 8.\n\n27 Mehta, _Liberalism and Empire_ , 9. Italics added. \"Given liberalism's universalism,\" he writes elsewhere, \"this is definitionally the case\" (48).\n\n28 Ibid., 20. Italics in original.\n\n29 Cooper, _Colonialism in Question_ (Berkeley, 2005), 235.\n\n30 Mehta, _Liberalism and Empire_ , 43, 50. Michael Bentley suggests that Mehta should simply acknowledge that the \"other tradition\" he identifies is an antiliberal conservative one, fully capable of \"recognising other cultures in and for their authenticity and selfhood.\" Bentley, review, _Victorian Studies_ , 43\/4 (2001), 620.\n\n31 While I here focus on these texts, chiefly because of their influence and the scope of their historical claims, numerous other scholars have explored aspects of the topic. For some of the most interesting accounts of British imperial liberalism, see Peter Cain, \"Empire and the Languages of Character and Virtue in Later Victorian and Edwardian Britain,\" _Modern Intellectual History_ , 4\/2 (2007), 1\u201325; Cain, \"Character, 'Ordered Liberty,' and the Mission to Civilise,\" _Journal of Imperial and Commonwealth History_ , 40\/4 (2012), 557\u201378; Gregory Claeys, _Imperial Sceptics_ (Cambridge, 2010); Daniel Gorman, _Imperial Citizenship_ (Manchester, 2006); Jeanne Morefield, _Covenants without Swords_ ; Morefield, _Empires without Imperialism_ ; Nicholas Owen, _The British Left and India_ (Oxford, 2007); Andrew Sartori, _Liberalism in Empire_ (Berkeley, 2014); Casper Sylvest, _British Liberal Internationalism, 1880\u20131930_. For the European context, see Matthew Fitzpatrick, ed., _Liberal Imperialism in Europe_ (Basingstoke, 2012).\n\n32 Muthu, _Enlightenment against Empire_ (Princeton, 2003), 268\u201369.\n\n33 Ibid., 282. Italics in original.\n\n34 Ibid., 4, 5 (and 258). Italics added.\n\n35 Pitts, \"Political Theory of Empire and Imperialism,\" _Annual Review of Political Science_ , 13 (2010): 218.\n\n36 Pitts, _A Turn to Empire_ (Princeton, 2005), 26. For the intriguing late-Victorian afterlife of Smith's ideas, see Marc-William Palen, \"Adam Smith as Advocate of Empire,\" _Historical Journal_ , 57\/1 (2014), 179\u201398.\n\n37 Pitts, _A Turn to Empire_ , 2. Italics added. Pitts argues that French liberalism followed a similar trajectory in the nineteenth century, split between an anti-imperial tradition represented by Constant and Am\u00e9d\u00e9e Desjobert and a republican-inflected imperial liberalism articulated in de Tocqueville's writings on Algeria.\n\n38 Mantena, _Alibis of Empire_ (Princeton, 2010), 45. Italics added.\n\n39 Ibid., 48.\n\n40 On Maine's life and thought, see also Alan Diamond, ed., _The Victorian Achievement of Sir Henry Maine_ (Cambridge, 2006); Raymond Cocks, _Sir Henry Maine_ (Cambridge, 1988).\n\n41 Mantena, _Alibis of Empire_ , 1, 48. For empirical confirmation of this policy trend outside of India, see Coel Kirkby, \"The Politics and Practice of 'Native' Enfranchisement in Canada and the Cape Colony, c.1880\u20131900,\" (PhD thesis, University of Cambridge, 2013).\n\n42 Mantena also develops a brilliant analysis of the recurrent instability of imperial ideology, which she convincingly applies to the recent conflict in Iraq and its aftermath ( _Alibis of Empire_ , 179\u201381).\n\n43 Ibid., 11. Italics in original.\n\n44 Ibid., 22\u201339. On this account, his universalism was heavily qualified by assorted empirical factors, leading to a more contextualized approach to imperial affairs.\n\n45 This reinforces other recent accounts of the imperial origins of the League and the United Nations, including Mark Mazower, _No Enchanted Palace_ (Princeton, 2009). On trusteeship, see also William Bain, _Between Anarchy and Society_ (Oxford, 2003). For a magisterial analysis of the Mandate system, see Susan Pedersen, _The Guardians_ (Oxford, 2015).\n\n46 For recent assessments, see Andrew Thompson, ed., _Writing Imperial Histories_ (Manchester, 2014); John Mackenzie, \"The British Empire,\" _Journal of Imperial and Commonwealth History_ , 43\/1 (2015), 99\u2013124; Dane Kennedy, \"The Imperial History Wars,\" _Journal of British Studies_ , 54\/1 (2015), 1\u201322.\n\n47 This is no longer the case. See, for example, James Belich, _Replenishing the Earth_ (Oxford, 2009); John Darwin, _The Empire Project_ (Cambridge, 2011); Marilyn Lake and Henry Reynolds, _Drawing the Global Colour Line_ (Cambridge, 2008); Gary Magee and Andrew Thompson, _Empire and Globalization_ (Cambridge, 2010). Cf. Duncan Bell, \"Desolation Goes before Us,\" _Journal of British Studies_ 54 (2015), 987\u201393.\n\n48 Balachandra Rajan, \"Excess of India,\" _Modern Philology_ , 95\/4 (1998), 490.\n\n49 Mehta, _Liberalism and Empire_ , ch. 5; Pitts, _A Turn to Empire_ , ch. 3; Whelan, _Enlightenment Political Thought and Non-Western Societies_ (London, 2009), ch. 4; Whelan, _Edmund Burke and India_ (Pittsburgh, 1996); Muthu, _Enlightenment against Empire_ , 4\u20135.\n\n50 Daniel O'Neill, \"Rethinking Burke and India,\" _History of Political Thought_ , 30\/3 (2009), 492\u2013523; Sartori, _Liberalism in Empire_ , 26. For an insightful account of Burke's imperialism, see Daniel O'Neill, _Edmund Burke and the Conservative Logic of Empire_ (Berkeley, 2016).\n\n51 Margaret Kohn and Daniel O'Neill, \"A Tale of Two Indias,\" _Political Theory_ , 34 (2006), 202.\n\n52 For accounts of Locke and colonialism, see Barbara Arneil, _John Locke and America_ (Oxford, 1996); Arneil, \"Citizens, Wives, Latent Citizens and Non-Citizens in the _Two Treatises_ ,\" _Eighteenth-Century Thought_ , 3 (2007), 209\u201322; James Farr, \"Locke, Natural Law, and New World Slavery,\" _Political Theory_ , 36 (2008), 495\u2013522; Duncan Ivison, \"Locke, Liberalism and Empire,\" in _The Philosophy of John Locke_ , ed. Peter R. Anstey (London, 2003), 86\u2013105; Jimmy Casas Klausen, \"Room Enough,\" _Journal of Politics_ , 69\/3 (2007), 760\u201369; Herman Lebovics, _Imperialism and the Corruption of Democracies_ (Durham, NC, 2006), ch. 5; James Tully, _An Approach to Political Philosophy_ (Cambridge, 1993), 137\u201376; Jack Turner, \"John Locke, Christian Mission, and Colonial America,\" _Modern Intellectual History_ , 8 (2011), 267\u201397. For qualified skepticism about Locke's imperialism, see David Armitage, _Foundations of Modern International Thought_ , chs. 6\u20137.\n\n53 Dunn, _The Political Thought of John Locke_ (Cambridge, 1969), 5.\n\n54 Mehta, _Liberalism and Empire_ , 4.\n\n55 Skinner, \"Meaning and Understanding in the History of Ideas,\" in _Visions of Politics_ , 1:73\u201374. While agreeing with the general thrust of this argument, and the methodological commitments that underpin it, in chapter 3 I suggest that Locke _became_ a liberal in the twentieth century through his retrospective incorporation into the (new) liberal tradition, but that this was part of a process of conceptual and ideological expansion that rendered liberalism such an amorphous category that it is usually unhelpful as a guide to theoretical or historical interpretation.\n\n56 For the striking absence of Lockean accounts of property in elite metropolitan discourse, see Andrew Fitzmaurice, _Sovereignty, Property, and Empire, 1500\u20132000_ (Cambridge, 2014), chs. 7\u20139. On the inapplicability of the category \"liberalism\" to early modern empires, see Fitzmaurice, \"Neither Neo-Roman nor Liberal Empire,\" _Renaissance Studies_ , 26\/4 (2012), 479\u201391.\n\n57 Andrew Sartori, _Liberalism in Empire_.\n\n58 Buller used the phrase \"shoveling out paupers\" to describe Robert Wilmot Horton's emigration scheme. See the discussion in H.J.M. Johnson, _British Emigration Policy, 1815\u20131830_ (Oxford, 1972), 168. A friend of John Stuart Mill, Buller was a liberal politician and active member of the colonial reform movement. On the \"somersault in British attitudes to emigration,\" see Belich, _Replenishing the Earth_ , 145\u201352.\n\n59 The economic debate is discussed in Winch, _Classical Political Economy_.\n\n60 Cairnes, \"Colonization and Colonial Government,\" _Political Essays_ (London, 1873), 30, 33. He added: \"The theory has now little more than an historic value\" (30).\n\n61 The most developed version of his argument can be found in Wakefield, _A View of the Art of Colonization_ (London, 1849). For other contributions to the debate, see Nassau Senior, _Remarks on Emigration_ (London, 1831); Nassau Senior, _An Outline of a Science of Political Economy_ (London, 1836); Robert Torrens, _Colonisation of South Australia_ (London, 1835); Torrens, _Self-Supporting Colonization_ (London, 1847); Merivale, _Lectures on Colonisation and Colonies_ , 2 vols. (London, 1841). For analysis, see Winch, _Classical Political Economy_ ; Peter Burroughs, _Colonial Reformers and Canada, 1830\u20131849_ (London, 1969); Tony Ballantyne, \"Remaking the Empire from Newgate,\" in _Ten Books That Shaped the British Empire_ , ed. Antoinette Burton and Isabel Hofmeyr (Durham, NC, 2014), 29\u201350. One issue on which there was considerable disagreement was the idea of a \"sufficient price\" for land. For differing perspectives, see Wakefield, _A View of the Art of Colonization_ , 338\u201369; Merivale, _Lectures on Colonisation and Colonies_ , lectures 14\u201316; John Stuart Mill, _Principles of Political Economy_ [1848], in _The Collected Works of John Stuart Mill_ , ed. John Robson (Toronto, 1963\u201391), (hereafter _Collected Works_ ), vol. 3, bk. 1, ch. 8.\n\n62 For a good account of the argument, see Cairnes, \"Colonization and Colonial Government,\" 30\u201335.\n\n63 Wakefield, _A View of the Art of Colonization_ , 148. See also Arthur Mills, _Systematic Colonization_ (London, 1847), 33\u201334.\n\n64 Marx, _Capital_ , vol. 1, in _Collected Works_ , by Marx and Engels (London, 1975), ch. 33. Indeed Marx regarded him as the most significant bourgeois political economist since Ricardo. For Victorian accounts of the importance of the colonial reformers, see Alfred Caldecott, _English Colonization and Empire_ (London, 1891), 131\u201333, who labeled them \"Benthamites\"; and Egerton, _A Short History of British Colonial Policy_ , (London, 1897), who, despite praising Wakefield and the movement, noted their \"un-English\" propensity for theorizing systematically about empire (4).\n\n65 Smith, _The Empire_ (London, 1863).\n\n66 Cairnes, \"Colonization and Colonial Government,\" 58.\n\n67 Mill, _Considerations on Representative Government_ 1861], ch. 18. For more on his argument for retaining the colonies on a voluntary basis, see [chapter 9. In 1864 Mill and Cairnes corresponded over the issue, with Mill rejecting Cairnes's arguments and reiterating the position elaborated in _Considerations_. See, for example, Mill to Cairnes, November 8, 1864, _Collected Works_ , 15:965. See also the discussion in Georgios Varouaxakis, _Liberty Abroad_ (Cambridge, 2013), 132\u201334.\n\n68 See H.C.G Matthew, _The Liberal Imperialists_ (Oxford, 1973), on liberal parliamentary support for empire and imperialism. Both served as presidents of the Imperial Federation League.\n\n69 Lecky, _The Empire_ (London, 1893), 15.\n\n70 Carnegie, _The Reunion of Britain and America_ (Edinburgh, 1893), 24; see also Carnegie, \"Distant Possessions,\" _North American Review_ , 167\/501 (1898), 239\u201348. For analysis of this idea, see Duncan Bell, \"Beyond the Sovereign State,\" _Political Studies_ , 62\/2 (2014), 418\u201334; Bell, \"Before the Democratic Peace,\" _European Journal of International Relations_ , 20\/3 (2014), 647\u201370.\n\n71 Quoted in John Darwin, _The Empire Project_ , 146.\n\n72 Caldecott, _English Colonization and Empire_ , 11. Caldecott was Dean of St. John's College, Cambridge; the book was designed for use on university courses.\n\n73 The distinction was a constant theme across the Victorian era and beyond. George Cornewall Lewis, _An Essay on the Government of Dependencies_ (London, 1841), 169\u201379; Arthur Mills, _Colonial Constitutions_ (London, 1856); John Stuart Mill, _Considerations on Representative Government_ , ch. 18; Alpheus Todd, _Parliamentary Government in the British Colonies_ (London, 1880); Henry Jenkyns, _British Rule and Jurisdiction beyond the Seas_ (Oxford, 1902), 1\u20139.\n\n74 Seeley, _The Expansion of England_ , 244.\n\n75 Gooch, \"Imperialism,\" in _The Heart of Empire_ , ed. C.F.G Masterman (London, 1901), 310.\n\n76 Lucas, \"Introduction,\" in _An Essay on the Government of Dependencies_ , by George Cornewall Lewis, ed. C. P. Lucas (Oxford, 1891), xxxiii.\n\n77 Mills, _The Racial Contract_ (Ithaca, 1997); Mills, \"White Right,\" in _Blackness Visible_ (Ithaca, 1998). For a different account of the \"settler contract,\" see Carole Pateman and Charles Mills, _Contract and Domination_ (Cambridge, 2007), ch. 2 (by Pateman). Note that Mills and Pateman employ \"contract\" in different senses.\n\n78 Lorenzo Veracini locates the origins of the concept (not the practice) in the period of decolonization in the 1950s and 1960s. \"Settler Colonialism,\" _Journal of Imperial and Commonwealth History_ , 41\/2 (2013), 313\u201333. Settler colonialism has been central to the work of J.G.A. Pocock, though he has written little about the nineteenth century, which is why I don't engage him at greater length in this chapter. See Pocock, _The Discovery of Islands_ (Cambridge, 2005); Richard Bourke, \"Pocock and the Presuppositions of the New British History,\" _Historical Journal_ , 53\/3 (2010), 747\u201370.\n\n79 For theoretical accounts of the practice, see J\u00fcrgen Osterhammel, _Colonialism_ , 2nd ed. (Princeton, 2005); Lorenzo Veracini, _Settler Colonialism_ (Basingstoke, 2010); Patrick Wolfe, _Settler Colonialism and the Transformation of Anthropology_ (London, 1999); Caroline Elkins and Susan Pedersen, \"Settler Colonialism,\" in _Settler Colonialism in the Twentieth Century_ , ed. Elkins and Pedersen (London, 2005), 1\u201320; Mahmood Mamdani, \"Settler Colonialism,\" _Critical Inquiry_ , 41 (2015), 1\u201319. For a useful summary of the distinctive, even antithetical, character of colonialism and settler colonialism, see Veracini, \"Introducing Settler Colonial Studies,\" _Settler Colonial Studies_ , 1\/1 (2011), 1\u201312.\n\n80 On settler sovereignty, see, for example, Lauren Benton, _A Search for Sovereignty_ (Cambridge, 2010); Lisa Ford, _Settler Sovereignty_ (Cambridge, MA, 2010). See also Ann Stoler, \"On Degrees of Imperial Sovereignty,\" _Public Culture_ , 18\/1 (2006). On practices and ideologies of settler colonialism, see also Fiona Bateman and Lionel Pilkington, eds., _Studies in Settler Colonialism: Politics, Identity and Culture_ (New York: Palgrave, 2011); Shaunnagh Dorsett and Ian Hunter, eds., _Law and Politics in British Colonial Thought_ (Basingstoke, 2010); Lynette Russell, ed., _Colonial Frontiers_ (Manchester, 2001); Annie Coombes, ed., _Rethinking Settler Colonialism_ (Manchester, 2006); Alyosha Goldstein and Alex Lubin, eds., \"Settler Colonialism,\" _South Atlantic Quarterly_ , 107\/4 (2008).\n\n81 Wolfe, \"Settler Colonialism and the Elimination of the Native,\" _Journal of Genocide Research_ , 8\/4 (2006), 393. Italics added. On settler violence, see Dirk Moses, ed., _Genocide and Settler Society_ (New York, 2004); Ann Curthoys, \"Genocide in Tasmania,\" in _Empire, Colony, Genocide_ , ed. Dirk Moses (New York, 2008), 229\u201353; Wolfe, \"Settler Colonialism.\" On racial exclusion from the franchise in the British settler empire, see Julie Evans et al., _Unequal Rights_ (Manchester, 2003); Kirkby, \"The Politics and Practice of 'Native' Enfranchisement.\"\n\n82 Wolfe, \"Settler Colonialism.\" See also Wolfe, \"Recuperating Binarism,\" _Settler Colonial Studies_ , 3\/4 (2013), 257\u201379.\n\n83 On humanitarian governmentality, see Alan Lester and Fae Dussart, _Colonization and the Origins of Humanitarian Governance_ (Cambridge, 2014).\n\n84 In the zone of greatest destruction, the population of Aboriginal Australians fell from over 750,000 to less than 50,000 during the colonial period. In the penal colony of Tasmania (once Van Diemen's Land), the local population was almost exterminated between 1803 and 1850 in a prolonged nightmare of rape, torture, disease, and murder. See Benjamin Madley, \"From Terror to Genocide: Britain's Tasmanian Penal Colony and Australia's History Wars,\" _Journal of British Studies_ , 47 (2008), 77.\n\n85 Wolfe, \"Settler Colonialism,\" 397. For a related discussion, see Jonathan Lear, _Radical Hope_ (Cambridge, MA, 2006). See also the comments in Duncan Bell, \"Making and Taking Worlds,\" in _Global Intellectual History_ , ed. Samuel Moyn and Andrew Sartori (New York, 2013), 254\u201382.\n\n86 Wolfe, \"Settler Colonialism,\" 388. For a useful comparative perspective, see Benjamin Madley, \"Tactics of Nineteenth Century Colonial Massacre,\" in _Theatres of Violence_ , ed. Philips Dwyer and Lyndall Ryan (New York, 2012), 110\u201325.\n\n87 Duncan Ivison, Paul Patton, and Will Sanders, eds., _Political Theory and the Rights of Indigenous Peoples_ (Cambridge, 2001); Mamdani, \"Settler Colonialism\"; Tully, _Strange Multiplicity_.\n\n88 Patrick Brantlinger, _Dark Vanishings_ (Ithaca, 2003).\n\n89 Wells, _The War of the Worlds_ (London, 1898), prologue.\n\n90 Merivale, _Lectures on Colonies and Colonisation_ , 2:152. After a spell as Professor of Political Economy at Oxford, during which time he delivered his famed lectures on colonies, Merivale held a series of senior imperial administrative posts, which culminated in his appointment as Permanent Under-Secretary for India in 1860.\n\n91 Caldecott, _English Colonization and Empire_ , 234. On the inevitability of extinction-through-contact, he wrote the following extraordinary passage: \"The past is irrevocable, and in the future men must move on. Some of these peoples are plainly passing away: they are unable to live when called upon to make a sudden and almost a spasmodic effort to live in a higher stage of culture. But even for them it is not difficult to determine what should be our attitude. What is our conduct to the sick and dying among ourselves? All the alleviations and comforts we can think of are placed cheerfully at their disposal. Let it be so for these sick and dying tribes. Let us work gently as in the sick-chamber, and be ministers to their closing years in comfort, patience, and tenderness\" (235).\n\n92 Murray, \"The Exploitation of Inferior Races in Ancient and Modern Times,\" in _Liberalism and the Empire_ , ed. Hirst, Murray, and Hammond, 157.\n\n93 Merivale, _Lectures on Colonies and Colonisation_ , 2:152.\n\n94 On the notion of mythscape, see Duncan Bell, \"Mythscapes,\" _British Journal of Sociology_ , 54\/1 (2003), 63\u201381; Bell, \"Agonistic Democracy and the Politics of Memory,\" _Constellations_ , 15\/1 (2008), 148\u201366. On settler narratives, see also Veracini, _Settler Colonialism_ , ch. 4.\n\n95 Metcalf, _Ideologies of the Raj_ (Cambridge, 1995).\n\n96 On Aryanism, see Tony Ballantyne, _Orientalism and Race_ (Basingstoke, 2002), and the discussion in chapter 13.\n\n97 Mehta, _Liberalism and Empire_ , 31\u201333; Chakrabarty, _Provincializing Europe_. See also Ashis Nandy, \"Reconstructing Childhood,\" in _Traditions, Tyranny, and Utopia_ (Delhi, 1987), 56\u201376.\n\n98 Cornewall Lewis, _Essay_ , 170. This definition was adopted by Cairnes, in \"Colonization and Colonial Government,\" 4\u20135. For Cornewall Lewis's account of colonial sovereignty, see Shaunnagh Dorsett, \"Sovereignty as Governance in the Early New Zealand Crown Colony Period,\" in _Law and Politics in British Colonial Thought_ , ed. Dorsett and Hunter, 209\u201328.\n\n99 Wakefield, _A View on the Art of Colonization_ , 16-17. \"A colony therefore is a country wholly or partially unoccupied, which receives emigrants from a distance; and it is a colony of the country from which the emigrants proceed, which is therefore called the mother country\" (16).\n\n100 Egerton, _A Short History of Colonial Policy_ , 8\u20139.\n\n101 Wakefield, _A View on the Art of Colonization_ , 17. Canada was an example of the former, Massachusetts of the latter. E. A. Freeman also referred to the United States as \"independent colonies.\" Freeman, _Some Impressions of the United States_ (London, 1883), 23. See also my discussion in chapter 13.\n\n102 Seeley, _The Expansion of England_ , 58.\n\n103 Muthu, _Enlightenment against Empire_ , 75.\n\n104 E. G. Wakefield, _England and America_ (London, 1833), 2:252n; Richard Mills, _The Colonization of Australia (1829\u201342)_ [1915] (London, 1968), 152\u201353; Philip Schofield, _Utility and Democracy_ (Oxford, 2006), 199\u2013220.\n\n105 Hobson, _Imperialism_ (London, 1902), 36, 27, 328\u201355. Hobson, though, did recognize the exterminatory dangers of settler colonization (e.g., 266\u201367). He later changed his mind about imperial federation. See Duncan Bell, \"On J. A. Hobson's 'The Ethics of Internationalism,'\" _Ethics_ , 125 (2014), 220\u201322; and chapter 14.\n\n106 Mehta, _Liberalism and Empire_ , 2\u20133n1.\n\n107 Patrick Brantlinger, _Dark Vanishings_.\n\n108 Hammond, \"Colonial and Foreign Policy,\" 207. See also Gooch, \"Imperialism.\" This emphasis wasn't accepted by all liberals. Charles Dilke, for example, argued that \"India ought always to be first in our minds.\" Dilke, _The British Empire_ (London, 1899), 17.\n\n109 Hobhouse, _Liberalism_ [1911], ed. James Meadowcroft (Cambridge, 1994), 115.\n\n110 A. C. Forster Boulton, \"Liberalism and the Empire,\" _Westminster Review_ , 151 (1899), 490. Forster Boulton was a successful barrister and writer.\n\n111 Morley, \"Democracy and Reaction\" [1904], _Critical Miscellanies_ (London, 1908), 4:282\u201383. He later served as Secretary of State for India (1905\u201310).\n\n112 Besant, _The Future of the Empire_ (London, 1897), 124.\n\n113 Seeley, _Expansion of England_ , 11.\n\n114 Smith, \"The Hatred of England,\" _North American Review_ , 150\/402 (1890), 558.\n\n115 Hirst, Murray, and Hammond, _Liberalism and the Empire_ , xv.\n\n116 Seeley, _The Expansion of England_ , 37. On what he meant by this, see Bell, \"The Victorian Idea of a Global State,\" in _Victorian Visions_ , ed. Bell, 159\u201386; and chapter 11.\n\n117 Hammond, \"Colonial and Foreign Policy,\" 207. The Earl of Rosebery is often credited with coining the term \"commonwealth\" to refer to the British empire, though it only became popular when adopted by the Round Table twenty-five years later. See Rosebery's speech in Adelaide, January 18, 1884, reprinted in _The Concept of Empire_ , 2nd ed., ed. George Bennett, (London, 1962), 283.\n\n118 Hobhouse, _Democracy and Empire_ , 116. I explore Hobhouse's views in chapter 14. As I discuss in chapter 8, this vanguard notion was repeated in a variety of forms across the twentieth century.\n\n119 Bhikhu Parekh, \"Liberalism and Colonialism,\" in _The Decolonization of Imagination_ , ed. J. N. Pieterse and Parekh, (London, 1995), 81\u201398; Mehta, _Liberalism and Empire_.\n\n120 In chapter 3, I develop a similar argument about how liberalism is now conventionally understood.\n\n121 Comte, _System of Positive Polity_ [1854], ed. and trans. Richard Congreve (London, 1877 [1854]), 4:430\u201331. He called, for example, for the \"noble restoration\" of Algeria to the Arabs (364).\n\n122 P. J. Cain, \"Capitalism, War, and Internationalism in the Thought of Richard Cobden,\" _British Journal of International Studies_ , 5\/3 (1979), 229\u201347; Anthony Howe and Simon Morgan, eds., _Rethinking Nineteenth-Century Liberalism_ (London, 2006); Claeys, _Imperial Sceptics_ , 27\u201336. For the context of free trade arguments against empire, see Anthony Howe, \"Free Trade and Global Order,\" in _Victorian Visions of Global Order_ , ed. Bell, 26\u201346.\n\n123 Cited in Donald Read, _Cobden and Bright_ (London, 1967), 205\u20136. He warned: \"I have a presentiment... that God's chastisement upon us as a nation will come from Hindoostan.\"\n\n124 Cobden, \"How Wars Are Got Up in India,\" in _Writings of Richard Cobden_ (London, 1886), 455, 458.\n\n125 Spencer, \"The Proper Sphere of Government\" [1843], in _The Man versus the State_ (Indianapolis, 1982), 220.\n\n126 Spencer, \"Imperialism and Slavery,\" in _Facts and Comments_ (London, 1902), 113.\n\n127 Spencer, \"The Proper Sphere of Government,\" 224.\n\n128 For a key positivist intervention, see Richard Congreve et al., _International Policy_ (London, 1866). On the positivists, see T. R. Wright, _The Religion of Humanity_ (London, 1986). For their views on empire, see Claeys, _Imperial Sceptics_ , 47\u2013122. However, as the example of Seeley shows (see chapter 11), positivism was compatible with different positions on empire.\n\n129 Harrison, \"Empire and Humanity,\" _Fortnightly Review_ , 27\/158 (1880), 298, 299. For his views on empire, see also H. S. Jones, \"The Victorian Lexicon of Evil,\" in _Evil, Barbarism and Empire_ , ed. Tom Cook, Rebecca Gill, and Bertrand Taithe (Basingstoke, 2011), 126\u201343; Claeys, _Imperial Sceptics_ , 47\u2013122.\n\n130 Harrison, \"Empire and Humanity,\" 294. For his account of the nature of moral obligations within and beyond the state, see \"The Modern Machiavelli,\" _Nineteenth Century_ , 42\/247 (1897), 462\u201371.\n\n131 Harrison, \"Empire and Humanity,\" 295, 297.\n\n132 Ibid., 290.\n\n133 Ibid., 299. Andrew Fitzmaurice argues that international law, rather than a simple vehicle of imperialism, as it has often been characterized in recent scholarship, was also a site of deep contestation over the legitimacy of empire, riven by clashes over the meaning of sovereignty and freedom: \"[I]nternational law was... one of the domains in which opposition to empire was most strongly articulated.\" Fitzmaurice, _Sovereignty, Property and Empire_ , 300. For another pluralist interpretation, see Jennifer Pitts, \"Boundaries of Victorian International Law,\" in _Victorian Visions_ , ed. Bell, 67\u201389. For an argument that stresses the complicity of international law in empire, see Martti Koskeniemmi, _The Gentle Civilizer of Nations_ (Cambridge, 2001).\n\n134 I find less evidence of martialist attitudes glorifying violence for its redemptive capacities among liberal thinkers, though no doubt they were occasionally expressed. Karma Nabulsi, who first formulated the category, argues that Seeley can be seen as an exemplary martialist. Nabulsi, _Traditions of War_ (Oxford, 1999), ch. 4. For a challenge to this attribution, see Duncan Bell, \"Unity and Difference,\" _Review of International Studies_ , 31\/3 (2005), 562\u201366.\n\n135 This distinction is drawn in Jedediah Purdy, \"Liberal Empire,\" _Ethics & International Affairs_, 17\/2 (2003), 35\u201347.\n\n136 On the history of the idea, see Brett Bowden, _The Empire of Civilization_ (Chicago, 2009); Michael Sonenscher, \"Barbarism and Civilisation\" in Richard Whatmore and Brian Young (eds.), _A Companion to Intellectual History_ (Oxford, 2016), 288\u2013302.\n\n137 See, for example, Morefield's discussion of Gilbert Murray's liberalism in _Covenants without Swords_.\n\n138 Chamberlain, \"The True Conception of Empire\" (1897), in _Mr Chamberlain's Speeches_ , ed. C. Boyd, (London, 1914), 2:3.\n\n139 Dunning, \"A Century of Politics,\" _North American Review_ , 179\/577 (1904), 812\u201313. Dunning was at the time a Professor of History at Columbia University. For more on his writing, see the discussion in chapter 3.\n\n140 Dunning, \"A Century of Politics,\" 814\u201315.\n\n141 Vitoria, \"On the American Indians (De Indis),\" in _Franciso de Vitoria: Political Writings_ , ed. Anthony Pagden and Jeremy Lawrence (Cambridge, 1991 [1539]), Question 1, Conclusion, sec. 23, 250\u201351.\n\n142 James Mill, \"Review of Voyage aux Indes Orientales,\" by Le P. Paulin De S. Barth\u00e9lemy, _Edinburgh Review_ , 15 (1810), 371.\n\n143 Mikael H\u00f6rnqvist, _Machiavelli and Empire_ (Cambridge, 2004); H\u00f6rnqvist, \"Machiavelli's Three Desires,\" in _Empire in Modern Political Thought_ , ed. Muthu, 7\u201330.\n\n144 Pitts, _A Turn to Empire_ , chs. 6\u20137.\n\n145 Stephen, \"Liberalism,\" _Cornhill Magazine_ , 5\/25 (1862), 82.\n\n146 It is arguable, though, that Stokes exaggerates the importance of Stephen. See here Frederick Rosen, \"Eric Stokes, British Utilitarianism, and India,\" in _J. S. Mill's Encounter with India_ , ed. Moir, Peers, and Zastoupil (Toronto, 1999), 18\u201333. On the variability of utilitarian responses, see also Bart Schultz and Georgios Varouxakis, eds., _Utilitarianism and Empire_ (Lanham, MD, 2005).\n\n147 Mehta, _Liberalism and Empire_ , 29\u201330, 198; Pitts, _A Turn to Empire_ , 223; Mantena, _Alibis of Empire_ , 38.\n\n148 His unconventional liberalism is discussed in James Colaiaco, _James Fitzjames Stephen and the Crisis of Victorian Thought_ (London, 1983); K.J.M. Smith, _James Fitzjames Stephen_ (Cambridge, 1988); Collini, _Public Moralists_ , 280\u201387. For a convincing account of his political thinking, see Julia Stapleton, \"James Fitzjames Stephen,\" _Victorian Studies_ , 41\/2 (1998), 243\u201346.\n\n149 Sidgwick, _Lectures on the Ethics of T. H. Green, Mr. Herbert Spencer and J. Martineau_ (London, 1902), 236; Sidgwick, _The Elements of Politics_ 1891], 3rd ed. (London, 1907), 256. See also the discussion in [chapter 10.\n\n150 Leslie Stephen, _The Life of Sir James Fitzjames Stephen_ (London, 1895), 398.\n\n151 Stephen, \"Deus Ultionum,\" _Saturday Review_ , October 15, 1867; Stephen, _Life_ , 225, 310, 394.\n\n152 Stephen, _Liberty, Equality, Fraternity_ [1873], ed. R. J. White (Chicago, 1990), 113. See also his attempt to justify the conquest, and celebrate Warren Hastings, in _The Story of Nuncomar and the Impeachment of Sir Elijah Impey_ (London, 1885).\n\n153 Stephen, \"Manchester on India,\" _Times_ , January 4, 1878, 3.\n\n154 On his friendship and \"intellectual sympathies\" with Froude, see Stephen, _Life_ , 585, 700; Ciaran Brady, _James Anthony Froude_ (Oxford, 2013), 3, 16.\n\n155 Stephen, \"Liberalism,\" _Cornhill Magazine_ , 5\/25 (1862), 82.\n\n156 Stephen, \"Foundations of the Government of India,\" _Nineteenth Century_ , 14\/80 (1883), 559, 554, 566.\n\n157 Ibid., 554, 556.\n\n158 Ibid., 551 (and 561\u201363).\n\n159 Mantena, _Alibis of Empire_ , 11, 6.\n\n160 The argument about Indian policy draws on Metcalf, _Ideologies of the Raj_.\n\n161 Mantena, _Alibis of Empire_ , 43.\n\n162 I stress the role in disillusionment with democracy on settler colonial ideology in Bell, _The Idea of Greater Britain_ , ch. 2. On liberals and democracy, see also Christopher Harvie, _The Lights of Liberalism_ (London, 1976).\n\n163 Wilson, \"Taking Europe for Granted,\" _History Workshop Journal_ , 52 (2001), 292.\n\n164 Sidgwick, _The Methods of Ethics_ (Cambridge, 1874). See also J. B. Schneewind, _Sidgwick's Ethics and Victorian Moral Philosophy_ (Oxford, 1977); Bart Schultz, _Henry Sidgwick_ (Cambridge, 2004). On idealism, see David Boucher and Andrew Vincent, _British Idealism and Political Theory_ (Edinburgh, 2001); W. J. Mander, _British Idealism_ (Oxford, 2011), ch. 7; Peter Nicholson, _The Political Philosophy of the British Idealists_ (Cambridge, 1990); Sandra den Otter, _British Idealism and Social Explanation_ (Oxford, 1996); Colin Tyler, _Idealist Political Philosophy_ (London, 2006).\n\n165 Stefan Collini, _Liberalism and Sociology_ (Cambridge, 1983); Michael Freeden, _The New Liberalism_ (Oxford, 1978); Avital Simhony and David Weinstein, eds., _The New Liberalism_ (Cambridge, 2001).\n\n166 David Runciman, _Pluralism and the Personality of the State_ (Cambridge, 1997); C\u00e9cile Laborde, _Pluralist Thought and the State in Britain and France, 1900\u20131925_ (Basingstoke, 2000); Marc Stears, _Progressive, Pluralists, and the Problems of the State_ (Oxford, 2002).\n\n167 Michael Freeden, \"The Coming of the Welfare State,\" in _The Cambridge History of Twentieth-Century Political Thought_ , ed. Terence Ball and Richard Bellamy (Cambridge, 2006), 7\u201345; Jose Harris, \"Political Thought and the Welfare State, 1870\u20131914,\" _Past & Present_, 135 (1992), 116\u201341.\n\n168 Herbert Samuel, _Liberalism_ (London, 1902), 348. One Indian civil servant and British liberal MP went so far as to argue that the civilizing mission had _already_ been successful, with British imperial education having prepared the Indians for immediate (though limited) self-government within an overarching imperial structure. Henry Cotton, \"The Political Future of India,\" _North American Review_ , 181\/584 (1905), 110\u201316.\n\n169 Samuel, _Liberalism_ , 325.\n\n170 Ibid., 330, 332.\n\n171 Caldecott, _English Colonization and Empire_ , 84\u201385. For further examples of advocacy of civilization progress, see chapter 5.\n\n172 J. Stanley Little, _Progress of British Empire in the Century_ (London, 1903), xv. Drawn from \"Lockesley Hall\" (1842), Tennyson's phrase the \"federation of Mankind\" was routinely employed in imperial discourse. For further discussion, see Duncan Bell, _Dreamworlds of Empire_ (forthcoming).\n\n173 Arnold, \"The Duty and Destiny of England in India,\" _North American Review_ , 154\/423 (1892), 170. \"But\u2014and here comes the point\u2014the question of questions is whether the democracy of great Britain, our household-suffrage men, who have of late come to supreme power in the realm, comprehend their Indian Empire and care to maintain it\" (187).\n\n174 MacDonald, _Labour and the Empire_ (London, 1907), 102\u20133.\n\n175 Ibid., 108\u20139.\nCHAPTER 3\n\nWhat Is Liberalism?\n\nLike the history of anything else, history of philosophy is written by the victors. Victors get to choose their ancestors, in the sense that they decide which among their all too various ancestors to mention, write biographies of, and commend to their descendants.1\n\n\u2014RICHARD RORTY\n\nBefore we can begin to analyze any specific form of liberalism we must surely state as clearly as possible what the word means. For in the course of so many years of ideological conflict it seems to have lost its identity completely. Overuse and overextension have rendered it so amorphous that it can now serve as an all-purpose word, whether of abuse or praise.2\n\n\u2014JUDITH SHKLAR\n\nLiberalism is a specter that haunts Western political thought and practice. For some it is a site of the modern, an object of desire, even the _telos_ of history. For others it represents an unfolding nightmare, signifying either the vicious logic of capitalism or a squalid descent into moral relativism. For others still, perhaps the majority, it is a mark of ambivalence, the ideological prerequisite for living a reasonably comfortable life in affluent democratic states\u2014the least-worst option.\n\nBut what is liberalism? Across and within scholarly discourses, it is construed in manifold and contradictory ways: as an embattled vanguard project and constitutive of modernity itself, a fine-grained normative political philosophy and a hegemonic mode of governmentality, the justificatory ideology of unrestrained capitalism and the richest ideological resource for its limitation. Self-declared liberals have supported extensive welfare states and their abolition; the imperial civilizing mission and its passionate denunciation; the necessity of social justice and its outright rejection; the perpetuation of the sovereign state and its transcendence; massive global redistribution of wealth and the radical inequalities of the existing order. Shklar's complaint that it is an \"all-purpose word\" is thus unsurprising, for liberalism has become the metacategory of Western political discourse.\n\nThere are several responses to \"overextension.\" One is simply to ignore it, deploying the term as if its meaning was self-evident. Ubiquitous across the humanities and social sciences, this unreflective impulse generates much confusion. Another is to engage in \"boundary work\"\u2014to demarcate and police the discourse.3 Some influential attempts to do so have figured liberalism as a capacious tradition of traditions, with Guido De Ruggiero and Friedrich Hayek, for example, bifurcating it into British and Continental forms. The most common variation on this theme is to distinguish \"classical\" and \"social\" liberalisms.4 Another popular response is to narrate liberal history as a story of rise or decline, triumph or tragedy. A familiar rendition bemoans the lost purity of the original. Thus Leo Strauss mourned the transition from virtuous \"ancient\" liberalism (reaching its apogee in Athens) to debased forms of \"modern\" liberalism (commencing with Machiavelli), while Sheldon Wolin averred that twentieth-century liberalism had disastrously forgotten its early skeptical enunciation.5 Some neoconservatives have claimed the mantle, seeking, with Irving Kristol, \"a return to the original sources of liberal vision and liberal energy so as to correct the warped version.\"6 Declension has also been a recurrent libertarian complaint. When he came to pen his defense of \"classical\" liberalism in 1927, Ludwig von Mises grumbled that from Mill onwards the ideology had degenerated into socialism, a warning that Herbert Spencer had flagged half a century earlier.7 But the development of liberalism can also be cast as progressive. Both L. T. Hobhouse and John Dewey, for example, celebrated the transfiguration of liberalism from an ideology of _laissez-faire_ to one that justified the use of systematic government intervention to reduce harmful disadvantages.8 The argument continues today with many libertarians condemning \"social\" liberalism as a form of socialism and many social liberals rejecting the liberal credentials of libertarianism. All sides claim to be heirs of the one true liberalism.\n\nA related policing strategy is to concede the intellectual diversity of liberalism while extracting its constitutive element(s)\u2014its ineliminable core. This too is contested terrain. Adopting the most common line, Shklar sought to create a \"modest amount of order\" by characterizing liberalism as a \"political doctrine\" with \"only one overriding aim: to secure the political conditions that are necessary for the exercise of personal freedom.\"9 Yet Jeremy Waldron is right that positing a commitment to freedom as the foundation of liberalism \"is to say something too vague and abstract to be helpful.\" Instead, he proposes that it is best defined by a \"requirement that all aspects of the social should either be made acceptable or be capable of being made acceptable to every last individual.\"10 Ronald Dworkin, meanwhile, asserts that \"a certain conception of equality... is the nerve of liberalism.\"11 Others insist on a cluster of commitments. The historian Gary Gerstle, for example, suggests that liberals have always endorsed three \"foundational principles,\" rationality, emancipation, and progress, while John Dunn once lamented the \"dismaying number of categories\" that have been claimed as central to liberal ideology, including political rationalism, hostility to autocracy, cultural distaste for conservatism and tradition, tolerance, and individualism.12 Even its supposed core has proven elusive.\n\nIn what follows I neither attempt to adjudicate between these competing interpretations nor present a new substantive liberal theory. Instead, I seek to reframe the way in which the liberal tradition is understood. I open with a critique of some existing interpretive protocols used to delimit political traditions, before introducing (in section 2) a new way of conceptualizing liberalism, suggesting that it can be seen as the sum of the arguments that have been classified as liberal, and recognized as such by other self-proclaimed liberals, across time and space. In the second half of the chapter, I analyze the emergence and subsequent transformation of the category of liberalism in Anglo-American political thought between 1850 and 1950. This serves as an illustrative case study of some of the methodological arguments I outline in the first two sections. While section 3 traces the evolution of the language of liberalism in nineteenth-century Britain, section 4 explores how the scope of the liberal tradition was massively expanded during the middle decades of the century, chiefly in the United States, such that it came to be seen by many as the constitutive ideology of the West. Above all, I contend that this broad understanding of liberalism was produced by a conjunction of the ideological wars fought against \"totalitarianism\" and assorted developments in the social sciences. Today we both inherit and inhabit it.\n\nConstructing Liberalism: Scholarly Purposes and Interpretive Protocols\n\nThere are at least three _types_ of answer that can be given to the question in the title, each of which serves a different scholarly purpose. _Prescriptive_ responses specify norms of correct or best usage. They delineate a particular conception of liberalism, branding it as more authentic\u2014more truly liberal\u2014than other claimants to the title. Such accounts vary in the core features recognized as constitutive, the interpretive methodologies utilized to identify them, and the normative stance assumed towards them. This is the most familiar type of answer. _Comprehensive_ responses attempt to chart the plethora of liberal languages. Rather than prescribing a favored conception they seek to identify the _actual_ range of usage, mapping the variegated topography of liberal ideology. These accounts differ in the interpretive methodologies employed and the temporal and spatial scope of inquiry. _Explanatory_ responses account for the development of liberalism(s), whether understood in prescriptive or comprehensive terms. They too vary in methodology and scope. Although each kind of response is legitimate in certain circumstances, problems arise when they are misapplied or conflated. In particular, prescriptive accounts are very poor guides to understanding the internal complexity and historical development of ideologies.\n\nScholars also adopt different methodological strategies\u2014 _interpretive protocols_ \u2014to answer the question. To argue about a political tradition\u2014to compare and contrast it; to chart its decline, crisis, or ascension; to pinpoint its flaws or celebrate its strengths\u2014it is first necessary to construct it as an object of analysis. Political theorists typically employ two main protocols, either individually or in combination: _stipulative_ and _canonical. Contextualism_ offers an alternative.13\n\n_Stipulative_ accounts identify necessary (though rarely sufficient) conditions for a position to count as a legitimate exemplar of a tradition. \"Liberalism\" is typically constructed from interpretations of the meaning and interrelation of core concepts, such as liberty, authority, autonomy, and equality. Such accounts employ definitional fiat to demarcate the legitimate boundaries of liberalism: only those adhering to a particular cluster of assumptions and arguments count as properly liberal. We have already encountered the contrasting formulations offered by Dworkin, Gerstle, Shklar, and Waldron. History is sometimes invoked in such accounts, but it is usually what Rawls aptly termed the \"philosopher's schematic version of speculative history,\" and while these arguments often cite historical figures\u2014above all Locke, Kant, Mill, and now Rawls himself\u2014their core normative arguments can be justified independently of any past expression.14\n\nTraditions are usually constructed around a canon of renowned thinkers, which serves simultaneously as a reservoir of arguments, an index of historical continuity, and a powerful source of intellectual authority. _Canonical_ approaches thus distil \"liberal\" theoretical structures from exemplary writings. The most frequent targets for this protocol are (again) Locke, Kant, Mill, and Rawls, though a host of other figures are sometimes marshaled to fit the occasion. Leo Strauss and his epigones have divined sweeping interpretations of liberal modernity from a handful of \"great books.\" Pierre Manent, for instance, charts the unfolding of liberalism through a procession of figures stretching back to Machiavelli and Hobbes.15 Far from being an exclusive Straussian strategy, however, this is arguably the most common protocol for constructing liberalism. As I discussed in chapter 2, for example, canonical formulations have structured arguments about the relationship between liberalism and empire. While Uday Singh Mehta grounds his influential argument that liberalism has an \"urge\" to empire on readings of Locke and Mill, most rejoinders\u2014including those by Jennifer Pitts and Sankar Muthu\u2014have likewise focused on canonical figures.\n\nBoth of these methodological strategies are valuable, even essential, for achieving particular scholarly aims. Stipulative protocols can be fruitfully employed in the elaboration of normative political philosophies and the construction of ideal types for conducting social analysis. Canonical scholarship, meanwhile, can generate insightful readings of individual thinkers. Yet neither are capable of underwriting plausible comprehensive or explanatory accounts because they cannot shed much light on the universe of liberal languages, the plethora of competing and often contradictory claims that travel under its name. Articulated in the register of philosophical abstraction, the stipulative genre is estranged from the vicissitudes of history and political practice. It is caught on the horns of a dilemma. Unless the stipulated commitments are conceptualized at a very high level of generality\u2014for example, that liberalism prioritizes individual freedom, or that liberals are committed to toleration, liberty, and constitutional government\u2014they will invariably fail to encompass the deep divisions between professed variants of liberalism, yet when pitched at that level they provide little guidance for pursuing the detailed reconstruction necessary for satisfactory description or explanation. Waldron's argument illustrates this mismatch. Maintaining that only those adopting his contracturalist view of justification count as properly liberal, he anoints Locke, Rousseau, and Kant as genuine liberals, while suggesting that John Stuart Mill and numerous other nineteenth-century figures (especially utilitarians) stand in an \"ambiguous relation\" to the tradition. On this account, then, liberalism simultaneously preexists its own self-conscious formulation and was misunderstood by many of those who played a fundamental role in its propagation. At least he admits that \"many liberals may not recognise\" the picture he paints.16\n\nThe problem with canonical protocols is that they can rarely support the generalizations they are invoked to underpin. As Mehta's argument shows, work in this vein often seems to assume that the ideas of canonical figures can stand in for, or be seen as sufficiently representative of, the tradition as a whole. This provides a defective foundation on which to build an analysis of a multifaceted political ideology. Given the internal diversity of liberalism, its national and regional variation, and its polyphonic evolution, it is exceptionally difficult to ground felicitous generalizations on the work of a handful of authors. A further problem is that this protocol often takes as given the very thing that should be investigated\u2014the construction of the canon. The idea of a canon of great thinkers standing at the heart of a preconstituted tradition is, in part, an artifact of the professional development of academic political theory during the twentieth century.17 It is the product of a particular moment in time, shaped by largely forgotten value-commitments and selection criteria, and arguments centered on claims distilled from the canon are thus conducted within a discursive echo chamber. Indeed studying the processes through which the canon crystallized can reveal as much (or more) about the dynamics of political thinking as the forensic analysis of purportedly exemplary texts.\n\n_Contextualist_ approaches need little introduction.18 The bulk of such work has focused on illuminating the patterns of early modern political thinking, and at present there are no general contextual histories of liberalism\u2014indeed its methodological precepts render such a project quixotic. Contextualists have nevertheless made an important contribution to the analysis of liberalism by challenging the assumption that it can be traced to the seventeenth century. Versions of this argument have been tendered by John Dunn, Mark Goldie, J.G.A. Pocock, Quentin Skinner, and James Tully. Pocock, for example, maintains that \"liberalism\" was \"not used in the eighteenth century, where the adjective 'liberal' did not bear its modern meaning, and though elements were present which would in due course be assembled by means of this formula, there was no system of doctrine corresponding to its later use.\"19 He concludes that no significant inferences about liberalism can be drawn from the earlier period. In particular, this strand of scholarship has repeatedly questioned Locke's elevated status as a (or the) foundational liberal.20 It is important to recognize that this is not principally a semantic argument about the absence of the word \"liberalism\" in the early modern period, but rather a claim about the range of concepts and arguments available to historical actors.21 It is about extant thought-worlds, not recoverable terminology. Yet while this body of scholarship has questioned conventional accounts of liberal history, it has rarely probed how and why that very convention emerged.\n\nMichael Freeden has developed the most systematic contextualist account of Anglo-American liberalism. It is, he argues,\n\n... that semantic field in which the political understandings of people who regard themselves as liberals, or who others regard as liberals, may be investigated. It is a plastic, changing thing, shaped and reshaped by the thought-practices of individuals and groups; and though it needs to have a roughly identifiable pattern for us to call it consistently by the same name, \"liberalism,\" it also presents myriad variations that reflect the questions posed, and the positions adopted, by various liberals.22\n\nHowever, even Freeden tends to blur prescriptive, comprehensive, and explanatory arguments. Identifying Millian liberalism as the most genuine manifestation of the ideology, he finds several alternative strands wanting, including contemporary libertarianism and \"American philosophical liberalism\" (social liberalism following Rawls). With its focus on state neutrality, neo-Kantian conceptions of autonomy, and the possibility of specifying fixed principles of justice, as well as its abstraction from practical political activity, the latter represents a \"decisive departure\" from prevailing modes of liberal thought, while the former lacks \"many of the attributes which bestow on the liberal profile its distinctive contours,\" and it is thus disqualified as \"a serious contender for the current mantle of liberalism.\"23 On this account, while liberalism contains no ineliminable transhistorical essence, a specific thread nevertheless expresses its most mature \"established\" form. Freeden's explicit anti-essentialism is thus qualified by prescriptive boundary-working methodological commitments. His general approach nevertheless points to a fruitful interpretive strategy. A comprehensive contextualist analysis of liberalism should provide a framework for grasping the diverse ways in which liberal languages emerge, evolve, and come into conflict with one another, rather than trying to distil an ahistorical set of liberal commitments from conceptual or canonical investigation.\n\nA Summative Conception\n\nThomas Nagel is surely right to proclaim that \"[i]t is a significant fact about our age that most political argument in the Western world now goes on between different branches of [the liberal] tradition.\"24 This ideological victory is acknowledged by both self-proclaimed liberals and their critics. At the turn of the new millennium, Perry Anderson protested that \"for the first time since the Reformation there are no longer any significant oppositions\u2014that is, systematic rival outlooks\u2014within the thought-world of the West: and scarcely any on a world scale.\" Writing more in sorrow than celebration, Raymond Geuss concurs: \"We know of no other approach to human society that is at the same time as theoretically rich and comprehensive as liberalism and also even as remotely acceptable to wide sections of the population in Western societies.\"25 Most inhabitants of the West are now _conscripts of liberalism_ : the scope of the tradition has expanded to encompass the vast majority of political positions regarded as legitimate.26 Today there is little that stands outside the discursive embrace of liberalism in mainstream Anglo-American political debate (and perhaps especially in academic political theory), and most who identify themselves as socialists, conservatives, social democrats, republicans, greens, feminists, and anarchists have been ideologically incorporated, whether they like it or not. Useful as they are for other tasks, stipulative and canonical protocols offer little help in interpreting this phenomenon. We thus need a comprehensive account that can accommodate the plurality of actually existing liberalisms, past and present, without smuggling in boundary-working prescriptive commitments. A plausible explanation, meanwhile, must unpack the dynamics of ideological conscription. This section introduces a comprehensive heuristic, while the remainder of the essay begins the task of explaining how the meaning of Anglo-American liberalism was transformed between 1850 and 1950.\n\nI propose the following definition (for comprehensive purposes): the liberal tradition is constituted by the sum of the arguments that have been classified as liberal, and recognized as such by other self-proclaimed liberals, across time and space. Let us call this the _summative conception_. Adopting it offers several benefits: it can help make sense of the discursive \"overextension\" and elastic usage of the term, while avoiding unhelpful claims about pure essence or authentic form. Moreover, it forces us to examine traditions as evolving and contested historical phenomena, conjured into existence by the work of many hands, shaped by scholarly knowledge-production and pedagogical regimes, and often fashioned and remade with specific politico-intellectual purposes in mind. It allows us to grasp, that is, the intricate dialectic of intentional human action and unintended consequences that structure any rich political tradition.27\n\nFreeden, as we have seen, points us towards \"that semantic field in which the political understandings of people who regard themselves as liberals, or who others regard as liberals, may be investigated.\" However, it is necessary to qualify the claim about those \"who others regard as liberals.\"28 The problem here is that the term is commonly used to tar opponents or to create linkages between liberalism and political positions that liberals invariably reject. Witness the current fashion for American ultra-conservatives to conflate liberalism with both fascism and Marxism.29 If we adopt an unqualified summative position\u2014defining liberalism as the totality of positions termed liberal\u2014then the tradition would now traverse the spectrum from fascism to communism. This is an implausibly expansive view. Hence the epistemic limit: only those positions _affirmed_ at some point in time by groups of _self-proclaimed_ liberals should be included. This allows us to map the universe of liberalism(s), though it raises another question: how widely held must a particular interpretation be for inclusion? Can any usage (by a self-proclaimed liberal) expand the boundaries of liberalism? There is no simple answer to this threshold question\u2014scholars will adopt different inclusion criteria depending on their purposes and methodological inclinations. My own view is that to stake a claim for inclusion there must be sustained usage by numerous prominent ideological entrepreneurs over at least two generations. Otherwise, the bar for inclusion is set too low. That H. G. Wells declared himself a \"liberal fascist\" is nowhere near enough to warrant incorporating fascism into the liberal tradition, for barely anyone else followed him along that idiosyncratic path.30 But contra Freeden and others, \"libertarianism\" clearly meets the entry criteria. So too do the social democratic arguments scorned by libertarians.\n\nThe temporal point is also important: I am not suggesting that only arguments labeled (and recognized) as liberal at Time T1 count as liberal. An argument is not expelled from the liberal tradition because it is later ascribed a different label or because liberals now happen to reject it. The tradition is constituted by the accumulation of arguments _over time_. Explicit justifications of imperialism, arguments seeking to limit suffrage on grounds of gender and racial difference, and eugenicist attempts to \"perfect\" the species all form part of the liberal tradition.31 As do rejections of these positions. Rather than attempting to sanitize or inoculate liberalism by ignoring aspects no longer considered palatable, or, more subtly, relegating those aspects to superseded historical circumstances while extracting a pristine transhistorical core, we should recognize that liberalism has become a hyper-inflated, multifaceted body of thought\u2014a deep reservoir of ideological contradictions.\n\nIn thinking about traditions, it is productive to distinguish between the identities of agents and the arguments they invoke\u2014between being an X (liberal, socialist, fascist) and employing forms of argument that are best characterized as X. The former is a claim about self-fashioning and the construction of personae, the latter about doctrine. Although this chapter has focused on academic debates, the argument also applies to practical politics. It may well be part of the self-understanding of an American Tea Party devotee that they are fundamentally opposed to liberalism, but this identity-claim does not entail that they reject arguments central to the liberal tradition (as construed by the summative conception). In other words, despite espousing virulent strains of antiliberalism they are nevertheless committed to paradigmatic liberal positions insofar as they defend (say) neoclassical economics, libertarian social policy, and the superiority of \"liberal democratic\" institutions. Within political theory, the same can be said for many self-proclaimed critics of liberalism, whether post-structural, critical-theoretical, republican, communitarian, or conservative.\n\nAnother consequence of adopting the summative conception is that it dissolves a familiar but misleading picture of traditions, which are still often conceived of as self-contained bodies of thought with relatively clear and stable boundaries.32 On this view, the interstitial spaces between established traditions are populated by hybrids\u2014liberal-socialists, liberal-conservatives, Christian-realists. However, this fails to grasp the ideological miasma of modern politics, in which most individuals simultaneously adopt positions that are claimed by assorted traditions. The most hardened Tory or Republican, contemptuous of moderate \"liberal-conservatives,\" is likely to propound ideas that have long been affirmed by mainstream liberals. When looking at an agent who has been classified in two or more ways\u2014say as a liberal and a conservative\u2014this could mean several different things. It might imply that one of the classifications is mistaken, or that they adopt a hybrid position, or alternatively that decomposing the argument will yield some elements that are genuinely \"liberal\" and others that are genuinely \"conservative.\" The main problem with these options, however, is that today it is impossible to convincingly classify values (such as liberty or equality) or public policies (such as free trade or democracy promotion) as _exclusively_ liberal _or_ conservative (or something else). They are\u2014they have become\u2014both at once.33\n\nThe scholarly implications of tradition-construction can be significant, as the work of Domenico Losurdo demonstrates. His remarkable \"counterhistory\" of liberalism places considerable emphasis on the social practices characteristic of British, Dutch, and American societies.34 He contends that the British slave trade peaked in the eighteenth century, well after liberalism was consolidated by the settlement of 1688, and that in North America chattel slavery reached its apogee in the early nineteenth century, following the victory of liberalism in the War of Independence. John Locke figures heavily in both narratives. If we adopt the current conventional understanding of liberalism, as Losurdo does, this throws up a disturbing puzzle about liberal attitudes to domination, hierarchy, and exploitation, and it underpins his sweeping critique. The normative conclusions that Losurdo draws about contemporary liberalism are derived from, and are only intelligible in relation to, his interpretation of the tradition. But the puzzle dissolves if we adopt (for example) a Pocockian interpretation, because on that account neither Britain nor the United States was liberal in any meaningful sense before the nineteenth century.35 Interpretations of tradition often shape contemporary understanding as well as historical investigation.\n\nLiberalism before Locke\n\nAt the turn of the twentieth century, the dominant prescriptive narrative about liberalism in the English-speaking world identified it as a product of the late eighteenth and early nineteenth centuries, part of a cluster of ideological innovations that also included socialism. At the turn of the twenty-first century, the dominant narrative views it as a product of the mid-seventeenth century or earlier. In the former, the French and American Revolutions and the global spread of capitalism play a starring role; in the latter, the Glorious Revolution of 1688 and the religious wars in Europe. In the former, utility, democracy, and political economy are the guiding topics; in the later, natural rights, the social contract, and constitutionalism. In the former, radicals like Jeremy Bentham take center stage; in the latter it is almost invariably John Locke. Indeed Locke's foundational role in liberalism is today a leitmotif of political thought, promulgated by critics and adherents alike. \"To the extent that modern liberalism can be said to be inspired by any one writer,\" Wolin counseled in _Politics and Vision_ , \"Locke is undoubtedly the leading candidate.\" Stephen Holmes agrees: \"The best place to begin, if we wish to cut to the core of liberalism, is with Locke.\"36 The transition from one conception to the other tells us much about the trajectory of modern politics, the sociology of knowledge, and the historicity of theoretical categories.\n\nIn his compelling account of American political thought, John Gunnell argues that liberalism only became a widely recognized category of general political discourse after the First World War, and only assumed an important role in academic political theory in the wake of the Second World War. Moreover, he contends that \"it was not until after 1950 that there was even any extended discussion of Locke as a liberal.\"37 Adding a British dimension to the story complicates this picture. Both the conception of liberalism as a tradition rooted in early modern political thought, and the identification of Locke as a foundational liberal, emerged slightly earlier in Britain than in the United States, and for different reasons. Yet despite this initial variation, British and American narratives converged during the ideological battles of the middle decades of the twentieth century, creating the expansive vision of liberalism that dominates scholarly discourse today.\n\nWhile the term \"liberal\" had long been used in English to denote assorted aristocratic dispositions, mores, and pursuits, it only assumed a specifically political meaning in the early nineteenth century. Borrowed from the Spanish _Liberales_ of the 1812 Constitution, the term was first employed in a derogatory manner by Tories to malign their Whig opponents. During the 1820s it was reclaimed by some radical Whigs, in a classical example of rhetorical redescription, to characterize individuals and policies dedicated to nonrevolutionary reform, although it also became associated with the small but vocal group of \"philosophic radicals,\" including the young John Stuart Mill. \"Liberal\" was increasingly utilized to describe the politico-economic demands of the emergent middle classes.38 Yet it was still an obscure and marginal category: during the 1820s and 1830s \"'liberals' were not a firmly defined group and 'liberalism' did not securely mark out a single intellectual phenomenon.\"39 It was only during the second half of the century that usage proliferated, though it remained closely tied to the creed of the recently named Liberal Party.40\n\nDespite its increasing visibility, there was little sophisticated or thorough discussion of liberalism as an intellectual tradition until the early twentieth century, and even then it was rare. It is barely visible in surveys of political thought written between the 1850s and the 1930s.41 The main political theory textbook employed in Cambridge and Oxford in the late nineteenth century, Bluntschli's _The Theory of the State_ , didn't use liberalism as an organizing category, and nor did Sidgwick's _Development of European Polity_ , which replaced it in Cambridge. The effort to construct an authoritative liberal tradition only gained ground during the perceived \"crisis of liberalism\" in the Edwardian era. Fighting acrimonious battles over the future of the British state, and challenged by an emergent politically conscious labor movement, some liberals elaborated edifying genealogies to underwrite the ideological legitimacy of their cause. The most common renditions of the tradition identified the transition from the eighteenth to the nineteenth century as the formative moment. W. Lyon Blease's _Short History of English Liberalism_ , published in 1913, was typical. A polemical defense of advanced liberalism written by a legal scholar, it argues that liberalism was the product of three revolutions: the industrial (starting in the 1760s), American, and French.42\n\nAccounts that emphasized the Revolutionary-era origins of liberalism, defined it prescriptively as expressing a commitment to both liberty and social equality (sometimes even democracy). This move excluded earlier Whig political thought. It was a constellation of ideas that could only have emerged after the tumult of the late eighteenth century and the rise of a powerful middle class demanding political representation. In 1862, in one of the earliest analytical accounts of liberalism, James Fitzjames Stephen pinpointed the connection:\n\nAs generally used... \"liberal\" and \"liberalism\"... denote in politics, and to some extent in literature and philosophy, the party which wishes to alter existing institutions with the view of increasing popular power. In short, they are not greatly remote in meaning from the words \"democracy\" and \"democratic.\"43\n\nForty years later, William Dunning, a prominent American historian and political theorist, argued that \"fundamentally, nineteenth-century Liberalism meant democracy.\"44 In an essay seeking to illuminate the \"Historic Bases of Liberalism,\" another writer distinguished liberals from Whigs by pointing to the aristocratic character and consequences of 1688. \"In none of the great documents of the time,\" he announced, \"do you find the suggestion that the people should share in the work of government,\" for such a conception only emerged in the wake of the French Revolution. It followed that liberalism could only be a product of the late eighteenth century.45 This view only began to lose popularity in the interwar years, though it did not disappear completely. In a textbook published in 1920, for example, the author declared that the \"essence of Whiggism has always been the belief in individual liberty combined with the denial of social equality\" and that as such \"this conception is rejected by Liberals who have a far wider experience on which to frame their social judgments.\"46 Other variants of the prescriptive protocol can also be discerned, including one that reduced liberalism to a species of utilitarian radicalism. Thus, A. V. Dicey wrote in 1905 of \"Benthamite individualism, which, in accordance with popular phraseology, may often be called conveniently liberalism.\"47\n\nIt is both striking and symptomatic that in Britain, so often seen as the incubator of liberalism, Locke was not widely regarded as a liberal\u2014let alone a paradigmatic one\u2014until nearly a century after liberalism emerged as an explicit political doctrine. Several generations of self-identified liberals somehow failed to recognize him as one of their own. While Locke's nineteenth-century biographers celebrated him as one of the greatest of philosophers, their verdicts on his political writings were far less positive. Acknowledging him as a leading Whig ideologue who exerted a major influence over eighteenth-century political thinking, they almost invariably rejected his theoretical arguments as defective and obsolete.48 In so doing they painted a microcosmic picture of his general reputation during the Victorian age: \"Locke meant the _Essay_ ,\" not the _Treatises_.49\n\nMost accounts of the historical development of modern political thought contended that there had been a radical break\u2014both intellectual and political\u2014at the end of the eighteenth century. A new world had dawned, and there was little space in it for Lockean political theory. Liberalism was figured as the progeny of this gestalt switch. The historicist sensibility that permeated nineteenth-century social and political thought was antithetical to the rationalist deductions of Locke, and accounts of natural rights, natural law, and above all the social contract were widely denigrated as primitive. The eminent legal scholar Frederick Pollock was reiterating a popular line of argument when he claimed that Hume had shown decisively that \"even as analysis the mere doctrine is useless.\" He concluded that Burke had been right to ridicule the contract as \"absurd.\"50 Henry Craik, a writer who later served as MP for the Combined Scottish Universities, used a more colorful insult, scorning it as \"the veriest figment of pedantic theorizing that any mystified scholastic ever dreamed.\"51 Another common response was to historically relativize Locke's work, viewing him as a man of (and trapped in) his time. Thus the idealist philosopher W. R. Sorley loftily declared that despite the palpable weakness of Locke's political theory, \"it served its purpose as a justification of the revolution settlement in accordance with the ideas of the time.\"52 Many also questioned Locke's originality, suggesting that his main political ideas were derived from others, above all Hooker. As G. P. Gooch wrote in his influential account of seventeenth-century democratic thought, \"there is little in Locke that he did not find in the thinkers of the Interregnum.\"53 These lines of criticism were synthesized in the first monograph on Locke's political philosophy (originally a doctoral dissertation at Columbia supervised by John Dewey): \"His moral and political philosophy may well be viewed as the summation of the best thought of the seventeenth century. Though he added few ideas of his own and developed the old ideas he took from others, he is rather the ripe fulfilment of the past than the herald of the future.\" The author concluded that \"Locke's theory of political society is decidedly weak\" and offered little to contemporary political theory.54 Locke spoke from and about a lost world.\n\nNineteenth-century philosophers rarely saw Locke as a liberal or written positively about his political theory. John Stuart Mill's assessment is indicative. In the _System of Logic_ he praised Locke as \"that truly original genius\" and a hugely talented \"metaphysician,\" yet in the vast corpus of Mill's work there are only a handful of references to Locke's political writings.55 His only sustained discussion is in a book review, wherein Mill follows custom in disparaging social contract theories and inalienable rights, while conceding that their proponents rightly identified the importance of limitations on government. \"This is the truth,\" Mill notes, \"which was dimly shadowed forth, in howsoever rude and unskilful a manner, in the theories of the social compact and the rights of man.\"56 _On Liberty_ contains one passing reference to Locke, while James Fitzjames Stephen's powerful riposte, _Liberty, Equality, Fraternity_ , didn't mention him at all.57 Elsewhere, Stephen belittled Locke as confused and outmoded. The _Second Treatise_ , he argued,\n\n... was in its day extremely popular, and its practical effects were no doubt great, as it furnished people with the best and most accessible popular justification for the Revolution of 1688. It would be difficult, however, to find a better illustration of the fact that we have travelled a very long road since Locke's time, and have carried the metaphysical principles of which he perceived certain aspects, to consequences which have made his political speculations appear altogether superannuated and bygone.\n\nHis conclusion was equally damning: it was worth studying once popular books \"to consider the reasons why they now fall so flatly among us.\"58\n\nHerbert Spencer was probably the most widely read English-language philosopher of the age. Across his voluminous output, Locke made only a handful of appearances, and in what he considered his finest work, _The Principles of Ethics_ , Locke's theory of property was casually dismissed as \"unsatisfactory.\"59 T. H. Green, the leading philosophical light of the final quarter of the century, shared Mill's deep skepticism about the foundations of early modern political thought, and while he expended considerable energy grappling with Locke's epistemological writings\u2014\"at once so plausible and so hollow\"\u2014he barely mentioned his political views. Dismissive of the state of nature, prepolitical rights, and contractualism, Green ultimately rejected Locke's arguments as incoherent and he never viewed him as a fellow (or proto) liberal.60 Nor did Henry Sidgwick, who characterized Locke as a philosophically misguided Whig ideologue.61 In the Edwardian era, Graham Wallas added a post-Darwinian twist to the story by arguing that Locke's \"plea for a government which should consciously realize the purposes of God\" was one of many philosophical utopias rendered irrelevant by modern science.62\n\nThe same pattern of omission, disavowal, and scorn emerges if we turn from political theory to historical scholarship. In Leslie Stephen's important _History of English Thought in the Eighteenth Century_ Locke's ideas were relegated to an archaic past. In relativizing mode, he termed Locke's arguments a \"formal apology of Whiggism\" and grudgingly admitted that they \"did well enough for the quiet time of the eighteenth century.\" They were then comprehensively superseded: \"That authority vanished when the French Revolution brought deeper questions for solution, and new methods became necessary in politics as in all other speculation.\"63 Published during the same decade, J. R. Green's hugely popular history of England classified Locke as a Whig philosopher of 1688 before noting that the social contract had long since been regarded as obsolete.64 Venerated throughout Europe for his prodigious erudition, Lord Acton acknowledged that Locke had been a significant historical actor while assailing the quality of his political theory: \"always reasonable and sensible, but diluted and pedestrian and poor.\"65 While Acton clearly regarded Locke as a notable member of the \"Party of Liberty,\" he didn't think of him as a member of the party of liberalism. In the seminal multi-volume _Cambridge Modern History_ , planned by Acton before his untimely death, Locke was again credited as an influential Whig apologist, albeit one whose political ideas \"had already been better expressed by Sidney.\"66 The great F. W. Maitland likewise held a low opinion of Locke, cataloguing the many \"grave faults\" of his arguments, above all a literal belief in the historical reality of the social contract.67 Across the Atlantic, Locke's reputation was barely higher. The standard history of political thought textbook, for example, presented a damning account of his \"illogical, incoherent system of political philosophy.\"68\n\nWidespread skepticism about the quality and relevance of Lockean political thought was fortified by the historicist \"comparative method,\" which did so much to shape scholarship during the late nineteenth century.69 Its proponents, the most influential of whom was Henry Maine, challenged deductive models of politics and sought to root the origins and development of customs, language, social structures, and legal forms, in long-term historical-evolutionary processes. Antipathetic to early modern natural law and utilitarianism alike, it provided yet another weapon to attack the political thinking of the seventeenth and eighteenth centuries. It exercised a profound influence on historical scholarship and the emerging social sciences\u2014perhaps especially political science\u2014on both sides of the Atlantic.70 In the _locus classicus_ of comparativism, Maine's _Ancient Law_ , Locke made a fleeting appearance as one of the many thinkers whose ideas about the state of nature and the origins of law were fundamentally mistaken.71 For J. R. Seeley, the leading ideologue of the late-Victorian empire, Locke's political thinking was simply too ahistorical to be of value, while he didn't even warrant a mention in E. A. Freeman's _Comparative Politics_ , the first book to apply the method to the development of political institutions across time and space.72\n\nTeaching in the elite English universities reflected both Locke's prominence as a \"metaphysician\" and his meager reputation as a political thinker. At Oxford in the 1870s the _Essay_ , though not the _Treatises_ or _Letter_ , was a compulsory text in moral and political philosophy.73 In Ritchie's appraisal of the political science curriculum in 1891, the key authors are listed as Aristotle, Hobbes, Bluntschli, Maine, and Mill.74 At Cambridge, William Paley's _Principles of Moral and Political Philosophy_ (1785) was the standard text during the first half of the nineteenth century. While Paley briefly paid lip service to Locke's historical importance, he ignored his arguments and rejected the social contract on utilitarian grounds. Locke's fortunes didn't improve during the closing decades of the century. When Henry Sidgwick surveyed the subject in the mid-1870s, Locke failed to make the list of set authors in political philosophy, though students were expected to be familiar with Plato, Aristotle, Cicero, Hobbes, Clarke, Shaftesbury, Butler, Smith, Hume, Kant, Paley, Bentham, Whewell, Mill, and Grote.75 The History Tripos paper in \"Political Philosophy and General Jurisprudence\" followed a familiar pattern. In 1875, for example, Aristotle, Guizot, Tocqueville, Mill, Gibbon, Blackstone, Austin, and Maine, but not Locke, were listed.76\n\nGiven Locke's tarnished reputation at the time, what are we to make of his current status as the ur-liberal? One possible answer is that it is based on a mistake\u2014that Locke simply wasn't a liberal.77 Another response is to insist that we have now corrected the error of earlier thinkers who failed to recognize Locke's liberalism. In other words, he had either always been a liberal or he was never one. Both positions are defensible: it is possible to extract conflicting meanings from Locke's work. But I suggest an alternative answer: Locke _became_ a liberal during the twentieth century. As part of a process of _retrojection_ his body of work\u2014or at least some stylized arguments stripped from it\u2014was posthumously conscripted to an expansive new conception of the liberal tradition.\n\nWars of Position: Consolidating Liberalism\n\nThe Lockean narrative was consolidated in Britain and the United States between the 1930s and the 1950s, as liberalism was reconfigured as the ideological other of \"totalitarian\" ideologies, left and right.78 This was achieved through two key discursive moves and across two main chronological phases. The first move deepened the retrojective extension of the liberal tradition that had already begun in both Britain and the United States. The early modern account moved from being a minority report to the dominant narrative. The second development was, if anything, even more significant: the emergence and proliferation of the idea of \"liberal democracy.\" As representative forms of political order came under sustained fire, intellectuals propagated an all-encompassing narrative that simultaneously pushed the historical origins of liberalism back in time while vastly expanding its spatial reach. For the first time, it was widely presented as either the most authentic ideological tradition of the West (a pre-1945 storyline) or its constitutive ideology (a view popular after 1945). This story began to coalesce during the 1930s, in a context of radical anxiety about the fate of liberalism. This was an era where, as Mussolini proclaimed, \"all the political experiments of our day are anti-liberal.\"79 Liberals and their critics fought an ideological war of position, attempting to delineate the true, prescriptive meaning of liberalism. The narrative was cemented in the more complacent postwar intellectual milieu as scholars from across the political spectrum, and from assorted academic disciplines, converged on this new all-encompassing narrative, even as they proffered radically different explanations and normative evaluations of it. Strauss, Laski, Macpherson, Hartz, and Wolin, among others, helped to fabricate the new ideological structure. Though rarely acknowledged or analyzed, the transformation of liberalism did not go completely unnoticed. In a lecture delivered in 1960, Eric Voegelin observed that \"in the course of the last 30 years the image of what liberalism is has changed completely.\"80 Wittingly or not, we are the heirs of this ideological labor.\n\nThe main conceptual shift that underpinned the emergence and popularization of the Lockean narrative in Britain was the conscription of Whig constitutionalism into a newly expansive vision of liberalism. This move was captured by de Ruggiero in 1933: \"The ambitious designs of the radicals, curbed by the tenacious forces of tradition, fused with the older Whiggism to form a composite liberalism in which the old and the new were gradually integrated and harmonized.\"81 Contra Ruggiero, however, this discursive \"fusion\" was largely a product of the twentieth century. Consequently, liberalism came to be viewed through a wide-angle lens, as a politico-intellectual tradition centered on individual freedom in the context of constitutional government. This expansion in ideological scope was also facilitated by shifts in the philosophical current. The eclipse of idealism in the early twentieth century, as well as powerful challenges to utilitarianism, helped to create an intellectual environment more conducive to natural rights arguments and contracturalism. Locke, the arch-Whig, was recast\u2014by default as much as design\u2014as a seminal liberal thinker and a source of inspiration for an individualist account of political life.\n\nThis retrojective process began in earnest during the Edwardian years. Hobhouse's _Liberalism_ , arguably the most popular and sophisticated discussion of liberal political theory published during the first half of the century, played an important role in establishing the lineaments of the (new) Lockean tradition.82 He posited the emergence of liberalism as coeval with the development of the early modern English state. In its original Whig iteration\u2014a theory of the \"Natural Order\" centered on inalienable prepolitical rights and the restraint of government\u2014it embodied a \"negative\" form of constitutionalism that sought to eliminate obstacles to human progress. \"It finds humanity oppressed, and would set it free.\" But, Hobhouse continued, the underlying theoretical architecture was fundamentally flawed, and only during the nineteenth century was a positive dimension added, first by utilitarians and more recently by \"new liberals.\"83 Thus Hobhouse presented the Whigs as pioneer liberals, albeit now superseded. In addition to providing fellow liberal reformers with a powerful constitutionalist genealogy, he had another motive for stretching the discursive boundaries of liberalism, as he was engaged in the attempt to craft a liberal socialist politics to replace the desiccated \"old liberalism\" of the \"Manchester School\" and the Benthamites.84 Yet this Lockean narrative, a precursor of things to come, remained marginal until the 1930s, and scholarly and popular discussions of liberalism were most commonly tied to the quotidian concerns of the often-embattled Liberal Party.85 When R. G. Collingwood wrote the translator's preface for Ruggiero's _History of European Liberalism_ in 1927, he still felt it necessary to inform his audience that the book addressed liberalism in the \"continental\" not the \"British\" sense, as a \"name for principles of constitutional liberty and representative government,\" rather than a party ideology.86\n\nThe First World War and its aftermath also saw early attempts to self-consciously define an American liberal tradition with its origins in the seventeenth century. Progressive scholars and publicists took the lead.87 The critic Harold Stearn was one of the first. He drew heavily on Hobhouse's account of the true meaning of liberalism, but his historical narrative had a different emphasis, focusing in particular on religious toleration and the catalytic role of Roger Williams, the seventeenth-century Protestant theologian and colonist.88 Despite dedicating a chapter to \"what liberalism is\" and another to the \"English heritage\" of American liberalism, Locke was absent from his analysis. Interpreting liberalism as an ideology centered on religious toleration become a popular theme in American scholarship, exemplified by Vernon Parrington's hugely influential _Main Currents in American Thought_ , published in the late 1920s though composed largely in the 1910s.89 Parrington argued that liberalism was articulated originally in the natural law theories of the early Puritan settlers, who had fled from a European environment inhospitable to their radical claims to a welcoming new world in America, where liberalism could truly flourish. Though Parrington stressed the importance of Williams\u2014\"England gave us her best\"90\u2014he also assigned Locke a prominent role. Connecting liberalism and toleration in this manner helped to place Locke at the center of the newly formatted tradition. Whereas parliamentary constitutionalism was central to the British appropriation of Locke (via the retrojection of the Whigs), it was religious toleration (via the retrojection of key elements of Puritanism) that did much of the ideological labor in the United States.\n\nAlthough some of the key building blocks were in place by 1918, the ultimate hegemony of the Lockean narrative was still far from secure. The discursive consolidation of the new account of liberalism was a product of the complex interweaving of geopolitical dynamics and disciplinary imperatives within the human sciences, especially political science and history. Indeed the academic disciplines that profess to instruct us about the nature of liberalism played a fundamental role in its transfiguration. The shift unfolded in the context of a transfer of scholarly authority from Britain to the United States. Whereas British commentators had shaped the contours of interpretation in the late nineteenth and early twentieth centuries, exerting a profound influence (alongside German scholarship) on the development of American political science and history, by 1945 a decisive shift across the Atlantic was apparent. The new liberal narrative was thus largely a product of the American human sciences, though it was mirrored in Britain. The change in meaning is captured in the evolution of George Sabine's influential conspectus of Western political thought, which was the standard textbook in the United States during the middle decades of the twentieth century. It was one of the first major scholarly texts to discuss liberalism in any detail. Published in 1937, the first edition located the tradition squarely in nineteenth-century Britain, figuring it as a distinct position between socialism and conservatism. (Locke was not classified as a liberal.) Moreover, like so many of his contemporaries, Sabine worried that it \"was a diminishing force in modern society.\"91 In the revised edition of 1951, however, his account of liberalism was both more capacious and more confident, and he asserted that it now had two main senses. The first, which he associated with Fascist and Marxist critics, saw it as the \"social philosophy of the industrial middle class\" and thus coterminous with _laissez-faire_ capitalism. Rejecting this critique, he endorsed a far broader account of liberalism as both the \"culmination\" of Western history and largely synonymous with democracy.92 Here he followed political theorist Frederick Watkins who had recently celebrated liberalism as the \"secular form of Western civilization\" and the \"modern embodiment of all the characteristic traditions of Western politics.\"93 Sabine concurred: \"[P]olitical liberalism has been deeply implicated in the whole development of Western culture.\"94 (The ultimately unsuccessful attempt to retroject liberalism back into the ancient Greek world, thus making it coterminous with Western civilization, was one of the signature ideological moves of the era.)95 An irony appears lost on Sabine. Whereas linking democracy and liberalism had, in the nineteenth century, served to delimit its chronological scope, it was now employed to buttress the claim that liberalism was the spiritual inheritance of the West itself.\n\nConfusion reigned. As liberalism's boundaries were conceptually stretched, so whatever fragile coherence it once had was lost. In the mid-1930s Dewey moaned that \"liberalism has meant in practice things so different as to be opposed to one another.\"96 It only got worse. A decade later, a noted philosopher could insouciantly observe that \"we, too, have our 'ideology,' inherited from the past as the liberal tradition, the American creed, the Judeo-Christian heritage of Western civilization or the like.\"97 For many, these ideas had become interchangeable. The tendency to construct legitimating genealogies for crude ideological ends provoked the ire of a young C. B. Macpherson, who complained that too many scholars charting the history of Western philosophy substituted serious analysis with assertions of political faith, \"using their history to show how long and honorable an ancestry that faith has.\"98 This was an accurate diagnosis. A new piece of conceptual technology was added when the term \"neoliberalism\" was coined in the late 1930s. Since the 1970s it has served as shorthand for the valorization of the minimal state and deregulated market, but (to add to the confusion) it originally identified a _via media_ between unrestrained capitalism and progressive statism.99 Commentators grumbled endlessly about the theoretical muddle. One frustrated scholar marveled in 1948 that \"[o]ne finds the term employed to defend everything from classical economics to the Soviet interpretation of communism.\"100 In 1955, Reinhold Niebuhr addressed the \"confusion,\" arguing that liberalism had come to denominate both a phase of human history, \"the rise of a modern technical society availing itself of democratic political forms and of capitalistic economic institutions,\" and a specific set of partisan political commitments. It also signified two \"contradictory\" claims, namely, that liberty necessitated both the unleashing of capitalism and its radical restraint.101\n\nA similar pattern can be discerned in Britain. The translation of de Ruggiero's _History of European Liberalism_ and the publication of Laski's _The Rise_ _of European Liberalism_ bolstered the early modern liberal narrative.102 It became the norm during the 1930s and 1940s.103 Skeptical of claims about seamless continuity, Isaiah Berlin summed up the nature and ideological appeal of what had become a popular position by 1950: \"European liberalism wears the appearance of a single coherent movement, little altered during almost three centuries, founded upon relatively simple foundations, laid by Locke or Grotius or even Spinoza; stretching back to Erasmus and Montaigne, the Italian Renaissance, Seneca and the Greeks.\"104 By the early 1960s Kenneth Minogue, a young theorist at the London School of Economics (LSE), could confidently assert that liberalism was a \"single and continuing entity... so extensive that it involves most of the guiding beliefs of modern western opinion\" and that John Locke was its \"founding father.\"105 This bold proclamation would have surprised the Fabians who had founded the LSE just over half a century before.\n\nThe new historical narrative was adopted by both critics and celebrants of liberalism. Converging on description, they diverged in both explanation and normative evaluation. From the left, for example, Laski depicted liberalism as an ideology with foundations bored deep into the bedrock of Western history: \"[L]iberalism has been, in the last four centuries, the outstanding doctrine of Western civilization.\" It supplied the ideological scaffolding of modern capitalism. Locke was elevated to the \"most representative prophet\" of the new age.106 This line of critique reappeared in the work of Laski's student Macpherson and is still popular today.107 On the political right, meanwhile, Strauss, Voegelin, and others, also pressed variations on the early modern theme. Self-proclaimed liberals were only too happy to vaunt the robust durability and deep historical roots of their creed, bolstering its ideological armature in the face of hostile competition. Narrative convergence helped produce discursive hegemony. It was against this imposing\u2014but quite new\u2014ideological edifice that the contextualist scholars of the 1960s fought their rear-guard action.\n\nArguably, the most significant conceptual move of the interwar era was the emergence of the idea of \"liberal democracy.\" Barely visible before 1930, in the ensuing decade it began to supplant existing appellations for Euro-Atlantic states.108 During the 1940s and 1950s it became a commonplace.109 As a global conflict over the proper meaning of democracy raged, the modifier \"liberal\" simultaneously encompassed diverse representative parliamentary systems while differentiating them from others claiming the democratic title, above all Italy, Germany, and the Soviet Union. The year after Hitler assumed power, Ernest Barker observed that the \"issue of our time is hardly a simple issue of democracy versus dictatorship. Dictatorship itself claims the quality of democracy; indeed it claims the quality of a higher, a more immediate, spontaneous democracy.\" This was, then, a clash between \"two types of democracy\u2014the parliamentary type... and the dictatorial type.\"110 _Liberal democracy_ was the name increasingly adopted to cover the former in its conflicts against the latter. Social scientists soon began to utilize the concept, usage that was refined and normalized after 1945. By 1954 Quincy Wright could assert confidently that the concept of \"liberal democracy\" originated in sixteenth-century Europe, especially in England, and was powerfully articulated in Locke's political philosophy.111 The Lockean narrative was frequently generalized into a broader claim about the Lockean-liberal character of Anglo-American (sometimes Western) societies, an interpretive strategy popularized by Louis Hartz and that was to have a profound effect on the nascent subfield of comparative politics.112 Conjoining \"liberal\" to democracy automatically (and vastly) expanded the scope of those purportedly encompassed by liberalism, as supporters of \"liberal democracy\" were conscripted, however reluctantly, to the liberal tradition. Liberalism was thus transfigured from a term identifying a limited and contested position within political discourse to either the most authentic expression of the Western tradition or a constitutive feature of the West itself. Again, this conceptual shift was rarely acknowledged, though it didn't pass completely unremarked. Strauss noted the peculiarity, and the \"serious difficulty\" for interpretation, that resulted from the \"fact that here and now liberalism and conservatism have a common basis; for both are based here and now on liberal democracy, and therefore both are antagonistic to Communism.\"113\n\nThe political instrumentalization of intellectual history was widespread across the Euro-Atlantic world, reaching its _reductio ad absurdum_ in Bertrand Russell's declaration that \"at the present time Hitler is an outcome of Rousseau; Roosevelt and Churchill, of Locke.\"114 It is thus unsurprising that history provided another disciplinary space for propagating the new vision of liberalism. The \"history of ideas,\" an emergent field combining history and philosophy that \"rose like a new sign in the zodiac over large areas of American culture and education,\" was, like political theory, transformed by \u00e9migr\u00e9 scholars, including Hans Baron, Ernst Cassirer, Felix Gilbert, Raymond Klibansky, Paul Kristeller, Hajo Holborn, and Erwin Panofsky.115 Its zealous proponents helped to define and defend a holistic \"Western\" civilization based on \"liberal\" values, and as such it was of \"strategic\" value in fighting totalitarianism.116 As the classroom became a powerful vector for the transmission of the new liberal-civilizational creed, so the _Journal of the History of Ideas_ , founded in 1940, served as the principal venue for its scholarly elaboration. It is no coincidence that it was the only academic journal to receive a secret subsidy from the CIA-sponsored Congress on Cultural Freedom.117 University curricula, then, provided institutional authority for the transvaluation of liberalism. \"Western civilization\" courses, which flourished from the end of the First World War until the 1960s, popularized \"an interpretation of history that gives the United States a common development with England and Western Europe and identifies this 'civilization' with the advance of liberty and culture.\" Helping to construct a mythopoeic narrative of the West as simultaneously ancient and modern, free and strong, they were the most widely taught history courses after the Second World War.118 While claims about the intellectual coherence, historical continuity, and ethico-political superiority of \"the West\" stretched back at least as far as the eighteenth century, it was only in the mid-twentieth century that this potent civilizational narrative came to be routinely classified as _liberal_. The victorious spread of liberalism and the rise of the West came to be seen as one and the same thing.\n\nConclusion: Conscripts of Liberalism\n\nThe nature of liberalism has been a core concern in political theory since its emergence as an academic specialism in the early twentieth century. I have criticized some prominent approaches to interpreting liberalism, introduced some methodological tools for thinking about the proliferation of liberal languages, and sketched an explanatory account of shifts in the meaning of liberalism in the Anglo-American world. The analysis has implications for both political theorists and historians. Above all, it suggests the need to be alert to the historical contingency and variability of our theoretical vocabularies and the power relations of tradition-construction. It also calls into question the general utility of \"liberalism\" as a category of political analysis. Current debates about the nature of liberalism\u2014in and beyond political theory\u2014are often distorted because of the ahistorical understanding of liberal ideology that they invoke. Conducted in a discursive echo chamber, they are often marked by a symptomatic form of collective amnesia, a problematic erasure of the political and intellectual dynamics that generated much of what is now articulated as scholarly common sense.\n\nThis chapter is intended as a modest contribution to the work of historical recovery. As Stephen wrote in 1862, \"the words 'liberal' and 'liberalism,' like all other such phrases, derive a great part of their significance from the time they were invented.\"119 The history of liberalism, though, is a history of constant reinvention. The most sweeping of these occurred in the middle of the twentieth century, when liberalism was increasingly figured as the dominant ideology of the West\u2014its origins retrojected back into the early modern era, it came to denote virtually all nontotalitarian forms of politics as well as a partisan political perspective within societies. This was partly a consequence of the delegitimation of political extremes, partly a result of the vicissitudes of domestic political strife, and partly a result of political and conceptual labor performed in the developing human sciences. Karl Popper once referred to _The Open Society and Its Enemies_ as his \"war effort,\" a contribution to the fight against totalitarianism. The consolidation of Lockean liberalism was a grander, more all-encompassing variation on the same theme.\n\n1 Richard Rorty, \"The Historiography of Philosophy,\" in _Philosophy in History_ , ed. Richard Rorty, Jerome Schneewind, and Quentin Skinner (Cambridge, 1984), 70.\n\n2 Judith N. Shklar, \"The Liberalism of Fear\" [1989], in _Political Thought and Political Thinkers_ (Chicago, 1998), 3.\n\n3 On the practice of boundary-work, see Thomas Gieryn, \"Boundary-Work and the Demarcation of Science from Non-Science,\" _American Sociological Review_ , 48 (1983), 785\u201395.\n\n4 De Ruggiero, _The History of European Liberalism_ [1927], trans. R. G. Collingwood (Boston, 1959); Hayek, \"Liberalism\" [1973], in _New Studies in Philosophy, Politics, Economics and the History of Ideas_ (London, 1978), 113. Alan Ryan complicates matters by distinguishing between modern, classical, social, and libertarian variants. _The Making of Modern Liberalism_ (Princeton, 2012), 23\u201328.\n\n5 Strauss, _Liberalism Ancient and Modern_ (Chicago, 1968); Wolin, _Politics and Vision_ (Princeton, 2004), 263.\n\n6 Irving Kristol, _Reflections of a Neoconservative_ (New York, 1983), 75.\n\n7 Mises, _Liberalism_ (Indianapolis, 2005), 153\u201354; Spencer, _The Man versus the State_ [1884] (Indianapolis, 1969).\n\n8 Hobhouse, _Liberalism_ [1911], ed. James Meadowcroft (Cambridge, 1994); Dewey, _Liberalism and Social Action_ (New York, 1935), 21.\n\n9 Shklar, \"Liberalism,\" 3. On liberty as \"normatively basic,\" see Gerald Gaus and Shane Courtland, \"Liberalism,\" _The Stanford Encyclopaedia of Philosophy_ , ed. Edward Zalta, <http:\/\/plato.stanford.edu\/entries\/liberalism\/>.\n\n10 Waldron, \"Theoretical Foundations of Liberalism,\" _Philosophical Quarterly_ , 37 (1987), 131, 127, 140.\n\n11 Dworkin, \"Liberalism,\" in A _Matter of Principle_ (Oxford, 1985), 183.\n\n12 Gerstle, \"The Protean Character of American Liberalism,\" _American Historical Review_ , 99 (1994), 1046; Dunn, _Western Political Theory in the Face of the Future_ [1979] (Cambridge, 1991), 33.\n\n13 Less common in political theory, _expressive_ protocols are widely utilized across the humanities and social sciences. They distil the meaning of liberalism through a form of reverse engineering, working backwards from observations on (aspects of) a society to the ideas purportedly underlying it. First, certain entities\u2014for example, public policies\u2014are classified as \"liberal,\" a classification usually based on the self-identification of the relevant agents or the alleged correspondence between the entity and a putative external (\"liberal\") standard. Second, the entities are taken to embody or express underlying ideas or values, which are then characterized as liberal. Thus: State A is classified as liberal; \"liberal state\" A enacts policy B. Policy B is therefore \"liberal.\" B embodies or expresses liberal value or idea C. An expressive protocol is arguably employed in Dworkin's \"theory of what liberalism is\" (Dworkin, \"Liberalism\"). This protocol has various problems, not least debilitating circularity.\n\n14 Rawls, _Lectures on the History of Political Philosophy_ , ed. Samuel Freeman (Cambridge, 2007), 11.\n\n15 Manent, _An Intellectual History of Liberalism_ , trans. R. Balinski (Princeton, 1996).\n\n16 Waldron, \"Theoretical Foundations,\" 128, 143\u201344. For another prominent example of historical gymnastics, see Stephen Holmes, \"The Permanent Structure of Anti-Liberal Thought,\" in _Liberalism and the Moral Life_ , ed. Nancy Rosenblum (Cambridge, 1989), 236\u201337. Holmes characterizes Spinoza, Locke, and Hume (among others) as straightforward liberals, but denies a place in the pantheon to Michael Sandel and Charles Taylor.\n\n17 John Gunnell, _The Descent of Political Theory_ (Chicago, 1993). On the politics of canon formation in literature, see John Guillory, _Cultural Capital_ (Chicago, 1993).\n\n18 For a seminal statement, see Quentin Skinner, _Visions of Politics_ , vol. 1 (Cambridge, 2002).\n\n19 J.G.A. Pocock, _The Machiavellian Moment_ , rev. ed. (Princeton, 2003), 579.\n\n20 Mark Goldie, \"Introduction,\" in _The Reception of Locke's Politics_ , vol. 1, ed. Goldie (London, 1999), xvii-lxxiii. For a recent powerful argument, see Tim Stanton, \"John Locke and the Fable of Liberalism,\" _Historical Journal_ (forthcoming).\n\n21 Ryan, _Modern Liberalism_ , 9, reads it as a straightforward semantic claim.\n\n22 Freeden, _Liberal Languages_ (Princeton, 2005), 20. See also Michael Freeden and Marc Stears, \"Liberalism,\" in _The Oxford Handbook of Political Ideologies_ , ed. Michael Freeden, Lyman Tower Sargent, and Marc Stears (Oxford, 2013), 329\u201348.\n\n23 Freeden, _Ideologies and Political Theory_ (Oxford, 1996), 227ff., 276, 278.\n\n24 Nagel, \"Rawls and Liberalism,\" in _The Cambridge Companion to Rawls_ , ed. Samuel Freeman (Cambridge, 2003), 62.\n\n25 Anderson, \"Renewals,\" _New Left Review_ , 1 (2000), 13; Geuss, \"Liberalism and Its Discontents,\" _Political Theory_ , 30 (2002), 320.\n\n26 For a parallel usage to which I am indebted, see David Scott, _Conscripts of Modernity_ (Durham, NC, 2004).\n\n27 Note that a comprehensive account is not suitable for constructing a coherent normative political theory.\n\n28 Freeden, _Liberal Languages_ , 20.\n\n29 For an example of the absurd genre, see Jonah Goldberg, _Liberal Fascism_ (London, 2007).\n\n30 P. Coupland, \"H. G. Wells' 'Liberal Fascism,'\" _Journal of Contemporary History_ , 35 (2000), 541\u201358. Goldberg uses this example to reach the opposite conclusion. Wells was suggesting that it was necessary to use methods learned from fascism to realize liberal ends.\n\n31 One objection to this argument is that some liberal ideas\/values\/commitments (e.g., the normative priority of liberty) are more central to the tradition than others. I agree with this as an empirical claim. But on my view it is neither a conceptual nor a normative necessity that all possible legitimate liberalisms will contain those ideas\/values\/commitments. We can imagine future iterations with a different core. Thus the centrality of, e.g., liberty is a historically contingent feature of liberalism.\n\n32 For prominent examples, see Sherri Berman, _The Primacy of Politics_ (Cambridge, 2006); Rogers Smith, _Civic Ideals_ (London, 2007).\n\n33 It follows that those values\/policies are also now part of the conservative tradition (and hypothetically others too).\n\n34 Losurdo, _Liberalism_ , trans. Gregory Elliott (London, 2011). Losurdo mixes canonical and expressive protocols.\n\n35 On the problems with characterizing the nineteenth-century United States as liberal, see Daniel Rodgers, \"The Traditions of Liberalism,\" in _Questions of Tradition_ , ed. Mark Salber Phillips and Gordon Schochet (Toronto, 2004), 203\u201333.\n\n36 Wolin, _Politics and Vision_ , 263; Holmes, _Passions and Constraint_ (Chicago, 1995), 15. Rawls's \"speculative\" history traces liberalism to the Reformation and the sixteenth-century religious wars ( _Lectures_ , 11).\n\n37 Gunnell, \"The Archaeology of American Liberalism,\" _Journal of Political Ideologies_ , 6 (2001), 131; Gunnell, _Imagining the American Polity_ (Philadelphia, 2004), 183\u2013219.\n\n38 J\u00f6rn Leonhard, \"From European Liberalism to the Languages of Liberalisms,\" _Redescriptions_ , 8 (2004), 17\u201351.\n\n39 D. M. Craig, \"The Origins of 'Liberalism' in Britain,\" _Historical Research_ , 85 (2012), 482. Cf. Daisy Hay, \"Liberals, _Liberales_ and _The Liberal_ ,\" _European Romantic Review_ , 19 (2008), 307\u201320. For the European context, see Maurizio Isabella, _Risorgimento in Exile_ (Oxford, 2009).\n\n40 The Liberal Party was created from a fissile coalition of Whigs, free-trading Tories, and Radicals. The name was first used officially in 1868, but it had been a common designation since the 1850s.\n\n41 See, for example, Frederick Pollock, _An Introduction to the History of the Science of Politics_ (London, 1890); William Graham, _English Political Philosophy from Hobbes to Maine_ (London, 1899); Ernest Barker, _Political Thought in England from Herbert Spencer to the Present Day_ (London, 1915); W. L. Davidson, _Political Thought in England from Bentham to J. S. Mill_ (London, 1915); Ivor Brown, _English Political Theory_ (London, 1920); Robert Murray, _The History of Political Science from Plato to the Present_ (Cambridge, 1926); Lewis Rockow, _Contemporary Political Thought in England_ (London, 1925); C. E. Vaughan, _Studies in the History of Political Philosophy_ , 2 vols. (Manchester, 1925). Harold Laski was an exception, identifying liberalism as an economic ideology produced by the Industrial Revolution, though with philosophical roots in the seventeenth century. _Political Thought in England from Locke to Bentham_ (London, 1920), ch. 7.\n\n42 Blease, _Short History of English Liberalism_ (London, 1913). Blease taught law at the University of Liverpool.\n\n43 Stephen, \"Liberalism,\" _Cornhill Magazine_ , 5 (1862), 72\u201373. See also Leonard Hobhouse, _Democracy and Reaction_ (London, 1904), 166.\n\n44 Dunning, \"A Century of Politics,\" _North American Review_ , 179\/577 (1904), 803.\n\n45 P. J. Macdonell, \"Historic Bases of Liberalism,\" in _Essays in Liberalism_ (London, 1897), 220. Hillaire Belloc also discussed the liberal tradition entirely in nineteenth-century terms (\"The Liberal Tradition,\" 1\u201330).\n\n46 Brown, _English Political Theory_ , 66. \"Locke had striven hard and striven successfully for more freedom, but he had never striven hard for more equality\" (66). On continuities between Whigs and Victorian liberals, see John Burrow, _Whigs and Liberals_ (Oxford, 1988).\n\n47 Dicey, _Lectures on the Relation between Law and Public Opinion in England during the Nineteenth Century_ [1914], 2nd ed., ed. Richard VandeWetering (Indianapolis, 2008), 67. The radical Whig Charles James Fox was occasionally identified as a founding father of liberalism. See A. C. Forster Boulton, \"Liberalism and Empire,\" _Westminster Review_ (1899), 486\u201391; N. W. Sibley, \"Edmund Burke,\" _Westminster Review_ (1897), 509; Macdonell, \"Historic Bases,\" 226\u201327. Thanks to Emily Jones for discussion on this point. Jones argues that conservatism was likewise crafted as a distinctive, coherent political philosophy (with Burke at the core) during the late Victorian and Edwardian years: Jones, \"Conservatism, Edmund Burke, and the Invention of a Political Tradition, c. 1885\u20131914,\" _Historical Journal_ , 58 (2015), 1115\u201339.\n\n48 Lord King, _The Life of John Locke_ (London, 1830); H. R. Fox-Bourne, _The Life of John Locke_ , vol. 2 (London, 1876), 524\u201340; Thomas Fowler, _Locke_ (London, 1880); A. Campbell Fraser, _Locke_ (Edinburgh, 1890); Samuel Alexander, _Locke_ (London, 1908).\n\n49 Hans Aarsleff, \"Locke's Influence,\" in _The Cambridge Companion to Locke_ , ed. Vere Chappell (Cambridge, 1997), 278. His writings on toleration were also well-known though they rarely fed into accounts.\n\n50 Pollock, \"The Social Contract in Hobbes and Locke,\" _Journal of the Society of Comparative Legislation_ (1907), reprinted in Pollock, _Essays in the Law_ (London, 1922), 109. See also his \"Locke's Theory of the State\" (1904), 80\u2013102. Pollock was unusual in suggesting that Locke envisaged the contract as hypothetical. For an example of the conventional criticism\u2014that the contract was an (absurd) empirical claim about human history\u2014see Edwin Wallace, \"John Locke,\" _Westminster Review_ , 107 (1877), 193.\n\n51 Henry Craik, \"John Locke,\" _Quarterly Review_ , 169 (1889), 490.\n\n52 Sorley, \"John Locke,\" in _The Cambridge History of English Literature_ , ed. Adolphus William Ward and Alfred Rayney Waller (Cambridge, 1912), 8:390. Sorely succeeded Sidgwick as the Knightbridge Professor of Philosophy at Cambridge, a post he held until 1933.\n\n53 Gooch, _The History of English Democratic Ideas in the Seventeenth Century_ (Cambridge, 1898), 358. Gooch did not connect Locke with liberalism, though he suggested that Locke's account of self-ownership provided the theoretical basis for socialism (358).\n\n54 Sterling Lamprecht, _The Moral and Political Philosophy of John Locke_ (New York, 1918), 6, 150\u201351. Representative of Locke's changing designation, Lamprecht characterized him as a \"Whig and a liberal.\"\n\n55 Mill, _System of Logic_ (1843), _Collected Works_ , vol. 7, ed. John Robson (Toronto, 1974), 29, 305.\n\n56 Mill, \"Use and Abuse of Political Terms,\" _Collected Works_ , 18:11. In the book under discussion, George Cornewall Lewis's _Remarks on the Use and Abuse of Some Political Terms_ (1832), \"liberalism\" is absent and Locke's views are ridiculed.\n\n57 Mill, _On Liberty_ [1859], _Collected Works_ , vol. 18; Stephen, _Liberty, Equality, Fraternity_.\n\n58 Stephen, \"Locke on Government\" (1867), _Horae Sabbaticae_ , vol. 2 (London, 1892), 142.\n\n59 Spencer, _The Principles of Ethics_ , vol. 2, [1897] (Indianapolis, 1978), 111\u201312. Locke warrants a few brief mentions in Spencer's earlier _Social Statics_ (London, 1851). In the earlier published version of this chapter, I overlooked these earlier mentions, though they do not change the general point.\n\n60 Green, \"Introduction to Hume's Treatise of Human Nature\" [1874], in _Collected Works of T. H. Green_ (Bristol, 1997), 1:13; Green, _Lectures on the Principles of Political Obligation_ [1886] (Bristol, 1997), 375. D. G. Ritchie was a partial exception. In the _Principles of State Interference_ (London, 1891), he linked English empiricism with liberalism, and praised the continuing political relevance of Locke's writings, though he derided their philosophical value (138, 128), while in his _Natural Rights_ (London, 1895), Locke was characterized as both an ideologue of 1688 and an early liberal (6, 239, 175, 186).\n\n61 Sidgwick, _The Development of European Polity_ (London, 1903), 364\u201367, 417\u201318. Locke is largely absent from Sidgwick's _Methods of Ethics_ (1874), _Principles of Political Economy_ (1873), or _The Elements of Politics_ (1891).\n\n62 Wallas, _Human Nature in Politics_ , 3rd ed. (London, 1909), 178.\n\n63 Stephen, _History of English Thought in the Eighteenth Century_ , vol. 2 (London, 1876), 150, 135. However, he later acknowledged that Locke had unwittingly laid the foundations for Bentham's radicalism: \"Locke, John (1632\u20131704),\" in _The Dictionary of National Biography_ (London, 1893), 34:32.\n\n64 Green, _A Short History of the English People_ [1874] (London, 1878), 601\u20132.\n\n65 Acton, _Lectures on Modern History_ , ed. John Figgis and Reginald Laurence (London, 1906), 217.\n\n66 Arthur Lionel Smith, \"English Political Philosophy in the Seventeenth and Eighteenth Centuries,\" in _The Cambridge Modern History_ , ed. Adolphus Ward, George Prothero, and Stanley Leathes (Cambridge, 1909), 6:805, 787.\n\n67 Maitland, _A Historical Sketch of Liberty and Equality_ (Indianapolis, 2000), 42, 52. Written in 1875, it was only published in 1911. In his _Constitutional History of England_ (Cambridge, 1908), Locke appeared very briefly as \"that excellent Whig\" (290).\n\n68 Dunning, _A History of Political Theories from Luther to Montesquieu_ (London, 1905), 368.\n\n69 On the comparative method, see Collini, Winch, and Burrow, _That Noble Science of Politics_ , ch. 7; Sandra den Otter, \"The Origins of a Historical Political Science in Late Victorian and Edwardian Britain,\" in _Modern Political Science_ , ed. Robert Adcock, Mark Bevir, and Shannon Stimson (Princeton, 2007), 37\u201366.\n\n70 Robert Adcock, _Liberalism and the Emergence of American Political Science_ (Oxford, 2014), ch. 5; James Farr, \"The Historical Science(s) of Politics,\" in _Modern Political Science_ , ed. Adcock, Bevir, and Stimson, 66\u201396; and chapter 13 in this volume.\n\n71 Maine, _Ancient Law_ [1861] (London, 1908), 101.\n\n72 Seeley, _Introduction to Political Science_ [1891], ed. Henry Sidgwick (London, 1919), 28; Freeman, _Comparative Politics_ (London, 1873).\n\n73 Mark Pattison, \"Philosophy at Oxford,\" _Mind_ , 1 (1876), 91.\n\n74 Ritchie, \"The Teaching of Political Science at Oxford,\" _Annals of the American Academy of Political and Social Science_ , 2 (1891), 88.\n\n75 Sidgwick, \"Philosophy at Cambridge,\" _Mind_ , 1 (1876), 235\u201346.\n\n76 Jean McLachlan, \"The Origin and Early Development of the Cambridge Historical Tripos,\" _American Historical Review_ , 9 (1947), 99.\n\n77 J.G.A. Pocock, \"The Myth of John Locke and the Obsession with Liberalism,\" in _John Locke_ , ed. Richard Ashcraft and J.G.A. Pocock (Los Angeles, 1980); Goldie, \"Introduction.\"\n\n78 There is a huge literature on totalitarianism. For the most comprehensive survey of the term, see Abbott Gleason, _Totalitarianism_ (Oxford, 1997).\n\n79 Mussolini, _Fascism_ (1935), cited in Ira Katznelson, _Desolation and Enlightenment_ (New York, 2003), 23.\n\n80 Voegelin, \"Liberalism and Its History,\" _Review of Politics_ , 36 (1974), 504\u20135.\n\n81 De Ruggiero, \"Liberalism,\" in _Encyclopedia of the Social Sciences_ , ed. E. R. Seligman (London, 1933), 11:438.\n\n82 As late as 1963, C. Wright Mills claimed that _Liberalism_ was the best account of the subject. _The Marxists_ (Harmondsworth, 1963), 25n.\n\n83 Hobhouse, _Liberalism_ , 24\u201325, 8. For another clear usage, see A. W. Benn, _The History of English Rationalism in the Nineteenth Century_ , vol. 1 (London, 1906), 111. Compare Herbert Samuel, _Liberalism_ (London, 1902), which does not mention Locke and makes little effort to trace a genealogy.\n\n84 Michael Freeden, _The New Liberalism_ (Oxford, 1978); Stefan Collini, _Liberalism and Sociology_ (Cambridge, 1983).\n\n85 Freeden, _Liberalism Divided_ (Oxford, 1986).\n\n86 Collingwood, \"Translator's Preface,\" vii. See also the comments on the difference between the narrow (British) and expansive (Continental) uses of the term in John Morley, _Recollections_ (London, 1917), 1:21. Morley adopts the latter in his discussion.\n\n87 On the transition from progressivism to liberalism, see Gerstle, \"Protean Character.\" On the transatlantic dialogue between British and American thinkers, see James Kloppenberg, _Uncertain Victory_ (Oxford, 1986); Marc Stears, _Progressive, Pluralists, and the Problems of the State_ (Oxford, 2002).\n\n88 Stearns, _Liberalism in America_ (New York, 1919), 11, 16\u201317, 33\u201334. Charles Merriam dismissed it as a shallow exercise in partisan propaganda. _American Political Science Review_ , 14\/3 (1920), 511\u201312.\n\n89 Parrington, _Main Currents in American Thought_ , 3 vols. (New York, 1927\u201330). Gunnell argues that Parrington's trilogy marked the \"threshold of the adoption of liberalism as an American political identity\u2014both in politics and political theory.\" Gunnell, \"Archaeology,\" 132. Thanks to Robert Adcock for discussion of this topic.\n\n90 Parrington, _Main Currents_ , 1:74.\n\n91 Sabine, _A History of Political Theory_ (London, 1937), 679. In 1941 he observed that \"[to] give a practical definition of liberalism is virtually impossible.\" Sabine, \"The Historical Position of Liberalism,\" _American Scholar_ , 10 (1940\u201341), 490.\n\n92 Sabine, _A History of Political Theory_ (New York, 1951), 620. In a review, Macpherson noted the shift in meaning and concluded that the \"ideological atmosphere in America\" made an understanding of both liberalism and Marxism \"increasingly difficult.\" _Western Political Quarterly_ , 4 (1951), 145.\n\n93 Watkins, _The Political Tradition of the West_ (Cambridge, 1948), ix. Watkins made liberalism coextensive with freedom under the law. For an influential conservative political-theological account that adopted the same timeline but reversed the normative conclusion, see John Hallowell, _The Decline of Liberalism as an Ideology_ (Berkeley, 1943); Hallowell, _Main Currents in Modern Political Thought_ (New York, 1950).\n\n94 Sabine, review of Watkins, _Political Science Quarterly_ , 64 (1949), 147\u201349.\n\n95 The phenomenon was noted in Francis Coker, \"Some Present-Day Critics of Liberalism,\" _American Political Science Review_ , 47 (1953), 1\u20132.\n\n96 Dewey, _Liberalism_ , 3.\n\n97 Arthur Murphy, \"Ideals and Ideologies, 1917\u20131947,\" _Philosophical Review_ , 56 (1947), 386.\n\n98 Macpherson, \"The History of Political Ideas,\" _Canadian Journal of Economics and Political Science_ , 7 (1941), 564\u201365.\n\n99 On neo-liberalism, see Ben Jackson, \"At the Origins of Neo-Liberalism,\" _Historical Journal_ , 53 (2010), 129\u201351; Angus Burgin, _The Great Persuasion_ (Cambridge, 2012). For a contemporary attempt to distinguish Ordo-liberalism and the work of the Mont Pelerin Society, see Carl Friedrich, \"The Political Thought of Neo-Liberalism,\" _American Political Science Review_ , 49 (1955), 509\u201325.\n\n100 Boyd Martin, \"Liberalism,\" _Western Political Quarterly_ , 1 (1948), 295.\n\n101 Niebuhr, \"Liberalism,\" _New Republic_ (1955). He endorsed the \"Lockean type of liberalism.\"\n\n102 Laski, _The Rise of European Liberalism_ (London, 1936), 9, 115. For a similar analysis, see Richard Crossman, _Government and the Governed_ (London, 1939), 69\u201380. Laski's analysis was not unchallenged: \"There is plenty of truth in this as a historical account, though it is a one-sided truth. But to speak of it as Liberalism shows a bad confusion of thought.\" G. C. Field, _Mind_ , 45 (1936), 527.\n\n103 See, for example, George Catlin, _The Anglo-Saxon Tradition_ (London, 1939); Catlin, _The Story of the Political Philosophers_ (New York, 1939); Michael Oakeshott, ed., _The Social and Political Doctrines of Contemporary Europe_ (Cambridge, 1939), xi-xviii; Thomas Cook, _History of Political Philosophy from Plato to Burke_ (New York, 1936), 710\u201311; J. P. Mayer, _Political Thought_ (London, 1939).\n\n104 Berlin, \"Political Ideas in the Twentieth Century,\" _Foreign Affairs_ , 28 (1950), 357.\n\n105 Minogue, _The Liberal Mind_ (London, 1962), 2.\n\n106 Laski, _Rise of European Liberalism_ , 9, 115.\n\n107 Macpherson, _The Political Theory of Possessive Individualism_ (Oxford, 1962); Losurdo, _Liberalism_.\n\n108 See, for example, M. Parmlees, \"Liberal Democracy, Fascism, and Bolshevism,\" _Annals of the American Academy of Political and Social Science_ , 180 (1935), 47\u201354; J. A. Leighton, _Social Philosophies in Conflict_ (New York, 1937); Alfred Zimmern, ed., _Modern Political Doctrines_ (Oxford, 1939), xiv-xix; Crossman, _Government_ , 286\u201387, 294\u201396; J. A. Hobson, \"Thoughts on Our Present Discontents,\" _Political Quarterly_ , 9 (1938), 47\u201357; E. H. Carr, _The Twenty Years' Crisis, 1919\u20131939_ (London, 1939), 37. See Oakeshott, _Doctrines_ , xvi-xix, for skeptical acknowledgement of the linguistic shift.\n\n109 A Google Ngram graph shows this post-1930 spike in usage: http:\/\/books.google.com\/ngrams\/graph?content=liberal+democracy&year_start=1800&year_end=2000&corpus=0&smoothing=3. Google Scholar also offers illustrative evidence. Scrubbed of false positives, the term \"liberal democracy\" is employed with the following frequency: 1900\u20131910: 6; 1911\u20131920: 33; 1921\u20131930: 24; 1931\u20131940: 143; 1941\u20131950: 216; 1951\u20131960: 374.\n\n110 Barker, \"Democracy since the War and Its Prospects for the Future,\" _International Affairs_ , 13 (1934), 757. On the threat, see Katznelson, _Fear Itself_.\n\n111 Wright, \"International Law and Ideologies,\" _American Journal of International Law_ , 48 (1954), 619.\n\n112 Hartz, _The Liberal Tradition in America_ (New York, 1955).\n\n113 Strauss, _Liberalism_ , vii. He also wrote, \"The conservatism of our age is identical with what originally was liberalism\" (ix). Cf. Voegelin, \"Liberalism,\" 507; Hayek, \"Liberalism,\" 113.\n\n114 Russell, _History of Western Philosophy_ (London, 1945\/1948), 711.\n\n115 Anthony Grafton, \"The History of Ideas,\" _Journal of the History of Ideas_ , 67 (2006), 1.\n\n116 Jotham Parsons, \"Defining the History of Ideas,\" _Journal of the History of Ideas_ , 68 (2007), 682\u201389.\n\n117 Francis Stonor Saunders, _Who Paid the Piper?_ (London, 1999), 338.\n\n118 Gilbert Allardyce, \"The Rise and Fall of the Western Civilization Course,\" _American Historical Review_ , 87 (1982), 706; Peter Novik, _That Noble Dream_ (Cambridge, 1988), 312.\n\n119 Stephen, \"Liberalism,\" 70.\nCHAPTER 4\n\nIdeologies of Empire\n\nThe world in which we live is largely the product of the rise, competition, and fall of empires. To attempt a survey of the role of ideology in this vast historical panorama would be hubristic\u2014that archetypical imperial vice. Consequently, in this chapter I limit my focus both geographically and temporally, concentrating attention on European, and principally British, imperialism during the last two hundred years. Moreover I confine it to a subset of the topics that it would be possible to discuss under the heading of ideology and empire. Even with these limitations in mind, my discussion will be synoptic and selective, drawing out some key issues while leaving many others unmentioned, or mentioned only in passing.\n\nThe terms empire and imperialism have no settled definition\u2014indeed the attempt to control and delimit their meaning has often formed a significant dimension of ideological disputation. Contemporary scholarly definitions come in narrow and broad varieties. On a narrow view, empire connotes the direct and comprehensive political control of one polity over another. It is, Michael Doyle writes, \"a relationship... in which one state controls the effective political sovereignty of another political society.\"1 Broad definitions, meanwhile, characterize an empire as a polity that exerts decisive or overwhelming power in a system of unequal political relations, thus encompassing very diverse forms of control and influence.2 The same variation holds for the concept of imperialism. On a narrow account, imperialism is a strategy or policy that aims to consolidate or expand a territorial empire. According to broader definitions it a strategy or policy\u2014or even an attitude or disposition\u2014that seeks to create, maintain, or intensify relations of inequality between political communities. A cross-cutting issue concerns the connection between formal and informal imperialism. Some restrict the term to direct intervention in, or control over, a given territory; others invoke imperialism to cover a wide range of formal and informal (nonterritorial) modes of influence.3 This can lead to substantial variation in the application of the terms. For example, utilizing a narrow definition it is possible to deny that the contemporary United States is an empire while acknowledging that it exhibits occasional imperialist aspirations, but adopting a broader definition supports the argument that it is and nearly always has been an empire.4 Empire and imperialism, then, are essentially contested concepts. Sidestepping these thorny conceptual debates, this chapter discusses positions from across the spectrum, not least because imperial advocates and critics have often mixed the different accounts together. Conceptual precision is vital for the scholarly analysis of empires, but impassioned ideological contestation rarely adheres to strict academic conventions.\n\nThe study of empire straddles the humanities and social sciences. The last three decades have witnessed a renaissance of interest in imperial history, a development that has recently catalyzed the increasingly popular field of \"global history.\"5 Following the work of Edward Said, Homi Bhabha, and Gayatri Spivak, among others, scholars of comparative literature have focused attention on the representation and legitimation of empire in diverse forms of cultural production, from the quotidian to the avant-garde.6 Such studies have illuminated the pivotal role of empire in the life-worlds of the modern \"West\"\u2014indeed in their very construction. Anthropology, a field once deeply implicated in the justification of imperial activity, now offers one of the most incisive scholarly sites for its investigation and critique. A similar case can be made about geography.7 Scholarship in all of these areas has been heavily influenced, though certainly not exhausted, by a range of \"postcolonial\" challenges to the \"Eurocentrism\" of Western scholarly and popular discourse.8 Rather ironically, international relations (IR), a field putatively dedicated to the analysis of world politics, has yet to engage adequately with the practices and the legacies of imperialism. Like many of the other social sciences, the origins and early disciplinary development of IR were bound up with imperial projects, but the dominant approaches continue to conceptualize global order, past and present, in terms of the relations between autonomous states acting under conditions of \"anarchy.\"9 However, as I discuss in chapter 2, scholars of politics have not ignored the imperial turn entirely. Spurred on by shifts in the wider world, historians and political theorists have begun to demonstrate the assorted ways in which the history of Western political thinking is profoundly entangled with imperial encounters.\n\nPractices of imperialism are not, of course, simply the product of a set of explicit theoretical arguments, and ideologies of empire cannot be analyzed solely through deciphering written texts. Studying ideology is an interdisciplinary endeavor, exploring social, economic, political, cultural, and intellectual phenomena. It encompasses the interpretation of texts, the study of social practices, and the analysis of visual and material culture, soundscapes, the built environment, and much more besides. For heuristic purposes it is worth drawing an ideal-typical distinction between theory, ideology, and imaginary. (In reality, the three blur together.) _Theories_ are systematic articulated bodies of argumentation\u2014the kind of accounts of empire produced by Hannah Arendt, Frantz Fanon, V. I. Lenin, John Locke, and John Stuart Mill. It is writing of this kind that has drawn the attention of historians of political thought in recent years. Following Michael Freeden, we can define _ideologies_ as \"clusters of ideas, beliefs, opinions, values and attitudes usually held by identifiable groups, that provide directives, even plans, of action for public policy-making in an endeavour to uphold, justify, change or criticize the social and political arrangements of a state or other political community.\"10 Such ideologies include liberalism, socialism, republicanism, conservatism, and fascism. Imperial ideologies, as I use the term in this chapter, are those elements of more general patterns of thought that relate to empire. Sophisticated theories often play a crucial role in such ideologies, but they do not exhaust them. The bulk of the chapters in this volume examine material falling in either or both of these categories. Finally, ideologies are nested within, and given shape by, _socialimaginaries_. Charles Taylor defines a social imaginary as \"the ways people imagine their social existence, how they fit together with others, how things go on between them and their fellows, the expectations that are normally met, and the deeper normative notions and images that underlie these expectations.\" Among other things, imaginaries constitute \"that common understanding that makes possible common practices and a widely shared sense of legitimacy.\"11 Imaginaries are more basic than ideologies insofar as they establish the background cultural and cognitive conventions that structure and animate them. Just as ideologies contain multiple and often competing theories, so imaginaries are compatible with varied ideologies. One of the central contentions of this chapter is that rival ideologies of empire often share key assumptions about the nature of the social world and that this can be explained through reference to underlying imperial imaginaries.\n\nIn the next section I explore aspects of the modern imperial imaginary. In the subsequent sections I distinguish three ideal-typical aspects of imperial ideology: justification, governance, and resistance. Ideologies of justification are those patterns of thought that provide reasons, explicit or implicit, for supporting or upholding imperial activity. They seek to legitimate the creation, reproduction, or expansion of empire. Ideologies of governance articulate the modalities of imperial rule in specific contexts. Particular ideologies of justification may be compatible with diverse and conflicting ideologies of governance, while precluding others. Finally, ideologies of resistance deny the legitimacy of imperial control. They too cover a broad spectrum, ranging from moderate positions that reject only some aspects of imperial rule and seek accommodation with the existing order, through to defenses of violent rebellion and the revolutionary transcendence of the system.\n\nImperial Imaginaries\n\nSocial imaginaries constitute \"the macromappings of social and political space through which we perceive, judge, and act in the world.\"12 Throughout history they have animated imperial ideologies, underwriting relevant conceptions of time and space, philosophical anthropologies, ethical assumptions, cosmologies, and metaphysical belief systems\u2014the \"deeper normative notions and images\" that Taylor suggests mold expectations about human collective life.13 In ancient China, for example, imperial authority was construed as mediating between heaven and earth, with the Han Emperor serving as the \"son of Heaven.\"14 Early modern European imperialism had to be legitimated in Christian terms. Modern imperial ideologies, too, are rooted in a widely shared set of assumptions and beliefs about the character of the social world.\n\nCharles Taylor and Manfred Steger have both probed the relationship between modern ideologies and social imaginaries. Steger argues that \"ideologies translate and articulate the largely pre-reflexive social imaginary in compressed form as explicit political doctrine\" and he contends that the key transition in the modern world is from a national imaginary to a global one, a process that was accelerated by the Second World War and is still unfolding today.15 The modern social imaginary, on this view, is constituted by various interlocking elements, including conceptions of linear time and progress, secularization, individualism, and forms of rationality and scientific knowledge. The spatial configuration of modern politics\u2014a system of territorial states\u2014is the institutional expression of this imaginary. Globalization signifies the ongoing and uneven transition to an emergent \"globalist\" system characterized by a growing consciousness of the world as an interconnected whole. For Taylor, meanwhile, the modern social imaginary is formulated in \"Lockean\" terms as a society of mutual respect among free autonomous agents, and it is institutionalized in the rise of civil society, popular sovereignty, and the capitalist system of market exchange.\n\nMy primary concern here is with what I will call the imperial imaginary: those aspects of social imaginaries that pertain to the justification or governance of empire. It is not clear how empire fits into Taylor's account, a lacuna that follows from his focus on the internal constitution of discrete societies\u2014what we might call his _methodological communitarianism_. For Taylor the modern moral order, in contrast to its medieval predecessor, \"gives no ontological status to hierarchy or any particular structure of differentiation. \"In other words,\" he writes, \"the basic point of the new normative order is the mutual respect and mutual service of the individuals who make up society.\"16 This fails to grasp the sociopolitical dynamics of modern imperialism, which is predicated on the hierarchical classification of peoples\u2014the sorting and categorizing of the world in ways that denied (either temporarily or permanently) equality and autonomy to large swathes of it. Moreover, imperial practices helped fashion the internal ordering of Western societies: empire cannot be bracketed off as something that happened elsewhere. As practitioners of the \"new imperial history\" rightly insist, imperial metropoles and peripheries need to be viewed as part of a \"single analytic field\"\u2014as dynamically connected and interpenetrating.17 Above all, the modern social imaginary, in its imperial dimensions, encodes \"civilizational\" (or racial) difference. This imaginary has framed European encounters with other peoples at least since the \"discovery\" of the Americas in the fifteenth century.18 In the remainder of this section, I discuss three elements of the modern Euro-American imperial imaginary: civilizational difference, conceptions of time and space, and what I will call \"the comparative gaze.\"\n\nPerhaps the most consequential element of the modern imperial imaginary is the way in which the world is envisioned as a space of inequality and radical difference.19 Peoples and societies are arrayed in a hierarchical manner. \"Civilization,\" the meta-concept of the modern imperial imaginary, is the term most frequently employed to characterize this stratification. It entered European political discourse in the mid-eighteenth century, first in France and then in England.20 But the underlying idea is not unique to modernity or to the West; the distinction was also common in Japan, China, and the Islamic states. The Chinese historiographical tradition, for example, \"invariably assumed that, by virtue of its superior civilization, China stood at the centre and apex of the universe, and that its emperor enjoyed a mandate from heaven not only to rule the empire, but also to exact deference and tribute from all other peoples known and unknown to the Chinese.\"21 Employing the language of \"civilization\" invokes a standard of assessment and a regime of difference\u2014it demands the drawing of normatively significant boundaries between \"advanced\" and \"backward\" societies, the latter to be viewed as inferior to (and hence open to rule by) the former.\n\nConceptions of civilization have varied considerably in modern imperial discourse. The appellation can mark either a process or a _telos_. It can be theorized in constructivist or essentialist terms: as the product of time, chance, luck, and skill, or alternatively as the result of ingrained (usually biological) difference. Conceptions of civilization come in both dynamic and static forms. The dynamic account, which from the late eighteenth century drew in particular on the historical sociology of the Scottish Enlightenment and later on universalistic theories of progress, holds that the differential levels of ethical and material development found in societies across the world are neither inevitable nor natural. This notion permeates assorted modern ideologies, including liberalism and socialism. Proponents of static accounts, which deny the implicit moral universality of dynamic perspectives, concentrate on the purportedly immutable markers of a people or \"race,\" arguing that progress amongst at least some groups (with Aboriginal Australians and sub-Saharan Africans regularly coded as paradigmatic) is virtually impossible. An extreme manifestation of this view, found in both scholarly and literary discourses throughout the nineteenth and early twentieth centuries, viewed the most \"uncivilized\" peoples as unable to socially reproduce in a world dominated by advanced white civilizations, and consequently as doomed to extinction. They were seen, in other words, as self-annihilating. As Patrick Brantlinger observes, this discourse was \"a specific branch of the dual ideologies of imperialism and racism.\"22 Most accounts of race and civilization in nineteenth- and twentieth-century imperial discourse blended together \"cultural\" and \"biological\" arguments to create a potent set of claims about the stratified character of world order. As such, they were figured as pervasive yet opaque _biocultural assemblages_.23\n\nAssumptions about European civilizational superiority were typically shared by enthusiastic imperialists and critics of empire alike, although they interpreted them in different ways. (This is one reason why the labels \"pro-imperial\" and \"anti-imperial,\" whilst perhaps unavoidable in some instances, are usually too crude for satisfactory historical and theoretical discrimination.) The justificatory argument from civilization was fairly straightforward: the civilized peoples of the world had a right, or even a duty, to spread civilization to the backward. Progress\u2014human \"improvement\"\u2014demanded it. Military and economic dominance proved to many Europeans the inherent superiority of their political and moral orders, justifying attempts to export their institutions and ideas across the globe. J. A. Hobson pinpointed the connection commonly drawn between material superiority and ethical orientation in dismissing the view that \"the power to do anything constitutes a right and even a duty to do it\" as \"the most 'natural' of temperamental fallacies.\"24 But it is important to recognize that civilization was also a key category for those critical of expansion. This position assumed several forms. First, a case could be made that the attempt to export civilization would invariably fail given the intrinsic difficulty of the task, and in particular the perceived recalcitrance of the target communities. This argument was increasingly popular towards the end of the nineteenth century, as anthropological and sociological accounts of the structure of \"native\" communities moved to the center of imperial debate.25 Alternatively, even if the spread of civilization was both feasible and universally beneficial there were more efficient or humane modes of transmission available\u2014a case made by many liberal internationalists, for whom the primary engine of transformation was international commerce. Finally, and most commonly, it could be argued that regardless of whether imperialism was an effective vehicle of civilization, it inevitably damaged the imperial metropole. The \"spirit of conquest,\" as Benjamin Constant famously labeled it, threatened the fragile achievements of civilization itself.26 This was the lesson that many post-Renaissance Europeans drew from the fall of Rome, and it formed a key element of the critiques of empire formulated by Bentham, Constant, Cobden, Spencer, and a long line of nineteenth-century radical political thinkers. It could also be argued, in an explicitly racist variation on this theme, that the pursuit of empire threatened the (racial) contamination of the civilized.\n\nConceptions of time and space structure the way in which ideologies and theories articulate political projects. Throughout history they have established the imaginative limits of the zones that empires set out to conquer and rule. In Victorian Britain, for example, novel communications technologies altered the way in which individuals perceived the physical world and the political possibilities it contained. Political forms previously regarded as utopian came to be seen as realizable. This was the period in which ideas about the \"annihilation of time and space\" began to be applied routinely to global politics.27 Once again, this aspect of the imaginary was pervasive but politically indeterminate. Many saw technological developments as facilitating, even necessitating, the construction of imperial institutions that in the past would have seemed the stuff of dreams, but to others they intensified the dangers of interpolity competition. As I explore in other chapters, this cognitive revolution acted as a condition of possibility for the emergence of ideas about a globe-spanning polity, a \"Greater Britain\" uniting Britain and its settler colonies in the South Pacific, North America, and southern Africa. It was claimed that instantaneous global communication could, for the first time in human history, sustain the bonds of identity between the members of a community\u2014the \"Anglo-Saxon race\"\u2014scattered across oceanic distances.28 Ideas about the potential scope of \"the people\" and the nature of \"the public\" were reconfigured, in a racialized precursor to contemporary debates about the emergence of a global public sphere.29\n\nFinally, the constitution of specific historical sensibilities has played a vital role in the imperial imaginary. The manner in which individuals and groups emplot historical trajectories, and the process through which these representations mold narrative constructions of the present and future, help to configure the scope and content of political discourse. They generate a repertoire of analogies, metaphors, \"lessons,\" and precedents that give shape to the field of action and determine assorted ethical imperatives about how and why to act. Cyclical conceptions of historical time have structured much Western imperial discourse. The trope of \"decline and fall\" infused accounts of empire from the ancient world until deep into the twentieth century\u2014a topic that I discuss in greater detail in chapter 5. Empires, on this account, are impermanent structures, subject to the vagaries of time, and as such they are either to be rejected (as bound to end in failure) or designed in such a way as to maximize their potential longevity (to defer failure for as long as possible). Modernity saw the emergence of a novel conception of historical time tied to open-ended notions of progress, and this in turn reshaped the ways in which the temporality of empires was conceived. While modern progressivist accounts have often been haunted by nightmares of eventual dissolution, they have not been burdened with the same sense of historical inevitability. History, on this account, need not repeat itself.\n\nModern imperial thought has also been shaped by a _habit of comparison_ , the imperial gaze stretching across the world and back through time. Other empires, past and present, have provided templates for ways of ruling, as well as cautionary tales about what to avoid. Historiography has been an authoritative mode of political thinking. European imperialists turned to the ancient world for validation, and Rome, above all, \"consistently provided the inspiration, the imagery and the vocabulary for all the European Empires from early modern Spain to nineteenth century Britain.\"30 Civic humanism offered ideological support for justifying global exploration, conquest, and occupation in early modern Europe, while the language of neo-Roman republicanism permeated eighteenth-century defenses of the British empire, especially in the North American colonies.31 The most obvious manifestation of this historicized sensibility, though, resided in the frequent reiteration of the classical debate over the corrupting relationship between empire and liberty.32 Yet comparisons between the ancients and the moderns were always selective and the imaginative resources extracted from Rome and Greece fed a variety of conflicting desires and demands.\n\nComparison could also be employed as a strategy to \"deflect moral anxiety\" about the governing practices of empire.33 The brutality of conquest and imperial rule could be relativized, and thus downplayed, either by comparing it favorably to the gross atrocities of past empires (usually the Spanish) or by arguing (as was widespread in British, French, and American debates) that the subject populations were better off governed by the most beneficent imperial power, whatever its defects, than by another more rapacious state. In a related move, it could be argued that Western imperial domination was invariably better than non-European alternatives. As James Mill once wrote about India, \"[e]ven the utmost abuse of European power, is better, we are persuaded, than the most temperate exercise of Oriental despotism.\"34 Counter-factual reasoning was routinely put at the service of imperialism.\n\nThese elements of the imperial imaginary continue to shape our world: Western political discourse is still shadowed by the specter of the civilizing mission. Although usage of the term \"civilization\" declined precipitously through the twentieth century, it is at least arguable that the underlying ideas never disappeared\u2014they were rearticulated in the form of \"modernization\" theory during the 1960s and 1970s and are now rendered in the more palatable language of \"development\" and \"democratization.\"35 Purportedly novel conceptions of time and space lie at the very heart of debates over globalization. During the twentieth century, the apparent \"shrinking\" of the world through advanced communications and transport technologies underpinned an array of proposals for trans-planetary political institutions\u2014regional unions, democratic alliances, even federal world-states.36 Finally, the fascination with the ancients and the power of the comparative gaze continues undiminished. In the post-9\/11 world, for example, both critics and admirers of the United States have routinely compared it with the nineteenth-century British empire and with Rome, seeking to identify patterns of similarity and difference that shed light on the contemporary condition.37 Defenders of liberal imperialism, meanwhile, still resort to cost-benefit calculations and counterfactual reasoning to argue that it was better than the available alternatives.38 _Plus \u00e7a change?_\n\nIdeologies of Justification\n\nJustifications of empire are often blended together in practice to form a powerful if inconsistent ideological amalgam. However, for the purposes of analytical clarity it is worth delineating some of the ideal-typical forms of argument that have been employed to justify conquest and rule in the modern era.39 I will briefly outline five: commercial-exploitative, realist-geopolitical, liberal-civilizational, republican, and martialist. They embody distinct logics, although they overlap in assorted ways. It is also worth noting that each kind of justification has found sophisticated expression in social scientific or historical explanatory theories during the last one hundred and fifty years. Ideological affirmation has transmuted into canons of systematic scholarship. For example, the everyday arguments of imperial strategists and military planners find their contemporary academic analog in \"realist\" explanations of imperial expansion offered by IR scholars and diplomatic historians. Meanwhile, arguments once adduced on behalf of the financial benefits of empire are now the raw material of economic historians of Western expansion. This highlights the complex entanglement of imperial politics and the evolution of the modern human sciences.\n\nRealist-geopolitical arguments focus attention on power politics. According to such views, imperial consolidation or expansion is often regarded as necessary to balance or trump the power of competing imperial states. The world is envisaged as a chessboard, with imperial strategy a vital ingredient of ultimate success. Imperialism is rarely seen as an end in itself but rather as a means to secure geopolitical advantage. This was the kind of argument proffered by Bismarck in Germany and Lord Salisbury in Britain. An underlying assumption is that scale translates into status; that the governance of large territorial spaces is a precondition for assuming the role of a \"great power.\" Realist-geopolitical arguments play a starring role in much IR and historical scholarship. For example, they were central to Robinson and Gallagher's seminal work on the \"official mind\" of British imperialism in the nineteenth century.40 In a recent iteration of the argument, Brendan Simms contends that the fulcrum of British foreign policy throughout the seventeenth and eighteenth centuries was to be found in Europe, not the empire, and insofar as Britain engaged in imperial activity in North America and Asia it was primarily to maintain the balance of power within Europe.41 One feature of this type of scholarship is that while it takes calculations of power and interest seriously, it pays little attention to wider ideological currents, focusing its attention on the views of small groups of elite policy-makers.\n\nCommercial-exploitative arguments justify empire principally in terms of the economic benefits that it generates for the metropole (or specific interests therein). Throughout history, empires have acted as engines of wealth extraction and redistribution, moving raw materials, manufactured products, and countless people\u2014whether administrators, domestic workers, family dependents, soldiers, or slaves\u2014through complex circuits of production and exchange. It is unsurprising, then, that economic concerns have stood at the heart of many imperial ideologies. But the particular form of justificatory argument employed has evolved over time, especially as the state of economic \"knowledge\" developed. There have been, in other words, performative consequences to the evolution of the discourse of political economy, from its origins in early modern Europe to the current dominance of its neoclassical variants. Commercial-exploitative arguments tend to focus on either the extraction of raw materials from an occupied territory or on opening new markets for trade. The shift in emphasis from the former to the latter represents one of the major ideological shifts in the modern history of empire.42 Whereas deep into the early modern era imperial conquest was often legitimated through mercantilist arguments\u2014with the Spanish Empire in the Americas serving as an exemplar43\u2014during the eighteenth century, political economists began to insist that free trade was the best strategy to secure national economic development. Adam Smith's critique of the \"old colonial system\" in the _Wealth of Nations_ was the most sophisticated elaboration of this argument. This shifted the burden of justification: imperial territories were increasingly regarded as either economic liabilities to be discarded or (more commonly) their role in the imperial order was reimagined. They were cast as nodes in a vast global trading system\u2014as reservoirs of cheap labor and goods, or as profitable zones for market exchange.\n\nThe relationship between capitalism and empire, then, stands at the core of debates over economic justifications of imperial rule. Marx was ambivalent about imperialism. While critical of the violence and cupidity of European expansion, he nevertheless approved of its power to transform societies stifled by moribund (\"oriental\") traditions.44 The task of developing a systematic theory of capitalist imperialism was taken up by many of his acolytes, among whom the most influential were Rudolf Hilferding, Rosa Luxemburg, Karl Kautsky, Nikolai Bukarin, and Vladimir Illich Lenin, who famously argued that imperialism was the \"highest stage\" of capitalism.45 With the partial exception of Luxemburg, all of them focused on the dire consequences for European politics, largely ignoring the impact of empire on those subjected to it. Marxist theorizing was later reworked by scholars in colonial and postcolonial states. Most influential of all were the _dependencia_ theories that emerged in the 1960s and 1970s, though as with earlier Marxist accounts, their advocates downplayed the role of ideology in seeking to explain the dynamics of imperialism.46 (Indeed the lack of attention paid to ideology was one of the main criticisms leveled at Marxist analyses by scholars working in a postcolonial idiom.) Arguments linking capitalism to imperialism are not, of course, the preserve of Marxists. Lenin himself drew on the writings of the British radical liberal J. A. Hobson, who dedicated his seminal _Imperialism: A Study_ to exposing the dynamics of the \"new imperialism\" of the late nineteenth century. Joining a long line of radical critics of empire, all of whom stressed the economic imperatives driving imperialism, Hobson had concluded that capitalism itself was not at fault, only a distorted financial variant of it.47 Other important analyses of the socioeconomic conditions generating European imperialism were penned by Hannah Arendt, Karl Polanyi, and Joseph Schumpeter. Most work linking capitalism and imperialism is critical of either one or both of them, but there are exceptions. Neo-imperialists like Niall Ferguson, for example, have been quick to praise the conjoined transformative energies of capitalism and liberal empire.\n\nIt would be foolish to deny the role of capitalism in motivating modern imperial activity, but it is nevertheless worth noting that, at least in the last two hundred years or so, few prominent thinkers have justified empire solely, or even primarily, in economic terms. Even Joseph Chamberlain, a British politician famous for his arguments about the economic benefits of empire, emphasized the absolute centrality of national honor and moral character in legitimating imperialism.48 What, then, is the relationship between imperial discourse and practice? One possibility is that the profession of noneconomic justifications is a self-serving distortion of reality\u2014ideology in the pejorative Marxist sense. Another possibility is that most imperial thinkers were motivated primarily by noneconomic factors. (This option is compatible with the claim that governments and capitalist enterprises were driven by economic imperatives.) Perhaps most plausible is the idea that reflective imperialists typically had mixed motives, interweaving views on the economic gains generated by empire with a variety of other arguments, including those emphasizing its ability to protect important national (or \"racial\") security interests and the world-transformative power of civilization. But not all advocates of empire were quite so Panglossian. Recognizing that trade-offs were necessary, John Stuart Mill, to give one prominent example, argued that the British should retain their settler colonies if possible, but that doing so would invariably amplify their military vulnerability.49 Costs had to be weighed against benefits. Difficult choices had to be made.\n\nThe relationship between liberalism and empire has generated a substantial body of scholarship\u2014including many of the chapters in this volume. Arguments range from the claim that liberalism is inherently imperial to the Schumpeterian position that the two are antithetical. Both poles of the spectrum are implausible, not least because liberalism is such an inchoate ideological tradition that generalizations about its content are usually misleading. It contains resources both to justify and to critique imperialism. Despite this qualification, it is undoubtedly the case that during the last two centuries a particular strand of \"liberal civilizing imperialism\" has thrived. Maintaining that liberal states have a right (even a duty) to spread \"civilization\" to the purportedly non-civilized peoples of the world, its advocates insist that empire is only legitimate if it is primarily intended to benefit the populations subjected to it. Any other benefits that it generates are derivative and incidental. As Mill argued in _On Liberty_ , \"[d]espotism is a legitimate mode of government in dealing with barbarians, provided the end be their improvement, and the means justified by actually effecting that end.\" Giuseppe Mazzini, writing in the early 1870s, likewise endorsed the \"moral mission\" of civilizing imperialism, suggesting that the Europeans were destined to transform Asia and that Italy \"should not lose out on this wonderful new movement.\"50 At the turn of the twentieth century, Chamberlain recorded the shift towards this \"altruistic\" vision of empire: \"[T]he sense of possession has given place to a different sentiment\u2014the sense of obligation. We feel now that our rule over their territories can only be justified if we can show that it adds to the happiness and prospects of the people.\"51 Most articulations of this argument link civilization to nationality and sovereignty. Civilization is seen as a necessary though not sufficient condition for the emergence of national self-consciousness, which in turn is regarded as essential to trigger liberal claims to the right of political self-determination. Once a society had developed to the point where it could be classified as civilized, and once it exhibited authentic national self-consciousness, it could justifiably claim independence, and the job of the liberal imperial power was complete. But the temporal coordinates were very rarely specified; freedom was deferred to some indefinite point in the future. In the meantime, attention was focused on refining the modes and modulations of imperial rule\u2014on ideologies of governance.\n\nLiberal civilizing imperialism coexisted with another kind of justificatory argument which we might characterize as \"republican.\" Republican imperialism is primarily motivated by a concern with the character of the imperial power, justifying empire in terms of a particular class of benefits that it generates for the state. Its proponents seek to foster individual and collective virtue in their compatriots, while upholding national honor and glory. Any other benefits that empire generates\u2014including economic gain and \"civilization\"\u2014are derivative and incidental. This kind of argument has deep roots in Western political thought, traceable to Rome. During the nineteenth century Alexis de Tocqueville, and a range of British commentators, including the historians J. R. Seeley and J. A. Froude, articulated republican defenses of empire. Though they employed the language of civilization to classify and order the world\u2014as we would expect, given its central role in the imperial imaginary\u2014they tended not to justify imperialism principally in terms of its civilizing agency. For example, although Froude often boasted about the greatness of the British empire, he placed little emphasis on \"civilizing\" occupied territories, focusing instead on the virtues that such power fostered in the British population.52 Republican justifications predate liberalism by centuries, and they offer a different kind of argument about the character and purpose of empire, as well as its potential fate.\n\nFinally, we can isolate a martialist justification of empire. Martialism is the view that \"war is both the supreme instrument and the ultimate realization of all human endeavour.\"53 It stresses the transcendent role of violence in shaping individual and collective character. The field of battle is seen as a space for enacting a form of warrior masculinity\u2014and for inculcating virility in a population. Although it found its most ardent supporters in _fin de si\u00e8cle_ Germany\u2014including Helmut von Moltke and Heinrich von Treitschke\u2014a \"martialist _Zeitgeist_ ,\" Karma Nabulsi contends, infused the thought and practice of many British soldiers, imperial administrators, and civil servants in the nineteenth century. It was expressed, though rarely in an explicit and straightforward sense, in the utterances of writers such as Thomas Carlyle and J. A. Cramb,54 and it can also be located in the works of some of the more jingoistic British poets of the age, such as W. E. Henley, who once proclaimed that \"War, the Red Angel\" was the lifeblood of the nation.55 Empire, on this view, is a space for forging character through exercising the will-to-power in rituals of destruction.\n\nIdeologies of Governance\n\nGovernance includes the discrete institutions of government but it also encompasses the assorted practices and structures\u2014educational systems, market orders, civil society actors, cultural agencies\u2014though which populations are administered and regulated. It focuses, then, on the multiple vectors for creating, maintaining, and contesting political legitimacy. The modalities of governance employed to rule empires, and to construct pliant imperial subjectivities, have varied greatly across time and space. For much of human history the ability of governments to rule territory was severely constrained by practical concerns, above all the difficulties of creating effective administrative systems. Only in the last couple of hundred years\u2014and in particular during the last century\u2014have states gained the capacity to systematically observe, measure, and regulate large populations, thus providing the necessary conditions for the comprehensive exercise of sovereign power.56 Governance of this kind has ascribed a central role to the construction and deployment of knowledge and expertise. In the British empire, for example, administrators and scholars were set to work classifying different castes in India, tribes in Africa, languages, legal systems, sexualities, geographies, even dreams.57 Such exercises created the \"colonial knowledge\" thought necessary to police and rule space, though it was rarely as effective as its advocates proclaimed.58 Mapping the \"human terrain\" as it has come to be called in the post-9\/11 era, was a vital element of imperial governance.\n\nThe question of whether formal or informal rule is the most effectual runs through modern imperial discourse. The scholarly debate on the topic was initiated by Robinson and Gallagher's famous argument about the \"imperialism of free trade\" in the nineteenth century. Where possible, they argued, the British preferred to subordinate other societies through economic instruments rather than formal occupation\u2014\"trade with informal control if possible; trade with rule when necessary.\"59 Exercising _de jure_ sovereignty over a political community was not indispensable to wielding profound and pervasive control over it. The mid-nineteenth century, then, was marked less by a retreat from empire, as was once commonly assumed, than a turn to novel nonterritorial forms of imperial governance. This kind of argument highlights how economic regimes\u2014specific configurations of state, market, and knowledge\u2014can shape modes of rule. Mike Davis, for example, argues that Britain's commitment to classical liberal economics facilitated the famines that ravaged the population of British India in the closing decades of the nineteenth century, killing uncounted millions.60 Linking imperialism directly to liberal economic ideology opens a space for arguing that the postcolonial world remains structured by imperialism. On this account, even if formal empires have retreated to the wings, imperialism remains embedded in the structures and ideology of the current global economic order. Neoliberalism can be seen as the latest manifestation of capitalist imperialism.61\n\nA key issue in imperial governance concerns the degree to which an imperial power tries to (re)construct the subjected society in its own image\u2014the extent to which empire becomes a totalizing project. This was a contested issue in the nineteenth-century debates over how and why the British should rule India. A new generation of liberal civilizing imperialists attacked what they saw as an outdated policy in which European intervention in local Indian affairs was minimized (whether this was a realistic picture is a separate question). They were adamant that the primary aim of empire was to civilize a barbarian land and not simply to extract revenue or provide an outlet for British geopolitical ambition. These contrasting ends implied very different governing means. In particular, the civilizational model demanded a much more intrusive governance regime. The character of public education assumed a fundamental role, spawning a famous ideological dispute between \"Orientalists\" and \"Anglicizers.\" Professing respect for Indian cultural achievements, the Orientalists favored allocating money to teaching Sanskrit and Arabic, while the Anglicizers insisted on making English the primary language.62 This was the occasion for T. B. Macaulay's notorious \"Minute on Indian Education,\" wherein he proclaimed that \"a single shelf of a good European library was worth the whole native literature of India and Arabia.\"63 English should be supported because it conveyed the teachings of a superior civilization\u2014language was a vehicle for progress. At stake here was a question about both the purpose and the most appropriate governing technologies of empire.\n\nAn important transition occurred in the governing ideology of the British empire in the closing decades of the nineteenth century. Karuna Mantena has characterized this as the shift from \"ethical\" modes of imperialism (exemplified by John Stuart Mill) to informal \"alibis\" of empire (exemplified by Henry Maine). On this account, the British pulled back from the attempt to create imperial subjects in their own image, thus preparing the ground for liberal self-government, and instead turned increasingly to modes of rule that they claimed protected fragile native communities from destruction. \"Rather than eradicated or aggressively modernized, native social and political forms would now be patronized as they became inserted into the institutional dynamics of imperial power.\"64 Although this argument understates the extent to which \"ethical\" justifications continued to circulate\u2014a theme I discussed in chapter 2\u2014the gradual emergence of more indirect styles of governance was nevertheless highly significant. The major practical impact of this ideological shift was the transition towards government by indirect rule in Britain's African colonies and the later development of notions of trusteeship under the League of Nations.\n\nSettler colonialism, as I dissect in various chapters in this volume, produced (and was produced by) a range of distinctive justificatory and governing strategies.65 In a standard conceptual move, Mill distinguished two classes of British \"dependencies\": those composed of people of a \"similar civilization\" that were \"capable of, and ripe for, representative government\" and those, defined in hierarchical opposition, that remained \"a great distance from that state.\"66 The former group included Australia, Canada, New Zealand\u2014and had once included the United States\u2014while the latter encompassed India and British territories in the Caribbean and Africa. Since the settler colonies were seen as already populated by civilized subjects, they were justified and governed in different ways from the rest of the empire. In India the primary target of imperial governance, and the postulated locus of the problem it sought to rectify, was the mind of the \"barbarian.\" Discussion of the settler empire was likewise saturated with the imagery of childhood, except here the referent was different. The target was not the people, who were after all descendants or relations of the inhabitants of Britain, but rather the polities in which they lived. The collective not the individual, the whole not the part, required supervision. It was Australia, Canada, and New Zealand that were \"young\" and \"immature.\" They were governed in a different manner from the rest of the British empire: from the middle of the nineteenth century, for example, they were granted increasing domestic political autonomy (\"responsible government\").67 Furthermore, from the 1850s onwards most advocates of settler colonialism argued that the formal connection between \"mother country\" and colonies was only legitimate if subject to reciprocal assent. This stands in stark contrast to attitudes to the rest of the empire, where subjects were not regarded as sufficiently developed\u2014politically, cognitively, or morally\u2014to enter into such voluntaristic relations.\n\nViolence, and the threat of violence, is a necessary element of imperial governance. Empires are typically administered through a complex pattern of central rule and local collaboration, but violence is an ever-present possibility, employed both to enforce the existing order and to challenge it. During the nineteenth century, the utility of violence triggered disagreement between otherwise putatively \"liberal\" defenders of empire. For Tocqueville, an ardent proponent of French rule in Algeria, empire sometimes required brutal extra-judicial measures. \"In order for us to colonize to any extent,\" he asserted, \"we must necessarily use not only violent measures, but visibly iniquitous ones,\" and as such it was sometimes acceptable to \"burn harvests,... empty silos, and finally... seize unarmed men, women, and children.\"68 This kind of position horrified John Stuart Mill and many of his followers.69 For Mill, upholding the rule of law and treating subjects with due consideration was an indispensable element of enlightened despotism, differentiating it from illegitimate imperialism. This belief underpinned support for the campaign, in which Mill played a prominent role, to bring Governor Eyre to justice for his abuse of power in Jamaica in the 1860s.70 However, liberal imperialists were almost invariably blind to the lived experience of imperial rule, failing to recognize that routinized violence was inescapable in governing conquered spaces. While Mill became increasingly perturbed by the prevalence of colonial violence towards the end of his life, he nevertheless continued to preach the benefits of civilizing imperialism.71\n\nIn recent years, the legacy of imperial governance has shaped various aspects of world order. Imperial administrative practices forged in the early twentieth century have found a new lease of life as trusteeships and protectorates have been retooled by the United Nations in the former Yugoslavia and elsewhere.72 Methods of colonial policing, meanwhile, have been widely employed in Iraq and Afghanistan, as \"counter-insurgency\" activities have been launched against resistance movements of various kinds. Western militaries are far more open about the colonial origins of such strategies\u2014forged in the battle spaces of Malaya, Algeria, and Vietnam, among others\u2014than the governments who sent them there. Indeed learning the lessons of previous colonial wars has been a central feature of the post-9\/11 national security apparatus. A further legacy of imperial governmentality can be seen in the deployment of social scientists\u2014and above all, anthropologists\u2014to the global south to provide the \"cultural knowledge\" necessary to combat insurgencies.73\n\nIdeologies of Resistance\n\nThere are as many ideologies of resistance as there are of justification and governance. Excavating them would involve working at multiple levels of analysis, and in a variety of scholarly registers, spanning what James Scott labels \"everyday forms of peasant resistance,\" through the ideas animating revolutionary movements, to the sophisticated theoretical critiques developed by philosophers.74 For the sake of convenience, we can divide such ideologies into two broad families. The first set emanates from the imperial metropole; they constitute a form of internal opposition to the practices of imperialism. The second set is produced by subjects of imperial rule. Historically the most prominent strands of metropolitan opposition focused largely (though not exclusively) on the damage that imperialism wreaks on the imperial power itself, paying scant attention to those subjected to the violence and the routine humiliation of empire. The second form of imperial resistance argument focuses largely (though not exclusively) on that violence and humiliation.\n\nThe term \"anti-imperialism\" is often misleading when applied to ideologies of resistance. Many of the arguments lumped under the umbrella do not reject imperialism in principle\u2014instead they focus on certain expressions of it. An important body of scholarship has sought to anatomize the tradition of \"liberal\" imperial critique in Western Europe, demonstrating that an array of important thinkers, including Diderot, Herder, Smith, Bentham, and Kant opposed imperial conquest.75 Edmund Burke has also been reinterpreted as an important source of anti-imperial theorizing, albeit less convincingly.76 Despite this opposition, however, it is worth bearing in mind that much \"Enlightenment\" thought was nevertheless shaped by the imperial imaginary. It is sometimes suggested that anti-imperial arguments were marginalized by the middle of the nineteenth century, supplanted by the unabashed liberal imperialism exemplified by John Stuart Mill. This is misleading, however, for the nineteenth century saw stinging attacks on empire\u2014as passionate and comprehensive as any launched by Smith, Bentham, or Kant\u2014from esteemed liberal philosophers (such as Herbert Spencer), politicians (such as Richard Cobden), and political economists (such as J. A. Hobson). Like the late eighteenth-century critics, though, they were rarely opposed to _all_ forms of empire; the \"anti-imperial\" critique only cut so deep. For example, many of them opposed the violent usurpation and rule of European powers in Asia, Africa, and Latin America while simultaneously endorsing the seizure of \"unoccupied\" lands by European settlers\u2014the kind of settler colonialism that led to the dispossession and death (sometimes through genocide) of innumerable people in Australasia and North America, among other places.77 Given the ubiquity of the imperial imaginary, it is unsurprising that arguments explicitly critical of empire were nevertheless typically underpinned by racial and civilizational assumptions.\n\nLiberalism was not an ideology confined to the metropole\u2014it was both a product and an agent of globalization. During the course of the nineteenth century it was spread throughout the world by European imperial powers, but it was then often indigenized, adapted to local circumstances and traditions to provide a repertoire of arguments that could be utilized as part of an anti-imperial struggle. As C. A. Bayly notes, the leaders of anti-imperial protests \"in places as far distant as Santiago, Cape Town and Canton invoked the notion of their 'rights' as individuals and as representatives of nations.\"78 An emergent Indian liberal tradition provided a powerful ideological resource to oppose empire.79 Modern Western empires often carried the ideological virus that eventually helped to kill them.\n\nLike liberalism, republicanism is capable of being utilized for both imperial and anti-imperial ends. Whereas republican imperialism contends that the pursuit of empire is important (or even necessary) for maintaining a virtuous political community, republican anti-imperialism asserts that the very existence of the republic is endangered by imperial activity: republican virtues are corroded by the \"spirit of conquest.\" According to republicans, Quentin Skinner argues, \"[y]ou can hope to retain your individual freedom from dependence on the will of others if and only if you live as an active citizen of a state that is fully self-governing, and is consequently neither dominating nor dominated.\" Offering a contemporary gloss on this venerable theme, Philip Pettit suggests that \"the free individual is protected against the domination of others by the undominating and undominated state.\"80 Republican anti-imperial arguments have been popular during the last couple of centuries, most notably in the United States, where the founding has been mythologized as an archetypal anti-imperial moment.81 Today they are deployed to challenge American hegemony. Chalmers Johnson, for example, laments that the American republic is being destroyed by militarism and the pursuit of global empire\u2014it faces nemesis, the product of hubris.82\n\nThe Marxist arguments I mentioned in the third section of this chapter can be seen both as attempts to explain the dynamics of imperialism and as contributions to ideologies of resistance. Marxism provided much of the intellectual impetus for anti-imperial praxis throughout the twentieth century, and variants of Marxism remain central to both anti-imperial social movements and to the politico-intellectual attack on the neoliberal order. In one of the most widely discussed recent interventions, Michael Hardt and Antonio Negri argue that we are witnessing the emergence of a new form of network \"Empire.\"83 On this interpretation, Empire is \"a _decentred_ and _deterritorialising_ apparatus of rule that progressively incorporates the entire global realm within its open, expanding frontiers.\" Empire, they continue, can \"only be conceived as a universal republic, a network of powers and counterpowers structured in a boundless and inclusive architecture.\"84 (Their argument is notable among other things for underplaying the continued salience of the United States.) Traditional styles of resistance, based on nationalist forms of belonging, are as obsolete as the territorial modes of imperialism they originally challenged. Instead, Empire spawns its own agent of resistance\u2014the \"Multitude,\" the \"productive creative subjectivities of globalization.\"85 An amorphous, heterogeneous assemblage of workers, the dispossessed and the oppressed, the multitude is (somehow) supposed to offer an alternative way of being.86 Empire dialectically generates the specific mode of resistance that will dissolve or transcend it. Other Marxist theorists have recoiled from Hardt and Negri's grandiose metaphysics of resistance, and focused instead on unraveling the social dynamics of contemporary forms of neoliberal imperialism and its alternatives.87\n\nA plethora of anticolonial movements and ideologies sprang up in the world's occupied zones during the twentieth century. While impossible to do them justice in such a short space, it is worth highlighting two influential but contrasting models: the Gandhian and Fanonian. Perhaps more than any other anti-imperialist, Gandhi combined theory and practice as part of a seamless whole.88 In _Hind Swaraj_ he sketched both a stringent critique of Western civilization and elaborated an alternative nonviolent form of nationalist politics rooted in the celebration of Indian cultural practices. For Gandhi, Western civilization was poisoned by its materialism, its moral myopia, and its destructive individualism\u2014it was hypocritical to the core. Adopting a strategy of \"reversal,\" he denigrated the claims to normative superiority used by the British to legitimate their empire while affirming many of the \"traditional\" practices that they had belittled, finding in Indian civilization a productive source of ethical guidance and spiritual development.89 True (Indian) civilization embodied the virtues\u2014self-abnegation, duty, good conduct, self-control\u2014that Western culture was incapable of sustaining.90 Mixing romantic nostalgia, hard-headed political criticism and an iconoclastic account of nationalism, _Hind Swaraj_ served as a seminal (though selectively appropriated) text for the Indian Nationalist Movement and a source of inspiration for later anticolonial thinkers.\n\nFrantz Fanon, an Algerian psychiatrist and journalist, defended a radically different kind of resistance. Drawing on Marxism and psychoanalysis, his work illuminated the complex intersections of race and economic exploitation undergirding European empires.91 In his analyses of the social and racial dynamics of imperialism\u2014most famously _The Wretched of the Earth_ \u2014he emphasized its extreme violence and the damaging psychic consequences for the oppressed. Like Gandhi he dissected the hypocrisy of Western universalism, deriding its claims to superiority: \"[W]hen the native hears a speech about Western culture he pulls out his knife.\"92 Yet he diverged from Gandhi in at least two important respects. First, he was highly ambivalent about nationalism. Recognizing it as a necessary stage of anticolonial politics, he ultimately sought to transcend it, for rather than offering a vehicle to escape colonial rule, nationalism promised to reinscribe its hierarchical structures in novel forms. Fostering national consciousness served as a symbolic way for the new postcolonial elites to mask the mimetic dynamics of exploitation. The problem of oppression was not resolved by granting formal freedom, because capitalism was necessarily exploitative and freedom-constraining. This line of argument marked a powerful move, for much early anticolonial thought and practice was framed within the terms of a national imaginary. Indeed the nationalist impulse of much anticolonial activism provided one of the main targets for a later generation of postcolonial scholars.93 The second, and most controversial, way in which Fanon diverged from Gandhi was in his defense of the utility of violence in colonial contexts. Violence was an essential part of the anti-imperial struggle, necessary both to overcome the crushing power of the colonial state and to provide a form of catharsis for its victims. Liberation\u2014both political and psychological\u2014was only possible through a brutal clash of wills. It is in part through the exercise of such violence that colonial subjects can regain their agency. \"At the level of individuals, violence is a cleansing force. It frees the native from his inferiority complex and from his despair and inaction; it makes him fearless and restores his self-respect.\"94 Fanon's arguments resonated widely in a world caught in the throes of anticolonial struggle, while generating sharp criticism from those who rejected his advocacy of violence, including Hannah Arendt and Michael Walzer.95\n\nWe are left with a question about what forms of resistance are appropriate in the contemporary world. Modern history offers a range of answers, each of which finds its contemporary exponents. Liberal and republican thinkers and activists have offered forceful criticisms of imperial action, while Marxism continues to inspire social movements throughout the world, its arguments and strategies adapted to new forms of oppression. Gandhian nonviolence still finds enthusiasts.96 What of violent resistance? This is a topic that is rarely explored in contemporary political theory, yet if the current global order is a site of vast injustice, as many theorists suggest, should violence be ruled out? After all, to deny victims the right to resist their oppressors seems to conspire in their subjugation.97 The ghost of Fanon has not yet been exorcised.\n\nConclusions\n\nOne of the most famous passages written about imperialism is found in Joseph Conrad's _Heart of Darkness_ :\n\nThe conquest of the earth, which mostly means the taking it away from those who have a different complexion or slightly flatter noses than ourselves, is not a pretty thing when you look into it too much. What redeems it is the idea only. An idea at the back of it, not a sentimental pretence but an idea: and an unselfish belief in the idea\u2014something you can set up, and bow down before, and offer a sacrifice to.98\n\nConrad here penetrates to the core of the issues that I have discussed in this chapter. Empire is never a \"pretty thing,\" and while no idea redeems it\u2014despite the claims of Conrad's narrator and the protestations of contemporary neo-imperialists\u2014modern imperialism cannot be understood adequately without grasping the ideas that have motivated its advocates, legitimated its practices, and animated resistance to it. We live in a world shaped by the histories, memories, and myths of past empires, and in which imperial power still determines the life chances of countless millions of people. It should remain a central topic of concern for students of political thought.\n\n1 Doyle, _Empires_ (Ithaca, 1986), 45. See also David Abernethy, _The Dynamics of Global Dominance_ (New Haven, 2000), 19.\n\n2 Michael Ignatieff, _Empire Lite_ (London, 2003), 109; Niall Ferguson, _Colossus_ (London, 2004).\n\n3 For discussions of different conceptions of (largely European) empire, see Anthony Pagden, _Lords of All the World_ (London, 1995); Patrick Wolfe, \"History and Imperialism,\" _American Historical Review_ , 102 (1997), 388\u2013420; David Armitage, ed., _Theories of Empire, 1450\u20131800_ (Aldershot, 1998); and James Muldoon, _Empire and Order_ (Basingstoke, 1999).\n\n4 Compare, for example, John Ikenberry, _Liberal Order and Imperial Ambition_ (Cambridge, 2006) and Niall Ferguson, _Empire_ (London, 2003).\n\n5 Dominic Lieven, _Empire_ (New Haven, 2002); Christopher Bayly, _The Birth of the Modern World_ (Oxford, 2004); John Darwin, _After Tamerlane_ (London, 2007); James Belich, _Replenishing the Earth_ (Oxford, 2009); Jane Burbank and Frederick Cooper, _Empires in World History_ (Princeton, 2010).\n\n6 Said, _Orientalism_ (London, 1978); Said, _Culture and Imperialism_ (London, 1993); Bhabha, _The Location of Culture_ (London, 1994); Spivak, \"Can the Subaltern Speak?,\" in _Marxism and the Interpretation of Culture_ , ed. Cary Nelson and Laurence Grossberg (Urbana, 1988), 271\u2013313.\n\n7 For anthropology, see, from a long list, Eric Wolf, _Europe and the People without History_ (Berkeley, 1982); Marshall Sahlins, _How \"Natives\" Think_ (Chicago, 1995); Bernard Cohn, _Colonialism and Its Forms of Knowledge_ (Princeton, 1996); Ann Laura Stoler, _Along the Archival Grain_ (Princeton, 2010). For geography: Felix Driver, _Geography Militant_ (Oxford, 2001); Derek Gregory, _The Colonial Present_ (Oxford, 2004); Gerry Kearns, _Geopolitics and Empire_ (Oxford, 2009).\n\n8 Partha Chatterjee, _Nationalist Thought and the Colonial World_ (London, 1986); Dipesh Chakrabarty, _Provincializing Europe_ (Princeton, 2000); John Hobson, _The Eurocentric Conception of World Politics_ (Cambridge, 2012); cf. David Scott, _Conscripts of Modernity_.\n\n9 David Long and Brian Schmidt, eds., _Imperialism and Internationalism in the Discipline of International Relations_ (Albany, 2005); Robert Vitalis, \"The Noble American Science of Imperial Relations and Its Laws of Race Development,\" _Comparative Studies in Society and History_ , 52 (2010), 909\u201338; Tarak Barkawi, \"Empire and Order in International Relations and Security Studies,\" in _The International Studies Encyclopaedia_ , ed. Robert Denmark (Oxford, 2010), 3:1360\u201379; Naeem Inayatullah and David Blaney, _International Relations and the Problem of Difference_ (New York, 2004). Notable exceptions include, Doyle, _Empires_ ; Alexander Motyl, _Imperial Ends_ (New York, 2001); Alexander Cooley, _Logics of Hierarchy_ (Ithaca, 2005); Daniel Nexon, _The Struggle for Power in Early Modern Europe_ (Princeton, 2009).\n\n10 Freeden, _Ideologies and Political Theory_ (Oxford, 1996), 6.\n\n11 Taylor, _Modern Social Imaginaries_ (Durham, NC, 2004), 23. Taylor distinguishes imaginaries from theories, the latter explicit bodies of doctrine, the former often-unstructured background features of social existence (24\u201325). In line with Manfred Steger, _The Rise of the Global Imaginary_ (Oxford, 2008), I suggest that ideologies occupy a middle position, nested within social imaginaries, but themselves (often) containing a variety of more or less distinguishable theories. Note that the categories are not mutually exclusive.\n\n12 Steger, _The Rise of the Global Imaginary_ , 6.\n\n13 Taylor, _Modern Social Imaginaries_ , 23.\n\n14 Alejandro Col\u00e1s, _Empire_ (Cambridge, 2007), 2.\n\n15 Steger, \"The Changing Face of Political Ideologies in the Global Age,\" _New Political Science_ , 31 (2009), 426.\n\n16 Taylor, _Modern Social Imaginaries_ , 12.\n\n17 Frederick Cooper and Ann Laura Stoler, \"Between Metropole and Colony,\" in _Tensions of Empire_ , ed. Cooper and Stoler (Berkeley, 1997), 4. Among historians of modern Britain there is a heated dispute about the extent to which society was (and is) shaped by empire: John Mackenzie, ed., _Imperialism and Popular Culture_ (Manchester, 1986); Catherine Hall, _Civilising Subjects_ (Cambridge, 2002); Bernard Porter, _The Absent-Minded Imperialists_ (Oxford, 2004); Andrew Thompson, _The Empire Strikes Back_ (London, 2005).\n\n18 On the dynamics of encounter, see Tzvetan Todorov, _The Conquest of America_ , trans. R. Howard (New York, 1992).\n\n19 The following discussion draws on material from Duncan Bell, \"Empire and International Relations in Victorian Political Thought,\" _Historical Journal_ , 49 (2006), 281\u201398.\n\n20 J.G.A. Pocock, _Barbarism and Religion: Vol. 4_ (Cambridge, 2005); Brett Bowden, _The Empire of Civilization_ (Chicago, 2009).\n\n21 Patrick O'Brien, \"Historiographical Traditions and Modern Imperatives for the Restoration of Global History,\" _Journal of Global History_ , 1 (2006), 18.\n\n22 Brantlinger, _Dark Vanishings_ , 1.\n\n23 For further discussion of this idea, see Duncan Bell, \"Beyond the Sovereign State,\" _Political Studies_ , 62\/2 (2014), 418\u201321.\n\n24 Hobson, _Imperialism_ (London, 1902), 157.\n\n25 Mantena, _Alibis of Empire_.\n\n26 Constant, \"The Spirit of Conquest and Usurpation and Their Relation to European Civilization\" [1814], in _Constant: Political Writings_ , ed. B. Fontana (Cambridge, 1988), 51\u2013165.\n\n27 Stephen Kern, _The Culture of Time and Space, 1880\u20131914_ (Cambridge, MA, 1983).\n\n28 Seeley, _The Expansion of England_. See also the discussion in Duncan Bell, _The Idea of Greater Britain_.\n\n29 I develop this argument in chapter 7.\n\n30 Anthony Pagden, _Peoples and Empires_ (London, 2001), 28.\n\n31 Andrew Fitzmaurice, _Humanism and America_ (Cambridge, 2003); Mikael H\u00f6rnqvist, _Machiavelli and Empire_ (Cambridge, 2004).\n\n32 David Armitage, _The Ideological Origins of the British Empire_ (Cambridge, 2000); Pagden, _Lords of All the World_ ; David Armitage, \"Empire and Liberty,\" in _Republicanism_ , ed. Martin van Gelderen and Quentin Skinner (Cambridge, 2002), 2:29\u201347.\n\n33 Cheryl Welch, \"Colonial Violence and the Rhetoric of Evasion,\" _Political Theory_ , 31 (2003), 235\u201364.\n\n34 Mill, \"Review of Voyage aux Indes Orientales,\" by Le P. Paulin De S. Barth\u00e9lemy, _Edinburgh Review_ , 15 (1810), 371.\n\n35 Nils Gilman, _Mandarins of the Future_ (Baltimore, 2004).\n\n36 Wesley T. Wooley, _Alternatives to Anarchy_ (Bloomington, 1988); Jo-Ann Pemberton, _Global Metaphors_ (London, 2001). I discuss this topic in more detail in chapter 8.\n\n37 For the British comparison, see Ferguson, _Colossus_ ; Porter, _Empire and Superempire_ (London, 2006); for Rome, see Charles Maier, _Among Empires_ (Cambridge, MA, 2006); Margaret Malamud, _Ancient Rome and Modern America_ (Oxford, 2008).\n\n38 Most notably, Ferguson, _Empire_.\n\n39 Inconsistency is no bar to the political efficacy of an ideology; indeed there are ideological benefits to vagueness. Freeden, \"What Should the 'Political' in Political Philosophy Explore?,\" _Journal of Political Philosophy_ , 13 (2005), 113\u201334.\n\n40 Robinson and Gallagher, with Alice Denny, _Africa and the Victorians_ (London, 1961).\n\n41 Simms, _Three Victories and a Defeat_ (London, 2007).\n\n42 Burbank and Cooper, _Empires in World History_ , 219\u201351; Pagden, _Peoples and Empires_ , 103\u201377.\n\n43 J. H. Elliott, _Empires of the Atlantic World_ (London, 2006); Pagden, _Lords of All the World_.\n\n44 Gareth Stedman Jones, \"Radicalism and the Extra-European World,\" in _Victorian Visions of Global Order_ , ed. Duncan Bell (Cambridge, 2007), 186\u2013225.\n\n45 Anthony Brewer, _Marxist Theories of Imperialism_ , 2nd ed. (London, 1990); Wolfe, \"History and Imperialism.\"\n\n46 Lenin, _Imperialism_ [1917] (London, 1996). On dependency theory, see Brewer, _Marxist Theories of Imperialism_ , 136\u201398.\n\n47 On Hobson's political economy of empire, see especially Peter Cain, _Hobson and Imperialism_ (Oxford, 2002); Gregory Claeys, _Imperial Sceptics_ (Cambridge, 2010).\n\n48 Cain, \"Empire and the Languages of Character and Virtue in Later Victorian and Edwardian Britain,\" _Modern Intellectual History_ , 4 (2007), 249\u201373.\n\n49 Mill, _Considerations on Representative Government_ [1861], in _Collected Works_ , ed. J. Robson (Toronto, 1977), vol. 18, ch. 18.\n\n50 Mill, _On Liberty_ [1859], _Collected Works_ (Toronto, 1977), 18:224; Mazzini, \"Principles of International Politics\" [1871], in _Cosmopolitanism and Nations_ , ed. Stefano Recchia and Nadia Urbinati (Princeton, 2009), 238.\n\n51 Chamberlain, \"The True Conception of the Empire,\" 2:3.\n\n52 For more on Froude's imperial thought, see chapter 12.\n\n53 Karma Nabulsi, _Traditions of War_ , 126.\n\n54 Ibid., 110\u201319.\n\n55 Henley, \"Epilogue\" [1897], in _Poems_ (London, 1926), 241.\n\n56 James Scott, _Seeing like a State_ (London, 1998); Scott, _The Art of Not Being Governed_ (New Haven, 2009). The work of Michel Foucault has proven especially insightful in delineating the various modulations of power and \"governmentality\" involved in imperial subjugation. See, for prominent examples, Timothy Mitchell, _Colonising Egypt_ (Berkeley, 1991); Mitchell, _Rule of Experts_ (Berkeley, 2002); and Ann Laura Stoler, _Race and the Education of Desire_ (Durham, NC, 1995).\n\n57 On imperial dreaming, see Erik Linstrum, \"The Politics of Psychology in the British Empire, 1898\u20131960,\" _Past & Present_, 215 (2012), 214\u201333.\n\n58 Bernard Cohn, _Colonialism and Its Forms of Knowledge_ ; Susan Bayly, _Caste, Society and Politics in India from the Eighteenth Century to the Modern Age_ (Cambridge, 1999); Nicholas Dirks, _Castes of Mind_ (Princeton, 2001).\n\n59 Robinson and Gallagher, \"The Imperialism of Free Trade,\" _Economic History Review_ , 6 (1953), 13.\n\n60 Davis, _Late Victorian Holocausts_ (London, 2003).\n\n61 David Harvey, _The New Imperialism_ (Oxford, 2003); Harvey, _A Brief History of Neoliberalism_ (Oxford, 2005); Alex Callinicos, _Imperialism and the Global Political Economy_ (Cambridge, 2009).\n\n62 Lynn Zastoupil and Martin Moir, eds., _The Great Indian Education Debate_ (London, 1999).\n\n63 Macaulay, \"Minute of 2 February 1835 on Indian Education\" [1835], in _Macaulay, Prose and Poetry_ , ed. G. M. Young (Cambridge, MA, 1957), 721.\n\n64 Mantena, _Alibis of Empire_ , 2. The shift in India is traced in Thomas Metcalf, _Ideologies of the Raj_. Again highlighting the interpenetration between the modern social sciences and empire, Mantena shows how the origins of modern social theory were inflected with imperial concerns, not least through the development of the category of \"traditional society.\"\n\n65 Lorenzo Veracini, _Settler Colonialism_ (Basingstoke, 2010).\n\n66 Mill, _Considerations on Representative Government, Collected Works_ , 19:562.\n\n67 James Belich, _Replenishing the Earth_ , argues that the early nineteenth century saw a \"Settler Revolution\" that led to the explosive settlement of two related geo-economic regions, the \"American West\" and the \"British West\" (Canada, Australia, New Zealand, and South Africa). This revolution cemented the rise of the \"Anglo-world,\" which continues to exert great power today. For a theoretical analysis of the racial-political formation, see Srdjan Vucetic, _The Anglosphere_ (Stanford, 2011).\n\n68 Tocqueville, \"Essay on Algeria (October 1841),\" in _Writings on Empire and Slavery_ , ed. J. Pitts (Baltimore, 2001), 83, 70.\n\n69 Pitts, _A Turn to Empire_.\n\n70 Rande Kostal, _A Jurisprudence of Power_ (Oxford, 2005).\n\n71 I trace Mill's shift in attitude in chapter 9.\n\n72 William Bain, _Between Anarchy and Society_ (Oxford, 2003); James Mayall and Ricardo Soares de Oliveira, eds., _The New Protectorates_ (London, 2011).\n\n73 John Kelly, ed., _Anthropology and Global Counterinsurgency_ (Chicago, 2010).\n\n74 Scott, _Weapons of the Weak_ (New Haven, 1985); Scott, _Domination and the Arts of Resistance_ (New Haven, 1990).\n\n75 Sankar Muthu, _Enlightenment against Empire_ (Princeton, 2003); Pitts, _A Turn to Empire_.\n\n76 See chapter 2 for further discussion of this line of interpretation. It is convincingly challenged in Daniel O'Neill, _Edmund Burke and the Conservative Logic of Empire_ (Berkeley, 2016).\n\n77 Dirk A. Moses, ed., _Genocide and Settler Society_ (New York, 2004); Moses, _Empire, Colony, Genocide_ (New York, 2008).\n\n78 Bayly, \"European Political Thought and the Wider World during the Nineteenth Century,\" in _The Cambridge History of Nineteenth-Century Political Thought_ , ed. Gregory Claeys and Gareth Stedman Jones (Cambridge, 2011), 835; Christian Reus-Smit, \"Struggles for Individual Rights and the Expansion of the International System,\" _International Organization_ , 65 (2011), 207\u201342.\n\n79 C. A. Bayly, _Recovering Liberties_ (Cambridge, 2012).\n\n80 Skinner, \"On the Slogans of Republican Political Theory,\" _European Journal of Political Theory_ , 9 (2010), 100; Pettit, \"A Republican Law of Peoples,\" _European Journal of Political Theory_ , 9 (2010), 77.\n\n81 David Mayers, _Dissenting Voices in America's Rise to Power_ (Cambridge, 2007). It was also present in Victorian Britain. See, for example, Stuart Jones's account of Frederic Harrison's republicanism, in \"The Victorian Lexicon of Evil,\" in _Evil, Barbarism and Empire_ , ed. Tom Cook, Rebecca Gill, and Bertrand Taithe (Basingstoke, 2011), 126\u201343. On Harrison, see chapter 2.\n\n82 Johnson, _Nemesis_ (New York, 2007).\n\n83 Hardt and Negri, _Empire_ (Cambridge, 2000); _Multitude_ (Cambridge, 2004).\n\n84 Hardt and Negri, _Empire_ , xii, 166.\n\n85 Ibid., 60.\n\n86 Hardt and Negri, _Multitude_.\n\n87 Harvey, _The New Imperialism_ ; Alexander Anievas, ed., _Marxism and World Politics_ (London, 2010).\n\n88 Bhikhu Parekh, _Gandhi's Political Philosophy_ (London, 1989); Steger, _Gandhi's Dilemma_ (Basingstoke, 2000); Karuna Mantena, \"Another Realism,\" _American Political Science Review_ , 106\/2 (2012), 455\u201370; Anthony Parel, _Gandhi's Philosophy and the Quest for Harmony_ (Cambridge, 2006).\n\n89 On anticolonial strategies of reversal, see Margaret Kohn and Keally McBride, _Political Theories of Decolonization_ (Oxford, 2011). \"Reversal describes attempts to undermine power relations by valorizing the cultural markers that the colonial system had denigrated as inferior.\"\n\n90 Gandhi, _Hind Swaraj and Other Writings_ [1909], ed. Anthony Parel (Cambridge, 1997), 67\u201368.\n\n91 Nigel Gibson, _Fanon_ (Cambridge, 2003).\n\n92 Fanon, _The Wretched of the Earth_ (London, 2001), 43.\n\n93 Chatterjee, _Nationalist Thought and the Colonial World_.\n\n94 Fanon, _The Wretched of the Earth_ , 74.\n\n95 Arendt, _On Violence_ (New York, 1970); Walzer, _Just and Unjust Wars_ (London, 1978), 204\u20136.\n\n96 See, for example, James Tully, _Public Philosophy in a New Key_ , 2 vols. (Cambridge, 2008).\n\n97 For further discussion, see Duncan Bell, \"To Act Otherwise,\" in _On Global Citizenship_ , ed. David Owen (Bloomsbury, 2014), 181\u2013207.\n\n98 Conrad, _Heart of Darkness_ , ed. Ross Murfin, 2nd ed. (London, 1996), 21.\nPART II\n\nThemes\nCHAPTER 5\n\nEscape Velocity\n\nAncient History and the Empire of Time\n\nFor a long time the greatness of the ancient world lay with an oppressive weight like an incubus upon the moderns.1\n\n\u2014J. R. SEELEY\n\n[T]here exists, no doubt, a prevalent feeling, that, in a certain sense, the doom of Athens is already ours.2\n\n\u2014HERMAN MERIVALE\n\nObsessed with decoding historical experience, the Victorians endlessly scoured the past for lessons about how best to comprehend and navigate their world. In his inaugural lecture at Cambridge in 1895, Lord Acton observed that the nineteenth century was saturated with \"historic ways of thought,\" which had come to be given the \"depressing names\" of \"historicism or historical-mindedness.\" Such was the power exerted by the injunction to seek knowledge and guidance from the annals of history that the constitutional theorist A. V. Dicey once complained that it \"was far better, as things now stand, to be charged with heresy, than to fall under the suspicion of lacking historical-mindedness, or of questioning the universal validity of the historical method.\"3 The imaginative construal of empire was no exception to this ubiquitous cultural practice. Debates over imperial order were inflected by two conflicting narratives of historical time, one cyclical, the other progressive.4 According to the former, empires followed a predetermined trajectory: they rose, they declined, and ultimately they fell. Counseling vigilance, Goldwin Smith, one time Regius Professor of History at Oxford, warned in the late 1870s that the \"decay of Empires is the theme of history.\"5 According to the other conception, the nineteenth century was an age of progress, of constant human improvement, with the British imperial state in the vanguard. The \"movement of humanity is not, as the ancients fancied, in cycles,\" declared the omnicompetent scholar-statesman James Bryce, \"but shows a sustained, though often interrupted, progress.\"6 Imperial discourse was shaped by an unremitting negotiation between the two positions, each of which can be seen as different modulations of historicism. Although they diverged over how the past informed the present, both posited historical experience as central to understanding contemporary politics. This was a clash of historical epistemologies, of what kind of knowledge could be ascertained from historical reflection. The progressivist view of empire was broadly Whiggish, divining in the evolution of ideas and institutions the teleological unfolding of cherished principles (most often liberty).7 The cyclical view encoded a model of eternal return, of repetition and recurrence, in which the destiny of the empire could be discerned by grasping the shape of the past.\n\nWhile belief in progress suffused Victorian political consciousness, the trope of proleptic decline supplied critics of empire with powerful ammunition. It implied that imperial orders always contained the seeds of their own destruction. Hence Smith's argument that in light of historical experience the British \"policy of aggrandizement\" was necessarily ruinous.8 However, it is important to distinguish between two different conceptions of imperial cyclicality, one universal, the other more institutionally specific. The universal variant, which could draw on Polybian archetypes or Christian providentialism, viewed all human institutions\u2014indeed all life\u2014as subject to the same temporal dynamics. Synecdochic exemplars, empires were an instance of a general historical pattern. While unusual in Victorian Britain, this position found eloquent defenders among liberal Anglican historians, including Thomas Arnold, though it was also articulated in other idioms, such as the modified classical republicanism of the historian J. A. Froude. The history of all living things, including commonwealths, Froude proclaimed in the late 1870s, was defined by \"recurring stages of growth and transformation and decay,\" and as such it was imperative to recognize the ephemeral quality of imperial governance.9 Despite its historical determinism, the universalist account allowed scope for human agency: impossible to defeat, historical fate could at least be deferred. \"The life of a nation, like the life of a man, may be prolonged in honour into the fullness of its time, or it may perish prematurely, for want of guidance, by violence or internal disorders.\"10 Knowledge of history could guide the wise statesman in battling time. The more popular cyclical vision regarded empire as atypical, a pathological form of political association fated to collapse due to its inherent weaknesses. Unlike the universal account, this view was compatible with the widespread Victorian belief in the sustained progressive development of humanity. It was deployed to characterize empire as an _untimely_ aberration, flagrantly rejecting the spirit of the age.\n\nMost imperialists maintained that the British empire was somehow exempt from historical precedent. Forestalling the cycle of imperial temporality, progress guaranteed an _escape velocity_ , the ability to break free from the gravitational pull of imperial declension. In what follows I explore two broad variations that were articulated across the human sciences and in public debate, focusing in particular on the writings of historians. In the first, the modern British empire was figured as uniquely progressive, as capable\u2014either in actuality or _in potentia_ \u2014of avoiding the social, economic, and political dynamics that had annihilated all previous specimens. This argument was most frequently employed in relation to India. The other strategy was to insist that the empire (or a part of it) was not really an empire at all, but rather a new form of political order that could circumvent the entropic degeneration of traditional imperial forms. To think otherwise was to make a category mistake. This argument was often applied to Britain and its settler colonies from the 1870s onwards. \"Greater Britain,\" as the settler colonial assemblage was often termed, could attain permanence, a kind of historical grace.\n\nThe Time of Empire: Narratives of Decline and Fall\n\nThe \"English,\" J. R. Seeley observed in 1880, \"guide ourselves in the great political questions by great historical precedents.\"11 Understandings of the past played a formative role in the construction, elaboration, and defense of political argument in Victorian Britain, and it was widely assumed that a proper appreciation of the vicissitudes of history could impart wisdom and sound judgment. \"History ought surely in some degree... anticipate the lessons of time,\" Seeley declared in _The Expansion of England_ , one of the key textbooks of the Victorian empire, and it was necessary to study it so that \"we may be wise before the event.\"12 Some epochs of history were far more important than others. The stories of Greece and Rome provided a common frame of reference, a claim of authority, and a productive repertoire of images and arguments for a classically educated elite to interpret contemporary culture and politics, and they played a privileged role in thinking about the nature of imperial rule.13 Yet the Victorians disagreed profoundly over which particular lessons to draw from which particular pasts, and the meaning of history was a topic of intense ideological contestation.\n\nThey inherited\u2014and sought to recalibrate or transvalue\u2014one of the most venerable Western accounts of historical temporality. The _Imperium romanum_ , Anthony Pagden reminds us, \"has always had a unique place in the political imagination of western Europe,\" infusing visions of self, society, state, and empire, and it supplied the \"ideologies of the colonial systems of Spain, Britain, and France with the language and political models they required.\"14 The Romans had bequeathed modern Europeans an evocative metanarrative of self-dissolution: the drive for expansion corrupted the polity and inevitably led to disaster. The _topos_ of decline and fall had for centuries shaped understandings of empire and the principles underlying historical development. Drawing on the history of Rome, as mediated by Sallust and Polybius, Machiavelli had argued in his _Discourses on Livy_ that states would inexorably seek to expand, but that in so doing would forfeit their liberty before collapsing under the moral and constitutional strain of the quest for _grandezza_.15 Subsequent critics of imperialism, including Montesquieu, Hume, Kant, Robertson, and Constant, likewise pointed to the moral and physical collapse of Rome to warn of a comparable fate for those who pursued rapacious military policies. As Hume once wrote, \"[t]here seems to be a Natural Course of Things, which brings on the Destruction of great Empires.\"16 Edward Gibbon's _History of the Decline and Fall of the Roman Empire_ imprinted the narrative deeply into British historical consciousness: the disintegration of Rome \"was the natural and inevitable effect of immoderate greatness.\"17 In such accounts, the imperial dynamic was naturalized, and thus posited as unchanging, indelible, eternal. The critique of empire propagated by the \"country party\" Whigs during the eighteenth century warned about the corruption that destroyed Rome and threatened Britain as it carved out an empire in South Asia and the Caribbean.18 Alive to this classical precedent, British imperial ideologists of the seventeenth and eighteenth centuries had routinely sought to avoid the fate of Rome by emphasizing the exceptional character\u2014commercial, maritime, and free\u2014of their new empire in North America.19 The narrative likewise exercised the imagination of both scholars and the political elite during the Victorian age. According to Seeley, the most significant imperial thinker of the period,\n\nEvery historical student knows that it was the incubus of the Empire which destroyed liberty at Rome. Those old civic institutions, which had nursed Roman greatness and to which Rome owed all the civilisation which she had to transmit to the countries of the West, had to be given up as a condition of transmitting it. She had to adopt an organisation of, comparatively, a low type. Her civilisation, when she transmitted it, was already in decay.20\n\nThe narrative of decline and fall, Julia Hell argues, is \"always already part of all acts of imperial mimesis, of their imaginaries and specific articulations of space and time.\"21 An inescapable bequest, and an epistemic burden, it helped to set the coordinates linking past, present, and possible futures. The premonition of the fall, of earthly annihilation, was etched into the iconographic order of empire, the reservoir of images and symbols that animated Victorian debate on the subject.22 It was captured by Kipling in his melancholy prayer-poem \"Recessional,\" published to mark Queen Victoria's Diamond Jubilee in 1897.\n\nFar called, our navies melt away;\n\nOn dune and headland sinks the fire\n\nLo, all our pomp of yesterday\n\nIs one with Nineveh and Tyre\n\nKipling's plaintive call to his compatriots was stark, even desperate: \"Lest we forget\u2014lest we forget!\"23 He later wrote that he had been \"scared\" by the national optimism accompanying the royal celebrations, and that he composed the poem as a \" _nuzzur-wattu_ ,\" \"an averter of the evil eye.\"24 But perhaps the most famous representation of declension was concocted by Macaulay in his depiction of the \"New Zealander.\" In a review of Ranke's _The Ecclesiastical and Political History of the Popes of Rome_ , he had marveled at the longevity of the Catholic Church, its centuries of uninterrupted existence. In comparison, other institutions seemed fragile, ephemeral, transient. \"She [the Church] may still exist in undimmed vigor when some traveler from New Zealand shall, in the midst of the vast solitude, take his stand on a broken arch of London Bridge to sketch the ruin of St. Pauls.\"25 Macaulay was utilizing a familiar rhetorical device, imagining the future ruins of the metropolis in order to place the contemporary within a historical frame defined by the rise and fall of civilizations. His own rendition identified early Victorian Britain with both the magnificence of Rome and its eventual fate.26 Thirty years later the monitory image was given haunting pictorial form in an engraving by Gustave Dore, with the \"tourist New Zealander upon the broken parapets, contemplating something matching\u2014the glory that was Greece\u2014the grandeur that was Rome.\"27 The New Zealander was the most famous Victorian example of a \"scopic scenario,\" an image that \"depicts the imperial subject contemplating the ruins of empire\" while simultaneously rendering the \"trope of decline and fall visible.\"28 By the mid-1890s the positivist Frederic Harrison could record that it had \"become a proverb, and is repeated daily by men who never heard of Macaulay, much less of von Ranke.\"29\n\nThe sepulchral voyager was put to very different ideological uses. In his unpublished _The New Zealander_ , penned as a social critique in 1855\u201356, Anthony Trollope admitted that the British empire would eventually decline and fall but nevertheless asserted that it was possible to \"postpone the coming of the New Zealander\" through a combination of moderate reform and a return to traditional values.30 Dissolution could be deferred by elevating political complacency to a principle. After inspecting the admirable sanitation facilities in New Zealand, Froude proffered a quotidian rejoinder to Macaulay's flamboyant imperial metaphysics, admitting that \"I have come to believe in that New Zealander since I have seen the country.\"31 Hostile to sociopolitical developments in Britain, he saw the future (or at least better toilet facilities) being constructed on the colonial periphery. Goldwin Smith invoked the time-traveler to reach a different conclusion. He drew a clear distinction between Britain and its empire, the former a site of productive energy, the latter destined to follow the pattern of all history. \"There is no reason why British virtue, energy, and industry should not continue as they are, or increase with the lapse of time; and therefore, there is no reason why the New Zealander should ever moralize over the ruins of the British nation; but the man of the future, whoever he may be, is pretty sure one day to moralize over the ruins of the British Empire.\" The lesson was clear: \"In England the strength of England lies.\"32 Joseph Chamberlain, the radical Secretary of State for the Colonies, dismissed the pessimism evoked by the image, vowing that the British empire was confidently embarked on a progressive trajectory. \"I do not ask you to anticipate with Lord Macaulay the time when the New Zealander will come here to gaze upon the ruins of a great dead city. There are in our present condition no visible signs of decrepitude and decay.\"33 In an equally bombastic vein Arthur Conan Doyle, fabulator of Sherlock Homes and passionate imperialist, observed in his justificatory account of the South African War that Macaulay, \"in his wildest dream of the future of the much-quoted New Zealander,\" never envisaged soldiers from that distant land coming to the relief of British forces in a conflict across the ocean.34 The New Zealander, then, did not travel the world to sketch the ruin of empire, but rather to help defend it against the very forces of dissolution that the image encoded. Macaulay's icon, became a fulcrum for contesting visions of the future.\n\nThe combination of narrative simplicity and analytical ambiguity helps explain the powerful resonance of the Roman plotline. At least three distinct (though often overlapping) interpretations of decline and fall percolated through Victorian political culture. First, it was frequently argued that Rome had collapsed principally as a result of the corrupting power of luxury, with moral debilitation issuing in political cataclysm. Luxury, it was thought, degraded both the political morality of the governing class and eroded the manly virtues of the populace. This account dominated both scholarly interpretation and vernacular renditions for much of the century.35 Froude offered a suggestive rendition of the story. \"Virtue and truth produced strength, strength dominion, dominion riches, riches luxury, and luxury weakness and collapse\u2014a fatal sequence repeated so often.\"36 It was favored by radical critics of empire who stressed the potential dangers of aristocratic nabobs, habituated to wielding despotic power, returning from colonial service and threatening British political virtue. \"Is it not just possible,\" asked Richard Cobden in 1860, \"that we may become corrupted at home by the reaction of arbitrary political maxims in the East upon our domestic politics, just as Greece and Rome were demoralized by their contact with Asia?\"37 Goldwin Smith worried about the political influence that wealthy Anglo-Indians might wield on their return to Britain. The danger to British national identity was clear: \"No political character could be stronger or more confirmed than that of the Roman, yet by Empire it was radically changed.\"38 Marshaling the authority of Gibbon (while ignoring his conclusions), Herbert Spencer claimed that \"in a conspicuous manner Rome shows how... a society which enslaves other societies enslaves itself.\" Extirpating the freedom of conquered peoples invariably corroded the freedom of the conquerors. \"And now what is the lesson?\" he demanded. \"Is it that in our own case Imperialism and Slavery, everywhere else and at all times united, are not to be united?\" Unfortunately, he complained, \"Most will say Yes.\"39 In his seminal _Imperialism: A Study_ , published as war in South Africa raged, the heterodox political economist J. A. Hobson answered Cobden's question by insisting that such corruption was \"inevitable.\" It is, he averred, \"a nemesis of Imperialism that the arts and crafts of tyranny, acquired and exercised in our unfree Empire, should be turned against our liberties at home.\"40 But the trope could also be deployed by advocates of imperialism, as both warning and call to action. In 1885 Montagu Burrows, Professor of History at Oxford, counseled that the \"danger of our not perceiving our real position is exactly the same as was experienced by the old Roman Empire. The decay of the center gradually makes its way to the extremities; and these drop off, one by one, till the seat of the Empire itself, unprotected and forlorn, goes down in the general crash.\"41 It could likewise serve as a salutary admonition that the problem was not empire itself but \"imperialism\"\u2014a militant, territorially-rapacious creed.42 With Disraeli in mind, Gladstone feared that like Rome, \"England, which has grown so great, may easily become little; through the effeminate selfishness of luxurious living; through neglecting realities at home to amuse herself everywhere else in stalking phantoms.\"43 Available to both critics of empire and its supporters, the trope was politically indeterminate.\n\nA second account blamed excessive imperial ambition. In the late 1870s Robert Lowe, a leading British liberal politician, suggested that the Roman precedent, and in particular the transition from the Republic to the Empire, taught important lessons. \"This signal and prerogative instance, to which it would be easy to add many others, seems to show that when a nation has attained a certain amount of freedom and self-government, no step can be more fatal than a career of successful conquests.\"44 \"I am amused at the people who call themselves Imperialists,\" wrote William Harcourt, another eminent liberal politician, for \"I always remember the first pages in Gibbon on the 'moderation of Augustus,' in which he shows how for the first two centuries of the greatest and wisest Empire that ever existed the cardinal principle was the non-extension of Empire, and whenever it was departed from they came to grief.\"45 Although acknowledging that \"moral decay\" engendered by luxury had played a role in the collapse of Rome, Seeley argued that the main problem was the lack of military manpower caused by over-ambitious expansion, a point reiterated by Herbert Samuel, \"new liberal\" thinker and later senior politician. Admitting that history demonstrated every previous empire had \"decayed and was dissolved,\" Samuel drew the lesson that imperial consolidation was preferable to further territorial conquest. \"Expansion that is too rapid and too wide may open the door to all three of the causes which, singly or in combination, have brought the downfall of the empires that have preceded\u2014attack from without, revolt from within, disunion and weakness at the centre.\" Benjamin Franklin, he continued,\n\n... in one of the darkest times of our history, offered to furnish Gibbon with materials for a new work, on the \"Decline and Fall of the British Empire.\" Four generations have passed since then, and events have not given room for a book on that subject. But if in a later day some historian is called upon to take up this melancholy task, it may well be that he would have to write down an excess of ambition as the chief cause of decay, and to point out that the most fatal danger which had faced the British Empire had been an over-fervent imperialism among the British people.46\n\nFinally, it was argued that the over-centralization of Roman institutions, and the concentration of power in the hands of the few, led to eventual collapse. This had been a major theme in Montesquieu's pioneering _Considerations on the Causes of the Greatness of the Romans and Their Decline_ (1734). The liberal historian and politician John Morley picked up the thread, arguing that the idea of imperial federation, popular in the 1880s and 1890s, presupposed the centralization that had destroyed the Roman Empire, and that as a consequence it represented a grave threat to British political liberty.47 Hobson too ascribed the fall of Rome to over-centralization, asserting that it conveyed \"in brief the real essence of Imperialism,\" its inescapable dynamic.48 Economic \"parasitism\" by the political elite led to ever-increasing centralization of the \"instruments of government,\" immiserating the populace and breeding the seeds of dissent and rebellion. In _Imperium et Libertas_ (1901) Bernard Holland developed another variation on the theme. \"The Roman Empire perished not from over-greatness but from over-centralization, and the destruction of the provinces in favour of the metropolis.\" Yet he drew a different conclusion from Hobson: the \"failure of the Roman experiment does not prove that an empire which avoided this peril might not beneficially endure for a much longer period.\"49 Imperial nemesis could be evaded.\n\nThe Greek model of colonization presented an alternative conception of political termination. \"The ancient Greek city,\" explained Holland, \"when its population became too large for its rocky island or edge of mainland shore, sent out a colony as a beehive sends out a swarm. The colonists took possession of a new territory and there built a city, maintaining a pious regard, except when interests clashed, for the Mother City, but not a true political connection.\" This system, noted Seeley, \"gives complete independence to the colony, but binds it in perpetual alliance.\"50 It allowed for successful expansion without the internally corrosive dynamics of empire. This prospect appealed to many early Victorians, and in particular those associated with the \"colonial reform\" movement, prominent from the 1820s until the 1840s. Indeed in a survey written in 1856 Arthur Mills observed that the \"model of Colonial policy most frequently and prominently exhibited for the emulation of modern States is that of Greece.\"51 The Roman alternative was, James Mill had argued in 1823, \"so very defective,\" for in it the \"Few\" dominated the \"Many\" to such an extent that expansion was pursued only in the interests of the aristocratic class. Mill and assorted radical \"reformers\" thus argued that the Greek style of colonization, premised on peopling distant lands and establishing self-governing communities with strong affective ties to the \"mother country,\" offered a more suitable model to emulate\u2014although in a significant departure from the ancient precedent they were generally loathe to demand immediate independence for the colonies.52 In the 1840s John Stuart Mill eulogized the Greek colonies for \"flourishing so rapidly and so wonderfully\" and for guaranteeing freedom, order, and progress, and he argued that they served as a template for British colonization.53 The philosophic radical MP J. A. Roebuck sang a similar tune. \"Their colonies were very unlike those of the Roman,\" and had far more in common with modern British experience. In particular, the Greeks were bound by a \"gentle, kindly tie\" between the \"mother city\" and her colonial offspring, of the type \"we also wish to exist, and we endeavour to create.\"54 The reformers drew inspiration from the classics even as they made arguments structured by post-Smithian political economy and Benthamite utilitarianism.\n\nThe popularity of the Greek model of colonial independence waned from the 1870s onwards as advocates of Greater Britain sought to forge a _permanent_ political union between Britain and the settler colonies. For the pugnacious historian E. A. Freeman\u2014the subject of chapter 13\u2014this unionist vision clashed disastrously with a proper understanding of colonization. He argued that although the British colonies had much in common with their esteemed Greek predecessors, there was one crucial difference: they were not _ab initio_ independent. Under the Greek system, the \"metropolis claimed at most a certain filial respect, a kind of religious reverence, which was for the most part freely given,\" whereas the British settler colonies, despite their high degree of internal self-government, were nevertheless ultimately subject to the sovereignty of the Crown. Thus arguments propounding an indissoluble Greater Britain were at once conceptually flawed and historically na\u00efve. \"Let us at least remember that what is proposed is unlike anything that ever happened in the world before.\"55 This was a damning verdict from a man so sensitive to the moral and practical value of precedent, and it is little surprise that he promoted independence for the settler colonies. In an obituary note about his friend, Bryce observed that \"the analogy of the Greek colonies\" helped motivate Freeman's scathing criticisms of the imperial unionists, for \"[h]e appeared to think that the precedent of those settlements showed the true and proper relation between a 'metropolis' and her colonies to be not one of political interdependence, but of cordial friendship and a disposition to render help, nothing more.\"56 History could not be ignored.\n\nBy the turn of the twentieth century, classical accounts of imperial corruption had been reinforced by anxieties about national and racial degeneration underpinned by a range of new scientific discourses.57 In 1908 the former Prime Minister, Arthur Balfour, argued that many political communities, including Rome, were corrupted by mysterious bouts of decadence, but that through a combination of science and industry the British empire could probably escape this fate.58 He thus sought to neutralize more pessimistic renderings of the future. Perhaps the most (in)famous had been elaborated by the Australian historian and radical politician C. H. Pearson in his best-selling _National Life and Character_ (1894). Although it discussed the demise of Rome in some detail, the text focused principally on the contemporary exhaustion of political space, when little territory was left for the \"higher races\" to colonize.59 Only the year before, Frederick Jackson Turner had warned that the closing of the American frontier would dissipate the creative energies of American democracy.60 Pearson predicted a similar process writ global, as the Western empires, Britain foremost among them, would be undermined by a lethal combination of their own success in conquering territory and the pernicious domestic consequences of the emerging \"stationary\" socialist state. After gifting civilization to the rest of the world, the imperial powers would be thrown back onto their own continent by ungrateful subjects. Torpor, luxury, and decline would follow. This account both drew on and subverted progessivist justifications of empire. While Pearson viewed empire as an agent of improvement, the combination of imperial blowback and the exhaustion of planetary space meant that the future looked grim. Implicit in this argument were two claims. First, that other, perhaps less enlightened, forms of empire might be capable of reaching escape velocity, and second, that if only new spaces were discovered the restless dynamism of empire could be effectively channeled in their direction. It was this kind of thought, perhaps, that found expression in Cecil Rhodes's wistful proclamation that he would annex the planets if he could.61\n\nThe Victorians, then, absorbed two contrasting lessons from their incessant meditations on the history of empire, ancient and modern. Inherited from centuries of European political thought, the first insisted that history demonstrated the inevitability of imperial decline and fall. Foretelling a future of retreat and weakness, it implied that sooner or later the British empire would dissolve, and with it the claims of the British to world-historical significance. The other lesson, more popular and widely disseminated, allowed for the possibility of imperial redemption. Decline was _conceivable_ but not _inevitable_ ; the future was left open. Human choice\u2014political decision\u2014was thus accorded a central role, one that imperialists never tired of emphasizing. Though haunted by the image of failure, they were rarely fatalists.\n\nHarnessing the Time Spirit: On Imperial Progress\n\nReflecting on his long life, Morley remarked that the nineteenth century had seen belief in progress emerge as the \"basis of social thought,\" supplanting religion as the \"inspiring, guiding, and testing power over social action.\" Progress, he mused, could be seen as the \"Time Spirit\" of the modern world.62 Soon after he penned those words the first English-language history of the idea appeared. Its author, J. B. Bury, a prodigiously gifted historian and classicist, declared that progress was the \"animating and controlling idea of western civilization.\" He defined it in appropriately capacious terms as the view that \"civilization has moved, is moving, and will move, in a desirable direction,\" where the desire was identified with increased human happiness. Like Morley he argued that it had displaced religion as a source of meaning: \"The fate of an ultimate happy state on this planet, to be enjoyed for future generations, has replaced, as a social power, the hope of felicity in another world.\"63 On this account, the death of God was a precondition for the emergence of the idea of progress, since an active, world-shaping sense of human agency needed to escape the sociopolitical fatalism inculcated by religion.\n\nWhile Bury suggested that the idea of progress was predicated on the renunciation of \"active\" providentialism, it came in many flavors\u2014theological, agnostic, and secular\u2014during the Victorian age. Ubiquitous and multivalent, belief in progress structured social and political thought in assorted ways. It was typically assumed to encompass material, institutional, and moral dimensions. Materially, it was indexed by extraordinary advances in science and technology, which transformed the conditions of both social existence and political association. \"[I]n every science which deserves the name,\" Macaulay marveled, \"immense improvement may be expected.\" In institutional terms it was linked primarily to the development of individual freedom and representative government. Thus Macaulay could declaim that the history of England \"is emphatically the history of progress. It is the history of a constant movement of the public mind, of a constant change in the institutions of a great society.\"64 And finally, it encoded the idea that these new developments were altering the manners and _moeurs_ \u2014\"character,\" in Victorian nomenclature\u2014of the people.65 Confidence in the unilinear improvement of society reached its peak in the mid-Victorian era, when the various elements of progress were often read as mutually reinforcing. Many late Victorians were rather less sanguine, believing that they did not necessarily cohere or even that they conflicted. It was a common apprehension, for example, that the relentless development of science and technology was eroding public morality, advances in one domain leading to regress in another. The impact of Darwinism, disillusionment with political reform, the dizzying tempo of social life, an increasingly tense geopolitical environment, fear of urban degeneration: all contributed to the emergence of a more melancholy attitude. Most late Victorian thinkers, however, continued to believe in the possibility of progress, of constant human improvement, even as they expressed skepticism about its inevitability.\n\nThroughout this shift in temper the empire remained a space for the projection of fantasies about progressive development. This followed from the way in which progress was figured as the advance of civilization. The great French historian Francois Guizot had remarked in his influential _General History of Civilization in Europe_ that the \"first idea comprised in the word _civilization_... is the notion of progress, of development. It calls up within us the notion of a people advancing, of a people in a course of improvement and melioration.\"66 The Victorians tended to concur. Imperialists divided the world into those civilized spaces capable of self-sustaining progress (with Britain in the vanguard) and those in which progress had stalled (such as India) or had never even begun (including most of Africa). The empire was typically figured as an engine of civilization, a means to bring enlightenment to the backward spaces of the earth. Even if progress was slowing or even under threat in the \"mother country,\" there was still work to be done\u2014a duty to be fulfilled\u2014civilizing the rest of the world. Such was the conceit of many British imperialists. The most common proposition for escaping the cycle of rise and decline, then, was to insist that the British imperial model was itself uniquely progressive, a global agent of human advance. Past experience meant nothing, except perhaps as a hortatory reminder about what not to do. Liberal empire was simultaneously a cause and a consequence of civilizational progress.\n\nArguing that confidence in imperial progress was undercut by the Sepoy Rebellion of 1857 and successive moments of resistance, Karuna Mantena has recently questioned the durability of this civilizational justification of imperial rule. On this account, crisis and progress were figured as irreconcilable, and a markedly different \"culturalist\" narrative emerged, chiefly under the influence of the eminent comparativist Henry Maine. Emphasizing the fragility of local communities and the sheer difficulty of transforming colonized spaces in the image of liberal modernity, it provided Maine and his followers with an \"alibi\" for the prolongation of empire on the grounds that Western intervention had so weakened traditional forms of life that withdrawal would herald disaster.67 Valuable as it is in delineating Maine's position, this argument underestimates the continuities in British imperial discourse.68 As I argued in chapter 2, the civilizing vision of empire remained a staple of British imperial ideology, even its core feature, throughout the 1890s and deep into the twentieth century. In an address to the Imperial Institute in 1892, the historian W.E.H. Lecky sketched a characteristically Whiggish paean to the glories of imperial progress.\n\nRemember what India had been for countless ages before the establishment of British rule. Think of its endless wars of race and creed, its savage oppressions, its fierce anarchies, its barbarous customs, and then consider what it is to have established for some many years over the vast space from the Himalayas to Cape Comorin a reign of perfect peace; to have conferred upon more than 250 millions of the human race perfect religious freedom, perfect security of life, liberty and property; to have planted in the midst of these teeming multitudes a strong central government, enlightened by the best knowledge of Western Europe, and steadily occupied in preventing famine, alleviating disease, extirpating savage customs, multiplying the agencies of civilization and progress.69\n\nW. T. Stead used his editorial platform at the _Review of Reviews_ to broadcast a vision of \"responsible\" imperialism\u2014or what he also liked to call \"[i]mperialism within limits defined by common sense and the Ten Commandments\"\u2014aimed at improving the \"semi-civilised or wholly savage races.\"70 Indeed he called on the United States to assume its own responsibilities in civilizing Latin and South America. This call to assume the \"White Man's burden\" echoed widely during the decade as British imperialists sought to share the role of civilizing the world. Samuel too was spouting a clich\u00e9 when in 1902 he lavished praise on the transformative potential of the British empire. \"A barbarian race may prosper best if for a period, even for a long period, it surrenders the right of self-government in exchange for the teachings of civilization.\"71 It took the industrial slaughter of the First World War to create a significant transnational intellectual revolt that challenged the civilizing mission, chiefly by questioning the link between technological development and moral progress, though even that wasn't enough to fully derail the imperial desire to reorder the world.72\n\nA recurrent theme in imperial discourse was that the British empire was unique in its propagation of constitutional liberty. (The subjects of imperial coercion no doubt saw it rather differently.) The happy conjunction of altruistic civilizing ambitions (in South Asia and Africa) and a high-degree of colonial self-government (in the settler empire) was routinely praised as a matchless achievement. Combining _imperium et libertas_ , as Disraeli once boasted, they had managed to achieve stable rule, ordered freedom, and beneficent civilization in a single progressive ensemble.73 In so doing the British, with their self-proclaimed \"genius\" for governing, had cracked the temporal code. This \"civilized\" and \"civilizing\" imperial formation could, if managed carefully, escape the fate of all previous empires. Or so it was claimed. Writing at the turn of the twentieth century, as controversy over the war in South Africa raged, Charles Beresford, Tory MP and Admiral in the Royal Navy, celebrated freedom as the unique gift of the British. In standard Polybian vein, he catalogued the traditional causes of decline.\n\nThe great weakness of the nationalities which have been engulfed by the irresistible march of time has been the despotism which underlay their governments, the corruption which sapped their liberties, the luxury and indolence which ate into their vitality, and the remarkable fact that they became worn out and vicious, while the countries they had conquered, and the dependencies they had absorbed, at last broke away, imbued deeply with the vices and but few of the original virtues of the sovereign state.\n\nBut the \"irresistible march\" could be halted. Through accident or design, the British had forged an empire that could avoid the fate that befell all others. \"The Anglo-Saxon has so far, chiefly owing to the mixture of blood in his veins, kept alive side by side both the military and the commercial spirit; and it is this unique combination of talents which offers the best hopes for the survival of the Anglo-Saxon as the fittest of humanity to defy the decaying process of time.\"74 Bathed in philosophical idealism, the conservative historian and classicist J. A. Cramb glorified war, praised violence as a purifying force, and conceived of empire as a grand metaphysical principle, the vehicle for reason in history. It was, above all, \"the highest expression of the soul of the State; it is the complete, the final consummation of the life of the State.\" The British empire was insulated from troubling precedents, for while the \"Roman ideal moulds every form of Imperialism in Europe, and even to a certain degree in the East, down to the eighteenth century,\" the British offered the world a new model, \"not Roman, not Hellenic.\" The emphasis on freedom and justice was unprecedented. \"From this thraldom to the past, to the ideal of Rome, Imperial Britain, first amongst modern empires, completely breaks.\"75 It was attuned to the time spirit.\n\nAs Cramb was penning his encomium to imperial power, J. M. Robertson, a prominent radical liberal, scornfully dismissed imperialist attempts to escape the shadow of Rome.\n\nOne of the most unpromising symptoms of our case is the uncomprehending way in which the British imperialist always scans the story of ancient Rome. Noting the decadence which is the upshot of the whole, he seems to suppose that somehow Christianity will avail to save later empires from the same fate, though Rome was Christianized during the decline; or that haply the elimination of chattel slavery will avert decay, though Christian Spain was free from chattel slavery at home, or that industrialism will avail, though the Moors and the Florentines were tolerably industrial. Any theory will serve to burke the truth that the special cause of decay is just empire.76\n\nUnmoved by special pleading on behalf of the British, Robertson insisted that empires always and everywhere ended in annihilation. Products of avarice and arrogance, they were devoured by their own internal pathologies. \"For persistent empire in the end infallibly brings the imperator, be the process slow or speedy; and with the imperator comes in due time the decadence of empire, the humiliation and paralysis of the spirit that had aspired to humiliate its kind.\"77 He repeated the message in a scathing attack on the idealist philosopher D. G. Ritchie's justification of liberal civilizing imperialism. \"It seems the more necessary to point out that the _pax Romana_ was of old a plea for the kind of policy defended by our imperialists to-day; and that the pursuit of that policy meant the final conquest of Rome by its own brutality and moral barbarism as surely as the conquest of the surrounding world.\"78 Contra the reassuring fantasies of Cramb and Ritchie, this was the true destiny of imperial Britain.\n\nTroubled by intimations of mortality, advocates of imperial progress often saw the empire as fragile, beset on all sides by challengers and skeptics. As Peter Cain has demonstrated, normative justifications of empire during the late nineteenth and early twentieth century depended on a complex dialectical dance of \"character.\" It was frequently argued that British imperial greatness was largely the product of the superior character of its people, individually and collectively, and that this greatness underwrote both the capacity (military and economic strength) and the moral obligation (to spread the benefits of this character to others) motivating the pursuit of empire.79 Moreover, the practice of imperial governance fostered the very greatness on which empire depended. \"The creed of the ultra-imperialists could be simply expressed. \"Character,\"... had given Britain its empire and, without that empire, character would atrophy and die and Britain's moment of greatness would quickly pass.\"80 Imperial dissolution would not protect Britain but instead heralded its ruination. John Ruskin's inaugural lecture as Slade Professor of the History of Art at Oxford in 1870 included a stirring call for further imperial conquest, as the only alternative was to \"perish.\" \"She must found colonies as fast and as far as she is able.\"81 Expansion was the only way to avoid declension. \"If the empire should dissolve,\" Holland warned, \"England would doubtless decay and decline, exhausted by the effort of creating so many new states.\"82 A process of _imperial involution_ beckoned, the dismantling of the periphery leading inexorably to the degeneration of the metropole.\n\nThe universities were central to propagating the civilizational endeavor. Their importance was underscored in 1907 when Curzon, in his Romanes Lecture at Oxford, hailed the spirit of imperial patriotism and demanded that the elite arrayed before him hold the line against the forces menacing Western civilization.\n\nTo our ancient universities, revivified and re-inspired, I look to play their part in this national service. Still from the cloistered alleys and hallowed groves of Oxford... let there come forth the invincible spirit and the unexhausted moral fibre of our race. Let the advance guard of Empire march forth, strong in the faith of their ancestors, imbued with sober virtue, and above all, on fire with a definite purpose.83\n\nEmpire, then, was a bulwark against degeneration, that insidious fear stalking _fin de si\u00e8cle_ Victorian culture, while the elite universities were construed as institutions that could foster the imperial virtues necessary to neutralize the threat. The human sciences were assigned a crucial role, with history and classics at the forefront. Oxford was the principal site of imperial pedagogy. From the 1850s Benjamin Jowett, classicist and Master of Balliol, had been instrumental in directing graduates to the Indian Civil Service (ICS), the entrance examination for which placed great emphasis on knowledge of the classics.84 The results were palpable. Between 1874 and 1914, 27.1 percent of Balliol graduates went to work in the ICS, while between 1888 and 1905 three successive viceroys of India were products of the College. Sidgwick and Seeley, among others, tried to replicate this intimate imperial connection in Cambridge, though with only moderate success.85 The bequest of Cecil Rhodes, himself a proud Oxford product obsessed with the ancient world, only deepened the links between the university and the empire.86 George Parkin, a fervent Canadian imperialist and Secretary of the Rhodes Trust, purred that \"the relation of Oxford to the Empire is exceptional.\"87 Milner's \"Kindergarden,\" that group of thrusting young imperialists who played such an important role in both the Round Table movement and the formation of the South African state, were virtually all Oxford educated.88 The close links between Oxford and the imperial elite persisted until the era of decolonization.89\n\nEven as the universities produced a steady stream of recruits for the empire, they were also generating knowledge that ultimately, though often unintentionally, helped to undermine some traditional narratives of imperial legitimation. The closing decades of the nineteenth century witnessed a tectonic shift in the scholarship on Rome. For much of the Victorian era, the popular mythopoeic narrative of decline and fall\u2014and above all the account of corruption and decay\u2014had been bolstered by scholarly authority. So too was the idea that the Roman world taught pertinent lessons for the present. Niebuhr's _R\u00f6mische Geschichte_ in particular exerted a huge influence in the early Victorian era, helping to (re)establish for the nineteenth century the \"plot of Roman history as the recurrent story of the world.\"90 Indeed Niebuhr himself stressed the similarities between the British and Roman empires. A series of liberal Anglican writers, including Thomas Arnold and Charles Merivale, followed Niebuhr's example in seeking to collapse the temporal distance between the ancient and modern worlds, deriving lessons for the latter from the vicissitudes of the former. Their narratives of ancient Rome were infused with a moralized vision of the cycles through which all polities moved.91 But the credibility of this approach was challenged by the great German scholar Theodor Mommsen, whose influence increased steadily throughout the second half of the century. Providentialism was gradually superseded by a model of historical positivism, whose proponents celebrated its purported objectivity and scientific superiority over earlier, primitive accounts. In Britain, this ambition was realized above all in the writings of Bury, Acton's successor at Cambridge. In addressing the purported connection between Rome and Britain, Bury argued that \"luxury and immorality do not constitute, and need not be symptoms of, a disease that is fatal to the life of States,\" and he condemned \"all reasoning founded on historical analogy\" as \"futile.\"92\n\nThe thesis of British exceptionalism was reinforced by a burst of prominent writings comparing the Roman and British empires that appeared after 1900. The main examples were Bryce's long essay on \"The Ancient Roman Empire and the British Empire in India\"; _Ancient and Modern Imperialism_ , a short tract written by Evelyn Baring, the Earl of Cromer, one-time British consul-general in Egypt, then serving as President of the Classical Association; and C. P. Lucas's _Greater Rome and Greater Britain_ , the product of an imperial administrator turned Oxford don.93 To varying degrees, all drew on the shift in scholarship, and while they would have demurred from Bury's strident denial of the value of historical analogies, they were nevertheless adamant that the Roman and British empires were divided by far more than they shared. This act of disavowal served an important ideological function, allowing them to celebrate the unique virtues and continuing vitality of the British empire. All suggested that the British escaped the worst aspects of the Roman precedent\u2014its despotism, its political centralization, its crude militarism and absence of economic creativity. Lucas, for example, asserted that \"loss of freedom\" cemented the unity of the Roman Empire, whereas the diffuse British empire became increasingly decentralized \"as freedom has grown.\"94 Writing in a symposium on his book, Cromer stressed the radical difference between the ancients and the moderns. \"The records of the ancient world may be searched in vain for any guidance to show whether modern democracy... is capable of sustaining the burthens of Empire at all.\"95 They acclaimed an empire committed to freedom and justice, driven by largely humanitarian impulses and ruling in a civilizing manner, and this allowed them to boast of British superiority over even the most magnificent of their predecessors. The only area where the Romans were more successful was their ability to \"assimilate\" different conquered races.96 Yet here too the point was framed to signal the ultimate superiority of the British, for Roman success was relativized as the product of a smaller, less complex polity. The British faced profound difficulties because their ambition and reach were so much grander. The texts conveyed the message that uniquely among empires the British had escaped the gravitational pull of history. All three authors were also clear about the appropriate object of analysis, insisting that only India was suitable for comparison with Rome. Governed by radically contrasting principles, the British settler colonies \"differ wholly in kind.\"97 Ontologically distinctive, they presented yet another way in which advocates of settler colonialism sought to circumvent the fate of empire.\n\nThe Transfiguration of Empire\n\nCasting a skeptical eye over the British empire in 1892, the American scholar and journalist Albert Shaw found little to celebrate. \"If having an 'empire' means the acquiring of control over the territory and government of people of the races who happen for one reason or another to be weak, I can see nothing in that to be ardent about.\" Britain assumed its place in the long inglorious history of oppressive imperial powers, and as such it stood \"before the world in the garb of a perpetual candidate for dissolution.\" Yet hope remained, if only the British could fundamentally reform their empire by establishing it on progressive foundations, a noble task that could be achieved by creating a true imperial federation modeled on the United States. \"It would be an empire consisting of self-governing Britishers, in which each individual one of 'God's Englishmen' would have rights as extensive as any of his fellows and in the central ordering of which each autonomous group would be as influential, in the proportion of its numbers, as any other.\"98 Although few went as far as Shaw, many British thinkers argued that the settler empire, \"Greater Britain,\" constituted (or could constitute) a novel form of _post-imperial_ political association. As such, it could avoid the pattern of decline and fall.\n\nThe discourse of Greater Britain contained two distinct claims about novelty. The first recognized that the settler colonial system formed an integral part of the wider empire, but that it was nevertheless a new kind of imperial polity. The other denied that Greater Britain was an empire at all. While it had originated as part of an imperial order, it was now assuming a completely novel form, transfigured from empire to state (or commonwealth). On either account, Greater Britain was an unprecedented phenomenon that could be inserted into a progressive narrative of historical development. The novelty, it was commonly proclaimed, resided in the degree of self-government accorded to its constituent members and the civil and political freedoms already enjoyed by its (white) inhabitants.\n\nAt midcentury, Arthur Mills had observed that all of recorded history showed the pattern of imperial \"dismemberment and decay\" resulting in eventual \"dissolution.\" \"Is there any known principle of political life,\" he inquired, \"which history permits us to hope will be exceptional and peculiar to that cluster of communities which now own the rule of England?\" He answered in the affirmative. Political decentralization, and above all the granting of self-government to the settler colonies, allowed the process of decay to be circumvented.99 Later imperial unionists sought to harness this freedom in an overarching political structure. Half a century after Mills had praised the potential of self-government, Holland argued that the British could escape the fate of Rome because they had avoided destructive over-centralization. Sacrificing \"imperium\" in favor of more extensive \"libertas,\" they had saved the empire from the clutches of time. \"In the British empire, apart from India, we have learned... to concede to the Colonies the fullest liberty consistent with the maintenance of a common tie.\"100 \"The British Empire of to-day, it cannot be too often repeated,\" intoned Hugh Egerton, another prominent historian of empire, \"is without precedent in the past,\" chiefly because the colonies had been granted \"responsible government.\" In light of this splendid achievement, Egerton cautioned his readers against drawing false inferences from the past: \"It is at once the glory and the responsibility of nations that in their case, no ceaseless law of change is operating, to make dissolution and decay inevitable. To each generation, in its turn, is given the privilege and power to shape its own destinies.\"101\n\nFor Seeley, the former Professor of Latin and editor of Livy, the ancient world presented no important lessons for the \"boundless expanses\" of the settler colonies. In particular, viewing Britain as an heir to Rome was a serious error.102 In _The Expansion of England_ he argued that \"[o]ur colonies do not resemble the colonies which classical students meet with in Greek and Roman history, and our Empire is not an Empire at all in the ordinary sense of the word.\" He cited various reasons to account for this difference, including the \"ethnological unity\" of the Greater British population and the development of new communications technologies that \"annihilated\" time and space, facilitating the creation of a common identity and enabling effective governance across planetary distances.103 This did not mean, however, that the classical world failed to offer Seeley any insights into the patterns of contemporary international politics, for the Roman archetype, he argued, bore some resemblance to the British mode of rule in India. While the analogy was far from exact, they did share the status of \"superior races\" intent on \"civilizing\" those under their control. As the Roman Empire in the West was \"the empire of civilisation over barbarism,\" so the British empire in India was \"the empire of the modern world over the medieval.\" Such comparisons, though, had nothing to do with the settlement colonies.\n\nThe colonies and India are in opposite extremes. Whatever political maxims are most applicable to one, are most inapplicable to the other. In the colonies everything is brand-new. There you have the most progressive race put in the circumstances most favourable to progress. There you have no past and an unbounded future. Government and institutions are all ultra-English. All is liberty, industry, invention, innovation, and as yet tranquillity.\n\nIndia, by contrast, \"is all past and, I may almost say, has no future.\"104 For Seeley, the British governed spaces defined by two contrasting temporal regimes. One was characterized by novelty, creativity, movement, and flux, and its boundless energies were perfectly suited for progressive historical development. The other was stagnant, immobile, rigid, and thus incapable of progress without exogenous shock. It was as if past and future coexisted in the same historical moment.\n\nTwo decades later William Peterson, \u00e9migr\u00e9 classical scholar and Principal of McGill University, was likewise emphatic that the British empire represented a departure from the patterns of history, and above all its only other competitor for historical splendor:\n\nIt is by no means to its disadvantage or discredit that the British Empire is not altogether as other Empires have been. It was by the sword that old Rome, for instance, held what she had won by the sword. To her modern successor and representative has been left the glory of reconciling the two elements, which many of Rome's subjects found incompatible\u2014\"Empire\" and \"liberty.\" A Constitution which secures equal rights for all under the ample folds of the British flag has given a new meaning to the old motto, \" _Imperium et Libertas_.\" Never before in history has the unique spectacle been presented to the world of sovereignty wielded by the parent State on the slender basis of mutual consent.\n\nIndeed the settler colonial world, he maintained, might be described as \"a system of democratic republics under the gentle sovereignty of the Motherland.\"105 Many advocates of Greater Britain deliberately eschewed centuries of imperial political thought and the historicizing trends of the time by actively dismissing the relevance of ancient empires for thinking about the future. They often sought authority in the image of America\u2014a country that had, through the creation of a continental federal system, managed to solve many of the political problems facing the British.106 Above all, the Americans taught that it was possible to sustain individual freedom in a vast polity, reconciling liberty and empire as Thomas Jefferson had once promised.107 William Greswell, formerly a Professor of Classics in South Africa, accentuated the fundamental differences between the ancient empires and the modern British, and he emphasized, echoing an argument made famous by Constant, the superiority of modern freedom. \"The Britannica _civitas_ is a far wider, and we may be allowed to believe a far more honoured, privilege. It is a _civitas_ built upon freedom not despotism, upon tolerance rather than upon force, upon voluntary effort and individual enterprise rather than upon bureaucratic orders and state diplomacy.\" Greswell demanded a \"confederacy of the British race,\" but added the qualifier that it was foolhardy to \"refer for guidance to ancient or modern confederacies.\" Rather, it was instructive to look to the edifying example set by United States.108 In a historical irony that Macaulay might well have enjoyed, London Bridge, the shattered perch of his ubiquitous New Zealander, today sits intact in the blasted heat of Arizona, an unwitting symbol of the _translatio imperii_ dreamt by many Victorian imperialists.\n\nThe purportedly federal (or quasi-federal) character of Greater Britain meant that it was something wholly new. This was yet another expression of British imperial exceptionalism. In the _Considerations on Representative Government_ , Mill had referred to the colonial empire as an \"unequal federation,\" while four decades later Leonard Hobhouse talked of the \"loose, informal, quasi-Federalism of the British Colonial Empire,\" which he contrasted with the \"strict\" American variant.109 Some went as far as proclaiming that it already comprised a state\u2014or, alternatively, that it should be transformed into one. Considered \"as a state,\" argued Seeley, \"England has left Europe altogether behind it and become a world-state,\" and he called for the consolidation of this nascent polity into a vast permanent transoceanic polity.110 The transmutation of empire into state implied by schemes for imperial federation was acknowledged by A. V. Dicey, the leading constitutional theorist in the empire, who complained that they were demanding a \"new federated state.\"111 In the Edwardian years it was increasingly accepted that burgeoning colonial demands for autonomy meant that new forms of political order had to be devised. But the idea of a global Anglo-state did not disappear. In 1905 W. F. Monypenny, a leading journalist with the _Times_ , conceived of the empire as a \"world state,\" a polity defined by cultural homogeneity and unity of interests. It was, he claimed, the embodiment of a \"new political conception,\" which \"transcends nationality\" while simultaneously allowing the flourishing of separate nationalities within it.112 Leo Amery, meanwhile, wrote of the colonial empire as a \"single united whole, a great world-State, composed of equal and independent yet indissolubly united States.\" This was, he marveled, a \"new ideal,\" a \"great federation\" that corresponded to the \"wider outlook and broader humanity of advancing civilization.\"113 The idea of an Anglo-Saxon commonwealth was also central to the Round Table movement during the Edwardian era and beyond.114 I pick up its echoes in chapter 8.\n\nOther arguments stressed the priority of the periphery to the metropole. According to this picture, Britain may well be subject to the relentless logic of decline, but the settler colonies, creative offspring of an old and vulnerable world, could reach escape velocity. While Lecky believed in the progressive nature of British imperialism, he still acknowledged the power of historical precedent: \"Nations, as history but too plainly shows, have their periods of decay as well as their periods of growth.\" But even if Britain succumbed, the future of the British \"race\" was guaranteed as it had spread beyond the confines of the homeland to occupy vibrant, prosperous colonies throughout the world. \"[W]hatever fate may be in store for these Islands, we may at least confidently predict that no revolution in human affairs can now destroy the future ascendency of the English language and of the Imperial race.\"115 The (colonial) empire assured the permanence of the British people, their ability to transcend the vagaries of political institutions. This echoed arguments that figured the colonies\u2014above all New Zealand\u2014as a utopian space, a \"better Britain.\"116\n\nOnce again, the universities came to play a vital role in legitimating empire. Even as the new wave of Roman scholarship was starting to undermine traditional narratives of luxury, decadence, and decline, so a new field of knowledge was beginning to emerge and others were being revitalized. In Oxford, the prodigious classicist Alfred Zimmern developed a modernizing interpretation of ancient Athens that inspired the \"commonwealth\" vision of the British empire articulated by Lionel Curtis and other members of the Round Table.117 The Greek model entered a period of renaissance. Meanwhile Seeley's project to inject the study of the empire into the core of the emerging professional discipline began to bear fruit. During the early years of the twentieth-century imperial history, a new academic subfield financially underwritten by imperial interests was created to proselytize a specific ideological vision: to delineate Greater Britain as a singular political unit and to insist on its central importance for the future of Britain and the world. It was the hymn sung from the newly endowed chairs of imperial history in Oxford, Cambridge, and the University of London, and its intellectual inheritance persisted long into the twentieth century.118\n\nThroughout the Victorian age, then, commentators on empire wrestled with the meaning of history. This resulted in a clash between a vision predicated on either the possibility or inevitability of political progress, and a cyclical vision in which empires followed predetermined trajectories. Negotiating these temporal narratives required considerable intellectual dexterity. Most advocates of empire acknowledged the previous cycles of imperial history, but suggested that there was something radically different about the age in which they lived and the kind of empire they defended. Avatars of progress, the British had managed to birth a new form of empire, one that was not only compatible with a progressive understanding of human development, but which played a pivotal role in it. Critics demurred from this Panglossian view, suggesting that the British empire was bound to follow the course of all others, and that in doing so it threatened the very things\u2014liberty above all\u2014which made Britain great in the first place. The muse of history whispered to the Victorians in different voices.\n\n1 J. R. Seeley, _Introduction to Political Science_ , ed. Henry Sidgwick (London, 1896), 161.\n\n2 Herman Merivale, \"The Colonial Question in 1870,\" _Fortnightly Review_ , 7 (1870), 153.\n\n3 Acton, \"Inaugural Lecture on the Study of History,\" _Lectures on Modern History_ , ed. J. N. Figgis and R. V. Laurence (London, 1906), 22; Dicey, _Introduction to the Study of the Law of the Constitution_ , 4th ed. (London, 1893), 14. For a powerful questioning of that method, see Henry Sidgwick, \"The Historical Method,\" _Mind_ , 11\/42 (1886), 203\u201319; Sidgwick, _The Elements of Politics_ , 2nd ed. (London, 1897), ch. 1. Sidgwick, like Dicey, was cognizant that he was arguing against the grain.\n\n4 This chapter updates and extends the analysis of imperial temporality in Duncan Bell, The _Idea of Greater Britain_ , ch. 8.\n\n5 Smith, \"The Policy of Aggrandizement,\" _Fortnightly Review_ , 22 (1877), 307.\n\n6 Bryce, \"An Age of Discontent,\" _Contemporary Review_ , 59 (1891), 29.\n\n7 It thus fits with what Mark Bevir calls \"developmental historicism.\" Bevir, \"Political Studies as Narrative and Science, 1880\u20132000,\" _Political Studies_ , 54 (2006), 583\u2013606.\n\n8 Smith, \"The Policy of Aggrandizement.\" For a similar critique of American empire, see Goldwin Smith, _Commonwealth or Empire?_ (New York, 1902).\n\n9 Froude, _Caesar_ (London, 1879), 2. On this dimension of Froude's imperial thought, see chapter 12.\n\n10 Ibid., 3\u20134.\n\n11 Seeley, \"Political Somnambulism,\" _Macmillan's Magazine_ , 43 (1880), 32. On the role of historical imagination in political thinking, see especially John Burrow, _Whigs and Liberals_ (Oxford, 1988); Collini, Winch, and Burrow, _That Noble Science of Politics_ , chs. 6\u20137.\n\n12 Seeley, _The Expansion of England_ , 169.\n\n13 There is a huge literature on Victorian appropriations of the classics. See, for example, Simon Goldhill, _Victorian Culture and Classical Antiquity_ (Princeton, 2012); Frank Turner, _The Greek Heritage in Victorian Britain_ (London, 1984); Richard Jenkyns, _The Victorians and Ancient Greece_ (Oxford, 1980); Norman Vance, _The Victorians and Ancient Rome_ (Oxford, 1997); Christopher Stray, _Classics Transformed_ (Oxford, 1998). For the imperial uses of the classics, see, inter alia, Mark Bradley, ed., _Classics and Imperialism in the British Empire_ (Oxford, 2010); Sarah Butler, _Britain and Its Empire in the Shadow of Rome_ (London, 2012); Christopher Hagerman, _Britain's Imperial Muse_ (Basingstoke, 2013); Phiroze Vasunia, _The Classics and Colonial India_ (Oxford, 2013).\n\n14 Anthony Pagden, _Lords of All the World_ (London, 1998), 11. See also Pagden, _The Burdens of Empire_ (Cambridge, 2015), 2\u20133.\n\n15 Machiavelli, _Discourses on Livy_ , ed. Julia Conaway Bondanella and Peter Bondanella (Oxford, 1997), bk. 2. See also David Armitage, \"Empire and Liberty,\" in _Republicanism_ , ed. Martin van Gelderen and Quentin Skinner (Cambridge, 2002), 2:29\u201346; J.G.A. Pocock, _Barbarism and Religion, Vol. 3_ (Cambridge, 2003), esp. pts. 3-5.\n\n16 Hume, \"Hume's Early Memoranda, 1729\u20131740,\" _Journal of the History of Ideas_ , ed. E. C. Mossner, 9 (1948), 517. Hume attributed Roman decline to constitutional failures rather than moral debilitation.\n\n17 Gibbon, _The History of the Decline and Fall of the Roman Empire_ , ed. J. B. Bury (London, 1905), 4:161. Gibbon, though, made little of the connection between the British and Roman Empire. John Robertson argues that he was more interested in the fate of universal monarchy. Robertson, \"Gibbon's Roman Empire as a Universal Monarchy,\" in _Edward Gibbon and Empire_ , ed. Rosamond McKitterick and Roland Quinault (Cambridge, 1997), 247\u201371. On the popularity of the trope, see Vance, _The Victorians and Ancient Rome_ , 234\u201335; Richard Hingley, _Roman Officers and English Gentlemen_ (London, 2000), ch. 3; Jenkyns, _The Victorians and Ancient Greece_ , 73\u201377.\n\n18 On the Whig narrative, see Burrow, _Whigs and Liberals_. On the transmission of the critique into nineteenth-century imperial debate, see Miles Taylor, \"Imperium et Libertas?,\" _Journal of Imperial and Commonwealth History_ , 19 (1991), 1\u201319.\n\n19 David Armitage, _The Ideological Origins of the British Empire_ (Cambridge, 1997).\n\n20 Seeley, _The Expansion of England_ , 246.\n\n21 Hell, \"The Twin Towers of Anselm Kiefer and the Trope of Imperial Decline,\" _Germanic Review_ , 84\/1 (2009), 86.\n\n22 For further discussion of the iconographic order, see chapter 7.\n\n23 Kipling, \"Recessional,\" _Times_ , July 17, 1897.\n\n24 Ibid., _Something of Myself for My Friends Known and Unknown_ (London, 1937), ch. 6.\n\n25 Macaulay, \"History of the Popes\" [1840], in _Critical and Historical Essays_ , ed. A. J. Grieve (London, 1907), 2:39.\n\n26 On the trope, see David Skilton, \"Tourists at the Ruins of London,\" _Cercles_ , 17 (2007), 93\u2013119. For the romantic background, see Lawrence Goldstein, _Ruins and Empire_ (Pittsburgh, 1977).\n\n27 Gustave Dor\u00e9 and Blanchard Jerrold, _London_ (London, 1872), 188 (the words are by Jerrold). See also Robert Dingley, \"The Ruins of the Future,\" in _Histories of the Future_ , ed. Dingley and Alan Sandison (Basingstoke, 2000), 15\u201333. On the general theme of ruination, see Julia Hell and Andreas Schonle, eds., _Ruins of Modernity_ (Durham, NC, 2010); and for a meditation on artistic representations, Brian Dillon, _Ruin Lust_ (London, 2014).\n\n28 Hell, \" _Katechon_ ,\" _Germanic Review_ , 84 (2009), 284.\n\n29 Harrison, _Studies in Early Victorian Literature_ (London, 1895), 74. As I explored in chapter 2, positivists, including Harrison, provided some of the most stinging attacks on empire during the century. See especially Gregory Claeys, _Imperial Sceptics_ (Cambridge, 2012).\n\n30 Trollope, _The New Zealander_ , ed. N. J. Hall (Oxford, 1972), 211.\n\n31 Froude, _Oceana, or England and Her Colonies_ , new ed. (London, 1888), 236\u201337.\n\n32 Smith, \"The Policy of Aggrandizement,\" 308.\n\n33 Chamberlain, \"The True Conception of Empire,\" 2:5.\n\n34 Conan Doyle, _The Great Boer War_ (London, 1900), 306\u20137.\n\n35 Linda Dowling, \"Roman Decadence and Victorian Historiography,\" _Victorian Studies_ , 28 (1985), 579\u2013608.\n\n36 Froude, \"Calvinism\" [1871], in _Short Studies on Great Subjects_ (London, 1907), 2:26.\n\n37 Letter to Richard Hargreaves, August 4, 1860, in John Morley, _The Life of Richard Cobden_ , 2 vols. (London, 1881), 2:361.\n\n38 Smith, \"Policy of Aggrandizement,\" 308.\n\n39 Spencer, \"Imperialism and Slavery,\" in _Facts and Comments_ (New York, 1902), 162, 165. He traces the consequences in \"Re-Barbarization\" (172\u201388).\n\n40 Hobson, _Imperialism_ (London, 1902), 158, 160. Hobson also stressed the profound difference between ancient and modern empires, seeing in the former a \"genuine element of internationalism\" absent from modern variants (6).\n\n41 Burrows, \"Imperial Federation,\" _National Review_ , 4 (1884\u201385), 369. An undistinguished historian, Burrows was Chichele Professor of Modern History at Oxford from 1862\u20131900.\n\n42 On the late Victorian distinction between \"empire\" and \"imperialism,\" see the discussion in chapter 2.\n\n43 Gladstone, \"England's Mission,\" _Nineteenth Century_ , 4 (1878), 584.\n\n44 Lowe, \"Imperialism,\" _Fortnightly Review_ , 24 (1878), reprinted in _Empire and Imperialism_ , ed. P. J. Cain (Bristol, 1999), 265. See also the warning in Frederic Seebohm, \"Imperialism and Socialism,\" _Nineteenth Century_ (1880), in _Empire_ , ed. Cain, 309.\n\n45 Harcourt, letter to Rosebery, September 27, 1892, in A. G. Gardiner, _Life of Sir William Harcourt_ (London: Constable, 1923), 2:197. Widely distrusted by imperialists, Harcourt was Chancellor of the Exchequer in 1886 and again in 1892\u201395.\n\n46 Seeley, \"Roman Imperialism, II,\" _Macmillan's Magazine_ , 20 (1869), 54, 47\u201348; Samuel, _Liberalism_ (London, 1902), 342\u201343. Note that Seeley was inconsistent on this point (cf. Seeley, _Natural Religion_ (London, 1882), 237).\n\n47 Morley, \"The Expansion of England,\" _Macmillan's Magazine_ , 49 (1884), 241\u201358.\n\n48 Hobson, _Imperialism_ , 388. Here he drew heavily on the American scholar Brooks Adams's, _The Law of Civilization and Decay_ (London, 1895).\n\n49 Holland, _Imperium et Libertas_ (London, 1901), 13\u201314 (though see also his extended comparison of Rome and Britain, 265\u201369). Holland was a barrister. The book was reviewed positively in the _Political Science Quarterly_ by the classicist John Finley and in the _American Historical Review_ by the historian A. L. Lowell.\n\n50 Holland, _Imperium et Libertas_ , 15; Seeley, _Expansion of England_ , 69.\n\n51 Mills, _Colonial Constitutions_ (London, 1856), xix-xx.\n\n52 Mill, \"Colony,\" _Essays from the Supplement to the Encyclopedia Britannica, Collected Works_ (London, 1995), 4, 5\u20139. See also the discussion of the differences between the Roman and Greek models in George Cornewall Lewis's influential, _Essay on the Government of Dependencies_ (London, 1841), 115\u201317, where he notes the similarity between British colonization in North America and the Greek experience. He also argued that governing a dependent empire damaged the \"political morality\" of the imperial power (251).\n\n53 Mill, \"Wakefield's 'The New British Province of South Australia,'\" in the _Examiner_ , July 20, 1843, reprinted in _Collected Works_ , 23:739. For his admiration of the \"Greek empire,\" see \"Grote's _History of Greece_ ,\" vol. 2, [1853], _Collected Works_ , 11:321\u201324. Edward Wakefield, key ideologue of early Victorian colonization and a major influence on Mill, also stressed the suitability of the Greek model: _A View on the Art of Colonization_ (London, 1849), 16\u201317.\n\n54 Roebuck, _The Colonies of England_ (London, 1849), 138. Utilitarian views of Greece were shaped heavily by George Grote's seminal _History of Greece_ (1846\u201356). See also, Grote, \"Institutions of Ancient Greece,\" _Westminster Review_ , 5 (1826), 269\u2013331.\n\n55 Freeman, \"Imperial Federation,\" _Macmillan's Magazine_ , 51 (1885), 436 and 437\u201338. See also Freeman, _History of Federal Government_ (London, 1863), 5\u201326; and chapter 13.\n\n56 Bryce, \"Edward Augustus Freeman,\" _English Historical Review_ , 7 (1892), 502. Influenced by Thomas Arnold, Freeman was himself committed to a cyclical view of history: \"Historical Cycles\" in _Historical Essays_ , 4th series (London, 1892), 249\u201358, though he tended to locate patterns of repetition _within_ a political community.\n\n57 Daniel Pick, _Faces of Degeneration_ (Cambridge, 1989).\n\n58 Balfour, _Decadence_ (Cambridge, 1908).\n\n59 Pearson, National Life and Character (London, 1894). The book caused a sensation. Prior to his political career, Pearson was Professor of Modern History at King's College, London (1855\u201365).\n\n60 Turner, \"The Significance of the Frontier in American History,\" in _Rereading Frederick Jackson Turner_ , ed. J. M. Faragher (London, 1998). Jackson's frontier thesis is cited in Lord Curzon of Kedleston, _Frontiers_ (Oxford, 1907), 56.\n\n61 Rhodes, _The Last Will and Testament of Cecil J. Rhodes_ , ed. W. T. Stead (London, 1902), 190. For an intriguing, and ultimately ambivalent, narrative of the future Anglo-Saxon colonization of outer space, set in the year 2236, see Robert Cole, _The Struggle for Empire_ , ed. Richard Bleiler (London, 2013). Written in 1900, Cole's novel is now regarded as the first \"space opera\" in science fiction. I discuss this text in Bell, _Dreamworlds of Empire_ (forthcoming).\n\n62 Morley, _Recollections_ (London, 1917), 2:27, 30.\n\n63 Bury, _The Idea of Progress_ (London, 1920), vii, 2. \"[I]t was not till men felt independent of Providence that they could organise a theory of Progress\" (73). For more recent reflection on the notion of progress, see Reinhart Koselleck, _Futures Past_ , trans. Keith Tribe (Cambridge, MA, 1985).\n\n64 Macaulay, \"Sir James Mackintosh\" [1835], in _Critical and Historical Essays_ (London, 1848), 2:219, 226.\n\n65 On ideals of character, see Stefan Collini, _Public Moralists_ (Oxford, 1993), and, on its collective expression, Peter Mandler, _The English National Character_ (London, 2006).\n\n66 Guizot, _General History of Civilization in Europe_ [1828], ed. G. Knight (New York, 1896), 11. On John Stuart Mill and civilization, meanwhile, see Duncan Kelly, _The Propriety of Liberty_ (Princeton, 2011), ch. 4. See also Duncan Bell, \"Empire and Imperialism,\" in _The Cambridge History of Nineteenth-Century Political Thought_ , ed. Gregory Claeys and Gareth Stedman Jones (Cambridge, 2012), 864\u201391.\n\n67 Mantena, _Alibis of Empire_ ; Mantena, \"The Crisis of Liberal Imperialism,\" in _Victorian Visions of Global Order_ , ed. Duncan Bell (Cambridge, 2007), 113\u201336.\n\n68 See also, P. J. Cain, \"Character, 'Ordered Liberty,' and the Mission to Civilise,\" _Journal of Imperial and Commonwealth History_ , 40\/4 (2012), 557\u201378; Peter Mandler, \"Looking around the World,\" in _Time Travelers_ , ed. Adelene Buckland and Sadiah Qureshi (Chicago, forthcoming).\n\n69 Lecky, _The Empire_ (London, 1893), 44\u201345. One of the most influential historians of the age, Lecky never held a formal academic post, though he was offered (and declined) the Regius Professorship of History at Oxford after Freeman's death in 1892. For an earlier version of the refrain, see James Fitzjames Stephen, \"Liberalism,\" _Cornhill Magazine_ , 5 (1862), 32.\n\n70 Stead, \"To All English-Speaking Folks,\" _Review of Reviews_ , 1\/1 (1890), 17. On Stead, see Lauren Brake et al., eds., _W. T. Stead_ (Chicago, 2012).\n\n71 Samuel, _Liberalism_ , 330.\n\n72 Michael Adas, \"Contested Hegemony,\" _Journal of World History_ , 15\/1 (2004), 31\u201363.\n\n73 Disraeli coined the (ungrammatical) phrase in 1851. Jenkyns, _The Victorians and Ancient Greece_ , 333. He claimed Roman pedigree when he reused it in 1879. Moneypenny and Buckle, _The Life of Benjamin Disraeli_ , 6 vols. (London, 1910\u201320), 6:495. As Norman Vance notes, however, his attribution was mistaken. Cicero once wrote of _imperio ac liberte_ , though he meant the power to uphold and enforce law, not territorial empire. Disraeli probably had Tacitus in mind, since he had famously been misquoted by Francis Bacon in _The Advancement of Learning_ (1605), where _principatum ac libertatem_ was rendered as _imperium et libertatem_ , before being translated by Bolingbroke in _The Idea of a Patriot King_ (1738) as \"Empire and Liberty.\" Vance, \"Anxieties of Empire and the Moral Tradition,\" _International Journal of the Classical Tradition_ , 18\/2 (2011), 251. Disraeli's phrase was widely employed in British imperial debate. See, for example, Freeman, \"Imperial Federation,\" 444; Herbert Spencer, \"Imperialism and Slavery,\" 117; Holland, _Imperium et Libertas_.\n\n74 Beresford, \"The Future of the Anglo-Saxon Race,\" _North American Review_ , 171\/529 (1900), 803, 806.\n\n75 Cramb, _Reflections on the Origins and Destiny of Imperial Britain_ (London, 1900), 216, 18, 23. Cramb was Professor of History at Queen's College, London. In Karma Nabulsi's terms, he can be seen as a \"martialist,\" one of the \"high priests of the temple of Janus,\" a species quite common in German intellectual circles at the time, though rarer in Britain. Nabulsi, _Traditions of War_ , ch. 4. See also my discussion of the category in Chapter 4.\n\n76 Robertson, _Patriotism and Empire_ , 3rd ed. (London, 1900), 151.\n\n77 Ibid., 157.\n\n78 Robertson, \"The Moral Problems of War,\" _International Journal of Ethics_ , 11\/3 (1901), 283. Cf. Ritchie, \"War and Peace,\" _International Journal of Ethics_ , 11\/2 (1901), 137\u201358.\n\n79 For relevant philosophical discussion of the civilizational obligations incurred by liberal empires, see J. H. Muirhead, \"What Imperialism Means,\" _Fortnightly Review_ , 68 (1900), 177\u201387; Ritchie, \"War and Peace.\"\n\n80 Cain, \"Empire,\" 269.\n\n81 Ruskin, \"Inaugural Lecture,\" in _The Works of John Ruskin_ , ed. E. T. Cook and A. Wedderburn, 39 vols. (London, 1903\u201312), 20:41. See also his _Stones of Venice_ (1851) on how moral decline leads to imperial collapse ( _Works_ , 9:17).\n\n82 Holland, _Imperium et Libertas_ , 265.\n\n83 Curzon, _Frontiers_ , 57\u201358. Curzon was serving as Chancellor of the University at the time.\n\n84 Richard Symonds, _Oxford and Empire_ (Oxford, 1991); Vasunia, _The Classics and Colonial India_ , ch. 5. Oxford graduates dominated the system (though Trinity, Dublin, also produced a disproportionate number of entrants): Symonds, _Oxford and Empire_ , 180\u201391. Jowett's project was continued by his successor at Balliol, J. L. Strachan Davidson.\n\n85 Collini, Winch, and Burrow, _That Noble Science of Politics_ , 354\u201355.\n\n86 Philip Ziegler, _Legacy_ (London, 2008). Unable to read the original languages, Rhodes employed a team of classicists to translate all of the references found in Gibbon's _Decline and Fall_ , as well as numerous other classical texts, an exercise in historical recovery that filled over two hundred volumes in his personal library. See Victoria Tietze Larson, \"Classics and the Acquisition and Validation of Power in Britain's 'Imperial Century' (1815\u20131914),\" _International Journal of the Classical Tradition_ , 6\/2 (1999), 211.\n\n87 Parkin, _The Rhodes Scholarship_ (London, 1912), 211.\n\n88 On the Kindergarten, see Symonds, _Oxford and Empire_ ; John Kendle, _The Round Table Movement and Imperial Union_ (Toronto, 1975).\n\n89 These connections have recently become the focus of student activism aiming to force the university to acknowledge its historical role in imperialism. The campaign, drawing on developments in South Africa, is conducted under the name \"Rhodes Must Fall.\" Andr\u00e9 Rhoden-Paul, \"Oxford Uni Must Decolonise Its Campus and Curriculum, Say Students,\" _Guardian_ , June 18, 2015.\n\n90 Dowling, \"Roman Decadence and Victorian Historiography,\" 595.\n\n91 Duncan Forbes, _The Liberal Anglican Idea of History_ (Cambridge, 1952).\n\n92 Bury, \"The British Empire and the Roman Empire,\" _Saturday Review_ , June 27, 1896, 645. Bury later discarded his early positivism, emphasizing contingency and rejecting the possibility of discerning general patterns of cause and effect. _Selected Essays of J. B. Bury_ , ed. Howard Temperley (Cambridge, 1930), chs. 1\u20135. This shift is traced in R. G. Collingwood's review ( _English Historical Review_ , 43\/186 (1931), 461\u201365).\n\n93 Bryce, \"The Roman Empire and the British Empire in India,\" in Bryce, _Studies in History and Jurisprudence_ (Oxford, 1901), 1\u201371; Baring, _Ancient and Modern Imperialism_ (London, 1910); Lucas, _Greater Rome and Greater Britain_ (Oxford, 1912). For context, see Vasunia, _The Classics and Colonial India_.\n\n94 Lucas, _Greater Rome_ , 141.\n\n95 Cromer, \"History and Politics,\" _Classical Review_ , 24 (1910), 116.\n\n96 Lucas, _Greater Rome_ , 91\u2013112; see also Bryce, \"The Roman Empire,\" 54\u201363; Baring, _Ancient and Modern_ , 72\u201395.\n\n97 Lucas, _Greater Rome_ , 142; see also Bryce, \"The Roman Empire,\" 4\u20136; Baring, _Ancient and Modern_ , 17\u201318.\n\n98 Shaw, \"An American View of Home Rule and Federation,\" _Contemporary Review_ , 62 (1892), 311\u201312. An Anglophile, Shaw was the editor of the _American Review of Reviews_ , and thus a close associate of W. T. Stead. For his role in the foundation of American political science, see Robert Adcock, _Liberalism and the Emergence of American Political Science_ (Oxford, 2014), ch. 5.\n\n99 Mills, _Colonial Constitutions_ , xxxix-xl.\n\n100 Holland, _Imperium et Libertas_ , 14.\n\n101 Egerton, _A Short History of Colonial Policy_ (London, 1897), 455, 478. At the time of publication, Egerton worked in the Emigrants' Information Office. On the back of its considerable success, he was elected (in 1905) the first Beit Professor of Colonial History at Oxford. He retired in 1920.\n\n102 Seeley, \"Introduction\" to _Her Majesty's Colonies_ (London, 1886), xviii. For the misleading argument that Seeley saw the British as heirs to Rome, see Reba Soffer, \"History and Religion,\" in _Religion and Irreligion in Victorian Society_ , ed. R. W. Davis and R. J. Helmstadter (London, 1992), 142\u201343; Hingley, _Roman Officers_ , 24\u201325.\n\n103 Seeley, _The Expansion of England_ , 51.\n\n104 Ibid., 51, 244, 176.\n\n105 Peterson, \"The Future of Canada,\" in _The Empire and the Century_ , ed. C. S. Goldman (London, 1905), 363\u201364.\n\n106 See Bell, _The Idea of Greater Britain_ , ch. 9, for more detail. Contra Mark Bradley, I do not deny that ancient precedents informed various aspects of British imperial discourse, only that advocates of Greater Britain tended to eschew them as models to emulate. Bradley, \"Introduction,\" in _Classics and Imperialism in the British Empire_ , ed. Bradley, 16\u201317.\n\n107 On this motif in American history, see Richard H. Immerman, _Empire for Liberty_ (Princeton, 2010).\n\n108 Greswell, \"Imperial Federation,\" in _England and Her Colonies_ (London, 1887), 7.\n\n109 Mill, _Considerations on Representative Government_ , 565; Hobhouse, _Democracy and Reaction_ [1904], ed. Peter Clarke (Brighton, 1972), 154. See also J. R. Seeley, \"Georgian and Victorian Expansion,\" _Fortnightly Review_ , 48 (1887), 136.\n\n110 Seeley, _The Expansion of England_ , 293, 169, 75. See also Seeley, \"Georgian and Victorian Expansion,\" 133.\n\n111 Dicey, _Introduction to the Study of the Law of the Constitution_ , 8th ed. (London, 1915), lxxxiv. Dicey presented his own vision of an Anglo-Saxon future, focusing on an Anglo-American \"isopolity\" (a space of common citizenship). Duncan Bell, \"Beyond the Sovereign State,\" _Political Studies_ , 62\/2 (2013), 418\u201334. On how federation was seen by many eighteenth-century thinkers, including the authors of _The Federalist_ , as a way to reconcile liberty and empire, see Armitage, \"Empire and Liberty,\" 45\u201346.\n\n112 Monypenny, \"The Imperial Ideal,\" in _The Empire and the Century_ , ed. Goldman, 23 and 27.\n\n113 Amery, \"Imperial Defence and National Policy,\" in _Empire_ , ed. Goldman, 181\u201382.\n\n114 See, for example, Lionel Curtis, _The Problem of Commonwealth_ (London, 1916), 68.\n\n115 Lecky, _Empire_ , 47.\n\n116 Lyman Tower Sargent, \"Utopianism and the Creation of New Zealand National Identity,\" _Utopian Studies_ , 12\/1 (2001), 1\u201318.\n\n117 Zimmern, _The Greek Commonwealth_ (Oxford, 1911). He was later appointed to the first chair of International Relations (IR) in the world, at the University of Wales, Aberystwyth, before returning to an IR chair at Oxford. See Jeanne Morefield, \"'An Education to Greece,'\" _History of Political Thought_ , 28 (2007), 328\u201361; Morefield, _Empires without Imperialism_ (Oxford, 2014), ch. 1; Tomohito Baji, \"Commonwealth: Alfred Zimmern and World Citizenship,\" PhD thesis, University of Cambridge (forthcoming).\n\n118 Amanda Behm, \"The Bisected Roots of Imperial History,\" _Recherches Britanniques_ , 1\/1 (2011), 54\u201377. On the \"British world\" scholarly network, see Tamsin Pietsche, _Empire of Scholars_ (Manchester, 2013).\nCHAPTER 6\n\nThe Idea of a Patriot Queen?\n\nThe Monarchy, the Constitution, and the Iconographic Order of Greater Britain, 1860\u20131900\n\nThe voice of Britain, or a sinking land,\n\nSome third-rate isle half-lost among her seas?\n\n_There_ rang her voice, when the full city peal'd\n\nThee and thy Prince! The loyal to their crown\n\nAre loyal to their own far sons, who love\n\nOur ocean-empire with her boundless homes\n\nFor ever-broadening England, and her throne\n\nIn our vast Orient, and one isle, one isle,\n\nThat knows not her own greatness1\n\n\u2014ALFRED TENNYSON\n\nTennyson, perhaps more than any other poet, expressed the profound symbolic connection between the institution of the monarchy, the heavily mediated persona of Queen Victoria, and the vast and \"ever-broadening\" expanses of the British empire. Victoria's long reign saw this connection grow in power and potency, as she assumed the role of an imaginative fulcrum at the center of an unprecedented global imperial system. In a later poem\u2014one of his most anthologized and parodied works\u2014Tennyson anointed her the \"Patriot Architect,\" and this chapter explores some of the ways in which this vision was articulated in the political theory of Greater Britain\u2014the political theory proclaiming the unity of the Anglo-Saxon settler colonies and the ostensible \"mother country\"\u2014during the closing decades of the nineteenth century.2\n\nIn his pioneering _Short History of British Colonial Policy_ (1897), H. G. Egerton argued that \"The Period of Greater Britain\" commenced in 1886.3 This was to place the starting point at least fifteen years too late, however, for debate over the future of the settler empire began in earnest in the early 1870s, drawing its terminological inspiration from Charles Dilke's popular travelogue _Greater Britain_ (1868).4 Faced with what appeared to be a momentous shift in the patterns of European and global politics, combined with the insidious fear of mass democracy following in the wake of parliamentary reform\u2014the latter an issue often marginalized or ignored by historians of imperial thought\u2014a considerable number of British political thinkers sought ways to consolidate or reinforce the apparently weakening position of the country; to secure the greatness of Britain. The most vociferous, as well as the most fractious, manifestation of this desire was the movement calling for imperial federation, a movement that at one time or another attracted luminaries as diverse as J. R. Seeley, Joseph Chamberlain, Cecil Rhodes, James Bryce, J. A. Froude, W. E. Forster, W. H. Smith, Lord Rosebery, W. T. Stead, and J. A. Hobson. The proponents of Greater Britain, and in particular the imperial federalists, represented one of a large number of competing and intersecting movements aiming to challenge and transform the way in which the British empire (and state) was understood. Drawing the support and opprobrium of some of the most prominent thinkers and politicians of the day, they expounded their views in the most high-profile outlets in British public culture, generating a large volume of articles, books, and pamphlets. Ultimately, however, they never gained substantial support outside sections of the metropolitan elite, nor did they convince enough of the leading politicians of the day, including Disraeli, Gladstone, and Salisbury, of the viability and necessity of their proposals. The campaigning drive for federation faltered and then collapsed in ignominy during the 1890s, although ideas about federal unity were to remain a staple of imperial debate until the eve of decolonization. The proponents of Greater Britain, whether they identified with the federalists or not, argued that it was essential to reconfigure relations between the \"mother country\" and the settler colonies, so as to form an enduring and closely integrated global polity, a worthy challenger to the reinvigorated United States, the purportedly rapacious Russians, and the nascent German state. Through a policy of massive and systematic emigration, moreover, they hoped simultaneously to strengthen the colonies and diffuse the conjoined dangers of over-population and \"socialism\" in the United Kingdom\u2014in the process transfiguring the emigrants into loyal imperial subjects.\n\nA variety of different models were proposed. For some, including both Dilke and Goldwin Smith, the key was to animate the idea of a planet-spanning British national-racial community and they stopped short of suggesting significant constitutional restructuring, believing it to be counterproductive.5 Instead, they relied on the moral power of kinship and sentiment. This vision ran parallel to an important strand in the federalist literature, which demanded the recognition and fortification of the (supposedly) strong emotional and cultural bonds between the people of the United Kingdom and the colonies. For others, however, the development of a powerful Greater Britain necessitated the creation of non-legislating Advisory Councils, or expanding the scope of the Privy Council, so as to give voice (but not substantive power) to the colonists.6 The more ambitious federalists demanded the construction of novel institutional structures, the establishment of a system of equal representation for the colonies, and, in its most radical form, the creation of a global federal state.7 As Seeley commented\u2014most probably drawing on Robert Browning's poignant imagery\u2014the result would be a \"world-Venice, with the sea for the streets.\"8\n\nThe monarchy played two important functions in the political theory of Greater Britain. Although analytically separable, both of these lines of reasoning were woven together through the fabric of imperial discourse. First, the institution, stretching back over centuries, could act as a temporal stabilizer, an anchor of permanence and constitutional fidelity in a reconstituted Greater Britain. Critics of such designs would be reassured that their fears of fundamental transformation were groundless\u2014that a thread of historical continuity ran through the proposals. The delicate balance between change and stability was an essential topic to confront in a Whiggish political culture that venerated the past, disdained revolutionary institutional upheavals, and drew constant inspiration from the evolutionary gradualism elaborated most famously by Edmund Burke.9 Secondly, Queen Victoria\u2014or at least an idealized representation of her\u2014served as the linchpin for a sense of global national identity. It was thought that the renown and respect that she (and the institution of monarchy itself) generated knit the distant peoples of her dominions in close communion. This sense of an imagined community was a necessary though not sufficient condition for the creation of a coherent global polity, and it was something that many of the advocates of Greater Britain, of nearly all political stripes, stressed repeatedly. Moreover, a specific (and largely inaccurate) image of Victoria figured in a distinctly \"civic humanist\" (or what might be labeled \"civic imperial\") strand of imperial political thought. Above the fray of party political intrigue, and acting as a beneficent and revered ruler\u2014indeed as a modified expression of the Bolingbrokian humanist ideal of the Patriot King\u2014she was seen as embodying the communal values essential for linking together the colonial populations and the \"mother country.\"\n\nThe British empire was a complex mosaic of political regimes, social institutions, and juridical forms. The proponents of Greater Britain were determined to carve out from this intricate multiracial assemblage a unified and homogeneous political-economic space. This was no easy task, and the conception of Greater Britain relied as much on the sentimental pull of the name and its associations as it did on any systematic theoretical explication. Its advocates often relied on the emotive force of what might be termed the _iconographic order_ of Greater Britain, the imaginative system of resonant symbols, stirring rituals, and vague poetic imagery that, in their writings and pronouncements, provided a coherent picture of a shared past, a troubled present, and a glorious destiny. This order comprised a constellation of semi-articulated markers of identity that sought to provide an authoritative conception of a (possible if not actual) harmonious, productive, and progressive global nation\u2014the Union Jack, Britannia ruling the waves, the ancient constitution, hardy and loyal colonists, the sacred freedoms of the English. Seeley, with typical condescension, argued that the people were \"necessarily guided by a few large, plain simple ideas.\"10 One of the most powerful of these ideas was that of the patriot monarch, standing watchful guard over her magnificent realms, and signifying permanence, unity, and strength.\n\nIn subsuming the scattered Anglo-Saxon colonies under a single, emotively charged name linked indelibly to the self-understanding of the British, the promoters of Greater Britain attempted to draw distant lands within the orbit, indeed to the very heart, of the metropolitan political imagination. The name itself implied two dimensions, one spatial, one moral. Spatially it referred to the vast scope of the British nation, stretching across the planet. This was an important issue in an age obsessed with the increasing size of political units. As one federalist warned, the \"present growth of the United States and Russia threatens to dwarf the old states of Europe, and wisdom counsels union to the English nation.\"11 Froude concurred: \"These are not the days for small states: the natural boundaries are broken down which once divided kingdom from kingdom; and with the interests of nations so much intertwined as they are now becoming, every one feels the benefit of belonging to a first-rate Power.\"12 Morally it referred to the superiority of both the people and the political system\u2014each interacting with and shaping the other in a complex dance of political progress\u2014of this great agglomeration of territory; Greater Britain was fully deserving of a providentially ordained position of global leadership. \"The fruits of political union will... be found,\" argued one excited federalist in 1885, \"in the progress of an intelligent and prosperous people, marching in the van of civilisation, for the benefit not only of themselves, but of mankind, bound together in one nationality, though widely scattered over the broad surface of the globe.\" He concluded: \"To this position the world's history offers no parallels; beside it Rome's range of influence sinks into comparative insignificance.\"13 But this vision was deeply unrealistic, not least because its devotees failed to comprehend either the skepticism of colonial elites or its lack of political feasibility in Westminster. The dissonance between fantasy and reality was typical of much of the imperial thought of the age.\n\nConstitutional Patriotism and the Monarchy\n\nThe use of the Queen, in a dignified capacity, is incalculable. Without her in England, the present English government would fail and pass away.14\n\n\u2014WALTER BAGEHOT\n\nThe popularity of the monarchy has waxed and waned over time. The nineteenth century saw considerable fluctuations in its fortunes, as the British political system underwent profound transformation: the compromise settlement of 1688 and the constitutional lineaments of the _ancien r\u00e9gime_ were uprooted and transfigured as a (quasi-)democratic polity slowly emerged. The monarchy demonstrated remarkable resilience and flexibility, adapting to the rapidly changing society, adopting new public faces and political roles. The Hanoverian monarchy had been associated with old age, infirmity, corruption, and greed, and the young queen Victoria, ascending to the throne in 1837, consequently appeared as a breath of fresh air, revitalizing the image of a moribund institution. Apart from a brief but vocal efflorescence of anti-monarchical sentiment in the late 1860s, Victoria was to remain a popular and venerated Queen.15 The reasons for this popularity are multiple and varied, and would include, at a minimum, the ideological functions of elaborate royal ceremony, the respect that her demeanor and apparent disdain for aristocratic mores generated, the vital role of the burgeoning mass media in projecting her into the imaginative lives of the public, and the close association of the monarchy with philanthropic endeavor.16 Historians continue to debate the balance between these factors, but for our present purposes what matters most is simply that \"Victoria was central to the ideological and cultural signifying systems of her age,\" and that this was likewise true of the iconographic order of Greater Britain.17\n\nDrawing on the ideas of the French syndicalist Georges Sorel, J.D.B. Miller once claimed that imperial federation was a \"utopian\" project.18 As such, in Sorel's terminology, it was an \"intellectual product,\" a fragile construct too weak to engender a powerful attachment to its cause. The \"effects of utopias,\" Sorel argued dismissively, have \"always been to direct men's minds towards reforms which can be brought about by patching up the system.\" As such, they were poor at galvanizing excitement and in generating affective bonds. This is a revealing way of comprehending the historical predicament of the proponents of a Greater British polity. However, it is not a self-portrait that they would have recognized. For many, the idea acted more as a Sorellian _myth_ , the antithesis of utopia. For Sorel, the myth acted as an ideal, a picture of the future, behind which people would coalesce and which served consequently to unify and motivate transformative action. Myths, he argued,\n\n... must be judged as a means of acting on the present; all discussion of the method of applying them as future history is devoid of sense. _It is the myth in its entirety which is alone important_ : its parts are only of interest in so far as they bring out the main idea.\n\nUnlike utopias, myths could not be refuted; they existed as an image in the mind, and acted as a guide to action in the present.19 They embodied the intuitive, emotional, and symbolic aspects of political action. Greater Britain was seen by many of its advocates in this sense, hence their common reluctance to propound any specific plans and their reliance on vague rhetoric about unity, glory, and destiny. Moreover, their ideas fell prey to the same problems that beset Sorel's thought. The main dilemma appeared in attempting to translate the myth of global unity, of a providential Greater Britain, into a plausible scheme in an intellectual and political environment both skeptical of their general ambitions and lacking in the revolutionary impetus that a Sorellian myth would require to function adequately (if at all).\n\nFor many of the promoters of Greater Britain, then, vagueness was a virtue. Rather than explicating systematic theoretical plans for the future, a course of action that many considered counterproductive, they often relied on passionate appeals to emotion, to shared values, and to the moral edification of their loosely sketched ideas. (This began to change in the late 1880s and through the 1890s, when the number of concrete proposals increased, with the result that, as the skeptics had warned, the plans were frequently dismissed as unworkable contributions to \"practical politics.\") One of the perennial problems of political theory concerns the complex relationship between ideas (and ideals) and the resources necessary to motivate action in their name. Far too often political theorists propound visions of society, and of the world more generally, that appear to most observers to be detached from the vicissitudes of everyday life. British imperial theorists were acutely aware of this problem. Not only were they keen to stress that their ideas fell within the domain of \"practical politics,\" they also placed great emphasis on the role of sentiment in political life. \"Patriotism,\" proclaimed Froude, \"may be sentimentalism, but it is sentimentalism nevertheless which lies at the root of every powerful nationality, and has been the principle of its coherence and growth.\"20 Such sentiments were generated and reproduced over time by the motivational power of a rich tapestry of symbolism, ritual, and myth. An idealized image of the constitution performed such a function in the iconographic order.21 \"All nations have their idols, the creatures of their own hands, which having manufactured, they bow down before as gods... The Englishman adores the British Constitution.\"22 It was, after all, the constitution, signifying strength and stability, which had kept at bay the revolutionary fervor that had washed over Europe, both in the 1790s and in the mid-nineteenth century.23 And it was the constitution, so it was thought, that guaranteed the conditions necessary for protecting freedom and encouraging prosperity, thus underpinning the fragile sense of progress, both moral and material, so vital in Victorian consciousness.\n\nThe monarchy was inescapably embedded in this Panglossian constitutional patriotism. Indeed, it was fundamental to the self-understanding of the vast majority of Victorians. It was a common imperialist claim that the monarchy generated, as Walter Bagehot had asserted, a \"mystic reverence\" and a \"religious allegiance\" amongst the people. A broadly Bagehotian understanding of the \"dignified\" elements of the constitution pervaded the discourse of Greater Britain. Bagehot wrote in the _English Constitution_ (1867) that the importance of the Queen lay in the fact that \"the mass of our people would obey no one else, that the reverence she excites is the potential energy\u2014as science now speaks\u2014out of which all minor forces are made, and from which lesser functions take their efficiency.\"24 Loyalty to, and affection for, the dignified elements of the constitution were far greater than that catalyzed by the \"efficient\" facets. Froude noted that the loyalty of British subjects worldwide was principally to the Queen.25 Egerton argued that there \"is in the Colonies... an abundant loyalty to the Queen and to the British flag, but there is little loyalty to the Imperial Parliament.\"26 Edward Salmon, a keen federalist, after stressing the \"innate loyalty of true Britons,\" likewise proclaimed that \"the great majority of Englishmen are enthusiastic supporters of the Throne.\" It is, he continued, \"an emblem of Imperial unity\u2014a golden incarnation of the brotherhood of Australia, Canada, the Cape, Great Britain, and other centres over which the Union Jack floats.\" \"What the disappearance of the monarchy would mean is pretty clear. With it would come the break-up of the Empire.\" The lesson of all of this was straightforward: \"[T]he Crown and the Colonies are rapidly becoming interdependent.\"27 Although this was perhaps more aspiration than astute political analysis, such beliefs led many of the proponents of Greater Britain to stress the importance of the monarchy in their plans for a global polity.\n\nThe relationship between crown and colonies would also be reciprocally beneficial. Imperial federation, and a strong association with the aims of Greater British unity, would aid the monarchy in times ahead. The royal family could and should play an active role in advocating, and in governing, the new polity. The future status of the colonial empire was uncertain, argued Salmon, and the chances of success for the federalist movement were slim without royal support: it was up to \"the action of the Crown\" whether or not Greater Britain had a future. And at a time of increasing criticism of the royal family, and in particular the more feckless offspring of Victoria, this would be a wise course of action. De Labilli\u00e8re suggested that the sons and brothers of the sovereign might act as colonial governors, thus entrenching the connections between the different parts of the colonial system. \"Its head, the Sovereign, and Royal Family, would be felt to belong, as much to Australia, Canada, South Africa, as to the people of the British Isles\u2014just as much as the Federal Parliament in which they would all be directly represented.\" And again: \"The sphere of its occupations, and of its usefulness might be greatly extended, by its members being brought into constant, advantageous and agreeable contact with the people in all our dominions.\"28\n\nNevertheless, despite the desire of many of the federalists and the understanding amongst the leadership of the Imperial Federation League (IFL) that royal patronage was essential if they were to succeed, royal attitudes to federation were mixed. Victoria was far more taken by the orientalist splendor of the imperial dependencies, India in particular, than she was with the settlement colonies. Her interest in the latter was \"intermittent at best.\"29 It would seem that the Queen's heart lay always, like that of her beloved Disraeli, in the East\u2014it was, after all, with the help of her loyal prime minister that she became Empress of India in 1876. Despite this, a number of other members of the royal family were active supporters of imperial federation. One of Victoria's daughters encouraged her to read _The Expansion of England_ : \"It is wonderful and so statesmanlike, so farsighted, clear, and fair.\" The Prince of Wales likewise expressed his admiration for Seeley's vision of Greater Britain.30 The most outspoken support came from Victoria's son-in-law, the Marquis of Lorne. A somewhat dilettantish man of letters, Liberal Unionist MP, and finally Governor-General of Canada, he argued in _Imperial Federation_ (1885) for relatively limited imperial reform, expressing his disquiet at more ambitious federalist plans advocating an overhaul of parliamentary institutions. Instead, he recommended the creation of an \"Advisory Council\" incorporated within a reconstructed Privy Council. Rather unsurprisingly, he emphasized the role of the Queen as a focus of global national identity, capable of generating loyalty and a sense of unity amongst her scattered subjects. During her reign, he maintained, the tie between the \"mother country\" and the colonies in particular was regarded,\n\n... with reverence and affection, and it is that which enables all citizens of this Empire to call themselves the subjects of the Queen. Her name has acquired a magic force, the strength of which can only be realized by those who have heard the national anthem sung by men, women, and children in regions many thousands of miles distant from England. It matters not whence it be heard, for in whatever part of the world her standard flies, that strain of music, and the thoughts which come with it, make the voices ring with the true loyalty that reverences women and loves the glorious sovereignty of freedom. The fervour to be heard in such notes should count for something in the calculation men are making as to the chance of keeping shoulder to shoulder wherever British hearts are beating.31\n\nVictoria was thus a central element in the iconographic order of Greater Britain, her name alone exerting a \"magic force,\" her image linked by musical and visual rituals of national identification to the idea of freedom itself. And, Lorne stressed, the power of such emotions was an important element in fashioning and sustaining global British unity, alongside more traditional concerns with shared security interests and cold economic calculation.\n\nAn especially clear evocation of the perceived role of the Crown was provided by Francis De Labilli\u00e8re, originally an Australian colonist, barrister of the Middle Temple, and a driving force behind the foundation of the IFL, of which he served subsequently as honorary secretary.32 De Labilli\u00e8re was a prolific booster of what he termed the \"great Constitutional Empire of Greater Britain,\" and the monarchy played an important role in his plans.\n\nFor our Empire... Monarchy, even were it not the existing form of government, will have the greatest advantages. It will impart to it greater dignity, in many ways. It would be preferable, were it only to save us from a periodical scramble for the chieftainship of the nation, between rival candidates, with months of noise, abuse, exaggeration, and party trickery.33\n\nIn this passage we witness, alongside the Bagehotian phraseology, an example of the widespread anxiety about the importation of American \"machine politics\" into British life, a fear that was especially pronounced during the 1880s.34 There was apprehension that public life would be degraded by incessant party squabbling, the unfortunate but inevitable consequence of democratic politics. In a Greater Britain, governed by a revered constitutional monarch, such a problem would be far less marked.\n\nFurthermore, focusing on the centrality of the monarchy allowed proponents of a federal Greater Britain to confront another challenge. One of the main criticisms leveled at federation, as a general mode of political organization, was that it ran counter to the notion of unitary sovereignty.35 It lacked, that is, a single determinate locus of political authority. For the federalists, Victoria, as sovereign, could provide a focal point, a substitute vision for that of the unitary sovereign state. In _Imperium et Libertas_ (1901) Bernard Holland argued that the Crown played a key role in the relations between the \"mother country\" and the colonies, providing a pivot for the \"confederate\" empire. However, as a new era was beginning to dawn, so too was there a \"rise in importance of the Throne.\" In a politically decentralized federal empire, the \"spiritual sovereignty\" of the Crown would be of ever-increasing significance. \"It is not merely the symbol but the real bond of unity\" and to this \"central point all lines converge from all the ends of the earth.\"36 As political power was devolved, so symbolic power was reaffirmed. A monarchical federation therefore offered the most effective way to avoid issues that had long plagued more conventional notions of federation. This partly explains why some federalists were keen to argue that the American constitution, which they so often held up as a model to emulate, was simply a derivation of the late eighteenth-century British constitution. J. N. Dalton, for example, presented the American brand as a subtle reworking of existing British political forms, and even claimed that the United States was governed by the \"Imperial Houses of Parliament in Congress.\"37 The President, in this vision, was a temporary elected monarch. American institutions were thus assimilable to the conventions of British political thought; their apparently anomalous, even antithetical, structures were merely an evolutionary development of long extant British ideas. Federation was not so alien after all. The federalists were selective in their cultural and political appropriation: in reading America through British eyes, they sought to square the circle of federation and centralized sovereign authority.\n\nThe liberal statesman W. E. Forster, a key imperial ideologue and the first president of the IFL, stressed the linkage between historical continuity, patriotism, and the Crown. In discussing the conditions necessary for the continuance of Greater Britain, he argued that \"allegiance to one monarch\" was at the top of the list, and that the \"very essence of such continuance is a common patriotism;\u2014the feeling throughout all the different communities that, notwithstanding the seas that roll between them, they are yet one nation; and that all their inhabitants are fellow-countrymen.\" He maintained that the English-speaking peoples of the world shared a common culture, for they \"look at life and its problems, especially the problems of Government, with much the same eyes everywhere.\" This included the Americans, and he claimed that the British monarchy had more in common with the United States republic than it did with any other state. Indeed, he argued that Britain had carried the torch of republicanism further than the Americans had done:\n\nMany millions of our race prefer a Republic to a Monarchy. Yes, but remember these facts: first, that we so treated their fathers that we almost forced them to become Republicans; Secondly, that many of them now acknowledge that at least it is a moot question whether, as regards the real meaning of the word, and its true significance, our Limited Monarchy is not a more complete Republic than their own.\n\nMoreover, the loyalty of the colonists was specifically to the Crown. Why was this so?\n\nNot merely because they honour and respect our Queen; not merely because of their personal feeling towards the Royal Lady under whose rule they have grown from childhood to lusty youth; but because they are as proud as we are of the traditions of our history, and as convinced as we are of the actual advantages of a hereditary executive.38\n\n\"Republicanism,\" the monarchy, and the empire were indissolubly yoked together.\n\nCivic Republicanism and the Colonial Order\n\nIt might seem that there is a certain irony attendant on linking the political theory of Greater Britain to the monarchy. After all, the phrase was coined originally by the radical liberal politician Charles Dilke, who was also one of the most reviled republicans of the age, a figure ostracized by Queen Victoria and her loyal followers.39 Miles Taylor has claimed, however, that Dilke was concerned more with the issues that had troubled the classical republicans and their post-Renaissance successors than with the existence of the monarchy itself.40 In other words, he was interested more in the nature of political authority\u2014in challenging the scope of and constitutional limitations on popular representation\u2014and the character of civic life than with any drastic anti-monarchical scheme. Attention to the protection of political stability, maintaining limits on the power of government, and encouraging an active and patriotic citizenry permeated _Greater Britain_ (1868). It is this version of civic republicanism on which the ensuing discussion focuses. It comprised an important but neglected strand of imperial political thought, infusing much of the debate over the future of the settler empire, and in particular the envisioning of a Greater British polity. I return to the topic in chapter 12.\n\nFor Stefan Collini, Victorian political thought was marked by \"survivals and mutations\" of the earlier language of civic humanism, and as John Burrow, Eugenio Biagini, and Frank Prochaska have all stressed, Victorian liberalism, amorphous and multidimensional as it was, frequently served as a vehicle for time-honored civic humanist ideas, which it incorporated and transformed in various ways.41 Translated via the transmission belts of Whiggism from the early modern debates into the late nineteenth century, republicanism played a significant, though by no means dominant, role in shaping political thinking. It was common at the time to identify Britain as a republic: Tennyson called the United Kingdom a \"crown'd republic,\" the positivist leader Frederic Harrison claimed that \"England\" was \"an aristocratic republic,\" whilst Bagehot argued that \"a Republic has insinuated itself beneath the folds of a Monarchy.\"42 None of these were pure republican ideals, all were partial, compromised, and mixed various political sensibilities and vocabularies\u2014as had their eighteenth-century predecessors.43\n\nCivic imperialism\u2014humanist language and themes applied to the expanses of the empire\u2014permeated the discourse of Greater Britain, centered as it (often) was on equalizing political relations between the \"mother country\" and the colonies, protecting the constitutional freedoms of its inhabitants, challenging the crass materialism and excess luxury of the modern age, and fostering a global nation of virtuous, vigorous, imperial patriots. Found in writers as diverse as Seeley, Dilke, and even Bryce, it was displayed most prominently in Froude's _Oceana_ (1886), a book written explicitly as an updated version of James Harrington's utopian fantasy _The Commonwealth of Oceana_ (1656). Froude's musings were pervaded by a sense of longing for the forgotten glories of the English past, of hardy yeomen, agrarian splendor, and the \"genius of English freedom\"\u2014republican nostalgia writ large, and drawn upon in the name of shaping the present and the future. A \"sound nation,\" he wrote,\n\n... is a nation composed of sound human beings, healthy in body, strong of limb, true of word and deed\u2014brave, sober, temperate, chaste, to whom morals are more important than wealth or knowledge\u2014where duty is first and the rights of man are second\u2014where, in short, men grow up and live and work, having in them what our ancestors called the \"fear of God.\"44\n\nSuch was Froude's dream for the British body politic\u2014simultaneously stretching back in time, and projected forwards. It was a dream common to many of the Greater British advocates, though most of their proposals were not quite as austere.\n\nVictoria was sometimes (though certainly not always) represented in the political theory of Greater Britain as the embodiment of a long-standing fantasy in British political consciousness: a nineteenth-century incarnation of the model found in Bolingbroke's late humanist tract, _The Idea of a Patriot King_ (1738).45 This was not an explicit comparison, a direct and self-conscious reference to a long-dead thinker, but key features and themes of earlier interpretations of patriot kingship were invoked frequently by imperial theorists. For Bolingbroke, the ideal monarch would stand above party strife, defending the constitution at home and promoting and protecting trade abroad. They would display three proud faces to the world: the enemy of corruption, the father of the people, and the strong but beneficent leader of a vibrant commercial people. Moreover, the patriot king was to stand firm against dangerous entanglement on the European mainland, secure in the belief in Britain's global maritime destiny. As David Armitage has demonstrated, this idea had multiple afterlives, and it was drawn upon by radicals, revolutionaries, and later by Tories in the impassioned ideological milieu of late eighteenth- and early nineteenth-century Britain. Due to its lack of specificity, the image was \"perennially applicable.\" Following the death of William IV, the last monarch to whom the direct appellation of \"Patriot King\" was applied\u2014more as desire than accurate representation\u2014explicit references to the humanist dimensions of the Bolingbrokian idea seem to have disappeared. Indeed, from the 1830s onwards, and in particular in the hands of Disraeli and the Young England movement, Bolingbroke was retrospectively incorporated into the Tory ideological field.46 This was not the end of the story: the ideas that he had propagated, and that had acted as common political currency for generations, remained in circulation and can be seen resurfacing, albeit in a translated form, in late Victorian imperial thought. To many of the proponents of Greater Britain, Victoria exemplified all the moral and leadership qualities that the patriot king was supposed to possess. This was the key to her symbolic power. She also faced similar dangers. Whereas the Bolingbrokian target was oligarchic corruption and the decay of virtue, so the proponents of Greater Britain were keen to confront the corrosiveness of materialism, the greed and purported lack of patriotism displayed by capitalist businessmen, the ideas of the utilitarian political economists, and the moral decline of Britain in general. Political action in the name of public duty and the common good, not private interest, was the guarantee of the continued greatness of Britain.\n\nSir Frederick Young provided perhaps the most explicit articulation of this vision. An ardent liberal, Young had been a close associate of E. G. Wakefield in the colonization of New Zealand, and was a long-standing and tireless proponent of imperial federation. Instrumental in establishing the Royal Colonial Institute, of which he served as honorary secretary, he was also a prominent voice in the IFL, and later the British Empire League.47 In his contribution to an 1876 collection of letters on federation published originally in _The Colonist_ , Young stressed the necessity of binding the \"whole Empire into a homogeneous and indissoluble whole,\" and he demanded a \"radical reconstruction of the Imperial representative body.\"48 Indeed, he thought that the whole scheme was best conceptualized as a planetary \"national federation.\"49 This was a dream to which he remained faithful until his death over thirty years later.50 The monarchy was central to Young's scheme. His most revealing comments on the topic are found in _Exit Party_ (1900), a book charting (with stunning inaccuracy) what he saw as the decline of party politics in Britain. He wrote in an ode to Victoria:\n\nHer Most Gracious Majesty has, thank God, been preserved to us to the present hour, if it could be imagined possible, winning more and more veneration, the admiration, and the love of many millions of her people at home and beyond the seas by her supreme tact as a ruler, no less than her charming and beautiful womanly sympathy prompting her constant and wonderful personal activity in her unceasing desire for the promotion of the welfare of her subjects, throughout the length and breadth of her world-wide dominions.51\n\nLike many other commentators, Young employed a heavily gendered conception of the Queen, as a mother figure displaying not only the traditional stereotypical \"masculine\" qualities of leadership\u2014strength, fortitude, strategic calculation\u2014but adding to them such \"feminine\" qualities as grace, tact, and sympathy; an iron fist in a velvet glove. Just as Britain was the mother country to the colonists, so Victoria was the figurative mother to all the peoples of the global nation. This was not, however, an entirely new addition to the multifaceted reception of the idea of the patriot king. Bolingbroke had, after all, looked backwards to Elizabeth as the embodiment of the values that he cherished and desired to see replicated in future leaders. It is not a coincidence that Victoria herself was often linked in the public imagination with Elizabeth.52 Indeed, the Elizabethan age played an important role in the iconographic order of Greater Britain. Froude celebrated the \"forgotten worthies\" of the time, the old sea dogs who had helped make Britain great.53 Seeley located the origins of the \"national\" policy\u2014expansion at its core\u2014in the years of Elizabeth's rule.54 In particular, Young admired Victoria for standing above the fray of political intrigue, guiding the ship of state without being distracted by wearisome party machinations. In this, he argued\u2014implausibly\u2014she differed from many of her predecessors. \"With regards to her Parliament... her relations have been of the utmost and most uninterrupted harmony from the first moment she ascended the throne.\"55 Writing at the end of her long reign, Young hoped that her legacy would endure. Above all, it was essential to have a constitutional monarch standing at the head of a global imperial state. Citing James Douglas, a Canadian resident in the United States, he believed that such a monarch,\n\n... would represent in his person the traditions of the past, and embody the historical continuity of the race. Powerless to interfere arbitrarily, but not therefore bereft of influence, the creature of his subjects, though nominally the controller of their fate, his right to avert injustice and enforce fair play would exert a restraining power. Such a nominal head, called by whatever name the republican principle of the Federation would allow to be applied, would be a less dangerous and more picturesque chief than an elected president.56\n\nVictoria was, De Labilli\u00e8re likewise contended, the \"most perfect constitutional Sovereign that ever presided over a free people.\"57\n\nThe gap between vision and reality was sizeable, even by the standards of imperial political thought. Not only was Victoria more enamored with India than with the colonies, the representation of her as a disinterested leader, above and beyond party, was wholly incorrect. The political power of the monarch had been in steady decline over the course of the century, but it was still considerable, and far exceeded the limited rights ascribed to it by Bagehot.58 Victoria meddled incessantly in the day-to-day affairs of her ministers, and she perceived her role\u2014especially the prerogative of forming ministries\u2014as central to the constitutional machinery of the state.59 But the notion of her as an impartial leader was a powerful illusion. Victoria's \"civic publicness\" had, as John Plunkett remarks, been fostered most especially in the early years of her reign, when she was seen to represent a radical departure from her staid Hanoverian predecessors and the residues of Old Corruption, and during the second half of the century a newly vigorous and pliant media helped to sustain a potent image of her role. This image lingered throughout the rest of her reign, despite shifts in the intensity of adoration.60 Victoria was certainly patriotic, but she was no patriot queen.\n\nConclusions\n\nIn 1837 there was much talk of dissolution; in 1897 there is thought only of unity.61\n\n\u2014EDWARD SALMON\n\nThe monarchy, the monarch, and the empire were threaded together in the iconographic order of Greater Britain. Fantasies for politically unifying Britain and its colonies were grounded in a palpable sense of anxiety; fear for the future drove the construction of an image of the world rewritten according to a British script. Imperial unity became a prominent topic during the second half of Victoria's reign because it was viewed as a necessary response to domestic political pressures and foreign competition in an age of increasing globalization. For many, it was the only way of keeping Britain great.\n\nThe monarchy was essential to this dream. This chapter has sketched the outlines of that vision\u2014a more detailed examination would also explore the important role played by the ideal of the patriot queen in post-Repeal Act, pre-Fenian nationalist Ireland during the 1850\u201360s, the debate over Canadian federation (1867), and the attempt to \"unite\" South Africa in 1879\u201380. In all, Victoria stood as a symbolic marker of national and imperial sentiment, a focal point for loyalty. As an imperial figurehead, the matriarch of the British nation, she played a critical function in the matrix of British global identity and power. It was in this role that she could be seen as picking up the mantle of the patriot queen. The royal family might be criticized for waste, profligacy, inefficiency, or any number of other failings, but its existence in the British constitutional order was rarely questioned, even if the degree of its power was a subject of constant debate. The proponents of Greater Britain, on the whole, tended to reflect this common understanding of the importance of a constitutional monarchy. By emphasizing the centrality of the monarchy in their conceptions of the future, they hoped to ameliorate fears about the radical nature of many of the plans being adumbrated, and to root them in the soil of British historical tradition. A planet-spanning imperial polity\u2014even a global state\u2014was to be their gift to Britain, the world, and posterity itself. A timeless embodiment of the glory of the nation, ensconced safely and soundly at the center of a stable constitutional order, the monarch was at the core of this vision.\n\n1 Tennyson, \"To the Queen\" [1859], in _Poetical Works_ (Oxford, 1953), 441. Italics in original.\n\n2 Tennyson, \"On the Jubilee of Queen Victoria\" [1887], _Poetical Works_ , 784. On Tennyson and the empire, see especially Matthew Reynolds, _The Realms of Verse, 1830\u20131870_ (Oxford, 2001), pt. 3; Tricia Lootens, \"Victorian Poetry and Patriotism,\" in _The Cambridge Companion to Victorian Poetry_ , ed. Joseph Bristow (Cambridge, 2000), 255\u201380.\n\n3 Egerton, _A Short History of British Colonial Policy_ (London, 1897).\n\n4 Dilke, _Greater Britain_ , 2 vols. (London, 1868). Other early texts include: John Robinson, \"The Future of the British Empire,\" _Westminster Review_ , 38 (1870), 47\u201374; John Edward Jenkins, \"Imperial Federalism,\" _Contemporary Review_ , 16 (1871), 165\u201388; J. A. Froude, \"England and Her Colonies,\" _Fraser's Magazine_ , 1 (1870), 1\u201316; Andrew Robert Macfie, \"On the Crisis of the Empire,\" _Proceedings of the Royal Colonial Institute_ , 3 (1871\u201372), 2\u201312.\n\n5 See Dilke, _Problems of Greater Britain_ (London, 1890), vol. 2. For Smith's comments on \"Greater Britain\" as a moral community, see his letter to Professor Tyndall, October 6, 1882, in _A Selection from Goldwin Smith's Correspondence_ , ed. Arnold Haultain (London, 1910), 137.\n\n6 See, for example, Earl Grey, \"How Shall We Retain the Colonies?,\" _Nineteenth Century_ , 5 (1879), 935\u201354; John Sutherland, _Imperial Federation_ (London, 1885).\n\n7 The most explicit account of global statehood is in Seeley, _The Expansion of England_ , pt. 1. For the details of his analysis, see chapter 11.\n\n8 Seeley, _The Expansion of England_ , 288. See also Robert Browning, \"A Toccata of Galuppi's\" [1855], in _Browning: Poetical Works, 1833\u201364_ , ed. Ian Jack (Oxford, 1970), 579.\n\n9 On the centrality of history and tradition in Victorian public culture, see, in general, Stefan Collini, _Public Moralists_ (Oxford, 1991); Burrow, _Whigs and Liberals_ (Oxford, 1988).\n\n10 Seeley, _The Expansion of England_ , 190.\n\n11 Samuel Wilson, \"Imperial Federation,\" _National Review_ , 4 (1884), 386.\n\n12 Froude, \"England and Her Colonies,\" 15. See also Froude, \"England's War\" [1871], reprinted in _Short Studies on Great Subjects_ , 5 vols. (London, 1907), 3:276.\n\n13 Young, _An Address on Imperial Federation_ (London, 1885), 23. On the role played by Rome and Greece in late Victorian imperial thought, see chapter 5.\n\n14 Bagehot, _The English Constitution_ [1867], ed. Paul Smith (Cambridge, 2001), 34.\n\n15 On the status and popularity of anti-monarchical republicanism, see Richard Williams, _The Contentious Crown_ (Aldershot, 1997); David Nash and Anthony Taylor, eds., _Republicanism in Victorian Society_ (Stroud, 2003); Anthony Taylor, \" _Down with the Crown_ \" (London, 1999); Frank Prochaska, _The Republic of Britain, 1760\u20132000_ (London, 2000). The majority of commentators now agree that there was little mainstream support for (anti-monarchical) republicanism. Craig, \"The Crowned Republic?,\" _Historical Journal_ , 46 (2003), 167\u201385.\n\n16 David Cannadine, \"The Context, Performance, and Meaning of Ritual,\" in _The Invention of Tradition_ , ed. Eric Hobsbawm and Terence Ranger (Cambridge, 1993), 101\u201364; William Kuhn, _Democratic Royalism_ (London, 1997); Walter Arnstein, _Queen Victoria_ , (Basingstoke, 2003), ch. 4; Dorothy Thompson, _Queen Victoria_ ; John Plunkett, _Queen Victoria_ (Oxford, 2003); Frank Prochaska, _Royal Bounty_ (London, 1995).\n\n17 The quotation is from Homans and Munich, \"Introduction,\" 2. For the historiographical debate, see Craig, \"The Crowned Republic?\"; Arnstein, _Queen Victoria_. On the importance of the monarchy for empire, see G. R. Searle, _A New England?_ (Oxford, 2004), 119; Thompson, _Imperial Britain_ (London, 2000), 7.\n\n18 Miller, \"The Utopia of Imperial Federation,\" _Political Studies_ , 4 (1956), 195\u201397.\n\n19 Sorel, _Reflections on Violence_ [1908], ed. Jeremy Jennings (Cambridge, 1999), 28\u201329, 116\u201317. Italics added. Miller intimates but does not develop this point.\n\n20 Froude, \"England and Her Colonies,\" 6. See, for other examples, Forster, \"Imperial Federation,\" _Nineteenth Century_ , 17 (1885), 205; Anon., \"The Federation of the British Empire,\" _Westminster Review_ , 128 (1887), 492.\n\n21 On the importance of the constitution, and the way in which it was contested, see the essays in James Vernon, ed., _Re-Reading the Constitution_ (Cambridge, 1996); J. P. Parry, _The Politics of Patriotism_ (Cambridge, 2006).\n\n22 Froude, \"England's War,\" 136.\n\n23 Leslie Mitchell, \"Britain's Reaction to the Revolutions,\" in _The Revolutions in Europe, 1848\u20131849_ , ed. R.J.W. Evans and Hartmut Pogge von Strandmann (Oxford, 2000), 83\u201399.\n\n24 Bagehot, _The English Constitution_ , 4, 167. Cf. Michael Bentley, _Lord Salisbury's World_ (Cambridge, 2007), ch. 6. Note that Bagehot himself was skeptical of the claim often made by the advocates of Greater Britain that a shared race (defined in cultural terms) resulted in shared interests: \"It is begging the question to assume that the ties of common race and language make nations better inclined to enter into active political alliance or better suited for harmonic acting.\" Bagehot, \"An Anglo-Saxon Alliance\" [1875], in _The Collected Works of Walter Bagehot_ , ed. Norman St John-Stevas (London, 1965\u201386), 8:356\u201357.\n\n25 Froude, _Oceana_ (London, 1886), 221\u201322.\n\n26 Egerton, _Short History_ , 459.\n\n27 Salmon, \"The Crown and the Colonies,\" _National Review_ , 14 (1889\u201390), 200 and 202. For his views on federation, see Salmon, \"Imperial Federation,\" _Fortnightly Review_ , 58 (1900), 1009\u201319.\n\n28 de Labilli\u00e8re, _Federal Britain_ (London, 1894), 248\u201349.\n\n29 Arnstein, _Queen Victoria_ , 180. On Victoria's longstanding love of and involvement with India, and the lack of connection between this and her public persona, see Miles Taylor, \"Queen Victoria and India, 1837\u201361,\" _Victorian Studies_ , 46 (2004), 264\u201374.\n\n30 Letter by the Crown Princess of Germany to Victoria, May 25, 1884, in _The Letters of Queen Victoria, 1879\u20131885_ , ed. George Buckle (London, 1926), 3:506; Sir Francis Knollys, letter on behalf of the Prince of Wales, to J. R. Seeley, May 13, 1887, Seeley Papers, University of London Library, MS903\/1B\/19. He was also President of the Royal Colonial Institute.\n\n31 Lorne, _Imperial Federation_ (London, 1885). In a letter to Sir Frederick Young, Lorne wrote that he had \"little faith\" in the idea of a new imperial parliament. Lorne to Young, April 10, 1884, Young Papers, Cambridge University Library, RCMS 54\/2\/3.\n\n32 On his pivotal role, see the letter from W. E. Forster, the president of the IFL, to de Labilli\u00e8re, May 24, 1885, in the IFL Minute Book, British Library Add Ms, 62778, 74.\n\n33 de Labilli\u00e8re, _Federal Britain_ , 248\u201349.\n\n34 See, for example, Paolo Pombeni, \"Starting in Reason, Ending in Passion,\" _Historical Journal_ , 37 (1994), 319\u201341; and Murney Gerlach, _British Liberalism and the United States_ (Basingstoke, 2001).\n\n35 Amongst the most prominent advocates of unitary sovereignty were John Austin, _The Province of Jurisprudence Determined_ (London, 1832), a book that became popular only posthumously; and A. V. Dicey, _Lectures Introductory to the Study of the Law of the Constitution_ (London, 1885).\n\n36 Holland, _Imperium et Libertas_ (London, 1901), 316\u201317, 318.\n\n37 Dalton, \"The Federal States of the World,\" _Nineteenth Century_ , 16 (1884), 109. This was certainly not a universally recognized federalist strategy. For a denial of such connections, see Seeley, _Introduction to Political Science_ [1896], ed. Henry Sidgwick (London, 1923), 210.\n\n38 Forster, _Our Colonial Empire_ (Edinburgh, 1875), 25, 22, 23.\n\n39 On Dilke, see especially David Nicholls, _The Lost Prime Minister_ (London, 1995).\n\n40 Taylor, \"Republics versus Empires,\" in _Republicanism in Victorian Society_ , ed. Nash and Taylor, 25\u201334. Cf. Prochaska, _The Republic of Britain_ , 115\u201324.\n\n41 Collini, _Public Moralists_ , 108\u201310; Burrow, _Whigs and Liberals_ ; Biagini, \"Neo-Roman Liberalism,\" _History of European Ideas_ , 29 (2003), 55\u201372; Prochaska, _The Republic of Britain_ , chs. 4\u20135. In the historiography of European political thought, the terms \"civic humanism\" and \"civic republican\" are often used interchangeably.\n\n42 Tennyson, \"To the Queen,\" 464; Harrison, \"Our Venetian Constitution,\" _Fortnightly Review_ , 7 (1867), 278; Bagehot, _The English Constitution_ , 44.\n\n43 On the mixed idioms of eighteenth-century republicanism, see J.G.A. Pocock, \"Between Gog and Magog,\" _Journal of the History of Ideas_ , 48 (1987), 325\u201346; Gregory Claeys, \"The Origins of the Rights of Labor,\" _Journal of Modern History_ , 66 (1994), 249\u201390.\n\n44 Froude, _Oceana_ , 1:154. See also Harrington, _The Commonwealth of Oceana_ (London, 1656). Froude wanted to see a \"commonwealth of Oceana,\" united \"as closely as the American states are united\" (91). He was, however, very critical of plans for a formal set of federal institutions, although he thought they may one day develop (395).\n\n45 Bolingbroke, _The Idea of a Patriot King_ [1738], in _Bolingbroke's Political Writings_ , ed. Bernard Cottret (London, 1997), 329\u2013421.\n\n46 Armitage, \"A Patriot for Whom?,\" _Journal of British Studies_ , 36 (1997), 417; Richard Faber, _Beaconsfield and Bolingbroke_ (London, 1961).\n\n47 See the brief biographical comments in Young, _A Pioneer of Imperial Federation in Canada_ (London, 1902), 215. For the extent of his advocacy, see his prolific correspondence with newspapers on federation, Young Papers, RCMS 54\/III\/21.\n\n48 Young, Letter 1, in _Imperial Federation of Great Britain and Her Colonies_ (London, 1876).\n\n49 Young, Letter, _Morning Post_ , September 2, 1897, Young Papers, 54\/III\/21.\n\n50 See, for example, Young, _Imperial Federation of Great Britain and Her Colonies_ , xix\u2013xx; Young, _On the Political Relations of Mother Countries and Colonies_ (London, 1885); Young, _Exit Party_ (London, 1900), 66; Young, _A Pioneer of Imperial Federation_ , ch. 8.\n\n51 Young, _Exit Party_ , 56.\n\n52 Nicola Watson, \"Gloriana Victoriana,\" in _Remaking Queen Victoria_ , ed. Homans and Munich, 79\u2013105; Burrow, _A Liberal Descent_ (Cambridge, 1981), 249.\n\n53 Froude, \"England's Forgotten Worthies,\" _Westminster Review_ , 2 (1852), 42\u201367.\n\n54 Seeley, _The Growth of British Policy_ (Cambridge, 1895). He argued that this policy did not fully triumph over its \"dynastic\" competitor until the eighteenth century.\n\n55 Young, _Exit Party_ , 56\u201357.\n\n56 Young, _A Pioneer of Imperial Federation in Canada_ (London, 1902), 221\u201322. The quotation is taken from Douglas, _Canadian Independence_ (New York, 1894), 19\u201320. Young says of these words that \"they express so forcibly and cogently my own general sentiments on the subject\" (222).\n\n57 de Labilli\u00e8re, _Federal Britain_ , 251\u201352.\n\n58 Bagehot, _The English Constitution_ , esp. chs. 2, 3.\n\n59 G.H.L. Le May, _The Victorian Constitution_ (London, 1979), ch. 3; Arnstein, _Queen Victoria_ , ch. 8.\n\n60 Plunkett, _Queen Victoria_ , ch. 1.\n\n61 Salmon, \"The Colonial Empire of 1837,\" _Fortnightly Review_ , 61 (1897), 870.\nCHAPTER 7\n\nImagined Spaces\n\nNation, State, and Territory in the British Colonial Empire, 1860\u20131914\n\nThe old colonial system is gone. But in its place no clear and reasoned system has been adopted. The wrong theory is given up, but what is the right theory? There is only one alternative. If the colonies are not, in the old phrase, possessions of England, then they must be part of England; and we must adopt this view in earnest.1\n\n\u2014J. R. SEELEY\n\nDuring the late Victorian age, and deep into the twentieth century, a fierce debate raged among members of the British political and intellectual elite over the future of the empire. Could it be adapted to new economic, social, and political circumstances? What form should it take? Fear about the future was generated by concern over both the domestic consequences of democratic reform and about the precarious geopolitical position. Britain's status as a global power was at stake. Democratic reforms, first in 1867 and then more deeply in 1884, reshaped the political landscape. Large numbers of the (male) population were enfranchised, while socialism became an evermore popular and vocal force. Many advocates of empire saw these developments as a threat, worrying that the new mass public would harbor anti-imperial sentiments. The problem was reinforced by various geopolitical trends, and above all the rise of three main competitor states. First, post-unification Germany was well on the way to becoming the dominant power on the continent, and it appeared keen to flex its muscles on the global stage. Second, Russia was seen as a menace to the empire in India, and thus to British power globally. Finally, the post-Civil War dynamism of the United States challenged British economic dominance, and as it enthusiastically embarked on foreign imperial adventures in the 1890s it was figured as a formidable geopolitical competitor. To make matters worse, during the closing decades of the century Britain suffered a prolonged and severe economic depression.2 The country seemed to be weakening at the very moment when its hegemonic position was being challenged. The dynamics between \"domestic\" and \"foreign\" were mutually reinforcing; they signaled a vicious circle, a precipitate decline.\n\nWhat could be done? One of the main answers proposed to address the crisis of imperial confidence was to unite Britain with its scattered settler colonies. Australia, Canada, New Zealand, and parts of South Africa could be fused together into a vast political-economic unit, straddling the planet. The movement advocating Greater Britain, as this behemoth was often called, appealed to people across the political spectrum. Its supporters ranged from Tory peers, through liberal \"public moralists\" to assorted socialist leaders, including H. M. Hyndman and Keir Hardie.3 All of them believed that it was essential, for Britain and the wider world, that the colonial empire prosper in an international system defined increasingly by huge omnicompetent political units. Yet they diverged over the ends this unity was supposed to produce, as well as over the means through which to bring about those ends. For radical liberals, always in the minority, colonial unity would help simultaneously to democratize Britain and the international system as a whole. It would constitute part of a progressive multilateral institutional order.4 In the early years of the twentieth century, following the war in South Africa, and against the backdrop of Chamberlain's tariff reform campaign, radical support for this vision dissipated, leaving the field dominated (although not exhausted) by conservative intellectuals and politicians.5 The dominant view, however, was that Greater Britain provided a way of securing British power while dampening the threat posed by democratic reform and any possible socialist challenge. Through a process of systematic emigration, the disruptive, corrosive potential of democracy would be neutralized as \"excess\" population was channeled from Britain (and in particular from its overcrowded and festering cities) into the huge open spaces of the colonies.6 This movement, it was argued, would simultaneously defuse the dangers of urban radicalism while populating the colonies with individuals who, as a result of a transformation in their natural and cultural environments, would be transmuted into rugged imperial patriots, citizen-subjects of the most powerful polity on earth.7\n\nIn this chapter I explore how _fin de si\u00e9cle_ imperialist intellectuals challenged some of the existing spatial categories used to map world politics, and in particular how they sought to erode the distinction between the \"domestic\" and the \"foreign.\" I focus on two related issues: the imagined _globalization of domestic politics_ and the emergence of ideas about a nascent _planetary public_. In the minds of many imperialists, the boundaries between the domestic and the foreign were fluid and changeable, and they developed an account of the \"domestic\"\u2014or _Innenpolitik_ \u2014as a space that stretched across the face of the earth, encompassing the vast settler colonies. This was often characterized in terms of a global British nation-state\u2014a political-cultural whole, bound by a strong sense of identity and belonging\u2014and it implied a novel conception of a \"translocal\" public sphere. Julius Vogel, a prominent New Zealand politician, objected to the view that the colonies were \"foreign\" territories; they were instead \"part of a mighty nation.\"8 The advocates of Greater Britain sought to reimagine the ontological and ethical status of home and abroad, while simultaneously emphasizing the important differences between the settler colonies and the rest of the empire. I am not suggesting that this novel line of argument led to any straightforward changes in government priorities or legislation. Rather, I focus on how and why a group of well-placed individuals located at the heart of the imperial metropole attempted to shift attitudes, to transform political consciousness, in order to redirect public policy. They were what contemporary theorists of international politics call \"norm-entrepreneurs.\"9 Through argument and political mobilization, they were seeking to alter the terms of the debate and to institute a new vision of global political order.\n\nSalvaging Empire\n\nWhile British society and politics were partially constituted through the imperial encounter, most advocates of empire thought that foreign and imperial affairs failed to register sufficiently in elite consciousness, let alone among the wider public. It was a commonplace lament during the period that domestic affairs, however trivial, took priority in all but the most momentous times in national history. Wars, such as the South African War, could occasionally stir the populace from its myopic slumber, at least if they were intoxicating or exotic enough, but little else did. Whether this picture was accurate or not, it was routinely argued that both the public and the political elite downplayed or ignored the importance of international affairs in general, and imperial affairs in particular.10 There was little new in this sense of alienation. In a speech in Westminster in 1833, Thomas Babington Macaulay complained that:\n\nA broken head in Cold Bath Fields produces a greater sensation among us than three pitched battles in India. A few weeks ago we had to decide on a claim brought by an individual against the revenues of India. If it had been an English question the walls would scarcely have held the members who would have flocked to the division. It was an Indian question; and we could scarcely, by dint of supplication, make a House.11\n\nHis sense of frustration is striking, and it was widely shared. Imperialists argued that their compatriots typically failed to grasp the precarious nature of British global power, or the roles and responsibilities associated with the possession of empire. Their writings and speeches were peppered with complaints about the failure of imperial interests and ambitions to register sufficiently with either the government or the people. John Stuart Mill was expressing a common grievance when in 1859 he bemoaned the \"indifference to foreign affairs\" displayed by the public, and when a decade later he castigated the \"indifference of official people in England about retaining the colonies.\"12 Another variation on the theme of indifference concerned the lack of vision displayed by British politicians. In a discussion of George Cornewall Lewis's ideas about the Suez Canal, for example, Walter Bagehot contended that, \"[t]hose who wish that the foreign affairs of England should be managed according to a far-seeing and elaborate policy will not like such voluntary short-sightedness; but the English people themselves rather have to have the national course fixed by evident, palpable, and temporary circumstances.\"13 The governing class, he implied, exhibited a distinct lack of leadership and foresight in foreign and imperial affairs, this absence mirroring the apathy of the people.\n\nWhile the charge of indifference was thought to apply to nearly all aspects of imperial and foreign affairs, it was often argued that the colonial empire suffered the most of all. In an essay published in 1870, the historian J. A. Froude set out the familiar indictment, grumbling that the public was \"alienated\" from the settler colonies.14 Indifference, it was argued, was leavened with ignorance, a lack of awareness about the nature and value of the empire. Speaking at the inaugural meeting of the Royal Colonial Society in 1869 the Marquis of Normanby, an eminent colonial governor, argued that \"[n]o person who takes an interest in colonial matters can help being struck with the extra-ordinary ignorance that exists in this country in regard to colonial matters.\" At the same meeting, Baillie Cochrane, a Tory MP and one of the original leaders of the Young England movement, lamented the \"indifference\" prevalent among the members of the public and the political class.15 Writing in the _Quarterly Review_ in 1870, John Martineau crystallized the frustration of many imperialists when he lambasted the \"carelessness and indifference with which the English Parliament, reflecting truly the apathy of the public, has treated the magnificent inheritance of our Colonial Empire.\"16\n\nImperial advocates tended to construct the situation as a _crisis_. They deployed the language of emergency to demonstrate the urgency of the problem, to insist on its immediacy and magnitude.17 Theirs was an imagined cartography of fear and foreboding. This emotive idiom made possible the claim that sweeping political change was imperative, that without it the empire, and British power itself, would dissolve. Imperialists had always been haunted by a sense of potential failure, of the fragility of dominance.18 The specter of Rome loomed over their warnings; as I argued in chapter 5, the trope of imperial decline and fall was etched into Victorian political consciousness. During the second half of the century, this apprehension of crisis intensified. The Sepoy Rebellion (1857) unsettled many Britons, who were simultaneously astonished at the lack of gratitude displayed by their imperial subjects and transfixed by the brutality of the revenge exacted, the \"war of no pity\" waged against the rebels.19 Focusing on the violent repression of an uprising in Jamaica in 1865, the Governor Eyre controversy generated a similar set of responses.20 Beset by unrest, populated by millions of potential insurgents, yet essential to British greatness, the empire came to be imagined as an arena of perpetual conflict and confrontation. Indeed from the late 1850s onwards the British empire was routinely figured as a space of permanent crisis. In his brilliant analysis of the conceptual history of crisis, Reinhart Koselleck writes that,\n\nApplied to history, \"crisis,\" since 1780, has become an expression of a new sense of time which both indicated and intensified the end of an epoch. Perceptions of such epochal change can be measured by the increased use of crisis. But the concept remains as multi-layered and ambiguous as the emotions attached to it. Conceptualized as chronic, \"crisis\" can also indicate a state of greater or lesser permanence, as in a longer or shorter transition towards something better or worse or towards something altogether different. \"Crisis\" can announce a recurring event, as in economics, or become an existential term of analysis, as in psychology and theology. All these possible uses can be applied to history itself.21\n\nAnd all of these possible \"uses\" can be found in British imperial discourse. The British _colonial_ empire was both part of the problem and one possible solution to it. The modality of crisis varied between the different forms of imperial connection: for the colonial empire the main fear was not about violence or insurgency, moral corruption or strategic overstretch, but rather about secession, the dissolution of the political bond. Yet if the government acted swiftly and surely to unify the empire, to treat the colonists as full citizen-subjects of a single polity, the colonies would be integrated into a permanent structure of British dominance impervious to the crises afflicting the rest of the empire. Or so it was claimed.\n\nThere were various ways to address the crisis, to overcome the indifference. The most practical was to mobilize on behalf of an alternative vision of the empire, and during this period numerous pressure groups and campaigning organizations, including the Imperial Federation League (IFL), were established.22 They lobbied hard for the importance of the colonial empire. The politics of knowledge assumed a starring role: indifference to empire, it was often argued, was generated and perpetuated by a lack of relevant information. Schools and universities were failing to equip their students, all future imperial subjects, with an adequate appreciation of the past and present glories of the British empire. This was one of the main complaints leveled at the British educational system in Seeley's best-selling book _The Expansion of England_.23 It is not a coincidence that the IFL, and cognate organizations, exerted considerable energy in supporting speaker tours, public lectures, and the production and dissemination of educational materials. It was vital, they thought, to shape the public mind. The Marquis of Lorne\u2014liberal politician, Queen Victoria's son-in-law, and future Governor-General of Canada\u2014argued in a speech to the Royal Geographical Society in 1886 that \"knowledge and sympathy are essential to the consolidation of the empire.\"24 The fact that this was thought necessary bears witness to the sense of indifference perceived by the proponents of empire. W. T. Stead, one of the pioneers of the \"new journalism,\" went so far as to propose that Seeley be placed in charge of a college dedicated to teaching the glories of the British nation.25 In short, the production of colonial knowledge was an integral element of the project to create a Greater British century.\n\nThe advocates of Greater Britain claimed some success in reshaping public views of the character and importance of the colonial empire, if not in fully redirecting British policy. But the feeling of indifference lingered. The historian C. P. Lucas, for example, commented in 1890 that while there had been a \"change in tone and feeling towards the colonies and dependencies\" over the course of the previous decade, a \"spirit of indifference\" was still pervasive.26 Moreover, the expanding scope of the demos brought forth a new set of worries. Leonard Hobhouse, a leading \"new liberal\" and qualified supporter of imperial federation, picked out one of the main concerns, borne of a sense of frustration with the rise of the mass media. The public, he worried, remained poorly informed, with the press acting as a bar to widespread interest in or knowledge about public affairs. Fed an impoverished intellectual diet, they were interested only in reading about battles and sport. \"In truth, there is not, and cannot at present be, any such thing as an effective popular control of foreign policy. The average man gives little time and much less thought to politics.\"27 This message resonated across the political spectrum.\n\nRemaking the People\n\nOne of the most intriguing elements of the debate over the future of the British empire was the way in which the imaginative scope of both \"the people\" and \"the public\" was reconfigured.28 I am using the idea of \"the people\" to refer to the set of individuals within a particular polity who are conceived of as bound together by\u2014and thus in some sense as unified through\u2014a range of common characteristics (most frequently \"race\" or \"nationality\" or some combination of the two). As such, \"the people\" is not coextensive with the totality of individuals falling under the jurisdiction of a particular system of governance, for many of those individuals, including resident aliens, fall outside of the recognized boundaries of community. (Indians, for example, were not regarded as a constitutive element of the British people.) But neither is the people coextensive with \"the public\"; the latter is a subset of the former. The public, as I am employing the term, refers to the set of the people accorded political significance within a particular polity. They are construed as belonging to a distinct and privileged group with at least a notional role in the governance of the state. This conception is closely linked to the set of the enfranchised, but it is not necessarily reducible to it. During the Victorian era both the size of the public, and the importance accorded to it, expanded considerably. During the twentieth century, with the extension of the franchise to include (nearly) all adult men and women, this gap narrowed further, though the two categories are still far from identical.29\n\nOne of the most prominent ways in which imperialists in the late nineteenth century attempted to address the \"crisis\" was by arguing that the very terms in which the trope of indifference was articulated were flawed. The future of the colonial empire was not, they argued, chiefly a problem of foreign or imperial policy; it was instead a problem of _domestic_ British politics. This argument required a significant cognitive shift, the willingness to recognize that the distant and scattered colonies (and colonists) were an integral part of the British polity. As Seeley argued, once this work of imagination was complete, \"Canada and Australia would be to us as Kent and Cornwall.\"30 Even the most common appellation for the unity of the United Kingdom with its settler colonies\u2014Greater Britain\u2014served to signal the seamless continuity between the \"mother country\" and the colonial diaspora. This represented, then, an argument for the globalization of domestic politics: the Anglo-Saxon population(s) of the British settler colonies constituted one unified \"people,\" spread across several noncontiguous geographical spaces.\n\nThis argument was premised on a reorientation in the perception of time and space.31 The links between political identity, territory, and the nation were, it was claimed, challenged fundamentally by new technologies. In particular, the development of transoceanic steam ships and (above all) the construction of a network of telegraph cables had a profound effect on the political imagination.32 The cables, boasted Rudyard Kipling, \"killed their father Time.\" 33 This death precipitated an imaginative rescaling of planetary space and a concerted effort to rethink imperial possibilities. Imperial discourse was soon saturated by a powerful form of techno-utopianism. Routinely exaggerating the capabilities of the new technology, imperial commentators celebrated the \"annihilation\" of time and space, arguing that this meant that the physical limits to political association had been transcended. Repudiating a long-standing argument about the impossibility of creating strong and enduring political institutions and identities across oceanic distances, advocates of colonial unity argued that a new era had dawned, an era in which nature, previously viewed as immutable, was capable of being reshaped by the powers of human technical ingenuity. Frederick Young, one of the most prolific imperial unionists, wrote that the \"marvellous and mysterious help of telegraphy\" had \"worked a veritable revolution in the affairs of the world.\"34 W. E. Forster, an influential liberal politician and one-time president of the IFL, argued in a speech in Edinburgh in 1875 that \"science has brought together the ends of the earth, and made it possible for a nation to have oceans roll between its provinces.\"35 He later stated that\n\nThe inventions of science have overcome the great difficulties of time and space which were thought to make separation almost a necessity, and we now feel that we can look forward, not to the isolated independence of England's children, but to their being united to one another with the mother-country, in a permanent family union.36\n\nThis radical shift in the plasticity of nature translated into a moment of political opportunity. The unification of the colonial empire was now both possible and necessary. According to F. P. De Labilli\u00e9re, an ardent proponent of the federal vision, \"[t]he prospect of a Federal Empire, which five-and-twenty years ago appeared very remote, and which 50 years since seemed almost a chimera, now assumes a pressing and tangible shape.\"37 \"It may be said,\" wrote the radical Australian barrister John Edward Jenkins, that at \"no very distant date steam communication with Australia will be so frequent, regular, and rapid, and the telegraph system so enlarged and cheap, that no practical difficulty would impede the working of a representative federal government.\"38 The shift in perceptions of time and space was a necessary though not sufficient condition for contending that it was now feasible to create a globe-spanning political institution underpinned by a powerful sense of cultural identity.\n\nThe debate was divided over the character of this identity, however. The vision of the globe-spanning British \"people\" assumed two main forms. One insisted that the key binding principle\u2014the social ontological foundation\u2014of the people was _race_. They were, above all, Anglo-Saxon members of the \"English race.\" As was typical in nineteenth-century Britain, usage of the term race was highly imprecise, but the definition usually focused on a combination of cultural markers\u2014historical memories, language, shared values, habitus\u2014circumscribed by \"whiteness.\"39 This view was compatible with (but did not entail) an argument that the populations of the individual colonies were themselves being transformed into new nationalities. The other account accepted the centrality of race, but emphasized the idea of a singular nationality: the (relevant) population of Greater Britain was the British nation writ global. Both conceptions sanctioned extensive exclusion. The indigenous populations of the settler colonies, and the vast majority of the people that Britain ruled over in the Caribbean, Africa, and Asia, fell outside the scope of either account of the people. (Class and gender exclusion was more pronounced in accounts of the public.) But none of these boundaries was fixed permanently: political contestation over the scope of both the public and the people constituted two of the main axes of British and imperial politics in the nineteenth and twentieth centuries.\n\nFor some imperial thinkers, the colonies were in the process of forming new nations, or had even done so already. This process of differentiation from the originary British nation was regarded as a consequence of the radically different physical environments, social structures, economic systems, and nascent cultural traditions in which the colonists were enmeshed. Recognition of the increasing power of colonial nationality could lead in several directions. It could bolster the view that the colonies should be allowed to separate, even that this was now inevitable, and that the future of Greater Britain lay (at most) in a moral community of the Anglo-Saxon race. This was the view of Goldwin Smith, a prominent radical historian who was regarded as a dangerous enemy by many imperialists.40 And as I explore in chapter 13, it was also the position advocated by the historian E. A. Freeman, who focused in particular on the \"Teutonic\" racial community binding Britain and its ex-colonies in North America. The radical liberal politician Charles Dilke, who had popularized the term \"Greater Britain,\" defended another variation on the theme. He sketched an environmental conception of national character, where physical and social conditions, in dynamic combination, shaped the personality of individuals and collectives alike: Canadians and Americans, despite their (as he saw it) common racial origins, were very different in \"type.\" But they were anchored in the same foundations, in a \"Saxondom\" that incorporated both the United States and Greater Britain: \"That which raises us above the provincialism of citizenship of little England is our citizenship of the greater 'Saxondom' which includes all that is best and wisest in the world.\"41 But the belief in the growing strength of colonial \"nationalism\" was more commonly used to motivate urgent calls to confront this dangerous process. Crisis loomed if no action was taken.\n\nThe most popular view among late Victorian imperial thinkers was that the population of Greater Britain comprised a single nationality. Seeley argued for the \"general proposition\" that \"Greater Britain is homogenous in nationality.\"42 De Labilli\u00e9re, hoping for \"the permanent political unity of our race,\" asserted that the \"spirit of national unity has been one of the most beneficent influences in the enlightened progress of modern times. It has made Italy; it has made Germany... National magnetism, with the power of a loadstone [ _sic_ ] is drawing together Great and Greater Britain in closer Indissoluble union.\"43 The historian Hugh Egerton talked of the \"common nationhood\" binding together the peoples of Greater Britain, while a pamphlet produced for the IFL argued that federation was \"a means of securing the continued Union of our nation throughout the world.\"44 The nation, in this sense, acted as a form of social cement connecting the scattered elements of the empire, and allowing it to be represented both as a natural outgrowth of England and as a cohesive whole.\n\nIn the Edwardian era, a multinational commonwealth vision began to eclipse the Seeleyan global nation-state, in recognition of the burgeoning colonial demands for national autonomy. In other words, while the notion of a global polity never disappeared, it was increasingly decoupled from the idea of a singular global nation.45 This theme had not been absent from earlier debates, although neither was it especially prominent. For example, Lord Rosebery argued in a speech delivered in Adelaide in January 1884 that Australia could no longer be seen as a colony, but was \"a nation not in aspiration or in the future, but in performance and fact.\" The empire, he maintained, should be regarded as \"a commonwealth of nations.\"46 It was this account that became increasingly popular over time, not least because it mirrored the views of the political elites in the colonies. In 1905 the eminent journalist W. E. Monypenny suggested that the empire constituted a \"world state\" that \"transcends nationality\" while simultaneously allowing the flourishing of separate nationalities within it. By escaping the clutches of both a petty-minded \"national exclusiveness\" and a grim centralized \"Caesarian despotism,\" it pointed the way to a new form of political order, a truly \"cosmopolitan ideal.\"47 The idea of an Anglo-Saxon commonwealth was, meanwhile, central to the Round Table movement, because, as Lionel Curtis wrote in 1916, \"Canadians, Australians, and South Africans each think of themselves as nations distinct from the people of the British Isles, just as the British think of themselves as a nation distinct from the citizens of the United States.\" They had acquired, that is, a \"national consciousness of their own.\"48 Both the nation-centric and the race-centric accounts, however, embodied an argument about the global singularity of \"the people.\"\n\nTranslocalism: Expanding the Public\n\nThe extension of the scope of the people went hand in hand with an expansion of the compass of the public, of those individuals regarded collectively as politically significant. During the nineteenth-century the size and shape of the public shifted along two dimensions: _horizontal_ and _vertical_. The vertical dimension refers to the degree of formal political inclusion of a given public. This has been the focus of a very large body of scholarship; it is, indeed, the story of the development of democracy in the United Kingdom (and also of the parallel but uneven development of democracy in the individual colonies). Horizontal extension, on the other hand, refers to the spatial extent of a given public\u2014the degree to which it is linked to particular configurations of territory. This topic has received far less scholarly attention. Yet the arguments promulgating the unification of the British colonial empire embodied a claim\u2014sometimes made explicit, often not\u2014about the existence (or potentiality) of an ocean-transcending public. This was a significant moment in the history of modern global consciousness, an early step on the road to the idea of a global public sphere.\n\nAt the peak of the globalization boom in the 1990s the anthropologist Arjun Appadurai argued that the contemporary nation-state\u2014conceived of as \"a compact and isomorphic organisation of territory, ethnos, and governmental apparatus\"\u2014was undergoing a profound crisis; it was in \"serious trouble.\"49 In particular, political loyalties and territorial sovereignty were being wrenched apart as individuals increasingly came to identify with\u2014and feel a sense of belonging to\u2014communities and groups that transcended, indeed challenged, the nation-state. While states remained territorial entities, political identities were often unconstrained by formal boundaries, escaping the relentless topological imperatives of modern politics. \"Translocal\" affiliations\u2014affiliations, that is, to imagined communities that burst the territorially circumscribed foundations of political identity\u2014assumed a pivotal role. \"The most important feature of these emergent cartographies is that they do not appear to require horizontally arranged, contiguous, and mutually exclusive claims to territory.\"50 While Appadurai maintained that translocalism could take many forms, he drew a sharp distinction between two main categories. In the first, the imagined spaces are separate from, and come into conflict with, existing state configurations. An example would be the Sikh idea of Khalistan or the Islamic ummah.51 In the second, the idea is to rework existing configurations by extending the reach and power of one community over others. Appadurai's example is the German neo-fascist view that the Aryan peoples should be united into a single political community, thus expanding the scope of the German state.\n\nAppadurai leaves open the question about whether such dynamics existed in the past. Here we can offer a response which gives some historical flesh to his theoretical account, while employing that account to help shed light on the dynamics of late Victorian intellectual life. First, translocal dynamics have formed a central part of the history of modernity, not least through the globalizing agencies of empire.52 Yet, second, we also witness a significant shift within the politics of modernity, a shift that signals an important moment in the history of global consciousness. This shift was catalyzed by the transformation in the perception of time and space discussed above. As the world appeared to shrink (and as time appeared to contract) so it became possible to argue\u2014however unrealistically\u2014that a strong sense of affiliation and belonging could be felt with individuals scattered throughout the world. Adam Smith once referred to British colonists living in North America as \"strangers.\"53 In the last three decades of the nineteenth century this common (and commonsensical) understanding was overturned: distance no longer entailed alienation. Communal identification need not be rooted in or constrained by geography. This was not a novelty of the post-1989 world; it is not unique to contemporary forms of globalization. It was instead a product of the nineteenth-century communications revolution, and it spawned a major rethinking of the nature of political association, territory, and space. It was as a result of these developments that proponents of colonial unity in late Victorian and Edwardian Britain can be seen as imagining a form of globe-spanning translocal politics. However, whereas many of the examples explored by Appadurai are \"counterhegemonic\"\u2014seeking to challenge the established power structures and sources of authority54\u2014the attempted reworking of British racial-national consciousness in the Victorian age was a hegemonic project, an effort to establish and prolong the dominance of an empire through novel articulations of political identity.\n\nYet that project does not fit neatly into either of the two categories identified by Appadurai. The imperial unionists were neither seeking to create a space outside of or in opposition to the existing state, and nor were they chiefly focused on extending the scope of British nationality by conquering other established states. Instead, they sought to extend the scope of the British polity to encompass, on equal terms, colonial spaces that had previously been regarded as subordinate communities. It was for this reason that many of the supporters of colonial union did not regard the colonies as part of the empire\u2014a term that connoted hierarchy and difference\u2014but instead as integral elements of a transcontinental British state.55 This imaginative projection involved a double process of deterritorialization and reterritorialization.56 The British polity was no longer to be conceived of as a small group of islands lying off the northwest coast of continental Europe (deterritorialization). Instead it was to be seen as encompassing a vast range of territories in North America, the Pacific, and Southern Africa (reterritorialization). This new space was a nascent form of global state.\n\nIn envisioning a translocal cartography, the idea of the public itself was refashioned. This was a direct challenge to conventional understandings of the scope of the public sphere, which had seen it as falling within, and indeed constrained by, the territorial boundaries of the British Isles. The conventional view was compatible with the claim that the colonies had their own emergent publics, but these were nevertheless regarded as separate from, and inferior and subordinate to, that of Britain. This was the standard position adopted until the last three decades of the nineteenth century. John Stuart Mill, a defender of the value of the colonial empire, articulated it clearly in the _Considerations on Representative Government_ (1861), arguing that one of the key reasons why a federation of the colonies would fail to satisfy the \"rational principles of government\" was that the colonists were \"not part of the same public\" as the British people.57 A basic harmony of both interests and sympathies was absent. The alternative vision\u2014the vision that found expression in the debates over Greater Britain\u2014was of a single, translocal public sphere, encompassing the publics of the United Kingdom and the settler communities. This allowed the most ambitious imperial unionists to outline plans for the creation of representative institutions, a federal constitution, even a new imperial senate, that would bind the various publics together in a new political order. This polity was to be the home of an innovative form of imperial citizenship.58 The public sphere, circumscribed by race, had been stretched over the face of the earth.\n\nConclusions\n\nDuring the late Victorian and Edwardian years numerous imperial commentators sought to reimagine the British state, nation, and empire. In seeking to challenge the purported indifference of their compatriots, in attempting to respond to the perceived threats posed by both domestic and geopolitical developments, and in light of the cognitive transformations wrought by new communications technologies, many of them argued for novel understandings of territory, borders, and political identity. This prominent group sought to globalize domestic politics by arguing that a vast polity, grounded in a single people and containing a single (albeit differentiated) public sphere, could already be discerned, but that it was in danger of being lost if urgent political action was not taken to secure and strengthen it. Such a failure, they warned, would hasten the decline and fall of the British empire. Their arguments implied a refashioning of the boundaries between local and global, domestic and foreign, nation and empire.\n\nThe views that they professed\u2014hubristic, conceited, and deeply na\u00efve\u2014echoed powerfully down the years, and can be seen again today in the growing interest in the so-called \"Anglosphere,\" the globe-spanning body of the heirs of the British colonial diaspora. The main difference now, of course, is that the internal balance of power has shifted firmly across the Atlantic, with Washington assuming the mantle of imperial metropolis.59 The echo can be heard too, albeit more indirectly, in the arguments propagating a league or concert of democracies. As Tony Smith observes, these visions often embody \"a claim to cultural superiority and an encouragement to belligerent behaviour\" that represent \"an update of race theory.\"60 They are the latest incarnation of a long-standing set of arguments about the duties of purportedly advanced states to spread, by force if necessary, the enlightened benefits of civilization to the benighted, \"barbaric\" corners of the earth. We would do well to ignore their dangerous clarion call.\n\n1 Seeley, _The Expansion of England_ , 158.\n\n2 For useful general accounts of British society and politics at the time, see Theodore Hoppen, _The Mid-Victorian Generation, 1846\u20131886_ (Oxford, 1998) and Geoffrey Russell Searle, _A New England?_ (Oxford, 2005).\n\n3 On socialist support for imperial federation, see especially Gregory Claeys, _Imperial Sceptics_ , ch. 3. Hyndman was leader of the Social Democratic Federation and a booster of Marx, while Hardie was a founder of the Labour Party. See also the discussion of Hobson and Hobhouse in chapter 14.\n\n4 See chapter 10 of this volume, and Casper Sylvest, _British Liberal Internationalism, 1880\u20131930_ (Manchester, 2009).\n\n5 Daniel Gorman, _Imperial Citizenship_ (Manchester, 2006); Peter J. Cain \"The Economic Philosophy of Constructive Imperialism,\" in _British Politics and the Spirit of the Age_ , ed. Cornelia Navari (Keele, 1996), 41\u201365.\n\n6 On the general fear of degeneration, see Daniel Pick, _Faces of Degeneration_ (Cambridge, 1989); John Burrow, _The Crisis of Reason_ (London, 2000). On republican imperialism, see also chapters 2 and  of this volume.\n\n7 For further discussion, see Bell, _The Idea of Greater Britain_ , ch. 2.\n\n8 Julius Vogel, \"Greater or Lesser Britain,\" _Nineteenth Century_ , 1 (1877), 813; Vogel, \"The British Empire,\" _Nineteenth Century_ , 3 (1878), 617.\n\n9 Martha Finnemore and Kathryn Sikkink, \"International Norm Dynamics and Political Change,\" _International Organization_ , 52 (1998), 887\u2013917; see also the discussion of \"innovating ideologists,\" in Quentin Skinner, _Visions of Politics_ (Cambridge, 2002), vol. 1, esp. chs. 7, 8, 10.\n\n10 There is considerable debate over the extent to which empire did register among the public and elites (and of what might follow from this). See, for example, Michael Bentley, _Politics without Democracy_ , 2nd ed. (Oxford, 1999), xviii, 182; Peter Durrans, \"The House of Commons and the British Empire, 1868\u20131880,\" _Canadian Journal of History_ , 9 (1974), 19\u201345; Bernard Porter, _The Absent-Minded Imperialists_ (Oxford, 2004); Catherine Hall, _Civilizing Subjects_ (Cambridge, 2002).\n\n11 Macaulay, \"Speech on the Renewal of the East India Company Charter\" [July 10, 1833], reprinted in Macaulay, _The Complete Works_ (London, 1898\u20131906), 11:558. Cold Bath Fields was a notorious prison in London.\n\n12 Mill, \"A Few Words on Non-Intervention\" [1859], in _Collected Works_ (Toronto, 1963\u201391), 21:17; Mill, letter to Henry Samuel Chapman, January 14, 1870, _Collected Works_ , 18:1685.\n\n13 Walter Bagehot, \"Sir George Cornewall Lewis\" [1863], in _Biographical Studies_ , ed. Richard Holt, 2nd ed. (London, 1889), 212\u201313.\n\n14 Froude, \"England and Her Colonies,\" _Fraser's Magazine_ , 1 (1870), 4\u20135; L. J. Trotter, \"British India under the Crown,\" _Contemporary Review_ , 15 (1870), 113\u201332.\n\n15 Both men were responding to Lord Bury's \"Inaugural Speech\" [March 15, 1869], reprinted in the _Proceedings of the Royal Colonial Institute_ , vol. 1 (1869\u201370), 51\u201362. George Phipps, Marquis of Normanby, had served as Governor of Nova Scotia in the 1840s; during the 1870s and 1880s he was Governor of Queensland, New Zealand, and Victoria.\n\n16 John Martineau, \"New Zealand and Our Colonial Empire,\" _Quarterly Review_ (1870), 128, 135.\n\n17 See, for example, Andrew Macfie, \"On the Crisis of the Empire,\" _Proceedings of the Royal Colonial Institute_ , 3 (1871\u201372), 2\u201312.\n\n18 Piers Brendon, _The Decline and Fall of the British Empire: 1781\u20131997_ , (London, 2007); John Darwin, \"The Fear of Falling,\" _Transactions of the Royal Historical Society_ , 5th series, 36 (1986), 27\u201345; and the discussion of time in chapter 5.\n\n19 Christopher Herbert, _War of No Pity_ (Princeton, 2007).\n\n20 Rande Kostal, _A Jurisprudence of Power_ (Oxford, 2006); Karuna Mantena, \"The Crisis of Liberal Imperialism,\" in _Victorian Visions of Global Order_ , ed. Bell (Cambridge, 2007), 89\u2013113.\n\n21 Koselleck, \"Crisis,\" _Journal of the History of Ideas_ , 67 (2006), 357.\n\n22 Andrew Thompson, _Imperial Britain_ (London, 2002).\n\n23 On the institutional ecology of imperial campaigning, see Seeley, _The Expansion of England_. In an obituary, H.A.L. Fisher commented: \"I question whether any historical work has exercised so great an influence over the general political thinking of a nation.\" H.A.L. Fisher, \"Sir John Seeley,\" _Fortnightly Review_ , 60 (1896), 193. For Seeley's imperial political theology, see chapter 11.\n\n24 Lorne, \"The Annual Address on the Progress of Geography, 1885\u20131886,\" _Proceedings of the Royal Geographical Society_ , 8 (1886), 420; Felix Driver, _Geography Militant_ (Oxford, 1999).\n\n25 Stead, in _The Life of W. T. Stead_ , ed. Frederick Whyte (London, 1925), 2:209\u201310.\n\n26 C. P. Lucas, \"Introduction\" to George Cornewall Lewis, _An Essay on the Government of Dependencies_ (Oxford, 1891), xxxviii, lviii.\n\n27 Hobhouse, _Democracy and Reaction_ 1904], ed. P. F. Clarke (Brighton, 1973), 144\u201345. For more on Hobhouse, see [chapter 14.\n\n28 I do not follow nineteenth-century usage, where there was no settled meaning for either the \"people\" or \"public.\" Boyd Hilton argues that the idea of a public, as we would understand it, did not really exist before 1850. _A Mad, Bad, and Dangerous People?_ (Oxford, 2006), 310\u201311. I use the concepts as analytical categories to help make some sense of a confused debate. For a useful theoretical discussion, see Margaret Canovan, _The People_ (Cambridge, 2005).\n\n29 On the philosophical issues involved, see Arash Abizadeh, \"Citizenship, Immigration, and Boundaries,\" in _Ethics and World Politics_ , ed. Duncan Bell (Oxford, 2010), 358\u201377, and, more recently, Sarah Fine, \"Democracy, Citizenship, and the Bits in Between,\" _Critical Review of International Social and Political Philosophy_ , 14\/5 (2011), 623\u201340.\n\n30 Seeley, _The Expansion of England_ , 63. Leo Amery, \"Imperial Defence and National Policy,\" in _The Empire and the Century_ , ed. C. S. Goldman (London, 1905), 182.\n\n31 For the widespread transformation in perceptions of time and space in European culture, see Stephen Kern, _The Culture of Time and Space, 1880\u20131918_ (Cambridge, MA, 2003); Nicholas Daly, _Literature, Technology, and Modernity, 1860\u20132000_ (Cambridge, 2004); Wolfgang Schivelbusch, _The Railway Journey_ (Oxford, 1986).\n\n32 The Atlantic was straddled in 1866 (after an abortive attempt in 1858). Cables reached Australia in 1872, New Zealand in 1876, and South Africa in 1879.\n\n33 Kipling, \"Deep-Sea Cables\" [1896], in _Rudyard Kipling's Verse, 1885\u20131932_ (London, 1932), 173.\n\n34 Young, _Proceedings of the Royal Colonial Institute_ , 8 (1876\u201377), 118\u201319.\n\n35 Forster, \"Our Colonial Empire,\" _Times_ , November 6, 1875, 9; Francis de Labilli\u00e9re, \"British Federalism,\" _Proceedings of the Royal Colonial Institute_ , 24 (1893), 110.\n\n36 Forster, _Imperial Federation_ (London, 1884), 27.\n\n37 de Labilli\u00e9re, _Federal Britain, or, Unity and Federation of the Empire_ (London, 1894), 12.\n\n38 Jenkins, \"An Imperial Confederation,\" _Contemporary Review_ , 17 (1871), 78.\n\n39 Peter Mandler, \"'Race' and 'Nation' in Mid-Victorian Thought,\" in _History, Religion, and Culture_ , ed. Stefan Collini, Richard Whatmore, and Brian Young (Cambridge, 2000), 224\u201345; Stuart Jones, \"The Idea of the Nation in Victorian Political Thought,\" _European Journal of Political Theory_ , 5 (2006), 12\u201321. Since this chapter was first published, I have further developed this argument about race as \"biocultural assemblage.\" Bell, \"Beyond the Sovereign State,\" _Political Studies_ , 62\/2 (2014), 418\u201334.\n\n40 Smith, _The Empire_ (London, 1863); Smith, \"The Empire,\" in _Essays on Questions of the Day_ [1893], 2nd ed. (New York, 1894), 141\u201395. On Smith, see Bell, _The Idea of Greater Britain_ , ch. 7.\n\n41 Dilke, _Greater Britain_ (London, 1868), 2:150, 156.\n\n42 Seeley, _The Expansion of England_ , 49; Seeley, \"Introduction\" to _Her Majesty Colonies_ (London, 1886), xxiv\u2013xxv.\n\n43 de Labilli\u00e9re, _Federal Britain_ , 35\u2013171; S. Wilson, \"A Scheme for Imperial Federation,\" _Nineteenth Century_ , 17 (1885), 590; Young, _An Address on Imperial Federation_ (London, 1885), 23.\n\n44 Egerton, _A Short History of British Colonial Policy_ , 477; \"What Is Imperial Federation?\" [1890], _Minute Book of the General Committee of the Executive Committee of the I.F.L_., BL, Add MS, 62779, 256.\n\n45 See also the discussion in Gorman, _Imperial Citizenship_.\n\n46 Speech in Adelaide, January 18, 1884, George Bennett, _The Concept of Empire_ , 2nd ed. (London, 1962), 283; Forster, \"Imperial Federation,\" _Nineteenth Century_ , 17 (1885), 201; Douglas Cole, \"The Problem of 'Nationalism' and 'Imperialism' in British Settlement Colonies,\" _Journal of British Studies_ , 10 (1971), 160\u201382.\n\n47 Monypenny, \"The Imperial Ideal,\" in _The Empire and the Century_ , ed. Goldman, 23, 27.\n\n48 Curtis, _The Problem of Commonwealth_ (London, 1916), 68; John Kendle, _The Round Table Movement and Imperial Union_ (Toronto, 1975).\n\n49 Appadurai, \"Sovereignty without Territoriality,\" in _The Geography of Identity_ , ed. P. Yaeger (Ann Arbor, 1996), 40\u201359; Appadurai, _Modernity at Large_ (Minneapolis, MN, 1996); Peter Mandeville, \"Territory and Translocality,\" _Millennium_ , 28 (1999), 653\u201367.\n\n50 Appadurai, \"Sovereignty without Territoriality,\" 51.\n\n51 Ibid., 55.\n\n52 A. G. Hopkins, ed., _Globalization in World History_ (London, 2002) and Tarak Barkawi, _Globalization and War_ (Lanham, MD, 2006); John Gerard Ruggie, \"Territoriality and Beyond,\" _International Organization_ , 47 (1993), 139\u201374; Friedrich Kratochwil, \"Of Systems, Boundaries and Territoriality,\" _World Politics_ , 39 (1986), 27\u201352.\n\n53 Smith, _An Inquiry into the Nature and Causes of the Wealth of Nations_ , ed. W. B. Todd (Oxford, 1976), 622.\n\n54 Appadurai cites (51n) Paul Gilroy, _The Black Atlantic_ (Cambridge, MA, 1993).\n\n55 Bell, \"The Victorian Idea of a Global State,\" in _Victorian Visions of Global Order_ , ed. Bell, 159\u201386.\n\n56 See Appadurai, \"Sovereignty without Territoriality,\" 54.\n\n57 Mill, _Considerations on Representative Government, Collected Works_ , 19, 564. See also the discussion in chapter 9.\n\n58 Gorman, _Imperial Citizenship_ ; J. Lee Thompson, _A Wider Patriotism_ (London, 2007).\n\n59 James C. Bennett, _The Anglosphere Challenge_ (New York, 2004); Bennett, _The Third Anglosphere Century_ (Washington, 2007); Robert Conquest and Andrew Roberts, among others, have been pushing a similar idea in recent years. Conquest, _Reflections on a Ravaged Century_ (London, 2000), 267\u201381; Roberts, _A History of the English-Speaking Peoples since 1900_ (London, 2006). For analysis of the idea, see Srdjan Vucetic, _The Anglosphere_ (Stanford, 2011).\n\n60 Tony Smith, _A Pact with the Devil_ (London, 2007), 108.\nCHAPTER 8\n\nThe Project for a New Anglo Century\n\nRace, Space, and Global Order\n\nI believe that the twentieth century is par excellence \"The Anglo-Saxon Century,\" in which the English-speaking peoples may lead and predominate the world.1\n\n\u2014JOHN RANDOLPH DOS PASSOS\n\nProphets have long dreamed of schemes to govern a violent and unpredictable world. This chapter sketches a synoptic intellectual history of a prominent variation on the theme: the attempt to unify the constituent elements of the \"Anglo-world\" into a single globe-spanning community, and to harness its purported world-historical potential as an agent of order and justice.2 Since the late nineteenth century numerous commentators have preached the benefits of unity, though they have often disagreed on the institutional form it should assume. These are projects for the creation of a new Anglo century.\n\nThe opening two sections of the chapter explore overlapping elements of the _fin de si\u00e8cle_ Anglo-world discourse. Synthesizing some of the arguments made in previous chapters in this volume, I first analyze the relationship between Britain and its colonial empire, before turning to a range of intersecting arguments over the future relationship between the empire and the United States. The third section traces the echoes of these debates through the twentieth century, discussing the interlacing articulation of imperial-commonwealth, Anglo-American, democratic unionist, and world federalist projects. Despite important differences between them, most versions of these grand supranational schemes were heirs of the earlier debates. In the final section I discuss contemporary accounts of Anglo-world supremacy. While none of the most radical plans came to fruition, the evolving debate over the nature of the Anglo-world formed a central element in the cultural construction of the \"West,\" and illustrates the extravagant hopes that have been invested in the \"Anglo-Saxons\" over the course of a brutal century. This constitutes, then, an important strand in the history of modern political thought.\n\nEmpire, Nation, State: On Greater Britain\n\nTo govern, Foucault argues, is \"to structure the possible field of action of others.\"3 The second half of the nineteenth century saw a profound transformation in both the scale of the field of action and the ways in which it could be structured. It witnessed the emergence of a novel governance _episteme_ \u2014an imaginative regime wherein established conventions and presuppositions about political order were overturned.\n\nDaniel Deudney aptly labels this the \"global industrial period.\" The spread of the industrial revolution was a \"primal development\" for global politics, as new technologies intensified interactions across the planet, reshaping the material and imaginative contexts in which debates over the future took place. \"As the scale and tempo of human affairs changed, a major and tumultuous reordering of large-scale political relationships and institutions seemed imminent and inevitable.\"4 The thinkers of the time\u2014the \"industrial globalists\"\u2014proselytized a wide array of schemes for transcending the anarchic international system, including pan-regional imperial structures, European union, the federation of the British empire, and even the future development of a world state. The debates about the Anglo-world were an integral element of this more general discourse.\n\nThis period also saw the rearticulation of the global politics of race. In 1900, at the meeting of the Pan-African Congress in London, W.E.B. DuBois predicted that the \"problem of the twentieth century\" would be \"the problem of the color line.\"5 Fears about racial contamination were rife. A civilizational dividing line was constructed between \"white\" peoples and others, resulting in the initiation of numerous exclusionary practices, including racist immigration controls. This was a paradoxical process: \"The imagined community of white men was transnational in its reach, but nationalist in its outcomes, bolstering regimes of border protection and national sovereignty.\"6 Those debating the future of the Anglo-world insisted on carving out a space within the general identity of whiteness, establishing a stratified geo-racial imaginary. Usage of the term \"race\" was highly imprecise, but it typically designated a combination of cultural markers\u2014historical mythscapes, habitus, shared language, cultural values, and political ideals\u2014circumscribed by \"whiteness.\" It was simultaneously cultural and biological. The French, the Germans, the Russians, and the Hispanics were all considered inferior to the Anglo-Saxons. They in turn ranked higher on the scale of civilization than other nonwhite racial constellations populating the world outside the Euro-Atlantic zone and its diasporic outposts. In this conception of world politics, the basic ontological unit was race, and political institutions, including the state, were only of derivative importance.\n\nThe sweeping debate over the future of the British colonial empire was conducted under the sign of \"imperial federation,\" while the assemblage of communities under discussion was frequently labeled \"Greater Britain.\"7 The debate formed a key building block in the ideological construction of the twentieth-century Anglo-world. As I argue in _The Idea of Greater Britain_ , and elsewhere in this volume, it was driven by two intersecting imperatives. Fear that British relative power was threatened by the rise of formidable states\u2014notably Germany, Russia, and the United States\u2014led many commentators to argue for the construction of a globe-spanning political association, encompassing Britain and its settler colonies in Australia, Canada, New Zealand, and (more ambivalently) South Africa, either to balance the new threats or to deter them from attempting to compete. These geopolitical concerns were reinforced by anxieties about the onset of democracy, with many imperial observers worrying that an expanding electorate would fail to recognize the importance of the empire, concentrating its energies and ambitions on domestic reform. It was feared\u2014prematurely as it turned out\u2014that a democratic polity would invariably be anti-imperial. Creating a federal Greater Britain, and populating it in part through an accelerated program of \"systematic\" emigration from the \"mother country,\" was thought to be one way of neutralizing these threats. Yet even some radical advocates of democracy, including J. A. Hobson, H. M. Hyndman, and Keir Hardie, saw benefits in imperial federation. For them, Greater Britain could simultaneously hasten the peaceful development of the international system and help to democratize Britain itself through the importation of progressive practices from the more egalitarian colonies.8\n\nAccording to Hobson, great federal political communities would dominate the future, and it was thus essential to erect a \"Pan-Saxon\" one. As he proclaimed in _Imperialism_ , \"Christendom thus laid out in a few great civilizational empires, each with a retinue of uncivilized dependencies, seems to me the most legitimate development of present tendencies and one which would offer the best hope of permanent peace on an assured basis of inter-Imperialism.\"9 Hobhouse, meanwhile, argued that imperial federation \"is a model, and that on no mean scale, of the International State.\"10 These arguments illustrate the two broad temporal logics that underpinned debates over Anglo-union deep into the twentieth century. In one of them, union represented the terminal point of future political development: the polity would take its place among other competing pan-racial or regional units. In the other, Anglo-union was figured as a transitional institutional formation, one that could serve as a template, catalyst, and leader of a future global political association.\n\nTime was of the essence. Haunted by memories of the American Revolution, many feared that the rapidly expanding colonies would secede, either establishing independent countries or fusing with another state\u2014most likely the United States\u2014thus further weakening Britain. The imperial advocates were determined to refute Alexis de Tocqueville's prediction, made in the closing lines of _Democracy in America_ , that Russia and America would dominate the future.11 Greater Britain was their answer.\n\nA significant number of British unionists fantasized about the incorporation of the United States within an imperial federation, though most of them recognized that this was unrealistic (at least in the short term). Nevertheless, America played a crucial role in imperial discourse. First, it was regarded as a potential challenger to British supremacy, thus motivating the call for action. This was especially apparent in the wake of the McKinley Tariff of 1890, which incited the demand throughout Britain and its colonies for the creation of a system of imperial preference.12 Second, the turbulent history of American-British relations, and in particular the War of Independence, preoccupied British imperial unionists, teaching them that the demands of colonial subjects had to be treated seriously. This meant granting them greater political autonomy. And finally, the United States demonstrated the power of federalism as a political technology by proving that individual liberty was compatible with vast geographical extent. This was welcome in an age in which it was commonly believed that the future belonged to huge omnicompetent political units. The radical politician Charles Dilke, author of the influential _Greater Britain_ , cautioned that \"[i]t is small powers, not great ones, that have become impossible.\"13 Three decades later Joseph Chamberlain, arch-federalist and Secretary of State for the Colonies, concurred: \"The days are for great Empires and not for little States.\"14 Size mattered.\n\nThe debates over Greater Britain generated hundreds of proposals, differing in ambition, detail, and rationale. Three general institutional models were discussed.15 The least ambitious was \"extra-parliamentary\" federation, wherein a group of distinguished individuals\u2014organized as an imperial Advisory Council\u2014would offer the British Parliament nonbinding advice on imperial affairs. A more constitutionally far-reaching model was \"parliamentary federalism,\" in which the colonies were to send elected representatives to sit in Westminster. This had been a common exhortation since the late eighteenth century, though it was much less popular in the closing decades of the Victorian age. Finally, \"supra-parliamentary federalism\" connoted the formation of a sovereign federal chamber supervening on the individual political assemblies of the empire. This model followed the example, above all, of the United States.16\n\nThe leading constitutional scholar A. V. Dicey observed that many imperial federalist proposals implied the creation of a \"new federated state.\"17 According to prevailing conceptions of statehood, all supra-parliamentary schemes\u2014and indeed most parliamentary ones\u2014could be viewed as demanding the construction of a globe-spanning Anglo-state, a polity composed of people belonging to the same nation and\/or race, governed by a system of representative institutions subordinate to a supreme federal legislative chamber. The local legislatures would have a high degree of autonomy over specified domains of policy, though supreme authority would reside in either a newly created imperial chamber (sometimes labeled a \"senate\") or a reconfigured Parliament in Westminster. This body would determine questions of war and peace, trade, and any other general issues that concerned the whole polity. The case of the extra-parliamentary advocates is less straightforward, for they were simply trying to reanimate the existing structure and were far less willing to promote significant constitutional engineering. Many of them did, however, predict radical developments in the future.\n\nYet not all advocates of Greater Britain proposed the development of a vast federal polity. For many of them the key to the future lay in the shared identity of the British people spread across the world, and they argued that further institutionalization was unnecessary\u2014it either fell outside the scope of \"practical politics\" or it was counterproductive. Instead, they maintained that it was essential to nourish the existing connections. This was the course that the British government ultimately followed. Dilke and Goldwin Smith, both leading public intellectuals and critics of imperial federal schemes, extolled the superiority of the British \"race\" and promoted a vision in which the Anglo-Saxons, acting as a collective of independent states, would shape the future. They supported the independence of the British settler colonies, but as a means to the end of Anglo-unity, not its termination. For Dilke, the \"strongest of arguments in favour of separation is the somewhat paradoxical one that it would bring us a step nearer to the virtual confederation of the English race.\"18 Both of them also included the United States in their vision. The cultural-racial conception of \"virtual confederation\" proved the most enduring; it remains an important factor in world politics to this day.\n\nArguments about both Greater Britain and Anglo-American union were premised on a cognitive revolution, a fundamental transformation in the perception of time and space. It was this, above all, that shaped the new governance _episteme_. In his _Considerations on Representative Government_ , John Stuart Mill argued, in an idiom common throughout the eighteenth and much of the nineteenth centuries, that physical distance thwarted the union of Britain and its settler colonies. It contradicted the principles of \"rational government\" and precluded the necessary degree of communal homogeneity.19 From the 1860s onwards, new communications technologies radically altered the way in which individuals perceived the physical world and the sociopolitical possibilities it contained, spawning fantasies about the elimination of geographical distance that prefigure late twentieth-century narratives of globalization. H. G. Wells declared that \"modern mechanism\" had created \"an absolute release from the fixed conditions about which human affairs circled.\" For J. R. Seeley, the leading intellectual of the imperial federalist movement, the \"unprecedented facility of communication which our age enjoys seems to be creating new types of state.\"20 A Greater British state was now realizable. Techno-utopianism underpinned arguments about the existence of a trans-planetary British political community. \"When we have accustomed ourselves to contemplate the whole [colonial] Empire together and call it England,\" Seeley proclaimed, \"we shall see that here too is a United States. Here too is a homogeneous people, one in blood, language, religion, and laws, but dispersed over a boundless space.\"21 Previously viewed as immutable, nature was now open to manipulation, even transcendence.\n\nAll of these projects depended on claims about the common identity of the dispersed Anglo people(s).22 As I discussed in the last chapter, the argument assumed two main forms. One insisted that the social ontological foundation of the people was _race_. They were, above all, Anglo-Saxon or members of the \"English race.\" This view was compatible with (but did not entail) an argument that the populations of the individual colonies were coalescing into new nationalities, and that the United States already comprised a distinct nation. The other account accepted the centrality of race, but emphasized the idea of a singular _nationality_ : the (relevant) population of Greater Britain was the British (or \"English\") nation writ global. Both conceptions sanctioned extensive discrimination. The indigenous populations of the settler colonies, and the vast majority of the people that Britain ruled over in the Caribbean, Africa, the Middle East, and Asia\u2014and that the USA came to rule over in Hawaii and the Philippines\u2014fell outside the scope of either account of the singular people.\n\nThe \"nationality\" view prevailed among late Victorian imperial thinkers. Seeley was only the most prominent to claim that \"Greater Britain is homogenous in nationality.\"23 During the Edwardian years, a multinational commonwealth vision began to eclipse the Seeleyean global nation-state. This alternative option was not without precedent, for Lord Rosebery, the future British prime minister, had argued in 1884 that the empire should be regarded as \"a commonwealth of nations.\"24 This position became increasingly popular over time, not least because it mirrored the views of the political elites in the colonies. Greater Britain morphed into a post-national (or multinational) political association. Both the nation-centric and the race-centric accounts, however, centered on an argument about the singularity of \"the people.\"\n\nThe imaginative extension of the scope of the people was conjoined with an expansion of the compass of the public\u2014of the set of individuals within the totality of the people regarded as politically significant. Arguments promulgating the unification of the British colonial empire (and also Anglo-America) embodied a claim about the existence or potentiality of an ocean-spanning public. As I discuss in chapter 7, this was a racially delimited precursor to the idea of a global public sphere. Indeed one of the most conceptually innovative features of the discourse, prominent especially in the early twentieth century, was the effort to inaugurate a system of Greater British imperial citizenship.25 It is possible to view the Anglo-racial imaginary as an example of what Arjun Appadurai terms \"translocal\" affiliation\u2014of an emergent cartography that escaped the topological imperatives of the modern territorially bounded nation-state.26 As time and space were reordered, so it was increasingly argued that a strong sense of identity and belonging bound Britain and its colonial populations. However, whereas many of the examples explored by Appadurai are \"counterhegemonic\"\u2014seeking to challenge extant power structures and sources of authority\u2014the attempted reworking of \"Anglo-Saxon\" racial-national consciousness in the Victorian age was a hegemonic project involving a double process of deterritorialization and reterritorialization.27 The British polity was no longer to be conceived of as a small group of islands lying off the northwest coast of continental Europe (deterritorialization), but rather as incorporating a vast range of territories in North America, the Pacific, and Southern Africa (reterritorialization). A similar georacial logic also helped underpin arguments about Anglo-American unity.\n\nThe Reunion of the Race: On Anglo-America\n\nThe unity of the Anglo-world was not preordained. For much of the nineteenth century, relations between the British empire and the United States were antagonistic. Resentment about the colonial past, incessant disputes over the Canadian border, the bitter divide over the Civil War and its aftermath, pervasive cultural condescension from the British, and widespread Anglophobia in American public life: all fanned the flames of antipathy. Mutual suspicion was the norm. It was only during the last two decades of the century, and in particular during the late 1890s, that the animosity thawed. This \"rapprochement\"\u2014and the subsequent creation of an Anglo-American security community\u2014has long been the subject of intense scrutiny by diplomatic historians and IR specialists. Yet insufficient attention has been paid to the political thought of the episode.\n\nIt was during the 1890s that the debate over Anglo-American union moved to the center of political debate. The Venezuelan boundary dispute (1895\u201396) led to acrimonious exchanges between Washington and London, but it also prompted anguished commentators on both sides of the Atlantic to recoil from the prospect of war. Numerous proposals for Anglo-American union appeared. The clamor for racial unity was partly a result of the new assertiveness of the United States, for although it had been engaged in imperial conquest since its founding, the annexation of Hawaii and the Spanish-American War (1898) signaled its first sustained burst of extra-continental imperialism. This was seen as marking a new phase in American history: either a moment when the country assumed its predestined role as a great power, or when it betrayed the founding principles of the republic. Many observers on both sides of the Atlantic insisted that the British and Americans should be united, not divided, under conditions of global imperial competition. Arguments ranged from a minimalist position that simply encouraged deeper political and economic cooperation between the two \"kindred\" powers, through intermediate proposals seeking a formal defensive alliance, to maximalist plans for uniting the two countries in a novel transatlantic political community.\n\nPlans for a formal alliance blended \"realist\" concerns over shared security interests with assertions about underlying cultural affinities. The British imperial commentator Arthur Silva White declared that schemes for a comprehensive political union were \"at present impossible,\" but that there \"remains but one expedient\u2014an alliance, or accord, which would pave the way to concerted action in the future.\"28 Yet many commentators were skeptical about such an alliance, either because they opposed closer connections in the first place, or because they thought it would instrumentalize (and potentially distort) a more fundamental form of unity.29 The esteemed American naval strategist Alfred T. Mahan argued that it was vital to \"avoid all premature striving for alliance, an artificial and possibly even an irritating method of reaching the desired end.\" Instead, he continued, \"I would dwell continually upon those undeniable points of resemblance in natural characteristics, and in surrounding conditions, which testify to common origin and predict a common destiny.\"30 A British military writer concurred, warning against the \"artificial and temporary arrangements miscalled 'alliances,' which provide occupation for European chancelleries.\"31 The \"organic\" bonds of \"kinship\" were sufficient. Fearful that talk about the Anglo-Saxons was dangerously triumphalist, Benjamin Harrison, the former US president, insisted that friendship was quite enough. \"Are not the continuous good and close relations of the two great English-speaking nations\u2014for which I pray\u2014rather imperilled than promoted by this foolish talk of gratitude and of an alliance, which is often made to take on the appearance of a threat, or at least a prophecy, of an Anglo-Saxon 'paramountcy?'\"32 This was a prescient warning.\n\nAt the core of the Anglo-American vision lay a novel set of arguments that ruptured the isomorphic relation between state, citizen, and political belonging. Advocates of racial unity frequently decoupled the state from both citizenship and patriotism. Citizenship was reimagined as a political institution grounded ultimately in racial identity, not state membership. Dicey offered the most sophisticated elaboration of the idea of common citizenship, or _isopolity_ , arguing in 1897 for \"the extension of common civil and political rights throughout the whole of the English-speaking people.\" Rejecting the idea of a transatlantic (or imperial) federation, he insisted that \"reciprocal\" citizenship would be enough to secure permanent unity. The idea was, he averred, simply a return to a prior condition, for such a connection had existed before the Anglo-Saxon peoples were ripped apart by the War of Independence.33 Patriotism, meanwhile, was also reconfigured as a form of allegiance owed, in the first instance, to the race. Arguments about \"race patriotism\"\u2014a term usually associated with Arthur Balfour, a future prime minister\u2014circulated widely.34 They implied that people were enmeshed in a concentric circle of belonging and affect, the outer (and most important) ring of which was the race. Alfred Milner, a leading imperial thinker and official, summed it up neatly: \"My patriotism knows no geographical, but only racial limits... It is not the soil of England, dear as it is to me, but the speech, the tradition, the spiritual heritage, the principles, the aspirations of the British race.\"35 Quoting Balfour, Charles Beresford, a British Tory politician and senior naval officer, observed that\n\n[I]n addition to our domestic patriotism and our Imperial or American patriotism, we also have an Anglo-Saxon patriotism, which embraces within its ample folds the whole of that great race which has done so much in every branch of human effort, and in that branch of human effort which has produced free institutions and free communities.36\n\nTraditional notions of state citizenship and patriotism were thus seen as acceptable only insofar as they were compatible with attachment to the wider racial encompassing group.\n\nAndrew Carnegie, the Scottish-born industrialist, argued repeatedly for racial fusion and the \"reunion\" of Britain and America. Though usually lauded or reviled as an anti-imperialist, Carnegie, like Hobson, highlights how opposition to certain kinds of imperial activity\u2014in his case, British occupation of India and Africa and the American assault on the Philippines\u2014was consistent with ardent support for projects of racial unity or superiority. Carnegie dismissed the idea of an Anglo-American alliance as failing to grasp the far more important issues at stake. \"Alliances of fighting power form and dissolve with the questions which arise from time to time. The patriotism of race lies deeper and is not disturbed by waves upon the surface.\" \"[M]y belief,\" he declared, is that \"the future is certain to see a reunion of the separated parts and once again a common citizenship.\" This federated \"British-American Union\" would constitute a \"reunited state.\" Yet this vision was irreconcilable with imperial federation: the British had first to grant independence to their settler colonies, which would then be welcome to join the union as equal members.37 Although perturbed by the South African War, and by the exuberant imperialism of the American administration, he kept faith in the transformative potential of the Anglo-Saxon race.\n\nSkeptics were quick to point to the empirical inadequacies of unionist plans. One of their main complaints focused on the pertinence of arguments about racial unity. America, they complained, was simply not a lineal \"Anglo-Saxon\" descendent of Britain. \"There is,\" one critic observed, \"no fundamental reason rooted in human nature by virtue of a community of blood and religion why Americans as a nation should regard England with instinctive sympathy and friendship.\"38 Another stressed the multi-ethnic composition of the American population. \"What about the descendants of French men, of Germans, of Slavs, and of Scandinavians, who do not admit Anglo Saxon superiority?\" And what about the Irish or African-Americans?39 But such demographic arguments failed to register with the proponents of unity, not least because their conception of race was fluid. As one unionist observed,\n\nIt is quite true that, if the census of descent were taken as the test, the sons or descendants of Englishmen by no means make up the majority of American citizens. But there is descent other than that of birth and a lineage beside that of blood. The unity of language, literature, and law between England and America is a threefold cord that cannot be broken. To have our English Bible, our English Shakespeare, our English Blackstone all absolutely American in reverence and influence outweighs, outvotes and overwhelms all questions of racial compositeness.40\n\nIn general, then, what identified the United States as an Anglo-Saxon country was its dominant political culture\u2014its White Anglo-Saxon Protestant institutions, values, and ideals. Pointing to his own Portuguese origins, Dos Passos celebrated the American polity as a machine for turning (white) immigrants into Americans, and thus into adherents to an Anglo-Saxon creed. The \"foreign element,\" he argued, \"disappears, almost like magic, in the bosom of American nationality.\"41 Carnegie, meanwhile, suggested that immigration had barely altered the racial composition of America: \"[I]n race\u2014and there is a great deal in race\u2014the American remains three-fourths purely British... The amount of blood other than Anglo-Saxon or Germanic which has entered into the American is almost too trifling to deserve notice, and has been absorbed without changing him in any fundamental trait.\"42 Moreover, skepticism about racial commonality did not preclude support for political union. The eminent Anglo-American archaeologist Charles Waldstein argued that the notion of \"Anglo-Saxon\" racial identity was both misleading and dangerous: \"[I]t opens the door to that most baneful and pernicious of modern national diseases, namely, Ethnological Chauvinism.\" Yet he was adamant that Britain and the United States shared enough features in common to constitute \"one nationality,\" and he toasted the future creation of \"a great English-speaking Brotherhood.\"43\n\nCecil Rhodes was another formidable proponent of Anglo-American unity. At the heart of his vision lay an account of the fractured nature of history: its progressive course had been diverted by the catastrophic estrangement of the United States and Great Britain. This could only be put right if the two great institutional expressions of the race were reunited permanently. As a self-proclaimed \"race patriot,\" Rhodes was largely agnostic about whether Britain or the United States should lead the Anglo-Saxons in fulfilling their destiny, suggesting that a \"federal parliament\" could rotate between Washington and London.44 One of Rhodes's most practical contributions to realizing the dream of global racial dominance was the establishment of the Rhodes Trust, endowed following his death in 1902 with the intention of strengthening bonds between the elites of the Anglo-world, as well (initially) as Germany, that other Teutonic power. The radical journalist W. T. Stead agreed with his friend Rhodes that the \"English-speaking race is one of the chief of God's chosen agents for executing coming improvement in the lot of mankind,\" and he utilized his position as a prominent author and editor to preach the gospel of Anglo-unity, seeking to \"constitute as one vast federated unity the English-speaking United States of the World.\"45 Like many of his contemporaries, Stead sensed a gradual intra-racial shift in the balance of power. In _The Americanization of the World_ , he argued that the Americans had overtaken the British in most aspects of social and economic life, observed that Britain itself was slowly Americanizing, and determined that those ruling in London now faced a stark choice: ally with the United States in a grand project of earthly redemption, or become increasingly irrelevant as the empire slowly weakened and the settler colonies sought independence and looked to Washington for leadership. This was a cause for celebration: \"[T]here is no reason to resent the part the Americans are playing in fashioning the world in their image, which, after all, is substantially the image of ourselves.\"46 American success was an expression of British power, institutions, and values. This was a common trope in British accounts of Anglo-America, with Dilke, for example, boasting that \"[t]hrough America, England is speaking to the world.\"47\n\nH. G. Wells also dreamt of an Anglo enunciation of modernity. In _Anticipations_ , published in 1902, he prophesized the emergence of a world state ruled over by a new techno-managerial class of \"efficients\"\u2014the \"kinetic men\" of the future.48 This was a theme he was to pursue, in one way or another, until his death in 1946. In this early vision, the unification of the \"English-speaking\" peoples assumed a central role: they were to serve as pioneers of the world-state-to-come. By the year 2000 the English-speaking people would constitute a federal state, united by \"practically homogenous citizenship,\" with its headquarters in the United States. They would govern all the \"non-white states of the present British empire, and in addition much of the South and Middle Pacific, the East and West Indies, the rest of America, and the larger part of black Africa.\"49 His vision was vanguardist in a double sense. Not only were the English-speaking peoples to lead the way to a further global \"synthesis,\" but this drive was itself led by a select group of individuals, men of energy, determination, and drive, who would help to dissolve\u2014either through social revolution or in the wake of war\u2014the remaining barriers to its realization found in \"deliquescing\" modern societies. The New Republicans would act as a largely uncoordinated \"Secret Society\" to help inaugurate a fresh dawn in human history. This notion of a clerisy acting behind the scenes to secure race unity was echoed by Rhodes and Stead.\n\nWells was not the only fiction writer to propagate Anglo-unity. Arthur Conan Doyle was another enthusiast, dedicating his historical novel _The White Company_ to \"the Hope of the Future, the Reunion of the English-Speaking races.\" He even enlisted Sherlock Holmes, who declaimed that history should not prevent \"our children from being someday citizens of the same world-wide country whose flag should be a quartering of the Union Jack with the Stars and Stripes.\"50 Writing to his brother William, Henry James observed in 1888 that \"I can't look at the English-American world, or feel about them, anymore save as a big Anglo-Saxon total, destined to such an amount of melting together that an insistence on their difference becomes more and more idle and pedantic.\"51\n\nWhile many of the proposals for unity were motivated by pragmatic security concerns, an equally large number made drastic claims about the world-transforming potential of racial unity. We can thus interpret aspects of the pre-1914 Anglo-race discourse as expressions of utopian desire.52 A political project can be considered utopian, I submit, if and only if it invokes or prescribes the transcendence or elimination of at least one of the pervasive practices or ordering principles that shape human collective life. These include poverty, inequality, war, the state, the biochemical composition of the environment, or the ontological constitution of human beings, including death itself. Utopianism is not best employed as a synonym for any ambitious project of political change or seen as a general feature of the human condition, a universal striving for a better life. Rather, it identifies a particular species of transformative social and political thought.\n\nThe utopianism of this racial vision resided in the belief that if the United States and Greater Britain were properly aligned, the \"Anglo-Saxon\" race would help to bring peace, order, and justice to the earth. Carnegie argued that the \"new nation would dominate the world and banish from the earth its greatest stain\u2014the murder of men by men.\" Lyman Abbott, a prominent American Congregationalist theologian, dreamed of an Anglo century\u2014even millennium. \"[T]hese two nations, embodying the energy, the enterprise, and the conscience of the Anglo-Saxon race, would by the mere fact of their cooperation produce a result in human history which would surpass all that present imagination can conceive or present hope anticipate.\"53 For Albion Tourg\u00e9e, American soldier, diplomat, and judge, the Anglo-Saxons were, quite simply, the \"peacemakers of the twentieth century.\" Rhodes once wrote: \"What an awful thought it is that if we had not lost America, or even if now we could arrange with the present members of the United States Assembly and our House of Commons, the peace of the world is secured for all eternity!\" In 1891, he predicted that union with the United States would mean \"universal peace\" within one hundred years. Stead agreed, envisaging that \"war would by degree die out from the face of the earth.\"54 This, then, was the promise of an Anglo-racial utopia.\n\nAfterlives of Empire: Anglo-America and Global Governance\n\nDuring the twentieth century, proposals for supranational political unions were divided among (at least) five models. One of them emphasized regional federation, and centered above all on combining the states of continental Europe. It was this vision that ultimately had the most practical effect, though only after the cataclysm of a genocidal war. The other four\u2014which I will label imperial-commonwealth, Anglo-American, democratic unionist, and world federalist\u2014placed the transatlantic British-American connection at the core of global order. All were descended, in part or wholly, from the earlier Anglo-world projects. Some offered only minor modifications to earlier imperial schemes, while others pushed out in new directions. Perhaps most importantly, though, the majority of the interwar and midcentury projects regarded the \"Anglo\" powers as a nucleus or vanguard. And even those schemes that expanded beyond the institutional limits of the Anglo-world were almost invariably liberal democratic and capitalist in form, and as such they exemplified, even embodied, the values and institutions on which the Anglo-world was based, and over which its advocates claimed paternity.\n\nThe imperial-commonwealth model focused on the continuing role of the British empire. During the Edwardian years and beyond, the Round Table and other British imperial advocacy groups continued to campaign on behalf of Greater British unity. The imperial federalist project reached its zenith during the First World War with the creation of an Imperial War Cabinet in 1917, which incorporated the prime ministers of the dominions. This was the nearest the dream of a politically unified Greater Britain came to fruition. Yet the war also accelerated calls for further independence in the colonies. While the efforts of the imperial federalists did not go completely unheralded in the United States, they found, perhaps ironically, a more receptive audience in continental Europe, with a number of them\u2014notably Philip Kerr (Lord Lothian)\u2014playing an important role in shaping the ideological foundations of European union.55\n\nDuring the 1920s the balance of power continued to shift within the British empire, and as the colonies were granted further autonomy they frequently came into conflict with London.56 In the interwar period it became increasingly popular to reimagine the empire as the \"British Commonwealth\"\u2014the two terms were often used interchangeably\u2014and to see it either as a self-contained system capable of balancing other great political orders, or as the embryonic form of a future universal political system. Britain and its settler colonies remained at the center of the model, although India and other elements of the empire were sometimes allotted subordinate roles. In the second half of the twentieth century, following decolonization, the imperial-commonwealth vision morphed into a postcolonial international organization.57 Today it lingers on, a pale shadow of the hopes once invested in it.\n\nThe Anglo-American model centered on the Anglo-Saxon\u2014or \"English-speaking\"\u2014peoples, and in particular on a British-American axis. Relations between London and Washington continued to strengthen in the wake of the late Victorian \"rapprochement,\" and the alliance was cemented during the First World War when the United States joined the Franco-British cause in Western Europe. It remained close for the rest of the twentieth century, though not quite as close as many of its cheerleaders, then as now, like to boast. The First World War had a catalytic effect on American foreign policy discourse, spawning the development of a powerful, though often fractious, East Coast policy elite oriented towards greater American involvement in world politics, in cooperation (even alliance) with Britain.58 During the interwar era, a variety of institutions and informal networks were created to foster closer links between the United States and Greater Britain. They constituted an emergent epistemic community dedicated to emphasizing the importance of Anglo-world global leadership. The Council on Foreign Relations in New York and the International Institute of International Affairs (Chatham House) in London served as institutional hubs of Anglo-world thinking, in both its Anglo-American and British imperial-commonwealth articulations.59\n\nWhile the 1920s saw constructive cooperation between Britain and the United States, relations during the 1930s were strained; it was only with the outbreak of war, and especially between 1940 and 1942, that the two powers were forced into a tight embrace.60 This peaked with the signing of the Atlantic Charter in August 1941, dedicated to the promotion of \"certain common principles in the national policies of their respective countries on which they base their hope for the common world,\" though tension continued between London and Washington over the future of the British empire. As American power increased, and it became clear that Britain would be a junior partner in any future relationship, so once again the dream of an Anglo-American order faded. Perhaps its last gasp can be found in Churchill's \"iron curtain\" speech in March 1946, in which he popularized the term \"special relationship\" and insisted that peace was impossible without \"the fraternal association of the English-speaking peoples.\"61 Like the contemporary Commonwealth, the \"special relationship\" in the postwar years was a weak imitation of the ideal that had inspired many British, and even a few American, commentators over the previous decades.\n\nAnother model envisioned the creation of a league (or concert) of democracies. Before 1945 this essentially meant a transatlantic union of the United States, Great Britain, and assorted western European countries. As such, it moved beyond the \"racial\" limits of the Anglo-world. In the 1950s this idea sometimes mutated into an Atlanticist vision centered on the NATO countries. The most influential interwar democratic unionist vision was propounded by Clarence Streit, a journalist with the _New York Times_. In _Union Now_ , he proposed a federation, on the model of the constitution of 1787, of the fifteen democracies of the Atlantic world. The union would serve three main purposes:\n\n(a) to provide effective common government in our democratic world in those fields where such common government will clearly serve man's freedom better than separate governments, (b) to maintain independent national governments in all other fields where such government will best serve man's freedom, and (c) to create by its constitution a nucleus world government capable of growing into universal world government peacefully and as rapidly as such growth will best serve man's freedom.62\n\nHe followed this up with _Union Now with Britain_ , in which he argued that the creation of an Anglo-American union would guarantee the defeat of the Axis.63 Streit's later work highlights the way in which the Cold War constrained the imagination of democratic unionists. The West, figured as an \"Atlantic community\"\u2014a term first used by Walter Lippmann64\u2014took center stage. In 1961 Streit published _Freedom's Frontier_ , suggesting that the fifteen countries of NATO already constituted the nucleus of an immanent Atlantic federal state: \"Atlantica.\"65 This fed into a popular Atlanticist current of thought. Expressing a common view, Livingston Hartley, a former State Department official, demanded \"the political integration of the Atlantic community, the citadel and the powerhouse of freedom.\"66 For many, European union and Atlantic union went hand in hand, the development of the former helping to strengthen the viability of the latter.67 For others, though, the creation of a European union threatened the more desirable goal of Atlantic union. For Streit, avatar of Atlanticism, America needed to take the lead in creating a new order, \"preferably teamed closely with Canada,\" while European integration threatened transatlantic division.68\n\nThe veteran British peace campaigner Norman Angell followed a similar trajectory to Streit. An early advocate of democratic federal union as a precursor to world federation, during the Second World War he too emphasized the vital leadership role of the Anglo-states (and the British empire) in this future global order. Like so many other post-state visionaries, he insisted that a \"nucleus of authority\" was required to catalyze and then direct the transition to world federation, and that this nucleus \"must be the English-speaking world,\" by which he meant the United States and the \"British peoples.\"69 Rather than the latest manifestation of Anglo-Saxon imperialism, he was adamant that this Anglo core could act as the embryo of a true universalism. The empire should, then, be transformed into a \"nucleus of integration\" rather than dissolved into independent sovereign states.70 By the late 1950s, in Streitian vein, he was arguing that \"the West\" as a whole should act as the advance guard in any future transformation. \"A world government would have to work on the basis of 80 or 100 nationalisms, emphasizing widely differing cultures and ways of life.\" The common social basis for political unity did not (yet) exist. As such, he concluded, the adoption of the \"federal principle\" was necessary to unify the West in the face of Soviet totalitarianism, and as an essential step on the road to a more wide-ranging union.71 The unionist axis had shifted from the British empire, through Anglo-America, to the West as a whole, but the Anglo-world remained at the heart of the project.\n\nThe major difference between \"Anglo\" and \"Democratic unionist\" models concerns the identity claim on which they are based. The Anglo model is confined to a finite set of British diasporic communities; its potential spatial extent is delimited by a specific historical trajectory. A league of democracies is in principle more expansive, designating a community that shares a minimal set of political values and institutions, all of them hypothetically exportable. Yet in practice, at the heart of this picture, were (and are) the Anglo-states. Moreover, the values and institutions associated with such a community\u2014the architecture of liberal-democratic capitalism\u2014were either implicitly or explicitly ascribed by contemporaries to the British and American intellectual traditions. Once again, social science offered authoritative epistemic support. The empirical analysis, and the normative affirmation, of the Anglo-world were high on the agenda of early postwar behavioral political science. Most notably, the hugely influential idea of a \"security community\" was forged in the crucible of Atlanticist politics. Pioneering political scientist Karl Deutsch argued, for example, that the North Atlantic security community was anchored in the most highly integrated states, namely the United States, Canada, and the United Kingdom.72\n\nThe final model was a universal world polity. Ideas about world government have percolated through the history of political thought, ebbing and flowing in popularity.73 The 1940s witnessed an efflorescence of utopian political thinking, catalyzed by the old Kantian premonition that the route to perpetual peace would most likely wind its way through the valley of death\u2014that a brutal war might, once and for all, force people throughout the world to recognize the necessity of federation. Advocates of a global polity typically conceived of it as a long-term ideal rather than something within immediate grasp.74 Nevertheless, many of them called for a federal institutional structure with an Anglo nucleus, while numerous advocates of democratic or Anglo-racial union saw their own more limited goals as temporary steps on the road to\u2014and often agents in the creation of\u2014a universal federation.\n\nPerhaps the most famous world federalist was Wells, who proselytized on behalf of a post-sovereign cosmopolitan order in a seemingly endless stream of publications. After the First World War he turned his attention to the creation of a functionalist world state, suggesting in vague terms that a future world polity would result from the coagulation of regional and racial groupings.75 Like most of his contemporaries, his account of a cosmopolitan world state never escaped the ethnocentric assumptions that had marked his earlier writings. Evolving through various iterations, his vision of a future global order was rooted in the purported superiority of the Western powers, and in particular the Anglo-Americans. He longed for the (re)union of the English-speaking peoples. In 1935, for example, he argued that \"the commonsense of the world demands that the English-speaking community should get together upon the issue of World Peace, and that means a common foreign policy.\" It also meant economic unification, for \"the world revival\" would not materialize \"unless we homologize the financial control and monetary organization of our world-wide group of people.\"76 Wells exemplified the technocratic aspect of the world federalist project, even flirting with fascist methods during the 1920s and 1930s in order to help bring about a new global order.\n\nWorld federalist thinking flourished in Britain and the United States in the 1940s and early 1950s, drawing in a wide array of intellectuals and politicians, from Albert Einstein and Aldous Huxley to Henry L. Stimson and John Foster Dulles. Campaigning organizations\u2014notably the United World Federalists (1947)\u2014were formed, politicians lobbied, newsletters and pamphlets circulated. Wendell Willkie's _One World_ sold over two million copies.77 Henry Usborne, a British Labour MP, created a Parliamentary Group for World Government and signed up over 200 MPs.78 Under the leadership of its president, Robert M. Hutchins, the University of Chicago created a Committee to Frame a World Constitution.79 House Concurrent Resolution 64, in 1949, was proposed as a \"fundamental objective of the foreign policy of the United States to support and strengthen the United Nations and to seek its development into a world federation.\" It secured 111 votes, including those of John F. Kennedy, Gerald Ford, Mike Mansfield, Henry Cabot Lodge, and Henry Jackson. The movement peaked in early 1950, with 150,000 members worldwide.80\n\nIn the shadow of the bomb, political realists had their own one world moment. John Herz and Hans Morgenthau, among others, argued that human survival demanded the creation of a world state, though both were skeptical of its plausibility.81 The world federalist movement was stifled by the onset of the Cold War.82 The dream of unity struggled on, finding a variety of intellectual outlets, including the World Orders Model Project most closely associated with Richard Falk.83 But it was an early victim of bipolar ideological confrontation. Once a topic of mainstream concern for scholars, public intellectuals, journalists, and politicians, Thomas Weiss argues that today ideas about a global federal state are \"commonly thought to be the preserve of lunatics.\"84 Yet there are signs of a revival of interest in the idea, at least among scholars.85 In IR, for example, Alexander Wendt and Daniel Deudney have offered theoretically sophisticated accounts of the plausibility, even inevitability, of a world state.86\n\nThe proponents of democratic leagues and world federation often drew inspiration from\u2014and shared personnel with\u2014the imperial federal movement. Lionel Curtis is a prominent example. An enthusiastic advocate of imperial and then world federalism over the course of five decades, his political thought was riddled with the tensions between universalism, Atlanticism, and imperialism.87 Curtis's magnum opus, the sprawling politico-theological treatise _Civitas Dei_ , posited that a federated British empire could serve as a kernel and a model for a future universal commonwealth of nations, because of all extant political communities it offered the most appropriate space for human personality to find its fullest expression.88 The most difficult stage in creating a world federal state was the first one; the \"most experienced commonwealths\" needed to show leadership. He identified the core of the global order in the union of Great Britain, New Zealand, and Australia.89 The Second World War only reinforced his belief in the necessity of political transformation. In the early 1950s Curtis angrily denounced intellectuals for upholding the myth of sovereign statehood; they were, he charged, \"responsible for the bloodshed of this century\" and \"answerable for the suffering, poverty, and death that millions are now facing.\" Federation, with an Anglo core, was the only way to escape the killing machine. An arch Anglo-supremacist who died in 1956, Curtis was frequently hailed as one of the pioneers of the world federalist movement.90\n\nA notable aspect of the debates over global order, in both the nineteenth and the twentieth centuries, was that the United States often served as a template for the future. Both American political experience and political philosophy were routinely cited as inspirational, even formative. Streit modeled his plan for an Atlantic union of democracies on the US Constitution. Indeed, he went so far as to call for a Federal Convention, similar to its namesake in Philadelphia in 1787, to deliberate over the desirability and potential form of a transatlantic union. This proposal gained the support of the Canadian Senate and dozens of US senators.91 Twentieth-century British imperial federalists, meanwhile, regularly invoked the genius of the American founders, often interpreted through the prism of F. S. Oliver's _Alexander Hamilton_. Curtis, for example, was explicit about his debt to the _Federalist Papers_ ; they taught him, he recorded, about both the problem of political order and the best solution to it, fundamentally influencing his views over half a century of federalist agitation.92 America was both model and motive. Indeed, many world federalist plans can be read as demanding the Americanization of the planet.\n\nMillennial Dreams, or, Back to the Future\n\nWhile today there are few advocates of a global federal state outside of universities and think tanks, the vision of a \"concert\" or \"league\" of democracies has resurfaced in public life. \"Democracy\" has supplanted \"civilization\" as the defining feature in discourses of global governance. Democratic unionist arguments have been given a powerful boost by the popularity of theories of the \"democratic peace,\" once again highlighting the complex entanglement of twentieth-century social science with projects for global order. This line of reasoning is directly descended from the mid-twentieth-century discourse. Michael Doyle, for example, identifies Streit as the first modern commentator to point to \"the empirical tendency of democracies to maintain peace among themselves.\"93 Uniting liberal internationalists with neoconservatives, the idea of a league of democracies has wide ideological appeal among members of the American political elite, even if it has resonated far less in Europe. Advisors to both Barack Obama and John McCain promoted the idea during the 2008 election campaign, and McCain endorsed it.94 It has found its most systematic articulation in the Princeton Project on National Security, coordinated by Anne-Marie Slaughter and John Ikenberry, which proposes the creation of a global \"Concert of Democracies\" to \"institutionalize and ratify the 'democratic peace.'\"95\n\nRecent years have also witnessed a brief flurry of arguments focusing on the Anglo dimension of world politics\u2014the imperial dream that never expires. They are variations on the earlier themes of imperial federation and Anglo-American unity. In addition to the old rubric of the \"English-speaking peoples,\" a new term (coined in a science fiction novel) has entered the lexicon: the \"Anglosphere.\"96 Advocacy of Anglo superiority has assumed different forms. One popular version, outlined in a bestselling book and a popular television series, is Niall Ferguson's paean to British imperial power, and the necessity of the American empire assuming the responsibility\u2014the old \"White Man's burden\"\u2014of hegemonic stabilizer and civilizing agent.97 Other widely discussed proposals have emanated from the American businessman James Bennett and the British historian Andrew Roberts.\n\nEchoing earlier discussions about the world-historical function of the telegraph, Bennett contends that the Internet can serve as a medium through which the geographically scattered but culturally and politically aligned members of the \"Anglosphere\" can come into closer communion, and act together for the planetary greater good.98 He sees this as both desirable and necessary, given the likely development of other competing network \"spheres\"\u2014Sino, Luso, Hispano, and Franco. He concludes that the inherited political and economic traditions of the Anglosphere mean that it is uniquely equipped to thrive in the coming century. Roberts, meanwhile, seeks to pick up where Churchill finished his own bombastic history of the English-speaking peoples.99 Rather than advocating formal union, he outlines a vision, grounded in a hubristic reading of twentieth-century history, in which the English-speaking peoples are united by \"common purposes\" and in defeating waves of totalitarianism, today exemplified by Islamic fanaticism. Superior political institutions mean that when they act in unison, the whole world benefits. Roberts's vision of the English-speaking peoples is limited to the United States, the United Kingdom \"and her dependencies,\" New Zealand, Canada, and Australia, as well as the British West Indies and Ireland\u2014though of the latter two, the first is largely ignored while the second is routinely assailed for failing to live up to the standards set by the others. Reproducing earlier arguments about race patriotism, Roberts decenters the state: the ontological foundation of his argument is a singular people, while the political units of this singularity play a secondary function. \"Just as we do not today differentiate between the Roman Republic and the imperial period of the Julio-Claudians when we think of the Roman Empire, so in the future no one will bother to make a distinction between the British Empire-led and the American Republic-led periods of English-speaking dominance.\"100 The book secured him an invitation to George W. Bush's White House.101\n\nNone of these authors proposes a formal political union, instead hymning the powers of shared culture, traditions, and interests. But the vision of an institutionalized Anglo-union has not disappeared completely. Robert Conquest, eminent poet and historian, has called for the \"English-speaking\" countries of the world to join a \"flexibly conceived Association,\" something \"weaker than a federation, but stronger than an alliance.\" A \"natural rather than artificial\" association, this \"Anglo-Oceanic\" polity would act as a progressive hyperpower.102 Like Roberts, Conquest is driven in part by a sense of anger at the duplicity of British politicians signing up to European integration, and thus betraying their true kin in the dominions and across the Atlantic.\n\nThere are notable continuities between the contemporary projects for an Anglo century and their predecessors. All have been framed by war or imperial action. While Cuba, the Philippines, and South Africa set the context for the first outburst of writing on Anglo-America, and the rise of Hitler, the Second World War, and then the onset of the Cold War helped initiate the second, today it is Iraq, Afghanistan, and the \"War on Terror\" that provide the general ideological milieu. All of them depend on a form of \"othering,\" an imaginative geography of fear and loathing. Over time, the Anglo-Saxons have been arrayed against Japan, France, Russia, Germany, the Soviet Union, and now an amorphous \"radical Islam.\" Each phase has also been predicated on hyperbolic claims about the power of new communications technologies to transform the nature and scope of political association. Since the late nineteenth century, radical visions of formal political union have been accompanied by more modest proposals for strengthening existing connections and fostering close cooperation. Yet all of these varied projects, however ambitious, have been based on claims about translocal identity and belonging. They have insisted that the members of the Anglo-world share much in common\u2014a language, a history, a set of values, political and economic institutions, and a destiny.\n\nBut there are also some notable differences. The _fin de si\u00e8cle_ and mid-twentieth-century debates about supranational political unions were much wider ranging and more prominent; they drew in many of the leading public intellectuals, journalists, and politicians of the day. While the current debate over the league of democracies has a high profile, the ambitions of its proponents are far more limited than those urged by their mid-twentieth-century precursors. They do not seek to replace the state system, only to carve out a powerful coalition within it.\n\nThe contemporary Anglospheric discourse, meanwhile, is a pale imitation of previous iterations. This is partly because of its ideological coloring. Whereas the older debate crossed political lines, the contemporary discourse is almost exclusively confined to the political right, and in particular to neoconservatives. Another significant difference is that the utopian dimension of the earlier projects is largely absent. In the reheated version, the Anglosphere is figured as a force for good in the world, securing and helping to spread freedom, democracy, and liberal capitalism\u2014it upholds the new civilizing mission. This is a form of imperial idealism, but it is not equivalent to the earlier claims that the unity of the Anglo-Saxon race would eliminate war, or that it would inaugurate a universal world state. The messianic impulse has dissolved.\n\nThe last one hundred and fifty years, then, have seen the elaboration of numerous projects to unify or coordinate the scattered polities of the Anglo-world. Initially they centered on British imperial federation, before the focus switched to the Anglo-American relationship. Proposals for a league of democracy, Atlantic union, even world federalism were heirs of this Anglo discourse, not discrete and incompatible models of global order. They emerged from the earlier imperial-racial debates, and many of the proposals for transcending the existing system were similar in form and ambition to the projects for Anglo-world imperium. To chart the \"growth of nations,\" Tocqueville once wrote, it is an imperative to remember that they carry with them \"some of the marks of their origin.\"103 The same is true of projects of global governance. We have yet to escape the will to empire and the seductive call of the civilizing mission.\n\n1 Dos Passos, _The Anglo-Saxon Century and the Unification of the English-Speaking People_ , 2nd ed. (New York, 1903), vii. Dos Passos, a prominent Republican lawyer and author, was the father of the famous novelist.\n\n2 For the term \"Anglo-world,\" see James Belich, _Replenishing the Earth_ (New York, 2009).\n\n3 Foucault, \"The Subject and Power,\" in _Michel Foucault_ , ed. Hubert Dreyfus and Paul Rabinow, 2nd ed. (Chicago, 1983), 221.\n\n4 Deudney, _Bounding Power_ (Princeton, 2007), 215, 219.\n\n5 See, in particular, the argument in DuBois, _The Soul of Black Folk_ (New York, 1903).\n\n6 Marilyn Lake and Henry Reynolds, _Drawing the Global Colour Line_ (Cambridge, 2008), 4.\n\n7 I expand on the argument in this section in Bell, _The Idea of Greater Britain_.\n\n8 On Hobson and Hobhouse, see chapter 14. The idea of importing reform from the colonial periphery was prevalent in wider social reform debates: Daniel Rodgers, _Atlantic Crossings_ (Cambridge, MA, 2000).\n\n9 Hobson, _Imperialism_ [1902], ed. Philip Siegelman (Ann Arbor, 1997), 332.\n\n10 Hobhouse, _Liberalism_ , ed. J. Meadowcroft (Cambridge, 1994), 116. Note that Hobson later abandoned his support for imperial federation. P. J. Cain, _Hobson on Imperialism_ (New York, 2002).\n\n11 Tocqueville, _Democracy in America_ [1835\u201340], trans. Henry Reeve, 2 vols. (London, 1862), 2:456\u201357.\n\n12 Marc-William Palen, \"Protection, Federation and Union,\" _Journal of Imperial and Commonwealth History_ , 38 (2010), 395\u2013418; P. J. Cain and A. G. Hopkins, _British Imperialism, 1688\u20132000_ (London, 2002), ch. 7.\n\n13 Dilke, _Greater Britain_ (London, 1868) 1:274, 48.\n\n14 Chamberlain, _The Life of Joseph Chamberlain_ [1902], ed. J. L. Garvin and J. Amery (London, 1968), 177.\n\n15 This schema is derived from Ged Martin, \"Empire, Federalism and Imperial Parliamentary Union, 1820\u201370,\" _Historical Journal_ , 16 (1973), 65\u201392.\n\n16 For an example of the former model, see Marquis of Lorne, _Imperial Federation_ (London, 1885); for an example of the latter, see Francis de Labilli\u00e9re, _Federal Britain_ (London, 1894).\n\n17 Dicey, _Introduction to the Study of the Law of the Constitution_ , 8th ed. (London, 1915), lxxxiv. On contemporary ideas about statehood, see Duncan Bell, \"The Victorian Idea of the Global State,\" in _Victorian Visions of Global Order_ , ed. Bell (Cambridge, 2007), 159\u201386.\n\n18 Dilke, _Greater Britain_ , 2:157.\n\n19 Mill, _Considerations on Representative Government_ (1861), in _Collected Works_ , vol. 19, ch. 18. See also the discussion in chapter 9 of this volume.\n\n20 Wells, _Anticipations_ [1902] (Mineola, NY, 1999), 38, 44; Seeley, _The Expansion of England_ , 62.\n\n21 Seeley, _The Expansion of England_ , 158\u201359.\n\n22 For further details, see chapter 7.\n\n23 Seeley, _The Expansion of England_ , 49.\n\n24 Bruce Bennett, _New Zealand's Moral Foreign Policy 1935\u201339_ (Wellington, 1962), 283.\n\n25 Daniel Gorman, _Imperial Citizenship_ (Manchester, 2006).\n\n26 Appadurai, \"Sovereignty without Territoriality,\" in _The Geography of Identity_ , ed. Patricia Yaeger (Ann Arbor, 1996).\n\n27 Ibid., 54.\n\n28 White, \"An Anglo-American Alliance,\" _North American Review_ , 158 (1894), 492\u201393; see also Walter Besant, \"The Future of the Anglo-Saxon Race,\" _North American Review_ , 163 (1896), 129\u201343.\n\n29 On the former, see in particular Henry Cabot Lodge, \"England, Venezuela, and the Monroe Doctrine,\" _North American Review_ , 160 (1895), 651\u201358. Indeed Lodge, a Massachusetts senator, regarded the British empire as a dangerous geopolitical competitor.\n\n30 Mahan, and Charles Beresford, \"Possibilities of an Anglo-American Reunion,\" _North American Review_ , 159 (1894), 554.\n\n31 G. S. Clarke, \"Imperial Responsibilities a National Gain,\" _North American Review_ , 168 (1899), 141.\n\n32 Harrison, \"Musings upon Current Topics II,\" _North American Review_ , 172 (1901), 354. On the history of the concept of the \"English-speaking peoples,\" usage of which originated in the 1870s and peaked during the early decades of the twentieth century, see Peter Clarke, \"The English-Speaking Peoples before Churchill,\" _British Scholar_ , 4 (2011), 199\u2013231.\n\n33 Dicey, \"A Common Citizenship for the English Race,\" _Contemporary Review_ , 71 (1897), 458.\n\n34 On Balfour's \"race patriotism,\" see Jason Tomes, _Balfour and Foreign Policy_ (Cambridge, 1997), chs. 2\u20134. On Milner, see J. Lee Thompson, _A Wider Patriotism_ (London, 2007).\n\n35 Milner, \"Credo,\" _Times_ , July 25, 1925.\n\n36 Beresford, \"The Future of the Anglo-Saxon Race,\" _North American Review_ , 171 (1900), 809.\n\n37 Carnegie, \"Americanism versus Imperialism,\" _North American Review_ , 162 (1899), 5\u20136; Carnegie, _The Reunion of Britain and America_ (Edinburgh, 1893), 9; Carnegie, \"The Venezuelan Question,\" _North American Review_ , 162 (1896), 132.\n\n38 Mayo Hazeltine, \"The United States and Great Britain,\" _North American Review_ , 162 (1896), 597.\n\n39 John Fleming, \"Are We Anglo-Saxons?,\" _North American Review_ , 153 (1891), 254.\n\n40 William Crosswell Doane, \"Patriotism,\" _North American Review_ , 166 (1898), 318.\n\n41 Dos Passos, _The Anglo-Saxon Century_ , 101, 104.\n\n42 Carnegie, _Reunion_ , 9.\n\n43 Waldstein, \"The English-Speaking Brotherhood,\" _North American Review_ , 167 (1898), 225, 230, 238.\n\n44 Rhodes, _The Last Will and Testament of Cecil J. Rhodes_ , ed. W. T. Stead (London, 1902), 73.\n\n45 Stead, _The Americanization of the World_ (New York, 1901), 100, 397.\n\n46 Ibid., 2.\n\n47 Dilke, _Greater Britain_ , 318.\n\n48 Wells, _Anticipations_ , ch. 8. On Wells, see also Deudney, _Bounding Power_ , pt. 3.\n\n49 Wells, _Anticipations_ , 146.\n\n50 Doyle, _The White Company_ (London, 1891); Doyle, \"The Adventures of the Noble Bachelor,\" in _The Adventures of Sherlock Holmes_ (London, 1892).\n\n51 Letter to William James, October 29, 1888, _The Letters of Henry James_ , ed. Percy Lubbock (New York, 1920), 1:141.\n\n52 For more on this argument, see Bell, \"Dreaming the Future,\" in _The American Experiment and the Idea of Democracy in British Culture, 1776\u20131914_ , ed. Ella Dzelzainis and Ruth Livesey (Aldershot, 2013), 197\u2013210.\n\n53 Carnegie, _Reunion_ , 12\u201313; Abbott, \"The Basis of an Anglo-American Understanding,\" _North American Review_ , 166 (1898), 521.\n\n54 Tourg\u00e9e, \"The Twentieth Century Peacemakers,\" _Contemporary Review_ , 75 (1899), 886\u2013908; Rhodes, _Last Will and Testament_ , 73, 66; Stead, _The Americanization of the World_ , 435. I develop this line of argument in Bell, \"Before the Democratic Peace,\" _European Journal of International Relations_ , 20\/3 (2014), 647\u201370.\n\n55 For the American reception, see, for example, William Roy Smith, \"British Imperial Federation,\" _Political Science Quarterly_ , 36 (1921), 274\u201397; George Burton-Adams, _The British Empire and a League of Peace_ (New York, 1919). On the impact on European debates, see John Kendle, _Federal Britain_ (London, 1997), ch. 6; Andrea Bosco, \"Lothian, Curtis, Kimber and the Federal Union Movement (1938\u20131940),\" _Journal of Contemporary History_ , 23 (1988), 465\u2013502; Michael Burgess, _The British Tradition of Federalism_ (London, 1995), pt. 3; John Turner, ed., _The Larger Idea_ (London, 1988).\n\n56 Margaret MacMillan, \"Isosceles Triangle,\" in _Twentieth-Century Anglo-American Relations_ , ed. Jonathan Hollowell (Basingstoke, 2001), 1\u201325.\n\n57 Timothy Shaw, _The Commonwealth_ (London, 2008).\n\n58 Priscilla Roberts, \"The Anglo-American Theme,\" _Diplomatic History_ , 21\/3 (1997), 333\u201364.\n\n59 Nicholas Cull, \"Selling Peace,\" _Diplomacy and Statecraft_ , 7 (1996), 1\u201328; Priscilla Roberts, \"The Transatlantic American Foreign Policy Elite,\" _Journal of Transatlantic Studies_ , 7 (2009), 163\u201383; Inderjeet Parmar, \"Anglo-American Elites in the Interwar Years,\" _International Relations_ , 16 (2002), 53\u201375; Paul Williams, \"A Commonwealth of Knowledge,\" _International Relations_ , 17 (2003), 35\u201358.\n\n60 David Reynolds, _The Creation of the Anglo-American Alliance, 1937\u201341_ (London, 1981); Reynolds, \"Roosevelt, Churchill, and the Wartime Anglo-American Alliance, 1939\u201345,\" in _The Special Relationship_ , ed. William Roger Louis and Hedley Bull (Oxford, 1986), 17\u201341.\n\n61 Robert Rhodes James, ed., _Winston S. Churchill_ (New York, 1974), 289. Churchill advocated a common citizenship between Britain and the USA. See Henry Butterfield Ryan, _The Vision of Anglo-America_ (Cambridge, 1987), ch. 3; Richard Toye, _Churchill's Empire_ (London, 2010), 240.\n\n62 Streit, _Union Now_ (New York, 1938), 2.\n\n63 Streit, _Union Now with Britain_ (New York, 1941).\n\n64 Lippmann, _US Foreign Policy_ (Boston, 1943), 83.\n\n65 Streit, _Freedom's Frontier_ (New York, 1961).\n\n66 Hartley, _Atlantic Challenge_ (New York, 1965), 92.\n\n67 Robert Strauz-Hupe, James Dougherty, and William Kintner, _Building the Atlantic World_ (New York, 1963).\n\n68 Streit, \"Atlantic Union,\" _Annals of the American Academy of Political and Social Science_ , 288 (1953), 8. While Streit routinely talked of uniting \"all democracies,\" he also stressed \"Atlantic Union,\" thus leaving unclear the role of the non-Atlantic parts of Greater Britain.\n\n69 See the argumentative shift between Angell, _The Political Conditions of Allied Success_ (New York, 1918), and Angell, \"The English-Speaking World and the Next Peace,\" _World Affairs_ , 105 (1942), 10.\n\n70 Angell, \"The British Commonwealth in the Next World Order,\" _Annals of the American Academy of Political and Social Science_ , 228 (1943), 65\u201370.\n\n71 Angell, \"Angell Sums Up at 85,\" _Freedom & Union_ (December 1958), 7\u201311.\n\n72 Deutsch et al., _Political Community and the North Atlantic Area_ (Princeton, 1957); see also Bruce Russett, _Community and Contention_ (Cambridge, MA, 1963).\n\n73 For analyses of such ideas, see Derek Heater, _World Citizenship and Government_ (Basingstoke, 1996); Jens Bartelson, _Visions of World Community_ (Cambridge, 2009).\n\n74 Jo-Ann Pemberton, _Global Metaphors_ (London, 2001); Wesley Wooley, _Alternatives to Anarchy_ (Bloomington, 1988).\n\n75 Wells, _The Outline of History_ (London, 1925), 708.\n\n76 Wells, _The New America_ (London, 1935), 24.\n\n77 Dulles, _War, Peace, and Change_ (New York, 1939); Willkie, _One World_ (New York, 1943).\n\n78 For further detail, see Joseph Preston Baratta, _The Politics of World Federation_ , 2 vols. (Westport, 2004), 162\u201364.\n\n79 Hutchins et al., _Preliminary Draft of a World Constitution_ (Chicago, 1948); See also G. A. Borgese, _Foundations of a World Republic_ (Chicago, 1953).\n\n80 Thomas Weiss, \"What Happened to the Idea of World Government?,\" _International Studies Quarterly_ , 53 (2009), 258; John Preston Baratta, \"The International Federalist Movement,\" _Peace & Change_, 24 (1999), 342.\n\n81 Craig Campbell, _Glimmer of a New Leviathan_ (New York, 2003); Deudney, _Bounding Power_ , ch. 8.\n\n82 Baratta, _The Politics of World Federation_. This transition was mirrored in the mutation of an \"astrofuturist\" discourse that focused on the possibilities of the exploration and conquest of outer space. This discourse emerged in the interwar years in the USA, Germany, Britain, and Russia, and flowered in the second half of the century, chiefly in the USA. It reached its apotheosis with the moon landing in 1969. During the interwar period it had been largely internationalist in orientation\u2014albeit infused with the justificatory strategies of imperialism\u2014whereas its post-1945 fortunes saw it tied increasingly to the priorities of the national security state. DeWitt Clinton Kilgore, _Astrofuturism_ (Philadelphia, 2003).\n\n83 Falk, _A Study of Future Worlds_ (New York, 1975). Falk drew on Louis Sohn and Grenville Clark, _World Peace through World Law_ (Cambridge, MA, 1958).\n\n84 Weiss, \"World Government?,\" 258.\n\n85 For discussion, see Luis Cabrera, \"World Government,\" _European Journal of International Relations_ , 16 (2010), 511\u201330.\n\n86 Wendt, \"Why a World State Is Inevitable,\" _European Journal of International Relations_ , 9 (2003), 491\u2013542; Deudney, _Bounding Power_.\n\n87 On his life and religious views, see Gerald Studdert-Kennedy, \"Christianity, Statecraft and Chatham House,\" _Diplomacy & Statecraft_, 6 (1995), 470\u201389; Deborah Lavin, _From Empire to International Commonwealth_ (Oxford, 1995).\n\n88 Curtis, _Civitas Dei_ , 3 vols. (London, 1937).\n\n89 Curtis, \"World Order,\" _International Affairs_ , 18 (1939), 309; cf. Curtis, _Civitas Dei_ , vol. 3. Curtis also expressed admiration for Streit's alternative Atlanticist plan. Curtis, \"World Order,\" 310; Curtis, \"The Fifties as Seen Fifty Years Hence,\" _International Affairs_ , 27 (1951), 273\u201384.\n\n90 Curtis, \"The Fifties,\" 284. On his role as a pioneer, see Streit, \"Lionel Curtis,\" _Freedom & Union_, 10 (1956), 10.\n\n91 Streit, \"Atlantic Union\"; Curtis, \"The Fifties,\" 275\u201376.\n\n92 Oliver, _Alexander Hamilton_ (London, 1906); Curtis, \"World Order,\" 302\u20137. Deudney's fascinating discussion of republican security in _Bounding Power_ is also modeled on American experience.\n\n93 Doyle, \"Liberalism and World Politics,\" _American Political Science Review_ , 80 (1986), 1162n2; cf. Ikenberry, _After Victory_ (Princeton, 2001), 178\u201379. For further discussion, see Duncan Bell, \"Before the Democratic Peace,\" _European Journal of International Relations_ , 20\/3 (2014), 647\u201370.\n\n94 McCain, \"An Enduring Peace Built on Freedom,\" _Foreign Affairs_ , 86 (November\/December 2007), 19\u201334. See also Ivo Daalder and James Lindsay, \"Democracies of the World, Unite,\" _American Interest_ , 2 (2007), 5\u201315; Francis Fukuyama, _America at the Crossroads_ (London, 2006); James Huntley, _Pax Democratica_ (London, 1998).\n\n95 Ikenberry and Slaughter, _Forging a World of Liberty Under Law_ (2006), Princeton Project on National Security, 2006), accessed July 22, 2011, <http:\/\/www.princeton.edu\/~ppns\/report\/FinalReport.pdf>, 7.\n\n96 For an insightful analysis, see Srdjan Vucetic, \"Anglobal Governance?,\" _Cambridge Review of International Affairs_ , 23 (2011), 455\u201374; Vucetic, _The Anglosphere_ (Stanford, 2011).\n\n97 Ferguson, _Empire_ (London, 2004).\n\n98 Bennett, _The Anglosphere Challenge_ (Lanham, MD, 2007).\n\n99 Roberts, _A History of the English-Speaking Peoples_. Cf. Churchill, _A History of the English-Speaking Peoples_ , 4 vols. (London, 1956\u201358). On the term \"English-speaking peoples,\" see Clarke, \"The English-Speaking Peoples.\"\n\n100 Roberts, _A History of the English-Speaking Peoples_ , 381.\n\n101 Jacob Weisberg, \"George Bush's Favourite Historian,\" _Slate_ , March 28, 2007, accessed July 26, 2011, <http:\/\/www.slate.com\/id\/2162837\/>.\n\n102 Robert Conquest, _Reflections on a Ravaged Century_ (London, 2000).\n\n103 Tocqueville, _Democracy in America_ , 13.\nPART III\n\nThinkers\nCHAPTER 9\n\nJohn Stuart Mill on Colonies\n\nThe question of government intervention in the work of Colonization involves the future and permanent interests of civilization itself.1\n\n\u2014JOHN STUART MILL\n\nDuring the last three decades, the study of imperialism has moved from the periphery to the center of work in the humanities and social sciences. The importance of viewing metropolitan and imperial spaces within a \"single analytic field\"\u2014as dynamically connected, interpenetrating, even mutually constitutive\u2014has been a key theme in this flourishing scholarship.2 This productive insight points historians of political thought in two main directions. First, to the value of comparative political theory, encompassing the study of non-Western traditions and the attempt to trace the manifold ways in which political ideas circulate across and around different geo-cultural zones. And second, in drawing attention to how past thinkers conceptualized the world, how they constructed and deployed categories including the domestic, the foreign, the imperial, and the colonial.\n\nIn this chapter I explore some important yet neglected aspects of John Stuart Mill's vision of global order. Mill has played a pivotal role in the recent wave of scholarship dedicated to unraveling the entanglement of Western political thought and imperialism.3 The reasons for this are obvious: he occupies a talismanic position in the liberal canon, and his career and writings provide fertile ground for analysis and critique. At the age of seventeen he began work at the East India Company, where he rose to high rank and left only after the company lost its charter in 1858. He continued to defend the British occupation until his death in 1873. While this scholarship has illuminated various aspects of Mill's imperial thought, especially his views on India, it has passed over other areas in near silence, and has often failed to account for the divergent ways in which he imagined and justified different modes of imperial rule. In particular, scholars have tended to ignore or downplay his extensive writings on (settler) colonization\u2014the establishment, as Mill saw it, of new \"civilized\" communities in North America and the South Pacific.4 (Throughout the essay, I use the term colonization to denote _settler colonization_ , not as a synonym for imperialism.) Historians of economic thought, meanwhile, have probed Mill's account of the political economy of colonization, but they have largely refrained from linking these arguments to other aspects of his social and political theory.5\n\nIn Victorian Britain it was common to delineate different types of imperial territory.6 Mill identified two classes of British \"dependencies\": those composed of people of a \"similar civilization\" that were \"capable of, and ripe for, representative government,\" and those, defined in hierarchical opposition, that remained \"a great distance from that state.\"7 The distinction between settler colonies and other imperial spaces encodes a problem, for it erases some of the key similarities between them. All forms of imperialism involved the violent dispossession of and rule over indigenous peoples. All had roots deep in the political and intellectual history of Europe. And all generated diverse forms of opposition, at home and abroad.8 Unreflexively reproducing the categories reinscribes the presumption underlying much nineteenth-century political thought, namely that the territories settled by Europeans were \"unoccupied,\" devoid of sovereign communities or rational autonomous agents.9 Marx was simply following convention when he referred to \"virgin soils, colonised by free immigrants.\"10 Nevertheless, the distinction is important for without understanding the uses to which it was put by historical agents, it is impossible to map the imaginative geography of empire. Despite the similarities between the forms of conquest, there were also key differences. Two are especially salient for interpreting Mill: the role of mass emigration and the desire to create _permanent_ \"civilized\" societies on distant continents.\n\nThis chapter explores Mill's defense of colonization. In his mind, Britain and its colonies (chiefly in Canada, Australia, and New Zealand) formed part of a single analytical field: they could not be viewed as discrete, autochthonous units. The singularity was itself predetermined by the theoretical machinery of utilitarianism and post-Ricardian political economy. He saw the world as a space of movement and exchange, the colonies and Britain as inextricably bound by flows of capital, labor, and information. This was reinforced by his belief that progressive colonies could play a catalytic role in the global \"improvement\" of humanity. Mill's arguments on the subject require reconstruction, drawing together material from books, journalism, official reports, and personal correspondence. In what follows, I analyze three key thematics in Mill's colonial writings: (1) his evolving account of the political economy of colonization; (2) his views on \"responsible government\" and character formation; and (3) finally, his elaboration of the role played by conceptions of physical space, and of the constitutional structure of the imperial system.\n\nI also pursue two subsidiary lines of argument. First, I identify how Mill's justificatory account of colonization shifted over time. We witness a movement from the particular to the universal, from arguments justifying colonization primarily in terms of the benefits that it generated for the British state (and especially the working classes) to arguments that stressed the value of colonization (and especially British colonization) for the world as a whole. This signaled a subtle but significant change in emphasis, a change that sheds light on his understanding of the trajectory of modern politics. It is explained chiefly by his mutating perception of prevailing conditions. His account of colonial order\u2014like his political thought as a whole\u2014was structured by the dynamic interplay of general principles and interpretations of the exigencies of social, economic, and political life. While circumstances did not radically transform his core philosophical commitments, they did qualify them or identify some political options (or institutional configurations) as preferable to others.\n\nThe other line of argument focuses on how Mill framed his narrative. David Scott has drawn attention to the literary modes of emplotment shaping anticolonial nationalist writings and much postcolonial criticism. Both construct history, he contends, as a romantic narrative of heroic overcoming and redemption.11 Jennifer Pitts, meanwhile, has emphasized the significance of \"rhetorical practices\" in structuring moral discourse about empire, arguing that there was a strong correlation between anti-imperialism and the authorial use of irony and humor. In Mill's \"imperial liberalism\" she identifies a distinct \"earnestness\" that distinguished him from Burke and even Bentham.12 In the colonial context we see a transition in Mill's writings from a broadly romantic narrative to a position I label _melancholic colonialism_. Mill's colonial romance charted a story of unfolding enlightenment, in which a vanguard of far-sighted \"philosophical legislators\" transcended a reactionary past, opening up new vistas of human possibility. It was an optimistic story, untroubled by misgivings or doubt. Melancholic colonialism, in contrast, was marked by anxiety, even despondency, about the direction of (colonial) history, but it ultimately refused to reject the ideal, suggesting that the worst excesses could be mitigated, if not eradicated entirely. The transition occurred in the last decade of Mill's life, and was engendered above all by his increased awareness of the pathologies of colonialism, and especially the prevalence of settler violence. It signals an important shift in the way in which he conceived of the ethico-political potential of colonization.\n\nWhile Mill regarded Britain and the colonies as part of a single analytic field, there were cognitive and theoretical limits to his vision. He always saw the colonies as embryonic nations, bound ultimately for independence, their sheer physical distance from Britain rendering them indissolubly separate. They did not constitute part of a _single political field_ \u2014a field in which the colonies and Britain were envisioned not simply as bound together by economic flows, shared interests, and webs of communication, but as comprising a durable political community grounded in a thick common identity. Mill never thought that Britain and its colonies formed (or could form) a single integrated polity. Around the time of his death this alternative vision, which underpinned a normative defense of the permanence of the colonial connection, came to dominate imperial discourse, pushing his position to the sidelines.\n\nOn Systematic Colonization: From Domestic to Global\n\nEarly nineteenth-century Britain was characterized by \"a constant sensation of fear\u2014fear of revolution, of the masses, of crime, famine, and poverty, of disorder and instability, and for many people even fear of pleasure.\"13 Profound apprehension shadowed, and helped to motivate, political thought. Mill's political economy of colonization was shaped by two intersecting debates. The first concerned the material benefits and burdens of colonization; the second concentrated on how best to respond to the social and political turmoil that gripped Britain following the defeat of Napoleon in 1815. Focused inwards on the apparently perilous state of Britain, these concerns drove Mill's earliest forays into colonial advocacy.\n\nPolitical economists had long disagreed over the value of colonies. Adam Smith had derided them as a sink for capital and labor, as had Bentham and James Mill.14 Yet during the 1820s and 1830s, an increasing number of thinkers, including Nassau Senior, Robert Torrens, and Herman Merivale, came to view colonies in a more positive light\u2014as potential sites of economic productivity, social amelioration, and civilizational potential.15 At the heart of this reorientation stood Edward Gibbon Wakefield, a rogue political economist who exerted a profound influence over mid-nineteenth-century colonial discourse.16 Marx's analysis of \"The Modern Theory of Colonisation\" in _Das Kapital_ focused almost solely on Wakefield's arguments, while Mill regarded him as \"one of the most vigorous and effective writers of our time.\"17 He was to play a key role in the development of Mill's colonial vision.\n\nWriting from a London prison\u2014where he was interned for abducting a young heiress\u2014Wakefield published his _Letter from Sydney_ in 1829.18 On his release, he founded the National Colonization Society (1830) to promote his views. The elderly Jeremy Bentham, a friend of Wakefield's father, was an early convert, as was the young John Stuart.19 In 1830 Mill, then a precocious twenty-four, described emigration as a \"momentous subject,\" constituting the \"only feasible mode of removing the immediate pressure of pauperism,\" and throughout the following decade he proselytized on behalf of state-sponsored systematic colonization.20 Above all, he argued, colonization could alleviate suffering among the British working classes. In 1834 he joined the recently founded South Australian Association, which included among its members a number of the other leading philosophic radicals, notably George Grote, whose work was soon to refigure the place of democracy in British political consciousness, and Sir William Molesworth, the editor of Hobbes.21 It campaigned vociferously for the creation of a new colony in South Australia, \"as like as possible to a country which is perfectly civilized, but not over-peopled.\"22 While he thought that many aspects of this project were novel, the result of innovative theoretical advances in moral philosophy and political economy, Mill also suggested that in some respects it resembled the noble experiments of the ancient Greeks.\n\nLike the Grecian colonies, which flourished so rapidly and so wonderfully as soon to eclipse the mother cities, this settlement will be formed by transplanting an intire society, and not a mere fragment of one. English colonies have almost always remained in a half-savage state for many years from their establishment. This colony will be a civilized country from the very commencement.23\n\nThe \"colonial reformers,\" as they came to be known, were the heroes of Mill's colonial romance, battling against tradition and the political establishment. And Mill himself was ready to practice what he preached: during the 1830s he considered emigrating to Australia.24\n\nJonathan Riley distinguishes between Mill's \"Ricardian science\" and his \"liberal utilitarian art.\" The science \"consists of abstract 'laws' or theorems which presuppose that any person is motivated primarily by a desire for wealth,\" while recognizing that this motive is sometimes constrained by other nonmaterial desires (such as the pursuit of leisure). The art, which was shaped by but not reducible to the science, takes the \"laws\" and \"converts and rearranges them into a system of practical rules, and then applies the rules in concrete circumstances to promote the general welfare.\"25 The distinction is important for understanding Mill's conception of colonization (although so too is recognition of Mill's deviations from Ricardian orthodoxy).26 The science specified the reasons for the economic and social turmoil, while the art identified colonization in general\u2014and systematic colonization in particular\u2014as a viable solution available to enlightened political leaders, if they were willing to grasp its potential. Mill came to regard this willingness as a marker of political imagination and maturity.27\n\nAccording to Wakefield and Mill, the social crisis in Britain was caused by a shortage of land and an excess of capital and labor. This produced low levels of growth, a stagnant labor market, and increasing unrest. Emigration to the underpopulated colonies offered the most effective answer.28 It rendered \"the vast productive resources of our colonies available for the employment and comfortable subsistence of the unemployed poor of our country,\" and it could provide \"material relief\" to the \"labouring classes from the pressure of their own excessive competition.\"29 But Mill was wary of unregulated flows of people; rational order was necessary to maximize utility. Emigration should be neither a piecemeal voluntaristic process nor a crude attempt to \"shovel out paupers,\" but instead part of a coordinated state-sponsored scheme of colonization.30 In pushing for the creation of further colonies in Australia, Mill waxed lyrical about the \"the enlightened view of Colonization\" and the \"honesty and patriotism\" that underpinned this ambition.31 He emphasized two aspects. First, it would relieve socioeconomic pressure at home. And second, it would be financially self-supporting. The latter, Mill thought, was unprecedented: \"[F]or the first time in the history of overpopulation, emigration will now be made to pay its own expenses; and whatever relief it can allow to the pressure of population against subsistence in our own country, will be clear gain\u2014pure, unalloyed good.\"32 Indeed he suggested that colonization was the most important factor in the progressive development of the working classes. It would, he argued in 1837, \"produce a more immediate and obvious benefit to the industrious classes generally, and to the labouring class above all, than even the great constitutional changes which we are contending for.\"33 It was more far-reaching, that is, than the extension of the franchise. Systematic colonization, combined with the repeal of the Corn Laws, would unleash the productive promise of the British economy and help to emancipate the \"labouring class.\"34\n\nMill's most thorough discussion of systematic colonization can be found in the _Principles of Political Economy_ , first published in 1848.\n\nThe system is grounded on the important principle, that the degree of productiveness of land and labour depends on their being in due proportion to one another; that if a few persons in a newly-settled country attempt to occupy and appropriate a large district, or if each labourer becomes too soon an occupier and cultivator of land, there is a loss of productive power, and a great retardation of the progress of the colony in wealth and civilization.35\n\nYet despite this obvious problem, the \"instinct... of appropriation\" meant that emigrant laborers typically tried to secure as much land as possible, aiming to \"become at once a proprietor.\" Consequently there were too few laborers to support the investment of capital. Systematic colonization would disrupt this self-defeating process, so that \"each labourer is induced to work a certain number of years on hire\" before assuming a proprietary role. This was necessary to create a \"perpetual stock\" of laborers for the provision of public goods\u2014roads, canals, irrigation projects\u2014and the development of thriving towns.36 He planned to \"check the premature occupation of land\" and the dangerous \"dispersion of people\" by instituting a strict regime of land pricing. The basic idea was to sell \"all unappropriated lands at a rather high price, the proceeds of which were to be expended in conveying emigrant labourers from the mother country.\" The income could finance colonial emigration, creating a steady flow of wage-laborers fit to service an expanding capitalist economy. Wakefield and Mill added further refinements. They insisted on the importance of urbanization for creating \"civilized\" communities.\n\nIt is a beneficial check upon the tendency of the population of colonists to adopt the tastes and inclinations of savage life, and to disperse so widely as to lose all the advantages of commerce, of markets, of separation of employments, and combination of labour.37\n\nMetropolitan concentration, not the frontier virtues of agrarian republicanism, offered the greatest moral and political promise.38 Bourgeois modernity was urban. Likewise, they argued that it was vital to prioritize the emigration of young families to normalize social relations and accelerate population growth.39 In short, they conjoined three different types of argument: a diagnosis of the social question, a prescription for solving it, and the identification of specific institutional mechanisms to realize their plans.\n\nIt is unsurprising that Wakefield's analysis drew Marx's attention. For Marx, \"virgin\" colonies offered the potential to serve as free spaces for labor. While Wakefield had identified correctly the \"anti-capitalist cancer of the colonies,\" he sought to excise it by privatizing property. Wakefield's \"great merit,\" Marx proclaimed, was to have\n\n... discovered in the Colonies the truth as to the conditions of the capitalist production in them. As the system of protection at its origin attempted to manufacture capitalists artificially in the mother country, so Wakefield's colonisation theory... attempted to effect the manufacture of wage workers in the Colonies.40\n\nNote, though, that for Marx the \"evils\" of British settler colonialism lay chiefly in the spread of capitalist social relations rather than in the injustice of occupation itself.41 He seemed to think that an uncorrupted form of colonial emigration might allow people to escape the relentlessly dehumanizing logic of modern capitalism. This pointed to an alternative, noncapitalist form of colonial romance.\n\nMill's advocacy of systematic colonization was not insulated from his wider social and political theory. In the next section I discuss how it related to his views on character and nationality. Here, however, it is worth stressing that in the _Principles_ the argument was embedded in an account of the legitimate role of government, and especially of the justified exceptions to the policy of _laissez-faire_. In his analysis of the \"functions of government in general\" in Book 5, Mill divided \"the province of government\" into \"necessary\" and \"optional\" aspects. The former were those functions that were \"either inseparable from the idea of government, or are exercised habitually and without objection by all governments,\" while the latter were those \"which it has been considered questionable whether governments should exercise them or not.\" This did not render the optional aspects unimportant, it meant only that the \"expediency\" of the government exercising those functions did not amount to necessity.42 Mill was concerned here, as elsewhere, with a dual task: defending a version of Ricardian economic science whilst identifying legitimate exceptions to a libertarian interpretation of the functions of government. He challenged the view that the state should only provide protection against \"force and fraud.\"\n\nMill introduced systematic colonization in a discussion of \"cases in which public intervention may be necessary to give effect to the wishes of the persons interested.\"43 These cases identify a collective action problem in which the uncoordinated (instrumentally) rational actions of individual agents resulted in suboptimal outcomes for everyone involved. While individuals might benefit in the short term, the colony was damaged by existing emigration practices.\n\nHowever beneficial it might be to the colony in the aggregate, and to each individual composing it, that no one should occupy more land than he can properly cultivate, nor become a proprietor until there are other labourers ready to take his place in working for hire; it can never be the interest of an individual to exercise this forbearance, unless he is assured that others will not do so too... It is the interest of each to do what is good for all, but only if others will do likewise.44\n\nThe lack of guaranteed reciprocity meant that there was an overriding case for government regulation. If colonization was to benefit everybody, the enterprise must \"from its commencement\" be undertaken \"with the foresight and enlarged views of philosophical legislators.\"45 Here we see an instance of Mill's long-standing belief in the role of disinterested expertise. Just as he thought that India was best governed by the bureaucracy of the East India Company, and that representative democracy was best regulated by the expertise of the enlightened, so he also thought that colonial development needed to be directed by a class of \"philosophical legislators\" who understood the art and the science of political economy, and who recognized the duty to seek the improvement of humanity. The need for such legislators only increased as the century wore on, as the colonies grew in strength and size, and as their institutions increasingly diverged from those in Britain. In a letter written in 1870, for example, he argued that because colonial societies were \"much more democratic than our own\" it required imagination to support them. \"[O]nly very exceptional persons in our higher and middle classes... could either reconcile themselves to it or have the foresight and mental adaptability required for guiding and organising the formation of such a community.\"46 By then he had come to realize, much to his dismay, that such persons were very rare.\n\nWhereas Mill's colonial advocacy in the 1830s and early 1840s had principally emphasized the domestic benefits of systematic colonization\u2014its ability to address the \"social problem\" in Britain\u2014this began to change in the late 1840s. The shift was apparent in the _Principles_ , and became increasingly pronounced in the following years. In the _Principles_ Mill stressed, in a way that he had not done previously, the global economic benefits of (British) systematic colonization.\n\nTo appreciate the benefits of colonization, it should be considered in its relation, not to a single country, but to the collective economical interests of the human race. The question is in general treated too exclusively as one of distribution; of relieving one labour market and supplying another. It is this, but it is also a question of production, and of the most efficient employment of the productive resources of the world.47\n\nLaborers in the colonies were more productive than those in Britain, and their migration would expand the colonial economies while easing the restrictions on domestic growth.48 This in turn would catalyze further productivity. Everybody would benefit. While this line of argument had been implicit in the logic of Mill's earlier writings, he had placed little weight on it. From the late 1840s onwards it moved to center stage.\n\nThis shift in emphasis was the product of a series of changes in British, colonial, and global politics. This confluence of events reoriented Mill's normative account of the main purposes\u2014the ultimate aims\u2014of colonization. In 1846, the Corn Laws were repealed. In 1848, Britain avoided the revolutionary tumult that gripped the continent, in part because of the \"safety valve\" provided by the empire.49 The Chartist agitation ended in a damp squib. The economy prospered, while the \"social question\" receded from the forefront of political consciousness. The ghost of Malthus was temporarily exiled.50 It was also a period during which the colonies were granted self-governing status (under the aegis of \"responsible government\"), and in which their populations and economies grew rapidly.51 Mill saw confirmation of his optimistic predictions. Writing to an Australian correspondent in 1856, he was cheered by the fact that the colonies \"seem to be the most prosperous and rapidly progressive communities.\" This \"unexampled growth,\" was chiefly the result of the \"Wakefield system.\"52 A glorious new era was unfolding. Overcoming obdurate politicians and an indifferent public, outfoxing recalcitrant colonial officials and fighting the historical baggage of the pernicious \"old colonial system,\" the once embattled colonial reformers had triumphed. This was the apotheosis of colonial romanticism.\n\nAs well as triggering a shift in the purposes of colonization, the change in empirical conditions also forced Mill to reassess the significance of specific elements of Wakefield's scheme. In the 1865 edition of the _Principles_ , for example, he added a new passage to his discussion of the most effective ways to relieve pressure on the labor market. The onset of free trade, combined with a \"new fact of modern history,\" had transformed the situation. While his argument for systematic colonization remained \"true in principle,\" material advances had rendered it less urgent. \"The extraordinary cheapening of the means of transport... and the knowledge which nearly all classes of the people have now acquired... of the condition of the labour market in remote parts of the world, have opened up a spontaneous emigration from these islands to the new countries.\"53 The new dispensation, then, had both material and epistemic dimensions. The lowering of costs, combined with an increase in wages, meant that more people than ever had the economic _capacity_ to emigrate without government support. As such, one of the key pillars of the Wakefield system\u2014the self-financing provision\u2014was less relevant than before.54 But equally important was _knowledge_ , and in particular a growing awareness of the opportunities available.55 The novel communications technologies that were beginning to shrink the world in the imagination of Mill's contemporaries simultaneously aided in the diffusion of information, which made ocean-spanning travel seem appealing and feasible. This \"new fact\" offered further openings for civilizing the British, and perhaps most of all for educating the workers into responsible citizenship. The respite had, he argued, \"granted to this overcrowded country a temporary breathing time, capable of being employed in accomplishing those moral and intellectual improvements in all classes of the people, the very poorest included, which would render improbable any relapse into the over-peopled state.\"56 Moreover, the perceived change in conditions meant that political priorities had shifted: \"[O]ur politicians,\" he wrote, \"have grown more afraid of under than of over population.\"57 As a result, any impetus to stimulate emigration would now have to come from the colonies.\n\nSoon after Mill added this qualifier to the _Principles_ , he was perturbed to discover that his arguments for the protection of infant industries were being utilized by advocates of protectionism in the United States and the colonies.58 He engaged in an extensive correspondence on the issue\u2014several of his letters were printed in the colonial press\u2014rebutting the suggestion that his arguments applied there.59 This led him to rethink aspects of his position. Indeed, he indicated in a couple of letters written in 1868 that he no longer supported protection, preferring instead the idea of an annual grant from the treasury.60 Once again, we witness his prescriptions\u2014aspects of his art\u2014shifting in light of unforeseen developments.\n\nFrom the start of his career, then, Mill advocated systematic colonization. During the 1830s, when the economic plight of Britain seemed desperate, he viewed it chiefly as a means to answer the \"social question.\" Yet the situation was dynamic: the rapid development of the colonies and the stabilization of Britain rendered this narrow justification obsolete. His account of the utility of colonization therefore shifted along with his interpretation of empirical conditions. In particular, we witness two moves. First, his arguments from political economy increasingly emphasized the universal benefits of colonization. And second, as I explore in the rest of this chapter, the political economy arguments were increasingly reinforced, if not displaced, by a new range of geopolitical and ethical concerns.\n\nColonial Autonomy, Character, and Civilization\n\nWhile both Mill and Wakefield agreed on the underlying economic causes of the crisis afflicting Britain, as well as the best remedy for it, they presented different visions of the future, although this was never made explicit. Wakefield was motivated by fear of revolution. In _England and America_ (1833), the text that had drawn Marx's ire, he warned of the impending dangers:\n\n[F]or a country now situated like England, in which the ruling and the subject orders are no longer separated by a middle class, and in which the subject order, composing the bulk of the people, are in a state of gloomy discontent arising from excessive numbers; for such a country, one chief end of colonization is to prevent tumults, to keep the peace, to maintain order, to uphold confidence in the security of property, to hinder interruptions to the regular course of industry and trade, to avert the terrible evils which, in a country like England, could not but follow any serious political convulsion.61\n\nHis conception of colonization was ultimately more conservative than Mill's. He wanted to transpose hierarchical British social relations onto the colonies, recreating the new societies in the image of the old. Mill's vision was dynamic; he viewed the colonies as spaces for innovation and forms of progressive self-fashioning. They provided an escape from the parochialism and class-bound rigidities of British life, allowing\u2014even demanding\u2014experimentation in ways of living.\n\nExperimentation was central to Mill's account of the development of \"character,\" both individual and collective.62 For Mill, character was not a biological given, but rather a product of the environment, and throughout his writings he stressed the \"extraordinary susceptibility of human nature to external influences.\"63 He saw the colonies, I would argue, as laboratories of character development, as vast case studies of his proposed science of \"ethology.\"64 Systematic colonization offered the opportunity to create new advanced political communities, populated by industrious, confident, democratic individuals. This points to a significant discrepancy between Mill's account of colonization and his views on India. Uday Singh Mehta suggests that liberalism \"found the concrete place of its dreams\" in empire.65 For Mill, though, different elements of the empire spawned different dreams. India was a site for the reformist utilitarian project, for the mission to bring civilized enlightenment to a \"backward\" corner of the earth. Imperial governance, on this view, was a political technology that aimed to reshape the people who already lived there, bringing into being a different form of life, new modes of subjectivity, a fresh cultural-political constellation. Settler colonization, on the other hand, did not aim to transform the character of indigenous populations, or even to radically refashion the emigrants. It sought instead to provide an environment in which their existing civilizational potential could be realized. Such environments were conducive to the production of virtuous individuals and communities. The romance of colonialism was thus premised on the ethological opportunities opened up in distant \"virgin\" lands.\n\nWhile Mill spent much of the early 1830s focusing on Australia, in the second half of the decade his attention was increasingly drawn across the Atlantic to Canada, which he had previously regarded as one of the decaying \"colonies on the old system.\"66 The rebellions in Canada in 1837\u201338 provided a rare chance to refound a corrupt polity. For Mill, the crisis was never simply about the status of Upper and Lower Canada. After all, he assumed that in the future Canada would achieve full political independence. It was important for two other reasons: the legitimacy of imperial rule _in general_ and the fate of British political radicalism. The colonies and the metropole were once again figured as part of the same analytic field.\n\n\"[l]n an evil hour,\" Mill later reflected, the Canada question \"crossed the path of radicalism.\"67 The lightning rod here was the unlikely figure of Lord Durham. A vain, sickly, hugely wealthy scion of the Whig aristocracy, Durham had managed to alienate his colleagues in government while attaining great popularity among liberal and radical thinkers. Mill viewed Durham as a potential leader for the Radical party that he was attempting to create. In December 1837, news reached Britain that the French Canadians of Lower Canada had risen up against the colonial government. The rebellion was swiftly extinguished.68 Durham, a man who had previously shown little interest in colonial affairs, was appointed Governor-General and instructed to resolve the situation. One product of his brief stay in Canada\u2014he resigned in October 1838 following government censure of some of his activities\u2014was his report on \"the affairs of British North America,\" which came to be seen as one of the key documents in nineteenth-century British imperial history.69\n\nThe Canadian rebellions threatened an imperial legitimation crisis. For Mill the moral justification of the settler empire was different from that of the Raj. Empire in general could be justified if, and only if, it benefitted those subjected to it, but if those subjects lacked sufficient rationality\u2014if they failed to pass a (fluid) threshold of civilization\u2014then they could claim little control over their own form of government. Unless or until they passed that threshold, their destinies were best left to more enlightened peoples. This was, of course, how Mill saw India, and it generated a paternalist justification of despotism.70 In settler communities, on the other hand, the purportedly civilized character of the populations meant that questions of recognition and reciprocity were paramount. The colonies were legitimate expressions of political power only insofar as this was accepted by those they ruled over. In this sense, the relationship was voluntaristic. Colonial rule depended on a stable normative order in which everyone knew their assigned place, and challenges to this order broke the compact between governments and subjects. Mill feared that an inappropriate response to the Canadian rebellion would threaten the legitimacy of the colonial empire. Britain, he argued, should treat its (settler) colonial populations fairly, on both intrinsic grounds (because justice demanded it) and for more instrumental reasons. It was vital that Britain maintained\u2014and was _seen_ to maintain\u2014its reputation for \"wisdom and foresight, for justice, clemency, and magnanimity\" in the \"eyes of all nations.\"71 Legitimacy was as much a matter of perception as right action.\n\nIn line with many of his fellow radical liberals, Mill argued that the Canadians, while imprudent, had a \"just cause\" for revolting, for they had challenged a tyrannical system of government, an oppressive \"foreign yoke\": \"They are styled rebels and traitors. The words are totally inapplicable to them.\"72 The justice of the rebellion was a product of the illegal and immoral way in which the British government had overridden Canadian constitutional arrangements. \"The people of Canada,\" argued Mill, \"had against the people of England legitimate cause of war. They had the provocation which, on every received principle of public law, is a breach of the conditions of allegiance.\"73 He insisted that it was important to \"understand\" and to address the legitimate grievances of the rebels. Refusal to do so undermined the legitimacy of British rule. He saw Durham's mission as an opportunity to transform Canada from an unjustly governed polity into a model colony. It was a \"tabula rasa,\" open to Durham to \"inscribe what character he pleases.\"74\n\nFollowing what he assumed were the outlines of Durham's proposal, Mill argued for the creation of a broadly federal system uniting Lower and Upper Canada.75 This would guarantee political justice to both sides. With skillful institutional design, minority protection could be assured. Moreover, in the long run it would also help to eliminate one of the residual problems encountered in Canada: the problem of nationalities. A positive side effect of federation, he claimed, was that it provided the \"only legitimate means of destroying the so-much-talked-of nationality of the French Canadians,\" compelling them to see themselves not as a \"separate body\" but as \"an integral portion of a larger whole.\" Combining the best characteristics of each \"race\" would create a \"nationality of country,\" a sense of commitment to the state as opposed to the particularism of ethnic interests. It would forge them into \"British Americans.\"76 But it was not to be. Following Durham's humiliating resignation, Mill attempted to defend him, suggesting that he had demonstrated his fitness to lead the \"great reform party of the empire.\"77 This represented the triumph of hope over reality. By 1840 the plan was dead: Durham's activities had alienated many radicals, and he was not interested in the role that Mill envisaged for him.78\n\nThe intersection of race, nationality, and colonization can also be witnessed in Mill's analysis of the Irish famine a few years after the Canadian turmoil. As Pitts observes, he had a far more sympathetic understanding of the travails of the Irish peasantry than he did of the Indians, ascribing to the former \"a moral dignity and rationality\" he never accorded the latter.79 Yet the Irish still remained subordinate in Mill's imperial topography; his sympathy did not translate into granting them civilizational equality. Once again, his comments on this issue emerged in relation to a set of ongoing arguments about how best to respond to crisis. Did state-sponsored colonization offer an apposite solution to the problems of Ireland? In a letter penned to Tocqueville's travelling companion, Gustave Beaumont, in October 1839, Mill argued that it did.80 Yet by the mid-1840s, as the famine began to wreak its terrible havoc, he had changed his mind. While acknowledging the very serious problems in Ireland, he contended that they could be resolved by enacting a system of peasant proprietorship on reclaimed waste lands.81\n\nHe offered two reasons why systematic colonization was inappropriate in Ireland. First, it was prohibitively expensive: there were simply too many people who would need financial support to emigrate. The second reason goes to the heart of Mill's views on race, nationality, and ethology. He did not consider the Irish suitable apostles of civilization; their characters were too deformed by their blighted environment. This differentiated them from the settler populations in Australia, New Zealand, and Canada. In a newspaper article published in October 1846, he argued that \"it is not well to select as missionaries of civilization a people who, in so great a degree, yet remain to be civilized.\" Encouraging Irish emigration would retard the progressive potential of colonization. \"It is a serious question,\" he continued, \"whether, in laying the foundation of new nations beyond the sea, it be right that the Irish branch of the human family should be the predominant ingredient.\" He thought it \"desirable\" that the Irish should \"enter into the admixture,\" as the Saxon race needed \"to be tempered by amalgamation with the more excitable and imaginative constitution and the more generous impulses of its Celtic kinsfolk,\" yet this process had to remain asymmetric, the Irish qualities tempering but not displacing the dominant Saxon racial configuration.82 Mill's argument centered, once again, on the issue of character. The modern Irish character was deformed by economic exploitation and religious subservience. The Irish, he continued, lack \"individual hardihood, resource, and self-reliance\"; they demanded instead \"to be led and governed.\" And, moreover, they had been \"made lawless and disorderly\" by centuries of British misrule.83 With this common liberal move, Mill simultaneously acknowledged an earlier British injustice while employing its results to undermine political claims in the present. Not only did the Irish fail to display the moral resources necessary for successful colonization, they now exhibited the potential to disrupt the colonial order through lack of discipline, even criminal excess. Their behavior would give colonization a bad name. Instead, he looked elsewhere: \"The English and Scotch are the proper stuff for the pioneers of the wilderness.\"84 Racial difference, figured as civilizational capacity, structured Mill's analytical field, identifying a hierarchy of peoples ranked according to their ability to fabricate civilization in wild and distant locations.\n\nMelancholic Colonialism and the Pathos of Distance\n\nDuring the last decade and a half of his life we witness a distinct shift in the _tone_ of Mill's colonial writings. The romance faded, to be replaced by something more somber, even downcast. We also witness an increasing emphasis placed on noneconomic arguments. The most extensive analysis of colonization in Mill's later career is found in chapter 18 of the _Considerations on Representative Government_ (1861). The direct economic benefits of colonization play only a subsidiary role in his analysis. His earlier concern with the urgency of emigration is also absent. Indeed Mill suggested that the material costs generated by the colonies offset the benefits. \"England derives little advantage, except in prestige, from her dependencies; and the little she does derive is quite outweighed by the expense they cost her, and the dissemination they necessitate of her naval and military force.\"85 Not only was it expensive to maintain a colonial empire, it was also potentially dangerous, leading to extensive global military commitments. Imperial overstretch beckoned. \"Great Britain,\" Mill concluded, \"could do perfectly well without her colonies.\" Despite this, he argued that the colonies were still valuable, for they produced a wide range of other benefits, both for Britain and (perhaps more importantly) the world.\n\nMill starts the chapter by noting that only in the \"present generation\" had the British realized the \"true principle\" of colonial government. Previously they had meddled incessantly in colonial affairs. This was a \"corollary\" of the \"vicious theory\" of colonization that had long guided European policy, and which was premised on the view that colonies existed primarily for economic exploitation. The habit of meddling had outlasted the mercantile system, and it was the \"persistence in domineering\" that had caused the Canadian rebellion. However, out of this disaster had flowed enlightenment, for the foresight of Durham, Wakefield, Buller, and Roebuck\u2014and of course Mill himself\u2014had led to the abandonment of the \"vicious theory.\" Durham's report had inaugurated a \"new era\" in which the colonies were granted \"the fullest measure of internal self-government.\" This system bore little relation to previous modes of coercive colonial rule. Indeed if the colonies were to remain part of the British imperial system, it had to be on a voluntary basis. \"[O]n every principle of morality and justice,\" he argued, \"she [Great Britain] ought to consent to their separation, should the time come when, after full trial of the best form of union, they deliberately desire to be dissevered.\"86 The lessons of the American Revolution were etched deeply into Mill's political consciousness.\n\nMill offered three separate reasons for maintaining the colonial empire. First, he sketched an argument about what international relations theorists refer to as the \"security dilemma.\" The dilemma arises when two or more states coexisting in a condition of anarchy\u2014lacking a global leviathan to regulate their interactions\u2014are drawn into a conflictual posture despite their (potentially) nonaggressive intent.87 In a condition of uncertainty, political leaders are compelled to engage in actions that can inadvertently generate further insecurity. The greater the number of sovereign units populating the international system, the greater the probability of conflict. Mill thought that the colonial empire helped to mitigate this problem. It was, he argued, a step \"towards universal peace, and general friendly cooperation among nations.\" He offered two distinct arguments. In the first instance, it \"renders war impossible among a large number of otherwise independent communities.\" It dampened the dilemma by reducing the number of units in the system. Second, it prevented any of the colonies \"from being absorbed into a foreign state, and becoming a source of additional aggressive strength to some rival power, either more despotic or closer at hand, which might not always be so unambitious or so pacific as Great Britain.\"88 It restrained the growth of potentially belligerent states while maintaining British predominance. A stable international system enhanced British security, as did the inability of other states to absorb the colonies. The rest of the world benefitted, moreover, for despite its faults Britain remained the most progressive of nations.\n\nMill's second reason for maintaining the colonial system concerned the moral and economic exemplarity of Britain's commitment to free trade. The existence of the colonies \"keeps the markets of the different countries open to one another, and prevents that mutual exclusion by hostile tariffs, which none of the great communities of mankind, except England, have yet completely outgrown.\" Britain could offer an alternative, and superior, model of economic organization to the protectionism that was sweeping Europe and the United States. Mill's final argument focused on liberty. The colonial empire, he contended,\n\n... has the advantage, specially valuable at the present time, of adding to the moral influence, and weight in the councils of the world, of the Power which, of all in existence, best understands liberty\u2014and whatever may have been its errors in the past, has attained to more of conscience and moral principle in its dealings with foreigners, than any other great nation seems either to conceive as possible, or recognise as desirable.89\n\nThis conceited picture was a staple of British political thought. The British frequently saw themselves\u2014and liked to think that they were seen by others\u2014as the avatars of liberty. Consequently, the greater the reach of their institutions, the greater the benefits for all. Even Mill, a man deeply critical of many aspects of his society, held this as an article of political faith.\n\nAs I have suggested already, until the early 1860s Mill presented a remarkably optimistic picture of the potential of settler colonialization. This was colonization as romance: an uplifting story of progressive forces overcoming numerous obstacles, supplanting a \"vicious\" theory with an \"enlightened\" one, and consequently heralding a bright new dawn for the peoples of Britain and the world. Yet in the last decade of his life his optimism faded, to be replaced by a more disenchanted, anxious stance. In part this was because reality had caught up with the fantasy: as the colonies grew in population and power, and as they secured significant political autonomy, Mill realized that they were failing to play their allotted roles. There were three main problems. First, the colonies were becoming increasingly protectionist, thus adopting an economic system that he had spent decades inveighing against. Second, the new colonial authorities had failed to deal properly with the land question. Finally, and perhaps most devastatingly, the colonists themselves seemed to be resorting to barbarism in their treatment of indigenous peoples. Granting colonial autonomy had undercut the civilizing potential of colonization. When enacted, sound liberal principles came into destructive conflict.\n\nAn early hint of Mill's disquiet can be found in the _Considerations_. He observed that an example of \"how liberal a construction has been given to the distinction between imperial and colonial questions,\" was seen in the \"uncontrolled disposal\" of \"unappropriated lands\" in the colonies. \"[W]ithout injustice,\" Mill lamented, the land could have been employed \"for the greatest advantage of future emigrants from all parts of the empire.\"90 In his correspondence he was adamant that in failing to fully implement systematic colonization the new colonies were undermining their own developmental potential. The \"unoccupied\" lands, he complained in 1871, should have been \"reserved as the property of the empire at large until much greater progress had been made in peopling them.\"91\n\nDuring the 1860s, Mill became increasingly critical of the violent behavior of the settlers.92 While he had occasionally lamented brutality in the past, his earlier work was marked by a notable silence over colonial violence. During the 1830s and 1840s, the years of his most intense interest in Australia, some of the colonists were perpetrating the genocide of the Tasmanians, and engaging in widespread aggression against indigenous populations elsewhere.93 Although this topic was discussed in Britain, Mill failed to address it. It would have disrupted his colonial romance. During the final decade of his life, however, he returned repeatedly to the topic, though never in print. The \"common English abroad,\" he wrote, were \"intensely contemptuous of what they consider inferior races\" and sought to attain their ends by \"bullying and blows.\"94 This injustice threatened the normative justification of colonization. Mill appeared genuinely perturbed, yet he pulled back from arguing that colonization was _inherently_ cruel, and thus from abandoning the colonial project. (His continued commitment to this project may explain why he refrained from publishing his concerns.) Instead, he implied that certain categories of people\u2014oafish settlers and inexperienced officials among them\u2014were more prone to violence than others. With the right policies and people the injustices could be corrected. This is an example of what Cheryl Welch calls \"antiseptic containment,\" the attempt to confine colonial violence in a quarantined space.95 By locating responsibility in this manner, Mill denied the possibility that violence and injustice were systemic. The main problem for Mill, and the source of his despondency, was that those best placed to control the colonists\u2014the Crown government in London\u2014no longer had the political power to do so. Rather than leading to progress, colonial autonomy facilitated injustice. This profound tension remained unresolved at the time of his death.\n\nOne final issue came to the fore in the 1860s, and it again goes to the heart of some core issues in Mill's political thinking. This concerned the most appropriate form of political organization suitable for coordinating a globe-spanning colonial empire. In the _Considerations_ , Mill argued that it already constituted a weak quasi-federal political order. \"Their union with Great Britain is the slightest kind of federal union; but not a strictly equal federation, the mother country retaining to itself the powers of a Federal Government, though reduced in practice to their very narrowest limits.\" This system was defensible, but it meant that the colonists had \"no voice\" in vital areas of foreign policy, above all in questions of war and peace.96 In denying that the Irish should be accorded self-government, Mill explained that they were actually better off than the semi-autonomous Canadians, for through their incorporation in Westminster they \"had something to say in the affairs of the empire,\" whereas Canada was but a dependency\" and consequently voiceless. \"A union such as this,\" he concluded, \"can only exist as a temporary expedient, between countries which look forward to separation as soon as the weaker is able to stand alone, and which care not how soon it arrives.\"97 Throughout the nineteenth century, various constitutional schemes had been proposed to give colonial governments an increased role in imperial decision-making, thus consolidating the colonial connection. Some advocated the representation of the colonies at Westminster, or, more radical still, the creation of a new supreme imperial legislature. The latter of these options was, Mill observed, a plan to constitute a \"perfectly equal federation.\" But he dismissed further political integration. The idea was doomed to fail, he argued, for an equal federation of the colonies and Great Britain was so inconsistent with the \"rational principles of government\" that it is \"doubtful if they have been seriously accepted as a possibility by any reasonable thinker.\" Quite simply, \"[e]ven for strictly federative purposes, the conditions do not exist, which we have seen to be essential to a federation.\" The main obstacle was physical distance.\n\nCountries separated by half the globe do not present the natural conditions for being under one government, or even members of one federation. If they had sufficiently the same interests, they have not, and never can have, a sufficient habit of taking counsel together. They are not part of the same public; they do not discuss and deliberate in the same arena, but apart, and have only a most imperfect knowledge of what passes in the minds of one another. They neither know each other's objects, nor have confidence in each other's principles of conduct.\n\nRepresentatives from Canada and Australia, he continued, \"could not know, or feel any sufficient concern for, the interests, opinions, or wishes of the English, Irish or Scotch.\"98 The size and spatial extent of the \"public\" was ultimately constrained by the immutability of physical space. Rational deliberation, the key to democratic development, was impossible across such vast expanses, as was the formation of a substantive political (national) identity.99 It was cognitively impossible. Mill defended, then, a variant of Edmund Burke's influential argument from nature against colonial representation: \" _Opposuit natura_ \u2014I cannot remove the barriers of the creation.\"100 Similar arguments were adumbrated by Adam Smith, who once referred to British colonists living in North America as \"strangers,\" and by Bentham, who asked incredulously of colonists whether it was to their \"advantage to be governed by a people who never know, nor ever can know, either their inclinations or their wants.\"101 On this view, which Mill reiterated until his death, geography circumscribed the spatial extent of political community. \"I do not think,\" he wrote to a correspondent in 1871, \"that the federal principle can be worked successfully when the different members of the confederacy are scattered all over the world,\" and he concluded that \"the English people would prefer separation to an equal federation.\"102\n\nThe importance of physical space\u2014and in particular of what we might call the pathos of distance\u2014runs through Mill's colonial writings. We have already seen that Mill (following Wakefield) insisted that spatial dispersion undermined the potential of civilization.103 Moreover, he argued that the role of distance was vital in shaping British attitudes toward various parts of the imperial system. This was one of the reasons why they were less prepared to tolerate dissent in Ireland than in Canada. \"Canada is a great way off and British rulers can tolerate much in a place from which they are not afraid that the contagion may spread to England.\"104 Finally, the remoteness of the scattered elements of the empire\u2014\"at the distance of half the globe\" from Britain105\u2014had profound psychosocial consequences. One implication of Mill's \"associationist\" conception of character formation, albeit one that he never discussed, was that the colonies would never be suitable for full integration into a globe-spanning British colonial polity. While civilization could be transplanted, it would invariably assume different and increasingly divergent forms across the world, as it adapted to the local environment and developed its own constellation of institutions and _moeurs_. Over time, then, the underlying cultural unity necessary for maintaining a healthy political community would dissolve.\n\nIt was the argument from nature, above all, that marked the difference between Mill's promotion of the colonial empire and the proselytizers of the following generation. Mill himself had intimated change in an extraordinary letter in 1866:\n\nOne of the many causes which make the age in which we are living so very important in the life of the human race\u2014almost, indeed, the turning point of it\u2014is that so many things combine to make it the era of a great change in the conceptions and feelings of mankind as to the world of which they form a part. There is now almost no place left on our planet which is mysterious to us, and we were brought within sight of practical questions which will have to be faced when the multiplied human race shall have taken full possession of the earth.106\n\nBlending anxiety and awe, Mill recognized, without being able to put his finger on it, the profound transformation in political consciousness generated by the revolution in communications technology\u2014the (purported) elimination of the \"mystery.\" This revolution meant that the types of argument proffered by Burke, Bentham, Smith, and Mill were soon pushed aside, although they never disappeared completely. Whereas for Mill nature imposed definite limits on the spatial extension of community, many of his successors adopted a more ambitious line. From the early 1870s onwards, it was increasingly argued that the colonial empire formed part of a _single political field_ , that it constituted a unified community stretching across the globe. As a result, it became a commonplace to argue that the federation of the British colonial world was feasible, even necessary.107 This new generation of colonial advocates saw \"the public,\" and with it the limits of political community itself, as open to reconfiguration by novel technologies. Deliberation across space was possible; the interests of Britain and the colonies could be harmonized. Likewise, Wakefield's ideas\u2014the very backbone of Mill's colonial thought\u2014fell from favor. While emigration remained an abiding concern for colonial advocates, the specificities of Wakefield's scheme seemed redundant. As the author of the 1878 entry on \"emigration\" in the _Encyclopaedia Britannica_ wrote, the \"discussion thirty or forty years ago on organized methods of colonization have mostly disappeared in these later times. We hear no more of Mr Wakefield's scheme.\"108 Mill's insistence on the political limits imposed by geographical space and his adherence to Wakefield's theoretical ideas meant that his arguments looked increasingly obsolete in the years following his death.\n\nConclusions\n\nRecent scholarship on Mill has deepened our understanding of how his political thought was shaped by questions of empire, civilization, and progress. Yet his evolving vision(s) of global order can only be grasped adequately by recognizing the importance that he accorded to settler colonization. This was an issue he returned to repeatedly over the course of forty years, although as I have argued we can discern various shifts in his thought over time. Above all, we see an increased emphasis on the universal benefits of colonization, and on geopolitical and moral, as opposed to political-economic, justificatory arguments. He always imagined the metropole and the colonies within the same analytical field, a field structured but not exhausted by his political economy and his utilitarianism, but he never regarded them as part of a single political field, as part of the same community of interests, identity, and affect. The colonies were, as they had been for Bentham, nascent independent countries, distant spaces of hope. Because of their far-flung locations they would never constitute an integral element of the British polity. Ideally, and like their ancient Greek exemplars, they would remain bound by ties of kinship, economic exchange, and the warm glow of a mythopoeic past.\n\n1 J. S. Mill, _Principles of Political Economy_ [1848], in _Collected Works_ , 3:963.\n\n2 Ann Laura Stoler and Frederick Cooper, \"Between Metropole and Colony,\" in _Tensions of Empire_ , ed. Cooper and Stoler (Berkeley, 1997), 4.\n\n3 See, for example, Uday Singh Mehta, _Liberalism and Empire_ (Chicago, 1999); Jennifer Pitts, _A Turn to Empire_ (Princeton, 2005); Martin Moir, Douglas Peers, and Lynn Zastoupil, eds., _J. S. Mill's Encounter with India_ (Toronto, 1999); Lynn Zastoupil, _John Stuart Mill and India_ (Stanford, CA, 1994).\n\n4 Valuable exceptions include: Margaret Kohn and Daniel O'Neill, \"A Tale of Two Indias,\" _Political Theory_ , 34 (2006), 192\u2013228; Katherine Smits, \"John Stuart Mill on the Antipodes,\" _Australian Journal of Politics and History_ , 51 (2008), 1\u201315. Both Nicholas Capaldi, _John Stuart Mill_ (Cambridge, 2004), and Richard Reeves, _John Stuart Mill_ (London, 2007) underemphasize colonization.\n\n5 Bernard Semmel, _The Rise of Free Trade Imperialism_ (Cambridge, 1970); Winch, _Classical Political Economy_ ; R. N. Ghosh, \"John Stuart Mill on Colonies and Colonization,\" in _John Stuart Mill_ , ed. John Cunningham Wood (London, 1987), 4:354\u201367; Samuel Hollander, _The Economics of John Stuart Mill_ , 2 vols. (Oxford, 1985), 2:753\u201358.\n\n6 George Cornewall Lewis, _An Essay on the Government of Dependencies_ (London, 1841); Arthur Mills, _Colonial Constitutions_ (London, 1856); Henry Jenkyns, _British Rule and Jurisdiction beyond the Seas_ (Oxford, 1902), 1\u20139.\n\n7 Mill, _Considerations on Representative Government, Collected Works_ , 19:562. He defines a dependency as: \"outlying territories of some size and population... which are subject, more or less, to acts of sovereign power on the part of the paramount country\" (562). See also Mill, \"The East India Company's Charter\" [1852], _Collected Works_ , 30:49\u201350.\n\n8 See also Robert Hind, \"'We Have No Colonies,'\" _Comparative Studies in Society and History_ , 26 (1984), 3\u201335. Cf. Bruce Buchan, _Empire of Political Thought_ (London, 2008).\n\n9 This type of argument is today often characterized in terms of _terra nullius_ \u2014the occupation of \"empty land.\" This idea is ancient (as are the practices of conquest that can follow from it), but the terminology is a product of the late nineteenth century. Andrew Fitzmaurice, \"The Genealogy of _Terra Nullius_ ,\" _Australian Historical Studies_ , 129 (2007), 1\u201315.\n\n10 Marx, _Capital_ , vol. 1, in Karl Marx and Friedrich Engels, _Collected Works_ (London, 1975), 35:751n.\n\n11 Scott, _Conscripts of Modernity_.\n\n12 Pitts, _A Turn to Empire_ , 6. On Tocqueville's rhetorical moves, see Cheryl Welch, \"Colonial Violence and the Rhetoric of Evasion,\" _Political Theory_ , 31 (2003), 235\u201364.\n\n13 Boyd Hilton, _A Mad, Bad, and Dangerous People?_ (Oxford, 2006), 31.\n\n14 Adam Smith, _An Inquiry into the Nature and Causes of the Wealth of Nations_ , ed. R. H. Campbell and A. S. Skinner (Oxford, 1976 [1776]), 4:556\u2013641; James Mill, \"Colony\" [1818], in _Essays from the Supplement to the Encyclopedia Britannica, Collected Works_ [1823] (London, 1995), 3\u201333. J. C. Wood, _British Economists and the Empire_ (London, 1983), ch. 1.\n\n15 William Nassau Senior, _Remarks on Emigration_ (London, 1831); Senior, _An Outline of a Science of Political Economy_ (London, 1836); Robert Torrens, _Colonisation of South Australia_ (London, 1835); Torrens, _Self-Supporting Colonization_ (London, 1847); Merivale, _Lectures on Colonisation and Colonies_.\n\n16 On Wakefield, see W. Metcalf, ed., _Edward Gibbon Wakefield and the Colonial Dream_ (Wellington, 1997).\n\n17 Marx, _Capital_ , vol. 1, ch. 33; Mill, \"Wakefield's Popular Politics,\" _Examiner_ , January 29, 1837, _Collected Works_ , 24:788. Mill still professed adherence to Wakefield's views decades later. Mill, \"The Westminster Election of 1865,\" [1], July 3, 1865, _Collected Works_ , 28:16; letter to A. M. Francis, May 8, 1869, _Collected Works_ , 27:1599.\n\n18 It was published initially (and anonymously) in the _Morning Chronicle_ ; it appeared as a book, edited by Robert Gouger, and entitled _A Letter from Sydney, the Principal Town in Australasia, Together with the Outline of a System of Colonization_ (London, 1830).\n\n19 For Bentham on colonies, see Philip Schofield, _Utility and Democracy_ (Oxford, 2006), ch. 8; Pitts, _A Turn to Empire_ , ch. 4. On his conversion, see Richard Mills, _The Colonization of Australia (1829\u20131842)_ [1915] (London, 1968), 152\u201353; Edward Gibbon Wakefield, _England and America_ , 2 vols. (London, 1833), 2:252n.\n\n20 Mill, \"The Labouring Agriculturalists,\" _Examiner_ , December 19, 1830, _Collected Works_ , 22:218.\n\n21 On the aims of the group, see Edward Gibbon Wakefield, _The New British Province of South Australia_ (London, 1838). The \"philosophic radicals\" were divided over Wakefield's ideas, with Bowring, Perronet Thompson, and the _Westminster Review_ , critical of them; the more influential, including Grote, Molesworth, Roebuck, Buller, both Mills, and the _London Review_ , supported the plan.\n\n22 Mill, \"Wakefield's _The New British Province of South Australia_ ,\" _Examiner_ , July 20, 1834, _Collected Works_ , 23:739, 742.\n\n23 Mill, 739. On his admiration for the \"Greek empire,\" see also Mill, \"Grote's History of Greece,\" vol. 2 1853], _Collected Works_ , vol. 11, esp. 321\u201324. On the role of Greek models in imagining British colonialism, see [chapter 5 of this volume.\n\n24 Capaldi, _John Stuart Mill_ , 107. He later bought land in New Zealand, although he never visited the country: letter to Henry Chapman, November 12, 1845, _Collected Works_ , 18:687.\n\n25 Riley, \"Mill's Political Economy,\" in _The Cambridge Companion to Mill_ , ed. John Skorupski (Cambridge, 1998), 294\u201395.\n\n26 Scholars disagree over whether Mill's support for Wakefield signaled a break from Ricardo and Say. Much turns on whether Wakefield's arguments on economic growth were\u2014as he proclaimed\u2014inconsistent with them, or whether he had misread Ricardo (as Mill claimed: _Principles_ , 735\u201336). Donald Winch argues that Mill only supported Wakefield's policy proposals (Winch, _Classical Political Economy_ , 139\u201340), while Samuel Hollander argues that Wakefield and Mill consistently extended Ricardian insights ( _Economics of John Stuart Mill_ , 1:166, 475\u201379). I here follow Hollander.\n\n27 For an example, see Mill, letter to Arthur Helps, March 28, 1870, _Collected Works_ , 17:1710.\n\n28 For an early articulation, see Mill, \"Wakefield's 'The New British Province of South Australia,'\" 740\u201341. Mill argued that emigration, while vital, remained insufficient ( _Principles_ , 194).\n\n29 Mill, \"The Emigration Bill,\" _Examiner_ , February 27, 1831, _Collected Works_ , 22:271\u201372.\n\n30 For the debates over the issue, see H.J.M. Johnson, _British Emigration Policy, 1815\u20131830_ (Oxford, 1972).\n\n31 Mill, \"The New Colony,\" [1], _Examiner_ , June 29, 1834, _Collected Works_ , 23:733\u201334.\n\n32 Mill, \"The New Colony\" [2], _Examiner_ , July 6, 1834, _Collected Works_ , 23:737.\n\n33 Mill, \"The Sale of Colonial Land,\" _Sun_ , February 22, 1837, _Collected Works_ , 24:792.\n\n34 Mill, _Principles_ , 711. See also Mill, \"Torrens's Letter to Sir Robert Peel,\" _Spectator_ , January 28, 1843, _Collected Works_ , 24:841; Mill, \"On the Necessity of the Uniting of the Question of Corn Laws with That of the Tithes,\" _Examiner_ , December 23, 1832, _Collected Works_ , 23:539. On emigration as \"palliative,\" see Mill, \"The Claims of Labour,\" _Edinburgh Review_ [1845], _Collected Works_ , 4:387.\n\n35 Mill, _Principles_ , 958.\n\n36 Ibid., 958.\n\n37 Ibid., 958\u201359, 965\u201366. See also Mill, letter to Cairnes, December 12, 1864, _Collected Works_ , 15:1046.\n\n38 For the republican view, see chapters 2, , and , in this volume.\n\n39 Wakefield, _England and America_ , 2:215\u201317; Mill, \"The Emigration Bill,\" 273. See also Mill, \"Female Emigrants,\" _Examiner_ , February 26, 1832, _Collected Works_ , 23:419.\n\n40 Marx, _Capital_ , 753, 758.\n\n41 On Marx's views on empire more broadly, see Gareth Stedman Jones, \"Radicalism and the Extra-European World,\" in _Victorian Visions of Global Order_ , ed. Duncan Bell (Cambridge, 2007), 186\u2013215.\n\n42 Mill, _Principles_ , 800.\n\n43 Ibid., 965\u201367. He also discusses hours of labor. On Mill and collective action, see Richard Tuck, _Free Riding_ (Cambridge, MA, 2008), 133\u201335.\n\n44 Mill, _Principles_ , 959.\n\n45 Ibid., 963. See also Mill's letter to John Campbell, April 4, 1866, _Collected Works_ , 26:1155.\n\n46 Mill, letter to Arthur Helps, March 28, 1870, _Collected Works_ , 17:1710.\n\n47 Mill, _Principles_ , 963.\n\n48 Ibid. Mill had long utilized the argument about differential labor productivity. \"The Emigration Bill,\" 272.\n\n49 Miles Taylor, \"The 1848 Revolutions and the British Empire,\" _Past & Present_, 166 (2000), 146\u201380.\n\n50 Hilton, _A Mad, Bad, and Dangerous People?_ ; Anthony Howe, _Free Trade and Liberal England, 1846\u20131946_ (Oxford, 1998)\n\n51 Increasing political independence was accompanied, however, by growing economic dependence. P. J. Cain and A. G. Hopkins, _British Imperialism, 1688\u20132000_ , 2nd ed. (London, 2002), ch. 8.\n\n52 Letter to Hardy (1856), 511. This was despite the fact, Mill stated, that the plan had only ever been properly executed in New Zealand. He wanted to show that Australian growth could not be explained by the gold rush in the early 1850s. He also claimed that the \"opinions\" of the Australians were generally \"ahead\" of those in Britain. Letter to Henry Chapman, October 5, 1863, _Collected Works_ , 15:888. Moreover, he wrote that he and Harriet \"read every book we can get about the Australian colonies always with fresh interest\" (Letter to Hardy [1856], 511).\n\n53 Mill, _Principles_ , 378. Cf. Karl Marx and Friedrich Engels, _The Communist Manifesto_ [1848], ed. Gareth Stedman Jones (Harmondsworth, 2002), 224.\n\n54 See also Hollander, _The Economics of John Stuart Mill_ , 2:754\u201355, 756\u201357.\n\n55 See, in general, Robert Grant, _Representations of British Emigration, Colonisation and Settlement_ (Basingstoke, 2005).\n\n56 The argument is found in Mill, _Principles_ , vol. 5, ch. 10, sec. 1.\n\n57 Mill, letter to W. L. Johns, January 22, 1867, _Collected Works_ , 16:1230. And conversely, \"the colonies will not allow us to cast our paupers into them.\" Letter to Henry Chapman, January 14, 1870, _Collected Works_ , 17:1685.\n\n58 See here Mill, _Principles_ , vol. 5, ch. 10, sec. 1.\n\n59 See, for example, his letters to Frederick Miles Edge (of the _Chicago Tribune_ ), February 26, 1866, _Collected Works_ , 16:1150\u201351; Henry Soden, May 2, 1865, _Collected Works_ , 16:1043\u201344; George Kenyon Holden, July 5, 1868, _Collected Works_ , 16:1419\u201320. He notes in a letter to the political economist J. E. Cairnes, on February 4, 1865 ( _Collected Works_ , 16:989\u201390), that he had modified various passages in the 6th edition (5:919\u201321) to \"give a fuller expression of my meaning.\"\n\n60 Mill, letter to Archibald Michie, December 7, 1868, _Collected Works_ , 16:1516; letter to Edward Stafford, December 11, 1868, _Collected Works_ , 16:1520\u201321.\n\n61 Wakefield, _England and America_ , 2:105\u20136.\n\n62 Stefan Collini, _Public Moralists_ (Oxford, 1991), ch. 3; Janice Carlisle, _John Stuart Mill and the Writing of Character_ (Athens, 1991); Duncan Kelly, _The Propriety of Liberty_ (Princeton, 2010); and, on India, Pitts, _A Turn to Empire_ , ch. 5.\n\n63 Mill, _The Subjection of Women_ [1869], _Collected Works_ , 21:277; cf. Mill, _System of Logic, Collected Works_ , vol. 8, bk. 6, pp. 904\u20135.\n\n64 On Mill's writings on women, democratic institutions, and himself, as ethological \"case studies\" see Terence Ball, \"The Formation of Character,\" _Polity_ , 33 (2000), 25\u201348.\n\n65 Mehta, _Liberalism and Empire_ , 37. For a critical discussion of this argument, see chapter 2 in this volume.\n\n66 Mill, \"New Australian Colony,\" _Morning Chronicle_ , October 23, 1834, _Collected Works_ , 23:750.\n\n67 Letter to Edward Lytton-Bulwer, March 5, 1838, _Collected Works_ , 13:382. See William Thomas, _The Philosophic Radicals_ (Oxford, 1979), ch. 8; Michael Turner, \"Radical Agitation and the Canada Question in British Politics, 1837\u20131841,\" _Historical Research_ , 79 (2006), 90\u2013114.\n\n68 A smaller uprising followed in Upper Canada in December 1837. See Peter Burroughs, _The Canadian Crisis and British Colonial Policy, 1828\u20131841_ (London, 1972); P. A. Buckner, _The Transition to Responsible Government_ (Westport, 1985).\n\n69 C. P. Lucas, ed., _Lord Durham's Report on the Affairs of British North America_ [1839] (Oxford, 1912). Wakefield played a significant role in formulating the report. For a harsh indictment, see Ged Martin, _The Durham Report and British Policy_ (Cambridge, 1972).\n\n70 Pitts, _A Turn to Empire_ , ch. 5; and chapter 12 in this volume.\n\n71 Mill, \"Lord Durham and His Assailants,\" _London and Westminster Review_ (1838), _Collected Works_ , 6: 448.\n\n72 Mill, \"Radical Party and Canada,\" _London and Westminster Review_ (1838), _Collected Works_ , 6:414. See also Mill, \"Penal Code for India,\" _London and Westminster Review_ (1838), _Collected Works_ , 30:30.\n\n73 Mill, \"Radical Party and Canada,\" 417. \"A constitution, once conferred, is sacred\" (418). The point at issue was a series of punitive resolutions passed at Westminster in March 1837, which removed various powers from the Lower Canadian assembly, including the power of refusing to grant money for local administration, originally enshrined in the 1791 Constitution.\n\n74 Ibid.,\" 429.\n\n75 Ibid., 433\u201334. See also Mill's letter to John Robertson, December 28, 1838, _Collected Works_ , 13:393\u201334. Mill's article on \"Lord Durham and His Assailants\" was heavily shaped by Charles Buller's inaccurate account of Durham's plans. Thomas, _The Philosophic Radicals_ , 402\u20133.\n\n76 Mill, \"Lord Durham and His Assailants,\" 458, 459. On Mill's \"heterotic\" view of national absorption, see Georgios Varouxakis, _Mill on Nationality_ (London, 2002), esp. 15\u201319. Compare this with Will Kymlicka, _Multicultural Citizenship_ (Oxford, 1995), 53, where Mill is accused of advocating \"coercive assimilation.\"\n\n77 Mill, \"Lord Durham and His Assailants,\" 461. See also Mill, _Autobiography_ [1873], _Collected Works_ , 1:164\u201366, 223.\n\n78 For Mill's recognition of this, see his letter to Robertson, April 6, 1839, _Collected Works_ , 13:396\u201397.\n\n79 Pitts, _A Turn to Empire_ , 148.\n\n80 Letter to Beaumont, October 18, 1839, _Collected Works_ , 17:1990\u201392.\n\n81 See, in general, Bruce Kinzer, _England's Disgrace?_ (Toronto, 2001), esp. chs. 2\u20133.\n\n82 Mill, \"The Condition of Ireland,\" (11), _Morning Chronicle_ , October, 26, 1846, _Collected Works_ , 24:915.\n\n83 Ibid., 973.\n\n84 Mill, (25), _Morning Chronicle_ , December 2, 1846, _Collected Works_ , 24:973. Mill argued that the abject conditions meant that \"Ireland was once more a tabula rasa, on which we might have inscribed what we pleased.\" Letter to the _Examiner_ , May 1848, _Collected Works_ , 25:1098.\n\n85 Mill, _Considerations_ , 565. For his defense of the colonial system, see also his letter to Cairnes, November 8, 1864, 964\u201366.\n\n86 Mill, _Considerations_ , 562\u201363, 565.\n\n87 For a useful analysis of the idea, see Ken Booth and Nicholas Wheeler, _The Security Dilemma_ (Basingstoke, 2007).\n\n88 Mill, _Considerations_ , 565.\n\n89 Ibid. On the debate over the morality of free trade, see Frank Trentmann, _Free Trade Nation_ (Oxford, 2008).\n\n90 Mill, _Considerations_ , 563\u201364, 92.\n\n91 Mill, letter to Arthur Patchett Martin, October 10, 1871, _Collected Works_ , 32:232. But, he argued, \"[t]he renunciation of them was by no means a necessary consequence of the introduction of responsible government\" (232). See also letter to Chapman (1870), 1865\u201366.\n\n92 As detailed in Smits, \"John Stuart Mill on the Antipodes.\" Cf. Pitts, _A Turn to Empire_ , 159\u201360. For an argument that there is a general shift in justifications of British imperial rule during the closing decades of the century, see Karuna Mantena, _Alibis of Empire_.\n\n93 Benjamin Madley, \"From Terror to Genocide,\" _Journal of British Studies_ , 47 (2008), 77\u2013106. The issue was raised, for example, in Herman Merivale's _Lectures on Colonisation and Colonies_ , 2:150. Mill certainly read the second (1861) edition of these lectures. Letter to J. E. Cairnes, November 8, 1864, _Collected Works_ , 15:647\u201348.\n\n94 Letter to A. M. Francis (1869), 1599. See also the following letters: to Robert Pharazyn, August 21, 1866, _Collected Works_ , 16:1194\u201396; to Henry Chapman, August 7, 1866, _Collected Works_ , 16: 1135\u201336; to Charlotte Manning, January 14, 1870, _Collected Works_ , 17:1685\u201387.\n\n95 Welch, \"Colonial Violence and the Rhetoric of Evasion,\" 251\u201352.\n\n96 Mill, _Considerations_ , 564. A similar account of colonial \"quasi-federalism\" can be found in L. T. Hobhouse, _Democracy and Reaction_ [1904], ed. P. F. Clarke (Brighton, 1972), 154. Cf. Bell, \"The Victorian Idea of a Global State.\"\n\n97 Mill, \"England and Ireland\" [1868], 4th ed. 1869, _Collected Works_ , 6:524\u201325.\n\n98 Mill, _Considerations_ , 564, 565. Mill thought that a \"loose federation\" of the European states was a future possibility: letter to E. Cliffe Leslie, August 18, 1860, _Collected Works_ , 15:703; letter to M. C. Halstead, January 19, 1871, _Collected Works_ , 17:1800\u20131801.\n\n99 On the importance of deliberation in his political philosophy, see Nadia Urbinati, _Mill on Democracy_ (Chicago, 2002).\n\n100 Edmund Burke, \"Speech on Conciliation with America\" (March 22, 1775), in _The Writings and Speeches of Edmund Burke_ , ed. W. Elofson and John Woods (Oxford, 1996), 3:152.\n\n101 Smith, _Wealth of Nations_ , 622; Jeremy Bentham, \"Emancipate Your Colonies\" [1830], in _Rights, Representation, and Reform_ , ed. Philip Schofield, Catherine Pease-Watkin, and Cyprian Blamire (Oxford, 2002), 292.\n\n102 Mill, letter to Arthur Patchett Martin (1871), 233. See also, Mill, letter to Henry Chapman (1870), 1865.\n\n103 A point also made in Mill, \"Civilization,\" _Collected Works_ , 18:117\u201349.\n\n104 Mill, \"England and Ireland,\" 525.\n\n105 Mill, \"Lord Durham and His Assailants,\" 460.\n\n106 Mill, letter to Henry Chapman, August 7, 1866, _Collected Works_ , 16:1137.\n\n107 See, for example, Seeley, _The Expansion of England_.\n\n108 Robert Somers, \"Emigration\" [1878], _Encyclopaedia Britannica_ , 9th ed. (London, 1875\u201389), 8:176. For a brilliant analysis of the nature of the encyclopedia, see Alistair Maclntyre, _Three Rival Versions of Moral Enquiry_ (South Bend, IN, 1990), ch. 1.\nCHAPTER 10\n\nInternational Society in Victorian Political Thought\n\nT. H. Green, Herbert Spencer, and Henry Sidgwick\n\n_With Casper Sylvest_\n\nI grew up as an ardent believer in optimistic liberalism. I both hoped and expected to see throughout the world a gradual spread of parliamentary democracy, personal liberty, and freedom for the countries that were at that time subject to European Powers, including Britain. I hoped that everyone would in time see the wisdom of Cobden's arguments for Free Trade, and that nationalism might gradually fade into a universal humanism.1\n\n\u2014BERTRAND RUSSELL\n\nIf... one were to press the theoretic issue, whether a state or nation is a morally independent being, or whether it is in some sense or degree a member of what maybe called an incipient society of states or nations, nearly everyone would sustain the latter view. 2\n\n\u2014J. A. HOBSON\n\nThroughout the Victorian era, British liberal attitudes to international order were shaped by a complex interplay between conceptions of universalism, sovereignty, progress, and civilization. This chapter explores a prominent idea that permeated the thinking of the British liberal intelligentsia in the closing decades of the century, at the very apogee of the imperial age: a vision of international society as both an empirical account of progressive trends identifiable in global politics and as a normative project.3\n\nThis chapter analyzes the overlapping ideas about international society to be found in the political thought of three leading late Victorian liberal thinkers: T. H. Green (1836\u201382), Herbert Spencer (1820\u20131903), and Henry Sidgwick (1838\u20131900). In so doing it focuses on what Stefan Collini has labeled the world of the \"public moralists\"\u2014the world, that is, of influential and well-connected British intellectuals who flourished in the universities, in Parliament, and in the press.4 During the late nineteenth century it is possible to identify amongst the liberal sections of this elite a widely shared, if often only vaguely articulated, belief in the existence of a nascent and evolving international society. It was a belief that was to survive both world wars, albeit in a more disenchanted key. This was the vision that Bertrand Russell grew up believing in, only to have his hopes dashed by the horrors of the atom bomb and the Holocaust, and that Hobson claimed was \"sustained\" by \"nearly everyone\" in 1920.\n\nDespite their manifold political and philosophical differences, Green, Spencer, and Sidgwick shared and articulated complementary visions of the past, present, and future of international society. This was not simply a happy coincidence of views\u2014it was an understanding of international politics generated from within their distinctive intellectual systems. They simultaneously reflected and contributed to late Victorian liberal thinking about international affairs. Their significance in this respect lies, at least in part, in their attempt to theorize liberal internationalism in a sophisticated manner, thereby giving it both intellectual respectability and political force. Moreover, by approaching this theme from different philosophical viewpoints they managed to provide internationalism with an ideological flexibility that proved crucial for its survival and development in a period witnessing both major shifts in the intellectual current and considerable turbulence in global politics.5\n\nThe structure of this chapter is as follows. Section 2 provides a sketch of the political context in which liberal internationalism flourished during the late Victorian era as well as a brief analysis of key arguments employed by its proponents. Section 3 examines the international thought of Green, Spencer, and Sidgwick, and the way in which they derived overlapping notions of international society from their divergent philosophical systems. Finally, section 4 highlights some of the ways in which their internationalism was circumscribed by ideas about the boundaries of civilization and the role of empire. It was the moral and practical standing of empire that brought to the surface the internal tensions, and the ethical limitations, of late nineteenth-century liberal conceptions of international society.\n\nProgress, Justice, and Order: On Liberal Internationalism\n\nDuring the late nineteenth century liberal internationalism was, like the liberalism that spawned it, a many-stranded phenomenon. Nevertheless, it had at its core a cluster of ideas about how best to organize and reform global politics, to which virtually all liberals subscribed, including, in their different ways, Green, Spencer, and Sidgwick. This liberal internationalism was founded on a belief that it was possible to build a just international order on the basis of existing patterns of cooperation between distinct political communities. Such thinking was neither strictly cosmopolitan (insofar as it did not attempt to transcend the state) nor was it crudely nationalist (insofar as it did not prioritize national self-interest over the interests of \"humanity\"). It drew on a combination of long-standing radical ideas about the dangers of militarism and aristocratic privilege and fused them with more mainstream liberal concerns about the value of commerce (and in particular free trade) in creating a morally acceptable international order. In short, liberal internationalists yoked a political project to the idea of sustained moral development.6 In doing so, they projected, in what is often labeled the \"domestic analogy,\" their conception of the nature and sources of domestic order onto the plane of international politics.7 War was not a tragic inevitability. Internationalists insisted that the problem resulting from the lack of an overarching global leviathan\u2014that determinate source of political authority identified by so many thinkers at the time (and today) as one of the primary causes of interstate conflict\u2014was surmountable without recourse to the dreaded singularity of universal empire.\n\nNineteenth-century British liberalism was marked by two defining characteristics. The first was its political and ideological ascendancy, especially in the early and mid-Victorian eras. The second was its polyphonic variation, which was most marked in the closing decades of the century.8 The two are not unrelated\u2014liberalism was many things to many people. This was both a strength and a weakness. Its strength lay in the possibility of coopting and coordinating a variety of different political interests and philosophical outlooks and uniting them behind a broad vision of economic, political, social, and international reform. Its weakness resulted from the fragility of this compound. Liberalism's hold over both the popular political imagination and the intellectual elite was very pronounced, and for a few decades in the third quarter of the century it lay at the core of political discourse, the position against which others were forced to define (and often defend) themselves. Scholars often argue that the mid-Victorian era was comparatively harmonious, characterized by \"stability, optimism, social solidarity, relative affluence, and liberality.\"9 It was a moment of heightened confidence. Liberalism flourished in this comparatively sunny climate\u2014although the \"equipoise\" was often qualified by the common dread of war. The \"generation of William Whewell,\" noted Henry Maine in 1887, \"may be said to have had a dream of peace,\" exemplified by the atmosphere in the years surrounding the Great Exhibition of 1851. But the \"buildings of this Temple of Peace had hardly been removed when war broke out again, more terrible than ever,\" and Maine pointed to the Crimean War as having inaugurated a new period of conflict, which to believers in the possibility of peace had been \"a bitter deception.\"10 John Morley concurred: \"Heavy banks of cloud hung with occasional breaks of brighter sky over Europe; and all the plot, intrigue, conspiracy, and subterranean scheming... was but the repulsive and dangerous symptom of a dire conflict in the depth of international politics.\"11 Optimism about the future was tempered by fear about the potential derailment of progress, a fear that increased in intensity, as winter succeeded autumn, in the closing decades of the century.\n\nFrom the late 1880s until their landslide electoral victory in 1906, liberals repeatedly found themselves cast in the party-political wilderness. Moreover, challenges to liberal ideology became evermore obvious to contemporaries, sympathetic and hostile alike. As L. T. Hobhouse wrote in 1911, \"[w]hether at home or abroad those who represented Liberal ideas had suffered crushing defeats... [i]ts faith in itself was waxing cold.\"12 In the domestic sphere the furore over Irish Home Rule, increasing class antagonism, and the emergence of socialism as a serious political force, together with challenges to the shibboleth of free trade amid disappointment with the results of democratic expansion after 1867 and 1884, all combined to dampen the confidence of liberals. This trend was exacerbated by escalating European militarization, catalyzed in particular by the unification of Germany following the Franco-Prussian War (1870\u201371), the ensuing \"scramble\" for imperial territories in Africa, fear about a Russian challenge to British supremacy in India, and the perception that the British economy was rapidly weakening relative to other major states. But liberal optimism did not disappear altogether, and indeed the grim international environment led to a redoubling of efforts to find a way out of the political impasse. It was in this ideological milieu that _fin de si\u00e8cle_ liberal internationalism was forged, drawing on classical liberal (and radical) themes, Gladstone's global messianism, and the ideas of the \"new liberals\" and philosophical idealists.13\n\nIn general, liberal internationalists advocated the development of international law, arbitration, free trade, and multilateralism as the most appropriate strategies for states to pursue in search of a just international order. They also predicted the development of various supranational structures, including political federations, at the regional, inter-imperial or international level, although they rarely pushed for the immediate construction of such institutions. Two analytically distinct logics can be discerned in internationalist thought during this period, although they were usually interwoven in the writings of individual figures. Witness, for example, the Cambridge international lawyer T. J. Lawrence. One line of thought held that reform would come about mainly through a shift in moral norms (\"international morality\"); another held that the best route was through institutional engineering. The former, dominant, logic focused on transforming the values of domestic society and in particular it promoted democracy while lambasting aristocratic militarism and excessive capitalist accumulation. Writing in the 1880s Lawrence claimed that the three greatest forces of modern life, \"Commerce, Democracy and Christianity,\" facilitated peace, and when he examined war \"in light of the theory of Development\" he \"found reason for believing that a state of perpetual peace will be gradually evolved upon earth.\" The second logic foreshadowed and promoted the creation of a variety of institutional structures. These included regional and imperial federations and, rather less ambitiously, international arbitration bodies, or what Lawrence called \"authoritative tribunals.\"14 For most internationalists writing prior to the First World War, including Lawrence, the two logics were usually sequenced in a particular manner; moral transformation was seen as a necessary first step before institutions could be created to harness and embed this internationalist vision.15\n\nCommerce and law were generally seen as the two key engines of liberal internationalism. They were assigned distinctive and complementary roles in bringing about a new moral order. In the case of commerce it was held that free trade led to increasing levels of interdependence and cooperation between states, and thus reduced the probability of violent conflict. In other words, political cooperation would follow from economic interaction. This view had found its most forceful advocate in Cobden, and was to reach its apotheosis in \"Norman Angellism\" during the late Edwardian era.16 It can be seen today in the stultifying debates over the pacifying powers of neoliberal globalization. The legal vision focused mainly on constructing a regime based on international legal norms that would lock into place certain types of behavior, including reciprocity and arbitration, with the expectation that over time states would become socialized into new modes of peaceable and cooperative interaction. As the liberal historian Frederic Seebohm wrote in 1871, \"we enter into commercial treaties, and become more and more dependent upon maintenance of international peace and justice,\" which in turn required \"more adequate security for international justice which shall at the same time be less injurious to the interests of nations.\"17 Law and commerce were not only symptomatic of the general progress of humanity but would also be the means of bringing about a more fundamental transformation: the necessary (if not inevitable) moral development of the species. For James Bryce, famed anatomist of democracy, this process could be identified in the unfolding of history, which, despite repeated frustrations, was moving ever \"upwards.\" The best evidence for this was to be found in the fact that \"evils which men once accepted as inevitable have now become intolerable.\"18 The liberal jurist Sheldon Amos concurred:\n\nWar, as modified by the laws and restrictions which the conscience of the civilised world, working in concurrence with the dictates of military and political convenience, imposes, marks an intermediate and, it may be hoped, transitory stage, between an absolute oblivion of moral obligations, and such an ascendancy of the sense of these obligations, as would render the cruel hardships and bitter passions, which are inevitable, even in the best conducted Wars, an anachronism.19\n\nThis fusion of moral and institutional technologies of reform characterized liberal internationalism from the mid-Victorian era through the early decades of the twentieth century.\n\nInternational Society: Green, Spencer, Sidgwick\n\nGreen, Spencer, and Sidgwick occupied important positions in late Victorian intellectual life. Whereas Green, White's Professor of Moral Philosophy at Oxford, was the most important figure in translating philosophical idealism into a British creed, Herbert Spencer, a man who never held an academic post, has some claim to be described as the single most influential philosopher of the nineteenth-century Anglo-American world\u2014and well beyond. The popularity of his social evolutionary ideas stemmed, at least in part, from their ability to crystallize the hopes and anxieties of educated Victorians, as well as quenching their thirst for knowledge of self and society.20 Henry Sidgwick, the Knightbridge Professor of Moral Philosophy at Cambridge, provided the most sophisticated defense of utilitarianism in the closing decades of the century. Unlike Green, whose writings focused primarily on philosophical topics, Sidgwick's published output ranged widely across philosophy, history, political economy, and contemporary politics, although he never attained the level of popularity enjoyed by Spencer.\n\nThe three philosophers differed very considerably in temperament and style, and they were often found on opposite\u2014and not always predictable\u2014sides of major intellectual and political debates. Green and Sidgwick were both skeptical of Spencer's social evolutionism and his attempt (as they saw it) to reduce moral philosophy to a science. Green was also sharply critical of Spencer's metaphysical assumptions, and in particular how these translated into his writings on psychology.21 Spencer and Sidgwick, meanwhile, remained unconvinced by the idealism that Green was so instrumental in elaborating. Spencer objected to what he saw as the speculative, \"continental\" nature of idealism, while Sidgwick was more concerned with Green's inability to address or resolve what he regarded as the fundamental conundrums of philosophy, such as the reconciliation of different modes of ethical reasoning.22 While the two professional academics conducted their conversations in a technical philosophical language, Sidgwick's utilitarian ethical system was ultimately more compatible with that of Spencer, the academic outsider. They also diverged politically. Green and Spencer's views on the relationship between the individual and the state stood poles apart\u2014indeed the idealist disciples of Green regarded Spencer's utilitarianism and radical individualism as one of their main targets, both theoretically (as an indefensible view of the self) and politically (as justifying damaging inequalities). And despite his support for an idiosyncratic form of socialism, Sidgwick was much more of a traditional individualist liberal, an exponent, as D. G. Ritchie put it, of utilitarianism grown \"tame and sleek.\"23\n\nNotwithstanding this plurality of ideas and ideals, when it came to international politics they shared a bifocal vision that implied, first, that an incipient international society was discernible, even if only faintly, in the existing configuration of global politics and, second, as a normative ideal, that it should be nourished, strengthened, and expanded in the future. In other words this society was immanent, if not imminent. While they differed on its potential structure as well as on the temporal dimensions of its full realization, their views coalesced behind a coherent (though vague) concern with the possibility of bringing a measure of order, justice, and tranquility to international politics. Moral transformation was central to this vision. But Green, Sidgwick, and Spencer thought that this transformation required some form of institutionalization, and they therefore advocated new legal mechanisms, including arbitration bodies; in the longer term it would mean working towards the creation of federal modes of government at the international level. Starting from very different philosophical premises, they ended up arguing for very similar political goals.\n\n_Thomas Hill Green_\n\nIn approaching Green's international thought, it is crucial not to be swayed by the hostile interpretation of idealism orchestrated at the beginning of the twentieth century, largely but not exclusively by Hobson and Hobhouse. In a characteristic formulation, Hobhouse argued, with direct reference to idealism, that if \"all that is real is rational, it is difficult to resist the view that what wins is right.\"24 The prevailing view today is that idealism was not of itself anti-internationalist.25 This is especially true of Green, who was, as Melvin Richter once remarked, \"the last person in the world to be convinced of the moral virtue of a nation by its success in war.\"26 There was always a radical tint to Green's liberalism, particularly in terms of foreign policy, as is illustrated by his great admiration for the anti-militarist internationalism of Bright and Cobden.27 Moreover, his intellectual trademark\u2014the focus on the ethical dimension and potential of \"man\"\u2014was always carefully phrased in language that precluded militarism.\n\nGreen's liberalism can be seen as a halfway house between the classical liberalism of Mill and the new liberalism of the early twentieth century.28 He valued individuality and freedom and defended a conception of persons as essentially communal and moral beings bearing social responsibilities and rights. The political implications of this philosophical vision were formulated most clearly in the posthumously published _Lectures on the Principles of Political Obligation_ (1886), where Green argued that\n\nthe claim or right of the individual to have certain powers secured to him by society, and the counter-claim of society to exercise certain powers over the individual, alike rest on the fact that these powers are necessary to the fulfilment of _man's vocation as a moral being, to an effectual self-devotion to the work of developing the perfect character in himself and others_.29\n\nAfter setting out the objective of freedom as self-development and self-realization, Green argued that the true function of government was to make possible this ideal. Although this reformulation has often been seen as a precursor to \"new liberal\" arguments about the role of the state in achieving social equality, to Green the implications were not straightforwardly interventionist.30 Although his view of state intervention was much more permissive than Spencer's, its task remained primarily ethical, being devoted to sustaining and harmonizing individual relations.31 The state was a facilitating space for individual self-realization. On the other hand, Green also stressed that the citizen ideally should be an active participant in political life, not simply a passive recipient of its benefits, a view that fitted with his conception of \"man\" as inconceivable apart from community.32 He was a persistent critic of dualisms\u2014citizen-state, individual-society\u2014and repeatedly insisted on their mutual interdependence. This philosophical notion of unity had a moral and political equivalent in Green's avowal of the social and individual dimensions of pursuing the common good, a common good that anchored collective life. With this guiding idea Green provided\u2014or was seen to provide\u2014an answer to materialistic hedonism in an age of increasing religious doubt.33 This answer also embodied a progressive element in which institutions (including the state), and the individuals composing them, were seen as gradually fulfilling their true nature.34\n\nGreen's conception of the international was continuous with this vision of moral development. Green began his lecture \"The Right of the State over the Individual in War,\" delivered in the academic year of 1879\u201380, with a discussion of the essential \"wrongdoing\" of war, arguing that even if it was undeniable that \"many virtues are called into exercise by war, or that wars have been a means by which the movement of mankind... has been carried on,\" this did not diminish the wrong committed. Green then turned to the relationship between the right of (particular) states to act in their own interest and the rights that individuals acquired through membership in (a universal) human society. For Green, though, this implied a false dichotomy, because \"the source of war between states lies in their incomplete fulfilment of their function; in the fact that there is some defect in the maintenance or reconciliation of rights among their subjects\":\n\nThere is no such thing as an inevitable conflict between states. There is nothing in the nature of the state that, given a multiplicity of states, should make the gain of the one the loss of the other. The more perfectly each one of them attains its proper object of giving free scope to the capacities of all persons living on a certain range of territory, the easier it is for others to do so; and in proportion as they all do so the danger of conflict disappears.35\n\nThis statement follows from Green's understanding of the relationship between state and citizen and was intended also as a challenge to the fatalistic view, which he associated with Spinoza and which he saw as resurgent in contemporary political life. In a previous lecture Green had discussed Spinoza's approach to war, and especially the view that \"two commonwealths are enemies by nature.\" He complained that among \"the enlightened... there has of late appeared a tendency to adopt a theory very like Spinoza's, without the higher elements which we noticed in Spinoza; to consider all right as a power attained in that 'struggle for existence' to which human 'progress' is reduced.\"36 Green was to spend much time attempting to counter such crude notions of struggle, whether they were employed in debate about domestic or international politics.\n\nThe fulfillment of the real purpose of the state would remove the motives and opportunities for war, \"while the bonds of unity become stronger.\" This development was linked directly to \"Manchesterism.\" Despite some reservations about free trade, Green held that increasing levels of trade would strengthen \"the sense of common interests\" between citizens of different states, which war would otherwise violate. This logic can point in the direction of cosmopolitanism and a universal society of humankind, and there is indeed some evidence that this is what Green sought. Throughout his short life he argued against militarist patriotism, and he lamented that in international politics people were rarely influenced by \"the idea of the universal brotherhood of men,\" and by the notion of \"mankind as forming one society with a common good.\"37 This suggests that Green was committed to a conception of what might be labeled \"transcendent\" community, the belief that ideally once individuals are members of one community they are members of all communities.38 Two factors, however, complicate a simple \"cosmopolitan\" reading. First, Green was no straightforward individualist. Although he argued that in a nation, \"however exalted its mission,\" there was nothing \"which is not in the persons composing the nation or the society\" and that our \"ultimate standard of worth is an ideal of _personal_ worth,\" he also insisted that individuals could not possess \"moral and spiritual qualities, independently of their existence in a nation.\"39 In thinking about morals, he suggested, we have to start with a notion of moral community that does not encompass the whole of humanity. Second, even if Green was a cosmopolitan, his attainable ideal, his view, that is, of what it was at least plausible to aim for, was premised on the existence of nation-states. This emerges from his discussion of the claim that projects \"of perpetual peace, to be logical, must be projects of all-embracing empire.\" Although Green conceded that there was some merit in this, he argued that a world of nations expressing particularistic sentiments was more realistic and perhaps also more fulfilling. If these were properly constituted and directed towards the common good, not only would \"the occasions of conflict between nations disappear,\" those nations would also by virtue of the same development acquire a more altruistic \"organ of expression and action\" for dealing with each other.40\n\nGreen's ideal was, then, of a society of rightly constituted nations coexisting in anti-egoistic ways and developing within a larger circle of humanity. Even in _The Prolegomena to Ethics_ (1883), wherein he discussed the possibility of communities widening continually so as to increase the range of persons whose common good was sought, he did not dispense with (nation) states as long as they fulfilled their potential. He employed, for example, the equivocal phrase \"the fraternity of men and nations.\" More importantly, Green acknowledged that the prime impediment to the maintenance and formation of a fellowship was selfishness, a problem that was exacerbated as they expanded in scale and scope. Nevertheless he confidently asserted that \"where selfishness of man has proposed, his better reason has disposed.\" Thus he saw the formation of independently law-governed nations and communities as an expression of reason because they facilitated both the subordination of the individual to the common good and underpinned the language of rights instrumental in realizing wider interpersonal commitments.41 It was against this background that he could \"dream of an international court with authority resting on the consent of independent states.\"42 As with his conception of the relationship between individual and society the relationship between (nation) states and the \"society\" they form was potentially harmonious. But such a development depended on states becoming more fully realized and thereby recognizing their common interests.\n\n_Herbert Spencer_\n\nUnmistakably a child of the English provincial radicalism that flourished in his home town of Derby, Herbert Spencer was a self-made thinker who, from the 1850s onwards, worked out a \"synthetic Philosophy\" spanning biology, psychology, sociology, and ethics.43 Following a brief career in the booming railway industry and as a journalist at the _Economist_ , he published _Social Statics_ in 1851. From an explicitly deist perspective, which he later abandoned, the book developed deductively a system of ethics for the perfect condition towards which mankind was progressing. In later life Spencer would move away from this exclusive focus on \"absolute ethics\" and begin to deal also with non-ideal \"relative ethics.\" At this stage, though, he had not yet identified the evolutionary mechanisms of progress even if its existence and direction was clear: \"Progress... is not an accident, but a necessity. Instead of civilization being artificial, it is a part of nature.\" This conviction was so strong that Spencer could proclaim that evil and morality would disappear and that man would become \"perfect.\"44 In this projected future condition, a principle of equal freedom\u2014\" _Every man has freedom to do all that he wills, provided he infringes not the equal freedom of any other man_ \"45\u2014would guide human action. Many essential elements of Spencer's utilitarianism and of his mature philosophical system were thus present in his early work.46\n\nSo too was his political liberalism. Spencer was a ruthless advocate of the ideal-typical \"nightwatchman\" state, as demonstrated both in _Social Statics_ and in a series of letters to the _Nonconformist_ entitled _The Proper Sphere of Government_ (1842\u201343). Progress meant progressively less government.47 The international consequences of this ideology corresponded with the arguments of the Anti-Corn Law League and its icons, Cobden and Bright, and as such Spencer can be located in a tradition of political radicalism highly critical of British foreign policy and imperialism.48 This emerges clearly in _The Proper Sphere of Government_ , where he argued that war was \"the source of the greatest of England's burdens.\" War made nations aggressive and hindered industry and commerce, \"the real sources of wealth.\" But it was the moral evils of war that exercised Spencer the most. It was, after all, \"inconsistent with the spirit of Christianity,\" tending \"greatly to retard the civilisation of the world,\" and it acted as \"the grand bar to the extension of that feeling of universal brotherhood with all nations, so essential to the real prosperity of mankind.\"49\n\nThe same notion of an incipient and immanent society of nations is found in _Social Statics_ , but at this stage he predicted that it would manifest itself in a global federal structure. It is vital to stress, however, that Spencer was not willing to actively advocate the establishment of such an institution. The logic was much more circumvented:\n\nA federation of peoples\u2014a universal society, can exist only when man's adaptation to the social state has become tolerably complete. We have already seen... that in the earliest state of civilization, when the repulsive force is strong, and the aggregative force weak, only small communities are possible; a modification of character causes these tribes and satrapies, and _gentes_ , and feudal lordships, and clans, gradually to coalesce into nations; and a still further modification will allow for further union. That the time for this is now drawing nigh, seems probable... The recognition of its desirableness foreshadows its realization. In peace societies, in proposals for simultaneous disarmament, in international visits and addresses, and in the frequency with which friendly interventions now occur, we may see that humanity is fast growing towards such a consummation. Though hitherto impracticable, and perhaps impracticable at the present moment, a brotherhood of nations is being made very practicable by the very efforts used to bring it about.50\n\nImpersonal forces governing human development would in time bring about a full manifestation of the international society that was then only discernable _in embryo_. Spencer indicated that this trajectory should be located in the larger timescales of history and that inter-societal conflict had acted as a crucial mechanism of development. In order to understand how this argument worked in any detail, it is important to briefly examine Spencer's understanding of social evolution.\n\nA rudimentary notion of evolution was clearly present in Spencer's earlier writings, but it was not until he conceived of the \"synthetic philosophy\" that it was theorized more thoroughly, and arguably its full realization was parasitic on the development of the various branches of the entire philosophical system. In Spencer's philosophical groundwork, _First Principles_ , published originally in 1860, evolution was defined as \"an integration of matter and concomitant dissipation of motion; during which the matter passes from an indefinite, incoherent homogeneity to a definite, coherent heterogeneity; and during which the retained motion undergoes a parallel transformation.\"51 At the core of this \"total evolutionism\" were two separate but interlinked concepts, individuation and differentiation.52 At a general level Spencer held that organisms became distinct from other organisms\u2014\"individualised\"\u2014by a process of the differentiation of organs, but this process also implied another kind of individuation as the organism in question simultaneously became more integrated. The mechanism of these evolutionary developments was Lamarckian rather than Darwinian\u2014that is, adaptation to the environment took place through the ability of organisms to inherit acquired characteristics from previous generations rather than through the more random Darwinian process of variation and selection. This allowed Spencer to conceive of progress in an orderly\u2014and almost speculatively guidable\u2014fashion.53 It points to a crucial feature of the interlocking nature of Spencer's political ideology and theory of evolution: while the latter was presented as a disinterested scientific theory, in reality it was constantly fashioned and refashioned so as to confirm the main impetus of the former.54\n\nSpencer's sociology, which encompassed what today we would term \"political science,\" is important in understanding how he conceived of this process.55 He contended that from the early stages of history the necessity for security and collective action caused humans to form groups, which in turn triggered a process of struggle that was followed by further \"compounding\" of groups and societies. In these early stages of history it was possible to discern an intercommunal struggle, where only the fittest survived and grew. These societies were mostly \"militant\" in an ideal-typical sense: hierarchical, oriented solely towards security and survival, and providing little space for individual freedom. As Spencer later described this turn in his thinking,\n\nIt had to be reluctantly admitted that war, everywhere and always hateful, has nevertheless been a factor in civilization, by bringing about the consolidation of groups\u2014simple into compound, doubly-compound, and trebly-compound\u2014until great nations are formed. As, throughout the organic world, evolution has been achieved by the merciless discipline of Nature, \"red in tooth and claw\"; so, in the social world, a discipline scarcely less bloody has been the agency by which societies have been massed together and social structures developed.56\n\nYet the power of war was also limited because human societies could escape this logic. For example, the activity of war produced the skills needed for voluntary cooperation, and when a particular stage was reached the advantages of war were exceeded by its disadvantages.57 According to Spencer, admitting the centrality of war in evolution was\u2014viewed in the long term\u2014not incompatible with \"the belief that there is coming a stage in which survival of the fittest among societies, hitherto affected by sanguinary conflicts, will be affected by peaceful conflicts.\"58 The outcome of the evolutionary process was the establishment of \"industrial\" societies characterized by, among other things, voluntary association, minimal government, individual freedom, and purely defensive military capabilities.59 This development was paralleled in the domain of ethics, where egoism was gradually replaced by social altruism and rational\/transfigured egoism until international conditions allowed for the emergence of internationalist altruism. Spencer could thus proclaim that there \"needs but a continuance of absolute peace externally, and a rigorous insistence on nonaggression internally, to ensure the moulding of men into a form characterized by all the virtues.\"60\n\nThere are numerous problems with this explanatory logic, many of which are connected to the relationship between Spencer's ideology and his \"science,\" but these can be left aside. It is more fruitful to focus on the consequences that followed for the way in which he viewed the future of international relations and, more specifically, the \"brotherhood of nations,\" the burgeoning international society that figured in his early writings. First, the concept of social evolution and the distinction between militant and industrial societies possessed considerable rhetorical power for Spencer as a critic of foreign policy. Progress could be thrown into reverse by militaristic adventures and misconceived visions of empire as an agent of civilization. Consequently Spencer castigated the actions and ideas of politicians and aristocrats, the clergy, historians, generals, and imperialists of all stripes.61 The lesson was obvious: accelerating social evolution was virtually impossible, but much could be done to obstruct the development of peace. Spencer's internationalism thus simultaneously embodied optimistic analysis and ferocious criticism. Second, it becomes clear that although he was not a nationalist (and certainly not a patriot), he was no straightforward cosmopolitan either. In line with many other liberals, Spencer seems to have \"naturalized\" the idea of the nation to the extent that a world without nations was unimaginable. However, the nation was not conceptualized in a sophisticated manner. Rather, Spencer's ideal demanded the development of complex industrial societies cooperating within a larger context of an evolving humanity. Indeed, the benign coexistence of nations amounted to an international society. This emerges again in the final pages of _The Principles of Sociology_ (1896), although by this stage the ideal is much more heavily institutionalized. In speculating about the international order of the future, which Spencer thought (and hoped) would be federal, he argued that \"future competitions\" between nations would follow the general law of evolution, displaying not only increasing heterogeneity (in terms of structural and cultural differences) but also the trait of the \"primary process of evolution,\" increasing integration. This development was necessary for completing human evolution; its potential benefits were obvious:\n\nAs, when small tribes were welded together into great tribes, the head chief stopped inter-tribal warfare; as, when small feudal governments became subject to a king, feudal wars were prevented by him; so, in time to come, a federation of the highest nations, exercising supreme authority (already foreshadowed by occasional agreements among \"the Powers\"), may, by forbidding wars between any of its constituent nations, put an end to the re-barbarization which is continually undoing civilization. When this peace-maintaining federation has been formed, there may be effectual progress towards that equilibrium between constitution and conditions\u2014between inner facilities and outer requirements\u2014implied in the final stage of human evolution.62\n\nSpencer, it should be stressed, did not advocate the construction of specific international institutions. In general, he held that the quality of political institutions was \"relative to the natures of citizens,\" meaning that moral transformation had to precede successful institutional engineering. And of course, for Spencer, such transformation was slow and, to judge by its contemporary manifestations, sometimes regressive. Here lay the kernel of his increasing disenchantment with the conduct of international politics. Human evolution still had a long way to go before peace could break out. As with so many other aspects of his thought, the purported existence of a peaceful international society was more ideological assertion than scientific forecast.\n\n_Henry Sidgwick_\n\nSidgwick appears at first markedly different from Spencer, and much more like his friend Green. Although he admired Spencer's ethical system, Sidgwick was unsympathetic to what he saw as its utopian implications. In particular he was critical of Spencer's (early) privileging of \"absolute ethics,\" describing it as \"an investigation not of what ought to be done here and now, but of what ought to be the rules of behaviour in a society of ideally perfect human beings.\" This was too far removed from political realities: \"Thus the subject-matter of our study would be doubly ideal: as it would not only prescribe what ought to be done as distinct from what is, but what ought to be done if a society that itself is not, but only _ought_ to be.\"63 Although both Sidgwick and Spencer took the pursuit of truth\u2014and perhaps especially moral truth\u2014extremely seriously, this disagreement reflects a difference in confidence. Spencer relegated metaphysical uncertainty to his notion of the \"Unknowable\" on which it was intellectually fruitless (and, for Spencer, unhealthy) to dwell; instead, he focused on the remaining intellectual terrain where he felt confident that truths could be ascertained and then proselytized. Sidgwick, in contrast, was more skeptical and self-critical, often lambasting the emerging field of sociology, of which Spencer was the leading British light, for its predilection for utopian prophecy.64 In a very un-Spencerian fashion, Sidgwick constantly agonized over the risk that ethical truths, like religious truths, were built on sand.65 John Maynard Keynes's notorious remark that Sidgwick \"never did anything but wonder whether Christianity was true and prove it wasn't and hope it was\" should be read in this light.66\n\nThe readiness to engage the world as it really appeared is also testimony to Sidgwick's proximity to the British political elite; he had, after all, a future prime minister and a future Archbishop of Canterbury as brothers-in-law. His close links to the Tory establishment also raise a question about labeling Sidgwick a liberal. Like some other leading public moralists, including Henry Maine and A. V. Dicey, Sidgwick became increasingly conservative towards the end of his life. Although he displayed relatively little of the inflated fears about collectivism that beset Maine and Dicey, he was still skeptical about many contemporary political developments, most obviously the Gladstonian push for Irish Home Rule.67 Sidgwick warmed to the Unionist perspective (sometimes even the Tory variant), and he was critical of party political liberalism. Nevertheless, the conservative elements in his thought should not be overestimated\u2014the legacy of the academic liberalism of the 1860s and 1870s weighed heavily on him, shaping his views on various domestic issues, including female education.68 Although he considered himself an independent, and although he has been described (with Maine) as a \"terrible political hypochondriac,\" Sidgwick also remained decidedly liberal in his views about international politics.69\n\nDespite these qualifications, Sidgwick and Spencer displayed close intellectual and political affinities. Unlike many later thinkers Sidgwick took Spencer's ideas very seriously, lecturing and writing widely on them. And as David Weinstein has argued, the philosophical differences between them should not be exaggerated.70 In terms of international politics, moreover, they shared a number of fundamental assumptions and a normative vision. Sidgwick agreed with Spencer\u2014reiterating an argument common at the time\u2014that there existed an irreversible tendency towards ever-smaller numbers of large omnicompetent political units.71 He shared (and often quoted) Spencer's dictum that \"ideal conduct... is not possible for the ideal man in the midst of men otherwise constituted.\"72 One of the lessons that both men drew from this dictum was that it was impractical to work directly for the establishment of new political institutions. Nevertheless, Sidgwick also shared with Spencer the view that the future would (or at least should) be federal; the nations of the \"civilized\" world would be united under one government that ensured order on a global scale, although his optimism about this potential development increased during the 1890s. Following an exposition of the various factors generating the tendency towards larger unions\u2014the dangers and economic burdens of war, increasing competition, the industrial character of modern societies, better facilities and habits of communication, and rising consciousness of a common civilization\u2014Sidgwick warned that it would be vain to expect the development of a singular European nationality and of \"an extensive federation of civilised states strong enough to put down wars among its members.\" In its pure form the ideal was not attainable, so Sidgwick opted for the second best:\n\nThe practically dominant political ideal of the present age does not include an extension of government beyond the limits of the nation. As in Greek history the practically dominant ideal is a society of City-states, independent, though observing in their mutual relations some kind of common law, so, in the period to which we belong, it is a society of Nation-states under \"International Law.\"73\n\nSidgwick's formulation of the internationalist ideal is interesting in several respects. First, his admiration of federalism grew stronger towards the end of his life.74 As the 1890s unfolded, Sidgwick seems\u2014despite his earlier criticisms of evolutionary optimism\u2014to have become more open to the idea of evolutionary progress, and this in turn made him more inclined to speculate about the future.75 In the final lecture of the course that was later published as _The Development of European Polity_ (1903), he felt \"disposed to predict a development of federality.\" As he argued, \"When we turn our gaze from the past to the future, an extension of federalism seems to me the most probable of the political prophecies relative to the form of government.\"76 Second, Sidgwick seems to have become steadily more internationalist during the 1890s. The tentative acceptance of evolutionary progress was indicative of his increasing optimism about international affairs\u2014or perhaps \"defiant optimism\" considering the political developments at the time\u2014which in turn might have catalyzed a more robust internationalist position. The most compelling evidence for such a development is to be found in some of the revisions Sidgwick made to writings published in the early 1890s.77\n\nFinally, Sidgwick's internationalism contained a practical dimension. After setting out the ideal of a society of nations under International Law, he attempted to delineate the ethical principles that this idea involved and compared these to existing international practices. Behind this analysis lay the conviction that order and ethical progress in world politics were not only possible but also necessary. Although Sidgwick accepted the special anarchical character of international relations\u2014the \"absence of a common government which has hitherto rendered wars between nations inevitable\"78\u2014he nevertheless had a habit of distinguishing only in degree between domestic and international politics.79 Despite the neo-Machiavellianism of \"respectable,\" mainly German, \"thinkers of our century,\" Sidgwick was adamant that statesmen and states were not exempt from the demands of public morality.80 He conceded that if (when?) states could not expect reciprocity in their political dealings with other states, they were allowed a \"corresponding extension of the right of self-protection, in the interest of humanity at large no less than in its own interest.\" But this did not mean that he drove a wedge between private and public morality, for a similar situation could also be imagined with regard to the dealings of individuals. Sidgwick pressed home the point that\n\nIn both cases equally it must be insisted that the interest of the part is to be pursued only in such manner and degree as is _compatible with the interests of the larger community of which it is part_ ; and that any violation of the rules of mutual behaviour actually established in the common interests of this community, so far as it is merely justified by its conduciveness to the sectional interest of a particular group of human beings, must receive unhesitating and unsparing censure.81\n\nSide-stepping the fundamental problem in this passage\u2014the question of what censure can achieve in the face of the violation of rules\u2014it is important to note how this insistence on viewing states as moral beings forming part of a \"larger community\" is as much a premise as it is a conclusion. If states are moral beings they form part of a community, and vice versa. The crucial point, however, is that insofar as moral progress is possible in international affairs (and Sidgwick clearly thought it was), such progress would manifest itself in strengthening that burgeoning international society that he had already identified.\n\nSidgwick was able to provide his readers with a more detailed discussion than Green and Spencer of what consequences for ethics followed from his internationalism, and in spelling this out he achieved a fuller balance between hardheaded analysis and ideological speculation. He was aware of the implausibility of internationalism ever gaining a complete victory, and in this sense he was a skeptic. But it was a skepticism that often translated into pragmatism rather than fatalism. It was this predilection for political pragmatism\u2014which from another perspective simply means falling prey to power\u2014and his criticism of Spencer's \"unphilosophical\" anti-imperialism, that with hindsight appear to compromise this brand of internationalism.\n\nCivilization, Empire, and the Limits of International Morality\n\nGreen, Spencer, and Sidgwick adumbrated compatible understandings of \"international society,\" and this vision formed part of their wider liberal internationalism, a generally optimistic picture of world order grounded on a progressive account of international development. However, they disagreed fundamentally over the role of empire, a topic that fiercely divided liberals in late Victorian Britain. Indeed many of the fault lines and silences in liberal thinking about empire that I explore throughout this book were reflected in their contrasting positions. In this section the limitations\u2014conceptual, territorial, and political\u2014of the liberal internationalist vision are explored.\n\nVictorian internationalists sketched a highly circumscribed picture of the present and future, their implied universality constricted by a civilizational narrative of human moral and political development. Only those societies characterized as \"civilized\" were included within the scope of international society, at least in the present; most, though, were not accorded sovereign equality and were not considered bound by norms of legal and moral reciprocity. John Stuart Mill, famously, excluded from the remit of his \"one very simple principle\" of liberty \"backward states of society in which the race itself may be considered as in its nonage.\"82 The spatial limits of civilization\u2014an elusive, always slippery concept\u2014were not, however, etched naturally into the fabric of the world. Liberal internationalism contained a dynamic conception of \"international society,\" a picture in which civilization always emanated outwards, in concentric circles, from a European core. Progress was defined by a dual track of development, not only by the degree to which the already civilized powers were socialized into new and increasingly pacific modes of behavior, but also by the extent to which the sphere of civilization could be widened. The idea was that over time, and often with the explicit intervention of imperial powers, the uncivilized could reach the level of development necessary for reclassification. This notion of potentially expansive inclusion underpinned a progressive evolutionary conception of historical time, projecting the circumscribed \"international society\" from its embryonic present into an optimistic, but almost always deferred, global future.\n\nThroughout the nineteenth century, liberal politicians and intellectuals contested the nature and boundaries of civilization. Debate tended to focus on \"liminal\" societies\u2014those that, like China, Japan, and the Ottoman Empire, were thought to possess the potential for full inclusion.83 Although opinions differed over the problems involved in bestowing the sacred moniker of civilization on these states, the overall trend was to argue that most societies were simply not prepared. Levels of civilization were calculated in relation to theological orientation, stage of technological development, ascribed racial characteristics, economic success, the form of political institutions that predominated, individual moral and intellectual competence, or (as was typically the case) some combination of these factors. It was, moreover, a common argumentative move to associate a civilized society with a particular form of political consciousness\u2014nationality. A country that was civilized possessed a sense of nationhood, and as such displayed the political (and moral) capacity for self-determination. This was a necessary, but rarely sufficient, condition of entry into international society. India was, in the most common articulation of this argument, frequently seen as failing to meet the criteria. There was also a specific temporal dimension embedded in internationalist discourse. \"Civilization\" was a marker of the present, and a guide to the future; it was a classification independent of any historical greatness. Whilst the Indians could offer up their contributions to architecture, science, and philosophy as indicators of their civilizational status, this was not seen to reflect accurately the \"barbarism\" of the present. The Chinese, likewise, were frequently lambasted for their \"stationariness,\" their failure to live up to the splendor of their own ancient history.84 Different regions, and even different countries within a region, were labeled and judged (albeit often in conflicting ways) and placed on a ladder, with the \"white\" countries, and especially Britain, perched at the top. But this account allowed for the possibility of movement up (and even down) the ladder, and thus for eventual inclusion in international society. This, at least, was the theory, although there were very few discussions of the actual timescale involved.\n\nQuestions of race, empire, and progress were woven through late Victorian political debate. Few internationalists followed Spencer in his almost complete opposition to empire (more on this below)\u2014and most ended up defending at least some aspects of its existence. Many distinguished between varieties of \"good\" and \"bad\" imperialism. The aggressive, militaristic \"jingo\" imperialism associated with Disraeli and, later, Joseph Chamberlain, which reached its pinnacle in the \"scramble for Africa\" and the South African War, was widely condemned by liberal internationalists, including Morley, Hobson, and Hobhouse.85 But empire itself was rarely considered unjustifiable. Two general lines of argument can be discerned; these were often but not always combined, although the weight afforded to each differed from individual to individual.86 The first was a long-standing one, articulated most powerfully in the writings of John Stuart Mill, which stressed the benefits that enlightened imperial governance could bring to the \"barbarous\" regions of the world. This was often phrased, to use a pervasive metaphor, in terms of adults training children for induction into society.87 Although faith in the \"civilizing mission,\" which reached its peak in the 1830s and 1840s, had been slowly undermined by a series of imperial crises (most notably the 1857 Sepoy Rebellion and the Eyre controversy of the 1860s) and by a more general loss of confidence in the ability of the British to remake the world in their own image, belief in the civilizing role of empire still carried considerable weight (a topic I discuss further in chapter 2).88 The empire, in this account, was seen as a giant engine for global social reform, the agent of civilization itself. The second line of argument focused more on the role of the settler empire, stressing the economic, cultural, political, and racial commonalities between the United Kingdom and Australia, New Zealand, and Canada\u2014and often the United States. This union of the \"Anglo-Saxon\" peoples, whether cast in terms of a formal political alliance (most frequently in terms of \"imperial federation\") or a vague moral unity, was seen by a number of prominent internationalists, including Hobson and Hobhouse, as a step on the road to a more pacific global order.89\n\nGreen, Sidgwick, and Spencer embodied the ambiguities and ambivalences, as well as many of the prejudices, of liberal internationalism. Green had the least to say about civilization and empire, although this was largely a consequence of the level of abstraction at which his work was pitched. His undergraduate essays, written in the mid-1880s, had supported the conventional civilizing rationale of the British empire, arguing that \"the progress of our dominion [in India] seems to have been the inevitable result of the action of civilization on barbarism.\"90 He was never especially critical of the consequences of empire for Britain's imperial subjects.91 However, in the _Lectures on the Principles of Political Obligation_ he argued, albeit in an aside, that British rule in India was both internally and externally destabilizing, leading to the propagation of an unhealthy \"military character\" in England while simultaneously contributing to dangerous international rivalry.92 Ironically, this muted critique was launched from Green's base in Balliol, an institution that, under the inspiring leadership of his former tutor, Benjamin Jowett (1817\u201393), primed young men for a life of service on the frontier: between 1874 and 1914, 27.1 percent of Balliol graduates worked in the imperial \"outposts of progress\" for at least two years.93 Moreover, Green's teaching deeply influenced many of the men who left Balliol to become imperial administrators, and the impact of idealism on Edwardian conceptions of imperialism, ranging from ideas about the Anglo-Saxon \"commonwealth\" through to Tory visions of global grandeur, was pronounced.94\n\nSidgwick frequently wrote in a racialized idiom, and his work is studded with examples of crude (albeit standard) civilizational stereotyping.95 It is the \"business\" of civilized nations to \"educate and absorb\" the savage nations, he wrote once when criticizing Spencer's ethics.96 He was an ardent defender of the British empire; indeed he sought to replicate in Cambridge the success of Oxford in training young men for imperial service.97 He argued that while the empire exhibited many potential downsides these were ultimately outweighed by its positive effects. The downsides included the loss of life involved (mainly but not only among the \"civilized\"), the geopolitical vulnerability to which it exposed Britain, the difficulty of defending such a globally extended frontier, and the temptation to drag other great powers into competition. These could in principle be offset, however, by a combination of material and moral benefits. Materially, imperialism could generate increased military power and national wealth, although this was by no means certain. Above all, though, it was ideas about Britain's civilizational task and \"spiritual expansion,\" the \"sentimental advantages, derived from justifiable conquests,\" that anchored Sidgwick's support for empire:\n\nSuch are the justifiable pride which the cultivated members of a civilised community feel in the beneficent exercise of dominion, and in the performance by their nation of the noble task of spreading the highest kind of civilisation; and a more intense though less elevated satisfaction\u2014inseparable from patriotic sentiment\u2014in the spread of the special type of civilisation distinctive of their nation, communicated through its language and literature, and through the tendency to imitate its manners and customs which its prolonged rule, especially if on the whole beneficent, is likely to cause in a continually increasing degree.98\n\nThis was a vision of liberal civilizational imperialism, remaking the manners as well as the map of the world, and drawing on a long-standing argument about the occupation of \"unoccupied\" territory leavened with late Victorian moralism about the duty of imperialists to indigenous populations.99\n\nHowever, as I have stressed throughout the chapters in this book, liberalism was far from monolithic when it came to justifying imperial ventures, and sweeping claims about the imperial logic inherent in liberalism, or of the essential connection between liberal political thought and empire, need to be treated with caution. Spencer was a vitriolic critic of empire and imperialism. He was at his most acute in identifying the \"re-barbarization\" of England, the reversion to militarism and authoritarian practices, a process that he argued was inseparable from imperialism. At the turn of the century he wrote that the \"coincidence in time between the South African war and the recent outburst of Imperialism, illustrates the general truth that militancy and Imperialism are closely allied\u2014are, in fact, different manifestations of the same social condition. It could not, indeed, be otherwise.\"100 As noted earlier, Spencer predicted the development of industrial societies and their peaceful coexistence. Although he had never specified a timeline, the closing years of the nineteenth century offered very little support for this prophecy. Spencer reacted by indicting the whole political culture of late Victorian Britain:\n\nFrom the people who daily read their Bibles, attend early services, and appoint weeks of prayer, there are sent out messengers of peace to inferior races, who are forthwith ousted from their lands by filibustering expeditions authorized in Downing Street; while those who resist are treated as \"rebels,\" the deaths they inflict in retaliation are called \"murders\" and the process of subduing them is named \"pacification.\"101\n\nMost people took their \"nominal creed\" from the New Testament and their \"real creed from Homer,\" and it was against this background that the by-now-agnostic Spencer claimed often to find himself trying to convert \"Christians to Christianity.\"102 This is not to suggest that he was free from the prejudices of his age; his writings are, after all, peppered with racialized turns of phrase (one only has to look closely at the passage just quoted).103 The point is that Spencer's biting radicalism and his sense of betrayal gave him a critical distance from the establishment and the policies it pursued, especially in contrast to Sidgwick's \"government house\" internationalism. It was this distance that made it possible for him to refer to dark and white savages in the same breath, to identify the \"diffusion of military ideas, military sentiments, military organization, military discipline... going on everywhere,\" and to lament the \"general retrogression shown in the growing Imperialism and accompanying re-barbarization.\"104\n\nConclusions\n\nDespite considerable political and philosophical differences, the views on international society articulated by Green, Spencer, and Sidgwick were overlapping. They emphasized the potential of a variety of trends discernible in international politics, in particular the importance of free trade and the evolution of international law, and they shared a broadly complementary normative vision of the future, of a pacific, stable, and expanding society of civilized states. Their conceptions of empire were, however, very different. The potential universalism of Sidgwick's vision was, like that of so many of his contemporaries, circumscribed by arrogance towards and ignorance about other societies. The sphere of civilization, whilst in principle capable of encompassing the whole planet, was still considered very small. This vision of international society was constrained, that is, by an account of racial difference. Green appears rather more ambivalent on this matter, whereas Spencer, while often prejudiced, was contemptuous of imperialism and feared the degrading effects of foreign dominion on British politics.\n\nThe intellectual life of the late Victorians was marked by often-vicious debate over a host of political issues. Despite the fissiparous nature of the period, it is nevertheless possible to identify a relatively coherent internationalist ideology promulgated by liberal public moralists. Green, Spencer, and Sidgwick were able to systematically theorize lines of thought which others held as articles of political faith. In the twentieth century the liberal ideal of international society was gradually, albeit incompletely, realized following two catastrophic world wars, reaching its formal legal recognition with the end of the drawn-out and bloody process of decolonization. Yet this new society embodied the Janus-faced approach to international order found in the tradition of British liberalism, one of its main intellectual progenitors. While finally achieving a form of universality through encompassing the entire globe, the new international society failed to completely escape the hierarchical differentiation associated with the always shifting standard of \"civilization.\" This remains the case to this day.\n\n1 Bertrand Russell, \"Hopes: Realized and Disappointed,\" in _Portraits from Memory and Other Essays_ (London, 1956), 46.\n\n2 J. A. Hobson, _The Morals of Economic Internationalism_ (Boston, 1920), 3\u20134.\n\n3 In the late nineteenth century the terms \"society\" and \"community\" were often used interchangeably; in this chapter, for the sake of consistency, we stick to \"society.\" In current international relations theory \"international society\" is associated with the \"English School\"; see Hedley Bull, _The Anarchical Society_ (London, 1977); Alex Bellamy, ed., _International Society and Its Critics_ (Oxford, 2004). We are not using it in this latter sense.\n\n4 Collini, _Public Moralists_ (Oxford, 1991).\n\n5 The degree to which their liberal internationalism permeated British society as a whole is, though, an open question. The dangers of over-generalization, often resulting from the frequent mismatch between authorial intention and audience reception, are manifest in many studies of Victorian political culture\u2014on which see Peter Mandler, \"The Problem of Cultural History,\" _Social and Cultural History_ , 1 (2004), 94\u2013118. However, it is not implausible to conjecture that this internationalist vision had a wide following outside the highbrow world of the public moralists, although in this chapter we limit our attention to this world. To take a few examples: the success of Gladstone's Midlothian campaign relied, at least in part, on the wide resonance of his views amongst significant elements of the electorate (H.C.G. Matthew, _Gladstone, 1809\u20131898_ (Oxford, 1997), pt. 2, ch. 2); moreover, as Anthony Howe argues, from the 1860s onwards free trade was an essential element in popular political identity: Howe, _Free Trade and Liberal England, 1846\u20131946_ (Oxford, 1997), 113, Furthermore, the relative prominence of the peace movement demonstrates the wide reception of broadly liberal internationalist ideas. Paul Laity, _The British Peace Movement, 1870\u20131914_ (Oxford, 2001); N. W. Summerton, \"Dissenting Attitudes to Foreign Relations, Peace and War, 1840\u20131890,\" _Journal of Ecclesiastical History_ , 28 (1977), 151\u201378. Finally, much of the outlook of the labour movement, including the groups that later coalesced into the Labour Party, can also been seen as liberal in the sense that we employ the term. Henry Winkler, _British Labour Seeks a Foreign Policy, 1900\u20131940_ (London, 2005), ch. 1. Popular liberalism could also be taken in a more militant (though not necessarily anti-internationalist) direction. See Eugenio Biagini, \"Neo-Roman Liberalism,\" _History of European Ideas_ 29 (2003), 55\u201372.\n\n6 On the continuity in radical attitudes, especially towards empire, see Miles Taylor, \"Imperium et Libertas?,\" _Journal of Imperial and Commonwealth History_ , 19 (1991), 1\u201323; Peter Cain, \"Radicalism, Gladstone, and the Liberal Critique of Disraelian 'Imperialism,'\" in _Victorian Visions_ , ed. Bell, 215\u201339.\n\n7 Hidemi Suganami, _The Domestic Analogy and World Order Proposals_ (Cambridge, 1989).\n\n8 On parliamentary and popular politics, see J. P. Parry, _The Rise and Fall of Liberal Government in Victorian Britain_ (London, 1993); John Vincent, _The Formation of the Liberal Party, 1857\u20131868_ (London, 1966); Eugenio Biagini, _Liberty, Retrenchment, and Reform_ (Cambridge, 1992).\n\n9 Lawrence Goldman, _Science, Reform, and Politics in Victorian Britain_ (Cambridge, 2002), 59; Martin Hewitt, ed., _An Age of Equipoise?_ (Aldershot, 2001).\n\n10 Maine, _International Law_ (London, 1888), 3\u20135.\n\n11 Morley, _The Life of William Ewart Gladstone_ , 3 vols. (London, 1903), 2:318\u201319.\n\n12 Hobhouse, _Liberalism and Other Writings_ [1911], ed. J. Meadowcroft (Cambridge, 1994), 103. See also John Morley, _On Compromise_ [1874], 2nd ed. (London, 1886), 29; A. V. Dicey, _Lectures on the Relation between Law and Public Opinion in England during the Nineteenth Century_ [1905], 2nd ed. (London, 1914), 444.\n\n13 On new liberalism, see Peter Clarke, _Liberals and Social Democrats_ (Cambridge, 1978); Michael Freeden, _The New Liberalism_ (Oxford, 1978); Avital Simhony and David Weinstein, eds., _The New Liberalism_ (Cambridge, 2001). On philosophical idealism see the references and discussion in section 3 below.\n\n14 Lawrence, _Essays on Some Disputed Questions in Modern International Law_ [1884], 2nd ed. (Cambridge, 1885), vii, 24, 240.\n\n15 See here Casper Sylvest, \"Continuity and Change in British Liberal Internationalism, c.1900\u20131930,\" _Review of International Studies_ , 31 (2005), 263\u201383; and, in general, Jens Bartelson, \"The Trial of Judgement,\" _International Studies Quarterly_ , 39 (1995), 255\u201379.\n\n16 See especially Norman Angell, _The Great Illusion_ (London, 1910).\n\n17 Seebohm, _On International Reform_ (London, 1871), 70, 91.\n\n18 Bryce, \"An Age of Discontent,\" _Contemporary Review_ , 49 (1891), 14\u201329.\n\n19 Amos, _Political and Legal Remedies for War_ (London, 1880), 340\u201341.\n\n20 Rom Harr\u00e9, \"Positivist Thought in the Nineteenth Century,\" in _The Cambridge History of Philosophy, 1870\u20131945_ , ed. Thomas Baldwin (Cambridge, 2003), 11\u201326; C. A. Bayly, \"European Political Thought and the Wider World during the Nineteenth Century,\" in _The Cambridge History of Nineteenth-Century Political Thought_ , ed. Gregory Claeys and Gareth Stedman Jones (Cambridge, 2011), 835\u201362.\n\n21 Green, _Mr. Herbert Spencer and Mr. G. H. Lewes, Collected Works of T. H. Green_ , ed., Peter Nicholson, 5 vols. (Bristol, 1997), 1:373\u2013541. Hereafter _Collected Works_. The first three volumes of this new collection are reprints of _Works of Thomas Hill Green_ , ed. R. L. Nettleship, 3 vols. (London, 1885\u201388).\n\n22 See, for example, Spencer to Alexander Bain, April 25, 1902, and Spencer to Professor Masson, April 26, 1902, in David Duncan, _The Life and Letters of Herbert Spencer_ (London, 1908), 457\u201358. See also Henry Sidgwick, \"Green's Ethics,\" _Mind_ , 9 (1884), 169\u201387, and the discussion in Bart Schultz, _Henry Sidgwick_ (Cambridge, 2004), 362.\n\n23 Ritchie, \"Review of Henry Sidgwick, _The Elements of Politics_ ,\" _International Journal of Ethics_ , 2 (1891\u201392), 256. See also Bernard Williams, \"The Point of View of the Universe\" [1982], in _Making Sense of Humanity_ (Cambridge, 1994), 153\u201371.\n\n24 Hobhouse, \"Introduction to the Second Edition\" [1909], in _Democracy and Reaction_ [1904], ed. P. F. Clarke (New York, 1973), 274. Hobhouse partly exonerated Green from this critique (276). See also Hobson, _International Government_ (London, 1915), esp. 178; Hobhouse, _The Metaphysical Theory of the State_ [1918] (London, 1960), 25. For an early, tentative suggestion along the same lines see Sidgwick, \"Public Morality\" [1897], in _Practical Ethics_ (London, 1898), 66.\n\n25 Peter Nicholson, \"Philosophical Idealism and International Politics,\" _British Journal of International Studies_ , 2 (1976), 76\u201383; David Boucher, \"British Idealism, the State, and International Relations,\" 671\u201394; Boucher, \"Introduction,\" in _The British Idealists_ , ed. Boucher (Cambridge, 1997), vii-xxxiii.\n\n26 Richter, _The Politics of Conscience_ (London, 1964), 89.\n\n27 On Green's admiration for Bright and Cobden, and his corresponding hatred of Palmerston and Louis Napoleon, see R. L. Nettleship, \"Memoir\" [1888], in _Collected Works_ , vol. 3, xx and xxiii-xxiv. Green was a staunch defender of the principle of non-intervention in international politics. See Green, \"Can Interference with Foreign Nations in Any Case Be Justifiable?,\" _Collected Works_ , 5:15\u201319; Christopher Harvie, _The Lights of Liberalism_ (London, 1976), 102. On his domestic radicalism, see Colin Tyler, \"T. H. Green, Advanced Liberalism and the Reform Question 1865\u20131876,\" _History of European Ideas_ , 29 (2003), 437\u201358.\n\n28 Michael Freeden, _Ideologies and Political Theory_ (Oxford, 1996), 179.\n\n29 Green, _Lectures on the Principles of Political Obligation_ [1886], _Collected Works_ , 2:347, sec. 21. Italics added.\n\n30 Mill, _Political Obligation_ , 345\u201346, sec. 18.\n\n31 Mill, \"Lecture on Liberal Legislation and Freedom of Contract\" [1880], _Collected Works_ , 3:365\u201386.\n\n32 Mill, _Political Obligation_ , 454, 436, secs. 143, 122. See also Peter Nicholson, \"Introduction,\" in _The Political Philosophy of the British Idealists_ , ed. Nicholason (Cambridge, 1990), 1\u20136.\n\n33 For a discussion of Green's theology, see Colin Tyler, \"T. H. Green,\" _Stanford Encyclopedia of Philosophy_ , <http:\/\/plato.stanford.edu>.\n\n34 Richter, _The Politics of Conscience_ , 105.\n\n35 Green, _Political Obligation_ , 473, 478, 476\u201377, secs. 163, 167, 166.\n\n36 Ibid., 357\u201359, 373, secs. 34\u201335, 50.\n\n37 Ibid., 483, 484, 464\u201365, secs. 174, 155. See also Richter, _Politics of Conscience_ , 207, 216. For examples of Green's criticisms of patriotism, see his undergraduate essay \"Loyalty\"; his speech \"Against Disraeli's Foreign Policy,\" January 26, 1878; and his speech on \"National Loss and Gain under a Conservative Government,\" December 5, 1879, _Collected Works_ , 5:12\u201314, 313\u201317, 347\u201355.\n\n38 See Green, _Prolegomena to Ethics_ [1883], in _Collected Works_ , vol. 4, bk. 3, 160\u2013314; Nettleship, \"Memoir,\" cxxxviii-cxxxix.\n\n39 Green, _Prolegomena to Ethics_ , 193, sec. 184. Original italics.\n\n40 Green, _Political Obligation_ , 480\u201381, 484, secs. 170\u201371. This notion of \"cosmopolitan nationalism,\" to use a slightly paradoxical formulation, was not uncommon. See Stuart Jones, \"The Idea of the National in Victorian Political Thought,\" _European Journal of Political Theory_ , 5 (2006), 12\u201321; Duncan Bell, \"Unity and Difference,\" _Review of International Studies_ , 31 (2005), 559\u201379; and Georgios Varouxakis, \"'Patriotism,' 'Cosmopolitanism' and 'Humanity' in Victorian Political Thought,\" _European Journal of Political Theory_ , 5 (2006), 100\u2013118. See also my discussion of J. R. Seeley's political thought in chapter 11.\n\n41 Green, _Prolegomena to Ethics_ , 218\u201319, 229\u201330, secs. 207, 216.\n\n42 Green, _Political Obligation_ , 485, sec. 175.\n\n43 On his life and career see J.D.Y. Peel, _Herbert Spencer_ (London, 1971); David Wiltshire, _The Social and Political Thought of Herbert Spencer_ (Oxford, 1978). Since this chapter was first published, another important biographical study has appeared: Mark Francis, _Herbert Spencer and the Invention of Modern Life_ (Ithaca, 2007).\n\n44 Spencer, _Social Statics_ (London, 1851), 65.\n\n45 Ibid., 103. Italics in original.\n\n46 See David Weinstein, Equal Freedom and Utility (Cambridge, 1998); M. W. Taylor, Men _versus the State_ (Oxford, 1992).\n\n47 Spencer, _The Proper Sphere of Government_ [1842\u201343], in _Man versus the State_ (Indianapolis, 1982), 187.\n\n48 For a valuable analysis (in which Spencer is not mentioned), see A.J.P. Taylor, _The Trouble Makers_ (London, 1957); and also Taylor, \"Imperium et Libertas?\"; Cain, \"Radicalism.\"\n\n49 Spencer, _The Proper Sphere of Government_ , 211\u201313.\n\n50 Spencer, _Social Statics_ , 272\u201373. Italics in original.\n\n51 Spencer, _First Principles_ (London, 1867), 396. The wording of this definition changed slightly as Spencer revised the work.\n\n52 The phrase is from Maurice Mandelbaum, _History, Man, & Reason_ (London, 1971), 90.\n\n53 See especially John Burrow, \"Historicism and Social Evolution,\" in _British and German Historiography, 1750\u20131950_ , ed. Benedikt Stuchtey and Peter Wende (Oxford, 2000), 251\u201364.\n\n54 This had already been noted by Sidgwick, who castigated Spencer for his \"irrepressible and unwarrantable optimism.\" Sidgwick, _Lectures on the Ethics of T. H. Green, Mr. Herbert Spencer and J. Martineau_ (London, 1902), 228.\n\n55 Spencer, _Principles of Sociology_ , 3 vols. (London, 1876\u201396), vol. 1, v.\n\n56 Spencer, \"The Filiation of Ideas\" [1899], in Duncan, _Life and Letters_ , 569.\n\n57 Mike Hawkins, _Social Darwinism in European and American Thought, 1860\u20131945_ (Cambridge, 1997), 92.\n\n58 Spencer, \"Filiation of Ideas,\" 569.\n\n59 The importance of the distinction between militant and industrial societies to Spencer's sociology is hard to overestimate. It is developed in most detail in Spencer, _Political Institutions_ , esp. chs. 17, 18; Spencer, _The Principles of Ethics_ [1879\u201393], 2 vols. (Indianapolis, 1978), 2.\n\n60 Spencer, _Principles of Ethics_ , 1, 504.\n\n61 See the discussion below in section 4.\n\n62 Spencer, _Principles of Sociology_ , 3:600, sec. 853.\n\n63 Sidgwick, _The Methods of Ethics_ [1874], 7th ed. (London, 1907), 18, and the accompanying footnote. Italics in original. See also Sidgwick, \"Mr. Spencer's Ethical System,\" _Mind_ , 5 (1880), 216\u201326; Sidgwick, _Lectures_ , 206. Already in 1873 Sidgwick felt moved to criticize Spencer \"somewhat severely.\" H. S. to F.W.H. Myers [February 1873], Sidgwick papers, Wren Library, Trinity College, Cambridge, Add.ms.100\/237.\n\n64 Sidgwick, \"The Scope and Method of Economic Science\" [1885] and \"Political Prophecy and Sociology\" [1894], in _Miscellaneous Essays and Addresses_ (London, 1904), 170\u201399, 216\u201334; Sidgwick, \"The Relation of Ethics to Sociology,\" _International Journal of Ethics_ , 10 (1899), 1\u201321.\n\n65 Sidgwick acknowledged this gulf between him and Spencer: A. and E. M. Sidgwick, _Henry Sidgwick, A Memoir_ (London, 1906), 421.\n\n66 John Maynard Keynes to Bernard Swithinbank, March 27, 1906 (Keynes Papers, King's College, Cambridge), quoted in Schultz, _Henry Sidgwick_ , 4.\n\n67 Spencer also opposed Home Rule. See Spencer to Auberon Herbert, June 16, 1890, and Spencer to the Earl of Dysart, May 27, 1892, both in Duncan, _Life and Letters_ , 300\u2013301, 315.\n\n68 On \"academic liberalism,\" see Harvie, _Lights of Liberalism_ ; on Sidgwick's reformist credentials, see Schultz, _Henry Sidgwick_.\n\n69 Collini, _Public Moralists_ , 279; Collini, \"My Roles and Their Duties,\" in _Henry Sidgwick_ , ed. Ross Harrison (Oxford, 2001), 9\u201349, esp. 38.\n\n70 David Weinstein, \"Deductive Hedonism and the Anxiety of Influence,\" _Utilitas_ , 12 (2000), 329\u201346. See also Sidgwick, \"Political Prophecy and Sociology,\" 222; Sidgwick, \"The Relation of Ethics to Sociology,\" 2.\n\n71 Sidgwick, _The Elements of Politics_ [1891], 3rd ed. (London, 1907), 218\u201319. Valorizing massive political units was common at the time, as for example in the writings of Sidgwick's colleague J. R. Seeley. For a liberal critique of the \"megalophiles,\" see J. M. Robertson, _An Introduction to English Politics_ (London, 1900), 251\u201358.\n\n72 See, e.g., Sidgwick, \"Public Morality,\" 72. Sidgwick, _Elements of Politics_ , 239\u201340nn. See also Spencer, _Principles of Ethics_ , 1:307.\n\n73 Sidgwick, _Elements of Politics_ , 219\u201320.\n\n74 Ibid., 267, 301\u20132, 310; Sidgwick, _Memoir_ , 576.\n\n75 Weinstein, \"Deductive Hedonism,\" 337.\n\n76 Henry Sidgwick, _The Development of European Polity_ , ed. E. M. Sidgwick (London, 1903), 439. This book differed from the _Elements of Politics_ in being inductive, historical, and avowedly \"scientific,\" focusing on what _is_ or _has been_ (as opposed to his previous, deductive, and ethical concern with what _ought to be_ ).\n\n77 See, for example, \"The Morality of Strife,\" in Sidgwick, _Practical Ethics_ , 83\u2013112 (first published in _International Journal of Ethics_ , 1 (1890), 1\u201315); and compare ch. 15 of the first (1891) edition of _The Elements of Politics_ to later editions (1896 onwards). See also Collini, \"My Roles and Their Duties,\" 27\u201329.\n\n78 Sidgwick, \"Public Morality,\" 77.\n\n79 See, for example, the simultaneous discussion of the ethical dimensions of domestic and international conflict in \"Public Morality\" and in the revised edition of \"The Morality of Strife.\"\n\n80 Sidgwick, \"Public Morality,\" 60. Sidgwick appears to have drawn this analysis from Lord Acton's introduction to Burd's edition of Machiavelli. Acton, \"Introduction,\" in _Il Principe_ , by Niccol\u00f2 Machiavelli, ed. Burd (Oxford, 1891), xix\u2013xl.\n\n81 Sidgwick, \"Public Morality,\" 81\u201382. Italics added.\n\n82 Mill, _On Liberty_ [1859], _Collected Works_ , 18:224.\n\n83 For debate amongst lawyers, see Jennifer Pitts, \"The Boundaries of Victorian International Law,\" in _Victorian Visions_ , ed. Bell, 67\u201389.\n\n84 On the trope of Chinese \"stationariness,\" see Collini, _Public Moralists_ , 108, 274.\n\n85 See also Bernard Porter, _Critics of Empire_ (London, 1968).\n\n86 For debates among progressives, including Hobson, Herbert Samuel, J. M. Robertson, and C. P. Trevelyan, on the question of empire and civilization that bear out the following discussion, see Michael Freeden, ed., _Minutes of the Rainbow Circle, 1894\u20131924_ (London, 1989), 45\u201346, 58\u201360, 69\u201379, 115\u201326.\n\n87 Ashis Nandy, \"Reconstructing Childhood,\" in _Traditions, Tyranny, and Utopia_ (Delhi, 1987), 56\u201376; Uday Singh Mehta, _Liberalism and Empire_ (Chicago, 1999), 28\u201336.\n\n88 Mantena, _Alibis of Empire_.\n\n89 Hobson, _Imperialism_ 1902], ed. Philip Siegelman (Ann Arbor, 1997), 332; Hobhouse, _Democracy and Reaction_ , 153\u201354. See also Bell, _The Idea of Greater Britain_. Hobson and Hobhouse later changed their positions on this issue, as I discuss in [chapter 14.\n\n90 Green, \"British Rule and Policy in India,\" _Collected Works_ , 5:22. See also Green, \"Interference with Foreign Nations,\" 15\u201319. In later writings the British empire, in India or elsewhere, is rarely mentioned.\n\n91 For example he argued that the only \"lasting defence of the Indian Empire is in contentment of the Indian people.\" See Green's notes on his speech on \"National Loss and Gain under a Conservative Government,\" delivered on December 5, 1879, in _Collected Works_ , 5:352.\n\n92 Green, _Political Obligation_ , 483, sec. 173.\n\n93 Richard Symonds, _Oxford and Empire_ (Oxford, 1991), 28\u201329, 306. Since the 1850s, Jowett had been instrumental in directing Oxford and Cambridge graduates to the Indian Civil Service. See Phiroze Vasunia, \"Greek, Latin, and the Indian Civil Service,\" _Proceedings of the Cambridge Philological Society_ , 51 (2005), 35\u201371, esp. 44\u201347. In the years between 1888 and 1905, three successive viceroys of India came from Balliol. Vasunia, \"Greater Rome and Greater Britain,\" in _Classics and Colonialism_ , ed. Barbara Goff (London, 2005), 34\u201368, esp. 45. For the phrase \"outposts of progress,\" see Joseph Conrad, \"An Outpost of Progress\" (1896\u201397), in _Heart of Darkness, and Other Tales_ , ed. Cedric Watts (Oxford, 2002). See also the discussion in chapter 5.\n\n94 E.H.H. Green, _Ideologies of Conservatism_ (Oxford, 2001), 42\u201372; Morefield, _Covenants without Swords_.\n\n95 See especially Sidgwick, _The Elements of Politics_ , 311\u201328; Schultz, _Henry Sidgwick_ , ch. 7.\n\n96 Sidgwick, _Lectures_ , 236.\n\n97 Collini, Winch, and Burrow, _That Noble Science of Politics_ , 354\u201355; Vasunia, \"Greek, Latin, and the Indian Civil Service.\"\n\n98 Sidgwick, _The Elements of Politics_ , 312, 313, 256.\n\n99 For a discussion of so-called _terra nullius_ arguments, see Anthony Pagden, \"Human Rights, Natural Rights, and Europe's Imperial Legacy,\" _Political Theory_ , 31 (2003), 171\u201399. Since this chapter was originally published, a comprehensive study has appeared: Andrew Fitzmaurce, _Sovereignty, Property and Empire, 1500\u20132000_ (Cambridge, 2014).\n\n100 Spencer, \"Imperialism and Slavery,\" in _Facts and Comments_ (London, 1902), 112\u201321, esp. 113.\n\n101 Spencer, _Principles of Ethics_ , 2:277.\n\n102 Spencer to E. Cazelles, December 6, 1896, in Duncan, _Life and Letters_ , 399\u2013400.\n\n103 Although see the discussion in Peel, _Herbert Spencer_ , ch. 6. Note also that Spencer did offer heavily qualified support for privatized forms of settler colonialism, as I discuss in chapter 2.\n\n104 Spencer to Cazelles, and also Spencer to Moncure D. Conway, July 17, 1898, in Duncan, _Life and Letters_ , 410; Spencer, \"Re-Barbarization\" and \"Regimentation,\" in _Facts and Comments_ , 236, 138.\nCHAPTER 11\n\nJohn Robert Seeley and the Political Theology of Empire\n\nWhen we have accustomed ourselves to contemplate the whole Empire together and call it England, we shall see that here too is a United States. Here too is a homogenous people, one in blood, language, religion, and laws, but dispersed over a boundless space.1\n\n\u2014J. R. SEELEY\n\nJohn Robert Seeley (1834\u201395) was the most prominent imperial thinker in late nineteenth-century Britain. His writings about the past, present, and future of British expansion were hugely popular, and his name became a byword for the world-straddling ambition of the country. Lord Acton crowned him \"the philosopher of national greatness.\"2 Published in 1883, his most famous book, _The Expansion of England_ , was an instant success, helping to set the terms of late Victorian debate about empire and remaining a standard reference point for decades to come. \"I question,\" H.A.L. Fisher wrote in an obituary, \"whether any historical work has exercised so great an influence over the general political thinking of a nation.\"3 A quarter of a century later, G. P. Gooch marveled that it occupied \"a place in political history as well as in a record of historiography,\" such was its impact.4 It remained in print until 1956, the year of Suez.\n\nSeeley set himself two main tasks in the book. First, he sought to rewrite the plotline of British historical development. Displacing the center of gravity from domestic constitutional reform to imperial expansion, he contended that modern Britain was forged chiefly in conflicts over territory and sovereign control in North America and Asia, not in the corridors of Parliament or on the battlefields of Europe.5 \"History,\" he boomed, \"is not constitutional law, nor parliamentary tongue-fence, nor biography of great men, nor even moral philosophy. It deals with states, it investigates their rise and development and mutual influence, the causes which promote their posterity or bring about their decay.\"6 He thus rejected the Whiggish line that the epicenter of the national story was the evolution of constitutional government and individual liberty. Secondly, he emphasized the significance of what we might term the _second settler empire_ in Australia, Canada, the Cape, and New Zealand, insisting that this transoceanic political association was both more durable and more important than India. \"When we inquire into the Greater Britain of the future we ought to think much more about our colonial than our Indian empire.\"7 Seeley presented these arguments as a case study of his historical method. Committed to the view that the main purpose of analyzing the past was to inculcate political knowledge in citizens and (especially) members of the political elite, he argued that history was a \"school of statesmanship.\"8 Through the rigorous inductive dissection of the historical record, and in particular through tracing the development of states, it was possible to cultivate political wisdom and foresight. If it was \"worth anything,\" he argued, history must surely \"anticipate the lessons of time. We shall all no doubt be wise after the event; we study history that we may be wise before the event.\" Studying the past necessarily involved a \"practical object,\" insofar as it shaped perceptions of the world, and in doing so (hopefully) conditioned ethical judgment and political action.9 \"Though he did not coin the phrase 'History is past politics, and politics present history,'\" G. W. Prothero once wrote, \"it is perhaps more strictly applicable to his view of history than to that of its author.\"10\n\nDespite its importance, and despite the apparent clarity of its argument, _The Expansion of England_ remains poorly understood. This is partly a matter of genre. Based on a course of undergraduate lectures, and rewritten for a general audience, it doesn't include any sustained discussion of the sources that Seeley drew from, the conceptual architecture underpinning his argument, or the political and intellectual positions he sought to overturn. In this chapter I argue that many of the ideas Seeley employed in his account of empire\u2014nation, state, history, science, civilization\u2014had specific theological connotations, and his political thought as a whole was underwritten by his eccentric interpretation of the sacred. Religion, he professed, was \"the soul of all healthy political organization,\" and on it \"depends the whole fabric of civilization, all the future of mankind.\"11 This silence may also have been a matter of intention. Seeley wrote two major works of theological reflection, _Ecce Homo_ (1866) and _Natural Religion_ (1882), the former a literary sensation, the latter his most systematic treatment of the subject, but they were published anonymously, and even when their authorship was widely known Seeley refused to put his name to them.12 Both _Ecce Homo_ and _The Expansion of England_ , \"each in its own sphere,\" Fisher later reflected, \"may be held to mark an epoch in the education of the Anglo-Saxon race.\"13 Seeley did not regard those spheres as distinct or separable.\n\nSeeley's brand of liberal political theology blended the impulse to transform aspects of society with a Burkean gradualism and respect for tradition. A willfully syncretic thinker, he drew on a variety of sources. Comtean positivism, Rankean historicism, German romanticism, the doctrines of Broad Churchmanship derived ultimately from Coleridge and transmitted through Thomas Arnold and F. D. Maurice, the \"comparative method\" so popular among late Victorian scholars: all found their allotted place in his capacious intellectual system. In the next section I dissect Seeley's understanding of theology and religion.14 Section 3 probes his views on the sacred character of nationality, and shows how he attempted to reconcile particularism and universalism in what I will call a \"cosmopolitan nationalist\" vision. In section 4 I argue that _The Expansion of England_ should be understood as an expression of his basic political-theological commitments, and I also make the case that he conceived of Greater Britain as a global federal nation-state, modeled on the United States. I conclude by discussing the role of India and Ireland in his polychronic, stratified conception of world order.\n\nEnthusiasm for Humanity\n\nSeeley followed an intellectual trajectory typical of the son of \"extreme\" evangelicals.15 Bypassing the early crisis of faith so common amongst his contemporaries, he glided from a youthful immersion in evangelicalism to a less unforgiving incarnationalism, from a harsh and apocryphal vision of the cosmos to a milder one in which the life of Jesus served as a noble example for human behavior. In particular, Seeley drew inspiration from the \"Broad Church\" theologians, A. P. Stanley, F. W. Robertson, and especially Thomas Arnold and F. D. Maurice.16 The term \"Broad Church,\" happily embraced by Seeley, had been introduced to encompass those sharing a more liberal theological sensibility in the face of the radical supernaturalism and biblical literalism that united the otherwise conflicting High (Anglo-Catholic, Tractarian-influenced) and Low (Evangelical) Churches.17 In the background hovered Samuel Taylor Coleridge, whose ideas about the relationship between Church and State influenced the Broad Church theologians, and whose notion of a \"clerisy\" Seeley also embraced and updated.18 Seeley's latitudinarianism seems to have been reinforced by the time he spent in London, where he moved in the overlapping circles of the emerging Comtean positivist movement and the Christian Socialists.19 Learning from both, he never fully joined either. Indeed he can be seen as a fairly conventional Broad Church theologian, focusing on the interrelationship between (the usually capitalized) Church and State, the quest to reconcile modernity and tradition, and a concomitant desire to fashion national unity through the eradication of interdenominational and class strife. Extremely critical of the Church of England, Seeley believed that it was failing in its appointed task of educating the nation morally, of providing a sense of concord and purpose for society.20 As the century unfolded, he began to shift the burden of this task away from traditional religious institutions and onto the shoulders of what he hoped would become a reconfigured historical discipline, a new clerisy. Historians were to act not simply as literary chroniclers of the past but as apostles of national destiny. It was their job to animate and inform public opinion and to guide wise statecraft.\n\nIn _Ecce Homo_ he outlined a view of Christian morality appropriate for the modern world. Bracketing off the supernatural abilities attributed to Christ he focused on the life of Jesus, figuring him as a luminous moral exemplar.21 Christians, Seeley averred, have a \"divine inspiration\" that should ideally allow them to identify the appropriate course of action in all circumstances, inspired by \"the passion of humanity raised to high energy by the contemplation of Christ's character, and by the society of those in whom the same enthusiasm exists.\"22 Jesus, according to Seeley, thus established a divine universal society dedicated to the \"improvement of morality.\"\n\nHis morality required that the welfare and happiness of others should not merely be remembered as a restraint upon action, but should be made the principal motive of action, and what he preached in words he preached still more impressively and zealously in deeds. He set the first and greatest example of a life wholly governed and guided by the passion of humanity.23\n\nCentral to Christ's revolutionary impact was a transformation of the idea of duty. \"The Christian moral reformation may indeed be summed up in this\u2014humanity changes from a restraint to a motive.\" By this, Seeley meant that an \"active\" dimension (\"thou shalt\") was added to the extant negative dictates of morality (\"thou shalt not\"), and as such the range of duties that human owed to one another was vastly expanded. \"To the duty of not doing harm, which may be called justice, was added the duty of doing good, which may properly receive the distinctively Christian name of Charity.\"24 This was both a historical assertion about the early development of Christianity, and a claim about the best way to understand morality in the present. Moral improvement was\u2014or at least should be\u2014the guiding task of Christianity, its continuing lesson and gift to the world. Much to the chagrin of his friend Henry Sidgwick, Seeley dismissed modern secular accounts of ethics as incapable of motivating right conduct, solely reliant as they were on rational argumentation. Only a system rooted in the passionate exemplarity of Christ was sufficient.25\n\nSeeley's political theology developed in critical dialogue with Comtean positivism. Throughout his writings he attempted to combine elements of positivism, not least its respect for the wonders of modern science and its universalism, with a specifically Christian conception of moral life. He was far from alone in attempting this kind of synthesis. During the second half of the nineteenth century, numerous theologians grappled with Comte's elaborate system, which was widely understood to present a deep challenge to the main tenets of Christianity, principally through its corrosive skepticism about the ability to know the unobservable world. B. F. Westcott, J. B. Lightfoot, F.J.A. Hort, Charles Kingsley, and Maurice, among others, sought either to domesticate or tame its more radical epistemological claims.26 Like many liberal theologians of the era, Seeley was both attracted to and repelled by positivism. We can catch a glimpse of his ambivalent attitude from a letter he wrote in 1869 to Kingsley, his predecessor at Cambridge:\n\nI certainly do not feel equal to the task of opposing Comte. But you are right in thinking that, if I could, I would oppose his atheism as strongly as yourself. But just at present Comtism seems so irresistibly triumphant, that I have contented myself lately with pointing out that it is in a sense a Christian movement and with trying to induce the Church to appropriate what is good in it.27\n\nThe influence of positivism was most pronounced in _Ecce Homo_ , though it also inflected many of the concerns and categories of _Natural Religion_ , including Seeley's advocacy of \"enthusiasm\" for humanity and his emphasis on love as the basis of morality. Throughout his writings, Seeley sought to undercut one of the main implications of Comte's teaching, the strict division, both epistemic and historical, between science and religion.28 Rather than condemning the latter to a past rendered obsolete by the former, he (like Maurice) asserted that science itself could be seen as a form of divine revelation. Contra Comte and his legion of followers, then, science and religion were not only compatible, both were necessary to underpin a progressive vision of humanity.\n\n_Ecce Homo_ spawned impassioned debate about both the identity of its author and its religious teaching. Some theologians, including John Henry Newman, dismissed it as an amateurish essay.29 The evangelical seventh Earl of Shaftesbury condemned it as the worst work \"vomited from the jaws of hell.\"30 Others, though, were far more receptive to its message. Among its greatest admirers was Gladstone, who published a sympathetic response and subsequently propelled Seeley into the Regius Professorship of Modern History at Cambridge.31 Four decades after its publication, the liberal theologian and historian Hastings Rashdall described it as \"the most striking expression of the appeal which Christ makes to the Conscience of the modern world,\" one that had \"proved a veritable fifth Gospel to many seekers after light.\"32 As the First World War engulfed the world Seeley had known, the American theologian Arthur McGiffert praised _Ecce Homo_ as \"epoch-making\" due to its role in shifting attention to the personal example of Christ, while as late as 1927 Charles Gore, the Christian socialist Bishop, could write that there was \"still no book about the teaching of our Lord which can rival _Ecce Homo_.\"33\n\nDespite the success of _Ecce Homo_ , or perhaps because of it, Seeley was determined to outline his basic theological commitments in a more comprehensive fashion. His friend Richard Jebb once asked him why he had not written _Ecce Deus_ , the sequel dedicated to the divine aspects of Christ promised in the preface to _Ecce Homo_. Much to Jebb's surprise, Seeley replied that he had done so in the _Life and Times of Stein_ , his three-volume study of the reformist Prussian statesman.34 This curious remark provides us with an insight into the profound relationship Seeley discerned between politics, history, and religion. His holistic vision was articulated in what he considered his two most important books, _Natural Religion_ and _Stein_.35 The former was an attempt to systematically explore the bases of belief and the purposes of faith in a world in which the naturalistic impulse, the will to science, was central. The latter was a detailed study of the career and ideas of a man whom Seeley regarded as a founding \"father\" of modern Germany, and as portending many of the crucial developments of the ensuing century. They were conceived and written during the same period and should be viewed as two elements of the same intellectual compound, one the articulation of his political theology, the other a case study of some of the most important aspects of this as put into political practice. They establish the conceptual architecture essential for understanding his argument in _The Expansion of England_.\n\n_Natural Religion_ never achieved the prominence of _Ecce Homo_. Anatomizing _The Varieties of Religious Experience_ , William James observed that it was \"too little read, I fear.\"36 It was, nevertheless, a well-respected contribution to theological discussion. In 1911 W. W. Fenn, Unitarian theologian and Dean of the Harvard Divinity School, acknowledged that it was \"almost forgotten\" but went on to praise its \"prophetic insight and power\" and judged it \"one of the most significant contributions ever made to the subject.\" He concluded that it should have \"marked a turning-point in thought concerning natural religion.\"37 Establishing the exact theological status of _Natural Religion_ proved difficult, which may partly explain its muted reception. Praising it as \"one of the most striking [books] in our theological literature,\" Alfred Caldecott argued that Seeley articulated a potent brand of \"ethical theism,\" while a decade later the American theologian Durant Drake characterised it as the \"clearest popular exposition of the pantheistic conception.\"38 The philosopher A. W. Benn assigned Seeley a leading role in his influential history of rationalism, arguing that _Natural Religion_ , more than any other book, marked the \"retreat of religious belief before reason.\"39 In contrast, the eminent church historian Francis Warre Cornish declared that Seeley, along with Arnold, had curbed the tide of the \"forces which, since 1789, under the garb of liberation, were tending to irreligion.\"40 Seeley would most likely have approved of the judgments of Caldecott and Cornish. He came not to bury existing religious practice, but to reanimate it. And in this he achieved some success. His writings, for example, exerted a powerful influence over the fledgling \"ethical society\" movement that flowered on both sides of the Atlantic from the 1890s onwards. One of its key texts listed the favored authors of the society as Matthew Arnold, Emerson, Milton, Burke, and Seeley.41 Stanton Coit, a socialist and leading figure in the society, even dedicated his _National Idealism and a State Church_ to Seeley, praising his visionary account of the moral mission of a national church.42\n\nIn _Natural Religion_ Seeley attempted to move beyond both eighteenth-century natural theology and nineteenth-century Comtean positivism, whilst incorporating the most valuable aspects of both. He argued that there were two distinct but related forms of knowledge, the _theoretical_ and the _practical_. In relation to the sacred\u2014\"in the realm of observing God\"43\u2014the two corresponded to theology (theoretical) and religion (practical). \"By theology the nature of God is ascertained and false views of it eradicated from the understanding; by religion the truths thus obtained are turned over in the mind and assimilated by the imagination and the feelings.\" Theology was concerned with \"the attitude of Nature towards human beings,\" where nature was defined as \"the uniform laws of the Universe as known in our experience.\"44 These included scientific laws of the kind revealed with ever-greater frequency during the nineteenth century, as well as social laws, such as those governing the formation and growth of nations. It also examined meta-ethical questions including the character of virtue, the nature of temptation, and the role and limits of human conscience. \"In one word,\" he inquired, \"is life worth having, and the Universe a habitable place for one in whom the sense of duty has been awakened?\"45 Since for Seeley the scientific analysis of nature was an exploration of the laws of the universe, science was \"in the strictest sense Theology,\" and since history was an exploration of the laws of social development, it was also, in the \"proper sense,\" theological.46 To read Seeley as a straightforward \"scientific\" historian or as a progenitor of a secular political science misses the point that his conceptions of history and science were themselves theological.\n\nReligion, on the other hand, was grounded on admiration, on the impulse to (and act of) _worship_. Whereas theology engaged reason, religion was concerned chiefly with sensitivity, empathy, and imagination. It was as much about emotion as it was about rationality. This capacious understanding of religion attracted much commentary at the time.47 Religion, for Seeley, was constituted by three elements: \"that worship of visible things which leads to art, that worship of humanity which leads to all moral disciplines, and principally the Christian, and that worship of God which is the soul of all philosophy and science.\"48 The third panel of this triptych focused on the worship of God-in-nature as clarified by the theological disciplines of history, natural science, and philosophy. _Natural Religion_ was concerned primarily with this aspect. The aesthetic focus of the first panel pointed towards Seeley's intense love of literature and poetry, and in particular the works (and the sensibility) of the great romantic writers.49 Like Maurice, Seeley admired Byron, Wordsworth, and above all Goethe, whom he regarded as the model of modern cultivation, the human embodiment of excellence in the simultaneous pursuit of art, science, and philosophy, and hence as a \"religious\" thinker of the highest rank.50\n\nThe middle panel of Seeley's triptych clarified his notion of morality: it was his understanding of religion as worship that underpinned his system of ethics. Again, when discussing Stein we can discern the lineaments of his own considered position: \"As religion without morality would be to him a monstrosity, so he cannot understand any morality without religion.\"51 In _Natural Religion_ Seeley continued his campaign against the relevance of secular philosophy for ethics, arguing that it lacked the affective power to motivate action. Earlier, he had written to Sidgwick that utilitarian ethics were insufficient, for reason alone was incapable of identifying the \"instinct for sympathy\" that lay at the root of morality. Nor, he continued, could the \"methodological\" teachings of the philosophers help to inculcate the \"one law which is to be obeyed for itself, viz., love.\"52 It was this insight that he attempted to systematize in _Natural Religion_ , and which remained the centerpiece of his moral vision. He was also deeply critical of a system of morality derived from supernaturalism, the belief that human behavior should be regulated by certainty in the eternal pleasures or punishments of the afterlife.53 This \"legal school of morals,\" as he termed it, was both theologically indefensible and the source of political inaction.54 \"To hope even with enthusiastic conviction for a future life is one thing; to be always brooding over it so as to despise the present life in comparison with it is another.\" Moreover, he continued, by \"the side of such a vision everything historical, all the destiny of states and nations, fades away, and men become quietists if not monks.\"55 Rather than subscribing to what he considered a fallacy of eighteenth-century deism, Seeley suggested that his view of natural religion as the worship of nature (broadly defined) could sustain a system of morality focused on the worship of humanity, of humans. People were to teach themselves, and be guided by the historical clerisy, to be generous and humane to one another. The religion \"that leads to virtue,\" he intoned, \"must be a religion that worships men.\"56\n\nIt is worshipped under the form of a country, or of ancestors, or of heroes, or great men, or saints, or virgins, or in individual lives, under the form of a friend, or mother, or wife, or any object of admiration; who, once seizing the heart, made all humanity seem sacred, and turned all dealings with men into a religious service.57\n\nThe ordering he gives to the objects of worship is indicative, for he places the \"country\" at the top of his list. The state is the sphere within which the other objects either live or lived, and as such it takes precedence over them. But as we shall see, not all states were created equal.\n\nOn Nationalist Cosmopolitanism\n\nSeeley was dismissive of the \"modern\" conception of the secular liberal state, in which religion was pressed into a hermetically sealed private sphere.58 It was both ethically problematic and historically anomalous, for the vast panorama of the human past was painted largely by the brush strokes of religious ferment. Religious institutions and patterns of belief had played a fundamental role in social and political development, indeed in the origins and evolution of the state system itself. The locus of religion in the modern world was the _nation-state_. For Seeley, any human community could be labeled, almost interchangeably, \"by the name State or Church.\"59 Common among Broad Church thinkers, this claim was derived from his view of the Church as an institution constituting \"the atmosphere of thought, feeling and belief that surrounds the State; it is in fact its civilization made more or less tangible and visible.\"60 An ahistorical understanding of the interpenetration of politics and religion, one that failed to grasp this point, was inadequate for the contemporary age. In Arnoldian vein, he thought that a life without religion was mechanical and largely meaningless.\n\nFor Seeley, the most important consequence of the \"Anti-Napoleonic Revolution\" was the increasing awareness and power of the \"nationality doctrine.\" In a quasi-Hegelian spirit, the nineteenth century witnessed the emergent self-consciousness of the nation-state. This phenomenon was witnessed first in Spain, where the armies of Napoleon had crushed the institutions of the Spanish state but had then faced the onslaught of the Spanish nation, which after surviving the initial destruction had sought to reclaim its political destiny. Seeley wrote admiringly that when \"the state fell to pieces the nation held together and proceeded to put forth out of its own vitality a new form of state.\"61 It was in this period that \"a new idea took possession of the mind of Europe. That idea was not democracy or liberty... it was nationality.\"62 This argument, and Seeley's vision of modern politics as a whole, presupposed a clear distinction between the \"state\" and the \"nation.\" The former, Seeley wrote in _Stein_ , \"is merely a machinery by which a number of men protect their common interests.\" It was an administrative unit, a specified territory ruled over by government institutions. The latter was a distinct group of people whose bonds \"are more instinctive, and as it were, more animal.\" Consequently, the \"state which is also a nation is an organism far surpassing in vigour and vitality the state which is only a state.\"63 In _The Expansion of England_ , Seeley argued that there were three essential preconditions for (nation) state unity: the existence of a community of race, a community of religion, and a community of interest.64 Of these, religion was the \"strongest and most important\"; it was the \"great state-building principle.\"65 Powerful nation-states would combine all three, and as both a presupposition and a consequence they would have to be socially and politically uniform to succeed. \"States are composed of men who are in some sense homogeneous, and not only homogeneous in blood and descent, but also in ideas or views of the universe.\"66 Modern history began with the completion of the state by the principle of nationality.\n\nSeeley's vision of nationality drew on two main sources: the ideas of the German romantics, especially as instantiated by Stein, and the theology of the Broad Church, which was itself, through the work of Coleridge, influenced by the currents of Germanic organic romanticism. Seeley praised Fichte's _Addresses to the German Nation_ (1807\u20138) for stressing the role of national education, promulgating a holistic ideal of national unity, and conceiving of the state as a moral entity.67 \"Here certainly is heard the tocsin of the anti-Napoleonic Revolution and of all the Nationality Wars that were to follow.\" Seeley discerned a foreshadowing of his distinction between the nation and the state. \"Fichte proclaims the nation not only to be different from the state, but to be something far higher and greater.\"68 Seeley's nationalism was ultimately a branch of his political religion, and the religiosity of his conception of nationality can be seen in his argument that, in Fichte's hands, the union of past and present in the doctrine of the nation \"secures to the actions of man an earthly immortality.\"69 It was the quest for the earthly immortality of the Anglo-Saxon race that ultimately shaped Seeley's vision of Greater Britain.\n\nSeeley's thought was marked deeply by the ideas of Coleridge, and Coleridge's follower, F. D. Maurice. In a discussion of the prophetic seers of British politics, those who he labeled the \"genius politicians,\" he focused on Milton, Carlyle, Ruskin, and Coleridge, arguing that the key to their powers as political thinkers was that they tended to have one simple idea that they reiterated tenaciously. For Coleridge, the \"one conviction\" that ran through his writings was \"the hollowness of all hand-to-mouth statesmanship, and the necessity of grounding politics upon universal principles of philosophy and religion.\"70 Seeley concurred wholeheartedly. Indeed, it is imperative to view Seeley's dogged intellectual exertion on behalf of Greater Britain in this light. Whilst he thought that Coleridge was the greatest philosopher, in formulating his conception of the state he drew more on Thomas Arnold and Maurice.71 Coleridge had argued that the Church of England should be legally recognized as an integral component of the constitution, as a balance to the great landed and commercial interests of the country. It was an essential but quasi-autonomous element of the political nation.72 Arnold went further, arguing that church and state were in a sense \"perfectly identical\" and, in his _Postscript to Principles of Church Reform_ (1833), that the \"state in its highest perfection becomes the Church.\"73 Maurice, meanwhile, provided a forceful exposition of the ideal of a spiritual nation, in which church and state were coterminous and mutually constitutive.74 Seeley's conception of nationality wove together the threads of Fichte's romantic nationalism and the reworking of liberal Anglican theology by Arnold and Maurice.\n\nHorace Bridges, leader of the Chicago Ethical Society, once called Seeley \"the one great modern English philosopher of religious nationalism.\"75 This underplays the universalism of Seeley's political theology. Indeed he is perhaps best characterized as a _cosmopolitan nationalist_. His conception of international politics and the empire was grounded in the idea of the ultimate (albeit only vaguely articulated) unity of humankind. And as we have seen, it was animated by an ethical system that centered on \"enthusiasm for humanity.\" The future, he predicted, \"will witness national religions flourishing inside a grand universal religion.\"76 We see here echoes of Maurice's ideal of a \"Universal Church\" in which all of humanity was united in a nonsectarian spiritual society.77 And it was the idea of love, expressed in the worship of humans, and grounded in a non-parochial attachment to national-political communities that underpinned this complex admixture. For Seeley, there were two churches: the universal church, accommodating all the species, believers and nonbelievers alike, and the national churches as institutionalized in the form of the modern state. The latter took priority, as the highest embodiment of human communal life, but it was embedded in the wider domain of the former. However, this neat binary was upset by Seeley's constant reference to a third (less clearly conceptualized) sphere; between the universal and the national he interposed an intermediary plane, namely Western Christendom, which he regarded as a form of transnational civilization.78 He argued that the states of Europe\u2014including their dynamic offspring in the United States\u2014constituted a \"society,\" bound to a certain extent by common values and a common culture.79 The \"European brotherhood of nation-states\" were between them responsible for the glories of modern civilization.80 Seeley thus adumbrated a multilayered and hierarchically arranged conception of global order, but one underwritten by a universal religious community.\n\nDespite his constant avowal of the glories of the nation, Seeley was not an uncritical proponent of nationalism. In 1870 he warned that if left unchecked, the \"more victories the nationality principle wins,\" the greater the likelihood that the world would be engulfed by a wave of violence, as \"energetic popular states\" waged war on each other with the \"unrelieved fierceness of national antipathy.\"81 A decade later he complained that the pure ideal had often been corrupted, that in practice it was usually \"too narrow and provincial.\"82 He worried about the increasing militarization of Europe, of the great armies eyeing each other suspiciously from one end of the continent to the other.83 Wary of the dangers of revolution, he was scathing of the Jacobite descent into terror. It was the association of the French Revolution with the thought of the _philosophes_ that led Maurice to prefer the use of the term \"humanity\" to the otherwise equally appropriate \"cosmopolitan\" when outlining his own vision.84 Given his admiration for Maurice, his hatred of Revolutionary France, and the theological vocabulary that he adopted, I think it plausible that Seeley's view was similar. In _Ecce Homo_ he scorned \"universal patriotism,\" which, without the instantiation of the state, was simply a form of \"Jacobinism.\"85 Critical of the abstract \"universal man\" of the Jacobins, he preferred to focus attention on individual persons and their communities. In _Stein_ he had sided with his hero's critique of the purportedly disembodied cosmopolitanism of Goethe and Herder, whilst, drawing on Coleridge, he defended the virtues of national patriotism.86 But as we can see from an earlier essay, his use of the term was qualified:\n\nThe abuse of patriotism is not to be cured by destroying patriotism itself; but patriotism is to be strengthened by being purified, by being deprived of its exclusiveness, and ultimateness. The Christian unity of mankind is to be taught as a final lesson, which will be easiest learnt, or rather will only be learnt, by those who have already realized the unity of the state.87\n\nThe nation was not an insular political order, the antithesis of wide human sympathies. Rather, it was a necessary condition for their practical realization. Once again, Seeley was following in the wake of Maurice, who had argued that \"Christ's Kingdom of Peace\" was \"a Kingdom for all _nations_. Unless there are Nations, distinct Nations, this Kingdom loses its character; it becomes a world Empire.\"88 And world empires were associated with despotism and the eradication of difference. \"I have endeavored to shew [ _sic_ ] you how much mischief has proceeded from every effort to constitute a Universal divine Society which shall swallow up... distinctions into itself.\"89 It is little wonder that Seeley was so critical of Napoleon and his attempt to revive the ideal of a universal monarchy, or that he refused to label Greater Britain an empire, preferring instead to call it a \"world-state.\" However, Seeley's cosmopolitanism was heavily attenuated. While his \"purpose\" was to seek an ideal of national coexistence within a wider framework of progressive humanity, it simultaneously helped to justify the existing power structures of international politics and the ethos of global racial hierarchy.\n\nExpanding England: Democracy, Federalism, and the World-State\n\nThe early years of Seeley's career provided few hints about his later role as the leading ideologue of a united Greater Britain. Indeed during the late 1860s and early 1870s he appeared sanguine about the possible future independence of the colonies.90 All of this was to change. During the 1880s the idea of strengthening the bonds between Britain and its settler colonies swept through the political elite, provoking numerous expressions of support and skepticism. The movement advocating unity coalesced under the rubric of \"imperial federation.\"91 _The Expansion of England_ was its bible, Seeley one of its chief prophets. \"I should like to be a working apostle of the doctrine which interests me so much.\"92 He was so successful that W. T. Stead, the most famous journalist of the day, proposed that he be placed in charge of a college designed to spread the gospel of Greater Britain.93 In 1894 Seeley was knighted at the instigation of Lord Rosebery, the prime minister and sometime president of the Imperial Federation League. The award, Rosebery wrote to him, was not merely a testimony to \"my admiration for yourself and your work, but to my staunch adherence to the principles of empire that you have so eloquently set forth.\"94 While those principles could be read in secular terms, as Seeley presumably intended, they were nevertheless grounded in his political theology.\n\nThe central argument of _The Expansion of England_ \u2014and of much of Seeley's subsequent writings\u2014was that the most important development of modern history was the steady growth of the English state into a globe-spanning empire. Furthermore, within the diffuse space of the empire, Greater Britain had developed into a distinct political community, even a nascent \"world-state,\" and it constituted the most fundamental element of Britain's enormous network of power. The most significant chapter in this story had been victory over France in the second \"hundred years' war\" during the long eighteenth century.95 Both the public and the historians whose role it was to shape the popular mind had missed the importance of these events due to the prevailing \"insular\" comprehension of British history, a form of parochial Whiggery that celebrated the history of parliamentary debate and the post-1688 evolution of liberty.96 Macaulay was the preeminent source of this erroneous view, with J. R. Green the latest popular exponent.97 This was as much a political as an intellectual failure, for in losing sight of the importance of Greater Britain, Seeley warned that the people and the historians had forgotten the foundations as well as the purpose of colonial unity. The mid-Victorian years had been pervaded by a dangerous \"system of indifference\" that nearly led to a repeat of the American fiasco: \"We began to provoke and suggest secession.\"98 Although things had improved since that dark time, Seeley thought it was still essential to reconnect the people to their grand inheritance, to educate them about their sacred role.\n\nPart of the background to this argument can be discerned in Seeley's outline of a theory of political development. For Seeley stagnation connoted political death.99 \"It is impossible that the history of any state can be interesting unless it exhibits some sort of development. Political life that is uniform has no history, however prosperous it might be.\" Associated habitually with \"Asiatic\" modes of political order, reverting to a \"stationary\" condition was a characteristic liberal fear during this period.100 Averse to violent revolution, and drawing on fashionable biological metaphors, Seeley suggested that political \"organisms\" demonstrated their health in perpetual change, in their active response to internal and external pressures. \"Surely we moderns do not believe much in cataclysms. Development is our word. The present grows out of the past.\"101 In a revealing passage analyzing the development of the Church, he argued that an \"institution is healthy in proportion to its independence of its own past, to the confident freedom with which it alters itself to meet new conditions.\" Elsewhere he wrote of the state that the \"development of its institutions [was] the result of the effort which organisms make to adapt themselves to their environment.\"102 To remain healthy, therefore, institutions needed to be adaptable, fitting comfortably into the evolving political environment in which they were embedded. Failure in this delicate process of adjustment and calibration would result in inexorable degeneration. Grasping what we might term this \"environmentalist\" conception of politics sheds light on the reason why Seeley considered imperial federation a necessity and also on his belief that it could be realized. The shifting\u2014and increasingly threatening\u2014geopolitical situation, combined with the febrile condition of British domestic politics, sparked both the internal and external stimuli for change. This in turn necessitated constitutional revision and the strengthening of Greater Britain. To stand still, frozen, was to court disaster. _The Expansion of England_ at once sought to alert people to the dangers and present them with the best solution.\n\nSeeley warned that the people of Greater Britain faced a stark choice: separation or federal unification. \"Such a separation would leave England on the same level as the states nearest to us on the continent, populous, but less so than Germany and scarcely equal to France.\"103 Shorn of its dominions, England would be dwarfed. \"The other alternative,\" he suggested, was that \"England may prove able to do what the United States has done so easily, that is, hold together in a federal union countries very remote from each other.\" If it achieved this goal, Greater Britain would become, \"in time far greater than any political union the world has known.\"104 As if to prove his disinterested \"scientific\" curiosity about the subject, he cautioned that, \"[w]e ought by no means to take for granted that this is desirable.\"105 His lectures sought, he stated, to explore the two options in order to divine which was best for the country. The answer, though, was predetermined by the very language, structure, and tone of his analysis, and it was underpinned by his suggestion that the aim of British policy should be to secure \"the foundation of a solid and permanent union.\"106\n\nIn _The Idea of Greater Britain_ I argued that debate over Greater Britain was motivated by two intersecting fears, of international geopolitical competition and of the dangers posed by mass democracy to British greatness. Many saw a united colonial empire as an answer to both challenges, a means to buttress British preeminence and to diffuse the worst excesses of democracy, the latter chiefly through the agency of large-scale emigration, which could neutralize the rise of socialism and the insurrectionary dangers fostered by intensive urbanization.107 Seeley was no exception. During the 1880s he too became increasingly nervous about democracy. In 1881, for example, he wrote to his sister that \"[w]e are nearer to a Revolution than we have been since before I was born.\" \"Radicalism,\" he fretted, \"is triumphant everywhere.\" By the end of the decade, he had become, he admitted, \"a great skeptic about the current political system.\"108 This skepticism was less about franchise extension and the institutional paraphernalia of representative democracy, than it was about the underlying social conditions, and in particular the pronounced deficit in the English \"character.\" \"We have everything except decided views and steadfast purpose\u2014everything in short except character! We have emotions, sentiment, thought, knowledge in abundance, only not character! And so to foreigners this nation seems degenerate\u2014a nation in decay.\"109\n\nThe British educational system (and the Church) was to blame for the debasement of culture, the rise of crass materialism, and the divorce of the majority of the population from their glorious national heritage. An appreciation of the \"higher\" aspects of life was conspicuously absent from society. \"That bareness in ideas, that contempt for principles, that Philistinism which we hardly deny to be an English characteristic, was not always so,\" he lamented.110 This was not simply the complaint of a cultural elitist (although it was that also), for as we have seen Seeley's conception of culture was ultimately theological, and it underlay his notion of the \"higher\" life of the nation. To be uneducated was to lack the refinement and knowledge necessary to imagine oneself as part of a community; it was to be deficient in the prerequisites of full citizenship. The \"man\" lacking a decent awareness of national literatures, suggested Seeley, \"can have no link whatever with the past, he can have no citizenship, no country.\"111 For Seeley, then, the lack of a proper education, including a wide schooling in English literature and history, as well as in the centrality of empire, was an important _political_ problem. Although it beset all classes, it affected the workers in particular for the majority of them were \"childishly ignorant of larger political questions.\"112 Their ignorance endangered the country: as well as being unaware of their heritage and lacking adequate national consciousness, they were still beholden to superstitions, including the belief in the possibility of a political \"utopia,\" such as that promised by socialists. This was a potential harbinger of revolution. \"In England the ideas of the multitude are perilously divergent from those of the thinking class.\"113 Now, more than ever, it was essential for the historian to fulfill his destiny as shaper of the national mind and as spiritual healer of the body politic. For Seeley, the ideal nation-state needed to strike a fine balance between democracy and aristocracy (understood in its classical sense as rule by the most suitably qualified).114 Progress was fragile and in need of constant sustenance and supervision. The lack of national bonds of unity led to alienation between the individual and the state, and also between the different classes. This portended the possibility of increasing unrest, even revolt. It is little surprise, then, that Seeley emphasized the importance of mobilizing the support of the working classes to create a viable Greater Britain.115\n\nSeeley fretted that the collective \"imagination\" and \"ways of thinking\" about the empire acted as a brake on necessary reforms. Most people continued to view the colonies as entirely separate from the homeland, fragments of foreign land scattered over the distant reaches of the planet. It was thus imperative for the historical clerisy to bring \"home to our imaginations\" the true nature of the situation, for until that task was achieved \"[w]e have not really then as yet a Greater Britain.\"116 Political consciousness preceded legislative action; shifts in imagination initiated parliamentary change. The \"true moment of revolution,\" he had written in a different context, \"is not so much that in which the new legislation takes place as that in which the conviction becomes universal that a change must come.\"117 National education and political mobilization were thus interwoven, and in particular Seeley emphasized the increasing influence of public opinion in shaping British politics.118 But public opinion needed to be organized and directed. The conditions were ripe, he argued, for the previous decades had witnessed the power of public opinion and the role of pressure groups in catalyzing momentous political change. One of the most important forces guiding the \"English Revolution of the Nineteenth Century,\" and one of the main reasons for the corrosion of the pervasive monopolies of the _ancien r\u00e9gime_ , was the influence of the assorted \"Leagues\" that had demanded the repeal of the Corn Laws, and extensive parliamentary and religious reform. \"These Leagues may be considered as a kind of occasional system of government set up for a particular purpose beside the permanent government of the country.\" It is in the context of his views on the efficacy of the \"occasional systems of government\" that Seeley's involvement with the Imperial Federation League should be understood.119\n\nThe year 1887 was, declared Seeley, a time of \"of depression, confusion, and anxiety.\"120 Despite this, and many similar proclamations, he was not an abject pessimist, and his views about the future were somewhat ambiguous. While at times he wrote in the vein of a doom-laden prophet, a latter-day Carlyle, he also preserved a large measure of optimism. Apprehensive about the political life of the \"mother country,\" he was also keen to stress that things had improved markedly since the first few decades of the century, and as he became increasingly concerned about the international situation\u2014warning of the \"international danger, the gigantic discords, the gigantic armies!\"\u2014so he was also keen to stress the increasing strength and unity of the colonial empire. The continued expansion of England, and its consolidation since the troubled midcentury years, represented the \"brightest side\" of the Victorian age, and it gave him great hope for the future.121 In Greater Britain lay a potential resolution to his fears about both the \"mother country\" and the wider world.\n\nBut what kind of polity did Seeley envisage when he wrote that \"England has left Europe altogether behind it and become a world-state,\" or when he argued that it was essential to create a \"great and solid World-State\" that would supplant the existing fragile one?122 I would argue that he had in mind a supra-parliamentary federal polity, a United States of Greater Britain. In the _Introduction to Political Science_ , based on lectures delivered in the mid-1880s, Seeley traced the various forms that states had assumed across time and space. Seeley initially defined the state so broadly that it encompassed nearly all forms of human community, and as such it might be argued that there was nothing unusual in his assertion that Greater Britain was a state.123 But in evaluating the status of Greater Britain, he was actually drawing on a much narrower conception of the \"nation-state.\" Recall his three essential preconditions for (nation) state unity: the existence of a \"community of race,\" a \"community of religion,\" and a \"community of interest.\"124 All existed in the colonial empire. Colonists were not simply deracinated migrants lost to distant, alien lands, but (echoing Robert Browning) citizens of a \"world-Venice, with the sea for the streets.\"125 While in the past there had been a Greater France, a Greater Spain, and a Greater Holland, the experience of the late Victorian British was unique, and the expansion of England, he maintained, \"can be paralleled by nothing in the history of any other state.\"126 Previous empires had neither the geographical extension nor the degree of cultural and political unity exhibited by Greater Britain. In an age that had witnessed the power of the \"nationality doctrine,\" a new form of global British political consciousness was beginning to emerge, fusing together the scattered components of a global state. Greater Britain, wrote Seeley,\n\n... is a vast English nation, only a nation so widely dispersed that before the age of steam and electricity its strong natural bonds of race and religion seemed practically dissolved by distance. As soon as it is proved by the example of the United States and Russia that political union over vast areas has begun to be possible, so soon Greater Britain starts up, not only a reality, but a robust reality.127\n\nSeeley acknowledged that it was hardest to make the case for a \"community of interest.\" Indeed one of the main criticisms leveled at the imperial federalists was that Greater Britain was little more than a sentimental dream, based on an inability to recognize the divergent interests of the far-flung colonies.128 In the _Considerations on Representative Government_ , Mill had argued that spatial dispersion of the colonial empire meant that it was incapable of \"rational government.\"129 Seeley rejected this line of reasoning, arguing that new conditions meant that the \"old Utopia\" of Greater Britain was now realizable\u2014indeed it was necessary.130 The construction of a \"great and solid\" political association was predicated on a cognitive and affective revolution. Spread so widely, the empire had until recently been \"practically dissolved by distance.\" Separated by great distances, and working under a warped mercantile economic system, the fragments of the first British empire did not share the same vital interests. But new communications and transport technologies had fundamentally reshaped the world and its political potential.131 \"Science has given the political organism a new circulation, which is steam, and a new nervous system, which is electricity.\" A world of glorious possibility was opening up. In the eighteenth century Burke \"thought a federation quite impossible across the Atlantic Ocean,\" but since then the Atlantic had \"shrunk till it seems scarcely broader than the sea between Greece and Sicily.\"132 This was an age, he hymned, \"when inventions have drawn the whole globe close together, and a new form of state on a larger scale than was known in former ages has appeared in Russia and the United States.\"133 Greater Britain was such a state\u2014or at least it could be.\n\nAlthough Seeley never discussed the institutional form that he thought Greater Britain would or should assume, I believe that he had in mind a fully-fledged federal state, encompassing the assorted settler colonies and Britain. During the closing decades of the ninetieth century, federation was a topic of intense interest among liberal political thinkers, chiefly due to the dynamic success of the United States. Sidgwick was far from alone in predicting that \"an extension of federalism seems to me the most probable of the political prophecies relative to the form of government.\"134 In \"The United States of Europe\" Seeley had argued that a \"close\" federation, modeled on the United States, was the only way to halt the internecine violence that plagued Europe. What was required was \"Europe constituted into a single State, with a Federal executive and legislature,\" wherein its \"authority must be brought to bear directly upon individuals.\"135 In the long term it might come about, following a social revolution, but there were many obstacles in the way. In particular, the divergent national identities of the European states generated a clash of interests, meaning that if aggregated they could not satisfy his three conditions for proper statehood. Without such unity, Seeley argued elsewhere, a successful federation was impossible\u2014it was, after all, \"an arrangement so extremely difficult\" to construct.136 Such problems did not afflict Greater Britain, which was, he argued in the _Expansion of England_ , \"on the whole free from that weakness which brought down most empires, the weakness of being a mere mechanical forced union of alien nationalities.\"137 The social and technological conditions for crafting a successful federation were in place.\n\nSeeley's most thorough examination of federalism is found in the _Introduction to Political Science_.138 He argued that the strict distinction drawn between \"federal\" and \"unitary\" states was misleading, as it was \"too purely formal and verbal.\" Since all large countries were ultimately composite states, insofar as they comprised a number of semi-autonomous administrative units, it made little sense to sharply differentiate them from federations. \"I deny, then, that between the unitary state and the federation or federal state there is any fundamental difference in kind; I deny that the one is composite in any sense in which the other is simple.\" As such, there was \"no fundamental difference in the kind of union\" between French Departments, American States, and British Counties. The key to assessing states was to determine the extent of authority vested in local government. \"Where locality prevails, we can call this federal, where centralization prevails, we can call this unitary.\"139 Indeed, he proclaimed that every \"political union which has not sufficient central power to deserve the name of a unitary state must in our system be called federal,\" and he surmised that \"almost all very large empires\" are federations, \"because in them the central power cannot act vigorously at such a great distance.\" Just as all polities could be called states, so all empires could be called federations. But once again Seeley had something much more specific in mind for Greater Britain. It was essential to distinguish between two different types of federal entity: the \"federal state\" and the \"system of confederate states.\" Seeley was very critical of confederations, arguing that they were intrinsically weak. The vast majority of empires fitted that category. Federal states, on the other hand, could prosper, but they required \"a complete apparatus of powers, legislative, executive and judicial... raised above all dependence on the State governments.\"140 He pointed to the United States as a \"vigorous, strongly and sufficiently organized\" example.141 And like the United States, successful federations were predicated on a unified nation. Once again, Greater Britain fitted the bill. Already an immanent polity, it had the potential to become a fully-fledged federal nation-state, if only the imagination of the people and their leaders could be reoriented.\n\nEmpire as Polychronicon: India and Ireland\n\nOne of the most striking things about Seeley's imperial political thought was the absence of Africa. In his 1887 Rede Lecture on \"Georgian and Victorian Expansion,\" published at the pinnacle of the European frenzy to carve up the world, he declared that the greatest achievement of the Victorian age was the expansion and consolidation of the British empire. Africa did not warrant a single mention. India and Ireland, on the other hand, were frequent points of reference in his writings.\n\nPart 2 of _The Expansion of England_ was dedicated to an analysis of the past, present, and future of British rule in India. Far more ambiguous about the benefits of the imperial mission in South Asia than he was about Greater Britain, Seeley maintained that the two zones were simply not comparable. While Greater Britain was populated by transplanted British citizens bound loyally to the mother country, India comprised a separate and degraded political order, its countless inhabitants falling outside the scope of the English state and nation. Drawing on the findings of contemporary philology he argued that the Indians were an Aryan race, but that this was where the similarity with Europe ended. Once great, they had fallen by the wayside of history. \"The country has achieved nothing in modern times.\"142 Now moribund, India displayed the unmistakable symptoms of a diseased body politic, denuded of the \"vigour\" that Seeley considered essential for a healthy political \"organism.\"\n\nThe colonies and India are in opposite extremes. Whatever political maxims are most applicable to one, are most inapplicable to the other. In the colonies everything is brand-new. There you have the most progressive race put in the circumstances most favourable to progress. There you have no past and an unbounded future. Government and institutions are all ultra-English. All is liberty, industry, invention, innovation, and as yet tranquility.\n\nIn contrast, India \"is all past and, I may almost say, has no future.\"143 This was a vision of empire as a polychronic space, carved into zones characterized by diverse temporal stages of development within an imagined universal history. The ancient, medieval, and modern were juxtaposed in Seeley's fertile imagination, the various constellations of territory and time forming stratified levels of civilization. Arrayed hierarchically, each was subject to different modes of assessment and political prescription.\n\nIn the _Introduction to Political Science_ Seeley divided states into two broad classes, the _organic_ and the _inorganic_ , and while the book was mainly dedicated to classifying the varieties of organic states, he occasionally drew comparisons between the two types. Organic states were typically vibrant and capable of progress, whereas inorganic states were inert, thus failing to meet the criteria of proper statehood. They owed any substantive unity that they displayed to interference from outside powers. Products of conquest, they manifested a \"similar appearance to the organic state\" only because they adopted and imitated \"the organisation of it.\" They were more accurately termed \"quasi-states,\" the two defining features of which were low vitality and massive size. Again with Seeley we find ambiguity on a key point. Given both his conceptual analysis and his reading of Asian history, India could be classified as an example\u2014perhaps the prime example\u2014of an inorganic state. It was composed of multiple nationalities, immense, lacking in political consciousness\u2014and it had been subjected to invasions for centuries. Never a \"conscious political whole,\" the \"homogeneous community does not exist there, out of which the State properly so called arises.\"144 Yet Seeley rejected the obvious inference. This is probably because he regarded such states as the victims of aggressive conquest, where \"everything is founded on violence and conquest\" and a grim despotism was the norm, and he didn't want to associate the British with this pattern of behavior.145 This is also the most likely explanation for his determination to prove that the English had never actually \"conquered\" India in the first place. To conquer a country, he argued, is to presuppose that it was a unified entity in the first place, and since India had \"no sense whatever of nationality\" there had been \"no India\" to defeat. Rather, the spread of the early British traders and later the East India Company was due to the fortuitous circumstance of an \"internal revolution.\"146 It was as if they were sucked into a political vacuum, and both for their own good and that of the Indians, took control and brought stability and order.\n\nFor Seeley, then, India was an artificial country populated by a mix of races and religious creeds. Indeed any unity it possessed was created, not extinguished, by the British. A condition of \"anarchy seems almost to have been chronic in India since Mahmoud,\" and \"it may be said that India has never really been united so as to form one state except under the British,\" at least during the Governorship of Lord Dalhousie. Self-determination meant nothing there, for the \"love of independence presupposes political consciousness,\" and the name India, he argued, \"ought not to be classed with such names as England or France, which correspond to nationalities, but rather with such as Europe, marking a group of nationalities which have chanced to obtain a common name owing to some physical separation.\"147 Since it did not constitute a nation, the \"fundamental postulate cannot be granted, upon which the whole political ethics of the West depend.\"148 The liberal maxims that Seeley applied to the states of Europe and North America were irrelevant. This was not to suggest that India would remain permanently locked in a servile position, for \"Brahmanism\" presented the \"germ\" of a potential nationality movement, but independence was not on the horizon, and for the moment the British should accede to such demands. \"It is impossible for the present to think of abandoning the task we have undertaken there.\"149 A man with no direct experience of or knowledge about Indian culture or political life, Seeley could discern no signs of it at the time.150 Two years after _The Expansion of England_ was published, the Indian National Congress was formed.\n\nSeeley's views on Ireland exhibit a family resemblance to his account of India. Underpinning his assessment of the Irish question was a fiercely critical portrayal of Catholicism. In this, he shared the prejudices of his fellow Broad Church thinkers, who saw Catholicism as embodying all that they rejected in religious life, most notably dogmatic and exclusive adherence to doctrine. Viewing it as the least developed of the Christian denominations, Seeley argued that Catholicism was bound by rigidity and prone to undermine the possibility of good government.151 The mysticism of the Indians and the feudal superstitions of the priests both obscured the horizon of progress. Ireland, like India, fell outside the boundaries of the British nation. Or so he argued in 1870.152 However, by the time he published _The Expansion of England_ his position had changed, and he claimed that all of Greater Britain (including Ireland, but still excluding India) was bound together as one consolidated nation. In order to argue against home rule he modified his understanding of the boundaries of nationality; theoretical consistency gave way to the convenience of political maneuver. In a letter to his wife written in 1887 he noted that the \"public struggle goes pretty well. The _Times_ is really tackling Parnell with some vigour.\"153 He would have regarded it as energy well spent. He also sought to improve relations between the English and the Irish, believing that the ideal solution lay in the trends that had fermented the nineteenth-century \"English Revolution,\" chiefly the destruction of monopolies, including the closed labor market in the industrialized North.154 In 1870 at least, he thought that such a course of action would create a more just relationship. But his optimism faded, and by 1885 he was writing that the Irish were \"more hopelessly alienated than ever.\"155 No solution appeared to be forthcoming. This was all the more reason to focus on a perceived British success story, to find in Greater Britain a distraction from the fraught situation in Ireland.\n\nLike numerous other Victorian liberals, Seeley was critical of many facets of the history of British expansion. He lamented British behavior in Ireland.156 He also regretted the \"unjustifiable means\" by which the early imperial pioneers in India acquired power. The greatest crime of all was slavery. In the seventeenth century, he reminded his audience, Great Britain had pioneered the abominable practice: \"From this date I am afraid we took the leading share, and stained ourselves beyond other nations in the monstrous and enormous atrocities of the slave trade.\" Even in the Victorian age, there was \"nothing to boast of\" in the treatment of indigenous populations under British control. But he always qualified his critique by arguing that that the behavior of the British was \"not as bad as many others,\" and he stressed that such \"crimes\" as had been committed \"have been almost universal in colonisation.\"157 He thus employed what Cheryl Welch calls a \"rhetoric of evasion.\"158 In particular, Seeley utilized the argumentative strategy of \"comparison as vindication,\" at once admitting that the British had acted reprehensibly at times but also that their record was morally superior to their competitors. Past injustice, on this account, was no bar continued British involvement in India.\n\nBut why? Given the polychronic variation between Greater Britain and the Indian empire, why not simply advocate the abandonment of the latter, perhaps (even especially) in order to strengthen the former? After all, Seeley was skeptical of the material advantages accrued by holding India: \"[I]t is not at once evident that we reap any benefit from it.\"159 While acknowledging the economic importance, he also stressed the substantial noneconomic costs that occupation imposed, notably the dangers of war with other great powers, and especially Russia.160 Despite these worries, and the priority he assigned to Greater Britain, he recoiled from separation. The debates over Greater Britain were infused by a marked dissonance between skepticism about the benefits of the Indian empire and a fervent but often poorly explained desire to hold onto it anyway.\n\nSeeley argued that in the distant future it might be necessary to leave India, but that in the meantime it was \"obligatory to govern her as if we were to govern her forever.\" This was nothing to do with honoring the past, for such groundless romanticism belonged to a \"primitive and utterly obsolete class of ideas.\" Rather, Seeley presented two arguments. The first was that the British had a duty to remain. Because they had incapacitated Indian governing institutions, the British could not simply depart, leaving chaos in their wake. If political judgments were to be made purely on the grounds of national interests, the British would probably be better off withdrawing; however, it was imperative to place the interests of the Indians first. A \"very moderately good Government,\" argued Seeley, \"is incomparably better than none. The sudden withdrawal even of an oppressive government is a dangerous experiment.\" This echoed the argument made by Henry Maine.161 The British, Seeley professed, had a duty to finish the mission, with \"vast and almost intolerable responsibilities\" to uphold.162 This was owed as much to themselves as to the Indians, for self-denying conceptions of duty were a central tenet in the moral and political discourse of the Victorians, a core component in the formation of an admirable character.\n\nThe second argument centered on what we might call a sacred conception of the \"civilizing mission.\"163 Seeley argued that the ancients taught a valuable lesson about the nature of good governance and the priorities of virtuous politics. Liberty was not the only admirable quality in politics, nor was it necessarily the most suitable at any given time. Bewitched by vague and illusory notions about the irreducibility of freedom, this was an important truth that many of his countrymen failed to grasp.164 Other great qualities included civilization and nationality. What distinguished, and also in a sense justified, the Roman and Greek Empires was that they were of a vastly superior level of civilization in comparison with those they were ruling.165 So too the British in India. His compatriots had huge reservoirs of knowledge to impart to a people stranded in time. A \"grand object of the modern Church,\" he proclaimed in _Natural Religion_ , \"would be to teach and organise the outlying world, which for the first time in history now lies prostrate at the feet of Christian civilisation.\" For Seeley, then, civilization had an explicitly sacred connotation: it was the \"public aspect\" of the religious impulse.166 His conception of the civilizing mission was religious not in the sense that its principal aim was to proselytize Christianity (though it might include that goal), but that the very practice of spreading civilization was itself a religious act, an expression of admiration and worship motivated by \"enthusiasm for humanity.\"\n\nWestern civilization was defined by three main features. Firstly, it facilitated and encouraged science and the set of attitudes towards truth and verification that accompanied it. Secondly, it presumed a cosmopolitan view of humanity, defined as the ability to think beyond the confines of the tribe or nation, and including such features as respect for women and the principle of liberty. And finally, it generated \"delight and confidence\" in nature, as opposed to the besetting superstition and mysticism of other, less sophisticated ways of life. Seeley thought it important to export this complex of values and beliefs to \"backward\" regions, both at home and abroad. It was necessary, he argued, to teach \"the races outside it or the classes that have sunk below it.\"167 India was one such target, a vast tissue of superstitious beliefs and torpid social and political institutions. It had been civilized once, and the British were not therefore dealing with a properly \"backward\" people, but rather with one stuck in time. England's sacred mission was \"to raise India out of the medieval and into the modern phase.\" It was ripe for education. We \"stand out boldly,\" he proclaimed, \"as teachers and civilizers,\" imparting the \"superior enlightenment we know we ourselves possess.\"168 This education required the erasure of indigenous traditions and knowledges, the wiping clean of the slate. \"The true view of the universe must be opened to the population of India, even though it should seem to blot out and cancel all the conceptions in which they have lived for three thousand years.\"169 Such was the nature of progress.\n\n1 Seeley, _The Expansion of England_ , 158\u201359.\n\n2 Acton, review of Seeley, _A Short History of Napoleon, English Historical Review_ , 2\/7 (1887), 598. The most detailed discussions of Seeley are Deborah Wormell, _Sir John Seeley and the Uses of History_ (Cambridge, 1980); David Worsley, \"Sir John Robert Seeley and His Intellectual Legacy,\" unpublished PhD, University of Manchester, 2001.\n\n3 Fisher, \"Sir John Seeley,\" _Fortnightly Review_ , 60 (1896), 193.\n\n4 Gooch, _History and Historians in the Nineteenth Century_ (London, 1920), 371. See also Gooch, \"Imperialism,\" in _The Heart of Empire_ , ed. C.F.G Masterman (London, 1901), 309. \"Its influence can be traced in the pronouncements of three generations of political leaders (of all political parties)\": John Darwin, \"Empire and Ethnicity,\" _Nations and Nationalism_ , 16\/2 (2010), 394.\n\n5 His claim about the primacy of Asia in eighteenth-century British history still sparks rebuttals. \"It was not: the history of eighteenth-century Britain was in Europe.\" Brendan Simms, _Three Victories and a Defeat_ (London, 2007), 1.\n\n6 Seeley, _Expansion_ , 151.\n\n7 Ibid., 11.\n\n8 Seeley, \"The Teaching of Politics,\" _Macmillan's Magazine_ , 21 (1870), 433\u201344. On his methodological claims, see Collini, Winch, and Burrow, _That Noble Science of Politics_ , ch. 7; Ian Hesketh, _The Science of History in Victorian Britain_ (London, 2011); Wormell, _Seeley_ , ch. 4.\n\n9 Seeley, _Expansion_ , 169, 1.\n\n10 Prothero, \"Preface,\" Edward Seeley, _The Growth of British Policy_ , 2 vols. (Cambridge, 1895). The phrase was coined by Freeman (see chapter 13). Seeley had his own less pithy formulation: \"Politics are vulgar when they are not liberalised by history, and history fades into mere literature when it lose sight of its relation to practical politics\" ( _Expansion_ , 166).\n\n11 [Seeley], _Natural Religion_ (London, 1882), 259, 218.\n\n12 With _Ecce Homo_ (London, 1866), he was keen to avoid upsetting his family; his reasons for keeping the authorship of _Natural Religion_ secret are less clear. For a discussion of his anonymity, see Ian Hesketh, \"Behold the (Anonymous) Man,\" _Victorian Review_ , 38 (2012), 93\u2013112.\n\n13 Fisher, \"Sir John Seeley,\" 183.\n\n14 Good discussions of Seeley's theological views can be found in Richard Shannon, \"John Robert Seeley and the Idea of a National Church,\" in _Ideas and Institutions of Victorian Britain_ , ed. Robert Robson (London, 1967), 236\u201367; Wormell, _Seeley_ , ch. 1. Neither, though, reads his conception of empire in theological terms (and nor does any other scholarship on Seeley).\n\n15 Boyd Hilton, _The Age of Atonement_ (Oxford, 1988), 334. His father was R. B. Seeley, a prominent religious publisher and author of _Essays on the Church by a Layman_ (London, 1834), a fierce antiliberal, evangelical tract. For a comparison of father and son, see Reba Soffer, \"History and Religion,\" in _Religion and Irreligion in Victorian Society_ , ed. R. W. Davis and R. J. Helmstadter (London, 1992), 133\u201351. On the \"familial\" context of Victorian patterns of faith, see Frank Turner, _Contesting Cultural Authority_ (Cambridge, 1993), 73\u2013101; David Hempton, _Evangelical Disenchantment_ (New Haven, 2008).\n\n16 By the late 1850s, in correspondence with his family, Seeley was expressing admiration for the Broad Church. J. R. Seeley to R. B. Seeley, September 29, 185?, Seeley Papers, MS903\/2A\/2 and J. R. Seeley to Mary Seeley, April 3, 1855, Seeley Papers, MS903\/2B\/1. See also Seeley, \"The Church as a Teacher of Morality,\" in _Essays in Church Policy_ , ed. W. L. Clay (London, 1868).\n\n17 See for example, W. J. Conybeare, \"Church Parties,\" _Edinburgh Review_ , 98 (1853), 273\u2013342. See also C. R. Sanders, _Coleridge and the Broad Church Movement_ (London, 1972); Tod Jones, _The Broad Church_ (Lanham, MD, 2003).\n\n18 Coleridge, _On the Idea of the Constitution of the Church and State_ (London, 1830). The most explicit of Seeley's (published) references to Coleridge can be found in \"Milton's Political Opinions,\" _Lectures and Essays_ , 99. On the shifting meanings of clerisy, see Ben Knights, _The Idea of the Clerisy in the Nineteenth Century_ (Cambridge, 1978).\n\n19 Wormell, _Seeley_ , ch. 1. His main contact with the positivists was through Edward Beesly. His educational environment was also liberal. John Burrow, \"The Age of Reform,\" in _Christ's_ ed. David Reynolds (London, 2004), 111\u201343.\n\n20 Seeley, _Natural Religion_ , 43, 135\u201337. See also Seeley, \"The Church as a Teacher of Morality.\"\n\n21 The degree to which Seeley \"got rid\" of the traditional deity and the supernatural paraphernalia accompanying it is far from clear: in _Ecce Homo_ he gestured repeatedly to a belief in the transcendent realm, in _Natural Religion_ his starting point was to disavow such a belief, and in the preface to the 3rd edition (1891) he restated his heterodox Christianity, therein describing supernaturalism as \"accidental\" to the religion.\n\n22 Seeley, _Ecce Homo_ , 180.\n\n23 Ibid., 188.\n\n24 Ibid., 186, 189.\n\n25 Ibid., chs. 13\u201314. Unsurprisingly, Sidgwick rejected this argument: \"Ecce Homo,\" _Westminster Review_ (1866), reprinted in _Miscellaneous Essays and Addresses_ , ed. Eleanor Sidgwick and Arthur Sidgwick (London: Macmillan, 1904). For analysis, see J. B. Schneewind, _Sidgwick's Ethics and Victorian Moral Philosophy_ (Oxford, 1977), 28\u201335, 45\u201347.\n\n26 For Maurice's engagement with Comte, see, for example, Maurice, _Social Morality_ (London, 1869), 18\u201319, Lecture 19. The positivists, as I discuss in chapter 2, were among the most ardent critics of imperialism. See Greg Claeys, _Imperial Sceptics_ , ch. 1 (and p. 118) for Beesly's criticism of Seeley's _Expansion_ as spreading the \"poison of Imperialism.\" The positivist flavor of Seeley's writings did not go unnoticed, and it was a prominent theme in conservative criticisms of his views. Charles Cashdollar, _The Transformation of Theology, 1830\u20131890_ (Princeton, 1989), 179, 198, 437. Rather surprisingly, Seeley plays no role in T. R. Wright's _The Religion of Humanity_ (Cambridge, 1986).\n\n27 Seeley to Kinglsey, 1869, quoted in Cashdollar, _The Transformation of Theology_ , 437. Kingsley had been tasked by Gladstone to sound out Seeley's views on Comte, before he recommended him for appointment to the Regius chair. See Sheldon Rothblatt, _The Revolution of the Dons_ (London, 1968), 153, 160\u201361, 177; Wormell, _Seeley_ , 41\u201342.\n\n28 Cashdollar, _The Transformation of Theology_ , 426\u201330. Cashdollar claims that Seeley's theological thought was so heavily influenced by positivism that it \"pushed the definition of Broad Church to its very limits, and some would have said beyond\" (427). This is an exaggeration.\n\n29 Newman, \"An Internal Argument for Christianity\" [1866], in _Discussions and Arguments on Various Subjects_ , 4th ed. (London, 1882), 363\u201398.\n\n30 Quoted in Wormell, _Seeley_ , 23.\n\n31 Gladstone, _Ecce Homo_ (London, 1868).\n\n32 Rashdall, _Philosophy and Religion_ (London, 1909), 62. See also Rasgdall, \"Professor Sidgwick on the Ethics of Religious Conformity,\" _International Journal of Ethics_ , 7\/2 (1897), where he described it as \"the book from which in great measure I have learned all that I have been trying to convey\" (166n).\n\n33 McGiffert, _The Rise of Modern Religious Ideas_ (London, 1915), 271; Gore, _Christ and Society_ (London, 1928), 59.\n\n34 Caroline Jebb, _The Life and Letters of Sir Richard Claverhouse Jebb_ (Cambridge, 1907), 85\u201386. The nonconformist Joseph Parker did publish an _Ecce Deus_ (Boston, 1868) in response to Seeley, arguing that the main problem with _Ecce Homo_ was that it had failed to take the incarnation of Jesus seriously. Thanks to Michael Ledger-Lomas for this reference.\n\n35 _Natural Religion_ was first published in serial form in _Macmillan's Magazine_ between 1875\u201378, during the period in which Seeley was researching and writing _Stein_. It was published in 1882, the year during which the lectures on which the _Expansion of England_ were being delivered.\n\n36 James, _The Varieties of Religious Experience_ (London, 1902), 77n.\n\n37 Fenn, \"Concerning Natural Religion,\" _Harvard Theological Review_ , 4\/4 (1911), 472.\n\n38 Caldecott, _The Philosophy of Religion in England and America_ (London, 1901), 361, 191\u201392; Durant Drake, \"Seekers after God,\" _Harvard Theological Review_ , 12\/1 (1919), 71\u201372. Formerly Dean of St. John's Cambridge, Caldecott was Professor of Logic and Mental Philosophy at King's College London. For his views on empire, see chapter 2.\n\n39 Benn, _The History of English Rationalism in the Nineteenth Century_ , 2 vols. (London, 1906), 2:441. Benn defined rationalism as the use of reason for the (partial or total) destruction of religious belief (\"Preface\").\n\n40 Cornish, _The History of the English Church in the Nineteenth Century_ , 2 vols. (London, 1910), 2:207. Cornish described Seeley as \"less brilliant, but perhaps a more solid student of religion\" than Thomas Arnold (206). Cf. Bridges, _Some Outlines_ , 8, on Seeley as \"liberator.\"\n\n41 Horace Bridges, Stanton Coit, G. E. O'Dell, and Harry Snell, _The Ethical Movement_ (London, 1911), 12. On the movement, see I. MacKillop, _The British Ethical Societies_ (Cambridge, 1986).\n\n42 Coit, _National Idealism and a State Church_ (London, 1907). See also Horace Bridges, _Some Outlines of the Religion of Experience_ (London, 1916), 8, 78\u201379, 232, 258. While Seeley admired the ambition of the Ethical Societies to incubate a broad ethical sensibility in a world that had lost its bearings, he cautioned against ignoring the role of the Christian churches. Seeley, \"Ethics and Religion,\" _Fortnightly Review_ , 45 (1889), 501\u201314\n\n43 Seeley, _Natural Religion_ , 52.\n\n44 Ibid., 53, 66, 68.\n\n45 Ibid., 66.\n\n46 Ibid., 56, 257.\n\n47 For positive accounts: Arthur McGiffert, _The Rise of Modern Religious Ideas_ (London, 1915), 67\u201368; James, _Varieties_ , 76\u201377. For rejection of his definition as \"excessively broad,\" see J. H. Leuba, \"The Definition of Religion,\" _American Journal of Theology_ , 16\/4 (1912), 644\u201345; Leuba, \"The Psychological Nature of Religion,\" _American Journal of Theology_ , 13\/1 (1909), 84. A. C. Bradley engaged Seeley at length in his 1907 Gifford lectures, faulting him for failing to adopt the absolutist idealist metaphysics propounded by his brother, F. H. Bradley. Bradley, _Ideals of Religion_ (London, 1940), ch. 5.\n\n48 Seeley, _Natural Religion_ , 131\u201332.\n\n49 Seeley wrote widely on literature, including essays on Milton and a book on Goethe: _Goethe Reviewed after Sixty Years_ (London, 1894). He also published some (bad) poetry of his own: [Seeley], _David and Samuel_ (London, 1869).\n\n50 Seeley, _Natural Religion_ , 96\u2013111; Seeley, _Goethe Reviewed_. See also Frederick Denison Maurice, _The Life of Frederick Denison Maurice_ , vol. 2 (London, 1884), 59. On Seeley's \"striking\" account of the aesthetic dimension of religion, see Caldecott, _Philosophy of Religion_ , 356\u201361.\n\n51 Seeley, _The Life and Times of Stein, or Germany and Prussia in the Napoleonic Age_ , 2 vols. (Cambridge, 1878), 3:556.\n\n52 Seeley, letter to Sidgwick, July 2, 1867, Sidgwick Papers, Trinity College, Cambridge, Add Ms c95\/64\u201373.\n\n53 Seeley, _Natural Religion_ , 160.\n\n54 Ibid., 166.\n\n55 Ibid., 254.\n\n56 Ibid., 166.\n\n57 Ibid., 168.\n\n58 Ibid., 183\u201385.\n\n59 Ibid., 185.\n\n60 Ibid., 200.\n\n61 Seeley, _Stein_ , 2:20.\n\n62 Ibid., 2:17. Italics added. See also Seeley, \"Georgian and Victorian Expansion,\" 126.\n\n63 Seeley, _Stein_ , 2:35, 17. See also Seeley, \"History and Politics, II,\" _Macmillan's Magazine_ , 40 (1879), 297; \"Georgian and Victorian Expansion,\" _Fortnightly Review_ , 48 (1887), 126.\n\n64 Seeley, _Expansion_ , 11, 50, 220. He sometimes casually slipped between \"state\" and \"nation-state.\"\n\n65 Ibid., 154.\n\n66 Seeley, _Political Science_ , 137.\n\n67 See the extensive discussion in Seeley, _Stein_ , 2:29\u201342. See also Fichte, _Addresses to the German Nation_ [1807\u20138], ed. Isaac Nakhimovsky, B\u00e9la Kapossy, and Keith Tribe (Indianapolis, 2013). For the context of Fichte's argument, see Isaac Nakhimovsky, _The Closed Commercial State_ (Princeton, 2011).\n\n68 Seeley, _Stein_ , 2:34.\n\n69 Ibid., 2:41.\n\n70 Seeley, \"Milton's Political Opinions,\" 99.\n\n71 The claim about Coleridge can be found in Seeley, \"Milton's Political Opinions,\" 98. He once wrote in a letter to his father that he was \"more of an Arnoldite than a Mauriceite.\" Seeley to R. B. Seeley, [n.d. 185?], Seeley Papers, MS903\/2A\/2. The respectful distance was reciprocated, as Maurice wrote of _Ecce Homo_ , which he admired greatly (Maurice to A. Macmillan, January 2, 1886, Seeley Papers, MS903\/3A\/1). Despite these proclamations, I would argue that whilst Seeley might have shared more theological ground with Arnold (at least in the 1850s), his political thought appears to owe considerably more to Maurice, although this might simply be because Maurice lived longer and thus wrote on questions which were also pressing to Seeley.\n\n72 Coleridge, _Constitution of the Church and State_.\n\n73 Arnold, \"The Church and the State\" [1839] and \"National Church Establishments\" [1840], in _The Miscellaneous Works of Thomas Arnold_ , ed. Arthur Stanley (London, 1845), 466\u201375, 486\u201392; Arnold, _Postscript to Principles of Church Reform_ (London, 1833), 19. This was a vision supported by many Whig MPs.\n\n74 Maurice, _The Kingdom of Christ_ (London, 1838); Maurice, _Social Morality_. On Maurice's social and political thought, see Jeremy Morris, _F. D. Maurice and the Crisis of Christian Authority_ (Oxford, 2008), chs. 4\u20135.\n\n75 Bridges, _Some Outlines of the Religion of Experience_ , 228. Bridges was a British emigrant to the United States.\n\n76 Seeley, _Natural Religion_ , 207. On the universalism of the church, see Seeley, letter to Sidgwick, May 15, 1866, Sidgwick Papers.\n\n77 _The Life of Frederick Denison Maurice_ , 1:166.\n\n78 This was most apparent in Seeley, \"United States.\"\n\n79 Seeley, \"Our Insular Ignorance,\" _Nineteenth Century_ , 18 (1885), 869. He continued: \"In the main I hold that it is healthy for a nation to live in society. Like an individual a nation should study its behaviour to its fellows, and for this purpose it should listen respectfully and anxiously to their opinion\" (869). See also Seeley, _Expansion_ , 225.\n\n80 Seeley, _Political Science_ , 88.\n\n81 Seeley, \"United States,\" 447.\n\n82 Seeley, _Natural Religion_ , 200.\n\n83 Seeley, \"The Eighty-Eights,\" _Good Words_ (1888), 380.\n\n84 Maurice, _Social Morality_ , 19.\n\n85 Seeley, _Ecce Homo_ [1866], ed. John Robinson (London, 1970), 121. See also the discussion in Shannon, \"John Robert Seeley,\" 245\u201346; Maurice, _Social Morality_ , 122\u201323.\n\n86 Seeley, _Stein_ , 2:384\u201388. On patriotism (and its absence), see Seeley, \"Our Insular Ignorance\" and \"Georgian and Victorian Expansion.\"\n\n87 Seeley, \"The Church as a Teacher of Morality,\" 277. In _Constitution of the Church and State_ , Coleridge had counterposed his conception of the national church with the universal church of Christ, which knew no legal or political borders. The two could coexist in the same space, but should not be confused.\n\n88 Maurice, _Social Morality_ , 209. Italics in original. On the connection between nationalism and internationalism, see Georgios Varouxakis, \"'Patriotism,' 'Cosmopolitanism' and 'Humanity' in Victorian Political Thought,\" _European Journal of Political Theory_ , 5 (2006), 100\u2013118.\n\n89 Maurice, _Social Morality_ , Lecture 13, 481.\n\n90 See, for example, Seeley, \"The British Race\" [1872], _Education_ , vol. 1 (1881), 309\u201328; Seeley, \"The British Empire,\" _Bradford Observer_ , March 22, 1872.\n\n91 I explore this debate in Bell, _The Idea of Greater Britain_.\n\n92 \"Sir John Seeley and National Unity,\" letter quoted by H. F. Wilson, _Cambridge Review_ , 16 (1895), 197.\n\n93 Stead, _The Life of W. T. Stead_ , ed. Frederick Whyte (London, 1925), 2:209\u201310. Influenced by Seeley, Stead was an ardent imperial federalist. See Stead, \"The English beyond the Sea,\" _Pall Mall Gazette_ , October 4, 1884, 1. He later wrote to his close confidant, Cecil Rhodes, that he was \"drawing up... a course of reading\" for Rhodes's assistant, \"beginning with Seeley's The Expansion of England.\" Stead to Rhodes, May 21, 1891, Rhodes Papers, Rhodes House Library, Oxford, MSS Afr. s 228 C28, ff. 43\u201345.\n\n94 Rosebery to Seeley, March 5, 1894, Seeley Papers, MS903\/1B\/14.\n\n95 Seeley, _Expansion_ , 26, Lecture 2; Seeley, \"Georgian and Victorian Expansion.\"\n\n96 In the most cogent critique of Seeley, John Morley argued that this claim to historiographical novelty was exaggerated. \"The Expansion of England,\" _Macmillans's Magazine_ , 49 (1884), 241\u201358.\n\n97 Seeley, _Political Science_ , 236, 253, 385; Seeley, _The Growth of British Policy_ , 1\u20132. Seeley later upset the young G. M. Trevelyan by dismissing his great uncle as a \"charlatan.\" David Cannadine, _G. M. Trevelyan_ (London, 1992), 27. Seeley cited Green's _Short History of the English People_ in the original manuscript of the _Expansion_ , but was persuaded to drop it by Alexander Macmillan, the publisher of both men. Leslie Howsam, \"Imperial Publishers and the Idea of Colonial History, 1870\u20131916,\" _History of Intellectual Culture_ , 5\/1 (2005), 5.\n\n98 Seeley, \"Introduction,\" to _Her Majesty's Colonies_ (London, 1886), xv. On the trope of indifference, see also chapter 7, section 2.\n\n99 Seeley, _Natural Religion_ , 61. See also Seeley, \"Roman Imperialism\" [1869], vol. 2, in _Lectures and Essays_ , 45.\n\n100 Seeley, _Expansion_ , 117. For Seeley's views on Asia, see \"Roman Imperialism,\" 3:66\u201368; _Natural Religion_ , 61. See, for other examples, Matthew Arnold, \"Democracy,\" in _Culture and Anarchy, and Other Writings_ , ed. Stefan Collini (Cambridge, 1993), 10, 21; John Stuart Mill, _On Liberty_ [1859], _Collected Works_ , 18:273.\n\n101 Seeley, \"Ethics and Religion,\" 514.\n\n102 Seeley, _Natural Religion_ , 217; Seeley, _Political Science_ , 340.\n\n103 Seeley, _Expansion_ , 15\u201316.\n\n104 Seeley, \"Introduction,\" xi, xii. Intriguingly, he also referred to America as a \"world state\" ( _Expansion_ , 293).\n\n105 Seeley, _Expansion_ , 16.\n\n106 Seeley, \"Georgian and Victorian Expansion,\" 139.\n\n107 Bell, _The Idea of Greater Britain_ , ch. 2.\n\n108 Seeley to Bessie Seeley, April 9, 1881, Seeley papers, MS903\/2B\/1; Seeley, \"The Impartial Study of Politics,\" _Contemporary Review_ , 54 (1888), 59. On the important role of Irish Home Rule in this switch, see Seeley, letter to Oscar Browning, April 6, 188[?], Browning Papers, Modern Archive Centre, King's College, Cambridge, OB\/1\/1455A.\n\n109 Seeley, \"Ethics and Religion,\" 503, 508.\n\n110 Seeley, \"Liberal Education in Universities\" [1867], _Lectures and Essays_ (London, 1870), 215.\n\n111 Seeley, \"English in Schools,\" _Lectures and Essays_ , 238.\n\n112 Seeley, \"Political Somnambulism,\" _Macmillan's Magazine_ , 43 (1880), 42.\n\n113 Seeley, \"The Political Education of the Working Classes,\" _Macmillan's Magazine_ , 36, (1877), 145; Seeley, _Natural Religion_ , 208.\n\n114 Seeley, _Introduction to Political Science_ , 357. For his extended discussion on the nature of aristocracy, see 321\u201331. He is here echoing a Coleridgian argument about the necessity of aristocracies of talent.\n\n115 Seeley, \"Sir John Seeley and National Unity,\" _Cambridge Review_ , 197; Seeley, \"Political Education of the Working Classes,\" 143\u201345.\n\n116 Seeley, \"Introduction,\" vii; Seeley, _Expansion_ , 8, 61.\n\n117 Seeley, \"The English Revolution in the Nineteenth Century,\" _Macmillan's Magazine_ , 22 (1870), 1:241, 2:353. See also the comments on public opinion (in regard to India) in _Expansion_ , 190.\n\n118 For context, see James Thompson, _British Political Culture and the Idea of \"Public Opinion,\" 1867\u20131914_ (Cambridge, 2013), 85\u201386, 93.\n\n119 Seeley, \"English Revolution,\" 2:353. On his support for the IFL, see Seeley, \"The Journal of the League,\" _Imperial Federation_ , 1\/1 (1886), 4; Seeley, \"The Object to Be Gained by Imperial Federation,\" _Imperial Federation_ , 1\/6 (1886), 206; Seeley, Speech to the Imperial Federation League in Cambridge, May 29, 1891, reprinted in \"Professor Seeley at Cambridge,\" _Imperial Federation_ , 6\/6 (1891), 176.\n\n120 Seeley, \"Georgian and Victorian Expansion,\" 124.\n\n121 Seeley, \"The Eighty-Eights,\" 380; Seeley, \"Georgian and Victorian Expansion,\" 127.\n\n122 Seeley, _Expansion_ , 293, 169, 75.\n\n123 Seeley, _Political Science_ , 16\u201318. On this broad account, \"human beings almost everywhere belong to states.\" This point is noted in Meadowcroft, _Conceptualizing the State_ (Oxford, 1995), 45\u201347; Jens Bartelson, _The Critique of the State_ (Cambridge, 2001), 52. The volume was, wrote philosopher D. G. Ritchie, \"a valuable addition to political science and, it might be added, to English literature.\" Ritchie, review of _Political Science, International Journal of Ethics_ , 7\/1 (1896), 114. For further discussion of Seeley's conception of the state, see Henry Ford Jones, _The Natural History of the State_ (Princeton, 1916), 4\u20135, 150\u201352. Jones was Professor of Politics at Princeton.\n\n124 Seeley, _Expansion_ , 11, 50, 220; also Seeley, _Political Science_ , 68\u201370.\n\n125 Seeley, _Expansion_ , 288. In \"A Toccata of Galuppi's\" [1855], Browning wrote of Venice: \"Ay, because the sea's the street there; and 't'is arched by... what you call \/... Shylock's bridge with houses on it, where they kept the carnival: \/ I was never out of England... it's as if I saw it all.\" Browning, _Poetical Works_ , ed. Ian Jack (Oxford, 1970), 579.\n\n126 Seeley, \"Introduction,\" xv.\n\n127 Seeley, _Expansion_ , 72\u201373, 75; Seeley, \"Georgian and Victorian Expansion,\" 138\u201339.\n\n128 See, for example, Robert Lowe, \"The Value to the United Kingdom of the Foreign Dominions of the Crown,\" _Fortnightly Review_ , 22 (1877), 618\u201330.\n\n129 Mill, _Considerations on Representative Government, Collected Works_ , 19, 564\u201365.\n\n130 Seeley, _The Expansion of England_ , 74. On utopianism and Greater Britain, see Duncan Bell, \"Dreaming the Future: Anglo-America as Utopia, 1880\u20131914,\" in _The American Experiment and the Idea of Democracy in British Culture, 1776\u20131914_ , ed. Ella Dzelzainis and Ruth Livesey (Aldershot, 2013), 197\u2013210.\n\n131 For further discussion, see Bell, _Greater Britain_ , ch. 3, and chapters 6 and  in this volume.\n\n132 Seeley, _Expansion_ , 74\u201375. Cf. Burke, \"Speech on Conciliation with America\" (March 22, 1775) and \"Address to the Colonists\" (January 1777), in _The Writings and Speeches of Edmund Burke_ , ed. W. M. Elofson (Oxford, 1996), 3:285, 152.\n\n133 Seeley, _Expansion_ , 257, 288; Seeley, \"Georgian and Victorian Expansion,\" 137.\n\n134 Sidgwick, _The Development of European Polity_ , ed. Eleanor Sidgwick (London, 1903), 439.\n\n135 Seeley, \"United States,\" 445, 443.\n\n136 Seeley, _Stein_ , 3:238.\n\n137 Seeley, _Expansion_ , 46.\n\n138 Like many other federalists, Seeley used the terms \"federation\" and \"confederation\" interchangeably (e.g., _Political Science_ , 63, 85, 205). As his later discussion made clear, however, he was well aware of the differences pertaining between different forms of federation. See Seeley, \"United States,\" 440\u201344.\n\n139 Seeley, _Political Science_ , 94\u201395. Rather confusingly, Seeley then proceeds to identify two kinds of unitary state, the centralised and decentralised, before moving on to discuss different types of federation (97).\n\n140 Seeley, \"United States,\" 440.\n\n141 Seeley, _Political Science_ , 97\u201399. See also the discussion in Seeley, \"United States,\" 440\u201343.\n\n142 Seeley, _Expansion_ , 242, 243. He (242n) cites Max M\u00fcller's, _India, What Can It Teach Us?_ (Oxford, 1883). On the discourse of Aryanism, see Tony Ballantyne, _Orientalism and Race_ (Basingstoke, 2001).\n\n143 Seeley, _Expansion_ , 51, 244, 176. For discussion of this passage, see also chapter 5.\n\n144 Seeley, _Expansion_ , 185\u201386, 202, 204. This is why only a localized \"village-patriotism\" could be found (206).\n\n145 Seeley, _Political Science_ , 73\u201374, 76, 367\u201368, 168.\n\n146 Seeley, _Expansion_ , 203, 207\u20138, 228. For a similar argument, drawing on Seeley, see Alfred Caldecott, _English Colonization and Empire_ , 69\u201370.\n\n147 Seeley, _Expansion_ , 228, 221.\n\n148 Ibid., 205. According to Charles Dilke, Seeley wrote \"more suggestively and more profoundly upon the history of British government in all parts of the world than any other writer,\" and yet when it came to India his analysis was contradictory. Dilke, _Problems of Greater Britain_ (London, 1898), 2:98. Dilke also disagreed with Seeley over the priority of the settler colonies, insisting that India was more important: Dilke, _The British Empire_ (London, 1899), 17.\n\n149 Seeley, _Expansion_ , 194.\n\n150 Ibid., 198, 224, 226\u201327.\n\n151 Seeley, _Natural Religion_ , 168\u201369; see also Seeley, \"English Revolution,\" 2:450.\n\n152 Seeley, \"English Revolution,\" 2:446.\n\n153 Seeley, letter to Mary Seeley, April 22, 1887, Seeley Papers, MS903\/2A\/1. See also Christopher Harvie, _The Lights of Liberalism_ (London, 1976), 225\u201326.\n\n154 Seeley, \"English Revolution,\" 2:446\u201348.\n\n155 Seeley, \"Our Insular Ignorance,\" 862. On his darkening view of British politics in the 1870s and 1880s, see Bell, _Greater Britain_ , 164\u201368.\n\n156 Seeley, \"English Revolution,\" 2:446.\n\n157 Seeley, \"Our Insular Ignorance,\" 135\u201336; Seeley, \"Introduction,\" xiii.\n\n158 Cheryl Welch, \"Colonial Violence and the Rhetoric of Evasion,\" _Political Theory_ , 31 (2003), 235\u201364.\n\n159 Seeley, _Expansion_ , 183.\n\n160 Ibid., 187, 191\u201392, 289\u201390. On the importance of Indian trade, see Seeley, _Expansion_ , 191, 258\u201359, 263\u201364, 304.\n\n161 On which, see Mantena, _Alibis of Empire_.\n\n162 Seeley, _Expansion_ , 194\u201396, 183, 195.\n\n163 Rather surprisingly, Deborah Wormell asserts that Seeley disdained the civilizing mission and criticized the moralizing vision of \"helping\" other races. Wormell, _Seeley_ , 159.\n\n164 Liberty, he argued, \"in all cases will be but comparative,\" and moreover it \"will appear to be a good, or a bad thing according to circumstances.\" Seeley, _Political Science_ , 26\u201327. To the American political philosopher W. W. Willoughby, Seeley analyzed the concept of liberty \"in a thoroughly philosophical manner, and the idea in its correct meaning is applied to concrete conditions in a way that cannot but afford sound practical information.\" Willoughby, review of _IPS, Political Science Quarterly_ , 11\/3 (1896), 548.\n\n165 Seeley, _Expansion_ , 238\u201339.\n\n166 Seeley, _Natural Religion_ , 221, 201.\n\n167 Ibid., 201\u20132.\n\n168 Seeley, _Expansion_ , 244\u201345, 248, 252, 260.\n\n169 Seeley, _Natural Religion_ , 243.\nCHAPTER 12\n\nRepublican Imperialism\n\nJ. A. Froude and the Virtue of Empire\n\nSo far as I can judge, the characteristics of modern mankind, French, English, or American, are levity and selfishness, and out of these qualities you cannot build up republics.1\n\n\u2014J. A. FROUDE\n\nIn recent years, much scholarly attention has been lavished on the ideology of \"liberal imperialism.\" Against a backdrop of the omnipresent debates over the dynamics and consequences of globalization and the aggressive foreign policy of the United States and its allies, historians and political theorists have revisited the history of Western political thinking in order to identify the conceptual structure and to track the diffusion of liberal visions of imperial rule. This has propelled some scholars back to early modern Europe, and in particular to the colonial writings of John Locke. The other most popular destination is the nineteenth century, the crucible of liberalism and a period during which the power, geographical extent, and sheer ambition of the Western empires reached an unprecedented level.\n\nFocusing on liberal imperialism in this manner, whilst an important exercise, often generates more heat than light. First, the term itself is problematic: \"liberal imperialism\" implies commonalities and coherence, where the political thought of the nineteenth century was marked by dissonance and diversity. As I argued in chapter 2, not all liberals were imperialists, and those who were diverged very significantly in the intensity of their support, the types of empires that they envisaged, and the justifications that they offered. For example, alongside the standard \"liberal imperial\" position there existed a parallel and frequently overlapping mode of justification that I term republican (or civic) imperialism.2 The main purpose of this chapter is to elaborate on this claim. I proceed as follows. Utilizing John Stuart Mill's writings for illustrative purposes, section 2 sketches the basic features of the \"liberal civilizational\" position. The following section outlines, in broad terms, the republican alternative. The complex relationship between empire and liberty has been a prominent theme in European political thought for over two millennia. For many writers, the two were intimately linked: liberty at home was compatible with (or even required) empire abroad\u2014although empire itself, if understood and enacted improperly, could pose a threat to that very liberty.3 Such concerns also permeated Victorian public debate. Sections 4 and 5 interpret the political thought of the eminent Victorian historian and public moralist J. A. Froude (1818\u201394) in republican terms.\n\nIn ideal-typical form, the two types of imperial justification differed in both motivational structure and geographical orientation. The Millian variant of liberal imperialism contended that in the modern world empire was legitimate if (and only if) it was primarily intended to benefit the populations subjected to it. Any other benefits that it generated were derivative and incidental. It sought to \"civilize\" the \"barbarian,\" and it focused consequently on specific spaces in the imperial archipelago (most commonly India). It is this line of argument that has been at the center of recent scholarship. Republican imperialism, on the other hand, was primarily motivated by a concern with the character of the imperial power, defending empire in terms of the benefits that it generated for the state. Its proponents sought to foster individual and collective virtue in their compatriots, while striving to defend or enhance national honor and glory. Any other benefits that it generated\u2014including the gift of \"civilization\"\u2014were derivative and incidental. Given these concerns, republican imperialism tended to focus more on the settlement colonies, most notably (in the British case) in North America and the South Pacific. Yet republican and liberal civilizational modes of imperial justification were not antithetical, either in theory or practice. Republican defenses of empire were offered by self-professed liberals, as well as by non-liberals, while advocates of the \"civilizing\" potential of empire could be found across the political spectrum. Like those today, Victorian languages of imperial justification were complex, contested, and frequently inconsistent.\n\nJohn Stuart Mill and Liberal Civilizing Imperialism\n\nLiberal imperialism is usually understood to center on the \"civilizing mission,\" the idea that liberal states have a right\u2014and, in a strong version of the argument, a duty\u2014to spread \"civilization\" to the purportedly non-civilized peoples of the world. It is thus structured by a bifocal vision, dividing peoples into two separate categories: \"civilized\" and \"barbarian\/savage.\"4 Societies are arrayed along (and judged according to their position on) a single developmental trajectory, where both the logic and pace of change, as well as the status to be realized, are characterized in terms of \"progress.\" Although this vision allows for considerable variation within each category, crossing the threshold from \"barbarity\" to \"civilization\" is conceived of as a monumental step, one which (depending on the version of the argument employed) will either take an inordinate amount of time given prevailing social and political conditions, or would be impossible without exogenous assistance.5 Both versions justify imperial rule, and both were common in the nineteenth century, above all in Britain, France, and Germany.\n\nMost articulations of this generic liberal imperial argument link civilization to sovereignty. Civilization is seen as a necessary if not sufficient condition for the emergence of a sense of national self-consciousness, which in turn is regarded as essential to trigger liberal claims about the rights of national self-determination. Since most political communities were not thought to exhibit a sense of nationality, imperialism was legitimate if (and only if) it was intended to help bring about a significant progressive change in the social, political, and moral status of the subject people. Once a society had developed to the point where it could be classified as civilized, and once it exhibited authentic national self-consciousness, it could justifiably claim independence, and the job of the liberal imperial power was complete. Froude, who as we shall see was a critic of this argument, summarized the narrative of liberal transformation as follows:\n\nAt present in our enthusiasm for self-government we imagine that our Eastern subjects are by-and-by to learn to govern themselves as we do. We are their trustees while they are in their political infancy. Our duty is to train them in our own image, that when they are fit to receive their inheritance, we may pass it into their own hands. The Asiatic, we are persistently told, is the inferior of the European only in the disadvantages with which he has been surrounded. If he be educated, as we are educated, lifted gradually into freedom, with his rights and powers enlarged as he shows himself capable of their exercise, we shall elevate him into an equality with ourselves, and our mission will be ended.6\n\nThe projected _telos_ of this liberal project, was a world of \"civilized\" nation-states coexisting on a formally equal basis under an expanding regime of international law and commerce. Imperialism was thus part of a wider international reformist vision.7 But the temporal coordinates of this process were very rarely specified; freedom remained deferred to some indefinite point in the future. In the meantime, attention was focused on refining the modes and modulations of imperial rule.\n\nJohn Stuart Mill was the archetypal nineteenth-century proponent of liberal civilizing imperialism. He was certainly not the first to preach the creed, and nor were his imperial arguments especially novel, but he was nevertheless one of its most systematic and forceful advocates. He stands at the heart of contemporary scholarship on the subject\u2014indeed at times he almost seems to exhaust it.8 This is partly a result of his prominence during the Victorian era, his reputation as a philosopher, political economist, social reformer, and public moralist.9 But it is also a function of his place in the canon of modern political thought, a canon that retrospectively classifies individuals as worthy of scholarly attention, and which often identifies them (sometimes explicitly, often implicitly) as representatives either of their age or of the politico-theoretical positions they articulated. Mill is thus often seen as a symbol of nineteenth-century liberalism, and through this, of liberal imperialism. Yet as I argue in chapter 2, and as I further elaborate on below, this type of identification can lead to misinterpretations of the wider ideological context. The reasons for Mill's identification with liberal imperialism, though, are not hard to fathom. Following in the footsteps of his father, he went to work at the East India Company at the age of seventeen, and there he remained, rising to senior rank, until the charter of the Company was revoked in 1858. Having left the services of the Company, he continued to ruminate on the nature and value of the British empire until his death in 1873.\n\nFor Mill, civilization was a rare and fragile achievement; it was a status attained by only a very few communities.10 India was not one of them. He had very decided views on \"barbarians.\"11 Like many of his contemporaries Mill argued that India had once been an advanced society, but that this was no longer the case. It was moribund, mired in superstition, and beholden to primitive traditions. The scope of his putatively universal ambitions was circumscribed\u2014spatially not temporally\u2014by the limits of civilization. His famed definition of liberty, the \"one very simple principle\" that governed his ideal conception of society, did not apply to those who had failed to reach the \"maturity of their faculties.\" Children, the mentally disabled, and those \"backward states of society in which the race itself may be considered as in its nonage\" were not included within its embrace. \"Liberty, as a principle, has no application to any state of things anterior to the time when mankind have become capable of being improved by free and equal discussion.\"12 This was the spatial limitation\u2014for Mill, this argument excluded the vast majority of the world's population. Only a select few states had reached the prescribed level of maturity. The link to national self-consciousness is clear. \"[B]arbarians,\" Mill stated in an essay published in 1859, \"have no rights as a _nation_ , except a right to such treatment as may, at the earliest possible period, fit them for becoming one.\"13 This was because they were incapable of reciprocity and of following rules. The \"minds\" of those lacking civilization, he wrote, \"are not capable of so great an effort.\"14 The universality was reinscribed in temporal terms: in the future the \"barbarians\" will reach civilization, and when they do they will be welcomed into a society of states regulated by binding laws and enforceable rights. The job of the liberal state was to help them in this process, to act as the midwife of modernity.\n\nFor Mill, ever the utilitarian, the British empire, and in particular the empire in India, was an engine of improvement. It provided a vast laboratory for his \"ethology,\" the science of individual and collective \"character\" that he sketched (although never fully developed) in the _System of Logic_ (1843).15 Since human character\u2014both individual and collective\u2014was relatively plastic, and could be (re)shaped by environmental conditioning, it was possible to transform barbarous societies into progressive ones, given time, patience, and skill.16 This was the only legitimate type of imperial rule in the modern world. As he wrote in _On Liberty_ (1859), \"[d]espotism is a legitimate mode of government in dealing with barbarians, provided the end be their improvement, and the means justified by actually effecting that end.\"17 He reiterated the point in the _Considerations on Representative Government_ , published two years later, arguing that imperialism as a\n\n... mode of government is as legitimate as any other, if it is the one which in the existing state of civilization of the subject people, most facilitates their transition to a higher stage of improvement. There are... conditions of society in which a vigorous despotism is in itself the best mode of government for training the people in what is specifically wanting to render them capable of a higher civilisation.18\n\nTraditional motives for conquest, whether financial gain, geopolitical rivalry, or national glory, were obsolete.\n\nMill argued, then, that the primary duty of an imperial power was, through a combination of coercion and example-setting, to help educate subject populations until they were \"capable\" of attaining responsible self-government. The key point for the present discussion is that for Mill\u2014and for many other liberals\u2014this was the _only_ way in which despotism could be justified. Empire may generate other benefits (and Mill certainly argued that it did so), but these were necessarily incidental to the transformative project.\n\nRepublican Themes in Victorian Political Thought\n\nThe term \"republican\" has played an important role in historical writing over the last few decades, although it has assumed a number of different and sometimes conflicting meanings.19 In applying it to British imperial discourse, it is essential to be clear about the nature of the claims being advanced. (For example, I am not employing republican in the sense it is often used to describe French imperialism, especially in the years of the Third Republic, a vision in which _la mission civilatrice_ played a constitutive role.)20 It is therefore necessary to explore briefly both the generic structures of republican argumentation and the ways in which scholars have discussed republican legacies in the Victorian era.\n\nHistorians have traced republican themes in various nineteenth-century contexts. Two stand out. Firstly, they have identified a powerful republican inheritance among radicals, a line of argument that was transmitted from Thomas Paine and through to the Chartists, and which lingered until the 1880s when it was supplanted by socialist theories of political economy (especially those inspired by Karl Marx).21 Radical republicans stressed the close connection between the ownership of property and liberty, they criticized the Crown and the aristocracy for holding arbitrary power over them, and they regarded the state as corrupt. The solution to these problems lay, they argued, in political (as opposed to economic or social) transformation. A second stream of research has charted how republican themes shaped various aspects of an emergent liberalism, focusing in particular on the transmission belts of Whiggism. These themes were expressed in a variety of commonplace Victorian tropes. Stefan Collini, for example, argues that eighteenth-century conceptions of \"virtue\" and Victorian notions of \"character\" shared a number of key features, most notably their asceticism and demanding political ethic. Victorian thought, he concludes, was marked by \"survivals and mutations\" of the earlier language of civic humanism.22\n\nWhat unites these streams of scholarship is that they bypass empire. Yet it is in the domain of empire that we hear some of the clearest and most consistent echoes of republicanism in the Victorian age. The key point of imaginative anchorage lay in the prevalence and cultural authority of narratives of imperial decline and fall (a topic I explore in chapter 5). The dangers and the dynamics of imperial corruption, heralded by Sallust and Polybius and rearticulated most famously by Edward Gibbon, infused Victorian political consciousness.23 Collini maintains that the Victorians and their civic humanist predecessors differed in at least one important respect: their \"sense of nemesis.\"24 This difference resulted from divergent conceptions of historical time, for the eighteenth-century humanists, he argues, feared corruption, grounded in a cyclical account of rise and decline, while the Victorians feared stagnation as a threat to their open-ended notion of a progressive future. For many of those with their eyes fixed on the fortunes of the British empire, however, the sense of nemesis remained exactly the same: the seemingly inexorable logic of imperial declension. The imperial imagination was partially structured by interpretations of the political dynamics of the ancient world.\n\nThe most significant context for republican imperialism was the late nineteenth-century debate over the future of the settler colonies. Because India has been the focus of so much recent research, the pivotal importance of Canada, New Zealand, Australia, and the Cape in the Victorian political imagination has often been overlooked. The three best-selling books on imperial questions published during the second half of the century\u2014Charles Dilke's, _Greater Britain_ (1868), J. A. Froude's, _Oceana_ (1886), and J. R. Seeley's, _The Expansion of England_ (1883)\u2014all stressed the primary importance of the settler colonies. And all exhibited, to varying degrees, the complex and diffuse legacy of republican thinking. Republican imperialism was opposed to radical individualism, emphasizing instead public duty, self-denying altruism, and the promotion of a virtuous patriotism; its proponents worried, to varying degrees, about the corrupting powers of materialism, capitalism, and \"luxury\"; they stressed duty above rights, politics above economics, and the enchanted national above the unencumbered cosmopolitan. They contrasted the passive subject with the active imperial patriot. They also repeatedly invoked the benefits bestowed by propertied independence, and especially the ownership and active usage of productive agricultural land (at home and especially in the colonies). This helps to explain the suspicion expressed by many Victorian imperialists about urbanization.25 This anxiety is not surprising given the deep historical roots, stretching back to Rome, of the connection between farming and the planting of people. After all, the Latin term _colonia_ , derived from the verb _colere_ , means to cultivate, or to farm.26 This imaginative link has been a central theme in the history of Western imperial expansion.\n\nThe late Victorian colonial debates were not an unmediated replay of the eighteenth-century clash over the respective merits of the ancients and moderns. Rather, republican imperialism was a language adapted to and shaped by the late nineteenth-century imperial context.27 Born of an industrial capitalist society, its advocates were simultaneously proud of the achievements of modern commerce and wary of the dangers of the commercial spirit extending too far. Republican imperialism was defined as much by what it was opposed to as by what it stood for. Among the main targets were liberals infected with the \"virus of Manchesterism.\"28 This strand of liberalism was characterized, it was claimed, by utilitarian reasoning, a debilitating individualism, and a narrow obsession with profit and the doctrines of _laissez-faire_ political economy. Above all else, it was seen to underpin an attitude critical of empire: during the 1860s in particular liberalism came to be associated, albeit inaccurately, with \"indifference, if not hostility, towards the Colonies.\"29 It was against these forms of liberalism (or at least a crude caricature of them) that the republican imperial position was articulated most forcefully. Materialism, it was thought, was destructive in three distinct ways, although they frequently overlapped. First, it could corrupt individuals. The perfidious sensuality and vice of the East rebounding to undermine the polity from within was a long-standing (orientalist) concern, rising to prominence in the eighteenth century where it was exemplified in Burke's dogged pursuit of Warren Hastings. It reverberated throughout the nineteenth century.30 Modern luxury could even damage those not directly involved in the empire, either by entrenching social and economic conditions that debilitated the working classes, emasculating their virile energies, or through the creation of a rich but effete ruling class. Combined, this fashioned a society unable to, and uninterested in, expanding its strength and glory. The second dimension reinforced this polarization. Commercial society generated increasing economic inequality, triggering potentially destabilizing political consequences as well as fueling fear of the working classes rising to challenge their oppressors. Finally, there was a further indirect effect: the commercial spirit, it was often argued, corroded patriotism and the belief in a transcendent common good. Individuals became increasingly egotistical, placing self-interest above public duty.31 The \"materialists\" were perfectly happy to see the empire either fall into a state of disrepair or, in some cases\u2014most notably that of the self-proclaimed \"last of the Manchester school,\" Goldwin Smith\u2014to demand the \"emancipation\" of the colonies.32 Julius Vogel, a former premier of New Zealand, warned in 1877 of the dangers of Britain, stripped of its colonies, \"sinking into a small money-loving State\u2014a second Holland.\"33\n\nThese lines of thought came together in a powerful defense of the virtues of settler colonialism. Much of the debate over \"Greater Britain\"\u2014as the unity of Britain and the settler colonies was frequently labeled\u2014centered on the type of character necessary for and produced by successful colonization. Emigration lay at the heart of this process.34 For much of the nineteenth century, emigration was looked upon either as a \"safety valve\" for social problems or as a means of escape for greedy young men and the less talented sons of the aristocracy. While political economists had repeatedly insisted on the financial benefits of colonies, the colonists themselves were frequently scorned. The \"colonial reformer\" and political economist E. G. Wakefield wrote in _A View on the Art of Colonization_ (1849), that \"speaking generally, colonies and colonists are in fact, as well as in the estimation of the British gentry, inferior, low, unworthy of much respect, properly disliked and despised by people of honour here, who happen to be acquainted with the state of society in the colonies.\"35 Throughout the century settlers were also routinely criticized for their brutality to indigenous populations, often by Britons (including John Stuart Mill) who supported the empire but were worried about how some of its constituent elements were governed.36 The debates over Greater Britain witnessed a sustained attempt to transform this negative image, both to help encourage further emigration and to shift the general perception of the value of the colonies. As I discuss in Chapter 2, the colonies were reimagined as integral elements of the \"mother country\"; the existing colonists as loyal, hardy, and rugged patriots.37 Republican imperialism was not exclusively found in Britain. It can be seen, for example, in Alexis de Tocqueville's writings on Algeria. Unlike many other French nineteenth-century thinkers, Tocqueville was not especially interested in \"civilizing\" imperial subjects. He was concerned primarily with the benefits that colonialism would bring to mainland France, and he sought to reinvigorate the _patria_ through foreign conquest. With \"time, perseverance, ability, and justice,\" he prophesized, \"I have no doubt that we will be able to raise a great monument to our country's glory on the African coast.\"38 This monument would restore French greatness and transform the citizenry. American political thought at the turn of the twentieth century expressed many of the same concerns. It was in nineteenth-century Britain, however, that we find some of the most powerful echoes of republican imperialism.\n\nJ. A. Froude and the Pathologies of the Moderns\n\nAn anatomist of religious crisis, an influential historian, and a fierce social critic, Froude was one of the leading \"public moralists\" of the second half of the nineteenth century.39 His monumental twelve-volume study of the English reformation, the _History of England from the Fall of Wolsey to the Defeat of the Spanish Armada_ (1856\u201370), sold tens of thousands of copies. His writings on empire reached a similarly large audience.40 In these writings we see the articulation of a distinctive republican argument.\n\nFroude is often characterized as a straightforward disciple of Thomas Carlyle. However, although he admired Carlyle enormously, and although he followed him in various ways, Froude was nevertheless an independent thinker, fully capable of carving out his own path. The complexion of his political thought has proven notoriously elusive\u2014something of which he would be proud. Michael Bentley characterizes him as a \"great liberal,\" Peter Mandler a \"liberal Carlylean,\" while for John Burrow he was a \"radical Tory.\"41 By the 1850s he had shed his youthful radicalism and he increasingly identified with conservative policies and politicians. His writings grew increasingly reactionary in tone and content. He hated Gladstone and was an enthusiastic admirer of Disraeli. He was no \"great liberal.\" But nor was he a great Tory. He liked to project himself as a man above and beyond trivial partisan struggles, his energies focused on the good of the \"commonwealth.\" Indeed his writings, like those of Seeley, abound with harsh criticisms of the factionalism and myopia of \"party.\" He once wrote:\n\n[I]t is the very nature of \"party\" that party leaders shall never see things as they really are, but only as they affect for the moment the interests of one section of the community. They are as men who, having two eyes given them by nature, deliberately extinguish one. There is the point of view from the \"right\" and the point of view from the \"left,\" and from each, from the nature and necessity of the case, only half the truth can be seen. A wise man keeps both his eyes, belongs to no party, and can see things as they are.42\n\nFroude's eyes were fixed on the multifarious failings of his contemporaries, on the lessons that could be drawn from both the character and the fate of the Roman Republic and, ultimately, on how to secure the future glory of the British \"race\" in the wide expanses of the colonies.\n\nFroude had nearly become a colonist. In the 1840s he was on the verge of emigrating to Hobart, in Van Diemen's Land, to take up a teaching position, before the offer was rescinded in the wake of the controversy generated by the publication of his autobiographical novel _The Nemesis of Faith_ (1849). Burned publicly in his Oxford college, the book cost him his cherished fellowship as well as a potential new career. Yet it was only in the 1870s that he turned to writing at length about the empire. In a series of essays and books published between 1870 and his death in 1894 (two years after being appointed Regius Professor of History at Oxford), Froude elaborated a distinctive republican vision of the empire. It was republican in two specific senses. First, his imperial thought was shaped by an interpretation of the corruption of the Roman republic. From this narrative, Froude drew lessons that he applied directly to the contemporary world, identifying the same (or analogous) mechanisms at work in Britain. This was a fairly common argumentative strategy amongst his contemporaries, although (as I show in Chapter 5) it could be used to defend a wide variety of positions. Second, in a more innovative move, he argued that the answer to this impending catastrophe lay in creating a global polity populated by individuals exhibiting many of the same virtuous characteristics that he discerned amongst the inhabitants of the Roman Republic. Both his diagnosis and his prescriptions were drawn from the Greco-Roman world. Froude mixed these arguments with an idealized view of the \"ancient\" feudal system in Britain. Although he often talked in vague terms about the greatness of the \"English Empire,\" he placed little emphasis on the providential rights and duties of the British to \"civilize\" the rest of the world, and he prioritized the settler colonies above all.43 They were, he argued, \"infinitely more important to us than even India.\" The reason for this was simple: \"[I]t is because the entire future of the English Empire depends on our availing ourselves of the opportunities which those dependencies offer to us.\"44 Indeed he barely touched on India, and when he did it was in terms that would have horrified Mill. He suggested that, due to its role in promoting national greatness, the British should stay in India in perpetuity. \"Our Indian Empire was won by the sword, and by the sword it must be held; and to suppose that we can ever abandon it except in defeat and disgrace is to surrender ourselves wilfully to the wildest illusion.\"45\n\nFroude saw corruption wherever he looked in the modern world. \"[W]e are passing,\" he warned, \"through a crisis in our national existence.\"46 Obsessed with the \"genius of English freedom,\" a genius he saw as largely consigned to the past, he believed that the only hope for the future lay in the unity of the settler empire. But it was important, he argued, to recognize that the colonies were not simple imperial possessions, and that \"[o]ne free people cannot govern another free people.\"47 With the necessary checks and balances they could govern a non-free people\u2014this is presumably how he saw India\u2014but to impose their will on a \"free\" people was both to commit an injustice (made worse in this case because they were \"English\" and therefore part of the same \"nation\") and also to potentially corrupt the polity.\n\nFroude's views on the specific content of \"freedom\" were rather elusive. He was not a systematic theorist, and his comments on the issue are scattered and frequently opaque. It is nevertheless clear what he was opposed to. The modern state, he argued, \"disclaims abstract considerations of justice, and knows nothing but expediency.\" It existed only \"to secure the greatest liberty to the greatest number\u2014liberty meaning the absence of constraint,\" and it was driven by a simple philosophy: \"Let every man prove his private advantage with all the faculties that belong to him, and nature and competition will take care of the rest.\"48 His own conception of freedom was much less clearly articulated. He repeatedly harked after an \"old\" England\u2014the dates of which remained unspecified\u2014where the people were free in a different sense; it was this historical phantasm that he often linked to (or conflated with) the early Roman Republic. In this feudal ideal, freedom was an attribute of citizenship granted for the performance of valuable social roles. In such a society everybody knew their place, recognizing that they were enmeshed in a complex web of obligations and duties. \"In the old days a 'freeman' was a master of his craft, and not till he had learnt to do, and do well, some work which was useful for society did he enter upon his privileges as a citizen.\"49 In such a world, \"[l]iberty in the modern sense, liberty where the rights of man take the place of the duties of man,\" was neither \"sought nor desired.\"50 He summarized this view in \"On Progress,\" arguing that:\n\nAs a member of society man parts with his natural rights, and society in turn incurs a debt to him which it is bound to discharge. Where the debt is adequately rendered, where on both sides there is a consciousness of obligation, where the rulers and ruled alike understand that more is required of them than attention to their separate interests, and where they discern with clearness in what the \"more\" consists, there is at once good government, there is supremacy of law... and there, and only there, is freedom.51\n\nAs long as they were enacted for the betterment of the commonwealth, laws were not (as liberals purportedly argued) impediments to liberty. \"Just laws are no restraint upon the freedom of the good, for the good man desires nothing which a just law will interfere with. He is as free under the law as without the law, and he is grateful for its guidance when want of knowledge might lead him wrong.\"52 But freedom was increasingly undermined by the logic of capitalism, for under the iron rule of the political economists, Froude argued, English workers were overly dependent on their masters. The worker existed in \"an enchanted circle of necessity\u2014that he must stay passive under the barest of wages which will keep life in him and his, under penalty of starvation if he resist to make an effort to escape.\" We \"mock him with the name of freedom,\" he declared.53 Independence, which he routinely (although inconsistently) tied to property, was the anchor of freedom; and the freedom of the individual and the freedom of the polity were intimately connected, for the \"units composing it [the state] are free in the freedom of the body. If they seek a separate freedom of their own, they can obtain it only by degradation.\"54\n\nDreaming of Rome: The Uses of History and the Future of \"Oceana\"\n\nIn order to understand the nature of and the inspiration for Froude's views on Britain and the empire it is necessary to turn to his interpretation of ancient history, and in particular the history of Rome. This was a constant point of reference in his writings, and it played a fundamental role in shaping his political thought. It is this imaginative engagement with the ancients, as much as anything else, that marks his distance from Carlyle. The early republic offered Froude a partial template for his global British polity; and the causes of its decline presented a stark warning about both the mechanisms and the consequences of corruption. \"To the student of political history, and to the English student above all others,\" he wrote in the opening passage of his biography of Julius Caesar, \"the conversion of the Roman Republic into a military empire commands peculiar interest. Notwithstanding many differences, the English and the Romans essentially resemble one another.\"55 The twilight of the republic was, he continued, a period \"in so many ways the counterpart of our own,\" and the \"[t]endencies now in operation may a few generations hence land modern society in similar conclusions.\" If this came to pass, \"free institutions\" would be destroyed.56\n\nThe reason that Rome seemed such an apposite exemplar derived, at least in part, from Froude's conception of historical time. He believed that all living things, including \"commonwealths,\" followed the same trajectory: \"recurring stages of growth and transformation and decay.\"57 This was one of the reasons why he was generally suspicious of the cult of progress that he discerned amongst his contemporaries. But the pattern of history was not fully predetermined. The speed at which decay metastasized through the body politic remained within the domain of human agency, and as such, Froude thought that the Commonwealth could be ruled in such a manner as to extend its existence\u2014and conversely, that certain courses of action would accelerate decline. Fate could not be defeated, but it could be held at bay. \"The life of a nation, like the life of a man, may be prolonged in honour into the fullness of its time, or it may perish prematurely, for want of guidance, by violence or internal disorders.\" The study of history offered one way in which to inculcate wisdom, for the causes of decline could be identified and acted upon.58 This was yet another reason why he insisted that the fall of Rome was of such \"peculiar\" interest to the \"English student.\" Although Froude dissented from Harrington's specific proposals for overcoming the tension between expansion and liberty, he nevertheless thought that through reordering the moral and political constitution of the British people, and through incorporating vast expanses of the colonies within an enlarged polity, the inevitability of decline could be resisted, perhaps even indefinitely.\n\nFroude's vision of \"Oceana\" demanded the translation of the virtues of the early Roman republicans into the contemporary world. This was partly a matter of recovering their personal virtues. The inhabitants of the \"early commonwealth of Rome,\" he wrote, were \"distinguished by remarkable purity of manners.\" The \"marriage tie was singularly respected\" and the \"Latin yeomen, who were the back-bone of the community, were industrious and laborious,\" living their lives \"with frugality and simplicity,\" and raising their children \"in a humble fear of God or the gods as rulers to whom they would one day have to give an account.\" This was a society where \"[t]he whole duty of man lay in _virtus_ \u2014virtue, manliness.\" Then corruption set in, and the last years of the republic were marked by the \"incredible depravity of manners, the corruption of justice, the oppression of the provinces [and] the collapse of the political fabric in a succession of civil wars.\"59 The result was catastrophic: the \"free institutions which had been the admiration of mankind were buried under the throne of the Caesars.\"60\n\nFroude argued that a sense of religion had regulated the life of the republicans, motivating and giving shape to the other virtues.61 Under the wise rule of Augustus, order and justice were reinstated, but following his death it soon became apparent that the moral fabric of the republic had disintegrated.\n\nThe administration of Augustus was the most perfect system of secular government ever known, and the attributes assigned to Augustus were the apotheosis of it. The principle of Augustus was the establishment of law and order, of justice and decency of conduct. Of the heroic virtues, or even the modest virtues of purity and sense of moral responsibility, such a system knew nothing, and offered no motive for moral enthusiasm. Order and law and decency are the body of society, but are a body without a soul; and, without a soul, the body, however vigorous its sinews, must die and go to corruption.62\n\nAnd so it came to pass. The reign of justice could not last, and the decline and fall of Rome ensued as corruption and vice spread widely and decisively. The moral orientation provided by an overarching religiosity disappeared, and the collapse of virtue invariably followed. Such was the story that Froude recounted. The focus on religion was unusual\u2014and drew directly from Froude's own fragile spiritual sensibility\u2014but the general narrative of rise and decline was firmly etched in the consciousness of educated late Victorians. The ancient republic provided Froude with a model for the future, and a way to judge\u2014and judge scathingly\u2014the world around him. The character traits that he most admired in the ancients\u2014a sense of public duty, hardiness and frugality, \"manliness,\" an intimate connection with the land, and so forth\u2014were those that he considered necessary to escape the debasement of the moderns.63 The mechanisms of corruption that had destroyed the republic were those that he feared were hollowing out his beloved England from within. Froude also employed the fate of Rome to inculcate a number of specific lessons. One concerned the depredations of urbanization. England, he warned, was in danger of becoming a \"country of cities.\"64 This had two main consequences. First, it was leading to the moral and physical degeneration of the population. He drew on a passage from Horace to illustrate the point. As people flocked from the fields to the cities they were exposed to ever increasing levels of vice. \"Decay is busy at the heart of them, and all the fate of Rome seemed to me likely to be the fate of England if she became what the political economists desired to see her.\"65 Second, it meant that the number of \"free holders\"\u2014those owning their own plots of land or with secure tenure\u2014went into rapid decline. The ownership of property, the very anchor of freedom, was being eliminated. The likely consequences could again be traced in the fate of Rome.\n\nThe armies which made the strength of the Roman republic were composed of the small holders of Latium and afterwards of Italy. When Rome became an empire, the freeholder disappeared; the great families bought up the soil and cultivated it with slaves, and the decline and fall followed by inevitable consequence.66\n\nA similar process was happening around him, for as the people left the countryside to work in the factories large landowners increasingly swallowed up the lands they had vacated.67 Many of these men sat in Parliament, which partly explained the shameful state of British politics, for their main interest lay not in defending the common good but in the pursuit of personal gain. \"Their grandfathers cared for the English commonwealth. It is hard to say what some of these high persons care for except luxury.\"68 Froude also looked to puncture what he saw as facile complacency about progress. Gibbon, he noted, had identified the period between the accession of Trajan and the death of Marcus Aurelius as the \"time in which the human race had enjoyed more general happiness than they had ever known before.\" But this was a fatal mistake, for \"during that very epoch, and in the midst of all that prosperity, the heart of the empire was dying out of it. The austere virtues of the ancient Roman were perishing with their faults. The principles, the habits, the convictions, which held society together were giving way, one after the other, before luxury and selfishness.\"69 As with the Romans, warned Froude, so with his compatriots.\n\nFroude argued that the problems of the modern world could be laid squarely at the feet of liberalism, or at least a species of it. Liberalism promoted three crippling vices: materialism, individualism, and a minimalist (\"nightwatchman\") conception of the state. Materialism was the popular religion of the country; and luxury, understood as the excessive accumulation of personal wealth and its ostentatious display, was its progeny. \"Luxury,\" he lamented, was \"no longer deprecated as an evil,\" as it was by the ancient writers, but was instead \"encouraged as a stimulus to labour.\" Again: the \"modern creed [of liberalism] looks complacently on luxury as a stimulus to trade. Fact says that luxury has disorganized society, severed the bonds of goodwill which unite man to man, and class to class, and generated distrust and hatred.\"70 Luxury was allowed to polarize society because the modern liberal conception of the state failed to provide the necessary resources to deal with the threat\u2014indeed it encouraged it. In this rendering, the state was no more than the uncoordinated aggregation of egoistic individuals, a hollow shell lacking common purpose. This vision itself was premised on a rampant individualism that, according to Froude, corroded the affective bonds necessary to unite communities, reconcile classes, and ensure greatness. \"In these modern times men govern themselves, and therefore their loyalty is to themselves.\"71 He hankered after an older understanding of self, society, and state, praising the \"ancient notion of a community,\" one which fostered virtues \"which Englishmen used most to desire,\" the virtues of \"Patriotism, loyalty, fidelity, self-forgetfulness, a sense of duty.\" In such a society the \"sense of what is due to a man's self\u2014his rights, as he calls them\u2014is conspicuously absent.\"72 Individuals should be bound by duty, not seen as possessing inalienable rights; society was a cooperative hierarchical arrangement united by common purpose and interests; and the state was a moral entity, the priorities of which were clear: \"To repress needless luxury, to prevent capitalists from making fortunes at the cost of the poor, and to distribute in equitable proportions the profits of industry.\"73 A \"sound nation,\" he declared,\n\n... is a nation composed of sound human beings, healthy in body, strong of limb, true in word and deed\u2014brave, sober, temperate, chaste, to whom morals are more important than wealth or knowledge\u2014where duty is first and the rights of man are second\u2014where, in short, men grow up and live and work hard, having in them what our ancestors called the \"fear of God.\"\n\nThis was, of course, exactly the way he had described the virtues of the inhabitants of the \"early republic.\" Unlike the radical republicans, Froude believed that democracy fostered rather than eliminated these dangers. In democracies, he warned, the \"pursuit of wealth becomes the predominant passion, degrades the national character, raises to eminence the least worthy of elevation, corrupts those who obtain it by luxury.\"74 The main counter to these tendencies was strong government and, ideally, a patriotic aristocracy ruling in the best interests of the commonwealth. \"The natural leaders in a healthy country are the gentry; public-spirited and patriotic because their own fortunes are bound up with the fortunes of their country.\"75 They would act as a bulwark against the vagaries of \"commercial speculation.\" Here lay the roots of his (qualified) admiration for Disraeli. Whereas Carlyle \"despised\" Jews and had regarded Disraeli as a \"fantastic ape,\" Froude described himself as a \" _quasi_ follower\" of the Tory politician, although this is unsurprising as he attributed to him a vision of politics that almost exactly mirrored his own.76 After all, he claimed, Disraeli venerated the \"old conception of the commonwealth,\" where a just and beneficent aristocracy ruled in the name of the people, and he hoped that some version of this might be restored if only the aristocrats could relearn \"the habits of their forefathers.\"77 Once again we witness Froude's admixture of classical ideals and a mythopoeic vision of the feudal past. Aristocratic rule provided the backbone for republican life.\n\nRepublics have held together as long as they have been strong with patrician sinews; when the sinews crack the republic becomes a democracy, and the unity of the commonwealth is shivered into a heap of disconnected atoms, each following its own laws of gravitation towards its imagined interests. Athens and Rome, the Italian Republics, the great kingdoms which rose out of the wreck of the Roman Empire, tell the same story.78\n\nAnd this story was repeating itself before his very eyes. In language strikingly similar to that he employed to chart the decline of Rome, he argued that the Reform Acts of 1832 and 1867 had created an environment in which individuals focused solely on their own interests, \"a process under which the English people are becoming a congregation of contending atoms, scrambling every one of them to snatch a larger portion of good things than its fellow.\"79 Froude's vision was a paternalistic one in which a beneficent elite governed a contented free people, bound together in loyalty to the nation and by the interdependence and mutual reliance of all classes.\n\nFroude argued that the cure for the assorted evils that he identified lay in the wide-open spaces of Greater Britain. His dream, which was never specified with any precision, was of a \"united Oceana,\" a polity \"united as closely as the American states are united.\"80 The colonies were important for two different, though related, reasons. The first concerned scale and power. \"These are not the days for small states: the natural boundaries are broken down which once divided kingdom from kingdom; and with the interests of nations so much intertwined as they are now becoming, every one feels the benefit of belonging to a first-rate Power.\"81 Only a united Oceana could secure the freedoms of the (global) English nation. Secondly, the colonies offered vast tracts of land that could absorb millions of emigrants from the \"mother country.\" Froude was obsessed with emigration\u2014both the dangers of the continuing flow of people to the United States, and also the need for the British government to finance a system of systematic emigration to the colonies. The former was a problem because it simultaneously weakened Britain whilst strengthening a formidable competitor. The latter was vital because of the increasing urbanization and consequent degradation of Britain. In the colonies emigrants would be transfigured into freemen and patriots\u2014rugged, hardy, and industrious. \"You who are impatient with what you call a dependent position at home, go to Australia, go to Canada, go to New Zealand, or South Africa.\"82 The vile cities could be halved in size, the colonies restocked. Fearful of the \"plagues which are consuming us,\" Froude argued that emigrants would be able to lead \"a happier and purer life\" in the colonies.83 \"If,\" he argued,\n\n... the millions of English and Scotch men and women who are wasting their constitutions and wearing out their souls in factories and coal mines were growing corn and rearing cattle in Canada and New Zealand, the red colour would come back to their cheeks, their shrunken sinews would fill out again, their children, now a drag upon their hands, would be elements of wealth and strength while here at home the sun would shine again, and wages would rise to the colonial level, and land would divide itself, and we should have room to move and breathe.84\n\nThe aim of British government policy should be to create a polity strong and \"healthy\" enough to postpone the inevitable, to \"defy the storms of fate.\"85\n\nWas Froude simply reiterating Carlyle's views on empire? Their positions overlapped on many points. Both contended that the settler colonies were more important than India.86 Both expressed horror at the state of British cities, demanded more support for emigration, and waxed lyrical about the revivifying open spaces of the colonies. Both called for an end to the reign of the political economists and a more interventionist role for the state. But their thinking was marked by numerous differences, and when they did concur it did not necessarily mean that they had arrived at their conclusions in the same manner.87 We should not be surprised by this: their writings on empire were produced in different political contexts. Carlyle's scattered remarks on colonization were published during the 1840s and 1850s (primarily in _Chartism_ and _Past and Present_ ), while Froude's date mainly from the 1870s and 1880s. Carlyle's conception of the spiritual value of labor shaped his views on colonization, whereas Froude, who did not share Carlyle's account, articulated a more instrumental position\u2014it was beneficial for everybody to have a trade so that they could be independent, and thus capable of securing their freedom.88 Whereas Carlyle looked benignly on British emigration to America, Froude was horrified by it, regarding the United States as a challenger to British preeminence.89 \"We have raised up against us a mighty empire to be the rival, it may be the successful rival, of our power.\"90 For Carlyle, the colonies were important mainly as an answer to the \"social question,\" and he placed little emphasis on geopolitics; for Froude, on the other hand, the domestic and the international were combined in an intricate dialectic. Due to a combination of geopolitical competition and internal decay British greatness was under threat, and the colonies offered the only solution. Finally, while Carlyle expostulated on the benefits of emigration and colonial life, he never conceived of the empire, or the settlement empire within it, as a distinctive and integrated social and political unit. Froude, meanwhile, dreamed of a united Oceanic commonwealth.\n\nConclusions\n\nRecent interest in tracing the history of \"liberal imperialism\" has illuminated important dimensions of nineteenth-century political thought and action. The relevance of this exercise for contemporary political theory and social criticism is palpable. Yet focusing exhaustively on ideas about the liberal desire to \"civilize\" the \"barbarian,\" and to transmit British manners, values, and institutions throughout the world, has also meant that the variety and complexity of Victorian imperial thought is often obscured. Many liberals, and indeed many non-liberals, looked on the map of the world as an open invitation for projects of transformation\u2014social, political, and moral. But not all did so. Other parallel, intersecting, and sometimes contradictory forms of argument were also common, offering different accounts of justification for overseas expansion, coercion, and rule. In this chapter I have highlighted one such position, which I have termed republican. Yet it is important to stress that republican imperialism was not a discrete autonomous \"tradition\" completely separate from other imperial ideologies\u2014it was instead a bundle of arguments, even a sensibility, concerning the sources, nature, and value of overseas conquest and government. It was possible, for example, to offer a republican defense of settler colonization and insist on the imperatives of the civilizing mission elsewhere. Republican themes were threaded through the tapestry of Victorian political thought, cutting across liberalism, conservatism, even socialism. The clearest and most consistent articulation of republican imperial argument can be found in Froude's writings. Much as Froude was indebted to Carlyle, his hero and often his inspiration, those interested in tracing the sources and character of his political thought need to pay more attention to the imaginative debt he owed to the ancient world, and in particular to his appropriation of Roman republicanism, than is usually the case. His understanding of the pathologies and potential of the British (global) polity was shaped by, and anchored in, his understanding of the practices and intellectual worlds of the early Romans. Only by drawing vital lessons from the pre-capitalist past, he insisted, would it be possible to map a glorious future for \"Oceana.\" Otherwise the fate of Rome would befall the corrupted British.\n\n1 J. A. Froude, letter to Theodor Stanton, 1888, reprinted in Waldo Hilary Dunn, _James Anthony Froude_ , 2 vols. (Oxford, 1961\u201363), 2:560. Stanton was a professor at Cornell.\n\n2 I am not arguing that this distinction captures all of the variety of nineteenth-century imperial thought, only that it helps us to understand some significant aspects of it. For other modulations of imperial ideology, see the discussion in Chapter 3.\n\n3 David Armitage, \"Empire and Liberty,\" in _Republicanism_ , ed. Quentin Skinner and Martin van Gelderen (Cambridge, 2003), 2:29\u201347; Andrew Fitzmaurice, _Humanism and America_ (Cambridge, 2003); Mikael H\u00f6rnqvist, _Machiavelli and Empire_ (Cambridge, 2004); Mikael H\u00f6rnqvist, \"The Two Myths of Civic Humanism,\" in _Renaissance Civic Humanism_ , ed. James Hankins (Cambridge, 2000), 105\u201343.\n\n4 It is important to note, however, that during the nineteenth century \"civilization\" remained a highly fluid concept, lacking specificity and open to various ideological uses. See here: Gerritt Gong, _The Standard of \"Civilization\" in International Society_ (Oxford, 1984); Bruce Mazlish, _Civilization and Its Contents_ (Stanford, 2005); Jennifer Pitts, \"Boundaries of Victorian International Law,\" in _Victorian Visions of Global Order_ , ed. Duncan Bell (Cambridge, 2007), 67\u201389.\n\n5 Most nineteenth-century European thinkers ranked the \"civilized\" powers according to a variety of criteria, usually placing their own society at the peak. See Georgios Varouxakis, \"'Great' versus 'Small' Nations,\" in _Victorian Visions_ , ed. Bell, 136\u201359. Non-Western peoples were also coded in hierarchical terms, often with indigenous Australians placed at the bottom, and the more \"warlike\" of the Indian peoples, as well as the Maoris of New Zealand, accorded a higher position. Some of these peoples were thought to be heading for inevitable extinction. Patrick Brantlinger, _Dark Vanishings_ ; Mark Hickford, \"'Decidedly the Most Interesting Savages on the Globe,'\" _History of Political Thought_ , 27 (2006), 122\u201367.\n\n6 Froude, \"England's War,\" _Fraser's Magazine_ , 1871, reprinted in _Short Studies on Great Subjects_ , 5 vols. (London, 1907) (hereafter _Short Studies_ ), 3:272\u201373.\n\n7 Some variations of this argument also envisaged the eventual creation of regional (and even global) federations. On liberal internationalism, see Jens Bartelson, \"The Trial of Judgement,\" _International Studies Quarterly_ , 39 (1995), 255\u201379; Casper Sylvest, _British Liberal Internationalism, 1880\u20131930_ (Manchester, 2009); and chapter 10.\n\n8 For examples, see the discussion in chapter 2. Notably absent from the recent wave of scholarship on Mill is recognition of the value he placed on (and the arguments he offered for) settler colonization. For correctives, see Katherine Smits, \"John Stuart Mill on the Antipodes,\" _Australian Journal of Politics and History_ , 51 (2008), 1\u201315; and the discussion in chapter 9.\n\n9 Yet it is important to note that while Mill was widely admired, he also had numerous detractors, including self-proclaimed liberals, and his political writings in particular were subjected to sustained attack, both during his lifetime and afterwards. He was not, in other words, a straightforward representative figure of any position. See, for example, Stefan Collini, _Public Moralists_ (Oxford, 1991), esp. chs. 4, 8; Bruce Kinzer, _A Moralist In and Out of Parliament_ (Toronto, 1992).\n\n10 Mill, \"Civilization\" [1836], in _Collected Works_ , 18:117\u201349.\n\n11 From a very early age Mill was exposed to his father's highly influential writings on India, which he seems to have absorbed. For Mill's shifting ideas about race in India, see Zastoupil, _John Stuart Mill and India_.\n\n12 Mill, _On Liberty_ [1859], _Collected Works_ , 18:224.\n\n13 Mill, \"A Few Words on Non-Intervention\" [1859], _Collected Works_ , 21:119. Italics in original. See also Mill, _Considerations on Representative Government_ [1861], _Collected Works_ , 19:566\u201367.\n\n14 Mill, \"A Few Words on Non-Intervention,\" 118.\n\n15 Mill, _A System of Logic_ [1843], _Collected Works_ , 7:861\u201375.\n\n16 This view of development was grounded in an \"associationist\" account of psychology, a view that Mill had inherited from his father. For the most illuminating account of how this was to work in practice, see Mill's account of his own education in his _Autobiography_ (1873).\n\n17 Mill, _On Liberty_ , 224.\n\n18 Mill, _Considerations on Representative Government_ , 416.\n\n19 For examples, see Skinner and van Gelderen, eds., _Republicanism_ ; Eric Nelson, \"Republican Visions,\" in _The Oxford Handbook of Political Theory_ , ed. John Dryzek, Bonnie Honig, and Anne Phillips (Oxford, 2005), 193\u2013211; Iseult Honohan, _Civic Republicanism_ (London, 2002). This section extends my discussion of civic imperialism in Bell, _The Idea of Greater Britain_ , ch. 5.\n\n20 Alice Conklin, _A Mission to Civilize_ (Stanford, 1998), esp. ch. 1. Nor am I employing it to map the history of \"republican\" arguments about freedom and security, as in Daniel Deudney's fascinating, _Bounding Power_ (Princeton, 2007).\n\n21 Mark Bevir, \"Republicanism, Socialism, and Democracy in Britain,\" _Journal of Social History_ , 34 (2000), 351\u201368. For examples, see Eugenio Biagini, \"Neo-Roman Liberalism,\" _History of European Ideas_ , 29 (2003), 55\u201372; Biagini, \"Radicalism and Liberty,\" in Peter Mandler, ed., _Liberty and Authority in Victorian Britain_ (Oxford, 2006), 101\u201325; Duncan Kelly, \"Reforming Republicanism in Nineteenth-Century Britain,\" in _Republicanism in Theory and Practice_ , ed. Iseult Honohan and Jeremy Jennings (London, 2006), 41\u201352; Gregory Claeys, \"The Origins of the Rights of Labor,\" _Journal of Modern History_ , 66 (1994), 249\u201390; and, most influentially, Gareth Stedman Jones, \"Rethinking Chartism,\" in _Languages of Class_ (Cambridge, 1983).\n\n22 Collini, _Public Moralists_ , 108\u201310. See also John Burrow, _Whigs and Liberals_ (Oxford, 1988). Some scholars have pointed to the continuities between Mill's language and that of the civic humanists of the eighteenth century (for example, Burrow, _Whigs and Liberals_ , 85), but this does not refer to his vision of empire.\n\n23 In his highly critical overview of eighteenth-century political thought, Leslie Stephen scoffed that the discourse of the time was comprised of \"generalities about liberty, corruption, and luxury.\" Leslie Stephen, _English Thought in the Eighteenth Century_ (London, 1876), 2:111. Mill made a similar point about Gibbon: \"Carlyle's French Revolution\" (1837), _Collected Works_ , 20:134, 136. On the pervasiveness of the classics in the Victorian era, see Frank Turner, _The Greek Heritage in Victorian Britain_ (New Haven, 1981); and Norman Vance, _The Victorians and Ancient Rome_ (Oxford, 1997).\n\n24 Collini, _Public Moralists_ , 108\u201310.\n\n25 In classical republican thought, the city was often viewed as the most appropriate site of political life. During the nineteenth century the idea of the city was transformed, in the wake of industrialism and the vast growth of urban populations. Cities were reimagined as vast spaces of vice and danger rather than the seedbed of virtue.\n\n26 Moses Finley, \"Colonies\u2014An Attempt at a Typology,\" _Transactions of the Royal Historical Society_ , 5th series, 6 (1976), 173.\n\n27 For an analysis of the wide-ranging eighteenth-century debates over luxury, see Istvan Hont, \"Luxury and Commerce,\" in _The Cambridge History of Eighteenth-Century Political Thought_ , ed. Mark Goldie and Robert Wokler (Cambridge, 2006), 379\u2013419.\n\n28 Edward Salmon, \"The Colonial Empire of 1837,\" _Fortnightly Review_ , 61 (1897), 863.\n\n29 The quotation is from Hugh Egerton, _A Short History of British Colonial Policy_ (London, 1897), 455. Froude concurred: _The Earl of Beaconsfield_ (London, 1890), 238\u201339.\n\n30 Miles Taylor, \"Imperium et Libertas?,\" _Journal of Imperial and Commonwealth History_ , 19 (1991), 1\u201323.\n\n31 Seeley's defense of classical notions of (merit-based) aristocracies, above party intrigue, noble, and acting in the name of the common good, can be seen as a response to this. Seeley, _Stein_ , 3:564; Seeley, _Introduction to Political Science_ , ed. Henry Sidgwick (Cambridge, 1896), 328\u201330.\n\n32 Goldwin Smith, _The Empire_ (London, 1863); Smith, \"The Expansion of England,\" _Contemporary Review_ , 45 (1884), 524\u201340; Smith, \"The Empire,\" in _Essays on Questions of the Day_ [1893], 2nd ed. (New York, 1894), 141\u201395.\n\n33 Vogel, \"Greater or Lesser Britain,\" _Nineteenth Century_ , 1 (1877), 831.\n\n34 On the importance of emigration, see Bell, _The Idea of Greater Britain_ , ch. 2.\n\n35 Wakefield, _A View on the Art of Colonization_ [1849], in _The Collected Works of Edmond Gibbon Wakefield_ , ed. M. F. Lloyd-Prichard (Glasgow, 1968), 837. See also Arthur Mills, _Systematic Colonization_ (London, 1847), 33\u201334.\n\n36 Mill, _Considerations on Representative Government_ , 771\u201372. This was one of the central concerns of the prosecutors of Governor Eyre. See here Rande Kostal, _A Jurisprudence of Power_ (Oxford, 2006); Smits, \"John Stuart Mill on the Antipodes.\"\n\n37 The representation of the colonies in publicity material often drew on classical images of the virtue (and purity) of femininity. Dominic David Alessio, \"Domesticating 'The Heart of the Wild,'\" _Women's History Review_ , 6 (1997), 239\u201369. On the gendering of colonialism, see also Robert Grant, _Representations of British Emigration, Colonisation, and Settlement_ (Basingstoke, 2005), ch. 8.\n\n38 Tocqueville, \"Second Letter on Algeria\" [1837], in _Writings on Empire and Slavery_ , ed. J. Pitts (Baltimore, 2001), 24. Though for a switch in tone and emphasis, see also his \"First Report on Algeria\" [1847], _Writings_ , 146. For a valuable discussion of Tocqueville's thought, which identifies its republican dimensions, see Pitts, _A Turn to Empire_ , chs. 6\u20137.\n\n39 Froude's writings on his brutalized youth ( _Shadows of the Clouds_ , 1847) and the spiritual turmoil of his early adulthood ( _The Nemesis of Faith_ , 1849) provide two of the most psychologically rich explorations of the Victorian crisis of faith. Julia Markus contends that he was the author of the most important pre-Freudian biography (on Jane and Thomas Carlyle) in the English language: Markus, _J. Anthony Froude_ (New York, 2005), 76. Other studies of Froude, none of which make the argument I am pursuing, include Dunn, _James Anthony Froude_ ; A. L. Rowse, _Froude as Historian_ (Gloucester, 1987); and Walter Thompson, _James Anthony Froude on Nation and Empire_ (London, 1998). Since this chapter was originally published, a major new intellectual biography has appeared: Ciaran Brady, _James Anthony Froude_ (Oxford, 2013). In relation to the empire, it is especially good on Ireland and the Caribbean.\n\n40 For his conception of history, see John Burrow, _A Liberal Descent_ (Cambridge, 1981); Jane Garnett, \"Protestant Histories,\" in _Politics and Culture in Victorian Britain_ , ed. Peter Ghosh and Lawrence Goldman (Oxford, 2006), 171\u201392; Rosemary Jann, _The Art and Science of Victorian History_ (Columbus, OH, 1985), 105\u201340; Jeffrey von Arx, _Progress and Pessimism_ (Cambridge, MA, 1985), 173\u2013200. Burrow also notes Froude's reliance on the \"language of Bolingbroke and the eighteenth-century Country Party\" ( _Liberal Descent_ , 282), though he does not make enough of the civic elements of his imperialism. On Froude's largely negative reception among professionalizing historians at the time, see Ian Hesketh, \"Diagnosing Froude's Disease,\" _History and Theory_ , 47 (2008), 373\u201395.\n\n41 Bentley, _Lord Salisbury's World_ (Cambridge, 2001), 225; Burrow, _Liberal Descent_ , Part III; Mandler, _The English National Character_ (London, 2006), ch. 3. Elsewhere, Mandler writes that Froude and Carlyle were \"as close to organic conservatives as British intellectual life gets,\" but that they were ultimately paternalists who believed in the ability of leaders to shape the people \"at will.\" Mandler, \"The Consciousness of Modernity?,\" in _Meanings of Modernity_ , ed. Bernhard Rieger and Martin Daunton (Oxford, 2001), 123. The letter to Stanton cited in note 1 above also indicated Froude's ambivalent attitude towards radicalism and political change during the 1880s: \"The future of Radicalism these days I conceive to be the burning up of rubbish. The grass will spring up again by and by out of the ashes. But the burning process is disagreeable to me however I may see it to be inevitable.\" He also referred to radical reformers as \"indispensable persons\" because they were at the forefront of criticizing corruption and excess luxury in government. Froude, \"Party Politics,\" _Short Studies_ , 4:351 ( _Fraser's Magazine_ , 1874).\n\n42 Froude, _Oceana_ , cited in Dunn, _James Anthony Froude_ , 523\u201324. He uses a similar formulation in \"Party Politics,\" 326\u201327. Froude's _Oceana_ is of course named after James Harrington, _The Commonwealth of Oceana_ (London, 1656).\n\n43 Aside from _Oceana_ , which focused mainly on Australia, the Cape, and New Zealand (as well as the United States), Froude also wrote _The English in the West Indies, or the Bow of Ulysses_ (London, 1888). Pessimistic and deeply racist, this is his most Carlylean book. It focuses more on the degraded state of the British settlers than on \"civilizing\" the nonwhite population. He very briefly mentions that Russia and Britain were both engaged in bringing \"civilization\" to the \"Eastern nations\" in _The Earl of Beaconsfield_ (244), but he did not expand on this issue.\n\n44 Froude, \"England's War,\" 276.\n\n45 Ibid., 274\u201375.\n\n46 Froude, _Oceana_ , 395.\n\n47 Ibid., 2.\n\n48 Froude, \"Reciprocal Duties of State and Subject,\" _Short Studies_ , 3:118\u201320 ( _Fraser's Magazine_ , 1870).\n\n49 Froude, _The Earl of Beaconsfield_ , 189.\n\n50 Ibid., 75\u201376.\n\n51 Froude, \"On Progress,\" _Short Studies_ , 3:173 ( _Fraser's Magazine_ , 1870).\n\n52 Froude, \"Reciprocal Duties of State and Subject,\" 138.\n\n53 Froude, \"England's War,\" 287; Froude, _The Earl of Beaconsfield_ , 189.\n\n54 Froude, \"Party Politics,\" 341.\n\n55 Froude, _Caesar_ (London, 1879), 1. See also Froude, \"Society in Italy in the Last Days of the Roman Republic,\" _Short Studies_ , 5:205.\n\n56 Froude, _Caesar_ , 4, 8.\n\n57 Ibid., 2 (and also 536). Carlyle also held to a cyclical conception of historical time, though his was more violent and destructive than Froude's. See the discussion in Burrow, _Liberal Descent_ , 253. Compare this with Mill's ambiguous view: Mill, _Considerations_ , 388.\n\n58 Froude, _Caesar_ , 3\u20134. \"[T]here are courses of action which have uniformly produced the same results\" (4).\n\n59 Ibid., 257.\n\n60 Froude, \"Divus Caesar\" [1867?], _Short Studies_ , 5:258, 257; Froude, \"Society in Italy,\" 215.\n\n61 Froude, \"Divus Caesar,\" 250, 290. In \"Party Politics,\" Froude wrote that religion leads people \"into a recognition of their higher destiny and of the obligations attaching to it\" (342). In _Caesar_ , he refers to the religion of the Romans as \"the foundation of the laws and rule of personal conduct\" (7). He also writes that: \"The 'virtues' which the Romans made into gods [valor, truth, good faith, modesty, charity and concord] contain in them the essence of real religion, that in them and in nothing else has the characteristic which distinguished human beings from the rest of animated things\" (14).\n\n62 Froude, \"Divus Caesar,\" 283. Froude's most famous discussion of the \"heroic\" virtues amongst his (Elizabethan) countrymen came in his early essay, \"England's Forgotten Worthies,\" _Short Studies_ , vol. 3 [1852].\n\n63 Froude's portrait of the early Romans mirrors his admiring description of Dutch colonists\u2014the \"true colonists\"\u2014in southern Africa. See his speech at Bloemfontein, December 1874, reprinted in Dunn, _Froude_ , 2:414. See also his positive assessment in \"Leaves from a South African Journal,\" 378, 397. Froude was keen to see the Boers and the English settlers confederate. He was sent on a mission by the Colonial Secretary, the Earl of Carnarvon, during 1874\u201375 to investigate this possibility. On this episode, see Dunn, _Froude_ , vol. 2, ch. 26.\n\n64 Froude, \"England and Her Colonies,\" _Short Studies_ , 3:19 ( _Fraser's Magazine_ , 1870).\n\n65 Froude, _Oceana_ , 10. Elsewhere he lamented \"the poisoned atmosphere of our huge and hideous towns.\" Froude, \"England's War,\" 278.\n\n66 Froude, \"England and Her Colonies,\" 21. The same was true, he argued, of the famous commercial cities\u2014Venice, Genoa, Florence: \"Their greatness was founded upon sand.\" See also Froude, \"On Progress,\" 153.\n\n67 There was one difference, however. While the \"Roman capitalists\" filled their lands with slaves, the same was not true of the moderns. While this meant that the specific mechanisms of decline were somewhat different, it did not alter the general picture of freedom being eradicated, and of a dangerous migration to the overcrowded cities. See Froude, _Caesar_ , 7, 8\u20139; and Froude, \"On the Uses of a Landed Gentry,\" _Short Studies_ , 4:310 [1876].\n\n68 Froude, \"The Colonies Once More,\" _Short Studies_ , 3:207 ( _Fraser's Magazine_ , 1870).\n\n69 Froude, \"On Progress,\" 151.\n\n70 Froude, \"Reciprocal Duties,\" 123; Froude, \"On Progress,\" 181.\n\n71 Froude, \"Reciprocal Duties,\" 118.\n\n72 Froude, \"Party Politics,\" 342\u201343.\n\n73 Froude, \"Reciprocal Duties,\" 122.\n\n74 Froude, \"Party Politics,\" 329\u201330.\n\n75 Froude, \"Landed Gentry,\" 312. He frequently criticized aristocracies, past and present, for failing in their duties. In his Rector's address at St. Andrews in 1869, he praised John Knox for challenging an \"unworthy aristocracy.\" \"Education,\" _Short Studies_ , 3:227. He scalded the existing British aristocracy for falling into the grip of luxury and for diverting its attention from the common good. Froude, \"England's War,\" 278; \"Party Politics,\" 356\u201357. _Caesar_ was a harsh indictment of the corruption of the Roman aristocracy.\n\n76 Froude, _Beaconsfield_ , 84, 92, 93. Italics in original. For Froude's assessment of Disraeli's political thought, see 107, 216\u201318. He ultimately remained ambivalent about Disraeli, regarding his years in office as a wasted opportunity (ch. 16).\n\n77 Ibid., 82, 107. The connections between this and the civic humanist vision are not, however, that distant. The key link\u2014at least for Disraeli\u2014was Viscount Bolingbroke, whose _Idea of a Patriot King_ (1838) was a key \"country party\" text (Disraeli, though, stripped much of the radicalism from Bolingbroke's prescriptions). See Richard Faber, _Beaconsfield and Bolingbroke_ (London, 1961); David Armitage, \"A Patriot for Whom?,\" _Journal of British Studies_ , 36 (1997), 397\u2013418. See also the discussion of Victoria as a patriot queen in chapter 6.\n\n78 Froude, \"Cheneys and the House of Russell,\" _Short Studies_ , 5:347\u201348.\n\n79 Ibid., 375. Elsewhere he wrote that in a democracy the state was in danger of being \"reduced finally to the congregation of self-seeking atoms\" (\"Party Politics,\" 356).\n\n80 Froude, _Oceana_ , 91, 354\u201356.\n\n81 Froude, \"England and Her Colonies,\" 29. On the geopolitical necessity of Oceana, see also Froude, \"Party Politics,\" 333\u201334; \"England's War,\" 276.\n\n82 Froude, \"Landed Gentry,\" 319.\n\n83 Froude, \"England's War,\" 282\u201383.\n\n84 Ibid., 283\u201384. The \"wealth of a nation,\" he argued in _Oceana_ , \"depends in the long run upon the conditions mental and bodily of the people of whom it consists, and the experience of all mankind declares that a race of men sound in soul and limb can be bred and reared only in the exercise of plough and spade, in the free air and sunshine, with country enjoyments and amusements, never amidst foul drains and smoke blacks and the eternal clank of machinery\" (8, 246).\n\n85 Froude, _Oceana_ , 15.\n\n86 For Carlyle's views on India, see John Morrow, _Thomas Carlyle_ (London, 2006), chs. 2\u20133.\n\n87 Even on these points, however, tracing a direct line of influence is far from straightforward, for many of them were commonplaces of imperial political discourse.\n\n88 For example: \"I accept without qualification the first principle of our forefathers, that every boy born into the world should be put in the way of maintaining himself in honest independence.\" Froude, \"Education,\" 240, and also, 250\u201351; see also, Froude, \"On Progress,\" 164\u201369, and for his admiring views of the multi-dimensional education (and the \"universal practical accomplishments\") of the Romans, _Caesar_ , 231. On Carlyle's metaphysical view of labor, see Morrow, _Thomas Carlyle_ , chs. 4\u20135.\n\n89 For Carlyle's views, see Carlyle, _Collected Works_ , 6:378; and, in general, K. J. Fielding, \"Carlyle and the Americans,'\" _Carlyle Studies Annual_ , 15 (1995), 55\u201364.\n\n90 Froude, \"Education,\" 249. Indeed he feared that unless they were united with Britain the colonies might seek to join the United States. Froude, \"England and Her Colonies,\" 29\u201330.\nCHAPTER 13\n\nAlter Orbis\n\nE. A. Freeman on Empire and Racial Destiny\n\nWhere there is Empire, there is no brotherhood; where there is brotherhood, there is no Empire.1\n\n\u2014E. A. FREEMAN\n\nFreeman was a celebrated historian in a culture that venerated the historical arts as a privileged source of truth about the human condition. His historical writing was always political; his political thinking always historical. Indeed he once defined history in Aristotelian terms as \"the science of man in his character as a political being.\"2 A scholar of prodigious energy, he pioneered the application of the \"comparative method\" to the study of politics and contributed to a wide range of contemporary debates. He was, that is, an archetypal public moralist. Freeman gave the role two distinctive twists. The first, inspired by Thomas Arnold, stressed the \"unity of history,\" denying any radical break between the ancient and the modern\u2014\"that wretched distinction\"\u2014and emphasizing continuities and \"survivals\" more than rupture and innovation. The \"great truth\" to be discerned from studying the past was that \"history is one,\" that \"every part has a bearing on every other part.\"3 This led him to see events in a deep (and often distorting) historical perspective and to express suspicion of novelty. Freeman's second characteristic move was to underscore the spatial dimensions of political life, contrasting the unity of historical time with the disunity of geographical space, the manner in which different constellations of geology, climate, and territory shaped political institutions, racial character, and individual subjectivities. Indeed he can be seen as an early exponent of geopolitics.4 In combination, these intellectual commitments produced a body of work at once expansive in ambition and attenuated in execution.\n\nOscillating between Burkean gradualism and sentimental radicalism, Freeman was a self-declared searcher after truth and justice, his political activity marked, he claimed, by \"zeal for right against wrong.\" Proud of his devotion to individual and collective freedom, he boasted that he was \"for the oppressed everywhere, whoever may be the oppressor.\"5 While his myopic vision of justice rarely extended beyond the limits of Western Christendom, it nevertheless underpinned his skepticism about imperial order. Unconvinced by the purported benefits of British rule in India and Africa, he was hostile to plans for further imperial expansion and advocated immediate independence for the settler colonies. Yet Freeman was no straightforward \"Little Englander,\" for he defended an alternative model of global racial imperium in which the \"Teutonic\" peoples, and above all \"the English folk,\" would order the world. The English nation, on this account, was an immanent community distributed across North America, Britain, southern Africa, and the South Pacific. Its potential as an agent of progress was undermined by the misguided pursuit of empire. The bonds of \"race\" were more fundamental than those of formal political institutions. \"Surely the burthen of barbaric Empire is at most something that we may school ourselves to endure; the tie of English brotherhood is something that we may rejoice to strive after.\"6\n\nI start by dissecting some of Freeman's arguments about time, space, and politics. The rest of the chapter analyzes his views on racial kinship and empire, focusing initially on his critique of the idea of imperial federation, one of the most prominent political debates of the 1880s and 1890s, before moving to his alternative conceptualization of global order. He argued that dismantling the British settler empire was both a matter of justice and a precondition for establishing the proper sense of racial \"brotherhood\" necessary to realize the higher purpose of the English-speaking peoples. The manifest destiny of the race was thus premised on recognition of the deep unity of Britain and the United States.\n\nPalimpsest: A World of Worlds\n\nOn us a new light has come.7\n\n\u2014E. A. FREEMAN\n\nFreeman once claimed that reading Aristotle taught him the \"power of discerning likenesses and unlikeness, of distinguishing between real and false analogies,\" and that this lesson informed both his historical and political thought.8 Supremely confident in his ability to decipher the palimpsest of human experience, Freeman carved multiple worlds from the historical record, each defined by a specific configuration of territory and social organization, each subject to the perennial forces of expansion, contraction, dispersal, and even annihilation. Populated by civilizations, races, empires, cities, and states, his imaginative geography ranged across different scales, from the local to the planetary, but the practice of worlding\u2014of classifying communities and assigning them meaning in a universal story of human endeavor\u2014was a recurrent theme in his writings. It enabled him to trace patterns of continuity and change across continents and centuries. The privileged role of the historian was to map the fate of worlds and divine salutary lessons from the perpetual cycle of creativity and destruction.\n\nThe most fundamental division was expressed in the \"eternal Eastern Question,\" the millennia-long struggle between East and West. Stretching from \"the opening chapters of Herodotus\" to \"this morning's telegrams,\" it was an epic battle between \"light and darkness, between freedom and bondage,\" an enduring topography of fear and loathing. Originally centered on the Greek conflict against the barbarians, its most recent incarnation was the clash between Christianity and Islam.9 His hatred of the \"Turk\" motivated Freeman's political interventions during the 1850s and 1870s, when he took a lead in campaigning against the depredations of the Ottoman Empire.10 The Ottomans\u2014with the insidious support of the \"Jew\" Disraeli\u2014presented a fundamental threat to the progressive Western world, centered on Teutonic Europe. Blending anti-Semitism with a vitriolic hatred of Islam and the barbarism of \"the Orient,\" Freeman's racism infected his political vision and his historical writing in equal measure.11\n\nFreeman was drawn above all to the ancient Greeks. The rediscovery of classical learning in the fifteenth and sixteenth centuries, he marveled, must have \"been like the discovery of a new sense,\" indeed like the \"discovery of a new world of being, as it opened up the vistas of human knowledge and experience, granting access to the manifold treasures that had been lost from view.\"12 The Hellenic world provided Freeman with a uniquely rich inventory of ideas and institutions to measure all other worlds against, and as we shall see this classicizing gaze undergirded his account of the pathologies of empire and the potentiality of racial kinship. It also shaped his understanding of historical pedagogy. He once wrote that the \"great lesson of history is that the nature of man, or at any rate of civilized European man, is the same in all times and places, and that there is no time or place whose experience may not supply us with some teaching.\"13 Yet some times and places taught the true philosophical historian more than others. By focusing on a great but comprehensible civilization, students and scholars could uncover universal truths about history, politics, and the human condition.14 A microcosm of human experience, the Greek world was a laboratory of enlightenment and political virtue. While Freeman's views can be read as an expression of bathetic nostalgia, he never yearned for a mimetic recreation of the past; rather, the ancient Greek order was a yardstick and a navigation aid, both map and compass, for helping to comprehend his own world.\n\nFreeman regarded the \"comparative method\" as the intellectual polestar of the nineteenth century, a \"new light\" arguably more significant that the Renaissance encounter with the ancients\u2014the illuminator of worlds.15 Scholars such as Max M\u00fcller and Henry Maine provided tools to analyze the Aryan race and its Teutonic heirs through the study of symbols, myths, and above all language. They had demonstrated that unity could be found in difference and that human progress was essentially the story of the Aryans and their offspring. \"Civilization,\" as Maine once declared, \"is nothing more than a name for the old order of the Aryan world, dissolved but perpetually reconstituting itself.\"16 But Freeman thought that more still could be achieved, that enacting the \"true philosophy of history\" required knowledge of the important _institutional_ similarities connecting descendants of the ur-race, and he thus sought to track distinctive \"forms of government\" across time and space\u2014this was the overarching aim of the field he named \"comparative politics.\"17 Chains of racial descent could now be ascertained beneath ephemeral surface phenomena.\n\nLike the revival of learning, it has opened to its votaries a new world, and that one not an isolated world, a world shut up within itself, but a world in which times and tongues and nations which before seemed parted poles asunder, now find each one its own place, its own relation to every other, as members of one common primeval brotherhood.18\n\nHarnessing this dazzling intellectual power necessitated the cultivation of a new scholarly identity. The creation and maintenance of scholarly personae express a form of spirituality, characterized as they are by \"an array of acts of inner self-transformation, of work on the self by the self,\" with the intention of fostering \"an open ended variety of ethical aspirations, psychological deportments, cognitive dispositions, public duties, and private desires.\"19 Freeman's historico-political project is a telling example. To become a true comparative scholar required arduous training in various scholarly arts and the mastery of a vast body of historical knowledge\u2014\"[o]f some branches he must know everything, but of every branch he must know something.\"20 Moreover, it fostered a cognitive disposition to view the sensory output of the everyday with suspicion, allowing the scholar to delineate the fundamental patterns of history and politics. This was a kind of second sight, a trained capacity to identify \"analogies which are to be seen between the political institutions of times and countries most remote from one another\" and in particular where the \"most profitable analogies, the most striking cases of direct derivation, are not those which are most obvious at first sight.\"21 He was exceedingly proud of his mastery of the method, his self-proclaimed ability to perceive the importance of the unfamiliar and the counterintuitive.\n\nThe project of comparativism was predicated on an account of racial descent, the original Aryan ur-people spawning assorted lineal descendants, the most important of which were the Greeks, Romans, and Teutons. These three races\u2014of which the Teutons were the greatest\u2014either had been or were the \"rulers and the teachers of the world.\"22 This was at once their burden and their sacred mission. While M\u00fcller and Maine had focused on the philological, mythical, and cultural connections between them, Freeman traced the descent of \"forms of government,\" including state, monarchy, and representative assembly.23 Whereas the splendor of the Greeks and the Romans lay in the past, the Teutons now stood as the foremost race in the world, with the English their dominant branch. The itinerant English had three homes: their primeval base on the European mainland, their main dwelling in Britain, populated by those who travelled with Hengst in the fifth century, and their newest offshoot in the United States.24 Whether they realized it or not, they were united by the indestructible bonds of kinship.\n\nThe intercalating of geography and politics shaped Freeman's conception of both the possibilities and limitations of British power. He presented Britain as an \"alter orbis,\" another world, due to its island status. This spatial accident was freighted with historical meaning. \"It is the insular character of Britain which has, beyond anything else, made the inhabitants of Britain what they are and the history of Britain what it has been.\"25 Geographical otherness was the most important fact about British history, more significant even than the Norman Conquest. It explained crucial variations between the \"insular\" and the \"continental\" branches of the Teutons, and in particular why the Romans (and romance languages) never fully colonized Britain.26 \"We grew up as a Teutonic people, in some things more purely Teutonic than our kinsfolk of the mainland. For we never accepted the law of Rome, we never saw a roman empire of the English Nation.\"27 Shaped by a fortuitous concatenation of history and physical geography, the liberty-loving character of the English was present wherever they settled, including the United States, that \"newer and vaster England beyond the Oceans.\"28\n\nSpace could be recoded\u2014at least in part\u2014by human agency. Like so many of his contemporaries, Freeman was fascinated by the power of machines to master nature, though rather unusually he thought that this induced a welcome sense of temporal dislocation. Technological prosthetics, above all the electrical telegraph, furnished the recovery of the greatest of Greek political gifts: active citizenship. Freeman followed convention by arguing that small city-states (and their analogues) provided the ideal ground for the creation of political \"character.\" In such communities\u2014with Athens the template\u2014men \"are raised to the highest level and sharpened to the finest point,\" as all citizens had a stake in the life of the society.29 Such social intimacy was impossible to recreate in large communities, but the wondrous products of Victorian technoscience finally allowed people separated by vast distances \"direct personal knowledge\" of political affairs, creating a bond of solidarity between individuals and groups who might never meet face-to-face. For Freeman, always the time-traveler, this meant that it was now possible to replicate the political ethos of the Greeks.\n\nVery few Englishmen ever saw or heard Walpole or Pulteney, Pitt or Fox. Now the whole land has well-nigh become a single city; we see and hear our leading men almost daily; they walk before us as the leaders of the Athenian democracy walked before their fellow-citizens; they take us into their counsels; they appeal to us as their judges; we have in short a share in political life only less direct than the share of the Athenian freeman, a share which our forefathers, even two or three generations back, never dreamed of.30\n\nThose inventions meant that the world of Freeman's fellow subjects was closer to that of Periclean Athens than to their Georgian predecessors. The same technological developments also made it both possible and necessary to harness the power of race and the links of kinship uniting the English-speaking peoples.\n\nThe \"Dark Abyss\": Freeman on Imperial Federation\n\n\"I am no lover of 'empire,'\" Freeman once declared. \"I am not anxious for my country to exercise lordship over other lands, English-speaking or otherwise.\" While such lordship was sometimes a necessary evil\u2014\"a solemn and fearful duty\"\u2014it was never a \"matter for rejoicing or boasting.\"31 His main intervention in imperial debates came during the 1880s and early 1890s, at a time when arguments raged about the possible unification of Britain and its settler colonies. Plans for \"imperial federation\" tended to fall into three categories. Some advocated parliamentary representation for the colonists, others called for the creation of an extra-parliamentary council (or some equivalent institution) to offer nonbinding advice to Parliament on imperial affairs, while the most radical plans envisaged a globe-spanning federal polity. Railing against the \"dark abyss\" of imperial federation, Freeman established himself as one of the most trenchant critics of the project.32\n\nA great admirer of federalism, Freeman was widely regarded as the leading British authority on the subject. He was prone to wax lyrical about its possibilities. _The Federalist_ , he once wrote to Bryce, \"[is] one of the wisest books ever written. I used to call Polybius and it the Old and New Testament on the subject.\"33 He was skeptical, though, that many of his compatriots understood the complexities of the system\u2014\"so few know,\" he complained.34 For a government to be classified as federal, Freeman had argued in his _History of Federal Government_ , it had to meet two conditions: \"On the one hand, each of the members of the Union must be wholly independent in those matters that concern each member only. On the other hand, all must be subject to a common power in those matters which concern the whole body of members collectively.\" An ideal federation, then, \"in its perfect form, is one which forms a single state in its relations to other nations, but which consists of many states with regard to its internal government.\"35 As such, an authentic \"federal commonwealth\" could be seen simultaneously as a state and a collection of states, as singular and plural. It all seemed to depend on the angle of vision. Yet he had been clear that colonies could not be parts of a federal commonwealth, for despite their high degree of internal independence their \"relations towards other nations are determined for [them] by a power over which the Colony nor its citizens have any sort of control.\"36\n\nTo Freeman's fastidious mind \"imperial federation\" could only be interpreted coherently in two senses: the federation of either the whole British empire or the totality of the English-speaking peoples.37 Both were fatally flawed. In the former, the nonwhite population of the Empire would have a huge numerical advantage, which denoted, he wrote to James Bryce, \"a Federation in which we shall be outvoted by Hindoos and Mahometans.\" This entailed the ludicrous conclusion that \"barbarians\" would rule over their racial superiors.38 Encompassing the English-speaking peoples, on the other hand, meant incorporating the independent United States while excluding most of the extant British empire.39 Although this would solve one problem\u2014getting \"rid of the barbarians\"\u2014it was predicated on the fantasy that the US would willingly rejoin the very colonial power against which it had rebelled.40 However, he at least acknowledged the possibility. \"I believe that no-one proposes that the Federation of the English-speaking people shall take in the United States of America; if any one does so propose, I honour him as being more logical than his brethren.\"41 In both cases, Freeman was being disingenuous. Most imperial federalists were explicit about the racial exclusivity of their plans and some did argue for the absorption of the United States.42\n\nHe lambasted imperialists for misunderstanding the true meaning of both federalism and empire. \"On the principle that language was given to man to conceal his thoughts, 'Imperial Federation' is surely the wisest name ever thought of. On any other principle it is surely the most foolish.\"43 Freeman found it hard to believe that any sentient being might support it, and he was astonished when Bryce accepted the Presidency of the Oxford branch of the Imperial Federation League. \"For to me,\" he wrote to his friend, \"Imperial Federation seems to be, not an intelligible proposal which one deems unjust or inexpedient, and therefore argues against, but a mere heap of vague, meaningless, and contradictory phrases.\" The reasoning was simple: \"[W]hat is Imperial cannot be Federal, and what is Federal cannot be Imperial.\"44 Derived from Roman usage, empire had a distinct meaning, \"the rule of some person or power over some other,\" whereas Federation was a system of government that implied \"the unity of certain powers or communities, presumably on equal terms.\"45 The former was premised on political hierarchy, the latter on parity. They were antithetical.\n\nFreeman contrasted the superior Greek model of colonization with the ruinous behavior of post-Renaissance Europeans. In the Hellenic world, political obligation and patriotic loyalty were directed to a fixed space: the city. \"The Greek was before all things a citizen.\" The modern European notion of personal allegiance, a type of feudal fealty that bound individuals to the sovereign, was alien to them: \"The Greek would have regarded himself degraded by the name of 'subject.'\"46 The difference between subjecthood and citizenship determined the modality of colonization, for \"while the active duties of the citizen of a commonwealth can hardly be discharged beyond the territories of that commonwealth, the duties of the subject of... a personal master, are as binding on one part of the earth's surface as on another.\" The Greeks planted free cities populated by free citizens, as Corinth seeded Syracuse.\n\nParent and child were on the political side necessarily parted; the colonist could exercise no political rights in the mother-city, nor did the mother city put forward any claim to be lady and mistress of her distant daughter. Still the love, the reverence, due to a parent was never lacking. The tie of memory, the tie of kindred, the tie of religion, were of themselves so strong that no tie of political allegiance was needed to make them stronger.47\n\nIn contrast, the modern European colonists, including the British, remained bound to their \"mother land\" by formal and subordinate ties of political allegiance.48 Freeman's sympathies were clear: the connections between metropole and colony were the \"brightest facts of Greek or Phoenician political life,\" while those of the modern colonial system were \"among the darkest.\"49 This history of subjection bestowed a dangerous legacy, for when the modern colony sought independence, as it invariably would, the relations between it and the \"mother country\" were often poisoned, as demonstrated by lingering Anglophobia in the United States.50\n\nFreeman suggested that imperial federation would be more theoretically intelligible if it drew on the Roman precedent: absorbing colonies within an expanded state. \"By this process the ruling state gives up nothing; it simply admits others, not so much to its own level as into its own substance.\"51 However, this act of constitutional transubstantiation would mean extending full parliamentary representation to the British settler colonies, an idea that Freeman thought open to a battery of objections. Perhaps the most important \"moral\" taught by Roman history, he argued, was that the quest for empire resulted in the extinction of freedom at home and abroad, with citizens demoted from citizenship to subjecthood.52 But there were also practical difficulties to overcome. Despite the wonders of modern science, the colonial empire was still too geographically dispersed for political unification.53 Moreover, the colonies would be unwilling to cede their _de facto_ autonomy to a federal government dominated by England. \"[S]ubjection, in short, formally abolished, would practically be made more complete.\"54 Many colonial subjects concurred.\n\nSir John Colomb's idea of \"Britannic Confederation\" struck Freeman as the most intellectually credible plan for colonial unity. Its name was not self-contradictory and its scope was clearly specified: a federation of Britain, Australia, Canada, and South Africa.55 Yet it was neither feasible nor desirable. Establishing a durable connection was impossible between geographically fragmented territories bound only by sentimental attachment, especially when that sentiment was directed at the metropole but not each other. Colonial affect was bidirectional not multilateral, and Freeman predicted that this augured badly for the longevity of the empire. He regarded competition between constituent units as a weakness of all federations, but he thought it would be exacerbated in a distended noncontiguous one. Finally, he pointed to the lack of historical precedent for creating such a political association.56 Neither space nor time were on Colomb's side.\n\nMany advocates of imperial federation had failed to grasp the implications of their plans for the fate of Britain itself. Federation, he complained to Bryce, meant \"the degradation, if not the destruction, of England and its institutions,\" chiefly because Parliament would either be abolished or transformed \"into the Legislature of a Canton.\"57 Elsewhere he compared the status of a federated England to that of \"the State of New York or the State of Delaware.\"58 Again, history offered no precedent. Federations were typically instituted when a number of small states banded together against an external threat, but the imperialists proposed to conjoin a dominant state with several weaker entities, and as such \"a great power, an ancient power, a ruling power, is asked to come down from its place, to rank for the future simply as one member alongside its own dependencies, even though most of those dependencies are its own children.\"59 This upset the natural order of things. The lack of precedent carried great epistemological and moral authority. The historian G. W. Prothero once observed that \"if a proposal threatened to change the fundamental character of a thing or an institution, then, for Mr Freeman, it stood condemned.\"60 Such was the case with empire. Absence of a precedent \"does not of itself prove the proposed scheme is either impossible or undesirable,\" he admitted, but it was \"a fact worth bearing in mind,\" and it was always \"dangerous to imagine a precedent where there is none.\"61 Bryce too acknowledged the role of past experience in shaping the political views of his friend. Freeman's reading of the Greeks prompted him to think \"that the relation between the 'metropolis' and her colonies to be one not of political interdependence, but of cordial friendliness and a disposition to render help, nothing more.\"62 The historical record taught colonial independence, not union.\n\nFreeman played a Janus-faced role in the debates over imperial federation, cited as an authority by advocates and opponents alike. Both Sir Frederick Young, enthusiastic unionist and Honorary Secretary of the Royal Colonial Institute, and Francis De Labilliere, one of the most radical federalists, drew inspiration from Freeman's earlier influential work on federalism.63 So too did liberal politician W. E. Forster, the co-President of the Imperial Federation League, who utilized Freeman's account in outlining his own vision of a federal Greater Britain.64 Freeman retorted that Forster was confusing the _Bundesstadt_ , the \"perfect\" type of federation, with the _Staatenbund_ , a much weaker form that was bound to fail, and he attacked those who claimed the colonial empire already constituted a nascent federation.\n\nAll the elements of federation are wanting. There is no voluntary union of independent states, keeping some powers to themselves and granting other powers to a central authority of their own creation. There is instead a number of dependent bodies, to which a central authority older than themselves has been graciously pleased to grant certain powers. This state of things is not federation, but subjection.\n\nThe colonies, indeed, were not \"states\" in the relevant sense, but rather subordinate \"municipalities on a great scale.\"65\n\nWhile he complained that his objections fell on deaf ears, numerous critics deployed Freeman's arguments to bolster their attacks on imperial federation.66 Imperial federalists, meanwhile, often felt the need to respond to him. George Parkin, an energetic Canadian proselytizer, sought to rebut Freeman's argument about the absence of intra-colonial sentiment.67 He also suggested that Freeman's failure to understand imperial federation could be traced to his admission that he knew little about commerce, manufacturing, or agriculture. Praising Freeman for keeping \"faith\" in federalism during the American Civil War, Labilliere \"regretted\" that the great historian had \"written decadently against Imperial Federation\" and questioned the significance of historical precedent. He also denied that imperial federation would damage relations with the United States.68 Others acknowledged the force of Freeman's objections while stressing their limited scope. The journalist W. T. Stead conceded that Freeman was \"quite right in pointing out... [that] Imperial Federation is an absurdity when used by those who are really aiming at the federation of all the English-speaking peoples,\" but insisted that \"this criticism advances the matter very little,\" presumably because such a union wasn't the main object of the debate. \"Against those who have plans and are ready with paper constitutions for an Imperial England,\" wrote Sir Robert Stout, a senior colonial politician, \"Mr Freeman's criticism may hold good,\" but it failed to challenge those \"who strive to prevent separation and who are as yet unable to formulate the new form of government.\"69 Indeed it was a common federalist trope that preaching the general _idea_ of unity was more important than specifying constitutional details. Vagueness, on this account, was a political virtue, albeit not one that Freeman would have acknowledged. Archly characterizing Freeman as a man \"with a keen sense for the political antiquities of political terms,\" the idealist philosopher D. G. Ritchie accepted that imperial federation was an \"absurd\" idea if projected onto historical empires, but he argued that modern political experience demonstrated its feasibility.\n\n[J]ust as representative government was the great political invention of the middle ages, so federation (as distinct from mere leagues or confederacies) is the greatest political invention of modern times. To the Greek philosopher a republican _nation_ would have seemed an impossibility. A federal Empire (like Germany), a federal republic, a federation of self-governing communities with dependencies more or less autocratically governed according to their degree of civilization\u2014all these forms now seem possible to us.70\n\nUltimately, though, Freeman's skepticism was more realistic and support for imperial federation drained away after the turn of the century. But it did not disappear. The leading post-Victorian theorist of imperial union, Lionel Curtis, drew mixed messages from Freeman's work. Writing during the First World War, Curtis embraced Freeman's Teutonism, and borrowed heavily from his account of ancient federalism, to construct a celebratory narrative about \"English\" racial destiny, but he dismissed his criticisms of imperial federation.71 Like Freeman, though, Curtis sought legitimacy in historical precedent, claiming that the principle of \"commonwealth,\" which he regarded as the chief intellectual justification for imperial federation, was itself a product of Teutonic political experience.\n\nOn Racial Solidarity\n\nTo me most certainly the United States did not seem like a foreign country; it was simply England with a difference.72\n\n\u2014E. A. FREEMAN\n\nAlthough skeptical of constitutional models of union, Freeman nevertheless propounded a form of racial \"brotherhood,\" declaiming that true greatness was to be found in the diffusion of the English people(s) across the world. His was one voice among many. While debates between imperial federalists and their critics were heated, the participants often shared more than they were willing to concede, including a commitment to the basic unity and superiority of the \"English-speaking peoples\" (or \"Anglo-Saxons\").73 Their disagreements centered on the best means of realizing this racialized form of global dominion. Thus Goldwin Smith, widely reviled as an anti-imperialist, insisted that he had the \"greatest respect for the aspirations of the Imperial Federationists, and myself most earnestly desire the moral unity of our race and its partnership in achievement and grandeur.\"74 Freeman promoted a similar vision. Racial unity was, he argued, \"a thought higher and dearer than any thought of a British Empire.\"75 Above all, he vested his hopes in the United States, \"brethren in a higher brotherhood, born of one ancient stock, speaking one ancient tongue, sharer under different forms of one ancient freedom.\"76 Race was the basic ontological category of global politics, far more significant than the state, let alone the artificial shell of empire.\n\nPrimed by the \"comparative method\" to recognize \"survivals\" of the Teutonic order, Freeman unsurprisingly found them wherever he looked during his 1882 visit to the United States. He regarded his public lectures as an act of filial persuasion, an attempt to remind Americans that they were part of one great racial family. \"The feeling of unity between the two severed branches is really present in the American breast, but it needs something special to wake it up.\"77 He was happy to serve as an alarm clock. Like many keen on strengthening cooperation with the United States, Freeman sought to defuse lingering Anglophobia, which he interpreted optimistically as a sign of familial intimacy, although he admitted that memory of the War of Independence and of 1812 remained \"a formidable historic barrier\" to reconciliation.78 As it was, the very existence of the British empire circumvented the transformation of sentiment necessary to unlock racial destiny. Not only did the existence of a large \"dependent colony\" (Canada) on the borders of the \"independent colony\" (the United States) stand as a permanent reminder of the historical injustice of British rule, \"inconsistent with the full acknowledgement of the general brotherhood of the English folk,\" but the mixture of dependent and independent polities in the English world meant that suspicion would remain the norm. This quandary could only be resolved by granting independence to the colonies.79 Intra-racial equality was a perquisite for justifying global inequality between races.\n\nIn a lecture delivered in Oxford in 1886 to commemorate the birth of George Washington, he criticized the imperial unionists and outlined an alternative vision. Entitled \"George Washington, the Expander of England,\" the lecture was a provocative riposte to J. R. Seeley's _The Expansion of England_ , the bible of the imperial federation movement. As I discuss in chapter 11, Seeley argued that the true greatness of British history lay in its imperial expansion during the eighteenth and nineteenth centuries rather that in a Whiggish unfolding of liberty, and he promoted the creation of a \"great and solid world-state.\"80 Freeman turned the historical argument on its head, arguing that Washington\u2014rebel and founder\u2014was the real \"Expander of England,\" not the men who had pilfered swathes of South Asia. True expansion meant establishing permanent independent communities, a feat that Washington had achieved through dismembering the British empire.81 The act of rebellion was thus a paradoxical but productive moment in the history of racial \"brotherhood.\"\n\nIn a world thrown into close communion by modern technoscience, it was possible to deepen those racial bonds through replicating the political ideas and ethos of the ancients. \"Geographical distance, political separation, fierce rivalry, cruel warfare, never snapped the enduring tie which bound every Greek to every other Greek. So the Englishman of Britain, of America, of Africa, of Australia, should be each to his distant brother as were the Greek of Massalia, the Greek of Kyr\u00ean\u00ea, and the Greek of Chers\u00f4n.\"82 Misunderstanding the power of affect, the imperial federalists failed to grasp that the \"tie of national brotherhood, the abiding feeling of the oneness of the folk, lives on through physical distance, through political separation, through political rivalry and wasting war.\"83 A heterogeneous assemblage of territories, peoples, and forms of government, \"patched up out of men of every race and speech under the sun,\" the empire failed even to approximate the necessary conditions for successful union. In prioritizing empire over the race-nation they endangered racial unity. He concluded his peroration on Washington by sketching a glorious future:\n\nI shall hardly see the day; but some of you may see it, when the work of Washington and Hamilton may be wrought again without slash or blow, when, alongside the Kingdom of Great Britain and the United States of America, the United States of Australia, the United States of South Africa, the United States of New Zealand, may stand forth as independent homes of Englishmen, bound together by the common tie of brotherhood, and bound by loyal reverence, and by no meaner bond, to the common parent of all.84\n\nHere, then, was a suitable application of federalism to the English-speaking world. Just as communications technologies had transformed the potential scope of citizenship, so they had reanimated federalism, allowing its extension across vast political spaces. \"It is by the help of modern discoveries that the federal systems of old Greece can be reproduced on a gigantic scale, that a single Union of States can embrace a continent stretching from Ocean to Ocean instead of a peninsula stretching from sea to sea.\" The United States exemplified the wonderful possibilities. It demonstrated that federal government was appropriate for uniting territorially contiguous colonial polities, thus fashioning powerful independent states like Australia that would constitute the elements of an immense racial brotherhood.85 But empire itself was of little value. \"The sentiment is possibly unpatriotic,\" Freeman wrote, \"but I cannot help looking on such a friendly union of the English and English-speaking folk as an immeasurably higher object than the maintenance of any so-called British Empire.\"86\n\nAlthough wary of formal political institutions, Freeman hinted at a political technology that could help to fuse the brotherhood: _common citizenship_. \"I have often dreamed,\" he wrote, \"that something like the Greek \u03c3\u03c5\u03bc\u03c0\u03bf\u03bb\u03b9\u03c4\u03b5\u03af\u03b1, a power in the citizens in each country of taking up the citizenship of the other at pleasure, might not be beyond hope; but I have never ventured to dream of more than that.\"87 Although he didn't live to see it, the idea of common citizenship attracted considerable support during the 1890s and beyond, its advocates including Bryce and A. V. Dicey.88 In the early 1890s the industrialist Andrew Carnegie demanded the \"reunion\" of Britain and America. His call resonated widely, feeding the intellectual currents helping to drive the \"rapprochement\" between the two powers. Carnegie commended Freeman's \"wider and nobler patriotism\"\u2014the elevation of race over empire\u2014and he likewise advocated \"a common British-American citizenship\" while calling for the independence of the British settler colonies as a precondition for racial union.89\n\nFreeman's greatest intellectual influence, though, was exercised in the \"western home\" of his beloved English folk. His Teutonist account of the racial foundations of the English-speaking peoples, and his outline of the field of \"comparative politics,\" played a formative role in the development of the human sciences in North America.90 His main disciple was the historian Herbert Baxter Adams, who established a famous \"seminary\" at Johns Hopkins University to train American scholars in the arts of \"historical and political science\"\u2014a veritable laboratory for constructing \"comparativists.\" Alongside Bluntschli and Maine, Freeman was one of its guiding lights, his pithy motto \"history is past politics and politics are present history\" adorning both the wall of the library, where it \"stares every man in the face who enters,\" and the front page of the influential _Johns Hopkins University Studies in Historical and Political Science_.91 During his visit to the United States, Freeman spent time with Adams and his students, lecturing on the \"eternal Eastern question.\"92 Adams hailed the sage: \"He had come to the Western Empire of the English people, which, expanding with the great Teutonic race from local centres, is repeating in the continental island of Atlantis and in the continent of Asia, with Egypt and Ocean between, the experiment of the Roman People upon a grander and nobler scale.\" He also endorsed Freeman's mission to inculcate \"national belief in the civic kinship and religious unity of Britain and America.\"93 Adams considered Freeman \"the founder of our new walls,\" the \"godfather\" of his project. Freeman reciprocated, contributing an article to the first edition of Adams's journal, arguing that local institutions in the United States were expressions of the Teutonic branch of the \"Aryan family.\"94 Contra Freeman, Adams praised the ambition to federate the Teutons, although he also recognized that the solidarity of race was stronger and more enduring than institutions. \"England and the United States will probably never be federated together in that magnificent imperial system which some people in your country are now advocating; but they will always remain one in blood and thought and speech, which are better ties than politics.\"95\n\nFreeman also exerted a powerful spell over the philosopher and historian John Fiske, who was arguably the most widely read Teutonist in the United States.96 \"No student of political development in our time,\" Fiske declared, \"has made more effective use of the comparative method,\" and none had done as much to establish the continuities in transatlantic Teutonic history.97 Fiske even shared Freeman's prejudices, congratulating him for expressing \"very sound and wholesome views of the unspeakable Turk and the Everlasting Eastern Question.\"98 Like many of its adherents, he translated Teutonism into a conservative and racist vision of the present, and it is no coincidence that he served as Honorary President of the Immigration Restriction League, for he believed that the Teutonic greatness of the people was threatened by an influx of racial inferiors. The admiration was returned. Praising Fiske's attempt to trace the Teutonic origins of American history, Freeman lamented that it \"is so strangely hard to get people on either side of the Ocean to take in the simple fact that Englishmen on both sides of the Atlantic are one people.\"99 \"Truly,\" Freeman wrote after reading Fiske's popular _American Political Ideas Viewed from the Standpoint of Universal History_ , \"you preach exactly the same doctrine as I do.\"100 Fiske later dedicated _The Discovery of America_ to Freeman, a \"scholar who inherits the gift of Midas, and turns into gold whatever subject he touches.\"101\n\nNot all American intellectuals were so impressed. Henry Adams, for one, derided Freeman's \"parade of knowledge\" and asserted that he had never written anything \"really solid.\"102 Unsurprisingly, the Teutonic interpretation of American institutions generated fierce criticism. Describing Freeman, Goldwin Smith, Froude, and Matthew Arnold as the most distinguished \"British chauvinists,\" one commentator talked of \"an idea received with enthusiasm by some here in America, with indifference by others, but by a large section of our people by dislike, because it is false and because it is offensive.\"103 The archaeologist Charles Waldstein called it a \"modern version of the old story of national lust for power,\" and dismissed the Saxonist account for its \"pedantic pretensions of its inaccurate ethnological theories,\" while historian H. Morse Stephens labeled it a \"perverted and inaccurate view of the past as a source for political arguments in the present.\"104 While popular during the 1880s and early 1890s, by the turn of the century Teutonism had largely been displaced as the central interpretive framework to understand American political development, though it claimed a dwindling band of enthusiasts deep into the twentieth century. As it sank, so too did Freeman's reputation in the most recent \"home\" of the English.\n\n1 Freeman, \"George Washington, the Expander of England,\" in _Greater Greece and Greater Britain_ (London, 1886), 102.\n\n2 Freeman, \"A Review of My Opinions,\" _The Forum_ (1892), 152; Freeman, _The Methods of Historical Study_ (London, 1886), 117.\n\n3 Freeman, _Comparative Politics_ (London, 1873), 293\u201394.\n\n4 This novelty was acknowledged. C.R.M., \"The Late Professor E. A. Freeman and His Services to Geography,\" _Proceedings of the Royal Geographical Society_ , 14 (1892), 401. Halford Mackinder critiqued Freeman in \"The Geographical Pivot of History,\" _Geographical Journal_ , 23 (1904), 423\u201324.\n\n5 Freeman, \"A Review of My Opinions,\" 150, 157. On this uneasy oscillation, as well as shifts in the emphasis of his thought between the 1860s and 1880s, see Collini, Winch, and Burrow, _That Noble Science of Politics_ , 219\u201326; Burrow, _A Liberal Descent_ (Cambridge, 1981), pt. 3.\n\n6 Freeman, \"George Washington,\" 84.\n\n7 Freeman, \"Unity of History,\" _Comparative Politics_ , 301.\n\n8 Freeman, \"Review,\" 152.\n\n9 Freeman, \"A Review,\" 155, 156. See Vicky Morrisroe, \"'Eastern History with Western Eyes,'\" _Journal of Victorian Culture_ , 16 (2011), 25\u201345; William Kelley, \"Past History and Present Politics,\" in _Making History_ , ed. G. A. Bremner and Jonathan Conlin (Oxford, 2015), 119\u201339.\n\n10 Richard Shannon, _Gladstone and the Bulgarian Agitation, 1876_ (London, 1963), 81, 223\u201330.\n\n11 On Freeman's racism, see the contrasting accounts in Vicky Morrisroe \"'Sanguinary Amusement,'\" _Modern Intellectual History_ , 10 (2013), 27\u201356; Theodore Koditschek, _Liberalism, Imperialism and the Historical Imagination_ (Cambridge, 2011), 240\u201350; Christopher Parker, \"The Failure of Liberal Racialism,\" _Historical Journal_ , 24\/4 (1981), 825\u201346.\n\n12 Freeman, \"Unity of History,\" 297. The downside, he continued, was that it led people to venerate the Greeks and the Romans at the expense of the rest of history.\n\n13 Freeman, \"Greater Greece and Greater Britain,\" _Greater Greece_ , 59.\n\n14 This was a thought that he tried to translate into pedagogical reform: R. N. Berard, \"Edward Augustus Freeman and University Reform in Victorian Oxford,\" _History of Education_ , 9 (1980), 287\u2013301. It is little surprise that one of his main political preoccupations was the fate of modern Greece: \"A Review of My Opinions,\" 148.\n\n15 Freeman, \"Unity of History,\" 301\u20132; Freeman, _Comparative Politics_ , 1, 18. On the \"comparative method,\" see Collini, Winch, and Burrow, _That Noble Science of Politics_ , ch. 7; Sandra den Otter, \"The Origins of a Historical Political Science in Late Victorian and Edwardian Britain,\" in _Modern Political Science_ , ed. Robert Adcock, Mark Bevir, and Shannon Stimson (Princeton, 2007), 66\u201396.\n\n16 Maine, \"The Effects of the Observation of Modern European Thought,\" in _Village Communities in the East and West_ , 3rd ed. (London, 1876), 230.\n\n17 Freeman, _Comparative Politics_ , 33, 19. Maine said that Freeman's lectures on the topic were the most interesting he had ever heard. Maine to Freeman, December 22, 1873, Freeman papers, John Rylands Library, University of Manchester, EAF\/1\/7.\n\n18 Freeman, \"Unity of History,\" 302.\n\n19 Ian Hunter, \"The Persona of the Philosopher and the History of Early Modern Philosophy,\" _Modern Intellectual History_ , 4 (2007), 574. See also the discussion in Duncan Bell, \"Writing the World,\" _International Affairs_ , 85\/1 (2009), 3\u201322, and Joel Isaac, \"Tangled Loops,\" _Modern Intellectual History_ , 6 (2009), 397\u2013424. For the sources of this argument, see especially Pierre Hadot, _Philosophy as a Way of Life_ , trans. M. Chase (Oxford, 1995).\n\n20 Freeman, \"Unity of History,\" 308.\n\n21 Freeman, _Comparative Politics_ , 18, 20. On his understanding of historical \"method,\" see Herman Paul \"'Habits of Thought and Judgment,'\" in _Making History_ , ed. Bremner and Conlin, 273\u201393.\n\n22 Freeman, _Comparative Politics_ , 38.\n\n23 Freeman, _Lectures_ 3\u20135. On Freeman and \"democratic Teutonism,\" see Peter Mandler, _The English National Character_ (London, 2006), 86\u2013105. On Freeman as a \"universal historian,\" see Arnaldo Momigliano, \"Two Types of Universal History,\" _Journal of Modern History_ , 58\/1 (1986), 235\u201346.\n\n24 Freeman, \"The English People in Its Three Homes,\" in _Lectures to American Audiences_ (Philadelphia, 1882), 7\u2013204.\n\n25 Freeman, \"Alter Orbis,\" _Historical Essays_ , 4th series (London, 1892), 221. See also Freeman, _Comparative Politics_ , 47\u201350; Freeman, _The History of the Norman Conquest of England, Its Causes and Its Results_ (London, 1870),1:556.\n\n26 Freeman, \"Alter Orbis,\" 223, 229.\n\n27 Ibid., 234.\n\n28 Ibid., 221\u201322.\n\n29 Freeman, \"Greater Greece,\" 13; Freeman, _History of Federal Government in Greece and Italy_ , ed. J. B. Bury (London, 1893), 29\u201332; Freeman, _Comparative Politics_ , 93\u201397.\n\n30 Freeman, \"Greater Greece,\" 14\u201315.\n\n31 Freeman, \"The Physical and Political Bases of National Unity,\" in _Britannic Confederation_ , ed. Arthur Silva White (London, 1892), 56; Freeman, \"George Washington,\" 90.\n\n32 Freeman, \"The Physical and Political Bases of National Unity,\" 45. On the debates over imperial federation, see Bell, _The Idea of Greater Britain_ , and the chapters in part II of this volume. Freeman's nemesis, J. A. Froude\u2014the subject of chapter 12\u2014was among the most prominent imperial federalists, which may well have stoked Freeman's animosity to the idea.\n\n33 Letter to Bryce, July 10, 1884, _The Life and Letters of Edward A. Freeman_ , 2 vols, ed. W.R.W. Stephens (London, 1895), 2:324.\n\n34 Letter to Bryce, May 22, 1887, _Life and Letters_ , 2:367.\n\n35 Freeman, _History of Federal Government_ (London, 1863), 3, 9. \"It is enough,\" he wrote, \"for a commonwealth to rank... as a true Federation, that the Union is one which preserves to the several members their full internal independence, while it denies to them all separate action in relation to foreign powers\" (15). Criticizing Freeman's definition, Murray Forsyth argues that once a polity is federal it takes on its own state-like properties and cannot be seen in this bifocal manner. Forsyth, _Unions of States_ (Leicester, 1981), 7.\n\n36 Freeman, _History of Federal Government_ , 3, 9, 26.\n\n37 Freeman, \"Imperial Federation,\" 140\u201341.\n\n38 Letter to Bryce, February 7, 1887, _Life and Letters_ , 2:359.\n\n39 Freeman, \"Greater Greece,\" 38\n\n40 Letter to Bryce, February 7, 1887, 359; Freeman, \"Greater Greece,\" 39, 87.\n\n41 Freeman, \"Imperial Federation,\" 141.\n\n42 S. R. Mehrota, \"Imperial Federation and India, 1868\u20131917,\" _Journal of Commonwealth Political Studies_ , 1 (1961), 29\u201340. For American incorporation, see, for example, John Redpath Dougall, \"An Anglo-Saxon Alliance,\" _Contemporary Review_ , 48 (1885), 693\u2013707.\n\n43 Freeman, \"The Physical and Political Bases of National Unity,\" 45.\n\n44 Letter to Bryce, December 16, 1886, 356; Freeman, \"The Physical and Political Bases of National Unity,\" 45. He also dismissed the idea of \"Greater Britain.\" Freeman, \"Greater Greece,\" 1.\n\n45 Freeman, \"The Physical and Political Bases of National Unity,\" 45.\n\n46 Freeman, \"Greater Greece,\" 18, 23; Freeman, \"Imperial Federation,\" 142.\n\n47 Freeman, \"Greater Greece,\" 29.\n\n48 Ibid., 23, 30, 27.\n\n49 Freeman, \"Imperial Federation,\" 121.\n\n50 Freeman, \"Greater Greece,\" 36.\n\n51 Ibid., 55.\n\n52 Freeman, _Comparative Politics_ , 99. On ancient models in imperial thought, see chapter 5.\n\n53 Freeman, \"Greater Greece,\" 56\u201357.\n\n54 Freeman, \"Imperial Federation,\" 125; Freeman, \"The Physical and Political Bases of National Unity,\" 53\u201355.\n\n55 Freeman, \"Political and Physical,\" 49; Colomb, \"A Survey of Existing Conditions,\" in _Britannic Confederation_ , ed. White, 1\u201331. Colomb was a Tory MP and prominent writer on naval affairs.\n\n56 Freeman, \"The Physical and Political Bases of National Unity,\" 52, 53\u201354.\n\n57 Freeman to Bryce, February 7, 1887, 360. See also his letter to Bryce (February 7, 1887), 360, where he picks out Rhode Island. Freeman had consulted A. V. Dicey on the constitutional status of the British colonies. Dicey to Freeman, February 21, 1885, Freeman papers, EAF\/1\/7.\n\n58 Freeman, \"Greater Greece,\" 52; Freeman, \"The Physical and Political Bases of National Unity,\" 55.\n\n59 Freeman, \"Greater Greece,\" 54\u201355; Freeman, \"Imperial Federation,\" 120; Freeman, _Federal Government_ , ch. 2.\n\n60 Prothero, _English Historical Review_ , 8 (1893), 385. Casper Sylvest, _British Liberal Internationalism, 1880\u20131930_ (Manchester, 2009), emphasizes Freeman's influence on Bryce. See also H. A.L. _Fisher, James Bryce_ (London, 1927), 1:113\u201314, 2:308\u20139.\n\n61 Freeman, \"Imperial Federation,\" 122.\n\n62 Bryce, \"Edward Augustus Freeman,\" _English Historical Review_ , 7 (1892), 502.\n\n63 Young, _On the Political Relations of Mother Countries and Colonies_ (London, 1883), 22; de Labilliere, _Federal Britain_ (London, 1894), 94\u201395.\n\n64 Forster, _Our Colonial Empire_ (Edinburgh, 1875), 31; Forster, _Imperial Federation_ (London, 1885), 1. See also James Stanley Little, _The United States of Britain_ (Guilford, 1887), 17.\n\n65 Freeman, \"Imperial Federation,\" 114, 117, 118\u201319.\n\n66 Letter to Bryce, February 7, 1887, 360. For examples, see: P. Glynn, _Great Britain and Its Colonies_ (Adelaide, 1892), 3; Anon., \"Greater Greece and Greater Britain,\" _Spectator_ , September 18, 1886, 15; E. Burton, \"Federation and Pseudo-Federation,\" _Law Quarterly Review_ , 5 (1889), 176; Alpheus Henry Snow, \"Neutralization versus Imperialism,\" _American Journal of International Law_ , 2:3 (1908), 569\u201370; G. W. Wilton, \"Solidarity without Federation,\" pts. 1 and 2, _Juridical Review_ , 4 (1892), 317\u201334; 5 (1893), 248\u201362.\n\n67 Parkin, _Imperial Federation_ (London, 1892), 40\u201343, 44n. See also, E. T. Stuart-Linton, _The Problem of Empire Governance_ (London, 1912), 60\u201361. For other responses, see H. Mortimer-Franklyn, _The Unit of Imperial Federation_ (London, 1887), 20, 24, 32, 41, 60; _Imperial Federation League in Canada_ (Montreal, 1885), 28; [Urquart Forbes], \"Imperial Federation,\" _London Quarterly Review_ , 4 (1885), 325\u201326.\n\n68 Labilliere, _Federal Britain_ , 89n1, 206\u20137, 213.\n\n69 Stead, _Review of Reviews_ , 4\/20 (1891), 164; Stout, \"A Colonial View of Imperial Federation,\" _Nineteenth Century_ , 21 (1887), 356.\n\n70 Ritchie, \"War and Peace,\" _International Journal of Ethics_ , 11 (1901), 152.\n\n71 Curtis, _The Commonwealth of Nations_ (London, 1916), ch. 2 (on Teutonism) and pp. 227\u201330, 594\u201395 (for criticism of Freeman). Curtis was the chief ideologue of the Round Table movement.\n\n72 Freeman, _Some Impressions of the United States_ (London, 1883), 10.\n\n73 Freeman rejected the designation \"Anglo-Saxon,\" largely on etymological grounds (Lectures, 38\u201367).\n\n74 Smith, \"Straining the Silken Thread,\" _Macmillan's Magazine_ , 58 (1888), 242.\n\n75 Freeman, _Some Impressions of the United States_ , 16.\n\n76 Freeman, _Lectures to American Audiences_ , 10.\n\n77 Freeman, _Some Impressions of the United States_ , 19. For an account of his trip, see Conlin, \"The Consolations of Amero-Teutonism,\" in _Making History_ , ed. Bremner and Conlin, 101\u201319.\n\n78 Freeman, _Some Impressions of the United States_ , 7\u20139, 21.\n\n79 Ibid., 23, 24.\n\n80 Freeman, \"George Washington,\" 66; Seeley, _The Expansion of England_ , 169, 75.\n\n81 Freeman, \"George Washington,\" 89, 69\u201370. A quarter of a century later, an American scholar was still praising the lecture: \"[T]he English historian was right, and the title was correct.\" Edwin Mead, \"The United States as a World Power,\" _Advocate of Peace_ , 75 (1913), 58.\n\n82 Freeman, _Some Impressions of the United States_ , 24.\n\n83 Freeman, \"George Washington,\" 72. See also Freeman, _Comparative Politics_ , 82\u201385.\n\n84 Freeman, \"George Washington,\" 102\u20133.\n\n85 Freeman, \"Greater Greece,\" 16. See also Freeman, _Federal Government_ , 4, 86\u201387.\n\n86 Freeman, \"Imperial Federation,\" 143.\n\n87 Ibid., 142. In a letter to Goldwin Smith, August 19, 1888, _Life and Letters_ , 2:384, he summarized the idea as the \"taking up of citizenship at pleasure\u2014between Great Britain, United States of America, United States of Australia, and so on.\"\n\n88 Bryce, \"The Essential Unity of England and America,\" _Atlantic Monthly_ , 82 (1898), 29; Dicey, \"A Common Citizenship for the English Race,\" _Contemporary Review_ , 71 (1897), 457\u201376. For an analysis of the idea, see Duncan Bell, \"Beyond the Sovereign State,\" _Political Studies_ , 62 (2014), 418\u201334.\n\n89 Carnegie, _The Reunion of Britain and America_ (Edinburgh, 1893), 22, 10. On Carnegie, see Duncan Bell, \"Race, Utopia, Perpetual Peace,\" in _Intellectual Histories of American Foreign Policy_ , ed. Jean-Francis Drolet and James Dunkerley (forthcoming).\n\n90 Anthony Brundage and Richard Cosgrove, _The Great Tradition_ (Stanford, 2007), 34\u201342; Dorothy Ross, _The Origins of American Social Science_ (Cambridge, 1991), 68\u201373; James Farr, \"The Historical Science(s) of Politics,\" in _Modern Political Science_ , ed. Adcock, Bevir, and Stimson, 66\u201396. On the role of the seminary at Johns Hopkins, see Robert Adcock, _Liberalism and the Emergence of American Political Science_ (Oxford, 2014), ch. 5. Freeman's Saxonism was also influential in Australia. Marilyn Lake and Henry Reynolds, _Drawing the Global Colour Line_ (Cambridge, 2008), 50\u201352.\n\n91 Adams to Freeman, July 10, 1883, Freeman papers, EAF\/1\/7. Freeman called the motto a \"chance proverb.\" \"A Review of My Opinions,\" 157. See also Adams, \"Is History Past Politics?,\" _Johns Hopkins University Studies_ , 13 (1895), 67\u201370. Following Adams's death in 1901 the motto was removed, symbolizing the shifting fortunes of the Teutonic thesis.\n\n92 Adams, \"Mr. Freeman's Visit to Baltimore,\" _Johns Hopkins University Studies_ , 1\/1 (1882), 10. On why Freeman's work\u2014and his historical method\u2014should play a central role in American education, see Adams, _The Study of History in American Colleges and Universities_ (Washington, 1887).\n\n93 Adams, \"Mr. Freeman's Visit to Baltimore,\" 11.\n\n94 Adams to Freeman, January 12, 1885, June 9, 1882, and December 25, 1882, Freeman papers, EAF\/1\/7; Freeman, \"An Introduction to American Institutional History,\" _Johns Hopkins University Studies_ , 1\/1 (1882), 13.\n\n95 Adams to Freeman, September 5, 1884, Freeman papers, EAF\/1\/7.\n\n96 Fiske, _American Political Ideas Viewed from the Standpoint of Universal History_ (Boston, 1885).\n\n97 Fiske, \"Edward Augustus Freeman,\" in _A Century of Science and Other Essays_ (Boston, 1899), 268.\n\n98 Ibid., 275.\n\n99 Freeman to Fiske, August 9, 1889, in John Spencer Clark, _The Life and Letters of John Fiske_ (Boston, 1917), 414.\n\n100 Freeman to Fiske, November 10, 1889, in _Life and Letters_ , 415.\n\n101 Fiske, _The Discovery of America_ , 2 vols. (Boston, 1892).\n\n102 W. C. Ford, _The Letters of Henry Adams_ (New York, 1930), 1:236.\n\n103 John Fleming, \"Are We Anglo-Saxon?,\" _North American Review_ , 153 (1891), 253.\n\n104 Waldstein, \"The English-Speaking Brotherhood,\" _North American Review_ , 167 (1898), 227; Stephens, \"Nationality and History,\" _American Historical Review_ , 21\/2 (1916), 227.\nCHAPTER 14\n\nDemocracy and Empire\n\nJ. A. Hobson, L. T. Hobhouse, and the Crisis of Liberalism\n\nWhat would the new century bring?\" At the close of the nineteenth century, according to Jay Winter, most European and American writers, politicians, and artists were sanguine about the coming era: \"[I]maginings of the twentieth century celebrated progress on a global scale and projected it optimistically into the foreseeable future.\" Although dark prognostications were penned by H. G. Wells and Joseph Conrad, among others, it was confidence that triumphed.1 Winter may be correct about the general tenor of literary and artistic life, but many of those in Britain concerned with the future of geopolitics were deeply anxious. Threats appeared to emanate from multiple directions, at home and abroad. British global power was being challenged: foreboding abounded.2 Thinkers across the political spectrum grappled incessantly with questions about the past, present, and future of world order.\n\nIn this chapter, I explore how two of the leading social and political thinkers in _fin de si\u00e8cle_ Britain\u2014J. A. Hobson (1858\u20131940) and L. T. Hobhouse (1864\u20131929)\u2014viewed the prospects for international affairs in the decade and a half before the outbreak of the First World War. A self-described \"economic heretic,\" Hobson was and is best known as the author of _Imperialism: A Study_ (1902), arguably one of the most influential political tracts of the twentieth century.3 Hobhouse, meanwhile, was trained as a philosopher, held the first chair in sociology in Britain, and quickly made a name for himself as an innovative political theorist. Both men were political radicals, pivotal in the emergence of the \"new liberalism.\"4 Both were public moralists, combining scholarship with abundant political campaigning and popular writing. And both wrote widely on international and imperial affairs. Their work provides a revealing insight into how reflective liberals thought about the future of world order as a new century dawned.\n\nHobson and Hobhouse have drawn considerable scholarly interest, and in what follows I do not attempt an exhaustive analysis of their political thought.5 Rather, I outline some of the key issues shaping political thought at the time, and then explore how Hobhouse and Hobson conceived of the relationship between democracy, empire, and international politics. I focus on two main themes, neither of which has received sufficient attention. First, I highlight how they figured themselves within narratives charting the evolution of liberal thought and practice, allowing them simultaneously to pay homage to their predecessors while carving out a space for the new liberal project. Second, I discuss their writings about the settler colonies in Australia, Canada, and New Zealand. Their accounts of colonialism undermine neat distinctions between \"domestic,\" \"international,\" and \"imperial\" politics and political theory. For Hobson and Hobhouse, as well as for many of their contemporaries, the colonies exhibited characteristics of all three: constitutive elements of the empire, they were nevertheless semi-autonomous states purportedly composed of people of the same nationality and race as the inhabitants of the United Kingdom. According to this perspective, the British colonial empire could be viewed as an embryonic intermediary institution occupying the space between the territorially delimited modern state and an all-encompassing world state. Grounded in and bound by the cultural singularity of the \"British race,\" it promised, if understood properly, to unite colonial communities scattered across the planet, creating a vast polity that would maintain or expand British geopolitical strength while acting simultaneously as an agent of global progress. This was the apotheosis of British imperial ambition.\n\nConfronting Modernity\n\nBritish international thought at the turn of the twentieth century was structured by a wide variety of assumptions and preoccupations, some old, others new. It is productive to interpret many of the thinkers in this period as wrestling with the politics of modernity\u2014as confronting, that is, a world that seemed to be undergoing a period of intense and rapid transition in which many of the existing categories and concerns of politics were being transformed, even revolutionized.6\n\nFirst, as I have stressed throughout this book, technology was radically altering the way in which individuals perceived the physical world. New sociopolitical possibilities\u2014new horizons of expectation\u2014were opened up as a result.7 From the 1860s onward, the electrical telegraph, which promised instantaneous global communication, spawned fantasies about the elimination of geographical distance, the \"annihilation of time and space,\" that prefigure late twentieth-century accounts of globalization.8 Vast ocean liners, the motorcar, and the airplane all reinforced this belief during the two decades straddling 1900.9 Yet the political conclusions drawn from these changes were indeterminate. Many saw technological developments as facilitating, even necessitating, the construction of institutions and modes of politics that in the past would have seemed the stuff of dreams. But to others, they were potentially threatening, intensifying the dangers of competition and conflict.10\n\nThis cognitive shift reinforced the sense that Britain's global position was under threat. The dominance of the mid-Victorian years, when the country was thought of as the \"workshop of the world,\" was superseded by a period of anxiety and tension, especially from the 1880s onward. The \"age of equipoise,\" of stability, prosperity, and untrammelled optimism, had come to an end.11 An economic depression bit deeply. The post-Civil War dynamism of the United States, the rise of Germany at the heart of Europe and of Russia at the periphery, and, in the early Edwardian years, the emergence of Japan as a formidable force in Asia, seemed to augur the end of British hegemony. A new geopolitical constellation was materializing. This was felt keenly throughout the British intellectual and political elite.\n\nPolitical thought in Britain, meanwhile, was in a state of transitional flux. As I discuss in chapter 3, liberalism was being revised and reformulated by a new generation of thinkers, Hobson and Hobhouse prominent among them. The emergence of the \"new liberalism\" pointed many liberals in a social democratic direction, eschewing the perceived atomism of an older generation of reformers and focusing instead on the value of an interventionist state and on questions of social justice. In this their arguments overlapped, and sometimes fused, with those made by socialists, who since the 1880s had become an increasingly significant force in British political culture, terrifying many conservatives while expanding the space of political debate. British international thought was dominated, though far from exhausted, by forms of liberal internationalism. Liberal internationalists insisted on both the possibility and the moral necessity of progressive change in the structures and norms of world order. They sought to tame, even to eliminate, conflict while intensifying cooperation between \"civilized\" states, chiefly through the powers of international commerce and international law.12 The question of empire, however, divided the new liberals as it had the old. It was also a point of contention among socialist writers.13 Although some thinkers argued that empire was inimical to progress, for others it was, if enacted properly, a virtuous agent of it. The contest for the souls of liberalism and socialism was mirrored in a diverse array of visions of global order.\n\nDuring the closing decades of the century, democracy came to play a central role in debates over domestic and global politics. For much of the nineteenth century, mass democracy in Britain was a liberal aspiration and a conservative nightmare, its possible impact predicted but not yet felt. America acted as a model\u2014often mediated through the writings of Alexis de Tocqueville\u2014for this new form of politics, but it was far from clear how it would function in a European context. The Reform Bills of 1867 and, above all, 1886 were seen by many, despite their manifold limitations\u2014not least the failure to enfranchise women\u2014to initiate a democratic age. Yet a general sense of disillusionment with the realization of democracy and its failure to live up to expectations soon set in. The relationship between democracy and empire, which came to a head during the South African War (1899\u20131902), became a touchstone for debates over the future of liberalism and world politics.\n\nIn light of these various challenges, many commentators came to regard federalism as an answer to the political perplexities of the modern age. In a world undergoing profound changes, institutional technologies that could reconcile unity with difference were eminently desirable. Federalism seemed to fit the bill. It was prescribed for local, regional, imperial, and global politics. Although federalism had often been floated as a possible answer to the internecine warfare of European politics, it had rarely been considered a realistic option for governing on a global scale. At the end of the nineteenth century, as the world itself seemed to shrink, this skepticism receded. In Britain, debate raged about the potential unification of the settler colonies into an \"imperial federation,\" a vast polity stretching across the face of the earth. The possibilities for international organization were reshaped. Federalism joined democracy as an object of desire, confusion, and endless debate. All of this helped to fuel an ever-increasing fascination with the past, present, and future of the United States.\n\nFinally, this was a period marked by a growing tension between specialist and expert knowledge.14 Intellectuals increasingly had to negotiate between appealing to an ever-expanding public hungry for information (and entertainment) and the imperatives of a rapidly professionalizing academic world. At the same time, universities were being transformed by the development of new disciplinary fields constituted by professional norms that derided, and institutional structures that hampered, existing models of knowledge production.15 Such pressures were reinforced by the emergence of a global news service that helped to expand the geographical scope of the \"public.\"16 These shifts complicated the role of the \"public moralist,\" for it became progressively more difficult to satisfy the conflicting demands of multiple audiences. Some managed to navigate the terrain, including Hobhouse and Hobson, but it was treacherously difficult.\n\nHobson and Hobhouse were both contributors to, and shaped by, these various political and intellectual trends. They addressed questions that many of their contemporaries were puzzling over and in doing so they drew on a wide range of existing intellectual resources. But they were also important agents in structuring the terms of those debates, outlining arguments that were to play a significant role in fashioning the political thinking of their age.\n\nHobhouse and the Ironies of Liberal History\n\nIn 1901\u20131902, Hobhouse published a series of hard-hitting essays in the liberal weekly the _Speaker_. These were republished, in amended form, as _Democracy and Reaction_ (1904). His central message was clear: in recent years, Britain had entered a period of \"reaction\" that infected most aspects of public life and threatened to undermine the progress that had characterized the previous century. \"The nineteenth century,\" Hobhouse wrote later, \"might be called the age of Liberalism, yet its close saw the fortunes of that great movement brought to their lowest ebb.\"17 This reaction, which manifested itself most obviously in the war in South Africa, demanded a reconsideration of the limits of and opportunities for progressive politics. In his writings between the turn of the century and the First World War, Hobhouse meditated on the ironies of history, the unintended effects of success, and the failures of judgment that had befallen him and his colleagues.\n\nHe identified two main problems infecting British political life. First, the victorious march of liberalism had helped to seed its nemesis, its triumph paving the way for its supersession. In this dialectical movement, progress was potentially, although not necessarily, self-undermining. The key to this historical tragedy could be found in the recent history of the empire, and in particular the settlement colonies. Second, the historical self-understanding of the new liberals had contributed to the growth of reaction by failing to grasp the similarities between the old and the new liberalism.\n\nLiberals, Hobhouse observed, were only very rarely opposed to all aspects of empire. Historically, they had denigrated the \"old colonial system,\" but this was often conjoined with support for the establishment of settler colonies, which were seen as pioneer outposts of civilization. Indeed, the phenomenal growth of the settler colonies during the nineteenth century, from minor appendages of the imperial order to large self-governing political communities, was attributable chiefly to the ideas and energy of the Benthamite radicals. \"Paradoxical as it may seem,\" Hobhouse argued, \"the new conception of empire had its roots, politically speaking, in the older Liberalism.\" Cloaked in the language of progress and freedom, the new imperialism was thus powerfully \"seductive\" to the \"modern liberal.\"18 Looking to the settler colonies, they thought that \"the problem of reconciling Empire with liberty had been solved.\"\n\nUnder this mild sway each component State of the Empire enjoyed full internal self-government, and yet the whole had advantages which small free States cannot claim. Over a great area of the world there was, it seemed, peace; there was the machinery for adjusting disputes between different parts, should such disputes arise; and there was the consciousness of a wider fraternity, of a vaster common heritage, than the citizens of any small community, however proud, could enjoy. In all of this taken in full sincerity, there was much to appeal to Liberals, little to repel them.19\n\nYet the seduction was dangerous. Some liberals, he observed later, were becoming \"imperialists in their sleep.\" Falling for the rhetoric, they ignored the squalid reality\u2014a form of dissonance that could be applied to numerous liberal advocates of empire, then and now. This was an acute failure of moral and political judgment, for a political theory \"must be judged not only by its profession but by its fruits.\"20 And the fruits of the new imperialism were strange indeed. \"Under the reign of Imperialism the temple of Janus is never closed. Blood never ceases to run. The voice of the mourner is never hushed.\"21 Imperialism, for Hobhouse, was antithetical to liberalism properly understood. The \"central principle\" of the former was self-government; that of the latter, the \"subordination of self-government to Empire.\" They were impossible to reconcile. Those liberals who had supported imperialism, above all in South Africa, had fallen into a trap, and were now committed to an incoherent set of beliefs. \"The trap laid for Liberals in particular consisted in this\u2014that they were asked to give in their adhesion to Imperialism as representing admiration for an Empire which more and more has been shaped upon Liberal lines. Having given their assent, they were insensibly led on to the other meaning of Imperialism\u2014a meaning which, for all practical purposes, these principles set aside.\"22 Liberal success in reshaping the colonial empire in the second half of the century, then, had dulled the senses of many liberals, anesthetizing them against the profoundly antiliberal character of modern imperialism.\n\nThe second problem was a function of the historical understanding and intellectual self-fashioning of the new liberals. Hobhouse argued that they had erred badly in traducing their immediate predecessors, ignoring their strengths while exaggerating their weaknesses. To mark their distance from the _laissez-faire_ liberals of the mid-Victorian years, the new generation had glossed over the points of similarity, the connections in \"spirit and intention\" that linked them. \"The old individualism was standing in our way and we were for cutting it down.\"23 The consequences of this act of youthful rebellion were deeply regrettable, for in their rush to fell the old liberalism, the new liberals had inadvertently aided their reactionary adversaries. \"The socialist development of Liberalism paved the way for Imperialism by diminishing the credit of the school which had stood most for the doctrines of liberty, fair dealing, and forbearance in international affairs.\"24 In _Democracy and Reaction_ , Hobhouse lavished praise on Cobden for his assiduous defense of freedom and his sustained anti-imperialism. In his classic volume _Liberalism_ (1911), he went much further, sketching a historical narrative that charted, albeit briefly and in rather vague terms, the origins and trajectory of liberalism. This account identified the \"old liberalism\" as a necessary step in the evolution of liberal political thought and practice.25 On this view, liberal history had largely comprised a \"negative\" account in which liberals fought against the excessive and unjust powers of state and church.\n\nThus Liberalism appears first as a criticism, sometimes even as a destructive and revolutionary criticism. Its negative aspect is for centuries foremost. Its business seems not to be so much to build up as to tear down, to remove obstacles which block human progress, rather than to point out the positive goal of endeavour or fashion the fabric of civilization. It finds humanity oppressed, and would set it free. It finds a people groaning under arbitrary rule, a nation in bondage to a conquering race, industrial enterprise obstructed by social privileges or crippled by taxation, and it offers relief.26\n\nThe closing years of the century had witnessed the emergence of a more constructive form of liberalism, marked by greater attention to questions of economic inequality, social justice, and the positive role of state intervention. It is arguable that Hobhouse's narration of liberal history was, at least in part, a belated response to his perception of the failures of liberals to recognize the continuities in their own tradition. And as I suggested in Chapter 3, it played an important role in the reimaging of the liberal tradition that took place during the Edwardian years.\n\nHobhouse viewed the relationship between old and new liberal views on international affairs through the same prism. Whereas the old liberalism had prescribed strict adherence to the doctrine of nonintervention and skepticism about international entanglements, the \"positive\" dimension of the new liberalism, adapted for a democratic age, necessitated instead the creation of powerful international institutions.27 Although the means differed, the ends remained the same: peace and cooperation in world politics. And the enemies of this vision remained the same also: the imperialists. The tragedy of the situation was palpable. Although Hobhouse deplored the avarice and violence found throughout the British empire\u2014he focused repeatedly on the issue of racial injustice, without wholly escaping many of the racialized assumptions of his age\u2014he was primarily concerned with the destruction wrought on British society and politics. In this, he followed in a long line of radical critics of empire, from Bentham and Constant through to Cobden, Spencer, and beyond. Above all, he feared that the imperialist reaction \"paralysed democratic effort at home.\"28 Imperialism, that is, threatened to undermine Britain from within, infecting both political institutions and public morality. Like Constant, writing nearly a century beforehand, Hobhouse worried that the corruption of political discourse\u2014triggered above all by the disingenuous recourse to justifying imperial aggression in terms of honor, glory, and national defense\u2014was as dangerous as imperial policy itself. It was, Hobhouse averred, perhaps more corrupting than \"the unblushing denial of right.\"29 The spirit of conquest was malevolently intoxicating.\n\nDemocracy had failed to live up to its promise. The period of reaction had confounded the commonplaces of political prophecy. \"Both the friends and enemies of democracy,\" he noted, had previously \"inclined to the belief that when the people came into power there would be a time of rapid and radical domestic change combined in all probability with peace abroad.\" Democracy was supposed to usher in a new world order, yet the democratic state had been slow to reform, and its people had been enthusiastic supporters of the unjust war in South Africa. Moreover, the \"humanitarian sentiment\" that had shaped much of nineteenth-century British politics was being eroded. Humanitarianism was concerned \"not merely with the direct alleviation of suffering and prevention of cruelty, but with the removal of fetters, the opening of opportunity to individual and national self-development, the utilisation of vastly increased material resources for the common benefit, the bringing in of the humblest to the banquet of civilisation.\"30 It was a constituent element of the emergent liberalism. The corrosion of humanitarianism was caused by a number of factors, but above all Hobhouse emphasized the role played by mistaken understandings of evolutionary biology and the rise of philosophical idealism, both of which he thought legitimated a potentially authoritarian account of the state. This latter worry became an increasing fixation, reaching its peak in his polemical attack on _The Metaphysical Theory of the State_ (1918). The combination of German metaphysics and notions of the \"survival of the fittest\" meant the naturalization of might over right, the validation of selfishness and aggression in politics.\n\nYet rather than dismiss evolution and democracy as fatally flawed, Hobhouse defended specific articulations of each of them. His general philosophy was grounded in an account of \"orthogenic\" evolution.31 As an essentially ethical process, he affirmed, evolution was capable of rational human control; its end result and index was cooperation, not conflict. It served as an antidote to brute competition, not its justification. The political implications of this vision were obvious. Progress was defined by increasing cooperation between individuals in society and between different societies. The logical conclusion was a form of global institution that simultaneously entrenched political and economic interdependence while fostering particularity, and especially nationality, which Hobhouse, in common with many liberals, regarded as a progressive force in world politics.32 Imperial federation, as we shall see, offered him a microcosmic variant of this ambitious project.\n\nDemocracy, properly understood, was both an agent and a _telos_ of progress. Democracy and imperialism, he argued, were opposed in principle: \"Democracy is government of the people by itself. Imperialism is government of one people by another.\" But although the theory of democracy was clear on the matter, Hobhouse wondered whether modern political and economic developments had rendered it obsolete. He focused in particular on the issue of scale. Was democracy impossible in a world of vast states? To answer this question, he delineated two conceptions of democracy: _direct participation_ and _popular sovereignty_. On the former view, democracy implied \"a direct participation of the masses of ordinary citizens in the public life of the commonwealth.\" This was an ideal that had nearly been realized in \"the great assemblies and large popular juries\" of ancient Athens. It meant that ordinary citizens were entrusted with complex public functions, despite having little appropriate training or expertise. The modern way to neutralize this tendency was the creation of a bureaucracy, a disinterested technocratic civil service. Popular sovereignty, on the other hand, implied that the people constituted the only legitimate source of authority, which was achieved in practice through the institutions of representative government and through free and full public discussion.33 \"Given these conditions, on the one hand the recognised supremacy of the law which it makes, on the other hand perfect freedom to inform itself and make itself heard, democracy in the sense of ultimate popular sovereignty, is not necessarily incompatible with vastness of territory or complexity of interests.\" But this alone did not eliminate the conjoined problems of scale and complexity, for local differences threatened to undermine the unity, and thus the viability, of modern political communities. Centrifugal forces challenged their \"democratic character.\"34\n\nFederalism presented the best answer to the conundrum. Although the United States offered the world the main example of \"strict federalism,\" there were other forms available. For example, the British colonial empire was linked by what Hobhouse characterized as a \"loose, informal quasi-Federalism,\" in which the \"development of internal autonomy for each separate part is the means of reconciling democracy with empire.\" Although he recognized the potential friction that might arise between the claims of a united colonial empire and the nationalist aspirations of the individual colonies, he nevertheless argued that democracy, federalism, and empire (not imperialism) were theoretically compatible, and that this compound was partly, if precariously, realized in the British colonial system. \"Democracy,\" he argued, \"may be compatible with Empire in the sense of a great aggregation of territories enjoying internal independence while united by some common bond, but it is necessarily hostile to Empire in the sense of a system wherein one community imposes its will on others no less entitled by race, education, and capacity to govern themselves.\" This was to distinguish between progressive and reactionary forms of imperial government, those that were on the right side of history from those that held it back. He concluded by arguing that whatever its fate in the British colonial context, federalism, \"as the natural means whereby over large areas unity can be reconciled with the conditions of popular government,\" had a bright future.35 This argument aligned Hobhouse with the numerous proponents of imperial federation, who had been campaigning actively on behalf of the ideal since the late 1870s. Imperial federation was a vague term, identifying plans that ranged from the moderate\u2014simply reinforcing existing ties between Britain and its colonies\u2014to the truly audacious\u2014including the creation of a globe-spanning racial-national state ruled by directly elected representatives sitting in a new imperial senate in London. However, the very vagueness of the project, or at least its elasticity, was also part of its strength, for it allowed individuals and groups, often with different agendas, to form a broad coalition to pressure the government over the direction of British foreign and imperial policy.\n\nIn an earlier article reviewing _Imperialism_ , Hobhouse praised the imperial federal project outlined by Hobson\u2014to which I will return later\u2014although his endorsement was qualified. \"It is true,\" he wrote, \"that a democratic Empire, or let us say a democratic world State, might be conceived as a possibility,\" but, he continued, such a \"state could only be built up by Federation, probably by a complex system of Federation within Federation, and it would rest not on the annihilation, but in the peaceful development of nationality.\"36 Once again, and more forcefully than Hobson, Hobhouse insisted on the need to reconcile nationality and imperial federation. If the correct balance could be struck between demands for national autonomy and the centralizing tendencies of an overarching political structure, imperial federation would be a normatively desirable objective. Returning to the issue in _Liberalism_ , Hobhouse sketched a powerful, albeit highly abstract, argument for the viability, even necessity, of imperial federation. A united British colonial empire could act as both a model for the future and a possible agent of global transformation. Modes of international organization had to adapt to a changing world. \"Physically the world is rapidly becoming one,\" he argued, \"and its unity must ultimately be reflected in political institutions.\" In this quasi-determinist account, new technologies were modifying the conditions of both political possibility and of necessity. These developments were generated by, and further helped to generate, the orthogenic evolution of mind. The result was the simultaneous growth of support for the principle of nationality and a challenge to traditional conceptions of state sovereignty. The \"old doctrine\" of \"absolute sovereignty\" was \"absolutely dead.\" The largest modern states, continued Hobhouse, \"exhibit a complex system of government within government, authority limited by authority, and the world-state of the not-impossible future must be based on a free national self-direction as full and satisfying as that enjoyed by Canada and Australia within the British Empire at this moment.\"37 Here the British colonies acted as the vanguard of a democratic future, harbingers of a global polity to come. The fate of the indigenous populations of these \"free\" states was not considered worthy of attention.\n\nAlthough liberalism was antithetical to the \"imperial idea,\" it was fully alive to the forces that bound the colonies together, that is, \"to the sentiment of unity pervading its white population, to all the possibilities involved in the bare fact that a fourth part of the human race recognizes one flag and one supreme authority.\"38 This raised an important challenge for the new liberals. Because the colonial communities were the most democratic in the world, their union with Britain was often viewed as a force for progress, and as such it was considered imperative that the empire was not left to the reactionary imperialists. It was therefore vital \"to devise means for the more concrete and living expression of this sentiment without impairing the rights of self-government on which it depends.\"39 This was a difficult balancing act. As a first step, he proposed the creation of an Imperial Council to coordinate relationships between the colonial states, although he failed to offer any details about how it might work. This move would constitute, he implied, an initial step toward a deeper union, a union that would help to bind together, and give institutional expression to, the \"sentiments\" of the English-speaking peoples. \"Such a union is no menace to the world's peace or to the cause of freedom. On the contrary, as a natural outgrowth of a common sentiment, it is one of the steps towards a wider unity which involves no backstroke against the ideal of self-government. It is a model, and that on no mean scale, of the International State.\"40 Like many thinkers of his generation, Hobhouse saw a dual challenge. Not only was it vital to calibrate relationships with the colonies, it was simultaneously important to deepen the connection with \"the other great commonwealth of the English-speaking people,\" namely, the United States. If the democratic peoples of the Anglo-Saxon race could be aligned, then progress could be secured.\n\nFor Hobhouse, then, _imperialism_ , understood as the aggressive foreign expansion of the state, offered a dangerous challenge to the progressive development of humanity. It was the ultimate manifestation of reaction, antithetical to democratic theory and practice. But _empire_ , if regarded as a political vehicle uniting the colonial communities, was not only compatible with democracy, it could help to bring about the democratization of the international system through strengthening the bonds, moral and political, that linked the various Anglo-Saxon communities scattered across the earth. History had come full circle. Although the success of liberalism had helped to spawn the period of reaction, the rise of imperialism in turn triggered the revival of liberalism, waking many\u2014though not all\u2014liberals from their slumber. In the preface to the second edition of _Democracy and Reaction_ , published in 1909, Hobhouse identified the span of the period of reaction as 1880 to 1902, although it had antecedents and \"some currents\" were \"still flowing.\"41 In _Liberalism_ , published two years later, he identified the key turning point as Campbell-Bannerman's famous speech delivered in 1901 on the \"methods of barbarism\" employed by the British in South Africa.42 \"Liberalism,\" he concluded, \"has passed through its Slough of Despond, and in the give and take of ideas with Socialism, has learnt, and taught, more than one lesson.\"43 It seemed that Minerva's owl had flown: the period of reaction could only be comprehended at the moment it drew to a close.\n\nHobson and the Crisis of Liberalism\n\nWhen Hobson came to reflect on _The Crisis of Liberalism_ in 1909, his analysis dovetailed neatly with that of Hobhouse.44 He sketched, albeit in less detail and with less finesse, a grim account of recent political and intellectual developments. Liberals, he argued, had \"shown defects of vision and of purpose,\" with the result that for \"over a quarter of a century Liberalism has wandered in this valley of indecision, halting, weak, vacillating, divided, and concessive.\" Hobson sought to anatomize and correct this drift.\n\nLike Hobhouse, Hobson thought that liberals were engaged in a bitter conflict with the forces of reaction. He maintained that the Tories controlled the press, the political machinery, the city, the church, the armed services, and even the sporting establishment.45 Yet he remained optimistic, interpreting the intensity of the conservative reaction as a sign of the popularity and power of new liberal ideas. In characteristic radical style, he distinguished the people from the elites who ruled (and manipulated) them, placing his hope in the progressive potential of the former. The vitality of the new liberalism was demonstrated above all by the fact that the \"vested interests\" defended their class privileges by appeals to reason and justice; they were forced, that is, to use the terms of their opponents. This appeal took two main forms. First, they denied the existence of (structural) social and economic problems, focusing instead on \"individual moralization\" as the engine of progress. This was an attempt to neutralize demands for systemic social reform. Second, they tried to \"foster the combative competitive instincts of the lower nature of man by urging the necessity and utility of industrial competition with other States.\" They legitimated brutal competition through a combination of misapplied biological arguments, which led to politics being conceived of as a \"struggle for life,\" and the \"authoritative conservatism of Hegelian dogmas.\"46 The overlap with Hobhouse is clear.\n\n_The Crisis of Liberalism_ was Hobson's call to arms, an attempt to inject fighting spirit into the liberals by reorienting their priorities. The new liberalism, he argued, stood for an assault on monopolies and \"unearned property.\" To achieve this, it demanded a \"new conception of the functions of the State,\" and a reinterpretation of the meaning of, and the conditions necessary for securing, individual liberty.47 Like Hobhouse, Hobson also sought to embed the new liberalism in a developmental history of liberal thought and practice. This historical emplotment allowed him to argue that although the older individualist liberalism was in many respects obsolete, it nevertheless contained important truths that should not be jettisoned. Principles always needed to be adapted to contemporary conditions. \"Each new generation of liberals will be required to translate a new set of needs and aspirations into facts.\" It also meant that time was of the essence; reaction had to be defeated before it was too late. \"This is the last chance for English Liberalism.\"48 Hobson stressed two points. First, that the older liberalism had never been as etiolated as both its critics and its heirs proclaimed. \"The negative conception of liberalism, as a definite mission for the removal of certain political and economic shackles upon personal liberty, is not merely philosophically defective,\" he contended, \"but historically false.\" Liberals had never been committed to a radically atomistic individualism. Although he aimed to save the older liberals from the condescension of posterity, he nevertheless criticized their arguments, maintaining that the \"old Radicalism\" had been \"crippled\" by \"positive hostility to public methods of cooperation,\" and had placed \"an excessive emphasis upon the aspect of liberty which consists in the absence of restraint, as compared with the other aspect which consists in presence of opportunity.\"49 Second, he identified the continuities between the old and the new, which centered on the value assigned to individual liberty. In seeking the \"fuller realization of individual liberty contained in the provision of equal opportunities for self-development,\" 50 the new liberals could be seen as completing the historical mission inaugurated by their predecessors.\n\nAgain like Hobhouse, he argued that liberal weakness and indecision had encouraged the enemies of liberalism, facilitating their assaults on its core achievements in politics and social policy. Above all, he lamented that imperialism, the \"great arch-enemy of the age,\" had \"found a too facile entrance among the ranks of her dejected followers.\" Its popularity, then, was partly a function of liberal vacillation and loss of confidence. Imperialism, he continued, had been exploited by the conservatives to derail projects for reform, and it served as a natural ally for economic protectionism.51 In a perverse turn of events, liberals were thus colluding in the destruction of their own creed and the overturning of their historical achievements. Few of Hobson's readers were likely to be surprised by this diagnosis. He was, after all, well known as the author of _Imperialism: A Study_ (1902), a coruscating attack on the \"new imperialism\" being practiced by the United States, Germany, France, and, above all, the United Kingdom. This volume had followed in quick succession from two earlier books, both based on his experiences as a correspondent for the _Manchester Guardian_ during the South African War.52\n\nDuring the first few years of his career, Hobson had been a fairly conventional supporter of the liberal imperial mission to civilize, only transmuting into a new liberal thinker, and avowed enemy of imperialism, in the early 1890s. Yet this transition was never complete, and pronounced traces of his earlier views remained. His political thinking selectively combined elements of Fabian thought, Spencer's political sociology of industrial modernization, utilitarianism, positivism ultimately derived from the writings of Auguste Comte, and Ruskin's conception of organic economic society.53 By the late 1890s, he became convinced that the \"new\" imperialism, unfolding mainly in Africa and Asia, represented an overriding danger to British democracy. It threatened \"peace, economy, reform, and popular self-government,\" catalyzing instead militarism, reaction, and jingoism.54 _Imperialism_ presented a multicausal explanation for the emergence of the \"earth hunger\" that had gripped the imperial powers since roughly 1870. Its \"leading characteristic\" was competition between great capitalist empires.55\n\nThe main stimulus was investment. Oversaving among capitalists and underconsumption by the masses meant that the rich could not invest their money profitably in the domestic market. In search of a high rate of return, they pushed for the opening of foreign markets, which in turn required territorial acquisitions. This system benefitted the few\u2014chiefly financiers and their allies in the political establishment\u2014at the expense of the many. The \"business interests of the nation as a whole are subordinated to those of certain sectional interests that usurp control of the national resources and use them for their private gain.\"56 Employing a common radical trope, he argued that imperialism was \"irrational from the standpoint of the whole nation,\" although \"it is rational enough from the standpoint of certain classes in the nation.\" Using various forms of manipulation and misleading propaganda, this profit-driven imperialism was disguised as necessary government policy; it was a \"calculating, greedy type of Machiavellianism\" wrapped in the evocative language of \"national destiny\" and the spread of \"civilization.\"57 Like Hobhouse, he warned against the corrupting effects of disingenuous language.\n\nEmpire was not the problem, only its malignant forms. Hobson never gave up on the idea that higher civilization bestowed rights on some states or peoples to override the claims to self-determination of others. He also offered a strong defense of the value of settler colonization, insisting on the \"radical distinction between genuine colonialism and Imperialism.\"58 An advocate of imperial federation, he once sketched out an ambitious outline of the future of international organization in which vast federations, each rooted in \"common blood, language, and institutions,\" dominated, and helped to pacify, world politics.\n\nHolding, as we must, that any reasonable security for good order and civilization in the world implies the growing application of the federation principle in international politics, it will appear only natural that the earlier steps in such a process should take the form of unions of States most closely related by ties of common blood, language, and institutions, and that a phase of federated Britain or Anglo-Saxondom, Pan-Teutonism, Pan-Slavism, and Pan-Latinism might supervene upon the phase already reached... Christendom thus laid out in a few great federal empires, each with a retinue of uncivilized dependencies, seems to me the most legitimate development of present tendencies and one which would offer the best hope of permanent peace on an assured basis of inter-Imperialism.59\n\nImperial federation would also derail the aggressive ambitions of the rapidly expanding colonies. Hobson worried that the colonies were in danger of turning into semi-autonomous imperial powers, seeking to dominate the \"lower races\" in their regions and dragging Britain into hazardous entanglements with other powerful states. The threat was the same as in the \"mother country\": the influence of local cohorts of financiers pushing for market expansion and plotting the \"subversion of honest, self-developing democracy.\"60 On this account, empires bred other empires, as the will to dominate and exploit spread from the \"mother country\" to its imperial outposts like a virus.\n\nIn a book long remembered as a model of anti-imperialism, Hobson unambiguously defended the benefits of imperial federation and the civilizing potential of global Anglo-Saxon power. However, over the course of the next few years, his views on imperial federation shifted, and by the time he came to publish _The Crisis of Liberalism_ , he had lost his earlier enthusiasm for the project. Indeed, he poured scorn on those who professed support for it\u2014while conveniently failing to mention his earlier advocacy. \"Those British imperialists who with the events of the last few years before their eyes, still imagine a closer Imperial federation in any shape or form practicable, are merely the dupes of a Kiplingesque sentimentalism.\"61\n\nWhat spurred his change of heart? Part of the answer lies in Hobson's changing views on the practical effects of federalism and the dynamics of colonial development. When he turned to discussing the postwar situation in South Africa, he noted that much support for the union of South Africa, which was to be achieved in 1910, emanated from those (notably Carnarvon and Chamberlain) who had long sought a \"larger federation, or other reconstitution of the self-governing sections of the British Empire.\" They had assumed that the federation of South Africa would be a step on the road to imperial federation, a vanguard that heralded wider transformation of the imperial system. Hobson doubted this logic, arguing that federation and state consolidation in Australia, Canada, and South Africa made imperial federation _less_ feasible, for as the colonies have \"grown in size and strength, they have increasingly asserted their larger rights of independent government.\" National federation acted as a centrifugal force, reducing the likelihood of the wider imperial federal project acquiring sufficient support among the newly emboldened colonists. The leaders of the colonies would not think it in their national interest to federate with the \"mother country.\" Contrary to popular belief, moreover, the links between the colonies and Britain were growing weaker despite the \"greater physical accessibility\" facilitated by new communications and transport technologies and that space-eliminating instrument of modern capitalism, the \"great machinery of modern investment.\"62 These were outweighed by countervailing tendencies demanding increased national autonomy. Such skepticism about the transformative powers of technology highlights the political indeterminacy of technological change.\n\nIn the movement of Joseph Chamberlain's ideas, Hobson divined the direction of imperial federalist discourse, and above all the shift from arguments propounding political federation to those focusing on economic unity. \"Mr Chamberlain,\" he wrote, \"soon saw that the front-door of political federation was shut, bolted and barred. He thereupon sought the tradesman's entrance, claiming to knit the colonies and the mother country into an indissoluble union by means of a set of preferences which he hoped might eventually give free trade within the Empire.\" But, Hobson continued, this new project was also doomed to fail\u2014it was \"futile\"\u2014and for the same reasons: the perceived national interests of the colonial states.63 As such, the only possible mechanism for drawing the empire together was imperial defense. Here too he was skeptical. In particular, he turned his attention to the hollowness of imperial rhetoric:\n\nIt might well appear a profitable and glorious task to co-operate in the protection of a \"free, tolerant, unaggressive Empire.\" But it is not equally glorious or profitable to enter a confederation under which a necessarily dominant partner can claim his blood and money to help hold down India, to quell some struggles for liberty in Egypt, or to procure some further step in the tropical aggrandisement at the bidding of some mining or rubber syndicate.64\n\nAlthough this was a powerful critique from the perspective of a metropolitan new liberal, it was not convincing in its own terms. As Hobson lamented in _Imperialism_ , the colonies themselves claimed a right to engage in their own imperial activities. Indeed, one of the reasons that he had originally defended imperial federation was that he thought it would limit their expansionist ambitions. He concluded his dissection of imperial federation with the summary claim that \"no abiding unity can be found for an Empire half autocratic and half self-governing.\"65\n\nA further reason for the unacknowledged switch lies in Hobson's interpretation of the nefarious role of Chamberlain. Although in the 1890s Hobson had been a cautious admirer of Chamberlain, he soon came to associate him with the forces of imperialist reaction, above all in South Africa.66 This was made all the worse by Chamberlain's early political radicalism; his subsequent trajectory was a gross act of betrayal. The tariff reform campaign, launched by Chamberlain in 1903, was the final nail in the coffin for Hobson.67 He was also confronted with empirical evidence that challenged the feasibility of any constitutional scheme for imperial federation. During 1905, Hobson traveled around Canada, writing reports for the _Daily Chronicle_ , which he soon turned into a short book. Two main themes ran through it: the increasing \"Americanization\" of Canada and the failings of protectionism as an economic policy. Canada, he argued, was undergoing a profound transformation. Following the lead of its southern neighbor, its people were displaying boundless optimism; the country was \"conscious, vocally, uproariously conscious, that her day has come.\" Despite the professed anti-Americanism he discerned among many of its elite, Canada was also becoming more American. The food, the architecture, the economic infrastructure, even the accents and physical dispositions of the people: all were more American than British. Average Canadians, he proclaimed, \"are American through and through,\" although they retained a substantial residue of Britishness. \"In fact,\" Hobson concluded, \"Canada presents as yet a sub-American variety of civilization, though in some ways rapidly assimilating to the States.\"68 He maintained that Canada's destiny was bound up with increasing economic interaction with the United States. Imperial federation, which was based on an assumption about the cultural unity of the global British diaspora, would find it extremely difficult to flower in this environment.\n\nCanada was also gaining a sense of national unity, drawing the distinct interests and peoples of the country together. \"Every visitor to Canada is powerfully impressed by a growing conscious spirit of nationality,\" a spirit that was bound to \"find expression in demands for even larger liberty than is enjoyed now.\" This further undermined schemes for imperial federation. Despite widespread sentimental attachment to the British empire\u2014Hobson discerned little enthusiasm for complete independence\u2014he contended that \"it would not be possible to devise, even in general terms, any scheme of Imperial federation to which the most pro-British group of Canadians would assent when they understood what it implied.\" This was a consequence of both national consciousness and democratic development. Canadians were not prepared to lose \"one jot of the power of self-government\" or shut themselves off from \"any further degree of independence to which they may aspire in the future.\" Yet this is exactly what any serious federal scheme would involve. \"For, either an Imperial Council would be an amiable farce, or it would be a real political body, capable of committing the peoples of the Colonies to some course of action, involving pecuniary and military obligations, and directing, at any rate, their foreign policy.\" The idea that a \"democratic country\" like Canada would \"hand powers over to some Privy Council committee\" was, he thought, \"preposterous.\" Democratic sentiment heralded the death knell for federalist dreams\u2014a diagnosis that was largely accurate. The future for Canada lay elsewhere: \"Canada is not staying as she was: both in sentiment and in practical policy she is moving along the road towards national independence, either within or outside the Empire.\"69 Whereas imperial federation had once seemed an appealing prospect\u2014and there is no reason to think that he changed his mind on the abstract arguments in its favor\u2014it had now been rendered obsolete by a combination of political developments. Not only was it less feasible than before, it had also been hijacked by the forces of reaction. Hobson clearly agreed with Hobhouse's injunction to take the \"fruits\" as well as the intentions of political theories seriously.\n\nYet despite his disavowal of formal schemes for imperial federation, Hobson did not give up on the civilizing potential of empire. The problem with contemporary imperialism, he argued, was its lack of accountability and the fact that it was often pursued for self-interested motives. The \"radical moral defect of Imperialism,\" he contended, \"is due to lack of any true sanction from a society of nations to the interference of an imperialist nation with the life of a lower people.\" This implied that if such sanctions could be enacted, then it would be possible to distinguish morally corrupt from just forms of imperial governance. Indeed, he looked forward to a paternalist form of multilateral imperialism, the legitimacy of which could be secured through the collaboration of a variety of \"civilized\" states.\n\nIf there existed a fairly developed form of international society, in which all peoples, great and small, were in some sense represented, and such a society delegated England or France in the interests of civilisation to take under her tutelage some backward or degraded people which lay on their borders, maintaining order, developing the natural resources of the country, and helping to teach the arts of civilisation, this would afford some moral basis for Imperialism. Actual imperialism differs widely from this condition.70\n\nIn a move that prefigures the arguments of many late twentieth-century liberal imperialists, and arguably some of the most powerful norms of the post-1945 international order, Hobson defended a vision of a benevolent multinational civilizing imperialism.\n\nConclusions\n\nIn the wake of the war in South Africa, a war that divided British liberals like no other, Hobson and Hobhouse set out a penetrating autocritique of the recent failings of liberalism and offered an alternative vision for the future. They focused their critical energies on the purported enemies of liberalism: neo-Hegelian philosophy, misapplied notions of evolution, and vested class interests. But they also addressed the failings of liberalism in general, and the new liberals in particular. These failings were both practical and cognitive. Liberalism had been a successful force during the nineteenth century, but it had grown weak and divided, hamstrung by the moral and political limits of the older liberalism and by the failure of the new liberals to recognize the powerful intellectual resources bequeathed by their predecessors. Liberalism, that is, had been partially undermined by the careless way in which its history had been narrated and absorbed by the new liberals. Hobson and Hobhouse sought to rectify this failure of historical judgment by offering an alternative account of development, one that simultaneously allowed them to praise the virtues and the foresight of the earlier liberals while insisting that new conditions meant that it was essential to adopt new arguments\u2014to at once acknowledge and redirect the legacy of their forebears. In doing so, they provide an early example of what would become common practice as the twentieth century wore on: the writing and rewriting of the \"liberal tradition,\" with a canon of great thinkers at its core. This had been largely absent in prominent nineteenth-century constructions of liberalism.\n\nEmpire played a central, although ambivalent, role in their political projects. Initially both Hobson and Hobhouse supported the federation of the British colonies, arguing that it could harness unity and diversity within a single political organization and provide an institutional foundation for further progress in international politics. It had the potential to become a democratic new liberal polity stretched across the globe. During the Edwardian years, however, Hobson changed his mind. He came to regard imperial federation as both impractical and reactionary. Hobhouse, meanwhile, appeared to strengthen his support for the idea, although he rarely engaged with concrete details. Their shifting arguments about empire exemplified the deep ambiguity of liberal visions of global order at the turn of the twentieth century.\n\n1 Winter, _Dreams of Peace and Freedom_ (London, 2006), 11.\n\n2 This sense of foreboding found literary expression in a genre of fiction imaging future wars: I. F. Clarke, _Voices Prophesying War_ , 2nd ed. (Oxford, 1992); Charles Gannon, _Rumors of War and Infernal Machines_ (Liverpool, 2005), chs. 1\u20134. Some of the stories are reprinted in I. F. Clarke, ed., _The Tale of the Next Great War, 1871\u20131914_ (Liverpool, 1995).\n\n3 Hobson, _Imperialism_ (London, 1902). His autobiography was entitled _Confessions of an Economic Heretic_ (London, 1938).\n\n4 See, for example, Peter Clarke, _Liberals and Social Democrats_ (Cambridge, 1978); Michael Freeden, _The New Liberalism_ (Oxford, 1978); Aviral Simhony and David Weinstein, eds., _The New Liberalism_ (Cambridge, 2001).\n\n5 Stefan Collini, _Liberalism and Sociology_ (Cambridge, 1979); Peter Cain, _Hobson and Imperialism_ (Oxford, 2002); Michael Freeden, ed., _Reappraising J. A. Hobson_ (London, 1990); Jules Townshend, _J. A. Hobson_ (Manchester, 1990); David Long, _Towards a New Liberal Internationalism_ (Cambridge, 1995); David Weinstein, \"Consequentialist Cosmopolitanism,\" in _Victorian Visions of Global Order_ , ed. Duncan Bell (Cambridge, 2007), 267\u201391.\n\n6 I pursue this line of argument in more detail in Bell, \"Dreaming the Future,\" in _The American Experiment and the Idea of Democracy in British Culture, 1776\u20131914_ , ed. Ella Dzelzainis and Ruth Livesey (Aldershot, 2013), 197\u2013210. For the connotations of modernity in Britain, see Martin Daunton and Bernhard Rieger, eds., _Meanings of Modernity_ (Oxford, 2001).\n\n7 On \"horizons of expectation,\" see Reinhard Koselleck, _Futures Past_ , trans. Keith Tribe (Cambridge, MA, 1985).\n\n8 In general, see Stephen Kern, _The Culture of Time and Space, 1880\u20131914_ (Cambridge, MA, 1983); on how this affected views of global order, see Bell, _The Idea of Greater Britain_ , ch. 3; Jo-Ann Pemberton, _Global Metaphors_ (London, 2001).\n\n9 Bernhard Rieger, _Technology and the Culture of Modernity in Britain and Germany, 1890\u20131945_ (Cambridge, 2005).\n\n10 The language of competition was also fueled by the popularity of evolutionary arguments, although they too were politically indeterminate. Mike Hawkins, _Social Darwinism in European and American Thought, 1860\u20131945_ (Cambridge, 1997); Paul Crook, _Darwinism, War and History_ (Cambridge, 1994).\n\n11 W. L. Burn, _The Age of Equipoise_ (London, 1964); Martin Hewitt, ed., _An Age of Equipoise?_ (Aldershot, 2000).\n\n12 For further discussion of liberal internationalism, see chapter 10.\n\n13 Gregory Claeys, _Imperial Sceptics_ , ch. 3.\n\n14 See, in general, Martin Daunton, ed., _The Organisation of Knowledge in Victorian Britain_ (Oxford, 2005); Amanda Anderson and Joseph Valente, eds., _Disciplinarity at the Fin de Si\u00e8cle_ (Princeton, 2002).\n\n15 Collini, Winch, and Burrow, _That Noble Science of Politics_ ; Robert Adcock, Mark Bevir, and Shannon Stimson, eds., _Modern Political Science_ (Princeton, 2007), chs. 1\u20136.\n\n16 See, for example, Simon Potter, _News and the British World_ (Oxford, 2003). On the perceived shift in the scope of the public, see chapter 7.\n\n17 Hobhouse, _Liberalism_ [1911], ed. J. Meadowcroft (Cambridge, 1994), 103.\n\n18 Hobhouse, _Democracy and Reaction_ [1904], ed. Peter Clarke (Brighton, 1972), 18. On Bentham's views, see Philip Schofield, _Utility and Democracy_ (Oxford, 2006), ch. 7; Jennifer Pitts, _A Turn to Empire_ (Princeton, 2005), ch. 4. On utilitarianism, see Bart Schultz and Georgios Varouxakis, eds., _Utilitarianism and Empire_ (Oxford, 2005).\n\n19 Hobhouse, _Democracy and Reaction_ , 24\u201325.\n\n20 Ibid., 107, 28.\n\n21 Ibid., 28.\n\n22 Ibid., 48. One definition of imperialism that he offered was \"the doctrine of racial ascendency and territorial aggression.\" Hobhouse, \"The Growth of Imperialism,\" _Speaker_ , January 25, 1902, 474. This conception of the empire spawned the view, upheld by \"Lord Milner and Mr. Rhodes,\" that it comprised a \"great gold-producing machine.\"\n\n23 Hobhouse, _Democracy and Reaction_ , 11, 210.\n\n24 Ibid., 12. For a spirited defense of classical liberalism against the charges leveled by the new liberals (among others), see Goldwin Smith, \"The Manchester School,\" _Contemporary Review_ , 67 (1895), 377\u201390.\n\n25 _Liberalism_ was once described by C. Wright Mills as the \"best twentieth-century statement of Liberal ideals.\" Mills, _The Marxists_ (Harmondsworth, 1963), 25n. On Cobden, see Peter Cain, \"Capitalism, War, and Internationalism in the Thought of Richard Cobden,\" _British Journal of International Studies_ , 5 (1979), 229\u201345; Claeys, _Imperial Sceptics_ , ch. 2.\n\n26 Hobhouse, _Liberalism_ , 8.\n\n27 See Casper Sylvest, _British Liberal Internationalism_ (Manchester, 2009), on the difference between \"moral\" and \"institutional\" conceptions of progress in international politics.\n\n28 Hobhouse, _Democracy and Reaction_ , 49.\n\n29 Ibid., 29. Constant, \"The Spirit of Conquest and Usurpation and Their Relation to European Civilization\" [1814], in _Political Writings_ , ed. B. Fontana (Cambridge, 1988), 51\u201381.\n\n30 Hobhouse, _Democracy and Reaction_ , 49\u201350, 58\u201359.\n\n31 See especially, Hobhouse, _Mind in Evolution_ (London, 1901); _Morals in Evolution_ , 2 vols. (London, 1906); _Social Evolution and Political Theory_ (New York, 1911); _Development and Purpose_ (London, 1913).\n\n32 On liberal conceptions of nationality, see H. S. Jones, \"The Idea of the National in Victorian Political Thought,\" _European Journal of Political Theory_ , 5 (2006), 12\u201321.\n\n33 Hobhouse, _Democracy and Reaction_ , 147, 148\u201349, 151. Without providing details, Hobhouse also argued that the idea of \"direct participation\" was \"held by observers to have materially influenced American public life, and not to have influenced it for the good,\" 149.\n\n34 Ibid., 152\u201353.\n\n35 Ibid., 154, 156\u201357, 155.\n\n36 Hobhouse, \"Democracy and Empire,\" _Speaker_ , October 18, 1902, 75. He concluded that \"Mr. Hobson's book will become one of the text-books of reviving Liberalism\u2014the Liberalism which is finding itself again in opposition to Imperialism, and is recognising that a choice must be made between Democracy and Empire.\" Hobhouse was far from alone in thinking that the end result of imperial federation was better characterized as a \"world state\" not an empire. Bell, _The Idea of Greater Britain_ , ch. 4.\n\n37 Hobhouse, _Liberalism_ , 105, 115.\n\n38 Ibid., 115\u201316. Note the conflation here between the \"white\" settler colonies and the remainder of the empire.\n\n39 Ibid, 116.\n\n40 Ibid.\n\n41 Hobhouse, _Democracy and Reaction_ , 247, 250. 1886 saw the rejection of Gladstone's Home Rule Bill while 1902 was marked by the Peace of Vereeniging, bringing hostilities in South Africa to a close.\n\n42 See here C. C. Eldridge, _Victorian Imperialism_ (London, 1978), 13; John Ellis, \"'The Methods of Barbarism' and the 'Rights of Small Nations,'\" _Albion_ , 30 (1998), 49\u201375.\n\n43 Hobhouse, _Liberalism_ , 107, 109.\n\n44 Hobson, _The Crisis of Liberalism_ (London, 1909). This volume, like _Democracy and Reaction_ , was composed of a series of previously published articles.\n\n45 Ibid., x. All of this was \"thrown together by the class instinct of self-preservation,\" 188.\n\n46 Ibid., 183\u201384, 185, 187. Like Hobhouse, Hobson thought that evolution, properly understood, generated \"mutual aid or conscious co-operation,\" 185.\n\n47 Ibid., xi. The American Progressive scholar Charles Beard observed that \"At Albany or Harrisburg, Mr. Hobson's philosophy would be instantly branded as 'rank socialism' and dangerous utopianism, but at Westminster things are different.\" Beard, _Political Science Quarterly_ , 25 (1910), 530.\n\n48 Hobson, _The Crisis of Liberalism_ , 135.\n\n49 Ibid., 92\u201394. Yet he painted liberalism with a very broad brush, for, as Michael Freeden notes, he expended little effort in engaging with past thinkers, even Mill, and preferred to discuss his contemporaries. Freeden, _Liberal Languages_ (Princeton, 2005), 94.\n\n50 Hobson, _The Crisis of Liberalism_ , xii. This was a \"more constructive and evolutionary idea of liberty,\" 93.\n\n51 Ibid., viii.\n\n52 Hobhouse, _The War in South Africa_ (London, 1901); Hobhouse, _The Psychology of Jingoism_ (London, 1901).\n\n53 On Ruskin and Spencer, see Cain, _Hobson and Imperialism_ ; on the links to positivism, see Claeys, _Imperial Sceptics_ , ch. 4; and on utilitarian themes, see David Weinstein, _Utilitarianism and the New Liberalism_ (Cambridge, 2007), ch. 6.\n\n54 Hobson, _Imperialism_ , 126.\n\n55 Ibid., 13, 19.\n\n56 Ibid., 46. Like many contemporary critiques of finance capitalism, Hobson's views were tainted with anti-Semitism (Cain, _Hobson and Imperialism_ , 84, 92\u201393). On earlier socialist and radical theories of finance imperialism, see Claeys, _Imperial Sceptics_. His account highlights that Hobson's argument about finance capital was not especially original.\n\n57 Hobson, _Imperialism_ , 47, 12\u201313. Claeys ( _Imperial Sceptics_ , ch. 4) shows that this was grounded in, among other things, a Vattelian argument about the rights of occupation of underutilized land. See also Andrew Fitzmaurice, \"The Resilience of Natural Law in the Writings of Sir Travers Twiss,\" in _British International Thinkers from Hobbes to Namier_ , ed. Ian Hall and Lisa Hill (New York, 2009), ch. 8.\n\n58 Hobson, _Imperialism_ , 36.\n\n59 Ibid., 332.\n\n60 Ibid., 345.\n\n61 Hobhouse, _The Crisis of Liberalism_ , 238.\n\n62 Ibid., 236, 237, 239.\n\n63 Ibid., 239. On Chamberlain's own change of heart, see Bell, _The Idea of Greater Britain_ , 56\u201358.\n\n64 Hobson, _The Crisis of Liberalism_ , 241.\n\n65 Ibid., 242.\n\n66 On his early support for and respect of Chamberlain, see Cain, _Hobson and Imperialism_ , 53, 61.\n\n67 On the debates around tariff reform, see, inter alia, Anthony Howe, _Free Trade and Liberal England, 1846\u20131946_ (Oxford, 1998); Frank Trentmann, _Free Trade Nation_ (Oxford, 2008).\n\n68 Hobson, _Canada To-Day_ (London, 1906), 3, 50\u201351. Although it had long been in use, the term \"Americanization\" was popularized by W. T. Stead, _The Americanization of the World_ (London, 1902).\n\n69 Hobson, _Canada To-Day_ , 99\u2013101, 103.\n\n70 Hobhouse, _The Crisis of Liberalism_ , 259.\nCoda\n\n(De)Colonizing Liberalism\n\nIn 2004, with American and British troops fighting in Iraq and Afghanistan, and a ferocious global \"war on terror\" in full swing, empire was once again high on the agenda. In a now infamous outburst an anonymous official in Washington boasted that \"[w]e're an empire now, and when we act, we create our own reality... We're history's actors... and you, all of you, will be left to just study what we do.\"1 Most of the protagonists I have (just) studied in this book would likewise have seen themselves as belonging to an exclusive group of history's actors, the handful of states that had fundamentally remade the world, shaping their own reality, and whose political and intellectual leaders often believed that they were entitled, even destined, to continue doing so deep into the future. Like empire, hubris is a transhistorical phenomenon.\n\nThe preceding chapters have addressed a variety of themes and thinkers in the history of modern British imperial ideology (and beyond). Although I have concentrated on the \"age of empire,\" the half century prior to the outbreak of the First World War, I have also pushed back into the early Victorian era to trace the development of assorted doctrines, and moved through the twentieth century and into the present, across decades in which the British empire dissolved and the United States achieved a long foretold position of global supremacy. Whether wittingly or not, the anonymous official hymning the power and virtue of contemporary American empire was a lineal heir of those earlier ideologists, imaginatively beholden to a mythopoeic vision of the British empire and its role in the long nineteenth century. My analysis has been motivated by curiosity about the ways in which historical actors made sense of their world, and a conviction that studying their ideas can shed light on key moments and movements in the past, while also helping to inform contemporary political thinking. I have probed the meanings of liberalism, forms of imperial argumentation, conceptions of time and history, and accounts of global racial order. In doing so, I have investigated the writings of various individuals, some still famous, venerated even, but the majority of whom have been lost to the condescension of posterity. Only by recovering the political concerns, languages, anxieties, and fantasies of such a motley cast of characters can we begin to apprehend the content and complexity of imperial political thought at the apogee of the largest empire in history.\n\nThroughout _Reordering the World_ I have emphasized the importance of both \"historical-mindedness\" and of settler colonialism in nineteenth-century imperial discourse. Emigration and settlement had long been a conspicuous theme in English (and later British) political discourse. The colonization of North America provoked vociferous debate, drawing in many of the leading minds of the age.2 The subsequent loss of the thirteen colonies haunted later imperial thinkers, prompting anguish about the future, and melancholy ruminations about what might have been if only the British empire had remained intact. Although I am skeptical that we can learn much about modern imperial ideology from studying the writings of John Locke, it is nevertheless clear that in order to understand the character of much early modern political thought it is necessary to grapple with attitudes to settlement and occupation.3 I have traversed less well-trodden ground, analyzing intellectual debates over what I call the second settler empire. Whereas the first settler empire was geographically concentrated in North America, and was fatally wrenched apart by what Seeley termed the \"Schism in Greater Britain,\" the second was spread across oceans and continents, encompassing vast territories (and more modest populations) in Canada, the South Pacific, and southern Africa.4\n\nThis new empire\u2014or imperial subsystem\u2014was slow to form and slower still to ignite the political imagination. It coalesced piecemeal from the scattered remnants of the late eighteenth-century colonial order and the steady accumulation of new territories. Initially maligned, frequently ignored, its inhabitants routinely derided, it was only during the second half of the nineteenth century that it came to be seen as part of a single integrated system.5 During the same period it was transvalued: colonization was recoded as a laudable ideal, the colonies reimagined as spaces of virtue and desire. This fundamental switch in fortunes had several sources, some deep-rooted, others proximate. The early nineteenth century was marked by what James Belich terms a \"Settler Revolution,\" the \"explosive\" development of two interconnected geo-economic regions, the \"American West\" and the \"British West\" (Canada, Australia, New Zealand, and South Africa). Although the seeds of the revolution could be located earlier, a phase of \"hyper-colonialism\" erupted with the \"settler transition\" of 1815\u201320, as emigration reached a critical mass and became a significant historical force. It was the joint product of novel transport technologies and a shift in collective psychology, such that embarking on life in the colonies came to seem both practicable and attractive to millions of people. It was sustained by a new ideology of \"settlerism,\" praising the manifold benefits, material and spiritual, of colonization.6 In a wave of creative destruction\u2014characterized by an economic cycle that saw frenetic booms followed by sudden collapse and then sustained periods of \"re-growth\"\u2014the settler world became a powerful engine of economic development and a space for the reproduction of Anglo-societies. The nineteenth-century \"great divergence,\" then, was powered by the astonishing rise of an Angloworld formed by the \"organic unity\" of the British settler empire and the United States.7\n\nEconomic vitality alone was insufficient to captivate and enthuse generations of liberal thinkers. It was the specific political status\u2014or at least self-image\u2014of the colonies that provided the key. The period of the \"great transition\" was also, as Lisa Ford argues, the moment when settler sovereignty was consolidated.8 Exclusive spaces of jurisdiction were established, such that (for example) indigenous resistance was no longer treated as a matter for diplomatic resolution between distinct communities but as an instance of domestic criminality to be dealt with by the settler legal system. Regulated by violence, this new regime of territorial sovereignty established the juridical and symbolic foundations of the settler state. Above all, though, it was the grant of \"responsible government\" in the 1840s and 1850s that elevated the colonies in the eyes of so many liberal thinkers, rendering them worthy subjects of sustained attention and affirmation. Imagining colonies as semi-autonomous, collectively self-governing communities, free of the feudal vestiges of British society, and populated overwhelmingly by energetic \"civilized\" white people, aligned them with liberal visions of political progress. Indeed it was this political transformation that many liberals later boasted was the major liberal contribution to the British empire during the nineteenth century. This was _their_ empire, something of which they could be proud and in which they could invest their hopes. While most were happy to claim the title of preeminent civilizing agent for Britain, many also felt that the occupied territories in India, the Caribbean, and Africa were ultimately fated for independence and that the despotism required to govern them, while in principle compatible with liberal ideology, was not something that they could endorse with the same confidence as the project of settler colonization. This is why I have suggested, contra Uday Singh Mehta, that it was in the colonies, not India, that many liberals found the concrete place of their dreams.9 Liberal support for settler colonialism was premised on the belief that the colonies had performed a remarkable act of political synthesis, reconciling liberty and empire in a manner unprecedented in the annals of Western history. It was usually based on a willful downplaying of the violence necessary to construct and govern settler communities. The colonies were polities based on the _herrenvolk_ principle of white racial supremacy.\n\nWhile liberals frequently celebrated the progressive dimensions of colonization, they disagreed fiercely about how best to institutionalize the settler world. At midcentury, one of the most common positions\u2014maybe even the dominant one\u2014was a modern variation on the ancient Greek template, which envisaged the colonies securing formal independence and thereafter remaining tightly bound to Britain through a dense web of economic interactions, migrant flows, and the power of racial affect. Encompassing a cluster of geographically dispersed states\u2014including the United States\u2014joined symbolically by shared culture, history, and political institutions, the Angloworld would comprise a microcosmic international order. Despite the mosaic of independent polities, however, its underlying racial unity meant that it would remain one of history's actors. Others, including John Stuart Mill, were keen to maintain the sovereign connection between the \"mother-country\" and the colonies, but only on a voluntary basis, anchored in common interests and mutual recognition.10 During the 1880s and 1890s plans for consolidating the settler empire shaped the terms of debate, often under the elastic rubric of \"imperial federation.\" Whether formal or informal, visions of colonial unity were predicated on a cognitive revolution, a transformation in perceptions of time and space, and thus of the parameters of political feasibility, that allowed the scattered fragments of the settler world to be imagined as a single united domain. For all the intellectual energy exerted on the subject, little came of plans to create a Greater British polity, though the idea of closer Angloworld collaboration advocated by more judicious imperialists sowed a far more enduring legacy.11\n\nAntoinette Burton has recently called on historians to study phenomena that cannot be enclosed within the imaginative or juridical boundaries of nation or empire.12 One such transversal was the ideology of whiteness, \"at once global in its power and personal in its meaning, the basis of geo-political alliances and a subjective sense of self.\"13 Claims about the nature and value of whiteness were central to debate over settler colonialism and imperial federation. During the 1880s and beyond, moreover, conceptions of whiteness (and in particular Anglo-Saxonism) underlay numerous calls to reconcile Greater Britain and the United States. Once again, liberals assumed a leading role. Ambitious demands emanated from such apparently incongruent figures as H. G. Wells, Andrew Carnegie, Cecil Rhodes, and W. T. Stead, who fired some of the opening salvos in the campaign to politically unify the Angloworld.14 This represented an attempt to wrestle with the problem of _translatio imperii_ , of calibrating the transition from one imperial order to another, only this time it was construed as both an interstate and an intra-racial predicament, a shift in the balance of power between polities that were composed of the same people. In chapter 13 I discussed one of the main intellectual sources for the ideology of transatlantic whiteness, namely E. A. Freeman's argument for the shared Teutonic foundations of Britain and the United States. For Freeman, race was the most basic ontological element of the sociopolitical world, and as such political institutions should be arrayed to reflect this primacy. The British empire failed this test, incorporating as it did copious \"alien\" elements while excluding the most significant political expression of the race. Some prophets of Angloworld unity, such as Rhodes and Wells, called for the foundation of a vast transatlantic Anglo-American polity.15 Less ambitious proponents, including Freeman and James Bryce, recommended the creation of an \"isopolity,\" based on shared (racial) citizenship.16 More cautious devotees of the Angloworld simply emphasized the importance of closer cooperation between its two main powers, destined to reorder the world between them. As I discussed in chapter 8, the overlapping discourses of Greater Britain and Anglo-America spawned a variety of other models of global governance during the twentieth century, including leagues of democracies and world federalism. They continue to inform debates about global order today.\n\n_Reordering the World_ makes no claims to comprehensiveness. A broader study of the thought-worlds of the settler empire would incorporate a greater range of material, as well as shifting between different modalities of historical investigation. It would need to scrutinize conceptions of the world produced in the colonies, identifying how they helped to mold local politics and how they circulated around the imperial commons. It would need to address the gendered character of colonial discourse, as well as its theological dimensions. It would need to engage with the complex legal arguments utilized to claim land and establish sovereign jurisdiction.17 It would need to move beyond elite discourses to excavate the political languages of a larger cast of individuals, organizations, and movements. It would need to recover, where possible, the intellectual production of the assorted indigenous communities that were the main victims of the \"settler revolution.\" It would need to address the interstitial status of Ireland, at once a zone of colonial settlement and an integral part of the British state. There is also much work to be done in analyzing the intellectual history of the metropolitan elite. In this book, and especially in part III, I have dedicated a considerable amount of space to the work of historians and philosophers. This choice is not accidental, insofar as they produced some of the most interesting and influential accounts of colonialism, but nor is it exhaustive. Poets and novelists were amongst the most searching colonial fabulists, and appraising their output offers rich rewards for students of political thought.18 Political economists, in particular, are due greater attention. Although I have touched on aspects of the political economy of settler colonialism\u2014for example, in my discussion of Mill's work\u2014I have not engaged it in depth. Metropolitan political economists were especially significant in shaping debate during the first half of the century, chiefly through the theoretical work and activism of the colonial reform movement, but they also played a significant role in arguments over imperial federation, and later returned to center stage in the Edwardian clashes over Chamberlain's plans for imperial tariff reform.19 A new comprehensive study of the economic thought of empire across the nineteenth century is long overdue.\n\nElucidating the impact of alien rule in the history of modern European political thought produces a relatively clear dividing line between supporters and critics of empire, facilitating the creation of canons of \"anti-imperial\" and \"imperialist\" thinkers, liberal or otherwise. Injecting settler colonialism back into the narrative blurs this distinction. Most so-called \"anti-imperialists\" from the late eighteenth century to the late nineteenth, from Bentham through Spencer to Hobson and Hobhouse, promoted settler colonialism of one kind or another. Although there is no necessary conceptual or theoretical connection between liberalism and settler colonialism, such that authentic liberals must sanction the practice, the historical record demonstrates that (British) liberals overwhelmingly endorsed it. This support was frequently conjoined with the rejection, even fierce denunciation, of empire-as-alien-rule. The crucial task of decolonizing liberalism thus needs to start with an acknowledgment that many (liberal) critics of imperialism were simultaneously proponents of settler colonialism. This Janus-faced attitude was at once simple and complex. It was simple insofar as it was based on a claim that colonization belonged to a completely different category of political order\u2014that \"[w]hatever political maxims are most applicable to one, are most inapplicable to the other,\" as Seeley put it in one of the pithier renditions of the mantra.20 They shouldn't be confused or conflated. The complexity resided in disentangling them, specifying exactly how and why settler colonies were different, when all forms of empire involved conquest and repressive governance. Here there was considerable disagreement, though most supporters concurred on a few basic points, above all the importance of racial similarity and self-government. The settler colonies were imagined as _white_ , as populated by civilized peoples capable of governing themselves (preferably within an overarching imperial framework) and of instituting sovereign control over territory that could be appropriated legitimately from its unworthy original inhabitants. The liberal case for exceptionalism, for transcending or escaping the despotic logic of traditional modes of imperial rule, was premised on a racialized picture of global hierarchy.\n\nThinking through the political and theoretical implications of settler colonialism, past and present, involves formidable challenges.21 Such states are usually founded on acts of systematic violence against indigenous peoples. (The same could of course be said of many other states as well). The United States is but the largest example. Throughout the eighteenth and nineteenth centuries a succession of presidents, including Jefferson, Jackson, Grant, and Roosevelt, were quite open about the genocidal character of the frontier wars waged against the \"Indian.\"22 Civilization or extermination: such was the choice. In a discussion of Michael Walzer's account of American citizenship, Mahmood Mamdani writes that the \"American [national] biography is written as the autobiography of the settler. The native has no place in it.\"23 As such, pluralism and multiculturalism \"flowered on a bed prepared by the conquest and decimation of tribes in America,\" and \"[t]he uncritical embrace of the settler experience explains the blind spot in the American imagination: an inability to coexist with difference, indeed a preoccupation with civilizing natives.\" \"American cosmopolitanism,\" he concludes, \"has been crafted through settler lenses.\"24 Facing up to this situation is not only a matter of recognizing an obligation to address past injustice, but admitting that the current political order is founded on, and continues to be shaped by, an ideology of settlerism. \"Engaging with the native question would require questioning the ethics and politics of the very constitution of the United States of America. It would require rethinking and reconsidering the very political project called the USA.\"25 Efforts to rethink and reconsider have been attempted with varying degrees of enthusiasm across the other elements of the British settler world in recent years, spawning controversial campaigns for restitution, apology, and new forms of political participation, though with mixed results.26\n\nI offer no solutions to this quandary. But if the legacy of empire in general, and settler colonialism in particular, is to be confronted properly it will require a fundamental reconsideration of the political institutions and norms of settler states, including the ideologies that they created and profess. Liberalism is one such ideology. This rethinking need not entail a wholesale rejection of liberalism\u2014if such a thing is even possible now. Even at the height of British imperial arrogance, liberalism contained resources to both justify empire (of various kinds) and to launch stinging critiques of it. If those criticisms were often muted, their very possibility at least offers some hope. Today liberalism has expanded so broadly that it virtually monopolizes political theory and practice in the Angloworld, and as such it is vital to establish whether there are liberal forms of anti-imperialism suitable for the contemporary world, and what they might look like. It is essential to creatively engage with liberalism, joining the conflict between its tessellated factions.27\n\nIn _Liberalism and Empire_ , Mehta argued that the \"liberal involvement with the British empire was largely coeval with liberalism itself.\"28 I have challenged this historical narrative, suggesting that it both misdates the origins of liberalism and oversimplifies the character of liberal attitudes to empire in the nineteenth century. The British empire was forged long before the emergence of liberal political ideology: liberalism supervened on, while adapting and supplementing, existing ideas and practices. A relentless focus on the assumptions, theoretical architecture, and political entailments of liberalism carries the risk of overlooking the deeper intellectual and political currents on which it drew and to which it was a response\u2014perhaps above all the coevolving relationship between the modern state and global capitalism.29 In particular, I would contend that British liberalism was broadly coeval with the second settler empire. It was, in large part, a product of the violent dissolution of the thirteen colonies in North America, the revolutionary upheavals in France, and the tidal wave of economic, social, and political change that they unleashed. Perhaps more importantly, the development of liberal political theory and the second settler empire was interconnected. The repercussions of this historical imbrication have yet to be fully explored. In order to decolonize liberalism, it is first necessary to (re)colonize it, acknowledging the vital role that the project and ideology of settler colonialism played in its emergence and historical evolution.\n\n1 Ron Suskind, \"Faith, Certainty and the Presidency of George W. Bush,\" _New York Times Magazine_ , October 17, 2004. The phrase is often attributed to Karl Rove. On the debate over American empire, see Paul Macdonald, \"Those Who Forget Historiography Are Doomed to Republish It,\" _Review of International Studies_ , 35\/1 (2006), 45\u201367; Craig Calhoun, Frederick Cooper, and Kevin Moore, eds., _Lessons of Empire_ (New York, 2006).\n\n2 For two important accounts of early modern colonization, see David Armitage, _The Ideological Origins of the British Empire_ (Cambridge, 2000); Andrew Fitzmaurice, _Humanism and America_ (Cambridge, 2007).\n\n3 For wide-ranging analyses of imperial justification and contestation, see Lauren Benton, _A Search for Sovereignty_ (Cambridge, 2010); Andrew Fitzmaurice, _Sovereignty, Property, and Empire, 1500\u20132000_ (Cambridge, 2014); Anthony Pagden, _The Burdens of Empire_ (Cambridge, 2015). For a brilliant meditation on the construction of political space in European political thought, see Annabel Brett, _Changes of State_ (Princeton, 2011).\n\n4 This is the title of chapter 8 in Seeley, _The Expansion of England_.\n\n5 For a near-contemporaneous account of the gestalt switch, see J. E. Cairnes, \"Colonization and Colonial Government\" (1863), in _Political Essays_ (London, 1873), 158. On some of the key midcentury protagonists, see Edward Beasley, _Empire as the Triumph of Theory_ (London, 2004); Beasley, _Mid-Victorian Imperialists_ (London, 2005).\n\n6 Belich, _Replenishing the Earth_ , 153\u201356. For a comprehensive account of emigration around the British empire, see Marjory Harper and Stephen Constantine, eds., _Migration and Empire_ (Oxford, 2010).\n\n7 Belich, _Replenishing the Earth_ (Oxford, 2009), 51.\n\n8 Lisa Ford, _Settler Sovereignty_ (Cambridge, MA, 2010). Her book is based on a comparative analysis of Georgia and New South Wales. See also the discussion in Russell Smandych, \"Colonialism, Settler Colonialism, and Law,\" _Settler Colonial Studies_ , 3\/1 (2013), 82\u2013101.\n\n9 The quote is from Mehta, _Liberalism and Empire_ , 37.\n\n10 Mill, _Considerations on Representative Government_ (1861), _Collected Works_ , vol. 18, ch. 18. For the details of his argument, see chapter 9.\n\n11 On the legacies of the Angloworld in twentieth-century global politics, see Srdjan Vucetic, _The Anglosphere_ (Stanford, 2011); Peter Katzenstein, ed., _Anglo-America and its Discontents_ (London, 2012). On the weaknesses of the imperial federal movement, see Duncan Bell, _The Idea of Greater Britain_ , ch. 10.\n\n12 Burton, \"Getting Outside of the Global,\" in _Empire in Question_ (Durham, NC, 2011), 279\u201380.\n\n13 Marilyn Lake and Henry Reynolds, _Drawing the Global Colour Line_ (Cambridge, 2008), 3. See also Bill Schwarz, _The White Man's World_ (Oxford, 2011).\n\n14 I analyze fantasies of Anglo-America in Bell, _Dreamworlds of Empire_ (forthcoming).\n\n15 Rhodes, _The Last Will and Testament of Cecil J. Rhodes_ , ed. W. T. Stead (London, 1902); _Anticipations of the Reaction of Mechanical and Scientific Progress upon Human Life and Thought_ 1902] (Mineola, 1999). For more detailed proposals for formal union, see W. T. Stead, _The Americanization of the World_ (London, 1902); John Dos Passos, _The Anglo-Saxon Century and the Unification of the English-Speaking Peoples_ , 2nd ed. (New York, 1903). See further discussion in [chapter 8.\n\n16 Bryce, \"The Essential Unity of England and America,\" _Atlantic Monthly_ , 82 (1898), 22\u201329. For Freeman's account, see chapter 13. On isopolity, see Duncan Bell, \"Beyond the Sovereign State,\" _Political Studies_ , 62 (2014), 418\u201334.\n\n17 See, for examples, Benton, _A Search for Sovereignty_ ; P. G. McHugh, _Aboriginal Societies and the Common Law_ (Oxford, 2004); Fitzmaurice, _Sovereignty, Property and Empire_ ; Mark Hickford, _Lords of the Land_ (Oxford, 2011).\n\n18 For recent examples of work on this topic, see Helen Lucy Blyth, _The Victorian Colonial Romance with the Antipodes_ (Basingstoke, 2014); Terra Walston Joseph, \"Bulwer-Lytton's _The Coming Race_ and an Anglo-Saxon Greater Britain,\" _Nineteenth-Century Contexts_ , 37 (2015), 233\u201348; Philip Steer, \"Greater Britain and the Imperial Outpost,\" _Victorian Review_ , 35 (2009), 79\u201395; Lyman Tower Sargent, \"Colonial and Postcolonial Utopias,\" in _The Cambridge Companion to Utopian Literature_ , ed. Gregory Claeys (Cambridge, 2010), 200\u2013223.\n\n19 See, for example, the discussion in A. C. Howe, _Free Trade and Liberal England, 1846\u20131946_ (Oxford, 1998); E.H.H. Green, _The Crisis of Conservatism_ (London, 1996), chs. 2, 7; Gregory Claeys, _Imperial Sceptics_ ; P. J. Cain, _Hobson and Imperialism_ (Oxford, 2002). As far as I am aware, there are no recent histories of political economy that focus on colonial thought from the early Victorian era to the First World War.\n\n20 Seeley, _The Expansion of England_ , 244. Seeley was comparing the settler colonies to India.\n\n21 The journal _Settler Colonial Studies_ is an excellent source of analysis. Now a vibrant, multidisciplinary enterprise, the field of settler colonial studies was in its infancy when I embarked on my research into discourses of Greater Britain. I have learned much from it since then. For a valuable overview, see Lorenzo Veracini, _The Settler Colonial Present_ (Basingstoke, 2015).\n\n22 Benjamin Madley, \"Reexamining the American Genocide Debate,\" _American Historical Review_ , 120 (2015), 109\u2013110.\n\n23 Mamdani, \"Settler Colonialism,\" _Critical Inquiry_ , 41 (2015), 596. For an excellent discussion that takes this settler dimension into account, see Aziz Rana, _The Two Faces of American Freedom_ (Cambridge, MA, 2010). See also Alyosha Goldstein, ed., _Formations of United States Colonialism_ (Durham, NC, 2014); Kevin Bruyneel, \"The American Liberal Colonial Tradition,\" _Settler Colonial Studies_ , 3 (2013), 311\u201321.\n\n24 Mamdani, \"Settler Colonialism,\" 598\u201399. He is critiquing a line of argument that runs through Michael Walzer, _What It Means to Be an American_ (New York, 1996). On the peculiar form of sovereignty enacted by indigenous populations in the US, see Kevin Bruyneel, _The Third Space of Sovereignty_ (Minneapolis, MN, 2007).\n\n25 Mamdani, \"Settler Colonialism,\" 602\u20133.\n\n26 On official policies of reconciliation and apology, see Miranda Johnson, \"Reconciliation, Indigeneity, and Postcolonial Nationhood in Settler States,\" _Postcolonial Studies_ , 14\/2 (2011), 187\u2013201; Dirk Moses, \"Official Apologies, Reconciliation, and Settler Colonialism,\" _Citizenship Studies_ , 15\/2 (2011), 145\u201359.\n\n27 For valuable attempts to rethink liberalism, see Duncan Ivison, _Postcolonial Liberalism_ (Cambridge, 2002); Tully, _Strange Multiplicity_ (Cambridge, 1995). 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Barth\u00e9lemy, _Edinburgh Review_ , 15 (1810), 363\u201384.\n\n\u2014\u2014\u2014, \"Colony\" [1818], in _Essays from the Supplement to the Encyclopaedia Britannica, Collected Works_ (London: Thoemmes, 1995), 3\u201333.\n\nMill, John Stuart, \"The Emigration Bill,\" _Examiner_ , February 27, 1831, _Collected Works_ , 22:270\u201372.\n\n\u2014\u2014\u2014, \"Female Emigrants,\" _Examiner_ , February 26, 1832, _Collected Works_ , 23:419\u201320.\n\n\u2014\u2014\u2014, \"On the Necessity of the Uniting of the Question of Corn Laws with That of the Tithes,\" _Examiner_ , December 23, 1832, _Collected Works_ , 23:534\u201339.\n\n\u2014\u2014\u2014, \"New Australian Colony,\" _Morning Chronicle_ , October 23, 1834, _Collected Works_ , 23:749\u201351.\n\n\u2014\u2014\u2014, \"The New Colony\" [2], _Examiner_ , July 6, 1834, _Collected Works_ , 23:735\u201336.\n\n\u2014\u2014\u2014, \"De Tocqueville on Democracy in America [I]\" [1835], _Collected Works_ , 28:47\u201391.\n\n\u2014\u2014\u2014, \"Civilization\" [1836], _Collected Works_ , 28:117\u201349.\n\n\u2014\u2014\u2014, \"Carlyle's French Revolution\" (1837), _Collected Works_ , 20:131\u201367.\n\n\u2014\u2014\u2014, \"The Sale of Colonial Land,\" _Sun_ , February 22, 1837, _Collected Works_ , 24:791\u201392.\n\n\u2014\u2014\u2014, \"Lord Durham and His Assailants,\" _London and Westminster Review_ (1838), _Collected Works_ , 6:437\u201344.\n\n\u2014\u2014\u2014, \"Penal Code for India,\" _London and Westminster Review_ (1838), _Collected Works_ , 30:17\u201330.\n\n\u2014\u2014\u2014, \"Radical Party and Canada: Lord Durham and the Canadians,\" _London and Westminster Review_ (1838), _Collected Works_ , 6:405\u201336.\n\n\u2014\u2014\u2014, \"Coleridge\" [1840], _Collected Works_ , 10:117\u201364.\n\n\u2014\u2014\u2014, _A System of Logic, Ratiocinative and Deductive, Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation_ [1843], _Collected Works_ , 7:861\u201375.\n\n\u2014\u2014\u2014, \"Torrens's Letter to Sir Robert Peel,\" _Spectator_ , January 28, 1843, _Collected Works_ , 24:836\u201340.\n\n\u2014\u2014\u2014, \"Wakefield's 'The New British Province of South Australia,'\" _Examiner_ , July 20, 1843, _Collected Works_ , 23:738\u201342.\n\n\u2014\u2014\u2014, \"The Claims of Labour,\" _Edinburgh Review_ [1845], _Collected Works_ , 4:363\u201390.\n\n\u2014\u2014\u2014, \"The Condition of Ireland [25],\" _Morning Chronicle_ , December 2, 1846, _Collected Works_ , 24:972\u201375.\n\n\u2014\u2014\u2014, _Principles of Political Economy_ [1848], _Collected Works_ , vol. 3.\n\n\u2014\u2014\u2014, \"Grote's _History of Greece_ ,\" vol. 2 [1853], _Collected Works_ , 11:271\u2013306.\n\n\u2014\u2014\u2014, \"A Few Words on Non-Intervention\" [1859], _Collected Works_ , 21:111\u201324.\n\n\u2014\u2014\u2014, \"Grote's History of Greece [IV],\" _Spectator_ , March 10, 1859, _Collected Works_ , 25:1128\u201335.\n\n\u2014\u2014\u2014, _On Liberty_ [1859], _Collected Works_ , 18:213\u2013310.\n\n\u2014\u2014\u2014, _Considerations on Representative Government_ [1861], _Collected Works_ , 18: 371\u201372.\n\n\u2014\u2014\u2014, _The Subjection of Women_ [1869], _Collected Works_ , 21:259\u2013340.\n\n\u2014\u2014\u2014, _Autobiography_ [1873], _Collected Works_ , 1:4\u2013290.\n\n\u2014\u2014\u2014, _The Collected Works of John Stuart Mill_ , ed. John Robson (Toronto: University of Toronto Press, 1963\u201391).\n\n\u2014\u2014\u2014, \"Use and Abuse of Political Terms,\" _Collected Works_ , 18:1\u201314.\n\nMiller, J.D.B., \"The Utopia of Imperial Federation,\" _Political Studies_ , 4 (1956), 195\u201397.\n\nMills, Arthur, _Systematic Colonization_ (London: John Murray, 1847).\n\n\u2014\u2014\u2014, _Colonial Constitutions_ (London: John Murray, 1856).\n\nMills, Charles Wright, _The Marxists_ (Harmondsworth: Penguin, 1963).\n\nMills, Richard, _The Colonization of Australia (1829\u20131842)_ [1915] (London: Dawsons, 1968).\n\nMilner, Alfred, \"Credo,\" _Times_ , July 25, 1925.\n\nMinogue, Kenneth R., _The Liberal Mind_ (London: Methuen, 1962).\n\nMises, Ludwig von, _Liberalism_ (Indianapolis: Liberty Fund, 2005).\n\nMonypenny, W. F., \"The Imperial Ideal,\" in _The Empire and the Century_ , ed. Charles Sydney Goldman (London: John Murray, 1905), 5\u201328.\n\nMonypenny, W. F., and G. E. 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David Boucher (Cambridge: Cambridge University Press, 1997), 237\u201352.\n\nM\u00fcller, Max, _India, What Can It Teach Us?_ (London: Longmans, 1883).\n\nMurphy, Arthur, \"Ideals and Ideologies, 1917\u20131947,\" _Philosophical Review_ , 56 (1947), 374\u201389.\n\nMurray, Gilbert, \"The Exploitation of Inferior Races in Ancient and Modern Times,\" in _Liberalism and the Empire_ , by F. W. Hirst, Gilbert Murray, and J. L. Hammond (London: R. B. Johnson, 1899), 118\u201357.\n\nMurray, Robert, _The History of Political Science from Plato to the Present_ (Cambridge: Heffer, 1926).\n\nNettleship, R. L., \"Memoir\" [1888], in _Works of Thomas Hill Green_ , vol. 3, ed. Richard Lewis Nettleship, (London, 1885\u201388), xi-clxi.\n\nNewman, John Henry, \"An Internal Argument for Christianity\" [1866], in _Discussions and Arguments on Various Subjects_ , 4th ed. (London: Pickering, 1882), 363\u201398.\n\nNiebuhr, Reinhold, \"Liberalism,\" _New Republic_ , July 4, 1955, 11\u201313.\n\nOakeshott, Michael, ed., _The Social and Political Doctrines of Contemporary Europe_ (Cambridge: Cambridge University Press, 1939).\n\nOliver, Frederick Scott, _Alexander Hamilton: An Essay on American Union_ (London: Constable, 1906).\n\nOman, Charles William, _England in the Nineteenth-Century_ (London: Edward Arnold, 1899).\n\nParker, Joseph, _Ecce Deus: Essays on the Life and Doctrine of Jesus Christ_ (Boston: Roberts, 1868).\n\nParkin, George, _Imperial Federation: The Problem of National Unity_ (London: Macmillan, 1892).\n\n\u2014\u2014\u2014, _The Rhodes Scholarship_ (London: Constable, 1912).\n\nParmlees, M., \"Liberal Democracy, Fascism, and Bolshevism,\" _Annals of the American Academy of Political and Social Science_ , 180 (1935), 47\u201354.\n\nParrington, Vernon, _Main Currents in American Thought_ , 3 vols. (New York: Harcourt-Brace, 1927\u201330).\n\nPattison, Mark, \"Philosophy at Oxford,\" _Mind_ , 1 (1876), 82\u201397.\n\nPearson, Charles H., _National Life and Character: A Forecast_ (London: Macmillan, 1894).\n\nPeterson, W., \"The Future of Canada,\" in _The Empire and the Century_ , ed. Charles Sydney Goldman (London: John Murray, 1905), 363\u201384.\n\nPlamenatz, John, _On Alien Rule and Self-Government_ (London: Longmans, 1960).\n\nPlatt, Charles Malcolm, \"A Triad of Political Conceptions: State, Sovereign, Government,\" _Political Science Quarterly_ , 10 (1895), 292\u2013323.\n\nPolanyi, Karl, _The Great Transformation: The Political and Economic Origins of Our Time_ (Boston: Beacon, 1944).\n\nPollock, Frederick, _An Introduction to the History of the Science of Politics_ (London: Macmillan, 1890).\n\n\u2014\u2014\u2014, \"Locke's Theory of the State,\" _Proceedings of the British Academy_ , (1903\u20134), 80\u2013102.\n\n\u2014\u2014\u2014, \"The Social Contract in Hobbes and Locke,\" _Journal of the Society of Comparative Legislation_ (1907), reprinted in _Essays in the Law_ , by Frederick Pollock (London: Macmillan, 1922), 80\u2013109.\n\nRashdall, H., \"Professor Sidgwick on the Ethics of Religious Conformity,\" _International Journal of Ethics_ , 7\/2 (1897), 137\u201368.\n\n\u2014\u2014\u2014, _Philosophy and Religion_ (London: Duckworth, 1909).\n\nRedpath Dougall, John, \"An Anglo-Saxon Alliance,\" _Contemporary Review_ , 48 (1885), 693\u2013706.\n\nRhodes, Cecil, _The Last Will and Testament of Cecil J. 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(London: Grant Richards, 1900).\n\n\u2014\u2014\u2014, \"The Moral Problems of War,\" _International Journal of Ethics_ , 11\/3 (1901), 273\u201390.\n\nRobinson, John, \"The Future of the British Empire,\" _Westminster Review_ , 38 (1870), 47\u201374.\n\nRockow, Lewis, _Contemporary Political Thought in England_ (London: Parsons, 1925).\n\nRoebuck, John Arthur, _The Colonies of England: A Plan for the Government of Portion of Our Colonial Possessions_ [ _sic_ ] (London: Parker, 1849).\n\nRuskin, John, _The Works of John Ruskin_ , 39 vols., ed. E. T. Cook and A. 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(Cambridge: Cambridge University Press, 1878).\n\n\u2014\u2014\u2014, \"History and Politics,\" pts. 1\u20133, _Macmillan's Magazine_ , 40 (1879), 289\u201399, 369\u201378, 449\u201358.\n\n\u2014\u2014\u2014, \"Political Somnambulism,\" _Macmillan's Magazine_ , 43 (1880), 28\u201344.\n\n\u2014\u2014\u2014, \"The British Race\" [1872], _Education I_ , 4, (1881), 309\u201328.\n\n\u2014\u2014\u2014, _Natural Religion_ (London: Macmillan, 1882).\n\n\u2014\u2014\u2014, _The Expansion of England; Two Courses of Lectures_ (London: Macmillan, 1883).\n\n\u2014\u2014\u2014, \"Our Insular Ignorance,\" _Nineteenth Century_ , 18 (1885), 861\u201373.\n\n\u2014\u2014\u2014, \"Introduction,\" in _Her Majesty's Colonies_ (London: William Clowes and Son, 1886), viii\u2013xxvi.\n\n\u2014\u2014\u2014, \"The Journal of the League,\" _Imperial Federation_ , 1\/1 (1886), 4\u20135.\n\n\u2014\u2014\u2014, \"The Object to Be Gained by Imperial Federation,\" _Imperial Federation_ , 1\/6 (1886), 205\u20136.\n\n\u2014\u2014\u2014, _A Short History of Napoleon the First_ (London: Seeley, 1886).\n\n\u2014\u2014\u2014, \"Georgian and Victorian Expansion,\" _Fortnightly Review_ , 48 (1887), 123\u201339.\n\n\u2014\u2014\u2014, \"A Midlands University,\" _Fortnightly Review_ , 42 (1887), 703\u201316.\n\n\u2014\u2014\u2014, \"The Eighty-Eights,\" _Good Words_ (1888), 272\u2013360.\n\n\u2014\u2014\u2014, \"The Impartial Study of Politics: Inaugural Address to the Cardiff Society for the Impartial Discussion of Politics and Other Questions, October 18th 1886,\" _Contemporary Review_ , 54 (1888), 52\u201365.\n\n\u2014\u2014\u2014, \"Ethics and Religion,\" _Fortnightly Review_ , 45 (1889), 501\u201314.\n\n\u2014\u2014\u2014, _Introduction to Political Science_ [1891], ed. 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(London: Macmillan, 1907).\n\n\u2014\u2014\u2014, \"Philosophy at Cambridge,\" _Mind_ , 1 (1876), 235\u201346.\n\n\u2014\u2014\u2014, \"Mr. Spencer's Ethical System,\" _Mind_ , 5 (1880), 216\u201326.\n\n\u2014\u2014\u2014, \"Green's Ethics,\" _Mind_ , 9 (1884), 169\u201387.\n\n\u2014\u2014\u2014, \"The Scope and Method of Economic Science\" [1885], in _Miscellaneous Essays and Addresses_ (London: Macmillan, 1904), 170\u201399.\n\n\u2014\u2014\u2014, \"The Historical Method,\" _Mind_ , 11\/42 (1886), 203\u201319.\n\n\u2014\u2014\u2014, _The Elements of Politics_ [1891], 2nd ed. (London: Macmillan, 1897).\n\n\u2014\u2014\u2014, _The Elements of Politics_ [1891], 3rd ed. (London: Macmillan, 1907).\n\n\u2014\u2014\u2014, \"Political Prophecy and Sociology\" [1894], in _Miscellaneous Essays_ , 216\u201334.\n\n\u2014\u2014\u2014, \"Editor's Preface\" to _Introduction to Political Science: Two Series of Lectures_ [1896], by J. R. Seeley, ed. 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J., ,\n\nBalliol College, Oxford, ,\n\nBaring, Evelyn, 1st Earl of Cromer, , \u2013; _Ancient and Modern Imperialism_ ,\n\nBarker, Ernest,\n\nBaron, Hans,\n\nBayly, C. A., ,\n\nBaxter Adams, Herbert,\n\nBeard, Charles, 355n47\n\nBeaumont, Gustave,\n\nBeesly, E. S., , 268n19, 270n26\n\nBelich, James, 109n67,\n\nBengal,\n\nBenn, A. W., 83n83,\n\nBennett, James,\n\nBentham, Jeremy, , , , , , , , , , , , , , , , , ,\n\nBentley, Michael, 29n30,\n\nBeresford, Charles, , \u2013\n\nBesant, Walter,\n\nBevir, Mark, 120n7\n\nBhabha, Homi,\n\nbiocultural assemblage, account of race, , 175n39. _See also_ race\n\nBismarck, Otto von,\n\nBlackstone, William,\n\nBlair, Anthony, 26n23\n\nBluntschli, Johann Casper, , , ; _Theory of the State_ ,\n\nBrett, Annabel, 364n3\n\nBuller, Charles, \u2013, 216n21, 227n75\n\nBoer War. _See_ South African War\n\nBolingbroke, Viscount, Henry St. John, \u2013, 308n40, 317n77; _The Idea of a Patriot King_ , , 317n77\n\nBosanquet, Bernard.\n\nBowring, John, 216n21\n\nBradley, A. C, 274n47\n\nBradley, F. H., 274n47\n\nBradley, Mark, 145n106\n\nBridges, Horace,\n\nBright, John, , , , ,\n\nBritish Empire League,\n\nBroad Church, \u2013. _See also_ Seeley, J. R.\n\nBrowning, Robert, ,\n\nBryce, James, , , , , , , , , , , , , ; \"The Ancient Roman Empire and the British Empire in India,\"\n\nBukarin, Nikolai,\n\nBurke, Edmund, , , , \u2013, , 76n47, , , , , , , , ,\n\nBurrow, John,\n\nBurrows, Montagu,\n\nBury, J. B., , \u2013\n\nBush, George W., ,\n\nByron, George Gordon Noel, 6th Baron Byron,\n\nCabot Lodge, Henry, ,\n\nCain, Peter,\n\nCairnes, J. E., \u2013, , 44n98, 223n59, 365n5\n\nCaldecott, Alfred, 36n64, , , \u2013, \u2013\n\n_Cambridge Modern History_ ,\n\nCampbell-Bannerman, Henry,\n\nCanada, , , , 44n101, , \u2013, , , \u2013, , , , , \u2013, , , , , , , \u2013, , \u2013, , , , , , , , , , , \u2013, , ; \"Americanization\" of, \u2013; rebellion, in (1837\u201338), \u2013,\n\nCape Colony, , , , , 309n43. _See also_ South Africa\n\nCaribbean, the, , , , , , 308n39, . _See also_ Jamaica; West Indies\n\nCarlyle, Thomas, , , , , , \u2013, ; _Chartism_ , ; _Past and Present_ ,\n\nCarnarvon, 4th Earl of, Henry Herbert, 314n63,\n\nCarnegie, Andrew, , , , , ,\n\nCassirer, Ernst,\n\nCecil, Robert Arthur, 3rd Marquess of Salisbury, ,\n\nCentral Intelligence Agency (USA),\n\nChakrabarty, Dipesh, ,\n\nChamberlain, Joseph, , \u2013, , , , , , , , \u2013,\n\ncharacter, idea of, , , , , , , , \u2013, , , , , \u2013, , , , ,\n\nchildhood, language of, , , , , , , , ,\n\nChina, , ,\n\ncitizenship, , , , , , , \u2013, , , 198n61, , \u2013, , \u2013, \u2013, , , ; common, conception of, , 145n111, \u2013, , , 198n61, ,\n\ncivilization, idea of, , , , , \u2013, , \u2013, , \u2013, \u2013, , , \u2013, \u2013, \u2013, \u2013, , \u2013, , , \u2013, , , \u2013, , , \u2013, , , , , , , \u2013, \u2013, \u2013, , \u2013, \u2013, , \u2013, , \u2013\n\ncivilizing mission, idea of, , \u2013, , , , \u2013, , , , , , , , , , , \u2013, , , , \u2013. _See also_ civilization; empire; liberalism\n\nChartism, ,\n\nChurchill, Winston, , , ; \"Iron Curtain\" speech,\n\nCicero, Marcus Tullius, , 135n73\n\ncities, fear of, , , 305n25, \u2013,\n\ncivic humanism. _See_ republicanism\n\ncivic imperialism, , . _See also_ republicanism\n\ncivilization, idea of, , \u2013, , \u2013, , , \u2013, \u2013, \u2013, \u2013, \u2013, , \u2013, \u2013, , , \u2013, , , \u2013, , , \u2013, , , , , \u2013, , , , , , \u2013, 309n43, \u2013, , ,\n\nClaeys, Gregory, 357n57\n\nClarke, Peter, 191n32\n\nClassical Association,\n\nCobden, Richard, , , , , , , \u2013, , , , , ,\n\nCochrane, Baillie,\n\nCoit, Stanton,\n\nCold War, , 20n5, \u2013,\n\nCole, G.D.H., ,\n\nCole, Robert, 131n61; _The Struggle for Empire: A Story of the Year 2236_ , 131n61\n\nColeridge, Samuel Taylor, , , , , , 285n114; _On the Idea of the Constitution of the Church and State_ , 280n87\n\nCollingwood, R. G., , 140n92\n\nCollini, Stefan, , , \u2013\n\ncollective action problem, \u2013\n\nColomb, J.C.R.,\n\nColonial Office,\n\ncolonial reform movement, \u2013, , , , , . _See also_ Wakefield, E. G.\n\nCommittee to Form a World Government,\n\ncommunications technologies, imperial role of, , , , , , , , \u2013, , , , \u2013, , , ,\n\ncomparison, habit of, \u2013. _See also_ comparative gaze\n\ncomparative gaze, imperial, ,\n\ncomparative politics, academic discipline, \u2013, ,\n\ncomparative method, , , \u2013\n\nComte, Auguste, , , , \u2013, \u2013, ,\n\nConan Doyle, Arthur, , ; _The White Company_ ,\n\nCongress on Cultural Freedom, . _See also_ Central Intelligence Agency\n\nCongreve, Richard,\n\nConquest, Robert, 181n59, \u2013\n\nConrad, Joseph, , ; _Heart of Darkness_ ,\n\nConstant, Benjamin, , 30n37, , \u2013, , ; \"The Spirit of Conquest,\" ,\n\nCooper, Frederick, \u2013\n\nCorn Laws, , , ,\n\nCornewall Lewis, George, \u2013, 78n56, 129n52, ; _Essay on the Government of Dependencies_ , 129n52\n\ncosmopolitanism, , , , , , , , \u2013, , , ,\n\ncosmopolitan nationalism, , 248n40, , \u2013\n\nCouncil on Foreign Relations, \u2013\n\nCraik, Henry,\n\nCrimean War (1853\u201356),\n\ncrisis, language of, , , \u2013, , , \u2013\n\nCromer, Earl. _See_ Baring, Evelyn\n\nCurtis, Lionel, , \u2013, \u2013, ; _Civitas Dei_ ,\n\nCurzon, George (Lord Curzon), 131n60,\n\n_Daily Chronicle_ , the,\n\nDalhousie, Earl, James Broun-Ramsay,\n\nDalton, J. N.,\n\nDarwinism, social, , , , , , 343n10\n\nDarwin, John, 6n19\n\nDavis, Mike,\n\nDe Ruggiero, Guido, , , ; _History of European Liberalism_ ,\n\ndecline and fall, trope of, , , , \u2013, \u2013, , \u2013, , \u2013, \u2013, , , \u2013,\n\nDejobert, A., 30n37\n\ndemocracy, , , , , , \u2013, \u2013, , , , , , , , , , , \u2013, \u2013; anxiety over, , , ; and empire, , , , \u2013, \u2013; league of, , , ,\n\ndemocratization, , . _See also_ civilizing mission; democracy\n\ndependency theory, of exploitation, . _See also_ Marxism\n\nDerby,\n\nDeudney, Daniel, , , 203n92, 303n20\n\nDeutsch, Karl,\n\ndevelopment, ideology of, , , , \u2013, , ,\n\nDewey, John, , ,\n\nDiamond Jubilee (1897),\n\nDicey, Albert Venn, \u2013, , , , , , , , 331n57,\n\nDiderot, Denis, , ,\n\nDilke, Charles, 46n108, , , , , , , , , 292n148; criticisms of imperial federation, ; _Greater Britain_ , , ,\n\nDisraeli, Benjamin, , , , , , , , , \u2013,\n\nDore, Gustave,\n\nDos Passos, John Randolph, ,\n\nDouglas, James,\n\nDoyle, J. A., ,\n\nDoyle, Michael, 25n22, ,\n\nDrake, Durant, \u2013\n\nDuBois, W.E.B.,\n\nDulles, John Foster,\n\nDurham, Lord, John George Lambton, \u2013,\n\nDurham Report, \u2013,\n\nDworkin, Ronald, ,\n\nEast India Company, British, , \u2013,\n\n_Economist_ , the,\n\nEducation, relationship to empire, 59n168, \u2013, , \u2013, ,\n\nEgerton, H. E., , , , , ; _Short History of Colonial Policy_ ,\n\nEgypt, , , , , , ,\n\nEinstein, Albert,\n\nemigration, \u2013, , , , , , \u2013, , , , , , \u2013, , \u2013, \u2013; systematic account of, , , \u2013, , \u2013,\n\nEnglish-speaking peoples, idea of, , , \u2013, \u2013, , \u2013, , \u2013, \u2013, . _See also_ Angloworld; Angloshpere; Greater Britain\n\nempire, theories of, \u2013, \u2013118; free trade, variant of, \u2013; Hardt and Negri, account of, \u2013; iconographic order of empire, concept, , \u2013; imaginary, \u2013; informal, conception of, \u2013, \u2013, ; involution, idea of, ; resistance to, , \u2013; settler colonialism, \u2013, \u2013, \u2013, , , \u2013, , \u2013, , \u2013, , , , \u2013, \u2013, \u2013, \u2013, , \u2013, \u2013, , , \u2013, , , , , \u2013, , \u2013, \u2013; second settler empire, concept, , , , . _See also_ Greater Britain; Imperial Federation; India, British empire in\n\n_Encyclopaedia Britannica_ ,\n\nEthical Societies, movement, ,\n\nevolutionary theory. _See_ Darwinism, social\n\nEyre, controversy, \u2013, , , 307n36\n\nFabianism, ,\n\nFalk, Richard,\n\nFanon, Frantz, , \u2013; _The Wretched of the Earth_ ,\n\nfederalism, as mode of political organization, , , , , \u2013, 161n44, \u2013, , \u2013, , , \u2013, , \u2013, \u2013, \u2013; Imperial, , , , \u2013, , \u2013, \u2013, , , \u2013, \u2013, , \u2013, \u2013, , , , \u2013, \u2013, , , \u2013, \u2013; world, , , , , \u2013, , ,\n\n_Federalist Papers_ , the, 528\n\nFenn, W. W.,\n\nFerguson, Niall, , , \u2013\n\nFichte, Johan Gottlieb, \u2013; _Addresses to the German Nation_ ,\n\nFiggis, J. N.,\n\nFirst World War (1914\u201318), , , , , , , \u2013, , , ,\n\nFisher, H.A.L., 172n23, ,\n\nFiske, John, ; _American Political Ideas Viewed from the Standpoint of Universal History_ , ; _The Discovery of America_ ,\n\nFitzjames Stephens, James, \u2013, , ; _Liberty, Equality, Fraternity_ ,\n\nFitzmaurice, Andrew, 51n133\n\nFoley, Tadhg, 7n23\n\nFoucault, Michel, 106n56,\n\nFord, Gerald,\n\nFord, Lisa,\n\nForsyth, Murray, 328n35\n\nFoster, William, , , , \u2013,\n\nFox, Charles James, 77n47\n\nFrance, 30n37, , , , , , , , , , , , , , , , , , , , . _See also_ French Revolution\n\nFranco-Prussian War (1870\u201371),\n\nFranklin, Benjamin,\n\nFreeman, Edward A., \u2013, , 44n101, , , \u2013, \u2013; _Comparative Politics_ , ; on federalism, \u2013; on history, , 131n56, \u2013, \u2013; _History of Federal Government_ , ; opposition to imperial federation, , ; on race, , \u2013, \u2013, \u2013; on the United States, 44n101, , \u2013, \u2013\n\nfree trade, \u2013, , , , , , , 238n5, \u2013, , , ; \"free trade imperialism\" ( _see_ empire)\n\nFreeden, Michael, \u2013, , , 355n49\n\nFriedrich, Carl, 86n99\n\nFrench Canadians, \u2013\n\nFrench Revolution, , , \u2013, ,\n\nFroude, James Anthony, , \u2013, , , \u2013, , , , , \u2013, , , ; as civic imperialist, , , , \u2013, 308n40, ; conception of Oceana, \u2013; on history, , \u2013, , \u2013; _History of England from the Fall of Wolsey to the Defeat of the Spanish Armada_ , ; on liberalism, \u2013, 308n41, \u2013; _Nemesis of Faith_ , ; _Oceana_ , , , , 309n42; on race, \u2013,\n\nfuture war, narratives of, 341n2\n\nGallagher, John, , . _See also_ empire\n\nGandhi, Mahatma, \u2013, ; _Hind Swaraj_ , \u2013\n\ngender, , , , , , 307n37,\n\ngenocide, colonial, \u2013, , , . _See also_ Tasmania\n\nGermany, , , , , , , , , , , , , \u2013, 202n82, , , , , , \u2013, , , , , \u2013,\n\nGerstle, Gary, ,\n\nGeuss, Raymond,\n\nGibbon, Edward, , , , , , , ; _History of the Decline and Fall of the Roman Empire_ , , 138n36\n\nGierke, Otto von,\n\nGilbert, Felix,\n\nGladstone, William Ewart, , , , , 238n5, , , 270n27, ,\n\nGoethe, Johann Wolfgang von, ,\n\nGooch, G. P., , ,\n\nGore, Charles,\n\nGreat Exhibition (1851),\n\nGreater Britain, idea of, 7n21, \u2013, , , , , , , , , \u2013, \u2013, \u2013, \u2013, \u2013, , , \u2013, \u2013, , , \u2013, \u2013, . _See also_ Angloworld; Anglosphere; Imperial Federation\n\nGreece, model of empire, , , , , , \u2013, , , , , , , , \u2013, , , \u2013,\n\nGreen, J. R.,\n\nGreen, Thomas Hill, , , \u2013, \u2013; _Lectures on the Principles of Political Obligation_ , \u2013, ; _The Prolegomena to Ethics_ , ; \"The Right of the State over the Individual in War,\"\n\nGreswell, William,\n\nGrote, George, , 130n54,\n\nGuizot, Francois, ; _General History of Civilization in Europe_ ,\n\nGunnell, John, \u2013\n\nHammond, J. L., , 26n25, ,\n\nHarcourt, William,\n\nHardie, Kier, ,\n\nHardt, Michael, \u2013\n\nHarrington, James, ; _The Commonwealth of Oceana_ , , 309n42\n\nHarrison, Benjamin, \u2013\n\nHarrison, Frederic, \u2013, ,\n\nHartz, Louis, 3n8, ,\n\nHarvard Divinity School,\n\nHastings, Warren, 56n152,\n\nHayek, Friedrich,\n\nHechter, Michael, 21n7\n\nHegel, Georg W. F., ,\n\nHell, Julia, \u2013\n\nHenley, W. E.,\n\nHerder, Johann Gottfried von, , ,\n\nHerz, John,\n\n_Herrenvolk_ ethics, concept. _See_ race\n\nHilferding, Rudolf,\n\nHilton, Boyd, 173n28\n\n\"historical-mindedness,\" concept, \u2013, , \u2013,\n\nHitler, Adolf, , ,\n\nHobbes, Thomas, , , ,\n\nHobsbawm, Eric, \u2013\n\nHobhouse, Leonard Trelawny, , , \u2013, , , , , \u2013, , , , \u2013, \u2013, ; on colonialism, , , \u2013; _Democracy and Reaction_ , , , ; on liberalism, \u2013, , \u2013, , , , \u2013, ; _Liberalism_ , , , ; _The Metaphysical Theory of the State_ ,\n\nHobson, John A., , , , , , , , , \u2013, \u2013, , \u2013, , , , , \u2013, ; _The Crisis of Liberalism_ , \u2013, ; on imperial federation, , \u2013; _Imperialism_ , , , ,\n\nHolborn, Hajo,\n\nHolland, Bernard, , , , ; _Imperium et Libertas_ ,\n\nHollander, Samuel, 217n26\n\nHolmes, Stephen, 67n16,\n\nHolmes, Sherlock, of Baker Street, . _See also_ Conan Doyle, Arthur\n\nHort, F.J.A.,\n\nHouse Concurrent Resolution  (1949), \u2013\n\nhuman terrain, mapping of,\n\nHume, David, , 67n16, , , \u2013\n\nHutchins, Robert M.,\n\nHuxley, Aldous,\n\nHyndman, H. M., ,\n\nidealism, philosophical, \u2013, , \u2013\n\nideology, account of, 6n20, , \u201318\n\nIgnatieff, Michael, ,\n\nIkenberry, John, ,\n\nImperial Federation, \u2013, , , , , \u2013, \u2013, 167n3, \u2013, \u2013, \u2013, \u2013, \u2013, , , , \u2013, , \u2013, , \u2013, \u2013, \u2013,\n\nImperial Federation League (IFL), 37n68, , , , ,\n\nimperial involution, concept,\n\nImperial War Cabinet (1916\u201319),\n\nIndia, British Empire in, , , , , \u2013, , \u2013, \u2013, \u2013, , \u2013, \u2013, , \u2013, , \u2013, , , , \u2013, , , , \u2013, , \u2013, , , , , \u2013, , 299n5, \u2013, , , , , , ,\n\nIndian Civil Service, , 261n93\n\nIndian Mutiny (1857). _See_ Sepoy Rebellion\n\nIndian National Congress, ,\n\nInternational Institute of International Affairs (Chatham House),\n\nInternational Relations (IR), academic discipline, 3n10, \u2013, 147n36, ,\n\nIraq, , 31n42, , ,\n\nIreland, , , , , , \u2013, \u2013, , , , \u2013, ; Home Rule, in, , , ,\n\nIslam, , , ,\n\nisopolitan citizenship, 15n41, 145n14, , . _See also_ citizenship, common\n\nisopolity, . _See also_ isopolitan citizenship\n\nItaly, , , ,\n\nJackson, Henry,\n\nJamaica, \u2013. _See also_ Caribbean, the; Eyre, controversy; West Indies\n\nJames, Henry,\n\nJames, William, , . _The Varieties of Religious Experience_ ,\n\nJapan, , , ,\n\nJebb, Richard, \u2013\n\nJefferson, Thomas, ,\n\nJenkins, John Edward,\n\nJohnson, Chalmers,\n\nJones, Emily, 76n47\n\nJones, Henry Ford, 287n123\n\nJowett, Benjamin, ,\n\n_Johns Hopkins Studies in Historical and Political Science_ ,\n\n_Journal of the History of Ideas_ ,\n\nKant, Immanuel, , , , , , , ,\n\nKautsky, Karl,\n\nKennedy, John Fitzgerald,\n\nKerr, Philip, 11th Marquess of Lothian,\n\nKeynes, John Maynard, \u2013\n\nKingsley, Charles,\n\nKipling, Rudyard, , , , ; \"Recessional,\"\n\nKlibansky, Raymond,\n\nKnox, John, 316n75\n\nKoselleck, Reinhart,\n\nKosovo, 26n23\n\nKristeller, Paul,\n\nKristol, Irving,\n\nKymlicka, Will, 227n76\n\nLabilli\u00e8re, Francis P. de, , \u2013, , , \u2013\n\nLabour Party (British), 167n3, 239n5\n\nLaski, Harold, 75n41, , \u2013\n\nLawrence, T. J., \u2013\n\nLecky, W.E.H., , ,\n\nLeague of Nations,\n\nLenin, V. I., , ,\n\n_Liberales_ , Spanish,\n\nLiberal Party (British), , ,\n\nliberalism, variations on, \u2013, , \u2013, \u2013, \u2013, , \u2013, \u2013, \u2013, , , , , , , , \u2013, \u2013, , \u2013, \u2013, , \u2013, , , , \u2013, \u2013, \u2013; canonical approaches to, , , , , , \u2013, \u2013, \u2013, , ; conscripts of, \u2013, ; contextualist approaches to, , \u2013; neoliberalism, variant, , , , , \u2013, ; summative conception of, \u2013; settler colonialism, prioritization of, \u2013, , , \u2013, \u2013, 292n148, \u2013, , \u2013, \u2013; stipulative conception of, \u2013,\n\n\"libertas et imperium,\" phrase, , , , , , ,\n\nLightfoot, J. B.,\n\nLippmann, Walter,\n\n\"Little Englander,\" idea of, ,\n\nLocke, John, , , , , \u2013, \u2013, , \u2013, \u2013, , , ,\n\nLosurdo, Domenico, \u2013\n\nLowe, Robert,\n\nLucas, C. P., , \u2013, ; _Greater Rome and Greater Britain_ ,\n\nLuxemberg, Rosa,\n\nMacaulay, Thomas Babbington, , , , , , \u2013, , , , ; \"Minute on Indian Education,\" ; \"The New Zealander,\" image of, \u2013,\n\nMacDonald, Ramsay, \u2013\n\nMackinder, Halford, 322n4\n\nMachiavelli, Niccol\u00f2, , , , , , ; _Discourses on Livy_ ,\n\nMacmillan, Alexander, 283n97\n\nMacpherson, C. B., , 85n92, ,\n\nMaitland, F. W., ,\n\nMaine, Henry, \u2013, , , \u2013, \u2013, , , , , , \u2013,\n\nMalaya,\n\nMalthus, Thomas,\n\nMamdani, Mahmood,\n\n_Manchester Guardian_ , the,\n\nManchester School, political economy, , . _See also_ free trade\n\nMandler, Peter,\n\nMansfield, Mike,\n\nMantena, Karuna, , \u2013, , \u2013, , ,\n\nmartialism, idea of, \u2013. _See also_ Nabulsi, Karma\n\nMartineau, John,\n\nMarx, Karl, , \u2013, 167n3, \u2013, , , , . _Capital_ ,\n\nMarxism, , , \u2013, \u2013, , . _See also_ Marx, Karl; Lenin, V. I.\n\nMaurice, Frederick Denison, \u2013\n\nMazzini, Giuseppe,\n\nMcCain, John,\n\nMcGiffert, Arthur,\n\nMcGill University,\n\nMcKinley Tariff (1890),\n\nMehta, Uday Singh, , \u2013, \u2013, , , , \u2013, \u2013, , , \u2013; _Liberalism and Empire_ , \u2013,\n\nmethodological communitarianism, problem with, . _See also_ Taylor, Charles\n\nmelancholic colonialism, concept, , , \u2013\n\nMerivale, Charles,\n\nMerivale, Herman, , ,\n\nMill, James, , \u2013, \u2013, , ,\n\nMill, John Stuart, , , , \u2013, \u2013, , \u2013, \u2013, , \u2013, , , \u2013, , , , \u2013, , \u2013, , , \u2013, , , , , , \u2013, 304n22, , , 356n49, ; on colonization, , , \u2013, \u2013, , , , \u2013, , , , , \u2013, ; _Considerations on Representative Government_ , \u2013, , , , , , , , , ; on India, \u2013, \u2013, , \u2013, ; on Ireland, \u2013; and liberalism, \u2013, , \u2013, , \u2013, , , \u2013, , , , 356n49; _On Liberty_ , , , ; _Principles of Political Economy_ , \u2013; _System of Logic_ , ,\n\nMiller, J.D.B.,\n\nMills, Arthur, ,\n\nMills, Charles, ,\n\nMills, C. Wright, 83n82\n\nMilner, Alfred, ,\n\nMilton, John, ,\n\nMinogue, Kenneth,\n\nMises, Ludvig von,\n\nMolesworth, William,\n\nMoltke, Helmut von,\n\nMommsen, Theodor,\n\nMontesquieu, Charles-Louis de Secondat, Baron de, , ; _Considerations on the Causes of the Greatness of the Romans and Their Decline_ ,\n\nMonypenny, W. F., ,\n\nMorgenthau, Hans,\n\nMorley, John, , 83n86, , , , , 282n96\n\nMuirhead, J. H.,\n\nM\u00fcller, Max, ,\n\nMurray, Gilbert, \u2013, , 52n137\n\nMuthu, Sankar, \u2013, , , ,\n\nNabulsi, Karma, 52n134, \u2013, 136n75\n\nNagel, Thomas,\n\nNapoleon Bonaparte, , , ,\n\nNegri, Antonio, \u2013\n\nNewman, J. H.,\n\nNew South Wales, 3n.3,\n\nNew York,\n\n_New York Times_ ,\n\nNew Zealand, , , , , , \u2013, , , , , , 170n15, 175n32, , , , , 216n24, 222n52, , , , 299n5, , , 310n43, , , , ; \"New Zealander,\" idea of, \u2013\n\nNiebuhr, Barthold Georg, ; _R\u00f6mische Geschichte_ ,\n\nNiebuhr, Reinhold,\n\n_Nonconformist_ , the,\n\nNorth Atlantic Treaty Organization (NATO), ,\n\nObama, Barack,\n\nOliver, F. S., ; _Alexander Hamilton_ ,\n\nOrientalism, Saidian, traditional conception of, \u2013, ,\n\nOsterhammel, J\u00fcrgen,\n\nOttoman Empire, ,\n\nPagden, Anthony, , ,\n\nPaine, Thomas,\n\nPaley, William, ; _Principles of Moral and Political Philosophy_ ,\n\nPalmerston, Viscount, Henry Temple, 245n27\n\nPan-African Congress,\n\nPanofsky, Erwin,\n\nParker, Joseph, 272n34\n\nParkin, George, \u2013,\n\nParliamentary Group for World Government,\n\nParrington, Vernon, ; _Main Currents of American Thought_ ,\n\nPatriot Kingship, idea of, \u2013\n\nPearson, Charles, ; _National Life and Character_ ,\n\npeople, idea of, \u2013, \u2013, \u2013, , 308n41\n\nPeterson, William, \u2013\n\nPettit, Philip,\n\nPhilippines, US imperialism in, , ,\n\nPitts, Jennifer, , , , \u2013, , \u2013, , , , , , , ,\n\nPlamenetz, John, 3n8,\n\nPlunkett, John,\n\npluralism, political, ,\n\nPocock, J.G.A., 39n78, ,\n\nPolanyi, Karl,\n\nPollock, Frederick,\n\nPolybius, , , , ,\n\nPopper, Karl, ; _The Open Society and its Enemies_ ,\n\npostcolonialism, theory, , , \u2013, , ,\n\nPrivy Council, , , \u2013\n\nPrinceton Project on National Security,\n\nProthero, G. W., ,\n\nPrussia, . _See also_ Germany; Franco-Prussian War\n\npublic moralists, , , , , , , , , , ,\n\npublic opinion, significance of, ,\n\npublic sphere, idea of, , , \u2013, \u2013, \u2013, ,\n\n_Quarterly Review_ ,\n\nQueen Victoria. _See_ Victoria\n\nrace, ideas about, , \u2013, , , , , \u2013, , , , , \u2013, , , , , \u2013, , , \u2013, , 155n24, \u2013, , \u2013210, \u2013, , \u2013, , , \u2013, , , \u2013, , \u2013, , \u2013; Aryan theory of, , , \u2013, \u2013, ; as biocultural assemblage, , 175n39; contract, racial, ; _Herrenvolk_ ethics, , ; patriotism of, \u2013, ; Teutonic theory of, , \u2013, , . _See also_ Angloworld; Anglosphere; Civilization; Greater Britain\n\nRanke, Leopold von, , , ; _The Ecclesiastical and Political History of the Popes of Rome_ ,\n\nRawls, John, \u2013,\n\nrealism, international relations theory, , , \u2013, , . _See also_ International Relations (IR), discipline of\n\nReform Act (1867),\n\nReform Act (1884),\n\nRegius Professorship of Modern History (Cambridge), , 270n27,\n\nRegius Professorship of History (Oxford), , , 134n69,\n\nrepublican imperialism, , 30n37, \u2013, , , , , , , \u2013, \u2013. _See also_ civic imperialism\n\nrepublicanism, political theory, , , , 30n37, \u2013, , , , , , , \u2013, , , , , \u2013, , 153n15, , \u2013, 203n92, , \u2013,\n\n\"responsible government,\" colonial, , , , , 232n91, \u2013\n\nResponsibility to Protect (R2P), doctrine, 27n23\n\n_Review of Reviews_ ,\n\nRhodes, Cecil, , , , \u2013, \u2013, 281n93, ; \"Rhodes Must Fall,\" movement, 139n89; Rhodes Scholarship, \u2013\n\nRicardo, David, , 36n64, , , 217n26,\n\nRichter, Melvin,\n\nRitchie, D. G., 79n60, , , , 287n123,\n\nRobertson, F. W.,\n\nRobertson, J. M., \u2013\n\nRobertson, John, 123n17\n\nRobinson, Ronald, , . _See also_ empire\n\nRoebuck, J. A., 216n21,\n\nRome, legacy of, \u2013, \u2013, , \u2013, \u2013, , , \u2013,\n\nRoosevelt, Franklin Delano,\n\nRoosevelt, Theodore,\n\nRorty, Richard,\n\nRosebery, Archibald Philip, 5th Earl of Rosebery, , 47n117, , ,\n\nRound Table movement, 334n71, 47n117, , , , \u2013,\n\nRoyal Colonial Institute, 156n30, , ,\n\nRoyal Geographical Society,\n\nRoyal Institute of International Affairs, \u2013\n\nRuskin, John, , ,\n\nRussell, Bertrand, , ,\n\nRussia, , \u2013, , , , 202n82, , , \u2013, , 309n43,\n\nRyan, Alan, \u2013, 63n4\n\nSabine, George,\n\nSaid, Edward, . _See also_ Orientalism\n\nSalisbury, Lord, ,\n\nSallust (Gaius Sallustius Crispus), ,\n\nSalmon, Edward, ,\n\nSamuel, Herbert, , ,\n\nSay, Jean-Baptiste, 217n26\n\nSchumpeter, Joseph, \u2013, ,\n\nShaw, Albert,\n\nScott, David, \u2013\n\nScott, James,\n\nSecond World War (1939\u201345), , , , , \u2013, ,\n\nsecurity community, concept, ,\n\nsecurity dilemma, concept,\n\nSeebohm, Frederic,\n\nSenior, Nassau, ,\n\nSeeley, John Robert, , , \u2013, , 50n128, 51n134, , , , , , , \u2013, , , , , , , , , , , , \u2013, \u2013, 225n71, \u2013, ,  306n11, , , ; as a cosmopolitan nationalist, \u2013; conception of ethics, \u2013; _Ecce Homo_ , , , \u2013, ; _The Expansion of England_ , , , , , , , , \u2013, , , , , , , , , , ; on federalism, \u2013; \"Georgian and Victorian Expansion,\" ; on history, , \u2013, , , \u2013, , \u2013, , , \u2013, ; on imperial federation, , \u2013, , , \u2013, , , , , \u2013, \u2013, ; on India, , \u2013, ; _Introduction to Political Science_ , , , ; on Ireland, \u2013; _Life and Timesof Stein_, ; _Natural Religion_ , , \u2013, ; political development, theory of, \u2013; on religion, , \u2013\n\nSepoy rebellion (1857), , \u2013, , ,\n\n_Settler Colonial Studies_ , 370n21\n\nsettler colonialism. _See_ empire\n\nSettler Revolution, idea of, , . _See also_ Belich, James\n\nShaftesbury, 7th Earl, Anthony Ashley-Cooper,\n\nShklar, Judith, \u2013,\n\nSidgwick, Henry, , , , , , 77n52, , , 119n3, , \u2013, , , ; _Development of European Polity_ , , ; on empire, , , \u2013; on federalism, \u2013, ; on liberalism, \u2013, , , \u2013; _The Methods of Ethics_ ,\n\nSeeley, Robert B., 268n15\n\nSilva White, Arthur,\n\nSkinner, Quentin, \u2013, 6n20, \u2013, ,\n\nSlaughter, Anne-Marie,\n\nSmith, Adam, , \u2013, , , , , , , ; _An Inquiry into the Nature and Causes of the Wealth of Nations_ , ,\n\nSmith, Goldwin, , , , , , , , , , , ,\n\nSmith, Tony,\n\nSmith, W. H.,\n\nSocial Darwinism. _See_ Darwinism, social\n\nsocialism, , \u2013, , \u2013, , 77n53, , , , , , \u2013, \u2013, , , , , , , , , , , \u2013, \u2013, 355n47, 357n56. _See also_ Marxism\n\nSocial Democratic Federation, 167n3\n\nSocial Question, the, \u2013, \u2013, ,\n\nSorel, Georges, \u2013\n\nSorley, W. L.,\n\nSouth Africa, , , , , 109n67, , , , , , , , 174n32, , , , , , , , , , , , , , , , , , , ; War in (1899\u20131902), , , , , , , , , , , , , , , . See _also_ Cape Colony\n\nSouth Australia, ,\n\nSouth Australian Association,\n\nSpain, , , , , ,\n\nSpanish-American War,\n\n_Speaker_ , the,\n\nSpecial Relationship, Anglo-American,\n\nSpencer, Herbert, , , , , , , \u2013, , , , , , , , \u2013, , , ; as critic of imperialism, \u2013, , \u2013, ; evolutionary theory of, \u2013; _First Principles_ , ; liberalism of, , , , , , , , \u2013, ; _The Principles of Ethics_ , ; _The Principles of Sociology_ , ; _The Proper Sphere of Government_ , ; settler colonialism, support for, , , 263n103, ; _Social Statics_ , ,\n\nSpinoza, Baruch, 67n16, ,\n\nSpivak, Gayatri,\n\nStanley, A. P.,\n\nstationariness, trope of, , ,\n\nStead, W. T., , \u2013, 141n28, , , , , , 360n68, ; _The Americanization of the World_ ,\n\nSteger, Manfred, 94n11,\n\nStephen, Leslie, , 304n23; _History of English Thought in the Eighteenth Century_ ,\n\nStimson, Henry L.,\n\nStokes, Eric, \u2013; _The English Utilitarians and India_ ,\n\nStout, Robert,\n\nStrachan-Davidson, J. L., 138n84\n\nStrauss, Leo, , , , ,\n\nStreit, Clarence, , , ; _Freedom's Frontier_ , ; _Union Now_ , \u2013; _Union Now with Britain_ ,\n\nSuez Canal, ,\n\nSutherland, John George Edward Henry Douglas, Marquess of Lorne and 9th Duke of Argyll, \u2013, ; _Imperial Federation_ ,\n\nSylvest, Casper, 300n7, 348n27\n\nTacitus (Publius Cornelius Tacitus), 135n73\n\nTariff Reform campaign, ,\n\nTasmania, 40n84, , , . _See also_ genocide\n\nTaylor, Charles, 67n16, \u2013\n\nTaylor, Miles,\n\nTea Party, American,\n\nTennyson, Alfred, , ,\n\nTeutonism, racial theory, , , \u2013, ,\n\n_Times_ , the (London), , ,\n\ntime and space, imperial significance of, , , , \u2013, , \u2013, , , \u2013, , \u2013, , ,\n\nTocqueville, Alexis de, \u2013, , , , , , , , , ;\n\n_Democracy in America_ ,\n\nTorrens, Robert, ,\n\ntotalitarianism, concept, , , , , , ,\n\nTurkey. _See_ Ottoman Empire\n\nTreitschke, Heinrich von,\n\nTrevelyan, G. M., 282n87\n\nTrollope, Anthony,\n\nUnited Nations (UN), ,\n\nUnited States of America, , , , , \u2013, , , \u2013, , , , \u2013, , \u2013, , \u2013, , , , , , \u2013, , , \u2013, \u2013, \u2013, \u2013, , , , , , \u2013, , , \u2013, , \u2013, \u2013, \u2013, 350n33, , , , , , \u2013, ; Civil War, , , ; first peoples, , , , \u2013; imperialism of, , , , , , \u2013, , , 120n8, , , , \u2013, \u2013, , , 309n43, , , \u2013; Revolution, , , , , , , , , , ; union with Britain, , , , , , \u2013, \u2013, , \u2013, . _See also_ Angloworld; Anglosphere\n\nUnited World Federalists,\n\nUsborne, Henry,\n\nutilitarianism, , , , , , , , \u2013, , , , , \u2013, \u2013, , , , \u2013, , , ,\n\nutopianism, , , \u2013, , , , \u2013, , , , ,\n\nVan Diemen's Land. _See_ Tasmania; genocide\n\nVenezuela boundary dispute (1895),\n\nVeracini, Lorenzo, 40n79, 370n21\n\nVereeniging, Peace of (1902), 353n41\n\nVictoria, Colony, 170n15\n\nVictoria, Queen, , , \u2013, . _See also_ Diamond Jubilee\n\nviolence, colonial, , \u2013, , , 51n134, \u2013, \u2013, \u2013, , , , , \u2013, , \u2013, . _See also_ Eyre controversy; genocide; martialism\n\nVitoria, Francisco de,\n\nVoegelin, Eric, ,\n\nVogel, Julius, ,\n\nWakefield, Edmund Gibbon, \u2013, , 129n53, , , , , \u2013, , , , , ; _England and America_ , ; _Letter from Sydney_ , ; _A View on the Art of Colonization_ ,\n\nWaldron, Jeremy, , \u2013\n\nWaldstein, Charles, ,\n\nWallas, Graham,\n\nWalzer, Michael, ,\n\nWarre Cornish, Francis,\n\nWashington, George,\n\nWatkins, Frederick,\n\nWeinstein, David,\n\nWeiss, Thomas,\n\nWelch, Cheryl, ,\n\nWells, H. G., , , , \u2013, , , ; _Anticipations_ , ; _War of the Worlds_ ,\n\nWendt, Alexander,\n\nWestcott, B. F.,\n\nWest Indies, the, , , , 309n43. _See also_ Caribbean, the; Jamaica\n\nWhelan, Frederick,\n\nWhewell, William, ,\n\nWilliams, Roger,\n\nWilloughby, W. W., 295n164\n\nWillkie, Wendell, ; _One World_ ,\n\nWilson, Jon,\n\nWolfe, Patrick,\n\nWolin, Sheldon, , ,\n\nWorld Order Model Project,\n\nWormell, Deborah, 295n165\n\nWright, Quincy,\n\nYoung, Frederick, \u2013, ,\n\nYoung England, movement,\n\nZimmern, Alfred, \n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":" \nTable of Contents\n\nTitle Page\n\nCopyright Page\n\nDedication\n\nAcknowledgements\n\nWHAT'S IN A NAME?\n\nTHE HARMONICA MAN\n\nCLUB OF CHAMPIONS\n\nSTOP, START, THEN STOP AGAIN\n\nCITY ACCESS\n\nAMERICAN SUCCESS\n\nDEBBIE MCCORMICK\n\nCURLING IN PRINT\n\nMOTOR CITY, CANADA\n\nSTONE STANDARD\n\nTHE 12 RULES OF CURLING\n\nSAY WHAT?\n\nBURNS ON CURLING\n\nTWO TIMES EIGHT\n\nPAUL SAVAGE\n\nAMERICAN ORIGINS\n\nMOVING INDOORS IN THE U.S.A.\n\nPASSPORT, PLEASE\n\nA BOY AMONG MEN\n\nTHE MEASUREMENT OF A CURLING STONE\n\nTHE FIRST CURLING STAR?\n\nCARVED IN GRANITE\n\nU.S. COLLEGIATE CURLING\n\nSIX-SHOOTER\n\nOUT OF THE COLD\n\nCROWDED HOUSE\n\nKEN WATSON, MR. CURLING\n\nSWEEP, THEN PUSH\n\nWARMING UP IS RUBBISH\n\nKNOW YOUR WIDTHS\n\nALL ABOARD\n\nWHAT A HACK\n\nTHE JUBILEE STONE\n\nPAPER GRANITE\n\nCURLING FIGHTS\n\nCURLING CLUB CHAIN GANG\n\nCURLING IN THE MOVIES\n\nHelp!\n\nMen with Brooms\n\nNAME THAT CORN\n\nTHE KING OF SWING\n\nWHAT IF MY ROCK...\n\nENFANT TERRIBLE\n\nDEAD HEAT\n\nTHE ICE KING\n\nAMERICA'S MAN, BUD SOMERVILLE\n\nTHE WRENCH SAID\n\nBETWEEN A ROCK AND A HARD PLACE\n\nCURLING COUPLES\n\nROCKS FOR ROCKERS\n\nBRIER BROADCASTER\n\nA FAMILY AFFAIR\n\nHIGH SCORE\n\nTRAVELLIN' MAN\n\nAGE-OLD INVENTION\n\nGREAT COMEBACKS\n\nPIZZA AND MEDALS\n\nOLE MEXICO\n\nLONG-GONE EQUIPMENT\n\nCentre skittle\n\nTassels\n\nCrampits\n\nThe Duster\n\nCLOSET CURLING FANS\n\nSPRINGFIELD GRANITE\n\nTHE CURSE OF LABONTE\n\nBRITISH GOLD\n\nIRON CURLING\n\nBROTHERS\u2014AND SISTERS\u2014IN BROOMS\n\nTANKARD TOTAL\n\nCHAMPIONSHIPS FOR EVERYONE\n\nCanadian Postal Employees Curling Championship\n\nRoyal Canadian Legion\n\nCanadian Firefighters Curling Association\n\nCanadian Blind Curlers Championship\n\nCanadian Clergy Championship\n\nCanadian Police Curling Championship\n\nThe Trans-Canada Telephone Employees' Championship\n\nThe Atlantic Oilworkers Championship\n\nFANTASTIC FERBEY\n\nROARING ALONG\n\nPLANES, TRAINS, AND AUTOMOBILES\n\nHOLEY SLIDER\n\nQUITE AN ORDER\n\nTHE WRENCH VS. THE WENCH\n\nSTICKING TO CURLING\n\nThe History of the Stick\n\nNO RESPECT\n\nSLIPS OF THE TONGUE\n\nRECORD MAN\n\nWHY HURRY?\n\nCURLING NICKNAMES\n\nPERFECT RECORD\n\nBABY BROTHER\n\nPLAY THE GAME\n\nHEAD(SET) GAMES\n\nGOING LOW\n\nTHE MAGICAL 8\n\nBIG ROCKS\n\nSTONE CUTTER\n\nOLYMPIC DOUBLE\n\nROCK HARD SUCCESS\n\nHAMMER TIME\n\nGOING LONG\n\nTHE REAL WORLD\n\nWORLD SERIES CURLER\n\nMARKKU THE MAGNIFICENT\n\nSLIDING ALONG\n\nALL-IMPORTANT CLUB\n\nWHAT'S IN A NAME?\n\nCHARACTER GUY\n\nPRESERVED IN GRANITE\n\nSUBSTITUTE CHAMPIONS\n\nVISIBLE MINORITY\n\nCLOSE TO PERFECTION\n\nA HEART OF PURPLE\n\nTANKARD TIME\n\nSPONSORS\n\nBATTLE OF THE SEXES\n\nSCIENCE OF CURLING\n\nREGAL CURLING\n\nWOMEN'S DATES\n\nJUNIOR-SENIOR\n\nBAD ICE\n\n1970 Brier\n\n1992 Olympics\n\n1981 World Curling Championships\n\n2001 Brier\n\n2005 Women's World Championship\n\nORIGINAL OLSON\n\nHISTORY ON DISPLAY\n\nCURLING IN THE BIBLE?\n\nLATE NIGHT CURLING\n\nCURLING ART\n\nTV PAY DAY\n\nCURLER STATS\n\nCURLING IN TELEVISION COMMERCIALS\n\nAdvertiser: Cialis (a drug for erectile dysfunction)\n\nAdvertiser: Labatt Beer\n\nAdvertiser: Scotties tissues\n\nAdvertiser: Office Depot\n\nROCK BOTTOM\n\nDEADLY BUSINESS\n\nPURPLE RAGE\n\nAMERICAN SUCCESS\n\nTHE MANITOBA BONSPIEL\n\nA SPIKED TROPHY\n\nNORTHERN AFFAIR\n\nSTONES OF A DIFFERENT MATERIAL\n\nTIME TO CURL\n\nON THE TUBE\n\nCURLING ROYALTY\n\nTHE LONG AND THE SHORT(ER) OF IT\n\nTIMELINE OF THE FREE-GUARD ZONE\n\nELECTRONIC EYE\n\nTAKEN FOR GRANITE\n\nGIVING UP\n\nA BLIND EYE\n\nRECORD-SETTING CURLING\n\nAGE-OLD ROCKERS\n\nDOUBLING UP\n\nPIN MOGUL\n\nTHE CURLING TERMINATOR\n\nTHE RICHARDSONS\n\nA WOMAN'S PLACE\n\nMULTI-TALENTED\n\nTHE SHOT\n\nWORLD CHAIR\n\nSTATS\n\nLONG-DISTANCE CURLING\n\nRYAN'S EXPRESS\n\nWHAT A CROWD\n\nVERA NICE\n\nMONCTON 100\n\nCRAZY FOR CURLING\n\nSPIEL OF A DIFFERENT KIND\n\nTHE LONG BRIER ROAD\n\nROCK-SOLID POLITICS\n\nROCKIN' RICK\n\nCUT SHORT\n\nTHE ICEMAN CURLETH\n\nMARILYN BODOGH\n\nHOG WILD\n\nSINGULARLY REWARDING\n\nPHOTO CREDITS\n\nINDEX\n\n**Copyright \u00a9 2008 by Bob Weeks**\n\nAll rights reserved. No part of this work covered by the copyright herein may be reproduced or used in any form or by any means\u2014graphic, electronic or mechanical without the prior written permission of the publisher. Any request for photocopying, recording, taping or information storage and retrieval systems of any part of this book shall be directed in writing to The Canadian Copyright Licensing Agency (Access Copyright). For an Access Copyright license, visit www.access-copyright.ca or call toll free 1-800-893-5777.\n\nCare has been taken to trace ownership of copyright material contained in this book. The publisher will gladly receive any information that will enable them to rectify any reference or credit line in subsequent editions.\n\n**Library and Archives Canada Cataloguing in Publication Data**\n\nWeeks, Bob\n\nCurling, etcetera : a whole bunch of stuff about the roaring game \/ Bob Weeks.\n\nIncludes index.\n\neISBN : 978-0-470-73889-4\n\n1. Curling. I. Title.\n\nGV845.W.964 C2008-902118-5\n\n**Production Credits**   \nCover design: Jason Vandenberg   \nInterior design and typesetting: Mike Chan   \nCover photo: Hulton Archive\/Getty Images   \nPrinter: Tri-graphic Printing\n\nJohn Wiley & Sons Canada, Ltd.   \n6045 Freemont Blvd.   \nMississauga, Ontario   \nL5R 4J3\n\nTR\n\nThis book is printed with biodegradable vegetable-based inks. Text pages are printed on 60lb. 100% PCW recycled paper.\n_To Peter, Alfie and Ken\u2014the guys who opened the door for me_\n**ACKNOWLEDGEMENTS**\n\nThis book exists because I have a strange capacity for remembering all sorts of useless bits of information. Well, useless may be too strong a word, but certainly unusual and offbeat. Over the many years that I've written about curling and covered curling events, I've always managed to store in my mind not only the winners and losers but small associated items that wouldn't make the main column. I never had a place to put all these items . . . until now.\n\nThis book is a collection of years of these tidbits, the sum of which I hope will intrigue you. However, as sharp as I believed my memory was, I was still a bit foggy on certain facts and needed verification from a number of sources. Chief among these was Warren Hansen, the Canadian Curling Association's director of competitions. He knows as much about curling as anyone and\u2014once again\u2014graciously passed on a correction or clarification of certain events. If there's someone who has done more for curling in this world, I've yet to meet them.\n\nMany others pitched in as well: Jeff Timson, Keith Wendorf, John Kawaja, Danny Lamoureux, George Karrys, and the late Doug Maxwell were the primary aids.\n\nI also couldn't have managed this project without the assistance of my co-publishers of the _Ontario Curling Report_ : Peter Birchard, Alfie Phillips Jr., and Ken Thompson. They are three wonderful guys who have as much passion for the game as they do for red wine.\n\nThere is a shrinking but still strong fraternity of curling media who also pitched in (whether they knew it or not): Alan Cameron, Paul Wiecek, Jim Bender, Bob Garvin, Jim \"Hollywood\" Henderson, Brian McAndrew, Bill Graveland, Terry Jones, Vicki Hall, Mike Burns Jr., and the web-heads Dallas Bittle and Gerry Guerts.\n\nMany of the game's best players also answered questions for me either in person, on the phone, or via e-mail. Thanks to Russ Howard, Glenn Howard, Richard Hart, Dave Nedohin, Mike Harris, Ed Werenich, Kevin Martin, Joan McCusker, Hans Frauenlob, and Randy Ferbey. A special acknowledgment to Paul Savage, who may have enjoyed the game more than anyone I know.\n\nThe gang over at Wiley continue to amaze me with their talent and enthusiasm. Karen Milner had the faith to give this project the go-ahead and led a team that has shown a lot of faith in the roaring game.\n\nFinally, to my family. My parents, Bill and Deane, are my biggest fans and the feeling is mutual. My sister, Carol, is simply the most remarkable person I've ever met. Her husband, Dennis, is a close second. And my son, Chris, I am so proud to be your father. You are the centre of my universe.\n\nBob Weeks  \nMay 2008\n**WHAT'S IN A NAME?**\n\nCurling did not get its name because the rocks arc as they travel down the ice. That's known because the sport was called curling long before there was any intentional turn applied to the stone. The name \"curling\" is believed to come from an old Scottish word, \"curr,\" which refers to the roaring sound the stones made as they slid over the frozen lochs.\n\nIn-turns and out-turns came much later. In the book _The History of Curling_ by Reverend John Kerr, published in 1890, the author details what was called the Twist:\n\n\"...to be able by a turn of the wrist to give the stone a rotary motion which shall make it run against the bias of the ice, or to transform an object of offence into one of defence by making the stone curve round the right or left side of a guard by an elbow-out or an elbow-in delivery, is one of the highest accomplishments in the art of curling and greatly increases the interest and skill of the player.\"\n\nKerr also referred to this type of shot as the Fenwick Twist because it was a group of curlers from a village of the same name who were the first to purposely utilize this type of shot.\n**THE HARMONICA MAN**\n\nPiping the players onto the ice before draws of major championships is standard practice these days, but it wasn't always so. At the first few Briers, held inside Toronto's Granite Club, the curlers were actually paraded onto the ice surface by a man playing a harmonica. Art Condie, who was one of the early directors of the Brier, would play his harmonica at both the opening and closing ceremonies of the competition, usually leading the curlers to the ice. In 1940, when the Brier moved into an arena in Winnipeg, Condie's harmonica was simply too quiet to be heard by the fans. Still, he was allowed to perform at the closing ceremonies and was listed in the program as the Official Brier Musician.\n**CLUB OF CHAMPIONS**\n\nThe Strathcona Curling Club in Winnipeg, Manitoba, holds the distinction of being the home club for the most Brier-winning teams. It has seven Canadian championships to its credit.\n**STOP, START, THEN STOP AGAIN**\n\nIt's not often someone retires, then un-retires only to retire all without playing a game. United States skip Bruce Roberts, however, did just that in 1984. Roberts was a three-time U.S. men's champion, winning in 1967, '76 and '77, also taking the 1976 World Championship. '76 and '77, also taking the 1976 World Championship. But after that run, the resident of Duluth, Minnesota, retired from competitive curling, in part due to injuries.\n\nBut the 1984 World Championship was hosted in Duluth, and Roberts decided he wanted to make one more try at the Silver Broom in front of his hometown fans. And so, with his brother Joe throwing last rocks, he made a comeback and played exceptionally well, losing just four competitive games all year en route to representing the U.S.A. at the world final.\n\nDespite the success, Roberts stated prior to the start of his comeback year that he would be retiring when the season was over. So, effectively, he announced his un-retirement and re-retirement all at the same time.\n\nRoberts and his American rink lost a final round-robin game to Germany to finish with a 5-4 mark, one game short of the playoffs. True to his word, the U.S. Curling Hall of Famer hung up his broom\u2014again\u2014at the end of the '84 World Championship.\n**CITY ACCESS**\n\nFor five years, two cities were given entry into the Brier. Teams representing Montreal and Toronto fielded rinks in the Canadian men's national championship from 1927 to 1931 before being dropped in favour of provincial entries only. In 43 games, the Montreal team won just 10 matches. Toronto's team played 46 games\u2014including three playoff contests\u2014and came out on top in 28 of those.\n**AMERICAN SUCCESS**\n\nThe Bemidji Curling Club in Bemidji, Minnesota, is easily one of the most suc-is cessful in the United States, if not the world. The club can lay claim to having 18 U.S. national championship teams and 50 state championship rinks, a record that most clubs can only envy.\n**DEBBIE MCCORMICK**\n\nOne of the most successful curlers in U.S. history, Debbie McCormick played in five World Junior Championships, six World Curling Championships, and two Olympics. A few notes on the American curler:\n\n\u2022 She is the only American woman to skip a team to the World Championship title.\n\n\u2022 Her World Championship title in 2003 was the first time she skipped in international play.\n\n\u2022 She was born in Saskatoon, Saskatchewan, but moved to Madison, Wisconsin, when very young, when her father was transferred there for business.\n\n\u2022 She posed nude for a calendar created to promote women's curling.\n\n\u2022 She won the U.S. national title four times.\n\n\u2022 Her father, Wally, played in two World Championships, finishing third both times.\n\n\u2022 Her good-luck charm is a ticket from the gold-medal women's curling game at the 1998 Olympics, autographed by the members of the winning Sandra Schmirler team.\n**CURLING IN PRINT**\n\nOne of the earliest mentions of curling in print is found in Thomas Pennant's book _Tour Through Scotland_ , published in 1772. He describes the game as follows:\n\n\"Of all the sports in those parts, that of curling is the favorite. It is an amusement of the winter, and played upon the ice, by sliding from one mark to another, great stones of 40 to 70 lbs weight, of a hemispherical form, with a wooden or iron handle on top. The object of the player is to lay his stone as near the mark as possible, to guard that of his partner which has been well laid before, or to strike off that of his antagonist.\"\n**MOTOR CITY, CANADA**\n\nCross-border curling: The Detroit Curling Club is a member of the Ontario Curling Association.\n**STONE STANDARD**\n\nFor many years, curling stones came in all sorts of shapes and sizes. While there was an attempt made to somewhat standardize the stones over time, in the early 1800s the Grand Caledonian Curling Club came up with a scale for the ratio of diameter to thickness, shown below. Prior to this scale, rocks were often twice as wide as they were thick.\n\n**The Scale**\n\nWhen the weight of the stone is under the maximum height not to be more than\n\n35 lbs| 4.25 inches  \n---|---  \n38 lbs| 4.5 inches  \n41 lbs.| 4.75 inches  \n44 lbs.| 5 inches  \n47 lbs.| 5.25 inches  \n50 lbs.| 5.5 inches\n\n\"Whatever the diameter or weight, the height ought never to exceed 6 1\/8 inches, nor be less than 4\u00bc inches. None [ought] to be allowed in a set game of greater diameter than 12 inches, nor of a greater weight than 50 lbs. Imperial.\"\n**THE 12 RULES OF CURLING**\n\nWhen the Toronto Curling Club began play in Canada's largest centre, it did so on the frozen shoreline of Lake Ontario. The club was originally made up mostly of transplanted Scots who came from a variety of villages in the homeland and, as a result, had a variety of rules owing to the changes from village to village. So one of the first tasks of the new group was to craft an original set of Rules of the Game, which they did in about 1840. There were just 12 \"laws\" set out for play, some of which are still in use today:\n\n1. The rink to be forty-two yards from tee to tee, unless otherwise agreed upon by the parties.When a game is begun the rink cannot be changed or altered unless by the consent of a majority of players, and it can be shortened only when it is apparent that a majority cannot play the length.\n\n2. The hog score must be distant from the tee one-sixth part of the length of the rink. Every stone to be deemed a hog, the sole of which, when at rest, does not completely clear the length.\n\n3. Every player to foot so that in delivering his stone, it shall pass over the tee.\n\n4. The order of playing adopted at the beginning must not be changed during a game.\n\n5. Curling stones must be of a circular shape. No stone to be changed during a game unless it happens to be broken; and the largest fragment of such stone to count, without any necessity of playing it more. If a stone roll or be upset, it must be placed on its sole where it stops. Should the handle quit a stone in delivery, the player must keep hold of it, otherwise he will not be entitled to replay the shot.\n\n6. The player may sweep his own stone the whole length of the rink; his party not to sweep until it has passed the first hog score, and his adversaries not to sweep until it has passed the tee\u2014the sweeping to be always to a side.\n\n7. None of the players, on any account, to cross or go upon the middle of the rink.\n\n8. If, in sweeping or otherwise, a running stone is marred by any of the party to which it belongs, it must be put off the rink; if by any of the adverse party, it must be placed agreeably to the direction which was given to the player; and if it be marred by any other means, the player may take his shot again. Should a stone at rest be accidentally displaced, it must be put as near as possible in its former situation.\n\n9. Every player must be ready when his turn comes and must take only a reasonable time to play his shot. Should he, by mistake, play a wrong stone, it must be replaced wherever it stops, by the one which he ought to have played.\n\n10. A doubtful shot must be measured by a neutral person, whose determination shall be final.\n\n11. The skip alone shall direct the game. The players of the respective skips may offer them their advice, but cannot control their directions; nor is any person except the skip to address him who is about to play. Each skip may appoint one of his party to take the charge for him, when he is about to play. Every player to follow the direction given to him.\n\n12. Should any question arise, the determination of which may not be provided for by the words and spirit of the preceding Rules, each party to choose one of their number in order to determine it. If the two so chosen differ in their opinion, they are to name an umpire whose decision shall be final.\n\n**Curling Quote**\n\n\"We can't bring him in, he spilled red wine all over his uniform.\"\n\n\u2014Richard Hart to skip Mike Harris during the 1997 Canadian curling trials. The team's second, Colin Mitchell, was hurt, and Harris wanted to bring in the team's fifth player\/coach and noted bon vivant, Paul Savage, to fill in. The clip was heard across the TSN broadcast of the event.\n**SAY WHAT?**\n\nMany of the terms used in the early days of curling have disappeared from the game's lexicon. Here are a few that used to be quite common in the late 1700s and early 1800s.\n\n**Term** | **Meaning**  \n---|---  \nBreak an egg on| To strike one stone very gently with another  \nBrough| The House  \nChuckle to| To rub off the inside of two or more guards en route to another stone.  \nDirector| The Skip  \nHindhand| The player who throws the last rock on his team, usually the skip  \nLie in the bosom of| To freeze to another rock  \nRedd the ice| to clear guards from the front of the rings\n**BURNS ON CURLING**\n\nThe great poet Robert Burns may not have been a champion curler, but he did mention the grand old game in his poem \"Tam Samson's Elegy.\" The fourth verse of the piece reads as follows:\n\n_When Winter muffles up his cloak,_   \n_And binds the mire like a rock;_   \n_When to the loughs the curlers flock,_   \n_Wi' gleesome speed,_   \n_Wha will they station at the cock? -_   \n_'Tam Samson's dead!'_\n\nThe standard English translation of that work was provided by the Robert Burns World Foundation:\n\n _When Winter muffles up his cloak,_   \n_And binds the mire like a rock;_   \n_When to the ponds the curlers flock,_   \n_With gleeful speed,_   \n_Who will they station at the cock (mark)? -_   \n_'Tam Samson is dead!'_\n**TWO TIMES EIGHT**\n\nScoring an eight-ender\u2014a perfect end\u2014is an achievement ranked as one of the most difficult in sport. Many players compete their entire career without even witnessing one. But in 1993 the team of Kim Gellard, Corie Beveridge, Lisa Savage, and Sandy Graham accomplished something that had never been done before or since. Playing in a school league, the team recorded consecutive eight-enders\u2014two perfect ends. \"It's amazing,\" commented Gellard, the skip. No curler alive would disagree.\n\nCurling Quote\n\n\"Blood is thicker than Screech.\"\n\n\u2014Russ Howard on why he was cheering for his brother, Glenn, over his former Newfoundland teammates, led by Brad Gushue in the 2007 Brier final\n**PAUL SAVAGE**\n\nPaul Savage has been around the game of curling since he was a teenager, growing up in Don Mills, Ontario, and following in the footsteps of another Ontario icon, Alf Phillips Junior. He won titles all over Canada and competed around the world, and is known as a talented and fun-loving player. A few notes about Paul Savage:\n\n\u2022 His first provincial title was the 1965 Ontario Schoolboy, which he won while representing Don Mills Collegiate Institute.\n\n\u2022 He appeared in the movie _Men With Brooms_ , playing a minor role as a curling broadcaster, calling the action of the film's ultimate match.\n\n\u2022 He was the fifth man on Mike Harris's Canadian Olympic team, which played in the 1998 Games in Nagano, Japan. To qualify for a medal, he was required to play at least one end. He actually played two, in a game against Germany in which Canada had already posted a healthy lead. That allowed him to earn a silver medal. At 50, he was the oldest medalist in the '98 Games.\n\n\u2022 Prior to leaving for the Olympics, he had the Olympic rings tattooed onto his rear end. A picture of the tattoo appeared on the front page of a Toronto newspaper.\n\n\u2022 He played in seven Briers, winning once as third for Ed Werenich in 1983, and finishing second on three other occasions.\n\n\u2022 After his playing career, Savage became an entrepreneur in the game, starting an Ontario-based skins game, which grew to become a nationally televised event pitting the top teams in Eastern Canada vs. those in Western Canada.\n\n\u2022 He was on the losing end of one of the greatest comebacks in Brier history. In the 1974 Brier, he was leading Hec Gervais by seven points after six ends but lost in an extra end\u2014the 11th.\n\n\u2022 He was given the nickname \"the Round Mound of Come Around\" by the Ontario Curling Report owing to his girth as well as his talent for playing the draw shot. It was a play on the nickname of NBA player Charles Barkley, who was known as the \"Round Mound of Rebound.\"\n\n\u2022 Paul's daughter, Lisa, was the 1994 World Junior champion.\n**AMERICAN ORIGINS**\n\nThe first curling club in the United States was formed in Orchard Lake, Michigan, in 1831, six years before the state officially joined the union that would become the United States of America.\n**MOVING INDOORS IN THE U.S.A.**\n\nAlthough curling was a popular sport in the United States at the turn of the century, it was rarely played indoors. An exhibition match in 1897 in Brooklyn, New indoors. An exhibition match in 1897 in Brooklyn, New York, is believed to be the first time curling was played in a covered rink in America, but it wasn't until 1910 that it was first played on an indoor rink. That event took place in Boston at the Boston Arena when three sheets were put into a skating rink in order to host a bonspiel.\n\nThe first United States Men's Curling Championship, however, took that to another level with a rather impressive start. The championship was held in Chicago in 1957 at the Chicago Stadium, an 18,000-seat arena that served as home to the NHL's Chicago Black Hawks and the NBA's Chicago Bulls. It was also broadcast on regional television. The winner of that inaugural contest was a rink from Hibbing, Minnesota, skipped by Harold Lauber.\n**PASSPORT, PLEASE**\n\nCanadian ex-pats have taken their game to many countries over the years and represented those countries at a high level.\n\nHere is a selection of Canadian-born skips who have represented countries other than their native land in the world championships:\n\nHugh Milliken\n\n**Canadian** | **Country Represented** | **Year First Represented**  \n---|---|---  \nBob Woods| Sweden| 1967  \nKeith Wendorf| Germany| 1978  \nRoger Schmidt| Germany| 1987  \nMaymar Gemmell| USA| 1991  \nHugh Milliken| Australia| 1992  \nPatti Lank| U.S.A.| 1997  \nDan Mustapic| New Zealand| 2001\n**A BOY AMONG MEN**\n\nThe youngest player to compete at the world championships was 15-year-old Sjur Loen, who skipped Norway's entry in 1974. At that time, there were no age restrictions, and Loen's team of Hans Bekkelund (16), Morten Sogaard (17), and Hans Okelsrud (18) managed a record of 2-7. The next year, the first World Junior Curling Championship was held in Toronto, and although Loen didn't compete in that event, he represented Norway from 1976 to 1979, with his best finish coming in 1976, when he ended third. Loen managed to make it into the men's world championship nine more times, winning it twice.\n**THE MEASUREMENT OF A CURLING STONE**\n\nCurlers throw rocks up and down the sheet hundreds, perhaps thousands of times in a season, but do they ever stop to consider just how wide or heavy the curling stone really is? While stones are generally consistent from club to club and rink to rink, there is some provision in the rule book for a bit of variety. Here's what the rule book dictates:\n\nCurling stones, including handle and bolt, shall weigh a maximum of 44 pounds (19.96 kilograms) and a minimum of 38.5 pounds (17.46 kilograms), shall have a maximum circumference of 36 inches (91.44 centimetres), and shall be a maximum of 5.5 inches (13.97 centimetres) in height, measured between the bottom and top of the stone.\n\nThe rules indicate maximums for circumference and height, and a maximum and minimum for weight, so there is room to create a shorter, narrower, and lighter rock. So far, however, most manufacturers use the maximums as the standard measurements.\n**THE FIRST CURLING STAR?**\n\nHoward Wood of Winnipeg was one of the first curlers to achieve notoriety across a wide swath of Canada. A three-time Brier champion, he was a vivacious, gregarious man who quickly became popular with opponents and fans. A few notes about Wood:\n\n\u2022 He began curling in 1903 on a backyard rink built by his father.\n\n\u2022 In 1908, he played in his first Manitoba Bonspiel, the first of what would be a remarkable 70 consecutive appearances in the grand championship. That mark put him into the _Guinness Book of World Records_. He managed to win the overall title on eight occasions.\n\n\u2022 In 1925, Wood and his team won an all-expenses-paid trip to tour Ontario and Quebec, and curl teams in that part of the country. The rink played 19 games and won 18 of them, several by more than 20 points.\n\n\u2022 Wood won his first Brier in 1930 playing skip. Two years later, he won again, but this time playing third for Johnny Congalton.While many players have won a Brier at lead, second, or third and then later won as a skip, dropping down in position as Wood did is a feat that wasn't matched again until Pat Ryan, who skipped the Canadian champions in 1988 and '89, won as third for Rick Folk in 1994.\n\n\u2022 Wood's son, Howard Jr., became an accomplished curler, and played third for his father when they won the Brier in 1940.To distinguish between the two, the senior Wood became known affectionately as Pappy.\n\n\u2022 The 1940 Brier was the first to be played in an arena, the Winnipeg Amphitheatre. The final round was played before 5,000 fans, and they were not disappointed. Wood and his Manitoba team beat Cliff Manahan's Alberta foursome 17-11 to clinch the title.\n\n\u2022 In 1947, Wood won the first Carspiel, a competitive event that awarded four cars as first prize.Wood had to play a delicate-weight double with his final shot to win the title. It appeared to be a shot that was next to impossible to make. But Wood threw the rock and without waiting for it to finish, calmly walked over to one of the cars that had been conveniently brought onto the ice as a marketing tool, opened the door, and sat down in the driver's seat, just in time to watch the rock make the perfect split and come to rest for a single point and the title. He and his team drove home from Nipawin, Saskatchewan, in four new Hudsons.\n\n**Curling Fact**\n\nAccording to the Canada Curling Stone Company, the average lifespan of a curling stone is 50 years, and it can travel up to two hundred kilometres a year, up and down a sheet of ice.\n**CARVED IN GRANITE**\n\nThe first Canadian men's curling championship was held in 1927 at Toronto's Granite Curling Club. The event was held there continuously until 1939 and one final time in 1941. Some facts about the original home of the Brier:\n\n\u2022 The club was started in 1875 by five prominent Toronto businessmen who were members of the Toronto Curling Club. They were unhappy at the direction of that club and its decision to build a new facility on Adelaide Street.\n\n\u2022 The first honorary patron of the new club was Sir John A. Macdonald, Canada's first prime minister.\n\n\u2022 The club's first site was on a parcel of land just east of Queen's Park, the provincial legislature. The land was leased and the club built for $700. In future years, the club moved to locations on Church Street, north of Wellesley, and then, in 1926, to St. Clair Avenue, just west of Yonge. Its current location is on Bayview Avenue.\n\n\u2022 One of the main reasons to build the facility on St. Clair was to install artificial ice. In 1924 and '25, because of mild conditions, there had been almost no curling at the Church Street club, which had natural ice. When completed, the new rink was called \"the largest single covered expanse of artificial ice on the American continent.\"\n\n\u2022 Curling was only one of many sports available to members of the Granite Curling Club. Tennis, golf, swimming, bowling, badminton, and skating were all part of the lineup although curling remained the primary focus for many years.\n\n\u2022 A hockey team from the Granite Curling Club won the gold medal at the 1924 Olympics.\n**U.S. COLLEGIATE CURLING**\n\nWhile it's not quite on the same level as the Rose Bowl, there is a U.S. collegiate curling championship held annually. College curling began with the Illinois State Curling Foundation, which was established to administer a trust left by Darwin Curtis, an enthusiastic curler from Wilmette, Illinois. It started with a program to introduce college-aged curlers to the game in the mid-1980s and has grown into a true national bonspiel. In 2007, 30 teams were in the event, now held annually in Madison, Wisconsin. Among the schools that field teams are Harvard, MIT, Rutgers, and the University of Minnesota.\n**SIX-SHOOTER**\n\nOnly once has a Brier held in an arena had more than five sheets of ice. In Hamilton in 1991, because the ice surface was built to handle international hockey (which has a wider rink than North American hockey), six sheets of ice were built on the floor of Copps Coliseum. That allowed organizers to run an event with no morning draws, the only time that's happened. In total, only 14 draws were held, and attendance reached 88,894.\n\n**Curling Quote**\n\n\"I'm sure it was boring to watch. We could hear some people yelling down at us on the ice. It was frustrating for us too.\"\n\n\u2014British Columbia skip Rick Folk commenting on his 3-2 loss to Pat Ryan in the final of the 1989 Brier, regarded as one of the most uninteresting, boring Canadian finals ever\n**OUT OF THE COLD**\n\nThe first indoor curling rink with artificial ice opened in 1907 in Crossmyloof, Scotland.\n**CROWDED HOUSE**\n\nBrier attendance records have been kept since 1946, although in the early days, they were little more than estimates. The highest attendance came in 2005 in Edmonton when 281,985 people watched the competition. The lowest was in 1971 in Quebec City when just 8,501 fans showed up. That's the only time since '46 that fewer than 10,000 people watched the Canadian championship, although it should be noted that a major snowstorm limited travel for much of the week.\n**KEN WATSON, MR. CURLING**\n\nIn the 1930s and '40s, Ken Watson was known across Canada as Mr. Curling, and a look at his record shows the name was justified. Watson won three Briers as well as a host of other notable events, and was instrumental in starting the Scotch Cup, which was the forerunner of the world championships. Here are some facts about Watson:\n\n\u2022 He was born in 1904 in Minnedosa, Manitoba, the son of a reverend.\n\n\u2022 He started curling at 15, and his first curling prize was a butter knife.\n\n\u2022 He skipped the Brier-winning rink in 1939, '42, and '49.\n\n\u2022 Many felt he would have won more Briers, but the championship was put on hold from 1943 to 1945 because of the Second World War, right at the peak of Watson's career.\n\n\u2022 He was one of the first people to slide while delivering the rock. He accomplished this by taking off his rubber, which all curlers wore on their shoes at the time, and sliding on the sole of his shoe. In later years, he affixed solder to the bottom of his shoe so he could slide even farther. He was roundly criticized by many traditionalists for this shocking delivery.\n\n\u2022 He wrote a best-selling book, _Ken Watson on Curling_ , which listed the Seven C's for Success: Compatibility, Concentration, Co-operation, Courage, Confidence, Competitiveness, and Consistency.\n\n\u2022 In 1959, against the wishes of the Canadian (then Dominion) Curling Association, Watson set up matches between the Canadian champions, the Richardsons, and Willie Young and his Scottish champs. That tournament led eventually to the start of the World Curling Championship.\n\n\u2022 For 20 years, Watson made his living as a high school teacher, but because of his notoriety, he went into the insurance business and was extremely successful.\n\n\u2022 Watson won the overall title in the Manitoba Bonspiel, the largest event in the world, a remarkable six consecutive times, from 1942-47.\n\nCharles Reid, Lyle Dyker, Grant Watson, and Ken Watson with their Brier trophy in 1949.\n\n**SWEEP, THEN PUSH**\n\nFor many years, push brooms were used almost exclusively in Europe, while North American curlers played with corn brooms. But in the 1970s, the tide turned, and much of the impetus to switch was the result of play at one curling club. The Calgary Winter Club was one of the first facilities in Canada to offer up push brooms for club use, putting them into play in the late 1960s. Curlers at that popular rink found that the push brooms were more effective because they never left the ice surface, less taxing on the body, and far less messy. Not surprisingly, the brooms took off.\n\nThe peak of success may have been 1975, when three teams from the club won national championships\u2014all sweeping with push brooms. The rinks won the Canadian mixed, Canadian junior boys, and the Canada Winter Games.\n\n\"They are made right in Calgary and I think they are comparable to the corn brooms in effectiveness. There are places where you can keep working with the push broom when you couldn't with a corn broom. You don't wear yourself out as much in a long playdown, and you don't get arm weary,\" said Les Rowland, who skipped his team to the 1975 national mixed\u2014the first Canadian championship team to use push brooms.\n**WARMING UP IS RUBBISH**\n\nIn most sports these days, warming up is par for the course. Players in baseball have batting practice, basketball players have a shoot-around, and hockey players skate circles prior to the puck drop. But in curling, warming up was not allowed until 1976. In major competitions such as national or world championships, even walking down the ice to the far end\u2014as skips were required to do\u2014had to be done at the side of the sheet. Walking down the middle of the ice before the first rock was thrown was tantamount to cheating. Sliding or sweeping on the sheet was also a breach of etiquette.\n\nBut in 1975 Warren Hansen, who was a member of the 1974 Canadian championship team, and Laurie Newton, a postgraduate student at the University of Alberta, prepared a report for the International Curling Federation (ICF, forerunner of the World Curling Federation) that showed sweeping to be \"one of the most vigorous movements in sports.\" As well, players could \"reduce strains, sprains, muscle pulls and cramps\" if they were permitted to slide before the contest.\n\nHansen made the presentation to the ICF, and while it was generally accepted, Robin Welsh, longtime secretary of the Royal Caledonian Curling Club, wasn't in that camp. He stated: \"I believe it is all a pile of rubbish, curling is a manly game.\"\n\nHowever, the majority was on Hansen's side, and on the basis of the document, a warm-up period was permitted at the 1976 Silver Broom, the first of its kind. The warm-up did not, however, include throwing any rocks. That didn't happen until 1978, when a 10-minute warm-up was allowed; however, the players were not permitted to practise on the sheet on which they were playing. Finally in 1980, each team was permitted 10 minutes to throw stones on their own sheet.\n**KNOW YOUR WIDTHS**\n\nDid you know that the hog line is actually thicker than the tee line or the back line? It's true\u2014the hog line is four inches wide, while the tee and back lines are a mere half inch. These measurements are set under the rules of the game.\n**ALL ABOARD**\n\nIn the 1940s and '50s, before air travel, a dedicated train travelled across the country, picking up Brier competitors en route to the host site. It was known as the Brier Special and allowed the competitors to get to know each other prior to the competition. The event sponsor, Macdonald Tobacco, added a bar car that became the focal point of the ride. However, the atmosphere often took its toll on the players.\n\n\"By the time I got off the train in Moncton,\" said Edmonton's Matt Baldwin of his trip to the 1956 championship, \"I was shaking. We'd been drinking for five straight days.\"\n\n**WHAT A HACK**\n\n**A** hack may be something many curlers take for granted, but in 1989, it underwent a revolution thanks to a Quebec curler. Marco Ferraro was a competitive curler who always had difficulty with hacks wherever he played. He felt they were inconsistent, didn't provide a good hold for the foot, and often got in the way of the delivery. \"It just became a case of put up or shut up,\" he said. The old-style hacks were sunk into the ice and were not ergonomically designed with the foot in mind.\n\nThe Marco Hack\n\nFerraro's first stop was Montreal's Olympic Stadium, where he spent time examining the runners' starting blocks.\n\n\"I figured that an athlete going for a gold medal isn't going to leave anything to chance. He's only going to put his foot in something that's perfect,\" Ferraro noted.\n\nHe took that information to a mathematician who provided information on the exact angles of the foot during the delivery and then produced some prototypes. Those were tested by several top-ranked curlers, who made suggestions, and the final product was brought to market. These days, just about anywhere in the world there's a curling rink, you'll find one of these hacks, which are emblazoned with the name MARCO across the top.\n**THE JUBILEE STONE**\n\nBefore standardization of stones, curling was played with implements of varying shapes, sizes, and weights. In fact, in some parts of Scotland, bigger stones were a sign of strength of the thrower. Players brought their own rocks to games, and the rocks were often plucked from rivers, which had worn them smooth. One of the most famous is known as the Jubilee Stone, which weighed in at a massive 53 kilograms (117 pounds). It was given its name when it was presented to the Royal Caledonian Curling Club at the governing body's Jubilee Meeting in 1888. It is on display at the club's headquarters in Edinburgh, Scotland.\n**PAPER GRANITE**\n\nGeorge Plimpton made a career out of trying various sports at the top level and then writing about it from the viewpoint of an amateur. His most famous book in this genre was probably _Paper Lion_ , in which he recounted his experiences playing quarterback for the Detroit Lions at the team's training camp. While his most notable works have been about sports such as football, baseball (he pitched to the American League team at the All-Star Game), and boxing (he sparred with Archie Moore), he once tried his hand at curling. Plimpton attended the 1976 Super Draw Curling Bonspiel. This event was a lottery that allowed winners to travel, all expenses paid, to Vernon, British Columbia, where they competed in a bonspiel playing for high-profile skips. Prior to the event, he admitted that the only brooms he had seen were in closets. However, he went out and skipped a team in three games, including his first with the members of Hec Gervais' 1974 Canadian championship team, while Gervais skipped three members of the media. Plimpton lost, and after he missed a takeout attempt during the contest he commented: \"[The stone] must have lost interest.\"\n**CURLING FIGHTS**\n\nCurling is thought to be a game played by gentlemen and women, and in most cases, it is. However, there has been the occasion where the decorum has slipped and, just as in Canada's other great winter ice sport, fights have broken out. Here are a few incidents of fisticuffs on the curling sheets:\n\n\u2022 During a club championship game in Winnipeg in the 1980s, two players decided that bodychecking should be a part of the game. Player A was sweeping his skip's stone into the house when it reached the tee line. At that point, Player B from the opposing team decided he wanted to sweep it as well, hoping to drag the rock farther back in the house. But his efforts to do so were stymied by Player A, who blocked him off, declaring, \"It's _my_ house.\" The two players battled for position, with Player B using his body to push Player A away from the stone. The result was plenty of pushing and shoving and tangled brooms.With the rock now stopped, the two players continued jostling, and then punches were finally thrown, with both players falling to the ice. The club president happened to be on the ice at the time and he raced over from Sheet 6 to break up the melee. Order was restored, and the game continued without any more punches being thrown.\n\n\u2022 In 1976 in Sarnia, Ontario, two curlers in a local bonspiel began arguing when one accused the other of not releasing the stone before crossing the hog line. The argument became so intense, the player who allegedly committed the foul left the ice with his team, forfeiting the game. However, the squabble continued in the club after that and resulted in the accuser throwing a knockout punch to the head of the rock thrower. Charges were laid, and the accuser ended up in court. \"Surely we aren't going to get into violence in curling,\" said Sarnia Judge Alan Fowler, before fining the man $250 or 25 days in jail.\n\n\u2022 In 1982 the president of the Ottawa Curling Club sent a letter of reprimand to a member for a certain indiscretion. The member was quite upset about receiving the letter and disagreed with its accusations. During one evening's curling, the president and the member in question were playing, when the member dropped his broom, went across three sheets of ice, and clocked the president, who fell to the ice.The member received another letter, this one telling him he was banned from the club for one year. That prevented him from attending the closing men's banquet, so the member sat on a lawn chair in the parking lot of an adjoining property and threw stones at the window of the lounge where his team was eating. His teammates brought him a beer so he could at least experience a small part of the evening.\n\n\u2022 One night at the Bobcaygeon Curling Club, Player A was celebrating his birthday prior to taking to the ice for his game. He had been knocking back the drinks, and by the time the game started, he was feeling no pain. During the game, his behaviour bothered his opposing skip, Player B, who finally confronted him, pushing his finger into his chest. The two players began pushing each other, and Player A started throwing punches, landing a few, but also slipping to the ice. Another curler ran over, grabbed the birthday boy, and put him in a headlock, keeping him that way until he tossed him out the front door of the club. The incident appeared over, but about an hour later, Player A re-appeared through the front door and challenged Player B to a fight in the parking lot. The police were called, and the Player A was removed from the property.\n**CURLING CLUB CHAIN GANG**\n\nWhen the curlers at one New York curling club throw rocks, they may not realize that their club was partially built by convicts from the state penitentiary. In 1996, the Utica Curling Club installed a new floor on which the ice for the curling club would rest. The construction crew was made up of cons who were paid 15 cents an hour for their efforts. The work program was put in place as a way to help rehabilitate the inmates. While they may not have realized it, they were supervised by one of the game's top icemakers, Dave Merklinger.\n**CURLING IN THE MOVIES**\n\n#  _**Help!**_\n\nIn the movie _Help!_ , the Beatles showed they knew a little bit about the roaring game. During a winter scene, George, Paul, John, and Ringo all take part in an outdoor bonspiel\u2014or that's what it appears is happening. George throws a rock while John and Ringo try to catch up to it and sweep. Paul is sweeping, but nowhere near the rock\n\nThe movie's villain, Algernon, then plants a bomb in a rock and slides it down the ice toward the four musicians. Ringo sweeps the stone, which is smoking at this point. The other three realize what is in the stone, grab Ringo, and run away. Algernon, who expected the rock to explode before the boys exited, goes to check on his bomb and arrives just as it explodes.\n\n#  _**Men with Brooms**_\n\nThe only feature film ever made that used curling as an underlying theme was _Men with Brooms_ , starring Paul Gross of _Due South_ fame. A few facts about the movie:\n\n\u2022 The title came from a meeting between Gross and Alliance Atlantis head Robert Lantos. When Gross told him he wanted to make a truly Canadian movie and use curling as the central theme, Lantos said: \"You mean that sport that has men with brooms?\"\n\n\u2022 The movie about curling drew some unusual reactions. In November 1999, Gross told the _Toronto Sun_ : \"When I was in Los Angeles recently, I told people I was doing this thing about curling. It was as though I had farted. They didn't know where to look.\"\n\n\u2022 A number of top curlers were given cameos in the movie, including two-time Canadian champion Jeff Stoughton as well as 1983 world champion Paul Savage, who played the role of the television announcer.\n\n\u2022 Paul Gross didn't know how to curl prior to his on-screen debut and said he used the book _Curling For Dummies_ as his bible during the filming.\n\n\u2022 Members of the rock group The Tragically Hip appeared as a curling team, representing Kingston, Ontario, their hometown.\n\n\u2022 James Alodi, who played Neil Bucyk, one of the members of the team at the centre of the movie, fell and injured both elbows during the movie's filming. His injury, bone chips, hurt so much he wasn't able to rest his elbows on a table for weeks.\n\n\u2022 The film opened on March 8, 2002, and set a Canadian record for opening weekend sales, with more than $1.1 million brought in at the box office. The movie opened on 213 screens. In the United States, however, it opened in September 2002 on a grand total of just 27 screens and brought in $14,765.\n\n\u2022 A number of curling errors show up in the movie. For one, the scoreboard rarely reflects the scoring as shown on the ice.\n\n\u2022 The budget for the movie was estimated at $7.5 million, quite small for a feature film.\n**NAME THAT CORN**\n\nAlthough they're not even made any more, corn brooms once ruled the ice, at least in North America. It wasn't until the 1970s that push brooms took over as the dominant choice for curlers of all levels. Over the years, many brooms came and went. Here are the names of a few of the more popular corn brooms of years gone by:\n\nRockmaster x-11   \nZebra   \nLittle Beaver   \nLittle Otter   \nLittle Mink   \nMississauga Rattler   \nPro Polka Dot   \nWildcat   \nThunder   \n8-Ender   \nWhipper Snapper\n\n**THE KING OF SWING**\n\nShorty Jenkins is well-known as the first truly great icemaker in curling. Over the years he has established many techniques for making the playing surface better, and in the process he has become a well-recognized figure at major curling events. Here are some facts about the man:\n\n\u2022 His first name is really Clarence.\n\n\u2022 He was raised in an orphanage in Victoria, British Columbia.\n\n\u2022 He served in the Canadian Air Force.\n\n\u2022 He competed in the 1974 Ontario men's curling championships and experienced such bad playing conditions, he decided he would do something about it and started a career as an icemaker.\n\n\u2022 He was the first person to time how long it took rocks to travel down the ice. He used his method to judge the condition of his surface, but it has become a much-used way of determining the changing speed of the ice by competitive teams.\n\n\u2022 He used an infrared gun to determine the temperature of the ice and learned that different colour rock handles can absorb different amounts of heat, which can affect their speed.\n\n\u2022 He starred in his own Tim Hortons television commercial, which was later spoofed by the Canadian comedy show _This Hour Has 22 Minutes_.\n\n\u2022 He is often seen at curling events wearing his trademark pink cowboy hat.\n**WHAT IF MY ROCK...**\n\nWhen it comes to stones, the rule book makes provision for unusual happenings in a game\n\nFor instance, although it's rare these days for stones to break\u2014even with the tremendous force with which they are thrown by some of the top players\u2014Rule 4 (2) covers just that situation. It reads as follows:\n\n\"If a stone is broken in play, a replacement stone shall be placed where the largest fragment comes to rest. The inside edge of the replacement stone shall be placed in the same position as the inside edge of the largest fragment with the assistance of a measuring stick.\"\n\nIf the stone doesn't break but merely flips over or comes to rest on its side, the rule book takes care of that situation in 4 (6): \"A stone that rolls over in its course or comes to rest on its side or top shall be removed immediately from play.\"\n\nSo it seems it's better to have your rock break than flip over.\n_**ENFANT TERRIBLE**_\n\nIn the 1970s and early '80s, Paul Gowsell gained a reputation for being curling's _enfant terrible_ , shocking curling audiences big and small with his outlandish appearance as well as his exceptional talent. Although most of his success came as a junior and he never reached the heights some had predicted for him, tales of his antics are still told frequently in curling circles. A few stories about Paul Gowsell:\n\n\u2022 On his way home from being honoured as Athlete of the Year in Calgary in 1977, Gowsell was stopped by police and charged with possession of marijuana.\n\n\u2022 Gowsell was extremely nervous between games. He would often eat at the opening banquet or Calcutta (a form of betting where the teams are auctioned off, usually held at a party) on the first night and then not again until the event was over.\n\n\u2022 Gowsell's team was the first high-profile Canadian rink to use push brooms, and it is generally credited with starting the nationwide move away from corn brooms.\n\n\u2022 At the 1976 World Junior Championships, Gowsell was turned away from a banquet because he wasn't wearing a jacket or tie. He went back to his hotel room, put on the appropriate clothes, but returned without shoes or socks.\n\n\u2022 At the closing banquet for the 1978 World Junior Championship, which Gowsell won, he was refused entry by a security guard who told him, \"This is a banquet for curlers, not hippies.\"\n\n\u2022 Gowsell was cut from his high school team in Grade 10 and 11. The following year he made the team and promptly won the Canadian junior title.\n\n\u2022 At a major bonspiel in Winnipeg, Gowsell arranged for a pizza to be delivered to him in the middle of a game. As 1,000 fans looked on, the delivery guy walked down the sheet, handed the box to Gowsell, and took his payment. Gowsell opened the box and asked his opposing number, Larry McGrath, if he wanted a slice.\n\n**DEAD HEAT**\n\nWant to win a mug of your favourite beverage from your curling friend? Here's a trivia question that might just do the trick: Can you name two occasions when, at the conclusion of an end, there are rocks in the house but no team scores?\n\nThe answer can be found in _The Rules of Curling,_ which is published by the Canadian Curling Association. The first occurs when two stones finish exactly the same distance from the centre. Under Rule 13 (8), if, after using a measuring stick, it can't be determined which of the stones is closer to the centre, then the end shall be declared blank. That is, of course, if there are no other rocks closer to the centre than the ones being measured.\n\nThe second situation happens when two rocks are so close to the centre that the measure can't be used, and it can't be determined visually which is closer. That would happen if two stones finished almost on top of the exact centre of the house.\n\n**Curling Quote**\n\n\"There's nobody out here that concerns me.\"\n\n\u2014Randy Ferbey, when asked his opinion on the field at the 2005 world championship\n**THE ICE KING**\n\nAt curling clubs around the world, a strange-looking machine is often seen preparing the surface for play, either by knee-sliding novices or world champions. The Ice King is a device that scrapes a fine layer off the top of the ice, levelling the surface and allowing a new layer of pebble to be applied. Before the invention of this motor-pebble to be applied. Before the invention of this motorized device, ice had to be scraped by hand, a laborious task, to be sure. A brief history of the Ice King:\n\n\u2022 The machine was invented by Harry Mather of London, Ontario, in the mid-1960s. Mather used it at his own club. It was essentially a long blade, about half the width of a curling sheet, anchored on a plow-like device that was powered electrically.The blade could be raised or lowered depending on how much ice needed to be shaved off.\n\n\u2022 By 1968, he'd convinced a few area clubs to buy machines that would help improve the conditions. Word spread quickly throughout Ontario, and Ice King became a viable company, selling machines.\n\n\u2022 By the mid-1970s, Ice King was selling machines across Canada and had made some improvements to the machine, mostly cosmetic.\n\n\u2022 In 1986, Larry Mayo and Fred Veale purchased the company from Mather and looked to improve the popular machine.\n\n\u2022 In 1993, Bill Wood made a simple improvement by changing the power source to a battery. No longer was it necessary to drag a long cord along the ice while scraping.\n\n\u2022 In 2006, Wood bought the Ice King business from Mayo and Veale. He currently sells four different models\u2014the Prince, the Super Scraper, the Super 06, and the Super 07.\n\n\u2022 Ice Kings have been used at virtually every major event from the Canadian men's and women's championships to the Olympics.\n\n\u2022 Ice Kings are used around the world, and models some 30 years old are still used on a regular basis.\n**AMERICA'S MAN,** **BUD SOMERVILLE**\n\nBud Somerville was the first American curler to skip a team to the world championship title, and in so doing he became the unofficial father of U.S. curling. A few facts about the legendary curler:\n\n\u2022 He was a gifted athlete but a heart ailment kept him from playing most sports. As a result, he turned to curling.\n\n\u2022 He first reached the U.S. finals in 1962, skipping a rink that included his father, Ray, at second, and his brother-in-law Bill Strum at lead. The team finished third.\n\n\u2022 In the middle of the 1965 national final against a team from Illinois, Somerville's pants split up the front, and he was forced to patch them together with tape and a safety pin. Undaunted, he finished out the game, winning his first national title.\n\n\u2022 The team became the first American rink\u2014and first non-Canadian\u2014to win the world championship when it captured the Scotch Cup in 1965. After the victory, the team received a telegram of congratulations from President Lyndon B. Johnson.\n\n\u2022 He won a second world championship in 1974.\n\n\u2022 Somerville's youngest son, John, died of cystic fibrosis at age 17, and Somerville has raised thousands and thousands of dollars for the research into the disease **.**\n\n\u2022 In 1992, Somerville, at the age of 55, represented the United States at curling's demonstration at the Olympic Games, becoming that country's oldest Olympian. He skipped the rink to a bronze medal. He also skipped the team at the 1988 Games.\n\n\u2022 When the U.S. Curling Hall of Fame was started in 1984, Somerville was the first inductee.\n\n\u2022 His son Tim won three U.S. Championships and represented the United States in the 2002 Olympics.\n\n**Curling Quote**\n\n\"Today I saw a bunch of Scotsmen who were throwing big iron balls like bombs on the ice, after which they cried, 'soop, soop,' and then laughed like mad.\n\nI think they are mad.\"\n\n\u2014A French-Canadian farmer, circa 1790, relaying his first impressions of curling, as quoted in _The Curling Companion_ by W.H. Murray\n**THE WRENCH SAID**\n\nHe is one of the most beloved curlers of all time, and part of the reason for Ed Werenich's popularity was his penchant for speaking his mind, often saying something politically incorrect but that many were secretly thinking. Here is a selection of some of Werenich's most memorable quotes:\n\n\"They look like they're going jogging. Or maybe going to a pyjama party.\"\n\n\u2014Werenich commenting on the new-style athletic gear being worn by several European teams at the 1990 World Curling Championships\n\n\"I don't want him as my coach. I've worked 32 years for this moment. I don't want someone like him jumping in.\"\n\n\u2014Werenich, after winning the 1990 Brier, when he would not accept Canadian Curling Association official and longtime rival Warren Hansen as his team coach for the World Championships\n\n\"I went to Sweden, drank beer in my room, and came home with a bouquet of flowers and a $5 silver tray.\"\n\n\u2014Werenich summing up his experience at the 1990 World Championships in Vasteras, Sweden\n\n\"They not only want me to look pretty, they want me to be able to dance, too. I just hope they don't ask me to use Grecian Formula and get my teeth fixed.\"\n\n\u2014Werenich, when told he would have to lose 22 pounds and do aerobic exercise if he hoped to qualify for the 1987 Olympic trials\n\n\"How do you think this would look on my ass, Leon?\"\n\n\u2014Werenich, while mooning Ontario Curling Association official Leon Sykes after Sykes had presented him with his Purple Heart for winning the 1981 Ontario championship. Werenich had battled officials all week over a problem with the playoff format.\n\n\"We went into this thing thinking we needed to be 8-3 to get into the playoffs. We've got the easy three over with. Now we have to go over the hard eight ones.\"\n\n\u2014Werenich at the 1984 Brier in Victoria after the defending champions started out 0-3\n\n\"They're four real jerks. I know where they can put their brooms.\"\n\n\u2014Werenich referring to the Swedish team in the 1983 World Championship, skipped by Mikael Hasselborg. The Swedes used messy corn brooms to sweep, a tactic Werenich believed was akin to cheating. For years after that incident, the Hasselborg team carried pictures of Werenich and teammate John Kawaja with them, saying they used them to get up for important games.\n\n\"When I'm on the curling ice, that's my office. I'll challenge anybody in the world on certain things, like calling strategy. I know curling, okay? But I really don't know anything else, just curling and firefighting.\"\n\n\u2014Werenich to author Jean Sonmor in the book _Burned By The Rock_\n**BETWEEN A ROCK AND A HARD PLACE**\n\nIn some places where curling isn't always a mainstream sport, curlers have had to make do with whatever they can to play their game. Here are a few unusual locations in which curling has been held:\n\n\u2022 In 1992, the Imperial Grand Ballroom of the Aladdin Hotel and Casino in Las Vegas, Nevada, was transformed into a curling rink to host the Desert Spiel, a curling pro-am in which players competed on teams skipped by Canadian, U.S., and world champions. Curlers from across North America descended on Vegas to play in the event on ice made by world-renowned ice technician Shorty Jenkins.\n\n\u2022 Vegas isn't the only place where curling has been held in a casino. In 2007, a made-for-television skins game was held in the Entertainment Centre at Casino Rama, near Orillia, Ontario. The location is usually reserved for singers and comedians, but the high-stakes shootout brought together Glenn Howard, Kevin Martin, Wayne Middaugh, and Brad Gushue.\n\n\u2022 On more than one occasion, the skating rink in front of Rockefeller Center in New York City has been changed into a curling rink for an exhibition of the roaring game. In 2007, television personalities were given a lesson in curling by American Olympians Cassie Johnson and Pete Fenson in the heart of Manhattan.\n\n\u2022 Curlers have been known to have the odd drink and so it might not be that big a surprise that a bonspiel was held in a location where some of this liquid is manufactured. No, not Scotland and Scotch, but California and wine. In 2007, a bonspiel was held in Vacaville, California, in the heart of Napa Valley. A local hockey rink was transformed into curling sheets, and the competitors threw rocks and sipped Merlot.\n\n\u2022 According to the _International Guide to Curling_ by Robin Welsh, in 1973, a bonspiel was held in C\u00f4te d'Ivoire in Africa. The event was held on an indoor rink in the Ivoire Hotel and included local teams as well as rinks from France. A second event was held and teams from Switzerland and the U.S.A. played.\n\n\u2022 According to _The Curling News_ , at a posh mall in Rabat, Morocco, the only skating rink in the country is regularly transformed into a curling rink and lessons provided to locals. Although most had never seen a skating rink before\u2014let alone a game of curling\u2014they weren't afraid to test it out, and thousands have given the game a go. Instead of scratching circles into the ice for rings, a system of lights is used to create the houses at either end of the sheet.\n\n\u2022 In the 1880s, Scottish residents of New York held an annual bonspiel on a frozen pond in Central Park. The match pitted former residents of northern Scotland versus those from the south. The contest involved numerous teams, and scores were a total of all the games. In 1883, for example, the final score was North 182, South 150.\n\nCurling in Vegas\n\n**CURLING COUPLES**\n\nCurling, as many who play will attest, is a social sport. For that reason, it's no big surprise that many curlers end up as couples, husbands and wives who share a love of rock tossing. Here are a few of the more successful curling couples.\n\n**Rick and Lorraine Lang** : Lorraine Lang was a Canadian champion in 1988 and '89, and took the world title in 1989. Husband Rick is a three-time Brier winner\u20141972, '82, and '85\u2014winning the world title in '82 and '85. Together, they captured the Canadian Mixed in 1981.\n\n**Dave and Heather Nedohin** : Dave throws last rock for the powerful Randy Ferbey team that won four Canadian and three world championships, while Heather has a world junior and world women's title on her resum\u00e9.\n\n**Ian Tetley and Erica Brown** : A cross-border couple. Ian Tetley is a three-time Canadian and world champion, while Erica has four U.S. women's titles to her credit, as well as two Olympic appearances.\n\n**Pat Perroud and Jane Hooper Perroud** : Pat won Canadian and world championships playing lead for both Al Hackner (1985) and Ed Werenich (1990), while wife Jane was a member of Marilyn Bodogh's squad, which captured the Canadian and world championship in 1996.\n\n**Wayne and Sherry Middaugh** : Wayne is a two-time Canadian and world champion while better half Sherry has won the Ontario title three times, reaching the semi-finals of the Canadian championship on all three occasions. Both curlers have competed in the Canadian Olympic curling trials.\n\n**Curling Quote**\n\n\"They told us to watch out for odd people when he got here. The first guy I saw was wearing a gopher on his head. Where do you start?\"\n\n\u2014A member of the security detail of Prime Minister Stephen Harper, who visited the 2007 Tim Hortons Brier in Hamilton, as told to the _Edmonton Sun_\n**ROCKS FOR ROCKERS**\n\nMembers of the Canadian rock band The Tragically Hip are curling fans. That became obvious during a concert tour in 2006. The band was playing in London, Ontario, and singer\/guitarist Ed Robertson told the assembled fans his tale of looking for curling stones so he could play on an outdoor rink he made each winter at his Ontario cottage. He had searched high and low, and finally found one company that made them\u2014Canada Curling Stone, located in London, but when he called he only received an answering machine message, which he turned into a little song:\n\n _Canada Curling Stone_   \n_Canada Curling Stone_   \n_Please don't try to phone_   \n_We're Canada Curling Stone_   \n_No one is at home_   \n_At Canada Curling Stone_   \n_All of our rocks are home_   \n_At Canada Curling Stone_   \n_We implore you to leave us alone_   \n_We're Canada Curling Stone_\n\nThe next morning, Robertson called the company again, and this time, Kim Tuck answered the phone, and when Robertson introduced himself, she told him she'd already received scores of calls and e-mails from those who were at the concert the night before, relaying his request. In the end, that request was fulfilled, and Robertson bought a full sheet of 16 stones and reportedly has regular outdoor curling events at his cottage.\n**BRIER BROADCASTER**\n\nBob Cole has made a career of calling hockey games. He's been the main play-by-play man for the CBC since 1980 and has been calling games for the network since 1973. He regularly calls the action for the Toronto Maple Leafs, and perhaps his most famous call came in 1976 during an exhibition game between the Philadelphia Flyers and the Russian club team CSKA Moscow. In the first period, the Russians became unhappy with the officiating and left the ice. From the press box, Cole said, \"They're going home. They're going home.\"\n\nWhile he became famous for that and more hockey broadcasting, Cole is also a curler of some note, having represented Newfoundland & Labrador in the Brier twice. In 1971 he finished up with a 4-6 mark, and in 1975 he went 1-10. Cole also skipped his province in the 1973 Canadian Mixed.\n**A FAMILY AFFAIR**\n\nCurling has always been considered a good family game, but at a 1998 bonspiel in Keene, Ontario, the Davises took that to a new level. The squad comprised Alan, Chris, Gord, and Jamie Davis\u2014great-grandfather, grandfather, father, and son\u2014four generations of the family all on one team.\n**HIGH SCORE**\n\nIt is a badge of honour for every curler to play in the Brier and another to set records. While New Brunswick's Ken Everett might like to remember the former, he might not be too excited about the latter. Everett represented his province in the 1957 Brier in Kingston, which was won by Garnett Campbell's team from Saskatchewan. Along the way, Everett managed to put his team into the record books. Unfortunately it was for all the wrong reasons. The New Brunswick team came out on the wrong side of the most lopsided contest in Brier history\u2014a 30-3 loss.\n\nAs well, in today's era of conceding games once the score seems insurmountable, it's unlikely that score will ever be topped.\n**TRAVELLIN' MAN**\n\nEarle Morris is a talented curler, but as a member of the Canadian military, he moved around the country a great deal. But that never hurt his success on the ice. Morris curled in the Brier three times, but represented three different provinces, the only player with such a distinction. In 1980, he represented Manitoba, in 1982 Quebec, and in '85 he wore Ontario's colours.\n\n**AGE-OLD INVENTION**\n\nJack Grossart of Toronto proved that curling isn't necessarily the domain of the young man. He started curling at the age of 65 and fell in love with the sport. A self-confessed problem-solver, at age 89, he decided to try to invent a better curling broom and came up with the Grossart Super Brush. The innovative design was one of the first to feature a hinged head, which allowed it to be moved to any angle, and removable \"friction pads\" that could be switched depending on the ice conditions.\n\nWhen asked why he started designing brooms at his age, he replied: \"It's just stupid-ness. I wish I'd never got started in this thing.\"\n\nGrossart eventually sold off his broom business but kept curling until the age of 99.\n**GREAT COMEBACKS**\n\nUsually, teams that are ahead by healthy margins or with few ends to play don't surrender the lead. Most world-ranked rinks can finish off a game in which they lead by a few points. But on occasion, they slip up, allowing for a memorable comeback. Here are a few notable ones:\n\n\u2022 In 1970, the ice at the Brier in Winnipeg was horrendous, and it contributed to a tremendous comeback by Hec Gervais. The ice was extremely heavy, and after four ends, Ontario's Paul Savage was leading 8-1. Starting in the fifth end, Gervais began calling for his team to draw to the outside rings, but they kept coming up light\u2014or so thought Savage. Gervais intentionally placed the rocks in front of the rings, fooling the youthful Savage as the Alberta team rallied to a 12-9 win. \"I was thinking, 'These guys can't make a draw,'\" recalled Savage. \"Big mistake. I found out a few years after these were corner guards and did they ever work.\"\n\n\u2022 Heading into the final three ends of the 2004 Brier, Nova Scotia's Mark Dacey trailed Randy Ferbey by four points and appeared to be headed for a silver medal. Certainly he was an underdog. Ferbey was gunning for his fourth consecutive Brier crown and seemed in control of this final. Undaunted, Dacey rallied for three in the eighth before surrendering a single in the ninth to trail by two heading home. But a combination of tremendous shots by the Nova Scotia rink and some stunning misses from the Ferbey team allowed Dacey to draw the four-foot for three points and a 10-9 victory.\n\n\u2022 In the 2001 Canadian Olympic trials Russ Howard, trailing by three points with one end left, contemplated conceding a game against John Morris. The wily veteran, however, decided to play out the final frame, and what followed was a case of experience winning out over youth. Howard used a corner guard to hide several stones, and rather than removing the guard, Morris tried to pick out the Howard stones, but missed each time. Eventually, Howard took four points, winning the game and sending Morris storming off the sheet, ripping his shirt into shreds in the process.\n\n\u2022 Playing the tenth end of the final of the 1985 Brier in Moncton, New Brunswick, Pat Ryan was leading 5-3 and appeared in complete control of the final frame. In fact, after his last shot, he came down the ice with his broom in the air, already starting to celebrate what he thought was a Brier victory. However, that proved premature. Northern Ontario's Al Hackner played what is regarded as one of the greatest shots in Brier history when he made a thin double takeout to score two points. He then led his team to a steal of one in the extra end for the win and the Canadian championship.\n\n\u2022 Ontario's Jenn Hanna was set to celebrate a victory in the 2005 Scott Tournament of Hearts in St. John's, Newfoundland. With just one rock left to be thrown, Hanna led by three points and had shot stone buried on the button. Manitoba's Jennifer Jones sat second, third, and fourth shot but had only one hope of getting to Hanna's stone\u2014that was to redirect her shooter off a stone sitting almost off the sheet. She called the shot, played it, and watched as it hit and then went on a perfect angle to remove the Ontario stone and give her team four points and the national title.\n\n**Curling Quote**\n\n\"I worked with French CBC during the Torino Olympics. I did a TV show with a French-Canadian speed skater, and during that show, he tried some curling. At the end he looked at me and said, 'Geez guys...how do you do that? You guys are real athletes.'\n\nComing from a 29-year-old, two-time gold medalist in prime athletic condition, that's a very good compliment.\"\n\n\u2014Guy Hemmings in the _Penticton Western News_\n**PIZZA AND MEDALS**\n\nPete Fenson was the skip of the first American team to win an Olympic medal in regulation play (American teams had earned medals in Olympic demonstrations). His rink, from Bemidji, Minnesota, took the bronze medal at the 2006 Games in Torino, Italy. As such, he became one of the best-known curlers in the United States. Here is a bit about this popular American curler:\n\n\u2022 Fenson's father, Bob, won the United States Men's Championship in 1979. He taught Pete how to curl and has continued to serve as coach for the team.\n\n\u2022 Fenson won his first national title in 1993, playing third for Scott Baird. He won again in 1994. He was a semi-finalist at the '93 world championship and finished fifth in '94.\n\n\u2022 In 1998, Baird took a year off, and Fenson moved up to skip, learning under the watchful eye of veteran third Mark Haluptzok. In 2003, Fenson skipped his team to the U.S. title and then finished eighth at the world final.\n\n\u2022 Fenson won the 2004 and '05 U.S. championships and then skipped the Red, White, and Blue to a bronze medal in the 2006 Games, earning that honour with an 8-6 victory over David Murdoch of the United Kingdom.\n\n\u2022 The team was named the U.S. Olympic Committee's team of the year for 2006.\n\n\u2022 Fenson owns two pizzerias, operating under the name Dave's Pizza.\n\n\u2022 On the U.S. Olympic Committee website, Fenson was asked which cartoon character he best resembled. His answer was the Road Runner.\n\n\u2022 In the summer of 2006, Fenson's Olympic team broke up as John Shuster, who played lead, left the squad to form his own rink.\n**OLE MEXICO**\n\nCurling isn't one of the more popular sports in Mexico, to be sure, but there are a few participants in the tropical country. In fact Josele Garza, a car racer who has participated in the Indy 500, is one of the country's original rock throwers.\n\nAfter seeing the sport in the 1998 Olympics, he organized a group intent on setting up the sport in Mexico. The group travelled to Winnipeg for some instruction and a crash course on strategy. With only five arenas in Mexico City, it's difficult to get ice, but thanks to Garza and his group, there is an official curling club, and Mexico is a member country of the World Curling Federation.\n**LONG-GONE EQUIPMENT**\n\nIt's been a long time since a straw broom appeared in any major competition around the world. In fact, straw brooms were last made in 2003, having succumbed to the success of the push broom. While only recently extinct, the straw broom is far from the only piece of equipment that has disappeared from the game over the years. Here are a few more items that were once common on curling rinks around the world.\n\n#  **Centre skittle**\n\nYears ago, before rings were permanently painted into the ice, a small wooden skittle was positioned at the exact centre of the ice. This allowed players at the throwing end of the sheet to have a visual idea of the location of the button.\n\n#  **Tassels**\n\nHard as it may be to believe, many years ago, rocks weren't identified by coloured tops. That's primarily because each player was required to provide his or her own pair of stones, and there was no idea of what team he or she would be on for that game. Instead a small piece of coloured wool was tied to the handle\u2014eight handles, actually\u2014to determine which rocks belonged to which team.\n\n#  **Crampits**\n\nThe name is perhaps more closely associated with mountain climbing, but a crampit (also called a crampon) was an attachment that was tied on to the bottom of a shoe or boot and had prongs on the underside that provided a hold on the ice. For a short time, players kept the crampit on their foot the entire game, while throwing and sweeping, which caused some horrendous conditions as they ran up and down the sheet. In later years, crampits were affixed to the ice and remained in position for the entire game, usually by putting the metal fixture into hot water and then melting it into the ice.\n\n#  **The Duster**\n\nThe name came from the fact this was usually a cloth, much like something used for dusting. It was placed on the ice to show where the rock was to come to rest. If it was placed on top of a rock, the shot was a takeout.\n\nThese French curlers are using a duster (just above the rock on the left) to show the centre of the house on this outdoor rink.\n\n**CLOSET CURLING FANS**\n\nAlthough they are better known for other endeavours, the three people listed below have a soft spot for the roaring game. It's just that nobody knew!\n\n**Wayne Gretzky** \u2014hockey's all-time scoring leader is a devoted curling fan who said he regularly follows the Brier and other events. And he admitted to another secret in a column he wrote in the _National Post_. \"You'd be surprised how many National Hockey League players can be found sitting in their hotel rooms in the middle of winter watching [curling] somewhere.\"\n\n**Canadian Prime Minister Stephen Harper** \u2014Harper became the first prime minister to sit through an entire draw at the Brier, attending an afternoon at the 2007 event in Hamilton. Before the match, he met and had his photo taken with Kevin Martin's Alberta team. Harper, who said he's not a curler, still loves to watch the Canadian championship on a regular basis. \"I've been following it for years and back about a decade ago when I was travelling a lot I happened to be in Winnipeg when they were having the Brier,\" he said, \"and I made a point of going. Then I decided every year to schedule a business trip to be wherever the Brier was.\"\n\n**Toby Keith** \u2014the award-winning country singer said he fell in love with curling while following it at the 2006 Olympics. During a concert stop in Nashville, Tennessee, Keith decided he would take that passion one step further. He learned there was a curling facility in town and booked some ice for him and his band to play. \"They're calling themselves the redneck curlers,\" commented Nashville Curling Club president Sean Gerster, who also admitted that Keith was a fast learner and showed promise. \"He said he was going to try and qualify for the 2010 Olympics.\"\n\n**Bruce Springsteen** \u2014the Boss reportedly rents out curling clubs when on the road. He is known as a keen watcher of curling when it's on television, and is an improving rock tosser.\n\n**Curling Fact**\n\nThe first European team to win the world championship was Kjell Oscarius of Sweden, who won in 1973.\n**SPRINGFIELD GRANITE**\n\nCurling went animated in 2002 when the sport was featured in an episode of _The Simpsons_. On February 17, episode 280-1311, \"The Bart Wants What it Wants,\" aired on FOX and saw America's favourite animated family travel to Canada, where at one point Bart and his friend Millhouse start a fight in a movie\/television studio. They brawl and eventually go through a door where a sign reads: _Curling for Loonies_ , a reference to the American television staple, _Bowling for Dollars_. This Canadian show is being taped in the adjoining studio in which Bart and Millhouse now find themselves. As the two brawl, the announcers are heard:\n\n**Announcer 1:** Well, we've seen some wild sweeping here today.\n\n**Announcer 2:** Yes, the broom handling has been truly dazzling. [At this point, Bart and Milhouse are seen fighting their way onto the ice.] What's this? Two young Yankee Doodles have turned this match into a Dandy.\n\n**Announcer 1:** [laughs] Both our viewers must be thrilled. A very special episode of _Curling for Loonies_.\n**THE CURSE OF LABONTE**\n\nOne of the more unusual finishes to a major curling competition took place in 1972 at the world championships in Garmish-Partenkirchen, Germany. The final was between Canada's Orest Meleschuk and Bob Labonte of the United States. Up to that point, Canada was undefeated and hoping to run the table in the final. Heading to the tenth end, the Americans led by two points, but Meleschuk had the hammer.\n\nIn order to score two points, Meleschuk needed to hit and stay inside the eight-foot. He played the shot, but the shooter apparently rolled too far, giving the game to the Americans. Frank Assand, the U.S. third, who had been sweeping the Canadian shooter as it rolled, judged where that rock had stopped and where his team's shooter sat and immediately threw his hands in the air. His skip, Labonte, also believing they had won, jumped into the air in celebration, but slipped and kicked the Canadian stone, moving it back toward the centre of the rings. Now it appeared Canada had scored the tying deuce. After consulting with the head official, Doug Maxwell, a measurement took place, and Canada scored two then went on to win the game in the extra end.\n\nA few more notes about the infamous burned rock:\n\n\u2022 At the time, there were no rules in place to deal with the situation that occurred. Maxwell was left with little option but to leave the rocks where they were and measure the burned stone and the American rock.\n\n\u2022 To show how the times have changed, Labonte managed to complete his jump and tumble all with a cigarette in his mouth.\n\n\u2022 In his book _Canada Curls_ , Maxwell revealed that the CBC, which was covering the event, had just introduced instant replay and was supposed to have it available at the world championship, but a labour dispute cancelled its availability.\n\n\u2022 A reporter came up with the Labonte Curse, supposedly dropped on Canadian curlers. The idea was the country would never win another world championship, the revenge for winning the 1972 event under such strange circumstances. For the next seven years, Canada didn't win the global title, its longest dry spell.\n\n\u2022 For many years, Labonte showed up at world championships, introduced himself to the Canadian team, and playfully put the hex on them again.\n\n\u2022 After the incident, Labonte was given the nickname \"Boots.\"\n**BRITISH GOLD**\n\nWhen Rhona Martin took top spot in the 2002 Olympics in Salt Lake City, Utah, the win set off a wild celebration back in Scotland (her country of residence) and across Great Britain. Some remarkable facts about Martin and that victory:\n\n\u2022 Prior to being selected to represent Britain at the Olympics, Martin had made it to 10 national championships and finished second a remarkable nine times. She did represent Scotland at the European championships but lost in the semi-finals five of six times and subsequently lost all five bronze medal games.\n\n\u2022 More than 7 million viewers in Britain tuned into the broadcast of the gold medal game even though it started at midnight local time. That set a record for the BBC.\n\n\u2022 It was the first gold medal for Britain in 19 Olympiads.\n\n\u2022 Martin and her team of Janice Ranin, Fiona Macdonald, and Debbie Knox became household celebrities across Britain, even receiving MBEs. However, their fame was fleeting. Five years later, Martin was living in part off social security after her husband left her. She later gained a job as a curling instructor.\n**IRON CURLING**\n\nWhile granite stones are the traditional implements of use in curling games around the world, it hasn't always been that way.\n\nFrom 1807 until the early 1920s in Quebec and the Ottawa Valley, curling \"irons\" were the choice\u2014markers made of metal that weighed up to 80 pounds. According to the book _Sports and Games in Canadian Life, 1700 to the Present_ , Maxwell L. Howell and Nancy Howell suggest that the first of these irons were derived from the metal-rimmed hubcaps of gun carriages. Handles were inserted into these to turn them into curling \"stones.\"\n\nIt was only in this area that irons were used, and one of the reasons they disappeared was a financial gesture of the Macdonald Tobacco Company. It wanted to start a national curling championship and needed Quebec curlers to participate. To entice them, the tobacco company spent thousands of dollars to buy granite stones for many curling clubs in Quebec, easing the transition to the rock era.\n**BROTHERS\u2014AND SISTERS\u2014IN BROOMS**\n\nCurling siblings have been common sights atop the podiums of major events, showing that perhaps the ability to draw the button is genetic. Here are some of the more successful curling siblings:\n\n**Russ and Glenn Howard:** The duo won two world championships together, and separately they've also been successful. Russ was a part of Brad Gushue's gold medal-winning squad at the 2006 Olympics, while Glenn won a third world crown skipping his own team in 2007.\n\n**Julie and Jodi Sutton:** The two won the Canadian championship in 1991, five years after combining to capture the national junior crown. Julie also has a bronze medal from the 2002 Olympics.\n\n**Jim and Tom Wilson:** The Wilson brothers were a feared front end in the late 1970s and early '80s, sweeping for Rick Folk's Saskatchewan rink. They helped the team win a Canadian and world championship in 1980.\n\n**Ernie and Sam Richardson:** Two members of the famed Richardson rink from Saskatchewan, which won four Briers in five years. Ernie was the skip while Sam (whose real name was Garnet) played second. Two other cousins, Arnold and Wes, were also members of the rink.\n\n**Ken and Grant Watson:** These brothers paired up to win three Brier crowns between 1936 and 1949, a record for siblings.\n\n**Connie, Corinne, and Janet Laliberte:** With Connie at skip, these three sisters swept their way to the Canadian championship in 1984. Connie and Janet combined for two more titles as well.\n\n**The Campbells:** Don, Garnett, Lloyd, and Sam won the 1954 Brier playing out of Saskatchewan. It's the only time four brothers have combined on a team to win a national championship.\n\nThe Campbells\n\n**Cassie Potter and Jamie Haskell:** The sisters from Bemidji, Minnesota, have been U.S. champions and represented their nation at the Olympics.\n**TANKARD TOTAL**\n\nWhen Labatt took over sponsorship of the Brier in 1980, it needed a trophy of some sort to present and decided that a budget of $5,000 would deliver it a suitable award. Labatt's Grant Waterman was put in charge of the job and he commissioned what would become a piece of Canadian sporting history, the Labatt Tankard, a large gold stein with the company's logo on the front. He managed to keep the trophy hidden from press and even his co-workers until an unveiling at a press conference in Calgary, site of the 1980 Brier, where the Tankard would be presented for the first time. When it was revealed to the press, the reaction was positive, and as photographers snapped away, Labatt vice-president Sid Oland sidled over to Waterman and congratulated him on the trophy.\n\n\"How much did it cost?\" he asked.\n\n\"$35,000,\" said Waterman.\n\nShocked, Oland asked what happened to the $5,000 budget.\n\n\"The case cost $10,000,\" Waterman exclaimed.\n\nWhile there were a lot of upset people in the Labatt financial department, the move paid off a few years later when the Tankard was valued at $350,000.\n**CHAMPIONSHIPS FOR EVERYONE**\n\nThe Tim Hortons Brier and Scotties Tournament of Hearts are well known as the men's and women's Canadian championships, respectively. But there are plenty more national titles up for grabs each year.\n\n#  **Canadian Postal Employees Curling Championship**\n\nStarted in 1967 in Winnipeg, this event was originally known as the Canadian Postal Curling Championship. It's been held annually and has teams from every province and a combined territories entry.\n\n#  **Royal Canadian Legion**\n\nFirst held in 1957, the Legion's spiel is known as the Dominion Championship and is open to members of the Royal Candian Legion.\n\n#  **Canadian Firefighters Curling Association**\n\nThis group not only has a championship but a full-blown association. It was started by Aubrey Neff, who started a curling league among members of the Vancouver Fire Department. He contacted firefighters in other provinces, and in 1960, a championship was held between five provinces. Today, all ten provinces, Northern Ontario, and the territories compete. Past winners include Ed Werenich and Neil Harrison.\n\n#  **Canadian Blind Curlers Championship**\n\nTen teams play down for this championship. Some represent cities and others provinces, while the defending champion enters as Team Canada.\n\n#  **Canadian Clergy Championship**\n\nThis competition\u2014known as the Friar's Brier\u2014had its start in 1978 and is for members of the Canadian clergy and their associates. It is held annually in the same city as the real Brier.\n\n#  **Canadian Police Curling Championship**\n\nBack in 1955, the Canadian Association of Chiefs of Police formed the Canadian Police Curling Association. In 1956, a \"national bonspiel\" was held at the Winnipeg Granite Club, and in 1972, it was transformed into a true national championship.\n\n#  **The Trans-Canada Telephone Employees' Championship**\n\nRegina played host to the first national championship in 1964. Seven provinces currently compete for the title.\n\n#  **The Atlantic Oilworkers Championship**\n\nAnyone who gets a paycheque from the Atlantic petroleum industry is eligible for this championship, which celebrated its 44th anniversary in 2008.\n**FANTASTIC FERBEY**\n\nRandy Ferbey has won more Briers than any other curler, a total of six. He won twice while playing for Pat Ryan (1988 and '89) and has earned four more titles as skip of his own team in the 2000s. Although he calls the game, third player David Nedohin throws last rock. A few notes on Randy Ferbey:\n\n\u2022 He appeared on a television commercial for sponsor Strauss Herbs looking somewhat like a raccoon. The day before the taping, he had been at his son's baseball tournament, spending the day outside wearing wrap-around sunglasses. He forgot to apply sunscreen, and his face went red, except for where he was protected by his glasses. He gained notoriety for his appearance...and ribbing from just about every opponent, not to mention his teammates.\n\n\u2022 Ferbey's team holds the record for scoring the most points in a single end at the world championship\u2014five, a mark he achieved twice during the 2005 world final.\n\n\u2022 His team of Nedohin, Scott Pfeifer, and Marcel Rocque became the first to win four Briers with the same lineup. The famed Richardsons of Saskatchewan also won four, but on one occasion had a different lead.\n\n\u2022 His team was the first to have a book written about it. _The Ferbey Four_ was written by Edmonton sportswriter Terry Jones.\n\n\u2022 He was one of the few high-profile curlers not to join a 2001 movement of teams that elected to play in the Grand Slam of Curling instead of the Brier. That set him apart from many of his peers, but he said at the time: \"Maybe to some of the players [the Grand Slam is] right up there but let's be honest. To the paying public the Brier is the event of the year. I don't care what anybody else says.\"\n\n\u2022 He appeared, along with lead Marcel Rocque, on the television program _Celebrity Chefs_ , where he showed off his prowess in the kitchen by preparing shrimp canap\u00e9s with homemade mayo and dill, smoked goose breast canap\u00e9s, pork loin chops (brined) with a port\/maple\/nut reduction, lightly steamed vegetables in garlic \/olive oil sauce. Rocque did most of the cooking.\n\n\u2022 Along with teammate Dave Nedohin, he made a cameo appearance on the television program _Corner Gas_ , playing himself.\n**ROARING ALONG**\n\nCurling is known at \"the roaring game.\" This moniker was given to the sport for the sound the stones made as they travelled down the ice. While rocks don't particularly roar these days on artificial playing surfaces in clubs, there was a definite hum when the sport was played outdoors on the frozen lochs of Scotland, and that's where the name originated.\n**PLANES, TRAINS, AND AUTOMOBILES**\n\nCurlers are certainly a determined bunch, but Rob Whalen and his rink from Sioux Lookout, Ontario, took that to extremes en route to the 1996 northwestern Ontario playdowns.\n\nThey had originally booked seats on a flight from their hometown to Thunder Bay, hoping to arrive the morning of the start of the competition. However, that morning, a massive snowstorm hit the area, closing the airport. Undaunted, the team piled into a four-by-four and started off on the 250-kilometre trek. At Ignace, Ontario, about halfway to their destination, police had closed the road, forcing the team to find yet another way.\n\nWhalen, who worked on the railway, headed to the rail yards and managed to convince the crew of a freight train headed to Thunder Bay to let them board. But that didn't work either, as the blizzard forced the train to stop and back up to Ignace to wait out the weather.\n\nBack into the four-by-four the team members went, and this time, Whalen drove an hour southwest to Fort Frances and then finally on to Thunder Bay, arriving at 4:30 a.m., having missed his first two games in the triple-knockout competition. To add to the disaster, after winning their first two games, the team lost in its third contest, one victory short of qualifying for the provincial final.\n**HOLEY SLIDER**\n\nIt may have been inexperience, it could have been just a case of being naive, but Lino Di Iorio changed the way people slide just two years after taking up the sport.\n\nDi Iorio is the creator of the BalancePlus Slider, an invention that stopped an age-old problem with Teflon sliders.\n\nAfter taking up the sport at 45, Di Iorio noticed that the slider on his curling shoe had curled up so the edges weren't on the ice surface. Looking at other players' shoes, he noticed it was a common problem. \"To me, it showed that although the foot is about four inches wide, people were only sliding on about two inches of that.\"\n\nCombining his background in physics with an affinity for solving problems, he created the new slider, which has a shallow hole in the centre of it.\n\n\"Most people just slide on the ball of their foot,\" Di Iorio said. \"By adding the hole, that part of the slider doesn't come into contact with the ice. In essence, the person's weight is spread out over a greater area.\"\n\nThe BalancePlus Slider was first used by players such as Kevin Martin and Ed Werenich, who raved about it. That led to a surge in demand for the slider with the hole in it, and Di Iorio's invention has become the best-selling slider in the game.\n**QUITE AN ORDER**\n\nThree Canadian curlers have been honoured with the Order of Canada, the highest civilian honour in the country. They are:\n\nKen Watson (invested 1975)   \nRon Northcott (invested 1976)   \nErnie Richardson (invested 1978)\n**THE WRENCH VS. THE WENCH**\n\nIt was billed as the Battle of the Sexes, and while there have been many male-versus-female curling games, none were as high profile as one that took place in 1986 between Marilyn Darte, at that time the reigning women's world champion, and Ed Werenich, the 1983 world champ and one of the top curlers of the day. Darte (now Bodogh) appeared on a sports talk show and, feeling(now confident, issued the challenge to Werenich, which he accepted.\n\nThe match was held during the world championships, which were being contested in Toronto. In the lead-up to the game, the two\u2014who never met a reporter they didn't like\u2014playfully tossed barbs back and forth. They appeared on national television and on the front page of national newspapers. A few notes about the infamous match:\n\n\u2022 The game drew the largest crowd of the week at the world championships with a sold-out audience in excess of 7,000.\n\n\u2022 Both teams came onto the ice by bursting through huge paper hearts\u2014purple for the men, red for the women. Boxer Shawn O'Sullivan, then at the height of his career\u2014led the way for the Werenich rink, while Bodogh's team came out turning cartwheels.\n\n\u2022 Werenich's teammates came out wearing firefighters' helmets with flashing lights and blaring sirens, while Werenich came through wearing a crown and cape. The cape was being carried by an extremely busty woman in a short skirt.\n\n\u2022 Werenich's usual third, Paul Savage, was replaced by Northern Ontario's Rick Lang for the game. During the fifth-end break, Savage led a parade of women, dressed in aprons and cooks' hats and banging pots and pans, around the ice surface.\n\n\u2022 At one point, a CCA official appeared and jokingly called Darte third Kathy McEdwards for a hog line violation. Instead of removing the rock, however, he picked up McEdwards and carried her off the sheet.\n\n\u2022 The contest was broadcast live on TSN and received a rating higher than any games from that week's world championship.\n\n\u2022 The men won the game 11-3, with the women only scoring in the last end.\n\n\u2022 A rematch was held in 1996, during the world championships, but it never grabbed the attention of the initial contest.\n**STICKING TO CURLING**\n\nCurling has a great record of being accessible to all, with regular championships for blind, wheelchair, and deaf players. But one of the greatest inventions for keeping people in the game has been known simply as the Stick.\n\nThe Stick is a pole with an attachment at the end that fits over the handle of the rock. It allows a player to deliver a stone without having to bend down in the hack to do so, allowing plenty of players with back problems to continue at the game.\n\n#  **The History of the Stick**\n\nSeveral people claim to be the original inventor of the Stick, but most lean towards Preston Featherstone of Hamilton, Ontario, as the originator. Featherstone started curling in 1960 and for many years played alongside his friend Wilber House. The two often played as many as 25 bonspiels each winter, developing a long-lasting friendship.\n\nIn 1992, at the age of 82, House developed arthritis in his back, which left him unable to curl, a situation that led him\u2014according to Featherstone\u2014to become irritable and depressed.\n\nIn desperation, Featherstone decided he needed to find a way to get his friend back curling, and he got his idea from one of House's other passions. When he wasn't curling, House was a noted shuffleboard player in Tampa, Florida, routinely reaching the finals of tournaments where five hundred experienced players entered. Borrowing on that idea and from a welding-rod holder he had invented for business many years prior, Featherstone developed a stick with an attachment at the end that fit over the rock handle with a hinge. House took to the stick, named the Featherstone CurlMaster, model Mark 1, and was soon back curling.\n\nRefinements have been made over the years, and other manufacturers have jumped into the game with their own models. The Stick even made an appearance at the Brier. In 2000, Northern Ontario alternate Paul Sauve played two shots in a game using his Stick. Shortly after that appearance, the device was banned in events leading to a national championship by the Canadian Curling Association. However, many jurisdictions around the world have separate Stick championships. More important, the invention by Featherstone has allowed many curlers with back and knee problems to continue playing.\n**NO RESPECT**\n\nCurlers have always had a hard time being treated seriously by mainstream media. Two examples:\n\n\u2022 It's not very often that the U.S. mainstream press covers curling, but a 1994 report in _USA Today_ on the Buffalo Bills did so\u2014in a backhanded manner. The story centred on how the Bills have become synonymous with losing in sport. It provided quotes from other areas of sports and business where the Bills\u2014who lost four consecutive Super Bowls\u2014were used as an analogy for losing. One was provided by Russ Howard when he won the 2001 Brier after losses in the previous two. \"I don't want to be compared to the Buffalo Bills,\" said Howard. The story then followed with this line: \"So it has come to this... The Bills are getting goofed on by curlers.\"\n\n\u2022 A newspaper ad in the _Toronto Sun_ for a pay-per-call sports handicapping service carried the following headline: \"You could earn big money in sports, with no noticeable athletic ability (just like pro curlers).\" The service later offered an apology and stopped the ad.\n**SLIPS OF THE TONGUE**\n\nPutting microphones on players during televised curling games goes back to the 1960s when it was done for the CBC Curling Classic. While it provides first-hand insight into the strategy of players, it also has all the inherent dangers of live audio. Here are a few of the more memorable microphone moments from curling:\n\nWinnipeg curler Orest Meleschuk was known for his foul language, and during coverage of a major cash bonspiel in Sudbury, Ontario, local viewers got a first-hand taste. At one point during the game, the big skip found himself in a tight situation with no apparent way out. He turned to his third, John Usackis\u2014and in the process, the television audience\u2014and said: \"What the fuck are we going to do here John, eh? What the fuck are we going to do? What the fuck are we going to do?\"\n\nIn the 1983 Brier, also in Sudbury, Ed Werenich and Paul Savage were discussing Werenich's final shot. Werenich said to Savage, in a comment that was picked up by the CBC microphones: \"I'll throw it narrow and let the boys sweep the piss out of it.\"\n\nA year later, in the final of the 1984 Brier, Werenich's Ontario team was facing Mike Riley of Manitoba. Savage was suffering some stomach problems, and during the fifth end, he raced to the washroom, forgetting completely that he was still wearing his microphone. Luckily the CBC was in a commercial break, but the staff in the production truck heard all the strange noises of Savage's visit to the washroom.\n**RECORD MAN**\n\nAs one of the most successful curlers in history, Russ Howard's name is understandably all over the Brier record book. Here are a few of his and his team's entries:\n\nMost wins*| 107  \n---|---  \nMost losses*| 56  \nMost games played*| 163  \nMost games as skip*| 163  \nMost blank ends in a game (1993)| 8  \nLowest combined score (1993)| 2-1  \nShortest game (1986)| 4 ends (Howard won 11-0)  \n _*individual records_\n**WHY HURRY?**\n\nCanadian, world, and Olympic champion Russ Howard is probably the best-known caller of sweeping instructions in the game. His famous call of \"Hurry hard,\" usually heard at a high decibel level, is as famous as any in the game. Here's how it came about:\n\nWhen Howard started skipping in the late 1970s, one of the most popular brooms was called the Rink Rat, a foam-synthetic model that caused a huge amount of noise, making it hard to hear when there were multiple games going on at the same time.\n\nOut of necessity, Howard came up with a phrase that would distinguish him from other skips who yelled \"Sweep,\" so his teammates could hear him above the din. He decided on \"Hurry hard,\" which stuck.\n\nNot everyone enjoyed hearing Howard yell\u2014which he did almost incessantly during major events\u2014and people told him in e-mails and face-to-face meetings. But most of them only had to listen for a few games. Longtime Howard second, Wayne Middaugh, got so used to listening to it during the five years he played for him, he had personalized licence plates made that read: \"HURREE.\"\n**CURLING NICKNAMES**\n\nCurlers have some of the most colourful nicknames in sport, a few of which can even be written in a family book. Here are the real names and nicknames of a number of Brier champions:\n\nTerry Braunstein\n\n**Curler** | **Nickname**  \n---|---  \nEd Werenich ('83, '90)| The Wrench  \nOrest Meleschuk ('72)| The Big O  \nPaul Savage ('83)| The Round Mound of Come Around  \nAl Hackner ('82, '85)| The Ice Man  \nKevin Martin ('91, '97)| K-Mart  \nEd Lukowich ('78, '86)| Cool Hand Luke  \nBarry Fry ('79)| The Snake  \nRod Hunter ('70, '71)| The Arrow  \nRon Manning ('67)| Moon  \nTerry Braunstein ('65)| Bronco  \nRay Turnbull ('65)| Moosey\n**PERFECT RECORD**\n\nGetting through the Brier with a perfect record is a nearly impossible feat. In fact, in almost 80 years only 13 rinks have managed perfect records.\n\nRandy Ferbey| 13-0| 2003  \n---|---|---  \nPat Ryan| 12-0| 1988  \nRon Northcott| 10-0| 1969  \nMatt Baldwin| 10-0| 1957  \nGarnet Campbell| 10-0| 1955  \nBilly Walsh| 10-0| 1952  \nDon Oyler| 10-0| 1951  \nKen Watson| 9-0| 1949  \nJimmy Welsh| 9-0| 1947  \nHoward Wood| 9-0| 1940  \nAb Gowanlock| 9-0| 1938  \nLeo Johnson| 7-0| 1934  \nGordon Hudson| 9-0| 1929\n**BABY BROTHER**\n\nWhile he might not have as much notoriety as his older brother Russ, Glenn Howard has enjoyed a great deal of success on the ice as well. A look at the career of Glenn Howard:\n\n\u2022 Glenn is six years younger than Russ.\n\n\u2022 Glenn has won three Canadian and world championships, one more than Russ.\n\n\u2022 While playing for his brother during the 1980s and early '90s, Glenn had a tremendous rivalry with Ed Werenich, with no love lost between the two. However, he later spent one year curling for Werenich after Russ moved to New Brunswick.\n\n\u2022 Howard made a guest appearance on the CBC comedy series _Little Mosque on the Prairie_. He played himself and was overlooked when the characters on the program were choosing sides for a big curling match. At first, the producers wanted to cast Kevin Martin in the spot, but the first assistant director, a former Canadian junior champion named Dave Manion, convinced them that Howard would be better.\n\n\u2022 His full-time job is running the Beer Store in Midland, Ontario.\n\n\u2022 In 2006-07, his team wore pink shirts and swept with pink-handled brooms as part of an awareness and fundraising effort for breast cancer.\n\n\u2022 Along with teammates Richard Hart, Brent Laing, and Craig Savill, he started a fantasy curling camp to allow curlers of all abilities to mix with and learn from the world champions.\n**PLAY THE GAME**\n\nRuss Howard has played the most Brier games in the history of the Canadian championship with 163. And second on the list? His younger brother, Glenn.\n\nHere is a ranking of the curlers who have played the most games up to 2007.\n\n**Curler** | **Briers** | **Games Played**  \n---|---|---  \nRuss Howard| 13| 163  \nGlenn Howard| 9 9| 115 115  \nPat Ryan| 9| 109  \nAl Hackner| 9| 106  \nRandy Ferbey| 8| 100  \nKevin Martin| 8| 100  \nRick Lang| 9| 99  \nDon Walchuk| 8| 97  \nPeter Gallant| 8| 89  \nEd Werenich| 7| 89  \nRobert Campbell| 9| 88  \nWayne Middaugh| 7| 88  \nDon Bartlett| 8| 85  \nPierre Charette| 9| 85  \nGrant Odishaw| 7| 81  \nMark O'Rourke| 9| 79  \nNeil Harrison| 7| 77  \nJeff Stoughton| 6| 74  \nBruce Lohnes| 6| 73  \nMark Butler| 7| 70  \nDon Westphal| 6| 68  \nMark Dacey| 5| 65  \nJohn Kawaja| 6| 65  \nScott Pfeifer| 5| 65\n**HEAD(SET) GAMES**\n\nThe 1989 Brier in Saskatoon saw one of the most unusual and infamous incidents in the history of the Canadian championship. Russ Howard, the Ontario skip and a notorious yeller when it came to shouting out sweeping instructions, began to lose his voice. Between the noise on the other sheets and the crowd, his sweepers were having trouble hearing his squeaky voice. To alleviate the problem, Howard elected to use voice-activated walkie-talkie headsets hoping he could communicate with front-end players Tim Belcourt and Kent Carstairs. Belcourt wore the second unit, and Carstairs picked up the sweeping instructions from him. The system worked and the Ontario team won its contest, but after the game, Howard was told by Canadian curling officials he wasn't allowed to use them. He asked what rule it violated, and when told there wasn't an infraction, he brought the headsets out for the next game.\n\nHere are a few more facts about the incident.\n\n\u2022 In the first end of the first game with the headsets, Glenn Howard was narrow with a shot, and Russ yelled quickly and with force, and for some reason, his full voice kicked in. Over the microphone, the call nearly blew off Tim Belcourt's ear.\n\n\u2022 Prior to the second game, Pat Ryan of Alberta came over to see what all the commotion was and asked Howard how the units worked. With Belcourt at the other end of the ice, Howard said softly into the headset,\"Hey Tim, how big is your thing?\" Belcourt immediately raised his hands over his head, holding them apart about three feet. Ryan laughed.\n\n\u2022 One argument the CCA officials gave to Howard as to why he shouldn't be allowed to use the walkie-talkies was that someone in the crowd could be relaying information to him.When that was relayed to the press, one asked smartly, \"And just what is someone in the stands going to tell Russ Howard?\"\n\n\u2022 After the next game, an RCMP officer faxed Howard and told him he'd lend him a wireless unit that wouldn't be seen by any CCA official.\n\n\u2022 Before every draw, Howard was handed several homemade remedies for his laryngitis by fans, and he was given throat lozenges by the basket full.\n\n\u2022 Howard ended up using the headsets for two games, after which his voice returned.\n\n **Curling Quote**\n\n\"[It's] one of the very few sports that combine the excitement of a heavy piece of granite sliding slowly across the ice with the excitement of chunky broom-wielding people in bowling attire sweeping furiously in the stone's path, like janitors on speed.\"\n\n\u2014 _Miami Herald_ columnist Dave Barry on curling after viewing it at the 2002 Olympics\n**GOING LOW**\n\nPrince Edward Island is Canada's smallest province, and when it comes to the Brier, it's also the smallest on the scoreboard. The record for the combined low score in a Brier game is three\u2014games that ended 2-1.\n\nThat's happened on three occasions, and all three times, it has involved teams from Prince Edward Island, all of whom came out on the wrong end of the score.\n\nIn 2000, Andrew Robinson lost to Manitoba's Jeff Stoughton, in 1993 Ontario's Russ Howard defeated Robert Campbell, and in 1990, Ted MacFadyen came up short against Jim Sullivan of New Brunswick. In the latter two games, the teams combined for eight blank ends, also a Brier record.\n**THE MAGICAL 8**\n\nThe eight-ender is the mark of perfection in curling\u2014every rock in the rings and counting. It's often compared to the hole-in-one in golf, but it's exceedingly more difficult because, in golf, your opponent doesn't try to keep you from scoring an ace. For an eight-ender, not only does one team have to make eight perfect shots, but the opposition has to miss as well.\n\nFor that reason, it's rare to see an eight-ender in competitive play. But it has happened. At the 2006 Players Championship, the finale of the World Curling Tour, Kelly Scott of Kelowna, British Columbia, led her team to a perfect eight over Edmonton's Cathy King. Here's how the last four rocks played out:\n\n1. Scott has six rocks in the rings, five counting. Four are in or touching the four-foot and another is on the eight-foot.The sixth rock is at the top of the rings, half in the twelve-foot. King has fifth shot fully in the twelve-foot at the ten o'clock position. With her first shot, King attempts to lightly tap back the shot rock at the top of the button but comes heavy, misses everything, and sails through the house.\n\n2. Scott plays a guard that stops at the top of the rings, half in the twelve-foot.\n\n3. King's only option is to try and redirect her shooter, playing a hit on her own stone. She hits her own rock too thick, spills across the rings, touching two Scott stones but then exiting the house, leaving Scott an open draw for eight.\n\n4. Scott's shot is slightly heavy but stops in the back of the house for eight points.\n**BIG ROCKS**\n\nThe town of Arborg, Manitoba, lays claim to having the world's largest curling rock. Located 100 kilometres north of Winnipeg, the town of 1,021 erected the stone in 2006 in hopes of using it as a drawing card for passersby. The stone weighs in at a tonne and a half, measures 4.2 metres across and 2.1 metres tall and is made of steel, foam, and fibreglass.\n\nThis oversized rock is just a little bigger than the previous record holder located in Thunder Bay, Ontario. Known as the Lakehead Rock, that stone, which measures in at six and a half feet high and almost six feet in diameter and is made of concrete, was built to celebrate the 1960 Brier held in Thunder Bay. It held the record for more than 40 years, and many residents weren't impressed with being overtaken by the Arborg stone. When asked about the new record holder, Alf Childs, the Thunder Bay stone's caretaker, told the Thunder Bay _Chronicle Journal_ : \"That's an affront to granite right there.\"\n**STONE CUTTER**\n\nThere are only two places in the world still making curling stones. One is Canada Curling Stone Company, located in London, Ontario. Over the years, it has refined the art of making stones and produces wonderful rocks that are used all over the world.\n\nHere is a brief, step-by-step plan of how a stone is made:\n\n1. Huge blocks of granite are located from a quarry in Wales. This quarry produces granite that has a very fine grain and has little or no quartz in it, the desired type for curling rocks. This granite has greater impact resistance than regular granite.\n\n2. The block is cut down into smaller slabs from which large plugs, just larger than a curling stone, are cut. These plugs are shipped to Canada Curling Stone.\n\n3. The first step for the plugs once they reach Canada is to have the centre hole cut through them. The hole is roughly half an inch in width.\n\n4. The sides of the plug are then rounded off so it more closely resembles the shape of the stone.\n\n5. Once the sides have been rounded, a small pocket on the bottom of the stone is cut out to allow for an insert to be put in place. The inserts often come from older rocks whose running surface has worn out. By cutting up these older stones of fine Scottish granite, inserts can be created. These inserts provide a better running surface for the stone and extend its life.\n\n6. Once the insert has been affixed, a cup is created in both the top and bottom of the stone to allow the small running edge to be the only part of the stone that touches the ice.\n\n7. The stone is then polished with diamond abrasive pads. The bottom is also run over sandpaper to give it more grit to allow it to grab the ice better.\n\n8. The striking band is put on next by blasting the stone under high pressure with glass beads.\n\n9. Finally a handle is attached to the stone, and it's ready for play.\n**OLYMPIC DOUBLE**\n\nIn 1924, curling made its debut at the Winter Olympics held in Chamonix, France. A few notes about that competition:\n\n\u2022 Four teams played in the competition: France, Great Britain, and two rinks from Sweden.\n\n\u2022 The games were 18 ends in length and played outdoors.\n\n\u2022 Britain, which was represented by a group of Scots, won its two games, defeating Sweden I 38-7 and knocking off France 46-4.\n\n\u2022 The two Swedish teams did not play each other and so there was a playoff for the silver medal between France and Sweden II, which the Swedes won. Remarkably, both Swedish teams were awarded silver medals while the French took the bronze.\n\n\u2022 In the playoff, Major D.G. Astley of Great Britain played for Sweden II. He was awarded a silver medal for leading that team to a win and also took home a gold medal as part of the British team, making him the only person in Olympic history ever to win two medals in the same event.<\n\n\u2022 For many years, the competition was viewed as merely a demonstration and not an official event. However, an investigation by _The Herald_ , a Glasgow newspaper, showed the 1924 curling competition was, at the time, seen as official. In 2006, the International< Olympic Committee upgraded the status of that curling playdown from demonstration to official.\n\n\u2022 Curling was held at the Olympics several times since the 1924 Games, but never as an official event. It was reinstated in 1998 in Nagano, Japan.\n**ROCK HARD SUCCESS**\n\nNewfoundland and Labrador has won just a single Brier title since joining the competition in 1951. That win came in 1976 when a team led by skip Jack MacDuff beat remarkable odds to capture the Canadian championship. For many years, the rinks from Newfoundland and Labrador were viewed as hapless pushovers, having compiled a win-loss record of 45-206 prior to '76. Here are some of the highlights of that historic victory.\n\n\u2022 The team's driver for the week was none other than Sam Richardson, of the famed Richardson family team that won four Briers. He not only drove the team but guided them through the ups and downs of the week, serving more as a coach than chauffeur.\n\n\u2022 Curling fans in Newfoundland and Labrador became almost rabid as the team kept winning games. The MacDuff team received so many telegrams that the bellboys were carrying them to their room by the armload, and the telegrams managed to cover every square inch of wall space in one of the team's hotel rooms.\n\n\u2022 Newfoundland Premier Frank Moores called the team midweek and said down the line, \"A lot of people here don't know a thing about curling, but they're going crazy anyway.\"\n\n\u2022 The last game of the round robin was against Ontario, and a win would give Newfoundland the Brier. In the 10th end of a 12-end game, Ontario gave up a steal of 3 to give MacDuff a 9-3 lead. Ontario skip Joe Gurowka went to concede the game and the title to the Newfoundlanders, but Doug Maxwell of the CBC came out and said, \"You have to keep playing, this game is on television and we've got another hour to go.\"\n\n\u2022 Prior to skipping his own team, MacDuff played three years for Bob Cole, best known as the longtime hockey broadcaster for CBC.\n\n\u2022 Following the win, MacDuff had his curling shoes bronzed and put on display at the St. John's Curling Club.\n\n\u2022 The team didn't fare so well at that year's world championship, compiling a record of 2-9, the worst by a Canadian rink.\n\n\u2022 So well known was Jack MacDuff 's win, he received a congratulatory card from Western Canada addressed simply to \"Jack MacDuff, Newfoundland.\"\n\n\u2022 The team's third, Toby McDonald, served as coach for Brad Gushue's team, which won the gold medal at the 2006 Olympics.\n**HAMMER TIME**\n\nLast rock is supposed to be a significant advantage to top teams, but that's not always the case. In 1986, Alberta's Ed Lukowich recorded an 11-0 win over Newfoundland's Fred Durant, and Lukowich stole all 11 points.\n**GOING LONG**\n\nIf a curling game goes long, expect Northern Ontario to come out on top. The record for the longest game in Brier history is 15 ends, which has happened twice. In 1927, the Brier's first year, all games were 14 ends. Twice, Northern Ontario had to go to an extra end to determine a winner. The first came against Toronto while the second was in a match against Quebec. Northern Ontario won both times by a score of 11-10.\n**THE REAL WORLD**\n\nUnlike most other top athletes, top curlers usually hold down full-time jobs and try to combine curling and work. Some players have rather unusual vocations. Here's a look at some notable curlers and their full-time occupations:\n\nColleen Jones| weather\/sports presenter, CBC  \n---|---  \nEd Werenich| firefighter  \nWayne Middaugh| golf professional  \nMarkku Uusipaavalniemi| Member of Parliament, Finland  \nGlenn Howard| beer store manager  \nPeter Corner Vic Peters| police officer golf course superintendent  \nPete Fenson| pizza parlour owner  \nHammy Macmillan| hotel manager\n**WORLD SERIES CURLER**\n\nNew Zealand curler Hans Frauenlob is the only player to compete in the World Curling Championships and have two Major League Baseball World Series rings.\n\nHuh, you say?\n\nFrauenlob, a competitive curler originally a Torontonian, worked for the Toronto Blue Jays in their IT department during the club's 1992 and 1993 World Series victories. As was every other Blue Jay employee, he was presented with a World Series ring after each of the club's wins.\n\nHe later moved to New Zealand where he continued his curling career, eventually making it all the way to the world championship.\n**MARKKU THE MAGNIFICENT**\n\nMarkku Uusipaavalniemi is best known for winning a silver medal for Finland at the 2006 Olympics. But he has been around the game for a long time and worked harder than most to reach world-class status. Some things you might not know about Uusipaavalniemi:\n\n\u2022 In 2007 he was elected to Finland's Parliament.\n\n\u2022 U.S. curler Pete Fenson nicknamed him M-15 because he was unable to pronounce his last name. He has also been called Uusialphabet.\n\n\u2022 As a student, he once had the highest mathematics score in a nationwide test and has reportedly solved a Rubik's Cube in 25 seconds.\n\n\u2022 Following his silver medal at the Olympics, more than 1,000 people turned up for weekly clinics, encouraged by his team's performance. He was fielding 150 e-mails a day and appeared on television weekly.\n\n\u2022 Uusipaavalniemi played in the 2002 Olympics, finishing fifth. He won the European championships in 2000 and has finished third at the world championships on two different occasions.\n\n\u2022 The gold medal game in 2006 between Finland and Canada drew a television audience of 5 million in Finland, where curling is not much more than a fringe sport.\n\n\u2022 Uusipaavalniemi built his own curling club in his hometown of Hyvinkaa.\n**SLIDING ALONG**\n\nMany curlers may not realize the impact Arnold Asham has had on their games, but the Winnipeg entrepreneur is one of the largest suppliers of curling equipment in the game. Whether it be a slider, a broom, or some clothing, Asham Curling Supplies has touched curlers around the world. A few notes on the man behind the company:\n\n\u2022 Asham is a M\u00e9tis who grew up in Kinosota, Manitoba, and started curling at age 13.\n\n\u2022 He started working for the Manitoba Department of Mines and Resources while curling competitively and stumbled upon a material that made for a great slider. He started selling his now famous red-brick sliders out of his basement but when demand took off, he left his government job and went into the curling shoe business full time.\n\n\u2022 Asham didn't come up with the original idea for the red-brick slider. A fellow club curler, who worked in the printing business and used this hard plastic material in his work, was the first to put the material on his curling shoe. Asham was attracted by the noise it made and he revolutionized the manner in which it was put on the shoe.\n\n\u2022 He sold more than $1 million worth of red-brick sliders.\n\n\u2022 He was one of the founders of the World Curling Tour. His company serves as title sponsor of the circuit.\n\n\u2022 He founded a square-dance group called the Asham Stompers, which competed in festivals wearing, of course, Asham curling shoes (without the slider).\n\n\u2022 In addition to five kinds of curling shoes, Asham also sells curling brooms, bags, slip-on grippers, gloves, slip-on sliders, and curling apparel.\n**ALL-IMPORTANT CLUB**\n\nThe Duddingston Curling Society lays claim to being \"the most important curling club in the world.\" Formed in 1795, the club was the haunt of choice for curlers in Edinburgh, who used the Duddingston loch as their venue. The most distinguished curlers from all over Scotland joined the Duddingston with the fee being three guineas. There were also medals struck, which members wore to \"distinguish the members from other gentlemen.\" There were also rules for the new group, which included a fine for talking politics.\n\nPerhaps the society's main contribution to the game was the establishment of curling's first set of rules. The document, which still exists, is dated January 6, 1804. Many of the rules in that code still exist in some part today, such as No. 10: \"A doubtful shot is to be measured by some neutral person whose determination shall be final.\"\n**WHAT'S IN A NAME?**\n\nEver wonder how the hog line got its name? According to Scottish curling history, it's a farming term. A hog, in livestock circles, was a name given to a weak member of a litter, a runt, so to speak, specifically with sheep. This hog was more than likely to die before the end of its first year, either at the jaws of a predator or from the farmer who would cull his flock. Similarly, a hogged rock is one that falls short of the line, not making it into play.\n**CHARACTER GUY**\n\nUp until the mid-1950s, curling had been a staid and reserved sport, even at the Canadian championship level. It wasn't considered proper for players to show a lot of emotion or to showboat in any way. But that changed with the arrival of Edmonton's Matt Baldwin. Not only was he a breath of fresh air for fans, he was also a remarkably talented player. Some facts about the three-time Brier winner:\n\n\u2022 The first indication that Baldwin was going to buck tradition came in the fi fth round of the 1954 Brier in Edmonton. After making his last shot to beat Northern Ontario 6-5 in a close match, Baldwin's third, Glenn Gray, jumped into the air and let out a scream. Baldwin raised a clenched fist and shook it as he came down the ice to celebrate with his team. That night at a banquet, one of the Brier trustees (the organizers of the event) told Baldwin his actions that day weren't acceptable and asked the Alberta skip to keep his emotions in check for the rest of the event.\n\n\u2022 Baldwin was one of the first curlers able to slide the entire length of the ice. In the '54 Brier, every time he stepped into the hack, the crowd would yell, \"Slide, slide.\"\n\n\u2022 At a major event at Maple Leaf Gardens in Toronto, Baldwin delighted the fans by sliding the length of the ice with the rock in front of him. Halfway down the sheet, he removed his hand from the stone, nonchalantly rubbed his nose and then replaced his hand on the rock, which was sliding along in front of him, still in position. He stopped the rock perfectly on the button.\n\nMatt Baldwin and Garnet Campbell\n\n\u2022 Baldwin became known as a man who never missed a party. After winning the '54 Brier, he went to a party at the host hotel and stayed late. \"I just got plastered,\" he stated of the evening.\n\n\u2022 Gunning for his third Brier win in 1957 in Victoria, Baldwin told the media about the host hotel, the Empress, \"All those ladies having tea are making so much noise we can't get our rest.\"\n\n\u2022 On the final day of the '57 Brier, Baldwin was suffering so badly from the flu, he brought a chair out onto the backboards and sat in it when his team wasn't shooting\n\n\u2022 At the 1971 Brier in Quebec City, a massive blizzard caused a power failure at the arena in the middle of a draw, sending the event into 15 minutes of darkness. When the power came back on the Baldwin team was nowhere to be seen, but on their sheet, all eight rocks were sitting in the four-foot. Baldwin and his team emerged from the bar to where they'd retreated to gales of laughter from the fans.The incident became known as the Baldwin Blackout.\n\n\u2022 Baldwin was known as one of the single best shooters in the game. For a number of years, an Edmonton television station conducted a singles competition between some of the top players in the game, Ernie Richardson and Garnett Campbell among them. Baldwin won it six consecutive years, and the station finally had to remove him from the event.\n**PRESERVED IN GRANITE**\n\nThe final game of the 1956 Brier is one of the most memorable in the event's history. It required a playoff game (prior to there being regular playoffs) because Ontario and Manitoba tied with identical 8-2 marks. In an extra end of the extra game, Ontario's Alf Phillips appeared to have the match won with a stone 90 percent buried on the button. Billy Walsh of Winnipeg, however, played a perfect come-around tap to score one and win the Brier. So remarkable was the final shot that a fan jumped over the boards, grabbed the winning stone, and disappeared into the crowd. A few weeks later, he presented Walsh with the winning stone mounted on a special plaque to commemorate the fantastic finish.\n**SUBSTITUTE CHAMPIONS**\n\nWhen the first Brier was held in Toronto in 1927, it was organized late in the curling year, and there was a scramble to assemble the representative teams.\n\nTwo members of Ontario's team, winners of the Silver Tankard, had to be called back from Florida, where they'd escaped to pass the winter. The team's second, Mel Hunt (father of the late Toronto sportswriter Jim Hunt), and Harry Watson (grandfather of hockey broadcaster Harry Neale) returned with just a few days to spare.\n\nThe Nova Scotia entry had its own difficulties.When locals received the invitation to come to Toronto for the first championship, they originally decided to send Murray Macniell's provincial championship rink. But the only one able to make the trip was the skip, so he selected three other skips to join him.The first time the team played together as a team was the opening draw of the Brier. It obviously worked, as the Halifax four became the first Canadian champions.\n**VISIBLE MINORITY**\n\nOnly one non-white has won the Canadian men's curling championship. Rudy Ramcharan, who played second for Kevin Martin's winning squad in 1997, is of Guyanese background. He disappeared from curling circles a few years later after trying to run a cash event, officially the World Open but known to many as the Rudy Spiel, with a purse of $500,000. However he was never able to secure the sponsorship, and a number of teams competed and were never fully compensated. Ramcharan became persona non grata among many of the top curlers.\n\n**Curling Quote**\n\n\"There's not too many guys who can really be entrusted with (the ice). Besides, you'd have to be nuts to do it anyway. The hours, the work, the stress, the pressure of it all and I don't even get to curl on it. I'm the only one held responsible. It doesn't matter if the rocks are no good, or if the weather is bad, in the end, it all reflects on me. So come on curling gods, keep taking care of me.\"\n\n\u2014Icemaker Dave Merklinger, who made the ice for the 2007 Tim Hortons Brier in Hamilton, as told to the _Hamilton Spectator_\n**CLOSE TO PERFECTION**\n\nThere has never been an eight-ender in Brier history, but there have been two occasions when it seemed almost certain the perfect end would be recorded.\n\n\u2022 In 1947 Jimmy Welsh of Manitoba played Prince Edward Island's Frank Acorn. In the eighth end, Acorn was looking at seven Manitoba counters, and his final rock was light, stopping just into the twelve-foot. Welsh needed to be better than that Prince Edward Island rock to score the magical eight, but he was heavy and ended up scoring seven.\n\n\u2022 In the 1936 Brier, Ken Watson's team was rolling to win after win, and in its seventh match it faced a winless Prince Edward Island squad. Prior to the game, Watson gave lead Charlie Kerr a cigar, which Kerr smoked as the game progressed. In the first end, with Watson sitting five, third Grant Watson threw a draw that appeared to be perfect but just a little light. Kerr and second Marvin McIntyre put the brooms to it and just as it approached the rings, an ash from the cigar dropped in front of the stone, and it ground to an immediate halt, inches from the target. When the next two Manitoba stones found the house, the team had a seven-ender that could have been eight were it not for the cigar ash.\n**A HEART OF PURPLE**\n\nThe Purple Heart is a highly sought-after crest for male curlers in Canada. It signifies participation in the Brier and a provincial champion. Curlers who have one can thank a team from Ontario for that honour.\n\nFor the first six years of the Canadian championship, Purple Heart crests were not awarded. Each curler did receive a small pin.\n\nAt the seventh championship, Gordon Campbell and his rink from the Hamilton Thistle Curling Club arrived at the championship with lavish crests presented to them by the Ontario Curling Association proclaiming them to be Ontario champions. Senator Jack Haig of Winnipeg, who was one of the Brier trustees (essentially the organizers) noticed the crests and asked Campbell about them. \"I think we should do something like that,\" he said.\n\nThe next year, every participant received the famous heart-shaped crest. However the original ones were not purple, but red. The colour changed in 1940 and has remained purple ever since.\n**TANKARD TIME**\n\nThe trophy presented to the winner of the Brier is known as the Macdonald Brier Tankard and has a long history, somewhat longer than the championship itself. It was not even created for the Brier but for the Manitoba Bonspiel where it was first awarded to the winner in 1925. Presented by Macdonald Tobacco, the cup itself was hand-tooled in Great Britain.\n\nIn 1927, however, Macdonald Tobacco, the sponsor of the Brier, elected to use the trophy for the new national championship. It remained the official trophy until 1979, when the tobacco company ended its sponsorship.\n\nFor the first 27 years of the Brier, the names of the four winners were engraved into a heart-shaped crest and affixed to a base. However, after that period, there was no room left, and the players' names were put onto a single plaque on the back of the trophy.\n\nWhen Labatt took over sponsorship in 1980, it brought in its own trophy, which was presented until 2000. At that time, Nokia assumed title sponsorship, and in consultation with the Canadian Curling Association, had the original Macdonald Tankard reinstated. It was upgraded to the tune of $10,000 and, with the addition of a series of new base levels, every winning team from 1927 onward had their names engraved onto a heart-shaped crest.\n\n**Curling Quote**\n\n\"A match for money even though the sum be devoted to charity, would drag down curling to the level of baseball.\"\n\n\u2014A director of the Grand National Curling Club (forerunner of the United States Curling Association) in response to an 1870 challenge from Scottish curler Sir William Elliot, who said he'd play any North American team for \u00a3500 sterling\n**SPONSORS**\n\nCurling has had a number of interesting sponsors over the years, and in comparison to many other sports, the sponsors have stayed for extended periods of time. Here's a list of some of the leading sponsors of major events, and the length of their support:\n\n**Canadian Men's**  \n---  \nMacdonald Tobacco| 50 years  \nLabatt| 20 years  \nNokia| 4 years  \nTim Hortons| 4 years*  \n **World Championship**  \nScotch Whiskey Company| 9 years  \nAir Canada| 18 years  \nSafeway| 2 years  \nFord| 14 years*  \nNo sponsor| 5 years  \n **Canadian Women's**  \nDominion Grocery| 7 years  \nMacdonald Tobacco| 8 years  \nScott Paper (later Kruger)| 27 years*  \nNo sponsor| 6 years  \n*on going| \n**BATTLE OF THE SEXES**\n\nAs long as male and female curlers have been throwing rocks, a war has been waged as to which sex is the better at curling. Over the years, there have been a number of highly publicized battles of the sexes. Here are a few notables:\n\n\u2022 In November 1972,Vera Pezer and her team of Canadian champions challenged reigning men's Canadian and world champion Orest Meleschuk to a game, one that eventually found its way onto the CBC. Pezer ended up winning the game 4-3 when Meleschuk missed his last shot of the game. The announcers, Don Chevrier and Don Duguid, summed up Meleschuk's sentiments:\n\n _Chevrier_ : \"I'm not sure Meleschuck can really believe it.\"\n\n_Duguid_ : \"He'll believe it tomorrow morning, Don.\"\n\n\u2022 In October 2005, multiple-Brier winner Randy Ferbey and his team took on Jennifer Jones, the reigning Canadian women's champion, in a skins-format gender battle. The game was broadcast across Canada on Sportsnet, and what viewers saw was a Ferbey domination. He won seven of the eight available skins.\n**SCIENCE OF CURLING**\n\nWhy a curling rock actually curls has been a mystery to many curlers, but the CBC radio program _Quirks and Quarks_ tried to de-mystify it during a 1980 broadcast. Here, according to Dr. Mark Shegelski, are the reasons a 40-pound piece of granite curls.\n\nWhen a rock is turning as it travels down the ice, one side is turning toward the direction the rock is travelling and the other away from it.\n\nThe speed of the two edges relative to the ice is different due to friction. When a rock is first thrown, the amount of friction is about the same. But as the rock slows, the edge that is turning back toward the curler (the right side on an in-turn) is turning more slowly because it is turning in the opposite direction to which the rock is travelling.\n\nBecause this side is turning slower, friction has a greater effect upon it. That causes the stone to deflect to one side (in the case of the in-turn, to the right).\n\nThe sharpest move a rock makes is often right at the end as it stops, because one side of the rock stops first while the other side continues to rotate.\n\nAnd now you know!\n**REGAL CURLING**\n\nFrederick Hamilton-Temple-Blackwood, first Earl of Dufferin, first Marquess of Dufferin and Ava\u2014the name may not mean much to curlers, but this gentleman served as Governor General of Canada from 1872 to 1878 and had a profound effect upon the sport of curling.\n\nA devoted enthusiast of the roaring game, in 1873, at his own expense, he added a curling rink to Rideau Hall, the Governor General's official residence. It exists to this day, along with the Governor General's Club, an exclusive and honorary club whose membership is made up of those who have given a great deal to the sport of curling.\n\nAnd he presented a trophy for annual competition, which came to be known simply as \"the Governor General's.\" It was awarded to the winners of the Ontario double-rink competition, and for many years was emblematic of the provincial championship. The competition ceased being held in 1996.\n**WOMEN'S DATES**\n\nA few notable dates in women's curling:\n\n\u2022 The first women's curling club in Canada was established in 1894 in Montreal. Prior to that, women were discouraged from coming to curling competitions due to liquor being present.\n\n\u2022 The Ladies Curling Association of the Canadian Branch of the Royal Caledonian Curling Club, which became the governing body for women's curling, was established in 1904. It looked after the rules> and competitions for the women's game in the Quebec and Ontario regions, although there were few formal events held.\n\n\u2022 The Canadian Ladies Curling Association was formed in 1960 (taking over authority from the above-mentioned body), and a year later, the first Canadian women's curling championship was held. Prior to the event, Dominion Stores, a nationwide chain of grocery stores, approached the fledgling association and asked if it could be the title sponsor, one of the few times a sponsor has come to the event and solicited involvement and not the other way around.\n\n\u2022 The United States Women's Curling Association has a longer history, having formed in 1947. The first national women's championship was held in 1949, although it wasn't until 1977 that it was formally recognized as the national championship. Prior to that, it was run as a bonspiel.\n\n\u2022 The first women's world championship was held in 1979 in Perth, Scotland, sponsored by the Royal Bank of Scotland.\n**JUNIOR-SENIOR**\n\nOnly eight male curlers have won both the Canadian Junior and the Canadian Men's championship. Here is the list, noting the first time they won each event:\n\n**Name** | **Junior** | **Men's**  \n---|---|---  \nEd Lukowich| 1962| 1978  \nNeil Houston| 1975| 1986  \nKevin Martin| 1985| 1991  \nDan Petryk| 1985| 1991  \nJon Mead| 1986| 1999  \nScott Pfeifer| 1994| 2001  \nCraig Savill| 1988| 2007  \nBrent Laing| 1988| 2007\n\n**BAD ICE**\n\nIcemaking has become a combination of art and science, and it's not often these days that curlers at major championships have to suffer with poor conditions. That hasn't always been the case, however. Following are some recent examples of horrible ice at significant events.\n\n#  **1970 Brier**\n\nThe ice at this championship was so heavy it removed almost all shotmaking abilities. Instead, players just heaved the rocks down the ice as hard as they could and hoped they'd make the rings. In one memorable game, British Columbia's Lyle Dagg came short of the rings with his last rock to lose to Ontario's Paul Savage. Dagg was playing a hit.\n\n#  **1992 Olympics**\n\nCurling was a demonstration sport at the '92 Games. The competition was held in the ice rink of Pralognan-la-Vanoise, a venue about 50 kilometres from the host city, Albertville. Right from the start, the refrigeration unit didn't work properly, and only one of the four sheets in the facility froze properly. The two middle sheets were unplayable and were covered with carpet, so the entire competition was reduced to two sheets. One was extremely frosty and the other always had a small film of water on it. The icemakers called in Canadian skip Kevin Martin, who had icemaking experience, to try to help, but when the opposing teams learned he was involved, they protested, and Martin was forbidden from helping. At the end of the week, Martin had the highest percentage of any curler at a ridiculously low 63, the lowest winning mark of any international championship on record.\n\n#  **1981 World Curling Championships**\n\nIn the final game between the United States and Switzerland, the ice plant at Thompson arena failed in the late ends, and the ice began to melt slowly. By the time the teams played the final end, a small layer of water covered the surface, making it almost impossible to get rocks in play. The U.S. team hogged its first four shots, and Switzerland went on to win the title by a score of 2-1.\n\n#  **2001 Brier**\n\nWhen players complained that the ice conditions were too straight, preventing any aggressive play, the Canadian Curling Association asked renowned icemaker Shorty Jenkins to come in and work his magic. Despite his reputation for making superb ice, he had never worked on the Brier ice before. However, with limited time and resources, Jenkins overdid it, and put too much curl onto the sheets, making it nearly impossible to play. Following two draws, the CCA returned to its existing icemaker and flooded the surface to start over.\n\n#  **2005 Women's World Championship**\n\nThe event was held at the Lagoon Leisure Centre in Paisley, Scotland, and icemakers had their work cut out for them at this global tilt thanks to a number of factors. First, the ice rink was located next to a swimming pool, and humidity\u2014curling ice's worst enemy\u2014was a constant factor. Also, because organizers refused to pay for a deionizer for the water that was used to pebble the ice, the first few draws had horrid conditions. Finally, the arena floor was concave, so the outside sheets were thicker ice than the inside ones, meaning significant differences in conditions between each sheet. Conditions were so bad, the fourth draw was actually cancelled. The event was also marred by officials who walked out after they learned they weren't going to be paid, and by low attendance\u2014often times there were more people on the ice than in the stands.\n**ORIGINAL OLSON**\n\n**A** lot of curlers have stepped on the name Olson over the years, and that's just fine with the family. Olson, you see, is synonymous with hacks, and for many years, the company that bears the name of the inventor made a majority of the toeholds in use across the world.\n\nElias Bjarni \"Ole\" Olson was the inventor of the rubber hack. Patented in 1939, it was the standard for almost 50 years. (Some are still in use today, although a newer model\u2014the Marco hack\u2014has taken over.)\n\nOlson came up with his idea while playing in a bonspiel in Saskatoon. During a crucial time in the game, Olson went to play a shot, and his foot slipped, causing him to miss. At that time, hacks were merely holes chipped out of the ice. On his way home from that bonspiel, he stopped at a tire company and purchased some raw rubber with which he began to experiment, moulding it into different shapes before arriving at the final product. So successful was his invention that he was swamped by orders from curling clubs around the world.\n\nOlson was also the first person to use paint on curling ice to distinguish the house, that coming in 1926, and he also invented a curling rink ice shaver as an inexpensive alternative to the Zamboni. Among his other inventions are a pebbling can and a rock measure.\n\nOlson passed away in 1964 and was posthumously inducted into the Canadian Curling Hall of Fame in 2000.\n**HISTORY ON DISPLAY**\n\nDon and Elva Turner enjoyed collecting all things curling. In fact, they liked it so much they turned their basement into a museum to house all their wares. The artifacts the couple assembled are thought to be the largest collection of curling memorabilia in the world.\n\nThe collection began in 1974 when Elva curled in the Canadian Seniors in Halifax and returned home to Weyburn, Saskatchewan, with a small collection of pins and some curling photos. From there, the collecting became voracious and soon the couple's basement was turned into a museum. School groups and avid curlers used to come by to see the displays.\n\nThat was great for a while, but eventually the collection outgrew their home. That's when their home city of Weyburn stepped up and allowed them to create the Turner Curling Museum in a 2,600-square-foot building attached to the city's recreation centre. The operation is the world's first curling museum.\n\nInside, visitors see rarities such as a set of circular curling irons with iron handles, used in the late 1800s in the Ottawa Valley. There is also an early rock sharpener used by the Queen City Curling Stone Co. of Regina in the 1930s. A prized possession is a pair of rocks awarded as a prize in the 1927 Brier, the first Canadian championship.\n\nBut undoubtedly the most impressive display is the massive collection of pins, collected through years and years of attending major curling events, especially the world championship. It's estimated there are 18,000 curling pins, and no one is quite sure if that is the largest collection in the world, but it is certainly impressive.\n\nDon Turner passed away in 2006, and Elva maintains the museum.\n**CURLING IN THE BIBLE?**\n\nAt the opening banquet for the 1966 Brier in Halifax, the speaker, Dr. J.B. Hardie, a professor at Pine Hill Divinity College, light-heartedly suggested that curling must have been around for a lot longer than originally thought. To back up this point, he gave a number of examples of curling being mentioned in the Bible. First he said that the purest of curlers must be the leads: \"He that is without sin among you, let him cast the first stone\" (John 8:7).\n\nThen he said there were a great many talented curlers back in the Holy Land: \"Among all this people, there were seven hundred chosen men left-handed; every one could sling stones at an hair breadth, and not miss\" (Judges 20:16).\n\nFinally, he argued, there's nothing like the Canadian men's championship: \"He that is best among them, is as a brier\" (Micah 7:4).\n**LATE NIGHT CURLING**\n\nCurling made it to late-night television in 2002 during its play at the Olympics in Salt Lake City, Utah. That's when the titans of American talks shows\u2014Jay Leno and David Letterman\u2014made light of the cult hit. Leno had a joke about it during his opening monologue on February 19, 2002, saying: \"Did you see the curling today? Pretty exciting. The gold medal ended up going to a Brazilian cleaning team.\"\n\nLetterman used curling as a theme for one of his famous Top 10 lists. It was titled: \"10 Ways to Make Curling More Exciting.\"\n\n10. How about calling it anything but curling?\n\n9. Instead of weird lookin' Norwegian dudes in sweaters\u2014babes in lingerie.\n\n8. Only allow French judges.\n\n7. Sweep the stone toward the hog line and then...okay, I don't know crap about curling.\n\n6. Is it too much to ask for one curler to bite another curler?\n\n5. Throw in one of them miniature-golf windmills.\n\n4. Instead of a granite stone, use the frozen head of Walt Disney.\n\n3. 40% of final score comes from the swimsuit competition.\n\n2. You don't think curling is exciting? What are you, insane?\n\n1. First place gets gold medal, the rest are sent to Camp X-Ray.\n**CURLING ART**\n\nThere are a number of remarkable curling paintings around the world, but few that match the impressiveness of Charles Lees' work of the Grand Match that took place January 25, 1848. Titled \"The Grand Match at Linlithgow Loch,\" it shows what appears to be a wild game of curling with men in top hats and full dress. According to historian Bob Cowan, the curling was between 35 teams from the north and 35 from the south. Reportedly, 6,000 people were present. The painting of this event showed only a small number of these folks, and many notables of Scottish curling are represented. In fact, Cowan stated, there is evidence to suggest that Lees travelled to the homes of curlers to sketch them. The painting was completed in 1849, and the Royal Caledonian Curling Club purchased it in 1898. For many years, it hung in the curling club at Perth. In 2006, Sotheby's appraised the work at \u00a3500,000. The work now hangs in the Scottish National Portrait Gallery in Edinburgh.\n**TV PAY DAY**\n\nEd Werenic and Russ Howard\n\nThe TSN Skins Game is an innovative, made-for-television event that was developed at a time when curling was suffering from plenty of low-scoring, defensive play that left audiences snoring. It not only became one of the most popular curling events for viewers, but also one of the most lucrative for curlers. A few notes about the skins:\n\n\u2022 The idea for the format was developed by Jim Thompson, then vice-president of TSN, and entrepreneur Doug Maxwell. They decided to break all the rules in building a new event that would sell to television audiences.\n\n\u2022 The event has been held in all ten provinces as well as the Yukon.\n\n\u2022 McCain Foods sponsored the tournament from 1989 to 2004, then it went dormant until 2007, when it was revived and held at Ontario's Casino Rama.\n\n\u2022 The highest payout for a single skins game came in 2004 when Kevin Martin earned $100,500.\n\n\u2022 Wayne Middaugh has been a member of seven winning teams and has earned a total of $365,750 in his skins game appearances.\n\n\u2022 A women's version of the skins game was held for eight years but dropped in 2003.\n**CURLER STATS**\n\nWho are curlers? If they live in Canada, there's a pretty good idea of their profile, demographically speaking, thanks to the Print Measurement Bureau, a research organization aimed at the print media.\n\nHere's who the Canadian Curler is as of 2006:\n\n\u2022 one of 754,000 Canadians\n\n\u2022 55 per cent are male\n\n\u2022 between the ages of 35 and 49\n\n\u2022 lives in a community between 500,000 and one million residents\n\n\u2022 lives in a rural prairie location\n\n\u2022 20 per cent have a university degree\n\n\u2022 had an annual household income between $75,000 and $99,000\n\n\u2022 49 per cent engage in volunteer activities\n\n\u2022 a majority also golfed or fished\n**CURLING IN TELEVISION COMMERCIALS**\n\nCurling has appeared numerous times in commercials, being used to sell everything from beer to cellphones. Here are some of the more memorable commercials.\n\n#  **Advertiser: Cialis (a drug for erectile dysfunction)**\n\nA man is shown delivering a stone, and in doing so falls and appears to be injured. His wife comes to comfort him, and he announces that he'd better quit because of the injury. The next scene shows the couple leaving the club for their car, and the woman confronts her husband about his \"injury,\" which appears to have suddenly healed. A large Cialis logo then appears.\n\n#  **Advertiser: Labatt Beer**\n\nA snowy street scene is the opening shot of this commercial, with a hot dog cart as the central feature. The operator of the cart is putting it into place for the day and drops a bag of buns. When he bends down to pick them up, he lets go of the cart, which starts to slide down the street, turning like a curling rock. Suddenly, people appear from everywhere, from their porches, from shovelling their driveways, from taxis, all with brooms, and begin sweeping the hot dog cart as if it's the shot to win the Brier. The vendor is barking out orders like a skip, and after encouraging the group to sweep, suddenly bellows at them to stop. The cart slowly stops sliding just before hitting a postal truck, and a close-up shows the mustard container rubbing part of the truck, wobbling, but not falling over. As the cart comes to a stop, there is a spontaneous cheer from the group.\n\n#  **Advertiser: Scotties tissues**\n\nA woman is shopping and places a box of Scotties tissues in her cart. As she walks forward with her cart, two women appear, one with a corn broom, the other with a push broom. They sweep the cart toward the cash register, stopping once, then restarting and concluding when the cart reaches its destination. They look at each other and nod in satisfaction. A voiceover states: \"Scotties, proud sponsor of women's curling for over 25 years.\"\n\n#  **Advertiser: Office Depot**\n\nAn advertisement that aired in the United States prior to the 2002 Olympics showed a man in what appears to be a lounge, watching television. A close-up of a rock being swept appears on the screen, and the obviously confused man says: \"What is that?\" The screen then shows the words \"But, if life was like Office Depot...\" The same scene is repeated, only this time, U.S. curler Don Barcome responds to the man's question by placing a curling rock on the table in front of him and saying: \"Curling, an ancient Scottish ice sport played with a 42-pound stone.\" The scene then cuts to an Office Depot store, where an announcer says: \"If you want expert answers whenever you need them, come to Office Depot.\" At the end of the commercial, a tag points out that the retailer is a sponsor of the U.S. Olympic team.\n**ROCK BOTTOM**\n\nThere are curling rocks in unusual places but perhaps none stranger than the several crates of stones that rest at the bottom of the Atlantic Ocean, somewhere off the coast of Newfoundland. How did they end up there? According to Doug Maxwell in _Canada Curls_ , in the early 1800s there was a challenge issued by a group of Scottish soldiers stationed at Long-Sault to a group of Scottish ex-pats living in Lachute, Quebec. The difficulty was that there were not enough curling rocks to hold such a match and so an order was put in to the homeland to ship 16 to Quebec. Unfortunately, the ship carrying the rocks sank off the Grand Banks, dropping the bits of Ailsa Craig granite to the bottom of the ocean.\n**DEADLY BUSINESS**\n\nCurling has played a small role in two tragic and notable events. The first was on April 30, 1912, 20 days after the sinking of the Titanic. On April 17, the Mackay-Bennett set sail from Halifax with the grim job of recovering bodies from the sinking of the ocean liner. Over the course of the next few days, men on the ship pulled in 306 bodies and after sailing home, delivered them to the Mayflower Curling Club, which served as the morgue. While the ship was at sea, coffins had been piled high at the club awaiting the grim arrival.\n\nThe second event was on December 21, 1988, when Pan Am Flight 103 was destroyed by a bomb over Lockerbie, Scotland. Many parts of the plane fell on the town, and the first medical officer on the scene was Dr. Graeme Adam. Just a few weeks earlier, Adam had won the Scottish men's curling championship and was soon to leave for the world championships in Milwaukee,Wisconsin. But his practice time was cut short for two reasons. First, he was busy dealing with the accident, and second, as in Halifax, the local curling club was transformed into a morgue to house the bodies of those killed in the crash. The curling ice was understandably not available for curling.\n\nAdam went on to finish with a 5-4 record at the world final.\n**PURPLE RAGE**\n\nCurling has a great deal of tradition, and as one organization found out, curlers don't want to lose that.\n\nIn 1980, when Labatt took over sponsorship of the Brier from Macdonald Tobacco, it decided to create a new crest to present to all participants. This was a replacement for the famed Purple Heart.\n\n\"We weren't really keen on keeping the Purple Heart,\" admitted Dick Bradbeer, head of marketing for Labatt at the time. \"We wanted something more Labatt-oriented.\"\n\nIn place of the heart was an oval-shaped crest that had images of the Purple Heart and the Macdonald Brier Tankard, the trophy that was presented to the winning team up until Labatt replaced it with its own tankard. Among the curlers, it became known as the Doily.\n\nBut curlers from coast to coast\u2014those who had played in the Brier and those who had merely watched it\u2014were enraged. How could this new sponsor replace the historic crest? There were petitions and plenty of media attention on the issue of a crest. A front-page editorial in the _Ontario Curling Report_ admonishing Labatt for the change. It read:\n\nThe Heart is symbolic of the Brier; it represents curling supremacy. After the Brier, all that remains are the fine memories and the Heart.\n\nEvery competitive male curler dreams of playing in the Brier. The Brier is the pot of gold at the end of the rainbow. The Brier is the Stanley Cup, the Super Bowl, the end all, be all.\n\nNow the new sponsors of the Brier have created a new symbol that they are incorporating into a crest. The new crest does not resemble the Heart, although they have tried to keep the coveted Heart by placing its design in the centre of this new symbol. This new creation destroys the image that has been established from 50 years of annual competition. Every curler in Canada identifies with the Purple Heart; it is the symbol of excellence.\n\nLabatt's sponsorship is a welcome addition to the game. However, curling has established legends built around the Heart. You can do anything with the design of the Heart but don't mess with the winner, the Heart of the game.\n\nThe paper was the final straw. \"When we saw that newspaper, we realized just how important the Purple Heart was,\" said Bradbeer. \"It wasn't that we were being stubborn, it was another case of not realizing the importance the curlers put on it.\"\n\nLabatt reissued the crest in the famous shape and colour to the delight of all. All the players from the1980 Brier\u2014the first sponsored by Labatt\u2014ended up with two crests: the Purple Heart and the Doily, now a rare collector's item.\n\n**Curling Quote**\n\n\"His sister said the car looked like it had hit a moose. So I guess John is built like a moose.\"\n\n\u2014Kevin Martin on his third, John Morris, who was hit by a car just days before the start of the 2007 Tim Hortons Brier\n**AMERICAN SUCCESS**\n\nBob Nichols and Bill Strum have won more World Curling Championships than any other Americans, with three wins to their credit. That's quite an achievement considering the U.S.A. has won the world title just four times.\n**THE MANITOBA BONSPIEL**\n\nThe Manitoba Bonspiel, also known as the MCA after the Manitoba Curling Association, which runs the event, dates back to 1884 when the first bonspiel in Winnipeg was held. There were 65 teams from all over the province at that first event, which led to the formal start to the Manitoba Bonspiel, which began five years later and continues to this day. Notes about the famed event:\n\n\u2022 In the early days, the event became so popular that for several years, the sitting of the Manitoba Legislature was cancelled due to the inability to get a quorum; so many members were on the ice.\n\n\u2022 In 1988, to celebrate the bonspiel's centennial, an all-out effort to attract teams produced the largest field ever for a curling event\u20141,280 teams.\n\n\u2022 The event is open to all teams of male curlers, and there are regular entrants from across Canada, the United States, Europe, and Asia.\n\n\u2022 Entries into the provincial championship are awarded to the top finishers in the bonspiel.\n\n\u2022 In recent years, the number of teams in the bonspiel has dropped and there was discussion about allowing women to enter but that was never passed by organizers.\n\n\u2022 Even with the drop in teams, the Manitoba Bonspiel remains the largest curling bonspiel in the world.\n**A SPIKED TROPHY**\n\nIn 1902-03, the first visit by a group of Scottish curlers to Canada took place, with the Scots playing a lengthy string of games that took them from Halifax to Winnipeg, with stops at most major cities in between. Such a success was the tour that in 1909, a group of Canadian curlers went the other way.\n\nWith the event becoming a friendly rivalry of significance, it began to catch the attention of a great many curling enthusiasts, including Donald Smith, Lord Strathcona and Mount Royal. Smith spent his early years in Canada, working with the Hudson's Bay Company, eventually becoming the president of the firm. He also was a Member of Parliament and was a founding member of the Canadian Pacific Railway, becoming such an important figure in that operation that when the transcontinental railroad was being completed, Smith was selected to drive the last spike.\n\nSmith returned to Great Britain in his later years to take his spot in the House of Lords. He so loved both continents and the game of curling that he decided to present a trophy for regular competition between the two sides of touring curlers. Thus, in 1909, the Canadian team was the first to win the Strathcona Cup.\n\nToday the Scots travel to Canada in years that end in a three, while the Canadians go the other way in years that end in an eight. The trophy used to make the transatlantic trip with the defending champions, but now is considered so valuable that it resides permanently in Scotland.\n**NORTHERN AFFAIR**\n\nEvery team in the Brier represents a single province or territory, with the exception of Northern Ontario. The reason it has a spot in the field is history and respect. While the definitive answer to its inclusion is unknown (some say the size of the province and the overall population necessitated two entries), when the first Brier was held in 1927, it is believed a rink from Northern Ontario was invited by Brier organizers to make the field an even number. Although two other teams\u2014Montreal and Toronto\u2014were removed from the invitation list in 1931, Northern Ontario remains.\n\nWhen asked why Northern Ontario stayed in the field, David M. Stewart, head of the Macdonald Tobacco Company, said, \"When you invite someone into your living room, you don't invite them to leave just because the numbers aren't right.\"\n**STONES OF A DIFFERENT MATERIAL**\n\nIt's rare today to see a curling stone made of something other than granite, but in the early days of the sport, when rocks were difficult to come by, ardent players used almost anything they could get their hands on to play their favourite sport. Here are a few examples:\n\n\u2022 **Cannonballs:** this story has never been conclusively proven, but as the story goes, in the late 1700s, British soldiers melted down cannonballs and used them to curl on the Plains of Abraham.\n\n\u2022 **Jam cans:** in western Canada, schoolchildren who were too small to play with the 42-pound granite stones used jam can \"rocks\"\u2014cans that were filled with rocks or cement with a piece of wire or other material stuck into them for a handle.\n\n\u2022 **Thunder mugs:** in some spots on the Prairies, thunder mugs (yes, those bedpans from days gone by) were, like jam cans, filled with granite and used for playing pieces.\n\n\u2022 **Irons:** perhaps a derivative of the cannonballs, iron \"stones\" were, as the name suggests, made of iron and about a third the size of a traditional curling rock. Their weight made it next to impossible to play takeouts. Irons were used prominently in Quebec and eastern Ontario.\n\n\u2022 **Wooden stones:** plugs of wood\u2014sometimes off the end of telephone poles\u2014were used to provide lightweight stones for young people. They were also utilized in areas where curlers were unable to afford regular rocks.\n\n\u2022 **Little rocks** : Developed in the 1990s, smaller versions of regular rocks made of plastic appeared in curling rinks across Canada. These allowed children as young as five to start playing, and resulted in a huge boom of pint-sized players.\n\nThis pint-sized curler is lining up a shot with a Little Rock, a scaled-down version of traditional granite stones.\n\n**TIME TO CURL**\n\nMost sports have time clocks, which tick off the amount of time for the game to be contested. In curling, however, for the longest time (excuse the pun) there was no such thing. Games lasted as long as they lasted. Some contests at major championships stretched to four hours. In one memorable Ontario provincial championship in the 1980s, an evening draw had to be delayed because a game from the afternoon draw was nearing its fifth hour.\n\nIn 1983, curling entrepreneur Doug Maxwell came up with the idea of a time limit for curling, but to make it fair, he decided each team should be timed independently. To test out his theory, he purchased a chess time clock and sat behind the ice at competitive games in the Toronto area. Each team was timed for how long it took them to play.\n\nTime clocks were introduced to competitive play at the 1986 TSN Skins Game, and the result was dramatic\u2014teams played to their limits, not wasting any time, especially in the early parts of an end when strategy decisions were less involved.\n\nA few years later, organizers of the 1989 World Curling Championships in Milwaukee were dealing with a time problem. The International Curling Federation integrated the men's and women's championships into one event, meaning four draws a day. In order to make this work and avoid curling around the clock, they elected to implement Maxwell's time clocks, giving each team a specified amount of time to complete their game. The results were a success and most other jurisdictions soon followed, adding time clocks to their championships.\n\nToday, time clocks are a regular part of every major curling event.\n**ON THE TUBE**\n\nThe first televised coverage of the Brier was in 1962, when, thanks to a last-minute okay from network executives, the CBC drove its cameras and trucks to Kitchener, Ontario, to cover the playoff game between Saskatchewan's Ernie Richardson and Hec Gervais of Alberta.\n\nRegularly scheduled coverage of the final draw started in 1973, and it didn't have a great beginning. In the era before playoffs, Harvey Mazinke's team from Saskatchewan played so well that the final draw of the round robin\u2014the one the CBC came to cover\u2014was meaningless; Mazinke won the title the previous evening.\n**CURLING ROYALTY**\n\nTwo curlers of some note have gone from the ice to the viceregal's chair. Errik Willis was part of a curling team that competed for Canada at the 1932 Olympic Games in Lake Placid, New York, where curling was a demonstration sport. On January 15, 1960, he was appointed Lieutenant-Governor of Manitoba, holding the office for a term of five years.\n\nIn 1986 Sylvia Fedoruk became Saskatchewan's Lieutenant-Governor, a role she kept until 1989. On the ice, Fedoruk was also a member of the team skipped by Joyce Potter that captured the first Canadian women's championship in 1961.\n**THE LONG AND THE SHORT(ER) OF IT**\n\nAt the semi-annual meeting of the Ontario Curling Association in 1906, officials passed a regulation changing the length of competitive games from 22 ends to 18.\n**TIMELINE OF THE FREE-GUARD ZONE**\n\nThe free-guard zone is regarded by many as a rule that saved championship curling. The rule allows for plenty of offence and lots of rocks in play, meaning scoring. That makes the game appealing for fans both at venues and watching on television. Prior to its introduction, curling was a defence game with low scores. Here is a timeline of how the rule came to be:\n\n**1986:** Russ and Glenn Howard develop a method of practice that is essentially a one-on-one game that doesn't allow takeouts on rocks unless they are in the rings.\n\n**1991:** Organizers of the Moncton 100, a lucrative bonspiel held to celebrate the centennial of the New Brunswick city, utilize what is known as the Howard Rule\u2014the first four rocks of any end cannot be removed regardless of where they come to rest.\n\n**1992:** A modified version of the Howard Rule, dubbed the free-guard zone, is used at the Olympics. It states that any of the first four rocks of an end that come to rest in front of the tee line and outside of the rings may not be removed. The World Curling Federation adopts the same rule for play in all international championships including the world final. Every member country of the WCF adopts the rule for national play, with the exception of Canada. The Canadian Curling Association elects to remain with the traditional rules and study the free-guard zone for two years.\n\n**1993:** Ontario becomes the first jurisdiction in Canada to change its rules, adopting a modified version of the free-guard zone, limiting it to the first three rocks of any end for its provincial finals. Russ Howard wins the Ontario, Canadian, and world championships using three different rules: three-rock free-guard zone at the Ontario final; no free-guard zone at the Canadian; four-rock free-guard zone at the world championship.\n\n**1994:** The Canadian Curling Association adopts a trial of the three-rock free-guard zone rule beginning with its 1994 national championships. It continues with the rule for almost a decade.\n\n**2003:** The CCA finally falls into line with the rest of the curling world and changes to the four-rock free-guard zone beginning with the 2004 championships. The Canadian Mixed becomes the first event in that country to use the four-rock rule.\n**ELECTRONIC EYE**\n\nIn 1986, the Canadian Curling Association instituted curling's equivalent of line judges, placing officials on the hog line to call infractions at the men's and women's national championships. The umpires were situated at either side of the hog line, and if both confirmed that a player failed to clearly release the stone before the hog line, the rock was removed from play.\n\nThe decision was not popular with all curlers, and over the course of the next 17 years there were many charges of incorrect calls, some which cost teams championships.\n\nThat all came to an end in 2003 when something known as Eye on the Hog was put in place. This system was a series of sensors, one in the ice and one in the rock.\n\nIf a player failed to release the rock before it reached the hog line, a red light on the handle flashed. If the player released the rock before the hog line, a green light went on.\n\nThe technological advancement not only ended all arguments about human error, but removed the cost of having numerous extra officials at the event.\n**TAKEN FOR GRANITE**\n\nCurlers might not think in too much detail about the material in the rocks they throw up and down the ice, but the granite used in curling rocks is very important. Over the years, there have been many different types of granite tried in curling stones, including Canadian granite as well as some from India.\n\nBut the best continues to be from Scotland and Wales. For many years, the best granite came from the Scottish island of Ailsa Craig, but quarrying there is no longer allowed. Almost all of the granite used to produce today's curling rocks comes from Garn For Quarry in northwest Wales.\n\nAccording to the Canada Curling Stone Company, here is a list of the various types of granite used in curling rocks currently in play around the world:\n\n\u2022 **blue hone:** light grey in colour with random white specks. Often has half-moon shaped chips in the strike band.\n\n\u2022 **red\/brown trefor:** light to dark reddish brown marked by larger grains with white and black flecks.\n\n\u2022 **blue trefor:** bluish-grey in colour with white and black flecks. It's prone to premature pitting.\n\n\u2022 **grey trefor:** greyish brown in colour, also with white and black flecks throughout.\n\n\u2022 **keanie:** pinkish in colour with large white spots and black flecks throughout.\n\n\u2022 **common green Ailsa Craig:** greenish in colour with large black flecks that usually have white deposits around them.\n**GIVING UP**\n\nConceding a game at the Canadian championship is an accepted practice these days. When one team feels it no longer has a chance to win, it can elect to quit. But that wasn't always the case. Prior to the 1973 Brier, teams were required to complete all 12 ends, no matter the score.\n**A BLIND EYE**\n\nIt's not unusual for individuals to take up curling when they retire, and that's just what Ray Kotanen of Thunder Bay, Ontario, did in 1991 when he turned 65.\n\nKotanen joined the Ezyduzit Curling League for retired men and proved to be not only enthusiastic but also a quick learner. However, he did have one limitation\u2014he couldn't see the other end of the ice, his skip, or his skip's broom. Diabetes robbed him of vision in his right eye and left him with limited sight in his left. Kotanen relied on verbal instructions relayed to him by the sweepers and managed to become quite proficient. Still, he disliked being dependant on others.\n\nAll that changed when friend Ray Paju decided to help out. Paju developed a high-intensity strobe light that fastened onto the handle of Kotanen's skips' broom. The light blinked a strong signal from the skip's end of the ice and was visible for Kotanen sitting in the hack. He no longer needed the verbal instructions\u2014he could see just fine. Another example of ingenuity allowing a curler to play the game he loves.\n**RECORD-SETTING CURLING**\n\nCamille Villeneuve of Chicoutimi, Quebec, is a guy who has trouble playing on a regular team. For that matter, he has trouble finding a steady club. But that's something he planned. Since 2005, Villeneuve has ventured across Canada and the United States playing in as many different curling clubs with as many different teammates as possible. He travels by camper, setting up games ahead of time often playing two or three a night. To date, he's competed at more than 611 clubs and played with more than 1,800 different teammates. Both marks are recognized in the _Guinness Book of World Records_. All of his adventures came late in life for Villeneuve. At the age of 79 years old, he's still going, hoping to reach 700 clubs by his 80th birthday.\n\n**Curling Quote**\n\n\"I'm actually looking forward to playing in a country where five feet (tall) might actually be the average.\"\n\n\u2014The diminutive Kelly Scott on playing the world championship in Japan in 2007\n**AGE-OLD ROCKERS**\n\nCurling is known as a game for all ages, and certainly that's proven to be the case over the long history of the sport. Here are a few examples of \"elderly\" competitors, elderly being a relative term:\n\n\u2022 At age 50 Russ Howard became the oldest person to win a gold medal at the 2006 Olympic Games, capturing the medal for Canada.\n\n\u2022 At age 55, Bud Somerville played for the U.S. team at the 1992 Olympics.\n\n\u2022 At 94, Einer Egilssen plays three times a week in Woodstock, Ontario. He's played the game for 60 years.\n\n\u2022 At 99, Jack Grossart played twice a week in Weston, Ontario.\n\n\u2022 Jack Watkins, at 93, has a certificate from the Guinness Book of World Records, stating he is the oldest living curler. He plays twice a week in Sudbury, Ontario.\n\n\u2022 In Regina, Phil Ward competed regularly at the Tartan Curling Club at the age of 102.\n**DOUBLING UP**\n\nDoubles, in sporting terms, usually conjures up images of tennis, where teams of two players take on similar teams.\n\nBut doubles is also now a part of curling\u2014mixed doubles, to be more precise, with teams comprised of one man and one woman, just as in tennis. The format had its genesis in another event, the Continental Cup, where teams representing North America and Europe compete in various formats, one of which is mixed doubles.\n\nEach end of mixed doubles begins with a rock sitting behind the button guarded by a stone in front of the rings. Each team delivers five shots, and the teams can decide which team member throws first, allowing any order on any given end. The player that throws the first stone of the end also throws the last one, with the other player delivering the middle three rocks.\n\nHoping to get at least one more discipline added to the curling program at the Olympics, the World Curling Federation promoted mixed doubles as a stand-alone event. It even created a separate world championship, with the first one held in Vierumaki, Finland, in March 2008.\n**PIN MOGUL**\n\nCurling pins have a long association with the sport, with clubs, events and even people producing their own unique ones. Because there are thousands and thousands of different pins, collecting them has become a passionate pastime for many, much like collecting baseball cards would be for a fan of that game.\n\nGo to any big curling event and you're sure to see pin collectors, both those who do the job seriously and put out massive displays, and others who are just trying to pick up a few while at the bonspiel or championship.\n\nNo matter what the level of interest, all these folks can thank one Saskatchewan resident for most of their fun. Laurie Artiss has become one of the world's largest makers of pins, and it all started thanks to his love of curling.\n\nArtiss started his association with curling in 1962, covering the Brier for the _Brandon Sun_. He moved to Regina in the late 1960s to take a job as a sports writer with the _Regina Leader-Post_ , and in 1970 he started a curling supply business. Around that time, he grew frustrated by the lack of decent lapel pins available for events and clubs. So, taking matters into his own hands, he began The Pin People, a company that has grown into one of the largest pin-making companies in the world. Since that time, he has made the pins for thousands of curling clubs, championships\u2014including most national and international events\u2014and in 1988, the Olympics. There are not many curling pins today that don't come from Artiss's company. And it's expanded into pin-making for just about every type of event or occasion\u2014sporting or otherwise\u2014imaginable. Each year, it produces hundreds of thousands of pins. For many years, the company was the official pin-maker for the Olympic Games.\n\nIn addition to his pin-making business, Artiss served as chairman of the 1973 World Championship as well as the 1976 Brier. For his efforts, Artiss was inducted into the Canadian Curling Hall of Fame in 2006.\n**THE CURLING TERMINATOR**\n\nEisschiessen is a popular game in Austria and is still played to this day. It is very similar to curling except that it uses \"eisstocks,\" which resemble bowling pins stuck on a Frisbee instead of stones. In many places around the world, Eisschiessen is played on curling rinks.\n\nWhile it doesn't take a great deal of muscle to get the eisstocks down the ice, one of Austria's past national champions of the sport is Arnold Schwarzenegger's father.\n**THE RICHARDSONS**\n\nJust as Gordie Howe is to hockey and Babe Ruth is to baseball, the Richardsons are to curling. A Saskatchewan family of two brothers\u2014Ernie and Garnet (known as Sam)\u2014and two cousins, Arnold and Wes, they were the first team to win four Brier titles. They accomplished this remarkable feat in just five appearances. A few notes about the famed family:\n\n\u2022 The four are the sons of three brothers and, just to confuse matters, two of them married sisters. Sam and Ernie are brothers, while Arnold and Wes are cousins.\n\n\u2022 Sam and Ernie attended the 1955 Brier in Regina and decided then and there that they wanted to play in that event. \"I don't think you'll make it. I think you should have started earlier if you wanted to get into that,\" their mother told the two boys in their early 20s.\n\n\u2022 The Richardsons are the only curling team to appear on the cover of _Maclean's_ magazine.\n\n\u2022 By 1960, the Richardsons were so popular, Ernie gave his name to a line of curling accessories\u2014sweaters, brooms, boots... even socks. The team ended up making about $100,000 from the sale of these items.\n\n\u2022 The team lost just seven games in five Brier appearances.\n\n\u2022 A lobster supper may have prevented the team from winning a fifth Brier. In 1964 in Charlottetown, the night before the final draw, the team attended a lobster dinner at the home of a friend, and the seafood didn't sit well in the stomachs of the Prairie boys. None slept well that night and they came out flat, losing their last game and any chance of a fifth title.\n\n\u2022 Although there were rumours of dissension on the team,Wes Richardson didn't play with the team when it won its record fourth Brier in 1963 because of a bad back. His replacement that year was Mel Perry.\n\n\u2022 After winning the Canadian title in 1959 and '60, the Richardsons lost out in 1962, never making it past the Regina city playdowns.\n\n\u2022 In 1960, before there were playoffs, the Richardsons secured the title with one draw left to play, a draw in which they had a bye. When the award ceremonies started, the four players walked down the ice holding hands in what fans thought was a show of team solidarity. In truth, they celebrated heartily during their bye and were trying to keep each other from falling down.\n\n\u2022 The team won the first World Curling Championship by defeating a team of Scots in the Scotch Cup. They followed up with three more world championship wins.\n\n\u2022 In 1960, the City of Regina planned a massive civic reception for the team but was unsure when they were to arrive home from Scotland and a second Scotch Cup victory. When they finally received word of the date, it was too early, and so despite having been away for three weeks, the Richardsons were told to spend three extra days in Toronto while the reception was organized.\n\n\u2022 The Richardsons were just the second team from Saskatchewan to win the Brier, after Garnet Campbell in 1955.\n\n\u2022 Despite several tries, the team was never able to make it back to the Brier, and they disbanded in 1968.\n**A WOMAN'S PLACE**\n\nShannon Kleibrink may be best known as the skip of Canada's team at the 2006 Olympics, but she holds another distinction of note: she is the only woman to skip a team to the Canadian Mixed championship.\n**MULTI-TALENTED**\n\nPierre Charette of Quebec is the only player to compete in a Brier at all four positions. In 1989 and '93, he skipped Quebec's entry. In 1996 he played lead; a year later, second; and a year after that he was third.\n**THE SHOT**\n\nIt's been called the greatest shot in the history of the Brier. It is certainly one of the most dramatic\u2014it's a tenth-end, last-rock double takeout made by Northerna Ontario's Al Hackner at the 1985 Brier to score two points and tie up the game against Pat Ryan of Alberta. Hackner went on to win in one of the most stunning comebacks in the event's history. Some background on what has come to be known as The Shot:\n\n\u2022 Ryan finished the round robin at 11-0, while Hackner was 7-4.\n\n\u2022 Ryan's team hadn't had an end stolen on them all week and gave up just one two-ender.\n\n\u2022 When Ryan played his last shot, he thought he'd made it impossible for Hackner to score two, and therefore won the Brier. He came down the ice with his broom over his head in a premature celebration. Others thought he'd won too as photographers jumped all over the ice even though Hackner's last rock was still to come. It took almost 10 minutes to restore order to allow Hackner to play his shot.\n\n\u2022 Neither Hackner nor his third, Rick Lang, saw Ryan's mini-celebration as they were busy lining up the final shot.\n\n\u2022 When Ryan got down to the other end, he saw he'd left Hackner a shot. \"From my perspective [at the other end], it looked as thought I had made the shot,\" Ryan said later. \"But actually I hadn't\u2014I'd lined it up.\"\n\n\u2022 Hackner's team had played three shots down the same path as his final rock that end, so he knew the ice.\n\n\u2022 After he made the shot, the fans in the arena went crazy. But Hackner slid stone-faced down the ice, and as he passed Ryan said one word: \"Sorry.\"\n\n\u2022 When Hackner arrived beside Lang at the other end, Lang congratulated his skip, but also pointed out another problem: \"Nice shot, skipper,\" he said. \"Now how the hell are we going to steal one.\" The shot only tied the game, sending it to an extra end.\n\n\u2022 In the extra end,Alberta second GordTrenchie missed both shots, and when Ryan came to throw his last rock, he needed to draw to a piece of the four-foot. His rock came into the rings, and Hackner swept it back enough that it gave them a single point\u2014and the Brier crown to Northern Ontario.\n\n\u2022 Lang normally swept the opposition rocks when they came into the house, but for some reason, on this occasion, as Ryan's stone neared the tee line, he didn't move, and Hackner jumped in at the last second to sweep it back.\n\n\u2022 Hackner believes that if Ryan played more aggressively early in that final game, he would have won the game easily.\n\n\u2022 Although happy at winning, Lang felt remorseful at defeating Ryan, who was the best team that week. \"There was almost a feeling of guilt,\" Lang admitted. \"We know how Ryan's team felt because it happened to us [in 1981]. It really took something away from winning.\"\n**WORLD CHAIR**\n\nIn 2002, the World Curling Federation sanctioned the first World Wheelchair Curling Championship. Although there were not a lot of competitors at first, the discipline has grown over the years, and made its first appearance at the Paralympics in 2006.\n\n**World Wheelchair Curling Champions**  \n---  \n2002| Switzerland  \n2003| No competition  \n2004| Scotland  \n2005| Scotland  \n2006| no event due to Paralympics (Canada)  \n2007| Norway  \n2008| Norway\n\n **Curling Fact**\n\nThe oldest sporting club in North America is the Royal Montreal Curling Club, founded in 1807.\n**STATS**\n\nThe best teams don't always win the championship. At least not when it comes to statistics. The Canadian Curling Association has kept individual and team shooting percentages at its national championships since 1982, and often times, the team with the best average isn't the champion.\n\nHere's a look at the all-time top team shooting percentages and the teams' final positions:\n\n **Women**\n\n**%** | **Team** | **Year** | **Finish**  \n---|---|---|---  \n85| Canada (Jones)| 2002| First  \n83| Saskatchewan (Betker)| 2007| Second  \n83| Saskatchewan (Lawton)| 2005| Fourth  \n83| Ontario (Hanna)| 2005| Second  \n83| Alberta (King)| 2002| Tied fifth  \n83| Ontario (Middaugh)| 2002| Third  \n83| Saskatchewan (Schmirler)| 1997| First  \n83| Canada (Peterson)| 1995| Third  \n83| Canada (Peterson)| 1994| First\n\n **Men**\n\n**%** | **Team** | **Year** | **Finish**  \n---|---|---|---  \n89| Ontario (Middaugh)| 2001| Third  \n88| Alberta (Ferbey)| 2004| Second  \n88| Ontario (Werenich)| 1990| First  \n87| Alberta (Martin)| 2007| Fourth  \n87| Alberta (Ferbey)| 2003| First  \n87| N.B. (Howard)| 2003| Fourth  \n87| Manitoba (Stoughton)| 2000| Second  \n87| Ontario (Howard)| 1993| First  \n86| Ontario (Howard)| 2006| Second  \n86| Alberta (Ferbey)| 2005| First  \n86| New Brunswick (Howard)| 2004| Fifth  \n86| Ontario (Corner)| 2000| Fifth  \n86| Quebec (Roberge)| 2000| Third  \n86| Ontario (Middaugh)| 1998| First\n**LONG-DISTANCE CURLING**\n\nSome teams will do anything for a shot at the Brier, but Bob Chilton and his rink, from the End of the Rail Curling Club, might take top prize if there was one for perseverance. The team played out of a club in Moose Factory, Ontario, a native reserve on an island across from Moosonee on the southern tip of James Bay. To reach their club to practise, the team travelled three miles across the Moose River by snowmobile\u2014which meant they had to wait until mid-December for the freeze-up.\n\nIn 1987-88, to reach their zone playdowns, the rink had to fly to Timmins (about 250 miles as the crow flies), but because of a snowstorm, the plane almost didn't take off. Timmins was only the first stop. After arriving there, the team had to drive three and a half hours through the blizzard to Kapuskasing, arriving just minutes before their first game. They won their zone that year, advanced through the association level, and made it as far as the provincial championship before losing.\n**RYAN'S EXPRESS**\n\nOne of the most dominant curlers of his era, Pat Ryan had a lengthy and distinguished career on the ice. A three-time Canadian champion, he continues to compete to this day. Some notes about Ryan:\n\n\u2022 He is one of just two curlers to play in Briers in four different decades ('70s, '80s, '90s, and '00s). The other is Peter Hollett of Newfoundland and Labrador.\n\n\u2022 In 1985, thinking he had won the Brier after his last shot, Ryan came down the ice with his broom in the air in celebration. However, Northern Ontario's Al Hackner played what is often regarded as the most dramatic last shot in Brier history to tie the game and then beat Ryan in an extra end.\n\n\u2022 He won back-to-back Briers in 1988 and '89 on the strength of an extremely defensive style of play, playing a vast majority of takeouts and winning low-scoring games.\n\n\u2022 He moved to British Columbia in 1991 and, in 1993, won another Brier playing third for Rick Folk. He became just the second player to win a Brier as skip and then at another position.\n\n\u2022 He created and marketed a series of curler trading cards that sold extremely well.\n\n\u2022 He has two other national titles to his credit. He won the 2007 Canadian senior and the 1986 Canadian Mixed.\n\n\u2022 Ryan's daughter, Lynsay, appeared nude in a calendar to raise awareness and funds for women's curling.\n**WHAT A CROWD**\n\nBrier attendance figures have steadily increased over the years. Here is a look at some notable milestones when it comes to the turnstiles:\n\nFirst Brier to reach 50,000 Regina, 1955 (51,725)  \nFirst Brier to reach 100,000 Brandon, 1982 (106,394)  \nFirst Brier to reach 150,000 Saskatoon, 1989 (151,538)  \nFirst Brier to reach 200,000 Calgary, 1997 (223,322)  \nFirst Brier to reach 225,000 Edmonton, 1999 (242,887)  \nFirst Brier to reach 275,000 Edmonton, 2005 (281,985)\n\nBrier opening ceremonies\n\n**VERA NICE**\n\nSaskatchewan curler Vera Pezer is one of the first stars of women's curling, with four Canadian championships in five years. Pezer has many other accomplishments in curling and her business life that make her one of the most remarkable people to play the roaring game. A few notes on the career of Vera Pezer:\n\n\u2022 She learned the game in her hometown of Meskanaw, Saskatchewan, on a two-sheet natural ice club her father maintained.\n\n\u2022 She won her first Canadian title in 1969, playing third for Joyce McKee. For the next three titles, she played skip while McKee moved to second.\n\n\u2022 After winning three consecutive titles, the team disbanded.\n\n\u2022 She holds a Ph.D. in sports psychology and served as sports psychologist for two Canadian Olympic teams.\n\n\u2022 She did some work with another Saskatchewan legend, Sandra Schmirler.\n\n\u2022 She is currently the chancellor of the University of Saskatchewan.\n\n\u2022 She wrote two books on curling: _Smart Curling: PerfectYour Game Through Mental Training_ and _The Stone Age: A Social History of Curling in the Prairies_.\n\n\u2022 She won two national fastball titles in 1969 and '70 as part of the Saskatoon Imperials, and played in two Canadian Senior Women's Golf Championships.\n**MONCTON 100**\n\nThe richest bonspiel in curling history took place in 1990 in Moncton, New Brunswick. The event was created to help celebrate the city's centennial and it pitted 16 top teams playing for $250,000. It is still the most lucrative bonspiel ever held and also one of the most significant in that it was the first to utilize rules that are now standard. Some notes about this legendary bonspiel:\n\n\u2022 The field included two women's teams, skipped by Heather Houston and Linda Moore, four European teams, and two from Atlantic Canada. The rest were hand-picked by the organizers from across the country.\n\n\u2022 This was the first major event to use a variation of the free-guard zone. The rule stated that leads could not play takeouts on rocks anywhere between the hog line and the tee line. It was a huge hit with the curlers.\n\n\u2022 The event was the first to include a separate singles' skills competition for an extra purse. The players in the main event also participated in the challenge, being scored on their ability to play a number of difficult shots. A similar challenge was later added to both the men's and women's Canadian championships.\n\n\u2022 It was the first event to use a draw to the button to determine last rock. All four players threw one stone, and the team with the lesser cumulative distance had last rock in the first end.\n\n\u2022 The teams were charged an entry fee of $1,000 but received free airfare to Moncton, complimentary hotel rooms and, if they lost all their games, $1,500 in prize money.\n\n\u2022 With the new free-guard zone rule in place, most games were high-scoring, close affairs... except for the final. Ed Lukowich defeated Russ Howard 13-2 to win the Moncton 100. Lukowich earned $100,000 for the victory.\n**CRAZY FOR CURLING**\n\nPeople called Ken Murphy crazy, and he didn't mind one bit. An enthusiastic curler from Wallaceburg, Ontario, Murphy was known as Crazy Legs for the manner in which he danced\u2014and for what he did on the curling ice. At his annual curling bonspiel at the Sydenham Curling Club, he would slide down a sheet of curling ice perched atop a stone, often waving flags or playing a trombone. At the extreme level, Murphy placed the legs of a ladder on four stones and then scrambled to the top rung, where he sat as the rocks travelled over the ice. He became so famous for his act that he appeared on television and at big curling events. He also ran a famous bonspiel that, at its peak in the late 1980s, had a five-year waiting list.\n**SPIEL OF A DIFFERENT KIND**\n\nEvery weekend during the curling season, there are bonspiels of all shapes and sizes held all over the world. Most fall into a couple of broad categories: men's, women's, or mixed; competitive or social; one-day or longer. However, a few almost defy description. Here is a sampling of some rather unusual bonspiels held over the years:\n\n**Heavyweight Spiel:** organized by legendary promoter Doug Maxwell on behalf of a Toronto delicatessen chain, the total weight of the team members could be no less than 1,000 pounds, and individually, no competitor could weigh less than 225.\n\n**Left-Handers Spiel:** Every spring at the Oakville Curling Club outside of Toronto, the World Lefthanders Championship is held where southpaws battle it out to become global port-sider champion.\n\n**Grits vs. Tories:** Back in the 1850s, this annual affair pitted the two sides of the government of the day with the losers required to buy a meal of oysters for the winners.\n\n**Summer Spud:** Capitalizing on being one of Canada's great summertime playgrounds, folks at the Crapaud Curling Club in Prince Edward Island hold an annual spiel... in August! It includes a lobster feast and 18 holes of golf.\n\n**Watson Lake Outdoor Bonspiel:** Curling outside in the middle of February in the Yukon Territory might not seem that appealing, but obviously some folks like it. Played on the lake from which the bonspiel takes its name, this is the longest-running outdoor bonspiel in Canada.\n**THE LONG BRIER ROAD**\n\nIn Canada, approximately 7,000 curlers enter the playdowns every year that lead to the Brier, the Canadian championship. Of course, at the end of it, only four stand atop the highest step on the podium.\n**ROCK-SOLID POLITICS**\n\nPaul Delorey proved that politics and curling do mix. Delorey represented the Yukon\/Northwest Territories at the 1987 Canadian Mixed. He is also the Speaker of the Northwest Territories Legislature.\n**ROCKIN' RICK**\n\nThunder Bay, Ontario, has produced many great curling champions, but the best may be Rick Lang, the three-time Canadian men's champion who some believe is the best third to have played the game.\n\nSome interesting facts about Lang:\n\n\u2022 Ed Werenich calls him the best curler ever to play the game.\n\n\u2022 Lang won his first Brier in 1975 playing for Bill Tetley. In 1985, he won his third with Bill's son, Ian, playing second.\n\n\u2022 Lang joined forces with skip Al Hackner in 1980 and lost the Canadian final. The very next year, Kerry Burtnyk scored three in the 10th end of the final to beat them 5-4.They finally won the title in 1982 and again in 1985.\n\n\u2022 At many events, Lang would bet anyone willing to put up $20 that he could throw a rock down a sheet and drink a beer before the rock arrived at the other end. With the money on the table, Lang would throw a slow draw with a mighty spin cranked on the handle so the stone turned like a 78 rpm record, thereby taking a long time to reach its destination. Lang could also drink a beer quickly.\n\n\u2022 On the way home from winning the 1985 World Curling Championships in Germany, a flight attendant, noticing there was a lot of attention being paid to Lang, said to him, \"Are you who we think you are?\" Lang, thinking they knew him as the curler, replied, \"Yes I am.\" The flight attendant squealed, \"Mr. Jagger, may I have your autograph.\" Lang bears a striking resemblance to Rolling Stones' lead man Mick Jagger.\n\n\u2022 Lang holds the dubious distinction of being the only Canadian curler to lose games at the world championship to both France and Italy.\n\n\u2022 Lang's wife, Lorraine, won two Canadian women's championships. Together, they won the Canadian Mixed.\n\n\u2022 In 2006, Lang and Hackner joined forces again to win the Canadian Senior Championship.\n\n**Curling Quote**\n\n\"Curling is not a sport. I called my grandmother and told her she could win a gold medal because they have dusting in the Olympics now.\"\n\n\u2014Former NBA star and now outspoken television commentator Charles Barkley\n**CUT SHORT**\n\nCurling is an extremely popular sport on television, so much so that networks and curling associations should know better than to mess with those watching. Two examples prove that out:\n\n\u2022 In 1987, the CBC showed the semi-final of the Brier between Mark Noseworthy of Newfoundland and British Columbia's Bernie Sparkes. The game went longer than expected, and the network elected to cut away from the curling in favour of the evening news. With five rocks left to play, the coverage left the curling to show the warm-up of a game between the Montreal Canadiens and the Philadelphia Flyers.The CBC switchboard was flooded with phone calls from irate curlers, and a new policy was put in place to allow any curling game to finish, regardless of the time.\n\n\u2022 In 2005, the Canadian Curling Association signed a new broadcast agreement with CBC that moved round-robin games away from fan favourite TSN to a subscription channel owned by the CBC called Country Canada. When the first game of the Canadian Women's Championship aired and curling fans were unable to find it on TSN, the Canadian Curling Association's head office received such an onslaught of phone calls, it shut down its phone line. A year later, under much pressure, the round-robin games returned to TSN.\n**THE ICEMAN CURLETH**\n\nAl Hackner was known in curling circles as \"The Iceman\" for the cool, emotionless demeanour he exhibited on the ice, even in tense situations. The curler from Thunder Bay, Ontario, won two Canadian and world championships and a great many cashspiels over his career. He is also credited with throwing the most dramatic shot in Brier history\u2014a nearly impossible 10th-end double takeout that led to his second Canadian championship. And he never let a party stand in the way of a good bonspiel. Here are some notes about Al Hackner:\n\n\u2022 He named his dog Tankard, after the trophy awarded to the Canadian champions.\n\n\u2022 He played second in the 1976 Canadian mixed championship for Alberta, while living in Edmonton.\n\n\u2022 He realized near the end of his career that he may have enjoyed himself a little too much during his heyday. \"I'll be the first to admit I probably wasn't disciplined enough,\" he said in _Curling: The History, The Players, The Game_ by Warren Hansen. \"When I played seriously, we'd always have beer and the stereo going.\"\n\n\u2022 After winning his first world championship, Hackner was voted the second most recognizable person in his home town of Thunder Bay. The mayor was first.\n\n\u2022 At the 1980 Brier, Hackner and his team decided they wanted to see if Paul Gowsell, who represented Alberta and was the game's leading money winner, was as wild a party animal as the stories made him out to be. For the first few days, Hackner and his front end of Bruce Kennedy and Bob Nicol went to Gowsell's room every night to drink beer. On the fourth night, they arrived to find the door locked, and claimed victory in the party wars.\n\n\u2022 Hackner started curling on natural ice in Nipigon, Ontario.\n\n\u2022 He worked for more than 30 years for CN, serving as a switcher, trainman, and conductor.\n\n**MARILYN BODOGH**\n\nOne of the most colourful figures in women's curling is Marilyn Bodogh, a two-time World Curling champion from St. Catharines, Ontario. Bodogh won titles in 1986 and '96, and was an active player on the competitive circuit for close to 20 years. A few notes about this lively lady:\n\n\u2022 She made her first appearance at the Canadian championship playing third for her sister, Christine Bodogh. When she won her first world championship, Christine (Jurgenson) played second.\n\n\u2022 She spent several years as a commentator on broadcasts of World Curling Tour events on Rogers Sportsnet.\n\n\u2022 In 2006, she ran for the position of mayor of St. Catharines, finishing third out of eight candidates.\n\n\u2022 Through marriage (when she was known as Marilyn Darte), she helped operate a family-owned funeral home, leading the _Globe and Mail_ to start a story on her with the following line: \"The only things certain in Marilyn Darte's life are death and curling.\"\n\n\u2022 In 1987, as defending champion, Bodogh was in Lethbridge, Alberta, to promote that year's national championship. She attended a press conference at a Lethbridge curling club, and when a photographer suggested going onto the ice to take some pictures, Bodogh walked out, interrupted a game being played by some seniors, put a rock on the button, and then, despite wearing a skirt, did a cartwheel behind the rock. The photographer got his shot.\n\n\u2022 Bodogh almost always wore a kilt when playing. As well, she wore green bloomers underneath.\n\n\u2022 In 2008, she played in the Ontario senior championships for the first time, finishing second.\n\n\u2022 Bodogh works as a motivational speaker.\n\n**HOG WILD**\n\nPrior to the introduction of the electronic hog line sensor, officials called violations on curlers who slid over the line without releasing the stone. The curlers who were called for the violations almost always disagreed,who and some did so vehemently. And the more significant the event, the more they disagreed. Here are two of the most controversial hog line decisions:\n\n\u2022 At the 2001 World Curling Championships in Lausanne, Switzerland, Canadian skip Randy Ferbey was playing the semi-final against Switzerland's Andreas Schwaller. Ferbey was called three times for hog line violations, with the penalty being the removal of his rock. The official was Swiss, and for some unusual reason, that week, most of the violations came against the opponents of the Swiss team. Canada lost the game 6-5 to Switzerland, and Ferbey made his mark by chewing out the official after the third pull. Television replays show Ferbey clearly releasing the stone before the hog line. \"It's unfortunate that something like that got to dictate the way of the game going,\" Ferbey said. \"All week long I had one hog line call and all of a sudden I have three. I definitely question how they came to determine how I was over the hog line.\"\n\n\u2022 In the semi-final of the 1987 Ontario championships, Paul Savage played Russ Howard. In the eighth end of a close game, Savage played a takeout for two points, but before the stones were kicked off, an official came out and called Savage for a hog line violation. Instead of Savage scoring two, Howard took one and went on to win the game. Savage was livid for a number of reasons. First, sliding over the hog line on a takeout was nearly impossible, and Savage didn't slide very long at the best of times. Second, instead of the necessary two hog line officials\u2014one on either side of the sheet\u2014there was only one. Third, in his many years of curling, Savage had never been called for a hog line violation. Even Howard said after the game he was surprised the rock was pulled.\n\n**Curling Fact**\n\nAt the first Brier, there was only one team from Western Canada, Ossie Barkwell's rink from Yellowgras , Saskatchewan . The foursome earned the invitation by winning the Manitoba bonspiel that year, and a week after that victory they left for Toronto, taking their own rocks along with them.\n**SINGULARLY REWARDING**\n\nAlthough curling is a team game, each year, many of the major championships hand out individual awards for various achievements. Here is a look at the awards and the criteria for winning:\n\n**PHOTO CREDITS**\n\nPage 6: _Ontario Curling Report_\n\nPage 17: Denis Drever \/ _Ontario Curling Report_\n\nPage 27: Powell Photo \/ Estate of Doug Maxwell\n\nPage 31: H.C. Fortier Limited \/ Estate of Doug Maxwell\n\nPage 32: Courtesy Marco Ferraro\n\nPage 40: _Ontario Curling Report_\n\nPage 41: _Ontario Curling Report_\n\nPage 45: Estate of Doug Maxwell\n\nPage 52: Courtesy John Kawaja\n\nPage 56: Estate of Doug Maxwell\n\nPage 62: Michael Burns Photography Ltd. \/ _Ontario Curling Report_\n\nPage 70: Office du Tourisme Meg\u00e8ve \/ Estate of Doug Maxwell\n\nPage 79: L.H. Shaw, _The Leader-Post_ \/ Estate of Doug Maxwell\n\nPage 87: _Ontario Curling Report_\n\nPage 97: Estate of Doug Maxwell\n\nPage 106: Chiang \/ _Ontario Curling Report_\n\nPage 112: Courtesy Hans Frauenlob\n\nPage 118: Estate of Doug Maxwell\n\nPage 120: Turofsky, Alexandra Studio \/ Estate of Doug Maxwell\n\nPage 124: Estate of Doug Maxwell\n\nPage 140: Courtesy TSN\n\nPage 153: _Ontario Curling Report_\n\nPage 162: _Ontario Curling Report_\n\nPage 169: _Kitchener-Waterloo Record_ \/ Estate of Doug Maxwell\n\nPage 178: _Ontario Curling Report_\n\nPage 188: Courtesy TSN\n\nPage 190: _Ontario Curling Report_\n**INDEX**\n\n##\n\nAcorn, Frank\n\nAdam, Dr. Graeme\n\nadvertising\n\nAilsa Craig (Scotland)\n\nAilsa Craig granite\n\nAir Canada\n\nair travel\n\nAladdin Hotel & Casino (Las Vegas)\n\nAlberta\n\nAlbertville (France)\n\nAlliance Atlantis\n\nAll-Star Game (baseball)\n\nAlodi, James\n\nAmerican League (baseball)\n\nAnn Brown Award\n\nArborg (MB)\n\narenas\n\nartificial ice\n\nArtiss, Laurie\n\nAsham, Arnold\n\nAsham Curling Supplies\n\nAsham Stompers\n\nAssand, Frank\n\nAstley, D.G.\n\nAtlantic Oilworks Championship\n\nattendance\n\nAustria\n\nawards\n\n##\n\nback line, width of\n\nback problems\n\nbad ice\n\nbagpipes\n\nBaird, Scott\n\nBalancePlus Slider\n\nBaldwin Blackout\n\nBaldwin, Matt\n\nBarcome, Don\n\nBarkley, Charles\n\nBarkwell, Ossie\n\nBarry, David\n\nBartlett, Don\n\nbaseball\n\nbasketball\n\nbattle of the sexes\n\nBeatles, The\n\nbedpans (playing piece)\n\nBekkeluns, Hans\n\nBelcourt, Tim\n\nBemidji Curling Club\n\nBeveridge, Corie\n\nBible\n\nblue hone granite\n\nblue trefor granite\n\nBobcaygeon Curling Club\n\nBodogh [Jurgenon], Christine\n\nBodogh, Marilyn ( _See also_ Darte, Marilyn)\n\nBoston Arena\n\nboxing\n\nBradbeen, Dick\n\n_Brandon Sun_\n\nBraunstein, Terry\n\nBrier: ; (1927) ; (1929) ; (1930) ; (1931); (1932); (1934); (1936); (1938) ; (1940); (1949) (1946); (1947), ; (1949); (1951) ; (1952); (1954) ; (1955), ; (1956), ; (1957); (1959); (1960), ; (1962), ; (1963); (1964) ; (1965); (1966) ; (1967); (1969) ; (1970); (1970) ; (1971); (1972; (1973) ; (1974); (1975) ; (1976); (1978); (1979); (1980); (1981); (1982); (1983) ; (1984); (1985); (1986); (1987); (1988); (1989) ; (1990); (1990); (1991); (1993); (1996); (1997); (1999); (2000) ; (2001); (2003); (2004); (2005); (2007) 21( _See also_ Labatt Tankard; Macdonald Brier Tankard; Tim Hortons Brier)\n\nBrier Special (train)\n\nBrier Tankard. _See_ Macdonald Brier Tankard\n\nBritish Columbia\n\nbrooms\n\nBrown, Erica\n\nBuffalo Bills\n\n_Burned by The Rock_ (Sonmor)\n\nburned stone\n\nBurns, Robert\n\nBurtnyk, Kerry\n\nButler, Mark\n\n##\n\nCalcutta (betting)\n\nCalgary Winter Club\n\nCalifornia\n\nCampbell, Don\n\nCampbell, Garnett\n\nCampbell, Gordon\n\nCampbell, Lloyd\n\nCampbell, Robert\n\nCampbell, Sam\n\nCanada Curling Stone Company\n\n_Canada Curls_ (Maxwell)\n\nCanada Winter Games\n\nCanadian Association of Chiefs of Police\n\nCanadian Blind Curler Championship\n\nCanadian Clergy Championship\n\nCanadian Curling Association\n\nCanadian Curling Championship: (1984); (1991)\n\nCanadian Curling Hall of Fame\n\nCanadian Firefighters Curling Association\n\nCanadian Junior Championship\n\nCanadian Ladies Curling Association\n\nCanadian Men's Championship\n\nCanadian Mixed\n\nCanadian Pacific Railway\n\nCanadian Police Curling Championship\n\nCanadian Postal Curling Championship\n\nCanadian Postal Employees Curling Championship\n\nCanadian Seniors Championship\n\nCanadian Senior Women's Golf Championship\n\nCanadian Women's Championship\n\ncannonballs (stones)\n\nCarstairs, Kent\n\nCasino Rama\n\nCBC\n\nCBC Curling Classic\n\nCBC radio\n\n_Celebrity Chefs_ (TV show)\n\nCentral Park (NYC)\n\ncentre skittle\n\nChamonix (France)\n\nchampionships ( _See also_ individual championships)\n\nCharette, Pierre\n\nChevrier, Don\n\nChicago Black Hawks\n\nChicago Bulls\n\nChicago Stadium\n\nChilds, Alf\n\nChilton, Bob\n\n_Chronicle Journal_ (Thunder Bay)\n\nCialis (drug)\n\nclergy, curlers\n\nclosing banquet (Brier)\n\nclosing ceremony (Brier)\n\nclothing\n\nCole, Bob\n\ncollectors\/collections\n\ncollegiate curling\n\nColin Campbell Award\n\ncomebacks\n\ncommercials\n\ncommon green Ailsa Craig (granite)\n\nCondie, Art\n\nCongalton, Johnny\n\nContinental Cup\n\nconvicts\n\nCopps Coliseum (Hamilton)\n\ncorn brooms\n\n_Corner Gas_ (TV show)\n\nCorner, Peter\n\nC\u00f4te d'Ivoire (Africa)\n\nCountry Canada (TV channel)\n\nCowan, Bob\n\ncrampits\n\nCrapaud Curling Club\n\ncrests\n\nCrossmyloof (Scotland)\n\nCSKA Moscow\n\ncurling\n\nconceding game\n\ndebut at Olympics\n\nduration of game\n\nlongest game\n\nmedia coverage of\n\norigin of name\n\nand politics\n\nrecord-setting\n\nroaring game\n\nrules of. _See_ Rules of the Game\n\nscience of\n\nsuccess, elements of\n\n_Curling Companion, The_ (Murray)\n\ncurling couples\n\n_Curling for Dummies_\n\n_Curling News, The_\n\ncurling pins\n\ncurling siblings\n\n_Curling: The History, The Players, The Game_ (Hansen)\n\ncurling shoes\n\nCurtis, Darwin\n\n##\n\nDacey, Mark\n\nDagg, Lyle\n\nDarte, Marilyn( _See also_ Bodogh, Marilyn)\n\nDave's Pizza\n\nDavis, Alan\n\nDavis, Chris\n\nDavis, Gord\n\nDavis, Jamie\n\ndeaf players\n\ndeionizers\n\nDelorey, Paul\n\nDesert Spiel\n\nDetroit Curling Club\n\nDetroit Lions\n\nDi Lorio, Lino\n\nDoily, the\n\nDominion Curling Association( _See also_ Canadian Curling Association)\n\nDominion Grocery\n\ndoubles. _See_ mixed doubles\n\nDuddington Curling Society\n\nDufferin, Earl of\n\nDuguid, Don\n\nDurant, Fred\n\nduster\n\n##\n\nEdmonton\n\nEgilssen, Einer\n\neight-ender\n\nEisschiessen (game)\n\n\"eisstocks,\"\n\nelectronic hog line sensor\n\nElliot, Sir William\n\nElmer Freytag Award\n\nEmpress Hotel (Victoria)\n\nEnd of the Rail Curling Club\n\nequipment\n\nantiquated\n\nsuppliers\n\nEverett, Ken\n\nEye on the Hog\n\nEzyduzit Curling League\n\n##\n\nfans, famous\n\nfantasy curling camp\n\nFeatherstone CurlMaster\n\nFeatherstone, Preston\n\nFedoruk, Sylvia\n\nFenson, Bob\n\nFenson, Pete\n\nFenwick Twist\n\n_Ferbey Four, The_ (Jones)\n\nFerby, Randy\n\nFerraro, Marco\n\nfights\n\nFinland\n\nFlorida\n\nFolk, Rick\n\nfootball\n\nFord (sponsor)\n\nfour rock free-guard zone\n\nFowler, Alan\n\nFrance\n\nFrances Brodie Award\n\nFrauenlob, Hans\n\nfree-guard zone\n\nFriar's Brier\n\nFry, Barry\n\n##\n\nGallant, Peter\n\nGarmish-Partenkirchen (Germany)\n\nGarn For Quarry (Wales)\n\nGarza, Josele\n\nGellard, Kim\n\nGemmell, Maymar\n\ngender battles. _See_ battle of the sexes\n\nGermany\n\nGerster, Stan\n\nGervais, Hec\n\n_Globe and Mail_\n\ngolf\n\nGovernor-General's Club\n\nGovernor-General's trophy\n\nGowanlock, Ab\n\nGowsell, Paul\n\nGraham, Sandy\n\nGrand Banks (NF)\n\nGrand Caledonian Curling Club\n\nGrand Match (1848)\n\n\"Grand Match at Linlithgow Loch\" (painting)\n\nGrand National Curling Club\n\nGrand Slam of Curling\n\nGranite Club (Toronto)\n\nGranite Curling Club\n\ngranite, types of\n\nGray, Glenn\n\nGreat Britain\n\nGretzky, Wayne\n\ngrey trefor (granite)\n\nGrits vs. Tories spiel\n\nGross, Paul\n\nGrossart, Jack\n\nGrossart Super Brush\n\n_Guinness Book of World Records_\n\nGushue, Brad\n\n##\n\nHackner, Al (\"The Iceman\")\n\nhacks\n\nHaig, Senator Jack\n\nHalifax\n\nhalls of fame. _See_ Canadian Curling Hall of Fame; U.S. Curling Hall of Fame\n\nHaluptzok, Mark\n\nHamilton (ON)\n\n_Hamilton Spectator_\n\nHamilton-Temple-Blackwood, Frederick. _See_ Dufferin, Earl of\n\nHamilton Thistle Curling Club\n\nHanna, Jean\n\nHansen, Warren\n\nharmonica\n\nHardie, Dr. J.B.\n\nHarper, Stephen\n\nHarris, Mike\n\nHarrison, Neil\n\nHart, Richard\n\nHarvard University\n\nHaskell, Jamie\n\nHasselborg, Mikael\n\nheadsets\n\nheavyweight spiel\n\nHec Gervais Award\n\n_Help!_ (film)\n\nHemmings, Guy\n\n_Herald, The_ (Glasgow)\n\n_History of Curling,The_ (Kerr)\n\nhockey\n\nhog line\n\ndecisions, controversial\n\norigin of name\n\numpires\n\nwidth of\n\nhog score\n\nHollett, Peter\n\nHouse, Wilber\n\nHouston, Heather\n\nHouston, Neil\n\nHoward Rule\n\nHoward, Glenn\n\nHoward, Russ\n\nHowell, Nancy\n\nHowell, Maxwell L.\n\nhubcaps (\"stones\")\n\nHudson, Gordon\n\nHudson's Bay Company\n\nhumidity\n\nhumour\n\nHunt, Jim\n\nHunt, Mel\n\nHunter, Rod\n\n##\n\nice, changing speed of\n\nIce King\n\nIllinois State Curling Foundation\n\nIndy 500,\n\ninstant replay\n\nInternational Curling Federation (ICF)\n\n_International Guide to Curling_ (Welsh)\n\nInternational Olympic Committee\n\nin-turns\n\nirons\n\nItaly\n\nIvoire Hotel (Africa)\n\n##\n\nJagger, Mick\n\njam can \"rocks,\"\n\nJames Bay\n\nJapan\n\nJenkins, Clarence \"Shorty,\"\n\nJohnson, Cassie\n\nJohnson, Leo\n\nJohnson, Lyndon B.\n\nJones, Colleen\n\nJones, Jennifer\n\nJones, Terry\n\nJubilee Meeting, Royal Caledonian Curling Club (1888)\n\nJubilee Stone\n\nJunior-Senior championship winners\n\n##\n\nKapuskasing (ON)\n\nKawaja, John\n\nkeanie (granite)\n\nKeene (ON)\n\nKeith, Toby\n\n_Ken Watson on Curling_ (Watson)\n\nKennedy, Bruce\n\nKerr, Charlie\n\nKerr, Rev. John\n\nKing, Cathy\n\nKingston (ON)\n\nKleibrink, Shannon\n\nknee problems\n\nKnox, Debbie\n\nKotanen, Ray\n\nKruger Products\n\n##\n\nLabatt\n\nLabatt Beer\n\nLabatt Tankard ( _See also_ Macdonald Brier Tankard)\n\nLabonte, Bob\n\nLabonte Curse\n\nLadies Curling Association, Canadian Branch, Royal Caledonian Curling Club\n\nLagoon Leisure Centre (Scotland)\n\nLaing, Brent\n\nLake Placid (NY)\n\nLakehead Rock\n\nLaliberte, Connie\n\nLaliberte, Corinne\n\nLaliberte, Janet\n\nLang, Lorraine\n\nLang, Rick\n\nLank, Patti\n\nLantos, Robert\n\nlapel pins. _See_ curling pins\n\nLas Vegas\n\nLauber, Harold\n\nLausanne (Switzerland)\n\nLees, Charles\n\nleft-handers spiel\n\nLeno, Jay\n\nLetterman, David\n\nlexicon, curling terms\n\nlieutenant-governors\n\n_Little Mosque on the Prairie_ (TV show)\n\nlittle rocks\n\nlocations, unusual\n\nLockerbie (Scotland)\n\nLoen, Sjur\n\nLohnes, Bruce\n\nLukowich, Ed\n\n##\n\nMcCain Foods\n\nMcCormick, Wally\n\nMacdonald Brier Tankard ( _See also_ Labatt Tankard)\n\nMacdonald, Fiona\n\nMacdonald, John A.\n\nMacdonald Tobacco Company\n\nMcDonald, Toby\n\nMacDuff, Jack\n\nMcEdwards, Kathy\n\nMacFadyen, Ted\n\nMcGrath, Larry\n\nMcIntyre, Marvin\n\n_Mackay-Bennett_ (ship)\n\nMcKee, Joyce\n\n_Maclean's_ magazine\n\nMacmillan, Hammy\n\nMacneill, Murray\n\nMajor League Baseball\n\nMartin, Kevin\n\nmade-for-TV games\n\nmale-versus-female games. _See_ battle of the sexes\n\nManahan, Cliff\n\nManion, Dave\n\nManitoba\n\nManitoba Bonspiel\n\nManitoba Curling Association\n\nManning, Ron\n\nMaple Leaf Gardens (Toronto)\n\nMarco hack\n\nMarg Mitchell Award\n\nMartin, Kevin\n\nMartin, Rhona\n\nMassachusetts Institute of Technology (MIT)\n\nMather, Harry\n\nMaxwell, Doug\n\nMayflower Curling Club\n\nMayo, Larry\n\nMazinke, Harvey\n\nMCA. _See_ Manitoba Bonspiel\n\nMead, Jon\n\nMeleschuk, Orest\n\n_Men with Brooms_ (film)\n\nmen's team statistics\n\nMerklinger, Dave\n\nMexico\n\n_Miami Herald_\n\nmicrophones\n\nMiddaugh, Sherry\n\nMiddaugh, Wayne\n\nMilliken, Hugh\n\nMilwaukee\n\nMitchell, Colin\n\nmixed doubles\n\nMoncton (NB)\n\nMoncton 100,\n\nMontreal\n\nMontreal Canadiens\n\nMoore, Archie\n\nMoore, Linda\n\nMoores, Frank\n\nMoose Factory (ON)\n\nMoosonee (ON)\n\nMorocco\n\nMorris, Earle\n\nMorris, John\n\nmovies\n\nMurdock, David\n\nMurphy, Ken (\"Crazy Legs\")\n\nMurphy, W.H.\n\nmuseum\n\nMustapac, Dan\n\n##\n\nNagano (Japan)\n\nNapa Valley (CA)\n\nNational Basketball Association (NBA)\n\nNational Basketball League\n\nNational Hockey League (NHL)\n\n_National Post_\n\nNashville Curling Club\n\nNeale, Harry\n\nNedohin, Dave\n\nNedohin, Heather\n\nNeff, Aubrey\n\nNew Brunswick\n\nNew York\n\nNew York City\n\nNewfoundland\/Labrador\n\nNewton, Laurie\n\nnicknames\n\nNichols, Bob\n\nNicol, Bob\n\nNokia (sponsor)\n\nNorthcott, Ron\n\nNorthern Ontario\n\nNorthwest Territories\n\nNorway\n\nNoseworthy, Mark\n\n##\n\noccupations\n\nOdishaw, Grant\n\nOffice Depot\n\nOkelsrud, Hans\n\nOland, Sid\n\nolder players\n\nOlson, Elias Bjarni (\"Ole\")\n\nOlympic Stadium (Montreal)\n\nOlympics : (1924); (1932) ; (1975); (1987); (1988); (1992), ; (1998); (2001); (2002) ; (2006) ; (2010)\n\nOntario\n\nOntario Curling Association\n\n_Ontario Curling Report_\n\nOntario double-rink competition\n\nOntario Senior Championship\n\nopening banquet (Brier)\n\nopening ceremony (Brier)\n\nO'Rourke, Mark\n\nOrchard Lake (NY)\n\nOrder of Canada\n\norder of playing rule\n\nOrillia (ON)\n\nO'Sullivan, Shawn\n\nOscarius, Kjell\n\nOttawa\n\nOttawa Curling Club\n\nOttawa Valley\n\noutdoor bonspiel\n\nout-turns\n\nOyler, Don\n\n##\n\npaintings\n\nPaju, Ray\n\n_Paper Lion_ (Plimpton)\n\npebbling can\n\nPennant, Thomas\n\n_Penticton Western News_\n\nPerroud, Jane Hooper\n\nPerroud, Pat\n\nPerry, Mel\n\nPeters\n\nPetryk, Dan\n\nPezer, Vera\n\nPfeifer, Scott\n\nPhiladelphia Flyers\n\nPhillips, Alf\n\nPhillips Jr., Alf\n\npin collectors\n\nPin People, The (company)\n\nPine Hill Divinity College\n\nplayers\n\nclergy\n\ncouples\n\nfull-time occupations\n\nheavy\n\nleft-handed\n\nmost Brier games\n\nnicknames\n\nolder\n\npolice\n\nin politics\n\nprofile of\n\nsiblings\n\nspecial needs\n\nvisible minority\n\nyoung\n\nPlayers Championships (2006)\n\nPlimpton, George\n\npolice curlers\n\nPotter, Cassie\n\nPotter, Joyce\n\nPralogna-la-Vanoise (Albertville)\n\nPrince Edward Island\n\nPrint Measurement Bureau\n\nPurple Heart\n\npush brooms\n\n##\n\nQuebec\n\nQuebec City\n\nQueen City Curling Stone Co.\n\n_Quirks and Quarks_ (radio show)\n\n##\n\nRabat (Morocco)\n\nRamcharan, Rudy\n\nRanin, Janice\n\nrecords\n\nred-brick sliders\n\nred\/brown trefor (granite)\n\nRegina\n\n_Regina Leader-Post_\n\nReid, Charles\n\nretirement\n\nRichardson, Arnold\n\nRichardson, Ernie\n\nRichardson, Garnet (\"Sam\")\n\nRichardson, Wes\n\nRideau Hall (Ottawa)\n\nRiley, Mike\n\nrink ice shaver\n\nRink Rat (broom)\n\nrinks\n\nRobert Burns World Foundation\n\nRoberts, Bruce\n\nRoberts, Joe\n\nRobertson, Ed\n\nRobinson, Andrew\n\nrock sharpener\n\nRockefeller Center (NYC)\n\nrocks\n\ngranite used in\n\nidentifying by colour\n\nlifespan of\n\nmaking of\n\nmeasure\n\nrules\n\nscale of\n\nscaled down\n\nstandardization of\n\nsunken\n\ntypes of\n\nworld's largest\n\nRocque, Marcel\n\nRogers Sportsnet\n\nRoss Harstone Award\n\nRowland, Les\n\nRoyal Bank of Scotland\n\nRoyal Caledonian Curling Club\n\nRoyal Canadian Legion\n\nRoyal Montreal Curling Club\n\nrubber hack\n\nRudy Spiel\n\nRules of the Game\n\nRutgers University\n\nRyan, Linsay\n\nRyan, Pat\n\n##\n\nSafeway\n\nSt. John's (NF)\n\nSt. John's Curling Club\n\nSalt Lake City (UT)\n\nSandra Schmirler Award\n\nSarnia (ON)\n\nSaskatchewan\n\nSaskatoon Imperials\n\nSauve, Paul\n\nSavage, Lisa\n\nSavage, Paul\n\nSavill, Craig\n\nShegelski, Mark,\n\nSchmirler, Sandra\n\nSchwaller, Andreas\n\nSchwarzenegger, Arnold\n\nScotch Cup (1965)\n\nScotch Whiskey Company\n\nScotland\n\nScotland-Canada competition\n\nScott, Kelly\n\nScott Paper\n\nScottie tissues\n\nScotties Tournament of Hearts\n\nScottish National Portrait Gallery\n\nseven-ender\n\nShegelski, Mark\n\nShot, The\n\nshuffleboard\n\nShuster, John\n\nsibling curlers\n\nSilver Broom\n\nSilver Tankard\n\n_Simpsons, The_ (TV show)\n\nSioux Lookout (ON)\n\nskins games\n\nskip(s)\n\nCdn. representing foreign countries\n\nrules\n\nsliders\n\nsliding, before contest\n\n_Smart Curling_ (Pezer)\n\nSmith, Donald. _See_ Strathcona, Lord\n\nSogaard, Marten\n\nSomerville, Bud\n\nSomerville, John\n\nSomerville, Ray\n\nSomerville, Tom\n\nsongs\n\nSonmor, Jean\n\nSotheby's\n\nSparkes, Bernie\n\nspiels\n\nsponsors\n\n_Sports and Games in Canadian Life_ (Howell)\n\nSportsnet. _See_ Rogers Sportsnet\n\nSpringsteen, Bruce\n\nStewart, David\n\nStick, the\n\n_Stone Age, The_ (Pezer)\n\nstones. _See_ rocks\n\nStoughton, Jeff\n\nStrathcona Cup\n\nStrathcona Curling Club\n\nStrathcona, Lord\n\nStrauss Herbs (sponsor)\n\nstraw brooms\n\nStrum, Bill\n\nSudbury (ON)\n\nSullivan, Jim\n\nSummer Spud (spiel)\n\nsunken rocks\n\nSuper Bowl\n\nSuper Brush\n\nSuper Draw Curling Bonspiel\n\nSutton, Jodi\n\nSutton, Julie\n\nSweden\n\nsweeping\n\nbefore contest\n\ninstructions, calling\n\nSwitzerland\n\nSydenham Curling Club\n\nSykes, Leon\n\n##\n\ntalk shows\n\n\"Tam Samson's Elegy\" (Burns)\n\nTartan Curling Club\n\ntassels\n\nTeam Canada\n\nteam statistics\n\ntee line, width of\n\nTeflon sliders\n\ntelephone employees championship\n\ntelevision ( _See also_ CBC; Rogers Sportsnet; TSN)\n\nterminology\n\nTetley, Bill\n\nTetley, Ian\n\n_This Hour Has 22 Minutes_\n\nThompson, Jim\n\nthree-rock free-guard zone\n\nThunder Bay (ON)\n\nthunder mugs\n\nTim Hortons (commercial)\n\nTim Hortons (sponsor)\n\nTim Hortons Brier\n\ntime clocks\n\nTimmins (ON)\n\n_Titanic_\n\nTorino (Italy)\n\nToronto\n\nToronto Blue Jays\n\nToronto Curling Club\n\nToronto Maple Leafs\n\n_Toronto Sun_\n\n_Tour Through Scotland_ (Pennant)\n\ntrading cards\n\nTragically Hip, The\n\ntransatlantic competition\n\nTrans-Canada Telephone Employees' Championship\n\ntrain travel\n\nTrenchie, Gord\n\nTSN\n\nTSN Skins Game\n\nTuck, Kim\n\nTurnbull, Ray\n\nTurner Curling Museum\n\nTurner, Don\n\nTurner, Elva\n\nTwist\n\n##\n\nUnited States Men's Championship\n\nUnited States Curling Association\n\nUnited States Curling Championship\n\nUnited States Women's Curling Association\n\nUniversity of Minnesota\n\nUniversity of Saskatchewan\n\nU.S. Curling Hall of Fame\n\nU.S. National Championship\n\nU.S. Olympic Committee\n\nU.S. Olympic team\n\n_USA Today_\n\nUsackis, John\n\nUtica Curling Club\n\nUusipaavalniemi, Maskku\n\n##\n\nVacaville (CA)\n\nVancouver Fire Department\n\nVeale, Fred\n\nVictoria (BC)\n\nVierumaki (Finland)\n\nVilleneuve, Camille\n\nvisible minority players\n\nvision-impaired players\n\n##\n\nWalchuk, Don\n\nWales\n\nwalkie-talkies\n\nWalsh, Billy\n\nWard, Phil\n\nwarming up\n\nWatkins, Jack\n\nWatson, Grant\n\nWatson, Ken\n\nWatson, Harry\n\nWatson, Ken (\"Mr. Curling\")\n\nWatson Lake Outdoor Bonspiel\n\nWaterman, Grant\n\nWelsh, Jimmy\n\nWelsh, Robin\n\nWendorf, Keith\n\nWerenich, Ed,\n\nWestphal, Don\n\nWhalen, Rob\n\nwheelchair players\n\nWillis, Errik\n\nWilson, Jim\n\nWilson, Tom\n\nWinnipeg\n\nWinnipeg Amphitheatre\n\nWinnipeg Granite Club\n\nwomen's curling: highlights; sponsors ; statistics\n\nWomen's World Championship: (1961); (2005)\n\nWood, Bill\n\nWood, Howard\n\nWood Jr., Howard\n\nwooden stones\n\nWoods, Bob\n\nWorld Curling Championship : (1972); (1973); (1974); (1976); (1980); (1981) ; (1983); (1984); (1985); (1989) ; (1990); (1996); (2001); (2003); (2005); (2007)\n\nWorld Curling Federation (WCF)\n\nWorld Curling Tour\n\nWorld Junior Curling Championship: (1975) ; (1976); (1994)\n\nWorld Lefthanders Championship\n\nWorld Open\n\nWorld Series\n\nWorld Wheelchair Curling Championship\n\n##\n\nYoung, Willie\n\nYellowgras (SK)\n\nyoung players\n\nYukon\n\n##\n\nZamboni\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":"\n## \"Oh, I understand you very well,\" said Louisa, her voice a little high with suppressed feelings.\n\n\"What a very disagreeable man you are, Mr. Savage, with your orders and arrogance. I should very much dislike having you as a patient.\"\n\nHis dark eyes snapped at her. \"You surprise me, Louisa. I should have thought it would have been the very thing, because I would be entirely at your mercy and you could wreak revenge to your heart's content.\" His silky voice had a nasty edge to it. He opened the door. \"Perhaps we'd better keep out of each other's way?\" he said.\n\nShe agreed stiffly and when she was alone again, wondered why the prospect left her with the feeling that life would be rather dull.\nRomance readers around the world were sad to note the passing of Betty Neels in June 2001. Her career spanned thirty years, and she continued to write into her ninetieth year. To her millions of fans, Betty epitomized the romance writer, and yet she began writing almost by accident. She had retired from nursing, but her inquiring mind still sought stimulation. Her new career was born when she heard a lady in her local library bemoaning the lack of good romance novels. Betty's first book, Sister Peters in Amsterdam, was published in 1969, and she eventually completed 134 books. Her novels offer a reassuring warmth that was very much a part of her own personality. She was a wonderful writer, and she will be greatly missed. Her spirit and genuine talent will live on in all her stories.\n\n## THE BEST OF BETTY NEELS\n\n## HEAVEN AROUND THE CORNER\n\n## CONTENTS\n\nCHAPTER ONE\n\nCHAPTER TWO\n\nCHAPTER THREE\n\nCHAPTER FOUR\n\nCHAPTER FIVE\n\nCHAPTER SIX\n\nCHAPTER SEVEN\n\nCHAPTER EIGHT\n\nCHAPTER NINE\n\n## CHAPTER ONE\n\nTHE SEPTEMBER SUN, shining from an early morning sky, cast its impartial light on the narrow crowded streets, the smoke-grimed houses, several quite beautiful churches and the ugly bulk of the Royal Southern Hospital, giving a glow to its red bricks and a sparkle to its many narrow windows. It was a splendid example of mid-Victorian architecture, crowned with cupolas and a highly ornamental balustrade and rendered even more hideous by reason of the iron fire escapes protruding from each wing. And inside it was even uglier, for here the sun was unable to reach all its staircases and passages, so that the dark brown paintwork and distempered walls tended to cast a damper on anyone passing through them.\n\nBut the girl going down the stairs two at a time noticed none of these things. Her neat head with its crown of light brown hair was full of excited thoughts. She had passed her State finals; she was a fully trained nurse at last\u2014the world was her oyster. She was determined on that, despite the Principal Nursing Officer's gracious speech as she was handed the fateful envelope. There was a place for her at the Royal Southern, that lady told her; Night Staff Nurse on the surgical wing and the prospect of a Sister's post very shortly, and there was no need for Nurse Evans to decide at once...\n\nBut Louisa Evans had already decided instantly; she was going to leave, not only the hospital, but if possible, England too, although she prudently forbore from saying so at the time. At the end of the day, when she went off duty, she was going to write her resignation and hand it in and then she would go home for her two days off and tell her stepmother. She checked her headlong flight for a second, dreading that, but it was something which had to be done, and she had made up her mind to that weeks ago when she sat her exams.\n\nShe went along a narrow corridor, up another flight of stairs, across a wide landing and through the swing doors leading to Women's Surgical. Just for the moment the future wasn't important, only the delicious prospect of telling Sister and the nurses on the ward that she was an SRN.\n\nAnd she had no need to tell anyone. Sister, coming out of her office, took one look at Louisa's happy face and said: 'You've passed\u2014congratulations, but of course I knew that you would.' And after that the news spread like wildfire, with the patients, only too glad to have something to talk about, telling each other, nodding their heads and saying, with hindsight, that of course Nurse Evans had been bound to pass, she was such a good nurse. And as for Louisa, she floated up and down the ward, doing her work with her usual efficiency while a tiny bit of her mind pondered the problems of what she should do and where she should go.\n\nA problem solved sooner than she had expected: She had been to her midday dinner\u2014a noisy meal she shared with friends who had reached her exalted position too\u2014and she was back on the ward, changing Mrs Griffin's dressing, when that lady asked her what she intended doing.\n\nLouisa, aware of how news, false as well as true, travelled with the speed of light round the hospital, said cautiously that she hadn't quite made up her mind, and rolling the lady carefully back into a sitting position, rearranged her pillows, smoothed the counterpane and prepared to depart with her dressing tray.\n\n'Well, don't go for a minute, Nurse,' begged Mrs Griffin. 'Listen to this: \"Trained nurse urgently required for lady patient travelling to Norway in a month's time for an indefinite stay. Good salary and expenses paid.\" What do you think of that?' She folded the Telegraph and handed it to Louisa, who read it carefully, and having an excellent memory, noted the telephone number. 'It sounds fun,' she observed cheerfully. 'Someone'll be lucky.' She drew back the curtains and with a parting nod raced off down the ward to clear the tray and get on with the next dressing. But before she did that, she jotted down the telephone number on to the hem of her apron.\n\nShe went off duty at five o'clock, composed her letter of resignation and handed it in for delivery to the office and then went to telephone from the box in the entrance hall. There was no one about; she could see the porter on duty, sitting with his feet up, sipping tea during his brief break. All her friends were already in the Nurses' Home, getting dressed for the party they were all going to later on that evening. She dialled the number.\n\nThe voice at the other end asked her to wait a moment and after a few seconds another voice spoke. Louisa had had all the afternoon to rehearse what she was going to say and she was listened to without interruption. When she had finished, the voice, a woman's, high and somehow breathless, said: 'I have interviewed several nurses already, but none of them suit me. Come and see me tomorrow morning about eleven o'clock.'\n\n'I'm on duty until the early afternoon...'\n\n'Oh, well, the afternoon then, about three o'clock. I'm at the Connaught Hotel, and ask for Miss Savage.'\n\nLouisa put the receiver down slowly. Miss Savage had sounded petulant; she wondered what complaint the lady suffered from, but the only way was to go and see her and find out. Even if she were offered the job, she need not accept it.\n\nShe started to stroll along the passage to the small door which opened into the Nurses' Home. On the other hand, if she were offered the job it would be like the answer to a prayer\u2014she had been longing to leave the hospital for some months now, not because she was unhappy there\u2014on the contrary, she had enjoyed every minute of the three years she had spent within its walls\u2014but because her stepmother, living not too far away, had been able to keep tabs on her for that time, knowing that she had set her heart on training as a nurse and wasn't likely to leave the Royal Southern and was therefore unlikely to escape. But now she could do just that... She quickened her steps, intent on not being late for the party.\n\nThey had all decided to dress rather grandly for the occasion. Louisa, burrowing around in her cupboard, wasted a good deal of time deciding whether the pale blue crepe would look better than the sage green silk jersey. On second thoughts she didn't like either of them, she had had them too long although she hadn't worn them all that much. She chose the green and rushed off to find an empty bathroom.\n\nHalf an hour later she was dressed and ready\u2014a rather small girl and a little too thin, with a face which wasn't quite pretty although her eyes, large and hazel and fringed with long curling lashes, redeemed it from plainness. Her hair, long and fine and silky, she had fastened back with a silver clasp because there hadn't been time to do anything more elaborate. Presently her friends trooped in and they all went into the hospital to the residents' room where the housemen and some of the students had laid on a buffet supper. The room was packed already, with everyone talking at once and quite a few dancing to a barely heard tape recorder. Louisa, popular with everyone because she was ready to lend an ear to anyone who wanted it, was quickly absorbed into a group of young housemen, all of whom looked upon her as a sisterly type to whom they could confide their troubled but fleeting love affairs, for she never told them how silly they were but listened to their outpourings, giving sympathy but never advice. For a girl of twenty-two she had a wise head on her shoulders, albeit a rather shy one. Her stepmother had taken care that she had had very little chance of making friends while she was at school and when she left, until she had succeeded at last in her ambition to train as a nurse; she had been kept too busy to do more than meet the people Mrs Evans approved of, most of them elderly or at least middle-aged, so that she still retained the feeling of not quite belonging among the young people at the hospital, certainly she had shied away from any of the young men of her acquaintance who had hinted at anything more serious than a kiss, and they, once they had laughed about her among themselves, but kindly, had taken to treating her like a sister.\n\nShe joined the dancers presently and except for short pauses for food and drink, didn't lack for partners for the rest of the evening. The party broke up around midnight and they all went their several ways, yawning their heads off and grumbling at the prospect of getting up at half past six the next morning. All the same, they made a pot of tea and crowded into Louisa's room to drink it and discuss the party, so that it was an hour later before she went finally to bed, too tired to give a thought about the next day.\n\nShe dressed carefully for the interview in a thin wool suit with a slim skirt and a short loose jacket, it was a pretty grey and she wore a silk shirt in navy to go with it; a suitable outfit, she considered, making her look older than her years, which she considered might be a good thing.\n\nThe hotel looked grand and she went inside feeling a great deal less calm than she looked, but the reception clerk was pleasant and friendly and she was led to the lift and taken several floors up and along a thickly carpeted corridor until the porter tapped on a door and opened it for her.\n\nLouisa had expected to be interviewed in one of the reception rooms of the hotel; presumably her patient was confined to her room. And a very handsome room it was too, splendidly furnished with wide french windows and a balcony beyond\u2014and quite empty. She walked into the centre of the room and waited, and presently a door opened and a chambermaid beckoned her. It was an equally luxurious room, this time a bedroom, and sitting up in the wide bed was, she presumed, Miss Savage.\n\nMiss Savage wasn't at all what Louisa had expected her to be. She had entertained the vague idea that the lady would be elderly and frail: the woman in the bed was still young\u2014in her thirties and pretty with it. She had golden hair cut in a fringe and hanging in a gentle curve on either side of her face, her make-up was exquisite and she was wrapped in soft pink, all frills and lace.\n\nShe stared at Louisa for what seemed a long time and then said surprisingly: 'Well, at least you're young.' She nodded to a chair. 'Sit down\u2014you realise that we may be in Norway for some time if you come?'\n\nLouisa said, 'Yes,' and added: 'Will you tell me something of your illness? I couldn't possibly decide until I know more about that\u2014and you must want to know a good deal more about me.'\n\nMiss Savage smiled slowly. 'Actually I think you'll do very well. You're young, aren't you, and haven't been trained long.'\n\n'I'm twenty-two and I became a State Registered Nurse yesterday. I've not travelled at all...'\n\n'Nor met many people? From the country, are you?'\n\n'My home is in Kent.'\n\n'You won't mind leaving it?'\n\n'No, Miss Savage.'\n\nThe woman picked up a mirror and idly examined her face. 'I've got a liver complaint,' she observed. 'My doctor tells me that I have a blocked duct, whatever that is, I'm not bedridden but I get off days and he insists that if I go to Norway I should have a nurse with me.' She shot a glance at Louisa. 'My brother works there\u2014he builds bridges\u2014somewhere in the north, but I've arranged to take a flat in Bergen for a month or so.'\n\n'You have treatment, Miss Savage?'\n\n'Doctor Miles looks after me, he'll recommend a doctor to treat me.'\n\n'Yes, of course. But if you can get about, will you require a full-time nurse?'\n\nMiss Savage frowned. 'Certainly I shall!' She sounded petulant. 'I often have bad nights\u2014I suffer from insomnia; you'll have more than enough to do.' She put the mirror down and began to buff her nails. 'I intend to go in a little over three weeks\u2014you'll be free then?' She glanced up for a moment. 'You'll be paid whatever is the correct rate.'\n\nLouisa sat quietly. It seemed a strange kind of interview, no talk of references or duties. She had the impression that Miss Savage wasn't in the least interested in her as a person. The job was just what she had hoped for, but there was something about this girl that she didn't like. That she was spoilt and liked her own way didn't worry Louisa overmuch, but there was something else that she couldn't quite put her finger on. On the other hand, if she didn't take what seemed like a heaven-sent chance, she might have to stay in England.\n\n'I accept the job, Miss Savage,' she said at length. 'You will want references, of course, and I should like a letter from you confirming it. Perhaps you'll let me know details of the journey and my duties later on? Will you be travelling alone or will your brother be with you?'\n\nMiss Savage gave an angry laugh. 'He's far too busy, wrapped up in his bridges...'\n\nWhy did she want to go? thought Louisa silently. Surely Norway, unless one went there for winter sports, would be rather an unsuitable place in which to convalesce? And she had the impression that the brother wasn't all that popular with his sister, but that was no concern of hers.\n\nAll the way back to the Royal Southern she wondered if she had done the right thing, and knew that when she got back there she had, for there was a letter from her stepmother, telling her that she was expected home on her next days off and threatening to telephone the Principal Nursing Officer if Louisa didn't go. There were guests coming, said the letter, and they expected to meet her, and why hadn't Louisa telephoned for a week? She was an ungrateful girl...\n\nLouisa skimmed through the rest of the letter; it was merely a repetition of all the other letters from her stepmother. She would go home because if she didn't there would be a lot of unpleasantness, but she wasn't going to say a word about the new job. Perhaps once she was out of the country and out of reach of her stepmother, she would be left to lead her own life. She wrote a brief reply, scrambled into her uniform and went back on duty.\n\nShe told Sister before she went off duty that evening, and later on, after supper, those of her friends who had crowded into her room for a final pot of tea before bed, and her news was received with some astonishment. Louisa had always been considered a rather quiet girl, well liked and ready to join in any fun but unlikely to do anything out of the ordinary. There was a spate of excited talk and any amount of unsolicited advice before they finally went to their own beds.\n\nThere were two days to go before her days off. She used them to good advantage, arranging to get a passport and recklessly drawing out quite a big slice of her savings to buy new clothes. Common sense made her pause though before doing that. Supposing Miss Savage changed her mind, she might need the money...\n\nBut Miss Savage didn't disappoint her; there was a letter confirming the job and a promise to advise her as to travel arrangements in due course. Louisa counted her money and promised herself one or two shopping excursions. But first she had to go home.\n\nShe caught an early morning train to Sevenoaks; she could have gone the evening before, but that would have meant another night to be spent at home, but now she would be there well before noon and if there were people coming to lunch, her stepmother wouldn't have much time to talk to her. She got into the Ightham bus and settled down for the four-mile journey, looking with pleasure at the country they were going through. The trees were beginning to turn already and little spirals of blue smoke rose in the cottage gardens where the bonfires had been started. And the village looked lovely, too, with its square ringed by old houses. Linda paused to pass the time of day with some of the people who knew her and then walked up the narrow lane leading to her home.\n\nThe house was old and timbered and stood sideways on to the lane, surrounded by trees and large gardens. Louisa opened the little gate set in a corner of the hedge, well away from the drive, then walked across the grass and in through a side door leading to a low-ceilinged room furnished with rather old-fashioned chairs and small tables. There were bookshelves on either side of the open hearth and a rather shabby Turkey carpet on the floor. She was halfway across it when the door opened and Mrs Evans came in.\n\n'There you are!' Her voice was sharp and held no welcome. 'You should have come last night\u2014Frank was here. And why on earth did you come in this way? You know this room isn't used.' She looked around her with a dissatisfied air. 'So shabby and old-fashioned.'\n\nLouisa put down her overnight bag. 'It was Mother's sitting room,' she said flatly, 'and Father loved it.'\n\nMrs Evans shrugged thin, elegant shoulders. 'Did you pass your exams?' and when Louisa nodded: 'Thank heaven for that, now perhaps you'll see some sense and settle down. I must say Frank's been patient.'\n\n'I've no intention of marrying Frank, and I'm rather tired of saying so.'\n\n'Then you're a fool. He's got everything\u2014money, that splendid house in the village, that gorgeous car and a villa in Spain. What more could a girl want? Especially when she's not pretty. You're not likely to get another chance like that.' She gave Louisa a quick look. 'You've not fallen in love with one of those young doctors, I hope?'\n\n'No. Why are you so anxious for me to marry Frank Little?'\n\nHer stepmother's answer was a little too careless. 'He's devoted to you and he'll be generous.'\n\nLouisa studied her stepmother; still quite young, pretty and very elegant; extravagant, too. She had been left everything in the will, but Louisa suspected that she had spent most of it during the last three years and had deliberately cultivated Frank Little, hoping for an amenable son-in-law who would pay her bills\u2014and an equally amenable stepdaughter who would marry him.\n\nWell, I won't, thought Louisa. If only her stepmother had been fifteen or ten years younger she could have married him herself. The fact of her father's marriage to a woman so much younger than himself still hurt Louisa. It wouldn't have been so bad if she had loved him. She still wondered at his marrying her; this scheming, clever woman who had twisted him round her little finger and had never forgiven Louisa for not allowing herself to be twisted too. She could think of nothing to say and picked up her bag.\n\n'There are several people coming to lunch,' said Mrs Evans. 'You'd better go and tidy yourself.' She turned and went out of the room ahead of Louisa and crossed the hall to the drawing room, and Louisa went upstairs to her room. While she did her face and tidied her hair she thought about leaving England; she would miss her home, but that was all. She would have to come once more before she went because her stepmother would demand it and if she refused she might wonder why. The temptation to tell her was very great, but Mrs Evans was clever enough to prevent her going. She knew so many people, influential people who could perhaps put a spoke in Louisa's wheel. A car coming up the drive and rather noisy voices greeting each other interrupted her thoughts. She gave her unremarkable person a final inspection in the pier glass, and went downstairs.\n\nThe drawing room seemed to have a lot of people in it, but only because they were all talking at once a shade too loudly. Louisa shook hands all round, took the sherry she was offered and made small talk. She knew the five people who had arrived, but only slightly; they were friends of her stepmother's who had never come to the house while her father was alive, but now they were regular visitors. There was one more to come, of course\u2014Frank Little.\n\nHe came in presently, a man in his late thirties, rather short and plump, with an air of self-importance which sat ill on his round face with its weak chin. He stood in the doorway for a moment, giving everyone there a chance to greet him, and then went straight to Louisa.\n\n'Your dear mother assured me that you would be here,' he stated without a greeting. 'I know how difficult it is for you to get away.' He took her hand and pressed it. 'I can only hope it's because you knew that I would be here that you came.'\n\nLouisa took her hand away. It was a pity he was so pompous; otherwise she might have felt sorry for him. 'I didn't have to make any special effort to come home,' she told him politely, 'and I didn't know you'd be here.'\n\nWhich wasn't quite true; he was always there when she went home. She moved a little way from him. 'What will you drink?'\n\nHe sat next to her at lunch, monopolising the conversation in his over-hearty voice, making no secret of the fact that he considered her to be his property.\n\nAnd he was at dinner too, ill-tempered now because she had escaped that afternoon and gone for a walk\u2014her favourite walk, to Ivy Hatch where the manor house of Ightham Moat stood. She had got back too late for tea and her stepmother had been coldly angry.\n\nAnd the next day was as bad, worse in fact, for Frank had waylaid her on her way back from the village and rather blusteringly asked her to marry him, and that for the fourth time in a year.\n\nShe refused gently because although she didn't like him she didn't want to hurt his feelings. Only when he added angrily: 'Your mother considers me to be the perfect husband for you,' did she turn on her heel and start walking away from him. As she went she said over her shoulder: 'She is not my mother, Frank, and I intend to choose my own husband when I want to and not before.'\n\nHe caught up with her. 'I'm coming up to see you this evening\u2014I'm invited for dinner and there'll be no one else there.'\n\nSo after tea she went to her room, packed her bag, told her stepmother that she was leaving on the next bus and went out of the house. Mrs Evans had been too surprised to do or say anything. Louisa, leaping into the bus as it was about to leave, waved cheerfully to Frank, about to cross the village square.\n\nShe arrived back at the Royal Southern quite unrepentant, prudently asked one of her friends to say that she wasn't in the home if the telephone went and it was her stepmother, and retired to soak in a hot bath until bedtime.\n\nThe ward was busy and she spent almost all her free time shopping, so that she was too tired by the end of the day to have second thoughts about her new job. And at the end of the week she received a letter from Miss Savage confirming it, asking her to call once more so that final details might be sorted out and giving her the day and time of their flight.\n\nAnd this time when Louisa got to the hotel, it was to find her future patient reclining on a chaiselongue and rather more chatty than previously. 'Uniform,' she observed, after a brief greeting. 'You don't need to travel in one, of course, but you'd better have some with you. Dark blue, I think, and a cap, of course. Go to Harrods and charge it to my account.'\n\n'Will you want me to wear them all the time?'\n\n'Heavens, no\u2014you'll get your free time like anyone else. Besides, I shall be going out quite a bit and I shan't want you around.'\n\nLouisa blinked. 'I think I should like to see your doctor before we go.'\n\nMiss Savage shrugged. 'If you must. He's a busy man\u2014you'd better telephone him. I'll give you his number.' She yawned. 'Take a taxi and come here for me\u2014a friend will drive us to Heathrow. Be here by ten o'clock.' She frowned. 'I can't think of anything else. I shall call you by your christian name\u2014what is it? You did tell me, but I've forgotten.'\n\n'Louisa, Miss Savage.'\n\n'Old-fashioned, but so are you. OK, that's settled, then. I'll see you here in ten days' time.'\n\nLouisa got to her feet. She had been going to ask about clothes; after all, Norway would be colder than London, or so she supposed, but somehow Miss Savage didn't seem to be the right person to ask. Louisa said goodbye in her composed manner and went back on duty. After her patients on the ward, with their diagnoses clearly written down and an exact treatment besides, she found Miss Savage baffling. Her doctor would remedy that, however.\n\nBut here she was disappointed. Miss Savage's treatment was to be negligible\u2014rest, fresh air, early nights, good food. 'Miss Savage is on Vitamin B, of course, and I shall supply her with nicotinic acid as well. I've already referred her case to a Norwegian colleague who will give you any information you may wish to know. You, of course, realise that she suffers from dyspepsia and a variety of symptoms which will be treated as they arise.'\n\nLouisa listened to the impersonal voice and when it had finished, asked: 'Exercise, sir?'\n\n'Let our patient decide that, Nurse. I'm sure you understand that she'll have days when she's full of energy\u2014just make sure that she doesn't tax her strength.'\n\n'And notes of the case?' persisted Louisa.\n\n'They'll be sent to her doctor in Bergen.'\n\nShe put down the receiver. Miss Savage was a private patient, which might account for the rather guarded statements she had just listened to. Certainly, from her somewhat limited experience of similar cases on the wards, the treatment was very much the same, and unlike the patients in hospital, the patient would probably have more say in the matter of exercise and food. As far as Louisa could see, she was going along to keep an eye on Miss Savage, and not much else. But at least it would get her away from Frank.\n\nThe thought was so delightful that she embarked on a shopping spree which left her considerably poorer but possessed of several outfits which, while not absolutely in the forefront of fashion, did a great deal for her ego. She went home once more and because it was the last time for a long while, endured her stepmother's ill-humour and Frank's overbearing manner. There was less than a week to go now and she was getting excited. It was a good thing that the ward was busy so that she had little time to think about anything much except her work, and her off duty was spent in careful packing and a great number of parties given as farewell gestures by her friends.\n\nShe wrote to her stepmother the evening before she left and posted it just before she got into the taxi, with such of her friends as could be missed from their wards crowding round wishing her luck. Once the hospital was out of sight she sat back, momentarily utterly appalled at what she was doing, but only for a brief minute or so. She was already savouring the heady taste of freedom.\n\nShe was punctual to the minute, but Miss Savage wasn't. Louisa, gathering together the bottles and lotions and stowing them tidily in an elegant beauty box, hoped they wouldn't miss the plane. But a telephone call from reception galvanised her patient into sudden energy and within minutes there was a knock on the door and three people came in\u2014a young woman, as elegant as Miss Savage, and two men. They rushed to embrace Miss Savage, talking loudly and laughing a great deal, ignoring Louisa and then sweeping the entire party, complete with bellboys, luggage and an enormous bouquet of flowers, downstairs. Louisa felt that she had lost touch, at least for the moment. Once they were on the plane she would get Miss Savage to rest\u2014a light meal perhaps and a nap...\n\nNo one spoke to her and they all piled into an enormous Cadillac and roared off towards Heathrow. She sat in the back of the car, with the young woman beside her and one of the men. Miss Savage sat beside the driver, and for someone with a liver complaint who was supposed to take life easy, behaved in a wild and excitable manner, but Louisa realised that it would be useless to remonstrate with her. She was bubbling over with energy, and the man who was driving was encouraging her.\n\nAt Heathrow they got out, and to Louisa's horror, they all booked in for the flight. One of the men must have noticed the look on her face, because he patted her on the shoulder. 'Not to worry, Nurse\u2014we're only taking Claudia to Bergen. Once she's there, she's all yours.'\n\nAnd a good thing too, thought Louisa, watching the gin and tonics Miss Savage was downing once they were in flight. They were travelling first class and the plane was barely half full, which was perhaps a good thing considering the noise she and her friends were making. They had gone quietly enough through Customs. They had arrived with only a few minutes to spare and there had been no time for chat, but once on board they had relaxed. They might have been in their own homes, so little did they notice their surroundings. To Louisa, tired and apprehensive, the flight seemed endless. She heaved a sigh of relief when the plane began its descent and through a gap in the clouds she saw the wooded islands and the sea below, and then a glimpse of distant snow-capped mountains. Just for a moment she forgot her patient and her problems, and thrilled with excitement. Here was a new world, and only time would reveal all its possibilities.\n\n## CHAPTER TWO\n\nBERGEN AIRPORT was small compared with Heathrow. It took only minutes for them to clear Customs, summon two taxis and start the drive to Bergen. Louisa, sitting in the second car with the elder of the two men, hardly noticed him, there was such a lot to see. The country was wooded and very beautiful and the road wound between trees already glowing with autumn colour. She had been surprised to see on a signpost that Bergen was twelve miles away to the north; somehow she had expected to plunge straight into the town's suburbs. Presently they came to a village and then another, and then after twenty minutes or so, the outskirts of Bergen. Louisa was a little disappointed, for the busy road they were now on seemed very like any other busy road anywhere in England, but only for a moment. Suddenly they were in the centre of the town, skirting a small square park surrounded by busy streets. Her companion waved a vague hand at the window. 'Nice little tea room there,' he volunteered, 'very handy for the shops\u2014Claudia's got a flat near the theatre.'\n\nWhich, while interesting, meant nothing to Louisa.\n\nThey turned off a shopping street presently and came upon another small park set in the centre of a square of tall houses, and at its head, the theatre. The taxis stopped half way along one side and they all got out. Miss Savage's flat was on the first floor of a solid house in the middle of a terrace of similar houses, a handsome apartment, well furnished in the modern Scandinavian style, with its own front door in the lobby on the ground floor. A pleasant-looking young woman had opened the door to them and shown them up the short flight of stairs and disappeared down a passage, to reappear presently with a tea tray. Louisa, bidden to pour tea for everyone, did so, and then at Miss Savage's casual: 'Have a cup yourself, Louisa, then perhaps you'd unpack? There's a maid somewhere, see if you can find her,' went to do as she was bid.\n\nThe flat was larger than she had supposed. She had opened doors on to three bedrooms, a bathroom and a cupboard before she came to the kitchen. There was another girl here, young and pretty and, thank heaven, speaking English.\n\n'Eva,' she said as they shook hands. 'I come each day from eight o'clock until seven o'clock in the evening. In the afternoon I go for two hours to my home.' She smiled widely. 'You would like coffee?'\n\nLouisa hadn't enjoyed the tea very much. 'I'd love a cup, but I was going to unpack.'\n\n'Then first I show you your rooms and then the coffee. You are the nurse, I think?'\n\n'That's right.' Louisa followed her back down the passage; first her own room, light and airy, well furnished too, with a shower room leading from it, and then her patient's, much larger, with a bathroom attached and a balcony looking out over the square. Louisa, fortified by the coffee and five minutes' chat with Eva, went back there presently and started to unpack. It took quite a time, for Miss Savage had brought a large wardrobe with her; for an invalid she appeared to expect a good deal of social life. Louisa arranged the last scent bottle on the dressing table, arranged the quilted dressing gown invitingly on the bed, and went in search of her patient.\n\nThe tea party was still in full swing, only now a tray of drinks had taken the place of the tea and Miss Savage's pale face was flushed. Before Louisa could say anything, one of the men called out: 'All right, nurse, we're just off\u2014got a plane to catch. Look after our Claudia, won't you?' He winked broadly: 'Keep her on the straight and narrow!'\n\nTheir goodbyes took another five minutes and when they had gone the room was quiet again. Quiet until Miss Savage burst into tears, storming up and down the room, muttering to herself, even waving her arms around. All the same, she managed to look as pretty as ever, like a little girl who couldn't get her own way. Louisa's kind heart melted at the sight of her; with a little difficulty she urged her patient to sit down and then sat beside her. 'You're tired,' she said in her quiet, sensible voice. 'It's been a long day, and it's not over yet. Suppose you have a nap for an hour and Eva and I will get a meal ready for you. You haven't eaten much, have you?'\n\n'I want to go home,' mumbled Miss Savage, and buried her head against Louisa's shoulder.\n\n'Then why don't you? We can pack up in no time at all and after you've had a good night's rest we can get a flight back...'\n\n'Fool!' declared Miss Savage. 'Do you really suppose I wanted to come? To leave my friends and all the fun...'\n\nLouisa, who hadn't taken offence at being called a fool, quite understanding that her companion was suffering strong feelings about something or other, had asked merely: 'Then why did you come, Miss Savage?'\n\n'He made me, of course. I have to live, don't I, and if he stops my allowance what am I to do?'\n\n'Who's he?' enquired Louisa gently. 'You don't have to tell me, only it might make it easier if you did\u2014perhaps we can think of something.'\n\n'My beastly brother. I detest him\u2014he's mean and high-handed and he made me come here so that he can make sure that I don't spend too much money\u2014and don't have my friends.'\n\n'Very unreasonable,' commented Louisa. 'And what about me? I cost money, don't I?'\n\n'Oh, he pays for you\u2014it was one of the conditions...' Miss Savage paused and rearranged her words. 'The doctor said I had to have someone to look after me...'\n\n'I should think so indeed!' declared Louisa indignantly. She still didn't like Miss Savage overmuch, but probably her way of life was the result of having a despot of a brother who bullied her. 'Does your brother know you came here today?'\n\nMiss Savage nodded. 'Yes\u2014but you needn't worry, he won't come here. He's miles away\u2014the last I heard of him he was north of Tromso, that's on the way to the North Pole\u2014well, it's a long way beyond the Arctic Circle.'\n\nLouisa produced a handkerchief and wiped Miss Savage's face for her. 'I can't quite see why you had to come to Norway. If your brother wanted you to lead a quieter life, couldn't you have gone to live for a time in the country in England? It would have been much cheaper.'\n\nShe couldn't see her patient's face so she didn't see the cunning look upon it. Miss Savage sounded quite convincing when she said: 'But my friends would still come and see me!'\n\n'You'll make friends here,' declared Louisa. 'I thought the town looked delightful, didn't you? In a few days, when you've rested, we'll explore. There are bound to be English people living here.'\n\nMiss Savage sat up. She said: 'You're much nicer than I thought you were. I daresay we'll have quite a good time here. You will help me, won't you? I mean, if I make friends and go out sometimes?'\n\nLouisa answered her cautiously: 'Yes, of course, but you have to rest, you know, but I don't see why we shouldn't work out some sort of a routine so that you can enjoy yourself. No late nights, at least until the doctor says so, and take your pills without fail and eat properly and rest\u2014that's important.'\n\n'It all sounds utterly dreary,' Miss Savage smiled charmingly at her, 'but I'll be good, really I will.'\n\nSuiting the action to the word, she went to her room, took off her dress and allowed Louisa to tuck her up under the duvet.\n\nLouisa unpacked, consulted with Eva about their evening meal and then, for lack of anything else to do for the moment, went to sit by the sitting room window. There were people in the street below, hurrying home from work, she supposed, taking a short cut across the little park and disappearing round the corner of the theatre at the far end. The sky was clear, but there was a brisk little wind blowing the leaves around and she wondered what it would be like when autumn gave way to winter. From what she had seen of the town she was sure she was going to like it. She hoped she had brought enough warm clothing with her: Miss Savage's luggage had contained thick woollies and a couple of anoraks and fur-lined boots, and there was a mink coat which one of the men had carried for her... Her thoughts were interrupted by the telephone and she went to answer it quickly before it disturbed her patient. A man's voice, slow and deep, asking something or other.\n\n'I'm sorry, I don't understand you...'\n\n'You are the nurse?'\n\n'I'm Miss Savage's nurse, yes.'\n\n'I should like to speak to her. Her brother.'\n\n'She's resting\u2014we only arrived an hour or so ago. Perhaps you'll ring tomorrow.' Louisa's voice was cool, but not nearly as cold as the man on the other end of the line.\n\n'I shall ring when it is convenient to me,' he said, and hung up on her, leaving her annoyed and quite sure that he was just about the nastiest type she had ever encountered. Why, even Frank seemed better!\n\nShe told Miss Savage later, when that lady, remarkably revived by her nap, joined her in the sitting room.\n\n'And that's the last I'll hear from him\u2014obviously he's no intention of coming to see me.' She sounded delighted. 'If he rings again, Louisa, you're to say that I'm shopping or asleep or something. I'm hungry, have you arranged something or shall I go out?'\n\n'Eva has cooked a meal for us; it's all ready being kept hot. Eva goes in a few minutes.'\n\n'What a bore! Oh, well, you'll have to do the chores.'\n\nIt hardly seemed the time to point out that she was a nurse, not a maid; Louisa prudently held her tongue and went to tell Eva that she could dish up.\n\nMiss Savage's vivacity lasted for the whole of the meal, although her appetite, after a few mouthfuls of the excellently cooked cod, disappeared entirely\u2014indeed, presently she got up from the table, leaving Louisa, who was famished, to hurry through her meal, which seemed a shame, for the pudding was good, too, and the coffee following it excellent. At least Miss Savage accepted coffee, lying back on the big sofa facing the window, looking suddenly as though she'd been on her feet for days and hadn't slept a wink.\n\n'Bed,' said Louisa firmly, 'a warm bath first\u2014do you take sleeping pills? The doctor didn't mention them...'\n\n'There are some in my bag, but I don't think I'll need them tonight.' Miss Savage yawned widely, showing beautiful teeth. 'I'll have breakfast in bed\u2014coffee and toast, and don't disturb me until ten o'clock.'\n\nLater, with her patient in bed and presumably sleeping, Louisa cleared away their supper things, tidied the kitchen ready for Eva in the morning and went back to the window. It was very dark outside, but the streets were well lighted and there were plenty of people about and a good deal of traffic. The pleasant thought struck her that if Miss Savage wasn't to be disturbed until ten o'clock each morning, she would have time to take a quick look round after her own breakfast. She could be up and dressed by eight o'clock and Eva would be in the flat then, so that if Miss Savage wanted anything there would be someone there. She didn't know much about private nursing, but it seemed to her that this case wasn't quite as usual; only the vaguest references had been made to off duty, for instance, and what about her free days? She should have made quite sure of those, but she had been so eager to get the job, and although it might not turn out to be exactly what she had expected at least she was out of England, beyond her stepmother's reach, and moreover, in a country which, at first sight, looked delightful.\n\nShe went to bed and slept dreamlessly all night.\n\nShe was up and ready for Eva when she arrived, and since Miss Savage hadn't said anything more about uniform, she had put on a pleated skirt and a thin sweater.\n\nEva was surprised to see her already dressed, but she wasted no time in making coffee and unwrapping the still warm rolls she had brought with her. She shared Louisa's coffee too, sitting at the kitchen table while she told Louisa where the shops were and how to go to them. It wasn't nine o'clock when Louisa, a quilted jacket over the sweater and a woolly cap and gloves, left the flat; there would be time to explore and perhaps she could persuade Miss Savage to go for a short walk once she was up. She crossed the little park as Eva had instructed her and turned into Ole Bull Pass and then into the main shopping street, Torgalmenning, where the shops were already open, although there weren't many people about.\n\nLouisa walked briskly down its length, intent on reaching the harbour Eva said she simply had to see, promising herself that the next time she would stop and look in all the shop windows. It didn't take her long; there was the harbour, bustling with life, ferries chugging to and fro, freighters tied up in the distance. It was overlooked on two sides by rows of ancient houses, many of them wooden and all of them beautifully cared for and most of them converted into shops. She walked a little way beside the water, looking across to the mountains in the distance and then nearer to the neat colourful houses clinging to the skirts of the mountains behind the town. There was a fish market too, but she didn't dare to stop to inspect it for more than a minute or two; quite a different matter from the fish shops at home, and she had never seen such a variety. She paused for another minute to stare across the water at a castle\u2014she would have to find out about that, too... She had no more time; she retraced her steps, aware that there must be another way back to the flat, probably shorter\u2014tomorrow she would discover it.\n\nShe had time to change into her uniform when she got back; there was more chance of Miss Savage doing as she was asked if she was reminded that Louisa was a nurse.\n\nAt exactly ten o'clock, Louisa tapped on the door and went in, put the tea tray down by the bed and drew the curtains. Miss Savage wakened slowly, looking very pretty but just as listless as the previous evening. She sat up slowly without answering Louisa's cheerful good morning, merely: 'What a hideous uniform\u2014it doesn't do anything for you at all, but I suppose you'd better wear it\u2014that doctor's coming this morning.'\n\n'Then you'd better stay in bed when you've had your breakfast,' said Louisa cheerfully, ignoring the bit about the uniform. 'He'll want to examine you, I expect.'\n\nMiss Savage yawned. 'I don't want any breakfast.'\n\n'Coffee? Rolls and butter and black cherry jam?' invited Louisa. 'I'll bring it anyway.'\n\n'Not for ten minutes.'\n\nIt was amazing what those ten minutes did for her patient. Miss Savage was leaning back against her pillows, looking quite different, positively sparkling. What was more, she drank her coffee, ate a bit of roll and then went to have her bath without any fuss at all. Louisa made the bed and tidied the room and had Miss Savage back in it seconds before the door bell rang.\n\nDoctor Hopland was elderly, portly and instantly likeable. His English was almost accentless and he appeared to be in no hurry. He listened to Louisa's rather scant information about her patient, nodded his head in a thoughtful way and observed that beyond keeping an eye on Miss Savage he thought there was little he could do. 'I have had notes of the case,' he told Louisa. 'Unhappily there are many such these days and you will understand that there is not a great deal to be done. Miss Savage is co-operative?'\n\nIt was hard to give an answer to that. Louisa said slowly: 'On the whole, yes, but she does like her own way...'\n\n'I understand. Well, nurse, all you can do is to persuade her to eat good wholesome food and rest whenever she is tired, and as well as that get her into the fresh air. She is in bed, I take it?'\n\n'I thought you might like to examine her, doctor.'\n\n'Certainly. Shall we do that now?'\n\nMiss Savage submitted very nicely to Doctor Hopland's services, in fact she was so meek that Louisa was astonished, but not nearly as astonished as she was an hour later, when Miss Savage, whom she had left reading a book in bed, came into the sitting room and declared that she was going out to see something of Bergen.\n\nSo they spent an hour or two looking at the shops and Miss Savage bought several expensive trifles and an armful of books which Louisa was given to carry. 'And how about a bottle of sherry in case anyone calls?' asked Miss Savage gaily. 'And don't frown like that, Louisa, I know I mustn't drink it. I wonder where we buy it?'\n\nThey couldn't see a drink shop and, on reflection, Louisa couldn't remember having passed one, so she went into the bookshop they had just left and asked one of the assistants.\n\n'The nearest one is on the other side of Torget, quite a walk away, and there are quite a lot of restrictions\u2014you can only buy drinks at certain hours.' She glanced at her watch. 'They're closed now and don't open until this evening.'\n\nMiss Savage's voice was high and peevish. 'I never heard such nonsense\u2014you must get it then, I suppose.'\n\n'Is it so urgent?' asked Louisa. 'I mean, do you know anyone here who's likely to come to see you?'\n\nThey were walking back to the flat. 'That's beside the point and no business of yours,' said Miss Savage nastily. The charming mood of the morning had quite gone, as Louisa expected, and she had a difficult afternoon and an even worse evening, with her patient lolling on the sofa, refusing meals and playing the tape recorder far too loudly. It was a relief when she was told to go and buy the sherry.\n\nShe didn't hurry. It was good to get away from the flat; besides, she was hungry, for she hadn't been given the time to eat her own meal at midday and when tea came, Miss Savage had demanded this and that so that by the time it had been poured out, it was tepid. So now Louisa whipped into a snack bar, had a coffee and a large satisfying bun, and feeling much better, walked on down to the harbour, along Torget, with its mediaeval houses lining the pavement, and then turned up the side street whose name she had carefully written down, and found the off-licence.\n\nIt seemed a great fuss for one bottle of sherry, she decided as she walked briskly back again. It was cold now, but the shops, although closed, were still lighted and there was still a lot of traffic. She went indoors reluctantly; Eva would be gone by now and if Miss Savage was still so peevish she saw little hope of enjoying a pleasant supper.\n\nMiss Savage was sitting at the window, watching TV and so amiable that Louisa almost dropped the bottle in surprise. What was more, her patient made no difficulties about supper. She sat down to the table and even though she ate almost nothing of it, pushed the beautifully cooked cod round the plate, chatting with the utmost good nature while Louisa thankfully ate. She went to bed presently, leaving Louisa to clear the table and then sit writing letters until she went to bed herself.\n\nOn the whole, not a bad day, thought Louisa as she laid her head on the pillow and in no time at all, slept dreamlessly.\n\nAnd that first day seemed to set the pattern of all their days for the next week. Miss Savage was unpredictable, of course, but Louisa had got used to that by now; she could cope with the near-hysterical condition her patient would work herself into within minutes. She even got her to eat at least a little of each meal and, for a time each day, go for a walk. It was a pity that Miss Savage had no interest in museums and no desire to take the funicular to the top of the mountain behind the town and walk around and admire the view which Eva assured them was spectacular. Louisa promised herself that when she had some free time to herself, she would do just that. There was a restaurant there too, so that she might even possibly have her lunch there. And though the tourist trips had ceased, there were regular small steamers going to Stavanger and Haugesund and several of the fjords not too far distant. Presumably they ran all through the winter. Coming back one evening from posting letters, Louisa decided that with her first pay packet she would invest in a thicker quilted jacket; a sheepskin one would have been nice, but she didn't think she would have enough money for that. She was certainly going to buy a couple of thick knitted sweaters with their matching caps and gloves; she had already bought wool and needles and embarked on a long scarf, and judging by the cold crisp air, she would be glad of it soon enough.\n\nIt surprised her rather that Doctor Hopland hadn't called to see his patient again. True, he had told her to telephone if she was worried at all, and she supposed that there was little that he could do. She carefully checked her patient's temperature and pulse each day, saw that she took her pills and did her best to see that she led a quiet pleasant life, but she felt uneasily that she wasn't earning her salary. On the other hand, if Miss Savage should take a turn for the worse, at least she would be there to nip it in the bud and get the doctor at once.\n\nShe found such a possibility absurd when she got back to the flat. Miss Savage was sitting in the big chair by the window, playing Patience with such an air of contentment that it was hard to imagine she had anything wrong with her at all. She was charming for the rest of the evening too and astonished Louisa by saying that she should have most of the next day to herself. 'Go out about eleven o'clock, once I'm up,' she suggested, 'and don't come back until it begins to get dark\u2014about four o'clock. I shall be fine\u2014I feel so much better, and Eva can get my lunch before she goes, and you know I like to take a nap in the afternoon.'\n\nLouisa looked doubtful. 'Suppose someone calls or telephones during the afternoon\u2014there'll be no one there except you.'\n\nMiss Savage shrugged her shoulders. 'I shan't bother to answer\u2014they can call again, can't they?'\n\nLouisa went to bed quite prepared to find that in the morning her patient would have changed her mind. But she hadn't. Indeed, she got up earlier than usual after her breakfast and urged Louisa to go out as soon as they had had their coffee. 'And mind you don't come back until four o'clock,' she called gaily.\n\nLouisa, walking smartly through the town towards the cable railway, reviewed the various instructions she had given Eva, worried for a few minutes about Miss Savage being by herself and then forgot it all in the sheer joy of being out and free to go where she liked for hours on end.\n\nThe funicular first, she had decided, and a walk once she reached the mountain top, then lunch and an afternoon browsing among the shops. There was a large department store she longed to inspect, but Miss Savage hadn't considered it worth a visit. And she would have tea at Reimers Tea Rooms, which Eva had told her was the fashionable place for afternoon tea or morning coffee. There was a great deal more to see, of course, she would have to leave Bergenhus Castle until the next time, as well as the Aquarium and Grieg's house by the Nordasvann lake, not to mention the museums. She hurried up the short hill which took her to the foot of the funicular, bought her ticket and settled herself in the car with a sigh of pure pleasure.\n\nIt was wonderful. She had never experienced anything like it\u2014she had a good head for heights and craned her neck in all directions as the car crawled up the face of the mountain, and at the top she was rewarded by a view of the fjords and mountains to take her breath and when she had got it back again she walked. There were paths everywhere, and everywhere mountains and lakes and scenery to make her eyes widen with delight, and when at last she was tired, she lunched in the restaurant\u2014soup and an omelette and coffee\u2014and then went back down the mountain in the cable car.\n\nIt was early afternoon by now, but the flat wasn't more than ten minutes' walk away from Torgalmenning. Louisa walked slowly, looking in shop windows at the silver jewellery, porcelain and beautifully carved wood, took another longer look at the winter clothes set out so attractively in the boutiques and came finally to Sundt, the department store, where she spent half an hour browsing from counter to counter, working out prices rather laboriously, deciding what she would buy later. It was almost time to go back to the flat; she would have time for a cup of tea first, though. She found the tea room without trouble and sat down at one of the little tables. It was already crowded with smartly dressed women, and Louisa, once she had overcome the few small difficulties in ordering a tray of tea and one of the enormous cream cakes on display, settled down to enjoy herself. She even had an English newspaper, although as she read it England seemed very far away.\n\nShe got up to go reluctantly, but content with her day; even the thought that Miss Savage might be in one of her bad moods didn't spoil her feeling of well-being. In fact she was quite looking forward to telling her about her outing. This happy state of mind lasted until she opened the door of the flat and started up the stairs. There were voices, loud angry voices, and then Miss Savage's all too familiar sobbing. Louisa took the rest of the stairs two at a time, opened the inner door quietly and made for the half open sitting room door. Miss Savage was lying on the sofa, making a great deal of noise. She had been crying for some time if her puffy pink eyelids were anything to go by and from time to time she let out a small gasping shriek. She saw Louisa at once and cried in a voice thick with tears: 'Louisa\u2014thank God you've come!'\n\nLouisa took stock of the man standing by the sofa. He was tall and spare, with dark hair and an aquiline cast of feature. Moreover, he looked furiously angry, in a towering rage in fact, so that she took a deep breath before she spoke.\n\n'I don't know who you are, but you will be good enough to go at once. Miss Savage has been ill and whoever you are, you haven't any right to upset her in this way.' She held the door open and lifted her chin at him and met dark eyes glittering with rage.\n\n'The nurse?' His voice was crisp. 'I'm Miss Savage's brother, and since this is strictly a family argument, I will ask you to mind your own business.'\n\n'Well, I won't,' said Louisa stoutly. 'You may think you can bully her, but you can't bully me.' She opened the door a little wider. 'Will you go?'\n\nFor answer he took the door away from her and shut it. 'Tell me, what is my sister suffering from, Nurse? Did the doctor tell you? Did she explain when you were engaged? And the doctor here? Has he said anything to you?'\n\nLouisa opened her mouth to speak, but Miss Savage forestalled her by uttering a series of piercing cries and then dissolving into fresh sobs. Louisa brushed past the man, wiped Miss Savage's face for her, sat her up against the cushions and only then turned her attention to him.\n\n'Your sister has a blocked bile duct, she also has dyspepsia. That's a kind of severe indigestion,' she added in case he didn't know, 'I believe you wanted her to come to Norway, presumably to convalesce. We had made some progress during the last week, but I doubt if your visit has helped matters at all. Quite the contrary.'\n\nIt was annoying to see him brush her words aside as though they didn't mean a thing. 'You're young. Recently trained, perhaps?'\n\nShe supposed she would have to answer him\u2014after all, it was probably he who was paying her fees. 'About six weeks ago.'\n\nHis laugh wasn't nice and she flushed angrily. 'Probably you're a good nurse,' he observed in a voice which gave the lie to the statement, 'but you're inexperienced\u2014just what Claudia was looking for.'\n\n'I don't know what you mean.'\n\n'No? I suggest that you put Claudia to bed\u2014she must be exhausted after such a display of emotion. Tell Eva to give her some tea and then come back here. I want to talk to you.'\n\n'I don't think there's much point in that.'\n\nHis voice was soft. 'Probably not, but I must point out that I employ you, even if it was my sister who engaged you.' He went to the door and opened it and stood waiting. He had his temper under control by now, and he looked dangerous. Louisa helped Miss Savage on to her feet and walked her out of the room. She said in a voice which shook only very slightly: 'You're despicable, Mr Savage.'\n\nHe gave a short laugh. 'Shall we say half an hour, Nurse?'\n\nShe didn't answer.\n\n## CHAPTER THREE\n\nHALF AN HOUR wasn't nearly long enough in which to regain her cool, thought Louisa, and walked, outwardly composed and inwardly quaking, into the sitting room. Mr Savage was standing at the window, looking out and jingling the loose change in his pockets, and she brightened a little. Perhaps he had recovered from his nasty temper\u2014but when he turned round she saw with regret that she was mistaken; his mood was as black as ever although at the moment he had it under control. She didn't much care for the iciness of his voice when he spoke, though.\n\n'Ah, Nurse, I was beginning to wonder if your courage had deserted you.'\n\nLouisa was, for the most part, a mild-tempered girl, prepared to give rather more than she took, but only up to a point. 'I can't quite see,' she observed in a reasonable voice, 'what I have to be courageous about. True, I dislike being bullied, but a loud voice and a nasty temper don't count for much, when all's said and done.'\n\nShe crossed the room and sat down on a small hard chair because it was easier to be dignified like that. Her companion's eyes narrowed. 'Clever, are you?' he wanted to know. 'I've a few questions to ask, and I want truthful answers.'\n\nShe stared back at him. 'I can lie with the best of them,' she assured him, 'but never about patients.'\n\nHe laughed unpleasantly. 'I'll have to take your word for that. Tell me, why did my sister engage you?'\n\nHer eyes widened. 'Well, she wanted a nurse to accompany her here.'\n\n'There were other applicants?'\n\n'Oh, yes\u2014she told me, but they were all older and she wanted someone younger.'\n\n'Ah, and inexperienced.'\n\nShe let that pass. 'Why?'\n\n'I'm asking the questions, Nurse. What's your name?'\n\n'Evans\u2014Louisa Evans.'\n\n'Well, Nurse Evans, presumably you saw my sister's doctor?'\n\n'Naturally, and he gave me my instructions and informed me as to the nature of Miss Savage's illness.'\n\nHe gave her a sharp look, eyebrows lifted in faint surprise. 'So you know all there is to know about her?'\n\nShe surveyed him coolly. So he thought her incapable of doing her job just because she was young and not greatly experienced, did he? She drew a breath and recited the details of her patient's condition, adding kindly, 'If you don't understand the medical terms I'll explain...'\n\nHe turned a fulminating look upon her. 'It would be unwise of you to be frivolous, Nurse Evans. I shouldn't try if I were you.'\n\n'I'm not. You're not a doctor, are you?'\n\n'I'm a civil engineer, I build bridges. The reason I asked you that question may not be apparent to you at the moment.'\n\n'It's not.' She got to her feet. 'At least, I daresay you think I'm not old or wise enough to look after your sister. I hope you feel better about it now. She's making a little progress, or was... I don't know why you had to upset her, Mr Savage, and I don't want to be impertinent, but your visit hasn't helped much, has it?' Her tongue tripped on, speaking the thoughts she had no intention of uttering. 'I can't for the life of me think why she had to come to Norway. She must have a home somewhere in England; I don't believe she lives in a London hotel; she told me that she came because you made her...but there's no reason for that, surely? You work miles away, don't you?'\n\nHe had come to stand close to her, his face expressionless, but all the same Louisa had an urge to retreat behind the nearest chair, sternly suppressed. She had the extraordinary feeling that he was on the point of telling her something and at the last minute changed his mind. When he did speak it was to say: 'I wanted her to be nearer to me so that I could visit her easily. I should perhaps explain that we're not the best of friends, Nurse Evans. Claudia is my stepsister, she's only a little younger than I, and we met for the first time when my father married her mother, who had been a widow for some years. We are, in fact, not related\u2014all the same, as we bear the same name I feel some responsibility towards her.' He looked down at her and actually smiled\u2014a thin smile. 'She's been seen by a doctor since you arrived here? I did arrange...'\n\nLouisa said impatiently: 'Yes, the doctor came. I have his phone number and he'll call again in a week's time.'\n\n'He gave you no further instructions?' Mr Savage's deep voice sounded curt.\n\n'No, none at all. He told me to carry on as before and to call him if I was worried about anything.'\n\nHe moved away from her at last and went to stand at the window again, half turned away from her. 'There seems little point in staying,' he said at length, and turned to look at her, frowning. 'I'm not sure if I'm doing the right thing...'\n\n'Well, you are,' said Louisa firmly. 'You upset Miss Savage and I can't think why you came if you don't get on together\u2014you could have telephoned.'\n\n'My dear good girl, we're talking at cross purposes.' He started for the door. 'I shall telephone from time to time and I shall expect a report from you.' He paused, took a notebook from his pocket, scribbled a number in it and tore out the page. 'You can reach me at this number if you should need to.' He saw her face and gave a crack of laughter. 'Something you don't intend to do; you think I'm a tyrant and a bully...'\n\n'As a matter of fact, I do,' said Louisa in a matter-of-fact voice. All the same, the room seemed empty and rather lonely when he had gone.\n\nA small sound made her turn her head; Miss Savage was standing in the doorway. 'He's gone?' She gave a sly smile. 'I'm not really like that, you know, Louisa\u2014making such a fuss\u2014I wanted him to go away, you see.' She twisted her hands together and added in a wheedling voice: 'You're not cross, are you? Was he very rude to you?'\n\nFor some reason Louisa found herself saying no when she should really have said yes. She said mildly: 'I think your brother only came to see if you were settled in\u2014I'm sure he has your interest at heart; he wanted to know just how you were...'\n\nMiss Savage gave a giggle. 'I bet he did! Did he ask about my friends? The ones who came over with us?'\n\n'No.' Louisa wasn't sure if she liked Miss Savage in this mood.\n\n'Oh, good. I didn't tell him and I didn't have time to ask you not to mention them. He doesn't like them.'\n\nUnderstandably so, thought Louisa; she didn't like them herself.\n\n'Well, he won't be coming again for ages,' said Miss Savage in a satisfied voice. 'They've just started another bridge somewhere at the back of beyond and once the snow comes travelling around isn't all that easy.'\n\nLouisa thought otherwise. There were domestic flights all over the country; she had collected handfuls of leaflets from a travel agency because she had an inquisitive mind that liked to know about such things. Besides, the friendly woman at the newspaper kiosk had told her that there was a daily steamer that sailed the entire length of the country, right to the Russian border, and back again, calling at dozens of isolated villages. Louisa didn't think that the snow made much difference to the Norwegians\u2014after all, they'd lived there for hundreds of years and by now would know how to deal with their weather. It did put her in mind of something else, though. 'Will we be staying here all winter?'\n\n'Fed up already?' demanded Miss Savage apprehensively. 'I'll make him pay you more... Don't go, Louisa.'\n\nLouisa smiled at her patient. 'I don't intend to, and I'm not in the least fed up. I think it's marvellous here. The reason I asked was because I'll have to buy some thicker clothes; it's almost November and I thought I'd get one of those quilted coats and some lined boots.'\n\n'Oh, is that all?' Miss Savage had picked up a copy of Harpers and was turning the pages. 'Why don't you get a fur coat? You'll get your wages in just a couple of weeks\u2014Simon said something about it, but I wasn't listening. I expect you know when it's due to be paid? You have to go to the Bergen Bank and ask for Mr... He wrote the name down somewhere.' She turned the magazine over: 'Here it is, written on the back\u2014Helgesen.' She added mockingly. 'Simon seemed to think you needed someone to keep an eye on your money, I suppose. The tight-fisted so-and-so!' Her voice became full of self-pity. 'He's got more money than is good for him and he gives me barely enough to live on.'\n\nProbably he was mean, thought Louisa; he certainly was unpleasant enough to add meanness to his faults, but after all, Miss Savage lived in great comfort and if a mink coat and hand-made Italian shoes were anything to go by, not to mention the luxurious flat in which they lived at present, then her ideas of meanness and Miss Savage's weren't on the same plane.\n\n'My room's in rather a mess.' Miss Savage looked up briefly from her magazine. 'Be a good girl and tidy it for me, will you? I'm exhausted.'\n\nLouisa went. Miss Savage was bone idle, but she had been ill. Louisa knew from experience that getting over an illness was as bad in some ways as actually being in the throes of one. The room looked as though it had endured an earthquake. Miss Savage had wreaked her rage on the soft furnishings to an alarming degree; the bed had its pillows flung in all directions as well as the duvet; there wasn't a cushion in its rightful place and not only had a bottle of perfume been smashed to bits but a jar of one of the expensive creams Miss Savage used had been flung on to the carpet, making a very nasty mess.\n\nLouisa set the room to rights and spent a long time clearing up bits of glass and lumps of face cream. By the time she got back to the sitting room, Miss Savage was asleep, the magazine fallen to the ground. Louisa stood looking at her and thought how very pretty she was, even with her mouth open. She frowned a little, because the prettiness seemed somehow blurred round the edges and was beginning to sag a little, but that was probably because Miss Savage had cried so long and so hard. She would let her sleep for another hour while she went to see what Eva had got for their supper, and presently when she wakened her patient, she was relieved to find that she seemed to have recovered completely from the afternoon's upset. Indeed, Miss Savage spent most of the meal planning their next few days. Rather to Louisa's surprise she suggested that they might visit the Museum of Arts and Crafts\u2014already several of the museums had closed for the winter\u2014and if they enjoyed it, they could visit the rest during the weeks ahead. 'Because there's nothing much else,' she declared. 'Piano recitals, if you like such things, and the cinema\u2014I'll need some new clothes too.' She yawned. 'It's going to be deadly here,' and at Louisa's enquiring look: 'Oh, I can't go back to London, Simon will stop my allowance if I do.' Her voice became plaintive. 'I depend on it utterly.'\n\n'Well, once you're quite well again,' began Louisa, feeling her way, 'could you get a job? You know all about clothes and some of those boutiques must be super to work in.'\n\nShe was rewarded with a look of horror which was quite genuine. 'Me? Work? My dear Louisa, you must be out of your tiny mind! I couldn't possibly\u2014I mean, it's all right for someone like yourself, presumably you expected to have to earn your living; even after you get married your sort usually do a job, don't you? I should die!' And just in case Louisa didn't see her point, she added pettishly: 'I'm still far from well.'\n\nThere was no point in arguing. Louisa went away to warm the soup Eva had left and inspect the contents of the casserole in the oven. She still didn't like Miss Savage, but she was sorry for her too; she was missing such a lot of fun. Who would want London anyway? As far as Louisa was concerned anyone could have it, just so long as they left her Bergen to explore. And there was plenty to do: the theatre, cinemas, some wonderful shops and caf\u00e9s, and, she hoped, the chance to ski; she had asked about that and been told that there were ski slopes not far away where she could be taught...once she could get Miss Savage to agree to her having a free day at least once a week. She set supper on the table and made soothing conversation with her patient and presently helped her to bed, since she had become lachrymose again.\n\nBut by the morning she was once more her normal self, eating little, it was true, and disinclined to get up, but once she was dressed, Louisa persuaded her to put on her mink coat and its matching cap and go into the town with her. It was a bright day but cold, and they went first to Riemers for their coffee before spending an hour wandering about the shops. The visit to the museum had been forgotten, of course, but Louisa was glad that Miss Savage was at least out of doors, taking an interest in things, and just for once not grumbling; indeed, over lunch she insisted that Louisa should have the afternoon off. 'Because it's getting cold and you'd better get that coat you were talking about. I hope you have enough money, because I've got none,' she finished carelessly.\n\nSo after settling her on the sofa with a pile of paperbacks and a light rug, Louisa went off on her own. She knew what she was going to buy. She had seen just what she wanted in Sundt's department store and she went straight there; a quilted jacket with a fleecy lining and a hood. She chose a green one with a brown lining and teamed it up with thick brown slacks and leather boots, then added a thick wool sweater to wear with it and matching mitts and cap. They all added up to a quite formidable sum, but she hadn't spent more than a handful of kroner since they had arrived and pay day wasn't far off. Feeling pleased with herself, she walked the short distance to Riemers and had tea, then started for the flat. It was almost dark by now and the sky had darkened; there had been snow for some weeks in the north of the country, a friendly waitress had told her, and any day now it would snow in Bergen. Louisa sped through the brightly lighted streets, dreaming of skiing and wishing she could get away for long enough to visit some of the nearby islands by the local steamers.\n\nAs she neared the flat she saw that its windows blazed with lights and a slight unease jellied into horrible certainty as she opened the door. Miss Savage had visitors; Louisa could hear their loud voices and louder laughter as she went up the stairs. She didn't need to open the door to know who they were.\n\nThe three of them turned to look at her as she went in across a room hazy with cigarette smoke. They all held glasses in their hands too, although Miss Savage, sitting on the arm of a chair, had nothing in hers.\n\nLouisa was greeted with shouts of welcome and when they died down Miss Savage called: 'Aren't I good, Louisa? No drinks, but you see how useful that bottle of sherry is being.' She giggled and they all laughed with her except Louisa, who, aware that she was being stuffy, nonetheless was unable to laugh. It was curious that the first thought that entered her head had been concerning Mr Savage; he would be furious if he knew that these rather wild friends of his stepsister's had arrived; without even asking she knew that he would never approve of them. When the hubbub had died down a little she said hullo in a pleasant cool little voice, refused a glass of sherry and waited to see what would happen next.\n\nIt was the woman who spoke\u2014Connie someone or other. She had a strident voice in which she was doing her best to make conciliatory talk. 'How marvellous our Claudia looks, nurse\u2014you're to be congratulated. We just had to see how she was getting on\u2014we're staying a couple of nights at the Norge. You'll let her come out to dinner this evening, won't you? We'll take great care of her.'\n\nIt was obvious to Louisa that it wouldn't matter what she said. Miss Savage would go if she had a mind to. She said briskly: 'Of course I don't mind, only don't be too late back, please.' She saw them exchange glances and knew exactly what they were thinking: that she was a bossy young woman who liked ordering people about. If she had said that on a hospital ward they would have accepted it without a murmur. 'And don't wait up,' said Miss Savage. 'Be an angel and run a bath for me, will you? I simply must change.'\n\nEva brought everyone coffee while they were waiting and presently Louisa excused herself on the plea of consulting with Eva about the next day's meals, and from the kitchen she was called to help Miss Savage fasten her dress, a curiously quiet Miss Savage, hardly speaking and then in a hesitant fashion.\n\n'Do you feel all right?' asked Louisa in a casual voice. 'If you'd rather not go, I'm sure Eva and I can get a meal for you all here.'\n\nMiss Savage was busy pinning a brooch in place. 'Of course I'm all right\u2014don't fuss, for God's sake.' She caught up the mink coat. 'I get little enough fun.'\n\nThe flat was gloriously peaceful when they had gone, and presently, when Eva had left for the day, Louisa went along to the kitchen and got her supper, then carried it through to the sitting room and ate it in front of the TV, not really watching it, but it was company. Not that she was lonely; she had plenty to occupy her thoughts, and at the back of her mind a nasty nagging worry that there was something wrong about Miss Savage. Looking back over the days, Louisa realised that her behaviour wasn't consistent; as bright as a button for an hour or so and then listless; bursting into tears for no reason at all and at other times so irritable. She worried round the puzzle like a dog with a bone and came no nearer the answer.\n\nIt was almost ten o'clock when the phone rang and she hurried to answer it. Miss Savage in the throes of dyspepsia, or suffering a violent headache. She lifted the receiver and the very last voice she wanted to hear spoke.\n\n'Nurse Evans? I should like to speak to my sister.'\n\nLouisa readjusted her thoughts. 'Good evening, Mr Savage. I'm afraid Miss Savage isn't here\u2014she's out with friends.'\n\nHis voice was sharp. 'You know these friends, Nurse?'\n\nShe said thankfully: 'Oh, yes\u2014they're from England,' and then wished she hadn't spoken. Miss Savage hadn't wanted him to know about their trip over with her, probably she wouldn't want him to know that they had come again, but it was too late now. The voice, no longer sharp but definitely unpleasant, went on: 'When did they arrive?'\n\n'While I was out this afternoon.' She could have cut through the heavy silence with her scissors.\n\n'You say you know these friends?' It was like being cross-examined.\n\n'I met them in London at Miss Savage's hotel.'\n\nHis voice had become silky. 'Ah, yes, just so. Connie, Willy and Steve\u2014I'm right?'\n\nLouisa gave a great sigh of relief. 'Oh, good, you know them, so that's all right.'\n\n'I know them, Nurse Evans, and it is not all right. These friends are one of the reasons why I wanted Claudia to come to Norway\u2014you must have seen how unsuitable they are for someone in her...' he hesitated, 'state of convalescence, and why did you not go with her?' He was coldly condemning.\n\n'Because I wasn't asked,' snapped Louisa. 'I'm not your sister's keeper, you know.'\n\nHe said, 'I beg your pardon,' with cool insincerity. 'You don't know how long they're staying in Bergen?'\n\n'They mentioned two nights at the Norge\u2014that's a hotel...'\n\n'I'm well aware of that, Nurse. You will endeavour to stay with her as much as possible until they leave. I'm unable to get away from here at the moment, so I must rely on you.' His tone implied that he was expecting the impossible.\n\nShe said stiffly: 'I'll do what I can, Mr Savage,' and was rewarded by a disbelieving grunt and the click of the receiver.\n\nLouisa marvelled at his rudeness. 'Almost as bad as Frank in quite a different way,' she observed out loud, and sat down to wait for Miss Savage to come home.\n\nIt was almost midnight when she did and even then her friends seemed to think that they should come in for a last drink, but Louisa, standing at the door, wished them a firm goodnight and shut it equally firmly. Miss Savage had had a splendid evening, she told Louisa, the food had been delicious and she had drunk only one glass of white wine. 'You see how good I am,' she observed as Louisa helped her to bed. 'I'm going to have lunch there tomorrow and drive out to Troldhaugen to see Grieg's house. You won't want to come, of course?'\n\n'I should like to come very much,' said Louisa quickly, aware as she said it that it was the last thing Miss Savage wanted. 'It's kind of you to ask me.'\n\nOut of the corner of her eye she could see Miss Savage's face screwed up with temper.\n\nThere was, Louisa decided at the end of the next day, nothing worse than being an unwanted guest. The expressions on the faces of Miss Savage's friends when they called for her in the morning were bad enough, but Miss Savage's ill temper was even worse. Louisa, mindful of Mr Savage's orders, resolutely ignored the cold shoulders, the snide remarks and the sidelong glances\u2014indeed, being a sensible girl, she ate her lunch with pleasure: lobster soup, cod cooked in a delicious sauce with crisp little potatoes and a sea of vegetables, followed by ice cream heaped with honey, fudge and lashings of whipped cream were things to be enjoyed in any circumstances. And afterwards she sat in the back of the hired car, squashed into a window and totally ignored, until they reached Grieg's cottage home on the shore. The house was shut now that it was winter, but it was quite beautiful by the fjord. Miss Savage, her arm in Connie's, wandered off with the two men behind them, calling to Louisa over her shoulder: 'There's a grave somewhere, if you're interested, Louisa, and a stave church in those woods\u2014it's only a few minutes' walk, so I'm told,' she added mockingly. 'Don't worry, we won't go without you.'\n\nSo Louisa went off on her own, walking fast because even in the new quilted jacket it was cold. She found the composer's grave, and his wife's beside it, and then followed the path to the church. Its strange pointed roof reminded her of an Eastern temple without the trimmings and she would have liked to see the inside too, but there again the season was over; it would stay quiet and solitary until May when the tourists would come again. She was glad she had seen it in winter, though. If she had the chance, she would come again, preferably when the snow had fallen. And that wouldn't be long now, judging by the thick grey sky, already darkening into an early evening.\n\nLouisa was surprised when Miss Savage refused to spend the evening with her friends. She was, she declared, tired and intended to go to bed early\u2014and indeed, when they had gone she asked, quite nicely too, if Louisa would bring her some tea, and settled on the sofa where she presently fell asleep, leaving Louisa to drink her tea sitting by the window, watching the first of the snow falling. And when she woke up an hour later, she was still pleasant. 'I think I'll go to bed before supper,' she declared, and yawned prettily. 'It's been quite a day\u2014but fun. They're going back tomorrow. Louisa, I want you to go to that wine shop and get another bottle of sherry\u2014I know we don't get many visitors, but there's none in the place now and probably the doctor will have a glass next time he comes.' She got up and stretched her arms above her head. 'I'll have a bath now.' She strolled to the door. 'Was my brother angry when he phoned yesterday?' Her voice was very casual.\n\nLouisa considered. Mr Savage always sounded angry, in her opinion. 'Surprised,' she essayed, 'anxious that you wouldn't get tired or spoil your good progress\u2014no, I don't think he was particularly angry. I'm sorry I mentioned your friends. He asked me where you were, you see, and I had to answer.'\n\nMiss Savage darted a sidelong glance at her. 'Of course,' she smiled. 'You don't have to worry about it\u2014you did tell him they were leaving tomorrow, didn't you?'\n\n'Yes.' Louisa had got to her feet too. 'I'll get your bath going, shall I? Is there anything special you'd like Eva to cook for your supper?'\n\n'I'm not hungry\u2014we had an enormous lunch, lots of coffee and an omelette.'\n\nButter wouldn't have melted in Miss Savage's mouth for the rest of that evening, and it was the same next morning, which she spent lying in bed reading. It was after an early lunch which she took in her bed that she urged Louisa to go and get the sherry. 'It'll be dark soon,' she pointed out, 'and it's going to snow again\u2014you'd better go while you can.'\n\nSo Louisa buttoned herself into her thick jacket, pulled her woolly cap well down over her ears and set out happily enough. It was nice to be out in the clear icy air after the centrally heated flat, and the snow, crisp and white, made the whole town sparkle under leaden skies. There would be more snow and Louisa looked forward to it. The shop was on the other side of the harbour and she walked briskly through the main streets, their shops already lighted, pausing here and there to take a look in the windows. Miss Savage had told her not to hurry back, had even urged her to go and have a cup of coffee on her way back, and there was time enough before tea. Louisa was glad that Miss Savage had elected to stay in bed after the excitement of her friends' visit. They hadn't stayed long enough to do any harm, but on the other hand they hadn't been all that good for her\u2014besides, Mr Savage didn't approve of them. Probably he didn't approve of anything much, only bridges.\n\nThe shop was only open for a short time each day. She bought the sherry and started back again, stopping on the way to buy an English newspaper and post some letters. It was still only mid-afternoon and already almost dark, but the streets were alive with people and there was plenty of traffic. She turned down past the Hotel Norge and crossed the little garden in the centre of the square and went into Riemers. It was full and cheerful. Louisa ordered a tray of tea instead of the coffee she usually had, and chose a large cream cake to go with it, eating it slowly while she scanned the headlines of the paper. It was quite dark by the time she went into the streets again and she hurried her steps for the short walk to the flat. Miss Savage's light was on, she saw with relief as she opened the door; probably she was still having her afternoon nap. She went in quietly and peered round the half open door.\n\nMiss Savage was fast asleep, breathing rather thickly, her face flushed. Louisa went close to the bed and bent down to look at her closely and was greeted by a heavy waft of some cloying perfume she didn't like. Disconcertingly, Miss Savage opened her eyes.\n\n'Snooping?' she asked sharply. 'Did my dear stepbrother put you on to that?'\n\nLouisa straightened up. 'Certainly not! He suggested no such thing. You were sleeping so heavily and you looked flushed, I thought you might have a feverish cold.'\n\nMiss Savage replaced the scowl on her face by a sugary smile. 'You really do look after me well, Louisa. I'm just tired and I suppose I've lain in bed too long. I'll get up.'\n\nShe was amiability itself for the rest of the evening, praising their meal although she ate almost none of it, and full of more plans for the days ahead, and afterwards as they sat, Louisa with her knitting and she leafing through a magazine, she said something suddenly. 'I forgot something today\u2014you'll have to go to the bank tomorrow morning and get some money for me. You won't need a cheque\u2014they've got instructions to pay the miserable pittance Simon allows me.' She nodded carelessly. 'And isn't it time you had some wages?'\n\n'Next week,' said Louisa, frowning over a difficult bit of pattern.\n\nPresently Miss Savage tossed her magazine down. 'How fast you knit.'\n\n'It's not difficult and very soothing. Would you like to try\u2014or do some of that gorgeous embroidery everyone seems to do here?'\n\n'Lord no\u2014I'd be bored in minutes.' Miss Savage yawned. 'I'm going to bed. You know, the thought of a whole winter here sends me round the bend. I could kill Simon!' She floated away, saying over her shoulder: 'Don't come near me until ten o'clock tomorrow, that's time enough for my coffee.' She didn't say good-night, but then she wasn't one for the small courtesies of life.\n\nShe was bright-eyed and in a splendid mood when Louisa took her coffee in the morning. 'I feel marvellous,' she declared. 'Go and put on your things and go to the bank, will you? I must pay Eva and there are a lot of food bills...'\n\nIt had been snowing again and it wasn't really light yet, but Louisa found it exciting crunching through the snow in her new boots and despite the winter weather the town looked bright and bustling. The Bergen Bank was an imposing building even from the outside. She climbed the wide steps to its enormous doors and went in, to find it even more so on the inside. It was vast with a lofty ceiling, a great many bright lights, and heavy furnishings. She approached the friendliest-looking clerk at the counter and handed him Miss Savage's note, and was rewarded by an instant smile.\n\n'You need to see Mr Helgesen,' he told her, and pinged a bell beside him, and she was led away down a wide corridor to another lofty room, much smaller this time and furnished with a large desk with a youngish man sitting behind it. He got up as she was ushered in and shook hands, which gave her a chance to study him. A nice face, rugged and good-natured, with blue eyes and close cropped hair. He was stoutly built and a little above middle height, and she took to him at once, and even more so at his friendly voice.\n\n'Miss Evans? Simon Savage told me of you.' He glanced at the note the porter had given him. 'You need money for Miss Savage?'\n\n'Please, she wants to pay her household bills.'\n\nThere was a little pause before he said: 'Of course. I'll arrange for you to collect the money she requires. Now sit down for a minute and tell me what you think of Bergen.'\n\nHe was the easiest man to talk to. Louisa hadn't realised how much she had missed being able to talk to someone\u2014one couldn't count Miss Savage, who never wanted to talk about anything but clothes and her own discontent... She had been talking for several minutes before she stopped herself with an apologetic: 'I'm sorry, I'm wasting your time and Miss Savage will wonder where I've got to.'\n\nThey walked to the door together and shook hands, and she felt a small thrill of pleasure when he observed: 'I've enjoyed meeting you, Miss Evans. I hope we shall meet again soon. If you need help of any sort please don't hesitate to call upon me.'\n\nShe beamed back at him. 'You're very kind. I'll remember that.'\n\nThe money safely in her purse, she went out into the cold again, not noticing it because she was wrapped in a warm glow of pleasure. To stay in Bergen for the entire winter was suddenly inviting.\n\nShe was crossing the street in front of Sundt's store, the pavement crowded with shoppers, when she thought she glimpsed the young woman Connie ahead of her, but the traffic lights changed and by the time she was on the opposite side of the pavement there was no sign of her. It couldn't possibly be her, anyway; she and the two men with her had gone back to England several days ago. Louisa, walking happily through the snow back to the flat, didn't think any more about her.\n\n## CHAPTER FOUR\n\nLOUISA REMEMBERED her mistaken view of Connie later that day. Miss Savage had been remarkably quiet, even drowsy all the afternoon, and over their cups of tea Louisa tried to rouse her interest with undemanding conversation. She was completely taken aback by Miss Savage's reaction to her casual remark that she had imagined that she had seen her friend that morning. Miss Savage's eyes had glittered with rage and she had put her tea cup down so suddenly that most of the tea spilled into the saucer. 'What utter rubbish!' she exclaimed. 'How could you have possibly seen Connie? They're all back home\u2014why can't you mind your own business instead of imagining things which aren't any of your business anyway? Just because you don't like my friends...'\n\nLouisa, soothing her companion as best she could, found her remarks quite uncalled-for and wondered why she had made them; perhaps she was homesick for London and its life and mentioning Connie had triggered it off. Presently Miss Savage had begun to talk, rather feverishly and about nothing in particular, and Louisa had followed her lead.\n\nThe next day or two were passed in a peace and quiet Louisa found surprising and unexpected. Miss Savage was amenable to any conversation made to her and even, when urged, made an effort to eat her meals. The only thing she steadfastly refused to do was to go out. She argued that the snow upset her, that it was far too cold, and that she had no reason to go out anyway. But she insisted that Louisa should go out each day, usually directly after she had taken in her patient's breakfast, 'Because,' as Miss Savage observed, 'it's the one time of day when I don't need anyone\u2014I never get up before eleven o'clock and I like to lie and doze or read.' So Louisa formed the habit of spending the mornings in the town, getting back to the flat round about noon when Miss Savage was usually up and on the point of exchanging her bed for the sofa in the sitting room.\n\nWinter or no, there was a great deal to do, and Louisa happily explored the town in all directions, delighted to find another, not quite as fashionable shopping centre on the farther side of the harbour.\n\nIt was a pity that most of the museums were only open in the early afternoons during the winter, but the Bryggens Museum was open for a few hours each day; she went twice to examine the remains of some of the oldest buildings in Bergen. She went to the Historical Museum at Sydneshaugen too, which meant a bus ride to the other side of the town, but she was beginning to feel so at home now that she planned several longer excursions if the weather allowed and Miss Savage would agree to her having a day off. She had broached the subject once or twice and met with evasive answers, and since she had little to do except act as a companion and see that her patient took her pills, ate a sufficient amount and led a quiet life, she felt that she could hardly complain.\n\nThe snow had stopped on the morning she went to the Bergen Bank to collect her salary. Rather to her surprise Miss Savage had asked her to get some more money at the same time. It had seemed a great deal when Louisa had handed it over such a short time ago; apparently housekeeping was an expensive business in Norway. She went to the same clerk again and was ushered into Mr Helgesen's office.\n\nAnd this time he wasn't alone. Mr Savage was there, sitting in one of the leather chairs. Both men got up as she went in, but only Mr Helgesen crossed the floor to shake hands; Mr Savage contented himself with a curt nod, his severe expression not altering one jot. And two can play at that game, thought Louisa as she turned a shoulder to him and addressed Mr Helgesen. 'I think perhaps the clerk made a mistake. I've only come to collect my salary.'\n\n'No mistake, Miss Evans.' Mr Helgesen looked delighted to see her again. 'Mr Savage wished to see you; he has come specially for that purpose.' He added gallantly: 'Of course I wished to see you, too.'\n\nShe smiled at him rather shyly. 'Thank you. Oh\u2014 I'm sorry, I almost forgot, I have another note from Miss Savage. She asked me to get her allowance while I was here.'\n\nThe two men exchanged glances. 'Did you not collect it when you were last here?'\n\n'Yes.' Louisa frowned a little. 'She said there wouldn't be any difficulty, that I was just to ask...'\n\n'Yes, yes, of course,' said Mr Helgesen soothingly. 'It shall be attended to\u2014if I might have her note?' He went to the door. 'I'll arrange matters with the clerk.'\n\nLouisa didn't much fancy being alone with Mr Savage. 'Couldn't I get it when I get my money?' she enquired, and made for the door, too.\n\n'Miss Evans,' said Mr Savage. His voice was quiet but not to be ignored. 'I wish to speak to you.'\n\nShe faced him reluctantly and saw his smile. It wasn't a friendly smile; she sat down without a word and waited.\n\n'How is my sister?'\n\nIt was a difficult question to answer truthfully, and she hesitated. 'I think she's making slow progress, but she's unpredictable. I mean, her moods vary all the time. But she sleeps well\u2014too much, perhaps\u2014and for the most part she seems content, although she doesn't like living here. She hardly ever goes out, but one can hardly blame her in this weather...'\n\n'You go out?'\n\n'But I like it, I think it's lovely, all the snow and the streets lighted...'\n\n'Spare me your raptures, Miss Evans. Claudia's friends haven't returned?'\n\nShe stared at him in surprise. 'But they went back to England\u2014Miss Savage was very upset.'\n\n'You are sure of that?'\n\nShe hesitated. 'Yes\u2014I should have seen them otherwise. I did think I saw Connie\u2014I don't know her last name\u2014a few days ago, but the pavement was crowded and I lost sight of her. It must have been a mistake.'\n\n'You didn't enquire at the Norge if she was there?'\n\nLouisa said patiently: 'I've just told you\u2014I don't know her name.'\n\nHe stared at her with hard eyes and picked up the phone on the desk\u2014a piece of impertinence, she decided, in someone else's office, too. Who did he think he was?\n\nOf course she didn't understand a word he said, but when he put the receiver down his face was as black as thunder. 'The three of them left yesterday evening.'\n\nShe said, 'Oh, dear,' and his lip curled. 'I shall accompany you back to the flat,' he told her. 'Does my sister expect you back immediately?'\n\n'As a matter of fact she told me to have two hours off because she intended to stay in bed until lunchtime.'\n\n'Just so,' said Mr Savage; she wouldn't have been surprised to have seen him grind his teeth and sighed quite audibly with relief as Mr Helgesen came back into the room. He glanced first at Mr Savage and then smiled at her. 'I have told the clerk to let you have Miss Savage's allowance. Mr Savage has opened an account for you here; he thought it wiser, since you were in a foreign country and might not realise...it is, I think, rather more expensive here than in England. You can draw any amount you wish, of course,' he laughed a little, 'provided there is still some money there.'\n\n'That's very kind of you, Mr Helgesen.' Louisa turned round to face Mr Savage getting himself into a sheepskin jacket. 'And I expect you meant to be kind, too, Mr Savage, but I am capable of managing my own affairs, thank you. I promise you that I shan't run up bills all over the town.'\n\n'And I'm too far away to keep you to that promise. Nurse, shall we go?'\n\nHe said something to Mr Helgesen and moved to the door, leaving them together. 'Remember that I will do anything to help you, Miss Evans.' Mr Helgesen engulfed her hand in his. 'Are you ever free in the evening? There is to be a recital of Grieg music at the end of the week, I should very much like to take you.'\n\n'And I'd love to come. But I'd have to ask Miss Savage first\u2014you see, I'd have to leave her alone...'\n\n'Perhaps we can think of something. I'll telephone you\u2014if I may?'\n\n'Oh, yes, please.' He really was a dear; what a pity that he and Mr Savage couldn't be in each other's shoes. She shook hands again and walked beside the silent Mr Savage to the desk, where she very defiantly drew out much more money than she needed, and received a bundle of notes for Miss Savage. She quite expected that her companion would make some snide remark, but he remained silent as they went out into the street, and, just as silent, strode beside her on the way back to the flat. Once or twice she was on the verge of some harmless comment, but then she remembered that he had begged her to spare him her raptures...\n\nThe flat was quiet as she opened the door; usually Eva was bustling round cleaning. Perhaps she was already in the kitchen... Louisa went along the passage and pushed open the half open door. Eva wasn't there, but Miss Savage was, sitting at the kitchen table, her bright head on her arms, snoring her head off. On the table was a glass, not quite empty, and beside it a half full vodka bottle. Louisa stood and stared, not quite taking it all in. It wasn't until Mr Savage spoke very quietly over her shoulder that she turned her head to take a look at him.\n\n'You may be a splendid nurse, Miss Evans, highly qualified and skilled and taught everything there is to know about your profession, but one thing no one taught you, and that was to recognise an alcoholic when you saw one.'\n\n'No,' said Louisa, and then: 'Why wasn't I told? The doctors\u2014you...'\n\n'I believed that either one or other of the doctors would have briefed you; I had no reason to think otherwise. Indeed, I suggested to Claudia when I arranged for her to come here that she should engage an older woman and that she should be told what exactly was wrong with her patient. Instead, I find a chit of a girl who hasn't a clue. There seemed no point in telling you at first, but when I heard that her three boon companions had been here again, I came down to see you and explain. As you see, I have no need to do so. The matter speaks for itself.'\n\nLouisa gave him a thoughtful look. 'You have no pity, have you?' she observed quietly. 'I think you're the most disagreeable man I've ever met. And now will you carry her through to the bedroom and I'll get her into bed. And then I think you owe me an explanation.'\n\nHe didn't answer her, only stooped to lift the still snoring Miss Savage into his arms and carry her down the passage. Louisa, ahead of him, straightened the bedclothes and then tucked her patient up. 'If you'll wait in the sitting room,' she suggested, 'there are one or two things I have to do. If you want coffee there'll be some in the kitchen.'\n\nShe didn't wait to see if he would do as she asked but got busy with Miss Savage, bathing her face gently, soothing her, smoothing her hair, wrapping her snugly, and then tidying the room which as usual looked as though it had been ransacked. Presently, when everything was tidy again and she was sure that her patient was still deeply sleeping, she went along to the sitting room. It surprised her that Mr Savage had carried through a tray from the kitchen with the coffee pot and two mugs on it. He poured for them both, gestured her to a chair and asked brusquely: 'Well, what do you want to know?'\n\nLouisa took a sip of coffee. 'All the things that I should have been told in the first place, Mr Savage.'\n\nHe sat back in his chair, drinking his coffee with the air of a man who had nothing on his mind. He said carelessly: 'Claudia has been an alcoholic for the last eight years. Everything has been tried\u2014and I mean everything. Once or twice it seemed that she had been cured, but she lapsed... These so-called friends of hers\u2014she asks them to get her whisky or vodka or anything else she fancies, and they do. It seems certain that that's why they came to see her again. Surely you would have noticed something?'\n\n'If I'd been warned beforehand, yes. As it was, I believed the doctor's diagnosis.' She added honestly: 'Of course, the diagnosis was correct and I daresay the doctor thought I knew about Miss Savage\u2014it's quite possible, you see, to have all her symptoms for other liver complaints. But now that I know\u2014yes, there were a number of signs I should have been suspicious about.'\n\n'I brought her to Norway because I hoped that away from her friends and the life she led, she stood a better chance of fighting her addiction. It seems I was wrong.'\n\nLouisa put down her cup and met the dark eyes staring at her so coldly. 'Then wouldn't it be a good idea to let her go back to England? She's not happy here; she didn't want to come\u2014she told me that...' She paused, seeking a nice way of putting it.\n\n'She had to, otherwise I should have stopped her allowance. Quite correct.' He got to his feet. 'No, I don't intend to let her go back to England. On the contrary, as soon as she is fit enough, she shall travel up to Tromso, and you will accompany her.'\n\nLouisa choked back an instant denial. 'Isn't that a town in the north?'\n\n'Yes. My work is some fifteen miles away from there\u2014a ribbon bridge is being built between two islands. There's a small community there with a few hundred people.' He passed his cup for more coffee. 'You ski?'\n\n'Of course I don't!' She spoke sharply. 'You don't intend that Miss Savage should live there?'\n\n'Indeed I do\u2014she will be under my eye, and so for that matter will you.'\n\nLouisa said with great dignity: 'I believe I can manage my own life without your help.' She added boldly: 'Perhaps your sister would have had a better chance without your interference.'\n\n'You believe in plain speaking, Nurse, but I'm afraid your opinion holds no weight with me, so let's keep strictly to the matter in hand.'\n\n'I'll take a look at Miss Savage first,' said Louisa. But that lady was still deep in a snoring slumber.\n\n'You have sufficient warm clothing?' enquired Simon Savage as she sat down again. She told him briefly what she possessed and he said at once: 'You'll need more than that\u2014get a pencil and paper, will you?' And when she had, 'I imagine Claudia has almost nothing suitable; you'll outfit her as well.'\n\nLouisa wrote obediently and then lifted her head to look at him. 'You're not really going to send her all that way? She'll be so lonely, and she doesn't like snow or mountains...'\n\n'What a persistent young woman you are! Can you not see that she's almost at her last chance? Perhaps such a drastic step as this will provide that chance. And now be good enough not to argue with me; my mind is made up.'\n\n'Oh, pooh to that,' declared Louisa, and trembled at his icy stare. 'Just supposing she's ill\u2014is there a doctor there?'\n\n'She could be taken to Tromso by motor launch in a very short time. There is a road, of course, but it will be closed until late April\u2014even May.' He smiled thinly at Louisa's look of horror. 'You don't care for the idea?' His voice was silky. 'Perhaps you wish to give up the case, especially as you've been so misled.'\n\nHe wanted to be rid of her; any doubts she had been harbouring were instantly squashed. 'Certainly not, Mr Savage! I came to look after your sister, and that's what I intend to do. As you said, such a drastic change in her life might be her salvation, and if there's anything I can do to help her, I shall do it.'\n\nHis laugh was quite genuine and she went red with embarrassment and rage. 'I daresay you'll want to be getting back,' she told him stonily, 'and there are several things I want to do before Miss Savage wakes up.'\n\n'Plenty of time for that, she won't stir until this evening or even tomorrow morning.' He walked to the door, picking up his jacket as he went. 'And I'm staying in Bergen until Sunday. I shall be round tomorrow to see Claudia, and by the way, if you want to go out with Helgesen on Saturday evening, I shall be here\u2014my stepsister and I have a good deal to discuss, and I daresay we shall do that better without your well-meaning interference.'\n\nWhich remark left her speechless. Eva came back with the shopping presently and Louisa, always a girl to get things settled in her mind, went along to the kitchen, and while lunch was being prepared, got Eva to tell her all she knew about Tromso.\n\nEva had looked at her in a puzzled fashion. 'But that is a very long way away from here,' she pointed out. 'Why do you wish to know?'\n\nLouisa explained, very carefully, letting it appear that Miss Savage's brother was taking her with him for the benefit of her health.\n\nEva nodded. 'That is a good idea. It will be beautiful\u2014cold, you understand, but most healthy, and they will have each other, that will be nice.'\n\n'I'm not sure if I was supposed to tell you,' said Louisa doubtfully. 'What happens to your job here?'\n\n'Not to worry, Miss Evans, this flat is rented for six months by Mr Savage and I am to be paid for that time, whether I am needed or not. That was the arrangement.'\n\n'Oh, good.' Louisa got up. 'I'm going to see if Miss Savage is quite comfortable\u2014she doesn't want any lunch, so I'll have mine here with you if I may and you can tell me some more about Tromso.'\n\nMr Savage returned the following day in the morning. He had been quite right; his stepsister hadn't roused until very late in the evening and then she had been difficult to manage. She had a headache for a start, she felt terrible and she had no wish to do any of the things Louisa suggested. But towards midnight she had quietened down and Louisa had been able to wash her face and hands, change her nightie and re-make her bed. She had gone to sleep almost immediately, which was a good thing, for with one thing and another Louisa was tired out. Disliking someone, she decided as she put her thankful head on her pillow, was more tiring than anything else she knew of. And it wasn't her patient she was thinking of.\n\nIt was Eva who answered the door, took his coat and assured him that she would bring coffee in only a moment. She seemed to like him and Louisa, coming out of Miss Savage's bedroom, couldn't think why. His 'good morning' to her was accompanied by a mocking smile and the polite hope that his stepsister was feeling more herself.\n\n'Well, she is,' said Louisa, who had just had a slipper thrown at her by that lady, 'much\u2014but she's also very irritable. Please don't upset her.'\n\n'Oh, I won't. I know what a hangover's like, Nurse. And don't look like that; I also know when to stop.' He sat down by the window. 'The weather's changing. We shall have more snow.'\n\n'Indeed?' queried Louisa coldly. 'You can't see Miss Savage yet, you know.'\n\n'Don't be bossy, Miss Evans. When I've had my coffee I shall see my stepsister\u2014I have a great deal to say to her.'\n\n'She has the most appalling headache...'\n\n'Of course she has.' He got up and took the tray from Eva as she came in and smiled so nicely at her that Louisa blinked; she had no idea that he could look like that\u2014quite human. 'Three spoonfuls,' he told her. 'I have a sweet tooth.'\n\nLouisa was glad of her coffee. She had been up early, ministering to Miss Savage, persuading her to drink black coffee, dealing with her headache, ignoring the screams and abuse and ill-temper. Never having been more than slightly tipsy herself, she could only guess how ghastly her patient must be feeling and do her best to get her rational again. She had succeeded to an extent, though. Miss Savage had stopped crying and carrying on and had drunk more coffee and now she was dozing fitfully. 'I won't have her upset,' said Louisa out loud.\n\n'So you have already said,' remarked her companion dryly. 'I suggest that you drink your coffee and go out for a brisk walk, there's nothing like fresh air for clearing the head.' And when Louisa would have protested: 'Have you sufficient money?'\n\n'Plenty, thank you.'\n\n'Very good. We'll discuss clothes and travelling and so on when you return.'\n\nShe was dismissed and it would be undignified to protest again. She peeped in at Miss Savage, lying back in her bed with pads on her eyes and the blinds drawn, and then went to her own room and got ready to go out. She was at the door when the telephone rang and when she went to answer it Mr Savage was lying back in his chair, his eyes closed. He looked formidable even like that. Louisa picked up the receiver and found herself smiling because it was Mr Helgesen, wanting to know if she were free on Saturday evening. 'Because if you are, we could have a meal first and then go on to the concert. Could I call for you just after six o'clock?'\n\n'Oh, I'd love that,' said Louisa happily, 'only I quite forgot to ask...' She hesitated and glanced at the figure in the chair. 'Miss Savage isn't feeling very well and I hardly like to...'\n\n'Women never listen,' observed Simon Savage nastily. 'I remember very clearly telling you that I would be here on Saturday evening. I daresay you're due quite a lot of off duty.'\n\n'Thank you very much,' said Louisa into the phone, ignoring Mr Savage, 'I'll be ready just after six o'clock.' They wished each other goodbye and she rang off. She said rather snappily to the somnolent Simon Savage: 'Of course I listened, but how was I to know you meant it?'\n\n'I always mean what I say\u2014you'll know that in future.'\n\nShe flounced out of the room and by a great effort of will, didn't bang the door.\n\nShe had a list of shopping to do for Eva and she went first to the fish market, not only to buy fish but to admire the flowers. It amazed her that they were still to be bought in such bitter weather, although at a price she was unable to afford, but just looking at them, spaced out in such an unlikely fashion among the stalls of fish, was a pleasure. She chose her cod with a careful eye, bought a bag of cranberries, went to the little kiosk by the market and bought a Telegraph, then started walking away from the harbour towards the shops, stopping on the way to spend ten minutes in one of the many bookshops. There were as many English paperbacks as there were Norwegian\u2014but then she had come to the conclusion that everyone in Norway must speak English as well as their native tongue. She did a little window-shopping after that; obviously she would have to buy quite a few more clothes and it would be as well to price them first. She wondered how long it would be before Miss Savage would feel like shopping, and when they would be going and how. By air, she supposed; there was an excellent domestic service in the country and surely at this time of year it was the easiest way to travel.\n\nIt might be the easiest way, but it wasn't going to be their way. She discovered that when she got back to the flat, to find Miss Savage, looking like something just put through the mangle, sitting back against her pillows listening to her stepbrother, who was sitting on the side of the bed, talking to her in a quiet no-nonsense voice. Without turning his head, he said: 'There you are\u2014just in time to hear the arrangements which have been made. Take off your things and come in here.'\n\nNo please or thank you, grumbled Louisa to herself, and took her time about tidying her hair and putting more powder on her nose. She was rewarded by an impatient frown as she went into the bedroom and sat down meekly on the dressing table stool. 'Before we start, Miss Savage, is there anything you'd like?' she asked.\n\nHer patient shook her head and then winced at the pain. 'Who cares what I like?' she moaned, 'Simon least of all.'\n\nMr Savage didn't appear to hear this; he said at once: 'The sooner you come the better, and since you refuse to fly, I'll arrange for you to travel on the coastal steamer. It will probably be rather rough at this time of year, but the journey only takes five days to Tromso and you'll see some remarkable scenery. In\u2014let me see, today is Wednesday...a week's time you'll be met at Tromso, and as it will be afternoon when you get there, you'd better spend the night there and you can finish the trip by launch.'\n\n'No ice?' asked Louisa a little faintly.\n\n'The Gulf Stream,' said Simon Savage impatiently. 'Inland there's plenty of snow, of course.'\n\n'And are you inland?'\n\nHe shook his head. 'An arm of Tromso Sound; a little rural perhaps. We're building a bridge between two islands where it joins the sea, they each have a town and a good scattering of houses but only one road on the larger island.'\n\nIt sounded bleak, thought Louisa, and peeped at Miss Savage's face. It looked bleak too. 'It does sound a very interesting journey,' she said bracingly. 'Is there anything to do on board?'\n\nSimon Savage's firm mouth remained unsmiling. 'Nothing at all,' he said blandly.\n\nMiss Savage burst into tears and he got to his feet. 'Perhaps tomorrow we should shop for your clothes,' he observed. 'As you're making this unexpected journey, Miss Evans, and you are employed by me, anything you may need will be charged to my account.'\n\nMiss Savage stopped crying long enough to ask: 'And what about me?'\n\nHe turned to look at her from the door. 'When have I ever failed to pay your bills, Claudia?' he asked and, not waiting for an answer, shut the door.\n\nThe doctor came shortly after that, pronounced Miss Savage fit to get up if she felt like it, made out a prescription for the headache and before leaving, followed Louisa into the sitting room and closed the door.\n\n'Miss Savage should be all right,' he told her. 'We must try again, but with discretion. Allow her a drink with her lunch and dinner, Nurse. One glass of whatever she wishes, that is necessary, otherwise the withdrawal symptoms will be too severe. Later, perhaps, we can cut it down to one glass a day, and eventually to none. It is a pity that she has no incentive\u2014if she were married...' He shook his head and sighed, because there was really nothing much that he could do.\n\n'It needs a miracle,' said Louisa again.\n\nShe coaxed Miss Savage to eat a little of the light lunch Eva had cooked for her presently and gave her the whisky she asked for, and then to distract her attention from her craving, made a great business of making a list of the clothes they were to buy. Miss Savage even got out of bed towards evening, and though she shivered and shook alarmingly, she spent an hour discussing her wardrobe. No expense was to be spared, Louisa noted, but if Simon Savage was prepared to foot the bills, it was no concern of hers. She tucked her patient up presently, gave her supper and another ration of whisky and then, after her own supper, sat up until midnight until she was quite sure that Miss Savage was soundly asleep.\n\nIt was after lunch before Simon Savage came, which was a good thing, because his stepsister had wakened in a bad humour, declaring that she couldn't live unless she had a drink at that very minute and throwing her breakfast tray at Louisa. But somehow, now that she knew what was wrong, Louisa didn't mind too much. True, there was an awful lot of mopping up to be done, but she was beginning to feel sorry for Miss Savage now and even to like her a little. After a good deal of coaxing, Miss Savage consented to get dressed and by the time Mr Savage rang the bell, she was at least approachable.\n\nMr Savage had taken the precaution of hiring a taxi for the afternoon. It took them from shop to shop and the driver waited patiently outside each one. It certainly made shopping easy, and since Louisa didn't have to worry too much about prices, she began to enjoy herself in a modest way. True, she didn't insist on a fur-lined jacket, a fur cap and suede slacks, but she was quite content with her woollen slacks and the waterproof poplin outfit which, Simon Savage assured her, she would find very useful even if she didn't ski. He ordered her to buy several woollen sweaters, too and a dark green woollen skirt with a quilted jacket to go with it. 'And you'd better have a blouse as well,' he suggested carelessly. 'Probably we shall go to Tromso and you'll need them for the hotel.'\n\nWhich remark sent his stepsister off into another small orgy of buying.\n\nOn the whole, the afternoon went off smoothly, and since by the time they got back to the flat Miss Savage was tired out, Louisa saw her into bed, took her tea and then tucked her up for a nap. All this took a little time, of course, but Simon was still there, in the sitting room, doing nothing. She felt bound to offer him tea too, which he accepted with the air of one who had hoped for something better but would make do with what he could get. And when she thanked him stiffly for the things she had bought, he told her peremptorily to say no more about it in such a bored voice that she drank her tea in silence and was quite relieved when he went.\n\nPossibly building bridges was conducive to ill humour and an inability to tolerate the shortcomings of those one met outside of this tricky profession. 'I wonder how they can make an arch without the middle falling into the water,' Louisa asked the empty room. 'One day when he's in a good mood, I'll ask him. Only he never is in a good mood.'\n\n## CHAPTER FIVE\n\nMISS SAVAGE was at her most difficult for the rest of that day, alternately begging for a drink and abusing Louisa when she didn't get one, and in between that poking sly fun at her. 'You never guessed, did you?' she crowed. 'You thought I was being so considerate, sending you out each morning\u2014and there we were sitting cosily here\u2014they brought the drinks with them, of course. You gave me a fright when you thought you'd seen Connie\u2014I thought it was all up then, only you never suspected, did you? I'm clever, you know. I told the doctor in London that you knew all about me so there was no need to say anything to you, and I told the one here just the same.' She went off into a peal of laughter. 'I wish I'd seen your face when you and Simon found me! I had a drop too much\u2014I didn't mean to fall asleep. But now you know...what are you going to do about it?' She added pathetically with a complete change of manner: 'You won't leave me, will you, Louisa?'\n\n'No,' said Louisa, 'I won't, and I don't know what to do about it anyway\u2014only do as the doctor tells me. And now if you'd put on that dress that's too long, I'll pin it up and get it sewn.' She went on carelessly: 'Do you think it might be a good idea to go to that nice bookshop we found and get half a dozen paperbacks\u2014just to keep us going until we've discovered our way around Tromso?'\n\n'Tromso's miles away from Simon's work,' said Miss Savage sulkily.\n\n'Not so far, and there's this launch... I don't see why we shouldn't go there from time to time, do you?'\n\n'You don't know Simon\u2014he hates anyone to be happy.'\n\nAnd presently, stitching up the hem of the dress, Louisa began to wonder why Simon Savage should take such a bleak view of life, or was it perhaps that his stepsister made it appear so? But upon reflection, she couldn't recall his smiling, only just that once to Eva. She bit off the thread with small white teeth, but on the whole, she decided, he was better than Frank.\n\nHe came the next morning with the tickets for their journey and to tell Louisa that he had arranged for them to be taken by taxi down to the ship. 'She sails at seven o'clock and there'll be dinner on board,' he told her, 'no dressing up or anything like that. If Claudia is feeling off colour I'm afraid you'll have to look after her yourself\u2014there are stewardesses to clean the cabins and so on, but I doubt if their English is very good. How is she?'\n\n'Getting dressed.'\n\nHe nodded. 'May I stay for coffee?'\n\nLouisa blinked her long lashes. 'Why, of course\u2014it's your flat, isn't it? I'll ask Eva to hurry up a little.'\n\nHe didn't stay long, his visit had been one of duty; he made casual conversation with them both and went with an air of relief. He did pause as he went to remind Louisa that she was going out with Lars Helgesen on the following evening, and would she be good enough to tell Eva that he would be there for dinner with his stepsister.\n\nLars Helgesen and Simon Savage arrived together, and Louisa, in one of the new dresses, a fine wool jersey in several shades of blue, got up from her chair to greet them. Miss Savage, sulking again because she had to spend a few hours with her stepbrother, was lying on the sofa, wearing a soft woollen rose-coloured housecoat and looking really very pretty despite the deep shadows under her eyes and the downward curve of her mouth.\n\n'Lars Helgesen,' said Mr Savage, 'my sister Claudia.'\n\nMr Helgesen advanced to the sofa and shook hands, looking bemused, and Louisa, watching him, had to admit that Miss Savage did look glamorous even if she was addicted to the bottle, and certainly was worth a second look. If only she could cure her... She frowned in thought and changed it to a smile as Mr Helgesen suggested that they should go.\n\nMr Savage hadn't said a word to her, nor did he as they went out of the room. She had been going to tell him that Eva had promised to stay on for a little longer that evening and serve supper, but if he couldn't be civil enough to wish her good evening, he could find out for himself.\n\n'Call me Lars,' said Mr Helgesen. 'I thought we'd walk, it's not far.' He took her arm and took her down a side street which led to the market, where they crossed Torget into Bryggen and stopped outside one of the old houses there. 'Here we are,' he declared. 'It is a well known restaurant in the town, and you shall eat some of their delicious fish.'\n\nIt was warm inside, old-fashioned, and the tables were well filled. Louisa took off her coat and sat down at the table they were led to. She felt happy; Lars was a pleasant companion, even on their brief walk she had discovered that. She looked forward to a delightful evening in his company.\n\nThey had sampled the hors d'oeuvres and were well into the fish when Lars abandoned his light chat and asked in a carefully casual voice: 'Miss Savage\u2014Claudia\u2014is she very delicate?' And before Louisa could answer: 'She is so very pretty and so charming, I\u2014I was much struck...'\n\n'She's recovering from a complaint which left her rather low,' said Louisa carefully. 'She has her ups and downs though.'\n\nLars offered her the sauce. 'Yes? She is still so young.'\n\nJust as carefully Louisa agreed.\n\n'Of course Simon has told me something about her\u2014that was necessary so that I might check her account from time to time\u2014it is understandable that so very pretty a lady should wish to spend money.' Louisa murmured something or other and he went on: 'Simon tells me that you are to go to the village where he works. He thinks it will be better for her. I shall miss you\u2014both of you.'\n\nLouisa smiled at his earnest face. 'It does sound a long way off, but I'm sure we shall be all right once we're there,' she assured him. 'Have you been there?'\n\nThey talked about a great many things after that, finishing their dinner and walking back to the concert hall, and then sat in companionable silence listening to the pianist playing Grieg's music, and when it was over, walking the short distance back to the flat.\n\n'You'll come in for coffee?' asked Louisa, and felt a little thrill of pleasure at his eager 'Yes, please!' It was such a pity that they would have no chance to see each other again, at least until Simon Savage decided to send them back to Bergen, and he might not do that, they might go straight back to England. It depended on his stepsister, didn't it?\n\nThey went up the stairs into the quiet flat and found Simon Savage standing by the window looking out into the dark night. His long lean back had the look of a man impatient to be gone. Miss Savage was still lying on the sofa, which surprised Louisa; she had thought that her patient would have had more than enough of her stepbrother's company by now. She turned her head as they went into the room and smiled, her gaze resting for a bare moment upon Louisa before lingering upon Mr Helgesen's face. He crossed the room to her at once. 'I was afraid you would be in bed,' he told her, and took her hand, smiling down at her. Louisa, watching them, allowed the faint, vague idea that Lars had been getting a little interested in herself to slide into oblivion. Well, it had been silly of her to imagine any such thing in the first place. She looked away and found Simon Savage's dark eyes bent upon her, and it was only too obvious from the look on his face that he had read her thoughts. She flushed angrily. 'I'll get the coffee,' she muttered, and escaped to the kitchen.\n\nHe followed her. 'A pleasant evening, Nurse?' he enquired blandly.\n\n'Yes, thank you.' She went on putting cups and saucers on a tray, not looking at him.\n\n'A nice chap, Helgesen.' He watched her through half closed lids. 'Do you have a boyfriend at home, Louisa?'\n\nIf she had been expecting that question she would have been ready with a bright answer; as it was all she could think of to say was 'No.'\n\n'I don't say I'm surprised.' He didn't qualify this remark and she didn't answer it, recognising it as bait to make her lose her temper.\n\n'Will you stay for coffee?' she asked sweetly.\n\nHe took the tray from her. 'But of course.'\n\nBefore the two men went it had been arranged that Lars should take them in his car to the ship\u2014moreover, Louisa heard him arranging to take Miss Savage out to lunch on the following day. She was sure that Mr Savage had heard it as well, but he didn't say anything, not until he was actually on the point of leaving. He said softly: 'You can safely leave it to me, Nurse.'\n\nIt surprised her very much when she returned to the sitting room to hear Miss Savage asking her quite humbly if she would mind her going to lunch with Lars Helgesen. 'And I know what you're thinking, but I promise you I'll not drink anything, only tonic water.' She went on dreamily: 'He's sweet, isn't he?'\n\nLouisa, clearing away the coffee cups, wondered if this was the miracle she had hoped for. If it was, she was going to help it along with all her might. 'He's very nice,' she agreed, 'and now what about bed? You want to look your best in the morning.'\n\nThere were only three days before they left, and it seemed to Louisa that Lars Helgesen was either at the flat or taking Claudia Savage out to one meal or another. Louisa had awaited her return from their first date in some trepidation, but she need not have worried. Her patient seemed a changed young woman. True, she still needed a drink twice a day, but her temper was no longer something to be reckoned with and she had stopped throwing things about. Moreover, she had asked Louisa to call her Claudia, which was a great step forward and made for friendlier relations all round.\n\nOf Simon Savage there had been neither sight nor sound. He had returned to his work, she knew, but he had made no attempt to telephone or write, nor had he come to say goodbye. She wondered several times what he had said to Lars about his stepsister; whatever it was had made no difference to his feelings towards that lady. Louisa packed, did last-minute shopping and laid in a small stock of books against Claudia's boredom during their journey. She foresaw difficult days ahead, for Claudia wasn't going to take lightly to not seeing Lars. It seemed a pity that they couldn't have stayed in Bergen now that there was an incentive for her to give up drinking, and it was even more of a pity that there was no way of getting hold of Mr Savage to tell him so. She could of course telephone him, but she had the feeling that if she did he would listen to her in silence and refuse to change his plans. Perhaps he was bent on punishing his stepsister, perhaps he really did believe that a stay in the north would be the means of curing her. Louisa didn't feel inclined to give him the benefit of the doubt.\n\nTheir last day came and with it Lars Helgesen to take them both out to lunch\u2014the Norge Hotel this time, and although he was equally attentive to both of them, Louisa found herself wishing that she wasn't there. The other two had so much to say to each other, although he was careful to keep their talk light and amusing, and Claudia replied in kind, sipping her one glass of white wine as though she had little interest in it. Over coffee Louisa had the bright idea of remembering that she still needed some wool to finish her knitting, and left them together with a promise to meet later at the flat where they would have tea before driving to the dock.\n\nThey weren't back when she got in, so she got the tea tray ready and sat down to wait. And when they did arrive, what with saying goodbye to Eva, last-minute packing and messages, there was barely time for them to drink their rather late tea before they had to leave.\n\nOn board, Lars went with them down the curved stairs to their cabin, a quite roomy one with a table and chairs as well as two narrow beds. There was a tiny shower room too and a good sized cupboard. Its large window looked out on to the deck alongside and Louisa found it quite perfect, although from the mutinous look on Claudia's face she guessed that her views were not shared. Certainly there was a tremendous difference between the cabin and the comfort of the flat, but there was all they could need. She murmured something about finding out mealtimes, said goodbye to Lars and left them together. She encountered nobody as she made her way back to the main hall. There was the ticket office there and here people were queuing to get their tickets to whichever of the stops they wanted. The ship would call at a number of places, some quite large towns, some fishing villages, some a mere cluster of houses. Louisa could imagine how welcome the sight of it must be, especially during the long winter, bringing supplies and mail and discharging passengers and taking others on.\n\nShe edged past a family group, complete with pram, small baby and a large dog, and went up another winding stair. The dining room was quite large with small tables and an air of cosiness, and a door from it led to the stern of the ship where, she discovered, the passengers who were travelling only part of the way could sit. There was a cafeteria there and a small bar where she was delighted to see that no spirits were sold, only wines, sherry and port. There were already a few people sitting about, and she went back the way she had come, out of the door again and into a lounge, running across the fore part of the ship, from side to side, with large windows on all sides. There was no one there either, so she went up another small flight of stairs and found another lounge, exactly like the one below but used, she guessed, for observing the scenery. She stood for a few minutes, watching the ship preparing to sail, craning her neck to see Bergen alongside and behind her, lights shining from the houses perched high on the skirts of the mountains behind the town. And in front of her the fjord leading to the open sea. It was a dark evening and she could see very little; probably it would be both cold and rough. She went below presently, studied the meals timetable, made her way through the increasing number of passengers back to the cabin and tapped on the door. Someone had just shouted something over the tannoy which she guessed was an order for people to go ashore, for she could feel the engines somewhere under her feet. They would be sailing at any moment now, and surely Lars would be gone.\n\nHe had, and Claudia was sitting slumped in one of the chairs, crying. The moment she caught sight of Louisa she shouted: 'I won't go, I won't! I want to stay with Lars\u2014it's cruel of Simon to make me just when I'm h-happy...'\n\nLouisa privately agreed with her. It was cruel of Mr Savage, but then from what she had seen of him he possessed very little of the milk of human kindness. She went and sat down on the edge of one of the beds close to Claudia and took one of her hands in hers. 'Look, it's not as bad as you think. Listen to me\u2014you're much better. You've been trying hard, haven't you, and each day will be easier. This place, wherever we're going, is quiet and very peaceful. You'll sleep well without pills and start eating properly and you'll feel so well that you won't be bored or tired of doing nothing. And the quicker you do that, the quicker you'll come back to Bergen. Don't you see, if you improve as much as that, your brother can't refuse to let you return? And Lars will be here, won't he, waiting for you?'\n\nClaudia pulled her hand away pettishly. 'Oh, what do you know about it? You've never been in love, you've no idea what it's like. When you meet someone and you know at once...'\n\n'It must be wonderful. I've never been in love, as you say, and perhaps I never shall be, but it's happened to you, hasn't it? And you've got to hang on to it. You're one of the lucky ones.'\n\nClaudia turned round slowly to look at her. 'We haven't much in common,' she said, and laughed a little, 'but for a nurse you're not a bad sort.'\n\nHer face crumpled again. 'Do you really think we'll come back soon? And that Lars likes me as much as he says he does?'\n\n'Yes to both questions.'\n\nClaudia was looking at her face in the little jewelled mirror she carried in her handbag. She said defiantly: 'I told him\u2014I told him I was an alcoholic and he just smiled and said that I didn't need to be any more because he was there. Do you suppose I could be cured, Louisa?'\n\nLouisa paused in her unpacking of an overnight bag. 'Yes, I'm quite sure you can. You see, you've got a good reason now, haven't you, and before you never had that, did you?'\n\nClaudia flung the mirror down on the bed. 'All the same, I shall go mad in this beastly little place we're going to, and if I do it'll be Simon's fault.'\n\n'Do you suppose Lars will come and see you?' asked Louisa, and was rewarded by a return of good humour.\n\n'He promised, but he doesn't know when.' Claudia got up and peered out into the dark outside. 'Have we started?'\n\n'Yes, a few minutes ago. Dinner is at eight o'clock. Would you like a glass of wine before then?'\n\n'Whisky.'\n\n'No, wine. You can't buy spirits on board ship, anyway, it's against the law.'\n\n'Oh, well, wine, I suppose.' Claudia looked round her disdainfully. 'I've never been in such a poky little place in my life before, and I've got to share it with you. I can't bear the idea...'\n\nLouisa choked back what she would like to have said. 'It's only for four days\u2014and we shall only sleep here, after all.' She felt the ship dipping its nose into the beginnings of the North Sea, heaving alarmingly. 'And if it's rough you may be glad to have someone here.'\n\nThere were barely a dozen passengers in the dining room and the steward led them to a window table where two people were already sitting, and when Louisa said, 'Good evening,' because Claudia was looking annoyed at having to share, she was answered to her relief, in the same language\u2014they were an elderly pair and now that she had time to look at them, American.\n\nThey leaned over the table to shake hands. 'Mr and Mrs Foster Kuntz,' they said, beaming, 'and I do believe we're the only English speaking passengers.'\n\nLouisa shook hands and Claudia did the same, ungraciously, and since she had nothing to say, Louisa said: 'Miss Savage is visiting her brother near Tromso. She hasn't been well, and I'm travelling with her.'\n\n'Tromso?' queried Mrs Kuntz. 'That's right in the north. We're going to Trondheim to see our daughter\u2014she's married.'\n\n'To a Norwegian?' asked Louisa hastily, because Claudia was ignoring everyone.\n\nMrs Kuntz laughed in a jolly way. 'No, he's from the USA, same as us. Got a good job too. We're from Texas\u2014San Antonio, cattle and petroleum; Foster here has done very well from them. We thought we'd have a nice long vacation in Europe and visit Cissie before we go home.'\n\nLouisa said, 'What fun for you both,' and picked up her spoon to start on the soup the steward had set before her. 'Have you enjoyed your trip?'\n\nMrs Kuntz's answer kept the conversation going in a rather one-sided fashion through the cod steaks and the pudding, so that it wasn't too noticeable that Claudia didn't speak at all. They left the dining room together and Mrs Kuntz whispered: 'Your poor friend\u2014I reckon she must have been good and sick\u2014she hasn't said a word.'\n\nLouisa seized her chance. 'Yes, she has been ill and she's still convalescing. You mustn't mind if she doesn't enter into conversation, she finds it exhausting, and I hope you won't mind if we have our coffee quietly in a corner, because I think she's pretty well exhausted. We'll have an early night; there's nothing much to see anyway, is there?'\n\nMrs Kuntz laid a kind hand on her arm. 'Sure, my dear, we understand. We'll see you at breakfast.'\n\nClaudia had gone to sit at the opposite end of the saloon, as far away from everyone else as she could manage. As Louisa sat down beside her, she muttered: 'I won't go\u2014it's ghastly, those dreadful people\u2014I'm going to get off at the first stop.' And then: 'I'll kill Simon!'\n\n'Rather pointless,' Louisa said calmly. 'We'd be stuck high and dry miles from anywhere and not nearly enough money to get home.'\n\n'I'll telephone Lars.'\n\nLouisa poured their coffee. 'I think Lars loves you very much, and I thought you loved him\u2014I thought you were doing this for him.'\n\n'You mind your own business!' snapped Claudia.\n\n'Well, I do usually,' agreed Louisa matter-of-factly, 'but it seems a shame that you should give in so easily. And Lars wouldn't believe it of you.'\n\n'You know a lot about him, don't you?' Claudia turned a furious suspicious face towards her.\n\n'No, but I think he's a very honest and kind man who wouldn't give his friendship or his affection lightly.'\n\n'My God, you sound pompous!' declared Claudia.\n\n'Yes, I know, but you did ask me, didn't you? And I do want to help you to get...well again.'\n\nClaudia gave a small sneering laugh. 'Then you'll be out of a job.'\n\nLouisa said soberly, 'Yes, so I shall.' She hadn't thought about that: somehow the hospital, her stepmother and Frank had all faded gently into the past and she couldn't imagine going back to it.\n\nDespite a disturbed night because Claudia was unable to sleep, Louisa was up early. It was still dark when she wakened Claudia and then put on her thick jacket and went outside on deck. It was cold, but the sky was clear and she could see lights ahead\u2014Maloy, a fishing centre, its harbour crowded with boats, its modern wooden houses already dimly seen under the bright lights of the dock. As they drew nearer she could see too that their bright red roofs were powdered with snow, as were the fishing boats. The ship docked and she watched, oblivious of the cold, while the mail was slung in its great net on to the dock, and was loaded with more mail. They were taking passengers aboard too, quite a number, bound for farther up the coast. She would have stayed watching the busy scene until they sailed, but the breakfast gong sent her back to the cabin to see how Claudia was faring.\n\nShe was dressed and almost ready, and in a foul temper. She barely spoke to Louisa, nodded to the Kuntzes at the table and sat crumbling toast and drinking coffee while Louisa had her porridge, egg, cranberry jam and toast, carrying on a friendly conversation with their companions at the same time.\n\n'I absolutely refuse to go on deck,' declared Claudia when they were back in their cabin. 'I'm worn out and bored, and what am I supposed to do all day on this ghastly ship?'\n\nLouisa produced a couple of paperbacks, a pack of cards and the latest copy of Vogue which she had hidden away in the luggage. 'We'll go to the saloon on the top deck,' she declared, 'and of course you don't have to go out if you don't want to\u2014there'll be plenty to look at through the windows.'\n\n'Mountains and sea. I hope to God there's a comfortable chair...'\n\nClaudia refused to face a window; Louisa settled her in a large, well upholstered easy chair in a corner, laid the books on a table beside her and went to take a look from the long window overlooking the bows.\n\nMaloy was already behind them, but she caught sight of a narrow ribbon bridge behind the village. 'Did Mr Savage build any of the bridges along this coast?' she asked.\n\nClaudia shrugged, already deep in Vogue. 'Oh, he had something to do with several of them, I believe. I've never been interested.'\n\nThe ship was sailing between the coast and protecting skerries, but presently it was the open sea\u2014the Norwegian Sea\u2014and the ship, incredibly sturdy despite its smallness, pitched and rolled its way round the headland of Stad, past the Runde bird-rock, just visible to the west, and presently into the calm of Alesund.\n\n'We're stopping here for a couple of hours,' observed Louisa cunningly. 'Shall we go ashore and get some coffee and take a quick look at the shops? Lunch isn't till one o'clock\u2014there's more than an hour...'\n\nClaudia was looking pale, although she hadn't complained at the rough trip. She said now: 'Louisa, I must have a drink.'\n\n'OK. You won't be able to get whisky, but there'll be sherry or wine. I'll get our coats.'\n\nThe few passengers were already crossing the quayside and making for the town, a stone's throw away. It had been snowing and the wind was icy, but both girls were warmly clad, and once in the narrow busy streets, it was warmer. Louisa found an hotel within minutes and sat Claudia down at a window table in the bar, sipping her coffee while her companion drank her sherry, and then ordering more coffee for them both. Claudia was better after that and Louisa walked her briskly up the main street, looking in its shops, buying an English newspaper and one or two more books before going back to the ship. And there once more she was delighted to see that Claudia looked decidedly better and even made an effort to eat some lunch. What was more, she answered, briefly, it was true, when the Kuntzes spoke to her. The ship sailed while they were drinking their coffee and Louisa watched the little town slide away into the distance. There was a mountain behind the houses; one could drive up to its top by taxi and get a splendid view\u2014something she would have loved to do...\n\nIt was dark when they reached Kristinasund, and even darker when they docked briefly at Molde, although the sight of the twinkling lights which seemed to cover the mountains behind the town was worth a few cold minutes on deck.\n\nClaudia slept better that night, although it was still rough, and she got up with fairly good grace in plenty of time for breakfast. They were sailing up the fjord to Trondheim where there was going to be a three-hour stop, and this time they were among the first to go ashore. There were taxis on the quayside. Louisa ushered Claudia into one of them, said hopefully: 'The shops, please,' and got in too.\n\nIt was a short drive, but Claudia hated walking, although she was happy enough to linger from one shop to the next, while Louisa, longing to visit the Nidaros Cathedral, which Eva had told her on no account to miss, wandered along beside her. Clothes could be bought anywhere in the world, she thought irritably, so why couldn't Claudia be interested in anything else? They had coffee presently, spent some time in a bookshop and then found another taxi to take them back. A successful morning, decided Louisa, and only two more days to go.\n\nShe tucked Claudia up in her bed after lunch and waited until she was asleep before putting on her jacket and going on deck again. The weather was still clear, but there was a grey film on the horizon which she guessed was bad weather of some sort. And it was getting dark again, although there was still a little daylight left as they entered the Stokksund Channel. The captain had told her at lunch to look out for that\u2014a twisting narrow stretch of water where the ships had to sound their sirens before each turn. Only the thought of a cup of tea sent her back to the cabin to rouse Claudia and go up to the dining room for the simple generous meal.\n\nThere were fewer passengers now. The Kuntzes had gone and several others had disembarked at Trondheim and those who had got on in their place were Norwegians. They were in the open sea again and it was rough. Claudia lay down on one of the settees in the saloon and promptly went to sleep, and Louisa got out her knitting. She was enjoying it and she felt reasonably happy about Claudia; with luck she would be able to hand her over to her brother in a much better state of health. Beyond that she didn't intend to worry about anything.\n\nThe weather worsened as they worked their way steadily up the coast. By morning there was only the dim outlines of mountains and rugged coast to be seen. It had been too dark on the previous evening to catch a glimpse of the land around, and too dark in the early morning to see the iron globe on top of the rock marking the Arctic Circle, although the ship had sounded her siren as she passed, but the clouds lifted briefly after breakfast, just long enough for her to see the Svartisen Glacier, far away in the distance, remote and terrifyingly high.\n\nThey stopped at Bodo during the morning and this time Louisa persuaded Claudia to go with her to see the Cathedral, modern and not very large, but beautiful in its way, and then as a sop to Claudia's impatient company, took her to a hotel where she could have her glass of sherry and then coffee. There were some interesting shops too; Claudia bought herself some silver jewellery\u2014dangling earrings and a thick bracelet, and went back, reasonably good-tempered, to the ship.\n\nThere was more open sea in the afternoon and just before the light faded completely Louisa, on deck once more, was rewarded with the sight of the Lofoten Wall on the horizon. It looked a mass of barren rock where no one could possibly live, and yet, two hours later, they had docked by a small quay, and tucked into the formidable mountains towering above them was an equally small village, ablaze with lights, boasting a hotel and several shops. Louisa was enchanted and longed to talk to someone about it. It was incredible to her that people could live out their lives amidst such bleakness and, moreover, make such homelike surroundings for themselves.\n\nShe managed to convey something of her feelings to the captain when he came into the dining room and he nodded his great bearded head.\n\n'We do not mind the loneliness,' he told her, 'and we are happy to live simply. We have electricity, warm homes, plenty of books and all the sport you could wish for.' He twinkled at her. 'It is a long way from London, Miss Evans.'\n\n'Thank heaven for that,' said Louisa decidedly. 'I could live here, I think\u2014it's possible.'\n\nThey reached Tromso the next day, stopping at Harstad and Finnsnes during the morning. They could have gone ashore at Harstad, but Claudia was morose and disinclined to do anything, so that Louisa packed for them both, contenting herself with a quick peep at both places as they docked. As they steamed through the narrow waters leading to the city, she noticed that the country had changed. There were mountains crowding in on all sides, but the country had got friendly and there were farms here and there, surrounded by birch trees, and everything powdered with snow. There was nothing to be seen of Tromso yet, there were too many bends in the waterway, but there were houses scattered along the shores of the islands on either side of them. Holiday homes, she guessed, and wondered how one got to them\u2014by boat, presumably, although presently she could see a road close to the fjord's edge running between the houses, but on the other side, although there were houses, some built high into the sides of the mountains, there was no road at all. And presently Tromso came in sight, built on an island in the middle of the fjord. Louisa could see the bridge now, linking it with the mainland, larger and longer than the slender pillar bridge linking Finnsnes and its neighbouring island, but just as impressive. It was a pity that she disliked Simon Savage so heartily, otherwise she could have found out a great deal more about them.\n\nShe went below reluctantly. Claudia was sleeping again; she woke her gently, listened calmly to her mounting grumbles, coaxed her into her outdoor clothes and observed: 'You'll be able to telephone Lars this evening.'\n\nIt acted like magic. Claudia's scowl turned to self-satisfied smiles and Louisa was able to go and find a steward to deal with their luggage and then go back for Claudia. Mr Savage had said that they would be met at Tromso, but that was all. Louisa debated the choice of staying in one of the saloons until they were found, or going ashore and waiting on the quay\u2014there was bound to be a waiting room there. On the whole, she thought it best for them to go to the saloon and wait. The reception area by the office was full of passengers waiting to disembark. Most of them had boarded the ship at Bodo and Harstad. The quay was thronged with people, presumably waiting for friends or relations or travelling still farther north, and there was a steady hum of voices and a good deal of toing and froing. It was difficult to imagine that they were surrounded by bare mountains and glaciers, snowbound roads and vast forests. Louisa felt excited and happy, and wished that Claudia could feel the same. She took her arm and pushed her gently into a corner and said: 'Once most of these people have gone, we'll go up to the saloon, it'll be quiet there.'\n\nBut there was no need. Someone tapped her on the shoulder and she turned round to find Simon Savage, looking somehow much younger and cheerful. An illusion, of course, for all he did was to nod at her in a casual fashion before asking his stepsister if she was ready to leave the ship. If he uttered one word of welcome, Louisa didn't hear it. She said clearly, 'Our luggage is by the office. We had a very good journey, thank you, but your sister is tired.' She glanced at Claudia, who hadn't uttered a word. 'She should rest as soon as possible.'\n\nJust for a moment he looked at her with narrowed eyes and then surprisingly he laughed. 'Bring Claudia, I'll get the luggage,' he said, and turned away.\n\nHorrible man! thought Louisa, watching him shoulder his way through the crowd. He was wearing a sheepskin coat and knitted cap in bright colours. Probably it was that which made him look different, or perhaps she had hoped he would be... She put an arm round Claudia's shoulders.\n\n'Come on,' she said cheerfully, 'let's find some tea.'\n\n## CHAPTER SIX\n\nTHERE WAS hard-packed snow on the quayside, and Louisa felt Claudia flinch as they stepped off the gangway behind Simon Savage and a short, dark, burly man carrying two of their suitcases, but they didn't have far to go. There was a Range Rover parked close to the ship and they were bidden to get in while their luggage was piled in beside them. Louisa barely had time to look around her and take a last look at the ship before they had left the quay behind, driving down a road which curved under a bridge and turned sharply through warehouses, to turn again and enter the town over a wide bridge. The long evening had started, although it was not yet four o'clock, and the shops were brilliantly lighted in what was obviously one of the main streets, its broad pavements lined with bare trees. It ended in an open square surrounded by shops and along one of its sides, a large, solid-looking hotel. Mr Savage parked the car, said over his shoulder: 'This is where you will spend the night,' and got out.\n\nIt was more than she had expected, thought Louisa as she joined him on the pavement and waited while he held a hand out to his stepsister, in fact it looked delightful. The thought of a comfortable bedroom, a hot bath and a good dinner brought a sparkle to her eye. Even Simon's growling, 'And you'd better make the most of it,' couldn't spoil her pleasure.\n\nIt was just as splendid inside: warm, the foyer close-carpeted and furnished with comfortable chairs and little tables and a pleasant, smiling clerk who welcomed them with friendly warmth. He seemed to know Mr Savage already, for they were whisked away to their rooms with no delay at all; cosy rooms next to each other and with a communicating door and each with its own bathroom. Claudia, who had barely spoken since they had been met, looked around her with a critical eye. 'You wouldn't think they'd be able to manage anything like this in such a godforsaken place,' she observed bitterly. 'You don't suppose people actually stay here, do you? I mean for holidays...'\n\n'I believe it's popular in the summer, loads of Norwegians come up here from the south\u2014there's a road all the way, you know.'\n\n'No, I didn't know, and I don't want to.'\n\n'I'll unpack your overnight bag. Mr Savage said something about tea. You'd like some, wouldn't you? Or shall I ask for it to be sent up?'\n\nClaudia had regained some of her old languid manner. 'My dear Louisa, after weeks of nothing but you and my own company, I wouldn't miss a chance to have a look at whatever bright lights there are.'\n\nShe turned away to the dressing table and Louisa went back to her own room, where she tidied up her hair, did her face and unpacked her own bag. She got out the green wool skirt and the quilted jacket too and shook out a cream silk blouse to go with them. Presumably they would dine later with or without Simon Savage. She wasn't sure if she wanted him to be there or not.\n\nThey went down presently and found him sitting at one of the small tables, the tea tray before him. He got up as they reached him, hoped that they had found their rooms comfortable in a colourless voice and begged someone to pour tea.\n\n'Oh, you do it, Louisa,' said Claudia, 'I'm too exhausted. That fearful voyage! I absolutely refuse to go back by ship.'\n\nHer stepbrother looked up briefly from the Times he was reading. 'There are plenty of flights\u2014or the road\u2014when the time comes.'\n\nClaudia drew a hissing breath, but before she could speak, Louisa prudently handed her a cup of tea. She did the same for Simon, then poured her own and sat sipping it until he put his paper down and passed the plate of cakes. He caught her eye as he did so and gave a short laugh.\n\n'You remind me forcibly of my old nanny,' he observed, 'urging me to remember my manners.'\n\n'I haven't said a word, Mr Savage.'\n\n'No, but your eyes did. I can recommend the little round ones with the chocolate icing.'\n\n'And now we're here, perhaps you'll tell us what happens next.' Claudia's voice was sharp.\n\n'We leave tomorrow morning. You can have an hour if you need to do any shopping.'\n\n'I should like to stay here, in this hotel.'\n\nHe didn't answer this but observed, 'You're looking better, Claudia, better than you've looked for several weeks. The sea journey did you good\u2014you're half way there, you know. Why not finish it properly this time?'\n\n'I hate you!'\n\nHe remained unperturbed. 'Yes, I know, but that's got nothing to do with it.' He glanced at his watch. 'Lars will still be in his office if you want to telephone him.' He waved a hand towards the telephone booth by the reception desk. 'Have you the number?'\n\nShe got up without answering and hurried across the foyer, and he handed his cup to Louisa for more tea. 'I must admit you have achieved a good deal in this last week or so, Nurse. Is Claudia drinking at all?'\n\n'Wine or sherry, mid-morning, and a glass with her dinner in the evening.'\n\nHe nodded. 'She's in love with Lars Helgesen, isn't she?'\n\n'Yes.'\n\nSimon passed her the cakes and then helped himself. 'Splendid, we must keep that alive at all costs, it might prove the incentive she has never had.'\n\nLouisa eyed him uncertainly. 'Yes, but supposing he doesn't...would he marry her?'\n\nHis look mocked her. 'My dear Louisa, if a man loves a woman\u2014really loves her\u2014he'll marry her. Even a termagant like my dear stepsister.'\n\nHe really was beastly; perhaps he was a misogynist.\n\nClaudia came back then, looking considerably happier, but presently she said to no one in particular: 'I don't want to come down to dinner\u2014I'll have something in my room.' She gave her stepbrother a quick look, defying him to argue with her, but all he said was: 'A good idea\u2014I'll get a menu sent up presently.' He looked across at Louisa. 'You will dine with me, Louisa? Shall we say half past seven?'\n\nClaudia had got up and she got up too. 'Thank you, Mr Savage.' She gave him a cool nod and followed Claudia to the stairs.\n\nAn hour later she was dressing. Claudia, tucked up in bed, with magazines, books and the most recent papers strewn around her, had chosen her meal and was painting her nails, a long and meticulous business. Louisa, bathed and with her hair newly washed, put on the long skirt, the blouse and the little quilted jacket. They made a nice change after days of wearing slacks and woollies and probably she wouldn't have the chance to wear them again for weeks. She did her face carefully, wishing she was strikingly beautiful, witty and self-assured enough to take the shine out of Mr Savage. If she had had more time she might have given herself an elaborate hairdo, but she doubted very much if he would notice anyway, and what did it matter? They both disliked each other so heartily; she had been surprised that he had suggested dinner together. She went to take a last look at Claudia and found a waiter arranging a prawn cocktail, lamb cutlets and a variety of vegetables, and a delicious-looking pudding on the bedtable. There was a glass of wine there too. Louisa, going downstairs, reminded herself to warn Simon Savage...\n\nHe was waiting for her in the foyer, very elegant in a dark suit, looking longer and leaner than usual. He also looked ill-tempered, and she sighed. She was hungry for her dinner, but it would be spoilt if he was going to sit in stony silence.\n\nIt seemed that he was on his best behaviour, for he offered a drink in a quite friendly voice, and when she ventured to mention the possibility of Claudia ordering something to drink without their knowledge, actually thanked her for saying so. 'Though you have no need to worry,' he assured her carelessly, 'I've taken the necessary precautions.'\n\nAnd she had to be content with that. She sipped her sherry and looked around her. There were quite a number of people now, all well dressed, which somehow seemed strange when she remembered the miles of barren snowy mountains and the cold, stormy sea they had travelled through. She said: 'I didn't expect this\u2014I mean, all this luxury so far away...'\n\n'There's an excellent air service, the coastal express calls every day except Christmas Day, and there's a first class highway running from Oslo to Nord Kapp.'\n\n'No trains?'\n\nHe raised amused eyebrows. 'Through or over the mountains, Louisa?' and when he saw her flush, he added more kindly: 'The nearest railway is from Narvik into Sweden, the main line comes as far north as Bodo.'\n\nAt least they had found something to talk about. 'I saw any number of bridges\u2014pillar bridges, as we came.'\n\n'Beautiful, aren't they? Quite a number of islands are no longer isolated, although there are still ferries running in all directions and several local airlines.' He actually smiled at her. 'If you've finished your drink shall we have dinner?'\n\nThey had a table by the long window, overlooking the street and the square beyond. There was plenty of traffic still and any number of people. And because the street lights were so bright and numerous, the snow-covered pavements had a charming Christmassy look. Which reminded Louisa to ask: 'Shall we be here for Christmas?'\n\nSimon glanced up from the menu he was studying. 'It depends on several things. Be sure I'll give you plenty of warning. Are you anxious to be in England for Christmas?'\n\nShe said: 'Oh, no!' in such a tone of alarm that he asked: 'You like Norway? Have you no family?'\n\n'I like Norway very much,' she told him, and added: 'I'd like soup, please, and then the cod.'\n\n'Trailing a red herring, Louisa, or should I say cod?' and when she didn't answer: 'You have a family?'\n\nHe gave their order to the waiter and sat back waiting for her to answer, his dark face faintly bored.\n\n'A stepmother, no one else. Well, aunts and uncles, but they live a good way away...'\n\n'Where?'\n\n'Wiltshire and Cumbria.'\n\nTheir soup came and she picked up her spoon, glad of something to do. She didn't think she liked this urbane manner any more than his usual curt behaviour, and she wasn't going to answer any more questions.\n\n'You don't care for your stepmother?'\n\nShe looked at him across the elegant little table with its lighted candles. 'No.' She supped the last of her soup. 'I'm not going to answer any more questions.'\n\nHe raised quizzical eyebrows. 'My dear girl, I'm making polite conversation.'\n\n'You're cross-examining me. Is your bridge almost finished?'\n\n'Yes, the main work was done before the winter set in; there's not much left to do now, and that mostly under cover.'\n\n'May we see it?' asked Louisa.\n\n'By all means, but I doubt if Claudia will want to do that.' He spoke sourly and gave her such a disagreeable look that she rushed on to the next question.\n\n'Are you going to build any more?'\n\n'Now who's being cross-examined? Yes, I have a contract for three more bridges, one farther north, the other two in the Lofotens.'\n\n'We stopped there at a very small village\u2014it began with an S...'\n\n'Stamsund. You liked it?'\n\n'It was dark, but I would like to have gone ashore... Lots of bright lights and\u2014and cosy, if you know what I mean.'\n\nThe waiter came with their cod and when he had gone again: 'You surprise me, Louisa, or are you putting on an act for my benefit?'\n\nShe paused, fork half way to her mouth. 'An act? Why ever should I bother to do that with you?'\n\nHis bellow of laughter sent heads turning in their direction. 'Aren't I worth it?'\n\n'No,' said Louisa roundly, and applied herself to her dinner. She was a little surprised to find that although she disliked him still she wasn't...scared wasn't the word\u2014intimidated any more.\n\nThe cod was beautifully cooked with a delicious sauce and lots of vegetables. She ate it all up with a healthy appetite and followed it by a souffl\u00e9, light as air, while Simon ate biscuits and cheese. They had drunk a white wine with their meal, which was perhaps why she found herself telling her companion about Frank. She hadn't meant to, but somehow his questions had led back to her life in England again\u2014the hospitals where she worked, the villages where she lived and quite naturally from there, Frank. It was only when she glanced at him and caught his dark eyes fixed on her so intently that she pulled herself up short.\n\n'I'd better go and see if Claudia is all right,' she said.\n\n'We'll have coffee first.'\n\nShe went back to the lounge with him and drank her coffee and talked about the weather, disliking him very much because she suspected that he was laughing at her. She escaped as soon as she could, thanked him for her dinner and asked what time they were to be ready in the morning.\n\n'Eleven o'clock\u2014and I mean eleven o'clock. Unless Claudia particularly wants to do any shopping, I suggest that she has breakfast in bed. We'll breakfast at half past eight precisely.' He looked down his nose at her. 'You're not one of those silly women who don't eat breakfast, I hope?'\n\nLouisa said pertly: 'Perhaps I should have it in my room, then you won't have the bother of talking to me, Mr Savage.'\n\n'I seldom talk at breakfast, Louisa. It will give me the opportunity of giving you any last-minute instructions should it be necessary.'\n\nShe gave him a steely glance, wishing she could think of something dignified and really squashing, but she couldn't\u2014though her 'good-night' was icy.\n\nClaudia was lying against her pillows, a box of chocolates open beside her, books scattered in all directions. She looked up as Louisa went in and said: 'Oh, hullo\u2014there you are. Has Simon let you off the hook? I've had a lovely evening,' and she stretched her arms. 'Such lovely comfort, and the nicest chambermaid\u2014I got her to fetch me some more books and some sweets. I suppose you're going to tell me to go to sleep now.'\n\nLouisa smiled. 'No, I won't. We're leaving at eleven o'clock in the morning. Would you like breakfast in bed so that you'll have plenty of time to dress? And do you want to go to the shops?'\n\n'No, but you can go for me\u2014I want some more of that hand cream and I'm almost out of nail varnish. I suppose Simon will allow us to come here to shop as often as we want to?'\n\n'I expect so,' said Louisa, thinking it most unlikely. 'I'll be up fairly early, I'll get anything you want and be back in time to do your packing.'\n\nClaudia nodded dismissal. 'OK. See you in the morning.'\n\nLouisa, back in slacks, boots and thick sweater after a night's sleep, and wishful to keep Simon Savage's mood as sweet as possible, presented herself in the dining room exactly on time. Claudia was still asleep and she took the precaution of asking the reception girl to get a menu sent up to her room within the next ten minutes. Claudia couldn't be hurried and Simon had said eleven o'clock and meant it.\n\nHe was there now waiting for her, dressed for the cold, she noticed, and she wondered just how remote and bleak their future home was to be. He wished her a perfunctory good morning and waved her to the table along one wall, set out with a vast assortment of food: bread, toast, butter, jam, dishes of fish in various sauces and a great bowl of porridge.\n\nShe wandered slowly round and presently joined him at their table, a bowl of porridge in one hand and a plate laden with toast, egg, jam and cheese in the other. He got up and took them from her and asked: 'Tea or coffee?'\n\n'Coffee, please.' And after that she didn't speak, but applied herself to her meal, quite undaunted by the open newspaper Simon Savage held in front of his cross face. It was a pity, she thought, that he always had to look so very disagreeable; life couldn't be all that bad. Perhaps he had been crossed in love? She giggled at the very idea\u2014no woman would dare\u2014and choked on it as the paper was lowered.\n\n'You were saying?' Simon Savage enquired coldly.\n\n'Nothing.' She gave him a sweet smile. 'I don't talk at breakfast either.'\n\nHe folded his paper deliberately and very neatly. 'Take care, Louisa, I'm not the mildest of men.'\n\nShe poured herself another cup of coffee. 'We don't agree about much, Mr Savage\u2014about that, though, we do! Will I be able to get all I want from that big shop across the square?'\n\n'Sundt? I imagine so, provided it's nothing out of the way.' He glanced at his watch. 'Don't let me keep you.'\n\nClaudia was having breakfast when she went back upstairs. Louisa warned her to get up as soon as she had finished, got into her jacket and woolly cap, and went out of the hotel. The shops were open, although it was still not light, and inside Sundt was warm and brightly lighted. Louisa bought everything on her list and spent ten minutes going from counter to counter. She would have to send her stepmother a Christmas present, she supposed, and cards to her friends at the hospital, as well as the aunts and uncles she so seldom saw. She had written once to her home, and told her stepmother that she was in Norway with a patient, but she had given no address and her friends to whom she had written were sworn to secrecy. She had never felt so free, nor, strangely, so happy.\n\nShe would have liked to have lingered in the shop, but a glance at her watch told her that there was little more than an hour before they were to leave. And it was as well that she went back when she did, for Claudia was still lying in bed, doing absolutely nothing. Louisa, by now well versed in the right tactics, persuaded her out of her bed, under the shower and dressed with half an hour to spare, and that would be barely enough time for the elaborate make-up without which Claudia refused to face the outside world. Louisa packed neatly and with speed, rang for their cases to be taken down and left in the foyer, so that Simon Savage's impatience would be tempered, and applied herself to getting Claudia downstairs on time. As it was they were only five minutes late, a fact which Simon silently registered by a speaking glance at the clock.\n\nIt was going to be a lovely day, the blue sky turning the snow even whiter than it already was, and as the Land Rover left the city's centre, the mountains came into view once more, their grey bulk almost covered with snow, making a magnificent background to the tree-covered slopes that skirted them. Simon Savage turned off at the bridge at the end of the main street and took a road running alongside the fjord, and presently stopped.\n\nThere were fishing boats and motor launches moored here, and Louisa saw the same man who had met the boat with him on the previous day coming to meet them. She half expected Claudia to make a fuss as they got out, but beyond a furious look at the two men she did nothing at all, and they were ushered on board a motor launch without further ado. It was a roomy enough vessel with a fair sized cabin, comfortably warm and well fitted out. Claudia, huddled in her thick clothes, curled up at once on one of the cushioned benches and demanded coffee, and Simon without turning his head told Louisa to pour coffee for them all. 'There's a galley,' he told her curtly. 'You'll find everything there.'\n\nIt was a small place, more like a cupboard, but it did hold an astonishing number of things, and the coffee was already bubbling in the percolator on top of the spirit stove. She found mugs, set them on a tray, found milk and sugar too, and went back into the cabin. They were all there; the man introduced as Sven smiled at her as he took his mug, but Simon gave her austere thanks without looking at her, and as for Claudia, she turned her head away.\n\nBut when the men had gone, she sat up, accepted the coffee for a second time and looked around her. 'What a dump!' she declared, looking about.\n\nLouisa, who knew next to nothing about boats, thought it to be the height of comfort, but she knew better than to argue with Claudia; there was a mood coming on, unless she could forestall it...\n\nShe fetched rugs from a shelf, persuaded Claudia to take off her fur coat and her cap and gloves, and tucked her up cosily. 'You're tired,' she observed. 'Close your eyes and have a nap. I daresay we'll be there by the time you wake up.'\n\nJust for once Claudia forgot to be arrogant. 'It's going to be sheer hell,' she whispered. 'It'll kill me!'\n\n'It'll cure you\u2014think how happy that will make Lars.'\n\nClaudia closed her eyes. 'Do you think it's very silly of me to make plans? Wedding plans, I mean. Do you think he'll risk marrying me? I'm an alcoholic...'\n\n'Not any more,' declared Louisa stoutly. 'Now close your eyes and make plans.'\n\nWhich Claudia did, and presently slept.\n\nThe launch was doing a good turn of speed, although the water was choppy. Louisa peered out of the windows and discovered that she couldn't see much for spray, so she put on her jacket again, pulled her woolly cap down over her ears and went outside. Simon Savage was at the wheel, well wrapped against the cold, but when he saw her he said something to Sven, who took it from him and crossed the few feet to the cabin door. He didn't say anything, only pulled her hood up and over her cap and tied the strings under her chin, then kissed her gently.\n\n'You look like a nice rosy apple,' he told her by way of explanation.\n\nShe was too surprised to say anything, which was perhaps just as well, for he went on in a matter-of-fact voice: 'If you look behind you'll see Tromsdaltinden. The snow came early this year, so it will be a long winter. Any number of people go there on a Sunday to ski. There's Finmark to the east, and in a few minutes you'll be able to get a glimpse of the Lyngen mountains\u2014these are islands on the port side, look ahead of you and you'll see the fjord divides\u2014we take the left arm, it runs between two islands, and it's there that we're building a bridge.'\n\nLouisa, oblivious of the icy wind, took the glasses he handed her and then looked her fill. 'People live along here\u2014I can see houses.'\n\n'Settlements\u2014fishing folk mostly\u2014they're not far from Tromso, and there are Hansnes and Karlsoy to the north; small villages, but there's a road to Tromso from Hansnes. Once the bridge is open it will shorten the journey to Tromso.' He gave her a long considering look. 'You like it here, don't you?'\n\n'Yes. It must be lovely in the summer.'\n\n'It is. That's when we do most of our work.'\n\n'Do you ever go home between bridges?' The moment she had spoken she was sorry. He turned away from her and said shortly: 'You'd better go inside and see if Claudia is awake; we shall be landing very shortly.'\n\nLouisa went at once. Just for a few minutes she had thought that they were beginning to lose their dislike of each other, and she had to admit that for her part she was on the verge of liking him, ill-temper and all, but it was obvious that he didn't share her feelings. Oh, well, once they were ashore, he'd be working, she supposed, and they wouldn't have to see much of him. It struck her then that life might be a little difficult for the next few weeks, with Claudia to keep amused. She would have to think of something to occupy them during the short days. She remembered vaguely that Claudia had told her that she had learned to ski as a child and there would surely be a suitable slope not too far away.\n\nShe looked out of the window; there were plenty of mountains, but they all looked quite precipitous. Craning her neck, she could just see the bridge ahead of them; some way off still, graceful and narrow, standing tall on its pillars. She would have liked to have gone back outside and taken a good look, but she suspected that Simon had got fed up with her company and sent her inside unnecessarily soon. A pity, because there was a lot to see now\u2014houses, their painted wood bright against the snow, scattered along the fjord's edge, the mountains at their back doors, and as far as she could see, no road. Racks of cod, minute coves sheltering a fishing boat or two, a solitary church, its short pointed spire covered by snow...\n\nShe put the coffee pot on the stove to warm up and wakened Claudia. She managed to keep the excitement out of her voice as she said: 'We're almost there,' because she knew that Claudia didn't share that feeling; indeed she groaned and declared that nothing would make her set foot on such a solitary snowbound spot.\n\n'Well, if you don't go ashore here, Lars won't know where to find you,' observed Louisa matter-of-factly, 'and I'm sure it's not nearly as bad as you think. I've some coffee for you, drink it up and get wrapped up again.'\n\n'You're nothing but a bully,' complained Claudia, 'every bit as bad as Simon. I'm hungry.'\n\n'We'll get lunch as soon as we land,' declared Louisa, and hoped that they would: it wouldn't take much to send Claudia off into one of her moods. They were very close to the land now; through the windows she could see a cluster of houses beyond a small quay, more cod drying on wooden racks and a larger building with 'Hotel' in large letters on its bright yellow painted wall. The houses were brightly painted too, blue and red and pink; they made cheerful spots of colour against the snow and the grey granite mountains all around them.\n\nThe cabin door opened and Simon poked his head inside. 'We're here', he told them. 'Come along\u2014 Sven will bring the luggage along.'\n\nThere was no one on the quay, just a few wooden sheds and a stack of boxes. The road ran left and right and they turned to the left between two rows of small houses. There was a shop and then the hotel, but they went on past it to the last half dozen houses or so. Simon turned off the road here and clumped through the snow to one of these; square, like all the rest, and like its neighbours, standing on its own, facing the fjord, the mountains nudging its small plot of ground. He opened the door and went in shouting something as he did so and turned to hold it wide for them to go in too. The hall was very small with a door on either side, and from one of these an elderly woman came hurrying out.\n\nSimon performed introductions in a perfunctory fashion and added: 'Elsa speaks a fair amount of English; she comes each day and cleans the house and cooks for me.' He opened the other door and ushered them into a small square room, warm from the wood-burning stove against one wall and furnished with simple comfort. 'Get your things off,' he suggested, 'Elsa is bringing coffee, then you can see your rooms before lunch. I'll be out this afternoon, but you'll have enough to do, unpacking and finding your way around.'\n\nThe coffee came, hot and delicious, and Sven came in with the bags and sat down to drink his, too; and presently Elsa led them upstairs to two small rooms, simply furnished and warm, with bright rugs and curtains. There was a bathroom too, and Louisa, who had expected a lack of modern amenities, was impressed. Claudia wasn't\u2014she went and sat on the edge of her bed, making up her face. 'What a dump!' she declared. 'It's ghastly\u2014we can't all use that poky little bathroom.'\n\n'Don't see why not,' said Louisa cheerfully. 'We don't all want it at the same time, I don't suppose. Let's get tidy and go down to lunch.'\n\nSomething Claudia refused to do. 'I'm tired to death,' she moaned, 'I'll have something on a tray and go to bed with a book.'\n\nAnd nothing Louisa said would change her mind. She left her sitting there and went downstairs and found the table laid and Simon at one end of it, bent over a large map and a bundle of papers. He looked up briefly as she went in. 'Where's Claudia?' And when she explained: 'She can come down for her meals or starve, I don't care which. Tell her that.'\n\nLouisa eyed him with disfavour. 'No, you tell her,' she said quietly, and then: 'You're too hard on her, you know.'\n\nSimon gave her a baleful stare. 'Don't preach to me, Nurse.' But he went past her and up the stairs and presently came down again, looking grim, with a seething Claudia behind him. Louisa made an uneasy third at table, sitting between the two of them, eating her cod and potatoes in a heavy silence.\n\nWith a muttered excuse Simon went away the moment he had finished eating, and Claudia burst into tears. Louisa gave her another cup of coffee, allowed her to cry her fill and then suggested that they should go upstairs.\n\n'I'll unpack,' she said with a cheerfulness she didn't feel, 'and you can have a nap or read, and we can have tea here, by the stove.' She urged a reluctant Claudia upstairs, bathed her face for her, settled her under the duvet, found a pile of books and started to put away clothes. By the time she had finished, Claudia was asleep and she was able to go to her own little room and do her own unpacking. That done, she went to look out of the window. It was almost dark, but there were lights in all the houses, making the snow sparkle. Tomorrow she would persuade Claudia to explore a bit\u2014a shop, even a small general store, would be somewhere to go, and perhaps they could get coffee at the hotel. And she was longing to get a closer look at the bridge. She sighed and pulled the curtains, then went downstairs to look for Elsa and ask about tea.\n\nClaudia had calmed down by tea time and when Louisa, who had been prowling round the little house, mentioned casually that there was a telephone in the hall tucked away in a dark corner under the stairs, she declared that she would ring up Lars at once, but before she could get there, there was a call from him. Louisa, roasting herself by the stove and watching the television programme she couldn't understand, heard Claudia's excited voice and heaved a sigh of relief. The call lasted ten minutes or more, during which time Simon came back, said hullo, in a perfunctory manner, and declared his intention of going across the hall to the small room he used as his office. At the door he paused. 'Any idea how you're going to fill in the time here?' he asked.\n\n'I've brought embroidery and knitting and books for both of us. We'll go out each day\u2014Claudia told me she could ski, but I can't.'\n\n'You can learn\u2014there's an easy slope close by. We'll make up a party on Saturday. The shop has books and the papers come with the postman by launch every third day.'\n\n'And perhaps we could go to Tromso once in a while,' asked Louisa, encouraged by these suggestions.\n\n'Perhaps.' He was non-committal about it. 'Claudia will probably give you the hell of a time.'\n\n'Yes, I expect that, but I expect her to get better too.' She spoke defiantly and he laughed.\n\n'I hope you're right.' His eyes narrowed. 'And understand this; any hint of backsliding and I want to know at once. Is that understood?'\n\n'Oh, I understand you very well,' said Louisa, her voice a little high with suppressed feelings. 'What a very disagreeable man you are, Mr Savage, with your orders and arrogance. I should very much dislike having you as a patient.'\n\nHis dark eyes snapped at her. 'You surprise me, Louisa. I should have thought it would have been the very thing, because I would be entirely at your mercy and you could wreak revenge to your heart's content.' His silky voice had a nasty edge to it. He opened the door. 'Perhaps we'd better keep out of each other's way?' he wanted to know.\n\nShe agreed stiffly and when she was alone again, wondered why the prospect left her with the feeling that life would be rather dull.\n\n## CHAPTER SEVEN\n\nCLAUDIA WAS STILL asleep when Louisa went down to breakfast the next morning, to find Simon already at the table, spooning up porridge as though he had a train to catch. He got up as she went in, however, wished her good morning and asked her if she preferred coffee to tea. 'And where's Claudia?' he asked indifferently.\n\n'In bed, asleep. I shall take her breakfast up later.'\n\nShe met his cold eyes. 'I see no reason why she should be pampered. I brought her here in the hope that the simple life led here would effect a cure.' He sounded impatient.\n\n'Probably you did,' she said equably, 'but there's no reason to rush things, is there? Why put her back up when there's no need? I shall take her breakfast up.' She began on her porridge and dropped the spoon at his sudden roar.\n\n'Are you defying me, Nurse Evans?'\n\nShe sugared her porridge. 'Well, yes, I believe I am,' she told him placidly. 'I don't interfere with your bridges, Mr Savage, I don't think that you should interfere with my nursing.'\n\n'Claudia doesn't need a nurse any more.'\n\nShe raised her eyes to his. 'You'd like me to go, Mr Savage? You have only to say so. After all, it's you who pays my wages.'\n\nShe watched him getting control of his temper while he helped himself to cranberry jam and took some toast. He said evenly: 'Nurse Evans, you may have carte blanche with my stepsister, but I advise you to be very careful. I'm not a man to be crossed lightly.'\n\n'Oh, I can see that,' said Louisa airily, 'but if you'll give me a free hand with Claudia, then I promise I won't interfere with your bridges.'\n\nAn unwilling laugh escaped him. 'I've never met anyone quite like you, Louisa.' He started gathering up the papers by his plate. 'And you seemed so quiet, almost timid... I shan't be in to lunch.'\n\nShe finished her breakfast in deep thought. Obviously he didn't intend to organise any activities for them, that was something she would have to do for herself. She cleared the table and went into the kitchen and under Elsa's kindly eye, prepared a tray for Claudia.\n\nIt was still dark outside; she prudently left the curtains drawn, switched on the bedside light and only then wakened Claudia, whose temper, never very sunny in the morning, improved a little at the sight of her breakfast tray.\n\n'However did you manage it?' she asked, and yawned hugely. 'I'm sure Simon said something about eight o'clock...'\n\n'Yes, he did, but we agreed that you should have breakfast in bed.'\n\n'Every day?'\n\nLouisa nodded. 'Why not? I've little enough to do, you know. I thought we might go out presently and take a look at that shop and perhaps have coffee at the hotel...'\n\n'And then what?' demanded Claudia pettishly.\n\n'I'm going to find out about skiing, I'm dying to learn\u2014do you suppose you could teach me?'\n\nClaudia was buttering toast. 'I suppose I could. God knows where I'll get the energy from\u2014it sounds a fearful bore.'\n\n'Perhaps we could try once or twice, and if I'm quite hopeless I'll give it up.'\n\nClaudia had picked up a magazine and was leafing through the pages. 'OK,' she said without much interest, 'I suppose it'll be something to do.'\n\nLouisa was at the door. 'I suppose Lars Helgesen skis beautifully.' She closed the door gently behind her.\n\nThere weren't many people about as they crunched through the snow towards the shop, but there was a fair amount of activity on the quay: a fork lifter stacking large cardboard boxes, parcels and bundles of all shapes and sizes being sorted; there were lights everywhere, of course, for it was still not light, although the sky was clear. Several men went past them on snow scooters, going out of sight where the last of the houses clustered on a bend of the fjord. The bridge lay in that direction; Louisa dearly wanted to see it, but she doubted whether Claudia would walk so far. They turned into the shop and were agreeably surprised to find that it housed almost anything they might need. What was more, the post had arrived and among the letters was one from Lars. Claudia tucked it into a pocket, her pale face pink so that she looked lovelier than ever, and Louisa vowed that nothing was going to stop her from making every effort to cure her of her addiction\u2014'nothing', of course, was Simon Savage being tiresome. They spent quite a time in the shop, delighted to find that there was a small stock of English paperbacks as well as a two-day-old copy of The Times. They bought chocolate, too and Louisa, finding that they could speak English, asked the young woman behind the counter about skiing. Her questions were met with instant offers of skis, boots, a guide to show them the way and someone to instruct her. Louisa explained about Claudia teaching her, but accepted the rest of the offer for the next morning and when she offered to pay met with such a vigorous refusal to take a single krone that she didn't say another word. 'You are family of Mr Savage,' she was told. 'He is our friend and we treat you also as friends\u2014friends do not pay.'\n\nThey went to the hotel next and were surprised again. It was a small wooden building, not much bigger than the houses round it, but inside it had a small cosy bar, an even smaller dining room and a much larger room where there was a billiard table, dartboard and a number of small tables and chairs. Louisa guessed that it was used for a great many things during the winter, for there was a small screen hung against one wall and a projector beside it, and in one corner there was a piano.\n\nThere was no one else there. They ordered coffee and the proprietor brought it himself and then sat down with them, proving to be a fount of information, imparted in English, which while not fluent, was easily understandable. The post came twice a week, they were told, books and magazines could be ordered at the shop and came at the same time. It was possible to go to Tromso whenever they wished provided the weather wasn't bad. There was a film show every Saturday evening in that very room and dancing afterwards. And when Louisa observed that there weren't all that number of people to come to it, he laughed cheerfully and told her that the people who lived along the shores of the fjord came in for the evening.\n\n'We are very happy here,' he told her. 'We have the mountains and the fjord and in the summer visitors come and camp along the shore and we are very busy. Besides, there is the bridge. The men who work on it sleep and eat here and go home at the weekends. My hotel is full.'\n\n'Won't it be rather quiet when they go?' asked Louisa.\n\nHe looked surprised. 'Oh, no\u2014it will be Christmas.'\n\nThey parted, the best of friends, presently, and walked back to the house to find that Elsa had their lunch waiting\u2014soup and bread and a number of little dishes filled with varieties of fish and cheese and pickles. Claudia declared that she was tired, although she had soup and coffee before making herself comfortable on the outsize couch before the stove. Louisa waited for her to ask for a drink, but she didn't, and by the time Louisa had cleared the table she was asleep.\n\nElsa would be in the house until the evening and was perfectly willing to keep an eye on Claudia. Louisa put on her outdoor things again and went back through the snow, past the last of the houses to where the rough road ended, but there was some sort of path once she had reached the curve of the fjord and she followed it carefully in the twilight which she realised was all there was in place of the daylight. The water looked cold and dark, whipped up into waves by a cutting wind, and she faltered for a moment. Suppose night descended and she couldn't see the path to go back by? And then she told herself that she was silly; the snow scooters had gone that way; it was well used and surely they would be returning soon? She pressed on to the next curve and was rewarded by a sight of the bridge, brilliantly lighted at each end, and she could see and hear men working. She was in two minds whether to go on, but a few flakes of snow sent her sharply back the way she had come, very aware of the looming mountains and the gathering darkness. She had reached the first house when a snow scooter skidded to a halt beside her and Simon Savage got off. He greeted her coldly; 'I shouldn't advise you to go off on your own until you're sure of the way. Only a fool would do that at this time of the year. It's easy enough to get lost.'\n\n'I wanted to see the bridge, and I wasn't being reckless, Mr Savage. I saw some men go this way before lunchtime, and I guessed there would be a path.'\n\nHe grunted. 'And Claudia?' It was snowing quite fast now; he looked enormously tall and bulky.\n\n'We had a very pleasant morning. There was a letter from Lars Helgesen. We went to the shop and then to the hotel for coffee.' She added defiantly: 'And I asked about skiing.'\n\n'Admirable Louisa! I'm sure you'll deal with skis as competently as you do with everything and everyone else. You have someone to teach you?'\n\n'Claudia.'\n\nHe gave a great shout of laughter. 'Of course!'\n\n'And there's no need to laugh like that, it will be something to occupy her. Besides, that nice girl in the shop says her brother will go with us. She arranged it all so quickly...'\n\nSimon stood still and looked down at her. 'Of course she did,' he said blandly. 'I'd already told her that you might enquire. Her brother is wholly to be trusted, he may even give you a few tips when Claudia gets bored with teaching you.'\n\nThey had reached the house and he parked the scooter in the lean-to and opened the door for her. Louisa took off her things and hung them in the hall, got out of her boots and went upstairs in her stockinged feet, not sure if she was pleased or vexed that he should have bothered to arrange everything for them.\n\nSurprisingly tea was a pleasant little meal, and afterwards Louisa got out a pack of cards and taught Claudia how to play Racing Demon while her stepbrother crossed the hall and shut the door firmly behind him. They met again at supper\u2014lamb chops this time followed by cranberry tart and a great pot of coffee\u2014and Simon was so obviously making an effort to entertain them with light conversation that Louisa took pity on him and helped him out as much as she could. Claudia did no such thing, however, either ignoring him or uttering gibes. Louisa could see him holding back his temper with a restraint which did him credit and prayed earnestly that he might not explode with rage before the meal was over. He didn't: as soon as he could decently do so, he wished them goodnight and went back to his work.\n\nWhen she went down to breakfast the next morning he wished her good morning with his usual austerity, but added at once: 'You were quite right; breakfast with Claudia at the table would be disaster. It's a pity that we dislike each other so heartily. Perhaps you were right and I shouldn't have brought her here.' He gave her a grim little smile. 'Aren't you going to say I told you so?'\n\nLouisa sat down composedly, helped herself to porridge and sprinkled sugar with a lavish hand. 'No, I'm not, because I'm sure you were right to do so. It's kill or cure, isn't it?' She frowned. 'I wish I knew more about it\u2014alcoholism, I mean, but she is trying, you know. Is Lars coming to visit her?'\n\n'Yes, but I don't know when. Probably next weekend\u2014he'll fly up to Tromso. I haven't told her.'\n\nShe nodded. 'That's three days away. Perhaps we could go skiing today?'\n\n'Why not? It's clear weather. I'll tell them to have everything ready for you at the shop, and arrange for Arne to go with you both.' He got up. 'You'll excuse me?' He was gone.\n\nThe morning was a huge success. Claudia, once her skis were strapped on, became quite animated, and she and Arne got Louisa between them bullying and encouraging her in turn, while she tripped up, fell over, crossed her skis and did everything wrong, but at the end of an hour or more she found herself actually in some sort of control of the things and began to enjoy herself. They went back to lunch, glowing with exercise. Claudia very pleased with herself because Arne had complimented her on her grace and speed, and Louisa even more pleased because she had almost got the hang of balancing, and best of all, Claudia had actually enjoyed herself; not once had she complained of boredom or evinced a desire to lie down with a book. She ate her meal with a better appetite and although she declared after it that nothing would make her stir out of doors again that day, she did so in a goodnatured fashion, merely requesting Louisa to make her comfortable on the couch, fetch her a book and a rug, and then go away and leave her in peace.\n\nFortunately for her own comfort, Louisa had no wish to stay indoors. She wrapped herself up once more and started to walk towards the other end of the road. Not very far, because there were only a handful of houses beyond the one they lived in, but once past these, she found herself walking along the edge of the fjord, going rather gingerly towards the spot where the shore thrust a thin finger into the fjord's water. There was a hut there and she went to peer inside it. Bare now but probably used in the summer, she supposed, and decided to retrace her footsteps to the quay which was after all the heart and soul of the little place. She was standing at its far end, peering down into one of the fishing boats when Simon Savage came to stand beside her. 'You enjoyed your skiing?' he asked, not bothering to greet her.\n\nIt surprised her very much that she was glad to see him. 'Very much indeed, and so did Claudia. We thought we'd go again tomorrow.'\n\n'Why not?' He wasn't looking at her, was not indeed the least bit interested. She said rather tartly: 'It's getting cold, I'm going back to the house.'\n\nShe hadn't expected him to go with her; they left the quay, went past the shop and when they reached the hotel, a few yards farther on, he stopped. 'Coffee,' he said, and took her arm. 'I know it's tea time, but a cup won't hurt you.'\n\nThere were several men in the hotel, sitting at tables, drinking coffee and reading their papers, and Louisa suffered a pang of chagrin as he pulled out a chair at one of these, nodded to her to sit down, said something to the two men already sitting there, and then sat down himself. 'Herre Amundsen, Herre Knudsen,' he introduced them, and then in English: 'Miss Louisa Evans, my stepsister's nurse.'\n\nThey were youngish men and probably glad to see a new face, because they talked eagerly about their work at the bridge, their homes in Tromso and their wives and families. They would be moving on soon, they told her, another week or so and the bridge would be opened. And how did she like Norway? they wanted to know. Louisa told them, delighted to find such friendliness. She drank her coffee, and when Simon ordered her another cup she drank that too, hardly noticing, listening to tales of winter storms, avalanches, the midnight sun, reindeer, the Laplanders...all the things she had wanted to know about. If Simon Savage had been more forthcoming she would have asked him days ago; but he had never encouraged her to ask questions, let alone talk... He sat back now, content to listen, it seemed, replying only briefly when addressed. Presently he said: 'We'd better go. Wait here while I book a table for Saturday evening.'\n\n'Does it really get so crowded?' asked Louisa, watching him talking to the landlord.\n\n'Very busy\u2014many people come to eat and watch the film and afterwards they dance. A splendid evening.'\n\nLouisa thought that it might not be all that splendid. Lars and Claudia would want to talk to each other, she and her stepbrother would probably not be on speaking terms, and she would be forced to drop inane remarks over the high wall of Simon Savage's indifference\u2014but there would be a film afterwards and she hoped devoutly that the men would outnumber the girls so that she would get a chance to dance. Simon was a write-off as far as dancing was concerned.\n\nShe thanked him for the coffee as they walked the short distance back and he muttered something to her in reply, and beyond a few necessary words during tea and later at their supper, he had nothing further to say to her.\n\nThe next few days passed surprisingly smoothly. They skied every morning, and now that she had got over her first fright, Louisa was loving it. Claudia was more or less docile, even grudgingly admitting that she wasn't as bored as she had expected to be; certainly she was looking better and years younger and since there wasn't a great deal of daylight, she had less time to spend in front of the mirror in the mornings and after lunch she was too healthily tired to do more than read by the stove. True, there had been one sticky moment when she had demanded to go to Tromso that weekend, and since Simon hadn't told her that Lars was coming, merely telling her curtly that it wasn't possible, he provoked a burst of temper and tears which took Louisa an hour or more to calm. Indeed, she had intervened and told him severely to go away. He had stared at her for a long moment before he turned on his heel, and she had the quite ridiculous feeling that he was silently laughing.\n\nLars arrived on Saturday morning while Louisa was cautiously skiing down a gentle slope at the foot of the mountains. Claudia had remained at the top with Arne and it was she who saw Lars first, coming down the slope in fine style to meet him. Louisa, not wishing to be an unwelcome third party, began her patient sideways plodding up the slope again and was halfway there when Simon Savage, coming apparently from nowhere, joined her.\n\n'Keep your skis together and then move your right foot up,' he advised her. She paused to look at him. He did look rather handsome, she had to admit, and not as forbidding as usual. 'Where did you come from?' she wanted to know.\n\n'I fetched Lars from the airport. While he was changing I came across the mountains...' He waved a vague arm at the forbidding heights all around them, and she said: 'But there's nowhere to go.'\n\n'Yes, there is, if you know the way. I'll show you one day.'\n\nThey had reached the top and Simon said something to Arne, who grinned and sped away back to the shop far below.\n\n'Now,' said Simon, 'let me see what you can do.'\n\nAn opportunity to show her prowess; the slope was white and inviting and not quite so frightening any more. Claudia and Lars had disappeared: she would show her companion just how good she was. She launched herself with what she hoped was effortless grace.\n\nHer skis crossed almost at once and she ended up upside down in the snow, quite unable to get up. Simon pulled her to her feet, dusted her down and turned her the right way. 'Now, start again, and forget about impressing me.'\n\nShe shot him a very peevish glance and then, surprising herself, burst out laughing. 'Serves me right, doesn't it?' she asked, and launched herself cautiously. And this time she managed very well and even managed to stop at the bottom without falling over again to turn round in time to see Simon Savage sailing down after all with a careless expertise which swamped her with envy.\n\nShe had no chance to tell him how good he was. 'Do it again,' he commanded, 'and this time keep your feet together and don't be so stiff\u2014you can bend in the middle, I hope?'\n\nLouisa had a great desire to burst into tears; she had done quite well and he hadn't even bothered to tell her so, only snapped at her about her feet. She muttered crossly: 'Oh, we're not all as perfect as you are.'\n\n'No,' he sounded quite matter-of-fact, 'but there's no reason why you shouldn't be in time, provided you work at it. Now, are you going to try again?'\n\nShe was cross-eyed with weariness by the time he had finished with her, but she had to admit that she had learnt to control her feet and had lost her poker-like stance. They skied down the slope for the last time and she stood quietly while Simon undid her skis for her and then tossed them over his shoulder with his own. They found Claudia and Lars at the house, very pleased with themselves, and when Claudia said rather pointedly that they were going to spend the afternoon round the stove, Louisa declared that she had letters to write in her room and to her surprise, Simon observed that since they were going out that evening he had some work to do after lunch.\n\nLouisa didn't write letters. The room was warm and comfortable enough but she was lonely. She got on to the bed presently, wrapped in the duvet and slept until Elsa came tapping on the door to tell her that tea was on the table.\n\nBut she was sorry that she had gone down, for Simon Savage had a cup in his workroom and the other two, although pleasant enough, quite obviously didn't want her company. She was trying to think of some good reason for taking her cup upstairs with her when the door opened and Simon came in intent on a second cup. On his way back to the door he suggested that she should join him, adding, presumably for the benefit of the others, 'You're interested in bridges\u2014I've just got the plans for the next one to be built. Bring your tea with you.'\n\nIt seemed the lesser of two evils. She followed him out of the room and when he stood aside went into the room on the other side of the hall. She hadn't been in it before; it was smaller than the sitting room, with a small wood stove, a square table, loaded with rolls of paper, notebooks and, she presumed, the paraphernalia of bridge building, and two or three chairs. He waved her to one of them, and sat down again at the table, where he became totally immersed in a plan he unrolled, she sat sipping her tea, studying the back of his neck; she rather liked the way his dark hair grew. After a couple of minutes' complete silence she suggested: 'Since I'm interested in bridges shouldn't I see the plans?'\n\nSimon lifted his head to look at her and she thought it such a pity that he looked so remote. 'My dear girl, I said that to get you out of the room. I'd not the least intention of showing you anything.'\n\nShe felt so hurt that it was like a physical pain inside her. She put down her cup and saucer on the table and got to her feet. 'That was kind of you,' she told him quietly. 'I won't trespass on your\u2014hospitality any longer.'\n\nShe had whisked out of the room, giving him no chance to reply. Not that she had expected him to.\n\nShe had a nice cry after that, although she wasn't sure why she was crying, and then had a shower and dressed slowly, ready for the evening. Claudia had told her that she was going to wear a long dress, a lovely woollen affair with a matching stole, so Louisa felt quite justified in putting on the long skirt and the quilted waistcoat. She put on more make-up than usual too and did her hair in a complicated style which she prayed would stay up for the rest of the evening.\n\nLars, who was staying at the hotel, had already gone there. It only remained for Simon Savage, very stylish in pin-stripes and a silk shirt under his sheepskin jacket, to escort them the very short distance to the hotel.\n\nThe dining room was almost full and they went straight to their table, and Louisa, who had been worrying about the drinks, was relieved to find that the men made no effort to go to the bar and drank the tonic and lemon Simon had ordered for them all without a muscle of their faces moving.\n\nThe dinner was delicious\u2014thick home-made soup, fish beautifully cooked, and fruit salad, followed by a great pot of coffee. They lingered over it, while Lars, bearing the lion's share of the talk, kept them all laughing, until the film was due to start.\n\nThe room was crowded and their entry caused a small stir among the audience, calling friendly greetings, offering them seats. In the end they settled in the middle of a row of chairs half way back from the screen, Claudia and Louisa in the middle, the men on either side of them. The film was The Sound of Music, which Louisa had seen more times than she could remember, not that that made any difference to her enjoyment. She sat, misty-eyed, her gentle mouth very slightly open, oblivious of Claudia and Lars holding hands beside her and Simon Savage, sitting well back and watching her face, with no expression on his own features at all. Anyone looking at him might have concluded that he had seen the film too and had gone into a trance until it was over.\n\nWhen the film was finished the dancing began. The men had surged to the bar, but at the first sound of Abba on the tape, they were back, swinging their partners on to the floor. Louisa, who had watched Lars and Claudia join the cheerful dancing throng, felt a wave of relief when a young giant of a man she had seen several times on the quay advanced upon her with a friendly: 'Yes?' and danced her off too. Only then did she admit to her fear of being left high and dry and Simon Savage coming to find her without a partner. He would have danced with her, of course, with the frigid politeness of someone doing his duty...\n\nThe tape came to an end and she was still exchanging small talk with her partner when the music started again, and this time it was Simon Savage who danced her off. A neat dancer, she conceded, and self-assured. After a few minutes she relaxed and began to enjoy herself.\n\n'You are enjoying yourself?' enquired Simon, way up above her head.\n\n'Very much, thank you.'\n\n'It compares not unfavourably with the more sophisticated night spots of London?'\n\nShe glanced up briefly. 'I wouldn't know\u2014I've never been to one.'\n\nHe didn't answer and she spent several fruitless moments trying to think of something light and amusing to say, but she couldn't\u2014and anyway, Simon was hardly eager for conversation. They danced in silence, and presently, when the tape was changed, they went on dancing, and except for a short spell with Lars and ten minutes of disco dancing with another young man who owned a fishing boat and who had passed the time of day with her on occasion, Simon continued to dance with her for the rest of the evening. He was, she felt, exceeding his duty by doing so, especially as there were several pretty girls there, but it seemed that his duty didn't include talking. Probably he was working out a new bridge.\n\nThe evening came to an end. Everyone put on layers of warm clothing and went out into the cold, calling good-nights as they went. Louisa was glad that the distance was short to the house. The idea of facing a trip on the fjord before one got home was rather more than one would wish for at that time of night. She went indoors thankfully and went at once to her room, leaving the others downstairs. It was to be hoped that Simon would have the sense to go to his room too and give the other two a chance to say goodnight before Lars went back to the hotel. She was undressed and in bed, almost asleep, when there was a gentle knock on her door and it was opened.\n\n'You're awake?' It was more a statement than a question, uttered in Simon's voice, surprisingly quiet. He came in, shutting the door behind him, and Louisa sat up in bed and switched on the bedside light.\n\n'Claudia\u2014I heard her come up to bed...'\n\n'Where she is now. There's been an accident\u2014a gust of wind overturned one of the launches\u2014three men on board, all saved but in poor shape. They are bringing them in now. Will you come down to the hotel as soon as you can?'\n\n'Give me five minutes.' She barely waited for him to be gone before she was out of bed, tearing off her sensible long-sleeved nightie, bundling into woollies, a sweater, slacks, her jacket, her woolly cap crammed down on to her flowing hair. She crept downstairs in her wool socks and wondered briefly if it was all right to leave Claudia on her own, but there was nothing much she could do about that. She closed the outer door quietly and felt the shock of the bitter wind and cold night as she hurried to the hotel.\n\nThe door was shut, but there were lights on downstairs. She opened it and went inside and found that the first of the men was already there, lying on one of the larger tables, covered with a blanket. Two men were bending over him, but they straightened up as she went to look and stood back a little. The man was young and suffering, she judged, from his immersion in the fjord, but his colour wasn't too bad and his pulse was fairly strong. She got the men to help her turn him on to his side, made sure that he had a free air passage, and began to strip off his outer clothes. Someone, she was glad to see, had already taken off his boots and there were plenty of dry blankets piled near. She set the men to rub his arms and legs once his clothes were off, took his pulse again and turned round as the second man was brought in\u2014an older man this time, and not a good colour. The four men carrying him laid him on another blanket-covered table and while she took a quick look at him, began to take off his clothes and boots too. Louisa removed false teeth, took a faint pulse and requested towels, and when they came set to to rub the man's legs and arms, presently handing over to her helpers while she went back to look at the first man. He was decidedly better and would be better still for a warm bed and a good sleep once he was conscious. She judged him to be safe enough to leave and went back to the other man.\n\nNo one had said very much, doing as she asked them without query, and now the landlord appeared, his wife behind him, carrying a tray loaded with mugs and coffee pots and the potent spirit Aqua Vitae, and hard on their heels came the third patient, carried carefully by another four men, Simon Savage being one of them. He looked across the room as they laid the man, little more than a boy, on a table and said briefly: 'I think he has a broken leg.'\n\nAs indeed he had, a nasty compound fracture of the tibia and probably more than that. Louisa set about covering the ugly jagged wound, thankful that he was unconscious still, and then with Simon Savage's help gently straightened the leg and splinted it. There might not be a doctor in the small community, but at least they had an excellent first aid equipment. The boy had had a blow on the head as well, there was a discoloration over one eye, but his pulse was good and his pupils were reacting. She finished her work with calm unhurry and said: 'They'll need to go into hospital. The first one is not too bad, but he'll have to have a check-up.'\n\n'Lars and some of the men are getting a launch ready now,' Simon told her. 'We'll take them up to Tromso. You'll come with us.'\n\nOrders, orders! thought Louisa. He could have said please, it would have made a trying situation a little less trying. She said, 'Very well,' and then, 'Claudia is alone.'\n\n'Lars is going up there for the rest of the night. Are we ready to go?'\n\n'Who are \"we\"?' She was taking pulses again, doing a careful last-minute check.\n\n'You, me, Arne and Knut, the boy you were dancing with.'\n\nLouisa took the coffee the landlord was offering her and took a heartening sip. She wasn't sure, but she thought that he had put Aqua Vitae into it, a good idea if they were to face the cold again. Simon Savage was gulping his down too and then Arne and Knut came in, swallowed their drinks, listened to Simon's instructions, and went away again. One by one the three men were carried down to the quay, into the launch and made comfortable. Louisa was barely aboard when Simon shouted for a man to cast off, and took the wheel. There was a hard wind blowing within a very few minutes, and Louisa quite understood how the boat the three men had been in had overturned; she only hoped the launch was made of sterner stuff. They lurched and slithered, and if she had had the time she would have indulged in seasickness, but what with keeping the three men on the benches, taking pulses, and when the first man regained consciousness, reassuring him, she had not a moment to spare.\n\nThe journey seemed unending and she wondered how the men on deck were faring. Now and then she heard them shouting to each other above the wind, but their voices were cheerful. The boy with the broken leg came to for a moment and she had a job to quieten him before he drowsed off again. His cries brought Simon Savage into the cabin, together with a blast of icy air. 'All right?' he wanted to know. 'We're coming in now. There should be an ambulance waiting\u2014I phoned ahead.'\n\nIt took a little while to manoeuvre the three men off the launch and on to the quay, where two ambulances were parked. Louisa, told by Simon to get into the second one, did so, looking round anxiously to see what everyone else was doing\u2014surely they weren't going to leave her here?\n\n'Don't worry,' said Simon laconically. 'Arne and Knut will wait here in the launch for us.' He shut the doors on her and a moment later they moved off.\n\nShe was very tired by now and cold to her bones. The hospital, when they reached it, was a blur of bright lights and briskly moving figures. Modern, she thought, escorting the boy into the casualty department, and well equipped. If she hadn't been so worn out she would have been glad to have looked around her. As it was she was told kindly to sit down and waved to one of the benches and someone brought her a cup of coffee. Everyone had disappeared by now. She closed her eyes and dozed, to be roused presently by Simon Savage. 'We're going back,' he told her. 'One of the ambulances will give us a lift to the launch.'\n\nShe nodded. 'The men\u2014will they be all right?'\n\n'Yes. You did a good job, Louisa\u2014thanks.'\n\nHe bundled her into the ambulance, beside the driver, and got in beside her, then hauled her out again and helped her on to the launch. 'Inside,' he said, and she sat down thankfully on one of the benches and would have gone to sleep again if Knut hadn't come in with more coffee, laced with Aqua Vitae, and stood over her while she drank it. She went to sleep within minutes, which was a good thing, as they were heading into a gale force wind which sent the launch heaving and shuddering and would have terrified her if she had been awake. As it was she had to be shaken when they finally got back.\n\n'Are we there already?' she asked querulously, and tried to go to sleep again, and when she got another shake, 'I must have gone to sleep.'\n\n'You're swimming in spirits,' said Simon. 'We came back in a gale and it seemed best to knock you out.' He hoisted her to her feet. 'Can you manage to walk?'\n\nThe cold air revived her and she managed very well, with his arm around her, and at the door she asked: 'What's the time? I seem to have lost track...'\n\nHe opened the door and pushed her gently inside. 'It's almost five o'clock. Are you hungry?'\n\nShe discovered that she was and nodded.\n\n'Go upstairs and get ready for bed and then come down to the kitchen.'\n\nLouisa nodded again and stumbled upstairs and into her room. The sight of her bed almost sent her into it, still dressed as she was, but she had no doubt at all that if she didn't present herself downstairs within a reasonable time, Simon would be wanting to know why not. She undressed and went back to the kitchen, wrapped in the thick dressing gown she had bought for warmth rather than glamour. Certainly there wasn't a vestige of glamour about her. White-faced, her hair in rats' tails, her eyes heavy with sleep, she wandered into the warm little room and found the table laid with plates and mugs and knives and forks. Simon, that most unlikely of cooks, had fried eggs in a pan, made a pot of tea, and cut slices off a brown loaf.\n\nThey sat opposite each other hardly speaking, and when they had finished they cleared the table, left everything tidy and went out into the little hall. 'Where will you sleep?' asked Louisa, suddenly remembering that Lars was there.\n\n'It won't be the first time I've slept in a chair.' Indeed, now that she looked closely at him, he looked tired to death.\n\nShe said in a motherly voice: 'Oh, poor you! I'll get some blankets and a pillow...'\n\nSimon shook his head. 'Go to bed.' He smiled down at her, a wide, tender smile that made her blink, and then bent his head to kiss her\u2014quick and hard and not at all like the other kiss he had given her. If she hadn't been three parts asleep she would have been filled with astonishment. As it was, she fell into bed aware of a complete contentment, although about what, she had no idea.\n\n## CHAPTER EIGHT\n\nIT WAS Elsa who wakened Louisa later in the morning with a cup of tea and the news that Mr Savage had gone to Tromso to see how the three men were faring, and Miss Savage and Herre Helgesen had gone skiing.\n\nLouisa showered and dressed and went downstairs, had a cup of coffee and a slice of toast in the kitchen and set about laying the table for lunch. Everyone would be back soon; it was almost one o'clock. But one o'clock came and passed and she went into the kitchen to confer with Elsa, who shook her head and said that she really didn't know. Miss Savage had taken a packet of sandwiches with her, but she had said nothing about not coming back at the usual time, and as for Mr Savage, he had said nothing at all, merely walked out of the house\u2014it was Herre Helgesen who had told her where he had gone. Luckily it was a meal which would come to no harm. She looked enquiringly at Louisa because she always went home after she had seen to the midday meal and it was already over her normal time.\n\nLouisa assured her that she could cope quite easily with the dishing up when the others came home and begged her to take extra time off as she had been so inconvenienced, so Elsa got into her outdoor things, wished her a pleasant Sunday afternoon, and hurried off, leaving Louisa to potter in the kitchen for a while and then go back to sit by the stove, but by now it was almost two o'clock and she was famished, so she went into the kitchen again, helped herself to a plate of Elsa's delicious casserole and ate it at the kitchen table and then, because she was still hungry, she cut a hunk of cheese and ate that before washing her plate and setting the tea tray. Somebody must come back soon, the light was already fading fast into black night. She set the kettle to boil on the wood stove in the sitting room and sat down again to read, but presently she let the book fall and allowed her thoughts to roam.\n\nIt seemed likely that she would be going back to England soon. Claudia didn't really need her now; Lars had been the miracle that was needed, if Claudia loved him enough she wouldn't drink again as long as she lived\u2014they would marry and live happily ever after in Bergen. And Simon? Presumably he would go on building bridges wherever they were needed in the world. He was entirely self-sufficient and content with his lot. Presumably he had a home somewhere in England. He might even marry one day; he would make a terrible husband, she considered, although just once or twice she had glimpsed a quite different man behind that dark austere face. He had been kind to her, too. She remembered his smile and smiled herself, thinking about it. Undoubtedly there was another Simon Savage tucked away somewhere...\n\nIt was warm in the room and she dozed off, thinking about him still, and awakened to hear Claudia's voice and Lars' deeper tones.\n\nThey stopped in surprise when they saw her. 'Have you been here all day?' asked Claudia, and started flinging her jacket and cap and scarf on to chairs and kicking off her boots. 'We thought you'd go with Simon.'\n\nLouisa tried to remember if he'd said anything about taking her out and couldn't\u2014how awful if he had, and she'd gone on sleeping when she should have been up and dressed and ready. 'I didn't wake up,' she said uncertainly.\n\nClaudia shrugged. 'Oh, well, probably he didn't want you, anyway\u2014only he said he was going to the hospital at Tromso, and that's your meat and drink, isn't it?'\n\nLouisa didn't answer but picked up the dropped clothes and asked if they'd like tea. 'There's dinner in the oven,' she explained, 'but it'll keep until you want it.'\n\nThey decided to have tea and Lars went into the kitchen to get the tray while Louisa whipped upstairs with Claudia's things. Claudia looked fantastically happy, but she looked tired too.\n\n'Where did you go?' Louisa asked when she got downstairs again.\n\n'Oh, miles and miles\u2014it was heaven,' Claudia answered her carelessly. 'Lars, must you really go back to Bergen?' She smiled at him beguilingly. 'One more day?'\n\nHe shook his head. 'No, my dear, I have to go, but I'll come again, as often as I can.'\n\n'Why can't I come with you?' Claudia's voice was dangerously high.\n\n'Because another week or two here is what you need; I want a healthy beautiful girl for a wife and I'm prepared to wait for her.'\n\nLouisa poured tea, feeling de trop, and after her first cup she escaped to the kitchen with a muttered excuse which no one listened to, made herself another pot of tea and sat at the table drinking it. She felt incredibly lonely.\n\nWhen she went back to the sitting room an hour later, the two of them were so absorbed in their talk that she had to ask twice when they wanted their supper.\n\n'We're going over to the hotel,' said Claudia. 'I daresay Simon will be back, and you can eat together.'\n\n'He'll be able to tell you about the men in hospital,' suggested Lars kindly. 'They're all talking about you, you know, saying how splendid you were.'\n\n'Oh, are they? I didn't do anything.' She smiled at them both and went back to the kitchen and stayed there until they left, calling cheerfully that they wouldn't be late back.\n\n'I've got a key,' said Claudia from the door. 'Go to bed if you want to.'\n\nLouisa went back to the sitting room, cleared away the tea things, plumped up the cushions, made up the stove and sat down. If Simon didn't turn up by seven o'clock she was going to have her supper; the casserole was more than ready and she was hungry.\n\nAll the same, it was half an hour after that time when she finally had her supper. She ate it on her lap, wondering if the launch had turned turtle on the way back from Tromso. It was more than likely that Simon had gone to a hotel there and had a slap-up meal\u2014probably with some lovely Norwegian lady, she thought gloomily, and then told herself sharply that it didn't matter to her in the least with whom he went out.\n\nBy ten o'clock she had had enough. She washed the dishes, tidied the kitchen and went up to bed. It wasn't long after that that she heard Claudia and Lars come in and after a murmur of voices, Claudia came upstairs. What seemed like hours later, she heard Simon Savage's deliberate footsteps coming into the house. She listened to him making up the stove, going into the kitchen, retracing his steps to his workroom and finally the clink of a glass\u2014whisky; perhaps he was chilled to the marrow, hungry, soaking wet... By a great effort she stayed in bed, although every instinct was willing her to go down and warm up the rest of the casserole. It was an hour or more before he came upstairs and it wasn't until then that she allowed herself to go to sleep.\n\nThe next day was a bad one. Claudia, without Lars to keep her happy, was at her very worst. She refused to get out of bed, she threw her breakfast tray at Louisa, declared her intention of leaving for Bergen that very morning, swore that she would kill anyone who tried to stop her, and then dissolved into a flood of hysterical tears. Louisa, picking up broken china, was just in time to meet Simon Savage, coming up the stairs like the wrath of God, and order him down again.\n\n'Don't you dare!' she admonished him. 'She's only upset because Lars isn't here\u2014it'll be all right presently...' She shooed him step by step until they were back to the hall. 'Go on,' she told him firmly, 'go and build your bridge! You don't understand women, even if you do know how to make a bridge stay up.'\n\nHis face, black with temper, suddenly broke into a smile. 'I think you may be right there, Louisa. How fierce you are!' He kissed the end of her nose and turned her round. 'Up you go!'\n\nHe was wise enough not to come back until well after tea time, and by then Claudia was at least trying for self-control. A phone call from Lars had helped, of course, and Louisa's patient, uncomplaining company. Halfway through a good wallow in self-pity Claudia paused long enough to observe: 'I don't know how you can put up with me\u2014I'd be gone like a bat out of hell if I'd been you.' But before Louisa could answer that she was in floods of tears again.\n\nSimon behaved beautifully when he did come back home. Bearing an armful of magazines and the newest papers, he put them down beside his stepsister, wished the room at large a good evening, and went into his workroom, where he stayed until Louisa summoned him to supper. And during that meal he talked with unusual placidity about Bergen, Lars' house, his work, his interest in sport, and from there he passed to the various churches in the city, remarking that Lars always went to St Jorgen Church. 'It might be a good place in which to marry,' he suggested mildly, 'because they hold English church services there as well.'\n\nClaudia looked up from the food she was pushing round her plate.\n\n'You don't mind if I marry Lars? You've always disagreed with everything I've wanted to do\u2014hated my friends...'\n\nLouisa watched his saturnine features, ready for an outburst. None came. He said mildly: 'Won't you in all fairness agree that I had good reason to dislike them? Do you really want them as friends?' He shrugged. 'Not that it's any business of mine any more, but I'm not sure if Lars will care for them.'\n\n'Oh, I know that\u2014you don't have to preach at me, but I won't want friends now, will I, I've got him.' She got up from the table. 'I'm not hungry. 'I'm going to bed. Louisa, you can bring me up some coffee and a sandwich later.'\n\n'If it were not for the fact that you would scold me severely, I would have made Claudia apologise for talking to you like that,' remarked Simon evenly.\n\n'She doesn't mean it\u2014she's unhappy...' Louisa gave him the briefest of glances, wishing to appear matter-of-fact after their meeting that morning.\n\n'And you? Are you happy?'\n\n'Yes. You see, Claudia is almost cured, isn't she? Oh, I know she's had relapses before, but this time there's Lars. I think he loves her so much that he's prepared to put up with a good deal.'\n\n'And would you like to be loved like that, Louisa?'\n\n'Yes, of course I should, but it doesn't happen to everyone, does it?'\n\nHe didn't reply, but presently said: 'I had planned to take you both to Tromso for a day's shopping, but the weather forecast is bad and it's too risky.'\n\n'Perhaps in a few days\u2014it would do Claudia a lot of good. How are the three men?'\n\n'In good shape; two of them will be coming back in a few days, the boy will have to stay for a bit, but he's got relatives in Tromso, so it won't be too bad for him.' He was staring at her steadily. 'Everyone here is proud of you, do you know that?'\n\nShe looked down at her empty plate and could think of nothing to say. Presently she broke a silence which had gone on for too long. 'Mr Savage...'\n\n'And that's another thing\u2014why am I always Mr Savage? We have Lars and Arne and Knut and Mr Savage, as though I were some mid-Victorian ogre. My name is Simon.'\n\nShe poured herself more coffee which she didn't want, but it gave her something to do. She said very quietly: 'But you were an ogre,' and heard his sigh, and the next moment he had got to his feet.\n\n'Well, I've some work to do,' he was icily bland. 'Goodnight.'\n\nShe didn't see him again until the following evening and by then she was tired and a little cross. Claudia had been very trying, although there were signs that she was pulling herself together again. After all, Lars had promised to come up for the following weekend. Louisa reminded her of this at frequent intervals and talked herself hoarse about the new clothes Claudia insisted she must have. 'I shall want a great deal of money, heaps of it,' she declared. 'Simon will just have to foot the bills. I'm not getting married without a rag to my back!' An inaccurate statement Louisa ignored, only too happy to get Claudia in a more cheerful frame of mind. She wasn't quite as happy when Claudia brought the matter up at the supper table. The conversation between the three of them had been a little forced and Simon looked tired and bad-tempered too. But to her surprise he agreed placidly that Claudia should have enough money to buy what she needed. He even suggested that she might like to fly to Oslo and shop there.\n\n'Does that mean that we can get away from here soon?' Claudia demanded.\n\n'Very soon now\u2014it's up to you, Claudia.'\n\n'I'm on the waggon,' she promised him. 'I swore to Lars that I'll not drink another drop, and I won't\u2014you see, I don't need to. What about Louisa?'\n\nHis glance flickered over her before he answered his stepsister.\n\n'I think we might dispose with Louisa's services very shortly,' he said casually. Just as though I'm not sitting here, thought Louisa indignantly, and quelled the temptation to ask when she was to go. Let him tell her, she couldn't care less. She just stopped herself in time from tossing her head.\n\nShe didn't have long to wait. 'How about the end of the week?' he asked smoothly. 'Lars is coming up for the weekend, isn't he? I shall be finished here in four or five days. I don't see why you and Lars shouldn't go back together, and we can put Louisa on a flight the day before that.'\n\n'To London?' asked Claudia without much interest.\n\n'Where else?' Again that quick glance.\n\nShe conjured up a smile and said brightly: 'Oh, how lovely, home for Christmas!'\n\nThe very thought appalled her. She would have to find another job before that\u2014go to an agency and take anything, preferably something that kept her so busy she wouldn't have a moment to remember Norway and Claudia or, for that matter, Simon Savage.\n\nNow that plans were made and Claudia felt secure in a happy future, she shed her bad habits like some old outworn skin. For the next two days she got up for breakfast, insisted on taking Louisa on to the slope to teach her more about skiing, made her own bed and spent barely an hour on her face and hair. Louisa could hardly believe that this was the same woman who had engaged her in London, the change was so great. Of course, Claudia still took little interest in anyone else but herself and Lars. Beyond supposing that Louisa would get herself another job quickly she didn't mention her going and even remarked that it would be delightful to be on her own\u2014at least until she married, she added quickly. 'You're not a bad kid,' she told Louisa, 'but it's like having a ball and chain attached to me, but I suppose you have to put up with that if you're a nurse\u2014a necessary evil, aren't you?' She had laughed and Louisa had laughed with her. No one had ever called her that before, it gave her a nasty cold feeling in her insides, but she would have died rather than let Claudia see how shattered she felt.\n\nAnd Simon made it much worse that evening, talking at great length and with remarkable fluency for him about the delights of the Norwegian Christmas. 'Everything shuts down at midday on Christmas Eve,' he informed her, 'and there's a traditional dish of dried lamb served in the evening and afterwards everyone gathers round the Christmas tree and sings carols before the presents. Christmas Day is much the same and on the next day\u2014our Boxing Day\u2014they give enormous parties with skiing and sleigh rides and masses of food.' He fixed Louisa with his dark eyes. 'You would have enjoyed it, Louisa.'\n\nShe gave him a cross look. Of course she would have enjoyed it, the idea of going back to England didn't appeal to her at all, but what else could she do? They had made it plain enough that she was no longer needed\u2014they would probably be relieved to see her go. She toyed with the idea of staying in Bergen. Christmas wasn't so far off and if she was careful, she would have enough money. There had been little or no chance to spend much, but if she did Claudia might think that she was staying deliberately in order to spy on her. Besides, she had made it plain that she would be glad to see her go. She said woodenly: 'I'm sure I should, it sounds delightful.' And as she said it she was struck by the sudden knowledge that that was what she wanted more than anything in the world\u2014to stay in Norway for Christmas, for ever, if necessary, just as long as she could be with Simon Savage. Falling in love with him had been the last thing she had expected to do. He was ill-tempered, brusque, impatient and intolerant. He was also, she now perceived, the only man she wanted to marry.\n\n'How utterly silly!' she muttered, and earned a surprised look from him. She said the first thing which entered her head: 'Do I fly direct to England or must I change planes?'\n\n'Tromso to Bergen and Bergen to Heathrow.'\n\n'How nice,' she observed idiotically, and waffled on about the journey, the delights of Christmas at home, seeing her friends again, so intent on painting a carefree picture of her future that she quite missed Simon's puzzled look which presently turned to speculation.\n\nAnd if she had hoped, during her wakeful night, for some small sign that he might want to meet her again at some time, she was disappointed. He was more austere than usual over the breakfast table, telling Claudia in a forthright manner that on no account were they to go skiing that day. 'There's bad weather coming,' he assured her, 'probably there'll be no flights to Tromso...'\n\n'Then Lars won't be able to come?'\n\n'Probably not.'\n\nShe shot him a furious look. 'Then I shall go to him.'\n\n'No, if you get to Tromso and the planes are grounded there, you might not be able to get back here. I suggest that you ring him during the morning.' He had gone before she could answer and Louisa was forced to listen to recriminations for the next ten minutes or so; not that she listened very hard, for her head was full of her own problems.\n\nLars telephoned during the morning. There were violent snowstorms in the south of the country and all flights had been cancelled and he would come just as soon as he could\u2014a statement which met with an outburst of tears on Claudia's part and an hysterical request to be taken to Bergen at once. Even Lars' promise that if the weather delayed him for too long he would travel by the coastal steamer did little to cheer her up. He rang off finally and Claudia went up to her room and locked the door.\n\nIt was getting on for midday when she came downstairs again, and daylight, which would last a mere two hours or so, had come. The sky was blue and there wasn't a cloud to be seen from the window and she pointed this out to Louisa. 'They've slipped up,' she said hopefully. 'There's not a sign of snow.'\n\nLouisa glanced out at the sky. 'We can't see a great deal from here,' she pointed out. 'Would you like me to start your packing?'\n\nClaudia sprawled in a chair and picked up a book. 'After lunch\u2014would you go to the shop for me? There are several things I simply must have\u2014I'll make a list while you get your jacket.'\n\nIt was quite a long list and Louisa read it with surprise. 'But you can get most of these in Bergen. I mean, none of them are urgent...'\n\nClaudia barely glanced up from her reading. 'Don't argue. I want them now\u2014unless you're too lazy to go and get them?'\n\nLouisa bit back an angry retort and went out of the house without a word. What did it matter, she asked herself tiredly; what did anything matter?\n\nIt took her fifteen minutes to do the shopping by the time she had waited her turn, waited while the various odds and ends were found and then had a short chat with Arne's sister. As she started back again, she could see that the fjord's waters were dark and heaving sluggishly and that the blue sky had become less vivid. Perhaps there was bad weather coming after all. She went into the house and straight into the sitting room. Claudia wasn't there, so she picked up her basket and went along to the kitchen. Elsa was standing by the table, getting the lunch and looking put out.\n\n'I am glad you are here,' she began. 'Miss Savage has gone out and there is bad weather coming fast. She would not listen to me. She has taken her skis too. I think that Mr Savage should be told, for she will be lost once the snow comes.'\n\nLouisa dumped her basket on the table. 'Did she say where she was going?' and when Elsa shook her head: 'How long ago?'\n\n'Ten minutes, perhaps.'\n\n'Then I'll try and catch her up and get her to come back. Make me some coffee, Elsa, and put it in a thermos, and I want a torch, and then telephone Mr Savage.' Louisa was searching around for the rucksack which hung in the kitchen and when she had it, rammed in some slices of bread Elsa had just cut and a slab of chocolate and a ball of string she saw on the dresser. She hadn't a very good idea of what one took on such a trip and probably there would be no need to use any of them, all the same she added the coffee and the torch. It had all taken a few precious minutes and Claudia might be miles away by now. She put on the rucksack, urged Elsa to telephone without delay, collected her skis from the back door and hurried through the snow, past the last of the houses, where she put on her skis and started cautiously up the slope where they usually went. Claudia had gone that way; she could see the ski marks very plainly. Once she got to the top she would be able to see in all directions.\n\nIt was an interminable time before she got there and in her haste she fell down twice and getting on to her feet again took all her patience and strength, but once there, she stood, fetching her breath, scanning the scene before her. The mountains stretched for miles, snow-covered, terrifying in their grandeur, but far more terrifying was the great bank of cloud, yellow at the edges, devouring the blue sky, and the first hint of the bitter wind hurrying it along at a furious pace. But it wouldn't help to study the sky. She lifted her goggles and surveyed the slopes ahead of her. It took her a minute to spot Claudia, who had skied down the reverse side of the slope and was just beginning to work her way up on the farther side. She was following the route she and Lars had taken together, Louisa guessed. There was a narrow valley which would take her back towards the fjord. Louisa trembled at the thought of the journey ahead of her; she had never ventured farther than the spot she was on at that moment and she was frankly scared. But the longer she stood there, the more terrified she would be. She let out a ringing shout in the hope that Claudia would hear her and for a moment the distant figure paused, but then went on again. Louisa put her goggles back on, took one despairing look at the clouds racing towards her, and set off.\n\nSurprisingly it wasn't as bad as she had expected. The slope was longer than the one she had practised on but no steeper. She reached the bottom, still scared to death but rather pleased with herself, too, and started the laborious climb up the other side. Claudia had disappeared over the ridge and heaven knew what nightmares waited on the other side. A few paper-dry snowflakes began to fall and Louisa, by a great effort, kept her pace deliberate. Hurrying would mean another spill and she hadn't the time to waste. By the time she reached the top the snow was falling in earnest and it was getting ominously dark. She stood at the top, gasping for breath, and looked around her. There wasn't much to see now, for there was a thick curtain of snow and the wind had gathered a ferocious strength. She gazed around helplessly. Claudia's ski tracks had already been covered by the snow, and there was no way of knowing which way she had gone. She wiped her goggles, turned her back to the wind and shouted with all her might.\n\nThere was an answering shout, very faint; impossible to tell from where it came. She couldn't see the lower slopes ahead of her. Suppose she skied to the bottom, passed Claudia and had to come back? She would lose her way and make matters worse. She said out loud: 'Oh, God, please give a hand,' and just for a few seconds the wind dropped and the snow thinned, and away to her left, half way down, she saw a small dark object.\n\n'Oh, thanks very much,' said Louisa fervently, and plunged downwards at an angle, going very carefully. She hadn't learned to turn on skis yet and she hoped she had got the direction right.\n\nShe had, she was on top of Claudia before she could stop herself, and they both fell in a m\u00eal\u00e9e of arms and legs and skis. Claudia was up first and pulled Louisa to her feet. She said bitterly: 'I've been all kinds of a fool\u2014I'm sorry, Louisa,' which was the first time she had ever apologised to her. And probably the last, thought Louisa, busy brushing snow off herself.\n\n'We'll have to make some sort of shelter,' she shouted above the wind. 'I asked Elsa to ring Simon, they'll be out looking for us by now, but we'll freeze if we stay here.'\n\nClaudia clutched at her arm. 'There's a hut somewhere close\u2014we passed it when we came this way, Lars and I. It's somewhere to the left, on an outcrop of rock, it's got a turf roof.'\n\nLouisa remembered the string in her rucksack. 'Let's find it,' she shouted back, 'but we'd better tie ourselves together.' She turned her back. 'In the rucksack.'\n\nIt was a botched-up job, what with thick mitts they dared not take off and granny knots which didn't stay done up, but in the end they achieved a double line of string fastening them together. It would certainly snap if one of them fell, but it was better than noth ing at all. The snow was falling so thickly now that they couldn't see more than a few feet in front of them; but through the gloom it was still possible to make out the outline of the mountains whenever the wind dropped and the snow stopped swirling around them. Claudia remembered that the hut was on the lower slope of a mountain with a peak which towered above the rest. They had to wait a little while before she could locate it and even when they did they weren't sure that they weren't skiing in circles. When they at last saw the hut in front of their noses after several false starts they were ready to cry with fright and relief and tiredness\u2014indeed, Claudia did burst into tears, and Louisa, on the verge of snivelling herself, told her sharply to stop at once. 'Unless you want to die of cold,' she said. 'Get inside, do\u2014 I've got coffee with me and some bread and chocolate and we'll do exercises to keep warm.'\n\n'No one will ever find us,' wailed Claudia.\n\n'Simon will,' declared Louisa stoutly. 'I'm going to shine my torch presently.' She had pushed Claudia into the tiny place and turned to look round at their surroundings. It was a very small hut but stoutly built, with no windows and an open small door, but at least it was shelter. She took off her rucksack, opened the coffee and gave some to Claudia, had some herself and then shared the food, and when they had devoured the last crumb she made Claudia jump up and down and wave her arms. It was difficult, the two of them in the tiny place, floundering about, bumping into each other, but she kept Claudia at it until they were both exhausted even though they were less frozen. Claudia sat down on the rucksack and declared that she had to rest even if she froze solid, and Louisa let her, for the time being at least.\n\n'Why did you do it?' she asked.\n\n'Oh, I don't know\u2014I suppose I was disappointed and upset, and I don't take kindly to not getting my own way, and I've always made a point of doing the opposite of whatever Simon has told me to do.' Claudia gave a choked laugh. 'If we ever get out of this I'll be a reformed character!' She glanced at Louisa. 'Why did you come after me?'\n\n'I'm still in Simon's employ.' The thought of him made her want to cry. She said matter-of-factly: 'I'm going to have a try with the torch. What's the time?'\n\n'Just after two o'clock.'\n\nIt seemed a lot longer than the two hours since she had started out from the house. Surely a search party would be out looking for them by now? She put her head cautiously round the edge of the door and saw that for the moment the snow had lessened, although the wind was still blowing hard. The thought of the journey back, if ever they were lucky enough to make it, made her feel sick.\n\nIt was a pity that she never could remember SOS in Morse, but surely any kind of light in such a desolate spot would attract attention\u2014if only it could be seen. And she had lost her sense of direction, too, which meant sending a beam to all points of the compass. Nothing happened; she repeated her flashes several times and then went to crouch inside again. Claudia had gone to sleep and Louisa wasn't sure if this was a good thing or not. She decided not to wake her for half an hour and got down beside her on the iron hard floor, holding her close so that they might share each other's warmth.\n\nThe half hour went slowly. At the end of it she got up again, wakened an unwilling Claudia and after five minutes waving their arms and stamping their feet, she poked her head out once more. It seemed to her that the appalling weather wasn't quite so appalling as it had been. She had no idea how long such storms lasted and as the daylight hours had already passed, it was too dark to see any possible landmarks, but she was sure that the snow was lessening. She flashed her torch and peered hopefully for a reply, and when there wasn't one, flashed it again. Nothing happened. She would wait ten minutes and then try again. She took one last look and turned round to scan the gloom behind her\u2014and saw a light.\n\nThe torch was still in her hand; excitement made her drop it. She searched for it frantically, quite forgetting to shout. She had to have the torch; whoever it was might miss them and they would die of cold and hunger. She was still grovelling round, sniffing and sobbing under her breath, when someone swished to a halt within inches of her, plucked her off the ground and wrapped her so close that she had no breath.\n\n'So there you are,' said Simon, and kissed her cold face hard and still with one arm round her, turned the torch slung round his neck so that it shone behind him. 'The others will be here in a minute. Where's Claudia?'\n\n'Inside.'\n\nHe pushed her back into the hut and followed. He spoke gently to Claudia, who was in floods of tears, and only grunted when she paused long enough to say: 'You took long enough\u2014I could have died, and I won't go back until the snow stops.'\n\nSimon had coffee with him. He shared it between them and they had barely finished it when men began crowding into the small place, cheerful men who declared that the weather was improving, offering more coffee, handing out sandwiches, making much of them. Arne, who had crouched beside Louisa, said kindly: 'You see that now you are a good skier\u2014you will no longer be afraid.'\n\nShe smiled back at him. 'Oh, but I shall! I'm a complete coward, and I'm so sorry that we\u2014we got lost; that you all had to come and look for us, and in this appalling weather.'\n\nShe didn't know that Simon was behind her. She spilt her coffee when he said quietly: 'You have no need to apologise, Louisa, it was very brave of you to follow Claudia, who should have known better. My God, what a trouble that woman has been to me, and how glad I am that Lars is fool enough to take her on for the rest of his life.'\n\n'They'll be very happy,' Louisa mumbled.\n\nThey had two sledges with them. Claudia was wrapped up and strapped into one of them, but Louisa absolutely refused to travel on the other. 'I'll manage very well,' she declared firmly. 'It's the last chance I'll have of skiing before I leave and I don't want to miss it.'\n\nThey travelled in two files and Simon stayed with her the whole way, and when she fell over, which she did several times, he picked her up, dusted her down, and urged her on again, almost without speaking. She had never been so happy in her life before. The snow and wind were suddenly wonderful, the mountains not terrifying at all; she could ski and Mr Savage had turned into Simon at last. She closed her eyes, remembering his kiss, and fell over once more. They were almost home by then. Heaven, she felt sure, was just round the corner.\n\n## CHAPTER NINE\n\nBUT HEAVEN WAS rather further away than Louisa had thought. There was a good deal of bustle and confusion once they were back at home. Claudia demanded a great deal of attention, declaring that she felt faint, that she must have a hot bath at once, that she needed food, that she must telephone Lars immediately. She had thanked the men perfunctorily before she had gone upstairs, and it was left to Louisa and Elsa to hand round coffee and pastries and thank them more warmly. And Simon, when she looked for him, had disappeared. She shook hands with their rescuers and when the last of them had gone, went slowly upstairs to Claudia, who was calling for her.\n\n'Where have you been?' she asked impatiently. 'I want you to rub in that cream for me\u2014my skin will be ruined. Lord, I'm tired!'\n\n'And so am I,' observed Louisa shortly, making quick work of the creaming and bustling Claudia into bed without giving her a chance to think of anything else she wanted done. 'Elsa's staying late, she'll bring you up your supper presently. I'm going to have a bath.'\n\nShe was still in it daydreaming about Simon when he came back into the house. He didn't stay long; Elsa told him that his stepsister was in bed and she thought Louisa was going to bed too. He thanked her quietly and went to the hotel and had a meal there\u2014which was a pity, because presently Louisa went downstairs, looking a little wan, but nicely made up and wearing one of her Norwegian sweaters and a thick skirt, all ready to have her supper with Simon. But the table, she saw at once, was laid for one and when she asked, Elsa told her that Mr Savage had only called in for a moment to see if they were all right before going to the hotel.\n\nAnd although she was tired and remarkably sleepy by now, Louisa waited patiently until Elsa had gone home and the clock struck the hour of ten. But Simon didn't come. If he had wanted to he would have been back by now\u2014and what a good thing, she told herself, for she would have made a fool of herself if he had. It was time she learnt that kisses could mean nothing. She had no doubt that when they met in the morning he would be Mr Savage once more.\n\nShe was right. She went down to breakfast alone, because Claudia was certain that she was going to have a cold, and found him already at table eating the heavenly porridge Elsa made so beautifully. He wished her good morning, barely glancing at her and enquiring after Claudia.\n\n'She thinks she's caught a cold,' said Louisa.\n\n'Impossible. The one thing you can't get in these parts is the common cold.' He spoke coldly, very sure of himself, and she gave his bowed head a loving look, suddenly conscious of the fact that tomorrow she would be having breakfast with him for the last time. She put down her spoon, quite unable to eat, and he said at once: 'What's the matter? Aren't you well?'\n\nHe sounded so impatient that she picked up her spoon again and made herself finish the bowlful. 'I've never felt better,' she told him. 'I'm getting excited about going home.'\n\nHe put down the paper he was studying. 'I find that hard to believe,' he observed evenly. 'You don't like your home\u2014besides, you kissed me very thoroughly yesterday.'\n\nShe went very red but met his eyes frankly. 'I was very glad to see you\u2014I thought we were going to die. I\u2014I got carried away.'\n\n'Ah, you kissed me in fact under great provocation.'\n\n'I\u2014well, yes, that's about it. I'm sorry, I expect people do silly things when they're a bit upset.'\n\nSimon lowered his eyes to the paper. 'And not only when they're upset,' he observed.\n\nAnd that was the sum total of their conversation. Louisa did have a try just once. She began: 'I do want to thank you...'\n\nHis laconic 'Don't' stopped her more effectively than anything else could have done.\n\nThe storm had blown itself out. There was a great deal more snow, and the waters of the fjord carried small chunks of ice on its steely grey surface, but the sky was clear. There would be more storms, of course, but planes and helicopters were flying again, Lars would be coming to fetch his Claudia back to Bergen and Louisa would leave as had been arranged. No one had given her a ticket yet, although Simon had mentioned casually that he had it. She took Claudia's breakfast upstairs, finished the last of her packing, and put on her outdoor things. There was nothing more for her to do until she left in the morning and her room, shorn of her small possessions, looked uninviting. The sky was clear and the brief day wasn't far off. The little huddle of houses, painted in their cheerful blues and pinks and greens, gleamed in the street lamps' bright beams and the snow reflected them, so that one hardly noticed the darkness. The shop was full and she went inside to say goodbye and then on to the quay to speak to Arne and several of the other men who had become her friends.\n\nShe stayed talking for a few minutes and then struggled through the snow to the curve of the fjord to get a last look at the bridge. It was finished, they had told her, and was to be opened very shortly. Men were busy there now, packing up the scaffolding and piling it tidily at either end. When spring came, it would be taken away and the little wooden huts where they had worked during the winter months would go too. It was a beautiful bridge, curving gracefully across the grey water. Louisa turned away wanting to cry, then made her way back to the hotel, where she had coffee and a long talk with the owner.\n\nThe afternoon dragged. There was no sign of Simon and Claudia had elected to stay in bed, exclaiming crossly that of course she had a cold and what did Simon know about it anyway. Louisa sat by the stove and tried to make up her mind what she would do. She had plenty of friends, but she had no intention of wishing herself upon them at no notice at all. And she couldn't face her stepmother\u2014she didn't give Frank a thought. Somehow he had slid away into a past which wasn't important any more.\n\nShe had a solitary tea and went on sitting there, sad and forlorn and quite unable to be anything else. Elsa went presently and she took Claudia up the supper she had asked for and then laid the table for two.\n\nSimon didn't come. Louisa ate her meal with a book propped up before her, staring at the same page without reading it, and presently went to bed. She hadn't expected to sleep, but she did, to wake heavy-eyed when her alarm went at seven o'clock. She was almost glad that she would be going within an hour or so; to get it over quickly was all she wanted. She showered and dressed and packed her overnight bag, then went downstairs.\n\nSimon was at the kitchen table eating his breakfast and she sat down opposite him and began on the porridge Elsa put before her. He had said nothing beyond 'Good morning', but there was an envelope beside her plate. She looked at it and then at him and he said shortly: 'Your salary, Louisa,' and added after a tiny pause: 'Thank you for all the care and attention you've given Claudia. It must have been tiresome for you. I hope you'll find something\u2014someone more congenial for your next patient.'\n\nShe glanced at him, her eyes very large and soft. She would have liked to have said something suitable in reply, but her throat had closed over. To her horror she felt tears pricking her eyelids and she pushed back her chair and got up. 'Simon,' she whispered without realising that she had said it. 'Simon...' She swallowed the lump in her throat and said in a breathy little voice: 'I'm not hungry. I must finish my packing.'\n\nShe went to her room and sat on her bed, and presently Elsa appeared without a word and put a tray of coffee down on the dressing table and went away again. Louisa drank all the coffee, tidied up her face, put on her outdoor things and went to say goodbye to Claudia.\n\n'Going?' Claudia was only half awake and not best pleased at being disturbed. 'Oh, well, goodbye\u2014we're not likely to see each other again, are we?' She added grudgingly: 'Of course if you should ever come to Bergen you must come and see us.' She rolled over and closed her eyes, and Louisa went and fetched her bag and went downstairs. The launch was leaving at eight o'clock and there was only five minutes left.\n\nElsa was in her outdoor clothes too and when Louisa started to say goodbye she said: 'I'm coming to see you off, Louisa,' and they walked down to the quay together with never a sight of Simon. Louisa gave Elsa a hug, shook hands once again with the little crowd who had come to see her off, and was helped into the launch\u2014and there was Simon, longer and leaner than ever, standing on the deck talking to Arne. He nodded when he saw her and the people on the quay shouted and waved as the launch slowly crept away from them, out into the fjord. She stood waving until they were distant spots under the bright lights of the little quay and then went into the cabin. She hadn't expected Simon to be there\u2014indeed, she hadn't been thinking rationally at all, for she still had no ticket. She hadn't opened the envelope either. Presently she would do so, and ask about her ticket too, but just for a moment she wanted to sit still and pull herself together. It would never do to let him see that her heart was breaking. He came into the cabin presently, taking up most of the space, and she asked him in a composed voice if she might have her ticket.\n\n'All in good time,' he told her. 'Are you warm enough?'\n\n'Yes, thank you.' Then she asked, 'Are you going to Tromso, too?' and blushed at the silliness of the question, but she was answered without a flicker of amusement:\n\n'Well, yes, I am.' And then: 'Don't come on deck, it's very cold.' He went again as silently as he had come.\n\nThe journey seemed so short, but only because she wanted it to last for ever. She could see the lights of Tromso as they sped round the last bend; in another five minutes they would be there. She had no idea where the airport was and she didn't much care. She supposed there would be a taxi for her. She wouldn't want to wait around, saying goodbye would be bad enough however quick it was.\n\nSimon came back into the cabin, bringing a gust of icy air with him. 'Ready?' he asked, and picked up her bag.\n\nThey had berthed when she went outside and there was a Land Rover parked on the quay. She shook hands with Arne and the boy with him and stepped on to the hard-packed snow, to be joined almost at once by Simon.\n\n'We're going in the Land Rover,' he told her, and when she stared up at him questioningly: 'I'm flying to Bergen\u2014in fact I'm flying to Heathrow with you.' He put her bag down and pulled her close. 'I didn't dare tell you,' and at her look of astonishment: 'You see, when we met I thought, \"There's a brown mouse of a girl with a sharp tongue,\" and then before I knew what was happening I was in love with you. Oh, I did my best to ignore it, and I thought that if I ignored you too I'd be safely back in my bachelor state in no time\u2014only it didn't work out like that. You were under my skin, in my bones, my very heartbeat. And I'd gone out of my way to make you dislike me so that it would be easier for me to get over you. Only I haven't done that, my darling.' He stared down at her, unsmiling, even a little grim. 'I've discovered that I can't face life without you, indeed I doubt if I could build another bridge. You had a wretched life with Claudia\u2014if only you could bear to take me on instead...'A snowflake fell on to her nose and he paused and brushed it off very gently. 'My dearest little Louisa, if only you'd marry me!'\n\nIt was bitingly cold and a few snowflakes followed the first one, but Louisa hadn't noticed. She wasn't aware of the men on the launch watching them, or the driver of the Land Rover, for that matter. She had never felt so happy or so warm in her life before.\n\n'Oh, dear Simon, of course I will! I love you, too; I never want to leave you.'\n\nHe kissed her then, long and hard and with so much warmth that she wondered in a dreamlike way how she could ever have considered him austere and cold. He was most satisfyingly not either of those things. She kissed him back and then leaned back a little in his arms. 'It's a funny place to have a proposal,' she added shakily.\n\nHe smiled at her. 'I suppose it is.' He looked round and caught Arne's interested eye and shouted something to him which sent him and the boy as well as the driver hurrying over to them to pump their arms and utter congratulations before they finally got into the Land Rover.\n\nLouisa sat with her hand in Simon's and at the airport she went through reception and Customs and boarded the plane without taking any note at all of her surroundings. She tucked her hand in his again as they were airborne, drank the coffee that was brought round, ate the sandwich she was given like an obedient child, and then went to sleep, her head on his shoulder. And at Bergen there was only a brief wait before they were on the flight to Heathrow. She ate lunch this time, far too excited and happy to have much appetite. They didn't talk much, only as they started the descent to the airport she asked: 'Where are we going?'\n\n'Home,' said Simon, 'to Wiltshire. Shall we be married there and go back to Norway for our honeymoon?'\n\n'Oh, yes, please!' She was still too excited to bother about the details\u2014besides, Simon was there to see to everything. She heaved a sigh of pure happiness and went to sleep again.\n\nThere was a car waiting for them when they let Heathrow\u2014a Daimler Sovereign. As Louisa settled into the seat beside Simon she asked: 'How did it get here\u2014this car? Is it yours?'\n\nHe nodded. 'When I go abroad I garage it close by and they bring it here for me\u2014it's convenient.' He dropped a kiss on her cheek. 'Not long now, love. About two hours' drive.'\n\nThey drove down the M3, through a rain-sodden landscape, strangely green after the snow and the mountains, and then took the road to Warminster, but before they reached it Simon turned off the road, down a country lane which wandered up and down the gentle hills until it reached a very small village. It had a church in its centre and a cluster of houses and cottages round it and standing well back, taking up all of one side of the square, a splendid Queen Anne house with large square windows and a beautiful front door with a fanlight over it and a white-painted porch. Simon drove through the open gate at the side of the narrow front garden and stopped the car.\n\n'Home,' he said, undid her safety belt and leaned across to open the door for her and then got out himself. By the time they had reached the door it was open with a plump smiling woman on the porch, beaming a welcome at them.\n\n'Mrs Turner, my housekeeper.' He corrected himself: 'Our housekeeper. Mrs Turner, this is my future wife, Miss Louisa Evans.' He waited while they shook hands and then swept Louisa across the hall and into a small room, lined with bookshelves, its great desk covered with maps and papers. He took Louisa in his arms and pulled the cap off her head.\n\n'This is where I start my bridges,' he said very quietly, 'and this is where our heaven starts, my darling.'\n\nLouisa put up her face to be kissed. 'I thought it would be just round the corner, and it was,' she told him. She would have explained further, but there seemed no point. To be kissed was far more satisfactory.\nISBN: 978-1-4592-3930-2\n\nHEAVEN AROUND THE CORNER\n\nCopyright \u00a9 1981 by Betty Neels.\n\nAll rights reserved. Except for use in any review, the reproduction or utilization of this work in whole or in part in any form by any electronic, mechanical or other means, now known or hereafter invented, including xerography, photocopying and recording, or in any information storage or retrieval system, is forbidden without the written permission of the publisher, Harlequin Enterprises Limited, 225 Duncan Mill Road, Don Mills, Ontario, Canada M3B 3K9.\n\nAll characters in this book have no existence outside the imagination of the author and have no relation whatsoever to anyone bearing the same name or names. They are not even distantly inspired by any individual known or unknown to the author, and all incidents are pure invention.\n\nThis edition published by arrangement with Harlequin Books S.A.\n\n\u00ae and TM are trademarks of the publisher. Trademarks indicated with \u00ae are registered in the United States Patent and Trademark Office, the Canadian Trade Marks Office and in other countries.\n\nwww.eHarlequin.com\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
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+{"text":" \n# METAPHOR AND FIELDS\n\n_Metaphor and Fields_ is an explanation and demonstration of the value of metaphoric processes and fields in psychoanalysis. In this book, S. Montana Katz articulates a future direction for psychoanalysis which is progressively explored, taking into account features essential to psychoanalysts of all persuasions, clinically and theoretically. In this way, psychoanalysis is brought into the postmodern future by fashioning an umbrella for the discipline. With this umbrella, the barriers to mutual understanding may be dismantled and a path permanently forged to the possibility of meaningful international, intercultural, interdisciplinary, and poly-perspectival psychoanalytic exchange.\n\n_Metaphor and Fields_ organically merges work on metaphoric processes with work on fields. The use of a framework with metaphoric processes and fields combined exhibits the uniqueness of psychoanalysis and shows how it explores and explains human experience. The relational fields of the North American school of relational theory, intersubjective matrices, self object matrices, and the ground breaking work of Madeleine and Willy Baranger are all examples of field concepts that have been successfully employed in theoretical frameworks and clinical technique. They show how other schools of thought can be understood as using an implicit field concept.\n\nThe chapters in this book approach the subject from diverse vantage points. Taken together, they form an intricate web of psychoanalytic thought that moves the scope of psychoanalysis beyond dispute towards the open, inclusive discussion of core concepts and technique. _Metaphor and Fields_ will be of interest to psychoanalysts, psychiatrists, mental health clinicians, psychologists, social workers, and a wide academic audience drawn from the fields of philosophy, linguistics, comparative literature, anthropology, and sociology.\n\n**S. Montana Katz** is a training and supervising analyst, and a member of faculty for the National Psychological Association for Psychoanalysis. She is in private practice in New York City.\n\n# PSYCHOANALYTIC INQUIRY BOOK SERIES  \nJOSEPH D. LICHTENBERG  \nSERIES EDITOR\n\nLike its counterpart, _Psychoanalytic Inquiry: A Topical Journal for Mental Health Professionals_ , the psychoanalytic inquiry Book series presents a diversity of subjects within a diversity of approaches to those subjects. Under the editorship of Joseph lichtenberg, in collaboration with Melvin Bornstein and the editorial board of _Psychoanalytic Inquiry_ , the volumes in this series strike a balance between research, theory, and clinical application. We are honored to have published the works of various innovators in psychoanalysis, such as Frank lachmann, James Fosshage, Robert Stolorow, donna orange, Louis Sander, L\u00e9on Wurmser, James Grotstein, Joseph Jones, Doris Brothers, Fredric Busch, and Joseph Lichtenberg, among others.\n\nThe series includes books and monographs on mainline psychoanalytic topics, such as sexuality, narcissism, trauma, homosexuality, jealousy, envy, and varied aspects of analytic process and technique. In our efforts to broaden the field of analytic interest, the series has incorporated and embraced innovative discoveries in infant research, self psychology, intersubjectivity, motivational systems, affects as process, responses to cancer, borderline states, contextualism, postmodernism, attachment research and theory, medication, and mentalization. As further investigations in psychoanalysis come to fruition, we seek to present them in readable, easily comprehensible writing.\n\nAfter 25 years, the core vision of this series remains the investigation, analysis and discussion of developments on the cutting edge of the psychoanalytic field, inspired by a boundless spirit of inquiry.\n\nVol. 41  \n _Metaphor and Fields: Common Ground,_  \n _Common Language and the Future of_  \n _Psychoanalysis_  \nS. Montana Katz (ed.)\n\nVol. 40   \n_Growth and Turbulence in the Container\/_  \n _Contained: Bion's Continuing Legacy_  \nHoward B. Levine & Lawrence J. Brown  \n(eds)\n\nVol. 39  \n _Nothing Good Is Allowed to Stand:_  \n _An Integrative View of the_  \n _Negative Therapeutic Reaction_  \nL\u00e9on Wurmser & Heidrun Jarass (eds)\n\nVol. 38  \n _Self Experiences in Group, Revisited:_  \n _Affective Attachments, Intersubjective_  \n _Regulations, and Human Understanding_  \nIrene Harwood, Walter stone, & Malcolm  \npines (eds)\n\nVol. 37   \n_The Abyss of Madness_   \nGeorge E. Atwood\n\nVol. 36  \n _Manual of Panic Focused Psychodynamic_  \n _Psychotherapy - eXtended Range_  \nFredric N. Busch, Barbara L. Milrod,  \nMeriamne B. singer, & Andrew C. Aronson\n\nVol. 35  \n _World, Affectivity, Trauma:_  \n _Heidegger and Post-Cartesian Psychoanalysis_  \nRobert D. Stolorow\n\nVol. 28  \n _Transforming Narcissism:_  \n _Refections on Empathy, Humor, and_  \n _Expectations_  \nFrank M. Lachmann\n\nVol. 27  \n _Toward a Psychology of Uncertainty:_  \n _Trauma-Centered Psychoanalysis_  \nDoris Brothers\n\nVol. 26  \n _Living Systems, Evolving Consciousness,_  \n _nd the Emerging Person: A Selection of Papers_  \n _from the Life Work of Louis Sander_  \nGherardo Amadei & Ilaria Bianchi (eds)\n\nVol. 25  \n _Sensuality and Sexuality_  \n _across the Divide of Shame_  \nJoseph D. Lichtenberg\n\nVol. 24  \n _Jealousy and Envy:_  \n _New Views about Two Powerful Feelings_  \nL\u00e9on Wurmser & Heidrun Jarass (eds)\n\nVol. 23  \n _Trauma and Human Existence:_  \n _Autobiographical, Psychoanalytic,_  \n _and Philosophical Refections_  \nRobert D. stolorow\n\nVol. 22  \n _Psychotherapy and Medication: The Challenge_  \n _of Integration_  \nFredric N. Busch & Larry S. Sandberg\n\nVol. 13  \n _Self and Motivational Systems:_  \n _Toward a Theory of Psychoanalytic Technique_  \nJoseph D. Lichtenberg, Frank M.  \nLachmann, & James L. Fosshage\n\nVol. 12  \n _Contexts of Being:_  \n _The Intersubjective Foundations_  \n _of Psychological Life_  \nRobert D. Stolorow & George E. Atwood\n\nVol. 10  \n _Psychoanalysis and Motivation_  \nJoseph D. Lichtenberg\n\nVol. 8  \n _Psychoanalytic Treatment:_  \n _An Intersubjective Approach_  \nRobert D. Stolorow, Bernard Brandchaft, &  \nGeorge E. Atwood\n\nVol. 2  \n _Psychoanalysis and Infant Research_  \nJoseph D. Lichtenberg\n\n **Out of Print titles in the PI Series**\n\nVol. 15  \n _Understanding Therapeutic Action:_  \n _Psychodynamic Concepts of Cure_  \nLawrence E. Lifson (ed.)\n\nVol. 11  \n _Cancer Stories: Creativity and Self-Repair_  \nEsther Dreifuss-Kattan\n\nVol. 9  \n _Female Homosexuality: Choice without_  \n _Volition_  \nElaine V. Siegel | Vol. 34  \n _Change in Psychoanalysis:_  \n _An Analyst's Refections on the Therapeutic_  \n _Relationship_  \nChris Jaenicke\n\nVol. 33  \n _Psychoanalysis and Motivational Systems:_  \n _A New Look_  \nJoseph D. Lichtenberg, Frank M.  \nLachmann, & James L. Fosshage\n\nVol. 32  \n _Persons in Context:_  \n _The Challenge of Individuality_  \n _in Theory and Practice_  \nRoger Frie & William J. Coburn (eds)\n\nVol. 31   \n_Toward an Emancipatory Psychoanalysis:_  \n _Brandchaft's Intersubjective Vision_  \nBernard Brandchaft, shelley doctors, &  \nDorienne sorter\n\nVol. 30  \n _From Psychoanalytic Narrative to Empirical_  \n _Single Case Research: Implications for_  \n _Psychoanalytic Practice_  \nHorst K\u00e4chele, Joseph Schachter, Helmut  \nTom\u00e4 & the Ulm psychoanalytic process  \nresearch study Group\n\nVol. 29  \n _Mentalization:_  \n _Teoretical Considerations, Research Findings,_  \n _and Clinical Implications_  \nFredric N. Busch (ed.)\n\nVol. 21  \n _Attachment and Sexuality_  \nDiana Diamond, Sidney J. Blatt, & Joseph   \nD. Lichtenberg (eds)\n\nVol. 20  \n _Craft and Spirit:_  \n _A Guide to Exploratory Psychotherapies_  \nJoseph D. Lichtenberg\n\nVol. 19  \n _A Spirit of Inquiry:_  \n _Communication in Psychoanalysis_  \n _Joseph D. Lichtenberg, Frank M. Lachmann,_  \n _& James L. Fosshage_\n\nVol. 18  \n _Kohut, Loewald, and the Postmoderns:_  \n _A Comparative Study of Self and Relationship_  \nJudith Guss Teicholz\n\nVol. 17  \n _Working Intersubjectively:_  \n _Contextualism in Psychoanalytic Practice_  \nDonna M. Orange, George E. Atwood, &  \nRobert D. Stolorow\n\nVol. 16  \n _The Clinical Exchange:_  \n _Techniques Derived from_  \n _Self and Motivational Systems_  \nJoseph D. Lichtenberg, Frank M.  \nLachmann, & James L. Fosshage\n\nVol. 14  \n _Affects as Process:_  \n _An Inquiry into the Centrality_  \n _of Affect in Psychological Life_  \nJoseph M. Jones\n\nVol. 7  \n _The Borderline Patient:_  \n _Emerging Concepts in Diagnosis,_  \n _Psychodynamics, and Treatment, Vol. 2_  \nJames S. Grotstein, Marion F. solomon, &  \nJoan A. Lang (eds)\n\nVol. 6  \n _The Borderline Patient: Emerging Concepts in_  \n _Diagnosis, Psychodynamics, and Treatment,_\n\n _Vol. 1_  \nJames S. Grotstein, Marion F. Solomon, &  \nJoan A. Lang (eds)\n\nVol. 5  \n _Toward a Comprehensive Model for_  \n _Schizophrenic Disorders: Psychoanalytic Essays_  \n _in Memory of Ping-Nie Pao_  \nDavid B. Feinsilver\n\nVol. 4  \n _Structures of Subjectivity:_  \n _Explorations in Psychoanalytic Phenomenology_  \nGeorge E. Atwood & Robert D. Stolorow\n\nVol. 3  \n _Empathy, Volumes I & II_  \n _Joseph D. Lichtenberg, Melvin Bornstein,_  \n& Donald silver (eds)\n\nVol. 1  \n _Refections on Self Psychology_  \nJoseph D. Lichtenberg & Samuel Kaplan  \n(eds)  \n---|---\nMETAPHOR AND FIELDS\n\nCommon Ground, Common Language,  \nand the Future of Psychoanalysis\n\n_Edited by  \nS. Montana Katz_\n\nFirst published 2013  \nby Routledge  \n711 Third Avenue, New York, NY 10017\n\nSimultaneously published in the UK  \nby Routledge  \n27 Church Road, Hove, East Sussex BN3 2FA\n\n_Routledge is an imprint of the Taylor & Francis Group, an informa business_\n\n\u00a9 2013 Taylor & Francis\n\nThe right of the editor to be identified as the author of the editorial material, and of the authors for their individual chapters, has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988.\n\nAll rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers.\n\n_Trademark notice_ : Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe.\n\n_Library of Congress Cataloging in Publication Data_  \nMetaphor and fields : common ground, common language and the future of psychoanalysis \/ edited by S. Montana Katz.  \np. cm.   \n1. Psychoanalysis. 2. Field theory (Social psychology)  \n3. Metaphor--Psychological aspects. I. Katz, Montana.  \nBF173.M38 2013  \n150.19'5--dc23 2012028007\n\nISBN: 978-0-415-63171-6 (hbk)  \nISBN: 978-0-415-63172-3 (pbk)  \nISBN: 978-0-203-07231-8 (ebk)\n\nTypeset in Garamond  \nby HWA Text and Data Management, London\n\nThis book is dedicated to the work of Madeleine and Willy Baranger, and to the possibilities for finding psychoanalytic common ground in field theory.\n\n# CONTENTS\n\n_Contributors_\n\n_Foreword_ _by Madeleine Baranger_\n\n1 Introduction  \nS. MONTANA KATZ\n\n2 Preliminary Foundational Concepts  \nS. MONTANA KATZ\n\n3 Metaphoric Processes   \nS. MONTANA KATZ\n\n4 Metaphor in Psychoanalysis and Clinical Data   \nROBERT WALLERSTEIN\n\n5 Metaphor and Conflict   \nL\u00c9ON WURMSER\n\n6 Metaphor, Meaning, and the Mind   \nARNOLD H. MODELL\n\n7 Metaphor in Three Psychoanalytic Perspectives   \nROBERT S. WHITE\n\n8 Metaphor and Metonymy as the Basis of a New Psychoanalytic Language  \nANTAL BORBELY\n\n9 Metaphor and Psychodynamic Research   \nROBERT F. BORNSTEIN AND NIKAYA BECKER-MATERO\n\n10 Psychoanalytic Field Concepts   \nS. MONTANA KATZ\n\n11 Context for the Barangers' Work on the Psychoanalytic Field   \nANTOINE COREL\n\n12 Metaphor in Analytic Field Theory   \nGIUSEPPE CIVITARESE AND ANTONINO FERRO\n\n13 Field Theory, the \"Talking Cure,\" and Metaphoric Processes   \nANA-MAR\u00cdA RIZZUTO\n\n14 Field, Process, and Metaphor   \nJUAN TUBERT-OKLANDER\n\n15 Metaphor, Analytic Field, and Spiral Process   \nBEATRIZ DE LE\u00d3N DE BERNARDI\n\n16 Other Fields Within the Analytic Field   \nCLAUDIO NERI\n\n17 The Analytic Relationship in Field Theory   \nELSA RAPPOPORT DE AISEMBERG\n\n_Bibliography_\n\n_Index_\n\n# CONTRIBUTORS\n\n**Nikaya Becker-Matero** , MA, is a Clinical psychology PHD candidate at Adelphi University, Garden City, NY. She completed internship training at albert Einstein College of Medicine's Bronx psychiatric Center, Bronx, NY, and is adjunct assistant professor in the department of psychology at Adelphi University. Ms. Becker-Matero has published in the _Journal of Personality Disorders_ , _Psychoanalytic Inquiry_ , and _Journal of Counseling Psychology_ ; she has presented her work at the society for personality assessment (spa) and society for psychotherapy research (spr). Her main research interests focus on conducting empirical studies of psychoanalytic and psychodynamic models of personality, particularly histrionic personality, and on self-concept, self-complexity, and social awareness. Additional interests include the links between assessment and clinical practice in personality disorders. She has worked on grants founded by the national institute of Mental health and the national science Foundation.\n\n**Antal Borbely** , MD, is a Board certified psychiatrist and a graduate and lecturer at the new York psychoanalytic institute. He is a member of the American psychoanalytic association. He is interested in questions regarding the centrality of time and metaphor in psychoanalytic theory and in the mind's functioning. He wrote the following papers regarding these topics: \"Towards a temporal theory of the mind,\" _Psychoanalysis and Contemporary Thought_ , 1987; \"A psychoanalytic theory of metaphor,\" _International Journal of Psychoanalysis_ , 1998; \"Towards a psychodynamic understanding of metaphor and metonymy: Teir role in awareness and defense,\" _Metaphor and Symbol_ , 2004; \"Metaphor and psychoanalysis,\" in _The Cambridge Handbook of Metaphor and Thought_ , 2008; \"The centrality of metaphor and metonymy in psychoanalytic theory and practice,\" _Psychoanalytic Inquiry_ , 2009; \"Metaphor and metonymy as the basis for a new psychoanalytic language,\" _Psychoanalytic Inquiry_ , 2011. He is presently working on the comparison between the bootstrapping aspects observed in evolutionary robotics and in free association (in preparation).\n\n**Robert F. Bornstein** received his phd in Clinical psychology from the state University of new York at Buffalo in 1986 and is professor of psychology at Adelphi University. He has published widely on personality dynamics, assessment, and treatment, wrote _The Dependent Personality_ and _The Dependent Patient: APractitioner's Guide_, and co-edited (with Joseph Masling) seven volumes of the _Empirical Studies of Psychoanalytic Theories_ series. Dr. Bornstein is a Fellow of the American psychological association, association for psychological science, and society for personality assessment; his research has been funded by grants from the national institute of Mental health and the national science Foundation. Dr. Bornstein received the society for personality Assessment's 1995, 1999, 2002, and 2008 awards for distinguished Contributions to the personality assessment literature, and the American psychological Foundation 2005 Theodore Millon award for excellence in personality research.\n\n**Giuseppe Civitarese MD, PhD** , a member of the Italian psychoanalytic association and of the American psychoanalytic association, is in private practice in Pavia, Italy. He has published several papers in the main international psychoanalytic journals. His books include: _The Intimate Room: Theory and Technique of the Analytic Field_ , The new library of psychoanalysis, Routledge, London 2010; _The Violence of Emotions: Bion and Post-Bionian Psychoanalysis_ , The new library of psychoanalysis, Routledge, London 2012; _Perdere la testa: Abiezione, confitto estetico e critica psicoanalitica_ , Clinamen, Florence 2012 [ _Losing One's Head: Abjection, Aesthetic Confict and Psychoanalytic Criticism_ ]; _I film della vita. Il cinema e l'interpretazione dei sogni_ [ _The Films of our Life. Cinema and the Interpretation of Dreams_ ] (in preparation). He has also co-edited _L'ipocondria e il dubbio: L'approccio psicoanalitico_ , Franco Angeli, Milano 2011 [ _Hypochondria and Doubt: The Psychoanalytic Approach_ ].\n\n**Antoine Corel** , MD, is a member of the argentine psychoanalytic association where he was trained, and member of the Paris psychoanalytic society. Since 1976 he has been in private practice in Paris. His main interests concern the psychoanalytic process approached as a transformation in time and the formulation of constructions. His activity as a film critic has continued around the relation between psychoanalysis and the cinema.\n\n**Antonino Ferro** is a training and child analyst for the Italian psychoanalytic society, IPA, and an Apsaa member. He has published several books translated into many languages \u2013 the most recent being _Mind Works: Technique and Creativity in Psychoanalysis_ , and _Avoiding Emotions, Living Emotions_ published by Routledge\/ new library. In 2007 he was selected as a recipient of the Mary S. Sigourney award. He is has been Chair since 2007 of the sponsoring Committee for the Turkish provisional society of psychoanalysis and Chair of the executives of the international appointments Committee of the _International Journal of Psychoanalysis_ elections. He was editor for Europe of _IJP_ for seven years and, since January 2011, a member of the editorial board of _Psychoanalytic Quarterly_.\n\n**S. Montana Katz PhD, LP** is a training and supervising analyst and on the faculty of the national psychological association for psychoanalysis. She is on the editorial boards of _Psychoanalytic Inquiry_ and _The Psychoanalytic Review_. S. Montana Katz has a private practice in new York City.\n\n**Beatriz de Le\u00f3n de Bernardi** is a Uruguayan psychoanalyst, and full member and training analyst of the Uruguayan psychoanalytic association (APU). She is past president of the APU and has formerly been director of the scientific Committee and editor of the _Uruguayan Journal of Psychoanalysis_. She is an editorial board member of the _International Journal of Psychoanalysis_. Currently she is also a representative for latin America in the international psychoanalytical association Board. She has published papers and books in diferent languages on psychoanalytic topics, mainly about the patient\u2013analyst interaction and the analyst's contribution to the analytic process, the notion of countertransference in latin America, and the thought of Madeleine and Willy Baranger and Heinrich Racker. She has researched and published on implicit theories in psychoanalytic practice. She has received the award of the Latin-American psychoanalytical Federation (FEPAL) in 1992 and the training today award in 2009.\n\n**Arnold H. Modell, PhD** practices psychoanalysis in newton, Massachusetts. He is the author of numerous papers and five books. The most recent is _Imagination and the Meaningful Brain_ (MIT Press). He is currently Clinical professor of psychiatry at harvard Medical school and a training and supervising analyst at the Boston psychoanalytic institute.\n\n**Claudio Neri MD, PhD** is a psychoanalyst and group analyst who lives and practices in Rome. He is a full member of the Societ\u00e0 Psicoanalitica Italiana and a training and supervising analyst in its institute; full member of the international psychoanalytic association, and the Group-analytic institute of London; full professor at the Faculty of Medicine and psychology, University la Sapienza of Rome; and visiting professor at the University Lumi\u00e8re-lyon 2 and Descartes-paris 5\u00b0. He is chief editor of the online journal _Funzione Gamma_ , and is the author and editor of numerous books, among which are: _Group_ (Jessica Kingsley publishers, 1998), and, with pines and Friedman (eds), _Dreams in Group Psychotherapy_ (Jessica Kingsley publishers, 2002).\n\n**Elsa Rappoport de Aisemberg** is a member and training analyst of the argentine psychoanalytic association; former vice-president of the argentine psychoanalytic association; member of the ipa new Groups for the sponsoring Committee of asunci\u00f3n; past Chair of scientific Colloquiums and advisor for the scientific department of the argentine psychoanalytic association; Chair of the research Group on psychosomatics at the argentine psychoanalytic association; and author of many papers and publications on sexuality and gender, psychosomatics, art and psychoanalysis and theoretical and clinical approach of the analytic field in psychoanalytic journals in spanish, english, French, German, and portuguese. Additionally, she is co-editor of _Psychosomatics Today, A Psychoanalytic Perspective, L_ ondon, Karnac, 2010.\n\n**Ana-Mar\u00eda Rizzuto MD** is a training and supervising analyst at the pine psychoanalytic Center, a member of the American psychoanalytic association and a member of the international psychoanalytic association. She is the author of _The Birth of the Living God. A Psychoanalytic Study_ (1979), The University of Chicago press, and _Why did Freud Reject God? A Psychodynamic Interpretation_ (1998), Yale University press. This book received in 2001 the Gradiva award for Best Book (religion subject), given by the national association for the advancement of psychoanalysis. She co-authored with W. W. Meissner and Dan H. Buie the book _The Dynamics of Human Aggression: Theoretical Foundations and Clinical Applications: Theoretical Foundations, Clinical Applications_ (2004), Brunner-routledge. She is the author of numerous articles on the psychodynamics of religion, language in psychoanalysis, aggression, the clinical situation, and other subjects. In 1996, she received the William C. Bier award, given by division 36, American psychological association, and in 1997 she received the oskar pfister prize, given by the American psychiatric association. Both prizes were given to her for her outstanding contributions to the psychology of religion. She is a regular participant in national and international psychoanalytic congresses and a frequent psychoanalytic lecturer in the USA, latin America, Europe, and Japan.\n\n**Juan Tubert-Oklander MD, PhD** is a psychoanalyst, group analyst, and family therapist who lives and practices in Mexico City. Originally from Argentina, he has been living in Mexico since 1976 and is presently a Mexican citizen. He is a full member of the Mexican psychoanalytic association, and training and supervising analyst in its institute; additionally he is a full member of the international psychoanalytic association, the argentine psychoanalytic association, and the Group-analytic society international. He is author of _The Learning Operative Group_ (in spanish), _Operative Groups: The Latin-American Approach to Group Analysis_ (with Reyna Hern\u00e1ndez-Tubert), _Hybrid Science: Psychoanalysis and Analogical Hermeneutics_ (with Mauricio Beuchot-puente, in spanish), and _Theory of Psychoanalytic Practice: A Relational Process Approach_ (in preparation).\n\n**Robert Wallerstein, M.D.** is emeritus professor and former Chair of the department of psychiatry of the University of California San Francisco school of Medicine, and emeritus training and supervising analyst, San Francisco Center for psychoanalysis. He is a former president of the American psychoanalytic association (1971\u201372) and a former president of the international psychoanalytical association (1985\u201389). He graduated from Columbia College (June 1941), the Columbia University College of physicians and surgeons (September 1944), and the Topeka institute for psychoanalysis (June 1958). He was director of research at the Menninger Clinic (Topeka Kansas) until June 1966, and then Chief of psychiatry at the Mount Zion hospital, San Francisco (1966-75). He was twice a Fellow at the Center for advanced study in the Behavioral sciences at Stanford, California (1964\u20135, 1981\u20132), a Fellow at the rockefeller Foundation study Center at Bellagio, Lake Como, Italy (1992), and given the Mary singleton Sigourney award for outstanding contributions to psychoanalysis in 1991.\n\n**Robert S. White** is a graduate and member of the Western new England psychoanalytic society, Faculty, and Western new England psychoanalytic institute. He is associate editor for the internet, Japa 2004\u20132009, and founder and moderator of the Japan online discussion group, 1997\u20132009. Since 2010 he has been Chair, IPA website editorial board, and is assistant Clinical professor of psychiatry at Yale University. He is in private practice in psychoanalysis and psychiatry, new haven, Connecticut, USA and publishes in the areas of intersubjectivity, interpersonal psychoanalysis and Bion studies.\n\n**L\u00e9on Wurmser MD, PhD hc** (honorary degree in philosophy, Humboldt University, Berlin), is a psychoanalyst and former Clinical professor of psychiatry, University of West Virginia, with regular and extensive teaching in Europe. He is the author of _The Hidden Dimension_ (1978); _The Mask of Shame_ (1981); _Flight from Conscience_ (1987, in German); _The Riddle of Masochism_ (1993, in German); _Magic Transformation and Tragic Transformation_ (1999, in German); _The Power of the Inner Judge_ (2000); _Values and Ideas of Judaism in Psychoanalytic View_ (2001, in German); _Torment Me, But Do Not Abandon Me_ (2007); and _Shame and the Evil Eye_ (in German, 2011) and co-author with Aeidrun Jarass of _Jealousy and Envy\u2014New Views on Two Powerful Emotions_ (2007), a monograph in the psychoanalytic inquiry Book series and _Nothing Good is Allowed to Stand_ (2012) in the same series. He is a training and supervising analyst for the new York Freudian society, and recipient of Egn\u00e9r and _Journal of the American Psychoanalytic Association_ prizes.\n\n# FOREWORD\n\n___Madeleine Baranger_\n\nI am extremely touched by the fact that dr. S. Montana Katz considers the work of the Barangers in the psychoanalytic field an important source for her own work and that she relates it to the concept of metaphor, which she has studied in depth.\n\nThe subject of this book, as refected in the title, is captivating: _Metaphor and Fields: Common Ground, Common Language, and the Future of Psychoanalysis_.\n\nIts purpose is to examine and address obstacles in understanding and dialogue between different psychoanalytic authors and schools and other types of professional institutions.\n\nShe is trying to demonstrate that the concepts of metaphor and of the field are valuable for psychoanalysis.\n\nThe book is structured to progressively explore a goal for the future that takes into account all of the psychoanalytic orientations that are usually recognized as constituents of a particular science. The goal is to convince readers to immerse themselves in the project, theoretically and clinically, so that, in a postmodern future, an \"umbrella field\" is created for psychoanalysis.\n\nRegarding this objective, the concepts she uses to illustrate her convictions originate from diverse sources.\n\nThis is an excellent example and model for thinkers and researchers who seek to evolve and present their own convictions and want a way to recognize the different concepts that have contributed to their development.\n\nAs a whole, the book is a project to present the psychoanalytic research and thought of a variety of current authors whose perspectives are considered building blocks of psychoanalysis. This is not just my definition; it is demonstrated by the variety of themes and developments that are presented.\n\nSo far, I have only made reference to the statements and intents of the book's editor. I would also like to focus on the most remarkable parts that manifest her conceptual way of thinking and expressing herself.\n\nThe book is organized and presented in an original manner. In the relevant portions, the editor\/contributor clearly indicates her own theories, which are referenced in the title. With a sense of fair and generosity, in addition to the usual quotations, she offers the reader complete texts from analysts she recognizes as influencing her work or from those who have made remarkable contributions to topics of her interest.\n\nThere is a lesson to be learned from the contributions of so many different points of view. It is not about adopting one wholeheartedly\u2014declaring ourselves disciples of some fellow scientist\u2014or about rejecting a point of view because of its maximal or minimal differences about the same topic.\n\nIt is necessary to have a very precise knowledge of one's own thinking, to feel it, and to want it to be in constant evolution around the same issues. This requires modesty alongside creativity. It does not involve a search for final certainty but eternal revisions and possible disillusions in order to acquire new knowledge.\n\nIt was wonderful to be able to compare many of the authors mentioned, along with the author.\n\nIn my case, I would like to mention the work of l\u00e9on Wurmser, with which I was not very familiar, and of other authors about whose valuable contributions I was not so aware.\n\nWe can deepen our own thoughts by recognizing the importance, whether major or minor, of an influence from or similarity with a colleague. Readers can learn a way to get to know themselves better, accepting or rejecting other people's concepts. This is a great example\u2014and a model\u2014for analysts committed to an endless education, as for any thinker or researcher with the same eagerness to learn and develop.\n\nThe book's richness and scientific rigor make it an essential resource for readers\u2014who will undoubtedly experience the same interest and pleasure I felt in discovering it.\n\n# 1\n\nINTRODUCTION\n\n_S. Montana Katz_\n\nAs the editor, I have multiple expectations for what can be accomplished with this book. For the reader unfamiliar with the use of either metaphoric processes or fields in psychoanalysis, I hope that this book will offer an explanation and demonstration of the use and value of these concepts. For all readers, I have striven to arrange the contents of this book such that a potential future direction for psychoanalysis is articulated and progressively explored, taking into account features essential to psychoanalysts of all persuasions. I have attempted to build a convincing case for readers to become immersed in the resulting framework, clinically and theoretically. In this way an attempt is made to bring psychoanalysis into the postmodern future by fashioning an umbrella field for psychoanalysis.\n\nA common language is constructed in this framework through which all psychoanalytic perspectives can find faithful expression. It is hoped that conference and dialogue among the different analytic perspectives about psychoanalytic theory and practice will be possible without ineradicable loss or confusion of meaning. It is further anticipated that, ultimately, the result could be an expanded potential for the integration of concepts, principles, and techniques across analytic positions. Construction of the shared core concepts that underlie analytic perspectives constitutes a significant clinical and educational tool and may thus have an impact on psychoanalytic training.\n\nThere are other potential and far-reaching consequences to a common base for the psychoanalytic perspectives. Under this umbrella, analysts may reach across the interdisciplinary divide on firm ground. Psychoanalysis may become more accessible to disciplines in the humanities. Its irreducibility to other sciences is also clarified. The model exhibits what is unique to psychoanalysis and how it cannot be subjected to a reduction to a physiological or any other kind of inquiry. A possible outcome is enhanced and genuinely interdisciplinary cooperation, discussion, and research. This may afford a way to describe the discipline of psychoanalysis across perspectives for quantitative research. It is, moreover, an umbrella through which psychoanalysis may have expanded exposure in higher education and other kinds of professional institutions.\n\nThis book will thus address the current situation, in which not only are there multiple branches of psychoanalysis\u2014each refecting a different theoretical and clinical perspective\u2014but also there is also a dearth of understanding among the branches. This situation is due to several historical and other factors, which have been written about elsewhere and in some of the chapters here. Such a project is of contemporary relevance and perhaps urgency. In the current climate, psychoanalysis has endured diminished status and recognition, as well as reduced educational outlets.\n\nCombining these factors with the lack of communication amongst the multiple branches of psychoanalytic theory and practice, it is unclear whether there is currently a discernable integrated field of psychoanalysis. This situation is unacceptable if psychoanalysis as a body of theory and as a clinical set of techniques for addressing issues in mental health is to thrive. Over the past decades, there have been repeated calls to find a common ground and to open genuine discourse and understanding among the various analytic perspectives.\n\nMost of the work for this book grew out of two issues of _Psychoanalytic Inquiry_ for which I was the editor (31[2] and 33[3]). Many of the chapters in this book were written for one or the other of those issues. The first issue brought the psychoanalytic use of metaphoric processes up to date, with a particular eye toward forging a common ground amongst different schools of thought in psychoanalysis. The chapters in this book from that issue are 4, 5, 6, 7, 8, and 9. Together, these papers form a compelling discussion of how common ground might be achieved.\n\nTaking an overview of the work on metaphor, I felt that something was lacking in the structure such that the emerging umbrella framework was not entirely cohesive or complete. The missing piece was supplied by the formulation of a generalized notion of the psychoanalytic field. This concept arose from a process of abstracting from specific kinds of fields used in different psychoanalytic perspectives. This was part of the subject of the second issue. The chapters in this book that appeared in the second issue of _Psychoanalytic Inquiry_ are 11, 12, 13, 14, 15, 16, and 17.\n\nIn the issue on fields, the discussion taken as a whole demonstrates the essential nature of this emerging family of field concepts and of the idea of a generalized psychoanalytic field in particular. Tat issue brought the discussion onto the cusp of a potential future direction for an integrated discipline of psychoanalysis. There a double language barrier was broached. First was the barrier of natural languages, in that much of the vast, important, and highly stimulating work on fields in psychoanalysis was just beginning to be translated into English. Second was the barrier of the difculty of translating the specifc languages of the diferent psychoanalytic perspectives; this situation was partially addressed in some of the papers in the first issue.\n\nField theory has emerged as an international psychoanalytic concept that may help bring not only a coherent underlying structure for disparate psychoanalytic perspectives, but also a way of fostering interactive exploration of the various uses of psychoanalytic concepts and techniques. Field concepts are not new to psychoanalysis. Since at least 1960, Madeleine and Willy Baranger have elucidated their formulations of analytic fields and have shown how they work with them clinically. The relational fields of the north American school of relational theory, intersubjective matrices, self object matrices of self psychology, and recent developments in Italian psychoanalysis resulting in a modified form of the field work of the Barangers are all examples where field concepts have been employed in theoretical frameworks and clinical technique.\n\nOther perspectives can be understood as using some form of field concept at the base of their theoretical structure, as well as underlying their clinical approach. In this way, the contents and process of what occurs in sessions conducted by an analyst of each perspective can be described in what will be explored in general field theory terms. In fact, each clinical way of working can be described as employing a specific kind of field. Thus, a general field structure that encompasses individual field configurations supplies an essential component for the psychoanalytic framework with which to move the new paradigm forward.\n\nThis book thus furthers the exploration of a merging of work on metaphoric processes and that on fields. The use of a framework with metaphoric processes and fields combined exhibits the uniqueness of psychoanalysis and shows how and with what concepts it explores and explains human experience. An umbrella for psychoanalysis may not dissolve disagreements amongst psychoanalytic schools of thought, but it may permit the schools to be more clearly rendered and more explicitly understood. Formulating an umbrella for the discipline does not have the objective of eradicating differences among perspectives, but rather to be able to understand, explore, and learn from each of them. Both similarities and differences amongst the different psychoanalytic perspectives may be clarified with such a model, which also shows how psychoanalytic perspectives are related and how they are more like each other by far than like any other discipline or clinical technique.\n\nWith this umbrella, the barriers to mutual understanding may be dismantled and a path permanently opened to the possibility of meaningful international, intercultural, and poly-perspectival psychoanalytic exchange. Thus, this book contains an attempt to shine a light on a possible future direction for psychoanalysis by building a framework that can be used to structure clinical work and the theoretical constructs of psychoanalysis. This framework builds on the complex and rich history of psychoanalysis and takes fundamental psychoanalytic principles and concepts as a foundation. The framework allows an exploration of what it means to thoroughly probe core psychoanalytic insights.\n\nIn particular, this book can be viewed as an exploration of building from the fundamental premise of the existence of unconscious processes and the discovery of the complex affective meaning of human experience. Every analytic perspective accepts the existence and infuence of some form of unconscious processes. Following from this, each perspective can agree to the use of a psychoanalytic conception of unconscious metaphoric process. From this, a general concept of unconscious fantasy emerges.\n\nPursuing the premise of multiple affective meanings embedded in every experience leads to the development of what is here called a general psychoanalytic field structure of human experience. Some analytic schools of thought explicitly employ field concepts. Others can be understood as having an operative, implicit field concept, each specific to and uniquely formed by the particular analytic perspective. What evolves from the multiple field concepts in use in psychoanalysis is the employment of metaphoric processes and a generalized understanding of psychoanalytic fields utilized as a way of comprehending and speaking about psychoanalytic processes, theory, and human experience, such that a psychoanalyst from any school of thought can engage with and speak a common language. With these building blocks, psychoanalytic work on metaphoric processes is united organically with the use of field theory.\n\nThe chapters in this book approach the subject from diverse vantage points. Taken together, they form an intricate web of psychoanalytic thought that moves the scope and frontier of psychoanalysis beyond the format of dispute and toward the open, inclusive discussion of core concepts and technique, in an era in which psychoanalysis is coming to terms with the conclusions and implications of postmodernism.\n\nIn Chapter 2, I discuss the first principles necessary to build a base for psychoanalysis in which all schools of thought can participate. In this brief chapter, I discuss the consequences of adopting the fundamental psychoanalytic premise of the existence of unconscious processes. Included in this chapter is a discussion of the implications of dualism and holism for psychoanalysis. Interpretation and fantasy processes emerge as essential to human experience. The multiple affective meanings of human experience are also explored.\n\nIn Chapter 3, I discuss the evolution and use of the concept of metaphoric processes in psychoanalysis. I describe a model of metaphoric processes by breaking them down into component parts and subsidiary concepts. The ingredients of metaphoric processes are then used to express fundamental psychoanalytic concepts. Psychoanalytic perspectives are characterized according to this model in order to display similarities and differences among the different perspectives within a single common base and resulting common language.\n\nIn Chapter 4, Robertallerstein revisits a pertinent aspect of psychoanalytic history in his discussion of the attempts to eliminate the use of metaphor in psychoanalytic theory with the purpose of rendering psychoanalysis more on a par with other sciences. Citing the work of lakof and Johnson, Wurmser, and others, Wallerstein discusses the ubiquity as well as the inevitability of metaphor in general, in all scientific theory andin psychoanalysis in particular. He cautions against the current trend to spread the concept of metaphor so widely as to render it devoid of content. Wallerstein calls for some way of drawing a distinction between the metaphoric and the literal, locating the latter in the data of clinical experience. Different theoretical perspectives are then viewed as employing different scientific metaphors, which serve as heuristic devices to guide clinical work. Common ground is located in the clinical concepts of transference, countertransference, defense, conflict, and compromise.\n\nIn Chapter 5, l\u00e9on Wurmser provides a philosophical and psychoanalytic discussion of metaphor. He locates metaphor in the tension between the realms it brings together. In this way, metaphor is discussed as uniquely suited to portray inner conflict in the widest sense. Building on his previous work, Wurmser finds common ground for psychoanalytic perspectives in the study of cultural historical metaphors for conflict, complementarity, and harmony. Both ancient Greek and Chinese traditions are discussed in this connection.\n\nArnold Modell, in Chapter 6, describes the evolution of his thought on the use of metaphoric processes in psychoanalysis. He locates the motivation for the genesis of different psychoanalytic perspectives alongside the rise in popularity of ego psychology. Modell identifies with Freud's early emphasis on the unconscious processing of memory and feeling, through which meaning making takes place. Modell elaborates and argues for his proposition that metaphor is the currency of the mind. In so doing, he refers to a potential common ground in psychoanalytic concepts rather than in psychoanalytic technique. Metaphoric processes, then, are the subject matter of both psychoanalytic theory and clinical work.\n\nIn Chapter 7, Robert White focuses on the concept of the _nondynamic unconscious_ , and in particular on three psychoanalytic perspectives in relation to this concept. The three theories are found in the work of Wilfred Bion, Cesar and sara Botella, and donnel stern. White discusses these theories in detail and emphasizes the metaphors contained in them. The three perspectives are then compared on this basis.\n\nAntal Borbely, in Chapter 8, envisions the possibility of forging understanding among diferent theoretical psychoanalytic perspectives and between psychoanalysis and cognitive science. He discerns closer alignment in practice among various schools of thought in their use of metaphoric process and temporality. Borbely characterizes the fundamental psychoanalytic concepts of transference, defense, and interpretation in terms of a conception of temporal metaphors. Tat is, the common ground amongst psychoanalytic perspectives is here identifed in core aspects of psychoanalytic process. These are modeled in terms of temporality, metaphor, and metonymy.\n\nIn Chapter 9, Robert Bornstein and Nikaya Becker-Matero discuss the role of metaphor in psychoanalytic process, psychoanalytic research, and interdisciplinary discussion. They show how psychoanalysis has and can make use of metaphors from other disciplines, and how psychoanalytic metaphors have been translated and transformed in the language of other disciplines. Included is a discussion of the use of metaphor in both the design of psychodynamic research and in understanding the results.\n\nIn Chapter 10, I describe extant field concepts in contemporary psychoanalysis. I then provide a structure for what I call _general psychoanalytic fields_. This structure is designed to express the principles and concepts of different psychoanalytic perspectives and aford a neutral language in which to be able to compare and discuss the concepts of each perspective.\n\nIn Chapter 11, antoine Corel describes the conceptual, social, and psychoanalytic antecedents to the development of the field concept by Madeleine and Willy Baranger. He describes the intellectual atmosphere in Argentina preceding their work and explains the development of psychoanalytic concepts in that time and place that led to the concept of the analytic field.\n\nIn Chapter 12, Giuseppe Civitarese and Antonino Ferro discuss the central role of metaphoric processes in analytic field theory, as both a clinical tool and a core component of a model of human experience. They explore the genesis and meanings of the field metaphor in Bion's work and in field theory in general. Civitarese and Ferro discuss the paradigm shift that occurred in psychoanalysis as a result of Bion's work and the development of field theory. The authors then offer rich clinical examples of work with metaphoric processes in a field theory context, expanding their discussion with retrospective refections.\n\nAna-Mar\u00eda Rizzuto, in Chapter 13, explores the analytic process from the perspective of the Barangers' work, with attention to the use, function, and evolution of the meaning of words and other forms of expression. She then reviews neuroscientifc, psychoanalytic, and other literature concerning communication, including verbal communication. Rizzuto argues that communication is fundamentally embodied. She further draws out the psychoanalytic implications of the embodied nature of word meaning, with emphasis on understanding the nature of the intersubjective. Rizzuto locates word meaning in experiential and afective interpersonal meaning.\n\nIn Chapter 14, Juan Tubert-oklander adds to the working concepts of this book\u2014metaphor and field\u2014two other concepts to be taken into account: process and analogy. He makes use of Matte Blanco's concept of _bi-logic_ to describe the diferences between primary and secondary process, and he reformulates the objectives of psychoanalytic process. Tubert-oklander ofers a fundamentally holistic account of human experience that integrates the concepts of field and process.\n\nBeatriz de le\u00f3n de Bernardi, in Chapter 15, reviews the development of field theory in latin America. She then explores the role of metaphoric processes implicit in analytic process within field theory. De le\u00f3n de Bernardi discusses the infuence of lacan's work and of the use of metaphor on field theory. She further discusses the psychoanalytic conceptions of _temporality_ and _spiral process,_ illustrating her discussion with clinical material.\n\nNext, in Chapter 16, Claudio neri discusses working within a field theory model with groups in psychoanalysis, and how this differs from field theory work with individuals. Neri discerns other kinds of fields that Analysands experience. He describes working with what he calls the _shadow_ of such fields in which the analysand is immersed. It is in the analytic field, Neri argues, that these other fields can be detected. He also explores how to analyze such fields by gradually bringing them into the work within the analytic field.\n\nElsa Rappoport de Aisemberg's contribution, Chapter 17, describes the history of the evolution of the concept of countertransference, and then of the Barangers' field theory. She describes a crucial element in clinical work: the movement from the intrapsychic to the intersubjective and then back to the intrapsychic. She discusses working with countertransference within contemporary field theory and offers clinical material in which this work was salient.\n\nThese chapters discuss and demonstrate different ways of understanding and working with metaphoric processes and with fields. They also suggest a language and a structure through which to express and ground each of the various psychoanalytic perspectives. As we move into the future, there may be a way to experience psychoanalysis as an integrated discipline and practice in which internal as well as interdisciplinary discussion and debate are fruitful. Greater familiarity with field concepts may help foster an interest in articulating other kinds of fields associated with schools of thought that are not currently expressed in terms of field work. Some of this work has begun on the following pages. The more that psychoanalytic education includes a framework such as the metaphor and field structure presented here, the more students will be able to readily grasp the connections between their institute's theoretical and clinical perspective and other perspectives. In this way, interperspectival understanding may come to be a matter of course in the future.\n\nThese chapters implicitly indicate another way in which the umbrella framework of metaphoric processes and fields opens an avenue into the future of psychoanalysis. This consists of drawing from a full exploration of the oneiric in everyday processes. Tat is, working with metaphor and fields as the basis of psychoanalytic work undermines the distinction that has at times been drawn between dream states and waking states in analytic process. In this way of looking at human experience, all communications in an analytic process are, in a general sense, infused with fantasy products. This makes explicit a fundamental aspect of psychoanalytic understanding: that in clinical work, there are no communications that are outside the process. Neither are there communications that can be understood solely on the manifest level. Psychoanalysis and postmodern thought together belie the possibility of such an utterance in any context. This framework brings this and other psychoanalytic working principles to the fore.\n\nIn conclusion, I wish to thank my colleagues and co-contributors who read or wrote and discussed different parts of this book. Joseph Lichtenberg offered the initial idea, encouragement and motivation for the book. Kristopher spring helped me to develop the initial conception of the book and Kate Hawes and her assistant Kirsten Buchanan saw the project to completion. Gina Atkinson was a thoughtful and invaluable reader, commentator and editor for Chapters 1, , , and . Laurie Erskine skillfully edited and prepared the manuscript. I would also like to thank _Psychoanalytic Inquiry_ for the permission to reprint most of the chapters in this book and _The Psychoanalytic Review_ for the permission to reprint excerpts that contributed to two chapters.\n\n# 2\n\nPRELIMINARY  \nFOUNDATIONAL CONCEPTS\n\n_S. Montana Katz_\n\nIn this chapter, I will explore some core principles of psychoanalysis from which the concepts of metaphoric process and of psychoanalytic fields (both general and specific) may be developed. These principles are ones that all psychoanalytic schools of thought could accept and make use of. This discussion revolves around neutral ways in which to understand and articulate human experience. In particular, some implications of what can be generally agreed upon amongst analytic perspectives\u2014that is, the existence of some form of unconscious process\u2014are explored. In this way, an underlying base for a neutral psychoanalytic umbrella framework is articulated.\n\nA conclusion that emerges from this chapter is that psychoanalytic conceptions of some form of fantasy process are essential to understanding human experience, and this conviction about fantasy grows out of the idea of unconscious process. This is integral to formulations both about metaphoric processes and about all kinds of fields. To reiterate, this belief in the central role of fantasy is not one specific to any particular school of thought; rather, fantasy is seen as a general process that transcends and transforms experience.\n\nA crucial aspect of the development of the concept of fantasy in psychoanalysis has been present from the beginning and has been emphasized in the postmodern era. This is the matter of the origins of and the potential for a foundational basis for human experience. That is, if unconscious processes in general and fantasy processes in particular are at the foundation of psychoanalysis, then it remains to be determined from where they derive: the body, the mind, or somewhere else.\n\nTo an extent, this remains an as-yet unresolved issue in psychoanalysis. The question involves consideration of the mind\u2013body dilemma. Discussions and disagreements about the relation between mind and body have endured in multidisciplinary contexts. It is a question about which a resting place is crucial to psychoanalysis and to the potential for forming an integrated discipline from disparate perspectives. The resting place outlined here is located in a holistic model.\n\n## **The Psychoanalytic Subject and Process in a Holistic Model**\n\nFor more than a century, psychoanalytic thought and practice have changed the way humans understand themselves\u2014their thoughts, feelings, motivations, and behavior. Psychoanalytic constructs are used in ordinary discourse and have had a substantial impact on the creative arts and on many other disciplines and professions. Psychoanalysis has also been influenced by historical and social trends. Many of the psychoanalytic perspectives developed over the last half century have arisen hand in hand with a sense of disillusionment with unified and reductionist theory. This same disillusionment has led to formulations of postmodern thought.\n\nClassical Freudian theory became identified with reductionist, positivist science and was therefore the subject of a range of critiques and, at moments, wholesale rejection. While a thorough understanding of the application of postmodern principles to psychoanalysis was lacking, postmodernism was used to support the development of new psychoanalytic conceptualizations and practices. Unnecessarily rigid camps were formed. While there have been erroneous conclusions drawn from postmodern principles, psychoanalysis as a discipline has yet to reconcile one way or another with what has become established contemporary thought. For example, the rejection of absolute forms of truth and reality can be incorporated even into a classical psychoanalytic approach (in fact, with Freud's notion of _nachtr\u00e4glichkeit,_ amongst others, this has been implicit all along).\n\nWith the advent of the structural model and its underlying vision of human development, psychoanalysis was set on a path to favor the transferential, intrasubjectively shared, present moment. A common belief in postmodern thought and some contemporary psychoanalytic perspectives is that there is no subject, but instead it is the interactive nexus that creates an individual; consequently, the psychoanalytic subject has been purported to exist only as it emerges from a relationship. But it turns out that, for postmodern psychoanalysis, this is not an appropriate conclusion. In the postmodern framework, there is no unstructured, presymbolic, or prereflective state. It follows, then, that there is also no state of fusion. Thus, in this framework, a possibility exists from the beginning of a psychoanalytic, individual subject and structured, idiosyncratic experience.\n\nThe analytic experience for each participant has begun by the time initial contact is made between analysand and analyst. Already at that point, metaphoric fantasy processes are being brought to bear on the initial and subsequent contact and on the ongoing analytic process. At the point of initial contact, there is the beginning of a shared language with which to express the underlying intrapsychic meanings of each member of the dyad, especially the analysand. There is also initial input from each, necessarily understood by each in a different way. The analyst attempts to explore with the analysand the analysand's understandings. These inputs, verbal and otherwise, give rise to a complex set of affects, meanings, and understanding. For every communication, there is a potential for multiple, layered, and complex affective understandings.\n\nEach communication contains conscious and unconscious components, the understanding of which by the other then incorporates both components as filtered through the conscious and unconscious structures of the listener. Each step of communication in the analytic process is filtered through the preceding communications and understandings. A complex language is built by the analytic couple in which all terms have rich meanings. That is, the ongoing interaction between the two intrapsychic subjects is part of building a language of the psychoanalytic process that attempts to explore and express the experience of the analysand and is part of the experience of both. From the beginning of an analytic process, there are two imperfect, idiosyncratic translations or interpretations operating; it could be said that part of the analytic process is about understanding, exploring, and modifying the psychoanalytic subject's translation function.\n\nA goal of this process is to arrive at constructions that conceptualize, express, clarify, and elaborate the analysand's experience. These constructions, which may be understood as co-constructions, arise out of the analytic material originating in the analysand and interpretations from the analyst, both understood in the sense of the Barangers (2009) as having content only when each participant finds meaning in them and can make use of them to further the analytic process. An analytic goal is for the constructions to be ever more similarly understood by analyst and analysand\u2014that is, to be utilizing the terms of the analytic language in more similar ways toward a fuller expression of the analysand's idiosyncratic structures.\n\nCounterintuitive to postmodern psychoanalytic discussion, postmodern principles afford the possibility of a model of psychoanalytic process that is intrapsychic and co-constructed. The individual psychoanalytic subject, the analysand, naturally exists as an individual prior to the psychoanalytic process, but he or she also develops through the process of precipitating the idiosyncratic elements of experience into the process via co-constructed structures and the specific, unique language of the psychoanalytic process. Thus, the umbrella framework for psychoanalysis that is both nonreductive and allows for intrapsychic experience is compatible with contemporary, postmodern thought.\n\n## **Dualism and Reductions for Psychoanalysis**\n\nIn Western culture at least since descartes, theoretical and clinical discourse has assumed and made use of a separation and severability between each individual's mind and body, to the extremes of portraying persons as mindless bodies and as bodiless minds. In recent decades, this has often been expressed as the problem of mind\u2013brain. The debate has evolved into various camps of more complex or more articulated forms of dualism and of monism, including but not limited to the forms that involve reductions of mind or body, one to the other. There have also been models that include the outright elimination of mind or body\u2014often, most recently, the elimination of mind. There has also been an opposite trend: to implicitly correlate meaning with mind and to diminish the salience of the body.\n\nSome neuroscientists view the mind as reducible to the brain. Some psychoanalysts, including those who focus on one strand of Freud's thought, view the mind as emerging from the body during the course of development. One of Freud's postulations has been called a _dual-aspect monism_ (solms, 1997a). His position is more complex than that, however, due to his sense of the individual's long-range development that reaches back through past generations to seed the components of the structural model. Overall, there has been an emphasis on the body as the base or foundation from which the mind is either derived or built. This is in part the case because it is difficult to refute the idea that humans are born with bodies. At the same time, some feel that suficient evidence is lacking for the presence of mind at birth.\n\nThe discussions about adopting dualist or reductionist frameworks make use of many premises, some of which rely on heuristic principles about human nature involving survival instincts and adaptation hypotheses (Fonagy & target, 2007). Developmental theory begins with bodies and builds minds, language, and individual persons from the base of bodily sensation. This is a contemporary version of the empiricist theories of past centuries. The body has been taken to be that which provides a containment schema for the self (Modell, 2007). Humans are characterized as embodied minds or bodily minds (Rizzuto, 2001).\n\nPart of the motivation for considering the body as basic and as that from which mind grows is the quest for an answer to how it can be that humans\u2014with everything that operates privately and internally in each, together with unique idiosyncratic experiences\u2014may nevertheless share languages, meanings, and be largely predictable in agreeing on a multitude of factors. One point of view holds that it is the overall similarity of bodies, despite differences, and the strong similarity of bodily development and experience that affords communication and overall likeness among ourselves. As lakoff and Johnson (1999) describe the situation\u2014a description that many psychoanalysts accept\u2014meaning stems from commonalities among bodies and environments. There is a compelling argument that underlies this thought process, but one that warrants attention to its assumptions and presuppositions. Alternative conceptualizations that also address the theoretical requirements of this model diminish the need to accept a reduction to the body.\n\nRelevant to this question and of central importance to psychoanalysis are affects. As Modell (1978) has said so clearly, the communication of affect is the perceptual base of psychoanalysis. The formulation of a psychoanalytic theory of affect may be the litmus test for a characterization of mind, brain, and body, whether a dualist one, a monist one, or something else. To have a model of mind, brain, and body that allows for a rich understanding of affect would be to have the framework for a model of human experience.\n\nAffects do not fare well in dualist or reductionist monist models of mind, brain, and body. Problems arise as a result of situations reminiscent of Freud's assertion that the drives are located at the frontier of the psychic and the somatic. Unless affects are characterized as squarely on one side of the fence or the other\u2014which at times they have been\u2014the interactionist problem of joining or linking the two sides becomes crucial. Using affect to provide links does not redress the problem, unless affects themselves are characterized without embedding the issue there (pally, 1998). Heidegger graphically observed in his zollikon seminars that tears cannot be adequately described in a fundamentally dualist or reductionistic monist framework. To give another example, the internal perception of a sinking feeling in the stomach cannot be fully understood as body or mind alone, or as body plus mind, without some organic way of joining the two. This is the very problem posed by dualism.\n\nA tendency to adhere to Western dualism may be partly the reason why the formulation of a theory of affects has remained obdurately intractable. Neuroscientists have characterized affects as emerging from the neurodynamics of brain circuits. One way that psychoanalysts have characterized affects is as bodily experiences of drive derivatives or representations\u2014or, alternatively, as the basis of drives (Kernberg, 2001). As yet there is no articulated model of affects that exhibits their nature as neither solely of mind nor body, but as essential to both, and, further, as an integral part of a nondualist model of human experience. Also lacking at present is a model that recognizes the fundamental role of affects in psychoanalytic theory and in clinical practice (Arlow, 1977). More generally, an adequate theory of affects requires a different sort of framework than the ones we have been working with to date.\n\nBeginning from either side of the traditional dualism, either mind or body, engenders the serious liability that it is likely that either an irreducibly dualist position or a reductive monism will follow. Meissner (2006) provided an extensive and comprehensive discussion of this, noting the unsatisfactory nature of any form of either reductionist monism or dualism. Meissner developed a unified position that does not explicitly involve reduction. His language, however, is very much steeped in the dualist tradition, and thus it is difficult to assess the degree of success of this unification; he seems to have accepted what he called a _methodological dualism_.\n\nNearly one hundred years ago, heidegger noted that the division between mind and body is embedded in our very language. To speak of the problem or the issues involved is to use a language that renders expression fundamentally dualistic. Thus, dualism is the default position when using language to discuss the issues, with reductionistic monism a close second. Reductionistic monisms can be readily described in dualistic terms by noting that one of the two recognized categories is reducible to the other. Terminology is not lacking to make this kind of statement. But such a bias built into the language makes it very difficult, if not impossible, to formulate genuine alternatives to dualism that attempt to undercut the very way of thinking that lends to dualism.\n\n## **Immediate versus Interpreted Experience**\n\nAn implicit and crucial assumption of forms of dualism and of reductionistic monism concerns the possibility of unmediated access\u2014for example, direct access to the body, including self experience. The assumption of the existence of direct access arises organically from the separation of mind and body, whether by dualistic or reductionistic means. If the body is a severable entity in itself, then it must have at least a degree of independence. The body would thus be able to do something apart from performing automatic functions such as breathing. That is, it can also have sensations, at least in some sense of the word. This means that there is a possibility of the body taking in both the raw data of sensation and direct affective experience, without the use of the mind and without the use of concepts. This would also hold true in monisms that effect a reduction to the body. However, the assumption of direct access that would be entailed is untenable, as will be presently discussed, and without it, dualism and reductions to the body are undermined.\n\nA relevant distinction related to this question involves a clarifcation of what sorts of things humans experience and which have priority. Relevant are two possible kinds of experience. The first kind is the direct experience of things, without the necessity of intermediary identifying concepts. To have this kind of predicative experience would be to have an experience of that thing, that something holds of or pertains to it. The second kind of experience, on the other hand, requires some sort of conceptual background in order to have experience involving the thing. This is propositional and contextual experiencing that something holds of the thing.\n\nBoth Heidegger (1953) and Meissner (1997) have argued that there can be no independent immediate experience\u2014that is, experience of the first kind described above. Schafer (1993) and solms (1997b) have also argued to similar conclusions, and related discussions can be found in Bruner (1986, 1990), Grossman (1992), and Katz (2001). In practical terms, it is evident in clinical work that no experience is purely such\u2014free from conceptualization, interpretation, or being laden with unconscious meaning.\n\nThis means that a degree of interpretation or conceptualization is present in all human experience at all times. Specifically, there is no such thing as a pure, direct bodily experience. Even were there to be the possibility of direct sensory experience, it would have no human meaning.\n\nSimilarly, there is no direct access to the internal world or to self experience. All experience, including affective and sensory experience, is perceptual. This means that it proceeds by means of progressive interpretation, impacted by the environment and by idiosyncratic experience. A nondualist, nonreductive, holistic framework of human experience is thus essential for psychoanalysis.\n\n## **Fantasy Processes as Essential and Transcendent**\n\nGiven that there is no direct access, what is left for the umbrella framework for psychoanalysis is a way of understanding human experience as operating via holistic processes from the beginning. Transcendent and transformational processes are crucial to the psychoanalytic base. Without unmediated experience, mental processes must primarily make use of some form of transcendent concepts. Transcendence may be understood in a sense akin to phenomenologists' usage, in that it concerns going beyond what is given in experience, beyond what is accepted as relatively real. What is transcendent is not sensorily conferred by experience. The transcendent is constructed by rendering portions of the stream of experience meaningful, and this occurs by means of interpretation in a general sense.\n\nThus, transcendence is a process that goes beyond particular experience to conjecture to or posit conceptualizations. In this sense, concepts and constructions are transcendent. A concept that collects and organizes, perhaps sharpens or clarifies, disparate previous experiences and perceptions is transcendent. The concept acquired then becomes part of the cadre of what might be called the _relatively real_. The relatively real can be used to predict and shape the future, the experience itself, and memories of the past.\n\nFor example, a transcendent process could be said to proceed via the psychoanalytic notion of fantasy. Fantasy activity operates on prior experience, prior conceptualizations, and prior fantasy products, and arrives at perception and belief that are not and cannot be wholly derived from experience. A psychoanalytic example of a transcendent process in this sense is a transference interpretation. The analyst conjectures and posits a transcendent conceptualization of the analysand's communications.\n\nIn psychoanalytic terms, perception of an object proceeds by means of a transcendent process. An object is not experienced as such in itself, but only on the basis of relatively real past experience, including the involvement of prior perceptions and fantasies of the object. One is interpreting in experiencing and making predictions about the object. Friedman's (2002) discussion of symbolizing is perhaps another way of stating that a fundamental human activity is transcendence in this sense.\n\nWhile abstraction, generalization, and assessments of similarity are often taken as basic human operations, each one proceeds by means of a capacity to form and acquire concepts. What must be involved in these operations is a general psychoanalytic form of fantasy activity at their base. The ability to fantasize is more fundamental than other capacities that have been taken to be basic human ones; in fact, the capacity for fantasy activity can be considered inborn and taken as fundamental and primary. Put differently, it is perhaps by means of fantasy that humans can have and make use of sensory and other experience.\n\nEmbedded in, for example, peterfreund's (1978) paper on psychoanalytic conceptions of infancy, and also supported in Erreich (2003), are implications that something like the capacity for fantasy activity, which gives rise to concepts, must be present from birth. The world is understood by an individual via transcendent and transformational processes. Fantasy activity is a core capacity that is essential to life, and one through which the individual is able to move about in the world. Because fantasy is an essential component of life, each experience contains multiple affective, interpretive meanings. It is an objective of the analytic process to explore links amongst such multiple meanings.\n\nThus, a component of the psychoanalytic umbrella framework is a holistic base, and psychoanalysis highlights a fundamental aspect of human experience and life that is not reducible to any purely physiological theory or science. This theoretical framework includes the acceptance that human experience proceeds by means of fundamental transcendent processes. Such processes are, in a psychoanalytic sense, forms of fantasy processes. These are called _metaphoric processes_ and are explored in the following chapter.\n\n## **Note**\n\n Parts of this chapter appeared in _The Psychoanalytic Review_ vol. 97 (2010), \"Holistic Framework for psychoanalysis,\" pp. 107\u2013135.\n\n# 3\n\nMETAPHORIC PROCESSES\n\n_S. Montana Katz_\n\nThe concept of metaphor was broadened beyond the verbal by Lakoff and Johnson (1980). As will be discussed in detail in subsequent chapters, the concept of metaphoric process is an extension of this broadened view through the addition of temporal, developmental, and functional dimensions. A metaphoric process can be thought of as an unfolding of an unconscious trail, which includes and encodes emotional, procedural, dynamic, and other unconscious ingredients of experience.\n\nMetaphor is often contrasted with the literal. Similarly, metaphoric processes might be seen in distinction from direct, reality-based experience. In the umbrella framework for psychoanalysis, these are relative terms. What is experienced as real is such as a result of the metaphoric processes that give rise to the experience. Thus, what emerges from metaphoric processes may become the (relatively) real of the future.\n\nIt is argued extensively in the preceding and subsequent chapters that metaphoric processes are inborn and involuntary. Metaphoric processes are essential to human life; that is, without the continuous, ongoing stream of metaphoric processes, there would be no human world. They are the means by which each individual has experience, learns, and understands. They are the way in which humans communicate, verbally and nonverbally, intrapsychically and intervivos. Metaphoric processes are already active in early childhood (Imbasciati, 2002, 2003, 2004, 2006). These early processes persist as strands in processes throughout life. We might consider the unthought known to be involved in such strands.\n\nModell (2009a) describes metaphoric processes as mappings that involve similarity-and difference-seeking activity. When similarity is salient, repetition, including transference, may be involved and may be clinically observable. When difference is salient in the activity of an individual's metaphoric processes, conceptualization and thought are relatively absent, according to the degree of difference discerned. When the degree of difference is not extreme, resistance may be clinically in evidence. When the degree of difference is high, linking is barred and conceptualization cannot be perceived.\n\nThe idea that metaphoric processes are mappings is a simplifying heuristic proposition. Mappings can be thought of as occurring in segments of metaphoric processes. A manifold of mappings could be open to view in time slices of metaphoric processes. That is, a given metaphoric process will contain multiple mappings, each of which is modified over time in form as well as in salience. It could be said that metaphoric processes may be viewed as systems of mappings during any given time segment. In their entirety, however, they are not mappings themselves. To add more complexity, a conceptualization may (and will be likely to) involve more than one metaphoric process.\n\nFor example, a subject's conceptualization of an object will in general involve segments of several metaphoric processes. Together, these segments coalesce into a temporal conceptualization of the object. This means that, at a given point in time, contained within segments of a set of related metaphoric processes, there is a conceptualization of an object. This conceptualization exists with respect to certain salient aspects. Part of the conceptualization will necessarily involve aspects of conceptualizations of other objects, including primary objects. Mappings contained in this moment of metaphoric processes could be viewed as stemming from conceptualizations of earlier objects and being transferred to aspects of one of the current object.\n\nAn inaccuracy involved in this pertains to time and where in time the mappings that make up metaphoric processes are located. During a time slice in the present, the subject does not have direct access to past conceptualizations embedded in past segments of metaphoric processes. What the subject has are current reconceptualizations of the early conceptualizations, embedded in current segments of metaphoric processes together with associated affect patterns. In that slice, these are then mapped onto aspects of the current conceptualization.\n\nTo take an extreme example for the purposes of clarity, the time slices of metaphoric processes involved in very early preverbal experiences are not accessible as such. In fact, it is not likely that the concepts that were involved are discernible in the mappings in such metaphoric processes. The conceptualizations involved may be of a radically different nature than later experiences. What carry through are associated affect clusters, including the derivatives of self experiences.\n\nAnother inaccurate shorthand is that time progresses in a measured, linear fashion. Yet it is rarely experienced or psychoanalytically understood that way. Transference is a much-discussed case of both nonquantifable and nonlinear, lived time. Metaphoric processes can be heuristically thought of as coursing through the life of an individual in conventional time, yet one thing that is crucially plastic in such a metaphoric process is time. A past event, feeling, or experience is continually brought into the present in its rearticulation by means of newly acquired experience imported into the metaphoric process. These elements refer back to, reinvent, and restructure the experience of the past, as well as informing the experience of the present.\n\nAt every moment, metaphoric processes are based in that moment. From the salient metaphors of a given moment in the experience of a subject\u2014including the current valences\u2014the categories of experience, the organizing principles (Feirstein, 2009), the templates (Freud, 1912c), or the structure (Modell, 2009a; Katz, 2004) can be discerned. The early metaphoric processes of an individual, for example, may contain elements of the experience of the maternal environment. Active metaphoric processes need not form a mutually consistent set. Contradictions and paradoxes abound within the life span of an individual, and this can be represented by contemporaneous metaphoric processes containing conceptions and structures that conflict with each other. Within an individual, as with everything unconscious, a metaphoric process is lifelong. A single metaphoric process may be salient and active in and for the individual at certain points, moderately active other times, and relatively dormant at still others.\n\nMetaphoric processes are continuously ongoing within a human being, and as Modell has described so clearly, they map from one domain to another, possibly dissimilar domain. Metaphor can be a form of transcendence, a mapping from the known, relatively real onto new conceptions of previous experience. This conception of metaphor is consistent with Arlow's (1969) discussion of fantasy in that metaphors are not only ongoing, but also provide the mental set with which humans function. Modell (1997a) states this similarly with respect to metaphor by saying that it is the _currency of the mind_. Freud, in his discussions of dreams and unconscious processes, emphasized visual components. Metaphor is multiperceptual. This includes multisensory elements as well as those of affect and conceptualization.\n\nWhen a metaphoric process within which an individual is functioning can be discerned, one strand of a layer of his or her life comes into high relief. This strand can at times be perceived more or less consciously, and at others may be active solely in the unconscious. Multiple metaphoric processes are ongoing in an individual's life at all times and can merge, diverge, overlap, combine, contradict, and conflict with each other. Unlike Husserl's undifferentiated, universal stream of consciousness, there is an idiosyncratic, differentiated stream of metaphoric processes that continuously course through time.\n\nWhile the concepts and constructions that an individual postulates are idiosyncratic, they are not incommunicable. A subject's experience and interpretations are unique, which is an essential premise of theoretical and clinical psychoanalysis. They are also largely unconscious. Unconscious individual heuristics are discoverable to consciousness through discourse with another (shapiro, 2005). This is made possible from at least two directions. First, the environment has an influence in shaping an individual's conceptions, from the earliest forms of his or her protothoughts and feelings. This normative conditioning occurs as part of the way that natural languages serve to carve human experience into discrete conceptualizations of the behavior of others\u2014especially their highly repetitive behaviors common to many individuals and present in the value systems of populations.\n\nFrom at least birth on, one begins to conceive of aspects of the world through social structuring, including by means of the acquisition of language. This means that, to a large extent, an individual processes experience by means of the conceptual apparatus of the primary language learned, and begins to do so possibly even prior to achieving language competence. That is, many of the concepts acquired or formed in early experience are derived from the way of carving up the world that is implicit and embedded in the language of primary caregivers. Thus, many of an individual's concepts\u2014and thereby his or her expectations\u2014are learned largely through the various media the individual encounters in the world.\n\n## **Metaphoric Processes Are Essential to Human Experience**\n\nTo the same degree that humans could not survive without oxygen and water, they could also not survive without unconscious fantasy activity, and therefore not without ongoing metaphoric processes. Metaphoric processes are essential for the formation, acquisition, and development of concepts within an individual, a community, and the human race as a whole. They are required for the formation of languages and other forms of symbolic representation and communication. What we are aware of and can conceive of\u2014objects, things, self, brains, bodies, minds, etc.\u2014are arrived at through perception and are thus interpretations. In a manner of speaking, they exist as discrete entities to the extent that they are conceptualized as falling into categorizations.\n\nFor humans, a world without metaphoric processes would not be an impoverished world; it would be no world at all. Without the ongoing capacity for metaphoric processes, human experience would not be identifable, discernable, or even describable. All perception would devolve into discrete and unusable sensory impressions. Without metaphor, the potentially infnite amount of sensory input at any given moment would be a bombardment of particulars without any sort of filtration or conceptualization. There would be no patterns, no observations, no predications or predictions\u2014in effect, nothing.\n\nModell has discussed aspects of situations in which the flow of metaphoric processes is diminished or restricted. Specifically, he has explored when and at which points the play of similarity and difference collapse into similarity-seeking processes only, resulting in a loss of the relatively free mobility of metaphor construction. Such cases eventuate in what Modell calls _frozen metaphor\u2014_ repetitions, including transference.\n\nAt the other extreme is the situation in which metaphoric play collapses into difference-seeking and discerning processes only. In this case, metaphoric processes are disabled to the same extent as the degree of the lack of similarity seeking. For example, if an analysand sees only difference between herself and the analyst or other objects, then points of reference with which to discuss this perception will be scarce to nonexistent. At the extreme end of difference discerning, with no similarities discerned overall, there are, in effect, no useful concepts to draw upon. A framework of human experience in which all concepts are singletons is not usable because of an absence of links among discrete sensations and perceptions. No patterns can be detected without categories into which things fall and in which they can be grouped together.\n\nAffective experience under such circumstances of solely difference seeking would be unlinked as well. There would be no linking of similar affective experiences from which humans learn about the world and themselves in it. Moreover, it would not be possible to link the affective expression of others, as is so crucial for development and growth, especially in infancy. The metaphoric capacity is disabled altogether in this extreme case, and is relatively disabled in less extreme cases.\n\nWithout ongoing metaphoric processes, the beginning of life would be entirely different. One aspect of early development is that affectively linked concepts are acquired and increasingly applied. The discernment of patterns of needs, satisfactions, and frustrations; progressive recognition of others and self; increasing control over mobility\u2014all these are in part the result of developing conceptual and perceptual apparatuses. Without this none of these developments can occur, seriously arresting maturation\u2014for example, in the emergence of conceptualizations of space and oneself in it as three-dimensional. In extreme cases, even basic intentional mobility would not be achievable.\n\nIt is not going too far to say that human life would not be possible without some capacity to detect similarity amongst even vast differences. While the situation of living with a diminished capacity to form links is well known to psychoanalysis and is treatable with analytic processes, human life entirely without that capacity is neither survivable nor even conceivable. Virtually by definition, the state of that experience cannot be described in a language that necessarily employs linking concepts.\n\nThis exploration of the role of difference in metaphoric processes again demonstrates the fundamental nature of metaphor to human experience and to life itself. Without some presence of the play of similarity\u2014that is, without some capacity for linking\u2014there is no human life. Modell's (1990, 1997a) statement holds: that metaphoric processes are involuntary and inborn, that \"metaphor is the currency of the mind\" (2009a, p. 555). Furthermore, metaphoric processes are present from the beginning of life and are the means by which humans experience, learn about, and understand the world, including themselves and all objects. The largest element of human commonality may be metaphoric processes. What is pervasive to our processing and experience is affective and interpretive.\n\n## **Components of Metaphoric Processes**\n\nOne way to articulate the concept of metaphoric process is to differentiate its components. The components are ingredients, or dimensions, of a given metaphoric process. As ingredients, each contributes to the totality of any given point or time slice of a metaphoric process. The discernment of components as various ingredients of metaphoric processes is for heuristic purposes; they may not be neatly isolable or readily observable in the flux of actual clinical experience. Four components in a given metaphoric segment are the _idiosyncratic_ , _local_ , _community_ , and _generalized community_ ingredients. Movement or influence within any one component may have ramifications and effects in each of the other components.\n\nIn normal development, the peak, active formation of idiosyncratic features of metaphoric processes will take place in the early, preverbal period. The segments of metaphoric processes that run through this preverbal period are unlikely to be retrievable with organizations or structures close to those originally involved in them. The acquisition of local and community configurations contributes to the transformation of prelinguistic, idiosyncratic elements. However, this does not mean that the latter disappear or that they have been rendered inactive.\n\nAt the other end of the spectrum from the idiosyncratic is the generalized community component. The contents of this related component are close to what have been called _primary metaphors_ (Lakoff & Johnson, 1980). This component arises in structures as that portion common to all humans, across individual experience and culture. It might be that this component of metaphoric processes, while universal for humans, is relative to specific eras of human existence.\n\nThe structures from the other two components, the local and the community, lie in between the idiosyncratic and the generalized community in their influence on strands of metaphoric processes. These are configurations that revolve around perceptions of early environmental experience and those of broader cultural experience throughout life, respectively. Using metaphor as a foundation, all levels that have input into human experience can be incorporated. The idiosyncratic, the self in early relation to primary objects, the larger environment and enculturated community, as well as the level of general human experience\u2014all these contribute to metaphoric processes across the life span.\n\nLife proceeds along a sinew of metaphoric processes. The sinew continues for the life of the person. If the sinews of different individuals were entirely different from each other, then the individuals could not meaningfully interact with each other. While one's own sinew is what makes one oneself through time and space, many of the elements of that sinew\u2014that is, metaphoric processes, as well as items in those processes\u2014can be overridingly similar, more similar than not, across individuals, and this is what makes intersubjective, and derivatively intrasubjective, human interaction possible. Trough early experience, the highly idiosyncratic conceptualizations embedded in the metaphoric processes give way and merge with elements of this sinew that are held in common with others. Language acquisition and exposure to wider social experience contribute to this giving-way and merging process. Even in the idiosyncratic, more private, early phase, the ingredients of metaphoric processes may be mostly shared as a result of the commonalities of _in utero_ and early experience.\n\n## **The Concept of the Psychoanalytic Subject in Terms of Metaphoric Processes**\n\nA person can be represented as a sinew\u2014a bundle of metaphoric processes. All that is identified with a person\u2014his or her life experiences, memories, thoughts, bodily experiences, etc.\u2014are part of the sinew of metaphoric processes associated with that person. Not all strands persist throughout the entire length of the sinew (that is, the lifespan of the individual). Some become dormant, some merge with other strands, and some may even disintegrate. Some strands commence in the middle of the sinew, while some split into multiple strands. Some segments of strands overlap with others. Each strand carries valences throughout the metaphor and may become stronger or weaker at different points and in relation to valences on other strands.\n\nA momentary cross section of an individual's sinew would display multiple metaphoric processes in that time slice. Each metaphoric process in the time segment is composed of combinations of the four categories of ingredients, together with the valences of each. In addition, each valenced time slice is impacted to some degree by any or all of the metaphoric processes in the sinew up until that point of the time slice. Valences that are the strongest at that moment give rise to a tendency to influence the individual toward movement along the components or strands to which those valences are attached.\n\nThis way of describing a self provides a structural portrayal of the complex aspect of human experience with which psychoanalysts work. Each metaphoric process in itself represents one pathway that organizes and motivates the future of the self with respect to a specific cluster of experience. In any given moment of a person's life, multiple clusters of experience, multiple metaphoric processes, all have bearing on the moment, each with its own internal set of affects. Some current elements of one metaphoric process may well stand in contradiction to, or in affect bundle opposite to, another current slice of a different metaphoric process. Thus, motivation, multiple function, overdetermination, and conflict can be understood within this framework.\n\nIn this framework, self-awareness, whether bodily or otherwise, is mediated by metaphoric processes. In principle, one has no more direct route to self-awareness than object awareness. Whether it is a self-awareness of something as basic as enjoying a certain taste, it involves multiple metaphoric processes in order to arrive at linking the discrimination of a certain taste and the experience of pleasure. This may occur without an understanding of the past experience that led to the pleasure. Awareness of objects is not different in kind, but at certain points in the lifespan, it may sometimes be more limited and at other times less limited than self-experience and awareness. It is the sinew of ongoing metaphoric processes that brings one to a moment of affective or other experience, rather than an immediate self-experience. This view of persons and personal experience is grounded in unconscious processes.\n\n## **Note**\n\n parts of this chapter originally appeared in _Psychoanalytic Inquiry_ 31(2): pp. 134\u2013146 as \"Unconscious Metaphoric processes as a Basis for an inclusive Model of psychoanalytic perspectives.\"\n\n# 4\n\nMETAPHOR IN  \nPSYCHOANALYSIS AND  \nCLINICAL DATA\n\n_Robert Wallerstein_\n\nSince the 1980 book, _The Metaphors We Live By_ , by Lakoff and Johnson, the cognitive-linguistic view of metaphor that they propound has come to be most widely accepted. Its characteristic features are that (a) metaphor is a property of the concept, not the words; (b) its function is to heighten understanding, not simply artistic or aesthetic; (c) it is often not based on similarity; (d) it is ubiquitous in ordinary language, not requiring special talent; and (e) it is an inevitable intrinsic aspect of all human thought and language. This is true of all speech, including the speech in and of psychoanalysis. Metaphor both amplifies and creates meaning. But it can also be misleading and produce conceptual errors of meaning. It should, therefore, not be reified or always taken literally, but should remain flexible and alterable, so that heuristically more relevant and more encompassing metaphor can readily be elaborated.\n\n## **The Meaning of Metaphor**\n\nOur language of discourse, daily conversation or literature and essay, has, as far back as it has been recorded, been saturated with metaphor. Zolt\u00e1n K\u00f6vecses (2002), a student of, and collaborator with, the noted American linguist, George lakoff, in his comprehensive book on metaphor\u2014called a _Practical Introduction_ \u2014calls metaphor a figure of speech that implies a comparison between two unlike entities, though with linking common features. He states that traditionally metaphor has had five characteristic features: a) it is a property of words, a linguistic phenomenon, b) it is used for rhetorical or artistic purposes, c) it is based on resemblance, d) it is a conscious and deliberate fashioning of words that requires special talent, quoting Aristotle who called it \"a mark of genius,\" and last, e) a figure of speech that we can well do without.\n\nThis view K\u00f6vecses declares to be dramatically challenged, and in his view superseded, by the \"cognitive-linguistic view of metaphor\" enunciated in the 1980 volume by Lakoff and Mark Johnson, in which five quite different\u2014and opposed\u2014characteristic features define metaphor: a) it is a property of the concept, not the words, b) the function is to heighten understanding, rather than simply an artistic or aesthetic purpose, c) it is often _not_ based on similarity, d) it is used effortlessly, and mostly unremarked, in ordinary language, not requiring any special talent, and e) it is far from being a superfluous, though pleasing, linguistic ornament, and is rather an inevitable, intrinsic aspect of human thought, reasoning, and speech.\n\nTough admittedly there may be strong proponents of both perspectives still continuing today, K\u00f6vecses devotes his entire volume to demonstrating, via seemingly endless examples, the clear superiority of the newer \"cognitive-linguistic\" perspective. The use of metaphor is so ubiquitous, and often so mundane and commonplace, that it is simply not noticed, being called in that case \"dead metaphor.\" two such examples are, \"a local _branch_ of this business\" (a plant metaphor of a tree), and \"the country was close to s _liding_ into war\" (a spatial metaphor). But these are really \"live metaphors\" since they frame our thinking and give it meaning; they are the metaphors we regularly live by. For example, our common metaphor of the human mind as a machine can be seen in another two of K\u00f6vecses' examples: \"How could any man ever understand the _workings_ of a woman's mind?\" or \"After my first cup of morning coffee, my brain was _ticking over_ much more briskly.\" and this common metaphor is evident in all visions of mental activity, of mind conceived as computer for example, by scientist and general public alike.\n\nIn this perspective, metaphorical language is not arbitrary and unmotivated, nor simply ornamental, but is embedded in and central to, our entire idea-creating, thinking process, originally arising from our basic bodily (sensorimotor) developmental experiences. And when we see ideas as food (\"I can't swallow that claim\") or life as a journey (\"We aren't getting anywhere\"), we are thinking about abstract concepts (ideation, or life) in ways that are deeply facilitated by the more concrete concepts of food, or a journey. In this sense; \"in the cognitive-linguistic view, metaphor is defined as understanding one conceptual domain in terms of another [more concrete] conceptual domain\" (K\u00f6vecses, p. 4). Thus it creates new meaning.\n\nAdam Bessie in his 2006 review of the literature on metaphor, also drawing centrally upon Lakoff and Johnson, states then the specific contention that \"metaphor is a foundational, constructive, and natural process by which we conceptualize the world\" (p. 6), and is therefore, \"a process for generating ideas\" (p. 5). Within this conception, \"all language is, at some level, metaphoric... not a matter for the artist alone, but a part of everyday life\" (pp. 10\u201311), and \"a way of thinking, a way to invent ideas, rather than [just] a way to clearly express thinking\" (p. 11). Metaphor has been moved, powerfully by Lakoff and Johnson, from mental product to mental process.\n\nBessie quotes peter elbow (1973) on _how_ metaphor generates new meaning. \"When you make a metaphor you call something by a wrong name... you are thinking in terms of something else... [each comparison] throws into relief aspects of the [topic] you might otherwise miss. You are seeing one thought or perception in terms of another\" (elbow, pp. 53\u201354). \"In essence... the writer discovers similarity, and between things which are at first, seemingly unrelated\" (Bessie, p. 13). And it is this \"discovery process [that] is generative; the writer develops new ideas atop old ones, seeing the world in new ways\" (p. 13).\n\nThis is what yields new insights, activating \"two separate concepts, bridging the two separate conceptual schemata\" (Bessie, pp. 21\u201322). And, of course, it also makes for the possibility of error. As James seitz (1999) said: \"Metaphor, in other words, represents language at its most vulnerable moment, not only because it stimulates multiple, unpredictable readings, but more importantly because it risks obfuscation that can result from calling _this_ by the name of _that_ \" (p. 42) and therefore, \"the metaphoric process... is not only one of finding comparisons between different things but [can become one of ] finding contrasts\" (Bessie, p. 17). And thus, can also produce conceptual errors in our process of taking \"what we know, to make sense of what we do not\" (Bessie, p. 14). Metaphor can also be used, deliberately or automatically, to influence, even to mislead, to further bias and advance ideology, as in political, economic, or cultural propaganda, or commercially, in product advertising. Examples are of course, everyday, and legion.\n\nAnd lastly, importantly, \"Given theory which suggests [that] metaphor is a matter of individual cognition 'difference' becomes contextualized within the individual, rather than universally. Thus, determining when a topic and vehicle are 'different' and thus metaphoric, is a matter of individual perception, and individual knowledge\" (Bessie, p. 18). In other words; \"What is metaphoric to one person, can well be literal to another\" (Bessie, p. 9).\n\n## **Freud and Metaphor**\n\nGiven this state of metaphor theory, with its still continuing varying perspectives, and its warning caveats on the pitfalls for the adherents of any of its perspectives, how can we situate the role and place of metaphor within psychoanalysis, both in its theory, and in its therapeutic applications, within that context? as is so often the case, sigmund Freud can be understood on both sides of this just stated question. On the one hand his descriptive-explanatory language is drenched in vivid metaphor, in both the clinical and the theoretical realms. A very well-known and oft-remarked _clinical_ example is his analogy of the psychoanalytic situation to a train ride, and the emergent free associations of the analysand to the recital of a railroad passenger seated at the window, describing the passing scenery to the companion in the adjacent seat (1913a, p. 135). An equally well-known and quoted _theoretical_ statement is his effort to explain how sense-impressions relating to what he calls the perceptual system and the mnemic systems become embedded memory through analogy with the operation of the then recently introduced contrivance of the \"Mystic Writing-pad,\" a writing-tablet from which notes could be erased by an easy movement of the hand (1925, p. 228). Every student of psychoanalysis has many more of Freud's examples at hand.\n\nHowever, given Freud's commitment\u2014under the guidance of his neuropathological mentor, von Br\u00fccke\u2014to the Helmholtz model of a natural science, physico-chemical basis for biological processes, he espoused lifelong his conviction that psychoanalysis, as an evolutionarily constituted, biologically grounded, psychological discipline would ultimately be firmly embedded in that same natural science framework. And, as corollary to that, would necessarily endeavor to eschew metaphorical language in favor of a more scientific mathematical language (a language direction in which Bion sought later to move, while himself, at the same time creating new metaphoric concepts like \"container-contained\").\n\nAt the same time Freud himself famously created numerous compelling metaphors, like those just indicated, to describe his advancing theoretical conceptions, such as id, ego, and superego, used to describe differing mental activities\u2014and to justify their heuristic use, as well as mark out his strong awareness of their provisional, and non-literal, nature. I cite two of his best-known cautionary expressions. In his 1914b paper, _On Narcissism,_ he said:\n\n> I am of opinion that that is just the difference between a speculative theory and a science erected on empirical interpretation. The latter will not envy speculation its privilege of having a smooth, logically unassailable foundation, but will gladly content itself with nebulous, scarcely imaginable basic concepts, which it hopes to apprehend more clearly in the course of its development, or which it is even prepared to replace by others. For these ideas are not the foundation of science, upon which everything rests: that foundation is observation alone. They are not the bottom but the top of the whole structure, and they can be replaced and discarded without damaging it. The same thing is happening in our day in the science of physics, the basic notions of which as regards matter, centres of force, attraction, etc. Are scarcely less debatable than the corresponding notions in psycho-analysis.\n> \n> (Freud, 1914b: p. 77)\n\nIn this pivotal paper, Freud clearly defended the necessity of metaphoric conceptions to the advancement of psychoanalytic theorizing\u2014and cited the quintessential natural science, physics, as also governed by comparable needs and strategies\u2014while expressing the implied hope that this might be only a way-station on the road to more scientific, i.e., mathematical, precision.\n\nAnd in his final years, in his 1937 paper, _Analysis Terminable and Interminable,_ he still made the identical point, even more dramatically, when discussing the instincts and their relation to the ego, \"if we are asked by what methods and means this result is achieved, it is not easy to find an answer. We can only say: 'So muss denn doch die Hexe dran!'\u2014the Witch Metapsychology. Without metapsychological speculation and theorizing\u2014I had almost said 'phantasying'\u2014we shall not get another step forward. Unfortunately, here as elsewhere, what our Witch reveals is neither very clear nor very detailed\" (Freud, 1937 p. 225). And here is clearly stated the presence of\u2014and the use of\u2014metaphor as central to the fabric of psychoanalysis from its very beginnings as an emerging science, but also, its limitations, and its possibility for obfuscation.\n\n## **The Struggle to Expunge Metaphor From Psychoanalysis**\n\nEver since, different theoreticians have thrown their weight on one or the other side of this struggle over the proper place, for better or worse, of metaphor within psychoanalytic conceptualizing. In the first decades after World War II\u2014and prior to the path-changing Lakoff and Johnson volume\u2014major theorists, concerned to make psychoanalysis more \"scientific,\" sought to progressively eliminate metaphor from its language. For example, else Frenkel-Brunswik (1954), schooled in Vienna in the logical positivist teachings of Moritz schlick, averred: \"While the psychoanalytic system comes closer to a truly scientific theory than most observers realize, psychoanalysis still contains many metaphors, analogies, and confusions between construct and fact which must in the end be eliminated\" (in Heiman & Grant, 1974, p. 226). And she explained away such metaphoric, and in her mind, logical, lapses that appeared in Freud's theorizing. \"When Freud ascribes some of the difficulties in his speculations concerning the instincts to our being obliged to operate with 'metaphorical expressions peculiar to psychology,' we must add in his behalf that for the type of problems with which psychoanalysis deals the mentalistic (introspectionist or animistic) vocabulary constitutes the precise counterpart of the pictorial vocabulary which has been stressed as a legitimate or at least _tolerable_ ingredient of the earlier stages of physical science\" (also p. 226, ital. Added).\n\nAnd H. J. Home (1966) warned of the danger of such lapses. \"If mind is not a thing then each time we speak about it as if it were a thing we are speaking metaphorically... If, however, we suppress or repress our consciousness of the metaphor and speak literally about the mind as a thing then we have created a metaphysical fact\" (p. 46), something to certainly be avoided.\n\nIt was under this anti-metaphorizing banner that two major American psychoanalytic theorists undertook to expunge metaphoric language from psychoanalytic discourse, though from different perspectives, Lawrence Kubie from a theoretical vantage point, and Roy schafer from a clinical one. Kubie (1966) undertook his campaign as the centerpiece of his effort to ground psychoanalysis within \"the future development of a psychophysiology of psychoanalysis\" (p. 196), in accord with Freud's own dream of this future for the discipline that he had almost single-handedly created. Kubie did acknowledge that he had as yet no methods to properly carry out this intent of a biologically grounded, i.e., truly scientific (in his sense), psychoanalysis. \"Unhappily we have as yet no precise methods by which to carry on such investigations. The development of appropriate techniques will constitute a major methodological breakthrough for all psychologies, but especially for psychoanalytic psychology\" (p. 196).\n\nAnd in decrying both Freud's topographic and structural metaphors, Kubie did endeavor to commit himself to the effort to expunge metaphorical language from psychoanalysis. \"I will make no further use of this metaphor [topographic aspects of mentation], however, nor of certain other metaphors which appear currently in psychoanalytic writings, and which are regularly miscalled 'hypotheses'\" (p. 191). As an example of the ill that he felt was done by the widespread use of Freud's structural metaphor of the mind (id-ego-superego), Kubie declared; \"Freud called this the 'structural' aspect of human mentation. This metaphor seems to me to have been even more unfortunate and misleading than the other [the earlier topographic model] because it does not increase the precision of our descriptions of mental processes, but blurs them by an inexact analogy, and also because it has no explanatory value itself. Indeed, the effort to use this analogy as an explanatory hypothesis has led us into a morass of anthropomorphic pseudo-explanations\" (p. 192).\n\nOf such statements, L\u00e9on Wurmser (1977), who later wrote in defense of metaphor as central to the creation of (all) science, including psychoanalysis, declared, \"But is a statement referring to 'the characteristics of behavior in which preconscious processing flows freely, dominating the psychic stream and furnishing a continuous supply of processed experiences for 'symbolic sampling'... in any way less metaphorical than the points of view, the metaphors and models, attacked by him?\" (pp. 468\u2013469).\n\nIt was, however, Roy Schafer who, from a clinical, rather than a theoretical, vantage point, mounted the most intense and prolonged effort, in a major sequence of papers (1972, 1973a, 1975, and others) culminating in a book (1976), to thoroughly eliminate metaphor from psychoanalytic work by shifting concretizing nouns, and their qualifying adjectives, so often cast within a passive voice, into active verbs and their adverbs\u2014all to be called \"action language\" (since the verbs would specify mental acts). This would restore the personal agency, and its inherent acceptance of personal responsibility, to personal behavior and its psychoanalytic unraveling. Schafer's battle cry was, \"We can no longer afford to maintain unchallenged the belief that there can be no Freudian psychoanalysis without Freudian metapsychology\" (1975, p. 41).\n\nIn this effort to rid psychoanalysis of all its spatial metaphors of the mind's various functions, and their interplay and their movements inside and outside, schafer (1972) declared, \"I have been re-examining psychoanalytic terms in the interest of eliminating from our theory confusing, unnecessary, and meaningless metaphors and the assumptions they both express and generate... I am... attempting to develop a sublanguage within the English language that will make it possible to specify mental facts in an unambiguous, parsimonious, consistent, and meaningful fashion: I refer especially to facts of interest to psychoanalysts and analysands\" (p. 421).\n\nHe does this because, \"we have complicated our thinking unnecessarily; we are using a pseudospatial metaphor from which it is all too easy to slip into concreteness of thought; once embarked on metaphor, we tend to develop a sense of obligation to be metaphorically consistent, and to involve ourselves in extravagant niceties of formulation, and perhaps we even introduce still another assumption into theory where none is needed. The history of the pseudoquantitative energy metaphor in Freudian metapsychology demonstrates what I mean\" (1972, p. 435).\n\nSchafer then went on to assert that, \"Even though such archaic thinking is widely used as metaphor in the adaptive communications of everyday life, it _cannot_ be used for exact clinical description and interpretation or for rigorous theoretical conceptualization\" (1973a, p. 47, ital. Added). And this is because it cannot be tested: \"There is no _it_ that metaphors capture and so there is no way of testing the truth of a metaphoric construction of experience when one has only the metaphor to work with. Ten it is self-contradictory to assert\u2014it is so often asserted\u2014that certain experiences can be expressed _only_ metaphorically; for if the assertion is true, then there is no way of assessing the metaphor against its referent and so no basis for making the claim in the first place\" (1976, p. 369). Tat, in essence was schafer's message, which he kept enlarging in a series of papers seeming to cover almost every aspect of psychoanalytic conceptualizing.\n\nThat Schafer's action language never won a significant constituency can be attributed, I think, to two reasons. First is the real ubiquity of metaphor in all our spoken language, whether in social or psychoanalytic discourse, as Lakoff and Johnson demonstrated so convincingly in 1980 (after the publication of the major bulk of Schafer's writings on the subject), so that the effort to totally expunge metaphor becomes an unending, and always failed, task. And second, because the endless sample alternatives that Schafer offered so often were strained and clumsy locutions that could not come easily into conversation. For example, in a chapter in his 1976 book devoted to the language of emotion, after giving many striking and common examples of the metaphor of the heart, used to describe emotional states (big-hearted, broken-hearted, warm-hearted, cold-hearted, and many more), Schafer offers substitutions like: \"A warmhearted person is someone who deals affectionately and generously with others. A chicken-hearted person is one who fearfully avoids dealing with ordinary dangers. A hearty person is one who does a variety of things vigorously, zestfully, and good-humoredly,\" etc. (p. 276).2\n\n## **In Defense of Metaphor in Psychoanalysis**\n\nBut metaphor in psychoanalysis has also had its determined, early defenders, in both its clinical and theoretical arenas. Given its conversational ubiquity, working with, i.e., understanding, metaphor has long been part of the clinical armamentarium of psychoanalysis. Rudolf Ekstein and Dorothy Wright in the 1950s made explicit what Ekstein called \"working within the metaphor.\" in a 1952 article, they described a \"schizophrenoid\" child, a delusional nine-year-old, massively phobic, given to suicidal fantasying, and troubled by severe asthma, who played out his psychic turmoil as a Five star General, commanding an armada of space ships engaged in destructive inter-galactic wars. He was labeled the \"space child\" because of the vast cosmological distances over which his internal wars with his all too powerful parents were presented.\n\nWorking within the metaphor was described as, \"When we speak of distance we refer to it in the physical, emotional, metaphoric sense, since his way of describing the man far away, his using the metaphor of hundreds and thousands of light years seemed to be nothing but an allusion to a psychological problem which he could not present in any other way. The mode of his defense, the way his ego attempted to master internal problems rather than the content of the conflict was attacked by psychotherapeutic work\" (Ekstein & Wright, 1952, p. 214). And after substantial therapeutic work the child's internal world was brought down from the distant galaxies to planet earth, where he now became Oscar Pumphandle, engaged in research in Arizona, improving the atom bomb, while his parents were also now earth-bound, but as dinosaurs (still distant in time). It was such changes, as in these mechanisms of distance, of space and of time, that Ekstein felt could be taken as indicators of therapeutic progress. It was \"defense through distance\" (p. 222) that was gradually undone.\n\nIn a successor paper two years later, the boy was now solidly on earth but moving time over great spans through a time machine that he had created. He could now move from our primeval evolutionary birth from a fish or reptile, through all of history, favoring William the Conqueror's 1066 conquest of England, and a trip as a tourist in Europe in 1425. His mission in going back in history was to intervene to change critical familial events, and thus by changing his past, saving his future. In this paper entitled \"The space Child's time Machine\" (Ekstein, 1954), the author stated that, \"Tommy has made use of many archeological metaphors\" (p. 505). Tommy's delusional states could be conceptualized as experiencing concretized metaphors, literally, i.e. Delusionally.\n\nClearly, work within the metaphor, or with the metaphor, is not always so explicit as with this very disturbed youngster, but more or less explicitly (or implicitly) it has long been an inevitable and accepted part of imaginative clinical psychoanalysis.3 how could it be otherwise, given the ubiquity of metaphor as an inextricable constituent of even the most ordinary language, let alone the usually more educated discourse within the psychoanalytic encounter. And it can be put to apt clinical use. When a patient expresses himself, for example, as hunting around for something, the alert analyst can at least wonder about buried aggressive connotations, hunting, hostile assaults, murderous fantasies, etc.\n\nBut the place of metaphor within the theoretical language of psychoanalysis, a discipline trying to warrant its claim to be a growing science, has always been more problematic\u2014witness the efforts by theorists like Kubie and schafer, intent to rid psychoanalysis of its metaphoric expressions, the one to legitimate its credentials as science by making its language ultimately more mathematical, and the other to enhance its power as therapy by making its clinical language more actively verbal and its agency more owned.\n\nIt was L\u00e9on Wurmser (1977)\u2014also writing, like Kubie and schafer, prior to the publication of the Lakoff and Johnson volume, which retrospectively gave powerful support to Wurmser's thesis\u2014who impressively made the case for the inevitability and the necessity, of metaphor as a central component of developing science. Wurmser began with a systematic critique of those who saw metaphor as either a distortion of the clinical process (like Schafer) or an anti-scientific turn (like Kubie), in both ways declared to be hurtful to psychoanalysis. Wurmser's response to Kubie, who he artfully showed was actually substituting one set of metaphors for another in the language of psychoanalytic theory\u2014since, as Lakoff and Johnson later demonstrated, there is no escape from metaphor when constructing speech or writing\u2014has already been earlier stated.\n\nOf Schafer, Wurmser said: \"As Schafer (1975) states in a recent article, his profound criticism would sweep away all of metapsychology and most of our clinical theory and erect a new theory based on psychoanalytic phenomenology. His criticism is based on two premises: first that metaphors derived from direct experience become concretized and therefore are dangerous, indeed ultimately evil;4 and second, that it is possible to form a theory of psychoanalysis based strictly on functional correlations which have shed all metaphorical impurities, and that he has found a key to build such a nonconcretized, nonreified theory\" (p. 471). But again, \"shedding all metaphorical impurities\" is a fruitless task, and the substituted language proved clumsy and less attractive, and therefore never caught on.\n\nWurmser then went on to stake out his own \"defense\" of metaphor in psychoanalysis, both clinically and theoretically. Essentially his argument is that, \"What is crucial is that our science, like any other science, is woven of the warp of observations and held together by the intricate woof of symbolism, of many layers of abstractions, of stark and faded metaphors, which 'interpret' for us ('explain' to us) the 'direct' facts which, as we know, are never really direct\" (pp. 476\u2013477). This led to the statement all in italics; \" _All science is the systematic use of metaphor\"_ (p. 477). Which is further explained by: \"Metaphors, taken literally, are unscientific. Metaphors, understood as symbols, are the only language of science we possess, unless we resort to mathematical symbols\" (p. 483). (The latter of which, of course, Bion attempted prematurely.)\n\nActually, this all follows ineluctably from the Lakoff and Johnson thesis that metaphor is of the very fabric of all language usage, even though as Bessie (2006, p. 7) has stated, \"Across fields there is [still] a great deal of debate over what metaphor is, and how it functions. [and] ironically, or appropriately, metaphor is an abstraction, one which it is difficult to define without resorting to metaphor... in fact, the very word metaphor, Seitz (1991) observes, 'derives from a metaphor: to transfer, to carry'\" (p. 389).\n\nSince metaphor is always there, the (scientific) interest of psychoanalysis in the use of metaphor in its clinical and theoretical discourse, \"is _, whether and in what forms and on what levels we choose symbolic representations_ for the specific experiences gained by the psychoanalytic method and the scientific inquiry based on this method\" (Wurmser, p. 482). For, \"The connection between symbol and fact is solely this functional relation... a means to predict consequences\" (Wurmser, p. 473). And Freud, whose dramatic and evocative prose style earned him the Goethe prize for literature, was so often masterful in his metaphoric language choices. Wurmser put it thus: \"What has been most _fruitful_ in analytic theory formation? one has only to read the works of Freud and a few other analytic theoreticians to discover that it was the richness and the systematic, coherent use of metaphorical constructs that added so much to our knowledge\" (Wurmser, p. 484).\n\nFreud, of course, was not always clear about _how_ he deployed and used metaphor. Talking about Freud's energy metaphor, designed to substantiate the economic viewpoint in metapsychology, Wurmser quoted, \"shope (1973) is probably right when he states that Freud saw the concept of energy not as metaphor, but as explanatory construct (p. 396); this should not hinder our re-evaluating it critically\u2014accepting it as useful in the former, as most dubious in the latter meaning\" (p. 487). Tough the energy metaphor has been substantially abandoned by much of the psychoanalytic world, replaced now by heuristically more useful metaphor, Wurmser did try to explain its long appeal to Freud (and to many others) as follows: \"The economic world in psychoanalysis is an attempt not to add yet a new physical content to those physical equivalent [energy in the natural sciences] but to establish metaphorically, by analogy, a _similar system 'of quantitative relations of equivalence'_ \u2014some novel form of lawful correlation between emotional phenomena\" (p. 486). And, of course, by now much of Freudian metapsychology of which the economic viewpoint was but one component, has been abandoned and replaced with more felicitous (i.e., more useful) conceptions. What are involved are continuing issues of judgment that try to find widening collegial resonance.5\n\nAt the new York University institute of philosophy chaired by sidney hook in 1958, devoted to an interchange between psychoanalysts (hartmann, Kubie, Kardiner, Arlow) and philosophers of science, the philosopher Arthur Danto was one participant who spoke to the same issues as Wurmser, and made the same comparison with the queen science, physics: \"a person who demands that every properly scientific term be redeemed (without remainder) with observational equivalents, merely betrays allegiance to a superannuated empiricism. It is hardly damaging any longer, therefore, to accuse psychoanalysis of being unscientific by virtue of its trafficking in unobservables. Providing that the theoretical terms function in psychoanalytical theories the way they do in (say) physical theories, and providing that psychoanalytical theories come up to the mark on syntactical grounds, the two could hardly be contrasted invidiously. So far as unobservableness goes, there is little to choose as between castration complexes and psi-functions\" (1959, p. 315).\n\n## **Current Psychoanalytic Understandings of Metaphor**\n\nBy now the Lakoff and Johnson \"cognitive-linguistic\" perspective, quoted in most current psychoanalytic contributions to the subject of metaphor, has come to be our almost universally accepted conceptual bedrock. There have been two prior issues of _Psychoanalytic Inquiry_ (2005, 2009) devoted to exploring the role, rather the centrality, of metaphoric thought to psychoanalysis, both issues edited by Alan Barnett and S. Montana Katz\u2014with this article in this third issue, with the same co-editors. Both prior issues acknowledge the pioneering role of Arnold Modell in fashioning the current very much broadened psychoanalytic conceptions of metaphor as what has been variously called the \"heart,\" or the \"currency,\" of psychoanalysis\u2014both of these words, themselves metaphors. Modell, himself, has a central article in both of those journal issues (2005, 2009a) and is referred to, as basic to their understanding, by almost all of the other authors in those issues, including even one (Fred levin) calling Modell his muse (2009, p. 70).\n\nBuilding on the Lakoff and Johnson thesis about the central role of metaphor in all thought and language, Modell expanded this framework to conceive of metaphor as the linguistic \"bridge\" from body to mind, from its origin in the sensorimotor biological building blocks of language acquisition, to being the lifetime \"bridge\" between (often unconscious) feeling states and verbalized speech (knowledge). And the whole array of fellow authors in the second issue of _Psychoanalytic Inquiry_ (2009) ranging from the self-declared neuro-psychoanalyst, Fred levin, to the prominent relationist, Donnel stern, each in their own way, fully support Modell's conceptions.\n\nSome sample quotations will demonstrate this wide concordance of seeing metaphor as _the_ \"royal road\" to meaning-making, underlying almost every central (psychoanalytic) linguistic conception, like the understanding of the unconscious, affect, thought transference, dream, etc.; even the whole of psychoanalysis itself. For example, \"Metaphor is at the center of the construction of meaning\" (Modell, 2009b, p. 93); \"a modern understanding of metaphor as the way we initially process and articulate new concepts\" (Aragno, 2009, p. 30); \"metaphor... transfers meaning between dissimilar domains, and, through the use of novel recombinations, transfers meanings\" (Barnett & Katz, 2009, p. 1). Which transfer of meanings is, of course, the essence of transference, as several of the contributors point out. And, of course, of dreams as well. \"Metaphorical thought\u2014understanding one thing in terms of another\u2014underlies and permeates dream-formation\" (Aragno, p. 40), and \"Metaphor points to one thing while signifying something else, just as dreams point to their manifest content while meaning their latent thoughts\" (aragno, p. 41).\n\nWhich brings us to the practical equation of the use of metaphor as the practically total explanation of the entire analytic process, in Modell's words, \"the currency of the emotional mind\" (2009a, p. 6); \"it is fundamentally embodied and is not simply a figure of speech\" (2009a, p. 68). Which leads to the full equation: \"In summary, contemporary analysts of all connections agree that analysis _is_ a metaphoric process, and that the patient's and the analyst's metaphoric processes and verbalized metaphors are essential for the transformations the analysand must undergo. This theoretical issue seems indisputable\" (Rizzuto 2009, p. 20). And even more encompassing is a summarizing statement by Aragno \"With respect to metaphor, psychoanalysts are indisputably privileged. We dwell in the realm of metaphor; of tropes, synecdoche, and metonymy: of irony, hyperbole, allusion, and illusion; of vital enactment and corresponding dream; of symptom, demonstration, meaning, and story as metaphoric _events._ Metaphor fills the space and the situation (even before the meetings have begun!); it permeates the process, its stages, phases, and exchanges...\" (p. 32).\n\nContrary voices in psychoanalysis, like those of Kubie and Schafer, seem to have died away. And nowhere are the cautionary notes, like those of the cognitive-linguists, or among analysts, like Wurmser, that metaphors can be poorly constructed, can point to irrelevant or false meanings, can thus obfuscate and derail psychoanalytic understanding, can even lend themselves to harmful interventions\u2014whether in clinical interchange or in theoretical construction\u2014at all mentioned. Nor is much specific attention paid\u2014aside from conventional metaphors that are broadly based, quite universally self-evident, and with consensually agreed-upon meanings\u2014to the specific individual contextualization of metaphoric meanings, that though clearly central to understanding individual therapeutic interchange, may create real difficulties in facilitating theoretical advance that is meant to be universally applicable and consensually understood.\n\nAnd beyond all this, what the contributors to _Psychoanalytic Inquiry_ (2005, 2009) have done, is to push the by now quite well accepted conviction that our language, in all its dimensions, is (almost) automatically and inextricably, saturated with metaphor (both conventional, and in more creative minds, quite idiosyncratic), pushed this to the contention that all of abstract thought, is necessarily metaphoric, that abstraction cannot be conceptualized except metaphorically. Thus metaphor could become properly declared by Modell the \"bridge\" from the latent unconscious thought to verbalized speech. This carries the risk, to me, of making every thought and every speech act, other than the exactly literal, into metaphor, and, in so doing, making metaphor itself, lose its special distinctness of meaning. To me, this can be beyond the Lakoff and Johnson thesis, and it strips metaphor of an essential element, that metaphor makes an _abstraction_ more understandable in terms of something more _concrete_ \u2014with all the potential dangers then, of course, of leading to reification, to potential risk, and also to possible misunderstanding, because of individually different contextualization. To me, this overall broadening trend both overburdens the conception of metaphor and conceals its limitations and hazards.\n\n## **Where Do I Stand?**\n\nI first became explicitly involved in considering the place and the meaning of metaphor in psychoanalysis when I gave my presidential address to the international psychoanalytical association in Montreal in 1987, and chose as my topic the issue of our increasing psychoanalytic diversity, or pluralism as we had come to call it, a pluralism of theoretical perspectives, of linguistic and thought conventions, of distinctive regional, cultural, and language emphases; and what it was, in view of this expanding diversity, that still held us together as common adherents of a shared psychoanalytic science and profession.\n\nAfter reviewing in some detail Freud's own lifetime strenuous efforts to define the parameters of his new science of the mind, and to hold it together as a theoretically unified enterprise, against both destructive or diluting pressures or seductions from without, and also against fractious human divisiveness from within, I outlined how this effort broke down, even in Freud's lifetime, with the emerging Kleinian movement in Great Britain, and then spread with other new theoretical perspectives emerging around the world, leading to the multiple competing metapsychologies we were facing at the time of my address in 1987\u2014and continuing still today.\n\nTo respond to the question of what, in the face of this, still held us together that I had posed, I took as my starting point the distinction posited for psychoanalysis by George Klein (1976), between the low-level and experience-near clinical theory, dealing with the actual observables in the interactions within the consulting room, and the more encompassing, more generally explanatory, and more causally developmental accounting of mental life from its earliest fathomable origins, the experience-distant general theories (or metapsychologies) which seek to \"explain\" the clinical phenomena described by the clinical theory. Tough Klein declared the clinical theory to be eminently testable, he stated that the canons of correspondence between the clinical theory and our varying general theories were too tenuous to be able to claim any possibility of establishing utility or validity for any of the general theories, and that indeed, the general theories were anyway all unnecessary to psychoanalytic understanding, and should therefore be severed and cast out by an action he dubbed \"theorectomy.\" This, of course, was our entire realm of differing metapsychologies, the Freudian ego psychological (now, modern conflict theory), the British object relational, the Kleinian, Bionian, Lacanian, Kohutian self-psychological, relational, etc.\n\nI illustrated this contention with a vignette, described by Kohut, of a specific clinical interchange where three theoretical explanatory systems, the Kleinian, the ego psychological, and Kohut's own self psychological, could each be invoked and could each be used to differently causally \"explain\" that same clinical interaction, each putting the clinical specifics into a different framework of plausible meaning, within an overall theoretical explanatory context. And each of these general explanatory systems would indeed be persuasive to the adherents of that viewpoint who in fact would look at it as _the_ most useful and natural way in which to understand the described clinical interaction.\n\nWhat Kohut made of this was that the described clinical context was insufficient to decide which of the three \"interpretations\" would be in this instance closest to the mark, and so he called all three of them examples, potentially, of \"wild analysis\"\u2014 until proven otherwise. What I was differently suggesting was that our _data_ are the clinical events of the consulting room, and that their interpretation, that could carry consensually agreed meaning, was embedded only in our clinical theory, the theory level of transference and countertransference, of resistance and defense, of conflict and compromise, in fact, the original fundamental elements of Freud's 1914 definition of psychoanalysis.6 This I stated to be our common psychoanalytic clinical ground that united us within our shared discipline.\n\nI also suggested that our pluralism of theoretical perspectives within which we try to give overall meaning to our clinical data in the present, and try to reconstruct the past out of which the present developed, represent the various scientific _metaphors_ that we have created in order to satisfy our variously conditioned needs for closure and coherence and overall theoretical explanation. Joseph and Anne-Marie Sandler had earlier (1983) approached this same conception in their statement that deep interpretations into the infantile past could be viewed as but metaphoric reconstructions. For example, \"It is our firm conviction that so-called \"deep\" interpretations can have a good analytic effect only because they provide metaphors that can contain the fantasies and feelings in the second system [what they called the \"present unconscious\"]. The patient learns to understand and accept these metaphors, and if they provide a good ft, both cognitively and affectively, then they will be effective. This view gives us a way of understanding the interpretive approach of some of our [Kleinian] colleagues\" (p. 424).\n\nI broadened and extended this thinking to the conception that all our general theoretical perspectives, Kleinian, but also ego psychological, and all the others, are but our varyingly chosen explanatory _metaphors_ , heuristically useful to us in terms of our varying intellectual value commitments, in explaining, i.e., in making sense of, the primary clinical data of our consulting rooms, the realm of the \"present unconscious\" in the Sandlers' terms, or the realm of our \"clinical theory\" in George\n\nKlein's terms. Put most simply, this conceptualization makes all our grand general theory (and all of our pluralism of general theory), nothing but our individually chosen array of metaphor.\n\nPut this way, my conception of the place of metaphor in psychoanalysis, though within the framework propounded linguistically by Lakoff and Johnson, of its inextricable ubiquity in all our thinking and verbalization processes, is less broad than its equation with the totality of the psychoanalytic process\u2014itself very refractory to consensually agreed definition, with so many stating that, in judging case presentations, they find it hard to try to define the process, but they just know it when they see it\u2014and is rather something less automatic, less totalistic, but rather something more personal, more individually constructed, more idiosyncratically determined, by our own developmental and personality dispositions, and the outlooks on life that they embed.\n\nA similar view that life values are distinctly involved in our choice of theoretical perspectives, i.e., our scientific metaphors, was clearly articulated by John Gedo (1984), though perhaps not in a form with which we would all agree. He said on this issue:\n\n> Each of these conceptual schemata [the various psychoanalytic theoretical systems] encodes one or another of the primary meanings implicit in human existence\u2014unfortunately, often to the exclusion of all other meanings. Thus, the view of man embodied in the libido theory, especially in the form it took prior to 1920, attributed primary significance to the satisfaction of the appetites. By contrast, Melanie Klein's psychoanalytic system teaches the need to make reparation for man's constitutional wickedness... in the 1970s, Heinz Kohut promulgated views that give comparable emphasis to the unique healing power of empathy while acknowledging man's entitlement to an affectively gratifying milieu... let me hasten to add that I am emphatically in agreement with the need to satisfy appetites, to curb human destructiveness, and to provide an affectively gratifying environment for our children. And I am for other desiderata to boot! Isn't everyone?\n> \n> (Gedo, 1984: p. 159)\n\nWhich is exactly my point extended to the role of metaphor. Our chosen explanatory metaphors are not inherent and automatic in our thought and speech construction, but are to significant extent chosen (and so often, very thoughtfully and deliberately chosen) in terms of the personality predilections that we have\u2014individually and differently\u2014come to live by.\n\nThis same point of Gedo's, that our theoretical positions in psychoanalysis, i.e., our chosen scientific explanatory metaphors, are inevitably embedded in our fundamental social, political, and moral value dispositions has been made strongly as the closing statement in Greenberg and Mitchell's 1983 book on object relations perspectives in (American) psychoanalysis, which they traced developmentally and historically through critical discussion of the work of the various major object relations theorists starting with such diverse contributors as Melanie Klein, W. R. D. Fairbairn, and Harry Stack Sullivan. The summarizing point that they make at the end of their book is that the drive theory perspective and the relational theory perspective are linked to differing views of the essential nature of human experience and acquired world view.\n\nDrive theory they linked philosophically to the positions of Hobbes and Locke, that man is an essentially individual animal, and that human goals and satisfactions are fundamentally personal and individual. The role of the state rests on the concept of \"negative liberty,\" that the state adds nothing to individual satisfaction as such, but just ensures the possibility of personal fulfillment. Relational theory they linked philosophically to the position of Rousseau, Hegel, and Marx, that man is an essentially social animal and that human goals and satisfactions are realizable only within an organized community. The role of the state rests here on the concept of \"positive liberty,\" to provide an indispensable \"positive\" function by offering its citizens that which they cannot provide for themselves in isolation.\n\nGreenberg and Mitchell stated in relation to this that, \"The drive\/structure and the relational\/structure model embody these two major traditions within Western philosophy in the relatively recently developing intellectual arena of psychoanalytic ideas\" (p. 402). And in this context they quoted Thomas Kuhn, the well-known philosopher and historian of (natural) science, that \"communication between proponents of different theories is inevitably partial...What each takes to be facts, depends in part on the theory he espouses, and... an individual's transfer of allegiance from theory to theory is often better described as _conversion_ than as choice\" (1977, p. 338, ital. Added). Which is my own overall point, that we can and do choose different, and conflicting, explanatory metaphors to explain the same phenomena, the same facts, even what we take to be the facts, that we are endeavoring to explain.\n\nWithin this overall context, I see our present day theoretical pluralism, our, to this point, diversity of explanatory metaphors, arising out of our different life experiences, our different personality predilections, and our different psychoanalytic trainings and allegiances, as an expression of our current state of development as a credible science. Each metaphoric explanatory system represents, for its adherents, the best possible current understanding of the phenomena displayed in our consulting rooms, and is therefore heuristically useful, even essential, to the followers of that system. In that sense, these varying explanatory metaphors are vital to the current position of psychoanalysis as an evolving science, seeing the place of metaphor, of course, in a less totalistic way than others who view it more broadly as the vital coin of the entire psychoanalytic process, as in fact, the indubitable engine of all of psychoanalysis. That argument I leave aside, as I affirm what I regard as the central and essential role of metaphor in all scientific theory construction.\n\nI don't, of course, expect that psychoanalysis will simply remain in this current state. Psychoanalysis is rather a continually evolving scientific endeavor. I have in two previous publications (Wallerstein, 2002a, 2002b), the first, talking about the growth and transformations over time of American ego psychology, and the second, an effort to prognosticate what I saw to be the continuing course of evolving converging trends within our currently pluralistic metapsychological (metaphoric) international psychoanalytic world, recounted in both the efforts of many clinical and theoretical contributors (most explicitly Kernberg and Sandler, but also Chodorow, Gabbard, Gill, Loewald, etc.) to reconcile\u2014even creatively amalgamate\u2014disparate metapsychologies and their dominant metaphors. These efforts, anchored at the clinical level, but aspiring \"upward\" towards the general explanatory level of metaphor, represent unifying trends, which to the extent that they mature, in consensually acceptable ways, will necessarily also lead to increasingly more encompassing (and, hopefully, more precise) explanatory metaphors. (The reader is referred to my two 2002 articles, for a detailed exposition of the development, the then current status, and the expected near-future developments of these converging psychoanalytic perspectives.)\n\nHow far such unifying tendencies\u2014with the concomitantly enlarging explanatory metaphors\u2014will progress, is unclear, but they are similar to the unifying thrust of all science, even the paradigmatic science, physics, where an entire current generation of theoretical physicists, are pursuing, via the promise of (super)string theory, the effort to create T.O.E. (theory of everything). T.O.E. Would finally unite two current major theoretical structures, Einstein's relativity theory which explains so well the very large world of cosmology (galaxies, the expanding universe, space and time), and quantum mechanics, which explains equally well the very tiny world of subatomic particles (quarks, mesons, gluons, etc.), with the dilemma being\u2014somewhat akin to that of psychoanalysis\u2014that the two theories, of the very large and the very small, though each presumably valid in its own domain, stand in total opposition to each other, with\u2014in physics\u2014the situation, that if the one theory is correct, the other must be false.7\n\nHow far psychoanalysis will progress in this direction is clearly not at present knowable. Sciences do, incrementally, evolve, though at different rates, and varyingly towards a more precise (non-metaphorical) language of mathematical equations and symbolisms. It is certainly an open question as to how far each science can (or should) evolve from the language of metaphor to the language of mathematics. Certainly none are wholly there now, and psychoanalysis is very far, indeed.\n\nFinally, in terms of the whole tenor of the argument that I have been advancing through this article, the question in my title seems somewhat misplaced. Since metaphor is an integral component of the construction of language, all language, even the language of science, the issue is rather that though metaphor can indeed be misleading, and a bane, if it is concretized and reified and taken literally, it is indeed (most often) a blessing when aptly created, in the sense of imparting (and explaining) new meanings which advance our scientific understandings. And, as Freud counseled us at our very beginning, metaphor is intrinsically both flexible and alterable, so that heuristically more relevant and more encompassing metaphor can readily be elaborated. Thus scientific propositions advance towards greater explanatory comprehensions, and ultimately, testability.\n\n## **Notes**\n\n This chapter originally appeared in _Psychoanalytic Inquiry_ 31(2): pp. 90\u2013106 with the title, \"Metaphor in psychoanalysis: Bane or Blessing?\"\n\n Schafer's cause did achieve significant literary support when Susan Sontag (1978), caught up with her own cancer, published a polemical essay decrying the dangers caused by the all too ready willingness to make \"mysterious\" and dreaded illnesses, like tuberculosis and cancer, and also others (leprosy, syphilis, and insanity) into \"morally, if not literally contagious\" (p. 6) happenings. With bountiful references from world literature, Sontag described the long romanticization of tuberculosis into an ailment of talented aesthetes, \"the sign of a superior nature\" (p. 34) (like Shelley and Keats), or cancer as a failure of expressiveness, reflecting the repression of violent feelings by life's losers. \"Contrariwise, my point is that illness is _not_ a metaphor, and that the most truthful way of regarding illness\u2014and the healthiest way of being ill\u2014is one most purified of, most resistant to, metaphoric thinking\" (p. 3). Rather than being the bearer of secret (and often shameful) taboos, disease is an \"ineluctably material reality\" (p. 56). And in a wholesale assault on any hint of psychosomatic thinking, \"psychological theories of illness are a powerful means of placing the blame on the ill. Patients, who are instructed that they have, unwittingly caused their disease are also being made to feel that they have deserved it\" (p. 57). And that, of course, can be a danger of metaphor!\n\n For further striking examples of the use of flagrant metaphor in clinical psychoanalysis, the reader can consult Aleksandrowicz (1962), Reider (1972), and Voth (1970). For somewhat more theoretical conceptualizations, see Lewin (1970, 1971) and Sharpe (1940).\n\n The risks in concretizing metaphor, and taking it literally, can be very real and can do great harm. When I entered psychiatry in 1949, the lobotomy operation was still being employed for the mitigation of the psychotic structure in instances of severe, and chronic, paranoid schizophrenia. At a hospital \"lobotomy conference\" that I knew, the lobotomy was \"explained\" and justified by the conception that the ego resided in the frontal cortex, and the turbulent id in the thalamus, so that surgically severing the thalamo-cortical projections, would release the weakened ego from the tyranny of the overpowering, chaotic id. This formulation was advanced by the psychoanalytic consultant. An extreme and tragic instance of the risks of concretized metaphor!\n\n The earlier widely noted 1964 article by William Grossman and Bennett Simon made essentially the same argument as Wurmser, but under the more narrowly focused conception of anthropomorphism in psychoanalysis, rather than Wurmser's umbrella of metaphor.\n\n Freud stated there, \"[T]he facts of transference and of resistance. Any line of investigation which recognizes these two facts and takes them as the starting point of its work has a right to call itself psycho-analysis, even though it arrives at results other than my own. But anyone who takes up other sides of the problem while ignoring these two hypotheses will hardly escape a charge of misappropriation of property by attempted impersonation, if he persists in calling himself a psycho-analyst\" (1914a, p. 16). Of course we must add here that the key words \"transference\" and \"resistance\" also imply the concepts of the unconscious, of psychic conflict, and of defense and compromise formation, the key building stones of our shared psychoanalytic edifice. And, of course, modern conceptions of the place and use of countertransference must be included. Further along in this _History_ , Freud elaborates this same definitional statement, using much the same words (1914a, p. 50).\n\n For a detailed explanation of this situation in physics, I refer the reader to the two general explanatory books by the Columbia University theoretical physicist and string theory researcher, Brian Greene (1999, 2004).\n\n# 5\n\nMETAPHOR AND CONFLICT\n\n_L\u00e9on Wurmser_\n\nThe chapter deals with a double idea: Metaphor itself, by bridging two domains of experience, lives in the tension, even contradictoriness, of what it brings together, and in that way may be uniquely suited to present a theory of mental life that centers on inner polarities and antitheses, i.e., inner conflict in a wide sense, not necessarily bound to the drive or structural metaphors. In turn, the concept of \"conflict\" itself entails a spectrum of warlike or violent metaphors, like defense, antitheses, clashing values or forces, being torn or broken apart, inner part personalities fighting with each other, etc. The history of the metaphors for various forms of inner conflict is traced back in Western and eastern literature (homer, plato, Bible, Talmud, St. Augustine, Confucius, and Lao Tzu), thus broadening the search for a common ground for psychoanalytic perspectives.\n\nThe concept of \"symbol,\" encompassing that of metaphor, is itself derived from a striking and ritualized metaphor of fitting together what has been broken apart, a ritual that is very similar in ancient Greek and Chinese tradition.\n\nIn 1977 I published my paper in the _Quarterly_ defending the use of metaphor in psychoanalytic theory formation against the attacks by Schafer, holt, Kubie, and others (Wallerstein, this volume). This paper does not repeat what has been presented there but is based on its main ideas.\n\n## **\"The Seal of the Mind\"**\n\nSince I wrote my paper defending the use of metaphor in theory formation in the sciences in general, in psychoanalysis in particular (Wurmser, 1977), there have been several pertinent developments. They have been ably summarized and examined in various perspectives in the previous issue of _Psychoanalytic Inquiry_ (2009, Vol. 29, no. 1). The most important step, it seems to me, was distinguishing metaphoric processes from metaphor proper. The latter is bound to language and is one form of symbolic formation. The former is a biologically deeply anchored process of cross modal equations which can already be observed in newborns (stern, 1985; Wurmser, 2000, p. 27; Aragno, 2009, p. 31). The new, broader view is simply put: \"The essence of metaphor is understanding and experiencing one kind of thing in terms of another... most of our normal conceptual system is metaphorically structured; that is, most concepts are partially understood in terms of other concepts\" (Lakoff & Johnson, 1980, pp. 5, 56). It goes beyond words and deals more generally with concepts, understanding and action: \"Metaphor is primarily a matter of thought and action and only derivatively a matter of language\" (Lakoff & Johnson, 1980, p. 153). Aragno (2009) speaks of \"metaphoric thought as a primary activity of mind\" (p. 33). Quoting Borbely, she refers to the _metaphorical process_ as being situated between primary and secondary process (ibid.). \"It is a fundamental _law_ of ideation, a principle of synthesis and integration\" (p. 36).\n\nI asked therefore (1989, p. 33): \"Is not all conceiving of truth [Erfassung der Wahrheit] lastly founded in the metaphoric action of the human being?\" More specifically and summarizing, I wrote in the same work:\n\n> Natural science does not rest until it has resolved everything into mathematical relations. The humanities trace back their phenomena to formal stylistic relations. Could it be that psychoanalysis has to put everything into relations of polarities? is the idiom specific for it that of metaphors for paradoxes, for multiple refractions of conflicts and polarities? does it live in the spirit of Socratic irony, like creativity in general, forever questioning all knowledge anew, disquieting, constantly on the way? \"Restlessness and dignity\u2013\u2013this is the seal of the mind (or spirit)\" [ _Rastlosigkeit und W\u00fcrde\u2013\u2013das ist das Siegel des Geistes_ , Thomas Mann, _Joseph und seine Br\u00fcder_ , 1933\/1966, p. 50]. And doesn't it therefore show, more than all the other symbolic activities of man, the dominating double principle of conflict and complementarity?\n> \n> (Wurmser, 1989, pp. 499\u2013500)\n\nThere is hardly any moment in psychoanalytic work where we are not aware of voices of the personality that contradict each other, of parts that struggle with each other. Such inner splits are the hallmark of the mind when studied with our method, an _a priori_ starting point for our systematic efforts to understand our inner life and our dialogue with others: \"We seek not merely to describe and to classify phenomena, but to understand them as signs of an interplay of forces in the mind, as a manifestation of purposeful intentions working concurrently or in mutual opposition. We are concerned with a _dynamic view_ of mental phenomena. On our view the phenomena that are perceived must yield in importance to trends which are only hypothetical\" (Freud, 1916, p. 67). \"It is important to begin in good time to reckon with the fact that mental life is the arena and battle-ground for mutually opposing purposes or, to put it non-dynamically, that it consists of contradictions and pairs of contraries. Proof of the existence of a particular purpose is no argument against the existence of an opposite one; there is room for both. It is only a question of the attitude of these contraries to each other, and of what effects are produced by the one and by the other\" (ibid., pp. 76\u201377).\n\nThe central concern for us as psychoanalysts is the consistent, systematic exploration of inner conflict, especially of unconscious inner conflict. No matter how we try to define our work, it always comes down to the fact that the focus, the center of our interest during our analytic work at its best, lies on inner conflict. Everything else moves to the periphery; it is not irrelevant, but our inner orientation is so that we notice it as part of the surrounding field, not as the beacon that guides us. In this way our inner life becomes the most prominent example for the word of Heraklitus, the pre-Socratic philosopher, that \"war is the father of all things\u2013\u2013 _polemos pater panton_.\" \"Polemos\" can certainly be translated as conflict.\n\nAs I described in 1977 in more detail there are other approaches to an understanding of the mind, especially those that look for the inner growth towards harmony and the full development of what Aristotle dubbed \"entelechy\": that try to achieve the indwelling essence of being, and correspondingly to rectify deviations from such a path and hence deficits and defects. But our approach centers on the vision of conflicts of contradictory forces or parts or values and their possible complementarity, i.e., that such opposites do not exclude each other, but complement them: \" _Contraria sunt complementa_.\"\n\nThe notion of inner conflict did not originate with Freud; its systematic use as explanatory device par excellence did. In his and even more so in our work, relevant _explanation_ more and more moves away from the short cut attempts at reducing our inner life to certain large factors, like trauma, stages of libido development, narcissism, masochism, repetition compulsion. If these concepts are taken as explanations of causality, the clinician soon discovers that their usefulness stops precisely there where the problem begins. They are the beginning, not the end of the search. Instead, the stopping point of such exploration is the concept of a specific inner conflict, specifically inner preconscious conflict that stands for, is derivative of, long range unsolved unconscious inner conflicts in multiple layerings. Thus psychoanalytic explanation rests in an understanding of _conflict causality_ : the causes of what we observe are seen in many layers of inner conflict. Conflict does not simply refer to that between drives and ego, drives and superego, ego and outer reality, but also between opposite ego aspects, between discordant superego parts, as between different ideals and values, between sharply split loyalties, even between opposing drives, between ideas and affects, between conformity and self-loyalty, etc. It is also not so that conflict psychology is synonymous with the exploration of Oedipal issues or even with the structural model, as important both are for conflict psychology; both of them deal with special forms of conflict. Nor does conflict understanding, including the analysis of unconscious conflict, have to be tied to drive theory (Modell, this volume). There are very many levels of inner conflict: between ideas, values, affects, entire \"subpersonalities\" within the self, as it were different selves, \"the soul as multitude of subjects, as community building of drives and affects\" (Nietzsche, 1885\/1976, p. 20), as \"dividua,\" as Nietzsche somewhere put it ironically.\n\nThus psychoanalysis is grounded in a philosophy that sees its center in _conflict and paradox, in polarity and complementarity_ , and that seeks on many levels the dichotomies of knowing, acting, and feeling. This vision did not originate with Freud, but is profoundly rooted in Western literature and philosophy, and hints of it may even be traced in Chinese thought. Our classical writings for thousands of years are replete with metaphors for such inner oppositions: for inner breaks and struggles and for the abyss that opens up when such contradictions are unbridgeable and unsolvable.\n\n## **The Centrality of Metaphor**\n\nAs stated earlier (Wurmser, 1977, 1989; Arlow, 1979; Sharpe, 1940; Caruth & Ekstein, 1966; Voth, 1970; Modell, 2003, 2005, 2009a), the analyst's work has to be largely _metaphorical_. Arlow spoke of the whole of psychoanalysis as a metaphorizing odyssey, it \"is essentially a metaphorical enterprise\" (Arlow, 1979, p. 373, quoted by Aragno, 2009 p. 45): \"The patient addresses the analyst metaphorically, the analyst listens and understands in a corresponding manner. Under the influence of neurotic conflict, the patient perceives and experiences the world in a metaphorical way\" (Arlow, pp. 373\u2013374), and he quotes Empson that it is ambiguity that makes metaphor possible: \"Ambiguity implies a dynamic quality to language which enables meaning to be deepened and enriched as various layers of it become simultaneously available\" (Arlow, p. 373).\n\n\"The language of dreams is entirely metaphorical,\" says Aragno (2009, p. 42). \"Metaphor is fictive, not factual; its message imaginative, not literal. Metaphors do not deliver data, but evoke _insight_ ; image and concept here fuse in thought\" (p. 43). Quoting Goodman, she adds: \"The oddity is that metaphorical truth is compatible with literal falsity\" (p. 36). \"Truth is always relative to a conceptual system that is defined in large part by metaphor\" (Lakoff and Johnson, 1980, p. 159); there is no absolute, objectivist truth.\n\nPrimary process thinking underlying both neurosis and dream follows the logical laws of mythical thinking. Because they work with images and because they overstep the lines between perceptual categories, metaphors appeal to mythical thinking. Already the etymology of the word \"metaphora\" indicates the close relationship to one of the basic concepts of psychoanalysis: it means \"transference\" (Wurmser, 1977; Grassi, n.d.).\n\nOne of the most fascinating discoveries in the research of early infancy is the newborn's and infant's striking \"capacity to transfer perceptual experience from one sensory modality to another\" (stern, 1985, p. 47). Such \"yoking of the tactile and visual experiences is brought about by way of the innate design of the perceptual system, not by way of repeated world experience. No learning is needed initially...\" (p. 48). This implies \"that the infant, from the earliest days of life, forms and acts upon abstract representations of qualities of perception\" (p. 51). In other words, _abstraction_ , i.e., the ability to transfer formal qualities between different modalities, exists from the very beginning, independent from all experience, and thus is an immediate given, is _a priori_. Metaphorical thought is only a special case of this fundamental characteristic of our mind. Metaphorical process is an inborn readiness and manifests itself independent from language.\n\nWhat Aristotle ( _Poetics_ , 22.16\/17; 1459 a) saw as the \"by far greatest token of genius\" ( _euphyias the semeion_ ) in the poet, i.e., the use of metaphor ( _poly de megiston to metaphorikon einai_ ), can by rights also be claimed for the analyst: \"Seeing what is similar\" (l.c.). Similes, figures of speech, are an important road that may very directly lead to what is unconscious. Philosophically, it means also a great deal that the analytic models of insight and of ordering the data are themselves of metaphorical nature.\n\nThis philosophical attitude does also greater justice to the complexity of inner life than a closed and dogmatic system of theories could do. Theoretical models as metaphorical renderings that allow approximation to \"the truth,\" but are not absolute; models which are more useful for this purpose than others; all the models of the different schools being attempts to order smaller or larger segments of observations, some handier than others; based on such models, the technical guidelines as being more or less effective, short or long term, helpfully, yet unfortunately also often harmfully\u2014these are the _pragmatic_ foundations upon which, in my own psychoanalytic work, the concept of truth is built (Wurmser, 2000). \"Each metaphoric explanatory system represents, for its adherents, the best possible current understanding of the phenomena displayed in our consulting rooms, and is therefore heuristically useful, even essential, to the followers of that system\" (Wallerstein, this volume).\n\n## **Metaphor as Representation of Conflict**\n\n\"If psychoanalysis is the art and scientific study of interpreting our inner life, especially those parts disguised and hidden from ourselves\u2013\u2013that is, if it is a form of symbolically connected, meaningful wholes, patterns, strands, sequences of experience\u2013\u2013then the science of analysis has to describe and develop as many comprehensive 'models,' 'frameworks,' 'myths' (metaphors) as are practically useful and theoretically consistent, coherent, and integrated\" (Wurmser, 1977, p. 493). Today I would add: in these theoretical endeavors at explanation, metaphoric systems that center on conflict and related concepts have to assume a privileged position.\n\nThe trivial definition of metaphor is \"a word _substituted_ for another on account of the resemblance or analogy between their significations\" (Whately, cited in Black, 1962). The one Aristotle uses is more specific and is based on the etymology of _metaphora_ = transference (Wurmser, 1977): \"Metaphor is the application of a strange term either transferred from the genus and applied to the species ( _epiphora... apo tou genous epi eidos_ ) or from the species and applied to the genus, or from one species to another or else by analogy ( _kata to analogon_ )\" ( _Poetics_ , 21.7; 1457 b; Aristotle, 1927, p. 80). According to Black it is a contracted comparison (1962, p. 36). As third Black suggests the \"interaction view\": \"In the simplest formulation, when we use a metaphor we have two thoughts of different things active together and supported by a single word, or phrase, whose meaning is a resultant of their interaction\" (Richards, cited in Black 1962, S.38). He comments: \"To speak of the 'interaction' of two thoughts 'active together' (or, again, of their 'interillumination' Or 'cooperation') is to _use_ a metaphor emphasizing the dynamic aspects of a good reader's response to a nontrivial metaphor\" (S.39). \"The metaphor selects, emphasizes, suppresses, and organizes features of the principal subject by implying statements about it that normally apply to the subsidiary subject\" (Black, S.44 ff.). Metaphor transforms and reorganizes the view. \"... The set of literal statements so obtained will not have the same power to inform and enlighten as the original\" (p.46).\n\nThis idea is deepened by Beardsley ( _Encyclopedia of Philosophy_ ) when he talks about the \"verbal-opposition theory\": \"This theory... rests upon 1) a distinction between two levels of meaning, and 2.) the principle that metaphor involves essentially a _logical conflict of central meanings_ \" (Bd.5, s.286).\n\nThis inherent difference and, I would add contradictoriness and tension, is implied, but not made explicit when Modell (1997a, p. 106) defines metaphor as \"the mapping of one conceptual domain onto a dissimilar conceptual domain... resulting in a transfer of meaning from one to the other\" (quoted by Bornstein & Becker, this volume). Similarly, the latter authors describe the metaphor (metaphorically, in an inevitable circularity) as \"the glue that links disparate aspects of human life, over time and across different contexts, enabling us to construct cohesive life narratives that give meaning to past and present experience\" (this volume).\n\nIn contrast, White (this volume) stresses \"the emphasis on collision, tension and opposition over collusion and similarity\" in modern metaphor. I understand it similarly when Borbely (issue) writes about \"the tension inherent in metaphor which keeps the target away from the source yet at the same time connects source and target.\"\n\nI would stress the \"logical conflict of central meanings\" as the nub of my argument. At the end of this essay, in connection with Lao Tzu, I will talk about indirect, i.e., metaphorical presentation of conflict, by using _logical and perceptual contradiction as an indirect presentation of affective conflict_.\n\nTaking this together we conclude that we may see in non-trivial metaphors the result of a conflict of mental contents that usually have a strong emotional significance. If the psychoanalytic method as the study of inner processes focuses above all on seeing their essence as conflict it is evident that metaphor has to be the instrument par excellence to represent conflict. Such symbolization of conflict by metaphor serves a causal understanding of mental processes and is specifically and essentially explanatory.\n\n## **\"Words Have an Ancestor\"** 2 **\u2013\u2013A History of Some Central Metaphors**\n\nI would like to suggest that the search for common grounds for our divergent perspectives may be considerably helped if we study the metaphors that have been central throughout history for the understanding of the mind, most specifically those for conflict and its opposite: harmony.\n\n### Fitting Together What is Broken\n\nMetaphor is a special form of symbol; metaphoric processes are paramount forms of symbolic processes. But there is an inevitable circularity involved: when we talk about this we can only do so by employing metaphors as well, faded, even unconsciously deployed metaphors to be sure, but metaphors and metaphoric processes nevertheless. Etymology is largely a study of the emerging and development of metaphors.\n\nThe next question is then: What is the original metaphor standing behind \"symbol\"? it has a fascinating history in both world cultures, the Western and the eastern.\n\nThe Greek word \" _symbolon\"_ is derived from the verb \" _symballein\"_ \"to throw together.\" Its original meaning is that of sign, of a contract, in particular the sign by which old friends, guest and host, recognize each other. This sign consisted of a little tablet or a ring which had been broken in two at the time of farewell. Now, at the reencounter, these two pieces should ft together (Benseler-K\u00e4gi, 1931; Tzermias, 1976). Thus the \"symbol\" fits together two disparate realities: things and significance, concrete and what we call abstract.\n\nIt is fascinating to observe that something parallel happened in China: The ideogram for minister, Q\u00edng, is derived from the sign for _q\u012bng,_ the image of a piece of wood or jade that had been broken in two. Here the two separate pieces have to signify and verify charge and honor: \"In ancient times the emperor, when investing the feudatories or officials, handed over to them one half of a piece of wood or of jade diversely cut out; the other half was used to make the proof, as the modern counterfoil. The two pieces gathered are the, _q\u012bng..._ When they appeared before the emperor, or when they held the functions of their office, the feudatories or officials had this kind of scepter in their hands. It was used also as a seal\" (Wieger, 1927, S.147). Astonishingly, even the modern word for symbol, _F\u00fah\u00e0o,_ uses another ideogram for the verification in front of emperor or king by such a fitting correspondence of pieces of bamboo, jade or bronze.\n\nTo return to the Greek, in Aeschylos' _Agamemnon_ the fiery message of Troy's fall transmitted from mountain top to mountain top is called \"proof and symbol\u2013\u2013 _tekmar... symbolon te.\"_ Here the word already has our meaning: the fire has only one signification, the one that had been previously agreed upon.\n\nOn the other side we find in Plato's _Symposium_ the original use in the famous myth of Eros: Zeus had cut apart the previously complete human being: \"So ancient is the desire of another which is implanted in us, reuniting our original nature; making one of two, and healing the state of man. Each of us when separated, having one side only, like a fat fish, is but the indenture of man _(anthropou symbolon),_ and he is always looking for his other half\" (Plato, p. 158).\n\nJust like in Chinese magical Taoism, _\"symbola\"_ can also in Greece be used in a mythical religious sense: in the orphic tradition about the mysteries of Dionysos the story goes that the god as child was lured away by the titans with the help of such _symbola,_ in particular by a mirror, then torn to pieces by them, buried or resurrected. Terefore, the mirror became the symbol for his death, to a mythically powerful, Paradoxically valued, sacred object because it also meant transmigration of the soul and liberation. It became a symbol for spiritual resurrection and fulfillment (Gu\u00e9pin, 1968, pp. 241\u2013251). It reappears in the mirror image of Narkissos and in our newer narcissism theories (Kohut, 1971).\n\n> Whereas in allegory something that can be represented is replaced by something else that is expressed, in the mystical symbol something that can be presented stands for another reality that is removed from the world of presentation and expression... A hidden life that has no expression finds it in the symbol. Symbol is sign, but more than sign.\n> \n> (Scholem, 1957, p. 29)\n\n### \"Fight, But Do Not Sin\"\u2013\u2013Conflict in the Western Tradition\n\nThe view of inner life as conflict is one that is, among others, intrinsic to the Western intellectual tradition. We find prototypes for it already in the Homeric epics: in the _Odyssey_ , when Odysseus is about to stab the Cyclops Polyphemos, he stopped: \"The second mind [thought] stopped me ( _heteros de me thymos eryken_ 9.302),\" the recognition of their own inability to remove the giant boulder from the entrance. And then there is the beautiful passage in the Iliad, 11. 402 ff: Left alone by the other Greeks in the middle of battle, Odysseus \"spoke to his own greathearted spirit ( _eipe pros hon megal\u00e9tora thymon_ ): 'Ah me, what will become of me? it will be a great evil if I run, fearing their multitude, yet deadlier if I am caught alone; and Kronos' son drove to fight the rest of the Danaans. Yet still, why does the heart [mind] within me debate on these things ( _alla tie moi tauta philos diel\u00e9xato thymos_ )? since I know that it is the cowards who walk out of the fighting, but if one is to win honor in battle, he must by all means stand his ground strongly, whether he be struck or strike down another.'\" (trans. Lattimore; cf. Also Dodds, 1951\/1968, pp. 16, 25, also for additional examples).\n\nAncient Greek tragedy revolves around the pivot of the tragic choice\u2013\u2013the necessity to decide between the opposing commitments to two enormously important values, ideals, loyalties. Many symbols or metaphors in Greek tragedy reflect this consciousness of inner conflict\u2013\u2013e.g., the \"blue clashing rocks\" or _Symplegades_ of Euripides' _Medea_ , the repeated use of the term _diphrontis_ , \"of two minds\" in the _Libation Bearers_ of Aischylos and in the _Hippolytos_ of uripides (i have gone into this in more detail elsewhere; see Wurmser 1981, 1989). It appears to refer with particular poignancy to what I have referred to as the shameguiltdilemma. Yet more generally, these presentations of the fatal consequences of tragic choice refer to the unresolvability of such basic, existential conflicts of conscience, i.e., that in this absolutely, extremely posed form, as it is put to the protagonists and lived out by them, it never can be resolved once and for all, that there cannot be a final, right, perfect solution, but that only the \"measure\" represented by the Chorus, the \"moderation,\" the acceptance of _both_ parts of conflict, and with that of the paradox inherent in human life, is compatible with the survival of individual and society, of the culture and its ideals (the Gods). This \"measure\" however entails the insight of \"wisdom\" that the opposite parts of inner conflict complement each other, i.e., that the understanding of inner life as conflict has to encompass the reconciliation of the hitherto clashing forces\u2013\u2013the drives, emotions, values, loyalties\u2013\u2013in the form of _complementarity_. I believe it is this that Anton Kris (1984, 1985, 1986, 1987) has recently presented in the duality of convergent and divergent conflict (cf. Also Rangell, 1963).\n\nThe consciousness of inner conflict accompanies Western thought and creativity throughout its history and with that the guiding metaphors for self-understanding. Speaking in the _Phaidros_ of \"the soul being like the combined force of the winged pair of horses and the charioteer,\" plato describes how \"the bad horse pulls the chariot down\" and then adds: \"And then there is pain ( _ponos_ ) and extreme conflict ( _agon eschatos_ ) inflicted upon the soul\" (246\/247).\n\nIn the _Talmud_ we hear: \"A man should always incite the good impulse to fight against the evil impulse ( _le'olam yargiz adam jetzer tov al yetzer hara'_ ). For it is written: Fight, but do not sin ( _rigezu we'al techeta'u_ [ps. 4.5]). If they overcome it, fine! if not, they should study the Torah. For it is written: speak with your hearts ( _imru bilvavchem_ )\" ( _Berakot_ , 5a). Seeing a man and a woman part without engaging in anything forbidden, Abaye who had followed them, said: \"'If it were I, I could not have restrained myself,' and so went and leaned in deep anguish against a doorpost, when a certain old man came up to him and taught him: The greater the man, the greater his evil inclination ( _Kol hagadol mechavero, yitzro gadol hemennu_ )\" ( _Sukkah_ , 52a).\n\nBefore our modern age, however, such inner conflict has been, to my knowledge, nowhere more keenly expressed and reflected upon than by Augustinus in the _Confessiones_ , even in its unconscious dimensions and with the very concept (metaphor) of conflict at its center: \"so stood two wills of mine in conflict with each other, one old, the other new, one carnal, the other spiritual, and in their discord they wasted out my mind. _Ita duae voluntates meae, una vetus, alia nova, illa carnalis, illa spiritalis, configebant inter se, atque discordando dissipabant animam meam_ (8.5).\"\n\n\"This was the controversy I felt in my heart, about nothing but myself, against myself. _Ista controversia in corde meo non nisi de me ipso adversus me ipsum_ \" (8.11). Here it is even the very word underlying \"conflict,\" namely the verb \" _confligere_ \": \"clashing together, crashing, fighting.\"\n\n\"... It was myself who willed it, and myself who nilled it; it was I myself. I neither willed entirely, nor yet nilled entirely. Therefore was I at strife with myself, and distracted by mine own self ( _Ideo mecum contendebam et dissipar a me ipso_ )\" (8.10). And crucially he immediately adds that there are many such inner conflicts: \"For if there be so many contrary natures in man, as there be wills resisting one another; there shall not now be two natures alone, but many. _Nam si tot sunt contrariae naturae, quot voluntates sibi resistunt, non iam duae, sed plures erunt_ \" (ibid.). There is a multiplicity of inner conflicts which tear apart the will and hence the consciousness of the self.\n\nHe even commented upon the complementarity between these opposite parts of his self: \"Hence it is that there be two wills, for that one of them is not entire: and the one is supplied with that, wherein the other lacks. _Et ideo sunt duae voluntates, quia una earum tota non est, et hoc adest alteri, quod deest alteri_ \" (8.9).\n\nHe gives an etiology for such an inherent inner discord\u2013\u2013for the existential nature of man's conflict\u2013\u2013in the _Civitas Dei_ : God commanded Adam and eve obedience because the fulfillment of their own will in opposition to that of their Creator's is destruction (14.12). It was a fitting punishment for their own disobedience that they suddenly were compelled to notice the disobedience of their own genitals, and with that the disobedience of their desires, the lack of control over their bodies; all mental activity, all reasoning becomes overrun (14.16), the entire human being is being totally taken by it. And on the other side this pleasure cannot be willed and compelled, even if one so decides and desires it (14.16). This powerlessness, this loss of control in the face of the overpowering force of the sexual parts necessarily fills man with shame, even if the sexual act is permitted and specifically engaged in for the procreation of children; even in front of one's own children it therefore has to be treated with secrecy (14.18).\n\nIn these excerpts the conflict is sharply delineated: the primary concern is the conflict between the sexual desires (and member) and the will led by reason and with that by Godly command. The loss of control over these desires and their executive organs is inherently a cause for shame. Yet this loss of control is in itself already the punishment for a deeper, prior conflict: the conflict between the wish to follow one's own will and the obedient submission under God's command. The first conflict is a shame conflict, the second, deeper and antecedent conflict is one leading to guilt, a guilt to be punished by that loss of control. The assertion of power and independence ( _potestas voluntatis_ ) is by itself evil; it leads to the secondary evil, \"the punishment\" by the omnipotence of lust.\n\nLooking back to the Talmudic sources, we see the same doubleness, although not as sharply divided: whenever there is talk about the _Yetzer haRa'_ \u2013\u2013the evil Inclination\u2013\u2013it always refers to sexual desire and lust; but this lust also is always equated with rebellion against God.\n\nYet farther back, in platon, the negative part of human nature that pulls the soul perniciously \"down\" and \"apart\" is sensuality altogether\u2013\u2013the attachment to the body and its desires\u2013\u2013against the autonomous power of reason and with that against the \"vision\" of the ideas.\n\nThe augustinean view came to dominate the value system of the Western world for about one millennium: sexual lust was the evil par excellence, prideful assertion of will power, even in the service of reason, ran a close second. The power of the faith in this value hierarchy is not completely broken even today.\n\nIt was Goethe who took up the concept of \"inner conflict\" as an explanatory metaphor when he described 1815 how shakespeare puts in the foreground \"the inner conflict\" between \" _Sollen_ \" and \" _Wollen_ ,\" between what man ought to do and what he wants to do.3 This inner conflict converges with an external one, \"a wanting that goes beyond what the individual is able to, is modern\"4 (Goethe, 1961).\n\n### The question of conflict and complementarity in Confucius (Kong Tzu) and Lao Tzu\n\nWhat do we find in the other great and continuous tradition of thought\u2013\u2013the Chinese world, as exemplifed by these two leading thinkers (both were said to have lived around 500bce although there is much controversy about the time of Lao Tzu)? There are a number of leading metaphors in opposition to each other that dominate the ethical, political, and metaphysical debates, centering around balance, harmony, the right path ( _dao_ ), the uncarved block, the great flow versus strife, disorder, doubt, what we would also call conflict.\n\n\"Harmony was seen as the great norm of both the natural and social worlds; Confucianism and Taoism were equally philosophies of balance, whether man's counterpoise was society or the natural cosmos. Imbalance would have meant man against man, man against nature, in either case a separation between the self and the 'other.' But Confucianism and Taoism, each in its way, meant union, oneness, the concord and stasis of the eternal pattern\" (levenson & schurmann, 1969, p. 113). \"Conflict between Confucianism and Taoism was abortive, a) because they had a common theme, harmony, and b) because that common theme, harmony, implied a philosophical deprecation of conflict\" (ibid., p. 116).\n\n\"By now it should be evident that basic among Chinese thought patterns is the desire to merge seemingly conflicting elements into a unified harmony. Chinese philosophy is filled with dualisms in which, however, their two component elements are usually regarded as _complementary and mutually necessary rather than as hostile and incompatible_. A common feature of Chinese dualisms, furthermore, is that one of their two elements should be held in higher regard than the other. Here again, therefore, we have an expression of the concept of harmony based upon hierarchical difference, such as we have already seen in the Chinese view of society\" (Bodde, 1953, p. 54).\n\nThis does of course not imply that there is no awareness of conflict or that there is a relative absence of social, historical or psychological conflict. Rather it appears that there is an overriding concern to shift the focus of attention away from conflict, to the point of denying its emotional relevance. Why Chinese culture and tradition, in spite of its inner orientation, its greatly creative and expressive inwardness, seems so peculiarly inimical to psychoanalysis may very well lie in this deep and abiding antipathy to inner conflict. This means also a different approach to ethical and psychological choice.\n\nIn discussing this issue, Fingarette ( _Confucius\u2013\u2013The Secular as Sacred_ , 1972, p. 22) refers to two passages in the _Lun Y\u00fc_ , the \"book of the discussions (or sayings)\" of Kung Tse (KongFuzi, Confucius): \"You love a man and wish him to live; you hate him and wish him to die. Having wished him to live, you also wish him to die. This is doubt\" ( _huo_ \u2013\u2013legge: \"delusion\"; 12.10). \"For a morning's anger to disregard one's own life, and involve that of his parents\u2013\u2013is not this a case of doubt (delusion, _huo_ )\" (2.21). \"In such conflict, the task is not posed as one of _choosing_ or _deciding_ but of distuinguishing or discriminating ( _bian_ ) the inconsistent inclinations. Furthermore, in each passage, we have no doubt about which inclination is the right one when we have discriminated one from the other. In short, the task is posed in terms of knowledge rather than choice. _Huo_ , the key term in the passages, means here 'deluded or _led astray_ by an un _li_ inclination or tendency.' it is not doubt as to which to choose to do\" (pp. 22\u201323).\n\nI interject here that the decisive word _huo_ which does not appear rarely in both Confucius and Lao Tse is usually translated as \"doubt, suspicion, deception.\" Yet as a symbol it is composed of _huo_ and _xin. Huo_ means \"either, or, if,\" _xin_ is \"heart, mind,\" the common radical associated with any emotional, or generally mental processes. The _huo_ used in this context can therefore etymologically be rendered as the \"either of the Mind,\" the \"or of the Mind.\" Fingarette is right that hardly anywhere is there an explicit formulation of inner conflict, and yet, it seems to me that the repeatedly emerging \"doubt,\" _huo_ , is something like a symbol for suppressed, hidden, veiled conflict.\n\nThis means, Fingarette continues, that \"we must recognize at once that the absence of a developed language of choice and responsibility does not imply a failure to choose or to be responsible... The task is posed in terms of knowledge rather than choice... This Confucian commitment to a single, definite order is also evident when we note what Confucius sees as the alternative to rightly treading the true path: it is to walk crookedly, to get lost or to abandon the path... It is the following of the Way itself that is of ultimate and absolute value... The imagery in the _Analects_ [ _Lun Y\u00fc_ ] is dominated by the metaphor of traveling the road\" (pp. 18\u201322).\n\nHe then refers to a passage which \"seems... To present a situation where the issue, as we would define it, is one of internal conflict in the moral code, a conflict to be resolved by personal choice.\" I quote from Legge's translation, adding some modiffers: \"The duke of she informed Confucius, saying: 'Among us here are those who may be styled ( _gong_ , meaning personally, self, own; I think this is what Legge translates as styled; Fingarette takes this word as a proper name Gong [Kung]) upright ( _zhi_ ) in their conduct. If their fathers have stolen a sheep, they will bear witness to the fact.' Confucius said: 'Among us, in our part of the country, those who are upright are different from this. The father conceals the misconduct of the son, and the son conceals the misconduct of the father. Uprightness is to be found in this'\" (13.18).\n\nIt is the conflict between the value of _Xiao_ , the loyalty and reverential commitment, the _pietas_ ( _Piet\u00e4t_ ) towards the parents, versus the value of _Zhi_ , honesty, sincerity, uprightness, straightforwardness (the very sign symbolizes \"straightness\"). Here two deep commitments stand in irreconcilable conflict. Fingarette comments:\n\n> When two profound duties conflict, _we_ must choose. And it is in this necessity to make a critical choice that lies the seed of tragedy, of responsibility, of guilt and remorse.... Confucius merely announces the way _he_ sees the matter, putting it tactfully by saying it is the custom in _Li._ 5 There is nothing to suggest a decisional problem; everything suggests that there is a defect of knowledge, a simple error of moral judgment on the duke's part... When we take into account Confucius's stature as a moralist and his insightfulness into human nature, his failure to see or to mention the problem of internal moral conflict in such a case as this can only be accounted for by supposing that his interests, ideas, concerns, in short his entire moral and intellectual orientation, was in another direction.\n> \n> (1972, p. 23 f.)\n\nZai Y\u00fc being asleep during the daytime, the Master said: 'Rotten wood cannot be carved; a wall of earth and dung cannot be covered with the trowel. This Y\u00fc! What is the use of reproving him?!' The Master said: 'At first, my way with men was to hear their words, and give them credit for their conduct. Now my way is to hear their words, and look at their conduct. It is from Y\u00fc that I have learned to make this change' (5: 9).\n\n\"Here the active disease, the fulminating wound of Augustine, is replaced by a state of mere deadness, of passivity and inherent insensitivity to moral values,\" comments Fingarette (p. 31). \"The proper response to a failure to conform to the moral order ( _li_ ) is not selfcondemnation for a free and responsible, though evil, choice, but selfreeducation to overcome a mere defect, a lack of power, in short a lack in one's 'formation.' The Westerner's inclination to press at this point the issue of personal responsibility for lack of diligence is precisely the sort of issue that is never even raised in the Analects\" (p. 35). \"Confucius's vision provides no basis for seeing man as a being of tragedy, of inner crisis and guilt; but it does provide a socially oriented, actionoriented view which provides for personal dignity. Moreover... We see then that the images of the inner man and of his inner conflict are not essential to a concept of man as a being whose dignity is the consummation of a life of subtlety and sophistication, a life in which human conduct can be intelligible in natural terms and yet be attuned to the sacred, a life in which the practical, the intellectual and the spiritual are equally revered and are harmonized in the one act\u2013\u2013the act of _li_ \" (p. 36). For Confucius man is not tragic since he is not determined by the inner crisis of choice, decision and guilt, but oriented towards action and towards the concentric circles of obligations surrounding him.\n\nThe center of gravity has entirely shifted away from the metaphors for what we would, analytically speaking, describe as the _choosing and deciding ego and to the absolutely (unconditionally) certain and commanding superego_. The side of the drives ( _y\u00fc_ ) is not often mentioned; they have to yield to the dictates of conscience. Since the ego itself is the site of inner conflict, its complete subordination under the inner authority of conscience amounts to a kind of _invalidation of inner conflict_.\n\nThis statement is predicated on the a priori assumption, as a basic vision of existence, that inner conflict is indeed an indispensable part of human nature. It is both a philosophical premise of vision (i.e., a metaphorical system) and a methodological premise of exploration of man's nature\u2013\u2013neither provable, nor refutable\u2013\u2013not merely of the psychoanalytic understanding of human nature, but of the Western understanding of Man in general.\n\nNow just a few references from the other great thinker who shaped Chinese culture for over two thousand years, Lao Tzu (\"the old Master\" or \"the old Child\").\n\n\"Nothing in the world is softer and more supple than water, yet when attacking the hard and the strong, nothing can surpass it. The supple overcomes the hard. The soft overcomes the strong. None in the world do not know this, yet none can practice it. That is why the sage says: to accept the filth of a nation is to be lord of the society.6 to accept the disasters (the ill omens) of a nation (country) is to be the ruler of the world.7 Words of truth seem contradictory\"8 (trans. Tam C. Gibbs and alternate interpretations, where indicated; Ch. 78). This last sentence is: \" _Zheng yan ruo fan\u2013\u2013Zheng_ : straight or regular or correct\u2013\u2013 _yan_ : words or speech\u2013\u2013 _ruo_ : is as, follows\u2013\u2013 _fan_ : to turn back, contrary, opposite, to rebel.\" I would paraphrase it: \"The direct talk also has the opposite meaning, turns into its opposite.\" The outer references, like water, dirt of the country, ruler, appear like metaphors for the inner truth: that our inner life incessantly moves in contraries, in opposites.\n\n\"Words have an ancestor; actions have a lord\" (Ch. 70). There is a past to one's thought; there is a context that gives it the meaning; \"if they don't know this, they cannot understand me.\" The first reminds us of the basic premise of our genetic understanding; the latter of the coherence theory of truth; the first of Freud, the latter of Wittgenstein and of the criterion for truth stressed precisely by Freud over that by correspondence and by pragmatism.\n\nOf special beauty is the 11th chapter (i quote from Waley's translation): \"We put thirty spokes together and call it a wheel; but it is on the space where there is nothing that the usefulness of the wheel depends. We turn clay to make a vessel; but it is on the space where there is nothing that the usefulness of the vessel depends. We pierce doors and windows to make a house; and it is on these spaces where there is nothing that the usefulness of the house depends. Therefore, just as we take advantage of what is, we should recognize the usefulness of what is not.\" What Waley circumscribes as \"the space where there is nothing,\" the Chinese has \" _wu you_ \u2013\u2013not having, nonbeing\"; the object is visible and concrete, yet its function _dang qi... Yong_ depends on the absence, the void, the no, the \"There is not.\" is this no not also the no to consciousness, the no inherent in all defense? are not these expressions very beautiful metaphors for the inner life we deal with in our work\u2013\u2013clearly, metaphors of a very different kind from those we use in our theory formation, yet nevertheless metaphors that should bridge the visible world of the Yes with the invisible, but far more powerful world of the No\u2013\u2013the _Wu_ or _Wu you_ or _Wu ming_ or _Wu wei_ (no, nonbeing, nameless, no action)?\n\nJust as the emptiness gives the objects their ability to function, so does the silence give to the mind and to the spoken words the dimension of depth. The _Tao The King_ itself is indeed like a finely woven, and yet mighty structure built of spare words and much silence. The contradictions open up abysses of meaning.9\n\nYet what is the central concern?\n\n\"'To remain whole, be twisted (Chan: yield)!' to become straight, let yourself be bent. To become whole, be hollow. Be tattered, that you may be renewed. Those that have little, may get more. Those that have much, are but perplexed ( _huo_ , see above, the 'Either-or of the heart or mind'). Therefore the sage clasps the primal Unity (Chan: the sage embraces the one), testing by it everything under heaven (Chan: and becomes the model of the world). He does not show himself; therefore he is seen everywhere. He does not define himself, therefore he is distinct. He does not boast of what he will do, therefore he succeeds. He is not proud of his work (loves himself), and therefore he endures. He does not contend ( _bu zheng_ ). And for that very reason no one under heaven can contend with him (Chan: it is precisely because he does not compete that the world cannot compete with him). So then we see that the ancient saying: 'To remain whole be twisted!' (Chan: 'To yield is to be preserved whole') was no idle word; for true wholeness can only be achieved by return ( _gui_ = home coming)\" (Ch. 22, trans. Waley).\n\nHere again, the contraries are seen as part of an overarching unity; the aim of the wise person ( _sheng ren_ ) lies in overcoming what is in conflict\u2013\u2013of what \"competes,\" _zheng_. The most expressive formulation, however, comes right at the beginning of the _Tao The King_ (Ch. 2). I follow Chan Wingtsit's translation: \"When the people of the world all know beauty as beauty, there arises the recognition of ugliness. When they all know the good as good, there arises the recognition of evil. Therefore: _Being and nonbeing produce each other_ ( _you wu xiang sheng_ ); _difficult and easy complete each other_ ; long and short contrast ( _jiao_ or, alternately, _xing_ compare; Waley: test) each other; high and low distinguish each other; sound and voice harmonize each other; front and behind accompany each other. Therefore, the sage manages affairs without action ( _wu wei zhi shi_ ), and spreads doctrines without words. All things arise, and he does not turn away from them. He produces them but does not take possession of them (Gibbs: [nature] gives birth but does not possess). He acts but does not rely on his own ability (Gibbs: it acts but does not demand subservience). He accomplishes his task but does not claim credit for it. It is precisely because he does not claim credit that his accomplishment remains with him.\" The first four of the six pairs of contraries are rendered by Gibbs as follows: \"Is and is not are mutually arising; difficult and easy are complementary; long and short arise from comparison; higher and lower are interdependent.\" The accompanying commentary by ManJan Cheng calls the pairs _mutual functions, reciprocity: hu xiang_ , and speaks of the _paradox of the mutual support of opposites_ : _xiang fan xiang cheng._ in all of the six pairs the third of the fourth words is _xiang_ , \"mutual,\" translated here as \"each other.\" Waley comments: \"But, says the Taoist, by admitting the conception of 'goodness,' you are simultaneously creating a conception 'badness.' nothing can be good except in relation to something that is bad, just as nothing can be 'in front' except in relation to something that is 'behind.' Therefore, the sage avoids all positive action, working only through the 'power' of Tao, which alone 'cuts without wounding' _transcending all antinomies_.\"\n\nTough there is no special word about or for _inner conflict_ ; there is thus the clear awareness of the centrality of opposites, of contradiction, and the insistence to overcome, as we would say, conflict by recognizing complementarity. SiMa Qian speaks of the _unity of spirit_ as being advocated by the Taoist school (Ch. 130, quoted by Fung Yulan, 1931\/1934, p. 170). We would say in our theoretical framework that there is a consistent transcendence of conflict in favor of the synthetic function of the ego that attempts to reconcile all the opposites within and without, as well as between inwardness and outside world, while letting the paradoxes stand\u2014\"the mysterious leveling\" ( _y\u00fcan tong_ , Ch. 56, trans. Waley): \"The sage 'discards the absolute, the allinclusive, the extreme'\" (Ch. 29, trans. Waley) \"it is percisely because he does not compete ( _bu zheng_ , lit.: 'no conflict') that the world cannot compete with him\" (Ch. 66, trans. Chan; cf. Also 68, 72, 73, 77, 78, 81). The very last sentence of the _Tao The King_ is, I believe not coincidentally: \"The Way of the sage is to act but not to compete\u2013\u2013 _Sheng ren zhi Dao\u2013\u2013wei er bu zheng_.\"\n\nIf we assume now in all these references that _zheng_ does not merely refer to outer conflict in the meaning of \"competition,\" but that it expresses, with the consistent equation of inwardness and outwardness, equally inner conflict, then we can conclude that one of the major aims of Lao Tse is the overcoming of all conflict, inner and outer, in favor of a great unity (e.g., \"embracing the one,\" _bao yi_ ) or synthesis. It is what is called in Ch. 68 _bu zheng zhi D\u00e9_ \u2013\u2013the power of no conflict (Chan: the virtue of noncompeting, Gibbs: the Teh of noncontention, Waley: the power that comes of not contending).\n\nInstead of the social virtues of Kong Fu zi to deal with inner and outer conflict, Lao Tzu postulates something that appears to be radically different: \"Banish learning, and there will be no more grieving\" (Ch. 20, trans. Waley). In the place of these societal concerns, of the loyalty towards outer norms now internalized, there is the loyalty to what Waley translates as the Uncarved Block _, bo_ , to an inner truth ( _chang_ , the \"constant\"), to spontaneity ( _ZiRan_ , the \"selfso\") and creativity ( _sheng_ , \"life, birth\") beyond all contraries, transcending all strife ( _zheng_ ). Putting it positively, he speaks of the \"three treasures: the first is deep love, the second is frugality, and the third is not to dare to be ahead of the world\" (Ch. 67, trans. Chan).\n\nMost explicitly the Confucian virtues appear to be disavowed in Ch. 19 (Chan trans.): \"Abandon sageliness and discard wisdom; then the people will benefit a hundredfold. Abandon humanity (better: human solidarity) and discard righteousness; then the people will return to filial piety and deep love. Abandon skill and discard profit; then there will be no thieves or robbers. However, these three things are ornaments and are not adequate. Therefore, let people hold on to these: manifest plainness, embrace simplicity, reduce selfishness, have few desires.\" Waley suggests for the latter portion: \"if without these three things they find life too plain and unadorned, then let them have accessories; give them simplicity ['raw silk'] to look at, the Uncarved Block to hold, give them selflessness and fewness of desires.\" Gibbs translates: \"I believe these three statements show that words are inadequate. The people should be made to adhere to these principles: 'Look to the origins and maintain purity; diminish self and curb desires.'\"\n\nI think all these translations struggle to approximate the original's interweaving of inward and outward, its deft, yet bewildering use of metaphors bridging both worlds, e.g., in the concluding sentence: \"Diminish 'self,' make desires scarce\" involves the symbol for self, _si_. It is derived from _si_ : \"a cocoon. It represents a silkworm that coils itself up and shuts itself in its cocoon. By extension, selfish, to care only for one's self, separation, private, particular.\" The compound used means: \"my share of grains. By extension, private, personal, partial, selfish\" (Wieger, p. 224).\n\nFor this kind of emphasis on the synthetic ego function\u2013\u2013especially in the sense of bridging resolutely the gap between inner world and outer world in spite of their disparate laws\u2013\u2013learning and reeducation, in the sense of Kong zi, can evidently not be as desirable, as a complete retreat from the entanglements in _zheng_ , in conflict, would be. Instead of dealing with conflict by subordinating oneself entirely to a superego modeled after the magical power of the sageKings of hoary antiquity and their impersonal representatives in the shape of rules and forms ( _li_ ), Lao Tzu suggests a much more determined withdrawal from choice, decision, will, wish, and action, especially, however, from all ambition and competition, in behalf of an ideal of the unity of opposites and of the power of yielding to \"the spontaneous Becoming\" ( _ZiRan_ , often now translated as Nature)\u2013\u2013a \"passivity,\" very akin to what I alluded to before as the stance of the analyst. It is very much a \"feminine superego,\" even far more pronouncedly so as the Confucian superego (which, after all, also suggests submission, renunciation of self and of competition): \"The good use of people is by putting oneself below\" (Ch. 68, my translation). \"The female always overcomes the male by tranquility, and by tranquility she is underneath... Thus some, by placing themselves below, take over (others), and some, by being (naturally) low, take over (other states)\" (Ch. 61, trans. Chan). \"Therefore 'the weapon that is too hard will be broken, the tree that has the hardest wood will be cut down.' truly, the hard and mighty are cast down; the soft and weak set high\" (Ch. 76, trans. Waley). \"The original power ( _y\u00fcan D\u00e9_ ) is so deep, so distant; it makes things so paradoxical ( _fan_ ). Thus one goes back until one reaches the Great Flow ( _Da Shun_ )\" (end of Ch. 65, my translation).\n\nOne removes conflict by undoing knowledge and desire; yet therewith something else is veiled: Culture and society are themselves expression of human nature, conflict itself is human nature, an indispensable basis of the _conditio humana_. It is the same dilemma as the one later on faced by Rousseau. That unity is only attained at the cost of denying such conflict. With social and cultural reality, with knowledge and social virtues, an entire part of the inner world is bypassed too\u2013\u2013 the fidelity to the need to know10 and to curiosity, the deep need for activity and symbolization\u2013\u2013all in favor of that overriding longing for synthesis. In our frame of reference, in our metaphorical system: the executive side of the ego\u2013\u2013the deciding and distinguishing function\u2013\u2013is sacrificed at the behest of the synthetic side. With that the attempt at synthesis appears to be itself subverted, undermined.\" if one desires to be in front of the people, one must speak as if behind them\" (Ch. 66, trans. Gibbs). Yet can this be done without deception? does not thus the very split to be avoided recur, the conflict reemerge as inner and tragic reality, as outer isolation and estrangement?\n\n> Wildly, endlessly, all men are merry, as though feasting upon beef or sitting on the veranda in the spring sunshine. I alone remain uncommitted, like an infant who has not yet smiled. I alone seem as mindless as one who has no home to return to. Everyone else has enough and more, yet I alone seem to be left with nothing. What a fool's mind I have! how muddled I am! Most people seek brightness and clarity. I alone seek dullness and darkness. Most people are imaginative and observant. I alone am stifled and mum; I am as unmoved as the ocean, as ceaseless as the wind high in the sky. Everyone else has something to do; I alone am ignorant and dull. I alone am different from the rest in that I value taking sustenance from the Mother.\n> \n> (Ch. 20, trans. Gibbs)\n\nIn contrast to this supreme identification with the Maternal as ideal in Lao Tzu we have the equally strenuous identification with the idealized paternal in Confucius\u2013\u2013 yet both in the service to avoid any power struggle and competition, be that of an anal or oedipalphallic nature. Clearly, however, the _Tao The King_ is by no means a pamphlet dedicated to the overthrow of the superego altogether. Rather it is, as I would postulate, _the overcoming of an archaic, mostly \"anal\" superego in favor of the positing of a new ideal_. It is a revolutionary superego, a protest against a value system that at least for us has become associated with Confucius. It is a superego that aspires to reach back to the \"origin\" ( _y\u00fcan_ ), a superego living from a new vision, a very different metaphorical system. There is, as already noted, clearly a radical shift in valuation, compared with the Confucian ethos, regardless if Lao Tzu preceded Confucius, as the tradition presumed, or followed him by centuries, as is assumed by many today\u2013\u2013a shift without requirements of faith, without a belief in a divinity in any customary sense, yet a deep spirit of reverence, a kind of \"philosophical belief\"\u2013\u2013 using a wonderful spectrum of metaphors without the fixation into any dogma.\n\nWhat does that new vision entail? The great connectedness of life is seen, the advice given that the encompassing cohesiveness of what we know never be lost. Purposive and ambitious doing interferes with such knowing of the whole context of Being. All forms of external power destroy such awareness and should be avoided. It is a grand vision of existence that treats all the external entities\u2013\u2013realm, war, ruler, plants, and animals\u2013\u2013as metaphorical help to formulate such inner truth. The most important, however, of all the insights of such an inwardness is that of _mutually conditioning_ attributes and actions, instead of the _absoluteness_ of any one thing, subject or object, its Eitheror. Nothing that is being put into words can claim unconditional truth:\n\n> There was something undifferentiated and yet complete, which existed before heaven and earth. Soundless and formless, it depends on nothing and does not change. It operates everywhere and is free from danger. It may be considered the mother of the universe. I do not know its name; I call it _Dao_ (Way). If forced to give it a name, I shall call it great. Now being great means functioning everywhere. Functioning everywhere means farreaching. Being farreaching means returning to the original point. Therefore _Dao_ is great. Heaven is great. Earth is great. Man is also great. There are four great things in the universe, and man is one of them. Man models himself after earth. Earth models itself after heaven. Heaven models itself after _Dao_. And _Dao_ models itself after nature.\n> \n> ( _ZiRan_ , Waley: the \"selfso\"; Ch. 25, trans. Chan;  \n>  except that I follow the reading \"Man\" _ren_ , not \"king\")\n\nStill the most fascinating question remains: What about the seeming merging of opposites, that what has been called _fan yan_ , the speaking in paradoxes\u2013\u2013that big is small, small is big, full is empty, old is new, strong is weak, weak is strong? how can that be understood?\n\nThe immediate response is: speaking and knowing are impotent. It seems to imply an advocacy of a return to the preverbal, to the all encompassing and global affects. Ten we think of such \"absurd\" reversals in dreams, that may imply: \"This is incredible, ridiculous!\"\n\nWhat does it entail? I believe it expresses a deep doubt on the perception of reality and on the validity of everyday logic. Thus, by its very movement from one opposite to the other, it gives metaphorical expression to the profound quandary: What is truth?\n\nAnd yet it goes deeper still: This is the language of the soul, the discourse of the inner world where we discover layer upon layer, where we can tear of mask behind mask. It represents the depth dimension of inner reality. This is its hallmark, in Dickens' expression: \"... Things are not always as they seem...\" ( _Our Mutual Friend_ , 1971, p. 321) and \"But seeming may be false or true\" ( _The Mystery of Edwin Drood_ , 1961, p. 262). The layering is laced with anxiety, it is a layering of defenses and of dangers.\n\nCould it therefore be that we deal here, in the _fan yan_ , with an indirect presentation of conflict, in the sense of using logical and perceptual contradiction, as an indirect presentation of affective conflict\u2013\u2013in our terms: of intrasystemic and intersystemic conflict (whereby it is, I would think, mostly the former)?\n\nIt is evident that in the _Tao The King_ metaphysics, ethics and politics are united, even amalgamated (Jaspers); but it is also clear how everything points back to the one central and original issue: that of the insight in the inner reality, of its manylayeredness and multiplicity of meaning, of its contradictoriness, and, ultimately and inevitably, of its roots in conflict and complementarity. However, at the same time, that insight says: inner and outer truth manifest each other in mutually reflecting mirrors. Therefore its discourse has to be eminently metaphorical: truth can only be approached with the help of images; it cannot be \"grasped\" and \"held.\" proceeding, it has to be \"cautious like crossing a frozen stream in the winter\u2013\u2013 majestic in appearance\u2013\u2013yielding, like ice on the verge of melting...\" (Ch. 15).\n\n## **Notes**\n\n originally published in _Psychoanalytic Inquiry_ 31(2): pp.107\u2013125 under the title \"Metaphor as Conflict, Conflict as Metaphor.\"\n\n Lao Tzu, Ch. 70.\n\n \"Die person, von der seite des Charakters betrachtet, soll: sie ist beschr\u00e4nkt, zu einem Besonderen bestimmt; als Mensch aber will sie. Sie ist unbegrenzt und fordert das allgemeine. Hier entspringt schon ein innerer Konflikt, und diesen l\u00e4\u00dft shakespeare vor allen anderen heraustreten.\"\n\n \"ein Wollen, das \u00fcber die Kr\u00e4fte eines individuums hinausgeht, ist modern.\"\n\n _Li_ is variably translated as propriety, beauty, holy ritual, sacred ceremony, used as metaphor for \"the entire body of _mores,_ or more precisely, of the authentic tradition and reasonable conventions of society,\" as Fingarette defines it, p. 6\/7.\n\n Better by Waley: only he who has accepted the dirt of the country can be lord of its soilshrines; Chan Wing Tsit: he who suffers disgrace for his country is called the lord of the land.\n\n Waley: Can become a king among those what dwell under heaven.\n\n Waley: straight words seem crooked [seem, as we would say, to be paradoxes]; Chan Wing Tsit: straight words seem to be their opposite.\n\n \"Diese mannigfachen Gestalten der Gegens\u00e4tze benutzt nun Laotse, um im Widerschein das Unsagbare sagbar zu machen, das sein im nichtsein, das Wissen im Nichtwissen, das Tun im Nichttun\" (Jaspers, 1958 p. 926).\n\n Aristotle's insight: \"All men naturally desire knowledge,\" the beginning sentence of the _Metaphysics_.\n\n# 6  \nMETAPHOR, MEANING,  \nAND THE MIND\n\n_Arnold H. Modell_\n\nMetaphor and metonymy are the primary and crucial cognitive tools of unconscious thought. Acknowledging this function of metaphor and metonymy might provide a unifying bridge between the disparate schools and factions of contemporary psychoanalysis. I suggest that we are more likely to find common ground, both within psychoanalysis and neighboring disciplines, if we view the unconscious mind as the area within which meaning is processed by means of metaphor, rather than the locus of a battleground between repression and instinctual forces.\n\nThe [original] title of this chapter refers to a judgment attributed to the quantum physicist Wolfgang pauli. A friend showed him the paper of a young physicist which he suspected was not of great value but nevertheless wanted pauli's views. Pauli remarked sadly, \"it's not right it's not even wrong.\" to claim that a scholarly or scientific paper is \"not even wrong\" suggests that the author and the critic do not share the same conceptual system so that a judgment is not even possible. I'm afraid this can be said of the sorry state of affairs that separate the various \"schools\" and factions of psychoanalysis at this time. A \"classical\" Freudian ego psychologist, a Kohutian self psychologist, a sullivanian interpersonalist and a Lacanian cannot communicate with each other as they do not share in common a set of conceptual assumptions.\n\nConceptualizing the unconscious in terms of the Freudian instinctual id is unacceptable to most of us and is certainly incompatible with contemporary neuroscience. I will suggest that a revised concept of the Freudian unconscious, where metaphor is the cognitive tool, might be a starting point that will provide some shared basic assumptions. If we can agree on fundamental assumptions perhaps we can begin to talk to each other.\n\n## **Why I Am Not an Ego Psychologist**\n\nIn our field, at the start of our careers, our basic assumptions and beliefs usually follow from our identification with an idealized mentor, hence we describe ourselves as Freudians, Kleinians, Kohutians, Sullivanians, Lacanians, etc. But as we gain clinical experience we should begin to question those assumptions that we have uncritically adopted from our mentors. Although I would still describe myself as a Freudian, I would more specifically claim to be an early Freudian inasmuch as I reject Freud's instinct theory and many aspects of ego psychology, especially the idea of defense mechanisms. Of course I don't reject the idea of defense but I do reject the impersonal concept of mechanism. The machine metaphor is totally incompatible with the highly individualized, self-organizing, self-selecting function that unconsciously chooses a specific mode of defense at any given point in time. What I fully embrace, and identify with, is the Freud of _The Interpretation of Dreams_ (1900). As I shall describe, Freud's early concept of the unconscious processing of memory and feeling as illustrated by the formation of dreams is significantly and radically different from the concept of the unconscious that he later elaborated in _The Ego and the Id_ (1923a). If we return to Freud's early idea of the unconscious as a meaning making process and not a battle ground between instinctual wishes and those agencies that oppose their expression, we have, I believe, a better chance of finding a common conceptual ground between the various disparate schools that characterize contemporary psychoanalysis.\n\nI believe that ego psychology has proved to be a major divisive force that has separated the various schools of psychoanalysis. Freud's conception of the id has prevented us from viewing \"the unconscious\" not as that area of the mind in which instinctual forces are held in check by repression, but as that area of the mind concerned with the unconscious processing of meaning.\n\nNot surprisingly, the development of my beliefs and conceptual assumptions were influenced by the impact of my clinical experience. After my graduation from the Boston psychoanalytic institute in 1961, I tried to test the limits of the psychoanalytic method by accepting patients for psychoanalysis who were seriously ill such as the so-called borderline case as well as some patients who were diagnosed as schizophrenic. I soon discovered that their relationship to me was central to their treatment and that interpretation of their unconscious thoughts and feelings was not always useful and at times was counterproductive. Such an observation is today self-evident. I would think every clinician knows that with the sicker patient the effect of the therapeutic relationship transcended the result of interpreting unconscious content. But at that time this two-person relational understanding could not be easily integrated into Freud's third person concept of the mind as a mental apparatus. Nor could this two-person relational understanding be reduced to or understood simply under the rubric of transference. We know of course that this gap between clinical observation and Freudian theory was subsequently filled with the emergence of various \"relational\" and inter-personal schools of psychoanalysis.\n\nTo continue with this account of my conceptual development, I discussed this issue of a two-person psychology and its relation to Freudian theory in _Psychoanalysis in New Context_ (1984) (Modell, 1984) where I stated: that Freud essentially oscillated between a one person stance, for example, dream interpretation, and a third person \"scientific\" account of human psychology. In that volume I wrote: (p. 11) \"The process that occurs between two people, between the subject and the object in psychoanalysis is referred to the mind of the subject, who is the patient. This produces in us a certain intellectual unease when, for example, we describe dependency, a process occurring between two people, as an event in the mind of one person. Traditional psychoanalysis has not yet acquired theoretical language that would enable it to describe process occurring between two separate personalities in terms encompassing the events in both individuals.\"\n\nFreud of course was not unaware of a two-person dialogical perspective as such a perspective is implicit in Freud's recognition of the unconscious communication that occurs in transference and in the process of free association. For example in his encyclopedia article Freud (Freud, 1923b) understood free association to be a \"means to catch the drift of the patient's unconscious with his own unconscious.\" But this implicit two-person system could not easily be ft into his instinct theory or his structural ego psychology. Furthermore, Freud thought that the third person perspective, of a \"mental apparatus,\" a concept central to ego psychology, supported psychoanalysis' claim to be a scientific discipline.\n\nTo find mentors whose work was consistent with my clinical experience I turned to Winnicott as I did in my 1968 book _Object Love and Reality_ (Modell, 1968). There I applied Winnicott's concept of the transitional object to certain aspects of the relationship that one experiences in the treatment of borderline and schizophrenic patients. The concept of the transitional object can be thought of as a conceptual metaphor that is a shared imaginative construction, present in the minds of both parent and child. In a transitional object relationship the person of the analyst is treated as a protective magical agent that is interposed between the individual and one's existence of the world. There is a clear analogy here to the child's creation of the transitional object, where a real object, a blanket or teddy bear is, by means of the imagination, magically transformed. In a broader context this process can be thought of as an interplay between the real and the imagined. The transitional object illustrates the interplay between the real, the actual object, and its transformation by means of metaphor. This interplay reflects the synergy between metonymy and metaphor. The real object, blanket, etc., is a metonymic object, in that the part substitutes for the whole\u2014the whole being the mother. This \"real\" object is then magically transformed by means of metaphor. This interplay of metaphor and metonymy, the real and the imagined, is a crucial process that determines the unconscious construction of the other person. As this process is not limited to the therapeutic relationship, this can be described as the transference of everyday life. In our imaginative transformation of the other person we invariable respond to actual perceptions, something that is \"real.\" Metaphoric process always requires the \"real\" of metonymy (Jakobson, 1995). This formulation is consistent with a broader view of the perceptive process, including other species, where a distinction is made between raw sensations and their subsequent interpretation by the unconscious self (pincus, et al., 2007).\n\n## **Reconstructing the Freudian Unconscious in the Light of Neuroscience\u2014Hoping to Find Common Conceptual Ground**\n\nAnyone who identifies themselves as a psychoanalyst would, I imagine, unquestionably accept the idea of unconscious determinism. But how unconscious processes are conceptualized is a subject of much discord and disagreement. How one understands unconscious process is linked to several other theoretical controversies. One such controversy is the extent to which one believes that unconscious processes are neuro-biologically determined. Another is the extent to which one believes that unconscious processes are determined by the past unconscious, that is to say, memory, or the extent to which one believes in the importance of the present unconscious that is embedded in the inter-subjectivity of the present moment. As you know there are analytic schools of thought that minimize the importance of the past and therefore the significance of unconscious memory in determining the meaning of current experience. Some claim a certain autonomy for the present moment. I am thinking, for example, of the Boston Change process study Group (2008) who seem to have ignored the Freudian concept of unconscious process although they do acknowledge the significance of metaphor. It is not that I deny the importance of the present moment, which I take to be an aspect of the real, but this view omits a consideration of an unconscious metaphoric process that organizes the affective memories of the past through which the present moment interpreted. I will suggest, as I described in _Imagination and the Meaningful Brain_ (Modell, 2003) that an unconscious metaphoric process, analogous to dreaming, occurs in the waking state.\n\nIt is my belief that Freud went down the wrong path when he reframed human psychology in terms of instinct theory. Originally, in _The Interpretation of Dreams_ , Freud (1900) viewed the unconscious as a knowledge processing system that gave metaphoric expression to the unconscious wish. This view of the unconscious was radically altered with Freud's elaboration of instinct theory and the development of ego psychology. This is I believe one of the root causes for the divisions that separate the various schools of contemporary psychoanalysis. Freud never disclaimed his description of unconscious processing in dreaming, but he viewed it as special instance and put it aside when he re-characterized the unconscious, not as an area in which knowledge is processed, but as an area of the mind in which there is a conflict between instincts seeking discharge and the forces of repression that prevent, instinctual derivatives, thoughts, feelings and fantasies, from being from becoming conscious. The primary function of this revised unconscious was not the processing of knowledge but to prevent unacceptable impulses, wishes and fantasies from becoming conscious. In his introduction to his 1915 paper _The Unconscious_ Freud (1915b) states that everything that is repressed must remain unconscious, but he also noted that the unconscious has a wider compass, that the repressed is only one part of the unconscious and does not cover everything. But Freud does not say what this part consists of. Freud writes in that paper \"the nucleus of the unconscious consists of instinctual representatives which seek to discharge their cathexis; that is to say, it consists of wishful impulses.\" in his 1915 paper Freud further states that \"the content of the unconscious may be compared with aboriginal population of the mind. If inherited the mental formation exists in human beings\u2014something analogous to instincts in animals\u2014these constitute the nucleus of the unconscious\" (1915b, p. 186). At the end of his life, when he wrote _An Outline of Psychoanalysis_ Freud (1940a) now viewed unconscious process not as potentially adaptive but as a danger to the self. The id was seen as the ego's internal enemy he said: \"[I]mmediate and unheeding satisfaction the instincts, such as the id demands, which all would often lead to perilous conflicts with the external world and to extinction.\" had Freud retained his earlier view of the unconscious as a knowledge processing system, there would today be fewer theoretical divisions amongst psychoanalysts.\n\nLet me now turn to another conceptual area that has contributed to the divisions that exist between various schools of psychoanalysis. There are those who claim that psychoanalysis should have nothing to do with neuroscience because of the problem of reductionism (Blass & Carmeli, 2007). As a consequence those psychoanalysts who were interested in neuroscience have of necessity formed yet another separate school. In 1976 Merton Gill in his influential paper \"Metapsychology is not psychology\" observed that \"metapsychology deals with neurology and biology, with the physical substrate of psychological functioning while clinical psychoanalysis is a 'pure' psychology which deals with intentionality and meaning.\" Gill's belief that intentionality and meaning, the heart of psychoanalytic understanding, is a subject that is divorced from any biological substrate is no longer true. Some neuroscientists (Freeman, 1999), but I grant you not many, describe neural events that serve the function of meaning construction and intentionality. It should be noted however, in Gill's defense, that his paper was written in 1976 prior to the expansion of cognitive science and neurobiology. However, I believe that there are many psychoanalysts today who still wish to keep psychoanalysis \"pure,\" that is uncontaminated by neuroscience. There are even some analysts who have recently argued that being influenced by neuroscience is actually dangerous for psychoanalysis (Vivona, 2009).\n\nOne of the aims of this paper is to show that this problem of reductionism can be avoided if we recognize that there are separate and different levels of unconscious processing so that unconscious psychological processes are not to be confused with neurophysiological events.\n\nAs unconscious processes cannot be observed directly they can only be noted by inference and analogy. As Freud famously noted, the dream is the royal road to the unconscious. We can be conscious of the dream itself, but the process that created the dream is undeniably unconscious. You will recall that Freud understood that the metaphoric processes observed in dream formation was the same unconscious process that contributed to symptom formation in hysteria (Freud, 1923b). The physical symptoms of hysteria Freud interpreted as the metaphoric expression of an unconscious wish. The dream was also interpreted as a metaphoric expression of an unconscious wish. _Metaphor is therefore a fundamental cognitive tool that is central_ _to unconscious mental process._ Freud described dreams as a factory of thought, but to follow the analogy of a factory, the basic machinery that this factory employs is predominantly that of metaphor. The transfer of meaning between different domains and the multiplicity of different meanings that can be attributed to a single dream element, what Freud described as condensation, attests to the ubiquity of the metaphoric process in dreaming. As I have repeatedly maintained: metaphor is the currency of the (unconscious) mind (Modell, 2003). This means that unconscious thoughts, whether in the dream or whether in response to sensory inputs in current time are cognitively organized through the medium of metaphor.\n\n## **Unconscious Metaphoric Process and the Meaning Attributed to Past Experience**\n\nIn my book _Imagination and the Meaningful Brain_ (Modell, 2003) I suggested that a metaphoric process analogous to dreaming is operative in the waking state. In that book I quoted the critic and novelist Cynthia Ozick (Ozick, 1991) who observed that \"Metaphor, like the Delphic oracle is a priest of interpretation, but what it interprets is memory.\" according to the Nobel prize laureate Gerald Edelmam (Edelman, 1998) memory carves both the inner and outer world into categories. Further, these categories are recontextualized through experience. What I have observed is: that emotional memory is categorized by means of metaphor. In health these memorial metaphoric categories oscillate between similarities and differences. In the face of trauma, however, this play of similarity and differences is lost and the metaphoric transfer of meaning is invariant.\n\nIn health, metaphoric process facilitates the recontextualization of autobiographical memory. We assume that old memories are constantly re-interpreted in the context of new experience. This is the process that Freud termed _nachtraglichkeit_ , the meaning of old memories are re-interpreted in the light of subsequent experience. (i discussed this process in greater detail in Modell, 1990.) Metaphoric matchings play a crucial role in this process. Traumatic memories may represent a failure in the transformative power of metaphor. In this example memory was not recontextualized by means of metaphor. Metaphor was used not to transform memory but to simply transfer memory so that an unyielding similarity is experienced between the past and the present.\n\nMy patient reported the following incident. Because his airline went out on strike, my patient was stranded in a distant city and unable to return home. He did everything possible to obtain passage on another airline: he cajoled and pleaded with the functionaries of other airlines, all to no avail. Although my patient was usually not unduly anxious and was in fact a highly experienced traveler, in this particular situation he experienced an overwhelming and generalized panic. He felt as if the unyielding airline representatives were like Nazis and that the underground passages of the airline terminal resembled a concentration camp. The helplessness of not being able to return home, combined with the institutional intransigence of the authorities, evoked the following memory, which had been unconscious.\n\nWhen this man was three years old, he and his parents were residents of central European country and, as Jews, were desperately attempting to escape the Nazis. They did in fact obtain airline passage to freedom, but until that point, the outcome was very much in doubt. Although my patient did not recall his affect the state at that time, his parents reported that he seemed cheerful and unaffected by their anxiety. And as in this example, this helpless inability to leave a foreign city, combined with the intransigence of the authorities, evoked a specific affect category that remained a potential memory of an unassimilated past experience. In this example, unconscious memory was metaphorically interpreted with the help of a metronomic association. His helpless inability to leave a foreign city combined with the intransigence of the authorities served as a metonymic trigger. The metaphoric process can be defined as the transfer of meeting between different domains in this case the different domains are that of unconscious autobiographical memory and the present moment. This example also illustrates my hypothesis that an unconscious metaphoric process operates in the waking state. It is a process that interprets the meaning of current experience in a manner that is analogous to the way a dream utilizes metaphor.\n\nThe similarity between dream process and the unconscious process that occurs while we are awake has received some support from neuroscience. The neuro-physiologists Llinas and pare have also seen an analogy between the dream state and waking unconscious process. They provide some experimental evidence that points to a similarity of the neural process that supports the unconscious mentation of dreams and an analogous unconscious process that occurs while awake (Llinas & pare, 1991). As a consequence of their experimental observations they made the following statement: \"[T]hese observations indicate that mentation during dreaming operates on the same anatomical substrate as does perception during the waking state.\" This means that my suggestion that an unconscious metaphoric process, analogous to dreaming, occurs in the waking state is not physiologically implausible.\n\nI shall attempt to further spell out this analogy between dreaming and a waking unconscious process. Neuroscience believes that dreaming is initiated by a self-generated excitatory process within the brain. The anatomical site of this process is correlated with the various stages in the sleep cycle (Llinas & pare, 1991). Let us label this as the deepest level of unconscious dream process; it can be thought of as the physical or the neuro-chemical dream. Let us further consider that the dream of which we are conscious, is the product of a higher level of unconscious processing as compared to the initiating neurophysiological events. This higher level unconscious process interprets the excitory signals, what may be described as the raw neuro-physiologic dream. This higher level represents the functioning of the unconscious self. The functioning of the unconscious self encompasses many tasks of the dream that Freud described. These functions would include the classical Freudian dream wish, the defensive functions in accord with internalized moral values of the self as well as intentional thoughts directed towards future actions in response to specific elements from the previous day's residue. In contrast to the deeper neurophysiologic level of unconscious processing, which like other physiological processes are shared by all, the functions of the unconscious self are highly individualized.\n\nI recognize that these ideas are speculative and undoubtedly controversial. But I firmly believe that a revised theory of \"the unconscious,\" or more properly speaking unconscious processing, is a useful starting point. It is a theory that recognizes the ubiquity of the metaphor process that is active both in dreaming and in the waking state. I suggest that we seek common ground in concepts rather than in matters of technique. Those analysts who favor one aspect of technique over another will find it impossible to prove their case. For the uniqueness and variability of selves are such that generalizations are nearly impossible. Controversies concerning menace of technique ultimately prove to be irresolvable.\n\nIt may be a Quixotic hope that some agreement regarding the nature of unconscious process and recognition of the ubiquity of metaphor will enable a dialogue between the various factions of contemporary psychoanalysis. But the alternative, the absence of dialogue is unacceptable. We should welcome conceptual controversies for without controversy a discipline lacks vitality. But in order for controversies to be fruitful there must also be some basic shared assumptions. If the various psychoanalytic factions accept the idea that metaphor is the cognitive tool of unconscious processing, it is possible that we may then be able to establish other areas of conceptual agreement.\n\n## **Note**\n\n originally published in _Psychoanalytic Inquiry_ 31(2): pp. 126\u2013133 with the title, \"Not even Wrong.\"\n\n# 7  \nMETAPHOR IN THREE  \nPSYCHOANALYTIC  \nPERSPECTIVES\n\n_Robert S. White_\n\nAdopting the lakoff and Johnson view that conceptual systems of the mind are inherently metaphoric and embodied, I examine theoretical metaphor in psychoanalytic theory as an example of the use of metaphor more generally in the mind. I have chosen concepts of the non-dynamic unconscious to explore representative metaphors. These include the theories of W. Bion, C. And S. Botella, and d. Stern. This chapter first outlines recent interest in the non-dynamic unconscious and then examines the theories of Bion, the Botellas, and stern in detail. Differences and similarities among the theoretical metaphors are explored. I suggest that theoretical metaphors progress both through the attempted destruction of existing metaphor and reshaping of existing metaphor into new meanings. I am interested in finding among the metaphoric collisions that there may be hidden collusions that can potentially lead to unifying concepts.\n\n## **Metaphor**\n\nThe modern view of metaphor was introduced by Lakoff and Johnson (1980a) in the now classic, _Metaphors We Live By_. In this work, our conceptual system is thought to be fundamentally metaphoric. All degrees of abstract thinking are built up of layers of metaphor. Conceptual metaphors consist of a mapping from a more concrete source domain onto a more abstract target domain. Meaning is created from such mappings. Lakoff and Johnson (1999) went on to claim that the mind is inherently embodied. Thinking is mostly unconscious and is built up out of sensori-motor experiences. This cognitive-linguistic approach is now widely accepted in psychoanalysis (Wallerstein, Chapter 4). Wurmser (1977, Chapter 5), Modell (1968, 1990, 2003, Chapter 6), Borbely (1998, Chapter 8) and Katz (2010a, 2011b) have been most instrumental in arguing for the centrality of metaphor. Wurmser believes that all scientific thinking is the systemic use of metaphor. Modell, drawing from lakoff and Johnson, proposes that metaphor is the currency of the unconscious mind. Katz and Borbely believe that meaning, created out of metronomic and metonymic processes, can be the primary organizing concept and bridge among disparate psychoanalytic schools.\n\nI would like to add a dialectical dimension found in the modern metaphor. In addition to unity, there is an emphasis on collision, tension, and opposition over collusion and similarity (harries, 1978). He suggests that, in modern poetry, metaphors become weapons directed against reality, to break the referentiality of language, to find a magical presence, a godlike self-sufciency. It is a refusal to owe anything to the world. Out of the destruction of the world, the poet creates his own poetic world. Inherited metaphor must be removed for the poet's more daring combinations. The poet seeks a presentness and instantaneousness, a perpetual creation of self. Transcendence means a world that would be truly objective and transparent, free from all perspectival distortions. In a poem, there is an invitation to leave familiar ground for the sake of a more profound transcendental vision of what is, to throw into relief and destroy beloved reality. A new predicative meaning emerges from the collapse of the literal meaning. It is the destruction of ordinary reference and the projection of new possibilities.\n\nUsing collusion over similarity gives another modernist twist. Collusion is defined as a secret agreement between parties for fraudulent or deceitful purposes. So even when there is apparent similarity and agreement, we see just beneath the surface the emergence of deceit and hiding of secrets. The collusion quickly shades into collision.\n\nAnother way to view this tension is the difference between a fox and a hedgehog (Berlin, 1951). These metaphors come from the Greek poet Archilochus: \"The fox knows many things, but the hedgehog knows one big thing.\" The fox pursues many ends even if unrelated and contradictory. This is a centrifugal vision that is scattered, diffuse, moving on many levels, finding the essence in many things. The hedgehog relates everything to a centripetal vision or system, a single and universal organizing principle. The major figures in psychoanalysis have been hedgehogs (strenger, 1997). They favor the development of a single, organizing system that guided the interpretation of every phenomenon. Hedgehogs provide magnets that shape possible voices into integrated visions. They push ideas to their logical extremes. Beauty, coherence, and nobility are prized above all others. Harries' modern poets are hedgehogs. Freud, Klein, and Bion are all hedgehogs. They attract schools and apostles. They wish to destroy in order to build a pure system. I think there is a universal human need to build pure systems. It is a fantasy of being uncontaminated and of being controlled by no one. Most people who write theory take one or more organizing principles and then see all of phenomena through the lens of these principles. Another theorist comes along and sees what is missing, then builds his or her theory around that. Freud's (1919a, p. 168) famous statement speaks to this: \"The large-scale application of our therapy will compel us to alloy the pure gold of analysis freely with the copper of direct suggestion; and hypnotic influence, too, might find a place in it again, as it has in the treatment of war neuroses.\" The pure gold of analysis has a magical draw in psychoanalytic theory.\n\nMost clinical practitioners are foxes, borrowing and using whatever theory seems to ft. In the real world of clinical work, the pure gold does not work. In thinking of the metaphor of gold and copper, we should note that pure gold is beautiful and precious, yet it is too soft to be useful in practical life. It must be alloyed with copper or other metals to make it useful. It is a pragmatic approach, a craft to serve people and ft local reality. The map must never be confused with the territory. Theory is a tool and not a map of reality.\n\nWe could think of psychoanalytic metaphor in three levels, metaphors of human nature, metaphors of psychoanalytic theory and metaphors in clinical practice. In this paper, I plan to concentrate on theoretical metaphors. Out of this, I will develop the following categories to use in analyzing psychoanalytic metaphor:\n\n1 What reality does the new metaphor attack and attempt to destroy?\n\n2 Is there preserved any continuity and similarity between the new metaphor and existing reality?\n\n3 What is the mental space that the new metaphor inhabits?\n\n4 To what extent does new metaphor aim for a transcendence of a unity of vision?\n\n5 In destroying existing reality, can a new unity be found that provides a new coherent vision?\n\nIn this project, I will choose a common psychoanalytic space, which can be described from several theoretical points of view. From the different theoretical points of view, I will select representative technical metaphors. Each theoretical school had developed metaphoric labels to reflect their core assumptions (Bornstein and Becker-Matero, this volume). These metaphors will be compared and contrasted, using the categories outlined above. The psychoanalytic space that I will use is non-symbolic codes. This will also give us a chance to examine the limits of metaphor when we examine non-linguistic mental space. The three theorists are all hedgehogs, who attack existing psychoanalytic metaphor and seek to organize psychoanalytic reality using new assumptions. This paper is written by a fox who admires hedgehogs but finds they do not ft the everyday reality of psychoanalytic work.\n\n## **Non-Symbolic Codes**\n\nThere is now widespread convergence among a number of psychoanalytic theories of the existence of dual codes in the mind, the symbolic and nonsymbolic (lecours, 2007). Symbolic codes are the characteristic targets of classical psychoanalytic theories. This would include mental conflict, signal affects, intrapsychic mental structures, unification of self identity, links between affects and representations, networks of unconscious wishes and pathological beliefs, and networks of defenses and compromise formations. Defenses based on repression are characteristic of symbolic conflict.\n\nThe persistence of non-symbolic codes in adult life can result from deficits in early development, from borderline and psychotic functioning and from severe trauma. The lack of symbolization results in the use of primitive defenses, organized around splitting and projective identification, and the compulsion to repeat in actions. Affects are unmodulated and eruptive. Mental structures are split into dissociated areas or fragmentation.\n\nTheorists from a number of traditions have articulated versions of non-symbolic code. Freud (1915a) developed a second theory of the unconscious; conscious ideas could be split into word-presentations and thing-presentations. In repression, the word-presentation is stripped of and only the thing-presentation is retained. The thing-presentation is the raw material of the sensory experience. Loewald (1978) argues that word-presentations are not a higher organization than thing-presentations. At the beginning of mental life, words are part of the undifferentiated total experience of the infant, a primordial density. Busch (2009), from American conflict theory and building on Loewald, describes action-language, where words become concrete acts. Green (1998, 1999a, 1999b) speaks of the work of the negative: disavowal, splitting, and foreclosure. Bucci and Maskit (2007), from an empirical orientation, suggest multiple coding systems in the mind: symbolic codes either verbal or non-verbal, and subsymbolic coding system which can occur in motoric, visceral or sensory modes.\n\n## **Tree Theorists**\n\nI will choose three theorists, each coming from different analytic cultures, to compare and contrast. Wilfred Bion comes out of the English Kleinian school with its roots in object relations. C\u00e9sar and S\u00e1ra Botella come out of the French school, with its roots in early Freud, Lacan and philosophy. Donnel stern comes from the American interpersonal school with its roots in H. S. Sullivan and interaction.\n\n### Wilfred Bion\n\nBion (1957, 1962a, 1965, 1989, 1995b) aims for a radical attack and recasting of basic Freudian and Kleinian metaphors. He used Greek letters for his major metaphors because he wanted to start fresh, without any pre-existing meanings. This is the opposite of Freudian theorists, such as loewald (1978) who aimed to extend existing metaphor and maintain a tradition. Bion's key metaphors would include \u03b2-elements, \u03b1-function, \u03b1-elements, reverie, K-link, and container\/contained.2\n\nBion recasts Freud's metaphor of primary process into a more modern theory of thinking, where there is a progressive increase in complexity and integration of thinking and transformation of preverbal into verbal thoughts. Bion is dissatisfied with the primacy of libidinal and aggressive drives. While he does not deny the existence of these drives, he postulates that human growth occurs primarily through the emergence of truth in knowledge. Drives are recast as links, l (love), H (hate), and K (knowledge). For Bion, these are not drives but emotional activities. The ability to think is born out of the ability of the person to tolerate frustration. The movement is from evading pain to the acceptance of painful truths. Thinking does not reduce psychic tensions but manages them. Bion discards the polarity of conscious\/ unconscious in favor of the metaphors, finite and infinite. Primary and secondary process is discarded and replaced with **\u03b2** and \u03b1-elements. The structural model is replaced with the metaphor of container\/contained  .\n\nBion postulated a psychic space that precedes and underlies the dynamic unconscious. It would correspond with Freud's (1915b) thing presentation and the repressed that never achieve consciousness (Freud, 1915a). For Bion (1995b), the mind starts out in catastrophe. Mental space cannot be represented, leaving an immensity that is accompanied by violent and psychotic fear. This space is filled with what Bion calls (\u03b2-elements.3 They are fragments and debris of the mental catastrophe. While for Freud, these objects are a form of thought, for Bion (\u03b2-elements are the matrix from which thoughts can arise. (\u03b2-elements can be stored and clog up the mind or can be evacuated by projection or through acting out. The only link possible with the analyst is projective identification because (\u03b2-elements can only be evacuated by projection (Bion, 1959).\n\nFor use in thought, (\u03b2-elements must be transformed by \u03b1-function into \u03b1-elements. \u03b1-elements are comprised of visual, auditory and other sensory patterns that are now available for dreaming and unconscious waking thought, what Ferro (2005b, 2005c) calls visual pictograms. Dreaming, for Bion, is a form of psychoanalytic work (ogden, 2004b), in which pre-conscious thoughts are pressing toward awareness. Attacks on \u03b1-function, from envy or hate, destroy the persons ability to make contact with herself or others. The self and objects become inanimate, lifeless, dead.\n\nBion uses the metaphor of a container to understand the communicative aspects of projective identification. In the metaphor of container and contained  , the infant projects (\u03b2-elements into the containing mother, who at first provides the \u03b1-function to transform the contained (\u03b2-elements into \u03b1-elements and feed them back to the baby at an appropriate moment (Bion, 1965). The mother must be in a state of reverie, a dreamlike state, in order to receive and contain the infants (\u03b2-elements. Over time, the infant can acquire his mothers \u03b1-function and perform his own transformations. The capacity for \u03b1-function makes possible the development of thinking and the possibility of thoughts.\n\n### C\u00e9sar and S\u00e1ra Botella\n\nThe Botellas (2005) propose another view of the non-verbal. Unlike Bion, they do not want to destroy existing theory but extend it. They would understand their project as completing an aspect of Freud's thought that was left unfinished at his death. But metaphors of the traumatic dream are bent and shaped into a much larger theory of trauma, so we end up much as in Bion with a completely new theory. Key metaphors include figuration, perceptual axis, and non-representation.\n\nThey suggest we conceptualize the psyche space as having two axes. One axis is familiar to psychoanalysis. It is the system of representations, the familiar world of drive \u2013 repression \u2013 fantasy. It is located in the Pcs and Cs. It encompasses all of what we ordinarily think of psychoanalytic technique: conflict, defenses, transference, the return of the repressed, memory and interpretation. Even primitive defenses such as splitting and projective identification utilize the representational system. It is the act of giving form, of developing linguistic and symbolic forms. The object representation is not just a memory but it also contains the meaning for the subject.\n\nWhat is new in their psychic space is the second axis, the perceptual system. This is drawn from Freud's metaphor of perceptual identity (Freud, 1900) and the unconscious work of representability (what the Botellas translate at figuration). They wish to emphasize that what is nonverbal cannot be understood by the same processes of normal representation. If progression of the sequence of drive to object-representation is blocked, the result is negating of representation, leading to disavowal. In this void, the mind has the capacity for creating the sensation of reality to fulfill a wish with a materialization through an hallucinatory actualization. It is transient, dazzling, and instantaneous. It is what will not go into words. We have a traumatic plunge into the loss of representation and the sudden emergence of hallucinatory phenomena. The Botellas call this the act of figuration. Freud had found in the experience of the uncanny, animistic thinking and the experiences of traumatic neurosis hints of this traumatic loss of inner objects (Freud, 1913a, 1919a, 1933b, 1939). It is ordinarily only found in night-time dreams but will emerge under traumatic conditions. Figurations carry the conviction of having grasped the truth, a hallucinatory experience of continuity projected onto the sensory realm. They are created to banish what is unfamiliar and disturbing. Perception of the object must be disavowed so that belief can be maintained as representation.\n\nIn psychic trauma, there can be a sudden experience of the loss of representation, either because of a lack of internalization or a traumatic rupture of the chain of representations. The trauma cannot be represented and can only be experienced as a negative, a violent and abrupt absence. There is a violent excitement. This is experienced as a negative, a void, an implosion, a psychic death. It completely erases the negative and provides a presence. This zone of non-representation exists at the heart of the psyche.\n\n### Donnel Stern\n\nIf Bion and the Botellas are both revising the basic Freudian canon, d. Stern (1983, 1990, 1997) has more of a radical revision. This goes back to a basic distinction between repression and dissociation. In _Studies on Hysteria_ (1895), Breuer explained anna O's hysteria as two states of consciousness existing side by side while Freud formulated repression, that of erecting a barrier that prevents emergence into consciousness. Traditional psychoanalysis is founded on the defeat of dissociation and the primacy of repression.\n\nEagle (2000) points out the key differences between repression and dissociation. In repression, certain mental contents are excluded from a unified ego or self. The repressed is constantly driven by drive pressure toward consciousness and requires continual repression to maintain unconsciousness \u2013 the return of the repressed. In dissociation, mental contents are split into sections that each are potentially accessible to consciousness.\n\nStern, coming out of the sullivanian tradition, proposes dissociation as a primary defense and the unconscious as the \"natural state of experience\" (1997, p. 85), where experience is outside awareness. Action and effort are then required to bring experience into consciousness. This reverses the Freudian theory of repression as a pressure to force out of consciousness. To make something conscious is to construct the experience in words. Consciousness is not a passive container but an active shaping and representing. What are dissociated, then, is differences in function, between formulated, largely verbal experiences and unformulated murky and poorly defined experience and images. Stern proposes that unformulated experience is the primary matrix of all thinking. Unformulated experience is mentation characterized by lack of clarity and differentiation, familiar chaos. It is experience that has never been articulated enough to enter into defensive operations. To be unconscious is something that is so much present that we live it rather than see it or understand it. Key metaphors include unformulated experience, construction, and dissociation.\n\nAction, an interpretive construction, is necessary for consciousness. The basic metaphor is of seeing, turning our eyes toward. Rather than forcing meaning and risking stereotyping, we let meaning come to us, to just appear directly. Language must be authentic and creative, bringing thoughts alive. The basic defensive process is one of prevention of interpretation in reflective awareness. It is a restriction on the experiences we allow ourselves. Instead of repressed content, we have familiar chaos and the refusal to allow prereflective experience to attain full-bodied meaning. Clinically we look for absences, gaps, contradictions, stereotypes, repetitions, and dead spots. Dissociation is a selective inattention, an avoidance of certain unformulated experiences, so they never reach reflective consciousness.\n\n## **Collisions**\n\nAll of the theorists aim to attack and destroy existing psychoanalytic theory and metaphor, while preserving what they consider pure metaphor. Bion attacks Klein's extension of object relations to birth and her extensive use of the death instinct, while wanting to preserve and enlarge on Freud's later thinking on primary and secondary process. The Botellas attack the Freudian unconscious while preserving and extending Freud's ideas about dream work. Stern attacks Freudian defense and the unconscious while preserving Freud's early work on dissociation and hysteria.\n\nThe most fundamental division among the theorists is the contrast between the model of stern and the models of Bion and the Botellas. Stern's unconscious is nondynamic, a \"natural state of experience,\" having never become conscious. The post-Freudian unconscious remains dynamic, a depository of the repressed or fragmented, what once had been conscious and now excluded from consciousness. For stern, the primary defense is dissociation, a selective including or excluding contents from consciousness. The main action of defense is not seeing, an unconscious shaping of what is allowed into consciousness. The flip side of defense is creativity, the active shaping of unconscious mentation into new and surprising forms. For the post-Freudians, the primary defense is repression, a force preventing the movement from unconscious to conscious. The unconscious is always forcing its way into consciousness and must be continually resisted. Creativity comes from a relaxation and reshaping of the defensive structures.\n\nA second division among the theorists would contrast Bion and stern against the Botellas. Bion, although he retains a Freudian dynamic unconscious, postulates a second non-dynamic unconscious with many similarities to stern. Both are unformulated and require a translation to move toward consciousness. Both nondynamic unconsciouses are filled with experiences and affects of early development, that both must be defended against and potentially provide creativity and life. The Botellas do not have a concept of the non-dynamic unconscious. At the bottom of the dynamic unconscious is the ultimate consequence of repression, non-representation. Non-representation is then covered over by the fash of figurability.\n\n## **Collusions**\n\nAll of the theorists would broadly ft into Modell's model of unconscious metaphoric process (Modell, this volume). In this view, all unconscious thoughts are cognitively organized through the medium of metaphor. Metaphor is crucial in creating more complex and more organized meaning states. The unconscious is not just a repository of repressed instinctual derivatives.\n\nBoth Bion and the Botellas have a dual unconscious. They postulate a psychic space that underlies and forms the dynamic unconscious, a second unconscious. Bion speaks of processing of \u03b2 into \u03b1 elements. The \u03b2 elements represent the concrete source domain and the \u03b1 elements the target domain. The mappings between domains are called links. The Botellas speak of a perceptual axis. The work of figurability is the act of giving form to what is unrepresentable. There is a similar mapping from the unrepresentable to the form of the hallucination.\n\nBoth Bion and the Botellas conceive of spaces of trauma and terror. For Bion, it is the space of \u03b2 elements. He speaks of \"an intense catastrophic emotional explosion\" (Bion, 1995a, p. 14) with immense fear and violence. The explosion results when either the contained blows up the container or the container cannot contain the explosive nature of the contained. This explosion destroys links and the resulting fragments are dispersed into an infinite space. The metaphor is of debris and fragments from the explosion floating in a vast space. For the Botellas, it is the perceptual axis. In the perceptual axis, there is the presence of animistic thinking in which representation, perception and motor activity become equivalent as a continuous universe. Rather than the terror of fragmentation, it is the terror of non-representation, of the metaphor of nothingness. There is a violent and abrupt collapse into nothingness. In the violent excess of excitation and distress, the ego murders the object and its meaning. The shadowy equivalent of the perception has disappeared, and the persecuting perception invades the scene. The metaphor is of a deep and dark hole that is patched out and hidden from view.\n\nBoth Bion and the Botellas talk of hallucinations yet they differ phenomenologically. Bion describes hallucinations among other types of fragmentary experiences. The mental event is transformed into a sense impression. They provide only pleasure or pain and a failure to yield meaning. This is a transformation into a \u03b2 element which can only be evacuated. There is a vicious cycle in which the patient continues to hallucinate to compensate for the missing meaning. Greed increases the hallucinations. Hallucinations are \"a state always present, but overlaid by other phenomena, which screen it\" (Bion, 1995a, p. 36). For the Botellas, the hallucination is a figuration, a defensive operation in which the hallucination is potentially reparative and integrating.\n\nStern and Bion have a concept of dissociation in common. Bion, in the Kleinian tradition, would understand \u03b2 elements as split of fragments, a type of dissociation. Stern enlarges the concept of the non-verbal to include the entire unconscious. He privileges dissociation as a primary mechanism over repression. For both of them, dissociation is the natural condition where the \u03b2 space or the unconscious contain elements that are widely separated and not linked.\n\nBoth Bion and stern are constructionists. The \u03b2 elements have to undergo a construction, what Bion calls \u03b1 process, before they can access consciousness. Stern postulates that all unconscious elements are unformed and undergo a construction to become conscious.\n\nBoth Bion and the Botellas think of this psychic space as containing fragments that cannot enter the dynamic unconscious. Both conceive of these elements as subject to projection. Both think of projection as a mean of communication. Both think of reverie as a receptive state. Yet these elements are quite different. For Bion, \u03b2-elements are a basic sensori-motor level of organization that directly incorporates the traumatic elements. For the Botellas, figuration is a hallucinatory experience that covers over and defends against the loss of representation.\n\nThere is a difference about the direction of psychic movement. For Bion and stern, the movement is forward, originating in the non-verbal unconscious and proceeding forward, achieving greater complexity and symbolization in the process. The movement is toward consciousness. For the Botellas, the movement is regressive and backward. Unacceptable psychic elements are repressed and regress backwards toward the perceptual and the void. In contact with the void, there is a violent and defensive push forward again in the figuration.\n\n## **The Limits of Metaphor**\n\nBorbely (this volume) provides a model of psychoanalytic process that uses metaphor as a basic template for framework language that is relevant for all the psychoanalytic schools. Source and target domains are separated by two dimensions, time and form. Defense, for example, is understood as a temporal metaphor. The defending part is associated with the present time and the defended against is associated with the past time. The repressed then becomes an interpretation of the present based on the past. The second dimension, form, is the domains of metaphor and metonymy. In trauma and neurosis, there is a loss of metaphoricity and replacement with metonymic relationship. This is the movement from abstract to concrete and rigid relationships. The defending part stands for, in a metonymic way, the defended against part.\n\nThis model works well to explain key dimensions in the traditional Freudian unconscious where the linguistic forms of metaphor and metonymy are maintained. In the non-verbal unconscious, there are no such forms. In addition, in a dissociative process such as splitting, there is not a temporal present and past relationship. The split of fragments are both in present time but kept separate. Or one might say they are both in the past but contemporary to each other. Borbely's model of temporal metaphors is a good ft for repressive defenses but not splitting defenses. Wurmser (this volume) suggests an answer. He distinguishes metaphorical processes from metaphor proper. Metaphoric processes are a biological aspect of the brain and a deep principle of the mind: \"processes of cross modal equations.\" Metaphor proper is the verbal and linguistic aspect of this larger process, bound to language and symbol formation. This would imply an inherent and biologically based process of progressive organization of mental functions. Could we think of metaphor proper as only the final stages of a larger process of progressive symbolization and differentiation of mental structures?\n\nBion implies such an organizing principle. \u03b2-elements are unmentalized fragments that have no links to each other or to more organized forms. Bion postulates a separate \u03b1-process, at first in the mother and later internalized, that transforms the \u03b2-elements, at first into more complex \u03b1 elements or pictograms and in a further process, into proto-symbols or metaphors. Bion does not specify how this \u03b1 process might work but it fits well with Loewald in a progress toward linkages and symbolization.\n\nThe Botellas also imply a progressive organizing function of the mind. In the trauma of nonrepresentation and nothingness, the figuration is a binding together into a sensory whole. It erases the negative and provides a presence. Representational thinking is a higher level of organization, arising out of the mirroring and doubling of mother and child. Like Loewald, they see a linking and symmetry of word and think presentation.\n\n## **A Unifying Proposal**\n\nStern asks the question, how can we refuse to spell-out an experience without first having spelled it out? (1997, p. 123). His answer is that the self has a consistent sense of coherence. What is not me is disavowed, not formulated. Yet does not this act of disavowal depend upon the self having some recognition of what is alien and erecting some sort of barrier?4 it is not logically possible for the unconscious to formulate its own barrier. Does this not bring repression and dissociation closer together conceptually? Both would have barriers between the unconscious and conscious. We could postulate different elements, some of which represent excluded conscious contents that retain a linguistic mode, while other elements are unformed and have never risen to full consciousness.\n\nIs there here a possibility of a unified theory of defense? defense could be conceptualized with two basic dimensions. One dimension is force. There is a variable degree of force that maintains access to consciousness of a mental element. The other dimension is separation. There is a variable degree of separation of mental elements as a means to control access to consciousness. Pure repression emphasizes the maximum degree of force to prevent consciousness and a minimum of separation. Pure dissociation emphasizes a maximum of separation and a minimum of force. Freud (1927, 1940c), late in his life, was trying to grapple with such complexities. In his concept of splitting of the ego, he finds an intermediate position between repression and dissociation. Freud's example is castration but we could read these papers as a theory of trauma. Under traumatic danger, there is simultaneously a recognition and a disavowal of the danger. When the danger is recognized, repression occurs; the instinctual pressure is forced out of consciousness. When the danger is disavowed, instinctual pleasure is allowed into consciousness but displaced or separated by placement in a new object, the fetish. Thus, for Freud, there are two types of defense that operate together, repression and displacement, a type of dissociation. Both originate in the ego. I think the Kleinians have come up with a different middle view. Repressive defenses are characteristic of higher level mental operations. More developmentally primitive defensive operations are based on splitting and dissociation. In the Kleinian view, all patients have a mixture of repressive and splitting defenses. There is a greater predominance of splitting in borderline and psychotic personalities.\n\nBion fundamentally changes the idea of splitting. Instead of a primitive defense originating in the ego as a pressure, splitting is a fundamental property of the nondynamic unconscious in which mental content exists as unlinked fragments. Yet there is also a sense of defense in which these unlinked fragments are further separated through evacuation via projective identification.\n\nWhile the Botellas do not directly address Freud's concept of the splitting of the ego, they refer to another type of splitting, that of the two axes of representation and perception, in which animistic and formal thinking exist side by side. Animistic thinking is a kind of dissociation, in which pleasure is allowed to attach to hallucinatory objects.\n\nFreud's concept of splitting also differs from both Bion and stern, for which dissociation is the natural state of the unconscious. Yet Bion and stern also differ in the origin of the dissociation. For Bion, \u03b2-elements are a result of the catastrophe of being born, of dangers that cannot be contained because there is no container. For stern, the mind is also born in a state of dissociation but he lacks the sense of danger. It is just the natural state of the unconscious.\n\n## **Conclusions**\n\n1 I have focused on theoretical metaphor in psychoanalytic theory to illustrate how we can conceive of theory through the eyes of metaphor.\n\n2 Psychoanalytic theory and its theoretical metaphors are born out of an attack and murder of existing theory and the erection of a new pure theory and metaphors.\n\n3 Psychoanalytic practitioners take aspects of pure theory and metaphor, and mix them pragmatically in their clinical work.\n\n4 In the formation of new theoretical metaphor, we can see the use of new metaphor that is thought to be uncontaminated with old meaning and the shaping of existing metaphor into new meanings.\n\n5 In the development of conflicting theory and metaphor, we can see a complex of similarities and differences.\n\n6 Examining such theoretical metaphors may provide insight into unifying concepts. I have given such an example in the differences and unities of splitting and repression.\n\n## **Notes**\n\n originally published in _Psychoanalytic_ _Inquiry_ 31(2): pp. 147\u2013158 with the title \"The non-verbal Unconscious: Collision and Collusion of Metaphor.\"\n\n of course, over time, Bion's Greek letters have become metaphors in themselves. In this paper, I treat his Greek letters as metaphors.\n\n This account of elements and functions is taken from what Ogden (2004a) calls early Bion, up to and including _Learning from Experience,_ where he does not depart significantly from Klein. Only in the later papers (Bion, 1995b) does he move beyond Kleinian theory (symington & symington, 1996).\n\n The Freudian definition of \"disavowal\" would include an active force coming from the ego that pushes the disavowal.\n\n# 8  \nMETAPHOR AND METONYMY  \nAS THE BASIS OF A NEW  \nPSYCHOANALYTIC LANGUAGE\n\n_Antal Borbely_\n\nMetaphors are \"in terms of\" relationships whereas metonymies are \"stands for\" or \"belongs to\" relationships. These relationships are basic on the linguistic, mental, and developmental level. They are therefore suitable for a psychoanalytic framework language capable of uniting the psychoanalytic schools and achieving a rapprochement to those cognitive sciences which already see the mind's functioning as based on metaphor and metonymy. Psychoanalysis with its dialectic between past, present, and future yields a temporal dimension to metaphor: Mentation at one time is understood in terms of mentation at another time\u2014therefore metaphorically (\"in terms of\"). If metaphoric \"in terms of\" flexibility is lost, a metonymic (neurotic) \"stands for\" or \"belongs to\" relationship holds between issues rooted in different times. It is this temporal dimension of metaphor and metonymy which can conceptually bridge the cognitive sciences with psychoanalysis. The main psychodynamic concepts _transference, interpretation,_ and _defense,_ if slightly reformulated, become relevant within and without the treatment setting. They all can be seen as relating issues from different times flexibly (metaphorically) or neurotically (metonymically) with each other. This leads to conceptualizing transference, interpretation, and defense as having two variants: a metaphoric (healthy) and metonymic (neurotic) one. Psychoanalytic theory was burdened by a one-sided focus on clarification at the expense of enigmatization, both being important aspects of metaphor. The enigmatization, not understood in its theoretical centrality, was therefore collectively enacted as a Babel-like confusion between psychoanalytic languages. The central importance of metaphor and metonymy was not theorized.\n\nWhy, after more than a century, are the penetrating insights of psychoanalysis underappreciated\u2014and largely ignored\u2014outside the field? Why isn't psychoanalysis more of a participant in the important discussions about the mind's functioning that have been going on within the cognitive sciences (Barcelona, 2000; Borbely, 2004; sweetser and Fauconnier, 1996; Gibbs 1994, 2008; Kittay, 1987; lakoff and Johnson, 1999)? Finally, why has there been such disagreement among the many competing schools within psychoanalysis about basic terms and concepts (Wallerstein, 2002b)? These questions are not unrelated. They deserve further inquiry.\n\nTo a large degree, psychoanalysis will continue to be a bystander to the great scientific and cultural debates, and psychoanalysts will continue to misunderstand or talk past one another, until a metaphor-based framework language can be formulated that could accommodate the divergent psychoanalytic schools, traditions, and languages. When intelligent, highly educated, and well-trained psychoanalysts find themselves to be adherents of so many divergent schools without being able to account for their choice, we should think of the possibility that we are witnessing a collective enactment of something suppressed. This deserves an inquiry.\n\nBefore I begin my argument, let me make a few obvious points. First, unlike the cognitive sciences, which are primarily focused on understanding the mind's normal functioning, psychoanalysis was developed as a way of understanding psychopathology. Although there was originally an expectation that psychoanalysis could serve as a basis for a general personality theory, the main psychodynamic concepts\u2014namely, transference, defense, and interpretation\u2014remained almost exclusively connected with what occurred in the therapeutic setting. Even today, these terms generally do not apply to the individual outside the consulting room.\n\nSeeing temporality, metaphor (Wurmser, 1977), and metonymy as central to all psychodynamic notions (Borbely, 2008, 2009) allows us, as we shall see, to comprehend transference, interpretation, and defense deeper, namely in their intrinsic, rather than only in their extrinsic, functional, relatedness. The fact that in psychoanalytic theories, the main psychodynamic concepts remained only extrinsically related to each other is, in my opinion, the main reason for the stagnation of psychoanalytic theory and for the splitting of psychoanalysis into different schools, as well as for the isolation of psychoanalysis from other cognitive sciences. Psychoanalysis, freed from such stagnation, could and should take its rightful place among the \"sciences of surprise\" (Casti, 1995, p. 15): theories of creativity, chaos, fractals, and complexity.\n\n## **Metaphor and Metonymy**\n\nTo begin, let me be clear about terminology. Metaphor is defined (Ricoeur, 1986) as seeing or understanding one thing _(the target)_ in terms of something else _(the source)._ in \"Juliet is the sun,\" the two objects or ideas that are being related belong to different semantic domains, namely the domain of human beings and the domain of celestial bodies. A nonlinear\u2014that is a complex, nonadditive, evocative, open-ended\u2014relationship exists between source and target located in these different domains.\n\nAnother noteworthy fact about metaphor: it is sensitive to the context in which it occurs (stern, 2000). For example, when Romeo exclaims, \"Juliet is the sun,\" we understand his meaning: as a lovesick young man he considers Juliet of supreme importance. If we were to consider the same statement in a different context\u2014say, as a remark made by a member of the Montague family\u2014it might have a more sinister quality. In that case, we might be invited to see Juliet as the sun that is blinding Romeo, making him unable to assess the danger he is in.\n\nMetaphor entails some features that are especially relevant for psychoanalysis and are labeled by us as _psychodynamics._ For the remainder of this article, I propose to focus among psychodynamic terms on the three important notions: _transference, interpretation,_ and _defense._ The connection between psychodynamics, metaphor, and metonymy is, at first, not easy to understand, but will later become clearer. Metaphor entails interpretation because the source interprets the target: in \"life is a journey,\" _journey_ interprets _life._ one aspect of such interpretation is what could be called transference, in the sense of the source transferring selectively, attributes to the target: in \"Juliet is the sun,\" some attributes of the sun get transferred; others concealed. The source, the sun, not only interprets the target, Juliet, but endows it with new attributes and, thus, changes its meaning. We can thus talk of a mutative interpretation. Another of metaphor's features can be called _tension_ or _defense:_ Metaphor invites us (Ricoeur, 1987) to consider a new mental organization of source and target remaining in tension with the previous organization of source and target. Metaphor thus also entails memory. The target, now understood in a temporal way as this new organization (of source and target), defends itself against undue intrusion by the source, now understood as the previous and subsequently transgressed organization. Trough the remembrance of these mental organizations, narrative coherence can be maintained. Consider the following example: When Freud metaphorized hitherto independently understood concepts such as motivation and the unconscious by proposing to understand one in terms of the other, the newly suggested organization of the two concepts, namely \"unconscious motivation,\" remained in temporal metaphoric tension with the familiar one. Because of this tension, a new metaphor in science can be both interesting and controversial. The new organization _defends itself_ against the old one by holding the latter in abeyance; the old one _defends itself_ against the new one by trying to maintain its staying power through an appeal to familiarity.\n\nTo summarize, metaphor entails, among many others features, the psychodynamic concepts interpretation, transference, and defense. We will later see the surprising fact that interpretation, transference, and defense are not only features of metaphor but have themselves a metaphoric structure. The point here is that the two concepts \"metaphor\" and \"psychodynamics\" can be metaphorized: one is seen in terms of the other.\n\nIn a metonymy, the name of one object or idea (the source) stands for or belongs to another (the target). We ask, \"have you read the latest philip roth?,\" thereby equating the writer with his work. We use the term \"the White House\" as a stand-in for United states policy, and the term \"the Crown\" for the person of the English king or queen. In a metonymy, unlike a metaphor, both the source and the target are seen as located in the same domain. Unlike metaphor, a metonymy expresses a linear relationship\u2014direct, one-to-one, literal, and closed\u2014between the source and the target.\n\nIn summary, we can say that metaphor articulates _in-terms-of_ relationships, where source, target, and context change relative to one another; whereas metonymy articulates _stands-for_ or _belongs-to_ relationships. The former could be likened to a storyline's plot, the latter to one of its scenarios. Obviously, plot and scenario are specific viewpoints focusing on transfiguration versus configuration of narrative elements. The narrative process is, itself, as we shall see, a metaphoric process. Such a process reassigns in an ongoing way what should be seen as part of a metonymic configuration, thus belonging to each other, and what as part of a metaphoric transfiguration, thus interacting with each other.\n\nA further point has to be made to understand the functioning of metaphor in health and of metonymy in neurosis. Metonymy, as used by linguists, gives access to something that belongs to it or for which it stands (Langacker, 1993). Consider, for example, the phrase: \"They went out for a drink.\" This phrase gives access to many other possible but not articulated phrases such as, \"They went to a bar,\" \"They had a good time.\" Thus, linguistically speaking, in metonymy one mental entity gives access to another mental entity.\n\nFor psychoanalysis, I introduced the concept of _negative metonymy_ (Borbely, 2004) to describe what happens when access to a mental entity is not given but barred, as in a neurotic defense. The defending mental entity (e.g., \"I love my brother so much!\") stands for a defended-against mental entity (\"I hate him also quite a bit!\") to which access is barred. This relationship is linear and rigid and has a _belongs-to,_ metonymic, quality. For the remainder of this article, unless otherwise noted, _metonymy_ will be used to mean negative metonymy.\n\n## **The Psychoanalytic Process as Metaphoric Process**\n\nAlthough there are substantial theoretical disagreements among psychoanalytic schools, most analysts of divergent persuasions would agree today that all schools attempt to and, in general, succeed in establishing a psychoanalytic process with their analysands. Given this consensus, we have to assume that the different schools are closer to each other in their practice than in their theories. Accordingly, as we search for a framework language within which to discuss the various theoretical conceptualizations and traditions, it is best to start with examining common elements within psychoanalytic practice.\n\nEarlier, we defined the linguistic concept of metaphor as seeing, understanding, or mutatively interpreting something in one semantic domain in terms of something in another domain. Temporality is not a central issue here. But because psychoanalytic practice aims at increasing awareness in an ongoing way, a process that entails the fundamental notion of temporality, we must expand the linguistic to a psychoanalytic _temporal metaphor_ concept. Temporality (Borbely, 1987) now becomes central within this metaphor concept as a reflection of the mind's changing in the course of time.\n\nThe psychoanalytic temporal metaphor concept relates to the linguistic one in the following way: linguistically, as just mentioned, the purpose of metaphor is to see something, understand something, or mutatively interpret something in terms of something else. Psychoanalytically, _in terms of something else_ becomes _in terms of another time._ in the enacted transference, the present is understood in terms of the past and in the interpreted transference the past is understood in terms of the present. An analysand misses a session, having overslept. The analyst's thoughts, guided by the present transference picture, move to the analysand's earlier experiences in life or in the analysis to find a possible hint for why the analysand's absence occurred. A specific problematic event in the present is, in principle, understood in terms of previous, now unconsciously reenacted, experiences. At the same time, such a present enactment can lead to new material from the past. For example, if the analysand were to experience a present vacation-related interruption of the analysis as abandonment, the analyst, drawing attention to this transference enactment, may gain access to childhood abandonment experiences, which can now be interpreted for the first time from an adult perspective.\n\nIt may turn out, for example, that what was originally experienced as abandonment was a separation due to a parent's illness. In both these just mentioned cases, the analyst will try to establish a metaphoric in-terms-of relationship between an experience in the past now resonating with an experience in the present. The aim is to overcome a sterile metonymic repetition in which the past cannot inform the present in a way that is sensitive to the new context.\n\nMetaphor as principle, structure, and process underlies the mind's functioning. Metaphoric processes, in an ongoing way, reinterpret and change one's self and one's world (Bruner, 1987). Given the discussion so far, attempts to integrate the concept of temporal metaphor with psycho- dynamic concepts of the mind are of obvious importance. Today, metaphor is also researched as an important principle, structure, and process not only of the mind, but also on the level of the brain's neuronal functioning (see Lakoff, 2008).\n\n### A Temporal View of Interpretation, Transference, and Defense\n\nTo integrate psychoanalysis and the theory of metaphor and metonymy, it is necessary to show that the main psychoanalytic dynamic concepts, namely transference, interpretation, and defense, actively structure the relationship between time domains\u2014either in a metaphoric way in the case of health, or in a metonymic way in the case of neurosis.\n\nLet us look at a temporal view of interpretation: in the case of health, where present and past can recursively reach each other, an interpretation is metaphorically mutative; in neurosis, where present and past are unable to communicate, an individual's self-interpretation becomes metonymic, nonmutative, and repetitious, and is in need of the analyst's interpretation.\n\nLet us look at a temporal view of defense: according to the classic theory of defense, defending and that which is defended against are seen as discretely opposed entities assignable to the specific agencies ego, id, and superego. Yet, such a nontemporal assignment runs into logical and clinical diffculties: What serves a defending function at one moment can be defended against in the next; and what was defended against can likewise assume the role of defender. Therefore, no matter how ego, id, and superego are defined, they can be found simultaneously on the side of defending as well as defended against mentation. Only a temporal, as opposed to a content- or function-related, view can help to differentiate between defending and defended: We can assign the defending to the present domain and the defended to a past domain. It is, after all, something that happened in the past that evokes a defending in the present so as to avoid anxiety.\n\nThis temporal view of defending and defended can accommodate clinical observations where passions like perversions defend against guilt-laden phantasies. In the received, logically and clinically flawed, parlance, this would amount to the id defending against the ego and the superego.\n\nAssertions regarding the superiority of drive theory, object-relations theory, intersubjective theories, and others, are closely connected to how the relationship between defending and defended parts of the mind are understood. A concept of defense based on temporality allows us to put aside the sterile discussions whether thoughts defend against drives or whether relationships in the here and now defend against relationships of the then and there, etc. Drives, object relations, intersubjective relations, self-objects, part-objects, are aspects of the simultaneously occurring defending as well as the defended parts of mentation, and there is, therefore, no need to play one theory out against the others. What is now relevant relates metaphorically or metonymically to what was then relevant, whatever we call it. In summary, the structure of the neurotic defense (the relationship between the defending and the defended-against aspects of defense) is a metonymic one; the structure of the healthy defense is a metaphoric one.\n\nThe point I am making here for psychoanalysis and, therefore, for the mind's temporal functioning, is this: in the optimal functioning or healthy mind, experiences have to be reinterpretable with the changing context of an individual's personal narrative. Experiences can be reinterpreted if they have been integrated in a context-sensitive, that is, a healthy way. Such integration means that the present experience can be seen metaphorically in terms of previous experiences, and the meanings of these previous experiences change in terms of the new experience (Johnson, 1987). The new experience interprets the old one, updating it and changing it so that it can become a meaningful precursor for the ever-changing narrative.\n\nAlthough psychoanalysis cannot change a person's past as it occurred, it can and must change the effects the past has on the present. The past continues to mutatively interpret the present. As indicated, we can assume that such mutative change between different time domains occurs quite naturally, and mainly unconsciously, also in life outside any treatment setting. Therefore, our psychodynamic concepts, once temporally redefined, can be used to describe neurotic, as well as healthy, functioning in and outside the treatment setting.\n\nWhen the mind functions optimally, present and past relate to each other bidirectionally, both forward and backward, like the source and the target in a metaphor (Borbely, 1998). In health, with the passing of time, one time domain changes its view of the other, and by informing the other of such a change, changes the other. This bidirectional, nonlinear dialogic relationship is also characteristic of the analytic situation in which the past and present are interpreted metaphorically in terms of one another and where, based on metaphor, \"the interpenetration of all systems of experience\" can occur (Coburn, 2002, p. 657).\n\nPsychological trauma leads to an overly concrete way of experiencing. It leads to a loss of context sensitivity and, with it, to an isolation of the traumatic experience from the context-sensitive, ever-changing, mainstream of narrative processes. After a traumatic experience, a new experience, touching on issues sequestered by trauma, cannot be interpreted in terms of the traumatic one (that is, it cannot be interpreted metaphorically). The sequestered experience metanymically determines (rather than metaphorically informs) the present by rigidly inducing a defense in order to avoid unbearable anxiety.\n\nFor example, an authority figure elicits fear for a young man not only in the context of the original experience in which he was abused by his father, but for all contexts involving authority figures. The structure of the relationship between the defending mentation, namely the fear of authority, and the defended-against mentation, namely the fear of the abusive father, has become metonymic. In other words, the fear of authority relates in a rigid, linear way to a target as yet unknown. Even though it is unknown\u2014in the sense that the man does not have conscious access to it\u2014such a target exerts its power by rigidly evoking a specific defense in the present. By falsely locating the source of anxiety in the present, rather than in the past, the past cannot inform and be integrated with the present and the future. As a result, the man's ability to comprehend the present is impaired, and his creative potential in the here and now is diminished. Thus he is said to be neurotic, or, put differently, time-confused.\n\n### The Metaphoric Process as Equivalence in Motion\n\nTo orient itself, the infant's and adult's mind has to be able to establish metaphoric and positive metonymic equivalences. This occurs within a supraordinate metaphoric _currency_ (Modell, 1997b) of meaningfulness across myriads of dimensions, so that concepts, sensations, categories, values, identities, needs, and plans become commensurable and, thus, translatable into one another regarding their narrative meaning. The metaphoric process is the making of new meaning (hausman, 1984, p. 92). It establishes a hitherto unknown equivalence in form of a meaningful anticipation. It is the currency within which changing mental organizations can be negotiated. As already mentioned, the metaphoric process reassigns, at each moment, which among the mental entities should be seen as relating in an in-terms-of and which in a belongs-to or stands-for relationship.\n\nLet us look at some such meaningful equivalencies across different sensory registers. For the infant, mother's soothing voice in the domain of sound is the same and not the same as her tender stroking in the domain of touching. Can these cross-modal sensations be understood metonymically as standing for something, for example, as two forms of satisfying a need? or are they to be understood metaphorically, in terms of something else, for example in terms of mother's mood at the moment? does mother's smile metonymically stand for her approval of the infant's behavior, or does it have to be seen metaphorically, in terms of something else going on in the mother? like the poet, the young child, to borrow a phrase from R. Posner (1982), \"makes use of non-precoded properties of language\" or observations (p. Ix).\n\nImmaturity or trauma can cause confusion regarding the metaphoric or metonymic connection between mental entities or relationships. The infant's immature mind might see the bottle metonymically as an extension, or stand-in, for the mother's breast. The child who has been beaten by the father may, from then on, see father\u2014and future authority figures\u2014almost exclusively as an authority to be feared. Father's metaphorical meanings in terms of a role model, a friend, a caregiver, or a loved-one subject to moods cannot any more be fully experienced. Both immaturity and trauma can degrade a potentially metaphoric integrative experience to a metonymic concrete one.\n\nThe fundamental importance of metaphor for understanding the mind's functioning cannot be overstressed, even though here we can only highlight a few further points. Metaphor, unlike metonymy, creates new categories that allow for learning, maturational change and innovation. Metaphor integrates the old with the new by bringing memory and anticipation into the here and now. Accordingly, it has aspects of both succession and simultaneity (Vrobel et al., 2008) and can move from discursiveness to image (Langer, 1957).\n\nConsider a situation in which the analyst is seen in a metonymical form of transference as an authority figure to be feared. Once interpreted metaphorically, the analyst can again be experienced as the coinquirer into the analysand's way of functioning; as a result, the analysand can become more creative and able to relate to the present more realistically, rather than to live in a pseudo-present filled with unrecognized ghosts of the past.\n\nBy showing how trauma can cause an event to be experienced metonymically, transference interpretation thus allows for the possibility of upgrading such experiencing to a metaphoric integration with its open-endedness and enigmatic resilience. It can bring together the relevant elements of different times into the simultaneity of a now (Vrobel, 2006), from which past, present, and future can be recast. Interpretation as curing means metaphorization of lost or lacking metaphoricity.\n\nThe metaphoric process is comparable to a tune connecting antecedent and subsequent. It is our ability to connect the memory of the preceding note, which still lingers on in our consciousness of the present, with the note we anticipate to follow it. This ability enables us to perceive a meaningful entity, a tune, as opposed to a succession of uncorrelated, isolated notes. Therefore, we must assume the now to be extended \"in order to host retention and protention\" (Vrobel et al., 2008, p. 5). The metaphoric process is the basis for narrative coherence regarding memory and anticipation.\n\n### Summary of the Expanded and Temporal Definition of Transference, Interpretation, and Defense\n\nTo accomplish the integration of psychodynamics with metaphor theory as so far outlined, the notions transference, interpretation, and defense have to be conceived in a somewhat broader but also simpler way. Seeing transference, interpretation, and defense as corresponding to their temporal metaphoric or metonymic structure can accomplish the three goals mentioned at the beginning of this discussion: to find a framework language through which divergent psychoanalytic schools can express themselves and communicate with each other; to bridge the gap between psychoanalysis and other cognitive sciences where there is an increasing consensus that the mind (and possibly the brain) functions metaphorically and metonymically; and that the basic psycho-dynamic concepts become equally useful to describe the neurotic and the non-neurotic aspects of the mind's functioning.\n\nLet us start with the expanded definition of _transference:_ all influences originating in the past and targeting the present will be seen as aspects of transference. There are three aspects of transference in this broader sense: (a) transference in the narrower, received sense; (b) the defended-against mentation; and, (c) the return-of-the-repressed mentation. These three aspects are, according to this redefinition, synonyms referring to transference in a specific clinical context.\n\nWe continue now with a broader definition of _interpretation:_ all influences originating in the present and targeting the past will be seen as aspects of interpretation. The three aspects of interpretation in this broader sense are: (a) interpretation in the narrow, received sense; (b) the defending mentation; and (c) the mentation holding the past in abeyance. These three aspects are, according to this redefinition, synonyms referring to interpretation in a specific clinical context.\n\nSince the direction of influence differs between transference in the broad sense and interpretation in the broad sense, we can construct temporally bidirectional pairings of above synonymous aspects. We get the following equivalences: _interpretation of transference_ is equivalent with _defending against the defended_ and with _holding in abeyance against the return of the repressed._ The pair _defending and defended against_ can be called _defense complex_ or, briefly, _defense._ We now come to the following important and clarifying formulation: \"Defense is the interpretation of transference.\" This formulation, with its temporal and metaphoric\/metonymic implications allows for a recasting of frozen parts of psychoanalytic theory in order to achieve the goals just mentioned.\n\nThe phrase _interpretation of transference_ is familiar to us from our practice, where it is one of the ways we try to promote insight. Seeing interpretation of transference as synonymous with _defending and defended against_ allows us to understand that the analyst's interpreting the transference is aimed at the change of a neurotic into a healthy form of defense.\n\nIn the example described earlier, concerning the analysand who was abused by his father, the analyst's interpretation is the transfiguration of a metonymically structured defense into a metaphorically structured one. Put differently, it is a remetaphorization of a trauma-based loss of metaphoricity. At first, the analysand experienced the neurotic part of the transference metonymically: he regarded the analyst as a childhood figure without the awareness that the tension between present and past had collapsed from two temporal domains into one. We recall here that, in linguistics, metonymy is defined as articulating a source and target within the same domain.\n\nWe have described the neurotic and healthy variants of transference, interpretation, and defense. As already indicated, we postulate that at any time the mind functions, in the main unconsciously, by interpreting its transferences such that the present and past maintain the metaphoric tension allowing for mutual and mutative interpretations.\n\n## **The Enduring Enigma of the Sphinx**\n\nThe process of metaphorization occurs not only within the changing mind but also within theory development. At one time, Freud metaphorized such hither to dualistically understood psychological concepts as motivation versus sexuality, motivation versus unconscious processes, personality development versus sexual development, remembering versus enacting, and many others, by seeing them in terms of each other. He discovered the intrinsic relationship between these hitherto only extrinsically related notions. His most famous metaphorization was the Oedipus complex, in which the triangular relationships between father, mother and child were seen in terms of passions conceived as incestuous sexuality and aggression.\n\nOedipus, according to the Greek legend, solved the riddle presented by the sphinx, which had caused such devastation for the population of Thebes. But in doing so, Oedipus bypassed the enigma contained in what we could call the sphinx complex: how was the sphinx able to tempt so many young men to their death? Why did these would-be heroes perish after not understanding something of great importance, which, as it turned out, had to do with the notion of the life cycle of childhood, adulthood, and old age? What kind of creature or event was half male, half female; half human, half animal? What was the function of the Sphinx's gravity defying wings? Why did the sphinx need to kill herself when Oedipus uncovered her secret? What was the great danger and great promise all about? (see Roheim, 1934, regarding the sphinx as representing the primal scene.)\n\nOedipus had to enact what he did not understand. He made the prophecy of filial rage and lust come to pass by killing his father and marrying his mother. When the truth was revealed, his mother, like the sphinx, killed herself. His unbearable guilt about having availed himself of mother's secret ended in self punishment through blinding himself. What one cannot metaphorize one has to enact, as is well known from clinical experience where enactments are observed when metonymic transferences remain without adequate metaphoric interpretation.\n\nIt was Freud's genius that solved the Sphinx's enigma by conceptualizing the Oedipus complex. What Oedipus understood too concretely, Freud was able to metaphorize. This is what the analyst does when interpreting. Metaphorizing means to make something more interesting by clarifying it while illuminating the ensuing enigma. But metaphorization needs to be kept up lest it becomes metonymic both clinically and theoretically.\n\nIn view of the puzzling existence of so many divergent psychoanalytic schools, we can now ask: What was it, in analogy to Oedipus, which Freud and his disciples were enacting and thus remained unaware of? it was building theory only on the level of metaphoric clarification\u2014and leaving out the crucial second step of metaphorization, namely enigmatization. Clarification without metaphoric enigmatization leads to dichotomies, thus reducing the flexibility of even the most creative concepts. As a result of this shortcoming, psychoanalytic theory became increasingly metonymic, filled with hard-to-resolve dichotomies resisting metaphorization. I am defining dichotomies as pairs of concepts that oppose or exclude each other and are left without mediation. This can be remedied by suffusing psychoanalytic theory with metaphor theory.\n\n### _**Psychoanalytic Schools and Their Pitfalls of Dichotomous Thinking**_\n\nMetaphor mediates between two separate entities, and thus can be used as an antidote to dichotomies. The concepts _primary process_ and _secondary process_ can serve as an example. Mediation between these exclusionary processes is achieved with the concept _metaphoric process._ The metaphoric process, like the primary process, entails displacements and condensations of meaning and, like the secondary process, is reality-oriented. The metaphoric process, neither fully irrational nor fully rational, can be said to represent imaginative rationality. As such, it is a process occurring between the edge of chaos and the edge of stagnation. It is the creative self-organizing process that occurs on a daily basis in parts of the mind that are not neurotically impaired. Metaphorizing has to be an ongoing process in order for the mind not to become metonymic.\n\nThe theories developed by the different psychoanalytic schools, having remained insuffciently metaphorized, are therefore burdened with a multitude of dichotomies. Starting with Freud and the orthodox Freudians, we encounter the following dichotomies, most of which we have only touched upon: The just mentioned primary versus secondary process was not mediated by conceptualizing a metaphoric process; psychodynamic concepts solely pertaining versus not solely pertaining to the treatment setting remained not mediated by a theory where the interplay of transference, interpretation, and defense is seen as occurring in and outside the treatment setting; defense versus defended against was not mediated by a theory of their metaphoric or metonymic relationship; transference versus interpretation versus defense were seen in their external, functional relationship and remained not mediated through a theory of their being congruent with each other as temporal metaphors; interpretation of transference versus defending against the defended was not mediated by a theory of their being synonymous; the concepts conscious versus unconscious were not mediated through a concept of awareness that could include both.\n\nThe Jungians, perhaps sensing the dichotomy of acceptable rationality versus unacceptable irrationality, developed theories trying to integrate enigmatic aspects of life. The Kleinians sensed, perhaps, the lack of an elaborated temporal theory as they developed a theory of successive paranoid and depressive positions, where patterns of organization rather than specific contents are emphasized as relevant for the interplay between developmental and transferential issues. The Kohutians sensed, perhaps, the dichotomy of drive-based motivation versus motivation resulting from interpersonal influences and, with it, the absence of a theory mediating self-interpretation and other-interpretation\u2014the analyst's or the parents'. They developed a theory integrating the influence of the parents' and the analysts' quality of empathy with the child\/analysand.\n\nAll psychoanalytic schools use their own metaphor language to connect transferential and developmental phenomena by seeing them as mutually illuminating. Each school, in its own way, brings the present transferential issues into metaphoric alignment with issues of the past, understanding one in terms of the other.\n\n## **Review and Outlook**\n\nAlthough psychoanalytic practice deals with temporality and metaphor in a mainly implicit but central manner, the psychoanalytic theories do not thematize temporality and metaphor as central notions. There are several reasons for this lag in theory: Metaphor, because of its open-endedness and its enigmatic vagueness (Tuggy, 1993), was not seen as a serious scientific subject; interpretation, an aspect of metaphor, was not seen as metaphorization of lost metaphoricity and, therefore, as both clarification and enigmatization: making something interesting, rather than being limited to solving a problem. The psychoanalytic process was not seen as a special case of ubiquitously occurring metaphoric processes in the mind. The dialogic recursivity between the present and the past time domains was not suficiently theorized. The psychodynamic concepts of transference, interpretation, and defense were, therefore, not understood as temporal metaphoric ones, and, in the case of neurosis, as temporal metonymic ones. The complexity theories' notions of nonlinearity and disequilibrium (prigogine, 1997)\u2014important aspects of metaphor\u2014were not known as essential attributes of the mind's functioning and were replaced by stifling notions of linearity and equilibrium. The notion of emergence, so important in the theory of metaphor and the developing theory of complexity, was, to some extent, thematized by psychoanalytic theory as the return of the repressed, as becoming conscious, and as getting in-touch with heretofore not integrated dynamics.\n\nMost important, transference was not generalized to mean the mutative interpretation of the present by the past and interpretation as the mutative interpretation of the past by the present. Transference, interpretation, and defense were, therefore, understood only in their extrinsic relationships. The notion of a defense complex with the two components of defending and defended was not theorized suffciently, and their relationship as source and target of a metaphor or metonymy remained unexplored. The psychodynamic pairing of these temporally bidirectional concepts, namely interpretation and transference on the one hand and defense as defending and defended against on the other hand, were not seen in their congruence. The important formula revealing the intrinsic connections between the main psychodynamic concepts, namely that _defense is the interpretation of transference,_ was not discovered. Interpretation of transference was conceptualized only as one of the analyst's activities, rather than as the mind's ubiquitous, mainly unconscious, and ongoing process in or outside any treatment setting. Accordingly, the extension of all psychodynamic concepts as relevant to the mind's general functioning, in or outside the treatment setting, could not occur because the psychoanalytic process was not seen as a special case of the mind's metaphoric processes.\n\nTo repeat, these theoretical shortcomings were the consequence of overlooking temporality and metaphoricity as the most central, albeit implicit, notions of psychoanalytic practice. The concept _metaphoric process_ remained unknown and thus could not forestall the sterile, metonymic dichotomies that became entrenched in psychoanalytic theories. Charismatic psychoanalysts, sensing the impediments of unacceptable dichotomies but not understanding their source, tried to overcome the problem by creating new theories, new languages, and new dichotomies. Many of these nonmetaphorically conceived theories had, nevertheless, staying power because they were still capable of grasping the metonymic, repetitive, neurotic aspects of the mind's functioning. Repetition was thematized, creativity (metaphor!) as a central concept of personality theory remained neglected.\n\nAs we contemplate, based on this discussion, the puzzling existence of divergent psychoanalytic schools, we should resist the following two suggestions advanced by contemporary theoreticians (Wallerstein, 2005) for solving this problem: We are asked to either research what these schools' theories have in common and hope for a diminishing divergence between them over time or find an ecumenical way of agreeing to disagree and see the burgeoning number of schools as a sign of vitality with which psychoanalytic theory advances. In both cases we would clarify, like Oedipus, a riddle but continue, like Oedipus, to enact confusion, instead of getting interested in the enigma of metaphorizing. Such enactment would further increase the distance to the cognitive sciences in general and to the unfolding complexity theory of the mind in particular. The latter, as well as the neural theory of metaphor, now in early formation (Lakoff, 2008) could be greatly advanced by introducing metaphor- and metonymy-based psychoanalytic notions.\n\n# 9  \nMETAPHOR AND  \nPSYCHODYNAMIC RESEARCH\n\n_Robert F. Bornstein and Nikaya Becker-Matero_\n\nIn recent decades psychoanalysts have examined the role of metaphor in psychodynamic theory and therapy, but the uses of metaphor in psychoanalytic research have received only modest attention. After briefly reviewing extant psychoanalytic writings on metaphor, we discuss how research from outside psychoanalysis (i.e., studies of embodied affect-space links, mental images and prototypes, and associative networks) can inform us about the nature of metaphor. We then explore the ways that metaphor deepens our understanding of psychodynamic research and its implications, focusing on metaphoric definitions of concepts, and the metaphoric features of experimental manipulations and outcome assessments. Implications of a metaphoric perspective for the empirical testing of psychoanalytic concepts are discussed, and future directions for exploration in this area are described.\n\nMetaphor has been defined as \"the mapping of one conceptual domain onto a dissimilar conceptual domain... resulting in a transfer of meaning from one to the other\" (Modell, 1997b, p. 106). As Lakoff and Johnson (1980a) noted, metaphor is not merely a rhetorical device, but a fundamental way of thinking and understanding. Metaphoric concepts connect ostensibly separate aspects of human experience, linking body and mind, emotion and memory, past and present, unconscious and conscious. Our ability to interact and communicate effectively with others depends upon a shared metaphoric understanding of ourselves and the world; intersubjectivity is inextricably grounded in metaphor. Formal definitions notwithstanding, perhaps the most useful conceptualization of metaphor is itself metaphoric: Metaphor is the glue that links disparate aspects of human mental life, over time and across different contexts, enabling us to construct cohesive personal narratives that give meaning to past and present experience.\n\nAlthough the concept of metaphor is rooted in linguistics, in recent decades psychoanalysts have noted the central role that metaphor plays in psychoanalytic theory and therapy (Borbely, 2009; Gargiulo, 2006; Katz, 2011b). Metaphor helps unify disparate psychoanalytic perspectives (e.g., drive theory, object relations theory, self psychology) and illuminates common elements of different models. Analysts have begun to explore the ways in which metaphor may be a useful tool for embedding psychoanalysis in a broader epistemological context as well, making explicit connections between psychoanalysis and other areas of inquiry (e.g., levin, 2009; Modell, 2005). In this respect metaphor has the potential to bridge the divide between psychoanalysis and other perspectives on personality (e.g., cognitive, humanistic), other areas of psychology (e.g., developmental, social), and fields outside psychology (e.g., art, physics).\n\nOne issue that has received only modest attention from analytic writers is the role of metaphor in psychoanalytic research\u2014the ways in which metaphor may help researchers test psychoanalytic hypotheses empirically, and utilize research findings from outside psychoanalysis to enhance psychoanalytic theory and therapy. This paper seeks to fill that gap by examining the role of metaphor in research, to facilitate meaningful dialogue in this area. After briefly reviewing extant psychoanalytic writings on metaphor, we address two issues in detail: 1) how research from outside psychoanalysis can inform us about the nature of metaphor; and 2) how metaphor can deepen our understanding of psychodynamic research and its implications.\n\n## **Theory, Process, and Treatment Dynamics: The Tree Prongs of Psychoanalytic Metaphor**\n\nFreud often relied on metaphor to describe psychoanalytic constructs and make esoteric concepts accessible to the reader. As Wachtel (2003) pointed out, many of these metaphors involved spatial and military imagery, sometimes in combination (e.g., Freud's [1923a\/1961] likening of fixation and regression to an army advancing through territories but leaving behind contingents of troops at various points along the way). For the most part metaphoric concepts have been applied in three domains of psychoanalysis: theory and metatheory, psychological process, and therapist\u2013 patient interaction.\n\n## **Theory and Metatheory**\n\nA diverse array of psychoanalytic constructs (e.g., psychic energy, displacement, preconscious, repression, libido) are fundamentally metaphoric. As Wurmser (1977) noted, this situation is not unique to psychoanalysis: novel concepts from various disciplines often emerge first in metaphoric form, eventually acquiring fixed labels as they become more widely accepted. Resistance to acknowledging the metaphoric underpinnings of psychoanalytic concepts can have myriad negative effects, however, leading to \"the error of misplaced concreteness\" (Gargiulo, 1998, p. 416) wherein metaphoric concepts are reified and treated as immutable entities rather than descriptive labels.\n\nMetaphor also plays an important role in psychoanalytic metatheory. Every major school of psychoanalytic thought (e.g., drive theory, self psychology, object relations theory) is identified by a metaphoric label which reflects the core assumptions characterizing that model (e.g., behavior as shaped by instinctual drives, mind-as-map, psyche as mental representations of self and significant figures). In some respects the evolution of psychoanalytic metatheory during the past 100 years has been a search for the ideal metaphor to capture in a single word or phrase all the key elements of intrapsychic functioning and interpersonal dynamics.\n\n## **Psychological Process**\n\nMetaphoric concepts have helped shape psychoanalysts' understanding of a broad spectrum of psychological processes, being applied most prominently to trauma, symbolization, memory reconstruction, and the dynamics of emotional memories. In this context, Modell (1997b, 2005) delineated the ways in which metaphoric processes help categorize and map emotional experience, providing structure and agency during periods of intense or overwhelming affect. Consistent with Modell's view, stern (2009) noted that dissociation occurs when this process fails, and memories of traumatic experiences are not infused with metaphor. As a result traumatic experiences become isolated and compartmentalized, and cannot take on new meaning: The patient is unable to apply new experiences to gain a more nuanced understanding of the traumatic event. As trauma gradually comes to be seen through a metaphoric lens, the patient can begin to experience the traumatic event as part of an evolving life narrative, linking the traumatic experience to aspects of the self and facilitating a therapeutic shift from knowing to feeling.\n\n## **Therapist\u2013Patient Interaction**\n\nSeventy years ago sharpe (1940) conceptualized free association\u2014the grist of the psychoanalytic mill\u2014as a metaphoric process in which preverbal events are expressed through speech. More recently Arlow (1979) suggested that psychoanalytic treatment _in toto_ is inherently metaphoric: The patient provides the analyst a metaphoric expression of unconscious fantasy, and the analyst engages the patient by adopting the perspective that the patient's metaphor requires. Consistent with Arlow's view, Ogden (1997) noted that a central curative element (or \"common factor\") in many psychodynamic interventions is that they help the patient replace concrete language with metaphorical dialogue.\n\nMetaphor not only provides the essential language of psychoanalytic process, but plays a key role in shaping transference by functioning as a \"pattern detector so that the meaning of an old relationship is unconsciously transferred into the here and now\" (Modell, 2005, p. 526). Borbely (1998, p. 933) captured nicely the central role of metaphor in these aspects of therapist\u2013patient interaction, noting that \"In order to be able to help the analyst must be in possession of a theory and technique of metaphor language, which is capable of conceptually encompassing the salient developmental stages, traumata and conflicts of childhood, as well as the events unfolding in the transference.\" in this respect different psychoanalytic schools may differ in the details, but they share a common goal of conceptualizing (and helping the patient conceptualize) psychological development, conflict, striving, and defense in metaphoric terms.\n\n## **How Research Informs Metaphor: Reifying the Unobservable**\n\nIn recent years psychodynamic theorists have used research findings from outside psychoanalysis to explore the ways that metaphor can enhance our understanding of a broad array of psychoanalytic concepts. The most widely discussed links involve neuropsychology, wherein research on brain structure and function has elucidated the biological underpinnings of unconscious mental processes, helped trace the evolutionary roots of human behavioral predispositions, and been used to examine the interplay of neuropsychological, social, and cultural influences on affective experience and emotional responding (e.g., Modell, 2005; slipp, 2000).\n\nDevelopmental studies\u2014especially those focusing on early infant-caregiver interactions\u2014have also garnered considerable attention. Research in this area has provided an empirical basis for distinguishing primary\u2014or \"root\"\u2014metaphors (i.e., metaphors that originate in pre-verbal bodily awareness), from metaphors that are more strongly shaped by experience (Modell, 1997b). Developmental studies have also enhanced analysts' understanding of the ways in which variations in infant-caregiver mirroring (itself a metaphoric concept) shape subsequent personality dynamics (stern, 2009).\n\nCognitive science has been a third area of emphasis, with cognitive research helping elucidate the role of metaphor in contextualizing memories, and the process by which retrieval of schema-based memories inevitably results in some degree of distortion and reconstruction (Michels, 2005). These latter findings have been particularly relevant for understanding the long-term negative effects of early trauma, and the obstacles to accessing and working through traumatic memories in psychoanalytic treatment.2\n\nBeyond these widely studied topics, a number of research programs from outside psychoanalysis have the potential to enhance our understanding of the psychodynamics of metaphor. Tree stand out.\n\n## **Metaphorizing the Environment: Embodied Affect-Space Links**\n\nCentral to contemporary psychodynamic models of metaphor is the assumption that there are inborn, pre-existing connections between affect and bodily experience, sometimes described as _embodied affect-space links_. For example, there appears to be an innate association between upward gaze or movement and positive affect (as reified in the assumption that heaven is skyward, and the common comment that \"things are looking up\"), and a parallel association between downward gaze or movement and negative affect (which is why hell is below us and sometimes we \"feel down\"). Until recently evidence for embodied affect-space links was primarily anecdotal, but research from social cognition has provided empirical support for psychoanalytic thinking in this area.\n\nFor example, Meier and Robinson (2004) found that evaluations of affectively positive words occurred more rapidly when those words were presented in the upper portion of the visual field, whereas evaluations of negative words occurred more rapidly when these words were presented in the lower portion of the visual field; presumably our tendency to associate \"up\" with positive affect and \"down\" with negative affect facilitated cognitive processing when affect and word position were concordant. In a subsequent series of studies Meier et al. (2007a) found that participants encoded God-related concepts more easily if those concepts were presented in a high (versus low) vertical position; the opposite pattern was obtained for devil-related concepts. A second study demonstrated that when participants were presented with God- and devil-related concepts and later asked to recall the physical location of each concept, they showed a bias toward misremembering God-related concepts as being high and devil-related concepts as being low. When shown pictures of strangers and asked to assess their religious beliefs, participants rated strangers as stronger believers in God when their pictures appeared high in the visual field.\n\nStudies further suggest that these highly automatized metaphor-affect links are not limited to vertical position. For example, Meier et al. (2007b) found that people perceive positive words as being brighter in color than negative words, which appear comparatively dark (even though all the words were actually presented in the same shade). Meier et al. (2008) demonstrated that, metaphorically speaking, bigger is indeed better: positive words were evaluated more rapidly when presented in a large font, whereas evaluations of negative words were more rapid when their font was small. These size biases occur for neutral words as well: in a follow-up experiment affectively neutral words were evaluated as being more positive when their font was large, and more negative when their font was small.\n\n## **Internalizing the External: Imagery as Metaphor**\n\nEach individual's internal world can be conceptualized as a metaphoric representation of the external world. We construct and retain mental images of significant figures (e.g., mother, father, self ) that have both physical attributes and affect qualities (e.g., benevolence, punitiveness, empathy, rigidity; see Blatt, et al. 1993). We construct mental images of other features of the external world as well (e.g., common objects, familiar environments), and like mental representations of significant figures, our mental images of inanimate objects are to some degree veridical, and to some degree distorted. These distortions reflect constraints inherent in the human information processing system (e.g., external percepts are reconstructed as they are encoded in memory), and psychodynamic processes as well (e.g., affective experiences which bias the ways in which we perceive and encode object features). Some of our internalized images need not reflect external reality at all: Many mental images depict people or places we have never actually seen (which is why we can generate an image of an ideal lover we've never met, or what the stairways inside the World trade Center must have looked like on 9\/11).\n\nResearch on the metaphoric aspects of mental imagery may point toward a deeper understanding of the ways in which person and object representations shape behavior and affective responding. Like affect-space links, our mental representations of self and others reflect innate predispositions to encode images in particular ways. Thus, cognitive scientists have shown that mental images must be conceptually categorized before they can be encoded in long-term memory (Finke, 1989; Kosslyn, 1994); there is no such thing as an \"uncategorized\" mental image. As we form mental images we integrate objective features of the stimulus with an array of expectancy and experience variables that modify the initial percept, transferring meaning into the image (thus, a photograph of a person is encoded differently when the person is identified as a criminal than when they are identified as a scientist; see Bornstein & Craver-Lemley, 2004).\n\nPrototypes\u2014exemplary members of a conceptual category\u2014also illustrate the ways in which mental images have metaphoric qualities (Corneille et al., 2004). When asked to picture a dog, few people generate an image of a dachshund, but instead generate a more prototypic dog, like a retriever. People judge retrievers to be \"doggier\" dogs than dachshunds, and hence more prototypic (Rosch, 1978). The same occurs with psychodynamically relevant prototypes, so that as transference occurs and an older male therapist takes on more and more paternal attributes, the therapist gradually comes to resemble the patient's \"father\" prototype. Metaphorically speaking, the therapist has replaced the father (see Borbely, 1998, 2009, for more general discussions of metaphoric aspects of transference).\n\n## **Metaphoric Associates: Accessing the Unconscious**\n\nCentral to the definition of metaphor is that meaning is transferred among ostensibly unrelated concepts; through this process connections among different objects, ideas, and experiences are created, and associative links are developed and maintained (Fosshage, 2005; Melnick, 2000). Some of these metaphoric connections seem logical and rational (as when unfamiliar authority figures take on parental attributes); other metaphoric connections have a more idiosyncratic, primary process quality (as when smiling clowns appear threatening and malevolent).\n\nMetaphoric links among tangentially related concepts can be quantified using the emotional stroop task (est; Riemann & McNally, 1995), a laboratory procedure designed to map an individual's associative network by determining the degree to which a concept within that network is active at any given moment. On the est a prime word (e.g., Father) is first presented, following which a target word (e.g., STRONG) appears. The target word is presented in one of several colors (e.g., blue, green, red), and the participant's task is to ignore the content of the target word and name the color in which that word is printed as quickly as possible. To the extent that the prime word (Father) is conceptually linked with the target word (STRONG) in the mind of the participant, the target word will be activated by the prime word, and reaction time will slow because the participant must devote additional attentional capacity to deliberately ignoring the activated concept and focusing on the color\u2014an effortful, time-consuming task (see William et al., 1996). Thus, est response times are typically slower when Father is followed by STRONG than when Father is followed by TABLE, suggesting that most people have a stronger associative link between the first two concepts than the latter two concepts.\n\nThe est can also be used to examine individual and group differences in associative links (Bornstein et al., 2005; Dozois & Backs-dermott, 2000), helping quantify the \"transfer of meaning from one to the other\" (Modell, 1997b, p. 106) that forms the basis of metaphor. For example, most psychodynamic frameworks would suggest stronger associations between Father and DANGEROUS in men than in women, so est response times for this word pair should be longer in men. Women who have been sexually abused by their father should show longer reaction times to this word pair than women who have not been sexually abused. To the extent that the Father = DANGEROUS equivalence has generalized metaphorically to other male authority figures, one would expect that abused women's reaction times for HUSBAND (or MAN) and DANGEROUS would also be lengthened.\n\nUsing similar logic, the degree to which therapist is metaphorically linked with Mother, Father, or parent can be evaluated using the est, as can the degree to which SICK is associated with POWERFUL (if, e.g., the clinician believes that a particular patient is motivated to remain symptomatic to gain influence within the family). Finally, it is worth noting that changes in associative linkages over the course of treatment can be evaluated using this procedure. For example, est reaction times for thin and Good should decrease in an anorexic patient during the course of successful treatment, but remain unchanged in an anorexic patient for whom treatment was less successful.\n\n## **How Metaphor Informs Research: Inside the Freudian Skinner Box**\n\nFreud's liberal use of metaphor has led some philosophers of science (e.g., Grunbaum, 1984) and critics of psychoanalysis (e.g., Crews, 1996) to describe Freud's work\u2014and much of the theorizing that followed\u2014as unscientific. Freudians are hardly alone in their reliance on metaphor to identify and describe unobservable constructs, however. Many core concepts in physics (e.g., black holes), biology (e.g., natural selection), and chemistry (e.g., molecular bonds) are metaphoric. As Wurmser (1977, p. 483) pointed out, \"Metaphors, taken literally, are unscientific. Metaphors, understood as symbols, are the only language of science we possess....\" Edelson (1983, p. 56) put it more directly: \"A scientific theory is a metaphor for reality... it is only through our studies of the metaphors of science that we can come to find out which is real.\"\n\nIn this respect a focus on metaphor may help inform psychodynamic research, and illuminate the ways in which the empirical testing of psychoanalytic hypotheses overlaps with and differs from the empirical testing of hypotheses in other domains. In the following sections we discuss the role of metaphor in delineating scientific concepts, developing useful experimental manipulations, and quantifying the impact of these manipulations on thought, emotion, and behavior.\n\n## **Naming the Unobservable: Metaphoric Concepts**\n\nNaming the unobservable is invariably metaphoric, and because all theories of personality invoke unobservable theoretical constructs, all rest upon metaphor. The left column of table 9.1 lists some widely used psychodynamic constructs, many of which are clearly metaphoric in nature (e.g., repression, ego, repetition compulsion). The right column of this table lists parallel labels for these concepts that were developed by researchers in other, more \"scientific\" areas of inquiry. Perusal of these alternative labels confirms that they too are metaphoric (e.g., cognitive avoidance, central executive, nuclear script). As Bornstein (2005) pointed out, even though operational definitions of the psychoanalytic and non-analytic versions of these constructs typically differ in certain respects, in every instance there is considerable overlap between the two versions of a given construct.3\n\nIt is important that psychoanalysts become familiar with the operational definitions of key psychodynamic concepts, and with the operational definitions of parallel non-analytic concepts, for two reasons. First, by doing this our theoretical frameworks will become more rigorous, and more firmly embedded in an appropriate nomological network of related constructs: researchers in other areas have much to teach us if we attend to their ideas and findings more closely. Second, by becoming familiar with the various definitions applied to a given concept we will be in a better position to prevent these concepts from being co-opted by researchers in other disciplines. Myriad seminal constructs originating in psychoanalytic theory (including those listed in table 9.1) have been renamed and reinvented by non-analytic psychologists, who gradually assumed intellectual ownership of the co-opted constructs (see Bornstein, 2005, 2007b). This process has contributed substantially to the decline of psychoanalysis within mainstream psychology in recent years.\n\n_Table 9.1_ Revisions and Reinventions of Psychoanalytic Concepts\n\n_Psychoanalytic Concept_ | _Psychoanalytic Concept_  \n---|---  \nUnconscious Memory (1900\/1953a) | Implicit Memory  \nPrimary Process Though (1900\/1953a) | Spreading Activation  \nObject Representation (1905\/1953b) | Person Schema  \nRepression (1910\/1957a) | Cognitive Avoidance  \nPreconscious Processing (1915\/1957b | Preattentive Processing  \nParapraxis (1916\/1963) | Retrieval Error  \nAbreaction (1916\/1963) | Redintegration  \nRepetition Compulsion (1920\/1955) | Nuclear Script  \nEgo (1923\/1961) | Central Executive  \nEgo Defense (1926\/1959) | Defensive Attribution\n\n_Note_ : Original Freudian sources are identified by year of original publication\/date of corresponding Hogarth Press _Standard Edition_ volume.\n\n## **Operationalizing Phenomenology: Metaphoric Manipulations**\n\nEvery experimental manipulation is a metaphor for in vivo experience; the more closely the phenomenological impact of a manipulation approximates that of the real-world experience we are trying to evoke, the more effective the manipulation. This principle can be restated in empirical terms: The external validity of an experimental manipulation is a function of the degree to which that manipulation produces the intended psychological impact in participants (e.g., evokes the desired emotional response, initiates a thought pattern, alters a motivational state).\n\nThus, when examining the impact of affect state on self-report and free-response measures of interpersonal dependency, Bornstein et al. (1996) asked participants to write brief essays regarding traumatic events, joyful events, or neutral events to induce a corresponding mood. In a subsequent investigation examining the impact of the presence (versus absence) of an authority figure on dependency related behavior, Bornstein (2006) employed an experimental manipulation wherein some participants were told that a psychology professor would soon arrive at the laboratory to evaluate their performance in the study, and other participants were told that no one but the undergraduate experimenter would have access to their data. In this instance the unseen professor was a metaphoric stand-in for authority figures in general.\n\nSimilar logic holds for other psychodynamically relevant research programs. For example, subliminal psychodynamic activation (spa) researchers frequently use the subliminal message MOMMY and I are one to evoke pleasurable feelings associated with Mahler's (1968) symbiotic stage, when infant and caregiver were psychologically merged (Weinberger & Hardaway, 1990). Conversely, I AM LOSING MOMMY has been used to induce feelings of helplessness and abandonment (Patton, 1992). Along somewhat different lines, Pennebaker (1997) has documented the positive effects of cathartic unburdening of negative affect by asking participants to write essays regarding traumatic events and experiences. In these studies essay writing replaces more traditional verbal disclosure (e.g., free association) as a method for accessing heretofore unexpressed thoughts and emotions.\n\n## **Quantifying Impact: Measurement as Metaphor**\n\nJust as experimental manipulations are metaphoric replacements for in vivo experiences, the outcome measures used in most studies are metaphors for in vivo responses. For example, the Rorschach inkblots are just that\u2014inkblots\u2014but descriptions of these inkblots are taken to represent respondents' perceptions and experiences of self and other people (see Exner & Erdberg, 2005). Put another way, when a respondent's descriptions of inkblots are filled with malevolent imagery, we assume (and data confirm) that these malevolent attributions taint the respondent's perceptions of actual people as well (Blatt, 1990; Lerner, 2005). Simply asking someone if they see others as dangerous is likely to produce a defensive reaction at best, and at worst outright hostility; asking someone to describe inkblots allows them to make malevolent misattributions without acknowledging (or even recognizing) their source (Bornstein, 2007a).\n\nThe notion that measurement is metaphor for in vivo response is not limited to inkblots, but occurs for a broad array of psychological assessment tools. Following Milgram's (1963) groundbreaking obedience studies there have been dozens of experiments examining conditions that exacerbate or inhibit people's willingness to behave aggressively toward others. But none of these investigations measured actual aggression (nor did Milgram): in every case aggression was operationalized metaphorically and assessed indirectly (e.g., willingness to shock another person during a \"learning study,\" severity of prison sentence assigned to a mock trial defendant, number of personal fouls committed during a hockey game).\n\nIt is important to recognize the metaphoric aspect of measured outcomes, because if we do not we risk erroneously equating the measurement with the underlying variable it is intended to represent. Such equivalence errors\u2014akin to Gargiulo's (1998, p. 416) \"error of misplaced concreteness\"\u2014are surprisingly common in psychology. For example, a survey of five leading personality disorder (PD) journals revealed that 80% of all PD studies published between 1991 and 2000 relied exclusively on self-reports to assess both personality pathology and its correlates; no behaviors were ever measured in these investigations (Bornstein, 2003). Such patterns would be troubling in the best of circumstances, but are especially problematic given the topic being examined. After all, a distinguishing feature of PDs is limited insight and distorted self-awareness (Kernberg, 1984; Millon, 1996). It is ironic (to say the least) that the vast majority of PD studies rely exclusively on questionnaires, when we know _a priori_ that the questionnaire responses of PD patients are almost certain to be unreliable.4\n\n## **Reconnecting Psychoanalysis to Mainstream Psychology: Can Metaphor Glue the Person Together Again?**\n\nPsychoanalysts' historical reluctance to embrace traditional empirical methods has had numerous unintended negative effects, including the co-opting of psychoanalytic ideas by researchers in other areas, and the marginalization of psychodynamic treatment in an increasingly cost-constrained managed care environment (Bornstein, 2001, 2005). Reconnecting psychoanalysis to mainstream psychology is crucial if psychodynamic principles and therapies are to regain the stature they had during the early part of the twentieth century. Although metaphor is essentially idiographic in nature (see Arlow, 1979; Gargiulo, 1998), it has the potential to contribute to a fruitful integration of psychoanalytic and non-analytic perspectives, and to nomothetic as well as idiographic research efforts. In this context the parallels between metaphoric and nomothetic understanding of internal and external reality, though subtle, are noteworthy. One function of metaphor is to contextualize emotional memories, tagging them with a sort of affect label that facilitates retrieval of these memories when similar situations arise in ostensibly unrelated contexts years\u2014even decades\u2014 later. Nomothetic research serves a similar function: it contextualizes discipline-wide principles (\"scientific memories\") to facilitate retrieval of these principles when similar results emerge in new, ostensibly unrelated contexts (see Bornstein, 2009, for a discussion of this process in the evolution of personality assessment, quantum theory, and nonrepresentational art).\n\nPsychoanalysis is in a unique position to conceptualize and study metaphor in the laboratory, as it has in the consulting room. Continued efforts in this area represent an opportunity to strengthen the empirical base of psychoanalysis, and increase the relevance of psychoanalytic research for clinicians. Equally important, a focus on metaphor may provide one of the best opportunities to identify those psychoanalytic constructs that have been co-opted, renamed, and reinvented by researchers in other disciplines. In this respect understanding the contrasting metaphoric labels used by psychoanalysts and others to identify similar psychological constructs represents a unique opportunity for us to reclaim what is ours.\n\nUnderstanding scientific metaphors is key, but scrutinizing the pseudo-scientific metaphors that are sometimes used to describe psychological constructs is important as well. Oftentimes patients have internalized misleading metaphors to understand mind and brain, leading them to develop inaccurate beliefs about psychological difficulties and unrealistic expectations regarding psychological treatments (e.g., that the effects of early trauma will dissipate immediately if repressed memories of the traumatic events can be accessed). Worse, countless patients have been harmed by well-meaning clinicians who internalized misleading metaphors (e.g., memory as film or computer hard drive rather than sketchpad, dissociative identity disorder as literally reflecting multiple personalities rather than a fragmented ego\/self ). Understanding how research informs metaphor (and vice versa) can help correct the distortions associated with reliance on pseudo-scientific metaphors in our patients, and in ourselves.\n\nA similar process of self-scrutiny may be useful in understanding the limitations of the _Diagnostic and Statistical Manual of Mental Disorders_ (DSM) as a tool for classifying psychopathology. Many DSM category labels have become metaphors for the syndromes they are intended to identify, and we find ourselves describing patients in metaphoric terms (e.g., \"a flaming borderline,\" \"a toxic narcissist\"). Exacerbating the problem, DSM category labels have become so widely used that many are now dead metaphors, having lost their metaphoric qualities. In this context one important contribution of the _Psychodynamic Diagnostic Manual_ (PDM) is that it calls our attention to the fact that DSM categories represent only one of many possible metaphoric frameworks for describing psychological syndromes. To the extent that the PDM helps clinicians see the metaphoric qualities of DSM labels more clearly, it can enhance the rigor of both diagnostic systems.\n\nFinally, as the study of metaphor moves forward, it may be time to shift our focus from general principles of metaphoric process to individual differences in metaphor use. Beyond emphasizing the fundamental role that metaphor plays in thinking and understanding, Lakoff and Johnson's (1980a) work illustrates how different groups(e.g., liberals and conservatives) differ in their use of metaphor to conceptualize various issues. Although initial research in this area focused on individual differences in political attitudes and beliefs, the same principles hold for other individual difference variables as well (e.g., gender, age, ethnicity). Examining differences in metaphoric process in different types of patients (e.g., histrionic versus borderline) may allow us to tailor our interventions more precisely and enhance the effectiveness of psychodynamic treatment.\n\nThus, in addition to elucidating the role of metaphor in psychoanalytic theory, and the ways in which metaphor may deepen our understanding of research and its implications, it is time to explore differences in metaphor as a function of gender, culture, personality style, and other psychologically relevant variables. A truly integrative twenty-first century psychoanalysis must not only combine clinical wisdom with empirical data, and embed its ideas and findings in the broadest possible epistemological context, but it must also refine its interventions to maximize treatment effectiveness for patients with a broad array of backgrounds and diverse life experiences.\n\n## **Notes**\n\n originally published in _Psychoanalytic_ _Inquiry_ 31(2): pp. 172\u2013184 with the title \"Reconnecting psychoanalysis to Mainstream psychology: Metaphor as Glue.\"\n\n although numerous analytic writers have drawn upon studies from cognitive science to test and refine psychodynamic concepts, Michels (2005) pointed out that many constructs in contemporary cognitive science are flexible enough that they can be incorporated into extant psychodynamic frameworks without altering these frameworks in substantive ways (cf. Bucci, 1997).\n\n Behaviorists might argue that behavioral models\u2014especially radical behavioral models\u2014are metaphor-free, but they would be wrong. Myriad behavioral constructs (e.g., generalization, discrimination, unconditioned stimulus, avoidance learning, intermittent reinforcement) are to varying degrees metaphoric.\n\n PD researchers are not alone in their implicit equating of self-reports with the underlying variables assessed by self-report measures. Although the Five Factor Model (FFM; Costa & McCrae, 1997) is far and away the dominant model of personality in scientific psychology today, the vast majority of FFM studies rely exclusively on self-reports to assess personality as well as its correlates.\n\n# 10  \nPSYCHOANALYTIC  \nFIELD CONCEPTS\n\n_S. Montana Katz_\n\nField concepts currently in use in psychoanalysis may be viewed as special cases of general psychoanalytic fields. Existing field concepts include the fields of relational, intersubjective, and interpersonal psychoanalysis, self object matrices, the analytic situation of Donnet, Green's thirdness, Ogden's thirdness, fields resulting from Faimberg's listening to listening, and the fields originated by the Barangers and elaborations of them. Each particular kind of field serves as a core concept of the psychoanalytic perspective in which it was created or implied. It is useful to parse clinical process as evolving within an environment that could be called a \"field.\" The specific kind of field employed depends upon several factors, including the psychoanalytic orientation of the analyst. This chapter describes the fields employed in different psychoanalytic perspectives and also the concept of a general psychoanalytic field.\n\n## **Relational, Self Psychology, and Constructivist Fields**\n\nForms of relational psychoanalytic perspectives have used field terms such as _relational field, intersubjective field, interactional field,_ and _interpersonal matrix_ to describe the medium in which the analytic process unfolds. The emphasis is on the here and now of the interaction between analysand and analyst. This real-time interaction is what constitutes the relational field. The clinical interaction between analysand and analyst is the medium in which meaning evolves. This meaning of, for example, the analysand's enactments with the analyst is construed and understood within the dyadic interaction in which both participate. Enactments are understood as the means of expression of unsymbolized affective experience, primarily of the patient but also of the analyst (Bromberg, 2008). Unconscious intersubjective patterns are live in the transferential matrix. Once lived through in the analytic setting, there is a potential for understanding transferential elements. The individual is understood to emerge from the relational process of co-constructed meanings.\n\nIn contrast, in a classical model the individual enters the psychoanalytic process, is the focus of it, and leaves the process the same individual, albeit ideally deeply affected by the process. In relational models, the two-person field is posited to constitute the analysand through the analytic process. In forms of relational models, there is a varying degree of tension concerning the individual roots of the meanings of enactments. That is, the degree to which repetition is involved varies in relational perspectives. The psychic structure said to emerge from an interactional field is considered a co-construction based on the unfolding understanding of the analysand's historical, relational patterns that come alive and are potentially modified in the field (Hirsch, 1995). Analyst and analysand are both considered fully present and active, albeit asymmetrically, in the process.\n\nSelf object matrices of self psychology could be described in terms of relational fields that include\u2014and, in the transference, emphasize\u2014developmentally early relational fields of the analysand as experienced in the present analytic process. Constructivism expands the relational framework. It emphasizes that the progressive understanding arrived at is a collaboration between the processes of both participants\u2014that it is original, that it necessarily leads to change in both analyst and analysand, and that each emerges from the field as a result of what transpired there (Hoffman, 1991).\n\n## **Tirdness**\n\nThe relational and constructivist perspectives indicate the possibility of a complement to the concept of the here and now (Green, 2004). In this regard, concepts of thirdness could be viewed as widening the psychoanalytic relational field. In its most general form, the third points to other significant influences beyond the dyad that are involved in the analytic interaction. A specific concept of the analytic third could be viewed as launching from a relational matrix to posit another subjectivity beyond that of the analyst and analysand within analytic processes. The analytic third is considered to be generated by the dialectic of the subjectivities of the analysand and the analyst. This third is both created by and creates the subjective experience of analysand and analyst (Ogden, 2009). The necessarily unique matrix that evolves from the interplay and creation of subjectivity and intersubjectivity within the analytic process becomes an aspect of the object of psychoanalytic study.\n\nA further widening of the concept of the psychoanalytic field derives from an emphasis on the impact of the analytic setting itself on the process, as described by Donnet (2001). Donnet's conception of the analytic situation recognizes the interaction of the analysand with the analytic site, which includes the analyst, the analytic process, and what it offers. This interaction includes the activity of the intersubjective third.\n\n## **Faimberg Fields**\n\nFaimberg (2007) refines the concept of _nachtr\u00e4glichkeit_ and in so doing in effect constructs a kind of field. In the model that arises from the work of Faimberg, a central part of the analytic process is the analyst's attention to how the analysand listens to the analyst's interpretations and to the unfolding exchange within the dyad (Faimberg, 2005; sodr\u00e9, 2005). That is, the analyst is attending to the conscious and unconscious ingredients in the analysand's understanding of the meanings of the analytic exchange.\n\nIn effect, a kind of field is created by this attentive analytic listening to listening. This field contains a detailed expansion of the metaphoric processes from within each expression in the analytic exchange. The expansion includes an ever-branching articulation of derivatives of the analysand's unconscious processes that are involved in her or his experience of the analytic exchange.\n\nThe intrapsychic is modeled as constructed and reconstructed within the intersubjective exchange in a Faimberg field. The construction of the intrapsychic in this model is related to that posited in relational and other fields. As a part of the field, neither participant can survey the entirety of the field nor make sound, general statements about it. The analyst thus cannot be considered an authority concerning herself, the analysand, or the field.\n\nIn most psychoanalytic perspectives, analytic fields are said to be asymmetrical. As Baranger (2009) points out, it is only the analysand who speaks associations aloud, not the analyst. This creates asymmetry. The training and objective of the analyst to attend to understanding the derivatives of the analysand's unconscious processes strengthen the existence of asymmetry in the process (Katz, 2011b).\n\nWith Faimberg's concept of _listening to listening_ , the assertion that the analytic process is asymmetrical can be understood and given more precise meaning. That is, it is the analyst whose focus is primarily to listen to the analysand's listening to the analytic process. The analysand may also engage in this, but it is an essential role of the analyst to do so.\n\n## **Baranger Fields**\n\nThe foregoing field concepts lead directly to a further elaboration that yields another conception of an analytic field. This concept of the analytic field was introduced by Madeleine and Willy Baranger (1961\u201362). The Barangers' work, based on Kleinian and especially on Bionian thought, has multiple influences, such as the Gestalt theory of Kurt Lewin, Merleau-Ponty's work, Pichon-Rivi\u00e8re's contributions, and Racker's work on countertransference. The Barangers developed a structure with which to describe and guide clinical work (de Leon de Bernardi, 2000; Lewkowicz & Flechner, 2005; Silverman, 2010; Zimmer, 2010). The analytic field concept is used to describe another conception of the analytic situation as a whole. The analytic field encompasses all aspects of the analytic situation, including the spatial, temporal, and functional. Employing such a conception of the analytic field broadens the understanding of the analytic relationship and process to explicitly include all these dimensions (Ferro, 2005a).\n\nWhile there are said to be asymmetries in the field between the participants, the analyst is not considered to have authority in the process. In the Barangers' model, as in the relational, constructivist, and Faimberg models, the analyst is not considered to be self-contained or solely an observing interpreter. Rather, the analyst is viewed as an active contributor to and participant in the production of what is called the _basic fantasy of the field_. Thus the analyst is also an immediate part of the object of analytic study within the psychoanalytic process.\n\nThe individuals participating in an analytic process are considered to be derivative from the field, as are their unconscious processes. Unlike what is seen in relational models, the analytic field itself is posited to contain an unconscious dynamic that is more than and different from the sum of the unconscious dynamics of each participant. In this model, the unconscious of the field and the concomitant fantasies, called basic fantasies, are the immediate objects of interest and exploration in the analytic process. The analytic object of interest is thus neither the analysand nor the two-person interaction.\n\nThe quality of the analytic field is described as oneiric and as a dream membrane (Grotstein, 2009). The field is conceived in important ways as atemporal and as embodying a virtual reality. The fantasies of the field arise within the field and are not simple or direct imports from either participant.\n\nSimilarly, the presences found in the field are the results of and take shape in the fantasies of the field, and are thus neither solely from the past nor from the current experience of either participant. Derivatives of the metaphoric processes of the analyst and of the analysand are in the field, as are multiple virtual presences of analyst, analysand, primary objects, and others, as well as combinations and permutations of the participants' metaphoric processes.\n\nThe field and its fantasies are viewed in this model as novel creations that could not have arisen or been constructed in any other circumstance. This means that there will necessarily be different fields associated with different analytic couples and therefore different analytic processes. The intrapsychic is considered to be derivative from the intersubjective creations of the field. The individual participants are understood as emerging from the field rather than as components of it. By observing and understanding the basic fantasy, the intrapsychic processes of the analysand can be understood. The intrapsychic is viewed as a precipitate of the basic fantasy of the field.\n\n## **Comparison of Field Concepts**\n\nIn the following, common labels for psychoanalytic perspectives will be used only to locate classes of perspectives and without the precision of specific instantiation. That is, none of the names of different perspectives\u2014such as classical, Kleinian, relational, and so forth\u2014here specifies a theoretical and clinical position, but rather points to a general orientation within which there are variations.\n\nIt can be asked what work in one kind of field looks like from the vantage point of another. It might be that viewing an alternative perspective involves the diminished emphasis or erasure of certain components of metaphoric processes, or possibly understanding them as something else. Each analyst views clinical material through the filter of the chosen form of field implied by the psychoanalytic perspective used. For example, classical Freudian and relational filters are different in important respects that render understanding and clarity between them difficult. That is why general psychoanalytic fields in their broad inclusiveness of elements can help bridge gaps in understanding and meaning.\n\nAs has been elaborated above, the contents of analytic fields of different psychoanalytic perspectives vary. Psychoanalytic perspectives can be differentiated as well as linked in terms of the kinds of fields employed, together with which components of metaphoric processes and their derivatives are emphasized within each model. The kind of field associated with classical theory takes shape as a result of the transferences that develop. This means that, while there are two persons in a consulting room, there is in effect one subject recognized, and the focus is on action and change for that subject, the analysand. The components of metaphoric processes that are emphasized are the idiosyncratic and the general community. What could be called early metaphoric processes and thereby early fantasies are not emphasized in a classical analytic process. The phase of peak idiosyncratic development of metaphoric processes and early local experience is not the principal focus in a classical perspective. Because of the centrality of oedipal issues in a classical perspective, at least some of the salient poles in a classical field will necessarily have prominent features of sex and gender identifications and will involve oedipal-configuration derivatives. The analytic process is understood as steeped in the timelessness of the unconscious metaphoric processes and emphasizes repetition in the transference.\n\nIn Kleinian theory, while the environment is acknowledged, the focus is on phantasy and objects, which are always internal. In terms of the language put forth here, as described above, early segments of metaphoric processes\u2014particularly from the idiosyncratic and general community inputs\u2014and the objects extracted there from are salient to analytic processes. The field contains the derivatives of the analysand's metaphoric processes and evolves with the projective identifications of the analysand. While a Kleinian perspective could be represented in this model as having much in common with a classical perspective, the positions differ in that a Kleinian perspective significantly emphasizes the peak idiosyncratic as well as the universal, general community input to the analysand's metaphoric processes.\n\nThe field associated with a self psychological perspective also might be described as placing an emphasis on the local component of metaphoric processes, and to some extent on elements of the general community. A self psychology field, or self object matrix, will have self object poles and will contain derivatives of the metaphoric processes of the analysand. Rather than emphasizing transference repetition, the self object function complements or supplements early object experience. Repetition is considered to be present and as what motivates and formulates the self object matrix.\n\nForms of relational perspectives view the action of an analytic process as taking place within relational fields that emphasize the local and community components of metaphoric processes. The metaphoric processes of an individual in a relational perspective consist of unconscious organizing principles that have evolved intersubjectively (stolorow & Atwood, 1996). Analyst and analysand bring the contents of their prereflective unconscious and its derivatives and share an ever-expanding field containing the intersection of their structures and derivatives, and in which transference and countertransference are the means by which the intersubjective field is woven together and takes shape. This field is a functioning whole and is the object of the psychoanalytic process (Stolorow & Atwood, 1989). Individuals coalesce as precipitates of the field. The field functions in present, real time. Repetition, strictly speaking, does not occur. Where organizing principles are activated, it is within the intersubjective intersected nexus, and these are not attached to an individual.\n\nThe notion of the unconscious developed in Baranger models is a departure from the understanding of it found in classical and most other psychoanalytic perspectives. The central unconscious is that of the field and is not associated with an individual. In this conception of the unconscious, repetition in a traditional or even a relational-theory sense does not occur. As a result, there is a potential for\u2014and, in fact, a certainty of\u2014creativity and novelty. In other models, accounting for creativity and novelty is problematic. When the main action in analytic processes is, for example, intrapsychic and transferential, repetition of the analysand's past experience is a major focus. From repetition, there is no clear route to the creation of genuinely new meaning. Similarly, if the emphasis is on the enactment of amalgams of historical ingredients, repetition remains at the center of the analytic process. Experience in both cases is thus considered to proceed on the basis of transference and fantasy, which are understood to derive, ultimately, from previous experience and meaning. This can lead to a reconfiguration of what was already experienced but not necessarily to creation.\n\nIn some relational models, it is not repetition of the analysand but the real-time interaction of analysand and analyst, including the contribution of transferential elements of each, that is the focus of clinical process. In this case also, the available ingredients to work with are the union of the experience of the two participants. The potential for the emergence of something novel is not significantly different from the classical, one-person-focused situation. In this regard, a constructivist model does not introduce the possibility of something genuinely new beyond relational or intersubjective models.\n\nThe tension between repetition and the possibility of creativity is a core psychoanalytic issue. This tension and the problem of accounting for genuine creation in the analytic setting are sometimes believed to be, but are not addressed in the concept of _nachtr\u00e4glichkeit_ as understood as involving retranscription. That is, the understanding in the present of experience from the past, through the lens of accumulated further experience, involves the rearrangement of existing ingredients, including the emergence of derivatives of unconscious processes and the reconnection of affect with memories. Still, while new understanding of experience may be evocative or transformative, it does not necessarily afford the emergence of something new.\n\n## **Psychoanalytic Process and Creativity in Fields**\n\nA general psychoanalytic field consists of bundles of metaphoric processes that potentially include all four elements: the idiosyncratic, local, community, and general community. An initial translation occurs when the idiosyncratic elements of an individual's experience become infused with those shared by the individual's local and extended communities, through natural language and other shared structures.\n\nA second level of translation involves the language built by analyst and analysand in the course of the analytic process. This language is unique to the couple. These two levels of translations are interpretations in a general sense and are necessarily imperfect and incomplete. This consequence lends weight to the associative method of psychoanalysis. Free association is the tool that allows for the translation and interpretation of the multiple systems of structuring by and with which an individual experiences. The way into these unconscious processes is by means of free association, which taps into and allows for the expression of the individual's metaphoric processes. The psychoanalytic process and the language built by the analytic couple seek to reverse the processes of the first level of translation with the acquisition of shared natural language and the socialization of the individual. That is, the analytic process attempts to precipitate idiosyncratic elements of the analysand into the constructs, understanding, and language of the couple, and bloom them in the analytic process in order to lay bare as much as possible of the analysand's unconscious idiosyncratic motivators.\n\nWhen two people come together to enter into an analytic process, a dialogue ensues. An utterance of either participant contains and potentially conveys multiple meanings. Included are the consciously intended meanings and derivatives of unconscious contents from the utterer. Once spoken, the utterance may take on other meanings, including those in the mind of the utterer. This is a commonly known event within analytic process. The one listening to the utterance may attend to some or all of these three sets of meanings. In addition, the listener will attach idiosyncratic meanings to the utterance, deriving from both conscious awareness and the listener's unconscious processes. The listener now takes in four potential sets of meanings at conscious and unconscious levels, all filtered by the listener's metaphoric processes.\n\nWhen a participant in the analytic process makes a contribution to the dialogical process, the utterer does not have control over the meanings of the utterance. In addition, when the utterer is the analysand, the analyst is explicitly attempting to attend to the derivatives of unconscious communication embedded in the utterance. Like all forms of perception, both participants are taking in more meanings of the utterances than they are consciously aware of. Such meanings taken in are the results of individual filtering and elaborations. What is absorbed by a participant will then impact on that participant's future contributions to the dialogical process. In this way, meanings associated with utterances necessarily give rise to their permutations.\n\nUnderstanding between the participants, given the multiple sets of meanings associated with any given utterance, can have several senses. When analyst and analysand have developed enough of a common language in which to work and understand each other well enough to have what is called _bipersonal understanding,_ several factors must be present. For an utterance of the analysand, for example, to be understood at least in some aspects by the analyst, there must be significant overlap in the conscious, intended meaning of the utterance by the analysand and the conscious understanding of the utterance by the analyst; there must be a significant overlap in the analysand's unconscious communication of the utterance with the conscious understanding of the utterance by the analyst; and there must also be a significant overlap in what the analysand understands of the utterance after having said it with what the analyst understands of the utterance. More will be absorbed by both parties in light of the utterance, and possibly other overlaps will emerge, but the foregoing is a minimal standard for mutual understanding of an utterance.\n\nWithin general psychoanalytic field theory, the lack of control over the meanings of utterances on the part of the participants in the analytic process gives rise to the possibility of the emergence of new meanings. The possibility of new meaning is not modeled on the interpretive understanding of its transferential repetition. Perceived repetition of the analysand's patterns in the present moment of therapeutic process is understood as the analytic pair's jointly fabricated pattern. This contains derivatives of the experience of the analysand. Such derivatives pertain to previous experiences, which correspond to what the current joint product appears to refer to in the analysand's past.\n\nBecause of the loss of control of meanings within the dyad and because two sets of derivatives of idiosyncratic unconscious processes are intermingling, patterns within the dyad are necessarily hybrid affairs. New meaning may emerge in this process of intermingling. In models in which transferential repetition is a straightforward concept, such as forms of classical theory, and in models that do not include idiosyncratic elements, such as forms of relational theory, genuine creation of new meaning can only be a premise.\n\n## **Ontological Commitments of General Psychoanalytic Fields**\n\nThe idea that the field is an object of psychoanalytic interest, that there is an unconscious process of and in the field that is different from and independent of the participants, has heuristic value clinically. It serves to focus the work on the unconscious derivatives present in the analysand's communications. It highlights the fact that the utterances of each participant convey more than is in the awareness of either party. The field concept is a way of modeling unconscious communication within an analytic process. Nevertheless, an ontology is potentially being posited by field models that bear understanding. The concepts of _thirds_ in their various formulations posit entities; for example, Baranger fields posit the third entity of a field, not a person, which has its own unconscious processes and fantasies.\n\nIn order to have more than heuristic value, the field concept and its ontological commitments need specification. A third, independent, nonhuman entity with its own unconscious process is not necessary to general psychoanalytic field theory. Rather, it is the conscious and unconscious transformations and permutations of elements in the analytic process that inform and are informed by the metaphoric processes of each participant. When a segment of a set of these meanings converges and coalesces, an insight has formed within one of the participants that may lead to an interpretation. Due to the factor of the lack of control over meanings, the unconscious processes and resulting fantasies are as independent of the participants as the Baranger or relational field models require. There is no loss of power to the model in paring down the ontology.\n\nOntological questions reemerge in further specifying the contents of fields. Psychoanalytic discourse proceeds as if persons, offices, thoughts, feelings, derivatives, and unconscious processes may all be elements of fields; thus, fields contain an ontological hybrid of ingredients. While there is heuristic value in this, it is also necessary to make explicit what is being posited underneath this manner of speaking. Psychoanalytic theory posits the existence of unconscious processes. The existence of individual humans and of space-time locations, such as consulting rooms, are further assumptions. All such entities are conjectured (Katz, 2010a). Just as there is no direct contact with the unconscious, neither is there with humans, couches, or other items purported to be in the world. The ontology of fields is relatively uniform and consists of derivatives.\n\n## **Two Kinds of Derivatives in Analytic Processes**\n\nA thread in an analytic process may be identified by the persistent presence of certain derivatives. Such a process could be considered constructive if it involves the articulation, elaboration, or connecting of these derivatives. A constructive process might culminate in the introduction of a construction. This would be a coalescing of derivatives into a formation that conveys emotional and other meanings to the participants, especially the analysand. A construction is an interpretation in the wide sense; an analytic interpretation proper is a special case. The latter consists of an interpretation that leads to the revealing or inciting of further derivatives and thus changes in the field.\n\nWhat can be worked with in general psychoanalytic fields are two kinds of derivatives, the first- and second-order derivatives of the participants' experience. Second-order derivatives are derivatives of derivatives. What are in evidence in the consultation room are linguistic and other expressions of the participants. Second-order derivatives consist of the meanings of expressions. These are derivatives of aspects of the participants' experience with embedded emotional valences attached to experience. First-order derivatives are the aspects of experience. These are themselves derivative of underlying unconscious metaphoric processes.\n\nWhen thinking in terms of field concepts, derivatives could also be thought of as precipitates. Every expression contains derivatives of both orders. Different psychoanalytic perspectives have different points of emphasis and goals in analytic processes and so make different use of derivatives to widen the scope of understanding the analysand. Different perspectives also emphasize different kinds of derivatives. For example, relational and constructivist theories in the United states rely on second-order derivatives. Classical models and those that use Baranger fields employ both orders of derivatives and emphasize first-order derivatives.\n\nDerivatives relate to aspects of the participants' experience and coalesce into different formations at different times. Derivatives are not perceived singly but as derivatives in coalesced states within constructions. Coalesced derivatives of either order are interpretations in the wide sense. First-order derivatives consist of aspects of experience and coalesce into interpretations (constructions) of metaphoric processes. Second-order derivatives consist of the meaning of the participants' expressions and coalesce into interpretations (constructions) of aspects of experience.\n\n## **Poles and Neighborhoods in Fields Represent Object Formation and Consolidation of Experience**\n\nOn the one hand, a field can be thought of as atemporal, as has been discussed throughout the history of psychoanalysis concerning the unconscious. Since multiple presences of the same person at different points of lived time can inhabit a given field and even be in contradictory relationship to each other, atemporality seems to describe fields. On the other hand, an analytic process is steeped in time (Birksted-Breen, 2003). What it has to work with is the present experience of the past and present predictions about the future. Thus, what an analytic process at any given moment has is what is contained in the field. It is not outside of it or located in the past of the analysand. In being wholly in and of the present, aspects of the field itself are both the subject and the object of analytic study. Interpretation and other aspects of analytic processes necessarily occur within and about aspects of the field.\n\nA field can be said to be inhabited by all kinds of presences. In terms of elements of fields, presences consist of coalescences of derivatives of segments of metaphoric processes. This includes a potentiality for multiple presences or aspects of experience of certain objects. These include the analysand and the analyst, primary objects\u2014especially of the analysand, and acquaintances of each of them, as well as public figures. All these presences inhabit the field, bearing multiple and possibly incompatible relationships to each other. In this medium, derivatives of the unconscious processes of both analysand and analyst co-mingle and combine.\n\nA field has poles that are consolidations of aspects of experience. Each pole could be thought of as having a _neighborhood_ or space around it, which consists of compact clusters of metaphoric processes. Derivatives of a metaphoric process within such a neighborhood have elements that pertain to the experience of the construct at the center of the pole. A field will contain poles of aspects of experience of objects, including at least one for the analysand and another for the analyst. A transference situation could be represented, for example, by the convergence or significant overlap of the neighborhoods around poles of a primary object and of the analyst.\n\n## **Field Representation of Change in an Analytic Process**\n\nIt is possible to filter a field for indexical items in aspects of experience and their derivatives. An indexical item of relevance in an analytic process is the temporal one. The filtering pertains to neighborhoods of poles. This might proceed in some way analogous to the way in which specific statements with indexical elements can be filtered out of a larger set of statements. In other words, it might be possible to compare aspects of experience and neighborhoods, making use of the filtering of certain kinds of indexical components. Derivatives and constructions might be considered congruent if they agree once they have been filtered for indexicals. When there is a change in a neighborhood across time, then there will also be concomitant change in aspects of experience, and therefore also change in the pole around which the neighborhood centers.\n\nFrom one point in time to another, nontrivial change might be described as a _nonindexical_ change in the elements within a neighborhood. That is, change could be said to take place if a neighborhood around a given pole is filtered for changes, from one time to another, that involve purely indexical item difference, while other differences remain. Change of this sort reflects movement in the sense of Faimberg (2005). When neighborhoods around a pole change, it follows that the pole itself within the time span has also been altered. When a neighborhood is stable, so is the pole within it. It could then be said that when there has been change in a pole, something has happened in the analytic process; there has been some therapeutic action. When there is no change, there is some sort of block, or _bastion_ in the sense of Baranger fields.\n\nPsychoanalytic perspectives place the locus of therapeutic action in various locations. In a model that uses Baranger fields, for example, the locus is in the unconscious of the field. In self psychological models, models implicit in Faimberg (2007), and classical models, the locus is in the unconscious process of the analysand. In Spezzano (2007), it is in the unconscious process of the analyst.\n\nThe use of unconscious metaphoric processes and psychoanalytic fields allows for a description of the increased complexity of psychoanalytic models. Within a psychoanalytic perspective, the specific kind of field used is posited to provide the medium of analytic process and a model of human experience. In the latter is a potential claim that human functioning inherently proceeds according to the structure of the elements of the kind of field used in that perspective. A series of debates in the history of psychoanalytic discussion can be rephrased to contain assertions that humans operate in one kind of field rather than others, and thus the analytic medium must be the designated kind of field.\n\n## **Perspective of Psychoanalytic Process From General Fields**\n\nA still greater increase in complexity emerges when we step back from specific perspectives to the vantage point of general fields. This affords a broader view and allows for a way of reflecting on what is being modeled by the different forms of field. Within general psychoanalytic field theory, each field model is to be viewed as a possible model of human experience that is related to and interconnected with other possible models. From this vantage point, it can be asked whether the different field models necessarily apply to the analytic pair, or instead to the individuals in the pair. That is, within general field theory, the question naturally arises whether it is possible to have more than one form of field operative at the same time within an analytic perspective. From within perspectives, this question is not intelligible.\n\nFrom the general field view, this can be further elaborated to the question of whether participants in an analytic process might each make use of different aspects of the process in such a way that each is active in a different field. The analysand, for example, might be understood as working in a Baranger field, while the analyst is working within a classical field. If this is conceivable, issues arise concerning communication between analyst and analysand.\n\nIt may make sense to wonder whether some of the impasses within a therapeutic process or misalignments between analyst and analysand may be understood as the result of a lack of awareness of the possibility that analyst and analysand are operating under different sorts of fields. A Pandora's box, so to speak, opens up here, of possibilities for understanding what is happening in the course of an analytic process. For example, it may make sense to understand the nature of the analytic field within a specific analytic process as determined by the analysand's state of mind rather than by the analyst's theory. It may also be plausible to view the form of the field as shifting throughout the course of a specific analytic process, either as the work progresses over time or session by session, or even possibly from moment to moment. More complex still, it may make sense to understand the kinds of fields operating as variable according to the different layers of unconscious processes at work. In this case, more than one kind of field is operating at the same time.\n\nPsychoanalytic fields may be used to model and describe what sort of experience is occurring at a given point in the analysis for the analysand. This might be effected in several ways. One is to determine which aspects of the field the analysand can make use of at that point. Another is to understand the analysand's experience of the field at that point\u2014that is, to appreciate what kind of field it is for the analysand. While the analysand's and the analyst's experiences of and in the field are necessarily different, the degree and kind of discrepancies also pertain to the analysand's experience. This is a way of expressing a generalization of Faimberg's (2005) concept of the distance between the analyst's understanding of an interpretation and how the analysand processes and understands it.\n\nAnalytic progress might be measured in some cases by the analysand's expansion of the kinds of fields within which the analysand is able to function. An eclectic perspective might entail the analyst changing the kind of field over the course of the analytic process, in tune with where the analysand is, as understood by the analyst. The analyst's assessments are made from the vantage point of the analyst's field. That is, there are choices to be made about whether a field model is considered to apply to what is occurring for the analytic pair, or for each individual of the pair, and by whom in the pair the field options are determined.\n\nEach analytic perspective, even an eclectic one, operates with a model of mental processes that is the foundation of that perspective's theory. This model then determines what kinds of fields can be used clinically within that perspective. That is, the field is a technical, psychoanalytic tool, and this points to another asymmetry of the field. The field is the field of the analyst, and it is determined and justified by the choice and assumptions of the psychoanalytic perspective within which the analyst works. Thus what is relevant is the analyst's field working with a specific analytic perspective, not that of the analysand. The analysand comes to treatment with a mass of experiences and active unconscious processes. The analyst works with the analysand progressively, making use of the field. Only general psychoanalytic fields include all possible elements. This is by design, in order that all perspectives may be included.\n\n## **Notes**\n\n some of the material for this chapter derives from _Psychoanalytic Inquiry_ 33(3) (May 2013) \"General psychoanalytic Field Theory: its structure and applications to psychoanalytic perspectives.\"\n\n# 11\n\nCONTEXT FOR THE BARANGERS' WORK ON THE PSYCHOANALYTIC FIELD\n\n_Antoine_ _Corel_\n\nThis chapter evokes the intellectual atmosphere and the ideas developed within the psychoanalytical movement in Argentina during the two decades that preceded the formulation of the concept of \"psychoanalytic field\" by Madeleine and Willy Baranger in 1961.\n\nHowever brief its existence, a magnetic field organizes forces that may carry powerful effects\u2014as happens in a dynamo. Nearer to our analytic domain, with F. De Saussure we speak of the semantic field that organizes meaning in language.\n\nThese associations to the word \"field\" would be met by Mad\u00e9 Baranger (and would have been met by Willy) with one of their characteristic, wise, and meaningful bursts of laughter. I am pleased to imagine this, as I set out to evoke the intellectual atmosphere in which they coined the concept of psychoanalytic field. It was a fruitful soil that met them in the Rio de la Plata after World War ii.\n\nIn the decade that preceded their arrival in Argentina in 1947, a dynamic group of psychoanalysts had gathered, coming from a variety of backgrounds. Angel Garma, a Spanish physician born in 1904, had obtained his psychoanalytic training in Berlin, where he was analyzed by Theodor Reik and had been accepted as a member of the society with a paper on \"Reality and the id in Schizophrenia\"\u2014a remarkable subject matter for the times, which we shall see reappear in the membership papers of Pichon-Rivi\u00e8re and Racker. Besides an interest in psychosomatic symptoms characteristic of those years, Garma insisted throughout his life on the traumatic origin of dreams.\n\nAs a consequence of the Fascist takeover of his country, Garma was unable to settle in Spain. In Paris, he met Celes C\u00e1rcamo (an argentine physician analyzed by Paul Schif who had become a member of the Paris Psychoanalytical society). They both went to Buenos aires, where, as the only two formally trained analysts, they joined several persons from various horizons and frames of mind who shared a passionate interest in the science created by Freud. Among them was Marie Langer, who had interrupted her analysis with Richard Sterba in Vienna to take refuge first in Montevideo (Uruguay), then in Buenos aires in 1942. And in December of that same year, the argentine psychoanalytic association was founded by C\u00e1rcamo, Garma, Langer, Enrique Pichon-Rivi\u00e8re, Arnaldo Rascovsky, and G. Ferrari Hardoy. With the exception of G. Ferrari Hardoy, who left to settle in the United states, they all became training analysts in 1943. Also in 1943, the _Revista de Psicoan\u00e1lisis_ was founded; in the first years of its existence, papers by Fenichel, M. Klein, Sterba, Reik, Tausk, K. Abraham, Frieda Fromm-Reichmann, Ferenczi, F. Alexander, H. Deutsch, and G. R\u00f3heim appeared, together with articles by the local members.\n\nEnrique Pichon-Rivi\u00e8re is the personality who should interest us most in retracing the intellectual environment in which the \"field\" concept grew. Born in 1907 in Geneva to French parents who eventually settled in the subtropical northeast region of Argentina, Pichon-Rivi\u00e8re began to develop his original ideas on mental illness as a psychiatrist at the Hospicio de las Mercedes in charge of admissions. For him, the mentally diseased patient is the spokesman of the family group. This led him to take innovative initiatives in terms of family and group therapies, and to consider the conditions under which the sick member might be reintegrated (or not) into a family who would attempt to keep the disease \"frozen\" upon him. Pichon-Rivi\u00e8re described two essential types of anxiety: fear of losing and fear of being attacked. Asserting that a person falls ill \"for love, of hate,\" in his dialectic way of conceiving of psychic functioning he came to consider there to be only _one_ mental disease\u2014while at the same time maintaining refined nosographical distinctions. He described the interplay of three areas: mind, body, and the external world; and he pointed out, for example, that the persecuting object is located, in melancholia, hypochondria, and paranoia, respectively, in each of these three areas. In a study devoted in 1938 to delusions according to the German and French schools, he declared that the future lies with a structural approach.\n\nThese concepts provided the basis for the psychoanalytic treatment of schizophrenics within a rigorous frame. His paper on becoming a training analyst in 1943, \"Contribution to the psychoanalytic Theory of schizophrenia,\" draws on these experiences. One of Pichon-Rivi\u00e8re's favorite metaphors refers to a \"spiral process,\" a dialectical way of thinking applied both to the therapeutic process and to the process of learning: the spiral consisting in meeting similar conflicts or configurations at successively upward, growing levels. Another of his ideas that he carried to practice is \"the operative group,\" whose members learn within a model that includes solving the psychic conflicts that preclude learning.\n\nPichon-Rivi\u00e8re resorted predominantly to the oral transmission of his ideas. He published sparsely, or late. Among the exceptions we could mention: the aforementioned paper on schizophrenia published in 1946; another on the same subject in the _Revue Fran\u00e7aise_ (1952); and a study on the poet Lautr\u00e9amont. Many of his papers were collected in 1970 in two volumes under the title _Del psicoan\u00e1lisis a la psicolog\u00eda social._ But the series of conferences he gave in APA in 1956\u20131957 on his original theory of linking\u2014which has inspired many authors who have later elaborated on the topic\u2014for example, was published posthumously, in 1980, as _Teor\u00eda del v\u00ednculo_.\n\nWith the group who gradually gathered around his teaching and practice (and in which the non-medical, such as Racker and the Barangers, also benefited from the contact with psychotic patients), Pichon-Rivi\u00e8re founded in 1960 the school of dynamic psychiatry, where the psychoanalytic ideas were presented and discussed in a four-hour-per-week course of three years. Jos\u00e9 Bleger, d. Liberman, E. Rolla, and F. Taragano contributed to this space of psychoanalytic thinking that appeared, as we must recall, at a moment of democratic rebirth of the society at large.\n\nJos\u00e9 Bleger (born in 1922) was perhaps the most brilliant exponent of that group, and certainly the thinker who carried the fruitful dialogue with Pichon-Rivi\u00e8re to its most achieved methodological and philosophical foundations. Perhaps Bleger's most widely internationally known contribution is \"Psychoanalysis of the psychoanalytic Frame,\" where he purports that, parallel to the frame proposed and established by the analyst in terms of space, time, and method, there exists a frame (tacitly, unconsciously) conceived by the patient that explodes to light at moments of change or crisis and should be the object of interpretation. Bleger shared with many of his colleagues in Argentina a peculiar sensitivity to the elements that may thwart the process\u2014we could say an \"ear\" to understand secret, stealthy forms of resistance.\n\nIn _Symbiosis and Ambiguity_ , Jos\u00e9 Bleger gave the largest and most systematic expression to his ideas. He there describes the psychotic part of the personality (Bion) as linked to a phase of indifferentiation in psychic development, which he terms \"glischrocharic\" (meaning an agglutinated nucleus), that logically, not chronologically, preceding the paranoid-schizoid position (M. Klein) may manifest itself throughout life in the phenomena mentioned in the title. Tough couched in Kleinian terms, both his clinical examples and his conceptual formulations in _Symbiosis and Ambiguity_ go far beyond M. Klein. They may be linked to ideas of Ferenczi and Winnicott and, of course, Bion, without detracting from their originality.\n\nJos\u00e9 Bleger is no exception in this sense. Arminda Aberastury, in collaboration with Marie Langer, translated and published in 1948 _The Psychoanalysis of Children_ ; contacts were established in supervisions, by letter and personally; Emilio Rodrigu\u00e9 went to London to be analyzed by Paula Heimann and participated in _New Directions_ with the paper \"Te analysis of a Three-Year-old Mute Schizophrenic\": these may suffice as examples that the ideas of M. Klein were widely known and accepted within the Argentinian group\u2014which nevertheless kept the width, originality, and elasticity of its views in accordance with the teachings of Pichon-Rivi\u00e8re that had also included the ideas of W. R. Fairbairn and of French authors\u2014among them, Lagache.\n\nOne more point about Jos\u00e9 Bleger. He himself considered one of the rare antecedents to the ideas he presented in _Symbiosis and Ambiguity_ to be the article by Madeleine Baranger titled \" _Mala fe, identidad y omnipotencia_ \" (1963), in which a form of ambiguous personality is described: by means of the \"Proteus defense,\" the subject aims at maintaining omnipotence by presenting a succession of internal divided characters.\n\nDavid Liberman (b. 1920) gave a systematic slant to his formidable clinical intuition when he described the phenomenon of \"stylistic complementarity\" that, unawares or deliberately, may be produced by the analyst in relation to the patient's style; for example, to a discourse in the obsessional mood, the analyst would tend to respond in a \"hysterical\/dramatic\" style. Liberman later carried his developments into the field of structural linguistics\u2014another way of inscribing, we might say, the analytic dyad into a larger \"third\" frame.\n\nAt this point, we should recall that in 1954, Luisa Alvarez de Toledo's paper \"Analysis of 'Associating,' of 'Interpreting,' and of 'Te Words'\" made a long-lasting, fundamental contribution to this topic.\n\nAnother essential participant in the intellectual atmosphere of the 1950s in Argentina was Heinrich Racker. A non-medical, trained in music and philosophy, analyzed by Jeanne Lampl de Groot until he was obliged to fee Vienna in 1939, and then by Marie Langer, Racker became a member of the argentine association with a presentation on \"Aspects of the psychoanalysis of a schizophrenic.\" From 1948 to 1959, he gave a series of papers on countertransference that had deep resonance in the thinking of that group. The fact that the analyst relates to the patient, contributes to the process with his own psychic functioning, including his conflicts, and is in absolute need of knowing this in order to help the patient and modulate the process: all these ideas so thoroughly developed became essential acquisitions both at the clinical and the theoretical level. Together with the contemporaneous papers by Winnicott and Paula Heimann, Racker's essays (gathered in Spanish as _Estudios sobre t\u00e9cnica psicoanal\u00edtica_ and published in English under the title _Transference and Countertransference_ in 1968) gave systematic bases to accepting countertransference as an element that cannot be neglected in the process. Racker died in 1961, at age 50.\n\nFinally, we should consider another author, Jorge Mom. With the seminal papers on phobias he published from 1956 on, Jorge Mom appears more concomitant than antecedent to the concept of field formulated by the Barangers. They had trained in the same milieu and kept up a lively scientifc dialogue, as evidenced by the contributions the three of them later brought to international congresses (e.g., \"Process and Non-Process\" in 1982, \"Te infantile psychic trauma From Us to Freud\" in 1988). But in the middle, there was another period in which they worked in close association.\n\nIn 1954, Madeleine and Willy Baranger settled in Montevideo with the task of developing the Uruguayan psychoanalytical movement. They organized the training system counting with the regular visits and contributions to seminars by Jorge Mom, Pichon-Rivi\u00e8re, David Liberman, and Jos\u00e9 Bleger. The Barangers took in analysis the candidates who would constitute the Uruguayan association. It was in that stimulating atmosphere in 1956 that they founded the _Revista Uruguaya de Psicoan\u00e1lisis_ , to which they gave numerous papers\u2014among them, in the first issue of 1961\u20131962, a certain \"Te analytic situation as a dynamic Field\"\u2014but that, as the saying goes, is another story.\n\n## **Notes**\n\n Originally published in _Psychoanalytic Inquiry_ 33(3) (May 2013).\n\n# 12\n\nMETAPHOR IN ANALYTIC FIELD THEORY\n\n_Giuseppe Civitarese and Antonino Ferro_\n\n> _... as I lay in bed, with my eyes shut, I said to myself that everything is capable of transposition..._\n> \n> Marcel Proust\n\nEach of the principal psychoanalytic models is underlain by certain key metaphors. For example, the archaeological and surgical metaphors, as well as that of the analyst-as-screen, all throw light on some of Freud's basic concepts. In classical psychoanalysis, however, metaphor still tends to be an illegitimate or secondary element. Analytic field theory, on the other hand, reserves a completely different place for it, both as an instrument of technique in clinical work and as a conceptual device in theoretical activity.\n\nMetaphor and the field are linked in a chiasm: the field metaphor transforms Kleinian relational theory into a radically intersubjective theory, which in turn places metaphor at a point along the spectrum of dreaming\u2014to paraphrase Bion, it is the stuff of analysis.\n\nFor the sake of illustration, we shall examine first the origins and meaning of the field metaphor in analytic field theory; we shall then consider the mutual implications of this particular development of post-Bion psychoanalysis and the modern linguistic theory of metaphor; and, finally, we shall put the theoretical hypotheses discussed in the first part of this contribution to work in the clinical situation.\n\n## **Origins of the Analytic Field Metaphor**\n\nMadeleine and Willy Baranger developed the notion of the analytic field on the basis of Gestalt theory; the ontology of Merleau-Ponty (1945, in turn influenced by the dialectic of Hegel and by Koj\u00e8ve's reading of it); Klein's concepts of projective and introjective identification; Isaacs's (1948) concept of unconscious fantasy; and Grinberg's (1957)2 notion of projective counteridentification (Etchegoyen, 1986). The Barangers' basic idea is that patient and analyst generate unconscious field fantasies, or couple fantasies, which may even become actual obstacles (\"bastions\" or \"bulwarks\") to the psychoanalytic process. These are bipersonal fantasies \"which cannot be reduced to [their] habitual formulation\u2014as, for example, in Isaacs\u2014that is, as an expression of the individual's instinctual life\" (Bezoari & Ferro, 1991, p. 48).\n\nAmong the nonpsychoanalytic sources, let us briefly consider Merleau-Ponty, because he furnishes a philosophical foundation for the field concept, which he emphasizes to such an extent as to make it the cornerstone of his own theory, and because his conception of corporeality is extraordinarily modern. By the metaphor of the field, Merleau-Ponty conceptualizes the rigorously interdependent relationship that comes into being between subject and context, the reciprocal and constant influence of self and other, and the dynamic continuity arising between consciousness and the spatiotemporal parameters of experience of the world (time and space not being containers within which the individual moves, but instead being born together with him3 )\u2014the intersubjective determinants of identity.4\n\nThe subject is formed on the basis of a substrate of anonymous, prereflective, and prepersonal intersensoriality\/intercorporeality even before any actual self-reflective capacity exists. An albeit still obscure precategorial background which, however, does not lack meaning, paves the way for the entry of the transcendental ego on to the world stage.\n\nIn this phase (which then remains as it were one of the constant dimensions of experience, given that the ego will never be able to free itself from the environmental context and from the contingency of a certain life situation), subject and object are not distinguished from each other\u2014that is to say, they are dialectically correlated. Rather than existing as positive entities, pure presences-in-themselves, except in an abstract sense, they mold each other in an incessant, fluid to-and-fro traffic of sensations regulated by the \"porosity of the flesh.\" subject and object \"co-originate\" in a primordial medium to which both belong. Touching something is at the same time being touched. Our sense of the world is not only an intellectual content, and cannot dispense with our experience of our bodies; it stems from our _fleshly_ existence and is present even before a consciousness of self forms. Hence Merleau-ponty's assertion: \"I am a field, an experience\" (1945, p. 473)\u2014that is, _a system of relationships_.\n\nThe Barangers' essay in which the French philosopher's vision is subsumed, \"Te analytic situation as a dynamic Field,\" dates from 1961\u20131962. Significantly, in the same years Winnicott and Bion were laying the foundations of a radically intersubjective psychoanalytic theory of the birth of the psyche. The dialectic that underlies subjectivity\u2014which could in Bion's sense be formulated in terms of the binary couple _narcissism\/socialism_ \u2014seen as an ongoing process, is the same as that which Winnicott sought to apprehend by his famous gerunds, such as _coming-into-being_ , _a going concern_ , _holding_ , _handling_ , _object-presenting_ , _realizing_ , or _indwelling_. In this way, as Ogden (1992, p. 620) explains, Winnicott\n\n> captures something of the experience of the paradoxical simultaneity of at-one-ment and separateness. (a related conception of intersubjectivity was suggested by Bion's [1962a] notion of the container-contained dialectic. However, Winnicott was the first to place the psychological state of the mother on an equal footing with that of infant in the constitution of the mother-infant [relationship]. This is fully articulated in Winnicott's statement that \"There is no such thing as an infant [apart from the maternal provision].\"\n> \n> (Winnicott, 1960)\n\nFor an ideal genealogy of the field metaphor in psychoanalysis, Bion is an unavoidable reference. While the Barangers do not quote him in their now classical paper, Madeleine Baranger5 (2005; Churcher, 2008) acknowledges his influence on her from the early 1950s on. At that time, Bion was already developing a highly original theory of the analytic field, although he did not use that metaphor.6\n\nIn his contributions on the \"basic assumptions\" (1948), which date precisely from those years (Ferro & Basile, 2009, p. 92f.), he develops the concept of unconscious fantasy within the group. The analytic couple is in fact already a group. In Bion's view, individuals are endowed with \"valences\"\u2014the term, borrowed from chemistry, denotes the propensity of atoms to bind together into molecules\u2014that is, the spontaneous and instinctive (unconscious, automatic, and inevitable) capacity to establish mutual emotional bonds, \"for sharing and acting on a basic assumption\" (Bion, 1948, p. 153), \"behaviour in the human being that is more analogous to tropism in plants than to purposive behaviour\" (ibid., p. 116f.). The basic assumption, whether pair, Fight-Flight, or dependent, gives rise to \"other mental activities that have in common the attribute of powerful emotional drives\" (ibid., p. 146). It is \"the 'cement' that keeps the group assembled\" (L\u00f3pez-Corvo, 2002, p. 39).\n\nValences and basic assumptions express the psychological function of an individual as dictated by the \"proto-mental system.\" The proto-mental system is one of Bion's more speculative concepts, in that it \"transcends experience\" (1948, p. 101). He coined it to explain the tenacity of the emotional bonds that keep the group together, linking its members in a common psychological situation, and to denote a dimension of the psyche in which the basic assumptions that are for the time being inactive can be accommodated. The proto-mental system is\n\n> one in which physical and psychological or mental are undifferentiated. It is a matrix from which spring the _phenomena which at first appear\u2014_ on a psychological level and in the light of psychological investigation _\u2014to be discrete feelings_ only loosely associated with one another. It is from this matrix that emotions proper to the basic assumption flow to reinforce, pervade, and, on occasion, to dominate the mental life of the group. Since it is a level in which physical and mental are undifferentiated, it stands to reason that, when distress from this source manifests itself, it can manifest itself just as well in physical forms as in psychological.\n> \n> (ibid., p. 102, our emphasis)\n\nThe absence of a distinction between the physical and the mental in the proto-mental system is of course reminiscent of the ambiguous status of the drives in Freud, as a \"concept on the frontier between the somatic and the mental,\" just as the valences call to mind the concept of libido (Fornaro, 1990, p. 55); the point here, however, is that \"proto-mental phenomena are a function of the group\" (Bion, 1948, p. 103). _The individual's proto-mental system is merely a part of a larger whole, namely the proto-mental matrix of the group, and cannot therefore be studied in isolation from it_.\n\nIt will be seen that, already for Bion\u2014who is here absolutely in unison with Merleau-Ponty\u2014the subject cannot be thought of except on the basis of the intrinsic intersubjective dimension of the proto-mental system, of the area of \"initial biopsychic emergence\" (Fornaro, 1990, p. 20, translated). Mental life extends beyond the physical boundaries of the individual; it is \"transindividual\" (ibid.). Hence the (relative) absence of a distinction between mind and soma in the individual is in some way correlated with the background of a substantial (relative) absence of distinction between individuals.\n\nWith regard to Merleau-Ponty's postulate of the ego-as-field and Bion's of the proto-mental area, the concept of projective identification now assumes powerful explanatory force, because it so-to-speak confers \"tangibility\" on the communication channels through which this common, unconscious psychological area can establish itself, as well as on the _way_ in which it can do so. It imparts \"visibility\"\u2014in Greek, _theorein_ means to see or contemplate\u2014to the concrete and indispensable points of contiguity whereby the processes of interindividual mental influencing take place.\n\nThese theoretical foundations show that, already with Bion, and even more with the developments that came after him and the transition to an analytic field theory, psychoanalysis underwent a change of paradigm of the kind described by Kuhn (1962). For example, it may be misleading to define the characteristics of the analytic field in terms of the use of the classical concepts of transference and countertransference, because these presuppose a configuration in which analysand and analyst \"face each other\" as two positive, pure, complete, and separate subjectivities, each somehow totally \"external\" to the other. Ogden comments:\n\n> I believe the use of the term _countertransference_ to refer to everything the analyst thinks and feels and experiences sensorially obscures the simultaneity of the dialectic of oneness and twoness, of individual subjectivity and intersubjectivity that is the foundation of the psychoanalytic relationship.\n> \n> (Ogden, 1994a, p. 8, n.)\n\nIn a theoretical framework inspired by a one-person psychoanalysis, the concept of projective identification too would assume an a-dialectic and substantially solipsistic meaning. If, however, subject and object are thought of as places in an intersubjective field, it will be realized, as Ogden (2008) writes, that when a patient goes into analysis, he so to speak _loses his own mind_. He reconnects with the reestablished proto-mental area. He initiates a communication which involves him in depth and can be channeled in such a way as to repair dysfunctional places in his internal group configuration, to restart the conversation that the various parts of the mind incessantly carry on among themselves, while always seeking better ways of thinking about his current emotional problem (however, terms such as unconscious thought, dreaming, thinking, and the like must be seen as virtually equivalent).\n\n## **Elements of Analytic Field Theory**\n\nAnalytic field theory fruitfully combines the contribution of the Barangers with the developments of post-Bion thought and certain ideas derived from modern narrativity known in the english-speaking world by the labels of _critical theory_ and _reader-response criticism_ , and developed in Italy by, in particular, Umberto Eco (Ferro, 1999b). Another important component, on the other hand, stems, via Luciana Nissim Momigliano (2001), from Robert Langs and his original conception of the spiraling progression of the unconscious dialogue between patient and analyst. Other significant notions are the emphasis by Ogden (1979) on the concept of projective identification in a strongly relational sense, and that author's more recent idea, avowedly inspired by Koj\u00e8ve's lectures7 on Hegel (!), of the \"intersubjective analytic third\" (1994a). Nor must one disregard the fundamental contribution of Bleger (1967) on the \"institutional\" nature of the setting and on everything involved in the formation of the individual's so-called _meta-ego_ (Civitarese, 2008).\n\nThese initial remarks already point to the reason for the central position of the metaphor\u2014and with it the \"philosophy\"\u2014of the field, perhaps because no other lends itself better to the construction of a radically intersubjective psychoanalytic model, which we consider to be most suited to a psychoanalysis for our time. By virtue of a whole set of theoretical increments, the metaphor of the field has succeeded in expressing all its theoretical and clinical potentialities, such as grasping\/ casting, characters of the session, narrative derivatives of waking dream thought, transformations in dream, weak or unsaturated interpretation, and the like (Ferro, 1992).\n\nThe field metaphor is of course borrowed from electromagnetic or gravitational field theory. Its essential properties are that it represents a _dynamic_ totality, and that it is _inclusive_ , _invisible_ (but deducible from its effects on its constitutive elements), and _delimited_ (even if constantly in the throes of contraction or expansion).\n\nThe field is intrinsically unstable and subjected to continuous displacements of energy. The forces concentrated at a given point in the field can have effects on other forces in locations remote from that point. Hence all the elements in a field are structured as a differential system in which each term is defined in relation to the others in a process of constant, mutual cross-reference. This is not very different from de saussure's conception of the structure of language, Lacan's of the system of signifiers in the unconscious, or derrida's of the text. Perhaps only chaos theory could offer an effective representation of the dynamism of the field, because it can model the complex vectorial manifestations that give rise to turbulence, catastrophic points, and ultimately changes of state.\n\nFurthermore, the field is delimited. It is a container. This does not of course mean that it is a closed system; instead, by causing itself to be contained, it is itself in a dialectical relationship with what is outside it\u2014that is, with other, broader containers (social groups, institutions, ideologies, etc.). However, the fact that the field is relatively closed permits account to be taken of what may be defined as _inclusiveness_. This is an aspect given an original interpretation by Antonino Ferro, who radicalizes the model of the field already outlined by the authors mentioned above, and invites us to see _any_ element within the fictional frame of the setting as (virtually) a function of the analytic field.\n\nIn clinical psychoanalytic work, the field concept effectively supports the extension of the dream paradigm of the session, to which it imparts rigor, because it puts to work in the couple Klein's concept of projective identification (albeit as revised and corrected by Bion and Ogden) and Bion's of \"waking dream thought\" (we dream not only at night but also during the day). There is no point in the field (whether an event, a memory, a dream, an enactment, a reverie, an association, an emotion, a sensation, or whatever) that is not touched by the \"electromagnetic waves\" of the intersecting projective identifications of patient and analyst, and that does not correspond to the recordings made of it by their respective alpha functions; it might in fact be better to invoke the alpha function of the field (or its _gamma function_ , as Francesco Corrao called it). This function represents the capacity of the couple, outside the rigid framework of a subject\/object dichotomy, to narrate, dream, think, and construct metaphors or myths in order to attribute a specific meaning to their joint experience. The field takes the form of \"a system dedicated to the transformation of sensory and emotional experiences into thoughts and meanings, [and confers life on a] theory of treatment centered on the transformations and developments of the psychoanalytic field (which includes the analyst, the patient, and theories) rather than on individuals and contents\" (Neri & Selvaggi, 2006, p. 182, translated).\n\nA limitation of the field metaphor is that it might suggest a two-dimensional situation. This may indeed be the case when a quasi-autistic type of mental functioning arises. Instead of actual characters, there are only fat, emotionless \"picture cards.\" The patient draws the analyst into an exclusively concrete world. Play is impossible. There are no metaphors, no dreams, and no reveries. If, however, these possibilities can gradually be introduced, that will be tantamount to adding new dimensions or worlds to the field. Moreover, except in these situations the field _is_ as a rule multidimensional\u2014it is a _pluriverse_.\n\nEach of the characters in the analytic dialogue, \"including those called the analyst and the patient\" (Ferro, 2010, p. 428, translated), and their internal worlds (!), represents a specific place in the analytic field. However, the following can also be places in the field: its scenic component (the ongoing formation and transformation of the characters); the analyst's mind; the countertransference; the place of formation of images (waking dream thought) and its derivatives; the analyst's actual countertransference dreams; his reveries; the internal worlds of the analyst and the patient; their histories; their relationship; enactments; projective identifications and all their vicissitudes; and the transgenerational elements of both protagonists (Bezoari & Ferro, 1991; Ferro, 2006a). The art of the analyst is to apprehend the patient's point of view, using the restrictions imposed from time to time on the field by the viewpoint that can be assumed by dwelling in one of its many different places.\n\nIt would of course be misleading to think of this situation in terms of a process of constant, hyperwakeful monitoring of the field, which would be mechanical and unproductive. The metaphor of virtual reality (Civitarese, 2008), which is basically an extreme form of the concept of the transference neurosis, can be used to show how a clinical and theoretical field model aims to keep two aspects in balance\u2014namely, the usefulness for the actors in and authors of the analytic dialogue of _losing themselves_ in the fiction established by the setting (which means intimacy, closeness, spontaneity, emotional intensity, and authenticity), and the need to _reemerge from it_ in order to gain access to the plurality of the possible worlds in which they are simultaneously living.\n\nIn this way it is possible to satisfy, on the one hand, a poetics and an aesthetics of emotional involvement (how to allow oneself to be captured by the text of the analysis, and why), and, on the other, a poetics and an aesthetics of disenchantment (how to achieve the insight that the text is a fiction, and in view of what effects). The analytic field might then perhaps be definable as a medium\u2014a means of communication\u2014in which the analyst seeks to achieve the best possible balance between immersion and interactivity, between semiotic transparency and self-referential demystification (like dreaming and waking from a dream, both of which are necessary for the definition of a dream). Unless the oscillations between these poles are made explicit, the result will be narrative interpretations or, in other words, transference interpretations (which are in fact nothing but metanarrations).\n\nWhen Ferro attributes an innate transformative capacity to the field and to the narrativities it expresses, he is on no account invoking some kind of magical virtue inherent in it, but rigorously articulating the intersubjective implications of the field metaphor and of analytic field theory. The mere fact of being in a room already modifies the chemical composition of the air breathed by its occupants. Likewise, any change in the medium in which they are immersed influences both patient and analyst, even if the change is coincidental and peripheral to the points of concentration of the system of forces in the field that correspond to the two subjectivities involved. If a cellphone rings, the field is modifed. The modification is even greater after a significant exchange in the analytic dialogue. Between the two \"places\" represented by the patient and the analyst, there occur interactions that are to a greater or lesser extent direct and of variable intensity and to a greater or lesser extent differentiated in terms of the continuum from metonymy to metaphor, from sensoriality\/intercorporeality to the exchange of concepts or to the vicissitudes of the unconscious projective and introjective processes.\n\nThe field, seen as a dynamic system that identifies with the analytic couple and interweaves narrations that tell instant by instant of its own functioning, is a viewpoint very different from that of an analyst acting as a screen for the patient's projections. If three \"negative\" characters appear in the first analytic session after the summer break, they may be regarded as three areas of emotional congestion, lumps of nonthinkability waiting to be narrated and broken up (like the crime featuring at the beginning of a traditional thriller)\u2014but without any need to be made explicit by interpretation, unless the actual psychoanalytic game of interpretation itself becomes a place in the field, or a character in the text of the analysis. If one of the three \"baddies\" were an incompetent lifeguard or a rude barman, the narration could develop along the lines of understanding why he behaves in this way, of making hypotheses, of getting to know them, of considering them from a number of different possible points of view, and of trying to guess the reasons for them\u2014in a word, with a view to seeing if it is possible to bring about a transformation that can rid the field of the initial atmosphere of persecution. Of course, the patient could perfectly well signal the change in the plot by allowing a new character to take the stage. Beneath the new mask, however, the analyst would have no difficulty in recognizing the same tangled ball of emotions in the process of transformation.\n\n## **Metaphor as a Rhetorical Figure and as a Basic Cognitive Mechanism**\n\nMetaphor, in the sense of a rhetorical figure, is a schema (a \"configuration\" according to Mortara-Garavelli, 2010) that serves to model the expression of thought. A synonym of a rhetorical figure is a \"trope,\" which means \"turn,\" denoting an effect of \"deviation and transposition of meaning.\" When the \"deviated use\" becomes habitual, the metaphor turns into _catachresis_ (this Greek coinage means \"misuse\"). The irregularity receives the sanction of law and even becomes the norm. A catachresis, like certain state pardons granted for especially common offenses, is the fruit of a \"necessity\": it provides a name for an object that did not previously have one. The institution of a catachresis is therefore governed by a principle of economy which is applied at the cost of a certain imprecision, while also involving an effect of polysemy, or expansion of meaning. It is only when a catachresis is awakened from its sleep\u2014as often occurs in analysis by virtue of the attention devoted to the play of the signifier, for example in the case of a parapraxis or a joke\u2014that its primal nature as a metaphor is revealed. The memory of the underlying abuse then comes to the surface. A catachresis is usually seen as different from _extinct_ or lexicalized metaphors, which are now completely unrecognizable as such except by exploring the derivation of the word concerned (for example, the Italian word _testa_ [head] comes from the identical latin word, which originally denoted the shell of a tortoise\u2014ibid.).\n\nMetaphor is deemed the queen of tropes, \"the easiest to recognize and the most difficult to define [...] a mechanism that is so universal and so within everyone's reach has resisted every attempt to explain it completely and homogeneously\" (ibid., p. 9, translated). After all, metaphor is not always the contraction of a comparison or a simile that is abbreviated or described as such. The analogy is in fact often not recorded but _created_. Metaphor is the invention of an intelligence that is \"sympathetic\" (de Beistegui, 2010, p. 35, translated) to the matter of the world, a way of assigning a personal meaning to it, and of impressing one's own \"style\" on it. It is not the fruit of an analysis of the similarities and differences between two terms\/objects thought of as always identical with themselves, but itself _generates_ the relationship. Establishing a metaphor is tantamount to the use of a kind of violence, to causing a slight shock; in this respect, it is more consonant with a psychoanalysis understood as a _development of narrations or opening up of possible worlds_ , and less with a psychoanalysis that translates the unconscious into the conscious and is inspired by a cold, distant, and objective intelligence, as, for example, Freud's surgical metaphor might suggest.\n\nIt is at any rate clear that, on the one hand, language is composed of a gradient of abusive acts (cf. De saussure's notion of the arbitrary nature of the link that joins the signifier to the signified, the word to the thing, or separates them from each other, or Aulagnier's idea of the \"violence\" of interpretation, 1975), while, on the other, it is nothing but a \"cemetery of tropes\" (Mortara-Garavelli, 2010, p. 11, translated): violence and mourning would appear to lie at the origin of language and culture. Be that as it may, metaphor's constant \"transportation\" of heterogeneous terms remote from each other, like the subterranean cars of a subway train between stations, serves the purpose of _seeing reality_ \u2014of seeing it for the first time, as children do; and children of course produce highly original metaphors. They also make it possible to see again with new eyes, a capacity possessed by poets in greater measure than anyone else. For this reason it is indeed the case that \"metaphors can be the ghosts of ideas waiting to be born\" (Bion, 1977, p. 418). They are ultimately the royal road to reality, because they express the functioning of what we sense to be a basic cognitive mechanism of the psyche\u2014an actual \"principle of knowledge rather than of recognition\" (de Beistegui, 2010, p. 44, translated).\n\nIn a famous passage from _Totem and Taboo_ , Freud discusses the way in which magic thought treats past situations as if they were present:\n\n> It is further to be noticed that the two principles of association\u2014similarity [\u00c4hnlichkeit] and contiguity [ _Kontiguit\u00e4t_ ]\u2014are both included in the more comprehensive concept of \"contact\" [ _Ber\u00fchrung_ ]. Association by contiguity is contact in the literal sense; association by similarity is contact in the metaphorical sense. The use of the same word for the two kinds of relation is no doubt accounted for by _some identity_ [ _Eine... Identit\u00e4t_ ] in the psychical processes concerned which we have not yet grasped.\n> \n> (Freud, 1913b, p. 85, my emphasis)\n\nFreud here identifies an essential, albeit problematic, quality of the mind that makes the creation of meaning possible. He postulates the existence on the infralinguistic level of a central psychic mechanism, albeit as yet indeterminate, and does so by invoking linguistics and rhetoric. He thus subordinates similarity (metaphor, from the Greek _metapherein_ , \"to transport\") and contiguity (metonymy, from the Greek _metonymia_ , \"exchange of name\"\u2014although what is involved here is not so much the classical definition of the figure as the type of semantic relationship, based on its implication of coexistence\/proximity) to \"contact.\" But when we say \"contact,\" are we not in fact still referring to an idea of contiguity? in other words, are we not stating that the second of the modes of relating, contact _in the direct sense_ , is primary? it is no coincidence that the English words, as well as their Italian equivalents, have a common root in the latin _contingere_.\n\nFreud here seems to be alluding precisely to the relationship between metaphor and metonymy, a figure (of \"contiguity\"\u2014Mortara-Garavelli, 2010, p. 23, translated) that is no less important and no less difficult to define. The debate is ongoing in the linguistic field: some hold that metaphor can be reduced to metonymy because it is the fruit of a twofold metonymy (\"'two metonymies short-circuited,' or, as it were, the product of two synecdoches\"\u2014ibid., p. 24, translated). From this point of view, metonymy is the only transformational device, or trope, that can be thought of both as a general function of semiosis, and as something that entails a strategy of thought _which cannot be further broken down_.8\n\nOrdinary usage of course relies on traditional definitions and customary practical distinctions. However, this hypothesis will facilitate the tracing of thought, and the huge gulf it can bridge in joining even the most diverse of objects in metaphor, back to their bodily and sensory roots (as Merleau-Ponty teaches); to the cheek-breast interface (a relationship of contiguity), an \"area of sensations of a soothing sort\" that is the first nucleus of subjectivity (Ogden, 1994b, p. 174); and to the first (the most elementary) \"translation,\" which Freud may have had in mind in 1895 when he wrote in the \"Project\" that, for an infant at the beginning of life, the object is his own cry. Metonymy would then in effect be metaphor in its ground state, and thought an extension (virtualization) of the concrete and direct interbody contact that acts as a matrix for a child's nascent psyche (or for the development of the rudimentary subjectivity\/alpha function with which a child might already be endowed at birth). _\" Transferred contact\" (i.e., contact at a distance) would then be referred to \"direct contact,\" the intellect to its sensory and bodily roots, and the isolated subject to the intersubjective field_.\n\nHowever, as (mostly verbal) rhetorical figures, do metaphor and metonymy not correspond, as Lacan maintains, to the two key dream mechanisms discovered by Freud, namely condensation and displacement? _So in trying to define metaphor and metonymy, are we not actually referring to the meaning of dreaming? After all, did Bion not say that we dream not only at night but also during the day, and that to dream is to think?_ here, then, linguistic theory and psychoanalysis, although starting from different vertices, are seen to converge in formulating the idea that _in order to name things (to think), it is necessary to construct metaphors or to dream (to displace\/to condense)_ , and that these are two modes of expression, albeit on different levels of abstraction, of one and the same basic psychological process.\n\nThis meeting between a new theory of dreams (and of reverie) and narratology (and the modern theory of metaphor) underlies the model of the mind that serves as a framework for analytic field theory. Let us therefore briefly consider this model before turning to clinical examples.\n\n## **A Model of the Mind**\n\nIn psychoanalysis, the realm of the image is the dream. Perhaps we should say \"was\" rather than \"is,\" at least since Bion provided us with a model of the mind involving the continuous production of images (that could be called pictograms) by a function (described as the alpha function) on the basis of the sensoriality that pervades us from whatever source. The sequence of images somehow soothes and pacifies the mind whenever the transformation is successful. The result is a sequence of such images or pictograms, called \"dream thought of the waking state.\" These images are normally unknowable in themselves. Given, for example, a sequence of powerful sense impressions such as relatively undefined proto-emotional states of rage \u2192 relief \u2192 longing, a possible sequence of pictograms might be:\n\nOf course, the choice and construction of an individual \"pictogram\" and of sequences of pictograms are extremely subjective. It is like one and the same \"subject\" painted by degas, and then by Caravaggio, Monet, Chagall, Picasso, etc.\n\nTis, then, is the mind's first locus of creativity. In Bion's terms, it would be the transformation beta (via the alpha function) \u2192 alpha.\n\nThere is also a second locus of creativity in the mind. In a manner that is again extremely subjective, the sequence of pictograms (waking dream thought) is \"narrated\"\u2014that is, put into words. Here too, an infinite number of narrative genres can be used to perform this transformation. In any case, _narrative derivatives_ of the pictograms (or of the alpha elements, or of waking dream thought) are the outcome.\n\nThe sequence in the above example could generate a set of stories differing in style but all characterized by one constant\u2014namely, the succession rage\u2013relief\u2013longing. A \"memory\" of infancy leads to a \"diary entry,\" a chronicled event, a fantasy, and so on.\n\nWe can also come into contact with a pictogram of the sequence that forms in our mind in (and outside) an analytic session, by the phenomenon we call reverie. Reverie enables us to make contact with the image synthesized by the alpha function\u2014for example, that of a \"storm.\"\n\nAnother situation in which a pictogram of the sequence originating in waking dream thought is \"seen\" is when the patient projects one of these images to the outside, thus endowing it with a strongly sensory character; this is not a true hallucination, because the meaning it conveys can easily be guessed. A telling example is that of the patient who responded to a request by one of the present authors for an increase in fees by exclaiming: \"Good heavens, I can see a chicken being plucked on the wall opposite!\"\n\nAccording to this model of psychic life, throughout the day an enormous number of pictograms (alpha elements) are constantly forming and being transferred to memory. These are acted upon by an \"alpha-megafunction\" (Grotstein, 2007, p. 271)\u2014a mental device that performs a kind of second pressing or weaving of this material, eventually giving rise to dream images. These are the most \"digested\" elements which our apparatus for thinking thoughts is capable of producing.\n\nIt is no coincidence that Ogden holds that a psychoanalyst's work consists of dreaming\u2014that is, of undertaking the transformations of sensory \"storms\" into images which the patient cannot perform by himself. It follows, too, that the aim of analysis is to develop in the patient the capacity to \"generate images,\" to create dreams out of the forms of concrete thought represented by symptoms.\n\nO'shaughnessy (2005) distinguishes Bion's notion of waking dream thought from Klein's conception that the infant mind possesses from the beginning a rich unconscious fantasy life manifested in sensations and affects. Both of these processes confer meaning on experience, even if waking dream thought entails something new\u2014namely, the idea of a primary process (situated upstream of unconscious fantasy) of transformation\/\"alphabetization\" of the crude data of experience.\n\nLet us try to describe what happens in the analyst's consulting room. The patient arrives with a variously sized bottle of ink (his anxieties and proto-emotions\u2014in the jargon, his beta elements), which he keeps pouring on to the special kind of blotting paper represented by the field. The field absorbs the ink and becomes thoroughly soaked in it. Analyst and patient dip their pens into this ink in order to write down the text of the session. What was previously a mere formless blot is transformed into stories, narrations, and constructions. In this way, what at first had a \"soiling\" effect becomes susceptible to thought, narration, and sharing.\n\nAnother image of the patient's problem might be that of a big horse, with \" _ferri_ \"(!)9 on its hoofs, which, as it gallops, clip-clop back and forth like the types of an old-fashioned typewriter. However, eventually the horse finds a groom to take care of it, and as its hoofs fail back and forth, it begins to write at first fragments of stories, and then complete stories. Moreover, in the process of writing it calms down, grows ever smaller, and ultimately ceases to be a problem.\n\n## **The Aesthetics of Metaphor and the Analytic Field**\n\nSo far we have considered the significance of the field metaphor as the organizing schema of a particular psychoanalytic model.10 examples include the use of the archaeological, military, and chess metaphors in Freud's theories; Bion's digestive and sexual metaphors; or the gastronomic or cinematographic metaphors employed by Ferro (1992, 1996). We then proceeded to examine metaphor as a rhetorical figure and an elementary psychological mechanism (cf. Also the now classical studies of Lakoff & Johnson, 1980a); _and, on the basis of a passage from Freud and certain cues from the linguistic theory of metaphor, we postulated the substantial identity of metaphors and dreams (and visual images)_. Last, we come now to the meaning and use of metaphor in both the broad sense (referring to the level _of_ discourse) and the specific sense (of an image or rhetorical figure involved _in_ discourse), as a technical device in clinical psychoanalytic work within a field model.\n\n### Playing with Metaphors\n\n#### __Not Just Herbivores__\n\nPaolo begins his analysis as the good boy that he is. In his first session, he tells me about his attempts to fix his \"Vespa,\" which has been lying about, forgotten for years. After a number of sessions devoted to this subject, I venture to suggest that \"sometimes a _vespa_ [Italian for wasp] will sting.\" A prolonged silence ensues.\n\nIn the next session Paolo, who has hitherto always come along with a laptop, tells me: \"My computer has been struck by lightning and it is literally completely burnt out.\" So I mitigate the pressure of my interpretations, which was intended to demechanize certain aspects of the patient, but when I later return to a more pungent interpretative regime, there appears \"the neighbor who collects weapons and who seemed to be aiming a threatening submachine gun.\" When I return to a more \"playful\" style of interpretation, Paolo mentions the neighbor again, saying that his gun\u2014now he has had a clear view of it!\u2014has a red plug on top of it. It is manifestly a toy weapon, so there is no reason to be worried.\n\nAs the analysis proceeds, he tells me about his grandmother's farm, which is populated by a whole menagerie of chickens, ducks, hens, sheep, cows, and so on\u2014until one day I ask him if he is not fed up with all these herbivores (!). Paolo at first reacts as if struck by a wave of persecution, but in the final session before the summer vacation, I am surprised to be given a present of little toy wild animals. On returning from vacation, he discovers, carved into the beams of the ceiling of my consulting room, a five-pointed star, the symbol of the red Brigades\u2014which neither I nor the patients on the couch had ever noticed in thirty or more years.\n\nI now realize that rage and revolution have entered the room. However, when I try to find the carving again, I cannot focus on it: these aspects of Paolo tend to disappear. On another occasion when he shows me the five-pointed star and the mark of the red Brigades, I take the opportunity of telling him that he has the eyes of a hawk. In this way, I am substituting the hawk for the lost little sparrow he kept in a cage, about which he had told me at length.\n\nThese more intensely passionate aspects make their entry into the sessions, albeit in \"bleached white\" form, when he receives a letter from his girlfriend, from whom he has heard nothing for a long time; after a prolonged silence on my part, he comments: \"I didn't know whether to tear it up or to open it with the letter opener.\"\n\nIt will thus be seen that metaphor in the strict sense of the term (as a word-related fact) belongs to the order of the narrative derivatives of waking dream thought, but also that the process whereby it comes into being is the same as that of unconscious thought. The transformations from sensoriality into narrative derivatives are \"metaphorical,\" and conversely the metaphors are narrative derivatives.\n\n### Metaphors Living or Dead?\n\n#### __The Check__\n\nAndrea tells me of the climate of anxiety into which he was plunged by a friend who made him fear that he would no longer receive his monthly check for his new job. In fact, it would not be very serious even if he did not receive this check, as that would enable him to look for a more satisfying, better paid job. However, his friend has succeeded in making him feel persecuted and threatened, as well as open to the envy of others.\n\nThe \"friend\" of course represents a kind of functioning in the patient himself which, in the absence of analysis at the weekend, manages to undermine his (wavering) basic level of confidence, plunging him into a climate of discomfort and distrust, and causing him to lose sight of the progress he has made.\n\nI now make a metaphorical intervention. I tell him that he reminds me of a competent swimmer who is told that his lifejacket might be removed or that he will not be given one, because he doesn't need it and it would get in his way. My point is that this image, however, is not a preconstituted metaphor, because it arises in me, with him, there, in real time, for the first time and simultaneously with his communications. It is a reverie produced on the spot, or rather, one whose discursive formulation arises out of a reverie\u2014which is not directly communicable in itself, in its visual form, just as a dream is not communicable except by a kind of intersemiotic \"transmutation\"\/translation; that is, after being transferred from one system of signs to another, different system of signs.\n\n### Introducing the Patient to the World of Metaphors, or the Resumption of Dreaming\n\n#### __Lucio's Grease Gun__\n\nI tell Lucio that I shall be away for a couple of weeks (for professional reasons). He begins the next session by saying that _he has not had any dreams_. He then tells me that he took the cat along to be neutered and that he feels quite calm. He adds that he has met with one of the leaders of a pacifist association, who has been abandoned by his wife and weeps inconsolably. His wife cheated on him, taking up again with a female fellow student with whom she had already had a relationship.\n\n_I tell him that, if we were to look at these two communications as if they were two dreams_ (that is always one of my listening vertices when a patient speaks to me), we might think that he was worried that, if the cat had not been neutered, it might perhaps scratch me. What is more, who knows what might happen if the member of the pacifist organization who cried because of _my_ cheating on him, even if the cheating was in a way \"justified\" (for a congress, as he tells me he has discovered on the internet), was actually the Mexican revolutionary Pancho Villa or simply the Italian national hero Garibaldi.\n\nLucio immediately gets my drift, and says that he has nevertheless begun to make some progress. He has not yet become Garibaldi, but has at least taken on some of that worthy's boldness of character. He has, for example, plucked up the courage to go to the pharmacy to buy a vaginal lubricant for his girlfriend, who suffers from a dryness in that region. In the past he would never have exposed himself in this way, but this time he felt no shame. He asked for a \"nonspermicidal vaginal lubricant.\" he then remembers the film _Kill Bill_ , in which a male nurse gave a jar of Vaseline to someone about to have sex with a woman whose vagina was so dry that \"without the Vaseline it would have been like sticking his penis into a can of sand.\"\n\nI tell him he has been quite Garibaldi-like in managing to show his needs to the \"pharmacist,\" but at the same time, it seems to me that he feels the need to lubricate his relationships because he wants to avoid any friction with others. Yet he is still leaving something \"alive,\" he is not eliminating everything. Lucio confirms my interpretation, telling me of some episodes from his childhood in which, so as not to upset his parents, he always avoided any \"friction\" with his classmates, in what was in fact a pretty turbulent class. In the same session, he makes a slip, when he tells me of his \"fear of not being able to stop\" (he meant to say the opposite), and then wonders whether he should see himself as a bull dressed up as an ox or an ox dressed up as a bull. We then work on these themes of containment\/ noncontainment, referring also to the Michael Douglas movie _Falling Down_ , and Lucio returns to the subject of lubrication as the end of the session approaches. As a boy, he tells me, he already enjoyed using a grease gun to lubricate the gears of his bicycle; it was a sort of elongated contraption with a nozzle that made a very good job of lubricating. I now tell him that it seems obvious to me that a bull likes making women grow fat,11 and what better way could there be of making them pregnant (referring to a wish to have children that cannot be made fully explicit).\n\nWe thus observe an entire spectrum of shades of defense concerning the \"bulls,\" the feared and uncontainable proto-emotions that extend from the production of autism to that of a bonsai, of a mechanism, and of lethargy. In particular, however, we see how, little by little, a space for dreaming is regained by a series of metaphorical openings\u2014in fact, amounting to a kind of _ongoing metaphor_.\n\n### Negative Reverie\n\nThe analyst's mind should be receptive and capable of absorbing and containing the patient's emotions\u2014that is, of transforming proto-sensory and proto-emotional states into images and hence into thought, and then of imparting the method to the patient. Any narration, however seemingly realistic, always tells us as analysts (and only as analysts) of something else: of the patient's internal world and, in particular, if we are able to listen, of the appropriateness or otherwise of his instruments (for feeling, dreaming, and thinking). In substance, analysis has to do with all the methods whereby these instruments (and apparatuses) can be developed (and sometimes created).\n\nA symptom often takes the form of a \"stopper\" to prevent the emergence of something unknown both to the patient and to ourselves, but about which we ought sooner or later to become capable of \"dreaming together.\" At the beginning of an analysis, and at the beginning of each session, we should deploy our \"negative capability\" (a PS without persecution), and be able to wait for a meaning to slowly take shape. Every hypothesis of meaning that we formulate, and every misused metaphor that we employ, should be rapidly set aside, so as to put ourselves into a mental state open to the new and unpredictable.\n\nTings do not always turn out that way. Our functioning is sometimes affected by various degrees of negative reverie (\u2013 R), partially or totally blocked reverie\u2014perhaps even a situation of reversed functioning, in which the mind that is supposed to receive and transform projects things into the mind that wants and needs to evacuate and find a space and method to manage proto-emotions. These forms of mental functioning\u2014these traumatic facts (trauma is basically exposure to more beta elements than one can receive and transform, either by oneself or with the other's help)\u2014are then, as always, narrated in an infinite number of scripts.\n\n#### __Gino__\n\nIn one of his sessions, Gino takes out a Barbie doll and says: \"How's the dancer today?\" The therapist interprets the question as directed to herself and answers: \"Very well, and how are you?\" \"I'm at the cemetery,\" he answers (this seems to be something that has actually happened; it is the only way Gino can deal with the despair he has felt in the interval between sessions). He says the girl he likes most was not in class and the teacher was not listening. Gino is immediately noticing that the therapist has failed to pick up his depression, and adds that he would like to touch the long, bushy hair of his female classmates. Disoriented by the concreteness of the communication, the therapist (whose hair is cut short almost to her scalp) fails to grasp his wish for a gentle, soft touch, and says: \"Does it turn you on?\" Now also disoriented, Gino mentions a girl in his class who removed the hand he had placed on her hair, and then tells the therapist that he saw a boy blowing on a girl's hair. The feeling of being repelled makes Gino puff, but the warm, emotional component of puffing is lost in the blowing.\n\nHe goes on: \"Our teacher came to school wearing an undershirt, so can the boys wear a T-shirt on top of their sweaters?\" He adds: \"They're speaking German.\" There is a coded message here; restoring the freeze-dried emotion that has been sucked away, the communication becomes: \"You told me something about yourself (being turned on), so can I reveal intimate things too instead of covering them up?\"\n\n_Gino is in effect constantly sucking in the emotional sap of metaphor, and what the therapist ought to be doing (but cannot because she is in \u2013R) is to restore sap and emotional and affective solidity to what (seemingly) has to remain totally neutral in order to be expressed._\n\nGino begins another session as follows: \"Do you have a short-sleeved T-shirt? take of your sweater!\" His meaning seems to be: \"Uncover yourself, show the emotions you have underneath!\" He then adds: \"Is my hair clean?\" He is afraid the therapist might think there is something dirty in his communication (the \"turning on\" mentioned by the therapist), whereas Gino's communication is innocent! he adds: \"I want to grow a pigtail; I also like people with a crest on their heads.\" Although this too could be seen as a sensualization or erotization of the communication, I do not think that is correct. Until not long ago, in his sessions Gino used to lean over the desk with his face as close as possible to the therapist's. It was like the tropism of a plant toward the light, a kind of \"vegetable\" behavior (but previously, locked up in his mute amimia, his behavior had been mineral in nature for years on end!). Unable to say \"I feel attracted by you,\" he _moves toward_ the other, like a climbing plant. He now feels that the next stage in his evolution is the leap from the plant world of _concrete metaphor_ to the animal world of proto-emotions, the pigtail, and the crest as representatives of a no longer vegetable world. This development could also be seen as possessing a sexual element, as a transition from pollination to a more sexual form of functioning of minds. An emotional thread is indeed beginning to form, binding the two minds together, even if it is still wrapped in thick layers of sweater\/insulation\/German.\n\n### Metaphor, Reverie, and Free Association\n\nThe dichotomy of living vs. Dead metaphor is reflected in that of reverie vs. Free association. There are differences between a free association and a reverie. The latter is characterized by direct contact with the pictogram that constitutes the waking dream thought. It comes into being upstream of interpretation, and in some way inspires or suggests it. It is an image (which is usually communicable to the patient only in exceptional cases, but would then come under the heading of self-disclosure) that is created in the mind\u2014spontaneously and not \"to order\"\u2014whose difficulty lies in organizing it in a pertinent, explanatory communication. Rather than in effect being taken from an encyclopedia (that is, from the harvesting of preformed metaphors present in language), this communication should be created there, in that place, for the first time, like a small fragment of a dream triggered by situations permeated with projective identifications or, if you will, beta elements. The only possible approach for bringing out this stratum of thought processes is a negative one (Bion's \"negative capability\").\n\nAny reverie could also be said to be a free association, but the opposite is not the case, even though the boundary is sometimes blurred. An association may share the nature of reverie if it is spontaneous and is received in a state of passivity. Mostly, however, it emerges among the entities that can be described as \"narrative derivatives\" (Ferro, 2006a) of waking dream thought. Unlike reverie, a free association can also be \"forced.\" A free association\u2014which may be a metaphor already recorded in language, either because it is banal or because it has become a catachresis\u2014arises at a less early stage of thought, downstream of waking dream thought, when the level of narrative derivatives has already been reached. It is, rather, a widening of narration.\n\nGiovanna's analysis has reached an impasse with no obvious way out, when I come into contact with\u2014I actually see\u2014a \"sailboat in a bottle,\" which provides me with a visual description of what is happening in the analytic field: the sailboat of the analysis is bottled up. Hence the interpretation: \"It seems to me that we are stalled, and I find myself imagining a sailboat in a bottle\u2014a boat made like the analysis for sailing...\" and so on.\n\nThe corresponding metaphor, on the other hand, would be if I were to use an example taken from one of Conrad's typical tales in which a sailboat is \"becalmed.\" I could then more readily describe a situation of which I am already aware, to which the image of the \"sailboat in the bottle\" belongs; indeed, it suggests, triggers, and inspires the interpretation.\n\n## **Transformations of the Field and Narration**\n\nAs these vignettes show, in an analytic field theory, the analyst's reveries and affective and visual transformations based on the patient's narration, together with any metaphors that stem from these, are the actual factors of growth. The analyst transforms anxieties and persecution feelings into affective images; he has a dream about the patient's communication. He shapes the alpha elements and passes them on to the patient\u2014but, in particular, he puts the patient in touch with his own functioning (his alpha function), which governs these transformations. It is not so much metaphor in itself, as a living metaphor, arising there and specific to that patient at that time, that bears witness to the oneiric functioning of the analyst's mind and supplies him with the method for performing this act (paradoxically, in some cases, even if he does not say or do anything). The same can be said of the situation in which the analyst \"reawakens\" one of the now lexicalized or extinct metaphors used by the patient or by himself.\n\nWith patients who are more seriously ill (or with the more seriously ill parts of all patients), only this level can permit the development of the alpha function\u2014that is to say, of the patient's own capacity to dream, both while awake and while asleep, because a more explicit offer of meaning might arouse a sense of persecution.\n\nThe session proceeds by a kind of oneiric reciprocity, both when the patient \"dreams\" (if he can) the analyst's intervention and mental state, and when the analyst \"dreams\" the response to give to the patient (Civitarese, 2006; Ferro et al., 2007). The more this response is \"dreamed\"\u2014that is, the fruit of unconscious thought\u2014the more it will be a factor in shaping the patient's alpha function or in mending any defects in it.\n\nHowever, what we have described for the sake of simplicity as belonging to the analyst and the patient actually takes place in a _dimension that transcends both, which is_ _that of the field_. This situation could therefore be redescribed from this other complex viewpoint in terms of turbulences and the alpha function of the field. The idea is that, if we creatively transform the field constituted by the two subjectivities, each will benefit\u2014in particular, the patient, because, by definition, he comes along with less capacity to dream experience, or, in other words, to assign a personal meaning to it, and hence to contain emotions.\n\nIf the drama undergone by a character in the tale comprising the analytic dialogue is resolved, the positive turn of the plot is a narrative form that reflects profound emotional transformations occurring in the common psychological area of the analytic field, which are therefore bound to be relevant to both members of the analytic couple, albeit as a rule asymmetrically (because, after all, the analyst should also be capable of a certain detachment). Of course, whereas this situation is in our view more correctly described in intersubjective or field terms, there is no reason why it could not be portrayed more abstractly or with its complexity simplified, for example by the fiction of two completely separate subjectivities, or indeed using less radical relational models.\n\nThe vignettes show that, from a field vertex, rather than \"giving interpretations\" or \"making interventions\" _directed to_ the patient, the need is to _attune oneself to_ the emotions that are not yet thinkable for the patient and to help him to give shape to them. Attention will then be paid more to the development of the container\u2014that is, to facilitating the growth of the capacity to think\u2014than to its contents. In order to be in unison with the patient, the guiding principle is to reach him at the point where he is, and to take account of the degree of truth about himself that proves _tolerable_ to him\u2014that is, as Eco (1984) says in connection with metaphors, of his _limit of acceptability_. For this reason, the analyst must pay attention to the derivatives of waking dream thought, as a basis for constantly attempting to apprehend the signals addressed to him by the patient about where he is and how he reacts to what he says (or does not say) to him. The essential aim is to weave together the emotional threads making for growth of the patient's capacity to dream\/think\/symbolize. To this end, the conversation often proceeds on a twofold level, in which the manifest text _metaphorizes_ the latent text of the unconscious\/field dimension of the relationship\u2014the invisible \"electromagnetic waves\" that establish it, exactly as in the case of play in the therapy of children.\n\nAs rhetorical figures involved in the text of the analysis, metaphors appear to us as _transformations_ (a becomes B; the real appears to us, on the phenomenal level, as a given reality) which are _narrative_ \u2014that is, expressed in words: there is a temporality, a becoming. Felicitous metaphors have a containing effect (the frightening and unknowable \"O\" is \"cooked\"). By virtue of their metonymic basis, they represent a point of equilibrium between emotions and thought, because they are pervaded with sensoriality (i.e., they retain the mark of things), while at the same time distancing themselves from things (which they symbolize). They are _sensible ideas_ (Carbone, 2008)\u2014that is to say, they combine emotion and thought. They therefore restore a bodily element to the mind; they reunite psyche and soma; they reforge the \"psychosomatic collusion\" (Winnicott) that is the foundation of subjectivity; they are dreams that _create_ reality and give it a personal meaning.\n\nIt will therefore be understood that, in order to live, rather than knowing how the mechanisms of the unconscious work or receiving logical or rational types of explanations, patients need good metaphors. As in the case of aesthetic experience in art, there is nothing like a good metaphor to give someone a feeling of truth about his existence. An apt metaphor is an image of which we can never have too much; it is an inexhaustible source of meaning. To be apt, however, in analysis a narration must be attuned to the patient; it must contain his most anxiety-inducing emotions at their point of urgency. The analyst must be capable of reverie, have a well developed alpha function, and be in a receptive state. Reveries give birth to living metaphors, while, conversely, metaphors are an excellent, if not the only, way of using reverie.\n\nIn the dialogue, priority is given to the clear text furnished by the patient, because the metaphorical discourse as a whole is open and unsaturated, conveys emotions, and creates meaning. In our view, analytic field theory is the approach that places the greatest possible emphasis on metaphors and on metaphorical discourse, because, by virtue of its strict inclusiveness (at least in principle), there is nothing that cannot refer to the field and to the transference, and hence nothing that is present only for itself, like a lexicalized or extinct metaphor. As Proust writes in _The Captive_ , and as quoted in the epigraph to this contribution, \"everything is capable of transposition.\" There is no fact, event, memory, account of a dream, and the like, that cannot stand for something else. If we accept the suggestion of one of us (Ferro and Basile, 2009) that we should precede everything the patient says (as well as everything that we say) with the words \"I dreamt that...,\" in order to recover an \"internal setting\" (Civitarese, 2011, in press), the frame of reference is immediately shifted, thus saving his (or our) words from running aground on a realism lacking in personal significance, reopening the way to the play of meaning, and revealing to the patient (and to ourselves) the path toward the resumption of dreaming one's interrupted or undreamt dreams\u2014i.e., one's very existence (Ogden, 2005).\n\nTranslated by Philip Slotkin MA Cantab. MITI\n\n## **Notes**\n\n Originally published in _Psychoanalytic_ _Inquiry_ 33(3) (May 2013) with the title \"The Meaning and Use of Metaphor in analytic Field Theory.\"\n\n The Barangers also took inspiration from Kurt Lewin, Heinrich Racker, and Enrique Pichon Rivi\u00e8re (de Le\u00f3n de Bernardi, 2008). Churcher (2008) points out that Lewin's name is replaced by that of Merleau-Ponty in the second, revised version of the Barangers' 1961\u20131962 paper as republished in 1969.\n\n [Translator's note: For convenience, the masculine form is used for both sexes throughout this translation.]\n\n The lectures delivered at the Sorbonne in the 1950\u20131951 academic year, \"The Child's relation With Others\" (published in English in 1964), demonstrate Merleau-Ponty's familiarity with Klein's works. Klein used the concept of projective identification as the basis of an intersubjective theory of the psyche that was both extraordinarily advanced and in some respects complementary to that of Merleau-Ponty. According to Angelino (2005, p. 374, translated), Melanie Klein fascinated Merleau-Ponty \"because her writings are rich in highly concrete, indeed brutal, and quite shocking descriptions of our relations with others and with things, which bear out what he thought about the role of corporeality and the drives (libido and aggression) in our relationship with the world.\" As we know, Klein studied in detail, to a degree bordering on obsession, the mechanisms of the first introjections\/projections and identifications of a child when still immersed in a state of partial nondistinction from the object. Klein admittedly accepts the existence of a primitive ego from birth, but, as Kristeva (2000, p. 62f.) notes, \"the fragile ego is not truly separated in the sense of a 'subject' separated from an 'object,' but it incessantly consumes the breast from within and ejects the breast into the outside world by constructing-vacating itself while constructing-vacating the other.\" The point, however, is that Klein's model proves valuable not only for representing the relationship between the subject and his environment at the stage described by Freud as that of primary narcissism, but _also when the subject is no longer in such an elementary phase of constitution of the ego_. Like Klein, Merleau-Ponty considers that identity can be thought of only in terms of difference, of the intersection between the subject's body and the world of things and other people. A person can be himself only by projecting himself outside his own self into the other, and vice versa. The subject (S) constructs himself only by transferring himself into the object (O), which is thereby transformed (O'), and by then reintrojecting from the object what he had deposited in it, thereby in turn being modified (S'); the structure of the chiasm\u2014the resulting notation seems to allude ironically to a kind of appeal to the other\u2014would be SOO'S'. Hence the approaches of Klein and Merleau-Ponty can be seen as complementary. Oddly enough, because Klein was interested mainly in the unconscious and in psychic reality, she in effect disregards the \"carnal\"\u2014feeling and felt\u2014aspect of the body (even though the body is absolutely the protagonist of the subject's unconscious fantasies). Merleau-Ponty's concentration on the experience of the body, on the other hand, leads him to develop theories very close to current notions of the unrepressed, or \"sensory,\" unconscious and of procedural, rather than declarative, memories.\n\n Cf. Baranger M (2005, p. 62f.): \"It was when we reviewed Bion's studies on small groups that we modified and added precision to our thinking in a direction different from transference\u2013countertransference interaction [...] We then understood that the field is much more than interaction and intersubjective relations [...] translating what is described as the group's 'basic assumption' to the individual analytic situation, we spoke of the 'basic unconscious phantasy' that emerges in the analytic situation, created by the same field situation [...] This phantasy is not the sum or combination of the individual fantasies of the two members of the analytic couple, but an original set of fantasies created by the field situation itself. It emerges in the process of the analytic situation and has no existence outside the field situation, although it is rooted in the unconscious of the members [...].\"\n\n However, consider the following passage from Bion's letter to Rickman of 7 March 1943: \"Te more I look at it the more it seems to me that some very serious work needs to be done along analytical and field theory lines to elucidate [...]\" (Conci, 2010, in press). The article published in _The Lancet_ in 1943 and signed by both, \"intra-group Tensions in Terapy\u2014Their study as the task of the Group\" (which subsequently became the first chapter of \"experiences in Groups\" [1948]), contains what is clearly a field theory (Civitarese, 2010, in press). Lacan (1947) had no hesitation in describing this article as miraculous!\n\n Koj\u00e8ve (1947, p. 43) concisely sums up Hegel's conception of the subject as follows: \"if they are to be _human_ , they must be at least _two_ in number.\"\n\n Cf. Eco (1984, p. 87): metaphor \"[...] a trope that seems to be the most primary will appear instead as the most derivative, as the result of a semantic calculus that presupposes other preliminary semiotic operations. A curious situation for a figure of speech that has been recognized by many to be the basis of every other.\"\n\n [Translator's note: literally horseshoes, but the Italian word is also the plural of _ferro_ , the name of the analyst and one of the authors of this paper.]\n\n New metaphors are among the \"mutations\" that cause a scientific paradigm to evolve (Kuhn, 1962).\n\n [Translator's note: The Italian word _grasso_ can mean either grease or fat.]\n\n# 13\n\nFIELD THEORY, THE   \n\"TALKING CURE,\" AND  \nMETAPHORIC PROCESSES\n\n_Ana-Mar\u00eda_ _Rizzuto_\n\nThe Barangers field theory considers the analytic situation as dialogical, bipersonal, and at the service of the interpretation of unconscious phantasies created in the field by the shared participation of patient and analyst. They ask about the power of words to offer meaningful interpretations and their potential to return to their earlier meanings in the patient's life.\n\nExamining the richness of the spoken word as a medium for the expression of private experiences to another I suggest that what counts in analytic work is the use of living words, linked to past and intra-analytic experiences. I suggest that in psychic life the semantic meaning of words is embedded in their experiential and affective interpersonal meaning. The words act as the medium to link the private experience of the analysand to the private experience of the analyst without a direct intersubjective communication. I illustrate my point with the example of the analyst's warm words being \"savored\" as warm milk by a regressed analysand.\n\nField theory offers a conceptual framework to describe and interpret what happens during an analytic treatment based on the therapeutic contract between two persons who have accepted to talk with each other under the conditions imposed by the analytic setting. It was introduced as a psychoanalytic conception by Madeleine and Willy Baranger in their seminal article _La situaci\u00f3n anal\u00edtica como campo din\u00e1mico_ published in the _Revista Uruguaya de Psicoan\u00e1lisis_ in 1961\u20131962 and translated into English in 2008. Willy Baranger (1959) had already asserted that psychoanalysis \"must accept its character as a science of dialogue\u2014that is, of bi-personal psychology\u2014its character as an interpretative science\" (cited in de Leon de Bernardi, 2008, p. 774). Willy and Madeleine Baranger considered in their later article \"that the essence of the analytic procedure is a dialogue\" (2008, p. 816). The field is created spontaneously and dynamically by the participants in the analytic process and it emerges as a result of their engagement in the total situation between them, which includes the past, the present, and the future (Churcher, 2008). The Barangers had borrowed some of their concepts from the Gestalt psychologists and the work of Kurt Lewin on social field phenomena. Later, they referred to the work of the French phenomenological philosopher Maurice Merleau-Ponty without explaining their motive for the selection of the new author. Merleau-Ponty insisted on \"the primacy of perception\" and proposed that our knowledge of the world is dependent upon and inseparable from our bodily condition.\n\nBased on their conception of the analytic process as a dynamic gestalt the Barangers offered their idea of the analytic field as a _heuristic model_ to understand facts present in the analytic situation (Canestri, 2004\u20132005, p. 1511, cited by Churcher, 2008). The field they describe is ambiguous and is characterized by the emergence of a bipersonal unconscious phantasy created by the analytic couple. Such phantasy may become a \"bastion\" of joined resistance to the progress of the analytic process. The analytic process may also bring about a \"point of urgency\" calling for the analyst's to offer an interpretation to the analysand: \"[W]e consider the point of urgency to be a moment in the functioning of the field when the structure of the dialogue and the underlying structure (the basic unconscious phantasy of the field) can come together and give rise to an insight. The analyst feels and thinks that he can and must interpret (formulate an interpretation to the analysand)\" (M. Baranger, 1993a, p. 18).\n\nIn their original paper _The Analytic Situation as a Dynamic Field_ (1961\u20131962\/2008) the Barangers question how words acquire their interpretive power:\n\n> our problem is therefore reduced to this: how can the interpretation reduce the \"gestalt\" of the manifest content to the \"gestalt\" of the urgent unconscious phantasy in the session? This leads us to the problem: how can the interpretation, as words, act upon the different structurings of the bi-personal field? in other words, what is the basis of the interpretative power of the word?\n> \n> (2008, p. 820)\n\nIn response to their question, they mention the work of Luisa Alvarez de Toledo (1954\/1996) who connects \"speaking,\" \"associating,\" and \"interpreting\" to a \"doing\" of the analyst with the patient based on early object relations and the maternal voice. The voice of the analyst carries not only meanings but also gratifcation, danger, and has the power to evoke phantasies. They believe that these considerations are not enough to understand the function of words in analysis: \"It is one thing for the patient to take our words as milk or stones, and quite another for the patient to understand their meaning and for this understanding to provoke an important modification in the patient's world. The specific problem is the relation between the word and the insight that the patient acquires with an adequate interpretation\" (Baranger & Baranger, 2008, p. 821). The Barangers' consider the patient's capacity for insight and change to be the final goal of analysis, achieved through \"the patient's increased awareness of his or her inner world (ibid., p. 822).\n\nThey consider that \"the word is equipped with three essential functions: it carries object relations and very primitive emotions, connects split of and isolated structurings in the field and differentiates the parts and aspects of the field thus reunified. Thus, the word again acquires the characteristics discovered by M. Klein (1930) in the process of symbol formation: the equivalence of symbol and symbolized, on the one hand, and differentiation between the two on the other hand. The absence or insufficiency of either of these two aspects constitutes a very great difficulty in the technique of interpretation\" (Baranger & Baranger, 2008, p. 822). They believe that the question to be asked is \"how words have lost their original power to reach deeply into internal life\" and conclude: \"Te role of interpretation is to overcome the weakening of words that made them lose their original global communicational function and transformed them into mere abstract signs\" (ibid., p. 823).\n\nHow do words manage to modify the field? \"Te word opens up the communications in the field, uniting its isolated or split of regions. But it also serves to locate, determine and differentiate its multiple aspects. It is both communication and control, and the function of interpretation can be lost if one of these aspects is exaggerated at the expense of the other\" (ibid., p. 823). A modification of the field occurs when concrete words related to \"primitive phantasies of object exchange\" have the abstract power to make intelligible \"the prevalent situation in the field\" (ibid.). When this situation obtains \"one of the parts of the patient that is split of and isolated or deposited in some sector of the field is re-integrated into the patient's self and recognized as the patient's own\" (ibid.). As a result\n\n> the ego also differentiates between its own aspects that have been attributed to the object and the internal objects (different from the ego) that contributed to the structuring of the external object. This is a double process: the ego recovers what belongs to it as its own and also assimilates something more from its internal objects which, in turn increases the Ego's \"real potential and improved contact with reality\".\n> \n> (Baranger & Baranger, 2008, pp. 823\u2013824)\n\nThe entire process reveals that the bi-personal field \"is an experimental field\" (ibid.) which in the end permits the analysand to see the analyst as the analyst and not as a projected figure. To arrive at this final point, the patient and the analyst, as participants in the field, must continuously confront ambiguity: \"It is essential for the analytic procedure that each thing or event in the field be at the same time something else. If this essential ambiguity is lost, the analysis also disappears\" (ibid., p. 799). The ambiguity even involves the bodily language of the patient during the analysis: \"The ambiguity of the body in the analytic situation sometimes becomes quite patent at the moment when the patient abandons his 'body' of the session in order to recover the body of his daily life\" (ibid., p. 801). The process affects the analyst as well who responds with \"his or her own body to the patient's unconscious communications. The analyst also elaborates a body language with which to respond to certain modifications of the field\" (ibid., p. 802).\n\nThe different meanings of ambiguous verbal and bodily languages converge in the field, which the Barangers call the \"third configuration\" where they consider that the very essence of the analytic process takes place (ibid., p. 804). The analyst strives to interpret the configuration of the field: \"Te analyst searches through the multiple latent situations that can be perceived in the material offered, which are also related to the manifest content and the current phantasy of the contract, to find the situation that is effectively interpretable\" (ibid., p. 804). The analyst selects from the configuration the one manifestation that is most vivid to the patient, the most urgent and sees in it the \"point of urgency\" that calls for an interpretation capable of modifying the field\" (p. 804). The analyst's interpretation and its potential to alter the analytic field reveals the asymmetry of the participation between the members of the bi-personal field.\n\nThe rereading of the Barangers' early paper and their later contributions fills me with respect and admiration for the richness of their clinical understanding and the complexity of their analytic model. I have selected out of their many conceptualizations their manner of understanding communication, verbal and bodily, as well as their key concept of the jointly constructed unconscious phantasy during analytic work with a clear intent in my mind. I believe that their ideas may find support and at the same time call for some modification if they are placed in the context of a comprehensive understanding of the function of the spoken word in human relatedness and transformative interactions. In the next part of my paper I intend to review the present-day understanding of the spoken word as a fully embodied human capability and its significance for the understanding of any human communication. Ten, these concepts can be applied to the analytic process as a well-structured continuous process of verbal and bodily communicative exchanges between two individuals in the analytic setting. First, I must attend to the development process that introduces the child to the spoken word.\n\n## **The Acquisition of the Spoken Word**\n\nChildren are enclosed in a speech situation before birth. The capacity to hear some sounds develops during the fifth month of gestation. Mothers seemed to know it because they speak to their babies while pregnant: one of my patients addressed her baby boy fetus who was moving inside her: \"Charlie, you make me laugh. You kick so much. Be quiet now\u2014 _we_ are in analysis.\" Kolata's (1984) research shows that babies who heard their mother's voice during gestation favor it over any other after birth. Butterfield and Siperstein (1974) have shown that four-month old babies prefer words over any other sound, even over music. Mothers seemed to know that babies experience pleasure in hearing their voice and speech because they talk to their babies to the point of keeping them \"bathed in sound\" (Mowrer, 1952). This is the first bi-personal situation and it involves\u2014among the many ministrations that mothers offer to their infants\u2014the constant accompaniment of directly speaking to the baby about them. Thus bodily care and the baby's experience of it are directly _integrated as a total situation_ with the maternal voice, its prosody, affective tone, and spoken relational engagement. However, mothers\u2014and fathers\u2014also talk to their babies when they do not have a specific need: they want to _engage_ the baby in a personal encounter, be it of playing or of describing the baby to himself or aspects of the world to the infant. It must be noticed that the tone of voice of the parents\u2014and other adults\u2014include modifications of melody, loudness, and pitch in order to _engage_ the child in the conversation. Snow (1977) has demonstrated that mothers create for their non-speaking infants the normal turn-taking structure of dialogue. After having spoken to the baby, they use any action on the infant's part as if were a verbal response while they include the time pause typical of a conversation before entering their new spoken turn. When the child begins to use words, the parents progressively guide her to master the accurate use of language to join them in spoken exchanges. In all these developments, the child's proper name and the parent's use of the pronoun \"you\" (Rizzuto, 1993a) facilitates the new individual's formation of an identity, a mode of experiencing itself, and a mode of being together with others. The above description suggests that: 1) we have never been outside a context of spoken words addressed to us; 2) the prosodic component of language and its affective impact goes beyond the perception of sounds and words: it affects the individual viscerally (Fernald, 1996) and somatically (Condon & sander, 1974) and assists him to somatically experience the affect of the other and its emotional investment during the spoken encounter; 3) the words we learn from parents and others are always richer in their associative and affective links than just giving names to things. Each person has its own affective experience of particular words in relation to the contexts of their use during development. I have called this process _the emotional history of words_ (Rizzuto, 2003); 4) in ordinary life, speech is bi-personal: it involves two persons engaged with each other in order to achieve something together. In this respect psychoanalysis consists in the technical use of the richness always present in the spoken exchanges between two people; 5) language is part of the more extensive interpersonal communication between mother and child (Trevarthen, 1979) that precedes the acquisition of words. Even adults with full mastery of language cannot help but to have their spoken exchanges embedded within conscious and unconscious communications from the past; 6) bodily expressions and speech need to be organized as processes at the service of communication in the _privacy of the subjective experience_ of the person who relates, speaks or listens to the bodily or spoken communication of the other. The resulting communication with its affective, motoric, expressive, and verbal components creates a bridge between the interlocutors, to facilitate access to the _private_ experiences each of them is having. The aim of the communication is to find a _medium_ that facilitates _some_ access to the respective subjective experiences and expressions of the two people involved. This means that each participant is consciously and unconsciously (Meissner, 1993) an active intentional agent capable orchestrating\u2014preconsciously and unconsciously\u2014through the perception and _interpretation_ of the communications of the other\u2014its own manner of participating in the exchange. I understand this to be an interpersonal dialectic, ever present in human exchanges at the service of establishing meaningful links between two subjects whose inner reality remains _unavoidably private_. Bodily affective communication and speech create a virtual field of exchange as a _medium_ to indirectly access subjective reality.\n\n## **Recent Teories About Language Formation, Usage, and Understanding**\n\nIn 1980 Lakoff and Johnson proposed that we live by bodily created metaphors. More recently, the discovery of mirror neurons mediated by visually perceived actions or acoustically presented action-related sentences suggest that embodied perception of the action of others is a mediated \"embodied simulation\" (Gallesse et al., 2007). Embodied simulation is a spontaneous process probably facilitated by mirror neurons. Gallese describes it: \"A _direct_ form of 'experiential understanding' of others is achieved by modelling their behaviours as intentional experiences on the basis of the equivalence between what others do and feel and what we do and feel\" (p. 3, my italics). He concludes: \"By means of a shared neural state realized _in two different bodies_ that nevertheless obey the same functional rules, the 'object other' becomes another self'\" (p. 3, my italics). The embodied simulation facilitates the understanding of the intentions of others: \"ascribing _intentions_ would therefore consist in _predicting_ a forthcoming new goal\" [of an action] (p. 8, my italics). In a later article Gallese et al. (2007) says: \"we employ the term embodied simulation as a mandatory, nonconscious, and prerefexive mechanism that is not the result of a deliberate and conscious cognitive effort aimed at interpreting the intentions hidden in the overt behavior of others, as implied by the theory-theory account. We believe that embodied simulation is a prior _functional mechanism_ of our brain. However, because it also generates _representational content_ , the functional mechanism seems to play a major role in our epistemic approach to the world\" (p. 143, my italics). The authors suggest, based on numerous experiments and previous theoretical contributions, in particular Lakoff and Johnson (1980a) that we used our embodied experiences to understand the nonverbal as well as the spoken language of others.\n\nThese fascinating discoveries do add a dimension to our understanding of the function of the direct or indirect _perception_ of the body, the actions, the feelings and the words of others, including their intentions. As a psychoanalyst, I consider that we must pay attention to the fact mentioned above by Gallese that the embodied simulation takes place between _two different bodies_ , that can be similar in their neurological functioning, but never identical. The innumerable factors present in the simplest experience of satisfaction (Rizzuto, 2003, pp. 296\u2013297), the variety of circumstances that affect the relational and historical life of the individual, and the never-resting process of fantasizing about them, gives each of us a _historically personalized_ body to put at the service of any mirroring process. The embodied simulation seems to be an actual _neural mechanism_ at the service of human relatedness. Yet, in my opinion, when we intend to understand the subliminal or obvious bodily expressions and verbal communications in analysis, we must take the mirroring processes and its _perceptual foundation_ for granted, but remember that our human organism has the capacity to create a _psychical reality_ based on all those phenomena plus two other functions that go beyond mirroring and embodiment: the need to interpret ourselves to ourselves by the mediation of imagery, metaphoric processes, narratives, and our untamable need to create fantasized scenarios to rehearse our wishes and fears. This brings us to the _representational content_ that Gallese asserts emerges in the person involved in mirror neurons embodied simulation. In my way of understanding it, the _representational process,_ includes the automatic mirror neuron registration of the perception of the action and words of others, to which the individual adds two _interpretations:_ what it means for the self he conceives himself to be and what is the meaning of the _relational scene_ between the self and the other in the context of the wishful and fearful expectations\/fantasies elicited by them. This includes the dimension of the relational future. Green (1978) mentions scientifically well-documented transformative process in perception, in which the percept is not a simple registration of sensory input but the person's active way of organizing and decoding that input according to its own modalities of perceiving (p. 267). Gazzaniga (1995), a cognitive neuroscientist, after reviewing the large number of processes that function outside awareness introduces the notion of interpreter: \"Catching up with all this parallel and constant activity seems to be the function of the left's hemisphere's interpreter module. The interpreter is the system of primary importance to the human brain. It is what allows for the formation of beliefs, which in turn are mental constructs that free us from simply responding to stimulus-response aspects of everyday life. In many ways it is the system that provides the story line or narrative of our lives\" (p. 1394).\n\nThe accurate mirror neuron perception of the experiential moment, creates the possibility of analytic redressing, when the analytic process assists the patient to examine his interpretations and fantasies built around them by returning in certain global manner to the bodily memory of the original mirroring perception, that is, of the bodily state that was experienced while being with the other. This process is part of the working through, in particular of the transference.\n\n## **Freud and the spoken words**\n\nHow did Freud understand the word? he presented his ideas early in his career in his monograph _On Aphasia_ (1891) _._ he considered the word to be composed of two representations: the object representation that is formed by the sensory perception of objects and the word representation, composed of the sound and the images of movement for the spoken word and the visual image for reading and writing. The replication of the sound and movements to pronounce the spoken word is a learned process resulting from the imitation of others. The object presentation originates from the sensory perceptions in the body periphery. They travel along neural pathways from the receptive sense organs on the body's surface and proceed to undergo transformative processes in their way to the cerebral cortex where they come to form the multisensory (auditory, tactile, visual, and other modalities) object representation. The neural transformative processes, Freud (1891) says explicitly, is organized to represent the body \"in a manner suited to the function [of language]\"(p. 53; Rizzuto, 1990). Freud makes a very strong statement about perception: \"'perception' and 'association' are terms by which we describe different aspects of the same process\".... \"We cannot have a perception without immediately associating it... In reality they belong to one single process\" (p. 57). In brief, for Freud, object representations are not only 'embodied,' but they have the automatic capability of establishing instantaneous associations to other perceptive and mental processes. Would Freud have said that the mirror neurons associate what they mirror to other experiences? to me, this is a further confirmation that people's neural systems are unquestionably alike, but also _highly diversified_ by the accumulation of private associative links. According to Freud, in normal functioning the complex formed by the object associations establishes a connection of their visual component to the sound component of the spoken word. In this manner _a meaningful psychical word_ has been formed. As a learned spoken word it shares a linguistic meaning with the speaking community; as the internal representation of an object and a verbal form it combines the accuracy of sensory perception of the words learned from others with the context of the private associative networks of the individual. Freud makes another remarkable point: \"all stimuli to spontaneous speech arise from object associations\" (p. 79), and repeats it several times: \"Every 'volitional' excitation of the speech centres... involves the region of the auditory representations and results in its stimulation by object associations\" (p. 84). What is he saying? My reading is that the _wish_ or the _need_ to speak find their source in representational processes of associated objects in the privacy of the individual's mind. Contemporary linguist ray Jackendoff (1988) says something very similar today: \"people have things to talk about only by virtue of having mentally represented them\" (p. 83). He concludes that what a person has not represented does not exist for him, even when it unquestionably exists in the world. We analysts know that our task is to assist people to represent and describe in words those aspects of their psychical or actual reality that their pathology has blinded them to. Furthermore, we can say that psychoanalysis is possible because there is always an unconscious connection between things that have been represented in the past and the subjective experience of the patient in the present, regardless of how early that experience has taken place. Assisting the patient to make that representation consciously available and namable during analysis is critical to our work.\n\n## **The Components of the Spoken Exchanged Between People**\n\nI have insisted that people talk when they have mental representations that motivate them to share them with another. Several questions emerge: to whom do I want unconsciously and consciously to talk about it? how many people am I addressing when I talk to just one person? how do I want to talk about it? What do I want to do to my listener when he hears me talking to her? What do I want her to feel for me, about herself, about us? What am I asking her to _really_ hear? What kind of contact do I want to establish with her? What kind of message do I want to give? What is the context in which I want to contact her and how do I create such context? how do I phrase what I want to say so that it can be heard by my interlocutor? or do I want to speak and not _really_ be heard? The linguist Roman Jakobson (1990) created a model in response to these questions describing the six components of the functions of language and the six factors of the speech event. The latter include: the _context_ [what they are talking about], a _code_ [a language understandable to both partners], a _contact_ [the physical and psychological connection between interlocutors], _a person who addresses_ another, and _a person who is addressed_ , and who receives a _message_ from the addresser. As for the functions, Jakobson describes the _emotive or expressive_ , that presents the speakers attitude about his words; the _conative_ , that indicates the attitude towards the person addressed; the _referential_ , that puts a denotation to the message; the _poetic_ function that organizes the entire structure of the communication and that is manifested in the form the spoken expression takes; the _phatic_ function is placed at the service of maintaining contact, as when one interlocutor asks: \"Do you hear me?\" Finally, the _metalingual_ function serves to check the state of the communication: \"Do you know what I mean?\" it is no necessary to agree with Jakobson linguistic theories to accept that his description of the factors and functions present in spoken language are for real. What the description offers is a clear understanding of how many simultaneous events, actions, feelings, and relational elements are involved in the simplest of speeches between two people. Spoken language, I conclude, is closer to an orchestra than to a single instrument.\n\nJerome Fieldman and srinivas narayanam (2004) outlined \"an explicit neural theory of language (NTL) that attempts to explain how many brain functions (including emotion and social cognition) work together to understand and learn language\" (p. 385). They propose that \"one does not expect to find brain areas specialized only for language or to find language processing confined only to a few areas\" (ibid.). More than a century earlier, Freud (1891) had defied the neurologists of his time by rejecting the theory of localization of language centers and proposing the involvement of large areas of the cortex in the speech function (Rizzuto, 1993a). Fieldman and Narayanam (2004) assert: \"The NTL assumption is that people understand narratives by subconsciously imagining (or simulating) the situation being described. When asked to grasp, we enact it. When hearing or reading about grasping we simulate grasping, being grasped, or watching someone grasp\" (p. 385). We embody the words presented to us: \"This ability to simulate or imagine _situations_ is a core component of human intelligence and is central to our model of language\" (p. 389, my italics). Their experiments argue in favor of \"the embodied meaning of action words. They also provide robust biological evidence that planning, recognition and imagination share a common representational substrate. Our model of actions and their use in narrative predicts that the same structures are being exploited in understanding language about both concrete and abstract events\" (p. 390). They conclude that \"the basic ideas on embodied word learning, active simulation, and metaphorical interpretation appear to form the basis for a biologically plausible model of language acquisition and use\" (p. 391). I conclude from these assertions that we understand language by preconsciously creating somatically based _imaginary scenes_ in relation to what we are talking about. The scenes involve the multitude of interpersonal events that occur in the simplest of conversations. I have placed above a long list of questions to give concrete form to all the events that take place as a result of the factors and functions present in ordinary speech. In analysis we must add the great complexity introduce by our capacity to fantasize, to repress our fantasies, and to create with others shared fantasies, whether we are aware of them or not. When we put it all together, we can say that when there are two people talking to each other we believe that as part of their exchange they create one or several multifaceted fantasies about what is happening between them and to each of them. In other words: they place themselves in a complex interpersonal scene. It is worth noticing that although Freud did not theorize about the concept of scene, it is one of the most used words in his vocabulary. According to the Freud's standard edition concordance he used the term in 564 instances.\n\nIf we now connect the conceptions of Fieldman and Narayanan with Jacobson description of the multiple simultaneous factors and functions that compose any spoken exchange, we have all the ingredients we need to form a conception of what the analytic field may be about.\n\n## **The Analyzing Situation and the Analytic Field**\n\nPsychoanalysis rests on a critical premise: if we are to understand the private and pathogenic reality of our patients we need to use words. There is _no other avenue_ to access the patients psychic reality, the subjective experiences, beliefs, fantasies that sustain his way of relating to himself and to others. Freud said it as early as 1890: \"words are the essential tool of mental treatment\" (p. 283). The analyzing situation involves by definition two people speaking exclusively to each other under the specific conditions of the analytic setting or frame. The setting creates a very specific _context_ for the subject matter of the communicative exchanges between them. Whatever the partners talk about is organized by the context that they are talking with each other to assist the patient to 'grasp' his difficulties, make sense of them, and overcome them. The _message_ s patient and analyst send to each other, consciously or unconsciously, will be located within the context of their therapeutic relationship. The _contact_ between them, mediated by spoken words, voice, bodily movements, attitude and other factors opens in analysis a much wider spectrum of experiences than in any other ordinary conversation. In ordinary circumstances the aim of establishing contact is \"to enter and stay in communication\" (Jakobson, 1990, p. 73). Yet, we as analysts know how many patients do their best not to communicate and _that_ is their manner of communicating. We also know how frightened, ashamed, defiant, oppositional and other modalities of avoiding contact they may bring to the process. The analyst is not exempt from developing a wish to avoid hearing communications that are conflicting for her and sometimes enact the wish by losing contact with the patient's experience of the moment.\n\nThe _code_ in the analytic exchanges is more multilayered than it is in ordinary circumstances. In analysis words are capable of carrying several meanings, intentions, connotations, allusions, together with the affects present in the communication. In the treatment the basic code is the actual language\u2014English, French, Spanish\u2014they use to communicate. The analyst, however is aware, and invites the patient to become progressively aware, that ordinary words convey in their apparent innocence and simplicity multitude of experiences and meanings. They link to memories, to the body that experienced the events of the memory, and also to wishes, fantasies, and fears, which the patient may or may not recognize, but which are present in the hearing of the analyst by the mediation of symbolic processes, unusual assonances, evoked imagery, bodily responses, and other phenomena. The analyst accesses them preconsciously by forming fleeting scenes with the assistance of nonconscious processes such as condensation and displacement. In other words, the listening analyst, who does master the spoken language as an accurate vehicle for meaning, listens to the analysand with her entire embodied being. She cannot help but transform the words heard under the guidance of the analytic context into _preconscious scenes_ that involve her, directly or indirectly, with the analysand, thus registering what she has heard and sensed as a bi-personal experience, which may assist her to orient herself in the direction of understanding the analytic moment as well as non-verbalized unconscious processes present between them. The analyst is not inventing the preconscious scenes: they are somewhat present in the embodied selection of the words the patient is using to communicate what is in his mind, which in turn evokes the analyst's conscious and unconscious personal experiences. Freud (1901) was aware about the impact of the patients words upon him by noticing how: \"[it] runs through my thoughts a continuous current of 'personal reference,' of which I generally have no inkling... It is as if I were obliged to compare everything I hear about other people with myself; as if my personal complexes were put on the alert whenever another person is brought to my notice\" (pp. 24\u201325). I am talking about the _referential function_ of the words present in the patient's communications, which convey unconscious and preconscious denotations far beyond the analysand's capacity to be aware of them. Ogden (1994a) has written about the use of reverie to access the analyst's private experience of the analysand's communications. When the patient speaks, he cannot help but to address the analyst as he, consciously and unconsciously, senses the kind of person the analyst is. The universal phenomenon of transference described by Freud makes it abundantly clear that the person we intentionally address is, somehow, like a Russian doll: it contains layered one upon the other peoples of other times and circumstances, loaded with the combined affects, beliefs, and feelings of the past in the present. The analytic situation enhances and exacerbates the normal transferential situation to transform it into what we call in technical terms transference and countertransference. In analysis, more than in any other circumstances, the addressed analyst is always much more than herself. As a result, the analyst's task consists of finding in the patient's words the hidden and unconscious aspects of his communications and shared narratives, that, in one way or another, involve her as the analyst in the present. All the functions of spoken language become greatly enlarged and enhance by the analytic situation: the messages embedded in the simplest of sentences include complex affective expressions of overt and forbidden wishes, hidden or explicit demands and commands, requests to be loved\u2014or rejected and humiliated\u2014all of it embedded in the orchestral playing of the form (poetic function) taken by the patient's actual words, prosody, bodily posture, attitude, and gestures, in brief in his verbal and bodily communications. While listening, we, analysts, attempt to hear it all, with our embodied mind, hoping that we can achieve a sort of _free hovering attention_ that excludes as little as possible. In few instances there is a single message in the patient's words. Most frequently than not conflicts, contradictions, forbidden emotions and desires appear as dissonant notes barely audible but present in the communication. This description is far from exhaustive, but it permits to glance at the extraordinary complexity of the words we hear and speak during a session.\n\n## **The Analytic Field and the Spoken Word**\n\nHow does all this lengthy description of words, spoken exchanges, and their connection with the analytic situation relates to the concept of the analytic field? First I want to say that the Barangers' (2008) original article is an unquestionable precursor to all I have said about the function of the spoken word in analysis. They attended to the patient's bodily communications, his manner of speaking, and of relating to the analyst. Their concept of the bi-personal field is valid, even though, in my opinion, requires clarification and needs to be located not in the entire analytic setting but on the private and overt _interpretations_ the participants make about themselves in the field. The Barangers' description of the field includes the spatial organization of the office, the temporal dimension that involves the times for meeting, the frequency of sessions, the length of the treatment, and the \"basic functional configuration contained in the initial commitment and agreement\" that \"explicitly _distributes the roles_ between the two participants in the situation: one agrees to communicate to the other, as far as possible, all his or her thoughts\".... \"Te other agrees to try to understand the former, to provide help in resolving conflicts through interpretation and promises confidentiality and abstention from any intervention in the other's 'real' life\" (p. 797, my italics). In a later definition M. Baranger (1993b) says \"in speaking of the analytic field, we are referring to the formation of a _structure_ which is a product of the _two participants_ in the relationship but which in turn involves them in a dynamic and possibly creative process\" (p. 16, my italics). She continues: \"Te advantage of being able to think in terms of a field is that the dynamics of the analytic situation inevitably encounter many stumbling blocks which are not due to the patient's or the analyst's resistance but reveal the existence of a pathology specific to this structure\" (ibid.). The field facilitates the formation of \"a basic unconscious fantasy which, as a _creation_ of the field, is rooted in the unconscious of each of the participants\" (p. 17, my italics). The analyst is responsible for understanding the fantasy and making sense of it. The analyst attends to three aspects of the analytic moment: \"(1) the patient's explicit discourse; (2) the unconscious configuration of the field (unconscious phantasy of the field), which includes the activated aspect of the transference\/countertransference; and (3) what corresponds at this point to _something unconscious in the analysand_ , which must be interpreted\" (p. 20, my italics). Madeleine Baranger concludes: \"it is by virtue of the mediation of the unconscious configuration of the field that the analysand's unconscious can express itself and the analyst can find an interpretation. We thus avoid the risk of arbitrariness: it is not just any sense that is appropriate, and not just any interpretation that is valid\" (p. 20). It must be noticed that the analyst uses the \"unconscious configuration of the field\" to make an analytic _inference_ about \"something unconscious in the analysand.\" That inference is conveyed in the verbal form of an interpretation. However the verbal interpretation is not based on the semantic\/symbolic components of language (de le\u00f3n de Bernardi, 2008, p. 783), but on the understanding of the unconscious phantasy of the field. Madeleine Baranger (1993b) clarifies that \"the analyst generally retains a certain distance from the field, and except in a few rare cases there is no actual blurring of the distinction between him and his patient\u2014something that really would be an identification\" (p. 1161). The field therefore is narrower than the analyst's capacity to take distance from it\u2014as the Barangers suggested when talking about the \"second look\" to restore the analytic process. Analyst and patient do preserve their capacity to interpret themselves in relation to themselves and the other, the interpretive function of Gazzaniga, while still participating in the field. Madeleine Baranger (1993a) takes some notions for granted: \"Let us start with intersubjectivity as a _self-evident basic datum_. Freud described one aspect of this intersubjectivity in referring to communication from unconscious to unconscious (1912a), which he stated to be bi-directional. The field is a _structure_ different from the sum of its components, just as a melody is different from a sum of its notes\" (p. 16, my italics). I am not sure that intersubjectivity is a basic datum. All our knowledge of the world, including of ourselves, comes from perception, intero- and exteroceptive, which as demonstrated not only by psychoanalysis, but by all the empirical studies on subliminal perception and mirror neurons among many others, needs not be conscious. The so-called direct communication from unconscious to unconscious described by Freud could today be understood as subliminal perceptual processes mediated by all the bodily and verbal exchanges that are inevitably present when two people are together in a relationship. Intersubjectivity as a concept confronts a similar problem. How can we access the subjectivity of another, except through perceptual processes? I agree with Meissner (1999b): \"[T]he subjectivity of the other cannot be known directly but only inferred from objective data. Intersubjectivity comes to connote relations between persons who are known to each other as objects whose subjectivity is _inferred_ or assumed\" (p. 383, my italics). This notion is supported by the fact that each participant in the analytic situation has its own body\u2014similar and different from the body of the other. They may have similar mirroring neurons or subliminal perceptions as non-conscious processes, but the non-conscious or conscious subjective associative processes and the interpretation of them in relation to the meaning to the self is private, particular, and idiosyncratic to each of them. This is the distinction Gallese makes that I mentioned earlier between the process of mirroring and the representations that emerge from it.\n\nI am therefore disagreeing with the concept of intersubjective communication while I agree that the process it purportedly describes is in fact, as Madeleine Baranger suggests, bi-directional. We are always unavoidably registering the slightest expressions and bodily communications of others. This is not an intentional activity on our part, but the way in which our neural organization has us programmed to register what other people do with us. Only pathological defenses may remove awareness of its conscious components\u2014in the case when the neural process, such as vision or hearing calls for awareness. All the other subliminal and non-conscious processes are perceptually registered and associated (as Freud said) with previous processes. They influence us, not by mysterious communications, but through the signals we send to and receive from the other whether we are aware of them or not. Subjectivity registers them only when I become aware within myself of my experience of those signals. Numerous non-conscious processes may accompany the moment. I may register them as subliminal perceptions without becoming consciously aware of doing it and therefore not being able to include them in my subjective experience. Meissner (1999a) attributes such actions to the self-as-agent: \"Agency is attributed to the self-as-agent, encompassing all actions of the self (conscious, preconscious, unconscious) while the self-as-subject is the author of all conscious (and by implication preconscious) mental action. Self-as-agent and self-as-subject are the same in all conscious activity, but not in unconscious activity. Unconscious action has no subject, only agency\" (p. 155). The conclusion seems clear to me: we cannot share our subjectivity; we must resort to a _medium_ that is capable of establishing a connection between what I experience in myself and what I consciously or unconsciously want to express or communicate to another. The other has to register unconsciously or perceive consciously my communication for us to establish a _partial correlation_ in his own subjectivity of what I have tried to express. In between our subjectivities there are always numerous _objective mediators_ , even in the simplest of communications: words, voice, prosody, gestures, bodily posture, actions, mirror neurons registrations and all the embodied processes we use to relate to each other. And even so, the understanding of the meaning of the communication is dependent upon context and codes and the communal meaning of bodily and verbal communications. I believe that the term intersubjectivity is misleading because it gives the false impression that it is possible to share our subjective experience in a direct and unmediated form, when the truth is exactly the opposite: we all, as ordinary humans, and we analysts in particular, have to go through great efforts to ascertain what the patient is consciously experiencing, and to assist him to bring to conscious awareness what he is afraid of experiencing.\n\nNone of these considerations require that we reject the _concept_ of the field as a heuristic tool to understand the extraordinarily complex events that occur in the _exchanges_ between the patient and the analyst. Psychoanalysts who have adopted the concept of the field consider, together with the Barangers, that it involves the total analytic situation, including the components of the setting and some details of it such as the furniture. I believe that the setting as time, space, payment, frequency of hours, and even the fundamental rule are the _context_ in which a field is created. The context _conditions_ the type of communications that are suited for the analytic situation and the ones that are expected in order to achieve its therapeutic goal. The patient has to give words to all that is in his mind. We know that _that_ is impossible and that what he manages to say and succeeds in concealing are at the very heart of the analytic process. His manner of interpreting and feeling subjectively what happens in the office between him and the analyst are the core of the process: not the furniture, but the meaning of the furniture for him in connection to the analyst. The Barangers understood it this way even though it is not that explicit in their papers. After having clarified my position about intersubjectivity, I want to offer my own understanding of the field.\n\n## **The Analytic Field as a Complex Emergence of Successive Converging and Diverging Interpersonal Scenes**\n\nLakoff and Johnson (1980a) suggested in their now-classical book that \"metaphors allow us to understand one domain of experience in terms of another. This suggests that understanding takes place in terms of entire domains of experience and not in terms of isolated concepts\" (p. 117). They add other claims: \"most of our normal conceptual system is metaphorically structured\" (p. 56); \"metaphor is not merely a matter of language. It is a matter of conceptual structure\" (p. 235). They also assert: \"Metaphor is primarily a matter of thought and action and only derivatively a matter of language\" (p. 153), and: \"Te primary function of metaphor is to provide a partial understanding of one kind of experience in terms of another\" (p. 154). They draw a strong conclusion: \" _In actuality we feel that no metaphor can ever be comprehended or even adequately represented independently of its experiential basis\"_ (p. 19, italics in the original).\n\nThe experiential component includes the _situation_ in which the metaphor is used: \"Understanding a sentence as being true in a given situation requires having an understanding of the sentence and having an understanding of the situation\" (p. 169). Lakoff and Johnson's conception of the metaphoric understanding of human relatedness and conceptual comprehension in language helps us see, as they say, that we live our lives metaphorically. We are like Moli\u00e8re's Monsieur Jourdain: we all have been speaking [metaphoric] prose for many years without having been aware of it. Today many analyst's concur that psychoanalysis _is_ a metaphoric process (see _Psychoanalytic Inquiry_ , 2011) _._ how do psychoanalyst's use their experiential and spoken metaphoricity to help their patients to modify their pathogenic experiences and find metaphors they can live with and by?\n\nThe Barangers and many contemporary analysts resort to the concept of field as the medium for the analytic process. The field at times is given some ontological reality by the Barangers as a _structure_ or a _third_ , while at other times they present it as a virtual process. Green (1975) proposes that \"the formation of the analytic object through symbolization\" must take into account \"the _third element_ , which is the setting, in the dual relationship\" (p. 21, my italics). Ogden (2009) describes the third: \"This third _subjectivity_ , the intersubjective analytic third... Is a _product_ of a unique dialectic generated by (between) the separate subjectivities of analyst and analysand within the analytic setting\" (p. 161, my italics). The many authors that use the field concept oscillate between the two positions: a virtual field or an actual third endowed with subjectivity. I want to be clear about my position: the field cannot have an _ontological reality_ of its own: its virtual existence depends upon the subjective experiences of the participants and the verbal and bodily perceptual channels available to them to communicate with each other. The third cannot have _subjectivity_ because it is not a subject. Only persons can be subjects.\n\nFurthermore, the field\u2014unlike what the Barangers and many others propose\u2014cannot have effects caused by itself, because being a medium, the field has _no agency_. Only people have agency to carry out expressive, communicative, and understanding actions. I propose that we limit the notion of field to the extremely rich processes of simultaneous, diachronic, and synchronic verbal and somatic exchanges between the participants. The word \"limit\" is almost a contradiction because the multitude of events taken place between the two people who are attempting to communicate with each other is staggering. I have listed in a previous section the orchestral complexity of any verbal communication. Our present-day knowledge of embodied communication, registered preconsciously and non-consciously, barely discloses the multiple channels available to us to give perceptually registerable signals to others: think of subliminal scents and pheromones, just to talk about what we know today.\n\nThe term \"field\" used in analysis is itself a metaphor, most frequently than not a spatial metaphor. Freud used the metaphor of the battlefield. The Barangers (2008) describe it as the spatial structure of the entire office and setting where patient and analyst meet (p. 796). They also describe the analytic situation as one \"between two persons who remain unavoidably connected and complementary as long as the situation obtains, and involved in a single dynamic process. In this situation, neither of the couple can be understood without the other\" (p. 796). I fully agree with this second description. However, I want to add that for me what constitutes the analytic field, its very essence, is the personal connectedness and complementarity ever present in their daily encounters. I also want to bring back Lakoff and Johnson's (1980a) point mentioned above: \"Understanding a sentence as being true in a given situation requires having an understanding of the sentence and having an understanding of the situation\" (p. 169). The same applies to the understanding of any bodily communication, be it subliminal or overt. The situation in psychoanalysis is a very specific one: all that the patient and analyst do together as part of the \"single dynamic process\" is to use what happens between them only and exclusively at the service of making sense of the patient's experienced life and psychic reality as he presents it to the analyst. Psychoanalysis is an _intentional_ enterprise on both sides: the analyst's and the patient's. Freud could not fail to observe that the patient's unavoidable difficulty in keeping his part of the intentional agreement and his inclination to seek other goals and to keep to himself what he had promised to share was at the very core of the process. Soon he would learn that the analyst must remain watchful of himself because he too might try to avoid, escape, or became entrapped in the web of demands coming from the patient to respond or to avoid them rather than making analytic sense of them.\n\nThe single dynamic process of the Barangers includes the words and bodily communications the analytic pair exchange hour after hour. I have described at length the multitude of interpersonal events present in any verbal exchange. To that we must add the bodily messages and signals ever present when two people are together. Both partners cannot help but to add almost instantaneously two _interpretations_ about: 1) what it all means for the self he conceives him\/herself to be, whether as an analyst\/person or as a patient\/person; 2) the meaning of the _relational scene_ that is just occurring between them in the context of the double positioning of themselves. It is here that the asymmetry of the analytic situation becomes most obvious. The patient is immersed in the analytic process under the motivational guidance of his unacceptable wishes, fears, beliefs, in one word, his pathology. The analyst has a double task: she must be totally immersed in the process if she is to access the patient's unconscious pathogenic processes. She must also keep her distance to be able to perceive what the patient is really saying and what is actually happening between them. When this process fails and the analyst finds herself entrapped in a \"bastion,\" the Barangers recommended that she takes a \"second look\" at herself and the analytic process when she is _outside_ the analytic situation as a way of recovering her analytic function. What is happening between them, in their communicative field holds the clues the analyst needs in order to understand the analytic moment and the scenic roles attributed to each other. The Barangers' original article provides no clinical example but they make an allusion about the patient's perceiving the analyst's words as warm milk or as stones thrown at him. Let me play with one of them as a scenic moment. The analyst speaks calmly and warmly about something the patient has said. The scene the analyst _intends_ to bring about is one of understanding in preparation for a broader insight. The patient however responds in such a way that it requires more clarifications from the analyst. At one point the analyst becomes aware of how the patient perceives the scene they are involved in: he wants more calm and warm words because they feel like warm maternal milk\/words to him. A crossmodal perception of warmth has been established between the analyst's affect in her words and voice and the patient's reactivated wishes for maternal care and warm milk in the present analytic moment. It is all profoundly metaphorical and experiential. Teir exchanges have revived in the patient bodily experiences that he still feels need satisfaction. How does the analyst make the transition from her scene of giving meaningful words to his scenes of \"drinking\" them as warm milk? The analyst arrives at that point\u2014according to my theorizing\u2014by observing what is _incongruous_ in their share dcommunicational field: the patient should have attempted to understand her words; instead the analyst senses, through complex verbal and bodily communications, that he is not listening to her words but \"savoring\" them. The analyst's perception of the total situation guides her to describe to the patient what is happening between them and to access his revived wishes. After they have together recognized what is happening an interpretation is possible. If the analyst remains unaware of what is happening, perhaps because of her own maternal inclinations towards the patient, they may create a joint transient or protracted fantasy in the field that her \"words\" are good for him. They have jointly and unknowingly created a fantasized enactment of the good mother with the good baby she wants to feed. In this manner it must be said that enactment and fantasy\/phantasy in the field go hand in hand. As the Barangers say, this very ordinary analytic event is at the core of the progress of the analysis. Now, patient and analyst together need to analyze what they have done and find a meaning that simultaneously helps them to understand their bodily and communicative stances. Let's suppose that after much work the patient \"recalls\" that the analyst's voice reminds him of his mother's voice when getting ready to feed the children. Ten, we know that a perceptual metaphoric equation has been established between the two situations and experienced by the patient as \"real\" in the analytic present. The very fact that he has experienced it as \"real\" gives the analytic moment what it needs to give meaning to the interpretation. Perhaps this is what the Barangers meant when they say that analysis has to return to words their original meaning as the basis for their interpretation. They also questioned how the patients understand the meaning of words to achieve insight and change.\n\nMy answer is that the activation of metaphorically experienced scenes in the present moment of the analysis gives the words exchanged between them a level of meaning that goes beyond semantics and reaches the bodily experiences of the present and of the past in a single unit of perception, which connects the experienced past with the analytic present. The metaphoric experiential process is the mediatory link between life and words. Obviously the maternal care of the analyst was exclusively metaphoric, but it found its bodily incarnation in her \"warm\" voice duly registered by the patient. The analysand's \"drinking\" her words as \"warm\" milk was also a metaphoric process that also found its bodily form in her \"hearing\" him \"savoring\" her words. The field composed of this metaphoric processes permitted the analytic pair to revive the memory of the analysand's childhood experience and wishes that contributed to the creation of the metaphorically verbalized field of that particular analytic moment.\n\nJoseph sandler (1962) created the concept of role-responsiveness as a phenomenon linked to the countertransference. He describes how he felt compelled to talk more than usual in the case of a man who ended his sentences with an interrogation. It turned out that they were both reenacting an early event of the patient's life: \"He would feel extremely anxious as a child when his father returned home from work, and would compulsively engage his father in conversation, asking him many questions in order to be reassured that his father was not angry with him\" (p. 45). Sandler points out that the analyst may \"tend to comply with the role demanded of him, to integrate it into his mode of responding and relating to the patient\" and that \"he may only become aware of it through observing his own behaviour, responses and attitudes, _after these have been carried over into action_ \" (p. 47, italics in the original). Sandler tried to differentiate role-responsiveness from a countertransference originating only in the analyst's mind. I believe that role-responsiveness _is_ a component of the creation of the metaphorical field of joint experience in which somatically and verbally based signals given by the patient to the analyst have induced him to respond with a matching behavioral pattern. Sandler and his patient unknowingly recreated in analysis the childhood scene of a frightened child trying to disarm a frightening father.\n\n## **Conclusions**\n\nI would like to sum up in a concise form the main points I have discussed in this chapter.\n\n1 Communication between subjects is never direct. It is mediated by perceptual registration of bodily and verbal communications organized as metaphorical experiences of the individuals involved in the exchange.\n\n2 The Barangers questioned how words can return to their earlier meanings. My response is that when they do, it is through the mediation of intra-analytic experiences in the communicational field in the present between patient and analyst. I prefer to say that one could return to an experiential moment in early life in which the word was used in a particular relational context. That means to say that in psychic life the semantic meaning of words is embedded in their experiential interpersonal meaning.\n\n3 The Barangers asked about the power of words to offer meaningful interpretations. I reflect that only _living_ words have the power to offer meaningful interpretations. I call living words those that have been used and recognized as part of shared metaphoric affective experience by the patient and analyst in the present of the analytic situation. In my playful example of the analyst's \"warm\" words \"savored\" as \"warm\" milk by the adult\/child patient, the word \"warm\" becomes alive between them as actual and complex metaphorical experiences they are having together, each in his own way. The word \"warm\" has acquired the capacity to name simultaneously, what the analyst was doing, what was happening between them, what did happened in his childhood, and what he had wished would continue to happen with his mother in the past and with his analyst in the present. In brief, the word \"warm\" provides access to his wishes\/needs in the past and the present in the context of a concrete analytic moment and becomes a key word to interpret his metaphoric and historically revived experience of that analytic moment. The interpretation is possible because the word \"warm\" is a living affectively significant word between patient and analyst.\n\n4 The Barangers search for the point of urgency to interpret. They describe how the analyst selects what \"is most vivid to the patient, the most urgent\" to offer \"an interpretation capable of modifying the field\" (2008, p. 804). I believe that in the example just discussed the word 'warm' with all its metaphoric experiential past and present meanings for both analyst and patient is the point of urgency that will modify the field and open a new understanding of the patient's experience and assist him in the understanding of himself.\n\n5 The Barangers also ask about how the words of the interpretation can modify the shared unconscious phantasy and the structuring of the bi-personal field. In the example of the words \"warm\" and \"milk,\" patient and analyst shared for some time the unconscious phantasy that she, as a good and caring mother, is feeding him the warm milk he needs as a child\/patient. The analyst's interpretation of what is happening between them instantaneously restructures the field by reorganizing the metaphorical experiential situation between them. The adult side of the patient comes to the fore to understand the child desirous of warm milk and the analyst redresses her metaphorical experiential participation as a warm mother to take up again her role as the analyst in charge of making sense of what is happening between them.\n\n6 Finally, I want to make a brief comment about the metaphorical entailments of the word \"insight\" in the analytic vocabulary. It implies that real psychical life takes place in some internal locus of the individual and that the events or meanings in that place have to be seen by some psychical eye to acquire meaning for the person. This metaphorical entailment is at odds with all I have said in this presentation. We understand ourselves only through embodied interpersonal metaphorical experiences that help us to make sense of ourselves and of others. When we achieve \"insight\" what we actually do is to modify our embodied metaphorical experience of ourselves and the words we use to describe them to ourselves.\n\nI hope that my presentation of how I understand the concept of field in psychoanalysis contributes to the clarification of a term that is dear to so many contemporary analysts.\n\n## **Note**\n\n Originally published in _Psychoanalytic Inquiry_ 33(3) (May 2013) with the same title.\n\n# 14\n\nFIELD, PROCESS, AND METAPHOR\n\n_Juan_ _Tubert-Oklander_\n\nThe proposal of juxtaposing and articulating the concepts of \"field\" and \"metaphor\" is both challenging and intriguing, since both concepts are necessarily related, as pointed out by S. Montana Katz (2012). On the one hand, the very idea of the field is a metaphor; on the other, metaphors generate a field in themselves, when considered as a form of mental activity. So, this promises to be a fruitful match. To this I have added yet another metaphor, that of a \"process\" which complements, from my point of view, that of the field, and shall develop a juggling act, which will include yet another concept, that of \"analogy,\" hoping that this play with ideas will clarify some of the issues raised by our present theme.\n\nI shall, therefore, explore this problem by approaching the various concepts sequentially, while at the same time showing their mutual relations, and finally expound my own ideas on the subject.\n\n## **Analogy and Metaphor**\n\nIt is clear for me, from the very start, that our interest in metaphor goes far beyond its restricted sense, as a figure of speech intended to embellish a linguistic expression, especially in poetry, but rather extends to the kind of problems studied by logic, epistemology, semiotics, and hermeneutics. It also deals with the psychological fact that a major part of our mental processes\u2014what Freud (1900) called the \"primary process\"\u2014is intrinsically metaphoric. So, I shall start from the widest possible perspective, before landing it on the more restricted purview of our discipline.\n\nMetaphor is a particular case of a much wider concept, that of _analogy_ , which has been acknowledged ever since the beginnings of Greek philosophy, even though it was Aristotle who made the first formal study of it. Unlike formal logic, which is based on _identity_ , analogical thinking deals with _similarity_. To say that two things are similar implies that they have something in common, but that they differ in other aspects. Consequently, analogy is particularly useful for exploring similarities and differences between things, either physical or mental, that would otherwise seem to be unrelated. The results of this kind of reasoning are never certain, but only _probable_ ; this accounts for the disdain that strictly logical thinkers have always displayed towards analogy, which they consider to be an inferior and unreliable form of thought. Yet, practical disciplines such as medicine (\"probable diagnosis\") and law (\"beyond reasonable doubt\") have always relied heavily on analogy. This is certainly the case of psychoanalysis. Besides, analogy may be the only feasible way to articulate the knowledge derived from disparate disciplines, such as psychoanalysis, group analysis, philosophy, social sciences, and neurosciences, and even from the diverse theories within our own profession.\n\nAnalogy is the main tool for the interpretation of texts, so that we are now stepping on the hallowed ground of Hermeneutics, where many analysts fear to tread. This has been defined as the \"theory and practice of the interpretation of texts,\" but \"text\" means here much more than a written document. _Textus_ originally meant \"fabric\"\u2014 as in \"textile\"\u2014so the term was really a metaphor for a set of words that have been weaved, much as warp and woof in a cloth, to form a meaningful whole. Originally, it referred to written documents, but then extended to speech, dialogue (with Hans-Georg Gadamer, 1960), intentional action, whether conscious or unconscious (with Paul Ricoeur, 1965, who was a true Freudian scholar), and to any other meaningful human expression. Hence, nowadays hermeneutics stands for the theory and practice of interpretation of anything that might act as a bearer of meaning, and this clearly includes psychoanalytic interpretation.\n\nEver since its beginnings in Greek philosophy, hermeneutics has taken one of three forms: univocality, equivocality, and analogy (Beuchot, 1997). _Univocality_ demands that each word, sign or text have a single unambiguous meaning; this breeds certainty, but also dogmatism\u2014what Isaiah Berlin (2001) called \"monism.\" Contemporary science implies a univocal conception of meaning. _Equivocality_ affirms that for any meaningful expression there is an indeterminate, perhaps infinite, number of disparate possible meanings, and that they all have equal value, so that an interpreter can only choose one among them on the basis of personal taste, practical convenience, tradition or whim. This opens the way for taking into account motivation and context\u2014both the author's and the interpreter's\u2014but paying the heavy price of forsaking the quest for truth and proclaiming the inevitability of total uncertainty\u2014this being what Berlin calls \"relativism.\" Finally, _analogy_ claims that there are a number of possible interpretations for any given text, though not an infinite one, but that these various interpretations may be more or less adequate in depicting some aspect of the highly complex nature of the text\u2014some of them may be good, others not so good, poor or outright bad. Yet there may be several good interpretations of a same text, depicting different aspects of it as seen from disparate perspectives\u2014what Berlin calls \"pluralism.\" The result is that the path of analogy does not renounce the search for truth, and indeed attains some degree of it, even though only a partial, perspectival, and humble truth, but good-enough to continue thinking and acting rationally (Beuchot, 1997, 2003a). Such a perspective seems particularly fitting for a discipline as psychoanalysis, which was not only defined by Freud (1904) as \"an art of interpretation\" (p. 252) that rejects any fixed meanings, but also has to deal with the coexistence of diverse theories that seem to have a common referent, and which have probably expounded each a part of the truth about it (Tubert-Oklander & Beuchot Puente, 2008).\n\nIn contrast with formal logical thinking, which cannot create any new ideas, since the conclusion is always already contained in the premises, analogical thinking follows the drift of successive analogues, propelled by their similarities, and arrives at radically new conclusions, based on their differences. This requires, of course, a new period of rigorous thinking, in order to winnow out the less satisfactory interpretations and retain the better ones. Nonetheless, these conclusions are never certain, but only probable, or even just plausible, but in any case, something one can live and work with.\n\nBut the term \"analogy\" also covers several linguistic and logical phenomena that are loosely related. In other words, analogy itself is analogical (McInerny, 1971, p. 4), as it comprises three\u2014or perhaps four\u2014quite different types: the _analogy of inequality_ , the _analogy of attribution_ , and the _analogy of proportionality_ , which can be further divided in two subtypes, _proper_ or _metonymical_ and _improper_ or _metaphorical_. This classification was posed in the early sixteenth century by the Dominican archbishop, theologian, and philosopher Thomas Cajetan (McInerny, 1971; Hochschild, 2001).\n\nIt may be argued that the _analogy of inequality_ is not a real analogy, since it merely states that the same word may be used to refer to quite disparate ideas. Thus, the word \"body\" may refer to a distinct mass of matter, the material substance of a living organism, a human being as such, the trunk of an organism, the main part of a text or document, a planet, a group or number of persons or things, the viscosity of an oily fluid, the firmness of texture of a fabric, the richness of favor of a beverage, the fullness or resonance of a singer's voice, the import of a literary work, the spiritual presence of Christ in the bread during Eucharist, the Christian Church conceived as a mystical organism with Christ as its head, among others (Merriam-Webster, 2002, see \"body\"). This is a highly complex set of associated and derivative meanings, and dead, dying, and active metaphors, all as a result of the semantic shifts involved in the development and evolution of a living language. As much as univocal theories of meaning may decry the vagueness of such polysemy, both dictionaries and the actual use of language are full of it, and this certainly applies to the basic terms of psychoanalytic theory. However, it is precisely this characteristic that determines the superiority of true languages over artificial univocal ones, such as those created by symbolic logic, as tools for human thought. This is so because living words do not only have a _denotation_ \u2014i.e., they refer to some entity or other\u2014but also a _connotation_ of ramified associations, and this gives the expression a particular complex favor, which links words by association to a whole set of related implied meanings, thus turning them into _symbols_.\n\nFor instance, the term that serves as the axis of our present discussion, \"field,\" is most certainly analogous. It may refer to the open country, a piece of enclosed land, the place where a battle is fought, an area of land containing a natural resource, an area in which a particular activity or pursuit is carried out, the scene of actual living observation in research, the area where some sport is practiced, the empty area where visual symbols are projected (as in fags or heraldry), a battle (by extension from the battle field), a set of players in a game, a continuously distributed entity in space that accounts for actions at a distance, a complex of coexistent forces which determine human experience and behavior, a limited or demarcated area of knowledge, the site of a surgical operation, among many others (Merriam-Webster, 2002, see \"field\"). This multiplicity of meaning forecloses any precise definition of the term, but it is also the source of its richness, its evocative power, and the strong conviction it provides when actually used in thinking.\n\nThe _analogy of attribution_ implies that there is a flow of meaning from an original primary object (idea, perception, wish, experience), called the _primary analogue_ , to a series of derivative signs, called _secondary analogues_ , increasingly removed from its initial term, which constitutes their final referent that gives them their meaning. For example, the term \"healthy\" strictly refers only to a living organism, but its use may be extended to apply to food, medicine, habits, thoughts, lifestyle, ideology, appearance or urine (as an indicator of health), all of them analogues of the primary meaning. The classical psychoanalytic theory of symbolism, as developed by Freud (1900), Klein (1930), and others, suggests that symbols are the result of a displacement from an original vital and organic experience, related to psychosexuality, to a series of substitutes that disguise and express their true meaning at one and the same time. This kind of analogy presupposes a single original primary meaning, which makes it more palatable for univocally minded thinkers.\n\nHowever, the links between the primary analogue and the successive secondary analogues is something more than a matter of psychological associations, since they represent a _causal_ relation. And here \"causal\" does not only mean the kind of active preceding cause that is the only one acknowledged by our contemporary natural science and corresponds to Aristoteles's \"efficient cause,\" but all four Aristotelian causes: _material_ , _formal_ , _efficient_ , and _final_. In this, the final or teleological cause is always the most important one, which is manifested by means of the other three (Beuchot, 2010). Leaving aside the possible ontological connotations of this statement, there is no doubt that psychic phenomena are always intentional, that is, that they always tend to some aim, as the young Freud soon learned in his philosophy courses with Brentano, a great Aristotelian thinker (Beuchot, 1998).\n\nThe _analogy of proportionality_ represents the original Greek meaning of _analogy as proportion_. This is an assertion that follows the following logical model: \"A is to B as C is to D\"\u2014for instance, \"as water is to a plant, so is friendship to man.\" it should be noted that this statement says nothing about each of its four terms, taken in isolation, but only about their relations, and that it really compares one relation to another. When studying figures of speech, it is traditional to distinguish between a _simile_ , in which the comparison is explicit (\"friendship is like water\"), and a _metaphor_ , in which it remains implicit (\"the water of friendship\").\n\nIn hermeneutic analysis, this type of analogy is usually divided in two subgroups: _proper_ and _improper_. A proper analogy of proportionality compares elements coming from a same semantic field; for instance, the word \"semen\" comes from \"seed,\" with the implied analogy between the biological functions of two products of living organisms (\"semen is to man as the seed is to the plant\"). This kind of reasoning is known as _metonymy_ , and remains within the realm of the literal. On the other hand, an improper analogy of proportionality, called _metaphor_ , compares elements from widely different semantic fields, on the basis of a partial resemblance in structure, function or meaning, which is thus spotlighted and maximized, sometimes revealed. An example of this would be the phrase \"the wings of imagination,\" which compares a bird's organ with a mental function, on account of their being operative in sustaining two different kinds of \"fight\"\u2014physical and mental.\n\nFor the logical positivistic mood that prevails in natural science in our time, metaphor appears as a kind of sloppy thinking, confuse, ambiguous, and unscientific at best, but in the tradition of the humanities it is the most approximate way of conveying and pointing at some essential human experience or complex relationship that cannot be actually said in unambiguous terms. It is therefore the very stuff of symbols. When Shakespeare puts in Hamlet's mouth the exacting task of determining \"Whether 'this nobler in the mind to suffer \/ The slings and arrows of outrageous fortune, \/ or to take arms against a sea of troubles, \/ and by opposing end them\" (hamlet: iii, 1), is he not using three different metaphors, including an outrageously mixed one, in order to say something meaningful about the human condition?\n\nPsychoanalysis, as a discipline, and we psychoanalysts, as practicing professionals, are in the very same situation as the other human sciences. Thus we make an extensive use of metaphor in our theories, in the interpretations we offer to our patients, and in the narratives of our professional experiences, both written and oral. But here we have a wider basis for justifying this procedure, since, unlike the other humanities, we have a special knowledge of the workings of the mind that sustain it, as we shall presently see in the next section.\n\n## **Metonymic and Metaphoric Processes**\n\nFreud's point of departure was his conviction, which he probably derived from his philosophy courses with Brentano (Beuchot, 1998), that mind and all its processes are by definition _intentional_ \u2014i.e., that they always tend towards some aim. Edmund Husserl, who was also one of Brentano's students, derived his phenomenology from the very same conviction, albeit he restricted it to the workings of consciousness. Freud, on the other hand, made the momentous discovery that _all human behavior and experience is intentional and bears a meaning, but that such intention and meaning are largely unknown and inaccessible to the subject who has these experiences and carries out these actions_ (Tubert-Oklander, 2000, 2006a). They are inaccessible because the subject exerts an ongoing effort, which goes also unnoticed, to avoid their open expression; this is what we call \"repression.\" hence, whenever we wish to explore the unconscious dimension, we have to apply a method and work in order to neutralize this effort of repression and allow the emergence of those intentions and meanings that had been actively ignored by the subject (Freud, 1912a, 1915b). This is the work of psychoanalysis.\n\nBut Freud (1900) went even further, when he discovered that unconscious mental processes are of a different nature and follow quite another path from that of their conscious counterpart, and accounted for this with his theory of the primary and secondary processes. Ignacio Matte-Blanco (1988), who studied this problem from the logical perspective, suggests that the main characteristic of the primary process is that it is ruled by a _symmetric logic_ , which allows a reversibility of all relations, this being the hallmark of unconscious thinking. This is in sharp contrast with the secondary process that rules conscious thought, working in accordance with the traditional Aristotelian logic, which deals with irreversible relations\u2014if John is Peter's father, peter is not John's father: this is _asymmetric logic_. But in the logic of the unconscious, all statements are reversible; thus, John and peter have a father\u2013son relationship, in which each of them can occupy any of its poles. This is the reason why it is easy to be alternatively a sadist and a masochist, passive and active, abuser and abused.\n\nBut with this reversibility of relations, all the other characteristics of the secondary process simply vanish. This is, for instance, the case of causal relations, which can only be thought in irreversible terms\u2014in medicine we say that Koch's bacillus causes tuberculosis, but not the other way round. The same happens with the concept of objective time, which requires an irreversible sequence of successive moments, as well as that of space, since, if any given place can be replaced by any other, spatial relations become meaningless. Thus, in unconscious thought, a house may emerge from a fire or a mouth be turned into a nipple.\n\nBut the most striking feature of primary process thinking is the reversibility of the class-member relation. For instance, Mary is a woman and a mother, hence we may conceive her as a member of the class of mothers, but this class is not a woman, just as humankind, conceived as the set of all human persons, is not a person. This is the irreversible asymmetrical logic of the secondary process. But in the reversible and symmetric logic of the primary process, we may say that Mary is, at one and the same time, a member\u2014i.e., a part\u2014of the set of all mothers, and that this set is a part of Mary. The relations between a whole and a part, and between a class and one of its members, just collapse, and we are left with a diffuse but overwhelming concept of Motherhood, in which Mary becomes the bearer of the Great Mother archetype, and the latter incarnates in the visage, the body, and the voice of a particular woman. But since every one of the members of the class of mothers participates in such reversibility, in this dimension any of them is equivalent to any other and all mothers are one. This is the basis of those two peculiar mental processes that we call \"condensation\" and \"displacement,\" which, together with plastic representation and symbolism, are the instruments of the dream work (Freud, 1900).\n\nIn terms of our previous hermeneutic analysis, we may say that conscious mental processes are mainly metonymical, while unconscious ones are metaphorical. But there is yet another most significant difference, which may well account for the two types of logic: conscious thinking works mainly in terms of verbal, conventional, socially acquired, and interpersonally shared language, while unconscious thought seems to be made of idiosyncratic images derived from sensuous experiences\u2014what we call _iconic signs_.\n\n_Verbal signs_ are conventional, in that there is no visible relation between the word \"dog\" and that gentle, furry, and loving mammal that sleeps happily on the carpet while I am writing these words. They are appropriate because they are shared by a linguistic community, but they could easily be replaced by others\u2014as they frequently are, when a living language evolves\u2014without a loss of meaning. _Iconic signs_ , on the other hand, are an attempt to reproduce a part of the experience of perception of a given object or situation. An instance of this is onomatopoeia, by means of which cats _meow_ , bees _buzz_ or a twig _snaps_ (of course, when a market _cracks_ , we have concocted a metaphor out of an onomatopoeia). Another one are photographs o portraits of a person, which clearly depict her or him, but what is the status of a political cartoon that draws a caricature of its subject? The latter clearly represents a more elaborate symbol, which highlights a more general characteristic of icons: that they do not only depict, but always imply an interpretation. For Charles Sanders Peirce there were three kinds of icons, according to their distance from sensuous experience: _images_ , _diagrams_ , and _metaphors_. All of them are clearly ways of depicting relations, rather than things.\n\nThe icon always signals a presence, rather than an absence, and it can always be perceived simultaneously, unlike verbal discourse, which is necessarily sequential. So, the very fact that primary process operates as iconic thinking may account for its characteristic features, such as timelessness, reversibility, lack of causal relations, which are replaced by relations of meaning, and the inability for negation. But whereas words are more precise in denotation, icons have a much greater capacity for connotation, so that they have a deeper emotional impact, when used in interpersonal or social communication. In the inner workings of the individual mind, secondary process and verbal thought are the bases for reason, logic, and science\u2014hence, metonymy. On the other hand, primary process and iconic thinking are the language of feeling, art, poetry, and religion\u2014i.e., metaphor.\n\nIf we accept these propositions, clearly derived from the Freudian concepts of the primary and the secondary processes, as much as from hermeneutics and Peirce's conception of semiotics, we should admit that, at the unconscious level, there cannot be any discrimination between subject and object, and that they may be easily identified or interchanged. In the analytic situation, this implies that, in the unconscious dimension of the encounter, analyst and analysand are inevitably identical and interchangeable, and that this applies to the former, as much as to the latter. It is only in the conscious dimension of experience, thinking, and acting, that the analytic asymmetry can and must be understood, remembered, and preserved.\n\nBut obviously the stuff of human beings is not restricted to the unconscious and the primary process. Consciousness and the secondary process also exist and have a major bearing on human existence, so that thinking always travels along two contrasting and complementary paths. This is what Matte-Blanco calls \"bi-logic,\" that is, the alternance and confluence of both kinds of logic, which are kept in a state of dialectic tension between them.\n\nAll this derives, not only from the Freudian discovery, but also from the Kleinian conception of an unconscious fantasy, which determines a type of experience of oneself, objects, and the world and its happenings that underlies and is quite different from ordinary conscious experience. Donald Meltzer (1981) asserts that \"Mrs. Klein... made a discovery that created a revolutionary addition to the model of the mind, namely _that we do not live in one world, but in two_ \u2014that we live in an internal world which is as real a place to live in as the outside world\" (p. 178, italics added). It may be argued that Meltzer is overstating his pro-Klein case, and that this discovery really comes from Freud. This is unquestionably so, as far as clinical discoveries go, but the author develops a convincing argument for his contention that the original causal-deterministic and quasi-physiological model of the _Project_ (Freud, 1950) prevented him from finding a place in his theory for an internal world, and completing his \"approach to transforming himself from a neurophysiological psychologist into a phenomenological one\" (Meltzer, 1981, p. 178).\n\nThis perspective brings about substantial consequences, both for our hermeneutic approach and for clinical practice. It is easy to see that any attempt to think exclusively in terms of the asymmetrical logic of secondary process will bring about a univocal interpretation and view of things, while any way of thinking ruled by the symmetrical logic of the primary process will generate an equivocal one; these would be the bases of monistic and relativistic thinking. Likewise, bi-logic would be the psychological substrate of analogical thinking. Now, according to Matte-Blanco, bi-logic is the true shape of human thought, but in most circumstances they are mutually alienated, so that conscious thinking tries to follow only the path of asymmetrical logic, while unconscious mentation takes that of symmetrical logic, generating a steady flow of _dream-thoughts_ (Meltzer, 1983), thus constituting that \"other scene\" (Freud, 1900) of a parallel invisible world.\n\nHowever, the conscious assumption and development of the capacity for bi-logic is a veritable maturational achievement, which should be expected as a result of a successful psychoanalytic treatment. This implies the assumption that the aim of psychoanalytic treatment may be framed as _the integration of the personality_ , so that its various components and processes may fuse into a functioning whole\u2014a far cry from Freud's (1933a) staunch belief that the secondary process should prevail (\"Where id was, there ego shall be. It is a work of culture\u2014not unlike the draining of the zuider zee,\" p. 80).\n\nNow, this dual world also reflects on the very nature of the analytic relationship. In these terms, there is a conscious level in which the analyst is an analyst, the patient is a patient, and they are both together in a closed room doing something called \"psychoanalysis\", however, this has been defined in their initial agreement. Nevertheless, this coexists with another level in which things occur quite differently; thus the patient may feel that interpretations turn into a venom that poisons him or her, or the analyst may have the unconscious experience of being a good mother that feeds a hungry baby, or becomes the pray of the cannibalistic impulses of a starving one.\n\nSuch description is, nonetheless, insuffcient, since it is trying to express an experience belonging to the domain of the symmetric logic of the primary process, in terms of the asymmetric logic of the secondary process. It is no use saying to a patient \"You are having the unconscious fantasy that my interpretations are a sadistic penetration that tears you inside,\" since such a formulation translates the unconscious fantasy into the discriminate terms of consciousness, which are the only ones in which there is a differentiation between analyst and analysand. So, it is a metonymical framing of a valid intuition of something that can only be approached by metaphor\u2014approached, but never fully reached or encompassed. Fortunately, the patient's metaphorical mental processes usually take hold of the interpretation and retranslate it into terms that are more adequate for the kind of understanding they are both striving to attain. In any case, the use of poetical (metaphoric) language is frequently more effective, at the time of interpreting, than that of a more concrete and precise (metonymic) one.\n\nA more serious objection is that this way of phrasing the interpretation is tantamount to affirming that the unconscious fantasy belongs only to the patient, and that the analyst is not a part of the session's unconscious dimension\u2014a claim that is clearly absurd and unsustainable. A more adequate formulation would perhaps be: \"something is happening to us that transforms my interpretations into a sadistic act, which may be compared to a violent and painful rape.\" This is the metonymic version, while a more metaphoric one would be \"it seems that I am raping you with my words.\" such an interpretation would be based, both on the patient's feelings of pain, humiliation or indignation, and on the analyst's experiences of guilt or sadistic pleasure, felt at the moment of verbalizing it. The concrete wording of the interpretation will obviously depend on the context and associative substrate, which would stem from the patient's dreams or associations and the analyst's countertransference occurrences (racker, 1968), as well as from their respective personalities and communicative styles, and the history of their analytic relationship.\n\nIn this, Matte-Blanco's contribution turns out to be much more complex and nuanced than Klein's original concepts. For the former, it is not a question of us living in two worlds\u2014that of consciousness, which is determined by reality, and that of unconscious fantasy, derived from instinctual motions\u2014but that our relation with reality\u2014the whole of reality, which includes both the external world facts, harvested by perception, and those of emotional life, which are experienced without any mediation\u2014is transformed through the various thinking processes: _symmetric logic_ , _asymmetric logic_ and _bi-logic_. The result is a highly complex and polysemic view of the world, in which there is a confluence of disparate elements of diverse origins, which might be compared with the world of Greek mythology, inhabited by many different beings: the titans, the major Gods of Olympus, mortals, demigods born from the coupling of the previous two, and a myriad minor gods who dwelled in the various spaces of the everyday world, such as woods, fountains, seas or crossroads.\n\nIn the previous paragraph, I have made an extensive use of metaphoric language and iconic representation, in order to convey a highly complex conception of the organization and functioning of mind. This is precisely the way in which psychoanalytic theorizing works, what Freud, in his letter to Fliess of May 25, 1895, called \"fantasizing\" ( _Phantasieren_ ). The full quotation says:\n\n> During the past weeks I have devoted every free minute to such work [of theory building]; have spent the hours of the night from eleven to two with such _fantasizing, interpreting, and guessing_ , and invariably stopped only when somewhere I came up against an absurdity or when I actually and seriously overworked, so that I had no interest left in my daily medical activities.\n> \n> (Freud, 1895, p. 129, italics added)\n\nSo, when facing the protean quality of human mental life, Freud felt he had to resort to a peculiar admixture of scientific and poetic thinking, which alternated between moments of imaginative frenzy (\"fantasizing, interpreting, and guessing\") and the more sober ones of checking these fights of fancy with actual clinical experience and the rigors of argumentation. The resulting theory is necessarily mixed, a hybrid of logical discourse and poetic language; hence the omnipresence of metaphor in psychoanalytic theory, which has been a source of vexation for many an epistemologist.\n\nWhat is specific of psychoanalysis is the psychoanalytic experience, which is emotional, interactive, and cognitive, all at once. And such experience may only be conveyed by poetic language, which is mainly metaphorical. It is only afterwards that this gives rise to a conceptual discourse, as a transformation of the former, which aims at a universality that it never fully reaches; this is what we call \"metapsychology.\"\n\nMetapsychology is to the clinical discourse that aims to recreate in the reader or listener something of the living experience of the analytic encounter and dialogue, as metaphysics is to poetry\u2014and this is a metonymic analogy, which follows Mexican philosopher Mauricio Beuchot's (2003b) ideas on \"the intercrossing of metaphysical and poetical discourses.\" For him \"poetry is pre-metaphysic, and metaphysics is post-poetic\" (p. 143), and their mutual influence and dialogue should result in \"metaphysical poetry\" and \"poetical metaphysics.\" The same may be said about the clinical-poetical and metapsychological-conceptual discourses in psychoanalysis; it is not that the latter serves as foundation for the former, or vice versa, but that they complement each other in their mutual encounter, uncovering their similarities and common ground, but without losing sight of their specific differences, not unlike what goes on in the psychoanalytic dialogue. We shall now consider how this complementarity works, in the case of the field concept in psychoanalysis.\n\n## **The Field Concept**\n\nThe concept of \"field\" was originally introduced in physics, in order to account for phenomena that implied an influence of one object on a distant other, without any visible intermediation between them, such as gravity or magnetism. Since the type of influence the former had on the latter seemed to irradiate in all directions, as if in concentrical circles with diminishing strength, the term was thereafter used to refer to a region of space in which a given effect of these characteristics exists. But it also implied a certain organization of such region, in which any change at a given point had effects on every other point of the field. Field theories implied an epistemological revolution in science, since they replaced linear causality, as an explanatory principle, by complex interdependence. They also gave up the assumption that a cause should always precede its effects; consequently, they had the characteristic of being atemporal, since they explained the phenomena that took place in the field in terms of the latter's organization and dynamics, without any reference to its previous history (Tubert-Oklander, 2007).\n\nThese concepts were imported into psychology by Gestalt theorists, who were particularly interested in the study of \"wholes,\" as opposed to that of \"parts\" (Koffka, 1935; Katz, d. 1943; Merleau-Ponty, 1942). From such perspective, _the whole was considered to be more than, prior to, and more elementary than the sum of its parts_. In other words, _the relationship between the whole and the parts constituted a field_. This meant that, in the complex organizations that characterize living phenomena\u2014such as organisms, their structure and functions, and their interactions with other organisms and their environment\u2014this complexity is a primary phenomenon, and its so-called parts are artificially created by our analytic activity, whether intellectual or physical. For instance, the kind of anatomical and functional dissection used by physiologists to create the \"systems\" they study, by means of isolating parts of the organism, falsifies the fact that the latter always acts as a whole, and generates a situation that is akin to, as Kurt Goldstein (1940) pointed out, that which characterizes pathological conditions. The same would apply to the effects of some of the research artifices introduced by Freud's technique, such as the fragmentation of the dream, in order to inquire and follow the associations forced by the analyst's questioning (Freud, 1900).\n\nIf we accept this point of view, we are bound to conclude that the results attained by an approach based on an analytic activity that fragments the integrity of an organism (or personality) in order to inquire into the nature, structure, and functioning of the \"parts\" that are thus created, can only be used for the understanding of normality if we identify the ways in which this isolation modifies the functioning of the whole, and take the necessary measures to compensate such distortion. This demands reintegrating this information into the functioning of the organism-as-a-whole, and restoring the organism to its normal context, from which it had been segregated when it was placed in the laboratory (or consulting room). The same applies to any study or conception of the individual in isolation. The human being always acts as a whole and is inserted in a relational and social context.\n\nOf course, when the integrity of personality and\/or its relations with others and groups is impaired by pathology, the partial aspects that result from splitting are real, and need be analyzed, in order to restore\u2014or perhaps institute for the first time\u2014their wholeness. In this, traditional clinical psychoanalysis has made a fundamental contribution.\n\nBut the field concept was brought to social psychology by Kurt Lewin (1951), who came, like Freud, from a natural science background, and tried to formulate his field concept in quasi-physical terms. For him, the human being existed in a \"vital space,\" conceived as a field in which many different forces interact, thus shaping his or her behavior and experience. This concept allowed him to map the effect on the individual of a series of disparate elements, such as childhood experiences, wishes and aspirations, membership in groups and institutions, organic characteristics and transformations, physical and social climates, the geographic milieu, language, cultural values, the structure and functions of institutions and society, political events, and accidental happenings. Even though these may seem to be so different as to become incommensurable, their interaction and mutual influence turn out to be cogent, if we consider that they are all psychological events, acting within a psychological field.\n\nThis is especially evident when we consider the relation of individual psychology to interpersonal and group events and situations, which, according to Lewin, also constitute a psychological field in which the whole\u2014the group\u2014is more than, prior to, and more elementary than the sum of its parts\u2014the individual members. Following the aristotelian conception of the human being as essentially social, the individual becomes an abstraction, as the behavior and experience of concrete human beings can only be understood in terms of the organization and the dynamics of the group field.\n\nThe field approach is based on a spatial metaphor, so that it develops an atemporal theory. This implies the methodological principle of taking into account _contemporary factors_ only. Everything is viewed in terms of the present, and the past and the future have a purely psychological existence, as remembrances of what has happened and expectations of what is to come. In this, it is belief and meaning, rather than actual occurrence, which determine the psychological relevance of any given event. This would seem to be in dire contradiction with the psychoanalytic approach, which seeks to explain the present in terms of the past, but this is so only in terms of Freud's ultimately unsuccessful attempt to turn psychoanalysis into a positivistic science (Freud, 1940b).2\n\nAnother different approach to the psychological use of the concept of field was that of Maurice Merleau-ponty, in his books _The Structure of Behavior_ (1942) and _Phenomenology of Perception_ (1945). Starting from Husserl's phenomenology and the Gestalt point of view, he took a different turn, since, instead of emphasizing the experimental study of perception, as the classical Gestalt psychologists, or that of motivation, as Lewin, he adopted the phenomenological-existential perspective, thus focusing on the study of _personal experience_. This brought him into contact with one possible way of understanding psychoanalysis, as a methodology for the study of unconscious experience.\n\nThis field perspective of human existence became quite attractive for those psychoanalysts who were particularly interested in its interpersonal and social dimensions. For instance, harry stack Sullivan (1953) was overtly sympathetic to Lewin's field concepts, although he differed from them, as he developed his own view of human existence in terms of the individual's participation in an interpersonal field.\n\nField concepts also found their way into the theory and practice of those psychoanalysts who initiated the clinical analytic inquiry of groups, thus creating what became known as \"group analysis.\" Enrique Pichon-Rivi\u00e8re, whose influence was acknowledged by Willy Baranger (1979a), as his analyst, teacher, and friend, explicitly referred to Lewin's concepts and techniques in his papers on his own approach to group analysis, which he called \"operative groups\" (Pichon-Rivi\u00e8re, 1971; Tubert-Oklander & Hern\u00e1ndez-Tubert, 2004). On the other hand, S. H. Foulkes (1948; Foulkes & Anthony, 1965), the creator of group analysis in Britain, denied having a Lewinian influence, but he shared with him an origin in Gestalt psychology, which he had received from his teacher, the neurologist Kurt Goldstein (1940). The fact that Lewin's models were physical, like Freud's, while those of Foulkes stemmed from the study of human biology and social science, determined a significant difference in their perspectives.\n\nBut the true inception of a field theory of the psychoanalytic situation and process came in 1961, when Madeleine and Willy Baranger published, in the _Uruguayan Review of Psychoanalysis_ , their seminal paper \"Te analytic situation as a dynamic Field\" (Baranger & Baranger, 1961\u20131962), which was later included in their 1969 book _Problems of the Psychoanalytic Field_ (Baranger & Baranger, 1969). This seminal text has only recently been published in English translation by the _International Journal of Psycho-Analysis_ , in 2008.\n\nThe Barangers' point of departure is methodological: the minimum dimension for psychoanalytic observation comprises two people, not one. In this they implicitly agree with British independents, such as Michael Balint, who pointed out the paradoxical effects of trying to account for what happens in a bi-personal situation, by means of a one-person theory. Hence, they define the nature of the analytic field as follows:\n\n> A situation between two persons who remain unavoidably connected and complementary as long as the situation obtains, and involved in a single dynamic process. In this situation, neither member of the couple can be understood without the other.\n> \n> (Baranger & Baranger, 2008, p. 796)\n\nHere they introduce the concept of \"field,\" which they import from Gestalt psychology, especially from Merleau-Ponty (1945), whose approach is more consistent with their whole approach to psychoanalysis, which is mainly philosophical and humanistic, in sharp contrast with Lewin's quasi-physical perspective.\n\nBut the structure and dynamics of the field include more than the two people involved; they also comprise the place and physical disposition of the consulting room, the temporal sequence of the sessions and the functional definition of both parties' roles, in sum, the analytic setting. In later papers, they also included the analyst's theories (Baranger, Baranger & Mom, 1978). What they did leave unmentioned was the participation of the social, historical, and political context in the constitution of the analytic field. This may be understood as a result of their traditional psychoanalytic focus on the intrapsychic, in spite of Willy Baranger's life-long interest on the study of ideology and its influence on the psychoanalytic situation (Baranger, 1954, 1957, 1958, 1992; Hern\u00e1ndez-Tubert, 2005; Tubert-Oklander, 2005, 2007).\n\nThis holistic approach to the analytic situation and process led them to a reformulation of some basic concepts of the theory of technique. Insight, for instance, came to be seen as a reorganization of the field, which generates new meanings (Baranger & Baranger, 1964). The essential ambiguity of the analytic situation paves the way for a certain degree of regression in both parties, and the emergence of a _field unconscious phantasy_.3 This is clearly derived from Melanie Klein's concepts (Isaacs, 1948; Klein et al., 1952), but with a major difference: this mental product cannot be considered as an expression of the individual's drives, but as a _phantasy of the couple_ , which cannot \"be considered to be the _sum_ of the two internal situations... [but as] something created _between_ the two, within the unit they form in the moment of the session, something radically different from what each of them is separately\" (Baranger & Baranger, 2008, p. 806).\n\nIn this, there is an obvious influence of the experience and theories of group analysis, which they received from Pichon-Rivi\u00e8re. This they explicitly acknowledge, when they write that \"we can only conceive of the basic phantasy of the session\u2014the point of urgency\u2014as a phantasy in a couple (in analytic group psychotherapy, the appropriate expression is 'group phantasy')\" (pp. 805\u2013806).\n\nAnother major point in their argument is that, when the patient's resistance becomes a _bastion_ ( _baluarte_ in spanish)\u2014understood as \"whatever the patient does not put at risk because the risk of losing it would throw the patient into a state of extreme helplessness, vulnerability and despair\" (p. 814)\u2014its analysis and final resolution shows that this was truly a field phenomenon, which included an unconscious participation of the analyst. This bi-personal bastion also includes the analyst's theories and technique (Baranger, Baranger, & Mom, J. M., 1978). In this they follow the path opened by Racker's (1958) pioneer work on the analyst\u00b4s counter-resistances.\n\nThe resolution of such bastions requires that the analyst take a \"second look\" at the developments in the analytic situation, taking himself or herself as an object of the analytic inquiry. This happens whenever the necessary asymmetry of the analytic relation, instituted by the initial contract, has been lost and substituted by a pathological symmetrical organization, which has to be solved by interpretation (Baranger, Baranger & Mom, 1983). When this interpretive effort is successful, the result is that reorganization of the analytic field that we call \"insight,\" and the asymmetry of the relationship is restored, thus reactivating a stagnated process, which they call a \"non-process.\"\n\nNow, this later formulation is more restricted than their initial statement that the analytic situation can only be fully understood as a bi-personal field. In their 1983 paper called \"process and non-process in analytic Work,\" the Barangers and Mom were more cautious, as they seemed worried about the risk implied by taking the field concept as an affirmation of a total symmetry of the positions of analyst and patient. Perhaps this was a reaction to some misreadings of their original text that emphasized a mutuality in the analytic relationship\u2014i.e., a relational perspective that they would be far from sharing (Tubert-Oklander, 2007). In any case, they were posing the problem of the alleged opposition between symmetry and asymmetry that emerges whenever the issue of _mutuality_ in analysis is discussed, ever since Ferenczi's bold experiments in mutual analysis (Ferenczi, 1932; Aron, 1996; Tubert-Oklander, 2004a, 2004b).\n\n## **The Author's Point of View**\n\nMy personal position vis-\u00e0-vis this problem is that the analytic relation needs be asymmetrical, since it is defined as a professional helping intervention; hence, the analyst's and the analysand's positions, functions, responsibilities, and rights are necessarily different and complementary. But this happens only at the differentiated level of conscious and preconscious experience, since the unconscious knows nothing about differences or professional obligations. Therefore, at the deepest level, not only are both parties symmetrical and interchangeable, but they are also completely undifferentiated, in a state of primeval unity (Loewald, 1951; little, 1960; Bleger, 1967a; Tubert-Oklander, 2006a, 2008). This is what creates a symmetrical unconscious field, which enters into a dialectic tension with the asymmetrical analytic relation, which the analyst strives to maintain, as the only possible tool for an understanding of the field. When this difference and tension is momentarily lost, it is high time for that second look, which may come from self-analysis, personal analysis or supervision, in order to salvage the analytic process.\n\nBut the field is not a \"thing,\" a discrete structure or event, which may or may not be present and is in need of explanation, but rather a different perspective, another way of organizing our perceptions and thinking about them. Classical psychoanalytic theory starts from the assumption that only the individual is \"real,\" and that dyads, fields, interpersonal and transpersonal processes, or collective entities such as groups, institutions, and communities, are secondary phenomena, or even fantasies. One instance of this is to be found in Bion's (1952) assertion that \"the belief that a group exists, as distinct from an aggregate of individuals, is an essential part of [the members'] regression, as are also the characteristics with which the supposed group is endowed by the individual.... [Te word] 'group'... [means] an aggregation of individuals all in the same state of regression\" (p. 142).\n\nThis brief text, which was written while the author was training as a psychoanalyst and in analysis with Melanie Klein, enters into a sharp contrast with his previous \"experiences in Groups\" (Bion, 1948), in which he poses an entirely opposite position:\n\n> In the group the individual becomes aware of capacities that are only potential so long as he is in comparative isolation. The group, therefore, is more than the aggregate of individuals, because an individual in a group is more than an individual in isolation.\n> \n> (Tubert-Oklander & Hern\u00e1ndez-Tubert, 2004, p. 90)\n\nBe it as it may, the unquestionable existence of the individual was clearly Freud's starting point, and from it he derived his research program of investigating psychic processes, considered as something \"inside\" the individual. The rationale seems to be that only material entities are \"real,\" and that the isolated physical organism is the only possible true substrate of mind. But this is an assumption that stems from his previously accepted conception of the world\u2014the materialistic metaphysics of modern science\u2014and not a result of the psychoanalytic inquiry (Hern\u00e1ndez-Tubert, 2004; Tubert-Oklander, 2004c).\n\nNonetheless, not all psychoanalysts share these positivistic assumptions, and there has been lately a sea change in a large sector of the psychoanalytic community towards holistic thinking. The idea that the psychoanalytic situation is an organic whole, whose parts cannot be understood without referring to each other and to the organized totality in which they are immersed, may be framed in more than one way (\"Being is said in many ways,\" said Aristotle in his _Metaphysics_ ). If one conceives it in atemporal terms, as a complex mutual interaction and influence between a number of elements that occur simultaneously, then you have a _field model_ of complexity. If, on the other hand, one looks at it in temporal terms, as a hypercomplex evolution with direction, course, and aim, this is a _process model_. Finally, if one constructs it as a model of personal relations in an imaginary group, as the ancient Greeks did with the Olympus and Freud (1923a) with \"Te ego and the id,\" the result is a _dramatic or mythological model_. There is no need for us to choose between these three kinds of models, since they have an epistemological and not an ontological validity; they are something like three different lenses or recording instruments, three basic metaphors for understanding, each of which gives a different image of one and the same thing (Tubert-Oklander, 2006b). And this \"same thing\" is human ontology, ever present and evolving, but never fully visible or knowable. This is the Being which is said in many ways and called by many names.\n\nHence, the three models that I have just described are but metaphors, coined in order to describe some aspect or other of the ineffable complexity of the analytic experience. They offer a metaphoric description, more akin to the symmetric logic of the unconscious and poetry, which is to be articulated with the literal or metonymic description, in terms of the asymmetric logic of consciousness and science, in order to attain an analytic bi-logical understanding of the experience we share with our patients.\n\nBut does the assertion that human existence is a highly complex totality imply that the individual be nothing but a creation of our thinking processes, a partial metaphor used to refer to an aspect of a complex whole? I would say it is, but so are relations, the field, the group, the community, and humankind. We are always striving to picture in our minds a hypercomplex, irrepresentable reality by building sketchy maps of our primary pre-reflective experience (Merleau-Ponty, 1945), and playing with them, like a child plays with building blocks.\n\nIn this, the group-analytic experience is the necessary complement of the traditional bi-personal psychoanalytic experience. Wilfred Bion's (1948) early incursion into groups led him to postulate the existence of _proto-mental phenomena_ , prior to any dreaming or wording of them. In the proto-mental level, there is no differentiation between body and mind, self and other, individual and group, since the proto-mental system is the matrix from which such entities are formed and emerge.\n\nIn the same vein, S. H. Foulkes, the creator of group analysis, stated\u2014in his _Introduction to Group-Analytic Psychotherapy_ , published in 1948, the very same year in which Bion's \"Experiences in Groups\" started to appear in _Human Relations_ \u2014that:\n\n> Each individual\u2014itself an artificial, though plausible, abstraction\u2014is basically and centrally determined, inevitably, by the world in which he lives, by the community, the group, of which he forms a part.... The old juxtaposition of an inside and outside world, constitution and environment, individual and society, phantasy and reality, body and mind and so on, are untenable. They can at no stage be separated from each other, except by artificial isolation.\n> \n> (Foulkes, 1948, p. 10)\n\nThe obvious corollary is that the group is also \"itself an artificial, though plausible, abstraction.\" in this, Foulkes was envisaging, just like Bion, a conception of existence as a hypercomplex undifferentiated whole, but whereas the latter conceived this as a primitive level, the former saw this systemic quality in all levels, from the apparently isolated individual through groups, institutions, and communities, up to the whole social and political reality.\n\nThe very same stance was taken by Enrique Pichon-Rivi\u00e8re, founder of the argentine psychoanalytic association and pioneer of psychoanalysis and group analysis in Latin-America, who, as we have already seen, had a major influence on the Barangers. He also conceived both psychoanalysis and human life in general as an organic whole, although he preferred the temporal metaphor of the process to the spatial one of the field. His conception of the \"spiral dialectic process\" of analysis was part of the inspiration for the Barangers' concept of the analytic situation as a dynamic field (Baranger, W., 1979a).\n\nIn pichon-rivi\u00e8re's thinking, there was never an opposition between individual and collective psychology, since they are two sides of one and the same mental phenomenon\u2014that of human existence. He used to refer to the metaphor of the island and the mainland, taken from John Donne's famous _Meditation XVII_ , in which the poet says: \"No man is an island, entire of itself; every man is a piece of the continent, a part of the main.\"\n\nThis poetic metaphor speaks for itself: neither the island, nor the continent are real entities, but only that part of a single irregular ground that can be seen over the level of the waters. Hence, the individual and the group are illusions, derived from our mind's tendency to split and splinter complex wholes, in order to be able to talk and think them through (Tubert-Oklander, 2011). Or, perhaps, rather than speaking of \"illusions,\" we should call them, after Foulkes (1948), \"artificial, though plausible, abstractions.\"\n\nSo, we are now back to our original problem of articulating _metaphor_ and _field_. The concept of \"field\" is now clearly a metaphor for the analytic situation, which is complemented by two other metaphors that depict other aspects of it: the _process metaphor_ , which highlights its evolution in time, and the _dramatic metaphor_ , which iconizes the mental processes in the analytic relation and dialogue, in terms of that \"other scene\" of fantasy and dream (Tubert-Oklander, 2006b).\n\nOn the other hand, the unconscious metaphoric processes that represent the mind's basic efforts to represent its dealings with the world are the very stuff of the analytic interaction, in its three aspects of field, process, and drama. In these deepest levels of minding, there is no differentiation between self, others, and the whole environment, and unconscious experience comprises everything there is; communication does not follow the ordinary, discrete, and perceptible paths, and neither does it occur in sequence, but rather as a simultaneous mutual influence\u2014i.e., field and process phenomena. This is what we try to depict and unravel by means of the analytic dialogue, in its double aspect of interpretation and explanation, which requires both metaphor and metonymy, which correspond to the poetic and argumentative uses of language (Ricoeur, 2008).\n\nThe end result is truly analogical, inasmuch as it finds a proportional midpoint in between the univocality of metonymy and science, and the equivocality of metaphor and poetry\u2014\"analogy\" originally meant \"proportion.\" and this requires, on the part of the analyst, an exercise of the Aristotelian virtue of _phronesis_ (prudence), which is the ability to give to all parties their due. The knowledge that is thus acquired is necessarily partial, since it is based on similarity, rather than identity, but enough for the analyst and the analysand to go on thinking and working together\u2014i.e., analyzing (Beuchot, 1997, 2003a; Tubert-Oklander & Beuchot Puente, 2008).\n\n## **Summary**\n\nThe concepts of \"field\" and \"metaphor\" are necessarily related. First, because the very idea of the field is a metaphor; second, because metaphors generate a field in themselves, when considered as a form of mental activity. The mind works in terms of two logics and two processes: the secondary process, which is verbal, realistic, logical, and scientific, and the primary process, which is iconic, fantastic, metaphorical, and poetic. The logic of the secondary process is asymmetrical and that of the primary process is symmetrical; the confluence and articulation of both is bi-logical. The analogical synthesis of both logics gives the fullest integration of the human mind.\n\nAt the unconscious level, there is no individuation and no differences, but rather a primeval fusion of subject, object, and environment; this is the psychological and logical basis of the bi-personal field and process, which include both patient and analyst in an evolving dynamic whole. There is necessary complementarity between psycho-analysis and group analysis, as there was between the Barangers' concept of the dynamic field and their teacher Enrique Pichon-Rivi\u00e8re's concept of the spiral process. These ideas originated from the group-analytic experience and found their way into the theory of psychoanalytic technique.\n\n## **Notes**\n\n Originally published in _Psychoanalytic Inquiry_ 33(3) (May 2013) with the same title.\n\n \"Psychology, too, is a natural science. What else can it be?\" (Freud, 1940b, p. 282).\n\n Here the unusual spelling of the word corresponds to the Kleinian usage (Isaacs, 1948), in which \"phantasy\" refers to the original unconscious mental processes and their iconic content, as something quite different from conscious \"fantasies,\" akin to daydreaming, and their repressed derivatives, as described by Freud (1908).\n\n# 15\n\nMETAPHOR, ANALYTIC FIELD,  \nAND SPIRAL PROCESS\n\n_Beatriz_ _de Le\u00f3n de Bernardi_\n\nThis chapter deals with field theory issues in the frame of latin American thought, linking it to the subject of metaphor in psychoanalysis.\n\nIn the first part, some general developments about the theme of metaphor and about metaphor in psychoanalysis are exposed. The author presents the concept of dynamic field theory in the vision of Madeleine and Willy Baranger, the metaphoric processes implicit in this theory, and interpretations formulated over different basic concepts.\n\nIn the second part, the author develops a personal perspective of the field theory, supporting herself with examples from her clinical practice. She describes the characteristics of moments of intense communication between patient and analyst and the metaphoric processes implicit in interpretations. These metaphoric processes enable the integration of different levels of the intersubjective experience created between patient and analyst. The author postulates a dialectic point of view that allows the articulation of a situational perspective that studies the specific intersubjective moments of change in the analysis, with a vision that considers the process of analysis through time.\n\nConclusions are formulated regarding the role of metaphor in analysis and the future of the field theory in the context of theoretical and technical pluralism of current psychoanalysis.\n\n## **Metaphor and Theory of the Analytic Field**\n\nMetaphor has been traditionally understood as a rhetorical figure used by poets and artists. Usually, it has been defined as \"a figure of speech in which a word or phrase is applied to an object or action that it does not literally apply to in order to imply a resemblance\" (Collins dictionary). Aristotle had already put the emphasis, in _Poetics_ and _Rhetoric_ , on the processes of transmission and extension of meaning that are characteristic of metaphoric creation. When a metaphor is created, we transfer an attribute from one subject to another subject to which it does not literally correspond. This transmission is accompanied by a figurative extension of the original meaning. From this perspective, Ricoeur (1986) considers that metaphors emerge to fill semantic vacuums. Processes of meaning extension that are present in metaphoric figures generate a new reference and new semantic pertinence that becomes impertinent with regard to the literal meaning and the usual reference of the term.\n\nIn a different posture, D. Davidson (1978) stated the pragmatic character of metaphor. From his point of view, what is relevant in a metaphor does not lie in the transmission of a meaning but in the promotion of conceptual changes and the creation of meanings in the listener. Thus, the metaphor does not create a figurative meaning, but the terms used in the metaphor keep meaning in a literal way. But the central aspect that this author highlights is that metaphors leave some degree of indetermination among related aspects, something that suggests new associations that are relevant to the listener. The way in which new connections are established, producing new meanings and emotions, depends on this listener (Quintanilla, 1999). In this approach, the function of metaphor is not mainly to give a message, but to provoke effects in the subjective experience of the listener. Following Davidson's point of view, authors such as Rorty (1989) have shown how the use of metaphors in communication also attempts to establish bonds with a strong emotional basis.\n\nAt present, the conception of metaphor does not gather only literary and philosophical reflection, but it has extended to the general processes of human cognition, the development of artistic and scientific thought, the different ways of communication and culture (Gibbs, 2008). The studies of Lakoff and Johnson (1980b, 1999) stated how metaphor is not only a figure of speech but is also part of daily expressions, being an intrinsic element of communication and of the thought processes since the origin of life.\n\nIn psychoanalysis, the subject of metaphor has been present in the reflection about the role of psychoanalytic theoretical conceptions and in elaborations about the characteristics of analytic communication. Authors such as G. Klein (1976), schafer (1976), and spence (1987) have understood, for example, how psychoanalytic theories may be seen as explanatory metaphors of unconscious psychic functioning. For some of these authors, this has been the reason why metapsychological constructions with a high degree of abstraction and generalization must be left aside in our practice. For others, however, this metaphoric character of psychoanalytic theory constitutes its greatest instrumental value.\n\nRecently, Wallerstein (this volume) critically reviewed the proposals of G. Klein and R. Schafer, who considered the metapsychological contributions as metaphors that must be left aside in their clinical application. Wallerstein, on the contrary, hierarchized the instrumental and descriptive value of the different psychoanalytic theories. He also stated how this value is lost if psychoanalytic theories are taken in their literal sense when in contact with the patient, because in a contact adjusted to the richness of the clinic and to the interpretative processes, \"Metaphor has been moved, powerfully by Lakoff and Johnson, from mental product to mental process\" (Wallerstein, this volume).\n\nAnalytic communication may also be understood, in a broad sense, as a metaphoric process that establishes connections between the literal meaning of the analyst's expressions, those of the patient and their unconscious meaning, between manifest and latent speech. Borbely (1998), for example, stated how the metaphoric process, inherent to interpretation, establishes relationships between the present and the past as a way to re-establish the polysemic flow of experiences interrupted by the neurotic suffering. The interpretation proposes new categorizations that question old conceptions about oneself:\n\n> All new insight leads to a greater or lesser extent, to a change to all previously established concepts. This mental change entails a re-conceptualisation of all previous concepts and their simultaneous re-categorization along new dimensions of relevance and meaningfulness.\n> \n> (Borbely, 1987)\n\nAs we see, considering the issue of metaphor in psychoanalysis includes different perspectives of approximation to the subject: that of metapsychological constructions of a more general and abstract character and the consideration of the specific way in which processes of metaphorization are established and the use of metaphors in the dialogue with the patient.\n\nThe perspective of the field theory constituted a model of clinical work that allowed M. And W. Baranger to establish connections between the more general and abstract levels of metapsychological constructions and the level of experience in the session. Teir reflection is placed at the phenomenological level, something that allows them to rethink different general notions of psychoanalysis in relation to its way of functioning in practice. This led them, as time went by, to permanently think and reformulate their own ideas questioned by their experience.\n\nField theory in the vision of M. And W. Baranger was understood as a metaphor of the analytic situation, and these authors' most meaningful publication about the subject is precisely entitled \"Te analytic situation as a dynamic Field.\" The different manifest aspects of the analytic field\u2014spatial, temporal, and functional\u2014supposed a \"radical ambiguity,\" an \"as if\" that enabled the analysis of the underlying unconscious phantasies.\n\n> It is essential for the analytic procedure that everything or every event in the field is at the same time something else. If this essential ambiguity is lost, the analysis also disappears.\n> \n> (Baranger & Baranger, 1961\u20131962a, p. 9; Baranger & Baranger, 2008, p. 799)\n\nIn this paper, I will first refer to the central notions of the field theory and to the vision of the analytic process of Madeleine and Willy Baranger, including references to Lacan's ideas, some of which were reviewed by these authors. I will analyze metaphoric processes in two interpretations, each formulated from a different conceptual basis.\n\nIn the second part of the paper, I develop my perspective of the field theory and of the analytic process. I describe the characteristics of moments of intense communication between patient and analyst and the metaphoric processes implicit in interpretations. These metaphoric processes enable the integration of different levels of the intersubjective experience created between patient and analyst. Starting from Pichon-Rivi\u00e8re's idea of the \"spiral process,\" I postulate a dialectic point of view that allows the articulation of a situational perspective that studies the specific intersubjective moments of change in the analysis, with a vision that considers the process of analysis through time. Finally, I will consider perspectives of the field theory and metaphor in the context of the theoretical and technical pluralism of current psychoanalysis, formulating some conclusions regarding the role of metaphor in analysis and about the future of the field theory.\n\n## **The Dynamic Field Theory in Latin America**\n\nThe analytic field theory emerged in Uruguay at the beginning of the 1960s with the appearance of the paper \" _La situaci\u00f3n anal\u00edtica como campo din\u00e1mico_ \" (\"Te analytic situation as a dynamic Field\") by Madeleine and Willy Baranger (1961\u20131962a). This paper was published in the _Revista Uruguaya de Psicoan\u00e1lisis_ 50 years ago, at a moment when psychoanalytic groups were being formed and consolidated in Uruguay and Argentina.2 That paper, which was recently reprinted in the _International Journal of Psychoanalysis_ (Baranger & Baranger, 2008), had a strong impact on the psychoanalytic thought of the time and continues to have influence today, as shown in publications and congresses of the Federaci\u00f3n de Psicoan\u00e1lisis de Am\u00e9rica Latina (Fepal).3\n\nThe field theory referred to the analytic situation (de Le\u00f3n de Bernardi, 2008),4 incorporating conceptualizations from philosophy, psychology, social psychology, and psychoanalysis developed at that time in both margins of the R\u00edo de la Plata. It also incorporated contributions from phenomenology, through Merleau-ponty's thought, especially from \"Te phenomenology of Perception\" (1945); from the psychology of Gestalt and through the thought of Kurt Lewin; and from social psychology through Enrique Pichon-Rivi\u00e8re, psychiatrist and psychoanalyst residing in Argentina, who theoretically and clinically conceptualized the effects of the social bonds in the structuralization of psychism, favoring group treatment of different problems.\n\nFrom psychoanalysis, the contributions of M. Klein, S. Isaacs, and W. Bion were central. These authors had, at that time, a strong impact on the region and meant to modify the classical Freudian points of view, centered on the role of instinct, libinal evolution, and childhood history, considered from an intrapsychic point of view. The importance given by Klein and those who continued his work to the primitive object relationships, with their anxieties and defenses when facing destructive impulses, the unconscious phantasy, and the conception of different paranoid and depressive positions along life, led to conceiving the analytic situation as an expression of primitive relationships in the \"here and now\" of the session.\n\nBion's Group Theory offered a vision of the unconscious root of certain group behaviors that went beyond individual psychology. In the same way, Kurt Lewin applied the notion of field, with its dynamism and directions, to social situations, which influenced the thought of Bion (Churcher, 2008). Enrique Pichon-Rivi\u00e8re (1998), from his experience as a doctor in a psychiatric hospital and later as psychoanalyst, was interested in developing group activity that would promote forms of more creative and healthier social adaptation. His experience as a psychiatrist and psychoanalyst led him to broaden the notion of object relationship, proposing the notion of bond.\n\n> The analytic investigation of this inner world took me to broaden the concept of \"object relationship,\" formulating the notion of bond, which I define as a complex structure that includes an individual, an object, and their interrelation with processes of communication and learning.\n> \n> (p. 10)\n\nThese different conceptions about the group experience influenced the analytic vision of M. And W. Baranger, which was understood as a situation of a couple.\n\nBut, in addition, the field theory had a heuristic value, offering an answer to epistemological preoccupations of Willy Baranger on the specificity of psychoanalysis and the need for validation of our interpretations.\n\n> The systematic exam of what occurs in the analytic bipersonal situation is the only access to an ideal of knowledge validation that is truly characteristic of psychoanalysis. This ideal currently conceivable is made\u2014without being formulated\u2014in several writings of the last years, which offer a very exhaustive description of the analytic situation with the interpretations and modifications that occur in limited temporal groups.\n> \n> (Baranger, W., 1959, p. 81)\n\nFrom my point of view, the field theory was conceived as a tool of knowledge and clinical investigation, representing an attempt to broaden the capacity of observation5 and perception of the analyst to the multiple manifest and latent aspects of the analytic situation. In this regard, it was logical that they would support themselves on ideas of the Gestalt psychology, which showed how the human mind could perceive elements in globalizing structures.\n\nM. And W. Baranger conceived the existence of a dialectic interrelation between the need for observation and the search for objectivity through acceptance and use of their own subjectivity. They considered the analyst's subjectivity as a determining factor of the field phenomena,6 but at the same time, they found the need for the analyst to be participant and observer, an idea that was highlighted by Racker in relation to countertransference.7\n\nIt becomes necessary that the analyst can establish in himself or herself \"a process of relative division, as an observer of the interpersonal situation\" (Baranger & Baranger, 1961\u20131962a, p. 168), which implies questioning their own emotional reactions and interventions, evaluating their impact in the interpersonal situation, at the same time converted in object of analysis. This attitude will lead them to postulate the need of a second look after the session, which would allow the review of what was experienced and acted by both participants of the situation. We have stated (Bernardi & de Le\u00f3n, 1993) that the second look implies the analyst's disposition to auto-analysis regarding the different ways of his or her participation in the bond with the patient. Establishing a second look during and after the session offers the possibility of testing alternative hypotheses and technical options, as we will see below.\n\n## **Metaphoric Process in the Field Theory**\n\nThe approach of the analytic situation as a dynamic field led to putting the target in the present of the session and in the characteristics of the analytic dialogue established in it.\n\n> The essence of the analytic procedure is dialogue, as Freud (1926) has defined it.\n> \n> (Baranger & Baranger, 2008, p. 89)\n\nS. Isaacs's ideas about unconscious phantasy gave the conceptual basis to understanding the latent sense of this dialogue. For Isaacs, unconscious phantasies are emotional structures, primitive ways of relating in their variants of love and hate, created in the contact with the first object relationships. Still far from verbal expression, they organize the foundations of psychism, of the perception of the self and the world, and they are re-lived in the transferential bond. In this approach, what basically guides the analyst is the \"logic of emotion.\" The point of \"urgency\" of the interpretation is determined by the type of anxiety, depressive or paranoid, and the defenses when facing it, captured by the analyst in his or her countertransference.\n\n> The primary phantasies, the representatives of the earliest impulses of desire and aggressiveness, are expressed in and dealt with by mental processes far removed from words and conscious relational thinking, and determined by the logic of emotion. The unconscious phantasy condenses visual images; auditory, kinaesthetic, tactile, taste, olfactory sensations, etc.\n> \n> (Isaacs, 1948, p. 84)\n\nIsaacs, as well as M. Klein, considered unconscious phantasy from an intrapsychic point of view. But the field perspective, especially influenced by Pichon-Rivi\u00e8re's idea of bond, integrated the intrapsychic with the intersubjective. The dialectic intergame of the individual with others modifies inner object relationships. The subject and the object are reciprocally constituted. It is from this perspective that the shared unconscious phantasy, in its game of reciprocal projective identifications, was placed in the center of the analytic communication in the session.\n\nFor the perspective of the analytic field, which gathers ideas of \u00c1lvarez de Toledo (1954), the words between analyst and patient acquire in the communication with the analyst a pragmatic character, being an expression of multiple actions and unconscious phantasies:\n\n> in addition to its semantic value, the word acquires concrete value, most particularly in analytic work, in terms of fantasied action: shooting arrows, throwing rocks, poisoning, suckling, caressing, etc.\n> \n> (Baranger, Baranger, & Mom, 1983, p. 4)\n\nThe analytic dialogue is compared to ways of exchange from early infancy.\n\n> In early infancy there are synaesthesias between sounds, smells, temperatures, shapes and feelings; the most frequent of these are synopsias (coloured hearing). A sensation corresponding to a given sense appears associated with one or more others, and arises regularly when the latter are stimulated... This is particularly relevant to the process of symbolization.\n> \n> (Alvarez de Toledo, 1954[1996], p. 299)\n\nI have noted (de le\u00f3n, 1993, 2008) proximities among these ideas with ideas emerged in investigations of early development that have shown the phenomenon of the unity of the senses and of the amodal transposition of the information in the bond of the child with his or her mother (stern, 1985b). These phenomena are comparable to the metaphors of poetic creation, which achieve their effects of meaning when they propose analogies and correspondences among different levels of the sensorial experience. It has called my attention to how d. Stern (1985b) and \u00c1lvarez de Toledo (1954) used the same poem by Baudelaire, \"Correspondances,\"8 to illustrate their ideas.\n\nAs we see, the interpretation in the perspective of the field theory, influenced by ideas of the Kleinian frame, supposed an implicit metaphoric process that attempted through the word of interpretation the symbolizing reunification of aspects of the split primitive experience, or fragmented in its emotional and bodily aspects. The word will attempt to integrate the sub-symbolic levels (emotional and bodily) with the symbolic ones (images and verbal representations).\n\nThis perspective is illustrated in an investigation about the \"Changes in the interpretation in the Uruguayan psychoanalytic Group\" (Bernardi et al., 1997). Interpretations of the decades of the 1960s and 1990s were studied in 93 papers of associated Member Work (theoretical-clinical papers on analytic processes presented by the candidates to end their training) and 443 interpretations that made latent contents explicit. A quantitative-qualitative analysis was made of them. From that investigation we extract a paradigmatic example by Aida Fern\u00e1ndez (1967) that shows the interpreting mode of the 1960s, influenced by Kleinian ideas and the conception of unconscious phantasy.\n\nA young homosexual patient, with \"a weak structure of the self\" and with confusional states that show difficulties in the differentiation of the self and the objects, suffers intensely the separations from his analyst, experiencing them as abandonment. With great difficulty, the patient narrates that after the session he has looked for promiscuous sexual contacts, which have generated great discomfort and guilt. When referring to them, the patient describes the uncontrollable impulse of sexual contact as \"a fire in my head\" that had blinded him and made him lose control:\n\n>... then I felt as a fire in my head; it seemed that it had blinded me. I don't know what happened to me; it was amazing...\n\nThe analyst answers, retaking the patient's expression:\n\n> You feel fire in your head due to rage, when you believe that I stop giving you here\u2014to give it to someone else\u2014on weekends. That is why you go searching and giving, relating through all the holes. You go searching outside what you believe I do not want to give you. You are taking revenge brutally\u2014leaving me alone\u2014as you feel yourself, alone and hungry when you reject me\n> \n> (Fern\u00e1ndez, 1967, p. 189)\n\nIn this interpretation, we see how the analyst recontextualizes the expression of the patient, giving a new meaning to it in the bond with her. The expression \"fire in my head\" is used as a metaphor that puts the anger with the analyst on the same level as the anger experienced when facing frustrations in the patient's primary bodily contacts.\n\nThe formation of metaphors and metaphoric processes in the analytic field shows a complex dynamism. In this case, the starting point is the feeling of the analyst of being \"brutally\" attacked by different actions of the patient that lead to self-destructive acts. The image of the \"fire in your head\" used in the interpretation contributes to the processing in the analyst of the impact generated in herself by the actions of the patient, at the same time that she attempts to facilitate processes of integration of the split emotional and bodily experience in the patient. The analyst transmits how she conceived this movement of integration and symbolization in analysis.\n\n> The countertransferential experience is, in this regard, very important, because it can condition all the relationship between analyst and patient. My interpretative task was to translate the act at the level of verbal thought, taking each detail of his movements, of the intention, and their meaning, patiently and carefully, using the healthy parts of the transferential bond. Those of the patient and those the patient felt in me, his analyst. In this way I was able to penetrate the primitive, unreachable world of his internal reality, stopped in the primary process. I consider that he gradually came to accept his acting out and showing what he wanted to communicate to me, that he started to understand, to think.\n> \n> (Fern\u00e1ndez, 1967)\n\nThe notion of bastion that was stated by W. And M. Baranger (1961\u201362a, 1983; 1983 with Mom) describes difficulties in this integration process. Splittings of the primitive self escape the flow of the verbal free association that may end up deceptive, slowing the process of analysis. In these cases, the implicit metaphoric processes in our interpretations fail. Racker's ideas on complementary countertransference (1957a) and the notion of projective counteridentification, which included the analyst's emotional and bodily reactions (Grinberg, 1956), described situations in which the analyst defensively assumed identifications with roles of objects from the inner world of the patient. If this was not understood, it could cause the formation of \"types of stereotyped patterns of experiencing and behaviour,\" of shared phantasies acted in the analytic interaction during a long period of the analysis. In these situations, the analyst put into play his own conflicts and impulses, especially the avoidance of his own destructiveness.\n\n## **New Developments and Changes in Interpretation**\n\nThe advent of Lacan's thought in the R\u00edo de la Plata at the end of the 1960s created a favorable atmosphere for the re-reading of Freud's works, introducing new ideas that differed from those postulated by the theory of object relationships. Ideas about language as the structure of the unconscious, the three registries\u2014symbolic, imaginary, and real\u2014introduced new metapsychological postulates.\n\nLacan's ideas about the influence of the other's desire in the structuring of psychism took him to first place himself in an intersubjective perspective, a position that was later modified together with the advance in his developments about the symbolic order. Lacan clearly differentiates the position of the analyst from the position of the patient. From his point of view, the ordering function of the analyst, exerted from a \"third\" place, is what makes restructuring the patient's psychism possible in relation to the limit of lack and castration. Lacan will question the approaches that highlight the relational or intersubjective aspects because they can cause the loss of analytic asymmetry.\n\nThe conception of metaphor had a central place in Lacan's ideas about the oedipal complex and the paternal metaphor, repression, and the mechanism of condensation. In reference to the condensation mechanism, Lacan takes up again contributions from Roman Jakobson (1956), who, based on studies about aphasia, distinguished the metaphoric axe of language, which allows the selection and substitution of linguistic items, and the metonymic axe, which allows their combination. He followed ideas of de Saussure when he considered metaphor to belong to the paradigmatic axe of _langue_ , while metonymy belonged to the syntagmatic one. Jakobson linked metaphor and metonymy to the fundamental mechanisms of the dream work described by Freud: metonymy with displacement and condensation and metaphor to identification and symbolism.\n\nLacan takes distance from Jakobson when he links metonymy with displacement and metaphor with condensation. From his point of view, interpretation has the effect of substitution of signifiers in a new game of metaphoric meanings. The metaphoric substitution and condensation of verbal signifiers as an effect of interpretation appears in a disruptive way, and it shows in the appearance of lapsus linguae and other formations of the unconscious, provoking ruptures in the known discourse of the conscious self and new restructuring in the patient's psychism.\n\nWhen it comes to hierarchizing moments of rupture, Lacan's approach is placed in the antipodes of Klein's and Isaacs's perspective, who highlighted the phenomenon of the emotional experience integration as an effect of interpretation. In the new perspective, language is what constitutes the structures of the world, as Wittgenstein would say, an outlook that prevails in structuralism influenced by L\u00e9vi-Strauss's thought. The floating attention of the analyst stops focusing on his or her own emotional reactions, to pay attention to the insistence of certain verbal signifiers in the associative discourse of the patient. This perspective necessarily made Lacan strongly question the notion of countertransference (de Le\u00f3n, 2000).\n\nThese ideas, developed within the frame of a growing theoretical and technical pluralism, had an influence on the listening of the analyst in the session in the R\u00edo de la Plata since the early 1970s (de Le\u00f3n, 2005). The previously mentioned paper about the changes in interpretation in the Uruguayan group (Bernardi et al., 1997) shows how interpretations become less saturated of sense and the analyst goes from an active and incisive attitude in his interpretations to an exploratory, interrogative, and expectant attitude toward the patient's associations, working on the basis of the implicit transference, differentiating from the way transference was explicitly worked into many interpretations of the 1960s.\n\nAn example of an interpretation influenced by Lacan's theory clearly appears in a more recent paper of the _Revista Argentina de Psicoan\u00e1lisis_ , Paulucci and Dujovne (2003), that I, myself, have commented on (de Le\u00f3n, 2003).\n\nThe author of the paper shows how a patient complains about his relationship with his partner, saying:\n\n> There is one _ensilladura_ (a Spanish word that literally means \"saddle,\" and that the patient here uses to mean \"tight relation\") between my professional relationship with J. And how mad his rudeness and the yelling he brings to the office make me.\n> \n> Then the analyst answers with an interrogative intervention: **_\"\u00bf_** _Ensilladura_?\"\n> \n> This intervention that attempts to highlight the ambiguity and opacity of the term _ensilladura_ evokes in the analysand the fragmentation of that word:\n> \n> \" _en \u2013 silla \u2013 dura_ \" (in Spanish, \"on hard chair\")\n> \n> To which (the analysand) adds, intensely moved: \"It looks as if I am always suffering on a hard chair.\"\n> \n> (Paulucci & Dujovne, 2003, p. 14)\n\nThe metaphoric game between _ensilladura_ and on \"hard\" \"chair\" opens the patient's later associations. This allows the analyst to conclude that this interpretative modality produced a clarification in the patient about \"his position of masochistic suffering.\"\n\nIn this case, the metaphoric process is guided by the appearance of a term in the patient's speech that is repeated by the analyst in an interrogative way. The patient transforms, substitutes, and surprisingly relocates the term in another context of meaning, linked to his masochistic identification, showing himself \"intensely moved.\" in this case, unlike the previous example, the analyst does not make any direct reference to transference.\n\nM. And W. Baranger reviewed the field theory in papers dated 1961\u201362a and 1983 (and 1983 with Mom). In these reformulations, they stated problems and limitations of the theory regarding the risk of carelessness of the patient's history, the exaggeration of the role of transferential interpretation and of countertransference that were confused, at the same time, with the mechanisms of the projective identification and projective counteridentification. These concepts could be extended in excess to explain clinical phenomena of a varied nature.\n\nM. And W. Baranger dealt with some of Lacan's questions about the risks of asymmetry loss in a bipersonal psychology and his approach to the opaque character of the unconscious (M. Baranger, 1993a). However, they kept the notion of bastion, which would lead to articulating this notion with the one of analytic process and non-process, in their papers dated 1961\u201362a and 1983 (and 1983 with Mom). The second look broadens then beyond the session, to the consideration of the unconscious guidelines of interaction established between patient and analyst, in a more extended period of the analysis.\n\n## **Dialectics of Temporality: \"Field\" Theory and \"In Spiral\" Process**\n\nAlthough in the paper dated 1961, the subject of temporality\u2014present, past, and future\u2014had been introduced in regard to the patient's history, it is twenty years later that Willy Baranger (1979a), when proposing the idea of \"spiral process,\" introduces the dialectics of temporality to the analytic process. This idea from Pichon-Rivi\u00e8re was developed by W. Baranger from a close exchange with Pichon that was established in Argentina and maintained in Uruguay between the years 1954 and 1958 (de Le\u00f3n, 2008).\n\n> The spiral process essentially aims to explain the temporal development of the analytic process, of its turns, repetitions, elaborations, in the alternation of regression and progression, of the dialectics of the history and the temporality that characterizes it.\n> \n> (W. Baranger, 1979a)\n\nThe notions of \"dynamic field\" and \"spiral process\" imply different perspectives. The metaphor of the \"field\" attempted to describe the permanent framing of the analytic work at the time that the characteristic elements that configure the analytic situation, in the synchrony of one given moment of analysis. The \"spiral\" metaphor used to describe the analytic process implied the vision of a succession of moments in time, from a diachronic perspective.\n\n> The concept of \"dynamic field\" is a neighbour of the \"spiral process\" concept, though it aims to describe the structures of minor temporal units. It enables to understand the reciprocal constitution of the individual and the object, and the need to understand one based on the other. Field designates both the frame and the configuration of the analytic situation.\n> \n> (Baranger, 1979a)\n\nThe fertile moments of interpretation and \"insight\" punctuate the analytic process, described by Pichon Rivi\u00e8re (1998) as a \"spiral process,\" an image which expresses the temporal dialectics of the process. \"Here, now, with me\" is often said, to which Pichon Rivi\u00e8re adds \"Just as there, before, with others\" and \"As in the future, elsewhere and in a different way.\" it is a spiral, each of whose turnings takes up the last turning from a different perspective, and which has no absolute beginning or given end. The superimposition of the spiral's curves illustrates this mixture of repetition and non-repetition which may be observed in the characteristic events in a person's fate, this combined movement of deepening into the past and constructing the future which characterizes the analytic process (Baranger M., Baranger W., & Mom J., 1983, p. 9).\n\nThe idea of \"spiral process\" did not only introduce the issue of the temporality of the patient's life \"Just as there, before, with others,\" but also the time in the history of analysis conceived as dialectic process.\n\nThe dialectic spiral in M. And W. Baranger's thought complements the Freudian notion of _Nachtr\u00e4glichkeit_ , which allows understanding of how not only the analytic situation will have prospective effects in analysis, but also that while in the process, situations and analytic moments of the past history of analysis will retroactively resignify. The concept of \"listening to the analysand's listening\" of H. Faimberg (2006) is an example of how different interventions of the analyst only acquire their sense with the advance of the analysis, in responses the patient gives to the interpretations of the analyst in _a posteriori_ time.\n\nTogether with the contributions of Pichon-Rivi\u00e8re and M. And W. Baranger, different authors in latin America have differentiated situation and process (Etchegoyen, 1986), reflecting on the characteristics and the way in which they are mutually conditioned. Bleger (1967a) proposed that the analytic situation is defined from the process, because all analysis needs certain permanent conditions, as the frame and the respect to essential aspects of the analytic situation. More recently, emphasis has been given to the internal setting of the analyst (Alizade, 2002), and to the fact that the dynamics of the process gradually determine the situation and the type of setting.\n\nThese two perspectives have been integrated, attempting to both describe essential aspects of the situation and the process. Isa\u00edas Melshon (1989, pp. 57\u201358) stated how in the session, \"the types of speech, intonation, rhythmic line, building modalities... The expressive movements of the body... Everything, becomes ordered around nodal points of organization and disorganization\" that follow one another and transform along the analytic process. Ruben Cassorla (2005), in his developments about enactment, studies phenomena of interaction over which pathological aspects of patient and analyst converge, which become chronic and prevent the advance of analysis. It is in certain moments in which these phenomena become acute that they can be perceived by the analyst in a retrospective look about the process.9\n\nFrom an integrating approach that takes into account the situational and temporal vision, I have proposed that the analytic process is constituted on the basis of moments of mutual link, in which an intense emotional contact and an intense psychic work happens between patient and analyst. These moments imply complex dynamisms in communication in which _\"_ facilitated by regression, a tight intergame of images, affects and words happens between patient and analyst\" (de Le\u00f3n, 1993). These moments of the analytic relationship intricately include transferential and countertransferential aspects, which, as formations of the unconscious, get installed in the field and must be unraveled in a retrospective look of the analyst, regarding the nature of his or her own participation and regarding the ways of interaction established up to that moment. In that sense, I believe that these moments constitute true neoformations of the analytic field, \"interactive dynamic nuclei\" that mark the history of analysis and establish \"the shared substratum of interpretation\" (de Le\u00f3n, 1993).\n\n## **Situational and Temporal Perspective of the Metaphoric Processes in the Analytic Field**\n\nPablo, aged 42, married, father of two daughters and one son, who had finished his treatment with me more than 15 years ago, recently returned for consultation. I had included a vignette of this analysis to exemplify my ideas about the characteristics of intense interaction moments between patient and analyst, in which implicit metaphoric processes take place, which allow integrating experiences expressed in different sensory registers (de Le\u00f3n, 1993). Meeting Pablo again demanded reviewing my vision of the dynamics of these clinical moments from a situational perspective, but at the same time, the fact of Pablo having consulted me again allowed me to consider them in a temporal dialectic of effects and retrospective new meanings.\n\nPablo had started his analysis with me at the end of his adolescence, expressing difficulties in his relationship bonds and questions regarding his professional future. After five years of analysis, we decided, by common consent, to end it. Pablo had accomplished many objectives that he had set for himself at the beginning of treatment.\n\nFirst, I did not remember a precise description of Pablo's analysis, and I preferred not to review my own written material about it, so as to be able to see the current situation with a new outlook, somehow \"without memory.\" however, during the days before the interview, one expression came to me, which I remembered was especially meaningful in his analysis. It was the expression \"\u00a1 _A cucha_!\" (a Spanish expression equivalent to \"shoo!\" in English), said to dogs when we want them to get far from us. I remembered that I had referred to it in the vignette narrated in my paper dated 1993, but I did not clearly remember how that word had emerged in the analysis and who had said it.\n\nThe reunion with Pablo impresses me because of the sudden, vivid, and pleasant recovery of the shared experience that seems to have stayed intact over time. Pablo has formed a family and achieved success in his professional life. However, he returned to consult because he is going through a period of great anxiety. His wife has been promoted at her job, which revives in Pablo strong feelings of abandonment and rejection, awakening paranoid ideas. At that point, I re-read my previous vision of the patient.\n\n### _**Twenty Years Ago: A Moment in Analysis**_\n\nAlmost 20 years ago, Pablo appeared to me as\n\n> an adolescent patient who consults after moments of great insecurity in his couple relationships in which he has felt rejected. This insecurity extends to other situations. He defends himself with intellectualizations and taking distance, attempting in that way to achieve better control of his feelings. He has problems handling his aggressiveness, which is usually denied and when it appears, it generates very unpleasant feelings to him. During his childhood he had problems with sphincter control, he presents an untidy aspect and sometimes impresses me as dirty.\n> \n> (de Le\u00f3n, 1993, p. 811)\n\nFrom the material of the analysis, I had selected a moment that occurred in a session immediate to an unexpected interruption of the analysis. When he referred to a sexual relationship he had with a girl that weekend, the patient had used the term _acuchar_ instead of the term _acostarse_ (Spanish for \"go to bed with\"). Following is the quote of my vision of that clinical moment:\n\n> The lapsus linguae _acuchar_ provokes certain commotion to me. When exploring my countertransferential experience I admit that it is true that this patient has raised certain rejection which reason I don't get to clarify completely. His dirty aspect, his demand of proximity, certain behaviour of lack of consideration that I connect with his aggressiveness...\n> \n> However, at this moment his lapsus has had in me the opposite effect... I feel a special type of proximity. I have immediately related his expression _acuchar_ with the exclamation \"\u00a1 _A cucha_!,\" and this one with feeling rejected, taken out of my office.\n> \n> The patient associates with childhood situations in which, having finished individual lessons, he waited for his mother to pick him up, feeling great anguish thinking that his mother would forget about him. At the same time he remembers episodes of enuresis and encopresis at school, in which he felt ashamed and rejected.\n> \n> Then, his waits for his mother, his loneliness and his great anguish get connected in me, the image of the animal and dirt. For the first time I feel that he opens a way to the understanding of my feeling of rejection that gets partly connected to this image of something \"animal,\" dirty, in a corner, and rejected that the patient transmits to me.\n> \n> I only verbalize his feelings in relation to having felt pushed away from his sessions during the interruption of analysis, as if I had told him, \"shoo!\" The patient keeps talking as if nothing had happened, but suddenly he gets quiet for a long time. Finally, when he resumes talking, he says that he can't explain why he has felt a very intense emotion, that he doesn't know how to understand it, and he associates with a poem he has read about creation.\n> \n> At that time, the patient dreams with the image of an animal in a cradle. It was a \"dog-fish,\" half dog (from the waist up) half fish (from the waist down). I recall once again the lapsus linguae of the patient and my associations.\n> \n> (de Le\u00f3n, 1993, p. 812)\n\nAt present, I agree with the characteristics that I had attributed at that clinical moment: the intricacy of the experiences of patient and analyst, the figurative character of them, and the way of multimodal functioning of the analyst's mind.\n\nThe exclamation \"\u00a1 _A cucha_!\" that had emerged in me condensed my tone of rejection and the inhibited gesture of pushing. This expression had unexpectedly revealed to me my own latent posture in the analytic situation. The halt due to the setting of the \"access to motility\" eased my gestures and emotions to regressively express in the image \"of the animal in the corner, and far in his dirt\" that imposed to me in the session.10 This image allowed me to capture an unconscious or preconscious identification of the patient, but also to visualize the scene I myself was involved in.\n\nIt was a moment of intricacy and reciprocal link between my experiences and those of the patient. I had alternatively placed myself in a complementary or concordant way with the patient (Racker, 1957a), with a phenomenon of regressive circularity between both. From the first moment in which I had been left in a place in a complementary way, pushing the patient far from me, I came to place myself concordantly in his place, which enabled me to perceive the quality of his subjective experience and produced the feeling of greater proximity in the session.\n\nThe dynamics of the metaphoric processes that occurred in the analysis show a process that is co-built between analyst and patient. But in this case, the metaphoric condensation is not made between verbal meanings only, but among different levels of the subjective experience expressed in emotions, in images that include primary bodily representations of the bond with the others (such as my gestures in the previous clinical example), and, finally, in verbal expressions. From my perspective, the multimodal functioning and the analyst's mind capacity for reverie make it possible that the analyst, being aware of the answers of the patient, may:\n\n> walk an alternative or simultaneously different registries of expression in himself or in the patient, attempting to give place to still unformulated phenomena. In this way, images, feelings, bodily representations and words can displace or condense in a representation, exchange themselves, re-translate themselves.\n> \n> Regressive understandings make possible that what is expressed in a register reaches its meaning for the patient and for ourselves in the other.\n> \n> (de Le\u00f3n, 1993, p. 819)\n\n### At Present\n\nDuring the early times of Pablo's re-analysis, I find again aspects perceived at that clinical moment but now lived in an amplified and dramatic way. Pablo is afraid that the current situation will cause him to take distance from his family; he feels out of balance and overwhelmed by anguish. His painful feeling of abandonment and rejection is updated. His oedipal conflict reappears re-lived by the current situation. Intellectualizations and obsessive thoughts, uncontrollable at moments, attempt to control his jealousy and paranoid ideas toward his wife. He attempts to control his aggressiveness, which, when it gets to be expressed, does so in an explosive and sadistic way, generating great discomfort and suffering. But what called my attention most was that in certain moments, his jealousy acquired the fixing of the delirious ideas, putting his phantasies and thoughts on a level with reality. In certain moments, he lives the breaking of his couple and his family as the only possibility.\n\nDuring the first months of the re-analysis, I have the impression that I am facing a crack in Pablo's psychism that cannot be reached by my words. The dimension of the \"as if \" is lost, and I feel that it is impossible to establish a metaphoric process that will restore it. Analysis becomes a place of catharsis, emotion processing, and prevention of his self-destructive actions.\n\n* * *\n\nUndoubtedly, this second meeting with Pablo resignified my vision of the clinical moment previously described. I had seen Pablo as an adolescent who reproached his mother her lack of attunement and her exaggerated dedication to his father and siblings during his childhood, which at that time, I thought essentially framed in his oedipal conflicts. Although I had found little intrapsychic permeability in Pablo and great difficulties for him to become conscious of his own aggressive impulses, I had attributed it to his steely obsessive defences. Today, I see that the oedipal conflicts and their tendency to isolate his emotions is reinforced by splitting mechanisms of a more primitive self, which make the integration of different aspects of his psychism difficult.\n\nThe second dream about the \"dog fish\" had made me think then of the castration anguish. Today, his identification with animals shows me difficulties in the integration of his bodily image and his emotions. His movements are rigid and inexpressive at times. Today, I see his bonds little discriminated, which has made his couple relationship difficult and has caused an exaggerated identification with her, which has contributed to the genesis of the current crisis. It has been difficult for him to feel that he is not her wife, and this repeats in his close bonds, where he exaggeratedly puts himself in the others' place, taking care of their problems. His good reflexive capacity is always at the service of the others, living through them and leaving aside his own desires and personal projects. In general, he avoids, in this way, expressing his aggressiveness.\n\nAfter three years of analysis, the storm calms down and pablo recovers his stability in his family life and his working capacity. He becomes gradually conscious of his dissociations, ambivalences, and contradictions, at the same time that his bonds become more discriminate, recovering his joy. However, he has warned me that \"it is better not to touch some things.\"\n\nThis second moment of Pablo's analysis has made me think about the limits of our task. But I have also proved how metaphoric processes established in the analytic field are a privileged way to convey the emotional communication between patient and analyst and intrapsychic modifications in the patient. The clinical situation described in the first analysis of Pablo perhaps did not have the scope that I gave it at that moment, but undoubtedly, it was a meaningful moment that enabled the understanding in the analysis of different aspects of the unconscious problematic of the patient and his integration at a mental and emotional level, something that allowed the analytic bond to sustain through time.\n\n## **Conclusions: Analytic Field and Metaphor**\n\nThe central focus of the dynamic field theorization attempted to illuminate how, beyond the manifest forms of analytic interaction, unconscious interaction patterns are built and mark the dynamism of analysis. These ways of interaction are undoubtedly conditioned by the individual past of the patient and analyst but, at the same time, are specific and new in the present of the bond and context in which each analysis is established.\n\nI think the metaphoric processes and metaphors that emerge in the analysis ease the analytic communication and the emerging of transforming moments of intersubjectivity. As the clinical moments described in this work show, these moments are dynamically co-built in a way that goes beyond the conscious will of the analyst. In that way, the relationship that is established in the analytical dialogue between the words _ensilladura_ (\"saddle\") and _silla dura_ (\"hard chair\") constitutes a field formation in its manifest and latent aspects that will determine the history of this analysis. This phenomenon imposes itself beyond the conceptual frame of the analyst, who apparently attempts not to get actively involved and only to participate, precisely highlighting an expression of the patient's speech.\n\nBut it is necessary to consider the limits of verbal language in our interventions and metaphors. Not only because, as in the case of pablo, rigid defensive mechanisms can make more difficult a more permeable and fluid verbal communication of the patient with us and with himself, but also because the metaphoric processes emerged in the analysis show through language only some of the multiple phenomena (attitudes, tones, etc.) inherent to the analytic communication.\n\nIn fact, different interpretative styles also imply attitudes toward the patient that may go unnoticed at first sight. Ten the explanatory style of the interpretation of the first clinical example may be accompanied by an active attitude, which may be experienced as instrusive by the patient, generating an attitude of submission to the analyst's point of view. On the contrary, the laconic style of the second case may be experienced by the patient as an indicator of a cold and indifferent analyst attitude. Pablo's case made me reflect on possible attitudes of rejection toward him that probably were present before the mentioned moment. These manifest attitudes, also in styles and voice tones, may answer to characteristics of the analyst or patient, but also to unconscious patterns of interaction that get established beyond verbal language, but which may have their meaning in the internal world of the patient. Becoming aware of them may avoid acute enactments, the installation of bastions, or impasse situations.\n\nIn psychoanalysis, interpretative processes of metaphoric character show the double function of the metaphor stated at the beginning of this paper: they transmit implicit meanings and produce unexpected effects in the patient or analyst, or in both, with the corresponding internal restructuration. One or another of these aspects, or both, may predominate along the analytical process. In this way, in the expression \"fire in your head\" used by the analyst, it predominates the intention of the analyst to transmit a meaning connecting the expression of the patient to different aspects of his unconscious subjective experience. In the second example, the patient is the one who, supported by the analyst's intervention, builds the connection between his own expressions _ensilladura_ and _silla dura_ , which allows him to become aware of his masochistic positions. In the case of pablo's analysis, it is an expression of the patient that awakens in me a second meaning and allows me to establish the connection of the lapsus linguae _acuchar_ with the expression \"\u00a1 _A cucha_!\" that produces in both a moment of \"insight.\"\n\nAs we saw before, in Davidson's perspective, the emerging of novel metaphors (not the ones integrated in the conventional language) has the effect of correlating emotions and meanings linked to subjective experiences of the listeners: \"Metaphor makes us see one thing as another by making some literal statement that inspires or prompts the insight\" (Davidson, 1978, p. 47).\n\nUndoubtedly, it calls to our attention the apparent coincidences between these developments and the analytic experience. In effect, the \"insight\" in psychoanalysis is a new and creative experience that produces similar effects to those caused by the listening to a poem or the contemplation of a piece of art, or when\u2014as Davidson states\u2014we feel that one metaphoric expression used in the communication makes us evoke experiences and emotions shared by those who surround us. In the Uruguayan psychoanalytic milieu, T. Bed\u00f3 (1987) stated how the experience of insight in analysis can be shared between patient and analyst in an \"insight \u00e0 deux.\"\n\nThe metaphoric processes that emerge in analysis are the product of a complex dynamism that includes specific moments that have to be considered, as in a dialectic spiral, in relation to different moments of the analytic process: retrospectively\u2014in the new meanings of previous moments\u2014as well as prospectively, in its possible effects. Besides, these processes are guided by a therapeutic preoccupation and, in this sense, the transformation of impulses, identifications, and unconscious defenses that imply emotional and primary bodily experiences that generate suffering to the patient.\n\nThe figurative language of our interpretations evokes not only childhood experiences but also concrete experiences of the present in the life of the patient in his bonds with those who surround him or her. Pichon-Rivi\u00e9re had already referred to the dialectic interrelation between the internal world and the external bonds: \"... All unconscious mental life, I mean the domain of the unconscious fantasy, has to be considered as the interaction between the internal objects (internal group) in permanent interrelation with the objects of the external world\" (1998, p. 42). This same posture is seen in the developments of Bleger about the situational, dramatic, and dialectic perspective (Bernardi, 2009).\n\nPablo's analysis was done in the context of his separation from his family of origin and the search of an independent way. At present, childhood experiences are reformulated regarding his bonds at work and especially the relationship with his wife and his own children. And my current vision is also influenced by my experience, the evolution of analytic thought, and my vital situation.\n\nThe notion of dynamic field formulated within the frame of phenomenology brought up a dialectic relationship between the intersubjective and the intrapsychic, between subjectivity and objectivity. In this vision, the idea of field itself provided two aspects. It supposed a scenery in which we are immersed like actors in an immediate relationship with the other, but also a scenery-field that may be seen from a more distanced and reflective second look. In this sense, moments of intersubjectivity and of certain symmetries that manifest in regressive syntony and in the use of a figurative language get dialectically entangled with moments of intrapsychic elaboration in analyst and patient, or moments of joint elaboration.\n\nThe notions of \"second look\" and \"participant observer\" refer precisely to the possibilities of elaboration by the analyst of the different ways of his or her participation. With the notion of second look, the field theory proposed an attitude of putting off-center our own participation and the ways of established unconscious interaction. But currently, this attitude becomes necessary also with regard to the way in which our theories influence our practice, in a moment in which the development of psychoanalysis is characterized by the plurality of theoretical and technical ideas that condition in a different way our interventions with the patient.\n\nIn effect, the metaphoric processes present in our interpretations, idiosyncratic to each analytic situation, implicitly condense different \"partial theories, models, or schemata\" (sandler, 1983, p. 37) that start processes of integration of the regressive experience of the analysis in the analyst, on a preconscious-conscious level.\n\nAbout the expression _\"\u00a1A cucha!,\"_ in my mind converged, in a blurry and partial way, constellations of ideas belonging to different theoretical frames: implicit ideas about countertransference\u2013transference and the mechanism of projective identification, Freud's ideas about the anal stage, and Kleins ideas about separation anxiety. But also the influence of Lacan's thought on my way of listening to the patients speech and the formulation of open interventions, not saturated of sense. As has been noted (Sandler, 1983),11 these groups of ideas or implicit mini-models (Leuzinger-Bohleber & Fischmann, 2006) do not look for internal coherence nor do they respect the no-contradiction principle. They emerge spontaneously in the analysts mind, searching to adjust to the personal characteristics of each patient. This theoretical\u2013clinical integration that is characteristic of the metaphoric processes of analytic communication seems to give the reason to F. Schkolnik's thesis (1985) that invariants exist beyond differences and Wallerstein's (1990, 2005) about the existence of a common clinical base, \"a common ground,\" over which different theoretical approaches of contemporary psychoanalysis converge, transcending the existing differences among them.\n\nHowever, it is also true that the implicit theoretical\u2013clinical integration in the moments of greatest emotional closeness with our patients opens the space of internal differentiation processes among different alternative hypotheses, which will be available to the \"attention\" and \"floating deliberation\" of the analyst (de Le\u00f3n, 2010). The participation and answers of the patient resignify (H. Faimberg) previous visions and hypotheses of the analyst, opening a space of reformulation, comparison, and validation of her interventions and of critical evaluation of the effects that the participation of the analyst has on different moments of the process. From the second stage of Pablo's analysis on, new hypotheses emerge. But his warning not to touch certain nuclei of his problems: is it part of a defensive bastion that protects him from an unmanageable unbalance, or a bastion of the field that implies me somehow?\n\nI consider it useful to hold the phenomenological and dialectic points of view on which the formulation of the field theory supported in latin America. The phenomenological point of view broadened the possibilities of observation and perception of the analyst, making the considered analytic situation available to the floating attention of the analyst as a whole, following the perspective of Gestalt theory. The dialectic point of view complements the previous one, as it makes us consider as central the reciprocal influence of unconscious character between analyst and patient, the interrelation among different moments of the analytic process in its retrospective and prospective meanings, and, finally, the consideration of the dialectic interrelation among the unconscious aspects and the possibilities of their integration at a preconscious-conscious level (Baranger, 1993a).\n\nIf the field theory emerged within the frame of Kleinian thought, later it showed itself to have a more independent approach, which, conserving some aspects of this one, could critically reformulate them according to the phenomena of the analytic experience. In this sense, the psychoanalytic theories about the unconscious must not be considered with an ontological character but as a partial approximation to the particular characteristics of the field, in the bond with a certain patient and in a certain moment of the analytic process. In the same way, the field perspective considered the dialectic interrelation that happens in the session and the analytic process between the unconscious aspects and the possibilities of their integration at a preconscious-conscious level (Baranger, 1993a). The validity of these points of view has caused the field theory to keep its value as a tool of knowledge and clinical investigation of the analytic practice until today.\n\n## **Notes**\n\n Originally published in _Psychoanalytic_ _Inquiry_ 33(3) (May 2013) with the title \"Field Theory as a Metaphor and Metaphors in the analytic Field and process.\"\n\n Madeleine and Willy Baranger, members of the Asociaci\u00f3n Psicoanal\u00edtica Argentina (Argentinian psychoanalytic association), lived in Uruguay between 1954 and 1965, helping to form the Group of the Uruguayan psychoanalytic association; they were founders of the _Revista Uruguaya de Psicoan\u00e1lisis_ ( _Uruguayan Journal of Psychoanalysis_ ).\n\n For example, the xxi Congress of Fepal in Mexico in 1995: \"Problems of the transference and Countertransference Field.\"\n\n The reflection about the analytic situation appeared in different thinkers of the time, as Enrique Pichon-Rivi\u00e8re, Heinrich Racker, Luisa Alvarez de Toledo, and Jorge Mom, among others, but we owe to M. And W. Baranger the more exhaustive study of the subject.\n\n It is interesting to confirm proximities between this approach and different current experiences in working groups formed by analysts from different regions, who with different methodologies attempt to observe and investigate specific aspects of psychoanalysis based on the study of clinical materials presented by analysts (IPA Berlin Congress and Chicago Congress, FEPALCongress).\n\n \"Te analytic situation should be formulated by an indefinite and neutral personage\u2014in effect of a person confronted by his or her own\u2014but a situation between who remain unavoidably connected and complementary as long as the situation obtains and is involved in a single dynamic process. In this situation neither member of the couple can be understood without the other\" (M. Baranger & W. Baranger, 2008, p. 796).\n\n \"Te true objectivity,\" says Racker, \"is based on a form of inner splitting that trains the analyst to take himself\/herself (their own subjectivity or countertransference) as object of continuous observation and analysis. This position also trains him\/her to be relatively 'objective' towards the analysand\" (Racker, H. [1948\/58] 1957a).\n\n \"La Nature est un temple o\u00f9 de vivants piliers \u2044 Laissent parfois sortir de confuses paroles; \u2044 L'homme y passe \u00e0 travers des for\u00eats de symboles \u2044 Qui l'observent avec des regards familiers. Comme de longs \u00e9chos qui de loin se confondent \u2044 dans une t\u00e9n\u00e9breuse et profonde unit\u00e9, \u2044 Vaste comme la nuit et comme la clart\u00e9, \u2044 Les parfums, les couleurs et les sons se r\u00e9pondent\" (Baudelaire, \"Correspondances\") (L. \u00c1lvarez de Toledo, 1954[1996], p. 299).\n\n This polarity between situation and process is present in the psychoanalytic reflection of different schools, which stress one of these aspects or the other. B. Joseph (1985), for example, from a Kleinian perspective, defines essential aspects of transference understood as total situation. From another theoretical posture, d. Stern (2004) analyzes the characteristics of \"present moments\" of the analytic relationship that show meaningful changes in the relating patterns. The already-mentioned perspective of Haide\u00e9 Faimberg, although it studies specific moments of analysis, also studies its effects in the process development. Thoma and Kachele (1989) referred in their interactive model of the analytic process to \"thematic nodal issues\" or \"interactive foci\" that happen one after the other along the analysis.\n\n Different authors have stated that the analyst's mind operates with similar mechanisms to those described by Freud in relation to the dream work, as shown Ferro and Cevitarese in this n\u00famero. W. Bucci (2001), in her theory of multiple codes, has shown how the interpretative activity allows to integrate the analogic subsymbolic, emotional, and bodily levels with the discrete, symbolic elements of image and word. The image or sequences of those which are characteristic of dreams and the expressions of the analyst or patient appear as intermediate nexus that allow integrating emotional and bodily experiences, several times split in the process of symbolization achieved by the access to the word.\n\n Sandler (1983) differentiated the public, official, or explicit theories, exposed in the scientific exchange with colleagues, from the theories used in the individual clinical practice, which he called private theories or implicit theories. This perspective has given origin to different contributions. Latin American thinkers also marked differences between the way in which theory works in the psychoanalytic session and in the field of scientific discussion with colleagues, such as Pichon-Rivi\u00e8re (1998), Liberman (1970), and Bleger (1969). Bleger was one of the first who, in the R\u00edo de la Plata, talked about implicit theory, noted that the \"theory developed and made explicit does not always coincide with the implicit theory in practice\" (288). He also notes \"the divergencies between psychoanalytic theory and implicit theory [in practice], not completely formulated nor assimilated\u2014this last one\u2014in the theoretical body of psychoanalysis\" (p. 289).\n\n# 16\n\nOTHER FIELDS WITHIN  \nTHE ANALYTIC FIELD1\n\n_Claudio Neri_\n\nThe main point of this chapter is the recognition that the patient doesn't create a field only with the analyst but also with other important people, with his workplace, and with some self-objects. The analyst may perceive how the patient's moods, feelings, and self-esteem change when entering each of these different fields. The analytic field created between the analyst and the patient is an important tool, a sort of Geiger counter, through which the analyst may detect the presence and the activity of these other fields. Isabel's brief case history illustrates a useful approach to deal with the negative effects of a very disturbing and confusing field she established with the company she worked for.\n\nAn original \"field theory\" has been developed in Italy, and many colleagues have contributed to this collective intellectual achievement. I will mention only a few here: Corrao, Ferro, and Gaburri, and in 1994, the Societ\u00e0 Psicoanalitica Italiana dedicated its x Congress to \"Te transformations in the analytical Field.\"\n\nThe field theory that was elaborated by Italian psychoanalysts differs from that of Madeleine and Willy Baranger in many ways. I will briefly mention only three here. First, in Italy the field theory was connected to Bion's alpha function and the idea of transformation of emotions in narration and vice versa (Emotions \u21d4 Narrations). Second, the field was not considered to be a product of exchange of projective identifications between the patient and analyst, and its existence was put into a relationship with the presence and pressure of \"thoughts without thinkers\" that can be taken on board and thought through by both the analyst and the patient. And, finally, the most important rules for the analyst\u2014during the session\u2014are the maintenance of a mental setup that is characterized by \"negative capacity,\" and the practice of \"unsaturated interpretation.\"\n\n## **Psychoanalysis and Group Psychotherapy**\n\nI used field theory in my practice as a group psychotherapist. In 1988, at Didier Anzieu's invitation, I presented a paper on the difference between field theory and transference theory in paris at the historical salp\u00eatri\u00e8re auditorium, the hospital where Freud had followed Charcot's lessons. In my opinion, this conceptual tool is of critical importance in group psychotherapy work.\n\nAfterwards, I tried to use field theory in the traditional psychoanalytic setting. In this case, however, I came up against great difficulty. It was immediately clear for me that not only a group but also the \"analyst\u2013patient couple\" produce and are immersed in a field; however, when I tried to use this theory extensively in psychoanalytical sessions, I was often dealing with the impression that it was not quite the right choice. There certainly were some advantages compared to the use of the relationship and transference concepts. For example, I managed to obtain an overall picture of the situation more easily. I was also more inclined to give a value to everything that in the sessions was non-verbal. However, the dialogue and the contact between the patient and me lost some spontaneity. In the back of my mind, the unpleasant perception that something was not working in the right way kept coming out. Discouraged, I sometimes thought about letting it drop. It could have been as in music: symphonies are for big orchestras, sonatas for two or four musicians.\n\n## **Other Fields That Influence the Patient**\n\nI don't wish to concentrate all the attention on the theme of the difference between the group setting and the psychoanalytic setting. Instead, I would like to speak about the first clinical circumstance when I used \"something similar to field theory\" with a patient and felt that it was something appropriate and effective. It happened when I put an idea I had to the test. What was important to pay attention to was not only the field that was established between the patient and me, but also, and above all, the \"shadow of other fields\" that the patient set up with other people with his self-objects, both positive and negative. The idea of using the field theory in this way came from the sudden appearance of a memory of the life of a comic-strip character, superman.\n\nSuperman was different from other superheroes such as spiderman, Batman, and robin, for one main reason. These latter heroes were normal people who became superheroes when they took on a secondary identity; superman's real identity was that of being someone from another planet. He was born on the planet Krypton and possessed all the abilities and powers of a Krypton inhabitant. When this planet was on the point of exploding, his parents put him into a spaceship and sent him to earth. Ten, after the explosion, some fragments of the planet Krypton struck earth. I will now come to the key point. When superman, the superhero, enters a room or an area where there is also a sliver of Kryptonite, he becomes weak, feels ill, and loses all his powers.\n\nSome of my patients have to face up to a similar catastrophic transformation that occurs not only in the presence of their mothers but also when they perceive something that makes them remember even the most distant existences of their mother. They become confused, afraid, exhausted as if they were under the effects of the powerful rays of the \"kryptonite minds of the mothers.\" Teir faces would become dull, and they would become almost unapproachable for me (and for anyone else) during the time that they found themselves under the influence of the toxic mind-of-the-mother field. Thinking about these patients to myself, I realized that i was using the expression \"field created by the mother's mind.\" Thus, I was using the term and the concept of field to refer to something with which the patient had come into contact, I wasn't using it instead\u2014which usually happens\u2014to indicate something that was between myself and the patient, between the analyst and the patient.\n\n## **Field and Non-Places**\n\nThe successive step in my process of reflecting was to recall other conditions in which a patient was under the influence of a \"field\" that was not produced by an imaginary figure (such as the \"toxic mother\") but by a social situation\u2014for example, a field that corresponded to working in a certain company. The summary of my analytical work with Isabel illustrates this situation and explains which clinical approach I honed to deal with the problem.\n\nI will mention a few facts. Six months after beginning the second part of her analysis, Isabel had begun to speak at length about a strong disturbance she felt regarding anything to do with work. I listened with great interest. For Isabel, her company was not an object that was totally differentiated from her. It was something that she was submerged in and, at the same time, something that pervasively occupied almost her whole life and thoughts.\n\nAt this part of the analysis, I also saw some changes that concerned the \"analytical field.\" I noticed difficulties on both our parts in not being able to perceive personal feelings. It was as if the \"analytic field\" was occupied by a silent and invisible force that was restraining and imprisoning it. Everything was fat and painfully the same, hour after hour, day after day. The heavy atmosphere in Prague after the occupation by soviet tanks that had retreated to the outskirts of the city came to mind.\n\nFor Isabel, what did the company world correspond to? Who were the tanks? her father? her mother? The family? had her life been divided into two by a traumatic break that had left a feeling of emptiness? For the moment, I left these questions in the background. I wanted to concentrate on that which seemed to present a more pressing need, the sharing of Isabel's concrete daily life. So I took the problem of living the company as a very serious problem indeed. I considered it to be a real situation. However, I didn't take it at face value, but rather as something that Isabel didn't really know, even though she did say that she knew about it, and that\u2014in a conventional and factual way\u2014Isabel did know. At the beginning, the difficulties and uneasiness that she felt appeared, both to me and to her, comparable to the experiences, the psychic processes, and the changes that a person who has entered into an organized group has to face (in Isabel's case, the company-group).\n\nIn analysis, speaking about the \"social field\" of the company and its dynamics, little by little, we managed to see the existence of a \"psychological field\" that corresponded to the \"social field\" only in part. This \"psychological field,\" which was characterized by something hazy and uncertain and waves of engulfing and discharging spurts, was fundamentally not suitable for taking on board any autonomous form of intellectual and affective life of an individual. This first knowledge of the nature of the \"psychological-company field\" didn't come about through a representation but through a sharing that occurred because my attentive and interested listening to her long accounts was like accompanying her to her place of work.\n\nAfter a few months, the picture changed once more. Loneliness, disorientation, the lack of a guide, and affective proximity for which Isabel had suffered during her infancy appeared with great force. Isabel didn't have anyone who was really close to her. Above all, she was lacking someone who could have given her some confirmation of being right about her perceptions. Immediately after the emergence of these painful memories and experiences, two positive things happened to her. The first was her discovery of a talent for writing short stories. She read me some during the sessions. The first one she read was about a little girl who comes out of school and sees the mother chatting among the other mothers. Listening to her, I thought that she could finally see herself with her mother. I also thought about some changes I had noticed in the analytical field. It was no longer rigid and immobile. On the contrary, it was possible to see the slight presence of a \"narrative field\" inside it\u2014that is, a place in which the experiences, sensations, and feelings are connected to words, scenes, and a narrating voice.\n\nThe second event related to the fact that Isabel, who had recognized the characteristics of the \"company field,\" was then able to recognize the characteristics of her own feelings and experiences that were connected to the company. Tis, in turn, had freed her from her immobility and impotence. Soon after, Isabel was also able to find a practical solution to her problems at work.\n\n## **Conclusion**\n\nIn presenting the second part of Isabel's analysis, I spoke about three different fields. The first one is the field of the company world; it is very concrete and, simultaneously, a very elusive field. At the beginning, when Isabel was under the influence of this field, she wasn't able to distinguish herself and her moods from the atmosphere and tension that were present in this field. Isabel also felt very unhappy and lonely. In Isabel's company-field, there were no feelings besides persecution and uneasiness. All the other feelings had either been ejected or inhibited. Later on, Isabel compared being in this field to \"being in a concentration camp.\" it is also possible to establish an analogy between Isabel's company-field and a labyrinth\u2014first, because there were no possibilities of reaching a sense of orientation, and second, because the people in this field appear and feel that they are like monsters and that other people are like monsters, like a Minotaur.\n\nThe narrative field is much less concrete and more livable than the company-field. It is a transformation of the company-field. This transformation takes place when the company-field becomes the subject of a repeated, friendly, and lively conversation between the patient and the analyst. The possibility of speaking in analysis besides the one just mentioned, the company-field also has other effects. First of all, the company-field can be seen through not just one position (being immersed in it), but from many vertices, as many as the different narratives. Second, being the issue of a human conversation, the company-field becomes a little bit more humane. Finally, the narrative field is full of images and feelings; some of these feelings may migrate and inhabit the company-field that was previously just a wasteland, a gulag.\n\nThe analytic field is governed by the rules of the analytic setting. Its characteristics are elements such as intimacy, directness, absence of intrusiveness from the analyst, and the continuity of the sessions with predetermined phases of suspension. The analytical field is not only a frame or structure. It is also a powerful detecting apparatus, a Geiger counter. The analyst may perceive the quality of other fields (e.g., the company-field, the mother-mind field, etc.), through either perturbations of the analytic field, or through non-verbal, extra-verbal, ultra-verbal, a communication from the patient such as body posture, facial expressions, unexpected breaks in the narration of a dream. It is as if a dream editor had introduced a cut and then continued with very different characters and feelings. Later on, the patient is able to glimpse the other fields from the secure base of the analytic field. Thus, he can begin talking about these fields, which in this way can be shared with the analyst and become objects of narrations.\n\n## **Note**\n\n1 Originally published in _Psychoanalytic Inquiry_ 33(3) (May 2013) with the title \"Isabel: social Field, psychological Field and narrative Field.\" it was also presented to the panel \"Te Field Theory\" at the IPA Congress (Mexico City, 5 august 2011).\n\n# 17\n\nTHE ANALYTIC RELATIONSHIP  \nIN FIELD THEORY\n\n_Elsa_ _Rappoport de Aisemberg_\n\nI focus my presentation on the patient\u2013analyst relationship within the frame of contemporary psychoanalysis. In order to do so, I take the Freudian origins of transference as a starting point, then move on to the evolution of the concept of counter-transference, and finally reach the essential point: the theory of the analytical field, such as it was described by Willy and Madeleine Baranger, including my own perspective of the subject.\n\nThe unconscious fantasy, common to both the patient and the analyst, the unconscious to unconscious communication, the relationship from the intrapsychic toward intersubjectivity and back, as well as neutrality, are all crucial concepts in the presentation, which ends with a clinical vignette in which my ideas are illustrated.\n\n## **Introduction**\n\nI celebrate that the Mexico Congress has stimulated us to think about the patient\u2013 analyst relationship, as we understand it today in contemporary psychoanalysis. First of all, why speak of a theory of the analytical field and of a contemporary psychoanalysis?\n\nI think that when Freud created our discipline based on the concepts of the unconscious, infantile sexuality, Oedipus, drives, and transference, he focused on the patient's problematic. With the vicissitudes of clinical work, there appeared difficulties that gave rise, among others, to the notion of counter-transference. In 1910 at the Nuremberg Congress, he referred to it as an obstacle to the cure, the analyst's blind spot, the need of the analyst to be under analysis present in the demand to set up the law or order over the young analysts' erotic counter-transference so as to bar their acting out. The formulation of the abstinence law and that of neutrality belong to the same problematic.\n\nAfter forty years of silence on this subject, only interrupted by Ferenczi's contributions, at the end of the 1940s and beginning of the 1950s there were Paula Heimann's conceptualizations in London and Enrique Racker's in Buenos aires introducing another dimension: counter-transference can be an obstacle, but it can also be a tool for the understanding of preverbal, sensorial elements previous to the word.\n\nIn a third stage, we have broader counter-transference or the use of the analyst's mind, which was started in 1961\u20131962 by the works of Willy and Madeleine Baranger on the analytical field. Later, other concepts were added: de M'Uzan's Chimera, Bion's _reverie_ , Winnicott's, Bollas's, Green's contributions, and C\u00e9sar and Sara Botella's statements on regredience, figurability, and the \"work by double\" in the session. We should also add Antonino Ferro's interesting developments with his particular conception of the analytical field.\n\nAs Madeleine Baranger clearly stated in her presentation in Athens in 2010, all this speaks of an evolution in our discipline. Science develops by overcoming crises and inevitable obstacles that must be transformed into new knowledge, as Freud taught us with his works. The new hypotheses we build based on our clinical work must be articulated with Freudian metapsychology to maintain psychoanalytical status.\n\nMoreover, the development and extension of our clinical work concerning the approach to narcissistic and non-neurotic functioning, added to classical psychoneuroses, has led us to an extension of our theories to account for the diversity of psychic functionings; this is what we call contemporary psychoanalysis.\n\n## **The Field Theory**\n\nWilly and Madeleine Baranger, both committed researchers into clinical work, thought their praxis articulating it with ideas from Gestalt psychology, from Merleau-ponty's phenomenology, and from other psychoanalysts such as Racker and Heimann, which led them to formulate in 1961\u20131962 the first model of the analytical field, understood as a product of projective identifications between patient and analyst. In this manner, they generated a hypothesis lying between the clinical work and metapsychology, coherent with their concern, shared by our analytical world, about the gap between clinical work and theory.\n\nIn a later paper, they added the idea of an encounter between two psyches generating a common basic unconscious fantasy, in the manner Bion describes for groups. To do so, they used the concept of unconscious fantasy put forward by Susan Isaacs (1952), another Kleinian author who thinks that fantasies are the primary content of unconscious psychic processes, first experienced as sensations, which later take up the form of plastic images and scenes. They refer primitively to the body and represent the instinctive movements of the libido and of destruction, oriented toward the objects.\n\nIn another theoretical model, in Freudian semantics, its equivalent could be the purposive-idea ( _Zielvorstellung_ ), as Laplanche and Pontalis (1967) point out. We should bear in mind that representation is the ideational component of the drive, while affect refers to quantity.\n\nIn 2004 Madeleine Baranger, after having widened her theoretical references, reformulated the concept of analytical field as a structure created between a patient and an analyst in the analytical situation\u2014a third one, which has both a mythic and a symbolic dimension. That is to say, these repetitions in the analytical field, which have a mythic dimension, can achieve symbolic transformation in the interplay of the analytical situation.\n\nI think that the patient\u2013analyst encounter, which has something of the original encounter with the primary object or other significant objects, is what the patient transfers to the analyst and, in turn, gives rise to the therapist's listening, who brings into play his own counter-transference.\n\nInstead, the symbolic level is the power of the setting, surely asymmetric, and of the interpretation that works as a third one that transforms the emotional experience shared by patient and analyst into what Green calls analytical object and what Ogden calls the analytical third one, thus paving the way for the construction of a representation in the analyst's mind, the origin of his intervention on transference.\n\n## **From the Intrapsychic to Intersubjectivity**\n\nIt is important to highlight that in this model of the theory of the field, to which I fully adhere, there is circulation from the intrapsychic to intersubjectivity and back, whereas in the intersubjective model, to my mind, there is a predominance of interaction rather than an encounter between two subjects with their unconscious, their drives, and their unconscious fantasies, as both Barangers state.\n\nThis leads me to remark on another similar theme, as follows.\n\n## **Unconscious to Unconscious Communication**\n\nAs Freud already wrote in his metaphor of the telephone in 1912, the physician \"must turn his own unconscious like a receptive organ towards the transmitting unconscious of the patient. He must adjust himself to the patient as a telephone receiver is adjusted to the transmitting microphone\" (1912b, _SE_ , 12, pp. 115\u2013116). The field theory and related formulations as well: de M'Uzan's chimera, Bion's _reverie,_ and Botellas' figurability try to account for the communication from unconscious to unconscious, which would give rise to \"perceived\" experiences without being aware of it, which would function as the day's residues that stimulate the use of the analyst's mind and that of the analysand. Thus I think the corporal perception of the relationship with the object is the origin of the unconscious to unconscious communication, which certainly must be transformed by the analyst. Who in these cases works as an \"auxiliary,\" lending her or his mental capacity as M. De M'Uzan pointed out in 1976, since the patient is not yet able to turn it into words or representations. In addition, this helps us to understand figurability or the analyst's dreams aroused by the patient's clinical material as a complementary remembrance activity in the analytical field.\n\n## **On Neutrality**\n\nI believe that we should not give up the aspiration for asepsis and neutrality even though we know it is impossible to reach. It is one of our many paradoxes, as Willy\n\nBaranger pointed out in 1957 in his work on \"Interpretation and ideology,\" since the analyst as a person and his or her presence inevitably act upon the patient, giving rise to diverse transferences, among others, idealized transference, which has to be deconstructed at one point during the analytical process to attain a good outcome. However, in the beginning, such transference favors the installation of the treatment, especially when there is a predominance of non-neurotic functioning.\n\nI believe that we as analysts are involved in our task all the time. To achieve our work\u2014aware of the asymmetry in the setting\u2014we have to let ourselves be partly affectively and sensorially involved in the patient's unconscious messages, besides the verbal listening. We must admit we are not entomologists, but it is also true that we have to understand, self-analyze, and resolve those experiences belonging to the transference-countertransference field and then decide whether to include them in our interpretative or constructive approach. This view is accepted by some colleagues and questioned by others, depending on their theoretical framework as well as their scientific or personal ideology.\n\nThis affective involvement has advantages and problems. One advantage is that it helps to understand the patient, true within the limits of our own insight. The problems lie in the blind spots shared by patient and analyst, what the Barangers call bastions, which demand a second gaze, either self-analysis or supervision. That is to say, in the transference-countertransference field that inevitably is created between patient and analyst, we oscillate between empathy and the need of a second gaze.\n\n## **Mar\u00eda**\n\nI shall illustrate my ideas with a clinical vignette.\n\nIt deals with Mar\u00eda, a patient who had analysis on the couch four times a week during six years. When she first came to see me, she was a young woman, 35 years old, very pretty and elegant, who produced a great aesthetic impact. She was married and had two children and a high income. She was a psychologist but not happy with her profession; she wanted to become a writer. She had tried to start writing but had difficulties.\n\nShe needed me to help her to overcome the inhibitions that prevented her from fulfilling her wish; in addition, she brought a passionate story. The object of her love was a close friend of the couple, also married and with children, who was close affectively and also geographically. On the other hand, or \"on the same hand,\" her husband was a very jealous man, a little paranoid, who for rational reasons kept a gun in their house.\n\nMar\u00eda let me know about her intense and urgent sexual desire for this friend as well as his desire for her and, at the same time, the image of a husband who noticed that something was going on and voiced it through scenes of violent jealousy or falling ill.\n\nI had the intuition that a situation out of Greek tragedy might burst out because Mar\u00eda was ready to break up her marriage, her friendship with her friend's wife, the friendship between their children, and her financially comfortable position by defying a jealous husband with a gun. On a counter-transference level I was very worried; I had to put aside\u2014the analysis of counter-transference and ideologies aims at that\u2014my bourgeois ideology. I told myself: this married woman, with children, with an attractive and well-of husband is ready to sweep all this away in order to fulfill her passion! I had to elaborate all this to maintain certain analytical neutrality.\n\nIf I respected the rhythm set by her desire and her passion, we were approaching an atmosphere of Greek tragedy. She described with anxiety scenes in which she and her friend exhibited their erotic desire before the husband and how he reacted with violence to this provocation. If I stopped her, leading her to reflection, Mar\u00eda had serious psychosomatic episodes. She had an accident with the car and also an infectious clinical picture lasting several months. Death anguish was floating in the air. Either she would destroy herself or she would be destroyed by her jealous husband.\n\nLike Mar\u00eda, I had to break with my own values, my ideas of a bourgeois woman, to accompany her in her growth so that she might find the way to realize her forbidden erotic desire without having to exhibit them before her husband, seeking punishment. She was able to do so; she succeeded in separating from her husband on friendly terms, taking care of the relationship with the children. She began to work to earn her living in something connected with writing and creation, and at the same time, she began to write novels.\n\nDuring her analytical process, we went through constructions and histories about a very poor childhood when Mar\u00eda used to share the bedroom with her brother, with incestuous, dangerous plays that were acted in the present passionate story. We also examined her guilt because of her present comfortable life in contrast with the poverty of her parents' home and also the fact that she was a survivor of a group of friends who had died during the years of state terrorism in Argentina.\n\nDeath runs through Mar\u00eda's history, and she put my psychoanalyst's ethical attitude to a test\u2014in the end with a good outcome for the shared task. I think that Oedipal conflicts in their dimensions of erotic and destructive desires and of prohibition and guilty feelings were dramatized in the analytical field constructed between the patient I call Mar\u00eda and myself. The elaboration of such conflict, where I was able to rescue my own feelings and ideas to understand the patient's truth, contributed to constructing a new way out of her Oedipal drama.\n\n## **In Conclusion**\n\nNowadays, we deal not only with what the patient repeats in the transference dimension, the repressed unconscious derivates, but also with what is dramatized in the patient\u2013analyst relationship, and this enables us to create something new that has no meaning yet, the expressions of the proper or genuine unconscious.\n\n## **Note**\n\n Originally published in _Psychoanalytic Inquiry_ 33(3) (May 2013) with the title \"Te Theory of the analytical Field.\"\n\n# BIBLIOGRAPHY\n\nAeschylus (1955). _Aeschyli septem quae supersunt tragoediae. R_ ecensuit Gilbertus Murray. Oxford, UK: Oxford University Press.\n\nAhumada, J. L. (1994). Interpretation and creationism. _International Journal of Psychoanalysis_ 75: 695\u2013707.\n\nAisemberg, E. R. (2008). 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Metaphor as conflict, conflict as metaphor. _Psychoanalytic Inquiry_ 31: 107\u2013125.\n\nYoung-Breuhl, E. & Bethelard, F. (1999). The hidden history of the ego instincts. _Psychoanalytic Review_ 86 (6): 823\u2013851.\n\nZimmer, R. (2010). _Psychoanalytic Quarterly_ 79 (4): 1151\u20131165.\n\n# INDEX\n\nabandonment , ,\n\nAberastury, a.\n\nabstraction , , ,\n\naction language \u2013\n\nAeschylos \u2013\n\naesthetics ,\n\nAffect \u2013; -space links \u2013\n\n_Agamemnon_\n\nagency ,\n\naggressiveness , , \u2013\n\nAhlvers, W.J.\n\nairlines \u2013\n\nalpha function , , \u2013,\n\nAlvarez de Toledo, l. , , \u2013\n\nambiguity , , , ,\n\n_Analects_ \u2013\n\nanalogy \u2013,\n\nanalytic field \u2013, \u2013; metaphor in , \u2013, \u2013, \u2013; other fields within , , ; spiral process \u2013, , , , ; \"talking cure\" , , , , \u2013 _see also_ fields\n\nanalytic situation \u2013, \u2013, \u2013, , , \u2013, \u2013, \u2013\n\n_The Analytic Situation as a Dynamic Field_ , , , \u2013\n\nanimism , ,\n\nanorexia\n\nanxiety \u2013, , ,\n\nAnzieu, D.\n\naphasia\n\nAragno, a. , ,\n\nArgentina , \u2013, , ,\n\nargentine psychoanalytic association \u2013, ,\n\nAristotle , , , , , , , , ,\n\nArlow, J. , , ,\n\nasymmetry , , , , \u2013, \u2013,\n\nAtemporality ,\n\nAugustine \u2013,\n\nAaulagnier, p.\n\nauthority figures \u2013,\n\nbabies  _see also_ infancy\n\nbalance\n\nBalint, M.\n\nBarangers xviii\u2013xix, \u2013, \u2013, , , , \u2013, \u2013, \u2013, , \u2013, \u2013, \u2013, , \u2013, \u2013, , \u2013, , \u2013\n\nBarnett, A.\n\nbastion , , , , , , ,\n\nBaudelaire\n\nBeardsley, M.C.\n\nBecker-Matero, N. , \u2013\n\nBed\u00f3, T.\n\nBerlin, I.\n\nBessie, A. ,\n\nbeta-elements \u2013, \u2013\n\nBeuchot, M.\n\nbi-logic , \u2013, ,\n\nbi-personal field \u2013, , , ,\n\nBion, W. \u2013, , , , \u2013, \u2013, , , \u2013, \u2013, \u2013, \u2013, , \u2013\n\nBlack, M.\n\nBlanco, M.\n\nBleger, J. \u2013, , ,\n\nbody , \u2013, \u2013, , , ;-language\n\nbonds , \u2013, ,\n\nBonner, S.\n\nBorbely, A. , , , \u2013, \u2013, ,\n\nBornstein, R.F. , \u2013\n\nBoston ,\n\nBotellas , , \u2013, \u2013\n\nBowers, K.S.\n\nbrain \u2013, , ,\n\nBrentano, F. \u2013\n\nBreuer, J.\n\nbridge ,\n\nBritain ,\n\nBruner, J.\n\nBucci, W.\n\nBuenos aires\n\nBusch, F.\n\nC\u00e1rcamo, C.\n\ncaregivers , , ,\n\nCassorla, R.\n\ncastration\n\ncatachresis ,\n\ncatastrophe ,\n\nCatejan, T.\n\ncausality , ,\n\nCaven, A.J.\n\nchange \u2013\n\nchaos theory\n\nchildren , \u2013, \u2013, ,\n\nchimera \u2013\n\nChina , , , \u2013\n\nchoice \u2013,\n\nChristianity\n\nCivitarese, G. \u2013, \u2013\n\n_Civitas Dei_\n\nclassical perspective \u2013,\n\ncode \u2013; non-symbolic \u2013\n\ncognitive sciences \u2013, , ,\n\ncognitive-linguistic view \u2013,\n\ncoherence ,\n\ncollusion \u2013, ; psychosomatic\n\ncommunication , , \u2013, \u2013, ,\n\ncommunity \u2013,\n\ncompany-field \u2013\n\ncomplementarity , , , , , , ,\n\ncomplexity theory \u2013\n\nconative\n\nconceptualization \u2013\n\ncondensation , , \u2013,  _conditio humana_  _Confessiones_\n\nconflict \u2013, \u2013, \u2013, \u2013,\n\nConfucius \u2013, \u2013\n\nconnotation ,\n\nconstructivism , \u2013, , \u2013\n\ncontact , \u2013\n\ncontainer \u2013, \u2013, , ,\n\ncontext , \u2013, \u2013,\n\ncontiguity \u2013\n\ncontradiction \u2013, , \u2013,\n\ncopper \u2013\n\nCorel, a. , \u2013\n\nCorrao, F. ,\n\ncountertransference , , , , , \u2013, \u2013, , \u2013\n\nCrawford, L.E.\n\ncreativity , ,\n\ncritical theory\n\ncurrency of the mind , , , , ,\n\ndanger\n\nDanto, A.\n\nDavidson, D. ,\n\ndefense , , \u2013, \u2013, \u2013, , , ,\n\nderivatives \u2013,\n\nDerrida, J.\n\nDescartes, R.\n\ndesire , \u2013, \u2013\n\ndevelopmental studies\n\ndevil  _Diagnostic and Statistical Manual of Mental_ _Disorders_\n\ndialectics , , , , \u2013, \u2013\n\ndialogue , , , ,\n\ndichotomies \u2013\n\ndickens, C.\n\ndifference , \u2013, ,\n\nDionysos\n\n_diphrontis_\n\ndisavowal \u2013\n\ndisplacement , ,\n\ndissociation \u2013, \u2013\n\ndistortions \u2013\n\ndogs , , \u2013\n\nDonne, J.\n\nDonnet, J.-L. \u2013\n\ndoubt \u2013\n\nDouglas, M.\n\ndramatic metaphor\n\ndream , , , \u2013, \u2013, , \u2013,\n\n130\u2013, \u2013, , ; -thoughts ;\n\nmembrane\n\ndrives , , , , ,\n\ndualism \u2013,\n\nDujovne, I.\n\ndyad ,\n\ndynamic field \u2013, \u2013\n\neagle, M.\n\neast ,\n\nEco, U. ,\n\neconomic viewpoint \u2013\n\nEdelman, G.\n\nEdelson, J.T.\n\nego , , \u2013, , , \u2013, ,\n\n_The Ego and the Id_\n\nego psychology , , \u2013\n\nEinstein, A.\n\nEitherOr ,\n\nEkstein, R. \u2013\n\nelbow, p.\n\nembodiment , , ;\n\nembodied simulation \u2013\n\nemergence\n\nEmotional Stroop Task (EST) \u2013\n\nemotions , , \u2013\n\nempathy\n\nempiricism\n\nenergy ,\n\nenigmatization , \u2013\n\n_ensilladura_ , \u2013\n\nentelechy\n\nequilibrium\n\nequivalence , ,\n\nequivocality\n\nEros\n\nErreich, A.\n\netymology\n\nEucharist\n\nEuripides\n\nEvil Inclination \u2013\n\nexchanges ,\n\nexperience \u2013; immediate\/interpreted\n\n12\u2013; private ; role of fantasy \u2013;\n\nunformulated\n\nfactory analogy\n\nFaimberg, H. \u2013, \u2013, ,\n\nFairbairn, W.R.D.\n\n_fan yan_\n\nfantasy \u2013, , \u2013, , , ; analytic relationship \u2013; field concepts \u2013; foundational concepts \u2013, \u2013; metaphoric processes \u2013; process \u2013 , ; spiral process \u2013, ; \"talking cure\" \u2013, , , \u2013, ,\n\nFascism\n\nfathers , \u2013, \u2013, \u2013,\n\nFieldman, J. \u2013\n\nfeminine\n\nFerenczi, S. , ,\n\nFern\u00e1ndez, A.\n\nFerrari Hardoy, G.\n\nFerro, A. \u2013, , \u2013,\n\nfields \u2013, , \u2013; Faimberg field \u2013; general psychoanalytic field , , \u2013 ; interpersonal field ; intersubjective field , , ; psychoanalytic field , ; relational field , \u2013, ,  _see also_ analytic field\n\nfigurability , \u2013, \u2013\n\nfiltering , \u2013\n\nFingarette, H. \u2013\n\nforce\n\nFoulkes, S.H. ,\n\nfoxes \u2013\n\nfragmentation \u2013\n\nfree association , , , \u2013\n\nfree hovering attention\n\nFrenkel-Brunswik, E.\n\nFreud, S. , \u2013, , \u2013, , \u2013, , , , \u2013, \u2013, , \u2013, \u2013, , \u2013, , , , , \u2013, \u2013, \u2013, , , \u2013, \u2013, \u2013, \u2013, , , ,\n\nFriedman, ,\n\nfurniture\n\nGaburri, E.\n\nGallese, V. \u2013,\n\nGargiulo, G.J.\n\nGarma, A.\n\nGazzaniga, M.S. ,\n\nGedo, J.\n\nGeneva\n\nGestalt , , \u2013, \u2013, \u2013,\n\nGibbs, T.C. \u2013\n\nGill, M.\n\nGod ,\n\nGods\n\nGoethe, J.W. von\n\ngold\n\nGoldstein, K. ,\n\nGreeks , \u2013, , \u2013, ,\n\nGreen, a. , , ,\n\nGreenberg, J. \u2013\n\nGrinberg, L.\n\nGrossman, W.I.\n\ngroup , , , \u2013\n\nguilt , ,\n\nhallucination , \u2013,\n\nhamlet\n\nharmony ,\n\nharries, K.\n\nhealth \u2013,\n\nhedgehogs \u2013\n\nHegel, G.W.F. , ,\n\nHeidegger, M. \u2013\n\nHeimann, P. \u2013,\n\nHelmholtz, H. von\n\nHeraklitus\n\nhermeneutics , , \u2013\n\nHobbes, T.\n\nholism \u2013, \u2013, ,\n\nHolt, R.\n\nHome, H.J.\n\nhomer\n\nHook, S.\n\nHospicio de las Mercedes\n\nhuman nature\n\nhumanities ,\n\n_huo_\n\nHusserl, E. , ,\n\nhysteria , \u2013\n\niconic signs \u2013\n\nid \u2013, , \u2013\n\nidentity\n\nidiosyncratic \u2013, \u2013; peak\n\nIliad\n\nimages \u2013, \u2013, , ,\n\nimagination ,\n\n_Imagination and the Meaningful Brain_ ,\n\nimmaturity\n\ninclusiveness ,\n\nindexical items \u2013\n\nindividualism\n\ninfancy , , , \u2013, , , \u2013,\n\n146\u2013,\n\ninsight , , \u2013\n\ninstincts \u2013, \u2013\n\nintentionality ,\n\ninteraction , \u2013, \u2013\n\ninterdisciplinarity ,\n\ninternalizing \u2013\n\ninterpretation ; fields \u2013, \u2013, ,\n\n145\u2013, , , \u2013; metaphor ,\n\n, \u2013, , \u2013, ; process \u2013,\n\n,  _Interpretation of Dreams_ ,\n\nintersubjectivity \u2013, \u2013, \u2013, , \u2013, , ,\n\nintrapsychic , \u2013, \u2013, , ,\n\nIsaacs, S. \u2013, , , ,\n\nItaly , ,\n\nJackendoff, R.\n\nJakobson, R. \u2013,\n\nJaspers, K.\n\nJohnson, M. , , , \u2013, \u2013, , , , , , , \u2013,\n\nKardiner, a.\n\nKatz, S.M. xviii, \u2013, , , \u2013,\n\nKleinians \u2013, , , , , , , , , , , , , , , \u2013, \u2013, , , \u2013, ,\n\nknowledge , ,\n\nKohut, H. \u2013, ,\n\nKoj\u00e8ve, A. ,\n\nKolata, G.\n\nK\u00f6vecses, Z. \u2013\n\nKris, A.\n\nKryptonite\n\nKubie,L. , , \u2013,\n\nKuhn, T. ,\n\nKung Tse _see_ Confucius\n\nLacan, J. , , , , , , , \u2013,\n\nLakoff, G. , , , \u2013, \u2013, , , , , , , \u2013,\n\nLampl de Groot, J.\n\nLanger, M. , \u2013\n\nLangs, R.\n\nLanguage , \u2013, , , , ; acquisition , ; barrier ; clinical data , ; dualist bias ; shared ; \"talking cure\" ,\n\nLao Tzu , , \u2013\n\nLaplanche, J.\n\nlatin\n\nLatin America , ,\n\nLegge, J.\n\nL\u00e9on de Bernardi, B. , \u2013\n\nL\u00e9vi-Strauss, C.\n\nLevin, F.\n\nLewin, K. , , \u2013,\n\nLiberman, D. \u2013\n\nliberty\n\nlinearity\n\nlinking , \u2013, ,\n\nlistening to listening\n\nliving words\n\nLlinas, R.R.\n\nlocal \u2013, \u2013\n\nLocke, J.\n\nLoewald, H ,\n\nlogic , \u2013, ; of emotion ; symmetric\/asymmetric\n\nlubrication\n\n_Lun Y\u00fc_ \u2013\n\nlust\n\nmagic\n\nMahler, M.S.\n\nMann, T.\n\nmappings \u2013, ,\n\nMarx, K.\n\nMaskit, B.\n\nmasochism \u2013\n\nmaterialism\n\nmathematics , \u2013,\n\nMatte-Blanco, I. \u2013\n\nmeaning \u2013, , \u2013, , , \u2013, , ; shared ; spiral process \u2013,\n\nmeasure \u2013\n\nmeasurement \u2013\n\nmechanism\n\nmedicine ,\n\nMeier, B.P. \u2013\n\nMeissner, W.W. \u2013, \u2013\n\nMelshon, I.\n\nMeltzer, D.\n\nmemory , \u2013, , ,\n\nmentation , ,\n\nmentors \u2013\n\nMerleau-Ponty, M. , \u2013, , \u2013, \u2013,\n\nmessages \u2013\n\nmetaphor: current understandings \u2013; frozen ; as rhetorical figure \u2013; working within \u2013\n\nmetaphoric processes \u2013, , , , ,\n\n_Metaphors We Live By_ ,\n\nmetapsychology , , \u2013, , , ,\n\n, \u2013\n\nmetatheory \u2013\n\nmetonymy , , , \u2013, \u2013, \u2013, \u2013, , , \u2013, ,\n\nMilgram, S.\n\nmilk \u2013\n\nmind , \u2013, , \u2013,\n\nMinotaur\n\nmirror \u2013\n\nmirror neurons \u2013,\n\nMitchell, S. \u2013\n\nModell, A. , , , \u2013, \u2013, , \u2013, ,\n\nMom, J. ,\n\nMomigliano, L.N.\n\nmonism \u2013,\n\nmonsters\n\nMontevideo ,\n\nmorality \u2013\n\nmothers , , \u2013, , , \u2013, \u2013, , \u2013, \u2013\n\nmotivation ,\n\nmutuality\n\nM'Uzan, M. de \u2013\n\n_nachtr\u00e4glichkeit_ , , , ,\n\nnarayanam, S. \u2013\n\nnarcissism , ,\n\nnarrative , \u2013, , \u2013, \u2013; derivatives , \u2013,\n\nNazis \u2013\n\nnegative affect \u2013,\n\nnegative metonymy\n\nneigborhood \u2013\n\nNeri, C. , \u2013\n\nneural theory of language\n\nneuropsychology\n\nneuroscience , , , \u2013, ,\n\nneurosis \u2013, , \u2013\n\nneutrality \u2013\n\nNietzsche, F.\n\nnomothetics \u2013\n\nnonlinearity\n\nnovelty\n\n_Object Love and Reality_\n\nobject relationships , \u2013,\n\n_Odyssey_\n\noedipal issues , \u2013, , , , ,\n\nOgden, T. , \u2013, , \u2013, , , ,\n\nOlympus ,\n\noneiric , ,\n\nonomatopoeia\n\nontology \u2013, ,\n\noperative group ,\n\norganism\n\nO'Shaughnessy, E.\n\nOzick, C.\n\nparadox , , \u2013,\n\npare, d.\n\nPauli, W.\n\nPaulucci, O.\n\nPeirce, C.S.\n\nPennebaker, J.W.\n\nperception , , \u2013\n\nPeterfreund, E.\n\n_Phaidros_\n\nphantasy _see_ fantasy\n\nphenomenology , , , , ,\n\n_phronesis_\n\nphysics , , , , ,\n\nPichon-Rivi\u00e8re, E. , \u2013, , , \u2013, \u2013, \u2013,\n\npictograms ,\n\nPlato , \u2013\n\npluralism \u2013, ,\n\npoetics , , , , \u2013, ,\n\npolarity \u2013, \u2013\n\nPontalis, J.-B.\n\npositive affect \u2013\n\npositivism ,\n\nPosner, R.\n\npostmodernism , \u2013\n\npreverbal ,\n\nprimary process , \u2013, , , , \u2013\n\nprivate experience\n\nprocess , ,\n\nproportionality \u2013,\n\nProteus defense\n\nproto-mental system \u2013, \u2013\n\nprototypes\n\nProust, M. ,\n\npsychism , , \u2013,\n\n_Psychoanalytic Inquiry_ , , ,\n\npsychodynamics \u2013, , , \u2013, \u2013, \u2013, ,\n\nPumphandle, O.\n\nquantum mechanics ,\n\nquestionnaires\n\nRacker, H. , \u2013, , , , ,\n\nRappoport de Aisemberg, E. , \u2013\n\nRascovsky, A.\n\nrationality , \u2013\n\nreality , , \u2013, \u2013, , ,\n\nreciprocity\n\nreductionism \u2013,\n\nregression \u2013\n\nreifcation , ,\n\nReik, T.\n\nrelational theory , , \u2013, , , ,\n\nrelatively real \u2013\n\nrelativism\n\nrelativity\n\nreligion\n\nrepetition \u2013\n\nrepresentation ,\n\nrepression , \u2013, \u2013,\n\nresponsibility \u2013\n\nreverie \u2013, , , \u2013, , \u2013, ,\n\n, , \u2013; negative \u2013\n\n_Revista Argentina de Psicoan\u00e1lisis_\n\n_Revista de Psicoan\u00e1lisis_\n\n_Revista Uruguaya de Psicoan\u00e1lisis_ , , ,\n\n_Revue Fran\u00e7aise_\n\nrhetoric\n\nRicoeur, P. ,\n\nR\u00edo de la Plata , , \u2013\n\nRizzuto, A.-M. , \u2013\n\nRobinson, M.D. \u2013\n\nRodrigu\u00e9, E.\n\nRolla, E.\n\nRomeo \u2013\n\nRorschach test\n\nRorty, R.\n\nRousseau, J.-J. ,\n\nSandler, J. , \u2013\n\nSaussure, F. de , , ,\n\nscene , \u2013; other ,\n\nSchafer, R. , \u2013, , ,\n\nSchif, P.\n\nschizophrenia \u2013,\n\nSchkolnik, F.\n\nSchlick, M.\n\nSchool of Dynamic Psychiatry \u2013\n\nSchools of thought \u2013, \u2013, , \u2013\n\nscience , , \u2013, ; natural \u2013, , ; as systematic use of metaphor  _see also_ cognitive science\n\nsecond look , , \u2013, , ,\n\nsecondary process , , , \u2013\n\nSeitz, J. ,\n\nself , ; -awareness ; -objects \u2013; experience \u2013; object matrices ,\n\nsemiotics ,\n\nsensation \u2013\n\nsensuality\n\nseparation\n\nsexuality , , \u2013, ,\n\nShakespeare, W. ,\n\nshame\n\nSharpe, E.F.\n\nShope, R.K.  _si_\n\nsigns , \u2013\n\nsimilarity , \u2013, \u2013, , , ,\n\nsimile\n\nsinew \u2013\n\nsleep\n\nSnow, C.E.\n\nSolms, M.\n\nsoul \u2013\n\nsource , ,\n\nspace child \u2013\n\nSpain\n\nspence, d.\n\nspezzano, C.\n\nsphinx \u2013\n\nspiral process , , \u2013, , ,\n\nsplitting \u2013\n\nspoken word , \u2013, \u2013, \u2013\n\nstate\n\nsterba, R.\n\nstern, d. , , , , \u2013, ,\n\nstyle ,\n\nsubjectivity \u2013, , , ; and metaphor \u2013, \u2013; spiral process , ;\" talking cure\" , \u2013,\n\nsubliminal psychodynamic activation\n\nsullivan, H.S. , , , ,\n\nsuperego , , \u2013, \u2013\n\nsuperman\n\n_Symbiosis and Ambiguity_\n\nsymbol , \u2013, , \u2013, ; symbolic codes ; symbolic order\n\n_symbolon_\n\n_Symposium_\n\nsynesthesia\n\nsynthesis \u2013\n\n_Talmud_ \u2013\n\n_Tao The King_ \u2013, \u2013\n\ntaoism , \u2013, \u2013\n\ntaragano, F.\n\ntarget , \u2013, , ,\n\ntemporality , \u2013, \u2013, \u2013, \u2013, , \u2013\n\ntension , , ,\n\ntexts\n\nTebes\n\nthing-presentations\n\nthirds \u2013, , , , \u2013,\n\ntime , \u2013, ; temporal metaphors \u2013\n\ntitans\n\ntorah\n\n_Totem and Taboo_\n\ntranscendence \u2013,\n\ntransference \u2013, , , \u2013, \u2013, ; in field theory , , , \u2013, \u2013; metaphor\/metonymy \u2013, , \u2013,\n\ntransformation \u2013, , ,\n\ntransitional object\n\ntranslation , , , ,\n\ntrauma \u2013, , \u2013, \u2013, , \u2013, , ,\n\ntropes \u2013\n\ntruth ,\n\nTubert-oklander, J. , \u2013\n\numbrella xviii, \u2013, \u2013, , \u2013\n\nunconscious \u2013, \u2013, , , ; analytic relationship \u2013; field concepts , , , ; meaning \u2013; nondynamic , , \u2013, ; process \u2013, ; \"talking cure\" \u2013\n\nunivocality \u2013\n\nunobservables , \u2013\n\nuprightness\n\nUruguay , , , \u2013,\n\n_Uruguayan Review of Psychoanalysis_ see _Revista Uruguaya de Psicoan\u00e1lisis_\n\nUs ,\n\nutterances \u2013\n\nvalences , \u2013\n\nverbal signs\n\nverbal-opposition theory\n\nVienna , ,\n\nvirtual reality\n\nvital space\n\nvoice \u2013\n\nvoid , ,\n\nWachtel, P.L.\n\nwaking , \u2013; dream thought , , \u2013\n\nWaley, a. \u2013\n\nWallerstein, R. , \u2013, ,\n\nWest , , , , \u2013,\n\nWhite, R. , , \u2013\n\nwill \u2013\n\nWinnicott, D.W. , \u2013, ,\n\nWittgenstein, l. ,\n\nwords , \u2013, \u2013, \u2013, \u2013\n\nWright, d.\n\nWurmser, L. xix, , , \u2013, \u2013, , , ,\n\n_xiang_\n\n_xin_\n\nzeus\n\n_zheng_ \u2013\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":" \n#\n\nDAVE EGGERS  \nZEITOUN\n\nDave Eggers is the author of six previous books, including _What Is the What_ , a finalist for the 2006 National Book Critics Circle Award and winner of France's Prix Medici. That book, about Valentino Achak Deng, a survivor of the civil war in southern Sudan, gave birth to the Valentino Achak Deng Foundation, run by Mr. Deng and dedicated to building secondary schools in southern Sudan. Eggers is the founder and editor of McSweeney's, an independent publishing house based in San Francisco that produces books, an eponymous quarterly journal, a monthly magazine _(The Believer)_ , and _Wholphin_ , a quarterly DVD of short films and documentaries. In 2002, with N\u00ednive Calegari he cofounded 826 Valencia, a nonprofit writing and tutoring center for youth in the Mission District of San Francisco. Local communities have since opened sister 826 centers in Chicago, Los Angeles, Brooklyn, Ann Arbor, Seattle, Boston, and Washington, D.C. In 2004, Eggers taught at the University of California\u2013Berkeley Graduate School of Journalism, and there, with Dr. Lola Vollen, he cofounded Voice of Witness, a series of books using oral history to illuminate human rights crises around the world. A native of Chicago, Eggers graduated from the University of Illinois with a degree in journalism. He now lives in the San Francisco Bay Area with his wife and two children.\n\nwww.zeitounfoundation.org  \nwww.voiceofwitness.org  \nwww.valentinoachakdeng.org  \nwww.826national.org  \nwww.mcsweeneys.net\n\n#\n\nALSO BY DAVE EGGERS\n\nMemoir\n\n_A Heartbreaking Work of Staggering Genius_\n\nFiction\n\n_You Shall Know Our Velocity!  \nHow We Are Hungry  \nHow the Water Feels to the Fishes  \nWhat Is the What  \nThe Wild Things_\n\nNonfiction\n\n_Teachers Have It Easy: The Big Sacrifices and Small Salaries of America's Teachers_ (with N\u00ednive Calegari and Daniel Moulthrop)\n\nAs Editor\n\n_The Best American Nonrequired Reading_\n\n_Surviving Justice: America's Wrongfully Convicted and Exonerated_ (with Lola Vollen)\n\n#\n\nAll author proceeds from this book go to the Zeitoun Foundation, dedicated to rebuilding New Orleans and fostering interfaith understanding.\n\nwww.zeitounfoundation.org\n_For Abdulrahman, Kathy, Zachary, Nademah,  \nAisha, Safiya, and Ahmad in New Orleans_\n\n_For Ahmad, Antonia, Lutfi, and Laila in M\u00e1laga_\n\n_For Kousay, Nada, Mahmoud, Zakiya, Luay, Eman, Fahzia,  \nFatimah, Aisha, Munah, Nasibah,  \nand all the Zeitouns of Jableh, Lattakia,  \nand Arwad Island_\n\n_For the people of New Orleans_\n\n# Contents\n\nAbout the Author\n\nOther Books by this Author\n\nTitle Page\n\nDedication\n\nNotes About this Book\n\nPart I\n\nChapter 1 - Friday August 26, 2005\n\nChapter 2 - Saturday August 27\n\nChapter 3 - Sunday August 28\n\nChapter 4 - Monday August 29\n\nChapter 5 - Tuesday August 30\n\nPart II\n\nChapter 6 - Tuesday August 30\n\nChapter 7 - Wednesday August 31\n\nChapter 8 - Thursday September 1\n\nChapter 9 - Friday September 2\n\nChapter 10 - Saturday September 3\n\nChapter 11 - Sunday September 4\n\nChapter 12 - Monday September 5\n\nChapter 13 - Tuesday September 6\n\nPart III\n\nChapter 14 - Wednesday September 7\n\nChapter 15 - Thursday September 8\n\nChapter 16 - Friday September 9\n\nChapter 17 - Saturday September 10\n\nChapter 18 - Sunday September 11\n\nChapter 19 - Monday September 12\n\nChapter 20 - Tuesday September 13\n\nChapter 21 - Wednesday September 14\n\nChapter 22 - Saturday September 17\n\nChapter 23 - Monday September 19\n\nPart IV\n\nChapter 24 - Tuesday September 6\n\nChapter 25 - Wednesday September 7\n\nChapter 26 - Thursday September 8\n\nChapter 27 - Friday September 9\n\nChapter 28 - Saturday September 10\n\nChapter 29 - Sunday September 11\n\nChapter 30 - Monday September 12\n\nChapter 31 - Tuesday September 13\n\nChapter 32 - Wednesday September 14\n\nChapter 33 - Thursday September 15\n\nChapter 34 - Friday September 16\n\nChapter 35 - Saturday September 17\n\nChapter 36 - Sunday September 18\n\nChapter 37 - Monday September 19\n\nChapter 38 - Monday September 19\n\nChapter 39 - Tuesday September 20\n\nChapter 40 - Thursday September 22\n\nChapter 41 - Friday September 23\n\nChapter 42 - Sunday September 25\n\nChapter 43 - Monday September 26\n\nChapter 44 - Tuesday September 27\n\nChapter 45 - Wednesday September 28\n\nChapter 46 - Thursday September 29\n\nPart V\n\nChapter 47 - Fall 2008\n\nThe Zeitoun Foundation\n\nAcknowledgments\n\nCopyright\n\n#\n\n_... in the history of the world it might even be that there was more punishment than crime..._\n\nCormac McCarthy, _The Road_\n\n_To a man with a hammer, everything looks like a nail_.\n\nMark Twain\n\n# NOTES ABOUT THIS BOOK\n\nThis is a work of nonfiction, based primarily on the accounts of Abdulrahman and Kathy Zeitoun (pronounced \"Zay-toon\"). Dates, times, locations, and other facts have been confirmed by independent sources and the historical record. Conversations have been recounted as best as can be remembered by the participants. Some names have been changed.\n\nThis book does not attempt to be an all-encompassing book about New Orleans or Hurricane Katrina. It is only an account of one family's experiences before and after the storm. It was written with the full participation of the Zeitoun family, and reflects their view of the events.\n\n# I\n# FRIDAY AUGUST 26, 2005\n\nOn moonless nights the men and boys of Jableh, a dusty fishing town on the coast of Syria, would gather their lanterns and set out in their quietest boats. Five or six small craft, two or three fishermen in each. A mile out, they would arrange the boats in a circle on the black sea, drop their nets, and, holding their lanterns over the water, they would approximate the moon.\n\nThe fish, sardines, would begin gathering soon after, a slow mass of silver rising from below. The fish were attracted to plankton, and the plankton were attracted to the light. They would begin to circle, a chain linked loosely, and over the next hour their numbers would grow. The black gaps between silver links would close until the fishermen could see, below, a solid mass of silver spinning.\n\nAbdulrahman Zeitoun was only thirteen when he began fishing for sardines this way, a method called _lampara_ , borrowed from the Italians. He had waited years to join the men and teenagers on the night boats, and he'd spent those years asking questions. Why only on moonless nights? Because, his brother Ahmad said, on moon-filled nights the plankton would be visible everywhere, spread out all over the sea, and the sardines could see and eat the glowing organisms with ease. But without a moon the men could make their own, and could bring the sardines to the surface in stunning concentrations. You have to see it, Ahmad told his little brother. You've never seen anything like this.\n\nAnd when Abdulrahman first witnessed the sardines circling in the black he could not believe the sight, the beauty of the undulating silver orb below the white and gold lantern light. He said nothing, and the other fishermen were careful to be quiet, too, paddling without motors, lest they scare away the catch. They would whisper over the sea, telling jokes and talking about women and girls as they watched the fish rise and spin beneath them. A few hours later, once the sardines were ready, tens of thousands of them glistening in the refracted light, the fishermen would cinch the net and haul them in.\n\nThey would motor back to the shore and bring the sardines to the fish broker in the market before dawn. He would pay the men and boys, and would then sell the fish all over western Syria\u2014Lattakia, Baniyas, Damascus. The fishermen would split the money, with Abdulrahman and Ahmad bringing their share home. Their father had passed away the year before and their mother was of fragile health and mind, so all funds they earned fishing went toward the welfare of the house they shared with ten siblings.\n\nAbdulrahman and Ahmad didn't care much about the money, though. They would have done it for free.\n\nThirty-four years later and thousands of miles west, Abdulrahman Zeitoun was in bed on a Friday morning, slowly leaving the moonless Jableh night, a tattered memory of it caught in a morning dream. He was in his home in New Orleans and beside him he could hear his wife Kathy breathing, her exhalations not unlike the shushing of water against the hull of a wooden boat. Otherwise the house was silent. He knew it was near six o'clock, and the peace would not last. The morning light usually woke the kids once it reached their second-story windows. One of the four would open his or her eyes, and from there the movements were brisk, the house quickly growing loud. With one child awake, it was impossible to keep the other three in bed.\n\nKathy woke to a thump upstairs, coming from one of the kids' rooms. She listened closely, praying silently for rest. Each morning there was a delicate period, between six and six-thirty, when there was a chance, however remote, that they could steal another ten or fifteen minutes of sleep. But now there was another thump, and the dog barked, and another thump followed. What was happening in this house? Kathy looked to her husband. He was staring at the ceiling. The day had roared to life.\n\nThe phone began ringing, today as always, before their feet hit the floor. Kathy and Zeitoun\u2014most people called him by his last name because they couldn't pronounce his first\u2014ran a company, Zeitoun A. Painting Contractor LLC, and every day their crews, their clients, everyone with a phone and their number, seemed to think that once the clock struck six-thirty, it was appropriate to call. And they called. Usually there were so many calls at the stroke of six-thirty that the overlap would send half of them straight to voicemail.\n\nKathy took the first one, from a client across town, while Zeitoun shuffled into the shower. Fridays were always busy, but this one promised madness, given the rough weather on the way. There had been rumblings all week about a tropical storm crossing the Florida Keys, a chance it might head north. Though this kind of possibility presented itself every August and didn't raise eyebrows for most, Kathy and Zeitoun's more cautious clients and friends often made preparations. Throughout the morning the callers would want to know if Zeitoun could board up their windows and doors, if he would be clearing his equipment off their property before the winds came. Workers would want to know if they'd be expected to come in that day or the next.\n\n\"Zeitoun Painting Contractors,\" Kathy said, trying to sound alert. It was an elderly client, a woman living alone in a Garden District mansion, asking if Zeitoun's crew could come over and board up her windows.\n\n\"Sure, of course,\" Kathy said, letting her feet drop heavily to the floor. She was up. Kathy was the business's secretary, bookkeeper, credit department, public-relations manager\u2014she did everything in the office, while her husband handled the building and painting. The two of them balanced each other well: Zeitoun's English had its limits, so when bills had to be negotiated, hearing Kathy's Louisiana drawl put clients at ease.\n\nThis was part of the job, helping clients prepare their homes for coming winds. Kathy hadn't given much thought to the storm this client was talking about. It took a lot more than a few downed trees in south Florida to get her attention.\n\n\"We'll have a crew over this afternoon,\" Kathy told the woman.\n\nKathy and Zeitoun had been married for eleven years. Zeitoun had come to New Orleans in 1994, by way of Houston and Baton Rouge and a half-dozen other American cities he'd explored as a young man. Kathy had grown up in Baton Rouge and was used to the hurricane routine: the litany of preparations, the waiting and watching, the power outages, the candles and flashlights and buckets catching rain. There seemed to be a half-dozen named storms every August, and they were rarely worth the trouble. This one, named Katrina, would be no different.\n\nDownstairs, Nademah, at ten their second-oldest, was helping get breakfast together for the two younger girls, Aisha and Safiya, five and seven. Zachary, Kathy's fifteen-year-old son from her first marriage, was already gone, off to meet friends before school. Kathy made lunches while the three girls sat at the kitchen table, eating and reciting, in English accents, scenes from _Pride and Prejudice_. They had gotten lost in, were hopelessly in love with, that movie. Dark-eyed Nademah had heard about it from friends, convinced Kathy to buy the DVD, and since then the three girls had seen it a dozen times\u2014every night for two weeks. They knew every character and every line and had learned how to swoon like aristocratic maidens. It was the worst they'd had it since _Phantom of the Opera_ , when they'd been stricken with the need to sing every song, at home or at school or on the escalator at the mall, at full volume.\n\nZeitoun wasn't sure which was worse. As he entered the kitchen, seeing his daughters bow and curtsy and wave imaginary fans, he thought, _At least they're not singing_. Pouring himself a glass of orange juice, he watched these girls of his, perplexed. Growing up in Syria, he'd had seven sisters, but none had been this prone to drama. His girls were playful, wistful, always dancing across the house, jumping from bed to bed, singing with feigned vibrato, swooning. It was Kathy's influence, no doubt. She was one of them, really, blithe and girlish in her manner and her tastes\u2014video games, Harry Potter, the baffling pop music they listened to. He knew she was determined to give them the kind of carefree childhood she hadn't had.\n\n* * *\n\n\"That's all you're eating?\" Kathy said, looking over at her husband, who was putting on his shoes, ready to leave. He was of average height, a sturdily built man of forty-seven, but how he maintained his weight was a puzzle. He could go without breakfast, graze at lunch, and barely touch dinner, all while working twelve-hour days of constant activity, and still his weight never fluctuated. Kathy had known for a decade that her husband was one of those inexplicably solid, self-sufficient, and never-needy men who got by on air and water, impervious to injury or disease\u2014but still she wondered how he sustained himself. He was passing through the kitchen now, kissing the girls' heads.\n\n\"Don't forget your phone,\" Kathy said, eyeing it on the microwave.\n\n\"Why would I?\" he asked, pocketing it.\n\n\"So you don't forget things?\"\n\n\"I don't.\"\n\n\"You're really saying you don't forget things.\"\n\n\"Yes. This is what I'm saying.\"\n\nBut as soon as he'd said the words he recognized his error.\n\n\"You forgot our firstborn child!\" Kathy said. He'd walked right into it. The kids smiled at their father. They knew the story well.\n\nIt was unfair, Zeitoun thought, how one lapse in eleven years could give his wife enough ammunition to needle him for the rest of his life. Zeitoun was not a forgetful man, but whenever he did forget something, or when Kathy was trying to prove he had forgotten something, all she had to do was remind him of the time he'd forgotten Nademah. Because he had. Not for such a long time, but he had.\n\nShe was born on August 4, on the one-year anniversary of their wedding. It had been a trying labor. The next day, at home, Zeitoun helped Kathy from the car, closed the passenger door, and then retrieved Nademah, still in her carseat. He carried the baby in one hand, holding Kathy's arm with the other. The stairs to their second-floor apartment were just inside the building, and Kathy needed help getting up. So Zeitoun helped her up the steep steps, Kathy groaning and sighing as they went. They reached the bedroom, where Kathy collapsed on the bed and got under the covers. She was relieved beyond words or reason to be home where she could relax with her infant.\n\n\"Give her to me,\" Kathy said, raising her arms.\n\nZeitoun looked down to his wife, astonished at how ethereally beautiful she looked, her skin radiant, her eyes so tired. Then he heard what she'd said. The baby. Of course she wanted the baby. He turned to give her the baby, but there was no baby. The baby was not at his feet. The baby was not in the room.\n\n\"Where is she?\" Kathy asked.\n\nZeitoun took in a quick breath. \"I don't know.\"\n\n\"Abdul, where's the baby?\" Kathy said, now louder.\n\nZeitoun made a sound, something between a gasp and a squeak, and flew out of the room. He ran down the steps and out the front door. He saw the carseat sitting on the lawn. He'd left the baby in the yard. _He'd left the baby in the yard_. The carseat was turned toward the street. He couldn't see Nademah's face. He grabbed the handle, fearing the worst, that someone had taken her and left the seat, but when he turned it toward him, there was the tiny pink face of Nademah, scrunched and sleeping. He put his fingers to her, to feel her heat, to know she was okay. She was.\n\nHe brought the carseat upstairs, handed Nademah to Kathy, and before she could scold him, kid him, or divorce him, he ran down the stairs and went for a walk. He needed a walk that day, and needed walks for many days following, to work out what he'd done and why, how he had forgotten his child while aiding his wife. How hard it was to do both, to be partner to one and protector to the other. What was the balance? He would spend years pondering this conundrum.\n\nThis day, in the kitchen, Zeitoun wasn't about to give Kathy the opportunity to tell the whole story, again, to their children. He waved goodbye.\n\nAisha hung on his leg. \"Don't leave, Baba,\" she said. She was given to theatrics\u2014Kathy called her Dramarama\u2014and all that Austen had made the tendency worse.\n\nHe was already thinking about the day's work ahead, and even at seven-thirty he felt behind.\n\nZeitoun looked down at Aisha, held her face in his hands, smiled at the tiny perfection of her dark wet eyes, and then extracted her from his shin as if he were stepping out of soggy pants. Seconds later he was in the driveway, loading the van.\n\nAisha went out to help him, and Kathy watched the two of them, thinking about his way with the girls. It was difficult to describe. He was not an overly doting father, and yet he never objected to them jumping on him, grabbing him. He was firm, sure, but also just distracted enough to give them the room they needed, and just pliant enough to let himself be taken advantage of when the need arose. And even when he was upset about something, it was disguised behind those eyes, grey-green and long-lashed. When they met, he was thirteen years older than Kathy, so she wasn't immediately sold on the prospect of marriage, but those eyes, holding the light the way they did, had seized her. They were dream-filled, but discerning, too, assessing\u2014the eyes of an entrepreneur. He could see a run-down building and have not only the vision to see what it might become, but also the practical knowledge of what it would cost and how long it would take.\n\nKathy adjusted her hijab in the front window, tucking in stray hairs\u2014it was a nervous habit\u2014while watching Zeitoun leave the driveway in a swirling grey cloud. It was time for a new van. The one they had was a crumbling white beast, long-suffering but dependable, filled with ladders and wood and rattling with loose screws and brushes. On the side was their ubiquitous logo, the words ZEITOUN A. PAINTING CONTRACTOR next to a paint roller resting at the end of a rainbow. The logo was corny, Kathy admitted, but it wasn't easy to forget. Everyone in the city knew it, from bus stops and benches and lawn signs; it was as common in New Orleans as live oak or royal fern. But at first it was not so benign to all.\n\nWhen Zeitoun first designed it, he'd had no idea that a sign with a rainbow on it would signify anything to anyone\u2014anything other than the array of colors and tints from which clients might choose. But soon enough he and Kathy were made aware of the signals they were sending.\n\nImmediately they began getting calls from gay couples, and this was good news, good business. But at the same time, some potential clients, once they saw the van arrive, were no longer interested in Zeitoun A. Painting Contractor LLC. Some workers left, thinking that by working under the Zeitoun Painting rainbow they would be presumed to be gay, that somehow the company managed to employ only gay painters.\n\nWhen Zeitoun and Kathy finally caught on to the rainbow's signifying power, they had a serious talk about it. Kathy wondered if her husband, who did not at that point have any gay friends or family members, might want to change the logo, to keep their message from being misconstrued.\n\nBut Zeitoun barely gave it a thought. It would cost a lot of money, he said\u2014about twenty signs had been made, not to mention all the business cards and stationery\u2014and besides, all the new clients were paying their bills. It wasn't much more complicated than that.\n\n\"Think about it,\" Zeitoun laughed. \"We're a Muslim couple running a painting company in Louisiana. Not such a good idea to turn away clients.\" Anyone who had a problem with rainbows, he said, would surely have trouble with Islam.\n\nSo the rainbow remained.\n\nZeitoun pulled onto Earhart Boulevard, though a part of him was still in Jableh. Whenever he had these morning thoughts of his childhood, he wondered how they all were, his family in Syria, all his brothers and sisters and nieces and nephews scattered up and down the coast, and those who had long ago left this world. His mother died a few years after his father passed on, and he'd lost a treasured brother, Mohammed, when he was very young. But the rest of his siblings, those still in Syria and Spain and Saudi Arabia, were all doing well, extraordinarily so. The Zeitouns were a high-achieving clan, full of doctors and school principals and generals and business owners, all of them with a passion for the sea. They had grown up in a big stone house on the Mediterranean, and none had strayed far from the shore. Zeitoun made a note to call Jableh sometime that day. There were always new babies, always news. He only had to reach one of his brothers or sisters\u2014there were seven still in Syria\u2014and he could get the full report.\n\nZeitoun turned on the radio. The storm that people were talking about was still far down in Florida, moving slowly west. It wasn't expected to make it up the Gulf for another few days, if at all. As he drove to his first job of the day, the restoration of a wonderful old mansion in the Garden District, he turned the dial on the radio, looking for something, anything, else.\n\nStanding in her kitchen, Kathy looked at the clock and gasped. It was all too rare that she got the kids to school on time. But she was working on it. Or planned to work on it as soon as the season calmed down. Summer was the busiest time for the business, with so many people leaving, fleeing the swamp heat, wanting these rooms or that porch painted while they were away.\n\nWith a flurry of warnings and arm movements, Kathy herded the girls and their gear into the minivan and headed across the Mississippi to the West Bank.\n\nThere were advantages to Zeitoun and Kathy running a business together\u2014so many blessings, too many to name\u2014but then again, the drawbacks were distinct and growing. They greatly valued being able to set their own hours, choose their clients and jobs, and be at home whenever they needed to be\u2014their ability to be there, always and for anything relating to their children, was a profound comfort. But when friends would ask Kathy whether they, too, should start their own business, she talked them out of it. You don't run the business, she would say. The business runs you.\n\nKathy and Zeitoun worked harder than anyone they knew, and the work and worry never ended. Nights, weekends, holidays\u2014respite never came. They usually had eight to ten jobs going at any one time, which they oversaw out of a home office and a warehouse space on Dublin Street, off Carrollton. And that was to say nothing of the property-management aspect of the business. Somewhere along the line they started buying buildings, apartments, and houses, and now they had six properties with eighteen tenants. Each renter was, in some ways, another dependent, another soul to worry about, to provide with shelter, a solid roof, air-conditioning, clean water. There was a dizzying array of people to pay and collect from, houses to improve and maintain, bills to deal with, invoices to issue, supplies to buy and store.\n\nBut she cherished what her life had become, and the family she and Zeitoun had created. She was driving her three girls to school now, and the fact that they could go to a private school, that their college would be taken care of, that they had all they needed and more\u2014she was thankful every hour of every day.\n\nKathy was one of nine children, and had grown up with very little, and Zeitoun, the eighth of thirteen children, had been raised with almost nothing. To see the two of them now, to stand back and assess what they'd built\u2014a sprawling family, a business of distinct success, and to be woven so thoroughly into the fabric of their adopted city that they had friends in every neighborhood, clients on almost any block they passed\u2014these were all blessings from God.\n\nHow could she take Nademah, for instance, for granted? How had they produced such a child\u2014so smart and self-possessed, so dutiful, helpful, and precocious? She was practically an adult now, it seemed\u2014she certainly spoke like one, often more measured and circumspect than her parents. Kathy glanced at her now, sitting in the passenger seat playing with the radio. She'd always been quick. When she was five, no more than five, Zeitoun came home from work for lunch one day and found Nademah playing on the floor. She looked up at him and declared, \"Daddy, I want to be a dancer.\" Zeitoun took off his shoes and sat on the couch. \"We have too many dancers in the city,\" he said, rubbing his feet. \"We need doctors, we need lawyers, we need teachers. I want you to be a doctor so you can take care of me.\" Nademah thought about this for a moment and said, \"Okay, then I'll be a doctor.\" She went back to her coloring. A minute later, Kathy came downstairs, having just seen the wreck of Nademah's bedroom. \"Clean up your room, Demah,\" she said. Nademah didn't miss a beat, nor did she look up from her coloring book. \"Not me, Mama. I'm going to be a doctor, and doctors don't clean.\"\n\nIn the car, approaching their school, Nademah turned up the volume on the radio. She'd caught something on the news about the coming storm. Kathy wasn't paying close attention, because three or four times a season, it seemed, there was some early alarmist talk about hurricanes heading straight for the city, and always their direction changed, or the winds fizzled in Florida or over the Gulf. If a storm hit New Orleans at all, it would be greatly diminished, no more than a day of grey gusts and rain.\n\nThis reporter was talking about the storm heading into the Gulf of Mexico as a Category 1. It was about 45 miles north-northwest of Key West and heading west. Kathy turned the radio off; she didn't want the kids to worry.\n\n\"You think it'll hit us?\" Nademah asked.\n\nKathy didn't think much of it. Who ever worried about a Category 1 or 2? She told Nademah it was nothing, nothing at all, and she kissed the girls goodbye.\n\nWith the thrump of three car doors, Kathy was suddenly and definitively alone. Driving away from the school, she turned the radio on again. City officials were giving the usual recommendations about having three days' worth of supplies on hand\u2014Zeitoun had always been vigilant about this\u2014and then there was some talk about 110-mile-per-hour winds and storm surges in the Gulf.\n\nShe turned it off again and called Zeitoun on his cell phone.\n\n\"You hear about this storm?\" she asked.\n\n\"I hear different things,\" he said.\n\n\"You think it's serious?\" she asked.\n\n\"Really? I don't know,\" he said.\n\nZeitoun had reinvented the word \"really,\" prefacing a good deal of his sentences with \"Really?\" as a kind of throat-clearer. Kathy would ask him any question, and he would say, \"Really? It's a funny story.\" He was known for anecdotes, and parables from Syria, quotations from the Qur'an, stories from his travels around the world. All of it she'd gotten used to, but the use of \"Really?\"\u2014she'd given up fighting it. For him it was equivalent to starting a sentence with \"You know,\" or \"Let me tell you.\" It was Zeitoun, and she had no choice but to find it endearing.\n\n\"Don't worry,\" he said. \"Are the kids at school?\"\n\n\"No, they're in the lake. My God.\"\n\nThe man was school-obsessed, and Kathy liked to tease him about it and any number of other things. She and Zeitoun spoke on the phone throughout every day, about everything\u2014painting, the rental properties, things to fix and do and pick up, often just to say hello. The banter they'd developed, full of his exasperation and her one-liners, was entertaining to anyone who overheard it. It was unavoidable, too, given how often they talked. Neither of them could operate their home, their company, their lives or days without the other.\n\nThat they had come to such symbiosis continually surprised Kathy. She had been brought up a Southern Baptist in suburban Baton Rouge with dreams of leaving home\u2014she did so just after high school\u2014and running a daycare center. Now she was a Muslim married to a Syrian American, managing a sprawling painting and contracting business. When Kathy met her husband, she was twenty-one and he was thirty-four and a native of a country she knew almost nothing about. She was recovering from an unsuccessful marriage and had recently converted to Islam. She wasn't even vaguely interested in getting married again, but Zeitoun had turned out to be everything she had not believed possible: an honest man, honest to the core, hardworking, reliable, faithful, devoted to family. And best of all, he very much wanted Kathy to be who and how she wanted to be, nothing more or less.\n\nBut it didn't mean there wasn't some fussing. Kathy called it that, their spirited back-and-forth about everything from what the kids ate for dinner to whether they should enlist a collection agency to help with a particular client.\n\n\"We're just fussin',\" she would tell her kids when they heard the two of them. Kathy couldn't help it. She was a talker. She couldn't hold anything in. I'm going to speak my mind, she told Abdul early in their relationship. He shrugged; that was fine with him. He knew that sometimes she just needed to blow off steam, and he let her. He would nod patiently, sometimes thankful that his English wasn't as quick as hers. While he searched for the right words to respond with, she would go on, and often enough, by the time she was finished, she had tired herself out, and there was nothing left to say.\n\nIn any case, once Kathy knew that she would be heard, and heard to the end, it softened the tone of her arguments. Their discussions became less heated, and often more comical. But the kids, when they were young, sometimes couldn't tell the difference.\n\nYears before, while Kathy was driving and fussing about something with Zeitoun, Nademah spoke up. Strapped into a car seat in the back, she had had enough. \"Dad, be nice to Mom,\" she said. And then she turned to Kathy. \"Mom, be nice to Dad.\" Kathy and Zeitoun stopped cold. They looked at each other, and then, in unison, back to little Nademah. They already knew she was smart, but this was something different. She was only two years old.\n\nAfter she hung up with Zeitoun, Kathy did what she knew she shouldn't do, because clients no doubt needed and expected to reach her in the morning. She switched off her phone. She did this every so often, after the kids had left the car and she'd turned toward home. Just to have that thirty minutes of solitude during the drive\u2014it was decadent but essential. She stared at the road, in total silence, thinking of nothing at all. The day would be long, it would be nonstop until the kids went to bed, so she allowed herself this one extravagance, an uninterrupted, thirty-minute expanse of clarity and quiet.\n\nAcross town, Zeitoun was at his first job of the day. He loved this place, a magisterial old house in the Garden District. He had two men on the job and was stopping by to make sure they were there, that they were busy, that they had what they needed. He jumped up the steps and strode into the house. It was easily 120 years old.\n\nHe saw Emil, a painter and carpenter from Nicaragua, kneeling in a doorway, taping off a baseboard. Zeitoun snuck up behind him and grabbed his shoulders suddenly.\n\nEmil jumped.\n\nZeitoun laughed.\n\nHe wasn't even sure why he did things like this. It was hard to explain\u2014sometimes he just found himself in a playful mood. The workers who knew him well were unsurprised, while the newer ones would often be startled, thinking his behavior a bizarre sort of motivational method.\n\nEmil managed a smile.\n\nIn the dining room, applying a second coat to the wall, was Marco, originally from El Salvador. The two of them, Marco and Emil, had met at church and had gone looking for work as a team of housepainters. They'd shown up at one of Zeitoun's job sites, and because Zeitoun nearly always had more work than he could handle, he'd taken them on. That had been three years ago, and Marco and Emil had worked for Zeitoun consistently since then.\n\nOutside of employing a number of New Orleans natives, Zeitoun had hired men from everywhere: Peru, Mexico, Bulgaria, Poland, Brazil, Honduras, Algeria. He'd had good experiences with almost all of them, though in his business there was an above-average rate of attrition and turnover. Many workers were transient, intending only to spend a few months in the country before returning to their families. These men he was happy to hire, and he'd learned a fair bit of Spanish along the way, but he had to be prepared for their short-notice disappearances. Other workers were just young men: irresponsible and living for today. He couldn't blame them\u2014he'd been young and untethered once, too\u2014but he tried, whenever he could, to instill in them the knowledge that if they kept their heads down and saved a few dollars a week, they could live well, could raise a family doing this kind of work. But he rarely saw a young man in this business who had an eye to the future. Just keeping them in food and clothing, chasing them down when they were late or absent\u2014all of it was exhausting and occasionally disheartening. He felt, sometimes, as if he had not four children but dozens, most of them with paint-covered hands and mustaches.\n\n* * *\n\nHis phone rang. He looked at the caller ID and picked up.\n\n\"Ahmad, how are you?\" Zeitoun said in Arabic.\n\nAhmad was Zeitoun's older brother and closest friend. He was calling from Spain, where he lived with his wife and two children, both in high school. It was late where Ahmad was, so Zeitoun worried that the call might bring grave news.\n\n\"What is it?\" Zeitoun asked.\n\n\"I'm watching this storm,\" he said.\n\n\"You scared me.\"\n\n\"You should be scared,\" Ahmad said. \"This one could be for real.\"\n\nZeitoun was skeptical but paid attention. Ahmad was a ship captain, had been for thirty years, piloting tankers and ocean liners in every conceivable body of water, and he knew as much as anyone about storms, their trajectories and power. As a young man, Zeitoun had been with him for a number of those journeys. Ahmad, nine years older, had brought Zeitoun on as a crewman, taking him to Greece, Lebanon, South Africa. Zeitoun had gone on to work on ships without Ahmad, too, seeing most of the world in a ten-year period of wanderlust that eventually brought him to New Orleans and to his life with Kathy.\n\nAhmad clicked his tongue. \"It really does seem unusual. Big and slow-moving. I'm watching it on the satellite,\" he said.\n\nAhmad was a technophile. At work and in his spare time he paid close attention to the weather, to developing storms. At the moment he was at his home in M\u00e1laga, a beach town on the Spanish Mediterranean, in his cluttered office, tracking this storm making its way across Florida.\n\n\"Have they begun evacuating?\" Ahmad asked.\n\n\"Not officially,\" Zeitoun said. \"Some people are leaving.\"\n\n\"And Kathy, the kids?\"\n\nZeitoun told him they hadn't thought about it yet.\n\nAhmad sighed. \"Why not go, just to be safe?\"\n\nZeitoun made a noncommittal sound into the phone.\n\n\"I'll call you later,\" Ahmad said.\n\nZeitoun left the house and walked to the next job, one block over. It was often like this, multiple jobs in close proximity. Clients seemed so surprised to work with a painter or contractor they could trust and recommend that through referrals and in rapid succession Zeitoun would get a half-dozen jobs in any given neighborhood.\n\nThis next house, which he'd worked on for years, was across the street from the home of Anne Rice, the writer\u2014he had not read her work, but Kathy had; Kathy read everything\u2014and was as stately and gorgeous a home as existed in New Orleans. High ceilings, a grand winding staircase descending into the foyer, hand-carved everything, each room themed and with a distinct character. Zeitoun had painted and repainted probably every room in the house, and the owners showed no signs of stopping. He loved to be in that house, admiring the craftsmanship, the great care put into the most eccentric details and flourishes\u2014a mural over the mantel, one-of-a-kind ironwork on every balcony. It was this kind of willful, wildly romantic attention to beauty\u2014crumbling and fading beauty needing constant attention\u2014that made this city so unlike any other and such an unparalleled sort of environment for a builder.\n\nHe walked in, straightened the drop cloth in the front hall, and made his way to the back of the house. He peeked in on Georgi, his Bulgarian carpenter, who was installing new molding near the kitchen. Georgi was a good worker, about sixty, barrel-chested and tireless, but Zeitoun knew not to get him talking. Once Georgi started you were in for a twenty-minute discourse on the former Soviet Union, waterfront property in Bulgaria, and his various cross-country motorhome trips with his wife Albena, who had passed away years ago and was greatly missed.\n\nZeitoun got in his van and the radio assaulted him with more warnings about this storm called Katrina. It had formed near the Bahamas two days earlier and had scattered boats like toys. Zeitoun took note, but thought little of it. The winds were still many days from being relevant to his life.\n\nHe made his way to the Presbytere Museum on Jackson Square, where he had another crew working on a delicate restoration of the two-hundred-year-old building. The museum had been a courthouse long ago and was now home to a vast and extraordinary collection of Mardi Gras artifacts and memorabilia. It was a high-profile job and Zeitoun wanted to get it right.\n\nKathy called from home. She had just heard from a client in the Broadmoor neighborhood. Zeitoun's men had painted a window shut and someone needed to come unstick it.\n\n\"I'll go,\" he said. Easier that way, he figured. He would go, he would do it, it would be done. Fewer phone calls, no waiting.\n\n\"You hear about the winds?\" Kathy said. \"Killed three in Florida so far.\"\n\nZeitoun dismissed it. \"This is not the storm for us,\" he said.\n\nKathy often poked fun at Zeitoun's stubbornness, at his unwillingness to bow before any force, natural or otherwise. But Zeitoun couldn't help it. He had been raised in the shadow of his father, a legendary sailor who had faced a series of epic trials, and had always, miraculously, survived.\n\nZeitoun's father, Mahmoud, had been born not far from Jableh, on Arwad Island, the only island off Syria, a landmass so small it didn't appear on some maps. There, most boys grew up to be shipbuilders or fishermen. As a teenager Mahmoud began crewing on shipping routes between Lebanon and Syria, on large sail-powered cargo boats, bringing timber to Damascus and other cities along the coast. He had been on such a ship during World War II, sailing from Cyprus to Egypt. He and his shipmates were vaguely aware of the danger of Axis forces targeting them as potential suppliers to the Allies, but they were astounded when a squadron of German planes appeared on the horizon and bore down on them. Mahmoud and the rest of the crew dove into the sea just before the planes began strafing. They managed to detach an inflatable lifeboat before their ship sank, and were crawling into it when the Germans returned. They were intent, it seemed, on killing all the crew members who had survived. Mahmoud and his fellow sailors were forced to dive from the dinghy and wait underwater until the Germans were satisfied that the crew had all been shot or drowned. When the surface seemed safe again, the sailors returned to their lifeboat and found it full of holes. They stuffed their shirts into the gaps and paddled by hand, for miles, until they reached the Egyptian shore.\n\nBut the story Mahmoud told most often when Zeitoun was growing up, the story he told when forbidding his children to live on the sea, was this one:\n\nMahmoud was returning from Greece on a thirty-six-foot schooner when they ran into a black and tortuous storm. They sailed through it for hours until the main mast cracked and dropped the sail into the water, threatening to drag the whole ship into the sea. Without thinking, Mahmoud climbed up the mast, intending to free the sail and right the hull. But when he reached the crack in the mast, it gave way completely, and he fell into the ocean. The ship was traveling at eight knots and there was no chance of turning it around, so the crew threw what they could to Mahmoud\u2014a few planks and a barrel\u2014and in minutes the boat was gone into the darkness. He was alone at sea for two days, with sharks below and storms above, clinging to the remnants of the barrel, when he finally washed ashore near Lattakia, fifty miles north of Arwad Island.\n\nNo one, including Mahmoud, could believe he had survived, and thereafter he vowed never to take the chance again. He quit sailing, moved his family from Arwad onto the mainland, and forbade his children to work on the sea. He wanted good schooling for them all, opportunities apart from fishing and shipbuilding.\n\nMahmoud and his wife went looking all over Syria for a new home, a place far from the water. They spent months traveling with their small children, inspecting this town and that house. But nothing seemed right. Nothing, that is, until they found themselves inside a two-story home, with enough room for all their current and future children. When Mahmoud declared that this was the place for them, his wife laughed. They were facing the sea, not fifty feet from shore.\n\nThere, in Jableh, Mahmoud opened a hardware store, sent his sons and daughters to the best schools, and taught his boys every trade he could. Everyone knew the Zeitouns, all of them hardworking and quick, and they all knew Abdulrahman, the eighth-born, a young man who wanted to know everything and who feared no kind of labor. As a teenager, he watched the tradesman in town whenever he could, studying their craft. And once they realized he was serious and a quick learner, they'd teach him whatever they knew. Over the years he'd learned every trade he could get close to\u2014fishing, ship rigging, painting, framing, masonry, plumbing, roofing, tile work, even auto repair.\n\nZeitoun's father would likely be both proud and bemused by the trajectory of his son's life. He hadn't wanted his kids to work on the sea, but many of them, including Zeitoun, had. Mahmoud wanted his children to be doctors, teachers. Zeitoun, though, was too much like his father: first a sailor, then, to provide for a family and to ensure that he lived to watch them grow up, a builder.\n\nZeitoun called Kathy at eleven. He'd freed the window in Broadmoor and now was at Home Depot.\n\n\"You hear anything new?\" he asked.\n\n\"Looks bad,\" she said.\n\nShe was online. The National Hurricane Center had upgraded Katrina to a Category 2. They had shifted the possible track of the storm from the Florida panhandle to the Mississippi\u2013Louisiana coast. The storm was crossing southern Florida with winds around ninety miles an hour. At least three people had been killed. Power was out for 1.3 million households.\n\n\"People here are worried,\" Zeitoun said, looking around the store. \"A lot of people buying plywood.\" The lines were long. The store was running low on plastic sheeting, duct tape, rope\u2014anything that would protect windows from the winds.\n\n\"I'll keep watching,\" Kathy said.\n\nIn the parking lot, Zeitoun looked to the sky for signs of the coming weather. He saw nothing unusual. As he pushed his cart to his van, a young man, pushing his own cart full of supplies, approached Zeitoun.\n\n\"How's business?\" the man asked.\n\nProbably an electrician, Zeitoun figured.\n\n\"Not bad,\" Zeitoun said. \"You?\"\n\n\"Could be better,\" he said, and introduced himself and his trade: he was indeed an electrician. He was parked next to Zeitoun, and began helping Zeitoun unload his cart. \"You ever need one,\" he said, \"I show up when I say I'll show up, and I finish what I start.\" He handed Zeitoun his card. They shook hands, and the electrician got into his own van, which Zeitoun noticed was in better shape than his own.\n\n\"Why do you need me?\" Zeitoun asked. \"Your van's newer than mine.\"\n\nThey both laughed, and Zeitoun put the card on his dashboard and pulled out. He would call the young man, he figured, sooner or later. He always needed electricians, and he liked the man's hustle.\n\nWhen he began working in New Orleans, eleven years earlier, Zeitoun labored for just about every contractor in the city, painting, hanging Sheetrock, tiling\u2014anything they needed\u2014until he was hired by a man named Charlie Saucier. Charlie owned his own company, had built it from scratch. He'd become wealthy, and was hoping to retire before his knees gave out on him.\n\nCharlie had a son in his late teens, and he wanted nothing more than to leave the company to this son. He loved his son, but his son was not a worker; he was shifty and ungrateful. He failed to show up for work, and when he did, he worked listlessly, and condescended to his father's employees.\n\nAt the time, Zeitoun didn't have a car, so he rode to Charlie's work sites on a bike\u2014a ten-speed he bought for forty dollars. One day, when Zeitoun was already in danger of being late, the bike blew a tire. After riding on the rim for half a mile, he gave up. He needed to get four miles across the city in twenty minutes, and it was looking like he would be late for work for the first time in his life. He couldn't leave the bike and run\u2014he needed that bike\u2014and he couldn't ride on the flat tire, so he threw the bike over his shoulders and started jogging. He was panicking. If he was late for this job, what would happen to his reputation? Charlie would be disappointed, and he might not hire him again. And what if Charlie talked to other contractors, and found he couldn't recommend Zeitoun? The consequences could be far-reaching. Work was a pyramid, he knew, built on day after solid day.\n\nHe ran faster. He would be tardy, but if he sprinted, he had a shot at being no more than fifteen minutes late. It was August and the humidity was profound. A mile or so into his run, already soaked in sweat, a truck pulled up next to him.\n\n\"What are you doing?\" a voice asked. Without breaking stride, Zeitoun turned to see who it was. He figured it was some smart aleck poking fun at the man running along the road with a bike over his shoulders. But instead it was his boss, Charlie Saucier.\n\n\"I'm going to the job,\" Zeitoun said. He was still running; in hindsight he should have stopped at this point, but he was in a rhythm and he continued, with the truck puttering beside him.\n\nCharlie laughed. \"Throw your bike in the back.\"\n\nAs they drove, Charlie looked over to Zeitoun. \"You know, I've been at this for thirty years, and I think you're the best worker I've ever had.\"\n\nThey were driving to the job site and Zeitoun had finally managed to relax, knowing he wouldn't be fired that day.\n\n\"I have one guy,\" Charlie continued, \"he says he can't come to work because his car won't start. I have another guy, he doesn't come because he slept late. He slept late! Another guy, his wife kicked him out of the house or something. So he doesn't show. I have twenty or thirty employees, and ten of them show up to work any given day.\"\n\nThey were at a stop sign, and Charlie took a long look at Zeitoun. \"Then there's you. You have the perfect excuse. All you have is a bike, and the bike has a flat. But you're carrying your bike on your back. You're the only guy I've ever known who would have done something like that.\"\n\nAfter that day, things moved quickly forward and upward for Zeitoun. Within a year, he had saved enough to buy his own truck. Two years later, he was working for himself and employing a dozen men.\n\nAt noon Zeitoun made his way to the Islamic Center on St. Claude\u2014a humble-looking mosque and community gathering place downtown. Though his siblings worshiped in a variety of ways, Zeitoun was perhaps the most devout, missing none of his daily prayers. The Qur'an asked Muslims to worship five times daily: once between first light and dawn; again after midday; at mid-afternoon; at sunset; and lastly an hour and a half after sunset. If he found himself near home during the afternoon prayers, he would stop, but otherwise he prayed wherever he was, on any job. He had worshiped all over the city by now, at job sites, in parks, and in the homes of friends, but on Fridays he always stopped here, to meet friends for the _jumu'ah_ , a ritual gathering of all the Muslim men in the community.\n\nInside, he first washed in a ritual cleansing called _wuduu_ , required of worshipers. Then he began his prayers:\n\n_In the name of God, the Most Beneficent, the Most Merciful:  \nPraise be to God, the Lord of the Heavens and the Earth.  \nThe Most Beneficent, the Most Merciful.  \nMaster of the Day of Judgment.  \nYou alone we worship, and You alone we ask for help.  \nGuide us to the straight way;  \nthe way of those whom you have blessed,  \nnot of those who have deserved anger,  \nnor of those who are astray..._\n\nAfterward he called Kathy.\n\n\"It'll be a Category 3 soon,\" she said.\n\nKathy was at home, checking the weather online.\n\n\"Coming at us?\" he asked.\n\n\"They say it is.\"\n\n\"When?\"\n\n\"Not sure. Maybe Monday.\"\n\nZeitoun dismissed it. Monday, to him, meant never. This had happened before, Zeitoun noted, so many times. The storms always raged across Florida, wreaking havoc, and then died somewhere overland or in the Gulf.\n\nKathy's call waiting went off; she said goodbye to Zeitoun and switched over. It was Rob Stanislaw, a longtime client and friend.\n\n\"You leaving or are you crazy?\" he asked.\n\nKathy cackled. \"'I want to leave. Of course. But I can't speak for my husband.\"\n\nRob had a similar predicament. His husband, Walt Thompson, was like Zeitoun\u2014bullheaded, always feeling like his information was better than what anyone else had access to. Rob and Walt had been together for fifteen years, and had been close with the Zeitouns since 1997. They had hired the Zeitouns to help with the renovation of a house they'd bought, and immediately the two couples had clicked. Over the years they'd grown to depend on each other.\n\nWalt's family was in Baton Rouge, and it was likely that Rob and Walt would go there for the weekend, he said. Rob and Kathy agreed to update each other throughout the day.\n\nShe was about to take a break from the internet when something caught her attention. A news item, just posted: a family of five was missing at sea. The details were few\u2014two parents, three kids aged four, fourteen, and seventeen. They had been sailing in the Gulf, and had been expected Thursday in Cape Coral. But when the storm came, they'd lost contact. Family and friends had notified the Coast Guard, and boats and planes were searching as best they could. That was all anyone knew for now, and it looked bad.\n\nKathy was a mess. Stories like this just wrecked her.\n\nKathy called her husband. \"Rob and Walt are leaving.\"\n\n\"Really? Walt wants to leave?\"\n\nZeitoun trusted Walt's judgment on just about everything.\n\nKathy thought she might have her husband tilting her way. \"Fifteen inches of rain, I hear.\"\n\nSilence from Zeitoun.\n\n\"Twenty-five-foot waves,\" Kathy added.\n\nZeitoun changed the subject. \"Did you get the DeClercs to approve that paint sample?\"\n\n\"I did,\" Kathy said. \"Did you hear about this family of five?\"\n\nHe had not, so in a breathless rush Kathy told him what she knew about the family lost at sea in their tiny boat, swept away in the hurricane, just as the Zeitouns might be swept away if they didn't flee its path.\n\n\"We're not at sea, Kathy,\" Zeitoun said.\n\nZeitoun had spent the better part of ten years on ships, carrying everything from fruit to oil. He worked as a crewman, an engineer, a fisherman\u2014he'd been everywhere from Japan to Cape Town. All along, his brother Ahmad had told him that \"If a sailor finds the right port or the right woman, he'll drop anchor.\" In 1988 Zeitoun came to the United States on a tanker carrying oil from Saudi Arabia to Houston. He began working for a contractor in Baton Rouge, and it was there that he met Ahmaad, a Lebanese American who became one of his closest friends and the conduit through which he met his bride.\n\nAhmaad was working at a gas station at the time, and Zeitoun was hanging drywall. They bonded over common ancestry, and one day Zeitoun asked Ahmaad if he knew any single women who might be appropriate for him. Ahmaad was married to a woman named Yuko, an American of Japanese ancestry who had converted to Islam. And Yuko, it turned out, had a friend. Ahmaad was conflicted, though, because while he liked and trusted Zeitoun and wanted to help, he was hoping this friend of Yuko's might be a match for another friend of his. If it didn't work out between his friend and Yuko's, he said, he would surely introduce her to Zeitoun. Zeitoun was willing to respect that boundary, but at the same time his interest was piqued. Who was this woman who was so prized that Ahmaad would not even mention her name?\n\nThat year Zeitoun became increasingly determined to find the right woman. He told friends and cousins he was looking for a down-to-earth Muslim woman who wanted a family. Knowing he was a serious and hardworking man, they provided many introductions. He was sent to New York to meet the daughter of an acquaintance. He went to Oklahoma to meet the cousin of a friend. He went to Alabama to meet the sister of a coworker's roommate.\n\nMeanwhile, Yuko's friend had been set up with Ahmaad's friend, and though they courted for a few months, that relationship came to an end. Ahmaad, as promised, let Zeitoun know that Yuko's friend was now single. It was only then that Zeitoun was told her name: Kathy.\n\n\"Kathy?\" Zeitoun asked. He hadn't known too many Muslims named Kathy. \"Kathy what?\"\n\n\"Kathy Delphine,\" Ahmaad said.\n\n\"She's American?\"\n\n\"She's from Baton Rouge. She converted.\"\n\nZeitoun was more intrigued than ever. It took a courageous and self-possessed woman to take such a step.\n\n\"But listen,\" Ahmaad said. \"She's been married. She has a two-year-old son.\"\n\nThis did nothing to dissuade Zeitoun.\n\n\"When can I see her?\" he asked.\n\nAhmaad told him she worked at a furniture store, and gave Zeitoun the address. Zeitoun formulated a plan. He would park out front and observe her unnoticed. This was, he told Ahmaad, Jableh style. He didn't want to make a move, or allow anyone representing him to mention his intentions, before he could see her. This was the way of doing things where he'd come from: observe from afar, make inquiries, gather information, then meet. He wanted no confusion, no hurt feelings.\n\nHe pulled into the furniture store's parking lot at about five o'clock one day, planning to wait and watch as she left at the end of her shift. He was just settling in for his stakeout when a young woman burst through the door, wearing jeans and a hijab. She was striking, and very young. She tucked a few strands of hair into her scarf and looked around the parking lot. And then she was walking again, striding with a powerful confidence, her hands flying about as if she were drying just-painted fingernails. Then she broke into a private smile, as if recounting something that had made her laugh. _What was it?_ Zeitoun wondered. She was beautiful, fresh-faced, and the smile was everything\u2014wide, shy, electric. _I want to make her smile like that_ , he thought. _I want to be the one. I want to be the reason_. He liked her more with every step she took toward him. He was sold.\n\nBut she was getting too close. She was heading straight for him. Did she know he had come to see her? How was this possible? Someone had told her. Ahmaad? Yuko? She was almost at his car. He would look foolish. Why was she coming right at him? He wasn't ready to meet her.\n\nNot knowing what else to do, he ducked. Crouching below his dashboard, he held his breath and waited. _Please God_ , he thought. _Please_. Would she pass by, or would she appear at his window, wondering about the man trying to disappear below her? He felt ridiculous.\n\nKathy, though, had no idea she was passing a man hiding under his steering wheel. Her car just happened to be parked next to his. She unlocked her door, got in, and drove off.\n\nWhen she was gone, Zeitoun righted himself, breathed a sigh of relief, and tried to settle his stampeding heart.\n\n\"I need to meet her,\" he told Ahmaad.\n\nIt was agreed that they would meet at Ahmaad and Yuko's house. There would be a casual dinner, with Ahmaad and Yuko's kids and Kathy's son Zachary. It would be low-pressure, just an opportunity for the two of them to talk a bit and for Kathy, who had yet to even see Zeitoun, to meet this man who had inquired about her.\n\nWhen she saw him, she liked his eyes, his handsome, gold-skinned face. But he seemed too conservative, and he was thirty-four to her twenty-one\u2014well beyond the age she had imagined for a husband. Besides, it had been just two years since she'd left her first marriage, and she felt unready to begin again. She could think of nothing she needed from a man. She could certainly raise Zachary herself; the two of them had become a very good and streamlined team, and there seemed no reason to upset the balance of her life. She couldn't risk the chaos that her first marriage had wrought.\n\nAfter he left that night, Kathy told Yuko that he was a nice enough man, but she didn't think it was a good match.\n\nBut over the next two years, she and Zeitoun saw each other occasionally. He would be at a barbecue at Ahmaad and Yuko's, but out of deference to her\u2014he didn't want her to feel uncomfortable\u2014when Kathy arrived, he would leave. He continued to ask about her, and once a year he sent an offhand inquiry through Yuko, just to be sure she hadn't changed her mind.\n\nMeanwhile, Kathy's outlook was evolving. As Zachary grew, she began to feel guilty. She would take him to the park and watch the other boys playing with their fathers, and she began to wonder if she was being selfish. _A boy needs a dad_ , she thought. Was it unfair to dismiss the possibility of a father figure in Zachary's life? Not that she was ready to act on these notions, but there was a slow thaw occurring within her. As the years went by, as Zachary turned three and then four, she grew more open to the idea of someone new.\n\n* * *\n\nKathy called Zeitoun in the early afternoon.\n\n\"Let's wait and see,\" he said.\n\n\"That isn't why I'm calling,\" she said.\n\nA client on the West Bank wanted a bathroom repainted.\n\n\"Really? We just finished that one,\" he said.\n\n\"She doesn't like how it looks.\"\n\n\"I told her that color was wrong. Tangerine.\"\n\n\"Well, now she agrees with you.\"\n\n\"I'll go now,\" he said.\n\n\"Don't rush,\" she said.\n\n\"Well, make up your mind.\"\n\n\"I just don't want you driving fast,\" she said. Kathy worried about his driving, especially when there were people worried about a coming storm. She knew Zeitoun considered himself a good driver, but when they rode together she was a jumble of nerves.\n\n\"Kathy, please\u2014\" he started.\n\n\"I just get scared when you drive!\"\n\n\"I ask you,\" he said, beginning what Kathy knew was one of his frequent thought experiments. \"Let's say the average person drives maybe two hours a day, every day, and that person gets, on average, two tickets a year. I drive maybe _six_ hours _each day_. How many tickets should I have? This is what I ask.\"\n\n\"I'm just saying, I personally get scared.\"\n\n\"I get only two, three tickets a _year_ , Kathy! I knew this man, a cab driver in New York for thirty years. No license, and this man\u2014\"\n\nKathy didn't want to hear about the man in New York. \"I'm just saying...\"\n\n\"Kathy. Kathy. In Syria we have a saying, 'The crazy person talks, the wise person listens.'\"\n\n\"But you're the one talking.\"\n\nZeitoun had to laugh. She always got the best of him.\n\n\"I'll call you later,\" she said.\n\nZeitoun headed to the West Bank to get a look at the tangerine bathroom. He tried to be amused by the fickle nature of clients' tastes; it was part of the job, and if he got exasperated every time someone changed their mind, he'd never survive. The upshot was that it ensured no day was dull. The intensely personal nature of his business, the subjectivity of taste, the variables of light and curtains and carpets, guaranteed that minds would reevaluate and work would have to be redone.\n\nStill, the most unusual requests often came from the most normal-seeming people. One customer, a Southern belle in her sixties, had called Zeitoun Painting and had been happy to talk with Kathy, with her chatty demeanor and familiar accent. But when the painters showed up to begin work on the exterior of her home, the woman immediately called Kathy.\n\n\"I don't like these men,\" she said.\n\n\"What's wrong with 'em?\" Kathy asked.\n\n\"They're swarthy,\" she said. \"I only want white people working on my house.\" She said it like she was choosing a kind of dressing for her salad.\n\n\"White people?\" Kathy laughed. \"Sorry, we're fresh out of those.\"\n\nShe convinced the woman that the men who had been sent\u2014all of them Latino, in this case\u2014were skilled professionals who would do an excellent job. The woman assented, but continued to call. \"He's too short to be a painter,\" she said about one worker, Hector, who was over six feet tall. Realizing that no matter how much she complained, she would not be able to replace these painters with taller, Caucasian ones, the Southern belle resigned herself to watching the men, checking on them frequently.\n\nOf course, every so often, would-be clients could not get past Zeitoun's last name. They would call for an estimate and ask Kathy, \"Zeitoun, where's that name come from? Where is he from?\" And Kathy would say, \"Oh, he's Syrian.\" Then, after a long pause or a shorter one, they would say, \"Oh, okay, never mind.\" It was rare, but not rare enough.\n\nKathy sometimes told Zeitoun about such incidents, sometimes not, and never at dinner. Usually he just laughed it off, but occasionally it got under his skin. His frustration with some Americans was like that of a disappointed parent. He was so content in this country, so impressed with and loving of its opportunities, but then why, sometimes, did Americans fall short of their best selves? If you got him started on the subject, it was the end of any pleasant meal. He would begin with a defense of Muslims in America and expand his thesis from there. Since the attacks in New York, he would say, every time a crime was committed by a Muslim, that person's faith was mentioned, regardless of its relevance. When a crime is committed by a Christian, do they mention his religion? If a Christian is stopped at the airport for trying to bring a gun on a plane, is the Western world notified that a Christian was arrested today and is being questioned? And what about African Americans? When a crime is committed by a black man, it's mentioned in the first breath: \"An African American man was arrested today...\" But what about German Americans? Anglo Americans? A white man robs a convenience store and do we hear he's of Scottish descent? In no other instance is the ancestry mentioned.\n\nThen Zeitoun would quote the Qur'an.\n\n_Be one who is staunch in equity,  \nwitnesses for God  \neven against yourselves  \nor ones who are your parents or nearest of kin;  \nwhether rich or poor,  \nfor God is closer to both than you are;  \nso follow not your desires  \nthat you become unbalanced;  \nand if you distort or turn aside,  \nthen truly God is aware of what you do_.\n\nKathy was astonished at how well he knew the book, and how quickly he could quote a passage appropriate for any occasion. Still, though, these monologues at dinner? It was good for the kids to have some awareness of such prejudices, but to see Zeitoun disappointed, to get him so worked up after a long day\u2014it wasn't worth it. In the end, though, Zeitoun could laugh this kind of thing off, but the one thing he could not abide was a client raising their voice to Kathy.\n\nThere had been one client, a young woman married to a doctor. She was thin, pretty, immaculately put together. She had not set off any alarm bells when Zeitoun had provided an estimate and begun work on painting her stairway and guest bedroom. She told him that she and her husband were expecting houseguests, and she wanted the stairway and guest room painted in five days' time. Zeitoun said the timetable would be tight, but would present no problems on his end. She was thrilled. No other painter had been able to commit to such a deadline.\n\nZeitoun sent a crew of three over the next day. The client, seeing the quick and efficient work Zeitoun's team was doing, asked him if they could paint her husband's office and her daughter's bedroom, too. He said they could. He sent more painters to the house, and she continued to add rooms and jobs\u2014including re-tiling and painting a bathroom\u2014and Zeitoun's men continued to execute the work quickly.\n\nBut not quickly enough. On the third day, Kathy phoned Zeitoun, near tears. The woman had called Kathy four times in rapid succession, cursing and carrying on. The house wasn't ready, the client had screamed, and her guests were coming in less than two days. Kathy had told her that Zeitoun's crew had finished the original work on the guest room in plenty of time. But this wasn't what the client wanted. She wanted everything\u2014all seven rooms and their myriad tasks\u2014done in five days. She wanted three times the work done in the same amount of time.\n\nKathy had tried to reason with her. She and Zeitoun had never promised that he could finish all of the additional work in five days. That schedule was irrational; no one, not even Zeitoun A. Painting Contractor LLC, could complete the work on that timetable. But the client was beyond reason. She barked at Kathy, hanging up, calling again, hanging up. She was loud, condescending, and cruel.\n\nKathy, in tears, reached Zeitoun on his cell phone while he was driving to a job on the other side of the city. Even before they hung up, he had turned his truck around and was barreling to the client's house as fast as was legal. When he got there, he walked calmly into the house and told his crew they were leaving. In the space of ten minutes, they packed their paint, ladders, brushes, and tarps, and loaded them into the bed of Zeitoun's truck.\n\nAs Zeitoun was backing out, the client's husband ran out to the truck. What's wrong? he asked. What happened? Zeitoun was so angry he could barely think of the words in English. It was better, in fact, that he did not speak. He waited a few seconds to say only that no one talked that way to his wife, that he was leaving the job, that this was over and good luck.\n\nWhen he arrived at the tangerine-bathroom house, he called Kathy to run through the prices for the materials they'd need. Looking around the orange room\u2014it really was difficult to look at\u2014he noted the clients' new tub, a huge claw-footed antique.\n\n\"It's big, but isn't it beautiful?\" Kathy asked.\n\n\"Yes, like you!\" he joked.\n\n\"Watch it,\" she said. \"I can lose this weight, but you're never growing that hair back.\"\n\nWhen they'd met, Kathy had been weight-obsessed, and was far too thin. She had been chubby as a child, at least to some eyes, and in her teens her weight fluctuated wildly. She binged and dieted and then cycled through it all again. When she and Zeitoun were married, he insisted that she get beyond the weight issues and eat like a normal person. She did, and now joked that she'd gone too far. \"Thank God for the abaya,\" she told friends. When she didn't want to bother worrying about clothes or how they looked on her, the shoulder-to-floor Islamic dress solved the problem, and tidily.\n\nThere was a knock on the door. Kathy went to answer it and found Melvin, a Guatemalan painter. He was looking to get paid before the weekend.\n\nZeitoun was relentless in his efforts to pay the workers well and promptly. He always quoted the Prophet Muhammad: \"Pay the laborer his wages before his sweat dries.\" Zeitoun used that as a bedrock and constant guide in the way he and Kathy did business, and the workers took note.\n\nStill, Zeitoun preferred to pay on Sundays or Mondays\u2014because when he paid on Fridays, too many of the workers would disappear all weekend. But Kathy's heart was soft, her resolve to withhold payment even an hour weakened in the presence of these workers soaked with sweat, knuckles bleeding, forearms yellow with sawdust.\n\n\"Don't tell Zeitoun,\" she said, and wrote him a check.\n\nKathy turned on the TV and flipped through the channels. Every station was covering the storm.\n\nNothing had changed: Katrina was still headed their way, and it was losing no power. And because the hurricane as a whole was traveling so slowly, about eight miles per hour, the sustained winds were causing, and would continue to cause, catastrophic damage.\n\nThe coverage was just background noise, though, until Kathy caught the words \"family of five.\" They were talking about the family lost at sea. _Oh no_ , she thought. _Please_. She turned up the sound. They were still missing. The father's name was Ed Larsen. He was a construction supervisor. _You're kidding me_ , she thought. He had taken the week off to take his family sailing on his yacht, the _Sea Note_. They had been at Marathon and were sailing back to Cape Coral when they'd lost radio contact. His wife and three kids were with him. They were on their way back to shore for a family reunion. The extended family had gathered only to realize that the Larsens were missing; the celebration turned into a vigil of worry and prayer.\n\nKathy couldn't stand it.\n\nShe called her husband. \"We have to go.\"\n\n\"Wait, wait,\" he said. \"Let's wait and see.\"\n\n\"Please,\" she said.\n\n\"Really?\" he said. \"You can go.\"\n\n* * *\n\nKathy had taken the kids north a handful of times when storms had gotten close. But she was hoping she wouldn't have to make the trip this time. She had work to do over the weekend, and the kids had plans, and she always came back from those trips more exhausted than when she'd left.\n\nAlmost without exception, whether it was fleeing a storm or for a weekend vacation, Kathy and the kids had to go without Zeitoun. Her husband had trouble leaving the business, had trouble relaxing for days on end, and after years of this vacationless life Kathy had threatened to pack the kids and just leave for Florida some Friday after school. At first Zeitoun hadn't believed her. Would she really pack up and leave with or without him?\n\nShe would, and she did. One Friday afternoon, Zeitoun was checking on a nearby job and decided to stop at home. He wanted to see the kids, change his shirt, pick up some paperwork. But when he pulled into the driveway, there was Kathy, loading up the minivan, the two youngest already buckled inside.\n\n\"Where you going?\" he asked.\n\n\"I told you I'd go with or without you. And we're going.\"\n\nThey were going to Destin, Florida, a beach town on the Gulf about four hours away, with long white beaches and clear water.\n\n\"Come with us, Daddy!\" Nademah pleaded. She had just come out of the house with their snorkeling gear.\n\nZeitoun was too stunned to react. He had a hundred things on his mind, and a pipe at one of the rental properties had just burst. How could he go?\n\nNademah got in the front seat and put on her seatbelt.\n\n\"Bye bye,\" Kathy said, backing out. \"See you Sunday.\"\n\nAnd they were gone, the girls waving as they left.\n\nHe didn't go that Friday, but after that, he no longer doubted Kathy's resolve. He knew she was serious\u2014that in the future he'd be consulted on vacation plans, but that trips to Florida or beyond could and would happen with or without him. So over the years there were other trips to Destin, and he even made it on a few of them.\n\nBut always his decision was made at the last minute. One time Kathy was late in getting started, and he was so late in deciding that he couldn't even pack. She was in the driveway, backing out, when he pulled in.\n\n\"Now or never,\" she said, barely stopping the car.\n\nAnd so he jumped in the car. The girls giggled to see their dad in the back seat, still in his work clothes, dirty and sweating\u2014as much from the stress of the decision as from the day's work. Zeitoun had to buy beach clothes when they got to Florida.\n\nKathy was proud that she'd gotten him to Destin once a year. Zeitoun didn't mind going too much because, given how close it was, he knew he could come back at any time\u2014and more than once, he had cut a vacation short because of some problem at one of the work sites.\n\nBy 2002, though, Kathy wanted something that really felt like a vacation. And she knew she had to do something drastic. In all their time together\u2014eight years at that point\u2014he had never taken more than two days off in a row. She knew that she had no choice but to kidnap him.\n\nShe started by planning a weekend in Destin. She chose a weekend when she knew things would be calm at work; it was just after Christmas, and there was rarely much work till well after New Year's. As usual, Zeitoun wouldn't commit till the last minute, so she took the precaution of actually packing a bag for him and hiding it in the back of the minivan. Because she had made sure the weekend was quiet, he came along\u2014as always, at the last minute. Kathy told him she'd drive, and because he was exhausted, he agreed. She made sure the kids were quiet\u2014they were in on the plan\u2014and he soon fell asleep, drooling on his seatbelt. While he slept, Kathy drove right on through Destin and onward down the paunch of Florida. Each time he woke up she would say, \"Almost there, go back to sleep,\" and thankfully he would\u2014he was so tired\u2014and it wasn't until an hour north of Miami that he realized they weren't going to Destin. Kathy had driven straight down to Miami. Seventeen hours. She'd checked on the computer for the warmest place in the country that week, and Miami was it. Being that far away was the only way to ensure he would take a real vacation, a full week's worth of rest. Every time she thought back on the gambit, and how well it had worked, Kathy smiled to herself. A marriage was a system like any other, and she knew how to work it.\n\nAt about two-thirty, Ahmad called Zeitoun again. He was still tracking the storm from his computer in Spain.\n\n\"Doesn't look good for you,\" he said.\n\nZeitoun promised he would keep watch on it.\n\n\"Imagine the storm surge,\" Ahmad said.\n\nZeitoun told him he was paying close attention.\n\n\"Why not leave, just to be safe?\" Ahmad said.\n\nKathy decided to go to the grocery store before picking up the girls from school. You could never tell when people would make a run on the basics before a storm arrived, and she wanted to avoid the crush.\n\nShe went to the mirror to adjust her hijab, brushed her teeth, and left the house. Not that she thought about it much, but any trip to the grocery store or the mall presented the possibility that she would encounter some kind of ugliness. The frequency of incidents seemed tied, to some extent, to current events, to the general media profile of Muslims that week or month. Certainly after 9\/11 it was more fraught than before, and then it had calmed for a few years. But in 2004 a local incident had stoked the fire again. At West Jefferson High School, a tenth grader of Iraqi descent had been repeatedly harassed by her history teacher. He had called Iraq a \"third-world country,\" had worried that the student would \"bomb us\" if she ever returned to Iraq. In February of that year, while passing out tests, the teacher had pulled back the girl's hijab and said, \"I hope God punishes you. No, I'm sorry, I hope Allah punishes you.\" The incident was widely reported. The student filed a lawsuit against him, and his termination was recommended by the Jefferson Parish School District superintendent. The school board overruled; he was given a few weeks' suspension and returned to the classroom.\n\nAfter the decision, there had been an uptick in minor harassment of Muslims in the area, and Kathy was aware of the invitation she was providing in going out in her hijab. There was a new practice in vogue at the time, favored by adolescent boys or those who thought like them: sneak up behind a woman wearing a headscarf, grab it, and run.\n\nOne day it happened to Kathy. She was shopping with Asma, a friend who happened to be Muslim but who wore no hijab. Asma was originally from Algeria, and had been living in the U.S. for twenty years; she was usually taken for Spanish. Kathy and Asma were leaving the mall, and outside, Kathy was trying to remember where she'd parked her car. She and Asma were on the sidewalk, Kathy squinting at the rows of gleaming cars, when Asma gave her a funny look.\n\n\"Kathy, there's a girl behind you\u2014\"\n\nA girl of about fifteen was crouched behind Kathy, her arm raised, about to yank the hijab off Kathy's head.\n\nKathy cocked her head. \"You got a problem?\" she barked.\n\nThe girl cowered and slunk away, joining a group of boys and girls her age, all of whom had been watching. Once back with her friends, the girl directed some choice words Kathy's way. Her friends laughed and echoed her, cursing at Kathy in half a dozen different ways.\n\nThey could not have expected Kathy to return the favor. They assumed, no doubt, that a Muslim woman, presumably submissive and shy with her English, would allow her hijab to be ripped from her head without retaliation. But Kathy let loose a fusillade of pungent suggestions, leaving them dumbfounded and momentarily speechless.\n\nOn the drive home, even Kathy was shocked by what she'd said. She had been brought up around plenty of cursing, and knew every word and provocative construction, but since she'd become a mother, since she'd converted, she hadn't sworn more than once or twice. But those kids needed to learn something, and so she'd obliged.\n\nIn the weeks after the attacks on the Twin Towers, Kathy saw very few Muslim women in public. She was certain they were hiding, leaving home only when necessary. In late September, she was in Walgreens when she finally saw a woman in a hijab. She ran to her. _\"Salaam alaikum!\"_ she said, taking the woman's hands. The woman, a doctor studying at Tulane, had been feeling the same way, like an exile in her own country, and they laughed at how delirious they were to see each other.\n\n* * *\n\nOn this day in August, the grocery-store trip went off without confrontation, and she picked up her girls.\n\n\"You hear about the storm?\" Nademah asked.\n\n\"It's coming toward us,\" Safiya added from the back seat.\n\n\"Are we going to leave?\" Nademah asked.\n\nKathy knew that her kids wanted to. They could go to one of their cousins' homes, in Mississippi or Baton Rouge, and it would be a vacation, a two-day sleepover. Maybe school would be canceled on Monday as the city cleaned up? This was surely what they were thinking and hoping. Kathy knew the workings of her children's minds.\n\nWhen they got home, it was five o'clock and Katrina was all over the news. The family watched footage of enormous waves, uprooted trees, whole towns washed grey with torrential rain. The National Hurricane Center was suggesting that Katrina would soon become a Category 3. Governor Blanco held a press conference to declare a state of emergency for Louisiana. Governor Barbour did the same for Mississippi.\n\nKathy was rattled. Sitting on the arm of the couch, she was so distracted that soon it was six o'clock and she hadn't started dinner. She called Zeitoun.\n\n\"Can you get Popeyes on your way home?\" she asked.\n\nAt home, Nademah arranged the tablecloth and placemats. Safiya and Aisha set out the silverware and glasses. Kathy threw together a salad and poured milk for the kids and juice for herself and Zeitoun.\n\nZeitoun arrived with the chicken, showered, and joined the family for dinner.\n\n\"Finish, finish,\" he said to his daughters, who were picking at their food, leaving huge swaths of it uneaten.\n\nHe had gotten used to it after all these years, but still, there were times when the waste got to him. The disposability of just about everything. Growing up in Syria he had often heard the expression \"If your hand doesn't work for it, your heart doesn't feel sorry for it.\" But in the U.S., it wasn't just the prosperity\u2014because New Orleans was not uniformly prosperous, to be sure\u2014there was a sense that everything could be replaced, and on a whim. In his children he was trying to instill a sense of the value of work, the value of whatever came into their house, but he knew that much would be lost in the context, the waste and excess of the culture at large. He had been brought up to know that what God hates as much as anything is waste. It was, he had been told, one of the three things God _most_ hated: murder, divorce, and waste. It destroyed a society.\n\nAfter dinner the girls asked if they could watch _Pride and Prejudice_ again. It was Friday night, so Zeitoun had no school-related reasons to block the movie. Still, it didn't mean he had to sit and watch it again. He'd liked the movie fine the first time, but the need to watch it a dozen times in as many days was beyond him. In the past week, he and Zachary had retired to other rooms to do something, anything, else. Kathy, though, was right there with the girls each time, and this time all of them draped over each other on the couch, misting up at the same parts they always did. Zeitoun shook his head and went into the kitchen to fix a cabinet door that had gotten loose.\n\nAll evening they paused the movie to watch the news reports about the storm's intensity and direction. Still moving slowly, the hurricane was heading up the coast with winds over one hundred miles per hour. The longer it lingered over any region, the more destruction it would bring. All the news was terrible, and when Kathy saw the picture of the family of five she was ready to turn it off. She was sure they were gone, and she would obsess over this family for weeks, thinking about all their relatives gathered for the reunion, now forced to mourn the loss of so many at once\u2014but then Kathy realized that the family was not lost. She turned up the volume. They had been rescued. They had docked their boat on a mangrove island near Ten Thousand Islands, and had ridden out the storm in the cabin of the yacht, praying and taking turns climbing up to look for help in the skies. Just hours earlier, the Coast Guard had spotted their boat and lifted them all to safety. The family of five had been saved.\n\nLater, after kissing Zachary goodnight, Kathy lay down in Nademah's bed and the girls arranged themselves around her, a mess of overlapping limbs and pillows.\n\n\"Who wants to start?\" Kathy asked.\n\nSafiya began a story about Pok\u00e9mon. The stories, which the girls told collaboratively, were often about Pok\u00e9mon. After Aisha introduced the protagonist, Safiya provided the setting and central conflict, and Nademah took it from there. They continued, taking turns advancing the plot, until Aisha was asleep and Nademah and Safiya were drifting off. Kathy looked up to find Zeitoun in the doorway, leaning against the frame, watching them all. He did this often, just watching, taking it all in. The scene was almost too much, too beautiful. It was enough to burst a man's heart wide open.\n\n# SATURDAY AUGUST 27\n\nZeitoun and Kathy woke late, after eight. When they turned on the TV they saw Michael Brown, director of the Federal Emergency Management Agency, telling all residents of New Orleans to leave as soon as they could, to head inland with all possible haste. The National Hurricane Center had issued a watch for central Louisiana and warned that the hurricane could become a Category 5 by the time it made landfall. Category 5 hurricanes had only struck the United States mainland three times before, and never New Orleans.\n\n\"Honey,\" Kathy said, \"I think we should go.\"\n\n\"You go,\" Zeitoun said. \"I'll stay.\"\n\n\"How can you stay?\" she asked.\n\nBut she knew the answer. Their business wasn't a simple one, where you could lock an office door and leave. Leaving the city meant leaving all their properties, leaving their tenants' homes, and this they couldn't do unless absolutely necessary. They had job sites all over the city, and any number of things could happen in their absence. They would be liable for damage if their equipment caused harm to clients' property. It was yet another hazard of the company they'd built.\n\nKathy was leaning strongly toward fleeing, and watching the news throughout the day it seemed that there were so many new indicators that this storm was unique that she didn't feel she could even contemplate staying in the city. They'd already closed down most operations at Louis Armstrong International Airport. The Louisiana National Guard had called four thousand troops into service.\n\nMid-morning, it was at least ninety-five degrees, the air leaden with humidity. Zeitoun was in the backyard, running around with the kids and Mekay, the dog. Kathy opened the back door.\n\n\"You're really staying?\" Kathy asked him. Somehow she thought that he might be wavering. She was wrong.\n\n\"What're you worried about?\" he said.\n\nShe wasn't worried, in fact. She didn't fear for her husband's safety, really, but she did have the feeling that life in the city would be very trying during and after the storm. The electricity would go. The roads would be covered with debris, impassable for days. Why would he want to struggle through all that?\n\n\"I have to watch the house,\" he said. \"The other houses. One small hole in the roof\u2014if I fix it, no damage. If not, the whole house is wrecked.\"\n\nBy the early afternoon Mayor Nagin and Governor Blanco had called for a voluntary evacuation of the city. Nagin told residents that the Superdome would be open as a \"shelter of last resort.\" Kathy shuddered at the thought; the year before, with Hurricane Ivan, that plan had been a miserable failure. The Superdome had been ill-supplied and overcrowded then and in '98, with Hurricane Georges. She couldn't believe the place was being used again. Maybe they'd learned from the last time and better provisioned the stadium? Anything was possible, but she was doubtful.\n\nKathy planned to leave as soon as the contraflow took effect, supposedly around four o'clock. The contraflow would allow all lanes of every highway to flow outward from the city. By then Kathy would have the Odyssey packed and ready in the driveway.\n\nBut where would she be going? She knew well that every hotel within two hundred miles would be booked already. So it was a matter of deciding which family member she'd impose on. She had thought first of her sister Ann, who lived in Poplarville, Mississippi. But when she called, Ann was considering leaving, too. Her home was technically within the area that would be affected by the high winds, and it was surrounded by old trees. Given the likelihood that one of them might fall through her roof, Ann wasn't sure she should stay there herself, let alone with Kathy and her kids.\n\nThe next option was the family headquarters in Baton Rouge. Owned by her brother Andy, it was a three-bedroom ranch in a subdivision outside the city. Andy traveled frequently and was currently in Hong Kong, working on a construction project. While he'd been gone, two of Kathy's sisters, Patty and Mary Ann, had moved in.\n\nKathy knew they would allow her family to stay, but it would be cramped. The house wasn't so big to begin with, and Patty had four kids of her own. With Kathy's family there, all told there would be eight kids and three sisters living together in a house that would likely lose electricity in the high winds.\n\nStill, it had been some time since the families had gotten together. This might bring them closer. They could all eat out, maybe go shopping in Baton Rouge. Kathy knew her kids would endorse the plan. Patty's kids were older, but they got along well with the Zeitouns, and anyway, eight kids always found something to do together. It would be cramped and loud, but Kathy found herself looking forward to it.\n\nThroughout the afternoon, Kathy tried to convince her husband to come with them. When had officials suggested an all-city evacuation before? she asked. Wasn't that reason enough to go?\n\nZeitoun agreed that it was unusual, but he had never evacuated before and he saw no need to do so now. Their home was elevated three feet above the ground, and rose two stories on top of that, so there would be no danger of getting stuck in an attic or on a roof, even if the worst happened. Zeitoun could always retreat to the second floor. And they lived nowhere near any levees, so they wouldn't get any of the flash flooding that might hit some of the other neighborhoods. It was East New Orleans, or the Lower Ninth, with its one-story houses so close to the levees, that were in the gravest danger.\n\nAnd he certainly couldn't leave before he secured all his job sites. No one else would do it, and he wouldn't ask anyone else to do it. He'd already told his workers and his foremen to leave, to be with their families, to get a head start on the traffic. He planned to go to every one of the nine job sites to gather or tie down his equipment. He had seen what happened when a contractor failed to do this: ladders careening through windows and walls, tools damaging furniture, paint all over the lawn and driveway.\n\n\"I better go,\" he said.\n\nHe set out, visiting the work sites, tying down ladders, packing up tools, brushes, loose tiles, Sheetrock. He was through about half the sites when he headed home to say goodbye to Kathy and the kids.\n\nKathy was loading up a few small bags in the back of the Odyssey. She had packed enough clothes, toiletries, and food for two days. They would return on Monday night, she figured, after the storm had come and gone.\n\nKathy had the minivan's radio on and heard Mayor Nagin repeat his instructions for residents to leave the city, but she noted that he had stopped short of a mandatory evacuation. This would embolden her husband, she was certain. She switched to another station, where they were issuing a warning that anyone who planned to ride out the storm in New Orleans should be prepared for a flood. Levee breaches could happen, they said. Storm surges might cause flooding. Ten or fifteen feet of water would be a possibility. Any diehards staying home should have an axe, in case they needed to chop through their attic to reach the roof.\n\nZeitoun pulled up and parked the van on the street in front of the house. Kathy watched him approach. She never doubted his ability to care for himself in any situation, but now her heart was jumping. She was leaving him to fend for himself, leaving him to chop holes in the attic with an axe? It was insane.\n\nHe and Kathy stood in the driveway, as they had many other times when she and the family were leaving and he was staying.\n\n\"Better hurry,\" Zeitoun said. \"Lot of people leaving at once.\"\n\nKathy looked at him. Her eyes, much to her own frustration, teared up. Zeitoun held her hands.\n\n\"C'mon, c'mon,\" he said. \"Nothing's going to happen. People are making a big deal for no reason.\"\n\n\"Bye, Daddy!\" Aisha sang from the back seat.\n\nThe kids waved. They always waved, all of his children, as he stood on the driveway. None of this was new. A dozen times they had lived this moment, as Kathy and his children drove off in search of sanctuary or rest, leaving Zeitoun to watch over his house and the houses of his neighbors and clients all over the city. He had keys to dozens of other houses; everyone trusted him with their homes and everything in them.\n\n\"See you Monday,\" he said.\n\nKathy drove away, knowing they were all mad. Living in a city like this was madness, fleeing it was madness, leaving her husband alone in a home in the path of a hurricane was madness.\n\nShe waved, her children waved, and Zeitoun stood in the driveway waving until his family was gone.\n\n* * *\n\nZeitoun set out to finish securing the rest of his job sites. The air was breezy, the low sky smudged brown and grey. The city was chaotic, thousands of cars on the road. Traffic was worse than he expected. Brake lights and honking, cars running red lights. He took streets that no one fleeing would use.\n\nDowntown, hundreds of people were walking to the Superdome carrying coolers, blankets, suitcases. Zeitoun was surprised. Previous experiments using the stadium as shelter had failed. As a builder, he worried about the integrity of the stadium's roof. Could it really withstand high winds, torrential rain? You couldn't pay him enough to hide there from the storm.\n\nAnd anyway, in the past it had been little more than a few hours of squealing winds, some downed trees, a foot or two of water, some minor damage to fix once the winds had passed.\n\nHe already felt good. New Orleans would soon be largely vacated, and being in the empty city always felt good, at least for a day or two. He continued to make his rounds, secured the last few sites, and arrived home just before six.\n\nKathy called at six-thirty.\n\nShe was stuck in traffic a few miles outside the city. Worse, between her own confusion and the unprecedented volume of cars, she had gone the wrong way. Instead of taking the I-10 west directly to Baton Rouge, she was on I-10 heading east, with no way to correct her error. She would have to cross Lake Pontchartrain and swing all the way back through Slidell and across the state. It was going to add hours. She was harried and exhausted and the trip had barely begun.\n\nZeitoun was sitting at home, his feet up on the table, watching TV. He made a point of telling her so.\n\n\"Told you so,\" he said.\n\nKathy and the kids were expected at her brother's house for dinner, but at seven o'clock she'd traveled less than twenty miles. Just short of Slidell, she pulled into a Burger King drive-through. She and the kids ordered cheeseburgers and fries and got back onto the road. A little while later, a foul odor overtook the Odyssey.\n\n\"What is that?\" Kathy asked her kids. They giggled. The smell was fecal, putrid. \"What _is_ that?\" she asked again. This time the girls couldn't breathe they were laughing so hard. Zachary shook his head.\n\n\"It's Mekay,\" one of the girls managed, before collapsing again into hysterics.\n\nThe girls had been sneaking the dog pieces of their cheeseburgers, and the cheese was clogging her pipes. She'd been farting for miles.\n\n\"That is awful!\" Kathy wailed. The kids giggled more. Mekay continued to suffer. She was hiding under the seat.\n\nThey passed Slidell and soon met up with I-190, a smaller road Kathy figured would have less traffic. But it was just as bad, an endless stream of brake lights. Ten thousand cars, twenty thousand lights, she guessed, extending all the way to Baton Rouge or beyond. She had become part of the exodus without entirely registering the enormity and strangeness of it. A hundred thousand people on the road, all going north and east, fleeing winds and water. Kathy could only think of beds. Where would all these people sleep? A hundred thousand beds. Every time she passed a driveway she looked at the home longingly. She was so tired, and not even halfway there.\n\nShe thought again of her husband. The images she'd seen on the news were absurd, really\u2014the storm looked like a white circular saw heading directly for New Orleans. On those satellite images the city looked so small compared to the hurricane, such a tiny thing about to be cut to pieces by that gigantic spinning blade. And her husband was just a man alone in a wooden house.\n\nZeitoun called again at eight o'clock. Kathy and the kids had been on the road for three hours and had only gotten as far as Covington\u2014about fifty miles. Meanwhile, he was watching television, puttering around the house, enjoying the cool night.\n\n\"You should have stayed,\" he said. \"It's so nice here.\"\n\n\"We'll see, smart guy,\" she said.\n\nThough she was exhausted, and was being driven near-crazy by her flatulent dog, Kathy was looking forward to a few days in Baton Rouge. At certain moments, at least, she was looking forward to it. Her family was not easy to deal with, this was certain, and any visit could take a wrong turn quickly and irreparably. _It's complicated_ , she would tell people. With eight siblings, it had been turbulent growing up, and when she converted to Islam, the battles and misunderstandings multiplied.\n\nIt often started with her hijab. She'd come in, drop her bags, and the suggestion would come: \"Now you can take that thing off.\" She'd been a Muslim for fifteen years and they still said this to her. As if the scarf was something worn under duress, only in the company of Zeitoun, a disguise she could shed when he was not around. As if only in the Delphine household could she finally be herself, let loose. This was actually the command her mother had given the last time Kathy had visited: \"Take that thing off your head,\" she'd said. \"Go out and have a good time.\"\n\n* * *\n\nThere were times, however, when her mother's loyalty to Kathy trumped her issues with Islam. Years earlier, Kathy and her mother had gone to the DMV together to have Kathy's license renewed. Kathy was wearing her hijab, and had already received a healthy number of suspicious looks from DMV customers and staff by the time she sat down to have her picture taken. The employee behind the camera did not disguise her contempt.\n\n\"Take that thing off,\" the woman said.\n\nKathy knew that it was her right to wear the scarf for the photo, but she didn't want to make an issue of it.\n\n\"Do you have a brush?\" Kathy asked. She tried to make a joke of it: \"I don't want to have my hair all matted for the photo.\" Kathy was smiling, but the woman only stared, unblinking. \"Really,\" Kathy continued, \"I'm okay with taking it off, but only if you have a brush...\"\n\nThat's when her mother jumped to the rescue\u2014in her way.\n\n\"She can wear it!\" her mother yelled. \"She can if she wants to!\"\n\nNow it was a scene. Everyone in the DMV was watching. Kathy tried to diffuse the situation. \"Mama, it's okay,\" she said. \"Really, it's okay. Mama, do you have a brush?\"\n\nHer mother barely registered Kathy's question. She was focused on the woman behind the camera. \"You can't make her take it off! It's her constitutional right!\"\n\nFinally the DMV woman disappeared into the back of the office. She returned with permission from a superior to take the photo with Kathy wearing her scarf. As the flash went off, Kathy tried to smile.\n\nGrowing up in Baton Rouge, it was a crowded house, full of clamor and extremes. Nine kids shared a one-story, 1,400-square-foot home, sleeping three to a room and squabbling over one bathroom. They were content, though, or as content as could be expected, and the neighborhood was tidy, working-class, full of families. Kathy's house backed up against Sherwood Middle School, a big multiethnic campus where Kathy felt overwhelmed. She was one of a handful of white students, and she was picked on, pushed around, gawked at. She grew to be quick to fight, quick to argue.\n\nShe must have run away from home a dozen times, maybe more. And almost every time she did, from age six or so on, she ran to her friend Yuko's house. It was just a few blocks away, on the other side of the high school, and given that she and Yuko were among the few non\u2013African American kids in the neighborhood, they had bonded as outsiders. Yuko and her mother Kameko were alone in their house; Kameko's husband had been killed by a drunk driver when Yuko was small. Even though Yuko was three years older, she and Kathy grew inseparable, and Kameko was so welcoming and dedicated to Kathy's well-being that Kathy came to call her Mom.\n\nKathy was never sure why Kameko took her in, but she was careful not to question it. Yuko joked that her mom just wanted to get close enough to Kathy to bathe her. As a kid Kathy didn't like baths much, and they weren't a great priority in her house, so every time she was at Yuko's, Kameko filled the tub. \"She looks greasy,\" Kameko would joke to Yuko, but she loved to make Kathy clean, and Kathy looked forward to it\u2014Kameko's hands washing her hair, her long fingernails tickling her neck, the warmth of a fresh, heavy towel around her shoulders.\n\nAfter high school Kathy and Yuko grew closer. Kathy moved into an apartment off Airline Highway in Baton Rouge, and they began working together at Dunkin' Donuts. The independence meant everything to Kathy. Even in her small apartment off a six-lane interstate, there was a sense of order and quiet to her life that she had never known.\n\nA pair of Malaysian sisters used to come into the shop, and Yuko began talking to them, questioning them. \"What does that scarf mean?\" \"What do you see in Islam?\" \"Are you allowed to drive?\" The sisters were open, low-key, never proselytizing. Kathy had no real inkling that they had made a great impression on Yuko, but Yuko was captivated. She began reading about Islam, investigating the Qur'an. Soon the Malaysian sisters brought Yuko pamphlets and books, and Yuko delved deeper.\n\nWhen she caught on to how serious Yuko was about it, it drove Kathy to distraction. They'd both been brought up Christian, had gone to a rigorous Christian elementary school. It was baffling to see her friend dabbling in this exotic faith. Yuko had been as devout a Christian as walked the Earth\u2014and Kameko was even more so.\n\n\"What would your mom think?\" she asked.\n\n\"Just keep an open mind,\" Yuko said. \"Please.\"\n\nA few years passed, and Kathy, through a series of missteps and heartbreaks, was divorced and living alone with Zachary, who was less than a year old. She was renting the same apartment off Airline Highway and working two jobs. In the mornings she was a checkout clerk at K&B, a chain drugstore on the highway. One day the manager of Webster Clothes, a menswear store across the road, had come into the drugstore and, admiring Kathy's ebullient personality, asked her if she'd be willing to quit K&B or, if not, take a second job at Webster. Kathy needed the money, so she said yes to the second job. After finishing in the early afternoon at K&B, she would walk across the highway to Webster and work there until closing. Soon she was working fifty hours a week and making enough to cover health insurance for herself and Zachary.\n\nBut her life was a struggle, and she was looking for some order and answers. Yuko, by contrast, seemed peaceful and confident; she'd always been centered, so much so that Kathy had been envious, but now Yuko really seemed to have things figured out.\n\nKathy began borrowing books about Islam. She was just curious, having no particular intention to leave the Christian faith. At first she was simply intrigued by the basic things she didn't know, and the many things she'd wrongly presumed. She had no idea, for instance, that the Qur'an was filled with the same people as the Bible\u2014Moses, Mary, Abraham, Pharaoh, even Jesus. She hadn't known that Muslims consider the Qur'an the fourth book of God to His messengers, after the Old Testament (referred to as the _Tawrat_ , or the Law), the Psalms (the _Zabur)_ , and the New Testament _(Injeil)_. The fact that Islam acknowledged these books was revelatory for her. The fact that the Qur'an repeatedly reaches out to the other, related faiths, knocked her flat:\n\n_We have believed in God  \nand what has been sent forth to us,  \nand what was sent forth to Abraham,  \nIshmael, Isaac, Jacob,  \nand the Tribes  \nand what was given the Prophets  \nfrom their Lord;  \nwe separate and divide not  \nbetween any one of them;  \nand we are the ones who submit to Him_.\n\nShe was frustrated that she hadn't known any of this, that she'd been blind to the faith of a billion or so people. How could she not know these things?\n\nAnd Muhammad. She'd been so misinformed about Him. She'd thought He was the actual god of Islam, the one whom Muslims worshiped. But he was simply the messenger who related the word of God. An illiterate man, Muhammad was visited by the angel Gabriel _(Jibril_ in Arabic), who related to him the words of God. Muhammad became the conduit for these messages, and The Qur'an, then, was simply the word of God in written form. _Qur'an_ meant \"Recitation.\"\n\nThere were so many basic things that defied her presumptions. She'd assumed that Muslims were a monolithic group, and that all Muslims were made of the same devout and unbending stock. But she learned that there were Shiite and Sunni interpretations of the Qur'an, and within any mosque there were the same variations in faith and commitment as there were in any church. There were Muslims who treated their faith lightly, and those who knew every word of the Qur'an and its companion guide to behavior, the Hadith. There were Muslims who knew almost nothing about their religion, who worshiped a few times a year, and those who obeyed the strictest interpretation of their faith. There were Muslim women who wore T-shirts and jeans and Muslim women who covered themselves head to toe. There were Muslim men who modeled their lives on the life of the Prophet, and those who strayed and fell short. There were passive Muslims, uncertain Muslims, borderline agnostic Muslims, devout Muslims, and Muslims who twisted the words of the Qur'an to suit their temporary desires and agendas. It was all very familiar, intrinsic to any faith.\n\nAt the time, Kathy was attending a large evangelical church not far from her jobs. Though not always full, it could seat about a thousand parishioners. She felt a need to connect with her faith; she needed all the strength she could find.\n\nBut there were things about this church that bothered her. She was accustomed to the kind of fiery preaching that the church offered, the extremes of showmanship and drama, but one day, she thought, they crossed a line. They had just passed the collection plates, and after they had gathered and counted the funds donated, the preacher\u2014a short man with a rosy face and a mustache\u2014seemed disappointed. His expression was pained. He couldn't hold it in. He chastised the congregation calmly at first, and then with increasing annoyance. Did they not love this church? Did they not appreciate the connection this church created with their lord Jesus Christ? He went on and on, shaming the congregants for their miserly ways. The lecture lasted twenty minutes.\n\nKathy was aghast. She'd never seen the collection counted during a Sunday service. And to ask for more! The congregants were not wealthy people, she knew. This was a working-class church, a middle-class church. They gave what they could.\n\nShe left that day shaken and confused by what she'd seen. At home, after putting Zachary to bed, she turned again to the materials Yuko had given her. She flipped through the Qur'an. Kathy wasn't sure that Islam was the way, but she knew that Yuko had never misled her before, that Yuko was the most grounded and sensible person she knew, and if Islam was working for her, why wouldn't it work for Kathy? Yuko was her sister, her mentor.\n\nKathy struggled with the question of faith all week. She lived with the questions in the morning, at night, all day through work. She had just started her shift at Webster one day when a familiar man walked in. Kathy recognized him immediately as one of the preachers at the church. She came over to help him with a new sport coat.\n\n\"You know,\" he said, \"you should come to our church! It's not far from here.\"\n\nShe laughed. \"I know your church! I'm there all the time. Every Sunday.\"\n\nThe man was surprised. He hadn't seen her before.\n\n\"Oh, I sit in the back,\" she said.\n\nHe smiled and told her that next time he'd look for her. He made it his business to make sure everyone felt welcome.\n\n\"You know,\" Kathy said to him, \"this must be a sign from God, seeing you here.\"\n\n\"How so?\" he asked.\n\nShe told him about her crisis, how she had been disappointed with aspects of the Christianity she knew, in some of the things she'd seen, in fact, at his own church. She told him that she had actually been considering converting to Islam.\n\nHe was listening closely, but he didn't seem worried about losing a member of the congregation.\n\n\"Oh, that's just the devil toying with you,\" he said. \"He'll do that, try to tempt you away from Christ. But this'll only make your faith stronger. You'll see come Sunday.\"\n\nWhen he left, Kathy already felt more certain about her faith. How could his visit not be a sign from God? Just at the moment she was having doubts about her church, a messenger from Jesus walked straight into her life.\n\nShe went to church that Sunday with a renewed sense of purpose. Yuko may have found comfort and direction in Islam, but Kathy was sure that she herself had been personally called by Christ. She walked in and sat near the front, determined that her new friend should see her and know that he had made a difference.\n\nIt didn't take long. When he looked down at the congregation and upon her, his eyes opened wide. He gave her an expression that made clear that she was the one he'd been looking for all day. She'd seen the same expression on kids spotting a birthday cake with their name on it.\n\nAnd then suddenly, in the middle of the service, her name was being called. The preacher, in front of a full room of almost a thousand people, was saying her name, Kathy Delphine.\n\n\"Come up here, Kathy,\" the preacher commanded.\n\nShe rose from her seat and stepped toward the blinding lights of the pulpit. Onstage, she didn't know where to look, how to avoid the glare. She shielded her eyes. She squinted and looked down\u2014at her shoes, at the people in the front row. She had never stood in front of so many people. The closest thing had been her wedding, and that had been only fifty or so friends and family. What was this? Why had she been called forth?\n\n\"Kathy,\" the preacher said, \"tell them what you told me. Tell us all.\"\n\nKathy froze. She didn't know if she could do this. She was a talkative person, rarely nervous, but to recount something she'd said privately to the reverend in front of a thousand strangers\u2014it didn't seem right.\n\nStill, Kathy had faith that he knew what he was doing. She believed she'd been chosen to remain in this church. And she wanted to serve. To help. Perhaps, like Reverend Timothy entering the store that day, this was another event that was meant to be, meant to bring her closer to Christ.\n\nShe was given a microphone and she spoke into it, telling the congregation what she'd told the reverend, that she had been investigating Islam, and that\u2014\n\nThe preacher cut her off. \"She was looking to Islam!\" he said with a sneer. \"She was considering\"\u2014and here he paused\u2014\"the worship of Allah!\" And with that, he made a snorting, derisive sound, the sort of sound an eight-year-old boy would make on a playground. This preacher, this leader of this church and congregation, was using this tone to refer to Allah. Did he not know that his God and Islam's were one and the same? That was one of the first and simplest things she'd learned from the pamphlets Yuko had given her: Allah is just the Arabic word for God. Even Christians speaking Arabic refer to God as Allah.\n\nHe went on to praise Kathy and Jesus and reaffirm the primacy of his and their faith, but by then she was hardly listening. Something had ruptured within her. When he was done, she sat down in a daze, bewildered but becoming sure about something right there and then. She smiled politely through the rest of the service, already knowing she would never come back.\n\nShe thought about the episode while driving home, and that night, and all the next day. She talked to Yuko about it and they realized that this man, preaching to a thousand impressionable and trusting parishioners, didn't know, or didn't care, that Islam, Judaism, and Christianity were not-so-distantly related branches of the same monotheistic, Abrahamic faith. And to dismiss all of Islam with a playground sound? Kathy could not be part of what that man was preaching.\n\nSo by fits and starts, she followed Yuko into Islam. She read the Qur'an and was struck by its power and lyricism. The Christian preachers she'd heard had spent a good amount of time talking about who would and wouldn't go to hell, how hot it burned and for how long, but the imams she began to meet made no such pronouncements. Will I go to heaven? she asked. \"Only God knows this,\" the imam would tell her. The various doubts of the imams were comforting, and drew her closer. She would ask them a question, just as she had asked questions of her pastors, and the imams would try to answer, but often they wouldn't know. \"Let's look at the Qur'an,\" they would say. She liked Islam's sense of personal responsibility, its bent toward social justice. Most of all, though, she liked the sense of dignity and purity embodied by the Muslim women she knew. To Kathy they seemed so wholesome, so honorable. They were chaste, they were disciplined. She wanted that sense of control. She wanted the peace that came with that sense of control.\n\nThe actual conversion was beautifully simple. With Yuko and a handful of other women from the mosque present, she pronounced the _shahadah_ , the Islamic pledge of conviction of faith. \"AshHadu An La Ilaha Il-lallah, Wa Ash Hadu Anna Muhammadar Rasul-allah.\" That was all she needed to say. _I bear Witness that there is no deity but Allah and I bear witness that Muhammad is His Messenger_. With that, Kathy Delphine had become a Muslim.\n\nWhen she tried to explain it to friends and family, Kathy fumbled. But she knew that in Islam she had found calm. The doubt sewn into the faith gave her room to think, to question. The answers the Qur'an provided gave her a way forward. Even her view of her family softened through the lens of Islam. She was less aggressive. She had always fought with her mother, but Islam taught her that \"heaven is at the feet of your mother,\" and this reined her in. She stopped talking back and learned to be more patient and forgiving. _It brought back a purity in me_ , she would say.\n\nHer conversion might have been a step forward in her eyes, but in the eyes of her mother and siblings it was as if she'd renounced her family and all they stood for. Kathy tried to get along with them nevertheless, and her family tried too. There were times when all was good, visits were enjoyable, uneventful. But for every one of those, there was one that spiraled into sniping and accusations, slammed doors and quick departures. There were a few of her eight siblings she wasn't in touch with at all.\n\nBut she wanted extended family. She wanted her own kids to know their aunts and uncles and cousins, and so the relief was profound when the Odyssey arrived at her brother's house in Baton Rouge at eleven-thirty. She unpacked the kids and they fell asleep, on couches and floors, in minutes.\n\nSettled, she called Zeitoun.\n\n\"Winds come?\"\n\n\"Nothing yet,\" he said.\n\n\"I'm gonna pass out,\" Kathy said. \"Never been so tired.\"\n\n\"Get some rest,\" he said. \"Sleep in.\"\n\n\"You too.\"\n\nThey said good night and turned out the lights.\n\n# SUNDAY AUGUST 28\n\nKathy woke before dawn and turned on the TV. Katrina was now a Category 5 storm with winds over 150 miles an hour. It was heading almost directly toward New Orleans, with the brunt of it expected to strike about sixteen miles west of the city. Meteorologists were predicting furious winds, ten-foot storm surges, possibilities of levee breaches, flooding everywhere along the coast. It was estimated that the storm would reach the New Orleans area that night.\n\nThroughout the day, as news of the hurricane grew more dire, clients called Kathy or Zeitoun, asking them to secure their windows and doors. Kathy collected requests and relayed them to Zeitoun. Zeitoun discovered that one of his carpenters, James Crosso, was still in the city, so the two of them spent the day driving around, rigging the houses on the list. James's wife worked for one of the hotels downtown, and the couple was planning to ride the storm out there. Zeitoun and James drove from job to job, a quarter ton of plywood in the back of the truck, doing what they could before the winds came. The roads were still crowded, a new surge of cars leaving, but Zeitoun didn't consider it. He would be safe in their house on Dart Street, he figured, far from any levees, with two stories, plenty of tools, and food.\n\nMid-morning, Mayor Nagin ordered the city's first-ever mandatory evacuation. Anyone who could leave must leave.\n\nAll day Zeitoun and James saw people lined up at bus stops\u2014those who planned to stay in the Superdome. Families, couples, elderly men and women carrying their belongings in backpacks, suitcases, garbage bags. Seeing them exposed like that, as the winds picked up and the sky darkened, worried Zeitoun. He and James passed the same groups, waiting patiently, on the way to their job sites and on their way back.\n\nIn Baton Rouge, the weather was dark and unruly. High winds, black skies at noon. The kids played outside for a while, but then came inside to watch DVDs while Kathy caught up with Patty and Mary Ann. The trees in the neighborhood swung wildly.\n\nThe power went out at five o'clock. The kids played board games by candlelight.\n\nKathy periodically went out to the car to listen to the news on the radio. The winds were smashing windows in New Orleans, knocking down trees and power lines.\n\nKathy tried to call Zeitoun, but the call went straight to his voicemail. She tried the home phone. Nothing. The lines were down, she assumed. The hurricane had not hit the city yet, and already she had no way to reach her husband.\n\nBy six o'clock, Zeitoun had dropped James off and was home and ready. He watched the news on TV; the reports had not changed much. The outermost edge of the hurricane was expected about midnight. He assumed that would be the end of the electrical grid for a few days.\n\nWalking through the darkening rooms, Zeitoun assessed all the possible dangers he would face during the storm. The house had four bedrooms\u2014the master bedroom on the first floor and the kids' rooms upstairs. He expected leaks up there. Portions of the roof might be compromised. A few windows might break\u2014the front sitting room, with its bay window, was at risk. There was an outside chance the tree in the backyard would fall on the house. If that happened, there could be significant damage, because nothing, then, could keep the water out.\n\nBut he was optimistic. And in any case he wanted to be in the house, on which he had spent untold thousands for improvements, to protect it in whatever way possible. His grandmother had stayed put during countless storms in her home on Arwad Island, and he planned to do the same. A home was worth fighting for.\n\nThe only thing that concerned him was the levees. Again and again the news reports warned of the storm surge. The levees were meant to hold back fourteen feet of water, and the storm surges in the Gulf were already nineteen, twenty feet high. If the levees were breached, he knew the battle would be lost.\n\nHe called Kathy at eight o'clock.\n\n\"There you are,\" she said. \"You disappeared.\"\n\nHe looked at his phone and saw that he'd missed three calls from her.\n\n\"Coverage must be spotty already,\" he said. His phone had not rung. He told her that nothing significant had happened yet. Just strong winds. Nothing new.\n\n\"Stay away from the windows,\" she said.\n\nHe said he would try.\n\nKathy wondered aloud if there was something foolish in what they were doing. Her husband was in the path of a Category 5 hurricane and they were talking about staying away from the windows.\n\n\"Say goodnight to the kids,\" he said.\n\nShe said she would.\n\n\"Better go. To save the battery,\" he said.\n\nThey said goodnight.\n\nThe kids asleep, Kathy sat on the couch in her brother Andy's house and stared at the candle in front of her. It was the only light left on in the house.\n\nJust after eleven o'clock, the front end of the storm arrived at Zeitoun's house. The sky was a brutal grey, the winds swirling and cool. Rain came in sheets. Every half hour brought an escalation in the mayhem outside. At midnight the power went out. The leaks began at about two or three. The first was in the corner of Nademah's bedroom. Zeitoun went down to the garage and retrieved a forty-gallon garbage can to catch the water. Another leak opened a few minutes later, this one in the upstairs hallway. Zeitoun found another garbage can. A window in the master bedroom broke just after three o'clock, as if a brick had been thrown through the glass. Zeitoun gathered the shards and stuffed the opening with a pillow. Another leak opened in Safiya and Aisha's room. He found another, bigger garbage can.\n\nHe dragged the first two garbage cans outside and dumped them on the lawn. The sky was a child's fingerpainting, blue and black hastily mixed. The wind was cooler. The neighborhood was utterly dark. As he stood on the lawn, he heard a tree fall somewhere on the block\u2014a crack and then a shush as the branches pushed down through other trees and rested against the side of a house.\n\nHe went inside.\n\nAnother window had broken. He stuffed another pillow into it. Branches clawed at the walls, the roof. There were unknown thumps everywhere. The bones of the house seemed to be moaning under the strain of it all. The house was under assault.\n\nWhen he next checked, it was four o'clock in the morning. He hadn't stopped moving in five hours. If the damage continued at this pace, it would be worse than he had predicted. And the real storm hadn't come yet.\n\nIn the small hours, Zeitoun had a thought. He didn't expect the city to flood, but he knew a flood was not impossible. So he walked outside, tasting the cool wind, and dragged his secondhand canoe from the garage and righted it. He wanted to have it ready.\n\nIf Kathy could only see him now. She had rolled her eyes when she saw him come home with that canoe. He'd bought it a few years before, from a client in Bayou St. John. When the client was moving, Zeitoun had seen it on his lawn, a standard aluminum model, and asked him if he was selling it. The client laughed. \"You want _that?\"_ he asked. Zeitoun bought it on the spot for seventy-five dollars.\n\nSomething about the canoe had intrigued him. It was well-made, undamaged, with a pair of wooden benches inside. It was about sixteen feet long, built for two people. It seemed to speak of exploration, of escape. He tied it to the top of his van and brought it home.\n\nThrough the living room window, Kathy saw him pull up. She met him at the door.\n\n\"No way,\" she said.\n\n\"What?\" Zeitoun said, smiling.\n\n\"You're crazy,\" she said.\n\nKathy liked to act exasperated, but Zeitoun's romantic side was central to why she loved him. She knew that any kind of boat reminded him of his childhood. How could she deny him a used canoe? She was fairly certain he would never use it, but having it in the garage, she knew, would mean something to him\u2014a connection to the past, the possibility of adventure. Whatever it was, she wouldn't stand in the way.\n\nHe did try, two or three times, to get his daughters interested in the canoe. He brought them to Bayou St. John, put the canoe in the water, and sat down inside. When he reached for Nademah, standing on the grass, she refused. The younger girls weren't having it, either. So for half an hour, as the girls watched from the grass, he paddled around by himself, trying to make it all look fun, irresistible. When he returned, they still wanted no part of it, so he put the canoe back on the roof of the van and they all went home.\n\nThe wind picked up after five o'clock. He couldn't tell when the hurricane actually made landfall, but the day barely brightened that morning. It went from black to a charcoal grey, the rain like pebbles thrown against glass. He could hear tree limbs succumbing to the wind, great exhalations as their trunks fell on streets and roofs.\n\nEventually he could not stay awake. Though his house was under attack, he lay down, knowing something would awaken him soon enough, and so, surrendering for now, he fell into a shallow sleep.\n\n# MONDAY AUGUST 29\n\nZeitoun woke late. He couldn't believe his watch. It was after ten a.m. He hadn't slept that late in years. All the clocks had stopped. He got up, tried the light switches in three rooms. The power was still out.\n\nThe wind was strong outside, the sky still dark. The rain was coming down\u2014not heavily, but enough to keep Zeitoun inside much of the day. He ate breakfast and checked for any other damage to the house. He put buckets under two new leaks. Overall the damage had remained at about the level it had been at before he fell asleep. He had slumbered through the worst of the hurricane. Through the windows he could see the streets were covered with downed power lines and fallen trees and about a foot of water. It was bad, but not much worse than a handful of storms he could remember.\n\nIn Baton Rouge, Kathy brought her kids to Wal-Mart to stock up on supplies and buy flashlights. Inside, there seemed to be more people than products. She'd never seen anything like it. The place had been bought out, the shelves nearly bare. It looked like the end of the world. The kids were scared, holding on to her. Kathy looked for ice and was told that the ice was long gone. Improbably, she found a package of two flashlights, the last one, and reached for it a split second before another woman did. She gave the woman an apologetic smile and went to the check-out counter.\n\n* * *\n\nIn the afternoon the wind and rain calmed. Zeitoun went outside to explore. It was warm, over eighty degrees. He estimated there were eighteen inches of water on the ground. It was rainwater, murky and grey-brown, but soon, he knew, it would drain away. He looked in the backyard. There was the canoe. It called to him, floating and ready. It was a rare opportunity, he thought, to be able to glide over the roads. He had only this day. He bailed the water resting in the hull, and in his T-shirt and shorts and sneakers, he stepped in.\n\nLeaving the yard was difficult. A tree across the street had been ripped from its roots and lay across the road, branches spread over his driveway. He paddled around them and looked back to the house. No great damage to the exterior. Some shingles missing from the roof. The windows broken. A gutter that would need remounting. Nothing too bad, three days' work.\n\nIn the neighborhood, other homes had been hit by all manner of debris. Windows had been blown out. Wet, black branches covered cars, the street. Everywhere trees had been pulled out of the earth and lay flat.\n\nThe quiet was profound. The wind rippled the water but otherwise all was silent. No cars moved, no planes flew. A few neighbors stood on their porches or waded through their yards, assessing damage. No one knew where to start or when. He knew he would be giving many estimates in the coming weeks.\n\nHe paddled only a few blocks before he began to have second thoughts. There were power lines down everywhere. What would exposed lines do if they made contact with his aluminum canoe? Besides, there wasn't enough water to paddle much. In some parts of the neighborhood, there was scarcely any water at all\u2014only a few inches. He ran aground, got out, turned the canoe around, and paddled back home.\n\nThroughout the afternoon, the water fled from the streets, a few inches an hour. The drainage system was working. By that evening, the water had receded completely. The streets were dry. The damage was extensive, but really no worse than a handful of other storms he could remember. And it was over.\n\nHe called Kathy.\n\n\"Come back,\" he said.\n\nKathy was tempted, but it was already seven o'clock, they were about to eat dinner, and she knew she wasn't about to drive through the night again with four kids and a flatulent dog. Besides, there was no power in New Orleans, so they would be returning to the same situation they were suffering through in Baton Rouge. The kids were still enjoying the time spent with their cousins\u2014the laughter rattling the house was testament to it.\n\nShe and Zeitoun agreed to talk about it again in the morning, though they both expected Kathy to be packing up the kids sometime the next day.\n\nShe went inside and the combined families, three adults and eight kids, ate hot dogs by candlelight. That her sisters had put pork on the table did not go unnoticed, but Kathy vowed not to make an issue of it. _Better to let it go_ , she said to herself. _Let it go, let it go_. She had so many battles to fight. There would be so many more in the coming days, she was sure, that she couldn't expend her energy on her sisters, on hot dogs. If they wanted to serve her children pork, they could try.\n\n* * *\n\nLater, when Kathy went to the car to steal a few moments with the radio, she heard Mayor Nagin echoing her reluctance to return. Don't come back yet, he said. Wait to see what the damage is, until everything is settled and cleaned up. Give it a day or two.\n\nIn the afternoon, Zeitoun got a call from Adnan, a second cousin on Zeitoun's mother's side. Adnan had done well since emigrating over a decade earlier; he owned and managed four Subway franchises in New Orleans. His wife Abeer was six months pregnant with their first child.\n\n\"You still in the city?\" he asked, assuming Zeitoun was.\n\n\"Of course I am. You in Baton Rouge?\" Zeitoun asked.\n\n\"I am.\" Adnan had driven up the night before with Abeer and his elderly parents. \"How is it there?\"\n\n\"Windy,\" Zeitoun said. \"Really? It's a little scary.\" He would never have admitted this to Kathy, but he could confide in Adnan.\n\n\"You think you'll stay?\" Adnan asked.\n\nZeitoun said he planned to, and offered to look after Adnan's shops. Before Adnan had left the city, he'd emptied the cash register at the City Park Avenue location and made sure bread was baked; he'd assumed he'd be back on Tuesday.\n\n\"You know any mosques in Baton Rouge?\" Adnan asked. All the motels were booked, and he and Abeer knew no one in Baton Rouge. They'd been able to place Adnan's parents in a mosque the previous night, but there were already hundreds of people there, sleeping on the floors, and they couldn't accommodate more. Adnan and Abeer had spent the night in their car.\n\n\"I don't,\" Zeitoun said. \"But call Kathy. She's with family. They'll take you in, I'm sure.\" He gave Adnan her cell phone number.\n\nZeitoun emptied all of the buckets in the house, put them under the holes in the roof again, and got ready for bed. It was warm outside, stifling inside. He lay in the dark. He thought about the strength of the storm, its duration, how oddly minimal the damage had been to this house. He went to the front window. Already, at eight o'clock, the streets were dry as bone. All that effort to flee, and for what? Hundreds of thousands of people rushing north for this. A few inches of water, all of it now gone.\n\nIt was quiet that night. He heard no wind, no voices, no sirens. There was only the sound of a city breathing as he breathed, weary from the fight, grateful it was over.\n\n# TUESDAY AUGUST 30\n\nZeitoun woke up late again. He squinted at the window above, saw the same grey sky, heard the same strange quiet. He had never known a time like this. He couldn't drive anywhere, couldn't work. For the first time in decades, there was nothing to do. It would be a day of calm, of rest. He felt strangely lethargic, ethereally content. He fell back into a shallow sleep.\n\nArwad Island, his family's ancestral home, was soaked in light. The sun was constant there, a warm white light that bleached the stone buildings and cobblestone alleys, that brought incredible clarity to the surrounding cobalt sea.\n\nWhen Zeitoun dreamt of Arwad, it was the Arwad he visited during the summers of his boyhood, and in these dreams he was doing boyish things: sprinting around the island's tiny perimeter, scaring seagulls to flight, searching in the tide pools for crabs and shells or whatever oddities had been thrown onto the island's rocky shore.\n\nBy the outer wall, facing the western expanse of the sea, he and Ahmad chased a lone chicken through the ruins around the outermost homes. The scrawny bird raced up a pile of garbage and rubble and into a cave of coral and masonry. They turned at the sound of a frigate dropping anchor, waiting to land at Tartus, the port city a mile east. There were always a half-dozen ships, tankers, and freighters waiting for a berth at the busy port, and often they would anchor close enough to cast a shadow over the tiny island. Abdulrahman and Ahmad would stare up at them, the hulls rising twenty, thirty feet over the sea. The boys would wave to the crew and dream of being aboard. It seemed a life of impossible romance and freedom.\n\nEven then, when Ahmad was a skinny, tanned boy of fifteen, he knew he would be a sailor. He was careful not to tell his father, but he was certain he wanted to steer one of those ships. He wanted to guide great vessels around the world, to speak a dozen languages, to know the people of every nation.\n\nAbdulrahman never doubted that Ahmad would do this. Ahmad was, in Abdulrahman's eyes, capable of anything. He was his best friend, his hero and teacher. Ahmad taught him how to spear a fish, how to row a boat alone, how to dive from the great Phoenician stones on the island's southern wall. He would have followed Ahmad anywhere, and often did.\n\nThe boys stripped to their underwear and set out for a narrow archipelago of rocks. Abdulrahman and Ahmad found the spear they kept hidden in the stones and took turns diving for fish. Swimming came naturally to the boys of the Zeitoun family, and to all the children of Arwad. They could swim as soon as they could walk and would stay in the water, swimming and treading, for hours. When Ahmad and Abdulrahman emerged they would lay on a low stone wall, the sea on one side and the town's outer promenade on the other.\n\nThe promenade wasn't much to look at, a wide, crumbling paved area, dotted with litter, evidence of the island's half-hearted attempts to attract tourists. Most of the residents of Arwad didn't much care if visitors came or not. It was home, and a place where real industry happened: fish were caught, cleaned, and brought to the mainland, and ships, strong wooden sailboats of one or two or three masts, were built using methods perfected on the island centuries before.\n\nArwad had been a strategic military possession for an endless succession of sea powers: the Phoenicians, the Assyrians, the Achaemenid Persians, the Greeks under Alexander, the Romans, the Crusaders, the Mongols, the Turks, the French, and the British. Various walls and battlements, in pieces and all but gone, spoke of past fortresses. Two small castles, scarcely altered since the Middle Ages, stood in the center of the island and could be explored by curious children. Abdulrahman and Ahmad often ran up the smooth stone stairs of the lookout tower by their home, pretending they were spotting invaders, sounding bells of warning, planning their defenses.\n\nBut usually their games took place in the water. They were never more than a few steps from the cool Mediterranean, and Abdulrahman would follow Ahmad to the shore and up the great Phoenician stones of the wall. From the top they could see into the windows of the higher-sitting dwellings of the town. Then they would turn to the sea and dive. After swimming, they would lay on the stone wall, the surface polished by the crashing waves and the feet of uncountable children. They warmed themselves with the heat of the rocks and the sun above. They would talk of heroes who had defended the island, of armies and saints who had stopped there. And they would talk of their plans, their own great deeds and explorations.\n\nSoon the two of them would grow quiet, near sleep, hearing the waves push against the island's outer walls, the ceaseless shushing of the sea. But in Zeitoun's half-dream, the sound of the ocean seemed wrong. It was both quieter and less rhythmic\u2014not an ebb and flow, but instead the constant whisper of a river.\n\nThe dissonance woke him.\n\n# II\n# TUESDAY AUGUST 30\n\nZeitoun opened his eyes again. He was home, in his daughter Nademah's room, under her covers, looking through the window at a dirty white sky. The sound continued, something like running water. But there was no rain, no leaks. He thought a pipe might have broken, but that couldn't be it; the sound wasn't right. This was more like a river, the movement of great volumes of water.\n\nHe sat up and looked down through the window that faced the backyard. He saw water, a wide sea of it. It was coming from the north. It flowed into the yard, under the house, rising quickly.\n\nHe couldn't make sense of it. The day before, the water had receded, as he had expected it to, but now it had returned, far stronger. And this water was different from the murky rainwater of the day before. This water was green and clear. This was lake water.\n\nAt that moment, Zeitoun knew that the levees had been overtopped or compromised. There could be no doubt. The city would soon be underwater. If the water was here, he knew, it was already covering most of New Orleans. He knew it would keep coming, would likely rise eight feet or more in his neighborhood, and more elsewhere. He knew the recovery would take months or years. He knew the flood had come.\n\nHe called Kathy.\n\n\"The water's coming,\" he said.\n\n\"What? No, no,\" she said. \"Levees broke?\"\n\n\"I think so.\"\n\n\"I can't believe it.\"\n\nHe heard her stifle a sob.\n\n\"I better go,\" he said.\n\nHe hung up and went to work.\n\n_Elevate_ , he thought. _Elevate, elevate_. Everything had to be brought to the second floor. He recalled the worst of the predictions before the storm: if the levees broke, there would be ten, fifteen feet of water in some places. Methodically, he began to prepare. Everything of value had to be brought higher. The work was simply work, and he went about it calmly and quickly.\n\nHe took the TV, the DVD player, the stereo, all the electronics upstairs. He gathered all the kids' games and books and encyclopedias and carried those up next.\n\nThings were tense at the house in Baton Rouge. With the weather windy and grey, and so many people sharing a small house, tempers were flaring. Kathy thought it best to make her family scarce. She and her kids put away their sleeping bags and pillows and left in the Odyssey, intending to drive around most of the day, going to malls or restaurants\u2014anything to kill time. They would return late, after dinner, only to sleep. She prayed that they could return to New Orleans the next day.\n\nKathy called Zeitoun from the road.\n\n\"My jewelry box!\" she said.\n\nHe found that, and the good china, and he brought it all upstairs. He emptied the refrigerator; he left the freezer full. He put all the chairs on top of the dining room table. Unable to carry a heavy chest, he put it on a mattress and dragged it up the stairs. He placed one couch on top of another, sacrificing one to save the other. Then he got more books. He saved all the books.\n\nKathy called again. \"I told you not to cancel the property insurance,\" she said.\n\nShe was right. Just three weeks before, he had chosen not to renew the part of their flood insurance that covered their furniture, everything in the house. He hadn't wanted to spend the money. He admitted she was right, and knew she would remind him of it for years to come.\n\n\"Can we talk about it later?\" he asked.\n\nZeitoun went outside, the air humid and gusty. He tied the canoe to the back porch. The water was whispering through the cracks in the back fence, rising up. It was flowing into his yard at an astonishing rate. As he stood, it swallowed his ankles and crawled up his shins.\n\nBack inside, he continued to move everything of value upward. As he did, he watched the water erase the floor and climb the walls. In another hour there was three feet of water indoors. And his house was three feet above street level.\n\nBut the water was clean. It was translucent, almost green in tint. He watched it fill his dining room, momentarily struck by the beauty of the sight. It brought forth a vague memory of a storm on Arwad Island, when he was just a boy, when the Mediterranean rose up and swallowed the lower-sitting homes, the blue-green sea sitting inside living rooms and bedrooms and kitchens. The water breached and dodged the Phoenician stones surrounding the island without any difficulty at all.\n\nAt that moment, Zeitoun had an idea. He knew the fish in his tank wouldn't survive without filtration or food, so he reached inside and liberated them. He dropped them in the water that filled the house. It was the best chance they had. They swam down and away.\n\nUsing his cell phone, he talked to Kathy throughout the day. They reviewed what couldn't be saved, the furniture too large to carry upstairs. There were dressers, armoires. He removed all the drawers he could, carried upstairs everything that could be removed and lifted.\n\nThe water devoured the cabinets and windows. Zeitoun watched, dismayed, as it rose four, five, six feet in the house\u2014above the electrical box, the phone box. He would have no access to electricity or a landline for weeks.\n\nBy nightfall the neighborhood was under nine feet of water and Zeitoun could no longer go downstairs. He was spent; he had done all he could. He lay on Nademah's bed on the second floor and called Kathy. She was driving around with the kids, dreading a return to the house in Baton Rouge.\n\n\"I saved all I could,\" he said.\n\n\"I'm glad you were there,\" she said, and meant it. If he hadn't been at home they would have lost everything.\n\nThey talked about what would become of the house, of the city. They knew the house would have to be gutted, all the insulation and wiring replaced, the plaster and Sheetrock and paint and wallpaper. Everything, down to the studs, was gone. And if there was this much water Uptown, there was more in other neighborhoods. He thought of them\u2014the houses near the lake and the houses near the levees. They didn't stand a chance.\n\nAs they talked, Zeitoun realized his phone was dying. Without electricity, they both knew, when his battery was gone there would be no reliable way to call out.\n\n\"Better go,\" he said.\n\n\"Please leave,\" she said. \"Tomorrow.\"\n\n\"No, no,\" he said, but even as he spoke, he was reconsidering. He had not anticipated being confined to this house for long. He knew there was enough food for a week or more, but now the situation would present a greater strain than he had planned.\n\n\"Tell the kids I said goodnight,\" he said.\n\nShe said she would.\n\nHe turned off his phone to conserve what power it had left.\n\nKathy was still driving. She'd exhausted all means of diversion and was about to go back to her brother's house when her phone rang again. It was Adnan. He was in Baton Rouge with his wife Abeer, he said, and they had no place to stay.\n\n\"Where'd you stay last night?\" Kathy asked.\n\n\"In the car,\" he said, sounding apologetic and ashamed.\n\n\"Oh my God,\" she said. \"Let me see what I can do.\"\n\nShe planned to ask Mary Ann and Patty once she got back to the house. It would be crowded, but there was no way a pregnant woman should be sleeping in a car when there was enough room at her family's house.\n\n* * *\n\nWhen Kathy returned to Andy's, it was ten o'clock and the rooms were dark. All the kids, save Nademah, were asleep in the car. She roused them and walked quietly into the house. After the kids were settled in their sleeping bags, Mary Ann appeared and confronted her.\n\n\"Where were you all day?\"\n\n\"Out,\" Kathy said. \"Trying to stay out of the way.\"\n\n\"Do you know how expensive gas is?\" Mary Ann said.\n\n\"Excuse me?\" Kathy said. \"I didn't know you were paying for my gas.\"\n\nKathy was exasperated, defeated. In the house, they were made to feel burdensome; now she was being scolded for leaving. She vowed to herself to get through the night and think of a new plan the next day. Maybe she could drive to Phoenix to stay with Yuko. It was a ludicrous idea, to travel fifteen hundred miles when her blood relatives lived fifty miles from New Orleans, but she'd run to Yuko's house before and could do so again.\n\nThe tension was bad enough already, but for Adnan and Abeer's sake, Kathy had to ask. After all, Mary Ann knew them; she'd met Adnan and Abeer many times. Couldn't they stay for one night?\n\n\"Absolutely not,\" Mary Ann said.\n\nOn the dark second floor, Zeitoun held a flashlight between his teeth, sifting through the pile of belongings he'd salvaged. He shelved the books he could. He boxed the certificates and pictures. He found pictures of his children when they were smaller, pictures from a vacation they'd all taken to Spain, pictures from their trip to Syria. He organized them, found a plastic bag, put them safely inside and then re-boxed them.\n\nIn another, older box he came upon another photo, sepia-toned and in a rickety frame, and paused. He hadn't seen it in years. He and his brother Luay and sister Zakiya were playing with their brother Mohammed, eighteen years older. They were all wrestling with him in the bedroom Zeitoun and Ahmad and all the younger boys had shared in Jableh. There little Abdulrahman was, on the far right, maybe five years old, his tiny fingers swallowed by Mohammed's huge hand.\n\nZeitoun stared at his brother's electric smile. Mohammed had everything then. He _was_ everything, the most famous and accomplished athlete in Syrian history. He was a long-distance ocean swimmer, one of the best the world had ever known. That he was from a country not well known for its coast made his achievements all the more remarkable. He had won races in Syria, Lebanon, and Italy. He could swim thirty miles at a stretch, and faster than anyone else. Faster than any Italian, any Englishman or Frenchman or Greek.\n\nZeitoun examined the picture more closely. Poor Mohammed, he thought, all his brothers and sisters swamping him. They did that to him whenever he was home. The races\u2014in Greece, Italy, the United States\u2014kept him away too long. He was feted by heads of state and featured in newspapers and magazines all over the world. They called him the Human Torpedo, the Nile Alligator, the Miracle. When he was home his siblings went wild, buzzing around him like flies.\n\nAnd then, at age twenty-four, he was gone. Killed in a car accident in Egypt, just before a race in the Suez Canal. Zeitoun still missed him terribly, though he was only six when it happened. After that, he knew Mohammed only through stories, photos, and tributes, and the monument to him that stood on the waterfront in Jableh, just down the street from their home. Growing up they had to pass it every day, and its presence made forgetting Mohammed, even momentarily, impossible.\n\nZeitoun sat and stared at the photo for a minute or so before putting it back in the box.\n\n* * *\n\nHe couldn't sleep inside the house. It was hotter this night, and in New Orleans he had never withstood this kind of heat without air-conditioning. Laying on sweat-soaked sheets, he had a thought. He looked in one of the upstairs closets for the tent he'd bought a few years back. The previous summer, he'd set it up in the backyard, and the kids had slept outside when the heat relented and allowed it.\n\nHe found the tent and crawled through the window of Nademah's room and onto the roof. Outside it was cooler, a breeze cutting through the stagnant air. The roof over the garage was flat, and he set up the tent there, securing it with books and a few cinder blocks. He dragged one of the kids' mattresses out and squeezed it through the tent's door. The difference was vast.\n\nLaying on the mattress, he listened for the movement of water. Was it still rising? He wouldn't be surprised. He would not be shocked if, come morning, there was twelve, thirteen feet of water covering the neighborhood.\n\nThe darkness around him was complete, the night silent but for the dogs. First a few, then dozens. From all corners of the neighborhood he heard them howling. The neighborhood was full of dogs, so he was accustomed to their barking. On any given night, one would become excited by something and set off the rest, an arrhythmic call-and-response that could last hours until they calmed, one by one, into silence. But this night was different. These dogs had been left behind, and now they knew it. There was a bewilderment, an anger in their cries that cut the night into shards.\n\n# WEDNESDAY AUGUST 31\n\nZeitoun woke with the sun and crawled out of his tent. The day was bright, and as far as he could see in any direction the city was underwater. Though every resident of New Orleans imagines great floods, knows that such a thing is possible in a city surrounded by water and ill-conceived levees, the sight, in the light of day, was beyond anything he had imagined. He could only think of Judgment Day, of Noah and forty days of rain. And yet it was so quiet, so still. Nothing moved. He sat on the roof and scanned the horizon, looking for any person, any animal or machine moving. Nothing.\n\nAs he did his morning prayers, a helicopter broke the silence, shooting across the treetops and heading downtown.\n\nZeitoun looked down from the roof to find the water at the same level as the night before. He felt some relief in knowing that it would likely remain there, or even drop a foot once it reached an equilibrium with Lake Pontchartrain.\n\nZeitoun sat beside his tent, eating cereal he had salvaged from the kitchen. Even with the water no longer rising, he knew he could do nothing at home. He had saved what he could save, and there was nothing else to do here until the water receded.\n\nWhen he had eaten, he felt restless, trapped. The water was too deep to wade into, its contents too suspect to swim through. But there was the canoe. He saw it, floating above the yard, tethered to the house. Amid the devastation of the city, standing on the roof of his drowned home, Zeitoun felt something like inspiration. He imagined floating, alone, through the streets of his city. In a way, this was a new world, uncharted. He could be an explorer. He could see things first.\n\nHe climbed down the side of the house and lowered himself into the canoe. He untied the rope and set out.\n\nHe paddled down Dart Street, the water flat and clear. And strangely, almost immediately, Zeitoun felt at peace. The damage to the neighborhood was extraordinary, but there was an odd calm in his heart. So much had been lost, but there was a stillness to the city that was almost hypnotic.\n\nHe coasted away from his home, passing over bicycles and cars, their antennae scraping the bottom of his canoe. Every vehicle, old and new, was gone, unsalvageable. The numbers filled his head: there were a hundred thousand cars lost in the flood. Maybe more. What would happen to them? Who would take them once the waters receded? In what hole could they all be buried?\n\nAlmost everyone he knew had left for a day or two, expecting little damage. He passed by their homes, so many of which he'd painted and even helped build, calculating how much was lost inside. It made him sick, the anguish this would cause. No one, he knew, had prepared for this, adequately or at all.\n\nHe thought of the animals. The squirrels, the mice, rats, frogs, possums, lizards. All gone. Millions of animals drowned. Only birds would survive this sort of apocalypse. Birds, some snakes, any beast that could find higher ground ahead of the rising tide. He looked for fish. If he was floating atop water shared with the lake, surely fish had been swept into the city. And, on cue, he saw a murky form darting between submerged tree branches.\n\n* * *\n\nHe remembered the dogs. He rested his paddle on his lap, coasting, trying to place the pets he'd heard crying in the dark.\n\nHe heard nothing.\n\nHe was conflicted about what he was seeing, a refracted version of his city, one where homes and trees were bisected and mirrored in this oddly calm body of water. The novelty of the new world brought forth the adventurer in him\u2014he wanted to see it all, the whole city, what had become of it. But the builder in him thought of the damage, how long it would take to rebuild. Years, maybe a decade. He wondered if the world at large could already see what he was seeing, a disaster mythical in scale and severity.\n\nIn his neighborhood, miles from the closest levee, the water had risen slowly enough that he knew it was unlikely that anyone had died in the flood. But with a shudder he thought of those closer to the breaches. He didn't know where the levees had failed, but he knew anyone living nearby would have been quickly overwhelmed.\n\nHe turned on Vincennes Place and headed south. Someone called his name. He looked up to see a client of his, Frank Noland, a fit and robust man of about sixty, leaning out from a second-story window. Zeitoun had done work on his house a few years ago. The Zeitouns would see Frank and his wife occasionally in the neighborhood, and they always exchanged warm greetings.\n\nZeitoun waved and paddled over.\n\n\"You got a cigarette?\" Frank asked, looking down.\n\nZeitoun shook his head no, and coasted closer to the window where Frank had appeared. It was a strange sensation, paddling over the man's yard; the usual barrier that would prevent one from guiding a vehicle up to the house was gone. He could glide directly from the street, diagonally across the lawn, and appear just a few feet below a second-story window. Zeitoun was just getting accustomed to the new physics of this world.\n\nFrank was shirtless, wearing only a pair of tennis shorts. His wife was behind him, and they had a guest in the house, another woman of similar age. Both women were dressed in T-shirts and shorts, suffering in the heat. It was early in the day, but the humidity was already oppressive.\n\n\"You think you could take me to where I can buy some smokes?\" Frank asked.\n\nZeitoun told him that he didn't think any store would be open and selling cigarettes this day.\n\nFrank sighed. \"See what happened to my motorcycle?\" He pointed to the porch next door.\n\nZeitoun remembered Frank talking about this motorcycle\u2014an antique bike that he had bought, restored, and lavished attention on. Now it was under six feet of water. As the water had risen the day before, Frank had moved it from the driveway up to the porch and then to his next-door neighbor's porch, which was higher. But now it was gone. They could still see the faint, blurred likeness of the machine, like a relic from a previous civilization.\n\nHe and Frank talked for a few minutes about the storm, the flood, how Frank had expected it but then hadn't expected it at all.\n\n\"Any chance you can take me to check on my truck?\" Frank asked. Zeitoun agreed, but told Frank that he'd have to continue on a while longer. Zeitoun was planning to check on one of his rental properties, about two miles away.\n\nFrank agreed to come along for the ride, and climbed down from the window and into the canoe. Zeitoun gave him the extra paddle and they were off.\n\n\"Brand new truck,\" Frank said. He had parked it on Fontainebleau, thinking that because the road was a foot or so higher than Vincennes, the truck would be spared. They made their way up six blocks to where Frank had parked the truck, and then Zeitoun heard Frank's quick intake of breath. The truck was under five feet of water and had migrated half a block. Like his motorcycle, it was gone, a thing of the past.\n\n\"You want to get anything out of it?\" Zeitoun asked.\n\nFrank shook his head. \"I don't want to look at it. Let's go.\"\n\nThey continued on. Soon they saw an older man, a doctor Zeitoun knew, on the second-floor porch of a white house. They paddled into the yard and asked the doctor if he needed help. \"No, I've got somebody coming,\" he said. He had his housekeeper with him, he said, and they were well set up for the time being.\n\nA few doors down, Zeitoun and Frank came upon a house with a large white cloth billowing from the second-floor window. When they got closer, they saw a couple, a husband and wife in their seventies, leaning out of the window.\n\n\"You surrender?\" Frank asked.\n\nThe man smiled.\n\n\"You want to get out?\" Zeitoun asked.\n\n\"Yes, we do,\" the man said.\n\nThey couldn't safely fit anyone else in the canoe, so Zeitoun and Frank promised to send someone back to the house as soon as they got to Claiborne. They assumed there would be activity there, that if anywhere would have a police or military presence, it would be Claiborne, the main thoroughfare nearby.\n\n\"We'll be right back,\" Zeitoun said.\n\nAs they were paddling away from the couple's house, they heard a faint female voice. It was a kind of moan, weak and tremulous.\n\n\"You hear that?\" Zeitoun asked.\n\nFrank nodded. \"It's coming from that direction.\"\n\nThey paddled toward the sound and heard the voice again.\n\n\"Help.\"\n\nIt was coming from a one-story house on Nashville.\n\nThey coasted toward the front door and heard the voice again: \"Help me.\"\n\nZeitoun dropped his paddle and jumped into the water. He held his breath and swam to the porch. The steps came quicker than he thought. He jammed his knee against the masonry and let out a gasp. When he stood, the water was up to his neck.\n\n\"You okay?\" Frank asked.\n\nZeitoun nodded and made his way up the steps.\n\n\"Hello?\" the voice said, now hopeful.\n\nHe tried the front door. It was stuck. Zeitoun kicked the door. It wouldn't move. He kicked again. No movement. With the water now to his chest, he ran his body against the door. He did it again. And again. Finally it gave.\n\n* * *\n\nInside he found a woman hovering above him. She was in her seventies, a large woman, over two hundred pounds. Her patterned dress was spread out on the surface of the water like a great floating flower. Her legs dangled below. She was holding on to a bookshelf.\n\n\"Help me,\" she said.\n\nZeitoun talked gently to the woman, assuring her that she would be taken care of. He knew that in all likelihood she had been there, clinging to her furniture, for twenty-four hours or more. An elderly woman like this would have no chance of swimming to safety, much less have the strength to cut a hole through her roof. At least the water was warm. She might not have survived.\n\nZeitoun pulled her out the front door and caught a glimpse of Frank in the canoe. His jaw had gone slack, his eyes disbelieving.\n\nNo one knew what to do next. It would be very difficult to fit a woman of her size into the canoe under normal circumstances. And lifting her into it would require more than two men. Even if they could lift her and fit her inside, they couldn't possibly fit all three of them. The canoe would certainly capsize.\n\nHe and Frank had a quick whispered conversation. They had no choice but to leave her and find help. They would paddle quickly to Claiborne and flag down a boat. They told the woman the plan. She was unhappy to be left alone again, but there was no choice.\n\nThey reached Claiborne in a few minutes and immediately saw what they were looking for: a fan boat. Zeitoun had never seen one in person, but they were familiar from movies. This was a military model, loud, with a great fan anchored perpendicularly to the rear. It was headed directly toward them.\n\nZeitoun thought it was very lucky to have found another craft so quickly, and he was filled with something like pride, knowing that he had promised help and could now deliver it.\n\nHe and Frank positioned their canoe in the path of the boat and waved their arms. The fan boat came straight for them, and when it was close, Zeitoun could see that there were four or five uniformed officers aboard; he wasn't sure if they were police or military, but he was very happy to see them. He waved, and Frank waved, both of them yelling \"Stop!\" and \"Help!\"\n\nBut the fan boat did not stop. It swung around the canoe holding Zeitoun and Frank, not even slowing down, and continued down Claiborne. The men aboard the fan boat barely glanced at them.\n\nThe fan boat's wake nearly tipped their canoe. Zeitoun and Frank sat still, gripping either side until the waves subsided. They hardly had time to exchange incredulous looks when another boat came their way. Again it was a fan boat, also with four military personnel aboard, and again Zeitoun and Frank waved and called for help. Again the fan boat swung around them and continued without a word.\n\nThis happened repeatedly over the next twenty minutes. Ten of these vessels, all staffed by soldiers or police officers, ignored their canoe and their calls for assistance. Where were these boats going, what were they looking for, if not for residents of the city asking for help? It defied belief.\n\nFinally a different sort of boat approached. It was a small fishing boat manned by two young men. Though Zeitoun and Frank were disheartened and unsure if anyone would stop, they gave it a try. They stood in the canoe, they waved, they yelled. This boat stopped.\n\n\"We need help,\" Frank said.\n\n\"Okay, let's go,\" the men on the boat said.\n\nThe young men threw a line to Zeitoun, who tied it to the canoe. The motorboat towed Zeitoun and Frank to the woman's house, and once they were close, the young men cut the engine and coasted toward the porch.\n\nZeitoun jumped into the water again and swam to her door. The woman was exactly as they'd left her, in her foyer, floating near the ceiling.\n\nNow they only had to figure out how to get her into the fishing boat. She couldn't lift herself into the boat; that wasn't an option. She couldn't drop down into the water for leverage. It was too deep and she could not swim.\n\n\"You have a ladder, ma'am?\" one of the young men asked.\n\nShe did. She directed them to the detached garage at the end of the driveway. Zeitoun dropped into the water, swam to the garage, and retrieved it.\n\nWhen he brought it back, he set it on the ground and against the boat. The plan was that the woman would let go of the bookshelf, grab the ladder, put her feet onto it, and climb up until she was above the boat and able to step into the hull.\n\nZeitoun held the ladder while the two young men steadied it against the boat, ready to receive her. It seemed an ingenious plan.\n\nBut she couldn't climb the ladder. She had a bad leg, she said, and couldn't put pressure on it. It took a certain degree of agility, and she was eighty years old, weakened by staying awake for twenty-four hours while floating near her ceiling, thinking only that she might drown in her own home.\n\n\"I'm sorry,\" she said.\n\nThere was only one option now, they decided. They would use the ladder as a sort of gurney. They would prop one end on the side of the fishing boat, and one of the young men would stand on the porch, holding the other side. They would then have to lift it high enough to get her over the lip of the boat, and far enough in that she could roll into the hull.\n\nZeitoun realized that two men, one on either end of the ladder, would not be enough to lift a woman of over two hundred pounds. He knew he would have to push from below. So when the two young men were in position, and the woman was ready, Zeitoun took a deep breath and went under. From below the surface, he could see the woman let go of the bookshelf and grab the ladder. It was awkward, but she managed to place herself atop it, as if it were a kind of raft.\n\nAs she put weight on the ladder, Zeitoun positioned his shoulders under it and pushed up. The motion was akin to a shoulder-press machine he'd once used at a gym. He straightened his legs, and as he did, the ladder rose from the water until he saw light breaking the surface, until he felt the air on his face and was finally able to exhale.\n\nThe woman rolled into the bed of the boat. It was not a graceful landing, but she managed to sit up. Though she was wet and breathing heavily, she was unhurt.\n\nZeitoun shuddered as he watched her recover. It was not right to watch a woman of her age suffer like this. The situation had stolen her dignity, and it pained him to bear witness.\n\nZeitoun climbed back into the canoe. Frank, smiling and shaking his head, stretched out his hand from the fishing boat.\n\n\"That was something,\" Frank said.\n\nZeitoun shook his hand and smiled.\n\nThe men sat in silence, letting the woman determine when it was time to go. They knew it was an impossible thing for her to see her house like this, untold damage and loss within. At her age, and with the years it would take to restore the home, she would likely never return. They gave her a moment. Finally she nodded and they arranged their convoy. Zeitoun was alone in the canoe, being towed behind. He was soaked and exhausted.\n\nWith Frank directing the fishing boat, they made their way toward the couple who had been waving the white cloth. On the way there, they heard another cry for help.\n\nIt was another older couple in their seventies, waving from their second-story window.\n\n\"You ready to leave?\" Frank asked.\n\n\"We are,\" the man in the window said.\n\nThe young fishermen brought the caravan to the window, and the couple, fit and agile, lowered themselves into it.\n\nWith six people now aboard the fishing boat, they arrived at the white-flag house. The couple living there lowered themselves down, making the number in the fishing boat eight. The young men had seen a temporary medical staging ground set up at the intersection of Napoleon and St. Charles, and they agreed that they would deliver the passengers there. It was time for Zeitoun and Frank to part ways with their companions. Frank stepped back into the canoe and said goodbye.\n\n\"Good luck with everything,\" one of the young men said.\n\n\"You too,\" Zeitoun said.\n\nThey had never exchanged names.\n\n* * *\n\nIn Baton Rouge, Kathy was again driving to kill time, her car full of children. Needing distraction from the news on the radio\u2014it was getting worse every hour\u2014she stopped periodically at whatever stores or restaurants were open. Zeitoun had sounded so calm on the phone the previous night, before his phone had given out. But since then conditions in the city had devolved. She was hearing reports of unchecked violence, widespread chaos, thousands presumed dead. What was her lunatic husband doing there? She tried his phone again and again, hoping he had somehow found a way to charge it. She tried the home phone, in case the water had miraculously dropped below the phone box and the wiring was undamaged. She got nothing. The lines were dead.\n\nOn the radio, they were reporting that another ten thousand National Guardsmen were being sent to the region, about one-third of them directed to maintain order. There would soon be twenty-one thousand National Guard troops in the area, coming from all over the country\u2014West Virginia, Utah, New Mexico, Missouri. How could her husband be so calm when every branch of the armed forces was scrambling?\n\nShe turned off the radio and tried Zeitoun again. Nothing. She knew she shouldn't worry yet, but her mind took dark turns. If she was out of touch with her husband already, how would she know if anything was wrong? How would she know if he was alive, in danger, dead? She was getting ahead of herself. He was in no danger. The winds were gone, and now it was just water, placid water. And troops were on their way. No cause for worry.\n\nReturning to her family's house in Baton Rouge, she found her mother there. She had come to deliver ice. She greeted all the kids and looked at Kathy.\n\n\"Why don't you take off that thing and relax?\" she said, pointing to Kathy's hijab. \"He's not here. Be yourself.\"\n\nKathy suppressed a dozen things she wanted to say, and instead channeled her rage into packing. She would take the kids and go to a motel, a shelter. Anywhere. Maybe to Arizona. It just wasn't working in Baton Rouge. And it was all so much worse not knowing where Zeitoun was. Why did that man insist on staying? It was a cruel thing, really. He wanted to make sure that his family was safe, but Kathy, his wife, wasn't afforded the same certainty. When they next spoke, she was determined to get him to leave the city. It didn't matter anymore why he wanted to stay. Forget the house and property. Nothing could be worth it.\n\nIn New Orleans, Zeitoun was invigorated. He had never felt such urgency and purpose. In his first day in his flooded city, he had already assisted in the rescue of five elderly residents. There was a reason, he now knew, that he had remained in the city. He had felt compelled to stay by a power beyond his own reckoning. He was needed.\n\nZeitoun and Frank's next stop was Zeitoun's property, back on Claiborne at number 5010. He and Kathy had owned the home, a two-story residence, for five years. It was a rental unit, with four to six tenants at any given time.\n\nWhen they arrived, they found Todd Gambino, one of Zeitoun's tenants, on the front porch, a bottle of beer in his hand. Todd was a stout man in his late thirties, and had lived there as long as the Zeitouns had owned the building. He worked as a mechanic at a SpeeDee Oil Change and Tune-Up franchise most of the week, and had a part-time job delivering lost luggage for the airport. He was a good tenant; they'd never had a late check or any sort of problem from him.\n\nHe stood up, incredulous, as Zeitoun approached.\n\n\"What're you doing here?\" he asked.\n\n\"Really? I came to check on the building,\" Zeitoun said, smiling, knowing how ludicrous it sounded. \"I wanted to check on you.\"\n\nTodd couldn't believe it.\n\nZeitoun and Frank got out of the canoe and tied it to the porch. They were both happy to stand on solid ground again.\n\nTodd offered them beers. Zeitoun passed. Frank accepted and sat on the porch steps while Zeitoun went inside.\n\nTodd lived in the first-floor unit of the building, and had brought all of his possessions up to the second floor. The front rooms and hallway of the house were full of furniture, chairs and desks stacked on tables and couches. Various electronics saved from the flood were now resting on the dining-room table. It looked like a haphazard estate sale.\n\nThe damage to the house was extensive but not irreparable. Zeitoun knew the basement would be a loss, and might not be habitable for some time. But the first and second floors had not been badly harmed, and this gave Zeitoun comfort. There was a lot of dirt, mud, grime\u2014much of it from Todd moving things upstairs and rushing in and out of the house\u2014but the damage could have been far worse.\n\nZeitoun learned from Todd that because the house's phone box was above the water line, the landline was still working. He immediately dialed Kathy's cell phone.\n\n\"Hello? I'm here,\" he said.\n\nShe almost screamed. She hadn't realized how worried she'd been. _\"Alhamdulilah_ ,\" she said, Arabic for _Praise be to God_. \"Now get out.\"\n\nHe told her he would not be leaving. He told her about the woman in the ballooning dress in the foyer, how he had lifted the ladder to save her. He told her about the fishermen, and Frank, and the two elderly couples. He was talking so fast she laughed.\n\n\"So when do you plan to leave?\" she asked.\n\n\"I don't,\" he said.\n\nHe tried to explain. If he left, what would he do? He would be in a home full of women, with nothing to occupy himself. He would eat, watch TV, and be left to worry from afar. Here, in the city, he could stay and monitor developments. He could help where needed. They had a half-dozen properties to look after, he reminded her. He was safe, he had food, he could take care of himself and prevent further damage.\n\n\"Really? I want to see this,\" he said.\n\nHe wanted to see everything that had happened and would happen with his own eyes. He cared about this city and believed in his heart he could be of use.\n\n\"So you feel safe?\" she asked.\n\n\"Of course,\" he said. \"This is good.\"\n\nKathy knew that she couldn't dissuade him. But how would she explain to her children, as they watched images of the city drowning, that their father was there by choice, paddling around in a secondhand canoe? She tried to reason with him, noting that the TV reports were saying that things were only getting worse, that the water would soon become infected with all manner of pollutants\u2014oil, garbage, animal remains\u2014and that diseases would soon follow.\n\nZeitoun promised to be careful. He promised to call back at noon the next day, from the house on Claiborne.\n\n\"Call every day at noon,\" she said.\n\nHe said he would.\n\n\"You better,\" she said.\n\n* * *\n\nThey hung up. Kathy turned on the television. The news led with reports of lawlessness and death. The media consensus was that New Orleans had descended into a \"third-world\" state. Sometimes this comparison was made with regard to the conditions, where hospitals were not open or working, where clean water and other basic services weren't available. In other instances, the words were spoken over images of African American residents wilting in the heat outside the Morial Convention Center or standing on rooftops waving for help. There were unverified reports of roving gangs of armed men, of guns being fired at helicopters trying to rescue patients from the roof of a hospital. Residents were being referred to as refugees.\n\nKathy was certain Zeitoun was unaware of the level of danger being reported. He may have felt safe where he was in Uptown, but what if there really was chaos, and that chaos was simply making its way to him? She was reluctant to believe the hyperbolic and racially charged news coverage, but still, things were devolving. Most of those left in the city were trying desperately to get out. She couldn't stand it. She called the house on Claiborne again. No answer.\n\nHe was already gone. Zeitoun and Frank were paddling back to Zeitoun's house on Dart Street. As they made their way home, passing a half-dozen fan boats along the way, it occurred to Zeitoun that he and Frank had heard the people they had helped, in particular the old woman floating inside her home, because they were in a canoe. Had they been in a fan boat, the noise overwhelming, they would have heard nothing. They would have passed by, and the woman likely would not have survived another night. It was the very nature of this small, silent craft that allowed them to hear the quietest cries. The canoe was good, the silence was crucial.\n\n* * *\n\nZeitoun dropped Frank at his house and made for home. His paddle kissed the clean water, his shoulders worked in perfect rhythm. Zeitoun had traveled five, six miles already that day, and he wasn't tired. Night was falling, and he knew he had to be home, safe on his roof. But he was sorry to see the day end.\n\nHe tied the canoe to the back porch and climbed up into the house. He retrieved a portable grill and brought it to the roof. He made a small fire and cooked chicken breasts and vegetables he'd thawed that day. The night fell as he ate, and soon the sky was darker than any he'd known in New Orleans. The sole light came from a helicopter circling downtown, looking tiny and powerless in the distance.\n\nUsing bottled water, Zeitoun cleaned up and prayed on the roof. He crawled into the tent, his body aching but his mind alive, playing back the events of the day. He and Frank really had saved that woman, hadn't they? They had. It was a fact. They had brought four others to safety, too. And there would be more to do tomorrow. How could he explain to Kathy, to his brother Ahmad, that he was so thankful he had stayed in the city? He was certain he had been called to stay, that God knew he would be of service if he remained. His choice to stay in the city had been God's will.\n\nToo excited to sleep, he went back through the window and into the house. He wanted to find the photo of Mohammed again. He'd forgotten who was with him in the picture\u2014was it Ahmad?\u2014and he wanted to see the expression on Mohammed's face, that world-conquering smile. He retrieved the box of pictures, and while looking for that one he found another.\n\nHe'd forgotten about this photo. There he was, Mohammed with the vice president of Lebanon. Zeitoun hadn't seen the image for a few years. Mohammed wasn't even twenty, and he'd won a race starting in Saida and ending in Beirut, a distance of twenty-six miles. The crowd was stunned. He had come out of nowhere, Mohammed Zeitoun, a sailor's son from the tiny island of Arwad, and stunned everyone with his strength and endurance. Zeitoun knew his father, Mahmoud, was somewhere in the crowd. He never missed a race. But it had not always been so.\n\nMahmoud wanted Mohammed, and all of his sons, working on dry land, so Mohammed spent his early teenage years as a craftsman, laying brick and apprenticing for an ironsmith. He was a powerfully built young man, and was finished with school at fourteen. At eighteen he looked much older, with a full mustache and a square jaw. He was both a workhorse and a charmer, admired equally by his elders and the young women in town.\n\nWith his father's grudging approval, Mohammed crewed on local fishing boats in the afternoons and evenings, and even at fourteen, after a full day of fishing miles from land, Mohammed insisted on swimming to shore. The other fishermen would have barely pulled in the last net when they would hear a splash and see Mohammed cutting through the sea, racing them to the beach.\n\nMohammed didn't tell his father about such endeavors, and he certainly didn't tell him when, a few years later, he decided that he was destined to be the world's greatest long-distance swimmer.\n\nIt was 1958. Egypt and Syria, reacting to a number of political factors, including growing American influence in the region, merged, creating the United Arab Republic. The union was meant to create a more powerful bloc, one that might grow to include Jordan, Saudi Arabia, and others. There was wide public support for the alliance, pride bursting from the streets and windows of Syria and Egypt, the citizens of both countries seeing the union as a step along the way to a broader alignment between the Arab states. There were parades and celebrations from Alexandria to Lattakia.\n\nOne of the commemorative events was a race between Jableh and Lattakia, in which swimmers from all over the Arab world would swim thirty kilometers through the Mediterranean. It was the first race of its kind on the Syrian coast, and eighteen-year-old Mohammed followed every step, from the preparations to the race itself. He watched the swimmers train, studying their strokes and regimen, longing to be part of it himself. He managed to be appointed to the crew of the guide boat for one of the competitors, Mouneer Deeb, which would keep pace with him along the race's route.\n\nAlong the way, unable to contain himself, Mohammed jumped in and swam alongside Deeb and the other contestants. He not only kept up with the professionals, he impressed one of the judges. \"That boy is great,\" the judge said. \"He is going to be a champion.\" From that day on Mohammed thought of little else but the fulfillment of that prophecy.\n\nStill only eighteen years old, he worked mornings as a mason and ironsmith, afternoons as a fisherman, and at night he began to train for the next year's race. He kept his training secret from his father, even when he undertook two long-distance tests, one between Lattakia and Jableh and another between Jableh and Baniyas. Soon enough, though, Mahmoud learned of his son's aspirations, and, fearing he would lose his son to the unforgiving sea that had almost taken his own life, he forbade him from swimming long distances. He wanted him out of fishing, away from the sea. He wanted his son alive.\n\nBut Mohammed could not stop. As difficult as it was to disobey his father, he continued to train. Telling no one in his family, Mohammed entered the next year's race. As he stepped out of the water in Lattakia, the cheers were deafening. He had won handily.\n\nBefore Mohammed could return home, an old friend of Mahmoud's, himself a champion swimmer, visited the Zeitoun house, congratulating Mahmoud on his son's victory. This is how Mahmoud learned that Mohammed Zeitoun was the best swimmer in all of Syria.\n\nBy the time Mohammed arrived home that night, Mahmoud had given up his resistance. If his son wanted this, and if his son was destined to swim\u2014if God had made him a swimmer\u2014then Mahmoud could not stand in the way. He bought Mohammed a bus ticket to Damascus to train and compete with the best swimmers in the region.\n\nZeitoun found another photo. Mohammed's first major victory came in that same year, 1959, in a race in Lebanon. The field was crowded, filled with well-known names, but Mohammed not only finished first, he did so in record time: nine hours and fifty-five minutes. This photo, Zeitoun was almost sure, was taken during the celebration afterward. Thousands were there, applauding his brother.\n\nHow old was Zeitoun at the time? He did the calculations in his head. Just a year. He was maybe one year old. He remembered nothing of those early wins.\n\nThe next year, Mohammed entered the famed race between Capri and Naples, a contest that attracted the best swimmers in the world. The favorite was Alfredo Camarero, an Argentinean, who had placed first or second in the race five years running. Mohammed was an unknown when the race began at six in the morning, and after eight hours, when he was approaching shore, he had no idea that he was in the lead. It wasn't until he stepped out of the sea, hearing shrieks of surprise and the chanting of his name, that he realized he'd won. \"Zeitoun the Arab has won!\" they cheered. No one could believe it. A Syrian winning the world's greatest long-distance competition? Camarero told everyone that Mohammed was the strongest swimmer he had ever seen.\n\nMohammed dedicated the victory to President Nasir. In return, Nasir made the twenty-year-old Mohammed an honorary lieutenant in the navy. The prince of Kuwait attended the race and celebrated him at an honorary dinner in Naples. The next year Mohammed won the Capri-to-Naples race again, this time breaking the course record set by Camarero by fifteen minutes. Mohammed was now indisputably the best ocean swimmer in the world.\n\nAs a boy, Abdulrahman was enthralled, proud beyond measure. To grow up in that house, with a brother like that, to bask every day in the glory he'd brought to the family\u2014his siblings' pride in Mohammed fueled how they felt when they awoke each day, how they walked and talked and were perceived in Jableh and Arwad and everywhere across Syria. It changed, permanently, how they saw the world. Mohammed's accomplishments implied\u2014proved, really\u2014that the Zeitouns were extraordinary. It was incumbent, thereafter, on each and every child to live up to that legacy.\n\nIt had been forty-one years since Mohammed's death. Mohammed's incredible rise and premature passing had shaped the trajectory of Zeitoun's family in general and of Abdulrahman in particular, but he didn't like to dwell on it. In his less generous moments he believed his brother had been stolen from him, that the unfairness of taking such a beautiful man so young put many things into question. But he knew he was wrong to think this way, and it was unproductive in any case. All he could do now was honor his brother's memory. Be strong, be brave, be true. Endure. Be as good as Mohammed was.\n\nZeitoun tucked himself into the tent and fell into a fitful sleep. All over the neighborhood, the dogs were mad with hunger. Their barking was wild, unmoored, spiraling.\n\n# THURSDAY SEPTEMBER 1\n\nBy six a.m., Kathy had the Odyssey packed and the kids buckled in. Her sisters were still asleep as she quietly backed out of the driveway, leaving Baton Rouge. It was fifteen hundred miles to Phoenix.\n\n\"Are we really leaving Mekay?\" Nademah asked.\n\nEven Kathy couldn't believe it, but what else could they do? She had begged Patty to let her leave the dog there for a week; she'd given dog food and money to one of Patty's teenage sons to care for poor Mekay. It was better than putting her in a kennel, and far better than trucking the dog all the way to Phoenix and back. Kathy didn't have the nerves for it. It was hard enough with four kids.\n\nThey were beginning what would be a three-day drive, minimum\u2014more likely four or five. What was she doing? It was crazy to drive four days in a car full of kids. And making the decision without her husband! It had been so long since she'd been in such a situation. But she had no choice. She couldn't stay in Baton Rouge for however many weeks it would be before New Orleans was habitable again. She hadn't even begun to think about school, about clothes\u2014they'd only packed for two days\u2014or about what they would do for money while the business was at a standstill.\n\nHeading west on I-10, she felt some measure of relief in knowing that at the very least, on the open road she would have some time to think.\n\nOut on the highway, she dialed the Claiborne house. Though it was hours before their agreed-upon time, she called in case Zeitoun had gotten there first and was waiting to call her. The phone rang three times.\n\n\"Hello?\" a man said. The voice was an American's, not her husband's. It was gruff, impatient.\n\n\"Is Abdulrahman Zeitoun there?\" she asked.\n\n\"What? Who?\"\n\nShe repeated her husband's name.\n\n\"No, no one here by that name.\"\n\n\"Is this 5010 Claiborne?\" she asked.\n\n\"I don't know. I think so,\" the man said.\n\n\"Who is this?\" she asked.\n\nThere was a pause, then the line went dead.\n\n* * *\n\nKathy drove for a mile before she could even wrap her mind around what had just happened. Who was that voice? It was not one of the tenants; she knew them all. It was a stranger, someone who had found a way into the house and was now answering the phone. Again her mind took quick turns downward. What if the man on the phone had killed her husband and robbed the house and moved in?\n\nShe pulled into a McDonald's and parked, calming herself down. She turned on the radio and almost immediately came upon a report from New Orleans. She knew she shouldn't listen, but she couldn't help it. The reports of lawlessness were worse than before, and Governor Blanco, in a statement directed to would-be criminals, warned that war-hardened U.S. soldiers were on the way to New Orleans to restore order at any cost. \"I have one message for these hoodlums,\" she said. \"These troops know how to shoot and kill, and they are more than willing to do so if necessary, and I expect they will.\"\n\nKathy knew she should turn the dial before the kids heard any of it, but it was too late.\n\n\"Did they say the city was flooded, Mama?\"\n\n\"Is our house under water?\"\n\n\"Are they shooting people, Mama?\"\n\nKathy turned the radio off. \"Please, babies, don't ask me questions.\"\n\nShe steeled herself and got back on the highway, determined to drive straight through to Phoenix. She just had to get to Yuko and she would be okay. Yuko would settle her. Of course Zeitoun was okay, she told herself. The man on the phone could have been anyone. There would be nothing unusual about people sharing a phone when most of the city's landlines had ceased to function.\n\nFor a few minutes she was calm. But the kids started in with the questions again.\n\n\"What happened to our house, Mama?\"\n\n\"Where's Daddy?\"\n\nThis got Kathy's mind going again. What if that man _was_ her husband's killer? What if she had just spoken to the man who had murdered him? She felt as if she had been watching, from above, the convergence of forces on her husband. Only she knew what was happening in the city, the madness, the suffering and desperation. He had no television, couldn't know the extent of the chaos. She had seen the images from helicopters, the press conferences, she had heard the statistics, the stories of gangs and rampant crime. Kathy bit her lip. \"Babies, don't ask me right now. Don't ask me.\"\n\n\"When are we going home?\"\n\n\"Please!\" Kathy snapped. \"Just leave it alone for a minute. Let me think!\" She couldn't hold it in anymore. She could barely see the road. The lines were disappearing. She felt it coming on and pulled over. She was blind with tears, wiping her nose with the back of her hand, her head against the steering wheel.\n\n\"What's wrong, Mama?\"\n\nThe highway flew beside her.\n\nIn a few minutes, she managed to gather herself enough to pull into a rest stop. She called Yuko.\n\n\"Don't drive another foot,\" Yuko said.\n\nWithin twenty minutes a plan was shaped. Kathy stayed put while Yuko's husband Ahmaad looked into flights. Kathy would only have to make it as far as Houston. Yuko would arrange for Kathy and the kids to spend the night at a friend's house there. Ahmaad would fly to Houston immediately, and in the morning he would meet her there and drive the family all the way to Phoenix.\n\n\"Are you sure?\" Kathy asked.\n\n\"I'm your sister. You're my sister. You're all I have,\" Yuko said. Her mother Kameko had passed away that year. The loss had been devastating to both Yuko and Kathy.\n\nThis got Kathy crying all over again.\n\nThat morning Zeitoun woke after nine, exhausted from the howling of the dogs. He was determined this day to find them.\n\nAfter his prayers, he paddled out over his flooded yard. The dogs seemed very near. He crossed the street and went left on Dart. Only a few houses down, he found the source.\n\nIt was a house he knew well. He paddled closer, and the dogs went wild, their desperate sounds coming from within. Now he had to find a way inside. The first story was flooded, so he assumed the dogs\u2014two of them, he guessed\u2014were trapped on the second. There was a many-boughed tree near the house. He paddled to it and tied the canoe to the trunk.\n\nHe lifted himself into the tree, climbing until he could see through a second-story window. He saw no dogs, but he could hear them. They were in that house, and they knew he was close. The tree where he was standing was about ten feet from the window. He couldn't jump. It was too far.\n\nAt that moment, he spotted a plank, a foot wide and sixteen feet long, floating in the sideyard. He climbed down, paddled to the plank, brought it to the house, and leaned it against the tree. He climbed up again and lifted the plank to create a bridge between the tree and the roof. He was about sixteen feet off the ground, about eight feet above the waterline.\n\nThe bridge he created was not so different from the scaffolding he used every day in his work, so after testing it quickly with the weight of one foot, he walked across and onto the roof.\n\nFrom there he pried a window open and ducked into the house. The barking grew louder and more urgent. He walked through the bedroom he'd arrived in, hearing the dogs grow more hysterical. As he strode through the second-floor hallway he saw them: two dogs, a black Labrador and a smaller mixed breed, in a cage. They had no food, and their water dish was empty. They seemed confused enough to bite him, but he didn't hesitate. He opened the cage and let them out. The Labrador ran past him and out of the room. The smaller dog cowered in the cage. Zeitoun stepped back to give him room, but he stayed where he was.\n\nFor the Labrador, there was nowhere to go. He tried the stairs and saw the water reached to just a few inches below the second floor. He returned to Zeitoun, who had a plan.\n\n\"Wait here,\" he told them.\n\nHe walked back across the plank bridge, climbed down the tree and into his canoe, and paddled back to his house. He climbed up to the roof, slipped through his window, and went down the few steps not underwater. Knowing Kathy kept the freezer stocked with meat and vegetables, he leaned down and removed two steaks, quickly closing the door to keep the finite cold from escaping. He walked back up to the roof, grabbed two plastic water bottles, and dropped them and the steaks into the canoe below. He shimmied down and returned to the house of the dogs.\n\nAgain they sensed him approaching, and this time they were both waiting by the window, their heads peeking over the sill. When they smelled the meat, frozen though it was, they began barking wildly, their tails wagging. Zeitoun refilled their water dish and they dove for it. After drinking their fill they went to work on the steaks, gnawing on them until the meat thawed. Zeitoun watched for a few minutes, tired and content, until he heard more barking. There were other dogs, and he had a freezer full of food. He went back to his house to prepare.\n\nHe stacked more meat into his canoe and went in search of the other animals left behind. Almost immediately after leaving his house he heard a distinct barking, muffled, coming from almost the same location as the dogs he'd just found.\n\nHe paddled closer, wondering if there was actually a third dog in the home he'd just been in. He anchored the canoe to the tree again, took two steaks with him, and climbed up. From the middle bough he looked this time to the neighboring house, the one on the left, and saw two more dogs, jumping against the glass.\n\nHe pulled the plank away from the first house and arranged it so it extended to the other. The dogs, seeing him coming, went wild, leaping in place.\n\nIn a moment, he had opened the window and stepped in, the two dogs jumping at him. He dropped the two steaks and the dogs pounced, forgetting about him entirely. He needed to give them water, too, so he again paddled home and brought more water bottles and a bowl back to them.\n\nZeitoun left the window open enough to allow the dogs to get fresh air, then walked across the plank again and climbed down the tree to his canoe. He paddled off, thinking it was about time to call Kathy.\n\n* * *\n\nAs he paddled, he noticed that the water was growing more contaminated. It was darker now, opaque, streaked with oil and gasoline, polluted with debris, food, garbage, clothing, pieces of homes. But Zeitoun was in high spirits. He felt invigorated by what he'd been able to do for the dogs, that he was there for those animals, and four dogs that almost certainly would have starved would now live because he had stayed behind, and because he had bought that old canoe. He couldn't wait to tell Kathy.\n\nBy noon he'd returned to the house on Claiborne. Today Todd was gone and the house was empty. He went inside and called.\n\n\"Oh thank God!\" Kathy said. \"Thank God thank God thank God. Where have you been?\" She and the kids were still driving to Houston. She pulled over.\n\n\"What're you worried about?\" Zeitoun asked. \"I said I'd call at noon. It's noon.\"\n\n\"Who was that man?\" she asked.\n\n\"What man?\" he asked.\n\nShe explained that when she'd called earlier that day, someone else had answered the phone. This was unsettling to Zeitoun. As they spoke, he looked around the house. There was no sign of theft or crime of any kind. There were no broken locks or windows. Maybe the man had been a friend of Todd's? He promised Kathy it was nothing at all to worry about, that he would get to the bottom of it.\n\nKathy, calmer now, was glad to hear that he had been able to help the dogs, that he was feeling useful. But she didn't want him in New Orleans anymore, no matter how many dogs he was feeding or how many people he was finding and saving.\n\n\"I really want you to leave,\" she said. \"The news coming out of the city, it's so bad. There's looting, killing. Something bad is going to happen to you.\"\n\nZeitoun could hear how worried she was. But he hadn't seen anything like the chaos she described. If it existed at all\u2014and she knew how the media was\u2014it would be downtown. Where he was, he said, it was so quiet, so calm, so otherworldly and strange, that he couldn't possibly be in danger. Maybe, he said, there was a reason he'd stayed, a reason he'd bought that canoe, a reason he was put in this particular situation at this particular time.\n\n\"I feel like I'm supposed to be here,\" he said.\n\nKathy was silent.\n\n\"It's God's will,\" he said.\n\nShe had no answer to this.\n\nThey moved on to practical matters. Her cell phone never worked well at Yuko's house in Phoenix, so she gave Zeitoun the landline there. He wrote it down on a piece of paper and left it by the Claiborne phone.\n\n\"Get the kids into school when you get to Phoenix,\" he said.\n\nKathy rolled her eyes.\n\n\"Of course,\" she said.\n\n\"I love you and them,\" he said, and they hung up.\n\nHe set out again, and immediately saw Charlie Ray, who lived just to the right of the Claiborne house. He was a blue-eyed carpenter in his fifties, a friendly and easygoing native Zeitoun had known for years. He was sitting on his porch like today was a day like any other.\n\n\"You stayed too,\" Zeitoun said.\n\n\"I guess I did.\"\n\n\"You need anything? Water?\"\n\nCharlie didn't, but said he might soon. Zeitoun promised to check in with him again, and paddled off, curious about how many people had remained in the city. If Frank stayed, and Todd and Charlie had weathered the storm, surely there were tens of thousands more. He was not alone in his defiance.\n\nHe continued on, knowing he should feel tired. But he was not at all tired. He had never felt stronger.\n\nThis day he ventured closer to downtown, passing families wading through the water, pushing laundry tubs full of their possessions. He paddled by a pair of women pushing an inflatable baby pool, their clothes and food inside. Each time, Zeitoun asked if he could help, and occasionally they would ask for a bottle or two of water. He would hand them whatever he had. He was finding so many things\u2014bottled water, MREs, canned food\u2014and whenever he saw anyone, he gave them whatever was in his canoe. He had plenty for himself at home, and didn't want any more weighing him down.\n\nHe paddled up to the I-10 ramp at Claiborne and Poydras, a concrete structure about ten feet above the waterline. Dozens of people were there, waiting for rescue. A helicopter had dropped off water and food, and they seemed to be well provisioned. They asked Zeitoun if he wanted any water, and he said that he had enough, but that he would bring it to those who needed it. They gave him a case. As he turned his canoe around he saw a half-dozen dogs with the group, most of them puppies. They seemed healthy and well-fed, and were keeping cool from the heat under the shade of the cars.\n\nZeitoun, assuming that whatever was ailing the city was likely worse downtown, chose not to get too close to the epicenter. He turned around and made his way back to Dart Street.\n\nAs Kathy was driving to Houston, Yuko was making arrangements for the family to spend the night with a longtime friend of theirs she called Miss Mary. Like Yuko and Kathy, Mary was an American, born into a Christian household, who had converted to Islam as an adult. Now her house had become a sanctuary for families fleeing the storm, and when Kathy's Odyssey pulled into the driveway there were already a dozen or more people there, all of them Muslims from New Orleans and other parts of Louisiana and Mississippi.\n\nMary, a bright-eyed woman in her forties, met Kathy and the kids in the driveway. She took their bags and hugged Kathy so tight that Kathy started crying yet again. Mary took them inside and showed the kids the pool in back, and within minutes the four of them were swimming and happy. Kathy collapsed on the couch and tried not to think of anything.\n\nWhen he got back to the house on Dart, Zeitoun found his tent in the water below. It had been blown off the roof\u2014probably, Zeitoun guessed, by a helicopter. He retrieved it and set it up again, dried the interior with towels, and then went inside the house to look for ballast. He brought out stacks of books, this time the heaviest ones he could find, and put them in the corners of the tent.\n\nAs he was inside stabilizing it, he heard another helicopter approach. The sound was deafening. He expected it to pass over his house on its way elsewhere, but when he poked his head out and looked up he saw that it was hovering over his house, over him. Two men inside were signaling to him.\n\nHe waved them off, trying to indicate that he was fine. But this only seemed to intrigue them more. The second man in the helicopter was beginning to lower a cage to him when Zeitoun thought to give the man a thumbs-up. He signaled to his tent and then to himself and gave the helicopter a series of frantic thumbs-ups and _a-okay_ signals. Finally understanding Zeitoun's intent to stay, one of the men in the helicopter decided to drop a box of water down to him. Zeitoun tried to wave him off again, to no avail. The box came down, and Zeitoun leapt out of the way before it knocked the tent flat and sent plastic bottles bouncing everywhere. Satisfied, the helicopter tilted away and was gone.\n\nZeitoun returned to restabilizing his shelter, beginning to get ready for bed. But like the night before, he was restless, his mind racing with the events of the day. He sat on the roof, watching the movement of the helicopters circling and swooping over the rest of the city. He made plans for the following day: he would venture farther toward downtown, he would revisit the I-10 overpass, he would check on the state of their office and warehouse over on Dublin Street. On the first floor there they kept their extra supplies\u2014tools, paints, brushes, drop cloths, everything\u2014and on the second floor they had their offices, with their computers, files, maps, invoices, deeds to the properties. He winced, thinking of what had become of the building, a rickety thing to begin with.\n\nAll night the helicopters roamed overhead. Besides them it was quiet; he heard no dogs. After his prayers, he fell asleep under a vibrating sky.\n\n# FRIDAY SEPTEMBER 2\n\nIn the morning Zeitoun rose early, climbed down to his canoe, and paddled across the street to feed the dogs. They whimpered as he approached, and he took it as relief and gratitude. He climbed the tree, stepped carefully across the plank to the house on the right, and crawled through the window. He dropped two large pieces of steak for the dogs and refilled their water dish. As they busied themselves, he climbed out of the window, stepped carefully over to the next-door roof, and made his way into the second house to feed the second pair of dogs. They barked and wagged their tails, and he dropped two pieces of lamb between them and refilled their water. He left through the window, climbed down to his canoe, and paddled off.\n\nIt was time to see what had become of his office building. It was about a half mile away, just off Carrollton, a nearby road lined with warehouses, chain stores, and gas stations. The water was filthy now, streaked with oil and spotted with detritus. Anyone left to wade through this would become sick, he was sure. But so far this day, he had seen no one in the water. The city was emptying. Every day there were fewer people wading, fewer faces in windows, fewer private watercraft like his.\n\nIt had been drizzling throughout the morning but now the rain began to pick up. The wind came on, and the day grew miserable. Zeitoun paddled into the wind, struggling to control the canoe, the wind rippling the brown-blue water.\n\nHe took Earhart over to Carrollton, and took Carrollton southwest on his way to Dublin. He expected that there might be people on Carrollton\u2014like Napoleon and St. Charles, it seemed a logical thoroughfare for rescue or military boats\u2014but when he got close, he saw no official personnel at all.\n\nInstead he saw a group of men gathered at the Shell station just across the street from his office. The station was elevated from the main road and was under only a few feet of water. The men, about eight or nine of them, were carrying full garbage bags from the station's office and loading them into a boat. It was the first looting he had seen since the storm, and these men were the first who fit the description of those Kathy had warned him about. This was an organized group of criminal opportunists who were not simply taking what they needed to survive. They were stealing money and goods from the gas station, and they were operating in numbers that seemed designed to intimidate anyone, like Zeitoun, who might see them or try to impede them.\n\nZeitoun was far enough away to observe without fear of them reaching him\u2014at least not quickly. Still, he slowed his canoe to keep a safe distance, trying to figure out a way to get to his office without passing directly by them.\n\nBut one of the men had already noticed him. He was young, wearing long denim shorts and a white tank top. He squared his shoulders to Zeitoun and made a point of revealing the handle of a gun he had holstered in his belt.\n\nZeitoun quickly looked away. He did not want to invite confrontation. He turned his canoe around and made his way toward the house on Claiborne. He would not check on the office this day.\n\nHe arrived before noon and called Kathy. She was still in Houston at Miss Mary's house.\n\n\"Won't be able to check on the office today,\" he said.\n\n\"Why?\" she asked.\n\nHe didn't want her to worry. He knew he had to lie.\n\n\"Rain,\" he said.\n\nShe told him that friends had been calling her, checking in to see where she and Zeitoun were, if they were safe. When she told them that her husband was still in the city, there was always a three-stage response. First they were shocked, then they realized it was Zeitoun they were talking about\u2014a man who did not inspire worry in any situation\u2014and finally they asked that while he was paddling around, would he mind checking on their property?\n\nZeitoun was all too happy to be given a mission, and Kathy obliged. She had just gotten a call from the Burmidians, friends of theirs for thirteen years. Ali Burmidian was a professor of computer science at Tulane University, and ran the Masjid ar-Rahmah, a Muslim student association on campus. They had a building on Burthe Street that housed a resource center and dorm for visiting students from the Arab world.\n\nDelilah Burmidian had just called Kathy, asking if Zeitoun could check on the building, to see what kind of damage it had sustained. Zeitoun said no problem, he would check on it. He knew the building well\u2014he'd been to functions there a few times over the years\u2014and he knew how to get there. He was curious, actually, to see what had become of the campus, given that it was on higher ground.\n\n\"Call again at noon,\" she said.\n\n\"Of course,\" Zeitoun said.\n\nBefore he left, Zeitoun called his brother Ahmad. After expressing great relief to hear from him, Ahmad got serious.\n\n\"You must leave,\" Ahmad said.\n\n\"No, no. I'm fine. Everything is fine,\" Zeitoun said.\n\nAhmad tried playing the big brother. \"Go to your family,\" he said. \"I really want you to leave. Your family needs you.\"\n\n\"They need me here more,\" Zeitoun said, trying not to sound too grandiose. \"This is my family, too.\"\n\nAhmad had no way to counter such a statement.\n\n\"This call is expensive,\" Zeitoun said. \"I'll call you tomorrow.\"\n\nWhen he arrived at Tulane, the water was so low there that he easily stepped from the canoe onto dry land. He walked into the tiled courtyard of the Masjid ar-Rahmah and looked around. The grounds were crosshatched with downed branches, but otherwise the property was undamaged. He was about to look inside when he saw a man emerging from the building's side door.\n\n\"Nasser?\" he said.\n\nIt was Nasser Dayoob. Also from Syria, Nasser had left the country in 1995, traveling first to Lebanon. From Beirut he stowed away on a tanker whose destination he did not know. It turned out it was heading to the United States, and when it made port Nasser jumped off and immediately sought asylum. He was eventually granted sanctuary, and by then he'd moved to New Orleans. He had stayed at the Masjid ar-Rahmah during his legal proceedings.\n\n\"Abdulrahman?\"\n\nThey shook hands and exchanged stories of what they had been doing since the storm. Nasser's home, in the Broadmoor neighborhood adjacent to Uptown, had been flooded, and he'd come to the student association for shelter, knowing it was on higher ground.\n\n\"You want to stay here or come with me?\" Zeitoun asked.\n\nNasser knew that he would be safe at the campus, with little possibility of flooding or crime, but still he went with Zeitoun. He too wanted to see what had become of the city and of his home.\n\nHe ran back into the building to get his duffel bag and then stepped into the canoe. Zeitoun gave him the other paddle and they were off.\n\nNasser was thirty-five and tall, with freckles and a thick mess of red hair. He was quiet, with a slightly nervous demeanor; when Kathy met him she'd thought he was a fragile sort of man. He was a sometime housepainter, and had occasionally worked for Zeitoun. They were not close friends, but running into Nasser here, after the flood, gave Zeitoun some comfort. They shared a lot of history\u2014Syria, emigration to America and New Orleans, work in the trades.\n\nAs they paddled, they talked about what they had seen so far, what they had been eating, how they had been sleeping. Both men had heard the dogs barking. Always the dogs barking at night. And Nasser, too, had fed dogs in the empty homes, on the streets, wherever he encountered them. It was one of the strangest aspects of this in-between time\u2014after the storm but before anyone had returned to the city\u2014the presence of these thousands of left-behind animals.\n\nThe wind was stronger now. Fighting through an angry horizontal rain, they paddled by the post office near Jefferson Parkway and Lafitte. The parking lot there had become a staging ground for evacuations. Residents who wanted to be airlifted out of the city could come to the post office and helicopters would take them, presumably, to safety.\n\nAs they paddled closer, Zeitoun asked Nasser if he wanted to leave. Not yet, Nasser said. He'd been hearing about the New Orleanians stranded under highway overpasses, and he didn't want to be among them. Until he heard more reliable reports of successful evacuations, he would stay in the city. Zeitoun told him he was welcome to stay at the Dart house or the house on Claiborne. He mentioned that there was a working phone on Claiborne, and this was a godsend to Nasser. He needed to call a half-dozen relatives, to let them know he was alive.\n\nThey paddled back to Claiborne, passing a full case of bottled water bobbing in the middle of the waterway. They lifted it into the canoe and continued on.\n\nWhen they arrived at the house, Nasser got out and began tying up the canoe. Zeitoun was stepping out when he heard a voice calling his name.\n\n\"Zeitoun!\"\n\nHe figured it was Charlie Ray, calling from next door. But it was coming from the house behind Charlie's, on Robert Street.\n\n\"Over here!\"\n\nIt was the Williamses, a couple in their seventies. Alvin was a pastor at New Bethlehem Baptist Church and wheelchair bound; Beulah was his wife of forty-five years. Zeitoun and Kathy had known them for almost as long as they'd lived in New Orleans. When the Zeitouns had lived nearby, Pastor Williams's sister used to come to Kathy for meals. Kathy could never remember how it started, but the sister was elderly, and liked Kathy's cooking, so around dinnertime, Kathy always had a plate ready for her. It went on for months, and it warmed Kathy to know someone would go to the trouble to eat what she'd made.\n\n\"Hello!\" Zeitoun called out, and paddled over.\n\n\"You think you could help us get out of here?\" Alvin asked.\n\nThe pastor and Beulah had waited out the storm but had now exhausted their supply of food and water. Zeitoun had never seen them look so weary.\n\n\"It's time to go,\" Alvin said.\n\n* * *\n\nGiven the rain and the wind, it was impossible to try to evacuate them in the canoe. Zeitoun told them he would find help.\n\nHe paddled up Claiborne, the wind and rain fighting him, to the Memorial Medical Center, where he knew there were police and National Guard soldiers stationed. As he approached, he saw soldiers in the alleyway, on the roof, on the ramps and balconies. It looked like a heavily fortified military base. When he got close enough to see the faces of the soldiers, two of them raised their guns.\n\n\"Don't come any closer!\" they ordered.\n\nZeitoun slowed his canoe. The wind picked up. It was impossible to stay in one place, and making himself heard was difficult.\n\n\"I'm just looking for help,\" Zeitoun yelled.\n\nOne of the soldiers lowered his gun. The other kept his trained on Zeitoun.\n\n\"We can't help you,\" he said. \"Go to St. Charles.\"\n\nZeitoun assumed the soldier hadn't heard him correctly. The wind was turning his canoe around, veiling his words. \"There's an old couple down the road that needs to be evacuated,\" he clarified, louder this time.\n\n\"Not our problem,\" the soldier said. \"Go to St. Charles.\"\n\nNow both guns were lowered.\n\n\"Why not call somebody?\" Zeitoun asked. Did the soldier really mean that Zeitoun should paddle all the way to the intersection of Napoleon and St. Charles when the soldier could simply call another unit on his walkie-talkie? What were they doing in the city, if not helping evacuate people?\n\n\"We can't call nobody,\" the other soldier said.\n\n\"How come?\" Zeitoun asked. \"With all this technology, you can't call someone?\"\n\nNow the soldier, only a few years older than Zeitoun's son Zachary, seemed afraid. He had no answer, and seemed unsure of what to do next. Finally he turned and walked away. The remaining soldiers stared at Zeitoun, holding their M-16s.\n\nZeitoun turned his canoe around.\n\nHe paddled to the intersection of Napoleon and St. Charles, his shoulders aching. The wind was making the work twice as difficult. The water grew shallow as he approached the intersection. He saw tents there, and military vehicles, and a dozen or so police officers and soldiers. He stepped out of his canoe and walked up to a man, a soldier of some kind, standing on the grassy median\u2014New Orleanians called it the _neutral ground_.\n\n\"I have a situation,\" Zeitoun said. \"I have a handicapped man who needs help, medical attention. He needs help now.\"\n\n\"Okay, we'll take care of it,\" the man said.\n\n\"Do you want the address?\" Zeitoun asked.\n\n\"Yeah, sure, give me that,\" the man said, opening a small notebook.\n\nZeitoun gave him the exact address.\n\nThe man wrote it down and put his notebook back in his pocket.\n\n\"So you'll go?\" Zeitoun asked.\n\n\"Yup,\" the man said.\n\n\"When?\" Zeitoun asked.\n\n\"About an hour,\" the man said.\n\n\"It's okay. They're on their way,\" Zeitoun said. \"They said one hour.\"\n\nThe pastor and his wife thanked Zeitoun and he returned to the Claiborne house. He picked up Nasser, and they set out to see what they could do. It was just after one o'clock.\n\nA thousand miles away, Yuko's husband Ahmaad was driving the Odyssey. Kathy was resting and the kids were in the back as they barreled through New Mexico. Ahmaad had been at the wheel for seven hours without a break. At this pace, they would make it to Phoenix by Saturday afternoon.\n\nAhmaad discouraged Kathy from listening to any news on the radio, but even on the rock and country stations snippets of information were leaking through: President Bush was visiting New Orleans that day, and had just lamented the loss of Trent Lott's summer home in coastal Mississippi. Heavily armed National Guardsmen had just entered the Convention Center, and though they had been led to believe their entry would be met with something like guerilla warfare, they had found no resistance whatsoever\u2014only exhausted and hungry people who wanted to leave the city. Kathy took comfort in this, thinking that perhaps the city was coming under control. The military presence, one commentator was saying, \"would soon be overwhelming.\"\n\nMaking their rounds, Zeitoun and Nasser found an abandoned military jeep and in it, a box of meals, ready-to-eat\u2014MREs. Shortly after, they encountered a family of five on an overpass, and gave them some water and the box of MREs. It was a tidy coincidence. Zeitoun didn't like to carry anything of value at all, and welcomed any opportunity to unload anything he'd found.\n\nIt was about five o'clock, the sky darkening, when Zeitoun and Nasser made their way back to the Claiborne house.\n\nZeitoun was sure that the pastor and his wife would have been rescued by that point, but just to be certain, he and Nasser made a detour and paddled over to Robert Street.\n\nAlvin and Beulah were still there, on the porch, their bags still ready, a light rain still falling on them. They had been waiting for four hours.\n\nZeitoun was furious. He felt helpless, betrayed. He'd made a promise to the pastor and his wife, and because he had been lied to, his promise had not been kept.\n\nHe apologized to the couple, explaining that he had first tried the hospital, where he was sent away at gunpoint, and then gone to St. Charles to tell the soldiers and the relief workers about their plight. The pastor expressed confidence that help was still on its way, but Zeitoun didn't want to take any chances.\n\n\"I'll figure something out,\" he said.\n\nWhen he and Nasser returned to the Claiborne house, they saw a small motorboat tied to the front porch. Inside the house, they found Todd Gambino sitting inside with a new dog. With the boat\u2014which Todd had seen floating under a ruined garage and figured he would put to use\u2014he'd been making his own rounds around the city, plucking people from porches and rooftops and bringing them to the overpasses and other points of rescue. He'd even found this dog, which was now happily eating food at Todd's feet, on a roof and had taken him in.\n\nAgain Zeitoun felt the presence of some divine hand. The Williamses needed help immediately, help he had not been able to provide, and here was Todd, with precisely the vehicle they needed, at precisely the right moment.\n\nTodd did not hesitate. Zeitoun agreed to care for the dog while he was gone, and Todd was off. He picked up Alvin and Beulah, cradling them one by one into the motorboat. Then he sped off toward the staging ground at Napoleon and St. Charles.\n\nThe mission took all of twenty minutes. Soon Todd was back, drinking a beer and relaxing again on the porch, his hand stroking the rescued dog's matted fur.\n\n\"Some things you just have to do yourself,\" he said with a smile.\n\nZeitoun had known Todd to be a good tenant, but he didn't know this side of him. They talked for a time on the porch, and Todd told him stories of his own rescues\u2014how he'd picked up dozens of people already, how he'd been shuttling them to hospitals and staging grounds, how easy it was with a motorboat. Todd had always been, to Zeitoun's mind, a bit of a wanderer, something of a playboy. He liked to have a good time, didn't want to be too tied down with rules and responsibilities. He smoked, he drank, he kept irregular hours. But here he was, his eyes alight, talking about carrying people to safety, how his arrival at any given house or overpass was met with cheers and thanks. A time like this could change a man, Zeitoun knew, and he was happy to see it happening here and now to Todd: a good man made better.\n\nThat night Nasser came back with Zeitoun to the house on Dart. They removed the last of the lamb from the freezer and barbecued on the roof, recounting what they had seen and what they had heard. But Nasser was exhausted, and faded quickly. He crawled into the tent and was soon fast asleep.\n\nAgain Zeitoun was restless. He was still angry about the pastor and his wife. Nothing upset him more than someone breaking a promise. Who had that man been, at Napoleon and St. Charles, who had said he would send help to the Williams couple? Why had he said he would come if he did not plan to come? Zeitoun tried to be generous. Perhaps he had been pulled away to another emergency. Perhaps the man had gotten lost along the way. But it was no use. There was no excuse that could suffice. The man had abrogated a simple agreement. He had promised help and he had not kept that promise.\n\nUnable to sleep, Zeitoun went back inside and sat on the floor of Nademah's room. Her smell, the smell of his girls, was faint now, replaced by rain and the beginnings of mildew. He missed them already. He could not think of more than a few times when he had been apart from them this long. It was always like this: the first day alone afforded a welcome sense of calm and quiet, but slowly the missing would begin. He would miss their voices, their bright dark eyes, the rumble of their feet up and down the stairs, their squeals and constant singing.\n\nHe opened one of the photo albums he'd saved and lay down on Nademah's bed, smelling her strawberry shampoo on the pillowcase. He found a picture from his first year at sea, aboard a ship captained by Ahmad. He marveled at his hair, so much of it then, and such vanity. He was about thirty pounds lighter then, a constant grin on his face, a man tasting the full feast of youth. His brother Ahmad had saved him, had opened to him worlds upon worlds.\n\nAhmad left home a year after their father's death, traveling to Turkey to study medicine. This was the presumption in the house, at least. Though Mahmoud had forbidden his sons from pursuing a life on the sea, Ahmad wanted nothing else. So he took a bus to Istanbul, telling his mother that his intention was to become a doctor. And for a while he did study medicine. But soon Ahmad left college and enrolled in a naval officer's training academy. When his mother learned Ahmad was to become a ship captain, she was surprised, but did not stand in his way. Two years later, Ahmad had graduated and was crisscrossing the Mediterranean and the Black Sea.\n\nZeitoun found one of Ahmad's photos. He had more pictures of Ahmad than he did of himself\u2014it was almost comical how many photos his brother took and kept and distributed to family members. He documented every port, every ship. In this one, he and his crew were grilling something, some kind of animal. Zeitoun stared at it. It looked like a greyhound. _Could it be?_ No. Zeitoun hoped it was not a dog. The banner above the men said EASTER 1978. In another picture, Ahmad was standing in the middle of downtown New Orleans. When he saw this photo, and so many others of Ahmad standing in front of this city or that monument, Zeitoun always thought of the people Ahmad had asked to take the pictures. Ahmad must have met a thousand people during these trips, chiefly in the pursuit of someone to help him document that _Ahmad Zeitoun, of Jableh, Syria, was here_. Here in Tokyo. Here in America. Here in India.\n\nWhile Ahmad was seeing every corner of the world in rapid succession, Zeitoun was back home in Jableh, and he wanted out. It was a hollow home, and Zeitoun couldn't stand it. During the days he worked at his brother Lutfi's construction-materials store, hearing the stories of Ahmad's continuing adventures, his trips to China, Australia, South Africa, Holland. Zeitoun knew his father would not have approved when he was alive, but he was gone now, and Mohammed was gone, too. Zeitoun did not want to be stuck in Jableh.\n\nHis mother knew his feelings. She had heard him pace back and forth on the second floor, had seen his eyes' longing look when he talked to Ahmad on the phone. So on her own accord, she called Ahmad one day and asked him to take his younger brother with him. It was time, she said, for Abdulrahman to leave Jableh and get away, if only for a spell, from their home so full of melancholy.\n\nAhmad called his younger brother and told him he'd be shipping out in a few weeks' time. Zeitoun was speechless. He kissed the phone. He kissed his mother and sisters. And when the time came, he gathered a sackful of things and met Ahmad in Greece.\n\nOn his first voyage, he was a deckhand, the youngest man onboard. The other crew members hailed from everywhere\u2014South Africa, Turkey, Nigeria\u2014and welcomed him warmly. Zeitoun was convinced Ahmad was treating him a bit more roughly than the others, to compensate for any suspicions of nepotism, but he didn't mind. He washed and painted and hauled. He did the jobs no one wanted to do.\n\nThey sailed from Piraeus to Naxos and back, and Zeitoun was in love with it all. He let his hair grow, he spent his free time on deck, looking out, watching the water come at the ship and disappear behind it. Though the schedule was grueling, four hours on and four off, all day and night, he didn't mind. He didn't need to sleep, not yet.\n\nHe had not known until then how badly he had needed this kind of freedom. He felt twice as strong, three times as tall. And finally Zeitoun knew Ahmad's secret, why he had become a sailor, why he had risked so much to become a captain. As they passed on deck or on their way to their different quarters, Zeitoun and Ahmad shared knowing glances, sheepish smiles. Only now did Zeitoun know liberation, and it was everything. Ahmad could see that his younger brother would not be returning to Jableh any time soon.\n\nTheir lives were at sea, together and apart, as they passed from their twenties to their early thirties. There were cargo ships, passenger ships, combinations of both. They brought Nebraskan wheat to Tokyo, Brazilian bananas to London, American scrap metal to India. They brought Romanian cement to Nigeria, and always in Nigeria there were stowaways; every time they left Lagos they could count on finding two or three men hiding, and always they made the same arrangement: earn your keep onboard, and when we reach the next port you're on your own.\n\nJobs on general cargo ships were prized most; they usually spent a week or two at port, giving the crew plenty of time to investigate the area. Zeitoun explored dozens of cities, always docking with a pocketful of money and no obligations to anyone. He would rent a car, devour the surrounding towns, explore the coast, visit famed mosques, meet women who would beg him to stay.\n\nBut he was a serious young man, perhaps too serious at times. It was no secret that seamen liked to play cards and enjoy a drink or two. Zeitoun didn't gamble and had never had a drop of alcohol, so when his own shifts were over, he went back to work, helping whoever needed it. And when there wasn't work to do, while his crewmates got stoned and took each other's money playing cards, he found a different diversion: he would go to the small pool onboard the ship and tie a rope around his waist. He would tie the other end to the wall, and then he would swim\u2014three hours at a stretch, strengthening his arms and back, testing himself. He was always testing himself, seeing how much his body could do.\n\nIn the end, Zeitoun spent ten years as a sailor. Aboard a ship called the _Star Castor_ he saw the Persian Gulf, Japan, Australia, and Baltimore. Aboard the _Capitan Elias_ , he saw Holland and Norway. He saw herds of humpbacks, breaching grey whales, schools of dolphins leading the ships to port. He saw the aurora borealis, meteor showers over tumbling black waves, night skies so clear the stars seemed within reach, hung from a ceiling by fishing wire. He served on the _Nitsa_ , the _Andromeda_ , he sailed all the way until 1988, when he landed in Houston and decided to explore inland. That brought him to Baton Rouge, and Baton Rouge brought him to Kathy, and Kathy brought him Zachary and Nademah and Safiya and Aisha.\n\nZeitoun prayed on the floor in his house, and then lay down on Nademah's bed, wondering where his wife and children were this night, if they had made it to Phoenix yet, thanking God that they were safe, that he was safe, that they would see each other soon.\n\n# SATURDAY SEPTEMBER 3\n\nIn the morning Zeitoun rose with the sun, prayed, and then checked the freezer. There wasn't much left, and what was left was thawing. It would be rotten by the following day. He figured it had to be eaten immediately, so he removed some hamburger for the dogs and figured he'd barbecue the rest that night. He'd invite Todd and Nasser and anyone else he could find. They'd cook all the meat that remained, and have some grim semblance of a party on his roof.\n\nHe paddled across the street to feed the dogs.\n\n\"How are you boys today?\" he asked the first two.\n\nThey whimpered, and ate, and licked his legs. He was amused by how grateful, how surprised, they were every day.\n\n\"Have a little faith,\" he said.\n\nHe climbed across the rickety board to the second pair of dogs. They whined as he climbed through the window.\n\n\"What're you so worried about?\" he asked them. \"Every day I come, same time. Don't worry.\"\n\nYuko's husband Ahmaad had driven through the night, stopping only once, and they finally arrived in Arizona midday on Saturday. They were both too dazed, too wired to sleep, and that first day at Yuko and Ahmaad's house was full of welcome distraction. Yuko and Ahmaad's five children loved the Zeitoun kids, and they loved their Aunt Kathy, particularly the boys. She was one of them, effortlessly so, and they treated her like a peer. They played video games and watched TV, and Kathy tried not to think about what had become of their home, where Zeitoun might be at that moment.\n\nZeitoun still feared getting near his office on Dublin\u2014the armed men were likely still nearby\u2014so he and Nasser had no set itinerary this day. They decided to do a thorough check of Uptown, to see if any neighbors were left, if any help was needed.\n\nPaddling south on Octavia Street, Zeitoun noted that with the strength of two, and without rain or wind, they were fast. They sped past homes, over cars, around debris.\n\nZeitoun had worked on a dozen or so homes on this street, and knew he would return when the waters fell away. With every passing day, the standing water went deeper into the homes, made it less likely anything within would be salvageable.\n\nNasser saw the helicopter first.\n\nThe helicopters were everywhere, but didn't usually hover so low for so long, and rarely in such a densely built neighborhood. Zeitoun could see this one through the trees and over the roofs long before he could see the water below it. Zeitoun and Nasser paddled toward it to find out what was going on. As they got closer, they saw a dark smudge in the water, a log or piece of debris. They continued paddling, now feeling the wind from the rotors, the ripples radiating outward.\n\nThe object in the water looked like a tire, shiny and bulbous\u2014\n\nIt was a body. They were sure now. It had turned, and now the head was visible. It was a man of average size, wearing a T-shirt and jeans, half-submerged, face-down.\n\nZeitoun looked up to the helicopter. Was it a rescue in progress? He looked closer. No. A man was pointing a camera at the body. He did so for a few more minutes and then the helicopter rose, tilted, and drifted off.\n\nZeitoun and Nasser maintained their distance. Zeitoun knew too many people in this neighborhood. If this was a neighbor or friend, he didn't want to see him this way.\n\nRattled, they paddled silently to the Claiborne house. Zeitoun had never imagined that the day would come that he might see such a thing, a body floating in filthy water, less than a mile from his home. He could not find a place for the sight in the categories of his mind. The image was from another time, a radically different world. It brought to mind photographs of war, bodies decaying on forgotten battlefields. _Who was that man?_ Zeitoun thought. _Could we have saved him?_ Zeitoun could only think that perhaps the body had traveled far, that the man had been swept from closer to the lake all the way to Uptown. Nothing else seemed to make sense. He did not want to contemplate the possibility that the man had needed help and had not gotten it.\n\nWhen Zeitoun tied the canoe to the Claiborne porch, the phone was ringing. He picked it up and found his brother Ahmad.\n\n\"I wish you would leave,\" Ahmad said.\n\n\"I'm fine. Safer every day,\" Zeitoun said. He had no plans to tell Ahmad about the body.\n\n\"My kids are worried about you.\" Ahmad's son Lutfi and daughter Laila had been watching CNN since the storm. They saw the images of devastation and desperation, and could not believe that their uncle was living amid all that.\n\n\"Tell them not to worry,\" Zeitoun said. \"And hello from me.\"\n\nZeitoun was grateful for his brother's constant concern. The Zeitoun siblings were all close-knit, but no one worried more, and spent more time collecting and updating addresses and phone numbers and photos, than Ahmad. Perhaps it was because he felt disconnected from them, living in Spain, but in any case he liked to know where his siblings were, what they were doing. And he focused on Abdulrahman in particular, so much so that one day, a few years before, Ahmad had called in the middle of the day in New Orleans and made a very strange proposal.\n\n\"What are you doing today?\" he'd asked.\n\nIt was a Saturday, and Zeitoun was about to go to the lake with Kathy and the kids.\n\n\"Do you know the corner of Bourbon and St. Peter?\"\n\nZeitoun said he did.\n\n\"I have an idea,\" Ahmad began, and then explained that he had found a website where he could tap into a live webcam at that corner. If Zeitoun went there, Ahmad could watch him, in real time, while sitting at his computer in Spain.\n\n\"You up for it?\" Ahmad asked.\n\n\"Sure,\" Zeitoun said. \"Why not?\"\n\nZeitoun packed the kids up in the van, drove the few miles to the French Quarter, and looked for the corner of St. Peter and Bourbon. Once there, he searched for the camera. He didn't find it, but figured he should at least stand there for a while. He and the kids stood on every corner, in fact, just in case. And when he got home, he called Ahmad, who was just about leaping through the phone.\n\n\"I saw you!\" he said. \"I saw you all! Next to the hot-dog stand!\"\n\nHe had watched them for five minutes, grinning the whole time. He had made a screen capture and emailed it.\n\nWhen he saw it, Zeitoun laughed, amazed. There he was, with all four kids. Nademah was just below the streetlight, Zachary was holding Safiya, and Zeitoun was holding Aisha. Ahmad, technophile and deeply protective brother, was, in very real ways, watching over Zeitoun at all times.\n\nOn the roof that night, Zeitoun and Todd and Nasser barbecued the remaining meat, noting that it was the first time any of them had been at any sort of social event since the storm. The conversation was awkward, and the humor had a dark edge to it. They talked about FEMA, about the Superdome and the Convention Center. They had been hearing isolated reports from the radio and others who had stayed in the city, and they were all relieved they had eschewed shelter there; they had known it would turn out poorly. None among them could live caged like that.\n\nThey talked about what the city would look like when the water was gone. There would be trees and trash everywhere\u2014the ground would look like that of a dredged lake. The roads would be impassable for cars and bikes, for almost any kind of vehicle.\n\n\"A horse could do it,\" Zeitoun said. \"We'll get some horses. Easy.\"\n\nEveryone laughed.\n\nAs the sky blackened, Zeitoun saw an orange light through the trees, less than a mile away. Soon all three men were watching the light grow, the flames twisting higher. Zeitoun was sure it had engulfed two or three buildings at least. Then he looked closer, realizing that the fire was very close to\u2014\n\n\"My office,\" he said.\n\nThere was paint there, hundreds of gallons. Paint thinner, lumber. So many toxic and flammable things.\n\n\"We have to go,\" he said.\n\nZeitoun and Todd climbed down the side of the house and into Todd's motorboat. They sped toward the fire until they could see the flames blooming white and orange between buildings and over treetops. When they got close, they saw that the fire encompassed an entire block. There were five houses alight, the flames grasping for a sixth. They had no tools to stanch a fire, and no plan at all for what they might do to put out a chemical inferno.\n\nZeitoun's office was unharmed, but it was no more than twenty feet from the fire. They tested the winds. It was a still night, with heavy humidity. There was no predicting where the fire would go, but it was certain that nothing could stop its course. There was a fire station four blocks away, but it was empty and flooded; there were no firefighters in sight. And with the phones down, with 911 inoperative, there was virtually no way to alert anyone. They could only watch.\n\nZeitoun and Todd sat in their boat, the heat of the fire pulsing at them. The smell was musky, acrid, and the flames swallowed the homes with remarkable speed. One was an old Victorian Zeitoun had always admired, and a few doors down was a house he had considered buying when it had been on the market a few years earlier. Both homes were devoured in a minute. The pieces disappeared into the dark water, leaving nothing.\n\nThe wind was picking up, blowing away from Zeitoun's office. If there had been any gust in the other direction, his building would have succumbed, too. He thanked God for this small mercy.\n\nAs they watched, they glimpsed a few other watchers, faces orange and silent. Other than the crackle of the fire and the occasional collapsing wall or floor, the night was quiet. There were no sirens, no authorities of any kind. Just a block of homes burning and sinking into the obsidian sea that had swallowed the city.\n\nComing back to the house on Dart, Zeitoun and Todd were quiet. The stars were out. Todd steered the boat like he was captaining a great yacht. He dropped Zeitoun at his house, and they said good night. Back on the roof, Nasser was already asleep in the tent.\n\nZeitoun stood there, watching the fire ebb and flow. The flood, and now the fire: it was difficult not to think of passages in the Qur'an that recounted the flood of Noah, the evidence of God's wrath. And yet despite the devastation visited upon New Orleans, there was still a kind of order to the night. Zeitoun was safe on his roof, the city was silent and still, the stars were in their place.\n\nHe had been on a tanker once, maybe twenty years earlier, navigating through the Philippines. It was late, after midnight, and Zeitoun was keeping the captain company on the bridge.\n\nTo stay awake and alert, the captain, a Greek man of middle age, liked to take up provocative subjects. He knew that Zeitoun was a Muslim and a thoughtful man, so he sparked a debate about the existence of God. The captain began by expressing his utter conviction that there was no God, no deity in the sky watching over the human world.\n\nZeitoun had been on the bridge with the captain for an hour at that point, watching him pilot the ship through the many islands, avoiding high shelves and sandbars, other ships and countless unseen dangers. The Philippines, with over seven thousand islands but only five hundred lighthouses, was known for its frequency of maritime accidents.\n\n\"What would happen,\" Zeitoun asked the captain, \"if you and I went below the deck, and just went to our bedrooms and went to sleep?\"\n\nThe captain gave him a quizzical look and answered that the ship would most certainly hit something\u2014would run aground or into a reef. In any event, disaster.\n\n\"So without a captain, the ship cannot navigate.\"\n\n\"Yes,\" the captain said, \"What's your point?\"\n\nZeitoun smiled. \"Look above you, at the stars and moon. How do the stars keep their place in the sky, how does the moon rotate around the earth, the earth around the sun? Who's navigating?\"\n\nThe captain smiled at Zeitoun. He'd been led into a trap.\n\n\"Without someone guiding us,\" Zeitoun finished, \"wouldn't the stars and moon fall to earth, wouldn't the oceans overrun the land? Any vessel, any carrier of humans, needs a captain, yes?\"\n\nThe captain was taken with the beauty of the metaphor, and let his silence imply surrender.\n\nOn his roof, Zeitoun crawled into his tent, trying not to wake Nasser. He turned his back to the fire and slept fitfully, thinking of fires and floods and the power of God.\n\n# SUNDAY SEPTEMBER 4\n\nIn the morning Zeitoun rose early, climbed down to his canoe, and paddled across the street to feed the dogs. He climbed up the tree, crawled through the windows, and fed them all the last of the meat.\n\n\"Like barbecue?\" he asked.\n\nThey did.\n\n\"See you tomorrow,\" he said, making a mental note to get some dog food from Todd.\n\nHe picked up Nasser, dropped him at the house on Claiborne, and went on alone. He wasn't sure where he would go today, so he chose a new route, this time going back to Dart, then east on Earhart, heading to Jefferson Davis Parkway.\n\nThis day was quieter than the few before it. There were no helicopters, no military boats. He was seeing far fewer people wading through the water, now green-grey and streaked everywhere with oil. It smelled dirtier every day, a wretched m\u00e9lange of fish and mud and chemicals.\n\nAs he approached the junction of Earhart, Jefferson Davis, and Washington, the land rose up a bit, and he could see dry grass, a wide intersection with a large green and brown patch in the middle. And on the grass there was an astonishing sight, especially given what he and his guests had been talking about the night before. There were three horses, chewing happily. They were free, with no riders or saddles. The scene was at once idyllic and hallucinatory. He paddled closer. One of the horses lifted its head, noticing Zeitoun. It was a beautiful animal, white and perfectly groomed. Seeing Zeitoun as no threat, the horse returned to its meal. The other two, one black and one grey, continued to eat. How they had gotten there was beyond Zeitoun's imagination, but they seemed ethereally content, luxuriating in their freedom.\n\nZeitoun watched them for a few minutes, then traveled on.\n\nZeitoun paddled down Jefferson Davis. He carried his canoe across the bridge over I-10 and continued on, reaching the residential stretch of the road. Near the corner of Banks Street, he heard a female voice.\n\n\"Hey there.\"\n\nHe looked up to see a woman on the second-floor balcony of a home. He slowed down and paddled toward her.\n\n\"Give me a ride?\" she asked.\n\nThe woman wore a shimmering blue blouse. Zeitoun told her he would be happy to help, and he steered the canoe to her steps. As she descended from the balcony, Zeitoun noticed her short skirt and high heels, her heavily made-up face, her small glittering purse. And finally he realized what might have been obvious to many: she was a prostitute. He didn't know what he thought about paddling around in his canoe with a prostitute aboard, but he didn't have time to turn her away now.\n\nShe was about to step into the canoe when Zeitoun stopped her.\n\n\"Can you take off the shoes?\" he asked.\n\nHe was afraid the high heels might puncture the boat's thin aluminum. She complied. She was going to Canal, she said. Could he drop her off there? Zeitoun said he would.\n\nShe sat in front of him, her hands on either side of the canoe. Feeling like a gondolier, Zeitoun paddled steadily and said nothing. He wondered if there was, only a few days after the hurricane, already a market for her services. Could she have been working in the home where he picked her up?\n\n\"Where you going?\" he asked, unable to quell his curiosity.\n\n\"To work,\" she said.\n\nAt the corner of Jefferson Davis and Canal, she pointed to the First United Methodist Church.\n\n\"Drop me here,\" she said.\n\nHe paddled to the pink brick building, where the water met the church's higher steps, and she lifted herself out.\n\n\"Thank you, honey,\" she said.\n\nHe nodded and paddled on.\n\nZeitoun came to the I-10\/Claiborne overpass again, and even from a distance he could see that the people who he had seen awaiting rescue there a few days ago had been taken away. The cars remained, as did piles of garbage and human waste. As he floated closer, something caught his attention: a patch of fur. In a moment he was close enough to see that it was a dog, lying on its side. He remembered that when he was last here, there had been a half-dozen small dogs, most of them puppies, taking shelter in the shade of the cars. As his canoe tapped against the overpass, he could see that there were ten or more animals, the same ones he'd seen before and a few others, in various positions on the road. He anchored his canoe to the overpass and climbed up onto the pavement. He gagged at the sight. They were dead. The dogs had been killed, each of them shot in the head. Some had been shot repeatedly\u2014head, torso, legs.\n\nHe paddled quickly back to the house on Claiborne, shaken. He called Kathy. He wanted to hear her voice.\n\n\"I saw the most terrible thing,\" he said. He told her about the dogs. He couldn't understand it.\n\n\"I'm so sorry,\" she said.\n\n\"I don't know who would do this.\"\n\n\"I don't know either, honey.\"\n\n\"Why kill them all?\"\n\nThey tried to make sense of it. Even if they were euthanizing the animals, it didn't add up. There were so many boats in the city. It would only take a moment to take them aboard and set them loose anywhere. But perhaps something had changed irrevocably. That this was considered a sane or even humane option signaled that all reason had left this place.\n\n\"How're the kids?\" he asked.\n\n\"Fine,\" she said. \"They miss you.\"\n\n\"Tomorrow you'll put the kids in school?\" he asked.\n\n\"I'll try,\" she said.\n\nHe tried to understand, but he was frustrated. The kids needed to be in school. But he was in no mood to argue.\n\nThey talked about what he planned to do that afternoon. There was both more and less to see each day. There were fewer people left in the city, even downtown, and yet the horses, the prostitute, the dogs\u2014it was growing ever more apocalyptic and surreal. He thought maybe he would relax this day. Think about it all.\n\n\"You should,\" she said. Any time he stayed home she felt more sure of his safety. \"Stay at home today.\"\n\nHe decided he would.\n\nHe tried to, at least. He lay there on Nademah's bed, trying to relax. But he couldn't stop thinking about the dogs. Who could shoot a dog? All those animals, needing, trusting. He tried, as always, to give the benefit of the doubt to whoever had done it. But if they could find their way to the dogs with guns and bullets, wouldn't it be just as easy to feed them?\n\nHe got out of bed and looked for his Qur'an. There was a passage he'd been thinking about, _al-Haqqah_ , \"The Reality.\" He took the book from Nademah's shelf and found the page. It was as he remembered it.\n\n_In the name of God,  \nThe Merciful, The Compassionate,  \nThe Reality!  \nWhat is The Reality?  \nWhat would cause you to recognize  \nwhat The Reality is?  \nThamud and Ad denied  \nthe Day of Disaster.  \nThen as for Thamud,  \nthey were caused to perish  \nby a storm of thunder and lightning_.  \n _As for Ad,  \nthey were caused to perish  \nby a fierce and roaring, raging wind.  \nHe compelled against them  \nfor seven uninterrupted nights and eight days  \nso you would have seen the people laid prostrate  \nas if they were the uprooted fallen-down palm trees.  \nThen see you any ones who endure among them?  \nPharaoh and those who came before him,  \nand the cities overthrown,  \nwere ones of iniquity;  \nthey rebelled against the Messenger  \nof their Lord,  \nso He took them with the mounting taking.  \nWhen the waters became turbulent,  \nwe carried you in the floating Ark,  \nthat We might make it a Reminder for you,  \nand attentive ears would hold onto it_.\n\nZeitoun crawled through the window and onto the roof. The sky was muddy, the wind cool. He sat down and watched the city in the distance.\n\nHe was struck by the possibility that those who had killed the dogs might not have been law-enforcement officers at all. Perhaps Kathy was right, and armed gangs were free in the city, shooting whatever they chose to.\n\nHe pondered his own possibilities for self-defense. What would he do if men came here, to him? He had seen no robberies in his neighborhood thus far. But what if they came here?\n\nAs the night darkened, Zeitoun wished he was not alone. He thought of returning to the other house, to talk to Todd and Nasser about what he'd seen.\n\nBut instead, he sat on his roof, pushing away thoughts of the dogs on the overpass. Perhaps he was weak in this way. He had always been soft when it came to animals. As a child, he had kept many. He'd caught lizards and crabs. He'd even kept a stray donkey in the back alley for a few days, wanting it to be his, to take care of it. His father scolded him for that, and for the pigeon-grooming operation he'd run with his brother Ahmad. It was Ahmad's idea, really\u2014another scheme into which he had enticed his little brother.\n\n\"Want to see something?\" Ahmad had said one day. Ahmad was sixteen, and Abdulrahman would follow him anywhere.\n\nAfter swearing Abdulrahman to secrecy, Ahmad brought him up to the roof and showed him a cage he had built from scrap wood and chicken wire. Inside was a nest of straw and newsprint, and inside the nest was a bird\u2014something, Abdulrahman thought, between a pigeon and a dove. Ahmad planned to keep dozens like this one on the roof, to feed and care for them, to try to train them to deliver messages. Ahmad asked if Abdulrahman wanted to help. Abdulrahman did indeed, and they agreed to care for the birds together. Abdulrahman, being younger, would clean the cages when necessary, and Ahmad, being older and more experienced in these matters, would find new birds, feed those who lived there, and train them when the time came.\n\nAnd so they spent hours there, watching the birds come and go, feeding them from their palms, exulting in the familiarity that allowed the birds to land on their arms and shoulders.\n\nSoon there were thirty or more birds living on their roof. Ahmad and Abdulrahman built more homes for them, until they had assembled a complex that looked not unlike the stone and adobe structures in their neighborhood, homes stacked upon each other, rising up from the ocean, interlocking like a crude mosaic, extending inland.\n\nAll was good until their father Mahmoud discovered their hobby. He considered the keeping of birds a terrible and unsanitary waste of time. Since Mohammed's death, Mahmoud had been impatient, irritable, and so the kids had tried to find diversions outside their grieving home. This hobby, Mahmoud insisted, was taking them away from their schoolwork, and if they forsook their education for pigeons, he would be stuck with not only the birds but two illiterate sons.\n\nHe demanded that they free the birds and dismantle the cages. The boys were despondent, and argued their case to their mother. She deferred to her husband, and he was unbending. Abdulrahman and Ahmad refused to do it themselves, so one day, as the boys were leaving for school, Mahmoud said he would do it himself while they were gone.\n\nThe boys returned that afternoon and ran straight to the roof to see what had been done. They found the birds still there, their homes untouched. Amazed, they ran down to the kitchen, where they found their mother beaming. Apparently when Mahmoud had gone up to the roof, the birds had flocked to him, alighting on his shoulders and arms, and he was so charmed that he couldn't send them away. He allowed the birds to stay.\n\nMahmoud died a few years later. The cause was heart disease, but the talk in Jableh was that it was simple heartache. He had never gotten over the death of his golden son, the glory of the family and all of Syria, Mohammed.\n\nZeitoun assumed Nasser was staying at the other house. If he wanted to be here, he could. Todd had a boat. So Zeitoun settled into the tent and went to sleep alone.\n\n# MONDAY SEPTEMBER 5\n\nIn the morning Zeitoun rose early, said his prayers, and paddled across the street to feed the dogs. He'd gotten a bag of dog food from Todd.\n\n\"No more steak, guys,\" he said. \"I'm out.\"\n\nThey didn't seem to mind. They devoured what he poured. They seemed to be doing well now, and were no longer in the same state of shock as a few days before.\n\n\"See? I come every day,\" he said. \"I always come.\"\n\nHe climbed down from the roof and paddled away.\n\nHe went by the Claiborne house and found Todd and Nasser on the porch, eating breakfast. He went inside and called Kathy.\n\n\"The cops are killing themselves,\" she said.\n\nTwo different officers, overcome by the storm and its aftermath, had taken their own lives. Sergeant Paul Accardo, a prominent spokesman for the department, was found in nearby Luling, in his squad car; he'd shot himself. Officer Lawrence Celestine had committed suicide on Friday, in front of another police officer.\n\nThis hit Zeitoun hard. He'd always had good relations with the police in the city. He knew the face of Sergeant Accardo well; the man was frequently on television, and projected an air of reason and calm.\n\nKathy mentioned the roving gangs, the toxic chemicals, the diseases that were being unearthed and spread. She was trying, again, to convince her husband to leave.\n\n\"I'll call you later,\" he said.\n\n* * *\n\nRob, Walt's husband, called Kathy to check on the Zeitouns, to see where they were staying and if they needed any help. When Kathy told him that Zeitoun was still in New Orleans, Rob was incredulous.\n\n\"What's he doing there?\" he asked.\n\n\"Oh, he's got his little canoe,\" Kathy said. \"He's paddling around the city.\" She tried to sound nonchalant.\n\n\"He's got to get out,\" Rob said.\n\n\"I know,\" Kathy said. \"That's what I tell him every day.\"\n\nAs they talked, Rob mentioned that he and Walt had left their cat when they fled the storm. They had tried to find her before they left, but she was an outdoor cat, given to roaming, and hadn't been in or near the house. Now he was hoping that if Zeitoun found himself in their neighborhood, he could look for any sign of her. If Zeitoun happened to make it over there, there was a generator in the garage that he was welcome to if he needed it.\n\nShe called the house on Claiborne. Zeitoun was still there, about to leave. Kathy told him about Rob's hope that he could check on the house. It was a good three miles away, and would require a portage over the highway, but Zeitoun was happy to have a clear-cut task. Kathy mentioned the possibility of the generator, but Zeitoun dismissed it. He preferred not to travel with any possessions at all. Besides being doubtful he'd be able to get the generator into the canoe, he was wary of picking up anything of value. He knew the police were looking for looters.\n\nHe and Nasser made their way to Walt and Rob's house. The day was warm and white. They decided to check on Nasser's house along the way, so they went up Fontainebleau to Napoleon. Nasser's house was at the corner of Napoleon and Galvez, and he wanted to see if anything could be salvaged.\n\nWhen they got there, the water had reached the eaves of the roof. There was no way to get into the house, and nothing inside would be worth it. Nasser had prepared himself for this sight, and it was exactly as he'd expected.\n\n\"Let's go,\" he said.\n\nThey took Jefferson Davis Parkway to Walt and Rob's. The water at the house was far lower, only about eighteen inches. Zeitoun got out of the canoe and walked up to the front door. The house would be fine. But he saw no sign of the cat. He considered jumping the fence to get to the backyard, but it was this kind of suspicious activity that police and neighbors would be looking for.\n\nThey turned the canoe around and left. On the way home, they passed the post office at Jefferson Davis and Lafitte, the staging ground for helicopter rescues. They saw no helicopters, but there were rescue workers milling in the parking lot.\n\n\"You want to go?\" Zeitoun asked Nasser.\n\n\"Not today,\" he said.\n\nThat night Zeitoun and Nasser prayed together on the roof of the house on Dart and barbecued hamburger meat on the grill. The night was humid and quiet. There was the occasional sound of breaking glass, the growl of a low-flying helicopter. But overall the city seemed to have reached a new equilibrium. Zeitoun fell asleep missing Kathy and the children, wondering if it was time to leave.\n\n# TUESDAY SEPTEMBER 6\n\nIn the morning, after his prayers, Zeitoun made his way to the dogs across the street and fed them more of the dog food Todd had acquired for his rescued pet. When he paddled back to the house to pick up Nasser, he noticed Nasser was carrying his black duffel bag.\n\nZeitoun nodded at it. \"You're ready to go?\"\n\nNasser said he was. He was ready to be evacuated. Zeitoun would be sad to see him go, but he was happy to know that his friend would be safe, and that, even better, Zeitoun would no longer have to share his tent. Nasser got in the canoe and they were off.\n\nThey made their way to the post-office parking lot. They had passed it together a half-dozen times, and always Zeitoun had asked Nasser if he was prepared to leave, but he had not been ready, not until now.\n\n\"There's your ride,\" Zeitoun said, pointing to an orange helicopter in the distance, resting on the ground.\n\nThey paddled closer and realized there was something strange about the helicopter. It was resting on its side.\n\n\"Oh no,\" Nasser said.\n\nIts rotor was broken, the grass blackened all around it.\n\n\"It crashed,\" Zeitoun said, awed.\n\n\"It crashed,\" Nasser repeated, in a whisper.\n\nThey coasted toward it. There was no one near it, no sign that anyone had been hurt. There was no smoke, no rescue crew. The crash must have been the day before. All there was now was a mound of orange steel. Nasser would not fly out this day.\n\nThey returned to the Claiborne house, dazed. Zeitoun called Kathy. He couldn't decide if he should tell her about the helicopter. He knew it would upset her, so he chose not to.\n\n\"You put the kids in school yet?\"\n\nKathy said she was trying, but it wasn't easy.\n\nZeitoun exhaled loudly.\n\n\"You're like the man who lost his camel and is looking for the rope,\" she said. It was one of his favorite expressions, and she relished using it against him. He would often say it when he felt Kathy was focusing on irrelevant details while ignoring the crux of a problem.\n\nHe wasn't amused.\n\n\"C'mon honey,\" she said.\n\nSchool wasn't the first thing on Kathy's mind. She had been determined, the night before and all morning, to convince her husband to leave the city. Mayor Nagin had ordered a forced evacuation of everyone remaining.\n\n\"A forced evacuation,\" she repeated.\n\nOfficials were concerned about the spread of E. coli, the risk of typhoid fever, cholera, dysentery. Unsanitary conditions would threaten the health of anyone still in the area.\n\n\"I'm not drinking the water,\" he said.\n\n\"What about the toxic waste?\" she asked. \"You know the crap buried underground there.\" She reminded him that parts of the city had been built on landfills containing arsenic, lead, mercury, barium, and other carcinogens. \"What if that stuff leaches through?\"\n\nZeitoun didn't know what to say.\n\n\"I'll be careful,\" he said.\n\nWhat he didn't say was that he was considering leaving. Everything was becoming more difficult, and there was less for him to do. Fewer people were left in the city, and fewer still needed help. There was only the matter of his properties, looking after them, and of course the dogs. Who would feed the dogs, if not him? For now, he told her it would be fine, that he would be careful. That he loved her and would call her in a few hours.\n\nHe set out alone for a while and before long, at the corner of Canal and Scott, he encountered a small boat. It was a military craft, with three men aboard: a soldier, a man with a video camera, and one holding a microphone and a notebook. They waved Zeitoun down and one of the men identified himself as a reporter.\n\n\"What are you doing?\" the reporter asked.\n\n\"Just checking on friends' houses. Trying to help,\" Zeitoun said.\n\n\"Who are you working with?\" the reporter asked.\n\n\"Anybody,\" Zeitoun said. \"I work with anybody.\"\n\nAs he paddled back to Claiborne, a hope flickered within Zeitoun that his siblings might see him on TV. Perhaps they would see what he was doing, that he had done something good by staying in his adopted city. The Zeitouns were proud, and there was plenty of sibling rivalry that had pushed them all to an array of achievements\u2014all of them measured against the deeds of Mohammed. None of them had ever done something like that, none had achieved on his level. But Zeitoun felt again that perhaps this was his calling, that God had waited to put him here and now to test him in this way. And so he hoped, as silly as it seemed, that his siblings might see him like this, on the water, a sailor again, being useful, serving God.\n\nWhen Zeitoun got back to 5010 Claiborne, he saw a blue-and-white motorboat tied to the porch.\n\nWhen he entered the house, there was a man inside, a man he had never seen before.\n\n\"Who are you?\" Zeitoun asked.\n\n\"Who are _you?\"_ the man asked.\n\n\"This is my house,\" Zeitoun said.\n\nThe man apologized. He introduced himself. His name was Ronnie, and he'd passed by the house one day, looking for a place that might have a working phone. He'd seen the phone box above the waterline and walked into the house. Since then, he'd been coming in periodically to make calls to his brother, a helicopter pilot. Ronnie was white, about thirty-five, six feet, two hundred pounds. He told Zeitoun that he worked for a tree company.\n\nZeitoun couldn't think of a good reason to ask Ronnie to leave. Zeitoun was happy to see anyone alive and well in the city, so he left Ronnie in the house and went upstairs to see if the water worked. He found Nasser on the second floor.\n\n\"You meet this man Ronnie?\" Zeitoun asked.\n\nNasser had, and had found him to be agreeable enough. They both felt there was a certain strength in numbers, and again, if the man wanted to use the phone occasionally, who were they to prevent him from communicating with the outside world?\n\nImpossibly, the water in the bathroom was still functioning. Zeitoun hadn't even thought to check it sooner. It was a miracle. He told Nasser he was going to take a shower.\n\n\"Be quick,\" Nasser said. \"I'm next.\"\n\nNo shower had ever felt better. Zeitoun washed away all the sweat and grime, and what he assumed was a fair amount of oil and raw sewage. Afterward, he came downstairs.\n\n\"All yours,\" he told Nasser.\n\nHe picked up the phone and called his brother in Spain. He wanted to check in with him quickly before calling Kathy.\n\nAgain Ahmad tried to convince him to leave.\n\n\"Do you realize the images we're seeing on TV?\" he asked.\n\nZeitoun assured him that he was far away from that kind of chaos. Not counting the armed man at the Shell station, Zeitoun had seen almost no danger in all the time he had been canoeing around the city.\n\n\"Hey,\" he said, excited, \"I might be on TV. Someone just interviewed me. Look for it. Tell Kathy.\"\n\nAhmad sighed. \"So you won't go.\"\n\n\"Not yet.\"\n\nAhmad knew better than to argue. But he did want to remind his brother that even if he felt safe now, danger could come at any time. There were roving gangs of armed men, he said. That's all the media could talk about\u2014that it was the Wild West out there. Ahmad felt powerless, and he hated the feeling. He knew his little brother considered him overly cautious. \"Won't you please consider leaving, for the sake of your beautiful family, before something happens?\"\n\nZeitoun was holding the piece of paper with Kathy's Phoenix number on it. He needed to call her before she started worrying. He was already ten minutes late. He was about to get off the phone with Ahmad when he heard Nasser's voice from the porch. He was talking to someone outside.\n\n\"Zeitoun!\" Nasser called.\n\n\"What?\" Zeitoun said.\n\n\"Come here,\" Nasser said. \"These guys want to know if we need water.\"\n\nZeitoun assumed it was more men like himself and Nasser\u2014people with boats who were roaming around, trying to help.\n\nWhen he put the phone down and looked toward the front porch, he saw a group of men, all of them armed, bursting into the house. Zeitoun hung up the phone and walked toward the door.\n\n# III\n# WEDNESDAY SEPTEMBER 7\n\nKathy woke up tense. She fed and dressed the kids, trying not to think about the fact that her husband hadn't called the afternoon before. He had promised to call. Yuko told her not to worry. It was silly to worry. It had barely been a day, and even the regular contact Zeitoun had maintained so far was remarkable. Kathy agreed, but she knew she would be anxious until he called again.\n\nAfter Yuko took her own kids to school, she helped keep Kathy's children occupied while Kathy paced, phone in her hand.\n\nAt nine, Ahmad called from Spain.\n\n\"You hear from Abdulrahman today?\" he asked.\n\n\"No. You?\"\n\n\"Not since yesterday.\"\n\n\"So you talked to him?\" she asked.\n\n\"I did.\"\n\n\"He called you and not me.\"\n\n\"He was about to call you. But he got off the phone quickly. There was someone at the door.\"\n\n\"Who was it?\" Kathy asked. Her stomach dropped.\n\n\"I have no idea.\"\n\nShe called the Claiborne house and let it ring a dozen times before hanging up.\n\nNow she was a wreck. _He must call today_ , she thought. _I'll kill him if he doesn't call at noon_.\n\nAt ten o'clock Phoenix time it was noon in New Orleans. Kathy waited. The phone did not ring at ten, ten-thirty, eleven\u2014one o'clock New Orleans time. By noon in Phoenix she was frantic.\n\nShe called the Claiborne house again. No answer.\n\nYuko tried to put it in context. It was miraculous that the phone line at the Claiborne house was working at all. Chances were that it finally gave way and died. He'll find a way to call, she said. He's in an underwater city, she said. Cut the man some slack.\n\nKathy was calmer now, but still she paced the living room.\n\nYuko took the kids to the mall. She didn't want to leave Kathy alone, but the pacing was worrying the kids. Yuko was sure Zeitoun would call while they were gone, so why not let the kids enjoy themselves? The mall had a food court, an arcade for Zach. They planned to be back at three.\n\nKathy called the Claiborne house again. No answer.\n\nWalt called. \"You hear anything from Zeitoun?\"\n\nKathy told him she hadn't.\n\nShe called Adnan, Zeitoun's cousin.\n\n\"I'm still ashamed,\" she said. Last they had spoken, Kathy had had to tell him that her sister would not allow Adnan and Abeer to stay with them. It had been painful.\n\n\"Don't worry. We're fine,\" he said.\n\nHe was still in Baton Rouge with Abeer and his parents. After spending two nights in their car, they had returned to the mosque, and had been sleeping on the floor there for the past week.\n\n\"How is Abdulrahman?\" he asked.\n\n\"I haven't heard from him. Have you?\"\n\nAdnan had not.\n\nAlone and seeking distraction, Kathy turned on the TV, avoiding the news, finding Oprah Winfrey. Or she thought it was Oprah's show. But soon she realized it was a news report replaying portions of the previous day's show, with New Orleans police chief Eddie Compass and Mayor Nagin as Oprah's guests.\n\nCompass was lamenting the extent of the crime in the Superdome. \"We had babies in there. Little babies getting raped,\" he said, weeping. From Mayor Nagin: \"About three days we were basically rationing, fighting, people were\u2014that's why the people, in my opinion, they got to this almost animalistic state, because they didn't have the resources. They were trapped. You get ready to see something that I'm not sure you're ready to see. We have people standing out there that have been in that frickin' Superdome for five days watching dead bodies, watching hooligans killing people, raping people. That's the tragedy. People are trying to give us babies that were dying.\"\n\nKathy turned the TV off again, this time for good. She called the house on Claiborne. The phone rang and rang. She paced. She walked outside, into the assaulting Phoenix heat, then went back inside. She called again. The rings began to sound hollow, desolate.\n\n* * *\n\nFour o'clock arrived and he hadn't called.\n\nShe called Ahmad in Spain. He hadn't heard from Zeitoun either. He had been calling the Claiborne house all day, to no avail.\n\nIn the late afternoon, the kids returned.\n\n\"Did Dad call?\" Nademah asked.\n\n\"Not yet,\" Kathy said, \"still waiting.\"\n\nShe held herself together for a few seconds but then imploded. She excused herself and ran to the guest room. She did not want her girls to see her this way.\n\nYuko came in and sat on the bed with Kathy. It's been just one day, she said. Just one day in the life of a man in a city with no services. He would call tomorrow. Kathy pulled herself together, and together they prayed. Yuko was right. It was one day. Of course he would call tomorrow.\n\n# THURSDAY SEPTEMBER 8\n\nKathy woke up with a better outlook. Maybe her husband didn't even realize he'd forgotten to call. He was likely saving any number of new people and animals and homes, and in the midst of it all he'd gotten overwhelmed. In any case, Kathy was determined to put on a brave face for the kids. She cooked their breakfast and pretended she was sane and content. She played GameCube with Zachary and killed the morning with diversions.\n\nPeriodically she pushed the redial button on Yuko's phone. The phone at Claiborne rang in an infinite loop.\n\nNoon came and went.\n\nKathy was losing her grip again.\n\n\"I need to go to New Orleans,\" she told Yuko.\n\n\"No you don't,\" Yuko said. She peppered Kathy with logistical questions. How would she get into the city? Did she plan to buy a boat and dodge the authorities and find her husband on her own? Yuko dismissed the notion.\n\n\"We don't want to have to worry about you, too.\"\n\nAhmad called Kathy. His tone had been neutral the day before, but now he sounded worried. This unnerved Kathy. If Ahmad, made of the same stuff her husband was\u2014and both of them made of the stuff of their father Mahmoud, who could survive two days at sea tethered to a barrel\u2014felt this to be a dire situation, then if anything, Kathy was underreacting.\n\nAhmad said he would try to contact the TV station that had interviewed Zeitoun. He would contact all the agencies that tracked missing persons in New Orleans. He would contact the Coast Guard. They agreed to call each other as soon they heard something.\n\nDate: Thu, 8 Sep 2005 19:08:04 +0200\n\nTo: SATERNKatrinaReliefUpdates@csc.com\n\nSubject: Ref. AMER-6G2TNL\n\nDear Sires,\n\nMany thanks for your answering.\n\nKindly please do your best to give us any good news about him.\n\nHe's my brother, he leave many years ago in New Orleans:\n\n4649 Dart St. New Orleans\n\nNew Orleans, LA\n\n70125-2716\n\nActually I'm at Spain, but her wife and childrens they left a day before Katrina hit to ARIZONA, his wife: Mrs. Kathy Zeitoun actual contact: 408-[number omitted]\n\nMore information:\n\nHe remained at home without phone, but he've a small boat and he went daily to: Mr. TODD at:\n\n5010 S. Claiborne Ave 70125-4941 New Orleans\n\nLast calling was on Sept 6 at 14:30 local time, after that till now no calls, no news. The phone which he used is ringing but no answering. Here I including his pictures maybe can help.\n\nMany thanks.\n\nSincerely,\n\nAhmad Zeton\n\nIn the afternoon, Zeitoun's family began calling from Syria. First it was Fahzia. A secondary-school teacher in Jableh, she spoke fluent English.\n\n\"Have you heard from Abdulrahman?\"\n\nKathy told her she had not for two days.\n\nThere was a long silence on the line.\n\n\"You have not heard from Abdulrahman?\"\n\nKathy explained that the phones were down, that it was likely that her husband was just trying to reach a working phone. This did not sit well with Fahzia.\n\n\"Again, please\u2014you have not heard from Abdulrahman?\"\n\nKathy loved the Zeitouns of Syria, but she did not need this extra burden. She excused herself and hung up.\n\nKathy did not attempt to sit at dinner. She paced the rooms, the phone an extension of her arm. She thought through the possibilities\u2014who she knew and what they could do to help. She didn't know a soul still in the city, she realized. It was paralyzing. It seemed impossible that in 2005, in the United States, there was an entire city cut off from all communication, all contact.\n\nLater, thinking the kids were asleep, she passed one of the bedrooms and heard Aisha talking to one of Yuko's kids.\n\n\"Our house is under ten feet of water,\" Aisha said.\n\nKathy held her breath at the door.\n\n\"And we can't find my dad.\"\n\nIn the bathroom, Kathy covered her face in a towel and bawled. Her body convulsed, but she tried not to make a sound.\n\n# FRIDAY SEPTEMBER 9\n\nKathy had no choice but to lie. She had never told a bald-faced lie to her children before, but now it seemed necessary. Otherwise they would all lose their composure. She planned to enroll them in school on Monday, and to have the strength to be thrown into such a situation they had to believe that their father was healthy and in contact. So at breakfast, when Aisha asked if she had heard from Dad, Kathy did not hesitate.\n\n\"Yup, heard from him last night,\" she said.\n\n\"On what phone?\" Nademah asked. They hadn't heard a ring.\n\n\"Yuko's phone,\" Kathy said. \"I got it on the first ring.\"\n\n\"So he's at the house?\" Nademah asked.\n\nKathy nodded. And as smart and skeptical as her kids were, they believed her. Especially Nademah and Zachary. Whether or not they sensed the lie, they _wanted_ to believe it. Safiya and Aisha were harder to read, but for the time being her kids' fears had been assuaged and now Kathy only had to worry about her own.\n\nJust after breakfast, the phone did ring. Kathy leapt to it.\n\nIt was Aisha, another sister of Zeitoun's. She was the director of an elementary school in Jableh, and also spoke English.\n\n\"Where is Abdulrahman?\" she asked.\n\n\"He's in New Orleans,\" Kathy answered calmly.\n\nAisha explained that no one had heard from him in days. He had been in touch a few times after the storm, and then nothing. She was calling on behalf of all the siblings, and she was worried.\n\n\"He's fine,\" Kathy said.\n\n\"How do you know?\" Aisha asked.\n\nKathy had no answer.\n\nKathy got online. Immediately she was swamped with horrific news from the city. Officials were reporting the death toll in and around New Orleans at 118. But Mayor Nagin estimated that the final number might climb as high as ten thousand. She checked her email. Her husband had never sent an email in his life, but she couldn't rule it out. She found an email from Zeitoun's brother Ahmad. He had cc'ed her on an email to another aid agency.\n\nFrom: CapZeton\n\nDate: Fri, 9 Sep 2005 22:12:05 +0200\n\nTo: [name omitted]@arcno.org\n\nSubject: Looking for my brother \/ Abdulrahman Zeitoun\n\nDear sires,\n\nKindly, would you please if it's possible to know from you about the persons which they forced to leave houses from New Orleans last Tue. Sept 6th, where they are now?\n\nI would like to have any news about my brother, which we lost the contact with him from Tue. Sept. 6th after 14:30 hrs, while he was at (5010 S. Claiborne Ave. 70125-4941 New Orleans) using a small boat. Moving to 4649 Dart St. where he stay.\n\nMy brother's details:\n\nName: Abdulrahman Zeitoun\n\nAge: 47 years\n\nAddress: 4649 Dart St.-New Orleans, LA 70125-2716\n\nFrom that time till now we haven't any news about him,\n\nKindly please do your best to help us.\n\nThanking you indeed,\n\nAhmad Zeton\n\nMalaga-Spain\n\nWhen it was noon in New Orleans Kathy called the Claiborne house. She let the phone ring, willing it to stop, to be interrupted by her husband's voice. She called all day, but the ringing had no end.\n\nWalt and Rob called. Kathy told them she had not heard from Zeitoun, and asked if Walt knew anyone who could help. Walt knew everyone, it seemed, and always had a solution. He said he would call a friend, a U.S. marshal, who he knew was near the city. Maybe he could get inside and get to the house on Claiborne.\n\nAs Kathy put the kids to bed that night, she forced herself to present a face of confidence. They asked if their house was underwater, and Kathy admitted that yes, there was some damage, but that lucky them, their father was a contractor, and that any damage could be quickly fixed.\n\n\"And guess what?\" she told them. \"Now you'll all get new bedroom sets!\"\n\n# SATURDAY SEPTEMBER 10\n\nWalt called. He had spoken to his friend, the U.S. marshal. The marshal had driven toward the house on Dart Street, but he couldn't get close. The water was still too high.\n\nWalt said he would call a friend he knew who had a helicopter. He hadn't thought it through beyond that\u2014where the helicopter would go or how they would scout for Zeitoun\u2014but he said he would make more calls and call Kathy back soon.\n\nJust as she had the day before, when it was noon in New Orleans she called the Claiborne house. Again the ringing had no end.\n\nZeitoun's family called.\n\n\"Kathy, where's Abdulrahman?\" they said. It was Lucy, one of his nieces. All of Zeitoun's nieces and nephews were fluent in English, and were translating for the rest of the family.\n\n\"I don't know,\" Kathy said.\n\nAnother cousin got on the phone.\n\n\"You need to go find him!\" she insisted.\n\nThroughout the morning Zeitoun's sisters and brothers called from Lattakia, from Saudi Arabia. Had Kathy heard from him yet? Why wasn't she in New Orleans looking for him? Hadn't she been watching the TV?\n\nShe told them she hadn't, that she couldn't bear it.\n\nThey filled her in. There had been looting, rapes, murders. It was chaos, anarchy. They repeated Mayor Nagin's assertion that the city had devolved into an \"animalistic state.\" And in this way she got the media's funhouse picture of the state of the city via her husband's relatives halfway around the world. God knows, she thought, what kind of spin the media was putting on things out there.\n\nTwenty-five thousand body bags have been brought to the area, they noted. How can you live in that country? they asked. You need to move back here. Syria is so much safer, they said.\n\nKathy couldn't deal with the questions and the pressure. She was overcome, helpless, trembling. She got off the phone as politely as she could.\n\nShe went to the bathroom and for the first time in days looked at her face. There were blue rings around her eyes. She removed her hijab and took in a quick breath. Her hair. She had had no more than ten grey hairs before all of this. Now there was a stripe of white hair rising from her forehead, as wide as her hand.\n\nYuko forbade Kathy to answer the phone when anyone called from Syria. Yuko fielded all the calls, telling them that Kathy was doing everything she could, everything humanly possible.\n\nYuko and her husband Ahmaad took Kathy and the kids to Veterans Memorial Coliseum, where the Red Cross had set up a shelter and triage unit for New Orleanians. Various missing-persons agencies were collecting information and trying to connect those separated from their families. Kathy brought a photo of Zeitoun and every piece of information she could find.\n\nAt the gym, it was a grim scene. There were dozens of people from New Orleans there, looking like they had fled that very day. Injuries were being treated, families sleeping on cots, piles of clothing everywhere. Kathy's girls clung to her.\n\nThe Red Cross took down all of Zeitoun's information and scanned the photo Kathy had brought. They were efficient and kind, and told Kathy that thousands of people had been located, that they were scattered all over the country and every story was stranger than the last. They told Kathy not to worry, that each day brought more order to the world.\n\nKathy left with some renewed hope. Perhaps he had been injured. He could be in a hospital somewhere, heavily sedated. He could have been found somewhere, unconscious and without identification. Now it was just a matter of time before the doctors and nurses looked through the missing-persons database to find him.\n\nBut now the kids were confused. Was their father safe or not? The signals were mixed. Kathy had told them he was fine, he was safe, he was in his canoe. But then why report him to the Red Cross? Why the missing-persons files, why the mentions of police and Coast Guard? Kathy tried to shield them from all this but it was impossible. She wasn't strong enough. She felt weak, porous.\n\nWhen they got home again Kathy called the Claiborne house. The phone rang and rang. Until now she had been telling herself that the phone might have been out of service, but this day she checked with the phone company. If the phone was not working at all, they told her, she would have gotten something like a busy signal, a particular sound to indicate that the lines were down. But the ringing persisted, and the ringing meant that the phone worked, but no one was there to answer it.\n\n* * *\n\nAisha was taking it the hardest. She seemed to swing between worry and fatalistic resignation. She was irritable. She couldn't concentrate. She withdrew and wept alone.\n\nThat night, after the other kids had fallen asleep, Kathy sat behind Aisha on her bed. She took her daughter's thick black hair in her hands and kneaded it with one hand, brushing it with the other. It was something she had done with Nademah to calm her before bed, and Yuko's mom had done the same with Kathy after their baths. It was soothing, meditative for both mother and daughter. In this case Kathy was humming a tune she couldn't even remember the name of, and Aisha was sitting, tense but accepting. Kathy was confident that this would ease her worry, would end with Aisha dropping back into Kathy's lap, contented and sleepy.\n\n\"You hear from him?\" Aisha asked.\n\n\"No, baby, not yet.\"\n\n\"Is he dead?\"\n\n\"No, baby, he's not dead.\"\n\n\"Did he drown?\"\n\n\"No.\"\n\n\"Did they find his body?\"\n\n\"Honey, stop.\"\n\nBut after a half-dozen strokes of her brush, Kathy took in a quick breath. Aisha's hair was coming out in clumps. The brush was full of it.\n\nAisha's eyes welled. Kathy bawled.\n\n_There is nothing worse than this_ , Kathy thought. _There can be nothing worse than this_.\n\n# SUNDAY SEPTEMBER 11\n\nIt had been six days since Kathy had spoken to Zeitoun. She could no longer explain his absence. It didn't make sense. The city was overrun with help. The National Guard was everywhere, and officials were insisting that the city was virtually empty.\n\nShe ran the possibilities through her mind again. If he was still there, canoeing around New Orleans, he would have called again from the Claiborne house. If the Claiborne phone no longer worked, by now he would have found another working phone. Or he would have encountered one of the soldiers and asked for help in contacting Kathy. There seemed to be no way that he was in the city and unable to call.\n\nWhich meant that he had left the city. He might have been running low on water or food. He might have accepted a ride out of the city from one of the helicopters or rescue boats. But if he had left, and had been brought to a shelter, he would have called immediately.\n\nShe knew that bodies had been found floating, unclaimed and uncovered in the water. _He could be dead_ , she told herself. _Your husband could be gone_. There had been murders, she knew. She did not truly believe the accounts of untethered mayhem, but she knew that some murders would have occurred. _It could have been a robbery_ , she thought. _Someone had come to steal from one of our properties, he had been there, he had fought back\u2014_\n\nHe could not have drowned. He could not have fallen victim to any other sort of calamity. She knew her husband too well. She could not picture any accident taking him. He was too smart, too wary, and even if he had had some kind of incident, he was indestructible. He would have survived, he would have gotten help.\n\n* * *\n\nWhen it was noon in New Orleans Kathy called the Claiborne house. She let it ring, needing to hear her husband's voice, but still the ringing had no end.\n\nShe had to think of life insurance. She had to think about how she would support her four children. Would she be able to run the business on her own? Of course not. But some semblance of it? She would have to sell the rental properties. Or maybe the rental properties would be something she could manage on her own. Too many questions. No, she would sell the painting and contracting business and hold on to the rentals. Or she could sell a few of the buildings, bring it down to a number she could manage on her own. Should she stay in New Orleans, or move the family to Baton Rouge? To Phoenix? It would have to be Phoenix.\n\nAnd how long would anyone wait before assuming the worst? One week? Two weeks, three?\n\nShe got online and found another email from Ahmad. This one was sent to the TV station that had broadcast the brief interview with Zeitoun. From his office in Spain, Ahmad had found out which station it had been, and had found the name of one of the producers.\n\nFrom: CapZeton\n\nDate: Sun, 11 Sep 2005 02:01:34 +0200\n\nTo: [name omitted]@wafb.com\n\nSubject: New Orleans Hurricane-impacted areas\n\nDear Sires,\n\nAs I informed from some friends in Baton Rouge, that you have on Sept. 5th a meeting with my brother:\n\nName Abdulrahman Zeitoun, 47 years old, at New Orleans effected zone 4649 Dart St. LA 70125-2716 where he stay, our friend saw him on your TV WAFB CH9 on Sept. 6th.\n\nFrom that time till this moment we lost the contact with him. Kindly would you please can you give me any information about the day and time when you met him? Or if you have any other information?\n\nThanking you indeed,\n\nAhmad Zeton\n\nMalaga-Spain\n\nKathy found a website with current photos of New Orleans from the air. She searched until she found Uptown, and zoomed in until she saw what was left of her home and neighborhood. The water was filthier than she could have imagined. It looked like the entire city was bathing in oil and tar.\n\nShe called every number of every person she knew who might still be in New Orleans. Nothing.\n\nYuko and Ahmaad consoled her.\n\n\"He's old school,\" Ahmaad said. It was normal for a man like Zeitoun, rugged and independent, to be out of contact for a few days. \"They don't make guys like that anymore.\"\n\nYuko kept Kathy away from the phones and the news. Still, Kathy caught snippets in the car. In the Odyssey, she heard President Bush's weekly radio address. The president compared the storm to 9\/11 and the War on Terror. \"America is confronting another disaster that has caused destruction and loss of life,\" he said. \"America will overcome this ordeal, and we will be stronger for it.\"\n\n# MONDAY SEPTEMBER 12\n\nIt was time for the girls to start school. They had been out for almost two weeks now, and no matter how awkward it might be to start classes in the middle of September, they needed some semblance of routine.\n\nKathy made the calls. The closest public school was Dr. Howard K. Conley Elementary School. \"Bring them right away,\" Kathy was told. Zach, as a high schooler, would have a more difficult entry.\n\nThe girls were nervous. They were not happy to be brought to a new school, where they knew no one and where they would be branded as refugees. Why couldn't they just wait until they returned to New Orleans? What would they study? The books and lesson plans would be different. What was the point? The point, Kathy said, was that their father wanted them in school, and that was enough.\n\nYuko and Ahmaad bought the girls a new set of school supplies, binders and notebooks and pens and pencils, and Pok\u00e9mon and Hello Kitty backpacks to carry all of it. This gave the girls some measure of comfort, but when Kathy dropped them off, leaving them all in the office of the Conley principal, she was devastated. She couldn't look at Aisha. Everything was in that girl's wet black eyes, every worry Kathy shared\u2014that these were the first days of their new life together, living in Phoenix, living without their father.\n\nDriving away from the school, Kathy caught the news on the radio. The official death toll in New Orleans was now 279. It seemed to be leaping by a hundred a day, and the search for bodies had only just begun.\n\nDid she have to prepare for a funeral? It had been seven days now. How long could she explain away his absence? President Bush had come to New Orleans two or three times at that point. If the president could make his way to Jackson Square for a press conference, her husband, if alive, could find a phone and call out.\n\n# TUESDAY SEPTEMBER 13\n\nWith the kids at school during the day, Kathy spiraled downward. She had more time to herself and more time to worry, more time to plan a wretched new life.\n\nShe called the house on Claiborne every hour. She called Zeitoun's cell phone in case he had found some place to charge it.\n\nThe death toll jumped to 423.\n\nShe found Todd Gambino's girlfriend's number and called her. She was in Mississippi, and hadn't heard from Todd in a week. This meant something. Perhaps something had happened to both of them? This was good news. It had to be. The two women agreed to stay in touch.\n\nFrom Spain, Ahmad called Kathy every day. He called the Coast Guard and the Navy. He wrote to the Syrian Embassy in Washington. Nothing from anyone. He looked into flights to New Orleans. What could it hurt to have him searching for his brother on the ground? He worried that his siblings expected him to go, given that he was the only one who might have any chance at all of entering the United States; getting a visa from Syria was hopeless. His wife ruled out the notion, but still, the idea burrowed into him.\n\n# WEDNESDAY SEPTEMBER 14\n\nThe death toll was at 648 and climbing.\n\nKathy checked in with the Red Cross every day. She soon had Zeitoun registered at half a dozen agencies dealing with missing persons. His photo was everywhere.\n\n* * *\n\nThe girls went to school, came home, watched TV. They found momentary distraction with Yuko and Ahmaad's kids, but their eyes were hollow. They too were planning lives without their father. Did they want to move to Phoenix? Would there be a funeral? When would they know what had happened?\n\nIn the countless hours of darkening thoughts, Kathy imagined again where she would live. Could she live in Arizona? She would have to find a house near Yuko's. Ahmaad would have to be a father figure. Kathy had already leaned so heavily on Yuko and Ahmaad, she couldn't imagine permanently thrusting her entire family onto them.\n\nShe thought of Zeitoun's family in Syria. There was such a support network there, a vast and tight fabric of family. She and Zeitoun had brought the kids there in 2003 for two weeks to visit, and it had been unlike anything she'd expected. First there was the snow. Snow in Damascus! They'd taken a bus north to Jableh, and all along she'd been shocked at what she saw. She'd had, she later admitted, an antique idea of Syria. She'd pictured deserts, donkeys, and carts\u2014not so many busy, cosmopolitan cities, not so many Mercedes and BMW dealerships lining the highway heading north, not so many women in tight clothes and uncovered hair. But there were vestiges of a less modern life, too\u2014merchants selling sardines and cabbage by the roadside, crude homes of brick and mud. As they drove north to Jableh, the road soon met the coastline, and they traveled along a beautiful seaside stretch, hills cascading to the sea, mosques perched above the road, side by side with churches, dozens of them. She'd assumed Syria was entirely Muslim, but she was wrong about this, and about so many things. She loved being surprised, coming to realize that in many ways Syria was a quintessentially Mediterranean country, connected to the sea and in love with food and new ideas and reflecting the influence of Greece, Italy, so many cultures. Kathy devoured it all\u2014the fresh vegetables and fish, the yogurts, the lamb! The lamb was the best she'd had anywhere, and she ate it whenever she had the opportunity. In beautiful seaside Jableh she'd seen the homes that Zeitoun's grandfather had built, saw the monument to his brother Mohammed. They stayed with Kousay, Abdulrahman's wonderfully life-loving and gregarious brother, who still lived in their childhood home. It was a gorgeous old place on the water, with high ceilings and windows always open to the sea breezes. There was family everywhere within walking distance, so many cousins, so much history. While Zeitoun darted around town, reconnecting with old friends, Kathy had spent an afternoon cooking with Zeitoun's sister Fahzia, and she'd done something wrong with the propane and almost burned down the kitchen. It was terrifying at the time but made for much hilarity in the coming days. They were such good people, her husband's family, everyone so well educated, so open and hospitable, each of their houses full of constant laughter. Would it be impossible to think that Kathy could take the kids and live there, in Jableh? It was a radical idea, but one that would put her in a place of such comfort, embraced by family; the girls would be surrounded by so many relatives that perhaps they wouldn't be quite so devastated at the loss of their dad.\n\nZeitoun's family in Syria became increasingly despondent and resigned to the loss of Abdulrahman. There were so many bodies being found. Almost seven hundred in New Orleans. Their brother was surely one of them; to believe otherwise was folly. Now they just wanted the peace of mind of knowing how he had died. They wanted his body. To cleanse it, to bury him.\n\n# SATURDAY SEPTEMBER 17\n\nYuko had forbidden her to watch TV or get on the internet, but Kathy couldn't resist. She searched for her husband's name. She searched for their address, their company. She searched for any sign that her husband had been found.\n\nShe found nothing about him, but found other, terrible things. All over the web she found news of the violence and evidence of its overstatement. One page would report hundreds of murders, crocodiles in the water, gangs of men rampaging. Another page would report that no babies had been raped. That there had been no murders in the Superdome, no deaths in the Convention Center. There was no end to the fear and confusion, the racist assumptions and the rumor-mongering.\n\nNo one debated that the city was in chaos, but now there was debate over where that chaos had originated. Was it the residents or was it those sent to bring order? Kathy's mind spun as she read about the unprecedented concentration of armed men and women in the city.\n\nFirst she read about the mercenaries. Immediately after the storm, wealthy businesses and individuals had called in private-security firms from all over the world. At least five different organizations had sent soldiers-for-hire into the city, including Israeli mercenaries from a firm called Instinctive Shooting International. Kathy took in a quick breath. Israeli commandos in New Orleans? That was it, she realized. Her husband was an Arab, and there were Israeli paramilitaries on the ground in the city. She leapt to conclusions.\n\nAnd the Blackwater soldiers. Blackwater USA, a private-security firm that employed former soldiers from the U.S. and elsewhere, had sent hundreds of personnel to the region. They were there in an official capacity, hired by the Department of Homeland Security to help maintain order. They arrived in full battle dress. Some carried badges as deputies of the Louisiana State Police.\n\nKathy became obsessed with all the guns. Her brother had been in the National Guard, and she knew how they were armed. She started doing the math. If all the Blackwater mercenaries were carrying at least two guns each, that would mean hundreds of 9mm Heckler and Koch sidearms, hundreds of M-16 rifles and M-4 machine guns.\n\nShe felt as if she had stumbled upon the answer to her husband's disappearance. Nothing else made sense. This seemed the most logical thing. One of these mercenaries, responsible to no one, had shot Zeitoun. Now they were covering it up. This is why she had heard nothing. The whole thing would be covered up.\n\nBut there were also so many American troops. Surely they had things under control. As well as she could surmise, there were at least twenty thousand National Guard troops in New Orleans, with more arriving every day. But then she thought of the guns again. If each one of those soldiers had at least one M-16 assault rifle, there were about twenty thousand automatic rifles in the city. Too many. And if Governor Blanco was right, that these were vets coming straight from Afghanistan and Iraq, it could not bode well for her husband.\n\nShe searched more websites, went deeper. There were 5,750 Army soldiers in the New Orleans area. Almost a thousand state police officers, many of them there with SWAT teams, armed for urban combat. Four hundred Customs and Border Protection agents and officers deputized for local law enforcement. This included more than one hundred men from Border Patrol Tactical Units\u2014men usually armed with grenade launchers, shotguns, battering rams and assault rifles. There were four Maritime Security and Safety Teams, the new Coast Guard tactical units that Homeland Security had formed as part of the War on Terror. Each MSST carried M-16s, shotguns, and .45 caliber handguns. There were five hundred FBI special agents and a U.S. marshals special-ops team. And snipers. They were sending snipers into the city to shoot looters and gunmen. Kathy added it up. There were at least twenty-eight thousand guns in New Orleans. That would be the low number, counting rifles, handguns, shotguns.\n\nShe couldn't look anymore. She turned off the computer and paced. She lay in bed, staring at the wall. She got up, went to the bathroom, inspecting the new swath of white hair on her head.\n\nAgain she returned to the computer in search of her husband. She was furious with him, with his stubbornness. If he had just gotten in the Odyssey with them! Why could he not simply surrender to the same logic hundreds of thousands of people had recognized? He had to be apart from that. He had to do more. He had to do something else.\n\nShe found an email Ahmad had sent to one of the missing-persons agencies. The pictures he had attached were now the only ones she had of her husband\u2014the only ones she had in Phoenix, anyway. They had been taken a year before, in M\u00e1laga. They'd gone, the whole family, and the picture was taken on the beach near Ahmad's house. When Kathy saw that beach, she could only think of the hike, that insane hike her husband had insisted they take. If ever there was a totemic memory that encompassed the man, it was that day.\n\nThey had been in M\u00e1laga for a few days when the older kids felt comfortable enough in Ahmad and Antonia's house to be left for the morning. Zeitoun wanted to take Kathy and Safiya for a walk on the beach, to be alone for a bit. Zachary and Nademah and Aisha, entertained with Lutfi and Laila and the pool in the backyard, barely noticed when they left.\n\nKathy and Zeitoun walked down to the beach, Zeitoun carrying Safiya. They walked for a mile or so down the shore, the water cool and calm. Kathy was as content as she had been in years. It was almost like a real holiday, and her husband actually seemed relaxed, like a regular person on an actual vacation. To have him this way, just walking on a beach for no real reason, just to feel the water between his toes\u2014it was a side of him she rarely saw.\n\nBut it didn't last long. Almost as soon as she took notice of his sense of peace and leisure, his eyes focused on something in the distance.\n\n\"See that?\" he asked.\n\nShe shook her head. She didn't want to see what he saw.\n\n\"That rock. See it?\"\n\nHe had taken notice of a small rock formation in the distance, jutting into the sea a few miles down the shore. Kathy held her breath, afraid of whatever notion was brewing in his mind.\n\n\"Let's walk there,\" he said, his face bright, his eyes alive.\n\nKathy did not want to walk to a particular destination. She wanted to stroll. She wanted to stroll, then sit on the beach and play with their daughter, then go back to Ahmad's. She wanted a vacation\u2014idleness, frivolity even.\n\n\"C'mon,\" he said. \"Such a nice day. And it's not so far.\"\n\nThey walked toward the rock, and the water was pleasant, the sun gentle. But after another thirty minutes, they had not gotten noticeably closer. And they had come upon a low promontory that separated one part of the beach from the next. It seemed a perfect place to turn around. Kathy suggested this, but Zeitoun dismissed it out of hand.\n\n\"We're so close!\" he said.\n\nThey were not so close, but she followed her husband as he climbed over the rock, holding Safiya with one hand, over the jagged ridge and down again to the next stretch of beach.\n\n\"See?\" he said when they landed on the wet sand. \"So close.\"\n\nThey walked on, Zeitoun transferring Safiya to his shoulders. They continued another mile, and again the beach was interrupted by a ridge. They climbed over this one, too. When they were again on level ground, the rock in the distance seemed no closer than when they'd set out. Zeitoun wasn't fazed.\n\nThey had been walking two hours when the beach was interrupted by another, much larger promontory, this one big enough that homes and shops had been built atop it. They had to climb up a set of steps, through the roads of this small town. Kathy insisted they stop for water, for ice cream. She drank her fill, but they did not pause for long. Soon he was off again, and she had no choice but to follow. They jogged down the steps on the other side to continue on the beach. Zeitoun never broke pace. He was barely sweating.\n\n\"So close, Kathy!\" he said, pointing to the rock in the distance, which looked no closer than before.\n\n\"We should turn around,\" she said. \"What's the point?\"\n\n\"No, no, Kathy!\" he said. \"We can't turn around till we touch it.\" And she knew that he would insist she do it, too. He always wanted his family along for his quests.\n\nZeitoun showed no signs of fatigue. He switched Safiya, now sleeping, from one arm to the other, and kept going.\n\nThey walked for four hours in all, up and over three hillside towns, across fifteen miles of beach, before they were finally close enough to the rock to touch it.\n\nIt was nothing much to see. Just a boulder jutting out into the sea. When they were finally upon it, Kathy laughed, and Zeitoun laughed too. She rolled her eyes, and he smiled at her mischievously. He knew it was absurd.\n\n\"C'mon, Kathy, let's touch the rock,\" he said.\n\nThey walked out to it and quickly climbed to its peak. They sat there for a few minutes, resting, watching the waves crash against the rocks below. And as ridiculous as it had seemed en route, Kathy felt good. She had married a bullheaded man, a sometimes ridiculously stubborn man. He could be exasperating in his sense of destiny. Whatever he set his mind to, even a crackpot idea of touching some random rock miles in the distance, she knew he would not rest until he had done it. It was maddening. It was strange, even. But then again, she thought, it gave their marriage a certain epic scope. It was silly to think that way, she knew, but they were on a journey that did sometimes seem grand. She had grown up in a small Baton Rouge house with nine siblings, and now she and her husband had four thriving kids, had been to Spain, to Syria, could seemingly achieve any of the goals they conjured.\n\n\"C'mon, touch it,\" he said again.\n\nThey were sitting on it, but she hadn't yet officially touched it.\n\nNow she did. He smiled and held her hand.\n\n\"It's nice, right?\" he asked.\n\nAfter that, it became a joke between them. Any time something seemed difficult and Kathy was ready to give up, Zeitoun would say, \"Touch the rock, Kathy! Touch the rock!\"\n\nAnd they would laugh, and she would find the strength to continue, partly out of a strange sort of logic: wasn't it more absurd to give up? Wasn't it more absurd to fail, to turn back, than to continue?\n\n# MONDAY SEPTEMBER 19\n\nKathy woke up having reached a new kind of peace. She felt strong, and was ready to start planning. She had been paralyzed for almost two weeks now, waiting for word about her husband, but this was folly. She needed to go home, to the house on Dart. She was suddenly sure that she would find her husband there. His family in Syria was right. The most dangerous thing was these roving gangs of men. That made the most sense. As the city emptied out, the looting likely grew more brazen and engulfed neighborhoods like Uptown. The thieves had come to the house on Dart, and, not expecting to find anyone there, had killed her husband.\n\nShe needed to get back to New Orleans, hire a boat of some kind, and return to the house on Dart. She needed to see him, wherever he was. She needed to find him and bury him. She needed all of this to end.\n\nAll morning she felt a new serenity. It was time to get serious, to stop hoping, and to start working toward whatever came next.\n\n* * *\n\nMidday, Kathy heard that another hurricane, this one called Rita, was bearing down on New Orleans. Mayor Nagin, who had planned to reopen the city, now canceled those plans. The storm, being tracked over the Gulf with winds above 150 miles per hour, was expected to hit September 21. Even if she could make it near New Orleans, the winds would again push her back.\n\nNademah came in the living room.\n\n\"Should we pray?\" she asked.\n\nKathy almost said no\u2014all she did was pray\u2014but she didn't want to disappoint her daughter.\n\n\"Sure. Let's.\"\n\nAnd they prayed on the living room floor. Afterward, she kissed Nademah's forehead and held her close. _I will rely on you so much_ , she thought. _Poor Demah_ , she thought, _you have no idea_.\n\nAnd then Kathy's cell phone rang. She picked it up. \"Hello?\"\n\n\"Is this Mrs. Zeitoun?\" a voice asked. The man seemed nervous. He pronounced _Zeitoun_ wrong. Kathy's stomach dropped. She managed to say yes.\n\n\"I saw your husband,\" the man said.\n\nKathy sat down. An image of his body floating in the filth\u2014\n\n\"He's okay,\" the voice said. \"He's in prison. I'm a missionary. I was at Hunt, the prison up in St. Gabriel. He's there. He gave me your number.\"\n\nKathy asked him a dozen questions in one breath.\n\n\"Sorry, that's all I know. I can't tell you anything else.\"\n\nShe asked him how she could get hold of Zeitoun, if he was being well cared for\u2014\n\n\"Look, I can't talk to you anymore. I could get in trouble. He's okay, he's in there. That's it, I've got to go.\"\n\nAnd he hung up.\n\n# IV\n# TUESDAY SEPTEMBER 6\n\nZeitoun was enjoying the cool water of his first shower in over a week. The water might shut off for good at any time, he knew, so he lingered for a few seconds longer than he should have.\n\nBut he was ready to go. The neighborhoods were emptying out, and it wouldn't be long before there was no one else to help and little left to see. He wondered when and how he might leave. Maybe in a few days. He could head up to Napoleon and St. Charles and ask the officers and aid workers there how he could get out. He would only need to get to the airport in New Orleans or Baton Rouge, and then fly to Phoenix. There wasn't much left to do here, he was running low on food, and he missed Kathy and the kids. It was time.\n\nHe walked downstairs.\n\n\"Shower's all yours,\" he told Nasser.\n\nZeitoun called his brother Ahmad in Spain.\n\n\"Do you realize the images we're seeing on TV?\" Ahmad asked.\n\nAs they were talking, he heard Nasser's voice from the porch. He was talking to someone outside.\n\n\"Zeitoun!\" Nasser called.\n\n\"What?\" Zeitoun said.\n\n\"Come here,\" Nasser said. \"These guys want to know if we need water.\"\n\nZeitoun hung up the phone and walked toward the door.\n\nThe men met Zeitoun in the foyer. They were wearing mismatched police and military uniforms. Fatigues. Bulletproof vests. Most were wearing sunglasses. All had M-16s and pistols. They quickly filled the hallway. There were at least ten guns visible.\n\n\"Who are you?\" one of them asked.\n\n\"I'm the landlord. I own this house,\" Zeitoun said.\n\nNow he saw that there were six of them\u2014five white men and one African American woman. Under their vests it was hard to see their uniforms. Were they local cops? The woman, very tall, wore camouflage fatigues. She was probably National Guard. They were all looking around the house as if they were finally seeing the inside of a building they had long been watching from afar. They were tense, each of them with their fingers on their triggers. In the foyer, one officer was frisking Ronnie. Another officer had Nasser against the wall by the stairway.\n\n\"Give me your ID,\" one man said to Zeitoun.\n\nZeitoun complied. The man took the ID and gave it back to Zeitoun without looking at it.\n\n\"Get in the boat,\" he said.\n\n\"You didn't look at it,\" Zeitoun protested.\n\n\"Move!\" another man barked.\n\n* * *\n\nZeitoun was pushed toward the front door. The other officers had already gathered Ronnie and Nasser onto an enormous fan boat. It was a military craft, far bigger than any other boat Zeitoun had seen since the storm. There were at least two officers pointing automatic rifles at them.\n\nAt that moment, another boat arrived. It was Todd, coming home from his rescue rounds.\n\n\"What's happening here?\" he asked.\n\n\"Who are you?\" one of the officers demanded.\n\n\"I live here,\" Todd said. \"I have proof. It's inside the house.\"\n\n\"Get in the boat,\" the officer said.\n\nZeitoun was not panicking. He knew there had been a mandatory evacuation in effect, and he assumed this had something to do with that. He knew it would all get straightened out wherever they were being taken. All he needed was to call Kathy, who would call a lawyer.\n\nBut Yuko's number was in the house, by the phone, on the hall table. If he didn't get it now, he would have no way to reach Kathy. He hadn't memorized it.\n\n\"Excuse me,\" he said to one of the soldiers. \"I left a piece of paper on that table. It's my wife's phone number. She's in Arizona. It's the only way\u2014\" He moved toward the house, smiling politely. It was everything, that number. The piece of paper was fifteen feet away.\n\n\"No!\" the soldier yelled. He grabbed the back of Zeitoun's shirt, turned him around, and shoved him onto the boat.\n\nThe four captives rode standing, surrounded by the six military personnel. Zeitoun tried to figure out who they were, but there were few clues. Two or three of the men were dressed in black, with no visible patches or insignia.\n\nNo one spoke. Zeitoun knew not to exacerbate the situation, and assumed that when they were interviewed by a superior, everything would be explained. They would be scolded for staying in the city when there was a mandatory evacuation in effect, and they would be sent north on a bus or helicopter. Kathy would be relieved, he thought, when she heard he was finally on his way out.\n\nThey sped down Claiborne and then Napoleon, until the water grew shallow at the intersection of Napoleon and St. Charles.\n\nThe boat cut its engine and coasted toward the intersection. There were a dozen men in National Guard uniforms there, and they all took notice. A smattering of other men in bulletproof vests, sunglasses, and black caps all looked up. They were waiting for them.\n\nThe moment Zeitoun and the three other men were led off the boat, a dozen soldiers descended upon them. Two men in bulletproof vests leapt on Zeitoun, tackling him to the ground. His face was pushed into the wet grass. He spat out mud. There was a knee in his back, hands on his legs. It felt like there were at least three men keeping him down with all their force, though he had not moved or struggled. His arms were pulled behind his back and he was handcuffed with plastic ties. His legs were tied together. All the while the men were barking orders: \"Hold still!\" \"Stay there, motherfucker.\" \"Don't move, asshole.\" Out of the corner of his eye he could see the other three men, Nasser, Todd, and Ronnie, all on the ground, face down, with knees on their backs, hands on their necks. Photographers were taking pictures. Soldiers were watching, their fingers ready on the triggers of their guns.\n\n* * *\n\nStruggling to gain their balance with their legs tied, the four men were lifted up. They were shuffled into a large white van. They sat on two benches inside, opposite each other. No one spoke. A young soldier stepped into the driver's seat. His face seemed open; Zeitoun took a chance.\n\n\"What's happening here?\" Zeitoun asked him.\n\n\"I don't know,\" the soldier said. \"I'm from Indiana.\"\n\nThey waited for thirty minutes in the van. Zeitoun could see the activity outside\u2014soldiers talking urgently to each other and on radios. This was a busy intersection that he passed every day. He could see Copeland's restaurant, where he'd often eaten with his family, right there on the corner. Now it was a military post, and he was a captive. He and Todd exchanged looks. Todd was a joker, and he'd had a run-in or two with the law, so even in the back of a military van he seemed amused. He shook his head and rolled his eyes.\n\nZeitoun thought of the dogs he had been feeding. He caught the attention of one of the soldiers passing by the open back of the van.\n\n\"I've been feeding dogs,\" Zeitoun said. \"Can I give you the address, and you can take them out, bring them somewhere?\"\n\n\"Sure,\" the soldier said. \"We'll take care of them.\"\n\n\"You want the address?\" Zeitoun asked.\n\n\"No, I know where they are,\" the soldier said, and walked away.\n\nThe van drove toward downtown.\n\n\"We're going to the Superdome?\" Todd wondered aloud.\n\nA few blocks from the stadium, they pulled into the crescent-shaped driveway of the New Orleans Union Passenger Terminal, where incoming and outgoing Amtrak trains and Greyhound buses docked. Zeitoun's earlier assumption\u2014that they were being evacuated by force\u2014seemed to be confirmed. He was relieved, and sat back on the bench. It was wrong that he hadn't been allowed to retrieve any possessions, and he felt that the treatment by the cops and soldiers had been rough. But the result was going to be simple and fair enough: they were being put on a bus or train and sent out of the city.\n\nZeitoun had picked up and dropped off friends and relatives at the station a handful of times over the years. Fronted by a lush lawn and palm trees, the Union Passenger Terminal had opened in 1954, an art deco\u2013style building once aspiring to grandness but since overtaken by a certain grey municipal malaise. There was a whimsical candy-colored sculpture on the lawn that looked like a bunch of child's toys glued together without reason or order. A few blocks beyond, the Superdome loomed.\n\nAs they pulled to the side of the building, Zeitoun saw police cars and military vehicles. National Guardsmen patrolled the grounds. The station had become a kind of military base. A few personnel were casual, talking idly against a Humvee, smoking. Others were on guard, as if expecting a siege at any moment.\n\nThe van stopped at the station's side door, and the captives were taken out of the van and led inside. When Zeitoun and the others entered the main room of the station, immediately fifty pairs of eyes, those of soldiers and police officers and military personnel, were upon them. There were no other civilians inside. It was as if the entire operation, this bus station-turned-military base, had been arranged for them.\n\nZeitoun's heart was thrumming. They saw no civilians, no hospital or humanitarian-aid workers, as had been common in areas like the Napoleon\u2013St. Charles staging ground. This was different. This was entirely martial, and the mood was tense.\n\n\"Are you kidding me?\" Todd said. \"What the hell is going on?\"\n\nThe four men were seated in folding chairs near the Greyhound ticket desk. With every passing minute, everyone in the bus station seemed to take more interest in Zeitoun, Nasser, Todd, and Ronnie.\n\nAll around there were men in uniform\u2014New Orleans police, National Guard soldiers, prison guards with the words LOUISIANA DEPARTMENT OF CORRECTIONS on their uniforms. Zeitoun counted about eighty personnel and at least a dozen assault rifles within a thirty-foot radius. Two officers with dogs kept watch, leashes wrapped tight around their fists.\n\nTodd was lifted from his chair and brought to the Amtrak ticket counter against the wall. As two officers flanked him, a third officer on the other side of the counter began to question him. The other three men remained seated. Zeitoun could not hear the interrogation.\n\nThe soldiers and guards nearby were on edge. When Nasser shifted in his seat, there were immediate rebukes.\n\n\"Sit still. Go back to your position.\"\n\nNasser at first resisted.\n\n\"Stop moving!\" they said. \"Hands where I can see them.\"\n\nZeitoun examined his surroundings. In essential ways, the station was still the same. There was a Subway franchise, various ticket counters, an information kiosk. But there were no travelers. There were only men and women with guns, hundreds of boxes of water and other supplies stacked in the hallways, and Zeitoun and his fellow prisoners.\n\nTodd was arguing with his interrogators. Zeitoun could hear occasional bursts as the questioning at the Amtrak desk continued. Todd was hotheaded on a normal day, so it didn't surprise Zeitoun that he was agitated during the processing.\n\n\"Are we going to get a phone call?\" Todd asked.\n\n\"No,\" the officer said.\n\n\"You have to give us a phone call.\"\n\nThere was no answer.\n\nTodd raised his voice, rolled his eyes. The soldiers around him stood closer, barking admonitions and threats back at him.\n\n\"Why are we here?\" he asked a passing soldier.\n\n\"You guys are al Qaeda,\" the soldier said.\n\nTodd laughed derisively, but Zeitoun was startled. He could not have heard right.\n\nZeitoun had long feared this day would come. Each of the few times he had been pulled over for a traffic violation, he knew the possibility existed that he would be harassed, misunderstood, suspected of shadowy dealings that might bloom in the imagination of any given police officer. After 9\/11, he and Kathy knew that many imaginations had run amok, that the introduction of the idea of \"sleeper cells\"\u2014groups of would-be terrorists living in the U.S. and waiting, for years or decades, to strike\u2014meant that everyone at their mosque, or the entire mosque itself, might be waiting for instructions from their presumed leaders in the hills of Afghanistan or Pakistan.\n\nHe and Kathy worried about the reach of the Department of Homeland Security, its willingness to contact anyone born in or with a connection to the Middle East. So many of their Muslim friends had been interviewed, forced to send in documents and hire lawyers. But until now Zeitoun had been fortunate. He had had no experience with profiling, hadn't been suspected of anything by anyone with real authority. There were the occasional looks askance, of course, sneers from people upon hearing his accent. Maybe, he thought, this was just one soldier, ignorant or cruel, wanting to stir things up. Zeitoun decided to ignore it.\n\nStill, Zeitoun's senses were awakened. He scanned the room for more signals. He and the three others were still being watched by dozens of soldiers and cops. He felt like an exotic beast, a hunter's prize.\n\nMoments later, another passing soldier looked at Zeitoun and muttered \"Taliban.\"\n\nAnd as much as he wanted to dismiss both comments, he couldn't. Now he was sure that there was a grave misunderstanding taking place, and that unraveling it, disproving it, was going to take days. Todd ranted, but Zeitoun knew it would do no good. The question of their innocence or guilt would not be answered in this room, not any time soon.\n\nHe sat back and waited.\n\nBefore them was an alcove housing a bank of vending machines and video games. Above the machines, wrapping around the interior of the entire station, was a vast mural that occupied, in four long segments, the upper half of the station's main walls.\n\nIn all, the mural was about 120 feet long, and it sought to depict the entire history of Louisiana in particular and the United States generally. Zeitoun looked up at it, and though he had been in the terminal before, he had never really seen this mural. Now that he did, it was a startling thing, a dark catalog of subjugation and struggle. The colors were nightmarish, the lines jagged, the images disturbing. He saw Ku Klux Klan hoods, skeletons, harlequins in garish colors, painted faces. Just above him there was a lion being attacked by a giant eagle made of gold. There were images of blue-clad soldiers marching off to war next to mass graves. There were many depictions of the suppression or elimination of peoples\u2014Native Americans, slaves, immigrants\u2014and always, nearby, was the artist's idea of the instigators: wealthy aristocrats in powdered wigs, generals in gleaming uniforms, businessmen with bags of money. In one segment, oil derricks stood below a flooded landscape, water engulfing a city.\n\nNasser was processed next. He was brought to the Amtrak ticket counter, and now Zeitoun saw that they were fingerprinting and photographing each of them.\n\nSoon after Nasser's interrogation began, his duffel bag created a stir. A female officer was removing stacks of American money from the bag.\n\n\"This isn't from here,\" she said.\n\nNasser argued with her, but this discovery only got the building more excited.\n\n\"That _ain't_ from here,\" she said, now more certain.\n\nThe money was laid out on a nearby table and soon there was a crowd around it. Someone counted it. Ten thousand dollars.\n\nThis was the first Zeitoun knew of the contents of Nasser's bag. When Nasser had brought it into the canoe, Zeitoun had assumed it contained clothes, a few valuables. He never would have guessed it contained $10,000 in cash.\n\n* * *\n\nSoon there were more discoveries. Todd had been carrying $2,400 of his own. The officers stacked it on the table in its own pile next to Nasser's. In Todd's pockets they found MapQuest printouts.\n\n\"I deliver lost luggage,\" Todd tried to explain.\n\nThis didn't satisfy the officers.\n\nIn one of Todd's pockets they discovered a small memory chip, the kind used for digital cameras. Todd laughed, explaining that on it were only photos he'd taken of the flood damage. But the authorities were seeing something more.\n\nWatching the evidence on the table mount, Zeitoun's shoulders slackened. Most municipal systems were not functioning. There were no lawyers in the station, no judges. They would not talk their way out of this. The police and soldiers in the room were too worked up, and the evidence was too intriguing. Zeitoun settled in for a long wait.\n\nTodd grew more exasperated. He would calm down for a time, then explode again. Finally one of the soldiers raised his arm, as if to strike him down with the back of his hand. Todd went quiet.\n\nThen it was Zeitoun's turn for processing. He was brought to the Amtrak counter and fingerprinted. He was pushed against a nearby wall on which height markers had been written by hand, from five to seven feet. Zeitoun had stood in this exact place before while waiting to buy train tickets for friends or employees. Now, while handcuffed and guarded by two soldiers with M-16s, his photograph was being taken.\n\nAt the ticket counter, he surrendered his wallet and was frisked for any other possessions. He was asked basic questions: name, address, occupation, country of origin. He was not told of the charges against him.\n\nEventually he was brought back to the row of chairs and was seated again with Todd and Nasser, while Ronnie was processed.\n\nMoments later, Zeitoun was grabbed roughly under the arm. \"Stand up,\" a soldier said.\n\nZeitoun stood and was led by three soldiers into a small room\u2014some kind of utility closet. Inside there were bare walls and a small folding table.\n\nThe door closed behind him. He was alone with two soldiers.\n\n\"Remove your clothes,\" one said.\n\n\"Here?\" he asked.\n\nThe soldier nodded.\n\nUntil this point, Zeitoun had not been charged with a crime. He had not been read his rights. He did not know why he was being held. Now he was in a small white room being asked by two soldiers, each of them in full camouflage and holding automatic rifles, to remove his clothes.\n\n\"Now!\" one of the soldiers barked.\n\nZeitoun took off his T-shirt and shorts and, after a pause, stepped out of his sandals.\n\n\"And the undershorts,\" the same soldier said.\n\nZeitoun paused. If he did this, he would live with it always. The shame would never leave him. But there was no alternative. He could refuse, but if he did, there would be a fight. More soldiers. Some sort of retribution.\n\n\"Do it!\" the soldier ordered.\n\nZeitoun removed his underwear.\n\nOne of the soldiers circled him, lifting Zeitoun's arms as he passed. The soldier held a baton, and when he reached Zeitoun's back, he tapped Zeitoun's inner thigh.\n\n\"Spread your legs,\" the soldier said.\n\nZeitoun did so.\n\n\"Elbows on the table.\"\n\nZeitoun couldn't understand the meaning of the words.\n\nThe soldier repeated the directive, his voice more agitated. \"Put your elbows on the table.\"\n\nHe had no options. Zeitoun knew that the soldiers would get what they wanted. They were likely looking for any contraband, but he also knew that anything was possible. Nothing on this day had conformed to any precedent.\n\nZeitoun bent over. He heard the sounds of the soldier pulling plastic gloves onto his hands. Zeitoun felt fingers quickly exploring his rectum. The pain was extreme but brief.\n\n\"Stand up,\" the soldier said, removing the glove with a snap. \"Get dressed.\"\n\nZeitoun put on his shorts and shirt. He was led out of the room, where he saw Todd. He was arguing already, threatening lawsuits, the loss of all their jobs. Soon Todd was pushed into the room, the door was closed, and his protestations were muffled behind the steel door.\n\nWhen Todd's search was complete, the two of them were led back through the bus station. Zeitoun was certain that he saw a handful of looks of recognition, soldiers and police officers who knew what had happened in the room.\n\nZeitoun and Todd were brought to the back of the station and toward the doors that led to the buses and trains. Zeitoun's thoughts were a jumble. Could it be that after all that, they _were_ being evacuated? Perhaps they had been stripped to ensure that they hadn't stolen anything, and now, deemed clean, they were being sent away on a bus? It was bizarre, but not out of the realm of possibility.\n\n* * *\n\nBut when the guards pushed open the doors, Zeitoun took a quick breath. The parking lot, where a dozen buses might normally be parked, had been transformed into a vast outdoor prison.\n\nChain-link fences, topped by razor wire, had been erected into a long, sixteen-foot-high cage extending about a hundred yards into the lot. Above the cage was a roof, a freestanding shelter like those at gas stations. The barbed wire extended to meet it.\n\nZeitoun and Todd were brought to the front of the cage, a few feet from the back of the bus station, and a different guard opened the door. They were pushed inside. The cage was closed, then locked with chain and a padlock. Down the way, there were two other prisoners, each alone in their own enclosure.\n\n\"Holy shit,\" Todd said.\n\nZeitoun was in disbelief. It had been a dizzying series of events\u2014arrested at gunpoint in a home he owned, brought to an impromptu military base built inside a bus station, accused of terrorism, and locked in an outdoor cage. It surpassed the most surreal accounts he'd heard of third-world law enforcement.\n\nInside the cage, Todd ranted and swore. He couldn't believe it. But then again, he noted, it was not unprecedented. During Mardi Gras, when the local jails were full, the New Orleans police often housed drunks and thieves in temporary jails set up in tents.\n\nThis one, though, was far more elaborate, and had been built since the storm. Looking at it, Zeitoun realized that it was not one long cage, but a series of smaller, divided cages. He had seen similar structures before, on the properties of his clients who kept dogs. This cage, like those, was a single-fenced enclosure divided into smaller ones. He counted sixteen. It looked like a giant kennel, and yet it looked even more familiar than that.\n\nIt looked precisely like the pictures he'd seen of Guant\u00e1namo Bay. Like that complex, it was a vast grid of chain-link fencing with few walls, so the prisoners were visible to the guards and each other. Like Guant\u00e1namo, it was outdoors, and there appeared to be nowhere to sit or sleep. There were simply cages and the pavement beneath them.\n\nThe space inside Zeitoun and Todd's cage was approximately fifteen by fifteen feet, and was empty but for a portable toilet without a door. The only other object in the cage was a steel bar in the shape of an upside-down U, cemented into the pavement like a bike rack. It normally served as a guide for the buses parking in the lot and for passengers forming lines. It was about thirty inches high, forty inches long.\n\nAcross from Zeitoun's cage was a two-story building, some kind of Amtrak office structure. It was now occupied by soldiers. Two soldiers stood on the roof, holding M-16s and staring down at Zeitoun and Todd.\n\nTodd raged, wild-eyed and protesting. But the guards could hear little of what he said. Even Zeitoun, standing near him, could hear only muffled fragments. It was then that Zeitoun realized that there was a sound, a heavy mechanical drone, cloaking the air around them. It was so steady and unchanging that he had failed to notice it.\n\nZeitoun turned around and realized the source of the noise. The back of their cage nearly abutted the train tracks, and on the tracks directly behind them stood an Amtrak train engine. The engine was operating at full power on diesel fuel, and, Zeitoun realized in an instant, was generating all the electricity used for the station and the makeshift jail. He looked up at the monstrous grey machine, easily a hundred tons, adorned with a small red, white, and blue logo, and knew that it would be with them, loud and unceasing, as long as they were held there.\n\nOne guard was assigned to them. He sat on a folding chair about ten feet in front of the cage. He stared at Zeitoun and Todd, his face curious and disdainful.\n\nZeitoun was determined to get a phone call. He reached for the chain-link fence in front of him, intending to get the attention of an officer of some kind he saw near the back door of the station. Todd did so, too, and was immediately set straight by the guard who had been assigned to watch them.\n\n\"Don't touch the fence!\" the guard snapped.\n\n\"Don't touch the fence? Are you kidding?\" Todd asked.\n\nBut the soldier was not joking. \"You touch the fence again I'll fuck you up.\"\n\nTodd asked where they were supposed to stand. He was told they could stand in the middle of the cage. They could sit on the steel rack. They could sit on the ground. But if they touched the fence again there would be consequences.\n\nThere were a dozen other guards roaming behind the terminal. One walked by, led by a German shepherd. He made sure to pause meaningfully at their cage, giving Zeitoun and Todd a look of warning before moving on.\n\nZeitoun could barely stand. There was a stabbing pain in his foot he had ignored until now. He took off his shoe to find his instep discolored. There was something wedged under his skin\u2014some kind of metal splinter, he thought, though he couldn't remember where or when he'd gotten it. The area was purple in the center, ringed by white. He needed to clear out the splinter or the foot would get worse, and quickly.\n\nZeitoun and Todd took turns sitting on the steel rack. It was only wide enough for one person, so they traded ten-minute shifts.\n\nAfter an hour, the doors to the station burst open. Nasser and Ronnie appeared, escorted by three officers. Zeitoun and Todd's cage was opened, and Nasser and Ronnie were pushed inside. The cage was locked again. The four men were reunited.\n\nUnder the rumble of the engine, the men compared their experiences thus far. All four had been strip-searched. Only Todd had been told why they were being held\u2014possession of stolen goods was the only charge mentioned\u2014and none had been read their rights. None had been allowed to make a phone call.\n\nNasser had tried to explain the cash he had in his knapsack. The police and soldiers were in the city to prevent the widespread looting everyone had heard about. Nasser, being equally concerned about the looting, had decided to keep his money, his life savings, with him.\n\nHis interrogators did not accept this. Nasser had had no luck explaining that legions of immigrants kept their money in cash, that trust in banks was tenuous. He explained that one reason a person in his position kept his money in cash was for the possibility, however remote, that he would be stopped, questioned, detained\u2014or deported. With cash he could hide it, keep it, direct its retrieval if he was sent away.\n\nThe four men didn't know what would happen to them, but they knew they would spend the night in the cage.\n\nThe Syrian names of Zeitoun and Dayoob, their Middle Eastern accents, the ten thousand dollars cash, Todd's cash and MapQuest printouts\u2014it all added up to enough evidence that the four of them knew that their predicament would not be straightened out anytime soon.\n\n\"We're screwed, friends,\" Todd said.\n\nIn the cage, the men had few options: they could stand in the center, they could sit on the cement, or they could lean against the steel rack. No one wanted to sit on the ground. The cement beneath them was filthy with dirt and grease. If they made a move toward the fence, the guards would yell obscenities and threaten retribution.\n\nFor the first hours in the cage, Zeitoun's overriding goal was to be granted a phone call. All the men had made the request repeatedly during processing, and had been told that there were no phones functioning.\n\nThis seemed to be fact. They saw no one talking on cell phones or landlines. There was a rumor that satellite phones were working and that there was one phone, connected to a fax line, in the upstairs office of the bus station.\n\nEvery time a guard passed, they begged for access to this or any phone. At best they got shrugs and glib answers.\n\n\"Phones don't work,\" a guard told them. \"You guys are terrorists. You're Taliban.\"\n\nThe day's light was dimming. Processing had taken three hours, and the four men had been in the cage for three more. They were each given small cardboard boxes with the words BARBECUE PORK RIB printed on the side. Inside was a set of plastic cutlery, a packet of cheese spread, two crackers, a packet of orange-drink crystals, and a bag of pork ribs. These were military-style meals, ready to eat.\n\nZeitoun told the guard that he and Nasser were Muslims and could not eat pork.\n\nThe guard shrugged. \"Then don't eat it.\"\n\nZeitoun and Nasser ate the crackers and cheese and gave the rest to Todd and Ronnie.\n\nWith the darkness coming, the sound behind them seemed to grow louder. Already he was tired, but Zeitoun knew that the engine would ensure that none of them slept. He had worked on ships before, in engine rooms, but this was louder than that, louder than anything he had ever known. In the glare of the floodlights, it resembled a great furnace, moaning and ravenous.\n\n\"We can pray,\" Zeitoun said to Nasser.\n\nHe had caught Nasser's eye, and he knew what he was thinking. They needed to pray, were urged to do so five times a day, but Nasser was nervous. Would this arouse more suspicion? Would they be mocked or even punished for worshiping?\n\nZeitoun saw no reason not to do so, even while being held in an outdoor cage. \"We must,\" he said. If anything, he thought, they needed to pray more often, and with great fervor.\n\n\"What about _wuduu?\"_ Nasser asked.\n\nThe Qur'an asked that Muslims wash themselves before their prayers, and there was no means of doing so here. But Zeitoun knew that the Qur'an allowed that if there was no water available, Muslims could use dust to cleanse themselves, even if only ceremoniously. And so they did so. They took gravel from the ground and rubbed it over their hands and arms, their heads and feet, and they knelt and performed _salaat_. Zeitoun knew their prayers were arousing interest from the guards, but he and Nasser did not pause.\n\nAs the night went black, the lights came on. Floodlights from above and from the building opposite. The night grew darker and cooler, but the lights stayed on, brighter than day. The men were not given sheets, blankets, or pillows. Soon there was a new guard on duty, sitting on the chair opposite them, and they asked him where they were supposed to sleep. He told them that he didn't care where they slept, as long as it was on the pavement, where he could see them.\n\nZeitoun didn't care about sleep this night. He wanted to stay awake in case a supervisor of some sort, a lawyer, any civilian at all, happened by. The other men tried to rest their heads on the pavement, in the crooks of their arms. No one slept. Even when someone would find themselves in a place where they might be able to rest, the sound of the engine, its vibrations in the ground, took over. There could be no sleep in this place.\n\nSomewhere in the small hours, Zeitoun tried to drape himself over the steel rack, stomach-down. He found a minute or so of rest this way, but it was a position he could not maintain. He tried to lean his back against it, arms crossed. It could not be done.\n\nOther guards occasionally walked by with their German shepherds, but the night was otherwise uneventful. There was only the face of the guard, his M-16 by his side, the floodlights coming from every angle, illuminating the faces of Zeitoun's fellow prisoners, all drawn, exhausted, half-mad with fatigue and confusion.\n\n# WEDNESDAY SEPTEMBER 7\n\nWhen the sky began to pale into dawn, Zeitoun realized he had not slept at all. He had closed his eyes for a few minutes at a time, but had not found sleep. He'd refused to lie on the pavement, but even if he could have brought himself to do so, even if he could quell the panic about his situation, his family, his home, the uninterrupted drone of the engine would have kept him awake.\n\nHe watched as the night guard left and was replaced by a new man. The new guard's expression was the same as his predecessor's, seeming to take for granted the guilt of the men in the cage.\n\nZeitoun and Nasser performed their _wuduu_ and their _salaat_ , and when they were done, they stared at the guard, who was staring at them.\n\nZeitoun became more alert, even optimistic, as the sky brightened. He assumed that with each day since the hurricane, the city would find its way toward some kind of stability, and that the government would soon send help. With that help, the chaos that had brought him to this cage would be reined in and the misunderstanding manifested here would be mitigated.\n\nZeitoun convinced himself that the previous day had been an aberration, that today would bring a return to reason and procedure. He would be allowed a phone call, would learn about the charges against him, might even see a public defender or a judge. He would call Kathy and she would hire the best lawyer she could find, and this would be over in hours.\n\n* * *\n\nThe other men in the cage, all of whom had finally found some rest during the night, woke one by one, and stood to stretch. Breakfast was brought. Again it was MREs, this time including ham slices. Zeitoun and Nasser ate what they could and gave the rest to Todd and Ronnie.\n\nAs the prison awoke, Zeitoun examined the chainlink structure closely. It was about 150 feet long. The razor wire was new, the portable toilets new. The fencing was new and of high quality. He knew that none of this had existed before the storm. New Orleans Union Passenger Terminal had never before been used as a prison. He did some rough calculations in his mind.\n\nIt would have taken maybe six flatbed trucks to get all the fencing to the station. He saw no forklifts or heavy machinery; the cages must have been assembled by hand. It was an impressive feat, to get such a construction project completed so soon after the storm. But when had they done it?\n\nZeitoun had been brought into the station on September 6, seven and a half days after the hurricane passed through the city. Even under the best of circumstances, building a prison like this would have taken four or five days. That meant that within a day of the storm's eye passing over the region, officials were making plans for the building of a makeshift outdoor prison. Fencing and razor wire would have had to be located or ordered. The toilets and floodlights and all other equipment would have had to be borrowed or requisitioned.\n\nIt was a vast amount of planning and execution. A regular contractor would have wanted weeks to complete the task, and would have used heavy machinery. Without machines, dozens of men would be needed. To do it as quickly as they had, fifty men would be needed. Maybe more. And who were these men? Who did this work? Were there contractors and laborers working around the clock on a prison days after the hurricane? It was mind-boggling. It was all the more remarkable given that while the construction was taking place, on September 2, 3, and 4, thousands of residents were being plucked from rooftops, were being discovered alive and dead in attics.\n\nAt midday, Zeitoun heard something strange: the sound of buses at the bus station. He looked up to see a school bus arriving at the far end of the lot. From it descended thirty or more prisoners, one woman among them, in orange jumpsuits.\n\nThey were the incarcerated from the Jefferson Parish and Kenner jails\u2014those who had been in jail before the storm. Within the hour, the long row of cages began to fill. And again, just like Guant\u00e1namo, all prisoners could be seen by anyone, from any angle. Now, with the orange uniforms completing the picture, the similarities were too strong to ignore.\n\nQuickly after each group was locked into a cage, they were warned about touching the fence. Any touching of any fence would result in severe consequences. And so they came to know the strange rules of their incarceration. The pavement would be their bed, the open-door toilet would be their bathroom, and the steel rack would be the seat they could share. But for the first hour, while the new prisoners got acquainted with their new cells, there was much yelling from the guards about where and how to stand and sit, what not to touch.\n\nA man and a woman were housed one cage away from Zeitoun, and soon a rumor abounded that the man was a sniper, that it had been he who had been shooting at the helicopters that had tried to land on the roof of a hospital.\n\nLunch was different than previous meals. This time the guards brought ham sandwiches to the cages and then stuffed them through the holes in the wire.\n\nAgain Zeitoun and Nasser did not eat.\n\nThe presence of dogs was constant. There were at least two always visible, their handlers sure to parade them past the cages in close proximity. Occasionally one would explode into barking at some prisoner. Someone in Zeitoun's cage mentioned Abu Ghraib, wondering at what point they'd be asked to pose naked, in a vertical pyramid, and which guard would lean into the picture, grinning.\n\nBy two o'clock there were about fifty prisoners at the bus station, but Zeitoun's cage was still the only one with its own dedicated guard.\n\n\"You really think they consider us terrorists?\" Nasser asked.\n\nTodd rolled his eyes. \"Why else would we be alone in this cell while everyone else is crammed together? We're the big fish here. We're the big catch.\"\n\nThroughout the day, a half-dozen more prisoners came through the station and were brought to the cages. These men were dressed in their civilian clothes; they must have been picked up after the storm, as Zeitoun and his companions had been. The pattern was clear now: the prisoners who were being transferred from other prisons came by bus and weren't processed, while those arrested after the storm were processed inside and brought through the back door.\n\nBy overhearing the guards and prisoners talking, Zeitoun realized the prison had been given at least two nicknames by the guards and soldiers. A few referred to it as Angola South, but far more were calling it Camp Greyhound.\n\nIn the afternoon, one of the guards approached a man in the cage next to Zeitoun's. He talked to an orange-clad prisoner for a few moments, gave him a cigarette, and then returned to the bus station.\n\nMoments later, the guard reappeared, leading a small television crew. The guard led them straight to the man he'd given a cigarette to. The reporter\u2014Zeitoun could see now the crew was from Spain\u2014conducted an interview with the prisoner, and then, after a few minutes, he approached Zeitoun with the microphone and began to ask a question.\n\n\"No!\" the guard yelled. \"Not that one.\"\n\nThe crew was ushered back into the station.\n\n\"Holy shit,\" Todd said. \"They bribed that dude.\"\n\nAs they were leaving, the cameraman swept his lens over the whole outdoor jail, Zeitoun included. There was a bright light attached to the camera, and being viewed that way, in the glare of a floodlight and shown to the world as a criminal in a cage, made Zeitoun furious. It was a lie.\n\nBut Zeitoun had a sudden hope, given that the crew was Spanish, that the footage might be broadcast to his brother in M\u00e1laga. Ahmad would see it\u2014he saw everything\u2014and he would tell Kathy, and Kathy would know where he was.\n\nAt the same time, Zeitoun couldn't bear the thought of his family in Syria knowing he was being kept like this. No matter what happened, if and when he was released, he could not let them know that this had happened to him. He did not belong here. He was not this. He was in a cage, being viewed, gaped at, seen as visitors to the zoo see exotic animals\u2014kangaroos and baboons. The shame was greater than any his family had ever known.\n\nIn the late afternoon a new prisoner was brought through the bus-station doors. He was white, about fifty, thin and of average height, with dark hair and tanned skin. Zeitoun thought little of him until his own cage was opened and the man was pushed inside. There were now five prisoners in their cage. No one knew why.\n\nThe man was dressed in jeans and a short-sleeved shirt, and seemed to have stayed clean during and after the storm. His hands, face, and clothing were all without dirt or stain. His attitude, too, bore no shadow of the suffering of the city at large.\n\nHe introduced himself to Zeitoun and the three others, shaking each of their hands like a conventioneer. He said his name was Jerry. He was gregarious, full of energy, and made jokes about his predicament. The four men had spent a sleepless night in an outdoor cage and did not have the energy to make much conversation, but this new prisoner more than filled the silence.\n\nHe laughed at his own jokes, and about the bizarre situation they found themselves in. Without prompting, Jerry told the story of how he had come to be arrested. He had stayed behind during the storm, just as he always did during hurricanes. He wanted to protect his house, and after Katrina passed, he realized he needed food, and couldn't walk to any stores nearby. His car was on high ground and was undamaged, but he was out of gas. So he found a length of tubing in his garage and was in the middle of siphoning gasoline from a neighbor's car\u2014he planned to tell his neighbor, who would have understood, he said\u2014when he was discovered by a National Guard flatboat. He was arrested for theft. It was an honest misunderstanding, he said, one that would be straightened out soon enough.\n\nZeitoun pondered the many puzzling aspects to Jerry's presence. First, he seemed to be the only prisoner in the complex entertained by the state of affairs\u2014being held at Camp Greyhound. Second, why had he been put in their cage? There were fifteen other cages, many of them empty. There didn't seem to be any logic to taking a man brought in for gasoline-siphoning and placing him with four men suspected of working together on crimes varying from looting to terrorism.\n\nJerry asked how the rest of them had come to be in Camp Greyhound. Todd told the story for the four of them. Jerry said something about how badly the four of them had gotten screwed. It was all common small talk, and Zeitoun was tuning out when Jerry changed his tone and line of questioning.\n\nHe began to direct his efforts toward Zeitoun and Nasser. He asked questions that didn't flow from the conversational strands he had begun. He made disparaging remarks about the United States. He joked about George W. Bush, about the administration's dismal response to the disaster so far. He questioned the competence of the U.S. military, the wisdom of U.S. foreign policy around the world and in the Middle East in particular.\n\nTodd engaged with him, but Zeitoun and Nasser chose to remain quiet. Zeitoun was deeply suspicious, still trying to parse how this man had ended up in their cage, and what his intentions might be.\n\n\"Be nice to your mom!\"\n\nWhile Jerry talked, Zeitoun turned to see a prisoner a few cages away from him. He was white, in his mid-twenties, thin, with long brown hair. He was sitting on the ground, his knees drawn up to his chest, and he was chanting the statement like a mantra, but loudly.\n\n\"Be nice to your mom! Treat her kind!\"\n\nThe other three detainees in the young man's cage were visibly annoyed by him. He had apparently been repeating these strange directives for some time, and Zeitoun had only begun to hear them.\n\n\"Don't play with matches! Fire is dangerous!\" he said, rocking back and forth.\n\nThe man was disabled in some way. Zeitoun watched him carefully. He was not right in the head. He seemed to have been stunted, mentally, at no more than five or six years of age. He recited basic rules and warnings that a very small child might be asked to memorize in kindergarten.\n\n\"Don't hurt your mom! Be nice to your mom!\"\n\nHe went on like this. His cage mates hushed him and even nudged him with their feet, but he took no notice. He was in something like a trance state.\n\nBecause the train engine was so loud, his chanting wasn't much of a nuisance for anyone else. But his child's mind could not seem to understand where he was or why.\n\nOne of the guards, sitting a few yards away from the man's cage, kept insisting that he stay in the middle of the enclosure, where he could be easily seen. Any movement left or right was forbidden. But the man in the cage didn't understand this. He would simply get up and move over to another side. What motivated the man to decide it was time to move from here to there was unclear. But the unprovoked and unsanctioned movement enraged the guard.\n\n\"Get back there! Where I can see you!\" he yelled.\n\nThe man didn't know he was being addressed. \"Brush your teeth before bed,\" he was saying. \"Wash your arms and hands. Go pee-pee now so you don't wet the bed.\"\n\nThe guard stood. \"Get back over there or I'm gonna come down on you, motherfucker!\"\n\nThe man remained where he was, in an unsanctioned part of the cage. There he continued to rock, squatting, focused on the space between his feet.\n\n\"I'm going to count to three,\" the guard yelled.\n\nThe man, in an almost deliberate provocation, reached out and touched the fence.\n\nThat was it. The guard got up and a few seconds later returned with another guard. The second guard was carrying something that looked like a fire extinguisher.\n\nThey opened the cage. As they did, the man looked up, suddenly afraid. His eyes were wide with wonder and surprise as they lifted him to his feet and dragged him out of the cage.\n\nA few feet away, they dropped him on the pavement, and with the help of two more guards, they tied his hands and feet with plastic handcuffs. He did not resist.\n\nThen they stepped away, and the first guard, the one who had warned him, aimed the hose and sprayed him, head to toe, with a substance Zeitoun could not immediately discern.\n\n\"Pepper spray,\" Todd said.\n\nThe man disappeared in the haze and screamed like a scalded child. When the smoke cleared, he was cowering in a fetal position, wailing like an animal, trying to reach his eyes with his hands.\n\n\"Get the bucket!\" the guard said.\n\nAnother guard came over and dumped a bucket of water on the screaming man. They didn't say another word. They left him screaming, and soon moaning, soaked and gassed, on the pavement behind the Greyhound station. After a few minutes, they dragged him to his feet and returned him to the cage.\n\n\"You have to wash the pepper spray off,\" Todd explained. \"Otherwise you get burned, blistered.\"\n\nThis night's MRE was beef stew. Zeitoun ate. The smell of pepper spray hung in the air.\n\nThe previous night had been calm compared to the day, but this night brought more fury, more violence. Other prisoners had been added to the cages throughout the evening, and now there were more than seventy at Camp Greyhound; they were angry. There was less space, more agitation. There were challenges issued by the prisoners to the guards, and soon more pepper-sprayings.\n\nAlways the procedure was the same: a prisoner would be removed from his cage and dragged to the ground nearby, in full view of the rest of the prisoners. His hands and feet would be tied, and then, sometimes with a guard's knee on his back, he would be sprayed directly in the face. If the prisoner protested, the knee would dig deeper into his back. The spraying would continue until his spirit was broken. Then he would be doused with the bucket and returned to his cage.\n\nZeitoun had watched elephants as a boy, when a Lebanese circus passed through Jableh. Their trainers used large steel hooks to pull the beasts one way or the other, to prod or punish them. The hooks looked like crowbars or ice picks, and the trainers would grab the elephants between the folds of their hide and then pull or twist. Zeitoun thought of the trainers now, how these guards too had been trained to deal with a certain kind of animal. They were accustomed to hardened maximum-security prisoners, and their tools were too severe to work with these men, so many of them guilty of the smallest of crimes\u2014curfew violations, trespassing, public drunkenness.\n\nThe night dragged on. There were bursts of screaming, wailing. Arguments broke out among prisoners. Guards would leap up, remove a man, put him in a new cage. But the fighting continued. The prisoners this night were wired, agitated.\n\nZeitoun and Nasser brushed whatever dust they could over their hands and arms and neck to cleanse themselves, and they prayed.\n\nThe guilt Zeitoun now felt was profound and growing. Kathy had been right. He should not have stayed in the city, and he certainly should not have stayed when she asked him, every day after the storm, to get out. _I'm so sorry, Kathy_ , he thought. He could not imagine the suffering Kathy was enduring now. She had said every day that something bad could happen, something unexpected, and now she had been proven right. She did not know if he was alive or dead, and every indication would point to the latter.\n\nAnything in this prison would be tolerable if he could only call her. He did not want to imagine what she was telling the kids, what kinds of questions they would be asking.\n\nBut why not allow the prisoners their phone call? Any way he approached the question, he couldn't see the logic in prohibiting calls. It was troublesome, maybe, to escort the prisoners into the station to make the calls, but wouldn't the calls end up relieving the prison of at least some of the jailed? Any municipal jail, he figured, expects many of their prisoners to leave within a day or two, through bonds or dropped charges or any number of outcomes for the small-time offender.\n\nThe ban on phone calls was, then, purely punitive, just as the pepper-spraying of the child-man had been born of a combination of opportunity, cruelty, ambivalence, and sport. There was no utility in that, just as there was no utility in barring all prisoners from contacting the outside world.\n\n_Oh Kathy_ , he thought. _Kathy, I am so sorry. Zachary, Nademah, Aisha, Safiya, I am so very sorry tonight that I was not and am not with you_.\n\nBy two or three in the morning, most of the prisoners were asleep, and those who remained awake with Zeitoun were quiet. Again Zeitoun refused to sleep on the pavement, and caught only occasional rest by draping himself over the steel rack.\n\nHe knew the conditions had begun to take a very real toll on his psyche. He had been angry until now, but he had been thinking clearly. Now the connections were more tenuous. He had wild thoughts of escape. He pondered whether something very bad might happen to him here. And throughout the night he thought of the child-man, and heard his screams. Under any normal circumstances he would have leapt to the defense of a man victimized as that man had been. But that he had to watch, helpless, knowing how depraved it was\u2014this was punishment for the other prisoners, too. It diminished the humanity of them all.\n\n# THURSDAY SEPTEMBER 8\n\nZeitoun woke to screams and curses. He had somehow managed to doze off in the early hours, while draped over the steel rack. He stood and saw that down the line of cages, more prisoners were being sprayed.\n\nNow the guards were shooting the pepper spray through the fencing. They didn't bother removing the prisoners from their cages. The tactic lessened the individual dosages, but spread the gas all over the complex. After Zeitoun and Nasser prayed, they and the rest of the prisoners spent the morning shielding their eyes and mouths with their shirts, coughing through the poison.\n\nThe splinter in Zeitoun's foot was now infected. It had darkened to a dull blue overnight, and he could no longer put any weight on it. He had seen his workers, most of whom were uninsured and afraid to register at a hospital, ignore their injuries. Broken fingers went unset, horrible cuts went untreated and led to all manner of sickness. Zeitoun had no idea what kind of object was lodged inside him, but knew he needed to take it out as soon as possible. All he needed was a moment of attention, a sterile needle, a knife even. Anything to carve into the foot and remove whatever was lodged inside.\n\nThe pain was intense, and Zeitoun's cage mates tried to help, to come up with a solution\u2014anything sharp to use on it. But none of them had even a set of keys.\n\nMinutes later, a man emerged from the station and came toward him. He was wearing green hospital scrubs and had a stethoscope around his neck. He was portly, with a kind face and a ducklike walk. The relief Zeitoun felt in the seconds he saw him approach was beyond measure.\n\n\"Doctor!\" Zeitoun called.\n\nThe man did not break stride. \"I'm not a doctor,\" he said, and continued on.\n\n* * *\n\nBreakfast again was MREs, an omelet filled with bacon, and again Zeitoun and Nasser gave their pork to Todd and Ronnie. But there was something new to the breakfast this day, Tabasco, and Zeitoun had an idea. He took the small bottle and slammed it on the cement, breaking it into shards and blades. He took the sharpest piece and cut into the swollen area of his foot, releasing far more fluid\u2014clear, then white, then red\u2014than he thought possible. Then he cut through to the dark object lodged inside, and after soaking his foot in blood, he pried it out. It was a metal sliver, the size of a toothpick.\n\nHe wrapped his foot in all the extra paper napkins in the cage, and the relief was immediate.\n\nThroughout the day there were more pepper sprayings, both individual treatments and more indiscriminate ones. In the late afternoon one of the guards brought out a thick-barreled gun and shot it into one of the cages. Zeitoun thought a man had been killed until he saw that the gun was shooting not bullets but beanbags. The victim writhed on the ground, holding his stomach. From then on, the beanbag gun became a favorite weapon for submission. The guards alternated between the pepper spray and the beanbag gun, shooting the men and women in the cages.\n\nJerry continued to engage Zeitoun and Nasser in conversation. He was pointedly uninterested in Todd and Ronnie. He asked Zeitoun more about his heritage, about Syria, about his career, about his visits back home. He churned through the same line of questioning with Nasser, always disguising it with good cheer and innocent curiosity. Nasser, reticent by nature, withdrew almost completely. Zeitoun tried to brush off the questions, feigning exhaustion. The presence of Jerry grew more unsettling by the day.\n\nWho was he? Why, when there were almost one hundred prisoners elsewhere in the complex, was he in their cage? Todd would later insist that he had been a spy, a plant\u2014meant to glean information from the Syrians in the cage. Of course he was undercover, Todd said. But if this were true, Zeitoun thought, he was a very dedicated public servant. He ate outside in the cage, and when night fell and the air cooled, he slept as Zeitoun's cage mates slept, without blankets or pillows, on the filthy ground.\n\nThat night, when it was his turn to lie over the guardrail in the cage, Zeitoun tried to do so comfortably but could not. There was a new pain in his side, coming from the area of his right kidney. The pain was sharp when he tried to drape himself over the steel rail, and when he stood in place it dulled but remained. It was yet another thing to think about, another reason he would not find rest this night.\n\n# FRIDAY SEPTEMBER 9\n\nAt midday, Zeitoun and the cage mates were told they would be moving out of Camp Greyhound. A series of school buses pulled into the far area of the lot.\n\nZeitoun was removed from his cage, handcuffed, and pushed toward one of the buses. He was lined up and then handcuffed to another prisoner, a man in his sixties. It was a simple school bus, decades old. Zeitoun and his companion were told to board. They shuffled up the steps, past the armed driver and a handful of armed guards, and sat down. Todd, Nasser, and Ronnie, all paired with new men, were brought onto the bus. None of the fifty prisoners onboard were told where they were going. Zeitoun looked for Jerry, but he was no longer with them. He was gone.\n\nThey drove out of the city, heading north. Zeitoun and the man to whom he was handcuffed did not talk. Few prisoners spoke. Some seemed to know where the bus was heading. Others could not imagine what was next. Still others seemed content that finally they were out of the bus station, that it could not possibly get worse.\n\nThey left the city and Zeitoun saw the first expanse of dry land he'd witnessed since the storm. It reminded him of reaching port after a long trip at sea; the temptation was to leap from the ship and dance and run on the solid and limitless earth.\n\nForty miles on, Zeitoun saw a sign on the highway indicating that they were approaching the town of St. Gabriel. He took this as a positive sign, or a darkly comic one. In Islam, the archangel Gabriel, the same Gabriel who in the Bible spoke to the Virgin Mary and foretold the birth of Jesus, is believed to be the messenger who revealed the Qur'an to the Prophet Muhammad. In the Qur'an, Gabriel is described as having six hundred wings, and is assumed to have accompanied Muhammad when he ascended to the heavens.\n\nThe bus slowed at what at first looked like a country club. There was a vast green lawn enclosed by a white fence, the kind typically surrounding a horse ranch. The bus turned and passed through a gate of red brick. On the entranceway Zeitoun saw a sign confirming where they were: the ELAYN HUNT CORRECTIONAL CENTER. It was a maximum-security prison. Most of the men on the bus seemed unsurprised. The silence was absolute.\n\nThey made their way down a long driveway lined with tidy trees. White birds scattered as they approached another gate, this one resembling a highway tollbooth. A guard waved the bus through, and soon they arrived within the prison grounds.\n\nHunt Correctional Center was a complex of one-story red-brick buildings laid out across an immaculate green campus. Everything was arranged in orderly grids. The fences, and the barbed wire atop them, gleamed in the sun. The grass was bright and newly cut. Sprinklers ticked and spun in the distance.\n\nThe prisoners were processed one by one, at tables placed outside. Zeitoun's entrance interview was brief and his hosts were polite. Two women asked him about his health, any medications he was using, his food restrictions. He was struck by how professional and respectful they were. It occurred to him that this level of professionalism might mean that standard procedure\u2014a phone call for the accused\u2014would be observed, and he would be free within a day or two. At the very least, Kathy would know he was alive. That was all that mattered.\n\nThey were brought into a changing room and told to strip naked. Zeitoun did so, in the company of a dozen other men, and with such numbers he did not fear strip searches or violence. He removed his shirt, shorts, and underwear, and they were taken away by prison workers.\n\nHe and the other prisoners were given orange short-sleeved jumpsuits. They were not given underwear. Zeitoun stepped into the jumpsuit, zipped it up, and put his shoes back on.\n\n* * *\n\nThey were put back on a bus and driven through the prison complex\u2014an array of geometrically arranged buildings with blue roofs. The bus stopped at what seemed to be the last prison block, in what was evidently the highest-security section of the prison.\n\nZeitoun and the others on the bus were led into one of the long cellblocks. He was brought down a long concrete hallway and then directed into a cell. It was no more than six feet by eight feet, meant for one prisoner. Nasser was inside already. The door closed. The bars were baby blue.\n\nThe cell was constructed entirely from cement. The toilet was molded from cement and placed in the center of the cell. The bed, on the side of the room, was made of cement, with a rubber mattress atop it. On the back wall there was a small window covered in thick Plexiglas. A vague white square was visible, presumably the sky.\n\nZeitoun and Nasser barely spoke. There was nothing to say. They both knew their predicament had just taken a far more serious turn. The two Syrian Americans had been isolated. When they had been caged with Todd and Ronnie, it seemed possible that the charges against them\u2014whenever they were actually leveled\u2014might be limited to looting. But now the two Syrians had been separated from the Americans, and there was no predicting where this would go.\n\nZeitoun remained certain that one phone call would free him. He was a successful and well-known man. His name was known all over the city of New Orleans. He only needed to reach Kathy and she would knock down every wall to get to him.\n\nAll day Zeitoun made it his business to sit by the bars, waving a napkin, pleading with the guards to grant him a call. The guards seemed to relish concocting variations of their denials.\n\n\"Phone's broken,\" they would say.\n\n\"Not today.\"\n\n\"Lines are down.\"\n\n\"Maybe tomorrow.\"\n\n\"What'll you do for me?\"\n\n\"Not my problem. You're not our prisoner.\"\n\nThis was the first but not the last time Zeitoun would hear this. He had not been processed in a traditional way, and was not assigned to Hunt for the long term. Therefore he was not technically a Hunt prisoner, and so was not bound by the institution's standard operating procedure. This was what Zeitoun was told many times by the guards:\n\n\"You're FEMA's problem.\"\n\nFEMA was footing the bill for his incarceration, they said, and that of all the other prisoners from New Orleans. The Elayn Hunt Correctional Center was renting space to warehouse these men, but otherwise made no claims to their welfare or rights.\n\nThe night came but was barely distinguishable from the day. The lights were out by ten, but the prison was full of voices. Prisoners talked, laughed, screamed. There were various unidentifiable sounds coming from all corners. Smacking, grunting. The smoke seemed to increase as the night went on. The smells were rancid\u2014cigarettes, marijuana, old food, sweat, decay.\n\nThe pain in Zeitoun's side had gotten worse. It was a throbbing ache, as if his kidney were inflamed. He never overworried about any such problems, but what if Kathy had been right, that toxins in New Orleans had found their way into his body? Or perhaps it was the pepper spray at Greyhound\u2014he had surely inhaled enough of the gas to cause some internal reaction.\n\nBut he dismissed the pain. He could think only of Kathy. It had now been four days since she had heard from him. He could not imagine her suffering. Where would his mind be if she went missing for four days? He hoped she had not told the children. He hoped she had not told anyone. He hoped she had found comfort in God. God had a plan, he was certain.\n\nIn the early hours, Zeitoun, weakened by lack of sleep and food and the grim nothingness of his surroundings, recalled the passage of the Qur'an called _al-Takwir_ , or \"The Darkening\":\n\n_In the Name of God  \nThe Merciful, The Compassionate  \nWhen the sun is darkening,  \nwhen the stars plunge down,  \nwhen the mountains have been set in motion,  \nwhen the pregnant camels have been ignored,  \nwhen the savage beasts  \nhave been assembled together,  \nwhen the seas have been caused to overflow,  \nwhen the souls have been mated,  \nwhen the buried infant girl has been asked  \nfor what impiety she was slain,  \nwhen the scrolls have been unfolded,  \nwhen the heaven has been stripped off,  \nwhen hellfire has been caused to burn fiercely_,  \n _when the Garden has been brought close,  \nevery soul shall know to what it is prone.  \nSo no! I swear an oath by the stars that recede,  \nby the ones that run, the setting stars  \nby the night, when it swarms,  \nby the morning, when it sighs,  \ntruly that is the saying of a generous Messenger,  \npossessed of strength,  \nsecure with the Possessor of the Throne,  \none who is obeyed and trustworthy.  \nYour companion is not one who is possessed_.\n\n# SATURDAY SEPTEMBER 10\n\nAgain Zeitoun had not slept. The night before, the fluorescent lights above had been turned off at ten p.m., and had come on at three in the morning. In this prison, three o'clock was considered the beginning of the day.\n\nAfter he and Nasser prayed, Zeitoun tried to exercise inside the cell. His foot was still raw, but he jogged in place. He did push-ups, jumping jacks. The pain in his side, though, only increased with the activity. He stopped.\n\nBreakfast was sausage, which he could not eat, and scrambled eggs, which were nearly inedible. He took a few bites and drank the juice provided. He and Nasser sat on the bed, side by side, barely talking. The only thing on Zeitoun's mind was making a phone call. There was nothing else in the world.\n\nHe heard the guard coming down the hallway, picking up the breakfast trays. As soon as the footsteps were close enough, Zeitoun leapt up to the front gate. The guard jumped back a step, startled by Zeitoun's sudden appearance.\n\n\"Please,\" he said, \"one phone call?\"\n\nThe guard ignored the question and instead looked around Zeitoun to Nasser, who was still sitting on the bed. The guard gave Zeitoun a quizzical eye and moved on to the next cell.\n\nAn hour later, Zeitoun heard the guard's footsteps again, and again Zeitoun rose up to meet him as he passed the gate. \"Please, can I make a call?\" he asked. \"Just to my wife.\"\n\nThis time the guard issued a cursory shake of the head before peering around Zeitoun to see Nasser, who again was sitting on the bed. Now the look the guard gave Zeitoun was suggestive, even lewd. He raised his eyebrows and nodded over to Nasser. He was implying that Zeitoun and Nasser were romantically engaged, and that Zeitoun, fearing detection, had leapt from the bed when he heard the guard approaching.\n\nBy the time Zeitoun realized what the guard was implying, it was too late to argue. The guard was gone, down the hall. But this implication, that Zeitoun was bisexual, that he would betray his wife, so enraged him that he could barely contain himself.\n\nAt midday, Zeitoun was taken out of his cell. He was brought to a small office, where a prison guard stood next to a digital camera. He instructed Zeitoun to sit down on a plastic chair. As Zeitoun waited for the next command, the photographer squinted at him and cocked his head.\n\n\"You eyeballing me?\" he yelled.\n\nZeitoun said nothing.\n\n\"Why the fuck you eyeballing me?\" the photographer yelled.\n\nHe went on about how difficult he could make Zeitoun's stay at Hunt, that a man with an attitude like that would not last long. Zeitoun had no idea what he had done to provoke the man. He was still cursing as Zeitoun was led out of the room and returned to his cell.\n\nIn the late afternoon, Zeitoun again heard footsteps coming down the hallway. He went to the front of the cell and there he saw the same guard.\n\n\"What are you two doing in there?\" the guard asked.\n\n\"What are you saying?\" Zeitoun hissed. He had never been so angry.\n\n\"You can't do that kind of thing in your cell, buddy,\" the guard said. \"I thought that was against your religion anyway.\"\n\nThat was it for Zeitoun. He let loose a barrage of expletives and threats to the guard. He didn't care what happened.\n\nThe guard seemed shocked. \"You really talking to me that way? You know what I can do to you?\"\n\nZeitoun was finished. He went to the back of the cell and folded his arms. If he were any closer, he would be too tempted to throw himself against the bars, grabbing for any part of the guard's flesh.\n\n# SUNDAY SEPTEMBER 11\n\nIn the morning the door was opened and four men were added to their cell. All four were African American, between thirty and forty-five. Zeitoun and Nasser nodded to them in greeting, and with a quick choreography about who would sit where, the new residents found places in the tiny cell. Three men sat width-wise on the bed, and three on the floor, against the wall. Cramped and soaked in sweat, they rotated every hour.\n\n* * *\n\nZeitoun no longer harbored any expectations of being granted a phone call from any of the guards he had seen thus far. He pinned his hopes on seeing a new guard, a new employee of the prison, some visitor. He had no idea how the prison worked, how any prison worked. But he had seen movies where lawyers walked the cellblocks, where visitors passed through. He needed to find someone like that. Any one person from the world outside\u2014someone who might grant one small mercy.\n\nThe men in the cell told each other how they had ended up at Hunt. All had been picked up in New Orleans after the storm. This entire wing of the prison, they said, held Katrina prisoners. \"We're all FEMA,\" one said. Two of the men had been arrested for moving furniture, in situations not unlike Zeitoun's.\n\nOne man said he was a sanitation worker from Houston. His company had been contracted shortly after the storm to come in and begin the cleanup. One morning he was walking from the hotel to his truck when a National Guard truck pulled up. He was arrested on the spot, handcuffed, and brought to Camp Greyhound.\n\nIt was his first time behind bars, and of all the prisoners doing \"Katrina time,\" as they'd termed it, he was the most perplexed by it all. He had, after all, come to New Orleans at the behest of his company. He usually picked up garbage in Houston, but after the hurricane, his supervisor said they had taken a contract in New Orleans. This prisoner, thinking it would be interesting to see what had become of the city and wanting to help in its cleanup, went willingly. He was in uniform, and had identification, the keys to his truck, everything. But nothing worked. He was charged with looting and put in the cages behind the bus station.\n\nAnother of the cellmates said he was a fireman in New Orleans. He stayed after the storm, just as he had been asked to stay. He was in his yard when he was picked up by a passing Humvee. They charged him with looting, loaded him into the back, and brought him to Greyhound.\n\nZeitoun learned that most of those brought to Camp Greyhound had been arraigned in a more or less standard fashion. Most had been brought inside the bus station the morning after their arrest, and in an upstairs office, a makeshift court had been arranged. There had been a judge, and at least one lawyer. The arrestees were told their charges, and most of them were offered a deal: if they didn't contest the charges, they would be given a misdemeanor conviction and would be required to perform community-service hours, starting immediately. Some of those who took the bargain\u2014thus accepting the permanent strike on their record\u2014were promptly brought to the police station downtown, where they began repairing and repainting the damaged offices.\n\nThe stabbing pain in his side, which Zeitoun had first felt at Greyhound, had now amplified tenfold. It felt like a long screw was being twisted, slowly, into his kidney. It was difficult to sit, to stand, to lay down. Whenever he switched positions, he would find relief for five minutes before the pain returned. He was not one to worry about such things. He had had so many injuries over the years and rarely sought treatment. But this felt different. He thought of infections, the many diseases Kathy had mentioned when trying to get him to leave the city. He needed to find help.\n\n* * *\n\nThere was a nurse who came through the cellblock once a day, pushing a cart full of medicine, handing pills to the prisoners.\n\nZeitoun stopped her as she wheeled by. He told her about the pain.\n\n\"Do you have a prescription?\" she asked.\n\nHe told her no, that the pain was new.\n\n\"Then you need to see the doctor,\" she said.\n\nHe asked how he could see the doctor.\n\nShe told him to fill out a form describing his pain. The doctor would look at the form and then decide if Zeitoun needed attention. The nurse handed him the form and wheeled her cart down the hall.\n\nZeitoun filled out the form, and when she came back on her way out, he handed it to her.\n\nAfter dinner Zeitoun's cellmates shared the stories they had heard from the other prisoners they'd encountered. The prisoners who had arrived at Hunt during the first days after the storm had lived through conditions beyond comprehension.\n\nThe thousands from Orleans Parish Prison, including those who were in jail for public intoxication, shoplifting, and other misdemeanors, had been left on the city's Broad Street overpass for three days. They'd been on television, a sea of men in orange sitting on a roadway filthy with feces and garbage, surrounded by guards with automatic rifles.\n\nWhen buses finally arrived, the prisoners were taken to Hunt. Instead of being housed inside the prison, they were brought to the football stadium on the property. There they were held for days more, outside, without any kind of shelter. Thousands of prisoners, from murderers and rapists to DUIs and petty thieves, were thrown together on the stadium grass.\n\nThere were no bathrooms. The prisoners urinated and defecated wherever they could. There were no pillows, sheets, sleeping bags, or dry clothing. The men were given one thin blanket each. The area on which Hunt had been built was marshland, and the ground grew wet during the night. The men slept on the mud, with no protection against the elements, bugs, or each other. There were multiple stabbings. Men fought over blankets.\n\nWater was received through two small pipes extending from the grass. The men had to wait their turn and then drink from their hands. For sustenance, prison guards took sandwiches, fashioned them into balls, and threw them over the wall of the stadium and onto the field. Whoever caught one ate. Whoever could defend themselves ate. Many did not eat at all.\n\nNone of the men in Zeitoun's cell knew whether or not these prisoners were still on the football field, or what had become of them.\n\n# MONDAY SEPTEMBER 12\n\nIn the morning, the other four men were removed from the cell, and Zeitoun and Nasser were alone again. They had nothing to do but wait for any new face, anyone who might lead to recognition from the outside world that they existed here.\n\nThe boredom was profound. They had been given no books, no paper, no radio. The two men could only stare at the grey walls, the black floor, at the baby blue bars, or at each other. But they feared talking too much. They assumed they were being monitored in some way. If a spy, Jerry, could be planted with them in an outdoor cage, it would be unsurprising if their conversations were being monitored here, in a maximum security prison.\n\nZeitoun sat against the bed and closed his eyes. He wanted only to pass these days.\n\nHe recounted their arrest, and the hours and days before it, countless times, trying to figure out what had brought such attention to them. Was it simply that four men were occupying one house? Such a thing, after a hurricane, when most of the city had been evacuated, was worthy of investigation, he conceded. But there had been no investigation. There had been no questions, no evidence seized, no charges leveled.\n\nKathy often worried about the National Guard and other soldiers returning to the United States after time in Iraq and Afghanistan. She warned him about passing groups of soldiers in airports, about walking near National Guard offices. \"They're trained to kill people like you,\" she would say to Zeitoun, only half-joking. She had not wanted their family to become collateral damage in a war that had no discernible fronts, no real shape, and no rules.\n\nAlmost twenty years earlier, he had been working on a tanker called the _Andromeda_. They had just brought Kuwaiti oil to Japan, and were returning to Kuwait for more. This was 1987, and Iran and Iraq were in the midst of their long and crippling war. Most of their own refineries had been destroyed during the fighting, so both nations had come to rely on imported oil, and routinely tried to blockade or damage any ships bringing oil to their enemy via the Straight of Hormuz. Zeitoun and his shipmates knew that entering the Gulf of Oman, en route to the Persian Gulf, meant risking the wrath of Iraqi or Iranian submarines and warships. The seamen were paid extra for the risk.\n\nZeitoun's bunk was over the fuel tanks, and he was asleep one early morning when he was jolted by an explosion below. He didn't know if it was one of the tanks, or if the ship had struck something. He quickly realized that if the tank had exploded, he would be dead, so they must have hit something, or had something hit them. He was rushing to the bridge to find out when another explosion shook the ship.\n\nThey had been struck twice by Iranian torpedoes. Together they created a hole big enough to drive a small motorboat through. But it was clear the Iranians didn't mean to sink the tanker. If they had wanted to, that would have been quite easy. They wanted only to send a warning, and to cripple the ship.\n\nThey managed to make it to Addan, and there they spent a month repairing the hull. While waiting to ship out again, Zeitoun decided that perhaps his father Mahmoud had been right. It was time to settle somewhere, time to build a family, to remain safe and constant, on land. A few months later, he got off the _Andromeda_ in Houston and began searching for Kathy.\n\n# TUESDAY SEPTEMBER 13\n\nZeitoun and Nasser did not discuss the possibility that they would not be released from this prison for many months, or even years. But they were both thinking it\u2014that no one knew where they were, which afforded the authorities, whoever it was who wanted them kept here, complete and unchecked power to keep them detained and hidden indefinitely.\n\nZeitoun could think of no indication so far that any measure could be taken to advance his case. He had not been allowed to make a phone call, and there was no hint that he would ever be allowed to do so. He'd had no contact with anyone from outside. There was the nurse, but she was a full-time employee of the prison. Professing his innocence to her was futile, as professions of innocence were likely all she heard all day. In fact, he knew that his very presence in a maximum-security prison likely proved his guilt in the minds of all who worked at the facility. The guards were used to overseeing men who had been convicted at trial.\n\nFurther, the prison was so isolated that there was no oversight whatsoever, no civilians who came to check on conditions. He had not been let out of the cellblock once, and had been let out of the cell only to shower; the shower itself had bars. If they had refused him a phone call for seven days now, why would they change their policy in the future?\n\nHe had one hope, which was to impart his name and innocence to every prisoner he might meet, so that in the event that one of them was someday released they might not only remember his name, but also bother to call Kathy or tell someone where he was. But again, who among them would believe he was one of the true innocents in the prison? How many other names and promises had they known and made?\n\nWhen he was originally arrested, Zeitoun had not been sure his country of origin had anything to do with his capture. After all, two of the four men in their group were white Americans born in New Orleans. But the arrest had taken on an entirely different cast by the time they were brought to Camp Greyhound. And though he was loath to make this leap, was it so improbable that he, like so many others, might be taken to an undisclosed location\u2014to one of the secret prisons abroad? To Guant\u00e1namo Bay?\n\nHe was not the sort to fear such things. He was not given to conspiracy theories or believing that the U.S. government willfully committed human rights violations. But it seemed every month another story appeared about a native of Iran, Saudi Arabia, Libya, Syria, or any one of a number of other Muslim countries who was released after months or years from one of these detention centers. Usually the story was similar: a Muslim man came to be suspected by the U.S. government, and, under the president's current powers, U.S. agents were allowed to seize the man from anywhere in the world and bring him anywhere in the world, without ever having to charge him with a crime.\n\nHow different was Zeitoun's current situation? He was being held without contact, charges, bail, or trial. Would it not behoove the Department of Homeland Security to add a name to their roster of dangerous individuals? In the minds of some Americans, the very thought of two Syrians paddling through New Orleans together after a hurricane would seem suspicious enough. Even the most amateur propagandist could conjure sinister implications.\n\nZeitoun did not entertain such thoughts lightly. They went against everything he knew and believed about his adopted country. But then again, he knew the stories. Professors, doctors, and engineers had all been seized and disappeared for months and years in the interest of national security.\n\nWhy not a house painter?\n\n# WEDNESDAY SEPTEMBER 14\n\nThe pain in Zeitoun's side was overtaking him. While standing or sitting in certain positions, he could barely breathe. He had to get help.\n\nWhen he heard the nurse's cart making its way down the cellblock, he jumped up to meet her at the bars.\n\n\"Did you give the doctor my form?\" he asked her.\n\nShe said she did, and that she would hear back soon.\n\n\"You look sick,\" Nasser said.\n\n\"I know,\" Zeitoun said.\n\n\"You've lost too much weight.\"\n\n\"The pain. It's so bad now.\"\n\nZeitoun had a sudden and strange thought, that the pain in his side could be caused not by infection or injury, but by sorrow. Maybe there wasn't a medical reason for it. Maybe it was just the manifestation of his anger and sadness and helplessness. He did not want any of this to be true. He did not want it to be true that his home and his city were underwater. He did not want it to be true that his wife and children were fifteen hundred miles away and might by now presume him to be dead. He did not want it to be true that he was now and might always be a man in a cage, hidden away, no longer part of the world.\n\n# THURSDAY SEPTEMBER 15\n\nNow Zeitoun knew the rhythmic ticking of the nurse's cart like his own heartbeat. He leapt to the bars again to meet her.\n\n\"What did the doctor say?\" he asked.\n\n\"About what?\" she said.\n\n\"About my condition,\" he said. \"You gave him the form.\"\n\n\"Oh, you know, I don't think he got it. You better fill it out again,\" she said, and handed him another form.\n\nHe did not see her again that day or the next.\n\n* * *\n\nZeitoun began to feel faint when he rose to his feet. He was not eating enough. It seemed that every meal had pork at its center. And even when he could eat what was offered, he was often too agitated or despondent to do so.\n\nAfter lunch three guards arrived. The gate to the cell opened, and they entered. Zeitoun was handcuffed and his legs were shackled, and he was led out from the cell. He was walked to another building, and was put into another, empty cell. Now he was alone.\n\nHe and Nasser had not spoken much, but the contrast in being alone was stark.\n\nZeitoun tried to remember how much his life insurance policy was worth. He should have bought a larger one. He had not thought hard enough about it. The woman at Allstate had tried to convince him to insure his life for more than a million dollars, given that he had four children, and how much the business relied on him. But he could not envision his death. He was only forty-seven. Too early to contemplate life insurance. But he knew that by now Kathy would have checked the value of the policy. She would have begun to imagine a life without him.\n\nWhen he pictured his wife having to make such plans, presuming him to be dead, his heart raged. He had wrathful thoughts about the police who had arrested him, the jailors who kept him here, the system that allowed this. He blamed Ronnie, the stranger who had come to the house on Claiborne, whom he didn't know and couldn't account for\u2014whose presence might very well have brought suspicion upon all of them. Maybe Ronnie _was_ guilty, maybe he _had_ done something wrong. He cursed Nasser's bag of cash. What a fool! He should never have been carrying around money like that.\n\nKathy. Zachary. The girls. The girls might grow up without a father. If Zeitoun was transferred to a secret prison, their lives would be reversed completely: they would go from the well-off children of a successful man to the disgraced children of a presumptive sleeper-cell mastermind.\n\nAnd even if he got out tomorrow or next week, their father had now been in prison. The scarring was inevitable\u2014to live in fear of their father's death, and then to find out he had been taken to prison at gunpoint, made a prisoner, made to live like a rat?\n\nHe clutched his side, pushing back at the pain, trying to contain it.\n\n# FRIDAY SEPTEMBER 16\n\nThe news came down to the prisoners that after lunch they would be allowed to go outside. It had been a week since Zeitoun had seen the sun.\n\nDuring the hour they were allowed in the yard, Zeitoun tried to jog, but felt light-headed. He walked around the yard, overhearing one bewildered story after another.\n\nHe met a man who said he had been moving furniture in his house just after the storm hit. The police spotted him and broke in. When he protested his innocence, they beat him up and left. A few days later, he came to the Greyhound station to complain. They arrested him and sent him to Hunt.\n\nNo story was more absurd than the tale of Merlene Maten. One of the prisoners had just seen her story on TV. She had been held next door, at Hunt's sister prison for women.\n\nMaten was seventy-three years old, a diabetic, and a deaconess at the Resurrection Mission Baptist Church. Before the storm, she and her husband, who was eighty, had checked into a hotel downtown, knowing that there they would be among other residents and guests. They would have access to help if they needed it, and would be safer, given that the hotel was on high ground. They drove to the hotel in their car and paid for the room with their credit card.\n\nThey had been at the hotel for three days when Maten went downstairs to get some food from their car. Mayor Nagin had told everyone in the city to have three days' food on hand, and she had duly packed enough into the car to last. The car was parked in the lot next to the hotel, and Maten had left a cooler inside, full of the foods her husband liked. She retrieved a package of sausages and was walking back to the hotel when she heard yelling and footsteps. It was the police, and they accused her of looting a nearby store.\n\nThe nearby Check In Check Out deli had just been looted, and the police were looking for anyone who might have benefited. They found Maten. She was handcuffed and charged with stealing $63.50 worth of groceries. Her bail was set, by a judge calling by phone, at $50,000. The usual bail for such a misdemeanor would be $500.\n\nShe was brought to Camp Greyhound, where she slept on the concrete. Then she was brought to the Louisiana Correctional Institute for Women, Hunt's sister prison, for more than two weeks. She was finally freed with the help of the AARP, volunteer lawyers, a private attorney, and an article about her plight published by the Associated Press.\n\nThe lawyers finally convinced a judge that a septuagenarian staying at a hotel would not need to loot a store for sausages. They proved that the store did not even sell the sausages she was carrying. Maten had never been in the store. Furthermore, to even enter the damaged store, strewn everywhere with debris and broken glass, would have required an agility that she did not possess.\n\nIn the late afternoon Zeitoun heard a group of guards enter the cellblock. He couldn't see them, but it sounded like at least four or five men. A cell down the hall rattled open. The guards yelled and cursed, and there was some kind of scuffle. Then quiet for a few minutes, and then the cell closed shut again. The process repeated itself half a dozen times.\n\nThen it was his turn. First he saw their faces, five men on the other side of the blue bars. He had seen one of the guards before, but the other four were strangers. They were all wearing black riot gear, dressed like a SWAT team. They had shields, padding, batons, helmets. They waited at the ready for the door to open.\n\nZeitoun was determined not to struggle. He would not present any appearance of opposition. When the cell door slid open, he stood in the center of the floor, his hands in the air, his eyes level.\n\nBut still the men burst in as if he were in the process of committing a murder. Cursing at him, three men used their shields to push him to the wall. As they pressed his face against the cinderblock, they handcuffed his arms and shackled his legs.\n\nThey brought him into the hallway. Three guards held him while the other two ransacked the cell. They threw open the bedding, overturned the mattress, scoured the tiny room.\n\nTwo of the guards unlocked Zeitoun's handcuffs and shackles.\n\n\"Take off your clothes,\" one said.\n\nHe hesitated. He had not been given underwear when he arrived at Hunt, so if he took off his jumpsuit he would be naked.\n\n\"Now,\" the guard said.\n\nZeitoun unzipped the jumpsuit and pulled it off his shoulders. It dropped to his waist, and he pushed it to the floor. He was surrounded by three men fully dressed in black riot gear. He tried to cover himself.\n\n\"Bend over,\" the guard said.\n\nAgain he hesitated.\n\n\"Do it.\"\n\nZeitoun complied.\n\n\"Farther,\" the guard said. \"Grab ankles.\"\n\nZeitoun could not tell who was inspecting him or how. He expected something to enter his rectum at any moment.\n\n\"Okay, get up,\" the guard said.\n\nThey had spared him this one indignity.\n\nZeitoun stood. The guard used his foot to slide Zeitoun's jumpsuit back into the cell, and then pushed Zeitoun in, too. While Zeitoun was putting on his clothes, they backed away from him, shields up, and out of the cell.\n\nZeitoun's door closed, and the guards assembled themselves at the next cell, ready for the next prisoner.\n\nFrom the other prisoners Zeitoun learned that these searches were common. The guards were looking for drugs, weapons, any contraband. He should expect such a procedure every week.\n\n# SATURDAY SEPTEMBER 17\n\nZeitoun lay in bed much of the day, wrecked by fatigue. He had not slept. He had run the strip-search through his mind most of the night, trying to erase all memory of it, but every time he closed his eyes he saw the men in their riot gear, at the other side of the cell door, waiting to flood in and take him.\n\nFor weeks, it seemed, he had been stealing hours of sleep during the day, a few at night. He could not remember the last time he had strung more than three hours of rest together.\n\nWhy had he done this to his family? There was something broken in the country, this was certain, but he had begun all this. He had refused to leave the city. He had stayed to guard his property, to watch over his business. But then something else had overtaken him, some sense of destiny. Some sense that God had put him there to do His work, to glorify Him with good deeds.\n\nIt seemed ridiculous now. How could he have been guilty of such hubris? He had put himself in harm's way, and by doing so had put his family in danger. How could he not have known that staying in New Orleans, a city under something like martial law, would endanger him? He knew better. He had been careful for so many years. He had kept his head low. He had been a model citizen. But in the wake of the storm, he'd come to believe he was meant to help the stranded. He believed that that damned canoe had given him the right to serve as shepherd and savior. He had lost perspective.\n\nHe had expected too much. He had hoped too much.\n\nThe country he had left thirty years ago had been a realistic place. There were political realities there, then and now, that precluded blind faith, that discouraged one from thinking that everything, always, would work out fairly and equitably. But he had come to believe such things in the United States. Things had worked out. Difficulties had been overcome. He had worked hard and achieved success. The machinery of government functioned. Even if in New Orleans this machinery was sometimes slow, or poorly engineered, generally it functioned.\n\nBut now nothing worked. Or rather, every piece of machinery\u2014the police, the military, the prisons\u2014that was meant to protect people like him was devouring anyone who got close. He had long believed that the police acted in the best interests of the citizens they served. That the military was accountable, reasonable, and was kept in check by concentric circles of regulations, laws, common sense, common decency.\n\nBut now those hopes could be put to rest.\n\nThis country was not unique. This country was fallible. Mistakes were being made. He was a mistake. In the grand scheme of the country's blind, grasping fight against threats seen and unseen, there would be mistakes made. Innocents would be suspected. Innocents would be imprisoned.\n\nHe thought of bycatch. It was a fishing term. They'd used it when he was a boy, fishing for sardines by the light of the moon they'd made. When they pulled in the net, there were thousands of sardines, of course, but there were other creatures too, life they had not intended to catch and for which they had no use.\n\nOften they would not know until too late. They would bring their catch back to shore, a mound of silver, the sardines dying slowly. Zeitoun, exhausted, would rest against the bow, watching the fish slowly cease their struggles. And once on shore, when the crew unloaded the nets, they would sometimes find something else. One time there was a dolphin. He always remembered this dolphin, a magnificent ivory-white animal shining on the dock like porcelain. The fishermen nudged it with their feet, but it was dead. It had gotten caught in the net and, unable to reach the surface to breathe, it had died underwater. If they had noticed it in time, they could have freed it, but now all they could do was throw it back into the Mediterranean. It would be a meal for the bottom-feeders.\n\nThe pain in Zeitoun's side was growing, rippling outward. He could not stay here another week. He would not survive the heartbreak, the wrongness of it.\n\nThere was no way to come out of this prison improved. Not the way he was being treated. He had seen parts of Hunt that seemed well-run, clean, efficient. When he first arrived and was being processed, he saw prisoners milling about freely in a grassy courtyard. But he had been confined twenty-three hours a day to his cell, with no distractions, no companionship or beauty. The environment would drive any sane man mad. The grey walls, the blue bars, the strip searches, the showers behind bars watched by guards and cameras. The lack of any mental stimuli. Unable to work, to read or build or improve himself, he would waste away here.\n\nHe had risked too much in the hopes that he might do something to match the deeds of his brother Mohammed. No, it had never been a conscious part of his motivation\u2014he had done what he could in the drowned city because he was there, it needed to be done, and he could do it. But somewhere in his gut, was there not some hope that he, too, could bring pride to the family, as Mohammed had so many years ago? Was there not some wish that he might honor his brother, his family, his God, by doing all he could, by circling the city looking for opportunities to do good? And was this imprisonment God's way of curbing his pride, tempering his vainglorious dreams?\n\n* * *\n\nAs the prisoners awoke, with their rantings and threats, Zeitoun prayed. He prayed for the health of his family. He prayed that they felt at peace. And he prayed for a messenger. All he needed was a messenger, someone to tell his wife that he was alive. Someone to connect him with the part of the world that still worked.\n\n# SUNDAY SEPTEMBER 18\n\nZeitoun had been napping through the morning, dazed and sluggish from the heat. His sweat had soaked through his orange jumpsuit. He heard notice that they would be allowed to walk outside again after lunch, and he wasn't sure he could stand to make it.\n\nHe was disappointed in himself. Part of him had given up, and the part that still believed stood apart from the broken half of his soul, incredulous.\n\nThe wheels of the nurse's cart echoed down the hallway. He had no reason to think she would help him, but he stood up and made ready to plead with her again. But when he looked down the hall, it was not the nurse, but a man he had never seen before.\n\nHe was pushing a cart of black books, and had stopped a few cells away from Zeitoun's. He was talking to whichever prisoners were there, and Zeitoun watched him, unable to hear the conversation. The man was black, in his sixties, and watching him interact with the prisoners down the row, it was clear he was a man of God. The books in his cart were Bibles.\n\nWhen he finished and passed by Zeitoun's cell, Zeitoun stopped him. \"Please, hello,\" he said.\n\n\"Hello,\" the missionary said. He had almond-shaped eyes, a wide smile. \"Would you like to hear about Jesus Christ?\"\n\nZeitoun declined. \"Please sir,\" he said. \"Please, I shouldn't be here. I committed no crime. But no one knows I'm here. I haven't gotten a phone call. My wife thinks I'm dead. Can you call her?\"\n\nThe missionary closed his eyes. It was obvious he often heard things like this.\n\n\"Please,\" Zeitoun said. \"I know it's hard to believe a man in a cage, but please. Can I just give you her number?\"\n\nZeitoun could only remember Kathy's cell phone number, and hoped it would work. The missionary looked up and down the cellblock and gave a nod. \"Be quick.\"\n\n\"Thank you,\" Zeitoun said. \"Her name is Kathy. My wife. We have four children.\"\n\nZeitoun had no pen or paper.\n\n\"This is against the rules,\" the missionary said, finding a pen in his cart. He had no paper. Now they were both nervous. The missionary had been too long at his cell. He opened a Bible and tore a page from the back. Zeitoun gave him the number. The missionary stuffed the page into his pocket and moved his cart quickly down the block.\n\nHope rose in Zeitoun's heart. He couldn't sit down for hours. He paced, hopped in place, elated. He pictured the missionary leaving the prison, getting to his car, retrieving the number, calling Kathy from the road. Or maybe he would wait till he got home. How long could it take? He counted the minutes until Kathy would know. She would know! He estimated the hours until Kathy would arrive here to free him. If she knew he was alive, he could wait. The process might take days, he knew. But he could wait if it meant seeing her. It would be no problem. He pictured it all. He would be free in a day.\n\nZeitoun struggled to sleep that night. There was a man in the world who knew he was alive. He had found his messenger.\n\n# MONDAY SEPTEMBER 19\n\nAfter breakfast two guards came to Zeitoun's cell. They told Zeitoun that his presence was requested.\n\n\"Where? With who?\" Zeitoun asked. _Already it's begun_ , he thought.\n\nThe guards told him nothing. They opened his cell, handcuffed him, and shackled his legs together. He was led out of the cell and down the hall. A few minutes later they arrived at another cell, where Zeitoun was deposited. He waited there for five minutes until the door opened again.\n\n\"Van's here,\" the guard said. The guard handed him to another guard, who walked him down another hallway and to a final gate. The gate opened, and Zeitoun was led to a white van waiting outside. He squinted in the full light of day. He was inserted into the van, the guard riding with him. They drove through the complex until they arrived at the main offices at the front of the prison.\n\nZeitoun was led out of the van and handed over to another guard, who led him into the building. Inside, they walked through an immaculate hallway until they arrived at a spare cinderblock office.\n\nOutside the office were Nasser, Todd, and Ronnie, sitting on folding chairs in the hallway. Zeitoun was surprised to see them all assembled, and they gave each other looks of mutual bewilderment. Zeitoun was led past them and into a small room.\n\nIn the room there were two men wearing suits. They sat down and gestured to Zeitoun that he could take a seat. They were from the Department of Homeland Security, they said. They smiled warmly at Zeitoun and told him that they needed to ask him some simple questions. They asked him what he did for a living. He told them that he was a painter and contractor. They asked him why he hadn't left the city when everyone had evacuated. He told them that he never left New Orleans during storms, and that he had a number of properties he wanted to watch over. They asked about Todd, Nasser, and Ronnie\u2014how he knew them. He explained his relationship to each. They asked him why he didn't have any money on him.\n\n\"What am I going to do with money in a canoe during a flood?\" Zeitoun said.\n\n\"But Nasser had money,\" one of the men said.\n\nZeitoun shrugged. He could not account for why Nasser had money with him.\n\nThe interview lasted less than thirty minutes. Zeitoun was struck by how friendly the men were, how easy the questions were. They did not ask about terrorism. They did not accuse him of plotting against the United States. At the end, they apologized for what Zeitoun had been through, and asked if there was anything they could do for him.\n\n\"Please call Kathy,\" he said.\n\nThey said they would.\n\n# MONDAY SEPTEMBER 19\n\nKathy was in a state. She'd just gotten the call from the missionary a few hours before. And now the phone was ringing again. Yuko, who had been fielding calls for days, no longer knew what to do. Kathy picked it up.\n\nA man introduced himself as belonging to the Department of Homeland Security. He confirmed that Zeitoun was at the Elayn Hunt Correctional Center.\n\n\"He's fine, ma'am. We have no more interest in him.\"\n\n\"You have no more interest in him? Is that good or bad?\"\n\n\"That's good.\"\n\n\"Well, what was he in there for?\"\n\n\"Well, they have 'looting' on his arrest sheet. But those charges will be dropped.\"\n\nThe call was brief and businesslike. When she hung up, Kathy praised and thanked God for his mercy. She shrieked and jumped around the house with Yuko.\n\n\"I knew he was alive,\" Yuko said. \"I knew it.\"\n\n\"God is good,\" they said. \"God is good.\"\n\nThey called Yuko's husband and made plans to get the kids out of school early. They had to celebrate. And plan. There were so many things to do.\n\nFirst of all, Kathy had to go. She knew she had to go. She had to leave that day for the prison. She didn't know where it was yet, but she had to go. Where was it? She looked it up online. St. Gabriel, less than an hour from Baton Rouge.\n\nShe called Hunt and was bounced around the various automated extensions until she reached a person. She could barely speak. She wanted to fly through the phone and be there with him.\n\n\"I'm trying to reach my husband. He's in there.\"\n\n\"The prisoner's name?\" the woman asked.\n\nKathy had to take a breath. She could not stomach the idea of her husband being called a prisoner. By naming him she was expanding this lie, the one being told by everyone involved in his incarceration thus far.\n\n\"Abdulrahman Zeitoun,\" she said, and spelled it.\n\nKathy heard the typing of computer keys.\n\n\"He's not here,\" the woman said.\n\nKathy spelled the name again.\n\nAgain the sound of typing.\n\n\"We have no one by that name,\" the woman reiterated.\n\nKathy tried to remain calm. She told the woman that she had just received a call from someone from Homeland Security, and that that man had told her that Abdulrahman Zeitoun was at that very prison.\n\n\"We have no record of him,\" the woman said. She went on to say that Hunt had no records for anyone who came via the hurricane. None of the prisoners from New Orleans were in their computer system. \"All of those records are on paper, and we don't have that paper. We have no actual records of any of those people. They're FEMA's.\"\n\nKathy almost collapsed. She was spinning, helpless. She didn't have a number for the Homeland Security man who had called; she cursed herself for not asking for a way to contact him. And now she was being told that her husband was not in the institution where the Homeland Security people and the missionary had seen him. Was this some kind of game? Had he been there at all? He might have been moved already. He had been a prisoner at Hunt but then some other agency wanted him. He had been spirited away to a secret prison somewhere\u2014\n\nShe had to go. She would go to Hunt Correctional Center and insist she see him. She had a right to see him. If he wasn't there she would demand they tell her where he'd been taken. It was the only way.\n\nShe told Yuko and Ahmaad she was going.\n\n\"Where?\" they asked.\n\n\"Hunt. The prison,\" she said.\n\nThey asked her if she was sure he was there. She was not. They asked if she was sure she would be allowed to visit. She was not. They asked where she would stay. Kathy didn't know. Already she was crying again. She didn't know what to do next.\n\nThey convinced her to stay in Phoenix for the time being, until she could be sure of Zeitoun's whereabouts and how she could actually help him. She needed to be smart, they said. They didn't want to worry about her, too.\n\nKathy called Raleigh Ohlmeyer, an attorney they had worked with before. Raleigh had helped a few of the Zeitouns' workers who had legal issues to straighten out. Raleigh's father was a well-known and powerful lawyer in New Orleans, and Raleigh, though in the family business, had chosen to break away, at least in his appearance. He wore his brown hair long, usually pulled back in a ponytail. He worked downtown and took on a wide variety of cases, from traffic tickets to criminal defense. Kathy was sure he would know how to straighten out this Hunt business.\n\nThere was no answer. She left a message.\n\nKathy called Ahmad in Spain and woke him up. She didn't care.\n\n\"He's alive!\" she said.\n\nHe yelled a string of Thank Gods and Praise Gods.\n\n\"Where is he?\" he asked. \"With you?\"\n\n\"No, he's in prison,\" Kathy said. \"But it's okay. I know where he is. We'll get him out.\"\n\nAhmad was silent. Kathy could hear him breathing.\n\n\"How? How will you get him out?\" he asked.\n\nKathy did not have a plan just yet, but she had a lawyer, had put in a call to him, and\u2014\n\n\"You need to go there,\" Ahmad said. \"You have to see him and get him out. You must.\"\n\nKathy was unsettled by Ahmad's tone. He seemed almost as worried by Zeitoun's incarceration as he had been by his disappearance.\n\nFahzia, Zeitoun's sister in Jableh, called soon after.\n\nKathy told her the good news. \"We know where he is. He's in prison. He's okay.\"\n\nAnother long silence.\n\n\"Have you seen him?\" she asked.\n\nKathy said she had not, but that she was sure she would soon.\n\n\"You need to see him,\" Fahzia said. \"You need to find him.\"\n\nIn the afternoon, Raleigh Ohlmeyer called Kathy back. He had fled the city just before the storm and had been staying in Baton Rouge. His house in New Orleans was under six feet of water.\n\nKathy told him what had happened to Zeitoun.\n\n\"What?\" Raleigh said. \"I just saw him on TV.\" He had seen the local news broadcast of Zeitoun in his canoe.\n\nKathy told him about the calls from the missionary and the Homeland Security officials, how they had seen him at Hunt.\n\nRaleigh was reassuring. He already knew all about Hunt. After the storm he had set up a makeshift office in Baton Rouge and was already working with prisoners brought to the prison.\n\nThe system's broken, he said. There was no means to post bail. It would take some time before it could be rectified. Raleigh promised that he would get Zeitoun released, but given the state of the courts\u2014there were none to speak of\u2014he could not predict or guarantee a timeline.\n\n# TUESDAY SEPTEMBER 20\n\nIn the morning Ahmad called Kathy, tense.\n\n\"Did you tell Fahzia that Abdulrahman was in prison?\"\n\nHis tone was severe.\n\n\"Yes, she asked and\u2014\"\n\n\"No, no,\" he said, and then softened. \"Let's not do that. Don't worry them. We cannot tell them he's in prison. We cannot do that.\"\n\n\"Okay, but I just thought\u2014\"\n\n\"We'll call them and tell them he's fine, he's home, it was a mistake. Okay? We need to tell them this. You don't understand the worry they'll have if they think he's in jail.\"\n\n\"Okay. Should I\u2014\"\n\n\"I'll call them and tell them he's fine. If they call you, tell them the same. He's at home, he's safe, all is fine. You made a mistake. Okay? This is what we tell them. Okay?\"\n\n\"Okay,\" she said.\n\nAhmad wanted to know which prison he was in. Kathy told him it was in St. Gabriel, and that because the legal system was in limbo, it would be some time before they could even hope to get Abdulrahman out. But she had spoken to a lawyer, and he was on the case. It was only a matter of time.\n\nBut Ahmad was thinking beyond simple cases of attorneys and bail. He did not want his brother in prison at all. A Syrian in an American prison in 2005\u2013this was not to be trifled with. Abdulrahman had to be seen. He had to be freed immediately.\n\nThe next time Kathy checked her email she saw a message from Ahmad; she had been cc'ed. He was trying to find Zeitoun, but he had gotten the city wrong. He had done an internet search for San Gabriel in the United States, had found a match, and had written this:\n\nFrom: CapZeton\n\nTo: ACOSTA, ALEX\n\nSubject: Urgent from Spain\n\nThe San Gabriel Police Department\n\nSan Gabriel, CA\n\nDear Sires,\n\nMy name is: Ahmad Zeton, from Spain\n\nReason: I'm looking for my brother (New Orleans Katrina evacuated). On Sept. 7th I missed the contact with my brother which we talked daily by phone after the Hurricane Katrina batch, I asked every place in order to have any news about him, lastly I learned that the Police Force him on Sept. 6th to evacuated his house in New Orleans and tacked him for San Gabriel, and he is actually still arrested at San Gabriel.\n\nKindly would you please if there is a possibility to learn if he is all right, and if it's possible to talk to him, or to call me by a collected call to my phone [number omitted].\n\nThe detail of my brother is:\n\nName: Abdulrahman Zeitoun.\n\nDate of berth: 24\/10\/1957\n\nAddress: 4649 Dart St., New Orleans, LA\n\nWell be very kind from you just to let me know if he's all right,\n\nThanking you indeed,\n\nAhmad Zeton\n\nMalaga-Spain\n\nKathy began to see the situation through Ahmad's eyes. What if the prosecutors, hoping to justify Zeitoun's incarceration, tried to make a case against him\u2014a connection, any distant connection, to some terrorist activity? Any connection, no matter how specious, might be used to justify his incarceration and extend it.\n\nKathy did not want to think this way.\n\n# THURSDAY SEPTEMBER 22\n\nShe called Raleigh Ohlmeyer again. He had just called Hunt, and they had confirmed that Zeitoun was there.\n\nKathy called Ahmad and told him the news.\n\n\"Yes, but has anyone seen him?\" he asked.\n\n\"No,\" she said.\n\n\"Then we can't be sure,\" he said.\n\n\"Ahmad, I'm sure that\u2014\"\n\n\"You have to go,\" he said. \"Kathy, please.\"\n\nHe apologized; he knew that he was pushing too hard, that he was calling Kathy too often, but his mind was filled with images of his brother on his knees, in an orange jumpsuit, in an outdoor cage. Every additional hour Zeitoun was in custody increased the chances of something taking a turn for the worse.\n\n\"I'll fly to New Orleans,\" he said.\n\n\"And do what?\" Kathy asked.\n\n\"I'll find him,\" he said.\n\n\"Don't. Don't,\" she said. \"They'll put you in jail, too.\"\n\n# FRIDAY SEPTEMBER 23\n\nBy now Raleigh was familiar with some of the judges and administrators working to process the post-storm prisoners being kept at Hunt. Hoping to get Zeitoun's case dismissed, Raleigh told Kathy it was time to come to Baton Rouge. She should fly out and be ready to come to the prison at a moment's notice; there was a chance she could visit him on Monday. Kathy booked a flight and called Adnan, Zeitoun's cousin.\n\n\"Abdulrahman?\" he asked, hesitant.\n\n\"He's okay,\" she said.\n\nHe exhaled. She told him the story of her husband's incarceration, and that she was coming to get him.\n\n\"You'll stay with us,\" Adnan said. After sleeping on the floor of a Baton Rouge mosque for that first week, he and his wife had rented an apartment for the month, and were living there.\n\nAdnan would pick her up and drive her to the prison.\n\n# SUNDAY SEPTEMBER 25\n\nThere was something wrong with the airplane. They were flying so low, descending too quickly. Kathy was certain the plane would crash. She no longer trusted anything about New Orleans, even the sky above the city. She gripped the armrest. She looked around to see if anyone else was alarmed. The pilot's voice came on the intercom. He announced that they were flying low over the city so the passengers could survey the damage. Kathy couldn't look.\n\nWhen they landed, the airport was desolate. There were airport security officers, New Orleans police, National Guardsmen, but few civilians. The passengers of Kathy's plane seemed to be the only people in the building. All the stores were closed. The lights were dim. There was detritus all over the floors\u2014garbage, papers, bandages and other medical supplies.\n\nAdnan picked her up and they drove to the apartment he and Abeer had rented in Baton Rouge. Kathy, exhausted and overwhelmed, fell asleep with her shoes on.\n\n# MONDAY SEPTEMBER 26\n\nZeitoun knew nothing about the work Kathy and Raleigh were doing. He still had not been allowed a phone call. All he knew was that he had been assured by both the missionary and the Homeland Security men that they would call his wife. But since then, he had no assurance that contact had been made.\n\nAfter lunch, Zeitoun was taken from his cell and again handcuffed and brought to the same building near the front gate of the prison. Inside he was brought to a small cinderblock room, where a table and a handful of chairs had been arranged. Sitting on one side of the table was a man in his late fifties, wearing a suit. On the other side were two men in coats and ties. Three other prisoners were seated in chairs at the back of the room. It was some kind of courtroom.\n\nA young man introduced himself to Zeitoun as the public defender. He would be representing Zeitoun that day. Zeitoun began to explain his case, the mistakes that had brought him to prison, and asked for an immediate phone call to his wife. The public defender closed his eyes to indicate that Zeitoun should stop talking.\n\n\"You're not here to be judged,\" he said. \"This is just a hearing to set bail.\"\n\n\"But don't you want\u2014\"\n\n\"Please,\" the young man said, \"just don't say anything. Let me speak for you. Just sit and be quiet if you can. Don't say a word.\"\n\nThe charges against Zeitoun were read: possession of stolen property valued at $500. The prosecutor suggested setting bail at $150,000.\n\nThe defender countered that Zeitoun had no prior record, and that the bail should be far lower. He suggested $35,000.\n\nThe judge set the bail at $75,000. That was the end of Zeitoun's hearing. The defender extended his hand to Zeitoun, and Zeitoun shook it. He was led out of the room as the defender opened the file for the next prisoner. On his way out, Zeitoun again asked for a phone call. The defender shrugged.\n\n\"But why set bail when I can't tell anyone I'm in prison?\" Zeitoun asked.\n\nFrom the judge, the prosecutor, and the defender, there was no answer. Zeitoun was brought back to his cell.\n\n# TUESDAY SEPTEMBER 27\n\nRaleigh called Kathy.\n\n\"Okay,\" he said, \"they finally have a system arranged, and we've got a court date. They want to clear the docket as much as we want him out of there. So gather as many people as you can to come to court and testify on his behalf. Character witnesses.\"\n\nThis seemed sensible enough to Kathy. It was a clear-cut task, and she dug in. But while making a list of friends to call, she realized she had forgotten to ask Raleigh where the courthouse was. She called him back and got his voicemail.\n\nShe called the New Orleans District Attorney's office. A recording gave her a number in Baton Rouge. She called it, expecting to get a recording, but to her surprise a woman answered the phone on the second ring. Kathy asked for the address of the courthouse.\n\n\"We don't have one right now,\" the woman said.\n\n\"What?\" Kathy said. \"I just need the address of the courthouse where the hearings are, the hearings for prisoners at Hunt? I just need the court address.\"\n\n\"We don't have one of those,\" the woman said.\n\n\"A court?\"\n\n\"Right.\"\n\n\"Where are people going to pay tickets?\"\n\n\"No one's paying tickets right now,\" the woman said.\n\nKathy asked to speak to a supervisor.\n\nShe was transferred, and this time a man picked up the phone. Kathy explained that she had just gotten word that her husband had been arrested, and now there was a court date. She only wanted to know where court hearings were being held.\n\n\"Oh, we can't tell you that,\" the man said.\n\n\"What? You can't tell me?\"\n\n\"No, that's privileged information,\" he said.\n\n\"Privileged for who? I'm his wife!\"\n\n\"I'm sorry, that's private information.\"\n\n\"It's not private! It's public!\" Kathy screamed. \"That's the point! It's a public court!\" She asked to speak to another, more knowledgeable person. The man sighed and put her on hold.\n\nFinally a third person, a woman, picked up the phone.\n\n\"What is it you want?\" she asked.\n\nKathy composed herself, hoping that perhaps the other two officials hadn't heard her clearly. She said, \"I want to know the location of the court. The court where sentencing and bail hearings are being held.\"\n\nThe woman's voice was even and firm: \"That is private information.\"\n\nKathy fell apart. She wailed and screamed. Somehow this, knowing that her husband was so close but that these layers of bureaucracy and incompetence were keeping her from him\u2014it was too much. She cried out of frustration and rage. She felt like she was watching a baby drown, unable to do anything to save it.\n\nWhen she'd gathered herself, she called CNN.\n\nShe reached a producer and told her the story: her husband's incarceration, the call from Homeland Security, the stonewalling, the courts that didn't even exist. The producer said she would investigate, and took Kathy's number.\n\nRaleigh called back. He apologized. Now he knew where the hearing would be held\u2014at Hunt itself. He told Kathy to call anyone she could and tell them to be at Hunt the next day, at nine a.m.\n\n\"I'm going to try to see Zeitoun today,\" he said.\n\nKathy prayed that he would.\n\nKathy began calling friends, neighbors, and clients. In two hours she managed to secure at least seven people who said they would come, including the principal of her daughters' school.\n\nZeitoun was again called out of his cell for a meeting. He was handcuffed, his legs were chained, and again he was led to the white van. He was driven to the front of the prison complex and was brought to another small cinderblock room, where he saw Raleigh, the first representative of the outside world he'd seen since his arrest.\n\nHe smiled, and they shook hands warmly.\n\n\"I want to get out,\" Zeitoun said.\n\n\"You have to pay to get out,\" Raleigh said. He sighed deeply. \"We've got a situation with this bail.\"\n\nZeitoun could either find and pay $75,000, and if he eventually won his case he would be refunded the full amount. Or he could pay thirteen percent of the bail to the courts and three percent to the bondsman\u2014about $10,000 total. And regardless of the outcome of his case, he would lose that amount.\n\n\"Isn't $75,000 a lot for petty theft?\" Zeitoun asked.\n\nRaleigh agreed it was. It was about a hundred times what it should be. Zeitoun could find the $10,000, but it seemed silly to him to throw away that much money. It would be, in effect, paying the government for incarcerating him for a month.\n\n\"Can't you reduce it?\" Zeitoun asked.\n\n\"I'll have to fight for it,\" Raleigh said.\n\n\"Well, then fight for it,\" Zeitoun said.\n\n\"What if it doesn't work?\" Raleigh asked.\n\n\"Then check if we can use my property as bail,\" Zeitoun said.\n\n\"You don't want to pay the bond?\"\n\n\"No,\" Zeitoun said.\n\nIf he paid for his release, what would he do, after all? He couldn't work. There was nothing to do in New Orleans, not yet. And by now he knew that Kathy and his kids knew he was alive. He trusted that he would be released. So he would be paying $10,000 to be free for a few extra days\u2014and he would spend that time pacing around Yuko and Ahmaad's living room. He would see his daughters, yes, but they knew he was safe now, and that money would be better spent elsewhere\u2014in their college trusts, for example. He had already been kept two and a half weeks; he could wait a few more days.\n\n\"I'll check about using your property as collateral,\" Raleigh said.\n\n\"Call Kathy,\" Zeitoun said.\n\n# WEDNESDAY SEPTEMBER 28\n\nKathy drove into Hunt, holding her breath. It was a surreal sight\u2014the tidy white fencing, the bright green lawn. It looked like a golf course. White birds scattered as she made her way down the long driveway and up to the gate.\n\nIn the parking lot, she stood outside and waited. It was eight-thirty in the morning, and she needed all the friends they had. They began to arrive a few minutes later. Rob and Walt had driven from Lafayette. Jennifer Callender, who worked with Walt and whose house Zeitoun had renovated, arrived with her husband and father. Tom and Celeste Bitchatch, neighbors on Claiborne, had driven from Houston. Nabil Abukhader, the principal at the girls' school, had driven from the French Quarter.\n\nThey all embraced. No one had been sleeping. They all looked terrible, and were shocked that such a thing had brought them together. But they were heartened, somewhat, to know that they would be able to speak about the character of Abdulrahman Zeitoun. They were confident that when the judge heard from them all and realized that the police had imprisoned a well-known businessman, the judge might very well release him that day. Perhaps they could all celebrate together.\n\nKathy couldn't stop thanking them. She was a wreck of tears and gratitude and anticipation.\n\nWhen Raleigh arrived, he was impressed. He gathered everyone together and gave them a brief rundown of how the proceedings would go. He wasn't sure exactly where the hearing would take place, or even what time. But he was confident that between Zeitoun's reputation, lack of any prior infractions, and this showing of character witnesses\u2014a wide swath of upstanding New Orleanians\u2014the judge would release Abdulrahman Zeitoun with profuse apologies.\n\nThey waited through the morning. No word. Finally Raleigh went to see what was happening. He came back out, his face a cloud.\n\n\"They won't see any of you,\" he said.\n\nThe hearing had been canceled. There was no explanation why.\n\n* * *\n\nNow the only chance was to post bail. Kathy would have to go back into the city and find papers proving ownership of their office building. They would use the building as collateral against the bond.\n\nAdnan insisted he drive Kathy into the city.\n\nThey took I-10 and exited at Carrollton. Immediately they were struck by the smell. It was so many things\u2014acrid, rotten, and even, from the branches and trees lying in the sun, sweet. But most of all the smell was overpowering. It was loud. Kathy wrapped her scarf around her face to blunt its power.\n\nThe city looked like it had been abandoned for decades. The cars, their colors washed grey from the toxic water, were strewn about like playthings. They took Carrollton to Earhart, and at one point had to cross over to the opposite lane to avoid downed trees. The debris was everywhere and bizarre\u2014tires, refrigerators, tricycles, couches, a straw hat.\n\nThe streets were deserted. They saw no one\u2014no human or vehicle\u2014until a police cruiser pulled up behind them a few blocks from the office. Kathy told Adnan to let her do the talking. It was a long-held strategy she developed with Zeitoun. It was always easier and quicker when she did the talking; a Middle Eastern accent would only provoke more questions.\n\nTwo officers approached their car, both with their hands on their sidearms. The officer at the driver's side window asked Adnan what he was doing in the city. Kathy leaned over to explain and extended her driver's license through the window.\n\n\"I live in the house down the street,\" she said. \"Just coming back to assess the damage, pick up anything that survived.\"\n\nHe listened to Kathy but turned back to Adnan. \"What are you doing here?\"\n\nKathy preempted him. \"We're contractors,\" she said. She gave the officer her business card.\n\nThe officer took it back to the squad car. He and his partner spent ten minutes there before returning to Adnan's window.\n\n\"Okay,\" the officer said, and let them go.\n\nThey decided to drive straight to the office, for fear that the next time they were stopped they would not be so fortunate.\n\nWhen they reached the building on Dublin, Kathy could see the remains of the homes that had burned to the ground. It seemed miraculous that the fire had stopped only a few yards away. The office appeared damaged from the outside, but not in a way that would hint at what they would find within. Kathy went to the door. Her key didn't work. The lock was rusted inside and out.\n\nAcross the street, Adnan spotted something. He jogged over to a neighbor's house and came back carrying an ancient, ruined ladder.\n\n\"I'm going up,\" he said. \"You stay here.\"\n\nHe set the ladder against the building and began to climb. The steps were crooked and some of them broken, but he went up carefully, and when he arrived at the second-floor window, he climbed through and quickly disappeared inside.\n\nKathy heard some thumps and scraping, and then it was quiet. Soon there was a voice from the other side of the door.\n\n\"Move away,\" he said. \"I'm kicking the door down.\"\n\nHe kicked it four times and the door gave way, falling flat.\n\n\"Be careful when you're going up the stairs,\" he said.\n\nInside, the building was ruined. It looked like it hadn't been inhabited in decades. The ceiling was half-destroyed, dotted with jagged holes. Exposed wiring and papers everywhere. A grey sludge covered the floor. The smell was strong. Mildew and rain and sewage.\n\nKathy and Adnan carefully climbed the stairs to the office. It was unrecognizable. The carpet squished with every step. She could smell the presence of animals, and there were scurrying sounds as they walked through the office. She opened a closet door and a dozen roaches fell onto her hands. She screamed. Adnan calmed her.\n\n\"Let's just get the papers and go,\" he said.\n\nBut nothing was where she remembered it. The file cabinets had shifted. The desk organizers were all over the floor. She searched through the cabinets and desk drawers, sweeping bugs off the few files left undamaged. Some of the files were so wet and soaked in mud that they were useless. She made a pile of the files that were unreadable, hoping that among the few that she could recognize was proof that they owned this building. It seemed so absurd, that she was searching through her own building, widely known as the headquarters of their well-known business, for a simple, filthy piece of paper that a makeshift court would accept in exchange for her husband. And what if she didn't find it? Her husband might fall deeper into the abyss of this broken judicial system for lack of this piece of paper?\n\n\"Please help,\" she asked Adnan, choking on the words.\n\nThey searched for an hour. They opened every drawer and every file, until she thought they were simply examining the same, few, undamaged files they'd already read repeatedly. But finally, in a drawer she was sure contained nothing of value, she found it, the act of sale for 3015 Dublin. She was on her knees, her abaya filthy, and she held it in her hands, and cried. She sat back and shook.\n\n\"This better work,\" she said.\n\n* * *\n\nWith the papers in hand, they returned to Raleigh's office in Baton Rouge. Raleigh prepared the paperwork and faxed it over to the bondsman. The bondsman confirmed that he had received it and that the bond had been paid. Raleigh called Hunt to confirm that all the paperwork had gone through for the surety bond. He was told that they had the paperwork, but that the office had closed early. It was three p.m.\n\nZeitoun would have to spend another night at Hunt.\n\n# THURSDAY SEPTEMBER 29\n\nIn the morning, Kathy and Adnan drove to the prison, arriving before eight. They went into the office and were told Zeitoun would be released that day. They waited in the same room where Zeitoun's friends had gathered two days earlier.\n\nThey waited until eleven. No word. Twelve. Nothing. It wasn't until one o'clock that they were given notice that he would be released any moment. Kathy was told to wait for him outside. A bus would be dropping him off at the gate.\n\nZeitoun was in his cell praying.\n\n_In the name of God, the Most Beneficent, the Most Merciful:  \nPraise be to God, the Lord of the Heavens and the Earth.  \nThe Most Beneficent, the Most Merciful.  \nMaster of the Day of Judgment_.\n\n\"Zeitoun!\"\n\nA guard was calling to him.\n\n_The guard can wait_ , Zeitoun thought. He had no idea that Kathy was at the prison and his release was imminent.\n\nHe continued his prayers.\n\n_You alone we worship, and You alone we ask for help.  \nGuide us to the straight way;  \nThe way of those whom you have blessed,  \nnot of those who have deserved anger,  \nnor of those who are astray_.\n\n\"Zeitoun!\" Now the guard was at his cell, yelling through the bars. \"Get ready!\"\n\nZeitoun continued his prayers until he was finished. The guard waited silently. When Zeitoun stood, the guard nodded to him.\n\n\"Get your stuff. You're getting out today.\"\n\n\"What?\" Zeitoun said.\n\n\"Hurry up.\"\n\nZeitoun fell against the wall. His legs had given way.\n\nKathy waited outside the prison with Adnan.\n\nA white bus arrived at the gate. A figure moved from within, from left to right, and then stepped down onto the pavement. It was Abdulrahman, her husband. He had lost twenty pounds. He looked like a different man, a smaller man, with longer hair, almost all of it white. Tears soaked her face. _He's so small_ , she thought. A flash of anger overtook her. _Goddamn those people. All of you people, everyone responsible for this_.\n\nZeitoun saw her. He smiled and she went to him. Tears all over her face, she could barely see. She ran to him. She wanted to protect him. She wanted to take him in the crescent of her arms and heal him.\n\n\"Get back!\"\n\nA heavy hand was on her shoulder. A guard had stopped her.\n\n\"Stay here!\" he yelled.\n\nKathy had crossed a barrier. It wasn't visible to her, but the guards had delineated an area within which the prisoners' relatives were not allowed.\n\nShe waited, standing a few yards away from her husband. They stared at each other, smiling grimly. He looked like a sad old man. He was wearing denim pants, a denim shirt, orange flip-flops. Prison clothes. They hung off him, two sizes too big.\n\nA few minutes later he was free. He walked to her and she ran to him. They held each other for a long moment. She could feel his shoulder blades, his ribs. His neck seemed so thin and fragile, his arms skeletal. She pulled back, and his eyes were the same\u2014green, long-lashed, touched with honey\u2014but they were tired, defeated. She had never seen this in him. He had been broken.\n\nZeitoun hugged Adnan, and then quickly pulled away.\n\n\"We should go,\" Zeitoun said.\n\nThe three of them quickly got in the car. They didn't want whoever was responsible for this to change their minds. It wouldn't have surprised them. Nothing at all would have surprised them.\n\nThey left the prison as fast as they could. They felt better after they passed through the main gate, and felt better still as they drove down the long white-fenced driveway and reached the road. Zeitoun turned around periodically, to be sure no one was following them. Adnan checked his rearview mirror as they sped down the rural route, trying to put as much distance as possible between themselves and the prison. They passed through a long corridor of tall trees, and with each mile they felt more sure that Zeitoun was absolutely free.\n\nKathy sat in the back seat, reaching forward, stroking her husband's head. But she wanted to be closer. She wanted him in her arms, she wanted to hold him and restore him.\n\nThey were only ten minutes away from the prison when Ahmad called Kathy's cell phone.\n\n\"We've got him!\" she said.\n\n\"What? You do?\"\n\nShe handed the phone to Zeitoun.\n\n\"Hello brother!\" he said.\n\n\"Is it you?\" Ahmad asked.\n\n\"It's me,\" Zeitoun said.\n\n\"Praise God. Praise God. How are you?\"\n\nAhmad's voice was trembling.\n\n\"Okay,\" Zeitoun said, \"I'm okay. Were you worried?\" He tried to laugh.\n\nNow Ahmad was crying. \"Oh praise God. Praise God.\"\n\n# V\n# FALL 2008\n\nKathy has lost her memory. It's shredded, unreliable. The wiring in her mind has been snapped in vital places, she fears, and now the strangest things have been happening.\n\nShe was at the bank in November, just to deposit checks from clients and withdraw cash for the week. She comes to this bank, Capital One, so often that everyone there knows her. This morning, like any other, the employees greeted her when she entered.\n\n\"Hi, Mrs. Zeitoun!\" they sang, and she waved and smiled.\n\nShe walked to one of the tellers and removed her checkbook and picked up a pen. She needed to write two checks, one for cash and the other to move money into the company's payroll account.\n\nShe wrote the first check and gave it to the teller, and when she returned her attention to her checkbook, she paused. She didn't know what to do next. She couldn't remember what her hand was supposed to be doing. She didn't know how to write, or what to write, or where. She stared and stared at the checkbook; it became more foreign by the moment. She couldn't identify the purpose of the checkbook on the counter or of the pen in her hand.\n\nShe looked around, hoping to see someone with these tools in their hands, to see how they were using them. She saw people, but they provided no clues. She was lost.\n\nThe teller said something but Kathy couldn't understand the words. She looked at the young woman, but the sounds coming from her mouth were garbled, backward.\n\nKathy couldn't speak. She knew, inwardly, that she was beginning to worry the teller. _Focus_ , she told herself. _Focus, focus, focus, Kathy!_\n\nThe teller spoke again, but the sounds were more distant now, coming, it seemed, from underwater, or far away.\n\nKathy's eyes locked on to the sliding wooden partition that separated this teller from the others. She lost herself in the blond wood grain, slipping into the elliptical lines of age on the wood's surface. Then she realized what she was doing, staring at the grain on the wood, and urged herself to snap out of it.\n\n_Focus!_ she thought. _C'mon_.\n\nHer hands felt numb. Her vision was blurry.\n\n_Come back! Come back!_\n\nAnd slowly she returned. The teller was talking. Kathy made out a few words. Kathy felt herself re-enter her body, and suddenly everything clicked into place again.\n\n\"Are you okay, Mrs. Zeitoun?\" the teller asked again.\n\nKathy smiled and waved her hand dismissively.\n\n\"Just spacing out for a second,\" she said. \"Busy day.\"\n\nThe teller smiled, relieved.\n\n\"I'm fine,\" Kathy said, and wrote the second check.\n\n* * *\n\nShe's been forgetting numbers, names, dates. She has trouble concentrating. She tells friends that she's going crazy, and laughs it off. She's not going crazy, she is sure and they are sure\u2014she's still the same Kathy almost all the time and certainly to most of the people she knows\u2014but episodes like the one at the bank are accumulating. She's not as sharp as she once was, and there are things she can't count on doing as she did before. One day she'll be unable to place the name of one of the workers she's known for ten years. Another day she'll find herself with the phone in her hand, the other end of the line ringing, and will have no idea who she is calling or why.\n\nIt is the fall of 2008 and the Zeitouns are in the process of moving into a new house. It's the same house, really\u2014the one on Dart\u2014but it's been gutted, expanded, tripled. Zeitoun designed an addition that will give all the children their own rooms, and will allow Kathy to work at home. There are balconies, gabled roofs, a large kitchen, four bathrooms, two sitting rooms. It is the closest thing to a dream house they will ever have.\n\nThe office on Dublin was a total loss. They went there a few days after Zeitoun's release from prison and found only mud and insects. The roof had given way, and everything inside was covered in the same grey mud. Kathy and Zeitoun took the few things they could salvage and eventually sold the building. They planned to move their office to their home. Now their house has an entrance on Dart, the residential address, and another one on Earhart Boulevard.\n\nThe Zeitouns have lived in seven apartments and houses since the storm. Their Dublin Street office was leveled and is now a parking lot. The house on Dart is still unfinished.\n\nThey are tired.\n\n* * *\n\nWhen they returned from Hunt, they stayed for two days on Adnan's floor in Baton Rouge, then moved into the studio apartment of their rental unit on Tita Street, on New Orleans' West Bank. There was no furniture, but it had been undamaged in the storm. Those first few nights, Kathy and Zeitoun lay on the floor, with borrowed blankets, talking very little. He did not want to talk about prison. He did not want to talk about Camp Greyhound. He was ashamed. Ashamed that his hubris, if that was what it was, had caused all this. Ashamed that he had been handcuffed, stripped, caged, treated like an animal. He wanted it all erased from their lives.\n\nOn that night and for many nights after, they lay on the floor and held each other, bitter and thankful and frustrated, and they said nothing.\n\nKathy fed him as much as she could each day. The day after his release, Kathy and Adnan took Zeitoun to Our Lady of the Lake Regional Medical Center, where the doctors found no major injuries. They could find no reason for the stabbing pain in his side. But he had lost twenty-two pounds. It would be a year before he was back to his previous weight. He'd lost hair, and what was left had gone grey. His cheeks were hollow, his eyes had lost their spark. Slowly, he regained himself. He grew stronger. The pain in his side dissipated, and this convinced Zeitoun it had been caused not by anything visible on an X-ray, but by heartbreak, by sorrow.\n\nAfter Zeitoun's release, their friend Walt loaned them a car from his Lexus dealership, and Kathy and Zeitoun drove it back into the city and to the house on Dart.\n\nThe smell was overpowering, a mixture of mold, sewage, and dead animals. Kathy pulled part of her hijab to her mouth to mute the stench. Zeitoun tried to flush one of the toilets and sewage poured out. More water had made its way into the rooms on the second floor. A shelf of books was ruined, as well as most of the electronics.\n\nWithout Zeitoun there to plug holes as they arose, the house had been devastated. He looked at the gaps in the roof and sighed.\n\nKathy leaned against the wall in the hallway. She was overwhelmed. Everything they owned was filthy. To think she had cleaned this house a thousand times!\n\n\"You okay?\" he asked her.\n\nShe nodded. \"I want to leave. I've seen enough.\"\n\nThey took the computer and some of the kids' clothes and put them in the car. Zeitoun started the engine but then ran back inside, retrieved the box of photos, brought it down, and put it in the trunk. He backed out of the driveway, turned down Dart, and remembered something else.\n\n\"Wait!\" he said. \"Oh no...\" He jumped out of the car, leaving the door open. _The dogs_. How long had it been? He ran across the street and down the block, his stomach spinning. _The dogs, the dogs_.\n\nHe knocked on the front doors of the two houses where he had fed them. No answer. He looked in the first-floor windows. No one. The owners had not come back.\n\nZeitoun went back to the tree. His plank was still there, and he leaned it against the trunk. He climbed up to his usual perch and then pulled the plank up. He stretched the plank across to the house on the right and walked to the roof. Usually the dogs were barking for him by now, but today he heard nothing.\n\n_Please_ , he thought. _Please God_.\n\nHe lifted the window and slipped inside. The stench hit him immediately. He knew the dogs were dead before he saw them. He found them together in one of the bedrooms.\n\nHe left the roof, stepped back to the tree, and arranged the plank to reach the second house. The dogs were just under the windowsill, a tangle of limbs, heads to the heavens, as if they had been waiting, for weeks, for him.\n\nAfter two weeks, Kathy and Zeitoun were still in the studio apartment, and the kids were ready to return to New Orleans. Zeitoun was nervous. \"Do I look like me?\" he asked Kathy. He was afraid he would scare them, having lost so much weight and hair. Kathy didn't know what to say. He did not look like him, not yet, but the kids needed to see their father. So Kathy and Zeitoun flew to Phoenix, and amid much crying and hugging, the Zeitouns were reunited. They drove back to New Orleans and returned to the apartment on Tita. For a month they slept together on the floor.\n\nOne day Kathy opened a letter from the Federal Emergency Management Agency. They were offering the Zeitouns a free trailer, a two-bedroom portable unit that would be delivered to them at their request.\n\nKathy filled out the appropriate forms and sent them back. She didn't expect much from the process, so she was startled when, in December 2005, an eighteen-wheeler pulled up in front of their apartment with a gleaming white trailer in tow.\n\nZeitoun was on his rounds, so he didn't see them install it. When he returned, he was puzzled. They hadn't connected the trailer to water or electricity. And it had been installed on a rickety tower of cement blocks, easily four feet off the ground. There were no steps to reach the door. It was so high that there was no way to get inside without a stepladder. And even if one reached the door, you couldn't enter the trailer, because the delivery team had failed to leave a set of keys.\n\nKathy called FEMA and let them know about these issues. They said they were doing the best they could, and would get to it as soon as possible. Weeks passed. No key was delivered. The Zeitouns watched every day for signs of any FEMA personnel. The trailer stayed where it was, unused, unconnected, and locked.\n\nAfter a month, a FEMA pickup truck arrived and dropped off a set of steps, about four feet high. They left no equipment that might attach the steps to the trailer. There was a foot-wide gap between the steps and the door. To get inside, one would have to jump. But the door still couldn't be opened. They had yet to provide the key.\n\nAfter another six weeks or so, a FEMA inspector appeared and gave Kathy the key to the trailer. But when he saw the trailer, he noted that because it was leaning, it was unsafe to use. He left, telling Kathy that someone would come to fix it.\n\nZeitoun and Kathy began to buy houses in their neighborhood. Their next-door neighbor had fled the storm and hadn't returned. She put the house on the market and the Zeitouns made an offer. It was half the value of the house before the hurricane, but she accepted. This was the most satisfying of all the transactions they made. Before the storm, they'd also bought the house on the other side of their own. Soon they were living in this house, while renovating their original house on Dart, and renting out the other house next door.\n\nMeanwhile, the FEMA trailer was still parked in front of the house on Tita. It had been there eight months, and had never been connected to water or electricity. A practical way to enter the trailer had never been devised, and now the Zeitouns didn't need it. It was an eyesore. Zeitoun had repaired all the damage to the Tita house, and they were trying to sell it. But the trailer was blocking the view of the house, and no one would buy a house where an immovable leaning trailer was parked out front.\n\nBut FEMA wouldn't pick it up. Kathy called every week, telling FEMA officials that the trailer had never been used and now was decreasing the value of their property. She was told each time that it would be removed soon enough, and that, besides, thousands of people would love to have such a trailer; why was she trying to get rid of it?\n\nIn June 2006, a FEMA representative came to collect the keys. He said they would return to take away the trailer. Months went by. There was no sign of anyone from FEMA. Kathy called again, and FEMA had no record of anyone picking up the keys.\n\nFinally, in April of 2007, Kathy wrote a letter to the _Times-Picayune_ detailing the saga of the trailer. At that point, the trailer had sat, unused and unusable, for over fourteen months. On the morning the letter ran, a FEMA official called Kathy.\n\n\"What's your address?\" he asked.\n\nThey took it away that day.\n\nKathy's problems with memory gave way to other difficulties, equally difficult to explain. She began to have stomach problems. She would eat any small thing, a piece of pasta, and her stomach would swell to double its original size. Soon she was choking on anything she tried to eat. Food would not go down some days, and when it did, she would have to gag and fight it down.\n\nShe grew clumsier. She knocked over glasses and plates. She broke a lamp. She dropped her phone constantly. Some days, when she walked, she would feel tipsy, swaying side to side, needing to rest against walls as if struck by vertigo. Some days her hands or feet would grow numb while she was doing normal everyday things like driving or working with the kids on their homework.\n\n\"Honey, what's happening to me?\" she asked her husband.\n\nShe went in for tests. One doctor suggested she might have multiple sclerosis; so many of her symptoms seemed to indicate some kind of degenerative illness. She was given an endoscopy, an MRI, and a barium swallow to test her gastrointestinal tract. Doctors administered tests of her cognitive skills, and she did poorly on those that measure memory and recognition. Overall the tests pointed to post-traumatic stress syndrome, though she has yet to decide on the strategy to manage it.\n\nKathy and Zeitoun had no intention of suing anyone over his arrest. They wanted it in the past. But friends and relatives fanned their outrage, and convinced them that those responsible needed to be held accountable. So they hired a lawyer, Louis Koerner, to pursue a civil suit against the city, the state, the prisons, the police department, and a half-dozen other agencies and individuals. They named everyone they could think of\u2014the mayor, Eddie Jordan, and everyone in between. They were told by everyone who knew anything about the New Orleans courts to get in line. There were hundreds, perhaps thousands, of cases against the city, the federal government, FEMA, police officers, the Army Corps of Engineers. Three years after the storm, few of the lawsuits had gone anywhere.\n\nA few months after Zeitoun's release, Louis Koerner found his arrest report. Kathy was shocked that it even existed, that any records had been made or kept. Finding the names of those who arrested her husband was satisfying at first, but then it only fueled her rage. She wanted justice. She wanted to see these men, confront them, punish them. The arresting officer was named Donald Lima, and this name, Donald Lima, seared itself into her mind. The other officer named on the report was Ralph Gonzales. Lima was identified as a police officer from New Orleans. Gonzales was a cop from Albuquerque, New Mexico.\n\nOut-of-state police could not make arrests, Kathy discovered, so on any arrest, a local officer had to be present along with any Guardsmen or contractors. Kathy and Zeitoun decided to name Donald Lima, the officer on the arrest report, in the lawsuit. The Zeitouns' lawyer contacted the New Orleans Police Department and found that Lima was no longer employed there. He had resigned in 2005, a few months after the storm. The department had no forwarding address.\n\nGonzales was easy to find. On the arrest report, he was identified as being an officer from Albuquerque, and he was still with that department in the fall of 2008. When he was reached by phone, he told his side of the story.\n\nGonzales had been a police officer for twenty-one years when, in August of 2005, his captain suggested that they send a team to New Orleans. The New Orleans Police Department had put out a nationwide request for law enforcement help, so Gonzales agreed to go, along with about thirty other officers from Albuquerque.\n\nThe New Mexico team arrived a few days after the storm, were sworn in as deputies, and began to assist with search and rescue operations. Before arriving in New Orleans, Gonzales and his fellow officers had heard a lot about the conditions in the city, and they were tense. They had heard about shootings, rapes, gangs of heavily armed and fearless men. They saw no such crime, but they saw plenty of death. They were one of the first units to investigate one of the hospitals. Gonzales didn't remember which one, but they found dozens of bodies. The smell was indescribable.\n\nConditions worsened every day. He and his fellow cops wouldn't go out at night. They could hear windows breaking and shots fired after dark. The entire city smelled of death and decay. \"Everyone was on guard,\" he said of his fellow cops. \"We thought we were in a third-world country.\"\n\nOn September 6, Gonzales was at the Napoleon\u2013St. Charles staging ground. Cops and soldiers and medical personnel gathered there every day to share information and receive assignments. Gonzales got word that there would be a search of a house down the road, occupied by at least four suspects presumed to have been looting and dealing drugs. It could be very dangerous, he was told, and they needed as many cops and soldiers as possible. It was the first law-and-order assignment he'd been part of since he had arrived.\n\nHe jumped on the boat wearing a bulletproof vest and carrying a pistol and an M-16. He was one of six cops, National Guard soldiers, and soldiers-for-hire on the boat. When they arrived, Gonzales was one of the first to enter. He saw a pile of computer components and stereo equipment on the dining room table, and he saw the four men. There was something in their attitude, he thought, which signaled that \"they were up to no good.\"\n\nThey arrested the four men, brought them to the staging ground, handed them to the authorities there. They were finished with the assignment in fifteen minutes. That was the extent, Gonzales asserted, of their duties. He never went to Camp Greyhound and was only vaguely aware that a jail had been installed there. Neither he nor any part of the arresting party secured the house or collected any evidence. In fact, none of them returned even once to the house on Claiborne.\n\nThe arrest of Zeitoun and the other three men on Claiborne Avenue was one of two arrests Gonzales made while he was in New Orleans. Every other task he performed was related to search and rescue. Ten minutes after bringing the four men to the staging ground, he was on another boat, looking for people in need.\n\nGonzales was asked how he felt about the fact that Abdulrahman Zeitoun, a middle-aged businessman and father of four, had done a month in maximum-security prison.\n\nGonzales seemed regretful. \"If he was innocent, then I feel very bad,\" he said. \"Here's the bottom line: I wouldn't want something like that to happen to me personally.\"\n\nGonzales talked about how the system is supposed to work: police officers investigate, make arrests, and then hand the process over to the judicial system. Under normal circumstances, if the men were innocent, he maintained, they would have been given a phone call and the opportunity to post bail.\n\n\"They should have gotten a phone call,\" he said.\n\nLima was more difficult to track down, but he had not gone far. He had left the New Orleans Police Department in 2005 and was living in Shreveport, Louisiana.\n\nHe knew that Zeitoun and the others had spent time in jail. He knew about Zeitoun's case because he'd been served papers when the lawsuit was undertaken. He didn't know how long the other men had spent in prison. He was quick to note that their imprisonment wasn't his doing. He only made the arrest.\n\nAt the time of Katrina, he was living in a five-thousand-square-foot house on Napoleon. During and after the storm, he stayed in the city with members of his family, guarding his house. He had two generators and enough food and water for three weeks. He also had over forty pistols and automatic rifles. During the day he traveled the city with other police officers and National Guard troops, making rescues. Each day he met with other law-enforcement personnel, and they would map out a plan of action. They divided up tasks and territory.\n\nThe National Guardsmen in the city had plenty of gasoline but were low on other supplies. In exchange for gasoline, Lima and other New Orleans police officers broke into convenience stores and took cigarettes and chewing tobacco. A majority of the National Guardsmen, Lima said, chewed tobacco and smoked Marlboros, so this arrangement kept both sides well supplied. Lima considered the looting a necessary part of the mission. The gasoline, he said, helped them make the rescues they did. He also needed it to power his home generators. When he couldn't find Guardsmen who had gas, Lima siphoned fuel from cars and trucks. His throat was sore from all the gas-siphoning he did after the storm, he said.\n\n\"The whole place was anarchy,\" he said.\n\nWhile making his rounds on a motorboat one day, Lima observed four men leaving a Walgreens carrying stolen goods. They left the Walgreens and put the goods into a blue-and-white motorboat. Lima had two rescuees with him, so he couldn't pursue the thieves at the time, but he made a mental note. He continued to make rounds, seeing dead bodies and being confronted by angry residents, many of them armed.\n\n\"My state of mind was rattled,\" he said.\n\nTwo days later he passed a house on Claiborne and saw the same blue-and-white boat tethered to the porch. He raced to the Napoleon\u2013St. Charles staging ground and gathered a crew of police and military personnel. They were \"heavily armed\" with sidearms and M-16s. He didn't know the other four men or the one woman who joined in the mission. Together they took a flatboat to the house. Lima was the lead cop on the arrest.\n\nWhen they entered, they saw what they thought were stolen goods on the dining room table. They found four men inside, and something about them and the scene seemed amiss. Lima was sure that these were the same four men he had seen leaving the Walgreens, so they arrested them and brought them to the staging ground.\n\n\"It was a fairly routine arrest,\" he said. \"All four of the guys were very quiet.\"\n\nThey handed the men over to National Guardsmen, and the Guardsmen put them in the white van. Lima filled out paperwork about the arrest and gave it to the Guardsmen, and they drove the arrestees to Camp Greyhound. Later, Lima went to Greyhound, where he saw the men's property laid out on a table. He saw Todd's maps, Nasser's cash, and the memory chips. \"They'd been up to something,\" he said.\n\nLima was not sure what goods he had seen the four men stealing. And he did not see any goods customarily sold by Walgreens in the house on Claiborne. He did not secure the house on Claiborne as a crime scene. No stolen goods were recovered. But he was certain the men in the house were guilty of something, though the extraordinary circumstances of post-storm New Orleans did not allow for the same degree of thoroughness as he would have liked.\n\nNor was the post-arrest procedure standard or fair, he said. In a normal situation, Lima said, they would have been arraigned properly, given a phone call and an attorney, and would have been out on bail within days. When he was a cop, he was frustrated by the revolving-door nature of the justice system. He would arrest someone in the morning and they would be out on the street in the afternoon. It was maddening for a police officer, but he admitted that this element of checks and balances would have been useful in this case.\n\n\"They should have gotten a phone call,\" he said.\n\nLima quit the NOPD in November 2005, and moved with his wife and daughter to Shreveport. He was a police officer in Shreveport for a time, but was treated, he said, \"like a second-class citizen.\" The officers there assume that all cops from New Orleans are corrupt, he said. So he quit, and now he's looking for a new career. Before joining the force, he was a stockbroker, and he was considering going back to that.\n\nThe Zeitouns were conflicted about what they heard about Lima and Gonzales. On the one hand, knowing that these two police officers had not purposely hunted and arrested a man because he was Middle Eastern gave them some comfort. But knowing that Zeitoun's ordeal was caused instead by systemic ignorance and malfunction\u2014and perhaps long-festering paranoia on the part of the National Guard and whatever other agencies were involved\u2014was unsettling. It said, quite clearly, that this wasn't a case of a bad apple or two in the barrel. The barrel itself was rotten.\n\nSoon after, a friend emailed Kathy a document that seemed to shed light on the state of mind of the soldiers and law-enforcement agencies working in New Orleans at the time.\n\nThe Federal Emergency Management Agency had been its own freestanding agency for decades, but after 9\/11 had been folded into the Department of Homeland Security. FEMA had historically been granted broad powers in the wake of a federal emergency; they could take command of all police, fire, and rescue operations. This was the case after Katrina, where it was necessary for FEMA to assume the responsibility for all prisoners being evacuated from New Orleans. And thus the prisoners, including Zeitoun, were overseen by the Department of Homeland Security.\n\nWhile Katrina bore down on the Gulf Coast, a four-page document was apparently faxed and emailed to law-enforcement agencies in the region, and to National Guard units headed to the Gulf area. The document, issued in 2003 by the Department of Homeland Security, was written by a \"red cell\" group encompassing representatives of the Department of Homeland Security, the CIA, the Marines, corporate security firms, and Sandia National Laboratories.\n\nThe authoring committee had been asked to \"speculate on possible terrorist exploitation of a high category hurricane.\" And though the authors admitted that it was unlikely that terrorists would act during or after a hurricane, they nevertheless enumerated the many ways they might do so. \"Several types of exploitation or attacks may potentially be conducted throughout the hurricane cycle\u2014hostage situations or attacks on shelters, cyber attacks, or impersonation of emergency response officials and equipment to gain access.\" These terrorists \"might even hope that National Guard and other units are less able and well-equipped to respond... because of deployments overseas.\"\n\nThen they broke their findings into three categories: Pre-Event, During Event, and Post-Event. Before the storm, the committee wrote, the terrorists would be most likely to use the occasion \"to observe precautionary measures to gauge emergency response resources and continuity of operation plans at critical infrastructures.\" They also warned that terrorists might target evacuation routes, creating \"mass panic\" and \"loss of public confidence in the government.\" Terrorist activity during the storm, the committee felt, was \"less likely due to the severe weather, unpredictability of the storm path and the difficulty of mobilizing resources.\" After the storm, the options for terrorists were few but potent. They might \"build on public panic to further destabilize the system by disseminating rumors\" and therefore \"increase media coverage\" and \"stress the public health system.\"\n\nThe committee had several recommendations to reduce the threat posed by such terrorists. They included: \"Institute increased security procedures (e.g. identification checks) at evacuation centers and shelters\"; \"Advise the first responder community, telecommunications personnel, and power restoration personnel to increase identification procedures to prevent imposters from gaining unauthorized access to targets\"; and \"Increase patrols and vigilance of staff at key transportation and evacuation points (for instance, bridges and tunnels), including watching for unattended vehicles at these locations.\"\n\nThe \"red cell\" committee thought it unlikely that an established terrorist group would work in the United States during a hurricane. Instead, they felt that \"a splinter terrorist cell, or a lone actor... would be more likely to exploit a hurricane on site. This includes persons pursuing a political agenda, religious extremists, or other disgruntled individuals.\"\n\nKathy isn't sure whether hearing things like this is helpful or not. She has moved on from Katrina in many ways, and yet the residual effects arrive at unexpected times. There are plenty of normal days. She drives the kids to school and picks them up, and in between she manages the affairs of the painting and contracting company. When the kids get home she makes them a snack and they watch TV and do their homework.\n\nBut the other day Kathy had to ask for Nademah's help. She was trying to get onto the Internet but couldn't make it work. She looked behind the computer and the wires were a chaos she couldn't decipher. \"D, can you help me get connected?\"\n\nNademah came to help. It was Kathy who had set up all the computers in the house, Nademah reminded her, and Kathy who had taught Nademah how to use them. Kathy knew this, but at that moment she couldn't remember which wires went where, which buttons did what, how everything was connected.\n\nCamp Greyhound has been the subject of investigative reports and a source of fascination for the city at large. Even employees of Greyhound and Amtrak are amazed at what became of the station after the storm. Clerks at the Amtrak desk will happily show visitors the place where prisoners were fingerprinted, where their heights were determined. The height chart is still there. Under a poster next to the counter, the handwritten marks are still there. You just have to move the poster to see them, just as they were in the days of Camp Greyhound.\n\nAs Zeitoun had suspected, the jail was built largely by hand. When he was incarcerated there, he couldn't imagine what workers were available and ready to work long hours a day after the hurricane, but the answer makes a certain amount of sense. The work was completed by prisoners from Dixon Correctional Institute in Jackson, Louisiana, and from the Louisiana State Penitentiary in Angola.\n\nAngola, the country's largest prison, was built on an eighteen-thousand-acre former plantation once used for the breeding of slaves. Meant to hold those convicted of the most serious crimes, it has long been considered the most dangerous, most hopeless prison in the United States. Among the five thousand men held there, the average sentence is 89.9 years. Historically the inmates were required to do backbreaking labor, including picking cotton, for about four cents an hour. In a mass protest decades ago, thirty-one prisoners cut their Achilles tendons, lest they be sent again to work.\n\nAt the time of the hurricane, Marlin Gusman, sheriff of Orleans parish, knew that there was a chance that the Orleans Parish Prison, where most offenders were kept while awaiting trial, would flood. So he called Burl Cain, warden of Angola. An arrangement was made to build an impromptu prison on high ground in New Orleans. Warden Cain rounded up fences and portable toilets, all of which he had available at the Angola campus, and sent the materials on trucks to New Orleans. They arrived two days after the hurricane struck the city.\n\nCain also sent dozens of prisoners, many of them convicted of murder and rape, and tasked them with building cages for new prisoners and those forced out of Orleans Parish Prison. The Angola prisoners completed the network of outdoor jails in two days, sleeping at night next door to the Greyhound station. Cain also sent guards. When the cages were finished, the Angola prisoners were sent back north, and the guards remained. These were the men who guarded Zeitoun's cage.\n\nWhen the prison was completed, Cain said it was \"a real start to rebuilding\" New Orleans. In the weeks that followed, more than 1,200 men and women were incarcerated at Camp Greyhound.\n\nThis complex and exceedingly efficient government operation was completed while residents of New Orleans were trapped in attics and begging for rescue from rooftops and highway overpasses. The portable toilets were available and working at Camp Greyhound while there were no working bathrooms at the Convention Center and Superdome a few blocks away. Hundreds of cases of water and MREs were readily available for the guards and prisoners, while those stranded nearby were fighting for food and water.\n\nThere have been times when someone speaks to Kathy in English and she can't understand what the person is saying. It happened the other day with Ambata, a woman the Zeitouns recently hired to help with office work. The kids had just come home from school, the TV was on, a stereo was playing\u2014there was noise throughout the house. Kathy and Ambata were sending out invoices when Ambata said something Kathy couldn't understand. She saw Ambata's mouth moving, but the words conveyed no meaning.\n\n\"Can you repeat that?\" she asked.\n\nAmbata repeated herself.\n\nThe words made no sense.\n\n\"I'm sorry,\" Kathy said. \"I have no idea what you're saying.\" She grew scared. She jumped up and, frantic, she turned off the TV, the stereo, and the computer. She wanted to eliminate any variables. She sat down again with Ambata and asked her to repeat what she said.\n\nAmbata did, but Kathy still could not parse the words.\n\nOne day, in 2006, Zeitoun was visiting his cousin Adnan at his Subway franchise downtown. Zeitoun occasionally stopped there for lunch, and was eating there that day when he saw an exceptionally tall African American woman enter. She was in tan-and-green fatigues, evidently a National Guard soldier. She looked very familiar.\n\nZeitoun realized why he recognized her. She was, he was almost certain, one of the people who had arrested him. She had the same eyes, the same short hair. He stared for a few long moments and tried to muster the nerve to say something. He couldn't devise the right thing to say, and soon she was gone.\n\nAfterward he asked Adnan about her.\n\n\"Have you seen her before?\"\n\n\"I'm not sure. I don't think so.\"\n\n\"If she comes in again, you have to ask her questions. Ask her if she was in New Orleans after the storm.\"\n\nZeitoun spent the day reliving his arrest and the weeks afterward. It wasn't every day that the arrest came to him, but late at night it was sometimes difficult to send away his anger.\n\nHe knew he couldn't live in the city if he felt he would continue to encounter people like this soldier. It was painful enough to pass by the Greyhound station. It was almost unavoidable, though, given how central it was\u2014within sight of the Home Depot. He had adjusted his habits in a dozen small ways. He was exceedingly careful not to commit any minor traffic infraction. He feared that because of the lawsuit he would be a target of local police, that they would manufacture charges against him, try to justify his arrest. But these were fleeting thoughts. He fought them off every day.\n\nOne confrontation was unavoidable.\n\nFour days after his release, Zeitoun had had time to sleep, and to eat a bit. He felt stronger. He didn't want to return to Camp Greyhound. But Kathy had insisted, and he knew she was right. They had to get his wallet back. It held his driver's license, and without it the only identification he had was the prison ID he had been given at Hunt. He and Kathy needed to fly to Phoenix to gather their children and drive home, and the only way he could do so was with his driver's license. They thought about it a dozen ways but couldn't find a better way. They had to return to the Greyhound station and retrieve the wallet.\n\nThey pulled into the crescent-shaped drive. All around were police cars, military Humvees, jeeps, and other military vehicles.\n\n\"How do you feel?\" Kathy asked.\n\n\"Not good,\" Zeitoun said.\n\nThey parked and stayed in the car for a minute.\n\n\"Ready?\" Kathy asked. She was primed for a fight.\n\nZeitoun opened his door. They walked toward the station. Outside the entrance, there were two soldiers.\n\n\"Please don't say anything,\" Zeitoun said to Kathy.\n\n\"I won't,\" she said, though she could barely contain her rage.\n\n\"Please don't,\" he repeated. He had warned her repeatedly that they could both be put in jail, or he could be returned to prison. Anything could happen. Anything _had_ happened.\n\nAs they approached the bus station, Zeitoun was trembling.\n\n\"Please be calm,\" he said. \"Don't make it worse.\"\n\n\"Okay, okay,\" Kathy said.\n\nThey walked past a dozen military personnel and into the building. It looked much like Zeitoun remembered. For the first time in his life, he tried to shrink. Trying to hide his face\u2014the very people who caged him might still be there\u2014he followed Kathy through the doors.\n\nThey were stopped by a pair of soldiers. They patted Zeitoun down and searched Kathy's purse. They directed them both through a metal detector. Zeitoun's eyes darted around the building, looking for anyone he recognized.\n\nThey were directed to a set of chairs, the same chairs Zeitoun had been questioned in, and were told to wait for a chance to meet with the assistant district attorney. Zeitoun wanted badly to get out as soon as possible. The situation was far too familiar. He had no faith that he would leave again.\n\nAs they waited, a man holding a tape recorder approached them. He told them that he was a reporter from the Netherlands, and that his friend had been held overnight at the station in one of the cages, and had just been released.\n\nHe began asking Zeitoun and Kathy why they were there. Kathy didn't hesitate, and began to tell him that her husband had been wrongfully arrested, sent to a maximum-security prison, held there for twenty-three days, and that now they were trying to retrieve his possessions.\n\n\"Get away from them!\"\n\nKathy looked up. A female officer in her fifties, wearing full camouflage, was glaring at them, and barking at the Dutch reporter. \"Get out of here,\" she said to him. \"Interview's over.\" Then she turned to a pair of National Guardsmen. \"If that man is seen in here again, arrest him and put him in a cage.\" The soldiers approached the reporter.\n\nKathy stood up and strode toward the woman.\n\n\"Now you take away my freedom of speech? Really? You took away my husband, you wouldn't let me speak to or see my husband, and now you take away my ability to speak freely? I don't think so! You know anything about freedom of speech?\"\n\nThe officer turned away from Kathy and ordered that the reporter be removed. Two soldiers guided him to the front door and led him outside.\n\nThe assistant district attorney, a heavyset white man, approached them and asked how he could help. Kathy reiterated that she needed her husband's wallet. The man led them to the gift shop, which had been converted into an office. It was a glass box in the middle of the station, full of Mardi Gras T-shirts and paperweights. Kathy and Zeitoun explained their situation.\n\nThe assistant DA said he was sorry, but the wallet was still being used as evidence. Kathy blew up. \"Evidence? How could his ID be used as evidence? You know his name. Why would you need his ID? He didn't commit a crime with his wallet.\"\n\nThe man sighed. \"I'm sympathetic, but you can't have it without permission of the district attorney,\" he said.\n\n\"You mean Eddie Jordan?\" Kathy asked. \"Where is he?\"\n\n\"He's not here,\" he said.\n\n\"When will he be here?\" Kathy asked.\n\nThe assistant DA didn't know.\n\nKathy and Zeitoun walked into the station lobby, not knowing what their next step was. But then, through the station's front window, she saw Eddie Jordan. He was standing out front, surrounded by a phalanx of reporters.\n\nKathy marched out the door to confront Jordan. He was dressed in a three-piece suit.\n\n\"Why can't we have his wallet?\" she asked.\n\n\"Excuse me?\" Jordan said.\n\nKathy told him a brief version of Zeitoun's situation, and reiterated her demand that the wallet be returned.\n\nJordan said that there was nothing he could do about it, and turned around, resuming his conversation.\n\nNow Kathy saw that the Dutch reporter was nearby. She wanted him and the other reporters to hear what was happening. She spoke as loudly as she could.\n\n\"You arrested my husband in his own house, and now you won't give him his wallet back? What's going on here? What is wrong with this city?\"\n\nJordan shrugged and turned away.\n\n\"We're going back inside,\" Kathy said to Zeitoun.\n\nZeitoun didn't see the point, but the fire in her eyes did not encourage debate. They went back in and walked directly up to the assistant DA. Kathy wouldn't allow that damned prison ID to define her husband, to be the only government-issued identification he owned.\n\n\"You have to do something,\" she said. She was near tears now, a mess of frustration and rage.\n\nThe assistant DA closed his eyes. \"Let me see what I can find,\" he said. He left the office. In ten minutes, he came back with the wallet and handed it to Zeitoun.\n\nZeitoun's driver's license and permanent-resident card were there, but all his cash, business cards, and credit cards were gone.\n\n\"Where are the other things?\" Zeitoun asked.\n\nThe man didn't know. \"That's all there was.\"\n\nKathy didn't care. All she wanted, for now, was proof that her country recognized her husband as a citizen.\n\n\"Thank you, sir,\" she said. \"Thank you.\" She wanted to hug him. He was the first person representing any part of the city or state government who had shown any humanity at all. Even this one easily executed task, retrieving the wallet of a man they'd held in a cage a few yards away, seemed, in the context, an act of great courage and empathy.\n\nThey left, satisfied that they had gotten the most crucial thing, the driver's license. Given the nature of the city's judicial system, it was miraculous that the wallet had been kept at all. Kathy had already canceled the credit cards. The rest they could replace.\n\nThat was the last time Kathy felt that focused, that angry. Now she is more diffuse. She gets angry, but not as often, and she can't focus her rage as she once could. Where she was once ready and willing to fight any battle, she prefers now to retreat, reinforce her defenses, double the locks on the doors. She finds herself fearful, always, that something will happen to her family. She doesn't like her kids playing in the neighborhood. She wants them where she can see them, even Nademah, who is thirteen now, and almost as tall as Kathy herself. She watches them sleep. She never did that before. She checks on them frequently during the night. She wakes up and has trouble getting back to sleep.\n\nNademah, always responsible, always whip-smart, is now sharing in the care of her sisters. Zachary is eighteen, lives with friends in New Orleans, and works at one of Adnan's Subway restaurants. Safiya and Aisha are the same as always: blithe, full of joy, given to bursts of song. All of the kids make life very easy for little Ahmad, born on November 10, 2006 at East Jefferson Hospital.\n\nAhmad is, by all accounts, a preternaturally content baby. He never wants for attention, with his sisters taking turns holding him, taking dangerous things out of his mouth, reading to him, dressing him in their old clothes.\n\nZeitoun was so thankful for a boy. And the name was never an issue. Ahmad was the first and only name.\n\nZeitoun's brother Ahmad, still living in Spain, now works as a ship inspector. He's waiting for his brother to bring the new baby to M\u00e1laga. It's time he saw his nephew, his namesake.\n\nKathy is working less these days. There's the baby to care for, and her mind is not sharp enough, not lately, to handle all the paperwork on her own. They have some help now, from Ambata and others, which gives Kathy some room to breathe, to be a mother, to try to make sense of the last three years.\n\nThere are appointments with doctors. Doctors to try to figure out why her hands go numb without warning. Doctors to investigate her digestive problems, memory problems.\n\nDoctors have asked Kathy what she thinks the most traumatic part of the Katrina experience was. She surprised herself and the doctors when she realized that it was after she knew Zeitoun was alive, and had been told he was at Hunt Correctional Center, but wasn't allowed to see him or even know where a court hearing might be held. It was that moment, being told by the woman on the phone that the hearing's location was \"private information,\" that did the most damage.\n\n\"I felt cracked open,\" she says.\n\nThat this woman, a stranger, could know her despair and desperation, and simply deny her. That there could be trials without witnesses, that her government could make people disappear.\n\n\"It broke me.\"\n\nShe finds herself wondering, early in the morning and late at night and sometimes just while sitting with little Ahmad sleeping on her lap: _Did all that really happen? Did it happen in the United States? To us?_ It could have been avoided, she thinks. So many little things could have been done. So many people let it happen. So many looked away. And it only takes one person, one small act of stepping from the dark to the light.\n\nShe wants to find out who that missionary was, the man who met her husband in prison and took her phone number\u2014the messenger. The man who risked something in the name of mercy.\n\nBut did he risk so much? Not really. Usually you needn't risk so much to right a wrong. It's not so complicated. It's the opposite of complicated. To dial a number given to you by a man in a cage, to tell the voice on the other end, \"I saw him.\" Is that complicated? Is that an act of great heroism in the United States of America?\n\nIt should not be so.\n\n* * *\n\nKathy worries that her husband is working too hard now. He works every day, even Sundays. He's home for meals, and bedtimes, but he works whenever he can. And how he does it while fasting on Mondays and Fridays\u2014he's become more religious\u2014is beyond her. He seems to eat even less than before, and works harder than ever.\n\nFriends who know what happened to Zeitoun after the storm ask why he hasn't left, why he hasn't gone to another city, another country\u2014even back to Syria\u2014anyplace removed from the memories embedded into New Orleans. He does have dark feelings when he passes by the Greyhound station, when he drives past the house on Claiborne where he and two friends and a stranger were carried off. When he drives by the home of Alvin and Beulah Williams, the pastor and his wife, he says a quick prayer for them. Beulah Williams died in 2007. Reverend Alvin Williams died in 2008.\n\nWhen he passes by the home of Charlie Ray, his neighbor on Claiborne, he waves if Charlie is on his porch, which he often is. One day after the storm, Charlie was visited by the National Guard. They told him that he should leave the city, and that they would help him. They waited for him to pack, and then carried his bags to their boat. They ferried him to an evacuation point, whereupon a helicopter flew him to the airport and he was given a free plane ticket to New York.\n\nHis rescue took place the same day Zeitoun was arrested. A few months after the storm, Charlie returned to New Orleans and still lives on Claiborne.\n\nTodd Gambino now lives in Mississippi. He spent over five months at Hunt Correctional Center. He was released on February 14, 2006. All charges against him were dropped. More than $2,400 had been confiscated from him when he was processed at Camp Greyhound, and when he was released, he attempted repeatedly to recover it. He was unsuccessful. He was not compensated in any way for the five months he spent at the maximum-security prison.\n\nAfter his release, he went to work on an oil rig in the Gulf of Mexico but was laid off in the fall of 2008.\n\nNasser Dayoob spent six months at Hunt. All charges against him were eventually dropped; when he was released, he tried to recover the $10,000 he'd had with him when he was arrested. No authorities had any record of it, and he never recovered the money, his life savings. In 2008 he moved back to Syria.\n\nRonnie spent eight months at Hunt. Since his release in the spring of 2006, the Zeitouns have not heard from him.\n\nFrank Noland and his wife have moved. Just about everyone in the Zeitouns' neighborhood has moved. Gone, too, is the woman Zeitoun found in her foyer\u2014the woman whose cries he heard because he paddled quietly. The new occupant of her house doesn't know where she went, but he has heard the story of Zeitoun's rescue.\n\nZeitoun thinks of the simple greatness of the canoe, of the advantages of moving quietly, of listening carefully. When he was released from prison, he and Kathy looked for the canoe where he'd last seen it, at the Claiborne house, but it was gone. The house had been robbed, too. Everything was stolen, because the soldiers and police who arrested Zeitoun had left the house unlocked and unguarded. Thieves walked in unimpeded and made off with all the tenants' belongings, everything Todd had gathered there in the front rooms to keep dry.\n\nAll those things were replaced, but he misses the canoe. He keeps his eye out for it, hoping he'll see it at a yard sale or in someone's sideyard. He'd pay for it again. Maybe he should get a new one, he thinks. Maybe his girls will like it more now. Maybe little Ahmad, like his uncle and father and grandfather and countless Zeitouns before them, will feel the lure of the sea.\n\nSome nights Zeitoun struggles to sleep. Some nights he thinks of the faces, the people who arrested him, who jailed him, who shuttled him between cages like an animal, who transported him like luggage. He thinks of the people who could not see him as a neighbor, as a countryman, as a human.\n\nEventually he finds his way to sleep, and in the morning he awakens to the sounds of his children\u2014four young ones in the house now, so many voices in this now-bigger house, the smell of fresh paint filling the home with possibility. The kids fear water, yes, and when a pipe burst last year there were screams and nightmares, but slowly they're growing stronger. For them he has to be strong, and he needs to look forward. He needs to feed them, to hold them close, and he needs to show them that God had a reason for their trials. He tells them that perhaps God, by allowing him to be jailed, saved him from something worse.\n\n\"Everything happens for a reason,\" he tells them. \"You do your duty, you do what's right, and the rest is in God's hands.\"\n\nHe has watched the progress of the rebuilding of the city. The first few years were frustrating, as legislators and planners bickered over money and protocols. New Orleans, his home, needs no speeches, no squabbling, and no politics. It needs new flooring, and new roofing, new windows and doors and stairs.\n\nFor many of his clients, it took time for the insurance money to come through, for the FEMA money to appear, for any number of complications to work themselves out. But now things are moving. The city is rising again. Since Hurricane Katrina, Zeitoun A. Painting Contractor LLC has restored 114 houses to their former states, or improved versions thereof.\n\nZeitoun bought a new van and drives through the city, through Uptown, the Garden District, the French Quarter, Lakeview, the West Bank, Broadmoor, Metairie, Gentilly, the Lower Ninth, Mirabeau Gardens\u2014and every time he sees a home under construction, no matter who's doing it, he smiles. _Build_ , he thinks. _Build, build, build_.\n\nAnd so he makes his rounds, checking in on his crews. They're working on some very good and important projects. Even with a slowing economy, there is much to do.\n\nThere's McDonogh #28, a three-story junior high school on Esplanade. It's been closed since the storm, but it can come back. Zeitoun is fixing the woodwork with caulk and putty, repainting the interiors with medium grey and sage-green and bone-white. That shouldn't take too long. It'll be good to see that school open again.\n\nIt would be easy, he knows, with that building and so many others, to simply tear them down and begin again. As a builder, it certainly is easier starting with a piece of flat, cleared land. But so much is lost that way, far too much is lost. And so for three years of rebuilding he has always asked, first, \"What can be saved?\"\n\nThere's the Leidenheimer Bakery on Simon Bolivar Avenue. The building is a wonderful brick structure, over a hundred years old, and the bakery is still run by the descendants of George Leidenheimer, an immigrant from Germany. Zeitoun was proud to get the job, as he always is with buildings of significance; he hates to see them torn down. The masonry weathered the storm just fine, but the windows and wood need refinishing or replacing. So he and his crew are doing that, and remodeling the inner office, installing some cabinets, painting the vents.\n\nAnd there's the St. Clement of Rome Parish Church on West Esplanade and Richland. The interior woodwork needs priming and refinishing. The exterior sustained some damage, so they'll pressure-wash it, sand and caulk it, and repaint every wall and window. He intends to oversee that project very carefully. He always does when hired to restore any house of worship. He is sure that God is watching the work he and Kathy and his men are doing, so it must be done with great care and even, he tells his crews, with soul.\n\nMore than anything else, Zeitoun is simply happy to be free and in his city. It's the place of his dreams, the place where he was married, where his children were born, where he was given the trust of his neighbors. So every day he gets in his white van, still with its rainbow logo, and makes his way through the city, watching it rise again.\n\nIt was a test, Zeitoun thinks. Who among us could deny that we were tested? But now look at us, he says. Every person is stronger now. Every person who was forgotten by God or country is now louder, more defiant, and more determined. They existed before, and they exist again, in the city of New Orleans and the United States of America. And Abdulrahman Zeitoun existed before, and exists again, in the city of New Orleans and the United States of America. He can only have faith that will never again be forgotten, denied, called by a name other than his own. He must trust, and he must have faith. And so he builds, because what is building, and rebuilding and rebuilding again, but an act of faith? There is no faith like the faith of a builder of homes in coastal Louisiana. And there is no better way to prove to God and neighbor that you were there, that you are there, that you are human, than to build. Who could ever again deny he belonged here? If he needs to restore every home in this city, he will, to prove he is part of this place.\n\nAs he drives through the city during the day and dreams of it at night, his mind vaults into glorious reveries\u2014he envisions this city and this country not just as it was, but better, far better. It can be. Yes, a dark time passed over this land, but now there is something like light. Progress is being made. It's so slow sometimes, so terribly so sometimes, but progress is being made. We have removed the rot, we are strengthening the foundations. There is much work to do, and we all know what needs to be done. We can only do the work, he tells Kathy, and his children, and his crew, his friends, anyone he sees. So let us get up early and stay late, and, brick by brick and block by block, let us get that work done. If he can picture it, it can be. This has been the pattern of his life: ludicrous dreams followed by hours and days and years of work and then a reality surpassing his wildest hopes and expectations.\n\nAnd so why should this be any different?\n\n# THE ZEITOUN FOUNDATION\n\nAll author proceeds from this book go to the Zeitoun Foundation, founded in 2009 by the Zeitoun family, the author, and McSweeney's. Its purpose is to aid in the rebuilding of New Orleans and to promote respect for human rights in the United States and around the world. The Zeitoun Foundation will serve as a grantor of funds generated from this book; the first group of recipients include the following nonprofit organizations.\n\n## REBUILDING TOGETHER\n\nRebuilding Together's Gulf Coast operations have focused on preserving and rehabilitating one thousand houses of low-income homeowners, which were damaged in the wake of Hurricane Katrina and Rita.\n\nwww.rebuildingtogether.org\n\n## THE GREEN PROJECT\n\nThe Green Project obtains and resells building materials salvaged in the New Orleans area. The purpose is to encourage recycling, thereby reducing waste; to enable residents of New Orleans to purchase low-cost materials; and to preserve the architectural history of the area.\n\nwww.thegreenproject.org\n\n## THE LOUISIANA CAPITAL ASSISTANCE CENTER\n\nAfter Hurricane Katrina, the LCAC was a leading force in locating the thousands of inmates who had been displaced, highlighting the plight of the prisoners who had been evacuated into terrible conditions, and securing the release of hundreds of inmates who were wrongfully imprisoned. The LCAC now aims to provide legal representation for defendants in Louisiana who are facing capital punishment, and seeks to address racism in the criminal justice system.\n\nwww.thejusticecenter.org\/lcac\n\n## INNOCENCE PROJECT OF NEW ORLEANS\n\nThis New Orleans\u2013based organization provides legal aid for people who have been wrongfully convicted, and helps them in their transition from incarceration to liberty. They focus on the states where incarceration rates (and rates of wrongful conviction) are highest\u2014Louisiana and Mississippi.\n\nwww.ip-no.org\n\n## MEENA MAGAZINE\n\n_Meena_ (\"port\" in Arabic) is a bilingual literary journal based in the port cities of New Orleans and Alexandria, Egypt. The journal publishes poetry, fiction, essays, travel writing, mixed-genre media, and art. _Meena_ hopes to exist as a port between the Western and Arab worlds by exchanging ideas about culture, language, conflict, and peace through writing and dialogue.\n\nwww.meenamag.com\n\n## THE PORCH SEVENTH WARD  \nCULTURAL ORGANIZATION\n\nAn organization committed to the Seventh Ward in New Orleans, The Porch is a place to come together and share culture and community. The Porch seeks to promote and sustain the cultures of the neighborhood, the city, and the region, and to foster exchange between cultural groups.\n\nwww.ny2no.net\/theporch\n\n## CATHOLIC CHARITIES, ARCHDIOCESE NEW ORLEANS\n\nCatholic Charities works with the entire community of New Orleans to respect the dignity of every human person. They are currently operating eleven community centers in the Greater New Orleans area to help with hurricane recovery. These centers provide case-management services, direct assistance, and other services as needed.\n\nwww.ccano.org\n\n## ISLAMIC RELIEF USA\n\nIslamic Relief strives to alleviate suffering, hunger, illiteracy, and diseases worldwide, without regard to color, race, or creed. In the event of man-made or natural disasters, it aims to provide rapid relief. Working with the United Nations World Food Program (UNWFP) and the Department for International Development, Islamic Relief establishes development projects in needy areas to help tackle poverty at a local level.\n\nwww.irw.org\n\n## THE MUSLIM AMERICAN SOCIETY\n\nThe Muslim American Society (MAS) is a charitable, religious, social, cultural, and educational not-for-profit organization. Its mission is to build an integrated empowerment process for the American Muslim community through civic education, local leadership training, community outreach, and coalition building. MAS also strives to forge positive relationships with other institutions outside of its community, in order to facilitate the protection of civil rights and liberties for American Muslims and all Americans.\n\nwww.masnet.org\n\n## THE NEW ORLEANS INSTITUTE\n\nThe New Orleans Institute is dedicated to engaged citizenry and is determined to cultivate local solutions. This is a networking alliance with a shared interest and commitment to fostering the resilience of New Orleans through innovation.\n\nwww.theneworleansinstitute.org\n\n## THE NEIGHBORHOOD STORYTELLING PROJECT\n\nIn 2004, the Neighborhood Story Project was founded by Rachel Breunlin and Abram Himelstein as a book-making project based in New Orleans, for New Orleanians. The NSP conducts workshops and facilitates the publishing of books by first-time authors in New Orleans, in an effort to tell the story of the city and its citizens.\n\nwww.neighborhoodstoryproject.org\n\n## MUSLIM STUDENT ASSOCIATION\n\nThe MSA is dedicated to developing an understanding of Islam and the Islamic culture among the Tulane University community. We seek to create a sense of awareness of Islam among the Tulane community by increasing their basic knowledge of Islam. We aim to give the Tulane community a firsthand experience with Islam and the Islamic culture.\n\nwww.tulane.edu\/\u223cmsa\/\n\n## THE NEW ORLEANS LENS\n\nThe New Orleans Lens is a nonprofit news-reporting site, dedicated to journalism in New Orleans. The Lens' strength lies in a highly qualified editorial and research staff, as well as a collaborative network of affiliated organizations including the Center for Public Integrity, Project on Government Oversight, and the national Investigative News Network.\n\n<http:\/\/thelensnola.org\/>\n\n## NEW ORLEANS CENTER FOR CREATIVE ARTS\n\nThe New Orleans Center for Creative Arts is a regional, pre-professional arts training center that offers secondary school-age children intensive instruction in dance, media arts, music (classical, jazz, vocal), theatre arts (drama, musical theatre, theatre design), visual arts, and creative writing, while demanding simultaneous excellence.\n\nwww.nocca.com\n\n# ACKNOWLEDGMENTS\n\nTHE ZEITOUN FAMILY WOULD LIKE TO ACKNOWLEDGE:\n\nAhmad Zeton; Mrs. Trufant; Yuko and Ahmaad Alakoum for putting up with us in our darkest hours; Mary Amarouni; Crystal and Keene Kelly; Celeste and Tom Bitchatch; the Callender family; Tom and Luke; Nabil Abukhader; Mohammed Salaam; Rob Florence; and all of those who helped us.\n\nTHE AUTHOR WOULD LIKE TO ACKNOWLEDGE THE WORK OF THE FOLLOWING JOURNALISTS AND RESEARCHERS:\n\nGwen Filosa, Rob Nelson, Bruce Nolan, Emmet Mayer III, Mark Schleifstein, John McCusker, _New Orleans Times-Picayune;_ Dr. Daniel L. Haulman, the Air Force Historical Research Agency; Tech. Sgt. Mark Diamond, the Air Force Medical Services Monthly Newswire; Jenny Carchman, Michelle Ferrari, Stephen Ives, Lindsey Megrue, Amanda Pollak, Mark Samels, _The American Experience;_ Donna Miles, Rudi Williams, the American Forces Press Service; Marina Sideris, Amnesty Working Group; Betty Reid, _Arizona Republic;_ Joseph R. Chenelly, _Army Times;_ Craig Alia, _Army Magazine;_ Lolita C. Baldor, Wendy Benjaminson, Rick Bowmer, Allen G. Breed, Melinda Deslatte, Linda Kleindienst, Marilynn Marchione, Brett Martel, Janet McConnaughey, Kevin McGill, Adam Nossiter, John Solomon, the Associated Press; Kelly Bradley, Lt. Col. Tim Donovan, Larry Sommers, _At Ease Magazine;_ Mickey Noah, _Baptist Press;_ Olenka Frenkiel, BBC; Amy Goodman, _Democracy Now!;_ Brandon L. Garrett, Tania Tetlow, _Duke Law Journal;_ Charlie Savage, _Boston Globe;_ Patrik Jonsson, the _Christian Science Monitor;_ Jamie Wilson, the _Guardian;_ Jason Carroll, Anderson Cooper, Jacqui Jeras, Chris Lawrence, Ed Lavandera, Rob Marciano, Ed Zarrella, Jeanne Meserve, Betty Nguyen, CNN; Tamara Audi, _Detroit Free Press;_ Neil deMause, Steve Rendall, _Extra!;_ Todd Stubing, _Fort Myers News-Press;_ Dave Reynolds, _Inclusion Daily Express;_ Adnan Bounni, Iran Chamber Society; Guy Siebold, _Journal of Political and Military Sociology;_ Stacy Parker Aab, The Katrina Experience Oral History Project; Alan Zarembo, _Los Angeles Times;_ Capt. David Nevers, _Marines Magazine;_ Jeremy Scahill, the _Nation;_ Staff Sgt. Jon Soucy, National Guard Bureau; Daniel P. Brown, Richard D. Knabb, Jamie R. Rhome, National Hurricane Center; John Burnett, Jeff Brady, National Public Radio; Ken Munson, _Nautical Notes;_ Diane E. Dees, _Mother Jones;_ Curtis A. Utz, Naval Historical Center; Ruth Berggren, _New England Journal of Medicine;_ Lou Dolinar, _New York Post;_ David Carr, Melissa Clark, N.R. Kleinfield, Merrill Perlman, Shadi Rahimi, Joseph B. Treaster, Richard W. Stevenson, Alex Berenson, Sewell Chan, Paul von Zielbauer, _New York Times;_ Sarita Sarvate, Pacific News Service; Kevin Callan, paddling.net; Yvonne Haddad, Fariborz Haghshenass, _PolicyWatch;_ Peter Henderson, Michael Christie, Jane Sutton, Reuters; Richard Burgess, _Sea Power Magazine;_ Jordan Flaherty, _Southern Studies: An Interdisciplinary Journal of the South;_ Morris Merrill, _Southern Quarterly;_ Fred Kaplan, _Slate;_ Angie Welling, _Salt Lake City Deseret News;_ Ken Kaye, Robert Nolin, _South Florida Sun-Sentinel;_ Jeff Schogol, _Stars and Stripes;_ Harry Mount, the _Telegraph;_ Amber McIlwain, _Times of London;_ Matthew Van Dusen, _Times of Northwest Indiana;_ Joel Stein, _Time Magazine;_ Anna Mulrine, Dan Gilgoff, _US News and World Report;_ Douglas Brinkley, _Vanity Fair;_ Renae Merle, Guy Gugliotta, Peter Whoriskey, Eugene Robinson, the _Washington Post;_ Michael Pope, Christiana Halsey, _Customs and Border Protection Today;_ the Center for Human Rights and Global Justice; Charles Janda, Chucksphotospot.com; Jordan Flaherty, _ColorLines;_ Eugen Tarnow, PhD, Cogprints.org; Amy Belasco, Steve Bowman, Lawrence Kapp, Department of Defense; Maj. Mark Brady, Capt. Lisa Kopczynski, Sgt. Les Newport, First U.S. Army in the News; Gary Mason, the _Globe and Mail;_ Hugh Hewitt, _The Hugh Hewitt Show;_ The Indy Channel; Indiana University, Bloomington; The Innocence Project; staff, _Killeen Daily Herald;_ Jason Brown, _Lafayette Daily Advertiser;_ Jamie Doward, _London Observer;_ Rosa Brooks, _Los Angeles Times;_ Chris Kelly, _MichelleMalkin.com;_ Michael Robbins, _Military History;_ staff, _Naples Daily News;_ staff, _NGAUS Notes;_ Lt. Col. Deedra Thombleson, National Guard; Erick Studenicka, National Guard Bureau; Navy Office of Information; Carl Quintanilla, Tony Zumbado, NBC News; New Orleans Copwatch; Jayne Huckerby, New York University Center for Human Rights and Global Justice; Gregory Smith MD, Woodhall Stopford MD, _North Carolina Medical Journal;peopleshurricane.org;_ Keith Woods, Poynter Institute; Eric Barr, Taylor Rankin, John Baird, _ThinkQuest;_ David Crossland, _Times of London;_ United States Coast Guard; Marina Sideris, University of California Berkeley Law School; Jerry Seper, the _Washington Times;_ Wrongful-Convictions.blogspot.com; Kelly Leosis, Katherine Yurica, _yuricareport.com; Neworleans.indymedia.org_.\n\nTHE FOLLOWING BOOKS AND REPORTS WERE CRUCIAL TO THE WRITING OF _ZEITOUN:_\n\n_The Great Deluge: Hurricane Katrina, New Orleans, and the Mississippi Gulf Coast_ by Douglas Brinkley (William Morrow, 2006); _Severe and Hazardous Weather_ by Bob Rauber, John Walsh, Donna Charlevoix (Kendall Hunt Publishing, 2005); _On Risk and Disaster: Lessons from Hurricane Katrina_ , edited by Ronald J. Daniels, Donald F. Kettl and Howard Kunreuther (University of Pennsylvania Press, 2006); _Hurricane Katrina: America's Unnatural Disaster_ , by Jeremy I. Levitt and Matthew C. Whitaker (University of Nebraska Press, 2009); _Come Hell or High Water_ by Michael Eric Dyson (Basic Civitas, 2006); _Disaster: Hurricane Katrina and the Failure of Homeland Security_ by Robert Block and Christopher Cooper (Henry Holt Books, 2006); _Down in New Orleans: Reflections from a Drowned City_ by Billy Sothern and Nikki Page (University of California Press, 2007); _The Essential Koran_ , translated and presented by Thomas Cleary (HarperCollins, 1993); _A Modern History of Syria_ by A.L. Tibawi (St. Martin's Press, 1969); _Fifty Years of Modern Syria and Lebanon_ , by George Haddad (Dar-al-Hayat, 1950); _Modern Syria, from Ottoman Rule to Pivotal Role in the Middle East_ , edited by Moshe Ma'oz, Joseph Ginat, and Onn Winckler, (Sussex Academic Press, 1999); _Supporting the Future Total Force_ , by John G. Drew, Kristin F. Lynch, James Masters, Sally Sleeper, and William Williams (RAND, 2007); _By the Numbers: Findings of the Detainee Abuse and Accountability Project_ by Human Rights Watch (Human Rights Watch, 2006); _Irreversible Consequences: Racial Profiling and Lethal Force in the War on Terror_ , by the Center for Human Rights and Global Justice (NYU School of Law, 2006); _Public Safety, Public Spending: Forecasting America's Prison Population 2007\u20132011_ , by the JFA Institute, the Public Safety Performance Project, and the Pew Charitable Trusts (Pew Charitable Trusts, 2007); _Abandoned and Abused: Orleans_ _Parish Prisoners in the Wake of Hurricane Katrina_ , by the National Prison Project of the American Civil Liberties Union, the American Civil Liberties Union of Louisiana, the American Civil Liberties Union Racial Justice Program, Human Rights Watch, the Juvenile Justice Project of Louisiana, the NAACP Legal Defense and Educational Fund, Inc., and Safe Street\/Strong Communities (American Civil Liberties Union and the National Prison Project, 2006); _Enabling Torture: International Law Applicable to State Participation in the Unlawful Activities of Other States_ , by the Center for Human Rights and Global Justice (NYU School of Law, 2006); _Beyond Guantanamo: Transfers to Torture One Year After Rasul v. Bush_ , by the Center for Human Rights and Global Justice (NYU School of Law, 2005); _Louisiana National Guard Timeline of Significant Events, Hurricane Katrina_ , by the Louisiana National Guard (Louisiana National Guard, 2005); _Torture by Proxy: International Law applicable to \"Extraordinary Renditions\"_ by the Association of the Bar of the City of New York and the Center for Human Rights and Global Justice (ABCNY and the NYU School of Law, 2004); _Use of Force: ATF Policy, Training and Review Process Are Comparable to DEA's and FBI's_ , by USGAO (United States General Accounting Office, 1996).\n\nTHE FOLLOWING AGENCIES AND ORGANIZATIONS PROVIDED ESSENTIAL INFORMATION:\n\n44th Medical Brigade Public Affairs; Air National Guard 920 Rescue Wing; American Civil Liberties Union; Blackwater USA; Bureau of Alcohol Tobacco and Firearms; Camp Pendleton Public Affairs; Center for Disease Control; DynCorp International; Defense Logistics Agency Defense Supply Center; Federal Emergency Management Agency; First Army Public Affairs; Fort Hood Public Affairs; Fort Hood Media Relations; Fort Carson Public Affairs; Fourth Infantry Division Public Affairs; Immigration and Customs Enforcement Public Affairs; Louisiana National Guard Public Affairs; Louisiana State Police; NASA; National Guard Association of the United States; National Oceanic and Atmospheric Administration; National Weather Service; National Hurricane Center; Office of the Attorney General; SOPAKCO; State of Michigan Department of Military and Veterans Affairs; State of Wisconsin Department of Military Affairs; Texas National Guard Community Relations; U.S. Army Public Affairs; U.S. Capitol Police; U.S. Department of Homeland Security, Department of Public Affairs; U.S. Marine Corps Public Affairs; U.S. Marshals.\n\nNOTES ABOUT THE QUR'AN QUOTED HEREIN\n\nMany translations of the Qur'an into English exist and many were consulted. The translation quoted in this book is by Laleh Bakhtiar, published in 2007 by Kazi Publications under the title _The Sublime Quran_. As is evidenced in the quotations included in this book, the Qur'an contains very powerful and surpassingly beautiful language, and this English edition reflects that beauty exceedingly well.\n\nAUTHOR NOTES ON PROCESS AND METHODOLOGY\n\nThe process behind this book started in 2005, when, shortly after Hurricane Katrina struck New Orleans, a team of volunteers from Voice of Witness, our series of books that use oral history to illuminate human rights crises, fanned out all over the Southeast to collect testimonies. From Houston to Florida, they interviewed residents and former residents of New Orleans about their lives before, during, and after the storm. The result was _Voices from the Storm_ , edited by Chris Ying and Lola Vollen and published by McSweeney's\/Voice of Witness in 2005. The book featured vivid narratives from dozens of New Orleanians, including Abdulrahman and Kathy Zeitoun. His story stuck with me, and the next time I was in New Orleans, to speak to students at the New Orleans Center for the Creative Arts (a great high school arts program), I visited the Zeitouns. From our first talk, it was clear that there was more to their story than we were able to include in _Voices from the Storm_. And so began an almost-three-year process of interviews and research that went into _Zeitoun_. During that time, I was able to get to know Abdulrahman and Kathy, as well as their beautiful family here and in Syria.\n\nAdditional notes:\n\n  * All events are seen through the eyes of either Abdulrahman or Kathy Zeitoun, so the view of events reflects their recollections. Todd Gambino was also a participant in the writing and fact-checking of this book. All conversations are reconstructed from the memories of the participants.\n\n  * Interviews with Officers Donald Lima and Ralph Gonzales were conducted by the author in 2008.\n\n  * I visited the Elayn Hunt Correctional Center in 2008. It seemed to be a very well-run prison, a progressive and rational place with a keen eye toward rehabilitation and re-entry, and toward giving prisoners the opportunity to advance their educations, whether academic or vocational. And yet Adbulrahman's experience there was not acceptable. I don't intend to denounce the operation of that prison; perhaps the institution was simply overwhelmed after Katrina and fell short of its higher standards.\n\nAUTHOR THANKS\n\nChris Ying and Lola Vollen laid the groundwork for this book and deserve vast thanks for encouraging me to pursue this story further. Billy Sothern, the New Orleans lawyer and author who conducted the initial interviews with Abdulrahman and Kathy Zeitoun for _Voices from the Storm_ , deserves profound thanks. He was a constant guide and mentor during the writing of _Zeitoun_ , and his own book, _Down in New Orleans_ , was both inspiration and roadmap. As deputy director of the Capital Appeals Project, he continues to fight every day in the defense of those left vulnerable to the judicial system's frailties and oversights. Annie Preziosi of the Louisiana Capital Assistance Center provided expert research at crucial junctures. Her colleague at LCAC, Julie Kilborn, was very helpful in providing context for the arrests and processing of prisoners after Katrina. Thanks also go to Pam Metzger at the Tulane University Law School and to Nikki Page, whose hospitality and warmth was appreciated always. Anne Gisleson, extraordinary New Orleans writer and teacher and activist, provided invaluable guidance and encouragement and was an expert reader of the manuscript. The courageous Todd Gambino provided fact-checking and context and important details. Elissa Bassist provided key and voluminous research early on. Yousef Munayyer and Mohammed Khalil provided gentle guidance in Arabic and Islamic matters. Naor Ben-Yehoyada provided expert counsel on the history and practice of _lampara_ fishing. Farah Aldabbagh translated a rare book about Mohammed Zeitoun from Arabic to English in a timely and expert manner. Peter Orner and Stephen Elliott provided surgical notes and deeply appreciated encouragement. Proofing and copyediting was provided by Lindsay Quella, Juliet Litman, Tess Thackara, Emily Stackhouse, and Henry Jones. Thanks to all at McSweeney's\u2014Jordan Bass, Heidi Meredith, Angela Petrella, Eli Horowitz, Mimi Lok, and especially to Andrew Leland, whose early read of the manuscript was crucial. Extraordinary and tenacious fact-checking was also performed by the indefatigable Chris Benz. Michelle Quint, associate editor at McSweeney's, was the day-to-day research director for this book. Her dedication, reliability, intelligence, and efficiency will never be forgotten, as this book would have been impossible without her. And of course life generally would not be possible without my wife Vendela, our children, and my brothers Bill and Toph.\n\nFinally, profound thanks go to the Zeitouns of America, Spain, and Syria. Captain Ahmad Zeton\u2014there are many ways to spell the name\u2014and his family in M\u00e1laga, Spain (Laila, Lutfi, and Antonia) were generous hosts and brought forth crucial memories. Ahmad was not only a champion of this project from the beginning, but also a meticulous record-keeper, and his photos, emails, and calls from before and after the storm were invaluable. Warm thanks and greetings go to the Zeitoun family in Syria, and to Qusay and young Mahmoud in Jableh in particular. The hospitality of all the Zeitouns knew no limits, and the beauty and laughter and warmth permeating every part of their extraordinary clan was inspiring and enriched this book and this author beyond measure. Most of all, thanks go to Abdulrahman and Kathy, and to their remarkable children, for their stunning personal generosity and for their unwavering commitment to the writing of this book. The process of bringing their story to print required a great deal of them, but they fought through unpleasant memories in the hopes that something constructive might come from their days of personal struggle. Their courage knows no bounds, and their faith in family and in this country renews the faith of us all.\nFIRST VINTAGE BOOKS EDITION, JUNE 2010\n\n_Copyright \u00a9 2009 by Dave Eggers_\n\nAll rights reserved. Published in the United States by Vintage Books, a division of Random House, Inc., New York.  \nPublished in Canada by Random House of Canada Limited, Toronto. Originally published in hardcover in the United States by McSweeney's Books, San Francisco, in 2009.\n\nVintage and colophon are registered trademarks of Random House, Inc.\n\nLibrary of Congress Cataloging-in-Publication Data  \nEggers, Dave.  \nZeitoun \/ Dave Eggers.\u20141st Vintage Books ed.  \np. cm.  \nOriginally published: San Francisco : McSweeney's Books, c2009.  \neISBN: 978-0-307-73943-8  \n1. Zeitoun, Abdulrahman, 1957\u2013 2. Zeitoun, Kathy. 3. New Orleans (La.)\u2014Biography. 4. Disaster victims\u2014Louisiana\u2014New Orleans\u2014Biography. 5. Arab Americans\u2014Louisiana\u2014New Orleans\u2014Biography. 6. Hurricane Katrina, 2005\u2014Social aspects\u2014Louisiana\u2014New Orleans. 7. Arab Americans\u2014Social conditions\u2014Louisiana\u2014New Orleans. I. Title.  \nF379.N553Z454 2010  \n305.892\u20327076335\u2014dc22  \n2010000757\n\nwww.vintagebooks.com\n\nv3.0\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":" \nAdvance Praise for\n\n\"When we strive to be somebody, we are actually striving to be somebody else. This somebody else is the root of all our problems. The key to awakening is being who you already are. But as Lama Marut dares to tell us in this delightfully written and wise book, this authentic somebody is nobody at all. Reading this book is easy, and understanding it is liberating. I invite you to do both.\"\n\n\u2014Rabbi Rami Shapiro, author of Perennial Wisdom for the Spiritually Independent\n\n\"In his refreshing and compelling new book, Be Nobody, Lama Marut gives us a road map to living life in the realm of an Everyday Joe in order to accomplish great happiness and connectedness and to begin to offer the very best we can access. He gives us a truly clear and vivid understanding of the present-day dilemma of the drive toward 'I' and the fact that this drive is leading to depression, isolation, and diseased thinking. And then he outlines a way that leads to joy by showing us how to practice a new thought pattern that encourages focus on anything but self. This is an amazingly powerful piece of work from a truly unique and dynamic nobody.\"\n\n\u2014Mary McDonnell, actress\n\n\"In his trademark emphatic and no-nonsense style, Lama Marut provides a much-needed critique of modernity that cuts to the root of every problem we currently face on the planet. Be Nobody exposes our culture of narcissism that precludes personal happiness, social equality, and ecological balance. Rather than taking us from our deluded state of alienated self-absorption to some exalted state of equally misguided self-annihilation, Marut guides us through an inner transformation and re-emergence as awakened altruists contributing to a sustainable future for all.\"\n\n\u2014Dr. Miles Neale, Buddhist psychotherapist and assistant director of the Nalanda Institute for Contemplative Science\n\n\"Here's some help in kicking your ego's butt so that you can create a genuine spiritual life. Instead of endless self-improvement, you're invited to let go of your self. This really is the only way to be happy. Lama Marut is brilliant, a Ch\u00f6gyam Trungpa for new generations mixed with a little Louis C.K.\u2013style humor.\"\n\n\u2014Lisa Selow, life coach and author of A Rebel Chick Mystic's Guide\n\n\"Lama Marut's Be Nobody fiercely examines our preoccupation with the 'I,' revealing how living on the 'Me Plan' can never satisfy the hungry ego. The antidote he offers is truly liberating, not only for oneself but for all sentient beings.\"\n\n\u2014Michael Bernard Beckwith, author of Life Visioning\n\n\"Writing with great sensitivity to the stress we all feel, Lama Marut helps us see that we strive to be valued by trying endlessly to be more and more special. We aim to be somebody, but only find tension and loneliness as we never reach the bar. What good is getting star billing if you never feel like a star? Laying out a clear spiritual alternative, he dares us to become nobody: a state of complete authenticity, where we are present to our lives and joyfully connected to all. This is no mystical pipe dream; the ideas in this book point to something every one of us can do. All of us want to be happy. We owe it to ourselves to become nobody. Put this transformative book by your bed, and read it again and again.\"\n\n\u2014Lindsay Crouse, Academy Award\u2013nominated actress\n\n\"Be Nobody is a great spiritual guide for people of all faiths. Lama Marut's description of our bondage to our egos is both entertaining and sobering. After providing an incisive diagnosis of the human condition, he not only offers an understanding of how to leave suffering behind, but also provides practical and achievable steps for doing so. I am recommending this book to all my friends and parishioners.\"\n\n\u2014Rev. Dr. Brian Baker, dean of Trinity Cathedral, Sacramento, CA\nThank you for downloading this Atria Books eBook.\n\n* * *\n\nJoin our mailing list and get updates on new releases, deals, bonus content and other great books from Atria Books and Simon & Schuster.\n\nCLICK HERE TO SIGN UP\n\nor visit us online to sign up at  \neBookNews.SimonandSchuster.com\n\nThe moment you want to be somebody, you are no longer free.\n\n\u2014Jiddu Krishnamurti\n\n## CONTENTS\n\nEpigraph\n\nPreface: Don't Give Me That Old-Time Religion!\n\nIntroduction: Living in the iEra\n\nPart I:\n\nDesperately Seeking Somebody\n\n1. Sticking Our Faces into Carnival Cutouts\n\n2. What Goes Up Must Come Down\n\nPart II:\n\nMaking a Better Somebody Out of Nobody\n\n3: Clutching at Straws and Chasing Shadows\n\n4: Nobody Makes a Better Somebody Possible\n\nPart III:\n\nLosing the \"Somebody Self\"\n\n5. Being Nobody for Others\n\n6. Going with the Flow\n\nPart IV:\n\nEverybody Is Nobody\n\n7. Living as an Ordinary Joe\n\nAcknowledgments\n\nAppendix: Dropping into Your True Nature\n\nAbout Lama Marut\n\nEndnotes\n\nSelected Bibliography\nThis book is dedicated to Cindy Lee, true companion, partner, muse, and the best friend I could have ever hoped for.\n\n## Preface:  \nDon't Give Me That Old-Time Religion!\n\nTraditions are group efforts to keep the unexpected from happening.\n\nBarbara Tober\n\nA gospel song I was taught in church as a kid advises us not to be all newfangled when it comes to our spiritual life. Instead of getting caught up in the modern world and its trappings, we should just stick with \"that old-time religion\":\n\nGive me that old-time religion\n\nGive me that old-time religion\n\nGive me that old-time religion\n\nIt's good enough for me\n\nWell, it wasn't good enough for me as an adolescent, and it's not good enough for me now either. A religion that isn't relevant to the current conditions under which we live is by definition irrelevant, isn't it?\n\nMy own spiritual life has been shaped by a variety of influences, and I suspect that this is the case for many of us. I was brought up a Christian (my father and grandfather were ordained Baptist ministers), was baptized and steeped in that tradition through many years of religious instruction (including formal graduate study in a divinity school), and to this day have a deep and abiding connection to the Christian faith.\n\nIn addition, for over thirty years of my life I was employed in the academic study of comparative religion with an emphasis on Hinduism, visiting India many times for my research. In the most extended of those sojourns, I made a deep connection to a learned and devout Hindu teacher who helped me not only with my Sanskrit but also with how to live a life guided by spiritual principles. My personal religious sensibilities have been profoundly enhanced by this teacher and by my acquaintance with Hindu Sanskrit classical texts that I have had the opportunity to teach to students in both academic and spiritual contexts over the past three decades. As will be evident to readers of this book, I have integrated the wisdom found in Hindu scriptures like the Upanishads, the Yoga Sutra, the Vijnana Bhairava Tantra, and the Bhagavad Gita into my overall understanding of the spiritual life.\n\nAnd in 1998, I began an intensive study and serious practice of Tibetan Buddhism, eventually taking ordination as a Buddhist monk and teaching the philosophy and training offered in that tradition. I have had a lifelong attraction to the Buddhist tradition and its emphasis on compassionate and mindful living as well as its mind-expanding teachings on the true nature of reality. And upon deeper study I discovered to my delight that in Buddhist texts there are oft-repeated directives encouraging the student to think for him- or herself; to not blindly accept on faith anything that one hasn't tested in practice; and to remain intellectually and spiritually open to what is useful and beneficial no matter where one encounters it. It seems to me that it is a Buddhist dogma to not be overly attached to any particular dogma. If I have correctly understood what is meant by the term \"Buddhist,\" I am proud to identify myself as one.\n\nSo the question of what or who I am when it comes to religion is not entirely clear\u2014even, or especially, to me. Am I a Christian, a Hindu, or a Buddhist? Is it important or even necessary to pick just one? How could I just erase years of experience with any one of these three main influences on my personal spiritual life?\n\nMany readers are probably at least as religiously complicated as I am. So many of us nowadays are religious hybrids, blended composites and combinations of a number of religious and philosophical traditions\u2014spiritual mongrels, if you will. Even those of us who closely relate to one or another of the world's religions have been exposed to and influenced by other religions in ways that are unprecedented in world history.\n\nIn the days of yore, most people lived in closed societies and were more excusably parochial, provincial, and unaware of the whole range of religious and cultural alternatives. Our world is a much bigger and more diverse place. We live in a global community of instantaneous communication and the World Wide Web; we reside in nation-states that are increasingly multicultural and religiously heterogeneous. The containers in which we once kept ourselves are now leaking all over the place.\n\nWe know way more about each other than ever before, and none of us is left unaffected by the mutual influencing and syncretistic blending that's occurring on all kinds of levels. There are significant ramifications of such intermingling when it comes to a spiritual life that isn't futilely trying to stay cloaked in \"that old-time religion.\"\n\nThese days, claiming a religious identification (or refraining from doing so) is an option, not just an unalterable accident of birth. While we may have been born and brought up as one thing or another (or without any religious training at all), we now exercise more choice than ever before about our personal beliefs, identities, and spirituality.\n\nFully 44 percent of Americans currently say they have a religious affiliation different from the one they were born into. No matter which religion our parents or guardians identified with, we spiritual crossbreeds now easily slip out of one category and into another.\n\nAnd in addition to all of us spiritual mongrels, there are increasing numbers who disavow any religious affiliation whatsoever. This trend toward religious nonidentification is growing. One recent study has predicted that organized religion is an endangered species\u2014probably \"set for extinction\"\u2014in no less than nine of the world's developed nations: Australia, Austria, Canada, the Czech Republic, Finland, Ireland, the Netherlands, New Zealand, and Switzerland. Another poll indicates that nearly two-thirds of those living in Great Britain no longer regard themselves as religious.\n\nEven in the United States, a country that is statistically much less disenchanted with institutionalized religion than most of Europe and other parts of the developed world, thirty-three million Americans now claim no formal religious association. According to a recent survey conducted by the Pew Forum on Religion and Public Life, the \"nones\" (\"none of the above,\" the religiously nonaffiliated) are the fastest growing group in America\u2014increasing by 25 percent in just the past five years\u2014and they're the only demographic that is expanding in every state. And the numbers are largest among younger people. According to the poll, 30 percent of the \"older millennials,\" born between 1981 and 1989, are counted among the \"nones\"; among the \"younger millennials\"\u2014those born between 1990 and 1994\u201434 percent are religiously unaffiliated.\n\nNonaffiliation with any particular religion does not necessarily mean a disinterest in living a spiritually oriented life. Sixty-eight percent of the \"nones\" in the United States say they believe in God, while 37 percent describe themselves as \"spiritual\" but not \"religious.\" One in five said that they pray every day. In Canada, according to a Forum Research poll, two-thirds of the population claim to be \"spiritual\" while only one-half say they are \"religious.\" But a quarter of those who say they adhere to \"no religion\" still profess a belief in God.\n\nIn addition to the religiously affiliated, the spiritual mongrels who have been shaped by several traditions, and the \"nones\" who prefer to remain religiously unidentified but spiritually alive, there is another category of those trying to live the good life in today's changed world. We can call them the \"undos.\"I\n\n\"Undos\" are those of us who are trying to break free from the confines of religious labeling without jettisoning the helpful teachings and methods found in those traditions. Being an \"undo\" is not quite the same as being a \"none.\" Divesting oneself of a particular religious designation presumes that you have had one to begin with\u2014that one has been trained in one or another of the world's spiritual traditions. To be an \"undo,\" a person must first have been a Hindu (or a Buddhist, Christian, Jew, Muslim, Sikh, or whatever). But having steeped him- or herself in this or that tradition, the \"undo\" chooses to drop the shell of religious identification in order to try just to be a good human being rather than an upstanding, card-carrying member of any one particular faith.\n\nWhatever the label\u2014affiliated, mongrel, none, or \"undo\"\u2014growing numbers of people are seeking a meaningful existence outside the confines of the traditional religious identities associated with \"that old-time religion.\" In light of such trends, the Dalai Lama recently declared (on his Twitter stream, no less!) that he is \"increasingly convinced that the time has come to find a way of thinking about spirituality and ethics beyond religion altogether.\" In his recent book Beyond Religion: Ethics for a Whole World, the Dalai Lama outlines a program for how to live the good life that presumes \"religion alone is no longer adequate\" for the task:\n\nOne reason for this is that many people in the world no longer follow any particular religion. Another reason is that, as the peoples of the world become ever more closely interconnected in an age of globalization and in multicultural societies, ethics based on any one religion would only appeal to some of us; it would not be meaningful for all. . . . What we need today is an approach to ethics which makes no recourse to religion and can be equally acceptable to those with faith and those without: a secular ethics.\n\nLiving an ethical life\u2014a life of selflessness rather than unbridled egoism, of integration and interconnection rather than alienation and myopic narcissism\u2014is not just for those who choose to follow one or another of the established religions. It is the key to true happiness for any individual, and the foundation for creating a better world. For \"when you have 'isms,' \" as Lama Surya Das once said to me, \"you have schisms.\"\n\nToo often, however, the identification with one or another of the institutionalized religions has become just another excuse to rehearse the need to be somebody in the ego's never-ending appetite for self-aggrandizement. When, in truth, the founders of the different religions of humankind become founders only retroactively. They weren't teaching \"isms,\" they were only conveying their understanding of life, of what is.\n\nAnd if there's one thing we know about the great spiritual exemplars of history, it's that they were humble. We don't admire and canonize people who pose as self-important and superior. There is no \"Saint Barry the Arrogant\" or \"Saint Tricia the Pompous.\" Our paragons of the past, as well as the present, are those who seem truly willing to be nobody, to be the servants, not the masters, of others.\n\nThe point is not to be a Buddhist but to learn how to become a Buddha; not just to identify with the label \"Christian\" but to live a Christlike life; not simply to join a religion as a way to strengthen one's sense of self but to actually live a good life, a life characterized by egoless concern for others.\n\n\"I am not a Hindu, nor a Muslim am I!\" declared the fifteenth-century Indian mystic Kabir. \"I am this body, a play of five elements; a drama of the spirit, dancing with joy and sorrow.\" Saint Paul similarly asserted in Galatians, \"There is neither Jew nor Greek, slave nor free, male nor female, for you are all one in Christ Jesus.\" The Buddha, it is said, \"did not teach any religion at all.\"II The practice of any spiritual path\u2014whether or not it is designated as such by one or another of the usual trademarks\u2014should lead not toward the elevation of the ego but rather to the self-negation and destruction of vanity that's entailed in being nobody.\n\nWhat? Be nobody? I've spent my whole life trying not to be just a nobody!\n\nBefore you throw this book off the nearest bridge, let's be clear about our terms. First off, there is a difference between the egoistic \"somebody self\" who regards itself as worthless\u2014a nothing, a complete zilch\u2014and being nobody. The latter does not refer to our sense of personal, individual identity that can and should be improved\u2014especially if it is insistent on its worthlessness. Somebody who thinks they're a nobody is self-consciously defining themselves as such, whereas somebody who has become nobody is unselfconsciously absorbed in something much greater.\n\n\"Nobody,\" as we use the term here, refers to our deepest nature, our \"true self,\" which is ever-present and in no need of improvement. It is our highest source of joy and strength, the eternal reservoir of peace and contentment to which we repair in order to silence the persistent demands and complaints of the insatiable ego.\n\nLetting go of our preoccupation with being important and significant will not be easy. Laboring at being somebody for so long digs deep ruts of habit, and some ingrained part of us will surely resist the required \"ego-ectomy.\" But there's a great relief in dropping the ego's restrictive inhibitions and demands for affirmation and magnification. We know this instinctually, and we crave such relief. Our deepest need is to identify not with something small and particular but with that which is greater, universal, and transcendent.\n\nWith the rise and vapidity of social networking and \"reality\" television, the veneration of the ego, celebrity, and instant fame, and the closed-minded arrogance of religious fundamentalism and fanaticism, the questions revolving around the nexus of spirituality and identity have never been more pressing, even as the quest for authenticity and genuine happiness remains perennial.\n\nWe all have the capability to be completely self-possessed and truly happy rather than neurotically self-obsessed and continuously discontented. We all have the potential to be the ocean and not just a wave, the clear blue sky and not merely a cloud passing through, the silence and not some particular name or label.\n\nSo before you burn this book or toss it in the can\u2014This is complete rubbish! Nonsense! I really am somebody, and the meaning of life is to be more of a somebody, not less!\u2014give that \"somebody self\" a bit of a rest and see if there isn't something to all this. If we lay aside our knee-jerk resistance, we'll soon realize that the happiness and self-satisfaction we all seek cannot be found through perpetually attempting to supersize our insatiable egos.\n\nThey say that nobody's perfect.\n\nSo why not be nobody?\n\n#### Notes:\n\nI. My use of the term \"undo\" is inspired by Swami Satchidananda, who writes the following in his book Beyond Words: \"People often ask me, 'What religion are you? You talk about the Bible, Koran, Torah. Are you a Hindu?' I say, 'I am not a Catholic, a Buddhist, or a Hindu, but an Undo. My religion is Undoism. We have done enough damage. We have to stop doing any more and simply undo the damage we have already done.' \" (Yogaville, CA: Integral Yoga Publications, 1977), 85.\n\nII. In chapter 13 of the world's oldest printed book, the Diamond Cutter Sutra, the Buddha asks one of his disciples, Subhuti, this provocative question: \"What do you think, Subhuti? Has the Buddha taught any religion at all?\" We imagine that good old Subhuti might very well have suspected this was some sort of joke, maybe a trick question. (What the hell, man? Why are you asking me this? What else have you been doing for all these years here in northern India except for teaching us religion? You weren't instructing us in better agricultural methods or how to yodel, now were you?) Instead, Subhuti gives the right answer: \"No, Lord. The Buddha has not taught any religion at all.\" In the passage cited here, the word I've rendered as \"religion\" is dharma\u2014admittedly not exact, but probably as close to our concept of \"religion\" as one gets in the Sanskrit texts. A very similar assertion is found in Nagarjuna's Root Verses on the Middle Way: \"Peace is the pacification of all perception and all conceptualization. No religion (dharma) whatsoever was ever taught by the Buddha.\" (24\u201325).\n\n## Introduction: Living in the iEra\n\nHumility does not mean thinking less of yourself than of other people, nor does it mean having a low opinion of your own gifts. It means freedom from thinking about yourself at all.\n\n\u2014\u2014William Temple\n\nWe're all desperately trying to be somebody. No one wants to be a loser, a small fry, a big zero, a washout, a nonentity. Nobody, it seems, wants to be just a nobody.\n\nWe're all en masse, and in pretty much the same ways, struggling to be unique individuals. This obsessive quest for distinctive identity drives us all equally, for we all believe that happiness and fulfillment will come through distinguishing ourselves, through being \"special.\" Our contemporary culture of consumerism, materialism, narcissism, and the worship of fame encourages the idea that we will be happy only when we become exceptional.\n\nBut maybe we've got it wrong\u2014exactly wrong.\n\nMaybe our deepest and most authentic happiness will be found only when we finally lay down this heavy burden of trying to be a somebody, of perpetual ego-enhancement and compulsive self-consciousness. Perhaps it is precisely in a state of egolessness, in an utter lack of self-preoccupation, that we will actually become nobody and thereby access something much larger, much more amorphous and less exclusive.\n\nMaybe true fulfillment in life requires an emptying, not a filling.\n\n### FROM THE \"ME DECADE\" TO THE \"IERA\"\n\nSelfishness and self-indulgence have always been with us. For thousands of years, the sacred texts of the world's great religious traditions have warned us of the danger of inordinate preoccupation with ourselves, just as they have also provided the most potent tools we have for overcoming it.\n\nBut arguably, over the past few decades, at least in the so-called developed nations, we've seen a dramatic rise in\u2014and a cultural validation of\u2014an all-too-human tendency toward self-indulgence. Now more than ever before, we seem to be increasingly preoccupied with \"me\"\u2014so much so that it seems no exaggeration to describe the whole zeitgeist as an obsession with the self. This excessive self-concern, now pervading virtually every aspect of our lives, is an example\u2014perhaps even the most salient example\u2014of a real \"First World problem.\"\n\nMore than thirty-five years ago, journalist Tom Wolfe dubbed the seventies the \"Me Decade.\" The social and political concerns and upheaval of the sixties had given way to a culture of individual self-centeredness. And in 1979\u2014at the tail end of this decade of self-preoccupation\u2014Christopher Lasch published The Culture of Narcissism, a scathing critique of \"the culture of competitive individualism, which in its decadence has carried the logic of individualism to the extreme of a war of all against all, the pursuit of happiness to the dead end of a narcissistic preoccupation with the self.\" Lasch's book remains one of the most accurate portraits of the world we still inhabit.\n\nLasch argues that every age produces a typical personality structure that accords with that particular society's characteristic patterns. \"Every society reproduces its culture\u2014its norms, its underlying assumptions, its modes of organizing experience\u2014in the form of personality.\" And the personality definitive of our time and culture, Lasch identified as \"narcissistic\":\n\nNarcissism appears realistically to represent the best way of coping with the tensions and anxieties of modern life, and the prevailing social conditions therefore tend to bring out narcissistic traits that are present, in varying degrees, in everyone.\n\nSuch traits revolve around an all-encompassing fixation on the self:\n\n  The insatiable greed, extravagance, sense of entitlement, and demand for immediate gratification that are the hallmarks of rampant consumerism\n\n  The end of the work ethic and its transformation into an ethic of leisure and hedonismI\n\n  The short-sighted exploitation of resources, personal and shared, without regard for future consequences or posterity\n\n  The total dependence on others for validation of one's self-esteem\n\n  The cult of celebrity and our vicarious fascination with the glamorous \"lives of the rich and famous\"\n\n  The \"culture of spectacle\" and entertainment that has infected just about everything, from politics to sports to religion\n\nThese defining trends, already recognizable in the late 1970s, have been magnified and multiplied in the years since. The culture of narcissism has mutated and grown in all kinds of ways. Among its many other expressions, it now saturates every aspect of popular culture.\n\nWe watch television shows and YouTube videos that revolve around the ennoblement of ordinary people into the suddenly famous: American Idol, The Voice, and the whole array of so-called reality shows on television; or viral YouTube footage that places a previously unknown talent into instant stardom (think Justin Bieber). We bob our heads to the lyrics of popular songs, many of which revolve around how totally awesome the surrogate singer is, not to mention the products he or she wears, drives, and consumes. We read magazines endowed with such revealing titles as Self (as if we need to be coaxed into thinking about ourselves even more than we already do!).\n\nThe narcissistic worldview informs the way we view politics as a popularity contest or \"race.\" It transforms news into another \"show\" to entertain us. Journalism today often centers far more on the journalist than it does on the subject matter of the report.\n\nAnd, of course, many advertisers shamelessly exploit our narcissism when creating our desire for cool new products: iPhones, iPads, iPods\u2014all the \"i\" gadgets pitched to the \"I\" and its insatiable hunger for attention.\n\nIt is also predominantly the neediness of the self, and not really an interest in others, that is reflected in our present addiction to nonstop communication. There are now 3.14 billion email accounts worldwide, from which we transmit millions of emails each day. We call each other all the time; we send each other nearly 200,000 text messages every second from the over six billion mobile phone subscriptions worldwide; and half a billion of us worldwide have Twitter accounts.\n\nAll of this emailing, calling, messaging, and tweeting is not so much to \"reach out and touch somebody,\" as a phone company slogan once had it. It is mostly about reaching out so that others will acknowledge and affirm us.\n\nAnd then there's the exponential increase in usage of the social networks, Facebook being the behemoth of them all, with well over one billion participants, or nearly 20 percent of all the earth's inhabitants. With Facebook, it's all about the thumbs-up \"likes,\" isn't it?\n\nDo you like what I just said? Do you like this photo of my cat?\n\nAnd beneath it all, the real question:\n\nDo you like me?\n\nSocial networks are amazing communication tools that can be (and occasionally are) employed for very beneficial purposes. Unfortunately, most often the postings are of the narcissistic order, some more blatant than others. It's sad, but it's also typical of our self-possessed times, staring at our monitors, that we peg our self-worth on how many Facebook friends give us a thumbs-up, with our Instagram hearts throbbing for more notches on the proverbial post. Like Narcissus, we are enamored of our own reflections in the (now digitized) mirror. When will we realize that we'll never get enough thumbs-up to satisfy the ego, no matter how many photos we share, no matter how many witticisms and observations on life we contribute to the Web's global conversation?\n\nFacebook doesn't have a \"don't like\" option, and that's definitely not an oversight. It's only the \"likes\" that any of us is really interested in. But it's disingenuous to think that the \"somebody self\" will ever feel like \"somebody enough\" by resorting to methods like this.\n\n\u2022 \u2022 \u2022\n\nYes, the \"Me Decade\" has stretched out into what I call the \"iEra,\" an epoch not just dominated by the glut of information but also by the magnification of the \"I\" who is situated at the nexus of this flurry of communication. But while we have been encouraged to maintain perpetual self-absorption and are inundated with \"iProducts\" and \"iMedia,\" the \"iEra\" can never wholly satisfy the \"I\" it ceaselessly entices. We remain unhappy and dissatisfied, now more than ever before.\n\nIn light of this unprecedented exaltation of the ego and its insatiable need to be acknowledged, fulfilled, pampered, and \"liked,\" it's worth reminding ourselves: There is not a single authentic spiritual tradition that enjoins us to be more self-preoccupied, more full of ourselves, or more narcissistic than we already are. When it comes to achieving happiness in life, obsession with the self has traditionally been identified as the problem, not the solution.\n\nAs C. S. Lewis wrote way back in 1952, \"Men have differed as regards what people you ought to be unselfish to\u2014whether it was only your own family, or your fellow countrymen, or every one. But they have always agreed that you ought not to put yourself first. Selfishness has never been admired.\"\n\nUntil now, perhaps\u2014and much to our detriment.\n\n### PROSPERITY, NARCISSISM, AND PANDEMIC DEPRESSION\n\nIs it just coincidental that, with the narcissism and self-obsession so enshrined in our society, we're simultaneously witnessing an equally breathtaking increase in the rate of mental illness?\n\nTake depression as just one example. Depression is a debilitating disease\u2014I know! I was hospitalized with a clinical case of depression when I was in my early thirties. I was a complete mess, incapacitated by the inner voice that repeatedly told me I was worthless and that there was nothing I could do to change that. And even run-of-the-mill self-esteem problems, as most everyone can attest, are no picnic in the park.\n\nThe statistics tracking our current condition are alarming: The US Department of Health estimates that over twenty million Americans currently suffer from depression. Another source claims that 15.7 percent of the population is depressed. Prescriptions for antidepressants have skyrocketed, rising 400 percent over the past twenty years, with more than one out of ten Americans over the age of twelve now taking these medications. In many places, depression has now become one of the leading causes of absenteeism from work.\n\nIt is not an exaggeration to say that depression has become pandemic. The World Health Organization has predicted that by 2020 it will be the second most fatal illness, trumped only by heart disease. Perhaps most shockingly, depression is increasing at astounding rates among young people. In the last thirty years, the United States has seen a 1,000 percent increase in the disease among adolescents.\n\nAnd it's not accidental that the precipitous rise in depression has occurred concurrently with two other modern trends, which themselves are interrelated: the dramatic increase in material prosperity in the developed nations, and the parallel obsession with the self, which consumerism encourages, aggravates, and excites.\n\n\u2022 \u2022 \u2022\n\nThe rates of depression\u2014as well as associated ailments like anxiety and stress, and mental illnesses such as bipolar disorder\u2014have risen precisely in those places where material prosperity has also substantially increased. In little more than a generation, we have gone from a society in which expensive consumer goods, once only available to the elite, are now readily purchasable by the masses: cars (now regularly equipped with cameras, computers, and talking GPS), televisions (now, like the movies, in realistic high-definition or 3-D), telephones (they've gotten so \"smart\"!), and computers (formerly only possessions of the government and large research universities, now standard issue, in constantly updated better, faster, and more compact versions). And leisure activities formerly reserved for the mega-rich\u2014including exotic holidays now made possible by nearly universal access to air travel\u2014are currently enjoyed by most of us commoners.\n\nYou can't afford to be depressed if you're just trying to stay alive. Depression is itself a kind of luxury good, available only to those for whom the material necessities of life are a given. It may not only be one of the entitlements of the economically privileged but also one of the entailments.\n\nIn the post\u2013World War II era, we were promised happiness through acquiring and consuming, and for sixty-plus years now we've dutifully been acquiring and consuming. We all got cashed up and started amassing all kinds of stuff. We began buying ovens and refrigerators even before they became self-cleaning and self-defrosting. We've obediently purchased pretty much everything they've brought into the marketplace, from transistor radios (remember those?) to iPods; from clunky black-and-white televisions to the sleek fifty-two-inch plasma flat-screens; from pocket calculators to handheld supercomputers.\n\nMaybe by now it has dawned on us that we've gotten everything they promised us and much, much more. And isn't it just as obvious that desires are being created and implanted in order to get us to buy more?\n\nYeah, so you already have the big black iPod, but now we've come up with this white itsy-bitsy model! Last year's car? It may still run fine, but it's so outdated!\n\nEither we got everything and are still not satisfied, or we had our expectations raised so high that we feel it's our right to have everything and then, when we don't get something, we feel cheated. In either case, since we've placed all our hopes for happiness on self-fulfillment through consumerism, when it doesn't bring us what we expected, well, then there's a big crash.\n\nOnce we have staked our claim on owning everything, we are left with not much of anything when it comes to inner peace and contentment.\n\n### IT'S NOT SELF-HELP IF IT'S ALL ABOUT YOU\n\nIt seems quite likely that many of us feel so bad not only because we are encouraged, at every turn, to remain dissatisfied (so we will buy more) but also because of an insistence that we continually brood about how we're feeling. We're all constantly keeping our fingers on our own pulse:\n\nAm I OK? Are my needs being met? Am I recognized and appreciated enough? Am I somebody enough yet?\n\nThis obsession with the self emanates not only from egocentrism but also from deep insecurity. There's a dark side to the culture of narcissism\u2014in fact, maybe there's only a dark side. According to the ancient texts, as we shall see in chapter 2, one of the karmic causes of depression is an overweening interest in oneself at the expense of thinking of others. In a time and place where \"it's all about me\"\u2014where the promotion of the first-person pronoun demands a \"me first\" attitude\u2014it's no wonder that we're plunging into depression in unparalleled numbers.\n\nThe self, as we'll see below, is both our best friend and our worst enemy. And it's only the \"best friend self\" that can save us from our own self-destructive tendencies; it's only by improving ourselves that we'll feel better about ourselves.\n\nTrivializing the pain and suffering that is associated with the mental afflictions brought on by the \"somebody-self\" mentality is neither compassionate nor fair. But neither is offering panaceas that don't get at the real root of the problem or, worse, aggravate it by promoting as the cure that which is in fact the cause. After all, there are effective and ineffective methods of self-improvement and self-help.\n\nIt's not self-help if it's all about you. It's not genuinely self-serving to live only in the service of the ego instead of in the service of others. It's only through cultivating real humility and an unselfish spirit, and not through indulging in yet more self-absorption, that a healthy and deeply felt self-esteem can emerge.\n\nIt's important that we not mistake humility for self-abasement or confuse depression with self-forgetfulness. An individual with low self-esteem who feels like a \"real nobody\" is not actually being nobody as we'll be using the phrase in this book. Rather he or she is somebody posing as a nobody\u2014and that's a very different thing.\n\nThere's a kind of perverse pride in the \"somebody self\" who feels special and exceptional in feeling so bad. And if we imagine that we can help ourselves through more, and not less, self-centeredness\u2014and that includes obsessing about how lousy we feel all the time\u2014our efforts to improve our self-image will inevitably backfire.\n\nAs stated in the preface, there is a difference between the egoistic \"somebody self\" who regards itself as worthless\u2014a nothing, a complete zilch\u2014and being nobody. Our limited, personalized, and individual self\u2014which may regard itself with healthy self-esteem or unhealthy self-debasement\u2014is distinct from the unlimited, shared, and universal \"nobody self.\" Identifying with the latter is quite different from identifying with something contemptible. \"Nobody\" refers to our ever-present \"true self,\" our greatest source of joy and strength, the eternal reservoir of peace and contentment to which we repair in order to silence the persistent demands and complaints of the insatiable ego.\n\nConsider this: We all know that it is in those moments when we completely lose ourselves\u2014engrossed in a good book or movie, engaged in an all-consuming task or hobby, or immersed in our child's or lover's gaze\u2014that we are truly happy. These experiences point to something extremely important: Our greatest joy comes when we vacate ourselves and give ourselves over to something or someone else. It is when we manage to \"stand outside of ourselves\" (exstasis) that we experience ecstasy.\n\nTrue and deeply felt self-esteem comes not through the exhausting quest for more and more ego inflation. It comes only when the ego and its endless demands are quieted and quenched, when the lower self is emptied and the fullness and plentitude of the Higher Self arise.\n\nIt is only when we stop narrating the play-by-play of our lives and actually start living in an unmediated and direct way that we become really present and fully engaged. It is only when that little voice inside our head finally shuts up that we become wholly assimilated with what's actually happening, and become truly happy.\n\nIt is important to have a good, healthy sense of self-worth, and the point of being nobody is certainly not to become servile, a doormat on which others can trample. But thinking that we will feel fulfilled only if we become more special than others leads to an increase, not a diminishing, of anxiety and dissatisfaction.\n\nWanting to be somebody unique\u2014or somehow \"more unique than others\"\u2014is actually quite common: there's nothing special about wanting to be special. But it is this very drive for radical individuality and superiority that keeps us feeling isolated and alone. In the end, the willingness to let go and be nobody is what's really extraordinary, and it is the only means for real connection with others and communion with what is real.\n\n\u2022 \u2022 \u2022\n\nAs the successor to A Spiritual Renegade's Guide to the Good Life (Beyond Words, 2012), Be Nobody takes the quest for real happiness into new territory. As with its predecessor, this book draws upon the universal truths of the world's venerable religious and philosophical traditions and distills them into an accessible, practical handbook for finding happiness and fulfillment in our modern, everyday lives. The principles may be ancient, but the presentation is up-to-the-minute.\n\nIt is a spiritual truism that only by loosening our grip on the lower, egoistic self will we discover our real potential. Be Nobody maps out this journey from egoism, selfishness, and the obsession with individual identity to the spaciousness and freedom of abiding in one's true and authentic nature. Such a goal\u2014living one's life fully and happily in the here and now\u2014is not just for the spiritual elite or the mystic but is achievable by anyone (\"religious,\" \"spiritual,\" \"secular humanist,\" or \"none of the above\") who understands and implements the right ideas and practices.\n\nThe desirability of such self-transcendence has been recognized for millennia by the world's spiritual traditions. The mystics have all encountered this blessed state, and acquiring a deep familiarity with it on a permanent basis seems to be what is meant by the Eastern terms satori, samadhi, nirvana, moksha, mukti, and so on.\n\nIn Christianity, too, one finds the concept of kenosis (from the Greek word for emptiness)\u2014the \"self-emptying\" of one's own ego in order to become entirely receptive to the divine will. As the great theologian of the last century, C. S. Lewis, writes in Mere Christianity,\n\nThe terrible thing, the almost impossible thing, is to hand over your whole self\u2014all your wishes and precautions\u2014to Christ. But it is far easier than what we are all trying to do instead. For what we are trying to do is to remain what we call \"ourselves\" . . .\n\nThe goal of a spiritual life is to bring true happiness to the practitioner. To that end, the purpose of spiritual cultivation is not to learn to become better than others, but rather to become better for them. The religious traditions, as opposed to the modern secular sensibility of narcissism, consumerism, and greed, have always recognized that the inflation of the egoistic self is not the solution; rather, it is the problem.\n\nBe Nobody unfolds in four sections:\n\nIn part 1, \"Desperately Seeking Somebody,\" we review one of the main sources of stress and anxiety in our lives: the interminable search for personal identity in what are only temporary and ever-shifting roles. We are forever trying to find some stable self in the guises we assume: \"I am a father\/mother\/son\/daughter\/friend\/lawyer\/doctor\/teacher\/surfer\/blogger\/Christian\/Buddhist\/secular humanist,\" and so on. Whether these roles are chosen by us or given to us to play, when we wholly identify with one or another of this cast of characters, we lose touch with our deeper, changeless nature. And when we take excessive pride in one or another of these individual or group identities, we not only separate ourselves from those who are not like us, we also imagine we're superior to them\u2014and by doing so, set ourselves up for a big fall.\n\nPart 2, \"Making a Better Somebody Out of Nobody,\" begins with a \"Where's Waldo?\" search for the self we are so sure we have\u2014a quest that leaves us clutching at straws and chasing shadows. We are not who we think we are, but by the same token we are nothing other than who we think we are. And this realization is the key to true self-improvement: the development of a better self-conception. Here we learn how karma really works to upgrade the \"somebody self\" into a happier, more self-satisfied model. And we also learn that it is by changing our sense of who we are that we change the world around us.\n\nPart 3 is entitled \"Losing the 'Somebody Self,' \" and in this section we explore the joy we feel when we drop our inner narratives and self-conscious facades and truly experience life as it is. We are happiest when we lose ourselves\u2014in empathetic love and compassion for others and in really \"getting into the zone\" when we are fully engaged in an activity with mindful unselfconsciousness. It is in these moments of self-transcendence that we find the real heart and soul of what it means to be alive.\n\nWe conclude with a return to the pressing question of self-identity in part 4, \"Everybody Is Nobody.\" Who or what is this \"nobody self\" that lies at the base of our being and that all of us somebodies universally share? And how can we live in a way that integrates more of our true nature into our daily lives? Posing less as a \"special somebody\" and being more of just an \"Ordinary Joe\" infuses our individual existence with more humility, more of a sense of connection to the world and the people in it, and much more true and abiding contentment and joy.\n\nEach chapter ends with an \"Action Plan\" exercise to help put this all into practice and further incorporate what we've talked about into our daily lives. It's one thing to read about how to live a happier, more fulfilling, more satisfying life. It's another to actually start doing it. It doesn't take much to make a significant change. But it does require at least some modification of our old patterns of thought and action\u2014old habits that, if we're honest with ourselves, have not really worked out the way we'd hoped.\n\nCollected at the end of the book in a section called \"Dropping into Your True Nature,\" you'll find very simple and brief meditations you can do whenever you have a free minute or two in the day. They are samplings from 112 such meditations found in a rather astonishing eighth- or ninth-century ad Indian text called the Vijnana Bhairava Tantra, \"Methods for Attaining the Consciousness of the Divine.\" The really remarkable thing about the techniques prescribed in this text is how mundane they seem. According to this ancient scripture, dropping into our true nature and communing with our Higher Self is way easier than we might think!\n\n\u2022 \u2022 \u2022\n\nLiberation from the anxiety of always feeling that you have to be \"somebody\" is found only in true selflessness and freedom from the ego's restrictions, where solace is found in relaxing into life rather than trying endlessly to micromanage it for one's own selfish ends. The following pages offer instruction for attaining such liberation from the lower self without having to seclude oneself in a monastery or retire to a cave in the Himalayas. This book is meant to challenge you to incite the biggest revolution of all: the overthrow of the self-centeredness and self-consciousness that are the root causes of our dissatisfaction, and the embrace of our true potential and source of our real happiness.\n\nHappiness is ours for the taking, but it cannot be achieved without doing the hard work of letting go of old habits of thinking and acting and plunging into the new and untried.\n\n#### Notes:\n\nI. This trait of the \"culture of narcissism\" has been coupled with, rather than superseded by, a \"cult of busyness\" that we'll discuss in chapter 7.\nI'm nobody! Who are you?\n\nAre you nobody, too?\n\nThen there's a pair of us\u2014don't tell!\n\nThey'd banish us\u2014you know!\n\nHow dreary to be somebody!\n\nHow public like a frog\n\nTo tell one's name the livelong day\n\nTo an admiring bog!\n\n\u2014\u2014Emily Dickinson\n\n## 1\n\n## Sticking Our Faces into Carnival Cutouts\n\nIt is possible to move through the drama of our lives without believing so earnestly in the character that we play. That we take ourselves so seriously, that we are so absurdly important in our own minds, is a problem for us.\n\n\u2014\u2014Pema Ch\u00f6dr\u00f6n\n\nIt's a funny thing how we adults so rarely stop to ponder the big questions in life: What's the meaning of it all? Is there a God? Why do bad things happen to good people, and vice versa? And just where did I put my car keys?\n\nYoung people in their teens and early twenties, as they are entering into adulthood, tend to pose and chew on these queries quite a bit. But apart from professional philosophers and those in the throes of a midlife crisis, we grown-ups get too busy with our families, professions, and ongoing responsibilities to stop and reflect much on these really important puzzles (except maybe for the location of the car keys).\n\nAnd of all the great mysteries, there's one that surely must count as the most pressing, persistent, and perplexing:\n\nWho am I?\n\n\"Know thyself,\" said Socrates, succinctly summing up the biggest of all life's challenges. Sounds good . . . and sounds a lot easier than it turns out to be.\n\nAlthough we spend the preponderance of each day, every day, preoccupied with and enamored of the self, we nevertheless are perpetually confused and uncertain as to who we are so fascinated by. \"What we are looking for,\" observed Saint Francis, \"is what is looking.\" But when we try to catch hold of this elusive self, it seems to evaporate into thin air.\n\nKnowing oneself seems to be an itch we can't quite scratch. And just like any unreachable itch, it's really driving us crazy.\n\nWhile there are lots of conundrums in life, genuine and deep self-knowledge is perhaps the biggest mystery of all\u2014as well as our biggest obsession. We instinctually feel that we must be somebody, but we can't quite put our finger on who that somebody might be. We are aware that we are aware, but we're a bit clueless as to exactly who it is that is aware.\n\nOr, as Alan Watts has cleverly put it in limerick form,\n\nThere once was a man who said, though\n\nIt seems that I know that I know,\n\nWhat I'd like to see,\n\nIs the I that knows me,\n\nWhen I know that I know that I know.\n\nPerhaps because locating the true self\u2014here depicted as the self that \"knows that I know that I know\"\u2014has proven to be so difficult, we gravitate to forged imitations of the real article in the hope that they might suffice. Because self-discovery turns out to be so perplexing, we attempt instead a self-fabrication. We create a character for ourselves and then elevate it\u2014temporarily, at least\u2014to the status of genuine identity.\n\nLike boardwalk tourists poking our faces in the two-dimensional carnival cutouts depicting the muscle man and bathing beauty, we are forever trying to find some authentic self in the multitudinous, temporary, and ever-changing roles we assume in life. We clutch at straws, claiming to actually be somebody to avoid the free fall that we fear is entailed in being nobody.\n\nWe find ourselves in relationships with others and then glom on to such guises as our true identity (\"I am a father\/mother\/son\/daughter\/friend\/lover\/husband\/wife,\" and so on). Or we identify with our jobs and professions (\"I am a carpenter\/lawyer\/doctor\/teacher,\" and so on). Or we earn degrees, certificates, and titles, and present them as our true identity (\"I am a licensed mechanic\/certified yoga instructor\/PhD\").\n\nWe have our hobbies and leisure pursuits (\"I am a surfer\/camper\/blogger\/roller blader\/stamp collector\") and our racial, religious, economic, and national personae (\"I am white\/middle class\/Christian\/American\"). We create online avatars or Facebook identities in the hope that a virtual persona will suffice for our self-image. We even, in a true act of desperation, identify ourselves with our past traumas (\"I am a recovering survivor of alcoholism\/drug addiction\/childhood abuse\/divorce\") or current feelings (\"I am angry\/happy\/jealous\/depressed\").\n\nWe try to find ourselves through these identifications, a word that derives from the Latin term \"to make the same.\" We make a role \"the same\" as the player of the role, or constitute the experiencer as \"the same\" as the experience the experiencer experiences.I\n\nBut who is the \"I\" that we at different times assert is one or another (or the sum total of all) of these guises? Who's the person that takes on all these personae? Who is it that's sticking his or her head into each of these two-dimensional cutouts?\n\n\"All the world's a stage,\" Shakespeare said, \"and all the men and women merely players. They have their exits and their entrances, and one man in his time plays many parts.\" These various roles are sometimes chosen and sometimes given to us to enact, but when we wholly identify with one player or another in this revolving cast of characters\u2014doing our best to keep up with the necessarily frequent costume changes\u2014we set ourselves up for confusion, dissatisfaction, and frustration. We are confused about which one of the multiple roles truly identifies us; we are dissatisfied by the attempt to make any one of these parts truly fulfill us; and we are frustrated by the limitations inherent in each and every one of these personae.\n\nBewildering when you actually think about it, right? All these different versions of \"me\"!\n\nA character played by Lily Tomlin in her one-woman show, The Search for Signs of Intelligent Life in the Universe, voices what may be a common sentiment: \"All my life, I've always wanted to be somebody, but I see now I should have been more specific.\"\n\nMistaking the authentic self for what are just multiple, transient, and conditional guises\u2014creating at best a fractured and confused sense of identity\u2014we are diverted from the quest to uncover our deeper, changeless nature. We identify with what has been called the \"lower self\"\u2014the ego, persona, personality, or \"self-image\"\u2014instead of communing with the real McCoy, what has been variously termed the higher or authentic self, the soul, the spirit, our true nature or being. \"We have a hunger for something like authenticity, but are easily satisfied by an ersatz facsimile,\" as Miles Orvell puts it.\n\nThe self, it seems, is in an ongoing identity crisis. We're spending our lives in a series of caricatures, impersonating somebody or another, substituting one persona after another for a real person.\n\nWhen it comes to self-realization, we've been settling for a bunch of wooden nickels. And trying to find our authentic self in such a weak currency has not, and will not, pay off.\n\n### THE COMMON WISH TO BE SPECIAL\n\nIf there's one thing we're pretty sure of when it comes to our perception of ourselves, it's that we are unique. We all, each and every one of us, want to think of ourselves as truly individual, as one of a kind. Most of us, and in much the same kind of way, think of ourselves as special\u2014and wish to be even more special, for it is in our hoped-for extraordinariness that we believe we will find true fulfillment and happiness.\n\nIn an age when depression has reached epidemic proportions in our so-called developed nations, it is important to foster a healthy sense of self-esteem in order to combat the spiraling trend toward self-abasement. We need to find ways to help reverse this trend\u2014for our own good and for the good of others who are also susceptible to this tendency, for the true causes and cures of this modern ailment are not the ones usually on offer in many therapeutic and \"self-help\" circles.\n\nNow, lest you think I'm telling you that you're not special, please know that I'm not saying that at all. You are indeed special, distinct, and one of a kind, and you should honor that. Fostering a good, healthy sense of self-acceptance is an essential basis for a happy life. And this process must begin early. Parents need to instill in their children a sense of self-worth. You've probably seen the meme\u2014a picture of a small child with the caption \"God made me, and God doesn't make junk!\" Every child deserves to believe that they are not \"junk.\"\n\nMr. Rogers\u2014surely one of our modern saints, who positively influenced a whole generation in America\u2014repeatedly told young viewers of his television show that they were his friends and he liked them just the way they are. The whole salubrious message was encapsulated in a song entitled \"You Are Special.\"\n\nYou're special to me . . .\n\nYou are the only one like you.\n\nThis beneficial promotion of self-affirmation, \"You are special,\" is also crucially important to convey to those who are, for one reason or another, cut off from some or all the ways a person's worth is measured in our society\u2014those without much money, whose profession (or lack thereof) is not afforded much status, or who are otherwise unable to draw upon the usual social props for their sense of self-worth.\n\nWhen I was a boy, my father occasionally took me on weekend trips from our home in St. Paul, Minnesota, to Chicago\u2014the big, big city for all us Midwesterners. We'd go to the Shedd Aquarium, the Museum of Science and Industry, Maxwell Street Market, and other places of urban wonder. And my dad, being a second-generation Baptist minister, would also bring me on Saturday mornings to a large auditorium for the weekly service conducted by a young and exceptionally dynamic pastor, the Reverend Jesse Jackson.\n\nThe organization was called Operation Breadbasket, an offshoot of the Southern Christian Leadership Conference, formed to help foster economic development among disadvantaged people like those living on the South Side of Chicago. And the highlight of the weekly service was when the charismatic Reverend Jackson would get behind the pulpit and do his thing, call-and-response style:\n\nRev. Jackson: Say, I am!\n\nCrowd: I am!\n\nRev. Jackson: Somebody!\n\nCrowd: Somebody!\n\nRev. Jackson: I may be poor.\n\nCrowd: I may be poor.\n\nRev. Jackson: But I am . . .\n\nCrowd: But I am . . . .\n\nRev. Jackson: Somebody!\n\nCrowd: Somebody!\n\nRev. Jackson: I may be young.\n\nCrowd: I may be young.\n\nRev. Jackson: But I am . . .\n\nCrowd: But I am . . .\n\nRev. Jackson: Somebody!\n\nCrowd: Somebody!\n\nRev. Jackson: I may be on welfare.\n\nCrowd: I may be on welfare.\n\nRev. Jackson: But I am . . .\n\nCrowd: But I am . . .\n\nRev. Jackson: Somebody!\n\nCrowd: Somebody!\n\nAnd on the chant went, reaching greater and greater pitches of enthusiasm:\n\nI may be small, but I am somebody!\n\nI may make a mistake, but I am somebody!\n\nMy clothes are different, my face is different, my hair is different, but I am somebody!\n\nI am black, brown, white. I speak a different language.\n\nBut I must be respected, protected, never rejected!\n\nI am God's child!\n\nI am somebody!\n\nI AM SOMEBODY\n\nAnd, of course, we all are indeed somebody, and we should all be a self-respecting somebody. Each of us has our own personality, shaped by our distinctive genetic makeup, personal history, life choices, and so on\u2014what the Eastern traditions would regard as the fruition of our individual karma. Accepting the cards you've been dealt is the condition of possibility for playing them well in the game of life.\n\nWe truly are, each and every one of us, special and unique like a snowflake, and we all should accept who we are with dignity and a certain sense of self-assurance and pride.\n\n### YOU: YOUR BEST FRIEND AND WORST ENEMY\n\nThe kind of healthy self-respect Mr. Rogers and Jesse Jackson encourage is unquestionably a positive thing. But feeling comfortable with one's individuality is really just the starting point for more advanced forms of self-discovery. Like possessing enough food, proper shelter, and leisure time, having a strong positive sense about one's distinctive individuality is a prerequisite for deeper spiritual pursuits.\n\nThe spiritual quest begins, one might say, where many of the traditional therapeutic processes leave off. Mental health therapy in its myriad forms\u2014from the rigors of psychoanalysis to the most user-friendly self-help book\u2014has, at bottom, the same function. The fundamental purpose of the therapeutic approach is to make us feel better about ourselves\u2014to make us feel that we're all somebody special.\n\nAnd that's great . . . as far as it goes.\n\nBut the spiritual approach, as opposed to the merely therapeutic, should regard a strong, positive sense of one's distinctive individual identity as the starting point, not the end result. \"One should raise up the self by oneself, and not degrade oneself,\" as it says in the great Hindu classic, the Bhagavad Gita. But the text goes on to note, \"For the self is its own best friend and its own worst enemy.\"\n\nBuilding a good, healthy ego is a necessary step in the task of true self-realization, but it is not sufficient in and of itself. The affirmation of the lower, personalized, and individual self is not, according to the religious traditions, true self-knowledge. In the deeper search for one's irreducible core, identifying with and clinging to the ego is in fact the obstacle. The best friend turns into the worst enemy.\n\nWe must, as the saying goes, lose the self to find it. We must get beyond the ego\u2014the \"special somebody\" self\u2014if we are to discover our deeper, more genuine, and more universal identity. In such a quest, feeling special and unique repositions itself as the problem, not the solution.\n\nThe journey to true self-knowledge is like climbing a ladder. One must start on the lower, foundational rungs. But to move higher, we must also be willing to ascend, leaving the lower rungs behind. Once we've established a proper sense of self-worth, individuality, and specialness, we are ready to take the next steps.\n\nWe must, in a word, have a good, healthy ego in order to proceed with the ego-ectomy necessary to discover our real nature.\n\n\"When there is no 'I,' there is liberation,\" as it says in another ancient Sanskrit text of the Hindu tradition. \"And when there is an 'I,' there is bondage.\" And this truth is repeated in countless ways in the scriptures and classics of other world religions:\n\n  \"Since all the disasters, sufferings, and fears in the world come about from the grasping to a self, then how is this grasping beneficial to me? Without abandoning the self, suffering cannot be abandoned, just as without avoiding fire one cannot avoid being burned\" (Shantideva, Buddhism).\n\n  \"Above all the grace and the gifts that Christ gives to his beloved is that of overcoming self\" (Francis of Assisi, Christianity).\n\n  \"He who attends to his greater self becomes a great man, and he who attends to his smaller self becomes a small man\" (Mencius, Confucianism).\n\n  \"There is an irreducible opposition between the deep transcendent self that awakens only in contemplation and the superficial, external self that we commonly identify with the first person singular. We must remember that this superficial 'I' is not our real self. It is our 'individuality' and our 'empirical self,' but it is not truly the hidden and mysterious person in whom we subsist before the eyes of God. The 'I' that works in the world, thinks about itself, observes its own reactions, and talks about itself is not the true 'I' that has been united to God in Christ\" (Thomas Merton, Christianity).\n\n  \"Owing to ignorance of the rope, the rope appears to be a snake; owing to ignorance of the Self, the transient state arises of the individualized, limited, phenomenal aspect of the Self\" (Shankara, Hinduism).\n\nWhile our unique individuality serves as a starting point, it cannot function as the end-all of the quest to \"know thyself.\" To move beyond our fascination and attachment to our particularity, we must gain an appreciation for what we share with all the other somebodies out there.\n\n### NEVER SOMEBODY ENOUGH\n\nThe need to feel special is not in and of itself special. We all want to portray ourselves\u2014to ourselves and to others\u2014as being in one way or another extraordinary. If we don't feel this foundational sense of specialness at all, it is indeed important to find ways to increase our sense of self-worth\u2014and there are plenty of resources available in the therapeutic establishment to facilitate that. And throughout this book, we'll be discussing some surefire methods for increasing self-esteem.\n\nBut what we also may start to suspect is that, at a certain point\u2014after shoring up the foundation of a necessary and beneficial sense of self-worth\u2014the interminable pursuit of being somebody can become a heavy load to carry.\n\nIf, for example, we believe that our \"specialness\" derives from what we have achieved rather than from who we really are, we will be forever striving to be important enough, famous enough, rich enough, loved enough, accomplished enough.\n\nThe eminent psychiatrist Thomas Szasz noted, \"People often say that this or that person has not yet found himself. But the self,\" Szasz argued, \"is not something one finds, it is something one creates.\" And it is true that most of us peg some important part of our identity to our accomplishments in whatever arenas of life we deem important. But if we overvalue the idea that self-worth is tied to a created specialness, most of us will never feel we have produced a special enough self.\n\nIf we fully buy into an accomplishment-based understanding of selfhood, we'll be perpetually trying, and endlessly failing, to be somebody enough.\n\nWhen we wholly identify with one or another of the roles we play in the ongoing drama that is life, we may begin to suspect that no matter how successful we are\u2014no matter how many promotions we win, how much money we accumulate, how much praise we receive\u2014it will never be sufficient. If this is the gauge of self-approval, the bar will always be moving higher; there will always be more hoops to jump through and more rivers to cross, with no end in sight.\n\nWe often glorify and idealize those who seem to really be somebody: the rock star, the Olympic athlete, the A-list actor, the mega-rich or supremely famous. But even off-the-charts superstars like Madonna can never quite measure up when it comes to this kind of achievement-based understanding of the self. As she candidly confessed in an interview, no matter how successful she became, she never quite felt that she was \"somebody enough\":\n\nMy drive in life comes from a fear of being mediocre. That is always pushing me. I push past one spell of it and discover myself as a special human being but then I feel I am still mediocre and uninteresting unless I do something else. Because even though I have become Somebody, I still have to prove that Somebody. My struggle has never ended and I guess it never will.\n\nMadonna fears \"being mediocre\"\u2014that is, not being \"Madonna enough.\" Similarly, the great hockey player Wayne Gretzky has complained that \"The hardest part of being Wayne Gretzky is that I get compared to Wayne Gretzky.\" Cary Grant also reportedly once declared, \"Everyone wants to be Cary Grant. Even I wish to be Cary Grant.\"II\n\nThese testimonials should give us a clue about pinning our hopes for identity and self-satisfaction on achievement alone. If Madonna can't be Madonna enough; if Wayne Gretzky can never quite live up to being Wayne Gretzky; and if even (the real) Cary Grant wanted someday to be (the ideal) Cary Grant, well, what hope is there for us less-than-superstars?\n\nThe ideal of a \"special self\" one wishes to construct through accomplishment tends always to outstrip the reality, leaving one feeling incomplete, inadequate, and continually running to try to catch up. The fear of not being so special after all\u2014the anxiety of being ordinary\u2014haunts and follows even those among us who seem to have reached the very apex of our chosen endeavors, and it is endemic among those of us who, by and large, are actually pretty ordinary when it comes to our abilities and our achievements.\n\nWhile Socrates encouraged us to \"know thyself,\" others have pointed out that self-knowledge is sometimes bad news! If the worth of the self we're trying to know and identify with is judged by performance-based criteria, we will usually find ourselves perpetually coming up short. We will encounter a self that is forever not special enough, a somebody who is not big enough.\n\nAlthough even the most ordinary of us apparently would rather not think of ourselves as such, the burden of being special is perhaps a much heavier weight to bear.\n\n### TOO SPECIAL FOR OUR OWN GOOD\n\nAnd then there's the other side of the coin. If we're not suffering from neurotic apprehension that we're not special enough, we're puffed up with the narcissistic arrogance of thinking we're somehow more special than others. The desperate need to be special easily morphs into a competitive quest to feel superior in one way or another. Fearing that we'll be seen as nobody and urgently trying to be somebody, we get too big for our britches. We become too special for our own good.\n\nAs Pema Ch\u00f6dr\u00f6n notes in the epigraph to this chapter, it's a mistake to overestimate the role and ignore who is really playing that role. It is a given that we are all unique individuals, but attaching to and elevating our uniqueness is not the recipe either for true happiness or for more comprehensive self-knowledge.\n\nIt's somewhat ironic that, driven by the belief that we'll be happy only by being distinctive, separate, and unique, we end up collectively pursuing this Holy Grail of redemptive individuality in very similar ways. The reader might recall a scene in that Monty Python movie, Life of Brian, in which a mob pursues Brian, the supposed messiah, and surrounds his home. The reluctant savior appears at the window and implores the assembled masses to stop being sheep and to think for themselves. Brian shouts to them, \"You're all individuals,\" and the crowd, en masse, answers, \"We're all individuals.\"\n\nBut then one lonely little voice at the back says, \"I'm not.\"\n\nAnd he's the one who got it right. It is truly an act of independence and freedom to recognize that we're all alike and that nobody is really more somebody than anyone else. The one who realizes he's no more special than others is the truly special one.\n\n### WE'RE ALL IN THE SAME BOAT: THE GREAT EQUALITY\n\nThe emphasis on being special\u2014embracing our uniqueness and individuality as if true self-fulfillment were to be found in being somebody or, even worse, being more of a somebody than others\u2014can blind us to the essential ways that we are fundamentally alike, and can serve to divide rather than bring us together in our shared humanity.\n\nClinging to the particular and the individual precludes opening ourselves up to the general and universal. It is only by laying down the burden of individuality that we can begin to embrace our larger Self, the true core of our being that we share with all others. It is getting in touch with this universal part of ourselves that brings us joy, in large part because it relieves us of the strain of having to be somebody in particular by plugging us into what we have in common with others.\n\nAs opposed to the modern, secular emphasis on individuality (which can so easily turn into narcissistic self-absorption and prideful superciliousness), the world's spiritual traditions emphasize our commonalities and kinship. Rather than focusing on what sets us apart, the spiritual traditions highlight what binds us together.\n\nWe can begin to receive intimations of a deeper sense of who we are\u2014an identity that transcends the anxiety of being somebody\u2014by recognizing that underlying our superficial differences is a great equality that links us with all others.\n\nThe Dalai Lama likes to emphasize that although we are indeed unique individuals, there are two basic desires we all share as living beings:\n\nIn our quest for happiness and the avoidance of suffering, we are all fundamentally the same, and therefore equal. . . . Despite all our individual characteristics, no matter what education we may have or what social rank we may have inherited, and irrespective of what we may have achieved in our lives, we all seek to find happiness and to avoid suffering during this short life of ours.\n\nPut simply, we all want to be happy and avoid pain, and we are all exactly alike in that we have these two fundamental wishes. And this, by the way, we share with all sentient life. It matters not if you're a squirrel or a CEO, an insect or the president of the United States. Every living being just wants to attain happiness and evade suffering.\n\nBut we are also equal in that we are not very savvy about how to obtain these goals. While we all want to avoid it, suffering is endemic to life. And while we all desire true happiness, few of us are very good at actually achieving it.\n\n\u2022 \u2022 \u2022\n\nAll religions are premised on the recognition that, in the absence of spiritual training, life will just repeatedly kick our helpless asses. Acknowledging this fact of life is the sine qua non for getting serious about finding an alternative to perpetual victimhood.\n\nIf life just flowed merrily on for us, there would be no need for self-cultivation. We could just relax and enjoy ourselves, like Adam and Eve in the Garden of Eden. But, as the myth in Genesis tells us, we are not in a paradisiacal garden anymore (in case you hadn't noticed). We're in a deep, dark, dangerous forest and need guidance to find our way out.\n\nThis acknowledgment of our collective predicament was emphatically encapsulated in the first words that came out of the mouth of the Buddha after he achieved his Awakening: \"Y'all are suffering,\" he declared (loosely translated). From the point of view of a truly self-realized being, all of us, equally, are in deep doo-doo.\n\nThis is the first of the four so-called Worthy Truths in Buddhism, and the starting point for any serious attempt at a spiritual life designed to bring an alternative.III \"Houston, we have a problem,\" as the astronauts said when they realized their spaceship wasn't working anymore. Our spaceships aren't working. We all have a problem. Our lives are shot through with difficulties, stress, dissatisfaction, and the like.\n\nSuffering, in a word.\n\nOh, Buddhists, they're so negative! What do you mean \"Life is suffering\"? Cheer up, already! Maybe you guys should get out more\u2014enjoy a movie or a nice dinner, or go dancing or something!\n\nOf course, the Buddha didn't mean that life for everyone is an unremitting series of tragedies\u2014although, for some of our fellow human beings living on this very same planet, daily life is indeed a relentless set of challenges. Billions go hungry every day; billions do not have proper shelter, clothing, water, and medical care, while nearly equal numbers do not have basic political freedoms, educational opportunities, or even the ability to read. Billions also suffer from deep-seated psychological and emotional problems that make their daily life a living hell.\n\nAnd all of us, no matter how privileged and sheltered we are from the more extreme forms of misery, are subject to misfortune. The things and people in our lives, even our own health and welfare\u2014all of it is precarious.\n\nIn fact, we can accurately consider ourselves to be perpetually in one of two possible situations: we are either in the midst of a disaster or between them. These are, for all of us equally, the only two options in this life.\n\nWhen we're in the middle of a disaster, the truth that life involves suffering is not debatable. We've all been there, and many of us are there right now. It's when tragedy hits that the scales of denial fall from our eyes.\n\nWhen it comes to traumatic experiences, everyone has their own tales to tell. One of mine occurred early on in my adult life. My first marriage, to my high school girlfriend, took place at the tender age of eighteen. Within a year it was over. These were the days before \"no fault\" divorces, so, in addition to the pain of having my wife leave me, I had to endure the further torment of having my friends testify in court about what a bad husband I had been. (This was not untrue, but nevertheless it hurt to hear it publicly declared by my own friends.) By age nineteen, the hopes and expectations I had had about what an adult life would look like had been cruelly crushed. I was completely devastated and spun into a deep depression.\n\nWhen we're in the middle of a disaster, the fact of suffering is viscerally felt and intellectually obvious. It is, at such times, painfully indisputable, and we don't need to be convinced then that life is suffering. But there are two things we do need to try to remember in those difficult but potentially eye-opening circumstances.\n\nThe first is that suffering isn't just random bad luck; rather, encountering misfortune is inevitably part of living life. We all lose loved ones. We all get sick, get old, and die. Or, as the Buddha summed it up, we don't get what we want, we do get what we don't want, and we don't get to keep forever the things and people we love.\n\nIt's not some strange anomaly when tragedy befalls us. Suffering is in the very nature of our lives. We are slapped in the face with this truth when we're in the middle of the disaster, but when we're in between disasters it's important to remember that the next one (when it comes, not if ) will greet us in the same manner as the last one.\n\nThe second thing to remember\u2014and this one is even harder than the first\u2014is that, when the suffering nature of life whacks you upside the head, it's not just you. As we have seen, we all want to feel special, and when we experience catastrophes we embrace those negative experiences also as something that distinguishes, or even defines, us. This is so unfair\u2014we often think at such times\u2014I have been singled out for this misfortune.\n\nWhen it comes our time to undergo difficulties, we all feel like poor Job in the Bible, who, shaking his fist toward the sky, demands to plead his case to the one who has unjustly rained such torment down on him.\n\nWhy me? Why me?\n\nThere's a story told in the Buddhist scriptures about a woman who has just lost her only child. She goes to the Buddha and pleads with him to restore her son to her. Surprisingly, the Buddha agrees\u2014but under one condition. \"Go to every home in the village,\" he instructs the grieving mother, \"and bring me a mustard seed from the household that hasn't had a tragedy like yours.\" The poor woman starts knocking on doors and, well, you can guess the outcome. Let's just say she didn't bring back any mustard seeds to the Buddha.\n\nSuffering doesn't make you special any more than the need to feel special makes you special. We have all been there, and we'll all be there again. Anyone who has been alive more than a few years has already taken huge hits, as any therapist, counselor, or clergyman who regularly listens to people's stories can attest. Everyone has tales of woe; we are all the walking wounded. When I hear about what people\u2014ordinary people, everyday people, just like you and me\u2014have gone through, I'm often amazed that any of us can even get out of bed and carry on.\n\nNo one is getting through life unscathed. We're all in the same boat, and when it comes to our susceptibility to suffering, that boat is the Titanic. And while the experience of disaster is ubiquitous, there are no objective criteria for measuring whose suffering is worse. There's no scale of suffering, such that yours is a 6.8 while someone else only scores 4.2.\n\nWhile we might feel our own trials to be greater than others, it is necessary to realize that suffering is subjective. What one person finds unbearable another might skate through, and what someone might find trivial is another's unmitigated nightmare.\n\nThere's a story about a young girl who had just begun college. She had been admitted to the same school both her mother and grandmother had attended. Both mom and grandma had also been active members in one of the school's most popular sororities; indeed, membership in that sorority had sort of defined their whole lives. Even as alumnae, this girl's maternal kinfolk continued to financially support the sorority, regularly attend the annual reunions, and so on. Most importantly for the story, they instilled in the young lady how crucially important it would be for her to also be inducted into the society of Alpha Delta Awesome, or whatever it was.\n\nGuess what happened? She didn't get in. Having heard about how great Alpha Delta Awesome was her whole life, and knowing full well the expectations her mother and grandmother had of her carrying on this family tradition, she was utterly devastated by the rejection.\n\nSo a bit of a thought experiment here: Was the suffering that this young lady experienced as a result of being rebuffed by some damned sorority comparable to what many of us would regard as a much more serious disappointment? Is it possible, or could it even be likely, that from her point of view the trauma was felt as deeply as, say, another might feel having a career tank, or having something precious get stolen or lost, or even having a major health problem or being in the midst of a divorce?\n\nRealizing that suffering is both subjectively experienced and universally encountered\u2014no one is having an easy life here!\u2014is a crucial step toward breaking out of the loneliness of individuality and recognizing what we share with all others. Personal suffering need not simply further and solidify our sense of distinctiveness, but can open us up to a compassionate empathy that enlarges our sense of self.\n\n\u2022 \u2022 \u2022\n\nNo one wants to suffer. All of us try to avoid it the best we can. And conversely, we all want to be happy and enjoy life, and this is the second way in which we are all exactly alike.\n\nThe desire for happiness (and for avoidance of pain) is fundamental to our nature as living beings. It drives us all day long, and it lies behind all of our life choices. As psychologist Mihaly Csikszentmihalyi puts it, \"While happiness itself is sought for its own sake, every other goal\u2014health, beauty, money, or power\u2014is valued only because we expect that it will make us happy.\"\n\nAlthough everything we do throughout the day\u2014throughout our whole lives\u2014is done with the hope that it will bring us more happiness (and less pain), many of us may perceive happiness as something that occurs accidentally, once in a while, through causes unknown and unknowable.\n\nThe very etymology of the word happiness contains within it the idea that it is, so to speak, haphazard. We feel hapless when it comes to obtaining real happiness; we have a sense that, when it seems that things are going right, it's all just a matter of happenstance. It might appear that happiness, like its opposite (a four-letter word for excrement, as one sees on bumper stickers), just happens.\n\nHappiness doesn't just happen; it is caused, like everything else. And there is a universally affirmed method taught in the spiritual traditions to achieve true and lasting happiness. That method involves less, not more, self-centeredness; it entails relinquishing the individual's insatiable demands and losing oneself in something larger.\n\nWhile we sometimes think of happiness as a randomly occurring phenomenon, we even more often associate true happiness with the pleasuring of the ego\u2014\"making myself happy\" through trying to find joy in what we label \"self-fulfillment,\" \"self-satisfaction,\" or any other of the myriad concepts that have \"self\" as the first component (\"self-respect,\" \"self-indulgence,\" \"self-importance,\" and so on). Although, as we've seen, it is essential to have self-esteem to be strong enough to move things to the next level, we must transcend egoism if we are to find both our true identity\u2014what unites us with all others\u2014and the real and authentic source of joy.\n\nCompulsively trying to be somebody, we keep ourselves imprisoned by our own egotistical addiction to being more, better, and higher.\n\nTrue happiness doesn't involve fulfilling the ego's needs for high status, the love and admiration of others, a beautiful body, or a trophy wife or arm-candy husband. True happiness, in other words, will not be an attribute of the lower, smaller, individual self. It is only when we access our higher, universal, true identity that we experience the profound and unshakeable euphoria we all seek.\n\nThe purpose of life is to find an alternative to ubiquitous suffering; the whole point is to find the lifeboat and get off the freakin' Titanic. And that's another way in which we are all the same: we all have the capability of discovering the lifeboat that's been there all along.\n\nWe all, equally, have this capacity for deep-rooted happiness, because we all, equally, have a spirit, universal in nature, at our core. This is the great and fundamental equality, assumed in all the world's spiritual traditions. In Christianity, we are taught that we all\u2014sinner and saint alike\u2014are capable of redemption and salvation. And similarly in Judaism, we are all regarded as equal before God. In Islam, the Qur'an declares that \"All peoples are a single nation,\" while in the Hindu tradition it is presupposed that we all have the potential to break through the illusion of individuality and realize the true nature we share in common.\n\nAnd in Buddhism, each and every living being is said to have what is called \"Buddha nature,\" the inborn potential to realize one's Higher Self.\n\nEveryone has this Buddha nature, and nobody has more of it than anyone else. When it comes to our true identity\u2014our deepest and happiest sense of self\u2014we are not hierarchically ordered individuals with different types and degrees of specialness. Rather, we're perfectly, 100 percent equal and alike.\n\nAccording to the Buddhist texts, recognizing this capability to achieve our highest destiny\u2014a potential we all have, each and every one of us\u2014is the true remedy for the depression and low self-esteem that many of us suffer as a result of our identification with a lower, individual self:\n\nNever be discouraged and think,\n\n\"How could someone like me become Awakened?\"\n\nThe Buddha, who speaks the truth,\n\nHas said these true words about this:\n\n\"Even those who were flies, gnats, bees, and worms\n\nObtained the highest enlightenment, so hard to obtain,\n\nBecause of their perseverance.\"\n\nBecause we are not really just the \"somebody\"\u2014the particular, discrete, and separate individual\u2014that we believe ourselves to be, we can reach the highest happiness. But it will require effort and perseverance to discover who we really are. It will especially demand a willingness to undergo the kind of de- and re-identification entailed in the ego-ectomy we spoke of earlier.\n\nWe must die to be born again. We must be prepared to let go of the caterpillar to which we are so attached if we are to soar free as the butterfly we are truly meant to be.\n\n### TWO BIRDS SITTING ON THE SAME TREE\n\nOur capital \"S\" Self, our Buddha nature, our soul\u2014whatever name one wishes to give it\u2014is definitely not the individual ego. There is a part of each and every one of us that has never been born and will never die\u2014an eternal, uncreated, and universal Self that is not \"somebody\" and has never been \"anybody,\" but is both \"nobody\" and \"everybody.\" And it is this part of us, labeled the \"wise one\" in the following verse from the ancient Indian Upanishads, that is truly extraordinary.\n\nThe wise one has never been born and never dies. It has not come from anywhere, nor has it become anyone. It is unborn, unchanging, eternal, and primordial. It is not killed when the body is killed.\n\nOur real specialness lies not in our uniqueness but in what we share with all others. It is who we really are, and it is who we really want to be. It is what makes it possible to overcome our sense of separation and aloneness and feel a part of a larger whole.\n\nWe long for it and take our greatest joy when we reconnect with it. According to Hindu scriptures, the little voice inside\u2014the mouthpiece of the ego\u2014quiets down, and the atomistic, unhappy self is enveloped into something much greater: \"Conceits such as 'This is who I am' or 'I am not this' are destroyed for the practitioner who has become silent, knowing that everything is encompassed within the true Self.\"\n\nReal self-knowledge requires us to drop the identification with the changing cast of personae that prevent us from knowing the real nature of the face that's peeking from behind those assorted carnival cutouts.\n\nThere is, in each one of us, a tension between our identification with a lower, individual self (we all want to be \"somebody\") and the yearning for union with the true Self. We are at war with ourselves; we are a house divided; we are existentially schizophrenic.\n\nAnd what is at stake in this internal struggle is our true happiness, our sense of fulfillment, and the end to the feelings of desperation, inadequacy, and victimization. One of the older Upanishads provides this metaphor:\n\nTwo birds, inseparable friends, perch on the same tree. One of them eats a tasty fig while the other looks on without eating. Sitting on that same tree, the lower, deluded self is overwhelmed by the belief that he is a powerless victim and he despairs. When he sees the other, the beloved Master, and realizes that all greatness is his, then his despair vanishes.\n\nIt is our own embrace of the personal, smaller, individual self\u2014the bird that always needs another tasty fig to feel like a better somebody\u2014that perpetuates our suffering and discontentment. And it is by knowing our true and universal self\u2014the bird that is always satisfied and never feels the compulsion to be more or better\u2014that we can end it.\n\nAnd we will know this true self not as ourselves but in the blissful relief of not having to be ourselves, of finding the peaceful and ever-satisfied \"beloved Master\" within.\n\n\u2022 \u2022 \u2022\n\nIn the following pages of this book, we will survey the different battlegrounds where war is being waged between the \"two birds perched on the same tree\"\u2014the ego or \"somebody self\" and the authentic \"nobody self.\" It is an inner conflict between our anxious striving to be somebody and our deepest feelings of contentment or \"at-onement\" that occur when we get back in touch with the stillness and the feeling of interconnectivity made possible only by being nobody.\n\nAction Plan: Generating Compassion for the Suffering of Others\n\nTake five or ten minutes each day to stop and reflect on the problems others are currently facing. Begin by thinking about your relatives and friends and the difficulties they are wrestling with in their lives. Generate what should be a natural sense of compassion for their suffering and make a plan for something you could do to help relieve at least some of their pain.\n\nThen have a look at the news of the day and reflect on what it must be like to be one of the millions of people who are currently in the midst of a major disaster. Try to overcome the tendency to let such news reports pass through the consciousness without touching the heart. These are people just like you, with the same desire to be happy and avoid pain, and they are currently experiencing a terrible catastrophe.\n\nResolve not to use current events as just another form of entertainment; rather, use them as a daily opportunity to generate empathy and a sense of connection to the suffering of others.\n\n#### Notes:\n\nI. Cf. Eckhart Tolle's observation in A New Earth: Awakening to Your Life's Purpose: \"One of the most basic mind structures through which the ego comes into existence is identification. The word 'identification' is derived from the Latin word idem, meaning 'same,' and facere, which means 'to make.' So when I identify with something, I 'make it the same.' The same as what? The same as I. I endow it with a sense of self, and so it becomes part of my 'identity' \" (New York: Penguin Books, 2005), 35.\n\nII. For these and other such examples\u2014including the groupie who said of every rock star she'd slept with, \"He's great, but he's no Mick Jagger,\" until she finally did bed Mick Jagger. She then reported, \"Great, but no Mick Jagger\"\u2014see Wendy Doniger's The Woman Who Pretended to Be Who She Was: Myths of Self-Imitation (New York: Oxford University Press, 2004).\n\nIII. The other three \"truths\" are (1) that suffering is caused (and not by anyone or anything other than ourselves), (2) that there is an alternative to suffering, and (3) that there is a method for attaining the true happiness that is our birthright.\n\n## 2\n\n## What Goes Up Must Come Down\n\nProud people breed sad sorrows for themselves.\n\n\u2014Emily Bronte\n\n### PRIDE AND PREJUDICE\n\nA healthy sense of self is the necessary foundation for further spiritual progress. We're all unique individuals\u2014everyone truly is a special snowflake\u2014and we should all honor our own singular gifts and achievements.\n\nBut when self-affirmation tips over into self-importance and vanity\u2014when that little \"somebody self\" birdie starts chirping a bit too loudly and arrogantly\u2014it becomes another part of the problem rather than a step on the way to the solution.\n\nPride is a major weapon in the ego's arsenal; it is closely associated with the compulsion to be somebody. Taking overweening pride in some particular and temporary personal characteristic or adventitious circumstance in order to feel superior to other people\u2014to be more special than others\u2014is a fool's game. It seizes on something we think makes us truly special (one personal trait among many\u2014beauty, youth, strength, intelligence, talent, or how much money one has, what one owns, or one's professional status or religious affiliation) and absurdly elevates it above all other possibilities in order to make ourselves supremely special.\n\nAnd if we set too much store by such fleeting and ephemeral phenomena, when they change or we lose them, we become devastated. Instead of taking pride in being somebody oh-so-exceptional, we crash hard, as this inflated sense of the special self is punctured and contracts.\n\nPride is universally identified in the world's religions as one of the biggest dangers for a spiritual practitioner; it often makes it onto the short list of vices. And what's most relevant at this juncture is that pride is the lifeblood of the \"somebody self's\" interest in feeling superior to others. As C. S. Lewis notes,\n\nNow what you want to get clear is that Pride is essentially competitive\u2014is competitive by its very nature\u2014while the other vices are competitive only, so to speak, by accident. Pride gets no pleasure out of having something, only out of having more of it than the next man.\n\nExcessively impressed with and attached to our sense of uniqueness and individuality, we distinguish ourselves from those over whom we tower. And with pride inevitably comes its twin sister: envy. We become jealous of and estranged from those who are even more special than we are (richer, smarter, better looking, more gifted or accomplished).\n\nFeeling too special alienates us from others\u2014from both those we suspect are above us and those we place below us. Our yearning to be somebody not only implicates us in the fear that we'll never be somebody enough; it also requires others to be less of a somebody than we are. With pride comes not only envy but prejudice.\n\nIt is not by further isolating and separating ourselves from others that we will find the genuine happiness we seek. True happiness will not come from feeling better than others any more than it will spring forth from envy and resentment toward those we feel are our betters. True happiness comes only through realizing what connects us to one another\u2014the unity that lies beneath superficial differences.\n\nTaking disproportionate pride in our individuality, we become enmeshed in judgment over those we deem inferior, thus further detaching ourselves from our fellow human beings. And most ironically, this attempt to feel better by ranking ourselves above others backfires and produces the exact opposite effect. For as we shall see in this chapter, it is pride that the spiritual traditions have identified as the main cause of low self-esteem.\n\nWhat goes up must come down. When we take pride in whatever we latch onto in order to pose as someone superior to others, the result is that we become somebody who thinks of themselves as just a worthless nobody.\n\n### TRYING TO BE SOMEBODY BY ASSOCIATION\n\nOne of the many ways we attempt to define and distinguish ourselves\u2014while also paradoxically trying to overcome the isolation and disconnection we abhor\u2014is through identification with a group. We fabricate at least a part of our personal sense of identity by subsuming ourselves within a collectivity.\n\nWe describe and designate ourselves, at least to some degree, by hitching our personal wagons to some communal star:\n\n\"I am an American, Australian, Japanese, German\"\u2014identifying ourselves with our native or adopted nation.\n\n\"I am white, black, Asian, indigenous\"\u2014identifying ourselves with one of the (remarkably few, given human diversity and millennia of interbreeding) racial groupings.\n\n\"I am poor, working class, middle class, upper middle class, or (more rarely and immodestly) stinking rich\"\u2014identifying ourselves with our economic status.\n\n\"I am a Democrat, Republican, progressive, democratic socialist, Green Party member\"\u2014identifying ourselves with our chosen political party.\n\nWe all have a strong desire to belong to something greater, to meld our unique little individual snowflake into a larger snowball.\n\nWhen it comes to the dynamics behind group affiliation, we once more butt up against the internal civil war between the compulsive drive to be somebody and the craving for the release and freedom that comes from being nobody.\n\nOn the one hand, it seems that our desire to join a community is inspired by an innate drive to transcend the loneliness and isolation of singularity. And as such, it is certainly a positive thing. The impulse to connect with others, to identify with a group, seems to be a variant of the urge we all have to drop the obsession with individualism and lose ourselves in something greater. Our interest in associating our discrete, isolated lower selves with a nation, a race, an economic class, or a political party is, from this point of view, motivated by a kind of secular expression of our spiritual longing to drop being ourselves and be nobody through connection to a larger whole.\n\nAs we know from personal experience, it is exactly in those times when we discard the burden of self-consciousness and the striving to be somebody that we feel a sense of relief, spaciousness, and fulfillment. And so it is that we can lose ourselves in a group, gaining a sense of belonging and camaraderie, which is all well and good . . . up to a point.\n\nIf we exaggerate the defining importance of any one of these group identities and take pride in our communal sense of self, we're asking for trouble. For each of them is a mere role we play (or have been given to play) in the game of life, and each is quite different from our essential and higher Self. If we focus monomaniacally on any one of these social personalities\u2014elevating it to a supreme position, and then submerging the lower individual self into this collective identity\u2014we have the complete formula for fanaticism and for a new kind of alienation from others.\n\nIndividual identification through the collecting and blending of various communal identities can at best only partly, and never essentially, define any of us. For an individual's connections with a set of groups is only a small component of what comprises that person. Each of us is much more (or, you might say, ultimately much less!) than the groups with which we are associated.\n\nWe are not wholly defined by being card-carrying members of one club or another, and when it comes to our true nature, our wallets are altogether empty of such nonessential credentials.\n\nOur attempts to forge some kind of special individual identity through our memberships in larger social groupings are all just more carnival cutouts into which we stick our particular faces. In the great internal war that we discussed at the end of the last chapter, it seems as though identification through association is most often aligned with the \"be somebody\" side of things rather than the \"be nobody\" faction.\n\nWhat over-identifying with one or another of our collective guises inevitably entails is not only being included in some group but also not being included in others. Groups are defined negatively as well as positively: If I'm an Australian, it means I'm not a New Zealander; if I'm a Democrat, I'm certainly not a Republican.\n\nFor while the ego is immersed in and defined by the group, the group is in turn usually defined by who is excluded. And when we constitute membership in one or another of these collectivities as exclusive, separating out an \"us\" from a \"them,\" we obscure or even deny the deep commonalities we share with all other living beings.\n\nWe seek to overcome the pangs of loneliness and isolation and gain a sense of community in such group identifications. But if we overestimate them and give them overweening dominance in how we think of ourselves, we re-create the conditions for estrangement from and animosity toward others. Submersion of one's distinct individuality into a group identity can end up being just a repositioning of the will to be somebody.\n\nAnd too often, being somebody requires that we not be somebody else, and once again we find ourselves alienated from others.\n\n### TOO HEAVENLY MINDED AND NO EARTHLY GOOD\n\nIt is especially ironic that religious identities have so often functioned to separate human beings into oppositional factions. As with our association with other groupings, identifying with and taking pride in one or another of the religious traditions\u2014\"I am a Buddhist, Christian, Hindu, Muslim,\" or whatever\u2014endows us with a sense both of belonging and of distinctiveness. But insofar as our connection to one or another of the organized and institutionalized religious \"isms\" is understood to preclude rather than enable our sense of a shared humanity, it has at least the same divisive, if not lethal, potential as national or political identities.\n\nLiving in an age when boundaries of all sorts are breaking down, traditional markers of religious identity are increasingly anachronistic. What really matters is not the particular group one adheres to, but rather the universally promoted spiritual message, which is one of tolerance, love, and respect for others, no matter what tribe they are a part of.\n\nThere was once a group of young Westerners who were visiting India back in the sixties, in the early days of the Tibetan exodus from Chinese persecution and the establishment of refugee communities in places like Dharamsala. The Dalai Lama at that time was not the famous international figure and Nobel Prize recipient he is today, and according to this anecdote the motley crew of European and American hippies walked right up to His Holiness's house and banged on his door.\n\nAnd the Dalai Lama, as the story goes, came to the door and said, \"Hello. What can I do for you?\" and joined the Westerners on the verandah for a bit of a chat.\n\nThe discussion, as one might guess, turned to the topic of religion. One of the Westerners was quite adamantly antireligious and got into his host's face about it: \"How can you in good conscience act as leader of a world religion? Religion has caused nothing but trouble throughout human history\u2014it's been nothing but a source of violence, dissention, and animosity! How can you justify yourself?\"\n\nThe Dalai Lama purportedly said this: \"Religion is really not about vertically dividing ourselves into separate compartments like Hindu, Buddhist, Muslim, Jew, Christian, Taoist, and the rest. Rather, it's better to draw the line horizontally. Those who practice religion, regardless of label, are pretty much all alike. And those who don't practice religion, whether formally affiliated or not, are also pretty much alike.\"\n\nSo what unites all the real practitioners of religion, regardless of which (if any) of the world's faiths they adhere to? Surely the core message of any authentic spiritual path is the cultivation of a universal love, leading to a sense of unity among all people, irrespective of differences in culture, race, economic standing, political belief . . . or formal religious affiliation (or the lack thereof). Those who are practicing religion (and this includes those who disavow formal association with any particular religion) are practicing being more expansive and inclusive in their love, compassion, empathy, and sense of interconnectedness with others. And those who aren't practicing the true intent of religion are in the business of creating more, not less, divisiveness and ill will among people\u2014often very loudly!\n\nReligion, it has been said, is like a swimming pool. All the noise is coming from the shallow end.\n\nBack in my academic days, I once had the opportunity to join a group of students who were having lunch with one of the eminent scholars of comparative religion at the time, Wilfred Cantwell Smith. At some point in the conversation, Professor Smith was asked whether he was a Christian. The answer was quite memorable: \"I can't really say. You'll have to ask those who know me\u2014my family and friends.\"\n\nTo be a real Christian (or Buddhist, Hindu, Jew, Taoist, and so on) means that you try to live like one. And surely that must include living a life guided by the universally extolled religious principles of kindness and love (not animosity and hatred) for others, and the cultivation of harmony and fraternity with (and not estrangement from and enmity toward) others.\n\nIf we want to claim to be a Buddhist, Christian, Muslim, Hindu, Taoist, and so on, we should try to act like one. And this will not involve trying to be somebody by means of exclusive religious branding, but rather will necessitate cultivating the willingness to be nobody through the practice of humility, universal brother- and sisterhood, and the abandonment of egoistical self-regard\u2014even, or especially, when enveloped in a religious guise.\n\nIf we're too obsessed with our religious identity, we can lose sight of our responsibilities to our fellow human beings. We become so \"heavenly minded\" that we're \"no earthly good,\" as the Johnny Cash song would have it:\n\nYou're shinin' your light, and shine it you should\n\nBut you're so heavenly minded you're no earthly good.\n\nOverweening pride of all sorts has disastrous consequences. If someone brags about standing, they surely will fall, as the Man in Black so aptly notes in the song. But there's no pride like spiritual pride. Taking undue self-satisfaction in our religious affiliation or, even worse, in our supposedly exceptional spiritual realizations, blinds us to the very thing a genuine path is supposed to lead to\u2014the end of the clinging to the little, egoistic self, and the realization of our true universal nature and interconnection with all others. If we're too heavenly minded and proud, we're no earthly good at all.\n\n### JUDGE NOT, LEST YE BECOME A JUDGMENTAL PRIG\n\nIt is easy to forget that learning to be nobody is both the ultimate goal of any authentic spiritual path and the royal road to true happiness. The very institution that throughout history has been responsible for transmitting this redemptive message has also repeatedly been usurped in order to subvert and invert the good news. Pride in one's religion has too often been used to shun those with beliefs that differ from one's own\u2014to judge and condemn outsiders in order to extol and congratulate the insiders.\n\nIt is, of course, not just religious people who are proud and judgmental. This is yet another way in which we are alike\u2014we all have the tendency to be forever placing ourselves above and judging others. But it's sad to say that, when it comes to being judgmental and feeling superior, so-called religious people often seem to excel.\n\nWe do not become better and happier people by elevating ourselves over others or through judging. Au contraire. Judging destroys our wisdom, our forbearance, and our love and compassion, and leaves us just feeling smug and isolated.\n\nHere's how it goes, if you're like me: We encounter a complex, constantly changing person or transitory situation, and then we freeze-frame the picture and impose some immutable characteristic on our snapshot: \"He is a bad person; she is a liar.\" Passing judgments like this\u2014and we all tend to do it, don't we?\u2014denies a basic fact of life: everything and everybody is impermanent and in a perpetual state of flux and change.\n\nWe know how complex we are\u2014each one of us is an incredibly intricate mass of experiences, proclivities, memories, opinions, influences, and feelings. We're so complex, it's hard to know who we really are! But when we encounter one another, we seem to forget that others are at least as complicated. When such meetings occur, it's like one tiny edge of the huge balloon that is \"me\" touches a minute portion of the massive balloon that is \"you.\" And on such paltry, fragmentary evidence, I make my determination: \"He is such an irritating person! She is so conceited!\"\n\n\"Judging,\" observes author William Young, always \"requires that you think yourself superior over the one you judge.\" And it is always in the service of ego-enhancement, for as Eckhart Tolle points out,\n\nThere is nothing that strengthens the ego more than being right. Being right is identification with a mental position\u2014a perspective, an opinion, a judgment, a story. For you to be right, of course, you need someone else to be wrong, and so the ego loves to make wrong in order to be right.\n\nJudging is, therefore, both deeply implicated in ignorance and precludes any sort of deep sense of kinship between ourselves and others. Instead of bringing us closer, the tendency to judge tears us apart. Rather than helping us appreciate our commonalities (including our common tendency to be judgmental!), judging imposes a rank order where (in our imaginations, at least) we're on top and others cower guiltily below.\n\nAs Mother Teresa said, \"If you judge people, you have no time to love them.\" And as Jesus advised long before, \"Judge not, that you be not judged.\" What goes around will come around: \"For with what judgment you judge, you will be judged; and with the measure you use, it will be measured back to you.\" We know how unfair and hurtful it feels to have others judge us to be essentially this or that\u2014wrong, bad, ugly, stupid, and so on. And yet, as usual, we create the causes for more of this by doing it to others.\n\n\u2022 \u2022 \u2022\n\nNow, let's be clear. To refrain from judging does not mean that we no longer are allowed to make distinctions among things. In Buddhism, the ability to discriminate is counted as one of the five physical and mental parts, or \"aggregates\" (samskaras), that make up our very being.I We cannot help but discriminate; it is innate to our nature, and without it everything would be one big indistinguishable blob.\n\nBut there is a difference between judgment and what we might call \"discernment.\" To discern means simply to recognize things as distinct from one another (from the Latin discernere, dis\\- meaning \"apart\" and cernere meaning \"to separate\"). And with its connotations of being able to recognize or comprehend something (\"He discerned a pattern in his behavior\"), it is not bound up in ignorance (as with judgment) but rather it is the essence of wisdom.\n\nWhile judgment inhibits learning, discernment is the very soul of it. It functions to distinguish, among other things, what works to bring happiness and what doesn't. Discernment involves identifying what is good for ourselves and others and what is not; what will be useful in our quest to live the good life, alone and in company, and what will only bring more pain.\n\nDiscernment is discrimination minus the self-righteousness and egoism that accompany judgment. It is fundamentally egalitarian rather than hierarchical\u2014what I correctly discern to be beneficial for myself will also be good for you. Hurting others, selfishness, self-cherishing, and, yes, judging are not conducive to happiness, either for me or for anyone else. Loving-kindness, compassion, equanimity, and wise discernment bring happiness to anyone who cultivates them.\n\nDiscernment helps us honor Jesus's advice to take care that there be no hypocrisy fouling our evaluations:\n\nAnd why do you look at the speck in your brother's eye, but do not consider the plank in your own eye? Or how can you say to your brother, \"Let me remove the speck from your eye\"; and look, a plank is in your own eye? Hypocrite! First remove the plank from your own eye, and then you will see clearly to remove the speck from your brother's eye.\n\nThere's a difference between different modes of differentiating. It's not discrimination that's the problem here. But we often exercise the discriminating capacity in a judgmental modality, a way of differentiating that is conducive neither to our own happiness nor to the betterment of our relations with others. This very same ability to discriminate can be used to appreciate the distinctive and unique beauty and goodness in every particular thing and being. We all are indeed special somebodies . . . equally special in our own way.\n\nOne way to foster a healthy exercise of discrimination is to note that in every person there are good attributes as well as bad; in every situation, no matter how difficult and challenging, there are positive aspects and things to learn. Every cloud has a silver lining; every \"problem\" can also be seen as an opportunity; every person possesses at least some admirable and loveable traits if we look for them.\n\nWe perversely are so drawn to the negative side of things that we systematically ignore the positives that are always present\u2014in ourselves, in another person, in a situation, and in groups (national, ethnic, social, economic, or religious) other than our own.\n\nIt's like when we get a small sore, cut, or scratch. The whole rest of the body is fine, but instead of thinking about all the bits that are OK, all the parts that are working well, we become obsessed with this one little scab and we keep picking at it. We fixate on the dark cloud instead of the silver lining.\n\nSince we all innately have the ability to differentiate, why not exercise that power to choose that which will bring more happiness to ourselves and others instead of less, and that which will bring us together rather than separate us?\n\n### BIG FISH IN A SMALL POND\n\nWhether we pride ourselves on our individual status, possessions, or accomplishments, or on our association with a national, ethnic, or religious group, when such vanity serves to prop up our sense of importance, it sets us up to fall.\n\nEgotistical pride is universally regarded as an obstacle to true spiritual progress, and therefore to true happiness. In the Tibetan Buddhist tradition, pride made it onto the list of the top five or six of the \"mental afflictions\" that militate against our sense of well-being and contentment. The whole of the religion known as Islam takes its name from the Arabic term for overcoming one's pride and practicing submission (islam) to God's will. And in Catholicism, pride is listed among the \"seven deadly sins\"\u2014and, indeed, is often regarded as the worst of them. C. S. Lewis calls it \"the essential vice, the utmost evil\":\n\nAccording to Christian teachers, the essential vice, the utmost evil, is Pride. Unchastity, anger, greed, drunkenness, and all that, are mere fleabites in comparison: it was through Pride that the devil became the devil; Pride leads to every other vice; it is the complete anti-God state of mind.\n\nPride is a vice not so much because it is \"bad\" but because it is self-destructive. From a karmic point of view, as we shall see below, pride is one of the principal causes of depression and low self-esteem. What is elevated too high will fall very low; what rises up into the stratosphere comes crashing down into the depths.\n\nPride sets itself up to lose, in both the short run and the long run. In the short run, pride can only sustain its illusion of superiority by remaining a big fish in a small pond.\n\nIn my own case, I have taken pride in my intelligence since I was in elementary school. I remember feeling quite pleased back then to think that I was the smartest kid in my class. This may or may not have been true\u2014relative \"smartness\" is slippery to measure, and memory definitely plays its tricks\u2014but in any case there were only twenty or thirty others to whom I could compare myself.\n\nConvincing myself that I was \"the smartest\" was less sustainable in high school\u2014especially since I nearly flunked eleventh grade due to truancy!\u2014and even harder to maintain in college (there was that course in logic that I just barely passed, and plenty of other ego deflators and reality checks along the way). But it really wasn't until I got to graduate school that this particular illusion was completely blown out of the water. The truth finally penetrated through all the levels of self-deception that sustained my pride. It became indubitable that there were plenty of people way smarter than me\u2014for there they were, lots of them, teeming around me at the university every single day.\n\nAnd then, of course, a new mental affliction arose: envy. But that's a different story.\n\nThe point is just that pride in anything (intelligence, wealth, technical skill, physical beauty or strength or flexibility, or even in one's supposed spiritual attainments) can only be maintained in willful isolation from those who would challenge it.\n\nWhile depression and problems associated with low self-esteem are on the rise, it is not contradictory to observe that it is actually the narcissistic overestimation of the self that lies at the heart of this beast. One modern expert has baldly stated, \"There doesn't seem to be a great deal of really low self-esteem. The average person already thinks that he or she is above average.\" This double-faced Janus\u2014simultaneously insecure and arrogant, self-abasing and self-absorbed\u2014is consistent with the neurosis that arises with the self-preoccupation definitive of our culture.\n\nSo here's one helpful hint for solving the problem of pride: If you're liable to take inordinate self-regard due to your intellect, go to Harvard or the University of Chicago and hobnob with some hardcore eggheads. If you are vain about your good looks, stop hanging around with people you feel are obviously uglier and enter a beauty contest! If you think you're so amazing because of your money, quit socializing with those who have less and chill with really rich people! If you think you're cool because of the flexibility you demonstrate when at your local yoga studio, go to an international yoga conference and check out the real competition.\n\nGet the fish out of the small pond and into the ocean!\n\nPride takes a lot of work to maintain and prolong\u2014not only in light of the constant real-life challenges to its inflated sensibility but also because of the impermanent and changing nature of the things we take pride in. The financial position or professional status, the popularity and fame, the cleverness or brainpower, and (especially!) the appearance and abilities of the physical body are unreliable. That's why pride and insecurity are actually two peas in a pod.\n\n### THE KARMIC CAUSES OF DEPRESSION\n\nBut it's the long run\u2014the karmic consequences of pride\u2014that we're especially concerned with here. So let's cut to the chase, shall we?\n\nLed by pride into the lower realms, they are even in this human life deprived of joy. They will be servants who feed on others' leftovers\u2014stupid, ugly, and weak. Stuck up with pride and miserable, they will be despised by everyone.\n\nAs we unpack this verse from the Buddhist classic Guide to the Bodhisattva's Way of Life, we see that, first of all, the karmic principle of \"What goes around comes around\" is here reformulated as \"What goes up must come down.\" The high shall be made low; the first shall be last. The proud will sink in the afterlife into \"lower realms,\" and even in this life will feel inferior, like \"servants\" of others. Those who take pride in their intellect will see themselves as stupid; those whose arrogance centers on their good looks will regard themselves as ugly; and those vain about their strength will feel weak. Having been too proud, one perceives oneself as inadequate intellectually and physically and, in general, will feel unloved by others (\"despised by everyone\").\n\nThe proud, according to the laws of karma, will become the depressed.\n\nBut what's really interesting and insightful about this passage is that it also states that the proud will remain proud, even after they have been brought low: \"Stuck up with pride and miserable,\" the text says, pointing not only to the idea that karma tends to replicate itself (one of the effects of pride being a future propensity to continue to feel pride), but also to the fact that one can be proud even while simultaneously feeling miserable, inadequate, and unloved.\n\nOr perhaps it's like this: it is possible to be proud of feeling miserable, inadequate, and unloved.\n\n\u2022 \u2022 \u2022\n\nMedical science has not identified any single cause of depression. A whole array of factors, external and internal, is said to be capable of triggering it in any given individual. External causes might include family conflict, interpersonal conflict, bereavement, job loss, major life changes, and drug or alcohol abuse. (Sounds like a description of life itself, doesn't it?) Internal causes seem a bit more vague: previous negative experiences (e.g., a history of depression), \"personality\" (e.g., a tendency toward perfectionism), medical illness, and \"family disposition\" (i.e., bad genes).\n\nAs one expert summarizes the situation, \"The precise causes of these [depressive] illnesses continue to be a matter of intense research.\" Decoded, that means, \"We really don't know exactly what causes depression.\"\n\nAncient Indian logic texts distinguish between a \"cause\" (hetu) and a \"condition\" (pratyaya). A \"cause\" is what's absolutely necessary if there is to be the effect. The cause must be there before the effect will be produced, and if the cause is not there, the effect can never come about. An oak tree cannot grow without an acorn to function as its seed.\n\nBut a cause isn't a cause until it's activated by the right circumstances. A \"condition\" acts as a sort of midwife to help the cause give birth to its result. The acorn is the cause of the oak tree, for without it you'll never get an oak tree. But the acorn needs certain conditions to occur for it to operate as the cause of the oak tree. It has to be planted in the right kind of soil and given water and sunlight. Without the proper conditions, the cause can't perform its function.\n\nWhen it comes to the origins and treatment of depression and low self-esteem, we should be careful not to mistake what are just conditions for real causes. The so-called external causes for depression listed above\u2014family or interpersonal conflict, loss of a loved one or job, and so on\u2014can't really properly be regarded as such. They certainly can act as conditions for enkindling the true cause. But there are plenty of people who suffer through such experiences in life without getting depressed, and depression can arise apart from undergoing such experiences.\n\nAnd the same is true with respect to the supposedly \"internal causes.\" It's not necessary to have had previous negative experiences or some personality defect or a medical illness or a particular genetic disposition in order to succumb to depression.\n\nHere, as in so many other areas of modern, secular life, is where we must push what I call the \"Why, Daddy?\" question. You know, like that little kid who won't quit asking Daddy or Mommy \"Why? . . . Why? . . . Yeah, but why?\" As adults, we should ask similar questions of our secular experts:\n\nWhy am I so depressed, Doctor?\n\nWell, you just lost your job.\n\nBut my friends at work were also laid off, and they didn't get depressed like me. Why am I depressed?\n\nYou lost your job, plus you have a genetic predisposition to depression.\n\nYeah, that's true, but my brother's been through all kinds of terrible experiences in life, and he's never been depressed! And anyway, how come my family has depression genes when other families don't? Why me, Doctor? Why?\n\nAnd just like the little kid who keeps asking \"Why, Daddy?\" eventually we get the same answer from the doctor that we give to our inquisitive four-year-old children:\n\nJust because. No reason. It's random. Bad luck.\n\nIn my case, it wasn't that I lost a job, but rather that I got one that seemed to set off my own depression. For twelve years, throughout college and graduate school, I had been told over and over by my professors that I probably wouldn't get a teaching position in my unmarketable, specialized field. Comparative religion with an emphasis on the religions of ancient India wasn't exactly a lucrative field of study with a huge demand that needed filling.\n\nAnd sure enough, when I finished my studies and went looking for a job in my field, there weren't many openings. And there were lots and lots of brilliant, well-trained applicants for each one of the very few available positions.\n\nIn the year when I was up for employment, I not only landed one of the few jobs advertised, I got the very best of them\u2014a plum position in the Ivy League. And within four months, I was checked into a local psychiatric ward and put on twenty-four-hour suicide watch.\n\nGetting the great job obviously was not what caused my depression, but none of the other possibilities I explored with my therapist seemed to sufficiently explain things, either: the difficult relationship with my father, past traumas that had been left unexamined, an \"imposter syndrome\" that made me afraid I'd be found out to be a sham. No one of these, nor any of the other possibilities that modern therapy could come up with, rose to \"acorn\" status; they were all just conditions (\"soil,\" \"sunlight,\" \"water\") that inexplicably came together to precipitate a cause that was yet to be identified.\n\nA depressed person feels like a \"real nobody,\" but, if there is to be a surefire cure for the malady, we should first identify the true source of the ailment.\n\n\u2022 \u2022 \u2022\n\nIt is within the spiritual traditions that we must look for the real causes of our experiences. Religions offer answers to the \"Why, Daddy?\" questions of life. But if we are to be empowered to really help ourselves, we cannot even here remain satisfied with answers that render us impotent victims. Agreeing to religious explanations like \"God's inscrutable will\" doesn't get us any further than secular, scientific answers like \"genetic predisposition.\" Both of them end up sounding like \"Too bad! Just your tough luck!\" and leave us in the same powerless and helpless place.\n\nFortunately, there are other explanations for what causes depression and low self-esteem. And knowing them gives us power: if we no longer create the cause, the effect will arise no more. But in order to gain the power, we have to accept the responsibility.\n\nThe truth of the matter is that we experience depression and low self-esteem because of specific kinds of actions we've done in the past. What goes around really does come around. We do in fact reap what we sow, and this is an absolute truism in every authentic spiritual path: good acts bring pleasant experiences; bad acts bring undesirable consequences.\n\nWhile the ancient texts offer several candidates for the karmic cause of depression\u2014including anger (animosity toward others boomerangs into hatred of the self) and \"idle speech\" (talking trash comes back at us as the feeling that we are trash)\u2014there's one that's by far the most glaring: pride. It serves as the cause and then repositions itself as the self-centered perpetuator of our self-esteem problems.\n\nIt seems paradoxical only because of our fundamental confusion and ignorance: low self-esteem is the consequence of high self-regard. And what's even less apparent is the fact that identifying oneself as a \"depressed person\" is just another way, albeit a sad and twisted one, to take pride in being somebody special.\n\n### BEING SOMEBODY SPECIAL AS NOBODY SPECIAL\n\nAmong the many nasty aspects of pride is the fact that it is good at concealing itself from those of us who have it (and, let's be honest, we all have some version of it). \"There is no fault which makes a man more unpopular,\" observes C. S. Lewis, \"and no fault which we are more unconscious of in ourselves.\" Pride can pretend it's not there, when really it has just relocated itself.\n\nAnd so it is that pride and overweening self-regard can even express themselves through self-deprecation. The individual self, in its desperate attempt to be somebody, can stake its claim to be somebody special because it feels so worthless\u2014and so it asserts its special status in just that way, as a \"depressed person.\"\n\nAs Eckhart Tolle has written, \"If you take away one kind of identification, the ego will quickly find another. It ultimately doesn't mind what it identifies with as long as it has an identity.\" The \"somebody self,\" if unable or unwilling to find confirmation in anything else, will go looking for validation in its own suffering. Physical and psychological disabilities can, as easily as anything else, become the individual's defining quality:\n\nYou can just as easily identify with a \"problematic\" body and make the body's imperfection, illness, or disability into your identity. You may then think and speak of yourself as a \"sufferer\" of this or that chronic illness or disability. . . . You then unconsciously cling to the illness because it has become the most important part of who you perceive yourself to be. . . . Once the ego has found an identity, it does not want to let go.\n\nIt may seem surprising to those who have never suffered from depression to learn that nobody thinks of themselves more than somebody who is depressed. But even those who have only experienced \"a bad day\" or just \"a little case of the blues\" will recognize the phenomenon: when you're feeling down, you aren't interested in much else besides how down you feel.\n\nDepression is a caricature of the main cause of depression. Depression is ultimately caused by thinking about oneself all the time, and is experienced as the inability to think about anyone other than oneself.\n\nMr. Karma (who is no one other than your own conscience and consciousness) has a sort of sick sense of humor. He notices when we're constantly preoccupied with ourselves\u2014What about me? What about me?\u2014and says, \"OK. You want to focus on yourself all the time? Try this!\" We get depressed, unable to get out of our own heads and stop the repetitive, broken record of how bad we feel.\n\nAnd then, performing another trick from its vast repertoire, the \"somebody self\" identifies with this \"depressed person\" it has fabricated. We are so desperate to be somebody that we're willing to stick our heads into even this kind of carnival cutout: If I can't be a good enough anybody else, at least I can be somebody as a nobody. The ego tries to solve the problem of low self-esteem by assuming the role of \"somebody with low self-esteem.\"\n\nAnd tragically, this designation of the self as \"a depressed self\"\u2014now more self-centered than ever and taking perverse pride in its self-defining misery\u2014re-creates the very cause that brought about this dismal state of affairs in the first place.\n\nDepression is a downward cycle, in more ways than one.\n\n\u2022 \u2022 \u2022\n\nThe culture of narcissism that encourages rampant self-obsession and self-congratulatory pride has had unfavorable ramifications when it comes to the pursuit of true happiness. The precipitous rise in depression and the steep plunge in self-esteem can be directly correlated to living in a society where the unconstrained preoccupation with the self has taken on pathological dimensions.\n\nWhile we've drawn the karmic correlations between, on one hand, egotism and pride, and on the other hand the calamitous fall into the bleakness of depressed self-absorption, you don't really even have to accept karma to perceive the relationship between the two. Selfishness doesn't make us feel better about ourselves, which we know if we check in on our own experience. And in fact it makes us feel much worse, depressingly so.\n\nThe karmic causes of depression\u2014anger; idle speech, either in the form of self-righteous gossiping about others or making promises that aren't kept; and the pride, arrogance, and judgmental mindset that cause us to place ourselves above others\u2014these are all expressions of a more fundamental root problem: self-centeredness. And correspondingly, the real causes of happiness (and the cures for depression) will all orbit around the same foundational source: selflessness and altruistic concern for our fellow human beings.\n\nIn the next chapter, we'll see that the usual forms of self-absorption are in fact based on a grand illusion. While in our culture of narcissism we invest so much time and effort in appeasing the needs of a divinized, egoistic self, the status of that deity is insecure\u2014and for very good reason. The \"somebody self,\" one might say, is in a perpetual identity crisis because it suspects (while at the same time it denies) that it isn't really real.\n\nWhen we actually go looking for the self we feel so intuitively is there\u2014it makes such constant demands, after all!\u2014a sneaking suspicion starts to grow that there's really nobody home. For the self we are so obsessed with and take such pride in has only an apparitional existence, and our obsession turns out to be no more than chasing a shadow.\n\nThis is not, however, the nihilistic tragedy we might fear. When we give up looking for the somebody who's not really there\u2014when we come up empty-handed in our futile search for some unchanging and all-controlling entity amidst our many and variegated personae and appearances\u2014we begin to realize that the nobody we're left with isn't just a big nothing.\n\nWising up about the real nature of the \"somebody self\" makes it possible for us to become a happier somebody. It's through accessing the infinite potentiality of being nobody that we can really begin to help and improve ourselves.\n\nAction Plan: Managing Pride\n\nMake a list of personal traits that you are proud of\u2014your looks or physical abilities, acquired skills, natural gifts, accomplishments, whatever. This is not the time to be falsely humble. We're all proud of something about ourselves.\n\nFirst off, consider whether these traits are permanent and will always be with you. Do you really suppose that you will always be beautiful, strong, clever, adept, successful, or famous? How will you feel when what you are proud of is diminished or lost altogether due to the ravages of time and changing circumstances?\n\nSecond, check to see whether the pride you take in these characteristics is only in relation to others who don't have them or who have only lesser versions of them. Isn't it always the case that what you're proud of depends on feelings of superiority to others?\n\nFinally, reflect on the fact that there are others who definitely have more or better versions of these traits. Be more realistic about your place in life: are you really the most talented, beautiful, rich, skilled, accomplished, or intelligent? Get the fish out of the small pond, at least theoretically, and realize your true place in whatever hierarchy you've bought into!\n\n#### Notes:\n\nI. The five aggregates that comprise the basis for our sense of self are the physical body, the ability to discriminate, consciousness, feelings, and mental imprints.\n\n## 3\n\n## Clutching at Straws and Chasing Shadows\n\nKnock, knock.\n\nWho's there?\n\nExactly.\n\n\u2014\u2014Author unknown\n\n### FREEDOM'S JUST ANOTHER WORD FOR NOTHING LEFT TO LOSE (OR GAIN)\n\nBeneath it all, it is only true contentment\u2014the glorious sensation of being utterly free, unencumbered, and relaxed\u2014that we all desire. The goals depicted in many religions reflect this understanding of what we are shooting for: moksha or mukti (both meaning \"liberation\") in Hinduism; nirvana (the great \"extinguishing\" or \"sigh of relief\" as one becomes free of all troubling thoughts and feelings) in Buddhism; the dropping of the old self and being \"born again\" into Christ; the release that comes from following God's will and law in Judaism and Islam.\n\nWe all want to be free. So what, exactly, are the chains that bind us? What is the nature of the prison that we feel encloses us?\n\nBeing free isn't just a matter of doing, saying, or thinking anything that comes into your head. That much should be obvious to anyone who has lived more than a few years in the company of other humans. We've tried that version of \"freedom\" over and over and over again, to no avail. Whenever some strong impulse arises, unless thwarted by fear of reprisal (or jail!), we usually just give in to it, consequences be damned! We yell back at those who yell at us, try to hurt those who hurt us, plot our revenge when we feel betrayed . . . just because we \"feel like it.\"\n\nUntil we have thoroughly trained ourselves, we are enslaved by our negative emotions, our mental afflictions. When anger, jealousy, pride, or lust raise their nasty little heads, we are usually rendered helpless in their thrall. Worse yet, we stick our head into the carnival cutouts of these irrational feelings and say, \"I am angry! I am depressed! I am jealous!\"\n\nAmong the large array of mental afflictions that plague and tyrannize us (the Buddha said we have 84,000 of them!), two lie at the root of our unhappiness and imprisonment.\n\nThey are desire and ignorance.\n\n\"Desire\" here really means perpetual dissatisfaction\u2014with what we have, with the life we are leading, and with who we are. It's like when we have an itchy mosquito bite. We scratch the itch, hoping that by doing so it won't itch anymore.\n\nWe're slaves to our itches, and that's one very important way in which we are not free. We get a hankering for a new iPhone and the itch begins: If only I had the new iPhone! You know, the one with that little computer voice named Siri that talks to you? Then I'd be happy. Or one or another of the myriad versions of the itch: If only that girl would pay attention to me. If only I had a better job. If only I were rich, famous, popular.\n\nI, I, I and if only, if only\u2014the repetitive call of incessant yearning and discontent, the \"somebody self\" always wanting more.\n\nAnd so we try scratching. We save our money for the iPhone, or try to get the phone number from the beautiful babe or stud-muffin dude, or apply for a different job, or try to be more (more wealthy, more famous, more popular, more attractive) of a somebody.\n\nAnd every time we scratch, it's in the hope that there won't be any more itches.\n\nWe all know what happens next. It's just like those pesky mosquito bites\u2014the more you scratch them, the more irresistibly the itch returns. The relief is at best temporary, and then after a brief respite the desire comes roaring back, more demanding than ever.\n\nAnd so freedom, we could say, is nothing more than the exalted state of itchlessness\u2014being satisfied with everything we have, with \"nothing left to lose,\" as Janis Joplin says in her famous song, and nothing more to gain.\n\nThe liberation we seek with all our scratching consists of simply not being beset with new and improved itches all the time. This is called by another name: \"contentment,\" and it is what we hope to attain with every attempt to satisfy our desires. We hope that, by fulfilling this particular craving, we won't want anything more. We hope that each scratch will be the last one; that finally, with this one last scrape, we'll be satisfied.\n\nMaybe there's more than just contentment at the end of our spiritual journey. Maybe there's heaven or a Pure Land with all kinds of rainbows in the sky and unicorns bounding about. And maybe we'll all be angels, blissfully flapping around with supernatural abilities and X-Men superpowers. I can't, in all honesty, say with any certainty that there won't be.\n\nBut I do know this: If we shoot for contentment\u2014the Great Itchlessness\u2014it won't matter one way or the other. Once we become content, it will be impossible to be discontented with our lives and ourselves\u2014with or without streets paved with gold and divine bodies made of beautiful light. It's win-win when it comes to contentment! If there's more in addition to that, great; and if there's not, well, that will be OK too, because we'll be content!\n\nAnd, of course, all this itching and scratching is in the service of being somebody. We believe that status and personal fulfillment will come through scratching, through obtaining something we don't already have or more (or less) of what we already possess.\n\nThis would be far more understandable if we were lacking the necessities of life. But for readers of this book, I'll wager, it's not for want of proper food or shelter or clothing, nor for lack of education or opportunities to make a decent living, nor due to the absence of friends and loved ones that we remain discontented with our lives.\n\nWe aren't among the three billion people living on two dollars and fifty cents a day or less, nor are we among the 80 percent of the earth's population subsisting on less than ten dollars a day, nor among the one billion fellow human beings dwelling in slums, nor among a similar number who remain illiterate.\n\nWhat we really desire is the freedom from endless desires, especially when we already have so much. It's liberation from our incessant whining about how we don't have enough or aren't somebody enough. As for the first, when it comes to wealth, consumer goods, leisure time, access to education and information\u2014the nuts and bolts of the good life\u2014there's really no excuse for folks like us. We're just forgetting the basic facts of our lives; we're just spacing out. Say the mantra:\n\nOm, I have enough, ah hum!\n\nOur problems\u2014our itches\u2014are \"First World problems,\" which hardly deserve the name \"problems\" at all. Since our \"problems,\" when it comes to what we own and the material lives we lead, are of such an entirely different order than what others face, we do have a real shot at being content with the material circumstances of our lives.\n\nBut when it comes to what is termed \"self-fulfillment,\" well, that, you might say, is a different kettle of fish.\n\nSo now let us turn to the second of our two great mental afflictions: ignorance. As we shall see, there is a fundamental misunderstanding when it comes to who we think we are, and it lies at the heart of our problems.\n\n### THE ROOT OF ALL EVIL\n\nIn the Eastern spiritual traditions, ignorance performs the same quintessential role, when it comes to our unhappiness, that disobedience plays in the West. Readers brought up in Western societies all know the story: In the beginning, everything was jake. Adam and Eve lived in the Garden of Eden and swung in hammocks all day long. When they got hungry, they would leisurely pick fruit from the trees that God had generously provided for them. But there was one tree whose fruit God commanded them not to eat. And we know how the story goes from there: of course, they perversely did the one thing they were told not to do, and the rest is history. Adam and Eve were cursed, and they were thrown out of the Garden to fend for themselves. And so, according to the myth, our tale of woe begins.I\n\nIn the religious traditions stemming from India, it is ignorance, not insubordination to God's will, that's at the root of our problems. And in these Eastern traditions, there's usually no myth of origins offered to show how ignorance came into our lives.II Ignorance has been with us since time with no beginning, and each of us is simply born with it. It's a standard-issue part of the makeup for us as human beings (not to mention other life-forms).\n\nBecause of this ignorance, we make fundamental mistakes about who we are and how to live a good life. We really don't get it when it comes to what's what. And because we don't get it, we're really in for it!\n\nIgnorance (avidya in Sanskrit) is not so much not knowing as it is mis-knowing. Our minds invert things; we mistakenly think things are one way when actually they are another. In the ancient Yoga Sutra, ignorance is (and this is the norm in South Asian scriptures) said to be the \"field\" or \"breeding ground\" in which all the other mental afflictions grow. As long as the \"root\" of these negative emotions remains uncut, we will continue to suffer through life instead of finding true happiness.\n\nThe Yoga Sutra's definition of this Mother of All Mental Afflictions is interesting and comprehensive:\n\nIgnorance is the belief that what is impermanent is permanent, what is impure is pure, what will bring suffering will bring happiness, and what is without an essence has an essence.\n\nThis is, I know, quite a mouthful. But it does, I promise you, have direct bearing on both the real cause of our unhappiness and the disastrously wrong view we have about our individual identity.\n\nSo let's look carefully at what is meant by each of these four ways in which ignorance works to turn things upside down in our lives:\n\n1. We believe what is impermanent to be permanent.\n\nDoes this ever happen to us, do you think? All the time! We are perpetually thrown for a loop when impermanent things, things we thought wouldn't change, actually do change\u2014or else don't change precisely the way we wanted them to.\n\nOur relationships, our financial situation, our jobs, our possessions, our very bodies and thoughts and feelings\u2014everything in our lives is transitory and fleeting. When our partners change (\"Don't go changing,\" sings Billy Joel\u2014but how can any of us not?); when our once-operative computer freezes up; when the boss suddenly alters our job description; when we get depressed, sick, old, or die\u2014what is it but impermanence smacking us upside the head? Wake up! Did you think this would last forever?\n\nNo, you might protest, I know that things and people change. But I wanted them to go this way and instead they changed that way! Well, welcome to reality. We can't govern the specifics of how external things and other people will change any more than we can magically stop change from occurring at all.\n\nWe'll return below to the fantasy of the \"controlling self,\" that ignorant sense that we can, in the moment, micromanage our lives and the events and people in them to suit our own whims. But here's the point: change is, and the exact direction of how things change is not within our control. Thinking that changing things won't change, or believing that we can decree the precise direction in which change will occur, sets us up for a big fall when reality makes its presence known.\n\n2. We believe what is impure to be pure.\n\nThe classic example of this misunderstanding involves the way we normally think about the human body. We sometimes, in our vanity, admire our own body for its good looks; even more often, we lust after the attractive, \"pure\" bodies of others.\n\nBut beauty, as they say, is only skin-deep, and really it's not even that. Even at skin level, up close and personal, we're all pretty much the same, and it's not that fetching. The epidermis of you, me, Angelina Jolie, and Johnny Depp is equally hairy, pocked, flaky, and mole-, pimple-, and freckle-marked.\n\nAnd when we go subterranean, deeper than skin-deep, well, it's sort of a horror show, isn't it? One Buddhist text describes this \"pure\" body we're so enamored of as a bundle of \"hair, nails, teeth, skin, flesh, sinews, bones, marrow, kidney, heart, liver, membranes, spleen, lungs, stomach, bowels, intestines, excrement, bile, phlegm, pus, blood, sweat, fat, tears, serum, saliva, mucus, synovial fluid [whatever that is\u2014we probably don't want to know!], and urine.\"\n\nNot a pretty picture, when we actually think about it\u2014which we definitely don't like to do, especially in the throes of either narcissistic self-admiration or sexual longing for another.\n\nOne of my teachers used to argue that supermodels, as they promenade down the runways exhibiting their external exquisiteness (here's me on the outside!) should also be mandated to carry and display a colostomy bag (and here's me on the inside!). But that would sort of spoil the show, wouldn't it? Our attraction to the physical body as something \"pure\" and desirable requires a dose of fantasy and a dollop of willful overlooking of the disagreeable details.\n\nWhile it's important to maintain a certain level of self-acceptance when it comes to our own bodies, and while there's nothing intrinsically wrong in being appreciative of or attracted to the physical beauty of another man or woman, our ignorance comes in being unrealistic about what the human body really is. We suffer because of our illusions about our physicality. And these illusions include thinking that beauty, youthful appearance, strength, and flexibility are inherent and unchanging in ourselves and in others. (See above for mistaking impermanent things for permanent ones.)\n\n3. We believe what will bring suffering will bring happiness.\n\nThis one is sort of a catchall category that describes our ignorance when it comes to what we think will really pay off for us. Throughout our lives, we scurry about pursuing money, things, experiences, and other people, in the hopes that somehow they will make us happy. But instead, we are repeatedly let down and perpetually left dissatisfied. What we thought would bring happiness ends up leaving us feeling unfulfilled and discontent.\n\nWe've set things (and people) up to fail. External things and beings don't have it in their power to make us happy; at best, they can only bring a temporary spike in pleasure. Only we have the power to create real, deep, and lasting satisfaction within ourselves and our lives.\n\nTrue happiness can only come from within. It's not \"out there\" somewhere, oozing out from something or someone else. And when we go looking for it in other people or external things, instead of discovering happiness we find ourselves disappointed, disheartened, and sometimes infuriated.\n\n4. We believe what is without an essence has an essence.\n\nWhen it comes to ignorance, this one's sort of the \"root of the root\" and will lead us directly to our mistaken view of ourselves: We think that things that have no \"essences\" (the word in Sanskrit is anatman, often translated as \"no self\") do have some kind of enduring and definitive quality or characteristic (an essential \"self\" or atman).\n\nHere's an example of this kind of mistake. Just imagine that you have an annoying person in your life\u2014an angry boss, an exasperating ex, or a troublesome relative. When we encounter (or even think about) such challenging people, we feel strongly that it's obvious to us that they are defined by the traits we ascribe to them: they are irritating, exasperating, or troublesome (or provocative, mean, hurtful\u2014pick the adjective that is apropos of your own annoying person). Any fool could see it! That's the way they really are\u2014essentially.\n\nThe proof that there actually are no essentially angry, exasperating, or troublesome people in the world is rather obvious, although we choose to ignore it all the time: These people have friends. They have loved ones. They have loads of people in their lives who do not find them angry, exasperating, or troublesome.III\n\nThis some find perplexing\u2014so much so that they go to the bother of trying to convince this annoying person's friends, family, and acquaintances how wrong they are. How can you be friends with her? Let me tell you the real deal about him! But alas, the annoying person's friends, family, and acquaintances often persevere in their error, don't they?\n\nI once had a student raise his hand in class and say what we all think before the filter goes up that prevents really stupid things from coming out of our mouths: \"I know someone who everyone would find annoying.\" Like we should all get on a bus and go on a field trip to visit the one essentially annoying person in the world. We'd all file by that innately objectionable person and go, \"Ooh, yeah, that's right . . . so annoying!\" Like a lighthouse casting its beam, this annoying being would just exude annoyance, and whenever we entered the purview of The Essentially Annoying Person, we could not help but be annoyed.\n\nThis is a self-justifying fantasy, and one that's often fortified when we find a few other people who agree with our evaluation of the person in question. See, we say to ourselves, she really is annoying. It's a groundswell, a veritable movement, a bandwagon of right-thinking folks, all of whom agree with me!\n\nWell, in fact, no. It's not that you and your fellow travelers correctly see some definitive unsavory essence that eludes the perception of others. It's that you (and, OK, perhaps some others) respond in a certain disagreeable way to some aspect of the personality of another. It's not that someone is annoying; it's that you are annoyed.\n\nWe don't see the world and the people in it as they are; we see them as we are. There are no difficult people in the world until and unless you find them to be so.\n\nAnd as a result of not comprehending this fundamental fact of life, we suffer. Instead of working on what it is in us that is aroused by the annoying person, instead of locating and then fixing the button inside of ourselves that gets pushed, we just complacently assume that the difficulties we experience with our annoying person are the annoying person's fault\u2014because \"annoying\" is what they are, not just what they seem to us to be.\n\nThe same error can be made in reverse. Let's say you enjoy Ben & Jerry's ice cream, as I do. Chunky Monkey flavor, let's suppose. Mmmm. Tastes so good! It is good-tasting ice cream, and anyone in their right mind would agree!\n\nAnd then we encounter someone who doesn't like Chunky Monkey! Maybe they don't even like the Ben & Jerry's brand. Possibly, they don't care for ice cream at all!\n\nIf Ben & Jerry's Chunky Monkey ice cream had the essence of being tasty, everyone with working taste buds, and who was not insane, would find it so. But (amazingly to those of us who like B&J's CM), there are people of apparently sound mind and taste buds who don't take a shine to it.\n\nThe qualities that we assume are in the people, objects, and experiences in life are not really there. These qualities are coming from us, not at us. We're projecting them, not perceiving them. Sure, we have our reasons. They say this or do that, and this pisses us off. But others hear or see the same things and don't get pissed off. We find a person \"difficult\" only because we have difficulties with him or her. They are not intrinsically, inherently, or essentially \"difficult\"\u2014in spite of the way they may appear to us.\n\nThinking otherwise is a serious blunder, and one that we make all the time, much to our detriment. This kind of error is the condition of possibility for the kind of judgmental attitude we talked about in chapter 2, and for all the nastiness that comes in its wake.\n\nThis is, bottom line, raw and unadulterated ignorance. Wisdom 101 is the dawning of the realization that we got it all wrong, all back-ass-wards.\n\n### THE \"WHERE'S WALDO?\" SEARCH FROM HELL\n\nThere's an even more fundamental application of our tendency to err in our perception of how things and people really are, one that lies even deeper than the mistake of thinking that our \"annoying person\" is annoying, or that Ben & Jerry's ice cream is delicious.\n\nIf the Mother of All Mental Afflictions is ignorance, the Mother of All Ignorance is the belief in a kind of a \"self\" that has never existed. What we have called the \"root of the root\" when it comes to ignorance\u2014thinking things have an inherent essence when they do not\u2014has a root of its own: the \"root of the root of the root\" is ignorance about the nature of the self.\n\nWe believe that we ourselves have a fixed, inherently existing, definitive essence, a self (atman)IV, when there actually is no such thing (anatman). And it is really this foundational error that not only undergirds all our misperceptions but also undermines any chance we have for finding true happiness and real self-knowledge.\n\nThe \"self\" here is not what we've been referring to as the true or higher self (the Self, Buddha nature, or soul) that we can and do access when we cease thinking we're somebody and relax into being nobody. What is meant here is an individual, particularistic lower sense of identity\u2014the egoistic self, the being somebody self, the little-voice-inside-your-head self.\n\nIt's \"you\" (say your name to yourself) that we're talking about here. It's the self that rises up in defense of itself when falsely accused\u2014\"You stole my car!\" \"No, no, I didn't!\"\u2014it's that \"I\" we're now focused on. It's the self that has a birthday, and so will have a death day. It's the \"itchy self\" that's unhappy, discontented, and dissatisfied, and that, fortunately, has no essential existence as such.\n\nAnd until we see this caterpillar for the chimera it really is, we'll only have a passing acquaintance with our true butterfly nature, that part of us that is free, spacious, and unbounded, that real Self who has never been born and so will never die.\n\nTrying to locate the individual \"somebody self\" that we're so sure, in our ignorance, is really there is like trying to find that bespectacled little guy with the red-and-white striped shirt and beanie known as Waldo (aka \"Wally\" in some markets), hidden inconspicuously within a vast crowd of people.\n\nOnly it's worse, because in this case \"Waldo\" isn't there at all. No needle to find in the haystack. Attempting to locate the self that we are so convinced really exists but can't be found is like playing the \"Where's Waldo?\" from hell!\n\n\u2022 \u2022 \u2022\n\nWhen we think of ourselves, who is it that we are thinking about?\n\nWho is it that we think sticks his or her head inside those carnival cutouts: the groups we identify with, the jobs that help define us, the roles we assume in our skein of relationships (father, mother, brother, sister, son, daughter, friend, enemy)? Who is it that we think is angry, jealous, proud, envious, or depressed?\n\nBeneath all the superstructure of personality makeup, memories, emotions, conditioning, and role-playing, who is the \"I\" that has a personality, a past, mental afflictions, an occupation, a set of relationships, and all these various roles to play?\n\nIn the Buddhist scriptures, it is said that the self we think exists but doesn't exist is one that (if it truly existed) would have three essential traits: it would be unitary, independent, and unchanging. But a particular, individual self\u2014the \"you\" that your name refers to\u2014with any of these three qualities is totally unfindable.V\n\nNow, dear reader, be forewarned: you might not appreciate how the proof for this unfolds. Your egoistic, self-infatuated but ultimately imaginary self will try to protect itself from being exposed for what it is. It will protest; it will feign boredom; it will say,\n\nOh, whatever. Let's take a break from reading this bit and get something to eat!\n\nHowever, ignorance is not bliss. The truth is what will set you free. But first, as Gloria Steinem once observed, it will piss you off.\n\nSo here we go . . .\n\nUnitary means we believe there's only one of us. Unless you have a serious case of multiple personality disorder, you think of yourself in the singular, not the plural. When we think or speak of ourselves, we say \"I,\" not \"we\" (monarchs using the royal \"we\" excepted).\n\nThe classical analysis when it comes to trying to find this particular Waldo is called \"The One or the Many.\" Is the self one thing, or is it many things? If the self were to exist in the way we think it does\u2014as a real thing, something perceptible\u2014it would have to be either one or the other.\n\nAlthough we normally assume that the egoistic, personalized self is unitary, we should ask ourselves, \"Does this supposed singular thing have parts?\" And yes, we could say we are indeed made up of two main components: physical and mental, the body and the mind.VI And we do, at different times, identify with one or another or both of these parts.\n\nIf I were to ask you, \"How old are you?\" and you gave me a number in response, you would have just identified with your body. And if in reply to the question \"How are you?\" you said \"I am upset, aggravated, pleased, OK,\" or whatever, you would have identified with your feelings, with your present state of mind.\n\nSo already there is a problem here. How can the one self be both the body (\"I am six feet tall\") and the mind (\"I am stressed out\")? That's two things, not one\u2014two kinds of selves, one physical and one mental, but not a unitary \"I.\"\n\nAnd when we look at either one of these two great portions of the supposed individual and indivisible self, we find that they themselves are not really single things either. What we call \"the body,\" as if it were one organism, is itself composed of many constituents\u2014the torso, the limbs, and then all those yucky things inside the body that we talked about earlier in this chapter. And each of these separate parts is infinitely divisible into its own constituent parts. Even a single finger can, upon investigation, be dissected into the part above the knuckle and the part below, the fingernail part and the part beneath the fingernail, the left side of the fingernail and the right side\u2014and on and on, ad infinitum.\n\nThere's no part of us that isn't further divisible into its own parts. That's what's entailed in saying \"a part\"; it's something that has a right side, a left side, a top, and a bottom (the parts of a physical object), which makes it different from other parts. And the same is true with a moment in time: a thought arises, lasts for a while, and then ends, and each of those three parts of the moment itself has a beginning, a middle, and an end.\n\nWhen we say something like \"right side\" or \"beginning,\" these parts of a part can always be further partitioned: \"right side of the right side, left side of the right side, top and bottom of the right side;\" or \"beginning of the beginning, middle of the beginning, end of the beginning.\"\n\nAnd so it is that if we think we are the body and\/or the mind, that self cannot be unitary, but in fact would be endlessly multiplied and fragmented.\n\nOh, come on! I didn't really think I actually was my parts. I'm not my body and mind; I have a body and mind. Now can we please stop thinking about this and get something to eat?\n\nOK then. So while we might sometimes carelessly identify with one or another of the various constituents of the self, maybe the \"I\" we think we are is separable from those parts. And this would be the second of the three qualities that we attribute to the personal self: independence.\n\nThe investigation applied to this second kind of misconception about the self is called \"The Same As or Different From?\" It goes like this: Is the self the same as the parts that comprise the self, or is it different from (i.e., independent of) those parts? And like \"the One and the Many,\" if the self really and truly exists the way we think it does, it can't logically be both. It's an either\/or proposition.\n\nSo let's check. If the self were the same as its parts, it couldn't be a unitary self, for as we've seen there are lots and lots of parts, physical and mental, that would comprise a self that was the same as its parts. If I were identical to the parts of me, there would be as many me's as there are parts to me.\n\nThat leaves the other option, that there's a self that is different from the parts. This would be a self that is independent of the parts, a self that has a body and mind. And \"independent\" means \"doesn't need them.\" The body and mind could then be heaped together in London while the self could somehow separately be in New York City.\n\nBut that's impossible, isn't it? For one thing, whose mind is it that's thinking about a self that exists apart from the mind that's thinking about such a self? And in any case, that's not the you-say-your-name-to-yourself self we are so sure must be somewhere floating around inside the mind-body complex.\n\nA room has four walls, but where is the room that has four walls? The self that we imagine has a body and mind is as unfindable as a unitary self that's the same as the body and mind. \"The self,\" like \"the room,\" cannot really exist independent of the parts that make its shadowy semblance possible.\n\nNow this is really enough! Why can't he just leave us alone? What about that snack?\n\nFinally, we turn to the third impossible thing that we believe when it comes to ourselves: the idea that there is an unchanging personal self. This is sometimes called the \"witness self\"\u2014an invariable \"I\" that has observed \"me\" growing up as a child, graduating from school, getting married, having a family, moving from one house to another, and is presently watching \"me\" get old and moving nearer and nearer to death.VII\n\nWe all have this sense that there is an unchanging witness self that carries on continuously as everything else\u2014life as a whole, one's thoughts and feelings, and every individual part of the body\u2014is perpetually and ceaselessly changing. So where's that Waldo? Can we really believe that there's a tangible, perceptible present self that is in any real way whatsoever the same as the self we were when we were three years old?\n\nYes, we can believe that, as long as we don't have to think about it, so just quit it already! Like Popeye said, \"I y'am what I y'am and that's all that I y'am!\" Why bother with all this! Let's just stop this thinking about things, OK? I'm hungry . . .\n\nTo \"The One or the Many\" and \"The Same As or Different From,\" we can now add a third kind of analysis to our \"Where's Waldo?\" search from hell: \"Changing or Unchanging?\" Where is the individual, particularistic self that remains unchanging as everything else in us and around us changes? Or more subtly, where's the self that undergoes change? If there's only a constantly fluctuating self, there's not also an unchanging witness self, let alone an unchanging self that also undergoes change.\n\nSo the exercise is now complete. Disoriented? Confused? Filled with objections? Well, it's no wonder. As I warned you above, the ego doesn't like this \"Where's Waldo?\" game one bit! All kinds of resistance arises in ourselves when we try to find the \"somebody self\" we think is ourselves!\n\nBut I just know I'm somebody! There's probably some trick here. How could it be that I'm really nobody when it feels so obvious that I am somebody? And I still didn't get my snack!\n\n\u2022 \u2022 \u2022\n\nAnd there is a trick here, actually. The self can be thought of as both unitary and plural, as both the same as and different from its parts, as both changing and continuous\u2014because the self is just an idea, not a thing. From one perspective, the self can be conceptualized as singular, independent, and unchanging; and from another perspective it can be thought of as plural, contingent, and fluctuating. It depends how you look at it\u2014because the \"somebody self\" is not really there at all apart from our thinking it's there.\n\nWhen it comes to the little, individual, particularistic, snowflake, caterpillar self, there is not a findable unitary, independent, unchanging entity either inside or apart from the body and mind. The \"somebody self\" is not a discrete, discernable object; it is only a conceptualized image.\n\nWhen we say we have a \"self-image\" or a \"self-conception,\" we're way more accurate than when we say we have a self or when we claim to be somebody.\n\nThe \"Waldo\" we try to find when we go looking for it turns out to be only imaginary. Remember the movie Harvey, with Jimmy Stewart? The one whose lead character was always accompanied by an invisible six-foot rabbit? Well, the self we think we are is just as imaginary as Jimmy Stewart's friend Harvey the rabbit.\n\nBut imaginary things can feel quite real and can function quite well to bring us a lot of difficulty in life. The Mother of the Mother of All Mental Afflictions\u2014ignorance about what kind of self we think we have\u2014leads to all kinds of problems.\n\nOur belief in the \"self-existence\" of the personal self\u2014the feeling that Waldo (or Harvey) is really there apart from our merely thinking he's there\u2014inevitably engenders what is called in the Buddhist texts \"self-cherishing.\" We become enchanted with and seduced by an illusory impression of the individualized self, and then we grasp and cling to it for dear life.\n\nAll the other mental afflictions\u2014desire, anger, lust, pride, jealousy, envy, greed\u2014arise either to defend or to promote what is, after all is said and done, just a misconception. Ultimately, we are imprisoned not by these negative emotions, but by the imaginary self who is adversely affected by them.\n\n### THE CAPTAIN KIRK SELF\n\nThere's another false notion we have about ourselves that we haven't examined yet. It's the sense we have that there's a self who's in control of the present, a \"master self\" that rules over the current state of the body, the mind, and, indeed, all aspects of our life.\n\nI like to think of this version of \"me\" as the \"Captain Kirk self.\"\n\nIn the original Star Trek television series, the spaceship Enterprise was overseen by Captain Kirk, played by William Shatner. He was often depicted sitting in his commander chair\u2014a replica of which I've seen for sale, priced at over two thousand dollars!\u2014on the upper deck of the starship, gazing out at the cosmos through that cool wraparound windshield. And Captain Kirk would bark out orders to his crew: \"Scotty, raise deflector shields!\" And Scotty would dutifully obey: \"Aye, aye, sir! Deflectors raised.\"\n\nSomewhere ensconced inside the head, just behind the eyes (our own personal windshield of our own personal Spaceship Me) is where we usually locate the Captain Kirk self. And just like the dear captain, that commander self barks out orders: \"Legs, prepare to walk!\" \"Mouth, commence talking!\" \"Mind, remember to pick up some milk!\"\n\nAnd often enough, our lackey crew obeys. The legs move when ordered to walk, the mouth flaps when instructed to speak (sometimes even before the mind is commanded to think!), and frequently we do remember to get the milk when Captain Kirk enjoins us to.\n\nThese kinds of experiences give us a strong conviction that this master self is in charge not only of what the body does and the mind thinks but also of everything else in our lives. And when confronted with incontrovertible evidence that contradicts our conviction, it's usually quite upsetting. When we don't get our own way, the old Captain tends to pitch a fit!\n\nIf there really were such an all-controlling self, why would that ruler ever decree that we have a bad day, or get upset at an annoying person, or have a headache, or get sick or old, or choose to be anything other than happy and content all the time? If our own personal Captain Kirk truly existed, wouldn't some of his commands seem sort of wacky? \"Scotty, let's get really gloomy today. Raise depressors!\" Wouldn't Scotty's clear retort be, \"Captain, are ye mad? Have ye gone insane?\"\n\nIn fact, there is no real Captain Kirk self, just as there's no unitary, independent, or unchanging personal self. And here's the real proof of that: we can't change the present in the present. If there were a Captain Kirk self, we would command everything in life to be just as we wished. And that's obviously not happening\u2014have you noticed?\n\nAs you can probably tell from all my references, I watched a lot of television as a kid. Readers of a certain age might actually remember viewing two shows I used to like from the 1960s\u2014Bewitched and I Dream of Jeannie. In the first, Elizabeth Montgomery played Samantha, a full-blown witch with all kinds of supernatural powers, married to a pretty hapless ordinary mortal named Darrin. When Samantha wanted to effect some change in a situation (often to fix something poor Darrin had messed up), she would simply wiggle her nose and\u2014shazam!\u2014the world would bend to her witchy will.\n\nBewitched met with some success\u2014it was the second most watched program on television in 1964, and nearly forty years later TV Guide magazine included it in a list of \"The 50 Greatest TV Shows of All Time\"\u2014so it wasn't long before a similar program, I Dream of Jeannie, went on the air. The premise again involved a match-up between a magic-making woman (a genie this time) and a normal guy (who was, however, an astronaut, whom his devoted wife called \"master\"\u2014a patriarchal fantasy, simultaneously subverted by the mismatch when it came to actual power).\n\nIn addition to offering a genie instead of a witch in the lead role, the other major difference in the two programs (product differentiation!) was that Jeannie didn't wiggle her nose to magically transform reality whenever she wished. Her modus operandi was to fold her arms and forcefully nod her head such that her long ponytail would flop around a bit. And that was enough to change anything she wanted, right there and then, in the moment.\n\nMost of us go through life wiggling our noses and shaking our ponytails, trying to miraculously transform the present in the present. But things don't work like that; we're not witches and genies, and the confirmation of this is all too apparent. The traffic doesn't unsnarl just because we wish it would; the headache doesn't disappear simply because we don't like having it; and the annoying person doesn't magically stop being annoying when we, metaphorically speaking, twitch our nose or bounce our ponytail. We can't wriggle our way out of tight spots just by wiggling our appendages!\n\nThe desire to change the present in the present is perhaps the biggest and most recurring itch of all, but it's the one we clearly can't alleviate by sorcery scratching. That mojo ain't working. The Captain Kirk\/Samantha\/Jeannie self is really (to switch the pop-cultural reference yet again) the Wizard of Oz, just a humbug behind the curtain, ineffectually moving nonfunctional levers and pulleys.\n\n### YOU ARE WHO YOU THINK YOU ARE\n\nThe realization that the \"somebody self\" is just an idea should come as really good news. If there were essentially a unitary, independent, and unchanging individual self, it would be, well, unchangeable. But luckily, as we've seen, there is no such self. And so it's a good thing that we are not really the somebody we think we are.\n\nBut, then again, you could equally say that we are just the somebody we think we are, and that's all the \"somebody\" any of us is. It's the conceptualization of somebody that makes us that somebody\u2014and really nothing more than that. As one ancient Indian text puts it, \"The one who thinks he is free is free; the one who thinks he is bound is bound. It is true what they say: You become what you think.\"\n\nTo say that the \"somebody self\" we usually desperately clutch to is illusory is not the same as saying it doesn't exist at all. The individual self does, of course, exist . . . but only as an idea, a concept, a label. As philosopher Julian Baggini puts it, \"The idea of the self as a construction is one that many want to resist, because it seems to imply that it is not real. But of course constructions can be perfectly real.\"VIII\n\nAnd there are different kinds of constructions or conceptualizations of the self, some more beneficial than others. The belief in a unitary, independent, and unchanging self; or the conviction that there really is an all-powerful Captain Kirk self\u2014these are not helpful concepts. Besides the fact that there's no findable \"Waldo,\" the very idea of a self like this leaves us feeling either paralyzed (how could we change such an unchangeable self?) or frustrated (Captain Kirk's commands so often go unheeded!).\n\nThe \"somebody self\" is just like the room we talked about above. The room has four walls, and there's no room without the four walls, but \"room\" is just a name and a concept that arises due to the empty space enclosed by the walls. And it's just the same with the individual self: it's nobody that makes somebody possible.\n\nWe're nobody apart from thinking that we're somebody, and when we stop thinking we're somebody, we're left with really nobody. This observation points us to the true methods for \"self-improvement,\" which we'll investigate at length in the next chapter.\n\nThe question is not whether our individual sense of identity exists. It obviously does; we hear that little voice inside our heads pretty much constantly. The crux of the matter is how such a self exists\u2014and how we could improve it.\n\nBy recognizing that we're nobody (that is, that we're not a hard-wired somebody who exists essentially and unchangingly), we have the possibility of conceptualizing ourselves as a better somebody\u2014a more contented, happy, and fulfilled person.\n\nAnd by doing so, we will have moved closer and closer to the Great Itchlessness we all desire.\n\nAction Plan: Scratching the Itch\n\nStop for five or ten minutes each day and pinpoint your biggest desires, your most persistent itches. First identify what it is that you want. Is it more money, a better house or car, or a new iPhone? Or is it an improved relationship with your partner, your family members, or with someone at work? Maybe it's more recognition and popularity, or a holiday in Bermuda. Or perhaps it's losing a few pounds or feeling healthier.\n\nOnce you've identified the itch, focus on what you hope will be the outcome if the itch gets scratched\u2014on what you think would happen if you actually obtained what you desire. See if you can't get to the realization that what, in fact, you wish for is actually just contentment\u2014the end of the itchiness itself.\n\nThen revisit the particular desire you've identified. Would getting what you want really bring about the hoped-for satisfaction, or would it just provide some partial and temporary relief from the wanting? While we may not be able to achieve contentment immediately, this action plan helps us train ourselves to be more aware of what it is we really desire.\n\n#### Notes:\n\nI. Overachieving, type-A personalities who are obsessed with their careers might recall that God's curse for humanity as he kicked Adam and Eve out of the Garden was to cause man and woman thereafter to work for a living and look after their children, instead of granting us a permanent holiday.\n\nII. There are some exceptions. For stories of how ignorance originated in the Hindu and Buddhist texts, consult Wendy Doniger O'Flaherty, The Origins of Evil in Hindu Mythology (Berkeley: University of California Press, 1980).\n\nIII. Another indication that people are not essentially the way they sometimes appear to be is that they don't always seem to be that way. Sometimes angry people appear angrier than at other times, and sometimes they don't appear angry at all. If the angry person were essentially an angry person, he or she would always be an angry person, to exactly the same degree. For an \"angry person\" would always be that and couldn't essentially be that and something other than that at the same time. Isn't that what \"essentially\" means, after all?\n\nIV. In some Indian texts, the Sanskrit word atman is used differently than it is here in the Yoga Sutra and in many Buddhist scriptures. Elsewhere it is synonymous with the \"true self\" as opposed to an individual, egoistic self (which is sometimes designated as the jiva to contrast it with the atman).\n\nV. The latest research in the neurosciences is validating the ancient Buddhist observations. As one recent summary puts it, an unchanging and continuous self, a \"unifer\" self, and an \"agent\" self (similar to the \"Captain Kirk self\" talked about later in the book) are all \"mistaken beliefs\" or \"illusions\" that \"do not withstand scrutiny.\" See the special issue of New Scientist magazine, \"The Self: The Greatest Trick Your Mind Ever Played\" (February 2013). See also Julian Baggini, The Ego Trick: What Does It Mean to Be You? (London: Granta Books, 2011).\n\nVI. There are neuroscientists nowadays who believe that the mind's activities\u2014consciousness, thought, emotions, and so forth\u2014can be reduced to the brain and its firing of neurons. While only a few researchers would be so reductive as to say there is absolutely no difference between the mind and the brain (most still acknowledging some sort of \"ghost in the machine\"), there does seem to be a trend toward the position that ultimately there are only physical parts to our being. While such a reductive view of the self does not accord with the assumptions of any of the world's spiritual traditions\u2014indeed, it is the opposite of a belief in anything spiritual\u2014it has no bearing on our argument here: Are we one thing (even if it's just a purely physical thing, just the body) or many?\n\nVII. The \"witness self\" spoken of here can be distinguished from one of the two \"birds\" we encountered in the passage from the Upanishads quoted toward the end of chapter 1. The \"bird\" who looks on impassively as the other \"bird\" (the individual self) eats and engages with the world, is the true Self\u2014the ocean as opposed to the individual wave; our nameless true nature, not you say your name-to-yourself.\n\nVIII. Baggini has coined this term \"ego trick\" to describe the play between the self we think exists and the conceptualization of the self that does exist: \"The Ego Trick is not to persuade us that we exist when we do not, but to make us believe we are more substantial and enduring than we really are. There may be an illusion as to what we really are, but not that we really are.\" Julian Baggini, The Ego Trick, 41, 152.\n\n## 4\n\n## Nobody Makes a Better Somebody Possible\n\nThere is only one corner of the universe you can be certain of improving, and that's your own self.\n\n\u2014\u2014Aldous Huxley\n\n### BECOMING A BETTER SOMEBODY\n\nIf the individual self is, at bottom, nothing but a conceptualization of the self, then one important part of the spiritual quest will be to improve that self-conception. While there may not be a findable essential \"somebody self\" to ameliorate\u2014and, remember, the real, oceanic \"nobody\/everybody\" butterfly self is in no need of improvement at all\u2014the personal self that does exist can and should be developed into a better edition.\n\nAs we noted toward the end of the last chapter, it is precisely because we are not stuck with the somebody we think we are now that we can upgrade ourselves into a more self-satisfied model.\n\nAnd there's nothing wrong with wanting to become a better somebody. Indeed, without a desire like this, we'll never get to the point where the Great Itchless State becomes possible, and where the peace and tranquility of being nobody can be fully experienced and appreciated.\n\nBecause it's possible, we should definitely strive for self-improvement. Because we're all really, deep down, nobody, everyone has the potential to become a different somebody. We can choose to continue to embrace a depressed, discontented, and perpetually itchy sense of self, or we can work toward creating a joyful and fulfilled personal identity that is nourished by the deep reservoirs of our true identity.\n\nWe can change. We can better ourselves. We can create a happier iteration of the self to replace the needy, greedy, twisted version that's driving us crazy. But self-improvement will be achieved not through trying to be more special than others, either through foolish pride or through laying claim to an exceptional status due to our suffering.\n\nIt's worth repeating: There's nothing inherently wrong with being \"self-interested.\" It's crucial to build a good, healthy sense of the individual self\u2014not as the final goal but as a necessary platform for the higher work of joyful self-transcendence and integration with the world around us. Enlightened self-interest entails wising up to what will really work to bring about an untroubled and contented personality, somebody who's ready, willing, and able to be less self-obsessed and self-centered.\n\nRemember, it's not really \"self-improvement\" if it's all about you.\n\n\u2022 \u2022 \u2022\n\nThe \"somebody self\" is an artifact of how we presently regard ourselves. And this, in turn, depends on the kind of past we think we had (for we are who we think we once were) and our expectations, hopes, and fears about the future (we are who we think we will become). The conceptualized \"somebody self\" is found at the nexus of two times\u2014the past and the future\u2014that themselves only exist as ideas within the present mind.\n\nThis \"somebody self\" is the product of moral training and positive self-development\u2014or the lack thereof. There's a huge difference in the self-perception of someone who has cultivated humility, modesty, and an unselfish and charitable attitude toward others and that of someone who is driven by inborn (and reinforced) selfishness, vanity, pride, and aggressive competition with others.\n\nWe've seen in the last chapter that we can't change the present in the present. Captain Kirk can't just dictate that things change at will in the moment, nor can any inner witch or genie work this kind of magic. This means that somebody can't just in the moment choose to be anybody; the \"somebody self\" can't immediately transform into somebody different. We can't go from zero (selfish, egotistical, and dissatisfied) to one hundred (humble, altruistic, and untroubled) in just a few seconds, or even a few days or weeks or months.\n\nThe lower, individual self is an idea of the self, but our self-conception is constantly in flux. This self, we could say, is a process, not a thing. To invoke a very common and ancient simile, the self is like a river\u2014let's say the Mississippi. What we call \"the Mississippi River\" is not an entity or a thing; it is only a name we give to a particular flow of water\u2014to a process. As Paul Robeson famously sings, \"Ol' Man River just keeps rolling along.\"\n\nWe mistake changing things for unchanging things. We assume that, because we have a name or a concept for \"the Mississippi River,\" the word and the idea must refer to some thing, when all it really designates is a flowing current, a movement, an activity.\n\nWell, our sense of personal identity is just like a river. Every part of what we include in our idea of \"me\"\u2014every physical and mental component of the self\u2014is changing, moment by moment. The kind of idea I have about \"me\" deceives me. I think my concept of \"me\" refers to a unitary, independent, and unchanging entity, when all it denominates is a flow.\n\nAnd so even what we mean by \"me\" changes over time, doesn't it? What Julian Baggini calls the \"autobiographical self\" provides a sense of continuity to the self: \"The unity and permanence we feel over time depends on our ability to construct an autobiographical narrative that links our experiences over time.\" \"But,\" Baggini goes on to observe, \"individual experiences and sense of self at any particular time can vary enormously. What is more, the autobiographical self is very good at self-revision. In effect, we are constantly rewriting our histories to keep our inner autobiographies coherent.\"\n\nThe self is mutating and therefore mutable. Otherwise what would be the point of a spiritual practice? If we weren't changing, we couldn't change! Every authentic spiritual tradition has always assumed that, because the \"somebody self\" is just a process and not a thing, the process we call \"me\" can be redirected and differently channeled.\n\nWe can transform our understanding and evaluations\u2014not only of ourselves, but also of other people and of everything about our lives. We can train ourselves to change our minds\u2014not in the blink of an eye, of course, but over time. We can gift ourselves with a different set of ideas about both our inner and outer worlds.\n\nAnd, as we shall see toward the end of this chapter, these two different conceptualizations of our reality\u2014inner and outer\u2014are in a symbiotic relationship.\n\nBy cultivating wisdom, we can learn to think differently about both ourselves and the people and things in our outer world (remember, no annoying people or intrinsically tasty ice cream out there). With more awareness of the changing nature of the \"autobiographical self,\" we learn to direct that change in a more positive way. Wisdom about the externals will help us act, speak, and think in such a way that we'll improve our sense of self\u2014and this, in turn, will transform our view of the world and the other people in it.\n\n### HOW KARMA REALLY WORKS\n\nAs we saw in the last chapter, we all have a bad case of the \"if only\" syndrome. We are convinced that if only we could adjust the external events in our lives to our satisfaction:\n\nIf only I had a better job, more money, a nicer home, a new iPhone, a holiday in Bermuda . . .\n\nAnd if only we could figure out how to make other people in our lives change to our liking:\n\nIf only my husband or wife were nicer to me . . . if only my boss weren't so demanding . . . if only I could make that annoying person stop being so annoying . . .\n\nThen, finally, we'd be happy. We're all pretty itchy, pretty much all the time.\n\nIn our ignorant and self-centered desire to work our will on the world, we usually just send Captain Kirk out on the case. We hope that the good old Cap'n will micromanage the external world and the people in it so that all will become pleasing instead of so problematic.\n\nBut as we've seen, the Captain Kirk self is an ineffectual humbug. It is therefore unsurprising that he is impotent to effect the changes we demand. Events in the outer world aren't modified at our command, and other people don't automatically adjust themselves and their actions in accordance with our mandates.\n\nWe are perpetually thwarted in our attempts to work the magic that would change the present in the present.\n\nThere is, however, a more efficacious method at hand for transforming our lives for the better. We can still hope for a happier future, but we must also accept that there will be a gap between the time of the cause and that of the effect. This gradual method for transformation is what the Eastern traditions would call \"changing your karma,\" or what Jesus spoke about in terms of \"sowing what you will reap,\" or what we colloquially mean when we say \"what goes around, comes around.\"\n\nThe basic \"laws of karma\" can be succinctly stated: \"No action in this world goes for naught or brings about a contrary result,\" as one ancient Indian text crisply puts it.\n\nThe first principle\u2014\"no action goes for naught\"\u2014proclaims that every action will have a reaction; everything we do, say, or even think will have future consequences. And the second rule\u2014\"no action brings about a contrary result\"\u2014asserts that the kind of outcome one will experience depends on the kind of action that produced it. No cause brings about a \"contrary result\": nothing bad can come from something good, and nothing good can come from something bad.\n\nThese principles are not the creation of any one religious tradition. They are found, in one form or another, in many and various places. In the Yoga Sutra we read, \"There is a causal connection between meritorious and blameworthy acts and their respectively cool and pleasurable or scorching and unpleasurable effects.\" Jesus put forward the same karmic law in more metaphorical terms by noting that you don't get grapes from thorns or figs from thistles:\n\nYou shall know them by their fruits. Do men gather grapes of thorns, or figs of thistles? Even so every good tree brings forth good fruit; but a corrupt tree brings forth evil fruit. A good tree cannot bring forth evil fruit, neither can a corrupt tree bring forth good fruit.\n\nWhat makes an action \"good\" or \"bad\"? An act (inclusive not just of physical acts but also those of speech and even thought) done with a good intention\u2014that is, with a selfless, kind, altruistic, compassionate motivation\u2014will bring about a good (that is, pleasant) result. Conversely, a bad act is \"bad\" because it is inspired by an intention fueled by one or another of the mental afflictions, all of which are instigated by selfishness. Such a negative action\u2014motivated by ignorance, self-aggrandizement, or the wish to harm others\u2014will bring an unpleasant consequence in the future.\n\nAll authentic spiritual traditions teach some form or another of \"karma.\" The fundamental principles we've just discussed form the very heart and soul of every moral system. There's no \"system\"\u2014and therefore no hope for willed self-improvement\u2014if there's not the assumption that:\n\n1. Every action has a consequence, and\n\n2. The type of result (pleasant or unpleasant) invariably correlates to the nature of the cause (kind or unkind, selfish or selfless).\n\nThe first principle denies randomness and therefore empowers us, while the second provides the basic method for governing the direction of one's karma in cultivating a better life.\n\nSo far, so good. But while the fundamental rules of karma are both easy to grasp and universally advocated in every ethical system, the actual operation of karma works at a level different from the one we usually think. The project of knowing how to improve the \"somebody self\" depends upon a belief in moral causality (which gives us confidence that improvement is possible), but also on an understanding of how such beneficial transformation can really occur.\n\nKarmic management\u2014creating the causes for a more agreeable life in the future\u2014can easily be misconstrued as just another attempt to magically bend the world and other people to one's self-centered will. When there's only a superficial grasp of karma, the Captain Kirk self is resurrected, albeit in a slightly different guise:\n\nOK, I get it now! I can still have my way with the world and with other people . . . I just have to be a little more patient! If I don't hurt others, in the future no one will hurt me. If I am generous, then the boss will someday give me a raise. If I'm patient with my annoying brother-in-law, he'll eventually change into a friendlier person.\n\nThis simplistic, mechanistic, and ultimately narrow-minded and self-seeking understanding of karma is really just the ego grabbing onto a new-and-improved technique in order to once again try to achieve its narcissistic ends. It's the \"if only\" syndrome at work all over again: If only others would behave themselves; if only I had more money; if only my brother-in-law were a nice guy.\n\nThe sole difference between this view and the usual version of such wishful thinking is that now we have come into possession of this cool spiritual tool called \"karma\" in order to realize our longings.\n\nNo matter what guise the Captain Kirk self assumes, the egomaniacal assumption persists: We will be able to get whatever we want from the world, and we can make other people behave exactly as we wish, if we can just somehow find and pull the right strings.\n\n\u2022 \u2022 \u2022\n\nThere are some presentations of karma that lend themselves to the mechanistic theory discussed above. But even in those versions of karmic causation, bets are very much hedged. For one thing, according to the texts of Tibetan Buddhism, the precise workings of karma are classified at the level of \"very subtle\" (as opposed to \"obvious\" or just plain \"subtle\") and they're knowable only to enlightened beings, who, unlike us, are supposedly omniscient.\n\nFuthermore, karmic results\u2014becoming famous through practicing humility, or getting money by being generous\u2014are said to ripen in one of three possible times: in this very life (could be tomorrow, could be seventy years from now), in the very next lifetime (when you'll be a dramatically transfigured version of \"you\"), or (wait for it . . .) in any lifetime after that.\n\nThe exact time when one will reap what one has sown is as unknowable as the exact form the reapage might take.\n\nThere's a joke that underlines this point. George is magically transported to heaven and meets with God. The visitor is astounded by how dissimilar God's paradise seems from life on earth.\n\n\"Wow, it sure is impressive here! So different from where I come from! Say, God,\" George asks, \"how much is a million dollars on earth worth in heavenly currency?\"\n\nAnd God answers, \"One penny.\"\n\nGeorge is, needless to say, quite impressed. Just one of God's pennies is the equivalent of a million dollars!\n\nSo he persists in his questioning: \"And how long is a hundred years in divine time?\"\n\nGod replies, \"One minute. One minute up here is equal to a hundred human years.\"\n\nGeorge, suitably dazzled but with his wits still about him, makes a request: \"Before I go back to earth, could I get one of your God pennies to take home with me?\"\n\n\"Sure,\" God answers. \"Just wait a minute.\"\n\n\u2022 \u2022 \u2022\n\nIt's best not to regard self-improvement through karmic management as a matter of manipulating and upgrading outer events and other people. Positive actions of body, speech, and mind will indeed have positive results. But it's more realistic to think about the fruit of good karma ripening internally, not externally.\n\nAs Tolstoy once observed, \"Everyone thinks of changing the world, but no one thinks of changing himself.\"\n\nKarma is not some kind of magical, mystical technique for genetically modifying difficult people or for physically re-engineering events in the material world. Karmic management is primarily a method for systematically changing one's self-perception. What we can most effectively, efficiently, and reliably transform is ourselves\u2014and not the world, let alone other people who have their own karma to work out.\n\nIn Shantideva's Guide to the Bodhisattva's Way of Life, we are given direction as to where to concentrate our efforts when it comes to changing our karma:\n\nAnd so, although I am unable to exercise control over external phenomena, I will restrain my own mind. What else is there that I can really control?\n\nThis verse points us to a more commonsensical understanding of causation and self-improvement. Karma isn't about creating the causes for altering the behavior of other people (I'm being nice so my husband will change and stop being mean to me) or directing the processes of the external world (I'm being generous so more money will come my way). It isn't about changing the data. The data will change all right, but always in unanticipated, unpredictable, and, as the text says, uncontrollable ways.\n\nIn any event, whether other people appear to us as \"nice,\" or whether a particular amount of money is \"enough\" are subjective interpretations and not objective, measurable phenomena. If one's subjective perspective changes, one's perspective on how much money makes you rich or how nice other people are will change as well.\n\nKarma is not like gravity; it is not some kind of invisible external \"law of nature.\" It is first and foremost an internal law governing our own state of mind. And so, karmic management is really about changing our own frame of reference\u2014\"restraining my own mind\" from creating negative karma\u2014so that our outlook on others and on life itself is not so distorted by our own mental afflictions. It's about transforming our perception such that it is conditioned not by our worst tendencies but rather by virtues like forgiveness, compassion, love, wisdom, and a magnanimous spirit.\n\nWhen we see ourselves struggling to overcome our own negative proclivities and replace them with goodness, we plant \"karmic seeds\"\u2014a metaphor for what we nowadays would call \"memories\" (conscious, subconscious, or even unconscious). And as we know, memory does not simply replay what really happened but what we think happened, which can and does change over time.\n\nIt is what we think we have done, said, or thought in the past\u2014in a word, our karma\u2014that defines us in the present. Our concept of our personal identity\u2014who we think we are\u2014is a function of who we think we used to be. And both our present sense of self and the memories that constitute it are perpetually changing and therefore changeable.\n\nIn the Buddhist texts, a big debate rages over where, exactly, the karmic \"seeds\" we planted in the past were \"stored\" until they were ready to ripen. Given that we always come up empty-handed in any \"Where's Waldo?\" search for an immutable and enduring individual self, how does karma persist from the time of its creation to the time of its fruition?\n\nThe answer is that karma is conserved in the \"simple me\"\u2014our basic sense of who we are at any given moment. Karma is memory\u2014again, conscious, subconscious, or unconscious\u2014and it is memory that comprises our current identity. If you don't believe me, try to imagine who you would be if you had no past! As filmmaker Luis Bu\u00f1uel has said, \"Life without memory is no life at all. . . . Our memory is our coherence, our reason, our feeling, even our action. Without it, we are nothing.\"\n\nThe \"me\" who created my past karma is long gone, but the \"me\" I presently conceptualize is an idea based on my memories of who I once was and the kinds of things I think I once did, said, or thought.\n\nThere's no enduring, abiding self that has karma. The conceptualization we have of ourselves is karma.\n\nThe memories that shape our self-image are called vasanas in Sanskrit. They pervade our consciousness in the same way that the fragrance of perfume lingers in a room even after the person wearing it has departed. The \"room\" that is our present identity is saturated with, and defined by, the aroma of our past karma.\n\nSo one way to improve the conception of the self is to rehabilitate the memories we are carrying around. The past is never like it used to be. It is forever undergoing reinterpretation. For individuals as for groups, there's no history except for revisionist history. As psychologist Mihaly Csikszentmihalyi has written, \"The past can never be literally true in memory: it must be continuously edited, and the question is only whether we take creative control of the editing or not.\"\n\nSince what we call our \"past\" is really only some part of our present mind, and since our present is constantly changing, our idea of the past is in flux too. Instead of carrying around\u2014and defining ourselves by\u2014a past replete with bitterness, recrimination, and disappointment, we can work at revising our personal histories in such a way that forgiveness replaces anger, gratitude takes the place of resentment, and acceptance supersedes thoughts of sadness and regret.\n\nPeople who have made peace with their past will have gone a long way toward improving their present sense of self-esteem. Not only will their memories have been altered and improved, but the very acts of forgiveness, gratitude, and acceptance will have modified their sense of self. Rather than thinking of oneself as an embittered, traumatized victim, one can begin to conceptualize the self in terms of the virtues one has practiced in relation to the people and events of the past.\n\nKarma can, in this way, work both retroactively and proactively. By practicing forgiveness, gratitude, and acceptance vis-\u00e0-vis our past, we create the causes that will result, over time, in a better self-image. And in the future, we will remember ourselves as someone who was trying to forgive, to be grateful, and to be accepting of all that has happened.\n\nIf karma is memory, and memory is what composes our self-image, then improving our sense of self is a matter of acting, speaking, and thinking such that we will look back at our lives with dignity instead of embarassment: I was the kind of person who tried to live a good life, a life guided by nonviolence, honesty, integrity, charity, and the other virtues. We practice being a better person today (not just in terms of our past, but in an ongoing way as we interact with the world and other people) so that we will think about ourselves in a better way tomorrow.\n\nFurthermore, by paying more attention to our ethical life, we will have also transformed even our present conception of ourselves. If we can generate conviction in the laws of karma, and if we start living our lives in accordance with what will bring us more happiness and less suffering, we will begin to see ourselves differently in the present. We will regard ourselves as a person who is guided by the karmic laws instead of someone who is just unthinkingly going through life on automatic pilot. Our current level of self-esteem will instantly rise when we become more cognizant of the consequences of the actions we take to enhance our future level of self-esteem.\n\nKarma shapes our perspective of ourselves\u2014and the idea of the self is the only self we have ever had. Trying to manipulate and master other people or external phenomena in order to feel better about one's own life is usually a pretty ineffectual gambit (have you noticed?).\n\nWhat I can change is myself. And, as the verse says, \"What else is there that I can really control?\"\n\n### \"IT'S LIKE THIS NOW\"\n\nSo now that we're acquainted with the theoretical blueprint of how self-improvement really occurs, it's time to put theory into practice. The secret to feeling better about ourselves and our lives, as we've seen, is not to expect the world and others to be different than what they are. It is rather to accept the hand we're dealt at any given moment, and then learn to play our cards in such a way as to improve our estimation of ourselves as a player.\n\nHere's a little mantra\u2014words of power\u2014that I've found to be extremely helpful for staying focused on the task at hand. It's a kind of acceptance mantra\u2014an embrace of reality as it is, not as we wish it would be. So let's call it \"the reality mantra,\" since it's meant to keep us concentrated on what is actually happening in reality:\n\nOm, it's like this now, ah hum.I\n\nOm traditionally marks the start of a mantra. It means, \"Here comes a mantra.\" And ah hum signifies the end of the incantation. \"It's like this now\" are words of absolute truth, and this is one aspect of their power.\n\nBecause it is always the case, right? It's always \"like this now,\" isn't it? The hand we've been dealt at any given moment is the only one we have to play.\n\nPlease note that the mantra is not \"It's like this now, and I wish it weren't.\" That's the usual spurious mantra of discontentment and non-acceptance. Nor is the mantra, \"It's like this now, and I wish it would stay like this forever.\" That's the fanciful mantra we recite to ourselves in those (relatively rare) times when things are going just the way we want them to.\n\nSo the mantra has to be continually repeated, because the \"now\" in \"It's like this now\" is perpetually on the move. If we are to stay in reality rather than drift off into fantasy, we have to keep up with the ever-changing present.\n\nThe first element of the actual practice of self-improvement is accepting what is rather than either wishing that it were different or that it would freeze-frame and stay the same.\n\nNow for the next step: Since it's like this now, what would be my most intelligent response? How to best play these cards I've been dealt? Instead of just unthinkingly reacting to situations, we try to stay mindful and rational and think:\n\nWhat can I do, say, and think in this situation that would enrich rather than diminish my self-image? Will what I do now be something I will regret in the future, or something I can look back on with satisfaction that I did my best?\n\nBecause we misunderstand the nature of our \"somebody self,\" we habitually respond to difficult situations and people with our untrained feelings rather than with an educated view of how the personal, individual self exists\u2014as a constantly changing and evolving idea or conception based upon karma.\n\nWe think of the self in an erroneous way, and therefore want always to preserve and enhance the identity we think truly does exist as a unitary, unchanging, independent, and Captain Kirk self. So when faced with difficult situations or people, we respond defensively or aggressively. Instead of using the rationality of our heads and the compassion and love in our hearts, we acquiesce to our selfish instincts and untrained habits.\n\nWhen someone is angry with us, we respond with anger; when someone hurts us, we feel we must strike back. When we are faced with an unwanted event, we flail about, trying to avoid or change it in the moment instead of thinking about how we could best preserve our present peace of mind and create better memories with which to define our future.\n\nBut in order to make the smart choice in any given situation, we have to fight our tendencies to succumb to our selfish negative feelings, our mental afflictions. The guidelines for an intelligent and compassionate response to any situation can be set out as simply as the laws of karma themselves:\n\n  Do unto others as you would have them do unto you.\n\n  Do not do unto others as you would not have them do unto you.\n\nJust as you don't want to suffer, others don't want you to return anger with anger, hurt with hurt, lies with more lies, untrustworthiness with some version of the same. Changing our habitual responses to the events and challenging people in our lives involves shifting the focus from what seems to be \"good for me\" (and harmful to others) at any given moment and concentrating instead on what will really be the best way to improve my sense of self\u2014here and now and also in the future.\n\nAnd from the karmic point of view, what's actually best for us will also be what's best for the others around us. Om, it's like this now, ah hum. So how, in every moment, can we act, speak, and think in such a way that we'll be happier and make the lives of those around us better, not worse?\n\nThe way to improve our self-image, the truly efficacious method for upgrading the \"somebody self,\" is to train ourselves to stop reacting negatively\u2014defensively or aggressively, protecting or promoting the self-centered ego\u2014and instead respond in such a way as to increase our sense of self-worth.\n\nWe must use our \"best friend\" self to overcome our \"worst enemy\" self. If we really want to improve and help ourselves, we must side with the angel inside of us, not with our demons.\n\nWho else will overcome your unhappy, depressed, discontented self if not you? Who else besides you will make you a better \"somebody self\"?\n\n### THE BIG SMACKDOWN, RAGE IN THE CAGE\n\nBecause self-improvement really is possible, it's our responsibility to make efforts to accomplish it. And it will take effort. It's na\u00efve to assume that responding wisely and kindly to difficult events or annoying people will be easy. Our contrary habits are deeply engrained. Our habitual responses are like knee-jerk reactions.\n\nWhen the mental afflictions arise\u2014rage, vanity, lust, jealousy, resentment, annoyance, self-deprecation, and so on\u2014there's a strong air of inevitability about them. We feel, in the moment, compelled to do, say, or think things we soon regret (or at least should regret). We excuse ourselves or apologize to others by saying, I'm sorry, but I just couldn't help it!\n\nWe all know how it goes. Someone says or does something that we don't like\u2014something that insults or injures or provokes our \"somebody self.\" A force is awakened, an energy that seems to have a life of its own. Like in the Alien movies, the affliction feels like an aroused monster that just pops out of our gut.\n\nAnd then the alien power starts to surge through our being. The negative feeling seems to rise up in us (one old expression for getting angry is that \"the ire rises\"). Left unchecked, the mental afflictions move from the solar plexus area and make their way up through our tightening chest and throat and quickly hijack our heads.\n\nThe negative emotion takes possession of us. We \"lose it,\" meaning we \"lose our temper\" or basically go temporarily insane. We become the puppet of the affliction and do, say, and think unpleasant, hurtful, and damaging things.\n\nIf we wish to free ourselves from the negative emotions\u2014if we are to change these foolish and self-destructive responses\u2014we must prepare ourselves for battle. Old habits are hard to break. We must gird our loins and train for the Big Smackdown, the Rage in the Cage, with our mental afflictions.\n\n\u2022 \u2022 \u2022\n\nI was a big wrestling fan when I was a kid (professional wrestling, not the more staid and rule-governed collegiate or Olympic version), and so was my grandfather. We'd watch televised matches between characters called \"Gorilla Monsoon\" and \"Dick the Bruiser\" and marvel at the feats of violence: one combatant would jump off the top rope in the ring and smash his elbow into the throat of his opponent lying prone on the mat\u2014stuff like that.\n\nBoth my grandfather and I were totally convinced that this kind of wrestling was real. It drove my dad bonkers! We would watch eye gouges, \"sleeper holds\" (pinching some \"nerve\" in the shoulder that would render the opponent instantly unconscious), death grips, and elbows to windpipes\u2014not to mention the fully illegal bashing with chairs and attacks with smuggled blackjacks, brass knuckles, and razor blades. All this, my dad adamantly maintained, had to be fake.\n\nYou know the adage? Grandparents and grandchildren generally get along so well because they share a common enemy. My granddad and I derived a certain perverse pleasure in the apoplectic response we got from my father as we held firmly to our faith that wrestling was a real \"sport\" and not just athletic \"theater.\"\n\nIf we are to defeat our mental afflictions, we have to be like the professional wrestlers. We need to get ready for the Big Smackdown. We have to be ruthless and brutal with our negative emotions, for they are our true foes. While our human \"enemies\" have lots of other things to do when they're not harassing us\u2014sleep, eat, carry on relationships, tend to business, pursue hobbies\u2014our mental afflictions have nothing else to do but destroy our happiness.\n\nThere's a big misconception about the spiritual life. There is a widespread assumption that the spiritual practitioner should always remain in a sort of otherworldly and catatonic state\u2014tranquilized, muted, and peacefully inert.\n\nBut the true spiritual renegade is not some namby-pamby navel-gazer, looking vague and flashing the peace sign at his or her negative emotions. It may come as a surprise to some that many spiritual texts use the language of violence and war in relation to the project of self-control.\n\nThe Buddhist classic Guide to the Bodhisattva's Way of Life by Shantideva, for example, urges us to be \"fierce warriors\" when it comes to overcoming what the text refers to as our \"congenital enemies.\" Just like soldiers on the battlefield, we should be brave when it comes to our own personal Rage in the Cage. Knowing that the struggle will not be easy, we should steel ourselves and resolve to persevere no matter how difficult it may be:\n\nIn the heat of battle, fierce warriors are able to swiftly kill those who, ignorant and unhappy, will die anyway. Although tormented by countless wounds from arrows and spears, they do not turn away until they've accomplished their goal.\n\nWhen I am intent on slaying my congenital enemies, the causes of all my continuous suffering, why am I now depressed and dejected, even if I must put up with hundreds of difficulties?\n\nWarriors on the battlefield, boxers in the ring, and, yes, professional wrestlers in their smackdowns get even more psyched when injured. And we too should become even more maniacal when the opposition puts up resistance in our personal struggle with our own worst inclinations.\n\nThe Guide also urges us to be not only strong-willed but also merciless when it comes to the Big Smackdown. We all have the tendency to make excuses for our thoughtless reactions. Even worse, we defend, justify, and rationalize our afflictions:\n\nSo what if I got angry and yelled? She deserved it! I just had to set her straight!\n\nAnd worst of all, we go so far as to identify with our negative emotions\u2014and thus define ourselves through them:\n\nI am jealous; I am proud.\n\nIn order to live happier lives, we must stop pampering, excusing, rationalizing, and identifying with the enemies of our peace of mind. If we leave the door open even a crack, they will surely rush in. If we continue to mollycoddle these nasty demons, they'll beat us every time.\n\nThat's why Shantideva exhorts us to get medieval on the little buggers!\n\nLet my guts ooze out and my head fall off\u2014whatever! But I will never, no matter what, bow before my enemy, the mental afflictions.\n\nNothing namby-pamby about that, right?\n\nLet the Rage in the Cage begin!\n\n\u2022 \u2022 \u2022\n\nWhat are the weapons we'll need to fight the mental afflictions? What kind of wrestling holds can we apply the next time one of them raises its ugly head? And what sort of \"illegal\" implements can we smuggle into the Rage in the Cage that might give us a fighting chance in our efforts to defeat our worst enemies?\n\nRecognition\n\nJust acknowledging the mental afflictions as harmful, rather than as necessary or even desirable constituents of our being, will go a long way toward helping us beat them.\n\nA smoker friend of mine refers to cigarettes as his \"little friends.\" They're always there for you, he explains. First thing in the morning with your coffee, all day long as you work, with a drink at the end of the day, after meals or sex\u2014you can always count on your \"little friends\" to help you get through life.\n\nMany of us regard our mental afflictions as our \"little friends\" instead of our worst enemies. Labeling them more accurately will help get us psyched for the Big Smackdown.\n\nUnderstanding\n\nMental afflictions always justify themselves. It is, in fact, part of the negative emotion's modus operandi to appear to be a reasonable response to a difficult situation. But this is a serious mistake. The mental afflictions are not rational at all; they are harmful emotional outbursts that reduce us rather than lead us to a better self-perception.\n\nI had a student who once told me that she was having a hard time breaking her habit of getting angry. \"I get such clarity when I'm mad,\" she reported. \"With anger, things really come into focus and I feel such certainty.\"\n\nAnd yes, as we all know, there is the sense of great lucidity that comes with a strong emotion like anger. Everything is indeed quite starkly black and white: I'm right; they're wrong.\n\nBut when the spell of the affliction is broken, we often realize that the seeming clarity that came with the negative emotion was actually a distorted, skewed view of the actual situation. A powerful feeling, wholly in service to the ego, was masquerading as a hyper-rational, objective evaluation.\n\nThe mental afflictions do not actually bring us real lucidity, and they do not arise out of rational, objective calculation. No one in the cold light of day chooses to have a mental affliction attack. No one, when faced with a problematic person or situation, judiciously, cogently, and reasonably considers their options and then elects to have a big meltdown.\n\nThis person just said something I didn't like. Hmm. I wonder what would be the best thing to do here, for my own present and future happiness and peace of mind? Oh, I know! I'll increase my blood pressure and heart rate, get all knotted up and tense inside, go red in the face, and say things\u2014maybe really loudly with lots of four-letter words\u2014that I'll probably regret a few hours from now!\n\nSo another major weapon we can develop and then bring into the Big Smackdown is wisdom and understanding. Remembering how karma works to create our sense of self, we remind ourselves that if we want to have a better self-conception we'll need to avoid the temptation to give in to the siren song of the afflictions. And so we dispel the affliction's spell of pseudo-rationality.\n\nWith wisdom we understand that it is never in our self-interest to be anything other than cool, calm, and collected. It's never intelligent to capitulate to a mental affliction. Giving rein to our worst inclinations is neither rational nor advantageous.\n\nSelf-improvement derives from self-control, not from self-indulgence.\n\nDe-identification\n\nDisassociating from the negative emotions gives us more power over them. We are not our jealousy, pride, envy, anger, or depression. A mental affliction may have arisen, but regarding it as an alien power will reposition it as something other than \"you.\" You will be fighting them, not integrating and identifying with them.\n\nDetermination . . . by any means necessary\n\nWe've already seen how important unwavering resolution is in our battle with our negative emotions:\n\nLet my guts ooze out and my head fall off\u2014whatever! But I will never, no matter what, bow before my enemy, the mental afflictions.\n\nAny other attitude we take with our afflictions will only sustain and invigorate them. The \"by any means necessary\" determination is perhaps the most powerful arrow in our quiver as we wage war against our inner enemies.\n\nAnd like the professional wrestlers I used to watch on television, we can't be too scrupulous about what methods we use to try to win the match. Full nelsons, scissor holds, kicks to the head, but also blackjacks, folding chairs, and razor blades\u2014we have to resort to whatever weaponry will help us emerge victorious from the Big Smackdown.\n\nOnce more, we let the Guide be our guide. In order to aid our good intentions, resolution, and determination to become a better, more self-controlled person, the text recommends a truly radical method, one that bends the usual rules. We are told how to smuggle the blackjacks and brass knuckles into the ring.\n\nWe are charged to use and direct the mental afflictions against themselves. As in some of the martial arts, we take the energy of our opponent\u2014and make no mistake about it: anger, jealousy, pride, and strong desire have great energy\u2014and we turn it to our own advantage.\n\nAnd so Shantideva draws a distinction between the mental afflictions that function as our enemies and the very same energies when utilized as our allies. The Guide recommends, for example, that we abandon patience (the usual antidote to anger) and get angry at our anger!\n\nStationed within my own mind, they are perfectly situated to destroy me. And yet I do not get angry. To hell with this inappropriate patience!\n\nI will be tenacious and intent on revenge! I will wage war against my mental afflictions\u2014except for the kind that are designed to obliterate mental afflictions.\n\nGet angry . . . about being a slave to anger  Be proud . . . of efforts to overcome pride. Be envious . . . of those without envy!\n\nAnd be strongly desirous. Desire the defeat of the opponent in the Big Smackdown, the Rage in the Cage. Desire self-improvement. Desire a better self-image, the reward of self-development through self-discipline and karmic management.\n\nAnd finally, desire with all your heart the end of desire, the Great Itchlessness that is the end of desire, contentment itself.\n\n\u2022 \u2022 \u2022\n\n\"I count him braver who overcomes his [negative, selfish] desires than he who conquers his [external] enemies,\" said Aristotle, \"for the hardest victory is over self.\"\n\nIt has been recognized since at least the ancient Greeks that it is hard to change self-destructive habits and replace them with beneficial ones. It's difficult for the self to overcome the self. It's totally worth doing\u2014and we should fervently desire it\u2014for it's the only way to really improve our self-esteem. But no one is saying it will be easy.\n\nAnd so, as we engage in our regimen of self-improvement through karmic management, we have to expect setbacks.\n\nWe won't always emerge from the Big Smackdown victorious. There will be plenty of times when the mental affliction du jour will defeat us, even when we put up our best fight. We may offer resistance, but there is a point of no return where we just capitulate:\n\nOh, the hell with this! I don't care if this affliction is bad for me! I don't care who I hurt\u2014myself or others!\n\nAnd we give in to the urgent demands of the affliction, and the negative emotion wins that round of the wrestling match.\n\nWhen we are temporarily vanquished by our own worst inclinations\u2014when we submit to the powerful wrestling holds of anger, desire, jealousy, resentment, and prideful arrogance\u2014it feels like we're a character in a cartoon. The affliction grabs us by the throat, and we become a rag doll as we are bounced against the wall and swung up and down and right and left for a while. We are in the throes of a force that is currently greater than the potency of the weaponry we are using to combat it.\n\nWe then must switch into a defensive rather than aggressive strategy. We cover up and try to protect ourselves the best we can in order to minimize the damage.\n\nThe first line of defense is to break our opponent's hold as soon as possible. Many of us are accustomed to letting our mental afflictions have their way with us for hours, days, weeks, or even months and years. A spiritual warrior will wait until the overwhelming force of the affliction lessens its death grip a bit. But when it does, he or she will immediately shake it off:\n\nOK, that's enough now. I gave in to my resentment, my arrogance, my anger, or my jealousy, but I will not let it ruin another minute of my life! I may have lost this round, but I will not concede the match!\n\nFreeing ourselves from its hold, we get back on our feet and ready ourselves for the next encounter with the enemy. We go back to the spiritual gym and work out some more. We fortify our weaponry in preparation for the next bout. We recognize that the afflictions are the real and only enemy to our happiness; we understand that self-improvement is a matter of fighting old habits and replacing them with new ones; we de-identify with these nasty tendencies; and we determine to be victorious in the next round of the Big Smackdown.\n\nA second defensive strategy to employ when we lose the Big Smackdown is to not use the setback as just another way to feel bad about ourselves. Regret, yes; but guilt, no\u2014and there's a difference. Feeling guilty about our failures, like the depression that often feeds on such guilt, is really just another form of narcissistic self-absorption. It doesn't help, and in fact it saps the energy we need to feel better about ourselves.\n\nRegret, on the other hand, is the acknowledgment that giving in to the mental afflictions hurts oneself and others. Regret always entails the resolve to try harder not to do that kind of thing again in the future. While guilt debilitates, regret inspires us to strengthen our willpower to become stronger and better prepared for the next confrontation.\n\nAnd a third defensive tack: we (once again) de-identify with whatever mental affliction has temporarily defeated us. We don't join enemy forces; we don't surrender to the provisionally victorious affliction and become its prisoner of war.\n\nEven Shantideva, Mr. \"Be a Spiritual Warrior,\" knows we won't always win the battle with our bad habits. And so we read,\n\nWhenever you fail, your cheeks should burn in humiliation and you should think: \"What can I do so that this doesn't happen to me again?\"\n\nWhen you fall off the horse, you dust yourself off and get back up on it for the next ride. This is called \"practice.\" We renew our efforts and strengthen our will. And this is the only road, rocky as it may sometimes be, to real self-improvement.\n\nRemember the \"reality mantra\":\n\nOm, it's like this now, ah hum.\n\nGiven that this mantra is perpetually relevant, we can deploy it also in those times of failure:\n\nIt's like this now. So what can I do now to avoid future defeat at the hands of my mental afflictions?\n\n### PLAYING FOR BIG STAKES\n\nThere is a very helpful spiritual maxim\u2014perhaps the most effective of all the tools we can employ in our laborious undertaking of self-improvement:\n\nIf you can't do it for yourself, then do it for others.\n\nThere's a tremendous power in altruism. I'm reminded here of news stories that tell of a small child pinned under a car. The child's mother, filled with adrenaline due to her panic and desperate wish to rescue her beloved offspring, just lifts up the car by the bumper, snatches the kid out of harm's way, and then drops the two tons of steel back on the ground.\n\nIn the next section of this book, we'll learn more about both the power and joy of self-forgetfulness. But even in our quest for self-improvement, thinking about others and not just ourselves is ultimately our greatest resource.\n\nCreating a better \"somebody self\" involves understanding how karma really works in order to gradually give one's self-image a makeover. And our self-conception begins to change immediately upon making the shift from ignorant self-indulgence to informed self-rehabilitation. We start to think of ourselves as someone trying to be a better somebody rather than as someone addicted to becoming more of a somebody. We begin turning our attention to others and how we can help rather than hurt them.\n\nWe focus on our ethical behavior and wage war against our mental afflictions, our true enemies who both destroy our current happiness and plant the seeds for an unhappy \"somebody self\" in the future. We hone and deploy the weapons of recognition, understanding, de-identification, and determination in our internal battle with our demons, and we do not get discouraged with the setbacks and failures that will inevitably be part of our path. We remember our mantra\u2014it's like this now\u2014and we play the hand we've been dealt with wisdom and skill, remembering that self-improvement is possible and knowing how it will be effectuated.\n\nWe try to play our cards smartly, but we should also recognize that the stakes are high. We are in every moment creating the causes for who we will be in the future. For our future happiness, or its opposite, depends on what we do, say, or think in the ongoing present.\n\nBut here's the real rub. Here's how high the stakes really are. Your world, and all the people in it, will change when you change.\n\nChange you, change the world.\n\n\u2022 \u2022 \u2022\n\nThis, I fully acknowledge, is extremely hard for any of us to believe. It is virtually inconceivable to think that we as individuals have this kind of power, as it is sort of overwhelming to be laden with this kind of heavy responsibility.\n\nIt's one thing to think that we can change and improve ourselves. While most of us assume this is possible, it seems far-fetched indeed that there's any correlation between an inner transformation and a change in the outer world.\n\nBut what we make of our lives has repercussions far beyond what we ordinarily believe. What we do, say, and think defines not only who we are but also what kind of world we live in and what sort of people we encounter. If we truly wish to help others and create a better world, helping ourselves turns out to be the best way to do that.\n\nAnd if we are to come to actually believe this, we'll have to very carefully go through the logic for why this is so, and we'll have to repeatedly rehearse the syllogism.\n\nReady?\n\nNone of us has an objective view of our external world.\n\nWhen we aren't actually thinking about it, we all feel that we see things, events, and people as they really are. But this is an illusion, another trick of the egoistic self. Nobody has a \"God's eye\" view on reality.\n\nIf we're honest with ourselves, we can't help but admit that we are human beings and not digital cameras or recorders. And as humans, we're not like detective Joe Friday in Dragnet, who gathers \"just the facts, ma'am.\" None of us is privy to \"just the facts\"; we're only privy to what we think \"the facts\" are.\n\nAnd as psychologist Mihaly Csikszentmihalyi writes, \"How we feel about ourselves, the joy we get from living, ultimately depends directly on how the mind filters and interprets everyday experiences.\"\n\nSince none of us has an objective take on things, each of us necessarily has only a subjective view of the external world.\n\nBecause we're not machines but living organisms called \"people,\" our respective perceptions of the world, events, and other people come from a subjective, and not an objective, perspective.\n\nPut otherwise, all the data received by our senses is strained through our subjective filter. We don't see, hear, feel, taste, or touch the outside world in an unmediated fashion. We interpret what we experience in order to experience it.\n\nAnd the way we interpret things, events, and people is determined by our conditioning, by our karma. There are a multitude of factors that constitute the subjective filter through which all the external data must pass in order to be comprehended. The language we speak and the linguistic categories with which we think, the cultural and historical conditioning and assumptions of our place and time\u2014these form one part of the subjective filter. But additionally there are even more individual factors, such as our personal history, the ideology or belief system we adhere to, our psychological make-up, even how we are feeling on any particular day, and the prejudices and biases that derive from and are shaped by all of these conditions.\n\nThe \"subjective filter\" is really just another name for what we've been calling the \"somebody self.\" And so it is that we see the world not as it is but as we are.\n\nIf you change your subjective perspective, you change your experience of the external world.\n\nIf you accept the above two premises, then here is the first of the necessary logical conclusions: when you change your interpretive lens, you change your perceptions. Change you, and you'll change your viewpoint on external events and other people.\n\nWe all have experience of this. One day you wake up on the \"right side of the bed\" and the world looks pretty good\u2014you're relatively happy with your life and the people in it. But the next day, when you wake up on the \"wrong side of the bed,\" that same world takes on a different hue.\n\nGeorge Eliot wrote, \"Will not a tiny speck very close to our vision blot out the glory of the world, and leave only a margin by which we see the blot? I know no speck so troublesome as self.\" Our \"somebody self\" blocks out much of the range of possibility and permits us to see only a fragment of potential reality. But when we alter the \"troublesome speck of the self,\" we gain a different perspective on the world around us.\n\nSo self-improvement improves not only your sense of who you are, but it also cleans the filter through which you process what's outside of you. When you feel better about yourself, the world and other people seem more approachable and less problematic.\n\nAs we've seen, the individual self is nothing other than the sum total of our karma. When we change our karma, we change our sense of self, and thereby also change the subjective filter through which we apprehend the world.\n\nOK so far?\n\nIf you have followed me through these first three steps of the reasoning, then here comes the real kicker.\n\nIf you change your subjective perspective, you change the world.\n\nWait a minute! What happened? That couldn't be. I've been tricked!\n\nNo, you've just followed the logic of the syllogism. Since none of us has an objective view of the external world, and since all of us only experience the world from our subjective perspective, if we change our subjective perspective, we change our perspective on the world.\n\nAnd the world seen from the subjective perspective is the only knowable world there ever has been, is, or will be for any of us. So we might as well just call it \"the world.\"\n\nChange you, change the world.\n\nGet it? No? Review the steps. We all need to work through it over and over again. Because if we have even an inkling of how self-improvement goes hand in hand with the amelioration of the world we live in, it will supercharge our efforts to better ourselves.\n\nThe stakes are high when it comes to self-improvement. And so, once again, when the going gets tough\u2014when the Big Smackdown with the mental afflictions seems too daunting\u2014remember the maxim:\n\nIf you can't do it for yourself, do it for others.\n\nAction Plan: The Daily Rage in the Cage\n\nSingle out your worst negative emotion, your number-one mental affliction. (If you need some help, ask someone who knows you well; they'll tell you!) Begin your own daily Rage in the Cage with the affliction, employing the techniques we've discussed in this chapter\u2014recognition, understanding, de-identification, and determination. Don't be discouraged when the negative emotion wins the Smackdown. Review the defensive strategies above, and get back into the ring for the next round!\n\nAnd remember, your indulgence of the mental affliction is not making the lives of those around you more pleasant. Take strength in your consideration for their well-being. If you can't do it for yourself, do it for others.\n\n#### Notes:\n\nI. I believe this mantra\u2014at least the \"it's like this now\" part\u2014originates with Buddhist teacher Jack Kornfield, although he may have gotten it from someone else too.\n\n## 5\n\n## Being Nobody for Others\n\nWhatever suffering there is in the world comes from the selfish desire for happiness.\n\nWhatever happiness there is in the world comes from the desire for the happiness of others.\n\n\u2014\u2014Guide to the Bodhisattva's Way of Life\n\n### WHAT CAN I DO FOR YOU?\n\nAny task is easier if it's done selflessly rather than egotistically, and that very much includes the big life project of improving the \"somebody self\"\u2014and thereby improving the world we live in.\n\nThe means to real self-improvement is, paradoxical as it might seem to the controlling, Captain Kirk self, a function of self-forgetting. We are happiest when we leave off assessing and evaluating our own relative happiness and become absorbed in something or someone other than ourselves.\n\nIn this section, we will examine two interrelated techniques for discovering more of the joy and fulfillment that being nobody can bring to our lives. Both methods involve losing the \"somebody self\"\u2014either by fully engaging in unselfconscious action (that's in the next chapter) or, as we'll see here, by freeing the ego from its endless itching through empathetically thinking about someone else and their wants and needs.\n\nIt is not through incessant self-consciousness but rather through dissolving ourselves in something or someone other than ourselves that we access the greatest source of transformational power we have available. It is when we can drop the demands of the \"somebody self\" and be available for others that we create the karma for improving our self-conception and the quality of life we lead.\n\nKarmic regulation, far from being just another method for ego-enhancement, is the only effective method of self-help. And at the very heart and soul of self-improvement through karmic management is the ability to put others and their interests first. Contrary to our usual unenlightened beliefs, the best thing we can do for ourselves is to consider how we can help others.\n\nAt first, it might seem a bit like driving a car with the accelerator floored while simultaneously stomping on the brake. Two apparently opposite operations occur simultaneously: we forget ourselves and turn our attention to others, all the time knowing that thinking about others and their needs is the best and only way to our own personal fulfillment.\n\n\u2022 \u2022 \u2022\n\n\"The most satisfying thing in life,\" writes Pierre Teilhard de Chardin, \"is to have been able to give a large part of one's self to others.\" We all know that some of our deepest and most rewarding experiences in life come when we can forget ourselves in service to another. We derive much of our joy in life from caring about and for other beings: our children, parents, lovers, friends, and even our pets.\n\nAs we witnessed in the last chapter, we usually can't trust either our untrained instincts or the mental afflictions they inspire. Or, it could also be said, we can trust them\u2014to be 180 degrees wrong. Just check for yourself: What responses do your instincts immediately advocate when someone hurts, offends, insults, or betrays you? These habitual reactions are in need of retraining, and this is the first task of self-improvement.\n\nFortunately we have certain instincts that we can trust, and those are the ones we should nurture and strengthen. Our deep-seated need to connect with others, to love and empathize with fellow human beings, is surely one urge we should cherish and nourish. The affection and concern a parent has for a child; the gratitude, respect, and responsibility a child feels for his or her parents; the heart-felt and intimate sense of union between lovers; the bonds of loyalty and camaraderie we share with close friends\u2014these are inborn positive emotions that our relationships with others inspire and call forth.\n\nThe inner angel strongly desires the self-forgetfulness\u2014or perhaps we should say, self-expansion\u2014that can accompany these kinds of links with other people. But the inner demon\u2014concerned only with the lower, egoistic, caterpillar self\u2014misconstrues and, often enough, subverts this aspect of our lives.\n\nAs we know all too well, the relationships we maintain with our significant others not only deliver the joys of interconnection and freedom from alienation; they can also inflict on us our greatest disappointments, aggravation, and animosity. That which is potentially one of the sources of our highest happiness can be (and, sad to say, often is) the cause of considerable frustration.\n\nThe spiritual project\u2014and the path to true contentment\u2014require that we tutor our self-destructive inclinations such that they can align with our deepest desire and purpose in life: to achieve the \"Great Itchless State\" so that we can help others achieve it too.\n\nWe ally ourselves with the inner angel\u2014that part of us that longs for the freedom that comes from relinquishing the purely egoistic orientation\u2014and we disavow the self-preoccupied \"me-first\" demon that keeps us tethered to our lower, individual self.\n\nGrasping to our individuality, to the little self we're so attached to, we invite unpleasant feelings of separation and isolation. Good relationships hinge on our ability to set aside the individual self's insatiable need to be venerated. The tiresome chant\u2014What about me?\u2014is replaced with a different incantation\u2014What can I do for you?\n\n### RELATIVITY THEORY\n\nNone of us is an autonomous, disconnected little island. We are inevitably and perpetually engaged in interactions with the other people in our world\u2014physical or mental, and for better or worse. These relationships not only affect our sense of self, they constitute it. Just as we don't have karma but are our karma, we also don't have relationships but are defined by them.\n\nThe personal self does not exist independently, only dependently. It is dependent on the body and mind that acts as the basis for the idea of the self (as we have seen in chapter 3), and on the karma or memories that fashion our self-conception (as we noted in chapter 4).\n\nBut we also exist in relation to our relationships. Every role we inhabit is made possible only in relation to somebody else. What Zen teacher Thich Nhat Hanh calls \"interbeing\" (as opposed to the \"illusion of our separateness\") describes not just our interpersonal relationships but our reality as a whole.\n\n\u2022 \u2022 \u2022\n\nWe have already encountered a negative description of how the world really exists: Things and people are not perceived by any of us objectively. Just as we ourselves do not have a hardwired \"self\" in the way we think we do (recall the \"Where's Waldo?\" search), it is also not possible to identify some kind of unchanging and definitive essence for anyone or anything. Remember our examples from chapter 3? There are no essentially aggravating people in the world, and there is no essentially tasty flavor of ice cream.\n\nBut this negative assertion must be carefully distinguished from the nihilistic idea that what's external to us doesn't exist at all, that it is some kind of fantasy conjured up by \"me\" (whoever that is!). The external world and other people in it do exist\u2014and here's the positive articulation\u2014dependently. There are aggravating persons, but this depends upon others being aggravated by them. Ben & Jerry's Chunky Monkey ice cream is delicious, but only to someone (like me!) who judges it so.\n\nAnd it's like that with everything. Everything, without exception, depends on something else, and that something else depends in turn on something else! And so this positively stated depiction of reality is more accurately put like this: everything and everyone exists interdependently, not independently.\n\nYou know that old puzzle? If a tree falls in the forest and no one is there to hear it, does it make a sound? The answer is of course not! And here's why:\n\nThere is nothing perceivable in the world until and unless it is perceived. There can be, for example, no audible sound like that of a tree falling in the forest until and unless it is heard by someone. And while we may have all kinds of objections to such an apparently audacious statement, what would it really mean to assert that a sound occurs when no one hears it? Wouldn't such a position have to posit an inaudible (that is, not heard by anyone) audible sound?\n\nWe're not talking here about a sound's potential to be heard. Potentially, all kinds of things are possible. What we're discussing here is how things really are. Something is audible only when it is heard by a hearer, and not until. Right?\n\nSimilarly, there is no visible object until and unless it is seen by someone\u2014for if there were, there could be an invisible visible object! There's no odor until and unless it's smelt, there's nothing tangible that isn't felt, there's no tasty thing (like ice cream!) without a taster. And there's no thought that exists independently of a thinker who thinks the thought.\n\nAn unthought thought, an invisible visible object, an inaudible sound, an unsmelled smell, an intangible tangible thing, an untasted taste\u2014these are impossible things, totally inconceivable!\n\nToo theoretical? Here's the cash-out.\n\nThis truth of interdependence buttresses the startling conclusion of the last chapter: Change you, change the world. Because the external, perceivable world exists (for any of us) only in relation to being perceived (by any of us), the way it exists (for any of us) depends upon us, on the perceiver. If you want to perceive the external world\u2014things, events, and other people\u2014in a better way, adjust the perceiver, the lens through which the world comes into existence. Change you, and you will change the world.\n\nBut here the other shoe drops: in accordance with the interdependence of things, it's not just that perceptible objects depend upon a perceiver in order to be perceptible; because things exist interdependently, it is also the case that perceivers become perceivers only when they perceive something.\n\nFor a seer to be a seer, he or she must see a visible object, right? Can't be a \"seer\" if you aren't seeing something! And you can't be a \"listener\" until and unless you hear some sound. In what sense are you a \"seer\" or \"hearer\" (actually, not potentially) until and unless you see or hear something? And the same is true with the smeller, feeler, taster, and thinker; they exist dependently on what they sense\u2014a smell, a tangible thing, or a thought\u2014just as what they sense depends on being sensed in order to exist as such.\n\nAnd here's the relevant consequence of that dropped shoe. It's the inverse of our previous formula: Change the world, change you. If our sense of self\u2014the perceiver\u2014depends upon what is perceived, then if we learn to perceive things, events, and people differently we will change as well.\n\nWe see things and people not as they are but as we are. But because of interdependence, it is also the case that we are what we see (and hear, smell, feel, taste, and think). The perceiver is defined by what is perceived, and vice versa, and that's another reason why \"it's all relative\"\u2014everything and everybody exists within the matrix of interdependence.\n\nIf, for example, we see \"problems\" as \"opportunities,\" we will feel less embattled and thwarted, and will instead view ourselves as more engaged and empowered. If we focus on the good qualities of our aggravating person, we will be less aggravated. And if we engage with others with love and compassion, we will experience those relationships, and ourselves, in a much more positive way.\n\n### \"I AM BECAUSE YOU ARE\"\n\nBecause everything exists interdependently and not independently, our sense of self is inextricably entwined in and constituted by our relationships with others. We depend upon other people to be who we are.\n\nThere's an African concept called ubuntu, which is summarized in the proverb \"I am because you are\" and explained by Archbishop Desmond Tutu in this way:\n\nMy humanity is caught up, is inextricably bound up, in theirs. We belong in a bundle of life. We say, \"A person is a person through other people.\" It is not \"I think, therefore I am.\" It says rather: \"I am human because I belong. I participate, I share.\"\n\nNone of us is somebody without other somebodies. All the roles we play\u2014every one of the carnival cutouts we stick our faces in\u2014are made possible by our relationships with others. We are fathers or mothers dependent upon having children; we're children only because we have parents. We're \"a friend\" because there is someone we're friends with, and we're \"a lover\" because there's someone (other than ourselves!) to love.\n\nOur professional identities are likewise always relational. A \"doctor\" can only be so because of patients, a \"teacher\" because of students, and a \"car mechanic\" because there are car owners whose vehicles need servicing. And as we observed in chapter 2, we also define our individual selves in relation to the communities we identify with\u2014our nationality, race, religion, or whatever.\n\nGroup identities, no less than individual ones, exist only in relation to others; they are forged in opposition to those who belong to different communities. As we've seen, we conceptualize ourselves as \"American\" because we're not \"Canadian\"; if we're \"Buddhist,\" it's dependent on us not being \"Christian.\" And so it is that we are also defined even by relationships with those we don't consciously identify with. We are annoyed because there are people who annoy us; angry and upset because others seem provocative; resentful or envious because of another's actions or status.\n\nWe are tied to those we dislike just as we are to those we more willingly associate with. Relationships fueled by negative emotion keep us chained to a self-conception marred by disaffection and unhappiness. As writer Ursula K. Le Guin observes, \"To oppose something is to maintain it.\" We can only think of ourselves as victims because we think of others as oppressors.\n\nWe can't be somebody all by ourselves, and the kind of \"somebody self\" we think we are exists dependently on the quality of our relationships. If we establish and maintain pleasant, loving, supportive relationships, we feel one way about ourselves. But if we are continually hassling with others, our self-image will suffer and our lives will continue to be troubled by these interpersonal difficulties.\n\n\u2022 \u2022 \u2022\n\nThe mental afflictions we spoke of in the last chapter almost always arise in relation to someone else. While we sometimes get angry, greedy, or prideful in relation to inanimate objects or events, it's when there are other people involved that we really get our backs behind the negative emotion.\n\nWe've talked about some of the tools available to us to combat those disturbing feelings as they rear their ugly heads:\n\n  Recognition: \"This mental affliction is not my 'little friend.' \"\n\n  Understanding: \"It's never in my self-interest to give in to such destructive emotions.\"\n\n  De-identification: \"This affliction is not me.\"\n\n  Determination: \"I will combat this feeling with all my might!\"\n\nAll of these methods involve turning inward. We introspectively identify and combat the negative feelings within ourselves as part of the project of self-improvement. The Rage in the Cage occurs within ourselves. But we also realize that, by changing ourselves through this kind of self-mastery, we will alter our perceptions of the people and situations that once evoked such destructive sentiments in us. We purify the subjective filter through which we perceive external things and beings and thereby clean our karma:\n\nChange you, change the world.\n\nBut as we've seen, there is a second method for transformation that stems from the theory of relativity and interdependence. Instead of focusing within, we turn our attention outward. If we can learn to perceive the things, events, and especially the other people in our world as beneficial instead of problematic, as targets of our positive feelings rather than our negative ones, we'll automatically gain a happier sense of self:\n\nChange the world, change you.\n\nAnd there is one powerful emotion, one virtuous state of mind, that we can direct outwardly in order to transform our perception of other people and thus our relationships with them.\n\n### FIND SOMEBODY TO LOVE\n\nThere's an old song made famous by Dean Martin, \"You're Nobody 'til Somebody Loves You\":\n\nYou're nobody 'til somebody loves you\n\nYou're nobody 'til somebody cares.\n\nDino croons on about how you might \"be king\" or possess all the riches of the world, maybe even the world itself, but no amount of riches can bring you true, lasting happiness. These lyrics convey a certain truth about the most important source of our self-esteem and self-worth. It's not our wealth, possessions, or professional achievements that now or in the end, when you're growing old, are of the greatest importance. We are indeed nothing without the meaningful, loving relationships we establish and maintain with others.\n\nWhen my dad was a resident in an assisted-living facility (what used to be known as the \"old folks' home\"), I would travel to visit him once or twice a year. It was not much of a sacrifice for me\u2014a couple days out of my life\u2014but it was a big deal for him. He would parade me around, introducing me to his friends at the facility, showing me off\u2014not so much for how special I supposedly was, but for the very fact that I was there at all, that I had come to visit him.\n\nIn conversations with my father and other elderly people at the old folks' home, I learned that what really mattered to them was not their former professions (no one spoke much about what or who they \"used to be\") or the possessions they had once acquired (now, for the most part, gone) or the exotic holidays they once enjoyed (just fading memories and tattered photographs).\n\nNone of this was that important to them anymore\u2014and none of it will be important to any of us if we're lucky enough to grow old before we die.\n\nWhat mattered to the elderly was who loved them. What was of greatest import was who cared about them enough to come visit, to spend a few hours of their lives with those who had been stripped of the more tenuous ego props we often rely on to feel like we're really somebody.\n\nAnd, of course, the old folks also talked a great deal not only about who loved them, but about those they loved. When the \"somebody self\" has been reduced to being just another inhabitant in a retirement facility, much of life is lived vicariously. The activities of the children and grandchildren, the nieces and nephews, take on greater significance. The focus in such a situation, almost by necessity, tends to turn away from the self and toward others.\n\nIt's like that, too, in times of crisis. When the chips are really down, we humans often rise to the occasion, break out of our self-imposed egoistic confines and instead think about how we can help those in need. There are, unfortunately, countless examples of such terrible times. The great tragedy of 9\/11 brought out the best in many New Yorkers, who selflessly aided and supported each other in the darkest of times. And there have regrettably been more recent and continuing incidents where a disaster elicits heroic responses of self-sacrifice and concern for others.\n\nBut it's not necessary to wait until old age or a crisis situation to exercise our greatest instinctual drive\u2014to love and care for someone other than ourselves.\n\n\u2022 \u2022 \u2022\n\n\"You're nobody 'til somebody loves you,\" as the song title states, but the lyrics continue to take things in a different direction:\n\nYou're nobody 'til somebody loves you,\n\nSo find yourself somebody to love.\n\nThe orientation shifts here. Instead of focusing on receiving love, we are advised to give it. \"Find somebody to love\"\u2014a recommendation put into our pop-cultural consciousness not just by Dean Martin, but also in tunes by Jefferson Airplane (\"Wouldn't you love somebody to love? You better find somebody to love\") and Queen (\"Can anybody find me somebody to love?\"), among many, many others.\n\nInstead of dwelling on ourselves and our own need for love, we think of others and how we can love them. Change the world\u2014through the power of love for someone else\u2014and you will change you.\n\n\u2022 \u2022 \u2022\n\nThe centrality of love is reflected in the fact that our popular culture continually shapes and gives expression to our deep need for it. From television shows and movies to Hallmark greeting cards, from the novels we read to the music we listen to, the theme of love recurs over and over again.\n\nBut the message we receive\u2014and often resonate with\u2014is not always helpful for a proper understanding of this all-important human emotion.\n\nIn preparation for remarks I was to give as the officiant at a wedding, I did some research and found a database that had compiled a comprehensive list of popular song titles. When I searched for those whose messages might be relevant for a couple that was getting married, I found that many of our so-called love songs conveyed a rather screwy idea of what love is.\n\nI found out that 191 songs have in their title the phrase \"you belong to me,\" and lots of others have variants on this theme:\n\n\"You Belong Here\"\n\n\"You Belong Here with Me\"\n\n\"You Belong in My Arms\"\n\n\"You Belong inside My Heart\"\n\n\"You Belong to Only Me\"\n\nThere is one song with the title that really cuts to the chase: \"I Own You.\" There are two, according to the database, with the title \"You Own Me.\"\n\nTwo songs are entitled \"I'm Your Woman.\"\n\nFive claim \"You're My Woman.\"\n\nSix are called \"You're My Man,\" while forty-five say \"I'm Your Man.\"\n\nAnd no less than 137 songs have titles that begin with the words \"you're mine\":\n\n\"You're Mine, I'm Yours\"\n\n\"You're Mine, Heart and Soul\"\n\n\"You're Mine Alone\"\n\n\"You're Mine Tonight\"\n\n\"You're Mine Forever\"\n\n\"You're Mine Only\"\n\n\"You're Still Mine\"\n\nAnd on it goes, the epitome of the genre being \"You're Mine, Mine, Mine.\"\n\nReal love is not about owning or possessing another. And love is also not about coercion, about \"making\" someone love you. Again, our popular so-called love songs reinforce this mistaken idea. Tunes with titles like \"I'm Gonna Make You Love Me\" or \"What Do I Have to Do to Make You Love Me?\" create the idea that we can somehow compel another's love for us.\n\nOr, much more often, we believe that the other can or should \"make us\" something or another, that our emotional life is putty in the hands of others. Sixty-seven songs begin with the phrase \"you make me\":\n\n\"You Make Me Feel Like a Natural Woman\"\n\n\"You Make Me Feel Like a Man\"\n\n\"You Make Me Want to Be a Mother\"\n\n\"You Make Me Feel Like Dancing\"\n\n\"You Make Me Feel So Young\"\n\n\"You Make Me Feel Brand New\"\n\nAnd, interestingly, \"You Make Me Real.\"\n\nConsider this title, a combination of both of the erroneous ideas about love\u2014as ownership and as compulsion: \"You Make Me Want to Make You Mine.\"\n\nWe are especially encouraged to think that a loved one has the power, and therefore also the obligation, to \"make us happy\"\u2014a message famously conveyed in the Blood, Sweat & Tears song \"You've Made Me So Very Happy.\"\n\nIf we believe that others have it within their power to \"make us happy,\" then soon enough we will also believe that they are capable of \"making us unhappy.\" Instead of taking responsibility for our own happiness and unhappiness, we cede it to others. We saddle them with a task they cannot perform (\"you make me so very happy\") and blame them for what they do not in fact have the ability to do (\"you make me so very unhappy\").\n\nTrue love\u2014whether it is romantic, fraternal, parental, filial, or whatever\u2014is neither about \"owning\" another person nor about what the other can or should do for you. Rather, it is about what you can or should do for another.\n\nReal love is about giving, not taking. It is the cessation of the \"me\" orientation and the generation of a selfless concern for another's happiness and well-being.\n\n\u2022 \u2022 \u2022\n\nThe mental afflictions we've been discussing can all be viewed as self-centered perversions of love. Anger (\"You're not loveable at all!\"), lust (\"I love you so much, I must have you to love me!\"), jealousy (\"You love somebody else and not me!\"), envy (\"You have something I don't that makes others love you more than me!\"), pride (\"I am so very, very loveable, don't you think?\")\u2014we can view the whole list of negative emotions in terms of our egotistical demands that others should love us.\n\nWhile we all want to be loved in order to feel like a real somebody, we also need to love in order to be loved\u2014and to do the latter, we must exercise self-forgetting. For it is when we suspend our self-centeredness and give ourselves over to others that we tap into the real power of love, the Higher Power, the god (or God) that is love.\n\nThe love of another is gratifying and helps us feel like a better somebody; but it is the love for another, premised on self-abnegation, that gives us a glimpse of our true nature and the real strength and bliss that come from being nobody.\n\nYou're nobody 'til somebody loves you, so you'd better find somebody to love. And when you do, you will truly love not as a somebody but as a nobody. As Bhagwan Rajneesh (aka Osho) remarked, \"When you love a person, you have to become a no-self.\"\n\n### EMPATHY, OR THE ART OF PUTTING YOURSELF IN ANOTHER'S SHOES\n\nTrue love\u2014again, not just romantic love but love in all its forms\u2014is an exercise in selflessness, the leap out of the stifling confines of our own individuality and into another's life and their desires, their cares, their difficulties.\n\nThe world's spiritual traditions have, in one voice, extolled such altruistic substitution for myopic self-absorption. This is not only because it's \"nice\" or \"good\" to be concerned with the well-being of others. It's also because, when we are able to think about somebody other than ourselves, we by necessity must drop the egoistic demands of the \"somebody self.\" The little voice inside stops its me, me, me refrain and a different mantra is heard: What about you? What can I do for you?\n\nThe essence of, and precondition for, selfless love is empathy, the ability to put oneself in another's position, to feel what they must be feeling and to relate to what they must be thinking. While the degree to which we are able to do this varies, the more we empathize with another, the less we are preoccupied with ourselves\u2014and therefore, the more relief we get from the isolation and burden of our disconnected individuality.\n\nEmpathy, the prerequisite of altruistic love and compassion, itself depends upon the assumption that others are essentially no different than us. This is why this kind of self-sacrificial emotion is relatively easy (although by no means always practiced) with our families, lovers, and friends. Because we identify with them, we can relatively easily love them \"as ourselves\"\u2014to \"love your neighbor as yourself,\" as Jesus put it.I\n\nBut it's not just those close to us who are like us. We saw way back in chapter 1 that \"we're all in the same boat\": we all equally are suffering, and we all equally have the desire, innate capability, and right to be happy.\n\nThis recognition of the fundamental equality of all human beings (or maybe it would be better to say of all living beings, for animals also share in these two big facts of life) lies behind the invariable principles that should guide all of our responses to others and their actions. We've mentioned them before; they are universally extolled and sometimes referred to as the Golden and Silver Rules:\n\n  Do unto others as you would have them do unto you.\n\n  Do not do unto others as you would not have them do unto you.\n\nBecause we know how we feel when others treat us either kindly or poorly, we know how we should treat them. It is the assumption of our basic equality that makes empathy possible, and, in turn, informs us about how to interact with others with love and respect\u2014friends as well as enemies.\n\n\u2022 \u2022 \u2022\n\nIt is also our ability to empathize\u2014to put ourselves in another's shoes\u2014that provides another clue as to why and how karma really works when it comes to our actions vis-\u00e0-vis others. Why is it a karmic \"law\" that what goes around unfailingly comes around? Why couldn't something bad come from something good, and vice versa?\n\nKarma, as we argued in the last chapter, is not operating \"out there\" as a \"law of nature,\" but rather works to determine our perception of ourselves and of the external world.II Karma as an explanatory system is not about why and how other people are the way they are, or about why and how events occur the way they do. It explains how and why we experience people and events (and also, of course, ourselves) the way we do.\n\nKarma in its causal dimension depends on intention. Because we know how it feels to be hurt, for example, we can formulate the intention to hurt others. Similarly, we know how to show compassion, goodwill, and respect because we have been on the receiving end of others' positive actions toward us. We know how it feels to be loved, and because of that we know how to love.\n\nBut, as in our previous discussion concerning interdependence, we have to again drop the other shoe: because we know what it feels like to intend to hurt others, we know what it feels like to be hurt.\n\nSuffering and pain don't come so much from the words of another\u2014they're just syllables and decibels until they are interpreted as words meant to be hurtful. Even when it comes to harmful physical actions done to us, although the body itself may be injured, we are nevertheless much more liable to excuse and forgive if we believe the damage has been done accidentally or unwillingly. It is, again, the cruel motivation that makes the deed most upsetting and least pardonable. The deeper pain is not in the words spoken or even in the physical abuse, but in the belief that it was the other's intention to hurt us.\n\nAnd on the positive side, we know what it feels like to be loved by another because we have loved others. The warmhearted intention we project onto the other is what makes us feel loved, and we can project that intention onto the other because we've already had that same wish ourselves.\n\nThis is interdependence when it comes to karma and our relationships with others: (1) Because we know how it feels to be hurt or loved ourselves, we can formulate the intention to love or hurt others; and (2) because we know what it feels like to intend to hurt or love others, we also know what it feels like to be loved or hurt, as we presume the same intention on the part of another.\n\nKarmic management therefore entails another principle: Think the best of others\u2014allow for the possibility that they are basically well-intentioned. Because of this assumption\u2014because of interdependence\u2014you'll think better about yourself, and you'll be more likely to formulate better intentions in your interactions with others. This, in turn, will promote the habit of assuming that others' intentions are fundamentally good, like yours are, and on it goes . . . in an upward spiral.\n\nThe usual proverb can be inverted: It is the road to heaven, and not to hell, that is paved with good intentions.\n\n\u2022 \u2022 \u2022\n\nWe should pause here to emphasize something about empathy. Empathy infused with love is not some chuckleheaded, na\u00efve, Pollyanna-ish attitude. Our capacity to put ourselves in another's position allows us to think well of others\u2014repeat this mantra: we're all just doing our best\u2014but it also recognizes that others are just like us in another way.\n\nWe're all equally fallible; we all make mistakes; we all are liable to succumb to our worst tendencies and to do and say things that we know, when the mental afflictions don't have their death grip on us, are wrong and hurtful.\n\n\"Homo sum, humani nihil a me alienum puto,\" wrote the playwright Terence nearly two thousand years ago. \"I'm a human being. Nothing human is foreign to me.\" And that refers both to our human capacity for virtue and to our common inability to always exhibit it.\n\nAnd so empathy also inspires us to consideration, tolerance, and forgiveness when it comes to the other people in our lives. Just as we hope others will cut us a break when we fail, similarly we can use empathy to give others the benefit of the doubt. This too is a form of seeing the best in others, for, as we all know, \"doing our best\" does not always mean we win the Big Smackdown with our own negative emotions. Sometimes our best when it comes to a particularly challenging situation does not reflect our idealistic best.\n\nThe smartest response to others' mistakes and shortcomings is guided not by self-righteousness rooted in pride and egoism; rather, it is guided by the exercise of our wisdom and compassion, both of which are grounded in a recognition of our common humanity.\n\nWe can both appreciate the goodness in others as well as acknowledge our shared failings if we exercise empathetic love. Such a perspective brings us closer to one another rather than keeping us apart. Such a point of view is essential for overcoming the separation we feel when we over-identify with the \"somebody self\" as if it were somehow cordoned off from other beings who are essentially just like us.\n\nReflection on the nature of our relationships with others helps us understand the artificial, and therefore porous and expandable, boundaries of our own selfhood. We all have the capacity to stretch the borderlines of our identity such that the small individual self encompasses others. And in the process, the ego is subsumed within a larger whole.\n\nWhen we lose ourselves in empathetic identification with others\u2014with our children or parents, our lovers or friends, but also with those we find difficult (and these are not mutually exclusive categories!)\u2014we get an inkling of the joys and benefits of dropping the \"somebody self\" and being nobody.\n\n### THE DOORMAT SYNDROME AND THE MYTH OF \"COMPASSION FATIGUE\"\n\nThere are two objections I often hear when it comes to the spiritual teachings on selflessness in relation to others.\n\nThe first objection concerns dysfunctional relationships involving repeated incidents of abuse. Our closest relationships can, unfortunately, be our most traumatic when they've gone seriously awry. Should I stay or should I leave is a question I'm often asked. And the inevitable answer is, \"It depends.\"\n\nIt is not a compassionate act to allow yourself to be a doormat. Obviously it's not good for you. Being the repeated object of another's aggression places you in the role of \"helpless victim\"\u2014and this is neither a pleasant nor beneficial carnival cutout to stick your face in. We are all equally entitled to respect from others\u2014and that includes you!\n\nBut a relationship characterized by such abuse is also not good for the one who's using you as the doormat. Entering into and perpetuating an association where we allow another person to hurt us over and over again is not good for that other person. Hurting others is wrong, and those who hurt others are creating some very nasty karma for themselves. Out of love and compassion for both yourself and your partner, you must put a stop to it.\n\nEmpathy can once again guide us. People who hurt other people are not happy people. We know this from our own experience. When we are deeply troubled inside, we often seek relief by taking it out on others. Misery, as they say, loves company. The proper response to the suffering of others\u2014even or especially the suffering that causes people to lash out in violent speech or actions\u2014is compassion.\n\nCompassion: to suffer together. And with such empathy for the other's pain, we can determine the best course of action should we find ourselves in an abusive relationship.\n\nStay or leave? It may be possible to stay and try to work things out, perhaps with the help of a good therapist, such that the cycle of mistreatment is broken. But it might also be necessary to leave in order to end an unhealthy codependency where negative karma for all concerned continues to be reproduced.\n\nIn either case, empathetic love will help point us in the right direction. Instead of basing our decision on what we think will be most advantageous for ourselves, we turn our attention to the other:\n\nWhat's best for him or her? Can I really help this person end the abusive behavior by staying, or do I need to vacate the relationship in order to stop perpetuating this unhealthy codependency?\n\nDon't forget: being nobody does not mean being a worthless nothing; being nobody is not the same as being a victimized, traumatized, doormat somebody. What is called for is the willingness to drop our inveterate self-centeredness. And also remember, if it doesn't bring the release that comes from laying down the burden of selfishness, it ain't really being nobody.\n\nThe other objection many of us have when it comes to losing the \"somebody self\" in our love for others is what has been labeled \"compassion fatigue.\" People in the helping professions, or just overtaxed parents and caregivers, sometimes claim to be burned out or drained from \"too much compassion.\" I give and I give and I give, and now I'm exhausted. I need a little \"me time\"!\n\nBut if we examine the notion of \"compassion fatigue\" from the karmic point of view, it turns out to be an oxymoron. One of the invariable principles of karma is that nothing bad can come from something good. Assuming that \"fatigue\" is not a welcome feeling, and that \"compassion\" is indeed a virtuous state of mind, the former cannot actually derive from the latter.\n\nAny \"fatigue\" we experience when engaged in helping others comes from self-concern, not from self-forgetfulness. Once we have truly lost ourselves in service to others, we tap into a source of energy and strength far beyond what the \"somebody self\" is capable of. Like the mother who lifts the car under which her child is trapped, when we give ourselves over completely to others we gain access to a tremendous reservoir of power\u2014the power that comes from being nobody.\n\nIt is not often, however, that we are able to be so completely self-effacing in our relationships. The demands of the hungry ego are very, very compelling. It is an extremely self-assured, self-confident person who can summon the courage and daring to willfully and completely set aside the imperatives of the \"somebody self.\"\n\nIn the next chapter we'll discuss the nature of selfless action\u2014activity that encompasses a kind of relaxed presence and playfulness quite different from what we think of as \"work.\" If we experience \"fatigue\" or \"burnout\" from our compassionate actions toward others, it ceases to be truly compassionate and truly selfless. It's no longer a choice but a chore.\n\nAnd so, with the understanding that it's not the compassion that fatigues you, when you feel the need, you must rest. When your charitable service to others threatens to subvert the virtuous inclination that led to it, it's time to take a break . . . before you break! Go ahead and grab some \"me time\" so that you can return later, refreshed, to the aid of those who need you.\n\nMany of the world's religions share the tradition of regularly observing holidays (\"holy days\") in order to rest and revitalize. In the Western religions, this is the purpose of the \"Sabbath,\" one day of vacation every week. And in the Eastern traditions, we find similar injunctions to nurture and protect our altruistic inclinations from burnout. Here's one such admonition:\n\nThe forces for helping us accomplish the goals of other living beings are willpower, steadfastness, joy, and taking a break when needed.\n\nThe text lays out the \"forces\" that keep us going even when the temptations to quit are great. Willpower\u2014the determination to overcome the stifling limitations of selfish egoism by \"finding someone to love.\" Steadfastness\u2014sticking with our resolution to pursue our enlightened self-interest through cultivating empathetic love and altruistic behavior. Joy\u2014being happy to have the opportunity to create the causes for our own true happiness by promoting the welfare of others.\n\nFinally, \"taking a break.\" The word I've translated as \"taking a break\" is mukti, which means \"freedom, release, deliverance from\"\u2014here in the sense of \"leaving off\" or \"releasing\" oneself from the task. This means taking a holiday\u2014or at least some \"down time\"\u2014in order to safeguard our charitable, altruistic inclinations from the self-preoccupation that can undermine them, and to restore ourselves such that we can think more clearly about the value of service to others.\n\n### WHAT IF GOD WERE ONE (OR ALL) OF US?\n\nLosing the self in service to others is a time-honored spiritual method for overcoming our innate egoism. An opposing inborn predisposition is called up: the desire to connect and identify with other people and rise above and beyond the arbitrary limitations through which we imprison ourselves.\n\nIt is because of the fact of interdependence, the truth that we are inextricably bound to others, that we can acknowledge and make use of interdependence to improve the quality of the relationships that, in their turn, define us. One of the two formulas of transformation is employed\u2014change the world, change you, the twin of the equally potent recipe: change you, change the world\u2014and we work the magic.\n\nWe think about others with the empathy that evolves from an assumption of basic equality. We wish that others be free from suffering and that they find happiness, just as we wish it for ourselves; and we interact with others with that kind of intention rather than with the more egoistic and injurious desires our mental afflictions motivate. And we also recognize that others, like us, are fallible and don't always live up to their highest ideals\u2014an exercise in empathy that invokes in us compassion rather than anger or judgment, forgiveness rather than resentment and a thirst for revenge.\n\nOvercoming our preoccupation with the self and its perverse misunderstanding of \"love,\" we realize that our love for another is the karmic cause of feeling loved by another\u2014for what goes around will come around. And we are wise enough to understand that empathy sometimes requires tough love and tough choices toward others (to avoid the \"doormat syndrome\") and the careful preservation and maintenance of our own efforts (to avoid associating \"compassion\" with \"fatigue\").\n\nIn the next chapter, we will see how our activities in general can be pursued more selflessly\u2014and joyously! Losing the self in the ongoing flow of life itself\u2014in our solitude as well as in our interactions with others\u2014provides us with another opportunity to be nobody in our everyday lives.\n\nBut let's conclude here with what has been called the greatest secret, the most esoteric and powerful practice, when it comes to our relationships with others:\n\nHear once more My highest words, the most secret of all, for you are surely dear to Me so I will tell you for your own good. Keep your mind on Me, be devoted to Me, sacrifice to Me, prostrate to Me. I promise that you will come to Me, for you are dear to Me.\n\nThese verses are from one of the world's religious classics, the Bhagavad Gita. Krishna is speaking to his friend and student Arjuna at the very end of the long dialogue that comprises the text. At one level, the \"highest words, the most secret of all,\" that Krishna communicates relate to the transcendence of the lower self and the realization of the Divine, the Great Unity that lies beneath all diversity that is the ultimate experience of being nobody.\n\nBut another dimension of Krishna's supreme teaching offers us a formidable strategy when dealing with others. It is one that we all can utilize in order to improve\u2014radically improve\u2014our relationships. In the Eastern traditions, this practice is called \"guru yoga\"\u2014seeing another person as a divine manifestation in your life, an emissary sent from HQ and assigned specifically to your case.\n\nThere's a lot of misunderstanding about the nature and function of the \"guru\"\u2014the Sanskrit term for the spiritual teacher\u2014so it is important to be clear about what this practice really entails before we can benefit from it.\n\nFirst of all, a guru is not essentially or objectively a guru, any more than the aggravating person is. A guru becomes a guru when a student voluntarily enters into this special relationship with him or her\u2014and not until. The guru-disciple bond, like all other relationships, functions interdependently: for the guru to act as a guru, he or she must have a student; and for a student to be a student, he or she must have a teacher.\n\nA second important point about the guru follows from the first. Your guru could literally be anyone. There's no factory that produces gurus, and there's no \"Gurus R Us\" website from which you could order yours. The guru comes into being when we designate someone to act in that capacity for us. And in a sense, that choice is arbitrary. Your guru could be a minister, rabbi, priest, imam, monk, or nun; but he or she could also be your wife or husband, boyfriend or girlfriend, son or daughter, father or mother, friend or relative\u2014or even (maybe especially!) whoever that aggravating person is in your life.\n\nAnd so it is that we can put into practice this most esoteric, secret technique for making our relationships extraordinary. We begin with the admission that we really don't know who other people are. We know how they appear to us, but we also acknowledge that we don't see others as they are, but rather as we are.\n\nAnd who we are is a complex bundle of possibilities. We alternate, even moment to moment, among a vast array of potential identities. We stick our faces into all kinds of carnival cutouts, and as we've observed in this chapter, we also define ourselves through our relationships with others.\n\nThe core of guru yoga involves intentionally deciding to see another as the reflection of our Highest Self. \"I am seated in the hearts of everyone,\" says Krishna. God is within us as well as without, a notion that is common to many of the world's spiritual traditions, especially in their more mystical strands.\n\nAnd so guru yoga can be understood as a mechanism for using another person as a mirror for catching a glimpse of what is best in us. By tapping into the truth of interdependence, we connect with our innate divinity by working to see the divine in another. Perceive it without, and you will recognize it within.\n\nBut now for a third crucial observation about guru yoga: Constituting someone as your guru does not mean that everything they say or do will automatically be \"good\" or \"right,\" and that the student's job is just to agree and obey. This is a dangerous misunderstanding of the practice and has gotten a lot of people into a lot of trouble!\n\nThe essence of guru yoga is to be constantly learning; the guru is the teacher and teachings can come in many forms. Sometimes teachings are easy, but sometimes they're hard. Sometimes teachings make us feel better about ourselves, but perhaps the most beneficial lessons are those that challenge us to look at what we need to change. Sometimes teachings make it easy for us to like the teacher, but sometimes they are presented in the form of a negative exposure\u2014cautionary examples about what we need to avoid in our own lives. There are even instances when the teaching the guru gives is that it's time to find someone else to fulfill that function\u2014a lesson in detachment that can be particularly hard.\n\nBut in every case, a teacher can only teach if a student learns. The proper practice of guru yoga always requires the student to take personal responsibility for the relationship and to think for him- or herself. One reflects on whatever the guru says or does and struggles to come to his or her own determination:\n\nWhat am I to learn from this?\n\n\u2022 \u2022 \u2022\n\nSome of us may choose to formally enter into a relationship with an \"official\" guru\u2014someone who represents a spiritual lineage and teaches us what has been handed down in a particular tradition. But all of us have the opportunity to avail ourselves of the power inherent in the practice of guru yoga. Whether one works with an \"authorized\" spiritual teacher or chooses to remain a \"none,\" guru yoga is the most efficacious way to transform our relationships and make quick progress in our spiritual journey.\n\nWe often have this somewhat na\u00efve notion that a real spiritual teacher should look and act in a particular way. They should, perhaps, wear certain clothing, adorn themselves with religious artifacts, or have a distinctive hairstyle (or lack thereof). They should, we might think, be capable of miracles, or at least have all kinds of charisma and charm. They should, we may assume, have some sort of signature \"spiritual\" demeanor, only speak softly and significantly, and (here's what we really hope!) always be nice to us.\n\nBut with the understanding that the guru could be anyone, what if we decided to bring the personage who occupies that special role for us a little closer to home? What if we took the guru off the pedestal and put him or her inside our living room? What if we tried to imagine that a divine being had moved in with us in order to help us improve ourselves?\n\nWhat if God were one of us, trying to help us see the divine that is in all of us?\n\nHere's the way it works\u2014and kids, do try this at home! Just make a decision that from now on someone in your life will serve as your guru. Just decide that your husband or wife, your flatmate, your son or daughter, your best friend, or even a very difficult person with whom you have a close relationship will function in this special way for you. From now on, you assume that this person is a divine being, working undercover (sometimes it will seem that they are deeply undercover!), trying to help you.\n\nFrom now on, everything this newly appointed guru says or does will be interpreted as a teaching meant especially for you.\n\nAnd then let the games begin! Occasionally things will indeed seem magical. Words and actions that you once paid little or no attention to will take on deep meaning. The relationship will assume the enchanted quality of our dreams:\n\nWow! I can't believe what she just said to me! Amazing!\n\nBut far more often, the practice will be a lot more challenging:\n\nWhy did he leave his dirty underwear on the floor?\n\nWhy did she forget my birthday?\n\nAnd why oh why did my guru just insult me?\n\nIn fact, it probably won't be but a few minutes into this practice that your newly appointed guru will do and say what will seem to be very \"un-guru-like\" things!\n\nThen it's up to you to think, \"What's the lesson here? What is this divine being trying to teach me?\" Maybe it's to be more like him or her, to imitate the positive qualities you have become keenly aware of while engaging in this practice of seeing the other as divine. But maybe it's to learn patience from a teacher posing as an irritating person; to learn to be more thoughtful of others as the teacher displays what it looks like to be selfish; to be careful that you're not doing to others what the teacher is now doing to you.\n\nNo matter whether the lesson is presented positively or negatively, the relationship becomes an ongoing opportunity to learn and grow. And that's the real magic inherent in the practice of guru yoga.\n\nWhile it's probably easiest to begin with one person you already see as sort of special, someone you love and who loves you, guru yoga has the capability of revolutionizing any relationship. It can be employed with equal benefit with loved ones and difficult people alike. It is the ultimate extension of thinking the best of others, of giving others the benefit of the doubt; of seeing the transformative possibilities inherent in any relationship; and of exploiting to the fullest the fact that if we alter our perception of others we will change our understanding of ourselves.\n\nAction Plan: Working with a Guru\n\nPick one person in your life to function as your \"guru.\" As we've said above, it could theoretically be anyone, but it might be best to start with someone close to you who you love\u2014a wife or husband, boyfriend or girlfriend, mother or father, sister or brother, son or daughter, or a very close friend.\n\nThe practice is simple to describe, but difficult indeed to stick with. Just decide that from now you'll regard this person as a kind of divine being\u2014an angel who is only trying to help you\u2014and everything, without exception, that this special person says or does is meant to be a teaching for you. What is it you need to learn about yourself from what the \"guru\" just said or did?\n\n#### Notes:\n\nI. When asked which of the commandments were most important, Jesus said: \"You shall love the Lord your God with all your heart, with all your soul, and with all your mind. This is the greatest commandment. And the second is like it: You shall love your neighbor as yourself.\" Matthew 22:37\u201339.\n\nII. In philosophical terms, we might say that karma isn't a metaphysical system but rather an epistemological one.\n\n## 6\n\n## Going with the Flow\n\nTo be too conscious is an illness\u2014a real thoroughgoing illness.\n\n\u2014\u2014Fyodor Dostoyevsky\n\n### GETTING INTO THE ZONE\n\nYou must lose the self, as Jesus said, to find it.I Or, to put it in the terminology we've used here, you must rise above the \"somebody self\" in order to gain some kind of access to the joyful unselfconsciousness of being nobody.\n\nThe empathetic expansion of identity to encompass others in our lives is one of the principal methods provided by our spiritual traditions to overcome the confines of mere individuality. But there is another spiritual technique designed to help us drop the self-consciousness and self-centeredness that are the ultimate sources of our unhappiness.\n\nThe method we'll explore in this chapter is designed to help us lose the self in action of all sorts\u2014not only in our relationships with others, but in each and every one of our everyday activities, alone or in company.\n\nWe use various colloquialisms to speak of being engrossed in action. When we're \"really into it,\" or when we're in \"the zone\" or \"the pocket\" or \"the groove,\" or when we're \"going with the flow,\" we're describing what it's like to be nobody because the \"somebody self\" has been wholly absorbed in an endeavor.\n\nWe all know what it feels like to be really consumed in an activity. When we say a book was a \"real page-turner\" or a movie was \"riveting,\" we are referring to this experience. When the concert was \"mind-blowing\" or the football match kept us on the \"edge of our seat,\" it's this sensation we're pointing to.\n\nWe are attracted to our hobbies, recreational activities, and games because they tend to launch us into this special state of mind. We're captivated by puzzles, and we love challenges at work for their capacity to bring us there. The rush we get while engaged in stimulating activities, especially those with a hint of danger (for me, it's riding my motorcycle), or when we're in the midst of an emergency\u2014these too can evoke this feeling. And, of course, it is this state of self-forgetfulness and ecstasy (derived from the word exstasis, \"standing outside of the self\") that lies behind the powerful attraction of heightened sexual experiences.\n\nIt's the feeling of not being there, or, we could also say, of totally being there\u2014of dropping the mental narrative and fully integrating with the experience itself. The inner play-by-play commentary on life ceases. Instead of the usual voice-over we superimpose on unfolding events, we are fully engrossed in the activity itself. The mind's monologue is silenced as unmediated awareness takes over.\n\nWe're all familiar with this unselfconscious state of consciousness that arises when we fully inhabit the here and now. It's the joy of being fully integrated into life itself. It's the exhilaration and elation we feel when we are deeply engaged in what we're doing. And it's another way we gain access in our everyday lives to the rapture of being nobody.\n\n\u2022 \u2022 \u2022\n\nMihaly Csikszentmihalyi has observed that we're happiest when we're in this condition of pure awareness. He has famously labeled it \"flow,\" defining it as the state \"in which people are so involved in an activity that nothing else seems to matter; the experience itself is so enjoyable that people will do it even at great cost, for the sheer sake of doing it.\"\n\n\"Really getting into it\" is the opposite of being \"out of it,\" of just spacing out and living life on cruise control. The flow state is characterized by extraordinary concentration on a task one finds captivating. \"Concentration is so intense that there is no attention left over to think about anything irrelevant, or to worry about problems,\" writes Csikszentmihalyi. When we are fully in the moment, completely occupied with the task at hand, we are unable to be simultaneously preoccupied with what comes next or \"post-occupied\" with what has already happened.\n\nThe flow state is the thorough engagement with the present, the utter embrace of reality as it's happening. It's like this now\u2014entirely accepted and embodied.\n\nMost importantly for our theme, this state of heightened awareness\u2014full absorption in what one is doing\u2014is also characterized by the loss of a sense of self-consciousness. \"Happiness,\" notes spiritual teacher Krishnamurti, \"is not something that you can seek; it is a result, a by-product,\" of self-abandonment:\n\nIf you pursue happiness for itself, it will have no meaning. Happiness comes uninvited; and the moment you are conscious that you are happy, you are no longer happy. . . . Being self-consciously happy, or pursuing happiness, is the very ending of happiness. There is happiness only when the self and its demands are put aside.\n\nThe \"somebody self\" disappears when we are truly happy; the inner voice shuts up. In fact, it is precisely the degree to which one loses the self in the activity that defines how deep the flow really goes.II Such \"peak experiences,\" as Abraham Maslow designated them, are moments of self-transcendence and contentment: \"Perception in the peak-experience can be relatively ego-transcending, self-forgetful, egoless, unselfish. It can come closer to being unmotivated, impersonal, desireless, detached, not needing or wishing.\"\n\nThese optimal, self-transcending states of mind are the bread and butter of religious mysticism. The \"oceanic feeling\" occurs when the individual feels herself or himself subsumed within some greater whole: \"God,\" \"ultimate reality,\" \"the Ground of All Being,\" one's \"Buddha nature,\" or whatever one wishes to call the nameless.\n\nIn the Eastern religious traditions, we are given a method designed to bring some version of this exalted state of mind into all our actions. In Taoism and Confucianism, the practice is called wu wei, or \"effortless action,\" and in Buddhism it's spoken of in terms of \"awareness\" and \"mindfulness\" in each and every one of our pursuits. In the Hindu tradition the phrase describing this spiritual technique for getting into the zone is particularly apt: karma yoga, or \"disciplined action.\"\n\nThese spiritual traditions posit that even in the ordinary activities of our daily lives we can enter the flow state. We don't need to wait for some extraordinary gift of grace to get a taste of the bliss, or sequester ourselves in a cave somewhere in order to bring about a mystical trip. And we don't have to continually and desperately search for exceptionally titillating \"peak experiences\" before we can get into the groove.\n\nEvery experience in life has the potential to be \"peak\"; every moment and every activity has the latent capacity to be \"optimal\" if we learn to let go of the \"somebody self\" and live in a more integrated and less self-conscious way.\n\nThere is, however, a difference between being mindlessly absorbed in an activity\u2014passively watching television or a movie or staring at the computer, for example\u2014and what we might call mindful unselfconsciousness in our actions. Karma yoga assumes both the disciplined \"mindfulness\" and the joyful \"unselfconsciousness\" that comprise \"being in the zone\" as opposed to just \"zoning out.\"\n\nThere's also a difference between hoping that some activity or another will seem captivating enough to push us into the flow, and the learned ability to put ourselves there. We all know and desire the joy of being completely engaged in what we're doing. But in between such \"optimal experiences,\" few of us stop to reflect on why and how they happen, and how we could potentially enter into any activity with this same intensity and attention.\n\nWashing the dishes offers the same potential for getting into the zone as motorcycling or rock climbing do. There's nothing in any Himalayan cave that's missing from the office when it comes to getting into the flow. Any action done with mindful unselfconsciousness can take us there.\n\n\u2022 \u2022 \u2022\n\nThe unexamined life, it has been said, is not worth living\u2014and that's true enough. It's important to be self-aware, in part because it is through self-awareness that one can come to realize that it is too much self-awareness that blocks us from the source of our greatest happiness. For the over-examined life can perpetually defer the actual living of it. \"Ask yourself whether you are happy,\" wrote J. S. Mill, echoing the Krishnamurti quotation cited above, \"and you cease to be so.\"\n\nOur deepest joy arises only when we cease taking our own temperature and, like the old Nike slogan says, just do it. Life does not run best when it's in neutral\u2014stalled out in continual self-analysis\u2014but when it's fully engaged.\n\n### GETTING UNBUSY\n\nYeah, but I'm already \"fully engaged,\" and it's totally stressing me out! I've got a million things to do\u2014so many responsibilities! I'm just so busy!\n\nNowadays most of us do indeed often feel the tension that accompanies having a lot to do. We have homework to complete, exams to pass, diplomas to acquire, and paying jobs to land. There are tasks at the office to accomplish, business problems to solve, and professional promotions to earn. The bills must be paid, forms must be filled out, and taxes must be filed.\n\nThe housework needs attention, the kids have to be driven to their soccer game, and there are birthday parties to be organized. There are home repairs that await us, meals to be prepared, and dishes, clothes, cars, and bodies to be washed. And there are, for some of us, book manuscripts to complete in order to meet the publisher's deadline.\n\nOur social lives can also sometimes seem a bit overwhelming, what with all the appointments, meetings, engagements, rendezvous, dinner parties, and lunch dates there are to juggle. We even fill our leisure time with plans, projects, schedules, and itineraries so as to not run the risk of\u2014gasp!\u2014boredom, the characteristically modern abhorrence of not having enough things to do.\n\nAnd the younger you are, the more likely that you're freaking out about all of this. A survey done on behalf of the American Psychological Association found that half of all \"millennials\" say their angst keeps them awake at night, and 39 percent of them said that their stress levels had increased in the past year.\n\nWe've done a good job of passing on this kind of anxiousness about life's tasks to our kids. When I was a teenager, I looked forward to sleeping in on Saturday morning (and we all know the amazing talent most teenagers have for sleeping in\u2014especially, I guess, if they've been kept awake the night before by stress!). But invariably my dreams were literally shattered as my father woke me at some ungodly hour (like maybe around 10:00 am) with the \"to do list\"\u2014the chores I was expected to get through that day.\n\nIdleness, I was told, was the devil's playground, and there would be no such demonic tomfoolery in this house! Let's get to work, son!\n\nAnd so most of us have internalized the idea that our self-worth consists at least in part in how busy we keep ourselves, with all the pressures and strains that come from such an attitude. Now more than ever before, we feel it's crucial to keep ourselves constantly occupied\u2014or at least thinking about all the things we have to do\u2014in order to be a real somebody.\n\nEven though such perpetual worry and frenetic activity is wearing us out and down, we nevertheless revel in what has become a cult of busyness.\n\nOur communications these days are often just to let each other know how much we've all got going on. Have you ever phoned up a friend and asked them how they're doing, only to sit there on the other end of the line, listening to them talk for fifteen minutes about how busy they are? Maybe you've found yourself doing the same when someone else asks after you. Our catch-up conversations turn into contests to see who's busier.\n\nAnd what's the unspoken message behind such tedious sharing and cataloging of our many activities?\n\nI'm really, really busy\u2014so see how important and valuable my life is?\n\nIn an article published in the New Statesman, Ed Smith writes that busy people \"are not rushing to arrive somewhere, still less to achieve anything. They are rushing because rushing is how they display how hard they work.\" The cult of busyness has become \"a cultural malaise.\" We're all trying to convince ourselves and others that our lives are significant because we are so busy working:\n\nIn every area of public life, we demand not only that people work harder, but, crucially, that they be seen to work ever harder. This is the age of professional martyrdom.\n\nOne of my spiritual teachers once pointed out that super-busy people are actually the very ones\u2014talented, energetic, and intelligent people\u2014who, if they paused their nonstop spinning long enough, would realize how relatively insignificant much of what they're busy doing actually is.\n\nBusyness for its own sake can keep us unaware of and unfocused on the more consequential things we have to do in life. And the busyness stresses us out, which often enough triggers major mental-affliction attacks. Anxiety about how many things there are to do does not help us do them better or more efficiently, let alone more wisely and calmly.\n\nInstead of putting us in the flow, busyness just sweeps us away in the current. Instead of the mindful unselfconsciousness that characterizes being in the zone, the cult of busyness instills a self-conscious mindlessness that keeps us stewing about how much we have to do instead of concentrating on what we are actually doing.\n\n\u2022 \u2022 \u2022\n\nStaying busy for the sake of busyness is not a spiritual technique for self-transcendence, happiness, or contentment. It is, rather, a recipe for agitation and turmoil, in addition to often being just another ploy to accentuate one's self-importance.\n\nThe spiritual methods for self-forgetfulness in action are quite different than this kind of hectic, chicken-with-its-head-cut-off urge to just keep busy all the time. And it's not mere inactivity that serves as the real antidote. Another cause of stress derives from worrying about all the things we should be doing that for one reason or another we are unable or unwilling to do.\n\nThe opposite of busyness is not paralysis. It's remaining active and engaged in life, but in a calm and relaxed manner. We must do what there is to do, but most of us need to get way more unbusy as we're doing it.\n\nGetting unbusy can mean cutting back on nonessential or meaningless activity in order to create a more uncluttered schedule. Reprioritizing what is really important puts what is not so essential in its proper place.\n\nIt can also mean taking more time off or simply enjoying the free time we already have without diluting it with obsessive worry, nonstop checking of email and text messages, and treating our days off and holidays as if they were just another opportunity to stay busy. We don't need to bring our work into our leisure time, and we don't need to turn our leisure time into work.\n\nGetting unbusy can also include introducing a relaxation or meditation practice into the daily schedule\u2014a time where you just sit and do nothing (except grabbing some peace of mind!), which is perhaps one reason why so many of us resist it. To the busyness fanatic, meditating seems so . . . unproductive.\n\nBut the main thing about getting unbusy is a change in one's attitude. Our duties in life, no matter how many or even how onerous, will not seem so overwhelming if we are not overwhelmed.\n\nStress does not arise in reaction to some quantifiable number of things one has to do. There are plenty of people\u2014I've personally known several\u2014who remain constantly occupied all day long without evincing much or any anxiety. And then there are folks who have, like, two things to do in the day and get themselves all balled up:\n\nOh, I'm so busy! I have a doctor's appointment at 9:30, and then this afternoon, I have this other thing to do!\n\nThere's a difference between staying active\u2014physically doing what needs to be done in the here and now\u2014and the mental feeling of being too busy. It's not that there aren't things in our lives that need attending to. There certainly are. What's being suggested here is definitely not that we ignore our jobs, our family obligations, or any of our other responsibilities. But these duties need not be a perpetual source of unhappiness by being regarded as drudgery instead of as opportunities for getting into the flow.\n\nAssuming an unbusy mindset allows for relaxed action instead of frenzied movement. Bhagwan Rajneesh (\"Osho\") has drawn a distinction between \"activity\" and \"action.\" \"Action is not activity,\" Rajneesh argues, and \"activity is not action.\"\n\nAction is when the situation demands it, you act, you respond. Activity is when the situation doesn't matter, it is not a response; you are so restless within that the situation is just an excuse to be active. Action comes out of a silent mind\u2014it is the most beautiful thing in the world. Activity comes out of a restless mind\u2014it is the ugliest.\n\nWhen the situation demands it, we act\u2014it's like this now, so we do what needs to be done. The opposite of busyness is not simple indolence or immobility, and it is certainly not shirking our obligations. But the agitation and restlessness\u2014the chronic impulse to just do something, anything!\u2014that accompanies what Rajneesh labels \"activity\" is the source of tension and anxiety.\n\nIndian deities and Tibetan Buddhist enlightened beings are often depicted with multiple arms to indicate the many beneficial ways they act in the world. They are portrayed as industrious\u2014it's a big job keeping the universe going and all! But none of them is pictured with brows all furrowed in angst. They're all totally Botoxed!\n\nActively and skillfully engaged, but not crazy busy\u2014this is the model for action in our own lives. Getting unbusy entails doing what there is to do efficiently and happily but without the incessant demands for frenetic activity associated with a stressed-out lifestyle that accompanies the cult of busyness.\n\n### FREEDOM FROM COMPULSIVE ACTIVITY\n\nTrue freedom, as we've been emphasizing, does not consist of just doing anything our untrained impulses suggest. Such an understanding of \"freedom\" keeps us locked in a prison of our own making. The happiness associated with spiritual goals depicted as \"liberation,\" \"deliverance,\" or \"release,\" requires first and foremost the end of this sort of bondage to our unrestrained mental afflictions, not the unconstrained expression of them.\n\nSo if you really must be busy, maybe it's best to get busy subduing these negative emotions that are the source of all our unhappiness. We feel more or less constantly a compelling need to change the way things presently are.\n\nBut living freely also mandates that we shake ourselves loose from the obsessive need to constantly accomplish, fix, or improve things through manic activity. We are enslaved not only by our mental afflictions but by our continuous attempts to direct future outcomes instead of fully concentrating on what we are doing in the here and now.\n\nAnd so the controlling, Captain Kirk self makes yet another appearance! Reinforced by the misguided idea that we need to keep busy in order to be of value, we feel compelled to be perpetually working to alter and change things. Motivated by stressful discontentment, the good old Captain turns out to be a full-blown neurotic!\n\nThis obsession with work and achievement is another way we try to scratch the perpetual itch of dissatisfaction\u2014in this case, the itch of always feeling like we have to do something in order to be somebody. It is the antithesis of the Great Itchless State.\n\nThe opposite of freedom, contentment, and perfect happiness is what the Eastern religions call samsara, the cyclical reproduction of suffering in our lives. And while there are many dimensions to what constitutes and causes this recurrent unhappiness, one definition of samsara found in the ancient texts is particularly striking for our present subject.\n\n\"Samsara,\" it is said in the Ashtavakra Gita, \"is nothing other than having something that needs to be done.\"\n\nThe crucial Sanskrit word in the verse, kartavya (\"having something that needs to be done\") refers to the compulsion to act, the niggling dissatisfaction that instigates panicky activity. The statement is rather radical and adamant, that this feeling of being compelled to act, and nothing other, keeps us from contentment.\n\nAt first blush, such an assertion might seem rather extreme\u2014But there are things I need to do! If I don't feed the kids, who will? If I don't go to work, how will I pay the bills? There are, of course, responsibilities that we all have to fulfill. But we'll complete them a lot more efficiently and happily if we lose the feeling that we are doing so under duress. It's not the obligation to act that's the problem. It's the neediness that spurs activity that causes us stress.\n\nThe idea that we are unhappy owing to a compulsion to act actually does pretty accurately sum up our unrest. We more or less constantly feel a compelling need to change the way things presently are. We are kept dissatisfied by our perpetual itchiness\u2014the desire for what we don't already possess and the yearning to rid ourselves of something we do have in our lives. These are the two forms of discontentment, and it is the cessation of both that brings us tranquility and peace.\n\nIt is the wish that things were not like this now that defines our unhappy state\u2014what we've called the \"if only\" syndrome. And in response to this discontentment, we feel the compulsion to get busy and start scratching all those nagging itches in the hopes of getting what we want and getting rid of what we don't.\n\nJesus, among many other great spiritual teachers, advised us long ago to just relax already. \"Therefore I tell you, do not worry about your life, what you will eat or what you will drink, or about your body, what you will wear.\" Constant fretting and stressing out about the future just ruins the present and, in general, spoils the limited time we have here on earth:\n\nIs not life more than food, and the body more than clothing? Look at the birds of the air; they neither sow nor reap nor gather into barns, and yet your heavenly Father feeds them. Are you not of more value than they? And can any of you by worrying add a single hour to your span of life? And why do you worry about clothing? Consider the lilies of the field, how they grow; they neither toil nor spin, yet I tell you, even Solomon in all his glory was not clothed like one of these. But if God so clothes the grass of the field, which is alive today and tomorrow is thrown into the oven, will he not much more clothe you\u2014you of little faith? Therefore do not worry, saying, \"What will we eat?\" or \"What will we drink?\" or \"What will we wear?\"\n\nThis famous passage from the Bible\u2014its message can be put succinctly: Don't worry, be happy!\u2014concludes with the following useful summary: \"So do not worry about tomorrow, for tomorrow will bring worries of its own. Today's trouble is enough for today.\"\n\nWe've got enough to take care of in the here and now without polluting our lives with anxiety and fear about future difficulties. There will be \"worries\" and \"troubles\" tomorrow\u2014let's rename them \"challenges,\" shall we?\u2014and when they arrive we'll need to deal with them. But the best way to prepare for tomorrow is to concentrate on today, for it is in the present that we are creating the causes that will govern our relative ability to deal with the events of the future.\n\nThere's another potential teaching on this subject that may be floating, so to speak, in your head somewhere.\n\nRow, row, row your boat, goes the song. We have things to do and responsibilities to fulfill, so keep rowing! The converse of keeping busy in compulsive activity is not slothful inactivity. But row your boat gently down the stream (and also merrily, merrily, merrily!) for life is but a dream\u2014and one day it will end.\n\nFlailing about with the oars in a frenzy of compulsive activity, worrying about what might be around the next bend, we forego the opportunity to leisurely enjoy the boat ride and do what we need to do in the present\u2014gently, merrily, and in a way that doesn't take the \"dream\" so very, very seriously.\n\n### KARMA AND ACTION FOR ITS OWN SAKE\n\nIt is important to do what we can to ensure a pleasant future. But such preparations are best accomplished through mindful attention to the present. The future will fall into place if we create the appropriate karmic causes in the here and now. And the most effective means for doing so is neither through harried busyness nor the compulsion to fix and change things that distracts us from what there is to do right now.\n\nThe compulsion to act is motivated by a perceived need to effect an \"improved\" situation in the future. It's just another instance of the \"if only\" syndrome. We ignore the present and the opportunities it affords when we obsess too much about the future. We feel compelled to get busy and start scratching in the hopes that we'll later obtain something better than what's going on now.\n\nIt was John Lennon who famously said, \"Life is what happens while you're busy making other plans.\" We become oblivious to the possibilities inherent in each moment of our lives when we're preoccupied with what will happen instead of centering on what is actually happening.\n\nThere is a spiritual technique to help us concentrate mindfully on what we're doing now. It is to act, not to gain some future reward, but simply because the task is there to do. This is the essence of what in the Bhagavad Gita is called karma yoga, the \"discipline\" (for this is what \"yoga\" really means) of action.\n\nTo do this sort of yoga there's no need to get a high-performance mat or buy expensive attire made of free-range organic cotton. A practitioner of karma yoga is defined as \"one who does what needs to be done while remaining unattached to the results of this action.\"\n\nMost of our actions, most of the time, are carried out as a means to achieve a desired end, expedients for reaching a desired goal. To be sure, every action will achieve some result\u2014there's a beginning, middle, and end to everything. But being \"in the flow\" puts our full attention on the action as it's happening\u2014on the middle bit, in \"real time\"\u2014and not on trying to arrive at an outcome as quickly as possible.\n\nLosing oneself in the activity at hand is by definition not \"goal-oriented.\" This is not to suggest that there isn't an end to be reached or a result to be eventuated. But in karma yoga, the means and the ends collapse so that the focus is on the action in and of itself.\n\nThis attention on the task at hand rather than on some projected result we hope to bring about is what we might call action done for its own sake.\n\n\"Action done for its own sake\"\u2014it's the very definition of being \"in the flow.\"III And while we are all happiest when we're mindfully unselfconscious and in the zone, the compulsion to act in order to attain a future objective tends to rule nearly every aspect of our everyday lives.\n\nIt's the inner angel and devil locking horns once again. We long to submerge ourselves in an activity and go with the flow, but at the same time we tell ourselves that such action for its own sake is somehow irresponsible. Given our desire to improve our own lives and the lives of those we love, we may think that losing ourselves in our present is somehow reneging on our obligation to try to create a better future.\n\nHere's another way to put this apparent quandary: There may seem to be a contradiction between action for its own sake and what we've talked about above in terms of \"karmic management.\" Can we simultaneously be fully and unselfconsciously absorbed in an activity while at the same time be working to create a better life for ourselves, for our loved ones, and for the world as a whole?\n\nWe observed in chapter 5 that according to the laws of karma every action will definitely have a corresponding reaction\u2014good acts bring pleasant consequences for our sense of self and happiness, while bad acts bring unpleasant results. The self-improvement enterprise\u2014which we've also argued is the best and really the only method for helping others (summed up in the formula change you, change the world)\u2014depends on wisely manipulating the karmic system.\n\nBut laboring to create the karmic causes for a better future might seem to be inherently goal-oriented; indeed, the whole concept of \"self-improvement\" might seem so. And neither would appear to mesh very well with a vision of \"action for its own sake.\"\n\nTo resolve this apparent contradiction, we'll need to review a few things about karma and then introduce some new observations pertaining to how the system really operates. And perhaps we will see that effective karmic management and action for its own sake turn out to be two sides of the very same coin.\n\nWe've already encountered one reason why there is actually no real conflict between creating new good karma\u2014acting in the present in order to create a better future\u2014and karma yoga, acting without attention to the fruits. The \"good\" acts we do are \"good\" to the degree that they are motivated by a selfless intention. The more we are motivated by self-interest, the less \"good\" that act is, and therefore the less pleasant will be the result.\n\nTo really work the karmic system, we must silence the demonic inner voice that always asks, What's in it for me? It is only a seeming paradox that the more selfless the intention behind any particular action the more beneficial that action will be to oneself. It's actually the very principle for generating good karma. It is intrinsic to the most effective management of karma that one loses oneself in action.\n\nPerhaps the easiest way to take the selfishness out of any activity is, as we've seen, to do it for someone else. Compassionate and empathetically inspired action\u2014What can I do for you?\u2014is a very effective surgical instrument for performing the ego-ectomy, extracting the self-interest out of the act.\n\nWhen we take our self-centered motivations out of the equation, we are able to concentrate more fully on the action itself instead of diluting it with futuristic projections of what we hope to personally gain from it. So from this angle we can see that karmic management\u2014directed by altruism and empathy\u2014entails the self-forgetting necessary for action done for its own sake. We can act unselfconsciously because our attention is focused on another.\n\n\u2022 \u2022 \u2022\n\nBut there's another dimension of why action for its own sake is built into the very system of karma. It is not the perpetual dissatisfaction with the present\u2014\"I'll do x so that I'll later obtain y\"\u2014that lies at the heart of the karmic enterprise. Creating the karma for a better future actually necessitates an opposite assumption.\n\nThe most effective karmic management assumes some version of contentment, and with contentment we have the possibility for pure action\u2014action done truly for its own sake.\n\nWhat goes around, comes around\u2014this is Karma 101. But for \"it\" to come around, \"it\" must go around first\u2014and herein lies an important secret when it comes to karma. We have to have some kind of sense that we already have \"it\" sufficiently before we become comfortable enough to give \"it\" away.\n\nLet's take one example. The feeling of prosperity or abundance\u2014for it is indeed a \"feeling\" and not a quantifiable commodity\u2014is the karmic result of generosity. Give and you shall receive, right? We may not always believe it, but we've heard the maxim plenty of times, from plenty of sources.\n\nThe example is a salient one, for generosity is one way of describing the whole karmic program. It is the willingness to give to others\u2014not just money and things, but also time and energy, love and compassion, respect and protection\u2014that lies at the very core of the care and maintenance of one's karma.\n\nKarmic management assumes some awareness of present fulfillment. Before we can even think about giving to others, we must believe we have enough to give\u2014enough material things, enough time, enough emotional gratification. We know that there will be future rewards\u2014that it will \"come around\"\u2014but even in the present there must be a certain sense of sufficiency, even excess, for us to first let it \"go around.\"\n\nEven the most self-interested, na\u00efve, and mechanistic understanding of karma has some degree of this sensibility that I have enough already. Even karma simplistically regarded as a kind of investment scheme\u2014\"I'll give this so that I'll get that in the future\"\u2014has some element of the notion that I have something I can afford to give right now.\n\nAnd a more informed understanding of how karma really works will bear an even deeper appreciation of this underlying secret: It is the feeling of plenitude and abundance, not the constant craving for more, that makes for truly efficacious karmic management.\n\nDo unto others as you would have them do unto you. Because I believe I have adequate material prosperity, I feel free to donate my money or things. Because I think I have enough time, I share my surfeit with others. If I feel a basic contentment within myself, I then feel able to give others the love and compassion that might help them feel more contentment too.\n\nSuch a recognition of self-sufficiency also helps us restrain ourselves from generating bad karma\u2014do not do unto others as you would not have them do unto you. If I feel safe and secure, I have no interest in harming others. When I am content with what I possess, I do not think of stealing. Because I feel enough love within, I am not tempted to infringe on others' relationships. And when I am satisfied with my own life I am not inclined to be envious or resentful of what others have.\n\nKarma yoga, in one sense, simply means disciplining one's actions in order to do good instead of bad, to be kind instead of cruel, to be other-oriented instead of egotistical. But we've also noticed that this method presupposes the latent assumption behind all karmically beneficial and unselfish activity. It is encapsulated in our contentment mantra:\n\nOm, I have enough, ah hum.\n\nAction done without expectation of personal reward presumes the recognition that one has been rewarded enough already. According to the Bhagavad Gita, \"No one becomes a yogi\" or true practitioner of karma yoga \"who has not renounced expectation of selfish advantage.\"\n\nBecause we don't need or expect recompense, we complete the action with the purest intention and the fullest attention on the act itself\u2014which, as we've repeatedly underscored, is the most powerful way to ensure that the act will have a positive karmic result.\n\n\u2022 \u2022 \u2022\n\nThere is no contradiction between karmic management and action done for its own sake. In fact, we do the former best when we are doing the latter. But, needless to say, we have a resistance to engaging in either.\n\nThe mental afflictions\u2014all of them revolving around egoistical self-cherishing\u2014militate against relying on the self-sacrificing principles of karma in our actions. The Big Smackdown, the Rage in the Cage, recurs over and over again as we fight our selfish inclinations in our attempts to live more wisely and joyously.\n\nAnd because of this same clinging to the self we resist, even while we yearn for, the experience of losing ourselves in an activity. Who would I be if I weren't somebody?\u2014a question we'll actually attempt to answer in chapter 7. But some part of us fears the very unselfconsciousness that brings us the euphoria of being in the flow\u2014of doing what needs to be done selflessly, efficiently, and with attention to the act itself and not to the fruits.\n\nKarma yoga as a discipline requires repeated practice. Our battles with the inner demon of egoistic self-centeredness are ongoing and arduous. And so in our quest to lose the self-consciousness and get into the flow of things when it comes to our everyday actions, we'll need to recall, over and over again, the benefits of doing so in order to strengthen the inner angel.\n\nTo reinforce our desire to act without selfish intention, we must remind ourselves how much pleasure there is in being in the zone, in the bliss of mindful unselfconsciousness, the exuberance of acting as nobody.\n\n### LIFE AS ART, WORK AS PLAY\n\nKarma yoga, or action done for its own sake, is a revolutionary method for living one's life. It is a radical procedure for removing the self-interest from our daily activities and becoming more attentive to what we're doing while we're doing it.\n\nOne of the principal ways of practicing karma is to replace the drone of What's in for me? with What can I do for you? Already this inverts our usual self-centered motivation and begins the revolution in our thinking about our everyday acts.\n\nUnderstanding the deeper principles of karma, we tune in to our own sense of self-sufficiency in order to give to others. Willfully suspending and foregoing any future personal rewards of action, we do what there is to do to the best of our ability, but for its own sake\u2014just because it's given to us to do.\n\nAnd there is another way of describing karma yoga that further highlights its revolutionary implications: Action done for its own sake is purposeless action.\n\nEvery action comes to an end and serves as the cause for a future effect. But action done for its own sake is focused not on the result but on the action itself. When the means and ends collapse, there is no particular purpose for doing something, other than that's what there is to do. The activity is enough in and of itself, not for what it achieves or brings about.\n\nPurposeless action does not imply that the activity is meaningless, and it certainly does not suggest that it need not be done at all or without giving it our full attention. If you're like me, you're accustomed to associate \"purposelessness\" with indifference and apathy. If you say there's no purpose, well, I guess there's no point.\n\nAction done for its own sake is purposeless but not pointless. To better understand this aspect of karma yoga, let's turn to two familiar examples of purposeless action: play and artistic expression.\n\n\u2022 \u2022 \u2022\n\n\"This is the real secret of life,\" declares Alan Watts\u2014\"to be completely engaged with what you are doing in the here and now. And instead of calling it work, realize it is play.\"\n\nWatts is by no means the first or only person to recommend that we concentrate fully on the task at hand; and he's also not alone in advising us to conceptualize all our activities in life as \"play\" rather than \"work.\" We naturally and easily do the first\u2014engage thoroughly with what we're doing in the here and now\u2014when we do the second, dropping the stress and compulsion to act and adopting instead a relaxed, playful attitude toward our daily tasks.\n\nWhen we are at play, it is not because we need to do something, but because we really want to do it. As opposed to the onerous demands associated with the idea of \"work,\" we play simply because it's fun. In play, we continue to row our boats\u2014and we do so quite assiduously and even strenuously\u2014but we also row merrily, because it's fun to play.\n\nOne of the reasons so many spiritual teachers, theologians, and secular scholars have taken play quite seriously is that when we are at play we don't take things so seriously. We relax (without losing focus) and shed the stressful anxiety that comes when we obsess about the outcome rather than really getting into the process.\n\nIt's been said that we should lighten up on our way to enlightenment, and thinking about all our activities in terms of \"play\" rather than \"work\" can help us to do this.\n\nJohan Huizinga, the author of the classic scholarly study on this subject, Homo Ludens: A Study of the Play-Element in Culture, refers to the irreducible \"fun element\" lying at the heart of play: \"Now this element, the fun of playing, resists all analysis, all logical interpretation. As a concept, it cannot be reduced to any other mental category.\" The essential purpose of play is that it has no purpose, which makes it both \"fun\" and quite different from our usual compulsive need to act. Play, Huizinga writes, \"stands outside the immediate satisfaction of wants and appetites.\"\n\nThe importance of the concept of play has been recognized for millennia in the world's spiritual traditions. In one branch of the religions of India, the concept of \"play,\" or \"sport,\" is known by the Sanskrit term lila, and it was originally introduced as a stratagem for solving a perennial theological question: Why did God create the universe? Did God\u2014who lacks for nothing and is complete in Him- or Herself\u2014nevertheless have some need to create, some purpose behind bringing the world into existence?\n\nIn response to the accusation that God can't be the creator of the world, since God, being God and all, has no motive or reason to act, it was countered that God did create the world\u2014but \"merely in play.\"IV As William Sax writes in his aptly titled The Gods at Play, \"The idea is that God's creation of the world is motivated not by any desire or lack, since these would be incompatible with his or her self-fulfilled and complete nature, but rather by a free and spontaneous creativity.\"\n\nIn the Bhagavad Gita, we are explicitly advised to imitate the divine in our own actions, in the ongoing creation of our own lives. Krishna tells Arjuna, his student and friend, to act\u2014to do what needs to be done\u2014but to act like God does, not out of a compulsive need for self-aggrandizement, but totally and selflessly unattached to the results:\n\nArjuna, throughout the three worlds there is nothing whatsoever that I need to do. There is nothing unattained that I need to attain, and yet I still engage in action. . . . While those who are ignorant perform actions out of attachment, the wise one, unattached, acts in order to maintain the world.\n\nLila describes action done out of freedom rather than necessity, out of a sense of prior and ongoing contentment rather than the neediness of the \"if only\" syndrome. It is the paradigm for action done for its own sake, the blueprint for karma yoga.\n\nThe purity of play has been seriously diluted in our modern, grown-up versions of \"games\" and \"sports\" and must be distinguished from them. The overweening emphasis on winning as the purpose, especially in professional sports, where fame and fortune depend on victory, have compromised the \"action for its own sake\" nature of play in its essential form.\n\nThe quaint old aphorism \"It's not whether you win or lose but how you play the game\" has largely been forgotten and replaced by football coach Vince Lombardi's famous dictum: \"Winning isn't everything; it's the only thing.\"\n\nThis preoccupation with victory is thoroughly tied up in the culture of narcissism we spoke of in the introduction. We're encouraged to think we're not \"somebody enough\" unless we're a real \"winner.\" And winners require losers. We often believe that we'll be a real somebody only if somebody else is less of one.\n\nI once met a professional speed skater who was very, very good at what he did\u2014so good, in fact, that he was sent to the Olympics, where he did very, very well. He came home with a silver medal. He was the second best skater in the world in his event.\n\nAnd guess what? He was disappointed, because he was only second best.\n\nPlay in its uncorrupted sense isn't about trying to be better than others. But it also does not preclude healthy competition. Action done for its own sake, whether done alone (competing against ourselves) or in the company of others (competing against competitors), can bring out the best in all of us.\n\nWhat the Tao Te Ching calls the \"virtue of non-competition\" is not about no competition, as the text makes clear. It is rather doing one's best\u2014and wanting others to do their best too\u2014all in the \"spirit of play\":\n\nThe best athlete\n\nwants his opponent at his best . . .\n\nAll of them embody\n\nthe virtue of non-competition.\n\nNot that they don't love to compete,\n\nbut they do it in the spirit of play.\n\nIn this they are like children\n\nand in harmony with the Tao.\n\nAnd so it is that to act in the \"spirit of play\" we are pointed to the example of children. Children, before they are taught that the point is to \"win,\" exemplify the pure version of playful activity. If you've been around small children (or if you remember being one), you know that kids get totally and tirelessly absorbed in what is, after all, purposeless action.\n\nImagine going to a playground and asking kids why they're doing what they're doing\u2014that is, asking what the purpose of the activity is. \"Why are you sliding down the slide, little girl? What is the purpose of all this swinging back and forth? Why the teetering, then the tottering? What is your objective in going around and around in circles on the merry-go-round? And what exactly is the reason for climbing up and down that jungle gym?\"\n\nThe kid would probably run away screaming to her mom or dad, terrorized and confused by such stupid questions coming from such a crazy grown-up!\n\nThe point of play is found not in the completion but in the process. As always, there's a beginning, middle, and end to the activity. You climb up the stairs of the slide and slide down, thus getting to the ground. Sliding ends when one reaches the bottom, but it's not in order to reach the bottom that one slides. In play, it's all about the sliding, not the having slid.\n\nThe kids got it right when it comes to action for its own sake. Play is not puerile or childish in the sense of being fatuous or foolish. But it is childlike to the degree that it embodies the simple, unencumbered sense of wonderment and joy involved in acting mindfully and unselfconsciously in purposeless action.\n\nIt is this simplicity in behavior, purity in action, and humility rather than self-promotion\u2014not believing that \"winning is the only thing\"\u2014that led Jesus to answer the way he did when asked by his disciples, \"Who is the greatest in the kingdom of heaven?\"\n\nHe called a child, whom he put among them, and said, \"Truly I tell you, unless you change and become like children, you will never enter the kingdom of heaven. Whoever becomes humble like this child is the greatest in the kingdom of heaven.\"\n\nAs an Indian text asserts, the wise spiritual practitioner \"does whatever comes to him to do, no matter if it's pleasant or unpleasant.\" The adult version of childlike simplicity entails facing every responsibility\u2014\"pleasant\" or \"unpleasant\"\u2014with the same playful and lighthearted attitude. And so, the text continues, she \"who is without desire in all undertakings behaves in a childlike fashion. Acts done by a pure one like this are without stain.\"\n\nOne final note about play. A serious person might, once again, object that using this analogy of \"life as play\" is immature and irresponsible. But as the ancient Greek thinker Heraclitus observed, \"Man is most nearly himself when he achieves the seriousness of a child at play.\"\n\nFor all those good-hearted but perhaps overly earnest people out there, remember what's been said above about the relationship between karmic management and action for its own sake: There's no contradiction between working to improve oneself and the world, on the one hand, and selflessly losing oneself in action\u2014making work into play\u2014on the other. As we've seen, the former is actually done best when the latter occurs.\n\nActing as if it were all \"just a game\" (\"life is but a dream\") is neither irresponsible nor uncompassionate, and we can once again return to the theology of lila to understand why. The \"sportive\" activity of God's play does not preclude the \"supportive\" or compassionate element of God's grace, as Norvin Hein has cleverly put it. They are reconciled in that they both are defined by the same absence of \"calculation of any selfish gain\":\n\nGod's sportive acts and his supportive acts are one because both are done without calculation of any selfish gain that might be made through them. Both are therefore desireless . . . and between God's lila and his grace there is no inconsistency.\n\n\u2022 \u2022 \u2022\n\nMany forms of artistic expression also exemplify the purposelessness of action done for its own sake. It's not usually to fulfill some practical function that one paints, dances, sings, writes poetry, plays an instrument, or sculpts\u2014although professional artists need to make a living too!\n\nWhile the artistic endeavor often results in a product\u2014a picture is painted, a form is sculpted, a dance has been danced\u2014even the finished \"work of art\" is aesthetic, not utilitarian. Andy Warhol once remarked, \"An artist is somebody who produces things that people don't need to have.\"\n\nAnd the process of artistic creation is arguably more important than the product. \"The object isn't to make art,\" observed painter Robert Henri. \"It's to be in that wonderful state which makes art inevitable.\" The purpose of artistic creation is to get into the flow of artistic creation. Like play, artistic activity in its pure form has no purpose other than itself.\n\nIn some instances, art is clearly created as ephemeral and transitory in order to highlight the importance of the creative process over the created product. Tibetan Buddhist monks labor for days, even weeks, painstakingly pouring colored sand to construct a mandala, an elaborate geometrical representation of the cosmos\u2014and then completely destroy it upon its completion. In a similar fashion, Andy Goldsworthy assembles equally intricate designs over the course of many hours, with icicles that melt in the sun, twigs that are blown away by a gust of wind, or rock structures that are swallowed by the sea when the tide comes in.\n\nGraffiti art (aka \"street art\") is also often quite detailed and time-consuming to create, but usually with the expectation that sooner or later the civic authorities will scrub it off or paint over it. And performance art of all sorts is by definition, well, performed\u2014it's the activity itself that's essential; not something else that is brought about by the activity.\n\nMusic and dance are particularly salient examples of artistic expression done purely for its own sake. There's no real purpose to either playing or listening to a piece of music other than the pleasure of aesthetic expression and appreciation. And we dance or watch others dance not because doing so produces some result or attains some goal, but simply because it's enjoyable to do or watch.\n\nThe meaning and purpose are in the music and the dance themselves. As Isadora Duncan memorably quipped, \"If I could tell you what it meant, there would be no point in dancing it.\"\n\n\"A strong relaxation and calm comes over me,\" reports another dancer. \"I have no worries of failure.\" Like with pure play, there's no winning or losing, success or failure, involved in pure artistic expression. While others might judge the dance or the poem to be \"good\" or \"bad\" according to some criterion or another, the creative experience of dancing or writing poetry is rewarding in and of itself.\n\nAs one nonprofessional dancer elegantly observed, when we give ourselves over to the dance, our mental afflictions temporarily evaporate, our sense of individual isolation dissolves, and we feel fully integrated with our surroundings:\n\nWhile I dance, I cannot judge. I cannot hate. I cannot separate myself from life. I can only be joyful and whole. That is why I dance.\n\nArt imitates life, it is said; and it's also said that life imitates art. From the point of view of karma yoga, we might also put forward the idea that life should imitate art, just as \"work\" should best be regarded as \"play.\"\n\n\"Art,\" declared philosopher Friedrich Nietzsche, \"is the proper task of life.\" And to fully engage in life as art, the artist loses him- or herself in the ongoing process of creation.\n\n### VIRTUE IS ITS OWN REWARD\n\nAny activity can be made much more enjoyable and rewarding if it's done for its own sake. Any act undertaken calmly and unbusily, free from the compulsion to act; any chore that's reconceptualized as play; any pursuit that's reconstituted as a kind of performance art\u2014in sum, any endeavor we do with mindful unselfconsciousness, can get us into the flow.\n\nI wish I could tell you that I knew of some quick and easy tricks for getting into the zone\u2014especially when the activity does not seem that intrinsically magnetizing. It's relatively easy for me to get into the flow when riding my motorcycle or playing in the waves at a beautiful beach. I too would be stoked to learn of some magic that would effortlessly launch me into action when it came to taking out the garbage, mowing the lawn, or doing my taxes.\n\nBut karma yoga, as we've mentioned before, is a form of \"yoga\" or \"discipline,\" and the main feature of this yoga is not physical. Karma yoga is a method that depends on mindfulness and awareness. The essence of this technique is continuously remembering our simple but always relevant formula:\n\nOm. It's like this now. Ah hum.\n\nThe only \"trick\" to karma yoga is to constantly recall this mantra. \"This is what's happening now; this is the task I have to do at present.\" There's no point in starting up the \"if only\" whine again. It's like this now, so let's just do it!\n\nIt is the complete acceptance of whatever the next scene is in the ever-changing drama of life that serves as the precondition for losing oneself in the play. Karma yoga is the discipline of integrating the \"somebody self\" into what we are doing in the here and now, and thereby assuming the guise of the \"nobody self\" when acting.\n\nSo among the other descriptors that characterize action for its own sake, the most important of them is egolessness:\n\nWhether he is seeing, hearing, touching, smelling, eating, walking, sleeping, or breathing, the disciplined one, who knows how things really are, would think, \"I'm not doing anything at all.\"\n\nIt's just the \"seeing, hearing, touching, and so forth\" that's happening. The \"I\" that's doing the \"seeing, hearing, touching\" is subsumed in the activity itself. \"I'm not doing anything at all\" because the self-consciousness required for awareness of the conceptualized \"I\" has been lost in complete engagement with what one is actually doing. The separation between the self and the world evaporates, and we become one with the life we are living.\n\n\u2022 \u2022 \u2022\n\nBefore concluding this discussion on \"losing oneself in action,\" it's important to emphasize that the kind of \"action for its own sake\" we're speaking of here is not a morally neutral exercise. There are better and worse ways to be \"in the zone.\" It's totally conceivable, to take one grisly example, that an ax murderer could really get into the activity of chopping up his victims.\n\nWhile our secular psychologists have extolled the \"flow state\" for the pleasant and rewarding feelings that naturally attend it, our spiritual teachers have always emphasized that it matters not only how we do what we do, but also what we do and why we do it.\n\nThe discipline of karma yoga assumes that we understand the \"karma\" part. It presupposes wisdom about how karma really works and the direction such wisdom moves us when determining what we will do with our lives. Most importantly, karma yoga assumes that we are clear about the why\u2014the intention or motivation behind any activity. The more aware we are that it is the selfless motivation that creates a happier life, the happier our lives will be\u2014in both the present and the future.\n\nThe ancient Stoic philosopher Seneca remarked, \"The real compensation of a right action is inherent in having performed it.\" Virtue, in other words, is its own reward.\n\nBut virtue is virtue only if it is its own reward. Virtuous actions pay off only to the extent that we forego the explicit and conscious expectation of future personal benefit and concentrate on doing what needs to be done\u2014to the best of our ability and out of the best of intentions.\n\nThere is pleasure to be found in any activity that puts us in the flow. But the rewards of virtuous action done for its own sake are doubled. Selfless action creates the karmic causes for future happiness: what goes around will come around. But action guided by karma yoga also entails contentment with our present situation and the opportunities it provides for acting wisely and happily in the here and now.\n\n\"The one who abandons attachment to the results of action,\" it says in the Bhagavad Gita, and \"who is always satisfied and independent, does nothing at all, even when he is engaged in action.\" Once again, with the loss of the \"I,\" it's nobody who's doing anything when action is done for its own sake.\n\nWhen we practice going with the flow, guided by karma yoga, we obtain relief from incessant self-consciousness, the inner chatter of the \"somebody self.\" We are also at least temporarily liberated from the itchiness of the \"if only\" syndrome. And we are propelled for the length of our mindful unselfconsciousness into an experience of the Great Itchless State, the place where the \"somebody self\" stops cogitating and scheming (\"I'm not doing anything at all\") and allows the \"nobody self\" to take over and play.\n\nAction Plan: Who's There When You're in the Flow?\n\nMake a list of the activities you engage in that bring you the most pleasure\u2014gardening, going to the beach, playing with your children, dancing at the club, getting absorbed in a challenging and enjoyable task at work, or whatever yours might be. When you are fully engaged in these happiness-producing activities, are you self-consciously monitoring yourself, or are \"you\" not really there at all?\n\nThen pay attention to the experience of doing what you truly enjoy next time you have the opportunity to do it. Check to see whether it is precisely the degree to which you can \"lose yourself\" in the activity that produces the joy and satisfaction you attribute to it.\n\n#### Notes:\n\nI. \"If you cling to your life, you will lose it; but if you give up your life for me, you will find it.\" Matthew 10:39.\n\nII. \"In flow, a person is challenged to do her best and must constantly improve her skills. At the time, she doesn't have the opportunity to reflect on what this means in terms of the self\u2014if she did allow herself to become self-conscious, the experience could not have been very deep.\" Mihaly Csikszentmihalyi, Flow: The Psychology of Optimal Experience (New York: Harper & Row, 1990), 65\u201366.\n\nIII. Compare Csikszentmihalyi's fancier label for this same idea: \"The term 'autotelic' derives from two Greek words, auto meaning 'self' and telos meaning 'goal.' It refers to a self-contained activity, one that is done not with the expectation of some future benefit, but simply because the doing itself is the reward.\" Csikszentmihalyi, Flow, 67.\n\nIV. The earliest example of this argument in Sanskrit literature is found in Badarayana's Vedantasutras, 2.1.32\u201333. The author answers the objection that God can't be the creator of the world since God has no motive or reason to act (na prayojanavattvat, 2.13.2) by saying God does so \"merely in play\" (lokavattu lilakaivalyam).\n\n## 7\n\n## Living as an Ordinary Joe\n\nWe have the choice of two identities: the external mask which seems to be real, and the hidden, inner person who seems to us to be nothing, but who can give himself eternally to the truth in whom he subsists.\n\n\u2014\u2014Thomas Merton\n\n### WHO DA HELL AM I?\n\nIn the futuristic movie Total Recall, the protagonist, played by Arnold Schwarzenegger, purchases a brain implant designed to endow him temporarily with a completely new persona. The procedure goes haywire and Arnie becomes seriously confused, wandering through the movie trying to remember his former, and real, identity.\n\nAt one point, the frustrated, amnesiac Teutonic hero cries out in anguish, \"If I'm not me, who da hell am I?!\"\n\nThis is the million-dollar question for all of us: \"Who da hell am I?\" And there's one thing that the world's spiritual traditions and modern science and philosophy agree upon when it comes to the self: We are not who we think we are. We are all amnesiacs like the Schwarzenegger character, wandering through life, trying to find ourselves.\n\nJulian Baggini has summarized the state-of-the-art findings in psychology, neuroscience, and modern philosophy in The Ego Trick, noting first that we're all pretty damned sure that there must be a real \"me\" in there somewhere: \"People almost invariably believe that there is such an essence, a core of self that holds steady through life,\" he writes. \"This is sometimes called the 'pearl' view.\" But the pearl inside the oyster is impossible to find: \"The problem is that no one seems to be quite sure where to locate this precious gem.\"\n\nDespite our certainty that there must be \"a core of self,\" we've seen that the \"Where's Waldo?\" search from hell for a unitary, unchanging, independent, Captain Kirk, essential pearl of a self inevitably leaves us empty-handed.\n\nThe Buddhist tradition has coined the term \"no-self\" (anatman) to describe this absence of the kind of \"me\" I think I am. But the recognition of the illusive nature of the personal, individual self is neither the sole discovery of any one religion nor nowadays even of religion itself.\n\nIt's become common knowledge that our commonsensical ideas about the self are in no way obviously or self-evidently true.\n\nThe self we think we have turns out to be just a kind of imaginary friend\u2014or, perhaps even more often, an imaginary enemy. So we can all join our voices with Arnie's and cry out in unison: \"If I'm not me\"\u2014if I'm not the \"me\" I think am\u2014then \"who da hell am I?\"\n\n\u2022 \u2022 \u2022\n\nHere's what we've discovered so far:\n\nEach of us is, in fact, a unique individual; we're all equally \"special,\" worthy of healthy self-respect and deserving of basic human rights. These are the givens when it comes to the question of personal identity\u2014I am somebody!\n\nYes, each of us is somebody, and we're all fundamentally equal as somebodies. We're all the same in that we suffer and have problems in life, and we're all equally entitled to and have the capacity for attaining true happiness. And we all, equally, make mistakes\u2014the worst of them stemming from our ignorance about who da hell the somebody we are really is.\n\nBut we delimit ourselves when we overidentify with the temporary and changing roles we play\u2014when we mistake the revolving series of carnival cutouts, which we employ to constitute either our individual or group identities, as being fully and essentially definitive of who we actually are. And we especially suffer when one or another of these cutouts pits us against the cutouts into which other people are sticking their faces. This desperate, if futile, quest to be a real somebody quickly devolves into the divisive competitiveness of trying to be more of a somebody than somebody else.\n\nOur ongoing culture of narcissism\u2014stretching from the \"Me Decade\" right through to the present \"iEra\"\u2014has magnified our attachment to the ego and its insatiable need to be admired and inflated. The elevation of self-centeredness as a culturally acceptable obsession has had obvious consequences, for what goes up must come down. The rampant pandemic of depression (and its less virulent but nevertheless serious twin, low self-esteem) can be directly linked to the excessive self-preoccupation that is both the real cause and the tragic expression of this debilitating disease.\n\nReal self-improvement is founded upon first wising up about the question of \"Who da hell am I?\" I'm not the \"me\" I think I am\u2014unified, changeless, independent, and a Master Controller of the present in the present. Who I am\u2014as somebody\u2014is an idea of me based on my parts: my body (can't be me without it!) and my mind (I'd really be in trouble without a mind!). \"We are nothing but our parts,\" writes Julian Baggini, \"but we are more than just our parts.\"\n\nThis \"more\" that makes us who we are is simply a label, a name, an idea. I am, in sum, a conceptualization made possible by the conglomeration of multiple physical and mental parts that are forever changing.\n\nI myself (!) have been many different me's (both internally and externally) over the course of lo these sixty years\u2014child me, rebellious youth me, family man me, academic me, surfer bum\/biker me, monk me, spiritual teacher me, and retired man-of-leisure me. In some of my interactions, I'm \"Dr. Smith, PhD,\" and in others, \"Brian K. Smith.\" In yet other circumstances I'm \"Lama Marut,\" but to friends and family, I'm just plain \"Brian.\" Each me is a different persona, each a different conceptualization of the self and role, which I (whoever that is!) assume depending on the context and type of relationship I have with others.\n\nAnd because who I am is merely a conceptualization on the basis of constantly evolving mental and physical parts, I can learn to re-conceptualize myself so as to become a happier me, no matter what role \"I\" am playing.\n\nWe've spoken in this book of many methods that function to help us improve our sense of self. Since who we think we are at any given moment is dependent on who we think we once were\u2014on our memories or past karma\u2014if we practice forgiveness, gratitude, and acceptance vis-\u00e0-vis our past, we will think of ourselves differently now. As we battle our selfish, destructive, and irrational mental afflictions in our own inner Rage in the Cage, we begin to think of ourselves as someone who is at least trying to be a good person, someone who is working to tame the worst of our habits.\n\nWhen we drop the egotistical me, me, me chant and substitute the What can I do for you? mantra, we advance the process of self-improvement ever further, knowing that the best thing we can do for ourselves is to think about how we can help others. Lovingly and empathetically putting ourselves in other people's places, we gain freedom from the artificial limitations we place on our self-identity. And when we lose ourselves in action and concentrate on joyfully doing what needs to be done rather than calculating what we personally will get from doing it, we practice mindfully unselfconscious living all day long, in each and every situation.\n\nIf we wish to think of ourselves as a better somebody, we must act, speak, and think in more selfless and less selfish ways\u2014in our relationships with others and in our everyday activities. We gain a better sense of self when we're not thinking about ourselves\u2014and this is the seemingly paradoxical key to true \"self-improvement.\"\n\nSo who da hell are you? And if you don't like the answer, make the necessary changes! \"Your worst enemy cannot harm you as much as your own unguarded thoughts,\" asserts the Dhammapada. \"But once mastered, no one can help you as much, not even your father or your mother.\"\n\nThere's no one who makes you \"you\" other than you, and you now have the necessary tools for the creative process of self-reinvention.\n\n\u2022 \u2022 \u2022\n\nThe question for us at this point is not \"If I'm not me, who da hell am I?\" I may not be the \"me\" I ordinarily think I am. But I am also no other than the \"me\" that I think I am. That's all the self there is when it comes to the particular, individual \"me\"\u2014the \"somebody self\" is a self-conception.\n\nThe really pertinent question at this concluding stage of our inquiry is \"When I'm not me, who da hell am I?\" We're nobody apart from thinking that we're somebody. And when we stop thinking we're somebody, we're really left with nobody.\n\nWe've said it before, and it's worth repeating: It's nobody that makes any and all somebodies possible. If we were really somebody\u2014if there were a hardwired, permanent, essential \"somebody self\"\u2014we'd be forever saddled with a static, unchanging, unimprovable, and very bored \"me.\"\n\nSo let's put it positively: because we really are, have always been, and will always be nobody, we can be the ever-changing somebody we are now, have been in the past, and will be in the future.\n\nIt's getting in touch with the nobody that we really are that helps us improve the somebody we think we are. Thomas Mann once said, \"No one remains quite what he was when he recognizes himself\"\u2014and this is especially true if we know which self is changed when which self is recognized.\n\nIt is in the close encounters of the third kind with our \"nobody self\"\u2014when we drop the self-consciousness, the self-grasping, and the self-centeredness\u2014that we plug into our true being and the real power that transforms us. It is by losing the little self that we discover the Higher Power that is our Higher Self. And it is those moments when we commune with our true nature that function to make us a better and happier somebody.\n\nSo in this concluding chapter, we'll be exploring the final frontiers of the question of self-identity:\n\nWho are we when we're not somebody?\n\nWe'll first look a bit more closely at who this \"nobody self\" we've been talking about really is. We'll then investigate the relationship between our personal identity and our universally shared true nature. Finally, we'll conclude with some tips on how the \"somebody self\" can further integrate with its real nobody-ness as it learns to live, not as someone desperately striving to be somebody special, but rather contentedly, as just an Ordinary Joe.\n\n### THE SELF THAT HAS NO NAME\n\nWhat we've called the \"nobody self\" has various names in different traditions: it is our \"true self\" or \"Buddha nature,\" the immortal soul, the Ground of Being, the atman, or the Tao. And the different traditions describe it in comparable ways, albeit with somewhat different vocabulary\u2014that is, when they are willing to describe it at all.\n\nThe \"true self,\" says one Hindu text, is \"pure, awake, dear, complete, unmanifest, and faultless.\" It \"has never been born and never dies,\" says another ancient Indian scripture. \"It has not come from anywhere, nor has it become anyone. It is unborn, unchanging, eternal, and primordial. It is not killed when the body is killed.\"\n\nAll of these descriptors point to the fact that the \"nobody self\" is the exact opposite of the \"somebody self.\" When our true nature is depicted, it is as a kind of reverse image of the limited, flawed, mortal, and basically disgruntled self we are so attached to.\n\nAnd in many of the world's religions, there is also the recognition that the \"nobody self\" can't really be depicted or characterized at all. It is the unspeakable, the inconceivable. The \"nobody self\" is, by definition, nameless:\n\nThe tao that can be told\n\nis not the eternal Tao\n\nThe name that can be named\n\nis not the eternal Name.\n\nThe unnamable is the eternally real.\n\nNaming is the origin\n\nof all particular things.\n\nWhereas the particular, individualized, lower self is really nothing other than a \"name\"\u2014an idea or concept\u2014the \"nobody self\" is the self that has no name . . . and is eternally unnamable.\n\nIn the ancient Indian traditions, this ultimate state is sometimes said to be nirguna, \"without qualities or characteristics,\" and from this point of view the only way to refer to it is negatively. It is neti, neti, \"not this, not that.\" \"Ultimate reality is indescribable and cannot be signified,\" as one text puts it. \"The blissful experience of one's own innermost self is accessible only when conceptual thought ceases.\"\n\nOr as another text declares, \"It is unseen, unattainable, ungraspable, and without distinguishing marks. It is unthinkable, indefinable, and its essence is the perception of only itself. It is the pacification of all projections\u2014peaceful, auspicious, non-dual. This is the true self; this is to be known.\"\n\nWhat is labeled our \"Buddha nature\" in the Buddhist tradition is similarly depicted as \"beyond conceptualization\" and description:\n\nBecause of its inexhaustible qualities, in nature it's like nothing else. Limitless, it acts as the only real refuge for living beings. It is always non-dual, beyond conceptualization. It has an indestructible quality since its true nature is uncreated. It is not born because it is permanent. It does not die because it is immovable. It is not harassed because it is in a state of peace. It does not decay because it is eternal.\n\nTurning to the Western traditions, in Islam there are said to be ninety-nine names for Allah (\"The Merciful,\" \"The Creator,\" \"The Bestower,\" and so on), but the hundredth name is the \"name that cannot be uttered.\" Jewish theologian Lawrence Kushner also declares that \"there is yet a higher Name for the One of Being,\" and this name is \"Nothing\":\n\nBeyond One there is only Nothing, for only Nothing can comprehend both good and evil, being and becoming, unity and duality, sea and dry land. Already hinted at in Kabbalistic tradition by the ultimate Name, Ayn Sof: literally, without end or utter Nothingness. It is here that our consciousness and the Name of God while still discrete, are no longer separate.\n\nAnd in the Christian tradition, this negatively enunciated depiction of what cannot be accurately or fully depicted is called the via negativa, \"apophasis\" (from a Greek word meaning \"to say 'no' \"), or \"negative theology\" (describing God or ultimate reality only by saying what it is not). Such an approach to the truly real can be found in many other ancient traditions as well\u2014including certain strands of modern Western philosophy.\n\n\"When you come to the ultimate,\" writes Rajneesh, \"when you come to your deepest core, you suddenly know that you are neither this nor that, you are no one. You are not an ego. You are just a vast emptiness.\"\n\nSo there's not much to be said about that of which we cannot speak. We, as particular somebodies, can really only point to the universal nobody we all really are, like so many fingers pointing to an indescribable moon. The great mystics have often said\u2014when they're talking about what can't be talked about at all\u2014that silence is probably the best strategy when it comes to our attempts to describe the \"nobody self.\"\n\nBut we can definitely say this: Being nobody is not being nothing. It is an absence (no-body) and not a presence (some-body), but it is the emptiness that makes the plenitude possible. It is the hole in the middle that makes a donut what it is; it is the empty glass that can hold whatever is poured into it; it is the undifferentiated ocean from which all particular waves arise, last for a while, and then return to their source.\n\nThis absence is the space in which all manifestation and life forms take place. It is nobody from which any and all somebodies arise and into which we are all reabsorbed. Nameless but not a nonentity, the ultimately real is the silence from which all sounds, words, names, and concepts emerge and back into which they dissolve.\n\nAnd there's another thing we should say about the inexpressible: in its presence, we stand in reverential wonderment. It is the ultimate Great Itchless State of pure bliss. If we space out on those times when we commune with the infinite spaciousness of our true being\u2014the self that cannot be named, conceptualized, or described\u2014we miss out on the possibility of being awestruck . . . and therefore dumbstruck.\n\nIt's like the difference between appreciating the awe-inspiring beauty of a gorgeous sunset and coldly calculating the angle of the light rays as they filter through the atmosphere. The latter is driven by curiosity and utilizes words and concepts; the former captures the wonder of open-mouthed astonishment and wordless stupefaction.\n\nAs Rajneesh says, if you haven't experienced that which is beyond words, you haven't really lived at all:\n\nEven in ordinary life you feel the futility of words. And if you don't feel the futility of words, that shows that you have not been alive at all; that shows that you have lived very superficially. . . . When for the first time something starts happening which is beyond words, then life has happened to you, life has knocked on your door.\n\n\u2022 \u2022 \u2022\n\nThroughout this book, we've talked about the opposition between the \"somebody\" and \"nobody\" selves as a tension between our sense of individuality and our longing for absorption into the universal. We've reviewed some of the various battlegrounds on which this inner war is waged, and we've spoken of the debate between the \"devil\" and the \"angel\" within. While we cling to our unique snowflake self, at some level we also long to merge into the cosmic avalanche\u2014or to melt away altogether, vaporized into what is truly real.\n\nBut these two fundamental aspects of our being\u2014the nameable \"somebody self\" and the unnamable \"nobody self\"\u2014need not be at war with each other, and we needn't feel torn between them. The inner house need not be divided, but can live in harmony.\n\nAnd to achieve this d\u00e9tente between our two selves, it's helpful to recognize that one does not exist without the other.\n\n### THE IN-BETWEEN STATE\n\nIn the Tibetan Buddhist tradition, the concept of the bardo is meant to explain where we go in between lives. In a system that presupposes rebirth, the bardo is thought of as a sort of a purgatory, betwixt and between the end of one life and the beginning of another.\n\nBut there is also a larger and more inclusive understanding of the term bardo. While living, we are in between birth and death; when we're middle-aged, we're in between youth and old age; when we're asleep, we're in between the end of last night's waking consciousness and the beginning of tomorrow morning's. And in this very moment, we're in between the past and the future.\n\nSo, from this point of view, we are always in some bardo or another. We're always \"in between.\"\n\nThe \"somebody self\" is who we are in between experiences of being nobody, and the \"nobody self\" is who we are when we are in between being somebody. That's the simplest way to answer the question \"Who da hell am I when I'm not somebody?\" You're nobody when you're in between being somebody.\n\nThe remarkable ancient Indian scripture that we'll use for the meditational exercises at the end of the book points to any number of these in-between states where we drop into our true nature of being nobody. What the Vijnana Bhairava Tantra calls \"the omnipresent state of ultimate reality\" is continuously available: it is \"on the radar even of ordinary people.\" Between the polarities and dualities\u2014between \"this\" and \"that\"\u2014is the potential for the \"highest realization\":\n\nOne should meditate on the perception of two things, and then place oneself in the middle between them. Dropping the two of them simultaneously, reality appears.\n\nOr:\n\nWhen the mind leaves one object and then is restrained from wandering to another object, being in the middle between two objects the highest realization then unfolds.\n\nAll day long, every minute, we have the opportunity to revisit and commune with our nobody self. It is who we are in between being aware of ourselves as somebody. This state is even findable in the gap between every breath we take in and let out.\n\nIt is in those in-between moments, in the gaps between being somebody self-consciously doing something, that our ever-present true nature shines through.\n\n\u2022 \u2022 \u2022\n\nThe two kinds of self, somebody and nobody, are mutually exclusive when it comes to our awareness of them. We can't be conscious of being nobody when we're thinking we're somebody, and we aren't consciously somebody when we've dropped the self-awareness and become nobody.\n\nAnd although we really are nobody all the time, we can't be nobody all the time. Our somebody and nobody selves exist, like everything else, interdependently\u2014you can't have one without the other.\n\nWe're the kind of somebody we are\u2014a changing, conceptualized self\u2014because we really are nobody. But it's also true that we can only be nobody when we stop being somebody.\n\nAnd we have to be somebody in order to stop being somebody!\n\nThe point is not to attempt to be nobody all the time. That's impossible. We'll always be somebody in between being nobody, because we're always in between. We alternate between our two selves, and each serves an essential purpose. We self-consciously plan our schedule and, if we're practicing karma yoga, unselfconsciously but mindfully carry out each task with our full attention, wholly integrated into the activity, like a child at play. We might make a decision to read a book, but, if we are self-consciously reading each word instead of getting into the flow of the story line, we're not really enjoying what we're doing.\n\nAlternating between the somebody and nobody selves is just in the nature of change, and our lives are in constant flux. Things arise, last for a while, and then end. And then there is the gap\u2014the in-between state\u2014before a new cycle begins.\n\nPeople who completely lose touch with their individual sense of self over a long period of time are, to put it bluntly, crazy. Clinical psychology calls such an unfortunate malady \"depersonalization,\" and this condition is \"associated with such unpleasant states of mind as fatigue, sleep deprivation, sensory deprivation, anxiety, depression, temporal lobe migraine, temporal lobe epilepsy, and so on.\"\n\nIt is healthy and normal to identify, at least to some degree, with the somebody self, and to rotate between it and the always present, unchanging, and eternal nobody self. As enjoyable as it is to be \"in the flow,\" if we were always in the flow there would be no one to emerge from the experience refreshed, revitalized, and energized. If we were in a state of self-forgetfulness all the time, the experience of self-loss would not result in any kind of self-transformation, for there would be no return to the self that could be transformed.\n\nNeuroscientist Susan Greenfield remarked in an interview, \"There are moments in most of our lives when we want to 'let ourselves go,' 'blow our minds.' \" But such Dionysian experiences of self-transcendence, enjoyable and rejuvenating as they are, cannot realistically be extended indefinitely, any more than it is healthy to only remain in the Apollonian state of uptight self-control:\n\nIf someone said to you, \"I want to do that all the time, I want to go to the rave every single moment I'm alive,\" on the whole, we'd feel rather sorry for someone like that, just as we'd feel sorry for someone that proudly declared they'd never let their hair down, they'd never let themselves go, they'd never had a sensational time in their whole lives.\n\nNo one really knows what happens to us after we die. Perhaps then we permanently merge into the nobody state forever and ever. But in this life\u2014and in future rebirths, if there are any in store for us\u2014we will always be somebody when we're not being nobody.\n\nSo the spiritual goal is not to somehow disappear the \"somebody self\" but rather to know it for what it is and detach from the belief that it's the only self that there is. Depictions of the enlightened state\u2014the person who is \"liberated in this very lifetime\" (jivanmukta) or one who has gone into \"nirvana with something left over\" (i.e., one who still has a body and continues to appear in this world)\u2014do not suggest that somebody who is free ceases to be somebody entirely.\n\nBut such a person is not only free from the illusions the rest of us carry around, he or she is also free from the grasping onto and full identification with those illusions. The liberated person has realized the true nature of both the individual self (transient, changing, finite, and restricted) and the universal self (eternal, unchanging, infinite, and universal).\n\nThe free man or woman lives \"like an ordinary person\" but also \"is completely different.\" And the difference lies in how they think of themselves\u2014or, we might say, how they don't think of themselves. The liberated person has emancipated herself or himself from the prison of a restricted self-conception that completely identifies with one's own individuality, distinctiveness, and separation from others\u2014and also from all the unhappiness that attends such a delimited understanding of the self.\n\n\u2022 \u2022 \u2022\n\nThe spiritual quest is ultimately not the freedom of the individual; it is the freedom from the individual. And one of the main reasons we are not free is that the \"somebody self\" resists its own dethronement as the sole monarch ruling the Kingdom of Me.\n\n\"You\" (say your name to yourself) will not somehow gain liberation as \"you.\" The \"somebody self\" will not become some supersized version of itself in nirvana or heaven; such a fantasy is just spiritual megalomania.\n\nAs the great modern Tibetan Buddhist teacher Ch\u00f6gyam Trungpa Rinpoche famously observed, enlightenment will be the ego's \"ultimate and final disappointment.\"\n\nActually we cannot attain enlightenment until we give up the notion of me personally attaining it. As long as the enlightenment drama has a central character known as me, who has certain attributes, there is no hope of attaining enlightenment, because it's nobody's project.\n\nAwakening is not somebody's project but nobody's. Salvation or liberation is freedom from both the complete association with the \"somebody self\" and the alienation from the \"nobody self.\" \"He who knows the true self is blessed,\" says one Indian text, and \"because of who he is\"\u2014because of this radical de- and re-identification\u2014\"when acting in everyday life he does not suffer like ordinary people.\" He or she has discovered and abides in the Great State of Itchlessness.\n\nSuch a person continues to \"act in everyday life\"; he or she remains \"a somebody\" in the world\u2014going to work, interacting with others, leading a life. But the liberated man or woman is a completely happy somebody, knowing he or she is just in between being nobody, and not grasping onto an illusory version of his or her identity:\n\nOne whose mind is completely at peace stays happy in his everyday life. He sleeps happily, he comes and goes happily, he speaks happily, and he eats happily.\n\n### THE TWO SELVES IN HARMONY\n\nWe are all split personalities when it comes to our identity. There are two of us within each of us\u2014the ever-changing \"somebody self\" that exists only conceptually, and the \"nobody self\" that truly exists but cannot be named.\n\nRemember the two birds sitting on the same tree we encountered back in chapter 1? They are described, you may recall, as \"inseparable friends,\" not as irreconcilable antagonists. One of them is actively engaged in the world (that's the lower, individual self) while the other only passively \"looks on\" (that would be the Higher Self). When the \"somebody self\" birdie perceives the \"nobody self\" birdie and \"realizes that all greatness is his, then his despair vanishes.\"\n\nThe personal self, being changing and therefore changeable, is improvable. But as we have seen, improving the \"somebody self\" is not accomplished through further inflating the ego in the attempt to become more of a somebody. Rather, it is by systematically deflating the self-centered self, and accessing the ever-present reality of being nobody, that we move forward in the reconceptualization of who we think we are.\n\nIt's when our two selves are reconciled and coordinated that we truly become complete. The two birds then sing in harmony; somebody and nobody peacefully coexist as inseparable friends.\n\n\u2022 \u2022 \u2022\n\nOur dual selves are spoken of in the Mahayana Buddhist tradition as two versions of our \"Buddha nature,\" that \"element\" (dhatu) or \"propensity\" (gotra) within every living being that serves as the \"womb\" for birthing an Awakened Buddha (tathagata-garbha). As it says in the Uttara Tantra,\n\nIt should be understood that the propensity comes in two types. . . . There is the propensity that is naturally present from time with no beginning, and that which has been perfected through cultivation.\n\nThe \"somebody self\" possesses the \"developable\" Buddha nature\u2014\"perfected through cultivation\"\u2014which is said to be like a seed. When watered and given sunlight\u2014when we cultivate the virtue that pivots on the development of humility, kindness, empathy, selfless action, and compassion and love for others\u2014this sort of Buddha nature is nurtured and propagated. We improve ourselves by learning to let go of our selfish needs and wants and the mental afflictions inevitably associated with them. The inner potential is activated little by little as we drop the ego's What about me? imperative and turn our attention to the What can I do for you? directive.\n\nThe second sort of Buddha nature is said to be \"innate\" and is in no need of improvement or development whatsoever. It is always and unchangingly present, eternally perfect, but also usually unrecognized. It's said to be like an undiscovered treasure trove of riches buried under a poor man's home.\n\nAlthough we may be unaware of its existence, we all have within us this precious treasure, which is our true nature, our \"nobody self.\" It is always with us, right under our house; it is always available and accessible. But we need to notice, embrace, and identify with it if we are to partake of this inner abundance.\n\n\"There is nothing whatsoever that needs to be removed from this, and nothing whatsoever that needs to be added,\" the text says. The innate Buddha nature within us\u2014our \"nobody self\"\u2014is always and already perfected. Simply by fully realizing who we truly are, we are freed from the monopolizing tyranny of who we think we are: \"It is from seeing reality that the seer of reality is really and completely liberated.\"\n\nThe integrated self is less fully identified with somebody and more with nobody. It is only our desperate clinging to the ego, and its insatiable desire to be a \"real someone,\" that keeps us from realizing our deeper identity and the balance that comes when the two selves are in harmony.\n\n### EMPTYING AND FILLING\n\nWhen we commune with the \"self with no name,\" we immediately gain what Jesus called the \"peace that surpasses understanding.\" Realizing who we are when we're not being ourselves, experiencing the great relief and itchlessness of being nobody, is thus more a matter of emptying than filling.\n\nWhen it comes to the deeper answer to the \"Who da hell am I?\" question, less is in fact more.\n\nIt is important to honor the personal self and its \"developable\" Buddha nature, and to continuously cultivate its transformation. But the less we grasp onto our particularity and individuality, the more we make ourselves available to our universal, eternal, blissful, and perfect \"nobody self.\"\n\nIn the Christian tradition, the relinquishing of the exclusive identification with the individual self is called kenosis (from the Greek word for emptiness)\u2014the \"self-emptying\" of one's own ego in order to become entirely receptive to the divine. In a passage from the New Testament, we are admonished to renounce the ego's \"selfish ambition\" and \"in humility\" lose ourselves in service to others:\n\nBe of the same mind, having the same love, being in full accord and of one mind. Do nothing from selfish ambition or conceit, but in humility regard others as better than yourselves. Let each of you look not to your own interests, but to the interests of others.\n\nThe more we are able to let go of thinking about \"me,\" the more we are able to think of ourselves as \"we.\" Self-emptying allows for the recognition not only of our true self but also of our commonality, of the bonds we share with all other somebodies. When somebody is emptied out and nobody remains, the space is created to refill and be everybody.\n\nThis passage from the Bible goes on to say that the self-emptying process also entails a kind of \"mind meld\" with Christ\u2014not with the Jesus Christ Superstar version but rather with the one who truly voided himself of all conceit and pride:\n\nLet the same mind be in you that was in Christ Jesus, who, though he was in the form of God, did not regard equality with God as something to be exploited, but emptied himself, taking the form of a slave, being born in human likeness. And being found in human form, he humbled himself . . .\n\nThe \"somebody self\" becomes more like nobody when it practices humility rather than pride, modesty rather than arrogance, connection rather than haughty (and unhappy) isolation. It is when we empty ourselves that we are filled with plentitude and realize the Great Commonality we share with all others.\n\nThe more we can put the \"somebody self\" aside, the more affinity we feel for all others and for life itself. We become more like Jesus\u2014humbled by his humanness rather than prideful about his divine origins\u2014and by doing so become more attuned to both the common humanity and universal divinity each of us shares with all others. As we are told in the Biblical passage cited above, it is through practicing \"looking not to your own interests, but to the interests of others\" that we train ourselves for increasingly melding our minds to that of the divine.\n\n\u2022 \u2022 \u2022\n\nWhen we empty ourselves completely, we automatically slip into our \"nobody self.\" As we've seen, we are nobody when we are in between being somebody. But even as a self-conscious somebody, we can practice taking on both the identitylessness and the sense of interrelationship with others that is entailed in being nobody. When a \"somebody self\" learns to be more of a nobody, they increasingly actualize their capacity to identify more with everybody.\n\nAs we have noted, selflessness and empathy lie at the very heart of what it means to create good karma rather than bad. The practice of karma yoga, you will remember, is action done without self-regard or personal reward\u2014action done for its own sake, knowing that virtue is its own reward. If our intention is motivated by selflessness and altruism, our activities will have a beneficial result on our self-image and on our outlook on the world.\n\nWe've discussed several methods for improving our self-image, all of which revolve around the premise that it is nobody that makes a better somebody possible. When we drop into our true nature and in one way or another turn off the self-centered inner narration\u2014through love and compassion for others, mindful unselfconsciousness in our actions, or virtuous action done for its own sake\u2014we experience the power and joy of being nobody.\n\nThe self-emptying project can be thought of not only as a hollowing out but also as an infusion of our true selfless nature into our \"somebody self\" identity. The latter gets itself out of the way and, in thought and action, becomes more nobody-like.\n\nThere are relatively simple ways in which we can start practicing being more of a nobody as we live in our daily lives as a somebody. On our way to final liberation, we can increasingly become more like our spiritual heroes and religious archetypes: more Christ-like, more Buddha-like, more nobody-like.\n\nInstead of reveling in and glorifying our individuality and uniqueness, we can practice living more as just a regular guy or gal, just an Ordinary Joe.\n\n### BE ANONYMOUS\u2014OR AT LEAST UNFABULOUS\n\nWe've seen that the \"nobody self\" is nameless and unnamable. By becoming more anonymous\u2014a word that derives from the Greek phrase \"no name\"\u2014we mirror and imitate our true nature.\n\nMy birth name is \"Brian Smith.\" The \"Brian\" part is the name my parents gave me, but the surname is a total invention. I might just as well be called \"Brian X\" or \"Brian Doe.\"\n\nHere's the story: My paternal grandfather (the professional wrestling fan) was left as an infant on the doorstep of some orphanage in late-nineteenth-century England. His parentage was unknown\u2014there was no note or anything pinned on the swaddling clothes. And so the staff gave him the most generic last name possible for that time and place: Smith.\n\nI know that there are some people who can trace their family lineage back to the Mayflower or whatever, but I personally am only a couple of generations removed from complete obscurity when it comes to my genetic origins. My bloodline disappears into namelessness and anonymity pretty quickly.\n\nAnd truth be told, no matter how far back your family genealogy can be traced, eventually we all discover that we end up as . . . well, no one in particular. We all, if we look into the matter, are of indeterminate origin. Despite the different names that distinguish us, at bottom we are really all just generic human beings.\n\nPracticing being more anonymous, and posing less as the amazing, special somebody we all think we are, is an acknowledgment of our basic commonality. It's not only our true nature, the \"nobody self,\" that we share with all others. Even as individual somebodies, we're all really \"just folks,\" and embracing our generic ordinariness leads to a closer affinity with our fellow human beings (themselves all \"just folks\" too).\n\nLittle acts done incognito teach us to be less and less identified with our sense of particularity, our ego, our \"somebody self.\" Acting as anonymous agents of good in the world, we train ourselves to be more of a hybrid, more of somebody who is practicing to be more nobody-like.\n\nThere are many, many ways in which we can think and act more anonymously in our lives. Here are just a few tips to get you started in your new career as Secret Agent 000:\n\n  If you live in a city that still has them, plug someone else's depleted parking meter and save them a ticket! And don't stand around waiting for the owner to come back so you can be thanked.(Putting money into someone else's parking meter is, by the way, illegal in many municipalities, so, by doing this little act of civil disobedience, you can also get in touch with your inner Che Guevara.)\n\n  Take a \"first-person-pronoun-free day\" where you avoid using the terms \"I,\" \"me,\" or \"mine\" for twenty-four hours. Trying to keep up this practice over an extended period of time will make you more aware of how often we think of (and talk about!) ourselves, and only ourselves.\n\n  Give presents to people without them knowing it was you who was the donor. You might want to stick on one of those little tags, filling out the \"To\" part but leaving the \"From\" line blank.\n\n  Do somebody else's job for them\u2014a task at work that your office mate is responsible for, or a chore at home that your partner usually takes care of\u2014and do it secretly and transparently.\n\n  Slip some money into the purse or wallet of someone that you know is having financial challenges. This reverse pick-pocketing will require the same sort of cleverness and stealth that criminals employ. And you will experience the same thrill that the successful thief enjoys, while simultaneously doing something nice for someone else!\n\n  It used to be a tradition on May Day to place a basket of food, flowers, or presents on a neighbor's doorstep, ring the doorbell, and then run away. Becoming Secret Agent 000 could singlehandedly revive this tradition, and not just on May 1.\n\n  Next time you're at a restaurant, pay for some stranger's dinner. Just randomly select someone, call the waiter or waitress over, and secretly pick up that person's tab. You can sneak a peek at the person's reaction when they are told that an anonymous benefactor has paid their bill, and surreptitiously share in the little unexpected spike of happiness you brought to someone else's life.\n\n  There's a similar practice that's currently gaining traction in some cities. Next time you go to Starbucks for your grande soy decaf nonfat sugar-free latte, lean in and quietly whisper to the barista that you will be paying for two coffees\u2014one for you and one for the next person in line. And be sure to tell the server not to mention who paid it forward.\n\n\u2022 \u2022 \u2022\n\nIf you can't be anonymous, at least work at being unfabulous. The individual self strives to be remarkable, cool, clever, important, and distinctive. Somebody who is trying to be more like nobody reverses this impulse and endeavors to be ordinary, common, simple, nondescript, and undistinguished.\n\nIn this day and age of reality television, of Facebook and Twitter self-promotion, of the endless quest to be more of a real somebody, it's really fighting the power to be content with being average and unfabulous.\n\nOne simple way to do this is to reduce one's preferences in life\u2014what one prefers to wear and to eat, which people we prefer to be around\u2014and learn to be more equanimous. Our preferences help to define us as unique individuals, and so being a little more non-preferential and impartial is another way to train somebody to be more nobody-like.\n\nI had a habit for several years of never buying new clothes. When I needed something to wear, instead of going to Macy's, I went to the Salvation Army. There's nice stuff at Sal's, especially at outlets located in affluent neighborhoods\u2014a dirty little secret for minimizing the austerity of this practice!\u2014and I saved a lot of money by shopping exclusively at such places.\n\nBut all the clothing at secondhand stores is, of course, used; it has been previously selected, bought, worn, and then discarded by someone you don't know. And there's something about wearing other people's clothes that makes an impression on one's psyche. You usually feel a little less fabulous, and a lot more like an Ordinary Joe, when you pull on a five-dollar secondhand shirt that you are aware used to belong to some stranger.\n\nLooking totally unfabulous was, of course, the original intent behind the robes worn by monks, nuns, priests, imams, and other clergy. These are uniforms, designed to make every individual look alike. Nowadays such a presentation often conveys the exact opposite impression\u2014\"Here's somebody dressed differently who must be special!\"\u2014and when I was wearing the robes it made me very uncomfortable to imagine people thinking this. The real purpose of such a uniform was to iron out particularities (and to make one's sartorial choices every morning much easier), not to confer some exceptional status.\n\nEven while I was still an ordained monk, I eventually made the decision to appear in public as an ordinary layman. Dropping the unusual veneer provided by the flowing red robes took down a barrier between me and the people around me. It was hard at first\u2014the costume does provide a kind of protective shield\u2014but the advantages of appearing \"normal\" outweighed the vulnerability that accompanied looking like an ordinary Clark Kent instead of giving the impression of being some kind of spiritual Superman.\n\nThere's a great virtue in appearing as an Ordinary Joe. Instead of setting ourselves apart by what we wear, we can send a different message when we don clothing more typical and common to whatever context we find ourselves in. For some this will mean an off-the-rack business suit rather than a tailored Brooks Brothers ensemble, while for others it will entail unbranded and inexpensive jeans and T-shirts rather than whatever new and cool garb is currently in fashion.\n\nAnother way to feel less distinctive is to minimize one's food preferences. I know there are plenty of people who really like those fungi known as mushrooms, and there are others who enjoy that fruit with the suitably unappetizing name \"eggplant.\" But I don't particularly care for either\u2014I am somebody, defined in part as a person who doesn't prefer such supposed edibles.\n\nAnd I avoid them if possible. But when someone has gone to the trouble of cooking a meal that includes such items, I eat them. It's not a big deal, but this act, in its small way, diminishes the ego's need to be a special somebody, distinguished by what one will and will not eat.\n\nThis practice may be a lot more challenging for self-defined vegans or vegetarians. But there's an ancient instruction for monks and nuns\u2014those who are professionally committed to humility and self-effacement\u2014to uncomplainingly accept and eat whatever is put before them, without making a fuss about \"being\" one thing or another when it comes to food.\n\nIt is a time-honored religious practice to be less picky and just eat what has been offered. One of my students spent several years living as a Buddhist nun in England, where they maintained this tradition. Every day, she told me, the monastics would go to the local village, begging bowls in hand, and stand and wait for edible donations. The villagers would come along and put whatever they could give into the bowls\u2014and in whatever order: carrots on top of ice cream, cheeseburgers piled onto lentils. And that was dinner; that's what the ordained would eat.\n\nOne need not go to such extremes to benefit from a practice of not being so particular about what one consumes. While there are undoubtedly many benefits to a vegetarian or vegan diet, being overly attached to what one prefers to eat strengthens rather than weakens the individual's sense of distinctiveness.\n\nBeing less preferential about what one wears and eats is just the tip of the iceberg when it comes to being unfabulous. There are countless ways in which we can train ourselves to be less demanding and more accepting, less exclusive and more inclusive, less of a special somebody and more of an Ordinary Joe.\n\nIt's like this now\u2014now there's only this one shirt that fits me on the rack; now there are mushrooms on my plate; now someone has prepared and served me a cheeseburger.\n\nAnd now I find myself with this kind of person. We all have preferences when it comes to the people we choose to be with. And we all tend to hang out with pretty much the same kinds of people\u2014people who are more or less like ourselves. Getting along with others who are not in our social clique is yet another way to be more nobody-like in our daily lives.\n\n\u2022 \u2022 \u2022\n\nIn the 1983 mockumentary Zelig, Woody Allen portrays a character who so badly wants to fit into his social surroundings that he literally takes on the physical characteristics of those around him. This \"human chameleon\" transforms into a rich patrician when around the Great Gatsby set, and then into a plain-speaking regular guy when he's with the servants. He becomes a Native American, an African American, and a Hasidic Jew when around such kinds of people.\n\nThis spoof displays, by means of an extreme caricature, the perils of conformity. But read in a different way, it also can be viewed as a comic version of the serious spiritual practice of living like an Ordinary Joe.\n\nAs we've argued in this book, the need to be unique and special is itself unexceptional and general to us all. It is not a sign of our distinctiveness to want to be distinctive. The deeper conformity we are all susceptible to is our common and quite ordinary desire to be extraordinary and set apart\u2014to be a real somebody.\n\nWhen with others, somebody who is trying to be more nobody-like tries to fit into the situation and to make others feel more at ease. Instead of clinging to our uniqueness and specialness, when we're with other people, especially those who appear different from ourselves, we remember the more fundamental ways in which we are all alike. The \"somebody self\" who is working at being more nobody-like feels more affinity to the others who come within his or her purview.\n\nWe are all human, and nothing human can be completely foreign to any of us. So when you encounter the checkout girl at the supermarket or the driver of your taxi or the fellow behind the counter at the dry cleaners, just ask about their day, tell a little joke, and treat them with respect. It doesn't take much to make another person's life a little better, but it does require acknowledging them as human beings fundamentally no different from oneself.\n\nWhen you're with people who are different from you\u2014whether they're a plumber from New York or a cowboy from Tucson\u2014take an interest in what that kind of life must be like, learn a little bit about what's entailed in doing that for a living. When you're around rich people, stop with the class struggle already and recall that they're essentially as ordinary as you are. When you're with people of different ethnic or racial backgrounds, remember that they're basically just like you\u2014burdened with the same kinds of problems, harboring the same desires for happiness, and endowed with the same fundamental true nature.\n\nIt was in part out of such considerations that, in October of 2013, I made the difficult decision to give back my monk's vows after living for eight years as an ordained monastic. While I have only admiration and respect for those who commit to this kind of life, for me personally being a monk in the Tibetan Buddhist tradition no longer seemed to accord with my developing nondenominational spiritual orientation, nor with the desideratum to try to live more as a nobody instead of a special somebody. The very terms \"monk\" and \"monastic\" are derived from the Greek word for \"alone\" (monos), and can be interpreted to refer to someone who has set themselves apart from others.\n\nAs the scripture says, \"Give up such distinctions as, 'I am so-and-so, but not such-and-such.' \" Working to be more of an Ordinary Joe in our interactions with others helps us to recognize the real bonds that we share with every other person.\n\nThis is not a matter of being inauthentic or pretending to be someone you're not\u2014you don't have to turn into Zelig, the \"human chameleon.\" But we can authentically think and act less like the special somebody we might believe we are, because we are all authentically and really nobody.\n\nAnd when we're in between being nobody, we're all authentically just \"everyday people,\" trying our best to get through life. So if you need some help as you interact as Ordinary Joe with others who seem quite different from yourself, you can hum the old Sly and the Family Stone song and remember the refrain:\n\nI'm everyday people, yeah yeah . . .\n\nOh sha sha\u2014we got to live together.\n\n### NOBODY IS EVERYBODY (AND VICE VERSA)\n\nYes (oh sha sha), we really do have to live together. None of us is an island; our human archipelago is actually one big land mass under the surface. As Zen teacher Thich Nhat Hanh has declared, the whole purpose of our lives is to overcome our sense that we are isolated, discrete individuals: \"We are here to awaken from our illusion of separateness.\"\n\nGrasping onto our individuality and uniqueness\u2014to the \"somebody self\" we've talked about so much in this book\u2014is premised upon and further propagates this \"illusion of separateness.\" Some of our strongest inborn instincts\u2014this is the \"devil\" part of us\u2014encourage the selfishness that detaches us from others. And our modern culture of narcissism and self-promotion ratifies and exacerbates our innate egoism.\n\nBut all this self-centeredness is based on illusion, not reality, and the inner \"angel\" who suspects this needs to have her voice amplified. The self we are so centered on\u2014independent, disconnected, and alone\u2014doesn't really exist at all, and the idea that we pursue our own happiness by feeding this phantom is wholly misguided.\n\nOur spiritual traditions have for millennia been telling us that our selfishness and egoism must be put aside if we are ever to find true happiness. And our scientists are now joining their voices in the chorus, pointing out that there is no findable \"pearl self\" at all; that what we call the self is just a bundle of functions wrapped together by our self-conception; and that the age-old religious virtues revolving around selflessness\u2014altruism, empathy, compassion, gratitude, and forgiveness\u2014will inevitably bring more happiness to one's life.\n\nAnd at least some of our scientists now agree with the long-standing spiritual claim that our sense of separation from others and the world around us is a misconception. \"A human being,\" observed Albert Einstein, \"is part of the whole, called by us 'Universe.' \"\n\nHe experiences himself, his thoughts and feelings as something separated from the rest\u2014a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty.\n\n\u2022 \u2022 \u2022\n\nSo we end by restating the million-dollar question, adding a million-dollar adverb:\n\nWho da hell am I . . . really?\n\nReally, beneath all our differences and distinctions, we are all equally nobody. And being really nobody is the condition of possibility for becoming a better somebody\u2014somebody who increasingly realizes that he or she is part of a much larger whole.\n\nWe'll always be somebody, so when we're in between being nobody we can live happier, more fulfilling lives by being more nobody-like, more of an Ordinary Joe and less of a special, distinctive little snowflake, set apart from others. Since we're all really nobody, everybody is really just like everybody else.\n\nRemembering that we all live in \"interbeing,\" we can think and act more in accordance with the interdependence that defines our existence in the world. Dispelling the illusion of our separateness, we can find solace in the reality of our interconnectedness, in being everybody.\n\nDetaching from the monopolizing claims of the atomistic \"somebody self,\" we can integrate more with the world around us and identify more with the fount of our very being, the ultimate reality that is our true self.\n\nThis is the path to real happiness, for happiness can only be founded in truth, not in illusion.\n\nRemember, they say nobody's perfect.\n\nSo why not be nobody?\n\nAction Plan: Secret Agent 000\n\nYour mission, should you choose to accept it, is to commit to one act of kindness for someone else every day\u2014anonymously. Spend a few moments at the beginning of the day making a plan for how you will pull this off. And keep your eye out during the course of the day to see if unexpected opportunities arise to help others incognito. Practice being Secret Agent 000 in all the little ways you can.\nKnock,\n\nAnd He'll open the door.\n\nVanish,\n\nAnd He'll make you shine like the sun.\n\nFall,\n\nAnd He'll raise you to the heavens.\n\nBecome nothing,\n\nAnd He'll turn you into everything.\n\n\u2014\u2014Rumi\n\n## Acknowledgments\n\nI am inexpressibly grateful to the phenomenal mother-daughter team Wendy and Cindy Lee for the time they took to read the earliest drafts of each chapter and for their invaluable advice and perspectives.\n\nDavid B. Fishman painstakingly went through the manuscript word by word and vastly improved the quality of my prose. It is a great mitzvah to have a full-fledged genius take the time to carefully review what an ordinary man has written.\n\nI have also been blessed to have superb editors at Beyond Words. Many thanks to Emily Han and Henry Covey for their help in making a much better book out of the original manuscript, as well as to my literary agent, Joelle Delbourgo, for her unflagging advocacy and support.\n\nI am very grateful to those who assisted me in my research\u2014Chantal Carleton, June Maker, Darin McFadyn, Claire Thompson, the Rev. Anne Deneen, Karl Whiting, and my daughter, Sophia Fleming-Benite\u2014and to the many volunteers who have transcribed oral teachings under the efficient management of Catherine Eaton.\n\nTo all whose generosity and hospitality make my life on the road so trouble-free, I cannot begin to thank you enough. And to my benefactors and patrons, I remain in your debt. I hope this book will be of some benefit to others and thus justify, at least to some extent, your support.\n\nThere is no way to repay what I owe to my teachers\u2014my spiritual mentors, academic guides, close friends, fellow travelers on the path, and those who pose as my students.\n\nFinally, although it may sound stupid, I'm really grateful to my computer and all it makes possible. I simply could not have written this book without the magic that has become available to us. We live in amazing times.\n\n## Appendix:  \nDropping into Your True Nature\n\nOur true nature is always with us. It has never been born and so can never die; it is eternally unchanging and ever-present; it is the \"nobody self\" that lies behind and beneath all iterations of every \"somebody self.\"\n\nAnd so it is always accessible. It is perpetually there whenever we quiet the ego's chattering, mute the ongoing inner narrative, and relax into the silence, spaciousness, and serenity of being nobody.\n\nIn what follows below, you'll find a set of simple meditative exercises, correlating to each of the seven chapters in this book, for dropping into that supreme state of bliss anytime you wish. They can be used as full-fledged meditations or merely as ways to catch a few moments of peace at any time during your day.\n\nThe exercises are drawn from 112 such meditations, or dharanas, that comprise the bulk of an ancient Sanskrit text from the Hindu tradition of northern India called the Vijnana Bhairava Tantra (VBT).I The VBT purports to be a conversation between two deities, Shiva (aka Bhairava, representing ultimate reality) and his beloved and inseparable partner Shakti (symbolizing the world of appearances and form). When Shakti asks Shiva to teach her how to discover the highest nature of things, the latter replies, \"Shakti is the very face of Shiva.\" That is to say, the deepest aspect of reality is found nowhere other than within the day-to-day world we live in.\n\nThe extraordinary is discoverable within the ordinary; the ultimate within the relative; the transcendent within the immanent. This same truth is summarized within the classical Buddhist scripture the Heart Sutra: \"Emptiness is not different from that which takes form, and that which takes form is not different from emptiness.\" The void and the plentitude are two sides of the same coin.\n\nIn the VBT, Shiva proceeds to teach Shakti an array of straightforward techniques for recognizing her true nature in the midst of everyday life. The methods are simple\u2014deceptively so. They aren't hard to do, but they do require paying close attention to what's happening to your consciousness when you're engaged in them. They are, after all, meditations.\n\nI hope you'll give these exercises a try. If you do, you'll find them to be relatively easy ways to get a little taste of what it feels like to be nobody. You'll be able to drop into your true nature whenever you want.\n\n### MEDITATION FOR CHAPTER 1\n\nLook at the clear blue sky with an unwavering gaze, keeping the body still. Immediately you will reach your true essence. . . . When one places the mind on outer space\u2014which is unchanging, without support, empty, all-pervasive, and free from limitation\u2014one enters the realm of spacelessness.II\n\nRemember how nice it was, when you were a kid, to just lie down on the grass and look up at the sky? Here's a quick, easy, and enjoyable way to break out of your limitations and get out of your own head, anytime during the day or night. Just take a moment to stop and go outside (or at least look through the window) and lose yourself in the unlimited expanse of the atmosphere or in the inconceivable vastness of outer space.\n\nThe mind takes the form of what it perceives. If what you perceive is the limitless, well, you've just dropped into your true nature.\n\n### MEDITATION FOR CHAPTER 2\n\nBecause of placing the mind at the meeting place of the two breaths, either inside (i.e., where the inhalation ends and the exhalation begins) or at the outer limit (i.e., where the exhalation ends and the inhalation begins), the yogi attains equanimity and becomes a proper vessel for knowledge.III\n\nEver heard the expression \"Just take a deep breath?\" We're breathing all day, every day, so here's a way to gain a little peace whenever you need it. Take a deep breath, but do so mindfully. Notice that at the end of each inhalation and exhalation there is a gap, a pause, before the next exhalation or inhalation, respectively. Gently, without holding the breath or interrupting the natural respiratory flow, place your mind fully on that pause and rest in the respite between breathing in or out.\n\nFall into the gap! And when done without self-consciousness of being in the gap, you've just found your true nature. There's no need to go to church or temple to find the sacred; it's there with every breath we take.\n\n### MEDITATION FOR CHAPTER 3\n\nOne who meditates nonconceptually on the emptiness of the body, even for just a moment, loses all conceptions and comes to possess the self-nature of what is beyond conceptual thought. . . . One should concentrate on just the skin encasing the body like a wall [while thinking], \"There is nothing inside.\" Meditating on that, one becomes joined with the imponderable. . . . [Then] meditate on the self taking the form of empty space, stretching out endlessly in all directions . . . [and] being freed from any resting place, then one sees his own true nature.IV\n\nWe're all pretty attached to the idea that we are our physical bodies, and so this brief meditation helps us to break out of our identification with our corporality at the same time it puts the mind on the infinite.\n\nFirst, imagine that inside the body there is nothing but empty space, like clear blue sky. Mentally empty out all the guts and bones until it is completely void, right up to the ends of the fingers and toes, encased only by the thinnest layer of skin.\n\nThen erase even the outline of the body and open up into the infinite empty space outside. Nothing to the left as far as you can imagine, or to the right, or up, or down, or in front, or in back.\n\nRelax and reside in complete spaciousness, and enjoy your true nature.\n\n### MEDITATION FOR CHAPTER 4\n\nWhen one experiences desire, anger, greed, delusion, intoxication, or jealousy, one should place the mind on it unwaveringly until only the bare essence of it remains.V\n\nWhen you're on the verge of losing the Big Smackdown with an incipient mental affliction, stop and do this meditation. Close your eyes and go deep within. Locate the feeling you're struggling with and then analyze it. Is it really one, complete, seamless, full-blown \"feeling\"?\n\nOr is it, upon investigation, separable into moments? Before it's designated \"anger\" or \"jealousy,\" isn't it just a series of momentary instances of consciousness over which the mind superimposes a label?\n\nIf you can get this far, then have a look at what makes up each of these little moments. Doesn't each instant of what we call \"anger\" or \"jealousy\" have its own beginning, middle, and end? And what about the beginning of each momentary fragment of what we name \"a feeling?\" Mustn't it also have its own beginning, middle, and end?\n\nAnd down you go. There are no partless parts, no moments of the so-called mental affliction that aren't further divisible. When you get tired of analyzing your feeling into parts of the parts of the parts of the parts, ad infinitum, you'll get to its \"bare essence,\" as the text says\u2014its emptiness, its true nature\u2014which is the same as yours!\n\n### MEDITATION FOR CHAPTER 5\n\nWhen one experiences great bliss, or when one sees a long-lost relative, one should meditate on the arising of the bliss and thoroughly dissolve the mind in it. . . . One should let the mind rest on things remembered or places one has seen. One's body will lose its support (i.e., one will forget one is embodied) and the Lord will arise.VI\n\nWe all spend at least some time every day daydreaming, so this little meditation should be easy. Take a moment to immerse yourself in a pleasant memory. Lose yourself completely in the reverie; stop thinking you're stuck inside your physical body. Fully relive being in some beautiful place, or the wonderful times you've had with a loved one, or any other memory of when you were perfectly happy. Focus on the feeling of bliss that arises, and completely merge your consciousness with it.\n\nThis simple exercise also has the potential to evoke a sense of gratitude in us for the good times we've had and the great people we've known in our lives. And gratitude, as it happens, is another very potent antidote and cure for depression and low self-esteem.\n\n### MEDITATION FOR CHAPTER 6\n\nOne should meditate on the pleasure that arises from eating and drinking\u2014the bliss of that tasty flavor\u2014and then the state of plenitude and great bliss arise. Through the unequalled joy of becoming absorbed completely in the sound of beautiful music and such, the yogi's mind is elevated and becomes one with that.VII\n\nOur true nature is accessible in even the most commonplace of activities, like eating and drinking. But we need that mindful unselfconsciousness in order to be fully absorbed in what we're doing when we taste the food or beverage. Try it. Use your daily meals and morning coffee or tea as a chance to encounter the \"nobody self.\"\n\nAnd the text gives us another method for relaxing into our true nature. Turn on one of your favorite pieces of instrumental music (no distracting lyrics). And then really get into it! Don't focus on individual notes or even the musical phrases, but lose yourself in the melody as a whole. When you're not there listening\u2014that is, when you've been wholly engrossed in the music\u2014there it is again! You've dropped back into your true nature.\n\n### MEDITATION FOR CHAPTER 7\n\nOne should realize that the consciousness in others' bodies is the same as in one's own. Having abandoned concern for one's own body, one soon becomes all-pervasive.VIII\n\nWe believe that we are really separate from others, not only because we have separate physical bodies but also because we have our own peculiar thoughts (some more peculiar than others!). And other beings have their own separate bodies and, we presume, their own particular thoughts too.\n\nThis meditation requires us to concentrate neither on the thinker inside the body nor on the particular thoughts the thinker thinks, but rather on the field of consciousness itself. What is the sphere or arena in which all thinking, in any body, occurs? The focus here is on what makes awareness of anything possible; it is on pure consciousness, not self-consciousness or any other consciousness of something.\n\nThis ability to be conscious\u2014regardless of what specific thoughts are being thought by which individual thinker\u2014is exactly the same in all living beings. Focus on that and the mind becomes \"all-pervasive,\" and we are drawn into the universal true nature we all share.\n\n#### Notes:\n\nI. For those interested in reading the full text, my complete translation is online at <http:\/\/lamamarut.org\/wp-content\/uploads\/2012\/01\/VijnaBhairavaTantraHandout.pdf>.\n\nII. VBT, verses 84 (with minor changes from the original) and 120.\n\nIII. VBT, verse 64.\n\nIV. VBT, verses 23, 48, and 92.\n\nV. VBT, verse 101.\n\nVI. VBT, verses 71 and 119.\n\nVII. VBT, verses 72 and 73.\n\nVIII. VBT, verse 93.\n\nCINDY LEE\n\nLama Marut (aka Brian K. Smith) holds a PhD in comparative religion and taught for more than two decades in the academic world, first at Columbia University and later at the University of California. He lived as a Buddhist monk for eight years and has served for the past fifteen years as a spiritual teacher to students around the world. Lama Marut is currently the spiritual director of eight Middle Way Centers located in North America, Australia, and Singapore.\n\nMEET THE AUTHORS, WATCH VIDEOS AND MORE AT\n\nSimonandSchuster.com\n\nauthors.simonandschuster.com\/Lama-Marut\n\n  BeyondWordsPublishing  \n  BeyondWordsPub\nWe hope you enjoyed reading this Atria Books eBook.\n\n* * *\n\nJoin our mailing list and get updates on new releases, deals, bonus content and other great books from Atria Books and Simon & Schuster.\n\nCLICK HERE TO SIGN UP\n\nor visit us online to sign up at  \neBookNews.SimonandSchuster.com\n\n## Endnotes\n\nPreface\n\n. Pew Research Center's Religion and Public Life Project, \"Religious Landscape Survey, Report 1: Religious Affiliation,\" <http:\/\/religions.pewforum.org\/reports>.\n\n. Jason Palmer, \"Religion May Become Extinct in Nine Nations, Study Says,\" BBC News, March 22, 2011, <http:\/\/www.bbc.co.uk\/news\/science-environment-12811197>.\n\n. John McManus, \"Two-Thirds of Britons Not Religious, Suggests Survey,\" BBC News, March 20, 2011, <http:\/\/www.bbc.co.uk\/news\/uk-12799801>.\n\n. Dan Merica, \"Survey: One in Five Americans Has No Religion,\" CNN Belief Blog, October 9, 2012, <http:\/\/religion.blogs.cnn.com\/2012\/10\/09\/survey-one-in-five-americans-is-religiously-unaffiliated\/?hpt=hp_c2>.\n\n. Ibid.\n\n. Kathryn Blaze Carlson, \"Organized Religion on the Decline? Growing Number of Canadians 'Spiritual but Not Religious, ' \" National Post, December 21, 2012, <http:\/\/life.nationalpost.com\/2012\/12\/21\/organized-religion-on-the-decline-growing-number-of-canadians-spiritual-but-not-religious\/>.\n\n. Dominique Mosbergen, \"Dalai Lama Tells His Facebook Friends That 'Religion Is No Longer Adequate,' \" Huffington Post Religion, September 13, 2012, <http:\/\/www.huffingtonpost.com\/2012\/09\/13\/dalai-lama-facebook-religion-is-no-longer-adequate-science_n_1880805.html>.\n\n. His Holiness the Dalai Lama, Beyond Religion: Ethics for a Whole World (Toronto: Signal Books, 2011), xii, xiv.\n\n. Cited in Acharya Peter Wilberg, Tantric Wisdom for Today's World: The New Yoga of Awareness (CreateSpace Independent Publishing Platform, 2009), 112.\n\n. Galatians 3:28. All Biblical citations in this book are from the New Revised Standard Version, found online at the Oremus Bible Browser, <http:\/\/bible.oremus.org>.\n\nIntroduction\n\n. Tom Wolfe, \"The 'Me' Decade and the Third Great Awakening,\" New York magazine, August 23, 1976, <http:\/\/nymag.com\/news\/features\/45938\/>.\n\n. Christopher Lasch, The Culture of Narcissism: American Life in an Age of Diminishing Expectations (New York: W. W. Norton, 1979). Some of Lasch's observations were foreshadowed not only by Tom Wolfe but also in Peter Marin's \"The New Narcissism,\" Harper's, October 1975. The \"world view emerging among us,\" wrote Marin, centers \"solely on the self\" and has \"individual survival as its sole good.\"\n\n. Lasch, ibid., 34.\n\n. Ibid., 50. Narcissism is elsewhere described as the \"distinctive personality type suited to the requirements of [our] culture,\" 238.\n\n. The continuing relevance of Lasch's portrait of our society is readily apparent. \"The personality of his time, it seems, is even more the personality of ours,\" writes Lee Siegel in his New York Times essay, \"The Book of Self-Love,\" February 5, 2010, http:\/\/www.nytimes.com\/2010\/02\/07\/books\/review\/Siegel-t.html?pagewanted=all&_r=0.\n\n. Justin Bieber, of course, became a superstar on the basis of a YouTube video posted by his mom, and later paid it forward by promoting on YouTube what would become, thanks to Bieber's home movie, an international hit song by Carly Rae Jepsen, \"Call Me Maybe.\" A YouTube-engendered star gives birth, via YouTube, to another instant celebrity.\n\n. There were 3.14 billion email accounts worldwide in 2011, according to Royal Pingdom, <http:\/\/royal.pingdom.com\/2012\/01\/17\/internet-2011-in-numbers\/>. An estimated 6 billion mobile phone subscriptions, from which 200,000 text messages are sent every second, according to World Mobile Media, <http:\/\/worldmobilemedia.com\/sponsor\/>. Twitter reaches half a billion accounts in 2012, according to a Semiocast study, <http:\/\/semiocast.com\/en\/publications\/2012_7_30_Twitter_reaches_half_a_billion_accounts_140m_in_the_US>.\n\n. Emil Protalinski, \"Facebook Passes 1.11 Billion Monthly Active Users,\" The Next Web, May 1, 2013, <http:\/\/thenextweb.com\/facebook\/2013\/05\/01\/facebook-passes-1-11-billion-monthly-active-users-751-million-mobile-users-and-665-million-daily-users\/>.\n\n. In fact, the addiction to Facebook seems to be having the opposite effect. Check out Stephen Marche, \"Is Facebook Making Us Lonely?\" The Atlantic, May 2012, <http:\/\/www.theatlantic.com\/magazine\/archive\/2012\/05\/is-facebook-making-us-lonely\/308930\/>. Marche not only links the addiction to Facebook to an increase in feelings of loneliness among some of its users but also cites research that has found \"a significant correlation between Facebook use and narcissism.\" \"In fact, it could be argued that Facebook specifically gratifies the narcissistic individual's need to engage in self-promoting and superficial behavior.\" Cf. Geoffrey Mohan's \"Facebook Is a Bummer, Study Says,\" Los Angeles Times, August 14, 2013, <http:\/\/articles.latimes.com\/2013\/aug\/14\/science\/la-sci-sn-facebook-bummer-20130814>.\n\n. C. S. Lewis, Mere Christianity (New York: HarperSanFrancisco, 1952), 6. See also Timothy Keller's observation in The Freedom of Self-Forgetfulness: The Path to True Christian Joy (Chorley, England: 10Publishing, 2012): \"Up until the twentieth century, traditional cultures (and this is still true of most cultures in the world) always believed that too high a view of yourself was the root cause of all the evil in the world. . . . Traditionally, that was the reason given for why people misbehave. But, in our modern western culture, we have developed an utterly opposite cultural consensus. Our belief today\u2014and it is deeply rooted in everything\u2014is that people misbehave for lack of self-esteem and because they have too low a view of themselves.\"\n\n. Patrice Lescoe, \"How Much Have Depression Rates Increased?\" eHow, <http:\/\/www.ehow.com\/way_5627919_much-depression-rates-increased_.html#ixzz2Le3SK2UA>.\n\n. Maia Szalavitz, \"What Does a 400% Increase in Antidepressant Use Really Mean?\" Time, October 20, 2011, <http:\/\/healthland.time.com\/2011\/10\/20\/what-does-a-400-increase-in-antidepressant-prescribing-really-mean\/#ixx2LS6bouMr>.\n\n. See Mental Health: A Call for Action by World Health Ministers (Geneva: World Health Organization, 2001), <http:\/\/www.who.int\/mental_health\/advocacy\/en\/Call_for_Action_MoH_Intro.pdf>.\n\n. This according to an article entitled \"In Defense of Self-Esteem,\" written by Senator John Vasconcellos, Robert Reasoner, Michele Borba, Len Duhl, and Jack Canfield: <http:\/\/www.self-esteem-nase.org\/amember\/newsarticles\/InDefenseofSelf-Esteem.pdf>. The article was published in response to a critique of the self-esteem movement written by Lauren Slater, \"The Trouble with Self-Esteem,\" New York Times Magazine, February 3, 2002, <http:\/\/www.nytimes.com\/2002\/02\/03\/magazine\/03ESTEEM.html>? . . .all.\n\n. Lewis, Mere Christianity, 197.\n\nChapter 1\n\n. Cited in John Broomfield, Other Ways of Knowing: Recharting Our Future with Ageless Wisdom (Rochester, VT: Inner Traditions, 1997), 73.\n\n. Alan Watts, The Book: On the Taboo against Knowing Who You Are (New York: Vintage Books, 1989), 55. For a more weighty enunciation of the same problem, here's eighteenth-century philosopher David Hume's frustrated cri de coeur: \"For my part, when I enter most intimately into what I call myself, I always stumble on some particular perception or other, of heat or cold, light or shade, love or hatred, pain or pleasure, colour or sound, etc. I never catch myself, distinct from such perceptions.\" David Hume, Treatise of Human Nature, ed. by L. A. Selby-Bigge (New York: Oxford University Press, 1978), book 1, part 4, section 6.\n\n. William Shakespeare, As You Like It, act 2, scene 7.\n\n. Jane Wagner and Lily Tomlin, The Search for Signs of Intelligent Life in the Universe.\n\n. Miles Orvell, The Real Thing: Imitation and Authenticity in American Culture, 1880\u20131940 (Chapel Hill: University of North Carolina Press, 1989), xxiii.\n\n. Fred Rogers, \"You Are Special,\" 1967. The complete lyrics to the song can be found online at <http:\/\/pbskids.org\/rogers\/songLyricsYouAreSpecial.html>.\n\n. For a rendition of the speech the Reverend Jackson did with a multicultural audience of small children on the television show Sesame Street, see <http:\/\/www.youtube.com\/watch?v=iTB1h18bHlY>.\n\n. The Bhagavad Gita 6.5. All translations from Sanskrit and Pali texts cited in this book are my own unless otherwise noted.\n\n. Ashtavakra Gita 8.4.\n\n. Guide to the Bodhisattva's Way of Life 8.134\u2013135.\n\n. Quoted in John Michael Talbot and Steve Rabey, The Lessons of Saint Francis: How to Bring Simplicity and Spirituality into Your Daily Life (New York: Plume, 1998), 49.\n\n. Quoted in Robert Wingate, Pocket Wisdom: Inspirational Quotations from East and West for Daily Living (CreateSpace Independent Publishing Platform, 2011), 65.\n\n. Thomas Merton, New Seeds of Contemplation (New York: New Directions, 1961), 8.\n\n. Quoted in Heinrich Robert Zimmer, Philosophies of India (Princeton, NJ: Princeton University Press, 1969), 462.\n\n. Quoted in Kathlin Austin, Wise People Quotes (CreateSpace Independent Publishing Platform, 2013), 15.\n\n. Lynn Hirschberg, \"The Misfit,\" Vanity Fair, April 1991. Reprinted in All about Madonna, <http:\/\/allaboutmadonna.com\/madonna-interviews-articles\/vanity-fair-april-1991>.\n\n. For one indication of the negative effects of the cultural emphasis on being \"special,\" see \"Why Generation Y Yuppies Are Unhappy,\" Huffington Post, September 15, 2013, <http:\/\/www.huffingtonpost.com\/wait-but-why\/generation-y-unhappy_b_3930620.html>.\n\n. Dalai Lama, Beyond Religion, 28, 29.\n\n. Mihaly Csikszentmihalyi, Flow: The Psychology of Optimal Experience (New York: Harper & Row, 1990), 1.\n\n. Qur'an 2:213. From the online translation found at <http:\/\/quod.lib.umich.edu\/k\/koran\/>.\n\n. See Guide to the Bodhisattva's Way of Life 7.2, where \"depression\" (vishada) and \"low self-esteem\" (atmavamanya) are listed among the obstacles to the cultivation of \"joyful effort,\" the enthusiastic energy needed to overcome unhappiness and suffering.\n\n. Guide to the Bodhisattva's Way of Life 7.17\u201318.\n\n. Katha Upanishad 1.2.18.\n\n. Ashtavakra Gita 18.9.\n\n. Shvetashvatara Upanishad 4.6\u20137.\n\nChapter 2\n\n. Lewis, Mere Christianity, 122.\n\n. Johnny Cash, \"No Earthly Good,\" The Rambler (Columbia Records, 1977). The complete lyrics can be found at www.lyricsondemand.com\/j\/johnnycashlyrics\/noearthlygoodlyrics.html.\n\n. William Paul Young, The Shack (Los Angeles: Windblown Media, reissue edition, 2011), 159.\n\n. Eckhart Tolle, A New Earth: Awakening to Your Life's Purpose (New York: Penguin Books, 2005), 67.\n\n. Quoted in Lama Surya Das, The Big Questions: How to Find Your Own Answers to Life's Essential Mysteries (Emmaus, PA: Rodale Books, 2007), 215.\n\n. Matthew 7:2\u20133.\n\n. Matthew 7:4\u20135.\n\n. Lewis, Mere Christianity, 121\u201322.\n\n. Professor Roy Baumeister, interview by Neal Conan, Talk of the Nation, National Public Radio, February 4, 2002, <http:\/\/donpugh.dyndns.org\/Psych%20Interests\/Self-esteem\/Questioning%20the%20conventional%20wisdom%20of%20self-esteem.htm>. Baumeister also makes reference to a study that found that 90 percent of us think we're above average drivers. Another research project discovered that none of the high school students surveyed thought they were below average in the ability to get along with others. Like Garrison Keillor's fabled \"Lake Wobegon,\" where \"all the women are strong, all the men are good looking, and all the children are above average,\" we often seem reluctant to say we're just average, even when we are. See <http:\/\/prairiehome.publicradio.org\/about\/podcast\/>.\n\n. Guide to the Bodhisattva's Way of Life 7.57\u201358.\n\n. Cf. ibid., 8.127: \"Because of my wish to be elevated in importance, I will find myself in unpleasant realms, ugly, and stupid.\"\n\n. Jack D. Maser, \"About Anxiety and Depression,\" Freedom from Fear, accessed November 29, 2013, <http:\/\/www.freedomfromfear.org\/AboutAnxietyandDepression.en.html>.\n\n. Lewis, Mere Christianity, 121.\n\n. Tolle, A New Earth, 44.\n\n. Ibid., 51.\n\nChapter 3\n\n. Anup Shaw, \"Poverty Facts and Stats,\" Global Issues, January 7, 2013, <http:\/\/www.globalissues.org\/article\/26\/poverty-facts-and-stats>.\n\n. Yoga Sutra 2.4; 2.13.\n\n. Yoga Sutra 2.5.\n\n. Maha Satipatthana Suttanta, verse 5. From Dialogues of the Buddha, trans. T. W. Rhys Davids and C. A. F. Rhys Davids (1910; repr., Delhi: Motilal Banarsidass, 2000), and cited in Edwin F. Bryant's The Yoga Sutras of Patanjali (New York: North Point Press, 2009), 180.\n\n. Jone Johnson Lewis, \"Gloria Steinem Quotes,\" About.com, \"Women's History,\" <http:\/\/womenshistory.about.com\/cs\/quotes\/a\/qu_g_steinem.htm>.\n\n. Ashtavakra Gita 1.11 (emphasis added).\n\nChapter 4\n\n. Julian Baggini, The Ego Trick: What Does It Mean to You? (London: Granta Books, 2011), 40.\n\n. Bhagavad Gita 2.40.\n\n. Yoga Sutra 2.4.\n\n. Matthew 7:16\u201318.\n\n. The Tolstoy quote is cited in a recent edition of Ralph Waldo Emerson's Self Reliance (The Domino Project, 2011), 50.\n\n. Guide to the Bodhisattva's Way of Life 5.14 (emphasis added).\n\n. Cited in Csikszentmihalyi, Flow, 121. Modern films like Memento and Total Recall (for the latter, see chapter 7) turn on the question of what becomes of self-identity when memory is erased.\n\n. Csikszentmihalyi, Flow, 133.\n\n. Guide to the Bodhisattva's Way of Life 4.37\u201338.\n\n. Guide to the Bodhisattva's Way of Life 4.44.\n\n. Guide to the Bodhisattva's Way of Life 4.29, 43.\n\n. See also the Guide to the Bodhisattva's Way of Life 6.41, where Shantideva says that it is better to get angry at anger itself than at a person who provokes anger in you.\n\n. Guide to the Bodhisattva's Way of Life 7.55\u201356: \"Everything should be conquered by me; I should be defeated by nothing! I should carry myself with pride, for I am the child of the Conquering Lions. Those pitiable beings who are defeated by pride are not those who possess pride. Those possessed of pride never become slaves of the enemy which is pride; others have turned into slaves.\" Compare this to French author Georges Bernanos's dictum: \"It's a fine thing to rise above pride, but you must have pride to do so.\" The Diary of a Country Priest: A Novel (Cambridge, MA: Da Capo Press, 2002), 224.\n\n. Quoted in Daniel Akst, We Have Met the Enemy: Self-Control in an Age of Excess (New York: Penguin Press, 2011), 2.\n\n. Guide to the Bodhisattva's Way of Life 7.72.\n\n. Csikszentmihalyi, Flow, 9.\n\n. Josie Billington, Eliot's Middlemarch, Reader's Guide (New York: Continuum, 2008), 89.\n\nChapter 5\n\n. Quoted in John Cook, comp., and Steve Deger and Leslie Ann Gibson, eds., The Book of Positive Quotations (Minneapolis: Fairview Press, 2007), 27.\n\n. Thich Nhat Hanh, Interbeing: Fourteen Guidelines for Engaged Buddhism, ed. Fred Eppsteiner, 3rd ed. (Berkeley, CA: Parallax Press, 1988).\n\n. Desmond Tutu, No Future without Forgiveness (Colorado Springs, CO: Image, 2000), 31.\n\n. Ursula K. Le Guin, The Left Hand of Darkness (New York: Ace Trade, 2000), 151.\n\n. Dean Martin, \"You're Nobody 'til Somebody Loves You,\" The Door Is Still Open to My Heart (Capitol Records, 1960). The complete lyrics can be found at www.metrolyrics.com\/youre-nobody-till-somebody-loves-you-lyrics-dean-martin.html.\n\n. Ibid.\n\n. Bhagwan Shree Rajneesh, Tantra: The Supreme Understanding (Poona, India: Rajneesh Foundation, 1975), 17.\n\n. Quoted in Alain de Botton, The Consolations of Philosophy (New York: Vintage, 2001), 146.\n\n. Guide to the Bodhisattva's Way of Life 7.31.\n\n. Bhagavad Gita 18.64\u201365.\n\n. Bhagavad Gita 15.15.\n\nChapter 6\n\n. Csikszentmihalyi, Flow, 4.\n\n. Ibid., 71.\n\n. Jiddu Krishnamurti, Think on These Things (Ojai, CA: Krishnamurti Foundation of America, 1964), 65.\n\n. Abraham Maslow, Religions, Values, and Peak-Experiences (New York: Penguin, 1970), 62.\n\n. John Stuart Mill, Autobiography, in Harvard Classics, vol. 25, ed. Charles W. Eliot (New York: P. F. Collier & Son, 1909), 94. Or as Csikszentmihalyi puts it, \"It is by being fully involved with every detail of our lives, whether good or bad, that we find happiness, not by trying to look for it directly\" (Flow, 2).\n\n. Tyler Kingkade, \"Millennials Are More Stressed Out than Older Generations,\" Huffington Post, February 8, 2013, <http:\/\/www.huffingtonpost.com\/2013\/02\/08\/millennials-stress_n_2646947.html>.\n\n. Ed Smith, \"What Some People Call Idleness Is Sometimes the Best Investment,\" New Statesman, July 19, 2012, <http:\/\/www.newstatesman.com\/business\/business\/2012\/07\/what-some-people-call-idleness-often-best-investment>.\n\n. For one analysis of how we are keeping ourselves constantly available for work even when we're supposedly on vacation, see Bob Sullivan's \"How the Smartphone Killed the Three-Day Weekend,\" CNBC, May 24, 2013, <http:\/\/www.cnbc.com\/id\/100765600>.\n\n. Rajneesh, Tantra, 73.\n\n. Ashtavakra Gita 18.57.\n\n. Matthew 6:25\u201334.\n\n. Quoted in Joe Tichio, Greatest Inspirational Quotes: 365 Days to More Happiness, Success, and Motivation (CreateSpace Independent Publishing Platform, 2013), 46.\n\n. Bhagavad Gita 6.1.\n\n. Bhagavad Gita 6.2.\n\n. Quoted in Suhail Murtaza, Reflections: A Collection of Essays on Life, Happiness, Roots, and Responsibility (New York: Perseus Press, 2007), 79.\n\n. Johan Huizinga, Homo Ludens: A Study of the Play-Element in Culture (1938; repr., London: Routledge, 2008), 3.\n\n. Ibid., 9.\n\n. 18 William Sax, ed., The Gods at Play: Lila in South Asia (New York: Oxford University Press, 1995), 4.\n\n. Bhagavad Gita 3.22, 25.\n\n. Quoted in Packers: Green, Gold and Glory (New York: Sports Illustrated, 2013), 53.\n\n. Lao-Tzu, Tao Te Ching, trans. Steven Mitchell (New York: Harper Perennial, 2009), chapter 68, <http:\/\/acc6.its.brooklyn.cuny.edu\/~phalsall\/texts\/taote-v3.html#75>.\n\n. Matthew 18:1\u20134.\n\n. Ashtavakra Gita 18.49.\n\n. Ibid., 18.64.\n\n. Quoted in Wayne W. Dyer, Wisdom of the Ages: 60 Days to Enlightenment (1998; repr., New York: William Morrow, 2002), 29.\n\n. Norvin Hein, \"Lila,\" in The Gods at Play: Lila in South Asia, ed. William Sax (New York: Oxford University Press, 1995), 15.\n\n. Quoted in Neal Ranzoni, The Book on \"Art Quotes\" (CreateSpace Independent Publishing Platform, 2012), 45.\n\n. Quoted in Cay Lang, Taking the Leap: Building a Career as a Visual Artist, 2nd ed. (San Francisco: Chronicle Books, 2006), x.\n\n. Quoted in Ellen J. Langer, Mindfulness (1989; repr., Cambridge, MA: Da Capo Press, 1990), 117.\n\n. Cited in Csikszentmihalyi, Flow, 59.\n\n. This quote, which circulates around the internet, is attributed to one Hans Bos, who apparently lives in Terre Haute, Indiana, and is neither a professional dancer nor writer. See <http:\/\/www.bdancer.com\/HansBos.html>.\n\n. Quoted in Joseph Campbell, The Inner Reaches of Outer Space: Metaphor as Myth and as Religion, 2nd ed. (Novato, CA: New World Library, 2002), 92.\n\n. Bhagavad Gita 5.8.\n\n. Quoted in Meredith Gould, Deliberate Acts of Kindness: Service as a Spiritual Practice (Colorado Springs, CO: Image, 2002), 70.\n\n. Bhagavad Gita 4.20.\n\nChapter 7\n\n. Baggini, The Ego Trick, 7. A little later in his book, Baggini says, \"The most important finding, which seems to be universally accepted by all researchers into the self and the brain, is that brain research has given up on the search for the pearl of the self\" (28).\n\n. Ibid., 69.\n\n. Dhammapada 3.42\u201343. The translation is Thomas Byrom's The Dhammapada: The Sayings of the Buddha (New York: Random House, 2010).\n\n. Quoted in James R. Miller, Voices from Earth: A Book of Gentle Wisdom (Victoria, BC: Trafford Publishing, 2006), 22.\n\n. Ashtavakra Gita 18.35.\n\n. Katha Upanishad 1.2.18.\n\n. Tao Te Ching, chapter 1, trans. Mitchell.\n\n. Vijnana Bhairava Tantra, verses 14\u201315.\n\n. Mandukya Upanishad 7.\n\n. Uttara Tantra 1.79\u201380.\n\n. Lawrence Kushner, The River of Light: Jewish Mystical Awareness (1981; repr., Woodstock, VT: Jewish Lights Publishing, 1991), 122.\n\n. For a comprehensive survey of ancient and modern \"apophatic discourses\" in the West, see William Franke, ed., On What Cannot Be Said: Apophatic Discourses in Philosophy, Religion, Literature, and the Arts (Notre Dame, IN: University of Notre Dame Press, 2007).\n\n. Rajneesh, Tantra, 12.\n\n. Ibid, 5.\n\n. Vijnana Bhairava Tantra, verse 124.\n\n. Ibid., verse 61.\n\n. Ibid., verse 62.\n\n. Roy J. Matthew, \"Psychoactive Agents and the Self,\" in The Lost Self: Pathologies of Brain and Identity, eds. Todd E. Feinberg and Julian Paul Keenan (Oxford: Oxford University Press, 2005).\n\n. Quoted in Baggini, The Ego Trick, 202\u2013203.\n\n. Ashtavakra Gita 18.18.\n\n. Ch\u00f6gyam Trungpa, The Myth of Freedom: and the Way of Meditation (Boston: Shambhala, 2002), 6.\n\n. Ibid., 104\u2013105 (emphasis added).\n\n. Ashtavakra Gita 18.65, 60.\n\n. Ashtavakra Gita 18.59.\n\n. Shvetashvatara Upanishad 4.6\u20137.\n\n. Uttara Tantra 1.149.\n\n. Uttara Tantra 1.154.\n\n. Philippians 4:7.\n\n. Philippians 2:2\u20134.\n\n. Philippians 2:5\u20138.\n\n. Ashtavakra Gita 15.15.\n\n. Sly and the Family Stone, \"Everyday People,\" Stand! (Epic, 1968). The complete lyrics can be found at www.lyricsmode.com\/lyrics\/s\/sly_and_the_family_stone\/everyday_people.html.\n\n. Quoted in Eleanor \"Ndidi\" Hooks, Finding Joy\u2014Finding Yourself (CreateSpace Independent Publishing Platform, 2013), 57.\n\n. Quoted in Jon Kabat-Zinn, Full Catastrophe Living: Using the Wisdom of Your Body and Mind to Face Stress, Pain, and Illness (New York: Delta, 1990), 165.\n\n## Selected Bibliography\n\nBaggini, Julian. The Ego Trick: What Does It Mean to Be You? London: Granta Books, 2011.\n\nByrom, Thomas. The Dhammapada: The Sayings of the Buddha. New York: Random House, 2010.\n\nCsikszentmihalyi, Mihaly. Flow: The Psychology of Optimal Experience. New York: Harper & Row, 1990.\n\nDalai Lama, H. H. Beyond Religion: Ethics for a Whole World. Toronto: Signal Books, 2011.\n\nDoniger, Wendy. The Woman Who Pretended to Be Who She Was: Myths of Self-Imitation. New York: Oxford University Press, 2004.\n\nHanh, Thich Nhat. Interbeing: Fourteen Guidelines for Engaged Buddhism. Edited by Fred Eppsteiner. 3rd ed. Berkeley, CA: Parallax Press, 1988.\n\nHuizinga, Johan. Homo Ludens: A Study of the Play-Element in Culture. 1938. Reprint, London: Routledge, 2008.\n\nKeller, Timothy. The Freedom of Self-Forgetfulness: The Path to True Christian Joy. Chorley, England: 10Publishing, 2012.\n\nKrishnamurti, Jiddu. Think on These Things. Ojai, CA: Krishnamurti Foundation of America, 1964.\n\nLao-Tzu. Tao te Ching. Translated by Stephen Mitchell. New York: Harper Perennial, 2009.\n\nLasch, Christopher. The Culture of Narcissism: American Life in an Age of Diminishing Expectations. New York: W. W. Norton, 1979.\n\nLewis, C. S. Mere Christianity. New York: HarperSanFrancisco, 1952.\n\nMaslow, Abraham. Religions, Values, and Peak-Experiences. New York: Penguin, 1970.\n\nMerton, Thomas. New Seeds of Contemplation. New York: New Directions, 1961.\n\nNew Revised Standard Bible. New York: Oxford University Press, 1989.\n\nO'Flaherty, Wendy Doniger. Origins of Evil in Hindu Mythology. Berkeley, CA: University of California Press, 1980.\n\nRhys Davids, T. W., and C. A. F. Rhys Davids, trans. Dialogues of the Buddha. 1910. Reprint, Delhi, India: Motilal Banarsidass, 2000.\n\nSatchidananda, Swami. Beyond Words. Yogaville, CA: Integral Yoga Publications, 1977.\n\nTolle, Eckhart. A New Earth: Awakening to Your Life's Purpose. New York: Penguin Books, 2005.\n\nRajneesh, Bhagwan Shree. Tantra: The Supreme Understanding. Poona, India: Rajneesh Foundation, 1975.\n\nTutu, Desmond. No Future without Forgiveness. Colorado Springs, CO: Image, 2000.\n\nWatts, Alan. The Book: On the Taboo against Knowing Who You Are (New York: Vintage Books, 1989), 55.\n\nWolfe, Tom. \"The 'Me' Decade and the Third Great Awakening.\" New York, August 23, 1976.\n\nZimmer, Heinrich Robert. Philosophies of India. Princeton, NJ: Princeton University Press, 1969.\n\n\u2022 \u2022 \u2022\n\nAll translations from Sanskrit and Pali texts cited in this book are my own unless otherwise noted:\n\nAshtavakra Gita\n\nBadarayana's Vedantasutras\n\nBhagavad Gita\n\nBodhicaryavatara (Guide to the Bodhisattva's Way of Life)\n\nKatha Upanishad\n\nMaha Satipatthana Suttanta\n\nMandukya Upanishad\n\nNagarjuna's Mulamadhyamaka Karika (Root Verses on the Middle Way)\n\nShvetashvatara Upanishad\n\nVajracchedika Sutra (Diamond Cutter Sutra)\n\nVijnana Bhairava Tantra\n\nYoga Sutra\n\nA Division of Simon & Schuster, Inc.\n\n1230 Avenue of the Americas\n\nNew York, NY 10020\n\nwww.SimonandSchuster.com\n\n20827 N.W. 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+{"text":"**_THE AMERICAN SLAVE COAST_** offers a provocative vision of US history from earliest colonial times through emancipation that presents even the most familiar events and figures in a revealing new light.\n\nAuthors Ned and Constance Sublette tell the brutal story of how the slavery industry made the reproductive labor of the people it referred to as \"breeding women\" essential to the young country's expansion. Captive African Americans in the slave nation were not only laborers, but merchandise and collateral all at once. in a land without silver, gold, or trustworthy paper money, their children and their children's children into perpetuity were used as human savings accounts that functioned as the basis of money and credit in a market premised on the continual expansion of slavery. Slaveowners collected interest in the form of newborns, who had a cash value at birth and whose mothers had no legal right to say no to forced mating.\n\nThis gripping narrative is driven by the power struggle between the elites of Virginia, the slave-raising \"mother of slavery,\" and South Carolina, the massive importer of Africans\u2014a conflict that was central to American politics from the making of the Constitution through the debacle of the Confederacy.\n\nVirginia slaveowners won a major victory when Thomas Jefferson's 1808 prohibition of the African slave trade protected the domestic slave markets for slave-breeding. The interstate slave trade exploded in mississippi during the presidency of Andrew Jackson, drove the US expansion into Texas, and powered attempts to take over Cuba and other parts of Latin America, until a disaffected South Carolina spearheaded the drive to secession and war, pushing the Virginians to secede or lose their slave-breeding industry.\n\nFilled with surprising facts, fascinating incidents, and startling portraits of the people who made, endured, and resisted the slave-breeding industry, _The American Slave Coast_ culminates in the revolutionary Emancipation Proclamation, which at last decommissioned the capitalized womb and armed the African Americans to fight for their freedom.\n\nCopyright \u00a9 2016 by Ned Sublette and Constance Sublette\n\nAll rights reserved\n\nFirst edition\n\nPublished by Lawrence Hill Books\n\nAn imprint of Chicago Review Press Incorporated\n\n814 North Franklin Street\n\nChicago, Illinois 60610\n\nISBN 978-1-61374-820-6\n\n**Library of Congress Cataloging-in-Publication Data**\n\nSublette, Ned, 1951-\n\nThe American slave coast : a history of the slave-breeding industry \/ Ned Sublette, Constance Sublette. \u2014 First edition.\n\npages cm\n\nIncludes bibliographical references and index.\n\nISBN 978-1-61374-820-6 (hardback)\n\n1. Slave-trade\u2014United States\u2014History. 2. Slave traders\u2014United States\u2014History. 3. Slavery\u2014Economic aspects\u2014United States. 4. Slaves\u2014United States\u2014Social conditions. 5. Slaves\u2014United States\u2014Sexual behavior\u2014History. 6. Slaveholders\u2014Southern States\u2014History. 7. Southern States\u2014History\u20141775-1865. 8. Slave-trade\u2014Southern States\u2014History. 9. Slave traders\u2014Southern States\u2014History. I. Sublette, Constance. II. Title.\n\nE442.S82 2015\n\n331.11'7340973\u2014dc23\n\n2015002493\n\nInterior design: PerfecType, Nashville, TN\n\nPrinted in the United States of America\n\n5 4 3 2 1\n_Although it is a record of horror it has an odd, matter-of-fact air about it simply because the infamies that are described were so completely taken for granted._\n\n\u2014Bruce Catton, reviewing the 1965 edition of  \n _Documents Illustrative of the History of the Slave Trade to the Americas_\n\n# **Contents**\n\nIntroduction\n\nPart One: The Capitalized Womb\n\n1 The Mother of Slavery\n\n2 Protectionism, or, The Importance of 1808\n\n3 A Literature of Terror\n\n4 Natural Increase\n\n5 Little Shadows\n\n6 Species of Property\n\nPart Two: The Chesapeake and the Lowcountry\n\n7 Rawrenock\n\n8 A Cargo of Shining Dirt\n\n9 Our Principall Wealth\n\n10 Maria's Land\n\n11 Barbados\n\n12 The Anglo-Saxon Model\n\n13 Carolina\n\n14 The Separate Traders\n\n15 Charles Town\n\n16 Savannah and Stono\n\n17 A Rough Set of People, but Somewhat Caressed\n\n18 Ballast\n\nPart Three: Silent Profit\n\n19 Newspapers as Money as People\n\n20 Lord Dunmore's Blackbirds\n\n21 The General Inconvenience\n\n22 The Fugue of Silences\n\n23 Ten Thousand Powers\n\n24 The French Revolution in America\n\nPart Four: The Star-Spangled Slave Trade\n\n25 The Cotton Club\n\n26 The Terrible Republic\n\n27 I Do Not Threaten the Government with Civil War\n\n28 These Infernal Principles\n\n29 The Hireling and Slave\n\n30 A Jog of the Elbow\n\nPart Five: The Slaveocracy\n\n31 Swallowed by Millions\n\n32 Democratizing Capital\n\n33 Old Robbers\n\n34 Wake Up Rich\n\n35 The Slave Trade to Cuba and Brazil\n\n36 Heaps and Piles of Money\n\n37 The Slave Power\n\n38 Manifest Destiny's Child\n\n39 A Letter from Virginia\n\n40 Communists in Blackface\n\n41 Hiring Day\n\nPart Six: The Revolution\n\n42 Vanish Like a Dream\n\n43 A Snake Biting Its Tail\n\n44 Assignment in Paraguay\n\n45 The Decommissioning of Human Capital\n\n46 A Weird, Plaintive Wail\n\nCoda\n\nAcknowledgments\n\nPicture Credits\n\nNotes\n\nReferences\n\nIndex\n\nKent News, _Chestertown, Maryland._\n\n# **Introduction**\n\nTHIS IS A HISTORY of the slave-breeding industry, which we define as the complex of businesses and individuals in the United States who profited from the enslavement of African American children at birth.\n\nAt the heart of our account is the intricate connection between the legal fact of people as property\u2014the \"chattel principle\"\u2014and national expansion. Our narrative doubles, then, as a history of the making of the United States as seen from the point of view of the slave trade.\n\nIt also traces the history of money in America. In the Southern United States, the \"peculiar institution\" of slavery was inextricably associated with its own peculiar economy, interconnected with that of the North.\n\nOne of the two principal products of the antebellum slave economy was staple crops, which provided the cash flow\u2014primarily cotton, which was the United States' major export. The other was enslaved people, who counted as capital and functioned as the stable wealth of the South. African American bodies and childbearing potential collateralized massive amounts of credit, the use of which made slaveowners the wealthiest people in the country. When the Southern states seceded to form the Confederacy they partitioned off, and declared independence for, their economic system in which people were money.\n\nOur chronology reaches from earliest colonial times through emancipation, following the two main phases of the slave trade. The first phase, _importation_ , began with the first known sale of kidnapped Africans in Virginia in 1619 and took place largely, though not entirely, during the colonial years. The second phase, _breeding_ , was the era of the domestic, or interstate, slave trade in African Americans. The key date here\u2014from our perspective, one of the most important dates in American history\u2014was the federal prohibition of the \"importation of persons\" as of January 1, 1808. After that, the interstate trade was, with minor exceptions, the only slave trade in the United States, and it became massified on a previously impossible scale.\n\nThe conflict between North and South is a fundamental trope of American history, but in our narrative, the major conflict is intra-Southern: the commercial antagonism between Virginia, the great slave breeder, and South Carolina, the great slave importer, for control of the market that supplied slave labor to an expanding slavery nation. The dramatic power struggle between the two was central to the Constitutional Convention in Philadelphia in 1787 and to secession in 1860\u201361.\n\n**Part One** is an overview, intended as an extended introduction to the subject.\n\n**Part Two** , which begins the main chronological body of the text, describes the creation of a slave economy during the colonial years.\n\n**Part Three** centers on the US Constitution's role as hinge between the two phases of slave importation and slave breeding.\n\n**Parts Four through Six** cover the years of the slave-breeding industry, from the end of the War of 1812 through emancipation: the rise, peak, and fall of the cotton kingdom.\n\nNote: This book describes an economy in which people were capital, children were interest, and women were routinely violated. We have tried to avoid gratuitously subjecting the reader to offensive language and images, but we are describing a horrifying reality.\n\n#   Part One\n\n# **The Capitalized Womb**\n\n#   1\n\n# **The Mother of Slavery**\n\n\"VIRGINIA WAS THE MOTHER of slavery,\" wrote Louis Hughes.\n\nIt wasn't just a figure of speech.\n\nDuring the fifty-three years from the prohibition of the African slave trade by federal law in 1808 to the debacle of the Confederate States of America in 1861, the Southern economy depended on the functioning of a slave-breeding industry, of which Virginia was the number-one supplier. When Hughes was born in 1832, the market was expanding sharply.\n\n\"My father was a white man and my mother a negress,\" Hughes wrote. That meant he was classified as merchandise at birth, because children inherited the free or enslaved status of the mother, not the father. It had been that way in Virginia for 170 years already when Hughes was born.\n\n_Partus sequitur ventrem_ was the legal term: the status of the newborn follows the status of the womb. Fathers passed inheritances down, mothers passed slavery down. It ensured a steady flow of salable human product from the wombs of women who had no legal right to say no.\n\nMost enslaved African Americans lived and died without writing so much as their names. The Virginia legal code of 1849 provided for \"stripes\"\u2014flogging\u2014for those who tried to acquire literacy skills. A free person who dared \"assemble with negroes for the purpose of instructing them to read or write\" could receive a jail sentence of up to six months and a fine of up to a hundred dollars, plus costs. An enslaved person who tried to teach others to read might have part of a finger chopped off by the slaveowner, with the full blessing of law.\n\nSo it was an especially distinguished achievement when in 1897 the sixty-four-year-old Louis Hughes published his memoir, titled _Thirty Years a Slave: From Bondage to Freedom: The Institution of Slavery as Seen on the Plantation and in the Home of the Planter._ Like the other volumes collectively referred to as slave narratives, it bears witness to a history slaveowners did not want to exist: the firsthand testimony of the enslaved.\n\nBy the time Hughes was twelve, he had been sold five times. The third time, he was sold away from his mother to a trader. \"It was sad to her to part with me,\" he recalled, \"though she did not know that she was never to see me again, for my master had said nothing to her regarding his purpose and she only thought, as I did, that I was hired to work on the canal-boat, and that she should see me occasionally. But alas! We never met again.\"\n\n_Louis Hughes's author photograph._\n\nThe trader carried the boy away from the Charlottesville area that had been his home, down the James River to Richmond. There he was sold a fourth time, to a local man, but Hughes \"suffered with chills and fever,\" so the dissatisfied purchaser had him resold. This time he went on the auction block, where he was bought by a cotton planter setting up in Pontotoc, Mississippi\u2014a booming region that had recently become available for plantations in the wake of the delivery of large areas of expropriated Chickasaw land into the hands of speculators.\n\nSlaves were designated by geographical origin in the market, with Virginia-and Maryland-born slaves commanding a premium. \"It was held by many that [Virginia] had the best slaves,\" Hughes wrote. \"So when Mr. McGee found I was born and bred in that state he seemed satisfied. The bidding commenced, and I remember well when the auctioneer said: 'Three hundred eighty dollars\u2014once, twice and sold to Mr. Edward McGee.'\"\n\nMcGee had plenty of financing, and he was in a hurry; he bought sixty other people that day. A prime field hand would have commanded double or more, but even so, the $380 that bought the sickly twelve-year-old would be more than $10,000 in 2014 money.\n\nLike the largest number of those forcibly emigrated to the Deep South, McGee's captives were all made to walk from Virginia to Mississippi, in a coffle.\n\nSouthern children grew up seeing coffles approach in a cloud of dust.\n\nA coffle is \"a train of men or beasts fastened together,\" says the Oxford English Dictionary, and indeed Louis Hughes referred to the coffle he marched in as \"a herd.\" The word comes from the Arabic _qafilah_ , meaning \"caravan,\" recalling the overland slave trade that existed across the desert from sub-Saharan Africa to the greater Islamic world centuries before Columbus crossed the Atlantic. With the development in the late fifteenth century of the maritime trade that shifted the commercial gravity of Africa southward from the desert to the Atlantic coast, coffles were used to traffic Africans from point of capture in their homeland to point of sale in one of Africa's many slave ports.\n\nBut the people trudging to Mississippi along with Louis Hughes were not Africans. They were African Americans, born into slavery and raised with their eventual sale in mind. Force-marched through wilderness at a pace of twenty or twenty-five miles a day, for five weeks or more, from can't-see to can't-see, in blazing sun or cold rain, crossing unbridged rivers, occasionally dropping dead in their tracks, hundreds of thousands of laborers transported themselves down south at gunpoint, where they and all their descendants could expect to be prisoners for life.\n\nPerhaps 80 percent of enslaved children were born to two-parent families\u2014though the mother and father might live on different plantations\u2014but in extant slave-traders' records of those sold, according to Michael Tadman's analysis, \"complete nuclear families were almost totally absent.\" About a quarter of those trafficked southward were children between eight and fifteen, purchased away from their families. The majority of coffle prisoners were male: boys who would never again see their mothers, men who would never again see wives and children. But there were women and girls in the coffles, too\u2014exposed, as were enslaved women everywhere, to the possibility of sexual violation from their captors. The only age bracket in which females outnumbered males in the trade was twelve to fifteen, when they were as able as the boys to do field labor, and could also bear children. Charles Ball, forcibly taken from Maryland to South Carolina in 1805, recalled that\n\nThe women were merely tied together with a rope, about the size of a bed cord, which was tied like a halter round the neck of each; but the men... were very differently caparisoned. A strong iron collar was closely fitted by means of a padlock round each of our necks. A chain of iron, about a hundred feet in length, was passed through the hasp of each padlock, except at the two ends, where the hasps of the padlocks passed through a link of the chain. In addition to this, we were handcuffed in pairs, with iron staples and bolts, with a short chain, about a foot long, uniting the handcuffs and their wearers in pairs.\n\nAs they tramped along, coffles were typically watched over by whip- and gun-wielding men on horseback and a few dogs, with supply wagons bringing up the rear. In the country coffles slept outdoors on the ground, perhaps in tents; in town they slept in the local jail or in a slave trader's private jail. Farmers along the route did business with the drivers, selling them quantities of the undernourishing, monotonous fare that enslaved people ate day in and day out.\n\nSometimes the manacles were taken off as the coffle penetrated farther South, where escape was nearly impossible. But since the customary way of disposing of a troublesome slave\u2014whether criminally insane, indomitably rebellious, or merely a repeated runaway\u2014was to sell him or her down South, drivers assumed that the captives could be dangerous. Coffles were doubly vulnerable, for robbery and for revolt, so security was high.\n\nThe captives were not generally allowed to talk among themselves as they tramped along, but sometimes, in the midst of their suffering, they were made to sing. The English geologist G. W. Featherstonhaugh, who in 1834 happened upon the huge annual Natchez-bound chain gang led by trader John Armfield, noted that \"the slave-drivers... endeavour to mitigate their discontent by feeding them well on the march, and by encouraging them\"\u2014 _encouraging_ them?\u2014\"to sing 'Old Virginia never tire,' to the banjo.\" Thomas William Humes, who saw coffles of Virginia-born people passing through Tennessee in shackles on the way to market, wrote: \"It was pathetic to see them march, thus bound, through the towns, and to hear their melodious voices in plaintive singing as they went.\"\n\nSometimes coffles marched with fiddlers at the head. North Carolina clergyman Jethro Rumple recalled them stepping off with a huzzah: \"On the day of departure for the West the trader would have a grand jollification. A band, or at least a drum and fife, would be called into requisition, and perhaps a little rum be judiciously distributed to heighten the spirits of his sable property, and the neighbors would gather in to see the departure.\" Rumple was speaking, needless to say, of \"heightening the spirits\" of young people who had just been ripped away from their parents and were being taken to a fate many equated, not incorrectly, with death.\n\nA coffle might leave a slave jail with more people than it arrived with. The formerly enslaved Sis Shackleford described the process at Virginia's Five Forks Depot (as transcribed by the interviewer):\n\nHad a slave-jail built at de cross roads wid iron bars 'cross de winders. Soon's de coffle git dere, dey bring all de slaves from de jail two at a time an' string 'em 'long de chain back of de other po' slaves. Ev'ybody in de village come out\u2014'specially de wives an' sweethearts and mothers\u2014to see dey solt-off chillun fo' de las' time. An' when dey start de chain a-clankin' an' step off down de line, dey all jus' sing an' shout an' make all de noise dey can tryin' to hide de sorrer in dey hearts an' cover up de cries an' moanin's of dem dey's leavin' behin'.\n\nAn enslaved person could always be sold to another owner, at any time. When Louis Hughes's coffle reached Edenton, Georgia, McGee sold twenty-one of his newly purchased captives, taking advantage of the price differential in the Lower South to post an immediate profit on a third of his Virginia transaction and thereby hedge his debt to his financier.\n\nCharles Ball described a deal that took place on the road in South Carolina:\n\nThe stranger, who was a thin, weather-beaten, sunburned figure, then said, he wanted a couple of breeding wenches, and would give as much for them as they would bring in Georgia.... He then walked along our line, as we stood chained together, and looked at the whole of us\u2014then turning to the women; asked the prices of the two pregnant ones.\n\nOur master replied, that these were two of the best breeding-wenches in all Maryland\u2014that one was twenty-two, and the other only nineteen\u2014that the first was already the mother of seven children, and the other of four\u2014that he had himself seen the children at the time he bought their mothers\u2014and that such wenches would be cheap at a thousand dollars each; but as they were not able to keep up with the gang, he would take twelve hundred dollars for the two. The purchaser said this was too much, but that he would give nine hundred dollars for the pair.\n\nThis price was promptly refused; but our master, after some consideration, said he was willing to sell a bargain in these wenches, and would take eleven hundred dollars for them, which was objected to on the other side; and many faults and failings were pointed out in the merchandise. After much bargaining, and many gross jests on the part of the stranger, he offered a thousand dollars for the two, and said he would give no more. He then mounted his horse, and moved off; but after he had gone about one hundred yards, he was called back; and our master said, if he would go with him to the next blacksmith's shop on the road to Columbia, and pay for taking the irons off the rest of us, he might have the two women. (paragraphing added)\n\nWomen with babies in hand were in a particularly cruel situation. Babies weren't worth much money, and they slowed down coffles. William Wells Brown, hired out to a slave trader named Walker, recalled seeing a baby given away on the road:\n\nSoon after we left St. Charles, the young child grew very cross, and kept up a noise during the greater part of the day. Mr. Walker complained of its crying several times, and told the mother to stop the child's d\u2014\u2014d noise, or he would. The woman tried to keep the child from crying, but could not. We put up at night with an acquaintance of Mr. Walker, and in the morning, just as we were about to start, the child again commenced crying. Walker stepped up to her, and told her to give the child to him. The mother tremblingly obeyed. He took the child by one arm, as you would a cat by the leg, walked into the house, and said to the lady,\n\n\"Madam, I will make you a present of this little nigger; it keeps such a noise that I can't bear it.\"\n\n\"Thank you, sir,\" said the lady.\n\nFrom the first American coffles on rough wilderness treks along trails established by the indigenous people, they were the cheapest and most common way to transport captives from one region to another.\n\nThe federally built National (or Cumberland) Road, which by 1818 reached the Ohio River port of Wheeling, Virginia (subsequently West Virginia), was ideal for coffles. It was the nation's first paved highway, with bridges across every creek. Laying out approximately the route of the future US 40, its broken-stone surface provided a westward overland transportation link that began at the Potomac River port of Cumberland, Maryland. From Wheeling, the captives could be shipped by riverboat down to the Mississippi River and on to the Deep South's second-largest slave market at Natchez, or further on to the nation's largest slave market, New Orleans.\n\nBeginning after the War of 1812 and continuing up through secession, captive African Americans were trafficked south and west by every possible method, in an enormous forced migration. \"A drove of slaves on a southern steamboat, bound for the cotton or sugar regions,\" wrote William Wells Brown in his 1849 autobiography, \"is an occurrence so common, that no one, not even the passengers, appear to notice it, though they clank their chains at every step.\"\n\nAs railroads extended their reach, captives were packed like cattle into freight cars, shortening the time and expense to market considerably. Some passenger trains had \"servant cars,\" though a cruder term was more commonly used. On his first trip to the South, in January 1859, the twenty-one-year-old New Englander J. Pierpont Morgan noted: \"1000 slaves on train.\"\n\nThey were trafficked by sea in oceangoing vessels that sailed the hard passage from the Chesapeake around the Florida peninsula to New Orleans, as well as in shorter voyages within that route. Ocean shipment was more expensive than a coffle, but it was quicker, so it turned the capital-intensive human cargo over more efficiently. Though exact figures do not exist, it is safe to say that tens of thousands of African Americans made the coastwise voyage from the Chesapeake and from Charleston to New Orleans and up the Mississippi to Natchez, as well as to Pensacola, Mobile, Galveston, and other ports. Maryland ports alone (principally Baltimore) shipped out 11,966 people for whom records exist between 1818 and 1853, and an unknown number of others before, during, and after that time.\n\nMore slave ships came to New Orleans from the East Coast of the United States than from Africa. In a shorter recapitulation of the Middle Passage of a century before, the captives were packed into the hold with ventilation slats along the side to keep them from suffocating. Upon arrival, they were discharged into one or another of New Orleans's many slave pens, where they were washed, groomed, and fed, their skin was oiled, and their gray hairs, if they had any, were dyed or plucked out. On sale day, they were put into suits of the finest clothes many of them would ever wear, with perhaps even top hats for the men. Most would be sent to the cotton fields, where inhuman levels of work would be extracted from them through torture, or to Louisiana's death camps of sugar.\n\nFollowing the precedent set by the Europeans, who referred to the coastal regions of Africa by their exports\u2014the Ivory Coast, the Gold Coast, the Slave Coast\u2014some writers have referred to the Chesapeake region as the Tobacco Coast.\n\nBut it would also be appropriate to call it the American Slave Coast.\n\n#   2\n\n# **Protectionism, or, The Importance of 1808**\n\n_Industry: A particular form or branch of productive labour._\n\n\u2014Oxford English Dictionary\n\nBY HEMISPHERIC STANDARDS, THE African slave trade to English-speaking North America was petty.\n\nAccording to database-backed estimates by David Eltis and David Richardson, only about 389,000 kidnapped Africans were disembarked in the ports of the present-day United States, the majority of them before independence. We say \"only\": that's an enormous number of captives to be dragged across the ocean, but Africans trafficked to the United States territory account for less than 4 percent of the estimated hemispheric total. An estimated 10.7 million Africans arrived alive to the Americas\u2014out of an estimated 12.5 million embarked, leaving 1.8 million dead at sea.\n\nThere is no way to figure the collateral damage to African populations from slave-raiding with even a rough level of accuracy. Slave-raiding, which was typically conducted by Africans, was notoriously wasteful of life, since only the young were taken and often the rest were killed. If one died for every one taken captive in slave raids\u2014a speculative and possibly conservative number\u2014that would mean the transatlantic slave trade killed or enslaved some twenty-five million Africans. It may have been double that; there's no way to know.\n\nBarbados, an island about the size of the New York City borough of Queens, appears to have taken in more Africans than the entire territory of the present-day United States\u2014493,000, according to Eltis and Richardson.\n\n**Region** | **Estimated number of African captives**  \n---|---  \nChesapeake (Virginia and Maryland) | 129,000  \nLowcountry (South Carolina and Georgia) | 211,000  \nNew England and Mid-Atlantic | 27,000  \nGulf Coast | 22,000  \n**Total present-day US** | **389,000**  \n**Barbados** | **493,000**\n\nEstimates vary, of course; historian James McMillin believes that the number for the United States and its colonial predecessors exceeded 500,000. But that difference is not an order of magnitude. Some captives were brought to North America from Barbados and other places in the West Indies, especially in the seventeenth century; while documentation is scarce, the numbers were small by comparison.\n\nAfricans were only the seed. By 1860, those few hundred thousand Africans had given way to four million African Americans. Each birth was, as Thomas Jefferson described it, \"an addition to the capital.\" The South did not only produce tobacco, rice, sugar, and cotton as commodities for sale; it produced people.\n\nVirginia had been slave breeding since the seventeenth century. It had the oldest, most deeply rooted African American population, and the largest. With far more slaves than any other state, and with much of the land already burned out for tobacco farming by the time of the Declaration of Independence, the agricultural productivity per laborer in Virginia was low. The most profitable thing for Virginia planters to do with their growing slave population was to sell young people to traders for shipment down South.\n\nThe existence of slavery in the United States was taken for granted by the delegates to the Constitutional Convention in 1787; there was little or no discussion of abolishing it. The African slave trade, however, was very much in contention.\n\nNone of the delegates assembled at the Constitutional Convention could know that there would soon be a revolution in Saint-Domingue (the future Haiti), much less that as a consequence Napoleon Bonaparte would make a snap decision to sign his claim to Louisiana over to the United States in 1803. But it was commonly understood that territorial expansion was coming. Everyone knew that the upriver hinterlands of New Orleans were being invaded by Anglo-American settlers who would eventually take the territory over through force of numbers. Charleston merchants had a long-established web of overland trade that spread a thousand miles, across Georgia and what we now call Alabama and Mississippi into Louisiana. The frontiersmen of Kentucky and Tennessee were itching to drive the Native Americans out of Alabama and take their rich, black land. Spanish Florida had from the beginning been a security threat to South Carolina and Georgia; it, too, would come under US control. The market for slaves was about to explode in volume, and everyone knew it.\n\nThe question of who would have the concession to supply slave labor to this plantation-empire-to-come was an obstacle to unity at the Constitutional Convention. Slaveowners in Virginia, and in smaller numbers Maryland, were uniquely positioned to sell slaves into the emerging markets. Unlike the sugar slaves in the rest of the Americas or the rice slaves of South Carolina, the tobacco slaves of the Chesapeake didn't die off. It was an unprecedented phenomenon in the hemisphere: their numbers increased every year.\n\nProhibiting the African trade, as the New England delegates wanted to do, would create a grand bonanza for Virginia slaveholders\u2014at the expense of South Carolina. But the delegates from Virginia had to compromise if they wanted South Carolina and Georgia to be part of the nation instead of an independent, belligerent, slave-importing competitor for power next door\u2014one, moreover, whose territory was the overland gateway to territorial expansion into the Deep South.\n\nCharleston, meanwhile, was the major receiving port in North America for kidnapped Africans, and South Carolina's delegates wanted no federal interference in their market-driven opening and closing of the trade. Chesapeake slaveowners, who were the only ones with sufficient surplus labor to sell off, wanted the African trade permanently closed. They compromised on a twenty-year guarantee that the foreign slave trade could exist on a state-by-state basis.\n\nAccordingly, Article 1, Section 9 of the United States Constitution reads:\n\n_This 1762 map portrays Virginia, Carolina, and Georgia as extending all the way out to Louisiana, across densely forested territories held by different Native American confederations._\n\nThe Migration or Importation of such Persons as any of the States now existing shall think proper to admit, shall not be prohibited by the Congress prior to the Year one thousand eight hundred and eight, but a tax or duty may be imposed on such Importation, not exceeding ten dollars for each Person.\n\n\"Importation of persons\" was a euphemism; the framers were not so indelicate as to use the word _slave._ It was an anomalous provision, containing as it did the only date in the Constitution, and moreover the only price\u2014the ten-dollar duty limit, which guaranteed that the African slave trade could not be taxed out of existence but implied that the slave trade might contribute revenue to the federal budget.*\n\nThat constitutionally stipulated deadline of January 1, 1808, is, from our perspective, one of the most important dates in American history, signaling as it does the transformation of the United States slavery industry.\n\nFor this reason, 1808 is also an essential date for understanding the making of African American culture. Kidnapped Africans had been arriving for almost two hundred years, repeatedly re-Africanizing American culture. No longer. The child was separated from the ancestors. With the changeover to a domestic slave trade, the long-established Afro-Chesapeake culture of Virginia and Maryland was diffused southward over several decades. Meanwhile, there was an overland march westward of the more recently Africanized Lowcountry of Carolina and Georgia across Alabama and into Mississippi and Louisiana, as well as vessels sailing around Florida to New Orleans. The two collided with each other in the presence of the smaller but potent creolized culture of Catholic Afro-Louisiana.\n\nWhile the forces involved were greater than any single historical figure, individuals do make a difference in history. We will interpret key events and figures of American history in the light of their relationship to the profit-seeking machine African Americans were caught in. In particular, three slaveowning politicians loom large in our narrative as principal enablers of the territorial expansion of slavery and, consequently, of the slave-breeding industry: Thomas Jefferson, Andrew Jackson, and James K. Polk\u2014a Virginian and two Tennesseans. All three were slaveholders, and like all slaveholders, their wealth was primarily stored in the form of captive human beings, so their entire financial base\u2014personal, familial, social, and political\u2014depended on high prices for slaves. To that end, they restricted the supply of captives by keeping the African trade closed; by opening new territory for US slavery to expand into, they expanded the demand for that restricted supply, greatly increasing as they did so the wealth and political power of the slaveowning class.\n\nFourteen years after the Constitution went into effect, on December 20, 1803, the territorial area of the new nation approximately doubled when French governor Pierre Cl\u00e9ment de Laussat handed New Orleans over to President Jefferson's men, the Virginia-born W. C. C. Claiborne and the Maryland-born James Wilkinson. From that date until Louisiana became a state in 1812, the territory was effectively a colony of Virginia.\n\nJefferson's pointedly undemocratic rule of the Louisiana Territory assured favorable regulatory treatment for Virginia slaveowners. He asked Congress for, and got, monopolistic commercial restrictions on the slave trade into Louisiana: importation into Louisiana of slaves from outside the United States was prohibited, but importation into Louisiana of slaves from within the United States was allowed.\n\nWith the Constitution having set the rules of the match, Virginia and South Carolina were in direct competition to supply the growing Louisiana slave market. It was an enormous business opportunity for Charleston's slave dealers, but time was running out. The twenty-year constitutional guarantee of protection for the African slave trade that South Carolina had insisted on had only four years to run. While Jefferson proactively worked to be sure that window was closed at the first possible moment, the Carolina merchants scurried to take maximum advantage of it.\n\nSouth Carolina legislators knew full well that the prohibition of the African slave trade by federal law was on President Jefferson's action list; accustomed to turning the trade on or off as economic conditions dictated, they rescinded their previous ban against the African trade as soon as the news of the acquisition of Louisiana arrived at the end of 1803. Disregarding the anger the move provoked elsewhere, they opened the port of Charleston to cargoes of kidnapped Africans. Louisiana couldn't legally import Africans but South Carolina could, and could then resell the Africans to Louisiana via the domestic trade. Even with a substantial markup, they could still undercut the price Virginia farmers charged for African Americans.\n\nThe Constitution did not require the federal prohibition of importation of persons as of 1808; it merely stipulated that federal law could not prohibit it before that date. But Jefferson, who legally owned more than six hundred people during his lifetime, proactively made sure that importation of persons would indeed be prohibited as of the earliest constitutionally permissible date. So as not to have slave importation one day more than necessary, on December 2, 1806, he gave his Sixth Annual Message and asked Congress for a measure to end the African trade\u2014more than a year before it could become effective. It was a move that was to his personal financial advantage as a Virginia slaveowner and to the disadvantage of South Carolina's wholesale slave importers.\n\nTo be sure, Jefferson framed ending importation of persons as a humanitarian act, and many historians have treated it that way, but it was not. Ending the African slave trade was protectionism on behalf of Virginia. It kept out the cheaper African imports so as to keep the price of domestically raised people high. Nobody in Chesapeake politics wanted more Africans coming in and devaluing their most significant assets. Over the long term, ending the African trade was a business coup on behalf of the slaveowners of Virginia, who were Jefferson's most loyal constituents throughout his increasingly disastrous second term as president (1805\u20131809).\n\nMoreover, ending the foreign slave trade to the United States was popular among other groups as well. Few white people wanted more black people in the country. Antislavery people wanted the African trade suppressed. The Southern public approved of ending the foreign slave trade as an antiterrorism measure: they were alarmed by the discovery of Gabriel's planned uprising in 1800, terrified by the bloody chain of events that had produced the newly declared nation of Haiti, and always frightened of the ever-present possibility of slave rebellion at their door.\n\nBut not everyone was happy about the prohibition of the African trade. Louisiana and Mississippi's burgeoning planter population wanted all the slave labor it could get, but once foreign sources were shut off pursuant to Jefferson's signature, no states besides Virginia and Maryland had quantities of laborers ready to sell. The French Creoles of Louisiana were particularly angry at having to pay high prices to the Virginians for English-speaking slaves when they could have gotten Africans much cheaper via Havana. But the United States shifted over to an entirely domestic slave trade in African Americans as of 1808\u2014albeit with some ill-documented smuggling of captives from outside for ten more years or so, particularly by the Lafitte brothers' operations in Louisiana and Spanish Texas.\n\nIn a frenzy of last-minute stocking-up during the last legal year, in 1807 South Carolina merchants imported the highest one-year volume of Africans in the history of the North American trade, with the result that the market became glutted and captives from diverse parts of Africa died on Gadsden's Wharf awaiting sale.\n\nThough the end of the African slave trade was a major commercial shift, its immediate impact was eclipsed by a mercantile catastrophe. Only a few days before the African trade ban went into effect, in one of the most radical economic actions ever taken by a president, Jefferson put an embargo on _all_ foreign commerce rather than respond militarily to naval aggression by the British and the French. From then until 1815, American business was paralyzed\u2014first by embargo, then by war\u2014during which time the large-scale domestic slave trade could not develop. But it grew spectacularly after that.\n\nWith the African trade halted, those slaves that continued to be bought and sold brought profit to US slaveowners, speculators, and slave trading firms instead of to British syndicates and African royals.\n\nSlavery required a slave trade, and with the trade in kidnapped Africans shut off, there was no slave trade without slave breeding. By deliberately creating a scarcity of slave labor from which profit could derive for those who could supply it, the 1808 cutoff of the African trade created an economic incentive for farmers to deliver as many homegrown laborers to market as possible, as fast as possible.\n\nThe Maine-born Episcopal clergyman Joseph Holt Ingraham, writing under deep cross-gendered cover as Kate Conyngham, reported from Virginia in the 1850s that:\n\nSo necessary is the annual decimation of slaves by sale to support these old decayed families, that it has become a settled trade for men whose occupation is to buy slaves, to travel through the \"Old Dominion\", from estate to estate.... Here he gets one, there another, and in a few weeks he enters Lynchburg, Alexandria or Richmond with a hundred or more.... As it is, slaves are raised here more as a _marketable_ and money-returning commodity than for their productive labor.\n\nFor Virginia's African Americans, Jefferson's legacy was unspeakably cruel. When the prohibition of importation of Africans made a massive business out of the already existing interstate slave trade in African Americans, black Virginians and Marylanders were trafficked in mass quantities to the newly opened territories, destroying family ties with every sale. The human cargoes that were driven in coffles and loaded onto ships were assembled by a network of traders' agents who fanned out through the farming territories of the Chesapeake, combing the slave-producing region to buy\u2014one could say harvest\u2014young people from farmers, often one at a time.\n\nWith the acreage under cultivation vastly expanding, the slave-selling industry touched the lives of everyone in the slave-trade zone, free or enslaved. It put a price on everyone\u2014including on slaveowners, whose wealth was stored in the bodies of their always-liquidatable slaves and whose available credit was a function of the size of their slaveholdings. In the absence of a domestic supply of coin, slaves collateralized the credit that created new money.\n\nThe growing nation of fortune hunters exerted a popular pressure to wrest more cotton-growing land from the Native Americans, a mission notably carried out by General Andrew Jackson under cover of the War of 1812, creating the land-and-slaves boom remembered as \"Alabama Fever.\" Jackson's subsequent taking of Florida by military conquest and removing the South's remaining Native Americans from their ancestral lands\u2014we now call it \"ethnic cleansing\"\u2014made the entire Deep South safe for plantation slavery and further increased the demand for slave labor.\n\nPresident James Monroe\u2014a Virginian, as were all his predecessors in the office except John Adams\u2014cracked down on what remained of the clandestine African trade, signing into law in 1820 a bill that declared participation in the foreign slave trade to be piracy and, as such, punishable by death. For the next forty-five years, the enslaved population of the United States was a closed system that expanded its numbers through sexual reproduction, more politely referred to as \"natural increase.\" As W. E. B. DuBois described it, \"slaves without [the African] slave trade became more valuable; with cotton culture their value rose still further, so that they were fed adequately and their breeding systematically encouraged.\" Over time, more states, including South Carolina, got into the business of exporting African Americans to new territories.\n\nWhile the North developed cities and industry, the South failed to build an infrastructure through which consumer goods could be distributed, and thus furnished no domestic market; instead, its profitable system of plantation-prisons expanded to new lands through imperial and military effort. After the worst depression the nation had yet suffered, President James K. Polk prosecuted the Mexican War to annex Texas for the Southern cotton kingdom, an action hotly contested by John Quincy Adams in the House and generally unpopular in the North. Once Texas was in the Union, Southern slave prices continued to climb, with only brief dips, until secession.\n\nPolk's success in extending the Southern slave regime to Texas instantly\u2014and predictably\u2014revalued slaveowners' human portfolios upward. Including his own: Polk bought slaves in secret from his office in the White House on an ongoing basis during his presidency in the hope of building up his nest egg while he worked to extend the reach of American slavery.\n\nA century and a half later, what vocabulary to use in talking about this is still something of a work in progress.\n\nIt's hard to describe business without employing a business vocabulary. That said, economists who have written on the subject have sometimes used the antebellum business vocabulary too readily, as in the 1958 study that made the hypothetical assumption that \"each prime field wench produced five to ten marketable children during her lifetime.\" The history of slavery is a study in euphemisms, beginning with the near-universal use by refined whites of the polite term \"servant\" to refer to the individuals they legally owned. The colloquial term of choice used by slave traders, more often spoken than written, was, of course, \"nigger,\" or, more politely, \"Negro,\" which was considered synonymous with \"slave\"; judging from available evidence, the n-word was used by the enslaved themselves as freely as it is on playgrounds today, even as the vocabulary of slavery times echoes in colloquial black speech: _bitch, buck_ , and the ultimate curse, _motherfucker_.*\n\nA number of people presently prefer to say \"enslaved person\" or some similar construction instead of \"slave,\" arguing that Africans and African Americans never accepted their enslaved condition. This phrasing can become cumbersome in an extended discussion, and in talking about our subject, it can lead to a paradox of parallel constructions. If one was not a slave, then one had no owner, and one could not be sold. True enough on a moral level, but unfortunately, what we are describing is precisely the legal ownership and sale of slaves. We have chosen generally, and perhaps not entirely consistently, to use the words \"enslaved\" or \"captive\" to refer to people in their human aspect and \"slave\" to refer to their economic function and social position, and we hope the reader will cut us some slack.\n\nThe term \"slave breeding\" was much in use when it was happening\u2014hurled as a charge on the floor of Congress and denounced as a damned lie by slaveowners.* But it wasn't merely an allegation: \"slave breeding\" was an ugly term that described a horrific reality.\n\nOur ambivalence about terminology extends to the naming of wars, which is a highly political pursuit. Slavery ended as a consequence of what American history generally chooses to remember by the name of the Civil War, and which in official US documents was called the War of the Rebellion. But revolutions generally are civil wars, and vice versa; we argue that, depending on one's perspective, the most common names for the two great national conflicts\u2014the Revolutionary War and the Civil War\u2014could be flipped.\n\nIn recent years, it has become more common for scholars to speak of the War of Independence from Britain (commonly memorialized as the Revolutionary War) as a civil war, as indeed it was frequently described during the independence struggle. We will argue that the War of Independence not only did not intend to end slavery, but was fought in part to protect slavery from the growing power of British abolitionism. From the perspective of the enslaved, meanwhile, the war usually called the Civil War was the revolutionary war, because it ended chattel slavery and, in removing the appraised resale value of human beings from the balance sheets, remade the basis of American money.\n\n*The ten-dollar duty was never imposed; South Carolina congressmen reacted with such fury when a Northern legislator proposed it that the measure was killed, and slave importation remained tax exempt.\n\n*Unlike the words _funk, the blues_ , or, for that matter, _nigger_ (in its one-g form, _Niger_ ), the formerly unprintable _motherfucker_ doesn't seem to have come from Britain. It's not clear how far back it goes, but it probably reaches back to slavery days as part of a vocabulary that ultimately became hipster lingo and emerged into print and recordings only slowly. The earliest written forms cited by the Oxford English Dictionary are two court cases from the South: in 1889 in Texas, \"that God damned mother-fucking, bastardly son-of-a-bitch!\" and, even more provocatively, in 1918, when the twenty-two-year-old African American soldier Sidney Wilson of Tennessee was court-martialed and sentenced to ten years at hard labor for having written a letter to the Memphis _Commercial Appeal_ that said, \"You is a line Mother Fucker, an' don't think the boys from Memphis is the onlyest one said that. We is goin' to straiten up this country, just as soon as we get some amonation,\" and another letter to his draft board that said, \"you low-down Mother Fuckers can put a gun in our hands but who is able to take it out?\" See Ellis, 89\u201390.\n\n*The general usage of the word \"breeding\" in reference to people was more common than it is today, as per the still occasionally heard phrase \"well-bred.\"\n\n#   3\n\n# **A Literature of Terror**\n\n_Were I about to tell you the evils of Slavery... I should wish to take you, one at a time, and whisper it to you. Slavery has never been represented; Slavery never can be represented. 1_\n\n\u2014William Wells Brown, address to the Female Anti-Slavery Society of Salem, Massachusetts, 1847\n\n\"SLAVERY IS TERRIBLE FOR men; but it is far more terrible for women,\" wrote Harriet Jacobs, under the pseudonym Linda Brent. \"Slaveholders have been cunning enough to enact that 'the child shall follow the condition of the _mother_ ,' not of the _father_ ; thus taking care that licentiousness shall not interfere with avarice.\"\n\nJacobs's memoir, _Incidents in the Life of a Slave Girl. Written by Herself_ , describes her abuse by \"Mr. Flint,\" whose real name was James Norcom of Edenton, North Carolina. One of only a few nineteenth-century slave narratives written by a woman, it is perhaps the frankest in its treatment of sexual exploitation:\n\nThe slave girl is reared in an atmosphere of licentiousness and fear. The lash and the foul talk of her master and his sons are her teachers. When she is fourteen or fifteen, her owner, or his sons, or the overseer, or perhaps all of them, begin to bribe her with presents. If these fail to accomplish their purpose, she is whipped or starved into submission to their will.... Resistance is hopeless.\n\nLike Louis Hughes's memoir, Jacobs's was one of more than a hundred slave narratives published in book form in the nineteenth-century United States. All but forgotten until the 1960s, these testimonies have now become more familiar outside specialist circles and are understood not only as an essential body of historical witness, but also a fundamental corpus of American literature. Frederick Douglass and William Wells Brown, foundational figures of African American letters, both wrote autobiographies detailing their experiences in slavery. Solomon Northup's _Twelve Years a Slave_ (1853)\u2014one of the best-written of the slave narratives, specific in its details, well-authenticated by scholars, and forgotten until the 1960s\u2014is now well known because of the 2013 movie version, but there are many others. The narratives participate in literary tropes and publishing conventions of the day, and many bear the influence of editors and cowriters. But even discounting for occasional possibly exaggerated or invented scenes in some of them, their composite picture of the workings of the regime of slavery is remarkably consistent, mutually corroborating, and credible. They speak up for one another.\n\n_A runaway ad for Harriet Jacobs placed by James Norcom in the_ Norfolk Daily Beacon _of July 4, 1835. This description of an abused slave makes clear the abuser's close familiarity, and stalker's fascination, with her, while affirming that the enslaved girl \"absconded\" without \"any known cause or provocation.\"_\n\nBethany Veney, from Paige County, Virginia, reinforced the testimony of Jacobs when she wrote in her 1889 memoir:\n\nMy dear white lady, in your pleasant home made joyous by the tender love of husband and children all your own, you can never understand the slave mother's emotions as she clasps her new-born child, and knows that a master's word can at any moment take it from her embrace; and when, as was mine, that child is a girl, and from her own experience she sees its almost certain doom is to minister to the unbridled lust of the slave-owner, and feels that the law holds over her no protecting arm, it is not strange that, rude and uncultured as I was, I felt all this, and would have been glad if we could have died together there and then.\n\nAlso essential to our understanding is the collection of more than twenty-three hundred oral histories of formerly enslaved elders taken under the general direction of folklorist John A. Lomax by the Federal Writers' Project of the Works Progress Administration between 1936 and 1938, and by earlier researchers from Fisk and Southern University in 1929 and 1930. These twentieth-century narratives are of variable quality and reliability. There are some issues of mistrust of white interviewers by black subjects (though some interviewers were black); questions of reliability without recording (though a few were recorded); questions of memory (interviewees were recalling seventy years previously, and some were too young to remember their lives in slavery, though older respondents could recall events as early as the 1840s); and a heavily dialectized transcription style (though the emphasis on phonetic precision is not without value). But even so, this collection provides the most extensive description extant of slavery from the inside, and, as with the nineteenth-century slave narratives, the many voices corroborate each other over and over again. It has served as a significant source for many books about slavery published since the 1970s and has a major advantage over the nineteenth-century narratives in the much higher percentage of women represented. Unfortunately, about half the Virginia interviews were lost or destroyed, and there are no interviews from Louisiana at all.\n\nThe silence from the eighteenth century is deafening. There were no slave narratives published in North America during the colonial era; there is only one known diary by a white indentured servant. With only a few exceptions, the essential witness of the enslaved is largely missing from the historical record for the colonial years, which is why there will be few black voices in that section of our book.\n\nNo less than any other form of capitalism, American slavery capitalism was premised on continual expansion. The growth of the Southern economy was tied directly to the productivity of the capitalized womb, a term we use to refer to the way enslaved women's bodies functioned as the essential production engine of the slave-breeding economy, which in turn fueled a global economy that processed slave-grown cotton into mass-produced cloth.\n\nThat individual plantation owners practiced slave-breeding through the rape of enslaved women is attested to repeatedly in the testimony of the formerly enslaved and elsewhere. But beyond that, we argue, with the importation of African captives shut off, antebellum slavery was in the aggregate a slave-breeding system.\n\nOne of the functions of this slave-breeding machine was to chew up the black family, systematically, in every generation. Why might elite whites want a machine with which to destroy the black family? Most immediately, because the family was the strongest unit of social cohesion and resistance to slavery. But longer term, because destroying family webs systematically in every generation was the best way to guarantee the perpetual existence of an abject underclass whose labor and upkeep would remain as cheap as possible.\n\nWith every generation, the American elite became collectively more entrenched as its family structures expanded while the enslaved became collectively more entrenched as an underclass as its family ties were systematically, recursively cut.\n\nFor enslaved women, who could be freely violated in the cellar, the barn, the field, or anywhere else a captor chose, it was a system of terror. Beyond the purely venal incentive of unrestrained sexual activity, the existence of a market in young people created a financial incentive for slaveowners to intrude into the reproductive lives of enslaved women, leading to what Richard Follett calls an \"intrusive policy of demographic engineering.\" A blunter way of saying it is forced mating: enslaved women could be assigned to enslaved men by slaveowners, or impregnated by white men who had access to them.\n\nForced mating was sufficiently widespread to be documented in a surfeit of examples, from the presidential-slaveholder level on down. During James K. Polk's presidency, his brother-in-law Robert W. Campbell, who was watching the plantation for him, promised the president in a letter to purchase \"young girls\" for him with the purpose of force-mating them with Polk's \"young men\":\n\nwhen I go down [to the plantation] I [will] act according to my best Judgment about the husbands & wives of your people[.] I want to take down likely young girls for wives for your young men as there are to[o] gr[e]at a proportion of men on your farm for the women.\n\nThe formerly enslaved Lueatha Mansfield of Bastrop, Louisiana, recalled that if a slaveowner \"saw a fine woman or man on another plantation, he would buy him or her for breeding purposes in order to continue to have good able workers. If he didn't bring them on the same farm, he would arrange for them to breed from each other.\"\n\nCharles Grandy, enslaved in Virginia, recalled that \"Marsa would stop de ole nigger-trader and buy you a woman. Wasn't no use tryin' to pick one, cause Marsa wasn't gonna pay but so much for her. All he wanted was a young healthy one who looked like she could have children, whether she was purty or ugly as sin.\"\n\nJames Green, half Native American and half African American, sold away from his mother at the age of twelve for $800, recalled at the age of ninety-seven in 1938 in San Antonio, Texas, that \"no one had no say as to who he was goin' to get for a wife. All de weddin' ceremony we had was with Pinchback's [the slaveowner's] finger pointin' out who was whose wife.\" Much less did the \"wife\" have any say.\n\nBefore abolitionists made the term too notorious to use beginning in the 1830s, slave-sale advertisements might bluntly extol one or another woman as a \"breeder,\" meaning that she had proven her ability to give birth to healthy children and recover to reproduce again at a time when many women died from childbirth. \"If a woman wern't a good breeder she had to do work with de men,\" said Green, \"but Pinchback tried to get rid of women who didn't have chillen.\"\n\nFannie Moore, interviewed in North Carolina in 1937, recalled that (as transcribed): \"De 'breed woman' always bring mo' money den de res', [even the] men. When dey put her on de block dey put all her chillun aroun her to show folks how fas she can hab chillun.\" Mary L. Swearingen of Bastrop, Louisiana, paraphrasing her enslaved grandmother, said, \"Whenever a woman was an extraordinary breeder, she was mated by the master to his own accord. Only sometimes the couples were happily married, and occasionally when a couple was happy, the master separated them by selling one or the other.\"\n\nResistance to forced breeding was described by Mary Gaffney, enslaved in Texas, who described chewing cotton root as a contraceptive (as transcribed):\n\nFact is, I just hated the man I married but it was what Maser said do. When he came to Texas he took up big lots of land and he was going to get rich. He put another negro man with my mother, then he put one with me. I would not let that negro touch me and he told Maser and Maser gave me a real good whipping, so that night I let that negro have his way. Maser was going to raise him a lot more slaves, but still I cheated Maser, I never did have any slaves to grow and Maser he wondered what was the matter. I tell you son, I kept cotton roots and chewed them all the time but I was careful not to let Maser know or catch me, so I never did have any children while I was a slave.\n\nWe can't quantify forced mating; Eugene Genovese, who tried, estimated that \"forced marriages affected perhaps one out of ten.\" Every slaveowner was free to set his own rules; just as some provided better material conditions for their captives than others, some allowed them leeway in choosing partners, and some did not. According to quantitative historian Daniel Scott Smith, the \"average slave\" lived on a plantation with forty-one slaves; on larger plantations, there would presumably have been somewhat more choice of mates while on smaller ones there were fewer options. But by virtue of being enslaved, no slave had fully free choice.\n\nMost Americans' familiarity with the notion of slave breeding comes from popular fiction\u2014in particular, from the 1957 Southern gothic novel _Mandingo_ , set on an imaginary slave-breeding plantation.\n\nThe general reputation of _Mandingo_ among critics is as a benchmark for bad writing. The first novel by the Illinois-born Kyle Onstott (1887\u20131966), previously the author of _The New Art of Breeding Better Dogs_ , it was published by Denlinger's, an independent publisher of dog books in\u2014where else?\u2014Richmond, Virginia. Though it has been out of print for years as of this writing, _Mandingo_ sold more than five million copies, mostly in mass-market paperbacks that sold for under a dollar at a time when strict controls on movie and television content made books the place to go for explicit material. It generated a franchise of fourteen novel-length sequels by various writers over thirty years; a Broadway play with Adolphe Menjou and Dennis Hopper that opened in May 1961 for eight performances; and, in the heyday of blaxploitation pictures, two big-budget movies with remarkably hateful dialogue.*\n\nWith its fictional stud-farm plantation\u2014Falconhurst, it was called\u2014that bred and raised people for market, _Mandingo_ disseminated an inaccurate and exaggerated vision, to say nothing of the stereotypes it promoted.\n\nNot that _Mandingo_ got it all wrong. As antebellum historical fantasy goes, its brutal, lascivious dystopia was closer to the truth of slavery than the nostalgic _Gone With the Wind_ of a generation earlier, in which slaves were never sold and captive women loved their masters' children more than their own. But much is missing from _Mandingo's_ fetishistic gaze.\n\nA generation of scholarly search has turned up no confirmed documentation of plantations devoted exclusively to breeding slaves, and some scholars have concluded they did not exist as such.\n\nThere is a compelling reason why such a plantation wouldn't make economic sense: human beings grow too slowly to raise them as a cash-producing monocrop. The overwhelming majority of the enslaved on such a plantation would be children, but children brought very little money on the market, so they would have to be raised to maturity. Meanwhile, most of the adults would have been women weakened from pregnancy, so the farm would not be able to produce income from the sale of staple commercial crops. It would take seventeen to twenty years of raising the farm's children until they reached peak sale age, adding up to a huge barrier to entry for all but the very well capitalized.\n\nSome farmers seem to have tried it. Drawing on a data sample from 1860 on farms in the Deep South\u2014not even including the major slave-selling states of Virginia and Maryland\u2014of 9,185 enslaved women between the ages of fifteen and forty-four and of 9,098 men, the economist Richard Sutch in 1972 identified forty-seven \"suspected breeding farms\" on which enslaved women and children substantially outnumbered enslaved men. A farm in Drew County, Arkansas, had only two men but twenty-two women and twenty-seven children. Another in Wake County, North Carolina, counted 28 men, 38 women, and 120 children. Michael Tadman, whose _Speculators and Slaves_ is the landmark study of the demographics of the interstate slave trade, suggests that there might be other explanations for the gender imbalance of Sutch's data; \"abroad marriages\" to another plantation, for example, were common, though it seems unlikely that that could explain away the Drew County farm. The meaning of Sutch's data, suggestive as it is, remains within the realm of speculation. But perhaps the most plausible explanation for the Drew County farm is that it _was_ a slave-raising plantation, possibly relying on what several Federal Writers' Project interviewees called \"stock\" men\u2014\"portly\" men who were used as studs for large numbers of women, as dramatized in _Mandingo_ , and who did not have to do as much fieldwork.\n\nThere is some testimony\u2014although not a lot\u2014from diverse parts of the South that at least a few such \"breeding men\" existed. Jeptha Choice, born in 1835 in Texas, noted that (as transcribed) his \"master was mighty careful about raisin' healthy nigger families and used us strong, healthy young bucks to stand the healthy nigger gals. When I was young they took care not to strain me and I was as handsome as a speckled pup and was in demand for breedin'. Later on we niggers was 'lowed to marry.\" West Turner of Whaleyville, Virginia, told of a \"stud man\": \"Joe was 'bout seven feet tall an' was de breedinges' nigger in Virginia. Didn't have no work to do, jus' stay 'round de quarters sunnin' hisself 'till a call come fo' him.\" Ida Blackshear Hutchinson, born enslaved in Alabama in 1865 and interviewed in Arkansas in 1937, recalled family lore:\n\nMy grandfather on my father's side, Luke Blackshear, was a \"stock\" Negro... six feet four inches tall and near two hundred fifty pounds in weight.... Luke was the father of fifty-six children and was known as the GIANT BREEDER. He was bought and given to his young mistress in the same way you would give a mule or colt to a child. Although he was a stock Negro, he was whipped and drove just like the other Negroes.\n\nThere was one particularly horrible kind of operation in which this kind of slave breeding would have been profitable, and it appears to have been an inspiration to Onstott, who as a teenager met \"Uncle Bob\"\u2014Robert Wilson, the direct inspiration for his character of Mede the Mandingo.\n\nAccording to Wilson's April 12, 1948, obituary in the _Elgin (IL) Daily Courier-News_ , the accuracy of which we could not independently verify, he was 112 years old when he died in the Elgin State Hospital for Veterans and was a black veteran who had served in the Virginia Infantry\u2014which was to say, the Confederate army\u2014in 1862 and 1863. (There are already two unusual, perhaps suspect, features to this story: Wilson's extreme longevity, and the very rare situation of a black soldier in the Confederate army.) The obituary did not mention Wilson's local-legend status for allegedly having fathered hundreds of children at different plantations, but Wilson himself talked about it freely. While it's not possible to confirm or deny Wilson's tales of being used vocationally as a rapist of enslaved women, it's clear that: 1) Onstott did not make Wilson or his story up; 2) Wilson told his story to a number of people; and 3) there are mentions, albeit not very many, in oral histories from diverse locations in the South of such stock men. Certainly there was no reason that such an arrangement could not be put into practice, and it is consistent with the dehumanizing logic of the slave market.\n\nIllinois journalist-historian Jon Musgrave fills in some details: though it was not legal to own slaves in Illinois, people did. Moreover, slaves were rented (or \"hired\") from Kentucky, sometimes more than a thousand of them, to work in the saltworks near Shawneetown. The Carolina-born John Hart Crenshaw, who began working as a young man in the violent, lawless environment of the saltworks, apparently raised his capital to get into business by kidnapping free people of color and illegally selling them away. He subsequently leased saltworks from the US government and became a very wealthy man, renting large numbers of slaves to do the brutal work of saltmaking.\n\nOver a criminal career that lasted from the mid-1820s (when he was indicted for kidnapping) until secession, Crenshaw appears to have kidnapped hundreds of free black people, including in 1842 his cook Maria Adams and seven or eight of her children, whom he sold for $2,000 to John G. Kuykendall, a slave trader based in the then-independent Republic of Texas, and his father, Lewis. He was said to have kept his victims in holding-pen cubicles on the upper floor of his mansion called Hickory Hill\u2014still standing today and known as the Old Slave House\u2014outside the ironically named town of Equality, Illinois.*\n\nAccording to Musgrave (and Onstott, who wrote an article about it in the October 1959 issue of _True: the Men's Magazine_ ), that's where Robert Wilson came in. Crenshaw purchased Wilson, apparently in Virginia at the age of twenty in 1856. He put him to work, so goes the story, to impregnate the women held captive at Hickory Hill\u2014a vocation Wilson claimed to have performed previously on other plantations\u2014either to sell the children into a record-high market or because pregnant women and mothers brought a higher price than women whose reproductive abilities had not been proven. That Crenshaw was a kidnapper-trader and that Wilson was Crenshaw's captive between 1856 and 1859 seems to be well established. Was the third floor of Hickory Hill a rape room, or was that a lurid tall tale?\n\nPerhaps this problematic, unverifiable, but possibly true story became the basis of a mega-bestseller in segregated 1957 because its narrative lent itself so conveniently to stereotypical libels of the black male and the black family. Although women, who had to do both field work and bear children, were doubly enslaved, it bears emphasizing that forced mating was a violation of enslaved men as well. The evidence\u2014and common sense\u2014suggests that enslaved men and women overwhelmingly worked as partners when they could and were emotionally devastated when their marriages were broken by sale.\n\nThat is not the story _Mandingo_ tells. Nor the corollary: forced mating was a violation of the most basic notions of genealogy, which is a basic element of much African religion, and of economic legacy, which is the accumulated consequence of family.\n\nFor all the anecdotal testimony, circumstantial evidence, and creepy local lore, no one has proved with documents the existence of a single full-time specialized slave-breeding farm with a monocrop of fatherless children, much less a network of such farms constituting a supply chain. The best argument, pretty much a clincher, against the existence of such businesses on any significant scale is that there seems to be no mention of them in existing slave traders' letters. If such farms existed, they would have existed to supply traders, and mentions of them would presumably have turned up in traders' records\u2014which, so far, they have not.\n\nSo, to be clear about the subject of our book: we do not contend that slave breeding was conducted by means of businesses specializing solely in human reproduction, though such operations may have occasionally existed. But that doesn't mean slave breeding didn't take place on a broad scale, only that it wasn't practiced as an isolated profession.\n\nSlaves weren't the same kind of cash crop as tobacco or cotton; domestically raised slaves and staple crops functioned together, complementing each other's economic function to bring financial stability to a farm operation. For a farmer, slave breeding commonly functioned as a long-term play to stabilize his finances, while adult slaves' labor produced the price-volatile monocrops that provided cash flow. The proportion of revenue deriving from the sale of crops versus the sale of young people varied from farm to farm. In Virginia and Maryland, where tobacco crops were increasingly poor and wheat needed fewer hands, it appears that many farms needed to raise tobacco in order to grow slaves, rather than the other way around.\n\n_Every_ farm where the enslaved had children was a slave-breeding farm, if only because every newborn slave child increased an estate's net worth. But some farms were net consumers of slaves, as was the case in the rest of the hemisphere, where the enslaved died more often than they were born: in the United States, the rice plantations of South Carolina and Georgia and the sugar plantations of Louisiana were slave-consuming areas. And there was a conversion cycle: as new land was cleared and farms established, territories that formerly bought slaves from settled areas joined the growing ranks of sellers of slaves to the frontier, becoming slave breeders instead of slave consumers. Slave breeding was premised on continual expansion.\n\nIt is unsurprising that a planter who denied the humanity of the people he held captive for life would have thought of his laborers as breeding stock. Farms were, and are, all about increase: the creation and sale of a surplus. A handful of seeds brought bushels, out of which a farmer fed his family and sold or bartered the surplus for things he could not produce. Animals were expected to perform reproductively: mares, heifers, sows, nanny goats, or ewes that did not breed were sold off or were eaten by the family as a matter of basic farm management. The stallion, bull, boar, billy goat, or ram that didn't do its job would suffer the same fate. Runts were killed without a second thought so that the mother's nourishment could go to the stronger offspring. Slaves, whose legal status was comparable to that of livestock, were expected to provide a farm owner with marketable children.\n\nThere are occasional mentions of inducements for women who hit a procreation target: a frock, a piglet, a few weeks off from field labor. Before laws prohibiting manumission were passed, the grand prize was emancipation, as in John Guthrie's 1761 will in Virginia, which stipulated that \"if Jeany brings ten live children\" she would be freed.* Slave breeding was premised on continual expansion.\n\nBut the real incentives were negative. \"I have known a great many negro girls to be sold off, because they did not have children,\" wrote an unnamed slave owner to Frederick Law Olmsted. The girl who tried to refuse being bred might be beaten, and, in the end, the girl who wasn't a \"good breeder\" could expect to be sold south, which was commonly understood to be the worst thing that could happen. There she would work among strangers under an overseer's lash in the cotton fields, or finish out her life after a few years on one of Louisiana's sugar plantations.\n\nIf, however, she was a good breeder, her children would suffer that fate instead.\n\nBreeding seems to have been something of an obsession for men of property, who wanted to create the fastest horses, the best dogs, the cotton bolls that most perfectly fit the human hand, and the strongest slaves. From African slave raids forward, marketing people was a process of selection for desirable traits as well as survival of the fittest, with clear eugenic implications.\n\nSome oral histories recall eugenic practices by slaveowners. Eighty-two-year-old Charlotte Martin, interviewed in Live Oak, Florida, recalled, as summarized by the interviewer, that her captor, Judge Wilkerson, \"selected the strongest and best male and female slaves and mated them exclusively for breeding. The huskiest babies were given the best of attention in order that they might grow into sturdy youths, for it was those who brought the highest prices at the slave markets. Sometimes the master himself had sexual relations with his female slaves, for the products of miscegenation were very remunerative. These offsprings were in demand as house servants.\"\n\nHenry H. Buttler\u2014born in Virginia, transported in a group to Arkansas in 1863 to escape Union forces, subsequently educated, and interviewed in Fort Worth, Texas, at the approximate age of eighty-seven\u2014recalled that \"the slaves were allowed to marry but were compelled to first obtain permission from the master. The main factor involved in securing the master's consent was his desire to rear negroes with perfect physiques.\"\n\nAbove all, masters wanted bigger, stronger laborers. The Alabama-born Thomas Johns, interviewed in Cleburne, Texas, at the age of ninety, recalled that\n\nIf a owner had a big woman slave and she had a little man for her husban' and de owner had a big man slave, or another owner had a big man slave, den dey would make the woman's little husban' leave, and dey would make de woman let de big man be with her so's dere would be big children, which dey could sell well. If de man and de woman refuse to be together dey would get whipped hard and maybe whipped to death.... Course even if it did damage de sale of a slave to whip him, dey done it, 'cause dey figured kill a nigger, breed another\u2014kill a mule, buy another.\n\nThe formerly enslaved Cornelia Andrews, interviewed in North Carolina at the age of eighty-seven, recalled a castration policy for eugenic purposes: \"Yo' knows dey ain't let no little runty nigger have no chilluns. Naw sir, dey ain't, dey operate on dem lak dey does de male hog so's dat dey can't have no little runty chilluns.\"\n\nAfrican Americans have been uncomfortably aware of the issue of eugenics all along, as when _Saturday Night Live_ comedian Leslie Jones, responding to _People's_ designation of _Twelve Years a Slave_ star Lupita Nyong'o as the world's \"most beautiful person,\" stirred up a tweetstorm during the May 2, 2014, broadcast with what was surely one of the few mentions of forced mating on network television, let alone in the context of comedy. Nyong'o, born in Mexico City to Kenyan parents\u2014in other words, not descended from American slavery\u2014had recently won the Academy Award for her role in _Twelve Years a Slave_ , in which she was stripped naked and whipped on camera. Jones, from Memphis and descended from slavery, contrasted her large physique with Nyong'o's petite one, drawing on the enduring power of the _Mandingo_ franchise to make her point:\n\nSee, I'm single right now, but back in the slave days? I would have _never_ been single. I'm six feet tall and I'm _strong_! I mean, look at me, I'm a _Mandingo_!... I'm just saying that back in the slave days, my love life would have been way better. Master would have hooked me up with the best brother on the plantation, and every nine months I'd be in the corner havin' a superbaby!\n\nIt was an attempt at transgressive humor: presenting herself as a product of a eugenic process achieved through recursive rape and euphemized as \"love life,\" she hurled the image of the blatantly exploitative _Mandingo_ at the studiedly artistic _Twelve Years a Slave._ After ebony.com senior editor Jamilah Lemieux (among others) took offense at what she saw as Jones's minstrelsy, Jones tweeted back, \"I would have been used for breeding straight up. That's my reality.\"\n\nWhen Sherry George of Birmingham, Alabama, was discovered in 2012 to be a distant white cousin of First Lady Michelle Obama, she responded to the news by saying, \"I'm appalled at slavery.... I know that times were different then. But the idea that one of our ancestors raped a slave... I would not like to know that my great-grandfather was a rapist. I would like to know in my brain that they were nice to her and her children. It would be easier to live with that.\"\n\nHer tormented words express the difficulty of coming to terms with the reality of antebellum American slavery. The idea that one's ancestor was \"nice\" to the people he kept imprisoned has comforted many slaveowner-descended families\u2014and, indeed, some were less cruel than others. But in the days when First Lady Michelle Obama's great-great-grandmother had a child fathered by the slaveowner's son, it was legal nonsense to speak of raping a slave.\n\nTo own a slave was to have a license for libertine behavior, because sexual violation was intrinsic to slavery. The slaveowner had the full legal right to do with his property as he saw fit, and sexual use was part of the portfolio of privileges. The oral-history interviewees described forced mating between the enslaved less frequently than they did sex forced on enslaved women by white men. Perhaps a rough index for quantifying sex between enslaver and enslaved is the census, which in 1860 counted 588,352 \"mulattoes,\" rating them as \"13.25 per cent. of the whole colored class.\" The census also attempted to explain why there were more mulattoes in the free states even though they were increasing faster in the slave states. It concluded that they were more likely to be manumitted (a phenomenon observable in the rest of the enslaved Americas as well): \"the greater number of mulattoes in the condition of freedom has arisen chiefly from the preference they have enjoyed in liberation from slavery.\" The census's summary further noted \"that of every 100 births of colored about 17 are mulattoes, and 83 are blacks,\" then went on to deplore the morals not of the white men who were impregnating captive black women, but of the free colored class.\n\nWith new additions to the gene pool entering via intercourse with white men, an increasing portion of the enslaved population became lighter-skinned with every passing generation. \"The time has passed by when African blood alone is enslaved,\" wrote the formerly enslaved Austin Steward in his 1857 memoir. \"In Virginia as well as in some other slave States, there is as much European blood in the veins of the enslaved as there is African; and the increase is constantly in favor of the white population.\"\n\nNor did enslaved women have legal protection against sexual abuse from enslaved men. In the 1859 case of _George v. the State of Mississippi_ , in which an enslaved man was accused of raping an enslaved female child, the Mississippi supreme court noted that \"a slave can only commit rape upon a white woman\" and held that \"the regulations of law, as to the white race, on the subject of sexual intercourse, do not and cannot, for obvious reasons, apply to slaves; their intercourse is promiscuous, and the violation of a female slave by a male slave would be a mere assault and battery.\"\n\nThere was, then, legally no such thing as the rape of an enslaved woman. A Missouri court effectively affirmed that rape was legally what Saidiya Hartman calls the \"normative condition\" for enslaved women in that state when it sentenced the slave Celia to death in 1855. Celia, who had no last name, was hung for having at the age of nineteen killed the man who had been raping her repeatedly since the day he purchased her at the age of fourteen.\n\nSlaveowners in the antebellum United States enjoyed full legal impunity for any sexual aggression they might commit against their human property. Concubinage with the master, the most privileged form of sexual servitude, tantalized enslaved women with the possibility of better living conditions and perhaps even the prospect of freedom, but it rested on the routine perpetration of atrocities, which often included selling the concubines, along with their children, after a few years. Enslaved concubines bedded down by the master watched their bastard daughters, lighter-skinned by half, grow up to do the same\u2014raised to the office, as it were. The stories mostly went untold. Thomas Jefferson's second-generation family concubine Sally Hemings must have strongly resembled his deceased wife, Martha, since, according to Madison Hemings (Jefferson's son by Sally Hemings), the two women had the same father (the slave trader John Wayles), but there is no portrait extant of either woman, nor did either one leave a record of her thoughts.\n\nIf a slaveowner wanted to enjoy the adolescent daughters of his work force, he had absolute authority over them. No one would say no\u2014not even his wife, who had few legal rights and who had perhaps grown up ignoring her own resemblance to the enslaved half sister who served her.\n\nSlavery was rape. A person who has no right to refuse has no consent to give, so even absent the use of physical force at the moment of the sex act, an enslaved woman could not have consensual sex with a white man. The lack of consent was explained away by what has become known as the Jezebel libel, which characterized black women as incorrigibly licentious, always willing, and irredeemably dishonored from birth.\n\nThe logic of capital required safeguarding the slaveowners' human assets by dividing society into two rigidly defined, inescapable, color-coded castes\u2014one of which was expected to reproduce according to moral protocols, and the other promiscuously. It was a common social understanding that did not need to be explained out loud, though visiting Northerners noticed and commented on it. The intermediate caste of free people of color, so prominent in other slave societies of the hemisphere, was very small in the slave societies of the United States, though in Louisiana and in the small Southern cities in general, their presence was acutely felt.\n\nBut whether a woman was white and respectably married, or black and laboring in the field, she was expected to reproduce as much as possible. Neither woman had the right to say no; Virginia law didn't even recognize spousal rape as a crime until 1986.\n\nJefferson, who by all accounts loved his wife, Martha Wayles Jefferson, dearly, nevertheless bred her to death with repeated pregnancies that killed her. John Quincy Adams nearly did the same: Louisa Catherine Johnson Adams, his cosmopolitan British-born wife, suffered depression and was in chronic poor health from her reproductive regime of fourteen pregnancies (Adams referred to them as \"illnesses\"), in which she miscarried nine times (five of them within the three and a half years before her first live birth). She had one stillborn child and four live children, one of whom died at the age of two.\n\nBut those women at least got to choose their husbands, and their children were not sold. If that was the fate of the wives of the great men of the land, imagine how the lowest of the low fared. The slave narratives give us a glimmering of an idea, but they have to stand in as paradigms for the unheard testimonies of millions.\n\n* _Mandingo_ (1975), starring James Mason; and _Drum_ (1976), starring Warren Oates. Boxer Ken Norton played the title roles of each. Reviewer Vincent Canby described _Drum_ as \"nasty, lascivious, sadistic, mean, rude, evil, and supposedly erotic\" (Talbot, 97, 207).\n\n*Hickory Hill subsequently became a popular tourist stop as a haunted house and has been designated by the National Park Service as part of its Underground Railroad Network to acknowledge the existence of a \"Reverse Underground Railroad\" of kidnappers' networks that funneled people from free territories into slavery.\n\n*Manumission: the voluntary freeing of an enslaved person by his or her captor.\n\n#   4\n\n# **Natural Increase**\n\n_One of slave trader Austin Woolfolk's early advertisements._ Baltimore Patriot and Mercantile Advertiser, _June 27, 1817._\n\nCASH FOR NEGROES, shouted the advertisements that ran in the newspapers of Virginia and Maryland.\n\nThe ads were running as early as 1810, but the War of 1812 brought them to a temporary halt. After the Battle of New Orleans in January 1815 put a final victorious stamp on the war that had ended before the battle was fought, they proliferated as the economy began a ferocious expansion. An 1818 item in the New York\u2014published _National Advocate_ reports traders going around the streets of the Shenandoah Valley town of Winchester, Virginia, with labels reading CASH FOR NEGROES displayed on their hats.\n\nThere was always a market for \"Negroes\" in an expanding country of uncleared agricultural land. The key word was \"cash.\" Slave traders dealt in cash, which could mean specie (silver or gold coins) but typically meant high-quality paper that could be readily exchanged for specie. That made their offers compelling in an environment where \"money\"\u2014almost always meaning not coins, but credit\u2014was otherwise hard to come by. In the antebellum plantation economy, slaves were far and away the easiest property to convert to cash that a farmer might have; when a crop failed or prices dived, slaveowners could cover their debts by selling some of their laborers. Land, by contrast, had little cash value. Traders often sold slaves on time-payment plans, but they paid cash when buying, so they were important financial intermediaries in the Southern agricultural economy, dispensing liquidity as they bought children and enlarging the overall supply of credit\u2014which was to say, of money\u2014through the terms they gave their customers. In other words, staple crops were a credit business, but slaves were a cash business; the Southern economy was the result of the way the two worked together.\n\nAs the United States threw itself into what has been retroactively called the \"market revolution,\" transitioning from commerce based on imports to an ever more broadly based domestic market of producers and consumers, the domestic slave trade was the expression of that movement in the South. Addressing the American Anti-Slavery Society in 1839, Connecticut abolitionist Henry Stanton used the common business-textbook metaphor of cash flow as blood circulation to describe the system that carried human chattels from the Upper South to the expanding Deep South: \"The internal slave trade is the great jugular vein of slavery; and if Congress [would]... cut this vein, slavery would die of starvation in the southern, and of apoplexy in the northern slave states.\"\n\nThe rest of the world was well aware of this commerce. Writing in _Die Presse_ of Vienna on October 25, 1861, the former _New York Daily Tribune_ columnist Karl Marx noted \"the transformation of states like Maryland and Virginia, which formerly employed slaves on the production of export articles, into states which raised slaves in order to export these slaves into the deep South.\"\n\nWe can't quantify the domestic slave trade with any certainty, but we have a rough idea. Local transactions, not interstate trades, were likely the majority of slave sales; Stephen Deyle believes that at least two million people were sold in all, two-thirds of them in local transactions. Tadman declines to put a total number on the interstate trade, but based on Tadman's work Deyle estimates that during the four decades or so prior to the end of slavery in the United States at least 875,000 enslaved people were taken southward, 60 to 70 percent of them trafficked in commercial transactions and the rest brought as a consequence of planter migration. More anecdotally, Illinois-born Frederic Bancroft, the path-breaking historian of the domestic slave trade, wrote in 1921 of trips he took to the \"Southwest\" in 1902 and 1907: \"I made it my business to inquire of every ex-slave I met as to how he or she came South, if not a native. In fully four cases out of five, they were brought literally by the traders.\"\n\nThe southward trafficking of domestically raised slaves from what we will call the Upper South (Chesapeake and inland) and the Lower South (Carolina, Tennessee, Georgia) down into the \"Southwest,\" or Deep South (western Georgia, Alabama, Mississippi, Louisiana, Arkansas, Texas), accompanied by a flow of money in the opposite direction, bound these distinct geographical regions together into a commercial circuit that made it possible to speak of \"the South\" as a single entity.\n\nThat in turn led members of the Southern elite to imagine themselves leaders of a nation built on the economic system of slavery, which thrived with a balance of cash crops and human property value. In the widely reproduced March 1861 words of Alexander Hamilton Stephens, the exultant, newly named vice president of the Confederate States of America, slavery was \"the chief stone of the corner in our new edifice.\"\n\nAntebellum slavery was, in Gavin Wright's essential phrase, \"a set of property rights.\" In a collision of the ancient institution of slavery with free-market capitalism, the modern nineteenth-century American slavery industry made laborers into financial products: merchandise, cash, productive capital, collateral, and, even, at the end of the chain, bonds.\n\nBesides working for the people who legally owned them, the enslaved could be \"hired\"\u2014rented\u2014out, generating an income stream that could pay off a mortgage on them. \"Negroes are a kind of capital which is loaned out at a high rate, and one often meets with people who have no plantation, but who keep negroes to let and receive very handsome sums for them every month,\" wrote a German visitor to Savannah in 1860. Enslaved children were often rented out, among them Frederick Douglass.\n\nBut revenue from slave labor was only part of the profitability of slavery. Selling slaves was part of the commerce at every little Southern junction. Most farmers who had slaves bought or sold them at one time or another. \"In slavery, niggers and mules was white folk's living,\" recalled an unnamed formerly enslaved woman in Tennessee, who said that her former master \"would sell his own children by slave women just like he would any others. Just since he was making money.... My mother sold for $1,000.\"\n\nThe most obvious method of profit-taking in the slave market was by selling one or a few people at a time, as a plantation's younger captives came of age while working on the staple crop with which the farm was at least nominally identified. Typically that crop was tobacco, in the case of Virginia and Maryland; the twin industries of slave raising and tobacco raising went on as complements to each other, but slave raising was for many the more lucrative.\n\nThe sale of surplus laborers wasn't as explosive a cash-flow generator as a bumper crop, but it was more dependable, and the profits were significant. Financial and legal historian Richard Holcombe Kilbourne Jr. writes that \"slaves represented a huge store of highly liquid wealth that ensured the financial stability and viability of planting operations even after a succession of bad harvests, years of low prices, or both.\" Meanwhile, the seller had the important social distinction of being a planter instead of a slave breeder.\n\nBut neither were slaves merely labor to be jobbed out and merchandise to be sold for cash; they were also collateral with which to generate credit. Planters were chronically indebted, perpetually a year behind. They lived on credit, financing their operations with loans to be paid off by next year's crops. The security pledged for such arrangements was most commonly the planters' slaves, who were seen by lenders as largely risk-free collateral, even as they provided the labor that made the crop. If the crop failed, the laborers could be seized and sold on the open market. Meanwhile, the debt they collateralized added to the wealth of the slaveholding South; it was bundled into bonds that were sold to investors in New York, London, and beyond.\n\nThe financialization of enslaved people made them fundamental to the economy of the credit-driven slave society. The value of slaves, said James Gholson in the great Virginia slavery debate of 1832, \"regulate[s] the price of nearly all the property we possess.\" Children born into slavery, blandly referred to as \"increase,\" were capital assets at birth. They were the only way a planter's assets could grow as inexorably as his debts compounded.\n\nWith human capital shoring up balance sheets as collateral for mortgages in a heavily indebted society, reproductive potential was factored into the price of enslaved women as part of a farm's value as assessed by creditors. A slaveholder wrote to Frederick Law Olmsted that \"a breeding woman is worth from one-sixth to one-fourth more than one that does not breed\"; the ratio would presumably have been higher had women not died in childbirth so frequently.\n\n\"Planters mortgaged their plantations, livestock, and slaves,\" writes Russell R. Menard of the colonial Lowcountry, \"to expand their estates by purchasing additional land, livestock, and slaves.\" Most of this value was in the slaves, who as human collateral were constantly exposed to the risk of sale away from their families and community.\n\nThat's how Thomas Jefferson funded the renovation of Monticello, by mortgaging the labor force that did the work. After he died in debt, his laborers were sold at auction. Often the decision was out of the slaveowner's hands. In Jefferson's case, the bitter end took the form of an estate liquidation after his death, so he never saw the human consequences of his impractical showpiece mansion and his extravagantly acquisitive ways: families separated forever on the auction block.\n\nMuch like a house mortgaged to a bank today, mortgaged slaves were security for those who put up the money for the mortgage, to whom the slaves were \"conveyed.\" A mortgage financier might be a merchant, a church with an investment portfolio, a college, a bank, or, commonly, a wealthy individual with a large slavehold. A slave put up for sale had to be warranted not only of \"good character\" (not criminal-minded or rebellious) but \"free of all incumbrance\" (not already mortgaged). Slaveowners had physical possession of, and legal title to, the enslaved, but to speak only of the slaveowners is to underestimate how broad was the stakeholding.\n\nIt is common today to hear people protective of the antebellum legacy go on the defensive by pointing out that the North profited from slavery too.\n\nCertainly people and businesses in the North profited from slavery. Northern slaveowners sold off slaves to the West Indies and the South as slavery was ending in their territories, cashing in and diffusing their black population southward, though the numbers were tiny compared with those of the Chesapeake. New York monopolized the shipping of plantation products across the Atlantic. Northern banks captured the credit and foreign exchange generated by slave-driven agriculture, and bought and resold bonds collateralized by slaves. Hartford insurance companies, including the still-existing Aetna, sold policies to slave shippers and slaveowners, as Lloyd's of London had done before. After the African slave trade was declared piracy, Northern merchants illegally financed and equipped expeditions to supply industrial quantities of African captives to the plantations of Cuba and Brazil.\n\nBut the capital invested in the expansion of the agricultural South does not seem to have mostly come from the North. Slavery created its own distinct circuit in the American economy, since its most valuable commodity, slaves, had no value outside the slavery bloc. By the last three decades of slavery, the South was largely funding itself, or, as Kilbourne puts it, despite the \"despair-filled declarations of Southern commercial boosters and conventions... most of the internal investment in the region was funded with savings that had been accumulated over several generations in numerous wealthy households throughout the Cotton Belt.\" Those \"savings\" overwhelmingly took the form of slaves, who were the basis of this massive intra-Southern credit-circulation system.\n\nThe Constitution gave Congress the power to coin money but in 1804, when Jefferson annexed Louisiana, the only US coins in common circulation were copper pennies. There was a chronic shortage in the South of \"Spanish dollars\"\u2014the silver _pesos_ minted in Mexico, also known as \"pieces of eight,\" which were accepted as legal tender in the United States, because until the discovery of gold in California in 1848, there were no large money mines in the United States. What little specie there was in circulation before the Gold Rush was rapidly pulled to the centers of banking in the North and, especially in colonial days, was sucked across the ocean by the manufacturing and commercial heavyweight of the world, Britain. The workhorse of Southern commerce was bank-issued paper money, but it entailed the risk that the bank might fail and it lost its value with distance from the issuing bank.\n\nEnslaved people were the savings accounts. In lieu of coin or trustworthy paper, people were money in the slaveholding South. Most economists will tell you, with variations in the wording, that three conditions must be met for a commodity to be considered money:\n\n1) a means for conducting transactions (\"medium of exchange\");\n\n2) retention of its worth over time (\"store of value\"); and\n\n3) a way to keep accounts (\"unit of account\").\n\nSlaves easily fit the first two criteria. They were a unique kind of money\u2014a \"money thing,\" economists today might call it. They weren't a convenient medium of exchange the way coins were, but coin was rare and when no reliable bank paper was available for a transaction a store debt could be paid with a child, whether through transfer of ownership or hiring out. A slave might be handed over in lieu of a debt from a land purchase or lost to a cardshark as a thousand-dollar bet in a high-stakes game.\n\nSlaves satisfied the second condition of being money as well. As a store of value, they were the most trusted form in which a slaveowner might save his money. They not only retained their value over time by maintaining their value through reproduction, but they increased that value by reproducing frequently, which is why slaveowners insisted on owning the children: people paid flesh-and-blood interest when they reproduced. This was a modern adaptation of an ancient concept, as David Graeber notes: \"in many Mediterranean languages, Greek included, the word for 'interest' literally means 'offspring.'\" Frederic Bancroft wrote that:\n\nA stock-raiser indifferent to enlarging his herd was not so rare nor so absurd as a large planter that did not count the annual births and values that grew with the slave children. This increase alone was conservatively estimated to yield a net annual profit of from five to eight per cent after deducting all losses from age, illness or death. And even careless and spendthrift planters had such a passion to increase the number of their slaves that this human interest was regularly added to the principal, and thus compounded. A slaveholder twenty-five years old having 40 slaves might reasonably hope, without buying any, to become the owner of 150, or perhaps 200, slaves by the time he reached the age of sixty.\n\nIf people were money, children were interest. That's why the rigidly enforced color-coded caste system of slavery offered no path to freedom even over multiple generations: no escape from the asset column could be permitted.\n\nAt first glance, it might seem that slaves didn't satisfy the third condition of being money, a unit of account. They were not what economists call a \"sovereign currency.\" No government accepted them for taxes, duties, fines, licenses, or fees. That honor went to the dollar, a denomination that Thomas Jefferson had (in the absence of any domestic sources of silver) modeled on the Spanish dollar combined with a French-inspired decimal system of cents, all in pointed contradistinction to the British pounds-and-shillings system.\n\nBut in another way, slaves _were_ a unit of account. The white South kept score in slaves. A rule of thumb for estimating a Southerner's wealth was the number of slaves he had. And, as we will discuss, the Constitution's notorious three-fifths clause* was explicitly designed to allow the South to vote that kind of wealth, making slaves a unit of account for what was literally political capital.\n\nBut if slaves were a kind of money, they were a nonconvertible domestic money, usable only inside the slave-trade zone. New York merchants wouldn't accept slaves in payment for manufactured goods from Britain. They did frequently become slaveowners via control of slaves pledged as collateral, but if slaves had to be seized in satisfaction of a debt, they could only be sold in the regions that used slave labor. Since slaves couldn't be used in trade outside the area of their circulation, they defined the economy of the region where they were traded.\n\nFor a money to be continually valuable, it must at times be defended by the government, even if the government is not the issuer. That happened in the case of slavery; Southern politicians were obsessively dedicated to preserving the monetary value of slaves, culminating in the cataclysmic war that ended the slave economy.\n\nOwning people entailed risk: the person claimed as property might die, escape, or rebel. Those possibilities were best absorbed by large fortunes; slave-holding, the ultimate in inequality, was dominated by the wealthy. But taking on risk was essential for those who wanted to grow their fortunes fast. The Southwest was a magnet for high-spirited gamblers, especially in the Jacksonian era of wildcat banks. Young men in the South wanted to get rich _now_ , before they died of some fever or distemper, so they went into cotton, plunging into debt to buy as many slave laborers, plant as much acreage, and get as fast a return as possible, then plow the profits into more land and slaves. But cotton acreage could only expand as fast as labor could be acquired to clear and cultivate it.\n\nThe reason slaves could not legally be created equal was not merely that appropriating one hundred percent of their labor was wildly profitable. Nor was it the many forms of comfort and pleasure they afforded their owners, nor even the owners' routinely expressed fear that if freed, the blacks would do to the whites what the whites had done to them.\n\nIt was that attributing fully human characteristics to the enslaved would have debased the coin of the Southern realm.\n\nThe four million enslaved in 1860 were not merely a labor force; they were the South's capital stock. Fanny Kemble quoted the words of \"a very distinguished Carolinian\" in her 1838\u201339 journal: \"I'll tell you why abolition is impossible: because every healthy negro can fetch a thousand dollars in Charleston at this moment.\"\n\nWhether a slave child was ever sold in the market or not, his or her birth _created_ money, in the form of credit, so the growth to four million enslaved people was in itself an economic expansion. The bottleneck in the creation of this unique form of sentient money was the capitalized womb.\n\nLarge landowners often preferred a strategy of buying slaves whenever they could get a good deal but never selling, whereas smaller farmers were more likely to need to sell an enslaved adolescent for cash to a regional trader's representative. The kingpin of the Jackson-era slave trade, Tennessean Isaac Franklin, grew his fortune by accumulating people, and then put the money they collateralized to work in the credit market of his place and time by lending to smaller fry, whose slaves were in turn pledged to him as collateral. An 1847 accounting of the deceased Franklin's estate valued the infants Andrew, George, Eliza, Larienia, Little Ann, Cynderrilla, Betsy, Shadrach, Sylvia, Lewis Edward, Noah, Isaac, Randolph, Washington, William, another Isaac, Meshac, and Matilda, along with \"an infant child of Tracy Butler,\" at $75 each (more than $2,000 each in 2014 dollars). They were not being priced for immediate sale, but expertly appraised for estate valuation.\n\nOlder slaves were depreciated. Minerva Granger, who had produced nine children while enslaved by Thomas Jefferson, was at the age of fifty-five appraised as being worth nothing. Historian Caitlin Rosenthal explains that planters \"appraised their inventory [of slaves] at market value, compared that with its past market value to assess appreciation or depreciation, calculated an allowance for interest, and used this to determine their capital costs. In a sense they were marking slaves to market.\" The on-paper value of a child increased as he or she survived and grew, picking up around the age of eight, when he or she could begin to do a day's work. The price peaked in the late teens, when the full-grown laborer could do a long day's work and be advertised for sale as a \"likely young Negro.\"\n\nThat now-archaic word \"likely,\" ubiquitous in slave sale advertisements, had a cluster of converging meanings: vigorous, strong, capable, good-looking, attractive, promising\u2014in other words, likely to reproduce.\n\n*Article 1, Section 2, Clause 3 of the Constitution, subsequently invalidated by the Thirteenth Amendment, allows for the counting of three-fifths of \"persons bound to service,\" i.e. slaves, in determining a state's representation in the House of Representatives, and, by extension, in calculating representation in the electoral college.\n\n#   5\n\n# **Little Shadows**\n\n_Common sense will tell us, that the consumption of a slave must be less than that of a free workman. The master cares not if his slave enjoy life, provided he do but live... even the soft impulse of sexual attraction is subject to the avaricious calculations of the master. 1_\n\n\u2014Jean Baptiste Say, _A Treatise on Political Economy_ (1803; 1821 translation)\n\nCAPITAL IS USELESS IF it is not being put to work, and slaveholders in every era were diligent in extracting the maximum return from their human capital.\n\nSlaves were not allowed to be idle. Black men, women, and adolescents worked long days under the punishing sun doing hard labor that would have killed a white man, or so said the white men who expropriated their labor. In cold weather, they shivered in the rain and froze their fingers in the ice and snow.\n\nIn the early days of Chesapeake colonization, working alongside indentured English, Scotch, and Irish paupers and convicts, the enslaved cut down the hardwoods, pulled up the stumps, turfed the slopes of the plantations, and manicured the grounds of the master's estate. They plowed, planted, weeded, harvested, and cured tobacco, rolled it in hogsheads down to docks they had built, and loaded it onto boats that enslaved boatwrights had constructed, piloted by enslaved navigators.\n\nThey fired the bricks with which they built the great houses that they painted, maintained, and staffed. Enslaved laborers built the stone walls, the zigzagging \"worm\" fences, and the roads, barns, sheds, smokehouses, and cesspools, as well as the cabins where they lived, six or eight or ten to a room. They forged the decorative ironwork, made the furniture, and except for hoes, chains, and a few other items, they even made the tools they made everything else with. \"Almost all the implements used on the plantation were made by the slaves,\" recalled Louis Hughes. \"Very few things were bought.\"\n\nThey were most commonly employed in repetitive monocrop farming, the kind that is most destructive to the land. Every future Confederate state except Virginia raised quantities of cotton, and there were regional monocrops of tobacco in the Chesapeake, rice in the Sea Islands and Tidewater of South Carolina and Georgia, and sugar in south Louisiana. From London, Karl Marx succinctly described the practice in an October 25, 1861, newspaper column:\n\nThe cultivation of the Southern export articles, cotton, tobacco, sugar, etc., carried on by slaves, is only remunerative as long as it is conducted with large gangs of slaves, on a mass scale and on wide expanses of a naturally fertile soil, that requires only simple labor. Intensive cultivation, which depends less on fertility of the soil than on investment of capital, intelligence and energy of labor, is contrary to the nature of slavery.\n\nOn this matter, which was more or less conventional wisdom, Marx agreed with his ideological adversary the _Economist_ , which had printed in 1859:\n\nThe truth is, that Slavery _could_ only be profitable on rich, large, and sparsely populated soils. The profit it yields it can only yield while the first fertility of a soil is unexhausted, and, therefore, where land is unsettled, and the labour need not be of a very earnest or skilful kind.\n\nWhen utilized this way, slave laborers were known for being utterly unenthusiastic workers. In some plantation regimes, the work was deliberately kept heavy so as to leave the labor force too tired to revolt. A note accompanying a hoe on display at Edisto Island Museum explains: \"Until after the Civil War, even large tracts of land on Edisto were cultivated primarily by slaves using hoes, not animal-drawn plows. With the natural increase in the slave population, it was considered 'good management' to keep the work force as busy as possible.\"\n\nPerhaps neither Marx nor the _Economist_ realized that slaves' labor was not only crude. They brought a wide variety of expertise to skilled work. Enslaved craftsmen were the artisan class of both the colonial and the antebellum South. They helped build the White House and the US Capitol. Their knowledge, together with the forced labor of enslaved muscle, transformed forest, bramble, and swamp into the Anglo-American idea of civilization.\n\nPlanters and merchants arranged for their particularly talented artisans to be taught special skills by European craftsmen, which had the side effect of establishing a knowledge base among the community of the enslaved. It enhanced their monetary value: slaves deemed to be \"skilled\" brought more money in the market for both renting-out and sale. They worked as mechanics and tradesmen, discouraging white tradesmen from immigrating. Skilled slaves did cabinetry, woodworking, ironworking, tailoring, dressmaking, and jewelry-making; they were usually better than white craftsmen, if only because white craftsmen, if they were any good, often quit their trade as quickly as possible to go into planting rather than compete economically with slaves, or bought a slave to do the work for them.\n\nKnowledge from Africa was basic to planters' fortunes, nowhere more than in the cultivation of rice. In the unhealthy marshes of the Lowcountry of South Carolina and Georgia, teams of enslaved laborers with interconnecting jobs\u2014specialized task labor, not gang labor like cotton\u2014operated complex plantations they had built with skills that were unknown to Europeans. They did this mostly in the absence of the masters, who fled their plantations in mortal fear of disease during the hot months, leaving only an overseer to run an all-black plantation.\n\nThe great rice plantations of the Lowcountry could never have been built and staffed with free labor. No one would have done that work voluntarily. Attacked by clouds of stinging insects in rattlesnake-ridden swamps, the rice slaves built dams, dug miles of ditches, burned the ground cover in spectacular nocturnal conflagrations, pulverized the earth, spent their days standing barefoot and waist-high in foul-smelling stagnant water, hoed endless rows of rice, regulated how much of the heavier salt water versus how much of the lighter fresh water to allow into the sluice gates they had designed and built, chased away the thick flocks of migrating bobolinks that could devastate a crop, winnowed the rice in baskets they had woven according to African practice, pounded the husks off with African-style tall pestles in mortars, and cut and hauled wood to build the barrels with, while also raising or catching much of the food they ate.\n\nThe homes of the enslaved brought little comfort after the work day. Josiah Henson, who published several iterations of his autobiography\u2014the bestselling of the slave narratives, because Henson was said to be the inspiration for Harriet Beecher Stowe's character of Uncle Tom\u2014recalled in the earliest (1849) and possibly most accurate version that:\n\nOur lodging was in log huts, of a single small room, with no other floor than the trodden earth, in which ten or a dozen persons\u2014men, women, and children\u2014might sleep, but which could not protect them from dampness and cold, nor permit the existence of the common decencies of life. There were neither beds, nor furniture of any description\u2014a blanket being the only addition to the dress of the day for protection from the chillness of the air or the earth. In these hovels were we penned at night, and fed by day; here were the children born, and the sick\u2014neglected.\n\nOld age was especially miserable for the enslaved. When Jefferson's slaves got too old to work, he routinely cut their rations in half. Aged slaves were a drag on a planter's profits, at which point it was cheaper to turn them loose and let them die off premises. The Virginia code of 1849 provided a fine of fifty dollars for \"any person who shall permit an insane, aged or infirm slave... to go at large without adequate provision for his support,\" which perhaps attests to how common the practice was. Isaac Mason, born enslaved in 1822 in Kent County, Maryland, recalled in his memoir that\n\nMy grandfather, in consideration of his old age and the time being past for useful labor, was _handsomely_ rewarded with his freedom, an old horse called the \"old bay horse\"\u2014which was also past the stage of usefulness\u2014and an old cart; but, alas! no home to live in or a place to shelter his head from the storm. (emphasis in original)\n\nThey labored and reproduced and died and were replaced, without retaining the proceeds of their labor for their own needs, while the people who claimed to be their owners generally spent as little as possible on their maintenance. Field laborers, who had little or no direct contact with the master and his family, wore rough, cheaply manufactured \"negro shoes,\" and covered their bodies with osnaburg, or \"negro cloth,\" of jute or flax, a little softer than burlap. George White of Lynchburg, Virginia, recalled that \"Dat ole nigger-cloth was jus' like needles when it was new. Never did have to scratch our back. Jus' wiggle yo' shoulders an' yo' back was scratched.\" They perhaps, but not necessarily, got summer and winter varieties. \"Do you recollect that you have not given your Negroes Summer clothing but twice in fifteen years past[?]\" wrote Georgia Sea Island plantation manager Roswell King to his boss, Constitution framer and absentee gentleman farmer Pierce Butler, at Butler's mansion in Philadelphia. Thomas Jefferson's captives got one blanket per family every three years, but when Monticello was leased out during his presidency, an overseer failed to distribute blankets for five years.\n\n_Isaac Mason's author photograph._\n\nThey did hard labor in the same clothes all day, every day. When 225 enslaved people asserted their freedom by escaping into the custody of British rear admiral George Cockburn during his invasion of the Chesapeake in the War of 1812, Cockburn feared that the dirty rags they came clothed in might spread disease. He issued the men bright red jackets, which, said his commanding officer, Admiral Alexander Cochrane, might \"act as an inducement to others to come off,\" and he gave them military training, which they had previously been kept away from.\n\nSometimes they worked without clothes at all. Enslaved children and sometimes even post-pubescent adolescents commonly were naked or barely clothed. Charles Ball recalled his first workday in a South Carolina cotton field after being trafficked from Virginia:\n\nMore than half of the gang were entirely naked. Several young girls, who had arrived at puberty, wearing only the livery with which nature had ornamented them, and a great number of lads, of an equal or superior age, appeared in the same costume.... [O]wing to the severe treatment I had endured whilst traveling in chains, and being compelled to sleep on the naked floor, without undressing myself, my clothes were quite worn out, I did not make a much better figure than my companions; though still I preserved the semblance of clothing so far, that it could be seen that my shirt and trowsers had once been distinct and separate garments.\n\nDenied basic hygiene, the laborers' funk bothered masters enough to become a conversational commonplace among slaveholders, who typically attributed it to a racial characteristic, referring if necessary to Thomas Jefferson's racist pseudo-factbook _Notes on the State of Virginia:_ \"they secrete less by the kidnies, and more by the glands of the skin, which gives them a very strong and disagreeable odour.\"\n\nEnslaved women made the soap the slaveowner washed with. They carded, combed, spun, weaved, knitted, cut out, sewed, mended, washed, starched, and ironed the fine clothes the master's family wore, and they worked into the night after a long day's labor to dress their own families a little better, though at times there were difficult to enforce laws that forbade slaves from dressing above their station. Domestics, who were on display to guests, typically dressed much better than field laborers, often in hand-me-downs of the master or mistress.\n\nIn eighteenth-century Maryland, liveried coachmen drove the imported \"chariots\" in which the masters rode. In wealthy antebellum Mississippi, they wore velvet topcoats in the heat as they drove the masters' barouches. Enslaved blacksmiths forged iron shoes for the horses that enslaved grooms put up at night. Enslaved fiddlers played at the Saturday night dances, and when the masters hunted foxes, enslaved houndsmen blew the hunting horns.\n\nThe enslaved brought to the masters' table the food they supplied and prepared, and they kept everything the guests saw spotless, all on an unforgiving schedule. Urban slaves generally had a better diet than those on the plantations, and African Americans seem to have generally eaten better than slaves did on Antillean sugar plantations. But the quality and availability of food varied sharply from plantation to plantation, and most had an insufficient diet by modern standards.\n\nThe enslaved laborers who built the University of Virginia were fed the basic slave diet: greasy fat bacon and cornmeal, purchased in industrial quantities. A hogshead of bacon could weigh 900 pounds or more, and plantations bought commensurate quantities of molasses. \"Some slaves enjoyed a wide variety of foods,\" write Kenneth Kiple and Virginia King, \"[but] others suffered from a seldom if ever supplemented hog-and-corn routine, while most existed on a basic meat-and-meal core with some supplementation.\" That monotonous diet of \"hominy and hog\" was the mainstay for the enslaved, as well as for poor whites, in much of the South, though the enslaved of the Chesapeake and Lowcountry generally ate better than those in the Deep South. Unfortunately, the Southern-raised white corn, the most commonly eaten variety, contained no vitamin A. Milk was in short supply in the South, so the enslaved often got little or no calcium. They shocked doctors with their high rate of geophagy\u2014eating clay or dirt, a malnutrition-related behavior especially associated with pregnant women\u2014which caused a range of health problems. Arguing in favor of feeding the enslaved in a way he considered adequate, the overseer Roswell King Jr. of Butler Island, Georgia, wrote of the plantation's 114 enslaved children in an 1828 letter published in the _Southern Agriculturalist_ that \"it cost less than two cents each per week, in giving them a feed of Ocra soup, with Pork, or a little Molasses or Hommony, or Small Rice. The great advantage is, that there is not a _dirt-eater_ among them.\"\n\nBlack cooks knew how to work with the animal parts the master's family didn't want\u2014the offal\u2014and they also knew how to prepare grand Christmas feasts. It was common for the enslaved to tend a garden patch after a long day of work, and Sundays, usually a day off, could be spent hunting or fishing if owners allowed it. But even so, slaves were often malnourished and therefore sickly; the typical food expenditure for an enslaved laborer in Virginia was about a quarter that of a free laborer. Henry Watson, born in 1813 near Fredericksburg, Virginia, who was sold six times and whose experience was especially harsh, recalled the routine he knew in 1820s Mississippi:\n\nIn the morning, half an hour before daylight, the first horn was blown, at which the slaves arose and prepared themselves for work. At daylight another horn was blown, at which they all started in a run for the field, with the driver after them, carrying their provisions for the day in buckets.... [They] worked until such time as the driver thought proper, when he would crack his whip two or three times, and they would eat their breakfasts, which consisted of strong, rancid pork, coarse corn bread, and water, which was brought to them by small children, who were not able to handle the hoe.\n\nAs soon as Harry, the driver, has finished his breakfast, they finish likewise, and hang up their buckets on the fence or trees, and to work they go, without one moment's intermission until noon, when they take their dinner in the same manner as their breakfast; which done, they go again to work, continuing till dark. They then return to their cabins, and have a half hour to prepare their food for the next day, when the horn is again blown for bed. If any are found out of their cabins after this time, they are put in jail and kept till morning, when they generally receive twenty-five or thirty lashes for their misdemeanor. (paragraphing added)\n\nCharles Ball recalled a scene he witnessed while accompanying his master on travels in South Carolina:\n\nAfter it was quite dark, the slaves came in from the cotton-field, and taking little notice of us, went into the kitchen, and each taking thence a pint of corn, proceeded to a little mill, which was nailed to a post in the yard, and there commenced the operation of grinding meal for their suppers, which were afterwards to be prepared by baking the meal into cakes at the fire.\n\nThe woman who was the mother of the three small children, was permitted to grind her allowance of corn first, and after her came the old man, and the others in succession. After the corn was converted into meal, each one kneaded it up with cold water into a thick dough, and raking away the ashes from a small space on the kitchen hearth, placed the dough, rolled up in green leaves, in the hollow, and covering it with hot embers, left it to be baked into bread, which was done in about half an hour.\n\nThese loaves constituted the only supper of the slaves belonging to this family for I observed that the two women who had waited at the table, after the supper of the white people was disposed of, also came with their corn to the mill on the post and ground their allowance like the others. They had not been permitted to taste even the fragments of the meal that they had cooked for their masters and mistresses. (paragraphing added)\n\nSlave cabins did not have kitchens; cooking, if done indoors, was done in the fireplace. On some plantations children were fed out of troughs, eating with their hands or improvised spoons out of a communally served mush of corn-bread, molasses, or whatever else was customary.\n\nBeginning with maternal, fetal, and infant malnutrition, it's hardly surprising that the enslaved were more susceptible than free people to most infirmities, including crib death, infant mortality of all kinds (including infanticide), death in childbirth, and injuries and deterioration to the mother from repeated childbirth, along with typhoid, cholera, smallpox, tetanus, worms, pellagra, scurvy, beriberi, kwashiorkor, rickets, diphtheria, pneumonia, tuberculosis, dental-related ailments, dysentery, bloody flux, and other bowel complaints. The health conditions of the enslaved were aggravated by overwork, accidents, and work-related illnesses such as \"green tobacco sickness,\" today known as nicotine poisoning, which plagued tobacco workers. The heavy work regimes they endured wore down their bodies and aged them prematurely, with childbirth-related fatalities limiting women's life spans even more than the men's.\n\nThe enslaved had a greater immunity to some diseases than the whites, though: the sickle-cell trait is believed to have evolved as a defense against malaria, to which many of the enslaved were immune, though they might become ill from sickle-cell disease. Some Africans were also immune to the yellow fever that on occasion killed large numbers of whites in fierce epidemics.\n\nAfricans brought a vast lore of medicines (and poisons) from Africa, and on occasion learned the use of local herbs and roots from the Native Americans. Attentive slaveowners learned from the medical knowledge of the enslaved, as in the case of smallpox vaccination, which spead in the hemisphere through the knowledge of Africans. In colonial Boston, Cotton Mather heard of smallpox vaccination from the enslaved Onesimus, whom Mather's congregation had given him as a present: \"Enquiring of my Negro-man _Onesimus_ , who is a pretty Intelligent Fellow, Whether he had ever had ye _Small-Pox_ he answered, both, _Yes_ , and, No; and then told me, that he had undergone an Operation, which had given him something of ye _Small-Pox_ , & would forever preserve him from it.\" Onesimus had been vaccinated for the disease in Africa, and told Mather it was a common practice among the \"Gurumantese\" (Akan or Twi people of the Gold Coast, now called Ghana), \"& who ever had ye Courage to use it, was forever free from ye fear of the Contagion. He described ye Operation to me, and shew'd me in his Arm ye Scar, which it had left upon him.\"\n\nEspecially in colonial days, slaveowners sometimes doubled as doctors. William Byrd II, the founder of Richmond, had a large medical library and gave his enslaved frequent \"vomits\" and \"purges.\" The enslaved were used as guinea pigs for experimental treatments that advanced the practice of medicine in the United States. An aspiring doctor or dentist in the South might buy an old or infirm slave to practice on. The nation's first teaching hospital, at the Medical College in Charleston, used live enslaved people for demonstrations and dead ones for dissection. The \"father\" of modern gynecology, generally portrayed in medical historiography as an innovative figure, was the South Carolina surgeon J. Marion Sims, whom one historian refers to as \"the Architect of the Vagina.\" Sims refined his innovations by operating experimentally on the genitals of enslaved women he kept for that purpose. In this way, he developed a surgical repair for vesico-vaginal fistulas, using an infection-resistant silver suture, and more generally he popularized the use of surgery for gynecological problems, becoming quite wealthy in the process. In a \"hospital\" he built in his backyard in Montgomery, Alabama, he operated on a woman named Anarcha thirty times, sewing her insides without anesthesia and giving her opium afterward. He also kept women named Lucy and Betsy for this purpose, describing the expense of their maintenance as a research cost. After perfecting his treatment, he subsequently moved to New York, where he founded the Woman's Hospital and continued experimenting surgically; since there was no slavery in New York, he practiced on poor Irish women, performing thirty surgeries on one Mary Smith.\n\nLater, there was an entire lucrative branch of \"slave medicine\" dedicated to \"negro diseases,\" in which naming a disease could be the road to prestige and higher fees for a physician. The Virginia-born Dr. Samuel A. Cartwright described at a professional conference a medical condition he had discovered called _drapetomania_ , in a paper reprinted in _DeBow's Review_ in 1851. Drapetomania's victims were \"Negroes,\" and its chief symptom was an irresistible urge to run away. When milder therapy failed, Dr. Cartwright prescribed \"whipping the devil out of them.\" He also described another purported disease, _dys\u00e6sthesia \u00e6thiopica_ , or \"hebetude of mind,\" whose symptom was commonly described by overseers as \"rascality,\" and which was \"much more prevalent among free negroes living in clusters by themselves, than among slaves on our plantations, and attacks only such slaves as live like free negroes in regard to diet, drinks, exercise, etc.\" Dr. Cartwright was serious; the Southern medical profession had taken up the call to demonstrate the purportedly separate and inferior physical and mental characteristics of what was considered to be the \"Negro race.\"\n\nSlaveowners had the power of life and death, and despite slaves' monetary value as human property, death came to some from \"punishments\"\u2014torture\u2014and other violence inflicted by the owner or his agents, as Fannie Berry recalled in Petersburg, Virginia: \"sometimes if [you rebelled], de overseer would kill yo'.\" Others committed suicide.\n\nIt was much preferable to be enslaved in town. The urban enslaved generally enjoyed better material conditions than those on the plantation, as well as more independence of movement and association, more chances to make money, and, especially in port towns, a better chance to escape to free territory. Most of the work in Southern towns was done by \"hired\" slaves; the urban South developed in direct proportion to the amount of slave-rental that went on. Such Southern industrial work as there existed was mostly done by the enslaved, who sometimes managed to collect a bit of incentive pay.\n\nRobert S. Starobin estimates that there were between 160,000 and 200,000 industrially employed slaves by the 1850s, 80 percent of them owned by the businesses' owners and the rest rented. Ironworking was heavily dependent on enslaved labor. Slaves mined lead, salt, and coal. Turpentine production, a large industry, was almost entirely done by enslaved laborers. They manufactured rope, tanned leather, baked bread, cut lumber out of the Dismal Swamp till all the trees were gone, and operated gristmills and printing presses. In shipyards and textile mills, they worked side by side with poor whites in a sometimes violently uneasy coexistence that worked to the disadvantage of the enslaved.\n\nEnslaved workers cleaned and repaired Southern streets, laid down turnpikes, and dredged canals. They marked twain, shoveled coal, and sometimes were scalded to death or blown up in boiler explosions on the riverboats, with the more dangerous jobs going to older, less salable men. They built almost all the railroads in the South, as a March 30, 1852, advertisement in the _Southern Recorder_ of Milledgeville, Georgia, illustrates:\n\nIMPORTANT SALE OF NEGROES, MULES, &C. ON THE 27TH DAY OF APRIL NEXT.\n\nThe undersigned having nearly completed their contract on the South Carolina Railroad, will positively sell, without reserve, on TUESDAY, the 27th day of April next, at Aiken, South Carolina to the highest bidder \u2013\n\n130 | NEGROES  \n---|---  \n85 | MULES,  \n3 | HORSES,  \n90 | CARTS and HARNESS,  \n25 | WHEELBARROWS  \n190 | SHOVELS,\n\nRailroad PLOWS, PICKS, Blacksmith's, Carpenter's and Wheel-right's Tools, &c.\n\nThese Negroes are beyond doubt the likeliest gang, for their number, ever offered in any market, consisting almost entirely of young fellows from the age of twenty-one to thirty years, some few boys, from twelve to sixteen years of age, and four women.\n\nAmong the fellows are first rate Blacksmiths, Carpenters, Coopers, Brick-moulders, Wheel-rights and Wagoners.\n\nAmong the women, one excellent Weaver and Seamstress, another one, a good Cook. All well trained and disciplined for Rail and Plank-road working....\n\nTerms Cash. J.C.SPROULL & CO., Aiken, S.C., immediately on the Railroad, 16 miles from Hamburg.\n\nIn the towns and cities no less than on the plantations, virtually all domestic servants were enslaved; a white Southern woman who hired out as a maid had fallen on hard times indeed. In some cities, notably New Orleans and Charleston, enslaved women were major vendors of foodstuffs, whose customers were typically enslaved domestics doing the mistress's shopping.\n\nSlaves learned the hard way to anticipate the master and mistress's slightest wishes. Having their ears boxed would be the least of it; they could be exposed naked to be brutally whipped with a knotted cowhide, leaving their backs and buttocks bloody raw. Slave narratives commonly contain accounts of severe punishment resulting in horrible scarring, maiming, or even death, for minor or even imagined infractions, for domestics no less than for field hands. A single example, selected almost at random from the literature, is J. D. Green's testimony: \"When I was fourteen years old my master gave me a flogging, the marks of which will go with me to my grave, and this was for a crime of which I was completely innocent.\"\n\nWhether the victims were female or male, the torture of the enslaved also had a sexual component. There is little or no documentation of male-on-male intercourse, something unspeakable in that era, but there is much testimony about slaves being stripped naked and flogged, which today we would call sexual abuse. There are many stories of deliberate sadism in the slave narratives. After Henry Watson was trafficked to Natchez, he was sold to a man who beat him daily:\n\nThe first morning I was severely flogged for not placing his clothes in the proper position on the chair. The second morning I received another severe flogging for not giving his boots as good a polish as he thought they had been accustomed to. Thus he went on in cruelty, and met every new effort of mine to please him with fresh blows from his cowhide, which he kept hung up in his room for that purpose.\n\nIsaac Mason recalled that\n\nwhenever I did anything that was considered wrong... I had to go to the cellar, where I was stripped naked, my hands tied to a beam over head, and my feet to a post, and then I was whipped by master till the blood ran down to my heels. This he continued to do every week, for my mistress would always find something to complain of, and he had to be the servant of her will and passion for human blood. At last he became disgusted with himself and ceased the cruel treatment. I heard him tell her one day\u2014after he had got through inflicting the corporal punishment\u2014that he would not do it any more to gratify her.\n\nThe enormous rawhide bullwhips were designed to lacerate; accounts mention whips cutting flesh to bone. Solomon Northup used the word \"flaying.\" \"Many a time I've heard the bull-whips a-flying,\" recalled Lizzie Barnett, a centenarian interviewed in the 1930s, \"and heard the awful cries of the slaves. The flesh would be cut in great gaps and the maggots would get in them and they would squirm in misery.\" These beatings\u2014and other tortures too numerous to mention\u2014could, and occasionally did, kill.\n\nThe enslaved had no right to refuse intimate services to the people who could order them beaten. Harriet Jacobs writes of her great-aunt Nancy, who \"slept on the floor in the entry, near [the mistress's] chamber door, that she might be within call\" through six of Nancy's pregnancies, all resulting in premature births.\n\nSometimes enslaved concubines got special treatment, but sometimes not. Henry Watson's owner had taken an enslaved woman \"to wife\" and had two children by her; she was \"out in the field all the day, and in his room at night.\" James Green recalled that \"de nigger husbands weren't the only ones dat keeps up havin' chillen. De mosters and the drivers takes all de nigger girls day want. One slave had four chillen right after the other with a white moster. Their chillen was brown, but one of 'em was white as you is. But dey was all slaves just de same, and de niggers dat had chillen with de white men didn't get treated no better.\"\n\nThe brutality of forced concubinage took place within the more fundamental brutality of being property: even the nicest master might be forced to pay his debts by selling his favorite slave, along with his children by her.\n\nIt mattered not whether white women disliked this state of affairs, since they had little or no legal standing themselves. The South Carolina plantation mistress Mary Boykin Chesnutt, author of a widely read diary and a good friend of Confederate First Lady Varina Davis, wrote angrily in 1861,\n\n[O]urs is a _monstrous_ system and [full of] wrong and iniquity... Like the patriarchs of old our men live all in one house with their wives & their concubines, & the Mulattoes one sees in every family exactly resemble the white children\u2014& every lady tells you who is the father of all the Mulatto children in every body's household, but those in her own, she seems to think drop from the clouds or pretends so to think.\n\nHarriet Jacobs said it even more bluntly:\n\nSouthern women often marry a man knowing that he is the father of many little slaves. They do not trouble themselves about it. They regard such children as property, as marketable as the pigs on the plantation; and it is seldom that they do not make them aware of this by passing them into the slave-trader's hands as soon as possible, and thus getting them out of their sight. I am glad to say there are some honorable exceptions.\n\nThere is much testimony like that of Savilla Burrell, interviewed at the age of eighty-three in Winnsboro, South Carolina, who recalled (as transcribed) that \"Old Marse wus de daddy of some mulatto chillun. De 'lations wid de mothers of dese chillun is what give so much grief to Mistress. De neighbors would talk 'bout it and he would sell all dem chillun away from dey mothers to a trader. My Mistress would cry 'bout dat.\"\n\nEnslaved women were used for milk extraction, in the common case of wet nurses, or \"sucklers\"\u2014women whose own babies had died or were pushed aside. Isabella Van Wagenen, better known as Sojourner Truth, born enslaved in New York in 1797, was said to have exposed her breasts to a proslavery crowd in Indiana that had questioned her gender while shouting that \"her breasts had suckled many a white babe, to the exclusion of her own offspring.\" Since enslaved women were pregnant so often, there was little need for a slaveowning white woman to feed her own baby, with the result that baby cotton planters grew up sucking from black women's breasts. Nursing women might be lent out to a family member, or rented out to a stranger. In the latter case, the slaveowner was selling the protein and calcium out of the woman's body.\n\nWhile a \"prime field hand\"\u2014young, healthy, strong, and male\u2014was the benchmark of the slave market, the premium-priced captives were young female sex slaves, or \"fancy girls,\" who were light skinned or even passable as white. A teenaged \"fancy girl\" purchasable either for private sexual use or pressed into commercial service by a pimp could bring a multiple of what even a \"prime field hand\" might command.\n\nA number of reports from the later days of slavery mention blond-haired, blue-eyed slaves on sale\u2014the children of enslaved women, despite their phenotype. Fredrika Bremer, the Swedish novelist who visited Richmond in 1851 as part of an extended journey, wrote in her widely read _Homes of the New World_ of visiting \"some of the negro jails, that is, those places of imprisonment in which negroes are in part punished, and in part confined for sale.\" She visited one \"where were kept the so-called 'fancy girls,' for fancy purchasers,\" and yet another where \"we saw a pretty little white boy of about seven years of age, sitting among some tall negro-girls. The child had light hair, the most lovely light-brown eyes, and cheeks as red as roses; he was nevertheless the child of a slave mother, and was to be sold as a slave. His price was three hundred and fifty dollars.\"\n\nThe enslaved caste grew with every generation. Escape, whether by flight or by manumission, was difficult to achieve; the census counted 1,011 escaped slaves in 1850, \"about 1\/30 of one percent\" of the enslaved. People in the Chesapeake might escape to free territory in the North, but in the Deep South, that was practically impossible. The lighter-skinned an enslaved person was, the greater the possibility that he or she might be able to steal away, escape the dragnet that routinely captured unaccompanied black people, and pass for white under a new identity; Thomas Jefferson allowed two of his four children by Sally Hemings to do so, under which cover they disappeared from the historical record.\n\nNotwithstanding the severity of the whippings that occupy such a prominent role in slave narratives, the threat of sale was the most powerful coercive weapon in the slavemaster's arsenal. As Isaiah Butler of Hampton County, South Carolina, put it: \"Dey didn't have a jail in dem times. Dey'd whip 'em, and dey'd sell 'em. Every slave know what 'I'll put you in my pocket, sir!' mean.\" No aspect of slavery was more emblematic of its horror than forced separation of families, which took place regularly and publicly in the theater of the slave auction.\n\nSlave marriages were not binding on the slaveowner, and forced mating was always possible, sanctioned by law and by custom. Even those whose families remained together knew that the fortunes of a slave could change in a heartbeat. The enslaved lived with the knowledge that they or a loved one\u2014a mate, a sibling, a child\u2014might at any moment be removed without warning from their familiar world and taken away from their family without so much as a fare-thee-well.\n\nThe slave trade routinely destroyed marital relationships, along with all other family ties, by selling one or the other partner away. Robert H. Gudmestad estimates that \"forced separation... destroyed approximately one-third of all slave marriages in the Upper South.\" Marriage between slaves was sometimes solemnized and celebrated on the plantation (\"jumping the broomstick\"), but it was a charade: there was no such thing as legal marriage for slaves. As Matthew Jarrett, born in 1848 and interviewed in Petersburg, Virginia, put it, \"don't mean nothin' lessen you say 'What God done jined, cain't no man pull asunder.' But dey never would say dat. Jus' say, \"Now you married.\"\n\nAn individual slaveowner might respect slave marriages, but when he died, the heirs would have to divide up the estate at auction.\n\nMasters often tried not to let slaves know in advance they were going to be sold, since they tended to run away if they knew. They ran away in any case, everywhere there was slavery. Among the many fragmentary song lyrics collected as part of the Federal Writers' Project oral histories, none appears more frequently than _Run, nigger, run \/ Patter-roller* catch you_, a song sung by both white and black in the South. The surveillance society was a reality to African Americans in slavery\u2014not that people didn't run away anyway. Maroons often hid out in their home region, sometimes hiding for years in underground dugouts or hard-to-access places, sometimes returning to the plantation surreptitiously at night for food and on occasion returning to the workforce after negotiating conditions for their return.\n\nMen ran away more than women, who might be gang-raped if caught, as described by the fugitive Lewis Clarke in 1842: \"They know they must submit to their masters; besides, their masters, maybe, dress 'em up, and make 'em little presents, and give 'em more privileges, while the whim lasts; but that ain't like having a parcel of low, dirty, swearing, drunk, patter-rollers let loose among 'em, like so many hogs.\"\n\nMasters grew up with \"little shadows,\" personal child servants who did everything for them, were not allowed to fight back when they were abused, and were in deep trouble if anything happened to their young master. The three-quarters white William Wells Brown was an enslaved \"playmate\" at the age of nine for a five-year-old master to whom he was related. The position carried the privilege of wearing a white linen suit; he had to audition for it against \"some fifteen\" others by doing gymnastics. After the family moved to Missouri, Brown recalled that\n\nWilliam had become impudent, petulant, peevish, and cruel. Sitting at the tea table, he would often desire to make his entire meal out of the sweetmeats, the sugarbowl, or the cake; and when mistress would not allow him to have them, he, in a fit of anger, would throw any thing within his reach at me; spoons, knives, forks, and dishes would be hurled at my head, accompanied with language such as would astonish any one not well versed in the injurious effects of slavery upon the rising generation.\n\nWhen masters became older, they sometimes bet and lost their childhood companions to strangers in card games, or they might be sold to pay an extraordinary expense. In Roswell, Georgia, a town founded by Pierce Butler's former manager Roswell King as a summer refuge for the wealthy, James Stephens Bulloch sold off four enslaved people to pay for his younger daughter Mittie's grand wedding at Bulloch Hall on December 22, 1853. Bulloch did not sell Mittie's personal slave, whose too-appropriate name was Toy. Nor could the \"shadow\" of Mittie's troubled half brother Daniel Stuart Elliott be sold, because Daniel had previously shot and killed him in a fit of temper. But Bess, the attendant of Bulloch's older daughter Anna, was sold together with her son John for $800. Anna, who had no husband and was therefore of no economic importance, subsequently became governess to Mittie's children, one of whom was the future president Theodore Roosevelt Jr.\n\n\"When your marster had a baby born in his family,\" recalled an unnamed formerly enslaved woman in Tennessee, \"they would call all the niggers and tell them to come in and 'see yur new marster.' We had to call them babies 'Mr.' and 'Miss' too.\" If a little white boy with a Roman-numeraled name said up was down, his captive black playmate had better agree. Once the boy was grown into a planter, if he said up was down, who dared correct a man who was accustomed to punishing disagreement with torture? Virtually all of the members of the Southern aristocracy that seceded from the United States grew up with such a regime, going back ten generations for the oldest families among them.\n\nUp became more down with every passing decade, and more incompatible with the outside world. The build out of the slavery ideology became more elaborate, more radical, and more delusional as each generation began from a more doctrinally inbred point of departure. Meanwhile, it became more belligerent, accompanied by a vigilant suppression of dissent.\n\nAntislavery opinions were not to be expressed publicly in the slave states. That was considered traitorous and was repressed with violence that was sometimes spontaneous and sometimes organized. Any perceived slight to the system of slavery could provoke a hair-trigger response. There was not even a pretense of free speech on the subject of slavery in the South, nor did slavery's defenders want anyone in the North to criticize, or even mention, slavery. The enslaved were, needless to say, not to speak against their captivity. They were to be happy, or else. They loved their master, or else.\n\nUnlike Africans\u2014or, more horrifying to slaveowners, the \"French Negroes\" of Haiti\u2014African Americans were believed to be docile, since scrupulous attention was paid to keeping them ignorant of military technique. That was one of the attractions of \"Virginia and Maryland Negroes\" in the market\u2014they had been raised to an unquestioning submission to the work regime, or so it was believed.\n\nThat belief was disproved daily. For all their powerlessness and the almost unimaginable degree of their exploitation, the enslaved were social actors\u2014of course they were\u2014who, despite their great disadvantages, had some ability to negotiate their conditions. They also had the dangerous power that stemmed from slaveholders' fear of them.\n\nRebellions existed wherever there was slavery, in every era, because everywhere, always, the enslaved were at war with their condition. Rebellions happened on the slave ships, on the plantations, and in the towns. Herbert Aptheker, writing in 1943, found \"records of approximately two hundred and fifty revolts and conspiracies in the history of American Negro slavery,\" defining such incidents as involving ten slaves or more and with the intention of obtaining freedom.\n\nSmaller rebellions were ubiquitous. Every runaway was a rebel, and there were runaways at almost every plantation. Often escape attempts were unsuccessful and violently repressed, while others were temporary with a negotiated end, and some were successful and permanent. Twenty-two-year-old Ona Judge, who was Martha Washington's personal servant, escaped from the President and First Lady of the United States in Philadelphia in 1796 after learning she was to be given away as a wedding gift. She married a free black man in Portsmouth, New Hampshire, and managed to avoid falling prey to the attempts at recapture that George Washington attempted against her until he died in 1799.\n\nEvery slave who got into a suicidal, or perhaps murderous, fight with an intolerable overseer was a rebel. Every slave who took something from the master (called \"stealing,\" as if the master were not the one stealing from his captives) was a rebel. Every enslaved person who learned to read was a danger. The now-common term \"day-to-day resistance,\" proposed by Raymond A. and Alice H. Bauer in 1942, expresses the ongoing inconformity of the enslaved with their status.\n\nThe larger rebellions, small though they were in military terms, were extraordinarily effective at bringing the war on slavery forward: the Stono rebellion (1739), the alleged New York conspiracy (1741), Gabriel's conspiracy (1800), the German Coast rebellion (1811), Denmark Vesey's alleged conspiracy (1822), Nat Turner's rebellion (1831), and others were sensational news when they happened. To slaveowners, they were a portent of apocalypse.\n\nMajor foreign wars were also occasions of slave rebellion, though it was folded into the larger context. Collectively the enslaved formed a Fifth Column in every war, siding with those who promised to deliver them from the death-in-life of slavery. In Saint-Domingue, black generals fought with the Spanish against the French, with Toussaint Louverture crossing over to the French once France had declared emancipation in North America. The enslaved of Virginia and points south defected to the British during the War of Independence and again during the War of 1812. Then in 1860 they supported the Union against the Confederacy, first as \"contrabands\" who decamped en masse, and then as soldiers. After they were allowed to fight against the Confederacy pursuant to the Emancipation Proclamation, the war was won.\n\nAbolitionist books and publications by David Walker, Benjamin Lundy, William Lloyd Garrison, Frederick Douglass, and others cast a long shadow. In the eyes of slaveowners, they were multiplied manyfold into a giant \"San Domingo,\" with the aid of demonized figures like John Quincy Adams, William Seward, Salmon P. Chase, and Charles Sumner. This was the much-decried \"Northern aggression,\" whose forces were, in the minds of the South's political class, gathering to swoop down on the defenseless South, when purportedly savage \"Negroes,\" would, it was believed, be let loose to rape, pillage, and kill, with nothing less than the destruction by murder and amalgamation of the white race as their object.\n\nA letter to a Fredericksburg, Virginia, paper in 1800 declared that \"if we will keep a ferocious monster in our country, we must keep him in chains.\" In other words, the omnipresent, entirely legal violence of slavery was an ongoing state of war.\n\n*patteroller = patroller\n\n#   6\n\n# **Species of Property**\n\n_Slavery was not the beautiful state of love and confidence between masters and slaves that we often see pictured in books. 1_\n\n\u2014Judge O. P. Temple, Knoxville, Tennessee, letter to Frederic Bancroft, 1904\n\nSLAVERY WAS THE CENTRAL fact of Southern life.\n\nSlaveowners formed the whole of the Southern political class and controlled Southern governments from top to bottom, with South Carolina the most proudly antidemocratic of all. The pro-slavery plutocracy of 1860\u2014the Slave Power, abolitionists not incorrectly called it\u2014had the full weight of American legal history behind it in claiming as its property 38.9 percent of the people of the slaveholding states (57 percent in South Carolina).\n\nThe legal systems of the Southern states were organized around maximizing slaveholder profit. In the towns, repressing the enslaved population was the principal goal of the policing system, which was not one of beat cops on patrol but of military-style squads that made street sweeps. In Charleston, these sweeps were done nightly by twenty to thirty officers at a time, which required much higher levels of manpower than Northern police forces.\n\nWith their enslaved assets fully capitalized, slaveowners were not merely wealthy; they were spectacularly wealthy. At the time of secession, two-thirds of the millionaires in the country lived in the slave states, with most of their wealth in the form of slaves. The Slave Power became wealthier with every territorial annexation for slavery: new territories meant new slave markets, which jacked up the resale value of existing slaveholdings.4\n\nProtecting and developing enslaved assets\u2014most definitely including reproductive value\u2014was slaveowners' first, second, and third political order of business. With the leisure provided by living on the proceeds of slave labor and in the absence of other profitable ventures in the largely nonindustrial South, they had plenty of time to pursue politics, in which they competed to be the most faithful to the ideal of slavery and its concomitant philosophy of states' rights.* Thanks to the compromises brokered at the Constitutional Convention and to the slaveowners' bloc-voting fraternity, they exercised disproportionate political power at the national level, right up through the collapse of their system.\n\nSlaveowners were an elite within their own geographically and ideologically isolated societies, with those who owned the most slaves at the apex of the social and political order. According to the detailed US census of 1860, which enumerated slaves and slaveholders in its \"Agriculture\" supplement, the 347,525 owners of one or more slaves constituted only 4.3 percent of the 8,039,000 \"whites\" in the fifteen slaveholding states (eleven of which would shortly secede) and 2.86 percent of the population of those states as a whole. If, as Frederic Bancroft did, we count the population of slaveholding families as five times the number of slaveowners, some 14 percent of the population of the slave states were of the slaveholding class. Perhaps one-half of 1 percent of the population of the slaveholding states owned a hundred slaves or more, and a few owned a thousand or more. It has been suggested that the 1860 census numbers might have underreported large slaveowners, but it's unlikely that large slaveholders\u2014again, almost the entire political class of the South\u2014amounted to even 1 percent of the population of their states.\n\nThe South's 1860 population of 3,953,742 enslaved people comprised or made viable an estimated four billion dollars' worth of private property, as per Mississippi's declaration of secession: \"Our position is thoroughly identified with the institution of slavery.... We must either submit to degradation and to the loss of property worth four billions of money, or we must secede from the Union.\"\n\nThis figure, which turns up in other contemporary writings, was an estimate of the South's capitalization. It apparently valued slaves at a blunt average of $1,000 per human being, or maybe something like $800 per human being and $200 for the land he or she worked on. Slaves were not all the property involved in that quick-and-dirty computation, but they were most of it, the rest being land and equipment that Southerners insisted would be valueless without slave labor. Some estimates said three billion dollars, and some said two billion; sporadic sales reports in Southern newspapers during the final years before the war, at the dizziest peak of the market, suggest that a thousand a head for a total of four billion dollars might not have been too high a figure to put on it. At the beginning of 1860, the _Albany (GA) Patriot_ reported an estate liquidation of 536 people\u2014one of the largest slave sales ever\u2014that brought an average price of $1,025 per person sold, making the total sale worth more than $15 million in 2014 dollars. Another estate sale from Columbus brought an average of $1,084. The _Mobile Daily Advertiser_ of January 18, 1860, reported a Mississippi sale with an average price of $1,145.\n\nFour billion dollars in 1860 was equivalent to about a hundred billion in 2010. It was more than 20 times the value of the entire cotton crop that year and 17.5 times all the gold and silver money in circulation in the United States ($228.3 million, most of it in the North). It was more than nine times the $435.4 million of currency in circulation\u2014which, pursuant to the dismantling of the national banking system by President Andrew Jackson, was issued by local banks whose notes depreciated over distance.\n\nFour billion dollars was more than double the $1.92 billion value of farmland in the eleven states that seceded.* Without labor Southern land lost what value it had, but even with labor Southern land in 1860 still was worth much less than land in the free states. In the census of that year, farmland in the mid-Atlantic states was valued at $28.08 an acre, and in New England at $20.27 an acre, but in the Southern states it was only worth $5.34\u2014even though the South was producing the big export crops. Farms in Pennsylvania, New York, Ohio, and Illinois were more improved, more diversified, better tended, more mechanized, better connected to market by infrastructure, and were worked by family or wage labor instead of by capital-intensive slaveholdings.\n\nIt was almost a laboratory experiment: two mutually exclusive economic systems competing for territorial expansion and financial supremacy, each one having at the start about the same number of inhabitants\u2014but one allowing enslaved human property and the other not. Slave societies were caught in a downward spiral. Slavery brooked no competition from free labor, and without a broad consuming class of wage laborers, the slavery bloc furnished no domestic market for the products of industry. Moreover, industrial working conditions involving complicated machinery proved a more problematic situation than field labor for workforce discipline, which often had to be resolved with some kind of incentive pay for the enslaved, something the politics of plantation slavery was resolutely opposed to. Without industry, the South slid further and further behind while the North modernized and grew in population.\n\nMeanwhile, the South had no foreign outlet for its other main product besides cotton: slaves. With slaveowners' encouragement, and sometimes their participation, the enslaved population was increasing by 25 percent or more every decade, even in the face of high mortality among the generally unhealthy enslaved.\n\nWith domestic labor needs being met, the South looked to territorial expansion for the growth of its slavery business. By 1860 North Carolina, South Carolina, Georgia, Kentucky, Tennessee, and Missouri\u2014and even Alabama and Mississippi\u2014were no longer importing enslaved laborers from their neighbors to the north but were exporting coffles as far west as they could go. As more states became slave sellers, having new territories to sell slaves into became a matter of ever greater urgency.\n\nFrom President Jefferson's time forward, the grand prize of territorial expansion was Cuba. In his first year of retirement from political office, ex-president Jefferson rhapsodized in a letter to his prot\u00e9g\u00e9, President James Madison, about his imperial dream that the United States would acquire Cuba with Napoleon Bonaparte's blessing, and would conquer Canada in war: \"We should have such an empire for liberty as she has never surveyed since the creation: & I am persuaded no constitution was ever before so well calculated as ours for extensive empire & self government.\" Then he described the weather and the condition of his gardens, and thanked Madison for the squashes he had sent.\n\nWhen a \"founding father's\" remarks about \"liberty\" don't seem to make sense, substitute the word \"property\" and they do. Taking over Havana would have created an empire of liberty, all right\u2014for slaveowners. Jefferson wasn't fantasizing about freeing the two hundred thousand or so slaves who were being systematically worked to death on Cuba's sugar plantations and replaced by new arrivals from Africa. Cuba was at that time a fantastically productive sugar machine that was still in the early phase of its multi-decade peak of importation of kidnapped Africans. Acquiring Cuba would have been a windfall for Virginia slave breeders and would have added two reliably pro-slavery senators.\n\nIn 1861, slaveowners went to war with the North over slavery, as South Carolina's planter class had been inciting them to do for decades. The idea that the South fought a war so that it could be left in peace to have slavery merely within its settled boundaries is sometimes voiced as a cherished myth today, but it does not fit the facts on the ground, nor did anyone think so at the time. Quite the contrary: the war was fought over the expansion of slavery. Southern rulers feared being restricted to the boundaries they then occupied. The dysfunctional-from-the-beginning Confederate States of America was set to have an aggressively annexationist foreign policy.\n\nPremised on infinite reproduction into an ever-expanding market, the slave-breeding economy was like a chain letter or a Ponzi scheme: sooner or later someone would be left holding the bag. Expansion into other territories was thus presented as a demographic imperative; in the last days of 1860, two Alabama \"secession commissioners\" sent to pitch secession to the North Carolina legislature announced that:\n\n[Alabama's black] population outstrips any race on the globe in the rate of its increase, and if the slaves now in Alabama are now to be restricted within the present limits, doubling as they do once in less than thirty years, the [white] children are now born who will be compelled to flee from the land of their birth, and from the slaves their parents have toiled to acquire as an inheritance for them, or to submit to the degradation of being reduced to an equality with them, and all its attendant horrors.\n\nThough the Jeffersonian \"empire for liberty\"\u2014which, like we said, meant slavery\u2014never managed to annex Cuba, it confiscated vast amounts of Native American territory as it pushed into western Georgia, Florida, Alabama, Mississippi, Louisiana, Arkansas, Missouri, and, after an international war of territorial conquest, Texas. Slaveowners fought bitterly but unsuccessfully to have slavery in New Mexico, California, and, in an 1854 armed confrontation of national dimensions, Kansas and Nebraska. Until Lincoln, they were used to having the president on their side.\n\nThe clash between slave labor and free-soil\u2014the \"irrepressible conflict,\" to use William Seward's phrase of 1858\u2014resulted in the overthrow of slavery. But it was not merely a clash between labor systems; it was a clash between monetary systems.\n\nWhen slavery was abolished and the on-paper value of flesh-and-blood capital disappeared from the balance sheet, the wealth of the South evaporated. Since the South's economy had been built entirely on a foundation of slavery, there was nothing to substitute for it. There were as many laborers as before, but they could no longer be coerced. There was nothing to pay labor with, because the labor had been the money. The security for hundreds of millions of dollars in debt walked away, leaving the obligations valueless, the credit structure imploded, the hundred-dollar Confederate notes trampled in the mud, and the planters owning worthless land.\n\nEmancipation destroyed an entirely legal form of property, which is why it was a revolution.\n\nBefore achieving independence, the thirteen quarrelsome colonies were already well along with the process of cleaving into two interdependent but hostile economies. As each new territory came into the Anglo-American system, its policies regarding slavery and slave trading occasioned a shifting of the balance of power in the economy. The tension was there all along, and it formed arguably the greatest obstacle to union at the Constitutional Convention. The difference was not merely one of large states versus small states, or protective tariffs versus free trade, or even wage labor versus enslaved labor; it went directly to the issue of property rights in people. Within that framework, however, there was a sharp competition between the two major centers of power in the slave societies: Virginia and South Carolina. The commercial and political antagonism between the two went back to colonial days.\n\nWe're going to turn back to the sixteenth century now, in order to describe the formation of the states of the Chesapeake and the Lowcountry, each in their differing social and political particulars. We begin just before the establishment of an English colony in North America, when the first known group of enslaved Africans brought to live in the present-day territory of the United States rebelled and escaped.\n\n*\"States' rights\" was not implicitly a slaveholders' project at first; Massachusetts nearly seceded during the War of 1812. But a states' rights slaveholders' doctrine can be traced from Patrick Henry to John Randolph to John C. Calhoun, who more than anyone made it the boilerplate of slavery.\n\n*Notwithstanding the thirteen stars on the Confederate battle flag, there were only eleven Confederate states (in order of secession: South Carolina, Mississippi, Florida, Alabama, Georgia, Louisiana, Texas, Virginia, Arkansas, North Carolina, Tennessee). The other two stars represented Kentucky and Missouri, slave states that did not secede, though a Confederate government proclaimed itself in Missouri in addition to the Union government.\n\n_John Smith's map of Virginia, showing the \"Virginian Sea,\" dated 1606 on the legend. North is to the right; the four major rivers on the western shore of the Chesapeake can be seen clearly._\n\n#   Part Two\n\n# **The Chesapeake and the Lowcountry**\n\n#   7\n\n# **Rawrenock**\n\n_It will rather hasten ye Spaniards rage, then retard yt; because he will see it, to grow every day harder for him to defeat us. 1_\n\n_\u2014A Justification for Planting in Virginia Before 1609_ , Records of the Virginia Company\n\n_Those who are now boastfully called popes, bishops, and lords have issued from] such a pompous display of power and such a terrible tyranny that no earthly government can be compared to it... we have become the slaves of the vilest men on earth.[ 2_\n\n\u2014Martin Luther, _Concerning Christian liberty_ (1520), trans. R.S. Grignon\n\nTODAY THE LAND AROUND Sapelo Sound is part of Georgia, but in 1526 the Spanish considered it part of the vaguely bounded territory Juan Ponce de Le\u00f3n had named in 1513: Florida.\n\nIt was probably somewhere near Sapelo Sound that the conquistador Lucas V\u00e1zquez de Ayll\u00f3n established a Spanish colony in 1526, bringing some six hundred people from Santo Domingo in six vessels\u2014including an unknown number of enslaved Africans, whose precise point of origin is also unknown, along with eighty or perhaps a hundred horses.\n\nIt was a mighty undertaking, the first since Ponce de Le\u00f3n had left the region, and Ayll\u00f3n carried a commission from Holy Roman Emperor and King of Spain Carlos V. Unfortunately, Ayll\u00f3n's short-lived town of San Miguel de Guadalpe became that archetypal horror of colonial history: a failed settlement in the wilderness. Ayll\u00f3n died of disease; the Africans rebelled, burning down the colonial prison; and one hundred fifty or so surviving Spanish colonists made their way back to the island of La Espa\u00f1ola (or Hispaniola).\n\nThe Africans appear to have been left behind to live or die among the Guale Indians, beginning Florida's tradition of marronage, a state of outlaw freedom for a self-emancipated slave.* Their ultimate fate is unknown.\n\nIn his explorations, Ayll\u00f3n had discovered the major watercourses of North America's east coast, including the Chesapeake Bay, which first appears on a map with the name Bah\u00eda de Santa Mar\u00eda. After various failed ventures, including a brief reign of slaughter and enslavement of Native Americans under Hernando de Soto in 1539, Spain gave up trying to colonize Florida. But the Spanish king's hand was forced by the appearance of a colony of heretics.\n\nMartin Luther's revolution (October 31, 1517) never took hold in militantly Catholic Spain. But in northern Europe, where dissident mobs attacked churches and monasteries, destroying statues and images in iconoclastic riots, what came to be called Protestantism was an active political project. It was a new kind of movement, disseminated by the booming technology of moveable-type printing, which thrived in northern Europe on Bible sales, creating as it did so a new political medium\u2014the printed tract\u2014that gloried in a rhetoric of freedom versus slavery that would carry forward into the coming centuries.\n\nAfrican slavery, introduced into Iberia by Portugal in 1441 or so, had not yet developed on a large scale in the Americas, nor did it exist in most of Europe, where slavery was associated with Spain and Portugal\u2014as were black people, who in England were called _blackamoors_ , reflecting their Iberian provenance. But though Martin Luther had no personal contact with slavery, he used the term frequently, describing conditions of the soul and of the church in terms of liberty versus slavery. In his theology, freedom was associated with reading the Bible in one's own language, and slavery was associated with Catholic ritual.\n\nAs Europe divided into Catholic and Protestant camps, a series of civil wars paralyzed France for four decades. Huguenots, followers of Jean Calvin who numbered at their peak a little more than a tenth of the French population, were mostly urban people, many of them tradesmen, at odds with a mostly rural, agricultural country. When they declared their church an established institution with a national synod in 1559, a crisis began.\n\nThen, the following year, a ten-year-old was crowned king of France\u2014Charles IX, whose affairs were guided by his Italian mother, Catherine de Medici, acting as regent. Catherine saw the growth of Protestantism as a threat to the state, and allied the French throne with Spain against it, while the Huguenots sought English and German support.\n\nOn February 18, 1562, the Huguenot sea captain Jean Ribaut embarked on a French colonizing mission across the Atlantic, which meant creeping into territory claimed by Spain. Flying the banner of his Catholic child-king, he founded the settlement of Charlesfort, at present-day Parris Island, in what later came to be called South Carolina.\n\nRibaut found the indigenous people* to be friendly, and when one of them showed the French the best place to land their vessel, Ribaut had him \"rewarded with some looking glases and other prety thinges of smale value\"\u2014the beginning of a long cycle of trade between Native Americans and Europeans in the area. As the richness of the unplowed land became apparent, and after Ribaut presented more gifts, he asked the question most on Europeans' minds:\n\nwe demaunded of them for a certen towne called Sevola [Cibola], wherof some have written not to be farr from thence.... Those that have written of this kingdom and towne of Sevolla... say that ther is great abound-aunce of gould and silver, precious stons and other great riches, and that the people hedd ther arrowes, instedd of iron, with poynted turqueses.\n\nRibaut kidnapped two of the natives but, to his apparent surprise, they did not want to be captives, and they escaped: \"We carried two goodly and strong abourd our shippes, clothing and using [treating] them as gentlly and lovingly as yt was possible; but they never ceassed day nor nyght to lament and at length they scaped away.\"\n\nLeaving twenty-eight men behind at Charlesfort, Ribaut returned home to raise money, but he found France's ports closed. Two weeks after he had embarked from France, the Duc de Guise had massacred a group of Huguenots at worship, and in Ribaut's absence, a religious civil war had begun. He went instead to London, a city he knew well and whose language he spoke, where in May 1563 he published a forty-four-page pamphlet whose short title is _The whole and true discouery of Terra Florida._ In it, he noted that the natives would trade for \"littell beades of glasse, which they love and esteme above gould and pearles for to hang them at there eares and necke.\"\n\nThe pamphlet brought Ribaut to a meeting with England's Queen Elizabeth, who wanted to mount an English expedition to Florida. She briefly gave Ribaut \"a salary of three hundred ducats and a house,\" as the Spanish ambassador duly reported to the Hapsburg monarch Felipe (Philip) II, but then she had him imprisoned in the Tower of London after he tried to escape with four French hostages Elizabeth was holding.\n\nBy then, the desperate, quarreling men Ribaut had left behind at Charlesfort had resolved to sail home. Running out of food and water on the voyage, they drank their own urine and turned to cannibalism, killing and eating an unfortunate outcast of their number before they were picked up by a British ship.\n\nA second, much larger, colonizing voyage from France brought both women and men to Florida when Ren\u00e9 Goulaine de Laudonni\u00e8re, Ribaut's former second-in-command, established the Huguenot colony of Fort Caroline (also named for Charles IX) on June 22, 1564, near the site of present-day Jacksonville, Florida. Laudonni\u00e8re brought an official expedition painter along, who depicted the sixteenth-century aristocrat dressed in \"a crimson, yellow, and blue costume,\" in yellow boots with red linings, and three colors of plumes in his hat. His colonists recorded eight births during the short life of their community. Unfortunately, they neglected to plant sufficient crops in the fall, so when famine struck they took an Indian chief hostage for a food ransom.\n\nEven more unfortunately, they were in the high-security Gulf Stream corridor.\n\nPonce de Le\u00f3n noted in his journal of 1513 that his three ships encountered a current they could not go against, despite favorable winds. He had discovered the strongest current in all the world's oceans\u2014a one-way express lane in the sea, where the water was warm even when the air was cold. More than two centuries later, Benjamin Franklin named it the \"Gulf Stream.\"\n\nDriven in a west-to-east direction by the Earth's rotation and intensified by the temperature differential between equatorial and polar latitudes, the Gulf Stream is stronger in the summer than in the winter. It originates after the waters of the Caribbean pass northward through the Straits of Yucat\u00e1n, pouring into the Gulf of Mexico and making the clockwise circuit in the Gulf now known as the \"loop current.\" The current is amplified again, and the waters become more turbulent, when it shoots eastward through the constricted passage of the Straits of Florida. Following along the eastern coast of the United States, it reaches its closest point to land near present-day Cape Hatteras, North Carolina, before gradually veering away from the coastline and out into the Atlantic. There it divides into two main branches, with one continuing up the North Atlantic along the \"great circle\" route to Europe, while another branch curves off eastward, leading to Spain.\n\n_Detail of the 1768 Franklin-Folger map showing the Gulf Stream, which diverges from the mainland off the coast of North Carolina._\n\nEvery year, a Spanish fleet bound for Sevilla sailed up the Gulf Stream out of the port of Havana, packed full of silver and gold ripped out of the bowels of Mexico and Per\u00fa. The volume of silver sharply increased as of 1557, when the Spanish mines began using an amalgamation refining process that involved indigenous slaves tromping in a toxic slurry of mercury, a labor force that was soon to be augmented with Africans.\n\nWhen the Spanish king Felipe II learned that French Protestants had established a colony on the mainland at a potential choke point for the route his treasure ships took, he commissioned the militantly Catholic Don Pedro Men\u00e9ndez de Avil\u00e9s as _adelantado_ (governor) of Florida, instructing him to establish a Spanish presence on the North American mainland that would remove the interlopers.\n\nWilliam Hawkins made what was probably the first African trading voyage\u2014but not a slave-trading one\u2014from England in 1536, traveling from England to \"Guinea\" (Africa) and then to Brazil. The first English company to finance commercial ventures to Africa seems to have been a London syndicate founded in 1540, but there was little further action until a highly lucrative voyage brought back gold, ivory, and hot peppers in 1553. It was followed by more expeditions, and Queen Elizabeth became an African-venture partner in 1561. These voyages, which did not entail carrying off kidnapped people, created good relations with the African traders, but Hawkins's son John changed that.\n\nThere are two previous documented incidents of Englishmen engaging in commerce of small numbers of slaves, but John Hawkins was the first to make a profitable \"triangular,\" or clockwise, slave trade. Moreover, he not only traded in slaves but participated in raiding for them, burning a town on the Gold Coast during his first voyage. He also seized them from other slave traders through piracy\u2014or rather, as a privateer.\n\nPrivateering\u2014the state endorsement of commercial piracy against vessels of other flags in furtherance of military and political objectives\u2014was an early form of capitalism as war. \"The setting forth of a privateer required considerable capital,\" writes Kenneth R. Andrews. \"Even in ventures consisting of one small ship, the joint-stock system of investment was used more often than not.\" In England, the partners were _adventurers_ , a word implying joint-investor commercial enterprise, as in the Company of Merchant Adventurers of London, apparently already in existence when it was chartered by Henry VII in 1407. Freelance piracy by English captains flourished during Queen Mary's reign (1551\u201358), but Queen Elizabeth, Mary's half sister and successor, gave the former pirates letters of marque to become privateers and used them as a tool of policy\u2014\"a privileged criminal class,\" in the words of Hugh F. Rankin.\n\nInvestment in privateering ventures was facilitated by the improved quality of English money during Elizabeth's long reign (1558\u20131603). Henry VIII had imposed what is remembered as the Great Debasement on his coinage as a money-making trick, sabotaging the value of the monarch's money. But Elizabeth's financial advisor Thomas Gresham accomplished the considerable feat of calling in the debased coinage and replacing it with newly minted gold sovereigns within a year (1560\u201361). Restoring value to the money created the conditions for a credit market to thrive, without which no long-distance trade could function. Gresham also impressed on Elizabeth the wisdom of raising money domestically from England's own internal commerce instead of from foreign bankers as the Spanish crown did. From Elizabeth's time forward, England was a financial center.\n\nBacked by a syndicate of investors, Hawkins took three ships to Sierra Leone in 1562 with the intention of capturing Africans to sell in La Espa\u00f1ola and thereby to violate the Spanish trade monopoly. Once arrived on the African coastline, he plundered Portuguese traders and made a slave-raiding alliance with an unnamed African king. He had some three hundred captives to sell by the time he arrived at La Ysabela, Columbus's now-vanished first settlement near present-day Puerto Plata in the Dominican Republic. Arriving with more soldiers than the Spanish had, he said he'd behave if he got to do business. After selling the Africans to eager customers, he acquired two more ships and loaded all five up with sugar, hides, ginger, and pearls for the return voyage to Europe, ultimately turning a profit for his investors.\n\nHawkins's second triangular voyage, heavily subscribed by merchant adventurers in 1564, brought back gold, silver, and pearls. On his return in August, he stopped at Fort Caroline in need of fresh water. There, in a gesture of Protestant solidarity against the Spanish, he saved the remaining Huguenot colonists by trading them food and a ship he didn't need in exchange for a Spanish brass cannon they had captured. During the months Hawkins remained there, Jean Ribaut arrived; released from the Tower of London, he had brought a fresh colonizing expedition of five hundred men and two hundred women.\n\n_Design for Sir John Hawkins's crest, depicting an African woman, bare-breasted and bound, 1568._\n\nIn Spain, Men\u00e9ndez's huge expedition to Florida was already in preparation when the news of Hawkins's arrival at Fort Caroline arrived. To the Spanish king, it seemed proof of an international alliance to break his control of the Americas, and he ordered Men\u00e9ndez to speed up his departure.\n\nMen\u00e9ndez had Felipe's trust. He had fought against the forces of the French Valois king Fran\u00e7ois I under Felipe's father, Carlos V, and he had successfully escorted Felipe to London in 1554 for Felipe's short-lived royal marriage to his Catholic second cousin, the English Queen Mary Tudor.* He was captain general of the Carrera de Las Indias, the transatlantic treasure route, during what is remembered as Spain's _Siglo de Oro_ , its Golden Age. With the security for Spain's entire money supply and commerce on his shoulders, as well as a fantastically lucrative upside should his franchise thrive, he took his responsibilities to God, king, and silver seriously. At enormous personal expense, he brought to Florida an armada of ten ships carrying 995 people, 300 of whom were veteran soldiers, along with 200 horses. They landed on the day of San Agust\u00edn (August 28, 1565), founding the town that today is still called St. Augustine\u2014the oldest continually occupied European-style city in the United States, though there are older Native American communities.\n\nShortly after Hawkins departed Fort Caroline, Men\u00e9ndez captured it in a surprise attack. As the massacre began, he gave an order to spare women and children under fifteen (though some were apparently dispatched before the order to spare them was communicated). One hundred forty-three men were killed, according to one source, although Laudonni\u00e8re escaped. Others were slaughtered in the countryside as they fled. The Spanish caught some two hundred of them, who had to be confirmed as members of the _nueva religi\u00f3n_ before being executed, because they could escape death if they declared themselves Catholics. When they refused, they were taken behind a sand hill in groups of ten with their hands bound, and their throats were cut.\n\nThe Spanish found six cases of the Huguenots' gilt-edged Bibles, which they burned. Ribaut got away with some 350 of his people, but their boat was shipwrecked near St. Augustine and Men\u00e9ndez caught them. Gonzalo Sol\u00eds de Mer\u00e1s, Men\u00e9ndez's official chronicler and brother-in-law, noted that Ribaut offered a ransom to spare their lives, but Men\u00e9ndez spared only \"the fifers, drummers, trumpeters, and four more who said that they were Catholics, in all sixteen persons: all the others had their throats cut,\" including Ribaut. One town had exterminated another town thirty miles away. The site is still known today as Matanzas (Massacre) Inlet. It was a small massacre, however, compared to the St. Bartholomew's Day massacre of August 1572, when the gates of Catholic Paris were closed and three days of killing of Huguenots began, followed by similar massacres in twelve other French cities that claimed an unknown number of thousands of victims.\n\nWith the Huguenots of Florida annihilated, the Spanish Fleet of the Indies continued its annual treasure runs from Havana through the Straits of Florida. To Christianize the natives, Men\u00e9ndez established a mission system that was the first interconnected circuit of European settlements in North America. He established firm military control over the region, sending a detachment up north to build a fort where the Charlesfort community had been, calling it Santa Elena (St. Helena in English). One of his captains, Juan Pardo, built Fort San Juan in western North Carolina, near present-day Morganton, the ruins of which were unearthed by archaeologists in the first decade of the twenty-first century. The area north of St. Augustine would remain a zone of conflict between Protestant and Catholic states for almost two centuries more.\n\nHawkins made his third and final slave-trading voyage in 1567, taking between four and five hundred captives, but Spain mounted effective resistance, and his expedition lost money. The English did not immediately continue the slave trade, but John Hawkins had started them in it.\n\nBy this time, Spain had purchased tens of thousands of Africans from Portuguese slavers to work in its silver and gold mines in Mexico and Per\u00fa. It was becoming clear how vulnerable the Spanish American possessions were to slave rebellion, given how badly outnumbered the whites were, and how vulnerable they were to attack from free black people whose arrival in the hemisphere predated that of the English. With the help of numerous maroons, as well as Huguenot privateers, Hawkins's nephew Francis Drake captured a fortune in gold\u2014he had to leave the silver behind for lack of vessels to carry it\u2014when he attacked one leg of the Spanish treasure fleet at Nombre de Dios, Panam\u00e1, in 1573.\n\nEngland's Queen Elizabeth knew well the traps that awaited women in royal marriage. She was the ex-sister-in-law of Spain's Felipe II, from his marriage to her half sister Mary Tudor. Her father, Henry VIII, had beheaded her mother, Anne Boleyn. For her refusal to subordinate herself, she became known as the Virgin (meaning unmarried) Queen.\n\nAccording to the writer remembered as John Taylor the Water-Poet, John Hawkins was the first person to bring tobacco to England, but it was popularized by Elizabeth's favorite, Sir Walter Raleigh. An Englishman who owned extensive tracts of land in Ireland, Raleigh was the fashionable figure who popularized \"tobacco-drinking,\" as it was called at first, puffing away on his long-stemmed silver pipe even in the presence of the snuff-dipping queen. When the Virgin Queen awarded Raleigh a charter in 1584 to a broadly defined area of North America, he named it Virginia in her honor.\n\nUnlike the Spanish colonies, which were developed as state projects and were often named for saints, Virginia was a commercial enterprise from the start, and its first colony, Roanoke, was named for money. _Rawrenock_ , as Captain John Smith spelled it, was the medium of exchange used by the Pamunkey people who lived there: \"white beads that occasion as much dissention among the salvages, as gold and silver amongst Christians,\" Captain Smith wrote. The settlement was founded in 1585 on an uninhabited island off the coast of present-day North Carolina that gave signs of having previously been the site of a massacre.\n\nVirginia was a challenge to Spain's hegemony in the Americas. Pushed by a \"war party\" among her advisers\u2014advocates of North American colonization who were locked out of commerce in the Americas by the Spanish monopoly\u2014Elizabeth authorized Francis Drake to conduct a 1585\u201386 raiding expedition to the West Indies. To accomplish his mission, Drake outfitted a large fleet of some twenty-five sailing ships and at least eight pinnaces (smaller oar-and-sail combos, used for boarding and reconnaissance). He press-ganged some of his crew, but captains were eager to serve under England's great sailor, warrior, profiteer, and anti-papist.\n\nShortly after setting out, a fever killed hundreds of Drake's men, but his surviving force sacked towns on the Cape Verde islands. Then, according to one sailor's account, on New Year's Day 1586 he landed a thousand men some \"9 or 10 miles distant from the Towne of Saint Domingo, the same day our men (by Gods helpe) tooke and spoyled the Towne.\" To dramatize their ransom demand, the English burned between half and two-thirds of Santo Domingo, starting with the poorest parts of town. They hanged two friars, took everything of value, and remained there a month before pushing on to Cartagena de las Indias in Nueva Granada (today Colombia), which they likewise \"spoyled,\" tormenting the Cartagenans for six weeks before moving on.\n\nIn both Santo Domingo and Cartagena, they burned Spanish galleys; a Mediterranean naval artifact out of place in the Caribbean, the ships were slower-moving and clumsier than Drake's vessels. They freed hundreds of galley slaves, some of whom joined Drake's forces\u2014a motley crew that included Africans, Turks, Frenchmen, and Greeks. Coming up the Gulf Stream along the coast of Florida, Drake spotted the watchtower of San Agust\u00edn, established twenty-one years before, and paused to allow his two thousand or so men to sack and burn the town.\n\nProceeding north, Drake's final stop on his American tour was the queen's colony of Roanoke. But when he arrived there, the colony was failing. He carried 105 dejected colonists home to England, so when Admiral Richard Grenville arrived with a supply ship shortly after, he found the colony abandoned. Leaving behind fifteen men, Grenville returned to England. When a second attempt at colonization with 150 colonists arrived in 1587, they found the colony abandoned yet again.\n\nDrake's campaign was not a profitable expedition for its joint-stock investors but it was costlier still for Spain, systematically dismantling as it did Spain's defenses and ports. After his assault, \"every sail upon the horizon conjured up the memory of Drake\" for the Spanish in their system of fortresses that they called _llaves_ (keys). It was the beginning of eighteen years of war between the two countries, during which England was allied with the Dutch.\n\nBent on retaliation for Drake's depredations, the Invincible Armada of Spain sailed for England in 1588, but it went down to humiliating defeat. First there was a devastating storm that was widely seen in England as God's intervention against popery and the Irish, then a battle in which England's use of signaling beacons, constructed at strategic points along the coast, revolutionized naval communications. The defeat of the armada marked the ascension of England to the status of world power and brought a knighthood for John Hawkins. An innovative shipwright, he was effectively the founder of the English navy, which grew out of picking at Spain piecemeal.\n\nOne casualty of the Anglo-Spanish war was the Roanoke settlement: no supplies could be shipped to the colonists. By the time a ship arrived in 1590, three years after the previous supplies had landed, they had disappeared once again. There has been much speculation over the centuries about the fate of the mysterious \"lost colony,\" but the simplest explanation is that they were killed by the Pamunkeys under Chief Powhatan, whose territory they were invading; according to Samuel Purchas, Powhatan \"confessed\" to Captain John Smith \"that he had bin at the murther of that Colonie.\"\n\nVirginia had failed on its first try.\n\nIn the wake of Drake, Spain began building up its American fortifications to withstand future assaults. But in defending its positions on the mainland and the \"vital artery of the treasure route,\" writes Kenneth R. Andrews, most significantly meaning Havana as well as Lima, Portobelo, Cartagena, and Veracruz, \"this inevitably meant that eastern Cuba, Jamaica, Hispaniola, Puerto Rico and the Lesser Antilles, though by no means abandoned, were more and more exposed to all forms of infiltration and attack.\" Men\u00e9ndez launched a newly formalized Spanish treasure fleet in 1566; that same year the Protestant Dutch, who had been under occupation by the Hapsburgs since 1482, launched a war for independence from Spain that dragged on in one form or another for some eighty years.\n\nSpain claimed a monopoly on commerce and shipping in the Americas, but its fortress colonies were increasingly being visited by freelance merchant-warriors from other nations, who often acquired their goods by piracy and wanted in on the mercantile action, drilling into the Spanish monopoly like so many termites. The Dutch, who with their shipping industry were creating the world's most dynamic economy in the Netherlands, made a grand business of attacking Spanish shipping. As the Anglo-Spanish war heated up, English privateers hammered at Spanish merchants and treasure ships, with profits accruing to the underwriters, who were often London merchants.\n\nDrake and Hawkins made the mistake in 1595 of attacking the early version of San Juan's formidable, well-defended Morro Castle, whose gunners and cannoneers had every possible angle of fire. The two despoilers of cities died in the aftermath of the assault, apparently of dysentery.\n\nElizabeth unified church and state under her sovereignty, formalizing the existence of the Church of England (or Anglican, or Episcopal church), which Henry VIII had broken out from the Catholic Church in 1534. The Anglican church retained much from Catholicism, but without the pope, without saints, and without the veneration of the Virgin Mary. The Lutherans and Calvinists thought the Anglicans corrupt, and the Catholics thought them heretical. While Elizabeth prioritized the avoidance of religious civil war in England, she brutally completed the conquest of Catholic Ireland that Henry had left unfinished, in a campaign that saw Spain side with its Irish co-religionists against England.\n\nElizabeth became alarmed by a small but increasing number of black people visible on London streets, and she ordered them deported in 1601, decrying the \"great numbers of Negars and Blackamoors\" in her kingdom and characterizing them as \"Infidels.\" She did not succeed in removing them, but she did establish a precedent in England for separating black people from others.\n\nElizabeth died\u2014unmarried, as per her vow, and without issue\u2014in 1603 after a forty-four-year reign. She took no part in choosing her successor, but advisor Sir Robert Cecil had negotiated a succession pact in favor of her second cousin, James Stuart, who had been crowned James VI, King of Scotland at the age of thirteen months. James had been raised as an Anglican; his Catholic mother, the conspiratorial Mary Stuart, Queen of Scots, had been beheaded on Elizabeth's reluctant orders in 1567 after eighteen years of imprisonment, in a botched execution that required three ax strokes to completely sever her head. James was considered a foreigner by the English, but no matter: at the age of thirty-seven he succeeded Elizabeth as King James I of England.\n\nElizabeth bequeathed James a much more powerful country than the one Henry VIII had left her. Elizabethan England had beaten Spain, finished the subjugation of Ireland, and\u2014not the least of its achievements\u2014stabilized the pound sterling. The House of Stuart, however, proved to be, as one historian succinctly put it, \"Europe's most hapless dynasty.\" Unifying the English and Scottish crowns, James was the first of a line of Stuart monarchs who would enrage Parliament.\n\nDespite the black people of London having been singled out as a distinct and undesirable class by Elizabeth, their presence was changing notions of style in the city. A fashionable white fascination for blackness was particularly visible in the worlds of art and music, as on Twelfth Night, January 6, 1605, when James's court attended _The Masque of Blackness_ , written by Ben Jonson at the request of James's wife, Queen Consort Anne of Denmark. \"It was her majesty's will to have them blackmoors at first,\" wrote Jonson by way of introduction; the ladies of the court who performed in the cast were dressed in high style\u2014which was the point of the exercise\u2014as Africans, with their faces blacked.\n\n*In Spanish the self-emancipated were called _cimarrones_ , a word deriving from the Ta\u00edno language that became _marron_ in French and _maroon_ in English.\n\n*Which group Ribaut encountered is unknown.\n\n*The daughter of Henry VIII, she acquired the nickname \"Bloody Mary\" by burning 283 Protestants at the stake in 1555 during the revolt that followed her marriage to Felipe; Felipe effectively left the marriage in 1556 when he assumed the throne of Spain, leaving Mary without an heir and thus halting her project of re-Catholicizing England.\n\n#   8\n\n# **A Cargo of Shining Dirt**\n\nSeagull, a sea captain. _Come, boys, Virginia longs till we share the rest of her maidenhead._\n\nSpendall, adventurer bound for Virginia. _Why, is she inhabited already with any English?_\n\nSea. _A whole country of English is there, man... the Indians are so in love with 'em that all the treasure they have they lay at their feet._\n\nScape. _But is there such treasure there, Captain, as I have heard?_\n\nSea. _I tell thee, gold is more plentiful there than copper is with us; and for as much red copper as I can bring, I'll have thrice the weight in gold. Why, man, all their dripping-pans and their chamber pots are pure gold; and all their chains with which they chain up their streets are massy gold; all the prisoners they take are fetter'd in gold; and, for rubies and diamonds, they go forth on holidays and gather 'em by the seashore, to hang on their children's coats, and stick in their caps, as commonly as our children wear saffron gilt brooches and groats with holes in 'em._\n\nScape. _And is it a pleasant country withal?_\n\nSea. _As ever the sun shin'd on; temperate, and full of all sorts of excellent viands: wild boar is as common there as our tamest bacon is here; venison, as mutton. And then you shall live freely there, without sergeants, or courtiers, or lawyers, or intelligencers.... You may be an alderman there, and never be a scavenger; you may be a nobleman, and_ never be a slave.\n\n\u2014from _Eastward Hoe_ (1605), a comedy by Ben Jonson, George Chapman, and John Marston, who were briefly imprisoned for their impudence (emphasis added)\n\nANYONE WHO GREW up in the southern United States knows that Jesus spoke seventeenth-century English.\n\nThat's because the King James Bible is the Word of God, at least as far as the English language goes. More or less concurrently with William Shakespeare, and together with the Anglican Book of Common Prayer, it effectively codified written English.*\n\nHaving a vernacular Bible was a matter of some urgency to King James. A connoisseur of theological argument and a self-proclaimed expert on witches, he believed that by the divine right of kings he was sitting on Jesus's throne on earth. He was, in short, blessed with no less beatific a vision of his own grandeur than the Spanish monarchs he hated. The English-language Bible he commissioned on behalf of the Church of England was begun in 1604, the first year of his reign as king of England, and was completed in 1611.\n\nReligion was politics in the post-Lutheran world, and commissioning this new Anglican Bible was a political act. An extremist group that enjoyed increasing power in Parliament, called \"Puritans\" by their enemies, aggressively opposed the monarch. In _Basilikon Doron_ , a how-to-be-a-king book that James wrote for his toddler son, Henry, subsequently published in Edinburgh (1599) and then in London, we read: \"as to the name of Puritanes,... they thinke themselves onely pure, and in a maner without sinne, the onely true Church, and onely worthy to be participant of the Sacraments, and all the rest of the world to be but abomination in the sight of God.\"\n\nAs the Bible was being translated, James chartered the joint-stock Virginia Company, whose first corporate settlement was, predictably, to be named Jamestown. No Puritans would be welcome there. Jamestown signified the exportation to America of the Church of England. Clergymen who wanted to come to Virginia had to audition, giving a trial sermon for the Virginia Company. If successful, their reward would be a terrifying weeks- or months-long voyage that might carry them to death from some combination of massacre, starvation, or any of a number of diseases.\n\nAs land-granted through latitude descriptions by King James to the venture capitalists of the Virginia Company on April 10, 1606, the Virginia territory comprised about 80 percent of the present continental United States. It extended all the way west across the unexplored continent, a distance seventeenth-century Englishmen did not comprehend. The directors of the company thought Virginia was an island and that on the other side of the mountains would be the ocean, which would provide the fabled passage to the riches of the Orient.\n\nBy the time the English in Virginia began privatizing land previously used as a commons, or \"enclosing\" it, they had had plenty of experience doing it at home. The planting of the Jamestown colony took place as political radicalism was growing in England in response to the mass dispossession of the people of the commons\u2014the \"commoners\"\u2014by enclosure.\n\nThe year Jamestown was founded, 1607, was the year of anti-enclosure riots in the English Midlands, erupting out of Northamptonshire. The rioters erased the boundaries of enclosure, filling in ditches and tearing down hedges, for which action they began to be called \"levellers.\" The social implication of the name was obvious; though they were not a forward-looking movement, the tendency the levellers represented, toward erasing social and financial distinctions in society, using violence if necessary, anticipated Marx's idea of communism by over two hundred years. The rioters were repressed on James's orders; dozens were killed, some by slow-death torture.\n\nAs the dispossessed, masterless people arrived in the cities, that liveliest and most squalid of slums was created: greater London. A huge city of two hundred thousand in 1600, when England's population was four million, it teemed with idle poor, far more than were needed as weavers by England's woolens industry, for whom the prospect of seven years' servitude in the New World could seem a rescue from freezing and starving.\n\nFor the English capital class, the colonies were a handy way to deal with a social problem by shipping it elsewhere. Besides finding gold and producing luxury goods, another of the intended functions of the foreign plantations was to draw down the excess laboring population that had become a drag on English society. Class tension, occasionally flaring into armed conflict, was a permanent fixture of English political life and was exported to Virginia with the first generation, along with a tradition of taverns.\n\nMeanwhile, another colonization scheme was occupying King James: the Ulster plantations in Northern Ireland. These were not \"plantations\" in the later sense of large staple-producing farms; this prior sense of the word meant (quoting the Oxford English Dictionary): \"the settling of people, usually in a conquered or dominated country; _esp._ the planting or establishing of a colony.\" Before colonies could be planted with crops, they had to be planted with people, who were called \"planters\" simply for being there.\n\nFor feudal Scotland, where land ownership was even more concentrated than that of England, northern Ireland was an escape valve. With the aim of securing the sparsely populated northern part of Ireland as a zone of British loyalty, it was Protestantized with planters. Vast tracts of confiscated land in the Ulster region were given to English (mostly Anglicans) and to Scots (mostly Presbyterian) who were being rewarded en masse by their countryman King James for their loyalty, or at least for their general political affiliation with him.\n\nThe thick woods of Ulster had to be cleared. Land was given to those bringing English and Scotch laborers, who had to be certified as Protestant. There was a racial mythology to go with this, one that cast the Scots as superior to the Celtic Irish.\n\nBy the time the English arrived in what they called Virginia, the Chesapeake Bay watershed had been populated for some eleven thousand years. An enormous estuary that connects North America's most complex river system to the Atlantic Ocean, it was created by global warming some twelve thousand years ago, when rising temperatures melted the last ice sheet and flooded the meteoric basin that had been an ancient riverbed.\n\nAbout 180 entirely navigable miles long from south to north, and about 30 miles across at its widest point, the Chesapeake is fed by nineteen principal rivers, all of them navigable, and by four hundred or so lesser creeks and streams, many of them navigable. The big rivers are on its western shore, carrying the force of continental drainage. Though the English didn't know it yet, this huge riverine system offered unrivaled possibilities as a transportation\u2014which meant, a communications\u2014network. The superstructure erected atop it became a global capital of power and influence: in the twentieth century, the world's most powerful military command center, the Pentagon, was built on a lagoon of the Potomac River, seventeen miles below the fall line, using sand dredged from the river.\n\nThe Spanish never occupied the Chesapeake. Since it was north of the Gulf Stream's bend away from the continent, it was safely out of the range of Spanish security concerns. But they went there as explorers, spreading diseases that killed natives who had never had face-to-face contact with Europeans.\n\nFrom that contact with the Spanish, the Pamunkey knew something of European culture, religion, and politics years before the English began referring to Pamunkey territory as Virginia. The seven-year-old son of a Pamunkey _werowance_ , or chieftain, had traveled with Spanish explorers to Mexico and on to Madrid, where he received a Jesuit education. Baptized as Don Lu\u00eds de Velasco, the young man returned in 1571 after ten years away, arriving via Havana with nine Spanish Jesuits who hoped to plant a colony. The Indians killed the Jesuits, apparently with Velasco's help.\n\nThe Pamunkey had long been at war with other natives of the region, and they may well have seen the English newcomers as one more variable in a complex scenario\u2014one more ally or one more enemy, and not necessarily always one or the other. But neither the Pamunkey nor the Virginia Company could have foreseen that they were the first point of encounter in a continent-wide war of enclosure.\n\nCaptain John Smith\u2014the rank referred to his onetime position in the Transylvanian army\u2014was the best negotiator with the indigenous people that Virginia ever had, and as such he was a key figure in the survival of the Jamestown colony. A bona fide war hero, he had fought against the Spanish both for the French and the Dutch, continued on to the Mediterranean, then went to the Balkans where he fought the Ottoman Turks. His coat of arms had three turbaned heads on it, representing the Turkish champions he had slain and ritually decapitated in three tournaments of mortal combat fought in lieu of confrontation between armies.\n\nSmith was an escaped former slave\u2014a white man who had worn an iron collar around his neck. Captured and enslaved by the Tatars, he ultimately escaped and was decorated, commissioned, and given a sinecure by Transylvanian prince Sigismund B\u00e1thory. Leaving his comfortable position at B\u00e1thory's court he returned to England, and then, at the age of twenty-seven, arrived at Jamestown with the first colonists on board the _Susan Constant._ He thereafter not only devoted himself to the mission of colonization but also became an outspoken advocate of the laboring colonist, to the point of being accused of being a leveller.\n\nThe colonists needed an advocate. From the beginning of the Virginia colony through the Boston Tea Party 166 years later, English policy-makers demonstrated over and over again an utter incomprehension of American realities. The tension between colony and metropolis that was to characterize Anglo-American relations was present from the first generation in Virginia, in the form of resistance to corporate governance. Not following foolish instructions was essential for survival, such as when the company sent to Virginia a disassembled ship. The colonists were to carry the five ship parts over the Blue Ridge Mountains, assemble them, and sail on into the ocean.\n\nReturning to England in October 1609 following a gunpowder explosion that apparently damaged his manly organs, Smith became a writer, and a good one at that. It was Smith who named New England and first described it, in 1610. His various books and pamphlets are full of firsthand historical information; he was one of the first autobiographers in England. In his masterwork, a classic of early hemispheric literature titled _Generall Historie of Virginia, New England, and the Summer Isles_ (1624), Smith described the Chesapeake region as \"a country that may have the prerogative over the most places knowne for large and pleasant navigable rivers, heaven and earth never agreed better to frame a place for man's habitation.... Here are mountaines, hils, plaines, valleyes, rivers, and brookes, all running more pleasantly into a faire bay, compassed but for the mouth, with fruitful and delightsome land.\"\n\nSmith was an autodidact cartographer. His maps did much to get Englishmen interested in North America; the _Mayflower_ Pilgrims who established the Plymouth colony relied on Smith's map when they crossed the Atlantic in 1620. An early example of Virginia branding, his map of the area labeled the region of the Atlantic Ocean outside the Chesapeake as the \"Virginian Sea.\" The colonists briefly tried calling their grand estuary Virginia Bay, but the name Chesapeake was already established, deriving from the Algonquian _chesapioc_ , \"village at big river,\" which implies the rivers' communicative function.\n\nAs with the Cuban hardwoods that built ships in Havana for the royal silver fleet of timberless Spain, the availability of Chesapeake lumber facilitated shipbuilding. Not only were there extensive stands of timber, they were located next to water\u2014which was necessary to make the lumber useful, since there was no practical way to haul it over land. The first members of the Shipwright's Guild arrived in Virginia in 1610, three years after the establishment of Jamestown. Over the next two centuries, the region became known for its innovative vessel design. A number of specialized craft were designed for the conditions of the shallow Chesapeake, which has an average depth of twenty-one feet but can be six feet or less. The number of vessels documented as sunk there over time exceeds three thousand, an indication of how much activity there was constantly on this vast aquatic highway system.\n\nWith so many rivers and streams, the Chesapeake abounded in rich alluvial deposits that were ideal for farming. Food could be fished, trapped, hunted, foraged, cultivated, or traded along the river system. The region was hospitable to horses and dairy animals. The Chesapeake ranges between freshwater and salty, so it supports both kinds of marine life in complex interlocking lifecycles. Crabs and oysters, the latter growing on giant underwater \"bars,\" could be harvested in quantities. There were terrapins, which in the nineteenth century would supply the kitchens of grand hotels in Baltimore, Philadelphia, New York, Boston, and other cities. There were so many waterfowl that in the early twentieth century commercial hunters illegally mass-harvested them using Gatling guns, bringing down dozens with a single volley.\n\nJamestown, however, was terribly situated. Colonist Thomas Gates described it as being\n\nin somewhat an unwholesome and sickly air, by reason it is in a marish ground, low, flat to the river, and hath no fresh-water springs serving the town but what we drew from a well six or seven fathom deep fed by the brackish river oozing into it; from whence I verily believe the chief causes have proceeded of many diseases and sicknesses which have happened to our people, who are indeed strangely afflicted with fluxes and agues.\n\nNo one knew what crops might grow or how to grow them. The colony was expected to provide England not only with gold and silver, but also with wine, olives, oranges, and almonds. These fancy foods grew in the Mediterranean on the same latitudes as Virginia, so the plan was to supply England with them from America. Unfortunately, the planners neglected to factor in America's colder climate. Moreover, since England wanted agricultural products that did not grow at home, the English had no knowledge of how to cultivate them. A period of desperate experimentation began to find a staple crop for the colony, involving repeated experiments with King James's personal hobbyhorse, silkworms. While Virginia did ultimately produce some silk, in the main the colony seemed destined to produce nothing finer than masts, pitch, tar, turpentine, hemp, flax, woad (a blue dye, later replaced by indigo), and madder (a red dye).\n\nThe Indians fed themselves easily, but the Jamestown colonists were frequently at the brink, and sometimes over the line, of starvation. Once they were disembarked into the deadly wilderness, the Virginia Company's \"planters\" attempted to replicate the bureaucratic and social structure of England. Idle, wealthy aristocrats kept tables for the colony's too-numerous gentlemen of fashion, attended by footmen who were themselves strangers to labor; meanwhile, others starved. There was a jeweler and a perfumer, but only one competent carpenter. During an investigation in 1623, Smith recalled that the company was at fault for \"maintaining one hundred men [servants and guards] for Governour, one hundred for two Deputies, fifty for the Treasurer, five and twenty for the Secretary, and more for the Marshall and other Officers who were never there nor adventured any thing, but onely preferred by favour to be Lords over them that broke the ice and beat the path, and must teach them what to doe.\"\n\nAfter Smith left Virginia, Jamestown hit its low point: the \"starving time\" of the winter of 1609\u201310 under the fatally inept administration of Smith's enemy, John Ratcliffe. Smith had managed to trade with the Indians, but after he left, Powhatan seems to have deliberately starved the colony, and settlers resorted to cannibalism as the population dwindled to sixty. Refugees who returned to England on board the _Swallow_ in 1610 brought tales that all London heard, though the Virginia Company denied them. The horrific stories were substantially true; a recent archaeological discovery indicates that a fourteen-year-old girl who died was subsequently butchered and eaten by other colonists.\n\nThe capitalistically named _Sea Venture_ , a vessel bringing colonists to Jamestown, was shipwrecked on the Bermuda archipelago, off the Florida coast, in 1609. The misadventure occasioned a ten-month island interlude for the colonists; some found it pleasant, spurning rescue to remain there. A publication about the experience, titled _A True Reportory of the Wracke, and Redemption of Sir Thomas Gates, Knight, upon, and from the Islands of the Bermudas_ , which begins with the words \"A most dreadful tempest,\" appears to have been one of the inspirations for Shakespeare's _The Tempest_ , performed in the presence of King James on November 1, 1611, and repeated the following winter.\n\nAmong the castaways rescued from Bermuda who went on to Virginia, arriving in the aftermath of the starving winter, was the young farmer John Rolfe, born in Norfolk, England, in 1585. Rolfe's experience on Bermuda had been cruel; he left buried there an infant daughter named Bermuda; his wife also apparently died, though her death is not noted in the historical record.\n\nRolfe was an \"ardent\" smoker who seems to have come to Virginia with the intention of trying tobacco cultivation. That wasn't in the Virginia Company's playbook. It certainly wasn't what King James wanted.\n\n*The King James Bible drew heavily on the vocabulary of William Tyndale's translation, which was published in the early days of Lutheranism, the 1520s and '30s. Tyndale was burned as a heretic in 1536. See Tombs, 196\u20139.\n\n#   9\n\n# **Our Principall Wealth**\n\n_A custome lothsome to the eye, hatefull to the Nose, harmefull to the braine, dangerous to the Lungs, and in the blacke stinking fume thereof, neerest resembling the horrible Stigian smoke of the pit that is bottomelesse._\n\n\u2014King James I on smoking, _A Counterblaste to Tobacco_ (1604)\n\nCHEW IT, SNORT IT, smoke it\u2014any way you use it, tobacco gets you high.\n\nNative Americans used it for ceremonial and medicinal purposes, but now an increasing number of Englishmen and women wanted regular doses of this addictive drug, imported or smuggled in from Spanish territories and sold in small quantities for a high price.\n\nLondoners began getting hooked on what they called sot-weed, for the way it intoxicated the smoker. So much money was spent on it that the balance of trade between Spain and England was affected. Spain guarded its tobacco monopoly jealously, but John Rolfe obtained the seed of a strain that grew in the Spanish colonies of Venezuela and Trinidad. It was industrial theft: Rolfe convinced a sea captain, who would have been hung by the Spanish had he been discovered, to smuggle the tiny seeds to him from Trinidad. Once Rolfe was himself planted in Virginia, he began raising his crop, naming his plantation Varina after the tobacco strain; it is still a working farm in Virginia today.\n\n_Indian tobacco pipe from Virginia. From Fairholt._\n\nWith Rolfe's first successful crop of tobacco in 1612, Virginia found its staple. Instead of providing delicacies for England's wealthy with olive groves and vineyards, the Virginians began supplying cheap, strong-smelling, habit-forming weed to the plebes. The tobacco the Virginians grew was universally accounted inferior to the leaf of Hispaniola, Cuba, Trinidad, Puerto Rico, or Venezuela, but it cost less.\n\nColonists quickly went over to cultivating the leaf. Tobacco required land and labor but not a fortune to get started, and it remained the most important American cash crop throughout the colonial years. The market was at first modest, but it swelled. Virginia's production reached thirty million pounds by the end of the seventeenth century, and one hundred million pounds fifty years later.\n\nIts widespread availability created a mass consumer culture in England. People were willing to work to have the money to buy tobacco, although, as the anti-tobacco King James ruefully (and correctly) noted, many a man had been known to \"smoke himselfe to death with it.\" James hated tobacco no less than he hated Raleigh, whom he ordered beheaded in 1618. Meanwhile, the English consumers' new nicotine habit sustained the colonial economy that brought it to them.\n\n_Rotterdam 1623: expelling smoke through the nose was the fashionable way to smoke. From Fairholt._\n\nWhen the new \"partners\" of the Virginia Company arrived in America, they found to their dismay that they were conscripts, coerced into gang labor under martial law. Everything they produced was to belong to the company, so they had no incentive to work.\n\nHalf or more of them died shortly after arrival. As word got out that Virginia was a death trap, agents, popularly known as \"spirits,\" went combing the streets for potential indentured servants for the colony\u2014a process that included abducting children, bringing the phrase _spirited away_ into popular usage, as well as the word _kidnap_. Some two hundred boys were taken from London in 1618, while groups of young women were dispatched in 1619 to provide wives for colonists; company officials were instructed to see that the women were not married against their will.\n\nMany of the desperately poor who went to Virginia were urbanites from London or Bristol, England's second city. There were indentured servants in England, but their term was a year and they received a wage. In Virginia, the term was between four and seven years, and the wages were paid up front in the form of a ticket for a transatlantic crossing.\n\nThe conditions of those crossings were described in a 1623 letter from Virginia that, according to the Oxford English Dictionary, provides the first known instance of the much older word _funke_ as meaning \"a strong smell or stink\": \"Betwixt decks there can hardlie a man fetch his breath by reason there ariseth such a funke in the night that it causes putrefaction of bloud.\" This was not a description of a slave ship; they smelled even worse.\n\nRealizing that there was little reason to come to Virginia and little incentive beyond mere survival to work hard once arrived, Virginia governor Thomas Dale threw open the door to private land acquisition in 1616, hoping to stimulate growth. He offered a good deal: the \"old planters\" who were already there got a hundred acres each, along with another hundred acres if they were company shareholders. Newcomers got fifty acres.\n\nThe colony had begun as a commons under military discipline, but by changing its regime to one in which individual colonists could become landowners, Dale created a real estate market, which in turn quickly became a land grab. But the land was worthless without labor. It now fell to individual entrepreneurs, not the Virginia Company, to address the labor problem in Virginia, and by 1617 the company was allowing semi-independent plantations, called \"hundreds,\" which transported their own labor.\n\nIndentures were probably under way in Virginia by 1617, but the first extant contract of indenture that has come down to us, issued by the Virginia partnership called the Berkeley Hundred, is dated September 17, 1619. That year, the colony's secretary John Pory wrote to London: \"All our riches for the present doe consiste in Tobacco, wherein one man by his owne labour hath in one yeare raised to himselfe to the value of 200\u00a3 sterling; and another by the meanes of sixe servants hath cleared at one crop a thousand pounds English.\"\n\nThen, as if thinking it through as he was writing, Pory corrected himself in the same paragraph:\n\n\"Our principall wealth (I should have said) consisteth in servants.\"\n\nWorkers were already capital assets.\n\nPlanters rarely imported specific indentured servants. Upon arrival, the survivors of the voyage were displayed in a market and\u2014they used the word\u2014\"sold.\" John Harrower, the Scottish indentured servant who left a journal of his tragically short life in Virginia, recalled the scene on May 16, 1774, still aboard the ship that brought him to Fredericksburg, Virginia; interestingly, he used the term \"soul driver,\" more commonly associated with the slave trade:\n\nThis day severalls came on board to purchase servts. Indentures and among them there was two Soul drivers. They are men who make it their bussines to go on board all ships who have in either Servants or Convicts and buy sometimes the whole and sometimes a parcell of them as they can agree, and then they drive them through the Country like a parcell of Sheep untill they can sell them to advantage.\n\nThis manner of labor distribution uncomfortably reminded some of the slave markets of the Muslim world, which those with military backgrounds might possibly have encountered (or, as in the case of Captain John Smith, been sold in).\n\nPlanters had a sweet deal, known as the \"headright\" system: they were given fifty acres of land for every indentured servant whose passage they paid\u2014so they not only got the benefit of several years of wageless labor, but also received the land to do it on. This facilitated the acquisition of large tracts of land by those with even modest amounts of capital. Headrights could be sold; by the 1650s, they were being traded for as little as forty or fifty pounds of tobacco. A real estate market had been created out of enclosed Virginia land, with any claims of sovereignty by Native Americans instantly discarded.\n\nThe urban poor who came as laborers were unskilled and unaccustomed to agricultural work. The descendants of multiple malnourished generations, they were not physically strong enough for the backbreaking task of clearing what George Washington would call \"this wooden Country,\" and their mortality rates after arrival were dreadful. They were, however, sufficient to amass large landholdings from headrights for those with the capital to sponsor them as land speculation began.\n\nJohn Rolfe is most remembered in popular history not for his pioneering of Virginia's great staple crop but for having married Pocahontas, a daughter of the Pamunkey chief Powhatan.\n\nPocahontas had learned English after being kidnapped by the Jamestown settlers in 1613, during which time she was Christianized and renamed Rebecca. As a prosperous tobacco farmer, Rolfe traveled to London in 1618 together with Rebecca\/Pocahontas and their infant son, Thomas, but she fell ill and died while preparing to return to Virginia. Fearing his son would not survive the voyage, Rolfe reluctantly left him in England and returned to America.\n\nBack in Virginia, Rolfe documented, rather off-handedly, the first known sale of African slaves in Anglo-America, from a passing Dutch vessel. One day \"about the latter end of August\" in 1619, as Rolfe described it in his historic letter of January 1620 (modern calendar) to Sir Edwin Sandys of the Virginia Company:\n\na Dutch man of Warr of the burden of a 160 tunnes arriued at Point-Comfort.... He brought not any thing but 20. and odd Negroes, wch the Governor and Cape Marchant bought for victualls (whereof he was in greate need as he pretended) at the best and easyest rates they could.\n\nIt was a good deal for the purchasers, and, since the seller got some much-needed food, perhaps a good deal for the seller as well. But if it was a win-win for buyer and seller alike, it was at the expense of those who were bought and sold.\n\nHistorians ever since have wished Rolfe had provided more detail. These were not, as has sometimes been claimed, the first black people to come to Virginia; a census five months earlier counted thirty-two. Nor were they the first slaves whose sale was documented. Already in _The Generall Historie of Virginia, New England, and the Summer Isles_ , John Smith had noted an inter-Indian slave trade of sorts, though it overlapped with the concept of marriage. Powhatan, Pocahontas's father, had sold a daughter of his, and Smith chided him for underpricing:\n\n[Powhatan said,] \"I have sold [my daughter] within this few days to a great Werowance, for two bushels of rawrenoke, three days journey from me.\"\n\nI replied... she was but twelve years old... he should have for her three times the worth of the rawrenoke in beads, copper, hatchets, &c.\n\nThe supremacy of Dutch maritime commerce was a mark of shame for the English. In a report submitted to King James, Sir Walter Raleigh had noted that the Dutch \"have a continual trade into this kingdom with five hundred or six hundred ships yearly with merchandize of other countries... and we trade not with fifty ships into their country in a year.\"\n\n\"The establishment of the American settlements,\" writes Philip A. Bruce, \"was the first step on the part of the English people towards a successful competition with the Dutch merchant marine.\" England was a heavy importer of raw materials from other European nations, for which it had to pay in scarce specie. Opening up North American colonies would make a whole array of products cheaply available to them: tar and pitch, salt and potash, iron and timber, hides and pelts.\n\nIt was not unusual for the Dutch to be nosing around the Chesapeake. In flagrant violation of England's rules, they carried Virginia and Maryland tobacco to their market in Amsterdam and gave better prices for peltry. The Dutch merchant fleet and credit services were far and away the world's most advanced. But as their commercial power grew globally, carrying goods was no longer enough for them, and they moved toward vertical integration.\n\nThe Dutch, who were not yet trading in slaves on an industrial scale, could not attack the Portuguese under the terms of their Twelve Years' Truce with Spain (1609\u20131621), because Portugal was under the Spanish crown between 1581 and 1640. But they occasionally sold slaves who had been taken as prizes from Portuguese slavers by English privateers. John Thornton argues that the \"20. and Odd Negroes\" were Kimbundu-speaking soldiers from Angola, captured during the large, formalized military campaigns of a war waged by the Portuguese against the kingdom of Ndongo. Historian Engel Sluiter provides evidence that they were nabbed by an English corsair in a raid on a Portuguese ship on its way to Veracruz. The raided cargo was then presumably swapped over for commercial liquidation to that \"Dutch man of warr\" (with an English \"Pilott\") that visited Jamestown in August 1619.\n\nIf so, the \"20. and Odd\" would have been Catholic, at least nominally. Some of them probably spoke some Portuguese.\n\n_Ruin of the Catholic church of S\u00e3o Salvador do Congo, known in Kikongo as_ kulu mbimbi, _\"strong place,\" built in 1491 at the royal seat of Mbanza-Kongo, in present-day northern Angola. July 2012._\n\nCentral Africa was Catholicized in 1491\u2014before Columbus crossed the Atlantic \u2014when the _manikongo_ (Kongo king) Nzinga a Nkuwu at his hilltop capital of Mbanza-Kongo converted\u2014not at sword's point, but enthusiastically and immediately upon the arrival of two missionaries. The _manikongo_ , who ruled the largest empire in Africa at the time,* accepted baptism and became King Jo\u00e3o I.\n\nJo\u00e3o seems to have grasped immediately the political uses of Catholicism. Converting his territory gave him a powerful new set of tools to establish his hegemony over the freelance priesthood of traditional Kongo religion, as well as allying him with powerful European patrons and giving him access to previously unknown manufactured goods, most especially including guns. Building churches throughout his vast kingdom, he established diplomatic relations with the Vatican.\n\nThe symbols and beliefs of Catholicism merged well with the symbols of traditional Bakongo religion, creating a syncretized version of Catholicism that was compatible with existing Kongo cosmology and continued ancient practices, which were arguably no more superstitious or magical than fifteenth-century Catholicism. The Bakongo already had a cross\u2014the _dikenga_ \u2014a cosmogram that signified the meeting in time of the land of the living with the land of the dead on the other side of the water. It was a midpoint cross, not a chest-high crucifix, but it was recognizable. The Bible that the priest revered was, to the Bakongo, clearly an _nkisi_ \u2014a power object.\n\nAs Central Africans became the most numerously slaved people of the African trade, the Kongo-Catholic syncretization\u2014a \"fully Africanized\" Christianity, in Thornton's words, which came into existence _before_ the Middle Passage\u2014was transported to all points of the Americas, serving as a fundamental backbone of African culture in the Americas. It took root easily in the Catholic territories established by Spain and Portugal, which would lead to enslaved Bakongo being suspected in the English colonies as potential allies of the Spanish.\n\nRolfe went on in his \"20. and odd\" letter to describe the colonists' fear of Spanish attack in the coming spring:\n\nwee have no place of strength to retreate unto, no shipping of certeynty (wch would be to us as the wodden walles of England) no sound and experienced souldyers to undertake, no Engineers and arthmen to erect works, few Ordenance, not a serviceable carriadge to mount them on; not Ammunycon of powlder, shott and leade, to fight 2. wholl dayes, no not one gunner belonging to the Plantaccon.\n\nBy that time, the Anglo-American tobacco economy in Virginia was well into a debt-driven boom, with interest typically at 6 percent per annum. With credit, people drank up the profits, then ordered another round. \"The first legislative assembly in Virginia in 1619 felt obliged to pass acts against excess in apparel and also against drunkenness,\" writes Edmund S. Morgan. \"The thirst of Virginians became notorious in England.... The ships that anchored in Virginia's great rivers every summer were, as one settler observed, moving taverns, whose masters, usually private traders, got the greater part of the tobacco that should have been enriching the colonists and the shareholders of the company.... There were sometimes as many as seventeen sail of ships to be seen at one time in the James River.\"\n\nThe colonists on occasion starved. Maybe it was self-destructive depression under the harsh conditions, or maybe the sheer ineptitude of their gentry-heavy colonial population. But you could also blame it on the weed: they were so determined to grow tobacco that they neglected to grow food. Colonists were officially required to cultivate a plot of corn, but many ignored the law and relied instead on the Native Americans to do the base labor of raising corn while they chased tobacco riches, but the natives didn't always want to sell their corn to the colonists, so sometimes the Virginians went and took it.\n\nThe income that in theory accrued to the Virginia Company was being systematically drained away by its shamelessly corrupt officials, who repressed dissent brutally as its investors lost money and colonists died of diseases, mysterious distempers, and violence. A massacre commanded by Pocahontas's uncle Opechancanough killed about a third of the colonists and kidnapped twenty women in more than thirty separate surprise attacks on March 22, 1622, with the aim of driving the English out. The ailing John Rolfe was a victim of the campaign: one of the raids destroyed his plantation, after which he died, though whether from violence or from illness is unknown.\n\nThat massacre, along with the concomitant destruction of productive facilities, was followed by yet another starving time. With fewer than a thousand colonists still alive, King James rescinded the Virginia Company's charter, reverting the colony to royal status\u2014a decision that earned James the vituperation of future Virginia historians. Edmund S. Morgan, in his landmark history of slavery in Virginia, responded: \"Because the Stuart kings became symbols of arbitrary government and because Sir Edwin Sandys [one of the proprietors of the Virginia company] was a champion of Parliamentary power and was even accused at the time of being a republican, historians for long interpreted the dissolution of the Virginia Company as a blow dealt to democracy by tyranny. Modern scholarship has altered the verdict and shown that any responsible monarch would have been obliged to stop the reckless shipment of his subjects to their deaths.\"\n\nColonial development in Virginia was going to be a long-term investment, far longer than the timetables of profit could hold out for. By the time the rescission of the Virginia Company's charter became final in 1624, investors in the company had lost \u00a3200,000 and more than three-fourths of the six thousand or so people who had emigrated since 1607 were dead.\n\nAnd by the following year, so was King James. But not before he empowered an enemy of Virginia.\n\nIn his capacity as King James's secretary, George Calvert was the monarch's man in Parliament to defend the proposed \"Spanish match,\" the never-achieved royal marriage of James's second son, Charles, to Hapsburg princess Maria Ana, daughter of Felipe III. The idea that Charles might take a Spanish-Austrian Catholic bride horrified the Puritans in Parliament. King James's older son, Henry, known for his upright Protestant morality, had been the great popular hope of the Puritans, but he died in 1612 at the age of eighteen, leaving younger brother Charles in line for the throne.\n\nIn the end the Spanish princess would not marry a Protestant, and though Charles traveled to Spain to court her, he would not convert to Catholicism, so the marriage never came to pass. But the fallout from the affair led to a deterioration of relations between England and Spain, followed by war. It also left Calvert on the outs politically. He resigned his position and came out of the closet as a Catholic. James rewarded Calvert for his services, and got him out of the way, by awarding him a barony in northern Ireland and a title in the Irish peerage: Lord Baron of Baltimore.\n\nThen Charles, the future king of England, scandalized the Puritans by marrying a French Catholic Bourbon princess, Henrietta Maria de Medici. That's Maria as in the Virgin Mary, and also as in the territory that was named for the new queen consort: Maryland.\n\n*Reaching from present-day Gabon to present-day Zambia.\n\n#   10\n\n# **Maria's Land**\n\n_Does my hair trouble you? 1_\n\n\u2014King Charles I to his executioner, January 30, 1649\n\nIN HER MARRIAGE CONTRACT, the fifteen-year-old Queen Consort Henrietta Maria was guaranteed the full practice of her Roman Catholic religion, which enraged the Puritans.\n\nBorn in 1609, nine years after her father King Henri IV's Edict of Nantes provided civil guarantees for French Protestants, Henrietta Maria came from France to England with a mission of spearheading Catholic power by means of strategic marriage. She had learned the art of queening at the knee of her mother, Marie de Medici, who commissioned a series of twenty-six allegorical paintings depicting her life from the prolific Peter Paul Rubens.\n\nShe brought with her from France eleven liveried musicians and three singing boys, who performed sacred music composed for her. The English crown was considerably less affluent than the French, and Henrietta Maria's retinue was smaller than the Bourbons were accustomed to in France, but it was large enough that her household staff included a \"keeper of the parrots\" and two dwarves, Jeffrey and Sarah, both of whom had servants. \"Pet\" dwarves were common figures in royal courts, but in the case of Charles and Henrietta Maria, they had the function of making the monarchs look bigger: Charles was five foot four, and Henrietta Maria was so short she only came up to his shoulder.\n\nEngland began its slide to civil war in 1629 when Parliament, with strong Puritan representation, refused to convene. For the Puritans, having a Catholic queen was a dreadful infamy; they saw Charles as soft on popish Spain. By that time, England's monarch had deferred to Parliament for over three hundred years, but now Charles attempted to run England without Parliament, a standoff that lasted eleven years. During that period the royals also had a tense relationship with William Laud, the Archbishop of Canterbury, who persecuted both Puritans and Catholics while discharging his responsibilities as head of the twelve-member Lords Commissioners for Foreign Plantations.\n\nThe ensuing migration of Puritans to America defined one of the principal power blocs of future American politics, as approximately twenty thousand dissenters came to the Massachusetts Bay Colony in the 1630s. Unlike most other immigrants to the Americas, these were not single young men, but families. Many were relatively prosperous, and the community they built was stable, productive, and repressive.\n\nPuritan New England, a culture of literate, industrious, small farmers, was on guard against tyranny and against witchcraft\u2014which, for them, included Catholicism. There was no doubt: the Antichrist was the pope, and the Spanish were his henchmen. Immigrants had to be formally admitted to New England: the Puritans required letters of recommendation for potential colonists, who could only be part of the Calvinist New England Congregationalist Church. They were anti-episcopal (didn't have bishops), and they were intolerant of the episcopal Anglicans, as well as of the Quakers, to say nothing of Catholics.\n\nIn 1629, the same year that Puritans began fleeing to New England, George Calvert, now titled Lord Baron of Baltimore, asked Charles I for a land grant. His short-lived Avalon colony in Newfoundland had been defeated by a harsh winter. Now he wanted the territory belonging to Virginia on both the western and eastern banks of the upper Chesapeake, as mapped out by Captain John Smith. He pitched the charter as providing a buffer zone to protect His Majesty's grand Chesapeake Bay from encroachment by the Dutch and Swedish. The former had founded Nieuw Amsterdam in 1625, while the latter, colonizing parts of what later became Delaware and Pennsylvania, named a river and a settlement after the Swedish Queen Christina.\n\nIf the Swedish queen had a settlement named in her honor, what homage befit the queen of England?\n\nCalvert died only weeks before his land grant was finalized, but it was bestowed on his son Cecil Calvert, who inherited his title. Writing in Latin, a priest gave an account of the colony in 1633, before the first colonists had sailed: \"The Most Serene King of England desired that it should be called the land of Maria or Maryland, in honor of Maria, his wife. The same Most Serene King, out of his noble disposition, recently, in the month of June, 1632, gave this Province to the Lord Baron of Baltamore and his heirs forever.\"\n\nPraying to the Virgin Mary was a razor-sharp dividing line between Catholics and Protestants, the former of whom saw it as a mystical experience and the latter of whom saw it as idolatry. Virginia had been named for the Virgin Queen, Elizabeth, whose Church of England had removed the worship of the Virgin Mary from its liturgical calendar. Now there would be another Virgin-inspired queen-named colony in the typhoidal swampland\u2014this one appropriate for Catholic pioneers, for whom Marianism was at once a religious and political imperative.\n\nMary's Land was to be tolerant, but Maryland would not be Catholic turf the way the Spanish domains were. Quite the contrary: Maryland was officially Anglican, the majority of its colonists were Anglican or Protestant, and no Catholic church was actually established there, though Jesuits manned missions.\n\nNever again would the Chesapeake be under the control of a single entity. Its division into upper (Maryland) and lower (Virginia) affected everything from the cultivation of tobacco\u2014the two colonies could never coordinate how much they would produce or even what the standard measure was\u2014to the two territories' opposing status in 1861, when Virginia went Confederate while Maryland remained in the Union.\n\nThe first Maryland colonists arrived in 1634 on the _Ark_ , traveling via the Antilles. The priest Andrew White, who crossed the Atlantic with them, wrote in his journal that \"we came before [the island of] Monserat, where is a noble plantation of Irish Catholiques whome the virginians would not suffer to live with them because of their religion.\" This first known written instance of the word \"virginian\" was, significantly, used in connection with Virginia's intolerance. Virginia was officially Anglican and remained intolerant until independence, although Virginia was not settled by religious dissenters and was not particularly pious. \"With no resident bishop and only a handful of ministers to watch over its rowdy, scattered populace,\" writes Paul Lucas, \"seventeenth-century Virginia became noted for its lack of religiosity.\"\n\n\"As for Virginia, we expected little from them but blows,\" wrote Father White. When they arrived, he was impressed by the \"Patomecke\" (Potomac) River, which the new colonists attempted to rename St. Gregory's; it was, he wrote, \"the sweetest and greatest river I have seene, so that the Thames is but a little finger to it.\"\n\nFather White brought with him a Portuguese-surnamed indentured servant of African descent, Mathias de Sousa, described as a \"molato,\" along with another \"molato\" named Francisco, so free men of color\u2014albeit indentured\u2014were among the founders of the colony. Father White assigned his headrights to one Ferdinando Pulton, who claimed land grants based on the importation of twenty-one people.\n\nThe Virginia colonists were already insolent. In a 1634 letter written from Jamestown, Captain Thomas Yong of the Maryland expedition wrote, \"I have bene informed that some of the [Virginia] Councellors have bene bold enough in a presumptuous manner to say, to such as told them that perhaps their disobedience might cause them to be sent for into England, That if the King would have them he must come himself and fetch them.\"\n\nVirginia was by that time relatively stable. Its food problem had largely been solved by the successful establishment of large herds of cattle and especially hogs, which can have two or more litters a year of up to a dozen piglets at a time. With so much land available for pasturage, raising meat animals was practical, and the easy availability of high-quality protein from meat and dairy products may have been the salvation of the Virginia colony.\n\nVirginia was impresarial, its founding the work of a corporation with investors, but Maryland was a proprietorship. Lord Baltimore _owned_ it. A number of counties in Maryland are named for his family members: Calvert (the family name), Cecil (for Cecil Calvert, the second Lord Baltimore), Charles (for Charles Calvert, the third Lord Baltimore), Anne Arundel (Cecil Calvert's wife, Charles Calvert's mother), and Talbot (Lady Grace Talbot, Cecil Calvert's sister).\n\nWritten in Latin, King James's charter granted to Lord Baltimore the _hactenus inculta_ , or uncultivated lands, \"partly occupied by Savages, having no knowledge of the Divine Being.\" As compensation, the king and his heirs and successors were to receive (according to contemporary translation) \"TWO INDIAN ARROWS of those Parts, to be delivered to the said Castle of _Windsor_ , every Year, on Tuesday in Easter-week; and also the fifth Part of all Gold and Silver Ore, which shall happen from Time to Time, to be found within the aforesaid Limits.\"\n\nThe Maryland charter covered both shores of the upper Chesapeake, creating a territory divided into two parts by water. The \"western shore\" and the \"Eastern Shore\" of Maryland do not meet, but must connect across water.* The Virginians had the Chesapeake's four great rivers in their territory, though they were not yet fully navigable\u2014from south to north, the James, the York, the Rappahannock, and the Potomac. Maryland occupied the northern bank of the Potomac, but never attempted to navigate it commercially.\n\nCalvert's territory did, however, have a grand harbor on its western shore. It would not be of much use for transatlantic traffic, but would later be the commercial powerhouse of the Chesapeake's communication with the westwardly expanding domestic market: Baltimore.\n\nThe Virginians were too few in number to have occupied the Maryland territory, but William Claiborne (or Clayborne, or Clairborne), a Virginian from Kent, England, was already invested in the territory and opposed Baltimore's plan. Claiborne, a member of the Virginia Council, had named and claimed proprietorship of Kent's (or Kent) Island, which sits in the middle of the Chesapeake adjacent to the Eastern Shore. He focused not on planting tobacco but on fur trading, which obliged him to have good relations with the Native Americans. Claiborne insisted that the charter's language could not apply to Kent Island, to which he asserted ownership rights. Planning for the island to be the hub of a mercantile empire he would build, he had convinced settlers to move there and plant it with orchards and vines. He set up a shipyard, where he had the pinnace _Long Tayle_ built in 1631, three years before the arrival of Lord Baltimore's colony\u2014\"the first boat built solely on the bay,\" writes Frederick Tilp.\n\nThe first naval battle in the Anglo-American colonies took place in 1635 between Maryland and Virginia, when Lord Baltimore's pinnaces defeated Claiborne's vessels at the entrance to the Pocomoke River. Claiborne attempted various times to get back what he considered his land, through military conflict and diplomatic wrangling, but he ultimately relinquished the struggle in 1657 after an intra-Chesapeake hostility that lasted more than twenty years. Remembered as the champion of Virginia's former grandeur, he was the founder of a still-prominent family line of politically connected American bluebloods that includes his great-great-grandson W. C. C. Claiborne (the Virginian who was the first American governor of Mississippi and Louisiana).\n\nPerhaps it was Calvert's experience with the failed colony at Newfoundland that led him to issue and enforce instructions to his colonists to grow food crops for themselves: \"that they cause all the planters to imploy their servants in planting of sufficient quantity of corne and other profision of victuall and that they do not suffer them to plant any other comodity whatsoever before that be done in a sufficient proportion wch they are to observe yearely.\"\n\nPlantations were anything but self-sufficient in food. As John Smith explained to a royal commission, \"Corne was stinted [valued] at two shillings six pence the bushell, and Tobacco at three shillings the pound; and they value a mans labour [in tobacco] a yeere worth fifty or threescore pound, but in Corne not worth ten pound.\" The capital-intensive nature of a plantation required the dedication of all land to maximum financial return, with supplies imported and paid for on credit. But Lord Baltimore's insistence that \"Mary's Land\" raise its own \"victuall\" implanted from the beginning a culture of expert and varied cultivation in the colony, with long-range consequences for the state's high-quality food supply.\n\nMaryland put itself to the cultivation of tobacco from early days, with the result that Virginia planters had competitors who could be expected to increase production if they held back.\n\nNew England (Connecticut, Rhode Island, Massachusetts, New Hampshire, and, later, Vermont and Maine) never developed a staple crop, or a plantation system. New England had slavery in the colonial years, but unlike Virginia, it never became a slave society, in which all social and economic relations revolve around slavery. One of the first slaveowners in Massachusetts, Samuel Maverick, was the object of a complaint from a captive African woman whom he had force-mated with an African man; but without plantations, and cooped up in the limited space of houses in town, New Englanders did not engage much in slave breeding. New Englanders bought slaves, but mostly in small numbers: Africans (or creoles) from the Antilles and, later, Native Americans from Carolina, who were generally destined to be household, urban, or small-farm workers. Nor was New England a heavy consumer of indentured labor.\n\n_The Eastern Shore is prominent in this depiction of Lord Baltimore's Maryland in 1732._\n\nNew England survived in its early days the way the French did in Canada: on the fur trade. Beaver pelts were a principal export, and King Charles provided a market for them all by himself. He particularly liked silk-lined beaver hats, worn with brightly colored hatbands, and bought them not only for himself but for his retinue. According to Nick Bunker, he bought \"sixty-four beaver hats in 1618, fifty-seven in 1619, forty-six in 1623, and forty-three in 1624.\" Bunker estimates that as the beaver hat became popularized as \"an emblem of status\" for the peerage and the landed gentry, a minimum of twenty-three thousand of them a year were needed to accommodate the demand.\n\nThe small farmers of New England exported a variety of food and commodities, especially corn, and they diversified into becoming fishermen, lumberjacks, and shipbuilders, then developed into shippers, merchants, bankers, and insurers.\n\nDavid Hackett Fischer's tracing of four English folkways in America provides a model for appreciating the cultural contrast: 1) the Puritans of southeast and northeast of London, who moved to New England; 2) the Royalists of the south and west, who moved to Virginia; 3) the up-country Quakers, to Pennsylvania; and 4) the \"Scotch-Irish,\" to the Appalachians. Fischer surveys the demographics of England from which each migration came and demonstrates strong cultural continuity between locales on either side of the Atlantic, each of which would develop into a distinct political tendency in the independent American republic.\n\nSlavery was not a new idea in English culture, particularly in the area from which the largest number of Virginia's early populators came. \"Virginia's recruiting ground,\" writes Fischer, \"was a broad region in the south and west of England\" of scarce urban development and large rural manors\u2014an area where slavery had earlier (though no longer) existed for centuries, going back to the Roman era. \"During the eighth and ninth centuries,\" writes Fischer, \"the size of major slaveholdings in the south of England reached levels comparable to large plantations in the American South. When Bishop Wilfred acquired Selsey in Sussex [in the late seventh century], he emancipated 250 slaves on a single estate. Few plantations in the American South were so large even at their peak in the nineteenth century.\"\n\nThe Puritans of New England and the Royalist Virginians, opposed to each other from the start, struggled to establish their respective colonies in America as the hatred between \"Roundheads\" (Puritans, so called because they cut their hair short, who in popular telling were commoners descended from Saxons) and \"Cavaliers\" (Anglicans, who wore their hair long and were said to be aristocrats descended from French Normans, who were in turn the descendants of Norsemen, or Vikings) erupted in 1642 into what has been remembered in England as the Civil War, which had a strong echo in America.\n\n_In this woodcut tobacconist's card from ca. 1700, Virginia cavaliers drink and smoke while black slaves labor behind them. Images of Africans at work appeared in a variety of English tobacco advertising materials in the late seventeenth century, along with (not depicted here) Indians depicted with black skin, in tobacco-leaf skirts and headdress, overtly promoting as part of the product's public image its origin as an \"Indian weed\" cultivated by slave labor in Virginia. From Fairholt._\n\nThe Puritans versus the Cavaliers: not coincidentally, in North America these words connoted the two power bases of New England and Virginia. The Royalist Virginia gentry, who were largely descendants of English family webs transferred to America, believed in aristocracy, hierarchical society, luxury, idleness, and servants. Their identification as \"Cavaliers\"\u2014a word meaning \"horsemen,\" or, more broadly, \"knights\"\u2014links them with the Spanish _caballeros_ and the French _chevaliers._ Like them, the Cavaliers had the opposite of the Puritans' work ethic. \"Many Virginians of upper and middle ranks aspired to behave like gentlemen,\" writes Fischer. \"The words 'gentleman' and 'independent' were used synonymously, and 'independence' in this context means freedom from the necessity of labor.\"\n\nThe stringently religious Puritans did not gamble, but Virginia planters gambled compulsively. The Puritans suspected them of being Catholic sympathizers. By the 1630s, the more affluent Virginians were buying African slaves from Dutch traders on an ongoing basis, while Virginia frontier traders, who were something of a renegade element in the colony, enslaved and sold Native Americans.\n\nHenrietta Maria opened her chapel at Somerset House in 1636, after seven years of work. It was a safe place to attend Mass, and thousands did. It was also the height of fashion. The chapel hummed with motets commissioned from the queen consort's preferred composers. Marian imagery was everywhere. \"Visitors thronged to see the mesmerizing decorative scheme,\" writes Erin Griffey, \"replete with paintings and a special sacristy. Conversions of prominent courtiers and aristocrats, ladies in particular, were not uncommon in 1637. [Archbishop] Laud was incensed by the public scandal.\" But pursuant to an anti-superstition act of the Puritan Parliament, Henrietta Maria's chapel was destroyed by a mob of iconoclasts in 1643. They tore its crowning work, Rubens's _Crucifixion_ , into bits and threw the pieces into the Thames, along with the rest of the painting and sculpture the chapel contained.\n\nBy then, the English Civil War was under way. The Puritans, whose New Model Army was the first modern army in England, beat the forces of King Charles in 1645 and established the Commonwealth of England in 1649. Parliament carried out one of the most radical acts in all of European history when it tried, convicted, and, on January 30, 1649, killed the king. Remembering the botched execution of his grandmother, Mary Queen of Scots, Charles Stuart put his long Cavalier hair away from his neck into a cap to allow his executioner (a professional, brought from France for the occasion) a clean shot at his neck, and was successfully beheaded with a single stroke.\n\nOnce Puritans no longer feared persecution in England, out-migration to New England stopped as suddenly as it had begun. The region would not receive another mass migration for nearly two centuries. There was even a reverse migration back to England, since previously closed doors were now open to well-connected Puritan businessmen.\n\nThe Puritan regicide further poisoned the relations between Catholic and Protestant Europe. The designation of the ambitious New Model Army leader and king-killer Oliver Cromwell as Lord Protector of England, Wales, Scotland, and Ireland in 1653 began an era of intolerance, during which the execution of heretics increased and theaters remained shut down.\n\nIn Maryland, the colonial assembly passed the Act of Toleration in 1649 at the Calverts' urging. The first law in the colonies concerning religious tolerance, it reiterated the tolerant policy that had been part of Lord Baltimore's instruction from the beginning. But after a ten-man Puritan council headed by Maryland's old nemesis William Claiborne took charge of Maryland in post-Cromwell 1654, a new law prohibited open practice of the Catholic faith. In 1658, Calvert managed to get the Act of Toleration reinstated. Still, on July 23, 1659, the council issued a directive to \"Justices of the Peace to seize any Quakers that might come into their districts and to whip them from Constable to Constable until they should reach the bounds of the Province.\"\n\nQuakers, who were antislavery and were therefore unwelcome, presented a new social and political problem for the nominally Anglican Cavaliers. The first seed of Quakerism was planted in Virginia in 1656 by the Londoner Elizabeth Harris, who remained in Virginia for a year or so and proselytized. Quaker George Wilson, who had been whipped from constable to constable through three different towns and banished from Massachusetts, arrived in Virginia in 1661 and was imprisoned until \"his flesh actually rotted away from his bones,\" in the words of a chronicler.\n\nUnder the Puritans, Royalists fled England for Virginia and Maryland, an exodus that continued even after the Restoration of 1660. \"From 1645 to 1665,\" writes Fischer, \"Virginians multiplied more than threefold and Marylanders increased elevenfold, while New Englanders merely doubled.\"\n\nOther Cavaliers fled hostile Puritan England for the island of Barbados, where a different kind of revolution was in progress: sugar.\n\n*By custom \"Eastern Shore\" is capitalized, but \"western shore\" is not.\n\n#   11\n\n# **Barbados**\n\n_The genterey here doth live far better then ours doue in England; thay have most of them 100 or 2 or 3 of slaves apes apiece] whou they command as they pleas: hear they may say what they have is thayer oune; and they have that Libertie of contienc [conscience] which wee soe long in England have fought for: But they doue abus it.[ 1_\n\n\u2014Henry Whistler, Barbados, 1655\n\nTHE ATLANTIC SUGAR PLANTATION system took shape in the late fifteenth century on the previously uninhabited island that the Portuguese called S\u00e3o Tom\u00e9, off the coast of Calabar, in the crook of Africa.\n\nSettled by explorer \u00c1lvaro Caminha in 1493\u2014the same year Columbus brought experimental sugar seedlings to the present-day Dominican Republic\u2014S\u00e3o Tom\u00e9 built on the previous model of Mediterranean sugar plantations but employed previously unthinkable quantities of labor to produce sugar on a new, large scale. The labor was available via S\u00e3o Tom\u00e9's ready access to slave markets; it was a transshipment point for slaves headed to the Americas. By the 1550s, S\u00e3o Tom\u00e9 had sixty sugar mills grinding, with individual plantations boasting workforces of as many as three hundred slaves.\n\nThe Portuguese applied the S\u00e3o Tom\u00e9 model to create the first great sugar industry of the Americas in northeastern Brazil, where a full-scale planters' aristocracy had entrenched itself by the mid-sixteenth century. There was one major difference, however: the labor force in Brazil was mostly made up of enslaved indigenous Brazilians, who quickly proved to be unsatisfactory laborers. In a pattern later replicated throughout the hemisphere, a transition began in Brazil to African slave labor.\n\nWanting in on the sugar plantation action, the Dutch captured S\u00e3o Tom\u00e9 in 1598\u201399. While paused from attacking Spanish and Portuguese merchant vessels during the Twelve Years' Truce (1609\u20131621), they built up their navy. They established Dutch outposts in North America, beginning in 1615 with Fort Nassau on the Hudson River and including, as of 1625, Fort Amsterdam\u2014the future New York City\u2014at the tip of Manhattan Island. With its defensive battery positioned on the site of present-day Battery Park, Fort Amsterdam provided protection for Dutch families who had been consolidated there from around the region.\n\n_The relative closeness of Africa and Brazil is depicted in this detail from the first map of the hemisphere, a 1562 collaboration between Spanish cartographer Diego Guti\u00e9rrez and Dutch engraver Hieronymous Cock. In the ocean between the two, the Portuguese fleet is depicted on its way to \"Calicute\" (India). In the lower portion of the image, a naval battle is depicted._\n\nNieuw Amsterdam was from the beginning dense, secular, tolerant (with Jews both Sephardic and Ashkenazi), and multilingual. The colony's first shipment of slaves, eleven in all, came in the colony's second year, making it the second colony (after Virginia) in the present-day United States to import African slaves.\n\nSlaves in Nieuw Amsterdam were corporately owned by the Dutch West India corporation. With time, they were manumitted and given land of their own, though they had to give a portion of their proceeds back to the company. On July 14, 1645, the free African Paulo d'Angola was granted a parcel of land on present-day Washington Square Park. Antony Congo was granted a parcel on the east side of the Bouwerie (from a point between present-day Houston and Stanton Streets to Rivington) on March 25, 1647. Francisco and Simon Congo were given nearby plots. They were exposed pioneers in a bad neighborhood, forming the buffer zone between the Dutch at the lower tip of Manhattan and the Native Americans to the north who might decide to raid.\n\nAs Dutch commercial policy became more aggressive, the Dutch fleet assaulted Portugal's markets in Asia, then in the 1620s began a war for the European sugar market, which was principally supplied at that time by the two Brazilian centers of Salvador da Bahia and Recife in Pernambuco. They took Recife in 1641, though they could not hold Salvador.\n\nFrom their vantage point in Brazil, the Dutch saw a double commercial opportunity nearby, on the English-controlled island of Barbados. In taking advantage of it, they created the Antillean sugar industry.\n\nBarbados was easy for a seventeenth-century navigator to miss. Located in the Atlantic a hundred or so miles to the east of the arc of the rest of the Lesser Antilles, it's a patch of land comprising only some 166 square miles. Off the main sea road, it was the farthest from the major Spanish bases in the Americas, and it offered a relatively easy sail to Europe.\n\n_Barbados_ means \"bearded ones\" in Spanish, though why the island was called that is a mystery. The Spanish had claimed the unoccupied island in 1511, but it was abandoned by the time the English occupied it in 1627, just as the Dutch were making their move into Brazil. Sent by a commercial syndicate in London, the English expedition to settle Barbados paused on the way to \"capture a prize\"\u2014i.e., plunder another country's vessel. They stole ten \"negro slaves,\" who were taken to Barbados along with the eighty settlers that disembarked on February 17, 1627.\n\n_In this detail from a 1639 Dutch map by Joan Vinckeboons, Barbados is the island sticking out to the east of the arc of the Lower Antilles._\n\nThe island had no native population, but Captain Henry Powell induced thirty-two agriculturally knowledgeable native people from Dutch-held Guyana to come to Barbados, then enslaved them once they were there. Starvation would not be an immediate problem: the island teemed with wild hogs, the legacy of a long-gone Spanish presence. The colonists killed them off in three years flat.\n\nThe Barbadian colonists tried raising tobacco at the same time it was being developed in Virginia and Maryland. But their product was of even poorer quality than the Chesapeake's, and they had problems getting labor because Barbados's checkered reputation in England made recruiting difficult. As happened over and over in the Americas, crooks and whores were sent as colonists, but they were far from satisfactory as plantation workers.\n\nThe trade balance between England and its colonies was projected to be even, via barter, without a need for settling accounts by a transatlantic flow of silver and gold that was wanted elsewhere. Since London made the rules and set the prices, London could tinker with the numbers as it liked. But just as the London planners were caught by surprise when Virginia became a tobacco exporter, they didn't count on the Dutch setting up English colonists in Barbados in the sugar business, from a base in Brazil.\n\nIt happened in the 1640s, while England was embroiled in the civil war between Roundheads and Cavaliers. Barbados had both political tendencies present but neither controlled the society definitively, and the island was practically independent during those years, enjoying what was effectively free trade with vessels of various flags.\n\nThe Dutch, not the English, made the Barbadians rich. Fueled by a substantial injection of Dutch capital\u2014something strictly forbidden by London\u2014the Barbadians learned how to make sugar, via Dutch intermediaries and also by firsthand observation from traveling to Brazil. The Dutch had a lot to offer the Barbadians, and they could take a profit at every step of the process. They provided the Barbadians with Europe's cheapest credit to get started making a fortune in sugar and waited until the sugar was on the market to collect and refinance. They sold them the machinery and technology. They refined the molasses into sugar in Europe, and sold the sugar in the lucrative Dutch markets.\n\nThe Dutch could also provide the crucial and most expensive element: the labor. As a complement to taking Brazil, in 1637 they took the Portuguese slave castle of Elmina, offshore from the Gold Coast. They established posts on the Slave Coast (present-day Benin) that were controlled from Allada (or Ardra). For a time the Dutch controlled Luanda and Benguela in Angola as well. The strategic reason to occupy the slave ports was to support the Dutch sugar venture in Brazil, where the labor force died or escaped to the wilderness in large numbers even as acreage under cultivation was increasing. As a consequence of their move into Africa, the Dutch had plenty of slave-trading capacity with which to service the English, who were not yet engaged in the commercial African slave trade.\n\nThe Dutch didn't rule the Brazilian northeast for long. The Brazilian planters rebelled against them in 1645, but by the time they drove the Dutch out definitively in 1654, the Barbadians had copied their techniques for making sugar and were making fortunes.\n\nThe sugar revolution transformed Barbados. Among the skills the Barbadians learned from the Dutch and the Brazilians was the management of hundreds of slaves on a single plantation. When they converted Barbados to slave labor, they did it massively and quickly. Barbados, then, became the first place where Englishmen surrounded themselves with large numbers of enslaved Africans. The Barbadian planters had been purchasing indentures of white servants, but they made an abrupt transition to purchasing the legal rights to the bodies and the future \"increase\" of black laborers. They imported large numbers of kidnapped Africans, because, as with later sugar regimes, their labor force was not self-reproducing: \"though we breed both Negroes, Horses, and Cattle,\" wrote Richard Ligon in Barbados, \"yet that increase, will not supply the moderate decays which we find in all those.\"\n\nAlong with the changeover to a slave society came accumulation by dispossession, with the mortgage as a primary tool.* The Dutch were conservative about whom they extended credit to, making for a concentration of large planters. The wealthy then extended credit to the less wealthy by means of a mortgage, and foreclosed when they could not pay, as land ownership consolidated. Many former indentured servants had been given small patches of ground at the end of their tenure; now the small farmholds of forty different farmers became the eight hundred acre property of a single sugar baron, one Captain Waterman.\n\nThe new Barbadian sugar planters quickly developed, in Richard S. Dunn's words, \"a code of conduct that would never be tolerated at home.... In the islands there were no elders, the young were in control, and many a planter made his fortune and died by age thirty. In short, Caribbean and New England planters were polar opposites; they represented the outer limits of English social expression in the seventeenth century.\" But these two outer limits did business with each other, as Barbados was dependent on New England for much of its food.\n\nBarbados's sugar revolution was well under way in 1645, when the island's black population was 5,680. Guadeloupe and Martinique, belonging to the enemy commercial system of France, quickly followed in the conversion to sugar with the help of Dutch exiles from Brazil. On the other side of the Atlantic, some of Glasgow's first factories were rum distilleries, which added value to the molasses Glaswegian merchants were importing from the Antilles already in the 1640s.\n\nAs Barbados was experiencing its first rush of sugar prosperity, the execution of King Charles in 1649 sent Cavaliers fleeing to the island. They seized control of its government following a pamphlet war and armed action, making the island into a Royalist stronghold. By the following year, Barbados had declared itself for Charles II, who was in French exile. Austere, regicidal, militarized, religious extremists: the Puritan government was unpopular at home, but Barbados was in open rebellion.\n\nMore consequentially, Barbados's practice of free trade with the Dutch antagonized the politically powerful London merchants and shippers, who were not happy about losing their captive market to foreign competition. An embargo, the Act of 1650, froze all English trade with Barbados as well as with the other Royalist colonies, including Virginia, and authorized the confiscation of all merchandise headed there. That became a hot issue in New England, whose trade with Barbados was its most profitable commercial activity.\n\nBarbados issued what was essentially a declaration of independence on February 18, 1651, charging Parliament with placing it in a state of \"slavery\"\u2014a word that would resound through pro-independence polemics on the North American mainland in the eighteenth century. Barbadian Cavaliers confiscated the lands of Barbadian Roundheads; according to an anguished letter written from Barbados, they had \"Sequestred 52 Gallandt plantations, who are Werth as all ye island besydes.\" Meanwhile, Barbadian royalists' lands in England, Scotland, and Ireland were confiscated by Parliament.\n\nThe Puritan Parliament passed a Navigation Act in 1651 that forbade trading with foreigners, requiring the use of English ships and captains for all commerce. That quickly led to war between England and the Netherlands, leaving Barbadian planters' Dutch business contacts on the wrong side of hostilities. Believing, perhaps not incorrectly, that Cromwell was out to destroy them, the Barbadian planters openly favored their Dutch commercial partners over their English colonial masters, effectively committing treason during wartime.\n\nWith instructions to seize Dutch merchantmen, Cromwell's admiral Sir George Ayscue blockaded the island in 1652. Then, despite having only a small force, he attacked with the support of scurvy-ridden troops who had detoured from their mission of subduing Virginia. He bluffed the Barbadian royalists into surrendering and established a government loyal to Parliament. But the damage was done to the British colonial system: Barbados had experienced independence and free trade.\n\nAyscue's victory was only the beginning of Cromwell's military designs. After making peace with the Dutch in 1654, he began a project\u2014the Western Design, it was called\u2014to drive the Spanish out of the Americas. Unfortunately, Cromwell sent an untrained, incoherent expedition of conquest to base itself in Barbados in 1655\u2014there to provision itself, on an island dependent on importation for its food. Depleting the island's scant resources, the English fleet funded itself by laying high duties on the island's imports.\n\nThat there was already a nascent slave-breeding business of sorts in Barbados is suggested by the journal of a member of the Western Design expedition, a Puritan named Henry Whistler, who noted in 1655 that children had a cash value at birth and that there was a market in them:\n\nThis Island is inhabited with all sortes: with English, french, Duch, Scotes, Irish, Spaniards thay being Iues Jews]; with Ingones [Indians] and miserabell Negors borne to perpetuall slavery thay and thayer seed: these Negors they doue alow as many wifes as thay will have, some will have 3 or 4, according as they find thayer bodie abell; our English heare doth think a negor child the first day it is born to be worth 511 [five pounds eleven shillings], they cost them nothing the bringing up, they goe all ways naked: some planters will have 30 more or les about 4 or 5 years ould: _they sele them from one to the other as we doue shepe._[ 17 (emphasis added)\n\nThe principle of _partus sequitur ventrem_ was already in place. \"By 1650 certainly, and probably a good bit earlier,\" writes Dunn, \"slavery in Barbados had become more than a lifetime condition. It extended through the slave's children to posterity.\" The idea that one caste of people, visibly different, could be born into bondage conflated the condition of slavery with the concept of \"race.\"\n\nBefore leaving Barbados on its mission of conquest, the English fleet recruited the island's dispossessed whites to join its soldiery, a job that entailed risking one's life but also brought the possibility of plunder, or even land. When the expedition sailed away on March 31, 1655, it took away some four thousand white Barbadians, mostly formerly indentured servants, who were never to return. In their wake were sent a rougher class: defeated Scotch and Irish soldiers captured in battle, sent as laboring prisoners, along with troublemakers, Catholics, and former landowners.\n\nThe Western Design expedition's attack on Santo Domingo was a murderous failure, repulsed definitively by the Spanish. But then the expedition turned its sights more successfully on Jamaica. Cromwell's navy invited pirates into Jamaica's gaudy, raunchy, now-disappeared capital of Port Royal, beginning a golden age of piracy in the Caribbean.* While England launched attacks against Spanish coastal towns, the pirates (most infamously Henry Morgan) attacked Spanish shipping, provoking a two-fronted war that expelled the Spanish from Jamaica in 1655, though it took another five years for the English to subdue the insurgency.\n\nThis first dislodging by force of Spain from an established colony sparked a new rush for riches as politically connected merchants jockeyed for position in Jamaica. Few if any of the former Barbadian yeomen who had come to Jamaica with the fleet benefited, however; most died of disease. Some surviving soldiers received land grants and became planters, amassing large fortunes through the use of slave labor and achieving that rare, coveted condition: class mobility.\n\nAfter Cromwell died in 1658, probably of a bacterial infection, the Roundheads in England deteriorated into bickering factions and the Cavaliers retook power. The extravagant, lecherous, French-raised Charles II, son of the beheaded Charles I, ascended to the English throne in 1660. Amid widespread rejoicing at the departure of the unpopular regime, the theaters of England, shuttered by the Puritans, reopened. In what has been remembered as the Restoration, London once more began to have a public life after more than a decade of Puritan sobriety, as an age of coffeehouses began.\n\nWith the Restoration came an aggressive new commercial policy designed to project an image of grandeur by maximizing the royal share of the world. Charles II was not much interested in governing, but he was attuned to the importance of the colonies; many places in the New World had been named for his father, and Maryland bore the name of his mother. In appreciation of Virginia's loyalty, he bestowed on the colony the title of Dominion, a name that persists as Virginia's nickname of \"Old Dominion.\"\n\nOwnership of Barbadian land was quite concentrated by this time, and sugar production increased precipitously. There were twenty thousand black captives on Barbados by 1660, twenty times as many as in Virginia. By 1676, the number had grown through importation to 32,473, and 46,602 in 1684. The island became one of the most densely populated areas in the world.\n\nNow that the labor force was mostly black, the situation required legal clarification. Barbados had a comprehensive slave code by 1661 that differentiated indentured servants from slaves, with provisions that were highly disadvantageous to the enslaved: killing an enslaved person was punishable only by a fine. The code came just in time to be useful to Jamaican lawmakers; Charles II formally annexed Jamaica for England in 1661.\n\nParliament passed another Navigation Act in 1660, requiring exclusivity of trade by the colonies, who could conduct commerce only with English ships that were captained by Englishmen and three-fourths of whose sailors were English. Subsequent Navigation Acts were passed in 1662 and 1663 and were followed up in 1673 and 1696, defining a policy that would in one form or another endure through the Napoleonic era. The Navigation Acts were highly consequential; by denying the Dutch access to American markets controlled by England, they consolidated England's position as the number-one commercial power.\n\nThey also empowered the New England colonists, though that was an unintended consequence. New England had been conducting some hemispheric trade since the 1630s. Now, since colonial ships counted as English, the Navigation Acts stimulated the New England shipping industry, turning the New Englanders into \"the Dutch of England's empire.\" New England's territorial advancement to the north was blocked by French Canada. Especially in the case of the Rhode Island colony, founded in 1636 by Massachusetts dissident Roger Williams, New England had little in the way of a hinterland. Rhode Island was like Portugal in that both places consisted mostly of coastline; like the Portuguese, Rhode Islanders turned to the sea to make money.\n\nThe colonists weren't allowed to manufacture, but New England ships could run down to the West Indies and exchange their farm and fishing products for molasses, which they brought home and distilled into great quantities of rum. The New Englanders also sold the Barbadians kidnapped Native Americans as slaves, but since New England was hemmed in by French Canada, their supply was limited.\n\nCharles II was more interested in trying to find gold than slaves when he chartered the Governor and Company of the Royal Adventurers Trading to Africa on January 10, 1662. Most of Africa had no gold, but the Gold Coast had for centuries provided a money supply to the Muslim world. Its gold, traded overland up through the Maghreb and into Europe, had been turning up in English commerce since at least the thirteenth century, when the Royal Mint was established. Though the Gold Coast's resources were partly depleted by the time of the Restoration, it was still a gold producer.\n\nAt that time, the Gold Coast was not an exporter of African slaves, but an importer: an intra-African coastal slave trade conducted by Portuguese captains brought laborers kidnapped from Calabar to labor in the Akans' gold works. Under pressure from the colonies to supply labor, English traders began to insist on taking slaves from the Gold Coast as well as gold and ivory. The company instructed its traders not to pay for slaves with gold but with barter, because the idea was to bring gold home. But African traders quickly began demanding gold for at least part of the price of slaves, the rest being made up of manufactured goods.\n\nThe Royal Mint began striking a new gold piece in 1663, the first machine-minted English coin, intended to be worth twenty shillings (actual exchange rates were different). A tiny elephant embossed on each one\u2014sometimes an elephant and castle\u2014let the world know that England's money was made with Africa's gold. The coins became known almost immediately as \"guineas,\" from the name of the long coastal stretch of West Africa between the mountain ranges of Sierra Leone and the Bight of Biafra. Elephant and elephant-and-castle guineas were minted until 1726, though later non-African-themed guineas were minted until 1813, the monarch pictured on the \"heads\" side changing with the throne.\n\n_Detail of a guinea._\n\nThe castle was a direct image of England's growing importance in the slave trade, while the coin's elephant image depicted another of the sources of wealth of the African trade: ivory, used in all manner of fine manufactures, notably including musical instruments. Ivory comes from killing a male animal (only the males have big tusks) of five tons or so in order to harvest the approximately 1 percent of its body weight that is dentine mass, while leaving the carcass for carrion eaters. As keyboards appeared all over Europe and America, the intelligent animals were slaughtered in large numbers so their teeth could produce ivory for the fingers of well-bred young ladies to caress, the market picking up when the piano began to be mass-produced in the nineteenth century. Ivory toothpicks became a necessary gentleman's item in Europe. In Africa, where hunting elephants was basic to survival and hunting lore was remembered in the form of song, the animal was consumed after slaughter and the tusks used as ceremonial trumpets across a wide range of the continent.\n\nEngland's creation of the guinea spearheaded an offensive in which it squared off against the Netherlands. Charles II's brother James (the future King James II), who bore the king's brother's traditional title of Duke of York, prosecuted a second Anglo-Dutch war, fought on multiple fronts in different parts of the world. The English attacked Dutch slave-trading positions on the African coast, and in 1664, they took control of Nieuw Amsterdam, renaming it New York in honor of the city's new royal master. But they were otherwise badly beaten in the war, which ended in 1667 with England's humiliating defeat. In the treaty negotiations, the English offered to trade New York back to the Dutch in exchange for the sugar-producing, moneymaking South American colony of Surinam, but the Dutch refused the offer. The English kept Manhattan, locking in their control of the Atlantic seaboard from New England down to Virginia.\n\nThat stretch of the North American Atlantic coast formerly claimed by the Dutch became property of the Duke of York, James Stuart; Charles II gave him all the land between New England and Maryland. James in turn dealt out the territory between the Hudson and Delaware Rivers to John Lord Berkeley and Sir George Carteret, never mind that people already lived there. It was divided into East Jersey and West Jersey, with the whole collectively known as, according to the document signed by James, \"New Caeserea or New Jersey,\" whose birth was thus pure cronyism. Up the Hudson, the Dutch Fort Nassau was renamed Albany, for James's Scottish title. Located on the Mohawk River, in the gap between the Catskills and the Adirondack Mountains, Albany was perfectly positioned for commerce with the West.\n\nThe Anglo-Dutch war badly damaged the ineffective Company of Royal Adventurers Trading to Africa, which was reorganized and renamed the Royal African Company in 1672. But the new company was also badly managed, and it made no attempt to get North American slaveowners the labor they wanted. The gap was filled by independent entrepreneurs.\n\nAs soon as there were slaves, there were conspiracies to rebel\u2014sometimes involving indentured whites as well, sometimes together with Native Americans. Herbert Aptheker lists the first \"serious conspiracy involving Negro slaves\" in English North America as occurring in Virginia in 1663, when there were still relatively few black people in Virginia and they had only just been declared to be slaves. The Virginia Assembly, in passing a 1672 act that authorized the killing of maroons, with reparations made at public expense to the individual slaveowners thus deprived of property, noted, \"it hath beene manifested to this grand assembly that many negroes have lately beene, and now are out in rebellion in sundry parts of this country and that noe meanes have yet beene found for the apprehension and suppression of them from whome many mischeifes of very dangerous consequence may arise to the country if either other negroes, Indians or servants should happen to fly forth and joyne with them.\" A similar authorization was passed in 1680, suggesting that the problem continued to vex the Virginians.\n\nA plot to murder the masters, neither the first nor the last, was discovered on Barbados in 1674. Whether it existed in reality or not is hard to say, since slave societies were particularly alert to potential uprisings, to the point of sometimes executing people for imagined crimes. According to a pamphlet published in London in 1676, the conspiracy was led by the \"Cormantee\"\u2014Akan people from the Gold Coast. The pamphlet's text is notable for its description\u2014complete with, supposedly, elephant-tusk trumpets\u2014of the artistry and artisanship attendant to Gold Coast royal pageantry, of which some seventeenth-century Barbadians would have had firsthand knowledge from slaving voyages. It also includes an early occurrence of the word _Baccararoe_ , i.e., _buckra_ , which would become a black term for whites throughout the English-speaking Americas:\n\nThis Conspiracy first broke out and was hatched by the Cormantee or Gold-Cost Negro's about Three years since, and afterwards Cuningly and Clandestinely carried, and kept secret, even from the knowledge of their own Wifes.\n\nTheir grand design was to choose them a King, one Coffee an Ancient Gold-Cost Negro, who should have been Crowned the 12th of June last past in a Chair of State exquisitely wrought and Carved after their Mode; with Bowes and Arrowes to be likewise carried in State before his Majesty their intended King: Trumpets to be made of Elephants Teeth and Gourdes to be sounded on several Hills, to give Notice of their general Rising, with a full intention to fire the Sugar-Canes, and so run in and Cut their Masters the Planters Throats in their respective Plantations where-unto they did belong.\n\nSome affirm, they intended to spare the lives of the Fairest and Handsomest Women (their Mistresses and their Daughters) to be Converted to their own use. But some others affirm the contrary; and I am induced to believe they intended to Murther all the White People there, as well Men as Women: for Anna a house Negro Woman belonging to Justice Hall, overhearing a Young Cormantee Negro about 18 years of age, and also belonging to Justice Hall, as he was working near the Garden, and discoursing with another Cormantee Negro working with him, told him boldly and plainly, He would have no hand in killing the Baccaroroes or White Folks; And that he would tell his Master.\n\nAll which the aforesaid Negro Woman (being then accidentally in the garden) over-heard, and called to him the aforesaid Young Negro Man over the Pales, and enquired and asked of him What it was they so earnestly were talking about? He answered and told her freely, That it was a general Design amongst them the Cormantee Negro's, to kill all the Baccararoes or White People in the Island within a fortnight. Which she no sooner understood, but went immediately to her Master and Mistris, and discovered the whole truth of what she heard, saying withal, That it was great Pity so good people as her Master and Mistriss were, should be destroyed.\n\nThis account exemplifies what was already a well-worn conspiracy theory, combining as it does three major tropes of white narratives of slave rebellion:\n\n1) decisions taken by a council of slaves from various plantations to stage an organized rebellion (as would in fact happen more than a century later in Saint-Domingue\/Haiti);\n\n2) the assertion by the chronicler of the intention of the black rebels to kill white men and take white women for sexual use; and\n\n3) the salvation of the whites by the intercession of a faithful domestic slave who betrays the conspiracy of the black rank-and-file out of love for her master's family.\n\nThese elements recur in masters' accounts of conspiracies throughout the hemispheric history of slavery, both black and indigenous. The following excerpt from the same pamphlet concludes with the characteristic final trope of the slave rebellion narrative, portrayed as a happy ending: the torture and massacre by the masters of a number of the enslaved. It also reports a common belief of Africans, reported in various parts of the Americas, that the enslaved would return to Africa upon death.\n\nSix burnt alive, and Eleven beheaded, their dead bodies being dragged through the Streets, at _Spikes_ a pleasant Port-Town in that Island, and were afterwards burnt with those that were burned alive...\n\nThe spectators... cryed out to _Tony, Sirrah, we shall see you fry bravely by and by._ Who answered undauntedly, _If you Roast me to day, you cannot Roast me tomorrow:_ (all those _Negro's_ having an opinion that after their death they go into their own Countrey). Five and Twenty more have been since Executed.\n\nIn this telling from a colonist, the death of Africans was only of importance as the cost of doing business.\n\n*The term \"accumulation by dispossession\" was suggested by David Harvey, who proposes it as an update to Marx's \"primitive accumulation.\" Harvey, 137.\n\n*Port Royal was permanently submerged by earthquake and tsunami in 1692.\n\n#   12\n\n# **The Anglo-Saxon Model**\n\n_It was not necessary to pretend or to prove that the enslaved were a different race... Anyone could tell black from white, even if black was actually brown or red. And as the number of poor white Virginians diminished, the vicious traits of character attributed by Englishmen to their poor could in Virginia increasingly appear to be the exclusive heritage of blacks. 1_\n\n\u2014Edmund S. Morgan\n\nTHE FIRST LARGE LAND distribution in Virginia was overseen by William Berkeley, royal governor as of 1642. A wit and playwright from the court of Charles I, he \"encouraged the cavaliers to come over in large numbers,\" wrote Philip A. Bruce, and made his cronies into large landholders. Berkeley remained as governor over a thirty-five year period, although he was out during the years of the Civil War and the Puritan reign. His years in power were on the whole prosperous ones, but his governorship ended badly with the suppression in 1676 of Nathaniel Bacon's rebellion, the largest colonial-era uprising in the territory of the future United States.\n\nBacon's Rebellion was a class war, in which \"the ambitions and fears of frontier planters clashed with the desire of the royal governor to maintain a monopoly of trade with the Indians.\" A tiny number of families\u2014the gentry\u2014had quickly come to control the affairs of each county, and they had the good coastal land locked up. The leading edge of the economy was on the west, pushing out into the wilderness. In a pattern that would be repeated in various forms during the long westward expansion across the continent, the pioneers made war on the Native Americans in order to enclose the land the \"salvages\" lived on. To that end, they wanted to get rid of the Indians as fast as possible\u2014abduct them and sell them to Barbados, thereby profiting, or simply kill them and consider the expropriated land adequate profit.\n\nBacon, recently arrived in Virginia, led a group that attacked the Pamunkey and then led an uprising against Berkeley in which he promised slaves their freedom if they would fight with him. Bacon was put down by Berkeley after a battle involving a thousand Redcoats sent from London; a battalion of eighty slaves and twenty indentured servants was one of the last to surrender. In the course of suppressing the rebellion, Berkeley heavy-handedly massacred a number of the rebels, and hung some as well, confiscating the property of anyone he deemed an enemy. Ebenezer Cook, the London-born Maryland poet remembered for his satirical poem \"The Sot-Weed Factor,\" composed his longest poem about Bacon's Rebellion. He described the rebels as \"Bullies, Ruffians, Debauchees, Cheats, Gamesters, Pimps, and Raparees,\" and characterized Berkeley's force as a mercenary one:\n\n_Berkley, whom the Mob detested,_\n\n_In Bacon's Absence had invested;_\n\n_Transporting from the Eastern Shore_\n\n_(T'augment the Force he had before)_\n\n_Of Arms and Ammunition Store,_\n\n_And Men, who fought for ready Pay,_\n\n_Twelve Pence a Head, for ev'ry Day;_\n\n_With Plunder of all that had taken_\n\n_Rebellious Oath to Col'nel Bacon._\n\nThere had been uprisings of the poor in England, but Bacon's Rebellion brought a new element into the mix that would become a permanent feature of American clashes: guns. Unlike England, Virginia was a gun culture. \"Whereas in England, only men with estates valued at above one hundred pounds sterling were allowed to own guns,\" writes Kathleen M. Brown, \"English men in Virginia at all levels of property ownership were _expected_ to own them, especially after the succession of Dutch threats to the colony during the late 1660s and early 1670s.\" Guns and slavery were intimately associated with each other; all slave-raiding relied on guns, and all slaveholding relied on armed repression.\n\nOne of the messages of Bacon's Rebellion as received by the Virginia gentry was that new poor freedmen emerging from indenture every year created a social problem. Enslaving them was not possible: Englishmen would not countenance enslaving other Englishmen. The solution was to shift over to African laborers. By replacing English laborers with African ones, they could, in Edmund S. Morgan's memorable phrase, \"enslave the poor,\" transforming the underclass from a political threat to a security issue with a color-coded caste system.\n\nLocked up and dispersed across isolated tobacco plantations, enslaved Africans were easier to control than indentured English, Scottish, and Irish freemen. Slavery was for life: manumission, common in Spanish territories, would not become so in Virginia. It was widely assumed that if slaves were freed, they would be a danger to the public at large, an assumption that drew on (and fed) a common belief that Africans were naturally more violent than Europeans and would become vicious if not repressed.\n\nThough tobacco required much less startup capital than sugar, Virginia nonetheless became a magnet for capital, much of which went into acquiring slaves. With slave labor, Virginia produced more tobacco than ever before. \"In the three generations that followed Bacon's Rebellion,\" writes Bernard Bailyn, \"a hierarchy of the plantation gentry emerged in stable form, dominated by a social and economic leadership whose roots can be traced back to the 1650s and whose dominance in politics was largely uncontested.\" The fact that this politicized gentry was principally invested in slaves would determine the course of policy for subsequent generations.\n\nLeaving future generations to deal with the consequences of a society divided into white masters and black slaves, the great planters of late seventeenth-century Virginia established dynasties of wealth in English North America, some of which continue into the present day. They locked the need for slavery into place by making it such a central part of the economy that, once implemented, it could not be eradicated\u2014at least, not without the destruction of the economic structures they had put in place and the erasure of their accumulated wealth. Future generations were born into a system they felt powerless to dismantle.\n\nThe move to a slave society in Virginia bound rich and poor whites together through the privilege of skin color. Landowning Virginians would be free to experiment with democracy, since their enslaved working class had no rights or vote. Lesser whites would identify with the masters, whose caste they were privileged to belong to, and not with the slaves. This implied a considerable commitment to the policing of caste boundaries, since this category of the poor would have to remain repressed and enslaved in perpetuity.\n\nBy the time of independence, some two-thirds of freemen were landowners. Their society was necessarily organized along different lines than that of England, nurturing the republican tendencies already present in English society and fostering an ideology of liberty that was taken to extremes, with guns aplenty. It was a frontier society, in which the most brazen won out.\n\nA Virginia slave regime was implemented by 1640, the earliest date at which \"surviving Virginia county records began to mention Negroes,\" writes Winthrop Jordan, who adds, \"sales for life, often including any future progeny, were recorded in unmistakable language.\" There was now a clear distinction between slave and indentured servant\u2014necessary not only in terms of civil and criminal law, but in terms of the market for their services: a transfer of indenture was considerably less valuable than a slave sale. While the changeover from indentured to chattel labor offered political and labor advantages, the greatest benefit for slaveowners was the property rights it conferred. It was the profitability of owning slaves as capital, added to their capacity for labor, that made slavery foundational to Virginia's economy.\n\nThere was \"no body of English law to invoke,\" writes James A. Rawley. \"Slavery may be considered a colonial invention, abetted by the English traders in slaves.\" A legal framework appeared in Virginia for dealing with slavery, one law and ordinance at a time, beginning in the 1650s. In 1662 the _partus sequitur ventrem_ passed to Virginia children the free or enslaved legal status of the mother, thus extending slavery to all future matrilineal generations, in perpetuity. Another law seven years later, headed _An Act about the Casuall Killing of Slaves_ , exempted slaveowners from being charged with felony murder if one of their slaves should die during \"correction,\" noting the difference in types of punishment dealt to indentured servants and slaves: \"The only law in force for the punishment of refractory servants resisting their master, mistris or overseer cannot be inflicted upon Negroes.\" In other words, since indentured servants could have their term extended as a punishment but slaves in perpetuity could not, it was necessary to use violence on slaves. The law even provided a philosophical justification that noted the value of slaves as multigenerational property: \"it cannot be presumed that prepensed malice (which alone makes murther ffelony [ _sic_ ]) should induce any man to destroy his owne estate.\"\n\nManagement of slave labor in the Americas generally took one of two forms. One, which Jacob M. Price calls the Latin model, protected the integrity of the plantation by treating slaves as immovable assets, or real estate, which could not be separated from the plantation as a whole. This model, employed in the Spanish, Portuguese, and French territories, tended toward maintaining family ties among the enslaved and may well have contributed to the rootedness of the Afro-Louisianan population that is notable into the present day.\n\nThe other, the Anglo-Saxon model, protected the creditor by treating slaves as chattel, or disposable personal property, like furniture, and allowed the dismantling of a plantation for the instant conversion of its labor force into cash, breaking family relations among the enslaved whenever it was financially expedient.\n\nThe Barbadian code at first considered slaves to be real estate but was amended in 1668 to reclassify them as chattel alienable from the land, conforming with facts on the ground. That quickly became part of Virginia law as well, where the forward-looking knew that massive importation of Africans would come soon. The logical consequence of capitalizing slaves as chattel was that creditors felt more secure investing in slaves. As the international slave market became stronger, the chattel principle also supported the creation of a locally traded market in slaves, who were a self-increasing source of riches\u2014an important domestic business during those days of restricted foreign trade.\n\nBy the time slave ships began to disgorge hundreds weekly into Virginia, a legal framework for slavery was already in place. This legal infrastructure would be subject to constant revision, but the basic questions were settled by the time of the great wave of African arrivals in the last days of the seventeenth century. By 1690 or so, perhaps a little earlier, Virginia's labor force was majority enslaved, not indentured. The society became even more unequal as large landowning slaveholders became very wealthy men and the formerly indentured were shut out of participation in the economy and from landowning.\n\nDespite the glamour of the Royalist Cavalier image, most British emigrants to Virginia were indentured servants, most of them young men. In marked contrast to Puritan New England, which was more middle-class and more egalitarian, Virginia received rich and poor, exalting the former and exploiting the latter.\n\nMany of the Virginia colonists confronting the daunting physical problems of clearing and planting wilderness land never bothered to establish formal title, and did not necessarily know how. Many would move on; their relentless, unrotated farming of tobacco exhausted the soil of the necessary nutrients after a few years, and the West was always beckoning with the promise of more land. Old Dominion became concentrated in large holdings, which ultimately facilitated the cultivation of tobacco and the importation of slaves.\n\nThe consequences for American society were permanent. \"During a brief period in the late seventeenth and early eighteenth century,\" writes Anthony S. Parent in his study of the creation of Virginia's slave society between 1660 and 1740, \"a small but powerful planter class, acting in their short-term interest, gave America its racial dilemma.\" A miserably fed, clothed, and housed force of enslaved black laborers was what planters wanted, and that's what they bequeathed.\n\nOnly the wealthy could afford to own an enslaved work force, so the influx of slaves created an additional competitive advantage for the larger planters, even as the enslaved people themselves counted as wealth for them. \"The workers who produced the crops,\" writes Lorena S. Walsh, sounding a note repeatedly expressed by writers on the subject, \"were almost invariably the most valuable asset that planters possessed.\" The rich of Virginia became richer, and the super-rich, or \"great planters holding thousands of acres and exceptionally large labor forces\" probably \"increased from fewer than a dozen in 1640 to around eighty at the close of the Seven Years' War [1763].\"\n\nWhile generally the colonial wealthy had unimpressive fortunes compared with the income English lords had, the Virginians had them beat in terms of luxurious living: they had slaves, who made the planters' lives comfortable in every detail.\n\nThe planters had to superintend their affairs closely, though; unlike the island confines of sugar-producing Barbados and Jamaica, the extensive tobacco lands of Virginia were not conducive to absentee ownership. Planter William Fitzhugh wrote about a proposed land deal in 1689: \"it is not worth two pence to anyone that is not actually upon the Spot.\"\n\nNot all farmers understood the importance of legal documentation, but it made a fortune for those with English legal training and connections. Holding public office in early Virginia was a direct path to personal enrichment on a drastic scale. Members of the oligarchy who knew best how to appropriate land helped themselves to large tracts. Claimed and commodified by England, this newly fenced land was given to individuals who were in a position to use it to create wealth. The laws were crafted so as to make rights of property\u2014both the enclosed land and the human labor\u2014sacrosanct at a foundational level to the society built atop the Chesapeake, creating a network of property owners whose descendants have traditionally been of high social importance in the region.\n\nWriting of the nineteenth century, Steven Deyle notes that white births were recorded in a Bible, black ones in a ledger. It was that way already when the big ships began sailing from Africa to Virginia. Black servitude was to be perpetual, including all future children of the enslaved person, and their children, and their children's children, founding a fortune of human property within a few generations through the power of what came to be called \"natural increase.\"\n\nConsider a hypothetical example of the economic power of the capitalized womb: if an enslaved girl brought from Africa in 1695 survived long enough to give birth to four children who survived long enough to be of reproductive age (which typically entailed giving birth to a number of other children who died), and if two of those four surviving children were girls and each similarly produced four surviving children, recursively over 165 years (twelve generations, supposing fifteen years to be a generation), a first-generation enslaved woman's womb would thus engender a population of 2,048 people by 1860, all of them legally considered property, each with a cash value.\n\nThe only thing hypothetical about that scenario is the numbers. Apart from that, it in fact happened: enslaved women began having children as soon as their bodies were able, and their children were handed down as inherited property from generation to generation. There was a white family's fortune to be accumulated from the \"increase\" of a single African kidnap victim. That Virginia planters understood this is clear from the records of one of the first planters for whom we have much documentation, who was also a lawyer.\n\nOn the strength of his correspondence, the English-born William Fitzhugh was a pioneer not only in the use of an enslaved labor force in Virginia, but also in comprehending the value of owning the laborers' children and descendants in perpetuity. Anthony S. Parent writes:\n\nHe did not have to purchase laborers; he could grow his own. He thought of his blacks as stock, not unlike cattle, that could be bred indefinitely. He boasted in 1686 that most of his twenty-nine enslaved workers were Virginia-born, and the Africa-born were as \"likely as most in Virginia.\"\n\nIn a 1681 letter about a slave cargo (the place of origin is not noted) expected to arrive into York, Virginia, Fitzhugh requested a colleague there \"to buy me five or six, whereof three or four to be boys, a man and woman or men and women, the boys from eight to seventeen or eighteen, the rest as young as you can procure them, for price I cannot direct therein because boys according to there age and growth are valued in price.\"\n\nHe used the word _breeders_. Writing of his holdings, Fitzhugh anticipated cheerfully that \"the Negroes increase being all young, & a considerable parcel of breeders, will keep that Stock good for ever.\" He does not appear ever to have purchased any more Africans. Were more documentation extant of the thoughts and actions of seventeenth-century colonists, one would presumably find more examples of this line of thinking, as per the 1696 deed in Hampton, Virginia, turning over \"one negro Lad nam'd Will and one Gray Mare & their Increse to him & his heirs for ever.\"\n\nEducated in England as a lawyer and elected to the Virginia House of Burgesses in 1676, Fitzhugh used his office to acquire vast parcels of land through abuse of the headright system. He had labor to work it, his workforce increasing as the long-range value of owning people's perpetual descendants worked its actuarial magic. When Fitzhugh died in 1701 at the age of fifty\u2014not an uncommonly early age to die in colonial Virginia\u2014he was a very wealthy man. He had not only been a highly successful accumulator of land, but had also watched his holdings of human beings increase on their own, or perhaps with his or his sons' help, as household sexual abuse of servants by gentlemen was common.\n\nFitzhugh's informative will makes clear the ideal of legacy in Virginia. Dividing out his possessions among his widow and five sons (his married daughter Rosamond was not included), it begins with bequests of land, awarding five parcels containing a total of 30,918 acres to his eldest son, also named William Fitzhugh, \"to have and to hold the said Tracts and parcels of Land to him & the heirs of his Body Lawfully begotten for ever.\" Dividing among his remaining sons and his widow a total of twenty-seven parcels comprising 49,500 acres, he described precisely from whom each parcel had been acquired and any details and conditions attaching to it, e.g., \"all that Tract or parcel that I bought to Mr. Waugh conta. 400 acres lying upon Rappahannock one half thereof being now Leased [to] William Yates.\"\n\nOnce the lands were bequeathed, Fitzhugh divided up his slaves. His style of disposition made clear that he saw them as the most valuable of his family's heirlooms, parceling out to different households in the region his fifty-one \"Negroes and Mulattoes,\" providing inadvertent witness that the multigenerational skin-lightening process had already begun in Virginia.\n\n_AND_ as for what Personal Estate God Almighty hath been graciously pleased to Endow me with I Give and bequeath as followeth[:] _Item_ I Give to my Dear and well beloved wife seven Negroes \u2013 (to say) Harry & his wife Katherine Kate Will and his wife Peggy, Hanna & her youngest child to her & her dispose forever... I Give to my said beloved Wife one silver Bason three silver Plates one of the Lesser silver Candlesticks a silver Salt half my silver Spoons in the house the second Best silver Tankard a silver Porringer & a large silver Ladle the Great silver Tumbler to her & her heirs forever [etc.]...\n\nThe enslaved Hanna left no record of her thoughts, so we do not know how she responded to the news that she was being bequeathed to Mrs. Fitzhugh along with her youngest child only, while her children Clory, Rose, and Robin went to one of Fitzhugh's sons, her family divided up like so many silver spoons. Still, there was some consolation: Hanna would be in the same county as her children, and perhaps they would see each other from time to time or could at least hear news of each other.\n\nVirginia's enslaved population grew its own extended communities through fragile webs of kinship that paralleled those of the masters, with the grapevine as a means of communication. Despite the regime of dehumanization that confronted the enslaved, a multigenerational African American community was forming in Virginia, which was as much home to Hanna's children as it was to Fitzhugh's heirs.\n\nSugar in Barbados, tobacco in the Chesapeake: following the whirl of the ocean gyre, a global production cycle, still in its early stages, took slave labor from Africa to raise crops in the Americas that were consumed in Europe.\n\nBut Barbados was full. Population pressures were already palpable there in the 1640s. After the Restoration, the Barbadian Royalists who had been loyal to Charles II during his years of exile, and who were now influential in his court, successfully petitioned the king to be allowed to create a colony in southern Virginia that would be christened with the Latin version of his name.\n\nCarolina wouldn't cost the king anything. It would be a buffer between Virginia and the Spanish territories, and it was the perfect expansion slot for Barbados.\n\n#   13\n\n# **Carolina**\n\n_Formerly when beavor was a comodity they sold about 1200 skins a year but no imployment pleases the Chicasaws so well as slave Catching. A lucky hitt at that besides the Honor procures them a whole Estate at once, one slave brings a Gun, ammunition, horse, hatchet, and a suit of Cloathes, which would not be procured without much tedious toil a hunting. 1_\n\n\u2014Thomas Nairne, _Journalls to the Chicasaws and Talapoosies_ , 1708\n\nTHE PRIME MOVER OF the idea to seek an American concession from Charles II for a proprietary colony was John Colleton, a Cavalier who had fled to Barbados after Charles I's execution. Returning to England after the Restoration, Colleton was knighted in return for the loyalty that had cost him the confiscation of his property by the Roundheads. He got a plum position: named to the Council for Foreign Plantations, he came into contact there with the heavy players of economic expansion for the revitalized monarchy, all of them happily and openly using their positions to enrich themselves.\n\nColleton joined with seven other power brokers, five of whom were members of the Council for Foreign Plantations. Together the eight asked His Highness for a royal charter, which was granted in 1663, of the territory to be owned by the eight True and Absolute Lords Proprietors.\n\nCarolina's north-to-south reach was described as being from 31\u00b0 to 36\u00b0 latitude, blithely ignoring Spanish or Native American claims to the territory. Its boundaries were expanded both northward and southward by a second charter two years later, including areas that were already colonized\u2014to the north, the Albemarle colony that had been settled by Virginians; to the south, the Spanish fortification of St. Augustine, even though that was unoccupiable by the English. To the west, the Carolina territory was defined as stretching all the way across the unexplored continent, and the Carolinians took that seriously; Carolina as natural master of the continent became part of an enduring ideology.\n\nA colony attempted by Barbadian adventurers at Cape Fear failed in 1667. It took until 1669 for the Carolina project to begin to take off, which it did after one of the lords proprietors, Baron Anthony Ashley-Cooper, took active charge, persuading the others to put up \u00a3500 sterling each in seed money for a settlement at Carolina's Port Royal.\n\nIn support of his utopian project of proprietary colonialism, Ashley-Cooper created an ambitious document, the Fundamental Constitutions of Carolina (1669). Though unsigned, it was largely drafted by John Locke, who was secretary to the lords proprietors and an investor in the Royal Adventurers and the Royal African Company, and who lived in Ashley-Cooper's house and tutored his children. Locke's _Two Treatises of Government_ , which popularized the notion of a social contract between governed and governors and established him as a founding philosopher of modern liberalism, was still twenty years away.\n\nAfter the trauma of a king beheaded, a Puritan interregnum, and a new king reseated on the throne, Carolina would exemplify royal grandeur amid separation of powers. Though the Fundamental Constitutions were never formally ratified and were roundly ignored by the colonists, they served as a kind of mission statement, sketching out in some detail how a system of nobility could function in Carolina and how a freeman might join that nobility. It proposed an elaborate structure, heavy on theory: though it hoped to \"avoid a numerous democracy,\" there would be a sort of system of checks and balances between the power of the nobles in the metropolis and the new nobility in the colony. Carolina would have representative government, elected by an oligarchy, with a parliament, a council, and a complicated court system to settle the many disputes that occur when an entire society is simultaneously engaged in land-grabbing.\n\nAt the head of it would be a hereditary aristocracy. Carolina would be a \"palatinate\": the eldest lord proprietor was designated the palatine, the direct representative of the king whose functions might be exercised by a local deputy called a landgrave or a lesser figure called a cazique.* Locke was named a landgrave in 1671, though he never traveled to America.\n\nThe colonists, the theory went, would pay the costs of establishing themselves in exchange for generous land grants\u2014though there were Native Americans living on the granted land\u2014and policies facilitating slaveowning, which was to be the economic backbone of the new colony. The proprietors, who in theory owned a fifth of the unsurveyed land, were assigned \"baronies\" of twelve thousand acres, and nobles received another fifth, but any intrepid colonist with even a little capital could acquire land, thanks to a generous headrights system that awarded 150 acres per servant imported\u2014triple what Virginia had offered. It must be a large territory indeed to be able to give away so much land, and indeed, they claimed all the land to the west.\n\nIn response to a request for clarification, the lords proprietors agreed that the headright for importation of servants would apply to slaves as well. They had a motive: with four of the eight lords proprietors having also been founders of the Royal African Company, Carolina was founded by slave traders. It was created to be slaveowners' heaven. Bring in a slave, get a hundred fifty acres free. Bring twenty, fifty, a hundred! Colonists could own their slaves securely, because, as in Barbados, these slaves would have _no rights at all._ Ashley-Cooper, writes M. Eugene Sirmans, \"inserted in all drafts of the Fundamental Constitutions a provision which became of crucial importance in shaping the development of Carolina. 'Every Freeman of Carolina,' it was stipulated, 'shall have absolute power and authority over his Negro Slaves, of what opinion or Religion soever.'\"\n\nConversion to Christianity would not free them. Carolina was not a religiously motivated colony, nor was it founded by refugees from persecution. Needing to attract settlers, it was relatively tolerant of religion; the Fundamental Constitutions included a limited guarantee of religious freedom, though Catholics were not welcome. The utopian vision of Carolina was the pursuit of individual profit by any means necessary.\n\nFor an aggressive young man starting out, it was as good a deal as could be, if he didn't die of the numerous diseases. The lords proprietors published pamphlets \"praising [South Carolina] as a healthy and temperate location, indeed a paradise for English bodies,\" writes Peter McCandless, but in reality, Carolina was even more unhealthy than Barbados. Malaria was not common in Barbados, but the Lowcountry had it, and yellow fever too, as well as parasitic worms and diarrheal diseases.\n\nBuffeted and blown off course by storms, the first South Carolina colonists spent seven grueling months at sea before arriving in March 1670. The travel experience was sufficiently horrible from the beginning that four colonists deserted when the ship stopped in Ireland. Stopping at Barbados on the way, they picked up the Royalist landowner John Yeamans, who brought his slaves with him, with the result that black people participated in the founding of Carolina, as they previously had in Barbados. Once landed, they planted their settlement, naming it after their king and patron: Charles Town. Yeamans, who had been instructed to choose a governor for the territory, chose himself and was proclaimed governor in 1672.\n\nVirginia received some Barbadian immigrant planters, but South Carolina was defined by them. It was, in Peter H. Wood's phrase, \"the colony of a colony.\" \"By the second summer of settlement,\" Wood writes, \"almost half of the whites and considerably more than half of the blacks in the colony had come from Barbados.\" It was even less polite than Virginia, as the colonists jockeyed to game the system and take profit at gunpoint. It was combative; with Florida to its south, it was the most exposed of any of England's territories to Spanish attack.\n\nThe largest immigration to South Carolina in the 1670s was a movement of Barbadian planters to a community near Goose Creek, off the Cooper River, which became a power base that dominated South Carolina politics throughout the proprietorship. Practiced hands at colonial survival, the \"Goose Creek men\" had no intention of being subject to the lords proprietors, and they quickly acted to take control of the fledgling colony's elaborate governing structure of council and parliament. There was a religious schism as well: the Goose Creek men were part of Carolina's Anglican contingent, which wanted the Church of England to be an official religion, with favoritism for its members and themselves running it.\n\nCarolina's business policies were from the beginning hostile toward Virginia, some of whose colonists had to a degree been trading with the Native Americans and in native slaves. As soon as the Carolinians arrived, they went directly to work at cutting the Virginians out of the Indian trade, and they were favorably located to do so. Virginia's natural connection was not to the southern part of the eastern seaboard but to the line of colonies to its north. By land, Virginia was hemmed in by the Appalachians on the west and the Dismal Swamp to the south. By sea, a vessel going south from Virginia would have to cross the rough Cape Fear barrier and go against the Gulf Stream. So Virginia's easiest commerce was to the north and with Europe; it had little maritime contact with Charles Town and points south.\n\nThe northern part of Carolina was hemmed in worse than Virginia\u2014blocked by barrier islands along the coastline, the Dismal Swamp on the north, and the Appalachians to the west. Forming a large buffer zone between Charles Town and Virginia, it would be formally partitioned as North Carolina in 1712. It was physically impossible to govern both Carolinas from a single seat; sea travel was the only practical access between them. But Charles Town was in charge commercially: North Carolina had no major seaport, and never developed a colonial aristocracy.\n\nThe two Carolinas were quite different from each other. Whereas North Carolina was settled principally from the north by frontiersmen and became mainly a domain of small farms, South Carolina was settled principally by sea, via immigration from England, Scotland, Ireland, and Barbados, and became a regime of large plantations. Its west and southwest were located below the Appalachians, leaving the way clear for overland travel on trails through thick forests to the vast region that we now call the Deep South\u2014the home of a complex, interlocking network of related native cultures that anthropologists call the Mississippian, which dated back to the innovation of maize cultivation and storage in the region around 1000 BC.\n\nNot only was North Carolina where the South began; South Carolina was where the Southwest began. South Carolinians fought the Native Americans and drove westward expansion. From South Carolina's earliest days, it saw itself as extending all the way out to New Mexico, where the first Spanish settlement had been established in 1598.\n\nThe indigenous peoples had long fought internecine wars among each other. The arrival of the Europeans increased the pressure of war that was already forcing the Native Americans into confederations, including:\n\n  * the Choctaw, who inhabited the Mississippi River region;\n  * the Chickasaw in present-day northern Mississippi and western Tennessee;\n  * the powerful Creek confederation, loosely divided into Upper Creeks (present-day Georgia) and Lower Creeks (Alabama);\n  * the mountain-dwelling Cherokee in eastern Tennessee and parts of South Carolina; and\n  * others: the Natchez of Mississippi, the Catawba of the Carolinas, the Tuscarora of North Carolina; as well as\n  * two that would play important roles in the South Carolina native slave trade: the Yamasee of South Carolina and the Shawnee (or Savannah) of the Savannah River area, where the town of Savannah was later founded.\n\nMeanwhile, the picture was complicated considerably by the entry into Louisiana of the French, who were strategically focused on the Mississippi River. The French, the Spanish, the English: three contenders for the same large Native American territory that later became the cotton kingdom, all enslaving the natives. But it was Carolina traders\u2014many of them Scots\u2014who massified the Native American slave trade.\n\nComing from Barbados, the Carolinians had ample knowledge of the workings of the global slave trade, and they also had business contacts on the island. They knew that there were no indigenous people on Barbados, but Carolina abounded with Native Americans, and the settlers immediately began trafficking in them to supply Barbados's, and the other English colonies', slave markets. They also exported kidnapped natives to England's enemy colonies of Saint-Domingue, Martinique, and Guadeloupe.\n\nFormerly, when Native Americans defeated rival tribes they tortured the men to death over a period of days and took the wives and children. Now, the losers could instead be sold to South Carolina traders. The Carolinians, in other words, paid Native American warriors with consumer goods to annihilate each other, escalating an already existing circle of recriminative violence whose origin predated the arrival of the Europeans. Carolina, then, took its first steps toward having an economy by building a Native American slave trade that would then fund the growth of a plantation system using black labor.\n\nThe lords proprietors had not contemplated this; like the Virginia Company previously, they wanted to reserve the trade in hides for themselves, for which reason they wanted good relations with the natives. Though African slavery was central to the proprietors' design, they were furious when Carolina's first industry became a trade in enslaved Native Americans. For one thing, they didn't get a cut from that business since the colonies, not the Royal African Company, supplied the market.\n\nThe merchants of Britain, the slaveowners of Barbados, and the traders of Carolina worked together through commerce to create a revolution against the lords proprietors. New England and Virginia had previously sold some native slaves, but the Carolinians had access to a much larger supply, and they set about it with a will. This Native American slave trade was completely illegal under the laws of the colony, in which free people were not to be enslaved except in \"just war.\" (Africans, however, were deemed to have been already enslaved at the time of purchase in Africa.) A set of additional rules for Carolina, written in Locke's hand in December 1671, specifically prohibited enslaving the natives. Too late. Traders in the two-year-old colony were already fomenting war among the local tribes for the purpose of slave-raiding, accumulating wealth by dispossession.\n\nThe Native Americans needed little encouragement from the English and Scottish to kill and enslave each other, and the Carolinians were eager to help them do it. The methodology had already been worked out by African slave traders. To create slave exports, the entrepreneurs producing slave-raiding wars had to create an arms race among the native people, whether they were the indigenous peoples of Mississippi or of Ouidah. As in Africa, slave-raiding in greater Carolina was done by the natives: the traders armed their Indian allies and bought the slaves they captured.\n\nFrom its earliest years, Carolina sought to extend its control over the entire region by means of its superior trading goods, which most especially meant guns and ammunition. In the last two decades of the seventeenth century, Carolina traders built a network that extended through the territories later known as Georgia, Alabama, Mississippi, and Louisiana. It was all South Carolina, at least in the minds of the Carolinians.\n\nThere were two main export products from this commercial wilderness trading circuit. One was deerskins, which were exported by the tens of thousands annually to European markets. Fashions in London changed with the availability of the new commodity, which was cheaper than New England beaver: stylish Englishmen began wearing breeches made of the comfortable, soft leather, and women wore deerskin gloves. But the more lucrative, and primary, commodity that Carolina traders sold was native slaves, who were exported to the Antilles as well as to New England. The farther west the traders penetrated\u2014by the 1690s they were operating in present-day Mississippi and Louisiana\u2014the less likely they were to be handling deerskins. The Native Americans preferred slaves as their long-distance export; they were more valuable and, unlike deerskins, which were a burden to be carried, captives could walk themselves to market.\n\nGenerally the Carolinians preferred to sell the Native Americans away rather than keep them as slaves locally; for one thing, the natives knew the territory better than the Carolinians did, and they had allies outside, so the potential for escape was high. But also, Africans were much preferred as workers.\n\n\"That slavery would be the accepted labor system of South Carolina was unquestioned from its earliest settlement,\" writes Elizabeth Donnan. \"Coming from Barbados, Jamaica, Antigua, and St. Kitts, slavery was the accustomed order, the bringing of slaves into the province the natural and desirable practice.\" Even before South Carolina was able to establish a major staple crop, it quickly developed a two-way slave trade: first, exporting Native Americans, then plowing the profits into importing Africans.\n\nThe flow of captives among the Anglo-American markets was a complex circuit in the years after South Carolina became a power in Native American slave trading.\n\nIn the late seventeenth century, there was a market for slaves at every port in the English colonies. Every colony wanted labor, and if it didn't come from the Royal African Company, so much the better. Boston, New York, Philadelphia\u2014they all bought slaves when they could get them, though the market was smaller in the North. The plantations of Virginia were an especially good market for any trader with laborers to sell, because the territory received few Africans. Barbados, Jamaica, Antigua\u2014the first stops after Africa on the trade routes of the clockwise loop\u2014were almost always ready to buy Africans, so there was no need for a slaver who could sell his cargo there to continue for weeks more to Virginia with prisoners who could erupt into violence or die in an epidemic. (Much the same thing would happen later with French slavers, who could always sell their cargo in Saint-Domingue and had no need to continue on the perilous way to Louisiana.)\n\nSo vessels packed with enslaved Africans came into the sugar islands in the 1660s, albeit in insufficient quantities to please the planters, but only rarely to North America, where slaves accordingly sold for high prices. The scarcity created business opportunities: needing desperately to diversify from the monocrop of sugar, Barbadians developed a minor trade in exporting small quantities of slaves to the mainland. Right up until the War of Independence, vessels coming to North America from the West Indies might carry a few slaves along as part of the cargo, generally new arrivals from Africa. A captain could buy them on his own account, paying with the gold coins the Barbadians otherwise had such a hard time getting. He would sell them for deerskins\u2014or, later, rice\u2014in Carolina or to Virginians for tobacco, then take that commodity to London, sell it for paper exchangeable for gold, and continue on another round with a new supply of coins. Alternatively, black slaves from the Antilles were exchanged for native slaves from Carolina, sometimes at a two-for-one exchange rate that reflected both the Carolinians' desire to rid their territory of Native Americans and their eagerness to acquire black slaves.\n\nThe sugar boom on Barbados thus indirectly provided a labor supply for the Chesapeake, even as the Barbadians bought Carolina natives. While presumably most of the black slaves trafficked to the Chesapeake were African-born, others were born in Barbados, or were what historians have begun to call \"Atlantic creoles\"\u2014a new cosmopolitan people who, writes Ira Berlin, \"might bear the features of Africa, Europe, or the Americas.\"\n\nThe native slave trade was not a small business; Alan Gallay, whose scholarship has informed our treatment of this topic, estimates that the Carolinians trafficked between thirty and fifty thousand Native Americans off to slavery. Perhaps ten to twenty thousand of them came from the Florida peninsula, which was largely depopulated as a result. There is little documentation of the traffic of either native slaves out of Carolina or of black slaves from the Indies up to the mainland. Gallay concludes that during the years of the Native American slave trade (until the Yamasee War put an abrupt stop to it in 1715), more native slaves were exported from Charles Town than African slaves were imported.\n\nWhatever the precise numbers, the direction was clear: over a period of more than 150 years, culminating in the Native American removals of the 1830s, the free, sovereign, native population of the entire Deep South was hollowed out and gradually replaced by an imprisoned African, then African American, population.\n\nThe creation of a voracious external market in abducted Native Americans was a much different proposition than pre-Columbian indigenous enslavement of natives by natives had been. It altered forever the political and social relations among indigenous people, none of whom could remain unaffected as Indian slave trade routes emerged across the densely forested Deep South. Tribal groups became well-armed colonial clients, racing toward each other's destruction.\n\nThis Charles Town trade web reached as far as Louisiana. Even before the Canadian Pierre Le Moyne, Sieur d'Iberville, brought his force to the Gulf Coast to establish the Louisiana colony in 1699, South Carolinian traders had already begun depopulating the region, removing enslaved indigenous people through their already well established frontier posts. On February 28, Iberville wrote that two Englishmen were leading Chickasaw war parties \"among all the other nations to make war on them and to carry off as many slaves as they could.\"\n\nThese Carolina traders, with their organized circuits, were the first Europeans to learn, however crudely, something of the political complexity of the indigenous Mississippian culture. They were also the first English to comprehend the plan of \"encirclement,\" by which the French hoped to control the entire circuit from the St. Lawrence in Canada down the continental backbone of the Mississippi River to the Gulf of Mexico, with the ultimate aim of driving the English out of the coastal Atlantic areas.\n\nThe Mississippi River did not figure much in the Native Americans' strategy; they dominated the land. Presumably they could have exterminated the European settlements had they not been so at odds with each other. Instead, they made alliances with the Europeans for protection against other tribes and for the guns and other consumer goods that the Europeans brought. Rarely did Europeans fight Native Americans directly, and though the European forces on occasion attacked each other's strongholds, in general they fought their wars through native clients, who attacked each other.\n\nThe French made allies of the Choctaw, whose enemies, the English-allied Chickasaw, were by then completely given over to a slaving economy. When the Chickasaw attacked the Choctaw, it was England attacking France. The large Creek confederation managed the feat of never allying with any of the three European powers in the vicinity, and thus became power brokers.\n\nThis early Carolina trading economy was the work of perhaps two or three hundred traders, some of whom were cattlemen as well. Trade was war: like the privateers of Elizabeth's time, these were merchant-warriors, known for their brutality.\n\nThe traders established \"factories\" in the wilderness and in the Native American towns. A word with roots in slavery, _factory_ derives from _factor_ , referring to the financial agents who, in the absence of banks in America, settled colonial accounts on behalf of the London syndicates. That's what they called the trading posts in Native American territories, as well as the hellish installations that similarly swapped merchandise for people along the West African coast: factories.*\n\nIn Africa, slave-ship captains assembled a live cargo over a period of weeks as local traders came downriver, sometimes waiting for a nearby battle to end so that war captives would be available for purchase. The captives' heads were shaved before they were packed belowdecks, a precaution against lice that also de-individualized them, along with stripping them of their names, identities, and culture. Likewise their clothes went: most were shipped naked, in violation of the traditional modesty of many African societies.\n\nThe modern sense of a _factory_ was already implicit, then, in what the slave trade did. Through a series of dehumanizing procedures, it processed the raw material of people into a value-added industrial product: slaves. As the American plantation system emerged, planters did not have to capture and enslave people; they bought African slaves, offered to them as a product by a slave factory.\n\nThe systematic crushing of the black family by the later antebellum slave-breeding industry began with the severance of African family ties. The elite of the Americas, whose successive generations tended to remain elite, and who had in many cases come from Europe with the advantage of family connections, did everything possible to make sure that the family structures of Africa, which in some cases included royalty, high priests, and military heroes, did not transfer their webs to the Americas.\n\nRipped from the families that had always been their strength, the captives were intended to be as close to human blanks as the slave traders could deliver\u2014though, as scholars have detailed in recent decades, there is abundant evidence to confirm what common sense suggests: that the enslaved struggled against their condition all along, and never accepted their captivity. Slave traders couldn't remove the Africans' heads, and in those heads the captives brought culture and knowledge, which in turn became their defense after they were sold\u2014captured, bound, imported, naked, packaged in chains, nameless, and, in the Duke of York's heyday, complete with corporate logo.\n\nWhen we speak of \"branding\" today, we should remember that it was at one time literal: with a hot iron pressed against human flesh. York literally put his name on his merchandise: many thousands of people were branded RAC, for Royal African Company, while thousands more were branded DY, for Duke of York. The brand functioned as a tax stamp, signifying that the person was to be considered a legally imported factory product.\n\nIn modern commentary, one sometimes hears the term \"feudal\" applied to the slaveholding South. That is incorrect;* instead of following a feudal model as prescribed by the Fundamental Constitutions, South Carolina agricultural slavery was capitalism in action. Enslaved black people in English North America did not have the advantages of serfs, who were attached to specific pieces of land and could at least remain with their families and communities.* Carolina slaves were, like Barbadians, chattel\u2014a different category of property, which allowed them to be separated from their family members and redistributed as necessary for financial advantage to the master or his creditors.\n\nA color-caste system of forced laborers to produce export crops for sale on the global market was as modern a notion as a new sugar factory, a more efficient sailing vessel, an insurance policy, or a London bill of exchange. It was based not on tradition\u2014English involvement in African slavery was still a recent phenomenon\u2014but on empirical, market-driven experience: African slaves had been proven in both Barbados and Virginia to be more profitable than indentured Englishmen.\n\nNot only through custom, but also as stipulated by law, the enslaved were routinely treated as if they were less than fully human. As such, they could be fed inhumanely: a low grade of Indian corn, imported from New England, would suffice, so that the maximum amount of land and agricultural labor could be devoted to cash crops.\n\nIncome from plantation produce arrived not in the form of coins but as credit, always leading production by a year, giving the perennially indebted planter an urgent incentive to produce, which was transmitted to his overseer, who in turn used his whip to communicate the economic imperative to the people in the field.\n\nIntroducing firearms, ammunition, and consumer goods, conspicuously including rum, into native societies had the effect of making the natives dependent on their Carolina allies. Meanwhile, the slave trade in indigenous people increased the collective temperature of rage among the tribes, who in the aggregate greatly outnumbered the Carolinians. The Europeans' dealings with the natives were thus highly political: these were not unions of tribes but confederations whose ancestrally distinct factions could turn hostile against each other and whose antagonisms could be stoked and played off against each other. Some tribes were eradicated entirely, as in the case of the small but violent Westo.\n\nThe Westo, who acquired that name only when they got to Carolina, had endured two forced migrations in fifteen years. First displaced from New York and Pennsylvania by the Iroquois Confederation\u2014the most highly organized of the native governments\u2014they went to Virginia, where they slave-raided on behalf of Virginia traders until the Pamunkey, who were themselves being displaced by the Virginia colonists, pushed them out. The Westo migrated down to Carolina, where they terrorized other tribes and sold the captives to traders, doing much business between 1675 and 1680. But they too were killed and enslaved when the Carolinians found a stronger trading partner, the Savannah, who would in turn be replaced by a confederation called the Yamasee, whose fighting men numbered perhaps twelve hundred and whose origins are unclear.\n\nIt was a deliberately genocidal business model. In Louisiana, Iberville told a Choctaw council in 1702 that, as summarized by Vernor W. Crane, \"within the last decade the Chickasaw had taken five hundred Choctaw prisoners at English instigation and had killed more than three times that many.\" By giving Native Americans a mercantile incentive to assassinate and capture one another, the English facilitated the murderous process of depopulation. So killing was the traders' business, and business was good, especially because credit could now be had. British business took enormous steps toward modernization during the period of the native slave trade out of Carolina, and the Carolina economy took full advantage of the financial innovations.\n\nThe Royal African Company was founded in 1672, a disastrous year for British business. The finances of the extravagant Charles II, who was supported by Louis XIV, were in such disarray that England defaulted on its debts. Carolina's earliest days, therefore, coincided with the rise of private banking in the face of Charles's default.\n\nPrivate banks issued readily transferable debt in the form of bills of exchange. These were something like checks that could be traded; their expansion came along just in time to play a key role in fueling South Carolina's economic growth. Bills of exchange had been used in England as early as the fourteenth century, arriving there as part of the credit footprint of Italian bankers. In the intervening centuries, they had played a key role in the humbling of monarchs by empowering the bourgeoisie. They allowed for the production of money without the intervention of the king, although\u2014and here's the catch\u2014the system required a stable sovereign currency to function well.\n\nAn individual bill of exchange might be passed around from hand to hand many times before being redeemed at the office of the original issuer. It was a lot easier than passing around pieces of gold, especially since there was rarely gold to be had in the colonies. In writing up a bill of exchange, the merchant in effect created money in the form of new debt. This system, as elaborated in late seventeenth-century England, created the conditions necessary for capitalism to thrive; it was copied throughout Europe.\n\nCharles Town, which was in close contact with London over the years, developed a powerful mercantile economy based on bills of credit. The increased availability of credit from London merchants facilitated Carolina's import\/export slave trade that in effect exchanged Native Americans for Africans, who then served as collateral for the creation of more credit.\n\nThe position of bills of exchange in commerce was illustrated by a report made to Thomas Starke, one of the first importers of African slaves direct to the Chesapeake (as of 1692) and one of London's largest tobacco importers. When in 1697 he sent an apprentice to Maryland to collect a large sum owed him by indebted tobacco planters and to sell dry goods, Barbadian rum, and slaves, the apprentice reported back that indentured servants were being paid for with tobacco (meaning tradable paper notes redeemable in tobacco), whereas slaves were being paid for with bills of exchange\u2014meaning that slaves were more valuable than indentured servants and had to be purchased with a higher-quality money.\n\nWhen Charles II died in 1685 without an heir, his younger brother James, the Duke of York and of Albany, became King James II. Though it was an orderly succession, it alarmed Protestant politicians. James, who like Charles had spent his formative years in exile in France, had converted to Catholicism in 1669\u2014more or less in secret at first, while continuing to attend Anglican services. A believer in a strong monarchy, James dissolved Parliament twice during the three years he was in power. When his Italian wife, Mary of Modena, gave birth to a Catholic heir in 1688, tensions grew until James was deposed by his own Protestant daughter Mary, who had married the Dutch prince Willem van Oranj (William of Orange).\n\nWilliam and Mary took power in 1688 at the invitation of the Protestants and in collusion with the Dutch, who had ample reason to hate James. Their anti-Catholic coup d'etat has been remembered as the \"Glorious Revolution,\" a term that put a halo and a political spin around the word \"revolution,\" which also described the movement of the heavens.\n\nVirginia and Massachusetts both exulted at the Glorious Revolution, though otherwise they rarely agreed on anything. The days of absolute monarchy\u2014and, they hoped, of rule by Catholics\u2014were definitively over. And so were the days of Catholics being able to hold office, or even vote, in Maryland, a situation that would not change again until independence.\n\nThe discontent that led to the Glorious Revolution stemmed in part from Charles's fiscal profligacy. Now there would be no more Stuart spendthrifts. King William III was placed on an allowance and had to go to Parliament for money. Meanwhile, under its Dutch king, English finance was penetrated by Dutch systems, the most modern of the day. The Bank of England was created in 1694, and a stock exchange came into being in London. Making use of Dutch innovations that were not available to or, apparently, understood by the French, English commerce flourished, with merchant-created \"credit-money\" (Geoffrey Ingham's term) becoming \"the most common means of transacting business,\" even as England created \"the strongest metallic currency in history.\" The merchants' bills of exchange were pegged to that now-solid currency.\n\nAll of this augured a more dramatic projection of England as a world power. After the accession to the throne of Mary's Protestant sister (and Charles II's niece) Queen Anne in 1702, the Union of Crowns in 1707 brought England and Scotland together into the new nation of Great Britain\u2014a powerful free-trade zone that did not include Ireland, which would remain an exploited colony.\n\nNeither Catholics nor Quakers were welcome in Virginia, but both thrived in Maryland and Pennsylvania. Meanwhile, not all the white settlers in Virginia were English, Scottish, Welsh, or Irish. There were Palatines, as German immigrants were called.\n\nAnd there were French Huguenots. By the beginning of the eighteenth century, after Louis XIV removed civil guarantees for Protestants in 1685 and began torturing them and confiscating their wealth following eighty-five years of tranquility, a migration was under way that made the Huguenots the largest continental group in the English colonies at that time. Iberville's strong military presence in Louis XIV's Catholic Louisiana foreclosed on the possibility of the hundreds of Huguenot refugees going to the Gulf Coast in 1700, and instead they established the colony of Manakin Town, some twenty miles north of Richmond, on the James River fall line.* Others went to South Carolina.\n\nBy this time the commercial struggle between South Carolina and Virginia for control of the Native American trade was well under way. South Carolina harassed the Virginians with duties on skins and on occasion seized traders' inventories. But South Carolina had much hotter conflicts on its hands; its founding inaugurated a border war with Spanish Florida that lasted more than a century. For the first decades, it looked as though one colony might annihilate the other, the way the Spanish had exterminated the French Fort Caroline. The Carolinians carried out an effective campaign of burning Spanish missions in the area.\n\nIn San Agust\u00edn, chronically underfunded by the Spanish, shortages were a way of life. But thinking there was a hoard of silver bars there, the English pirate Robert Searles attacked the town in 1668, burning it and killing some sixty people. The Spanish responded by fortifying their defenses, breaking ground on a fourteen-year construction project that began in 1672. Built by native and black slaves, convicts, and Spanish soldiers, the Castillo de San Marcos is today under the management of the United States National Park Service. Like similar, larger structures that can be seen in Havana, Santiago de Cuba, San Juan, Cartagena, Luanda, and other places around the former Iberian empire, it's still impressive. During multiple attacks on the city, its formidable walls were never breached. When a 1702 attack by the South Carolina governor (and Goose Creek Indian slave trader) James Moore razed the town of San Agust\u00edn and besieged the castle for two months, the population retreated to safety within its walls.\n\nBy contrast, a Scottish settlement in South Carolina, at present-day Beaufort, was annihilated. Stuart's Town (or Stuart Town), established in 1684, competed with Charles Town for the Native Americans' alliances. But after the Yamasee attacked a Spanish mission, Santa Catalina de \u00c1frica, killing some fifty people and taking away indigenous and African people to sell to Stuart Town traders, the Spanish attacked and burned Stuart Town in retaliation, destroying it in 1686.\n\nBesides direct assault, the Spanish had a powerful ultimate weapon to use against Charles Town: the lure of freedom for those who wanted to accept Catholicism or who, like the Bakongo, had been baptized Catholic in Africa. This allowed manumission to be part of what Gerald Horne calls \"leverage\" for the enslaved that resulted from the Catholic-Protestant enmity. The Spanish were not, of course, motivated by kindness; offering freedom to those who would defect was a tactic.\n\n_The Castillo de San Marcos as seen from the town of St. Augustine, Florida. June 2013._\n\nThe first recorded instance of defection was in 1687 when, writes Jane Landers, \"Florida's governor, Diego de Quiroga, reported to Spain that eight men, two women, and a nursing child had escaped from Carolina to San Agust\u00edn and were requesting baptism into the 'True Faith.'\" In the succeeding years, more groups of escapees arrived, occasioning a complaint to San Agust\u00edn's governor by John Colleton.\n\nSpanish Florida made use of slave labor, but it was a military outpost, not a plantation empire. The territory's de facto status as a haven for enslaved people wishing to be baptized Catholic was formalized by a November 7, 1693, edict from the feeble Spanish king Carlos II. The last Hapsburg king of Spain, he was believed to be bewitched but was actually the product of generations of royal inbreeding; his decisions, presumably including this one, were largely made by his regent mother, the Austrian queen Mariana.\n\nOffering freedom was an effective measure: the promise of a safe haven for slaves within marching distance kept South Carolinians afraid of domestic revolt, to say nothing of their fear of nearby Spanish armies, which commonly had black soldiers.\n\nWith the death of Carlos in 1700, the Bourbons took the Spanish throne, with Louis XIV's grandson Philippe d'Anjou becoming Felipe V. This union of French and Spanish crowns alarmed the rest of Europe. The War of Spanish Succession, known in America as Queen Anne's War, began in 1701 with England, the Netherlands, and the Austrian-centered Hapsburg Empire as allies against France and Spain. In local terms, that meant intensifying the conflict between South Carolina and Florida, between South Carolina and Louisiana, and between the English-allied Chickasaws and the French-allied Choctaw.\n\nIberville formulated a plan for a joint French-Spanish expedition against Charles Town, which would in theory continue on to Virginia and New York. He was perhaps the most able military man in the Americas at the time, and it is possible he could have taken Charles Town, but he died before he could carry out the assault, apparently of yellow fever, in Havana in July 1706. It went on without him in September, launched from Havana, with both black and indigenous troops joining the combined French and Spanish forces. But the invaders were defeated with the substantial participation of citizen militia, and the assault failed miserably.\n\n*The word \"landgrave,\" previously associated with the Holy Roman Empire, referred to an officer of the border guard, which was indeed Carolina's strategic buffer-zone function; \"cazique\" was a Ta\u00edno word for chieftain that apparently crept into the vocabulary via Spanish.\n\n*Muscle Shoals, Alabama, famous in the annals of recorded music, was at one time the site of such a Native American\u2013trading factory.\n\n*Though there was later an idealized affinity in the antebellum South for the fantasy medieval life depicted by Walter Scott in his 1820 novel _Ivanhoe._\n\n*Disclosure: the Sublette (or Soblet) family arrived in America as part of this migration.\n\n#   14\n\n# **The Separate Traders**\n\n_Most of the wealth consists in slaves or negroes.... These negroes are brought annually in large numbers from Guine and Jamaica (the latter of which belongs to England) on English ships. They can be selected according to pleasure, young and old men and women. They are entirely naked when they arrive, having only corals of different colors around their necks and arms. They usually cost from 18 to 30 pounds between about $3,900 and $6,500 in 2014 dollars]. They are life-long slaves and good workmen after they have become acclimated. Many die on the journey or in the beginning of their stay here, because they receive meagre food and are kept very strictly. Both sexes are usually bought, which increase afterwards.[ 1_\n\n\u2014A Swiss visitor to Virginia, 1702\n\nIn the face of the Royal African Company's continued inability to provide planters with all the slave labor they wanted, independent entrepreneurs ignored the royal monopoly, rushing contraband slave ships to Africa in numbers.\n\nThe West Indian planters, who were influential in Parliament, wanted the Royal African Company's monopoly broken. After experimentation with individual licenses, the African trade was deregulated in 1698. Independent merchant syndicates (called \"separate traders\") could now trade, provided they paid a 10 percent duty to the company on merchandise they exported or brought back, except for \"red-wood\" (a dyestuff, with a duty of 5 percent) and for the significant exception of \"Negroes,\" on whom no duty was charged.\n\nThe separate traders were also allowed to maintain their own factories in Africa, where they spread rumors that the RAC was bankrupt and lured factors away from the company into their service. Many were based in Bristol, which began its ascent as a major slaving port after the deregulation. The RAC had established itself at some thirty to forty factories along the African coast, from Elmina to Luanda, and many of these were taken over by separate traders, whose competition drove up prices at the African source.\n\nAnother financial innovation of the time was an insurance sector. The investors of Lloyd's coffeehouse in London began insuring in 1688, and, since the transatlantic slave trade was a high-risk enterprise, the rise of separate trading grew Lloyd's business considerably.\n\nDeregulation was effective at stimulating the traffic in kidnapped Africans. The black population of Virginia approximately tripled over the twelve years after the opening of separate trading, and only with separate trading did large-scale trafficking of Africans to South Carolina begin. By the end of that period, the arrival of large numbers of African laborers had, predictably enough, raised Virginia and Maryland's production levels dramatically, causing a glut of tobacco on the market. The price plunged to crisis levels, causing numerous defaults on payments for slaves bought on credit from the RAC. Cutting its losses, the company stopped voyages to Virginia in 1706, but the separate traders continued pouring in Africans, as this comparison for the years between 1698 and 1707 shows:\n\n| **Jamaica** | **Virginia** | **Maryland**  \n---|---|---|---  \nSeparate traders |\n\n35,718 | 5,692 | 2,938\n\nRoyal African Company |\n\n6,854 | 679 | 0\n\nThe separate traders' aggressive importation consolidated the power of the slave plantation in the Chesapeake, making Virginia into a full-blown slave society. As planters reinvested their profits in more slaves, they ran up a trade deficit sufficiently alarming to cause the Virginia assembly in 1710 to levy a five-pound duty on each imported captive\u2014Virginia's first domestically generated tariff\u2014with the result that for five years only a few slaves entered the territory, until the balance of payments problem eased.\n\nThe large slaveowners who made up the Virginia assembly were in favor of restricting the entry of new slaves. Not only did they have all the captive laborers they needed to run their plantations at peak efficiency, but the laborers were surviving and reproducing instead of dying off, creating capital gains for them. A slaveholder's on-paper worth, and therefore his credit, was based on the price he could command if he sold his surplus labor; as the century rolled on, Virginians complained frequently of the English slave trade, which drove down the value of their enslaved assets. The simple device of keeping the price of domestically born enslaved human property artificially high through import restriction was to be fundamental to the economy of Virginia, right up through emancipation.\n\nVirginia and Maryland charged duties to each other's vessels. Scofflaws could find their slaves confiscated and sold for the commodity money of tobacco to the colonial government's benefit. After Maryland relocated its capital away from the upper bank of the Potomac and needed a statehouse at its new site of Annapolis,* the Maryland Assembly in 1695 imposed a per-slave import duty of ten shillings to pay for it, and doubled the duty the following year.\n\nAcross the Chesapeake from Annapolis, slavery was the first order of business for the new port of Chestertown. It was right up top, in the language the Maryland Assembly used when it created the little town on April 19, 1706, designating a plantation waterfront on the Chester River as one of a number of official customs posts where \"all Ships and Vessells trading into this Province shall unlade and put on shoare all Negroes Wares goods merchandizes and Comodities.\"\n\nThat the first dutiable item mentioned in the creation of the new town was \"Negroes\" reflected the growing importance of the slave trade as a source of revenue for colonial government. That the law specified \"Negroes\" rather than \"servants,\" \"slaves,\" or even \"Africans\" reflected that the criterion for enslavement was a two-tone caste system, because \"Negroes\" was a color word, from the Spanish and Portuguese _negro_ , meaning black. That \"Negroes\" were separately broken out on the list implied that although the enslaved were being sold along with \"Wares goods merchandizes and Comodities,\" there was something different about selling human beings.\n\nThe importation of indentured English, Scotch, and Irish paupers, who had previously constituted the Chesapeake labor force, had slowed after the Glorious Revolution of 1688. A large-scale importation of convict laborers was still in the future. The trade was in Africans.\n\nA \"servant\" could be any of several different classes of people; one writer has discerned \"nine or ten varieties of servitor,\" with indentured whites at the top of the hierarchy and \"negro slaves\" at the bottom. The term applied equally to indentured Irish, Scottish, or English paupers and to African slaves, to people doing brutally hard field labor and to artisans, valets, cooks, or tutors. What they all had in common was that they did not generally receive wages. The trade that shuttled them to their destinations was as bare-knuckles a business as could be, and constantly provided a fat target for taxation.\n\nThe new separate-trading legislation empowered Bristol, whose captains made fortunes in pauper, convict, and African labor; and the new high-volume capital of the African trade, Liverpool, whose captains would trade as many slaves as Bristol and London together.\n\nThe business transformed with the arrival of the biggest commercial contract of the day: the _asiento_ , a word literally meaning \"seat\" that refers to a contract between the government and a private concern. Spain had been purchasing slaves by means of the _asiento_ since the sixteenth century, mostly from the Portuguese, without developing a major slaving industry of its own. As the long War for the Spanish Succession was ending, Spain in 1713 sold the _asiento_ to Britain to supply 4,800 African slaves a year to its colonies, and it was then awarded in turn to the recently created South Sea Company by Queen Anne Stuart, James II's younger daughter.*\n\nAnne died the following year at the age of forty-nine. Gout was the stated cause of her death, but she had been weakened by the eighteen pregnancies she experienced before becoming queen; eleven were miscarriages and none of them resulted in a surviving heir to the throne. She was succeeded by her second cousin, King George I, a Protestant descendant of the Stuarts from the house of Hanover, whose first language was German.\n\nHugh Thomas calls the _asiento_ the \"El Dorado of commerce.\" Not only was it a thirty-year monopoly to sell slaves, but since it allowed British ships into Spanish ports, it gave British merchants practical, though not legal, access to all sorts of other commerce.\n\nThe resulting investor hysteria in London culminated in the South Sea bubble, infamous in business history, when a mania for shares in the company drove prices sky-high, with the inevitable crash. Many of London's best-known figures\u2014Alexander Pope, John Gay, and Sir Isaac Newton, among thousands of others\u2014were burned when their investments in the slave trade went sour.\n\nBut the slave trade itself continued being profitable as the age of large-scale British slaving got under way. About 4,000 Africans arrived in Virginia between 1715 and 1718, and then 5,170 came on thirty-five ships between 1719 and 1721. The problem of tobacco overproduction predictably returned, and prices for the commodity were depressed throughout the 1720s. Complicating the market further was that the wide-open competition of freelance traders to supply slaves bid the price up in Africa even as it fueled intra-African wars that fed the trade in captives, depopulating some areas (especially in Central Africa), and creating ever wealthier, ever more rapacious African elites\u2014and, as economist Warren Whatley argues, promoting polygyny in Africa and the development of small, fragmented African states over large ones.\n\nWith the advent of high-volume freelance slave trading, colonial assemblies levied duty after duty on what the US Constitution would later politely call \"importation of persons.\" Not that cash actually changed hands at the customs post: as the colonists had no gold or silver, tobacco was used as money\u2014\"commodity money\" is the economist's term. But passing around hogsheads of tobacco was impractical; paper notes backed by tobacco were issued as early as 1727, and perhaps earlier, in Virginia. Around the Chesapeake, duties, fines, commissions, and prices of all sorts were quoted in pounds of tobacco and paid by tobacco notes. When the Kent County courthouse in Chestertown was torched by an arsonist in 1719, a new one was built at the cost of fifty-five thousand pounds of tobacco and was renovated in 1750 at the cost of fifty thousand pounds more.\n\nOnce planters had enough slaves for themselves, they were happier if no one else did, especially not their emerging competitors to the west. The colonies were political battlefields of conflicting interests with constant tension between settled areas and the newer communities on the western frontier. The planters and merchants of the former tended to have control of colonial assemblies, while the farmers of the latter constituted a market to exploit. Meanwhile, the African slave trade\u2014not to be confused with slavery itself\u2014made many in the colonies uneasy, because it was seen as introducing a dangerous population into the colonies. It also had another deleterious effect: it sucked specie out of the colonies and put colonists in debt to British merchants, who for their part were very pro\u2013slave trade.\n\nLondon's policy was to encourage importation of enslaved and indentured labor whether the colonists liked it or not. The more labor, the more profit: there was profit in the agricultural commodities that were produced, but also in shipping them; in financing, selling, and shipping the labor; and in taxing the sales.\n\nProhibitively high duties on slave importation were laid at times by colonial assemblies, but the laws they made could always be overridden by London, where slave-trade interests, sometimes including the king, prevailed time and again to roll the duties back. A group of Liverpool merchants successfully lobbied for a rollback of a 1728 Virginia duty, while a similar effort resulted in the denial of South Carolina's attempt to impose a duty of \u00a310 per head in 1731.\n\nSlaves were frequently purchased on credit, typically twelve months or less but sometimes as long as three years, by means of the planter's giving a postdated bond with one or two cosigners. As the colonial legislatures began erecting a fence of measures to protect planters against debt collection by British merchants, the traders of Liverpool, Bristol, and London brought pressure to bear on Parliament to pass the Colonial Debts Act of 1732, which allowed creditors to seize \"lands, houses, chattels, and slaves\" in satisfaction of debts. This new law, abhorred by the colonial planters, strengthened the merchants' hand: their factors working in the colonies could collect on a planter's bond if he could not pay it when due.\n\nBy clarifying that slaves could be seized and sold in satisfaction of obligations, the Colonial Debts Act expanded significantly the available credit for slave purchasers, and made the use of planters' bonds the most common credit instrument in the Virginia slave trade. It also provided for the legal, forcible separation of the enslaved from their families by a debt collector. The logical consequence was that creditors felt more secure investing in slaves.\n\nSugar\u2014the crop for which most of the 12.5 or so million Africans were embarked in chains to the Americas\u2014systematically brought death to its laborers. Cutting cane is backbreaking labor, but that was not the worst of it. Cane had to be boiled and reduced to molasses on the spot, as it was too bulky and perishable to transport, so sugar plantations were full-scale factories. They were hot, smoky, and physically dangerous, but even so, the deadliest factor was the unbearably long hours the laborers were forced to work.\n\nSugar-making was both labor intensive and seasonal. Rather than work a full complement of laborers ten hours a day and have to maintain them during the \"dead time\" when there was nothing for them to do, it was cheaper to make half as many workers go for as many as twenty hours a day in the peak periods, replacing them with newly arrived Africans when they finally expired.\n\nThe system of sugar plantation management that the English sugar planters learned from the Dutch and the Brazilians followed the logic of free-market capitalism: _x_ pounds for equipment, _y_ number of African laborers who cost _z_ pieces of gold and live _m_ years, to get _n_ amount of molasses that brought _p_ amount of money in _q_ time. The result of these multivariable calculations, which pushed the limits of eighteenth-century accountancy, was that self-interested rationally acting plantation owners with no moral scruples could make the most money by working laborers to death.\n\nCompared with sugar, cultivating and packing tobacco was milder work. Tobacco was a less intensely seasonal crop; it did not require as many hands, and its planters had no financial incentive to work their slaves to death. In the off time, when hands were not needed for tobacco, they were put to work raising food crops and doing artisanal and construction work. \"Planters placed few demands on the outside world, in these respects, and supplied little to the outside world,\" write Anderson and Gallman.\n\nFernando Ortiz, who wrote what was perhaps the first work of structural anthropology, _Cuban Counterpoint of Tobacco and Sugar_ , described the distinct lifestyles associated with those two crops as constituting the poles of the Cuban personality. About sugar, he wrote, \"capital was needed to buy slaves, to bring in experts and administrators and all the machinery for milling, boiling, evaporating, and decanting. Even aside from the land required, sugar production was necessarily a capitalist enterprise.\"\n\nAbove all, sugar required access to slave labor. To facilitate the capitalist enterprise of sugar, there was another capitalist enterprise at work: procuring and selling the laborers that produced the sugar. That required financing, credit, international contacts, political contacts, market information, insurance, ships, shore facilities, and crews.\n\nSugar plantation populations typically had fewer women than men. Wherever in the hemisphere enslaved laborers were applied to sugar, they had negative reproduction rates. But in the milder climate of Virginia, with the relatively milder work of tobacco, with more women among the enslaved population and more adequate food, the numbers increased. By the 1710s, Virginia's enslaved population was growing by reproduction\u2014an \"unprecedented event for any New World slave population,\" writes Philip D. Morgan. Despite the arrival of so many Africans, \"natural increase\" was such that by 1720 Virginia-born slaves accounted for about half the colony's total. (It would take about another thirty years for gender balance of the enslaved to even out.) This was something that did not happen elsewhere in the Americas, and it was the key to Virginia's developing a slave-breeding industry.\n\nIn South Carolina, it was very different.\n\n*Named in 1694 for Princess Anne, who became Queen Anne in 1702.\n\n*\"South Sea\" referred to the South Atlantic.\n\n#   15\n\n# **Charles Town**\n\n_You ain't got no supper in Beaufort unless you got some rice. You ain't finished cookin' yet, until you've cooked a pot of rice. 1_\n\n\u2014Sea Island folklorist Anita Singleton-Prather in her performance persona as Aunt Pearlie Sue\n\n**Question.** _I see it hazardous for a man to give so much Money for a Slave, and that Slave may soon die, then all his Money is lost...._\n\n**__ Answer _]._** _Is it not so here If a Man purchase Cattle or Horses, how can he be assur'd of their Lives? Yet we have a greater Encouragement to buy Slaves, for with good Management and Success, a Man's Slave will, by his Labour, pay for his first Cost in about four Years at most, besides his Maintenance, so, the Remainder of his Life, you have his Labour as free Gain, we esteem their Eating and Wearing as little, for that rises on the Plantation, and is little cost out of Pocket.[ 2_\n\n\u2014John Norris, _Profitable Advice for Rich and Poor_ , promotional London pamphlet pitching emigration to South Carolina, 1712\n\nTHE GROWING CONDITIONS OF Virginia and Carolina were as different as their topographies, necessitating different crops.\n\nIt took Virginia between sixty and a hundred years to become a slave society, but South Carolina began as one. \"By the late seventeenth century,\" writes Philip D. Morgan, \"Virginia had a plantation economy in search of a labor force, whereas South Carolina had a labor force in search of a plantation economy.\" Virginia had defined its staple crop for decades before massive importation of Africans began, staffing the fields mostly with indentured servants, whereas South Carolina, founded by slave traders, began as a slave society that had not yet found its staple crop.\n\nA 1708 census of the Carolina colony, which did not count free Native Americans, gave the population as 9,580\u2014with a distribution of 42.5 percent white, 42.5 percent black, and 15 percent enslaved Native Americans. Most of the captives brought to the colony in the late seventeenth century were \"seasoned\" slaves, brought up from the West Indies. But Carolina colonization began as England was beginning to get involved in the African trade on an industrial scale. The first known slave ship to travel from Africa to South Carolina arrived in 1696, about the same time quantities of African captives were beginning to come to Virginia and Maryland.\n\nAfter that, the floodgates opened. \"The first quarter of the eighteenth century saw the enactment of numerous laws laying import duties on the incoming slaves,\" Elizabeth Donnan writes, \"the reason offered being sometimes 'the great importation of negroes,' which threatened the safety of the province, and sometimes the need for a revenue, easily provided by a duty on slave importations.... Despite occasional outbursts of anxiety over the menace of a [']barbarous['] population greatly outnumbering the planters themselves, the lure of profit which slave labor held out prevented the success of any consistent policy of limitation.\"\n\nSugar, chocolate, and coffee came from the warmer latitudes. Virginia and Maryland were growing tobacco. But what would Carolina produce? So far, it was an exporter of Native American slaves and deerskins. It took some decades of experimentation, but by the beginning of the eighteenth century Carolina had found its principal staple crop: rice. Tradition has it that the first crop was made with seed from Madagascar, brought in by a privateer.\n\nInvesting in the Madagascar trade from East Africa\u2014a striking exception to the flow of slaves from West and Central Africa\u2014was a New York specialty, though others were in it too. During the Royal African Company's monopoly (through 1698), wealthy New Yorkers made fortunes doing an end run around it, trading illegally in slaves and other African merchandise by opening a commercial corridor to Madagascar, where the RAC's vessels did not go.\n\n_Scottish trader and Indian agent Thomas Nairne's 1711 map, made for the lords proprietors, shows South Carolina's territory as including present-day Georgia, Alabama, much of Florida, and part of Mississippi. The only named towns are Charles Town, Port Royal, and Augustine; the \"South Bounds of Carolina\" is shown as well south of Augustine. Native American locations are precisely described, with a count of the warriors: \"Chicasa 600 Men,\" etc._\n\nThe Scottish-born merchant Robert Livingston was one of a number of New York merchants who became rich investing in African trading expeditions. The son of a Scottish Presbyterian minister who had fled Charles II's compulsory Anglicanism in 1663 for Rotterdam, he ultimately emigrated to America. After marrying the wealthy Albany Dutch widow Alida Schuyler Van Rensselaer in 1679, Livingston became the head of a family that came to own about a million acres of land. With the disappearance of Dutch commerce from New York after the definitive English takeover in 1674, the established merchant families of the former Nieuw Amsterdam took greater control, consolidating commercial dynasties headed by the city's old money, and by 1690, Livingston was a halfpartner in the _Margriet_ , a ship that traded slaves, sugar, and tobacco on an illegal trading voyage to Madagascar, Barbados, and Virginia.\n\nThe first rice seed may have come to Carolina from Madagascar, but the cereal grain was grown across a wide area of Africa. Rice was indigenous to Africa as well as to other places, and an African strain was domesticated there; Mande people had built the Malian empire in part on the technical achievement of cultivating it. The Europeans did not know how to produce rice, but West Africans were familiar with its complicated cultivation, and they brought their knowledge to Carolina. Virginia had unsuccessfully attempted to grow rice during Berkeley's governorship, but its climate was not hot enough. Planters competed to buy slaves from a vaguely defined part of West Africa referred to in slave-sale advertisements as the Rice Coast\u2014a name it received not because Africa exported rice, but because it exported kidnapped farmers who knew how to grow it.\n\nThe \"Rice Coast\" often meant the Windward Coast, but could mean anywhere from Senegal down to present-day Ghana. A slave-sale advertisement from the _South Carolina Gazette_ of March 18, 1769, makes clear the involvement of Africans in rice culture:\n\nTO BE SOLD\n\nOn Wednesday the 29th Instant\n\nA CARGO of Two Hundred and Ninety\n\nSLAVES\n\nREMARKABLY HEALTHY\n\nJust arrived in the Ship Sally, Capt. George Evans, from CAPE MOUNT A RICE COUNTRY on the WINDWARD COAST, after a SHORT Passage of Five Weeks.\n\nThat these captives were from \"a rice country\" (in present-day Liberia) was an incentive for rice farmers to purchase them.\n\nCarolina quickly became the largest supplier of rice in the world. In his landmark study _Black Majority_ , which called attention to the African genesis of the Carolina rice industry, Peter H. Wood observes that \"during precisely those two decades after 1695 when rice production took permanent hold in South Carolina, the African portion of the population drew equal to, and then surpassed, the European portion.\" As South Carolina out-imported Africans over any other territory, becoming a black majority society, the Sea Islands off its coast became not only black but diversely so, with people from disparate regions of Africa.\n\nBoth South Carolina rice and, a little later, indigo relied on African agricultural and processing knowledge. That was also the case in Louisiana, where the first slave ships brought rice seedlings and Senegambians who knew how to grow it, and where indigo was also grown and processed into dye.\n\nImports of Africans increased dramatically as diversified farming gave way to a plantation society in South Carolina. Big operators gobbled up freeholds; as planters became wealthy, small farmers became impoverished, and the population became blacker. \"Put simply,\" write McCusker and Menard, \"rice brought the demographic regime of the sugar islands to South Carolina.... In long-settled plantation districts spread along the tidewater in both directions from Charleston, the black share of the population approached 90 percent by 1740, roughly the proportion in the sugar islands.\"\n\nRice was a miserable crop to tend. It had to be weeded constantly, which meant bending over all day long while standing in mud. Disease thinned the laborers' numbers constantly. The standing water of the rice plantations incubated mosquitos that bore maladies usually associated with more tropical climates, while the density of workers rendered rice plantation slaves especially vulnerable to epidemics.\n\nRice wasn't for small family farms; it required an operation of at least thirty workers to be profitable. The fatality of the environment was a disincentive to voluntary immigration. Rice could only be produced on a commercial scale in the Lowcountry with slaves, who lived unspeakably miserable lives.\n\nThe enslaved population of the rice plantations exhibited characteristics seen in the sugar islands with mortality exceeding births as laborers were worked to death. Africans in South Carolina had a negative growth rate, and the burned-out laborers would have to be replenished by new arrivals. It took until the 1770s for African Americans to become the majority of the black enslaved in South Carolina, fifty years after it happened in Virginia and more than a century after black slaves had first been brought there.\n\nA boosterish book by John Norris, published in London in 1712 to stimulate emigration, contrasted the two ethnic slaveries that coexisted in South Carolina. Norris mentioned perpetual enslavement of Native American slaves' descendants while pointing out their provenance from \"French\" (Louisiana) or \"Spanish\" (Florida) territories:\n\nThose we call Slaves are a sort of Black People, here commonly call'd Blackmoors, some few kept here in England by Gentry for their Pleasure... but their proper Names are Negroes.... When these People are thus bought, their Masters or Owners, have then as good a Right and Title to them during their Lives as a Man has here to a Horse or Ox after he has bought them....\n\nThere is also another sort of People we buy for Slaves, call'd Indians, bred on the Continent, but far distant from us, belonging to the French and Spanish Territories in America. They are a sort of Red Dun, or Tan'd Skin'd People, who are also Sold us by Merchants or Traders that deal with several Nations of our Native Indians, from whom they first buy these People, whom we then make Slaves of, as of the Negroes... they are never Free-Men or Women during their Life, nor their Children after them, who are under the same Circumstances of Servitude as their Parents are, during their Lives also.\n\nNorris described how a hypothetical \u00a31,500 investment should be spent to yield a plantation producing \u00a3400 annually. His first item of expense was \"Fifteen good Negro Men at \u00a345 each,\" followed by \"Fifteen Indian Women to work in the Field at \u00a318 each,\" \"Three Indian Women as Cooks for the Slaves, and other Household-Business,\" and \"Three Negro Women at \u00a337 each, to be employ'd either for the Dairy, to attend the Hogs, Washing, or any other Employment.\"\n\nThe many twists and turns of the conflict between slave-raiding South Carolina and the shifting alliances of Native Americans with the French and Spanish are beyond the scope of this volume. Suffice it to say that Carolina's slave trade in Native Americans was ended by a full-scale war between the Carolinians and an alliance of native tribes that lasted for two years, an enormously long campaign in the context of indigenous struggles against the Europeans.\n\nOn the morning of April 15, 1715, the Yamasee, in alliance with the Creeks, struck in a coordinated attack and massacred the frontier traders. Thomas Nairne, the Scottish trader who had led an expedition to the Mississippi and was the most capable frontiersman in South Carolina, was captured and slowly roasted to death by means of burning splinters stuck into his body over a period of days. The Indians did not attack Charles Town, which became a citadel for frightened people from the countryside.\n\nRemembered by the Carolinians as the Yamasee War, the uprising changed direction with the entry of the Cherokees as South Carolina's allies against the Creeks, and it was over by 1717. The remaining Yamasee fled to Florida; the Creeks, the most powerful of the confederations, migrated west and retained their status as a crucial regional power while nursing a special hatred of the Cherokees.\n\n\"This war,\" writes Alan Gallay, \"marked the birth of the Old South, just as Appomattox later marked its death.\" The turning point in the consolidation of the rice-plantation economy, it led to the end of the proprietorship and the reversion of Carolina to royal colony status.\n\nIt is worth underscoring that the end of trading in native slaves came about as the direct result of a focused attack by Native American alliances, and also that this native rebellion was a black rebellion as well. Black soldiers fought together with Native Americans in the Yamasee War; the Carolinians, meanwhile, were so desperate that they armed some of their slaves.\n\nSouth Carolina's war with Native Americans underscored how exposed the English were on their southern flank. With the flight of the remaining Yamasee to Florida and the Creeks' move west, the southern frontier was depopulated, even of Native Americans, which represented a grave security issue. And the land that the Yamasee had abandoned was prime rice-growing land.\n\nThe lords proprietors' claims to own the land to the southwest had foreclosed on the possibility of settlers there, but now, under the pressure of the Spanish threat from Florida, a convention of colonists (with the militia's support, expressed by flying colors) rose against the lords proprietors. After fifty years of proprietary government, what South Carolina remembered as the Revolution of 1719 led ten years later to the final return of the colony to crown status. After the Carolinians successfully petitioned to change the colony's status in 1729, the lords proprietors took a lowball buyout.\n\nThe Yamasee War made the Native Americans more powerful relative to the South Carolina colonists than they had previously been and diminished England's influence against the Spanish and French in the region. But the French colony had arrived at its own crisis with the Native Americans. On November 28, 1729, Natchez Indians attacked Fort Rosalie, the nucleus of the later town of Natchez and the hub of the fledgling French agricultural effort, worked by enslaved natives and Africans. They killed much of the town's population\u2014between 230 and 240 settlers, mostly men\u2014and kidnapped 62 more, mostly women and children, and 106 slaves, and they destroyed all the crops. On April 10, according to Marc-Antoine Caillot, a clerk for the Company of the Indies, \"a Natchez Indian woman whom the Tunicas had captured\" was slow-tortured, dismembered, and burned to death by the Tunicas in New Orleans, Indian-style, with the permission of the French, in reprisal for the Natchez torture of their captives. The destruction of the colony's agriculture signaled the end of the active French colonization effort in Louisiana, as that colony reverted to crown status in 1731, two years after South Carolina had done so.\n\nThe Carolina economy had to be rebuilt after the Yamasee War, something that took most of the 1720s to accomplish, during which time the transition to a rice-plantation economy based on African labor was consolidated. Once again, the importation of Africans increased the threat of slave rebellion, both real and imagined. An \"anonymous letter addressed to a Mr. Boone in London, and dated 'Carolina June 24, 1720'\" mentions a purported slave conspiracy:\n\nI am now to acquaint you that very lately we have had a very wicked and barbarous plott of the designe of the negroes rising with a designe to destroy all the white people in the country and then to take the town [Charles Town] in full body but it pleased God it was discovered and many of them taken prisoners and some burnt some hang'd and some banish'd.\n\nRecords from the period are scanty, but there is reason to believe that this slaughter of \"negroes\" was far from the only one in South Carolina. A letter from Charles Town dated August 20, 1730, describes a purported plan for an uprising much like the purported 1674 Barbados conspiracy and not unlike the one successfully executed sixty-one years later in Saint-Domingue, the future Haiti. This one was organized around a dance:\n\na bloody Tragedy which was to have been executed here last Saturday night (the 15th Inst.) by the Negroes... some of them propos'd that the Negroes of every Plantation should destroy their own Masters; but others were for Rising in a Body, and giving the blow at once on surprise; and thus they differ'd. They soon made a great Body at the back of the Town, and had a great Dance, and expected the Country Negroes to come & join them; and had not an overruling Providence discovered their Intrigues, we had been all in blood.\n\nBy this time, more than two thousand Africans a year were coming into Charles Town. Samuel Wragg testified before the board of trade in 1726 that he\n\nhad been a Trader to Carolina Seventeen or Eighteen years. That that Country formerly had but very few Negroes, but that now they employd near 40,000. That they now usually import 1,000 per Ann: whereas they formerly imported none, and sometimes 2 or 300. At the same time Mr. Platt, also of Carolina, reported that the colony imported about 1000 negroes per annum, at prices ranging from \u00a330 to \u00a335 sterling.\n\n\"Even though Wragg were greatly exaggerating both the yearly importation and the number of slaves in Carolina,\" writes Elizabeth Donnan, \"it is evident that by this decade the trade had become of sufficient importance to merit the fostering care of the home government and the constant solicitude of British and Carolina merchants, foremost among whom were the Wraggs, Joseph and Samuel.\"*\n\nThe frontier between Carolina and Florida had never been agreed on, much less defined. Carolina's colonists, who were influential in London, pressed for a new boundary colony that would buffer them against the Spanish, the French, and the Native Americans. Promotional literature began circulating in London in favor of a new colony below South Carolina. The first one to circulate, in 1717, continued the feudal fantasy of the still extant proprietorship, proposing a colony that would be headed by a hereditary official called a margrave. The name of the new colony was to be the Margravate of Azilia.\n\nIt took fifteen more years for a colony to be planted there. When it was, it was named for King George II: Georgia.\n\nThere was to be no slavery in Georgia.\n\n*When Joseph Wragg died in 1751, the obituary in the _South Carolina Gazette_ called him \"an eminent Merchant of this Town, who formerly dealt pretty largely in the Slave Trade.\"\n\n#   16\n\n# **Savannah and Stono**\n\n_As the staples of Carolina were valuable, and in much demand, credit was extended to that province almost without limitation, and vast multitudes of negroes, and goods of all kinds, were yearly sent to it. In proportion as the merchants of Charlestown received credit from England, they were enabled to extend it to the planters in the country, who purchased slaves with great eagerness, and enlarged their culture. 1_\n\n\u2014Alexander Hewatt, 1779\n\n_If We allow Slaves we act against the very Principles by which we associated together, which was to relieve the distressed. Whereas, Now we Should occasion the misery of thousands in Africa, by Setting Men upon using Arts to buy and bring into perpetual Slavery the poor people who now live free there. 2_\n\n\u2014James Oglethorpe to the Trustees, January 17, 1738\/9\n\nLONDON NEWSPAPERS HAILED THE initiative to found Georgia. It was the product of humanistic and philanthropic movements in London, and also of public relations. The colony's visionary founder, James Oglethorpe, spent two years directing the colony's promotional campaign before sailing for America.\n\nOglethorpe was an aristocrat formerly allied with the Stuarts. He had studied classical antiquity at Oxford's Corpus Christi College, then went to military school in Paris and fought against the Turks in the 1717 siege of Belgrade. Becoming radicalized after his scholar friend Robert Castell died in debtor's prison, Oglethorpe wanted to help the poor better themselves in the autocratic, militarized utopia he would build. Georgia was intended to be a site of relief where debtors could have a fresh start\u2014though in practice, no debtors were among the colonists\u2014while functioning as the avant-garde of England's North American empire, protecting South Carolina from Florida.\n\nDrawing on his studies of Greece and Rome, Oglethorpe devised a unique plan for a city: a matrix of connected rectangular plazas\u2014twenty-four were built\u2014each one serving as a commons around which were to be housed ten families, with garden plots for subsistence located within walking distance. Because of that plan, and with help from the lush vegetation, historic Savannah today is one of the most beautiful urban environments in the United States.\n\nThe colonists carved out their plots from a densely wooded area on a bluff overlooking the Savannah River, beginning the construction of Oglethorpe's meticulously planned community of 240 freeholders. He also founded several other communities in Georgia: Darien; Frederica; James Brown's future home town of Augusta, on the South Carolina border; and Ebenezer, a community of persecuted Protestants from Salzburg who were dead set against slavery. A group of forty-one Jews, all but seven of them Sephardic Portuguese, arrived on July 11, 1733, and founded a short-lived congregation in 1735. After checking with lawyers in Charles Town as to whether Jews could be admitted to Georgia, Oglethorpe was advised that they could be, since they weren't papists. Their arrival upset the trustees in London, but they were powerless to do anything about it.\n\nOglethorpe, who had been deputy-governor of the Royal African Company, saw slavery as a bad system that would lead to problems in Georgia\u2014and not only because the ever-present potential for rebellion was aggravated by San Agust\u00edn's offer of freedom directly to the south. He also saw it as a corrupting influence on white colonists. Oglethorpe felt the same way about rum, prohibiting its sale, though wine and beer were permitted. Nor did he want a real estate market; in Oglethorpe's Georgia, land given to colonists was passed on by entail: it could not be sold, only inherited, and only by men.\n\nAs the first houses of Savannah were being built and moved into, Oglethorpe lived in a tent to set an example of self-sacrifice for the others. But there was trouble from the beginning, and in an isolated community riven by vicious personal rivalries and much disagreement, slavery was a divisive issue.\n\nCharles Town did more to destroy Oglethorpe's utopia than Florida. Carolina merchants ran trade routes all through the area, and Savannah was dependent on them for many kinds of supplies. But Oglethorpe didn't want his colony buying the supplies the Carolinians most wanted to sell: slaves. Moreover, Georgia's resistance to rum impeded the Carolinians' business of selling it to the Native Americans along with the guns and ammunition they were selling them, which created friction.\n\nAs slaveowners would do more than a century later in Missouri and Kansas\u2014and would even attempt to do in Southern California\u2014the South Carolinians infiltrated pro-slavery colonists into Georgia. The Carolinians who moved down into Georgia had no more respect for Oglethorpe's restrictions than they previously had for the lords proprietors'. From South Carolina, Eliza Lucas Pinckney complained in a September 1741 letter of Oglethorpe's \"Tyrannical Government in Georgia,\" presumably because its residents were denied the freedom to own slaves, plant large plantations with staple monocrops, deal in rum, or buy and sell land. Noting ill treatment of indentured servants in Savannah that had caused some to desert, colonist Thomas Jones wrote: \"The Carolina Temper, of procuring Slaves, and treating them with Barbarity, seems to be very prevalent among us.\"\n\nCharles Town merchants thus began making money importing Africans from British slave traders for re-export into Georgia, a market that would keep them rich for generations. Prosperity reigned; in 1732, the year Georgia was planted, Benjamin Franklin's ex-apprentice Lewis Timothy founded the _South Carolina Gazette_ , with Franklin as a silent partner. The South's second newspaper to appear, it was as strategic a media rollout as the times afforded: South Carolina's economy, heavily centralized in Charles Town, was booming. By 1735 Charles Town was sufficiently wealthy and cultured to found the St. Cecilia concert society. Its fast-growing wealthy elite consumed luxury goods. It was _the_ prime underserved advertising market.\n\nMeanwhile, another migration to North America was picking up: the so-called Scotch-Irish, whose Presbyterianism made them a dissenting sect in Anglican Ulster. They had to settle to the west, because the good coastal land was taken. After the first such colony moved to South Carolina to receive land grants near the Santee River, establishing Williamsburg in 1732, they were in \"low and miserable circumstances,\" wrote Alexander Hewatt, until they too bought slaves from the Charles Town merchants and their lands \"in process of time became moderate and fruitful estates.\"\n\n_A view of Charles Town, as depicted in 1739 by artist Bishop Roberts and etcher W. H. Toms, emphasizes the constant activity in its port._\n\nThe border was still dangerous. Having Georgia as a buffer between South Carolina and Florida made Carolina that much more secure. But England and Spain were still facing off in the region; the Spanish responded by inducing more of the English colonists' slaves to escape.\n\nThere were already small communities of free blacks around San Agust\u00edn, but in October 1733 a Spanish edict reiterated that people reaching Florida and accepting the Catholic faith would be free, increasing the flow of runaways. To further bedevil the Carolinians, a free black garrison town, called Gracia Real de Santa Teresa de Mose, was established in 1738 about two miles north of San Agust\u00edn, providing a first line of defense for the Spanish.* Its governor was Francisco Men\u00e9ndez, the leader of Florida's black militia. A Mandinga who was born a Muslim, Men\u00e9ndez had been kidnapped to Barbados as a boy and then taken to South Carolina. He defected to the Yamasee Indians at the time of the Yamasee War in 1715 and ultimately escaped to Florida, where he accepted Catholicism and was baptized with his Spanish name. There was a price on his head in South Carolina, but no matter: he was fighting for the Spanish, and he had weapons. The news traveled: a free black town on the side of the Spanish, with Bakongo soldiers among its residents, within marching distance.\n\nIn 1738, the Spanish at San Agust\u00edn announced that runaways would be given freedom and land, sweetening the attraction the Florida territory already had for Carolina slaves. Benjamin Franklin's _Pennsylvania Gazette_ , with its good contacts in South Carolina, ran the following item on October 8, 1739:\n\nExtract of a Letter from Charlestown in South Carolina.\n\nThe Spaniards of St. Augustine near Georgia, have issued a Proclamation, giving Freedom to all white Servants and Negro or Indian Slaves, belonging to Carolina, Parrisburg or Georgia, that will go over to them, and have allotted them Land near St. Augustine, where upwards of 700 have been receiv'd to the great Loss of the Planters of those Parts, which will prove their Ruin if a Stop is not put to such a villanous Proceeding. This is a certain Proof of their Intent to attack Georgia, in which Case these Servants and Slaves are to be their Pilots and our worst Enemies.\n\nThe feared uprising had already happened but word of it hadn't reached Philadelphia yet. Remembered as the Stono Rebellion, it erupted about twenty miles from Charles Town on September 9, 1739. The anonymous sole firsthand description of the event is not too long to reproduce in its entirety.\n\nAN ACCOUNT OF THE NEGROE INSURRECTION IN SOUTH CAROLINA\n\nSometime since there was a Proclamation published at Augustine, in which the King of Spain (then at Peace with Great Britain) promised Protection and Freedom to all Negroes Slaves that would resort thither. Certain Negroes belonging to Captain Davis escaped to Augustine, and were received there. They were demanded by General Oglethorpe who sent Lieutenant Demere to Augustine and the Governour assured the General of his sincere Friendship, but at the same time showed his Orders from the Court of Spain, by which he was to receive all Run away Negroes.\n\nOf this other Negroes having notice, as it is believed, from the Spanish Emissaries, four or five who were Cattle-Hunters, and knew the Woods, some of whom belonged to Captain Macpherson, ran away with His Horses, wounded his Son and killed another Man. These marched f [ _sic_ ] for Georgia and were pursued, but the Rangers being then newly reduced [ _sic_ ] the Countrey people could not overtake them, though they were discovered by the Saltzburghers, as they passed by Ebenezer. They reached Augustine, one only being killed and another wounded by the Indians in their flight. They were received there with great honours, one of them had a Commission given to him, and a Coat faced with Velvet.\n\nAmongst the Negroe Slaves there are a people brought from the Kingdom of Angola in Africa, many of these speak Portugueze [which Language is as near Spanish as Scotch is to English,] by reason that the Portugueze have considerable Settlement, and the Jesuits have a Mission and School in that Kingdom and many Thousands of the Negroes there profess the Roman Catholic Religion. Several Spaniards upon diverse Pretences have for some time past been strolling about Carolina, two of them, who will give no account of themselves have been taken up and committed to Jayl in Georgia.\n\nThe good reception of the Negroes at Augustine was spread about, Several attempted to escape to the Spaniards, & were taken, one of them was hanged at Charles Town. In the later end of July last Don Pedro, Colonel of the Spanish Horse, went in a Launch to Charles Town under pretence of [taking] a message to General Oglethorpe and the Lieutenant Governour.\n\nOn the 9th day of September last being Sunday which is the day the Planters allow them to work for themselves, Some Angola Negroes assembled, to the number of Twenty; and one who was called Jemmy was their Captain, they suprized a Warehouse belonging to Mr. Hutchenson at a place called Stonehow [Stono]; they there killed Mr. Robert Bathurst, and Mr. Gibbs, plundered the House and took a pretty many small Arms and Powder, which were there for Sale. Next they plundered and burnt Mr. Godfrey's house, and killed him, his Daughter and Son. They then turned back and marched Southward along Pons Pons, which is the Road through Georgia to Augustine, they passed Mr. Wallace's Ta[v]ern towards day break, and said they would not hurt him for he was a good Man and kind to his slaves, but they broke open and plundered Mr. Lemy's House, and killed him, his wife and Child. They marched on towards Mr. Rose's resolving to kill him; but he was saved by a Negroe, who having hid him went out and pacified the others.\n\nSeveral Negroes joined them, they calling out Liberty, marched on with Colours displayed, and two Drums beating, pursuing all the white people they met with, and killing Man Woman and Child when they could come up to them. Collonel Bull Lieutenant Governour of South Carolina, who was then riding along the Road, discovered them, was pursued, and with much difficulty escaped & raised the Countrey. They burnt Colonel Hext's house and killed his Overseer and his Wife. They then burnt Mr. Sprye's house, then Mr. Sacheverell's, and then Mr. Nash's house, all lying upon the Pons Pons Road, and killed all the white People they found in them. Mr. Bullock got off, but they burnt his House, by this time many of them were drunk with the Rum they had taken in the Houses.\n\nThey increased every minute by new Negroes coming to them, so that they were above Sixty, some say a hundred, on which they halted in a field, and set to dancing, Singing and beating Drums, to draw more Negroes to them, thinking they were now victorious over the whole Province, having marched ten miles & burnt all before them without Opposition, but the Militia being raised, the Planters with great briskness pursued them and when they came up, dismounting; charged them on foot. The Negroes were soon routed, though they behaved boldly several being killed on the Spot, many ran back to their Plantations thinking they had not been missed, but they were there then taken and Shot, Such as were taken in the field also, were after being examined, shot on the Spot, And this is to be said to honour of the Carolina Planters, that notwithstanding the Provocation they had received from so many Murders, they did not torture one Negroe, but only put them to an easy death.\n\nAll that proved to be forced & were not concerned in the Murders & Burnings were pardoned, And this sudden Courage in the field, & the Humanity afterwards hath had so good an Effect that there hath been no farther Attempt, and the very Spirit of Revolt seems over. About 30 escaped from the fight, of which ten marched about 30 miles Southward, and being overtaken by the Planters on horseback, fought stoutly for some time and were all killed on the Spot. The rest are yet untaken. In the whole action about 40 negroes and 20 whites were killed.\n\nThe Lieutenant Governour sent an account of this to General Oglethorpe, who met the advices on his return from the Indian Nation[.] He immediately ordered a Troop of Rangers to be ranged, to patrole though Georgia, placed some Men in the Garrison at Palichocolas, which was before abandoned, and near which the Negroes formerly passed, being the only place where Horses can come to swim over the River Savannah for near 100 miles, ordered out the Indians in pursuit and a Detachment of the Garrison at Port Royal to assist the Planters on any Occasion, and published a Proclamation ordering all the Constables &c. of Georgia to pursue and seize all Negroes, with a Reward for any that could be taken. It is hoped these measures will prevent any Negroes from getting down to the Spaniards.\n\nA brief account of this uprising in the _Pennsylvania Gazette_ on November 8 read:\n\nWe hear from _Charlestown_ in _South-Carolina_ , that a Body of Angola Negroes rose upon the Country lately, plunder'd a Store at _Stono_ of a Quantity of Arms and Ammunition, and murder'd 21 white People, Men, Women and Children before they were suppress'd: That 47 of the Rebels were executed, some gibbeted and the Heads of others fix'd on Poles in different Parts, for a Terror to the rest.\n\nJohn Thornton underscores the probable military background of the \"Angola Negroes.\" They were likely not Kimbundu-speaking Angolans, relatively few of whom came to North America, but their immediate neighbors to the north, who were Bakongo. The term \"Angola,\" Thornton writes, \"surely meant the general stretch of Africa known to English shippers as the Angola coast,\" though the possibility exists that some people from various central African origins were mixed in. In a world divided by religion, that these Africans were Catholic made them instant allies of the Spanish.\n\nAs the slave trade created business opportunities in Africa, African despots formed regularly organized armies and battled each other, the losers being sold into slavery. The result was that the ranks of the enslaved in the Americas included increasing numbers of combat-seasoned veterans of gun-toting African armies. In her history of Kongo Catholicism, C\u00e9cile Fromont identifies the ceremony that preceded the Stono uprising as \"a typical central African _sangamento_ , a martial performance in preparation for battle, in a manner similar to that used by contemporary Kongo armies.\" The mention of drums and singing ties the Stono rebellion in with later rebellions as well as with Kongo military and spiritual influence, in Saint-Domingue and Cuba. African drums were a means of military communication, as the British well understood. Since 1699 the law in Barbados had stipulated that\n\nWhatsoever Master, &c., shall suffer his Negro or Slave at any time to beat Drums, blow Horns, or use any other loud instruments, or shall not cause his _Negro-Houses_ once a week to be search'd, and if any such things be there found, to be burnt... he shall forfeit 40 s. Sterling.\n\nThe _South Carolina Gazette_ ran no articles about the Stono uprising, apparently fearing even to mention the subject where the black majority might learn of it. But a Charles Town merchant wrote in a letter of December 27 of that year, \"We shall Live very Uneasie with our Negroes, while the Spaniards continue to keep Possession of St. Augustine.\" \"For several years after [Stono],\" writes Peter H. Wood, \"the safety of the white minority, and the viability of their entire plantation system, hung in serious doubt.\"\n\nBelieving foreign slaves to be the most dangerous, South Carolina raised the duty on slave importation from \u00a310 to a prohibitive \u00a350. But that made for considerable lost income for local government in a territory where slaves had accounted for two-thirds of customs revenues in 1731, so in 1744 the duty was lowered back to its previous level. Previously, South Carolina had imposed double duties on slaves _not_ coming from Africa, apparently in order to discourage the unloading of incorrigible West Indian slaves into their territory.\n\nThe author of an 1825 pro-slavery pamphlet in Charles Town noted that the Stono rebellion was also remembered as the Gullah War.* In recent years, Y. N. Kly has been arguing for the use of the term \"Gullah War\" as a blanket name for the ongoing black resistance struggle in South Carolina, Georgia, and Florida that lasted from Stono until 1858, with the end of what is usually called the Third Seminole War. This Gullah War can be seen as part of the larger war against slavery, fought in ways large and small by the enslaved. From this perspective, slave rebellions reveal themselves not to be isolated struggles, as they have been frequently characterized, but rather as eruptions of a widespread, ongoing state of resistance. Their tactics ranged from day-to-day resistance, to absconding, to full-out uprising, to actions taken by the enslaved in major wars.\n\nIn the wake of Stono, the South Carolina legislature on May 10, 1740, passed a detailed new slave code. \"An act for the better ordering and governing Negroes and other slaves in this province,\" or, more simply, the Negro Act, had long been in preparation but some had thought it severe; its passage was catalyzed by the crisis atmosphere. Under its regulations, teaching a slave to write\u2020 became punishable by a fine of one hundred pounds; masters had to apply to the legislature for permission to manumit; and it even forbade slaveowners to allow their slaves to dress in \"clothes much above the condition of slaves.\"\n\nAimed at making impossible the kinds of public assemblies that could turn into mobs or hatch conspiracies, Article 36 (out of 58) paraphrased the existing Barbadian regulation to stipulate that \"whatsoever master, owner or overseer shall permit or suffer his or their Negro or other slave or slaves, at any time hereafter, to beat drums, blow horns, or use any other loud instruments or whosoever shall suffer and countenance any public meeting or feastings of strange Negroes or slaves in their plantations, shall forfeit ten pounds, current money, for every such offence.\" One long-term consequence of this and similar legislation was that African hand drums, so rigorously prohibited by the British colonists, do not turn up in popular African American music until they came into the United States via the Cubans in the mid-twentieth century. That African drums were played on some Southern plantations is documented, but they do not seem to have flourished outside their immediate context.\n\nAnother clause of the Negro Act forbade slaves from engaging in sales, and yet another restricted gatherings of \"great Numbers of Negroes, both in Town and Country, at their Burials and on the Sabbath Day.\" All this was in marked contradistinction to New Orleans, where Sunday gatherings were already taking place at the commons later known as Congo Square.\n\nThe Negro Act was not discussed in the _South Carolina Gazette._ Days after the legislature adjourned, a slave conspiracy was uncovered (or perhaps imagined) in June 1740 among plantation slaves planning to strike in some numbers against Charles Town. The undoing of that conspiracy\u2014also unreported in the _Gazette_ , though other colonial newspapers took up the slack\u2014resulted in the hanging of fifty people, in daily batches of ten. The following year, after a purportedly murderous slave conspiracy was uncovered in New York, the second largest black city after Charles Town, magistrate Daniel Horsmanden executed or exiled over one hundred people. Horsmanden, who may have dramatically exaggerated an existing plot or may have even imagined it all, linked the never-realized black insurrection to an alleged Catholic plot involving the Spanish. Between 1730 and 1760 there were twenty-nine slave revolts reported in North America, about one a year, with an unknown number of others of smaller dimensions going unreported.\n\nWhen a calamitous fire in Charles Town on November 18, 1740, \"in a very short time laid the fairest and richest part of the town in ashes, and consum'd the most valuable effects of the merchants and inhabitants,\" it was said at first that the fire had been set by slaves, though this apparently was not true. The clergyman Josiah Smith preached a sermon, subsequently published with the title \"The Burning of Sodom,\" that spoke of the fire as God's punishment for wickedness. Smith excoriated the whites of the town for defiling themselves by having sex with their slaves\u2014not because they were taking unfair advantage of their captives but because they were cohabiting with inferiors. Reverend Smith insisted there was a great deal of fornication going on:\n\nthere has been too much _Affinity_ in _our Sins_ and those of _Sodom_ , as there has been in _our Punishment._ \u2014Whether we have any _Sodomites_ in our Town strictly so, I can't say.\u2014Such abandon'd Wretches generally curse the Sun, and hate the _Light_ , lest their Deeds should be reproved.\u2014But in some Respects and Instances we declare our Sin as _Sodom;_ we hide it not\u2014We have proclaim'd on the _House-Top_ what we should be asham'd of in _Secret..._ Let us enquire seriously, Whether our Filthiness be not found in our Skirts?\u2014Whether our _Streets, Lanes_ and _Houses_ , did not burn with _Lust_ , before they were consumed with _Fire?_... That unnatural Practice of some _Debauchees_ , that Mixture and Production, _doubly spurious_ , of WHITE AND BLACK; and taking those to our _Bed_ and _Arms_ , whom at another Time we set with _the Dogs of our Flock_ , ought to stand in _red Capitals_ , among our _crying_ Abominations! I know not, if _Sodom_ had done this\n\nThe news of Stono arrived in Georgia concurrently with the confirmation that, as rumored, England and Spain were at war yet again. It was especially unhappy news because tensions along the disputed Georgia-Florida border had been the catalyst for the hostilities.\n\nBritain's enduring, disingenuous name for the resulting war was applied to it much after the fact, in 1858, by Thomas Carlyle: the War of Jenkins' Ear. This referred to an incident that occurred off the coast of Florida in 1731, eight years before the war began. A Spanish coast guard patrol boat from San Agust\u00edn boarded a British brig, during which action the Spanish officer Juan de Le\u00f3n Fandi\u00f1o cut off the ear of the British captain Thomas Jenkins, taking in vain the name of the British king as he did so; the pickled ear was subsequently exhibited on the floor of Parliament.\n\nRemembering the conflict as the War of Jenkins' Ear might suggest that the war was somehow trivial or silly. In Spain, however, the war was remembered not by that anecdotal incident but by its underlying financial cause: the _Guerra del Asiento._ British merchants commonly used their slave shipments to the Spanish colonies as trojan horses to smuggle in all sorts of other prohibited goods. Worse, the British government had stopped making its payments for the _asiento_ to Spain as called for.\n\nWith England and Spain at war, Oglethorpe led a monthlong siege of San Agust\u00edn in 1740 but failed to take it; its defenders included about a hundred black militiamen from Gracia Real de Santa Teresa de Mose, led by Yamasee War veteran Francisco Men\u00e9ndez. Meanwhile, a dissident faction in Georgia, dubbed the Malcontents, were uninterested in small, self-sufficient, inalienable farms. They wanted to get rich via large, debt-driven, plantation slavery, and they wanted a functioning real-estate market so that they could buy out or seize the farms of others. Oglethorpe thought them in league both with the Charles Town merchants (which they were) and the enemy in San Agust\u00edn (perhaps not). Oglethorpe wrote the trustees on May 28, 1742:\n\nThe Mutinous Temper at Savannah now shows it self to be fomented by the Spaniards, & that the Distruction of that Place was but part of their Scheme for raising a general Disturbance through all North America.... They found three Insuperable obstacles in their way in driving out the English from this Colony. 1st. The People being white & Protestants & no Negroes were naturally attached to the Government. 2dly. The Lands being of Inheritance, as Men could not Sell, they would not leave the Country so easily, as new commers would do, who could Sell their Emprovements. 3d. Distilled Liquors were prohibited which made the Place Healthy.\n\nTheir Partizans laboured to get those who Perhaps intended no ill to bring about what they Desired. 1st. To Obtain Negroes being secure that Slaves would be either Recruits to an Enemy or Plunder for them. 2dly. Land Alianable which would bring in the Stock Jobbing Temper, the Devill take the Hindmost. 3d. Free Importation of Rum & Spirits which would Destroy the Troops & Laboring People here. (paragraphing added)\n\nThe war with Spain made Savannah's Jewish community particularly nervous, since they had fled the Inquisition. The community collapsed in 1741, and some of its members relocated to Charles Town where a congregation was organized in 1749, with the community divided between \"Portuguese\" (Sephardic) and \"German\" (Ashkenazi).\n\nOglethorpe defeated a Spanish invasion of St. Simons Island in the descriptively named Battle of Bloody Marsh on July 6, 1742, effectively consolidating Britain's ownership of the Spanish-claimed territory of Georgia. The force that attacked St. Simons Island was a large one: about a thousand Spanish regulars and five hundred or so black militiamen from Cuba, where a quarter or more of the soldiery was _pardo_ (mulatto) or _moreno_ (black). Alexander Hewatt, a Scottish Presbyterian minister who wrote the first history of South Carolina and Georgia (after being expelled from Charles Town as a Loyalist in 1777), recalled the frightening impression made by the presence of uniformed black soldiers:\n\nAmong their land forces they had a fine company of artillery, under the command of Don Antonio de Rodondo, and a regiment of negroes. The negro commanders were clothed in lace, bore the same rank with white officers, and with equal freedom and familiarity walked and conversed with their commander and chief. Such an example might justly have alarmed Carolina. For should the enemy penetrate into that province, where there were such numbers of negroes, they would soon have acquired such a force, as must have rendered all opposition fruitless and ineffectual.\n\nThe war was mostly over by 1742, after an attempted occupation of Cartagena by some thirty thousand British troops was repulsed, though hostilities continued through 1748. During the war, Spanish ships (joined in 1741 by French ones) preyed on shipments bringing American tobacco to London, denying the Chesapeake's tobacco farmers access to their market in Britain. This further encouraged the farmers in their ongoing switch to wheat, which had a domestic market, took fewer weeks of labor than tobacco, and needed less tending as it grew.\n\nMeanwhile, the British were cut off from their supply of indigo in the French West Indies, spurring the development of indigo production in South Carolina.\n\nThe first crop of indigo was brought in 1744 about five miles from the site of the Stono Rebellion by the twenty-one-year-old Eliza Lucas. A true godmother of American slavery, Lucas had lived most of her life in Antigua, where her father was the lieutenant governor. After trying her hand at raising ginger, alfalfa, cotton, and cassava at her father's South Carolina plantations, which she managed in his absence, she found she could grow indigo with seeds of the West Indian variety that her father sent her\u2014but she could not process the plant into dye until her father sent her a \"negro man\" who knew how. After the success of her crop, she distributed seed to her neighbors and married Charles Pinckney of Charles Town, becoming Eliza Lucas Pinckney.\n\nBritain paid a bounty for indigo cultivation in order to have a supply of dye for its growing textile manufactures, though the South Carolina product was inferior in quality to the indigo they had been receiving from India. Indigo was the perfect complement to rice. Both called for large amounts of labor and, most importantly, they grew in different seasons, allowing for one overworked labor force to produce two different staple crops in a year. Both crops required disagreeable, unhealthy work.\n\nAccounts of indigo production describe the terrible stench it gave off as the plants decomposed after infusion. It attracted grasshoppers and clouds of flies, was toxic to the workers, depleted the soil, and ruined the surrounding land for cattle, which were needed to provid basic nourishment for the region. But once processed, it was a perfect long-distance export: a small amount of the concentrated, solid dyestuff had a high value. It was even more profitable than rice. The success of indigo made South Carolina much more profitable, further stimulating British trade, most especially the slave trade, to the colony.\n\n_Charles Town, at the confluence of the Ashley and Cooper Rivers, at the end of a defensible channel behind barrier islands, as depicted in a 1780 map by William Faden. Sullivan's Island, to the right, was the entry and quarantine point for upwards of a hundred thousand Africans._\n\nOglethorpe returned to England for good in 1743, leaving behind William Stephens as governor. Stephens followed Oglethorpe's principles\u2014at tremendous personal cost, since his son Thomas had become a leader of the Malcontents\u2014but in 1749 he admitted defeat, advising the trustees that the prohibition against slavery was no longer enforceable. Slavery was legalized in Georgia as of January 1, 1751, and by 1752 the trustees had washed their hands of the place as the territory reverted to crown colony status. The itinerant traders who brought slaves in from South Carolina became known by a name that would outlive them: Georgiamen.\n\nTwenty years after its founding as the first free-soil territory in the nascent British Empire, Georgia was firmly established as a satellite of South Carolina's world of plantation slavery. Though slaveowners frequently accused Britain of having forced the system of slavery on them, the case of Georgia offered an unambiguous model to the contrary: the British who established the colony wanted no slavery, but some of the colonists\u2014and the South Carolina merchants\u2014did.\n\n*The site of Gracia Real de Santa Teresa de Mose was found in a 1986 architectural dig and is now a Florida state park.\n\n*The name of the creolized African American people called \"Gullah\" in South Carolina likely derives from \"Ngola,\" or Angola, though there are other theories; in Georgia, the population is known as \"Geechee,\" the name presumably deriving from the indigenous-named Ogeechee River.\n\n\u2020Writing was taught separately from reading in those days. Slaveowners feared that slaves who could write would forge the passes that every slave traveling alone was required to carry and thus escape.\n\n_The coast of Georgia as depicted in a British map of 1780, showing the Sea Islands down to Amelia Island, claimed by Florida. Savannah is in the upper right._\n\n#   17\n\n# **A Rough Set of People, but Somewhat Caressed**\n\n_... that Cargo Sold at pretty good prices tho they were a month about it... it was a most butifull Cargo of the Sort chiefly young People from 15 to 20 which are not accustom'd to destroy themselves like those who are older. 1_\n\n\u2014Henry Laurens, letter to Liverpool slave trader John Knight, May 28, 1756\n\nTHROUGHOUT GEORGE WASHINGTON'S CAREER, it would never be forgotten by the British, the French, or the Spanish that when the young land speculator was a twenty-one-year-old lieutenant colonel in the British army, he played a key role in starting the war that deprived France of its North American real estate.\n\nAs French troops from Louisiana made incursions into the unexplored Ohio Valley, trying to connect France's Canada positions with Louisiana and thus box the British in on the Atlantic coast, they were ambushed on July 3, 1754, in what is now southwestern Pennsylvania, by a detachment led by Washington, with one column of British troops and one column of Native Americans. The British troops had been sent there by Virginia governor Robert Dinwiddie, in part to protect the land claims of the Ohio Company of Virginia, of which Washington's half brother Lawrence was a cofounder.\n\nAfter a skirmish that led to the death in captivity of the French commander Jumonville at the hands of Washington's indigenous ally Tanacharison, Washington was captured and released after signing a confession in French, which he could not read. The Ohio Valley conflict escalated into a global war, with London and Paris as the principal belligerents. In America it became known as the French and Indian War, and in Europe as the Seven Years' War. Its outcome drastically altered the course of hemispheric history, driving the French out of North America and giving control to Britain of New France, or Canada.\n\nIn the final phase of that war, after Spain's Bourbon king Carlos III foolishly entered the conflict on the side of his cousin, Louis XV of France, Britain occupied the great harbor of Havana, the hub of Spain's gold- and silver-shipping empire, for about ten months. At war's end, victorious Britain, in another net territorial gain, returned Havana to Spain in exchange for Florida.*\n\nAfter 198 years as a Spanish Catholic town, San Agust\u00edn was now to become St. Augustine, a British Protestant town. Britain promptly divided Florida into West and East, with the Apalachicola River as the eastern boundary between the two. Pensacola, founded as a fort in 1698, was the capital of West Florida, which had the Mississippi as its western boundary abutting French Louisiana and controlled the access to the sea for the Gulf Coast hinterland. St. Augustine was the capital of East Florida, which included the entire peninsula.\n\nLondon began giving away\u2014mostly to politically connected Scots\u2014massive amounts of the depopulated Florida land it now claimed, as well as large tracts in Georgia. It was the first, but not the last, boom in Florida real estate: \"during the great speculation in American lands that preceded the American Revolution,\" writes George C. Rogers Jr., \"there was more interest in the real estate of East Florida than in the property of any other region of British America.\" In the years from 1764 to 1770, 2,856,000 acres of East Florida were distributed.\n\nVirginia's tobacco was the largest American export, but the Lowcountry's rice and indigo was the second largest. Moreover, Virginia's exports were declining, while shipments from Charles Town's harbor, one of the colonies' busiest, were increasing. As plantations proliferated in South Carolina, Georgia, and Florida, Charles Town was the great mercantile supplier to all of them, with slaves far and away the highest-value merchandise supplied. Debts incurred purchasing slaves mounted up so fast that importation of Africans was suspended from 1766 to 1769, and disputes over taxation with England depressed importation in 1770\u20131, but in 1772 and especially 1773, importation was enormous. These slaves were often sold in gangs, with the result that, as in the sugar territories, people from a single African point of origin wound up on the same plantation, a consciousness that has remained in black Sea Island folkways, where different islands are understood to have different African cultural influences.\n\nFlorida was to embody, once again, the British dream of enormous landholdings. One of the first in the door was a leading British capitalist: the Scottish slave trader, commodity trader, shipping magnate, army contractor, planter, and stock market investor Richard Oswald, who was one of six owners who built Bance (or Bunce) Island in the Sierra Leone River into a major slave-trading factory. Oswald received twenty thousand acres in 1764, almost as soon as Florida was open for business. African slaves were brought directly to Florida for the first time, and Oswald soon had a hundred of them on his plantation.\n\nA dinner at a meeting of the East Florida Society of London, founded in 1766, brought together a group of men that included Richard Oswald and Benjamin Franklin, who thought Oswald an \"honest\" man. Oswald's firm was at the time on the first year of its unprecedented five-year contract with a French society to bring regular shipments of slaves to the war-damaged plantations of Saint-Domingue and Guadeloupe from their Sierra Leone River base at Bance Island\u2014a job only achievable by a modern factory, requiring as it did the coordination of regular supplies of people captured in slave raiding and war, with shipping schedules and cash flow, year in and year out. This type of venture marked a new level of professionalization in a business that had largely been the province of individual merchants working with captains who assembled cargoes as best they could. By the time Grant, Oswald & Co.'s French contract expired in 1770, they had delivered 4,847 people. Oswald had a remarkable record of picking winners, but his venture in Florida was a bust, as were most of the others: the land was unsuited for rice or for sugar.\n\nWith the handover of Florida to Britain, more than three thousand of the Spanish colony's people evacuated, most of them fleeing to Cuba, where many established themselves in the communities of Guanabacoa and Regla, now part of metropolitan Havana. Residents of the free black town of Gracia Real de Santa Teresa de Mose founded the community of San Agust\u00edn de la Florida in Matanzas province. The western part of Cuba, meanwhile, was being reconfigured by sugar. Control of the sugar market had been a major object of contention during the Seven Years' War, and after the abrupt British withdrawal from Cuba the island entered into its era of sugar prosperity. During its ten months as an occupier in Havana, Britain had begun aggressive slave importation there, giving new life to Cuba's moribund sugar industry. Cuba had been home to Africans for almost two and a half centuries at that point but had not had massive plantation slavery; now that began to change. Liverpool slave captains serviced much of this new Cuban market, bringing large numbers of captives supplied by their African trading partners in the Bight of Biafra, the region known as Calabar. The African traders of Bonny and Old Calabar were particularly powerful and did not allow the establishment of factories by Europeans, giving them a trade advantage.\n\nRemoving the Spanish antagonist from St. Augustine was a godsend for Carolina and Georgia slaveowners. Meanwhile, in compensation for the loss of Florida, the French Louis XV gave Louisiana (in secret, at first) to the Spanish Carlos III. Spain was occupied with reasserting Spanish authority in Cuba, where planters had tasted British commerce and weren't going back, so no Spanish governor was sent to Louisiana until 1768, during which time the French and Creole elite of New Orleans further developed its already pronounced independent streak.\n\nSpain had no choice but to take Louisiana when the French king handed it over. Though Louisiana produced little of value, it was an essential buffer zone for protecting Spain's Mexican silver mines from the English. So, for approximately the last third of the eighteenth century, the governor of Louisiana reported to the captain general in Havana, with enormous cultural consequences for the town of New Orleans, which under the Spanish took on the structure of a city and started to be a port of importance.\n\nThe London economy suffered a panic in 1772, which, coupled with a quickly withdrawn incentive plan to encourage poor Protestant immigrants, brought in thousands of desperate Scots, Irish, and especially Scotch-Irish to South Carolina. In the four days between December 19 and 22, 1772, four ships from Northern Ireland disgorged more than a thousand people into Charles Town. These were poor and uneducated Ulsterpeople, nominally Presbyterians but in fact barely churched. Henry Laurens, who dealt in indentured servants as well as slaves, wrote of a group of them:\n\nI have been largely concerned in the African trade... yet I never saw an instance of Cruelty in ten or twelve Years experience in that branch equal to the Cruelty exercised upon those poor Irish... Self Interest prompted the Baptized Heathen in the first case to take care of the wretched Slaves for a Market, but no other care was taken of those poor Protestant Christians from Ireland but to deliver as many as possible alive on Shoar upon the cheapest terms, no matter how they fared upon their Voyage or in what condition they were landed.\n\nThe coastal land was taken, so most of the new arrivals went upcountry.\n\nThe little more than a decade between the end of the Seven Years' War and the Declaration of Independence was a time of great political transformation and opportunity for enterprise. With peace and stability, the Lowcountry plantation economy boomed. The growth of rice cultivation expanded enormously owing to the adoption of a new method of irrigation that used sluices to bring in sea water mixed with fresh to make aquaculture possible in the Tidewater, instead of merely in the inland swamps.\n\nSouth Carolina was the opposite of the decentralized Chesapeake: it was highly centralized in Charles Town, an empire whose commercial relations extended for hundreds of miles. The only place in South Carolina that could be described as a city, it traded via small oceangoing vessels with coastal North Carolina, Georgia, and Florida, and by land, selling the native confederations and the new arrivals upcountry guns to kill each other with, as well as having its own prosperous residents to import goods for. Leila Sellers described it as \"a sort of city-state, drawing to itself all the wealth of the surrounding country, which gave it a prestige the memory of which has never faded.\"\n\nThe easy upward social mobility the slave society offered white men was described by Alexander Hewatt in 1779, in the course of explaining why he thought (correctly) that industry would not develop in South Carolina:\n\nNor is there the smallest reason to expect that manufactures will be encouraged in Carolina, while landed property can be obtained on such easy terms. The cooper, the carpenter, the brick-layer, the shipbuilder, and every other artificer and tradesman, after having laboured for a few years at their respective employments, and purchased a few negroes, commonly retreat to the country, and settle tracts of uncultivated land.... Though the wages allowed them are high, yet the means of subsistence in towns are also dear, and therefore they long to be in the same situation with their neighbours, who derive an easy subsistence from a plantation, which they cultivate at pleasure, and are answerable to no master for their conduct.\n\nEven the merchant becomes weary of attending the store, and risking his stock on the stormy seas, or in the hands of men where it is often exposed to equal hazards, and therefore collects it as soon as possible, and settles a plantation. Upon this plantation he sets himself down, and being both landlord and farmer, immediately finds himself an independent man. Having his capital in lands and negroes around him, and his affairs collected within a narrow circle, he can manage and improve them as he thinks fit.\n\nHe soon obtains plenty of the necessaries of life from his plantation; nor need he want any of its conveniences and luxuries. The greatest difficulties he has to surmount arise from the marshy soil, and unhealthy climate, which often cut men off in the midst of their days. Indeed in this respect Carolina is the reverse of most countries in Europe, where the rural life, when compared with that of the town, is commonly healthy and delightful.\n\nHewatt wrote that Charles Town \"may be ranked with the first cities of British America.\" He estimated its 1765 population to be between five and six thousand white inhabitants and between seven and eight thousand \"negroes,\" while his estimate for South Carolina as a whole was forty thousand whites and eighty to ninety thousand blacks. When the Declaration of Independence was signed, Charles Town was the fourth largest city in the colonies, far behind Philadelphia and New York in population and somewhat behind Boston. It was a town of young people, as Hewatt noted: \"There are few old men or women to be found in the province, which is a sure sign of the unhealthiness of the climate. We cannot say that there are many in the country that arrive at their sixtieth year.\"\n\nIn Charles Town, slaves were crucial to a merchant's offerings, since they drew customers who might then purchase their dry goods from him. \"Before the Revolution,\" writes Elizabeth Donnan, \"at least one hundred [Charles Town] firms had offered [slave] cargoes for sale, some advertising but one, others one a year for a number of years, while Brailsford and Chapman, in the year 1765, handled nine cargoes, two of which numbered four hundred slaves each.\" That was exceptional: a big cargo was a lot to handle, and even a large merchant would normally not handle more than two or three in a year. But there were a lot of merchants.\n\nHenry Laurens was the number-one dealer in Africans. During 1760, his firm Austin, Laurens, and Appleby advertised 1,010 slaves for sale; for purposes of comparison, 3,573 slaves were sold in all of Charles Town for the year beginning November 1, 1759. In surveying accounts of duties paid, Daniel J. McDonough identifies Laurens as involved in the importation of some 6,900 people. That was synonymous with being well capitalized; Charles Town's slave distribution network reached North Carolina, upcountry South Carolina, Georgia, Florida, and beyond, but only very wealthy merchants could lay out the sums necessary for such operations. Since the trade was highly seasonal (April to November, primarily because the cold months killed too many of the captives), capital drain was concentrated in time. On the sale end, the trader had to extend credit and collect, a process that sometimes took years; Laurens estimated that he often had more than \u00a310,000 sterling out. Advising a pair of young brothers who were hoping to get started as slave traders, Laurens wrote, \"We experimentally know that a large Capital is requisite to negotiate a Trade in this Country for 7 or 800 Negroes a Year in the way we take them.\" He took his profits in slaves; by 1776 he owned 797 of them, and plantations for them to work on.\n\nBut smaller, less-capitalized merchants could also participate in this chain of value creation. The 1,108 slave cargoes known to have been brought to colonial Charles Town (almost no place else in South Carolina received Africans) were received by 405 different merchants and factors. There was no business easier to make a profit in. Slaves were sold everywhere commerce was conducted in Charles Town, from Gadsden's Wharf, large merchants' warehouses, auction houses, plantation grounds, and the \"Negro yard,\" to small dry goods stores and on many public occasions that included, in Leila Sellers's description, \"at the race course between the heats of the races.\" Slaves were still coming in from Barbados and Antigua, and occasionally Jamaica, in one- and two-digit quantities, but most of the vessels by now were from Africa, perhaps making a stop in the West Indies first, and bringing hundreds at a time.\n\nThe traders had a paper money supply that facilitated their commerce. There was little specie in South Carolina for cash purchases, but bills of exchange from reputable London merchants were circulating in some numbers, though the supply was subject to sharp fluctuation. Carolina's paper money, first issued in 1703 when North and South Carolina were still one polity, \"established a security and stability rare in the colonies,\" writes John J. McCusker; the seven-to-one rate of exchange between South Carolina currency and London pounds sterling remained in effect from the 1730s until shortly before South Carolina's declaration of independence from the British Empire.\n\nHenry Laurens's letter to a London trading firm on August 25, 1763 noted a spectacular ninefold markup realized in a slave sale that mixed people from two disparate regions of Africa: \"Negroes have yielded great prices hitherto & will continue do so thro the Year unless the Importations should be excessive. A Cargo of Angola's lately averaged \u00a332 Sterling round & 50 prime Gold Coast Negroes bought in Antigua at \u00a334 per head sold in one lot at \u00a3300 round.\"\n\nThough we have no specific details of the settlement of that sale, it's close to impossible that a horse-cart loaded with tons of silver trudged through the streets of Charles Town. Sales were accomplished with transferable credit of one type or another, and could not have been effected at all unless London merchants were willing to extend credit to the purchasers. In effect, the profit reported by Laurens that day was money that had not previously existed, but had been written into being at the moment of sale, in the form of bills of exchange. These sales actively turned people into money. Laurens's firm may have been Charles Town's biggest factorage, but the factors' profits were small compared to those realized by the British merchant houses they were affiliated with. Laurens was proud of his association with his \"worthy Friend\" Richard Oswald, whose firm of Grant, Oswald, and Co. shipped 12,742 Africans across the Atlantic that are documented, and an unknown number of others, between 1748 and 1770.\n\nArriving in Charles Town to sell a quantity of flour in 1765, the Connecticut merchant Pelatiah Webster found a town of \"about 1000 houses, with inhabitants, 5000 whites and 20000 blacks\"\u2014a considerable exaggeration in the latter case, but one based on appearances. Webster wrote an enthusiastic account of his \"sauntering about town as much as the great heats will permit\" and dining as the guest at the magnificent tables of a succession of Charles Town merchants, all of whom sold slaves as a significant part of their business. In the course of making the social business circuit, he \"passed some hours... with some Guinea captains, who are a rough set of people, but somewhat caressed by the merchants on account of the great profits of their commissions.\"\n\nThe slave ship captains may have been coarse, but according to Webster, the merchants who sold human beings by the boatload were anything but. Thomas Smith, of Brewton and Smith, was \"a reputable merchant in this town & in very fine business: is an agreeable sensible kind man.\" His brother, Benjamin, one of the wealthiest men in South Carolina, had made a great fortune in the slave trade; by then retired from active trading, he was \"a Gent about 50\" who was \"cheerful, easy & generous.\" Thomas Shirley, of Shirley and Martin, was \"a very polite English Gent. residing here in very genteel fashion: is an ingenious ready man: was bread a merchant, has traveled much, understands several modern languages.\" Thomas Liston was \"a man of great openness and politeness, of generous sentiments and very genteel behavior\"; Webster traveled with him to Sullivan's Island, the entry point for slave cargoes, where there \"were 2 or 300 negro's performing quarantine with the small pox\" in the local pest house. After hearing some \"very fine airs on the harpsichord by Mr. ____, an English organist,\" he found Charles Town an \"agreeable and polite place,\" noting that \"the laborious business is here chiefly done by black slaves of which there are great multitudes.\"\n\nGeorgia received its first cargo direct from Africa in 1766, when a Liverpool captain brought in a vessel coming from Senegal with seventy-eight kidnapped people in the hold. The following year, Savannah built a pest house to quarantine new arrivals, like the one at Sullivan's Island for Charles Town, where incoming slaves were expected to remain for a minimum of ten days. But in the absence of capital to handle a sizable African cargo, a larger percentage of Georgia's imports came in smaller shipments from the Antilles\u2014especially Jamaica, but also Antigua, Barbados, St. Christopher, St. Kitts, Grenada, Cura\u00e7ao, and others. Even today, you can hear in the Gullah and Geechee way of talking a marked resemblance to black speech of the British West Indies.\n\nSouth Carolina was already at least occasionally exporting enslaved African Americans to neighboring regions by sea, as when Laurens shipped a \"parcel\" of \"country Negroes\" to British-controlled St. Augustine in 1768.\n\nWith Jamaica and Saint-Domingue both taking large numbers of Africans, the African slave trade was reaching its hemispheric peak. Liverpool, London, Bristol, and Lancashire captains competed to open up new sources of supply in Africa.\n\nBoth forced African immigration and voluntary European immigration to the colonies reached new levels after the Seven Years' War, increasing the colonial population by 10 percent or so. There were newcomers in every town. Many were getting ready to push west, out where one could own land, albeit at the price of defending one's claim from the Indians. The moving frontier of westward expansion, still in its early stages, kept the market for slaves strong.\n\n*Britain wanted the island of Guadeloupe, but had to keep Canada\u2014which was producing much less revenue\u2014instead.\n\n#   18\n\n# **Ballast**\n\n_She [Phillis Wheatley] does not seem to have preserved any remembrance of the place of her nativity [Senegal], or of her parents, excepting the simple circumstance that her mother poured out water before the sun at his rising._\n\n\u2014\"written by a collateral descendant of Mrs. Wheatley\" for the 1834 edition of _Memoir and Poems of Phillis Wheatley, a Native African and a Slave_\n\nIRON WAS FUNDAMENTAL TO any kind of industrial development. England had been making iron since the Roman era, but by the beginning of the eighteenth century, British furnaces had slowed down\u2014not for lack of iron ore, but for lack of fuel, the forests having been consumed. Britain had been importing iron from Sweden but the coronation of King George I in 1714 put an end to that because George was at war with Sweden.\n\nWith commerce between Britain and Sweden frozen, Britain was eager to get iron from its colonies. Maryland made it governmental policy to encourage iron furnaces as of 1719, and the Chesapeake became a leader in colonial iron production. These ironworks produced only bars, or \"pigs,\" because as codified in the Iron Act of 1750 the colonists were not to have rolling, plating, or slitting mills, much less to make steel of their own. The colonials were to be consumers, not manufacturers, so they weren't allowed even to work iron into the rods used in the manufacture of nails, because supplying nails to plantations was a British business. Americans were expected to buy their iron back in the form of finished nails from the West Midlands naileries, with the cost of two ocean voyages factored into the price.\n\nBy the early 1720s, the Principio Company was already up and running in Maryland from a base in Cecil County and with holdings throughout Maryland. Owned by English investors, it employed English ironmasters as well as enslaved workers. Using slaves in an industrial setting was something of an experiment, but black men producing iron was not: iron was a longtime African specialty.\n\nA list of Principio's laborers enumerates twenty-six paid laborers, ten wageless indentured laborers who had last names, and thirteen enslaved laborers who did not have last names: Ben, Cuzo, Quash, Quamini, Tantaro, Tom, Prince, Joe, James, and Pohick.  The enslaved laborers seem to have started at the bottom of the Principio labor chain, as woodcutters feeding the endlessly hungry furnaces, but by 1750 several of them were listed as skilled laborers and they received incentive pay of a shilling per ton of iron blooms produced. Prince was still working at Principio in 1781 at the age of sixty-five, and was classed as a skilled forgeman, along with fifty-five-year-old Harry, sixty-five-year-old Dancer, and thirty-seven-year-old Ellick and Will.\n\nEven the highest-ranking white wage laborers at Principio did not necessarily receive their pay on time. Much of their salary was taken in the form of credit at that notorious institution, the company store, \"which seems to have been the first part of the enterprise... to go into operation,\" writes Michael W. Robbins in his history of the company. Needless to say, the black laborers were treated worse than white employees. A 1781 inventory of the facilities of one iron company, the Kingsbury Furnace, includes both a kitchen and a \"Negro kitchen,\" suggesting that the enslaved ate separately, and, to be sure, more poorly. Caloric requirements for the hard labor were high, and though they ate a monotonous diet based on corn, they had to have enough to keep moving. On their feet they wore what were listed in budget lines as \"negro shoes,\" bought in large quantities. They lived crowded into shanties and crude cabins where privacy was unknown. They were corporately owned, in what could amount to as many as 150 enslaved laborers on an iron plantation. Large numbers of support personnel were needed to sustain the ironworkers; a few of the enslaved in the ironworks were women, who cooked and sewed\u2014and occasionally were ironworkers as well.\n\nCharles Carroll the Settler arrived from Ireland to Lord Baltimore's colony in 1688. Determined to become wealthy in spite of the discrimination against Catholics in the wake of the Protestant coup of the Glorious Revolution, he became the largest landowner and the largest lender in Maryland. He began a family line that included a number of people named Charles Carroll, who then needed another name to differentiate them, so that Charles Carroll the Settler's son was Charles Carroll of Annapolis, whose only child and heir was Charles Carroll of Carrollton.\n\nCharles Carroll of Annapolis also had a distant relative in the area, known as Dr. Charles Carroll, who was the father of Charles Carroll the Barrister. But unlike the previously named Charles Carrolls, Dr. Charles Carroll's branch of the family was not Catholic but Anglican, so in Annapolis they spoke of the Catholic Carrolls and the Anglican Carrolls.\n\nHoping to diversify their holdings, Dr. Carroll and four partners\u2014including Charles Carroll of Annapolis\u2014were eagerly looking for alternatives to tobacco as a way to put their capital to work. They started the Baltimore Iron Works (or the Baltimore Company), in 1731 on a choice plot of about thirteen hundred acres north of the Patapsco River that Dr. Carroll had purchased. The second ironworks in Maryland, it was well situated: the little village of Baltimore was next to a thick vein of iron ore and had a deep-water harbor.\n\nBefore committing to founding the company, Dr. Carroll even drew up a business plan of sorts, which concluded that profitability could be reached in a mere two years. In his operating budget, the largest single expense was the purchase of laborers, who were capital acquisitions and were resalable. This earliest of Baltimore industries used a combination of free, indentured, and slave labor, beginning the diverse mix of workers that would later characterize the city. By 1734, the Baltimore Iron Works had forty-three enslaved black laborers, eight of them cooks.\n\nThirty years later, when Charles Carroll of Annapolis was the richest man in Maryland, he listed his holdings for his son and heir's benefit. Valuing at \u00a310,000 his one-fifth interest in the company's holdings of thirty thousand acres and \"150 slaves young and old,\" he listed as part of his estimated \u00a388,380.97 personal wealth \"20 Lots in Annapolis with the houses thereon,\" valued at \u00a34,000, and \"285 Slaves on my different Plantations at \u00a330 Ster,\" valued at \u00a38,550.\n\nTwenty built-up lots in Annapolis was a substantial holding, but 285 human beings were worth more than twice as much. That letter's addressee, Charles Carroll of Carrollton, became the only Catholic signer of the Declaration of Independence, as well as the wealthiest. Charles Carroll of Carrollton was already price-conscious at the age of twenty-nine when he wrote his father's partner Walter Dulany on August 29, 1767, that \"I am informed that negroes sell cheap in Virginia: as they are much wanted at the works would it not be pro[per] to direct Clt. Brooke to attend the Sales? Next Octbr. I am told will be the best time to purchase when it is probable the gentleman says from whom I had my information, young likely country born negroes may be bought at \u00a325 or 30 Sterling.\"\n\nDulany wrote back: \"I shou'd be for purchasing Negroes in Virginia, since they are to be had so cheap there as Mr. carroll mentions\u2014I know of but one Reason against doing it of this Side of Winter, which is that we shall probably have them all to cloath with Goods bought here, for it is very uncertain whether our Goods will come in in time from England; however I am willing to run the Risque.\"\n\nApparently the purchasing did not go forward as Charles Carroll of Carrollton wished. He wrote a circular letter to the other four partners in 1773 complaining that, \"In 1769 I procured from our Clerks a list of hirelings wages at the furnace, and at the three forges, which I have often mentioned in my Letters to the Company, to induce them to purchase Slaves to save that enormous expence, but hitherto without success.\" He then computed in detail the costs of purchasing slaves, concluding that an\n\nannual saving of 901.5.0 would not be the only Advantage the Company would reap from the purchase of 40 Slaves: the business would be carried on with more Alacrity, and fewer disappointments; we should encrease our Stock of negroes, and be greatly benefited by that encrease, in case the company should hereafter come to the resolution of selling their Lands, or leasing them, selling their Stock, and breaking up the Iron works.\n\nIt was good business to own slaves instead of rent them, and the richer one became, the easier it was to do. By purchasing slaves, not only did the partners save on labor costs in day-to-day operations, they acquired human capital that could then be sold or rented out. A few years later, on December 3, 1773, the seventy-one-year-old Charles Carroll of Annapolis wrote a good-news letter to his only son and heir, Charles Carroll of Carrollton:\n\nI have taken a very Exact Acct of all the Negroes Here, I was Closely employed 5 Mornings from Breakfast to Dinner & two long Evenings in Comparing the last with my present List, they Amou[nt] to 330 including the 3 Jobbers with You. My Love & Blessing to You...\n\nNegroes as pr List taken Decr:1st: 1773 | 330  \n---|---  \nDo: as pr List taken Decr:1st: 1767 | 273  \nIncrease in 6 years |\n\n57\n\nCarroll's return on investment in \"Negroes\" was almost 21 percent in six years. Those extra fifty-seven people also increased Carroll's liquidity, since slaves could be disposed of more readily than any other holdings.\n\nAs the South developed what little industry it would have, slave labor was omnipresent, positing a model of industrial slavery in which either the workers and their children were corporate assets, or the workers were hired from local owners via employment agents specializing in slave labor. But slave labor was problematic in an industrial setting. Gang labor in the field was a blunt instrument, and agricultural slaves were notoriously recalcitrant. That spirit couldn't be set loose on expensive factory machinery. Enslaved factory laborers had to be paid incentives to work properly, but paying wages to slaves was seen by slaveowners as a hazardous practice. Indeed, many slaveowners believed that paying wages to _anyone_ set a dangerous precedent.\n\nThe legacy of the old days is visible all over the Eastern Shore of Maryland. In Crumpton, the effects of a fine old house were auctioned one day in January 2011. Among the items the auctioneer turned over was a two-piece ring of iron, just big enough to fit around someone's neck. It was a slave collar, found in the basement of the house. When it was knocked down for ninety dollars, the ghost of slavery threw off yet another commission for an auctioneer.\n\nChestertown's population was 5,252 in the 2010 census, not much more than in the late eighteenth century. Like many English colonial towns, Chestertown has, besides a Queen Street, a High Street, and, adjacent to the harbor, a Water Street (also known as Front Street), where the building known as the Custom House dates to 1746 or so. Located as it is on the waterfront of the Chester River on the Eastern Shore of Maryland, the Custom House was at one time the home of a wealthy merchant who traded in slaves and convicts: Thomas Ringgold IV.*\n\nIn America as in England, much of the business of African slavery belonged to Roman-numeraled generations of wealth. With a surname that spoke directly to money, Thomas Ringgold I was one of many Anglicans who left England during the Puritan regime (1647\u20131660). Only sixteen years after the _Ark_ and the _Dove_ brought the first Maryland colonists, he arrived in Maryland with his two sons in 1650. He acquired an Eastern Shore estate in 1657 by marrying a widow, a common means of enrichment for men in a land of high mortality and few rights for women.\n\nBy great-great-grandson Thomas Ringgold IV's time in the mid-eighteenth century, Chestertown was the most important port on Maryland's Eastern Shore, second only to Annapolis in all of Maryland, and the Ringgolds were its leading family. Together with his son, Thomas Ringgold V, and his brother, William Ringgold, the energetic Thomas Ringgold IV imported a variety of goods besides British manufactures: the strong, sweet, fortified wine the colonists drank (from Portugal, England's oldest trading partner); West Indian molasses; and indentured servants, convict labor, and African slaves. It was his good fortune to be at his peak during the boom years for colonial merchants after the French and Indian War, when explosive, immigrant-driven population growth made for an active commercial world throughout the bustling colonies. As merchants profited from supplying the new arrivals, the newly wealthy were furnishing exquisite new mansions. Ringgold IV bought the almost-new Custom House from its tavern-keeper builder in 1749, and it became both his residence and his place of business. He appears to have been the wealthiest man in Kent County, though he had competition from his next-lot neighbor Thomas Smyth, whose magnificent Georgian mansion Widehall, built in 1769, still stands on the former Water Lot #16, across High Street from the Custom House.\n\nEighteenth-century businessmen were necessarily diversified, and Ringgold IV was an attorney, planter, import\/export merchant, and retailer. He shipped out tobacco and iron\u2014the two went together, with the iron serving as ballast\u2014and by the 1760s, with the Chesapeake already making a transition out of tobacco, he was loading wheat onto an increasing number of ships.\n\nFueled by the growth in mercantile revenues, building after solid building went up in Annapolis, the small, wealthy colonial capital that had been designed in the European style. Its peculiar baroque pattern of streets radiating outward from two circular plazas (called Church and State, they were joined by a road to symbolize the Anglican union of the two) was unlike the square grid pattern already in effect in Philadelphia and in Burlington, New Jersey. With overhead cabling and signage having been removed in the mid-twentieth century to enhance the time-capsule effect, Annapolis is today a living reminder of the Enlightenment's rational organization of space: a logical order imposed on a small, urban area.\n\nAt the peak of Annapolis's influence, about a third of its population was enslaved, mostly in domestic service. With a population of only a thousand or so, Annapolis was the most stylish town of its size in the North American colonies, the social leader of the Chesapeake. A theater opened in 1771, where Annapolitans saw what had decades before been the most popular works of the London stage: Joseph Addison's _Cato_ , John Gay's _The Beggar's Opera_ , and Isaac Bickerstaffe's afterpiece _The Padlock_ , with its comic, Spanish-derived, black-faced character Mungo, the precursor of black minstrelsy. Annapolis even had a colonial version of \"macaronis,\" the young, effeminate, Italianate dandies with comically big hair who burst on the London scene in 1772, as lampooned in \"Yankee Doodle.\"\n\n_Fast-changing Macaroni fashions in London, from Thomas Wright_ , Caricature History of the Georges, _1904._\n\nMany of the wealthy men who founded the American nation passed through Annapolis and Chestertown, which were cheerful stops on the dreary overland route between Virginia and Philadelphia. The only road that ran south from Philadelphia divided in Delaware, one branch going to the Eastern Shore and the other to the western. The Eastern Shore branch, the quicker of the two, ran through Chestertown, from where it continued on to connect to the ferry that as of 1762 ran between the Eastern Shore's Rock Hall (later a small town, but then a terminal) across the Chesapeake to Annapolis.\n\nPublishing magnate Benjamin Franklin, traveling home to Pennsylvania from Virginia on official business after having been appointed deputy postmaster general of the colonies, attended a January 1754 meeting of Annapolis's celebrated Tuesday Club. This was a social club in the London style where participants took on funny names (Franklin, internationally famous as a scientist, was dubbed \"Electro-Vitrifrice,\" or electric glass-stroker), made ribald jokes (\"longstanding members,\" that sort of thing), and sang drinking songs. In Chestertown, Franklin, whose postmaster position paid little but was of great benefit to his newspaper business, handed over his Eastern Shore accounts receivable for the _Pennsylvania Gazette_ to Ringgold IV for collection.\n\nAcross the bay from Chestertown, Ringgold IV's partner Samuel Galloway III (1720\u20131785), was one of the most important merchants of Annapolis. Galloway was a Quaker and thus a second-class citizen; there were even whispers among Anglicans that the Quaker ranks concealed Catholics in disguise. Spanning both sides (\"shores\") of the Chesapeake, the Galloway-Ringgold partnership was a commercial force linking Annapolis and Chestertown, locked down with strategic weddings: Thomas Ringgold V (1744\u20131776) married Galloway's daughter Mary, while Galloway's other daughter, Anne, in turn married into another merchant family, the Chestons.\n\nWhen the Mount Vernon planter George Washington ordered from a merchant \"a Pipe [about 126 gallons] of your best Lisbon Wine,\" the price to be drawn against an account in London, he asked that it \"receive a Freight in any of Mr Galloway's, or Mr Ringold's vessels.\" That Washington should be on friendly terms with Galloway and Ringgold was hardly surprising: the wealthy of Virginia and Maryland formed a tight society, with interlocking kinship by marriage at the heart of the business network. By marrying the widow Martha Custis, Washington had become a large slaveowner and a rich man\u2014rich enough, in the long run, that he could wear his own custom-designed uniform when he served eight years at the head of the Continental Army without pay, and rich enough that he could be a racing enthusiast.\n\nThoroughbred racing, an amusement for the truly wealthy, had become popular in England after the Restoration of Charles II in 1660. It came to Virginia quickly, where it became a central social activity of the ruling class, and arrived in Annapolis in 1745. Washington's wealth wasn't sufficient to put him in the league of racehorse owners, but he traveled hundreds of miles to hobnob at Annapolis, noting in his ledger on October 10, 1772, \"Cash lost on the Races 1.6 pounds.\" On occasion he enjoyed the hospitality of Tulip Hill, Galloway's country estate, which still exists.\n\nGalloway was the owner of Selim, \"the most famous native colonial Chesapeake racer,\" whose heyday was at the height of the town-house era, between 1766 and 1772. Wealthy slaveowners were investing in the expensive hobby of horse breeding that attends a racing culture: twenty-seven stud farms have been identified in colonial Virginia. Selim had cost Galloway \u00a3178 on three years' credit, a heavy outlay at a time when an enslaved male laborer might be had for \u00a335. Even so, Selim was profitable. Besides winning races, he earned stud fees by covering the mares of Maryland's wealthiest. As did those sired from him: in 1793, it was advertised in Chestertown that one of Selim's grandsons\u2014named Liberty, of course\u2014\"will cover at SIX DOLLARS each mare, the season,\" noting that \"Country produce, at market price, will be received\" to pay for the stud service. Galloway kept a detailed Stud Book, now in the possession of the Maryland State Archives.\n\nGalloway was diversified. He planted tobacco and wheat, invested in ironworks, and owned a stand of oak trees that \"was the envy of all ship builders along the eastern seaboard,\" writes J. Reaney Kelly. In 1757, during the French and Indian War, he built and outfitted an eighteen-gun privateer and advertised for a crew. He tried and failed at launching a distillery, which was an essential asset for going into the African slave trade from North America.\n\nColonial documents contain pages-long lists of the fine things and basic necessities merchants imported: horses, cheese, candles, glass, paper, carpets, overcoats, hats, shoes, and on and on, in many varieties. Merchants also imported money, in many different forms, functioning in essence as mini-banks. They had to be agile mental calculators, since the currency they handled\u2014in a non-decimal-denominated system of twenty shillings to a pound and twelve pence to a shilling\u2014was issued by myriad sources, each with its own exchange rate or discount reflecting varying degrees of confidence in the solidity of the issuer. Frequently, debts were collected in merchandise, which meant keeping track of commodity price trends. The merchandise then had to be resold or traded for something else; that could be done at the Ringgolds' store on the ground floor of the Front Street building.\n\nRinggold IV traded in real estate as well, of course, but the way to make real estate valuable was to apply labor to it. No merchandise was more urgent, or potentially more lucrative, than laborers.\n\nIn front of a house on Queen Street in twenty-first-century Chestertown, the trees are set off from the sidewalk by a perimeter of \"rounded, water-worn stones,\" that, as Peregrine Wroth described them in 1871,\n\nare not natives of our alluvial district, being entirely different from any that I have ever seen in Kent [County]... Traditionally we are informed that they were brought to this country in ships from England which traded for Tobacco, as ballast; in the early times of the colony, tobacco being our staple crop for exportation. The stones being thrown out to take in the cargo, were afterwards used to pave the approach to the wharves.\n\n\"If I can procure him iron,\" wrote Ringgold of an arriving sea captain, \"I shall get his ballast wch I want to compleat my wharf.\" Pigs of iron made for a profitable cargo going back to London. The commerce in question was not the notorious clockwise, or \"triangular,\" trade, but a less efficient, colonially disadvantageous, back-and-forth monopoly circuit between North America and England. Ballast was necessary in both directions, but more of it was needed on the long westbound trip to America, because there was less cargo in the hold on the outbound voyage. Tobacco, the Chesapeake colonies' principal export, was a bulky commodity; the goods a ship would bring from London in exchange took up much less room. Freight was expensive, and shipping stones from England to Maryland was unprofitable. But the slack in a lopsided balance of trade is taken up by cheap labor, and an unprofitable cargo of ballast stones could share the hull with a profitable cargo of unfortunate people.*\n\nThat's where Ringgold and Galloway came in. They imported British convicts\u2014a product line with a dependable supply, as there were always plenty of prisoners on hand in Britain, already processed into the penal system. A steady flow of convicts in irons was a colonial merchant's dream, and was a specialty of the English port of Bristol. Ringgold was a factor, or agent, for the Bristol firm of Sedgely, Hilhouse, and Randolph, whose deported convicts received pardons for their crimes in exchange for indentures to labor in America. Some were felons, pirates, rogues, or dissenters, but others were merely indebted; and to judge from a number of advertisements in the _Maryland Gazette_ for the return of various runaways described as a \"Convict Servant Lad,\" a number of them were boys between sixteen and nineteen years of age. Convicts and paupers were in any case bundled together in the servant business, mixing the truly dangerous with the merely malnourished. While the number of convicts who were brought to America is difficult to state with any precision, the high-quality records of Annapolis indicate that by 1776, that port had handled 8,846 convicts, making the merchants who sold them rich.\n\nThe difference between indentured and enslaved labor was often negligible in terms of the actual work performed by the laborer. From the beginning of indentured servitude in America, tales circulated in England about how the indentured were made to work alongside the enslaved. It was common to refer to the \"purchase\" of indentured laborers, as per the 1774 letter from Charles Carroll of Carrollton authorizing a Baltimore Iron Works representative \"to Purchase 5 Negroes & 5 white Servants\" for industrial labor. But there was a significant difference between the two: the convict laborer was not bound for life, but the black slave was. Nor was the indentured servant's potential for \"natural increase\" part of the deal, as it was with the enslaved.\n\nIn the television miniseries _Roots_ , as in Alex Haley's novel on which it was based, the fictional protagonist Kunta Kinte was brought from the Gambia and sold at Annapolis in 1767. That was when Samuel Galloway was conducting slave sales at Middleton's Tavern, like the one he advertised in 1761, presumably of captives brought up from the West Indies, since they were \"seasoned\":\n\nTO BE SOLD\n\n_At the House of Mr._ Samuel Middleton, in Annapolis, _on Saturday next, being the 22d Instant,_\n\nA CHOICE PARCEL of Healthy Seasoned\n\nNEGRO MEN.\n\n... S GALLOWAY, and Company.\n\nA \"parcel\" might be two to four dozen people, less than a \"cargo,\" which could be hundreds. Ringgold and Galloway sold at least one cargo in 1761, but it was not a good sale.\n\nJuly 29, 1761.\n\nJ U S T I M P O R T E D\n\n_In the Snow_ Alexander, _Captain_ Neilson, _from the Coast of_ AFRICA,\n\nA CARGO of Choice Healthy SLAVES, and to be Sold on Tuesday next, being the 4th of _August_ , at _Annapolis_ , for Bills of Exchange or Cash, by THOMAS AND WM. RINGGOLD,\n\nSAMUEL GALLOWAY\n\nThe promise of \"Choice Healthy SLAVES\" was a barefaced lie. They were the wretched captives who arrived on the _Alexander_ , a vessel that had been outfitted to carry 320 humans as if they were sardines. The _Alexander_ had met with \"misfortune,\" Ringgold and Galloway wrote the ship's owners in Bristol afterward, resulting \"in the Loss of so great a part of her Slaves. We had but 105 left alive to sell, 11 of them so bad we were glad to get \u00a311 Ster. P Head for them, 6 of the 11 since dead and many of the others in very bad Condition.\" It is unknown whether the \"misfortune\" was smallpox, typhoid, measles, or any of a number of other diseases that could carry away shiploads of people.\n\nIt took a while to work through the undesirable inventory, but slaves rarely went unsold. Ringgold wrote Galloway on August 15 of the liquidation: \"We sold 14 of the Negroes yesterday very well considering the Cond'n they were in. The wenches and 1 man at 60 each, 1 man \u00a368, 1 Boy \u00a360, Girls at \u00a356, 2 sickly Girls cheap, the Maits [mate's] Boy for \u00a370, the small poor Boy died coming up. We have only The 2d Maits Fellow and 2 Girls hope they go today.\"\n\nThis was business correspondence\u2014formal and decorous, in the manner of colonial merchants, and devoid of remorse for over two hundred deaths, let alone the partners' responsibility in them. Then Ringgold delivered what he saw as the really bad news: \"But the worst of it twas chiefly on some Credit.\"\n\nNo Chesapeake merchants were exclusively slave traders in those days, but the converse of that was that many merchants might handle some slave trade, and every merchant was aware that the slave trade was murderous. But then, life was precarious in the colonies, where children routinely died, childbirth was every woman's hazard, and the wealthiest citizen might take sick and be gone within hours. The crews on occasion had higher mortality rates than the people who made up the cargo; slave ships were death ships, the bottom of the employment ladder for sailors. Stephen D. Behrendt, analyzing the mortality of 58,778 crewmen on 1,709 slave voyages out of Liverpool from 1780 forward, found 10,439 deaths, or 17.8 percent, about half of them killed by the captives. The \"seasoning\" process for newly arrived Africans was often more deadly than the crossing. Some emaciated arrivals expired dockside. Others died unattended in the pest house, where the healthy were locked up together with the dying in quarantine. Still others took mortally ill within months after sale.\n\nSlave buyers and merchants had a definite hierarchy of desirable African ethnicities. Gambians were at the top of the list, both in the Chesapeake and in South Carolina. One reason was that the voyage from that northernmost part of the West African slaving territory was significantly shorter than from farther south, and there was less time for the captives to sicken and die. As Ringgold IV put it in a letter: \"Gambia the best and generally comes in best helth as the Passage is quick from thence to this place,\" though the passage surely seemed to last an eternity for those chained in the hold.\n\nThe cultivation of tobacco was well suited to Senegambians' existing agricultural skills. Conveniently, they were at the time easy to get, an availability that peaked in the first three decades of the eighteenth century, as intra-African conflicts in that region threw war captives onto the market. The Bambara, the Wolof, the Mandinka, the Fulani: they brought with them not only agricultural skills, but all kinds of cultural skills, including music. They brought the banjo and a bowed fiddle (the latter a specialty of the nomadic Fulani), which they used to play a highly ornamented dance music. They brought a sense of swing, in which pairs of notes were not of equal length, but were long\/short. They brought a bardic poetic tradition that informed their way of singing, and, not least, they brought a centuries-old history of contact with Islam. The musical styles of the Muslim world affected their way of playing music greatly, and aspects of it\u2014melisma, pitch-bending, and heterophony (a loose sense of unison)\u2014would surface in a new African American music. Senegambians were early populators of all three major African American cultural areas: the Chesapeake, the Lowcountry, and Louisiana. But there were people from all seven of the major slaving regions of West and Central Africa (and perhaps a few from the eighth, Southeast Africa) in Chesapeake society.\n\nEven the biggest tobacco planters didn't purchase labor in the quantities Antillean sugar planters did. Most slaves in the Chesapeake were bought in small numbers, many in ones and twos; even large plantation workforces were assembled piecemeal out of hetergeneous sources. Annapolis was a breakup point, where cargoes were separated into smaller \"parcels\" for local distribution.\n\nOnce the captives had been sold, they were plantation bound, so their next journey was to be shipped along the watercourse of the Chesapeake river system and possibly marched over land. In their traumatized condition, often half-dead from their ordeal, they were traded and re-traded around the waterways, along with other merchandise, traversing a web of traders and planters. They were all connected by water along the decentralized Chesapeake system's thousands of miles of fractal coastline and riverbank.\n\nAfricans had long worked as sailors in European navies. Now Africans' descendants, raised in the intricate world of Chesapeake creeks and marshes, would become its boatmen, pilots, and navigators.\n\nBy contrast with the convict trade, the African slave trade was unpredictable. It was a high-stakes venture, with a remunerative upside but facing hazards unlike those of any other business. Given the dangers of the trade, a slave ship might never return. Even on a successful run, it could be incommunicado for a year or more, collecting one or a few captives at a time on the African coast, bargaining anew for each one, on occasion waiting for slave raids or nearby battles to end so that fresh victims could be procured.\n\nThough the upside was high, outfitting African slave-trade expeditions was a nerve-wracking business. \"There are more disasters in these Voyages than any others whatever,\" Ringgold wrote Galloway. The return on investment was at best excruciatingly slow, and, as with the other risks of slavery, it was best absorbed by large fortunes.\n\nColonial merchants sent their own expeditions to Africa as early as 1643, when a ship from Boston brought African captives to Barbados. But even for men of Galloway and Ringgold's wealth, it was hard to outfit an expedition to Africa from America. For one thing, the African traders who sold captives to the Guineamen wanted specific merchandise for their domestic markets in exchange, and most of it wasn't available in the colonies.\n\nThe African market was known for its \"fastidiousness,\" both in terms of the goods it would accept and the variety of them it demanded. Willem Bosman, the Dutch West India Company's factor at Elmina, wrote in 1703 that \"to trade on this Coast, about a hundred and fifty several sorts of Commodities are necessary,\" though he pleaded that the specific list was a trade secret. African merchants' conditions had many regional variations, but generally they wanted gold and silver, guns and gunpowder, textiles, hardware, brass basins and pans, luxury goods (principally rum and tobacco), and vast quantities of copper, which was a common material for adornment and, in the form of rods or bracelets called manillas, was Africa's most common currency.\n\nExcept for the rum and tobacco, none of this came from the colonies. Accordingly, rum was of central importance to the portion of the African slave trade outfitted from America. Beginning in Newport in the 1720s, Rhode Island's slaving activities grew out of its rum manufacturing; that in turn depended on molasses illegally imported from Saint-Domingue, whose syrup was cheaper than the Jamaican variety. The unusually well-documented voyage of the Providence slaver _Sally_ was probably typical; it went loaded with more than seventeen thousand gallons of rum, along with tobacco and onions, to be introduced into the African market in exchange for people. With its many distilleries, Rhode Island was the only North American colony to specialize in outfitting African slavers\u2014approximately a thousand voyages, accounting for an estimated 111,000 captives over its trading life.\n\nRhode Island ran a clockwise loop trade that carried New England rum to Africa in exchange for Africans, who were in turn taken to the West Indies (or sometimes North America) and exchanged for molasses, which was then brought to Rhode Island for distilling into rum, and so on recursively, in theory with a profit taken at every stop. In this way, Rhode Island in the eighteenth century became the largest outfitter of slaving voyages in North America, with Newport sometimes referred to as the \"American Liverpool.\"\n\nConspicuously, this commercial triangle did not include England. Nor did it necessarily include much hard currency, if the African slave traders could be persuaded to accept rum and tobacco, though they usually wanted manufactured goods or money too.\n\nSouth Carolina did little smuggling; its commerce largely followed British rules. But New England was a hotbed of contraband. According to Britain's routinely ignored 1733 Molasses Act, importation from the French colonies was to be prohibitively taxed. In the face of the need to raise revenue against Britain's debts from the French and Indian War, the Sugar Act of 1764 halved the molasses tax but included measures to enforce it, causing widespread alarm throughout New England, where distilling was a major business. The merchants of Providence responded by sending London a ringing defense of their right to smuggle molasses, pointing out that the rum thus produced gave them the revenues with which to pay for the British manufactures they consumed. Recalling the era, John Adams wrote in an 1818 letter, \"I know not why we should blush to confess that molasses was an essential ingredient in American independence... these articles of molasses and sugar, especially the former, entered into all and every branch of our commerce, fisheries, even manufactures and agriculture.\" The antislavery Adams discreetly neglected to mention the vital role molasses had played in the slave trade.\n\nTo give the devil his due, Rhode Island's slave trade was an extraordinary achievement given the obstacles to it, a feat Maryland did not replicate. The only known African slave voyage outfitted from Maryland was sent by Ringgold and Galloway in 1762, together with two other partners, though Galloway may have invested in others of which there is no record. It was a fiasco.\n\nIn an effort to stock their Africa-bound ship with commodities for trade, Ringgold traveled to Philadelphia. The decentralization of the Chesapeake had worked against the creation of urban centers in favor of widely scattered individual wharves, a situation pleasing to price-gouging English merchants. In doing so, it created a commercial vacuum for Philadelphia to exploit. Philadelphia, which had surpassed Boston as the largest city in the colonies in the 1750s, was the commercial capital, with the best-supplied marketplace. But even there, as Ringgold wrote Galloway:\n\nI found a great deal of Trouble and Diligence required to get anything and severel Things I did not get... so I was obliged to supply the Defects by Manchester Goods in Immitation as well as I coud.... I was put to great Difficulty ab't Gunns could not find any of the Trading Gunns but 21 in Town... Getting so few Gunns in Philada. I wrote to Mr. Freman to try to pick me up 100 or Less at York of the Cheap sort and send with the Rum.\n\nThe Scottish slave trader Richard Oswald, by contrast, in 1754 notified the British government of his intention to ship \"one hundred and twenty barrels of gunpowder, one hundred & twenty chests containing three thousand trading guns & thirty cases containing three thousand cutlasses\" to Africa. But even British slave traders had difficulties coming up with enough trade goods. \"Assembling an export cargo normally took several months,\" writes Kenneth Morgan, who argues that one of the advantages Liverpool traders had over those of Bristol and London was their proximity to the Isle of Man, a duty-free zone where until 1765 Dutch shippers could transship cheap products from Asia that included cowry shells (used as money in many parts of Africa) as well as those perennial trade offerings to Africa, textiles and lethal weaponry.\n\nCoin was equally difficult for even an affluent American to obtain; merchants rarely received it. \"I wrote him also as to Dollars,\" Ringgold's letter continued, referring to silver pesos, \"not one of them to be got in Philad[elphi]a.\"\n\nThe partners' slave ship made it to Africa and back, but the kidnapped Gambians never reached Maryland; to their consternation, the captain stopped off in Antigua and sold them there. \"If he was to go to the nearest place,\" fulminated Ringgold, \"why did not he take Barbados? Where slaves are wanted and would have sold well.\" Though the captain's side of the story appears to be lost to history, it might have been that much of his cargo had died and he feared losing it all if he continued any farther. At any rate, that's why Eseck Hopkins, captain of the previously mentioned _Sally_ , dumped onto the Antiguan market in 1765 the 87 naked, emaciated captives who remained alive out of the 196 he had embarked from Africa with instead of bringing them father north.\n\nThese were complicated deals. \"Dear Sir,\" Ringgold wrote Galloway in 1764, \"I have been looking over our Guinee Accts since I came home, and They really are almost got out of my Hand. I wish we could get them settled whilst we can understand them.\"\n\nLike other merchants' letters, Ringgold's correspondence is full of complaints about business, but he was making money. In 1767, he added to his portfolio the property with enclosed grounds at Water and Cannon Streets, a block upriver from the Custom House, commissioning Virginia architect William Buckland to tie together two existing structures to create a grand new mansion with a double staircase, a style that was becoming popular among the wealthy. Today it is known as the Hynson-Ringgold house, and is the presidential residence of Washington College.\n\n_Charles Willson Peale's portraits of Thomas Ringgold IV, who is depicted writing, and Anna Maria Ringgold._\n\nThe Baltimore Museum of Art has portraits of the Ringgolds by American master Charles Willson Peale, but there are no portraits extant of \"Sue, Fender, Milford, Betty, Sukey, Sarah, Cinthia, Darkey, and Will Harding,\" whom Ringgold bequeathed to his wife, Anna Maria, when he died in 1772 at the age of fifty-seven. Born into a fortune, he left a greater one to his only son.\n\nIn the tradition of the time and place, the Ringgolds were hospitable. When George Washington passed through one night in 1773, he \"lodgd at Ringgolds,\" referring to the Hynson-Ringgold house, home of Thomas Ringgold V, who went into the family business of buying and selling, and continued the family tradition of politics. Along with his uncle William Ringgold and neighbor Thomas Smyth, Ringgold V was one of seven Kent County signers of the Maryland Declaration of Independence in Annapolis on July 26, 1775, and he was a delegate to the Annapolis Convention, which met on May 8, 1776, to draft a constitution for the state. But he died unexpectedly on October 26 of that year, at the age of thirty-two. The short-lived Ringgold V left behind a will, in which he bequeathed the Chestertown mansion to his mother. He also left her his car\u2014not a motorcar, of course, but \"my imported chariot,\" the three-seat coach with a perch for an enslaved driver and a roost for an enslaved footman, in which she rolled up and down High Street.\n\nBecause Annapolis is so well documented and preserved, and because so much archaeology has been done there, we know that under the steps leading down into a basement room in Charles Carroll of Carrollton's mansion, Nanny the cook placed a spirit bundle. Known throughout a wide area of Africa in different forms, these bundles in their North American manifestation include such specific items as bent nails (Zarabanda, they call him in Cuba, the Kongo blacksmith spirit with the power secret of iron) and four-hole buttons, as well as organic ingredients that did not survive the centuries. It seems likely that more spirit materials will turn up, especially now that there is a greater awareness of their existence. They're not that easy to identify, though, because they're mostly mundane objects. It's the combination of them that gives them away as spirit materials. None have been identified from the seventeenth century in the Chesapeake; the earliest known is from Virginia in 1702, while the earliest in Maryland dates from 1790.\n\nChristianity was a religion of the book, and slaves were not supposed to know how to read. Even as slaveowners prohibited the use of African drums on their plantations, they often preferred that the enslaved not be Christianized, and many of them never were, especially in the colonial era. But there was never a moment when the enslaved were not spiritually conscious. In the new land the Africans had been dragged to\u2014across the ocean to the land of the dead, according to Kongo cosmology\u2014they fashioned a set of religious practices that developed, with significant regional variations and with Native American influence, into a broadly generalized African American religion that was also a social mediator and a medicinal practice. Katrina Hazzard-Donald calls this set of practices \"the old Hoodoo religion,\" arguing that it developed in available \"safe spaces,\" and proposing that the mid-eighteenth century must have been a crucial time in the crystallization of this wide-reaching system.\n\nIn different regional forms, this old hoodoo religion radiated outward from the three great fountainheads of African American culture\u2014the Chesapeake, the Lowcountry, and the Gulf South. Its persistence was described by Louis Hughes in his 1897 autobiography:\n\nIt was the custom in those days for slaves to carry voo-doo bags. It was handed down from generation to generation; and, though it was one of the superstitions of a barbarous ancestry, it was still very generally and tenaciously held to by all classes. I carried a little bag, which I got from an old slave who claimed that it had power to prevent any one who carried it from being whipped. It was made of leather, and contained roots, nuts, pins and some other things. The claim that it would prevent the folks from whipping me so much, I found, was not sustained by my experience\u2014my whippings came just the same. Many of the servants were thorough believers in it though, and carried these bags all the time.\n\n\"Because it concerned the transformation of a variety of traditional African religions into one spiritual tradition,\" Hazzard-Donald writes, \"Hoodoo must have involved a major confrontation of spiritual forces.\" Mande speakers from the Islamized Sahel; Akan from the Gold Coast, Fon from the Slave Coast, Igbo from the Calabar, and many other peoples from the zone of West African traditional practice; Bakongo from Catholicized Central Africa\u2014their cosmologies all had elements in common, and all played a part in the composite religious understanding of the enslaved.\n\nBecause Monticello has been so thoroughly scrutinized by archaeologists, we know that Thomas Jefferson's enslaved kept pits under their floors, a common practice among the enslaved of Virginia at the time. What did they keep in those pits? Anything valuable. Anything they didn't want Master Tom, or the other members of their community, to see. Goods that could be considered stolen\u2014which, since they could have no legal property of their own, might mean anything of value. Spirit materials.\n\nThe tour guide to Monticello's Mulberry Row, an entire street of slave cabins and workhouses that in Jefferson's day was hidden from the big house's view by mulberry trees, will tell you that cowrie shells\u2014historically used as money in many parts of Africa\u2014were \"passed to later generations\" by Monticello's laborers and were worn as jewelry or attached to clothing. Some of the people at Monticello wore pierced silver Spanish coins around their necks or ankles. They were not mere adornment; the formerly enslaved Silvia Witherspoon recalled in 1937, in Alabama, that (as transcribed) \"sometimes I wears dis dime wid de hole in it aroun' my ankle to keep off de conjure.\"\n\nPortable spirit bundles were carried by nomadic and migrating Africans, in societies that counted the departed as living presences. Called by various names in different territories of Africa and the New World, a portable spirit bundle\u2014though not containing ancestors' remains as in the motherland\u2014was known in the southern United States as a _mojo_ ( _moyo_ , a Kikongo word meaning something like \"soul force\"). Mentions of a \"mojo hand\" are familiar from blues lyrics, and mojo hands of one kind or another continue being made and used today.\n\nAnother version of the mojo hand was called by an English name: a _toby._ As per the first line in Charles Burnett's film _To Sleep With Anger_ , about spirit combat in South Central Los Angeles: \"I was looking through my trunk and I can't find my toby\"\u2014a foreshadowing that bad things are about to happen.\n\nHow did it come to be called a toby? We can't prove this, but there is some intriguing circumstantial evidence:\n\nIt was in the 1760s, the heyday of Annapolis and Chestertown, and of Galloway and Ringgold, that a modern kind of consumer item became ubiquitous: industrially produced, gaily painted, lead-glazed beer vessels from the child-labor pottery workshops of Staffordshire. Shaped in the form of a comically figured man (who was sometimes styled as a king), they were called _filpots_ , but more commonly were referred to as _toby jugs._ Their popularization as household objects was preceded for several decades by what J. A. Leo Lemay characterizes as \"a minor subgenre of poetry concerning drunks who were transformed into liquor containers,\" as per \"Dear Sir, this Brown Jug that now foams with raild Ale \/ Was once Toby Filpot a thirsty old soul.\" Such works as the witty Boston clergyman Mather Byles's \"The Transformation of Bug-Barret into a Brandy Bottle\" inspired the twenty-seven-year-old _Pennsylvania Gazette_ printer Benjamin Franklin to publish his mock \"Meditation on a Quart Jugg\" (1733)\u2014in which he compared the soul in the jug to an abused slave:\n\nAlas! what Power, or Place, is provided, where this poor Mug, this unpitied Slave, can have Redress of his Wrongs and Sufferings? Or where shall he have a Word of Praise bestow'd on him for his Well-doings, and faithful Services?... Poor Mug, unfortunate is thy Condition! Of thy self thou wouldst do no Harm, but much Harm is done with thee! Thou art accused of many Mischiefs; thou art said to administer Drunkenness, Poison, and broken Heads: But none praise thee for the good Things thou yieldest\n\nIn the Catholic territories, iconic statues of saints abounded, and were syncretized by Africans for their own religious purposes. The _santo_ that the priest called Santa B\u00e1rbara, for example, who holds a hatchet in her hand, became for the enslaved the image of Chang\u00f3, the womanizing, ax-wielding warrior, apotheosis of masculinity, the greatest dancer, the owner of thunder and drums whose colors are red and white and who is called by specific rhythms that are known to millions of Cubans. This kind of syncretization is often said not to have existed in the Protestant Anglo-American territories, where saints did not exist, to say nothing of sacred statues. But the figurative power of the toby jug seems to have spoken to the African-born and to the not-yet-Christianized African Americans, who carried bound-up spirits with them.\n\nThe toby jug, it would appear, lent its name to a syncretized African practice in the eighteenth-century Chesapeake that was unseen and uncomprehended by the merchants who sold both the jugs and the people. A container that holds a soul: that needed no explanation to Africans. It fit right into the needs of the old hoodoo religion. In their captivity, the enslaved could bring nothing with them but their souls, their minds, and the bodies that contained them. While the slaveowners repurposed the ballast stones from England for wharfing, the enslaved repurposed what they found in their hostile new world, trying to protect themselves however they could\u2014with nails, spirit bundles, cowries, coins, resistance, readiness to take flight, and rebellion.\n\n*Disclosure: today the Custom House is the home of Washington College's C.V. Starr Center for the Study of the American Experience, where the first half of this volume was drafted.\n\n*Ballast was needed with human cargoes, because people move around.\n\n_One of thirty-nine human prizes at a raffle, co-organized by twenty creditors including George Washington. Rind's_ Virginia Gazette, _November 23, 1769._\n\n#   Part Three\n\n# **Silent Profit**\n\n#   19\n\n# **Newspapers as Money as People**\n\n_There is to be sold a very likely Negro Woman aged about Thirty Years who has lived in this City, from her Childhood, and can wash and iron very well, cook Victuals, sew, spin on the Linen Wheel, milk Cows, and do all Sorts of House-work very well. She has a Boy of about Two Years old, which is to go with her. The Price as reasonable as you can agree._\n\n_And also another very likely Boy aged about Six Years, who is Son of the above said Woman. He will be sold with his Mother, or by himself, as the Buyer pleases. Inquire of the Printer._\n\n\u2014Advertisement, Benjamin Franklin's _Pennsylvania Gazette_ , May 3, 1733\n\nFROM THE BEGINNING OF newspapers in America, the forced-servitude business was a steady part of their revenue stream.\n\nAmerican newspapers and slavery helped grow each other. The first regularly published American newspaper\u2014issue number one of the _Boston News-Letter_ in 1704\u2014contained an \"advertisement\" that read:\n\nThis News Letter is to be continued Weekly; and all Persons who have any Houses, Lands, Tenements, Farmes, Ships Vessels, Goods, Wares or Merchadizes, &c to be Sold or Lett; _or Servants Run away;_ or Goods Stoll or Lost, may have the same Inserted at a Reasonable Rate.  (emphasis added)\n\nThe _Boston News-Letter_ was distributed at the Boston post office and printed by the colonial postmaster, a linkage that would continue into the age of postmaster-printer Benjamin Franklin. Advertisers were slow in coming to the publication, but among the earliest, in issue number seven, was a slave-sale ad:\n\nTens of thousands more would appear over the next 154 years. Maryland had a newspaper as of 1727, the _Maryland Gazette._ Published in Annapolis, it ceased publication in 1734; the printer, William Parks, moved to Williamsburg, the bustling port on the James River, where in 1736 he started the _Virginia Gazette._ (A second _Maryland Gazette_ appeared in 1747, from a different printer.)\n\nThen as now, the unique economics of newspapers necessarily relied on income from diverse sources. The popularity of the word _Gazette_ in so many colonial newspapers' names derived from its then-current connotation of \"official record,\" which allowed the paper to get government business printing public notices. But newspapers also derived a steady, dependable income from slavery-related advertisements.\n\nNewspapers ran two main kinds of slavery-related advertisements: for apprehension of runaways, and for sale or hiring. In the former case, the existence of this new advertising medium strengthened slavery by creating a system of vigilance that made long-term escape less of a possibility. In the latter, newspapers not only ran advertisements for slave sales but also facilitated them through brokerage, by furnishing venues for a sale to take place, and even by consignment of slaves to the paper's printer.\n\nIn turn, the soul-driving business grew and prospered with the marketing power afforded by this up-to-date medium, as per the advertisement in the _Pennsylvania Gazette_ of November 18, 1731:\n\nTo be Sold, A Likely Negro Wench, about Fifteen Years old, has had the Small-pox, been in the Country above a Year, and talks English. Enquire of the Printer hereof.\n\nThe \"Printer\" was twenty-five-year-old Benjamin Franklin, who bought the _Pennsylvania Gazette_ in 1730 after its founder, Samuel Keimer, went to debtor's prison. Keimer, though English, was a follower of the \"French prophets,\" a millennial sect of Huguenots in London; in an account of his sufferings he referred to himself as a \"white Negro,\" predating Norman Mailer's use of the term by more than two hundred years. He relocated to Barbados, where he began the _Barbados Gazette_ , which ran many slavery-related advertisements.\n\nWith Franklin's newspaper and his retail location in Philadelphia, he brokered slave sales like the one at the beginning of this chapter for a girl at the beginning of her childbearing years. Franklin, the only one of the \"founding fathers\" to have been an indentured servant,* owned slaves for thirty years or so.\n\nA concerned student of the problems of creating and retaining wealth, Franklin fused what we now call \"the media\" with political power in America via networking and new technology. A vegetarian in his youth (the \"Pythagorean regimen,\" as it was called), he was also an amateur avant-garde composer who invented musical instruments and, while living in France, wrote in the then-new string quartet idiom a striking, unique-sounding three-movement work played entirely on open strings.\u2020\n\nFranklin franchised his newspaper operation, partnering with printers in other towns. We have previously noted his silent partnership in the _South Carolina Gazette._ When William Parks was preparing to start the _Virginia Gazette_ , Franklin advised him to build his own papermill\u2014the first in the Southern colonies\u2014and sold him the rags he needed to make the paper from. \"By the mid-1740s,\" writes David Waldstreicher, whose _Runaway America: Benjamin Franklin, Slavery, and the American Revolution_ has informed this section of our narrative, \"Franklin was the largest paper dealer in the colonies.\" He controlled paper itself and saw its uses as medium and as money.\n\nFranklin's influence as an economic theorist was all the more significant because his ideas were grounded in real-world practice. He made his _Pennsylvania Gazette_ into a new kind of newspaper. \"As no one quite had before,\" writes Waldstreicher, \"he learned to make his printed manufactures\u2014the newspaper and the annual almanacs\u2014essential goods in the booming economy.\" As part of that process, Franklin got himself named postmaster of Philadelphia in 1737\u2014a significant and profitable office for a newspaperman, since newspapers constituted the bulk of what the postal system carried. He subsequently became deputy postmaster general for British North America, and ultimately postmaster of the United States, creating the US Postal System. For much of his adult life he used the post office as a base from which to dispense patronage and build his personal network as the North American economy grew.\n\nFranklin was an anti-monetarist: in an economy where he might have to accept (and store, and sell) a quantity of tobacco as payment in lieu of silver, he was a strong proponent of paper currency. From his perspective in America, where land was cheap but labor was dear, Franklin saw wealth in terms of labor, not silver.\n\n\"Franklin's writings of the 1730s and 1740s pivot repeatedly around... notions of money as akin to people, and people as capital,\" writes Waldstreicher. Karl Marx, who quoted Franklin approvingly in _Das Kapital_ , described him in 1859 as the man \"who formulated the basic law of modern political economy.\" Marx was referring to Franklin's anonymously published pamphlet (in 1729, when Franklin was twenty-three) titled \"A Modest Enquiry into the Nature and Necessity of a Paper-Currency\":\n\nTrade in general being nothing else but the Exchange of Labour for Labour, the Value of all Things is... most justly measured by Labour....\n\nBy Labour may the Value of Silver be measured as well as other Things... Thus the riches of a country are to be valued by the _quantity of labour_ its inhabitants are able to purchase.\n\nSomewhere between 6 and 10 percent of the population of Philadelphia at the time was enslaved and was therefore purchasable labor. The Pennsylvania legislature dropped the duty on slaves from ten pounds to twenty shillings in the 1720s, and throughout the 1730s an ever-increasing number of kidnapped Africans were arriving. Franklin owned at least two slaves, though he found them troublesome; in a 1748 letter to his elderly mother about domestic matters, he wrote of an enslaved couple that \"we conclude to sell them both the first good opportunity, for we do not like Negro servants.\"\n\nFranklin lived to be eighty-four, and in his late years, he became a vocal abolitionist. But that was after he made his fortune with newspapers that acted as clearing houses for slave sales and runaway advertisements. Using the unpaid labor of black slaves, indentured servants, and his wife, Deborah, Franklin operated a book and stationery shop on the street level of his printing house. In a cash-poor society, Franklin frequently had to take payment in the form of South Carolina rice or West Indian sugar, selling it at his store, and on at least one occasion accepted a slave as partial payment for a debt.\n\nNot for nothing did 1990s rappers speak of $100 bills as \"the Benjamins.\" Franklin saw paper money as a democratization of capital, and thereby as a broader franchise for the wider civic participation he favored\u2014though that did not include the participation of \"Negroes,\" to whom a cash value was assigned. In the wake of the smallpox epidemic of 1731, Franklin published a calculation in his newspaper: \"The Number of those who died here of that Distemper, is exactly 288.... 64 of the Number were Negroes; if these be valued one with another at 30 pounds per Head, the Loss to the City in that Article is near 2000 p o und s.\"\n\nIn a sense, Franklin's newspaper and his almanac were his money, since they were paper he could exchange for commodities. But Franklin also literally printed money\u2014more than \u00a3770,000 worth of notes for Pennsylvania between 1731 and 1764, as well as notes for Delaware and New Jersey. As a newspaper publisher, he had a bird's-eye view of the variety of contemporary commerce. He routinely had to handle complex transactions entailing a mix of barter, credit, and occasionally cash, with heightened insight into the workings of the colonial credit economy. He understood clearly how \"money\" could take on various forms.\n\nFrance had tried a disastrous experiment with paper money in 1717, urged on the Regent Duke of Orleans by John Law, the gambler son of an Edinburgh goldsmith. Law created a paper money for France, backing it with future revenues from the infant colony of Louisiana, which had neither a staple crop nor a labor force. To that end, a cedar swamp was cleared in 1718 and New Orleans was built. As he privatized France's foreign debt into a single, paper-issuing, monster corporation, there followed a speculative bubble in which Law's notes traded at ten times their face value in Paris, with the inevitable crash coming in 1721. After that, France was soured on paper money until the nineteenth century. The crash was more or less concurrent with the London South Sea bubble, but Britain bounced back much better.\n\nAs Virginia, Maryland, and Delaware bulked up with slaves, South Sea Company ships from Africa pulled up into the ports of the Chesapeake. Discharged from widely disparate West and Central African slaving territories, the cargoes were sometimes very large, as per this advertisement from Williamsburg's _Virginia Gazette_ on April 8, 1737, the second year of the paper's existence:\n\nAlexander Hewatt in 1779 described the situation of South Carolina forty years previously:\n\nAdventurous planters in Carolina, eager to obtain a number of negroes, always stretched their credit with the traders to its utmost pitch; for as negroes on good lands cleared themselves in a few years, they by this means made an annual addition to their capital stock. After obtaining this credit, it then became their interest to maintain their superiority in assembly, and discharge their debt to the merchants in the easiest manner they could. The increase of paper-money always proved to them a considerable assistance, as it advanced the price of those commodities they brought to the market, by which they cancelled their debts with the merchants; so that however much this currency might depreciate, the loss occasioned by it from time to time fell not on the adventurous planters, but on the merchants and moneymen who were obliged to take it.\n\nIn other words, slaves were safer money than paper currency. This would continue to be true in the slave territories of the United States until the end of slavery.\n\nThe newspaper runaway ads of Virginia and Maryland in the 1730s were more often for indentured servants than for black slaves. The descriptions of the absconded, often quite detailed, provide the closest we have to thumbnail sketches of the white servant population. But by the 1750s, black slaves, many of them described as \"Virginia born,\" dominated the runaway ads.\n\nSlave-sale advertisements appeared in the _Virginia Gazette_ from its earliest numbers in 1736. They were numerous by the 1760s, by which time they stressed the \"Virginia-born\" provenance of the human merchandise. Four advertisements that appeared on page four of the January 8, 1767, issue of the _Virginia Gazette_ offered \"Sixty odd exceeding fine Negroes, all, except two, _Virginia_ born\"; \"Sundry Valuable Virginia Born Slaves\"; \"About 100 choice Negroes, most of them _Virginia_ born\"; and \"Sixty choice Virginia born Slaves.\"\n\nThe opposite of \"Virginia-born\" was \"outlandish,\" a word that subsequently came into common use in a more general sense. \"Virginia born\" laborers had a number of advantages in the market over the \"outlandish.\" They were English-speaking, were trained in plantation work, were \"seasoned,\" i.e., had immunities to American diseases\u2014and, importantly, they were considered to be more docile and were carefully kept away from military training. Outlandish Negroes might have military experience. The destabilization of Africa occasioned by the slave trade created a legacy of war, as well as a means of funding those wars. They provided captives for slave traders: African soldiers, captured in battle, were sold in American markets. In Virginia, a preference for slaves with no military knowledge was reflected in higher prices.\n\nRaised from birth to a slave work regime, the Virginia-born had never known freedom. They did not file their teeth sharp, an African tradition that in the Americas became a means of defense for people who were not allowed to carry weapons. Those scary-looking filed teeth turned up in an August 20, 1761, advertisement placed in the _Maryland Gazette_ by the twenty-seven-year-old George Washington, who, ever the alert commander, was prepared with precise descriptions of his servants and slaves in case any of them decamped. When he advertised for the return of four \"Negroes\" named Peros (perhaps P\u00e9rez?), Jack, Neptune, and Cupid, he advised that Jack had \"Cuts down his Cheek, being his Country Marks,\" and Neptune, his teeth \"fil'd sharp,\" and his \"Back, if rightly remember'd, has many small Marks or Dots running from both his Shoulders down to his Waistband, and his Head was close shav'd.\" This was the British military method of identifying black soldiers, of whom there were many. Washington, an acute observer, differentiated the runaways' language skills, though he couldn't pinpoint their origins within Africa. Neptune and Cupid, he wrote, \"were brought in an African ship in August 1759, and talk very broken and unintelligible English; the second one, Jack, is Countryman to those, and speaks pretty good English, having been several Years in the Country. The other, Peros, speaks much better than either, indeed has little of his country Dialect left, and is esteemed a sensible judicious Negro.\"\n\nQuite possibly, though we do not know, an enslaved fiddler played for the dancing at the splendid ball of April 26, 1738, in Williamsburg. Surely Mrs. Degrassenreidts' guests that night were waited on by liveried black servants, even as her soir\u00e9e was enlivened by a show of cruelty, a slave sale in the form of a raffle, as advertised in the _Virginia Gazette:_\n\nFor more than a century, slaves were occasionally sold by raffle in Virginia, where gambling was a mania. The seller hoped to realize more money from a raffle than from an auction, and the ticket buyers got the entertainment value of seeing who won the human prizes. What will you draw? The carriage? A garden tool? A couple of children? The only losers were the people being raffled for fun and profit\u2014but then, it was a common (and convenient) belief among slaveowners that \"negroes,\" being a lesser kind of being, did not feel the sorrows of parting from kin as deeply.\n\nDirectly below that advertisement was another one, for the following night, which combined a raffle of a young man with \"Grotesque Dances\":\n\nSometimes the raffle method was even used to liquidate a large estate. Henry Wiencek calls attention to an advertisement (in one of two concurrent, competing _Virginia Gazette_ s) for an estate liquidation to take place in Williamsburg, in which fifty-five slaves were announced to be raffled off in thirty-nine lots.\n\nThis form of dispersing an estate at random guaranteed the maximum degree of dismemberment of the family and community structures that had existed on the plantation prior to being liquidated. There was little chance, for example, that \"A Negro Woman named _Kate_ , and a young Child, _Judy\"_ would be won by the same person who won \"A Negro Girl, _Aggy_ , and Boy, _Nat;_ Children of _Kate._ \"\n\nGeorge Washington was the third of twenty co-organizers listed for that raffle. The advertisement is too long to reprint in full, but suffice it to say that one of the lots offered as a raffle prize was \"a fine breeding Woman named _Pat_ , lame of one Side, with Child, and her three Children, _L\u00e6t, Milley_ , and _Charlotte.\"_ The advertisement ran in the April 14, 1768, issue of Rind's _Virginia Gazette_ , with no date for the sale specified.\n\nThe sale apparently took more than a year and a half to pull off, being advertised once again in the issue of November 23, 1769, with a date of December 13 set for the drawing. The \"fine breeding Woman\" Pat was once again represented as being \"with Child\" a year and a half later.\n\nIt was done at a tavern, with all the conviviality that implies, and animated by the thrill\u2014not of buying, but of _winning_ Pat and her children, or maybe children who were being separated from their mother.\n\nWashington seems to have taken part in drawing the lottery winners, to judge from his journal entry: \"went to Southalls in the Evening to draw Colo. Moores Lottery,\" a process that took three nights. As Wiencek puts it, \"Washington himself was raffling off slaves.\" Before Wiencek's book was published in 2003, no previous biographer of George Washington had called attention to his participation in this utterly depraved practice. Wiencek then attempts to account for the transformation of Washington into the man who in his last will took the then-unusual step of freeing his (though not Martha's) slaves. Washington, it should be noted, was free to liberate his slaves: he was not under crushing debt when he died, so they were not seized and sold. He had no natural heir, having not sired any children with Martha. If he had had a son to inherit his property, it would have been seen as a betrayal to devalue his estate like that.\n\n\"I think God has a Quarrel with you for your Abuse of and Cruelty to the poor Negroes,\" wrote English preacher George Whitefield in _A Letter to the Inhabitants of Maryland, Virginia, North and South Carolina, Concerning their Negroes._\n\nThe cross-eyed Whitefield had a mighty voice, and he was the first big-hit performative evangelist to travel throughout the colonies.* He was one of the founders of Methodism, along with the brothers John and Charles Wesley, in approximately 1729 while they were all students at Oxford; his version was Methodist Episcopalism, a Calvinist offshoot of Anglicanism. His speaking had intrigued, though not converted, Benjamin Franklin, who after hearing him speak and making some calculations concluded that his reputation for addressing tens of thousands at a time in England was probably not exaggerated.\n\nThat was the sort of thing that caught Franklin's attention. Though he had no interest in the new sect of Methodism Whitefield intended to implant in North America, he was a media man, and he was clearly fascinated by the sense of communication this phenomenal figure created. His _Pennsylvania Gazette_ published the schedule of Whitefield's high-profile journey through the colonies during the second of his seven American tours. On April 17, 1740, he devoted his front page to Whitefield's sensational open letter that said bluntly, \"considering what Usage they commonly meet with, I have wondered, that we have not more Instances of Self-Murder among the Negroes, or that they have not more frequently rose up in Arms against their Owners.\" It was the first antislavery tract in any colonial newspaper, and the only one that would run for another thirty years.\n\nAnglican clergymen read droning word-for-word sermons that they might not even have written themselves, but Whitefield was dynamic. He had a theatrical\u2014which was to say, a disreputable\u2014background, and his revivals were a kind of popular theater. In South Carolina, he was denounced by Anglican pastor and naturalist Alexander Garden. Alexander Hewatt wrote that he was\n\nnot unlike one of those strange and erratic meteors which appear now and then in the system of nature. In his youth, as he often confessed and lamented, he was gay, giddy, and profligate; so fondly attached to the stage, that he joined a company of strolling actors and vagabonds, and spent a part of his life in that capacity. At this period it is probable he learned that grimace, buffoonery and gesticulation which he afterwards displayed from the pulpit.\n\nWith theater still in its early days in the colonies as of 1740, this evangelical \"Great Awakening\" (a cynic might call it the Great Wave of Superstition) was the first cultural phenomenon to tie together Northern and Southern colonies.\n\nMethodism already had a base in Georgia. The brothers Wesley had been there since 1736, when Oglethorpe invited them to minister to his colony. The Wesleys in turn invited Whitefield to come to Savannah, where he started the Bethesda Orphanage, raising a sizable amount of funds to do so. But they differed on doctrinal issues: Whitefield's Calvinist Methodism held that God's elect would be the only ones go to heaven no matter what, but John Wesley, in what was called the Arminian heresy by its enemies, democratized salvation by insisting that anyone could attain it\u2014a free-will doctrine that would be fundamental to African American Christian belief as well.\n\nAfter Whitefield's celebrity arrival in the colony, the trustee's secretary William Stephens wrote that he hoped the clergyman would focus slaveowners' minds away from rape and incest, though he didn't use those words: \"It may be hoped That Good Work is lately begun from Mr. Whitfields so daily gaining on the affections of the people: but [there remains] the practice of open Lewdness, in first making Whores of their Female Servants; then cohabiting with them and their Bastards, from whence a continuation of the same Course may be presumed.\" Whitefield's followers had a tendency, distressing to slaveowners, to go out and convert the enslaved, who on one occasion chose the occasion of being converted to go \"raving in the Woods for some time till their Masters were oblig'd to take them under Discipline.\"\n\nWhile Alexander Hewatt acknowledged grudgingly that \"religion in America owed not a little to the zeal, diligence, and oratory, of this extraordinary man,\" he was troubled by Whitefield's converts in South Carolina who became abolitionist preachers for a time, before they were repressed: \"After him a servile race of ignorant and despicable imitators sprung up, and wandered from place to place, spreading doctrines subversive of all public order and peace.\"\n\nThe \"subversive\" Whitefield preached the gospel to white and black both. Methodism in its early days was doctrinally antislavery, and some black South Carolinians converted. But South Carolina had a miniscule population of free blacks, and enslaved blacks on the plantations were kept far away from evangelists. The big wave of conversion would have to wait until after independence, when religious intolerance became constitutionally prohibited and itinerant evangelists had a freer hand.\n\nDespite his early abolitionist posture, however, Whitefield came to feel that Georgia could never be profitable without slave labor. He bought slaves to work at his orphanage, spoke up in favor of legalizing slavery in Georgia, and ultimately became a plantation owner in South Carolina. He was said to treat his slaves kindly, which is to say that he was a founding father of the school of Christian slaveowning that would later dominate Southern ideology, which historians generally refer to as paternalism.\n\nShockingly to many, Whitefield preached to the enslaved; in the eighteenth century, almost no effort was made to Protestantize them. Slaveowners were by and large not eager for their captive labor force to be Christianized. Kongos arrived pre-Catholicized, though their version of Catholicism was Kongo all the way down. Other captives, from Senegambia and elsewhere, practiced a sub-Saharan form of Islam. Various belief systems of West Africa were active, and the old hoodoo religion was everywhere. Hewatt wrote of South Carolina in 1779 that \"the negroes of that country, a few only excepted, are to this day as great strangers to Christianity, and as much under the influence of Pagan darkness, idolatry and superstition, as they were at their first arrival from Africa.\"\n\nBut Christianization of the enslaved was moving forward. When Whitefield died in 1770, a poem was published eulogizing him that caused a sensation. \"An elegiac poem, on the death of that celebrated divine, and eminent servant of Jesus Christ, the late reverend, and pious George Whitefield,\" by \"PHILLIS, a Servant Girl of 17 Years of Age, Belonging to Mr. J. WHEATLEY, of Boston: \u2013 And has been but 9 Years in this Country from Africa\" was the poem that made Phillis Wheatley famous.\n\nBorn in Senegal, Wheatley gained a first-rate command of English in only a few years. Her spiritual poetry had an edge to it that might not be easily apparent to a modern reader. Her best-known poem, \"On Being Brought from Africa to America,\" was practically a civil-rights demand to be allowed to participate in the evangelical movement:\n\nRemember, _Christians, Negros_ , black as _Cain,_\n\nMay be refin'd, and join th' angelic train.\n\nHer ardor for Africans to achieve spiritual greatness was fully present at her debut, in her eulogy to Whitefield:\n\nTake HIM ye Africans, he longs for you;\n\nImpartial SAVIOUR, is his title due;\n\nIf you will chuse to walk in grace's road,\n\nYou shall be sons, and kings, and priests to GOD.\n\nSlaveowners took pains to disabuse the notion, popular among the enslaved, that Christianity was a path to freedom. There was to be no path to freedom, not for the enslaved and not for their descendants. The South was from the beginning dependent on the economic magic of slave reproduction, deeply integrated as it was into the very basis of credit. There could be no climb-down position. \"The permanent riches of the country,\" wrote Hewatt of South Carolina in 1779, \"consisted in lands, houses, and negroes; and the produce of the lands, improved by negroes, raw materials, provisions, and naval stores, were exchanged for what the province wanted from other countries.\"\n\nFrom very early on, there were only two choices for the South. Ending slavery would have meant watching the vast on-paper wealth of its oligarchy disappear; that wasn't going to happen. The other course was to commit fully to a two-caste system: the perpetually free and the perpetually enslaved.\n\n*Franklin was indentured to his older brother, a newspaper printer in Boston, from whom he ran away to the forty-one-year-old town of Philadelphia in 1723.\n\n\u2020There has been a question of attribution of authorship about this singular work, but there is no strong evidence in favor of any other composer. Besides the traditional attribution to him, our ultimate reason for believing it to be Franklin's is subjective: its wit, style, and above all its sense of invention.\n\n*Jonathan Edwards began holding revivals in the early 1730s that on one occasion paralyzed an entire Massachusetts town as it got the religious fever and on another occasion led to a wave of religiously motivated suicides, but he never left New England.\n\n#   20\n\n# **Lord Dunmore's Blackbirds**\n\n_Your petitioners apprehend we have in common with all other men a natural right to our freedoms without being depriv'd of them by our fellow men as we are a freeborn people and have never forfeited this blessing by any compact or agreement whatever._\n\n\u2014\"Petition of a grate number of blackes\" to General Thomas Gage, the recently inaugurated royal governor of Massachusetts, May 25, 1774\n\n_The late resolution of the Quakers in Pennsylvania to set at liberty all their negro slaves may satisfy us that their number cannot be very great. Had they made any considerable part of their property, such a resolution could never have been agreed to. 1_\n\n\u2014Adam Smith, _An Inquiry into the Nature and Causes of the Wealth of Nations_ , 1776\n\nWITH THE END OF the French and Indian (or Seven Years') War, Prime Minister John Stuart, the Scottish Third Earl of Bute, decided not to demobilize the army but to station ten thousand troops in America. Previously British troops had appeared in the colonies to fight the colonists' enemies, but now they were going to be a police force.\n\nWorse, the colonists were told to pay for it. The colonies had long endured trade regulations that gave them access to British ports but cut them off from competing markets and otherwise imposed intolerable conditions on the merchants, but they had never been \"internally\" taxed (as opposed to \"external\" taxes, such as duties). Now Parliament laid a tax on them.\n\nBoston merchant banker John Hancock denounced the Stamp Act as \"slavery.\" Hancock, who never bought or sold slaves but grew up served by slaves in the house of his wealthy merchant uncle, was exaggerating. In reality, the 1765 Stamp Act was a tax\u2014not, thought the British, a terrible one, given what had been expended to protect the colonists from the French and Indians, but a maddening one to colonists who had to pay with hard coin for the new stamped paper that would be used in any officially recorded transaction.\n\nContrived to make all levels of society pay, the Stamp Act was a serious miscalculation on the part of the clueless British officialdom. Nothing was more calculated to infuriate the legal class than the Stamp Act, since it mandated use of stamped paper for legal documents. It angered the poor: it required a one-shilling stamp on a deck of playing cards\u2014a particular annoyance, since gambling required frequent replacement of the deck\u2014and a whopping ten shillings on a pair of dice. And it was a call to arms as well for newspaper printers, who were expected to print on officially stamped and purchased paper, and who retaliated with all the ink at their disposal.\n\nIn Boston, where the first insurrections of colonists against Britain exploded, two distinct social levels were active, each of which had their own motives: the merchants, and the motley crew that made up the mob. We speak today of \"the mob\" most commonly with reference to the Sicilian-style Mafia, as transplanted to America via New Orleans in the late nineteenth century. But in the 1760s another kind of mob was already well established in Boston, though it was more loosely structured. The mob culture of Boston was a principal actor in the early days of the American Revolution.\n\nPuritan Boston didn't have any Catholic churches, nor did it celebrate Christmas or Easter, nor did it have a theater. As in Connecticut and Rhode Island, \"stage-plays\" were prohibited in Massachusetts and were not part of the public consciousness, so Bostonians had not seen Addison's influential _Cato_ , nor did Boston have that part of social life that centered around the theater. Boston's theatrical urges played out differently: in the form of participatory mass actions in the street, as happened every year on November 5, or \"Pope's Day.\" Known in England as Guy Fawkes Day for the radical Catholic who had tried to blow up Parliament with gunpowder in 1605, the holiday had replaced the pagan All Hallows' Eve. In Boston, some people observed it by dressing as devils and popes for a carnival of misrule that might include attacking Catholics\u2014a practice imported from London\u2014should any be detected.\n\n\"Rioting in Boston was almost a ritual,\" writes Hiller B. Zobel. Boston's street culture meshed with its heritage of Protestant dissent, which had long expressed itself in resistance to the colonial government. An anti-impressment riot in 1747 lasted three days, during which a multiethnic, mutinous mob of sailors that grew to some three thousand participants battled press gangs, took hostages, burned boats, and physically confronted the governor\u2014\"literally a case,\" write Linebaugh and Rediker, \"of the people's fighting for its liberty, for throughout the eighteenth century the crew of a ship was known as 'the people,' who once ashore were on their 'liberty.'\"\n\nBy the time of the Stamp Act, the Mob\u2014they wrote it with capitals\u2014was a focused force that took direction and had been repurposed as a political weapon. The leader of the Mob in Boston (which divided into antagonistic North and South Boston factions) was a twenty-eight-year-old shoemaker named Ebenezer Mackintosh. Zobel writes:\n\nDuring the years from 1765 to 1770... although the rioters seemed uncontrolled and uncontrollable, they were in fact under an almost military discipline. On one notable occasion, according to the Tory Peter Oliver, Mackintosh \"paraded the Town with a Mob of 2,000 Men in two Files, & passed by the Stadthouse, when the general Assembly were sitting, to display his Power: if a Whisper was heard among his Followers, the holding up of his Finger hushed it in a Moment: & when he had fully displayed his Authority, he marched his Men to the first Rendezvouz, & Order'd them to retire peacably to their several Homes; & was punctually obeyed.\"\n\nPerhaps the figure of two thousand is an exaggeration; that number represented well over half of the town's adult male population. But there is no doubting that in Boston more than anywhere else, the hatred of the British and of those thought to collaborate with them generalized and transcended social class. And Boston had no police force to speak of.\n\nMackintosh's Mob, performing some of the functions of a militia, wound up being the street enforcers of a group called the Loyal Nine, a club of mid-level merchants and businesspeople that included Benjamin Edes, printer of the _Boston Gazette_ , as well as a ship's captain, a jeweller, and two distillers who bought much forbidden molasses from Saint-Domingue.\n\nFrequently present at Loyal Nine meetings, though not a member, was Harvard graduate and failed businessman Samuel Adams Jr. Possibly the most fully committed revolutionary to appear during the entire independence process, he was thirteen years older than his second cousin John Adams. When the Stamp Act crisis came to a head, Adams seems to have been one of the principal ligatures between merchants and Mob, a connection that was a significant tactical achievement of the urban American insurgents. At the height of the action, he was perhaps the most powerful man in Boston.\n\nAdams had been affected by the experience of Boston's 1747 impressment riots, and subsequently began a radical newspaper, the _Independent Advertiser._ He had come to consciousness in the midst of the fierce political struggle between the \"popular\" party (which dominated the Massachusetts House of Representatives) and the \"court\" (pro-British, aristocratic) party.\n\nMany Americans today have the impression that the uprisings in Boston were directed solely against British occupiers, but despite his close collaboration with the crown, the Massachusetts merchant Thomas Hutchinson was as much an American as Samuel Adams. The Hutchinsons were the ruling class; they had a reputation for tight, strategic intermarriage among three clans that had literally come to be Boston's ruling family. They dedicated themselves exclusively to commerce and officeholding. After a prolonged \"bank war\" between a crown-associated \"silver bank\" and a populist-associated \"land bank\" went badly for the latter, Samuel Adams's family hated the Hutchinson clan obsessively\u2014especially Thomas Hutchinson, who simultaneously served as governor, legislator, and supreme court justice.\n\nThe Loyal Nine were at the center of the first provocative actions of what came to be called the American Revolution, dispatching physical intimidation as a primary tactic. The presence of printer Benjamin Edes was critical: the first confrontations exploded amid a torrent of radical pamphleteering, which, amid the proliferation of printers and newspapers, was the new-media component of the American Revolution. The message Edes never stopped printing was that a standing military force was tyranny, and the very presence of troops an affront.\n\nThe Loyal Nine were absorbed into the Sons of Liberty, a self-appointed action group with chapters in all the colonies. The many merchants in their ranks intended to be on the winning side when their wealthy loyalist competitors had been hounded out of town, a process they eagerly threw themselves into. They hanged in effigy the wealthy merchant Andrew Oliver on the hot night of August 14, 1765, for collaborating with the Stamp Act. While that might seem relatively mild as compared with, say, breaking on the wheel, as was done to rebellious slaves in Louisiana, it was a terrifying experience for the victim.\n\nOn August 26, violence erupted as the Mob stormed Thomas Hutchinson's house, using axes to break their way into the fine house, built seventy-five years previously by Hutchinson's grandfather. Hutchinson's family, who had been having supper, fled as the Mob destroyed the furniture, took everything of value\u2014clothes, rings, cash\u2014and, in Bernard Bailyn's words, \"destroyed or scattered in the mud all of Hutchinson's books and papers, including the manuscript of volume I of his _History_ and the collection of historical papers that he had been gathering for years as the basis for a public archive.\" They did their best to pull the building down: \"only the heavy brickwork construction of the walls prevented their razing the building completely, though they worked at it till daylight.\"\n\nThe violence of the Boston Mob, whom the aristocrats saw as \"levellers,\" astounded their bourgeois sponsors. They got away with it\u2014not only with impunity, but with glory. In a systematic campaign of intimidation directed largely at merchants, the Mob enforced a nonimportation edict. To anyone suspected of not supporting nonimportation, they made life unbearable. The violence was strategic, implying both a command structure and a financed campaign.\n\nThey showed up at targets' homes en masse, carrying clubs. They beat people up, and they inflicted the signature torture of the American Revolution: tarring and feathering. They stripped their victims naked in front of a crowd, covered them first with scalding hot tar (making them black) and then with goose feathers (making them Indians), and paraded them in that condition about town for perhaps three hours to be the object of ridicule and beatings before being left half dead. As a public humiliation and street theater, tarring and feathering dates back at least to the twelfth century in England, but it seems to have made its first appearance in the colonies in the hands of the self-proclaimed Patriots.\n\nThe Mob hounded Thomas Hutchinson's nephew, the merchant Nathaniel Rogers, with more than a year's worth of attacks on his house, physical threats, and intimidation of his family, until he left Boston. Then they had their Sons of Liberty soldiers in New York hound him out of that city. But New York did not mobilize like Boston had.\n\nWith its relatively homogenous population, accustomed as it was to the focus and discipline of Puritan society, Boston was unique. In New York, heterogenous and multilingual from the moment of its founding by the Dutch, coordinated movement was less likely. The Sons of Liberty tried the same tactics there, but the mobs lacked organization and merely went trashing, vandalizing the rich and on one occasion destroying a newly built theater.\n\nThe colonists' violent reaction to the Stamp Act caught the British\u2014and some of their factors\u2014by surprise. In South Carolina, the radical who stirred up mob action was Christopher Gadsden, a temperamental merchant who was the most aggressive local figure in defying colonial governors. Writing under the pseudonym of Homespun Freeman, Gadsden denounced the Stamp Act as a Scottish plot. He went to New York in 1765 as a delegate to the Stamp Act Congress, which asserted that only colonial assemblies had the right to tax the colonies, and he returned to Charleston an ardent member of the Sons of Liberty. He was a kindred spirit and warm correspondent with Samuel Adams; their friendship was emblematic of the close ties of insurgency between New England and South Carolina. It was Gadsden who designed the \"Don't Tread On Me\" rattlesnake flag for John Paul Jones to hoist over the _Alfred_ , the first ship of the American navy, as the \"special standard\" of the US Navy's first commander in chief, the former Rhode Island slave-ship captain Eseck Hopkins.\n\nGadsden in 1767 invested his fortune in the seven-year project of building his 840-foot wharf, the largest in the colonies, which shipped out enormous amounts of rice. It is notorious in American memory as the site where Africans were taken for sale after their period of quarantine at Sullivan's Island; perhaps more than one hundred thousand Africans were sold from Gadsden's Wharf before the African trade was prohibited.\n\nThe anti\u2013Stamp Act mob in Charles Town rioted for nine days. Henry Laurens, a conservative businessman who prided himself on doing things legally, was in favor of complying with the Stamp Act, and so was targeted by the mob, which came to Laurens's house bent for, as he put it years later while confined in the Tower of London, \"seizing the Stamp'd Paper just arrived in Charles Town & for awing the Officers appointed to distribute it.\" But Laurens successfully talked the mob down, demonstrating the crowd-handling skill he subsequently deployed as president of the First Continental Congress.\n\nRadicalism was a double-edged sword for the merchants. Many were invested in commercial alliances in England, and destabilization was not good for business. War would disrupt shipping. But being constantly at the mercy of British trade regulations seemed to them to be \"slavery,\" the word they invariably used. Independence would give merchants ownership of their commerce\u2014which in some cases, needless to say, included slave trading\u2014and would put them in charge of regulation. The Loyalists weren't going to be the winning side, and knocking them out would remove competition.\n\nAs the \"Patriots\" seized power in all thirteen colonies, merchants who didn't dance to the broadly popular tune of revolution might be labeled Tories and find themselves the object of mob action. As Henry Laurens discovered, it was a better bet to be the one leading the mob. In Chestertown, Maryland, Thomas Ringgold IV cast his lot with change. Besides being a member of the Maryland assembly, Ringgold was a founder of the local chapter of Sons of Liberty and a member of the Stamp Act Congress. He became a slave-trading revolutionary, and not the only one.\n\nWhile the repeal of the Stamp Act on March 17, 1766, temporarily averted a crisis, it was accompanied by the Declaratory Act, which held\n\nthat the said colonies and plantations in _America_ have been, are, and of right ought to be, subordinate unto, and dependent upon the imperial crown and Parliament of _Great Britain;_ and that the king's Majesty... had, hath, and of right ought to have, full power and authority to make laws and statutes of sufficient force and validity to bind the colonies and people of _America_ , subjects of the crown of _Great Britain_ , in all cases whatsoever.\n\nWith the Declaratory Act, London reaffirmed its right to strike down colonial law at will. \"Every colony had been established by a document from the king that authorized a colonial legislature to enact laws for the colony so long as they were 'not repugnant to the laws of England,'\" write Alfred and Ruth Blumrosen. \"Thus the British government retained a kind of superintending power over the colony's behavior. This was well known in the colonies.\" That was a problem: while the Declaratory Act aroused no popular protest in the colonies, its implications were clear to the colonial ruling class. Meanwhile, Southern slaveholders were become increasingly alarmed by the abolitionist movement that had been growing in Britain since the 1760s, fed by the increasing popularity of Methodism and Quakerism, both antislavery.\n\nNowhere did British and colonial law differ more sharply than on slavery. William Blackstone, the ranking British jurist of his day in 1765, praised liberty in terms that infuriated the Virginians: \"[the] spirit of liberty is so deeply implanted in our constitution, and rooted even in our very soil, that a slave or a Negro, the moment he lands in England, falls under the protection of the laws and so far becomes a freeman.\"\n\nSlaveowning colonists were particularly alarmed by the 1772 _Somerset_ decision. James Somerset was the slave name of a man who had been kidnapped from Africa at the age of nine. After landing in Virginia in 1749, he caught the eye of the young Scottish-born tobacco merchant Charles Stewart of Norfolk, whom he served for more than two decades as his \"body servant,\" performing whatever personal services Stewart required.\n\nWhen Stewart took Somerset along to London in 1771, Somerset escaped. Stewart recaptured him with the aid of professional slave catchers, who existed in London because there were enough enslaved people there, belonging to colonists both visiting and resident, that this kind of thing happened on an ongoing basis. The displeased Stewart avenged his humiliation by having Somerset bound and put on a ship to be sold in Jamaica\u2014a reminder that a slave could easily be removed from the most relatively privileged urban echelons to a tropical death camp.\n\nBefore the vessel could sail, however, Somerset was dramatically rescued by the abolitionist Granville Sharp, who paid for Somerset's defense in court. The unprecedented case was a striking example of using litigation to steer social policy and was reflective of the maturity of the British justice system at the time. It put slavery on a show trial, occasioning widespread debate in the press, and it thrust the eminent, conservative jurist Lord Mansfield into the hot seat.\n\nTo the objection by Stewart's lawyer that freeing the estimated fourteen thousand slaves held in Britain would cost their owners a catastrophic \u00a3700,000, figured at \u00a350 a head, Mansfield replied, \"\u00a350 a head may not be a high price.\" But he judged the case narrowly. He felt the issue was one for Parliament to take up, urging them to do so in his decision freeing Somerset: \"The state of slavery is... so odious, that nothing can be suffered to support it but positive law. Whatever inconveniences, therefore, may follow from the decision, I cannot say this case is allowed or approved by the law of England; and therefore the black must be discharged.\"\n\nThe decision, widely reported in colonial American newspapers, effectively prohibited chattel slavery in England (Scotland had a separate body of law), and unquestionably was a great victory for the antislavery movement. At bottom, it established that Somerset had the rights of a person, which went directly contrary to the current of colonial law. Somerset was feted at a party in London attended by two hundred free people of color, an event also reported in colonial papers, including the _South Carolina Gazette._ Benjamin Franklin, who was in London in 1772 when the _Somerset_ decision came down, wrote in full cry:\n\n_Pharisaical Britain!_ to pride thyself in setting free _a single Slave_ that happens to land on thy coasts, while thy Merchants in all thy ports are encouraged by thy laws to continue a commerce whereby so many _hundreds of thousands_ are dragged into a slavery that can scarce be said to end with their lives, since it is entailed on their posterity\n\nThe passage above has sometimes been cited as a proof of the non-plantation-owning Franklin's humanitarian bent. But if we read this with a pragmatic politician's understanding, we see less a simple cry against the immorality of slavery than that favorite trick of the political debater: changing the subject. And it was disingenuous: as Franklin well knew, Rhode Island captains had carried tens of thousands of Africans, and he himself made money from advertisements for slave sales in his newspapers, especially in South Carolina.\n\nThe British Parliament never picked up the gauntlet Lord Mansfield had thrown down. Slavery in Britain would never be made legal by affirmative law. It had been implemented in the colonies by English merchants, officials, captains, and by the colonists who had written laws to support it there, but there was never any groundswell of public opinion in its favor at home.\n\nStamped paper and tea are iconic in American popular history, but only recently have historians begun to consider the _Somerset_ case much in the narrative of American independence. _Somerset_ posed a more basic kind of threat to a slaveowner than stamped paper. It jeopardized the basis of Southerners' wealth: property consisting of human beings.\n\nHenry Laurens was in London when _Somerset_ was being argued. Before the verdict was delivered, he took a sarcastic tone in a letter of May 29, 1772: \"They say that supper is ready, otherwise I was going to tell a long and comical Story, of a Trial between a Mr. Stuart and his Black Man James Somerset, at King's Bench, for Liberty.\" Thirteen years later, he argued in a letter that \"nor is it quite a decided fact that the moment a Negro sets his foot on British Ground he becomes a freeman. Lord Mansfield left this a moot point.\" But Laurens was arguing against the tide: Mansfield's shocking decision was strongly felt, as evidenced by the 1774 newspaper advertisement in Virginia for return of a runaway that said, \"He will probably endeavor to pass for a Freeman by the name of John Christian, and attempt to get on Board some Vessel bound for Great Britain, from the Knowledge he has of the late Determination of Somerset's Case.\"\n\nA British crackdown on smuggled molasses and tea inevitably led to confrontation. In Providence, the wealthy slave trader and rum distiller John Brown was one of the (at the time) unidentified leaders of a group of sixty or so who on the night of June 9, 1772, with their faces blacked, boarded and blew up the British blockade ship _Gasp\u00e9e_ , wounding the vessel's master in the struggle.* The assault on the _Gasp\u00e9e_ was tremendously popular among the people of Providence; no one would identify Brown or the other combatants, let alone testify.\n\nIn response to the Tea Act of 1773, which laid a threepenny duty on a vast surplus of tea that was otherwise being dumped on the American market, militants disguised with soot-blacked faces and Indian feathers on December 16 staged what later became known as the Boston Tea Party, arguably the detonating act of the American Revolution. Other anti-tea events followed in every colony, with a general boycott of tea that created a sense of revolutionary unity in the face of collective caffeine deprivation. In Annapolis, the ship _Peggy Stewart_ was burned; the vessel's owner, Anthony Stewart, was compelled to torch it himself, with its load of tea. Samuel Galloway, perhaps with a there-but-for-the-grace shudder at the loss to his colleague and competitor, noted in a letter of October 24, 1774, that Stewart was not allowed even to place a handbill in the newspaper. \"This is Liberty with a Vengence,\" Galloway wrote to Thomas Ringgold V. For his part, Ringgold insisted the whole incident was cooked up by Stewart to curry favor with London and wrote his father-in-law and merchant partner that he was \"glad the people have shewn so much spirit.\"\n\nPhiladelphia, meanwhile, was riled up by the _Centinel_ , written in various issues of the _Pennsylvania Journal and Weekly Advertiser_ beginning March 24, 1768, by Francis Alison, John Dickinson, and George Bryan, which warned of a plan to install an Anglican bishopric in the colonies, something that, despite the colonies' official status as Anglican, had never been done. Evangelicals and other religious dissenters, a major force in the independence struggle, feared that an \"American Episcopate\" would bring religious oppression to tolerant, multi-sected Pennsylvania. _Centinel_ #1, which warned of the danger to religious dissenters, charged that \"Enemies of America,... are exerting their utmost Endeavours to strip us of our most sacred, invaluable and inherent Rights; to reduce us to the State of Slaves; and to tax us.\" Needless to say, this came from people who knew full well that the \"State of Slaves\" involved far more than taxation.\n\nThere was plenty to enrage the colonists, including the Quebec Act of 1774, which would have extended the province of Quebec down to the Ohio and Mississippi Rivers. But all of that aside, and allowing for the argument that the colonies had in fact largely been independent since their foundation, the slave-society colonies of the South had their own compelling reason to secede from Britain: only independence could protect slavery from the growing power of British abolitionism.\n\nThe British army came with a display of intimidating grandeur. Malcolm Bell Jr. describes the arrival in 1765 of the mostly Irish Twenty-Ninth Regiment of Foot in Halifax on the ship _Thunderer:_ \"Ten black drummers, all former slaves captured from the French on the island of Guadeloupe, gave the band a special air. In their brilliant uniforms of scarlet pantaloons, silver-buttoned yellow jackets, Hessian boots, feathered turbans, and Persian scimitars, they won the admiration of all who saw them perform.\"\n\nTraveling with that regiment was Major Pierce Butler. An Irish Anglican, proud and even defensive throughout his life of his (somewhat questionable) aristocratic lineage, he was a third son and as such not in line to receive an inheritance in the age of primogeniture. The Americas were a fortune-hunting ground for younger sons; when Butler was eleven years old, his family purchased him a commission in the king's army. He came to North America at the age of fourteen during the French and Indian War, then subsequently returned to service in Ireland, and was sent again to Canada in 1765 with the rank of major.\n\nButler traveled to Philadelphia in 1767 with other officers to determine where best to post the regiment, then traveled alone down to Charles Town, arriving December 11, 1767, and remaining there through April 1769. During that time, in September 1768, his regiment was posted to insurgent Boston, which, with about sixteen thousand residents, was far and away the most rebellious of American towns and was the only site of resistance that British politicians were concerned about. There were no barracks in Boston to quarter the troops, who were hated as occupiers by the townspeople. Minor street beefs became confrontations between civilians and military, who otherwise mingled in various ways. Some soldiers deserted; others supplemented their regimental pay by doing casual day labor in Boston's ropeworks.\n\nThe twenty-one-year-old Major Butler (as he would be referred to throughout his life) had wider latitude. While in Charles Town, he caused a scandal by eloping with a fifteen-year-old heiress, but her stepfather intervened and thwarted the marriage, to the amusement of local society. When she married the following year, her fortune was quantified in the newspaper as \"Thirty Thousand Pounds Sterling,\" with an implicit mockery of Butler, who was reported in the same issue to be leaving town and who never quite lived down his reputation as a fortune hunter.\n\nBroke and experiencing problems with receiving his pay, Butler returned to his regiment in Boston, at a time when the town was at a peak pitch of anticolonial furor. He was apparently present, though not in uniform, on March 5, 1770, when members of his regiment killed five people after provocation, committing what was immediately trumpeted by propagandists as the Boston Massacre, and, reported Thomas Hutchinson, brought Massachusetts to the brink of\u2014a commonly used term at the time\u2014\"civil war.\"\n\nReturning to Charles Town in January 1771 with only his military commission to his name\u2014not an insubstantial holding\u2014Butler quickly married Mary Middleton, whose deceased father, Thomas, had in the 1750s been one of the largest slave traders in Charles Town. The young heiress had received not only Middleton's legacy, but an even larger fortune from her maternal grandmother.\n\nIt was a prosperous time for South Carolina's businessmen, but Thomas Middleton left a legal mess behind, with much property and much debt. Butler became property manager for his wife's portfolio, which catapulted him into the ranks of the large planters. He now owned hundreds of slaves, many of them originally kept back from general sale by Middleton, who as a slave trader had first pick and a practiced eye.\n\nIt appears that one of the first things Butler did was to put hot-iron brands on their skins. There is nothing to suggest that Butler subsequently continued this practice, but the year after his marital windfall, he advertised in the _South Carolina Gazette_ for two runaway slaves, thanks to which advertisement we know that they wore his initials for life:\n\nRUN AWAY\n\n_From the Subscriber's Plantation in_ Prince William's _Parish,_\n\nT W O N E G R O F E L L O W S\n\n_Named_ MINOS, and CUDJOE; \u2014 they are both strong-made Fellows.\n\nMinos appears to be near 40 Years old. Cudjoe about 26: \u2014 They are marked a little above the right Breast with the Letters PB...\n\nPIERCE BUTLER.\n\nDespite having married into the Charles Town gentry, Butler was still an officer in His Majesty's Army. The Crown was still giving away land to settlers counted loyal to the king, and Butler managed a substantial land grab as a Loyalist. \"In the years immediately following his marriage,\" writes Bell, \"Pierce Butler made numerous requests for property and was awarded in excess of ten thousand acres, of which more than eight thousand was in the Carolina back country.\" Butler, who ultimately made a considerable fortune in real-estate deals, was described approvingly in 1785 by no less a profiteer than Henry Laurens as a \"great Speculator\" who \"loves to make money.\" There was no question that all this land would be cleared and planted by newly arrived Africans.\n\nButler maintained the fiction of loyalty as long as he could, but as his regiment was preparing to ship back out to Britain, he resigned from the British army in 1773. Selling his military commission, he plowed the receipts from cashiering himself into purchasing a seventeen-hundred-acre plantation on St. Simons Island off the coast of Georgia. With his hundreds of slaves and the excellent land he had acquired, Butler began producing rice and premium-priced long-staple cotton. His fortune was made.\n\nHe was collaborating actively with the independentists by 1775, and with the coming of the war, he became South Carolina's adjutant general against his former army, charged with whipping a backwoods militia into shape as a military force. Keenly aware that South Carolina's defense was obstructed by the reluctance of men to leave their homes and families unguarded against Native American attack or slave insurrection, he requested a force of five thousand troops from the North to protect the Lowcountry\u2014from the British, officially, but also from domestic enemies.\n\nThe Scottish naturalist Alexander Garden, who arrived in Charles Town in 1752, \"had not been in South Carolina very long before he was told by both doctors and laymen of their concern that people were being poisoned by their slaves,\" write Edmund and Dorothy Smith Berkeley. \"It was widely believed that plant poisons were being administered in food or drink, especially in tea. When he inquired concerning what plants were suspected of being used, he found that no one had a very clear idea.\" Dr. Garden came to the conclusion that many of the local cases of \"poisoning\" were actually other maladies.\n\nIt was not, however, an unfounded fear. Knowledge of poisons was the same as knowledge of medicines; both were African specialties, and there were many cases of terror by poison in the slave societies of the hemisphere, perhaps most notably the sorcerer-poisoner Makandal, counted as a foundational figure in Haitian political iconography. Regardless of whether the poisonings in Charles Town were real or imagined, they were vivid in white Charles Townians' imaginations, as was another perceived danger: the free black and enslaved tradesmen who formed Charles Town's artisan class had access to all sorts of potentially lethal objects. Alexander Hewatt wrote in 1779, and note the use of the word _breed:_\n\nFrom [enslaved] labourers in the field the colonies have perhaps less danger to dread, than from the number of tradesmen and mechanics in towns, and domestic slaves. Many negroes discover great capacities, and an amazing aptness for learning trades, where dangerous tools are used, and many owners, from motives of profit and advantage, breed them to be coopers, carpenters, bricklayers, smiths, and other trades.\n\nOut of mere ostentation the colonists also keep a number of them about their families, who attend their tables, and hear their conversation, which very often turns upon their own various arts, plots, and assassinations. From such open and imprudent conversation those domestics may no doubt take dangerous hints, which, on a fair opportunity, may be applied to their owners hurt.\n\nThey have also easy access to fire arms, which gives them a double advantage for mischief. When they are of a passionate and revengeful disposition, such domestic slaves seldom want an opportunity of striking a sudden blow and avenging themselves, in case of ill usage, by killing or poisoning their owners. Such crimes have often been committed in the colonies, and punished; and there is reason to believe they have also frequently happened, when they have passed undiscovered. Prudence and self-preservation strongly dictate to the Carolineans the necessity of guarding against those dangers which arise from domestic slaves, many of whom are idle, cunning and deceitful. (paragraphing added)\n\nOut on the western edge of Anglo-American expansion, concerns were different. A 1772 panic in London's financial markets caused widespread hunger among the poor, triggering a translatlantic exodus of Scots, Irish, and so-called \"Ulster Irish\" or \"Scotch-Irish,\" who, though often referred to simply as \"Irish,\" were Scots from Northern Ireland. In South Carolina, the Scotch-Irish Presbyterians and the German immigrants of the rugged upcountry would have loved to have had the luxury of worrying about stamps and tea, let alone plantations full of slaves. Pillaging by bandits and annihilation by the natives were daily threats to them. They had no representation in the colonial legislature, nor were they under the protection of any state. Any policing they had, they did themselves by means of regulators, practicing vigilante justice.\n\nSouth Carolina's Congress was in session in June 1775 when news of the first blood of Lexington arrived. The assembled oligarchs responded immediately; from the steps of the majestic building now known as the Old Exchange, they declared South Carolina to be the first independent provisional government. Henceforth Her Majesty's government was disregarded by Charles Town's political class, who considered this independence from Britain to be their second revolution, the first having been against the lords proprietors in 1719. Henry Laurens signed the document that created a thirteen-man Council of Safety and three committees: a General Committee; a Secret Committee of five persons with broad, vaguely defined powers; and a Special Committee, which was an extension of the Secret Committee and which had the repression of black people as its primary mission.\n\nAccording to nineteenth-century South Carolina historian Edward McCrady, the rationale for the latter appears to have come from a private letter received from London, \"intimating that a plan had been laid before the Royal government for instigating the negroes to insurrection, which seems to have been believed, and to have been regarded as more alarming because it was known that some of the negroes entertained the idea that the contest was for their emancipation. To meet, therefore, whatever might arise, a _Special Committee_ was appointed to form such plans as they should think immediately necessary to be carried into execution 'for the security of the good people of the colony.'\" The Secret Committee also managed to tar and feather a couple of Roman Catholics, who, it was feared, might be in league with the \"Negroes.\"\n\nThen came the edict that shocked the slaveowners, and made clear what was at stake for them.\n\n\"Hell itself could not have vomitted anything more black,\" wrote a Philadelphian in a letter published in the _Morning Chronicle and London Advertiser_. The proclamation by Lord Dunmore, the Scottish governor of Virginia, on November 5, 1775, read in pertinent part:\n\nI do hereby... declare all indented Servants, Negroes, or others, (appertaining to Rebels,) free that are able and willing to bear Arms, they joining His MAJESTY'S Troops as soon as may be, for the more speedily reducing this Colony to a proper Sense of their Duty.\n\n_I... declare all... Negroes... free._ These were the words of slaveowners' nightmares. It did not apply to those enslaved by Loyalists. At least in theory, slaveholding colonists who were not taking up arms against the king had nothing to fear, because they could stay home and keep their slaves on lockdown. But those rebels who left their plantations to fight might first find their capital running away and then find themselves facing off against the very people they had brutalized, now with guns in their hands. The insurgents responded by raiding the plantations of those they demonized as \"Tories,\" or Loyalists, and confiscating their slaves, who were put to military support work.\n\nDunmore had been thinking about this for a few years. In 1772, he had written:\n\nAt present the Negroes are double the Number of white people in this Colony, which by the natural increase, and the great addition of new imported ones every year, is Sufficient to allarm not only this Colony, but all the Colonies of America... in case of War (which may probably often happen) with Spain, or indeed any other power... the people, with great reason tremble at the facility that an enemy would find in procuring such a body of men; attached by no tye to their Masters or to the Country... by which means a Conquest of this Country would inevitably be effected in a very Short time.\n\nBy threatening to take away the Southerners' principal source of wealth, Dunmore's proclamation galvanized wavering elements of the white population of Virginia and South Carolina into supporting the \"patriots,\" or, as the British called them, the \"rebels,\" who defended the idea of enslaved property. The struggle against the British in the Southern colonies became profoundly identified with the struggle of the white population against emancipation of the black population. The newspapers printed rumors that Dunmore was paying the \"savages\" (Native Americans) in specie to attack. \"We have a right to take up arms in self-defense,\" read a letter to the _Virginia Gazette's_ printer \"Mr. Purdie\" in the December 8 edition, \"since we have been threatened with an _invasion_ of _savages_ , and an _insurrection_ of _slaves_ , and have had our _negroes_ and _stocks_ piratically taken from us.\"\n\nDunmore was obliged to flee, retreating offshore to a flotilla of more than a hundred vessels, where he remained while the enslaved flocked by the hundreds to seek the protection of the Union Jack. Dunmore needed them; reinforcements from Britain were not forthcoming, since for reasons inexplicable to him they were sent to North Carolina instead. Almost immediately, he formed what became known derisively as Lord Dunmore's Ethiopian Regiment. Their first skirmish was the Battle of Kemp's Landing, ten days after Dunmore's Proclamation, in which, as a correspondent for Purdie's _Virginia Gazette_ wrote, \"23 members of the _Scabby race_ went as volunteers, with 200 regulars.\" The British won the battle, with the result that Colonel Joseph Hutchings of the colonial militia was taken prisoner by one of his former slaves.\n\nOn December 14, the _Pennsylvania Evening Post_ reported that: \"Late last night, a gentlewoman, going along Second street, was insulted by a negro, near Christ church; and upon her reprimanding him for his rude behaviour, the fellow replied, \"Stay you d----d white bitch, till lord Dunmore and his black regiment come, and then we will see who is to take the wall.\"\n\nSo it was that the rebels, patriots, insurgents, continentals, call them what you will, were at war with the British and those suspected of being loyal to them, most especially the \"Negroes.\" An article in the March 22, 1776, issue of Purdie's _Virginia Gazette_ demonstrates Dunmore's effectiveness at getting under the colonists' skins. Laden with racist scorn, the article not only notes the presence in Virginia of the balafon (a marimba-type mallet instrument known across a wide region of Africa), called in Virginia _barrafoo_ , but implies that it was something familiar to the readership:*\n\nWe hear that lord Dunmore's _Royal Regiment of Black Fusileers_ is already recruited, with runaway and stolen negroes, to the formidable number of 80 effective men, who, after doing the drudgery of the day (such as acting as scullions, &C. on board the fleet) are ordered upon deck to perform the military exercise; and, to comply with their _native_ warlike genius, instead of the drowsy drum and fife, will be gratified with the use of the sprightly and enlivening _barrafoo_ , an instrument peculiarly adapted to the martial tune of _\"Hungry Niger, parch'd Corn!\"_ and which from henceforward is to be styled, by way of eminence, the BLACKBIRD MARCH.\n\nThe British used armed, emancipated former slaves who knew the terrain. The most prized defectors were pilots and navigators, masters of the marshy nooks and crannies in which they had been born and raised. Others were former African soldiers. In all cases, they were highly motivated in going to war against the masters they had escaped, who might kill them, torture them, or sell them away if they were recaptured. On the other side, in South Carolina and Georgia the independentists confiscated slaves from Loyalists and put them to work as military laborers. Patriot soldiers in Virginia, South Carolina, and Georgia were paid with slaves; according to Malcolm Bell Jr., in Georgia slaves were given \"to public officials as salary, and were exchanged for provisions for use by military units.\"\n\nAfter a battle on December 29, 1778, the British took Savannah and held it until 1782, despite a thirty-two-day siege of the city that ended with a failed assault by French and American forces on October 18, 1779. Men of color had been serving as French soldiers on foreign missions since the beginning of French Antillean slavery, and the bloody siege of Savannah is rembered for the participation of the 750-man Chasseurs-Volontaires de Saint-Domingue, a free-black volunteer corps that provided about a third of the expedition's manpower, and in which, it is popularly believed (it may be true), future Haitian leader Henri Christophe served as a drummer boy.\n\nOne sometimes reads that black soldiers fought on both sides in the War of Independence. That's technically correct, but misleading. Some did fight in Northern pro-independence regiments, but in the South, where most black people were, they ran away and joined the British if they could. Both sides used mercenaries and foreign troops: in 1780, there were more Americans fighting for the British than for the Continental Army, including a number of formerly enslaved African Americans.\n\nIn the War of Independence, as in every other conflict involving slave societies, the constant potential for slave insurrection was taken into account in every military calculation. In the plantation societies, more than anywhere else, the war between Britain and the colonists was a revolutionary war\u2014at least on the part of the formerly enslaved black soldiers, who were fighting with the British against the slaveowning Patriots for their liberty.\n\n*Brown, along with his abolitionist brother Moses, was later a cofounder of Brown University. See Rappleye.\n\n*The indentured servant John Harrower described a \"barrafou\" in 1775: \"The body of it is an oblong box with the mouth up & stands on four sticks put in bottom & cross the [top?] is laid 11 lose sticks upon [which?] [the player] beats.\" Harrower, 89.\n\n#   21\n\n# **The General Inconvenience**\n\n_sold Sandy to Col. Chas Lewis for \u00a3100. paiable in June. from which deduct \u00a39.4.8 my present debt with him; leaves \u00a390.15.4. to be received. 1_\n\n\u2014Thomas Jefferson, Memorandum Book, January 29, 1773\n\nPATRICK HENRY WAS BY accounts a good fiddler, a singer of tavern-ballads, and an engaging character. Jefferson, who first encountered him in 1760 when Henry's store had failed, recalled that \"his manners had something of coarseness in them; his passion was music, dancing, and pleasantry. He excelled in the latter, and it attached everyone to him.\" A slaveowning tobacco planter and a seditious orator, Henry strikingly personifies the fundamental paradox of the early American experience: how liberty could be intimately bound up with slavery.\n\n\"Give me liberty, or give me death!\" Henry's hyperdramatic, rhetorical ultimatum, the most popular and durable slogan of the independence movement, subsequently venerated as patriotic scripture, was in support of what was basically his own declaration of war against Britain, arguing in favor of placing the entire state on an emergency mobilization. Henry's speech has been widely credited with moving Virginia to declare independence from Britain. It took place, so we are told (though there is no contemporary record of it), on March 20, 1775, from the third pew of the left central section of St. John's Church in Richmond.\n\nHoping to avoid escalation of hostilities, the pro-American Irish statesman Edmund Burke warned in a speech given in London two days after Henry's peroration that \"in Virginia and the Carolinas they have a vast multitude of slaves... these people of the southern colonies are much more strongly, and with a higher and more stubborn spirit, attached to liberty, than those to the northward... such will be all masters of slaves, who are not slaves themselves. In such a people, the haughtiness of domination combines with the spirit of freedom, fortifies it, and renders it invincible.\"\n\n_Interior of St. John's Church, Richmond, June 2013._\n\nIt required five weeks minimum, and often much longer, for a message to travel from America to England, so Burke's speech was not a direct response to Henry, but his words described Henry perfectly. Henry's polemical evocations of liberty and slavery were framed by his concrete, daily experience of denying the most basic freedoms to an entire community of people over whom his word was law, and who lived in misery at his grudging expense.\n\nHenry's famous line was reworked from Joseph Addison's _Cato_ , a play the founders of the American republic knew well. Written in 1712 and published the following year, _Cato_ might be understood as a parable: Britain, once a vassal of the Roman Empire, was now the center of an empire modeled on Rome. Addison's sober neoclassical tragedy of liberty versus tyranny was set in Mediterranean North Africa, with Roman exiles as the heroes. The word \"Africa\" is heard frequently in the mouths of the actors in _Cato_ , perhaps for its resonant value, though the play is ambiguous about it. By Addison's time, London coffeehouses were getting coffee from Martinique; the transformation that African labor in the colonies had wrought in the metropolitan economy lurked offstage as well as on. The African character, Juba, is a figure out of history: the king of Numidia (Algeria), then under the control of the Carthaginians. When Juba wants the hand of Cato's daughter, Marcia, Cato responds with a nonanswer to his request: \"It is not now time to talk of aught \/ But chains or conquest, liberty or death.\"\n\nArguably the most politically consequential play in the history of British theater, _Cato_ was carefully bipartisan and scrupulously inoffensive. At its premiere, Whigs and Tories competed to applaud the loudest at the mention of the word \"liberty.\" To be a patriot, a son of liberty, a free man and not a slave\u2014that was a British oratorical legacy, imperial in scope and carried over to the colonies. In England, writes Bernard Bailyn, \"a flood of what has been called 'Whig panegyric verse'... poured from the presses from 1700 to 1760 and... echoed from the stage in play after play... No writer, however famous or obscure, could afford to neglect the theme of British liberty and power.\"\n\nThe Americans saw themselves as Cato's conspirators, called to sacrifice against a British Caesar. The first professional theater companies in the colonies performed _Cato._ Excerpts of its soliloquies were printed in colonial newspapers. It was staged by students at William and Mary College. Benjamin Franklin could recite chunks of it from memory. Its line \"What a pity it is \/ That we can die but once to serve our country\" proved inspirational for the martyred Nathan Hale. George Washington, who saw _Cato_ various times, referred to it in letters and had it performed near the front lines at Valley Forge on May 11, 1778, within earshot of the British troops.\n\nThere's a good reason modern audiences have not seen _Cato:_ it's not Shakespeare. Today it would seem stiff, stilted, and interminable. A celebration of stoicism in the face of tyranny, it lacks complex characters. Cato is noble and good; Caesar, the villain, is an unseen oppressor who has no part in the drama. Amateur theatrics were popular in the isolation of plantation Virginia, and _Cato_ was, writes Jane Carson, \"a favorite vehicle for amateurs because it requires little acting ability; the characters simply strike an attitude and declaim noble sentiments in high-flowing oratory.\"\n\nPatrick Henry was something of a \"ham actor,\" notes biographer George F. Willison, and as he gave his riveting oration in Richmond, he dramatized it. Not that we know exactly what he said: unlike Jefferson, who even as president declined to speak in public but left us a massive record of his thought in written form, Henry's most famous words live today only as hand-me-downs. There is no contemporaneous transcription of the full text; what follows, likely assembled from the recollection of jurist St. George Tucker, was published seventeen years after Henry's death:\n\nIt is vain, Sir, to extenuate the matter. Gentlemen may cry peace, peace; but there is no peace. The war is actually begun!...\n\nIs life so dear, or peace so sweet, as to be purchased at the price of chains and slavery?\n\nForbid it, Almighty God!\n\nI know not what course others may take. But as for me\u2014give me liberty, or give me death!\n\nWhen Henry shouted \"Give me liberty!\" he paused for effect, and poised a letter opener in his right hand, pointed at his chest\u2014an ivory letter opener, a product of Africa. When he said \"or give me death!\" he thumped his right hand containing the letter opener of death against his breast, as if stabbing himself. John Roane, who was present, recalled that \"When he said, 'Is life so dear, or peace so sweet, as to be purchased at the price of chains and slavery?' he stood in the attitude of a condemned galley slave, loaded with fetters, awaiting his doom. His form was bowed, his wrists were crossed, his manacles almost visible.\"\n\nPatrick Henry knew what a manacled slave looked like. He had received six people as a wedding present from his father-in-law, and later sold them to raise money to set himself up in an ill-fated storekeeping venture. For that matter, slaves were routinely sold in front of the Virginia House of Burgesses in Williamsburg, where a fair-weather auction outside would have been audible through the open windows of the building.\n\nHenry's bound-slave gesture can be read as an example of how the struggle for independence from Britain branded itself as a \"revolution\" against \"tyranny.\" To judge from the writings and recorded speeches of the self-proclaimed Patriots, they were obsessed with slavery, as per a New York protest of 1770, typical of the genre: \"The Right of a People to tax themselves is essential to their Liberty; and the Power of imposing Taxes on them, when exercised by others, subjects that People to the most abject Slavery.\" The word \"slave\" turns up repeatedly in their discourse, as the essence of what they would never allow themselves to become. This was nothing new: describing those in opposition to oneself in terms of slavery and freedom was an ingrained English trope of at least two centuries by then, heard routinely from the pulpit in the sermons of every denomination.\n\nHenry's liberty-or-death message carried the clear blame-the-victim implication that those who submitted to slavery were unworthy of liberty. The protest against Britain thus doubled as a taunt at the colonists' enslaved laborers. It was a libel routinely asserted against African Americans: that they were complicit in their degradation.\n\nMeanwhile, the use of _slavery_ as a political fighting word continued in use in England as well. \"Shall our fate be national bankruptcy, poverty, oppression and slavery?\" asked a 1772 London pamphlet castigating the East India Company. Looking at a dismal future as a colony, in which their sole purpose would be to enrich Britain, the wealthy North American colonial elite saw an analogy with the way the slave only existed for the benefit of the master. But the word \"slavery\" did not only compel colonials as an abstract metaphor; the Americans brought something different to the use of the term. For those who were born into full-fledged slave society as masters, some of their most profound, complex, and unrestrained relationships were with their slaves.\n\nPatrick Henry owned slaves when he was a sermonizing radical, and he owned them when he was the first governor of independent Virginia, where he was second in popularity only to George Washington. Like other liberty-loving Virginians, he bewailed the necessity of having slaves. Henry acknowledged the contradiction in a 1773 letter to his Virginia planter friend Robert Pleasants. A devout Quaker, Pleasants had educated and freed his slaves at an enormous personal cost of \u00a35,000 (more than $700,000 in 2014 dollars) and had sent Henry an antislavery book. \"Would anyone believe,\" asked Henry rhetorically, \"I am master of slaves of my own purchase? I am drawn along by the general inconvenience of living here without them. I will not, I cannot, justify it.\" This was, it should be emphasized, in a private letter; there is no record of his expressing such sentiments publicly. \"I believe a time will come,\" the letter continued, \"when an opportunity will be offered to abolish this lamentable evil... I could say many things on this subject, a serious view of which gives a gloomy perspective to future times.\"\n\nHis gloomy perspective was well-founded. The general inconvenience of living without slaves would have meant not merely having to empty one's own slop jar. It would have meant not living on the capital they embodied. Ending slavery would have required a different kind of revolution than the one Henry championed.\n\nThe liberty Patrick Henry was willing to trade for death (not his own martyrdom, as it turned out; others did the dying) was, as his other discourses and letters bear out, the freedom to own\u2014which inescapably meant the freedom to breed and sell\u2014slaves. Henry's revolution did nothing to change slaves' status as chattel or creditors' valuation of them as collateral. Whether or not Henry believed, as he wrote to Pleasants, that the time for abolition would someday come, he clearly believed it had not come yet, and he worked to delay it until long after his generation had departed.\n\nHenry argued against freeing slaves even as he dramatized the evil of slavery. \"Slavery is detested,\" he wrote in a letter. \"We feel its fatal effects, \u2014 we deplore it with all the pity of humanity... we ought to lament and deplore the necessity of holding our fellow-men in bondage. But is it practicable, by any human means, to liberate them without producing the most dreadful and ruinous consequences?\"\n\nWas it practicable? It would indeed have been possible to free the slaves voluntarily. Thousands of slaveowners did, including Robert Pleasants, in some cases because they got religion and in others simply because they despised the slave system they had been born into as hereditary slaveowners. But it was not \"practicable\"\u2014not because, as Henry, Jefferson, and most other slaveowners assumed, freeing the slaves would unleash the criminality they believed was inherent in the enslaved, but because to do so would have made their former owners poor.\n\nTo manumit one's slaves was to make a ruinous financial sacrifice. Without slaves, Virginia would be destitute; with them, she was the wealthiest of the states. With slavery having been built into the deepest levels of the colonial Virginia economy during the seventeenth century, there was no way to get rid of it by Patrick Henry's time, short of all of the slaveowners voluntarily impoverishing themselves. The historical record amply demonstrates that most slaveowners were not only not willing to do this, but would hurl the poorer class of their society against cannonballs first.\n\nThat the War of Independence resulted in the strengthening, not the termination, of slavery was not an unexpected outcome for Southerners: protecting slavery had been the point of the war for them. It was the principal Southern political goal at every moment until slavery was destroyed.\n\n\"Here's to the next insurrection of negroes in the West Indies,\" said the proudly anti-American Dr. Samuel Johnson as he offered a toast at Oxford. In a thirteen-thousand-word pamphlet called _Taxation No Tyranny_ that mocked the inflated rhetoric of the colonists in the last days before war, he wrote in the spring of 1775, \"How is it we hear the loudest yelps for liberty from the drivers of Negroes?\"\n\nPatrick Henry, the loudest of all the voices for liberty, was the perfect example of the colonists being caricatured by Johnson, though no one who heard Henry orate ever described his voice as a \"yelp.\" Dr. Johnson continued his essay by proposing to arm the colonists' slaves:\n\nIt has been proposed, that the slaves should be set free, an act, which, surely, the lovers of liberty cannot but commend. If they are furnished with firearms for defence, and utensils for husbandry, and settled in some simple form of government within the country, they may be more grateful and honest than their masters.\n\nAs Dr. Johnson knew full well, though the colonial tax protestors might feel emboldened to stand up to London, their more serious threat came from closer to home. After Dunmore's proclamation, which put the idea espoused by Dr. Johnson into practice, enslaved people in Virginia began voting with their feet.\n\nBy December 23, 1775, Henry was writing Edmund Pendleton, who as president of the Virginia Committee of Safety was Virginia's highest-ranking official, from Williamsburg: \"SIR: I have the pleasure to inform you... that we have taken a Vessel of the Govt. bound to the Eastern shore for provisions, commanded by Capt. Collett & manned with 16 Negroes.\" Not only the \"Govt.,\" but \"Negroes,\" were Henry's enemies in war. The enslaved overwhelmingly sided not with Henry's vision of liberty, which was their slavery, but with the British who offered them freedom.\n\nThe paradox of liberty versus slavery at the nation's birth is no paradox at all. Liberty was the right to property. Slaves were property. Liberty for slaveowners meant slavery for slaves.\n\nViewed from the slaveowners' perspective, liberty _was_ slavery. It was made much easier by\u2014indeed, almost required\u2014believing something that resonated with the Calvinist doctrine of predestination: those who were enslaved were those who were naturally inferior. God had made them that way for a reason, and they were easy to visually identify.\n\nIn Thomas Jefferson's celebrated reworking of George Mason's \"all men are by nature equally free and independent\" into the catchier, more deistic \"all men are created equal,\" the thirty-three-year-old Virginian was not envisioning a republic in which Barack Obama would be president. In Jefferson's society, black people did not have the legal status as people\u2014\"personhood,\" we call it now\u2014that Lord Mansfield had acknowledged in the _Somerset_ case.\n\nThe later pro-slavery propagandists of the Confederacy were right in insisting that, like them, Jefferson did not intend those words to mean \"all men.\" This is not merely a statement about Jefferson's psychology; there was an existing framework for interpretation of the phrase. When George Mason wrote his version of the phrase as part of the preamble to a new Virginia constitution, it met with objections from planters, who saw it as an incitation to slave rebellion. Donald L. Robinson writes: \"Defenders of Mason's language replied that the clause could not have this effect because it did not apply to Negroes, since Negroes were not 'constituent members' of the society being formed.\" Nor did anyone think it applied to Native Americans. \"All men\" did not mean _all_ men, any more than it meant women, but it was a politically useful phrase, since those opposed to slavery could read into it what they wanted.\n\nIn drafting the document (his authorship of it was generally not known at the time), Jefferson needed to please the French, who wanted a political commitment on the Americans' part before they in turn would commit to an overt war against Britain in America yet again, after having gotten kicked off the continent not twenty years before. Though Britain's naval power was supreme, its army boasted nowhere near the manpower of France's, which was the largest in Europe.\n\nNor, despite the citation of it fourscore and seven years later in Lincoln's Gettysburg Address, was Jefferson declaring the existence of a new nation. The Declaration announced the birth of, in Garry Wills's words, \"not one country, but thirteen separate ones\" that were forced to form a \"league\" in order to attract foreign aid for the war they were fighting together.\n\nJefferson's document was not the legal declaration of independence; that had been made by the Continental Congress on July 2, with the passage of the Virginian Richard Henry Lee's resolution that \"these United Colonies\" were \"free and independent states,\" and note the plural. Jefferson's Declaration, which took on a mythical glow with the passage of years, announced the passage of Lee's resolution. The French participation in the American uprising took two more years to codify, in the commercial treaty of February 6, 1778.\n\nDespite Jefferson's expressed misgivings about slavery during his early years and his frequently quoted bits of antislavery-sounding rhetoric and philosophical reflection, his actions make it clear where he stood on the subject in practical terms: African Americans in republican Virginia were property, period. He did his best to sound like a French _philosophe_ when he inserted that word: life, liberty and the pursuit of... _happiness._ But whether Jefferson's captives, whom he described as laboring for his \"Happiness,\" lived at his mountaintop prison of Monticello or on one of his other parcels of land, they had no right even to keep their own children, though they were mostly allowed to. Nor did Jefferson at any time express any intention of ultimately extending the franchise to them, ever.\n\nIn his draft of the Declaration, Jefferson included a complaint against the king for the slave trade:\n\nhe has waged cruel war against human nature itself, violating it's most sacred rights of life & liberty in the persons of a distant people who never offended him, captivating & carrying them into slavery in another hemisphere, or to incur miserable death in their transportation thither. this piratical warfare, the opprobrium of infidel powers, is the warfare of the CHRISTIAN king of Great Britain. determined to keep open a market where MEN should be bought & sold, he has prostituted his negative for suppressing every legislative attempt to prohibit or to restrain this execrable commerce...\n\nThen he evoked the terrorism of Lord Dunmore:\n\nand that this assemblage of horrors might want no fact of distinguished die, he is now exciting those very people to rise in arms among us, and to purchase that liberty of which he had deprived them, & murdering the people upon whom he also obtruded them: thus paying off former crimes committed against the liberties of one people, with crimes which he urges them to commit against the lives of another.\n\nIt was slickly done. The slaveowner denied all American agency in slavery. He threw all the blame for the slave trade on Britain, thereby exonerating the slave-ship captains of Rhode Island, the many slave dealers throughout the colonies, and the eager buyers who patronized slave sales. The slave trade was an easy target: it was genuinely unpopular, and not only for its sheer ugliness. The traffic to North America was mostly conducted by British ships, with a corresponding loss of profit to Americans. It was out of the control of colonial legislatures, which at times wanted to regulate the supply of Africans on the market by shutting it off. Every slave ship lowered the resale value of slaves already in the colonies, and Virginia already had an oversupply. The arrival of so many Africans was terrifying to the nonslaveowning majority of whites, who tended to see them the way they were generally portrayed in the political discourse of the day, as a socially destabilizing and potentially violent element.\n\nThough Jefferson cloaked his complaint in \"moral dress\" (Robinson's term), it was a complaint against the African slave trade, not against slavery itself; but the section was struck out at the insistence of the congressmen from South Carolina and Georgia, who were not against the slave trade at all.\n\nWhile Jefferson was a member of the Virginia House of Delegates between 1776 and 1779, he obtained a prohibition of the slave trade into the state\u2014but, tellingly, not out of it. One of his best-known achievements of those years was his successful campaign to end the aristocratic institutions of primogeniture (the first son received the entire inheritance) and entail (landholdings could not be broken up) in Virginia. Georgia was the first state to ban primogeniture and entail entirely, in its constitution of 1777; all the other states prohibited them as well. Though these institutions were not vigorously in force in Virginia at the time of their prohibition, abolishing primogeniture and entail was unquestionably a democratizing move\u2014for whites. But the resulting distribution of land among more men of the family (and thus the franchise, for only men of property could vote) meant breaking up more black families, who were divided up along with the estate.\n\nJefferson biographer Dumas Malone recalled in 1967 his conversation with \"a traditional Virginia lady more than forty years ago. This _grande dame_ began by asserting that 'Mr. Jefferson undermined the family.' Her reference was to the abolition of entails and primogeniture, which were supposed to safeguard family estates and family lines. Continuing, she said, 'he wrecked the church,' the reference being to the disestablishment in Virginia shortly after the American Revolution. 'In fact,' she triumphantly concluded, 'the only decent institution he left us was slavery.'\"\n\nThis flurry of lawmaking could have proceeded along a different line than it did. The Virginia delegates did not throw out the established body of law and create a new one from scratch; instead, they retained and modified the existing law regarding slavery. John Quincy Adams commented retrospectively on the process in 1831:\n\nThe principle of setting aside the whole code of their legislation would of itself have emancipated all their slaves. In renovating their code, they must have restored slavery after having abolished it; they must have assumed to themselves all the odium of establishing it as a positive institution, directly in the face of all the principles they had proclaimed....\n\nIt was easier to abolish the law of primogeniture... the bill on the subject of slaves was a mere digest of the existing laws respecting them, without any intimation of a plan for a future and general emancipation.... Mr. Jefferson contents himself with a posthumous prophecy that [emancipation] must soon come, or that worse will follow.\n\n_Partus sequitur ventrem_ came through the Revolution intact, as did the rest of Virginia law regarding slaves, all of which had been made by the Virginia House of Burgesses and none of which was British law.\n\nWhen Patrick Henry was governor of Virginia, at war in 1777, he signed a bill written by Jefferson to regulate and discipline the militia. Every free man in Virginia was expected to join it, including indentured servants and free men of color, with a list of exceptions (professors at William and Mary, for example). Jefferson stipulated that \"the free mulattoes in the said companies or battalions shall be employed as drummers, fifers, or pioneers,\" which meant that men of color were to be required to participate in combat, but were not to have guns.\n\nLord Dunmore had offered freedom to the enslaved, and military commissions, but the best Jefferson could do was to put free people of color on a battlefield as \"pioneers.\" That word may evoke covered wagons to some, but its prior military use meant those who went out in front of the army to dig trenches, one of the most dangerous of positions. _Pioneer_ is etymologically related to _pawn_ and to _peon_ , and roughly synonymous with the French military term _avant-garde._ Virginia's militia, according to Jefferson, was to be an all-white force except for the musicians and the free black avant-garde, who would not have weapons to defend themselves with.\n\nWriting from Charlottesville on January 20, 1779, Thomas Anburey, a lieutenant in the British army who kept an extensive journal and who was clearly not a sympathetic observer, described in detail the typical Virginia planter as an idle character, then went on to outline the work day:\n\nIt is the poor negroes who alone work hard, and I am sorry to say, fare hard. Incredible is the fatigue which the poor wretches undergo, and that nature should be able to support it; there certainly must be something in their constitutions, as well as their color, different from us, that enables them to endure it.\n\nThey are called up at day break, and seldom allowed to swallow a mouthful of homminy, or hoe cake, but are drawn out into the field immediately, where they continue at hard labour, without intermission, till noon, when they go to their dinners, and are seldom allowed an hour for that purpose; their meals consist of homminy and salt, and if their master is a man of humanity, touched by the finer feelings of love and sensibility, he allows them twice a week a little fat skimmed milk, rusty bacon, or salt herring, to relish this miserable and scanty fare. The man at this plantation, in lieu of these, grants his negroes an acre of ground, and all Saturday afternoon to raise grain and poultry for themselves. After they have dined, they return to labor in the field, until dusk in the evening; here one naturally imagines the daily labor of these poor creatures was over, not so, they repair to the tobacco houses, where each has a task of stripping allotted which takes them up some hours, or else they have such a quantity of Indian corn to husk, and if they neglect it, are tied up in the morning, and receive a number of lashes from those unfeeling monsters, the overseers, whose masters suffer them to exercise their brutal authority without constraint. Thus by their night task, it is late in the evening before these poor creatures return to their second scanty meal, and the time taken up at it encroaches upon their hours of sleep, which for refreshment of food and sleep together can never be reckoned to exceed eight.\n\nWhen they lay themselves down to rest, their comforts are equally miserable and limited, for they sleep on a bench, or on the ground, with an old scanty blanket, which serves them at once for bed and covering, their cloathing is not less wretched, consisting of a shirt and trowsers of coarse, thin, hard, hempen stuff, in the Summer, with an addition of a very coarse woollen jacket, breeches and shoes in Winter. But since the war, their masters, for they cannot get the cloathing as usual, suffer them to go in rags, and many in a state of nudity.\n\nThe female slaves share labor and repose just in the same manner, except a few who are term'd house negroes, and are employed in household drudgery.\n\nThese poor creatures are all submission to injuries and insults, and are obliged to be passive, nor dare they resist or defend themselves if attacked, without the smallest provocation, by a white person.\n\nIn 1779 at the urging of Jefferson, who had at this time been elected governor of Virginia, the state's capital was moved inland from Williamsburg to Richmond\u2014farther away from Washington's home turf and closer to Jefferson's. In the first days of 1780, Jefferson and his family fled Richmond for Monticello\u2014his wife Martha Wayles Jefferson had an infant in her arms\u2014to escape Benedict Arnold's troops as they entered the new capital.\n\nThe British began a victorious forty-day siege of Charles Town on March 5, 1780, and after the city surrendered en masse, they occupied the city until the end of 1782, almost three years, with an army whose ranks included\u2014to the white population's great discomfort\u2014armed black men. Escaped slaves came to occupied Charles Town to seek refuge.\n\nLord Charles Cornwallis invaded Virginia in 1781, plundering and bringing liberated slaves along in an entourage that was larger than any town in Virginia, but from there, he went directly on to defeat at Yorktown. During that invasion, shortly after Jefferson's term as governor expired, the Jeffersons\u2014Martha was pregnant\u2014fled the British again, this time from their home in Monticello, to escape a troop led by Cornwallis's Lieutenant Colonel Banastre \"Bloody\" Tarleton. Adding to the insult, Cornwallis used Monticello as a base for a few days while the Jeffersons hid.\n\nIt was as close to being in combat as Jefferson ever came, unless you count peering through the Venetian blinds of his carriage in the streets of Paris in 1789. He was subsequently called on to defend his alleged cowardice as governor in a formal proceeding, which Jefferson believed to have been instigated by Patrick Henry. Sixteen years later, when Jefferson was running for president against John Adams, his nemesis Alexander Hamilton wrote mockingly (and pseudonymously) of the occasion that the \"governor of the ancient dominion dwindled into the poor, timid philosopher and, instead of rallying his brave countrymen, he fled for safety from a few light-horsemen and shamefully abandoned his trust.\"\n\nBut then, Hamilton was a bona fide war hero. Born illegitimate in Charlestown, the capital of the tiny Antillean island of Nevis, he had distinguished himself in active military service during the long War of Independence, serving as Washington's aide-de-camp during the horrendous winter at Valley Forge. Rising through war, in 1780 he married one of the most eligible rich young women in New York\u2014Elizabeth Schuyler, a slaveowner.\n\nIn April 1780, George Washington received word that Louis XVI was sending six thousand troops in ten ships of the line* and thirty transports, with one of France's most distinguished generals, Jean-Baptiste-Donatien de Vimeur, Comte de Rochambeau, at the head, all to be placed under Washington's command. Financed via Havana, the white-uniformed French troops, who tripled the size of the US army, paid for their purchases in gold and silver, endearing them to local merchants. Virginia was grateful to Louis XVI, and on May 1, Governor Jefferson signed the Virginia General Assembly's charter for a new port town: Louisville, on the Ohio River in the part of Virginia that would become Kentucky.*\n\n_French cannon, dated 1761, on the grounds of Yorktown battlefield, June 2013._\n\nIn the late days of the war, there were various plans and proposals to arm black regiments, as in Maryland in 1781, when Charles Carroll of Carrollton wrote his father indicating he would not oppose such a measure: \"nothing but the exigency of the occasion, & the total want of money can excuse such hars[h] & violent measures.\" Henry Laurens tried to act as though he were taking seriously his son John's proposal for a black regiment in South Carolina, but no such plan came to fruition.\n\nOne of the decisive battles of the War of Independence was not fought by Americans at all. The Battle of the Capes was a days-long encounter at sea between Fran\u00e7ois Joseph Paul de Grasse's French fleet\u2014whose expedition was financed by a substantial loan from Havana, because Spain also had an interest in defeating the British\u2014and Sir Thomas Graves's smaller British fleet. Beginning September 5, 1781, the French blockade at the mouth of the Chesapeake resulted in the British Navy's withdrawal to New York, cutting off Cornwallis and his army from escape by sea.\n\nThe decisive assault of the Siege of Yorktown, the storming of the redoubts with bayonets on October 19, was accomplished by two stealth groups of four hundred handpicked troops that included black troops from the Rhode Island Regiment on one side, commanded by Alexander Hamilton, and a French team on the other. Once the redoubts had been attacked, two columns attacked the British: George Washington led the left column, and Rochambeau the right. In that decisive campaign against the British, French soldiers formed the majority of those on the battlefield.\n\nAbout half of the British forces were sick with malaria. Cornwallis abandoned the escaped slaves in his train, many of whom were dying. Jefferson noted that besides destroying his crops and livestock, Cornwallis \"carried off also about 30. Slaves,\" 27 of whom he believed had died \"from the small pox & putrid fever then raging in his camp.\" He and his compatriots expected idemnification from the British for their property.\n\nThe Americans' southern flank in the war was covered by Louisiana's Spanish governor, the general Bernardo de G\u00e1lvez, who led a group that took back West Florida (Mobile), though not East Florida (Pensacola), for Spain. A number of G\u00e1lvez's troops were black\u2014battalions of _pardos_ and _morenos_ constituted about a third of Spain's fighting force in the Americas generally\u2014and a number of them were what might fairly be called Cubans, though a distinct Cuban national identity did not yet exist.\n\nNegotiations for war's end began in April 1782, culminating in the signing in November 1783 of the Treaty of Paris. The British side of the negotiations was led by the man George III believed the \"fittest Instrument for the renewal of... friendly intercourse\": the slave trader Richard Oswald, who had lived in Virginia and unlike most other Britons had a realistic notion of what America and the Americans were like. Oswald seems to have been chosen in part because of his acceptability to American negotiator Benjamin Franklin, to say nothing of another American negotiator, Oswald's former factor Henry Laurens, who arrived late in the process. Oswald allowed his old friend to insert at the last moment a clause prohibiting the \"carrying away any Negroes or other property of the American Inhabitants.\" When the treaty was ratified by the Confederation Congress in Annapolis in 1784, Laurens was its president.\n\nAmong its other accomplishments, the Treaty of Paris retroceded East Florida from Britain to Spain; Oswald knew from experience that Florida was, in Laurens's words, \"a Paradise from whose Bourn no Money e'er returns.\" Africans had been imported to Florida as plantation slaves during twenty years of British rule, and during the War of Independence the territory had been a haven for Loyalist planters fleeing the war with their slaves. Now it would be Spanish again, and again San Agust\u00edn could be a haven for the escaped enslaved of Georgia and Carolina.\n\nThough the Treaty forebade the carrying away of human property, Sir Guy Carleton, the Irish commander-in-chief of British forces in North America, considered that those who had crossed behind British lines were free, and as soon as the spring weather of 1783 permitted, he began a flotilla that between April and November took some three thousand of Britain's black allies to Nova Scotia, beyond the reach of re-enslavement. Their names were recorded in a document called _The Book of Negroes;_ descendants still live in Canada, mostly in Halifax. But life was difficult in Nova Scotia, and more than twelve hundred of them went on to Sierra Leone in 1792.\n\nOther black soldiers opted for military careers in the Black Carolina Corps, formally organized in 1779. A career outfit, it was evacuated to Jamaica following the defeat at Yorktown in 1781. Its success spurred the further Africanization of Britain's army in the Caribbean, leading in 1795 to the creation of the West India Regiment\u2014a standing infantry of free black and enslaved soldiers. In order to fill out its ranks, the British army on occasion resorted to buying African captives off the slave ships and putting them to work as soldiers. Buying some 13,400 slaves for this purpose between 1795 and 1808, at the considerable cost of about \u00a3925,000, the British government became one of the largest customers of the same African trade that many in Parliament were working to abolish.\n\nAs peace negotiations got under way, some French aristocrats remained in North America, where they were the toast of society. The Marquis de Chastellux, a major general at Yorktown under Rochambeau, took Jefferson up on his invitation to visit him at Monticello in April 1782, where Jefferson was living in what he said was retirement from public affairs. Chastellux remained at Monticello for four days with his entourage of ten, six of whom were servants.\n\nMartha Wayles Jefferson had to provide hospitality for them. She had been pregnant almost constantly for ten years, throughout the war, and though she was, in Chastellux's description, \"amiable,\" she was in the habit of retiring early and seems to have been depressed, as she was, in Chastellux's words, \"expecting her confinement at any moment\" in the pregnancy that would finally kill her. Chastellux and Jefferson stayed up after Mrs. Jefferson had gone to bed, talking about, among other topics, their mutual enthusiasm for the poems of Ossian\u2014about which, more later.\n\nMartha gave birth in May for the last time, and died in September. Jefferson, who attended her for four months continually as she declined, was prostrate with grief on his wife's death. This has provided a dramatic scene in many Jefferson biographies, though his obvious agency in her repeated pregnancies has often gone circumspectly unmentioned.\n\nThere is no clue in Jefferson's papers that he saw himself as playing any part in his wife's death through continual impregnation in the face of her continually weakening condition, despite Jefferson's clear awareness of the mechanics of sexual reproduction. Nor was Jefferson unaware of what we now call family planning, as per his description of Native American women in _Notes on the State of Virginia:_ \"The women very frequently attending the men in their parties of war and of hunting, child-bearing becomes extremely inconvenient to them. It is said, therefore, that they have learnt the practice of procuring abortion by the use of some vegetable; and that it even extends to prevent conception for a considerable time after.\"\n\nLet us be clear that we are not guilty of the present-day bugaboo of \"presentism\" by noting that women in Jefferson's day were expected to be pregnant constantly. Our point is to call attention to the difference between the mindset of Jefferson's world and that of ours: it was commonly considered women's duty to produce babies nonstop, whether it killed them or not. We differ, however, with the interpretation offered by Jon Meacham, who suggests that Martha Wayles Jefferson's fatal continuum of pregnancy (Meacham suggests she may also have had tuberculosis) was evidence of \"no shortage of physical passion between them.\" We propose an alternate interpretation: that her repeated, debilitating pregnancies might be evidence that a dutiful wife had no right to say no.\n\nOn her deathbed, according to the later recollections of the enslaved women who attended her while dying, she exacted an oath from Jefferson never to remarry, which would have compromised their daughters' inheritance. But we don't know what Martha Wayles Jefferson thought, confined to die in her bed on that isolated mountaintop. Jefferson, so conscious of his own immortality through writing, burned her letters, thus erasing her voice from historical memory. We have not even a picture of her.\n\nThe forlorn widower returned to public life, accepting the appointment to serve the presidentless, moneyless American Confederation as US Minister Plenipotentiary\u2014basically, the trade representative\u2014to France in 1784, where he remained until 1789. John Adams, who unlike Jefferson was an experienced diplomat, performed the same function in London.\n\nChastellux, who helped get Jefferson's daughter Patsy into a good school in Paris, published in 1786 an account of his travels that helped promote the Jefferson mystique in France\u2014an early flash of the enduring legend of the mountaintop sage of Monticello. In it, he noted the abject condition of Virginia's poor whites and connected it to the Virginia slaveowners' desire for \"increase\":\n\nHumanity [suffers] from the state of poverty in which a great number of white people live in Virginia. It is in this state, for the first time since I crossed the sea, that I have seen poor people. For, among these rich plantations where the Negro alone is wretched, one often finds miserable huts inhabited by whites, whose wane looks and ragged garments bespeak poverty.... I have since learned that all these useless lands and those immense estates, with which Virginia is still covered, have their proprietors. Nothing is more common than to see them possessing five or six thousand acres of land, but exploiting only as much of it as their Negroes can cultivate. Yet they will not give away or even sell the smallest portion of it, because they are attached to their possessions and always hope to eventually increase the numbers of their Negroes.\n\nIn Paris, where printing was much cheaper than in America, Jefferson in 1785 privately published _Notes on the State of Virginia_ , first drafted in 1781 as an answer on the part of Virginia to a questionnaire put to the various states by Fran\u00e7ois de Barb\u00e9-Marbois, the secretary of the French legation to the United States. The only book Jefferson ever published, it was intended to pitch the wonders of his state to the wealthy French. Jefferson printed two hundred copies privately and semi-anonymously (the author was \"M. [Monsieur] J***\") for individual distribution in elite circles only. When he sent one to James Madison, he wrote, perhaps disingenuously, \"I shall only send over a very few copies to particular friends in confidence and burn the rest... in no case do I propose to admit them to go to the public at large.\" But they did.\n\nA French bookseller who acquired a copy after its owner unexpectedly died jobbed it out to a \"hireling translator\" and published it in French in 1786. The book was favorably reviewed in the _Mercure de France_ , who proclaimed the barely anonymous author a _philosophe._ Jefferson, who disliked the translation, then allowed his English version to be published in London the following year.\n\nIn composing what amounted to an intellectual investment prospectus for the state he represented, Jefferson faced the problem of having to explain to the French why the enslaved of his country would never be freed. Most of his friends in France were abolitionists who expected the postrevolutionary United States to bring slavery to an end. But Jefferson's Virginia countrymen overwhelmingly had no intention of ever freeing their slaves and thus losing their property, and were touchy about the issue.\n\nJefferson did not make the true argument, which would have been that he and all his relatives, friends, and constituents would be paupers without slaves. Rather, his justification was that the \"negro\" was inferior\u2014something he seems to have truly believed\u2014and moreover dangerous, and therefore had to be kept in a state of slavery for everybody's good. This problem, as Jefferson insisted throughout his career, was due not to the greed of the colonists themselves, but to British insistence on imposing slavery on the colonies in the first place, leaving the wealthy of Virginia no choice, so went the story, but to soldier on with their white man's burden of ever-increasing human property.\n\nIt's not an oversimplification to say that Jefferson despised blackness. The most inflammatory quote from _Notes_ has been frequently reprinted in recent years after being largely overlooked, and we too will include it for purposes of clarity, with apologies to the reader:\n\n[T]he difference [of \"the negro\"] is fixed in nature, and is as real as if its seat and cause were better known to us. And is this difference of no importance? Is it not the foundation of a greater or less share of beauty in the two races? Are not the fine mixtures of red and white, the expressions of every passion by greater or less suffusions of color in the one preferable to that eternal monotony, which reigns in the countenances, that immovable veil of black which covers the emotions of the other race? Add to these, flowing hair, a more elegant symmetry of form, their own judgment in favor of the whites, declared by their preference of them, as uniformly as is the preference of the Oranootan for the black woman over those of his own species.\n\nWith his evocation of \"the Oranootan\" copulating with black women, Jefferson provides an early instance of the fundamental racist trope that Felipe Smith calls the ape libel. Because \"negroes\" were an inferior \"race,\" Jefferson argued, they could not be freed. To do so would require their immediate deportation, he insisted, in order to avoid the amalgamation that would stain the purity he detected in the white \"race\":\n\nThis unfortunate difference of colour, and perhaps of faculty, is a powerful obstacle to the emancipation of these people... The [Roman] slave, when made free, might mix with, without staining the blood of his master. But with us [in America] a second is necessary, unknown to history. When freed, he is to be removed beyond the reach of mixture.\n\nThe notion of \"racism\" did not yet exist; the French term _racisme_ was coined in the late nineteenth century. But if this call to maintain purity of blood is not racism, the word has no meaning. James Madison, who never freed any of his slaves in life or death, was a racist of the same stripe, who believed abolition impossible because of \"the physical peculiarities of those held in bondage, which preclude their incorporation with the white population.\"\n\nWith _Notes of the State of Virginia_ , Jefferson definitively established himself as a founding theorist of white supremacy in America, laying out in condensed form key points of racialized thought that pro-slavery writers would consistently reaffirm and that would echo in the cant of modern day white supremacists. He linked his ideas to a deportation scheme that was, in effect, a foolproof way to avoid ending slavery, though he didn't package it like that. Quite the contrary: he pitched his impossible project as the only way slavery could be ended.\n\nJefferson insisted that manumission required the immediate deportation of the emancipated. This would be necessary, Jefferson explained, in order to avoid \"convulsions which will probably never end but in the extermination of the one or the other race.\" To avoid this conjectured race war of annihilation, emancipation required what is now called ethnic cleansing: Jefferson stamped that demand with a founder's seal and a philosopher's sigh.\n\nThe reviewer for the _Mercure_ waxed enthusiastic about Jefferson's solution for the problem of slavery. That Jefferson would consider emancipation under _any_ circumstances and would speak badly of slavery, even in abstract terms, was enough to trip the hair-trigger anger of many American slaveowners, which is perhaps why he had wanted to keep the book off the general market. It cost him some political support, especially in South Carolina.\n\nJefferson's plan was to deport flotillas of black youth, in wave after wave, year after year. He would \"by degrees, send the whole of that population from among us,\" until the \"race\" itself was gone, and simultaneously replace them with white immigrant laborers\u2014a plan for total removal that did not acknowledge the presence in the United States of free people of color. In _Notes on the State of Virginia_ , he proposed:\n\nthat they should continue with their parents to a certain age, then be brought up, at the public expence, to tillage, arts or sciences, according to their geniusses, till the females should be eighteen, and the males twenty-one years of age, when they should be colonized to such place as the circumstances of the time should render most proper, sending them out with arms, implements of household and of the handicraft arts, feeds, pairs of the useful domestic animals, &c. to declare them a free and independant people, and extend to them our alliance and protection, till they shall have acquired strength; and to send vessels at the same time to other parts of the world for an equal number of white inhabitants; to induce whom to migrate hither, proper encouragements were to be proposed.\n\nTo better understand what Jefferson had in mind, we flash forward to a February 4, 1824, letter he wrote to Jared Sparks, the Unitarian minister who published the _North American Review._ In it, the eighty-year-old Jefferson outlined a scheme for accomplishing the \"colonization\" that would rid the United States of its proliferating African Americans once and for all, before they got any more numerous, and proposed a timetable for accomplishing the expulsion of about a sixth of the nation's population:\n\nthere are in the US. a million and a half of people of colour in slavery. to send off the whole of these at once nobody conceives to be practicable for us, or expedient for them. let us take 25. years for it's accomplishment, within which time they will be doubled. their estimated value as property, in the first place, (for actual property has been lawfully vested in that form, and who can lawfully take it from the possessors?) at an average of 200.D. each, young and old, would amount to 600. millions of Dollars, which must be paid or lost by somebody.\n\nJefferson went on to propose the creation of a fund, financed by the sale of western lands, for purchasing infants on the cheap, raising them as wards of the state, and deporting them\u2014to \"St. Domingo\" (he did not ever use the name \"Haiti\"). But, he suggested:\n\nthe estimated value of the new-born infant is so low, (say 12 \u00bd Dollars) that it would probably be yielded by the owner gratis, and would thus reduce the 600,000,000 millions [ _sic_ ] of Dollars, the first head of expence, to 37 millions & a half. leaving only the expense of nourishment while with the mother, and of transportation.\n\nJefferson calculated that though it would take twenty-five years to accomplish the entire project, by the last nine years, the number of \"breeders\" (he used the word) would have diminished considerably. He imagined a fleet of fifty vessels recursively sailing away full of black youth and coming back empty for more until every last one of _them_ was gone:\n\nsuppose the whole annual increase to be of 60 thousand effective births, 50 vessels of 400 tons burthen each, constantly employed in that short run, would carry off the increase of every year, & the old stock would die off in the ordinary course of nature, lessening from the commencement until it's final disappearance. in this way no violation of private right is proposed.\n\nThe \"private right\" Jefferson was talking about was, of course, that of all those men who were created equal. Black people did not have \"private right.\" But separating them from their children was not all that bad, thought Jefferson, because, as he explained in _Notes,_\n\nTheir griefs are transient. Those numberless afflictions, which render it doubtful whether heaven has given life to us in mercy or in wrath, are less felt, and sooner forgotten with them. In general, their existence appears to participate more of sensation than reflection.\n\nThis was the classic rationalization for minimizing the damage caused by systematically destroying African American families, and it was a libel: being simple creatures, they'd get over it. Accordingly, Jefferson concluded his letter to Sparks: \"The separation of infants from their mothers... would produce some scruples of humanity. But this would be straining at a gnat, and swallowing a camel.\"\n\nWere the United States not purged of its black people soon, Jefferson warned Sparks, the demographics guaranteed armed slave resistance: \"A million and a half are within [slaveowners'] control; but six millions, (which a majority of those now living will see them attain,) and one million of these fighting men, will say, 'we will not go.'\" This did in fact happen, though the numbers were different: there were four million enslaved African Americans in 1860, not six million; and there were officially 186,097 soldiers and sailors who fought in the US Army and Navy against the Confederacy, in effect saying, \"we will not go.\"\n\nConfiscate all African American children from their mothers and ship them off to thrive or die: _that_ was Jefferson's vision of a final solution for the Negro problem. Presumably such a massive expulsion as Jefferson contemplated would have required a fully totalitarian state apparatus to implement, and would have resulted in the death of many of the deported; mortality rates were high in the few miserable \"colonization\" attempts that were made.\n\nJefferson had not suddenly gone mad in his dotage. This had been his idea all along, as he explained to Sparks: \"This was the result of my reflections on the subject five and forty years ago, and I have never yet been able to conceive any other practicable plan. It was sketched in the Notes on Virginia, under the fourteenth query.\" If this kind of massive deportation couldn't be achieved, he insisted throughout his career, emancipation could not take place. This conviction would be strengthened by the Haitian Revolution that erupted in 1791 and by Gabriel's unenacted rebellion of 1800, and would be taken as gospel by pro-slavery Southerners. It would spur the founding of the American Colonization Society, whose ostensible mission was to deport all free people of color.\n\nHaving outlined the \"physical\" reason for exile in _Notes_ , Jefferson proceeded to the \"moral\" reason, pursuant to which he described a long list of inferiorities attributed to \"them,\" which we will not quote here. This was perfectly in line with the thinking of many European intellectuals. Citing David Hume, the leading light of the Scottish Enlightenment, Immanuel Kant had written in _Observations on the Feeling of the Beautiful and the Sublime_ (1764) that \"The Negroes of Africa have by nature no feeling that arises above the trifling. Mr. Hume challenges anyone to cite a single example in which a Negro has shown talents and asserts that among the hundreds of thousands of blacks who are transported elsewhere from their countries [etc]...\" But the point was less urgent to Kant, whose wealth did not consist of black people, than to Jefferson and Madison.\n\nA mere seventy-five years later, as Southern states left the Union, prosecessionist radicals argued to their unconvinced countrymen some of the same points as Jefferson's: the \"negro\" was inferior and not the equal of whites; emancipation would result in a race war to the death, or in the purity of the white race being sullied by the horror of mongrelization; and slaveowners' property rights must be respected.\n\nThere was, however, a solution of sorts to the perceived problem of black overpopulation, and it was highly profitable: if Virginia's black people could not be emancipated and deported, they could be sold away into the new territories.\n\nAll the states had prohibited the African slave trade by the time non-importation cut off exterior commerce during the independence struggle, so Africans had not been entering the colonies for years. With independence achieved, South Carolina and Georgia, whose labor forces had massively taken flight or died, reopened their slave trades. As Charles Town's slave market boomed, it changed its name in 1783 to the less regal Charleston. According to James McMillin, \"between 1783 and 1787 nearly one hundred Charleston merchants handled slave sales ranging from one person to cargoes of more than four hundred Africans.\" But there was soon a glut on the market as slavers from multiple territories, most numerously British but also from Rhode Island, tried to get in on the action, depressing point-of-sale prices in America and raising point-of-supply prices in Africa.\n\nThe slave trade continued being a cash business for the captains who brought in the cargoes, so an intermediate class of British factors\u2014still very much active in the independent republic\u2014brokered the sales to the planters on easy terms, with up to two years to pay. Though some of the factors became wealthy, there wasn't much money coming into the territory. The large market for American indigo died with independence, never to return, because Britain ended the subsidy that had made it profitable. The rice economy recovered only slowly.\n\nA boom in slave sales meant a debt problem as well. The eagerness of planters to buy slaves drained the supply of specie from the economy, and many individuals were carrying excessive debt burdens. \"The great quantity of negroes now pouring in upon us, occasions every planter to wish an increase of his stock,\" said Thomas Bee before the South Carolina Enquiry into the State of the Republic in 1785. \"The sight of a negroe yard was to[o] great a temptation for a planter to withstand, he could not leave it without purchasing; in short, there seemed to be a rage for negroes, without any consideration how they were to be paid for.\" Then Charleston's economy crashed, and in 1787, drowning in debt, the South Carolina legislature prohibited slave importation after a spirited debate.\n\nSouth Carolina's closure of the foreign slave trade increased the traffic to Georgia, where the trade remained open until 1798, with an illicit trade continuing afterward. More Africans entered Georgia after independence than before, but not so many as the planters would have liked: less credit was available to Georgia planters from merchants, so the state's economy incurred less of a debt burden than it might have, but since less labor was imported, production came back only slowly. During Georgia's period of importation, two revolutionary developments charted the nation's course:\n\nIn Philadelphia, the Constitution. In Savannah, the sawtooth cotton gin.\n\n*Ships of the line were large, heavily armed vessels that, in battle, formed a line.\n\n*Kentucky was entirely occupied by Native Americans until the first settlement at Harrod's Town, later Harrodsburg, on a surveying expedition ordered by Lord Dunmore in 1774.\n\n#   22\n\n# **The Fugue of Silences**\n\n_Mr. Madison thought it wrong to admit in the Constitution the idea that there could be property in men. 1_\n\n\u2014from James Madison's notes, August 22, 1787\n\n_The bargain between freedom and slavery contained in the Constitution of the United States is morally and politically vicious... The consequence has been that this slave representation has governed the Union. 2_\n\n\u2014John Quincy Adams, 1820\n\nLIKE THE FUGUES OF J. S. Bach (1685\u20131750), the United States Constitution is an exemplary eighteenth-century machine. Like the Bible, it has been taken as scripture by those who imbue it with mystical authority.\n\nNegotiated and agreed on in 1787 at Philadelphia, ratified the following year, and effective as of March 4, 1789, with a ten-amendment Bill of Rights that became effective December 15, 1791, the Constitution is synonymous with the American republic. It prescribes a carefully contrived system of representation that regulates our national life to this day.\n\nIt's the oldest constitution in effect among the world's nations today, and the hardest to amend. It's remarkably terse, which has contributed to its enduring quality. The later constitutions of some other nations go on for dozens or even hundreds of articles, making promises that cannot be achieved and specifying points of law rather than general principles, with the result that they have to be rewritten at intervals.\n\nAnecdotal evidence would suggest that many twenty-first-century Americans confuse the Constitution, which is the source of US law and was largely drafted by James Madison, with the more poetic Declaration of Independence, which has no legal force and was drafted by Thomas Jefferson. The president swears to uphold the former, but not the latter.\n\nThere is much that the Constitution does not do. It does not state that all men are created equal, nor does it guarantee life, liberty, and the pursuit of happiness. It does not create a democracy; _democracy_ was a dirty word, synonymous with mob rule, when the Constitution was written. With seven articles and ten amendments that have grown to twenty-seven, the US Constitution is a carefully composed fugue of silences that stipulates and limits government's powers.\n\nUntil the adoption of the Thirteenth Amendment on December 6, 1865, the Constitution did not prevent individuals from enslaving or trading in the enslavement of other individuals. Its rhetorical discretion was noted at the time by the Philadelphia physician and Declaration of Independence signer Dr. Benjamin Rush, a cofounder of the first American abolitionist society, who sarcastically wrote, \"No mention was made of _negroes_ or _slaves_ in this constitution, only because it was thought the very words would contaminate the glorious fabric of American liberty and government.\"\n\nThe silences went beyond euphemism. As ratified in 1788, the Constitution neither explicitly prohibited nor permitted slavery, but merely acknowledged its existence as a fact, without even naming it or defining it. But by means of that acknowledgment and its otherwise careful limitation of powers, it gave tacit permission to the long-established practice of enslavement.\n\nThe Constitution implied that there was a class of people\u2014persons \"held to service\"\u2014for whom rights might not apply. It nowhere suggested that enslaved people had any rights at all. It left the way clear for state and local government, and, in practice, for individual slaveowners and slave traders, to construct the world enslaved people would live in.\n\n_We are slaves to Britain!_ the rebels had shouted. It had been absurd for slaveowners to complain they were being subjected to \"slavery,\" but it was the strongest, loudest thing they could say, the most potent word in their political lexicon, the most extreme rhetoric they could deploy. When it came time to write their Constitution, however, the word _slavery_ vanished from the vocabulary, as had the word _negro_ , though there was a considerable body of states' law dealing with \"negroes,\" which the Constitution left untouched.\n\nIn its strategic silence, the Constitution perhaps resembled that genre of painting so popular in the parlors of the eighteenth-century plantocracy, as described in John Michael Vlach's _The Planter's Prospect._ These canvases, which provided bread and butter for skilled American painters, typically depict a static scene organized around an accurately rendered vision of the grand mansion. A pink, chubby, perfectly dressed family poses in front, on their expansive grounds, perhaps with topiary hedges.\n\nNo one is seen working in the idealized plantations of these paintings, though in reality these places were never still but were run by squadrons of slaves. There is nothing in the images to indicate how such a complex system might actually run, or who actually did the work, or what the work was\u2014not so much as a child with a watering can\u2014let alone who did the hard offstage agricultural labor that paid for it all.\n\nWe see no one singing in these paintings, nor are there fiddles, banjos, or bones players. These paintings are lattices of silence. Black people are entirely absent from this visual representation of a life that depended at every moment not merely on their labor, but also on their skills.\n\nThe enslaved workers who made it all run were as absent from the Constitution as they were from the paintings.\n\nAs we have emphasized, slavery is a central fact of American history, not a sidebar. Nor, despite the textual silence, was it a sidebar issue to the Constitution. In devising a national government and a system of representation, the Constitution created lasting political institutions. But the major sticking point was cutting a deal over slavery. How to compromise on an issue about which there could be no compromise? How to speak of a human right to own other people as property? How to stipulate the freedom to enslave?\n\nAnd there was a problem that would only get worse: how to work constructively with violence-prone countrymen who became instantly belligerent the moment slavery was criticized, or even mentioned?\n\nAs early as 1775, John Adams had argued the need for the North American colonies to \"set up a Republican government, something like that of Holland.\"\n\nUpon independence, the former colonists did not form a new nation called America, though that subsequently became its de facto common name, as if the rest of the Americas did not exist. Borrowing a nomenclatural model from the Dutch United Provinces\u2014whose emblem, a lion with nine arrows representing nine provinces in his paw, is echoed in the thirteen arrows in the talons of the eagle in the great seal\u2014they were the United States. They were a crazy-quilt confederation with distinct histories of governance and political identities, and nowhere more so than in the states' differing approaches to slavery.\n\nA collection of individual, independently functioning states would inevitably work at competitive cross-purposes with each other, and would lead to currency wars, tariff wars, even shooting wars. The Articles of Confederation governing the thirteen ex-colonies' alliance had failed. State banks each issued their own money, which complicated interstate commerce considerably. There was no provision to raise funds to run a national government. Against the background of a sharp credit squeeze, Shays' Rebellion\u2014an armed antitax and anti-debt revolt by disaffected elements in rural Massachusetts, including many unpaid war veterans from mid-1786 to mid-1787\u2014pointed up the need for a stronger government to repress insurrections, as well as to find a mechanism for settling the war debts. Jefferson, who was in Paris and thus in no danger from Shays' Rebellion, applauded it from afar, prompting his remark so beloved of the twenty-first-century far right: \"What signify a few lives lost in a century or two? The tree of liberty must be refreshed from time to time with the blood of patriots and tyrants.\"\n\nMeanwhile, a continuing external military threat imperiled American shipping and provided ample potential for conflict\u2014especially with Britain, which did not in practice recognize American sovereignty on the high seas. Spain was in control of the Gulf Coast from Florida to Texas, and of all of Mexico and Cuba. With Indian attacks and slave rebellion as constant worries, a common defense was necessary. Or, to look at it from another perspective: a substantial military force would be needed if the United States was to seize neighboring territory, as South Carolina's elite hoped to do in expanding their empire of slavery, and as some acquisitive New Englanders hoped to do with Canada, which had declined to declare independence as the fourteenth colony.\n\nThe most memorable achievement of the Congress of the Confederation was the poorly drafted Northwest Ordinance, which formally annexed the territory northwest of the Ohio River. It allowed for the settling of present-day Ohio (which became the seventeenth state in 1803), Indiana (the nineteenth, in 1816), Illinois (twenty-first, 1818), Michigan (twenty-sixth, 1837), Wisconsin (thirtieth, 1848), and part of Minnesota (thirty-second, 1858). Britain had restricted immigration to these territories in 1763, following the end of the Seven Years' War, to the frustration of would-be settlers, especially those who had participated in military action against the French and Indians to keep the territory in British hands.\n\nArticle VI of the Ordinance provided that \"There shall be neither slavery nor involuntary servitude in the said territory otherwise than in the punishment of crimes, whereof the party shall have been duly convicted\"\u2014a phrase that would echo in the Thirteenth Amendment of 1865. This was notwithstanding the fact that there were already slaveholders in the territory, but it provided for no enforcement, and there was in any case no federal government to speak of under the Articles of Confederation. The ordinance seemed to confirm the admissibility of slavery south of the Ohio, and it even contained a fugitive slave clause, the first appearance of that explosive notion in American law.\n\nArticle VI was inserted at the last minute in the proceedings by Nathan Dane of Massachusetts, with no prior discussion of slavery and no debate. It's something of a mystery exactly why and how this happened. The immediate model for Article VI was the Land Ordinance of 1784, which provided a mechanism for new states in the Western territories previously claimed by New York and Virginia to enter the United States upon attaining a population of twenty thousand free inhabitants.* The Land Ordinance was largely drafted by Jefferson, who wanted to name the new states Cherronesus, Metropotamia, Saratoga, Polypotamia, Illinoia, Assenisippia, Michigania, and Sylvania, and who, four years before the publication of _Notes_ , already had his eye on possible territories where emancipated black people could be deported. His draft contained a clause prohibiting all slavery in the new territories after 1800, and though that clause was removed at the behest of delegates from farther south, it included a significant exception that echoes down to the twenty-first century: convict labor would be permitted. The Land Ordinance has been pointed to as Jefferson's principal attempt at taking any kind of antislavery action (as opposed to rhetoric); if so, it was also his last. It can also be seen as establishing the template for the ruinous competition for territorial expansion between free-soil North and slavery South. With its language regarding convicts, it might also be interpreted as the first faint stroke of a uniquely American regime of carceral labor.\n\nNo slaves were freed as a result of the Northwest Ordinance, and once the Constitution was adopted, it no longer had legal force. Its major long-range impact seems to have been discouraging the immigration of slaveholders to the Northwest as a new, non-slave system began to assert itself there. The free Northwest of Ohio and beyond became a magnet for European immigration and a bulwark of antislavery politics; it was the region from which Lincoln, Grant, and Sherman emerged.\n\nThe die was cast, then, for a larger country divided into free and slave states. The ordinance was approved on Friday, July 13, 1787, which was also the day that at the Constitutional Convention in Philadelphia enslaved people were transformed into political capital.\n\nThe story of the Constitution's making in 1787 has been told any number of ways, typically suffused with a cue-the-kettledrums aura of religiosity and an assumption of American triumphalism. Constitutional historians have tended to portray their subject as the most important political document in world history, in the greatest nation in history. In extreme cases this has involved elevating the framers to a sort of secular sainthood, as in the post-Reagan years, when a school of constitutional interpretation called \"originalism\" emerged in American jurisprudence. Most prominently associated with archconservative Supreme Court Justice Antonin Scalia, originalism is a fundamentalist movement that seeks in effect to construe the Constitution as static and unchanging by mind-reading the intentions of the presumably divinely inspired Framers\u2014a word Scalia writes with a capital F, the way they did it in the eighteenth century. His opinions are shot through with variations on phrases like: \"The Framers recognized...,\" \"The Framers contemplated...,\" \"The Framers viewed...,\" and \"The Framers' experience...\" This is a peculiarly subjective lens through which to view a document created by so many people, at such sharp cross-purposes with each other.\n\n\"Aware that the South would not join a Union that prohibited slavery,\" writes Scalia's generally dissenting colleague, Supreme Court Justice Stephen Breyer, who does not capitalize \"framers,\" \"the framers in effect postponed the question of slavery's continued existence by writing into the Constitution a series of compromises.\" But if we were to follow the notion of original intent from the point of view of the South Carolina Framers, we would see the Constitution as protecting the right to own and trade in slaves.\n\nThe deliberations for the Constitution began on May 14, 1787, before most of the delegates had arrived. They were done in secret, behind closed doors, with the press excluded. The official minutes were poor, so historians have to rely largely on the nightly recaps written by policy wonk and principal drafter James Madison while many of the other framers were busy drinking.\n\nSlaveowners were on the defensive. When Vermont broke away from New York during the War of Independence to become an independent republic from 1777 to 1791, its constitution abolished slavery outright\u2014the first such constitutional prohibition in the Americas. In 1783, a judicial decision interpreted the 1780 constitution of Massachusetts as abolishing slavery. Pennsylvania, Connecticut, and New Hampshire had all introduced phase-outs. Even Jefferson, in drafting a radical new constitution for Virginia in 1783\u2014it was not even considered, much less adopted\u2014had proposed: \"The General assembly shall not have the power to... permit the introduction of any more slaves to reside in this state, or the continuance of slavery beyond the generation which shall be living on the 31st day of December 1800; all persons born after that day being hereby declared free.\"\n\nEven so, white supremacy was assumed. Washington, who chaired the Convention, brought his lifelong personal manservant Billy Lee. Madison, perhaps fearing a runaway, did not bring any of his slaves to attend him in Philadelphia, but his fellow Virginian George Mason brought at least two of his more than three hundred slaves.\n\nTo achieve the truce that the Constitution represented, it had to be, and was, a pro-slavery document. It was made such largely at the insistence of South Carolina but done with the acquiescence of all. South Carolina's delegates to the Constitutional Convention supported a strong national government as long as they entered it on the most advantageous terms possible. The Lower South had suffered from foreign occupation during the War of Independence more than anywhere else. South Carolina and Georgia were militarily the weakest of the colonies, in no small part because so much of their population, being enslaved, was motivated to fight for the slaveowner's enemy; slaveowners remained at home to suppress slave rebellion and defection rather than fight.\n\nExposed on its southern flank to Spanish Florida, vulnerable to Indian attack and to slave uprisings, South Carolina needed the protection of a larger entity that could provide its defense. But even so, South Carolina's delegates were determined to protect slavery and the African slave trade, and they arrived ready to walk if they didn't get what they wanted.\n\nVirginia\u2014the largest, most populous, and wealthiest state\u2014took the lead at the Convention. Delegate James Madison had seized the advantage in the constitutional negotiations by arriving first with a draft all prepared. His \"Virginia Plan\" was put forth on May 29 by Virginia governor Edmund Randolph, the American-born son of an English aristocrat and an aide to Washington during the War of Independence.\n\n\"Many of the delegates were stunned,\" writes Richard Beeman, \"by the revolutionary character of the proposal so boldly laid before them.\" Madison's plan radically reshaped the structure of what until then had been a weak confederacy into a national government that would be superior to the states. With Beeman's choice of the word \"revolutionary,\" he places the accent of revolution where John Adams would have placed it\u2014not on the military act of separating from a colonial master, but squarely on the civilian idea of making thirteen competing states into one self-governing republic.\n\nThis had not been the grand design everyone was working toward in the long, grinding civil war by which the colonies obtained independence from Britain. The wealthy rebels in each colony had seen themselves as leaders of sovereign states, not provincial officials of a larger entity. Subordination to a federal republic would take power away from them personally, and from their\u2014note the word again\u2014states.\n\nImmediately the question arose of how states would be represented in this supra-state government. The Virginia Plan proposed two ways the \"rights of suffrage\" could be calculated: they would be \"proportioned to the Quotas of contribution\"\u2014that is, they would get votes based on how much in taxes each state put into the kitty\u2014\"or to the number of free inhabitants, as the one or the other rule may seem best in different cases.\"\n\nPopulation or wealth\u2014whichever way it went, Virginia was on top. South Carolina definitively favored voting based on wealth. Max Farrand's compilation of the existing deliberation records reads:\n\nGov. Rutledge [John Rutledge, of South Carolina] moved... that the proportion of representation ought to be according to and in proportion to the contribution of each state.\n\nMr. Butler [Pierce Butler, of South Carolina] supported the motion, by observing that money is strength; and every state ought to have its weight in the national council in proportion to the quantity it possesses.\n\nWealth as the direct basis for apportioning political representation: now _that's_ original intent. As incorporated via the three-fifths clause, it sought to make the new nation into a plutocracy. The Constitution, in somewhat veiled form, made the idea of voting wealth structural to the new nation, capitalizing the enslaved as a way to do so, even as the colonies' transformation into a constitutional republic enhanced the resale value of the Chesapeake's enslaved population.\n\nAccording to James Madison's notes:\n\nOn the motion of Mr. [Edmund] Randolph, the vote of saturday last authorizing the Legislre. to adjust from time to time, the representation upon the principles of _wealth_ & numbers of inhabitants was reconsidered by common consent in order to strike out \"Wealth\" and adjust the resolution to that requiring periodical revisions according to the number of whites & three fifths of the blacks.\n\nMadison also noted the response by Gouverneur Morris of New York:\n\nA distinction had been set up & urged, between the Nn. & Southn. States.... Southern gentlemen will not be satisfied unless they see the way open to their gaining a majority in the public Councils.... If the Southn. States get the power into their hands, and be joined as they will be with the interior Country they will inevitably bring on a war with Spain for the Mississippi. This language is already held. The interior Country having no property nor interest exposed on the sea, will be little affected by such a war. He wished to know what security the Northn. & middle States will have agst. this danger.\n\nPierce Butler retorted, \"The security the Southn. States want is that their negroes may not be taken from them which some gentlemen within or without doors, have a very good mind to do.\"\n\nWhen we speak of the Framers, we do not often speak of Founding Father Pierce Butler, who in a show of unconvincing modesty in a letter to a friend wrote that he had \"some small part in frameing\" the document. Though he was a South Carolina delegate, the very wealthy absentee plantation owner lived, attended by his slaves, in his Philadelphia mansion. In the four-man South Carolina delegation, he was the number-two eminence behind the state's governor, John Rutledge, whose nickname was \"Dictator John.\" One of the eight foreign-born of the fifty-five delegates to the Constitutional Convention, and one of the Constitution's thirty-nine signers, Butler pushed the limit in the negotiations to safeguard slavery.\n\nButler took a few pages of notes at the Convention, on the final page of which he\u2014surely reflecting the tedium of the proceedings\u2014doodled and drew cartoons, preserved today as part of the documentation of the framing of the Constitution. An opinionated, theatrical debater, Butler wore a powdered wig, a velvet neckcloth with a silver buckle, and a gold-laced coat as he delivered outspoken orations calculated to provoke. He was a proponent of a strong national government, an electoral college system, and slavery.\n\nTo placate the Carolinians, the Scottish-born Pennsylvania delegate James Wilson proposed a compromise of sorts, one that took advantage of the prestidigitation of turning people into property. His proposal substituted for the phrase \"quotas of contribution\" the language that became known as the \"three-fifths\" clause, allowing slaveholding states to be represented based on three-fifths of their enslaved inhabitants. The measure was immediately seconded by South Carolina's Charles Pinckney, who in a previous plan had been the first to suggest a three-fifths figure.\n\nThe only compromise South Carolina made was that they didn't get to vote on behalf of 100 percent of their enslaved inhabitants, only 60 percent of them. Butler wanted to hold out for 100 percent representation. But neither was three-fifths an arbitrary formula; Pinckney knew it was the maximum the South could get away with. The three-fifths clause did not mean, as some have complained, that the enslaved were considered only three-fifths human. Politically, the enslaved were zero-fifths human. The three-fifths clause was a politically acceptable accounting gimmick for figuring out how much to rig the national vote on behalf of slaveholders, and it distorted political realities in the United States for as long as slavery lasted.\n\n_Pierce Butler: Notebook from the Constitutional Convention, last page. Philadelphia, 30 May 1787\u201316 July 1787._\n\nEarlier in this volume we have spoken of slaves as money. With the three-fifths clause, we might consider that, at least in one sense, the transformation of slaves into money was complete. To recapitulate:\n\nCondition One, _medium of exchange:_ from their first appearance in the colonies, slaves had been exchanged for anything money could buy, and moreover were a fundamental part of the collateral that numerous distinct credit systems were based on.\n\nCondition Two, _retains its value:_ by virtue of owning descendants in perpetuity, slave property did not die, but had eternal life the way real estate or gold does, and even provided an annual increase to counter interest and inflation (though the inclusion of slaves in the monetary system contributed to inflation). More simply: if people are money, children are interest.\n\nAnd Condition Three: slaves were now _units of account_ for what was literally political capital. At the level of national politics, the South voted its wealth, and that wealth was slaves, quantified and multiplied by three-fifths. Thanks to the demands of the South Carolinians, the slaveowners' privilege of voting their collective human wealth was enshrined into the Constitution. Though based on population, the three-fifths clause was explicitly understood to be a way of basing voting power on wealth\u2014but only one kind of wealth: slaves.\n\nNo other region's principal form of wealth was taken as a basis for representation. Massachusetts delegate Elbridge Gerry bristled that \"The idea of property ought not to be the rule of representation. Blacks are property, and are used to the southward as horses and cattle are to the northward; and why should their representation be increased to the southward on account of the number of slaves, than horses or oxen to the north?\"\n\nWilson's pragmatic purpose in proposing the three-fifths clause was to enlist the large slaveholding states in resolving the large state \/ small state debate and thereby break up the logjam that had divided the convention along the lines of those two blocs. Rhode Island, the smallest state, had boycotted the convention. The holdout was Connecticut, whose delegates ultimately proposed the formula that gave the United States its Senate\u2014the American analog of the House of Lords, with two votes per state\u2014and, corresponding to the House of Commons, a lower House of Representatives, based on population and, unlike senators, directly elected. The result of this compromise is that today a vote in Wyoming (pop. 563,626 in the 2010 census) has more national influence than one in, say, New York (pop. 19,378,102).\n\nThe balance of free versus slave states would prove an even thornier issue than the size of the states. There were seven mostly free states, assuming Rhode Island was in (slavery still existed in some Northern states, but not in large numbers), and there were six slave states (Delaware, Maryland, Virginia, North Carolina, South Carolina, Georgia). They would each get two senators, tilting the balance toward the free states.\n\nBut the South would get extra weighting in the House of Representatives and a guarantee that they could import more, and since the House of Representatives was the only body authorized to initiate budget legislation, the South had disproportionate power in that as well. South Carolina's three-fifths weighting also gave it disproportionate clout in the presidential selection process, via the electoral college's arbitrary formula of adding the number of senators and representatives to make the number of presidential electors. It was an enduring compromise: the Confederate Constitution retained the three-fifths clause in 1861.\n\nIn looking at the Constitution from the point of view of South Carolina, we are not attempting to reduce the many varied interests and motives of the new nation to those of the most politically extreme state, nor to deny the crosscurrents of opinion in every territory. But in order to understand what subsequently happened, it is necessary to understand the Constitution according to South Carolina's original intent: all slavery, all the time, and if you don't like it, you are the enemy.\n\nA national government, announced Pierce Butler to the Constitutional Convention, \"was instituted principally for the protection of property.\"\n\nIt was Butler who proposed the fugitive slave clause to the Constitution (and took credit for writing it, though he probably did not), something that had not existed in the Articles of Confederation. The immediate background for it was a 1783 Massachusetts court case that freed ten slaves out of thirty-four abducted four years previously from South Carolina plantations by an invading British privateer. The privateer had in turn been captured by a Spanish vessel (at the time allied with American independence), then recaptured by the British, and finally taken over by American warships and brought into Boston. When the Massachusetts court freed the ten enslaved men who had not yet been returned to South Carolina four years later, there was a hue and cry from down south.\n\nFull protection of fugitive property, in Massachusetts or anywhere in the nation, was on the list of South Carolina's nonnegotiable demands at the Constitutional Convention. All the delegates knew that full well, which is perhaps why no one opposed Butler's fugitive slave clause. There is no record of any delegate\u2014not Franklin, Madison, Mason, nobody\u2014objecting to it. Reworded by the committee chaired by the antislavery Gouverneur Morris before being incorporated, it read in the evasive language characteristic of the Constitution regarding slavery:\n\nNo Person held to Service or Labour in one State, under the Laws thereof, escaping into another, shall, in Consequence of any Law or Regulation therein, be discharged from such Service or Labour, but shall be delivered up on Claim of the Party to whom such Service or Labour may be due.\n\nThe fact of acknowledging the existence of a \"person held to service\" gave constitutional permission for the existence of slavery. Of the various clauses protecting slavery in the Constitution, the fugitive slave clause was the only one that required non-slave states to be proactive in enforcing it, and it implied that no state could prohibit slavery entirely on its terrain. It gave rise to the Fugitive Slave Act of 1793, and then to the Fugitive Slave Act of 1850 and the subsequent _Dred Scott_ decision (1857) that accelerated the nation's downward spiral to war. By then, posses of people-snatchers were abducting free blacks from the North to sell them down South.\n\nThe fugitive slave clause meant that no state could become a haven for marronage. There was, however, still such a haven to South Carolina's southern flank in Spanish-controlled East Florida. To take that out would require a strong national government; South Carolina was incapable of doing it alone. So much manpower was needed to repress the black majority of South Carolina that little was available for external military ventures.\n\nThe most important non-mention of slavery in the Constitution from our point of view is one of the least-known by the general public, the first paragraph of Article One, Section Nine, which we take the liberty of reproducing for a second time:\n\nThe Migration or Importation of such Persons as any of the States now existing shall think proper to admit, shall not be prohibited by the Congress prior to the Year one thousand eight hundred and eight, but a tax or duty may be imposed on such Importation, not exceeding ten dollars for each Person.\n\nThough vaguely enough worded that \"importation of persons\" could apply to indentured servants, it was a twenty-year guarantee that the African slave trade could not be banned or prohibitively dutied. (No one ever figured out what the framers meant by \"Migration.\") It did not mean that the slave trade would have to be prohibited as of 1808; it meant that the slave trade could not be prohibited by the federal government before then.\n\nThe \"importation of persons\" clause is singularly out of place in the Constitution. It's the sort of thing that would normally be the subject of legislation, concerned as it was with then-current conditions. But its presence in the Constitution made the twenty-year guarantee of being able to reopen the slave trade in some sense structural to the new nation.\n\nIn practice, South Carolina merchants didn't want importation to be open at that time. The same South Carolina legislature that sent four delegates to the Constitutional Convention to argue for the protection of the slave trade in 1787 also voted to suspend South Carolina's slave trades, both foreign and interstate, for three years, though they subsequently changed their mind about the interstate trade the following year.\n\nSouth Carolina's legislature, home to the most practiced slave-dealers in the thirteen colonies, turned the spigot of the foreign and domestic slave trades on and off as market conditions dictated, though not without tremendous clashes of internal interests in the process. Seesawing between prohibiting and facilitating the foreign trade was partly due to the fluctuations of intrastate labor politics. Charleston and the Lowcountry coastal gentry, who controlled the South Carolina legislature, had plenty of slaves. It was the new settlers out west who wanted more of them. The black-to-white ratio in the Lowcountry was 3:1, but upcountry it was 1:4; the Lowcountry was twelve times as black as upcountry. If an African trade were to dump vast numbers of new Africans onto the market, the cash value of Lowcountry planters' human capital would drop. It would only make sense for them to allow the African trade if there was a vast new market opening up that South Carolina could not supply with its own slaves, but could service via importation and re-exportation.\n\nThe question was taken up at the Constitutional Convention on August 21, 1787. Such records as we have of the debate over this measure, as summarized by James Madison and more vaguely by the Constitutional Convention's bad note-taker James McHenry, make clear that everyone understood the stakes of prohibiting or permitting the foreign slave trade. According to Madison's summary, Rutledge of South Carolina put it bluntly: \"Religion & humanity had nothing to do with this question\u2014Interest alone is the governing principle with Nations\u2014The true question at present is whether the Southn. States shall or shall not be parties to the Union.\"\n\nBy this point, the three-fifths clause had been approved. With that in hand, the four South Carolina delegates drove home their right to expand their disproportionate franchise with all the Africans they could import. They backed their demand with the ever-present threat to walk, insisting that, as South Carolina's Charles Pinckney put it, \"South Carolina can never receive the plan if it prohibits the slave trade. In every proposed extension of the powers of Congress, that State has expressly & watchfully excepted that of meddling with the importation of negroes.\"\n\nGeorgia was South Carolina's ally in this; Virginia, on the other hand, was an adversary to South Carolina in this showdown, with Maryland as Virginia's ally. Continuing importation of Africans would do nothing to profit Virginia slaveowners; quite the contrary. George Mason made a speech whose fire burns through Madison's paraphrase, beginning with the standard disclaimer that \"this infernal trafic originated in the avarice of British Merchants. The British Govt. constantly checked the attempts of Virginia to put a stop to it.\" That said, he went on to point out that \"the evil of having slaves was experienced during the late war. Had slaves been treated as they might have been by the Enemy, they would have proved dangerous instruments in their hands,\" meaning that had Britain been more adept at exploiting the enslaved population, much more damage could have been done.\n\nMason argued for uniform conditions: \"Maryland & Virginia he said had already prohibited the importation of slaves expressly. N. Carolina had done the same in substance. All this would be in vain if S. Carolina & Georgia be at liberty to import.\" What Mason described did in fact subsequently happen: \"The Western people are already calling out for slaves for their new lands; and will fill that Country with slaves if they can be got thro' S. Carolina & Georgia.\" Mason went on to catalog the ills of slavery for a society: \"Slavery discourages arts & manufactures. The poor despise labor when performed by slaves. They prevent the immigration of Whites, who really enrich & strengthen a Country. They produce the most pernicious effect on manners. Every master of slaves is born a petty tyrant. They bring the judgment of heaven on a Country...\"\n\nThe key point was expressed by South Carolina's Charles Cotesworth Pinckney on August 22. The son of Charles Pinckney and indigo doyenne Eliza Lucas Pinckney, he was referred to as \"General Pinckney\" to differentiate him from his cousin Charles Pinckney, who was another of South Carolina's four delegates to the convention. General Pinckney described correctly what would happen in the future. In Madison's paraphrase: \"S. Carolina & Georgia cannot do without slaves. As to Virginia she will gain by stopping the importations. Her slaves will rise in value, & she has more than she wants. It would be unequal to require S.C. & Georgia to confederate on such unequal terms.\"\n\n_Virginia's slaves will rise in value. She has more than she wants._ That was the economic argument, in a nutshell. Ending the African trade would be a bonanza for Virginia, which stood to dominate the domestic slave trade. Mason noted that the Carolinians were poised to profit if allowed to import; Pinckney countered by pointing out that if importation were not allowed, Virginia would have that lucrative market cornered.\n\nVirginia's interstate slave trade was already going on. A few months after Pinckney's words, the Richmond _Virginia Independent Chronicle_ carried an advertisement by Moses Austin & Co. If the name seems familiar, that's because he was the father of Stephen F. Austin, who later brought Southern slavery to Texas and for whom the Texas capital was named. The senior Austin, who began the American lead industry, was at the time a dry goods merchant, and though he was not a full time slave trader, on December 26, 1787, he was offering to dispose of troublesome slaves by selling them South, probably to Georgia:\n\n_W A N T E D_ , ONE HUNDRED NEGROES, From 12 to 30 years old, for which a good price will be given. They are to be sent out of the state, therefore we shall not be particular respecting the character of any of them\u2014Hearty and well made is all that is necessary.\n\nThe question of slave breeding (Virginia) versus slave importation (Carolina) to supply the demand for labor in whatever new territories might be annexed in the next twenty years was so financially momentous that it almost derailed the Constitution. McHenry's notes from the Constitutional Convention summarized the situation:\n\n[The three-fifths clause] gave the slave States an advantage in representation over the others.\n\nThe slaves were moreover exempt from duty on importation.\n\nThey served to render the representation from such States aristocratical.\n\nIt was replied\u2014That the population or increase of slaves in Virginia exceeded their calls for their services\u2014That a prohibition of Slaves into S. Carolina Georgia etc\u2014would be a monopoly in their favor. These States could not do without Slaves\u2014Virginia etc would make their own terms for such as they might sell.\n\nSuch was the situation of the country that it could not exist without slaves\u2014That they could confederate on no other condition.\n\nThey had enjoyed the right of importing slaves when colonies.\n\nThey enjoyed as States [ _sic_ ] under the confederation\u2014And if they could not enjoy it under the proposed government, they could not associate or make a part of it.\n\nThen, on Saturday, August 25, in Madison's words, \"Genl Pinkney moved to strike out the words 'the year eighteen hundred' (as the year limiting the importation of slaves), and to insert the words 'the year eighteen hundred and eight.'\" Pinckney was prescient, as South Carolina's slave-importation bonanza would not begin until after the acquisition of Louisiana at the end of 1803, something no one could have predicted.\n\nCharleston had built great fortunes by re-exporting Africans to the neighboring territories. Now it was poised to service the future market when the nation grew to the South and the West. No one knew exactly when, or under what conditions, that might happen.\n\n*Raised to sixty thousand in the Northwest Ordinance.\n\n#   23\n\n# **Ten Thousand Powers**\n\n_It appears that Mr. Henry is not at bottom a friend._\n\n\u2014James Madison to George Washington, October 28, 1787\n\nWHEN THE SOUTH CAROLINA House of Representatives met to ratify the successfully negotiated Constitution in January 1788, former South Carolina governor Rawlins Lowndes congratulated Charles Cotesworth Pinckney by unleashing a blast of anti-Northern bitterness.\n\n\"Negroes were our wealth, our only natural resource,\" Lowndes said, \"yet behold how our kind friends in the North were determined soon to tie up our hands, and drain us of what we had,\" with palpable sarcasm on the word \"friends.\"\n\n\"We are at a loss, for some time,\" Pinckney responded, \"for a rule to ascertain the proportionate wealth of the states. At last we thought that the productive labor of the inhabitants was the best rule for ascertaining their wealth.\" Pinckney struck the already familiar tone of intra-sectional rivalry as he continued:\n\nyour delegates had to contend with the religious and political prejudices of the Eastern and Middle States, and with the interested and inconsistent opinion of _Virginia, who was warmly opposed to our importing more slaves._\n\nI am of the same opinion now as I was two years ago... that, while there remained one acre of swampland uncleared of South Carolina, I would raise my voice against restricting the importation of negroes. I am... thoroughly convinced... that the nature of our climate, and the flat, swampy situation of our country, obliges us to cultivate our lands with negroes, and that without them South Carolina would soon be a desert waste. (emphasis added)\n\nYet, Pinckney insisted, there was a reason for South Carolina to have negotiated over this issue and to have joined the newly constituted republic: facing potential or actual threats from the English, the Spanish, the Native Americans, the free blacks of Florida, and its own captive labor force, South Carolina needed the other states to defend it.\n\nWe are so weak that by ourselves we could not form an union strong enough for the purpose of effectually protecting each other. Without union with the other States, South Carolina must soon fall. Is there any one among us so much a Quixotte as to suppose that this State could long maintain her independence if she stood alone, or was only connected with the Southern States? I scarcely believe there is... By this settlement we have secured an unlimited importation of negroes for twenty years. Nor is it declared that the importation shall be then stopped; it may be continued. We have a security that the general government can never emancipate them, for no such authority is granted; and it is admitted, on all hands, that the general government has no powers but what are expressly granted by the Constitution, and that all rights not expressed were reserved by the several states. We have obtained a right to recover our slaves in whatever part of America they may take refuge, which is a right we had not before. In short, considering all circumstances, we have made the best terms for the security of this species of property it was in our power to make. We would have made better if we could; but, on the whole, I do not think them bad.\n\nThe two points had been made, yet again: one, without enslaved black labor, South Carolina would be desperately poor; two, without a defensive alliance, South Carolina could not survive. It was equally true in Georgia; as George Washington wrote in a letter of January 17, 1788: \"if a weak state [Georgia], with powerful tribes of Indians in its rear and the Spaniards on its flank, do not incline to embrace a strong _general_ government, there must, I should think, be either wickedness or insanity in their conduct.\"\n\nThe word \"slave\" may have been silent in the Constitution, but not in the nationwide ratification debate. It required considerable persuasion to sell the ratification of the Constitution up North in the face of increasing antislavery sentiment. The provision for possibly ending the African slave trade after twenty years had to be touted as a step toward ending slavery, which it was not.\n\nThere was no debate in South Carolina as to whether the Constitution gave sufficient protection to slavery: it did. South Carolina had gotten what it wanted, and ratified the Constitution easily, despite protests from upcountry farmers who saw themselves as self-sufficient. David Waldstreicher writes that \"strikingly few people\" in the Lowcountry \"criticized the Constitution for being insufficiently pro-slavery.... The relative absence of debate on the topic in North Carolina, South Carolina, and Georgia speaks volumes.... The only reason North Carolina did not ratify was because slavery-dominated districts did not outnumber those where small farmers predominated.\"\n\nThe South Carolina Assembly voted in 1786 to move the capital to an upcountry site and to name it Columbia. It ratified a carefully drafted state constitution in 1790 that, like Britain, required property-holding and tax-paying in order to be able to exercise the voting franchise, with higher property-holding requirements for important officeholders. In effect, this excluded non-slaveholders from government. These requirements were partly expressed as a number of \"negroes,\" so that a state representative was expected to \"be legally seized and possessed in his own right of a settled freehold estate of five hundred acres of land and ten negroes, or of a real estate of the value of one hundred and fifty pounds sterling, clear of debt.\" The governor was required to have an estate of fifteen hundred pounds sterling. From then until after the end of slavery, South Carolina's governor, US senators, and congressmen would not be chosen by popular vote but by the assembly, which was utterly dominated by planters; nor did the people at large have a vote in the presidential election.\n\nThe Constitution owed its existence to two Virginians: Washington, who chaired the convention and lent his prestige to it, and Madison, the principal drafter. But even so, Virginia, less in need of defense from invasion than South Carolina, was less eager to ratify. There was extensive sentiment in Virginia that the proposed Constitution gave too much power to a federal government. With eight states having ratified the Constitution out of nine needed, Virginia was widely seen as the swing state for ratification (though as it played out, New Hampshire became the ninth to ratify), and it was sharply divided.\n\nThe opposition was led by Patrick Henry and George Mason. Henry had declined appointment to the Constitutional Convention, worrying James Madison, who with characteristic precision correctly predicted what Henry would do: \"Besides the loss of his services on that theater [of the Constitutional Convention], there is a danger I fear that this step has proceeded from a wish to leave his conduct unfettered on another theatre where the result of the Convention will receive its destiny from his omnipotence.\" Mason, however, had participated in the Constitutional Convention but did not like the result.\n\nHenry saw Virginia as a \"country\" that would lose her sovereignty by demotion to membership in a \"general\" government. \"What is become of your country?\" he asked rhetorically. \"The Virginian government is but a name.\" He warned that if you \"give up your rights to the general government,\" then that government would have the terrible power to end slavery. Sounding the tocsin of sectional antagonism, he warned that the Constitution would put slaveowners at risk for losing their property. \"Among ten thousand powers which they may assume,\" thundered Henry (imagine exclamation points), \"they [the general government] may, if we be engaged in war, liberate every one of your slaves if they please. And this must and will be done by men, a majority of whom have not a common interest with you. They will therefore have no feeling for your interests.\"\n\nPatrick Henry believed that the Articles of Confederation were adequate. An isolated provincial by then at the age of fifty-one, he was out of touch with the world beyond Richmond. James Madison, whom Henry directly confronted in the ratification debate, knew the complexities of American politics at that moment as well as anyone alive, and he knew the Articles of Confederation weren't working. Much of the country was in a state of near anarchy, with no visible control at any higher level than the local. A pro-Constitution essay in the Winchester, Virginia, _Gazette_ of January 18, 1788, said plainly, \"At the American Revolution there was not only an end to the power of the crown, but a total dissolution of government.\" The South Carolinians, who were in favor of a national government that would defend them from external attack even as they demanded protection for slavery, were in much better contact with the real world of commerce than Patrick Henry. In a sense, Henry was arguing for imposing the decentralization of Chesapeake society on the nation.\n\nThe Constitution and Patrick Henry were on a collision course as regards rhetoric as well. The Constitution was everything Henry wasn't: concise and restrained. Henry's style was to sweep the listener away with cathartic discourse, the opposite of Madison's neoclassical rationality. The clash between Henry and Madison in the Virginia House of Delegates wasn't a fair fight, oratorically speaking. Madison was small, analytical, and a mumbler\u2014\"Mr. _Madison_ added other remarks which could not be heard\" is one of many such notations in the debate minutes\u2014while Henry was an expansive, emotional orator who filled in the silences about slavery in Madison's document.\n\nHenry, who literally talked for days, warned on June 17, 1788, in the Virginia Convention that had been called to debate ratification, that a national Congress could do the most horrifying thing possible: free Virginia's slaves. The Constitution did not give Congress the power of emancipation, but Congress could, in the reporter's paraphrase of Henry, \"lay such heavy taxes on slaves, as would amount to emancipation; and then the Southern States would be the only sufferers.... He considered the clause which had been adduced by the Gentleman as a security for this property, as no security at all. It was no more than this\u2014That a run-away negro could be taken up in Maryland or New-York. This could not prevent Congress from interfering with that property by laying a grievous and enormous tax on it, so as to compel owners to emancipate their slaves rather than pay the tax.\"\n\nIn case of war, Henry warned on June 24, \"may Congress not say, that every black man must fight?\u2014Did we not see a little of this last war?... acts of Assembly passed, that every slave who would go to the army should be free.\" Then he looked into the abyss. \"May they [Congress] not pronounce all slaves free?\" He continued: \"The majority of Congress is to the north, and the slaves are to the south. In this situation, I see a great deal of the property of the people of Virginia in jeopardy, and their peace and tranquility gone away.\" That the \"property of the people of Virginia\" consisted of other people of Virginia does not seem to have bothered Henry.\n\nThe old rhetorician knew when to deflate himself and jab his audience with something more vernacular. Though it does not appear in the official account of his speech, there is this tidbit in an 1850 account by Hugh Blair Grigsby, the nineteenth-century historian of the Virginia Convention and an influential thinker in secessionist circles:\n\nOn one of the occasions which the reporter passes over with some such remark as, \"Here Mr. Henry declaimed with great pathos on the loss of our liberties,\" I was told by a person on the floor of the Convention at the time, that... he suddenly broke out with the homely exclamation: _\"They'll free your niggers!\"_ The audience passed instantly from fear to wayward laughter; and my informant said that it was most ludicrous to see men who a moment before were half frightened to death, with a broad grin on their faces.\n\nWhatever the truth of this secondhand account, \"They'll free your niggers!\" is indeed a homely summary of what Patrick Henry was saying, and at the very least, Grigsby's quoting of it suggests the continuity that later slaveowners saw with Henry.\n\nUltimately, the opposition of Henry and Mason (along with Jefferson's influence over Madison, exercised from Paris by letter) helped prompt the insertion of the Bill of Rights in 1789. It is in no small part to Henry's resistance that the Constitution owes the Second Amendment in particular\u2014the one that promises \"the right to keep and bear arms\" in order to have \"a wellregulated militia\"\u2014and it too was, in part, about slavery, because in the South, the militia was understood to be identical with the slave patrols that were constantly on guard.\n\nThe Constitution gave Congress a measure of control over the militia, which Henry virulently opposed. He wanted assurances that Congress would not use that control to disarm the militia. The Constitution empowered Congress \"to provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions.\" This mention of insurrections, while broadly phrased, was made at a time when slave rebellion and Native American uprising were an ever-present threat. Nor was the repelling of invasions by foreign armies something the undisciplined American militias were capable of doing, as would be demonstrated in the War of 1812.\n\nThe Second Amendment was intended in part to insure that Northerners could not interrupt or halt Southern repression of black people and Native Americans\u2014though many, notably including Jefferson, incorrectly thought militias adequate for defending the country, too. The goal of slaveowners was to make the entire South a prison from which no enslaved person could escape; militias were the police force. What was intended by a militia, at least from the point of view of South Carolina, was expressed by Alexander Hewatt in 1779 and agrees with the functions enumerated in the Constitution:\n\nAs all white men in the province, of the military age, were soldiers as well as citizens, and trained in some measure to the use of arms, it was no difficult matter to complete the provincial regiment. Their names being registered in the list of militia on every emergency they were obliged to be ready for defence, not only against the incursions of Indians, but also against the insurrection of negroes.\n\nWhen the Bill of Rights was ratified two years later, it did not lay a hand on slavery, nor did it extend a hand to Americans enslaved at the time the United States was born. The Fifth Amendment provided that \"no person\" could be \"deprived of life, liberty, or property, without due process of law.\" At that time, there were 694,280 legally enslaved people, who lived in a far more abject relationship to the people who were legally their owners than the colonists had to their king, and to whom the Fifth Amendment would not apply.\n\nSouthern slavery democratized the divine right of kings. No matter how poor a plantation owner might seem to a London merchant, on the grounds of his plantation he was the head of a royal family where his word was law. Every man of property was a little king, with the power to order sexual reproduction or summary execution. With their labor to provide his income and the collateral of their bodies to secure his credit, he could be free to ponder great things and spend his days in politics. The South's down-home kings had the Constitution at their back, with a Bill of Rights that safeguarded their slave-patrolling militias from being disarmed by abolitionists up North who might at some future point take charge of the federal government, even though the South was disproportionately over-represented in Congress and in presidential elections.\n\nThe South got yet another benefit from the Constitution: Article 1, Section 8 contemplated (but did not mandate) the creation of a \"District (not exceeding ten Miles square) as may, by Cession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States\"\u2014a neutral ground that would not be part of any state to house the federal capital. With so many Quakers in Pennsylvania, to say nothing of so many free people of color, and with Pennsylvania having passed the Gradual Abolition Act in 1780 (which granted birthright freedom to children born in Pennsylvania but did not affect those already enslaved), slaveholders did not consider Philadelphia a comfortable seat for a government that they expected to safeguard slavery. The Virginians knew where they wanted that federal district to be\u2014right by where George Washington lived.\n\nDuring the First Congress, Second Session, of 1790, Pennsylvania Quakers presented petitions calling for the abolition of slavery, triggering a strongly worded rebuttal. Offended by the Quakers' imputations, South Carolina representative William Smith responded to the petitions with an extended defense of his state. He asked rhetorically of the Quakers, \"had any of them ever married a negro, or would any of them suffer their children to mix their blood with that of a black?\" He then\n\nread some extracts from Mr. Jefferson's Notes on Virginia, proving that negroes were by nature an inferior race of beings; and that the whites would always feel a repugnance at mixing their blood with that of the blacks. Thus, he proceeded, that respectable author, who was desirous of countenancing emancipation, was, on consideration of the subject, induced candidly to allow that the difficulties appeared insurmountable.\n\nJefferson in 1790 brokered a deal over dinner with Hamilton: Jefferson would get a Southern capital if Hamilton could begin his financial plan. As a result of the deal, Hamilton created the national debt and the Bank of the United States that issued bonds to back it, paid the veterans of the independence struggle what they were owed, and restored the United States' international credit, while Jefferson set out to create the federal city.\n\nThe one-hundred-square-mile District of Columbia was created out of sixty-one square miles of Maryland land on the north side of the Potomac, where the capital was sited, together with thirty-nine square miles of Virginia land south of the Potomac, including the town of Alexandria, whose harbor was designated by Washington, Jefferson, and Monroe as the Potomac's official port of entry in 1784. Building the new capital city of Washington out of swampland was good for business; it employed lots of slave labor, rented from Virginia and Maryland slaveowners. As construction began, the slave-selling business in Alexandria picked up from the federal stimulus.\n\nSixty years later, the Beaufort, South Carolina, arch-secessionist Robert Barnwell Rhett would call the Jefferson-Hamilton deal a \"corrupt bargain\" in which Jefferson sold out the South. For the political class of South Carolina, who saw themselves as rulers of a sovereign state, the creation of Washington City centralized power in the Chesapeake and legitimized a system of national debt, the payment of which, they believed, would be extorted from them in the form of tariffs. Indeed, the First Congress in 1789 passed a tariff that South Carolina and Georgia saw as a transfer of wealth from South to North, prompting Pierce Butler in 1790 to warn that, in William C. Davis's paraphrase, \"the doctrine of protective tariffs, if pursued, might one day destroy the Union.\"\n\nDuring the thirty-one-month interval between the Constitution taking effect and the Bill of Rights taking effect, the French and Haitian Revolutions erupted. It was one long upheaval: American independence was a French-supported project that occurred in parallel with France's revolution, though the American side erupted first. The two movements were inextricably tied together, with communication between the two and an overlapping cast of characters that included Jefferson and the Marquis de Lafayette.\n\nIn Europe, where American independence was seen primarily as a victory for France against England, the fall of the Bastille on July 14, 1789, was a far greater shock. Not only had the French monarch been powerful, but France was wealthy: the island colony of Saint-Domingue was the most profitable piece of ground on earth, contributing perhaps as much as 40 percent of France's annual income with its products. In 1789 it supplied \"about 60 percent of the coffee sold in the western world\"; only Jamaica could compete with it as a producer of sugar; and it produced indigo, cotton, and tobacco. It was a high-volume consumer of kidnapped Africans; forty thousand arrived in 1789 alone, after a six-year period that had seen Saint-Domingue's agricultural production double. As such, it generated a vast cash flow for the trans-African slave trade at its height. This capital \"fertilized\" the crops, as C. L. R. James put it: \"though the bourgeoisie traded in other things than slaves, upon the success or failure of the traffic everything else depended.\" The great revenues from Saint-Domingue created the prosperity that was the source of the power France projected internationally. But it was not royal power; the fortunes of the slave trade were made by the bourgeoisie.\n\nSome of the bourgeoisie of Saint-Domingue were free people of color, though they were discriminated against. Stewart King, who analyzed Domingan notarial records, estimates that as many as 30 percent of the slaves in Saint-Domingue were owned by free people of color, who were approximately half the free population. There were about thirty thousand whites and about thirty thousand free people of color in Saint-Domingue, and approximately half a million slaves, about two thirds of them African-born. No comparable-sized piece of ground in Africa had ever sustained such a population. They were angry, and among them they had a considerable body of military knowledge to draw on.\n\nIn the hodgepodge of African nations compacted together under the harsh discipline of the plantation, the Senegambians of Saint-Domingue, from an Islamized region, brought a concept of _jihad._ From farther south in Africa, the Fon-speakers from Ardra (in present-day Benin) followed traditional African practices and called their spirits _foddun_ (from which, _vodou)_ , alongside representatives of other traditional African practices. From farther south yet, in West Central Africa, the most numerous group, the Bakongo, whose military techniques seem to have predominated, had been Catholicized, while continuing their traditional practices. The body of spiritual practices called _vodou_ , which developed along with the Haitian nation, became an umbrella concept, an _e pluribus unum_ of African religion that allowed for different traditions to continue within an overall framework of _nanchons_ , or nations. Under this umbrella, the spirits multiplied.\n\n#   24\n\n# **The French Revolution in America**\n\n_Suppose a negro man of 25. years of age costs \u00a375. sterling: he has an equal chance to live 30. years according to Buffon's tables; so that you lose your principal in 30 years. 1_\n\n\u2014Thomas Jefferson, letter to George Washington, June 18, 1792\n\nBEING ANTI-MONARCHIC AND PRO-REPUBLICAN to the bone, Thomas Jefferson was sympathetic to the French revolutionaries, who in turn idolized him as a hero of the American revolution.\n\nThey misunderstood Jefferson so badly that in 1788, while Jefferson was United States Minister Plenipotentiary in Paris, Jacques-Pierre Brissot de Warville invited him to become a member of the organization he had founded. Inspired by Thomas Clarkson's Society for Effecting the Abolition of the Slave Trade in Britain, the _Societ\u00e9 des Amis des Noirs_ (Society of the Friends of the Blacks) was the first French antislavery society.\n\nWith the insincerity that was Jefferson's political hallmark, he declined Brissot's invitation, using what the editors of Jefferson's papers, speaking of another occasion, refer to as a \"polite diplomatic fiction.\" In it, he distinguished abolition of slavery from abolition of the slave trade:\n\nI am very sensible of the honour you propose to me of becoming a member of the society for the abolition of the slave trade. You know that nobody wishes more ardently to see an abolition not only of the trade but of the condition of slavery: and certainly nobody will be more willing to encounter every sacrifice for that object. But the influence & information of the friends to this proposition in France will be far above the need of my association. I am here as a public servant; and those whom I serve having never yet been able to give their voice against this practice, it is decent for me to avoid too public a demonstration of my wishes to see it abolished.\n\nWhen the Bastille fell, Jefferson was in Paris, preparing to leave for home. He'd been packed since April, and he decamped in September 1789 for his mountaintop in Virginia with his daughter Patsy, and\u2014though he had told Brissot that \"nobody would be more willing\" than he to \"encounter every sacrifice\" to end slavery\u2014he brought home as well Patsy's enslaved attendant, the pregnant fifteen- or sixteen-year-old Sally Hemings, who was the deceased Martha Wayles Jefferson's half sister (one of six half siblings Martha had owned) and thus Patsy's illegitimate aunt.\n\nMuch has been written about Hemings in recent years, and we will not summarize her story once again here. It is ironic that she has come to define Jefferson in the modern popular image, with her captivity cast as a love story in some narratives. The fact that she was, as was typical of enslaved concubines, only one-quarter black made her acceptable to Jefferson for cohabiting. As he explained in _Notes_ , elaborating on his pseudoscientific notion of black inferiority: \"The improvement of the blacks in body and mind, in the first instance of their mixture with the whites, has been observed by every one, and proves that their inferiority is not the effect merely of their condition of life.\"\n\nThere was in the last third of the twentieth century a long historiographic scandal over Jefferson's parentage of Sally's children Beverly, Harriet, Madison, and Eston\u2014who, far from being \"removed beyond the reach of mixture,\" were seven-eighths white. We consider the issue of Jefferson's paternity of them to have been resolved and will forbear discussing the literature on the subject here. For us, the key point is not whether Jefferson fathered Hemings's children, but that he _owned_ the children, and could sell them if he wanted.\n\nReturning home from France to what was now a constitutional American republic, Jefferson brought an extraordinarily large cargo of goods he had purchased. The list has delighted Jefferson biographers ever since, with its furniture, cheeses, musical instruments, gadgets like the portable copying machine he had commissioned in London, and 680 bottles of wine. All of it would ultimately be paid for by his slaves, who produced all his revenue.\n\nJefferson answered Washington's call to join his administration and became the first secretary of state, a position that brought him into frequent conflict with his great enemy, Alexander Hamilton, whom Washington named secretary of the treasury.\n\nThe Antillean colony of Saint-Domingue stopped being profitable for France in August 1791, when, in the instability after the French Revolution, with radicals on the ascendant and talk of liberty in the air, another revolution began. A little more than two years after the fall of the Bastille, the enslaved Boukman Dutty\u2014a visionary troublemaker who had been traded into the colony illegally from British Jamaica\u2014led a brilliantly organized, intensely violent August 1791 rebellion on the northern plains of Saint-Domingue. It was the beginning of a complicated struggle, in two main phases with a tense interregnum, that continued until January 1, 1804, when Jean-Jacques Dessalines issued the Declaration of Independence of the Republic of Haiti, taking the new country's name from the indigenous Ta\u00edno language.*\n\nThe military aspect of Boukman's experience was informed by both African and European techniques of war, and by the body of African spiritual practices that in Haiti came to be collectively known as vodou.\n\nBy the time the US Bill of Rights went into effect on December 15, 1791, the sugar plantations of the northern plain of Saint-Domingue lay in ash heaps. The consequences were immediate: Europe's sugar and slavery industries were remade overnight. The principal supplier of sugar abruptly disappeared from the world market, though it would re-emerge to a lesser degree under Toussaint Louverture, who reinstated the plantation system with conscripted labor.\n\nCuba stepped in to fill the breach in sugar supply. The island had received its first shipment of African slaves in the 1520s, but for most of that time it had principally been a transshipping center for silver and gold from Mexico and Peru; without a plantation system, it had not been a major importer of slaves. Though Africans had been in Cuba for almost three centuries by then, the first four decades of the nineteenth century would be Cuba's peak period of importation of kidnapped Africans\u2014a tremendous source of revenue for those who supplied the captives\u2014as well as Havana's peak of prosperity, as sugar plantations proliferated.\n\nThe Domingan slaveowners were internationally notorious for sadism toward the enslaved. The uprising was everything they had feared, and the convulsive violence of it was made even worse in the telling of it by slaveowners, who were the sources of much of the printed discourse around it. \"Their standard was the body of a white infant impaled upon a stake,\" read a pamphlet widely read in France and in England, though there is no corroborating evidence that such a baby on a pike existed. The message hardly needed reinforcing: the natural state of the \"Negro\" was to be a baby-murdering, devil-worshipping savage. Accounts circulated in the slaveholding South of the spectacular violence directed against the bodies and plantation properties of the whites in the northern agricultural plain of Saint-Domingue. Word spread through the black Americas what had happened: the enslaved heard it through the inter-plantation grapevine, and they heard their aghast masters talking about it.\n\nThe United States' 1778 treaties with Louis XVI, which created the framework pursuant to which France substantially helped the United States win the War of Independence, committed the American republic to recognize France's claim on Saint-Domingue. No one in Washington's administration\u2014not Hamilton, and certainly not Jefferson\u2014wanted to see slave revolt there. The United States weighed in, and by 1792 had proactively spent some $726,000 in \"supplies, arms, and equipment\" to support the Domingan planters against the black rebels.\n\nIn a letter to President Washington, Secretary of State Jefferson attempted in 1792 to answer some questions about American agriculture posed by the English agricultural expert Arthur Young, whom Jefferson knew from Paris. In calculating the relative value of hired versus owned laborers, he observed that \"our families of negroes double in about 25. years, which is an increase of the capital, invested in them, of 4. per cent over & above keeping up the original number.\"\n\nThis is unambiguous: Jefferson was describing African Americans as self-reproducing merchandise that could meet a capital returns target. The consequences for Jefferson's personal economy of this calculation were that, in Henry Wiencek's words, \"he had realized that he was making 4 percent profit every year on the birth of black children.\"\n\nIn reply, Young disputed Jefferson's figures for wheat\u2014because, he said, it was impossible to raise as much wheat as Jefferson projected without proper land management (not something Virginia was known for), which meant letting land lie fallow, which in turn would call for more cows and sheep to graze it than Jefferson projected. He scoffed at Jefferson's projection of \u00a360 profit annually from slave-breeding, noting that \"to have a considerable value in slaves, is a hazardous capital; and there is no man in the world who would not give 60 _l._ a year on six thousand acres, to be able to change slaves to cows and sheep: he cannot otherwise command labour, and therefore must keep them; but the profit in any other light than labourers, is inadmissible.\"\n\nYoung may have understood the economics of wheat-raising better than Jefferson, but as he acknowledged in his letter, he was not on the ground in Virginia. The English economist does not seem to have fully understood how Virginians were wringing multidimensional profits from their labourers over and above their capacity to labor. Which is to say, he did not comprehend the nascent slave-breeding industry. In the process of explaining it to him, Jefferson seems to have improved his own comprehension of it.\n\nIn a response to Washington about Young's reply, Jefferson pleaded inexperience with macroeconomics, as he had not already had these figures on the ready but had to create them from scratch. He wrote, \"I had never before thought of calculating what were the profits of a capital invested in Virginia agriculture\"\u2014an extraordinary admission, it might seem, for a debt-burdened owner of a large slave plantation. But then, Hamilton, not Jefferson, was the money man in the Washington administration; though Jefferson was a compulsive record-keeper who kept minutely detailed lists of expenditures, he \"abandoned any effort to balance credits and debits in 1770,\" writes Alan Pell Crawford. Other large slaveowners who were more adept financial managers than Jefferson, like Charles Carroll of Annapolis, had been calculating their profits on \"natural increase\" all along.\n\nSlaveowners knew that their wealth increased with every enslaved birth, of course. The revelation for Jefferson was to think of it in terms of capitalism. It was a subtle perceptual shift that seems obvious to us now: translate that knowledge into a dollar figure that could be compared with other investments as an abstract rate of return. In comparing those figures, Wiencek suggests, Jefferson had realized that raising slaves was his best business. Wiencek's interpretation of this correspondence as a pivotal moment in Jefferson's thinking was attacked vociferously, and, in our opinion, incorrectly, by Hemings family biographer Annette Gordon-Reed, who legalistically argued that Jefferson \"was not speaking about his slaves at Monticello\u2014he was speaking about farms in Virginia generally.\" But that seems a false distinction: Jefferson's phrase was _\"our_ families of negroes,\" emphasis added. He identified personally with what he was describing.\n\nMore to our point, however, is that, as Gordon-Reed indicated, Jefferson was telling Young (and Washington) that slave reproduction was increasing Virginia's capital stock by 4 percent every year, whether there was a good crop or a bad one. That had obvious implications for him, both as a Virginia politician and as a large slaveowner. Laden with debt and entirely invested in the human capital of slaves, Jefferson was representative of the slaveowning class.\n\nAlexander Hamilton was not interested in monetizing slaves. Along with Aaron Burr, he was a member of the New York Manumission Society, which kept lists of slave traders and urged they be boycotted and which played a role in urging the end of slavery in New York.\n\nHamilton and Jefferson were the public faces of the England-France split of the country, which meant something close to civil war. Neither were pro-democracy ideologues. Hamilton loathed the idea of democracy, which he referred to as \"poison\" in a letter written the last night of his life, while, as Lucia Stanton notes, \"democracy\" was \"a word Jefferson rarely used and never in the way we do today.\"\n\nThe Federalist money of New England and New York was pro-British, while Republican Virginia was mostly pro-French. The Jeffersonians painted President Washington as an aristocrat and monarchist mouthing pro-British words supplied to him by the manipulator Hamilton, who was understood to be a threat to slavery.\n\nWashington, the father of the Constitution, didn't want political parties. All the specifications in the Constitution about representatives and senators didn't contemplate that they would be members of one of two political parties. More than any other individual, Jefferson was responsible for creating a party system in the United States, and he did so in direct opposition to Washington, while he was Washington's secretary of state. Washington, perhaps understandably, took it as a personal betrayal.\n\nJefferson had watched the workings of parties in revolutionary France. He created his own propaganda organ out of patronage by giving printer Philip Freneau a job in the Department of State, thereby supporting the publication of Freneau's highly partisan _National Gazette._ As of October 31, 1791, it published unsigned attacks by Jefferson and Madison, among others, against Hamilton, Washington, and the policies of the very administration from which Jefferson was a political renegade.\n\nWhen the French Republic was declared to exist in 1792, the radical Girondins were in power, though they were soon to be displaced (and many of them executed) by the more radical Jacobins. Believing in the radicalism of the American revolution, the more idealistic of the Girondins dreamed of a political union between the American and French republics, a free trade zone where _citoyens_ of one country would be citizens of the other. The Girondins had no strong hierarchy, but their de facto leader was the writer Jacques-Pierre Brissot de Warville, he who had previously invited Jefferson to join his abolition society; they were sometimes known as Brissotins.\n\nBrissot had traveled in the mid-Atlantic and Upper South of the United States, where he attempted to help organize antislavery societies, and published a narrative of his observations in 1791. A significant chunk of his book is about his contacts with slavery in America. He wrote of Jefferson's home state: \"Every thing in Maryland and Virginia wears the print of slavery; a starved soil. Bad cultivation, houses falling to ruin, cattle small and few, and black walking skeletons; in a word, you see real misery and apparent luxury, insulting each other.\" Still, Brissot idealized America and he admired Jefferson, who had advised Lafayette during the drafting of the Declaration of the Rights of Man\u2014betraying, as some saw it, America's independence ally Louis XVI.\n\nBrissot, momentarily in a position of power in 1793, dispatched the loose cannon Citizen Edmund-Charles Gen\u00eat as the Minister Plenipotentiary to America, advising him to trust Jefferson over all other Americans. Gen\u00eat's father had been a courtier to Louis XV, and he had grown up at Versailles, so he had the necessary skills and contacts for the mission Brissot entrusted him with: to escort the royal family\u2014Louis XVI, Marie Antoinette, and the young Dauphin\u2014out of France to a safe exile in America. But before Gen\u00eat could depart, the Jacobin faction pressed the momentous vote on death for the monarch, with Brissot as one of 387 convention members voting for regicide. Eleven days after guillotining King Louis XVI on January 21, 1793, the Girondins declared war on Britain and the Netherlands.\n\nGen\u00eat went on to the United States alone, with a diplomatic brief, basically, to be a saboteur\u2014to export the French revolution, consolidate the alliance with the United States, and, in the words of Gen\u00eat's biographer Meade Minnigerode, \"to do all the harm he could to England and Spain in America.\" He was also supposed to collect Louis XVI's $2 million war debt from the Americans so they could use it in the war in Saint-Domingue. (Hamilton had been making timely payments, but the French wanted the principal.) The charming, thirty-year-old Gen\u00eat's instructions gave him a budget of sixty thousand _livres_ , with the laughable instruction to draw it from the United States Treasury\u2014meaning, he was supposed to get it from Alexander Hamilton\u2014to be deducted from the American war debt to France.\n\nOn his way to America, Gen\u00eat paused his voyage so that his vessel, the _Embuscade_ (Ambush), could engage in privateering against British merchants. He took several prizes before being blown off-course and landing on April 8, 1793, in Charleston rather than the intended destination of Philadelphia. Despite the urgency of his diplomatic mission, the delighted Gen\u00eat determined to travel up the coast from Charleston by land.\n\nThe day after Gen\u00eat arrived in Charleston, the April 9, 1793, issue of _The Apollo; or Chestertown Spy_ (Maryland), was headlined by the shocking, just-arrived news of the execution of Louis XVI eleven weeks earlier. A smaller, more locally oriented, article was also significant:\n\nOn Tuesday last the _Corner Stone_ of the AFRICAN CHURCH, was laid in Fifth Street, between Walnut and Spruce Streets, Philadelphia, by four of the members of the Church. One of them afterwards kneeled down upon the stone and prayed in a fervent manner, for the success and usefulness of the undertaking.\n\nThis church will be forty-six feet in front, and sixty feet in depth.\n\nThe Bill of Rights' guarantee of freedom of religion gave protection to the movement of free black people toward becoming churched. The Free African Society, founded in Philadelphia in April 1787, was a mutual aid organization that aimed to create a nondenominational black church.\n\nWith the disestablishment of the Anglican church, or any other, guaranteed by the Bill of Rights, the murderous religious divisions that had long plagued Europe and carried over to the colonies\u2014between Catholic and Protestant, between Anglican and evangelical\u2014were moderated. Instead, there was a division between white and black that extended into the spiritual sphere. The church whose construction was announced in the _Spy_ was the African Episcopal Church of St. Thomas, founded by the Free African Society's Absalom Jones. After a split along Anglican\/Methodist lines, the society's Richard Allen founded the African Methodist Episcopal Church. Both churches taught reading to children.\n\n\"Mother Bethel,\" the A.M.E. church, which began as the Blacksmith Shop Meeting-House, was consecrated on July 29, 1794, as a great wave of evangelization was sweeping over First Amendment America, with numbers of African Americans taking to Jesus as their liberator. Methodism was still associated with antislavery, and abolition societies already existed in the 1790s, as per the notice in the _Chestertown Spy_ , enlarged and reproduced here.\n\nThere were no such societies in the Lowcountry, where such a thing would not have been tolerated. Nor were the enslaved there allowed to preach, as Frederick Law Olmsted quoted a slaveowner in 1853, \"unless a white man hears what they say.\"\n\nCharlestonians were known for extending a generous, courteous welcome to foreigners of a certain social rank, with which they hoped to win over ambassadors for the goodness of slavery. Gen\u00eat was given a superstar's welcome in South Carolina, where he met leading men of the state\u2014\"Dictator\" Rutledge, Senator Ralph Izard, Thomas Pinckney. While not many of the Federalists in Charleston turned out to greet him, most of the Southern elite supported the republicans in France. It comported flatteringly with the Charlestonians' view of their own importance that the emissary of the greatest nation in the world had come to see them first.\n\nWith South Carolina governor William Moultrie's full permission, Gen\u00eat commissioned four privateers (one of them named the _Citizen Gen\u00eat)_ , which began attacking English shipping and bringing the prizes into Charleston harbor.\n\nThat activity, which Jefferson ultimately made him stop, carried the possibility of bringing down retribution or even a declaration of war against the United States by the British navy, the world's most powerful. It provided the direct motivation for the passage by the next Congress of the Neutrality Act of 1794, which prohibited freelance warmongering.\n\nGen\u00eat wrote that Izard told him\u2014though he disregarded the advice\u2014that Jefferson and Madison \"pretend to be great republicans... They will do everything in their power to secure you on their side and will be friendly to you as long as your country or yourself may be serviceable to their ambitious views. Place no confidence in them.\" When Gen\u00eat answered that \"I shall have no other friends in America but those who will be friendly to France and to the cause of liberty,\" Izard replied, according to Gen\u00eat, \"oh[,] then[,] I see that you are going to fall into the snares of Mr. Jefferson and his party, and very probably will become their victim.\"\n\nJefferson indeed befriended young Gen\u00eat. The Virginia trio of Jefferson, Madison, and James Monroe saw American support for republican France as essential. In a letter to James Monroe of June 4, 1793, Jefferson, looking forward to dual citizenship for all, wrote: \"France has explained herself generously.... she wishes to promote [our prosperity] by giving us in all her possessions all the rights of her native citizens, and to receive our vessels as her vessels. This is the language of her new minister. Gr. Britain holds back with the most sullen silence and reserve.\"\n\nWashington took Jefferson's advice to receive Gen\u00eat, but did it standing in front of portraits of the murdered Louis, who had supported him in the War of Independence, and Marie Antoinette, who had not yet gone to the guillotine. By recognizing Gen\u00eat, the pro-British Washington was not merely recognizing the French Revolution, but actively harboring a hostile agent against Britain. Gen\u00eat proposed a commercial treaty\u2014a family compact, he called it\u2014that Jefferson was in favor of but Washington shot down, which would have ultimately had the effect of making the United States France's ally against Britain in war.\n\nThe radical Montagnard faction of the Jacobin Club came to power in France, on June 2, 1793. The execution of King Louis XVI was the beginning of the ascent to power of the _terroristes_ \u2014Danton, Marat, Robespierre\u2014as the Montagnards began liquidating all opposition, with the Girondins as their main political targets. Gen\u00eat, who like all transatlantic diplomats had to contend with a lag of five weeks minimum, and often months, to receive word from home, continued prosecuting his agenda. Meanwhile, Brissot and twenty-one other Girondins went to the guillotine on October 31, 1793; one of the charges against Brissot was his responsibility for Gen\u00eat's mission.\n\nAccording to Gen\u00eat's account, the popularity of the French Revolution in the United States brought a group of Philadelphians to ask him for advice on what to name their Jacobin club, the constitution of which had been drawn up by Pennsylvania secretary of state Alexander Dallas. Gen\u00eat diplomatically suggested they call it the Democratic Club. Soon every American city had a club with a variety of names, collectively remembered as the Democratic-Republican societies, which were in favor of the French Revolution and which began the formalization of the opposition into a Democratic-Republican party, with Jefferson as its leader.\n\nIn Saint-Domingue, the Jacobin revolutionary civilian commissioners L\u00e9ger-F\u00e9licit\u00e9 Sonthonax and \u00c9tienne Polverel came into open confrontation with General Fran\u00e7ois-Thomas Galbaud du Fort, the Royalist head of the French fleet and an absentee landowner in Saint-Domingue, who had assumed authority. After Galbaud attacked Cap Fran\u00e7ais, sending two thousand or so sailors and newly unchained political prisoners to run riot in that city on June 20, 1793, they were driven away by an army of black freedmen fighting on the side of Sonthonax and Polverel. In a battle that lasted several days, the city of Cap Fran\u00e7ais\u2014Saint-Domingue's largest port, and a center of arts and culture\u2014burned to the ground. Galbaud evacuated with about ten thousand people, whom he brought to Baltimore first; by August, his fleet had dropped anchor in New York, from which base his ships began cruising up and down the coast. Gen\u00eat tried to have Galbaud arrested, but he had broken no US law.\n\nRefugees had fled Saint-Domingue with the first insurrection in 1791; now, in a new wave, more refugees traveled down the Antilles\u2014Guadeloupe, Puerto Rico, Trinidad\u2014or to next-door, British-controlled Jamaica, while the largest number sailed up the Gulf Stream to the East Coast of the United States.\n\nOnly a few went to New Orleans at the time, though later the US-controlled New Orleans would become a magnet for what Nathalie Dessens describes as the ultimate \"convergence zone\" of a \"real Saint-Domingan diaspora\" that kept in touch with family, friends, and business connections, both by correspondence and by travel. But New Orleans was not an immediate destination in 1793: it was not as accessible by sail as Atlantic North America because of the loop current in the Gulf. Moreover, the Spanish government of Louisiana was not welcoming to French refugees, some of whom were evangelists for revolution.\n\nA convoy of 137 ships carrying Domingan refugees arrived in Norfolk, Virginia, in July 1793; from there, they went to cities up and down the coastline. Many went to Charleston, where there was already a community of French-speaking Huguenots. Bringing a new wave of Catholicism to the city, they effectively took over an Irish church there. John E. Baur notes that \"St. Domingue's creoles, many of them republican, tended to go to the Southern states, while French-born Royalists generally settled in New England and the Middle Atlantic states.\" About four thousand Domingans went to New York.\n\nIn Philadelphia, the nation's capital and largest city, refugees who began arriving from Saint-Domingue in the spring were widely believed to have brought the city's first yellow fever epidemic in 1793, which killed over 10 percent of the town's population, causing many residents to flee, while the Free African Society cared for the sick and dying. Erupting out of the dockside area, it paralyzed the city and the US government. Dr. Benjamin Rush identified the disease on August 19, and it abated in mid-October, when the weather cooled and mosquitoes stopped biting (though their agency as disease vectors was not yet realized), and it did not spread anywhere else.\n\nDuring this crisis and in the months before, French privateers had been openly using the United States as a base. Their vessels, fitted out in the United States, had been taking British prizes\u2014and Spanish, and even American\u2014and bringing them into American harbors\u2014Charleston, New York, Wilmington, Boston. This was inviting war with Britain, but, as Jefferson insisted in a cabinet meeting, \"the French have by treaty a right to come into our ports with prizes.\" Finally, realizing that Gen\u00eat's attacks on British shipping from a US base could put them at war with England, Washington, Hamilton, and Jefferson concurred that he had to stop passing out letters of marque to privateers.\n\nThe summer of 1793 stands out for the electric political turmoil in Philadelphia. The mounting death toll from the epidemic, combined with the convulsive energy emanating from the Terror in Paris and from Saint-Domingue, kept the town agitated, as political clubs increased in number and in aggression. Washington's government was nearly overthrown, as Adams angrily reminded Jefferson in an exchange of letters twenty years later:\n\nYou certainly never felt the Terrorism, excited by Genet, in 1793, when ten thousand People in the Streets of Philadelphia, day after day, threatened to drag Washington out of his House, and effect a Revolution in the Government, or compell it to declare War in favour of the French Revolution, and against England. The coolest and the firmest Minds, even among the Quakers in Philadelphia, have given their Opinions to me, that nothing but the Yellow Fever... could have saved the United States from a total Revolution of Government. I have no doubt You was fast asleep in philosophical Tranquility, when ten thousand People, and perhaps many more, were parading the streets of Philadelphia.... What think you of Terrorism, Mr. Jefferson?\n\nJefferson rationalized the mass guillotinings in Paris, even though some of his friends had fallen victim. But then the Jacobins brought terror to Jefferson, in the form of an emancipation proclamation.\n\nThe black army was the strongest force in Saint-Domingue, and it was better to be with it than against it; the French navy was an enemy; and Britain and Spain were both trying to take the colony over. Needing allies, Sonthonax and Polverel offered freedom to slaves who would join them\u2014at first within a limited geographic range, then widening its scope. Justified by strategic considerations, and consistent with their own revolutionary principles, they unilaterally abolished slavery by proclamation in the northern province of Saint-Domingue on August 29, 1793. Over the next two months the decree was at least theoretically extended to the rest of the island, though the commissioners did not control all the territory. They needed as unified a force as possible: in September, the British invaded Saint-Domingue from their base in Jamaica, attracting the support of pro-British planters.\n\nThough Jefferson was alarmed by Gen\u00eat's reckless actions, he was the administration member identified with the French. He had tried to resign before; now, in the wake of the turbulence that trailed Gen\u00eat, his opposition to the Washington administration made his position untenable. Jefferson left the post of secretary of state on December 31, 1793, announcing his return to Monticello. Vice President John Adams's comment in a letter to his son John Quincy Adams attributed Jefferson's resignation to his not making enough money as vice president to support his \"habit\" of expensive living, adding:\n\nJefferson thinks by this step to get a reputation of an humble, modest, meek man, wholly without ambition or vanity. He may even have deceived himself into this belief. But if a prospect opens, the world will see and he will feel that he is as ambitious as Oliver Cromwell, though no soldier.\n\nIt was time to make some money. As Jefferson prepared to leave public life, he wrote the iron merchant Caleb Lownes, asking for sixty to ninety days' credit on an order for iron rod, to be made into nails: \"I suppose one ton will serve me the first quarter of the year by the end of which I shall be ready to work up two or three times as much every quarter.\" He was going to go into business for himself, installing a cottage-industry nail factory with a workforce that Jefferson described as \"a dozen little boys from 10. to 16. years of age.\" They were given extra rations of meat and fish, and a suit \"of red or blue\" for the best workers. Needless to say, they were kept away from reading and writing, and spent their formative years in captivity, living together and making nails together all day until they were sixteen, when they were transferred to field labor. From 1794 to 1797, while Jefferson was at Monticello and supervising it daily, his slave-labor nail factory was a profitable operation.\n\nSonthonax and Polverel's declaration of emancipation was ratified and extended to all those enslaved in French territories on February 4, 1794, by the National Convention in Paris. It was the most radical achievement of the French Revolution: the immediate emancipation of all slaves, with no period of transition. When the ratification was confirmed, the general Toussaint Louverture stopped fighting under the Spanish flag in Saint-Domingue and came over to fight under the French.\n\nSlaves in Saint-Domingue had risen up and killed not only their masters, but slavery itself. Speaking of a hypothetical war that might pit the United States allied with France against Britain, Ralph Izard, who had lived in both London and Paris, and who had welcomed _citoyen_ Gen\u00eat to Charleston with open arms, wrote:\n\nBy a decree of the Convention of France, all the Slaves in their Colonies are emancipated. A joint war with France, under the present circumstances, would occasion a prodigious number of the lower order of Frenchmen to come to this Country, who would fraternise with our Democratical Clubs, & introduce the same horrid tragedies among our Negroes, which have been so fatally exhibited in the French Islands. Are the inhabitants of South Carolina ignorant of these things; or is it the will of God that the Proprietors of Negroes should themselves be the Instruments of destroying that species of property?\n\nFrom Georgia up to Virginia, slaveowning whites entered a new era of panic that at times crossed over into mass hysteria over the prospect of black revolutionary infiltration from the island. \"Our town swarms with strange Negroes,\" wrote the Norfolk County commandant Colonel Willis Wilson from Portsmouth, Virginia, to Governor Henry Lee in August 1793. In a panic, Wilson demanded that Lee send troops to defend against the \"many hundreds [of] French Negroes\" in the Portsmouth streets.\n\nThe looming post-Sonthonax fear in the slaveowners' collective imagination of infiltration by black warriors augured rising prices for suppliers of domestically born people. No one wanted a foreign slave trade now, not even South Carolina.\n\nBy this time, Jefferson was positively bullish on the profits to be made from reproduction of the enslaved. In April 1794, he wrote to Madame Plumard de Bellanger, a friend from Paris whose relative, J. P. P. Derieux, was living in Charlottesville and doing poorly. Blaming Derieux's bankruptcy on the Haitian Revolution, Jefferson politely asked Madame Plumard to send her relative money. He promised to see to it that her money would be put in the most conservative investment possible, the capitalized womb: \"I think I may pledge myself that it shall be every farthing of it laid out in lands and negroes, which besides a present support bring a silent profit of from 5. to 10. per cent in this country by the increase in their value.\"\n\nExiled Domingan planters, many of whom clung to the belief that they would return to claim their rightful real and human property, told terrifying tales that became further elaborated in the telling, further radicalizing US slaveowners.\n\nBut the exodus from Saint-Domingue to North America did not only bring paranoia. The Domingans were the world leaders in plantation technology. They brought skills, techniques, and knowledge everywhere they went, to say nothing of arts and culture. In eastern Cuba and Puerto Rico, they introduced the cultivation of coffee, subsequently a mainstay for those mountainous territories, along with a creolized music and other cultural paradigms that still resonate in those islands today. In South Carolina, they showed the few farmers who were still growing indigo new chemical reagents they could use in the process.\n\nIn Baltimore, which conducted much maritime trade with Saint-Domingue under Toussaint's leadership, the Domingans' influence was profound. Their boatwrights, both enslaved and free, knew French boatbuilding techniques, plus they knew all about building pirate ships, and Baltimore was heavily invested in the pirate-ship business. We can read \"French\" as meaning \"Domingan\" in the advertisement in the June 17, 1795, issue of the _Maryland Journal and Baltimore Universal Daily Advertiser_ that offered a \"New Vessel for Sale[:]... built at Baltimore and launched the latter part of last month. She is built with live-oak and cedar, nailed and finished _after the French manner_ (emphasis added), being calculated for extraordinary sailing.\" The Domingans brought new ideas of construction and finish to what was becoming a uniquely Baltimorean style of boat: the steeply raked, low-draft, fastest-thing-on-the-water vessel that would later become known as the Baltimore clipper.\n\nWith virtually all of Antillean trade being illegal according to the laws of one or another European country, vessels had to be fast and light, so everything was sacrificed to speed in this new model, which carried less freight than state-sanctioned merchant marines. These vessels were narrow and shallow, so they could go places large ocean-going vessels couldn't. The crew slept on deck. Many were fitted with \"sweeps\" (oars), so they could drop their sails and creep unseen when they set sail at night, in the dark of the moon. With their strongly raked masts, they could outfly any ship if they were to its windward. They looked dashing; the Baltimore boatwrights prided themselves in the quality of their construction.\n\nThough the major influx of Domingans did not come to Louisiana until 1809, the professions of journalism and law there were begun by Domingans; they founded newspapers and participated in the writing of the state's constitution of 1812, which was debated and written in French, then sent to Washington in translation. Stars of Saint-Domingue's theater scene took refuge in New Orleans, where their language was understood. The first great US piano virtuoso and arguably the greatest nineteenth-century US composer was the Domingan-descended New Orleanian Louis Moreau Gottschalk. Naturalist and artist John James Audubon was Domingan-born.\n\nOne celebrated refugee of the Haitian Revolution went to Spanish-controlled Florida. The black, Domingan-born general Georges Biassou was an early leader of the slave uprising\u2014he had received a blessing from Boukman himself\u2014and was subsequently Toussaint Louverture's superior officer in the Spanish army. Toussaint went over to the French army after the National Convention ratified Sonthonax's emancipation proclamation, but Biassou remained with the Spanish. The two wound up fighting each other before Biassou ultimately evacuated.\n\nBiassou was a fully commissioned general of the Spanish army in good standing when he arrived in Florida in early 1796 with an entourage of twenty-three, including five family members and one slave. \"The black general strolled through the streets of St. Augustine in fine clothes trimmed in gold,\" writes Jane Landers, \"wearing the gold medal of [Spanish King] Charles IV, a silver-trimmed saber, and a fancy ivory and silver dagger.\" As slaveowning planters in Florida\u2014many of them English speakers who had come in from the north\u2014watched in horror, Biassou and his men received land grants and began clearing the ground for plantations. They spoke of more of their black countrymen being on the way, though Spain wasn't about to let that happen.\n\nA black man who had killed slaveowners was living in comfort, with full military authority, in Florida. Nothing could have been more calculated to disturb the Georgians and Carolinians, who for their part were experiencing an agricultural revolution that would create a vast new market for slaves.\n\n*Since the nation of Haiti did not exist until January 1, 1804, we use \"Saint-Domingue\" to refer to the territory prior to that date; contemporary reports often refer to \"St. Domingo,\" not to be confused with the city of Santo Domingo on the Spanish-speaking side of the island. We call the people \"Domingans,\" reserving the word \"Haitian\" for those in or coming from Haiti after the existence of that republic. We refer to the entire conflict as the Haitian Revolution, while acknowledging that the name obfuscates the multi-threaded nature of the conflict.\n\n_The_ Lynx, _a replica of a privateer from the War of 1812, flying the fifteen-star flag (1795\u20131818)._\n\n#   Part Four\n\n# **The Star-Spangled Slave Trade**\n\n#   25\n\n# **The Cotton Club**\n\n_The experiments made in planting Annual Cotton has generally prov'd successful in respect to quantity and quality. But unless some engine be found as will take out the Seed agreeably to that Sort which is rais'd in the West Indias, no great quantity can be obtain'd. That of the West Indias will not produce Cotton here and is easily divested of its' Seed; But the Sort which grows here is far more difficult, and at present is no otherwise cleans'd than by a tedius picking. 1_\n\n\u2014Thomas Causton, letter to the Trustees of Georgia, 1741\n\nCOTTON CROPS HAD BEEN grown in the North American colonies every year from 1607 forward, but American cotton was not wanted by the English during colonial days, nor was mass production of cotton textiles yet possible.\n\nBritish policy was protective of its woolens industry. But Britain was running out of land on which to raise sheep for wool, and a series of industrial inventions caused the manufacture of cotton textiles to overwhelm the older woolens manufacture. Machines could card the cotton (untangle its fibers) and comb it (align the fibers, making a more compact, tightly weavable yarn). Hargreaves's spinning jenny (1764) spun the yarn into thread multiple strands at a time. All the different machines were combined under one roof into a single, integrated textile factory, and then there were a thousand such factories. Remembered as the Industrial Revolution, its input was cotton, and cotton's input was enslaved children.\n\nCotton's desirability for manufacturers rested on its unique strength: each cotton fiber (the \"lint\") is a single cell. First the fibers grow long, then, after seventeen days, the cellulose walls begin to thicken. There are only four species of domesticated cotton, which emerged independently in isolated parts of the world. Of the two that would grow in the Americas, one, _Gossypium barbadense_ , became known as long-staple, or \"Sea Island,\" or \"black-seed\" cotton, while the other, _Gossypium hirsutum_ , was short-staple, or \"upland,\" or \"green-seed\" cotton. The two were genetically isolated from each other and did not easily interbreed.\n\nThe fibers of _G. barbadense_ were longer and stronger, and it was easier to separate the fibers from the seeds and the lint; but in North America, it would only grow on the Sea Islands and inland for thirty miles or so. This was the crop that Thomas Causton was lamenting would not grow in Savannah, but in 1786 it was successfully raised for the first time in Georgia with seed brought from the Bahamas. The fibers could be removed from the seed mechanically by means of a roller gin\u2014a machine with rollers that plucked the fiber off, preserving its length and orientation.\n\nThe other variety of cotton, _G. hirsutum_ , which today accounts for more than 90 percent of the world cotton crop, could be cultivated across a much broader area, and it had a higher yield than long-staple; unfortunately, as Causton noted, it was too labor-intensive to clean by hand. Planters were growing it in areas where Sea Island cotton would not grow, using several types of cumbersome, labor-intensive foot- or hand-and-foot-operated gins to pull the fibers from the seed.\n\nA mechanical solution to that problem could open up vast new possibilities for cotton, and Thomas Jefferson wanted to find it. The US Patent Office, established in 1790, was his responsibility as secretary of state. He wrote in 1792 to William Pierce of New Jersey, who was advertising a machine that would mechanically tear the fibers from the boll and sweep the seeds away, but Pierce failed to answer the letter. The following year, however, Jefferson received a drawing of such a machine from Eli Whitney, a newly minted Yale graduate and mechanical prodigy from Massachusetts. While staying as a guest on the Mulberry Grove plantation near Port Wentworth, Georgia, Whitney built a prototype cotton gin. Jefferson expedited the patent, writing Whitney on November 16, 1793:\n\nThe only requisite of the law now uncomplied with is the forwarding a model, which being received your patent may be made out & delivered to your order immediately.\n\nAs the state of Virginia, of which I am, carries on household manufactures of cotton to a great extent, as I also do myself, and one of our great embarrassments is the cleaning the cotton of the seed, I feel a considerable interest in the success of your invention for family use.\n\nJefferson's term \"family use\" referred, as was customary, to his extended \"family\" of captives, as per Whitney's sales-talk answer to Jefferson: \"It is the stated task of one negro to clean fifty [pounds]... of the green-seed cotton Per Day. This task he usually completes by one oClock in the afternoon.\" Whitney's machine, a sawtooth, or \"saw,\" gin, solved the problem of cleaning cotton by redefining it. The twenty-six-inch-long tabletop machine didn't pull the fibers off, leaving them intact and combable, like the roller gin; it used teeth to chomp them off, so it could not be used on long-staple cotton without destroying its value. It produced an inferior fiber, a third the length of roller-ginned Sea Island cotton, that was not what textile manufacturers wanted to use for high-value goods.\n\nBut massification was happening. While the _hirsutum_ cotton processed by Whitney's gin was of lower quality, the South could turn out a tremendous amount of it. Having transitioned to highly productive steam-powered Watts-engine mills, Lancashire's textile businesses had the capacity to handle all the cotton the South could produce. The immediate consequence of Whitney's saw gin was to give upcountry South Carolina and Georgia their new staple crop\u2014the two states produced the majority of United States cotton until 1821\u2014but its long-term consequence was to create the cotton kingdom of the South.\n\nIt was not simply a switch that was flipped on in 1793: improvements and accommodations had to be made, including to the machines of Britain, which had to be refitted for the shorter-staple cotton. The power loom, first used in 1785, took until about 1820 to become reliable, but once it was, it gave Britain's textile industry capacity far in excess of the available supply of cotton thread. At first the gins were powered by horses, then by steam. Another invention, the screw press, compacted cotton into bales, which were then compressed into place in the holds of vessels by \"screwmen\"\u2014highly paid, muscular artisans who used specialized equipment to apply enormous screw-pressure to the already compressed bales.\n\nThe success of the saw gin sparked new enthusiasm for premium long-staple Sea Island cotton as well, which, processed by the roller gin, sold for three times as much per pound as _hirsutum_ , in much smaller quantities.\n\nMore or less concurrently with the rise of cotton, Spanish Louisiana became a late arrival to the longtime major staple crop of the hemisphere: sugar. Amid the market scramble caused by the Saint-Domingue rebellion, sugar was fetching high prices that caused explosive growth of canefields in Cuba to the south and east of Havana. The port of Matanzas, which the British had not even bothered with when they occupied Havana in 1762, would soon begin its career as the cultured, affluent \"Athens of Cuba.\" Cuba was in constant communication with Spanish Louisiana, whose governor reported from New Orleans to the Spanish captain general in the strategic hub city of Havana.\n\nUnlike Cuba, Louisiana could not make sugar. Louisiana freezes in the winter, and its nine months' growing season was thought to make sugar production unfeasible, since a crop of sugarcane was considered to require some thirteen to fifteen months of growth and several months of harvest. But in 1795, working with a Domingan sugar chemist, the planter \u00c9tienne de Bor\u00e9 found a way to produce a light, sweet syrup from the sucrose in Louisiana cane; the method required the labor force to work long hours in damp cold. There had been other such initiatives, but Bor\u00e9's sugar crop, produced by forty enslaved laborers, was the famous one: after it brought him $12,000, sugar plantations sprang up along both sides of the Mississippi. By the following year there were ten sugar refineries in operation.\n\nSugar operations were large and capital-intensive: those with fortunes could make their fortunes larger, but it was much easier to get started in cotton. The sugar plantations of south Louisiana became the highest-priced farmland in the South as the area around the lower Mississippi filled up with slave labor camps and the mansions they supported.\n\nThe sugar regime had come to North America, creating a voracious new demand for labor. But there was a complication: the Pointe Coup\u00e9e slave rebellion conspiracy was uncovered in the spring of 1795. The testimony from the promptly held trials made it clear that radical ideas from the French and Haitian Revolutions had reached Louisiana. According to the testimony, conspiracy leader Jean Baptiste said, \"we could do the same here as at Le Cap [Cap Fran\u00e7ais in Saint-Domingue].\" Twenty-three people were promptly tried and executed, and Spanish authorities, already nervous about infiltration of Jacobin radicals into the French-speaking population they uneasily governed, banned slave importation, even as labor-hungry plantations were springing up along the banks of the river, where the conspirators' heads were placed at intervals, impaled on pikes.\n\nBut the planters were determined to acquire slaves, and their regime had only begun.\n\nThe pro-French turmoil in Philadelphia pushed the Federalists closer to Britain.\n\nThe 1794 treaty that John Jay negotiated with Britain at President Washington and Treasury Secretary Hamilton's behest resolved a number of issues stemming from the War of Independence and laid the groundwork for ten years or so of relative peace between Britain and the United States, which was a boon for American shippers. However, Jay, a pro-British Federalist who had been against American independence and who detested slavery, dropped a major sticking point from the negotiations: the issue of compensation for slaveowners for the loss of their slaves during the war. The treaty was then more easily resolved, but at the domestic political price of cutting the Southern claimants loose. Moreover, the treaty appeared to be an alliance with Britain, which in those tense times meant against France.\n\nBeginning with Jefferson, who had filed a claim for compensation, Southern slaveowners were furious about Jay's dropping their demands, and they made their displeasure felt. Henceforth, US diplomats in negotiations with foreign powers, whatever their domestic position on slavery\u2014even John Quincy Adams\u2014maintained \"a unanimity in favor of guarding slavery from foreign harm,\" in Ward M. McAfee's words, \"even to the extent of claiming it as a constitutionally recognized national institution.\"\n\nIn Nashville, the twenty-eight-year-old Andrew Jackson thought Jay's treaty had created an \"alarming situation\" and wondered, \"will it End in a Civil warr[?]\" In Paris, Jay's treaty was seen as aggression. As the pro-French Democratic-Republican societies in the United States protested, the partisan breach in American politics widened. English and French alike identified the party of Hamilton as pro-English and that of Jefferson as pro-France.\n\nJay's Treaty seems to have been a spur for Manuel Godoy, the \"Prince of Peace\" in charge of Spanish affairs for King Carlos IV, to cut a deal with the Americans. On October 27, 1795, negotiations with Spain by Thomas Pinckney (Charles Cotesworth Pinckney's younger brother) yielded the Treaty of San Lorenzo, by which Spain acknowledged the United States' \"right of deposit\"\u2014i.e., to place goods for transshipment\u2014at the port of New Orleans, which meant that the cotton and sugar that was beginning to be cultivated in large quantities could find an outlet, along with all the other products that came from the growing upriver population.\n\nThe Treaty of San Lorenzo temporarily resolved a part of the Florida controversy by ceding to the United States a portion of the territory that comprised about the lower third of present-day Mississippi and Alabama. This Mississippi Territory did not extend down to the Gulf Coast, but it included the Mississippi River port of Natchez. It was a tremendously useful acquisition for the businesses of cotton and slaves, but the all-important coastal zone, including the port of Mobile, remained part of Spanish-controlled West Florida.\n\nAs part of organizing the Mississippi Territory, the Anglo-Americans marked an international boundary in 1798 by hacking out a neutral ground between their territory and that of the Spanish: a sixty-foot gash in the forest growth from the Mississippi River eastward all the way to Georgia\u2014cut by slave labor, needless to say. Foreign slave importation into the new territory was strictly forbidden; the labor would have to be purchased from domestic sources.\n\nIn Paris, the five-man Directory, three of them Jacobins, brought a more conservative government to power on November 2, 1795. The Royalist Charles Maurice de Talleyrand-P\u00e9rigord, who had lived unhappily in Philadelphia after fleeing the Terror (unlike Gen\u00eat, he was never officially received by President Washington), returned home on September 25, 1796, and became foreign minister for the Directory in July 1797, just before the Coup of 18 Fructidor (September 4) brought a disastrous group to power within the Directory. Authoritarian and incompetent, this new Directory repressed journalists and declared the state bankrupt, stiffing France's creditors, even as the Corsican general Napoleon Bonaparte was conquering Italy in the name of France.\n\nAt a time when candidates did not campaign for office in the public way we have since become used to, John Adams beat Thomas Jefferson in the 1796 presidential election, one that entailed a Virginia-South Carolina split: Adams's running mate was South Carolina Federalist Charles Pinckney, and South Carolina failed to support Jefferson. But Jefferson got the second highest vote total, so under the laws then in force, he, not Pinckney, became vice president, though he was Adams's political enemy. (Adams may have had occasion to recall the words of diplomat Arthur Lee, who in 1788 when sending a copy of the draft Constitution to Adams in England, complained about the creation of the office of vice president, \"whose sole business seems to intrigue.\")\n\nBy then, the diplomatic break between France and the United States was complete. With Talleyrand as its would-be head, the Directory looked to restore the colonial project that the Seven Years' War had arrested thirty years previously: to control the North American continent, even as France expanded its empire to control the rest of the world. By 1796, six hundred US merchant ships were doing business in Saint-Domingue. But when French privateers started attacking, hundreds were lost. When three American diplomats (John Marshall, Elbridge Gerry, and Charles Cotesworth Pinckney) tried to resolve the issue, Talleyrand sent go-betweens to solicit an enormous bribe\u2014$250,000\u2014before he would allow them to be received as diplomats. This was the \"XYZ Affair,\" so called because French diplomats' names were redacted from documents that, to Talleyrand's surprise, the Adams administration released to the public.*\n\nAmerican indignation over XYZ was the spark, though not the reason, for the Quasi-War with France, an undeclared war during the second half of the John Adams administration, from 1798 to 1800. The affair cost Talleyrand his post with the Directory, though he soon worked his way back into power via his alliance with the ascendant Napoleon.\n\nThe number-one reason for the Quasi-War, as enumerated by the Federalist Secretary of State Timothy Pickering (leader of a disunionist movement for New England to secede and establish a Northern confederacy), was \"spoliations and maltreatment of [US] vessels at sea by French ships of war and privateers.\" The pro-British Federalists began what has been remembered as \"black cockade fever,\" wearing long trailing black ribbons from the back of their hats. As Republicans countered with red\u2014or red, white, and blue\u2014ribbons, Philadelphia divided into two color-coded camps.\n\nSome Federalists believed that the democratic frenzy was the result of a conspiracy of a secret society of Illuminati, with French and Domingan membership. The Republican position was expressed by Virginia senator Henry Tazewell in a letter to Andrew Jackson: \"The Contest between them [England and France] is a Contest of political principles. One or the other must be annihilated... Either monarchey or Republicanism must be rooted out of Europe, or the War will not cease. If England succeeds, Monarchy will become more formidable then ever to the liberties of mankind... If France succeeds liberty will at least for a time be emancipated from the despotism of Kings.\"\n\nAttempting to combat a prolonged period of domestic political unrest following the French Revolution and war with France, and pushed by Pickering, the Adams administration passed the Alien Act, with which they hoped to deport French people\u2014they were never used for prosecution, but they motivated some French-speakers to leave the United States\u2014and the Sedition Act, which they used against the highly partisan press.\n\nIn response, Jefferson drafted the Kentucky Resolutions of 1798, in which he argued that states could find federal laws unconstitutional and oppose them. He did this anonymously, while he was Adams's vice president and as such was in theory part of the administration that had promulgated the Alien and the Sedition Acts. His stalking horse was Kentucky state representative John Breckinridge, who introduced the resolutions in the Kentucky House as his own, keeping Jefferson's involvement secret.\n\nThough the Kentucky Resolutions are largely forgotten today, they became a touchstone for antebellum separatists because in them Jefferson put the soon-to-be-a-buzzword \"nullification\" into the American political vocabulary: \"[T]he several states who formed [the Constitution], being sovereign and independent, have the unquestionable right to judge of its infraction; and that a nullification, by those [states], of all unauthorized acts... is the rightful remedy.\" Madison in 1799 drafted a similarly anonymous, somewhat milder, document, the Virginia Resolutions, which did not use the word \"nullification.\"\n\nBy the time Toussaint negotiated a British withdrawal in 1798, some fifteen thousand British soldiers had died during Britain's ill-advised campaign to take Saint-Domingue. One of the great military debacles of British history, it marked in blood the point at which Britain turned away from its sponsorship of plantation slavery. By this time, Toussaint was firmly in control in Saint-Domingue, and, as life became more orderly there, some planters even began returning.\n\nIn France, the Coup of 18 Brumaire (November 9), 1799, definitively put an end to dreams of democracy and republicanism, deposing the Directory in favor of the French Consulate government. This left only one republic in the world: the United States. Talleyrand was the coup's chief political strategist and, as of February 7, 1800, its head was First Consul Napoleon Bonaparte, who had returned from a failed two-year mission in Egypt days before.\n\n\"The recovery of colonial power was the first of all Bonaparte's objects,\" wrote Henry Adams, and every \"decisive event in the next three years of his career was subordinated to it.\" Bonaparte's Consulate intended to re-establish France's lost colonial plantation empire in the Americas, but, in the words of biographer Steven Englund, \"the measures proved to be such a failure that posterity has stopped seeing the policy as foundational.\"\n\nNapoleon's ascendancy was the definitive end of the abolition movement in France. A new French Constitution specifically exempted the colonies from metropolitan law, which was tantamount to re-legalizing slavery. Saint-Domingue was still theoretically under the French flag, but Toussaint was in charge and had restored some of the colony's sugar production using conscripted labor. In order to re-establish French control of Saint-Domingue, it was necessary to pacify the high seas so as to have clear sailing for the fleet, which Talleyrand and Napoleon did by making peace with the United States\u2014easily accomplished\u2014and with Britain, which took longer.\n\nRelations between Toussaint Louverture's government in Saint-Domingue and the United States were not bad under President Adams. Saint-Domingue, still in theory a colony of France, was exporting coffee and sugar again under Toussaint, and US merchants, especially those from Baltimore, were doing business in its port cities despite the problems. During the Quasi-War, Toussaint had taken the extraordinary step\u2014for which, along with related offenses, he paid with his life\u2014of brokering a separate peace with Adams, because supplies from North America were essential to Saint-Domingue's survival. An arrangement between the United States and Britain brought the British navy to patrol Saint-Domingue, allowing for commerce to continue, though the conservative British prime minister William Pitt the Younger was horrified by the idea of a black government.\n\nThe Adams administration went so far as to support Toussaint with the US Navy (the first intervention by the US military in another country's war) in a decisive 1800 battle in the south of Saint-Domingue between forces commanded by Toussaint's general Jean-Jacques Dessalines and those of Andr\u00e9 Rigaud.\n\nAs the United States entered into war with France, there was renewed fear in the South that slaves would once again become weapons of war in the hands of the enemy. Henry Knox, the former secretary of war, in the words of Alexander DeConde,\n\nurged Adams to raise an army for protection against a possible attack by \"ten thousand blacks\" recruited by the French. He feared that the invaders would land at \"the defenceless ports of the Carolinas and Virginia,\" where slaves would join them in a march of conquest.\n\nRumors spread saying that special Negro agents were distributing arms among the slaves in preparation for the French attack. These rumors were repeated in a Federalist pamphlet published in April. \"Take care, take care, you sleepy southern fools,\" a Federalist gazetteer warned. \"Your negroes will probably be your masters this day twelve month.\"\n\nThough Spain was the pre-eminent colonial power of the Americas, it was increasingly subordinate to France. Louisiana had been founded by France, but had been given over to Spain in 1762 as part of France's disgrace at the close of the Seven Years' War. Now Napoleon made a secret pact with Carlos IV, the Italian-born Bourbon king of Spain to recover Louisiana. Carlos, who flattered himself Napoleon's ally but was more like his stooge, was known as El Cazador (The Hunter), for the avidity with which he hunted game on his private preserve, to the neglect of affairs of state. In exchange for Louisiana, Napoleon swapped Carlos the Italian Duchy of Parma as a kingdom for his son-in-law. Key to this retrocession of Louisiana from Spain to France was Napoleon's promise not to alienate\u2014not to give away or to sell\u2014Louisiana.\n\nNapoleon's intention in retaking control of Louisiana was to use it as a supply base for the plantation empire he was planning to re-establish on Saint-Domingue, where every bit of ground was to be used to produce cash crops. The English sugar islands were being provisioned from the United States, and in the absence of a French supply base, so would a French island colony have to be.\n\nHostilities between France and the United States ended on September 30, 1800, when Napoleon's brother, Joseph Bonaparte, signed with the Adams administration the Convention of Mortefontaine, named for the lesser Bonaparte's country estate. But, writes Henry Adams:\n\nThe next day, October 1, [Louis Alexandre] Berthier [Napoleon's chief of staff] signed at San Ildefonso the treaty of retrocession [of Louisiana to France], which was equivalent to a rupture of the relations established four-and-twenty hours earlier. Talleyrand was aware that one of these treaties undid the work of the other. The secrecy in which he enveloped the treaty of retrocession, and the pertinacity with which he denied its existence, showed his belief that Bonaparte had won a double diplomatic triumph over the United States.\n\nNapoleon's plan to establish an empire in the Americas was moving forward. Meanwhile, Saint-Domingue's legacy of emancipation via violent rebellion was percolating throughout the slave societies of the hemisphere.\n\nIn Cuba, practitioners of the Kongo religion speak of Zarabanda, \"Nsalabanda,\" the blacksmith god of iron and war. In Haiti, there is Ogou Feray, the creolized Yoruba blacksmith liberation-fighter _lwa._ In Richmond, in 1800, a well-planned conspiracy was discovered, led by one Gabriel, a literate, enslaved blacksmith who could split a grain scythe down the middle to make a pair of fearsome swords and had stockpiled a number of them. Gabriel had been sentenced to hang the year before, when he bit off the ear of a white overseer who had whipped him, but he was too valuable for his captor, Thomas Prosser, to lose, so Gabriel was allowed to take advantage of an archaic law that commuted his sentence to being publicly branded if he could quote a Bible verse. Let off on the condition of good behavior, with a brand burned into his skin, he was soon jailed again, forcing Prosser to post a thousand dollars to get him back, an indication of how lucrative the rented-out services of a blacksmith could be.\n\nVirginia had modernized its penal code as of 1796, reclassifying twenty-seven different kinds of offenses as punishable by prison time instead of corporal abuse and restricting capital punishment to murderers. To deal with the new prison population this change would generate, Jefferson's friend, the English-born architect Benjamin Henry Latrobe, the first professional architect working in the United States, received his first major American commission in 1797, to build the Virginia State Penitentiary in 1797. The first penitentiary to be built as such in the United States, it was an Enlightenment-era prison, part of an agenda that emphasized a notion, advanced by Jefferson, of reform over punishment, with the architectural innovation of individual cells that facilitated the carceral innovation of solitary confinement. It quickly became a hellhole, was rebuilt in 1905, and was closed in 1992.\n\nGabriel's conspirators planned a surprise attack on that partly finished penitentiary, where the militia's weapons were stored but were only lightly guarded. After that, it was said, they would burn the city and hold Governor James Monroe hostage. Gabriel's plot was quite real, and could well have achieved those tactical objectives. Terrifyingly for the slaveowners, it was, like Boukman's uprising, widely networked among agents on different plantations. It grew out of routine socializing among the enslaved of the region, who might see each other in a number of ways, ranging from clandestine nighttime visits to church socials on Sunday.\n\nGabriel and his network of conspirators were animated by an ideology that resonated fearfully in the post-Saint-Domingue world: with the bold paralysis of the apparatus of state and the violent chaos they intended to cause as leverage, they planned to demand freedom for the slaves of Virginia. For the terrified slaveowners of Richmond, \"the most commonly repeated notion of how far the slaughter of whites would go simply held that all whites would be killed,\" writes Lacy K. Ford, \"except Quakers, Methodists, and Frenchmen, whom Gabriel planned to spare because they had tried to help the slaves win freedom.\"\n\nMuch the same way that the Stono Rebellion was a clear demonstration of the threat posed by Spain, Gabriel's plan was understood to be a signal of the perceived vulnerability of the slave regime to the revolutionary abolitionism of the French, even though in fact the viciously anti-abolitionist Napoleon was now in charge there. As with the later scapegoating of \"outside agitators\" in the civil rights era, saboteurs were thought necessary to catalyze uprisings among enslaved laborers, who were believed to be otherwise inert. Quite possibly there had been a \"Frenchman\" or two trying to foment slave uprising, or perhaps it was a figment of the paranoia of the times; the implication of two unnamed Frenchmen by witnesses at the trial cast a pall of suspicion over all the \"French\" people in Richmond, whether French-born or merely Huguenot-descended. The press denounced \"the French principle of liberty and equality,\" an idea that was self-evidently un-Virginian, because it was incompatible with slavery.\n\nGabriel's rebellion was foiled by a spectacular storm\u2014in Monroe's words, \"checked by the extraordinary torrent of rain which fell\"\u2014on the night the assault had been planned for, which was interpreted by both conspirators and townspeople as divine intervention. The plot was then betrayed by Pharoah and Tom, two enslaved informers fearful of the rebellion's consequences, who were subsequently purchased from their owners by the State of Virginia for five hundred dollars each and were not only emancipated as a reward, but also ultimately received an annuity of fifty dollars each a year. Amid fears that the conspiracy might still be active and moving forward, Monroe initiated a manhunt for Gabriel, who was described by Prosser as \"twenty four years of age, six feet two or three inches high, darkish complexion, long visage, with a gloomy insidious brow, short black knotty hair, some scars on his head.\"\n\nMonroe informed Jefferson on September 9 that \"about\" thirty prisoners were being held. There was considerable concern that the new, untested penitentiary would not be able to hold them; adding to the tension, it also turned out that four thousand muskets delivered to the militia and stored in the penitentiary were shoddy goods that were \"improperly constructed\" and \"badly executed.\"\n\nThough the conspiracy had not resulted in any bloodshed, trials began on September 11 and hangings began the following day. On September 18, thirteen men from Richmond petitioned the Henrico County court to move the executions somewhere out of sight, \"as the frequent Executions that have lately taken place, has been extremely distressing to the view of our families\u2014especially the female members.\" In response, three of the condemned were halted \"in the cart\" on their journey to the gallows for a reprieve until the place of execution could be moved.\n\nWith a price of three hundred dollars on his head, the \"Black General\" Gabriel escaped Richmond by boat, but ran aground four miles below Richmond. Taken up by a schooner that was going to Norfolk, he was brought back to Richmond under heavy guard on September 28, a few hours before Monroe's youngest child died after a few days' illness, overwhelming him \"with grief,\" as he wrote to Madison the next day.\n\nMonroe and Gabriel\u2014whom Monroe referred to not by his name, but as \"this slave\"\u2014had what must have been a dramatic face-to-face: \"From what he said to me,\" wrote Monroe, \"he seemed to have made up his mind to die, and to have resolved to say but little on the subject of the conspiracy.\" Gabriel attempted no defense at his trial but requested that his execution be postponed so that he could be hanged together with the others who would also be convicted. The request was granted, and Gabriel was hanged on October 10 together with George Smith, Gilbert, Tom, William, and Sam Graham. By October 24, twenty-six people had been executed.\n\nWith presidential voting about to begin October 31, it was a time of great political tension between Federalists and Democratic-Republicans. Jefferson was running for president again, and this time he was the leading candidate.\n\nThe poison-pen propagandist James Callender wrote to his employer, Thomas Jefferson, on September 13 from the Richmond jail, where he was serving his six-month sentence, that \"nothing is talked of here but the recent conspiracy of the negroes.\" Callender, who had fled Scotland one step ahead of the law in 1793, was one of only ten people convicted under President Adams's Sedition Act, for his book _The Prospect Before Us._ Funded by Jefferson, it was a sleazy work of character assassination that attacked Hamilton and Adams as monarchists while praising Jefferson in immodest terms.\n\nTwo days later, Monroe informed Jefferson that \"the plan of an insurrection has been clearly proved, & appears to have been of considerable extent. 10. have been condemned & executed, and there are at least twenty perhaps 40. more to be tried, of whose guilt no doubt is entertained.\" Twenty-six conspirators were hanged. Jefferson, whose preferred method of dealing with troublemakers on his plantations was to sell them to Southbound traders, wanted them disposed of by sale instead of hanging, and nine conspirators were, thereby realizing some income.\n\nIn the Richmond _Virginia Argus_ of October 3, 1800, Callender\u2014still loyal to Jefferson\u2014responded to charges that had been levelled against him of having somehow been involved in Gabriel's rebellion by changing the subject back to vilifying Alexander Hamilton:\n\nIf an idea so monstrous as that of promoting an African conspiracy can have entered into the head of any white man, he must have been a _Federalist;_ for this plain reason. An insurrection, at the present critical moment, by the negroes of the southern States, would have thrown every thing into confusion, and consequently, it was to have prevented the choice of electors in the whole, or the greater part of the States to the south of the Potomac. Such a disaster must have tended directly to injure the interest of Mr. Jefferson, and to promote the slender _possibility_ of a second election of Mr. Adams.\n\nI do not, for my part, believe that any white person whatever was concerned in the business. But if the country contains one man capable of conceiving such a project, it corresponds, in preference to the character of any other person, with that of Alexander Hamilton, the theoretical incendiary of Pittsburg,* and the grand Patriarch of American calamities.\n\n\u2014 JAMES T. CALLENDER.\n\nRichmond Jail.\n\nCallender subsequently wrote a second volume of _The Prospect Before Us_ , also funded by Jefferson.\n\nGabriel's plot sensitized electorate and politicians alike to the dangers of slave rebellion, with obsessive focus on the possibility of ideological contamination from Saint-Domingue. Virginia had a far greater slave population than anywhere else in the United States. Its 345,796 enslaved were overwhelmingly (322,199) in the eastern district, with only 23,597 of them in the non-plantation west of the state. Virginia slaveowners had been terrorized by the nightmare that \"the horrors of St. Domingo\" could happen to them; now, they thought, it was coming closer. The popular panic facilitated the adoption of the \"Negro Acts,\" which had been previously been considered too harsh to pass. These were new state laws directed at slaves, and partly also at pro-emancipation evangelicals, particularly Methodists and Baptists. A suite of laws forbade masters from manumitting, removed rights of assembly for blacks and all assembly by them at night, and forbade religious instruction of slaves\u2014though after pressure from evangelicals, the law was amended to allow religious gatherings if a majority of white people were present. A new military-style police organization, the Public Guard, was created as part of the militia in Richmond in 1801.\n\nPresident Jefferson wrote his minister to Britain, Rufus King, in 1802 that \"the course of things in the neighboring islands of the West Indies appears to have given a considerable impulse to the minds of the slaves in different parts of the US. A great disposition to insurgency has manifested itself among them, which, in one instance, in the state of Virginia, broke out into actual insurrection,\" though of course Gabriel's conspiracy did not break out into actual insurrection but was merely planned. Jefferson, who thought the many hangings resulting from Gabriel's conspiracy\u2014\"between 20. and 30. I believe\"\u2014too severe, affirmed that they had caused public revulsion: \"so extensive an execution could not but excite sensibility in the public mind.\" In other words, as terrified as the Virginians were, the repression was too grisly. The purpose of Jefferson's letter to King\u2014at the request of the Virginia legislature, he noted\u2014was to ask him to make inquiries in London into the possibility of using the English Sierra Leone colony not only as a \"receptacle\" for \"insurgents\" but also for future \"emancipated negroes.\"\n\nRichmond's African American burial ground was rediscovered in the 1990s, and there is now a state historical marker for this potter's field at Fifteenth and Broad. The wide expanse is partly covered over by I-95 and was for years partly buried under a Virginia Commonwealth University parking lot. Before that, it had been the dog pound, and, before that, the site of the Richmond City Jail. The lot was transferred to the city in response to community initiatives, resodded, and rededicated. It is now a flat, grassy memorial space framed by the interstate high overhead on one side and rail cars on the other.\n\n_A circle marks the approximate site of the execution of Gabriel. Richmond, June 2013._\n\nTo mark the gallows where Gabriel and five coconspirators were hanged in 1800\u2014not that the exact spot is known\u2014there is nothing more than a yellow cord strung around ground-level wickets, making a barely perceptible circle of power in the immensity of the field. To one side are two large trees with sashes tied around them, and, when we visited, small altars in the African manner. No one is allowed to play sports or picnic on the large field, respecting the space's memorial status as the trucks and train cars roll by above. It's walking distance from where Patrick Henry made his \"Liberty or Death\" speech, a quarter-century before Gabriel.\n\n*It was first referred to as the WXYZ affair, in which \"W\" was Caron Beaumarchais, who had acted as a go-between; Beaumarchais is also remembered as the librettist of Mozart's class-conflict opera farce _Le Nozze di Figaro._\n\n*Referring to the recent Whiskey Rebellion in Pennsylvania, which had erupted in response to a tax Hamilton had tried to impose.\n\n#   26\n\n# **The Terrible Republic**\n\n_Slaves!... Let us leave that qualifying epithet to the French themselves: they have conquered to the point of ceasing to be free. 1_\n\n\u2014Haitian Declaration of Independence\n\nGEORGE WASHINGTON DID NOT live to see Thomas Jefferson become president, nor were the two men on speaking terms when Washington expired, along with the eighteenth century, on December 14, 1799. Washington's widow, Martha Custis Washington, is said to have thought Jefferson \"one of the most detestable of mankind.\"\n\nLacking South Carolina's support, Jefferson had lost the 1796 election to John Adams. Open campaigning was at the time thought to be beneath the dignity of a presidential candidate, but as 1800 came around, lest anyone in South Carolina think the emancipation\/deportation proposal of _Notes on the State of Virginia_ meant that he was soft on slavery, Jefferson let it be known via Charles Pinckney that he \"authorized his friends to declare as his assertion\" that the Constitution did not give Congress the right to \"touch in the remotest degree the question respecting the condition or property of slaves in any of the states.\"\n\nAfter a complicated election, culminating in a protracted standoff over a tie vote with Aaron Burr in the House of Representatives, Jefferson prevailed over the incumbent Adams, becoming president on March 4, 1801, with Burr as vice president. For the next twenty-four years, the presidency would be occupied by a \"Virginia dynasty\" of Jefferson and his prot\u00e9g\u00e9s\u2014actually, a Piedmont dynasty, from the Shenandoah Valley above the fall line of the James River, where Jefferson, Madison, and Monroe were relative neighbors. During those years (and subsequently, for that matter) foreign and domestic policy alike would reflect the concerns of the Southern states, and specifically Virginia: protecting slavery (which meant expanding it); preventing slave rebellion (which meant isolating Haiti); free trade (with the significant exception, in Virginia's case, of protectionism for the domestic slave trade); hard money (though an all-metal currency regime was utterly unworkable); a weak federal government (though once the Republicans took power, they came to like wielding it); and a budgetary conservatism that excluded projects for the public good.\n\nJefferson's ascent to the presidency was the first peaceful transfer of political power to another party in recorded history. He seems to have truly believed, as he expressed in an 1819 letter, that his election was a \"Revolution of 1800\" that was as significant a revolution as the one his younger self had personified with the Declaration of Independence. The new Democratic-Republican party, usually just known as Republicans but sometimes as Democrats, attempted to implement Jefferson's philosophy of governance, which proved to be impractical.\n\nJefferson wanted an agrarian republic, where the \"chosen people of God\" would \"labor in the earth.\" For the general operations of manufacture, \"let our workshops remain in Europe,\" he wrote in _Notes_ , though he subsequently founded a nail factory. He didn't want there to be _cities_ , which he compared to \"sores\" on a body, and to that end he starved Washington City of infrastructural funds during his presidency, so that the capital consisted of two magnificent buildings in a malarial, muddy swamp.\n\nJeffersonian democracy, as it came to be called, held that states' rights were paramount, and central government was at best a necessary evil. Debt was an evil to Jefferson, something to be cancelled as quickly as possible. Banks were an evil. Slavery was a great evil, but we have no alternative to the riches it brings.\n\nKeeping a standing army was, as Madison expressed it during the Virginia ratification debate, \"one of the greatest mischiefs that can possibly happen.\" Jefferson attempted to defend the country from foreign aggression entirely by commercial sanction, a method he called \"peaceable coercion.\" There would be nothing peaceful, however, about the coercion employed domestically to repress slave escape or rebellion. The constitutionally sanctioned \"well-regulated militia\" could put down rebellions and apprehend black people traveling without a pass, selling them to a trader if no one claimed them.\n\nAs president, Jefferson committed to his theory of governance by paying down the debt quickly rather than investing in defense. Moreover, in spite of having a long coastline to defend, he dismantled what military readiness the nation had, reducing the army from five thousand to three thousand, and, in a backhand blow to New England, mothballing the successful United States Navy that Adams had built.\n\nA compulsive tinkerer, Jefferson couldn't resist refitting the navy, though he had no firsthand knowledge of naval affairs. He was taken with the idea of light, portable gunboats carrying a crew of twenty or so. These were heavily used in the Barbary War that the US Navy fought from 1801 to 1805 in Mediterranean North Africa, although the navy also relied on frigates and brigs in that war. Jefferson's remarkably bad idea was to make the entire navy into a fleet of the theoretically cheaper gunboats, relying on them as a domestic defense force.\n\nUnfortunately, in that capacity the gunboats were almost useless; vessels that plied the relatively placid Mediterranean couldn't go to war in the stormy Atlantic, and they were dangerous and demoralizing for the sailors who manned them. They also turned out to be unexpectedly expensive. Some of them, however, were built in Virginia.\n\nPresident Jefferson pardoned James Callender from his Sedition Act conviction and gave him fifty dollars, one-quarter of his fine, but Callender interpreted the gesture, wrote Jefferson, \"not as a charity but a due, in fact as hushmoney.\" Believing himself entitled to the postmastership of Richmond, Callender turned viciously on Jefferson, publishing their correspondence. In an article published in the Richmond _Recorder_ on September 1, 1802, he broke the story that Jefferson \"keeps, and for many years past has kept, as his concubine, one of his own slaves. Her name is SALLY... There is not an individual in the neighbourhood of Charlottesville who does not believe the story; and not a few who know it.... The _African venus_ is said to officiate, as housekeeper at Monticello.\" Callender's role in American history ended the following year, when he drowned while drunk in three feet of James River water on July 17, 1803.\n\nThe years of Jefferson's and, subsequently, Madison's administrations were years of war between England and France, a war in which the United States was in many ways a participant, even as it declared its neutrality.\n\nIn this chaotic maritime war, American merchant vessels fell victim to seizures by predators of both countries. Jefferson had no effective response, and piracy became more common, a situation Jefferson's gunboats did nothing to abate.\n\nThe federal government had for years been trying to stop piracy, which overlapped with the slave trade. Responding to antislavery petitions, Congress passed the Act of 1794, subtitled \"An Act to Prohibit the Carrying on the Slave Trade from the United States to any Foreign Place or Country,\" which went so far as to provide for money penalties, though not imprisonment, for outfitting vessels for the foreign slave trade. A subsequent congressional measure in 1800 authorized the taking of slavers as prizes, and in the last days of the Adams administration, the US Navy began capturing slavers in the West Indies. In the days of the gunboats, however, enforcement dropped off. During Jefferson's first term, by one estimate, US slavers carried 16 percent of the African slave trade, up from 9 percent the previous decade.\n\nJefferson's policy toward Toussaint Louverture was markedly different from that of the non-slaveowner John Adams. He refused even to write a personal letter for his new consul to Saint-Domingue to carry to Louverture, as was diplomatic custom, nor would he direct the credentials to Louverture's attention, sending them merely to \"Cap Fran\u00e7ais,\" an insult that Toussaint was quick to perceive.\n\nSaint-Domingue had never declared independence from France, though Toussaint had infuriated Napoleon by sending him a new constitution for Saint-Domingue and declaring himself Governor for Life. As Jefferson described it in a November 24, 1801, letter to James Monroe, in Saint-Domingue \"the blacks are established into a sovereignty de facto, and have organized themselves under regular law and government.\" Jefferson wrote in the context of wondering whether Saint-Domingue might be a possible colony on which to offload black people \"exiled for acts deemed criminal by us, but meritorious perhaps by him.\" By \"him,\" Jefferson meant Toussaint Louverture, but apparently could not bring himself to write the name, referring to him merely as \"their present ruler.\"\n\nOn this issue, at least, Jefferson and the First Consul coincided. Jefferson's explicitly racialized hatred of Toussaint was shared by Napoleon, who referred to Toussaint as the \"gilded African,\" while Jefferson, in a letter to Burr, referred to Toussaint's men as \"the Cannibals of the terrible republic.\" But Jefferson still didn't know about Napoleon's secret plan to occupy Spanish Louisiana when, four months into his presidency, Louis-Andr\u00e9 Pichon, the French minister to Washington, broached the possibility of an armed French intervention in Saint-Domingue to prevent Toussaint's declaring independence. Jefferson replied that, given the hostility between Britain and France, Britain had to sign on first. Pichon reported Jefferson's words back to Paris: \"in order that this concert may be complete and effective, you must make peace with England, then nothing will be easier than to furnish your army and fleet with everything and to reduce Toussaint to starvation.\"\n\nTo Pichon's delight, the new President Jefferson, a veteran political intriguer with no military experience, had just conditionally greenlighted a hypothetical invasion of the Americas by Napoleon Bonaparte. But once Jefferson realized the implications for Louisiana, he withdrew his support.\n\nNapoleon instructed Talleyrand in a letter of November 13, 1801, how to spin for British consumption his forthcoming invasion of Saint-Domingue: with racism. A black republic, it was assumed, would be a pirate state and a center of terrorism. Napoleon matter-of-factly wrote of \"the course which I have taken of annihilating the government of the blacks in Saint-Domingue.\" Without his intervention, he warned, \"the scepter of the New World would sooner or later fall into the hands of the blacks... the shock that would result for England [would be] incalculable, even as the shock of the blacks' empire, as relates to France, has been confused with that of revolution.\"\n\nThe British saw Napoleon's plan for what it was. \"The acquisition [of Louisiana],\" reported Rufus King, Jefferson's envoy to Britain, paraphrasing British foreign secretary Lord Hawkesbury, \"might enable France to extend her influence and perhaps her dominion up the Mississippi; and through the Lakes even to Canada. This would be realizing the plan, to prevent the accomplishment of which, the Seven Years' War took place.\"\n\nWith the Treaty of Amiens on March 25, 1802, Britain and France made a peace that was more or less a capitulation on Britain's part. Though Prime Minister Henry Addington would declare war on France less than a year later, for the time being, the peace cleared the way at sea for French intervention in the Americas. While negotiations with Britain were in progress, Napoleon wasted no time in preparing his trusted brother-in-law, General Charles-Victor-Emmanuel Leclerc, to lead an expedition of some thirty thousand men, the largest fleet that had crossed the Atlantic to that date. \"Troops were directed to ports, and shipyards in France, Holland and Spain intensified their activity in armaments,\" wrote Lieutenant General Baron Pamphile de Lacroix, who served in Leclerc's campaign. \"The purpose of these armaments could not be doubted; they were self-evident... the most superficial observer could conclude, without mental effort, that immediate action was being taken to put Saint-Domingue back under the power of the metropolis.\"\n\nCap Fran\u00e7ais in Saint-Domingue was only to be the first landing. While Leclerc's fleet was crossing the ocean during the brief window of peace between France and England, Jefferson's minister to France, Robert Livingston, correctly reported to Rufus King on December 30, 1801, that: \"I know... that the armament, destined in the first instance for Hispaniola, is to proceed to Louisiana provided Toussaint makes no opposition.\"\n\nBonaparte's intention was to invade the hemisphere under cover of subduing a slave rebellion, portraying his move internationally as a preemptive expedition against black terrorists, confining the English-speaking population along the East Coast and eventually driving them out, while controlling the rest of the hemisphere through puppet Spanish and Portuguese kings. Accordingly, Leclerc's brief was to subdue the _noirs_ of Saint-Domingue, ship their leaders back to France in irons, and then proceed immediately on to Louisiana. Needless to say, Leclerc never complied with the latter instruction, because the black army of Saint-Domingue, together with the _Aedes aegypti_ mosquito, beat the French. Leclerc's men died of yellow fever even more often than they died in combat with an organized if ill-equipped black military whose soldiers were, terrifyingly, not afraid to die.\n\nWhen Leclerc's fleet appeared in Cap Fran\u00e7ais, Domingan general Henri Christophe burned the newly rebuilt town on February 4, 1802, torching his own house first and repositioning his forces in the mountains. After Leclerc betrayed Toussaint on June 7, kidnapping him to France to die in a freezing mountain prison cell after inviting him to a meeting, the command passed to Jean-Jacques Dessalines, who had formerly served as a general for the French.\n\nAt the time Dessalines took charge, Bonaparte still believed he was winning. He wrote to his minister of the marine, Denis Decr\u00e8s, on June 19, 1802: \"My intention is to take possession of Louisiana with the shortest delay, and that this expedition be made in the utmost secrecy, under the appearance of being directed on St. Domingo.\" In July, the news arrived in Saint-Domingue that Napoleon had signed a decree reinstating slavery in Guadeloupe, and the resistance against France intensified. Dessalines gave an order that he is remembered for: _koupe t\u00e8t, boule kay_ \u2014cut off heads, burn houses.\n\nThe South was terrified.\n\n_Articles warning of an imaginary invasion of \"French Negroes\" in the_ Courier of New Hampshire, _November 11, 1802._\n\nFear of \"French negroes\" was general, not just in the slaveholding South but in Cuba as well, where slaveowners were prohibited from importing slaves who had lived in foreign colonies, and in Spanish Louisiana. A 1797 insurrection plot in South Carolina that may or may not have been real was attributed to \"French negroes.\" Five years later, as the carnage in Saint-Domingue mounted, a more serious eruption of popular fear had its origin in New York, where, writes Lacy K. Ford, the rumor began that \"the French planned to release incendiary black 'brigands' up and down the Atlantic coast.\" An unidentified ship in the waters near Georgetown, South Carolina, in 1802 set that heavily black area \"on the razor's edge of alarm,\" so that \"the sighting of a single black man, allegedly of French background, traveling without a pass on a Saturday evening prompted the rapid spread of reports that an armed brigade of French-speaking Caribbean insurrectionists had finally come ashore at Georgetown.\" In a fit of panic, the state militia was mobilized to resist a phantom invasion. The panic was transmitted in the popular press, as newspapers published accounts describing the imaginary landing of \"French negroes.\"\n\nWhile this panic was occurring, the French invaders were dying by the thousands in Saint-Domingue. With Leclerc's forces dwindling, he embarked on a campaign of genocide, reporting to Napoleon on October 7 that \"we must destroy all the mountain negroes, sparing only children under twelve years of age. We must destroy half the negroes of the plains, and not allow in the colony a single man who has worn an epaulette.\" There were no further communications from Leclerc, who died on November 2 of yellow fever. His successor, General Donatien-Marie-Joseph de Vimeur, the vicomte de Rochambeau, was the son of the French general who had saved the United States at Yorktown and had served his father as an aide-de-camp during the American war. He attempted to continue Leclerc's genocide, importing some five hundred bloodhounds from Cuba trained to rip their victims apart, though most of the dogs were apparently eaten by starving French troops.\n\nNapoleon, who never hesitated to make a far-reaching decision fast and act on it at once, effectively gave up on his American plan when he learned of Leclerc's death; though he retained Martinique and Guadeloupe, he was determined to spend no more money on Saint-Domingue, where some fifty thousand French soldiers had perished. Already assembling the resources for his coming campaign to conquer Europe, he cut off support for the American venture, leaving his soldiers to twist in the wind without reinforcements. Rochambeau was captured by the British while ingloriously fleeing the island and remained imprisoned for more than eight years.\n\nIn Paris, the US ambassador Robert Livingston had been instructed by Jefferson to try to purchase New Orleans and the Floridas. West Florida, with Mobile and Pensacola, was already interdependent with New Orleans for trade, and controlled the access to the sea of the rivers that emptied into the Gulf of Mexico. Without that access, frontiersmen had no outlet for their products. Then a crisis erupted: on October 18, 1802, the Spanish intendant at New Orleans, Juan Ventura Morales, suspended the \"right of deposit\" that allowed citizens of the United States to transship goods via that port.\n\nNeeding to look like he was doing something, Jefferson dispatched Monroe on an \"extraordinary mission\" to Paris in January 1803, though Livingston was already on the case. \"The fever into which the Western mind is thrown by the affair at N. Orleans,\" wrote Jefferson in a hasty letter to Monroe, \"stimulated by the mercantile, & generally the federal interest, threatens to overbear our peace.\" Three days later, he wrote Monroe again: \"The agitation of the public mind on occasion of the late suspension of our right of deposit at N. Orleans, is extreme.\"\n\nLivingston was no stranger to land deals; as the great-grandson of the landowner and slave trader Robert Livingston, he had inherited the town of Clermont, New York, where the British had burned his mansion during the War of Independence. But he was astounded when Talleyrand offered him not only New Orleans, but the whole vast Mississippi watershed west and north of Louisiana, albeit with little geographical precision\u2014or, more accurately, offered him France's claim to the territory. By the time James Monroe arrived to join him as a special envoy, sick from his ocean journey, Livingston had already made the deal, though Monroe received the credit for it in America. The price they agreed on for the territory was sixty million francs (approximately $15 million)\u2014a bargain, but enough money that it could fund Napoleon's war in Europe.\n\nWas it Napoleon's to sell? The North American purchase in effect legitimated Napoleon's claim to Louisiana. But it was exactly what Napoleon had promised Carlos IV he would never do. The furious Spanish king took the position that by alienating Louisiana, France had lost its claim and that therefore Louisiana was rightfully Spain's.\n\nIn Charleston, where newspapers had been chiding Jefferson for not acquiring New Orleans, the Louisiana Purchase was seen as a \"greater treasure to the western part of the US than a mountain of gold.\"\n\nBut it wasn't Florida.\n\nAcquiring Louisiana was a coup, but Livingston and Monroe had failed to accomplish their mission. They were supposed to get the Floridas along with New Orleans, to lock in the whole Gulf Coast. Instead, they got the west bank of the Mississippi and the uncharted, undeveloped territory upriver.\n\nFlorida was an obsession, and a permanent security threat. Controlling the Floridas would secure the entire southeast of the continent from European invasion. It would allow full-scale removal of Native Americans to begin, so that slave-driven plantation agriculture could flourish outward from the slave-supply center of Charleston down into Florida, and through Georgia and Alabama, into Mississippi.\n\nAs President Jefferson explained to Congress, the Americans didn't even have a map of Louisiana. No sooner was the Louisiana deal done than Livingston and Monroe\u2014and President Jefferson, and Secretary of State Madison\u2014began claiming that Florida was part of the deal, though they all knew it was not. Florida was still a Spanish possession and had never been ceded to Napoleon. The United States' baldfaced attempt to claim rights to Florida became the subject of considerable diplomatic wrangling and was a major international issue through the War of 1812 and beyond. Jefferson's minister to Spain was his South Carolina campaign supporter Charles Pinckney, the Constitution framer from South Carolina, who\u2014unfortunately but typically for an American diplomat\u2014did not speak Spanish.\n\nHistorians have argued about exactly why Napoleon made the sudden strategic decision to make Louisiana available to the United States at a fire-sale price, but two motives are clear: one, he wanted money right then for his European war; and, two, he didn't want the British to have it. Empowering America would provide a check on British expansionism.\n\nThat's certainly what the British thought. They saw Jefferson, as they had since his days in Paris, as a French lapdog, and understandably resented his funding of Napoleon's war against them. The American Federalists, who sided with Britain against France, were furious.\n\nPresident Jefferson wanted to get rid of the Indians by the old traders' device of predatory lending\u2014ensnaring the chiefs in personal debt, then foreclosing on the commons of the tribes they represented. He advocated this method to General William Henry Harrison on February 27, 1803:\n\nto promote this disposition [on the part of the Native Americans] to exchange lands, which they have to spare & we want, for necessaries, which we have to spare & they want, we shall push our trading houses, and be glad to see the good & influential individuals among them run in debt, because we observe that when these debts get beyond what the individuals can pay, they become willing to lop th[em off] by a cession of lands.\n\nHe continued in a tone that perhaps illustrated how the doctrine of \"peaceable coercion\" applied at home:\n\nit is essential to cultivate their love. as to their fear, we presume that our strength & their weakness is now so visible that they must see we have only to shut our hand to crush them.\n\nThe annexation of Louisiana was a political blockbuster. New England was cold to the acquisition, pointing out correctly that Jefferson had exceeded his constitutional limits in making it. But though it was opposed by New Englanders in both houses of Congress\u2014with the significant exception of John Quincy Adams, a pro-expansionist who crossed regional and party lines to side with Jefferson\u2014it approximately doubled the size of US territory overnight. It changed the national balance of power even as the innovations of the cotton gin and a method for making sugar from Louisiana cane made practical the cultivation of these two highly profitable slave-labor crops. Virginia was set to be the primary vendor for the large numbers of slaves that Louisiana planters would want. Jefferson was well aware that a commercial network already existed in which itinerant traders and small-time merchants bought Virginia slaves for trafficking down South, and he knew it was a handy way to get rid of troublemakers, because he took advantage of it repeatedly.\n\nAfter Cary, one of the imprisoned teenage boys who worked in his slave-labor nail factory at Monticello, attacked another one, Brown Colbert, with a hammer, he was sent away under Jefferson's orders. \"It will be necessary for me to make an example of him in terrorem to the others,\" he wrote to his son-in-law, Thomas Mann Randolph Jr., from the White House on June 8, 1803. \"There are generally negro purchasers from Georgia passing about the state, to one of whom I would rather he should be sold than to any other person. [I]f none such offers, if he could be sold in any other quarter so distant as never more to be heard of among us, it would to the others be as if he were put out of the way by death.\"\n\nJefferson, then, was not only well aware of the Georgiamen and their southbound interstate slave trade, but also understood their process as a tool with which to terrorize\u2014\"in terrorem to the others\"\u2014his factory's workers, who were imprisoned children, and who had a cash value even as felons.\n\nLouisiana's Anglo-American settlers were primarily from Kentucky, a territory that had been carved out of Virginia and settled by Virginians. While the Louisiana Territory was being organized, President Jefferson sent his proven ally John Breckinridge\u2014now a senator from Kentucky\u2014a top-secret letter on November 24, 1803, enclosing two cramped double-column pages of proposals for a markedly undemocratic rule of Louisiana by a pro-American oligarchy that he referred to as an \"Assembly of Notables.\" As with the previous Kentucky Resolutions, Jefferson cautioned Breckinridge to pass the work off in the Senate as his own and not reveal his hand in it:\n\nIn communicating it to you I must do it in confidence that you will never let any person know that I have put pen to paper on the subject and that if you think the inclosed can be of any aid to you will take the trouble to copy it & return me the original. I am this particular, because you know with what bloody teeth & fangs the federalists will attack any sentiment or principle known to come from me, & what blackguardisms & personalities they make it the occasion of vomiting forth.\n\nIt was the first time that Congress had dared contemplate making any determination as to whether slavery should be allowed somewhere, but there was no alternative if the territory was to be organized. Breckinridge put forth Jefferson's proposals as his own, perhaps with some modification (no copy survives of his bill as introduced). Having amply demonstrated his loyalty, he became Jefferson's attorney general in 1805.\n\nFor our purposes, the most interesting feature of Jefferson's plan for Louisiana as contained in the Breckinridge-tendered proposal was that he wanted to prohibit the foreign slave trade but allow the domestic. There was no question that Louisiana would continue to buy imported slaves. The payday for Virginia slaveholders was that slaves could not be brought to Louisiana from Africa or Havana, but would have to be imported from the United States\u2014a move that substantially revalued every Chesapeake slaveowner's holdings upward and substantially increased Virginia's share of the nation's capital stock.\n\nBut on the same day Jefferson wrote Breckinridge, South Carolina's governor James Richardson sent a message to his state's General Assembly calling for the reopening of the foreign slave trade to South Carolina. The following day, Jefferson wrote Breckinridge again, adding text to his previous letter: \"Insert in some part of the paper of yesterday 'Slaves shall be admitted into the territory of Orleans from such of the United States or of their territories as prohibit their importation from abroad, but from no other state, territory or country.' salutations. Nov. 25. 1803.\"\n\nJefferson's added clause was specifically aimed at denying South Carolina the right to import slaves for reshipment to New Orleans. Though Jefferson's general plan became law, the prohibition of importation from South Carolina did not survive; when the Louisiana bill came before the Senate, James Hillhouse, a Connecticut Federalist, attached an amendment that prohibited slaves from \"without the limits of the United States,\" but made no other distinction. With legal obstacles removed, South Carolina unilaterally and legally reopened the African slave trade in order to service Louisiana with freshly imported Africans rebranded as domestic product, undercutting the Virginia slaveowners substantially.\n\nThe United States formally took possession of Louisiana from France on December 20, 1803, twelve days before Commander in Chief Jean-Jacques Dessalines issued the Haitian Declaration of Independence that proclaimed the existence of the Republic of Haiti on January 1, 1804. It largely consisted of an extended and strongly worded cry of hatred for France, but nevertheless offered an olive branch to the rest of the hemisphere that acknowledged the fear that Haitians would become exporters of terrorism:\n\nLet us ensure, however, that a missionary spirit does not destroy our work; let us allow our neighbors to breathe in peace; may they live quietly under the laws that they have made for themselves, and let us not, as revolutionary firebrands, declare ourselves the lawgivers of the Caribbean, nor let our glory consist in troubling the peace of the neighboring islands.\n\nBut then Dessalines went from town to town, personally supervising the execution of the French remaining in the territory\u2014while exempting the Polish soldiers who had fought on the side of the Haitians, who were made honored members of the new society, and the many US captains who were happily doing business in the ports of the new republic. Dessalines served as Haiti's first president for less than three years before being murdered by other Haitians, and ultimately (unlike the Catholic Toussaint) became a _lwa_ of Haitian vodou.\n\nJames Wilkinson was upset to see the black militiamen of New Orleans in uniform and carrying weapons. A traitor who acted as a Spanish secret agent while commanding the US Army, Wilkinson had previously proposed that Kentucky declare independence from Virginia and become allied with Spain instead. But he nevertheless was tolerated by Jefferson, who made Wilkinson the head of the US Army in Louisiana.\n\nJefferson's Virginian-via-Tennessee prot\u00e9g\u00e9, W. C. C. Claiborne, a blue-blood descendant of Kent Island's William Claiborne, became the territorial governor of Louisiana. Claiborne, who spoke neither French nor Spanish, had since 1801 been governor of Mississippi, a position awarded him by Jefferson. As the Americans took charge in Louisiana, Claiborne's agent Dr. John Watkins, who had reconnoitered the country, pointed out in a report of February 2, 1804, the most important political issue:\n\nNo Subject seems to be so interesting to the minds of the inhabitants of all that part of the Country, which I have visited as that of the importation of brute Negroes from Africa. This permission would go farther with them, and better reconcile them to the Government of the United States, than any other privilege that could be extended to the Country. They appear only to claim it for a few years, and without it, they pretend that they must abandon the culture both of Sugar and Cotton. White laborers they say, cannot be had in this unhealthy climate.\n\nThe \"Kaintucks\"\u2014a minority in Louisiana\u2014had a marked preference for American-born slaves. But the Creoles of Louisiana wanted slaves from Africa. They didn't want English-speaking slaves, they didn't want Protestant slaves, and they didn't want to pay the much higher prices charged by the speculators who brought slaves from Virginia and Maryland.\n\nClaiborne wrote to Madison on March 10, 1804, of unrest on the part of both planters and slave traders:\n\nIn a Paper which was received by the last Mail from the Seat of Government, it was stated that a Law had passed the Senate prohibiting the foreign importation of Slaves into this Province. This intelligence has occasioned great agitation in this City and in the adjacent Settlements.\n\nThe African Trade has hitherto been lucrative, and the farmers are desirous of increasing the number of their Slaves. The prohibiting the incorporation of Negroes therefore, is viewed here as a serious blow at the Commercial and agricultural interest of the Province. The admission of Negroes into the state of South Carolina has served to increase the discontent here. The Citizens generally can not be made to understand the present power of the State Authorities with regard to the _importation of persons:_ \u2014they suppose that Congress must connive at the importation into South Carolina, and many will be made to believe, that it is done with a view to make South Carolina the Sole importer for Louisiana.\n\nAnd, indeed, that is what happened. Louisiana was a colonized territory, and as such, it was subject to trade restrictions that benefitted the metropolis\u2014principally Virginia, but Carolina had found a way to horn in.\n\nClaiborne's power during the territorial era was frequently and not inaccurately described as dictatorial, though the picture that emerges from his letters is that of a man who has a French-speaking tiger by the tail.* Contemplating the impending prohibition of both the African slave trade and the interstate trade to Louisiana as of October 1, he wrote Secretary of State Madison on May 8:\n\nI am inclined to think that previous to the 1st of October thousands of African Negroes will be imported into this Province; for the Citizens seem impressed with an opinion, that a great, very great supply of Slaves is essential to the prosperity of Louisiana: Hence Sir you may conclude that the prohibition as to the importation Subsequent to the 1st of October, is a source of some discontent; Nay Sir, it is at present a cause of much clamour.\n\nAnd on July 12:\n\nAt some future period, this quarter of the Union must (I fear) experience in some degree, the Misfortunes of St. Domingo, and that _period_ will be hastened if the people should be indulged by congress with a continuance of the African Trade.\n\nAfrican Negroes are thought here not to be dangerous; but it ought to be recollected that those of St. Domingo were originally from Africa and that Slavery Where ever it exists is a galling yoke. I find however that an almost universal sentiment exist in Louisiana in favour of the African traffic.... Slaves are daily introduced from Africa, many _direct_ from _this_ unhappy Country and others by way of the west India Islands. All vessels with slaves on bord [ _sic_ ] are stopped at Plaquemine, and are not permitted to pass without my consent. This is done to prevent the bringing in of Slaves that have been concerned in the insurrection of St. Domingo.\n\nThe foreign slave trade into Louisiana was never again legalized. But under pressure from Jefferson to respond to Claiborne's urgent drumbeat that the citizens of Louisiana wanted more slaves, Congress legalized the domestic slave trade to Louisiana in March 1805, to be fully effective October 1.\n\nThat the black territory freed from France should call itself a republic was seen by whites as a grotesquerie.\n\nFor the slaveowners in the United States government to have diplomatic relations with slaves who had killed their masters was unthinkable; it would, they thought, amount to rewarding their actions. Although Haiti was the second republic in the hemisphere, the United States didn't extend diplomatic recognition to it until 1862, and then only because President Abraham Lincoln saw it as a potential site for \"colonization,\" or deportation, of emancipated slaves.\n\nYet the Southerners owed the Haitians a lot. At a time when Washington, DC, was a squalid, barely built village and the US Army had only about three thousand troops, Haiti stopped the French troops' forward march into the Americas. To put it another way: though it was not their objective, Dessalines and his troops prevented Bonaparte's forces from invading Louisiana and controlling commerce on the Mississippi. Historians don't deal in counterfactuals\u2014what might have happened\u2014but it is tempting to imagine scenarios: if Leclerc had been able to comply with his orders to continue on from Saint-Domingue and occupy Louisiana with ten thousand men or more, controlling the great New Orleans gateway to the sea? Could the French have managed a permanent occupation that would have been hard to dislodge? Certainly the United States governing class had not expected to be able to expand across the continent so quickly and easily.\n\nSpain's military involvement in Saint-Domingue was its last gasp as a world power, the prelude to losing its colonies one by one, and Saint-Domingue was the graveyard of British colonial expansion in the Americas as well. The expense and horrendous loss of life were a spur to the British in stopping the African slave trade\u2014though not British colonial slavery, yet\u2014via an act approved in Parliament on March 25, 1807, a mere three years after the establishment of the Republic of Haiti.\n\nBritain could afford to get out of the slave trade. As profitable as slaving could be, British commerce was so large, and so diverse, that losing the slave trade didn't make a dent it. Trinidad, Britain's last-acquired Caribbean colony, was ceded to Britain by France in 1802. It had been Spanish, French, and now English in succession. The Africans who were subsequently brought to Trinidad were not brought as chattel slaves but as indentured workers from the British empire in Africa.*\n\nNew England merchants did a brisk business in Haiti, to the disgust and alarm of Southerners, trading arms along with other commodities and consumer goods. Napoleon, who refused to recognize Haitian independence, was furious about American commerce with Haiti; Jefferson, who hoped to have Napoleon's cooperation in taking over Florida, wanted to keep him happy. Congress passed sanctions against commerce with Haiti in 1806, amid arguments that to trade with Haiti against France's wishes was to recognize Haitian independence. That would be, Jefferson's son-in-law John Wayles Eppes shouted in the House, \"a system that would bring immediate and horrible destruction on the fairest portion of America.\"\n\nSoutherners were on permanent high alert for terrorism, and never backed down. The specter of Haiti informed all future discourse\u2014every dinner-table conversation, every political calculation, every speech\u2014about slavery in the Southern United States. The \"French Negroes\" were thought to carry the contagion of insurrection, and prophylactic measures were thought necessary to keep them from infiltrating; there was even concern, utterly unwarranted, that Haiti might attack the United States.\n\nHere as on other occasions, Southern slaveowners revealed how terrified they were by the ferocity of black fighters. Haiti had a significant population of black men who had served in European and\/or African armies or in colonial militias, and their military knowledge embraced both European and African military tactics and systems of organization.\n\nThe clock was ticking. The Constitution allowed the federal government to stop the foreign slave trade as of January 1, 1808, and President Jefferson wanted that trade shut down for good. Prohibiting the slave trade was easily represented to a panicked public as antiterrorism.\n\nBut it also partook of that other great issue: prohibiting the African slave trade protected the market so that a new class of American traders could come forward, supplied with homegrown captives born into slavery on Virginia and Maryland farms. The conditions were right for a massive forced migration of enslaved Chesapeake laborers down South, and it did not have to be a one-time drain: a continuing domestic slave-breeding industry was now possible.\n\nThis was something new. Taking the long historical view, African American historian William T. Alexander wrote in 1887:\n\nSlave breeding for gain, deliberately purposed and systematically pursued, appears to be among the latest devices and illustrations of human depravity.... That it was cheaper to buy slaves than to rear them, [had been] quite generally regarded as self-evident. But the suppression of the African slave trade, coinciding with the rapid settlement of the Louisiana purchase and the triumph of the Cotton Gin, wrought here an entire transformation. When field hands brought from ten to fifteen hundred dollars, and young slaves were held at from ten to fifteen dollars per pound, the newly born infant, if well formed, healthy, and likely to live, was deemed an addition to his master's stock of not less than one hundred dollars, even in Virginia and Maryland. It had now become the interest of the master to increase the number of births, in his slave cabins, and few evinced scruples as to the means whereby this result was obtained.\n\nThe Spanish had had the most permissive slave regime ever to exist in the territories that now make up the United States. Under Spanish law, the enslaved had a right to have a hearing to establish a price by which they could purchase their freedom. This practice, called _coartaci\u00f3n_ , was hated by the planters, and it ended in 1807.\n\nIn Louisiana, both free people of color and the enslaved found themselves in transition to the hemisphere's psychologically harshest racial regime: the Anglo-American mode of slavery, which provided no path to freedom even for future generations of descendants. The Virginians brought them a kind of slavery that was not only lifelong, but perpetual.\n\n*When in 1807 Jefferson tried to prevail on James Monroe to take the Louisiana governorship, he pitched it as the \"2d office in the US. in importance.\" _PJMon_ , 5:288.\n\n*The old ways persisted, however; Trinidad's carnival was a Mardi Gras, and when its characteristic musical form of calypso later appeared, it was in the French Creole tongue, as were many of the old _bombas_ of western Puerto Rico, where Domingans also went.\n\n#   27\n\n# **I Do Not Threaten the Government with Civil War**\n\n_The] facility with which the sugar Planters amass wealth is almost incredible. It is not uncommon with 20 working hands to make from 10 to 14 thousand Dollars and there are several planters whose field Negroes do not exceed forty who make more than 20,000 Dollars each year.[ 1_\n\n\u2014Louisiana governor W. C. C. Claiborne, letter to President Thomas Jefferson, July 10, 1806\n\nGEORGIA, THE ONLY STATE to have legally imported slaves from Africa since the Constitution took effect, finally banned both African and interstate slave trade in 1798, at a time when maritime commerce was disturbed by war. During the years the trade was open, Charleston merchants and factors had sold large cargoes of slaves in Savannah, and a class of Georgia traders had grown up as well. Slave trading continued after the ban, but illicitly, not subject to legal regulation or protection.\n\nIn 1802 the South Carolina legislature renewed the prohibition against both the foreign and interstate slave trades. As had previously been the case in both Chesapeake and Carolina, it was a regional issue. About half the population of Charleston at this time was enslaved; upcountry, the enslaved population comprised only about one-fifth of the total. Not only did the Lowcountry's large slaveholders, who were firmly in control, want to disempower their upcountry competition by denying them labor, they wanted to control the labor market so that upcountry would have to buy its labor from the Lowcountry, without having access to competitors from Virginia and Maryland.\n\nCharleston newspapers published excited reports of the productivity of the new Louisiana Territory, with the clear implication being that Louisiana had insufficient slave labor. South Carolina could easily supply it, since Charleston had since the 1790s carried slaves to New Orleans via its commercial, albeit treacherous and irregular, coastwise shipping route around the Spanish-held Floridas to New Orleans.\n\nFor South Carolina legislators, long attuned to fast-changing market conditions, it was time to act. \"To the surprise of many political observers,\" writes Lacy K. Ford, \"in late November 1803, just one year after its desultory rejection of inland cotton growers' pleas for a reopened slave trade, the South Carolina legislature suddenly began a serious reconsideration of the issue, undoubtedly prompted by both persistent backcountry pressure and the prospect of supplying legions of slaves to the lower Louisiana Territory for handsome profits.\" The two interests cut a deal: the merchants of Charleston got the African slave trade, whose victims they could resell to Louisiana and Mississippi, and the upcountry planters got the interstate trade, which would allow them to buy enslaved laborers from the Chesapeake.\n\n\"The news had not been five hours in the city,\" wrote Charleston bookseller E. S. Thomas, \"before two large British Guineamen, that had been lying on and off the port for several days expecting it, came up to town; and from that day my business began to decline.\" For the next four years, available resources went to investing in slaves.\n\nIt was not yet clear what the laws of an American-controlled Louisiana would be, but in adjacent Mississippi, under Claiborne's governorship, Congress had since 1798 allowed the interstate but not the foreign trade, requiring planters to buy from American slave vendors. With the cotton boom underway, Natchez was already a developed slave market, and Louisiana could\u2014and, as it happened, did\u2014radically widen that opportunity. It was clear that though the interstate trade to Louisiana was at that moment prohibited, the territory was being set up as a market for Virginia slaves, and South Carolina wanted in on the action.\n\nBeyond the simple lure of making sales, there was an additional, compelling reason for South Carolina to sell slaves to Louisiana: Louisiana had a hard-money supply, courtesy of the Spanish. Spain did its business the old-fashioned way, paying bills with silver mined out of the ground in Mexico. Claiborne reported from New Orleans to Secretary of State James Madison on June 16, 1805, that \"Two Spanish Schooners from Vera Cruz, have arrived at this Port, and are consigned to the Marquis of Casa Calvo. They brought with them a large Sum in Silver, report says One Hundred thousand Dollars, but it is believed the real Amount is much greater. This money is said to be destined for the payment of the Pensions allowed to persons residing in Louisiana, and to meet the expences which the Marquis has or may incur as Commissioner of Limits.\"\n\nSouth Carolina had no such shipments coming in. Louisiana offered a chance for Carolina merchants to get silver, instead of paper that might depreciate or become worthless. The Creoles had silver Spanish dollars, and they were eager to buy slaves.\n\nThe previous peak of South Carolina importation of Africans was 1773, when an estimated eight-thousand-plus slaves were brought in. This time, when South Carolina reopened the African trade, they brought in far and away the largest single concentration of victims that came to North America in any comparable period, as this table of estimated embarkations (using the Eltis and Richardson numbers) shows:\n\n1804 |  7,643  \n---|---  \n1805 |  8,592  \n1806 | 15,551  \n1807 | 23,174  \n1808 |  498  \n**total** | **55,458**\n\nEltis and Richardson show an estimated 12.7 percent death rate, with 47,281 arriving alive. Some estimates of the traffic are higher; James McMillin believes that more than seventy thousand Africans\u2014a phenomenal number\u2014arrived into the Lowcountry during the four years from 1804 to 1807.\n\nSome of these newly arrived Africans were sent on to Jamaica, Barbados, or other Antillean territories, and it's unclear how many of them were re-exported to Louisiana. At least five thousand, believes Lacy K. Ford\u2014more than 10 percent of the Eltis and Richardson estimate of Africans trafficked to South Carolina\u2014but the number could be larger. There was definitely a commercial corridor in slaves: Gwendolyn Midlo Hall's Afro-Louisiana database shows that between 1806 and 1810, 76 percent of captives that she was able to obtain documentation for who came into the port of New Orleans arrived from South Carolina, versus only 3 percent for other US ports of origin (a sample that does not include the migration of some ten thousand people, about a third of them enslaved, to New Orleans from eastern Cuba in 1809\u201310). Her statistics for 1811 and 1812 show 67 percent from South Carolina. A committee report to Congress on February 17, 1806, stated flatly, \"African slaves, lately imported into Charleston, have been thence conveyed into the Territory of Orleans; and, in their opinion, this practice will be continued to a very great extent, while there is no law to prevent it.\"\n\nSome of the Africans were taken past New Orleans to Natchez, though in the pre-steam days it was hard work getting a boat up the Mississippi River. The _Lucy_ left Charleston on July 4, 1806, \"carrying 50 negroes insured from Charleston to Natchez, the premium 7\u00bd per cent.\" During the Missouri Compromise debate of 1820, South Carolina senator William Smith, arguing in favor of unlimited slavery, entered into the congressional record the following passage about the importations of 1803\u201307, which shows how little the Carolinians were involved in the actual business of importation (as opposed to selling the captives):\n\nThe whole number imported by the merchants and planters of Charleston and its vicinity were only two thousand and six. Nor were the slaves imported by the foreigners, and other American vessels and owners, sold to the Carolinians, only in a small part. They were sold to the people of the Western States, Georgia, New Orleans, and a considerable quantity were sent to the West Indies, especially when the market became dull in Carolina.\n\nSo a number of the slaves brought into Louisiana through 1810 came from Africa through South Carolina via the coastwise trade. The manifests before 1818 were lost, but the one stray surviving manifest from 1807 is for a \"new negro man\"\u2014i.e., African-born\u2014coming to New Orleans from Charleston.\n\nProbably Charleston was the source from which George W. Morgan received the cargo of thirty people\u2014twenty adults, ten children\u2014from two widely separated regions of Africa that he advertised in the _Orleans Gazette and Commercial Advertiser_ of August 13, 1806, though they could also have been plucked by pirates off a ship headed for Cuba:\n\nBut there was also competition from the Chesapeake, as per this February 5, 1807, advertisement from the same paper:\n\nAnother advertisement in the same issue, reproduced here, shows the participation of Charlestonians in the business, offering \"140 NEGRES BRUTS, DE NATION CONGO\" to francophone buyers:\n\nRe-exporting Africans was not a business that benefited most South Carolinians, nor did most of the money stay in Charleston. The Carolinians were middlemen, not suppliers. They had a harbor, but not a transatlantic shipping industry of their own, so the profits from carrying went elsewhere. As a \"Planter from Pedee\" wrote during the non-importation movement of 1769\u201370, \"purchasing Negroes is in fact purchasing British manufactures.\"\n\nCharleston customs entries for 1806 show thirty-three slave ships from Africa as being owned by British proprietors, followed by thirteen from Rhode Island, then three from New Jersey, three from Charleston, and two from Ireland. Breaking down a customs count of 39,075 slaves declared as entering into Charleston between 1804 and 1807, Elizabeth Donnan found 19,949 of them entering on British ships, 7,958 on Rhode Island vessels, and only 2,006 imported by \"merchants and planters of Charleston and vicinity,\" presumably the same 2,006 cited by Smith.\n\nThe Carolinians tried to make their money on volume, in an unprecedented mass retailing experiment. Their greed was matched by that of the shippers, the largest number of whom were in Liverpool; they knew the market would be closing soon.\n\nThe Liverpool slavers' heaviest shipping period was the last ten years of the trade. During that time, they also sold slaves to the British Army, who purchased them for conscription into the West India Regiment, an arrangement that only ended with the end of the African slave trade. From January 1, 1806, through the prohibition of the trade on May 1, 1807\u2014the height of the South Carolina importation\u2014185 ships from Liverpool carried 49,213 Africans.\n\nIn this free-for-all slave importation scene, people from widely different parts of Africa turned up in Charleston\u2014from Kongo, Sierra Leone, the Gold Coast, and other regions. Omar ibn Said, an Islamic scholar from Senegal, a Fula, who arrived in Charleston in 1807, described his experience in a fifteen-page 1831 autobiography, one of fourteen manuscripts that he wrote in Arabic while enslaved:\n\n... there came to our place a large army, who killed many men, and took me, and brought me to the great sea, and sold me into the hands of the Christians, who bound me and sent me on board a great ship and we sailed upon the great sea a month and a half, when we came to a place called Charleston in the Christian language. There they sold me to a small, weak, and wicked man called Johnson, a complete infidel, who had no fear of God at all. Now I am a small man, and unable to do hard work so I fled from the hand of Johnson and after a month came to a place called Fayd-il. [Fayetteville, North Carolina.]\n\nThe unilateral reopening of the slave trade by South Carolina caused much anger in the rest of the country, both in the Upper South and in the abolitionist strongholds. Newspapers in North Carolina, Tennessee, Maryland, and Virginia all strongly criticized South Carolina's decision, but the Carolina press became especially defensive when the criticism came from the North, as in this piece from the _Charleston Courier_ of July 10, 1806, which takes on a mocking tone not unfamiliar in other eras of American politics:\n\nAs to the epithet of thieves, which [an unnamed Philadelphia editor] applies to those who bring Slaves from Africa, we shall presently see whether we cannot apply it to the pure, the immaculate, and demure Philadelphian, and some other of the Northern cities, where they are bellowing out, humanity! humanity! humanity! Oh! the rights of dear insulted human nature!\n\nAs captives died awaiting sale, Charlestonians were irritated by the captains' practice of disposing of the corpses on the cheap by throwing them overboard, \"in consequence of which,\" reported traveler John Lambert, \"no body would eat any fish.\" A city ordinance of 1805, printed in the _Charleston Courier_ , noted that \"since the importation of Slaves from Africa, several incidents have occurred of dead human bodies having been thrown into the waters of the Harbour of Charleston\" and provided that not only should a fine of one hundred dollars be imposed, but that the offender's name should be published in \"the several gazettes of Charleston, to hold up every such offender to public detestation.\" Still, the numerous advertisements for luxury goods in the four pages of the previously mentioned issue leave no doubt that, bodies floating in the harbor or not, the Charlestonians were prosperous. But since all those goods had to be imported, either from the North or from Europe, their money quickly left the city again on northbound boats.\n\nLooking forward to the January 1, 1808, expiration of the constitutionally specified guarantee that the African slave trade could exist, President Jefferson's Message to Congress of December 2, 1806, proactively called for its prohibition as of the first constitutionally permissible day. In defending the urgency of his proposal as necessary to forestall a final cycle of African expeditions, Jefferson also presented it as a moral issue:\n\nI congratulate you, fellow citizens, on the approach of the period at which you may interpose your authority constitutionally to withdraw the citizens of the United States from all further participation in those violations of human rights which have been so long continued on the unoffending inhabitants of Africa, and which the morality, the reputation, and the best of our country have long been eager to proscribe. Although no law you may pass can take prohibitory effect until the first day of the year 1808, yet the intervening period is not too long to prevent by timely notice expeditions which can not be completed before that day.\n\nA bill was duly proposed the following day.\n\nHowever moral it may have seemed to Jefferson to lament \"violations of human rights,\" ending the transatlantic slave trade did nothing to end slavery itself. Instead, it replaced one inhumane slave trade with another. This action of Jefferson's has been praised as, in one historian's words, \"his greatest act of humane egalitarianism.\" Perhaps in his layers of intellectual complexity, Jefferson thought so himself; we will resist the temptation to psychoanalyze. But in practice, it was no such thing. It was an act to transform American slavery into a purely domestic industry, reducing the nation's dependence on foreign sources of supply for slaves and bringing the entire slave trade under Virginia's control. Nor was this an unforeseen consequence; it was the predictable, desired outcome, which is why South Carolina and Georgia opposed the bill, albeit unsuccessfully.\n\nThe bill was referred to a House committee of four Southerners (from Georgia, Virginia, Maryland, and North Carolina) and three Northerners, with Peter Early of Georgia as chair. In debate, Early answered John Smilie of Pennsylvania, who wanted capital punishment for slave importers, with words that put Jefferson's high-flown appeal in perspective:\n\n[Mr. Smilie] has said that, in the Southern States, slavery is felt and acknowledged to be a great evil, and that therefore we will execute a severe law to prevent an increase of this evil. Permit me to tell the gentleman of a small distinction in this case. A large majority of the people in the Southern States do not consider slavery as a crime. They do not believe it immoral to hold human flesh in bondage. Many deprecate slavery as an evil; as a political evil; but not as a crime. Reflecting men apprehend, at some future day, evils, incalculable evils, from it; but it is a fact that few, very few, consider it as a crime.\n\nIt is best to be candid on this subject. If they considered the holding of men in slavery as a crime, they would necessarily accuse themselves, a thing which human nature revolts at. I will tell the truth. A large majority of people in the Southern States do not consider slavery as even an evil.\n\nThis was a long way from Mason, Jefferson, Henry, and even Pierce Butler and Henry Laurens's protestations that slavery was an evil forced upon North America by Britain, one to which there was unfortunately no effective end in sight because free blacks could supposedly not live together with whites. South Carolina was the center of an expanding commercial empire, with slavery at the heart of that vision. To hear Carolina slaveowners tell it, slavery was a positive good for mankind. This sentiment, soon to be institutionalized by South Carolina's John C. Calhoun, had already become common.\n\nWhat to do with enslaved people rescued from slave ships was a problem as well; should the federal government sell them at auction? When it was proposed that they be indentured for a term in a free state, Early responded by threatening civil war (while claiming the contrary), according to the minutes in the _Annals of Congress:_\n\nMr. Early said the inhabitants of the Southern States would resist this provision with their lives. We want no civil wars, no rebellions, no insurrections, no resistance to the authority of the Government. Give effect then to this wish, and do not pass this bill as it now stands.\n\nMr. Smilie. \u2014 This opens such a scene as I never expected to witness in this House. If it were not owing to the impulse of the moment, and the influence of passion, I should think it extremely reprehensible. Are we to be threatened with civil war? that our laws will be resisted at the peril of life? Sir, this is new doctrine. The gentleman must know that we are not to be terrified by a threat of civil war.\n\nMr. Early said the gentleman from Pennsylvania (Mr. Smilie) had made a palpable misrepresentation of his sentiments. I do not threaten the Government with civil war. I only communicated the idea that military force would be necessary to carry the law into execution.\n\nThe Senate added to the bill a prohibition against the coastwise slave trade for ships of less than forty tons burden, which made it impossible for small vessels intercepted at sea bearing slaves from the Antilles to claim that they were engaging in domestic coastwise trade. This infuriated the Southerners; Virginia's senior senator, the voluble, unhinged, but not unperceptive John Randolph, who owned some four hundred slaves, argued that (as summarized by the congressional reporter):\n\nThe provision of the bill touched the right of private property. He feared lest, at a future period, it might be made the pretext of universal emancipation, he had rather lose the bill, he had rather lose all the bills of the session, he had rather lose every bill passed since the establishment of the Government, than agree to the provision contained in this slave bill. It went to blow up the Constitution in ruins. Mr. R[andolph] said, if ever the time of disunion between the States should arrive, the line of severance would be between the slaveholding and the non-slaveholding states.\n\nOver Randolph's objections, the forty-tons clause remained, setting in place a mechanism that favored larger operators in the coastwise slave trade.\n\nThe Senate version also included a requirement that the ship's captain submit a manifest naming each enslaved passenger to the customs collector or surveyor both at the port of departure and at the port of arrival, with the customs officer performing a roll call at either end. New Orleans was the principal port of arrival, but far from the only one; the trade stretched to Galveston. The result of this requirement is that both inward and outward manifests exist. Many have been lost, but even so, these filled-in, commercially preprinted forms constitute the best record of the trade.\n\nJefferson signed the act prohibiting the African trade on March 2, 1807, to take effect the first day of 1808. Britain, meanwhile, having lost tens of thousands of men in its attempt to take Saint-Domingue, and under strong domestic pressure from abolitionists who had organized themselves into an effective political movement, put an end to its lucrative involvement in the slave trade by a measure that received royal assent on March 25, 1807. The British law did not have to wait until the first of the year to be effective so it took effect before the already passed American prohibition did. Though a British abolition law would have to wait until 1833, ending the transatlantic slave trade was a major turning point. Over the next decades, the British Navy enforced it at sea not only with respect to British ships, but stopping slave ships from other nations as well.\n\nAs the shutoff approached, South Carolina traders turned the spigot as wide as it would open. By the final year, the market was glutted, with fatal consequences for the Africans who piled up in holding pens. John Lambert reported that in 1807:\n\nthe sales for slaves was extremely dull, owing to the high price which the merchants demanded for them. The planters, who were pretty well stocked, were not very eager to purchase, and the merchants knowing that a market would ultimately be found for them, were determined not to lower their demands; in consequence of which, hundreds of these poor beings were obliged to be kept on board the ships, or in large buildings at Gadsden's wharf for months together.\n\nExhausted and sick, many of the captives died; McMillin believes that \"as many as sixteen hundred newly arrived Africans may have perished on the Charleston wharf over four months.\" By November, the major traders seem to have agreed to hold captives back from the market. With Jefferson having shut the African trade off, Virginia and Maryland traders settled into their newly protected domestic slave trade.\n\nWilliam Dusinberre's comment about another president, James K. Polk, is equally applicable in the case of Jefferson: \"His political conviction was congruent with what appeared to be his own financial interest.\" For Jefferson as for other large slaveholders, the end of African importation was a crucial step in protecting and growing their net worth, which perhaps explains the support Jefferson received from Virginia and the South in general during his subsequent measure, unique in the annals of American history: a complete embargo of all overseas trade.\n\n#   28\n\n# **These Infernal Principles**\n\n_From the best information I could obtain, this city contains nearly three hundred houses, and about three thousand inhabitants, including all colours. There are several extensive mercantile houses established here, and one at least which imports goods directly from England. There are two printing-offices, and consequently two newspapers, which are published weekly... The gentlemen pass their time in the pursuit of three things: all make love; most of them play gamble]; and a few make money. With Religion they have nothing to do; having formed a treaty with her, the principal article of which is, \"Trouble not us, nor will we trouble you.\"[ 1_\n\n\u2014The traveler Christian Schultz, describing Natchez in 1808\n\nUS MERCHANT SHIPPERS WERE caught in the crossfire between implacable opposed forces that would not allow them to act without subterfuge. Both the belligerent conservative government in Britain and Napoleon's government in France were increasingly taking a policy that there were no neutrals, pursuant to which they claimed the right to seize American vessels.\n\nNapoleon's Berlin Decree of November 21, 1806, prohibited trade with Britain and its allies, and allowed the capture of ships and the blockading of ports in service of that goal. However, it was not put into force against the United States for almost a year, so that in British eyes, the Jefferson administration was getting special treatment from Napoleon and was therefore not neutral but pro-French, as Jefferson had been deemed to be by the British all along. Indeed, Jefferson acquiesced to the Berlin Decree \"without effectual protest,\" as Henry Adams put it. Britain responded with the draconian Orders in Council of November 11, 1807, an opaquely worded declaration of commercial war against neutrals that was squarely aimed at the United States, even as Bonaparte began applying the Berlin Decree to American ships.\n\nJefferson's \"peaceable coercion\" theory of defense was about to be sorely tested. Henry Adams, whose nine-volume history of the Jefferson and Madison administrations examines the matter in detail, wrote bluntly, \"Jefferson and his government had shown over and over again that no provocation would make them fight; and from the moment that this attitude was understood, America became fair prey.\" Both France and Britain were seizing American merchant ships, but Britain's bullying was more aggressive, leading to the galvanizing seizure of one of the few ships of the American navy, the _Chesapeake_ , by the British ship _Leopard_ off the coast of Norfolk, Virginia, on June 22, 1807.\n\nDramatizing the stakes was the fate of Denmark. In Europe, both powers pressured the Danish king to support them, the endgame of which was that Britain bombarded Copenhagen from September 2 through 5, 1807, destroying about half the city, killing some two thousand people, and confiscating some $10 million worth of merchandise in Danish vessels. Adams wrote that \"the annihilation of Denmark left America almost the only neutral, as she had long been the only Republican State.\" (Not counting Haiti, that is, but the United States, England, and France alike refused to recognize Haiti's claim to be a republic and considered it an outlaw that still rightfully belonged to France.) According to Adams, the undefended United States' \"offences... had been more serious than those of Denmark, and had roused to exasperation the temper of England. A single ship of the line, supported by one or two frigates, could without a moment's notice repeat at New York the tragedy which had required a vast armament at Copenhagen.\"\n\nDuring the seven years of his presidency, Jefferson had discarded his previously declared Republican ideals of limited government one by one. Now, in the commercial emergency posed by Britain's Orders in Council, Jefferson imposed the Embargo Act, signed on December 22, 1807. His secretary of the treasury, Albert Gallatin, described it as \"an act prohibiting the sailing of ships or vessels from the ports and harbors of the U. States to any foreign port or harbor\"\u2014in other words, nothing less than a self-imposed embargo on all US maritime commerce and travel. This unparalleled real-world economic experiment was a hopeless attempt to resolve British and French incursions on US sovereignty at sea. It badly depressed the US economy, made Jefferson widely hated during his last year in office, and did nothing to dispel the tensions that ultimately erupted in the War of 1812.\n\nWhen the prohibition against the slave trade kicked in on January 1, 1808, then, it happened against the backdrop of the general embargo, which had unleashed a panic in American (and European) commerce that made even the African trade seem a minor issue. Even had the slave trade not been specifically prohibited, there would have been no one to ship slaves from Africa to South Carolina. The merchants of Liverpool, who provided the bulk of the slave shipments, had been shut down from London, because Britain now prohibited their trade and would soon be sending its imperial navy to chase down slavers. Nor would Rhode Island's slave-trade specialists have been able to take up the slack, because even had their slave ships somehow not been prohibited along with all other foreign commerce by Jefferson's embargo, they would have been subject to confiscation at sea by the British navy, or possibly by French ships taking prizes for Napoleon.\n\nWhile the embargo did stimulate American manufactures, it was received in New England as a plot by the French agent Jefferson to destroy American commerce. In New York, wrote the traveler John Lambert, \"the grass had begun to grow upon the wharves.\" But the full brunt of the embargo fell on the South, where two consecutive crops could not get to market. \"Virginia society could neither economize nor liquidate,\" wrote Henry Adams. \"Tobacco was worthless; but four hundred thousand negro slaves must be clothed and fed... with astonishing rapidity Virginia succumbed to ruin, while continuing to support the system that was draining her strength.\" With more than a little sarcasm, he added, \"No episode in American history was more touching than the generous devotion with which Virginia clung to the embargo, and drained the poison which her own President held obstinately to her lips.... the old society of Virginia could never be restored... President Jefferson himself woke from his long dream of power only to find his own fortunes buried in the ruin he had made.\"\n\nThe indecisiveness of Jefferson's solution prolonged the agony, as the external threat to commerce did not let up. Jefferson had begun his second term riding the popularity in the South of his greatest achievement as president: the annexation of Louisiana, to which New England's legislators had been opposed. Now, even in the wake of the unpopular embargo, he still had support in Virginia. He was, in the final analysis, the slavery president, and he had given his home-state constituents the means of monetizing their inert labor force.\n\nNot for another eight years, until the resolution of the War of 1812 finally ended the crisis of seizure at sea, would the coast be clear for something like normal commerce to resume\u2014and for Virginia planters to take advantage of the great gift Jefferson had given them by selling large quantities of black Virginians down South.\n\nJefferson was humiliatingly forced to sign the removal of the embargo on March 1, 1809, days before a new president was inaugurated\u2014another Virginian, Jefferson's prot\u00e9g\u00e9 James Madison.\n\nThe election had not been an inspiring one from the point of view of New England. It was a Virginia versus South Carolina election, pitting the Republican James Madison of Virginia, principal author of the Constitution, against Federalist Charles Cotesworth Pinckney of South Carolina, he who at the Constitutional Convention had insisted on a full twenty years' protection for the African slave trade. In his first term, President Madison more or less continued the policies he had pursued as Jefferson's secretary of state\u2014which had left a sectionally divided country, a damaged economy, a restless Louisiana that chafed under Anglo-American rule from the Chesapeake, an unresolved stalemate with an angry Britain, and an unbridled Napoleon\u2014who, despite having dumped Louisiana, was still intent on controlling the Americas.\n\nOn the pretext of subduing Portugal for having engaged in commerce with its centuries-long trading partner England, Napoleon introduced his forces into Spain in 1807 with the intention of taking control of the ports of Lisbon and C\u00e1diz, key bases for reaching across the Atlantic. With his troops installed in Iberia, he humiliated Carlos IV and his son Fernando VII before the world by installing his brother Joseph Bonaparte on the Spanish throne as King Jos\u00e9 I.\n\nNapoleon's defenestration of the Spanish government was a green light for independence movements in Spain's American territories. But Cuba remained loyal to the Spanish crown, and in eastern Cuba (known as Oriente), the French speakers who had relocated as refugees from the Haitian Revolution came under suspicion.\n\nAlready there had been justified concern that the _franceses_ might secede from the island and take over Oriente for themselves as per the model of the neighboring island Hispaniola, permanently divided between contentious French and Spanish speakers. Now the thirty thousand (a best-guess number) who had escaped the unraveling of Leclerc's genocide by fleeing as immigrants to eastern Cuba from Saint-Domingue were seen as potentially subversive by the loyalist Spanish government of Cuba. Those who did not take a loyalty oath to Spain or marry Spanish citizens found it expedient to leave for New Orleans, taking their slaves with them.\n\nIn the course of this flotilla, a report published by New Orleans mayor James Mather counted 9,059 people as entering New Orleans on some sixty ships, many of them privateers, mostly during the last three months of 1809. In this number, 3,225 of them (36 percent) were slaves, and only 962 of those were men over fifteen. Since this took place after the January 1, 1808, cutoff, \"importation of persons\" was by then prohibited by federal law, so it took an act of Congress to disembark the enslaved passengers, who were impounded for months in the harbor of what was then called the Territory of Orleans. They were thus the last slaves to be legally imported into the United States.\n\nAs they had previously done in Santiago de Cuba, the newly arrived Domingans transformed the French part of New Orleans\u2014the old part, which came to be known as the French Quarter for the language spoken there. New Orleans by then was well along in becoming two adjacent towns: a fast-growing English-speaking one and a much larger French- (and Spanish-) speaking one, separated by the no-man's-land (\"neutral ground\") of Canal Street (named for a canal that was never dug). While the Domingans' arrival helped push Louisiana's population a little farther toward the minimum of sixty thousand free inhabitants required for statehood, it also slowed the pace of Americanization of New Orleans for the next thirty years and brought a new layer of culture and skills to an already complex Afro-Louisianan population. Despite the peculiarity and isolation of Louisiana, it had been a colonial cousin of Saint-Domingue, Martinique, and Guadaloupe. Six of the twenty-three French slave ships that came to Louisiana were from Ouidah in present-day Benin, from whence the word _vodou._ Domingan vodou found fertile ground in Louisiana, since it was kin to practices that had been going on in Louisiana since the first contact with Africa.\n\nEnding the African trade signaled a major cultural shift in black America. Africans had been entering the colonies on an ongoing, though not continual, basis for almost two centuries.\n\nThere were 1,191,364 slaves in the United States according to the 1810 census, an increase of 33.4 percent over 1800. It seems reasonable to assume that fewer than one hundred thousand were African-born, with most of those in the Lowcountry. The next five decades would each show a growth of the enslaved population of never less than 24 percent\u2014a tremendous level of growth for a population not being supplemented by imports and routinely devastated by high child mortality\u2014but never again would the 1800 to 1810 rate of growth in the slave population be reached, combining as it did massive importation in combination with reproduction of the domestic population.\n\nDuring that decade, the population of the southwestern corner of Mississippi quadrupled. Most of the new nation's frontiers pushed westward, but the expansion of plantations into Mississippi unrolled in a northeasterly direction. Natchez, in the southwest of the territory, was at the edge of a vast forest of uncleared land. The nearest Anglo-American towns to the east were hundreds of miles away. Nor was it easy to get to Natchez from New Orleans; as Christian Schultz was leaving Natchez downriver in April 1808, his boat passed one going the other way whose cargo of enslaved laborers were doing the hard upriver slog that required physically pulling the boat forward: \"we met a brig at the Fausse Rivi\u00e8re, one hundred and sixty-five miles above New-Orleans, which was then forty-two days from that city. This vessel had part of her cargo of slaves on board, and was bound to Natchez; and though she had the advantage of extraordinary assistance from her slaves, she had performed only one half of her voyage. I have no doubt that her whole voyage from city to city took up more than eighty days.\"\n\nNatchez was already the second biggest slave market of the Deep South. Sitting at the end of the distribution line, it paid the highest prices. As had happened in the Chesapeake and Carolina, there was a political cleavage between the planters already established around Natchez, who had plenty of slaves and wanted to see the value of their holdings appreciate, and those on the frontier, who wanted to buy more slaves, cheap.\n\nWhen Jefferson left office at the beginning of 1809, the US economy was in tatters from his embargo, with New England's shipping industry having suffered especially badly. As shipping resumed, Britain and France returned to impounding American vessels, and the new president, James Madison, continued to swallow the insults.\n\nAs when Madison had been Jefferson's secretary of state, the acquisition of Florida continued to be a strategic obsession. A new Native American group had formed there: the Seminoles were a composite people, most numerously a breakaway group of Creeks who had incorporated a number of black escapees into their ranks. These \"Black Seminoles,\" as they were called, were largely Gullah people making use of Native American social identity while living in marronage.\n\nAll over the Southeast, settlers pushed onto Native American land, and they wanted more of it. In Congress, the perhaps twenty-one representatives and senators who clamored for war with Britain were overwhelmingly Southern and Western. Their Federalist enemies dubbed them the \"War Hawks.\" Kentucky's thirty-four-year-old Henry Clay made his debut on the national stage when, after two weeks as a senator, on February 22, 1810, he announced, \"The conquest of Canada is in your power... I verily believe that the militia of Kentucky are alone competent to place Montreal and Upper Canada at your feet.\"\n\nClay was trying to appeal to annexationists in New England, but he also wanted the Native Americans, Spanish, and British cleared out of the way of the Southern river arteries that could carry Kentucky's products to the Gulf of Mexico via the West Florida ports of Mobile and Pensacola. When Madison invaded the short-lived, self-proclaimed independent Republic of West Florida, which the United States had no claim to other than conquest, Clay defended the action on Christmas Day, 1810, with these words:\n\nI am not, sir, in favor of cherishing the passion of conquest, but I must be permitted, in conclusion, to indulge the hope of seeing, ere long, the new United States, (if you will allow me the expression,) embracing, not only the old thirteen States, but the entire country east of the Mississippi, including East Florida, and some of the territories to the north of us also.\n\nExposed to attack from without and within, the Chesapeake was leery of war. Virginia congressman John Randolph argued restraint because of \"the danger arising from the black population,\" as the congressional recorder summarized it during a December 1811 oration. \"The French Revolution had polluted\" them, declaimed Randolph with his characteristic rhetorical extravagance, and was teaching them\n\nthat they are equal to their masters; in other words, advising them to cut their throats... What was the consequence? Within the last ten years, repeated alarms of insurrection among the slaves, some of them awful indeed. From the spreading of this infernal doctrine, the whole Southern country had been thrown into a state of insecurity.... God forbid, sir, that the Southern States should ever see an enemy on their shores, with these infernal principles of French fraternity in the van! While talking of taking Canada, some of us were shuddering for our own safety at home.\n\nHe then evoked the fearful specter of Gabriel's rebellion, reminding everyone to be afraid of the slaves' potential for violence: \"The night-bell never tolled for fire in Richmond that the mother did not hug her infant more closely to her bosom.\"\n\nSouth Carolina's twenty-nine-year-old John C. Calhoun, as new in Congress as Clay, was at the beginning of a career that would see him become the embodiment of pro-slavery doctrine. Calhoun was the first upcountry South Carolina politician to make a name on the national stage; if he was representative, upcountry was an angry place.\n\nCalhoun was a brilliant writer and debater, and to judge from the extensive documentation that exists, he was an unhappy, strict man whose single goal in life was to become president. Harriet Martineau wrote in 1838 of Calhoun that \"I know of no man who lives in such utter intellectual solitude. He meets men and harangues them by the fire-side as in the Senate. He is wrought like a piece of machinery, set going vehemently by a weight, and stops while you answer. He either passes by what you say, or twists it into suitability with what is in his own head, and begins to lecture again.\"\n\nGeorge C. Rogers Jr. writes that \"Calhoun considered diplomacy too slow\u2014the tool of the effete coastal aristocrat.\" Slavery was Calhoun's irreducible demand, and he treated it as synonymous with the human dignity of his people; an affront to slavery was an affront to a Southerner. He replied to Randolph by bragging about how much better South Carolinans were than Virginians at keeping their enslaved ignorant:\n\nOf the Southern section, I, too, have some personal knowledge; and can say, that in South Carolina no such fears in any part are felt... however the gentleman may alarm himself with the disorganizing effects of French principles, I cannot think our ignorant blacks have felt much of their baneful influence. I dare say more than one half of them never heard of the French Revolution.\n\nThe awareness of what had happened in Haiti may well have reached more enslaved ears in Carolina than Calhoun imagined; but in Louisiana, the enslaved had definitely heard of the French Revolution. Up the Mississippi from New Orleans, on the riverbank that had since 1795 become a home to the death camps of sugarland, the mulatto Charles Deslondes\u2014not a Domingan, but fully aware of what had happened there\u2014led the largest peacetime slave revolt in US history: the \"German Coast rebellion\" that began on January 8, 1811. The uprising was ruthlessly suppressed by South Carolina's Wade Hampton, who would later become a Louisiana planter.\n\nClay, who urged armed confrontation with Britain, was also one of the Southern and Western legislators who pushed to allow the twenty-year charter of the First Bank of the United States to expire in 1811, with unfortunate consequences when the war began.\n\nIt requires an effort for a modern person, accustomed to a national currency, to imagine the monetary situation of the early United States.\n\nThe Constitution gave the federal government monetary authority, reserving for it the exclusive right \"to coin Money, regulate the Value thereof, and of foreign Coin.\" No state could \"enter into any Treaty, Alliance, or Confederation; grant Letters of Marque and Reprisal; coin Money; emit Bills of Credit; [or] make any Thing but gold and silver Coin a Tender in Payment of Debts.\"\n\n\"Bills of Credit\" meant paper money. The Constitution explicitly prohibited the printing of money by the states, so there couldn't be, say, Massachusetts dollars and Virginia dollars. But, perhaps because the debate would have been endless, the Constitution was silent on the issuance of paper money by the federal government, and silent on its issuance by banks. The most desirable money\u2014many would tell you, the only real money\u2014was specie, minted gold or silver coins that were usable around the world as money, most commonly in the form of Spanish coins. President Washington signed the Coinage Act in 1792, which adopted the dollar as the monetary unit, \"each to be of the value of a Spanish milled dollar,\" and allowed for the coining of money, expressed in dollars and bearing an image \"emblematic of liberty.\" Foreign gold and silver coins continued in circulation and were legal tender until 1857.\n\nBut there weren't enough silver dollars to conduct daily commerce with, nor was moving all the available precious metal around in daily circulation the best way to use it. Paper money was a practical necessity. A bank would own a given amount of specie and would issue notes \"backed\" by it. The notes could be redeemed in person at the bank for their face value in silver, but for most transactions this was an unnecessary step. The system worked because at any given time, much paper would circulate, serving the needs of commerce, while only a relatively small amount of paper would actually be exchanged for specie. In order to be assured of being able to cover their obligations, banks were expected to maintain \"fractional reserve\" requirements at a reasonable level, though that requirement was frequently ignored.\n\nThe First Bank of the United States, the only federally chartered bank, was a creation of Alexander Hamilton, modelled in part on the Bank of England. It was not under the control of the Department of the Treasury, though the government owned 20 percent of it and Treasury had access to its books, and it had a monopoly on receiving deposits of the government's revenues, some 90 percent of which were tariffs collected at seaport customs houses. It was well-run and profitable, and by 1811 its high-quality notes constituted about 20 percent of the nation's money supply.\n\nThe state banks, most of which were chartered after the First Bank of the United States was chartered in 1791, disliked the competition from a national bank that acted to some degree as a regulator on the amount of paper money they could issue, and they wanted the deposits of specie that were going to the national bank. Jefferson in particular had been vehemently opposed to Hamilton's bank, as he was to banks in general. The hard Jeffersonians were united in their ideologically based opposition to the bank; meanwhile, the state banks leaned on senators and congressmen to take their competition out. In a political triumph for South Carolina's Langdon Cheves, who was Speaker of the House, Congress refused to renew the bank's charter, overriding the objections of the only competent member of Madison's undistinguished cabinet, Secretary of the Treasury Albert Gallatin.\n\nWithout a national bank, then, the War of 1812 was fought without financing by a government whose principal source of revenue\u2014customs duties\u2014had been devastated by wartime conditions since the embargo of 1807. Nor was there much of an army. The military structure was plagued by a surfeit of officers, many of them incompetent, and a deficit of troops, who suffered unspeakable hardships. The militias were undisciplined, as they would demonstrate when they turned and ran by the thousands at the Battle of Bladensburg (August 24, 1814), opening the door for the burning of the federal city. The navy, the most competent branch of the military, had been crippled by Jefferson's gunboat debacle.\n\nNapoleon's towering influence on the course of American history extended to causing the breach in which the Spanish colonies could move toward independence. In forcing Carlos IV's abdication in 1808, he put a definitive end to Spain's status as a world power. As Spain's empire disintegrated, the fortress-city of Cartagena declared independence on November 11, 1811, beginning a series of bloody South American independence wars.\n\nThe Lafitte brothers\u2014French-born pirates who had relocated from Saint-Domingue to Cuba and then to Louisiana\u2014received letters of marque from Cartagena giving them legal cover as privateers to do what they were already doing: preying on Spanish slave ships bound for Cuba. They sold the human merchandise by the pound, cheap, from their well-guarded grey-market base at Barataria, west of New Orleans. Mostly they sold to the French-speaking creoles of southern Louisiana, who preferred to get their slaves from pirates than from the Georgiamen.\n\nLouisiana's colonial status ended on April 30, 1812, when it was admitted to the Union. It was the best way to secure the largely French-speaking state's dubious loyalty to the United States before going to war against Great Britain on June 18, four days before Napoleon declared war on Russia. By going to war against Britain, the United States effectively became an ally of Napoleon, who was quite popular in New Orleans.\n\nJefferson's presidency, which began with his great popularity, had ended in disaster; now Madison's was failing. \"Successive generations of scholars have never ceased to wonder,\" writes J. C. A. Stagg, who edited Madison's presidential papers, \"how the creative statesman who 'fathered' both the Federal Constitution and the Bill of Rights, to say nothing of the Republican Party of the 1790s, could be as incompetent and as unsuccessful as he seemed to be as a chief executive.\" Stagg describes an enduring image of Madison as \"the weak and indecisive statesman who handled the disputes with Great Britain over maritime rights so badly that he lost control of his policies to a congressional faction of 'War Hawks,' whose members, after November 1811, stampeded him into a conflict which he did not want and which he then mismanaged to the extent that he remains to this day the only president ever to have been driven from the nation's capital by an invading army.\" Stagg supplied this description in an attempt to dispel it as a stereotype, but while it is admittedly incomplete as a summary of Madison's presidential career, it is not incorrect.\n\nRemembered by the ideologically neutral name of the War of 1812, this conflict was crucial to the development of the republic. It was effectively the United States' participation in the final stage of the Napoleonic Wars, and it can be seen as a second War of Independence, since one of its most important outcomes was the definitive acknowledgment by Britain of American sovereignty. In New England, where many were antiwar, it was a failed war to annex Canada. In the South, where it was a war against Native Americans and free blacks, it was an essential step in the expansion of slavery that would fill in the territory from Louisiana to Florida with plantations.\n\nThere were four main fronts to the thirty-two-month war with Britain:\n\n1) Canada, which the United States repeatedly attempted to assault, without success;\n\n2) the Chesapeake, whose commerce was blockaded by the British from the start of the war and which was invaded by an army that burned the White House and the Capitol. The blockade was not impermeable, however, as the British admiral John B. Warren wrote to headquarters: \"Several large Clipper Schooners of from two to three hundred Tons, strongly manned and armed have run thro' the Blockade in the Chesapeak, in spite of every endeavour and of the most vigilant attention of our Ships to prevent their getting out, nor can any thing stop these Vessels escaping to Sea in dark Nights and Strong Winds.\"\n\n3) Alabama, a front not generally mentioned as such in summaries of the war, because it did not directly entail fighting with Britain but with Native Americans, who were massacred. In Alabama, the United States achieved its military goals with what has been remembered as the Creek War, undertaken as part of the War of 1812. It's something of a commonplace that no territory changed hands as a result of the War of 1812, but that's not so. Under cover of war with Britain, the United States\u2014in the person of the most effective general in the US Army, Andrew Jackson\u2014grabbed a vast area of Native American land in Georgia and Alabama; and\n\n4) the Gulf South, whose seaports of New Orleans, Mobile, and Pensacola were essential for control of trade with the interior. There the British were vanquished under the iron command of Andrew Jackson, in a tremendous victory for Southern slaveowners against the power that had dared offer freedom to their property.\n\n#   29\n\n# **The Hireling and Slave**\n\n_No refuge could save the hireling and slave_\n\n_From the terror of night or the gloom of the grave_\n\n_Oh, say, does that star spangled banner yet wave [etc.]..._\n\n\u2014Francis Scott Key, \"Defense of Fort McHenry,\" third verse\n\nTO DESCRIBE MORE FULLY the Jacksonian context, we will briefly backtrack our chronology to quote a journal entry by a clergyman from the year Andrew Jackson was born\u20141767\u2014and the place: Waxhaw, deep in the wooded, swampy hinterlands on the North Carolina side of the border between the Carolinas.\n\nThe most detailed account we have of this frontier life, albeit a biased one, is that of Anglican pastor Charles Woodmason, who was appalled. Woodmason had been shunned by Charleston society for having accepted a commission as a Stamp Act collector in 1765. He changed his life after that; apparently motivated by spiritual concerns, he was ordained so that he could become a circuit-riding Anglican (or Episcopal) priest on the frontier, where the Church of England had no institutional presence but where there were New Light Baptists, Presbyterians, Dunkards, Quakers, and more. (He ultimately returned to Britain after being stigmatized as a Tory.)\n\n[I went to] the Settlement of Irish Presbyterians called the Waxaws, among whom were several Church People.... This is a very fruitful fine Spot, thro' which the dividing Line between North and South Carolina runs... a finer Body of Land is no where to be seen\u2014But it is occupied by a Sett of the most lowest vilest Crew breathing\u2014Scotch Irish Presbyterians from the North of Ireland\u2014They have built a Meeting House and have a Pastor, a Scots Man among them\u2014A good sort of Man\u2014He once was of the Church of England... His Congregation is very large\u2014This Tract of Land being most surprisingly thick settled beyond any Spot in England of its Extent\u2014seldom less than 9, 10, 1200 People assemble of a Sunday\u2014They never heard an Episcopal Minister, or the Common Prayer, and were very curious.\n\nWoodmason's memoir leaves no doubt that if politics was the popular entertainment of the cities, religion was the great organized participatory experience for the unlettered people of the frontier, as per his outraged description of a New Light Baptist service:\n\nThere are so many Absurdities committed by them [New Light Baptists], as wou'd shock one of our _Cherokee_ Savages; And was a Sensible Turk or Indian to view some of their Extravagancies it would quickly determine them against Christianity. Had any such been in their Assembly as last Sunday when they communicated, the Honest Heathens would have imagin'd themselves rather amidst a Gang of frantic Lunatics broke out of Bedlam, rather than among a Society of religious Christians, met to celebrate the most sacred and Solemn Ordnance of their Religion. Here, one Fellow mounted on a Bench with the Bread, and bawling, _See the Body of Christ_ , Another with the Cup running around, and bellowing\u2014 _Who cleanses his Soul with the Blood of Christ_ , and a thousand other Extravagancies\u2014One on his knees in a Posture of Prayer\u2014Others singing\u2014some howling\u2014These Ranting\u2014Those Crying\u2014Others dancing, Skipping, Laughing and rejoycing. Here two or 3 Women falling on their Backs, kicking up their Heels, exposing their Nakedness to all Bystanders and others sitting Pensive, in deep Melancholy lost in Abstraction, like Statues, quite insensible\u2014and when rous'd by the Spectators from their pretended Reveries Transports, and indecent Postures and Actions declaring they knew nought of the Matter. That their Souls had taken flight to Heav'n, and they knew nothing of what they said or did. Spect[at]ors were highly shocked at such vile Abuse of sacred Ordinances\n\nWhile Dr. Woodmason never adapted to such a performative religious experience, he did become a voice for the settlers, helping them draft a remonstrance when they organized as \"regulators\"\u2014vigilantes\u2014in their own defense against roving gangs of bandits. Plantation slavery had not been developed upcountry yet; according to Woodmason, that was because the hazards of warlordism made it hard for white settlers to bring in slaves:\n\n... the people wearied out with being expos'd to the Depredations of Robbers\u2014Set down here just as a Barrier between the Rich Planters and the Indians, to secure the former against the Latter\u2014Without Laws or Government Schools or Ministers\u2014No Police established\u2014and all Property quite insecure\u2014Merchants as fearful to venture their Goods as Ministers their Persons\u2014The Lands, tho' the finest in the Province unoccupied, and _rich Men afraid to set Slaves to work to clear them, lest they should become a Prey to the Banditti_ \u2014No Regard had to the numberless petitions and Complaints of the people\u2014Thus neglected and slighted by those in Authority, they rose in Arms\u2014pursued the Rogues, broke up their Gangs\u2014burnt the dwellings of all their Harbourers and Abettors\u2014Whipp'd and drove the Idle, Vicious and Profligate out of the Province, Men and Women without Distinction and would have proceeded to Charleston in a Regular Corps of 5000 Men, and hung up the Rogues before the State House in Presence of Governor and Council.\n\nFor the Mildness of Legislation here is so great and the Clemency of the Cheif [ _sic_ ] in Authority has been carried to such Excess that when a notorious Robber was with Great Pains catch'd and sent to Town, and there try'd and Condemn'd he always got pardon'd by Dint of Money, and came back 50 times worse than before. The fellows thus pardon'd form'd themselves into a large Gang, ranging the province with Impunity. (emphasis added)\n\nThat was the world Andrew Jackson grew up in: militantly defensive, self-reliant, and deeply distrustful of government. As a young man, Jackson relocated to the western part of North Carolina, which was now being called Tennessee and was where many veterans of the war with the British were settling. Jackson set up shop as a lawyer in the frontier town of Nashville, which was becoming a business center for the settlers who were pouring into the area. By 1789, he was traveling down the hazardous Wilderness Road\u2014a 450-mile forest path through Native American territory plagued by \"land pirates\"\u2014to do business in Natchez.\n\nNatchez was already functioning as a slave market in the late 1780s, when the region's agricultural output was still relatively minor, consisting mostly of tobacco and indigo. It had the distinction of having been a French town, a Spanish town, a British town, and a Spanish town again, with elements of all those populations. It was the site of the Indian uprising that ended French colonial plans for Louisiana. A 1790 report called it \"an English [meaning, English-speaking] settlement, subject to the Spaniards,\" and by then it had \"many negroes,\" in the words of Mississippi historian Charles S. Sydnor.\n\nJackson was a product of the militia system, in which he was a leading officer. Like other merchants, he bought and sold slaves as part of his commercial activity. He was also a horse breeder and a racing enthusiast; a lawyer, land speculator, and plantation owner; a pathological hater of English, Spanish, Creek Indians, and anyone who crossed him; and a master of intimidation\u2014all of which was consonant with being a slave trader.\n\n\"Between court terms in Tennessee,\" writes Jackson's biographer Robert V. Remini, \"Jackson frequently dropped down to Natchez, where he brought [to Natchez traders] such items as cotton, furs, swan skins and feathers for bedding, lime, pork, beef, boats, and\"\u2014the final word in the list seems discreetly tucked in\u2014\"slaves.\" In Remini's delicate words, Jackson carried slaves \"frequently\" from Nashville to Natchez as a \"courtesy\" to \"his friends,\" though that belies the physical effort necessary to transport a prisoner through 450 or so miles of wilderness in the late eighteenth century.\n\nA young white man's first significant investment on the road to wealth acquisition might well be a young black woman, rather than what the slave trade called a \"prime hand.\" Such seems to have been the case with Jackson when he was twenty, as per a November 17, 1788, \"Bill of Sale from Micajah Crews to Andrew Jackson Esquire for a Negro Woman named Nancy about Eighteen or Twenty Years of Age.\" Nancy was the first slave that we have any record of Jackson having purchased, and her purchase was one of his first transactions of any sort of which we have a record. He may have purchased her with the intention of reselling her; we know nothing about what kind of use he put her to, nor do we know anything else about her. The bill of sale is the only indication that Nancy existed. Between 1790 and 1794, writes Remini, Jackson purchased \"at least sixteen slaves... They measured his steady progress toward economic security\" while he pursued a career as a merchant and a real estate speculator.\n\nIn July 1794, Jackson made a great real estate deal when he became co-owner of some five thousand acres of the lower Chickasaw Bluff, marvelously situated on the Tennessee side overlooking the Mississippi River, where the Wolf River empties into it. The land's previous owner, the trader John Rice, had bought it in 1783, while it was still part of North Carolina\u2014though under then-current law North Carolina had no right to sell it, as it was Chickasaw land. Rice was killed by Native Americans on his way back from a Nashville-Natchez run in 1791, throwing the property onto the market. The lawyer and slave trader John Overton, a Virginia-born Nashville transplant, purchased it in partnership with Jackson, his lifelong close ally.\n\nThough the area was as yet unpopulated by whites, it was the best site for a town along a far stretch of the Mississippi. Four decades later, in 1830, when steamboats ruled the transportation economy, Overton retroactively credited himself with foresight: \"I always... considered that at some day, the water privilege attached to the banks would be worth more than all the lots and lands about the place.\" Jackson had little to do with the property, other than making a profit on his share when he sold it; a third partner, General James Winchester, gave the settlement its fanciful Nile-istic name: Memphis.\n\nThe Mississippi Territory was organized in 1798, and the United States took over administration of it in 1801. The United States Army went to work building the Natchez Trace\u2014a road of sorts, along the route of the Wilderness Road, to connect the town with Nashville. Fortunately for Jackson, his friend from Tennessee and former colleague in Congress, President Jefferson's prot\u00e9g\u00e9 William Charles Cole Claiborne, was now the Mississippi Territory's first US governor. Claiborne, who addressed Jackson effusively in his letters, made Jackson's family emissary John Hutchings welcome, helped him find buyers for slaves and horses he had brought, and helpfully advised Jackson of the progress by mail. Claiborne wrote him on December 9, 1801:\n\nThe Races in this District, commenced yesterday, and will hold for three days; Mr. Hutchings has attended the _Race_ today, and will proceed from _thence_ , to Mr. Green's, where he has left the Negroes & Horses. Mr. H. will be at my House, next Week; in the mean time, I will try to find a purchaser for your Horses, as for Negroes, they are in great demand, and will sell well.\n\nClaiborne wrote Jackson again on December 23, informing him of young Hutchings's accomplishment as a slave trader: \"The Negro Woman he has sold for 500 dolls. in Cash, and I belive he has, or will in a few days sell the Boy, for his own price, to Colo. West.\"\n\nJackson must have been an effective frontier businessman. A violent man and an eager duelist, he once challenged another lawyer for mocking his knowledge of the law. Whether dealing with slaves, soldiers, or politicians, he was an authoritarian leader who, in Remini's words, \"could hate with a Biblical fury and would resort to petty and vindictive acts to nurture his hatred and keep it bright and strong and ferocious.\" When in 1804 he advertised in the _Tennessee Gazette_ for the return of a runaway slave, he made the extraordinarily vicious offer of \"ten dollars extra, for every hundred lashes any person will give him, to the amount of three hundred.\"\n\nJackson got a bad reputation when he killed Charles Dickinson in a May 30, 1806, duel. After Jackson's pistol jammed and did not fire during the first exchange, he was allowed to recock his pistol and fire a second shot. With a disadvantaged opponent, the gallant move would have been to fire the pistol into the air, shake hands, and considered honor avenged. But there was no doubt that Dickinson had intended to kill Jackson. Dickinson, who made his money on the interregional slave trade by, as Jackson later described, \"purchasing Negroes in Maryland and carrying them to Natchez & Louis[ian]a,\" had put a bullet into Jackson that fractured a rib or two and, in Remini's words, \"lodged in the chest cavity close to his heart and impinged on his left lung.\" Streaming blood from his chest wound, Jackson took aim and shot Charles Dickinson in cold blood from a distance of twenty-four feet. The bullet entered Dickinson's intestines, and he lived with no hope of recovery, in mortal pain, until he expired about ten o'clock that night. The bullet in Jackson's body remained there the rest of his life, one of a number of excruciating pains he lived with. The duel had been over a quarrel stemming from a horse race with a $3,000 purse.\n\nLike many other merchants, Jackson traded in slaves along with everything else\u2014horses, cattle, dry goods, and especially land speculation, which was the foundation of a great many fortunes in Jackson's day. Jackson made much money selling Tennessee plots to land speculators in Philadelphia, for which he typically got paid in paper, which he traded for goods, which he then had to sell at his own stores. Slaves, however, were cash transactions, as we see in a letter from Jackson's nephew Donelson Caffery, who was attempting to get started as a merchant, apparently in partnership with Jackson. Caffery wrote him from Bayou Sarah in West Feliciana Parish on May 20, 1810, which was at the time part of the nominally Spanish-controlled area that was about to briefly declare itself the independent Republic of West Florida and would come under Claiborne's control by year's end:\n\nI am sorry to inform you that I fear from the situation of this Country business cannot be done to advantage[.] It is true Goods may be sold on credit, but contrary to the opinion I had form'd from the accounts of people; There is no such thing as making collections... As soon as I can make sale of some Negroes, I will go to New Orleans to buy Groceries[.] it's the only business that can be done here for Cash.\n\nThere are various instances of Jackson's using \"negroes\" in settlement of accounts. A 1795 letter to him requesting him to purchase land for one Joseph Anderson notes that \"it would suit me to pay for it, either in a negro and Horses, or in Horses and some Money.\" Jackson's slave-trading past became a political hot potato when he later ran for president. During the election of 1828, a pamphlet authored by a man with whom Jackson had been in litigation over land deals, Andrew Erwin, bore the memorable title of _Gen. Jackson's Negro Speculations, and his Traffic in Human Flesh, Examined and Established by Positive Proof._ It brought up a story about which Jackson had to issue a clarification: in a not unusual transaction for the time and place, the mercantile firm of Jackson & Hutchings in 1806 accepted a thirteen-year-old \"negro boy\" as partial payment to close out a three-year-old debt. In Jackson's words, \"The negro boy was recd. & the account with Rawlings & Bradford closed.\" As was all too common in such stories, it had a sad ending: the boy, whose name was Charles, was kept at the Clover Bottom racetrack, run by Jackson's friends. One of them, William Preston Anderson, bet him in a race and lost him, and Charles subsequently died from an unspecified disease.\n\nJackson was the partner with capital and credit in Coleman, Green, and Jackson, founded in 1810 to sell cotton and tobacco from Nashville to Natchez. After losing money on a cotton deal, the partners attempted to recoup the expenses by going into slaves, buying a group of them from a tavern dealer in Virginia. The men, as Jackson later noted, were received naked; it was not uncommon for a seller to palm off the expense of clothing them on the buyer. The junior partner, Horace Green of Natchez, took the slaves down to Natchez by boat in the summer of 1811, but no one was buying. Business was terrible. Britain was hammering at American shipping pursuant to its Orders in Council, and commerce was dead. It was clear that war was coming with Britain, and there would likely be a naval blockade that would prevent taking the cotton crop out of New Orleans.\n\nFinding a weak market, Green traded a few of the unfortunate people for horses before Jackson arranged for John Hutchings to take them over and house them at his nearby plantation until he could come down personally to salvage what he could of the fiasco. Failing to sell the slaves himself, Jackson drove the unsold slaves back to Nashville, taking the unheard-of step of driving a coffle of slaves from the destination back to the point of origin, through Choctaw and Chickasaw territory. From Natchez he wrote his wife, Rachel, on December 17, 1811:\n\non tomorrow I shall set out from here homewards, on the Biopierre [Bayou Pierre][.] I expect to be detained Some days preparing the negroes for the wilderness[.]... I shall bring home with me from twelve to Twenty\u2014I hope to be able to sell some of them on the way at good prices\u2014but many of them I Shall be obliged to bring home and as most of that number will be females I leave you to point out to Mr. Fields [the overseer] where to have the house built for them.\n\nMeanwhile, an apocalyptic fear ran through the region. The New Madrid earthquake, with its epicenter in Arkansas, still believed to be the strongest earthquake ever to hit that part of the country, had struck on December 16, and the aftershocks were continuing. Navigating the Mississippi had become impossible, creating economic havoc in New Orleans. On the way back to Nashville with his coffle, Jackson, already in a bad mood, ran afoul of the federal Choctaw Indian agent, Silas Dinsmore, whose post on the road between Nashville and Natchez, as mandated by law, required passports for slaves being transported. Dinsmore was in the habit of confiscating undocumented slaves, thus creating a barrier for slave traders along the main trading artery. Jackson, who saw Dinsmore as a \"highway robber,\" defied him, bringing his train through with a conspicuous show of arms. He subsequently began a campaign to have Dinsmore removed from his post, writing to Tennessee governor Willie Blount a letter that bluntly threatened arson and murder: \"from the conduct of Silas in this as well as in other cases he must be removed, or our citizens will rise and burn his Tavern and Store with Silas in the middle of them.\"\n\nJackson subsequently refused to pay his partner Green's invoiced expenses, charging that Green was padding the bill to pay his gambling debts, that his transportation and provisions expenses were too high, and that he had hired the \"negroes\" out in Natchez and pocketed the proceeds. Like a number of items of Jackson's correspondence, his letter to the arbitrator appears to have been composed in a fit of passionate anger, but from it we can learn something about the deal. Needless to say, it shows not a bit of concern for the victims of his business, who had been trafficked from Virginia to Natchez, then made to trek through the wilderness back up to Nashville. Jackson's concern was that he was being cheated on the money:\n\nI also found from examining the ac[coun]ts of Negroes sent to Markett that the expence never averaged more from here than fifteen dollars a head except one wench and three children, who had been subject to the fits remained better than six months in the Natchez, she cost with her children twenty five dollars...\n\n[F]rom every inquiry I have made on the subject, [I find] that fifteen dollars pr head is about the usual expence, and finding this to amount including the amount of the price of the Boat, and not taking into view the children at the breast, it makes the cost on each negro $44.66 2\/3\u2014this as I am advised is more than double what is usual...\n\nThree months of provisions was talked of as necessary to be laid in as an outfit... let us take the soldiers ration for the Basis\u2014there was 25 grown negroes with two sucking children they always count with the mother\u2014then say 25 for three months will take 1125 lb. Beacon [bacon]... let us give $60 for cloathing (there was 13 wenches one habit each[,] the fellows recd naked)...\n\nIt was agreed on all hand that the Natchez was glutted with negroes... a sacrafice will be upon the negroes of at least $1500 if not $2000.\n\nThe trip was, unsurprisingly, hard on the captives. Jackson wrote his sister-in-law, Mary Caffery, who was eager to purchase a laborer: \"The negro fellows that I brought through with me owing to their exposure in the wilderness have all been sick and were the[y] _well_ neither* of them is such that I could recommend to you.\" Jackson never described the condition of the women and children, torn away from their families, who endured the round-trip forced march.\n\nGiven the documentation of this episode that exists, it appears safe to say that Andrew Jackson is the only US president that we know of who personally drove a slave coffle. But then, Jackson was also the first president to have been a merchant.\n\nNew England did not want the War of 1812; the Southerners did. They got what they wanted: under cover of war with Britain, a substantial chunk of the Deep South was made safe for plantation slavery when Andrew Jackson vanquished the Creek Nation and took its land.\n\nJackson was at home at the estate outside Nashville that he called the Hermitage when word arrived: a thousand or so Creek Indians had on August 30, 1813, committed a massacre of some 250 men, women, and children at Fort Mims in Alabama, in retaliation for a murderous attack on them by two settlers who had taken refuge there. They dashed out the brains of children, it was said, swinging them by their legs to bash their heads against the walls, and they slit open the bellies of live pregnant women. They carried off the slaves to be their servants\u2014meaning, they stole the most valuable property there. Among the dead at Fort Mims were 160 unfortunate soldiers under the command of W. C. C. Claiborne's brother, Ferdinand L. Claiborne, who escaped harm.\n\nCreek Indians were the very devil to white Tennesseans. South Carolina had fought the two-year Yamassee War against them almost a century before. Georgians had been fighting them since their colony was established. The people of Jackson's society considered it their duty to kill them as a matter of their own survival. For Jackson, the Indians were the flunkeys of the British, as were the Spanish; Britain and Spain were at this point allies, after the humiliation Napoleon had wreaked on Spain. With the United States at war with Britain at last, he sought to neutralize the British in the South by repressing their indigenous allies.\n\nWhen word of Fort Mims arrived, the forty-eight-year-old Jackson was nursing a broken arm with a slug newly embedded in his shoulder, ten days after a seven-man gun battle in the town's streets against future senator Thomas Hart Benton and his brother. With a seemingly limitless tolerance for pain, he set out on horseback with his swollen arm in a sling to command a militia that would accomplish the white settlers' agenda: the ethnic cleansing of Native Americans from the entire South east of the Mississippi. It took Jackson multiple campaigns over many years to finish the job, which required his attainment of the presidency to complete. Remini describes Jackson's intention:\n\nCertainly by 1813, if not earlier, Jackson's course of action was fixed. He intended to eliminate all foreigners along the southern frontier as a necessary prelude to the systematic destruction of the Indian menace and the territorial expansion of the American nation.\n\nJackson described his immediate mission unequivocally: \"to _carry_ a _campaign into_ the _heart_ of the _Creek nation_ and _exterminate them.\"_ 25 Though the Creeks were feared for their ambushes, they were unsuccessful at defending themselves against pursuit by organized armies hell-bent on killing them. The conflict had begun as a civil war among the Creeks, pitting the traditionalist Red Sticks, allied with Britain, against the more accommodationist Lower Creeks. Exploiting the division, Jackson ended by wiping out the Creek Nation, burning Native American towns wherever he found them and defeating a force he estimated at four thousand warriors; the Creeks had black slaves, who also participated in combat against US forces and were killed. As the defeated Red Sticks retreated to Spanish Florida, Jackson treated his allies among the Creeks as harshly as if they had been the losers, forcing hard terms on them and expropriating some twenty-two million acres of their land in what is now Alabama and southern Georgia.\n\nJackson did it without much in the way of resources with which to arm, feed, clothe, and pay his troops, who were frequently in a state of near or actual mutiny. Without a national bank, the federal government had to borrow from state banks, but the largest amount of specie was unavailable for Southern use, because it was in Massachusetts and Connecticut banks, who lent it to Britain instead. During the War of 1812, \"New England banks were financial agents of the enemy,\" writes Henry Adams. \"Boston bought freely British treasury notes at liberal discount, and sent coin to Canada in payment of them.\" Another embargo, from December 1813 to April 1814, cut off Southern exports, resulting in a net outflow of what specie there was from that region to New England.\n\nAt the end of the Creek War, Jackson returned eighteen \"negroes\" who had been captured by the Creeks at Fort Mims to their lawful owners. In three Native American camps, his men found \"one hundred and fifty scalps the greater part of which were females supposed to be taken at Fort Mimms.\"\n\nThe enslaved of the Chesapeake began slipping away to the British invaders as soon as they arrived. They were particularly valuable defectors, because they could serve as guides to the area. This ongoing drain became formalized as a military strategy on April 2, 1814, when, much as Lord Dunmore had previously done, Admiral Alexander Cochrane, the new British commander, issued a proclamation from Bermuda \"that all those disposed to emigrate... will have their choice of either entering into his Majesty's sea or land forces, or of being sent as FREE settlers to the British positions in north America or the West Indies.\"\n\nCochrane was attempting to incite slave revolt. Knowing the white Southerners' fear of black violence\u2014especially in Louisiana, which had so many white survivors of Saint-Domingue\u2014he imagined thousands of runaway slaves joining his troops. A diversionary force sent to harass coastal South Carolina and Georgia under Rear Admiral George Cockburn included black West Indian troops, with the explicit intention of instilling the fear that a British-supported slave insurrection was under way. One hundred thirty-eight of Pierce Butler's slaves ran away, a loss for him calculated by Roswell King Jr. at $61,450.\n\nUnfortunately for the Americans, the British invasion came at a time when Britain had a surplus capacity of well-trained, victorious soldiers. A beaten Napoleon had abdicated on April 11, 1814, and in August, Cockburn's troops landed in Maryland and marched toward Washington. After the Baltimore militia turned tail and fled at the Battle of Bladensburg on August 24, the British entered the capital city. President James Madison left the debacle at Bladensburg, and returned to Washington to find the White House in the process of evacuating. He fled to the countryside, humiliated.\n\nBritish forces under Admiral Cockburn entered Washington, burning the White House, the Treasury, part of the Capitol, and whatever was in the Library of Congress up to that point, while sparing civilian property. Their targeted arson in the capital city was widely believed to have been undertaken in reprisal for the inexcusable American plundering and partial burning of York (Toronto) in April 1813. A providentially violent thunderstorm blunted the British invasion of Washington, and they quickly retreated, having made their point.\n\nThe British offensive into the Chesapeake was stopped at Baltimore.\n\nThe War of 1812 is not well remembered today\u2014except for its two most heroic tableaux, both of which inspired familiar songs.\n\nWhen the British forces continued on from Washington to Baltimore on the night of September 13, 1814, they failed to get past Fort McHenry, which controlled the access to the town at the mouth of the Patapsco River. The Americans had plenty of gunpowder\u2014the factory of E. I. du Pont de Nemours was in nearby Wilmington, Delaware\u2014and there was a prolonged cannonade that stopped the British advance. \"For two hours,\" writes Harold R. Manakee, \"houses in Baltimore, four miles distant, trembled on their foundations.\"\n\nOne week after the battle, Francis Scott Key's lyric \"Defense of Fort McHenry\" was published in full on page two of the two-page _Baltimore American and Commercial Daily Advertiser_ of September 21, 1814, though it subsequently became better known as \"The Star-Spangled Banner.\" To indicate how it should be sung, it was sufficient to place at the head of Key's lyric the name of the risqu\u00e9 and ubiquitous English glee club drinking song his words had been composed to fit: \" _Tune_ \u2014 Anacreon in Heaven,\" the final two lines of which read in the original:\n\n_And besides, I'll instruct you like me to entwine_\n\n_The myrtle of Venus with Bacchus's vine._\n\nFrank Key, a twenty-five-year-old lawyer from Georgetown,* was a slaveowner and, as he would demonstrate in his later career, a thoroughgoing white supremacist. As of 1806, he was the brother-in-law of Roger B. Taney, another politically savvy slaveowning Maryland lawyer. Out of the successful defense of Baltimore, as witnessed by Key from aboard a British ship, he spun a disastrous war into something victorious.\n\nThe third, or \"vengeful,\" verse of Key's poem (quoted in this chapter's epigraph), which is _never_ sung today, brags of terrorizing and killing \"the hireling and slave,\" implying that the British soldiers were mercenaries and explicitly condemning the renegade ex-property who fought as enemies of the star-spangled banner.\u2020\n\nThe tune was already being sung with a patriotic lyric, \"Adams and Liberty,\" in praise of John Adams, but Key repurposed it\u2014a political act, right there, which he had already attempted with an earlier lyric (in praise of Jefferson's actions against the Barbary Pirates) that had included the phrase \"the star-spangled banner.\"\n\nThe other great heroic-tableau moment of the War of 1812 was, of course, kept alive in popular memory through Johnny Horton's 1959 recording of \"The Battle of New Orleans,\" composed by songwriting Arkansas schoolteacher Jimmie Driftwood (\"We fired our guns and the British kept a-comin'...\") The war had been ended by the Treaty of Ghent before the battle took place, but no one in America knew that yet. For Andrew Jackson, the war against Britain was never over.\n\nNew Orleans, which Jackson was tasked with saving, was well on its way to becoming one of the world's great ports. The first steamboat arrived in New Orleans from Pittsburgh in 1811. The patrician Livingston brothers, early American practitioners of the political revolving door, were in the steamboat business with Robert Fulton (whose first steamboat was named the _Clermont_ , the name of the Livingston estate). Robert Livingston, negotiator of the Louisiana Purchase and Fulton's principal backer, died in February 1813, but his brother Edward, in disgrace over missing funds during his tenure as New York district attorney, had relocated to yellow-feverish New Orleans in 1804\u2014with, wrote John Quincy Adams in his diary, \"one hundred thousand dollars of the public money.\" After his first wife died, he married a nineteen-year-old aristocratic Domingan beauty and became the attorney for slave trader and pirate Jean Lafitte. As of 1814, Livingston and Fulton were offering infrequent but regularly scheduled steamboat runs up the Mississippi from New Orleans to Natchez and back, despite the tendency of the boilers to explode, scalding workers and passengers to death, and despite the many lethal obstacles that were so many wooden land mines in the still-uncleared river.\n\nSugar and cotton went downstream, and now slaves could be shipped upstream: New Orleans and Natchez were already the major slave distribution hubs of the emergent Deep South. With Alabama pacified by Jackson and Louisiana a newly minted state, an economic boom was already under way, especially in New Orleans, even under wartime conditions. New Orleans was going to get the benefit of joining the United States: military aid.\n\nThe Creek War had transformed Jackson's image from that of disreputable brawler to one of savior. He repeatedly asked James Monroe, who was doubling as secretary of state and secretary of war, for permission to seize Spanish-governed Pensacola, with the self-assigned task of driving the British and Indians away. Monroe responded \"that you should at present take no measures, which would involve this Government in a contest with Spain.\" Jackson did it anyway. \"This will put an end to the Indian war in the South,\" he wrote when he informed James Monroe what he was about to do, \"as it will cut off all foreign influence.\" After leaving Pensacola, he wrote Monroe, \"I flatter myself that I have left such an impression on the mind of the [Spanish] Governor of Pensacola, that he will respect the American character.\"\n\nJackson had popular-hero status by the time he arrived in New Orleans to supervise its defense against the British, hatred and fear of whom united the town's Anglos and French in one of the few known cases of their agreeing on anything. After the shame of Jefferson's pacifism, when it seemed that the United States would rather swallow any insult from Britain or France than fight, and after more than two years of war in which the United States had fought and lost miserably, with the government's headquarters in the nation's capital a smoking ruin, here at last was a general who could not merely defend a town, but slaughter the enemy. While in New Orleans, Jackson censored the local press and became the first US general to impose martial law.\n\nThe British had been so sure of their victory that some of the officers had brought their wives, ready to assume their colonial posts after the locals were subdued. But the British troops were caught in a crossfire between massive volleys from behind earthworks and bombardment from the ship _Louisiana._ The one-sided killing of so many British was unprecedented in the history of two wars fought between the United States and Britain.\n\nThe Kentucky militia that came down to fight as part of Old Hickory's motley crew didn't even have flints for their guns. As had previously happened with Washington at Yorktown, a combination of black soldiers and Frenchmen\u2014in this case, the Lafitte brothers' well-trained, experienced pirate force\u2014played key roles in carrying the day.\n\nJackson emerged from the slaughter covered in glory. The burning of the capital city was avenged. America would defend itself. The Mississippi River would remain open to commerce. Almost immediately the price of cotton went up sharply, giving an enormous shot in the arm to the nascent cotton kingdom and its associated slave trade.\n\nThe slaveholders of the South paid a price for the war in lost slaves, because, as in the War of Independence, once again slaves had accepted the British offer of freedom. But after mediation by the czar of Russia, the British paid $1.2 million in compensation to the slaveowners, which they could use to restock their fields with young people. The slaveowners were the ones who had wanted to go to war in the first place, and as a class, they were the solid victors of the War of 1812. Jackson's land grab from the Creeks had made vast new acreage available for plantation slavery.\n\nMany of the black soldiers who fought on the British side retreated to East Florida, which was still in Spanish hands and was only weakly guarded. Secretary of War William Crawford wrote Jackson on March 15, 1816, instructing him to remove a maroon community that occupied a fort built by the British in 1814 in West Florida: \"It appears... that the negroe fort, erected during the war, at the junction of the Chathouchie and Flint rivers, has been strengthened since that period, and is now occupied by between two hundred and fifty and three hundred blacks, who are well armed, clothed and disciplined. Secret practices to inveigle negroes from the frontiers of Georgia, as well as from the Cherokee and Creek nations, are still continued by the negroes, and hostile Creeks.\" Jackson's subordinate Edmund P. Gaines reported to him that \"the Negroes are attempting to raise Corn... They have red Coats and are supplied with a large quantity of British muskets, Powder and other supplies.\"\n\nFree blacks wearing British redcoats, carrying guns, and teamed up with Indians: nothing could have provoked Jackson more violently. When gunboats from the US Navy attacked the \"Negro Fort,\" a lucky shot from their first volley hit the fort's powder magazine. The spectacular explosion killed 270 of the 334 people in the fort\u2014men, women, and children\u2014and wounded all but three of the rest.\n\nMeanwhile, the number of cotton plantations was exploding. As large amounts of cotton shipped out of the port of New Orleans bound for Lancashire, tens of thousands of African Americans were forcibly relocated into the area\u2014by oceangoing vessel, by flatboat, and in coffles.\n\n*i.e., none.\n\n*Part of Maryland at the time Key was born, Georgetown was redistricted as the third town in the District of Columbia, along with Washington and Alexandria.\n\n\u2020 _Hireling and the Slave_ was subsequently the name of a lengthy 1855 pro-slavery poem that, according to the Oxford English Dictionary, furnishes the first known occurrence of the term \"master race.\" Written by William J. Grayson of Beaufort, South Carolina, it was prominently serialized in _DeBow's Review._\n\n#   30\n\n# **A Jog of the Elbow**\n\n_While the Bank is my goddess, its desks are my altars, And all my \"fine phrenzy\" is spent on defaulters. 1_\n\n\u2014Nicholas Biddle, 1823\n\nTHE WAR WAS OVER, and at last Britain was respecting the American flag at sea. Money was flowing, albeit along unpredictable courses.\n\nNo energy was being consumed in partisan warfare; the Federalists had all but disappeared as a political force. Jackson didn't only crush the Creeks; his victory at New Orleans gave the coup de grace to the disgraced Federalist Party, members of which had been threatening New England's secession since 1793 and had openly sided with Britain during the conflict.\n\nFor the first time since the early days of the Washington administration, there was only one functional political party in the United States. At its head was Jefferson's former law student James Monroe, who as a teenager had crossed the Delaware with Washington and as an adult had taken credit for the Louisiana Purchase. It was Monroe who dispatched Jackson to New Orleans, and he came into peacetime a national hero. Facing no serious opposition in the presidential election of 1816, he became the third consecutive president from the Shenandoah Valley of Virginia.\n\nAfter the extreme partisan battles during what some historians describe as the First Party System, the relative political tranquility of a one-party nation led a derri\u00e8re-garde New England Federalist newspaper editor in 1817 to coin the sarcastic phrase \"the era of good feelings,\" a term that passed into general retrospective use to identify Monroe's first (but not the second) presidential term. It was an era of especially good feelings for all those connected to the fast-growing commercial web spun out of cotton.\n\nMonroe is the only US president to have an African capital city named after him: Monrovia, in Liberia, a country whose name betrays its intention as a destination of exile for manumitted ex-slaves. The American Colonization Society, which proposed to implement the self-deportation of free African Americans, was cofounded by Francis Scott Key, two years after he published \"Defense of Fort McHenry.\" Over the years, a plethora of famous political names attached themselves to the society, including James Madison, Henry Clay, Daniel Webster, John Randolph, Andrew Jackson, and even Abraham Lincoln. The chimera of \"colonization\"\u2014the white dream of mass black deportation that would comply with the vision Jefferson had projected in _Notes on the State of Virginia\u2014_ lasted until secession. Disclaiming any connection with abolitionism, it was a way of doing nothing about slavery. John Quincy Adams flatly called the Society a \"fraudulent charitable institution.\"\n\nThe word \"colonization\" implied that African Americans would somehow establish American colonies, which would have meant freeing slaves to go establish foreign beachheads for the slavemasters. The idea was widely hated by free black people, who were subject to various odious restrictions but for the most part had no intention of leaving their homes, and some three thousand people of color assembled at Mother Bethel in 1817 to protest the formation of the society. Harriet Martineau, who in 1834 visited James Madison in retirement at his Montpelier plantation a week after he had sold \"a dozen of his slaves,\" wrote that \"he accounted for his selling his slaves by mentioning their horror of going to Liberia, a horror which he admitted to be prevalent among the blacks.\"\n\nThe idea of colonization was hated just as much by hard-slavery Southerners, who saw it as soft on abolitionism and tending toward keeping a smaller portion of the population enslaved, when what they wanted was to see as much of the population enslaved as possible.\n\nThe party of Jefferson and Madison had discovered the uses of executive power, shifting considerably from its radical anti-federal stance of the first years of the republic. As they began rebuilding the White House and the Capitol, the Republicans now saw the federal government as a functional entity able to make the \"internal improvements\" that the fast-growing nation needed. A reliable paper money was needed, and the government needed a fiscal agent to support its wartime debt, much of it owed to foreign financiers. To that end, the Second Bank of the United States was chartered, for twenty years as the first had been, in 1817. Much of its capital stock was drawn not from its shareholders' gold and silver, but from their holdings of public debt. The bank was also heavily invested in British bills of exchange.\n\nWith the War of 1812 over, shipowners had surplus privateering boats to sell. But besides privateering, these fast, maneuverable vessels were also in use by slave traders, who bought used privateers and commissioned new vessels as well. Baltimore-style \"clippers,\" made in Baltimore and many other places as well, would be the vessel of choice for an African slave trade that no longer came to the United States but would still carry perhaps more than a million kidnapped Africans to Cuba and Brazil. The misery of the experience would have been heightened by the boats' characteristics: being light and fast made for even worse seasickness. This era of the slave trade was notorious for its tight-packing: the tiny below-decks compartments were typically only three feet or so high, so when the captives were put away at night, they rode lying down, packed tightly together; and since clippers \"rode wet,\" taking on large quantities of sea water, they were damp and cold.\n\nWith the Chesapeake unblockaded, coastwise vessels could freely ply the route from Baltimore to New Orleans; those CASH FOR NEGROES advertisements began appearing in newspapers around the Chesapeake as of 1815. But it was a slow expansion at first, because the Second Bank of the United States tightened credit in 1818.\n\nSouth Carolina's Langdon Cheves, who had been a War Hawk and who had killed the First Bank in Congress, was named the Second Bank's director in March 1819. On the question of the balance of credit versus metal, Cheves was all the way at the hard-money end of the scale. He was in favor of lavish personal spending coupled with extreme governmental restraint, and he was against the very concept of fractional reserves, the basis of modern banking. He continued tightening credit, accumulating governmental income in the form of inert specie while refusing to extend loans against it. That drove the Panic of 1819 into a depression the following year, during which he continued his extremely conservative management while many were ruined. Under his stewardship, the bank required each of its branches to make their own decisions with the capital they were allotted; by the time he resigned, Cheves had, in Howard Bodenhorn's words, \"effectively taken a national organization and transformed it into a network of independent banks operating under the loose direction of the parent institution in Philadelphia.\" The result was an uncoordinated interregional cash flow, and a differential of exchange rates from region to region\u2014not a good basis for a national commerce.\n\nCheves resigned in 1822, proud of the soundness of his overcapitalized bank, and was replaced by board member Nicholas Biddle in January 1823. Biddle\u2014who, in a poem he wrote at a lady's request shortly after he was named director, sang the praises of \"that simplest, sublimest of truths \u2014 six per cent\"\u2014began letting credit out again, and organized specie shipments. Precious metal could be purchased like any other commodity, and Biddle brought in shiploads of silver from Mexico\u2014now independent from Spain, and more tractable. The silver entered the bank's system at its New Orleans branch, as New Orleans entered into its peak era of national influence. Biddle created a domestic exchange operation that could make capital easily mobile throughout the country, with a national currency supplied by him that was worth the same amount at any of the bank's national branches.\n\nThe appropriation of the Creek lands was a textbook case of accumulation by dispossession. Now the formation of a new capital class could begin, with confiscated lands as the basis of new wealth\u2014if enough slave labor was available to clear it and make it produce.\n\nAlabama's liberation-for-slavery set off the great land rush remembered as \"Alabama fever.\" The US land office did land-office business, privatizing the newly available territory taken from the Native Americans and handing out the land in vast quantities on liberal credit terms. For slave traders, the takeover of Alabama by the cotton kingdom was the beginning of a long boom.\n\nCotton was a different kind of crop from tobacco or rice, and its cultivation imposed a different kind of brutality on its laborers. The whip-driven regime of cotton was like nothing known in Virginia. Tobacco cultivation was artisanship by comparison; rice cultivation was task labor, in which individual workers had specific, differentiated tasks to attend to. But cotton was based on the uniform, infinite repetition of the same tasks, requiring much in the way of manual dexterity and endurance.\n\nThe society of the enslaved of the cotton kingdom was a far cry from the family structures that still existed in Virginia and Maryland; the plantation populations that worked the cotton fields were the isolated remnants of destroyed families, jumbled together like the prison population they were. In the first years of the boom, about a third of them came from Virginia or Maryland, but they also came from Kentucky, Tennessee, Missouri, and, increasingly, points south. The arrival of so many occasioned a new cultural collision among the enslaved, as black, English-speaking former Marylanders found themselves having to converse with Gullah speakers from the Lowcountry or French-speaking Louisianans\u2014and, of course, until 1820 or so there were still some Africans coming in via piracy.\n\nSome farmers left their played-out farms and set out for Alabama with their slaves; others went to market to buy as many slaves as they could get. Some planters traveled north to the Chesapeake, hoping to get better prices by buying slaves directly from planters who were selling; others formed small partnerships to travel around on buying trips\u2014placing newspaper ads, visiting planters, attending auctions. They found eager vendors on the Eastern Shore of Maryland, where Easton began an annual slave auction in 1818, selling off its surplus young farmhands away from their families for the convenience of the Alabama-fevered.\n\nStates farther North got in on the action. New York and New Jersey both still had slavery in 1819, and slaveowners in both states took advantage of the opportunity to sell slaves off to Alabama. The numbers were nothing like Southern numbers, of course; the 1820 census showed 7,557 slaves in New Jersey out of a population of 277,575, and by 1830 the slave count was down to 2,254. Most of the diminution was from manumission, but some hundreds of enslaved people in eastern New Jersey were trafficked down South. By that state's Act of Gradual Abolition in effect since 1804, they were supposed to give their consent to leave the state, but that consent was easily forged.\n\nThe message was heard all through those states that still permitted slavery: raising slaves was a good business.\n\nFlorida\u2014the prize that had eluded Monroe at the time of the Louisiana Purchase\u2014was at last within reach. Spanish forces were stretched thin, engaged as they were in failing to suppress the independence wars being led in South America by Sim\u00f3n Bol\u00edvar and Jos\u00e9 de San Mart\u00edn.\n\nMonroe sent an eager Jackson to march some five thousand men into Spanish East Florida in 1818, in a de facto declaration of war on Spain without congressional consent. The expressed aim of Jackson's invasion was to stop Native American terrorists from making raids into US territory, though the skirmishes had been bidirectional, with Georgians also raiding into Florida for livestock and slaves. Jackson's Florida campaign was overtly a war on free black and indigenous people; his report of it made repeated reference to the enemy as \"Indians and negroes\":\n\nTo chastise a savage foe, who, combined with a lawless band of negro brigands, have for some time past been carrying on a cruel and unprovoked war against the citizens of the United States, has compelled the president to direct me to march my army into Florida. I have penetrated to the Mickasuky towns and reduced them to ashes.\n\nEarlier we have spoken of the concept of an ongoing Gullah War; this was one of the major hostilities of its long course. Jackson's marauders burned hundreds of houses, destroyed forts, killed an unknown number of Native Americans, and hung two native leaders in front of their people.\n\nJackson almost started another war with Britain by executing two British subjects in front of the black and native populations, impressing on them that they could not look to Britain for an alliance. The Englishman Alexander Arbuthnot, who had accurately warned the Seminole chief Billy Bowlegs that \"the main drift of the Americans is to destroy the black population of Suwannee,\" was hanged from the yardarm of his own schooner, while the Scotsman Robert C. Ambrister was shot by a firing squad. They were, Jackson wrote, \"exciters of this savage [i.e., Native American] and negro war; legally condemned, and most justly punished.\"\n\nJackson was burning to go on to Cuba, where there were no Indians but many Africans. Security of maritime commerce was not fully assured, he insisted, until Cuba also was under US control. \"I will insure you cuba in a few days,\" he promised Monroe, if given the necessary support.\n\nMonroe was alarmed by the international implications of Jackson's aggression in Florida, though he wanted the territory. Secretary of War John C. Calhoun liked the idea of taking Cuba, but not of the war with Spain that it would entail, and denied Jackson the forces to continue. (Calhoun was apparently also afraid that Jackson's military ambitions might be Napoleonic and that he would take over civilian government.) He attacked Jackson in the closed meetings of the cabinet, demanding Monroe censure him\u2014though Jackson only learned about that years later, when Calhoun was his vice president. The only member of the cabinet to defend Jackson's action was Secretary of State John Quincy Adams, who no less than Monroe saw Florida as essential to national security. Adams, who was far and away the most experienced diplomat of the time, proceeded to negotiate Jackson's win against Spain to an annexationist conclusion that resulted in major territorial gains for the United States.\n\nThe Adams-On\u00eds treaty of 1819 ceded East Florida to the United States and ended lingering controversies about West Florida. It also promised that the United States would not try to annex Texas; Adams perhaps believed that to be a keepable promise, but Jackson certainly did not. The treaty also ceded Spain's claim on Oregon to the United States, extending the border to the West Coast, in a \"joint occupation\" with Great Britain, whose Hudson Bay Company competed with John Jacob Astor's company for the fur trade there.\n\nMississippi, as yet sparsely populated and with Natchez its largest city, became a state in 1819. Most of it was still Choctaw or Chickasaw land, and there was popular discontent from Georgia westward about the slowness of the process of Indian removal. In 1820, Calhoun called in Andrew Jackson, a firm believer in deportation of Native Americans, together with Thomas Hinds, a Mississippi veteran of the Creek War, to negotiate\u2014more like, arm-twist\u2014the Treaty of Doak's Stand with Jackson's former ally, the Choctaw chief Pushmataha, which conveyed Choctaw land to the United States with a chunk of land beyond the Mississippi River ceded to them in return. (In practice, the Choctaw were unwilling to remove themselves, and it took until the 1830s, with Jackson as president, for their forced exile from the state of Mississippi to be accomplished.)\n\nMemphis was developed into a town in 1819 by former Tennessee superior court judge John Overton, who would become for a time the richest man in Tennessee. Incorporated in 1826, it quickly became the regional distribution hub for large areas of Mississippi, Tennessee, Arkansas, and Missouri. As a slave-trade center that serviced the new plantations of the large, fertile region, it boasted Mississippi River connections to Natchez and New Orleans.\n\nGrateful to Andrew Jackson, the politicians of Mississippi in 1821 named their newly created capital city for him. Located on the bluffs overlooking the Pearl River, at the site of a trading-post stop on the Natchez Trace, the town of Jackson connected by water to New Orleans via Lake Ponchartrain. Unfortunately, it wasn't easy to get to and from Jackson. The governing elite of Natchez, which was the only important commercial center in Mississippi at the time, blocked internal improvements that would have removed the sunken logs that booby-trapped the Pearl River, which was, said Senator Thomas Buck Reed in 1826, \"useless to the inhabitants, or nearly so, from the want of resources in the State to adapt it for the purposes of commerce.\" Roads were rudimentary.\n\nSpain's empire continued to deteriorate; Mexico became independent in 1821, the same year the Spanish evacuated San Agust\u00edn for the second and last time pursuant to the Adams-On\u00eds Treaty. The combat-averse Thomas Jefferson could not have imagined a less likely figure than Andrew Jackson to realize his dream of snatching the Floridas. Jackson had done it not by ensnaring the Indians in debt as Jefferson had imagined but by forcibly evicting them, even as he fought a war of repression against the free black people who lived among them. With the same stroke, he accomplished the Carolinian dream: now there was no free territory to the south that the enslaved of South Carolina and Georgia could escape to, or organize insurrections from.\n\nThe South had been made safe for plantation slavery. There was no more Native American threat, no more maroon havens, no more Spanish, no more British. It no longer needed the protection of the United States from enemies south and west. South Carolina could now afford to become even more uncooperative with the federal government.\n\nMonroe sent Jackson to install the Florida state government, but he resigned after only nine and a half months in St. Augustine, amid complaints of dictatorial behavior, and went back to Tennessee to become a senator. The Americans built a new town near the site of the long-disappeared Huguenot community of Fort Caroline, called\u2014what else?\u2014Jacksonville.\n\nSectional politics resulted in one of the nation's historic political struggles, fought in 1819\u201320, over whether the sparsely populated territory of Missouri, acquired as part of the Louisiana Purchase and previously a slave territory under the French and Spanish, would be admitted to the Union as a free or slave state. The prize at stake was control of the Senate, which was crucial for the slaveholders. The House was coming under control of the North, because in terms of population the North was handily outpopulating the South through immigration. It had already outstripped the three-fifths constitutional advantage, and the gap was widening.\n\nAnother prize was the concession to sell slaves to Missouri pioneers; needless to say, Virginia was enthusiastically in favor of Missouri's annexation as a slave state. Senator Henry Clay of Kentucky began earning his nickname of \"the Great Compromiser\"\u2014which was not a compliment in South Carolina\u2014by leading through Congress the Missouri Compromise, which admitted Missouri with slavery to the Union as the twenty-fourth state in 1821. In exchange, Maine was detached from Massachusetts and admitted as the twenty-third state, thus maintaining the Senate in a stalemate.\n\nBut as part of the compromise, slavery was outlawed west of the Mississippi and north of a line at 36\u00b030\u2033 latitude. The planter class of South Carolina, who could not expand their system into the West without slaves, was outraged; this, they shouted, was federal overreach. Frederic Bancroft wrote that slaveowners\n\nhad not previously believed that their chief interest was in danger. The far-seeing were now convinced of this. The whole South was sure to be permanently sectionalized if the politico-antislavery North ever became thoroughly organized. The political strength of the North depended on the development of interests and the extent to which prejudices and fears could be excited. Formerly sectionalism had usually been mild and courteous. Henceforth it was rarely to be either mild or courteous.\n\nMissouri had been acquired as part of the Louisiana Territory by Jefferson, who in his retirement saw what would happen. His remark in a letter of April 22, 1820, to John Holmes of Maine, is well known: \"A geographical line, coinciding with a marked principle, moral and political, once conceived and held up to the angry passions of men, will never be obliterated; and every new irritation will mark it deeper and deeper.\" But Jefferson was unambiguously on the slavery side of the question, agreeing with the Southerners that Congress had no right to legislate such matters for the states. Jefferson, ever the champion of exile for free black people, convinced himself that slaves trafficked to Missouri would be... _happier:_\n\nThe cession of that kind of property, for so it is misnamed, is a bagatelle which would not cost me a second thought, if, in that way, a general emancipation and _expatriation_ could be effected... But as it is, we have the wolf by the ears, and we can neither hold him, nor safely let him go. Justice is in one scale, and self-preservation in the other. Of one thing I am certain, that as the passage of slaves from one State to another, would not make a slave of a single human being who would not be so without it, so their diffusion over a greater surface would make them individually happier.\n\nHe finished the letter by absolving himself and his generation and dismissing his juniors: \"I regret that I am now to die in the belief, that the useless sacrifice of themselves by the generation of 1776, to acquire self-government and happiness to their country, is to be thrown away by the unwise and unworthy passions of their sons.\"\n\nDuring all this time, kidnapped Africans had been smuggled into American seaports, especially via Jean Lafitte's pirate\/privateer operation in the Gulf of Mexico. With Napoleon gone and the British once again allies, the US Navy concentrated on eradicating piracy. The milestone in the closing of the African slave trade was the 1819 Act to Protect the Commerce of the United States and Punish the Crime of Piracy, which was amended in 1820 to include the foreign slave trade as piracy, a crime carrying the death penalty. The ruling families of South Carolina saw that as an insult, but the slaveowners of Virginia liked it, and they were in charge in Washington.\n\nThe domestic slave trade was going full tilt. Finally, the competition from African importations was completely gone. With the British navy no longer harassing American ships, there was now a safe, legal ocean corridor for shipping slaves South in the domestic slave trade.\n\nThe legally mandated domestication of the slave trade put a sharp cap on how fast plantations could expand; they could only grow as fast as the enslaved women of the South could turn out babies.\n\nThe demand was intense. Over the next twenty years, as the power looms of Lancashire sucked up all the cotton the South could grow, enslaved wombs were not merely sources of local enrichment but were also suppliers in a global system of agricultural input, industrial output, and financial expansion.\n\nHow well or how harshly to treat an enslaved mother was a principal issue in plantation management, affecting as it did the survivability of children. Those farmers more inclined to long-term profit from \"increase\" than to shorter-term profit from labor were obliged to \"promote their health and render them prolific,\" as one writer put it.\n\nIn a now-notorious letter of January 17, 1819, that was in another era routinely ignored by Jefferson biographers, the seventy-six-year-old ex-president, plagued by debt and frustrated by the death in infancy of some of his human capital, emphasized urgently that producing children was a specialized occupation, on a par with other skills enslaved laborers might have:\n\nThe loss of 5. little ones in 4 years induces me to fear that the overseers do not permit the women to devote as much time as is necessary to the care of their children: that they view their labor as the 1st object and the raising their child but as secondary.\n\nI consider the labor of a breeding woman as no object, and that a child raised every 2. years is of more profit than the crop of the best laboring man.... I must pray you to inculcate upon the overseers that it is not their labor, but their increase which is the first consideration with us.\n\nBy this time, the interstate slave trade that Jefferson had done so much to facilitate was taking off, and the market it created for his slaves' \"increase\" offered the only hope for escaping his crushing burden of debt. In telling the overseer to ease off on hard labor for \"breeding\" women, Jefferson laid out the financial tradeoff that careful farm managers had to consider in deciding how to apply their female labor: how much time women should spend working the land versus how much to spend reproducing. This could involve calculations against market prices for crops\u2014high prices meant more field labor, low prices more birth labor. Or, since poor land required more labor to be applied to it, it could mean balancing the fertility of a patch of land against the fertility of an enslaved woman.\n\nJefferson's one-child-every-two-years quota was, it should be noted, not the worst: an even more rapacious owner could insist on faster breeding. Martha Jackson, born in 1850 and interviewed in Livingston, Alabama, recalled that her \"Antie\" was a \"breeder 'oman [who] brought in chillun ev'y twelve month jes' lack a cow bringin' in a calf.\" Indeed, Jefferson had established the two-year limit experientially, because, as previously noted, his own frail wife had died at the age of thirty-three from six pregnancies in less than ten years, her health growing visibly worse with each confinement.\n\nNot that that was unusual: white or black, women commonly were pregnant that often, and they not infrequently died during and especially after childbirth. One might wonder: if the reproductive ability of enslaved women was so valuable, why did they consistently sell for lower prices than men? Perhaps because women weakened from repeated pregnancy were less productive in the field, but also because women were a riskier purchase, often dying in their twenties because the prevailing unsanitary methods of childbirth were so deadly.*\n\nIn testimony during an 1839 court case in Warren County, Mississippi, about a farm at which \"the policy is not to make large crops but to raise young negroes,\" Tobius Stephens \"suggested rating 'breeding women' at half a hand,\" writes Christopher Morris: \"[Stephens wrote] 'If breeding women are worked hard on the hills, it is likely to produce abortion & sickness.' A witness for the plaintiff thought the current administrator had not managed the plantation very well, and offered as evidence his observation of women working in fields.'\" Concern for the women's well-being was not the issue in the court case, needless to say; what was being decided was the financial acumen of the manager. Jefferson was nothing if not consistent in his promotion of a two-year cycle of commercial human reproduction. In a letter of June 30, 1820, to John Wayles Eppes, in the course of justifying a plan to sell off twenty enslaved people in families rather than only laboring men, he discussed his captives in terms otherwise applicable to livestock management, as per the use of the verb _stocking:_ \"I know no error more consuming to an estate than that of stocking farms with men almost exclusively,\" Jefferson wrote. \"I consider a woman who brings a child every two years as more profitable than the best man of the farm. what she produces is an addition to the capital, while his labors disappear in mere consumption.\"\n\nAn addition to the capital! The variant word _capitalism_ had not yet been coined, but the term _capital_ had remained in Jefferson's lexicon twenty-eight years after his \"4 percent\" letter to Washington, and it still applied to slaves. Jefferson understood clearly how the concept of capital applied to his society. Capital is money that makes more money, and slaves were property who made more property\u2014including more slaves, who could be used as money when the need arose. It was therefore advisable to \"stock\" a farm with enslaved women, who would \"breed\" every two years, and in doing so would make a per annum capital growth target, as Jefferson had identified in his 1792 letter to Washington.\n\nEppes, the recipient of Jefferson's letter, was the recently retired US senator from Virginia and was Jefferson's son-in-law, having been married to Jefferson's daughter Maria (or Mary, or Patsy), who was his first cousin. Maria had died in childbirth-related complications sixteen years before, in 1804, as her mother Martha (or Patty) Wayles Jefferson had died from childbirth before her, and as her grandmother had died after giving birth to her mother. As Maria's confinement approached, Jefferson perhaps failed to reassure the frightened twenty-four-year-old when he wrote her from the White House: \"You are prepared to meet it [childbirth] with courage, I hope. Some female friend of your mamma's (I forget whom) used to say it was no more than a jog of the elbow.\"\n\nMaria knew better, having watched her mother die and having given birth twice already. She gave birth in February and died in April. The bereaved Eppes took up with a woman who may also have been Jefferson's daughter, at least according to present-day Hemings family oral tradition and local belief. By the time Jefferson wrote his \"addition to the capital\" letter, Eppes was cohabiting with Betsy Hemings, whom Jefferson had given to Eppes and Maria as a wedding present. If she was indeed Jefferson's daughter, she would thus have been the deceased Maria's half sister, making a creepy parallel with the way her aunt Sally had been the deceased Martha Wayles Jefferson's half sister. All the above-named (except for Jefferson himself) were descended from John Wayles. After Eppes died, Betsy Hemings was never sold, and she is buried alongside him. Whoever Betsy Hemings's father was, the Hemingses had provided the Wayles-Jefferson family with three generations of what Madison Hemings, Sally's son, referred to as \"concubine\" in a March 13, 1873, interview in the _Pike County_ (Ohio) Republican, in which he declared Jefferson to have been his father and which is our only record of his thoughts.\n\nJefferson died on the same day as John Adams, on the mystically suggestive date of July 4, 1826, the fiftieth anniversary of the date of the Declaration. His unpopularity as president had begun to fade with the growth of a patriotic cult around the Founding Fathers, fueled by Henry Clay's popular mythologizing discourse.\n\nJefferson had desperately hoped to grow his way out of the debt that tormented him in his final years. Like many Southern planters, he failed. When he died, the boom in Virginia-born slaves was only starting to get under way.\n\nWilliam Barry, who visited Monticello in 1832, wrote, \"All is dilapidation and ruin.\" Most of the gadgetry, maps, and fixtures in the interior of the present-day Monticello that is so impressively maintained by the Thomas Jefferson Foundation is a loving work of collection, restoration, and re-imagination. Jefferson's things were sold off, as were all his slaves but the ones descended from Betty Hemings. Among the other things that it is, the shrine that is present-day Monticello is a well-kept window into the practice of slavery, complete with (as of 2015) rebuilt slave cabins.\n\nLucy Cottrell, the woman in this picture, was fifteen on January 15, 1827, when she was put on the auction block\u2014one of 140 people sold, along with the farm implements, crops, and livestock of Monticello. She was bought, together with her mother, Dolly, by the Germanborn University of Virginia modern languages professor George Blaetterman, who had been vetted by Jefferson before being hired. Blaetterman was booted from the faculty in 1840 for horsewhipping his wife\u2014twice in a single week, \"once on the public road.\" It was around 1845 that the family had a daguerreotype made of Blaetterman's granddaughter Charlotte in the arms of the woman who attended her, making Cottrell one of the first African Americans to have been the subject of a portrait photograph. After Blaetterman died, his widow took Lucy and Dolly Cottrell to Maysville, Kentucky, around 1850, where she freed them five years later.\n\n_The woman holding the child in this picture, made from a daguerreotype taken ca. 1845, is Lucy Cottrell, formerly enslaved by Thomas Jefferson._\n\nBy the time Monticello was liquidated, the self-reproducing capital represented by slaves was about to be subjected to a new kind of profit-extracting process unknown in Jefferson's generation. Louisiana, the commercial giant of the South, created a new way of financing plantation agriculture: the property bank. After the Louisiana legislature chartered a bank called the Consolidated Association of the Planters of Louisiana in 1827, capitalized at two million dollars, that bank began to bundle mortgages\u2014largely collateralized, as were most Southern mortgages, by slaves, who thus made up a large part of the \"property\" of the \"property bank.\" Shored up by a guarantee from the State of Louisiana, the bank began to sell bonds in the financial capitals of the North, and in England and Europe. Edward E. Baptist, who calls attention to this securitization process, writes that \"a British bank could now sell a completely commodified slave: not a particular individual who could die or run away, but a bond that was the right to a one-slave-sized slice of a pie made from the income of thousands of slaves.\" Florida, Alabama, and Mississippi followed suit.\n\nWhen Jefferson took office in 1801, the African slave trade was still open. When Monroe left office in 1825, that trade was a distant memory, and the domestic slave trade in African Americans was on the verge of its great boom era. Managing that transition was one of the achievements, if one wishes to regard it as such, of the Virginia Dynasty.\n\nThe liquidation of Monticello in which Lucy and the others were sold was supervised by Jefferson's eldest grandson, Thomas Jefferson Randolph, with the help of his brother-in-law Nicholas P. Trist, a young Virginia-born Louisiana sugar planter who had married Jefferson's granddaughter Virginia Jefferson Randolph. We will meet Mr. Trist again.\n\nAs the center of population gravity shifted westward, the stage was set for the change from a political machine based in Virginia to one with roots in Tennessee. Intending to follow James Monroe as the fourth consecutive Jeffersonian president, Andrew Jackson won the popular vote and a plurality of the electoral vote in the 1824 presidential election. But it was taken from him by John Quincy Adams in what Jacksonians branded as the \"corrupt bargain,\"* for the backroom agreement Adams was alleged to have made to appoint the ambitious Henry Clay to the post of secretary of state in exchange for his electors.\n\nAppointing Clay doomed Adams's presidency from the start. Enraged at the outcome of the election, Jackson declined Adams's invitation to serve as secretary of war. Instead, with a group of advisors that included the New York professional politician Martin Van Buren and communications-magnate-in-the-making Amos Kendall, he built a powerful political machine that reshaped the nation and trained its political firepower on Adams, whose every initiative was blocked in Congress. The next four years was a full-time campaign for a Jackson presidency.\n\nAdams's career had been marked by his distaste for political parties, and he did not have a political organization. The Jacksonians had a populist platform: land and gold. Adams, a cosmopolitan, Puritan-descended intellectual who spoke the language of diplomacy in erudite phrases laden with classical references and did not have the popular touch, wanted a federal government that would make infrastructural improvements and improve education. But Jackson, a ruffian who spoke the plain language of a warrior, wanted a weak federal government that would distribute as much former Indian land and as much specie as possible to individuals in an expanding slave society. Adams thought Jackson \"a barbarian who could not write a sentence of grammar and hardly could spell his own name,\" but he learned a rough lesson at Jackson's hands about communicating with the public. At a time when newcomers with no inherited wealth were increasing the free population faster than established families could hand wealth down, Jackson's party harnessed the political power of this new force.\n\nPresidential candidates still were expected to remain somewhat aloof from campaigning, though candidates for lower offices showed no such restraint and traveled a lively circuit of political barbecues. Jackson spent the next four years running for president while pretending not to, burnishing his heroic aura. The Port Gibson, Mississippi, _Correspondent_ of November 3, 1827, reported his words as:\n\nI have saved your women and children from the tomahawk and scalping knife. I have protected your great emporium from flames, and from British myrmidons, and when all other resources failed, have obtained and annexed to your State, an extensive domain, adding wealth and numbers to your restricted limits.\n\nThe Jacksonians assembled what became the Democratic Party, with institutional continuity to the one we have today, whose bases were Nashville in the South and New York in the North. John C. Calhoun, who had been vice president under Adams, switched sides and ran with Jackson, who was elected president by a landslide in 1828. As Jackson had done in the 1824 election and would do again in 1832, he carried every county in Mississippi.\n\n*Despite black women's lower level of nutrition and generally poorer conditions, they may have been less at risk in childbirth than white women in one respect. Black women, who sometimes gave birth in the field and who followed African birthing practices that required them to squat, were likely more frequently successful at expelling the placenta; the mistresses, who gave birth lying on their backs according to then-current medical protocol, may have been less successful in expelling the placenta, with a correspondingly greater danger of infection or hemorrhage.\n\n*\"Corrupt bargain\" was already a well-worn phrase in Anglo-American political discourse by the time the Jacksonians hung it on Adams and Clay.\n\n_Three advertisements from the Natchez_ Mississippi Free Trader, _December 22, 1852._\n\n#   Part Five\n\n# **The Slaveocracy**\n\n#   31\n\n# **Swallowed by Millions**\n\n_I do believe that Virginia is become another Guinea, and the Eastern Shore an African coast._\n\n\u2014William Lloyd Garrison, _The Liberator_ , October 5, 1833\n\n_I have known what it is to be dragged fifteen miles to the human flesh market and be sold like a brute beast. I am from a slave-breeding state\u2014where slaves are reared for the market as horses, sheep, and swine are. 1_\n\n\u2014Frederick Douglass, 1846\n\nALREADY THE DOMINANT COMMERCIAL American city, New York took a major step toward consolidating its supremacy at the beginning of 1818, when \"packet\" boats began running monthly between New York and Liverpool.\n\nPackets left at a scheduled departure time whether they were full of cargo or not, making shipping more predictable, and they had to do it in all kinds of weather, fighting their way across from Liverpool to New York even if it was stormy and icy. Especially in winter, the westbound, or \"uphill,\" trip from England to America, going against the Gulf Stream, was the most dangerous passage a sailor could make, anywhere in the world. Because vessels couldn't sail directly against the prevailing westerly winds, they had to \"tack\": set their sails at a forty-five-degree angle to the wind in a series of successive adjustments that allow the craft to make an arc in the windward direction. Accordingly, they traveled farther than they would have, and much slower, than if the winds had been in their favor. Ships sailing from England to America typically could expect to travel anywhere from four to seven hundred miles more than when they were going the other way.\n\nThe Gulf Stream was also an obstacle for the American coasting trade southward down around Florida to New Orleans. North Carolina was a navigational menace, with sandbars outlining its shores; Capes Hatteras, Lookout, and Fear all posed dangers for passing vessels. But it was also where vessels began to have to go against the Gulf Stream. Then, going around Florida, there were coral reefs, shoals, keys, sandbars, eddy currents, and shallow water, to say nothing of the difficulty of passing through the Straits of Florida against the force of the current. Maritime insurers rated the accident rate from New York to New Orleans at 1\u00bc to 1\u00bd percent, more dangerous than the trip from New York to Liverpool though not more dangerous than the trip from Liverpool to New York.\n\nNew York's monopolization of the carrying trade was bitterly resented by the cotton growers of the South, but there was nothing they could do. Even from Charleston, the \"great circle\" northern route was the shortest way from America to England. Though wealthy planters were beyond-conspicuous consumers, there were so few of them that the South didn't buy enough imports to make regular direct round-trip transatlantic shipping from Liverpool to Charleston worthwhile\u2014ships would have arrived in America with their holds full of ballast. The shipping profit from sending cotton out and receiving imported goods in return went to New York, where the products were handled.\n\nCoasting packets took Carolina and Georgia cotton to New York, where it was loaded onto transatlantic packets. When ships arrived at New York carrying merchandise from Britain, the part of it that was destined for the Lowcountry traveled on a coasting packet, so British goods cost more in South Carolina than they did in New York. And needless to say, when specie was shipped from Britain to pay for purchases, it came to New York.\n\nBaltimore had the best harbor in the Chesapeake, and some of the best shipping facilities in the country, but it had no chance of competing with New York for European commerce. Instead, it was perfectly positioned to specialize in servicing the expanding domestic market, and it grew with the republic. Its shipyards built the lightweight, high-speed schooners that began darting back and forth along the coast as packets, bringing regular news from one place to another. The run was especially profitable between Baltimore and New Orleans: since both cities were rich emporia, ships could go full in both directions.\n\nMaryland, a border state with diversified agriculture that counted a number of Quakers in its population, was increasingly divided over slavery. On the Eastern Shore, there was much slave agriculture but also antislavery sentiment. In the northern part of the state especially, slavery was on the decline after 1820, as it was in Delaware. Limited terms of service were becoming increasingly common for Maryland slaves, raising them almost to the category of indentured servants. Slave-sale advertisements naming individuals generally specified whether they had a term of service or were \"slaves for life.\"\n\nFast-rising Baltimore had slave labor, but it was not a slave society the way Richmond or Charleston was. Seth Rockman describes the diverse mix of the early nineteenth-century Baltimore workforce as \"a continuum of slaves-for-life to transient day laborers\u2014with term slaves, rented slaves, self-hiring slaves, indentured servants, redemptioners, apprentices, prisoners, children, and paupers occupying the space in between.\" He argues that the reason slavery remained viable in the dynamic Baltimore labor market at all was the enslaved laborer's capitalized value: \"the perpetuation of slavery in a place like Baltimore owed less to the actual labor compelled from enslaved workers and more to the fact that plantation purchasers in Charleston, Augusta, New Orleans, and throughout the South were willing to pay hundreds of dollars for Baltimore slaves.\"\n\nOne of those enslaved laborers in Baltimore was Frederick Douglass, who ultimately escaped on a boat leaving the port. Though he remembered that \"going to live at Baltimore laid the foundation, and opened the gateway, to all my subsequent prosperity,\" while working as a hired slave at the Fell's Point shipyard he was beaten by \"four of the white apprentices\" in a fight \"in which my left eye was nearly knocked out, and I was horribly mangled in other respects.\" He described the relations between classes of laborers there:\n\nThe white laboring man was robbed by the slave system of the just results of his labor, because he was flung into competition with a class of laborers who worked without wages. The slaveholders blinded them to this competition by keeping alive their prejudice against the slaves as men\u2014not against them as slaves. They appealed to their pride, often denouncing emancipation as tending to place the white working man on an equality with negroes, and by this means they succeeded in drawing off the minds of the poor whites from the real fact, that by the rich slave master they were already regarded as but a single remove from equality with the slave. The impression was cunningly made that slavery was the only power that could prevent the laboring white man from falling to the level of the slave's poverty and degradation.\n\nTo make this enmity deep and broad between the slave and the poor white man, the latter was allowed to abuse and whip the former without hindrance.... these poor white mechanics in Mr. Gardiner's ship-yard, instead of applying the natural, honest remedy for the apprehended evil, and objecting at once to work there by the side of slaves, made a cowardly attack upon the free colored mechanics... The feeling was, about this time, very bitter toward all colored people in Baltimore, and they\u2014free and slave\u2014suffered all manner of insult and wrong. (paragraphing added)\n\nThe Baltimore waterfront was a key site for slave trading. There were twenty-four wharves along the harbor, to any one of which Maryland captains of local packet-boats coming from Easton, Chestertown, Kent Island, or other Eastern Shore points of origin might bring along a slave or two to sell. Most were sold without newspaper ads, but some surviving examples testify to the practice.\n\n_Baltimore_ American and Commercial Daily Advertiser _of December 21, 1818. This nameless \"mulatto,\" sold in payment of a debt, might have remained in Baltimore, perhaps hired out at the shipyard by his new owner, or perhaps ultimately taken down South. In the latter case, it is doubtful that his freedom date seventeen years hence would have meant much._\n\nIt is clear that there was already an export market for slaves out of Maryland by this time, though not much direct documentation of it survives. An 1816 grand jury report in Baltimore stated:\n\nThere are, in this city, houses appropriated to this trade, as prisons for the reception of the Negroes intended to be carried to other states. Slaves are crowded together, male and female, in one common dungeon. They are loaded with irons, confined in their filth, and subjected to various species of cruelty and tyranny from their keepers.\n\nThe earliest shipment of slaves by water from Baltimore to New Orleans of which we have a record\u2014though clearly not the first to take place\u2014was in December 1818, when, in Ralph Clayton's description, \"twenty-four slaves, boarded by six different shippers, were brought to the dock over a four day period\" to be put on the brig _Temperance_. In addition to slaves consigned from traders on the hard sail South, the packets might take migrating farmers transporting their labor forces, or passengers accompanied by enslaved personal servants.\n\nAustin Woolfolk Jr. was only nineteen when he began running his CASH FOR NEGROES advertisements in the Baltimore press in 1816, almost as soon as the coast was clear of the British. Working with his father, he had built up a stake in his hometown of Augusta, Georgia, by supplying slaves to planters relocating to newly available Alabama land. There were no quantities of slaves available in cotton-mad Georgia, so he went northward in search of supply\u2014to the farmers of Maryland's Eastern Shore, whose eagerness to sell slaves had already been amply demonstrated.\n\nWoolfolk was not the first slave trader to offer cash in newspaper advertisements, but he became emblematic of the practice. Spending liberally on advertising, traders helped anchor the Upper South's newspaper industry, running ads in every issue, all season long, of every small-town paper in their regions of coverage. Most merchants handled a variety of merchandise, but Woolfolk, who embraced as part of his pitch the term \"Georgiaman,\" dealt only in slaves, and unlike other slave traders, he did not run coffles, but only shipped captives by water.\n\nTo maximize profits, a slave trader had to cover both ends of the transaction: buy young people cheaply from farmers in Virginia and Maryland, transport them to the Deep South, and sell them there at premium prices. Woolfolk could bypass intermediaries by canvassing farms directly, offering farmers more for young African Americans than the Richmond-bound traders could. That meant having operations at both ends, with all the complexities of interstate law, taxation, and banking, all the complications of transport, and a large network of contacts. It meant a cash-flow-intensive business that had to respond quickly to changing political, economic, or weather conditions, and it entailed having offices and slave-processing facilities in different cities, with partners or agents in those cities. In Woolfolk's case, as with many merchants, his family provided them.\n\nThe Woolfolks developed the most effective network for canvassing the farms of the Eastern Shore for slaves to buy, establishing a base of operations headed by Woolfolk's brother Joseph at Easton. Once the harvest was in and farmers were ready to sell, Woolfolk's agents scoured the area, visiting every farm they could. Throughout the region they established temporary headquarters at one or another inn, distributed handbills, and took out CASH FOR NEGROES newspaper ads. They sailed the captives downriver to the Chesapeake Bay and on to Baltimore, where they were held in Woolfolk's jail until he had a full gang for shipment.\n\nWoolfolk \"generally consummated just a few sales at a time\" when buying in Maryland, writes William Calderhead, \"and from one to four slaves per purchase. Most chattels were in their teens and males outnumbered females by a ratio of 8 to 5. Slaves were not purchased in families, but on occasion a mother and child would be acquired as a unit.\" But only \"on occasion.\"\n\nLike everyone else in his trade, Woolfolk routinely separated families. John Thompson, born in Maryland in 1812 on a plantation with about two hundred slaves, had as one of his earliest childhood memories a visit to the jail where his sister was about to be sold, as his mother wept:\n\nthe first thing that saluted my ears, was the rattling of the chains upon the limbs of the poor victims. It seemed to me to be a hell upon earth, emblematical of that dreadful dungeon where the wicked are kept, until the day of God's retribution, and where their torment ascends up forever and ever.\n\nAs soon as my sister saw our mother, she ran to her and fell upon her neck, but was unable to speak a word. There was a scene which angels witnessed; there were tears which, I believe, were bottled and placed in God's depository, there to be reserved until the day when He shall pour His wrath upon this guilty nation.\n\nThe slave-buyers chatted up the locals to find out who might be going out of business, who needed cash, who might have an extra laborer to sell. It was much like what horse traders did, and not a few people who wound up doing this kind of work were former horse-traders who had moved over into trading in slaves; their successors would move back to selling horses again after emancipation. The working vocabulary of the slave trade overlapped that of the livestock business, as per the use of a term like \"stock\"\u2014specificially a breeding term\u2014to describe a labor force.\n\nA few slave dealers advertised themselves as \"negro traders,\" but most were identified more generically as brokers, commission merchants, auctioneers, et cetera. The network of the slave trade was not limited to the trader's own agents. The commerce spread its largesse around Maryland, and especially around Baltimore, through an informally organized network whose meeting-places were inns and taverns, some of which were especially known for their involvement in the business. \"Bartenders were often used as agents,\" writes Ralph Clayton. \"Their exposure to numerous travelers... placed them in an ideal position to act as go-betweens. A number of ads often reflected the seller or buyer's desire to have information left ' _at the bar_.'\" Clayton has compiled a list of Baltimore spots where traders did business: Mr. Lilly's Tavern, Fowler's Tavern, Fountain Inn, Sinner's Tavern, Mrs. Kirk's, the General Wayne Inn, William Fowler's, John Cugle's, the Columbian Hotel, the Globe Hotel, et cetera. This pattern was consistent throughout the South, where hotels commonly had secure lockup rooms that ranged from individual cells to full-fledged jails.\n\nSlave jailing was an informally organized, widely distributed system of forprofit prisons. Traders in many towns maintained their own jails, which passing coffle-drivers could use, with the advantage of possibly being able to sell or buy through contacts there. In other towns, the local lawman might be happy to rent space in the town jail for a night. Speaking of the 1850s, Bancroft wrote:\n\nEvery Southern city, and some mere villages, had slave-jails, slave-pens, or slave-yards, as they were variously called. They differed much in size and character. Some were carefully built, while others were old buildings, houses, sheds or stables, slightly altered. They usually had some of the characteristics of a poor barrack, a boarding stable and a prison.... At the best of the public ones, where slaves were fed and watched for any stranger, the usual charge was twenty-five or thirty cents a day\u2014hardly as much as the feeding and care of a horse at any public stable. Their food was almost as plain as a horse's and they often had less that could be called a bed. They slept on the hard floor, and considered themselves fortunate if, in addition to their bundle of clothes, which they used for a pillow, they could get an old blanket.\n\n_One of nine such advertisements in an issue of the Easton, Maryland_ , Gazette, _October 18, 1828._\n\nLocal sheriffs were good contacts for Woolfolk's agents, because they were in a position to flip runaways, whose disgusted owners might authorize handing them over to Woolfolk in exchange for a cash settlement, or who might be sold unclaimed. Surviving records from Baltimore show fifteen handovers of runaways to him between 1829 and 1836: Liz, on August 10, 1835; Kitty, on November 5, 1835; Henry Hazelton, December 3, 1835, et cetera.\n\nSome \"runaways\" might be free people kidnapped off the street, as in the case of Fortune Lewis, who was abducted in 1822, taken to Woolfolk's jail, and sent to Washington, where he was able to prove his freedom and was released. But such a happy resolution for the victim was unusual. The free black people of Baltimore\u2014and, indeed, free black people throughout the North\u2014lived with the knowledge that they could be kidnapped and sold.\n\nAustin Woolfolk's early growth was slowed by national economic difficulties. Much as the First Bank of the United States had previously done in 1792, the Second Bank of the United States caused a panic soon after it was chartered.*\n\nThe depression remembered as the Panic of 1819 took two years to bottom out and two more to come back, though its effects were lighter in the newly wealthy Deep South. \"Not till 1821 did [Woolfolk] ship more than one hundred slaves south annually,\" writes Calderhead. That was the year he moved into his Pratt Street quarters, complete with his own slave jail. \"In the following year his scale of operations doubled, and for the next six years he shipped from 230 to 460 slaves south on an annual basis.\"\n\nWoolfolk's main source of supply was the farms of Maryland's Eastern Shore; like those of Virginia, their well-fed, hard-working young farmhands were established as a premium brand. Calderhead notes that \"as for sellers, many who dealt with the traders once were inclined to do so again.\" For those repeat vendors, selling slaves had become a regular part of their economic cycle\u2014which is to say, they had become slave-farmers who sold perhaps one or two teenagers a year.\n\nLike many traders, Woolfolk lived on his jail site, in a house that was part of a complex where dozens of people might be chained up at a time. The size of Woolfolk's operation made him the public face of the \"negro-trader\" and his name the terror of the enslaved. He had a kind of bogeyman status for enslaved children\u2014except, unlike the bogeyman, he was real.\n\nFrederick Douglass grew up in fear of Woolfolk. Like many who were born enslaved, Douglass had been separated from his mother at an early age and did not know the exact date of his birth, which he reckoned to have been in 1818. Before he was hired and sold away, Douglass was one of about a thousand people Edward Lloyd owned on Maryland's Eastern Shore, near Easton. That kind of estate took generations to accumulate; Lloyd was descended from seventeenth-century Maryland old money, and the core of his property is still in the hands of his descendants today. Lloyd was at various times a congressman, senator, and the governor of Maryland; it is ironic that he is most remembered for owning the plantation where Frederick Douglass was born and lived as a child.\n\nLloyd's captives labored on a network of neighboring agricultural prisons administered from a central location. Douglass, who described the brutalities of Lloyd's regime, recalled of the central plantation that \"if a slave was convicted of any high misdemeanor, became unmanageable, or evinced a determination to run away, he was brought immediately here, severely whipped, put on board the sloop, carried to Baltimore, and sold to Austin Woolfolk, or some other slave-trader, as a warning to the slaves remaining.\"\n\nWoolfolk accounted for 53 percent of the 4,304 people documented as sent by the oceangoing trade from Baltimore to New Orleans between 1819 and 1831, but despite his outsized historical footprint, there were many other traders. A person with \"Negroes of either sex to dispose of\" might, for example, stop by the New Bridge Hotel and leave word for the Kentucky trader David Anderson, who accounted for 223 of the 1,400-plus people known to have been shipped by water from Baltimore to New Orleans between 1818 and 1822.\n\nWoolfolk knew better than to parade the grim spectacle of loading his ships before the eyes of the town. When it was time to sail, the captives were marched under cover of predawn darkness out of his complex, located near present-day Oriole Park, down seven or so blocks to Fell's Point. From there, they sailed around the peninsula of Florida, and many were ultimately sold out of the Woolfolk firm's New Orleans office at 122 Chartres Street. Others were taken to Natchez, where Woolfolk also sold slaves, as an advertisement in the Woodville, Mississippi, _Republican_ that ran for three months in late 1826 \/ early 1827 announced:\n\nNEGROES FOR SALE. The subscriber has on hand _seventy-five_ likely young Virginia born Negroes, of various descriptions, which he offers to sell low for cash, or good acceptance; any person wishing to purchase would do well to call and suit themselves. \u2014 I will have a constant supply through the season. \u2014 I can be found at Purnell's Tavern.\n\nNatchez, December 1st, 1826. \"Austin Woolfolk.\"\n\nFrederick Douglass recalled:\n\nWhen a child... I lived on Philpot Street, Fell's Point, Baltimore, and have watched from the wharves, the slave ships in the Basin, anchored from the shore, with their cargoes of human flesh, waiting for favorable winds to waft them down the Chesapeake. There was, at that time, a grand slave mart kept at the head of Pratt Street, by Austin Woldfolk [ _sic_ ]. His agents were sent into every town and county in Maryland, announcing their arrival, through the papers, and on flaming \"hand-bills,\" headed CASH FOR NEGROES. These men were generally well dressed men, and very captivating in their manners; ever ready to drink, to treat, and to gamble. The fate of many a slave has depended upon the turn of a single card; and many a child has been snatched from the arms of its mother by bargains arranged in a state of brutal drunkenness.\n\nThe flesh-mongers gather up their victims by dozens, and drive them, chained, to the general depot at Baltimore. When a sufficient number have been collected here, a ship is chartered, for the purpose of conveying the forlorn crew to Mobile, or to New Orleans. From the slave prison to the ship, they are usually driven in the darkness of night; for since the antislavery agitation, a certain caution is observed.\n\nIn the deep still darkness of midnight, I have been often aroused by the dead heavy footsteps, and the piteous cries of the chained gangs that passed our door. The anguish of my boyish heart was intense; and I was often consoled, when speaking to my mistress in the morning, to hear her say that the custom was very wicked; that she hated to hear the rattle of the chains, and the heart-rending cries. I was glad to find one who sympathised with me in my horror.\n\nA coastwise trip took three weeks or so, depending on the weather, versus seven or eight weeks to make the grueling walk from Maryland to New Orleans. Economic historians Herman Freudenberger and Jonathan B. Pritchett found that eight passages\u2014\"shipments\" was the term\u2014from Norfolk to New Orleans took an average of nineteen days in transit, at a cost of seventeen dollars per slave. But the transit time, they found, was only 18 percent of the time elapsed between receiving a certificate of good conduct (affirming that the enslaved person in question was not dangerous) and sale. The time of actual transport was sandwiched between weeks of being held in pens at either end. Though an individual interstate trade could be a process of between two and three months, there were cases that took a year\u2014a process of mental agony for the captive. Enslaved women were frequently pregnant, and on occasion women gave birth while in a holding pen or at sea.\n\nThe advantages of coastal speed over the overland trade were obvious. Coastal trade turned capital around quicker, essential in a cash-intensive business; market conditions could be responded to more quickly; a minimum of two weeks' expenses of provisions was saved; and, most important, the enslaved arrived in better condition\u2014especially children, who had a hard time keeping up with a coffle's pace\u2014which meant a higher price. There were relatively few onboard fatalities among these young people, who had, after all, been selected for their relative health and appeal. Long months of confinement in pens, followed by weeks at sea, facilitated the spread of diseases, but these were not the Middle Passage crossings that averaged something like a 15 percent mortality en route.\n\nThe inward shipping manifests show a disturbing phenomenon one digit at a time: the number of children under ten sold away from their mothers and sent for sale alone. Louisiana put a stop to that in 1829 with a unique law that harmonized with the rules of the old Code Noir, prohibiting the sale of children under ten without their mother unless documented proof of orphanhood was furnished. \"This statute markedly lowered the number of sales in Louisiana of out-of-state, unaccompanied young slave children,\" writes Judith K. Schafer. \"Immediately before passage of this law, 13.5 percent of the slaves sent from Virginia to New Orleans were under the age of ten years. Immediately following passage of the act, shipments from Virginia of slave children under ten declined to 3.7 percent, and none of these were unaccompanied by their mothers.\" Which is to say that, in Austin Woolfolk's heyday, until a regulation to control it was implemented, 9.8 percent of the involuntary passengers shipped south were motherless children under ten. For that matter, most of the rest of the passengers were little more than children, in the early years of their reproductive lives. Ninety-three percent of the enslaved people whose passage Freudenberger and Prichett could document were between the ages of eleven and thirty. But then, it was a young country. Black or white, people didn't live all that long. Over 40 percent of Baltimore was fifteen or younger in 1820.\n\nThere were dangers connected with oceangoing ships: piracy and mutiny. Both happened to ships carrying slaves for Woolfolk. The mutiny happened on April 20, 1826, when the schooner _Decatur_ left for New Orleans with thirty-one enslaved people on board. When the veteran captain made the mistake of allowing small groups of them on deck unchained, two men took him by surprise and threw him overboard. The mate, attempting to come to his aid, was also thrown overboard. The mutineers had hoped to escape to \"San Domingo\" (Haiti, which since 1822 had taken over the entire island of La Espa\u00f1ola), but lacking navigation skills, they instead floated aimlessly and were overtaken.\n\nUltimately fourteen men from the _Decatur_ were brought into New York, where, incredibly, they escaped into the city. Only one man, William Bowser, was apprehended, and he alone was tried for the murders of the captain and the mate.\n\nCoffles came via the National Road to Wheeling, Virginia, all the time during coffle season, there to be sent down the Ohio River, which empties into the Mississippi. Recalling his days as a nineteen-year-old saddler in Wheeling, Benjamin Lundy wrote, \"My heart was deeply grieved at the gross abomination. I heard the wail of the captive; I felt his pang of distress; and the iron entered my soul.\"\n\nAfter resettling a few miles away to raise his family on the other side of the borderline of emancipated Ohio, Lundy began an antislavery society and, in 1821, moved it to eastern Tennessee, where a manumission society existed. He took over a faltering antislavery publication, renamed it _Genius of Universal Emancipation_ , and made it the first substantial antislavery publication in the United States. By 1824 he was publishing in Baltimore and traveling extensively. He wasn't only a propagandist, but also an organizer, helping found other antislavery societies. He traveled to Haiti in 1825\u2014still thirty-seven years away from being recognized by the United States\u2014to make an arrangement with the Haitian government to take emancipated people. When in 1826 he arranged for the American Convention for the Abolition of Slavery to be held in Baltimore, there were \"directly or indirectly, eighty-one societies\" represented, \"seventy-three being located in slaveholding States.\"\n\nLundy began hammering at Woolfolk in print. He reprinted the _New York Christian Inquirer_ 's account of William Bowser's trial and execution:\n\nOne woman, [Bowser] said, who was confined in Woolfolk's prison, first cut the throat of her child, and then her own, rather than be carried away!... he was carried to the place of execution, when a few minutes before his exit he addressed the spectators in a few words, stating his willingness to die, and exhorting them to take warning by him to prepare to meet their God. As _Woolfolk_ was present, he particularly addressed his discourse to him, saying he could forgive him all the injuries he had done him, and hoped they might meet in Heaven; but this unfeeling \"soulseller,\" with a brutality which becomes his business, told him with an oath, (not to be named,) \"that he was now going to have, what he deserved, and he was glad of it,\" or words to this effect! He would have probably continued his abusive language to this unfortunate man, had he not been stopped by some of the spectators who were shocked at his unfeeling, profane and brutal conduct. In a few moments after this, the unfortunate man was launched into eternity.\n\nLundy ended his peroration with the words, \"Hereafter let no man speak of the humanity of Woolfolk.\"\n\nIn the South, such an insult against a gentleman would demand satisfaction in a duel, but Woolfolk did not pretend to be a gentleman, nor did he consider Lundy to be one. A few days after the article ran, Lundy was, as he put it in his memoir, \"assaulted and nearly killed\" when Woolfolk caught up with him on the street in Baltimore on January 9, 1827. Woolfolk beat Lundy severely, stomping on his head and leaving his face \"in a gore of blood\" that left him with a long recuperation and permanent damage. According to the coverage in _Niles' Weekly Register,_* when Woolfolk was tried for the assault on Lundy, he denied having been in New York during the execution, but admitted\n\nthat he was guilty of a breach of the law, but in mitigation of the penalty they read several articles in the Genius of Universal Emancipation, which Lundy acknowledged he had written and published, in which the domestic slave trade from Maryland to the southern states was spoken of in the heaviest and bitterest terms of denunciation, as barbarous, inhuman and unchristian; and Woolfolk was called a \"slave trader,\" \"a soul seller,\" &c., and equally guilty in the sight of God with the man who was engaged in the African slave trade....\n\nChief justice Brice, in pronouncing sentence, took occasion to observe, that he had never seen a case in which the provocation for a battery was greater than the present\u2014that if abusive language could ever be a justification for a battery, this was that case\u2014that the traverser was engaged in a trade sanctioned by the laws of Maryland, and that Lundy had no right to reproach him in such abusive language for carrying on a lawful trade\u2014that the trade itself was beneficial to the state, as it removed a great many rogues and vagabonds who were a nuisance in the state\u2014that Lundy had received no more than a merited chastisement for his abuse of the traverser, and but for the strict letter of the law, the court would not fine Woolfolk any thing. The court however was obliged to fine him something, and they therefore fined him _one dollar_ and costs.\n\nWoolfolk won the battle but lost the war; this violent clash of slave trader versus abolitionist was a propaganda victory for the burgeoning antislavery campaign, which in its early stages tactically consisted largely of attempts to prohibit the interstate slave trade.\n\nIt was not surprising that Lundy should receive street justice at the hands of a crude man like Woolfolk; physical threats and intimidation were a regular part of the arsenal of defending slavery. But Lundy's prot\u00e9g\u00e9, William Lloyd Garrison, had the effrontery to call out the respectable merchant Francis Todd\u2014from Garrison's hometown of Newburyport, Massachusetts\u2014in the _Genius of Universal Emancipation_ issue of November 13, 1829. Todd had allowed his vessel to be used to take eighty or so enslaved people from Herring Bay in Anne Arundel County, Maryland, down to New Orleans at the behest of a Louisiana planter who had purchased an entire plantation's worth of labor.\n\nGarrison, who was only beginning his career, was not impressed that, according to Todd's testimony, the whole gang boarded cheerfully at the thought of being transported South to work together rather than to be broken up and sold separately; he wrote that Todd should be \"SENTENCED TO SOLITARY CONFINEMENT FOR LIFE.\" Todd sued him for libel, and Garrison was jailed for inability to pay approximately one hundred dollars in fine and costs after his conviction; ultimately, he was ransomed by a wealthy abolitionist. From his incarceration (which he was allowed to pass under conditions more like house arrest), he wrote a letter to Todd, printed in the Boston _Courier:_\n\nHow could you suffer your noble ship to be freighted with the wretched victims of slavery?... Suppose you and your family were seized on execution, and sold at public auction: a New-Orleans planter buys your children\u2014a Georgian, your wife\u2014a South Carolinian, yourself: would one of your townsmen (believing the job to be a profitable one) be blameless for transporting you all thither, though familiar with all these afflicting circumstances?\n\nGarrison went on to publish _The Liberator_ , which began on January 1, 1831, and he formed the New England Anti-Slavery Society one year later to the day. The most consistently outspoken voice of the movement, _The Liberator_ continued for thirty-five years, during which it focused on the slave trade as emblematic of the evils of slavery, and as slavery's most vulnerable point. Local and state antislavery societies appeared, with the National Antislavery Society being formed in Philadelphia in late 1833.\n\nAbolitionism already had a decades-long history in Britain, going back to the days of the _Somerset_ decision. Nicholas Biddle derided its presence in America as part of \"the latest English fashions of philanthropy and dress.\" Abolitionism was a much more radical position than merely being antislavery. One could be antislavery without actually intending to do anything about it, while barring free blacks from one's state and letting the South continue having slaves. Abolitionists, who were both black and white, and both male and female, wanted slavery extinguished, immediately, where it existed\u2014converted to free labor, without compensation for the slaveowners. As such, abolitionism was a revolutionary ideology. If implemented, it would have had the effect of impoverishing many of the richest men in the United States, devaluing their capital suddenly to zero. It would destroy the basis of Southern credit.\n\nEven John Quincy Adams, who as a congressman delivered up sheaves of abolition petitions to the House of Representatives, wrote in his diary after spending an afternoon with Lundy:\n\nLundy... and the abolitionists generally are constantly urging me to indiscreet movements, which would ruin me and weaken and not strengthen their cause. My own family, on the other hand\u2014that is, my wife and son and Mary\u2014exercise all the influence they possess to restrain and divert me from all connection with the abolitionists and with their cause. Between these adverse impulses my mind is agitated almost to distraction. The public mind in my own district and State is convulsed between the slavery and abolition questions, and I walk on the edge of a precipice in every step that I take.\n\nBona fide abolitionists were relatively few among the white population in the early days of the movement, though their numbers grew in the 1850s. The hard core of abolitionists, of course, were the enslaved themselves, along with free people of color, who constituted most of the first five hundred subscribers to _The Liberator._ 37\n\nDuring the summer of 1822, the city of Charleston was convulsed by the investigation of an alleged conspiracy headed by Denmark Vesey, an ex-sailor and free man of color who had cofounded Charleston's African Methodist Episcopal church, where he was known as a radical abolitionist preacher.\n\nVesey, whose first name came from his origin (if not his birthplace, which is unknown) on the Danish Caribbean island of St. Thomas, came with a suspect background: he had been enslaved in Saint-Domingue for a time as a boy. In South Carolina, he purchased his freedom from the sea captain Joseph Vesey with lottery winnings in 1799. Vesey was alleged to have organized a plot, said to be French-influenced, to kill white people, supposedly on Bastille Day, and flee for Haiti. Scholars have argued as to whether the conspiracy actually existed\u2014many now believe it did not\u2014or whether it was only in the imagination of Charleston mayor James Hamilton Jr., who made political hay out of it along with Robert J. Turnbull and Robert Y. Hayne, all of whom would in a few years become known as Nullifiers. But whether there was a conspiracy or not, the repression of a known revolutionary and the destruction of the \"African Church\"\u2014the AME, affiliated with Philadelphia's Mother Bethel\u2014was real. One hundred thirty-five men were tried, and Vesey, sentenced to death on June 29, was one of thirty-five who were hanged, becoming a martyr. The AME church was burned by a mob, and its ministry exiled.*\n\nAmong the condemned was the African-born Jack Pritchard, or \"Gullah Jack,\" a conjurer who was part of the AME congregation and who was alleged to have been Vesey's recruiter. African power objects were seen as part of the alleged plot's military process, as expressed by South Carolina magistrate L. H. Kennedy's reference to \"powers of darkness\" in pronouncing sentence on Pritchard on July 9:\n\nIn the prosecution of your wicked designs, you were not satisfied with resorting to natural and ordinary means, but endeavoured to enlist on your behalf, all the powers of darkness, and employed for that purpose, the most disgusting mummery and superstition. You represented yourself as invulnerable; that you could neither be taken nor destroyed, and all who fought under your banners would be invincible.\n\n_Advertisement in the_ Augusta _(Georgia)_ Chronicle, _October 22, 1822._\n\nWhen the brig _Sally_ carried twenty-five slaves from Charleston to Mobile on February 12, 1823, the manifest noted that they \"were cleared of [involvement in] the recently attempted insurrection in Charleston.\" The Vesey conspiracy provoked a series of retaliatory measures that included the formation of a new repressive organization, the South Carolina Association. The Negro Seamen's Act provided for imprisoning free black sailors while their ships were docked in Charleston; in open defiance of federal law, it put South Carolina in the provocative position of detaining black British sailors. All emancipation petitions were to be denied; the entry of free people of color into the state was prohibited, as was all education for free or enslaved blacks. A kind of security fence bearing a medieval name became popular in Charleston: the chevaux-de-frise.\n\nDavid Walker was probably in Charleston when the post-Vesey repression began. If Vesey had a plot, he might have been part of it. Walker, the first militant African American writer, was born with free status (free mother, enslaved father), probably in Wilmington, North Carolina (though there is no documentation), probably in 1796 or '97, and he became literate, probably through Biblical education in the African Methodist Episcopal church in Wilmington. When he was grown, he moved to Charleston, where a small community of free blacks worked as craftsmen and entrepreneurs. An evangelical Christian, he probably attended the same AME church as Vesey and Gullah Jack. He moved on to less repressive Boston, probably in 1825 or '26, where he married. He kept a used-clothes store in Beacon Hill, where he sold second-hand sailors' uniforms. He was a subscription agent for the short-lived _Freedom's Journal_ , the first African American newspaper; edited by Samuel Cornish and John Russwurm, it was outspokenly abolitionist and anticolonization.\n\n_A chevaux-de-frise at the Miles Brewton House on King Street, Charleston, June 2013._\n\nIn the tradition of that foundational genre of American literature, the insurrectionary pamphlet, Walker published _Walker's Appeal in Four Articles; Together with a Preamble, to the Coloured Citizens of the World, but in Particular and Very Expressly to Those of the United States of America_ in September 1830. It demanded the immediate overthrow of slavery.\n\n_Walker's Appeal_ explicitly talked back to Jefferson. As the idea of \"colonization\" for free people of color\u2014which meant, deporting people like David Walker\u2014grew, the legacy of Jefferson's philosophical racism in _Notes on the State of Virginia_ was being, in Walker's words, \"swallowed by millions of whites,\" adding that \"unless we try to refute Mr. Jefferson's arguments respecting us, we will only establish them.\" But beyond calling for black responses to Jefferson, Walker's treatise was a call to action for immediate self-emancipation:\n\nin the two States of Georgia, and South Carolina, there are, perhaps, not much short of six or seven hundred thousand persons of colour; and if I was a gambling character, I would not be afraid to stake down upon the board FIVE CENTS against TEN, that there are in the single State of Virginia, five or six hundred thousand Coloured persons. Four hundred and fifty thousand of whom (let them be well equipt for war) I would put against every white person on the whole continent of America. (Why? why because I know that the Blacks, once they get involved in a war, had rather die than to live, they either kill or be killed.) The whites know this too, which make them quake and tremble.\n\nWalker smuggled quantities of his _Appeal_ into the South, where anyone remotely connected with its circulation would be considered guilty of sedition. The first place the _Appeal_ turned up was Walker's old home town of Wilmington, where the North Carolina legislature responded by meeting in a secret session to enact a slew of repressive measures against slaves but especially against free people of color. By the time Walker was mysteriously found dead on his own doorstep on June 28, 1830, the state of Georgia had a price on his head: $10,000 alive, $1,000 dead. The rumor spread that he had been poisoned, but no autopsy was done and no one stepped forward to claim the reward.\n\n_Walker's Appeal_ was blamed by nervous Southerners for the bloody revolt in Virginia on August 21, 1831, when at least fifty-seven people were killed in an uprising at Southampton, a few miles inland from Norfolk. Led by the mystical evangelical preacher Nat Turner and four other enslaved men, the conspiracy had at least seventy followers. Turner was hanged on November 11, following which his dead body was skinned.\n\nReaction to Turner's rebellion was swift. Louisiana, Mississippi, and Alabama all banned out-of-state traders for a time, though state residents could still bring slaves in, and could still sell them. The fear that Turner's collaborators might show up in their territory corresponded to a frequently expressed belief in the Deep South, not entirely unfounded but certainly exaggerated, that the interstate slave trade was bringing in \"the dregs of the colored population of the states north of us,\" in the words of a correspondent to a Georgia newspaper. Louisiana's prohibition lasted until 1834, when the immediate terror had passed and planters would wait no longer. Mississippi's new constitution, to take effect in 1833, included a ban on slaves introduced \"as merchandize.\" There was an immediate outcry in Mississippi to lift the ban, and though it remained on the books, it was unenforced. The Mississippi legislature imposed a 2\u00bd percent tax on slave sales, subsequently reduced to 1 percent. Mississippi's flourishing slave trade was thus unconstitutional but not illegal, and it continued in a gray era until the state again prohibited importations in 1837.*\n\n_Excerpt from a broadside headlined_ Horrid Massacre in Virginia, _1831._\n\nIn Maryland, where much of the state no longer used slave labor, the reaction to the Turner uprising was to prohibit almost entirely the growing trend of manumission in 1832. At the same time, Maryland's traffic to Louisiana, which had been drawing down the numbers of enslaved people in the state, stopped. These two reactions, writes Calderhead, \"practically ended Maryland's chances of eventually becoming a free state.\"\n\nNat Turner's vision was apocalyptic, but most of the enslaved were more pragmatic. Africans had believed they would return home after death; African Americans _were_ home, in a high-security prison on perpetual lockdown. There was no place for most of the enslaved to escape to\u2014no occupying armies to defect to as in 1775 and 1814, no foreign-held territory in Florida, no Indians left to hide out with.\n\nIn Virginia, where many whites were already alarmed by having so many black people in their midst, the result of Turner's rebellion was the debate of 1831\u201332 on the abolition of slavery, the only such debate in a Southern legislature ever. Among the many quotable statements of the session was the disapproving declaration by Charlottesville's representative Thomas Jefferson Randolph, grandson of the recently deceased ex-president: \"It is a practice, and an increasing practice, in parts of Virginia, to rear slaves for market.\"\n\nSome individual slaveowners voluntarily impoverished themselves by freeing their slaves in the wake of the Turner rebellion. But after considering the matter, Virginia legislators unsurprisingly declined abolition, passing instead a repressive new slave code.\n\nThomas Dew, a respected academic who subsequently became the president of William and Mary College, published his much-read _A Review of the Debate in the Virginia Legislature of 1831 and 1832_ in Richmond. In it, he argued that ending slavery would reward Turner's violence and legitimize the massacre. John Quincy Adams called Dew's 140-page landmark pro-slavery work \"a monument of the intellectual perversion produced by the existence of slavery in a free community.\" A full discussion of Dew's argument, which cites classical, Biblical, and European authors, is beyond the scope of our work, but we note two points:\n\n1) Estimating the annual outflow of slaves into the Deep South market, Dew approvingly spoke of the fecundity of the capitalized womb as an economic engine for the state, affirming that \"Virginia is in fact a _negro_ raising state for other states; she produces enough for her own supply and six thousand for sale.\" (emphasis in original) He was if anything conservative in his figure of six thousand annually exported; Frederic Bancroft believed the number might be double that, and some estimates are higher.\n\n2) He reported that the post-Turner legislation was actually _good_ for business, with more Louisiana and Mississippi planters journeying up to buy slaves in Virginia in the absence of a mechanism for importing:\n\nThe Southampton massacre produced great excitement and apprehension throughout the slave-holding states, and two of them, hitherto the largest purchasers of Virginia slaves, have interdicted their introduction under severe penalties. Many in our state looked forward to an immediate fall in the price of slaves from this cause\u2014and what has been the result? Why, wonderful to relate, Virginia slaves are now higher than they have been for many years past\u2014and this rise in price has no doubt been occasioned by the number of southern purchasers who have visited our state, under the belief that Virginians had been frightened into a determination to get clear of their slaves at all events; \"and from an artificial demand in the slave purchasing states, caused by an apprehension on the part of the farmers in those states, that the regular supply of slaves would speedily be discontinued by the operation of their non-importation regulations;\" and we are, consequently, at this moment exporting slaves more rapidly, through the operation of the internal slave trade, than for many years past. (quotations in original, unsourced)\n\n_An inward manifest documenting the passage of six enslaved people from Charleston to New Orleans in 1832._\n\nEven with Louisiana having closed its markets to outside traders from 1832 to 1834, there were still slaves coming into Louisiana, because New Orleans\u2013based traders were still free to import, as per a manifest from September 24, 1832 (pictured), which shows the New Orleans trading firm Amid\u00e9e Gardun et fils as \"owners or shippers\" of six people sent on the schooner _Wild Cat_ from Charleston to New Orleans. One tries to imagine the stories behind the names and the descriptions by sex, age, height, and skin tone: Willis, Jack, Hector, Adam, Maria, and seven-year-old, three-foot-six Mary.\n\nThe business that Dew had enthusiastically described as \"negro raising\" was too important to stop. Meanwhile, Louisiana's cutoff of importation, combined with the wild Jacksonian credit boom and the new availability of Mississippi land, stimulated the slave market at Natchez beyond anything previously experienced.\n\n*Cycles of capitalism in the United States have been remarkably consistent: too much easy credit, followed by strain to the system resulting in the failure of key financial institutions, after which credit vanishes and the economy goes into a long tailspin.\n\n*A widely read Baltimore magazine, edited by the antislavery Quaker Hezekiah Niles.\n\n*The 1891 building of the Charleston A.M.E., \"Mother Emanuel,\" was the site of the 2015 Charleston Massacre of nine African Americans, including pastor and state senator Clementa Pinckney.\n\n* The _Groves v. Slaughter_ case, which went to the US Supreme Court in 1841, turned on the repudiation by a slave purchaser in Mississippi of a promissory note he had given a slave trader in payment by claiming that the state Constitution prohibited the sale. The Court ruled in favor of the trader.\n\n#   32\n\n# **Democratizing Capital**\n\n_I leave this great people prosperous and happy. 1_\n\n\u2014Andrew Jackson, presidential farewell address, 1837\n\nTHE UPWARD TREND OF the American economy accelerated further, and again New York was in the lead, when governor DeWitt Clinton's great public works project, the Erie Canal, opened on October 26, 1825. Consolidating the power of New York City as a trade center, it was an audacious engineering feat that connected the Hudson River with the far western reaches of the country and tied New York State together by means of a commercial waterway.\n\nThe Erie Canal project needed as many people as it could hire. It was an economic stimulus even while it was being built, lifting all boats, so to speak, before the locks were even in operation. Whatever skills or labor a worker could offer was useful in such a massive undertaking: calculating, carpentry, cooking, driving mules, ditch-digging. The people who lived in the area prospered by selling the laborers food, liquor, clothes, lodging, and services.\n\nIt was one of the young country's proudest can-do moments. In the eight years it took to build, the canal employed some nine thousand wage laborers, many of them Irish, but also including free black laborers, including, from Saratoga, New York, the young Solomon Northup, later the author of _Twelve Years a Slave._ The Erie Canal was not built by slave labor. This was what a non-slave economy could do, and indeed by 1827 slavery ended in New York, following a period of gradual emancipation, providing the culmination of what some historians call \"the first emancipation,\" that of the North.*\n\nThe 360-mile Erie Canal supplied an unprecedented level of infrastructural improvement, connecting the vast land beyond the Great Lakes via the Lake Erie port of Buffalo to the state capital of Albany on the Hudson River, which ran 150 miles or so down to New York City.\n\nBy making it practical to get wheat from the western part of the state to New York's harbor for export, the canal caused the value of New York State's agricultural land to appreciate sharply, even as it created a path for distribution of finished goods from New York far into the interior\u2014and it was a toll road, on which New York got paid coming and going. Because it was the only northern channel that crossed the Appalachians, it instantly became the major route to market for farmers and home manufactures across a large territory.\n\nFast-growing New York City had overtaken Havana in population sometime in the 1810s; now the Erie Canal, together with New York's control of the Liverpool route and its Wall Street stock market, made the city definitively the number-one commercial center in the United States. It caused a massive appreciation of property values to the west as far as Chicago, which in the early 1830s was the subject of a tremendous real estate boom based on its position as a hub for water transportation. Goods from St. Louis and the \"northwest\" could now be brought to market via Chicago and New York instead of New Orleans. By 1836, the State of Illinois was digging a canal to connect Chicago directly to the Mississippi River, though it did not open until 1848.\n\nPrivate capital had been insufficient to build the Erie Canal. It was a project of New York State, financed without levying taxes. The state bank sold bonds, and happily for the investors, they were easily paid back by the toll receipts the state collected. Every state wanted that kind of success. In Maryland, the ninety-one-year-old Charles Carroll of Carrollton, the last surviving signer of the Declaration of Independence and the wealthiest man in Maryland, whose family's industrial arc had gone in two generations from colonial pig iron to republican railroads, turned over the first spade of earth on the Baltimore and Ohio, the nation's first \"common carrier\" railroad, in 1828.\n\nA mania for infrastructural improvement seized the nation, but the political class of the South was dead set against this kind of project. It would be a bad precedent for the labor regime of slavery if the federal government paid large numbers of free people to work. They were rentiers, living off their capital, and their capital was also their labor. If anything was to be built in their territory, they wanted it built by slaves rented from them, and they certainly didn't want improvements elsewhere to be paid for by taxes or tariffs on them. Henry Clay's \"American System\" of federally sponsored improvements, which counted among its successes the Second Bank of the United States and the National Road, was hated by Southern politicians and had been definitively stopped. With Andrew Jackson in the White House as of March 4, 1829, everyone knew that an extreme shift to limited federal government was about to begin.\n\nJacksonian rhetoric had freely levelled the charge of corruption against Adams, Clay, and the Bank of the United States. But Jackson's party was utterly corrupt. His campaign had freely promised governmental positions in exchange for support, and once in office, his administration began purging public employees, especially postmasters, in order to replace them with political hacks in what became known as the \"spoils system.\"\n\nJackson continued the job of exiling Native Americans, conducted with the accustomed attitude of patronizing benevolence in the native negotiators were expected to, and some did, address him as \"Father\" and refer to themselves as \"your children,\" as he took their homeland away. The urgency of the process was accelerated by a minor discovery of gold in Georgia in 1829.\n\nAlong with a number of other Native American groups, the so-called Five Civilized Nations (Choctaw, Chickasaw, Creek, Cherokee, Seminole) still inhabited the region; Jackson in 1830 signed the Indian Removal Act, which authorized him to \"negotiate\" for them to leave. A series of treaties were signed, and the first deportations began in 1831. During the decade, perhaps as many as a hundred thousand Native Americans were \"removed\" westward in the Trail of Tears. Evicting them was a money-maker: politically connected businessmen could receive a $10,000 contract for \"Indian removal,\" which gave them an incentive to do it cheaply. The forced migration had perhaps a 15 percent mortality rate, which was about the same as the transatlantic slave ships\u2014and indeed, much of the travel was by water, along river routes. More than three hundred Creeks died on the night of October 31, 1837, when the steamboat _Monmouth_ , which was carrying them, collided with another vessel and sank.\n\nThe Seminoles, some of whom were black, would not leave and in 1835, a war began that lasted seven years. After capture, the Seminole chief Osceola, whose heritage was part Creek and part English and Scotch-Irish, was imprisoned in the old Spanish citadel at St. Augustine (by then called Fort Marion) and then moved to Fort Moultrie on Sullivan's Island, South Carolina.\n\nNo sooner had Native Americans withdrawn from a spot than a town sprang up; expansion onto the formerly occupied lands that Jackson had taken went as fast as the credit system would allow. Some 80 percent of the Chickasaw cession of the 1830s, sold cheap at the public land office, passed through the hands of speculators.\n\nThe economic storm that raged during the eight years of Jackson's presidency and for another decade or so afterward drew its energy from a variety of sources. At the eye of it was Jackson, who opened up credit as wide as it would go and threw away the controls. The economy had been subject to the characteristic cycles of capitalism all along, of course, but the bubble of the 1830s was spectacular. Fueled by a conjuncture of forces international and domestic, it took the slave trade to new heights.\n\nThe boom-and-bust of the 1830s took place in the context of a radical economic experiment in decentralization and deregulation in which President Jackson took a wrecking ball to the country's financial structure, restructured it to operate without oversight, definitively abrogated a national role in the issuance of paper money, and shocked the system with abrupt rule changes. This is not to say that other crises would not have occurred had he not done that; but what _did_ happen was the Panic of 1837, which led to the most severe depression in American history until the Panic of 1929.\n\nIt is ironic that the name of a man as autocratic as Andrew Jackson is associated with the word _democracy._\n\n\"Jacksonian democracy,\" that great trope of American history, grew out of, and expanded the reach of, that other great trope, \"Jeffersonian democracy.\" Jacksonians were loudly faithful to many of the ideals of the Jeffersonians. But whereas Jefferson imagined an agrarian rural republic of franchised property owners, Jacksonian democracy incorporated poor white men\u2014the yeomanry of the Western frontier and the towns, the kind of person Jackson himself had been\u2014into the franchise, thus promoting caste solidarity among white men of all classes at the expense of blacks. Indeed, it implicitly promised to poor whites that, being unenslaveable, they might someday become slaveowners, especially with so much land and credit available cheap. Enfranchising them invested them in white supremacy; Jacksonian democracy promoted white caste solidarity at the expense of black personhood.\n\nRiches had never flown around so fast. Slavery could be incredibly profitable, especially when there was plenty of virgin Western land available and an unquenchable market for cotton that yielded cash returns as soon as slave labor could be applied to formerly native land. But even as a project for a racist democracy, or, as Sean Wilentz called it, \"Master Race democracy,\" Jacksonian democracy had little appeal to the patricians of South Carolina; uninterested in democracy of any sort, they formed a separate power bloc from Jackson, who in many ways represented political continuity with the old Virginia dynasty.\n\nIt is also ironic that Jackson's picture is on the twenty-dollar bill, because Jackson hated \"ragg money\" and wanted to get rid of it. Unfortunately, as his administration set out to, as the humorist Joseph Glover Baldwin satirically put it in a memoir of the era, \"democratize capital,\" Jackson's actions made paper money less reliable than it had ever been, made government more economically inefficient, and drove the South to rely more on its human savings accounts.\n\nJackson was a hard hard-money man. John Quincy Adams described Jackson's final presidential message as containing an \"abundance of verbiage about gold and silver and the injustice of bank paper to the laboring poor.\" Jackson would have liked silver coins to have been physically exchanged for every transaction, like when he sold slaves for silver in Spanish Natchez. There wasn't enough coin for the transactions of an expanding nation, but never mind, Jackson hated paper money, banks, and debt\u2014a point of view that was understandable from a small-town merchant, but disastrous when applied to the nation's economic system.\n\nJackson especially hated Henry Clay, whose party was for a time called the Anti-Jackson party; in a coalition with the Adams followers, they became the Whigs, with Clay as their losing presidential candidate in 1832. In what has been remembered as the Second Party System, these two main parties and a welter of smaller ones attempted to be national parties, connecting North and South. That was an attempt to straddle the fundamental dividing line of American politics, which was overwhelmingly slavery versus free soil. In both cases, making a national party required accommodating the slavery interest. Antislavery people in the North were growing in number, while Southern delegates grew steadily less interested in compromise.\n\nWhigs, who came in slaveowning and antislavery varieties, were modernizers. Most merchants were Whigs, in favor of banks and corporations, federally sponsored internal improvements, protective tariffs, and national currency regulation\u2014what we now call \"big government.\" Democrats, who saw all this as tyranny, were in favor of states' rights, limited federal government, an agrarian republic, hard money, and were for the most part aggressively or reluctantly pro-slavery, though there were antislavery Jacksonian Democrats as well.\n\nModern Americans are accustomed to thinking of Mississippi as the poorest of fifty states, but in 1831, when it was growing explosively with new plantations amid a landgrab and a slave boom, it had, in Biddle's words, \"more rich proprietors than... any where else assembled.\" Mississippi was the hottest lending location in the country, so in the spring of 1831, the Second Bank of the United States opened a branch\u2014its last one, as it turned out\u2014in Natchez. The Bank was not merely a presence in Natchez; it was aggressive, at one point concentrating 10 percent of its resources there.\n\nThe Bank's arrival transformed the state's credit-hungry business environment. It was the legally mandated depository of federal funds, receiving federal income as it came in. By marketing federal debt to state and private banks, it controlled the money supply. It was far bigger than any state-chartered bank, and it kept something of a lid on the state banks by accepting their notes (\"discounting,\" it was called, reflecting the percentage adjustments that had to be made when using paper obligations), and immediately redeeming them for specie. It thus acted as a kind of regulator on how much paper the state banks could issue; its national reach allowed it to move liquidity around and help keep the entire system flowing smoothly. Biddle called it a \"commercial railroad\"; it was the main channel of exchange at the national level. The Bank was not unpopular, and it was powerful politically, being at the center of multiple webs of patronage\u2014something Jacksonians wanted to monopolize. The paper money it issued could be exchanged for specie at any one of the Bank's national branches, but in fact it was not necessary to do so, because its paper was known to be high-quality and was easily accepted by everyone, including slave traders.\n\nAs competition from the Bank's new Mississippi branch forced the already existing State Bank of Mississippi (later called the Agricultural Bank) toward what would ultimately be liquidation, another bank appeared in the state: the Planters Bank. The Mississippi state legislature had chartered it in 1830, disregarding a state pledge made at the time of the first bank's charter not to charter another bank. It was theoretically capitalized at $4 million dollars, half of it subscribed to by the state and paid for with 6 percent state bonds. Its charter promised to \"by a creation of revenue relieve the citizens of the State from an oppressive burden of taxes, and enable them to realize the blessings of a correct system of internal improvement.\"\n\n_This lost-purse advertisement from the_ Baltimore American and Commercial Advertiser _of April 1, 1819, gives a sense of what managing cash was like, listing money from different banks separately; the Second Bank of the United States's note, the safest, most usable currency available, is listed up top as the largest denomination._\n\nExcept for the national bank's notes, all paper money was local money, and negotiating it anywhere but its place of issuance was much like doing a foreign-exchange transaction today. As hundreds of banks appeared with licenses to print money, they all wanted to get as much of the money they printed into the public's hands as possible, crowding the other banks' paper out.\n\nAs the two state banks of Mississippi competed with the national bank to write mortgages, it was never easier to buy slaves on terms. The Natchez slave market soared; with Louisiana closed to out-of-state dealers in the wake of Nat Turner, the competition in Mississippi heated up. The banks' bulging loan portfolios were capitalized largely by slaves, who trudged down into Mississippi in coffle after coffle.\n\nBoth sides in the presidential election of 1832 made the bank their major campaign issue. The Bank's twenty-year charter was set to expire in 1836, but in the face of Jackson's harassment of it, and at the urging of Clay and Daniel Webster, Biddle, the Bank's president, proposed a recharter in 1832, gambling that Jackson would not dare kill it with the presidential election coming up, sneering at one point that \"this worthy President thinks that because he has scalped Indians and imprisoned Judges, he may have his way with the Bank. He is mistaken...\" (ellipsis in original)\n\nIt was a bad idea to call Andrew Jackson's bluff.\n\nWe have previously noted Jackson's capacity for hatred. When Jackson hated, it was not only he who hated. It was a popular movement of hate, sanctioned by God, and it was a political mechanism of hate. To hate the Whigs was to hate the Second Bank of the United States, which was aligned with them to the point of having financially supported Henry Clay, who for his part had the bad idea of making the Bank recharter an election issue. Moreover, Jackson's first falling-out with the now-enemy Calhounites had been over the issue of the Bank, which they supported.\n\nDestroying was what Jackson did best, and destroying the Second Bank of the United States was his obsession. Jackson saw the Bank as a federally sanctioned private monopoly, but whatever his ideological reasons for hating it, there was perhaps a more basic reason: it was the most powerful institution in the United States not under his control, and that alone was enough to seal its doom. The Bank's recharter passed Congress, but was boldly vetoed by Jackson a week later, who issued an economically incoherent veto message authored by his bank-hating advisor and political fixer Amos Kendall that stoked sectional rivalries\u2014not simply South against North, but positioning Jackson on the side of the good West versus the bad East, understood to be associated with the South and the North, respectively that \"it is obvious that the debt of the people in that section to the bank is principally a debt to the Eastern and foreign stockholders; that the interest they pay upon it is carried into the Eastern States and into Europe, and that it is a burden upon their industry and a drain of their currency.\"\n\nWhile Jackson was staring down the Bank, he also went up against the political chiefs of South Carolina. Four days after the veto, he signed the Tariff of 1832, or, as South Carolina politicians called it, the Tariff of Abominations. It was a laundry list of protectionisms with something for New England and something for the mid-Atlantic states; it had proved a vote-getter for Jackson nationally, who needed to shore up his political base in the North.\n\nThe slaveholding region saw it as a tax on them. Many in the South were not opposed merely to this specific tariff, but to tariffs in general, seeing them as tribute extorted by the North in a situation where the South produced the wealth but the North took the profits. In Mississippi, where nothing was manufactured and everything had to be imported, a writer to the Woodville _Mississippi Democrat_ lamented that \"there are ten spinning wheels and two looms in the county\u2014such a thing as a slay, harness, shuttle or spindle is unknown, and if we want one of either we must send to yankee town for them.\"\n\nFor South Carolina's politicians, Jackson's signing of the tariff was a blunt dismissal of their political importance. They resisted with a level of virulence and extreme rhetoric that astonished other congressmen. Indeed, the vehemence of their \"discontent\" was not entirely rational, unless it was understood that the point of it was polarization: the tariff was a smokescreen issue with which ambitious politicians hoped to focus Southerners' anger in order to drive a wedge against the North, with the ultimate end of fomenting disunion and provoking confrontation.\n\nFor two years or so, Calhoun had been promoting the doctrine of \"nullification\" that he had formalized, taking the name from Jefferson's 1798 Kentucky Resolutions. In Calhoun's vision, a state had the right to \"nullify\" a federal law within its borders, which also meant that the federal government had no right to impose tariffs. Never mind that federal revenue depended on tariffs, that was the idea: big slaveowners wanted a powerless federal government.\n\nGeorge McDuffie, from near the Georgia border, who had been \"taken from labor in a blacksmith's shop by Mr. Calhoun\" to become a landed cotton planter and Calhoun's loyal political lieutenant, was the grim-faced oratorical star of the 1832 South Carolina Nullification Convention. McDuffie, who was known to be irritable because of the painful wounds dueling had left him, had come up with something retroactively called the Forty Bale Theory, which held that a 40 percent tariff equaled taking away forty bales of cotton for every hundred a planter produced. That was utter nonsense, but it had the advantage of simplicity, and the Calhounites used the aggressive messaging technique that in more recent times has become known as \"repeat until true.\" Secession was threatened in congressional debates. Reprints of apocalyptically worded speeches, charged Representative John Reed of Massachusetts,\n\nwere dispersed, thick as autumnal leaves, through the whole region of the South, with other incendiary tracts, all calculated, if not intended, to rouse the whole South to madness... We were told in this hall that the protective system [of tariffs] was a vampyre, by which the North was sucking the warm blood of the South; that the free States were prairie wolves, gorging their jaws by instinct in the blood of the South, whilst oppression, robbery, and plunder were sounded to every note of the gamut. Is the result surprising?\n\nThe argument over the tariff was in part a clash of factions in Jackson's government. Van Buren, who was Jackson's favored successor, had devised the tariff; Vice President John C. Calhoun made killing it his mission. As vice president under Adams, Calhoun had in 1827 cast the deciding Senate vote to kill a tariff, condemning it \"as a sectional measure designed to impoverish the slave South,\" in Manisha Sinha's words. But it was hard for Calhoun to stay ahead of the pack of radicals at home who were pushing him to the right. William C. Davis describes their objectives as to \"defeat protectionism and contain the growth of central power in Washington,\" which was pretty much the same thing as maintaining the political power of slavery. As always, the dynamics in South Carolina were different: in much of the rest of the country, the voting franchise had been expanding, but not in South Carolina, where a two-party system barely took root, and where, as Sean Wilentz put it, \"they had no use for the democratic dogma that appeared to be sweeping the rest of the nation.\"\n\nCalhoun, Jackson's backstabbing former ally, had become his open enemy\u2014both socially (after Calhoun's wife, Floride, ostracized Peggy Eaton, the wife of another cabinet member) and politically (after President Jackson belatedly learned that Calhoun had worked against him in the cabinet during his Florida conquest). Like Clay, Webster, and Benton, Calhoun had seen himself as a contender for the presidency. By now, it was clear that would never happen. But he could be president of an independent Southern nation, if one were to exist.\n\nAs a senator, Calhoun could more effectively promote nullification. He was appointed to the Senate by the South Carolina legislature\u2014the state didn't have the bother of a popular vote\u2014on December 12. He resigned the almost powerless office of vice president on December 28, 1832, finalizing his break with Jackson. The South Carolina legislature, meanwhile, passed a bill that committed South Carolina to raising a military force to resist the tariff. Calhoun insisted that nullification did not necessarily mean secession, but then again, it might. As he started a short-lived Nullifier Party, the thrilling idea of secession\u2014which would make the most belligerent politicians of South Carolina into the rulers of a sovereign state, as they insisted they already were\u2014was in the air. Not all of South Carolina was in favor of nullification, but Unionists were derided and intimidated. Sinha writes that \"the election campaign of 1832 was the bloodiest in the state's history. Duels, which were usually personal affairs of honor, became the stuff of politics.\" South Carolina went it alone; even in Mississippi the nullifiers lost.\n\nMany years later, after Martin Van Buren had pivoted around to an anti-slavery stance, he wrote of the nullification standoff that \"a more alarming crisis in the affairs of this country had never existed since the establishment of her independence.\" But the nullifiers overplayed their hand when they went up against Jackson. He was pro-states' rights, but as the last president to have personally suffered the violence of the War of Independence, he was a Union man until death. He denounced nullification in a ringing proclamation in December 1832, written by Secretary of State Edward Livingston. Capitalizing on his immense personal popularity and vowing to use fifty thousand troops if necessary to enforce the law, Jackson rallied the country to his side state by state, leaving South Carolina isolated.\n\nIt almost came to the point of an armed intra-Southern clash. According to Van Buren, Jackson was ready to get on a horse and personally direct an invasion of South Carolina, using Upper South troops to take out the Calhounites:\n\nHe had at this time... an inclination to go himself with a sufficient force, which he felt assured he could raise in Virginia and Tennessee, as ' _a posse comitatus_ ' of the Marshal and arrest Messrs. Calhoun, [Robert] Hayne, [James] Hamilton and [George] McDuffie in the midst of the force of 12,000 men which the Legislature of South Carolina had authorized to be raised and deliver them to the Judicial power of the United States to be dealt with according to law.\n\nSouth Carolina backed down. Jackson, who later expressed regret that he had not hung Calhoun when he had the chance, was re-elected president in 1832 by a landslide. In the wake of the nullification of nullification, a compromise tariff bill passed that would give South Carolina a climbdown from the failure of its insurrectionist posture by reducing tariff rates slowly. In the congressional debate over that bill, Representative Nathan Appleton, who as one of the founders of the New England textile industry and of the manufacturing center of Lowell, Massachusetts, was one of America's heaviest domestic cotton customers and one of Boston's richest men, asked point-blank:\n\nDoes the South really wish the continuance of the Union? I have no doubt of the attachment of the mass of the people of the South to the Union, as well as of every other section of the country; but it may well be doubted whether certain leading politicians have not formed bright visions of a Southern confederacy. This would seem to be the only rational ground for accounting for the movements in South Carolina. A Southern confederacy, of which South Carolina should be the central State, and Charleston the commercial emporium, may present some temptations for individual ambition.\n\nTwo days before the beginning of his second term, on March 2, 1833, Jackson signed the compromise tariff that Southern legislators had voted for. But he also signed the revenue collection act that Northern legislators had voted for; known in South Carolina as the \"Force Act,\" it allowed him to use the military to collect tariffs and to close any port he desired.\n\nThough the South Carolina legislature passed an act nullifying the Force Act in South Carolina, there was no armed insurrection against the federal government\u2014this time. The experience left South Carolina more isolated, and its politics even more extreme than before.\n\n\"I have had a laborious task here, but nullification is dead;\" wrote President Jackson in a letter on May 1, 1833, \"and its actors and exciters will only be remembered by the people to be execrated for their wicked designs to sever and destroy the only good government on the globe.\" The nullification struggle had been over the \"Tariff of Abominations,\" not slavery; but nullification was thoroughly identified with slavery and secession, and the crisis had been a rehearsal for leaving the Union, as Jackson saw clearly. The letter continued with his much-quoted observation that \"the tariff was only the pretext, and disunion and southern confederacy the real object. The next pretext will be the negro, or slavery question.\"\n\nFor Jackson, as for Nathan Appleton and many other contemporary observers, the issue was the personal ambition of Calhoun and his argumentative countrymen.\n\nMartin Van Buren's autobiography describes Jackson\n\nstretched on a sick-bed a spectre in physical appearance... Holding my hand in one of his own and passing the other thro' his long white locks he said, with the clearest indications of a mind composed, and in a tone entirely devoid of passion or bluster\u2014\"The bank, Mr. Van Buren is trying to kill me but _I will kill it!_ \" [punctuation _sic_ ].\n\nStopping the Bank's recharter wasn't enough for Jackson. \"The hydra of corruption is only _scotched, not dead,_ \" he wrote James K. Polk on December 16, 1832, after learning of Biddle's plans to reintroduce a recharter. In response, Jackson drove a stake through the Bank's heart to make sure the \"Money Power,\" as he called it in his 1837 farewell address, was dead. The Bank's charter would be in force until 1836, but in September 1833, after two consecutive secretaries of the treasury had resigned rather than announce that the federal government would no longer deposit its funds in the Bank, Jackson's new secretary of the treasury, Roger B. Taney, did it. At the time Jackson killed the Bank, it was operating twenty-five branches throughout the nation, though its operations in New England were much less significant because New England had a powerful banking system already in place. Jackson was the first president of whom we can speak as having \"managers,\" and there was a political payoff in destroying the Bank for one of them, New York's Martin Van Buren. Wall Street was happy; the Bank had been the last remaining power base of Philadelphia in US finance. Jackson and Van Buren's successful building of a national Democratic party was thus accomplished as a business alliance between slavery capitalism in the South and finance capitalism in the North.\n\nIn vetoing the Bank's recharter, Jackson abrogated the federal government's authority over paper money. He had hoped to do away with state banks next, but with the national bank gone, there was no alternative to state banks. But since the Constitution specifically denied to states the right to issue bills of credit, that left only private banks to print money. For the next thirty years, the United States had no uniform currency, as commercial institutions printed a massive uncontrolled emission of paper monies. This privatization of the money supply determined the commercial contours of the following decades, until the secession of the South provoked a new assertion of federal power by the Lincoln administration.\n\nJohn Quincy Adams, whom Jackson defeated in the 1828 presidential election, was elected to Congress in 1830\u2014the only ex-president to take such a step\u2014and began a remarkable second career. His diary, which he began keeping at the age of twelve in 1779 and maintained for sixty-nine years until his death in 1849, is the most extensive by any American historical figure, and is a gripping record of the times and of a conscience. As it makes clear, he had always been antislavery; but as one of the major figures in increasing the territorial reach of the United States, he had been known as a pro-expansion president rather than an antislavery one. On his first day in Congress, however\u2014December 12, 1831, only months after Nat Turner's rebellion\u2014he took advantage of his appointment as committee chair to present \"fifteen petitions, signed numerously by citizens of Pennsylvania, praying for the abolition of slavery and the slave-trade in the District of Columbia,\" and had one of them read out loud.\n\nIt drove the Southerners in Congress mad. From then on, Adams delighted in presenting all the antislavery petitions he received. From the time he entered the House until he collapsed at his desk there in 1848 (remaining in the Capitol until he died three days later), no one in the US government opposed slavery more consistently or effectively.\n\nAdams saw Jackson's shuttering of the Bank as a baby-with-a-loaded-gun scenario, writing in dismay, \"His experiment is to stake the revenue, the credit, and the currency of the country upon the State banks.\" Petitions and even deputations came in from around the country: no, _don't do this._ \"They have all had interviews with the President,\" wrote Adams, \"who treated them all politely, but declared his irrevocable determination never to consent to the restoration of the deposits, and never to assent to the chartering of a Bank of the United States.\" Slave trader Jourdan M. Saunders approved of Jackson's action, writing his business partner David Burford on September 28, 1833: \"We are looking out for hard times in the money market on account of the anticipated removal of the government diposits[.] The small [unclear: fry] are quaking[.] For my part I Glory in the Old Cocks [Jackson's] inflexible determination to rid the country of a growing evil[.]\"\n\nThe Bank's charter was to extend until 1836, but Jackson didn't wait until then to stop the flow of federal deposits to it. The federal government began depositing its tariff revenues into twenty-three non-networked state banks, a number later expanded to sixty, and then to ninety-three, and then to fewer, and to fewer, as so many of them failed. Referred to by Jackson's numerous enemies as \"pet\" banks, they were tools of the Jacksonian Democratic Party's immense patronage machine, with which Jackson put the financial power of the federal government at the service of his political party.\n\nBiddle had maintained a conservative 2:1 paper-to-specie ratio in the bank, but these new banks\u2014\"wildcat banks,\" they were called\u2014issued four, five, ten times as much paper money as they had specie to back it with. Sometimes they didn't have specie at all, just other banks' paper.\n\nBiddle responded to Jackson's choke order by pursuing policies consistent with liquidation, contracting credit sharply at all the bank's branches, calling in loans and redeeming notes from state banks around the country, leading, predictably enough, to a panic in early 1834. Many criticized Biddle as trying to make the economy scream in a contest of wills, but his actions were consistent with Jackson's order.\n\nIn Mississippi, the Bank of the United States strained the Planters Bank's resources locally by taking away a major local source of credit and calling in its notes at the same time. The Planters Bank became one of the new depositories for federal funds, but unfortunately, when it finally received the first federal deposits, which came later than expected, \"only a small percentage of the funds was in United States Bank notes or specie; a vast amount was in the paper of banks in Tennessee and Alabama, while the largest portion consisted of notes issued by the Planters Bank itself.\" The government receipts that were being deposited were mostly revenues from the sale of public lands, which were being paid for in increasingly worthless paper.\n\nAlong with this, as a government depository, the Planters Bank also had the responsibility of paying out governmental obligations. If a government employee got paid with paper in Natchez, he no longer received paper money from the national bank, redeemable for silver coins at any bank branch in the United States. Instead, he got Planters Bank money, which, if he tried to use it in, say, New Orleans, would only be accepted at a discount from its face value.\n\nMoney, which had been moving in the direction of becoming a national commodity, became newly provincialized. Now that there was no national bank, and with lots of \"virgin\" land on the market whose new owners were in the market for slaves, the newly flush pet banks began competing aggressively to write mortgages. Meanwhile, state legislatures began granting bank charters freely as new operators got into the business. Against a backdrop of general inflation that was acutely felt by the increasing numbers of urban poor in the North, demand in Mississippi for slaves spiked, while supply remained constant.\n\nSeveral bumper crops of cotton in a row had been sold into a growing industrial market in Britain. The British textile industry was continuing to expand, and there had been bumper crops of wheat in Britain, so British domestic consumers (who provided about half the market for British textiles), were relatively flush. Industrial capacity was growing: power looms in Britain grew from 14,500 in 1820 to about 100,000 in 1833, even as they were growing in size and becoming more efficient. This full-bore Industrial Revolution, which was creating wealth on a previously unknown scale, had enormous capacity to consume cotton. The French also bought American cotton, as did Lowell, Massachusetts, though its textile industry was tiny compared to the British juggernaut. Writing in humorist's hyperbole, Joseph G. Baldwin later recalled Mississippi during these \"flush times\":\n\nEmigrants came flocking in from all quarters of the Union, especially from the slaveholding States... Money, or what passed for money, was the only cheap thing to be had.... The State banks were issuing their bills by the sheet, like a patent steam printing-press its issues; and no other showing was asked of the applicant for the loan than an authentication of his great distress for money... Under this stimulating process prices rose like smoke.\n\nIn these times, there was a double incentive to buy large numbers of slaves: 1) those in possession of cotton-growing lands could make big money fast, if only they could get enough labor; and 2) the most obvious way to capture and store the value of the easy money flying by was to lock it down in the form of slaves before it devalued.\n\nIn Britain, a frantic dance of the millions took place in the great ballrooms of the economy: London, with its huge financial centers; Liverpool, the shipping emporium; and Lancashire, the industrial capital\u2014all dancing as fast as they could, taking in cotton and turning out cloth for the world. As Peter Temin has pointed out, there was a surfeit of silver on the British market, partly because the Chinese were accepting opium instead of silver in trade from Britain. In another global trade first, Britain had addicted large numbers of Chinese to the product, flooding the market with opium cheaply grown in British-controlled India, sometimes shipped in Baltimore clippers built specially for the opium trade, in shipments sometimes financed by New England merchants, and licensed by the East India Company. Eighteen thirty-four, wrote Karl Marx in an 1858 article in the _New York Daily Tribune_ , \"marks an epoch in the history of the opium trade\": Britain's East India Company was prohibited from trading in China, and opium was thrown open to separate traders, who began smuggling it into China aggressively, increasing the volume of the trade dramatically and demanding silver in return, depleting the Celestial Empire of the metal as the opium-seller's customers multiplied.\n\nThe growth of New England manufactures, together with the strong exports of cotton, shifted the balance of trade between Britain and the United States somewhat. As silver became cheaper on the British market, more of the silver Britain paid for cotton and other staple crops remained in America instead of being sent back out. That east-to-west trade winds influenced the economic collapse does not, however, make Jackson's ideologically driven recklessness fade to insignificance. The global interconnection went both ways: the revenue derived from American cotton provided conditions for the storm to intensify.\n\nBetween 1830 and 1836, the number of state-chartered banks went from 329 to 730; they issued circulating banknotes and long-term bonds.  State governments borrowed heavily to finance internal improvements, most of which were never built. \"From 1834 to 1836 the money supply grew at an average annual rate of 30 percent,\" writes Jane Knodell, \"compared to 2.7 percent between 1831 and 1834.\" Canal, railroad, and bank projects all moved forward, with the Deep South states investing especially heavily in banks. During that time American indebtedness to foreign creditors doubled, from $110 million to $220 million. The state governments were on the hook for much of it. Intended to finance internal improvements, the money flowed through the American economic system; when it got to the South, it stimulated the market in slaves.\n\nNicholas Biddle rechartered his bank under Pennsylvania state law as the United States Bank of Pennsylvania. Though it was still a giant in terms of capitalization, it was no longer the federal government's agent and no longer had the advantages of national branches. But once again, its most extensive operations outside of Pennsylvania were in Mississippi.\n\nJackson, meanwhile, achieved the conservative dream of paying off the national debt in January 1835. Unfortunately, that left the Treasury empty. Treasury coffers relied on income from tariffs, and now that the Nullifiers had succeeded in getting the tariffs down though not removed, there was a sharp drop in federal income. But with the switch to what in theory was a debt-free federal government, it was time for some other source of revenue, and the only contender was land sales.\n\nThere were vast quantities of newly available, unplowed land to privatize. It couldn't go on indefinitely, but the federal government could make lots of money right now by selling the Native Americans' land cheap, as fast as the natives could be evicted. Having an inside track on this market was valuable; as always with the Jacksonians, patronage was crucial to political power.\n\nThe Jacksonians opened up the floodgates of massive land speculation and currency at about the same time. Between January 1835 and December 1836, some fifty thousand square miles were sold at a fixed price of $1.25 an acre. Much of it was snapped up by speculators who flipped it, creating a real estate bubble, while banks issued paper money feverishly. Banks that were politically allied with the administration to be under the control of Secretary of the Treasury Levi Woodbury had the free use of millions of dollars of public money, on which they were utterly dependent, as few of them had much in the way of assets otherwise.\n\nThe Whigs, wrote a nineteenth-century financial historian, \"perceived that the system was exciting wild speculation, and that by it money was drawn from the great commercial centres and stored in remote banks to be loaned to the profit of those who had proved their loyalty to the administration and its 'revered chief.'\" One writer estimated in March 1837 that banknotes in circulation had been increased by $80 million since the veto of the bank charter in 1832.\n\nField hands, meanwhile, might sell for $1,000 or more, so it was clear where economic power resided: in owning slaves. That was where the profit was taken, as gains made in dubious paper were converted into the safer instrument of laboring bodies.\n\nSlave mortgaging was essential to the functioning of the Southern credit system, but the practice has not been much discussed by historians, and we do not have a good overview of the numbers. No one at the time seems to have compiled statistics about how much mortgaging was being done, whether of land or of slaves. Looking at South Carolina, Bonnie Martin found that \"year in and year out... private mortgage contracts were quietly filed across the South, but no published tallies exposed the number of mortgages made or the amount of capital raised.\"\n\nThe function of banks in the antebellum mortgage market was different than the way we think of it now. Most antebellum mortgages were funded not by bank capital but by private individuals in local networks. The credit networks of the time were informal, and often banks were not the lenders but merely the places of payment, where loans were facilitated by the issuing of paper. Martin writes that of the publicly recorded mortgages that she was able to analyze, \"banks, churches, merchants, and building societies were only 19 percent of the lenders who accepted human collateral in South Carolina. Interpersonal lending accounted for 81 percent.\" The financiers and banks made money, of course, and so did states and municipalities that collected taxes and fees and, through the court system, did buying and selling of their own.\n\nIt's clear that enslaved collateral was a significant part of the mortgage action: in the more than eight thousand mortgages she analyzed from Virginia, South Carolina, and Louisiana, Martin found that \"the 41 percent of them that included slaves as all or a portion [of] the collateral raised 63 percent of the capital.\"\n\nThe price of slaves fluctuated with the rise and fall of cotton, but over the long term, those fluctuations were superficial disturbances of steadily increasing prices.\n\nThe era between the War of 1812 and secession can be thought of as divided into two periods of bumpy boom followed by devastating busts. The first of these booms ended in the complicated series of events remembered as the Panic of 1837, the exact dynamics of which historians have argued about ever since.*\n\nAfter what we now call a \"dead cat bounce\" in 1838, the economy in 1839 crashed a second time, harder, landing in a depression that bottomed out in 1842 and did not immediately recover. By then, more than two hundred banks had failed. But for the strongest, most disciplined traders, there was still business to be done. In a letter of November 16, 1839, that somehow wound up in print in an abolitionist tract of 1846, the small-scale slave trader G. W. Barnes, of Halifax, North Carolina, informed the big trader Theophilus Freeman of New Orleans of the names of and prices at which he had shipped six \"girls\" to him, then wrote: \"I have a great many negroes offered to me, but I will not pay the prices they ask, for I know they will come down. I have no opposition in market. I will wait until I hear from you before I buy, and then I can judge what I must pay.... Write often, as the times are critical, and it depends on the prices you get to govern me in buying.\"\n\nThe stimulus that got the economy pumping again was provided by the annexation of Texas in 1845, which stimulated the slave trade. It accelerated further with the discovery of gold in California in 1848 and the increasing penetration of railroads, and rose along with cotton to new heights. It dipped briefly with a Panic of 1857 that was caused in part, thought Natchez planter Benjamin Wailes, by \"River lands at most unwarrantable prices & negroes at $1,500,\" though the South was actually the least affected by the downturn. Then the slave trade went higher than ever, reaching unheard-of levels by 1860. That boom ended with secession, though the trade continued and even accelerated during the first three years of the war. But by then there was no longer any reliable money with which to compare prices, because the Confederacy was not part of the US financial system.\n\nNot without a sense of irony, we will use white supremacist and onetime dominant-in-the-field-of-slavery historian Ulrich B. Phillips's data showing prices in four major slave markets, not including Natchez, the highest-priced large market. While Phillips's racist conclusions are thoroughly discredited, his numbers, in this case based on examining three-thousand-plus bills of sale, have been more or less generally accepted. As visually estimated by Robert Evans Jr. from Phillips's graphs, the curve of five-year average slave prices (for \"prime male field hands\") looks like this:\n\nThe effect of the post-1837 depression is clearly visible here, as is the economic tonic effect of annexing Texas in 1845. We see an impressive price rise over the fifteen years from 1845 to 1860, especially in Georgia. But a deeper wave was building that only broke with the ruin of war:\n\n_Slave prices inflated continuously as compared with the price of the cotton the slaves produced._\n\nHere are Phillips's figures for the Georgia cotton belt, which incidentally give a sense of how profitable slave trading was. With the importation of Africans no longer possible, the supply of African Americans onto the market could not keep pace with the amount of new cotton acreage continually being brought under cultivation, so the demand for labor always exceeded the supply. The degree of inflation slowed in hard times, but even then, the trend was upward.\n\n**Year** | **Price of a prime field hand expressed in pounds of ginned cotton**  \n---|---  \n1800 |  1,500  \n1809 |  3,000  \n1818 |  3,500  \n1826 |  5,400  \n1837 |  10,000  \n1845 |  12,000  \n1860 | 15,000\u201318,000\n\nAt these intervals, we see no depression, only slowed growth. The price of a field hand in Georgia fell from $1,300 to $650 between 1837 and 1845, but measured against the price of cotton, over the course of those years, the field hand appreciated in value from ten thousand pounds of cotton to twelve thousand. Over the six decades of antebellum slavery, even as agricultural innovations gradually increased per-hand productivity, slave labor was steadily becoming a more valuable property than the staple crops the labor produced.\n\nThe mere fact of holding slaves, then, brought substantial capital gains. The pressure of this curve, as we need not remind readers, was felt in unsubtle ways by enslaved women, who were pressured to bear children. Newborn black babies were worth more on paper all the time, their poor life expectancy actuarialized through traders' firsthand experience of discounting the substantial death rates. William Dusinberre believes that \"about 46 per cent of slave children died before reaching the age of fifteen,\" compared with a 28 percent mortality rate for free children. The higher mortality rate is no mystery, and it was needlessly high, as it turned on planters' reluctance to spend on the health and welfare of the enslaved.\n\nEven clean drinking water was sometimes seen as an unnecessary expense, which might explain the higher death rates of the enslaved from cholera. \"Good water is far more essential than many suppose,\" wrote a planter signing himself \"A Citizen of Mississippi\" in an article about plantation management titled \"The Negroes\" in _DeBow's Review_ of March 1847, \"or than I could be persuaded myself until within a few years.... Cistern water not too cold will on any plantation save enough in doctor's fees to refund the extra expense.\"\n\nBut money spent on slaves' welfare came right out of the plantation's immediate profits. Some planters who could take the longer view\u2014those who were not being ground down by debt\u2014could see that any money that was spent on the health and welfare of the enslaved was of direct economic benefit to the slaveowner, and could also be cited as proof of the slaveowner's purported kindness to his captives. \"The great object,\" continued the Mississippi planter, \"is to prevent disease and prolong the useful laboring period of the negro's life. Thus does interest point out the humane course.\"\n\nThe word _humane_ was frequent in slaveowner vocabulary. On some large estates, children were taken off the various different parcels of land, away from their parents, and raised together in a collective nursery that made easily visible the slave-breeding nature of the Southern slavery project. A planter in North Carolina told the British geologist Charles Lyell in 1842 that, given the frequent necessity of breaking up families by sale, that \"he defended the custom of bringing up the children of the same estate in common, as it was far more humane not to cherish domestic ties among slaves.\" That is, since domestic ties were only going to be broken anyway, it was better not to create them in the first place. Labor that was capital had no family.\n\nDespite its shorter average life span, the enslaved black population of the South grew faster than the white population, and faster than the small population of free people of color. The capitalized wombs of the South supplied boys, who were sold to traders, who sold them to planters so they could produce the cotton that would feed the steam-driven mills of Britain, France, and even New England. And they supplied girls, who could pick as much cotton as the boys, and who would themselves become captive baby makers. The slave-breeding industry was going full tilt.\n\n*Until 1840, out-of-state visitors could bring slaves to New York with them for a period of nine months.\n\n*The title of Jessica Lepler's book _The Many Panics of 1837_ conveys something of the fragmented, unsynchronized quality of the multisited crisis.\n\n#   33\n\n# **Old Robbers**\n\n_The Slaver led her from the door,_\n\n_He led her by the hand,_\n\n_To be his slave and paramour_\n\n_In a strange and distant land!_\n\n\u2014Henry Wadsworth Longfellow, \"The Quadroon Girl,\" 1842\n\nTHE STURDY BRICK DWELLING-HOUSE at 1315 Duke Street in Alexandria, Virginia, was built in the 1810s, when Alexandria was part of the District of Columbia. From 1828 to 1837, it was the home office and shipping entrep\u00f4t of Franklin and Armfield, the largest slave-trading company in American history, whose existence almost exactly coincided with the two terms of Andrew Jackson's presidency. Inscribed in the National Register of Historic Places in 1978, it now houses the Urban League of Northern Virginia and their Freedom House Museum.\n\nThe house was the master structure for a complex with three now-vanished courtyards. Enclosing the courtyards was a two-story multi-structure jail, \"neatly whitewashed,\" in the words of Ethan Allen Andrews, an antislavery Bostonian who paid a surprise visit there in July 1835, and was readily admitted and given a tour by John Armfield. It had separate facilities for men (the west yard) and women (the east), a kitchen, a tailor's workshop, and a stable. Andrews allowed that the facility was clean and that the inmates \"were well dressed, and everything about them had a neat and comfortable appearance, _for a prison.\" 1_ (italics in original)\n\nThe 1830 census enumerated 145 people being held there, though the evenness of the numbers suggests that the census-taker might have accepted Armfield's word rather than count heads:\n\n**Age** | **Male** | **Female**  \n---|---|---  \nUnder 10 |  1 |  4  \n10\u201324 | 50 | 50  \n24\u201336 | 20 | 20\n\nThe captives were mostly strangers to each other, freshly and forcibly removed from their families and their familiar worlds. They were being held until the next ship sailed or until the annual coffle began marching. If they had been purchased during the off season, they might remain there for months. Andrews noted \"that they are often chained at night, while at the depot at Alexandria, lest they should overpower their masters.\"\n\nAlexandria had formerly been a thriving port, but it was losing out to Baltimore. Federal law stipulated that public buildings could only be erected on the other, northern, side of the Potomac\u2014that is, on the Maryland side\u2014so Alexandria, on the Virginia side, got no federal offices. Instead, the slave trade was a key business for the town.\n\nAcross the Potomac, six miles away, the slave trade was disturbingly visible in Washington City. Coffles tramped through the streets of the nation's capital daily. Everyone knew where the slave jails were, and everyone walked past the open-air auctions.\n\nForeign diplomats were astounded to see such a thing in the country that propagandized so heavily its commitment to liberty. There was no comparable spectacle in Europe, where chattel slavery did not exist. Antislavery people saw it, not incorrectly, as a shameful proof that slaveowners ran their government. Many townspeople heartily disliked it, especially the women.\n\nBut slavery was fundamental to Washington City. Slaves built it, and slaves ran it on a daily basis. Starved of infrastructural resources by conservative politicians from Jefferson on, legally unable to govern itself, boasting a grand Capitol and the White House but lacking gaslight in its dark streets until 1848, Washington City was a dirty, disease-ridden fen that abounded with crooks, prostitutes, slaves, slave traders, and congressmen, the latter of whom typically lived in boardinghouses. About 6 percent of the city's residents were free black people in 1800, a percentage that grew after 1806, when Virginia began requiring manumitted slaves to leave the state.\n\nThe District of Columbia was the perfect site from which to command the slave trade from the Upper to the Lower South, with Alexandria as the port. Its water communication via the Potomac to the Atlantic made it practical to sail captives down to the Gulf of Mexico, up the Mississippi to New Orleans, and on to Natchez, leaving South Carolina out of the loop entirely. Financial and legal expertise was easily at hand in the nation's capital. It was adjacent to the largest, most prestigious, slave-selling territories\u2014those of Virginia and Maryland. Alexandria rose as a slave-trade center with the building of Washington City. By 1802, an Alexandria grand jury grievance decried\n\nthe practice of persons coming from distant parts of the United States into this District, for the purpose of purchasing slaves, where they exhibit, to our view a scene of wretchedness and human degradation, disgraceful to our characters as citizens of a free government. True it is that these dealers, in the persons of our fellow men, collect within this District from various parts, numbers of those victims of slavery, and lodge them in some place of confinement until they have completed their numbers. They are then turned out in our streets and exposed to view, loaded with chains as though they had committed some heinous offence against our laws.\n\nThis was the world of small-time tavern traders. By 1806, if not earlier, slaves were being sold in Alexandria at the Indian Queen at King and Water Streets, which was licensed to sell horses and carriages. The Indian Queen then came under the management of Elias P. Legg, who had previously traded in slaves while he was tavernkeeper at the Bell Tavern, where he had done well enough to open his own operation. As Legg worked his way up to buying a plantation, his tavern became for a time the main slave market of Alexandria. An advertisement in the _Alexandria Gazette_ of February 15, 1825, gives Tennessee\u2014still a slave-importing state\u2014as a destination:\n\nAlexandria Gazette, _March 22, 1817._\n\nSLAVES WANTED: The subscriber will at all times, pay the highest price in cash for slaves, either single or in families. Letters addressed to me in Alexandria, will be promptly attended to. Sixty or seventy slaves at this time, expressly to go to Tennessee. E.P. Legg.\n\nPrior to 1812, a slave taken from Alexandria County to Washington County for the purpose of sale became free. Then Congress passed an act on June 24, 1812, that allowed slaveowners from one of the counties to remove slaves to the other, but did not allow a person from Alexandria to purchase a slave in Washington (or vice versa) for removal to Alexandria (or vice versa). The exact legal situation of slave commerce between the two counties thus had a somewhat unsettled status under the law, but generally, the presumption was that while slaves could be sold in the District, they could not be brought into the District for the purpose of sale. The District of Columbia, then, major communications hub that it was, functioned mainly as a transshipment point for slaves bought in Maryland and Virginia (or kidnapped from the North), and destined for the South.\n\nAs the interstate slave trade became big business, its largest player was Isaac Franklin (1789\u20131846), whose astute business sense allowed him repeatedly to time the market right. Born in territorial Tennessee, the grandson of a Huguenot, Franklin had two brothers who were already in the slave trade, with an office in New Orleans. They brought him in at the age of eighteen to make runs down the Cumberland, the Ohio, and the Mississippi, thus familiarizing him with the territory.\n\nFranklin had the good fortune to be from Nashville, which served as a base for both Andrew Jackson and James K. Polk. He built up his stake plying the same course Jackson had a generation earlier: trafficking slaves from Nashville to Natchez, which Franklin was doing by 1819, if not earlier. In 1824, during a Virginia slave-purchasing trip, he struck up a friendship with North Carolina slave trader John Armfield, a stagecoach driver who was doing the same. The two became partners, and, in the classic merchant-family manner, Armfield married Franklin's niece Martha Franklin and moved to Alexandria.\n\nWith good relationships at multiple banks, Franklin was the best networked and best capitalized slave trader. He understood clearly the implications of the country's demographic shift to the Southwest, and the advantages for a slave-trading firm of having a presence over the entire geographical footprint of the slave-labor system. By establishing a headquarters in Alexandria and sealing the partnership with a strategic marriage, Franklin connected his Nashville base to the nation's capital. From there, he connected by water with the nation's great internal port, Baltimore; the great exporting port, New Orleans, which was approaching the peak of its national influence; and on to Natchez.\n\nUnder the antiregulatory climate of the Jackson administration, Franklin brought a new level of professionalism to the interstate slave trade. Franklin and Armfield's business co-partnership was founded on February 29, 1828, and their first newspaper advertisement offering to buy slaves ran in May:\n\nCASH IN MARKET.\n\nThe subscribers having leased for a term of years the large three story brick house on Duke street, in the town of Alexandria, D.C., formerly occupied by Gen. Young, we wish to purchase one hundred and fifty likely young negroes of both sexes between the ages of 8 and 25 years. Persons who wish to sell will do well to give us a call, as we are determined to give more than any other purchasers that are in market, or that may hereafter come into market.\n\nAny letters addressed to the subscribers through the Post Office at Alexandria, will be promptly attended to. For information, enquire at the above described house, as we can at all times be found there. FRANKLIN & ARMFIELD\n\nThere was, needless to say, no federal opposition to this perfectly legal trade, especially during the Jackson years (1829\u20131837). But because Congress made the laws for the District of Columbia, the slave trade in the District was a focal point of antislavery activism. Congressman Charles Miner of Pennsylvania, in his final days as a lame duck before vacating his seat, bravely introduced in 1829 a resolution into the House of Representatives\u2014one that he knew would not pass\u2014for the gradual abolition of slavery in the District. His speech in support of the measure, reproduced in the emerging abolitionist press, began:\n\nSlave dealers, gaining confidence from impunity, have made the seat of the federal government their head quarters for carrying on the domestic slave trade.\n\nThe public prisons have been extensively used (perverted from the purposes for which they were erected) for carrying on the domestic slave trade.\n\nOfficers of the federal government have been employed, and derived emoluments from carrying on the domestic slave trade.\n\nPrivate and secret prisons exist in the District for carrying on this traffic in human beings.\n\nThe trade is not confined to those who are slaves for life, but persons having a limited time to serve are bought by the slave dealers, and sent where redress is hopeless.\n\nOthers are kidnapped, and hurried away before they can be rescued.\n\nInstances of death, from the anguish of despair, exhibited in the District, mark the cruelty of this traffic.\n\nInstances of maiming and suicide, executed or attempted, have been exhibited, growing out of this traffic within the District.\n\nFree persons of colour, coming into the District, are liable to arrest, imprisonment, and sale into slavery, for jail fees, if unable, from ignorance, misfortune, or fraud, to preserve their freedom.\n\nThere was slave trading in all three towns of the District of Columbia. John Beattie's business at what became the 3200 block of O Street in Georgetown was established in 1760; in the nineteenth century, McCandless's tavern at M Street and Washington Avenue was a notorious slave-trade spot. Particularly visible in Washington, because of their location, were Robey's Tavern, at Seventh and Maryland, and, one block over and two blocks down, Williams's slave jail at Eighth and B Street (now Constitution Avenue). Williams's was where the kidnapped Solomon Northup regained consciousness after being kidnapped, and where he was beaten by trader James Birch (Burch, in Northup's spelling) before becoming one of the captives Birch regularly shipped to Theophilus Freeman, his partner in New Orleans.\n\nThe US jail in Washington made money by housing captives in transit. Representative Miner noted that 742 people being trafficked by traders had been housed there during the previous five years, and told Congress of how, when visiting the jail, he saw a female prisoner with \"three or four children with her\u2014one at the breast,\" and asked her story:\n\nShe was a slave, but had married a man who was free. By him she had eight or nine children. Moved by natural affection, the father labored to support the children; but as they attained an age to be valuable in the market, perhaps ten or twelve, the master sold them. One after another was taken away and sold to the slave dealers. She had now come to an age to be no longer profitable as a breeder, and her master had separated her from her husband, and all the associations of life, and sent her and her children to your prison for sale. She was waiting for a purchaser, and seemed to me to be more heart-broken than any creature I had ever seen.\n\n_The house on Duke Street, as depicted in an 1836 abolitionist engraving. Armfield is characterized by his accessories: a broad-brimmed hat and a whip._\n\nThough many slave traders were operating, Franklin and Armfield's operation quickly dominated the market. Armfield held down the Alexandria office on Duke Street, supervised the buying, and ran the shipping.\n\nArmfield also drove a large annual coffle southward in the summer. Since the firm had its own jail, Armfield could afford to buy one or a few slaves at a time and pen them up at Duke Street until he had accumulated a coffle-full, then drive the coffle down to get a jump on the fall slave-selling season in Natchez. Most coffles contained fifty, sixty, or at most a hundred captives, but G. W. Featherstonhaugh estimated the coffle of Armfield's that he encountered as having three hundred, which, if not an exaggeration, is as large as coffles ever got, and represented a major logistical and security effort.\n\nBy chance, Featherstonhaugh encountered Armfield a second time on a stagecoach. He described him as \"a queer tall animal about forty years old, with dark black hair cut round as if he were a Methodist preacher, immense black whiskers, a physiognomy not without one or two tolerable features, but singularly sharp, and not a little piratical and repulsive.\" Armfield was dressed entirely in black except for \"a huge broad-brimmed white hat, adorned with a black crepe,\" the latter perhaps worn in homage to Andrew Jackson, who perpetually wore mourning crepe for his deceased wife, Rachel. Featherstonhaugh quoted Armfield as saying of Jackson, \"The old Gineral is the most greatest and most completest idear of a man what had ever lived.\" Armfield's enslaved valet, Pompey, explained to Featherstonhaugh that the trader was overfond of onions and brandy, which kept him feeling ill.\n\nExcept for the summer coffle, Franklin and Armfield did all their trafficking by sea, connecting the Chesapeake, the source of wholesale supply, with the retail markets of New Orleans and Natchez. Franklin's first recorded slave sale in New Orleans took place in 1828, and the following year he took a two-year lease on a house with adjoining vacant lots at Esplanade and Casa Calvo (now the continuation of Royal Street) just below the French Quarter in the Faubourg Marigny, renewing it two years later. He seems to have kept his inventory of slaves for sale in a prison on the premises. A curiously ambiguous clause in his 1831 lease renewal stipulated that the lease was \"as a dwelling house and not for the business which the said Isaac Franklin now carries on that is to say that of selling negroes, although it is not the intention... to deprive the said lessee of the privilege to Keep His slaves in the said house and therein to carry on his aforesaid business.\"\n\nThough the District of Columbia was an important slave-exporting outlet, it was quickly overtaken by Richmond. Virginia's capital city was the great intake center for the slave trade, where traders could buy locally raised people for trafficking down South. Because Richmond traders sold fast, in quantities, to busy, professional resellers in a high-volume, competitive market, they conducted a high proportion of their sales by open-outcry auction, the kind at which the people being sold were routinely and ritualistically stripped naked and examined, typically in another room or area off to the side. Richmond's power was supplemented by a big local market for rented slaves, since the town's tobacco factories always needed labor.\n\nHaving a partner in Richmond was the key to a successful national slave-trade operation, and Franklin's man was Rice C. Ballard, whom he and Armfield had encountered at Eli Legg's tavern in Alexandria. Ballard too had his eye on the long-distance interstate market; he was already selling slaves into New Orleans and Natchez by 1828, if not earlier.\n\nBallard's friends addressed him as \"colonel,\" which was (and still is) the honorific of an auctioneer. Though Ballard was based in Richmond, he shipped slaves out of Norfolk, which was Virginia's major seaport, and where Franklin and Armfield's oceangoing brigs could make a stop. Franklin formed a second high-volume partnership with him that worked in parallel with his Armfield partnership.\n\nFranklin was the business visionary, the senior partner, the big-picture guy, the strategist who directed the other partners by mail and made the far-flung parts of his organization work together. He handled the point of sale, where the money was made, and he handled the banking. He created a slave-trade operation that was national in scope in a way that no one had done before, or would do after him, from a base in Tennessee that was very near the president's.\n\nRetail slave prices could vary by the day, and Franklin called the shots for when to buy and when to hold off. Besides watching market conditions carefully, he also paid close attention to crop forecasts, credit conditions, and political threats to the slave trade\u2014and, most important, to keeping the firm's cash flow moving and maintaining its credit in A-1 condition.\n\nEvery year Franklin passed tens of thousands of dollars to Ballard and Armfield, in the form of drafts on any of eight or so northern banks. In return, they sent him young African Americans. He successfully addressed the problem of a decentralized slave supply network in the Chesapeake by building a region-wide web of slave-harvesting associates who combed the plantations of Virginia and Maryland, as per the firm's advertisement that ran in every issue of the _Daily National Intelligencer_ and other papers during large parts of 1833 and '34. Their 1828 advertisement had solicited purchase of people between the ages of eight and twenty-five, but now the lower age limit had moved upward to twelve, presumably reflecting Louisiana's 1829 prohibition of children under ten:\n\nCASH IN MARKET\n\nWE will pay Cash for any number of likely Negroes, of both sexes, from 12 to 25 years of age, Field Hands. Also, Mechanics of every description. Apply to\n\nR.C. Ballard & Co. Richmond, Va.\n\nJ.M. Saunders & Co. Warrenton, Va.\n\nGeorge Kepheart & Co. Fredericktown, Md.\n\nJames F. Purvis & Co. Baltimore.\n\nThomas M. Jones, Easton, Eastern Shore of Md.\n\nOr, to the subscriber, at their residence in Alexandria.\n\nPersons having likely servants to dispose of, will do well to give us a call, as we at all times will pay higher prices in cash than any other purchaser who is now or may hereafter come into market.\n\nAll communications promptly attended to.\n\nFRANKLIN & ARMFIELD\n\nIn shipping by water, Franklin and Armfield at first followed the prevailing practice of consigning slave cargoes to captains as necessary. But then, marking a new level of national reach and vertical integration for a domestic slave trading company, they went into the carrying trade, establishing their own packet lines. The firm may have purchased the brig _United States_ as early as 1828. Three other brigs were subsequently added to the fleet: the _Tribune_ , the _Uncas_ , and, custom-built specifically for the needs of the domestic slave trade, the modern, copper-bolted _Isaac Franklin._\n\nBy establishing a packet line, Franklin and Armfield brought the slave trade into the modern world, where time is money. At first, they announced they would sail every two months from Alexandria to New Orleans, but by 1835 they were sailing the first and fifteenth of every month, shipping over a thousand slaves that year. Other traders could board their captives at Duke Street for as long as necessary at twenty-five cents per head, per night. By consigning them to Franklin and Armfield for handling during shipment, the other traders in effect subsidized the firm's shipping costs. Franklin and Armfield's size and greater capitalization in turn gave them more clout for purchasing young people in the countryside, as they began to enjoy advantages of scale.\n\nFranklin's firm, then, was a modern business that, as Bray Hammond described antebellum enterprise generally, was \"served by waterpower, steam, and credit.\" Franklin and Armfield proudly advertised that their vessels were fitted out as sail-steam hybrids in order to \"steam up the Mississippi.\" Steam power was not usable on the open Atlantic until 1838, so the brigs had to unfurl their sails down the Atlantic and into the Gulf. It was not an easy sail down the coast, going against the Gulf Stream from North Carolina forward, but the last crawl was the worst. The sixty miles or so up the river from the alluvial \"bird-foot\" of lower Louisiana to New Orleans was a longtime shipping bottleneck that could take a month without steam. By steaming up the Mississippi as far as New Orleans, and then on to Natchez, the traders could save precious time, turn their money around faster, and have fewer of the people who constituted their cargo arrive dead. This faster, safer delivery gave them a previously impossible competitive advantage in that highest-priced of slave markets.\n\nThe Reverend Joshua Leavitt, a cofounder of the New York City Anti-Slavery Society, who was allowed to go on board the _Tribune_ in 1834, reported that\n\nThe hold is appropriated to the slaves, and is divided into two apartments. The after-hold will carry about eighty women, and the other about one hundred men. On either side were two platforms running the whole length; one raised a few inches, and the other half way up to the deck. They were about five or six feet deep. On these the slaves lie, as close as they can stow away.\n\nThere does not seem to have been a standard security protocol for carrying slaves on the coastwise route. When Frederic Bancroft interviewed two people who had been carried south by sea, one of them, Nathan Ross, interviewed in Donaldsville, Louisiana, in 1902, recalled having been taken down to the James River to Portsmouth, Virginia, circa 1846, then put on a ship with thirty or forty others. He remembered that they were allowed to walk on deck and were only put into the hold at night and when it stormed. By contrast, seventy-two-year-old Washington Taylor, who had been taken to Richmond and put on a ship for New Orleans with some eighty others, recalled being kept in the hold all the time except when there was a storm; then, in Bancroft's summary, \"they were let out, lest all should be lost if the ship sank.\"\n\nDuring the off season, Franklin and Armfield's brigs carried commodities and occasionally ballast. They offered passenger fares on their line, but it's not clear how successful they were, as slave ships carried a stigma. These runs were dangerous; the potential hazards included not only epidemic and rebellion, but shipwreck. The brig _Comet_ , which probably belonged to Franklin and Armfield, left Alexandria in December 1830 with 164 captives on board, but went off course and broke up on the coast of Bermuda. The British governor of Bermuda set the captives free, but Franklin had insured seventy-six of them, and he collected $37,555, about a million 2014 dollars. That sum was left to the insurance companies to collect from the government of Great Britain, which in 1840 settled the claim.\n\nThe _Comet_ was followed two years later by the _Encomium_ whose forty-six captives were set free; by the brig _Enterprise_ , which while taking seventy-eight African Americans from Alexandria to Charleston in 1835 was forced by bad weather to put in at Bermuda; by the _Hermosa_ in 1840; and by the _Creole_ \u2014the most sensitive of the cases, since it put in at the Bahamas as the result of onboard slave rebellion, exactly what the slaveowners feared would happen if the enslaved had the incentive of being freed by the British. A diplomatic standoff ensued that lasted for years, as US diplomats to Britain defended slaveowners' rights and pressed for compensation for what was considered stolen property.\n\nWith Franklin's nephew James Purvis as their agent in Baltimore, Franklin and Armfield poached Austin Woolfolk's business and even his agents, outcompeting him in every way. It didn't help Woolfolk that he had a reputation for dishonesty. His business fell off quickly, and by October 1832 he was reduced to running a strange newspaper ad that ran for weeks in the Baltimore _Republican & Commercial Advertiser._ It read:\n\nA. WOOLFOLK wishes to inform the owners of Negroes in Maryland, Virginia, and N. Carolina, that he _is not dead_ , as has been artfully represented by his opponents, but that he still lives, to give them CASH and the HIGHEST PRICES for their NEGROES.\n\nHope Hull Slatter, the major Baltimore trader after A. Woolfolk, began operating in 1835 out of Owing's Globe Inn, at the corner of Howard and Market. He opened his jail on Pratt Street in 1838, digging a two-block tunnel beneath the city's streets to hide his coffles as they went from headquarters to wharf, and he continued selling slaves out of Baltimore until 1847, when he retired to Mobile.\n\nCASH FOR NEGROES.\n\nI WISH to purchase from 75 to 100 Negroes, of both sexes, from the age of 8 to 25 years, for which I will pay liberal prices. I can always be found at Owing's Globe Inn, corner of Howard and Market streets, Baltimore; and in my absence at any time, a lien left at the bar will be attended to, immediately on my return.\n\nHOPE H. SLATTER\n\nN.B. I wish particularly to purchase several seamstresses and likely small fancy girls for nurses. I will also purchase several families. \u2014Baltimore _Republican_ & _Commercial Advertiser_ , Feb. 2, 1835.\n\n\"Small fancy girls\" meant light-skinned female children, salable as sex slaves. It was a discreet phrase, but not a mysterious one: everyone understood it.\n\nThe New Orleans market specialized both in selling difficult-to-dispose-of \"vicious slaves\" to sugar plantations and in supplying high-priced craftsmen, skilled domestics, \"body servants,\" and sex slaves (the light-skinned \"fancy girls\") for urban use. New Orleans was notorious for its slave auctions, but auctions seem to have constituted only about half of the sales; traders did much of their business by private sale out of their own retail showrooms, clusters of which were located in both the French- and English-speaking parts of town.\n\nThe Natchez market, by contrast, did not have regular auctions, but mostly sold retail, directly to cotton planters, out of a compound that housed several hundred captives at any one time. \"From early in the century to 1860,\" wrote Frederic Bancroft, \"the Natchez market, apart from its actual location, changed perhaps less than any other large market in the South, for its patrons were mainly of the planter class.\" Natchez purchasers were mostly end-users, as opposed to the resellers who dominated the market in Richmond and were also well represented in Charleston and New Orleans.\n\nNatchez was a split-level pair of towns. The city proper, high atop the bluff two hundred feet above the Mississippi River, was where the old Natchez aristocracy lived and where Isaac Franklin did his business; it connected socially and commercially with the rural planters. Down below, at the foot of the bluff, was Natchez-under-the-Hill, a sleazy row of taverns, gambling halls, brothels, and merchants who dealt with the river traffic. A traveler from Kentucky wrote of Natchez in an 1803 journal that \"there are about 500 dwellings in this place. They are mostly Americans from South Carolina and Georgia... I suppose from what I have seen that Natchez is, or the inhabitants of the town are, as much given to luxury & dissipation as any place in America.\" Natchez was the crossroads where the major water route, the Mississippi River, met the major land route, the Natchez Trace. As such, it was the principal destination for coffles as well as boats coming up from New Orleans. At the end of the slave-selling chain, Natchez consistently paid the highest prices. Natchez was Franklin and Armfield's cash cow.\n\nLouisiana's post\u2013Nat Turner prohibition on slave importation caused inventory problems. In a letter from New Orleans of February 28, 1831, Franklin wrote to Ballard in Richmond: \"I will have a petition tomorrow before the house for our relief\u2014should that fail god knows what will be the consequence. I will do the best I can for all concerned & if nothing better can be done I will declare myself a citizen of the state. I am much depressed & if we have to rely entirely on the Mississippi market we have more in this shipment than can be sold to advantage.\" In November, facing a wipeout with the closing to out-of-state traders of the Louisiana market, Franklin conveyed \"his entire lot of slaves\" to his brother and agent James R. Franklin in Natchez, who sold them all by December. After that, Franklin didn't sell into New Orleans again until 1834.\n\nMeanwhile, Natchez was heating up as a spot for sales. But epidemics were a constant problem, especially after a global pandemic of Asiatic cholera reached the United States in 1832. Symptoms \"appeared almost simultaneously in Montreal, Philadelphia, and New York,\" write Kiple and King. For reasons that are still unclear, but quite possibly related to the lower levels of sanitation available to the enslaved, the ravages of cholera were more severe among the black population; many physicians in the hemisphere thought of it as a \"negro disease.\"\n\nAt first Franklin was afraid that the inmates of Ballard's slave jail in Richmond might die, but then he advised him to hold back from selling and wait for prices to climb as the epidemic did its work: \"... best hold on. The more negroes lost in that country the more will be wanting if they have the means of procuring them.\"\n\nOn December 8, 1832, he wrote Ballard of casualties from cholera: \"the last two weeks we have Buried... 9 Negroes and 6 or 7 children and we have 7 or 8 Negroes sick... the way we send out dead Negroes at night and keep Dark is a sin.\" \"Buried\" was a euphemism, because he hadn't buried them; to the great disgust of the polite citizens of Natchez, he opted to dump their bodies in a swamp, hoping not to be detected as he created a health hazard for the terrified town.\n\nThat a slave trader could easily bring an epidemic of deadly diseases into town was part of the social stigma attached to the profession. Africans brought in on the earlier transatlantic slave ships had passed through a period of quarantine in a \"pest house,\" but there were no quarantines in interstate commerce. Yellow fever, malaria, typhoid, smallpox, cholera: slave pens were a notorious breeding ground for epidemics.\n\nFrightened by the possibility of contagion in their midst, the citizens of Natchez kicked the slave traders out of the city proper in 1833. They were banished only a mile out of town, to a site where slaves were already being sold: the Forks of the Road, a crossroads where the ironically named Liberty Road, which led east to Georgia, crossed Washington Road, which led to the Natchez Trace and on to Tennessee. If Natchez was a crossroads, the Forks of the Road was the crossroads of the crossroads.\n\nCue Robert Johnson: slave jails were often at the crossroads. However you care to read the image of the crossroads in the blues, remember that in Mississippi, the most notorious crossroads was the state's largest slave market, where Robert Johnson's great-grandfather's generation was sold.\n\n_A display of manacles embedded in concrete on the ground, part of a memorial at the site of Natchez's Forks of the Road, March 2014._\n\nMany locals referred to the Forks of the Road as Niggerville, as in an advertisement that ran in the Natchez _Free Trader_ of February 26, 1835:\n\nNEGROES FOR SALE.\n\nTHE subscribers offer for sale at Niggerville, one mile from Natchez, six carpenters and three blacksmiths. They will be first tried as to their capacity, in their different branches of business, with a full guaranty as to title and soundness of the same. To be disposed of either for cash, or on time, for good acceptances. All persons that may be in want of such mechanics, would do well to call and look at them before they are purchased elsewhere.\n\nEATON FREEMAN.\n\nNiggerville, Feb. 26-30-3t.\n\nIn a letter to Ballard of April 24, James R. Franklin wrote from Natchez, \"our negroes are getting much better but they have been very sickly. So much so the City Council Compells us all to leave the limits of the Corporation in two days. We shall have to take to the woods.\" By May 7, in the dreary woods amid sick and dying captives and sick himself, James R. Franklin's tone sounded desperate: \"I do assure you it is dreadful I have 4 or 5 down at present,\" but he held out hope that he could still sell his diseased cargo: \"I am in hopes all the fools are not yet dead and some one eyed man will buy us out yet.\" The term \"one eyed man,\" which turns up at various places in the firm's correspondence, seems to have been a private but easily understandable joke: maybe some dickhead will buy our inventory of slaves before they all die.\n\nIn a letter of February 2, 1834, James R. Franklin warned Rice C. Ballard not to ship any more \"Negroes,\" giving him the bad news that smallpox had broken out on two or three plantations, and that slaves imported by their firm were suspected of having brought it. Then, amid a litany of complaints about uncooperative banks and piratical customs agents, he wrote: \"I never wanted to leave any place so bad as I do want to leave this damn hole.\"\n\n\"I have commenced upon a new years work, and am purchasing negroes much faster than usual at fair prices,\" wrote Franklin's associate Jourdan M. Saunders from the buying territory in Virginia to his partner David Burford in Nashville in April 1832.\n\nThe boom was underway. Franklin wrote Ballard from Natchez that \"the US Bank and the Planters Bank at this place has thrown a large amt of cash into circulation.\" Franklin was positioned to scoop up that cash. In a letter of November 1, 1833, he urged Ballard to buy heavy, reminding him that \"as to the money we can raise in a short Time any Amt that may be wanting.\" He went on to advise him that \"we have sold all of our negroes for Good prices & Good profits accept [except] some old negroes say 18 in number... [they] will keep house until next Spring if they do not Die before that time[.] [We] could have sold as many more if we had of had the right kind.... [We sold] men from $8 to 900 Dollars[,] field women large & likely from 6 to 650 Dollars.\"\n\nBut then he complained, \"We have no young Girl on hand... There are Great Demand for fancy maid[.] I do believe that a likely Girl and Good seamstress could be sold for $1000[.]\" That complaint was also personal: \"I was disappointed in not finding your Charlottsvill maid that you promised me[.] you must ship all the first rate house servants by the first shipment after you Receive this.\"\n\n\"First-rate house servants\" was, of course, a euphemism. The \"fancy maid\" was named Martha; according to a letter from James R. Franklin, she also answered to \"Big Cuff.\" Apropos the term _fancy_ , Walter Johnson suggests that \"the word 'fancy'... refers to appearances perhaps or manners or dress. But the word has another meaning; it designates a desire: he fancies.... The slave market usage embarked from this second meaning: 'fancy' was a transitive verb made noun, a slaveholder's desire made material in the shape of a woman.\"\n\nNew Orleans was the capital for selling fancy girls, whose earnings could keep a riverboat gambler doubling as a pimp\u2014not necessarily selling their services by the hour, but perhaps receiving regular rent on long-term concubinage contracts, beginning at as young an age as twelve. An anonymous 1850 booklet called _New Orleans As It Is_ quotes a price of twelve to twenty dollars a month for a girl to pay her \"owner\"\u2014until, it goes on to say, \"she is cast off as a useless and worthless thing.\"\n\nThe wealthy planters of Natchez could easily afford to purchase personal sex slaves as luxury goods. Franklin, Armfield, and Ballard certainly dealt in them, and, as slave traders commonly did, they raped them in the process. This was facilitated by the fact that traders generally owned the captives in their custody. Planters often retained ownership of their cotton until it was sold in Liverpool, moving it along through a series of consignments and commissions, by means of \"huge\" syndicates they formed for the purpose of marketing their cotton. Not so slaves; they were generally sold outright as they moved through each stage of the distribution chain. Slave narratives commonly mention having been sold four or five times, and ten times over a lifetime was not unheard of.\n\nSince traders were the legal owners of the slaves they were selling, they could mistreat them any way they wanted. The law was quite clear that slaveowners' power was absolute. The 1830 opinion of North Carolina Supreme Court judge Thomas Ruffin in the _North Carolina v. Mann_ case that \"the power of the master must be absolute, to render the submission of the slave perfect\" echoed through the South with its sexual subtext intact.\n\nA trader was assumed to enjoy a surfeit of sex slaves; it was part of the culture of the slave trade, a notoriety that contributed greatly to the general disrepute traders were held in. A number of traders remained unmarried, preferring to enjoy the sexual benefits of being in the slave trade, cohabitating with enslaved women, who were frequently \"mighty near white,\" until they perhaps left the trade for a more respectable life.\n\nOn the evidence of their correspondence, sexual exploitation was part of the corporate culture of Franklin and Armfield. These \"fancy girls\" were the highest-priced slaves, the premium class of the market, consistently outpricing even prime field hands. While Franklin waited to get the best prices possible for them they belonged to the firm. Wendell Holmes Stephenson, Franklin's admiring 1939 biographer, obtusely notes that Franklin was party to a sale in Natchez in which \"Chloe Ann, yellow, aged sixteen, was sold on June 30, 1821, for $700, an unusual price for that period unless the slave were a skilled laborer.\" It was not, however, an unusual price for a light-skinned sex slave.\n\nThe archetypal fancy girl was a \"quadroon\"\u2014one-quarter black, three-quarters white\u2014or lighter. Not that black women didn't have to do sex work, but their owners commanded a lower price for it. While awaiting sale in New Orleans, they might be sent from a slave jail for a night's work in the lower class of brothel to earn the trader some money. They didn't have to travel far for that; it was no coincidence that New Orleans had both the nation's largest slave market and was the leading city for prostitution\u2014which also meant it was pimp city,* a profession that overlapped with gambling. New Orleans may have even outsyphilized her big sister city Havana. In some areas of the town, the brothels occupied \"the windows and doors of every house as far as the eyes can recognize them,\" according to one writer. The heavier the slave trade got, the lewder New Orleans grew.\n\nFranklin seems to have raped a number of young women who were in his power. From this we can infer that the sexual use of young women did not harm the prices paid for them, or he probably wouldn't have done it. Quite the contrary: it might have been seen as adding value as part of the enslaving process, so that the girls, officially sold as seamstresses or maids, would arrive having been broken in and be more \"compliant,\" a word that turns up in one letter of the Ballard correspondence collection, referring to a female sex slave. Franklin had the Charlottesville \"fair maid Martha... and our white Caroline\" on sale in 1832.\n\nFranklin and his associates used their own peculiar lingo in intra-firm correspondence. Besides the previously noted \"one eyed man,\" they referred generically to black people by the stereotypical name of \"Cuffy\" (Kofi, an Akan name). Franklin jokingly referred to Rice Ballard as well as to himself as an \"old robber.\" The firm's extant correspondence contains barely coded references to the sexual use of captive women, as per Franklin's notorious letter to Ballard of January 11, 1834. Written from New Orleans as the Bank of the United States was contracting credit, Franklin began with the gloomy news that retail prices for slaves had not gone up there even though the Nat Turner\u2013inspired importation ban that had closed the New Orleans slave market to him for more than two years was on its way to being lifted. He continued with an account of his depression in the face of low prices, continual rain and snow, the bad conditions of the coming sugar crop, and his fear of a concomitant downward pressure on the next year's market as surplus sugar hands would be sold rather than new ones bought.\n\nThen Franklin transitioned into complaining that Ballard had not sent him \"the Fancy Girl from Charlottesville,\" whom he had previously requested but whom Ballard had detained, asking \"will you send her out or shall I charge you $1100 for her[?]\" His spirits seemed to perk up as he began talking about the fancy girls they were passing between themselves. \"I thought that an old robber [i.e. Ballard] might be satisfyed with two or three maids.\" In a postscript, he began fantasizing about another kind of business operation: \"The old Lady and Susan could soon pay for themselves by keeping a whore house... let it be kept for the benefit of the consern... it might be... established at your place Alexandria or Baltimore for the exclusive use of the cosern [sic] and... [its] agents.\"\n\nFranklin's notoriety for his sexual use of \"likely\" girls was such that at a hearing over his estate after his death, attorneys for the plaintiff (Franklin's brother) against the defendant (Franklin's widow) tauntingly submitted as a cross-interrogatory for two witnesses the question: \"in describing the domestic comforts [of Franklin's Fairvue plantation],... was there, at that place, several very likely mulatto girls [?]\" One witness responded, \"There were at the place several likely mulatto girls; the servants that he kept about the house were all of the likeliest description, both male and female,\" though he hastened to add that all was above board.\n\nAndrew Jackson owned about 160 slaves by the time he was elected president\u2014which is to say, he was wealthy, but not super-wealthy. There's no question that Jackson had been a slave trader, but, like most of the domestic slave traders of his generation, he was a relative amateur at that business. Isaac Franklin was not. Even though Jackson was president, Franklin in some ways had better market information than his fellow Tennessean.\n\nWe do not know how Franklin arrived at his decision to quit while he was ahead. Perhaps he was merely reacting fast to the increasing financial disarray that he had a close-up view of, or perhaps he was activating a long-term plan, or perhaps both. But only seven years after starting Franklin and Armfield, Franklin announced his departure from the retail slave trade, and took quick, decisive steps to exit the business. Designating a New Orleans factorage firm to handle his affairs, he unloaded parts of the business onto his partners while retaining an ownership stake. His last known slave sale in New Orleans was on April 17, 1835. An advertisement of March 6, 1836, in the _Daily National Intelligencer_ for the firm's packet boat line the following year lists only Armfield's name, and at the close of the slave-selling season the firm's name listed Armfield first, as per the advertisement of April 5, 1836:\n\nFOR NEW ORLEANS. \u2014 The last Packet this season. \u2014 The Brig UNCAS, Captain BOUSH, will sail as above about the 20th instant. Persons wishing to ship will please to make early application to ARMFIELD, FRANKLIN, & CO. Alexandria\n\nAn advertisement in the same paper of November 7 shows that the partners had found a one-eyed man to take the brigs off their hands:\n\nWASHINGTON CITY AND NEW ORLEANS PACKETS. \u2014 The subscribers having purchased of Messrs. Armfield, Franklin, & Co. two of their splendid New Orleans packets, intend running them regularly between the two ports, leaving each place on the 1st of each month.\n\nThe brig Tribune, Captain Boush, master, will leave this place on the 1st of next month, (December.) The brig Uncas, Nathaniel Boush, master, on the 1st January.\n\nThose wishing to ship had better have their servants at this place a day or two previous to the vessels sailing. Servants can be kept at 25 cents per day.\n\nFreight and passage as heretofore.\n\nWM. H. WILLIAMS & CO.\n\nIt wasn't easy turning off the largest slave-trading firm in the United States. But while Franklin didn't manage to extricate himself completely from long-running business issues, he was way ahead of everybody else. With perfect timing, he cashed out just before the Panic of 1837. Franklin exited the retail slave trade at the peak of the boom and managed a substantial, though not total, escape before the crash. He had moved many of his obligations onto other shoulders by the time Jackson's Specie Circular shook American finance, and did well when others were vulnerable.\n\nFranklin was \"a man of gentlemanly address, as are many of these merchants, and not the ferocious, Captain Kidd looking fellows, we Yankees have been apt to imagine them,\" as Joseph Holt Ingraham described him, without being so indelicate as to mention him by name. Ingraham, then a young clergyman with literary ambitions, went on to explain that slave traders' \"admission into society, however, is not recognised. Planters associate with them freely enough, in the way of business, but notice them no farther.\" Franklin was, however, a determined social climber, and after he became very wealthy, he changed direction dramatically at the age of forty-six, transforming himself from a despised slave trader to a respectable planter with an increasing fortune. Though he had created the basics of a functional corporate structure with interregional reach that had made him very wealthy, he seems to have been thinking not in terms of building a permanent, expandable company, but of enriching himself enough to jump to the next social station. From his new platform, Franklin worked nonstop to further develop the ample resources he had acquired during his career in the slave trade.\n\nIn 1830, Franklin acquired a prime tract of land about four miles from Gallatin, Tennessee\u2014up the Cumberland River from Nashville, in a beautiful bluegrass region where buffalo had once run. First he put up an overseer's house, then slave quarters, then a mill and gin. After that, he built the mansion of Fairvue, which he filled with perhaps ten thousand dollars' worth of furniture; then a garden, a yard, an ice-house, and a stable where he kept blooded horses. He put his slaves to work raising cotton and food crops that he could sell downriver to Nashville.\n\nFairvue was the grandest house in Tennessee. After Franklin's untimely death, a neighbor testified:\n\n[The] house and everything about it is finished in most splendid and costly style; the mantle pieces are made of the finest Irish Kilkenny marble, which cost, as I understood from Mr. Franklin himself, $500 a mantle piece. The house, in part, is covered with fine cedar shingles, which were painted before they were nailed on; the other and flat part of the roof is covered with copper sheeting. This house has attached to it a beautiful yard, finely ornamented with a variety of shrubbery and a splendid garden, that is decidedly superior to any garden I have ever seen in Tennessee; the yard, garden and horse stables are beautifully enclosed with fine brick walls; there are two large brick barns or stables, and a great many brick negro houses, and very splendid family vault, enclosed by a superior stone wall. I am well acquainted with the improvements of the hermitage, the house of Gen. Andrew Jackson, and consider those belonging to the Fairvue estate as decidedly superior to them.\n\n\"Brick negro houses\" were anything but common, but Fairvue was a grand showpiece. Those houses were the public face of Isaac Franklin. He had made the transition: he was no longer a slave trader\u2014a man who raped light-skinned teenagers for amusement and dumped corpses in the swamp\u2014but a reputable planter and a gentleman horse breeder.\n\nSuch a fine house would surely find a mistress. According to an unsourced but not implausible story in the privately printed _The Saga of Fairvue_ , when Adelicia Hayes was brought by friends to see Fairvue, she wrote in the guest book with a fortune-hunter's frankness: \"I like this house and set my cap for its master.\" She had something to offer that he badly needed: respectability. He had something she wanted: that house. She was a twenty-two-year-old Presbyterian minister's daughter, which put her almost past marriageable age, and he was a fifty-year-Old Robber who had remade himself.\n\nIt was the first marriage for both of them. The evidence of Franklin's prior career was discarded: one of Franklin's associates, William Cotton, with Ballard's help, whisked Franklin's enslaved mistress Lucinda and their child away to be sold in Louisville. In their six years of marriage, Adelicia Hayes Franklin gave birth to a son who died in infancy and three daughters, none of whom lived to adulthood.\n\nIn his new career, Franklin continued to do business in slaves, because that was what planters did. But now his commerce was on a higher level than merely retailing flesh in a stinking slave mart; he was a financier, accumulating human capital through dispossession of smaller slaveowners.\n\nThere weren't a lot of different investment opportunities available in the all-slavery South. Savings most commonly took the form of slaves, which in turn were viewed by lenders as almost risk-free collateral. Large slaveowners therefore had lots of credit, collateralized by their slaveholdings, which they resold piecemeal to smaller fry. These well-capitalized individuals, whom Kilbourne calls \"accommodation endorsers,\" thus lent out their credit. Writing mortgages heavily collateralized by the debtor's slaves, they foreclosed on the weaker members of planter society as they went down, appropriating the bankrupt estates in the process. A neighbor recalled that \"I have seen [Franklin], with his family, boarding at the St. Charles [Hotel], in New Orleans; he had a very large debt uncollected, both in Mississippi and Louisiana, and was in the habit of renewing notes from year to year, and taking mortgages, &c., which required his attention a great deal in the winter season.\"\n\nMost mortgage lending was done privately, using banks as \"amplifiers,\" as Kilbourne put it. At deal's end, the lenders either collected their interest or took over the collateral. In the latter case, they either sold the slaves and the land, taking a profit, or kept them, realizing a capital gain and commanding still more credit.\n\nThat's how Franklin came into possession of his other signature property besides Fairvue: some forty-eight hundred acres of prime land in East Feliciana Parish, Louisiana, that had formerly belonged to an unlucky man named Francis Routh. Franklin began acquiring the property, which Routh had acquired from different owners, by purchasing a one-half interest on May 29, 1835, when Routh's finances were faltering and Franklin was transitioning out of the slave trade. The property already had three developed plantations on it, with the French, Irish, and Scottish-nostalgic names of Bellevue, Killarney, and Lock Lomond (or Lochlomond). After Routh was ruined in the Panic of 1837, Franklin purchased the other half of the estate at two sheriff's sales on December 22, 1837, and January 7, 1838.\n\nAn appraisal of February 26 valued the entire property at $159,507. Almost 60 percent of that value, $94,950, resided in the 224 individually named and expertly appraised slaves of the three working plantations. An enslaved man named Thomas Jefferson was worth $350; Plato Goodwin was appraised at $600; Nelly at $400, and her child French at $150; Catherine, one year old, at $100. Only two of them\u2014fewer than 1 percent\u2014were worth four figures, and unlike any of the others their professions were listed alongside their names: a blacksmith named Claiborne was worth $1,000. John Theodore, a carpenter, $1,500.\n\nThere were 134 slaves at Bellevue, the best-developed of the plantations. But there were only 47 at Lock Lomond and 43 at Killarney. This density of slave labor, low for a plantation, was because much of Franklin's Louisiana land was still undeveloped. He set to work building it up.\n\nBellevue became Franklin's residence when he was on the plantations, which was as little as possible. Although the main dwelling-house wasn't up to the luxurious standards of Fairvue, it did have the basic comforts, including a piano. He migrated north to Fairvue annually when the \"sickly season\" of summer settled into Louisiana and people began to die of yellow fever and other diseases, then returned south in mid-October to develop his Louisiana properties, which entailed putting up buildings and acquiring slaves and machinery.\n\nAfter giving Routh and his family some \"compassion money\" and evicting them from the property, Franklin began developing a fourth plantation to be \"sufficient for sixty hands\" on some of the estate's uncleared land. He set it up as a sawmill and gristmill, feeding it the timber that grew in profusion on his plantations-to-be, and tried selling Spanish moss harvested from the trees. He gave his newly developed Louisiana plantation a curious name:\n\nAngola.\n\n*Pimp = _mec_ in French, anglicized to _mack._\n\n#   34\n\n# **Wake Up Rich**\n\n_INCENDIARY TRACTS AND PAPERS._ \u2014 _The Mail brought by the Steam Packet Columbia, arrived this morning, has come not merely laden, but literally overburthened, with the Newspaper called \"The Emancipator\" and two Tracts entitled \"The Anti-Slavery Record,\" and \"The Slave's Friend,\" destined for circulation all over the Southern and Western Country.... If the General Post Office is not at liberty to act in this matter, it is impossible to answer for the security of the Mail in this part of the country, which contains such poisonous and inflammatory matter._\n\n_\u2014Southern Patriot_ , Charleston, July 29, 1835\n\nEVEN TO SPEAK OF slavery, much less to criticize it, was likely to \"excite the affections\" of Southern congressmen.\n\nThe South erected an informational firewall so that its alternate reality could not be disturbed. The censorship of mail in the South was general; ideologically suspect literature was routinely confiscated. People in the South could rely only on Southern sources to tell them of the supposed horrors that the abolitionists were planning for them.\n\nDistrict attorney Francis Scott Key ran Benjamin Lundy out of Washington City in 1833 for having printed an article in the _Genius of Universal Emancipation_ that said, \"There is neither mercy nor justice for colored people in this district [of Columbia].\" More than half the black people in Washington were free, and Key, one of the most prominent deportationists, was still district attorney in Washington two years later, in August 1835, when a white mob ran riot for two nights and destroyed black schools, churches, and homes.\n\nA sensational pamphlet that described a plan for a Christmas Day slave uprising throughout the South created a panic in central Mississippi during the hot summer of 1835. It was widely believed that a criminal named John Murrell had a huge gang and planned to incite a massive slave rebellion to facilitate plundering the towns. Murrell, a murderous highwayman and notorious kidnapper of slaves, was serving ten years in the Tennessee State Penitentiary at the time for \"negro-stealing,\" but that didn't stop the rumors. \"Many Mississippians were led to believe that the state was indeed threatened with the fate of Santo Domingo,\" writes Edwin Arthur Miles. In fact, there was no uprising, and no white people were killed by black people, but respected citizens formed extralegal vigilante groups that extracted confessions and lynched a dozen white men, five of them gamblers, and an unknown number of black people. Similar groups hunted gamblers and other transients in towns and settlements up the Mississippi and the Ohio Rivers.\n\nEighteen thirty-five was the summer of abolition propaganda, when a mail campaign by the American Anti-Slavery Society sent tens of thousands of Garrison-published pamphlets down south via the postal system. \"They have raised funds to support and circulate inflammatory newspapers and pamphlets gratuitously,\" wrote John Quincy Adams, \"and they send multitudes of them into the southern country in the midst of swarms of slaves, which is causing great excitement and fermentation in all parts of the Union.\"\n\nMany Southern newspapers carried alarmed reports of the arrival of sheaves of abolitionist literature at the local post office. Charleston postmaster Alfred Huger wrote to his counterpart in the New York post office that\n\nthe most respectable men of all parties gather'd about our doors and windows, and in a little time I was formally summoned to give up the \"incendiary publications\" which were known to be in my possession, and at the same [time] told with very little ceremony, that they would be taken from me, if I did not... I could only resolve that when the mail became the object of attack, I would make it the object of defence; but seeing plainly the excitement and exasperation which were every Moment increasing, I came to the determination to Separate the obnoxious papers, from the rest of the Mail, not doubting that otherwise, the whole might be destroy'd between the Office and the Rail-Road.\n\nPostmaster and key Jackson adviser Amos Kendall approved. In a letter to Huger that was published in various newspapers, he wrote, \"We owe an obligation to the laws, but a higher one to the communities in which we live, and if the former be perverted to destroy the latter, it is patriotism to disregard them.\"\n\nFrancis Scott Key would not be outdone in rooting out terrorism. \"Are you willing, gentlemen, to abandon your country; to permit it to be taken from you, and occupied by the Abolitionist, according to whose taste it is to associate and amalgamate with the Negro?\" he shouted in 1836. It was part of his sensational prosecution of the young doctor Reuben Crandall for having possessed a trunkful of copies of _The Liberator_ and _The Anti-Slavery Reporter_ in his home in Georgetown. Key kept Crandall in jail for months, and though Crandall was found not guilty, he contracted tuberculosis in prison and died two years later. Key remained district attorney until the Whigs moved into the White House in 1841, using his position to suppress abolitionism wherever he found it.\n\nNor was the hostility only in slavery territory. In Boston, William Lloyd Garrison was nearly lynched after being captured by a mob that came to attack a meeting of the Boston Female Anti-Slavery Society. Abolitionist meetings were broken up by mobs in New York, where there was much Southern sympathy.\n\nMeanwhile, traders continued trafficking young African Americans southward. On his first trip South in 1835, William Henry Seward saw a disturbing sight in Virginia, as summarized by his brother and biographer, Fredrick W. Seward:\n\nA cloud of dust was seen slowly coming down the road, from which proceeded a confused noise of moaning, weeping, and shouting. Presently reaching the gate of the stable-yard, it disclosed itself. Ten naked little boys, between six and twelve years old, tied together, two and two, by their wrists, were all fastened to a long rope, and followed by a tall, gaunt white man, who, with his long lash, whipped up the sad and weary little procession, drove it to the horse-trough to drink, and thence to a shed, where they lay down on the ground and sobbed and moaned themselves to sleep. These were children gathered up at different plantations by the \"trader,\" and were to be driven down to Richmond to be sold at auction, and taken South.\n\nIn New Hampshire, the young Jacksonian Franklin Pierce, a prot\u00e9g\u00e9 of Levi Woodbury, was appalled at the formation of an Anti-Slavery Society in his home state in 1835. He wrote to a friend, \"One thing must be perfectly apparent to every intelligent man. This abolition movement must be crushed or there is an end to the Union.\"\n\nJames Madison died in 1835, leaving the legal ownership of his slaves to his wife Dolley. His writings bear witness that he had repeatedly agonized about the wrongness of slavery, though not as much as his slaves must have agonized about it. Madison did not leave Dolley in good financial condition, and the Panic of 1837 exacerbated her problems. It was a typical Southern widow's situation: Dolley Madison's slaves were her nest egg, and despite language in Madison's will forbidding her to sell them without their consent, she sold them off to pay her ne'er-do-well son's debts. Montpelier itself was sold to a Richmond merchant in 1844.\n\nAlong with the explosion of abolitionist propaganda in the 1830s came a new kind of argument, one championed by an emerging generation of free black abolitionists, that focused on the degradation forced on the enslaved. Frederick Douglass expressed it in his Fourth of July speech of 1852 in Rochester, New York: \"The feeling of the nation must be quickened; the conscience of the nation must be roused; the propriety of the nation must be startled; the hypocrisy of the nation must be exposed; and its crimes against God and man must be denounced.\"\n\nDouglass was so radical that he called for full political rights for women. A nascent American women's-rights movement drew energy from women's activity in the antislavery movement, their largest participation in American politics up to that time. Often denied membership in men's political organizations, and without the right to vote, they formed \"ladies'\" political clubs, collecting signatures for the petitions that John Quincy Adams lay on the table by the hundreds in the House of Representatives.\n\nThe coffles marching through the nation's capital became the number-one target of the antislavery movement. The District of Columbia was Congress's responsibility, so grassroots organizations\u2014local clubs\u2014flooded both houses of Congress with petitions to close the slave trade in the federal capital. The term \"slave-breeding\" became a part of the antislavery polemic, the interstate slave trade the visible symbol of slavery.\n\nIn response to John Quincy Adams's continued presentation of abolition petitions, Speaker of the House James K. Polk in 1836 cut him off with the \"gag rule\" requiring that nothing relating to the subject of slavery could be introduced or discussed. The gag rule, which was reinstated every year with ever more restrictive language until 1844, became a cause c\u00e9l\u00e8bre for the anti-slavery movement. Adams, outraged, focused on breaking it, exposing himself to censure for receiving and submitting petitions. The more petitions he laid on the table, the more came in. By the 1837\u201338 term, there were 130,200 petitions calling for the end of slavery in the District of Columbia. Others called for abolition nationally, for abolishing the interstate slave trade, for lifting the gag rule, against the annexation of Texas, against dueling, and, during the winter of 1838\u201339, more than two hundred petitions for the recognition of Haiti, which was a busy trading partner of US merchants while officially remaining a pariah country.\n\nThe arrival of master-race Jacksonian Democracy, the eruption of abolitionism as a movement, and the radicalization of the nullification movement combined to make a new, unapologetic attitude toward slavery that was felt especially along the southwestern frontier. In Mississippi, which had grown from twenty-six counties in 1832 to fifty-five in 1836 as former Choctaw and Chickasaw lands became occupied, Seargent S. Prentiss, newly elected to the Mississippi House of Representatives in 1836, introduced a resolution that the people of the state \"look upon the institution of slavery, as it exists among them, not as a curse, but as a blessing, as the legitimate condition of the African race... and that they hope to transmit this institution to their posterity, as the best part of their inheritance... we will allow no present change, or hope of future alteration in this matter.\"\n\nIn the decade between 1830 and 1840, as the plantation system exploded into the newly available lands, Mississippi's free population increased by a factor of 2.54 to 180,440 (free people of color were only 1,366 of them), but the enslaved population almost tripled, to 195,211. Mississippi now had a black majority.\n\nIn Mississippi, as in Carolina, there was no doubt, at least among the slaveholders: God himself was pro-slavery.\n\n\"I am a nullifier!\" shouted South Carolina's Robert Barnwell Rhett in 1837, in his first major speech as a congressman.\n\nHaving unsurprisingly outed himself as a Calhounian with that declaration, Rhett's speech pivoted into another kind of discourse as he unwound into over-the-top hyperbole. Rhett, who had no military experience, romanticized war and even annihilation in the service of the glorious cause of state sovereignty over the federal government, which in the case of South Carolina was to say, in the service of slavery. As he extolled martyrdom, which he had no intention of personally experiencing, he gave the House its sharpest taste yet of the belligerent, self-apotheosizing oratory of the new generation.\n\nAfter shouting chains of rhetorical questions, Rhett spoke defiantly of the resistance that, he insisted, would have met Jackson had Jackson invaded South Carolina during the nullification crisis:\n\nHad South Carolina been invaded, upon the first gleam of the bayonet along our mountain passes, he would have seen and known what the chivalry of the South really was, not in bloodless tropes and metaphors, but in the stern realities of the tented field. Not only Carolinians, but thousands of volunteers from the whole South, whose names are upon the file, would have met you in that fierce contest [etc. etc.]... We knew the mighty inheritance for which we were to contend\u2014that soil over which, for two centuries, we had been the lords; and those altars at which our fathers knelt and we had received our brides. We won it by the sword, and we were prepared to keep it by the sword.\n\nRhett had taken his political stage name just before running for office. Following a fashion in South Carolina to rename one's self after one's most illustrious ancestors, Robert Barnwell Smith and all his brothers changed their common laborer's last name to the more romantic-sounding Rhett. It was a Gaelic-style spelling of the name of a matrilineal ancestor, a Dutchman named Raedt, whose claim to fame was having captured Stede Bonnet, Charleston's only pirate of note.\n\nMargaret Mitchell took two of the Lowcountry's best-known pro-slavery political names for her fictional character of Rhett Butler in _Gone With the Wind_ , but Robert Barnwell Rhett was no Clark Gable. Balding on top by his thirties, he tried to disguise it with a comb-over, his red face framed by a hightop starched collar. There is little favorable commentary about him. He was ambitious, arrogant, belligerent, and an implacable foe with a martyr complex who attacked no one as ferociously as those who almost agreed with him. His biographer William C. Davis speculates that there might have been favorable commentary about him in documents that were destroyed when Charleston fell, and concedes that \"it is something of a struggle to present a balanced portrait of the man, especially since out of his own mouth he so often offends.\" Rhett was self-righteous, utterly convinced of the rightness of slavery, and careless with the truth. To that we could add, again quoting Davis, \"the inability to follow others and compulsion to enforce his own will, his unwillingness or inability to countenance any ideas but his own, and his constant scheming.\" He was aggressively religious, having had a kind of born-again experience, while remaining within the Episcopal fold.\n\nRhett's view of history was decidedly odd and self-serving, believing as he did that Charles Pinckney, and not Madison, was the real father of the Constitution. One might be forgiven for thinking Rhett barking mad, but that is an insufficient explanation for the phenomenon he presented. He was arguably the single most influential individual in pushing the South to secession; he referred to himself as a \"lucifer,\" a matchstick that lit the blaze. Rhett had been a force in the nullification movement, and played an active if complicated role in Calhoun's increasing radicalization. Under his former name of Robert Barnwell Smith, he had for years been pushing Calhoun to the right from his position in the South Carolina General Assembly, a powerful body that chose the state's governor, senators, and representatives.\n\nRhett was from Beaufort, the wealthy town by the site of the former Huguenot settlement of Charlesfort and the Spanish Santa Elena, in the heart of the region that produced long-staple, or Sea Island, cotton. At Beaufort College in South Carolina the aristocratic young planters flatly rejected the notion of the Age of Reason, and believed fully in the natural right of the oligarchy. Beaufort was Ground Zero of secessionism; the \"secession house\" in that town, owned in the 1850s by brother Edmund Rhett, was a central meeting place for the secession apostles who became known as the Fire-Eaters.\n\nBy the time Rhett arrived in Congress, he had not merely declared (in 1829), that \"I am a Disunionist! I am a Traitor!\" In the wake of the Force Act, he proposed what might lie beyond secession: a confederacy. He was the prophet of an independent slave nation, commanded from South Carolina. In what was perhaps a veiled dig at the most famous Jacksonian poet, Rhett declaimed at the States Rights and Free Trade Party convention of 1833 that \"The star-spangled banner no longer waves in triumph and glory for me. Sir, if a Confederacy of the Southern States could now be obtained, should we not deem it a happy termination\u2014happy beyond expectation, of our long struggle for our rights against oppression?\"\n\nRhett and his clan built the most powerful political clique in Charleston. Any serious politician needed a newspaper, and Rhett's brother-in-law John A. Stuart owned the _Charleston Mercury_ , the most radical paper in the South. The family also came to control the _Columbia South Carolinian_ in the state's capital. There were Rhett brothers in the state legislature, and they had control of the Bank of South Carolina.\n\nIronically, Rhett was a distant cousin of John Quincy Adams. When they were much younger, the two had met in private life. Describing Rhett's congressional speech, Adams drily noted his recent name change: \"Robert Barnwell Rhett (Smith heretofore) moved a long amendment, and literally howled a nullification speech. I say howled, for his enunciation was so rapid, inarticulate, and vociferous that his head hung back as he spoke, with his face upward, like that of a howling dog.\"\n\nIn an 1838 speech before Congress, Rhett explained his economic theory of the superiority of slavery: according to him, slaves were better off than free laborers, because they were both capital and labor, and self-interest would mandate their better treatment. In the midst of his lengthy lecture in political economy, he said, \"there is but one state of society in the world, where labor and capital are identical in interest; and that is where domestic slavery exists... Labor, there, is capital, and capital is labor.\"\n\nAccording to Rhett, that was what South Carolina was fighting for, with God's full approval: for labor to be capital.\n\nOf course, that meant there had to be a capital market. Rhett owned over a hundred slaves, whom he had bought pursuant to a promise not to sell them off. But his obsession was political power, and like many other slaveowning politicians, he was inattentive to his business as a planter, so he sold thirty-six people away to traders to cover his losses.\n\nSALE OF SLAVES. \u2014 I will sell at public auction, on Monday, the 23d October, at 4 o'clock P.M. at the auction room of Edward Dyer, in Washington City, D.C. the following slaves, purchased by me upon the 22d of August last, from Rezin Orme, and who were warranted sound in bodies and in mind, to wit, Dorcas Allen, and her two surviving children, aged about seven and nine years, (the other two having been killed by said Dorcas in a fit of insanity, as found by the jury who lately acquitted her.)\n\nTerms of sale cash, as said slaves will be sold on account of said Rezin Orme, who refuses to retake the same and repay the purchase money, and who is notified to attend said sale, and if he thinks proper to bid for them, or retake them, as he prefers, upon refunding the money paid, and all expenses incurred under the warranty given by him.\n\nJAMES BIRCH\n\nEDWARD DYER,\n\nAuctioneer.\n\nFour years before John Quincy Adams delivered the winning argument in the well-known _Amistad_ case, he went up against District of Columbia slave trader James Birch, with less successful results. A diary entry of October 23, 1837, notes that:\n\nThere was in the National Intelligencer this morning an advertisement signed James H. Birch, and Edward Dyer, auctioneer, headed \"Sale of Slaves\"\u2014a sale at public auction, at four o'clock this afternoon, of Dorcas Allen and her two surviving children, aged about seven and nine years (the other two having been killed by said Dorcas in a fit of insanity, as found by the jury who lately acquitted her). The advertisement further says that the said slaves were purchased by Birch, on the 22d of August last...\n\nI asked Mr. Frye what this advertisement meant. He seemed not to like to speak of it, but said the woman had been sold with her children, to be sent to the South and separated from her husband; that she had killed two of her children, by cutting their throats, and cut her own to kill herself, but in that had failed; that she had been tried at Alexandria for the murder of her children, and acquitted on the ground of insanity; and that this sale now was by the purchaser at the expense of the seller, upon the warranty that she was sound in body and mind.\n\nAdams visited the slave jail and spoke to Dyer, letting the traders know someone in Congress was watching:\n\nI learnt from Dyer that the woman had been the slave of a white woman who had married a man named Davis, who lived at Georgetown and was a clerk in the War Department; that this white woman had died, and had before her death promised Dorcas her freedom; that on her death-bed she had made her husband (Davis) promise her that he would emancipate Dorcas; that he did actually liberate her, but gave her no papers; that she lived twelve or fifteen years at large, married, and had four children; that in the mean time Davis married a second wife [Maria], and afterwards died, without granting to Dorcas her papers of freedom; that Davis's widow [Maria] married a man by the name of Rezin Orme, and that he sold Dorcas and her four children, on the 22d of August last, for seven hundred dollars, to Birch, who is an agent for the negro slave-traders at Alexandria; that Dorcas and her four children were on the same day removed to one of the slave-prisons in Alexandria; that in the night of that day she killed the two youngest of her children\u2014one, a boy four years of age, and the other, a girl under twelve months; that she attempted to kill the other two, but was prevented\u2014their screaming having roused some person in the house, who went into the cell where she was confined and took her surviving children from her; that she was tried at Alexandria for the murder of her two children, and was acquitted by the jury on the ground of insanity.\n\nAdams discussed the case with district attorney Francis Scott Key, who \"appeared to interest himself,\" Adams thought, in the plight of Allen's desperate free black husband, and proposed a fund to purchase her freedom, to which Adams contributed fifty dollars. But, Adams wrote dejectedly on November 2, \"if their freedom from Birch's sale should be purchased, they might still be reclaimed by Davis's creditors.\" Eight days later, he wrote: \"Upon conversing with [Mr. Key], I found he would give no assurance that Dorcas Allen and her children will be free if they should be purchased from Birch. By the law of the place, they are assets of the estate of Gideon Davis, upon which there never has been any administration; neither his widow nor her second husband... had any right to sell them.\"\n\nWhat ultimately happened is left a cliff-hanger in Adams's diary, but Key doesn't seem to have come through for Dorcas Allen. By November 13, she was with her husband, and her two children were back in Birch's jail. \"Mr. Key told me,\" Adams wrote, \"that if upon a writ of habeas corpus Birch's title should be disproved, still they were slaves; they could not be discharged.\"\n\nIn his diary, Adams routinely referred to his Southern congressional opponents as \"the slavers\" and to their Northern supporters as \"the serviles.\" On December 22, 1837, he recounted \"banter\" with Ratliff Boon of Indiana, who, recounts Adams, \"said that if the question ever came to the issue of war, the Southern people would march into New England and conquer it. I said I had no doubt they would if they could, and that it was what they were now struggling for with all their might.\"\n\nThe land-value bubble burst, but it was worse than that.\n\nIn a feat of election-year politicking, Congress passed, and Jackson signed, the Whig-sponsored Deposit Act, which directed that most of the federal government's surplus achieved from approximately $35 million in land sales be distributed beginning in January 1837 to the states in proportion to their number of electoral votes, a formula proposed by Calhoun.\n\nUnfortunately for Mississippi, the state was only entitled to receive about a half million dollars in the distribution, but its deposit banks had ten million dollars' worth of revenues from land sales in the region and therefore were going to have to send away 95 percent of their capital.\n\nMeanwhile, there was an explosion of commercial banking in which new institutions were chartered as if broadcasting seed, with no oversight. Florida banking operations of that time were satirized years later by Ellen Call Long, the daughter of Florida's governor during that era (former Jackson aide Richard K. Call, who had prosecuted the Seminole War):\n\nYou want to know how it operates? Well, you see a man can mortgage his land or negroes; draw from the bank two-thirds (in money) of their value, which will be re-invested in more land and more negroes. One or two crops of cotton will redeem all obligation to the bank; so you see that it is the best thing afloat; a man can just go to sleep, and wake up rich.\n\nThe riches obtained from this kind of maneuver, needless to say, were not in the form of gold pieces, but \"negroes,\" who remained as capital in the planter's possession when the cotton was sold and who could always be used to collateralize a loan.\n\nAfter Jackson promoted the obliging Roger B. Taney to chief justice of the Supreme Court, he named Secretary of the Navy Levi Woodbury to be his fourth secretary of the treasury. As speculators bought public land with increasingly questionable paper, Woodbury on July 11, 1836, issued the document that snapped the overextended banking system: the Specie Circular. Taking effect August 15, it announced an abrupt shift to hard money on the part of the government, which would henceforth require payment for public lands in specie. The plan, apparently, was to remove all notes from circulation under $20 (a little more than $500 in 2014 dollars) and replace them with coins, with paper money being reserved for larger transactions. To make these coins a series of new mints was built, including the US Mint in New Orleans, one of the city's enduring landmarks.\n\nThis move created a demand for coin that sucked specie reserves out of eastern banks. As paper money spiraled toward worthless and banks suspended specie payments, silver and gold pieces were physically repositioned among the states. Biddle wrote in an unsigned piece in 1839 that \"the monetary affairs of the whole country were convulsed\u2014millions upon millions of coin were _in transitu_ in every direction, and consequently withdrawn from useful employment. Specie was going up and down the same river, to and from the South and North and the East and West at the same time; millions were withdrawn from their usual and natural channels, and forced against the current of trade.\"\n\nThe term that was used to describe the westward movement of specie was the same used for the westward movement of Native Americans: removal. The Specie Circular was not the only thing that brought down the American economy, but it was Jackson's crowning achievement to that end.\n\nAs Jackson was preparing to leave office, still riding a national wave of adulation, he warned, according to his biographer Parton, that a \"paper money system and its natural associates, monopoly and exclusive privileges, have already struck their roots deep in the soil, and it will require all your efforts to check its further growth and to eradicate the evil.\"\n\nPaper money was... _evil._ No moral relativism: evil. Only gold and silver were good.\n\nFast-growing New Orleans had broken into three pieces. The French speakers (in the downtown \"French Quarter\") and the uptown Anglophone businessmen had long been at loggerheads, physically separated by Canal Street, which was a filthy, muddy, no-man's-land, or, as they say in New Orleans, \"neutral ground.\"\n\nThough immigrants generally did not come to the South, they did come to New Orleans, the second largest destination for them after New York. They encountered a vicious nativist movement; one New Orleans newspaper was called the _True American._\n\nThe uptown Anglo-Americans in fast-growing New Orleans in effect seceded from the city (though historians have generally refrained from using that term in speaking about it) on March 8, 1836, separating themselves off from their French-speaking counterparts, whom they saw as receiving an excessive share of the public purse. The city split into three municipalities, each in charge of its own revenues.\n\nThe First Municipality, French-speaking and Catholic, was the old town below Canal Street (the French Quarter). The Second, English-speaking and Protestant, was the Faubourg St. Mary, uptown above Canal Street (today's Central Business District). The Third, French-speaking and Catholic (and unpaved and unlighted), was the Faubourg Marigny, downriver from the First below Esplanade. These municipalities, which were more or less antagonistic, each had their own police force, complete with hostilities between the respective departments, whose primary duty was slave patrol. Each municipality built its own levees and administered its own infrastructure.\n\nThe Anglo-Americans of the Second Municipality intended to corner railroad commerce. A proposed railroad, the New Orleans and Nashville, planned to link the major trade terminus of Tennessee with Carrollton, a suburb of New Orleans named for railroad hero Charles Carroll of Carrollton, who had died in 1832 at the age of ninety-five. \"There is very little doubt,\" hummed an 1835 editorial in the _New Orleans Bee_ , \"of the New Orleans and Nashville railroad being completed in 3 or 4 years.\"\n\nThe local spur line to Carrollton was built entirely within the Anglo-controlled part of town. In seceding from New Orleans, the Anglo-American Second Municipality made off with that new railroad link, which began operations on September 22, 1835. But the Nashville railroad was never built; the only part ever completed was the local link, from present-day Lee Circle to Carrollton. Though it never became a freight corridor connected to a mighty railroad, the link became instead the anchor of uptown New Orleans development. Carrying passengers (it even had a ladies' car), it made the far-flung Carrollton Hotel a chic place for downtowners to repair to for supper and encouraged the development of the territory in between. The space between New Orleans and Carrollton filled in alongside the train, whose track became the extension of the former stub street of St. Charles. The rail line became public transport through what became known as the Garden District, and is today the main streetcar line that connects downtown with uptown. The New Orleans streetcar line was thus approximately tied with New York (the Long Island Rail Road) as the first in the US to connect city with suburb by rail.\n\nBut the failure to connect to the national rail network betokened the beginning of New Orleans's long decline. Meanwhile, the breakup of the city left the English speakers without the year's biggest fun. Mardi Gras was a French thing, done at that time in New Orleans more or less on the Parisian model. The pre-Lenten carnival season was celebrated with masked balls galore in the French Quarter, the masks being the main difference between carnival balls and the year-round schedule of dances.\n\nThe first organized Mardi Gras parade that we know of in New Orleans took place in 1837, less than a month before the inauguration in Washington of President Martin Van Buren, which was only six weeks before the New Orleans _True American_ published its sensational reportage on the failure of Hermann, Briggs, and Co.\n\nHeaded by America's most famous war hero, with Martin Van Buren, Amos Kendall, James K. Polk, Sam Houston, John Tyler, James Buchanan, and the young Franklin Pierce; Taney and Woodward on the Supreme Court; and Francis Scott Key as the capital's district attorney, the Jackson dynasty was the most powerful political force the United States had seen.\n\nVan Buren's election was to be its consolidation. Matty Van, or the \"little magician\" (for his short stature and political cunning), the \"red fox\" (for his hair), \"O.K.\" (Old Kinderhook, for his New York home town), or the \"wily Dutchman\" of the \"Albany Regency,\" as one of Polk's correspondents unflatteringly put it, was the first president born after independence, the first presidential candidate to campaign openly, and the first professional politician to become president.\n\nBut the chickens came home to roost on his head. Six weeks after Van Buren was inaugurated on March 4, 1837, his one-term presidency was wracked by economic convulsions as banks began suspending specie payments.\n\nThe winds of global trade had shifted again. The British financiers most heavily exposed to American debtors were insolvent; the Bank of England, which had its own problems, constricted credit. The invention of the telegraph was still seven years away, and steamships did not yet ply the Atlantic: the Panic of 1837 was in part a crisis of slow-moving financial information.\n\nThe panic seems to have begun in New Orleans when the cotton factorage firm Hermann, Briggs, & Co. failed. Perhaps because its proprietor Louis Florian Hermann was a German Jew, the New Orleans _True American_ printed a sensational story about it that traveled far and wide, spreading the worry. Then J. L. & S. Joseph & Co., a New York firm that was Hermann, Briggs's creditor, failed too. Meanwhile, the price of cotton plunged in Liverpool to \"a staggering fifty percent of what the cotton brokers had extended to the planters,\" writes Jessica M. Lepler. There was not yet class solidarity among bankers, so the directors of New Orleans's sixteen (!) banks did not take concerted action or even, apparently, talk to each other as the crisis accelerated. They all suspended specie payments in April, then the failure spread to New York on May 8.\n\nThe 1840 census showed New Orleans as the nation's third largest city, with 102,193 residents, effectively tied with Baltimore's 102,313 for second place. New Orleans, the number-one port in the United States, was unlike the rest of the South in many ways. It was urban. It had a substantial business community and a local economy dominated by factors; a waterfront that shipped the world's greatest quantities of cotton and much sugar; and, since the plantations of Louisiana and Mississippi required enormous amounts of credit, it had a large banking sector, heavily capitalized by captive human beings.\n\nBut though the port's overall receipts continued to grow, the panic was the end of New Orleans's peak period of national influence, and its share of the nation's expanding commerce grew progressively smaller. In particular, New Orleans failed to get in on rail transport, the competition from which was cutting into the river trade more every year. The Mississippi River had formerly been the only way for a wide swath of the United States to get its goods to market. But as railroads slowly extended their reach\u2014slowly, because laying a railroad was a big operation that required solid financing\u2014the rivers would matter less. New Orleans continued growing, but it would never again be tied for second largest city in the nation.\n\nNew Orleans was, however, the largest slave market in the United States. At least half if not more of its sales, and probably most of its high-value deals, were conducted by private sale out of dealer showrooms. Some of the buildings are still there, though the spectacular main auction venues are long gone. Some dealers made slaves stand out on the sidewalk from nine to four, trying to entice buyers. The horrors of slave auctioning have been amply detailed elsewhere, and we will not describe these wrenching scenes here, citing as merely one example the testimony of the formerly enslaved Stephen Jordon, many years after he was sold in New Orleans:\n\nI tell you, people were miserable in that old slave-pen. They used to make them open their mouths so that they could examine their teeth; and they used to strip them naked, from head to foot, to see whether they were perfectly sound. And this they did to women as well as men. I tell you, my dear child, it used to seem to me so brutal to see poor women treated in that way by brutal and heartless men. I declare, child, I can't understand it, although I've been right in it. When they would put them naked that way they used to switch them on the legs to make them jump around so that buyers could see how supple they were.\n\nDealers generally got better prices at private sale than at auction, but not necessarily. Auctions in New Orleans, typically conducted bilingually in French and English, were conducted to turn over large numbers of people as quickly as possible. It was a fast way to get rid of less desirable slaves or, on the other end of the profit scale, to maximize the value of a white-looking beauty or a first-rate cabinetmaker.\n\nThe New Orleans market sent large numbers of young men to the sugar plantations, which always wanted fresh victims, so the gender ratio of people sold in New Orleans skewed disproportionately toward males. But with so many wealthy people in the city, New Orleans also served the nation's largest market for domestic servants and skilled artisans, and it was the number-one retail market for fancy girls, with either Natchez or the horse-racing and gambling center of Lexington, Kentucky, perhaps a distant second in that category.\n\nWith so much money flowing through town, it was a great moment for architecture, not all of which survives. The St. Louis Hotel, which ran the length of the block from Royal to Chartres on St. Louis Street, is long gone. Frederic Bancroft visited its abandoned shell in 1902 and wrote of the \"blaze of light\" from the dome that illuminated the floor where slaves were sold daily. With its front entrance on St. Louis Street, the British visitor J. S. Buckingham described it in 1839:\n\nThe entrance into the Exchange at the St. Louis, is through a handsome vestibule, or hall, of 127 feet by 40, which leads to the Rotunda. This is crowned by a beautiful and lofty dome, with a finely ornamented ceiling in the interior, and a variegated marble pavement.... in the Rotunda, pictures are exhibited, and auctions are held for every description of good. At the time of our visit, there were half a dozen auctioneers, each endeavouring to drown every voice but his own, and all straining their lungs and distorting their countenances in a hideous manner. One was selling pictures, and dwelling on their merits; another was disposing of ground-lots in embryo cities, and expatiating on their capacities; and another was disposing of some slaves.\n\nThese consisted of an unhappy negro family, who were all exposed to the hammer at the same time. Their good qualities were enumerated in English and in French, and their persons were carefully examined by intending purchasers, among whom they were ultimately disposed of, chiefly to Cr\u00e9ole buyers; the husband at 750 dollars, the wife at 550, and the children at 220 each.\n\nThe middle of the Rotunda was filled with casks, boxes, bales, and crates; and the negroes exposed for sale were put to stand on these, to be the better seen by persons attending the sale. Often as I had witnessed this painful scene in the old times of the West Indies, and in several of the countries of the East, it had lost none of its pain by repetition; it appeared, indeed, more revolting here, in contrast with the republican institutions of America.\n\nThe St. Louis was far from the only auction venue. Banks' Arcade, an enormous building that ran from Gravier to Natchez Street on Magazine, hosted them. (A small part of Bank's Arcade still stands, as do a number of now repurposed former slave dealer showrooms in New Orleans.) It was at Banks' on October 15, 1835, that a meeting of the \"friends of Texas\" promised financial and military support to the Anglo-American provisional \"government\" in Texas, in blatant violation of US neutrality laws.\n\nMexico after its independence in 1821 prohibited slavery, but the territory was only sparsely settled; hoping to populate it, the Mexican government invited in settlers from the United States, giving them land. But once the settlers moved in, they declared it theirs. Moses Austin, who had become one of the country's major producers of lead, was a major promoter of the Texas colonization movement. With his eyes on Mexico's lead mines, Austin had sworn allegiance to the Spanish crown in 1798. His son, the Virginia-born, Missouri-raised land speculator Stephen F. Austin, brought slavery to Texas and fought to keep it.\n\nIt was an article of faith throughout the South that American slavery must expand into Texas and beyond. There was no question that Texas would be an ultimate destination for young African Americans who were being born and raised all over the cotton kingdom. Stephen Austin wrote his sister Emily from New Orleans in August 1835, the summer of the Southern abolition panic: \"It is very evident that Texas should be effectually, and fully, Americanized... Texas must be a slave country. It is no longer a matter of doubt. The interest of Louisiana requires that it should be. A population of fanatical abolitionists in Texas would have a very dangerous and pernicious influence on the overgrown slave population of [Louisiana].\"\n\nAndrew Jackson had mentored Sam Houston, the Scotch-Irish-descended, Virginia-born, Tennessee-raised land speculator, politician, and military leader. Houston had served under Jackson in the Creek War, and had been the Jacksonian governor of Tennessee, before fleeing to Texas to escape a disastrous marriage. He was one of fifty-nine signers of the Texas Declaration of Independence on March 2, 1836, four days before the massacre at the Alamo. As a general in the Texas army, he was the hero of the decisive Battle of San Jacinto that took Mexican general Antonio L\u00f3pez de Santa Anna prisoner. On October 22, Jackson's prot\u00e9g\u00e9 became the first president of the Republic of Texas.\n\nThere was much opposition in the North to annexing Texas, because it meant the expansion of US slavery. With Jackson's anointed successor Van Buren fighting hard to be elected president, annexation was too politically controversial and would provoke a sectional controversy instead of strengthening the national party the Democrats had built. James Hamilton of South Carolina printed a report in the _Telegraph_ , a Jacksonian organ that presented \"the Texans as a people struggling for their liberty, and therefore entitled to our sympathy,\" as John Quincy Adams disgustedly wrote in his diary. He continued: \"The fact is directly the reverse\u2014they are fighting for the establishment and perpetuation of slavery, and that is the cause of the South Carolinian sympathy with them.\"\n\nBut for all his involvement in the Texas project, Jackson didn't annex the territory. Instead, one of his last acts as president was to recognize the independent Republic of Texas. Houston tendered an annexation offer, but John Quincy Adams stalled the annexation of Texas in Congress. Houston took it off the table in 1839, with the result that Texas and the United States dealt with each other for about ten years as independent nations.\n\nMeanwhile, two real estate speculators from New York who intended to develop a town obtained permission to use Sam Houston's name. Incorporated on June 5, 1837, the town of Houston\u2014a city named for the sitting president\u2014served as the capital of the Republic of Texas until the capital was moved to Austin in 1839. That year, the Texas Congress adopted the Lone Star banner, representing the territory's readiness to go it alone, as the national flag. It subsequently became, and remains, the state flag of Texas.\n\nIt sounds impressive: the Mississippi and Alabama Railroad Company. More familiarly known as the Brandon Bank, it was chartered in Brandon, Mississippi, in 1836\u2014supposedly to build a railroad, but it never even tried. In 1837, with most of the state's plantation land already mortgaged, the Brandon Bank began making cash advances on cotton crops, paying $0.12 per expected pound. Unfortunately, by July 1838, the price for cotton was down to $0.083 a pound, and moreover, many farmers delivered no cotton to the bank at all. By the fall of that year, the bank's money was circulating in Jackson at 30 to 40 percent off face value.\n\nThe sell-off of the public lands continued; John Quincy Adams wrote in his diary in June 1838 that \"the thirst of a tiger for blood is the fittest emblem of the rapacity with which the members [of Congress] of all the new States fly at the public lands. The constituents upon whom they depend are all settlers, or tame and careless spectators of the pillage. They are themselves enormous speculators and land-jobbers.\" The nation's economy seemed to recover in 1838, as banks warily resumed specie payments, but it didn't last. The US government was broke, and couldn't make the final payment on the redistribution of the long-gone surplus.\n\nThree Mississippi bank commissioners traveled to Philadelphia, where they sold Nicholas Biddle $5 million in Mississippi bonds. Biddle sent the bonds on to London, where \"the United States Banks' London agency sold $2 million of them to European investors and transferred the remaining $3 million to London and Amsterdam bankers as collateral security.\" They wound up in the hands of the Rothschilds, the Baring Brothers, and others who knew quite well that they were purchasing shares in slaves. James T. MacIntosh writes that \"when the specie resulting from the sale of the bonds finally reached Mississippi, people celebrated in the belief that their financial woes were at an end.\" Edwin Arthur Miles writes that the entire population \"regarded those five millions as an especial Godsend... Wagon after wagon was seen conveying a portion of those five million in hard dollars to the vaults of the bank.\" With that money in hand, loans were made supporting cotton production\u2014which was to say, purchasing the bodies of young African Americans, trafficked from more settled regions of the country.\n\nSeveral other states also indebted themselves wildly in the British and other capital markets. \"In a very short period,\" writes Alasdair Roberts, \"American states had accumulated obligations roughly equal to the combined national debt of Russia, Prussia, and the Netherlands.\" Then, prompted by a bad wheat harvest in England that made Britain a food importer, the price of cotton in Liverpool crashed again in April 1839. Prices of slaves, so fundamental to the Southern economy, took a precipitous tumble\u2014the only major slide in the dollar value of slaves during the antebellum decades. As mortgages crashed and liquidation sales put thousands of enslaved laborers for sale in a depressed market, the interstate slave trade slowed down. In Mississippi, the Union Bank lasted less than two years from its creation before its charter was withdrawn by Governor Alexander G. McNutt on July 10, 1840. By 1841, both of the Mississippi state banks had suspended interest payments on their $7 million worth of bonds. Eight states defaulted on their bonds, plus the Territory of Florida. All but Mississippi and Florida eventually resumed payment on at least some of them, though Louisiana, Arkansas, and Michigan repudiated part of them.\n\nThe Republic of Texas, which had no extradition treaty with the United States, quickly became notorious as a haven for busted farmers escaping their debts\u2014G.T.T., gone to Texas\u2014and for deadbeats and crooks of all sorts. Texas had no money to speak of, but when Texans did have money\u2014often meaning, when they could borrow it\u2014they tended to spend it on slaves. Sam Houston wrote General William G. Harding of Nashville on July 17, 1841, trying to explain why he hadn't paid back a $500 loan yet:\n\nI have offered every sacrifice in property, but there _is no money in Texas_ , but our depreciated notes. I have upward of twenty five thousand dollars due me, and some of it for years, and I cannot collect as much as will pay one fourth of my land Tax! In addition, two valuable negro boys for which I had paid in cash $2100 previous to my visit to Nashville, ran away last spring to Mexico. Thus you see I am in bad luck\n\nThe State of Mississippi's answer was simple: rather than impose a tax to pay its obligations, it flat-out stiffed its creditors. Alleging legal technicalities, Governor McNutt proposed debt repudiation to the legislature on January 5, 1841. It was blatant theft, based on a bogus legalistic argument, and it became a divisive campaign issue in the subsequent state election. The pro-repudiation forces won, and passed a constitutional amendment that forbade repaying the bonds. Occasioning litigation that dragged on into the twentieth century, the default ruined the name of Mississippi in Europe, and even affected the ability of the US government to borrow there, although the federal government had a clean credit record.\n\nBill collectors prowled Mississippi. When England threatened to invade the state on behalf of its burned creditors, John Quincy Adams moved on March 2, 1843, that any state that found itself at war as a result of repudiating its debts \"will cease thereby to be a State of this Union, and will have no right to aid in her defense from the United States, or any one of them.\"\n\nWhen the Southern states seceded not twenty years later\u2014repudiating debts in the process\u2014British financiers were not eager to lend money.\n\n#   35\n\n# **The Slave Trade to Cuba and Brazil**\n\n_The fruit, thus far, of the measures against the slave-trade, has been the substitution of small, sharp, wet clippers, for the large, clump, dry vessels, of double and treble the tonnage which would now be employed to transport the same number of persons; and there is no telling how far this process of reduction may be carried. 1_\n\n\u2014Nicholas B. Trist, 1839\n\nAT SUNDOWN ON JULY 31, 1834, some 775,000 enslaved people (sources vary as to the exact number) in the British West Indies became free\u2014technically, at least, though most remained as \"apprentices\" until 1838. Twenty million pounds was allocated to compensate slaveowners for their lost property, but the newly freed Afro-Antilleans were not paid compensation for their stolen labor or their stolen persons. Some forty-seven thousand claimants filed for compensation as ex-slaveowners; the 6 percent of them who were absentees received 8.2 million pounds, or 41 percent of the money. Britain's economy was large enough and diverse enough to be able to easily buy out the slaveowners, something that would have been impossible in the American South.\n\nThe end of slavery in Jamaica was followed by a sharp drop in sugar production there, subsequently cited by Southerners as a boilerplate cautionary tale: there was no production without the whip. Meanwhile, Cuban sugar planters, who continued using the whip, had their greatest opportunity since Saint-Domingue disappeared from the market forty years before.\n\nCuba didn't have a domestic slave trade. Like every place else that raised sugar, the growth rate of its enslaved population was negative. Cuba's slave market clamored for more Africans. Now that Britain was no longer trying to stop American commerce and was, pursuant to treaty, respecting American vessels at sea, blockade runners and privateers were no longer called for. But the Baltimore shipyards still did business building their fast-sailing boats, which could elude capture by the British Navy better than any other vessel. Even as Baltimore traders were shipping African Americans down South, the city's maritime industry was doing a big business illegally servicing the African slave trades to Cuba and Brazil with impunity, in the absence of any will to prosecute. Its prolific shipyards turned out schooners with special-shaped hulls for the thoroughly prohibited African slave trade, which was operating massively to Cuba and Brazil.\n\nFernando VII of Spain\u2014remembered as the \"Felon King,\" he dispensed with Spain's short-lived constitutional government to restore absolute monarchical power\u2014accepted a payment of \u00a3400,000 from Britain in return for criminalizing the African slave trade to his domains as of May 30, 1820. After he signed the compact, Spain and Britain set up a Mixed Court in Havana with officials from both countries to emancipate Africans from captured ships. In Brazil, the world record-holder for numbers of African slaves by far, a similar Mixed Court of Portuguese and British was established.\n\nFernando all but laughed in Britain's face. Cuba's prosperity\u2014 _his_ prosperity\u2014depended on a constant flow of slaves, with the creole and Spanish planters of Cuba for a market. The global cholera epidemic had reached the sugar plantations of Cuba, where by 1833 thousands of slaves had died and \"nearly depopulated... several estates,\" intensifying the demand for labor, even as new lands continued to be converted to sugar.\n\nParticipation in this trade by US citizens was defined by US law as piracy and punishable by hanging. But President Jackson didn't care, and he wasn't in an enforcing mood. His consul in Havana was Nicholas Philip Trist, whose credentials, both as a Jacksonian and as a staunch pro-slavery man, were impeccable for this important patronage position.\n\nWell-educated and suavely mannered, Trist was a link between the worlds of Jefferson and Jackson. He had been tutored in law personally by his wife's grandfather Thomas Jefferson in their hometown of Charlottesville. He had been Jackson's private secretary in 1831 and was a lesser member of Jackson's unofficial circle of advisors that the Calhounites dubbed the Kitchen Cabinet.\n\nHe arrived in Havana in 1833, the year before General Miguel Tac\u00f3n became the Spanish captain general of Cuba, and remained there until 1841, bringing Virginia Jefferson Randolph Trist there to live with him. Trist, who gave slave captains of various countries permission to fly the star-spangled banner, seems to have come to an understanding with Tac\u00f3n.\n\nAs the British captured slave ships, they sent most of the slaves thus emancipated to Sierra Leone, but some thousands were also brought to Havana, where they were supposed to be set free. Unfortunately for them, Tac\u00f3n and his colleagues, principally including monopolist fishmonger Francisco Mart\u00ed (\"Pancho Marty\"), had a business reselling the _emancipados_ back into slavery, until the British in 1835 realized what was happening and stopped handing them over. One formerly emancipated African woman wound up being the property of Trist, who hired her out, collecting $2.50 a week for her services.\n\nNow that slave ships were illegal pursuant to Fernando's deal with Britain, they had to make payoffs, which, it was charged, made their way up the Spanish political channels. A slaver who played the game got preferential treatment, including a privilege no one else had: to enter the harbor after dark. Tac\u00f3n took a cut from the traders, reportedly a half-ounce of gold per captive. Slavers could well afford the payoffs; by 1840, Cuba was producing 21 percent of the world's cane sugar. Trist estimated in an 1839 letter that Tac\u00f3n was making more than $200,000 a year from the slave trade, \"a sum which, however respectable in itself, does not appear of very startling magnitude when compared with the value of twenty thousand slaves, which is about the number landed within the region.\"\n\nWe don't have a number for what Trist made. It seems unlikely that he turned the US consul's office into a slave-trading clearing house as a purely charitable act. But though his household finances had been damaged by Jefferson's impoverishment, he did not leverage his activities into permanent wealth: he constantly complained about his debts, he continued as a government functionary, and he was poor later in life. Working for perhaps the most anti-British president ever, he seems to have seen his enabling activity as a patriotic, pro-slavery act, designed to give the British navy as much trouble as possible.\n\nAccording to the British commissioner J. Kennedy in Havana, Trist in 1836 \"declared he would not even open a letter from us in future.\" The British commissioners repeatedly complained to the US government about Trist, and he was finally recalled to Washington. Horace Greeley's antislavery the _New-Yorker_ reported in October of that year that _\"Mr. N.P. Trist_ , Consul at Havana, has been ordered home by the President, to make answer to the serious accusations against him. The charge of fitting out _slavers_ from Havana with American papers is the most formidable.\"\n\nAfter John Quincy Adams interceded, Alexander Hill Everett was sent to Havana to investigate Trist's dealings with the slave traders. What he found was shocking: Trist had been registering slavers as US ships and allowing them the use of the American flag, along with false bills of sale and blank registries with his signature that could be filled out to show Spanish or Portuguese ownership. John Quincy Adams thought it \"perfectly conclusive of the guilt of Trist in conniving at, aiding and abetting, by all means in his power, the African slave-trade by Americans, Portuguese, and Spaniards.\" The British commissioner J. Kennedy told Everett that \"prior to 1836 we have no account of any vessel sailing hence under the United States flag to Africa, to be employed in Slave Trade,\" but in October 1836 five American vessels left Havana for Africa, a month after arriving from the United States\u2014apparently from Baltimore\u2014\"equipped for the slave trade,\" carrying lumber with which the crew would construct a belowdecks level once the vessel reached Africa. Eleven American-flagged vessels sailed from Cuba for Africa in 1837. As it became clear that the traffic could be conducted with impunity, it picked up: in 1838, there were nineteen American-flagged slave ships; and in 1839, twenty-three. The post of Portuguese consul in Havana was vacant for almost two years, and Trist filled in, authorizing Brazilian slave deals as well, thus servicing the two major African-buying territories.\n\nNewly built boats sailed from Baltimore to Havana, then on to Africa with an American captain, or an American pretending to be the captain, or sometimes a foreign captain pretending to be an American, with an all-Spanish or Portuguese crew or even with an American crew, often switching flags once they arrived in Africa and took on captives. Without the American flag on the way back, the ships were susceptible to boarding and confiscation by the British navy, but the danger of being captured before the return voyage had been eliminated, and if caught, the crews were not criminally chargeable: only the ship and the human cargo were subject to confiscation. Many traders thought the rewards great enough to justify the risk.\n\nTrist brokered one deal in 1838 for a Spanish slave trader in Cuba to buy a Baltimore schooner that sailed for Africa with a Spanish crew, under an American captain and flag, with the name _Ontario of Baltimore_ painted on her stern. The British captain's report read, \"Her sale was, no doubt, effected at Havana, although the bill of sale mentioned it to have taken place in Brass [present-day Nigeria]. In this instance the American flag gave unqualified protection to the slave trade.\" At some point, the flag was taken down; the captain apprehended the _Ontario_ \"with 220 slaves on board. She was under Spanish colors, but had no papers whatever.\"\n\nGeneral Tac\u00f3n remained at his post for fifteen years; the money from his wide-open clandestine slave trade paid for a building spree of historic dimensions in Havana, adjacent to the old city in what is now called Centro Habana. Pancho Marty built one of the largest and finest theaters in the world, Havana's Gran Teatro Tac\u00f3n, which opened during Carnaval on February 18, 1838, with five floors corresponding to social classes. According to a British Commissioners' report to Parliament in 1839:\n\nan astonishing number of new estates have been opened throughout the island within the last two years. In the district of Cienfuegos, of 40 estates now working there, 27 have been of recent formation... many [new plantations] have been commenced by American and some even by British subjects, who will thus, of course, give considerable impetus to the Slave Trade by means of their capital, industry, and skill.\n\nThe British rear admiral George Elliot, tasked with enforcing the ban on the slave trade, asked for clarification of his orders on February 6, 1839:\n\nThe probable object of using the American flag will be to protect the vessels up to the time of the cargo being ready for shipment; then to go through the farce of selling the vessel to a Portuguese or Spaniard.\n\nBut, in case of the capture of vessels with _slaves on board, under the American flag_ , I should beg to know what is to be done with the man passing for the American captain?\n\nA week later, he wrote: \"the use of the American flag is becoming rapidly more general in the protection of the Spanish slave-vessels.\" Elliot began capturing ships whose captains claimed to be naturalized US citizens. \"Several of the slave-dealers,\" he wrote, \"have declared their intention to have an American sailing-master in each vessel, and American colors.\"\n\nThe traders sold slaves into the Republic of Texas, which was a haven for illegal slave trading. Hugh Thomas writes that Charles David Tolm\u00e9, the British consul in Havana, \"in 1837 thought that 1,500 slaves might have been secretly carried to Texas in the previous few years.\" The Virginia-born Sam Houston put a stop to that, when on December 19, 1836, he signed a \"Proclamation Against the Slave Trade,\" which declared that \"the importation or admission of Africans or negroes into this Republic\" was \"forever prohibited and declared to be piracy,\" with one significant exception: if they came from the United States of America. In other words, he locked down Texas as a market for the US domestic slave trade.\n\nThe _Baltimore American_ of July 4, 1838, reported that \"A noble corvette ship, the Venus, Captain Wallace, pierced for 18 guns, built in this city on foreign account, is also ready for sea. She is, we learn, the sharpest clipper-built vessel ever constructed here, and according to the opinion of nautical men, must outsail any thing that floats.\" Her Majesty's judge in Havana saw this item reprinted in the _Diario de la Marina_ , when the ship arrived in ballast with a cargo of bricks after making the twenty-four-day sail from Baltimore to Havana, quoting it in a report that continued:\n\nThe Venus is destined for Mozambique, and is arranged to bring as many even as 1,000 negroes; in which case, it is said, she would clear to the speculators from $100,000 to $200,000 in her first voyage\u2014her cash price being estimated at $50,000, and the expenses of cargo and slaves at another $50,000.\n\nOn the subject of vessels going equipped under the American flag to the coast of Africa, there to be pretended to be transferred for the first time to some Portuguese or Spanish owner, I have had several conversations with the American consul at this place [Trist], a gentleman of high character and of considerable reading and observation. I regret, however, to say that I have received only the most discouraging replies on every point relating to the prohibited traffic; and to add, that this seems the general feeling here of the American community. They all seem to declare that... England may as well think of closing up the work-shops of Birmingham, where they say the bolts and shackles are manufactured, as call on America to forbid the sailing of vessels equipped with them. In answer, I have not hesitated to express my disbelief of the shackles coming from Birmingham, and to declare my full conviction that at no port whatever, in England, would they allow any such articles to be shipped, had they any idea of their being intended for such a purpose.\n\nI regret to have also to inform your lordship that, during the suspension of the Portuguese consul, as I have previously stated, the American consul has been acting _pro tempore_ in that character.\n\nThe cargoes\u2014the masses of imprisoned humans down in the hold\u2014were getting larger; the _Venus_ arrived back from Africa in Havana's harbor with 860 captives on board. Out of Havana, then, slave vessels carrying large numbers of Africans were being run by Spanish, Cuban creole, Portuguese, Brazilian, and United Statesian operators under the protection of the US flag. Some returned from Africa to Cuba, others to Brazil. The British captain Brunswick Popham wrote to Admiral Elliot that he did not want to exceed his instructions by arresting an American, \"feeling that I should not be borne out, in interfering with a citizen of the United States; of which, it appeared to me, the American Government evinced no disposition to tolerate, _even in very extreme cases.\"_ 23 (emphasis in original) Popham closed his letter with:\n\nIt has been mentioned by Spaniards and Portuguese slaving on this coast, that, were it not for the very active co-operation of the Americans, the slave-trade would very materially decline\u2014in fact, be but feebly carried on. I do not doubt, from all that I hear, that the citizens of the United States (generally of Baltimore) are more deeply interested in the slave-trade to Havana and Brazil than is generally supposed.\n\nAmong the papers dealing with the affair that were published as part of Van Buren's annual message at the end of 1840 was Trist's rambling defense, in which he professed indignation at the slave trade while demonstrating a close knowledge of it, and resorted to a change of subject to the classic y'all-do-it-too pro-slavery trope: insulting the British for profiting off the labor of a hypothetical girl working in the Lancashire textile mills.\n\nTrist (for whom a middle school in Meraux, Louisiana, is named) figures in the best-known case of American slavery law from the period. He authorized the voyage of the _Tecora_ , whose captives from Sierra Leone were transferred in Havana to the schooner _Amistad_ , which coasted along toward Puerto Pr\u00edncipe (Camag\u00fcey). The captives on the _Amistad_ overpowered the ship and tried to sail back to Africa. But they didn't know how; the mates, hoping to have the mutineers all captured, brought the ship on a northwest course instead. They were ultimately captured by the US Navy floating off Long Island, New York.\n\nThe Cuban slaveowners sued to have their property returned. John Quincy Adams argued the case for two days in 1841 before the Taney Supreme Court and won the Africans' freedom, based on the notions that the United States had no jurisdiction and that they could not have been legally enslaved. He asked the court: \"my clients are claimed under the treaty [of 1795, between the US and Spain] as merchandise, rescued from pirates and robbers. Who were the merchandise, and who were the robbers? According to the construction of the Spanish minister, the merchandise were the robbers, and the robbers were the merchandise. The merchandise was rescued out of its own hands, and the robbers were rescued out of the hands of the robbers. Is this the meaning of the treaty?\"\n\nTrist lost his post in 1841, with the coming of the Whigs. He faced no criminal charges for dozens of cases of using the American flag to cover blatant felonious activity, which would have made him an accessory to the slave trade that was defined as piracy by US law. As Adams remarked in the _Amistad_ argument: \"Say it was a Baltimore clipper, fitted for the African slave trade, and having performed a voyage, had come back to our shores, directly or indirectly, with fifty-four African victims on board, and was thus brought into port\u2014what would be the assistance guarantied by our laws to American citizens, in such circumstances? The captain would be seized, tried as a pirate, and hung!\" Trist's guilt was never proved in a court, nor was he censured by Congress.\n\nSuccessive administrations of the United States government turned a blind eye to American involvement in the African slave trade that had reopened following the Napoleonic Wars, and did little to enforce the law against it as US shipbuilders, captains, financiers, and officials facilitated the trade to Cuba and Brazil. But these African slave ships did not come to the United States. The government _did_ effectively police the importation of Africans to the United States, because that was a protected market.\n\nWithout that protection, Virginia's economy would probably have collapsed. James Henry Hammond of Columbia, South Carolina, noted in his diary after dining with \"Dr. Carter of Virginia\" on February 12, 1841, that \"he told me that in Virginia now planters realized nothing except from raising slaves and the increase in the value of their lands in consequence of improvements from marling [spreading quicklime].\" Then, with a bit of snark, he added, \"I suspect the rise in lands is rather imaginary.\"\n\n_Butler Island, Georgia, May 2013._\n\n#   36\n\n# **Heaps and Piles of Money**\n\n_You cannot think (to return to the songs of my boatmen) how strange some of their words are: in one, they repeatedly chanted the \"sentiment\" that \"God made man, and man makes\"\u2014what do you think?\u2014\"money!\" Is not that a peculiar poetical proposition? 1_\n\n\u2014Fanny Kemble\n\nPIERCE MEASE BUTLER HADN'T wanted his impulsive, high-spirited, strong-willed, self-absorbed, talkative wife, Frances \"Fanny\" Kemble Butler, to come South, but she wouldn't take no for an answer. In late 1838, she traveled to the Sea Islands of Georgia to spend fifteen disturbing weeks as plantation mistress of Butler Island. Her husband had inherited the property from his grandfather the framer: Major Pierce Butler, the father of the fugitive slave clause to the Constitution, who in his day had been the second largest slaveowner\u2014which is to say, the second richest man\u2014in Georgia.\n\nKemble was the superstar young actress who revitalized British theater, then came to America for a year of performances in 1833\u201334 that inspired American girls to wear their hair in \"Fanny Kemble curls.\" Butler assiduously devoted more than a year to courting the famous young woman nearly full-time, which he could do because he did not work, or even have an identifiable profession other than spending money.\n\nIn spite of the sums she was earning from her performances, Kemble's finances were spread thin by her family's expenses, and the handsome, self-assured Butler seemed to offer, among other things, financial stability. But then she found out what being married to a slaveowner meant, in the context of a nineteenth-century marriage. Living with her husband in Philadelphia, she found that Mrs. Pierce Butler was expected not to have a stage career, publish her writing, associate with her former friends, or disagree with her husband in any way. Kemble had not declared herself to be an abolitionist before her marriage, but her diaries suggest that she made a personal connection between her condition as a married woman and that of the enslaved. She lived out her contradictions in public, via her twin careers as writer and actress, in one of the high-profile marriage disasters of the century.\n\nKemble had apparently believed Butler's assurances that he was one of the \"good\" slaveowners. But after he became the full owner of his grandfather's Sea Island estate following the death of his brother in 1836, she saw the reality. Kemble is most remembered today for _Journal of a Residence on a Georgian Plantation in 1838\u20131839_ , her account of the months she passed there. A collection of privately circulated letters, harshly critical of slavery, she ultimately allowed it to be published in 1863 in London in the hope it might help keep Britain from siding with the Confederacy.\n\nIn it, to Butler's everlasting humiliation that his wife had gone so far out of his control, she matter-of-factly blew the whistle on slavery as a system of concubinage and breeding. She wrote of rewards and privileges for childbearing women that were \"indirect inducements to reckless propagation... a woman thinks, and not much amiss, that the more frequently she adds to the number of her master's live-stock by bringing new slaves into the world, the more claims she will have upon his consideration and good-will.\"\n\nKemble shared in the racism of the times, as in her ape-libel description of one of the enslaved who was possessed of a beautiful singing voice (in which, incidentally, she references the African American use of the word \"brother\"):\n\nBy-the-by, this individual _does_ speak, and therefore I presume he is not an ape, ourang-outang, chimpanzee, or gorilla; but I could not, I confess, have conceived it possible that the presence of articulate sounds, and the absence of an articulate tail, should make, externally at least, so completely the only appreciable difference between a man and a monkey, as they appear to do in this individual 'black brother.' Such stupendous long thin hands, and long flat feet, I did never see off a large quadruped of the ape species. But, as I said before, Isaac _speaks_ , and I am much comforted thereby.\n\nAt the same time, she saw the mote when it was not in her own eye:\n\nOne of their songs displeased me not a little, for it embodied the opinion that 'twenty-six black girls not make mulatto yellow girl'; and as I told them I did not like it, they have omitted it since. This desperate tendency to despise and undervalue their own race and colour, which is one of the very worst results of their abject condition, is intolerable to me.\n\nKemble was appalled by \"the meritorious air with which the women always made haste to inform me of the number of children they had borne, and the frequent occasions on which the older slaves would direct my attention to their children, exclaiming, 'Look, missis! little niggers for you and massa, plenty little niggers for you and little missis!'\" After Butler forbade her to continue carrying him requests for better treatment from the enslaved, she received a visit from the pregnant women whose owner she did not want to be, but whose labor supported her and provided a legacy for their two daughters:\n\nThe women who visited me yesterday were all in the family-way, and came to entreat of me to have the sentence (what else can I call it?) modified which condemns them to resume their labor of hoeing in the fields three weeks after their confinement . . Their principal spokeswoman... implored me to have a kind of labor given to them less exhausting during the month after their confinement, I held the table before me so hard in order not to cry that I think my fingers ought to have left a mark on it.\n\nOnce Kemble saw what Butler's fortune really depended on\u2014and realized that he too had been fornicating with enslaved women\u2014the marriage was over, though ending it took years, created a public spectacle, and set in motion a lifelong battle for the affections of the couple's two daughters. Divorce was uncommon in those days, and the law was not friendly to it. South Carolina did not allow divorce at all (until 1949). The suit was filed in Philadelphia, where state laws were relatively liberal on divorce; but the presumption was that children belonged to the father, and Butler kept the daughters. In a legal narrative drawn up for Butler by his attorneys in the course of divorce proceedings, which Butler published and circulated privately, he expressed his view of marriage as a contract between unequal partners:\n\nOne reason, and perhaps the fundamental one, for the ill success which attended my marriage, will readily be found in the peculiar views which were entertained by Mrs. Butler on the subject of marriage... She held that marriage should be companionship on equal terms\u2014partnership in which, if both partners agree, it is well; but if they do not, neither is bound to yield\u2014and that at no time has one partner a right to control the other.\n\nHe recalled that \"although we resided in Pennsylvania, where slavery does not exist, the greater part of my property lies in the State of Georgia, and consists of plantations and negroes. Mrs. Butler, after our marriage, not before, declared herself to be in principle an abolitionist...\"\n\nBut that was before Kemble met Die, who\n\nhad had sixteen children, fourteen of whom were dead; she had had four miscarriages, one had been caused by falling down with a very heavy burthen on her head, and one from having her arms strained up to be lashed. I asked her what she meant by having her arms tied up; she said their hands were first tied together, sometimes by the wrists, and sometimes, which was worse, by the thumbs, and they were then drawn up to a tree or post, so as almost to swing them off the ground, and then their clothes rolled round their waist, and a man with a cow-hide stands and stripes them. I give you the woman's words; she did not speak of this as of anything strange, unusual or especially horrid and abominable; and when I said, \"Did they do that to you when you were with child?\" she simply replied, \"Yes, missis.\" And to all this I listen\u2014I, an English woman, the wife of the man who owns these wretches, and I cannot say, \"That thing shall not be done again[.\"]\n\nOnce independent, she went back to work, paying her family's expenses by giving one-woman readings of Shakespeare plays.\n\nPrices for slaves might go down, but there was always a market for them. After all the banks had suspended specie payments, and planters by the thousands had sworn never to deal with banks and paper money again, there were still hundreds of thousands of enslaved people, whose bodies were the most reliable store of value.\n\nNo free black youth in the North was entirely safe from the \"negro stealers.\" One of the best-known slave narratives, meticulously adapted into an Oscar-winning movie in 2013, has as its full title _Twelve Years a Slave: Narrative of Solomon Northup, a Citizen of New-York, Kidnapped in Washington City in 1841 and Rescued in 1853, from a Cotton Plantation Near the Red River in Louisiana._ It describes how Northup was lured in 1841 from Saratoga, New York, to Washington, DC, with the promise of work. He was kidnapped and sold, becoming a captive of two slave traders infamous for their brutality. At the shipping end was James Birch of the District of Columbia, the same trader who had put Dorcas Allen and her children up for sale. After protesting that he was a free man from New York, Northup received a severe beating from Birch, described in detail, with the threat never again to say such a thing or he'd be killed. \"I doubt not he understood then better than I did,\" Northup wrote, \"the danger and the penalty of selling a free man into slavery.\"\n\nWhile imprisoned in Washington, a woman named Eliza arrived, with a son Randall and a daughter named Emily, who, recalled Northup,\n\nwas seven or eight years old, of light complexion, and with a face of admirable beauty. Her hair fell in curls around her neck, while the style and richness of her dress, and the neatness of her whole appearance indicated she had been brought up in the midst of wealth. She was a sweet child indeed. The woman also was arrayed in silk, with rings upon her fingers, and golden ornaments suspended from her ears. Her air and manners, the correctness and propriety of her language\u2014all showed evidently, that she had sometime stood above the common level of a slave. She seemed to be amazed at finding herself in such a place as that.\n\nAfter two weeks imprisoned in Washington, Northup and the pen's other captives were marched to a steamboat in the dead of night and taken down the Potomac, then transferred to stagecoaches and finally taken by rail to Richmond, where they were examined and where Northup was chained together in the pen with Robert, a kidnapped free-born black man from Cincinnati. They were put on an oceangoing brig that took on four more slaves at a stop in Norfolk; as they were sailing to New Orleans, Robert died of smallpox. Arriving there, they were taken charge of by Theophilus Freeman, one of New Orleans's largest slave dealers; Northup, who had contracted smallpox, was taken to Charity Hospital and managed to recuperate.\n\nNorthup watched as Freeman sold Eliza's son Randall away, then sold Eliza, refusing the buyer's offer, urged by Eliza's desperate pleading, to sell her daughter Emily to him as well:\n\nHe would not sell her then on any account whatever. There were heaps and piles of money to be made of her, he said, when she was a few years older. There were men enough in New-Orleans who would give five thousand dollars for such an extra, handsome, fancy piece as Emily would be, rather than not get her. No, no, he would not sell her then. She was a beauty\u2014a picture\u2014a doll\u2014one of the regular bloods\u2014none of your thick-lipped, bullet-headed, cotton-picking niggers\u2014if she was might he be d--d.\n\nWhen Eliza heard Freeman's determination not to part with Emily, she became absolutely frantic.\n\n\"I will _not_ go without her. They shall _not_ take her from me,\" she fairly shrieked, her shrieks commingling with the loud and angry voice of Freeman, commanding her to be silent.\n\nAs an unidentified formerly enslaved man, born circa 1845, recalled: \"I've seen them sell women away from little children, and women would be cryin' and they'd slap 'em about cryin'.\"\n\nBiddle's United States Bank of Pennsylvania failed in February 1841. The settlement of its outstanding liabilities on behalf of creditors took years. To try to collect on its debts, the British trustees created the Bacon Trust, headed by John Bacon, which was assigned $12.5 million in assets to recover; 41 percent of them were in Mississippi and another 30 percent were in New Orleans and Mobile.\n\nLouisiana passed a measure allowing debtors to settle at twenty-five cents on the dollar, and in Louisiana, since slaves were considered \"immovables,\" they could not be seized and separately sold. Neither of those conditions held in Mississippi, where the Bacon Trust became the biggest financier and \"probably ranked among the largest slaveholders\" in the state, says Richard Holcombe Kilbourne, who assembled its history out of a mass of archival documents.\n\nThe Bacon Trust's man on the ground, Joseph L. Roberts, actively managed as many as four plantations at a time. The value of mortgage debt, he found, was often compromised by the prior removal of \"the slaves which ma[de] mortgaged debts most safe.\" Once again, coined labor beat coined land: Roberts could not accept land in satisfaction of debts, because it was not salable; slaves, however were: \"Negroes,\" he wrote, \"c[ould] be sold & attain th[e] object but land not.\" The Bacon Trust thus involved itself repeatedly in the person-selling business. Prices were still \"dull,\" but, as Roberts wrote, \"good Negroes I am told will sell readily altho they will not bring high prices.\" Accordingly, Roberts accepted slaves as security, sometimes large numbers of them, and sold them, sometimes at sheriff's sales, sometimes buying them back on his own account.\n\nIn 1846, after Roberts had taken over a Louisiana plantation from a scam artist who had run the place down, his agent \"reported a wretched state of things\u2014Only 53 Negroes large & small; they received 60 Negroes with the place & their natural increase, inclusive of deaths, ought now to have made on the place at least 75 in number\u2014several of the Negroes now there are sickly & inefficient from overwork & exposure\u2014some frost bitten, some ruptured, some branded on their hips as runaways\u2014all without shoes & most of them without winter clothing or blankets.\"\n\nThe frost-bitten people who were property had to be discounted by the British banks' representative. Perhaps their fate was that nightmare of the enslaved: being sold at auction as \"refuse slaves.\"\n\n#   37\n\n# **The Slave Power**\n\n_A slave dreads the punishment of stripes more than he does imprisonment, and that description of punishment has, besides, a beneficial effect upon his fellow-slaves._\n\n\u2014Representative James K. Polk on the floor of the House, April 27, 1830\n\nTHERE NEVER WAS A president of the United States from Mississippi. But Tennessean James K. Polk was the absentee owner of a plantation in Mississippi, for which he bought slaves on an ongoing basis while he was a congressman, and then while he was president.\n\nPolk's father, Sam Polk, was a land speculator in Tennessee, of the same generation as land speculator Andrew Jackson, who was an occasional visitor to the household when Jimmy Polk was growing up. Though Polk was as frail as Jackson was tough, the diminutive, sickly Scotch-Irish-descended lawyer was Jackson's loyal follower. Polk, who suffered all his life from bowel disorders, was apparently sterile and perhaps impotent as the result of an unfortunate operation to remove a urinary stone, performed without anesthetic when he was sixteen. His devoted and religious wife, Sarah Childress Polk, who had no children to occupy her, was instead an active participant in Polk's political career. She allowed no work or amusements on Sunday, would not serve spirits stronger than wine with dinner at White House functions, and would not sponsor balls with dancing. In order to cut down on the expenses of running the White House, which had to be borne by the president, she discharged its ten-member staff and replaced them with slaves who lived in the White House basement, which had drainage problems and frequently flooded.\n\nFirst elected to Congress in 1825, Polk carried Jackson's water in the House, and with his backing became Speaker for two terms. Hoping in vain to live to an old age in which his plantation income would support him while he lived in a big house in Nashville, he bought young people, typically one at a time, as the opportunity came along or as his farming needs seemed to require.\n\nPolk kept a diary, intended for posterity, that does not mention slaves. But perhaps because he died suddenly, his correspondence was never sanitized, and it contains an extensive paper trail, including a number of letters that document the amount of time and money he spent buying slaves while in office as well as his injunctions to keep it secret. The title of William Dusinberre's book on the subject expresses it: _Slavemaster President: The Double Career of James Polk._ In his spare time, while directing a war of conquest that would expand slavery and thus sharply increase the valuation of existing slaveholdings, Polk also directed from the White House, via an overseer, a slave-labor plantation of which he was an inept absentee landlord.\n\nIn keeping with the common capital accumulation scenario of the South, Polk rarely sold slaves; he bought them in order to grow his value through their appreciation in price and increase in number. People frequently came offering deals on slaves to his brother-in-law, who bought for him. His collected correspondence contains frequent reference to the business of \"negroes\" until late in his life, as well as frequent references to their illness.\n\nPolk's slaves were a miserable, unhealthy lot who couldn't even sustain \"natural increase\" over the years. Instead, Polk tried to increase his wealth by buying more slaves\u2014which meant people twenty-one or younger. Every one of them would have been torn away from a family before being sold, so that the social composition of his plantation labor force followed the Deep South cotton-plantation model: a collection of young people bought like mules and cut off from their familiar lives, with few natural or local connections among them, in an atmosphere of violent, daily repression.\n\nLike any absentee plantation owner, Polk had to rely on his overseer, who whipped the workers unmercifully. An overseer's worth was measured in short-term results\u2014making the best crop possible _this_ year\u2014so his interest was at cross-purposes with the owner's stake in the workers' longevity. In 1832, during the cholera epidemic, Polk, then a congressman, received a letter from overseer Herbert Biles, revealing that in spite of the entire work force being sick, Biles had made them produce twenty-five thousand pounds of cotton:\n\nI hav bad news to writ to you. Lucys youngist Child died on the 16th of the instant and the little orphin Child died yester Day and the other little girl I am afraid will go the same way.... Seasor has bean under the Doctr ever senc you ware hear with the Liver Complaint but is likley to recover. The rest of the niggars the most of them has bean sick.... I hav got out About twenty five thousand lb of Cotton and hav got on[e] lo[a]d Reddy to send down but the Colry [cholera] got to Memphis and Alarmed the people so that thay ware Afraid to gone thair.\n\nPolk's farm must have been a true horror. His slaves ran away much more than was usual on a well-run plantation. One of them, Gilbert, did it _ten_ times. After Chunky Jack and Ben had absconded and been apprehended, Polk's brother-in-law and business advisor Silas M. Caldwell wrote him on January 4, 1834: \"Your negroes here are very much dissatisfied. I believe I have got them quieted. Some others spoke of running away...\" Caldwell's letter continued, reporting a crib death (which at then-current market rates meant a loss of perhaps $75 to Polk's net worth), and note the reference to the deceased child as \"it,\" and apparently to the labor force as \"stock\":\n\nElizabeths child died last night; she smothered it somehow. No person knew it was dead until this morning. It was a very fine child... I had it Buried to day. Maria has a fine boy about one Month old. I Bot you a very fine mule and Brot down with me. I gave $100 for it out of a drove. Your stock looks very well here, your negroes have plenty of Milk.\n\nAnother brother-in-law and business adviser, James Walker, wrote Polk that \"I am not sure that to sell some of your most refractory negroes to _real negro traders_ would not be the best thing you could do to reduce the balance to subjection, and if _Chunky_ Jack, could with propriety be sold it ought to be done.\" (emphasis in original)\n\nBy September 1834, Polk had sold his Tennessee plantation and was already on the trail of acquiring more labor in expectation of getting some of that unplowed Mississippi farmland that Jackson had \"negotiated\" away from the Indians. Hours after having closed the deal, he wrote to Sarah, telling her to keep \"the negroes\" ignorant of it, and bragged about having gotten a new slave and hoping to acquire another, all without spending any cash:\n\nI am resolved to send my hands to the South, have given money to _James Brown_ to buy a place & have employed _Beanland_ as an overseer.... I bought Mariah's husband a very likely boy\u2014about 22 years old for $600. And paid for him with the notes I held on his master for land which I sold him several years ago....\n\nP.S.... The negroes have no idea that they are going to be sent to the South and I do not wish them to know it, and therefore it would be best to say nothing about it at home, for it might be conveyed back to them....\n\nN.B. Since writing it occurs to me, that I will have to go a day or two out of my way, with the hope of getting a negro in payment of a debt due me by Silliman to whom I sold land.\n\nPolk's whip-happy overseer Ephraim Beanland wrote him on October 4 that Chunky Jack had disappeared into Shawnee Town, opposite Memphis across the Mississippi River, a hidey-hole that would have been a terrifying place to a white farmer: \"On last nite I got home from the Arkensis and I hearde of Jack but never co[u]ld get Site of him and it Is supposed that he is in Shauney villige which I was advised not to go theire for they is A den of thieves and to tell you the fact I donte [think] that you will ever git him.\"\n\nWalker, who together with partners ran a stagecoach line from Nashville to Natchez that relied on post office contracts and kept the family connection hidden through the use of a front man's name, advised Polk on October 15, 1839, of strategies for creating an annuity for the family of Polk's deceased brother:\n\nThe question... would be, in what kind of stocks the money could be invested with perfect safety. I should say not Bank Stock, for experience has proved that not a perfect safe investment. State Bonds bearing an interest of 6 pr. Cent would do and I think would certainly be safe. This investment could now you know be readily made. It is however probable, that a still better & more secure investment could be made, and the money and interest undoubtedly secured, by being upon land and negroes to double the amount.\n\nIn order to keep Tennessee from falling to the Whigs, Democratic party enforcer Polk left the House to run for governor in 1839 for a two-year term; he was elected, but then was subsequently turned down by voters for a second term, then lost the next election two years later.\n\nIsaac Franklin, who according to testimony \"was warm and decided in his politics,\" was a \"strong Polk man.\" We have found no documentation of Polk and Franklin having met, done business, or corresponded, but there is no way Polk didn't know Isaac Franklin, who had the finest house in his state, was one of his wealthiest supporters, was a kingpin of the trade of which Polk was such an eager customer, and moreover was a man who knew the value of connections.\n\nPolk was the slave traders' candidate. Indeed, he was the embodiment of what the one-term antislavery Ohio senator Thomas Morris, in a speech of February 9, 1839, accompanying his presentation to the Senate of abolition petitions with \"thousands of signatures,\" called the \"slave power of the south.\" Morris juxtaposed this image with what he saw as the other great evil, the \"banking power of the north.\" \"The cotton bale and the bank note,\" he declaimed, \"have formed an alliance; the credit system with slave labor.\" Morris noted the outsized capitalization of the South in slaves, noting Henry Clay's valuation of it at $1.2 billion and declaring that sum larger than the world's money (i.e., precious metal) supply, which was an exaggeration but not an unthinkable one:\n\nPermit me to tell the country now what this power behind the throne, greater than the throne itself, is. It is the power of SLAVERY. It is a power, according to the calculation of the Senator from Kentucky, which owns $1,200,000,000 in human beings as property; and if money is power, this power is not to be conceived or calculated; a power which claims human property more than double the amount which the whole money of the world could purchase.\n\nMeanwhile, the experience of slavery was getting worse as plantation management became more efficient. The antebellum cotton plantation of the Deep South was a much harsher regime than that of the Upper South; life as a worker there was hell on earth. Cotton planters extracted continually increasing amounts of labor through torture via a system not unlike modern time-metric monitoring of workers that Edward E. Baptist memorably calls \"the whipping machine.\" Under this regime, failure to meet production targets was punished by vicious, lacerative whippings at the end of the long work day. And the production targets were continually increased, pushing the worker ever harder. With this abusive, efficiency-conscious system in place, cotton production reached levels not seen again until mechanization.\n\nMartin Van Buren's entire presidency was spent combating the post-panic economic depression, and he was beaten by a Whig in the 1840 election. The Whigs had decided that if the American people wanted a warrior president, they'd run one. Their candidate, Virginia's William Henry Harrison, hadn't beaten the English like Jackson had, but he'd massacred Native Americans in the battle of Tippecanoe twenty-nine years earlier and had cheated them out of some three million acres of land in what we now call the Midwest. This land was above the Missouri Compromise line and as such would be free soil, but Harrison had hoped to make it slave territory the way he'd tried to make free-soil Indiana into a slave state when he was its territorial governor in 1804. The ticket's rhyming, alliterative slogan, permanently engraved in American memory, was \"Tippecanoe and Tyler too\"; Harrison's running mate, John Tyler, was an erstwhile Jacksonian and a very conservative states'-rights man\u2014a slaveowner whose family went back to the seventeenth century in Virginia, and whose father had participated in the ratification of the Constitution.\n\nLooking back at Van Buren's term, Adams wrote in his diary:\n\n[Jackson's] personal popularity, founded exclusively upon the battle of New Orleans, drove him through his double term, and enabled him to palm upon this nation the sycophant who declared it glory enough to have served under such a chief for his successor. Both the men have been for twelve years the tool of Amos Kendall, the ruling mind of their dominion.\n\nHarrison was president for only thirty-two days before he caught a cold and died, occasioning the first vice presidential succession: Tyler took office on April 4, 1841. Adams and Clay were outraged that Tyler did not meekly assume the post of \"acting president\" but, with all but a month of a four-year term to serve, declared himself a full president, which has been the model for vice presidential succession ever since.\n\nIn later life, Tyler's states'-rights enthusiasm was directed toward the cause of secession, and in his final days he was elected a member of the Confederate House of Representatives. As president, not surprisingly, Tyler was an aggressive booster of Texas annexation. Adams referred to him in his diary as \"the slave-breeder.\"\n\n\"This was a memorable day in the annals of the world,\" Adams wrote on April 22, 1844. \"The treaty for the annexation of Texas to this Union was this day sent in to the Senate; and with it went the freedom of the human race.\" Adams had been a pro-expansionist, but not any more. For both abolitionists and slaveowners, Texas was about nothing but expanding slavery. That was the year the gag rule in the House of Representatives was finally overturned, and John C. Calhoun threatened that \"if the annexation of Texas is to be defeated by the same sperit [ _sic_ ] which has induced the reception of abolition petitions, it is difficult to say, what may be the consequence.\"\n\nThen a freak accident brought John C. Calhoun into the position of secretary of state as an emergency replacement for Tyler's secretary of state, Virginian Abel Upshur, who was killed, along with seven others, when an enormous wrought-iron gun on board a new steam-powered iron warship he had commissioned exploded at its public demonstration. (Tyler was on board but survived.) As secretary of state, Calhoun's support for Texas annexation merged entirely with his impassioned defense of slavery. In a classic case of diplomatic overreach, Calhoun portrayed the annexation of Texas as an act of self-defense for the Southern states against the possibility\u2014for which there was no credible evidence\u2014of the infiltration by Britain of abolitionists into Texas. He did this in a calculatedly offensive letter to British ambassador Richard Pakenham, which, when leaked by Senator Benjamin Tappan of Ohio and published on April 27, 1844, made explicit to the whole country in ringing, paranoid tones the notion that annexing Texas was essential to preserving slavery. Attempting to show that \"in all instances in which the States have changed the former relation between the two races, the condition of the African, instead of being improved, has become worse,\" Calhoun reached for the census of 1840, citing figures from its demographic category of \"deaf and dumb, blind, idiots, and insane Negroes.\"\n\nFormer president Martin Van Buren seemed like a favorite to be nominated in 1844, but he was against the annexation of Texas. Jackson, seventy-six and dying, took that as a betrayal. Had Van Buren been the one to run against Clay, Texas would not have been an issue in the election, because neither were annexationists. But Jackson wasn't about to let that happen, and instead he threw his support to James K. Polk.\n\nAfter twenty-five years as a professional politician, Polk appeared to be a has-been. But he was pro-slavery, pro-expansion, and anti-tariff, and was thus the perfect presidential candidate for Southerners. For sectional balance, his running mate was George M. Dallas, former mayor of Philadelphia and James Buchanan's great rival in Pennsylvania.\n\nThe election turned on the issue of bringing Texas into the Union. William Seward described in a letter to Thurlow Weed a Whig rally at which \"one of the banners, and the most popular one, was a white sheet, on which was Polk dragging a negro in chains after him.\"\n\nLouis Hughes recalled in his memoir that when he was being taken by coffle down South at the age of twelve,\n\nas we passed along, every white man we met was yelling, \"Hurrah for Polk and Dallas!\" They were feeling good, for election had given them the men that they wanted. The man who had us in charge joined with those we met in the hurrahing. We were afraid to ask them the reason for their yelling, as that would have been regarded as an impertinence, and probably would have caused us all to be whipped.\n\nThe term Thomas Morris had popularized\u2014the Slave Power\u2014became a commonplace of abolitionist political discourse. A transform on Jackson's demonized \"Money Power\" of financial capitalism, it was a useful phrase with which to describe something that really did exist. Eric Foner writes, citing Marvin Meyers: \"If... the Money Power was the 'master symbol' for the Age of Jackson, the Slave Power was equally effective as a symbol for all the fears and hostilities harbored by northerners toward slavery and the South.\"\n\nOnly the abolitionists wanted to end slavery in the Southern states immediately; no ranking governmental official proposed such a thing, certainly not Adams. Despite the spectacularly belligerent reaction by the Slave Power to abolitionist literature, white abolitionists were few in number in the 1830s and '40s. But many non-abolitionist white northerners were antislavery, less because of compassion for black people than because they saw slavery as setting an unacceptably low floor for working conditions.\n\nThe sectional controversy over slavery was about its expansion to the new territories. Free labor did not want to go where there was slavery, and slaveowners felt locked out of any place where they couldn't sell slaves. Would the nation be a slave-labor nation with a free-labor section confined to the northeast, or a free-labor nation with a slave-labor section confined to the southeast? Or would it be all one way or the other: all-slavery or all-free? In 1844, Texas was the battleground.\n\nOf the ten United States presidents up to that point, only two had been antislavery, both of them named Adams. Martin Van Buren, who grew up in a household that owned slaves who worked at the family tavern in Kinderhook, New York, had been \"servile\" to the Slave Power, in John Quincy Adams's words, while riding Jackson's power train.\n\nAs president, Van Buren had resisted the clamor for prohibition of slavery in the District of Columbia, but now he had been purged by his own party, from Jackson on down, over the annexation of Texas as a slave state.\n\nFor many observers, Polk's nomination represented the final takeover of the Democratic Party by the Slave Power, even though South Carolina, responding to John C. Calhoun's wishes, did not participate in the nominating convention and remained standoffish.\n\nBoth major parties held their 1844 conventions in Baltimore, an indication of how central the city had become to the country's communications. Polk's nomination was announced by the newly patented electrical telegraph, a machine that would make Samuel F. B. Morse's well-connected business partner Amos Kendall very wealthy. Committing from the outset to be a one-term president, Polk won the election, barely. He was what in another era was called a wonk\u2014focused on his agenda, which was to take as much of Mexico's territory as he could, all the way out to California, and to settle the Oregon question with Britain.\n\nThe lame duck Tyler signed the Joint Resolution for Annexing Texas on March 1, 1845. It contemplated dividing Texas up into five states, each of which, needless to say, would get two senators. After becoming president, Polk signed the Joint Resolution for the Admission of the State of Texas into the Union, which did not contain the five-state clause, on December 29.\n\nMexico's government had long since announced that it would consider the annexation of Texas by the United States to be an act of war.\n\nPolk was eager to have a Mexican War.\n\nThe Mexican conquest was a warmup for the war that would be fought fifteen years later between Richmond and Washington. Many of the generals who fought in the later war, both Union and Confederate, knew each other from serving together in the Mexican War. Ulysses S. Grant, a junior officer in that war, later wrote in his memoir that \"I was bitterly opposed to the measure [of annexing Texas], and to this day regard the war which resulted as one of the most unjust ever waged by a stronger against a weaker nation.\" Grant's quick summary of it will do for our purposes:\n\nAmericans who had received authority from Mexico to colonize... paid very little attention to the supreme government, and introduced slavery into the state almost from the start, though the constitution of Mexico did not, nor does it now, sanction that institution. Soon they set up an independent government of their own, and war existed, between Texas and Mexico, in name from that time until 1836, when active hostilities very nearly ceased upon the capture of Santa Anna, the Mexican President. Before long, however, the same people\u2014who with permission of Mexico had colonized Texas, and afterwards set up slavery there, and then seceded as soon as they felt strong enough to do so\u2014offered themselves and the State to the United States, and in 1845 their offer was accepted. The occupation, separation and annexation were, from the inception of the movement to its final consummation, a conspiracy to acquire territory out of which slave states might be formed for the American Union... the Southern rebellion was largely the outgrowth of the Mexican war.\n\nFlorida, the obsession of presidents from Jefferson to Jackson, finally became a state on March 3, 1845. Its first senator was a secessionist who would ultimately join the Confederate Congress: the sugar planter David Levy, who was already serving as Florida's territorial representative to Congress. Levy, who owned some thirty thousand acres in the Jacksonville area, and whose Sephardic Moroccan-born father Moses Levy had been a weapons dealer in Puerto Rico and made a fortune in shipping in Cuba, became the first Jewish US senator. The following year he married a politically connected Christian woman, changed his name to David Yulee, and raised his children as Christians.\n\nThe South's black-or-white two-caste system worked to the advantage of Jews. In the North, where anti-Jewish sentiment could be intense, they were Jews; in the South, they were white people. \"For Southern Jews, loyalty to the Confederacy was often a matter of intense personal gratitude,\" writes Howard M. Sachar. In Richmond, New Yorker Frederick Law Olmsted noted their presence with racialized distaste: \"very dirty German Jews... abound, and their characteristic shops (with their characteristic smells, quite as bad as in Cologne), are thickly set in the narrowest and meanest streets, which seem to be otherwise inhabited mainly by negroes.\"\n\nThough more Jews went to the urban areas of the North than to the South\u2014Robert N. Rosen estimates 120,000 in the North versus 25,000 in the South\u2014Southern Jews played an important role as commercial intermediaries in the emerging slavery nation. The Jewish peddler, a fixture in many places of the world during the nineteenth century, and seen in every part of the United States, found a special niche among the plantations of the South. Charleston, home of the first Reform congregation in the United States, had the nation's largest Jewish community in 1820\u2014about seven hundred\u2014until New York surpassed it. Until about 1830, Jews were part of Charleston's elite, and, like most of Charleston's white population, most of them were slaveowners.\n\nPerhaps no story better illustrates how the explosive profits to be made in the cotton kingdom were foundational to American business than that of Chaim (or Heyum) Lehman, a twenty-two-year-old cattle dealer and wine merchant who arrived into New York's harbor on September 11, 1844. He was one of perhaps one hundred thousand Ashkenazi immigrants who came from Central Europe and the German states in the years between 1800 and 1860, transforming the American Jewish community, which had previously been dominated by Sephardim. Lehman had been forced to leave his Bavarian hometown of Rimpar, where the law required the departure of second and subsequent sons of a Jewish family. Changing his name to Henry, he sailed down to Mobile and traveled upriver, where he began a career as an itinerant peddler, one of many who sold dry goods and supplies to plantations and also served as conduits for news. The workaholic, well-informed merchant quickly built up enough of a stake to open a general store in Montgomery a few months before it became the state capital in 1846.\n\nWith the banking system still in post-Jackson disarray and hard currency nowhere to be had, farmers paid for goods at Lehman's store in cotton, which he happily accepted. His brother Emanuel came over to join him; then in 1850 came another brother, Mayer. Though the Lehmans did not convert to Christianity as some did, they assimilated; they ate pork, did business on Saturday, spoke English with Southern accents, and were pro-slavery.\n\nWe do not know whether Lehman ever sold slaves, but it would not be surprising if he did. It was certainly not illegal, it could be profitable, and few merchants did not at one time or another, in one way or another, become involved in a slave sale. Jacob Barrett, a Jewish merchant in partnership with his brother Judah in Columbia, South Carolina, and another brother, Isaac, in Charleston, sold:\n\ndry goods, groceries, provisions, liquors, (both at wholesale and retail,) hardware, crockery, shoes, hats and saddles. Besides all this, he sometimes bought a drove of hogs and made bacon for sale. He also speculated in negroes, horses and real estate.... a cargo of government soldiers' condemned coats or jackets, bought at a great sacrifice, were readily taken by the planters for their negroes at an advance of one or two hundred per cent. over cost. A gang of some twenty negroes from Charleston he soon disposed of at very large profits, keeping for his own use Armstead Booker, a good-looking, active carriage driver and barber, who attended to his horses and in the store, and Aunt Nancy, a first-rate cook, with her children.\n\nBarrett subsequently \"married the daughter of his cousin, Jacob Ottolengui of Charleston, another speculator in Negroes, and claimed before the Civil War to have around a thousand slaves working his rice plantations near the Savannah River,\" in the words of Bertram Wallace Korn.\n\nAll Southern towns of any size had Jewish residents in their business community. Some of them were, like other Southern merchants, slave traders, but the domestic slave trade was in no way a specialty of Jewish merchants. Jews were a tiny minority and were not disproportionately represented in the ranks of slave traders, nor were any of the biggest slave traders Jewish. Bancroft's list of seventy slave traders in Richmond lists only three Jews. The most important Jewish slave-trade firm was probably the Davis family of four brothers in Petersburg and Richmond, Virginia, who were named in Harriet Beecher Stowe's _The Key to Uncle Tom's Cabin_ , quoting a letter from abolitionist Gamaliel Bailey: \"The Davises, in Petersburg, are the great slave-dealers. They are Jews, came to that place many years ago as poor pedlers; and, I am informed, are members of a family which has its representatives in Philadelphia, New York, &c! These men are always in the market, giving the highest price for slaves. During the summer and fall they buy them up at low prices, trim, shave, wash them, fatten them so that they may look sleek, and sell them to great profit. It might not be unprofitable to inquire how much Northern capital, and what firms in some of the Northern cities, are connected with this detestable business.\"\n\nBut a regionally bounded business like slaves wasn't Henry Lehman's interest, nor was tying up cash in long-term physical assets. He was into cotton and credit\u2014which was inseparably bound up with the slavery industry, of course, but which was not the same thing. Slave property may have anchored Southern plantation mortgages, but it was the marketing of the cotton that consumed the credit from New York, which in turn consumed credit from London. It was the cotton, and not the slaves, that was shipped to Lancashire and sold by the pound, and in doing so, produced a hot cash flow. Handling that cash flow put Lehman in the fastest-rushing part of the global marketplace.\n\n\"In the years before 1845,\" writes Richard Holcombe Kilbourne, \"the credit market was in many respects localized.\" But with the regrouping of the economy after the prolonged post-Jackson depression and the annexation of Texas, the old institution of factorage became a principal provider of credit, and H. Lehman & Brother, as it was called at first, became a cotton factorage. Providing credit to cotton planters put the Lehmans in constant contact with New York banks\u2014and, presumably, meant accepting slaves as collateral from planters. The firm in 1854 purchased a fourteen-year-old girl named Martha for $900, and Mayer Lehman ultimately owned seven slaves. But he did not invest his profits in growing large holdings of enslaved people, the way planters did; he was a more modern kind of businessman. After Henry died of yellow fever in 1855, Emanuel moved to New York and established an office at 119 Liberty Street, while Mayer remained in Montgomery. The two became major financiers of the cotton trade in time for the boom years before secession. The Lehman brothers connected the slave-labor agriculture of the South with the financial world of New York in a direct way.\n\nLazarus Straus, a friend of the Lehmans from Bavaria, came over in 1848. Beginning as a peddler based out of Oglethorpe, Georgia, he moved to the small town of Talbotton, where he opened a store stocked with goods he managed to get on credit in Philadelphia, then in 1854 sent for his family.\n\nSam Houston arrived at the Hermitage a few hours too late on June 8, 1845: Andrew Jackson had died. As Houston's son watched, he lay his head on the dead Jackson's chest and mourned.\n\nJackson left his thousand-acre plantation and the approximately 150 slaves who worked it to his wastrel adopted son. As an anecdotal account of how he was remembered by one local African American, we turn to the memory of an elderly, formerly enslaved woman from the Nashville area, a former washerwoman whose name apparently went unrecorded when she was interviewed in 1929 or 1930 by a team from Fisk University:\n\nDid anybody ever tell you about old General Jackson? He was mean... In General Jackson's old place they had a whipping room, and they say now you can hear strange noises out there in that old house. I used to wash out there, after the War, but I never would go to the room to try to hear anything.\n\n#   38\n\n# **Manifest Destiny's Child**\n\n_We have bought at this place, a very likely girl, 13 years old well grown & smart, active &c. for $405.00, and Col. Campbell has just left with her for home. I consider it a fine bargain._\n\n\u2014Letter from John W. Childress in Nashville to President Polk in Washington, July 22, 1846\n\nAS THE PROSPECT OF annexing Texas for the cotton kingdom created a speculative boom in young African Americans, the price of slaves shot up by about 30 percent. Anticipating the sustained bull market that did in fact set in, President Polk bought a total of nineteen people, quietly, from his perch at the White House between 1845 and 1848. Except for a dip occasioned by the Panic of 1857, slave prices never went down again, but surged higher than ever.\n\nIn an article supporting the annexation of Texas, the Democratic Party propagandist John L. O'Sullivan coined the term _Manifest Destiny_ , a phrase that has never gone away. O'Sullivan's article is notable for its fusion of antiblack and anti-Mexican racism in a way that would become a permanent part of the social landscape of the American Southwest. In attempting to deny that annexing Texas was about slavery, O'Sullivan asserted in wordy prose typical of the era the principle that became known as \"diffusionism\": that the Upper South would become free of its slaves by selling them to Texas. Expecting, as many did, that Texas would be carved up into several states, he used the metaphor of waste water to describe the enslaved population, as he anticipated the day when slavery would no longer be necessary and black people could be flushed into Mexican society:\n\nThat [annexation] will tend to facilitate and hasten the disappearance of Slavery from all the northern tier of the present Slave States, cannot surely admit of serious question.\n\nThe greater value in Texas of the slave labor now employed in those States, must soon produce the effect of draining off that labor southwardly, by the same unvarying law that bids water descend the slope that invites it. Every new Slave State in Texas will make at least one Free State from among those in which that institution now exists... it is undeniably much gained for the cause of the eventual voluntary abolition of slavery, that it should have been thus drained off towards the only outlet which appeared to furnish much probability of the ultimate disappearance of the negro race from our borders.\n\nThe Spanish-Indian-American populations of Mexico, Central America and South America, afford the only receptacle capable of absorbing that race whenever we shall be prepared to slough it off\u2014emancipate it from slavery, and (simultaneously necessary) to remove it from the midst of our own. Themselves already of mixed and confused blood, and free from the \"prejudices\" which among us so insuperably forbid the social amalgamation which can alone elevate the Negro race out of a virtually servile degradation even though legally free, the regions occupied by those populations must strongly attract the black race in that direction. (paragraphing added)\n\nThe project branded as Manifest Destiny was thus based in an utterly racist vision of ethnic cleansing\u2014not only of Native Americans, but of African Americans.\n\nThe boundaries of Texas were not yet defined. The Republic of Texas's claims extended south to the Nueces River, but Polk went farther south and west, to the Rio Bravo del Norte (or R\u00edo Grande). Insisting on having the wide strip between the two rivers that was still populated mostly by wild horses (grassland then, barren and dusty now), he sent troops under the command of General Zachary Taylor, a wealthy Virginia-born Louisiana sugar planter who owned 147 slaves\u2014even though Polk distrusted Taylor because he was a Whig. Taylor positioned his men on the banks of the Rio Grande and provoked an incident, creating the pretext to invade Mexican territory and take as much of it as possible, all the way out to California.\n\nPolk asserted a new level of executive power, daring Mexico to fight and daring Congress to stop him. He signed the congressional act declaring war on Mexico on May 13, 1846. Almost at once, he advised his cabinet that he intended to acquire not only Texas, but California and New Mexico (the latter territory included the present states of Arizona, Utah, Colorado, and Nevada) as well.\n\nThere was also a legacy of conflicting claims to Oregon, but the South did not want a war with cotton-consuming Britain over it, so there wasn't one. Occupied with the fighting in Mexico, Polk compromised with Great Britain to divide up the Oregon territory, the lower part of which was already receiving American settlers in covered wagons. Ratified on June 18, 1846, the Oregon Treaty gave up American claims to \"54\u00b040\u2032 or fight\" that would have extended American ownership up to Alaska, accepting instead the forty-ninth parallel (the present US-Canada border) that definitively brought present-day Oregon and Washington, including the highly desirable Puget Sound harbor, under US control. Oregon would not be a slave territory, but when it applied for admission to the Union as a state in 1858, its constitution forbade free black people from entering the state, as well as denying the ones who were already there the rights to testify in court, make contracts, and own property. Similar prohibitions would forbid the entry of free blacks into the free-soil states of Illinois, Indiana, and Iowa.\n\nIn August 1846 Polk asked Congress for an appropriation of two million dollars to support negotiations with Mexico in anticipation of victory, but antislavery members of the House on August 8 tacked onto the appropriations bill the proviso that would make Pennsylvania representative David Wilmot's name execrated throughout the South. The Wilmot Proviso prohibited slavery in any territory to be acquired from Mexico, following the theory that Wilmot explained in 1847: \"Keep [slavery] within given limits... and in time it will wear itself out. Its existence can only be perpetuated by constant expansion.\" When the Wilmot Proviso passed the House, eighty-five to seventy-nine, it wasn't on a party-line vote, but a sectional vote, North versus South, a harbinger of things to come. It failed in the sectionally balanced Senate. The South was furious that it had been proposed at all.\n\nAntislavery politicians had no influence in the Senate, the Supreme Court, and certainly not in the executive branch. But free states dominated the House of Representatives. As the slave states slipped farther and farther behind in population, they became more insistent on keeping their balance of senators, which meant: add more slave states. As Wilmot had argued, slavery could only be perpetuated by constant expansion.\n\nThough pressed by his duties as commander in chief of a war of conquest, Polk found the time to advise his recently widowed sister Eliza that she should invest what little money she had in buying people. In a letter of August 16, 1846, he suggested she move in with their mother and \"apply [the money she had saved] to an increase of your [slave] force on your plantation, so as to enlarge your yearly income.\"\n\n\"The Mexican War occupies much of my time at present,\" Polk wrote, in a classic understatement, to a correspondent on October 7. A letter written to him two days later documents how his farm made twenty-five dollars, less commission, on a deal to acquire a girl who could be put to childbearing. With his hands full, Polk was more reliant than ever on his brothers-in-law, and one of them, Robert Campbell Jr., wrote him about some recent and planned purchases, including one in which he posted a small profit at a widow's expense through flipping the ownership of an enslaved boy in exchange for a \"likely\" girl at the beginning of her reproductive years. Bragging on his deal, Campbell discussed the children like they were mules:\n\nI have Sold the boy Jim that I bought for you [that] I gave $392 for to the Widow Colbern for $450 & bought a girl (Jane) 20 lb heavier for $425 and likely[,] 12 or 13 years old[.] it is one of the best trades I have made[.] I would have given the boy for the girl even[.]\n\nGeneral Winfield Scott, who like Taylor was distrusted by Polk as a Whig, bombarded the historic city of Veracruz for eighteen days in March 1847. When the troops entered the city to occupy it, they found starving people and rotting corpses. As Mexico capitulated, Polk didn't have the ideal negotiator at hand. But Secretary of State James Buchanan recommended his clerk, the number-two man at the State Department, who ran the department during Buchanan's extended absences: Nicholas P. Trist.\n\nTrist's political credentials were impeccable, and after his years in Cuba he spoke Spanish. As negotiations dragged on, Polk fired him, but he remained on the job, negotiating the Treaty of Guadalupe Hidalgo with no official status whatever. Moreover, he didn't comply with his instructions, which had been to secure Alta and Baja California both: Mexico retained Baja California, which the United States had, after all, not conquered. Trist did manage, however, to secure the grand harbor at San Diego as the southernmost border of the territory to be acquired.\n\nPolk was angry at losing Baja California, but he had a treaty, public support was waning, and the 1848 elections were looming. He made the deal, paying about $15 million for California and the New Mexico territory\u2014about a third of Mexico, including its best farmland and the Northern California goldfields that would be discovered mere months after the purchase. Polk vindictively made sure that Trist did not receive his back salary for the time spent in the negotiations. It was the end of Trist's governmental career, and for the rest of their lives, he and Virginia Randolph Jefferson Trist lived in poverty.\n\nThe United States hoped to annex Cuba as well, and a suitor came calling to broker the deal. There were no tickets available for the sold-out performances in New York by Havana's opera company, the grandest in the hemisphere, of Giuseppe Verdi's new smash hit _Ernani_ , but as noted in the _New York Herald_ of June 28, 1847, they gave a special performance in honor of President Polk, while he was visiting New York. If Polk attended\u2014there is no mention of it in his diary or letters\u2014it is difficult to imagine that, with his chronic bowel complaints, he enjoyed the four-act Italian opera much, nor is it likely that such a spectacle was Sarah Polk's cup of tea. The company's impresario was none other than slave trader and fish dealer Pancho Marty, who had imported the best Italian talent to staff his troupe. The performance in honor of Polk was a demonstration not only of the riches and high level of imported culture in Cuba, but of who the right man was to make a deal with for Cuba\u2014Pancho Marty.\n\nThe following year, John L. O'Sullivan began having meetings with Polk to urge him to acquire Cuba. In June 1848, Polk offered Spain $100 million for the island. Declined, thank you.\n\nO'Sullivan, and a host of adventurers, made plans to take Cuba by conquest.\n\nNew Orleans could be a hellhole of disease in the warm months, and Isaac Franklin took ill there. After traveling back to his Bellevue plantation, he died suddenly, on May 4, 1846, at the age of fifty-six from what the doctor called \"congestion of the stomach,\" which was likely cholera. A month later, after his distraught wife, Adelicia, had returned to Tennessee, she helplessly watched as two of their three daughters died two days apart from sudden cases of \"croup and bronchitis.\"\n\nAt the time of Franklin's death, he was possibly the richest man in President Polk's home state of Tennessee. He owned ten thousand acres of land in Tennessee, Louisiana, and Mississippi, plus claims in Texas, railroad bonds, and a large, continually increasing number of slaves. His estate was managed by his father-in-law and John Armfield as trustees, each receiving a 2\u00bd percent commission, so that Armfield was still working for Franklin. By 1851, when the trustees got rid of the responsibility and turned his estate over to the widow, it was worth almost $710,000 (perhaps $21.5 million in 2014). Sixty-nine percent of the value of Franklin's six Louisiana plantations was in its more than six hundred slaves, who were worth $363,927.80 out of the estate's total value of $525,674.85.\n\nDuring the five years of Armfield and Hayes's trusteeship, the slaves registered thirty deaths and eighty births, realizing a profit from \"natural increase.\" The deaths and births were broken out and inventoried in separate schedules in the estate proceedings, in which one can see that the average age at death was twenty-nine, all but four of the deceased having died before the age of fifty. The births\u2014eighty children of four or younger\u2014were listed by name, mother, age, and color: \"Madison, child of Caroline, 3, black; Bradley, child of Martha Winchester, an infant, black; Milly, child of Matilda Trottman, 4, griff; Len, ditto, 1...\"\n\nWhat would they be worth in a few years? An April 1857 article in _DeBow's Review_ cheered the high prices fetched at a sale of children in Texas, with terms of one and two years, and 10 percent interest. DeBow printed the names, ages, and prices fetched: \"Caroline, 11 years old, $1,100; Frank, 9, $805; Little Allick, 7, $810; Catharine, 10, $700; Flora, 6, $695; Sarah, 9, $890; Dick. 7, $650; Sam, 3, $450; Phoebe, 10, $655; Ben, 6, $405.\"\n\nIn his will, made in 1841, Franklin directed how many more hands were to be purchased for each of the plantations, and specified how the executors were to improve his holdings with two more plantations, called Panola and Loango, to be developed alongside the four already existing on the land. It's not clear why Franklin wanted to have two plantations (Loango and Angola) named after Central African slave markets on opposite sides of the Kongo River, since he didn't do business in Africans. But Angola is what the biggest antebellum slave trader called his plantation. The prison by that name today on those same grounds in East Feliciana Parish is Franklin's infamous bequest to Louisiana's cultural life.\n\nSo New Orleans saxophonist Charles Neville was right when he said that the land occupied by the Louisiana State Penitentiary was formerly a \"slave-breeding plantation.\" Neville spent three and a half years there for having had two reefers. Any Louisiana musician can sing you:\n\n_Now six months ain't no sentence_\n\n_One year ain't no time_\n\n_They got boys in Angola_\n\n_Doin' nine to ninety-nine._\n\nIsaac Franklin left a large footprint. His idyllically situated Fairvue mansion today anchors a beautiful, upscale residential development, with more than eight hundred large homes, a golf course, a country club, and Franklin's mansion and tomb.\n\n_Isaac Franklin's former mansion of Fairvue, now a private residence, March 2014._\n\nA tale of two plantations: at the other end of the desirability scale from Fairvue, Isaac Franklin's Louisiana land ultimately passed to the State of Louisiana, retaining the name Angola to cover all five previously distinct plantation tracts. In the last decades of the nineteenth century, it was run as a plantation using convict labor. Since 1901 it has been home to the Louisiana State Penitentiary, known internationally as Angola\u2014a singular institution even in the harsh annals of American penology. The former agricultural prison has remained an agricultural prison: a self-sustaining plantation that forces its inmates to get their hands cut up, because at Angola they still pick cotton by hand instead of using machinery. Angola houses sixty-three hundred inmates\u201476 percent of them black and 71 percent serving life sentences\u2014and it employs eighteen hundred people to keep them incarcerated. The continuity of Angola prison ties the historical slave trade to a living modern legacy of unequal treatment, income disparity, social pathology, and mass incarceration. The penal regime it imposes on convicts bears a chilling resemblance to the antebellum slave experience.\n\nAdelicia Franklin married twice more after Issac Franklin died. Her first remarriage, at Fairvue on May 8, 1849, was a major social event, as per ex-president Polk's diary entry:\n\nThis evening Mrs. Polk and myself attended the marriage of Mrs. Franklin, a wealthy widow of this City. She was married at her own house to Mr. Acklin of Huntsville, Alabama. The supper and whole entertainment was upon a magnificent scale. I met at the wedding many leading Whigs & democrats, and was courteously and kindly treated by all.\n\nIt was one of Polk's last social events. He had just returned to Nashville after leaving the presidency. On his trip home from Washington, worn out from prosecuting the war with Mexico, he noted in his diary the presence of cholera on the boat. At every stop he was given balls, public dinners, and received enormous numbers of visitors, despite suffering from \"a derangement of stomach & bowels\" and feeling \"greatly wearied and worn down.\" In New Orleans, Mayor Abdiel Crossman denied there was a cholera epidemic (there was) and insisted the fatigued ex-president come to a public dinner with 250 guests. As Polk continued on by riverboat, there was cholera on board again; various passengers died. Once in Nashville, he noted in his diary various people in the town being taken ill with cholera. His penultimate entry, on June 1, ends, \"During the prevalence of cholera I deem it prudent to remain as much as possible at my own house.\" But he too died of it, on June 15, a little more than ten weeks after leaving the presidency.\n\nIn his one term, Polk had reshaped the nation. In the process, he had reached the westward limits of slavery expansion. Slavery was exploding in eastern Texas, but it would grow no more to the West beyond that, though the Slave Power would fight hard in a losing battle for California.\n\nWhile most of the value of Polk's estate consisted of slaves, he wasn't worth a tenth of what Isaac Franklin was worth. In his will, Polk, ever the politician, wrote that \"Should I survive her [Sarah], unless influenced by circumstances which I do not now foresee, it is my intention to emancipate all my slaves, and I have full confidence, that if at her death she shall deem it proper, she shall emancipate them.\" But, as in the cases of Martha Washington and Dolley Madison, who like Sarah Polk were survivors of slaveholding presidential husbands, she didn't \"deem it proper\" to emancipate them. Wearing black for the rest of her life, she lived to be eighty-eight at Polk Place, the mansion they had occupied together for only three months, with her husband's tomb in the front yard. She had not been weakened by multiple childbirths and miscarriages like so many women of her era, and she was wealthy and savvy. In 1860, she cashed out, selling a one-half interest in her plantation, including all but six of her fifty-six slaves, to a relative for $28,500\u2014over $800,000 in 2014 dollars.\n\nIt was a fraction of what Adelicia Franklin got.\n\nIn terms of territorial gains, Polk's Manifest Destiny war with Mexico did very well, bringing under US control more than half a million square miles, sparsely populated even by Native Americans. As the Texans began slowly learning the Mexican ways of handling horses and cattle that became known as cowboying, and learned a new way of cooking, they called themselves \"white people\" in opposition to the Mexicans, whom they typically treated as an inferior \"race.\"\n\nThe \"white people\" began expelling the Mexicans from their towns. For one thing, in a frontier society that was chronically short of women, Mexican men were taking enslaved women away, thereby robbing the slaveholders of the future increase that they saw as their due. A newspaper reported:\n\nMATAGORDA. \u2014 The people of Matagorda county have held a meeting and ordered every Mexican to leave the country.... [They] have no fixed domicile, but hang around the plantations, taking the likeliest negro girls for wives; and... they often steal horses, and these girls, too, and endeaver to run them to Mexico.\n\nThe annexation of Texas kicked the Southern slave market into gear. But as the market for slaves heated up, no single firm dominated the trade the way Franklin and Armfield previously had. No slave-trading firm grew like Lehman and Brother did dealing cotton, and there was no major slave-retailing corporation that survived the war to trade in something else. Instead of the market consolidating after Franklin, it fragmented. Slave traders were mostly small shops, including many part-timers who left no records and a much less coherent paper trail than Franklin's company. Perhaps no one else had the ability to focus so many partners on a common set of business goals across the full geographic area, much less accomplish the complex task of keeping the money flowing smoothly at all times.\n\nThe 1840 census showed 2,487,355 slaves, and the 1850 census registered a 28.8 percent increase, for a total of 3,204,313. American slavery had never stopped growing since its beginnings in seventeenth-century Virginia. It could never stop growing, or the whole system would collapse of its own weight. More and more slave states were looking to export their young. People from every slave state could be found on sale in the market at New Orleans, where many were bought for Texas. But even so, the value of \"Virginia and Maryland negroes\" held as a premium brand, and shipments continued from Baltimore, Alexandria, Richmond, Norfolk, and lesser ports.\n\nAustin Woolfolk's operation had been profitable; Freudenberger and Pritchett calculate that after the expenses of maintaining slave jails at both ends, feeding the captives for weeks, buying all the newspaper advertisements, chartering a vessel, et cetera, Woolfolk's firm had a 14 percent rate of return. Woolfolk married, had five children, and was substantially out of the business by 1842, though he continued shipping slaves until 1846. He too moved to plantation land he had bought in Louisiana. He died of tuberculosis in 1847, \"reduced to a mere skeleton,\" as his uncle described it in a letter, in a tavern in Auburn, Alabama, leaving behind property in Louisiana, Alabama, and Maryland. More than thirty years later, his son, Austin Jr., sued his own mother, Emily Woolfolk, over the partitioning of the estate, which even with slavery no longer in existence was still worth a six-figure sum.\n\nBaltimore's outbound slave shipments in the 1840s exceeded those of the previous decade, as more major traders got into the act. In Alexandria, the Franklin and Armfield headquarters on Duke Street were taken over by their former associate George Kephart, who was for a time the biggest dealer in Alexandria, then by \"Price, Birch, dealers in slaves,\" James Birch's firm. Kephart's business declined by 1843, and from then until secession the biggest Alexandria slave trader was the firm of Bruin & Hill (Joseph Bruin and Henry Hill), whose slave jail at 1707 Duke Street is now on the National Register of Historic Places, though it's not open to the public. Bruin seems to have sent most of his victims South in coffles\u2014for which, unlike oceangoing vessels, there were no manifests to survive for the historical record.\n\nAs abolitionists continued to bombard Congress with petitions to end slavery and the slave trade in the capital city, Alexandria in 1847 requested, and was allowed, to leave the District of Columbia and rejoin Virginia, so that the present-day District of Columbia is entirely on land ceded by Maryland.\n\nThree years later, as part of a series of compromises that occupied the nation's political class for an entire year\u2014the Compromise of 1850\u2014slave trading, though not slavery itself, was at last prohibited in Washington.\n\n#   39\n\n# **A Letter from Virginia**\n\n_The little Boy has one of his toes cut off. I don't think that will lessen his value... Doct Ingram has Known the Boy for a length of time and Says he never Gives him medicine but once for Belly Ache.] he is Smaller than I like but it is hard to Buy at any price up here.[ 1_\n\n\u2014Sumterville, SC, purchasing agent A. J. McElveen to Charleston dealer Ziba B. Oakes, November 7, 1853\n\nIN HIS WILL, ISAAC Franklin directed that the income from his plantations support a school to be named the Isaac Franklin Institute, but his widow Adelicia got the court to void the provision, on the grounds that it would create a \"perpetuity,\" which in this case would have rested on the perpetual reproduction of the estate's enslaved. Instead, she got the assets, including Fairvue.\n\nThe trustees' management of Franklin's estate terminated with the resolution of the widow's court proceeding. During the five years or so of their management, seemingly every receipt submitted for every expense was collected and printed as part of the 918-page legal document titled _Succession of Isaac Franklin_ , which thus provides an unusually detailed snapshot of the mercantile realities of the time. The trustees bought laudanum, morphine, calomel (mercury chloride, a toxic compound then believed to have medicinal value and often used as a laxative), and a host of other preparations for when the \"negroes\" were sick. They bought \"negro shoes\" from the Tennessee State Prison, which used convict labor to make salable products. They sold cotton and lumber.\n\nAdelicia was presented to Queen Victoria when she visited London and was complimented on her riding skills by the horsewoman Princess Victoria Eugenie of Battenburg. It was Adelicia who brought Spanish palominos to breed in Tennessee. With her new husband, Joseph Acklen, she became a leading light of the Nashville social scene at her new thirty-six-room mansion on her estate called Belmont, which besides ten thousand square feet of living space had a bear house and a zoo, and where her daughter Emma died of diphtheria.\n\nJohn Armfield too became a respectable planter, and was a principal benefactor at the founding of the University of the South at Sewanee, Tennessee. Franklin's former Richmond partner Rice C. Ballard became a planter as well, though he continued to be involved in the slave trade. He married and moved to Louisville, though he seems to have spent a great deal of time in Natchez, to judge from the letters he received there from his wife begging him for money.\n\nBallard became friends, and then a business partner with, a Natchez judge named Samuel S. Boyd, with whom he co-owned a string of cotton plantations worked by perhaps five hundred slaves in Mississippi, Louisiana, and Arkansas. Boyd and Ballard's man in New Orleans was a Louisville-based slave trader named C. M. Rutherford, whose office in New Orleans was at 159 Gravier Street, between Baronne and Carondelet, and who also sold slaves in Natchez.\n\nIt was advantageous for Ballard to keep a hand in slave retailing. He and Boyd at one point closed down a plantation and sold the entire labor force South, a few at a time. Ballard provided working cash for Rutherford to buy with, and Rutherford knew what Ballard liked, as when he offered him a woman \"19 years old black likely and all rite as tall and likely as the one you wanted of white, price $700.\"\n\nBoyd was cruel to women. The Natchez attorney J. M. Duffield had owned a woman named Maria, and though he was fond of her and had a sexual relationship with her, he wound up through financial pressures losing her to Boyd's ownership. On May 29, 1848, Duffield wrote Ballard about Maria and her daughter (who may have been his daughter), asking him to intervene after she had been whipped \"like an ox, until the blood gushes from her.\" Another letter from Duffield reported on August 5 that \"Mr. Boyd will part with her now as her health is such that she must be a charge on any owner,\" as she suffered from \"womb complaint dreadfully brought on by unkindness and injuries, bodily injuries, and... [now that she can leave Boyd,] she can now recover though she will probably linger out to several years.\" Unfortunately, Duffield didn't have any cash right then. He offered another slave as security, promising to pay \"any price you might think she ought to bring, and perhaps prolong her life, which will soon be shortened where she is [now].\"\n\nSouthern Business Directory, _1854._ 3\n\nOn February 27, 1853, Rutherford wrote Ballard from New Orleans about a troublesome slave named Virginia, which may have been the name her mother gave her or may have simply been where she was purchased. Virginia was being sent as far away as Rutherford could manage, along with her swelling belly and her two children, who, though he didn't need to mention it, looked like Judge Boyd. While Rutherford was trying to decide whether to \"send her to Texas... or send her to Mobile,\" she kept trying to run away.\n\nMeanwhile, it was good to know a judge. On April 2, 1853, Boyd came to Ballard with a dirty deal\u2014the lucrative prospect of selling a whole plantation full of freed slaves back into slavery:\n\nHave lately learned of an opportunity to buy a lot of negroes at a very reasonable rate, next January.\n\nOld man Baldwin, of Jefferson County, directed his slaves to be sent to Liberia. This will be declared void at the present term of the High Court, and as nearly all the heirs reside in New Jersey, they do not want the slaves, & are willing they should be all sold together, to a good master, at a reasonable rate, according to the will, if it cannot be carried out. {Name indecipherable}, one of the Executors, has informed me he thinks they can be had at... $27000 for fifty two. He is to furnish me with a list soon, and will endeavour to obtain authority to close the trade.\n\nThe same day, Rutherford wrote Ballard that he'd decided to send Virginia to Texas, but it was going to cost: he had \"a friend there I can send her to but the vessels will not take any negro unless under the charge of some white person.\" So eager were the partners to get rid of Virginia that Rutherford hired an escort to deliver her personally to Texas. From New Orleans, Rutherford handled her case to the point of final sale, offering easy terms, as Rutherford reported on April 19:\n\nI have this morning shiped Virginia & children to S.B. Ewing Houston Texas with special instructions to sell her not to return to this place or Miss[issippi.] I gave her character and did not limit the sale when sold to permit account sales & nett proceeds to [factors] Nalle Cox & Co of this place for your benefit[.] I will give Nalle Cox & Co a copy of my letter of instructions[.] I had to hire a young man to go with her to Galveston.\n\nA letter from Boyd three days later that refers to Virginia only as \"the woman\" makes clear that she didn't go quietly: \"Rutherford was to ship the woman & her children to Texas on Tuesday last, by the steamer Mexico. She gave him a load of trouble.\"\n\nThere exists a letter from the heavily pregnant Virginia to Ballard, written in the desperation of the moment. The dimensions of her story are apparent, even though much is unknowable about the events referred to. A facsimile is available online; we will present it here as we have transcribed it, adding full-stop periods, capital letters, and paragraphing for readability, with question marks indicating transcription queries, brackets around reasonable guesses, and Xs signifying missing bits of text.\n\nHouston May 6th 1853\n\nDear Sir permit me to address you a few lines which I hope you will receive soon. I am at present in the city of Houston in a Negro traders yard for sale by your orders. I was present at the Post Office when Doctor Ewing took your letter out through mistake and red it a loud, not knowing I was the person the letter alluded to.\n\nI hope that if I have ever done or said any thing that has offended you that you will for give me for I have suffered enough cince in mind to repay all that I have ever done to anyone[.]\n\nYou wrote for them to sell me in thirty days. Do you think after all that has transpired between me & the old Man )I don't call names( that its treating me well to send me off a mong strangers in my situation to besold without even my having an opportunity of choosing for my self. Its hard in deed and what is still harder\u2014for the father of my children to sell his own offspring yes his own flesh & blood. My god is it possible that any free born American would brand his charites with such a stigma as that, but I hope before this he will relent & see his error for I still beleave that he is possesst of more honer than that.\n\nI no too that you have influence and can assist me in some measure from out of this dilema and if you will god will be sure to reward you, you have a family of children & no how to simpathize with others in distress.\n\nall I require or ask [is] for an agent to be appointed hear to see to me, XXXXX to Earn the money, honestly, to buy my XXXXX I have to work my finger ends off I will earn XXXXXay evry dime I do think in justice [the] children should be set free XXXX[As] for my self altho my youthfull days [were worn] out in [t]he service and grattification of the [person that] now wants me & his children sold is it posible that such a change could ever come over the spirit of any living man as to sell his child that is his image[?] I don't wish to return to harras or molest his peace of mind & shall never try get back if I am steall with family.\n\n_The first page of Virginia Boyd's letter._\n\nI no that you have been prejudist a gainst me, by what {name unclear} told you one day you will find who is the rascal & who has injured you most I have no motive in saying to you any thing but the pure truth, when you come to know all that she has said relative to you & matters concerning your family you will prehaps not have so great a confidence in all the tales she fabricates[.] I wish you to reflect over the subject and see if some little could be shown me for that mercy & pity you show to me god certainly will show you[.]\n\nWhat can I say more if I ever have spoken hastly that which I should not I hope you will for give me for I hope god has, I am humbled enough all reddy, hear a mong strangers without one living being to whom I have the least shadow of claim upon, my heart feels like it would burst a sunder[.] It will not be long ere I am confined, & the author of my suffering to be the means of my being thrown upon the charity to strangers in XXXX when I most need a simpathizing friend is XXXXX that XXX to receive for making so mXXXX for his sattisfaction.\n\nWill y[ou le]t me hear from you & say what yo[ur feelings] are relative to the proposition I make[?] [I know you are an] honerable high minded man and in your XXXX moments you would wish justice to be done to all, & if I am a servent there is some thing due me better than my present situation.\n\nI have writen to the Old Man in such a way that the letter cant faile to fall in his hans & none others. I use any precaution to prevent others from knowing or suspecting any thing. I have my letters writen & folded put into envelope & get it directed by those that dont know the contents of it for I shall not seek ever to let any thing be exposed, unless I am forced from bad treatement.\n\nVirginia Boyd\n\nSome of the elisions in Virginia Boyd's letter are accidental, some strategic. We can imagine the story; indeed, we have to in order to parse what we read. But there's much we don't know. Who is the \"Old Man,\" the father of her children she's referring to? Presumably Boyd. She's signing Boyd's name as hers, with the clear indication that her children are to carry that name too. But Ballard was the one giving the sale order\u2014apparently because Virginia was owned by the partnership, and Ballard handled slave sales.\n\nUnlike Maria, Virginia at least got away from Boyd without being maimed. All three of the traders in the loop knew her; she indicates a personal familiarity with Ballard, who was a frequent visitor to Natchez, and to her co-owner\u2014and who, she believes, has been turned against her by lies told by another enslaved female. We can make up stories about what _that_ was about, but we don't know.\n\nWhat else might we know about Virginia? According to Rutherford's earlier letter, she already had two children. She felt that her \"youthfull days\" were behind her. She might have been twenty-five, ready to be discarded as too old. What did she look like? She'd been the mistress of a slave trader, so she was presumably light-skinned. She wasn't a field hand; she had been accustomed to privileges, and perhaps had imagined the goal of freedom for herself and her children to be getting closer. She expected to be able to \"choose for myself,\" suggesting perhaps that even her enslaved status had been in question at some point, but she has now been \"humbled.\"\n\nThe level of literacy in her letter is at least as good as the traders'. There is no reason to assume that it was written by a scribe; its twists and turns seem the product of a coordinated mind, voice, and hand. Somehow, we don't know how, she had the ability to get letters sent by private channels out of the trader's yard\u2014one to Boyd, apparently, and this one to Ballard. And, she warns, if \"forced from bad treatment\" she could write another one that would tell what somebody doesn't want known.\n\nThe blackmail threat did her no good. She was sold into the hard conditions of the Texas frontier. There's no known record of her further existence. Her plea to free her children was ignored; slave traders didn't set children free, they sold them, and they were inured to\u2014perhaps even enjoyed\u2014desperate pleas. Virginia was sold together with her younger child, whose gender we don't know, for a thousand dollars. If that child was Boyd's daughter, by light-skinned Virginia, she would have been \"mighty near white\"\u2014a fancy girl, the slave trader's premium prize. In a typical slave-trader move, Virginia's older child, a girl, was kept back.\n\nA letter of August 8 from Rutherford to Ballard said: \"I recd a letter this morning informing me of the sale of Virginia & her Child reserving the eldest Child for $1000[.] I wrote Mr. Ewing not to sell the oldest child untill he heard from me... I recollect you wanted to reserve her before she went away which can be done now if you wish let me hear from you on the subject.\"\n\nFive months after Virginia was disposed of, Rutherford wrote Ballard from Natchez:\n\nSince writing I have seen Judge Boyd[.] he tells me that he thinks you will want 10 to 15 more females[.] I have on hand I think 12 more but they are the kind you would not buy[.] I know they are such as I would not buy for you although they are large... you cannot buy anything like a fair woman here for less than $1000 any that you would have[.] I know a lot of Georgia negroes at Memphis that I think you could buy the women for $900... I told the judge if you wished me I would go up there and buy you ten or fifteen & and charge you nothing but my expenses... Judge is in favor of my going if you say so.\n\nIt may be that Isaac Franklin's fantasy of a company \"whore house\" was not such an exaggeration.\n\nIn 1856, the year the secessionist leader and former governor James Henry Hammond was elected senator from South Carolina, he wrote his twenty-two-year-old son Harry a remarkably candid letter regarding the disposition of two sex slaves in the latest version of his will.\n\nHammond was something of an outlier in sexual behavior, as his confessional diary reveals. He wrote some of the only antebellum letters that survive documenting a sexual relationship between two men (with Thomas Jefferson Withers), and confessed in his diary to molesting all four of his teenage nieces from the marriage of Wade Hampton II to his wife's sister. Hammond had purchased Sally Johnson, a \"mulatto\" seamstress, when she was eighteen, along with her (presumably lighter-skinned) one-year-old daughter Louisa, who became his concubine when she was twelve. He had children by both women\u2014which is to say that, besides those children's complicated relationship to each other, they were his son's half siblings, as he explained in the letter to his son:\n\nIn the last will I made I left to you, over and above my other children Sally Johnson the mother of Louisa and all the children of both. Sally says Henderson is my child. It is possible, but I do not believe it. Yet act on her's rather than my opinion.\n\nLouisa's first child may be mine. I think not. Her second I believe is mine. Take care of her and her children who are both of your blood if not of mine and of Henderson. The services of the rest will I think compensate for an indulgence to these. I cannot free these people and send them North. It would be cruelty to them. Nor would I like that any but my own blood should own as Slaves my own blood or Louisa.\n\nI leave them to your charge, believing that you will best appreciate and most independently carry out my wishes in regard to them. Do not let Louisa or any of my children or possible children be slaves of Strangers. Slavery in the family will be their happiest earthly condition. (paragraphing added)\n\nAmong the greatest misfortunes Hammond considered himself to have suffered was that his captives died so frequently\u2014\"I have lost 89 negroes and at least 50 mules and horses in 11 years,\" he lamented in his diary. Perhaps, he wrote, he should move their quarters to a less unhealthy spot.\n\n_The Maxcy-Rhett house, informally known as \"secession house,\" in Beaufort, South Carolina. By 1850, the political class of Beaufort was already determined to secede. June 2013._\n\n#   40\n\n# **Communists in Blackface**\n\n_Give us SLAVERY or give us death _\n\n\u2014Edward Bryan, South Carolina, 1850\n\nTHE DISCOVERY OF GOLD in California was a turning point on the way to Southern secession.\n\nPresident Polk announced the find to the nation in his year-end message of 1848. Some ninety thousand gold-seekers arrived in northern California in 1849, staking their claims and displacing and murdering Native Americans en masse: the native population of the region dwindled in short order from about 150,000 to about 30,000.\n\nLured by the boom, immigrants came from Latin America and Europe to California and to the United States in general, and this on top of the massive Irish potato-famine migration that began arriving in numbers in 1847. Asian trade developed, Hawaii's economy thrived, and Chinese workers, principally Cantonese, came to both Hawaii and California. As gold fever spread, men (who were perhaps as much as 95 percent of the early migrants) left home and family to go West; Nantucket found itself \"drained\" of \"one-quarter of its voting population\" in nine months. A song from the period described the mania:\n\n_The people all went crazy then, they didn't know what to do_\n\n_They sold their farms for just enough to pay their passage through_\n\n_They bid their friends a long farewell, said \"Dear wife, don't you cry,_\n\n_I'll send you home the yellow lumps a piano for to buy.\"_ 3\n\nWith the discovery of other mines in the West, billions of dollars' worth of new money was extracted over the ensuing decades. It was an immediate game-changer, with global implications. So much gold was sucked to Britain, the United States' creditor and the world's economic powerhouse, that it was easily able to consolidate its already in-progress shift to the gold standard.\n\nEurope was troubled by a wave of revolutions. Beginning with a revolt in Sicily in January 1848 and a much bigger one in France the following month, insurrection spread to most of the continent. But it was put down within a year, and economic problems faded as the new money supply worked its way into the continent.\n\nA mint was established at San Francisco as the United States issued unprecedented amounts of its own gold coinage:\n\n**Year** | **Amount of gold minted into coins** 4  \n---|---  \n1848 |  $3,775,000  \n1850 | $31,981,000  \n1851 | $62,614,000  \n1852 | $56,846,000\n\nThe flood of coins brought down the price of gold and drove silver out of circulation. With a domestic supply of gold, the United States could at last ban foreign money\u2014most especially, the \"Spanish dollar\"\u2014from circulation in 1857. The total amount of paper money issued by banks, in circulation and on deposit, went from $231 million in 1848 to $392 million in 1854, and $445 million in 1857\u2014and the paper was of higher quality for having so much more gold in the system. Bankers and businessmen had a newfound sense of confidence and optimism, which made them more eager to speculate. The British were investing.\n\nCalifornia was an immigration magnet. But it was as hard to get to San Francisco from New York as from Chile, and Chilean gold-seekers were indeed arriving. The Eastern US wanted a transcontinental railroad, and the United States government wanted control of the Central American portage crossing\u2014whether in Honduras, Nicaragua, or, the ultimate choice, Panam\u00e1, the latter of which was then part of Colombia but would be pried away to become a zone of US influence.\n\nIt was the richest injection of precious metal into the global economy since the Hapsburgs had capitalized the world with gold and silver from Mexico and Per\u00fa. As the dimensions of the gold find became clear in 1849, the statehood of California was suddenly an urgent matter, before some other country tried to move in or before the miners decided to declare themselves an independent republic.\n\nUnlike Louisiana, which had been slave territory before Washington took it over, California had been free territory under Mexico, and even slaveowner President Zachary Taylor was against establishing slavery there. But there was a powerful economic interest in favor of it: slavery in California would, it was widely believed, make the value of existing slaveholdings appreciate sharply.\n\nA few slaveowners moved with their slaves to southern California, hoping to establish it as slave territory and take over the government, as had happened in Texas. But moving a plantation's worth of captive laborers even a few hundred miles was a big undertaking, let alone the near-impossibility of taking coffles the fourteen hundred parched miles from Houston to Los Angeles.\n\nSoutherners saw gold mining as something that should be done by slave labor, purchased from them. But up in the north, the forty-niner gold miners, who drafted their own legal codes requiring small, continuously worked claims, weren't about to have slaves working on massive gold plantations. They didn't want slave labor or free black people, either one; for them, California was white man's country. When a group of Texans headed by Thomas Jefferson Green tried establishing claims on the Yuba River in the names of their sixteen slaves in July 1849, miners informed them that \"no slave or negro should own claims or even work in the mines,\" and physically expelled them all.*\n\nThe large state of California, extending all the way down to San Diego, requested annexation with a free-soil constitution in 1849, putting checkmate as they did so on the westward expansion of slavery. One delegate at the California constitutional convention, Henry Tefft, matter-of-factly referred to the slaveowners as \"capitalists\" when he warned the assembly that the young white male miner population \"would be unable, even if willing, to compete with the bands of negroes who would be set to work under the direction of the capitalists. It would become a monopoly of the worst character. The profits of the mines would go into the pockets of single individuals.\" A clause that would have barred free blacks from entering the territory was voted down.\n\nIn South Carolina, Robert Barnwell Rhett, outraged that a group of gold-digging migrants could declare themselves to define California and thus exclude slavery, derided the California constitution as \"squatter sovereignty,\" _squatter_ being the preferred aristocratic epithet for poor rural whites, who often lacked legal title to the land they lived on. The states were the owners of the territories, argued the Fire-Eaters, and the slave states must be allowed to bring their property to their property.\n\nHenry Clay, together with Stephen A. Douglas of Illinois, attempted to placate the Slave Power with a grand compromise in January 1850 that was packaged by Mississippi unionist Henry Foote into a single \"Omnibus\" bill, which was then disassembled and recast into a series of laws known as the Compromise of 1850. It proposed admitting California as a free state and giving territorial status to Utah (later divided into Utah and Nevada) and New Mexico (later divided into New Mexico and Arizona), while disregarding Texas's claims to New Mexican territory.\n\nIn Clay's final grand speech after decades of fame as an orator, he attacked Massachusetts senator John Davis's charge that Texans were trying to establish the \"breeding\" of slaves in New Mexico, a territory that was useless for plantation agriculture but which Texas was intent on annexing as slave territory. Davis, perhaps intimidated, denied having used the term, but Clay wouldn't let him off the hook. He rhapsodized about how kind slaveowners were to their slaves and how sale into the market only was a painful last resort. Then he demonized abolitionists. He thus discredited himself in the eyes of posterity as a pandering apologist for slavery, while failing to please the Fire-Eaters, who wanted much more than Clay was prepared to give. Clay was a Unionist, and for him the Union meant the compromises that only he was adroit enough to manage.\n\nThe Compromise of 1850 included prohibition of the slave trade in the District of Columbia. Since Alexandria had left the District and returned to Virginia precisely over this issue, the interstate trade was not seriously disrupted, and in any case, slavery was not abolished in the District. But the secessionist project that was already well under way considered compromise to be treason, and the Fire-Eaters screamed bloody murder anyway.\n\nFor the North, the most offensive compromise was a new Fugitive Slave Act. Aimed at shutting down the Underground Railroad that emboldened the enslaved to escape, and building on the constitutional requirement to hand over fugitive \"persons held to service,\" it required lawmen to capture and deliver anyone in any state accused of being a fugitive slave, with no right of denial on the part of the accused. It gave kidnappers a legal apparatus.\n\nOutraged by the \"aggression\" of ending the slave trade in the District of Columbia, Southern members of both houses of Congress met in a caucus and produced _The Address of the Southern Delegates of Congress to their Constituents._ Mostly written by the aged, embittered John C. Calhoun, it warned of emancipation's awful consequences, expanding out into rings of ever more apocalyptic fantasy clad in the robes of prophecy. We offer one of its key passages as a glimpse into the routinely voiced Southern fear that white people would be on the receiving end of the violence of slavery:\n\n_The Fugitive Slave Act stimulated Southern slave-catchers to expand their operations into the free-state North, as per this September 1850 mailing piece by Maryland firm Kinsel & Doyle, which boasts of its network in Pennsylvania. The legal occupation of fugitive-catcher easily served as a cover for illegal kidnapping operations targeting free people._\n\nIf [emancipation ] ever should be effected, it will be through the agency of the Federal Government, controlled by the dominant power of the Northern States of the Confederacy, against the resistance and struggle of the Southern. It can then only be effected by the prostration of the white race; and that would necessarily engender the bitterest feelings of hostility between them and the North.\n\nBut the reverse would be the case between the blacks of the South and the people of the North. Owing their emancipation to them, they would regard them as friends, guardians, and patrons, and centre, accordingly, all their sympathy in them. The people of the North would not fail to reciprocate and to favor them, instead of the whites. Under the influence of such feelings, and impelled by fanaticism and love of power, they would not stop at emancipation.\n\nAnother step would be taken\u2014to raise them to a political and social equality with their former owners, by giving them the right of voting and holding public offices under the Federal Government. We see the first step toward it in the bill already alluded to\u2014to vest the free blacks and slaves with the right to vote on the question of emancipation in this District. But when once raised to an equality, they would become the fast political associates of the North, acting and voting with them on all questions, and by this political union between them, holding the white race at the South in complete subjection.\n\nThe blacks, and the profligate whites that might unite with them, would become the principal recipients of federal offices and patronage, and would, in consequence, be raised above the whites of the South in the political and social scale. We would, in a word, change conditions with them\u2014a degradation greater than has ever yet fallen to the lot of a free and enlightened people, and one from which we could not escape, should emancipation take place (which it certainly will if not prevented), but by fleeing the homes of ourselves and ancestors, and by abandoning our country to our former slaves, to become the permanent abode of disorder, anarchy, poverty, misery, and wretchedness. (paragraphing added)\n\n_John C. Calhoun._\n\nFrederick Douglass answered Calhoun's negrophobic blast, referencing the Fugitive Slave Act:\n\nWe say to the slaveholder, Insist upon your right to make Northern men your bloodhounds, to hunt down your slaves, and return them to bondage. We say, let this be insisted upon, the more strenuously the better, as it will the sooner awaken the North to a sense of their responsibility for slavery, not only in the District of Columbia, and in forts, arsenals, and navy-yards, but in the States themselves; and will the sooner see their duty to labor for the removal of slavery from every part of this most unhallowed Union. In any case, nought but slaveholders have anything to fear.\n\nJohn C. Calhoun died of tuberculosis in March 1850, \"with treason in his heart and on his lips,\" in the words of his Senate adversary Thomas Hart Benton, who, like Henry Clay and Daniel Webster, was by that time largely a spent force. When Calhoun began fomenting pro-slavery disunion, he was the only such figure on the national stage. His followers competed to be the most radical. In his final years, Calhoun had pushed aside Robert Barnwell Rhett, his longtime lieutenant, and had visibly passed his mantle to the man Rhett would come to hate most, Mississippi senator Jefferson Davis, who had war-hero status from the Mexican War.\n\nOne of the first two senators from California was William Gwin, Andrew Jackson's old crony from Isaac Franklin's hometown of Gallatin, Tennessee. Gwin, who owned two hundred or so slaves, was an embodiment of the Slave Power. After becoming a congressman from Mississippi, he wrote Jackson on March 14, 1842: \"I want a slaveholder for President next time regardless of the man believing as I solemnly do that in the next Presidential term the Abolitionists must be put down or blood will be spilt.\" Relocated to San Francisco, he participated in California's 1849 constitutional convention, where, presumably understanding that the free-soil measure would pass, he acceded to it graciously. Though he failed in his quest to bring slavery to the state, he was a happy man: he was the first slave baron to become a gold baron, having bought a mine that struck it rich. He organized the pro-slavery Democratic political faction in the California legislature\u2014the so-called Chivalry wing, informally known as the Chivs.\n\nGwin's case was not typical. Slavery wasn't in control of the gold mines, and as the world's economy was transformed by the new money, the specie failed to go South. Ultimately, the California gold strike was the death knell for an archaic modality of agrarian capitalism. But the South had no way out; it was locked into holding its wealth in the form of slaves, with human fecundity still the road to monetary increase, while slavery was locked out of the Gold Rush.\n\nEnormous tracts of land were coming on the market as East Texas cotton fields bloomed under the hands of trafficked-in slave laborers. Amid a generally inflationary environment, the price of slaves went up, up, up. But the largest movement of slaves South and West had already been completed; Texas and Arkansas were viable new markets, but Mississippi was already reaching its saturation point.\n\nSouth Carolina's overfarmed cotton land was playing out. Planters migrated westward, a little at a time, drawn by the lure of cheap land and a better deal. \"By 1850 more than 50,000 South Carolina natives lived in Georgia,\" writes Lacy K. Ford, \"more than 45,000 lived in Alabama, and some 26,000 lived in Mississippi.\" The cultural swath they cut as they brought laborers from the most Africanized population of North America remains a permanent part of American culture.*\n\nSouth Carolinian politicians had been actively constructing an ideology for secession since the 1820s, if not all along, one that cast the Constitution as an instrument of oppression now that its original meaning had been perverted by abolitionists. By 1850, they were working to export the secession project to the rest of the South.\n\nThe more of a state's land was under cultivation by slave labor, the more its politicians were apt to favor secession. Most of South Carolina was covered by plantations, with only a few counties in the north of the state not primarily slave-driven. In the plantation counties, nearly all the white population's prosperity depended, one way or another, on the continuance\u2014which meant, the exportation\u2014of slavery. South Carolina, so heavily dependent on slave property, had the most concentrated core of support for secession, arguably followed in zeal by Mississippi.\n\nIn Maryland, only a minority were in favor of secession, though they were vocal. But slavery in Maryland was on the decline. Much of Maryland did not rely on slave labor; between manumission and sale of slaves down South, its enslaved population was actually decreasing. As Bancroft put it, \"counting slave property as so much interest-producing capital, Maryland's course, viewed superficially, was spendthrift, for it was steadily eating into the principal.\"\n\nThe enslaved of Maryland had the most chance to escape via the Underground Railroad; all they had to do was get across the border to Pennsylvania, then push on to Canada. From Baltimore, they might have a chance of slipping away on a boat, the way Frederick Douglass did. While the number of escapees via the Underground Railroad may have been statistically small, the existence of a path to freedom was psychologically significant. The South was a prison, but the enslaved knew there was an escape to the North.\n\nWith the West Coast becoming all free-soil, Southerners were desperate for an outlet to the Pacific. As the \"Great Debate\" over the new western territories continued, Congress mulled the possibility of admitting a state of Deseret (ultimately admitted as Utah), and there was talk of war as slave-soil Texas attempted to annex free-soil New Mexico.\n\nThe march of slavery had been halted at Texas. California was a free state. Now the South's great obsession was its old dream of taking Cuba. A Cuban state in the Union would have two reliably pro-slavery senators. There was no way to make Cuba a free state; its slaves were creating too much wealth. Annexing Cuba would have dramatically boosted the values of extant North American slaveholdings\u2014which is to say, the slave-breeding industry. The United States would not only annex Cuba, but also its enormous slave trade, which as part of the United States would no longer be supplied with Africans, but would have to buy slaves entirely from US sources. Virginia alone would not be able to supply such a demand.\n\nNarciso L\u00f3pez, a Venezuelan adventurer, briefly invaded Cuba in 1848, hoping to annex it to the United States as a slave state. With the backing of secessionist Mississippi governor John Quitman, who hoped to make Mississippi into a slave-breeding state for Cuba's market, right across the Gulf, and with a cheering section that included John L. O'Sullivan, the _New Orleans Delta_ , and the New York _Sun_ , L\u00f3pez invaded Cuba a second time. He organized his venture at the same jumping-off point as Austin's Texas invasion: Banks' Arcade in New Orleans. The one-star flag he flew, based on the Lone Star flag of Texas, first flew on Fulton and Nassau Streets in New York above the offices of the Sun; it was later adapted to become the flag of Cuba, and, with the colors reversed, Puerto Rico.\n\nLanding at the northern Cuban port of C\u00e1rdenas with some six hundred men in May 1850, L\u00f3pez found taking Cuba more difficult than he had imagined. Nor did he learn until he had safely escaped back to New Orleans that a number of Cuban slaves had stowed away in his boats, hoping to escape the plantation; they were returned to Cuba. L\u00f3pez faced indictment for violation of the Neutrality Act, and Quitman was ultimately forced to resign his post as governor.\n\nL\u00f3pez invaded Cuba a third time, in 1851. He was captured and publicly garroted in Havana, using a screw-turn device that crushed his windpipe as he sat in a chair. In the wake of L\u00f3pez's failure, a secret society of Cuban exiles and Southern-rights supporters was formed in the United States to further the work of annexing Cuba and of the expansion of slave territory in general: the Order of the Lone Star, or OLS. Founded in Lafayette, Louisiana, with Pierre Soul\u00e9 as its first president, the organization came to claim\u2014almost certainly hyperbolically\u2014some fifteen thousand members in ten states, with its greatest strength in the Alabama-Texas corridor.\n\nIn response to the controversy over the Compromise of 1850, and growing out of a previous call by the late John C. Calhoun, Mississippi politicians announced a convention to be held at Nashville beginning June 1, 1850.\n\nSouth Carolina was the only state to send a full delegation of four to the Southern Convention, also known as the Nashville Convention. Ostensibly held to discuss ways to preserve the Union, it was promoted by the South Carolinians to legitimize the idea of secession and, not incidentally, to position themselves as the leaders of the movement. Only nine of the fifteen slaveholding states sent delegates; most of those who attended were Tennessee locals.\n\nWe know what the room smelled like. The church where the convention was held had to replace its carpet afterward because of all the tobacco juice and cigar ash. We know that the delegates were entertained by a troupe of Swiss bell ringers. The _Nashville True Whig and Weekly Commercial Register_ noted that, in St. George L. Sioussat's paraphrase, \"there was a noticeable identity in personnel between the southern advocates of the Nashville convention and the promoters of the expedition of General Lopez for the conquest of Cuba\"\u2014most notably Governor Quitman. \"The refusal to admit Cuba as an independent Southern state into the Union,\" said the newspaper, \"is another 'alternative,' vaguely hinted at by Mr. Calhoun... to which 'disunion' would be preferred by the extreme Southern factionists.\"\n\nHeld in the city that was the heart of Jacksonism, the Nashville Convention drove another wedge into the crevasse between secessionists and Jacksonian unionists. In a letter to James Buchanan, the late President Polk's close Tennessee ally Cave Johnson wrote: \"Be not surprised if you should hear even me with my fifty or sixty negroes denounced for favoring the abolitionists because I will not yield to the mad projects of disunion that are now so freely talked of.\"\n\nRhett's aggressive political strategy was much like South Carolina's: take the most extreme position and fight from there. He was disappointed by the lack of secession fever from the other states, whose more moderate members, including unionist Sam Houston, carried the day. Only the South Carolina, Mississippi, and Georgia delegates\u2014the states with the highest concentrations of slave labor\u2014had been strongly in favor of secession. But more significant than the results was that delegates from Southern states had convened to talk about remaining in the Union\u2014which was to say, to talk about secession.\n\nLouisiana did not send delegates to the Nashville Convention, but the excitable French-born Louisiana senator Pierre Soul\u00e9 proposed to the Senate on June 24 the extension of the Missouri Compromise line out to the West Coast, as the convention had recommended. Soul\u00e9 wanted to divide California into two states, with the southern, slaveholding one to be called \"South California.\" Brandishing the by-now standard threat of disunion, he warned that not to leave South California open to slavery would be\u2014he must have shouted it, because it was printed in all caps in the _Congressional Globe_ \u2014\"TO EXCLUDE THE SOUTH FOREVER FROM ALL SHARE IN THE TERRITORIES, THROUGH SPOLIATIONS OF HER RIGHTS AND A DEGRADATION OF HER SOVEREIGNTY, WITHOUT AN ALTERNATIVE THAT DOES NOT END IN AN INGLORIOUS SUBMISSION, OR A RUPTURE OF THE UNION!\"\n\nAs the California debate dragged on, President Zachary Taylor became the second Whig war-hero president to die in office, succumbing suddenly from cholera on July 9, 1850, leaving behind an estate of 131 slaves to be divided among his three children by his lawyer, Judah P. Benjamin. As the nation lauded him, the _Charleston Mercury_ was spiteful.\n\nTaylor was succeeded by Vice President Millard Fillmore, who cleaned house and brought in his own cabinet. Fillmore, from Buffalo, New York, had been a moderately antislavery congressman who voted against the annexation of Texas. But President Fillmore refused to submit the New Mexico constitution to Congress, because it would have brought in another free-soil state and thus would have disturbed the balance in the Senate. \"What is there in New Mexico that could by any possibility induce anybody to go there with slaves?\" asked Daniel Webster in Congress. \"Who expects to see a hundred black men cultivating tobacco, corn, cotton, rice, or anything else on lands in New Mexico, made fertile only by irrigation?\"\n\nTexas's motive for trying to take a big chunk of New Mexico may have been hostage-taking. The Republic of Texas had run up a heavy debt selling bonds that the State of Texas could not pay. Though Fillmore stood up to Texas's attempted annexation of New Mexico, threatening to send troops, Texas got a bailout from its debts as ransom.\n\nFillmore signed the compromise into law, and California became a state on September 9, 1850, which is why Fillmore's name survived in San Francisco to become the name of a rock-concert palace in the 1960s; another of the city's main thoroughfares is named Polk. But signing the compromise into law meant signing the Fugitive Slave Act, which cost Fillmore much support in the North and likely the election of 1852, which he lost.\n\nSlavery had lost the contest for western expansion. But if the intense polemic from Calhoun and his successors had done nothing else, it had made leaving the Union thinkable in the South, and whatever the specific political issue being fought over, it was all about slavery. Increasing numbers of people in the slave states had severed the emotional attachment with a country that could harbor unprosecuted abolitionists. The nation's churches had largely split into Northern and Southern over slavery. Slaveowners wanted Cuba badly, and the secessionists imagined that they were sure to have Mexico, Central America, all the way down.\n\nWhen a second session of the Nashville Convention was called for November, the moderates stayed home. On November 14, 1850, the delegates heard the seventy-three-year-old veteran South Carolina politician Langdon Cheves deliver an oration that presented the case for immediate secession in fiery terms\u2014 _if_ four states would do it. Since three were already in the bag, he was trying to convert just one of the attending delegations.\n\nThe South was not a particularly hospitable place for any Yankee, but for a Northern reporter deep cover was especially necessary. Joseph Holt Ingraham, a Maine-born Episcopal clergyman who discreetly published his letters under the name Kate Conyngham, saw Cheves as a \"hale, white-headed old gentleman, with a fine port-wine tint to his florid cheek.\" Cheves denounced abolitionists as communists, a term recently current from its use during the European-revolutionary year of 1848 in Marx's _Communist Manifesto_ and which would carry racialized connotations in Southern rhetoric into the Jim Crow era, when the Communist Party was the only one to call for full racial equality. Cheves conflated communism with democracy, as well as with jacobinism and anarchy. He denounced them all as equivalent to abolitionism, which he then dismissed with a minstrelic metaphor that referenced the old practice of blacking up one's face before engaging in group attacks:\n\nWhat we call the rights of man, or the admission of great masses to the power of self-government, has brought into action the minds of persons utterly unqualified to judge of the subject practically, who have generated the wildest theories.... This agitation has recently reached the United States. It has been introduced by European agents, and has brought under its delusions the subject of African slavery in the Southern States. It is of the family of communism, it is the doctrine of the anarchist] Proudhon, that property is a crime. It is the same doctrine; they have only _blacked its face to disguise it._[ 27 (emphasis added)\n\nSliding into his big finish, Cheves called for southern unity by evoking a master-race utopia:\n\nUnite, and your slave property shall be protected to the very border of Mason and Dixon's line. Unite, and the freesoilers shall, at their peril, be your police to prevent the escape of your slaves; California shall be a slave State; the dismembered territory of Texas shall be restored, and you shall enjoy a full participation in all the territory which was conquered by your blood and treasure. Unite, and you shall form one of the most splendid empires on which the sun ever shone, of the most homogeneous population, all of the same blood and lineage.\n\nCheves's speech was no fluke: proslavery writers formulated the first generation of American anticommunist rhetoric. Southern ideology had coalesced into a vision of a worthy elite who governs while the unworthy multitude suffer, with South Carolina taking the philosophical lead.\n\nThough the turnout at the Second Nashville Convention was disappointing, Rhett followed up by developing a plan with Quitman to call a secession congress in 1852. On May 7 of that year, Rhett abruptly resigned the Senate seat he had been recently returned to. Taking full control of the _Charleston Mercury_ , the Fire-Eatingest newspaper in the entire South, he installed his son, Robert Barnwell Rhett Jr., as editor.\n\nPeople were being convicted of abolitionism in South Carolina courts, though it was early yet in the building curve of hysteria that took nine more years to become cannonfire. It was not safe to voice even moderate antislavery views. The pro-secession British consul Robert Bunch wrote:\n\nPersons are torn away from their residences and pursuits; sometimes 'tarred and feathered'; 'ridden upon rails,' or cruelly whipped; letters are opened at the Post Offices; discussion upon slavery is entirely prohibited under penalty of expulsion, with or without violence, from the country.\n\nThe Whig party barely outlived Henry Clay. It had divided into sectional wings, and by 1852 it was disintegrating. Former Whigs and antislavery Jacksonians met in the new Republican Party, which did not exist in the South.\n\nThe South Carolinian writer, editor, and statistician James Dunwoody Brownson De Bow began publishing his _DeBow's Review_ in New Orleans in 1846. A deluxe business-news publication, with articles on scientific agricultural management and new developments in technology, it was a voice of the modernizing wing of the pro-slavery movement. Perpetually in financial straits, because its subscribers tended not to pay up, the composition and printing of the magazine was done in the North, where the cost was a third what it would have been in the South, and the quality better. During the Pierce presidency, De Bow was placed in charge of the Seventh Census of 1850, the most detailed US census up to that time. As the 1850s passed, the _Review_ 's pro-slavery, pro-secession positions became more extreme, as it looked toward a more industrial, technocratic, slave-driven South.\n\nBy the 1850s, in the wake of the Fugitive Slave Act, the antislavery movement was making itself felt in the popular arts. Harriet Beecher Stowe published _Uncle Tom's Cabin_ in 1852\u2014a bestselling book that reached even more people in its numerous unauthorized stage adaptations.\n\nWilliam Wells Brown, previously the author of _Narrative of William W. Brown, A Fugitive Slave_ (1847), became the first African American to publish a novel, though it could not be published in the United States at the time. _Clotel, or the President's Daughter_ (1853), was about fictional slave children descended from Thomas Jefferson, who was named in the book. Brown, at the time a fugitive from slavery\u2014or, rather, from the Fugitive Slave Act\u2014fled the United States for London, where the novel was published. He published other versions of it later, including an 1864 American edition that changed the fictional protagonist's parentage from Jefferson to being \"the granddaughter of an American Senator.\"\n\nSlave narratives became an established publishing genre. Solomon Northup, one of the few kidnapped free people to have descended into slavery and then been rescued, returned to his life in Saratoga, New York, and told his story in _Twelve Years a Slave_ (1853), dedicated to Harriet Beecher Stowe. John Thompson, a literate slave who escaped Maryland via the Underground Railroad and became a whaler in New England and a stern Methodist preacher, self-published his autobiography in Massachusetts in 1856: _The Life of John Thompson, a Fugitive Slave; Containing His History of 25 Years in Bondage, and His Providential Escape. Written by Himself._ To out himself as a fugitive slave was a provocation in 1856, when lawmen anywhere in the United States were obligated to hand accused fugitives over without further proceedings. It was a public dare: here I am, come and get me.\n\nSentimental popular songs referred to the interstate slave trade: in response to Stowe's book, Stephen Foster's \"My Old Kentucky Home,\" premiered in 1853 by Christie's Minstrels, was at first titled \"Poor Uncle Tom, Good Night,\" before Foster rewrote it. It's now the state song of Kentucky, but they don't sing the third verse any more:\n\n_The head must bow and the back will have to bend,_\n\n_Wherever the darkey may go:_\n\n_A few more days, and the trouble all will end_\n\n_In the field where the sugar canes grow._\n\n_A few more days for to tote the weary load,_\n\n_No matter, 'twill never be light,_\n\n_A few more days till we totter on the road,_\n\n_Then my old Kentucky Home, good night _\n\nThat's a song about a black man from Kentucky being worked to death in a sugar prison camp in Louisiana. Benjamin Hanby's tearjerking \"My Darling Nelly Gray\" (1856), which Hanby based on a story told him as a child by a black man named Joseph Selby, sang of an enslaved couple broken apart by a sale of the woman to Georgia:\n\n_O my poor Nelly Gray, they have taken you away,_\n\n_And I'll never see my darling anymore;_\n\n_I'm sitting by the river and I'm weeping all the day,_\n\n_For you're gone from the old Kentucky shore. 32_\n\nThis genre of songs continued after the Civil War (James Bland's \"Carry Me Back to Old Virginny\"), when they were bowdlerized and, bizarrely, repurposed into a nostalgia for the Old South.\n\nAnthony Burns, a self-emancipated twenty-year-old man who had escaped from Virginia via the Underground Railroad, was apprehended in Boston on May 24, 1854, by a US commissioner acting on the behest of a slave-catcher hired by Burns's former master. His case became a cause c\u00e9l\u00e8bre; one man was killed when a mob unsuccessfully tried to storm the courthouse to free him. But he was extradited to Richmond, where he was put into isolation at Lumpkin's Slave Jail. The Boston journalist Charles Emery Stevens published a book about the case, which described the conditions under which Burns was held for four months:\n\nThe place of his confinement was a room only six or eight feet square, in the upper story of the jail, which was accessible only through a trap-door. He was allowed neither bed nor air; a rude bench fastened against the wall and a single, coarse blanket were the only means of repose. After entering his cell, the handcuffs were not removed, but, in addition, fetters were placed upon his feet. In this manacled condition he was kept during the greater part of his confinement.\n\nThe torture which he suffered, in consequence, was excruciating. The gripe of the irons impeded the circulation of his blood, made hot and rapid by the stifling atmosphere, and caused his feet to swell enormously. The flesh was worn from his wrists, and when the wounds had healed, there remained broad scars as perpetual witnesses against his owner. The fetters also prevented him from removing his clothing by day or night, and no one came to help him; the indecency resulting from such a condition is too revolting for description, or even thought. His room became more foul and noisome than the hovel of a brute; loathsome creeping things multiplied and rioted in the filth. His food consisted of a piece of coarse corn-bread and the parings of bacon or putrid meat. This fare, supplied to him once a day, he was compelled to devour without Plate, knife, or fork.\n\nImmured, as he was, in a narrow, unventilated room, beneath the heated roof of the jail, a constant supply of fresh water would have been a heavenly boon; but the only means of quenching his thirst was the nauseating contents of a pail that was replenished only once or twice a week. Living under such an accumulation of atrocities, he at length fell seriously ill. This brought about some mitigation of his treatment; his fetters were removed for a time, and he was supplied with broth, which, compared with his previous food, was luxury itself....\n\nOne day his attention was attracted by a noise in the room beneath him. There was a sound as of a woman entreating and sobbing, and of a man addressing to her commands mingled with oaths. Looking down through a crevice in the floor, Burns beheld a slave woman stark naked in the presence of two men.\n\nOne of them was an overseer, and the other a person who had come to purchase a slave. The overseer had compelled the woman to disrobe in order that the purchaser might see for himself whether she was well formed and sound in body. Burns was horror-stricken; all his previous experience had not made him aware of such an outrage. This, however, was not an exceptional case; he found it was the ordinary custom in Lumpkin's jail thus to expose the naked person of the slave, both male and female, to the inspection of the purchaser. A wider range of observation would have enabled him to see that it was the universal custom in the slave states....\n\nAfter a while, he found a friend in the family of Lumpkin. The wife of this man was a \"yellow woman\" whom he had married as much from necessity as from choice, the white women of the South refusing to connect themselves with professed slave traders. This woman manifested her compassion for Burns by giving him a testament and a hymn-book. Upon most slaves these gifts would have been thrown away; fortunately for Burns, he had learned to read, and the books proved a very treasure. Besides the yellow wife, Lumpkin had a black concubine, and she also manifested a friendly spirit toward the prisoner.\n\nThe house of Lumpkin was separated from the jail only by the yard, and from one of the upper windows the girl contrived to hold conversations with Anthony, whose apartment was directly opposite. Her compassion, it is not unlikely, changed into a warmer feeling; she was discovered one day by her lord and master; what he overheard roused his jealousy, and he took effectual means to break off the intercourse. (paragraphing added)\n\nBurns was sold at auction after four months to a planter, but his freedom was subsequently purchased by L. M. Grimes, a minister who had established a church for runaway slaves in Boston. Fugitive slaves had become pop culture by this point; according to Stevens, P. T. Barnum offered the newly freed Burns $500 to be an exhibit in his museum in New York, which Burns indignantly turned down, reportedly saying, \"He wants to show me like a monkey!\"\n\nN.B. FORREST, Dealer in Slaves, No. 87 ADAMS STREET.\n\nHAS just received, from South Carolina, twenty-five likely young Negroes, to which he desires to call the attention of purchasers. He will be in the regular receipt of Negroes from North and South Carolina every month.\n\nHis Negro Depot is one of the most complete and commodious establishments of the kind in the Southern country, and regulations, exact and systematic cleanliness, neatness and comfort being strictly observed and enforced, and his aim is to furnish to customers No. 1 servants and field hands, sound and perfect in body and mind.\n\nNegroes taken on Commission. \u2014 Memphis _Eagle and Enquirer_ , June 2, 1857.\n\nThe western Tennessee river port of Memphis was a jumpoff point for selling slaves into the new territories of Arkansas and Texas. Memphis was a mature slave market by 1852, when the thirty-year-old slave trader Nathan Bedford Forrest begins to appear in the city's records. The hotheaded Forrest was at least as rash a man as Jackson, but had even less education. He instilled fear in those around him, and he didn't stay business partners with anyone very long; for a year he worked in a partnership called Forrest & Jones; then, with the more established Byrd Hill, he cofounded Hill & Forrest; and by 1855 was partners with Josiah Maples in Forrest & Maples. He bought a double lot on Adams Street\u2014named for John Adams, between Washington and Jefferson Streets\u2014using 85 Adams for his house and 87 Adams for his jail, and soon he began to run the customary 500 NEGROES WANTED advertisements in the paper, while opening depots in other towns. He seems to have procured his merchandise in what had become the standard way: canvassing planters personally and via agents, buying people one at a time. It was no longer necessary to go to the Eastern Shore of Maryland to find farmers willing to sell slaves. These were the high-priced years of the slave trade, and profits came fast.\n\nIn a mythologizing account written at the time of Forrest's funeral in 1877, Lafcadio Hearn, who was passing through Memphis at the time, wrote that Forrest was \"reported to have been 'kind' to his slaves, yet to have 'taught them to fear him exceedingly.'\" White people were afraid of him, too. He did not hesitate to escalate to lethal action, as when he put a gun up to a tailor's head for having delivered a bad suit. He made a lot of money in the slave business, some of which he invested in land, before winding it down in 1860 and getting out of it by 1861. Other traders continued in the business after the South seceded, but Forrest went to war, which allowed him to further develop the talent for blunt violence that had served him so well in slave trading.\n\n_A broadside advertisement for Nathan Bedford Forrest's slave dealership in Memphis._\n\n*The _Oxford English Dictionary_ notes the emergence in 1856, in the United States, of a new word: _vigilante._\n\n*From its platform in Mississippi, the \"Delta blues\" reaches back across the southeast to South Carolina and Georgia. Georgia was the birthplace of the three singers who did the most to bring the vocal dynamics of the black church into the mainstream popular repertoire: Ray Charles, Little Richard, and James Brown.\n\n#   41\n\n# **Hiring Day**\n\n_INSURE YOUR NEGROES IN THE AETNA LIFE INSURANCE COMPANY, OF HARTFORD, CONN. RATES REDUCED. Z. GIBBONS, Gen'l Ins. Agt., No. 3 Upper Street Lexington, KY_\n\n\u2014Lexington (KY) Semi-Weekly _Statesman_ , Feb. 21, 1860\n\n\"SEPARATION OF FAMILIES? YES, indeed,\" said the fugitive Lewis Clarke at an antislavery meeting in Brooklyn in 1842.\n\nIf the gentleman had been in Kentucky at New Year's time, he wouldn't need to ask that question. Of all the days in the year, the slaves dread New-Year's day the worst [of] any. For folks come for their debts then; and if anybody is going to sell a slave, that's the time they do it; and if anybody's going to give away a slave, that's the time they do it; and the slave never knows where he'll be sent to. Oh, New-Year's a heart-breaking time in Kentucky\n\nNew Year's Day, a day for settling debts, was also the occasion of a great annual party thrown by white people throughout the antebellum South: slave-hiring day. (\"Hiring\" is the customary term, though \"rental\" might be more appropriate.) A single tavern might be the stage for renting hundreds of legal nonpeople. They stood in the seasonal bitter cold for as long as it took, while drink flowed freely from the bar for prospective purchasers. Those too poor to own slaves could come and gaze at the possibilities. For the enslaved, it was the day when they learned where they would be sent next, whether back to the same place as last year or to a new and dangerous job far away.\n\n\"To the slave mother New Year's day comes laden with peculiar sorrows,\" wrote Harriet Jacobs. \"She sits on her cold cabin floor, watching the children who may all be torn from her the next morning; and often does she wish that she and they might die before the day dawns.\" For some, this system made the traumatic experience of being auctioned off into an annual event. \"Them ole red headed yaps would bid us off to the highest bidder and we couldn't do nothin' but pray,\" recalled a formerly enslaved Tennessean. \"Yes, fine times for them, but awful for us po' niggers. Yes'm, they would cry you off to the highest bidder for the next year. One by one, we had to get up on that block, and he bid us off.\"\n\nAll sorts of service occupations throughout the South were done by rented-out slaves, who on a year's contract typically earned their owners between 10 and 20 percent of their sale value besides relieving him or her of the necessity of housing, clothing, and feeding them. \"Those wages must represent exactly the cost of slave labor,\" noted Frederick Law Olmsted; they were typically paid to the slaveowner at year's end though sometimes monthly or quarterly, with a security deposit and a bond required. For an enslaved person, this could be a relatively advantageous situation, as it was much preferable to be enslaved in town than on a plantation, and it was way better than being sold down South. Or it could be atrocious.\n\n_Hiring contract in Petersburg, Virginia, dated January 2, 1865, for \"negro slave\" Cely and her children Rosie and Mary._\n\nSlave hiring was particularly common in Virginia, where there was less plantation work to do and where there was a variety of other kinds of work suited for slave labor. By the 1850s, Virginia's economy had diversified. After lying fallow, some of its worn-out tobacco land had been restored to productivity for other kinds of uses, though none had the income-generating power of tobacco.\n\nFrederic Bancroft described \"hiring\" as \"a restricted kind of slave trade,\" and emphasized the importance of prestige to both slaveowner and slave-hirer: \"the hirer as well as the owner was popularly considered as belonging to the slaveholding class.\"\n\nIt boosted the hirer's prestige to have a slave working for him. At the same time, it provided the owner a lucrative alternative to selling slaves, which would have indicated a drop in his or her social standing. If that had to happen, it was best to keep it on the down low. \"Richmond was the best place in the State to sell nearly all kinds of slaves at good prices without publicity as to ownership,\" wrote Bancroft.\n\nRichmond might not have looked like much of an industrial city to a Northerner, but it was the most developed in the South. Meanwhile, the sale of so many young people to traders over the decades had brought in plenty of capitalized labor to work with. Virginia had the most railroad mileage of any Southern state\u20141,771.16 miles in 1860, more than four times that of Maryland. \"The completion of several rail lines in Virginia coincided with a dramatic surge in the prices of tobacco, wheat, and corn,\" writes John J. Zaborney. \"The railroads so reduced transport costs that Virginia farmers shipped more of their products, more cheaply, to Virginia's growing urban centers.\"\n\nRailroads made possible the cultivation of new lands, increasing the state's development. They also made it easier to ship slaves; as a visitor can still perceive today despite the subsequent destruction of the town's core, Richmond's teeming slave-mart district of the 1850s was located by the town's railroad center. A traveler in 1856 wrote:\n\nYou notice... that every train going south has just such a crowd of slaves on board, twenty or more, and a \"nigger car,\" which is very generally also the smoking-car and sometimes the baggage-car. You notice also that these slaves whom you constantly meet going south in the trader's hands are not old men and women or by any means malicious-looking ones.... but are for the most part apparently picked slaves, boys and girls or young men and women, eighteen-twenty, twenty-five...\n\nThe trade in Richmond was located in an approximately thirty-block area between Fifteenth and Nineteenth Streets in the low-lying part of town called Shockoe Bottom, for which the large, comfortable Odd Fellows Hall between Fourteenth and Fifteenth on Franklin served as an auction site. The extension of Fifteenth Street, between Broad and Franklin, was called Wall Street, and was also known as Lumpkin's Alley for its tenant Robert Lumpkin, who operated the best known of the city's many slave-trading posts, and was more informally known as the Devil's Half Acre. Lumpkin's Slave Jail has become emblematic of Richmond's slave trade, but Lumpkin was only one of dozens of traders, and his jail was one of several.\n\nRecords show that as of 1840 Lumpkin owned an eight-year-old girl named Mary, by whom he subsequently had five children. As the pending acquisition of Texas stimulated the Virginia trade, he bought three lots on Wall Street in 1844, which were assessed at $6,000 in 1848. Lumpkin was not the first trader to operate on that site; the Richmond trader Bacon Tait was operating there in the early 1830s, and he built the brick jail Lumpkin later used. Tait sold it to the trader Lewis A. Collier, who made further improvements but was ruined in the post-Jackson depression; the Bank of Virginia took possession of the property in 1844, and sold it to Lumpkin.\n\nAs was typical of the larger slave jails, there were four buildings to the compound. One was a boardinghouse for visiting traders; another was a kitchen\/canteen. The filthy Shockoe Creek ran through the property, and the slave jail itself was down at the bottom of the embankment, on the lowest, muddiest, least desirable piece of ground.\n\nLike other such jails, it had a whipping room; the Reverend A.M. Newman of Opelousas, Louisiana, who as a boy was sent to be whipped there in 1862, recalled that \"on the floor of that room were rings. The individual would be laid down, his hands and feet stretched out and fastened in the rings, and a great big man would stand over him and flog him.\"\n\nLumpkin lived in the main building, together with Mary, now his concubine\u2014the \"yellow woman\" who had given Anthony Burns a hymnal\u2014and their five white-looking children, Martha, Annie, Robert, Richard, and John. Martha and Annie were sent to be educated at Mrs. John C. Cowles's Female Seminary in Ipswich, Massachusetts, where they ran no risk of being sold as fancy girls if their father should fall into debt; ultimately, all five were sent to live in Pennsylvania, where Lumpkin owned property. He had freed Mary by 1857, when she appears as a free woman of color in Richmond court records. However, while Mary may have been referred to in daily parlance as his \"wife,\" the state of Virginia prohibited \"interracial\" marriages until the United States Supreme Court's _Loving v. Virginia_ decision of 1967.\n\nThe prices in Richmond were the lowest of any of the major slave markets because it was primarily a wholesale mart for export, so some enterprising Virginians found it an attractive business proposition to buy slaves there specifically in order to rent them out locally, doubling their money in a few years.\n\nMany small slaveholders lived on the income that one or a few enslaved laborers earned by working for others; this was an especially important nest egg for slaveholding widows, and even for mentally incompetent persons who had inherited slaves. Churches received income by renting out the services of captives. To transact all this business, there were specialized employment agents dedicated to renting out slave labor; every Southern town had them. Southern municipalities made money from taxes and fees on slave-rental, sometimes requiring the purchase of a numbered badge that had to be worn by a rented slave.\n\nEven those people who were too old to be sold to a trader for export as cotton-field labor might still bring in a comfortable income locally as domestic servants or other types of workers. Hotel and boardinghouse guests were commonly attended to by rented slaves; Frederick Law Olmsted marveled at the quality of service he received in his hotel at Richmond, where a middle-aged enslaved man named Henry, who, according to the hotel owner, would have been worth $2,000 if he had been a little younger, \"becomes your servant while you are in your room; he asks, at night, when he comes to request your boots, at what time he shall come in the morning, and then, without being very exactly punctual, he comes quietly in, makes your fire, sets the boots before it, brushes and arranges your clothes, lays out your linen, arranges your dressing gear, asks if you want anything else of him before breakfast, opens the shutters, and goes off to the next room.\"\n\nEvery kind of work could be contracted for, from wet nursing to piloting a boat. \"Fieldhands, washers and ironers, cooks, porters, waiters, house-maids, plain mechanics of various kinds and half-grown boys and girls were numerous in nearly all hiring markets,\" writes Frederic Bancroft. For the enslaved, a job in even a small city was much preferable to field labor; besides making it easier to abscond, it allowed access to merchandise and opportunities to do business, which many did with great eagerness when they had the opportunity.\n\nWhile visiting Macon, Georgia, in April 1907, Bancroft interviewed a formerly enslaved man named Henry G. Griffin, who was, he said, bought twice via mortgage, once at the age of eleven months and again at the age of sixteen years. At first he \"worked in a store nearly like a clerk,\" as Bancroft put it; then, in Griffin's words, \"I sampled cotton for E.A. Wilcox, who paid [to Griffin's \"owner\"] at the rate of $30 a month for me. All the sample cotton was given to the samplers. Sometimes there was 40 or 50 pounds a day.\" That gave him a steady stream of something saleable. Griffin was treated rather well, he recalled, meaning that he was not separated from his family and could make some money at his job.\n\nGriffin took Bancroft sightseeing Southern style, to the barred windows of the brick city guardhouse on the east side of Fourth Street between Cherry and Poplar where, as was the norm in Southern jails, slaves could be sent for whipping. Speaking as an eyewitness, Griffin recalled that they were beaten in the most common slave-whipping position: stretched out face down with their hands and feet tied. Women, said Griffin, were stretched on the ground with a hole beneath their bellies, \"so that there was no chance of striking their stomachs,\" wrote Bancroft. Or, though Bancroft didn't put it this way, if they were pregnant, the valuable fetus would be protected while the mother was being\u2014the customary term was \"corrected.\"\n\nThe great peril of being hired out was that the hirer, who had no long-term stake in the laborer's well-being, might work him or her abusively hard, assign a dangerous job, or simply beat the daylights out of him or her. Accidents of all types were common, nowhere more than in the industrial jobs given to slaves. Underground mining was particularly dangerous, but many types of occupational accidents were common. Slaveholders typically required the hirer to take out insurance, so slave-hiring was a boon to insurance companies.\n\nBy custom, slave-hiring contracts were for one year, commencing on January 2 and ending on Christmas Eve, when the contract became payable. Then the hired-out people would return home for a brief, heartbreaking reunion with their families, perhaps learning that loved ones had died or been sold away during the year.\n\nSome enslaved people, typically the highest skilled workers such as carpenters, were sometimes allowed to hire themselves out. The repeated laws against the practice make it clear how common it was for them to handle the transaction themselves and live in their own quarters in town, paying their \"owner\" his or her fee and keeping any surplus for themselves.\n\nBut many were merely transferred from abusive master to abusive master. John J. Zaborney cites the case of a slaveholder who wrote a letter to a man who had rented a woman named Delphia from him, which perhaps provides one demonstration of the workings of pro-slavery theology:\n\nI am sorry to hear that Delphia is so impudent but glad to be able to recommend a cure which I have often tried with certain success. Let the overseer take Delphia and give her fifty lashes, on her bare and repeat the dose morning after morning...\n\n... Delphia is... no inconsiderable part of your household and I humbly suggest that it is your duty to command her that she may keep the way of the Lord, to do justice and judgments (see Genesis 18 chap.) What is due from Delphia to you? Service, labour\u2014ready, willing faithful service unquestioned obedience. If she fails in this she keeps no[t] the way of the Lord to do justice and judgment. (paragraphing added)\n\nIn 1850s Richmond, the larger hirers of young enslaved males were the tobacco factories, which prepared raw tobacco for chewing or smoking. Zaborney estimates that about half the tobacco factories' labor force consisted of hired slaves in 1850, and two-thirds in 1860, by which time there were forty-nine tobacco factories in the town hiring about thirty-four hundred laborers. The tobacco factories did not house workers, but gave them an allowance to rent lodgings in town, creating an entire class of enslaved urban consumers with a little pocket money.\n\nMusicians at a Saturday night dance were commonly enslaved workers, whose musical skills sometimes allowed them an opportunity to make a few coins for themselves. But in one case the scale was much larger. The South's best-known concert attraction was a slave: Blind Tom (Thomas Wiggins). With a mental age of six or so, Wiggins was what was then called an idiot savant and might today be called severely autistic. Born in Columbus, Georgia, in 1849, he had an eidetic memory for sound. He could do little else but play piano, which he did all day, every day. He could reproduce verbatim an entire political speech in all its sonic detail without understanding any of it; he could simulate convincingly the sounds of a rainstorm on the piano, or a battle; he could play music after hearing it once, and was said to know some seven thousand pieces; and he composed music, of which we have no recording or piano roll, though some sheet music was published, presumably bearing a dubious relationship to what he actually played.\n\nTom's curious, extreme talent probably saved him from the common fate of handicapped slave children, an early death. His master, the Columbus lawyer known as \"General\" James Neil Bethune, made a fortune touring Wiggins, taking in over $100,000 a year from London concerts alone in 1866, with a guardian agreement negotiated in 1864 that allowed Bethune to retain 90 percent of his no-longer-enslaved client's earnings. Until the end of slavery, Blind Tom did not play in the free-soil states, where he might have been subject to confiscation from Bethune. But he was a familiar figure on the concert circuit in the South. What a model for musical labor relations: the manager owned not merely the artist's contract but also the artist, and could sell him if he chose. Louis Hughes noted the impact of Blind Tom's concert in Memphis:\n\n_The \"Oliver Gallop,\" a piece of sheet music published ca. 1860, composed by the autistic, enslaved piano virtuoso Thomas Wiggins, or \"Blind Tom.\"_\n\nPeople came from far and near to hear him. Those coming from the villages and small towns, who could not get passage on the regular trains, came in freight or on flat bottom cars. The tickets were $5.00 each, as I remember, Boss said it was expensive, but all must hear this boy pianist. Many were the comments on this boy of such wonderful talents. As I drove our people Home they seemed to talk of nothing else. They declared that he was indeed a wonder.\n\nAfter secession, fearing the worst should he be removed from Bethune, the frightened, mentally impaired, blind teenager declared himself in favor of the Confederacy, making him its best-known black supporter.\n\n_There are not many slavery-era paintings depicting slave auctions. The people conducting them did not want them portrayed, and an artist caught sketching might find himself in trouble. This 1862 painting by Lefevre Cranstone, titled_ Slave Auction, Virginia, _depicts eight women being sold, three of them with children, as men leeringly assess them. The painting was first exhibited in London in 1863._\n\n#   Part Six\n\n# **The Revolution**\n\n#   42\n\n# **Vanish Like a Dream**\n\n_My soul is tormented with fears! Ah! they are dead! Their swords are red from the fight. O my brother! my brother! why hast thou slain my Salgar? why, O Salgar! hast thou slain my brother? Dear were ye both to me! what shalt I say in your praise? Thou wert fair on the hill among thousands! he was terrible in fight. Speak to me; hear my voice; hear me, song of my love! They are silent; silent for ever! Cold, cold, are their breasts of clay! Oh! from the rock on the hill, from the top of the windy steep, speak, ye ghosts of the dead! speak, I will not be afraid! Whither are ye gone to rest? In what cave of the hill shall I find the departed? No feeble voice is on the gale: no answer half-drowned in the storm!_\n\n\u2014Ossian [James Macpherson], _Songs of Selma_\n\nUPRIVER FROM THE GULF of Mexico port of Mobile, William Rufus DeVane King cofounded the town of Selma, naming it for the city in _Songs of Selma_ , an over-the-top, internationally popular literary fraud.\n\nPurportedly a collection of Celtic texts by an ancient Gaelic bard named Ossian, _Songs of Selma_ was accepted by the reading public as genuine, but it was the fabrication of one James Macpherson, who seems to have dressed folktales up in ludicrously overwrought language. Marking a worldwide literary trend toward kitschy hyperromanticism, the _Songs of Selma_ became a staple of a strain of pseudo-Celtic-nationalist mythology in spite of their bogosity.\n\nKing's family had done so well in the land scramble that they were the largest slaveholding family in the state, and King became Alabama's first senator in 1819. He was, according to an anonymous campaign biography, \"about six feet high, remarkably erect in figure, and is well proportioned.\" Some in Washington called him \"Aunt Fancy\" behind his back, while Andrew Jackson is known to have referred to King's good friend James Buchanan as \"Miss Nancy.\" Tennessee congressman Aaron Brown, in a letter to Sarah Childress Polk, referred to King as Buchanan's \"wife.\" Buchanan and King were a pair of lifelong bachelors who were not attracted to women, and it was \"somewhat common,\" writes Robert P. Watson, for Washingtonians and others to refer to them mockingly as women. Perhaps they were just good friends, but from our contemporary perspective, they look like a gay couple. And, yes, queerness\u2014or gayness, or call it what you will\u2014existed then, though it was less well understood in James Buchanan's rural southern Pennsylvania birthplace than in the big cities.\n\nBuchanan and King met in 1834 and moved in together in 1836, maintaining a stable household in Washington. Both had nieces who posthumously burned a number of their uncles' letters to each other. They domiciled together until 1844, when King left the country to be Polk's minister to France.\n\nIf there had been same-sex marriage with community property, Buchanan could have been a large slaveholder, because King owned over a hundred slaves. Though Buchanan lived in the free state of Pennsylvania, he was from the state's south, the borderland with slave territory, and he was ardently pro-slavery, to say nothing of duplicitous. \"I cannot rely upon his honest and disinterested advice,\" Polk wrote in his diary about Buchanan when he was Polk's secretary of state. Polk's admiring biographer Robert W. Merry calls Buchanan \"self-centered, devious, dishonest, and cowardly.\"\n\nThe power couple's plan was for Buchanan to be president and King to be vice president. It went awry: Buchanan didn't get the nomination in 1852, losing on the forty-ninth ballot to the former Mexican War general Franklin Pierce, with Buchanan thus being edged out by the most pro-slavery New Englander. But King got the vice presidential nomination, apparently in the hope that Buchanan would help out in the battleground state of Pennsylvania. After the nominating convention in Baltimore, New Hampshire congressman Edmund Burke wrote to Pierce, addressing him as \"General\": \"I think we did right in putting King on the ticket. You know he is Buchanan's bosom friend and thus a great and powerful interest is conciliated.... The slave states will fall into our laps like ripe apples.\"\n\nThe Democrats won, but King was ill with tuberculosis, and he took the oath of office for vice president of the United States from his convalescence in Cuba, a political feat that has not been repeated since. Wasting away, he barely made it home to Selma in time to die, forty-five days after the beginning of his term, on April 18, 1853.\n\nFor the rest of Pierce's term, the office of vice president was vacant.\n\nEven Franklin Pierce's biographers can't find much good to say about him. A Jacksonian in politics and a romantic in literary taste, Pierce was the only president from New Hampshire. Once in office, he named his close friend and campaign biographer, the perpetually broke writer Nathaniel Hawthorne, to the plum post of US consul in Liverpool. In the biography he wrote of Pierce, the New Englander Hawthorne had eagerly stoked sectional tension, disparaging \"those northern men... who deem the great cause of human welfare as represented and involved in this present hostility against southern institutions.\" (At the risk of redundancy, we will remind our reader that \"southern institutions\" centrally included the legal right to force-mate adolescent girls and sell the resulting children.)\n\nHawthorne went on to explain Pierce's position on slavery: it was God's problem, not the president's. He characterized slavery as \"one of those evils which divine Providence does not leave to be remedied by human contrivances, but which, in its own good time, by some means impossible to be anticipated, but of the simplest and easiest operation, when all its uses shall have been fulfilled, it causes to vanish like a dream.\"\n\nThe country was torn in half over slavery, the Fugitive Slave Act was in effect, the Whig party was crumbling, Southern radicals were organizing to secede, and Hawthorne promised that one day slavery wouldn't be a problem.\n\nElected on a strongly pro-Southern platform that included the annexation of Cuba, Pierce named the Mexican War veteran and already-declared secessionist Jefferson Davis as his secretary of war, giving him on-the-job training in the management of armies. For his part, Davis was urgently interested in a southern route for the proposed transcontinental railroad, though it was a disadvantageous route from an engineering standpoint, and he enthusiastically promoted what became known as the Gadsden Purchase, negotiated in 1854 by James Gadsden, the Jacksonian US ambassador to Mexico.\n\nGadsden was a Charleston aristocrat. His grandfather, Christopher Gadsden, had built Gadsden's Wharf; a second cousin, Thomas Gadsden, was one of Charleston's most prominent slave dealers of the 1850s, though there was quite some competition for that title. Gadsden was an old-line Jacksonian who had served in the Seminole campaign. At a time when the secession project was already well under way, the $10 million Gadsden Purchase was the last major acquisition of territory by the continental United States, giving Washington control of what is now the southerly strip of Arizona and New Mexico. The reason for the Gadsden purchase, with its farthest-South-possible location, was the same reason a wealthy South Carolinian's name was on it: rail shipment would be the only practical way to export slaves from the South to southern California, as well as the best way to bring California gold back. A railroad was needed; the South wanted it.\n\nThe Compromise of 1850 that admitted California as a free-soil state had not removed the South's dream of slavery in a separate Southern California. Far from it: speaking of an elderly slaveowner in 1855 who wished to sell out, Frederick Law Olmsted noted that \"he thought of taking them to Louisiana and Texas, for sale; but, if he should learn that there was much probability that Lower California would be made a slave State, he supposed it would pay him to wait, as probably, if that should occur, he could take them there and sell them for twice as much as they would now bring in New Orleans.\" Olmsted also quotes a politician whose campaign in 1855 argued that \"if slavery were permitted in California, negroes would sell for $5,000 apiece.\" That was, of course, pure conjecture; but it was what slaveowners wanted to hear. With even Mississippi approaching saturation point for enslaved labor, population pressures militated for new territory to sell the ever-increasing human capital into. In other words, the slave-breeding industry was reaching critical mass for unraveling\u2014unless the expansion of slavery territory could postpone the collapse. From California, it would have to expand outward into Asia, and this was discussed on occasion.\n\nDescribing the slave-labor \"Colony under my lead\" he would build in California, Gadsden wrote in an 1851 letter to General Thomas Jefferson Green in San Francisco:\n\nNegro Slavery, under Educated & Intelligent Masters can alone accomplish this:\u2014They have been the Pioneers & basis of the civilization of Savage Countries... Let us feed our own People & add Cotton Corn & Rice to the Gold export... and No power can vie with that which is washed by the Pacific... Our Men could thus at the season for mining be employed in extracting the Gold, while the Women & Boys could raise their food & raiment... [I will] Make our Road as we go by an organised Corps of Pioneers & Axe men & reach California with both Negroes & animals in full vigor to go to work.\n\nMeanwhile, schemes for expanding the empire of slavery into Latin America proliferated. As president, Pierce managed to remove Buchanan from his immediate sphere of intrigue by sending him to England in 1853 as ambassador to the Court of St. James, where he worked toward the longtime dream of the annexation of Cuba. He traveled to Ostend, Belgium, where he met with Pierre Soul\u00e9 and Virginia's John Mason, the former of whom was then Pierce's minister to Spain and the latter minister to France, to formulate an aggressive document, largely written by Soul\u00e9. Published in October 1854, the Ostend Manifesto announced US plans to acquire Cuba\u2014by purchase if possible, but if not, it warned, in a classic piece of Southern hyperbole, \"by every law, human and divine, we shall be justified in wresting it from Spain, if we possess the power.\"\n\nThe manifesto also made a different case for the annexation of Cuba, that of self-defense against slave rebellion, invoking the possibility that an \"Africanized\" Cuba might become \"a second St. Domingo,\" and arguing that taking Cuba would be justified \"upon the very same principle that would justify an individual in tearing down the burning house of his neighbor if there were no other means of preventing the flames from destroying his own home.\"\n\nBankrolled by Cuban exiles, John Quitman, who by 1853 was the leader of the secret Order of the Lone Star, tried to organize an invasion of Cuba that never sailed. But another filibuster, the Nashvillean William Walker, a great admirer of Napoleon, invaded and took over Nicaragua in 1855. Walker had previously been acquitted by a sympathetic jury of violating the Neutrality Act for taking over Baja California and declaring it the Republic of Southern California. An anonymous correspondent to _DeBow's Review_ called on Virginians to relocate with their slaves to Walker's Nicaragua, pooh-poohing the problem of yellow fever and exulting:\n\nHere is a new State soon to be added to the South, in or out of the Union\u2014here is the first piece of Mexico in fact, the whole of which, in a short lifetime, will fall into the hands of the white men of North America, and it behooves you to begin in time to secure your portion of the prize, for you are going to find it no easy task. I speak of Mexico (including of course, Central America in the same destiny) with absolute confidence. The expulsion of the Spanish masters has left that country to the red man\u2014the Spanish Indian\u2014an inferior and incompetent race, and the result is altogether analogous to the result of emancipation in the West Indies, just as the cause is similar. In both instances, the support of the strong will and high intelligence of the white man has been withdrawn, and, forthwith the red man and the black man, liberated but incapable and helpless, have sunk down from the position in which they had been held up and sustained, and lapsed rapidly towards their original and natural barbarism.\n\nThe boosterism reflected the fact that every newly acquired slave territory revalued a slaveowner's human holdings upward drastically. President Pierce obligingly recognized Walker's Nicaraguan government in 1856, but Walker was driven out in 1857. He was captured and turned over to Honduras in 1860, where he was promptly executed by the Honduran government.\n\nThe great issue of Franklin Pierce's presidency was his signing of Stephen Douglas's disastrous Kansas-Nebraska Act on May 30, 1854, as pro-slavery bandits attempted to implement slavery in Kansas through murderous intimidation, with two rival state constitutions, one slave and one free, vying for recognition. The clashes were a precursor of the violence of the coming war over slavery, right down to the lethal participation of the abolitionist terrorist John Brown, who in 1856 was a commander in two battles in Kansas. It was after expressing his outrage in the Senate over a massacre in Lawrence that abolitionist Senator Charles Sumner was viciously beaten while seated at his desk on the Senate floor by South Carolina representative Preston Brooks.\n\nDouglas's Kansas-Nebraska act sent shock waves through the North, because in declaring that Kansas and Nebraska could be slave territory, it effectively repealed the Missouri Compromise, which had been the basis of the entire deal between North and South since 1821. In doing so, it cut the fragile tethers of a frayed peace treaty loose.\n\nPierce left office unpopular, after one term, in 1857.\n\nThe oldest living Jacksonian still in a major position of power, the eighty-year-old Roger B. Taney, had been chief justice of the Supreme Court for twenty-four years when he handed down one of the most notorious decisions in the history of American jurisprudence: _Dred Scott v. Sandford._ The court had been deliberating the case for two years, but it held the decision until a slightly less old Jacksonian, sixty-five-year-old James Buchanan, was inaugurated as president in 1857. It was Buchanan's fourth try to reach the presidency by appealing as cravenly as possible to the slaveowners' wish list; this time, it worked.\n\nThe annexation of Cuba\u2014which would have been an enormous windfall for slave breeders\u2014was Buchanan's major campaign issue. Had he been able to do it, he would have joined Jefferson, Jackson, and Polk in the pantheon of territorial expanders. Spain wasn't about to let it happen. Meanwhile, Cuban agriculture was changing, and a few planters were looking to emulate the US slave-breeding model for sale to their own voracious domestic slave market. A boosterish 1859 article in _Harper's_ extolled the practice of one:\n\nIn former times, before the introduction of machinery, the number of negroes employed was greater, and, in consequence of the short space of time allowed for the manufacture of sugar, the mortality among the laborers was excessive. Ten per cent. per annum used to be a common average of deaths on plantations managed by reckless and unwise agents; in such cases the negroes worked twenty hours out of the twenty-four during the season. Since the introduction of steam the negro mortality has been much less, and the number of hands employed has been largely diminished. A force of a hundred field hands will now suffice to work a very large plantation.\n\nExperience has also shown the mischief of overworking the men. Mr. Drake, of Havana, long since proved that by allowing his negroes a fair amount of sleep and nutritious food, they could not only perform far more work than the hands of his neighbors, _but could add yearly, by natural increase, a large sum to his estate._ On many estates in Cuba, it is known, though the female slaves are quite numerous, the natural increase is comparatively nothing. (paragraphing and emphasis added)\n\nPresident Buchanan did not acquire Cuba, but he began one of the most remorselessly pro-slavery administrations ever. Buchanan not only knew in advance from Taney what the _Dred Scott_ decision would be; he improperly and without precedent interfered with the decision-making process, pressuring judges. Two days before the decision was announced, Buchanan lied in his inaugural address about not knowing what the result would be. He promised disingenuously that \"to their decision, in common with all good citizens, I shall cheerfully submit, whatever this may be,\" though he already knew the outcome. That was what we now call a \"dog whistle\"\u2014a message to those who could hear it.\n\nThe ruling caused much anger in the free-soil states. Among other improper actions Buchanan took regarding the decision, he lobbied one court member from the North to support the majority ruling so as to make it look like less of a coup d'etat by the South. The _Dred Scott_ decision was political hardball; a blatant attempt to remodel American law to conform with the pro-slavery agenda, it far overreached the limits of the case. It was the first overturning of a federal law by the court, the previous _Marbury v. Madison_ having struck down only a single clause. _Dred Scott_ declared the Missouri Compromise unconstitutional.\n\nThe case had been making its way up the judicial pipeline since 1842. First it had turned on the enslaved plaintiff Dred Scott, who had been taken by his captor into the free states of Illinois and Wisconsin, and thus, Scott's lawyers argued, had become free. As the case progressed, it turned on a widow who wanted to keep Scott and his family enslaved; it became more complicated when the widow assigned the supposed ownership of Dred Scott to John F. A. Sanford,* a New York lawyer. Now, before the Supreme Court, Sanford was arguing that never mind that as Scott's owner he lived in the free state of New York, Scott as a slave was not a US citizen and therefore had no standing to sue. Taney agreed with him, delivering his rambling, expansive opinion on March 5, 1857. In what Frederick Douglass called a \"hell-black judgment,\" Taney held that slavery was a constitutionally protected form of property, as he affirmed the constitutionality of the hereditary perpetuity of slavery unto the nth generation throughout the United States. In his opinion, charged with key points of pro-slavery ideology, he specifically addressed the Declaration of Independence's assertion that \"all men are created equal\":\n\nIt is too clear for dispute that the enslaved African race were not intended to be included, and formed no part of the people who framed and adopted this declaration, for if the language, as understood in that day, would embrace them, the conduct of the distinguished men who framed the Declaration of Independence would have been utterly and flagrantly inconsistent with the principles they asserted, and instead of the sympathy of mankind to which they so confidently appealed, they would have deserved and received universal rebuke and reprobation.\n\nYet the men who framed this declaration were great men\u2014high in literary acquirements, high in their sense of honor, and incapable of asserting principles inconsistent with those on which they were acting. They perfectly understood the meaning of the language they used, and how it would be understood by others, and they knew that it would not in any part of the civilized world be supposed to embrace the negro race, which, by common consent, had been excluded from civilized Governments and the family of nations, and doomed to slavery. They spoke and acted according to the then established doctrines and principles, and in the ordinary language of the day, and no one misunderstood them. The unhappy black race were separated from the white by indelible marks, and laws long before established, and were never thought of or spoken of except as property, and when the claims of the owner or the profit of the trader were supposed to need protection.\n\nJefferson's famous phrase was not law. But in drawing on it, Taney explained the common Southern understanding of it, and he did so while ruling for the United States that \"negroes\" could not be citizens, whether enslaved or free. They had, he approvingly noted, for\n\nmore than a century before been regarded as beings of an inferior order, and altogether unfit to associate with the white race either in social or political relations, and so far inferior that they had _no rights which the white man was bound to respect_ , and that the negro might justly and lawfully be reduced to slavery for his benefit. (emphasis added)\n\n_Dred Scott_ declared that there was no safe haven in the United States where slavery could not exist; if slaves remained slaves when their masters took them into free-soil states, then all states were slave states. It also meant that free people of color had no access in any state to the courts, to contracts, or to owning property, since they could not be citizens and thus had no legal basis to exist as free people, anywhere in the country.\n\nAs the implications of _Dred Scott_ sank in, the question emerged: why not just... enslave them all? After all, women were already slaves, noted Richmond's George Fitzhugh, a descendant of William Fitzhugh. In the _Dred Scott_ year of 1857, Fitzhugh published _Cannibals All! Or, Slaves without Masters:_\n\nThe husband has a legally recognized property in his wife's services, and may legally control, in some measure, her personal liberty. She is his property and his slave.\n\nThe wife has also a legally recognized property in the husband's services. He is her property, but not her slave.\n\nThe father has property in the services and persons of his children till they are twenty-one years of age. They are his property and his slaves.\n\nAfter deciding who was and wasn't a slave, Fitzhugh warned the North that abolitionists were really Communists who were using the slavery issue as a Trojan horse:\n\nEvery one of the leading Abolitionists is agitating the negro slavery question merely as a means to attain ulterior ends, and those ends nearer home. They would not spend so much time and money for the mere sake of the negro or his master, about whom they care little. But they know that men once fairly committed to negro slavery agitation... are, in effect, committed to Socialism and Communism... to no private property, no church, no law, no government, \u2014to free love, free lands, free women and free churches....\n\nSocialism, not Abolition, is the real object of Black Republicanism. The North, not the South, the true battle-ground.... The agitators of the North look upon free society as a mere transition state to a better, but untried, form of society.\n\nThat was the kind of thing Southern men said to each other as their butlers brought them brandy, but Fitzhugh went further than most. It was not necessary, he explained, to have a racial boundary. Prefiguring the radical capitalism of Ayn Rand, he saw the \"strong\" as natural masters of the \"weak.\" \"It is the duty of society,\" he asserted, \"to enslave the weak.\" In the _Richmond Enquirer_ of December 15, 1855, he wrote that anyone could be a slave if they were inferior: \"Nature has made the weak in mind or body slaves... The wise and virtuous, the strong in body and mind, are born to command.\" Dispensing as it did with the Jacksonian notion of white caste solidarity, _that_ was an extreme position, even in the South, and it was not a widely popular one: the color line was too useful, and too sacred, to be discarded.\n\nBut if Fitzhugh was a fringe theorist, he was widely read, and, writes Eugene Genovese, \"the Southern intelligentsia certainly appreciated him.... The notion that slavery was a proper social system for all labor, not merely for black labor, did not arise as a last-minute rationalization; it grew steadily as part of the growing self-awareness of the planter class.\"\n\nAs the genetic distinction between European and African continued to erode, the skin-lightening process was well underway in the upper echelons of enslaved society. Frederick Law Olmsted had noted in his much-read travel account that in Virginia, \"I am surprised at the number of fine-looking mulattoes, or nearly white-coloured persons, that I see. The majority of those with whom I have come personally in contact are such.\" Travelers' accounts of Southern slave auctions commonly mentioned seeing one or another \"white\"-looking person being sold as a \"negro.\"\n\nAs slavecatchers kidnapped free people for sale down South, even white people began to feel personally threatened: if, for example, a white man's daughter were to be denounced as a fugitive slave, the local lawmen would be required to deliver her to the marshal without so much as a hearing. With the Fugitive Slave Act compelling the deliverance of an accused slave to a slavecatcher without due process, it seemed that there might be no place where free labor didn't have to compete with slave labor. It seemed that if the Southerners got their way, all labor would be slave labor, whether black, white, or, to use the then-current term, amalgamated.\n\nSlaveowners incorrectly thought that the North would enslave them by making their black slaves into their masters. Increasingly, the laborers of the North correctly thought that the South wanted slavery everywhere.\n\n*The court documents referenced him as \"Sandford,\" but that was an error.\n\n#   43\n\n# **A Snake Biting Its Tail**\n\n_Labor to supply the demands of the South can be obtained only from Africa; and the laws of this country prevent the Southern people from obtaining this labor, branding those engaged in furnishing it with the opprobrious epithet of \"pirates,\" and inflicting on them the punishment due to those guilty of the crime of piracy!_\n\n\u2014Mobile _Daily Register_ , January 1, 1858\n\nTHE COMING OF RAILROADS ushered in a new era of capitalism on a scale impossible in the days when markets were linked only by water. Railroads required enormous sums of money to create, with a national organization that functioned simultaneously everywhere. But _Dred Scott_ threw western expansion plans into chaos, railroad bonds dropped in price, and there was a Panic.\n\nThe Ohio Life Insurance and Trust Company failed in August 1857, raising fears of a bank run. Then the SS _Central America_ , which sailed from Panam\u00e1 via Havana for New York, sank on September 12 in a hurricane 160 miles off the coast of Charleston. Down with the ship went 425 people (153 more were saved) and a double-digit number, perhaps fifteen or sixteen, tons of gold from California that was headed for the New York banks.* Paper money could be replaced in the system, but not metal money; the loss was by one estimate equivalent to about 20 percent of the nation's gold reserves. In what has been remembered as the Panic of 1857, credit contracted sharply, and the banks stopped specie payments for three months or so.\n\nThe panic originated in New York in part as a consequence of the local shortage of coin and in part as a consequence of excessive speculation, with the buying of stocks to sell rather than hold having become a common financial activity. It was worsened by the credit contraction that banks imposed in response. The commercial crisis was strongly felt in the North, while the South to some degree escaped it. Unfortunately, this led some to believe that the South could go it alone. Certainly, some Southerners were ruined when cotton prices dipped that year, and the disruption of commerce from New York occasioned the loss of money by many planters. A German observer wrote:\n\nIn 1857, the year of the commercial crisis in America, many planters were compelled to sell a portion of their slaves in order to raise ready money, which at that time was not to be had on the best security even at 50 per cent. interest; and I saw a planter bring a hundred slaves to market at one time, who certainly after that sale must have been obliged to leave half his plantation uncultivated.\n\nWhen a planter had a debt crisis, his captives were dispersed. As failures became larger, hundreds of people were occasionally sold at once, fragmenting an entire community each time. James Gadsden, of Gadsden Purchase fame, bought the Cooper River plantation of Pimlico in 1852; after his death six years later, his 235 slaves \"accustomed to the culture of Rice and Provisions\" were sold to thirty different buyers in a sale advertised throughout the South, all the way to Texas.\n\nThe Panic of 1857 was strongly felt in the West, leading New York businessmen to focus their commerce even more closely on the cotton-producing South, offering long credit terms, even as leading Southerners focused on finding ways to become economically independent from New York. Slave prices dipped in 1857, but slaves held their value better than cotton, and prices quickly recovered and climbed with yet another bumper crop. As the economy rebounded, slave prices reached new highs, raising the entry barrier to planter status yet further.\n\nThere could be no quicker way to get the price of slaves down than to reopen the African slave trade, which would create enormous profits for Charleston slave merchants while investing a new generation of purchasers in the slavery system. An article in _DeBow's Review_ pitched the idea as a solution to the problem of white social inequality in the South:\n\nAt present prices, it is almost impossible that the mere laborer can ever [own slaves].... However much he may wish a share in that desirable commodity of slave labor, it is done up in packages too large for common use... The foreign slave trade will bring slaves enough for all, and at prices which poorer men may purchase.... it will thus bring all the ruling race to the same social stand point; it will thus reintegrate and erect our social system; it will abolish the odious distinctions between slave owners and non-slave owners; it will increase the laboring element of our population; it will thus extend our capacity for production, and, in doing all this, will give the promise of a more abundant wealth, and open the prospect to a broader and a brighter future than was ever yet expanded to the eye of man.\n\nThough Virginians, needless to say, opposed reopening the African trade, it was an editorial priority of the Charleston papers, beginning about 1853. As South Carolina systematically attempted to expand its influence, measures promoting the importation of African labor appeared in the legislatures of South Carolina, Georgia, Alabama, Mississippi, Louisiana, and Texas\u2014none of which succeeded, perhaps because they would have been in overt defiance of federal law. It was not a popular notion among the mass of Southern whites, who did not want new Africans complicating their society, nor even for all slaveowners, but for some, it would have been a bonanza, and it was a useful political cudgel. Though the trade was not reopened, the initiative was not without effect, as W. E. B. DuBois pointed out: \"The agitation did succeed in sweeping away nearly all theoretical opposition to the trade, and left the majority of Southern people in an attitude which regarded the reopening of the African slave-trade as merely a question of expediency.\"\n\nIn South Carolina, where reopening the African slave trade at critical moments was a political and commercial tradition dating back to colonial days, agitating to reopen the foreign trade was a way of putting pressure on Virginia. There was a tactical problem that went back to the negotiations over the Constitution: an independent Southern confederacy would need Virginia's heft, strategic location, and money, but reopening the foreign slave trade was a deal-breaker that would have devalued the Virginians' slave property.\n\nOutside the cotton belt, there was always substantial political will to keep the African trade closed. The specter of a reopened African slave trade appeared in the Lincoln-Douglas debates of 1858, when the two men were contending for the position of senator from Illinois. Though neither of the two men was in favor of reopening the African trade, Lincoln went on the offensive. Stephen Douglas advocated \"popular sovereignty\" regarding slavery, which meant that each state was free to make its own determination about the institution. In what became known as the \"house divided\" speech, Lincoln argued that the logical consequence of this would be the reopening of the trade: \"For years he [Douglas] has labored to prove it a sacred right of white men to take negro slaves into the new territories. Can he possibly show that it is less a sacred right to buy them where they can be bought cheapest? And, unquestionably they can be bought cheaper in Africa than in Virginia.\"\n\nIn spite of bumper crops, the overheating slave market was threatening agricultural prosperity. The Mobile _Daily Register_ warned of dangerous levels of credit exposure:\n\n[January 19, 1859.] _High Prices for Negroes._ \u2014 Our exchanges from all parts of the South and West, are teeming with notices of the extraordinary high prices at which negroes are now selling, either on the block or at private sale, and the question naturally presents itself, what is the cause of it? Can the present high price of cotton be the cause?\n\nIf so, a return in the value of the product of the negro, sufficient to justify a purchase, at the prices now ruling cannot be the case, and all reasoning based on the proposition, proves ephemeral, for the influx of slaves this season into the cotton and sugar growing States is enormous. It is supposed that from Augusta, Ga., alone, for the last three months, that the shipments South and West, by the trains, average 200, daily, while the tide of emigration by way of other points is proportionately as great. Some estimate the import of negroes into the cotton growing States alone, will increase the next crop 200,000 bales.\n\nThe present amount of home slave labor should be sufficient to till the lands now open and under cultivation, but with this large increase of laborers, new lands must be opened and cultivated, and their yield [must be on sale] in the market next season. Now will the demand for cotton be equal to the supply?...\n\nIf the negroes have been purchased on time, and we are satisfied that such is the case with a large portion of them, a decline of a few cents in cotton would produce a reaction that must, necessarily seriously embarrass the planting interest, that have purchased on these terms. It is too much the custom for planters to anticipate their crops in dollars and cents, and shape their liabilities accordingly.\n\nThe demand for laborers is good, but we do not think that it justifies the exorbitant and high rates which prevail, although the South was never more solvent than now. (paragraphing added)\n\nCapital for a new African slave trade would have been easily available in New York, where businessmen were still financing an African trade to Cuba. At least 350,000 Africans were carried to Brazil in the 1840s, and, writes Don E. Fehrenbacher, \"at least half of those importations were achieved with American help of some kind.\" But the British navy, which had been actively pursuing slave traders for thirty years, cut off the Brazilian trade sharply in 1850, finishing it entirely by 1852. Besides British coercion, there was a familiar economic logic to the shutdown: the established Brazilian planters had imported so many that they had more than enough for their needs. Now, as new plantations were carved out of the forest in southern Brazil, a domestic slave trade began from the old slave area to the new one, as a forced north-to-south migration began in Brazil.* Similar to the United States's interstate trade, this interprovincial trade was the only other sizable such trade in the hemisphere.\n\nAfter 1850, only Cuba was left importing Africans. It was done with extensive connivance from within the United States, whose ships were by treaty immune from belowdecks search by British cruisers. Slaving above the Bight of Benin had largely been stopped, but whole villages were still being ripped out of Yorubaland by Dahomeyan slave raiders and carried off to sugar mills in the area of Matanzas, Havana, and elsewhere, and the Central African ports continued selling slaves.\n\n\"We don't care for the English squadron,\" boasted an imprisoned slave ship captain in New York in an 1855 interview published in the antislavery _New York Evangelist_ and reprinted in the pro-slavery _DeBow's Review._ \"We run up the American flag, and if they come on board all we have to do is show our American papers, and they have no right to search us.\" The captain estimated that his brig had cost $13,000 to outfit and brought in $220,000 on one run to Cuba\u2014a rate of return from which one successful venture could absorb the costs of several failed ones. Affirming that New York was the king of the trade, the captain was asked how he outfitted his ships:\n\nI can go down to South street, and go into a number of houses that help to fit out ships for the business. I don't know how far they own the vessels or receive the profits of the cargoes. I had rather not have American owners; I prefer Spaniards or Portuguese. But these houses know all about it. They know me. They see me sail out of port with a ship, and come back a passenger... They know [that]... when a cargo of slaves is landed, the vessel is often destroyed, not to be a witness against her officers and crew.\n\nThe colonial-era delay of months on the African coast while assembling a cargo piecemeal was a thing of the past. The African side of the business had gotten steadily more industrial, so slavers in the 1850s were frequently able to pull up to their African destination port and choose a cargo of as many as twelve hundred people from among those held captive in what amounted to a wholesale warehouse maintained by factors. The captain continued:\n\nThe boys and women we kept on the upper deck. But all the strong men\u2014those giant Africans that might make us trouble\u2014we put below on the slave deck.\n\n_Did you chain them or put on handcuffs?_\n\nNo, never; they would die. We let them move about.\n\n_Are you very severe with them?_\n\nWe have to be pretty strict at first\u2014for a week or so\u2014to make them feel that we are masters. Then we lighten up for the rest of the voyage.\n\n_How do you pack them at night?_\n\nThey lay down upon the deck, on their sides, body to body. There would not be room enough for all to lie on their backs.\n\n_Did many die on the passage?_\n\nYes, I lost a good many the last cruise\u2014more than ever before. Sometimes we find them dead when we go below in the morning. Then we throw them overboard.\n\nMortality was decreasing on the voyages, because steam vessels now made the cruise from Africa to Cuba in as little as eighteen days. The year-end 1859 British report from Havana to Her Majesty's commissioners on the slave trade noted that Madagascar had become a new staging ground for East African Arab traders selling people principally from Mozambique (referring to Mozambique Island, off the coast of the present-day country of Mozambique), to slavers bound for Cuba:\n\nSuch expeditions not unfrequently originate in the United States of America, from whence they take their departure; and there are at present here, we understand, agents from Boston and from New Orleans, who are engaged in completing the subscriptions for shares, which have been already in part filled up by American capitalists. One of these schemes is, for a ship of 900 tons to bring 2,000 slaves, under charge of an experienced slaver, who has made no less than thirteen successful voyages.\n\nIt seems that negroes are to be had on the East Coast of Africa for about 28 dollars each; and even so, they are paid for in goods, upon which there is at the least 100 per cent. of profit.\n\nWe learn that the ships to be employed in this unholy Traffic, with their goods for barter on board, and prepared with sufficient iron-fitting tanks for a supply of water, proceed from the United States, under American colours, to a port in Madagascar; there the slave-deck is laid in safety and without hindrance, and there they take in their cargoes of human misery, the victims being brought over from the opposite Coast of Africa in Arab vessels: and we have been told that such are the facilities and arrangements that a very large cargo of slaves can be completed in two or three days.\n\nThe commissioners accounted for 12,744 Africans introduced illegally into Cuba in 1858; of the twenty voyages that brought them, eleven were in American vessels. Certain that there was more traffic than they knew about, the commissioners rounded their estimate up by a third, to almost seventeen thousand.\n\nWith Africans selling in Havana at $1,000 or more, the profits on such voyages were immense; a merchant could afford to pay out bribes, and even burn the ship if necessary. New York merchants especially were involved in the financing, but a wide variety of US maritime centers participated in the trade, including Baltimore and New Orleans. W. E. B. Dubois's list, compiled from congressional documents, shows vessels from Portland, Maine; Portsmouth, New Hampshire; Boston; Rhode Island; Mystic, Connecticut; and Philadelphia.\n\nThe _Echo_ , a brig carrying 475 slaves (out of about 625 it had started with), was captured by the US Navy off the coast of Cuba in August 1858, and though the captain and crew were found not guilty at their trials, the captives were sent to Africa\u2014not back to their homes, but to Monrovia, Liberia, where, inevitably, a new composite culture was developing among people from various parts of Africa who had been left there.\n\nThe American ship _Haidee_ , which had left Kilongo on the Angolan coast with 1,145 captives, brought the 903 of them who were still alive into the Cuban port of C\u00e1rdenas on September 8, 1859. Juli\u00e1n Zulueta, the enormously wealthy Basque trader who had commissioned the voyage together with partners, took them to an \"estate\" with \"an escort of about 200 armed men. The bribes on this scandalous occasion are said to have amounted to about 200,000 dollars.\" By the end of 1859, reported the British judge in Havana: \"We have had information of the introduction of no less than thirty-nine cargoes, with 22,855 negroes; add to which one-third, as usual, and we have the enormous number of 30,473 landed here in this year.\" Reporting from Luanda, where more than three centuries of the slave trade had depopulated the countryside, Her Majesty's acting commissioner wrote: \"It is obvious that the only flag which the guilty adventurers in the Slave Trade now assume to cover their crime is the American.\"\n\nThe slaveowners of the Lowcountry saw all this as another instance of Northern hypocrisy: Americans in free-soil states were building fortunes illegally in the foreign slave trade. But since none of the slaves came to the United States, Carolina planters were denied the use of cheap African labor, while they continued paying a protectionist markup on slaves to Virginia's benefit, and Carolina merchants were denied the use of their harbor as a slave depot.\n\nDespite all the illegal African slave trading, with the exception of the well-known cases of the _Wanderer_ in 1858 and the _Clotilda_ in 1860, and perhaps a few others that left little trace, Africans were not imported directly into the American South. When in late 1859 President Buchanan sent a secret agent, Benjamin F. Slocumb, to travel from North Carolina to Texas as a potential slave buyer with a mission of looking for evidence of African slave vessels arriving, Slocumb found that \"reports concerning the landing of Africans, except in the case of the yacht 'Wanderer,' were unreliable, in fact mere fabrications.\" Joseph Bruin, the large New Orleans slave trader, told Slocumb there were none in town, as it was not a \"Safe business,\" but that \"about 100 [Africans] had been sold in and about New Orleans last Spring, and hurried away.\" Some historians believe that some or many clandestine shipments of Africans came to the Gulf Coast from Havana, while others say that cargoes were smuggled along the Georgia coastline. It is certainly possible, but there is no direct documentation\u2014there wouldn't be\u2014and, moreover, there is no trace of them in documentation about the markets, where Africans did not, as far as we know, turn up. If such shipments did come, they presumably went directly to large plantations under high secrecy, but high secrecy was not all that easy in polemical, newspaper-heavy, nineteenth-century America. Africans for sale in the open market would have been news, and would certainly have been mentioned in slaveowners' and traders' letters. For the labor networks of the South to have been supplied with African bodies in any more substantial way would have had to have left traces that do not exist. Whether some Africans came in clandestinely via Havana or not, the slave-breeding industry remained well-protected.\n\nThe two African slave ships that we do know of were highly conspicuous. The _Wanderer_ was outfitted by Charles Augustus Lafayette Lamar, a loose-cannon financier and speedboater from Savannah. Lamar was the son of New York bank president G. B. Lamar, who would shortly be part of a cockamamie plan, supported by pro-Confederate New York City mayor Fernando Wood, to have the city secede in sympathy with the South. His voyage was an open secret, intended in rebuke and defiance of the federal ban. Lamar's investors included several major slave traders, who were all taking a considerable risk since they were committing a capital crime. One was Nathan Bedford Forrest, whose business by this time reached from Texas to Georgia, and who bragged about his \"interest\" in the _Wanderer_ expedition to a newspaper reporter in 1869. Savannah historians Sheehy et al. write that Lamar \"calculated that if he could maneuver this confrontation into his own back yard of Savannah, he could win. This victory would in turn undermine the federal law banning the importation of African slaves.\" Win or lose, \"he hoped the importation of Africans would drive a wedge between the North and South and elect a Republican Party president\u2014something he was sure would trigger secession.\"\n\nAt the Angolan slave port of Benguela, 487 people were densely packed onto Lamar's _Wanderer_ , a small, fast-sailing vessel built as a pleasure craft that flew the flag of the New York Yacht Club. They were young, in keeping with market requirements, and many were children. About 409 of them were still alive when the _Wanderer_ came ashore on Jekyll Island, a little south of Savannah, on November 28, 1858. The crew was arrested immediately, but Lamar got the ship back and quickly disposed of the slaves. One African boy, the only remaining witness, was abducted at gunpoint from jail and never seen again. The crew members were put on trial and acquitted. Secret agent Slocumb's previously mentioned report to President Buchanan contains some information about what happened to the _Wanderer's_ captives: none of them went to Charleston, he reported from that city; some had passed through Mobile on the way to Louisiana; thirty were sold in Vicksburg by Nathan Bedford Forrest; and seven in Memphis, also by Forrest. Some wound up in Texas.\n\nLamar, also a horse racer, owned the Ten Broeck Race Course in Savannah, where on March 2 and 3, 1859\u2014a little more than three months after the _Wanderer_ arrived\u2014Georgia's all-time biggest slave auction was held to pay down the debts Pierce Mease Butler had incurred speculating in the stock market. The broker conducting the sale, Joseph Bryan, owned the largest slave jail in town, on Bryan Street facing Johnson Square, but even so, he couldn't manage an inhouse sale of that size, so he moved it to Ten Broeck. The people to be sold were housed in the stables.\n\nA Northern newspaper reporter attempting to take notes at the sale would have been ejected if not violently abused, so Mortimer Thomson, writing for Horace Greeley's _New York Tribune_ , went incognito, posing as a buyer. When his article, \"Great Auction Sale of Slaves at Savannah, Georgia, March 2d and 3d, 1859,\" was published on March 9, it caused an international sensation and was a public relations disaster for Savannah. Writing under the name Q. K. Philander Doesticks, Thomson reported hearing at the auction strong sentiments in favor of reopening the African slave trade, and described the scene:\n\nFor several days before the sale every hotel in Savannah was crowded with negro speculators from North and South Carolina, Virginia, Georgia, Alabama, and Louisiana, who had been attracted hither by the prospects of making good bargains. Nothing was heard for days, in the bar-rooms and public rooms, but talk of the great sale.\n\nThe community on Butler's Sea Island plantations numbered about nine hundred. Half of them were owned by the estate of Butler's deceased brother John, but Butler's 436 went to the auction block, there to be sold by what Southerners reckoned a \"humane\" method, in families, though of course such sales still broke family ties. So half the community would remain, and half would disappear. The auction realized $303,850 (about $8.7 million in 2014 dollars). The sale was particularly painful, since this community was so deeply rooted. \"None of the Butler slaves have ever been sold before, but have been on these two plantations since they were born,\" wrote Thomson. \"Who can tell how closely intertwined are the affections of a little band of four hundred persons, living isolated from all the world beside, from birth to middle age? Do they not naturally become one great family, each man a brother unto each?\"\n\nThomson reported as a conversation whose \"sentiment\" was \"more than once repeated\" a negative response by a prospective purchaser when asked if he would be buying a woman named Sally: \"Well, Major, I think not. Sally's a good, big, strapping gal, and can do a heap o' work; but it's five years since she had any children. _She's done breeding, I reckon.\" 26_ (emphasis in original)\n\nThe Ten Broeck sale is popularly remembered by the phrase \"the weeping time,\" which also refers to the weather; four straight days of rain stopped when the sale ended. The auction was up in the grandstand, a room about a hundred feet long, where they lined up and waited their turn to go on the block. Thomson tells us that as \"the wind howled outside, and through the open side of the building the driving rain came pouring in,\" auctioneer Thomas J. Walsh announced the terms: \"one-third cash, the remainder payable in two equal annual instalments, bearing interest from the day of sale, to be secured by approved mortgage and personal security, or approved acceptances in Savannah, Ga., or Charleston, S.C. Purchasers to pay for papers.\"\n\nAs the sale wound down, Pierce Butler moved among his former slaves carrying canvas bags from which he sorrowfully handed to each one of them four gleaming new twenty-five cent pieces, fresh from the mint, a dollar apiece, as if to say, it wasn't my fault. But when the sale was concluded, Butler's debts were paid, and he was a rich man again. He celebrated by going on an extended trip to the Mediterranean.\n\nThough Butler experienced the auction as a terrible humiliation, it turned out in the long run to have been a good business move: he cashed out his slave-holdings while they were still worth something. While it was not hard to tell in 1859 that war was coming, there was no reason for planters to believe the end of chattel slavery was around corner. Quite the contrary; it was a time-honored institution that had never been stronger. There were more slaves than ever; the cash value of the approximately four million people then enslaved in the United States embodied a phenomenal sum of money.\n\nThough the Ten Broeck race course no longer exists as such, a historical marker was placed in a small commemorative area on the former site on March 2, 2008\u2014another spot of sacred ground marked and acknowledged.\n\nIt was about the same time as the Ten Broeck sale\u2014sometime in early 1859\u2014that a \"castle\" of the Knights of the Golden Circle opened in Baltimore. Founded in 1854, and based in the free territory of Cincinatti, Ohio, the KGC was a pro-slavery secret society that had consolidated with the Order of the Lone Star, which had been somewhat directionless after the death of John Quitman in July 1858.* The KGC wanted to secede from the United States and take over Mexico.\n\nIn Virginia, the cherished diffusionist notion that the slave population would be eliminated by selloff had not become reality. Four and a half decades after the Battle of New Orleans, Virginia was still exporting slaves to the Deep South. Although planters had been living for generations off the earnings of slave-breeding, exactly as abolitionists charged, Virginia's slave population had increased by 1860 to 490,865, even though Maryland's and Delaware's had diminished.\n\nAn editorial in the Richmond _Enquirer_ of May 25, 1858, made clear the extent to which the Virginia economy still depended on the export to the South and West of domestically raised African Americans, as well as how alarming the loss of its protected status to a reopened trade would be:\n\n\"If a dissolution of the Union is to be followed by the revival of the [African] slave trade, Virginia had better consider whether the South of the Northern Confederacy would not be far more preferable for her than the North of a Southern Confederacy. In the Northern Confederacy Virginia would derive a large amount from the sale of her slaves to the South, and gain the increased value of her lands from Northern emigration \u2013 while in the Southern Confederacy, with the African slave trade revived, she would lose two-thirds of the value of her slave property, and derive no additional increase to the value of her lands.\n\nThe South Carolinians would make sure that the Virginia slave-breeders would not be able to sit their war out.\n\nJohn Brown's attempt to ignite a slave rebellion at Harpers Ferry in what is now West Virginia, at the confluence of the Potomac and Shenandoah Rivers, began on October 16, 1859, and was suppressed two days later by Lt. J. E. B. Stuart under the command of Colonel Robert E. Lee.\n\nFrederick Douglass was one of perhaps eighty people who knew about John Brown's raid on Harpers Ferry in advance. Though he tried to talk Brown out of the suicidal act that lit the match for war, he didn't inform on him, which was enough to make him a conspirator. Douglass fled the country to Canada and on to London, returning home the following year.\n\nRobert E. Lee's report, filed on October 19, described Brown's action not as Northern aggression, but as \"the attempt of a fanatic or madman, who could only end in failure.\" But Brown's attempt to start a slave rebellion galvanized the South, where it was seen by the political and intellectual class as proof of what the \"Black Republicans\"\u2014a contemptuous name for the party of Chase and Seward\u2014had in store for them. The _Charleston Mercury_ noted on October 20 that three New York newspapers with different political affiliations\n\nall concur in opinion as to the desperate condition of the democratic party throughout the North, and the imminent prospect of a Black Republican Speaker of the House of Representatives and President of the United States being lifted to power. Let none, however, expect Seward to be the candidate of that party. We, at least, have never thought so; but we are confident some one less committed, yet equally Black Republican\u2014such as [Salmon P.] Chase or [Supreme Court] Judge [John] McLean\u2014would be put forward.... But whether Seward, or Chase, or McLean, to the South the difference is small. It is the candidate of a hostile sectional party, whose success must put the South, as unprotected tributaries, at the feet of inimical rulers.\n\nIt wasn't just about Lincoln. In the eyes of the _Mercury_ , any \"Black Republican\" president would have been cause for war. The number of Southern vigilance committees grew.\n\nJohn Brown wasn't hanged until December 2, and that wasn't soon enough for slaveholders, because he didn't stop talking until he was hanged, and never strayed from his calm, righteous tone. Brown's execution (witnessed by the wealthy, successful, well-connected, radical young actor John Wilkes Booth, a member of the Knights of the Golden Circle) elevated him to the status of martyr. In his memory, new lyrics were put to an old campfire meeting song with the stirring chorus of \"Glory, Hallejulah\" to make the great song of the military campaign that ended slavery: _John Brown's body lies a-moulderin' in the grave..._\n\nAfter the _Wanderer_ , only one more slave ship containing Africans is known to have arrived in the United States. On an unknown date in the summer of 1860, the _Clotilda_ brought to Magazine Point on Mobile Bay 110 captives from Ouidah, in the Fon-speaking state of Dahomey. \"Ouidah was a more cosmopolitan city than Mobile,\" notes Sylviane Diouf in her study of the _Clotilda_ shipmates, which tells us that most of the captives were the people now called Yoruba (though that ethnonym was not yet in general use), practitioners of the orisha religion. The _Clotilda_ 's captives had been taken by the Dahomeyan king Gl\u00e8l\u00e8; some were from Atakora, in what is now northwest Benin; others were Fon speakers from Dahomey; still others were Muslim. One, Gumpa, who became known as Peter Lee, was a Dahomeyan nobleman who practiced vodun. This ship, which could as easily have gone to Havana or Matanzas, was more or less representative of the dramatic, high-volume African cultural transplantation to Cuba that was by then in its final days and would prove highly consequential for twentieth-century Afro-Cuban culture.\n\nOne survivor of the _Clotilda_ , Cudjoe Lewis, lived until 1935. One of the relatively few Yoruba to be brought to United States territory,* he described the slave raid in which he was captured, recalling that the warriors who killed the unsalable people and kidnapped the remainder were women\u2014the Dahomeyan kings favored the use of female soldiers\u2014and that as they took him to Abomey, they wore hanging from their belts the severed heads of the captives' unfortunate family members who had been slaughtered in the raid. After three days, the heads were decomposing, so the coffle stopped along the way for nine days as the soldiers smoked the heads over a fire to preserve them. The heads, along with the live slaves, were to be ceremonially sold to the king of Dahomey, a state organized for the purpose of slave-raiding.\n\nMost of the _Clotilda_ captives remained enslaved in the Mobile area. With the end of slavery, many of them reassembled; in 1866, they established their community under Gumpa's leadership as African Town, which he led for thirty years or so. After Gumpa's son with his shipmate Josephina was born, writes Diouf, they had the baby tattooed on the chest with the image of a snake biting its own tail. Ultimately, as many vodouisants in Haiti have subsequently done, Gumpa became a Baptist. Descendants still live in the area.\n\nBy the time the _Clotilda_ sailed, the African trade was already feeling the heat of President Buchanan's program of stepped-up American anti-slave-trade enforcement off the African coast. But as we have previously emphasized, suppressing the slave trade was a different issue than abolishing slavery, which President Buchanan had no intention of doing. Many secessionists approved of his stopping the illegal African slave trade. They weren't making any money from it, and harassing it kept the ships of the tiny US Navy busy\u2014far, far away.\n\n*There are different estimates of the amount of gold on board, but it was substantial. The wreck was found in 1988 and has not been completely excavated as we write. What has been brought to the surface so far includes 43 gold bars of up to 54 pounds, \"1,302 $20 double-eagle gold coins, 37 $10 eagle gold coins, and 9,053 10-cent silver coins,\" some of which dated back to 1823. Winter, Michael.\n\n*Brazil was the last country in the hemisphere to end slavery, in 1888, developing a mass abolition movement in the final years; Cuba, still a colony of Spain, ended slavery in 1886 in the face of growing independentist sentiment.\n\n*Quitman died of something later called \"National Hotel Disease,\" which he along with several hundred other people contracted attending the inauguration of James Buchanan.\n\n*The bulk of Yoruba slaving happened after the fall of the Oy\u00f3 empire to an Islamic jihad that began in the 1820s and culminated with the empire's collapse in 1836. By this time, the United States no longer allowed the African slave trade, but Yoruba were taken in numbers to Cuba, Brazil, and, as indentured servants, to Trinidad.\n\n#   44\n\n# **Assignment in Paraguay**\n\n_Both thy bondmen, and thy bondmaids, which thou shalt have, shall be of the heathen that are round about you; of them shall ye buy bondmen and bondmaids._\n\n_Moreover of the children of the strangers that do sojourn among you, of them shall ye buy, and of their families that are with you, which they begat in your land: and they shall be your possession._\n\n_And ye shall take them as an inheritance for your children after you, to inherit them for a possession; they shall be your bondmen for ever: but over your brethren the children of Israel, ye shall not rule one over another with rigour._\n\n\u2014Leviticus 25:44\u201346\n\nPRESIDENT BUCHANAN CONDUCTED HIS administration in such a way as to leave his successor crippled.\n\nSome of Buchanan's few biographers have defended him against the charge of being part of a Southern conspiracy. But however one cares to address the topic, the notion that Buchanan could have been unaware of having methodically put the Union in the most disadvantageous position possible does not pass the smell test. His contemporaries certainly thought that was what he was doing.\n\nBuchanan announced at the beginning of his term that he, like Polk, would be a one-term president, in effect setting the secession clock ticking. He sent the US Navy as far away as he could, where its personnel would not be easily available for duty in the event that, say, Carolinians or Mississippians should declare independence, as their leaders were constantly threatening to do. In 1858, he ordered \"a fleet of nineteen ships\"\u2014seven of them chartered merchant vessels\u2014\"of two hundred guns manned by twenty-five hundred sailors and marines\" on an unprecedented mission to Paraguay (!), where a US sailor had been killed in a river incident three years previously. Paraguay is a landlocked country, so the navy had to ascend three rivers. Most of the vessels stopped at Rosario, Argentina, and two continued on to the Paraguayan capital of Asunci\u00f3n, where they demanded an apology and extorted a new commercial treaty.\n\nFollowing the completion of that expensive, time-consuming errand, Buchanan sent the navy to the African coast to police the slave trade\u2014and indeed, for the first time, American enforcement did make a dent in it. The only captain ever hanged according to the legal penalty for engaging in the slave trade, one Nathaniel Gordon, was executed in 1862 under Lincoln, but he had been prosecuted and convicted during the Buchanan administration.\n\nRiddled with procurement scandals, bribery, and \"emergency loans,\" and spending extravagantly on military adventures, Buchanan's administration proved to be highly corrupt. Entering office with a $1.3 million surplus, Buchanan left behind a $25.2 million deficit, while government debt ballooned from $28.7 million to $76.4 million. Buchanan's secretary of the treasury was Howell Cobb, his old Jacksonian friend and Georgia cotton planter, and at one time owner of a thousand slaves. Ostensibly a Unionist and the ex-Speaker of the House of Representatives, Cobb in 1856 had published _A Scriptural Examination of the Institution of Slavery_ , a Bible-thumping defense of divinely ordained property rights in slaves that execrated various individual abolitionists, in which he complained\u2014this is a mere sample\u2014that:\n\nAmongst the most successful schemes of mischief brought forth by abolitionists, may be reckoned what is familiarly called the Under-Ground Railroad: by this means, many owners have been deprived of their property by persons esteeming themselves, and being esteemed by their associates, pious.\n\nAsserting that enslaved women reproduced \"like rabbits,\" the slave-breeding Cobb in 1858 told the Georgia Cotton Planters Association (of which he was secretary) that \"the proprietor's largest source of prosperity is in the negroes he raises.\" He was one of the key people informally known as the \"Buchaneers\" who helped make the Buchanan presidency a fiscal scandal of historic proportions. With him at the helm of Treasury, Buchanan ran his _entire term_ on deficit financing, which Andrew Jackson would have regarded as a mortal sin if not treason. Such a thing might not seem so strange to modern readers, since the Federal Reserve can now print money to meet the government's obligations, but this was an era in which there was no national paper currency. After three decades of a Jacksonian fiscal regime, the federal government was required to shift the physical location of pieces of gold and silver in order for federal spending to occur.\n\nBesides the naval operations in Paraguay and Africa, Buchanan sent the US Army to Utah in 1857, to confront the theocratic Mormon state of Deseret. That was before there was a railroad to get the troops out there; they had to go on horseback, far from telegraph lines. Though hostilities ended in 1858, the army remained in Utah through the remainder of Buchanan's presidency.\n\nBuchanan's vice president was Kentuckian John C. Breckinridge, the grandson of the man who had introduced Jefferson's anonymous Kentucky Resolutions that first branded the doctrine of nullification. As the Democrats split into Northern and Southern factions, Vice President Breckinridge ran for president in 1860 on the Southern Democratic ticket, with a platform that was essentially a threat that if he lost, the South would secede. He did, and it did. When Lincoln won the election, it was with a plurality of votes on a four-way split; his name had not even been on the ballot in the Southern states.\n\nIn his final, lame-duck State of the Union Address on December 3, 1860, Buchanan explained the problem to the nation\u2014the abolitionists made them do it: \"The long-continued and intemperate interference of the Northern people with the question of slavery in the Southern States has at length produced its natural effects.\"\n\nBy this point Northern bankers were refusing to buy Treasury notes for fear the money would go South; nor were they likely to invest in a situation in which the South was poised to repudiate its debts. Rhett's _Charleston Mercury_ wanted a new government, now. There was no time to lose: strike while the South has the momentum and the North is in transition.\n\nMany in the North had thought the Southern hotspurs wouldn't really secede. The plan to defeat the unprepared\u2014and, the South thought, irresolute\u2014North hinged on the idea of a quick mobilization. Howell Cobb had advised the secessionists to wait until the day of Lincoln's inauguration, which would have saved their old friend Buchanan considerable embarrassment, but they ignored his advice, so Cobb resigned as secretary of the treasury on December 8 to get in on the ground floor of the new country.\n\nIt was clear what Cobb had done, wrote Henry Adams in the _Boston Daily Advertiser_ of December 13: \"Everyone knows that [Buchanan] has neglected to garrison Fort Moultrie; that Secretary Cobb has so managed the Treasury as to weaken the new administration as far as possible; and that Mr. Floyd [John Floyd of Virginia, secretary of war] has as good as placed large amounts of national arms in the hands of the South Carolinians.\"\n\nAs secession was declared in one state after another, Buchanan did nothing to stop it. Instead, he let them go to form a slaveholders' confederacy that would attack and invade the United States\u2014once he was gone, and a less compliant president inaugurated.\n\nBefore Lincoln took office in March, unidentified thieves removed all the remaining specie from the federal treasury in Washington. In William P. MacKinnon's words, \"By the time Abraham Lincoln took office in March 1861 the country's largest military garrison was in the desert forty miles southwest of Salt Lake City, and the new administration could neither buy stationery nor meet the federal payroll. The two circumstances were not unrelated.\" What little money the United States government had was in the form of pieces of metal scattered around the far-flung country. That was how the South wanted it. Moreover, the secession of seven states from the Union meant that many Northern creditors would be burned if not ruined, seizing up the nation's commercial cash flow. Many of the merchants had been in favor of appeasing the South; but once they were stiffed by their Southern debtors, they became staunch Unionists.\n\nThe secession campaign was planned and executed by a wealthy group of men who had been at war with the government years before they equipped an army against it. Their propaganda machine ran full blast: disunion was the only permissible stance. With the _Charleston Mercury_ leading the charge, newspapers throughout the South hammered it home every day. When word of Lincoln's election came, the Fire-Eaters were already mobilizing; Robert Barnwell Rhett and others founded the Minute Men for the Defence of Southern Rights, an action group, in October 1860, while the Knights of the Golden Circle were establishing paramilitary forces elsewhere.\n\n_This Currier and Ives print in response to Florida's secession on January 10, 1861, depicts South Carolina leading Florida, Alabama, Mississippi, and Louisiana off a cliff. South Carolina is shown as riding a pig in pursuit of a butterfly labeled \"secession humbug,\" and saying, \"We go the whole hog... Old Hickory is dead, and now we'll have it.\" Georgia is depicted as deviating from the path, though in fact it seceded on January 19, before Louisiana did (January 26). The rider personifying Mississippi is saying, \"Down with the Union! Mississippi repudiates her bonds!\"\u2014referring to the self-ruination of Mississippi's credit on global markets almost twenty years before._\n\nSouth Carolina had been the state most likely to secede since the beginnings of the nation\u2014indeed, had barely joined the United States except for reasons of defense, which had been moribund since the removal of the Spanish, the British, and the local Native Americans following the War of 1812.\n\n\"All the slaves in Maryland might be bought out now at half-price with a liberal discount for cash,\" wrote Henry Adams the week before South Carolina seceded. Not all the slave states were determined to secede, however, and in order to evangelize on behalf of disunion, the governors of Mississippi and Alabama sent \"secession commissioners\" to the various slave states.\n\nAlabama's commissioner to South Carolina, John Archer Elmore, arrived in time to address the first evening session of the South Carolina Secession Convention on December 17, 1860, warning them of what they already believed: that Lincoln's election was \"an avowed declaration of war upon the institutions, the rights, and the interests of the South.\" The directorates that sent out secession commissioners tried to send natives of the states they were sent to, so Mississippi's commissioner to North Carolina was North Carolina\u2014born Jacob Thompson, President Buchanan's secretary of the interior. It was straight-up treason: Thompson was still a cabinet officer when he arrived in Raleigh on December 18 to deliver a barnburner of a speech characterized by the \"message of emancipation, humiliation, subjugation, and ruin\" that ran \"through the commissioners' messages like a scarlet thread,\" writes Charles B. Dew in his history of the secession commissions.\n\nThe South Carolina convention voted unanimously on December 20 to secede from the Union. Anyone who might have dissented had long since been weeded out. When it was Robert Barnwell Rhett's turn to ascend to the stage and take his turn signing the secession papers in the presence of three thousand cheering Carolinians, the most tireless and pugnacious disunionist of all \"fell to his knees, lifted his hands upward toward the heavens, and bowed his head in prayer,\" writes his biographer.\n\nSouth Carolina sent out well-coached secession commissioners, focusing them on the idea of a constitutional convention at Montgomery. Their commissioner to Alabama was John C. Calhoun's son Andrew. Raised from birth at a high pitch of pro-slavery hysteria, the younger Calhoun had in November recalled that the Haitians had risen up \"with all the fury of a beast, and scenes were then enacted over a comparatively few planters, that the white fiends [of the North] would delight to see re-enacted now with us.\"\n\nAs the appeals to secede became more intense, they became less economic and more emotional: if you don't support the slaveowners, you will be the victim of the slaves. After winding himself up for several pages, Alabama secession commissioner Stephen F. Hale reached the boiling point of negrophobia that Haiti represented in this by now ritualized discourse, augmented as usual by the image of the violation of white women:\n\nThe election of Mr. Lincoln cannot be regarded otherwise than... an open declaration of war, for the triumph of this new theory of government destroys the property of the South, lays waste her fields, and inaugurates all the horrors of a San Domingo servile insurrection, consigning her citizens to assassinations and her wives and daughters to pollution and violation to gratify the lust of half-civilized Africans. Especially is this true in the cotton-growing States, where, in many localities, the slave outnumbers the white population ten to one.\n\nBut the economic argument predominated. In a December 27, 1860, letter to Kentucky governor Beriah Magoffin, Hale put it down squarely to property rights in human beings: \"African slavery has become not only one of the fixed domestic institutions of the Southern States, but forms an important element of their political power, and constitutes the most valuable species of their property, worth, according to recent estimates, not less than $4,000,000,000; forming, in fact, the basis on which rests the prosperity and wealth of most of these States.\"\n\nHowell Cobb supervised the hasty, secretive drafting of the Confederate Constitution at Montgomery, Alabama, with a team that included his brother Thomas, Robert Toombs, Robert Barnwell Rhett, and Alexander Stephens. This constitution explicitly mentioned slavery\u2014ten times. Cobb served as temporary head of the six-state Confederate States of America for two weeks, until Jefferson Davis was selected president of the self-declared new nation and was inaugurated on February 18, 1861.\n\nAlexander Stephens of Georgia was declared vice president of the Confederacy. President-elect Lincoln had written Stephens on December 22 that, as the Republicans had insisted throughout the campaign, he had no intention of abolishing slavery where it existed, only of prohibiting its spread to other territories.\n\nBut of course, to stop slavery's expansion would have been to end it.\n\nSo effective was the sermon _Mutual Relation of Masters and Slaves as Taught in the Bible_ at the First Presbyterian Church of Augusta, Georgia, on January 6, 1861, that the congregation quickly raised the money to publish it.\n\nIts author, the twenty-five-year-old clergyman Joseph Ruggles Wilson, based his text on Ephesians 6:5-9; the passage begins, \"Servants, be obedient to them that are your masters according to the flesh, with fear and trembling, in singleness of your heart, as unto Christ.\" Affirming that the Greek word translated as \"servants\" \"distinctly and unequivocally signified 'slaves,'\" Wilson saw slavery as a permanent Christian institution. Expounding the Southern churches' doctrine, which had occasioned a break with their Northern denominations' counterparts, he proposed that as servants of Christ, masters should treat their slaves with love and slaves should work hard. This was the doctrine known as \"paternalism,\" in which slaves and master were portrayed as forming a big family\u2014until it was time to sell some of the family.\n\nOnly fifteen days before Georgia seceded, Wilson told his parishioners to prepare for the upcoming victorious struggle, speaking of slavery as something to \"cherish\":\n\nWe should begin to meet the infidel fanaticism of our infatuated enemies upon the elevated ground of a divine warrant for the institution we are resolved to cherish....\n\n[The Apostle Paul] as much as says, that it is unnecessary to fear that this long-cherished institution will first give way before the enemies who press upon it from without. If slaveholders preserve it as an element of social welfare, in the spirit of the christian religion, throwing into it the full measure of gospel-salt allotted to it, and casting around it the same guardianship with which they would protect their family peace, if threatened on some other ground\u2014they need apprehend nothing but their own dereliction in duty to themselves and their dependent servants.\n\nHe closed by anticipating prosperity for slaveowners and holiness for the enslaved:\n\nOh, when that welcome day shall dawn, whose light will reveal a world covered with righteousness, not the least pleasing sight will be the institution of domestic slavery... which, by saving a lower race from the destruction of heathenism, has, under divine management, contributed to refine, exalt, and _enrich_ its superior race  (emphasis added)\n\nWe do not know whether Wilson's son, Woodrow, attended his father's sermon that Sunday during secession winter, because he had just turned four. But his subsequent writings as a historian and his adult actions suggest that he absorbed the racist message of his father, with whom he had a lifelong loving relationship.*\n\nRather than \"submit\" to the \"Black Republicans\"\u2014so went the rhetoric\u2014Mississippi seceded on January 9, 1861, followed by Florida (which had only been a state for fifteen years) on January 10, Alabama on the eleventh, and Georgia on the nineteenth.\n\nOn January 21, five Southern Senators withdrew from Congress. In his brief valedictory speech, Jefferson Davis, owner of 113 slaves, said:\n\nIt has been a belief that we are to be deprived in the Union of the rights which our fathers bequeathed to us, which has brought Mississippi to her present decision. She has heard proclaimed the theory \"that all men are created free and equal,\" and this made the basis of an attack upon her social institutions; and the sacred Declaration of Independence has been invoked to maintain the position of the equality of the races.\n\nDavis went on to explain, as slaveowners frequently did and as the US Supreme Court had affirmed, that \"all men were created equal\" had not been intended to mean all men. Jefferson's youngest grandson, George Wythe Randolph, who as a boy stood by Jefferson's deathbed, apparently agreed: he was the Confederate secretary of war for eight months in 1862.\n\nNeither Virginia nor Maryland had seceded when, with Louisiana's P. G. T. Beauregard giving the orders, slavery \"fired on the flag,\" in Ulysses Grant's words, on April 12, 1861, at Fort Sumter.\n\nVirginia did much business with the North and was decidedly ambivalent about seceding. The Confederate Constitution, signed as of March 11, offered Virginia both a carrot and a stick. The document was modeled on the US Constitution, complete with a three-fifths clause, but with explicit protections for slavery written into it. However, even despite the latter-day clamor to reopen the African slave trade, the Confederate Constitution prohibited the foreign slave trade into the Confederate States with what might as well have been called the Virginia clause.\n\nThe carrot, then, was that a Confederate Virginia could continue to slave breed and thus retain a market capitalization of its enslaved population. With importation prohibited and conquest continuing, Virginia slaveowners could sell black people into new domains for the foreseeable future. But the stick was that since no foreign slaves could be traded into the Confederate States, if Virginia did not secede she would have no Southern market in which to sell African American youth.\n\nVirginia gave in and joined the Confederacy. Facing the loss of the state's slave-breeding industry, a Virginia secession commission voted provisionally to secede on April 17\u2014five days after South Carolina fired the first shot at Ft. Sumter, and after Lincoln had called for seventy-five thousand troops from all the states remaining in the Union. After Virginia ratified secession on May 23, West Virginia, where slave labor had never been much in use, seceded from Virginia, voting itself a Union state on October 24.\n\nThe day after Virginia seceded, Union troops moved into Alexandria, beginning the longest occupation of a long war. They surprised the Confederate cavalry eating breakfast at the Duke Street slave-shipping compound that had formerly been Franklin and Armfield's, and at that time was on its fifth owner, Charles M. Price, who had been a partner with James Birch in Price, Birch. \"The firm had fled,\" wrote Virginian M. D. Conway, \"and taken its saleable articles with it; but a single one remained\u2014an old man, chained to the middle of the floor by the leg. He was released, and the ring and chain which bound him sent to the Rev. Henry Ward Beecher.\" The \"Slave Pen,\" as it was known, was repurposed as a prison for captured Confederates.\n\nA divided Maryland did not secede, but continued to have slavery and was heavily occupied by the military. It was a fundamental priority for the United States to keep Maryland, because if Maryland went, Washington would be surrounded.\n\nKentucky did not secede. John C. Breckinridge was seated as a senator from Kentucky, subsequently enlisted in the Confederate army, and was formally expelled from the Senate as a traitor on December 2, 1861. Missouri, the most bitterly divided state, did not secede, but a faction announced a provisional Confederate government in the town of Neosho.\n\n_The captured Price, Birch & Co., \"Dealers in Slaves.\" Photograph: Andrew J. Russell, sometime between 1861 and 1865._\n\nThe capital of the Confederacy was moved from Montgomery to Richmond by a May 20, 1861, vote of the Confederate Congress. In eighty-two years, Richmond had gone from being the capital of Virginia's secession from Britain, to being the great wholesale center of the domestic slave trade, to being the Confederate capital. Prices for slaves remained strong, and slave sales continued until the city fell to the Union in 1865. Richmond versus Washington: the capitals of North and South were only a hundred miles apart.\n\nAmong the defects of Steven Spielberg's 2012 film _Lincoln_ was the short shrift it gave Elizabeth Keckley.\n\nThough depicted in the movie as a servant, she was the first African American couturier of note. Born enslaved in Virginia, and badly abused during slavery, after manumission Mrs. Keckley (as she was addressed) married and divorced, then opened her own dressmaker's shop as a modiste in Washington, DC. At one point she had simultaneously as clients both Varina Davis (the wife of Jefferson Davis, at the time a Mississippi senator) and Mary Todd Lincoln.\n\nShe became the confidante of the unpopular Mrs. Lincoln and was frequently present in the White House. Her 1868 memoir, _Behind the Scenes, or, Thirty years a Slave, and Four Years in the White House_ , was written with the abolitionist journalist James Redpath, who probably transcribed and tweaked her speech to create an \"as told to\" text. It would make a fine movie, complete with a unique, close-up view of Lincoln and his short-lived son Tad watching their pet goats play on the White House grounds. In it, Mrs. Keckley reported a conversation with Varina Davis:\n\nWhile dressing her one day, she said to me:\n\n\"Lizzie, you are so very handy that I should like to take you South with me.\"\n\n\"When do you go South, Mrs. Davis?\" I inquired.\n\n\"Oh, I cannot tell just now, but it will be soon. You know there is going to be war, Lizzie?\"\n\n\"No!\"\n\n\"But I tell you yes.\"\n\n\"Who will go to war?\" I asked.\n\n\"The North and South,\" was her ready reply. \"The Southern people will not submit to the humiliating demands of the Abolition party; they will fight first.\"\n\n\"And which do you think will whip?\"\n\n\"The South, of course. The South is impulsive, is in earnest, and Southern soldiers will fight to conquer. The North will yield, when it sees the South is in earnest, rather than engage in a long and bloody war.\"\n\n\"But, Mrs. Davis, are you certain that there will be war?\"\n\n\"Certain!\u2014I know it. You had better go South with me; I will take good care of you.... Then, I may come back to Washington in a few months, and live in the White House. The Southern people talk of choosing Mr. Davis for their President. In fact, it may be considered settled that he will be their President. As soon as we go South and secede from the other States, we will raise an army and march on Washington, and then I shall live in the White House.\"\n\nThe Yankees wouldn't fight. Varina Davis would live in the White House. New York would collapse without the money it stole from Southern cotton producers, and the poor would riot and burn down the mansions on Fifth Avenue. It was a common belief. Lazarus Straus's son Oscar, who would have been nine or ten years old at the time, vividly recalled hearing Georgia senator Robert Toombs speaking at Columbus's Masonic Temple: \"He drew a large, white handkerchief from his pocket with a flourish, and pausing before mopping his perspiring forehead, he exclaimed: 'The Yankees will not and can not fight! I will guarantee to wipe up with this handkerchief every drop of blood that is spilt!'\"\n\nToombs's ghost must be mopping up the blood still. At the time he made that extravagant remark, he hoped to become the Confederate president, as did Howell Cobb. But Jefferson Davis had the most military credentials, and running a war was going to be pretty much the Confederate president's only job. Davis's older brother Joseph had for years been promoting him as the obvious chief executive of an inevitable Southern republic. In order to keep his talented sibling free of financial worries, Joseph had given him the plantation called Brierfield, twenty miles south of Vicksburg, whose captives were capably overseen during Jefferson Davis's extended absences by an enslaved man, Davis's longtime \"body servant\" James Pemberton.\n\nMany in North and South alike believed that Lincoln would be no match as a warrior for Davis, who was unanimously named president of the Confederate States of America by the hastily convened Confederate Congress, which met in secret during its entire existence.\n\n*When he was president of Princeton, Wilson kept out black students; as president of the United States, he implemented Jim Crow in the federal government, requiring job applications to include photos.\n\n#   45\n\n# **The Decommissioning of Human Capital**\n\n_Every intelligent man knows that coined money is not the currency of the country. 1_\n\n\u2014Rep. Samuel Hooper (Massachusetts), arguing in favor of the Legal Tender Act, February 3, 1862\n\n_After the Civil War was over, ole Marsa brought some money in a bag and says to his wife that it wasn't no count. What was it they called it? Confederate money? You know when the War ceased money changed\u2014greenbacks, yes'm. 2_\n\n\u2014Unidentified informant, Fisk University, 1929\u201330\n\nTHE FEDERAL GOVERNMENT COST a million dollars a day, maybe more, to run. There was nothing to run it with.\n\nLincoln did not merely inherit a ransacked treasury and a government in debt from James Buchanan and Howell Cobb. He inherited more than thirty years of Jacksonian hobbles on the financial powers of federal government. In the years since Jackson had first become president, the United States had become an industrial and financial power fueled by earnings from the massive export of cotton, but its enormous economic growth had not been matched by an increase in federal resources, which were limited by a welter of archaic constraints. Bray Hammond writes:\n\nTo keep relations between the government and the economy \"pure\" and wholesome, tons of gold had to be hauled to and fro in dray-loads, with horses and heavers doing by the hour what bookkeepers could do in a moment. This, moreover, was not the procedure of a backward people who knew nothing better; it was an obvious anachronism to which, in keeping it tied around the federal government's neck, a mystical virtue was imputed. Actually its only beneficiaries were handlers of gold and speculators in it.\n\nThere had been no national currency since before the Panic of 1837. The nation's finances had taken the Jeffersonian small-government path instead of the Hamiltonian strong-government system of managed debt, and had ended up plucked clean. State power had been exalted and federal power demeaned, and the federal government had come apart. Cobb and Buchanan's systematic wasting of the Treasury had left the Jeffersonian-Jacksonian tradition bankrupted. The way was clear for the remaking of government along a Hamiltonian path\u2014or possibly even Franklinian, since it necessarily entailed paper money, and lots of it.\n\nWith the slavery interest, which had been the hard core of resistance to a strong federal government, having decamped, Lincoln now asserted federal powers in a way that had never been politically possible.\n\nIn a desperate effort to fund the government's short-term obligations as it went to war, Treasury Secretary Salmon P. Chase, a lawyer who was not a banker and was a hard-money man, reluctantly issued US Treasury notes. These quickly became known as \"greenbacks\": the first federally issued paper money.\n\nGreenbacks were not redeemable for gold or silver. They were what some economists call \"fiat money\"\u2014money that is worth something because the government says it is. Conceived by Elbridge G. Spaulding, the congressman from Buffalo, New York, who introduced the Legal Tender Act, greenbacks were a radical experiment born of the desperation Buchanan had left behind. Bray Hammond suggests that they were in effect a bankruptcy settlement. Though not convertible to specie, they were legal tender, meaning that their acceptance was mandatory for all obligations of the federal government.\n\nGold was coming in from California, where it was being found in creeks and rocks. Gold was coming in from England, which had become dependent on US wheat after its own crops failed, again. The federal government took in the gold and paid out greenbacks, which carried no interest and bore no date of maturity. They were simply intended to pass from one hand to another, and never be redeemed, only replaced.\n\nThere was a model for the Legal Tender Act: New York's free banking act of 1838, which dealt out money to the state's banks based on the amount of state bonds the bank had purchased and placed on deposit with the state. It was a hard fight to approve the act in Congress, after years of hard-money fiscal orthodoxy had taught that paper money was a diabolical swindle. Many believed that, as Jackson had insisted, the Constitution forbade such a thing. Lincoln signed the Legal Tender Act on February 25, 1862, and the first notes went into circulation on April 5, after the government had gone a long three months without money; $150 million were printed, though $60 million replaced demand notes being withdrawn from circulation, leaving a net $90 million of new money. Two months later, Chase asked for, and received, another $150 million.\n\n_A greenback: the silver front and green back of an 1862 US dollar, with Salmon P. Chase's picture._\n\nThe obverse was a silvery gray, and the reverse was all green, giving the new paper dollar its nickname. Chase put his picture on the one-dollar bill, and Lincoln's on the ten.\n\nThere was, however, still a gold dollar in existence, so there were effectively two standards; the value of gold went up compared to the value of paper when the South won a victory, and down when the North won. The notes began depreciating, and after another $150 million were printed in the aftermath of Lincoln's call for three hundred thousand more troops, they depreciated more.\n\nThe banks had wanted the Legal Tender Act, and it was followed by the National Bank Act of 1863, which created a national banking system. That year Chase's supporter John Thompson founded First National, the bank that subsequently became Citibank.* The banks took the greenbacks in from the government and they paid them out to customers; at least they had something to use for money.\n\nGreenbacks were popular. People wanted paper money; everyone was heartily sick of the patchwork system of privatized money issued by local banks, which was increasingly becoming irredeemable as the crisis of war deepened. Many newspapers wanted paper money and evangelized on its behalf. Now, for the first time since Jackson killed the Second Bank of the United States, there was a paper money that had the same value everywhere in the country. The new federal notes had the effect of knitting together the roughly two-thirds of the country's population* who were still flying the United States flag, because everyone had a stake in the survival of the currency, which meant, in the survival of the Union.\n\nThe bills depreciated substantially but did not become valueless. By 1863, they were trading at 61 percent of their face value, not bad considering the convulsions that the economy had undergone in wartime and the unresolved problems of a dual gold\/greenback system. There were only three issues of greenbacks, which were withdrawn from circulation at war's end, but the changeover had happened: though the course was not smooth, from then on the United States was committed to having a national paper currency.\u2020\n\nGreenbacks were as much an assertion of federal power as they were an economic innovation. Unlike the Confederate States of America, the United States had a functional government. As the Union created itself as a war machine, more initiatives issued from the federal government. Congress authorized, and Lincoln signed, an income tax. The Treasury sold the banks large amounts of long-term bonds. The Homestead Act was put into place\u2014something that the South had been strenuously opposed to but that now could pass in the absence of their obstruction of it, though free black people were excluded. The Land Grant Act apportioned land to public colleges across the country. The National Bankruptcy Act was implemented. The Yosemite wilderness was set aside as a national park. And spectacular new possibilities were opened up for corruption as vast amounts of Western land were granted to railroads, ushering in the age of the tycoons.\n\nWe will not attempt to replay the great conflict in these pages. For our purposes, we think of it as two successive, overlapping wars.\n\nThe first we could call the War of Southern Conquest, which was started in the expectation of a quick takeover of the US government by force. Its advance was quickly stopped, and it was definitively over by the time of the double Confederate losses at Gettysburg (July 3, 1863, which ended the South's invasion of the North), and Vicksburg (the next day, which ended the South's control of the Mississippi River). The Southern leadership\u2014Jefferson Davis in particular\u2014had no plan B, and it seems as though they wanted to prolong the misery as long as possible. Having committed to the total war that treason against the republic signified, expecting to pay the maximum penalty in the case of a Northern victory without a negotiated settlement, they dug in and continued fighting against a much larger, better equipped enemy, as the corpses mounted.\n\nBut they still had their slaves. And property rights in human beings still had multiple benefits, one of which was allowing the owners to avoid combat. After the Confederate Congress passed the first conscription act in April 1862, providing for three years of compulsory service (though one could hire a substitute), it passed on October 11 the so-called \"Twenty Nigger Law,\" which exempted from the draft one white man per plantation with twenty or more slaves\u2014in order to guard against rebellion. Overseers were also granted exemption. It stimulated a wave of desertions, already ongoing, by the poor whites of the South, who were overwhelmingly the ones dying on the battlefields in support of slavery. A catchphrase was popularized that has persisted in subsequent conflicts: rich man's war, poor man's fight.\n\nThe Confederate regime acted very much like an occupier on its own territory, especially in those rugged pockets with fewer slaves and consequently less interest in defending slavery. To fund its military operations, it imposed \"tax-in-kind,\" giving army officers the authority to take anything they wanted in a government-sanctioned banditry\u2014everything from the horse that pulled the wagon, to the ham in the smokehouse and the corn in the garden plot, to the cloth women had woven to make clothes for their children. By 1862 already in Davis's Mississippi, crops were not being planted for lack of manpower and supplies. Young men were conscripted on pain of death into the Confederate Army where they were miserably treated; unlike their officer class, Confederate troops frequently went without uniforms, tents, shoes, or food, even in the war's early days, though they were well-supplied with ammunition. Nor did it escape their notice that many planters were occupying themselves not with fighting so much as with blockade-running their cotton to market. What, then, united the South's poor yeomanry with its wealthy elite? Why did perhaps as many as a million Confederate soldiers experience untold misery and mass death to fight for the rights of 347,525 slaveowners?\n\nOne dependable, long-term force that held the white classes together was a culture of negrophobia: the visceral fear of annihilation in the race war they were certain would follow emancipation. This deeply embedded, centuries-old belief was unsubtly stoked at every turn. The War of Southern Conquest was from the beginning portrayed as the defense of white women and children against conjectured mass violence by black marauders, stoked against whites by monstrous abolitionists. But there were also poor yeoman farmers who regarded the Confederacy as a plague on them. There were Union volunteers from every slave state, and even in hardcore Mississippi, Jones County announced its independence from the Confederacy.\n\nAfrican Americans were entirely on one side in this war. But at the outset of hostilities, they weren't allowed to fight. US law prohibited black soldiers from enlisting in the army (though there were already black sailors in the navy), and Lincoln did not at first attempt to change it, so African American volunteers were turned down. The war went badly for the North during this time.\n\nDespite the South's insistence that the \"Black Republicans\" would force abolition on them, Lincoln had never proposed to end slavery in the Southern states. He had begun by insisting that it was not a war about slavery, but to preserve the Union. But on September 22, 1862, prodded by Seward and Chase as the carnage dragged on, and as Frederick Douglass had been urging all along, Lincoln issued the preliminary Emancipation Proclamation, followed by the definitive proclamation on January 1, 1863. It only applied to those enslaved in the seceded territories; Maryland, Delaware, New Jersey, Kentucky, Missouri, and the District of Columbia, as well as some occupied territories, continued to have slavery while remaining in the Union, with New Jersey using the euphemism of \"apprentices.\" But the Emancipation Proclamation transformed the meaning of the war.\n\nOnly after the North committed unambiguously to emancipation could the war be decisively won. Lincoln had not previously claimed to be prosecuting a war on slavery, but now that was unquestionably what it had become. This, then, was the second phase of the war, which we will call the War on Slavery.\n\nArtist Francis Bicknell Carpenter, who painted an imagined scene of Lincoln reading the proclamation to his cabinet, wrote that Lincoln told him, \"I felt that we had reached the end of our rope on the plan of operations we had been pursuing; that we had about played our last card, and must change our tactics, or lose the game.\" Why had Lincoln not started that way? According to Carpenter, Lincoln told him that \"it is my conviction that had the proclamation been issued even six months earlier than it was, public sentiment would not have sustained it. Just so, as to the subsequent action in reference to enlisting blacks in the Border States. The step, taken sooner, could not, in my judgment, have been carried out.\" In short, political will.\n\nEffective January 1, 1863, the Emancipation Proclamation's effect was somewhat symbolic, since it did not apply to those still held enslaved in Union territory and mostly applied to areas the Union did not control, but it nonetheless marked a change in the purpose of the war. The Fire-Eaters had long charged that the North was planning to impose abolition on them. Now, for the first time, it was a policy goal. And in allowing for the enlistment and arming of black soldiers, the Emancipation Proclamation was not symbolic at all. \"I further declare and make known,\" it read, \"that such persons of suitable condition, will be received into the armed service of the United States to garrison forts, positions, stations, and other places, and to man vessels of all sorts in said service.\"\n\nLincoln's game-changer came as a shock to the Confederates. What Patrick Henry warned against had finally happened: enslaved assets\u2014the property whose value had governed every Southern political initiative since colonial days\u2014were no longer legally recognizable as such. In a long message to the Confederate Congress on January 12, Confederate president Jefferson Davis\u2014who was never president of a functional government, but was commander in chief of a losing war\u2014denounced the \"execrable measure\" by which \"several millions of human beings of an inferior race, peaceful and contented laborers in their sphere, are doomed to extermination, while at the same time they are encouraged to a general assassination of their masters.\" Up till that point, the Confederate hierarchy had considered the possibility that a negotiated outcome to the war might yet result in a reunited nation on their terms. No more.\n\nSlaveowners' wealth had crumbled to dust. There would be no more securitizing Southern banks' collateralized slaveholdings by Northern banks, nor would European lenders buy into enslaved assets that Washington had pronounced worthless. Lincoln had been the wheat candidate; Britain, which had suffered bad harvests and needed Northern wheat, was siding with the North despite considerable Confederate sympathy in Lancashire. Nor did France save the day for Jefferson Davis, as it had for George Washington; instead, with the United States otherwise occupied, France invaded Mexico in 1861.\n\nThe Emancipation Proclamation decommissioned the capitalized womb. Labor was no longer capital. African American children were no longer born to be collateral. Their bodies were no longer a better monetary value than paper. The US economy was no longer on the negro standard. Not only were the slaves emancipated; so was American money.\n\nThe Emancipation Proclamation and the coming of the greenback were concurrent and were intimately related. Once the enormous appraised value of the bodies and reproductive potential of four million people was no longer carried on the books as assets, dwarfing other sectors of the economy on paper and generally distorting the economy, the financial revolution of a national paper money was able to happen. The end of the slave-breeding industry was crucial to the remaking of American money.\n\n_This engraving depicting three enslaved laborers was used on several different Confederate notes._\n\nThe Confederacy, meanwhile, was not receiving gold from California or from wheat sales to Britain. Instead, it took in its supporters' accumulated savings in gold and silver and in return, it gave them some seventy varieties of engraved notes, many of them bearing pictures of slaves working. Some had a written promise on the notes to pay them back with interest once the war was over. These notes were not usable to pay import duties; only specie and bond coupons were allowed for that. Among the many notes featuring the picture on this page was a one-hundred-dollar Confederate note issued at Richmond on December 11, 1862, whose hopeful legend promised an excellent rate of return: \"Six Months after the Ratification of a Treaty of Peace between the Confederate States and the United States of America, the Confederate States of America will pay to the bearer on demand One Hundred Dollars with interest at two cents per day.\" The back side of the bill was blank.\n\nThe South's banks were forced to buy worthless Confederate bonds on pain of being labeled treasonous to the Southern cause, so they effectively had their assets confiscated by the Confederacy. Unsurprisingly, the Southern banking system did not survive the war. With it went the commercial network that had connected the South's slave-driven finance with that of the rest of the country.\n\nThere was still money to be made by the intrepid. Cotton had become a cash market, attracting middlemen willing to take personal risk in pursuit of high profit. Despite the difficulty of shipping, the sky-high prices that cotton fetched encouraged farmers to keep planting it instead of food. After Joseph Acklen died on the Angola plantation in 1863, his widow, Adelicia (previously Isaac Franklin's widow), is said to have slipped into Louisiana from Tennessee to negotiate the illegal sale of twenty-eight hundred bales of cotton to an English merchant for an exorbitant sum of gold, said to be $750,000 or more, which she subsequently collected in person in London.\n\nDespite the worthlessness of Confederate money, some people made a profit with it. When New Orleans was occupied by the Union in 1862, Julius Weis, a merchant in Natchez, managed to sell his firm's inventory of ready-made clothing to Confederate soldiers for Confederate money, \"which was then nearly at par,\" he recalled. \"I took $15,000 of this money and bought a piece of property in Memphis, which I sold after the war for a like amount of greenbacks.\" Still having \"faith in the ultimate success of the Confederacy,\" he spent another $18,000 in Confederate money for \"a fine-looking mulatto, to whom I took a fancy.\"\n\nAfter the Southern rebellion began, the Lehman Brothers were well-positioned, having a New York office, and after the Union occupied the factorage capital of New Orleans in 1862, they established an office there. They became blockade runners, exporting such cotton as they could sneak out of the South.\n\n_\"Six months after the ratification of a treaty of peace between the Confederate States and the United States, the Confederate States of America will pay two dollars to bearer.\" Judah P. Benjamin on an 1864 two-dollar Confederate bill, one of at least seventy issues of paper money during the Confederacy. Poorly printed, this note was cut out with scissors. The back is blank._\n\nBlockade runners have been much romanticized, with tales of how they brought in British-made guns to the Confederates; but much of what the blockade runners brought back was luxury goods, because some of the wealthy continued to make money. After the war began, Charley Lamar became a blockade runner, slipping in and out of Charleston harbor on moonless nights in unlighted ships painted the color of water, past what Isidor Straus counted one night as twenty-one blockading steamers. The Strauses too went into blockade running. After a local grand jury excoriated what it called the \"evil and unpatriotic conduct of the representatives of Jewish houses,\" Lazarus Straus moved his family from Talbotton to Columbus, Georgia, the Confederacy's second most important industrial center after Richmond, in 1863, when Confederate money was trading five cents to the dollar in gold.\n\nNew Orleans's Jewish community, tightly connected with that of Charleston, had perhaps doubled in size in the years preceding secession, and numbered about four thousand in 1861. Its merchants were clustered in the area of Canal Street, the dividing line between the town's Anglo and Creole populations. It contributed the Confederacy's most brilliant legal mind: Judah P. Benjamin, a St. Croix\u2013born former sugar planter, former slaveowner, and a cosmopolitan attorney. He had been the second Jewish US senator (in 1852) and was a second cousin of the first Jewish senator, David Levy\/Yulee, though neither he nor Yulee were practicing Jews. A key advisor of Jefferson Davis, he became the attorney general of the Confederacy, then its secretary of war, then its secretary of the treasury.\n\nThe role of Jewish merchants as financial intermediaries irritated General Ulysses S. Grant. \"The Jews seem to be a privileged class that can travel anywhere,\" he wrote to Assistant Secretary of War C. P. Wolcott in 1862. Then and today, this complaint of \"privilege\" was a central tenet of anti-immigrant rhetoric, with which Grant was unfortunately familiar, as his political background included a strong nativist streak and he had in the winter of 1854\u201355 briefly joined a lodge of the xenophobic \"Know-Nothing\" movement in Missouri.\n\nGrant's General Order No. 11 of December 17, 1862, ordered the expulsion within twenty-four hours of all Jews \"as a class\" from Kentucky, Tennessee, and Mississippi. It was an attempt to stop cotton smuggling, but what it meant was that Jews who lived in those states were expected to pick up and leave their homes overnight. Grant's order all too easily fell into a pattern of anti-Jewish language\u2014some of it casual, some of it deeply believed\u2014that fell on occasion from the lips and pens of antislavery figures that included William Tecumseh Sherman, William Lloyd Garrison, Henry Wilson, John Quincy Adams, and Henry Adams. It was the culmination of a series of measures that on November 10 had included an instruction to railroad conductors not to accept Jewish passengers. General Order No. 11 had a predictably demoralizing effect on the seven thousand or so Jewish soldiers in the Union army, subjecting them to taunts from other soldiers and causing one Jewish officer, Captain Philip Trounstine of the Fifth Ohio Cavalry, to resign in protest. A Jewish protest to Lincoln quickly resulted in the rescission of the order on January 6, 1863, and Grant subsequently apologized for having issued it.\n\nThere were about three thousand Jewish soldiers in the Confederate army, most of whom were poor immigrants. Jewish merchants in the South, meanwhile, found themselves denounced in the Confederate Congress and on the receiving end of accusations from townspeople of disloyalty and extortion. The worse the war went for the South, the more vulnerable to scapegoating they were.\n\nIt is instructive to unpack the first words of Lincoln's Gettysburg Address again:\n\n_Four score and seven years ago our fathers brought forth on this continent, a new nation..._\n\nLincoln thus dated the republic as beginning eighty-seven years previously\u2014not from the 1789 Constitution, but from 1776, though the Declaration of Independence does not mention a new \"nation.\" In affirming that the thirteen colonies were a nation in 1776 rather than a confederation of thirteen states, Lincoln was providing a revisionist take on the Declaration. He then attempted to reclaim the words of the Southern hero Thomas Jefferson:\n\n_... conceived in Liberty, and dedicated to the proposition that all men are created equal._\n\nWith abolition now at last the official post-Emancipation Proclamation US policy, Lincoln was repudiating _Dred Scott_ 's interpretation of Jefferson's \"all men,\" declaring that the inspirational words might at last include those who had not been conceived in \"Liberty.\" At last, liberty no longer meant liberty for slavery.\n\nEverybody knows what happened to Lincoln.\n\n*In 1877, Thompson founded the bank whose successor still bears his friend's name: Chase.\n\n*Union population: ~23 million; Confederate: ~9.1 million (~5.1 million free, ~4 million enslaved).\n\n\u2020Convertibility to gold was restored in 1879, and ended under President Nixon in 1971.\n\n#   46\n\n# **A Weird, Plaintive Wail**\n\n_Savannah, Ga., Dec. 22 [1864]._\n\nTo His Excellency, President Lincoln:\n\n_I beg to present you as a Christmas gift, the city of Savannah, with one hundred and fifty heavy guns and plenty of ammunition, and also about twenty-five thousand bales of cotton. 1_\n\n(Signed.) W. T. Sherman, Major-General\n\n_When de war ended, I goes back to my mastah and he treated me like his brother. Guess he wuz scared of me 'cause I had so much ammunition on me. 2_\n\n\u2014Formerly enslaved Civil War veteran Albert Jones, Portsmouth, Virginia, January 8, 1937\n\nNOW THE WAR COULD be won: as with previous proclamations by Dunmore and by Sonthonax and Polverel, emancipation meant black soldiers in combat, even as it emboldened the many enslaved who heard about it throughout the South.\n\nPursuant to the Emancipation Proclamation, 166 black regiments were created. The number of African Americans who fought is officially around 180,000, but it seems likely there were more than that. By war's end, about 10 percent of the US Army was black. Though they were not commanded by black officers, they were known as dedicated fighters. For them, the war was even more dangerous than it was for white soldiers.\n\nIn his previously quoted message, Jefferson Davis announced his post\u2013Emancipation Proclamation intention to treat all captured Union officers as guilty of \"exciting servile insurrection,\" which was to say, to execute them. The Confederate hierarchy construed all black soldiers to be guilty of that crime and deserving of death.\n\nFrom the first encounters between black soldiers and Confederates in battle pursuant to the Emancipation Proclamation, the Confederates waged \"black flag\" or \"no quarter\" war. Atrocities were routine; taking no prisoners, they slaughtered wounded black soldiers, on occasion bayoneting them repeatedly or beating their brains out with clubs. Confederate soldiers frequently made every effort to kill black soldiers on the battlefield, murdering them in cold blood if they were captured, including, writes Gregory J. W. Unwin, \"those who attempted to surrender and wounded men too weak to offer resistance.\" Captured black soldiers who were not killed were frequently enslaved. Confederates also typically targeted for murder the white commanders of the black regiments; the knowledge that any whites associated with black troops would be flat-out killed was intended to drive a wedge between white and black Union soldiers.\n\nAfraid of the consequences, the Union refrained from calling for no-quarter war in reprisal, thereby leaving their black troops to be sacrificed. There were thus two different war regimes operating, one for white prisoners and the other, even more horrible, for black prisoners. \"Confederate war crimes far exceeded those of the Federals by every measure,\" writes George S. Burkhardt, who called attention to it in _Confederate Rage, Yankee Wrath._ 4\n\nConfederate violence in battle was genocidal toward black people, reaching a pitch comparable to the final moments of that other major bloody American war of abolition, the Haitian Revolution. The mere fact of a black man in a military uniform with a weapon was cognitive dissonance: in the Confederate worldview, this was not possible. As they saw it, the enemy was less than human, and was their own escaped property. In the words of a South Carolina woman: \"Just think how infamous it is that our _gentlemen_ should have to go out and fight niggers, and that every nigger they shoot is a thousand dollars out of their own pockets!\" The most notorious massacre, though not the largest, was committed by the troops of Nathan Bedford Forrest at Fort Pillow, an army post of no great strategic importance on a Tennessee bluff overlooking the Mississippi River, on April 12\u201313, 1864. Forrest had enlisted in the Confederate army as a private, but quickly became a lieutenant colonel, then one of the most celebrated Confederate generals. He was a cavalryman, said to be one of the best horsemen in the army, whose principal military technique was the aggressive assault.\n\nAfter charging into Fort Pillow, the troops under Forrest's command killed in cold blood perhaps as many as five hundred Union soldiers who had surrendered (there is no definitive count) over a period of two days. Most of them were black. The _New York Tribune_ reported that five soldiers were buried alive. Forrest's _New York Times_ obituary in 1877 recalled the massacre:\n\nWithout discrimination of age or sex, men, women, and children, the sick and wounded in the hospitals, were butchered without mercy. The bloody work went on until night put a temporary stop to it; but it was renewed at early dawn, when the inhuman captors searched the vicinity of the fort, dragging out wounded fugitives and killing them where they lay. The whole history of the affair was brought out by a Congressional inquiry, and the testimony presents a long series of sickening, cold-blooded atrocities... The news of the massacre aroused the whole country to a paroxysm of horror and fury.\n\nAn 1865 interview with Forrest, conducted by a reporter for the New Orleans _True Delta_ and reprinted in other newspapers, asked him if the investigators' (the \"Yankees'\") report of Fort Pillow was accurate. He answered, \"Yes, if we are to believe anything a nigger says.\" Then he added, \"When I went into the war I meant to fight. Fighting means killing. I have lost twenty-nine horses in the war, and have killed a man each time.\"\n\nThere were many witnesses to the Fort Pillow massacre, which contributed to its visibility as a media event, but Fort Pillow was not an anomaly; the level of hatred displayed toward black soldiers was consistent wherever Confederates fought. A Virginia colonel described the wholesale slaughter of prisoners at the disastrous Battle of the Crater outside Petersburg, Virginia, in July 1864: \"Our men, who were always made wild by having negroes sent against them... were utterly frenzied with rage. Nothing in the war could have exceeded the horrors that followed. No quarter was given, and for what seemed a long time, fearful butchery was carried on.\"\n\nBlack troops made \"Remember Fort Pillow!\" into a battle cry and became increasingly disposed to give no quarter. Burkhardt quotes a New Jersey officer: \"The Rebel prisoners are very fearful of being left to... colored troops as they fear their own acts of inhumanity will be repaid.\" Forrest's troops continued their homicidal career in June, a little north of Tupelo, Mississippi, at Brice's Cross Roads, where Forrest scored his greatest victory of the war against an enemy superior in numbers. After routing a Union force of eight thousand under the incompetent direction of Brigadier General Samuel Sturgis, Forrest's men hunted down and killed members of Colonel Edward Bouton's Colored Brigade who had survived the battle. In April 1865, Forrest directed a massacre of Union troops near Selma while they were sleeping.\n\nThe month after the Fort Pillow massacre, General William Tecumseh Sherman, who liked neither black people nor abolitionists, began his Atlanta campaign. Entering Georgia from Chattanooga on the north, he burned the strategic rail depot in Atlanta, a small town whose population had multiplied under the pressure of war. Some of Atlanta was torched by Sherman's troops, and some by the Confederate general John Bell Hood; about half the city went up in flames. It was tremendous news in the North.\n\nSherman followed up Atlanta on November 15 with his sixty-mile-wide, three-hundred-mile long March to the Sea without supply lines, forcing his sixty-two thousand troops to eat their way through the country as they tore up railroad tracks and burned industrial, governmental, and military facilities and cotton crops along the way. Sherman's march, tactically aimed at destroying what remained of the Southern railroad system and strategically aimed at stopping the war once and for all, has been traditionally portrayed in the South as an orgy of cruelty, acquiring a mythical reputation as Exhibit A of Northern aggression. Sherman's troops certainly caused suffering, in part because they destroyed food supplies as well as cotton, but they concentrated primarily on strategic targets rather than residences. Some homes were burned, especially those of the planters; Sherman took special care to make sure that Howell Cobb's plantation was burned to the ground.\n\nBut the property that Sherman's troops fired was the least of the wealth they destroyed.\n\nThey burned slavery to the ground.\n\nWhatever else Sherman's march symbolized, for the enslaved it was a march of liberation, as one of the war's best-known songs, composed by Henry Clay Work, recalls:\n\n_Hurrah! Hurrah! We bring the jubilee!_\n\n_Hurrah! Hurrah! The flag that makes us free!_\n\n_And so we sang the chorus from Atlanta to the sea_\n\n_While we were marching through Georgia._\n\n\"Marching Through Georgia\" took its place alongside the most popular anthem played by Northern military bands: the stirring \"John Brown's Body,\" for which Julia Ward Howe had written new lyrics, still familiar today, as \"The Battle Hymn of the Republic.\" Noah Andre Trudeau quotes a letter written during the campaign by General William P. Carlin of the First Division that described what happened on one occasion when the band played that song:\n\nAbout a dozen young African-American girls came out of nearby houses, \"formed into a ring around the band at the head of the column, and with a weird, plaintive wail, danced in a circle in a most solemn, dignified, and impressive manner,\" wrote Carlin years afterward. \"What their meaning was I did not know then, nor do I now, but I, of course, interpreted it as expressive of goodwill to our cause.\"\n\nCarlin was hearing a ring shout, a collective song of spiritual power sung and danced in a moving counterclockwise circle. One of the oldest known forms of African American music, heavily Kongo in influence, the ring shout is known in the Sea Islands and points west, all the way to the Louisiana \/ Mississippi delta region, where it became part of the Baptist tradition of \"rocks.\"*\n\nMeanwhile, Jacob Thompson was plotting the mass murder of Northern civilians on behalf of the Confederacy. Funded with a million dollars in gold and sent by Judah P. Benjamin to be head of Confederate Secret Service operations in Canada, Thompson dispatched incendiary attacks on New York and Chicago. These terrorist attacks were to be coordinated with occupation by the former Knights of the Golden Circle, as of 1864 called the Sons of Liberty, whose membership was said, perhaps hyperbolically, to number in the hundreds of thousands. That never happened; but had Confederate colonel Robert Martin been less inept in scouting locations and in using his \"Greek fire\" phosphorus firebombs, the plot for eight infiltrated Confederate officers to burn down New York City in a massive conflagration on November 25, 1864, might well have succeeded, in which case the Confederacy would have exacted a civilian death toll of possibly historic proportions. The fires were set, but in closed spaces, where they burned out for lack of oxygen.\n\nThe Confederate commander General William D. Hardee fled Savannah with ten thousand troops rather than confront Sherman, and he did not burn the town on leaving, nor did Savannahans put up resistance, so the fine houses of Oglethorpe's jewel of a city were spared the torch. Instead, Sherman established his headquarters there. A train of thousands of former slaves followed Sherman's troops into Savannah, creating a refugee problem.\n\nNot until Sherman's arrival in Savannah did the town's slave trade stop. Some traders escaped the city with captives, while others were less successful, and at least two traders, E. M. Blount and W. C. Dawson, fell victim to revolt, as the horrified trader Henry Bogardus wrote his sister: \"Blount's Negroes killed him and Dawson is not much better.\"\n\nFor the whites of Savannah, Sherman's occupation was defeat. But among black Savannahans, as the Reverend James Simms recalled, \"The cry went around the city from house to house among our race of people, 'Glory be to God, we are free!'\" Almost immediately, the black community of Savannah organized the Savannah Education Association. The Montmollin building, previously a Savannah slave trader's headquarters, was occupied by a school. It still had bars on the windows, and all they had to use for paper was the blank back sides of a stack of bills of sale for slaves, which were thus lost to history, but at least some children learned how to read and write.\n\nSherman continued on to Charleston, which fell in February 1865 after a siege of 545 days. Charleston had already suffered a devastating fire in December 1861; now, as most of the city's white population fled, Confederate troops set fire to the cotton in the warehouses and the ships in the harbor, and blew up their explosives, generating a great blaze that killed at least 150 civilians before Union troops put it out. In the chaos, two Northern journalists broke into the hastily abandoned slave mart on Chalmers Street. Charles Carleton Coffin, who reported for the _Boston Journal_ , took the gilt letters that read MART as a souvenir. James Redpath of the _New York Tribune_ , who had previously announced that he was not only an abolitionist but a reparationist, scooped up 652 letters to slave trader Ziba B. Oakes from his regional purchasing agents, which he donated to William Lloyd Garrison and which since 1891 have been in the Boston Public Library.\n\nThe people of Richmond had become accustomed to the sound of artillery fire, but now they too had to flee Grant's army. \"My line is broken in three places and Richmond must be evacuated,\" wrote Robert E. Lee to Confederate president Jefferson Davis, who ordered the evacuation of the Confederate capital on April 2, 1865. As Davis ran with the members of his government to board the Danville train, Robert Lumpkin hurried amid the chaos to evacuate the captives from his slave jail, setting out with one final coffle.\n\nThe classic account of the fall of Richmond is Coffin's report:\n\nMrs. Davis had left the city several days previous.... There was no evening service. Ministers and congregations were otherwise employed. Rev. Mr. Hoge, a fierce advocate for slavery as a beneficent institution, packed his carpet-bag. Rev. Mr. Duncan was moved to do likewise. Mr. Lumpkin, who for many years had kept a slave-trader's jail had a work of necessity on this Lord's day,\u2014the temporal salvation of fifty men, women, and children! He made up his coffle in the jail-yard, within pistol-shot of Jeff Davis's parlor window, and a stone's throw from the Monumental Church. The poor creatures were hurried to the Danville depot. This sad and weeping fifty, in handcuffs and chains, was the last coffle that shall tread the soil of America.*\n\nSlavery being the corner-stone of the Confederacy, it was fitting that this gang, keeping step to the music of their clanking chains, should accompany Jeff Davis, his secretaries Benjamin and Trenhold, and the Reverend Messrs. Hoge and Duncan, in their flight. The whole Rebel government was on the move, and all Richmond desired to be. No thoughts now of taking Washington, or of the flag of the Confederacy flaunting in the breeze from the dome of the national Capitol!\n\nHundreds of officials were at the depot, waiting to get away from the doomed city. Public documents, the archives of the Confederacy, were hastily gathered up, tumbled into boxes and barrels, and taken to the trains, or carried into the streets and set on fire. Coaches, carriages, wagons, carts, wheelbarrows, everything in the shape of a vehicle, was pressed into use. There was a jumble of boxes, chests, trunks, valises, carpetbags,\u2014a crowd of excited men sweating as never before: women with dishevelled hair, unmindful of their wardrobes, wringing their hands, children crying in the crowd, sentinels guarding each entrance to the train, pushing back at the point of the bayonet the panic-stricken multitude, giving precedence to Davis and the high officials, and informing Mr. Lumpkin that his niggers could not be taken.\n\nO, what a loss was there! It would have been fifty thousand dollars out of somebody's pocket in 1861, and millions now of Confederate promises to pay, which the hurrying multitude and that chained slave gang were treading under foot,\u2014trampling the bonds of the Confederate States of the America in the mire, as they marched to the station; for the oozy streets were as thickly strewn with four per cents, six per cents, eight per cents, as forest streams with autumn leaves.\n\n\"The faith of the Confederate States is pledged to provide and establish sufficient revenues for the regular payment of the interest, and for the redemption of the principal,\" read the bonds; but there was a sudden eclipse of faith; a collapse of confidence, a shrivelling up like a parched scroll of the entire Confederacy, which was a base counterfeit of the American Union it sought to overturn and supplant, now an exploded concern, and wound up by Grant's orders, its bonds, notes, and certificates of indebtedness worth less than the paper on which they were printed.\n\nJefferson Davis was trying to get to Texas, to continue the war from there. Did Lumpkin think he was taking his coffle to Texas too? There was nowhere to take a coffle. Those fifty people weren't going to be anyone's property now.\n\nIn a dramatic show of defiance, the Confederate general Richard S. Ewell torched a large area of Richmond, definitively ruining many of the city's businessmen. It was done with the acquiescence of his superior, Confederate secretary of war John C. Breckinridge, who was present in the city. The Richmond _Whig's_ report of April 4, 1865 seemed to suggest that the city had been ridded of an occupier with the departure of the Confederate government of which it had been the capital\u2014an occupier that destroyed much of Richmond as it fled:\n\nBy noon the flames had transformed into a desert waste that portion of the city bounded between 7th and 15th streets, from Main street to the river, comprising the main business portion. We can form no estimate at this moment of the number of houses destroyed, but public and private they will certainly number 600 to 800.\n\nAt present we cannot do more than enumerate some of the most prominent buildings destroyed.\u2014These include the Bank of Richmond; Traders Bank; Bank of the Commonwealth; Bank of Virginia; Farmers' Bank, all the banking houses, the American Hotel, the Columbian Hotel, the _Enquirer_ Building on 12th street, the _Dispatch_ office and job rooms, corner of 13th and Main streets; all that block of buildings known as Belvin's Block, the _Examiner_ office, engine and machinery rooms; the Confederate Post Office department building, the State Court House, a fine old building situated on Capitol Square, at its Franklin street entrance; the Mechanic's Institute, vacated by the Confederate States War Department, and all the buildings on that Square up to 8th street, and back to Main street; the Confederate Arsenal and Laboratory, 7th street.\n\nAt sunrise on Monday morning, Richmond presented a spectacle that we hope never to witness again. The last of the Confederate officials had gone; the air was lurid with the smoke and flame of hundreds of houses sweltering in a sea of fire.\n\nCoffin reported that:\n\nTo prevent the United States from obtaining possession of a few thousand hogsheads of tobacco, a thousand houses were destroyed by fire, the heart of the city burnt out, \u2014all of the business portion, all the banks and insurance-offices, half of the newspapers, with mills, depots, bridges, foundries, workshops, dwellings, churches,\u2014thirty squares in all, swept clean by the devouring flames. It was the final work of the Confederate government.\n\nRichmond's slave trade had continued full tilt, with a large population in the traders' jails when the Union entered the city. Chaplain Garland White, an African American soldier who entered Richmond with Indiana's Twenty-Eighth Regiment, described his experience in a letter written shortly after leaving the city: \"a vast multitude assembled on Broad Street, and I was aroused amid the shouts of ten thousand voices, and proclaimed for the first time in that city freedom to all mankind. After which the doors of all the slave pens were thrown open, and thousands came out shouting and praising God, and Father, or Master Abe, as they termed him.\"\n\nOn April 4, Elizabeth Keckley visited Richmond, as she accompanied Mary Todd Lincoln on the steamer _River Queen_ up the James, \"the river that so long had been impassable, even to our gunboats,\" to join the presidential party, with Lincoln at the head, to examine the city's condition.\n\nThe Presidential party were all curiosity on entering Richmond. They drove about the streets of the city, and examined every object of interest. The Capitol presented a desolate appearance\u2014desks broken, and papers scattered promiscuously in the hurried flight of the Confederate Congress.\n\nI picked up a number of papers, and, by curious coincidence, the resolution prohibiting all free colored people from entering the State of Virginia. In the Senate chamber I sat in the chair that Jefferson Davis sometimes occupied; also in the chair of the Vice-President, Alexander H. Stephens. We paid a visit to the mansion occupied by Mr. Davis and family during the war, and the ladies who were in charge of it scowled darkly upon our party as we passed through and inspected the different rooms.\n\nAfter a delightful visit we returned to City Point. (paragraphing added)\n\nFive days after Lee's surrender to Grant, on Good Friday, April 14, Lincoln became the first president in US history to be assassinated. John Wilkes Booth's conspiracy also gravely wounded Secretary of State William Seward and members of his family, and unsuccessfully targeted Vice President Andrew Johnson of Tennessee, who had been drunk at his swearing-in as vice president not six weeks previously on March 4, 1865.\n\nBooth was killed during capture, before he could be questioned. Eight people were convicted and executed for participating in his conspiracy; Jacob Thompson spent the rest of his life trying to clear his name of a rumored involvement in it. Was there a conspiracy involving Thompson's terrorist organization or other elements in the Confederate hierarchy? None has been proved, and Booth has often been portrayed as a fanatic in popular historiography, but that's too simple. Writing of the monk who assassinated the French king Henri III, the historian Geoffrey Treasure called him \"not mad, but _exalt\u00e9_ [exalted]: a recognisable type, not an isolated individual but representative, doing what many wished to see done.\"\n\nIf Calhoun, Rhett, Davis, Stephens, Cobb, Forrest, and their many colleagues were not \"madmen,\" neither was Booth. If they were madmen, at what point did madness set in? At Forrest's wholesale butchery? At Rhett's bizarre paean to martyrdom? At Calhoun's insistence that slavery was a positive good for humanity? At Jackson's genocide and ethnic cleansing? At Jefferson's scheme to deport all black people?\n\nThe madness was there all along. It was the madness of slavery.\n\nIn the Civil War's final battle east of the Mississippi, for Columbus, Georgia, on April 16, 1865, the forces of Union general James H. Wilson, who had not received word of Lincoln's assassination two nights before, defeated those of former US secretary of the treasury, now Confederate major general, Howell Cobb.\n\nOn May 2, President Johnson signed a proclamation offering $100,000 for Jefferson Davis's arrest in connection with Lincoln's assassination, and a manhunt for Davis ensued. Whatever the conspiratorial mechanism, Lincoln's assassination was a coup d'etat that carried a number of benefits for former Confederates who might reasonably have expected to hang for treason. Johnson was a pro-Union white supremacist who was uninterested in prosecuting Confederate leaders or in helping freedmen. He issued presidential amnesties and pardons for former Confederates, and restored confiscated lands\u2014thus ensuring that there would be no \"forty acres,\" as Rufus Saxton of the Freedmen's Bureau had promised, to compensate the destitute, largely illiterate mass of formerly enslaved for their multigenerational legacy of confiscated labor. There were no war crimes trials for the mass murder of black troops under cover of battle.\n\nBut the fundamental change had been made. The Southern economy had suffered its final, fatal collapse, the one long feared by slaveowners: their property had ceased to be their property. They were not compensated by the taxpayers for its loss, as the Jamaican slaveowners had been.\n\nNo more counting children as interest. No more multigenerational wealth accumulating from reproduction of enslaved humans to be passed on as legacies to slaveowners' children. No more paying debts in a bad year by cashing out and selling adolescents: the liquidity of the financial system vanished when ownership of the human capital was transferred from landowners to the laborers themselves.\n\nNo more forced mating. No more fancy girls. No more sex slaves.\n\nThe Ponzi scheme of the slave-breeding industry had crashed. Since laborers were no longer property, they were no longer mortgageable. Without enslaved women producing ever-increasing numbers of slave children to borrow against, the South suffered a massive credit implosion, whiplashing from a credit economy to a cash-poor cash economy, floating on a sea of bad debt.\n\nMany proud families never forgot the humiliation of losing their slaves, and some were downright hateful about it. Some former masters found it demeaning to have to share a sidewalk with black people who did not jump out of the way. Others were surprised to find that they could no longer slap black workers with impunity. There were still black laborers, of course, but they would no longer work sunup to sundown to make an ever-increasing, whip-enforced quota for bacon and corn mush in return. Some planters decamped for Brazil, which had slavery and plenty of land, and others for Mexico; a Confederate diaspora fanned northward up to Canada and out to the far West.\n\nThe poor whites of the South had a miserable time of it in the economically devastated postwar years. As the Southern states rejoined the country they had repudiated, many formerly wealthy Southerners occupied themselves by suing each other over old debts for which the collateral had vanished. But others had found ways to keep their money, or even made money during the war. They could no longer live off human capital as rentiers, but the elite were still the elite, and elite families have remarkable staying power over multiple generations, in every society. Since the planters' estates weren't broken up and distributed to the freedmen, they still had their land, which would be the basis of new fortunes. They still had their education, their family webs, their control of local institutions, their business and political contacts\u2014and they still had cheap black labor, which they kept as abject as possible by terrorizing them with a new racist regime that would come to be known as Jim Crow, enforced all over the former slave nation.\n\nMany of the formerly enslaved, whose dispossession was so complete that they had not even family names, got little more out of Reconstruction than an assigned surname, which was the bare minimum necessary for the creation a civil identity. Their new Anglo-Saxon names were in many cases assigned to them: Williams, Johnson, Smith, Jones, Brown, Jackson, Jefferson, Washington.\n\nSome of the elite who had the resources relocated with style\u2014the so-called \"Confederate carpetbaggers\"\u2014to New York, Chicago, and other urban centers. Some renewed Northern commercial contacts or business partnerships that had been active before or even during the war and found that little stigma was attached to their former treasonous activities, which were now recast as Southern patriotism.\n\nSouthern gynecologist Marion Sims, who had developed his surgical innovations by practicing on enslaved women, went to Europe during the war, where he operated on women of social importance for high fees. Returning to America, he established a private practice on Fifth Avenue and presented himself as a popular vision of a fabulously wealthy doctor-celebrity. He was \"instrumental\" in founding the nation's first cancer hospital, Sloan-Kettering Cancer Center, though he died the year before the project came to fruition in 1884.\n\nIsidor Straus spent much of the war in Europe, returning to America at war's end with about $10,000 in gold he had made in London trading Confederate bonds. His father Lazarus Straus relocated the family's retailing firm from Columbus, Georgia, to New York, where they became the owners of R. H. Macy's department store, then bought an interest in the store that became Abraham & Straus. Isidor Straus died in the 1912 sinking of the _Titanic_ , together with his wife Ida.\n\nEmanuel Lehman, already based in New York, also made money during the war selling Confederate bonds in England, at one point uncomfortably encountering his New York neighbor Joseph Seligman, who was selling Union bonds. After the war, Lehman Brothers put up $100,000 for Alabama's constitutional convention. Mayer Lehman moved up to New York, where he organized the first futures market in cotton; two of his former slaves came to New York to work for him as servants. The brothers parlayed their warehouses full of cotton into a business that continued through many transformations until the Panic of 2008, when Lehman Brothers filed for the largest bankruptcy in American history, intensifying a worldwide economic crisis.\n\nWidely suspected of being a planner of the Lincoln assassination, Judah P. Benjamin fled to London and became a barrister there. He wrote the standard legal work* on the sale of personal property, became legal counsel to Queen Victoria, and died, quite wealthy, in Paris in 1884.\n\nAdelicia Hayes Franklin Acklen Cheatham, one of the wealthiest women in the United States, died at the age of seventy, in 1887, in New York's Fifth Avenue Hotel, of pneumonia contracted while on a shopping trip.\n\nJ. D. B. De Bow, who in the South had been the most influential proslavery business publisher, started his _DeBow's Review_ right back up in New York in 1866, but died the following year.\n\nHowell Cobb's plantation was up and running again soon after the war. According to Cobb, the problem was that the formerly enslaved laborers were ungrateful, as per a December 1866 letter: \"The truth is I am thoroughly disgusted with free negro labor, and am determined that the next year shall close my planting operations with them. There is no feeling of gratitude in their nature.\" Cobb, who was as guilty of treason as anyone in the Confederate project, received a presidential pardon and died of a heart attack in New York City in 1868; his son continued the plantation.\n\nPierce Mease Butler's Georgia plantation survived the war intact. The places that had been occupied by the Union earliest\u2014Louisiana, the Sea Islands, Alexandria, etc.\u2014suffered less destruction, and the Union had occupied Butler's land from early in 1862, which likely saved it. Since the plantation was not broken up and distributed to the former slaves, Butler remained the owner. Though there was no longer slave labor, many of his former slaves returned to the plantation\u2014presumably less because they loved the Butlers than because the plantation was their home, and was the ancestral home of their close-knit community, or perhaps, as in other cases involving slaves who returned to the plantations they knew, because they were starving. Without a doubt, they would have preferred a small plot of land of their own in what sociologist Jean Casimir, speaking of Haiti, has called a \"counter-plantation\" system: \"a refusal... of the plantation system itself, [involving] the creation of a very different way of living, one focused on production for oneself and for surplus within a local market.\" But that was not on offer.\n\nFrances Kemble finally published her _Journal_ of life on Butler's plantation as a book in 1863, in post\u2013Emancipation Proclamation wartime. It became popular reading for abolitionists and caused a sharp rift with her pro-Confederate younger daughter Fan. After Pierce Mease Butler died of the archetypal Low-country disease, malaria, in 1867, Fan took the plantation over and tried to make it produce. But she couldn't make a go of it, blaming the labor force's disinclination to work as hard as necessary.\n\nJefferson Davis never surrendered. As long as Robert E. Lee continued, the war went on, but even after Lee surrendered on April 9, Davis did not; he was captured on May 10 in Virginia while trying to escape to Texas and was imprisoned for two years. He never asked for a pardon, never apologized, never swore allegiance, failed at his business initiatives, and spent much time being a traveling guest of honor until he died in a mansion in New Orleans's Garden District in 1889. In 1881 he published the stultifying 1,515-page _The Rise and Fall of the Confederate Government_ , in which he insisted that \"to whatever extent the question of _slavery_ may have served as an _occasion_ , it was far from being the _cause_ of the conflict.\" The cause, he explained, was \"sectional rivalry\" and \"political ambition\" that \"happened\" to have \"coincided\" along the \"line of demarkation\" of slavery versus free labor. He also maintained that \"African servitude among us [was]... the mildest and most humane of all institutions to which the name 'slavery' has ever been applied.\"\n\nRobert Lumpkin barely outlived the war. He died in 1866 at the age of sixty, his livelihood of slave trading destroyed. Shortly before he died, he named his former slave Mary executor of his estate and granted her the right to use the name \"Lumpkin.\" Provided she did not remarry, she became the sole proprietor of his properties in Richmond and Philadelphia.\n\nMary Lumpkin thus became the owner of the property she had lived on since she was twelve. Formerly known as Lumpkin's Slave Jail, it had been famous to every trader in Virginia, and notorious to the thousands of African Americans who had passed through it. It was nearly worthless. Desperate like everyone else for income in the charred ruin of Richmond, she rented it for $1,000 a year to the Rev. Nathaniel Colver, a Boston minister, to be used as the School for Former Slaves, subsequently Virginia Union University. White landlords wouldn't rent their property for such a purpose, so the newly freed students had to go down the muddy embankment at Shockoe Bottom. Unfortunately, Mary also inherited Lumpkin's debts, and she died poor.\n\nLumpkin's competitor, Silas Omohundro, whose slave jail adjoined his, had done something very similar before he died in 1864, leaving the use of his properties in Richmond and Pennsylvania to his formerly enslaved common-law wife, Corinna, with whom he had six children. Corinna fared better than Mary Lumpkin; she came to own her own confectionery.\n\nLouis Hughes did not escape from slavery in Mississippi until 1865; he went behind Union lines, and from there managed to rescue his wife and children. After moving around, the family settled in Milwaukee, where he worked as a nurse, and where, in 1897, he published his autobiography, _Thirty Years a Slave._\n\nFrederick Douglass's house in Rochester, New York, was burned down in 1872, apparently an arson. From late 1889 to mid-1891 he served as the US minister to Haiti; he died of heart failure in 1895, at the approximate age of eighty-seven. Though he was the leading African American literary and political figure of the nineteenth century, his writing was largely forgotten until a rediscovery that began in 1945, when historian Philip Foner edited a multivolume anthology of his work.\n\nWilliam Wells Brown largely devoted his post-emancipation years to activism on behalf of the temperance cause, and practiced medicine in Boston, specializing in homeopathy. On the occasion of his return to his birth state of Kentucky, he was kidnapped by the Ku Klux Klan, but escaped. He died at the age of seventy in Massachusetts.\n\nAfter Harriet Jacobs escaped from Edenton, North Carolina, to Philadelphia with the help of a boat captain in 1842, she lived in fear of being captured, especially after the passage of the Fugitive Slave Law. She became well known in abolitionist circles with her self-publication in 1861 of _Incidents in the Life of a Slave Girl_ , which came back from the printer shortly after the first wave of Southern states seceded. A vocal advocate of an emancipation proclamation, with great dignity she organized relief for the \"contrabands\"\u2014the homeless, impoverished refugees from slavery who poured into Washington and other cities in the early days of the war. With the post\u2013Emancipation Proclamation entry of black soldiers into the war, Jacobs was active in aiding convalescent soldiers in Washington, and together with her daughter founded a free school after the war. She was largely forgotten after her death, and had to be rediscovered; Jean Fagan Yellin's biography of her, from which we extract the above information, was published in 2004. Indeed, Jacob's memoir was considered by many critics to be fiction until Yellin authenticated it in 1987.\n\nElizabeth Keckley founded the Contraband Relief Organization in 1862, attempted to raise money for Mary Todd Lincoln, and published her book in 1868. She died in poverty in 1907, a resident of the National Home for Destitute Colored Women and Children in Washington, for which she had helped raise founding funds.\n\nGeneral Sherman went on to supervise the building of the transcontinental railroad during the Grant administration, which meant completing the killing of the buffalo herds and what Sherman referred to in an 1872 letter as \"the final solution to the Indian problem,\" in which the West's Native Americans were slaughtered or moved onto \"reservations.\"\n\nIf anyone in the Confederate ranks might have seemed a candidate for hanging, it would have been Nathan Bedford Forrest. By the time he was pardoned by Andrew Johnson instead of being tried as a war criminal, he had already returned to violence. Not two years after the Fort Pillow Massacre, in the fall of 1866, he was sworn in at Maxwell House in Nashville as the Grand Wizard of the Invisible Empire of the Ku Klux Klan. Beginning as a posse of malicious night-riding pranksters, complete with a fanciful, carnivalesque pedigree that cast them as Scottish knights, the Klan quickly expanded into other states to become the nation's most notorious, though not the only, white supremacist paramilitary organization as Forrest prosecuted a race war. In what was arguably the largest terrorist campaign in US history, the Klan and similar organizations murdered thousands of people, black and white, as part of a successful effort to suppress Reconstruction and black self-determination.\n\nPresident Ulysses S. Grant, inaugurated in 1869, believed that the sacrifice of so much blood in the war had to be redeemed by fully enfranchising the formerly enslaved. That was precisely the proposition the Ku Klux Klan was determined to reverse, but after Grant made clear his determination to prosecute the Klan, Forrest officially disbanded it in February 1869. By then much of their work had already been done. In subsequent testimony before Congress, Forrest added perjury to his list of crimes by denying his involvement with the Klan.\n\nWith no more slave trading business to do, Forrest ventured his net worth on a proposed Memphis & Selma Railroad, which was never built. As his railroad plan deflated, Forrest, thinking there might be war with Spain and that it might take place in Cuba (where slavery still existed, though it was fading), offered his services to\u2014of all people\u2014General Sherman, as reported in the _New York Times_ of December 3, 1873: \"I hereby tender you my services as a volunteer. I think I could enlist from 1,000 to 5,000 men who served in the Southern army during the late war, and at short notice, and who could rendezvous at New-Orleans, Mobile, Pensacola, and Key West, either as cavalry or infantry.\" Sherman politely explained that he did not believe there would be a war with Spain in Cuba; ultimately, there was one, but it happened twenty-five years later.\n\nForrest spent the rest of his life trying to live down Fort Pillow, for which his name was popularly held in contempt, though in the South there was no lack of apologists for him. In the perhaps sarcastic words of his _New York Times_ obituary on October 30, 1877:\n\nHis last notable public appearance was on the Fourth of July in Memphis, when he appeared before the colored people at their celebration, was publicly presented with a bouquet by them as a mark of peace and reconciliation, and made a friendly speech in reply. In this he once more took occasion to defend himself and his war record, and to declare that he was a hearty friend of the colored race.\n\nSlave trader, war criminal, the KKK's top terrorist: if Nathan Bedford Forrest's reputation could be sanitized, anyone's could be. A high school named for Forrest exists in his hometown of Chapel Hill, Tennessee; another, in Jacksonville, changed its name in 2014.\n\nForrest's final business venture was a plantation that used captive labor, under the postbellum name of \"convict leasing.\" He contracted in 1875 with the Shelby County jail to put 117 prisoners (39 of them white) to work for a term of five years (though he died in 1877), paying the jail ten cents a day for their otherwise uncompensated labor, employing seven guards to watch over them.\n\nThe slaves of the South had been emancipated by then, of course. But the Thirteenth Amendment, adopted on December 18, 1865, to prohibit slavery, left a loophole: prisons. It reads in its entirety:\n\nNeither slavery nor involuntary servitude, _except as a punishment for crime whereof the party shall have been duly convicted_ , shall exist within the United States, or any place subject to their jurisdiction. (emphasis added)\n\nIt has been argued that the framers of the Thirteenth Amendment did not intend to tolerate slavery, and that the phrase \"except as a punishment for a crime\" should be parsed as only modifying \"involuntary servitude\" and not \"slavery.\" A clearer version had been proposed: \"Slavery being incompatible with a free government is forever prohibited in the United States, and involuntary servitude shall be permitted only as a punishment for a crime.\" But it was Thomas Jefferson's phrasing and vision that prevailed: the amendment's framers copied the more ambiguous language of the Northwest Ordinance of 1787, which in turn had taken it from Jefferson's draft of the Land Ordinance of 1784: \"after the year 1800 of the christian era, there shall be neither slavery nor involuntary servitude in any of the said states, otherwise than in punishment of crimes whereof the party shall have been convicted to have been duly personally guilty.\"\n\nFrom Jefferson's ambiguity forward, convict labor has been part of American commerce, and, as twenty-first-century readers are well aware, it continues.\n\n*We don't know exactly what Carlin heard, but we can get an idea from hearing latter-day ring shout groups, which were recorded as early as 1934 by Alan Lomax. An annual ring shout, known as Easter Rock, is still performed in Winnsboro, Louisiana. See Jackson.\n\n*It was not; there were still coffles wherever the Union had not entered, notably Texas.\n\n*Still being updated today, it's known as _Benjamin's Sale of Goods._\n\n_The entrance to Angola, the former Louisiana plantation of the nation's largest slave trader, Isaac Franklin. Located at the dead end of a twenty-two-mile road that goes only there, it is now the penitentiary of the number-one incarcerator state of the number-one incarcerator nation of the world, with Death Row situated on the part of the property adjoining the Mississippi border. On its grounds, imprisoned people are forced to perform unmechanized field labor; it is understood by many, including the prisoners, as a re-creation of the slavery experience. March 2014._\n\n# **Coda**\n\n_Again we have deluded ourselves into believing the myth that capitalism grew and prospered out of the Protestant ethic of hard work and sacrifice. The fact is that capitalism was built on the exploitation and suffering of black slaves and continues to thrive on the exploitation of the poor\u2014both black and white, both here and abroad. 1_\n\n\u2014Martin Luther King Jr., \"Three Evils of Society\" speech, August 31, 1967\n\nIF ANYONE READING THIS book in the future wants to know the American historical context in which it was composed, the drafting was finished in August 2014, while the national trauma of Ferguson was going on, and the finishing touches were made during the aftermath of the Charleston Massacre of June 2015.\n\nToday, people are no longer sold like livestock in the public market, but the racism slavery engendered has been resilient, having become a seemingly systematic disfigurement of American society.\n\nThe post-emancipation history is a gloomy one. The only group that was brought to America against their will is still on the bottom. After the brief period of Reconstruction that saw much progress, including the establishment of black colleges, the freedmen were abandoned by the North to the mercy of Southern sheriffs by the time of the Hayes-Tilden Compromise of 1877. Their rights and possibilities were severely limited by ever more discriminatory \"black codes\" that locked white supremacy into place. While they were no longer legally treated as chattel, African Americans were systematically excluded from educational, professional, and housing opportunities, were frequently denied the possibility of relocating, were sometimes forced to labor, and were generally the victims of a nearly century-long postwar campaign of domestic terrorism. They suffered through peonage, debt servitude, sharecropping, and a sustained campaign of lynching.\n\nThe golden age of the American economy following the Second World War\u2014in which the working class did better relative to the wealthy than at any other time in American history\u2014pointedly excluded black people. African Americans' collective struggle took until the 1960s to result in full legal rights: enforcement of _Brown v. Board of Education_ , the Civil Rights Act of 1964, the Voting Rights Act of 1965, the Housing Act of 1968.\n\nThe counter-revolution to this \"Second Reconstruction\" was immediate. African Americans were further ghettoized: black neighborhoods around the country were lacerated and even destroyed by the Eisenhower Interstate Highway System, whose construction began in 1956. The interstate rammed elevated highways through the poorer parts of many cities,* demolishing black business districts and isolating existing housing projects in cul-de-sacs, while black applicants were denied mortgages in the suburbs that the new highways facilitated. African Americans ended up clustered in the old city cores that the whites abandoned, with their children attending dilapidated, underfunded, black-only schools.\n\nBeginning in 1971 with President Richard Nixon's \"war on drugs,\" along with \"three strikes\" laws and other mandatory sentencing guidelines, and a plea-bargaining system that made jury trials practically a thing of the past, the US prison population exploded in size, including millions of nonviolent drug offenders. As we write, the United States has for some years been the world's number-one incarcerator by far, holding at present (according to the most commonly cited figure) around 25 percent of the world's prisoners. In what has come to be known as the \"cradle-to-prison pipeline,\" black men are incarcerated at about six times the rate relative to population of white men, and black women at about double the rate of white women. The prison population is heavily skewed toward the South: ten of the top eleven American incarcerators are former slave states, with Louisiana number one and Mississippi number two. Private, for-profit prisons began in 1984, with their growth stimulated by a 1995 model \"Prison Industries Act\" introduced into state legislatures around the country in an organized campaign by the right-wing American Legislative Exchange Council (ALEC). Convicted felons have a hard time getting a job, and since felons are disfranchised in many states, black people have been disproportionately removed from the voting rolls.\n\nLast hired, first fired: increased post-civil rights economic and professional opportunities were countered by a redistribution to the wealthy that picked up steam in the post-Reagan years. Education and medical care have been repriced out of the reach of the poor, and increasingly require legal sophistication to navigate. The new inequality hit the long-term disadvantaged the hardest, a tendency that accelerated dramatically in the _post-Bush v. Gore_ years. The financial crisis that began in late 2007 wiped out gains that had been made by many African Americans, especially those targeted by predatory lending. \"Plunder in the past made plunder in the present efficient,\" writes Ta-Nehisi Coates, referring to the twenty-first-century subprime mortgage crisis that disproportionately affected black homeowners. Meanwhile, police brutality and murder, a longstanding problem, has emerged as a national issue in the age of video documentation, when it is no longer possible to pretend it doesn't happen, while open-carry and other firearm laws favor increased aggression by white supremacist hate groups, whose numbers \"skyrocketed\" during the Obama presidency.\n\nTo be sure, society does not look like it did when the Civil War Centennial began in 1961. Some African Americans occupy high professional and political positions. But the economic gap between black and white has not been bridged. Black unemployment remained more than double that of whites in the fifty years from 1963 to 2013, with African Americans earning on the average two-thirds as much; 27.6 percent of African American households were in poverty in 2013, compared with 9.8 percent for whites. Multigenerational wealth and multigenerational poverty seem to be nearly intractable forces, especially under the protection of a government by the wealthy, for the wealthy.\n\nIn talking about this book-in-progress with friends and strangers, we have frequently heard people say: but slavery is still going on today.\n\nThe highly charged S-word\u2014sometimes used metaphorically, sometimes not\u2014is a broad term that can take in many different kinds of inhumane practices; scholars today speak of \"slaveries.\" Our brief in writing this book has not extended to covering the postbellum forms of unfree labor, some legal and some not, which have been amply documented elsewhere: the postbellum neoslavery of convict leasing that made Birmingham, Alabama, a steel capital and continued in the South until the Second World War; the prison-industrial complex of the modern mass incarceration state; contemporary migrant exploitation, sex trafficking, and other forms of coerced labor; sweatshop and agricultural labor; and present-day work of all kinds performed in an environment of social brutality and under surveillance.\n\nThat people persist in describing these as \"slavery\" is perhaps a measure of the continuing weight of antebellum slavery and its burdensome shaping influence on our consciousness and our society, for which there have never been adequate reparations.\n\nOver the years we have been researching our nation's history, we have seen repeatedly that no matter how bad we thought slavery was, it was even worse. There's no end to it.\n\nNo one living today can fully understand what the enslaved endured in the total-slavery world of the Old South, where the economy was dependent on the production of chattel laborers by female reproduction workers who could be forcibly impregnated for that purpose, with their sexual violation approved by law.\n\nUnfortunately, the agenda of the slave society seems all too familiar to us in the twenty-first-century world.\n\nAntebellum slavery required a complex of social, legal, financial, and political institutions structured to maximize profits that flowed only to a small elite, while leaving the rest of the population poor. It wanted no legal oversight beyond the local, no public education, and no dissent. For laborers, it wanted no person-hood: no wages, education, privacy, clothing, human rights, civic identity, civil rights, reproductive rights, or even the right to keep a stable family. It existed at the cost of everything else in the society, including the most basic notions of humanity.\n\nThe history of the slave-breeding industry demonstrates how far the unrestrained pursuit of profit can go.\n\n*Four examples: the Bronx, New Orleans, Miami, and San Juan, Puerto Rico.\n\n# **Acknowledgments**\n\nIn visiting as many of the sites mentioned in this book as possible during the writing process, we were impressed over and over again by initiatives, many of them local, to make history known. From Gabriel's gallows circle in Richmond, to the manacles in the concrete in Natchez, to the museum at Charleston's Old Slave Mart and the Freedom Museum in Alexandria, to performative and ceremonial events like the Gullah-Geechee festival in Beaufort, Juneteenth in Galveston, and every Sunday in New Orleans, we salute those people in every community who are fighting to commemorate their local sacred places. We would also like to thank the workers of the National Park Service, who are tasked with managing heritage sites all across the country while being crippled by constant budget cuts.\n\nWe are indebted to the brave and singular work of Frederic Bancroft (1860\u20131945), who turned over the rock other historians would not look under. His _Slave Trading in the Old South_ (1931) employed the then-novel device, learned from German anthropology, of field interviews. Besides collecting documentation, he spoke in 1902 with formerly enslaved people, former slave traders, and other firsthand witnesses to the slave trade, and demonstrated that the commercial exploitation of human reproduction was indeed central to the antebellum system of slavery. _Slave Trading in the Old South_ has been largely vindicated and appears a more important work with every passing decade. Though scholars commonly cite Bancroft today, the disturbing implications of his privately published book were not incorporated into the mainstream narrative of American history until fairly recently. In composing our narrative, we have been informed by a critical reading of Bancroft, including some of his notes, sources, and the typescript of never-completed work by him in the Rare Book department of Bancroft's alma mater, Columbia University.\n\nThis book would not have existed without our nine months' residency in Chestertown, Maryland, at the C. V. Starr Center for the Study of the American Experience at Washington College, where Ned was a Patrick Henry Writing Fellow in 2010\u201311 and where Parts One through Three were drafted. In the years since the fellowship ended, Chestertown has continued to be a part of our lives. We are profoundly grateful to Washington College and to Starr Center director Adam Goodheart, and to Jill Ogline Titus, Michael Buckley, Lois Kitz, Jenifer Emley, Mitchell Reiss, the staff of Miller Library, and Kevin Hemstock of the _Kent County News._ To other friends and colleagues in Chestertown, more than we can name here: Peter Heck and Jane Jewell; Craig and Katie O'Donnell; Kenneth Schweitzer; Diane Daniels at the Historical Society of Kent County; the staff of the Kent County Public Library; Leslie Prince Raimond at the Kent County Arts Council, as well as to Vincent Raimond, whose spirit has now joined the great Spirit of the Place. Very particular thanks are extended to Ellen and Frank Hurst of next door, Cynthia Saunders from across the street, and Carol Mylander, just up the way\u2014the best neighbors and friends newcomers could ever have. We would also like to thank posthumously someone we never met: J. A. Leo LeMay, whose former personal library is in the Fellows' residence. We failed in our attempt to read it all, but we tried.\n\nMuch of Parts Four through Six was drafted at Bobst Library at New York University, with thanks to Franses Angelica Rodriguez and to the Circulation Department, and at the Mina Rees Library of the CUNY Graduate Center. Our ongoing research overlaps from project to project, so we would like to acknowledge fellowships that Ned held before this book project began as such. Studies undertaken while Ned was a Cullman Center Fellow at the New York Public Library, a Tulane Rockefeller Humanities Fellow at the Stone Center for Latin American Studies at Tulane University in New Orleans, and a John Simon Guggenheim Fellow all contributed significantly to our understanding of the subject as reflected in this volume. A Knight-Luce Fellowship for Reporting on Global Religion allowed Ned to make research trips to Mbanza-Kongo in 2012 and Port-au-Prince in 2013, and the final stages of work on this volume were done while he was a New York Foundation for the Arts Fellow in Nonfiction Literature.\n\nWe must thank more people for their help, support, and conversation than we can possibly list, so if your name is not here, please accept our thanks anyway. First, very special thanks to Julie Skurski and to Jason King. Thanks to Donald Harrison, David Rubinson, Michael Zilkha, Kip and Nancy Hanrahan, Howard Hunter and Metairie (Louisiana) Country Day School, Sarah Hill, Madison Smartt Bell, Ted Widmer, Roger Trilling, Lambert Strether, Gwendolyn Midlo Hall, Eric Weisbard, John Cummings, Ibrahima Seck, Ina Fandrich, Joyce Jackson, Robert Farris Thompson, C. Daniel Dawson, B\u00e1rbaro Mart\u00ednez Ruiz, Nzinga Paiva, Henry Wiencek, Laurent Dubois, Peter H. Wood, Warren Whatley, James Shinn, Freddi Evans, T. R. Johnson, Joel Dinerstein, Felipe Smith, Christopher Dunn, Beverly Trask, Shawn Hall, Mark Bingham, Susanne Hackett, Garnette Cadogan, Scott Aiges, Pat Cruz, Michael Zwack, Louis Head, Colin Dayan, Jerry Carlson, Sybil Cooksey, Dylon Robbins, Nadia Ellis, Kandia Crazy Horse, Linda Goldstein, Karen Goldfeder, Ken McCarthy, Blanca Lasalle, Ben Socolov, Peter Gordon, and Ronald Robboy, as well as Ned's colleagues at _Afropop Worldwide:_ Sean Barlow, Georges Collinet, Banning Eyre, Michael Jones, and Sam Backer.\n\nThanks go to our agent, Sarah Lazin, who helped us craft our ideas into a coherent proposal, and especially to our publisher, Chicago Review Press, which has published Ned's previous three books over the last ten years, and whose faith in us we have noted and appreciated. Our singular editor, Yuval Taylor, who developed Ned's previous books, is a valued and principled collaborator who has given us advice and editorial direction. Our gratitude goes to publisher Cynthia Sherry and to Michelle Williams, Mary Kravenas, Caitlin Eck, and Meaghan Miller.\n\nWe view this work as the continuation of a forty-year process of collaboration between the two of us that began long before either of us had published a book, and we are grateful to everyone who has helped us over the years. Thanks to the readers of our work, whose dialogue with us has been important to our understanding, and to the independent booksellers who have been a vital part of the process.\n\n# **Picture Credits**\n\n **** Map Division New York Public Library   **** Map Division New York Public Library   **** Library of Congress   **** College of Arms London   **** Arents Tobacco Collection New York Public Library   **** Arents Tobacco Collection New York Public Library   **** Photo by Ned Sublette   **** Map Division New York Public Library   **** Arents Tobacco Collection New York Public Library   **** Library of Congress   **** Library of Congress   **** British Museum   **** Photo by Ned and Constance Sublette   **** Huntington Library   **** New York Public Library   **** Library of Congress   **** Library of Congress   **** Maryland Historical Society   **** Photo by Ned and Constance Sublette   **** Photo by Ned and Constance Sublette   **** The Gilder Lehman Institute of American History   **** Photo by Ned and Constance Sublette   **** Photo by Ned and Constance Sublette   **** New York Public Library   **** Kentucky Gateway Museum Center Maysville   **** Special Collections University of Virginia Library   **** Photo by Ned and Constance Sublette   **** Photo by Ned and Constance Sublette   **** Photo by Ned and Constance Sublette   **** Rice C. Ballard Collection Wilson Library University of North Carolina at Chapel Hill   **** Photo by Ned and Constance Sublette   **** David M. Rubenstein Rare Book & Manuscript Library Duke University   **** New York Public Library   **** Columbus State University Archives   **** Virginia Historical Society   **** Library of Congress   **** Library of Congress   **** Photo by Ned and Constance Sublettet\n\n_Note:_ We have not hesitated to retouch newspaper advertisements in the interest of readability.\n\n# **Notes**\n\nChapter 1: The Mother of Slavery\n\n. Hughes, 5.\n\n. Virginia Code of 1849, 747.\n\n. In his history of Shelby County, Mississippi, John E. Harkins says that the planter's name was Edmund (not Edward). Harkins, 53.\n\n. Harkins, 53.\n\n. Historical dollar conversion figures are intended only as rough approximations. This and subsequent conversions are queried from Sahr.\n\n. Hughes, 12.\n\n. Tadman, 141, 147\u201351.\n\n. Ball, 37.\n\n. Featherstonhaugh, 1:122\u201323.\n\n. Humes, 33.\n\n. Rumple, 254.\n\n. _The Negro in Virginia_ , 173.\n\n. Ball, 72\u201373.\n\n. Brown, William Wells 1849, 49.\n\n. Brown, William Wells 1849, 32.\n\n. Strouse, 88.\n\n. Clayton 2002, 133.\n\nChapter 2: Protectionism, or, The Importance of 1808\n\n. Eltis and Richardson, 4, 17.\n\n. Eltis and Richardson, 18.\n\n. McMillin, 118.\n\n. Letter, Thomas Jefferson to John Wayles Eppes, June 30, 1820. http:\/\/founders.archives.gov\/documents\/Jefferson\/98-01-02-1352.\n\n. US Constitution, Article 1, Section 9.\n\n. For a detailed account of Jefferson's second term, see Adams 1889\/1986.\n\n. Ingraham 1860, 523.\n\n. For a discussion of credit in the creation of money, see Ingham, 107\u2013133.\n\n. DuBois, W. E. B. 1933, 44.\n\n. There are numerous references to slave purchases in Polk's letters _(CJKP);_ William Dusinberre's _Slavemaster President_ covers the subject in detail.\n\n. Conrad and Meyer, 105\u201306.\n\n**Chapter 3: A Literature of Terror**\n\n. Brown, William Wells 1847, 4.\n\n. Jacobs, 79\u201380, 117\u201318. See also _HJFP_ , 1:lxxvi.\n\n. Veney, 26.\n\n. Perdue _et al_ , 11.\n\n. Harrower.\n\n. Follett, 48.\n\n. _CJKP_ , 11:346.\n\n. Cade, 307.\n\n. _The Negro in Virginia_ , 83\u201384.\n\n. _TAS_ , supp. 2:5:1580.\n\n. _TAS_ , supp. 2:5:1580.\n\n. _FWP_ , North Carolina narratives, 11:2, 131.\n\n. Quoted in Cade, 306.\n\n. _TAS_ , supp. 2:5:1453.\n\n. Genovese 1974, 464.\n\n. Smith, Daniel Scott, 86.\n\n. Talbot gives a thorough accounting of the _Mandingo_ product line.\n\n. See, for example, Tadman, 121\u201325.\n\n. Sutch, 38\u201339.\n\n. Tadman, 124.\n\n. _FWP_ , Texas narratives, 16:1, 218..\n\n. _The Negro in Virginia_ , 171.\n\n. _FWP_ , Arkansas narratives, 2:3, 369.\n\n. Talbot, 11.\n\n. Musgrave, 264\u201367.\n\n. Catterall, 1:75.\n\n. Olmsted 1861, 55n.\n\n. _FWP_ , Florida narratives, 3:166.\n\n. _FWP_ , Texas narratives, 16:1, 180.\n\n. _FWP_ , Texas narratives, 16:2, 203\u201304.\n\n. _FWP_ , North Carolina narratives, 11:1, 31.\n\n. Lemieux; Jones.\n\n. Swarns, 2012a.\n\n. Escott, 44.\n\n. US Census (1860), x.\n\n. US Census (1860), x.\n\n. Steward, 151.\n\n. George, 317.\n\n. Hartman, 85.\n\n. <http:\/\/law2.umkc.edu\/faculty\/projects\/ftrials\/celia\/celiahome.html>\n\n. Purcell, 338.\n\n**Chapter 4: Natural Increase**\n\n. Bancroft 1931\/1996, 24.\n\n. Quoted in Lightner, 5.\n\n. Marx 1937, 67.\n\n. Deyle 2005b, 296.\n\n. Deyle 2005b, 289.\n\n. Frederic Bancroft, Letter to Winfield Hazlitt Collins, Dec. 13, 1921. _FBC_ , Box 89.\n\n. _TWOTR_ , ser. 3, 4:355.\n\n. Wright, Gavin, 2.\n\n. _FBC_ , Box 88, 109D.\n\n. _TAS_ , 19:298\n\n. Kilbourne 1995, 5.\n\n. Olmsted 1861, 55n.\n\n. Menard, 18.\n\n. Stephenson, 227.\n\n. Kilbourne 1995, 4.\n\n. Adams, Henry 1883, 59.\n\n. See, e.g., Rutherford, 371.\n\n. Graeber, 192.\n\n. _FBC_ , Box 84, 2:5, 3.\n\n. See Jefferson, \"Notes on Coinage,\" in _PTJ_ 7:175\u201385.\n\n. Kemble, 78.\n\n. _SIF_ , 559\u201360.\n\n. Stanton, 127.\n\n. Berinato.\n\n**Chapter 5: Little Shadows**\n\n. Say, 1:318.\n\n. Hughes, 34.\n\n. Marx 1937, 67.\n\n. \"The Impending Crisis in the Southern States of America\" (1859), _The Economist_ , Dec. 24, p. 1429.\n\n. Henson, 7.\n\n. Wiencek, 156\u201357.\n\n. Virginia Code of 1849, 458.\n\n. Mason, 13.\n\n. Quoted in _The Negro in Virginia_ , 71\u201372.\n\n. Quoted in Camp, 559.\n\n. Stanton, 23.\n\n. Smith, Gene Allen, 103\u201304.\n\n. Ball, 47.\n\n. Jefferson 1788, 148.\n\n. Kiple and King, 88.\n\n. Kiple and King, 89.\n\n. See Kiple and King, 74\u201378.\n\n. King, Roswell, Jr., 1:527.\n\n. Watson, 16\u201317.\n\n. Ball, 63\u201364.\n\n. See Cade, 300. There is a child-feeding trough in the collection of artifacts at Whitney Plantation in Louisiana.\n\n. www.cdc.gov\/mmwr\/preview\/mmwrhtml\/00020119.htm.\n\n. See Grandin, 40\u201341n.\n\n. Mather, 422.\n\n. Barker-Benfield, 85\u2013112.\n\n. _DeBow's Review_ (1851). 11:3, 332\u201333.\n\n. _FWP_ , Virginia narratives, 17:2.\n\n. Starobin, 11\u201312.\n\n. Zaborney, 121.\n\n. _FBC_ , Box 88, 70.\n\n. Green, J. D. 10.\n\n. Watson, Henry, 13.\n\n. Mason, 20\u201321.\n\n. Northup, 250.\n\n. _FWP_ , Arkansas Narratives, 2:1, 113.\n\n. Jacobs, 217.\n\n. Watson, Henry, 16.\n\n. _TAS_ , supp. 2:5:1580.\n\n. Chesnut, 29.\n\n. Jacobs, 57.\n\n. _FWP_ , South Carolina narratives, 14:1, 150.\n\n. In a letter by William Hayward. Truth, 139.\n\n. Bremer, 3:340.\n\n. US Census (1860), xvi.\n\n. _FWP_ , South Carolina narratives, 14:1, 158.\n\n. Gudmestad, 42.\n\n. Perdue et al., 158.\n\n. Clarke.\n\n. Brown, William Wells 1863, 17.\n\n. McCullough, 55.\n\n. McCullough, 47.\n\n. _TAS_ , 18:300.\n\n. Aptheker, 162.\n\n. Dunbar.\n\n. Bauer and Bauer, 338\u2013419.\n\n. Quoted in Aptheker, 235.\n\n**Chapter 6: Species of Property**\n\n. Letter, O.P. Temple to Frederic Bancroft, February 8, 1904, _FBC_ , Box 88.\n\n. Rousey, 19\u201324.\n\n. Kilbourne 1995, 6.\n\n. See Adams, Henry 1883, 36\u201337, 269\u201371.\n\n. _A declaration of the immediate causes_... See also, for example, Townsend, 19; Davis, Jefferson, 107.\n\n. _FBC_ , Box 88.\n\n. US Census (1860), \"Agriculture,\" vii.\n\n. Letter, Thomas Jefferson to James Madison, April 27, 1809, _PTJRS_ , 1:169.\n\n. Quoted in Dew, Charles B., 35.\n\n. Kilbourne 1995, 7.\n\n**Chapter 7: Rawrenock**\n\n. Kingsbury, 1.\n\n. Luther, 357\u201358.\n\n. See Landers, 13; Pickett and Pickett, 22\u201327; Milanich, 62.\n\n. Treasure, 3ff.\n\n. Ribaut, 67.\n\n. Ribaut, 75.\n\n. Ribaut, 93.\n\n. Ribaut, 93.\n\n. Lowery, 37.\n\n. Mercado, 16.\n\n. Thurber, 106\u201307.\n\n. Bennett 2001, 21.\n\n. Laudonni\u00e8re, 103\u2013122.\n\n. Scott, William Robert, 2:3\u20138.\n\n. Andrews, 20.\n\n. Rankin, 3.\n\n. Scott, William Robert, 2:8, 60\u201365.\n\n. Mercado, 9\u201310.\n\n. Mercado, 92; Bennett 2001, 37.\n\n. Laudonni\u00e8re, 138n; Bennett 2001, 38.\n\n. Bennett 2001, 38.\n\n. Sol\u00eds de Mer\u00e1s, 122.\n\n. Wilford.\n\n. Scott, William Robert, 89.\n\n. Taylor, 278.\n\n. Smith, John 1624, 58.\n\n. Keller, 66.\n\n. For a discussion of the term \"motley crew,\" see Linebaugh and Rediker, 27\u201328 and _passim_.\n\n. Andrews, 36.\n\n. Purchas, 4:1728.\n\n. Andrews, Kenneth R. 37.\n\n. See Bartels, 305\u2013322.\n\n. Tombs, 204.\n\n**Chapter 8: A Cargo of Shining Dirt**\n\n. Lemay 1991, 210.\n\n. Smith, John 1624, 21\u201322.\n\n. Tilp, 100.\n\n. Purchas, 4:1753.\n\n. Quoted in Lemay 1991, 184.\n\n. O'Brien.\n\n. See Linebaugh and Rediker's chapter on this interlude, 8\u201335.\n\n**Chapter 9: Our Principall Wealth**\n\n. Lemay 1991, 24\n\n. Smith, Abbot Emerson, 12.\n\n. Fischer, 227; McCusker and Menard, 242.\n\n. Morgan, Edmund S. 1975, 126.\n\n. Bruce 1895, 1:186.\n\n. See Parent's chapter, \"The Landgrab,\" 9\u201354.\n\n. Quoted in Tyler, Lyon Gardiner, 284.\n\n. Harrower, 39.\n\n. Morgan, Edmund S. 1975, 171.\n\n. Letter, George Washington to Robert Cary, February 13, 1764. _PGW_ , A:7:286.\n\n. Kingsbury, 243; see also www.encyclopediavirginia.org\/_20_and_odd_Negroes_an_excerpt_from_a_letter_from_John_Rolfe_to_Sir_Edwin_Sandys_1619_1620.\n\n. Sluiter 1997, 376n.\n\n. Smith, John 1624, 117.\n\n. Quoted in Anderson, Adam, 2:217.\n\n. Bruce 1895, 1:58.\n\n. Thornton 1998, 421.\n\n. Sluiter 1997.\n\n. Thornton 1983, 63.\n\n. Thornton 1983, 63.\n\n. Quoted in Kingsbury, 243.\n\n. Morgan, Edmund S. 1975, 111, 113.\n\n. Morgan, Edmund S. 1975, 101\u201302.\n\n. Lucas, 73; Mann, Charles C.\n\n**Chapter 10: Maria's Land**\n\n. Heath and Philips, 220.\n\n. Hibbard, 119.\n\n. Hall, Clayton Colman, 5.\n\n. Hall, Clayton Colman, 33, 40.\n\n. Lucas, 114.\n\n. Hall, Clayton Colman, 38.\n\n. Allan.\n\n. Hall, Clayton Colman, 61.\n\n. Tilp, 78.\n\n. Tilp, 12.\n\n. \"Lord Baltimore's instructions to his colonists.\" In _The Calvert Papers_ , 1:131.\n\n. Smith, John 1884, 615.\n\n. Adams and Pleck, 37\u201338.\n\n. Bunker 2010, 242.\n\n. Fischer, 240, 243.\n\n. Fischer, 366.\n\n. Walsh 2010, 10.\n\n. Griffey, 182.\n\n. For an account of the iconoclastic riots, see Eire.\n\n. Brugger, 21.\n\n. Harrison, 104.\n\n. Weeks, 13.\n\n. Weeks, 20.\n\n. Fischer, 226.\n\n**Chapter 11: Barbados**\n\n. Quoted in Firth, 146.\n\n. Schwartz, 13.\n\n. _The Bowery Historic District_ , Sec. 8, p. 9.\n\n. Fisher, 102\u201303.\n\n. Harlow, 5.\n\n. Harlow, 82, 86.\n\n. Price 1991, 297; Dunn, 61.\n\n. Price 1991, 299.\n\n. Price 1991, 297; Dunn, 61.\n\n. Ligon 2011, 188.\n\n. Harlow, 162\u201368.\n\n. Dunn, 10, 337\u201338.\n\n. Nisbet, 116.\n\n. Quoted in Harlow, 59.\n\n. Harlow, 84.\n\n. Bunker 2014, 412\u201313.\n\n. Quoted in Firth, 146.\n\n. Dunn, 288.\n\n. Dunn, 266; Harlow, 44.\n\n. Dunn, 245.\n\n. McCusker and Menard, 92.\n\n. Scott, William Robert, 17.\n\n. Garrard, 71.\n\n. _The Duke of York's Release_.\n\n. Aptheker, 165.\n\n. Hening 2:299\u2013300.\n\n. \"Great news from the Barbadoes,\" 339\u2013341.\n\n. \"Great news from the Barbadoes,\" 342.\n\nChapter 12: The Anglo-Saxon Model\n\n. Morgan, Edmund S. 1975, 386\n\n. Quoted in Fischer, 212.\n\n. Slotkin and Folsom, 17.\n\n. Morgan, Edmund S. 1975, 327.\n\n. Brown, Kathleen M., 177.\n\n. Morgan, Edmund S. 1975, 383.\n\n. Breen, 241.\n\n. Bailyn, 97.\n\n. Jordan, 75.\n\n. For an extended discussion, see Wright 2006, 14\u201347.\n\n. Rawley, 84.\n\n. Hening, 2:270.\n\n. Price 1991, 296.\n\n. Morgan, Kenneth, 719\u2013720.\n\n. Price 1991, 10.\n\n. Parent, 2.\n\n. Walsh 2010, 17, 233.\n\n. Davis, Richard Beale, 253.\n\n. Deyle 2004, 215.\n\n. Parent, 72.\n\n. Fitzhugh, William, 44.\n\n. Davis, Richard Beale, 175.\n\n. Goodheart 2011a, 304.\n\n. Davis, Richard Beale, 54.\n\n. Davis, Richard Beale, 373\u201377.\n\nChapter 13: Carolina\n\n. Nairne, 47\u201348.\n\n. This summary of South Carolina's political backstory substantially follows the contours of Eugene Sirman's.\n\n. Armitage, 607.\n\n. Armitage, 608.\n\n. Sirmans, 14.\n\n. McCandless, 10.\n\n. McCandless, 7.\n\n. Sirmans, 16.\n\n. Wood, Peter H., 24.\n\n. Gallay, 225.\n\n. Gallay, 23\u201331.\n\n. Our account of this indigenous political geography is indebted to Gallay, 1\u201339.\n\n. Armitage, 610.\n\n. Donnan, 804.\n\n. Berlin, 17.\n\n. Gallay, 299.\n\n. Gallay, 6\u20137.\n\n. Crane, 45.\n\n. Le Moyne d'Iberville, 119.\n\n. Crane, 19.\n\n. See Gallay, 40\u201369, and Crane, 6\u201321.\n\n. Gallay, 56\u201357.\n\n. Crane, 112.\n\n. See Ingham, 107\u201333.\n\n. Ingham, 127\u2013131.\n\n. Price 1984, 26\u201331.\n\n. Ingham, 129.\n\n. Gallay, 212.\n\n. De Quesada, 6.\n\n. Horne, 3.\n\n. Landers 1999, 24.\n\nChapter 14: The Separate Traders\n\n. Quoted in _DIST_ , 4:68.\n\n. Scott, William Robert, 23.\n\n. Behrendt 2007, 68.\n\n. Parent, 79; Rawley, 86.\n\n. figures from Price 1991, 305.\n\n. Catterall, 1:53\u201354.\n\n. Thomas, Hugh, 236.\n\n. Furdell, 245.\n\n. Thomas, Hugh, 235.\n\n. Parent, 93.\n\n. Whatley.\n\n. Bourne, Michael, 46.\n\n. Rawley and Behrendt, 182; Ridley, 27.\n\n. Morgan, Kenneth, 719\u2013720.\n\n. Anderson and Gallman, 32.\n\n. Ortiz 1947, 268; Ortiz 1978, 358.\n\n. Morgan, Philip D. 1998, 81.\n\n**Chapter 15: Charles Town**\n\n. At the Gullah Geechee Festival, Beaufort, South Carolina, May 26, 2013.\n\n. Norris, 58\u201359.\n\n. Morgan, Philip D. 1998, 1.\n\n. Gallay, 200.\n\n. Donnan, 804\u201305.\n\n. Wood, Peter H., 57n.\n\n. Wilder, 50; Leder and Carroso, 20\u201330.\n\n. See Carney, 32ff. for an extended discussion.\n\n. Bruce 1895, 1:331.\n\n. Wood, Peter H., 36.\n\n. See author's interview with Gwendolyn Midlo Hall for _Afropop Worldwide Hip Deep_ , <http:\/\/www.afropop.org\/11166\/gwendolyn-midlo-hall>.\n\n. McCusker and Menard, 181\u201382.\n\n. Mancall et al, 630.\n\n. McCusker and Menard, 235.\n\n. Norris, 17\u201318.\n\n. Norris, 93.\n\n. Quoted in Gallay, 328.\n\n. Gallay, 338.\n\n. Caillot, 125n, 146\u201368.\n\n. Quoted in Aptheker, 175.\n\n. Quoted in Aptheker, 181.\n\n. Quoted in Donnan, 805.\n\n. Donnan, 806.\n\n**Chapter 16: Savannah and Stono**\n\n. Hewatt, 2:300.\n\n. Egmont Papers, http:\/\/fax.libs.uga.edu\/egmont\/14203\/index.djvu?djvuopts&zoom=100&page=ep142030229.djvu.\n\n. Baine, 101.\n\n. Wilson, Thomas D., 12.\n\n. Wilson, Thomas D., 38\u201340.\n\n. Greenberg, 28.\n\n. See Wilson, Thomas D., 107.\n\n. Pinckney.\n\n. _CRG_ , 23:57.\n\n. Hewatt, 63\u201364.\n\n. Landers 2010, 1\u20133.\n\n. _CRG_ , 22:2:232\u201336.\n\n. Thornton 1991.\n\n. Fromont, 11.\n\n. Epstein, 39, 59.\n\n. Quoted in Wood, Peter H., 321.\n\n. Wood, Peter H., 320.\n\n. Hill, William, 93.\n\n. Seabrook, 13.\n\n. Kly, 18ff.\n\n. Wood, Peter H., 322.\n\n. See Lepore for an account.\n\n. Aptheker, 190.\n\n. Smith, Josiah, ii; Aptheker, 190.\n\n. Smith, Josiah, 10\u201311.\n\n. Landers 1999, 35\u201345.\n\n. _CRG_ , 23:332\u20133.\n\n. Greenberg, 35.\n\n. Hewatt, 2:114.\n\n. Zaborney, 10.\n\n. Pinckney, Eliza Lucas, memorandum of January 1742.\n\n**Chapter 17: A Rough Set of People, but Somewhat Caressed**\n\n. Letter, Henry Laurens to John Knight, May 28, 1756. _PHL_ , 2:204.\n\n. Rogers 1976, 479.\n\n. Melvin Gibbs, private communication.\n\n. Hancock, 205\u2013208; Rogers 1976, 488.\n\n. Behrendt 2007, 68.\n\n. Sellers, Leila, 112.\n\n. Letter, Henry Laurens to William Fisher, Nov. 9, 1768. _PHL_ , 6:149\u201350.\n\n. Sellers, Leila, 25.\n\n. Hewatt, 129\u2013130.\n\n. Hewatt, 291\u2013292.\n\n. Hewatt, 294.\n\n. Donnan, 810\u201311.\n\n. _DIST_ , 4:375.\n\n. McDonough, 21.\n\n. Sellers, Leila, 97.\n\n. Letter, Henry Laurens to Samuel and William Vernon, June 15, 1756, _PHL_ 2:219.\n\n. Rawley, 82.\n\n. Higgins, 206\u2013217.\n\n. Sellers, Leila, 97\u201398.\n\n. McCusker, 220.\n\n. Letter, Henry Laurens to Smith and Baillies, August 25, 1763, _PHL_ , 3:539.\n\n. \"worthy Friend\": see., e.g., Letter, Henry Laurens to Gabriel Manigault, March 2, 1772, _PHL_ 8:202; Oswald: Hancock, 205, 213.\n\n. Webster, 4\u201316.\n\n. _New Georgia Encyclopedia_ , www.georgiaencyclopedia.org\/nge\/Article.jsp?id=h-686.\n\n. Morgan, Philip D. 2010, 27.\n\n. Sellers, Leila, 97\u201398.\n\n**Chapter 18: Ballast**\n\n. Chance, 54.\n\n. Robbins, 2.\n\n. See Sublette 2004, 45.\n\n. Robbins, 100\u201301.\n\n. Robbins, 110.\n\n. Robbins, 120.\n\n. Robbins, 108.\n\n. Robbins, 256.\n\n. Carroll and Carroll, 1:438\n\n. Carroll and Carroll, 1:438\n\n. Carroll and Carroll, 2:707\u201308.\n\n. Carroll and Carroll, 2:706.\n\n. For a genealogy see Reamy and Reamy, 28.\n\n. Lemay 2009, 342.\n\n. _PGW_ , A:7:146.\n\n. _PGW_ , A:9:111.\n\n. Cohen, Richard, 374.\n\n. Carson, 114.\n\n. _The Apollo; or, the Chestertown Spy_ , April 9, 1793.\n\n. Cohen, Richard, 374\u201376.\n\n. Kelly, 360.\n\n. Wroth, 274.\n\n. Letter, Thomas Ringgold to Samuel Galloway, July 10, 1763, _TRP_.\n\n. Beirne, 79.\n\n. Robbins, 98.\n\n. Carroll and Carroll, 2:710.\n\n. See Minchinton for more about the forms slaving vessels took; Wax 1978.\n\n. Letter, Thomas Ringgold to Fowler, Easton and Comp., September 17, 1761, _TRP_.\n\n. Letter, Thomas Ringgold to Samuel Galloway, August 14, 1761, _TRP_.\n\n. Behrendt 1997, 55.\n\n. Letter, Thomas Ringgold to Samuel Galloway, September 17, 1761, _TRP_.\n\n. Parent, 62\u201364.\n\n. See Sublette 2004, Ch. 12. __.\n\n. See Walsh 1999.\n\n. Letter, Thomas Ringgold to Samuel Galloway, November 21, 1762, _TRP_.\n\n. Bosman, 91.\n\n. Herbert, 124, 200\u2013205; Metcalf, 380.\n\n. Rappleye, 58\u201359.\n\n. Eltis and Richardson, 71.\n\n. Letter, John Adams to William Tudor, August 11, 1818. _WJA_ , 10:345.\n\n. Letter, Thomas Ringgold to Samuel Galloway, December 15, 1760, _TRP_.\n\n. www.abdn.ac.uk\/slavery\/resource1b.htm\n\n. Morgan, Kenneth 2007, 67.\n\n. Letter, Thomas Ringgold to Samuel Galloway, November 1, 1762, _TRP_.\n\n. See _Voyage of the slave ship Sally_ , http:\/\/cds.library.brown.edu\/projects\/sally.\n\n. Letter, Thomas Ringgold to Samuel Galloway, May 6, 1764, _TRP_.\n\n. Beirne, 79.\n\n. www.thevalleyfamily.org\/getperson.php?personID=I1167639417&tree=fitzvalley.\n\n. Conger, 63.\n\n. Hazzard-Donald 2011, 195, 200; Hazzard-Donald 2012, 40.\n\n. Hughes, 108.\n\n. Hazzard-Donald 2012, 35.\n\n. See Samford.\n\n. Alabama narratives, 1:341.\n\n. Lemay 2006, 73.\n\n. Lemay 2006, 74.\n\n**Chapter 19: Newspapers as Money as People**\n\n. April 17\u201324, 1704; see also Thomas, Isaiah, 13.\n\n. www.vagazette.com\/our_newspaper\/about_us.\n\n. Waldstreicher 2004, 76. This chapter draws on Waldstreicher's analysis of Franklin's economic ideas.\n\n. Brissot de Warville, 1:182.\n\n. www.vagazette.com\/our_newspaper\/about_us.\n\n. Waldstreicher 2004, 121.\n\n. Waldstreicher 2004, 88.\n\n. Waldstreicher 2004, 88.\n\n. Marx 1970, 55.\n\n. _PBF_ , 1:149.\n\n. Waldstreicher 2004, 21.\n\n. Waldstreicher 2004, 79.\n\n. Quoted in Hawke, 82.\n\n. _Pennsylvania Gazette_ , July 8, 1731.\n\n. Grubb 2006, 7.\n\n. See the discussion of the Law company in Sublette 2008, 45\u201355.\n\n. Hewatt, 2:57.\n\n. Wiencek 2003, 178\u201379.\n\n. Hewatt, 2:169.\n\n. _CRG_ , 22:1: 203.\n\n. _CRG_ , 23:245\u201346.\n\n. Hewatt, 2:171\u201372.\n\n. Hewatt, 2:100.\n\n. Hewatt, 2:54.\n\n**Chapter 20: Lord Dunmore's Blackbirds**\n\n. Smith, Adam, 2:89.\n\n. For an extended discussion of the term \"motley crew\" and its application to this era, see Linebaugh and Rediker, 211\u2013247.\n\n. Zobel, 26.\n\n. Linebaugh and Rediker, 216\u201317.\n\n. Zobel, 28\u201329.\n\n. Bailyn 1974, 35.\n\n. Bailyn 1974, 135.\n\n. Rogers, 493.\n\n. Gadsden, 111, 316.\n\n. Gadsden, 92, 95.\n\n. _PHL_ , 5:24n.\n\n. Quoted in Morgan, Edmund S. 1959, 155.\n\n. Blumrosen and Blumrosen, 17.\n\n. Blackstone _et al_., 1:123.\n\n. Blumrosen and Blumrosen, 9\u201311.\n\n. Blumrosen and Blumrosen, 15.\n\n. \"The Somersett Case and the Slave Trade.\" _London Chronicle_ , June 18\u201320, 1772.\n\n. _PHL_ , 8:353.\n\n. _PHL_ , 16:533.\n\n. Quoted in Blumrosen and Blumrosen, 24\u201325.\n\n. Quoted in Kelly, 376.\n\n. Nybakken, 13, 85, 114.\n\n. Bell, Malcolm, 1.\n\n. Quoted in Bailyn 1974, 157.\n\n. Quoted in Bell, Malcolm, 22.\n\n. Bell, Malcolm, 22\u201323.\n\n. _PHL_ , 16:557.\n\n. Bell, Malcolm, 26.\n\n. Berkeley and Berkeley, 31.\n\n. Hewatt, 2:97\u201398.\n\n. McCrady, 3\u20134.\n\n. McCrady, 24.\n\n. Quoted in Willard, 233.\n\n. _DIST_ , 153\u201354.\n\n. Purdie's _Virginia Gazette_ , Dec. 29, 1775.\n\n. Bell, Malcolm, 33.\n\n. For a discussion of the conditions within Domingan society for men of color participating in the Chasseurs-Volontaires, see King, Stewart, 65\u201377.\n\n**Chapter 21: The General Inconvenience**\n\n. Jefferson 1997, 1:334\u201335.\n\n. Quoted in Unger, 13.\n\n. Burke, 51\u201352.\n\n. Bailyn, 18.\n\n. e.g., _Virginia Gazette_ , November 19, 1736.\n\n. Fuller, 132; Carson, 43.\n\n. Carson, 43.\n\n. Willison, 268.\n\n. See Cohen, Charles.\n\n. Willison, 267\u201368.\n\n. _Maryland Gazette_ , Aug. 16, 1770.\n\n. Quoted in Bunker 2014, 148.\n\n. Quoted in Willison, 485\u201386.\n\n. Tyler, Moses Coit, 389.\n\n. Boswell, 1:154.\n\n. Henry, William Wirt. 3:4.\n\n. Robinson, 84.\n\n. Wills, 332.\n\n. _Journals of the Continental Congress_ , 5:429.\n\n. Letter, Thomas Jefferson to Angelica Schuyler Church, Nov. 27, 1793. _PTJ_ , 27:449.\n\n. _PTJ_ 1: 243\u2013247.\n\n. Robinson, 80\u201383.\n\n. Malone, 131.\n\n. _MJQA_ , 8:284\u201385.\n\n. _PTJ_ , 2:350.\n\n. Anburey, 2:192\u20133.\n\n. Adams, William Howard, 279.\n\n. _Phocion_ 9 (1796). _Gazette of the United States_ , October 21. See also Chernow, 313.\n\n. Idzerda, 170.\n\n. Carroll and Carroll, 1443.\n\n. See Lewis, 83\u201399.\n\n. Letter, Thomas Jefferson to Dr. William Gordon, July 16, 1788, _PTJ_ , 13:362\u201364.\n\n. Quoted in Hancock, 391.\n\n. Quoted in Hancock, 160.\n\n. Buckley, 4, 22, 35\u201336, 55.\n\n. Parton, 262.\n\n. Jefferson 1788, 186.\n\n. Meacham, 58, 144.\n\n. Chastellux, 2:438\n\n. Letter, Thomas Jefferson to James Madison, May 11, 1785, _PTJ_ , 8:147.\n\n. Jefferson 1788, 147.\n\n. Smith, Felipe, 24.\n\n. Jefferson 1788, 154.\n\n. Letter, James Madison to Frances Wright, September 1, 1825.\n\n. Jefferson 1788, 147.\n\n. Jefferson 1788, 147.\n\n. Letter, Thomas Jefferson to Jared Sparks, February 4, 1824. _LOC_ American Memory.\n\n. Letter, Thomas Jefferson to Jared Sparks, February 4, 1824. _LOC_ American Memory.\n\n. Letter, Thomas Jefferson to Jared Sparks, February 4, 1824. _LOC_ , American Memory\n\n. Jefferson 1788, 148\u201349\n\n. Letter, Thomas Jefferson to Jared Sparks, _LOC_ American Memory\n\n. Letter, Thomas Jefferson to Jared Sparks, _LOC_ American Memory\n\n. Kant, 110\u201311.\n\n. McMillin, 76.\n\n. McMillin, 76\u201380.\n\n. _DIST_ , 4:482.\n\n. McMillin, 84\u201385.\n\n**Chapter 22: The Fugue of Silences**\n\n. Farrand, 2:417.\n\n. _MJQA_ , 5:11.\n\n. Letter, Benjamin Rush to John Coakley Lettsom, September 28, 1787, _DHRC_ 13:262.\n\n. _PJA_ , 2:178\u201379.\n\n. Letter, Thomas Jefferson to William Stephens Smith, Nov. 13, 1787, 12:356.\n\n. Finkelman 1986, 346.\n\n. Finkelman 1986, 349.\n\n. See Freytag v. Commissioner (90\u2013762), 501 U.S. 868 (1991).\n\n. Breyer, 33.\n\n. Beeman, 309, 320.\n\n. David Waldstreicher's _Slavery's Constitution_ develops this theme at length, using the term \"proslavery,\" as well as tracing the history of this interpretation of the Constitution.\n\n. Beeman, 91.\n\n. Farrand, 1:204.\n\n. Farrand, 1:603\u2013605.\n\n. Bell, Malcolm, 231.\n\n. Lipscomb, xxiii\u2013iv.\n\n. Farrand, 1:205\u201306.\n\n. Farrand, 1:580\u201381.\n\n. Hutson, 68.\n\n. See Ford, Lacy K. 2009, 82\u201383.\n\n. Bell, Malcolm, 88.\n\n. Farrand, 2:364.\n\n. Farrand, 2:364.\n\n. Farrand, 2:370.\n\n. Farrand, 2:370\n\n. Farrand, 2:371.26.\n\n. Reproduced in Deyle 2005, 37.\n\n. Farrand, 2:378.\n\n. Farrand, 2:415.\n\n**Chapter 23: Ten Thousand Powers**\n\n. Farrand, 3:253.\n\n. Farrand, 3:253\u201355.\n\n. _DHRC_ , 3:263.\n\n. Waldstreicher 2009, 119.\n\n. South Carolina State Constitution (1790), Art. II, Sec. 2.\n\n. Letter, James Madison to George Washington, March 18, 1787. Quoted in _LDC_ , 24:149\u2013150.\n\n. _DHRC_ , 10:1284, 1486.\n\n. _DHRC_ , 10:1473.\n\n. _DHRC_ , 8:311.\n\n. _DHRC_ , 10:1341.\n\n. _DHRC_ , 10:1476.\n\n. _DHRC_ , 10:1477.\n\n. Grigsby, 157n.\n\n. Hewatt, 2:245.\n\n. _AC_ , House of Representatives, 1st Congress, 2d Session, 1505.\n\n. Davis, William C., 17\u201319.\n\n. Trouillot 1990, 37.\n\n. See James, 45\u201355.\n\n. King, Stewart, 84.\n\n. James, 35, 56, 64.\n\n**Chapter 24: The French Revolution in America**\n\n. \"Notes on Arthur Young's letter to George Washington,\" _PTJ_ , 24:95.\n\n. _PTJ_ , 26:xli.\n\n. Letter, Thomas Jefferson to Jacques-Pierre Brissot de Warville, February 11, 1788. _PTJ_ , 12:577\u201378.\n\n. Jefferson 1788, 151.\n\n. See Foster et al; see also Stanton, 93\u2013104.\n\n. See Dubois 2004, 99\u2013101.\n\n. Mathewson, 321.\n\n. \"Notes on Arthur Young's letter to George Washington,\" _PTJ_ , 24:98.\n\n. Wiencek 2012, 8.\n\n. _WTJ_ , 7:114n.\n\n. Letter, Thomas Jefferson to George Washington, June 28, 1793. _PTJ_ , 26:396.\n\n. Crawford, 121.\n\n. Gordon-Reed.\n\n. Letter, Alexander Hamilton to Theodore Sedgwick, July 10, 1804. _PAH_ , 26:309; Stanton, 87.\n\n. Brissot de Warville, 244.\n\n. Minnigerode, 146.\n\n. Olmsted 1861, 107.\n\n. Ammon, 44.\n\n. Letter, Thomas Jefferson to Edmond Charles Genet, June 5, 1793. _PTJ_ , 26:195.\n\n. Minnigerode, 188.\n\n. Letter, Thomas Jefferson to James Monroe, _PTJ_ , 26:190.\n\n. Minnigerode, 146.\n\n. Minnigerode, 220.\n\n. Dessens, 20.\n\n. Dessens, 67; Baur, 398.\n\n. Baur, 395.\n\n. _PGW_ , C:14:55n.\n\n. \"Cabinet opinions on relations with France and Great Britain,\" September 7, 1793, _PTJ_ , 27:49\u201350.\n\n. Letter, John Adams to Thomas Jefferson, June 30, 1813, _AJL_ , 347\u201348.\n\n. Letter, John Adams to John Quincy Adams, _AFC_ , 10:4.\n\n. Letter, Thomas Jefferson to Caleb Lownes, Dec. 18, 1793. _PTJ_ , 27:586.\n\n. Letter, Thomas Jefferson to Jean Nicolas Demeunier, _PTJ_ , 38:341.\n\n. \"red or blue\": the recollection of former nailery slave Isaac Granger, quoted in Stanton, 7.\n\n. Stanton, 81\u201385.\n\n. Quoted in Brady, 609.\n\n. Sidbury 1997, 539.\n\n. Letter, Thomas Jefferson to Madame Plumard de Bellanger, April 25, 1794, _PTJ_ , 28:59\u201360.\n\n. Quoted in Chapelle, 5.\n\n. Chapelle, 13.\n\n. Bruchey, 106.\n\n. Ward, 1292.\n\n. Landers 2010, 82.\n\n**Chapter 25: The Cotton Club**\n\n. _CRG_ , 23:158.\n\n. Hills, 41.\n\n. Lakwete, 47\u201348.\n\n. Letter, Thomas Jefferson to Eli Whitney, _PTJ_ , 27:392\u201333.\n\n. Letter, Eli Whitney to Thomas Jefferson, _PTJ_ , 27:433.\n\n. Quoted in Hall, Gwendolyn Midlo, 351.\n\n. McAfee, xi.\n\n. Andrew Jackson letter to Nathaniel Macon, October 4, 1795, _CAJ_ , 1:17.\n\n. Sydnor 1938, 18\u201319.\n\n. _DHRC_ , 8:34.\n\n. _Naval documents related to the Quasi-War..._. 1:1.\n\n. Letter, Henry Tazewell to AJ, July 20, 1798, _CAJ_ , 1:53.\n\n. Geggus, 285.\n\n. Adams, Henry 1889\/1986, 248.\n\n. Englund, 178.\n\n. Popkin, 214.\n\n. DeConde, 84.\n\n. Adams, Henry 1889\/1986, 250.\n\n. _PJMon_ , 4:398n; Egerton, 33\u201334.\n\n. _PJMon_ , 4:345n.\n\n. Sidbury 2002, 210.\n\n. _PJMon_ , 4:398n.\n\n. Ford, Lacy K. 2009, 51.\n\n. Schwarz, 87.\n\n. _PJMon_ , 4:410.\n\n. Schwarz, 63, 10, 215, xxxiii.\n\n. _PJMon_ , 4:412.\n\n. _PJMon_ , 4:404.\n\n. _PJMon_ , 4:421.\n\n. Schwarz, 81.\n\n. \"Account of Richmond trials,\" September 18, 1800, <http:\/\/founders.archives.gov\/documents\/Jefferson\/01-32-02-0109>.\n\n. _PJMon_ , 4:420\n\n. _PJMon_ , 4:423.\n\n. Egerton, 108\u201311.\n\n. Schwarz, xxx\u2013xxxii.\n\n. Schwarz, 54.\n\n. Schwarz, 64\u201365.\n\n. US census figures for 1800.\n\n. See Schwarz, 97, for one of many examples of the use of this phrase.\n\n. Rousey, 21.\n\n. Letter, Thomas Jefferson to Rufus King, July 13, 1802, _PTJ_ , 38:54.\n\n**Chapter 26: The Terrible Republic**\n\n. Jenson, 89.\n\n. Quoted in Henriques, 122.\n\n. Quoted in Beard, 375.\n\n. Letter, Thomas Jefferson to Spencer Roane, September 6, 1819, <http:\/\/www.loc.gov\/exhibits\/jefferson\/137.html>.\n\n. Jefferson 1788, 175.\n\n. _DHRC_ , 10:1272.\n\n. Letter, Thomas Jefferson to James Monroe, May 29, 1801. _PJMon_ 4:516.\n\n. Drescher, 31.\n\n. Letter, Thomas Jefferson to James Monroe, _PTJ_ , 35:720.\n\n. Letter, Thomas Jefferson to Aaron Burr, 31:22.\n\n. Quoted in DeConde, 323.\n\n. Letter, Bonaparte to Talleyrand, November 13, 1801, _CN_ , 7:320.\n\n. Letter, Rufus King to James Madison, June 1, 1801, _State papers and correspondence bearing upon the purchase of the territory of Louisiana_.\n\n. Lacroix, 2:59\u201360.\n\n. Letter, Robert Livingston to Rufus King, _State papers and correspondence bearing upon the purchase of the territory of Louisiana_ , 10.\n\n. Letter, Bonaparte to Denis Decr\u00e8s, June 4, 1802, _CN_ , 7:485.\n\n. Ferrer, 60\u201372.\n\n. Ford, Lacy K. 2009, 85\u201391.\n\n. Quoted in Stoddard, 342.\n\n. See \"Canine Warfare in the Circum-Caribbean\" in Johnson, Sara E., 21\u201348; also Ferrer, 159.\n\n. Letter, Thomas Jefferson to James Monroe, January 10, 1803, _PTJ_ , 39:306.\n\n. Letter, Thomas Jefferson to James Monroe, January 13, 1803, _PTJ_ , 39:328.\n\n. Quoted in Ford, Lacy K. 2009, 97.\n\n. _AC_ , November 14, 1803.\n\n. Letter, Thomas Jefferson to William Henry Harrison, February 27, 1803, _PTJ_ , 39:590\u201391.\n\n. Letter, Thomas Jefferson to Thomas Mann Randolph, June 8, 1803, _PTJ_ , 40:505.\n\n. Letter, Thomas Jefferson to John Breckinridge, November 24, 1803, _WTJ_ , 10:52.\n\n. Shugerman, 274.\n\n. Quoted in Scanlon, 152\u201353.\n\n. Scanlon, 153.\n\n. See Dayan, 30ff.\n\n. Claiborne, 2:10.\n\n. Claiborne, 2:25.\n\n. Claiborne, 2:184.\n\n. Claiborne, 2:245\n\n. _AC_ , 9th Cong., 1st Sess., 515.\n\n. Alexander, William T., 180\u201381.\n\n**Chapter 27: I Do Not Threaten the Government with Civil War**\n\n. Claiborne, 3:363.\n\n. Shugerman, 8.\n\n. Shugerman, 15.\n\n. Ford, Lacy K. 2009, 97.\n\n. Thomas, E.S., 35\u201336.\n\n. Claiborne, 3:96.\n\n. Queried from _The Trans-Atlantic Slave Trade Database_ , www.slavevoyages.org\/tast\/database\/search.faces.\n\n. McMillin, 48.\n\n. Ford, Lacy K. 2009, 121.\n\n. Shugerman, 282.\n\n. _AC_ , H of R, 9th, 1st, 472.\n\n. _DIST_ , 4:513.\n\n. Shugerman, 19.\n\n. Quoted in Sellers, 219.\n\n. _DIST_ , 4:516.\n\n. _DIST_ , 4:525.\n\n. Table appears in Brooke, 234.\n\n. Said, 793.\n\n. Lambert, 2:406.\n\n. _Charleston Courier_ , Nov. 22, 1805.\n\n. Wilentz 2004.\n\n. _AC_ , H of R, 9th, 2d, , 238\u20139.\n\n. _AC_ , H of R, 9th, 2d, 477\u2013478.\n\n. _AC_ , H of R, 9th, 2d, 626.\n\n. The surviving inward bound manifests from the Port of New Orleans are in record group 36 of the National Archives in Washington, and they have also been digitized by ancestry.com.\n\n. Lambert, 2:406.\n\n. McMillin, 114.\n\n. McMillin, 113.\n\n. Dusinberre, 124.\n\n**Chapter 28: These Infernal Principles**\n\n. Schultz, 2:133\u20134.\n\n. Adams, Henry 1889\/1986, 984.\n\n. Adams, Henry 1889\/1986, 978\u20139.\n\n. Adams, Henry 1889\/1986, 973.\n\n. Adams, Henry 1889\/1986, 973.\n\n. Quoted in _Richmond Courier_ , December 29, 1807.\n\n. Lambert, 2:158\n\n. Adams, Henry 1889\/1986, 1:1121.\n\n. _Moniteur de la Louisiane_ , January 18, 1810.\n\n. Schultz, 2:137\u201338.\n\n. _AC_ , Senate, 11th, 2d, 579\u201380.\n\n. _AC_ , Senate, 11th, 3d, 63\u201364.\n\n. _AC_ , 12th, H of R, 1st, 450\u201351.\n\n. Martineau, 1:244.\n\n. Rogers 1962, 394.\n\n. Calhoun, 2:8.\n\n. Article I, Sections 8, 10.\n\n. Temin, 29.\n\n. Stagg, 2.\n\n. Dudley, 2:308.\n\n**Chapter 29: The Hireling and Slave**\n\n. Woodmason, 14.\n\n. Woodmason, 101\u201302.\n\n. Woodmason, 27.\n\n. Quoted in Sydnor 1938, 15.\n\n. Remini 1977, 55.\n\n. _PAJ_ 1:15.\n\n. Remini 1977, 56.\n\n. Capers, 26\u201328.\n\n. Quoted in Keating, 173.\n\n. Capers, 31.\n\n. Letter, W.C.C. Claiborne to Andrew Jackson,, Dec. 9, 1801. _PAJ_ , 1:261.\n\n. Letter, W.C.C. Claiborne to Andrew Jackson, Dec. 23, 1801. _PAJ_ , 1:265.\n\n. Remini 1977:378.\n\n. _PAJ_ , 2:41.\n\n. Letter, Andrew Jackson to Thomas Eastin, c. June 1806. _PAJ_ , 2:106; Remini 1981, 1.\n\n. Letter, Donelson Caffery to Andrew Jackson, May 20, 1810, _PAJ_ , 2:246.\n\n. Letter, Joseph Anderson to Andrew Jackson, December 3, 1795. _CAJ_ , 1:18\n\n. Letter, Andrew Jackson to William Berkeley Lewis, August 5, 1828. _PAJ_ , 6:486\u201387.\n\n. _PAJ_ , 2:261\u201362, 286\u2013290.\n\n. Letter, Andrew Jackson to Rachel Jackson, December 17, 1811. _PAJ_ , 2:273.\n\n. Letter, Andrew Jackson to Willie Blount, Jan. 25, 1812, _PAJ_ , 2:277\u201379.\n\n. Letter, Andrew Jackson to \"an Arbitrator,\" Feb. 29, 1812, _PAJ_ , 2:286\u201389.\n\n. Letter, Andrew Jackson to Mary Caffery, February 8, 1812, _PAJ_ 2:281\u201382.\n\n. Remini 1977, 191\u201392.\n\n. Letter, Andrew Jackson to Willie Blount, _CAJ_ , 1:416.\n\n. Adams, Henry 1889\/1986a, 886\u201387.\n\n. Letter, Andrew Jackson to David Holmes, April 18, 1814, _CAJ_ , 1:504\u201305.\n\n. _Niles' Weekly Register_ , June 11, 1814.\n\n. Owsley, 130.\n\n. Bell, Malcolm, 182.\n\n. Manakee, 35.\n\n. _MJQA_ , 8:188.\n\n. Letter, James Monroe to Andrew Jackson, October 21, 1814, _PAJ_ , 3:171.\n\n. Letter, Andrew Jackson to James Monroe, October 26, 1814, _PAJ_ , 3:173.\n\n. Letter, Andrew Jackson to James Monroe, November 20, 1814, _PAJ_ 3:191.\n\n. Warshauer, 2.\n\n. Haynes, 234.\n\n. Letter, William Crawford to AJ, March 15, 1816. _PAJ_ , 4:15\u201316.\n\n. Letter, Edmund P. Gaines to AJ, May 14, 1816. _PAJ_ , 4:31.\n\n. _PAJ_ , 4:15.\n\n**Chapter 30: A Jog of the Elbow**\n\n. Quoted in Simpson, 65.\n\n. _MJQA_ , 9:41.\n\n. Martineau, 1:192.\n\n. Kilbourne 2006, 12.\n\n. Chapelle, 108.\n\n. Chapelle, 111.\n\n. For a discussion of this balance in the Jacksonian era, see Green, George D.\n\n. Bodenhorn, 169.\n\n. Quoted in Simpson, 65.\n\n. See Bodenhorn, 169\u2013177.\n\n. Calderhead, 198.\n\n. Gigantino, 281\u2013296.\n\n. _Niles' Weekly Register_ , Dec. 26, 1818, 313.\n\n. _Niles' Weekly Register_ , Dec. 19, 1818, 311.\n\n. Letter, Andrew Jackson to James Monroe, June 2, 1818. _PAJ_ 4:215.\n\n. Fortune, 260\u201366.\n\n. _Gales & Seaton's Register of Debates in Congress_ (1829), 3:12.\n\n. _FBC_ , Box 85, IV:i, 44.\n\n. Letter, Thomas Jefferson to John Holmes, April 22, 1820. _MCMTJ_ , 4:324.\n\n. _American Cotton Planter_ , 1:10, 295, October 1857.\n\n. Letter, Thomas Jefferson to Joel Yancey, January 17, 1819. Jefferson 1953, 43.\n\n. FWP, Alabama narratives, 1:222.\n\n. Morris, 70.\n\n. Letter, Thomas Jefferson to John Wayles Eppes, Jne 30, 1820. http:\/\/founders.archives.gov\/documents\/Jefferson\/98-01-02-1352\n\n. Letter, Thomas Jefferson to Mary Jefferson Eppes, December 26, 1803. Rayner, 295.\n\n. Jacques.\n\n. Rasmussen and Tilton, 70.\n\n. Rudolph, 157.\n\n. \"Family histories: a beginning\" www.monticello.org\/site\/plantation-and-slavery\/family-histories-beginning.\n\n. Lislet, 2:394\u2013406.\n\n. Baptist 2014, 248.\n\n. Neu, 550.\n\n. An account from the Jacksonian perspective is Remini 1981, 94\u201399.\n\n. _MJQA_ , 8:546.\n\n. Miles 1960, 17.\n\n**Chapter 31: Swallowed by Millions**\n\n. Sheffield _Mercury_ , Sept. 12, 1846.http:\/\/docsouth.unc.edu\/neh\/douglass\/support5.html.\n\n. Albion, 9.\n\n. Albion, 11.\n\n. Rockman, 7.\n\n. Douglass 1855, 310\u201311.\n\n. Quoted in Clayton 2002, 44.\n\n. Clayton 2002, 45.\n\n. Clayton 2002, 59.\n\n. Calderhead, 197.\n\n. Calderhead, 198.\n\n. Thompson, John, 14.\n\n. Clayton 2002, 29.\n\n. _FBC_ , Box 85, I:iv, 10.\n\n. \"Flight to Freedom.\"\n\n. Clayton, 62.\n\n. Calderhead, 200.\n\n. Calderhead, 198.\n\n. Douglass 1845, 10.\n\n. Clayton 2002, 44.\n\n. Quoted in Sydnor 1966, 151.\n\n. Douglass 2000, 198.\n\n. _cf_. Freudenberger and Pritchett, 470\u201373.\n\n. Komlos and Alecke, 449.\n\n. Schafer 1997, 165\u201366.\n\n. Rockman, 39.\n\n. Clayton 1998.\n\n. Lundy, 15.\n\n. Wilson, Henry, 1:170.\n\n. _Genius of Universal Emancipation_ , Jan. 2, 1827.\n\n. Lundy, 29; _Genius of Universal Emancipation_ , Jan. 20, 1827.\n\n. \"Law case.\" (1827.) _Niles' Register_ , 32:206. May 19.\n\n. _LWLG_ , 1:92.\n\n. _LWLG_ , 1:93\u201394.\n\n. Bancroft 1900, 1:68.\n\n. Quoted in Kilbourne 2006, vi.\n\n. _MJQA_ , 8:365.\n\n. Lightner, 90.\n\n. The article disputing the conspiracy's existence of the conspiracy is Johnson, Michael P.; for a rebuttal, see Paquette and Egerton.\n\n. Egerton 1999, 16\u201320.\n\n. Egerton 1999, 73\u201374.\n\n. Egerton 1999, 118\u201320.\n\n. _City Gazette and Daily Commercial Advertiser_ , Charleston, August 21, 1822.\n\n. Quoted in Wesley, 163.\n\n. For a biography of Walker, see Hinks.\n\n. Walker, 18\u201319.\n\n. Walker, 71.\n\n. Quoted in Deyle 2005, 54.\n\n. Calderhead, 207n.\n\n. Quoted in Stowe 1853, 363.\n\n. _MJQA_ , 9:23.\n\n. _FBC_ , Box 85, I:iv, 2.\n\n. Dew, 50\u201351.\n\n**Chapter 32: Democratizing Capital**\n\n. Currier, 311.\n\n. Miles 1960, 118.\n\n. Wilentz 2005, 198 _et passim_.\n\n. Baldwin, 82.\n\n. _MJQA_ , 6:317.\n\n. Kilbourne 2006, 109.\n\n. Kilbourne 2006, 28.\n\n. Quoted in Kilbourne 2006, 47.\n\n. Quoted in _Sound Currency_ , 232.\n\n. Letter, Nicholas Biddle to Joseph Hopkinson, February 21, 1834. McGrane, 222.\n\n. President Jackson's veto message. (1832). <http:\/\/avalon.law.yale.edu\/19th_century\/ajveto01.asp>.\n\n. Quoted in Miles 1960, 61.\n\n. Poore, 81.\n\n. January 22, 1833. _Gales & Seaton's register of debates in Congress_, 1205.\n\n. Sinha, 19.\n\n. Davis, William C., 17.\n\n. Wilentz 2005, 375.\n\n. Sinha, 44.\n\n. Van Buren, 542.\n\n. Van Buren, 544.\n\n. January 22, 1833. _Gales & Seaton's register of debates in Congress_, 1194.\n\n. Letter, Andrew Jackson to Rev. Andrew J. Crawford, _CAJ_ , 5:72.\n\n. Van Buren, 625.\n\n. _CJKP_ , 1:575.\n\n. _MJQA_ , 8:434.\n\n. _MJQA_ , 9:93.\n\n. _MJQA_ , 9:93.\n\n. Letter, Jourdan M. Sanders to David Burford, September 28, 1833, _DBP_.\n\n. Miles 1960, 74.\n\n. _CSS_ 1536; Hills, 117.\n\n. Roberts, 27.\n\n. Baldwin, 82\u201389.\n\n. Temin, 22, 80\u201388.\n\n. Marx, Karl. \"Free trade and monopoly,\" _New York Daily Tribune_ , September 25, 1858.\n\n. Marx, Karl. \"Trade or opium?\" _New York Daily Tribune_ , September 20, 1858.\n\n. Roberts, Alasdair, 31.\n\n. Knodell, 542.\n\n. Kilbourne 2006, 59.\n\n. Roberts, Alasdair, 36.\n\n. Kilbourne 2006, 109.\n\n. Roberts, Alasdair, 10\u201311.\n\n. Bourne, Edward G., 17.\n\n. Bourne, Edward G., 14n.\n\n. Martin, Bonnie, 819.\n\n. Martin, Bonnie, 846.\n\n. Martin, Bonnie, 821\u2013822.\n\n. Wilberforce, 22.\n\n. Sydnor 1938, 95.\n\n. Evans, 199; Phillips, 266.\n\n. Dusinberre, 6\n\n. _DeBow's Review_ , 3:5, May 1847.\n\n. Lyell, 1:147.\n\n**Chapter 33: Old Robbers**\n\n. Andrews, E.A., 135\u2013138.\n\n. Andrews, E.A., 142\u201343.\n\n. Quoted in _The Friend_ 2:164.\n\n. Yagyu, 131\u201335.\n\n. 2 Stat. 755. See also, _Fenwick v. Tooker_ , Circuit Court, District of Columbia, 4 Cranch, O. C. 641, Nov. term 1835.\n\n. Laprade, 31.\n\n. Stephenson, 15, 22.\n\n. Stephenson, 23; Yagyu, 141.\n\n. Stephenson, 23.\n\n. _The Friend_ , 2:162.\n\n. Northup, 41\u201347, 75\u201378.\n\n. _The Friend_ , 2:163.\n\n. Featherstonhaugh, 1:120.\n\n. Featherstonhaugh, 1:166\u201370.\n\n. Quoted in Stephenson, 70.\n\n. Hammond, 15.\n\n. Quoted in Jay, 157\u201358.\n\n. _FBC_ , Box 88, 179A.\n\n. Stephenson, 40\u201342.\n\n. Gudmestad, 32.\n\n. Clayton, 83, 87, 98.\n\n. _FBC_ , Box 88, XIV, B6.\n\n. Rothert, 433.\n\n. Stephenson, 76.\n\n. Kiple and King, 148.\n\n. Quoted in Yagyu, 105.\n\n. Letter, Isaac Franklin to Rice C. Ballard, December 8, 1832, _RCBP_.\n\n. Letters, James R. Franklin to Rice C. Ballard, April 24, May 7, 1833, _RCBP_.\n\n. Letter, James R. Franklin to Rice C. Ballard, Feb. 2, 1834, _RCBP_.\n\n. Letter, Jourdan M. Saunders to David Burford, April 3, 1832, _DBP_.\n\n. Letter, Isaac Franklin to Rice C. Ballard, Jan. 9, 1832, _RCBP_.\n\n. Letter, Isaac Franklin to Rice C. Ballard, Nov. 21, 1833, _RCBP_.\n\n. Letter, James R. Franklin to Rice C. Ballard, April 16, 1834, _RCBP_.\n\n. Johnson 2000, 17.\n\n. _New Orleans As It Is_ , 43\u201344.\n\n. Kilbourne 2006, 17, 30.\n\n. _North Carolina v. Mann_ , 13 N.C. 263\n\n. Stephenson, 65.\n\n. See _New Orleans As It Is_ , 44; Schafer 2009 3.\n\n. For an extended treatment of these letters, see Baptist 2005.\n\n. Letter, Isaac Franklin to Rice C. Ballard, January 11, 1834.\n\n. _SIF_ , 272, 282.\n\n. Stephenson, 92.\n\n. Ingraham 1835,\n\n. _SIF_ , 299.\n\n. Warden. There are various versions, more or less similar, of this story and quote.\n\n. See Kilbourne 1995, 18\u201325.\n\n. _SIF_ , 280.\n\n. Kilbourne 2006, 1.\n\n. Stephenson, 131\u2013146.\n\n. Quoted in Stephenson, 152.\n\n**Chapter 34: Wake Up Rich**\n\n. Miles 1960, 124.\n\n. Miles 1957, 48\u201358.\n\n. _MJQA_ , 9:257.\n\n. Quoted in Gatell, 194.\n\n. Quoted in Miles 1957, 57.\n\n. Quoted in Finkelman 2007, 46.\n\n. Seward, 271.\n\n. Wallner, 28.\n\n. Douglass 1855, 445.\n\n. Fehrenbacher, 116.\n\n. Quoted in Miles 1960, 123.\n\n. comparison of US Census figures, 1830 and 1840.\n\n. Davis, William C., 4.\n\n. Davis, William C., 88, 671.\n\n. Davis, William C., 189.\n\n. Davis, William C., 165.\n\n. Davis, William C., 20.\n\n. Davis, William C., 75.\n\n. _MJQA_ , 9:386.\n\n. _Appendix to the Congressional Globe_ , 25th Cong., 2d Sess., 507.\n\n. _MJQA_ , 9:417\u201318.\n\n. _MJQA_ , 9:425.\n\n. _MJQA_ , 9:427\u201328.\n\n. _MJQA_ , 9:429.\n\n. _MJQA_ , 9:455.\n\n. Long, 84.\n\n. \"Suspension of specie payments.\" (1839). _The New-Yorker_ , 8:5, 76, October 19. The attribution to Biddle is by publisher Horace Greeley.\n\n. Parton, 3:626.\n\n. Quoted in Miller, Edward L., 6.\n\n. _CJKP_ , 1:472.\n\n. Lepler, 108ff.\n\n. Quoted in Albert, 105.\n\n. _FBC_ , Box 85, I:iv.\n\n. Buckingham, 1:334\u201335.\n\n. Miller, Edward L., 72.\n\n. Quoted in Miller, Edward L., 32.\n\n. _MJQA_ , 9:332.\n\n. Miles 1960, 140.\n\n. _MJQA_ , 10:19.\n\n. Kilbourne 2006, 109.\n\n. _PJD_ , 2:46n.\n\n. _PJD_ , 2:42n.\n\n. Miles 1960, 149.\n\n. Roberts, Alasdair, 51.\n\n. _WSH_ , 3:10.\n\n. Adams, Henry Carter, 395.\n\n**Chapter 35: The Slave Trade to Cuba and Brazil**\n\n. _Public documents_ 1841, 135. (26th Cong., 2d sess.)\n\n. Morgan, Kenneth 2007, 191\u201392\n\n. _The Legacies of British Slave-ownership_ website databases information given in slaveowners' claims for compensation. www.ucl.ac.uk\/lbs.\n\n. British Parliamentary Papers, _Correspondence relative to the slave trade_ , 28:4.\n\n. _CBC_ 1834, 2.\n\n. _CBC_ 1839, 276.\n\n. Thomas, Hugh, 642.\n\n. Klein and Vinson, 87.\n\n. Letter, N.P. Trist to John Forsyth, 23 May 1839, Despatches from US Consuls in Havana, Cuba, 1783\u20131906, Record Group 59, National Archives, College Park, MD. Thanks to James Shinn.\n\n. _CBC_ 1839, 275.\n\n. _The New-Yorker_ , 8:5, 75, October 19, 1839.\n\n. _MJQA_ , 10:440.\n\n. _CBC_ 1839, 272\u201373.\n\n. _Message from the President of the United States_ , 193.\n\n. _Public documents Printed by Order of the Senate_ (1841), 171.\n\n. See Sublette 2004, 129.\n\n. _AP_ 1839, 20:103.\n\n. _Message from the President of the United States_ , 189.\n\n. _Message from the President of the United States_ , 188\u201389.\n\n. Thomas, Hugh, 642.\n\n. _WSH_ , 1:510\u2013511.\n\n. _Message from the President of the United States_ , 185\u201386.\n\n. _Message from the President of the United States_ , 133.\n\n. _Message from the President of the United States_ , 133\u201334.\n\n. Adams, John Quincy 1841.\n\n. Bleser, 32.\n\n**Chapter 36: Heaps and Piles of Money**\n\n. Kemble, 219.\n\n. For an extended account, see Clinton.\n\n. Kemble, 122, 60.\n\n. Kemble, 218.\n\n. Kemble, 219.\n\n. Kemble, 183.\n\n. For more on antebellum divorce, see Goodheart 2011.\n\n. Butler, 9.\n\n. Butler, 13.\n\n. Kemble, 200.\n\n. Northup, 61, 85\u201388.\n\n. _TAS_ , 18:253.\n\n. Kilbourne 2006, 108\u201309.\n\n. Kilbourne 2006, 127.\n\n. Kilbourne 2006, 137.\n\n. Kilbourne 2006, 138\u201339.\n\n. Kilbourne 2006, 134.\n\n**Chapter 37: The Slave Power**\n\n. For more on Polk as slaveowner, see Dusinberre.\n\n. Bordewich, 281.\n\n. Letter, Herbert Biles to James K. Polk, November 23, 1832, _CJKP_ , 1:529\u201330.\n\n. Letter, Silas M. Caldwell to James K. Polk, Jan. 4, 1834, _CJKP_ , 2:219.\n\n. Letter, James Walker to James K. Polk, February 14, 1834, _CJKP_ , 2:315.\n\n. Letter, James K. Polk to Sarah Childress Polk, Sep. 26\u201327, 1834, _CJKP_ , 2:508\u201309.\n\n. Letter, Ephraim Beanland to James K. Polk, Oct. 4, 1834, _CJKP_ , 2:514.\n\n. Letter, James Walker to James K. Polk, Oct. 15, 1839, _CJKP_ , 5:261\u201362.\n\n. _SIF_ , 296, 359, 360.\n\n. _Congressional Globe_ , 25th Cong., 3d. sess., 167\u201368.\n\n. Baptist 2014, 135n _et passim_.\n\n. _MJQA_ , 10:556.\n\n. _MJQA_ , 11:382.\n\n. _MJQA_ , 12:13\u201314.\n\n. Quoted in Sinha, 65.\n\n. Quoted in Stahr, 96.\n\n. Hughes, 13.\n\n. Foner, Eric, 91.\n\n. www.tsl.texas.gov\/ref\/abouttx\/annexation\/march1845.html.\n\n. Grant, 40\u201341.\n\n. Sachar, 72.\n\n. Olmsted 1861, 51.\n\n. Rosen, 34.\n\n. See Diner, 86\u2013108.\n\n. Rosen, 17.\n\n. Chapman, 1, 5\u201312.\n\n. Scott, Edwin J., 82.\n\n. Korn, 41.\n\n. Stowe 1853, 151.\n\n. Kilbourne 1995, 3.\n\n. Chapman, 23.\n\n. _TAS_ , 18:301.\n\n**Chapter 38: Manifest Destiny's Child**\n\n. Letter, John W. Childress to James K. Polk, July 22, 1846, _CJKP_ , 11:251.\n\n. Dusinberre, 53.\n\n. In the July\u2013August 1845 issue of the _United States Democratic Journal_.\n\n. Quoted in Foner, Eric, 116.\n\n. Quoted in Dusinberre, 17; not included in _CJKP_.\n\n. Letter, James K. Polk to John Catron, Oct. 7, 1846. _CJKP_ , 11:345.\n\n. Letter, Robert Campbell, Jr. to James K. Polk, Oct. 9, 1846. _CJKP_ , 11:345\n\n. Stephenson, 116.\n\n. _SIF_ , 482, 549.\n\n. _DeBow's Review_ (1857), 22:4, 439.\n\n. In the film _Bayou Maharajah_ , dir. Lily Keber.\n\n. For more about Fairvue, there is a \"Historical Fireside Chat\" video with area historians at www.fairvueplantation.com\/history.php.\n\n. Polk, 4:429.\n\n. Polk, 4:408, 393.\n\n. Polk, 4:439.\n\n. Dusinberre, 79.\n\n. Quoted in Montejano, 28.\n\n. Freudenberger and Pritchett, 476.\n\n. Clayton 2002, 77.\n\n. Quoted in Clayton 2002, 77; _Reports and cases argued and determined..._ , 140.\n\n. _Reports and cases argued and determined..._ , 140\u201347.\n\n**Chapter 39: A Letter from Virginia**\n\n. Drago, 61.\n\n. Warden, 8.\n\n. _Southern Business Directory_ (1854), 163.\n\n. Yagyu, 334\u201335.\n\n. Yagyu, 343.\n\n. Letter, C.M. Rutherford to Rice C. Ballard, April 19, 1853, _RCBP_.\n\n. Letter, Virginia Boyd to Rice C. Ballard, May 6, 1853, _RCBP_.\n\n. http:\/\/www2.lib.unc.edu\/mss\/inv\/b\/Ballard,Rice_C.html#folder_191#1.\n\n. Letter, C.M. Rutherford to Rice C. Ballard, Dec. 14, 1853, _RCBP_.\n\n. Bleser, 19.\n\n. Bleser, 101.\n\n**Chapter 40: Communists in Blackface**\n\n. Quoted in Sinha, 102.\n\n. Roske 1968, 243\u201345.\n\n. _Put's Original California Songster_ , 7\u20138.\n\n. Based on Roske 1963, 211.\n\n. Roske 1963, 210.\n\n. Richards, 67\u201368.\n\n. Quoted in Richards, 76.\n\n. _Appendix to the Congressional Globe_ , 31st Cong., 1st sess., 1409.\n\n. _The Address of the Southern Delegates_ , 13\u201314.\n\n. _North Star_ , February 9, 1849.\n\n. Quoted in Bordewich, 203.\n\n. Davis, William C., 308\n\n. Quoted in Sellers, Charles G., 2:24.\n\n. See Richards, 72\u201376.\n\n. Ford, Lacy K. 1988, 38\u201339.\n\n. _FBC_ , Box 88, p. 11.\n\n. Keehn, 10\u201312.\n\n. Davis, William C., 273.\n\n. Sioussat, 329n.\n\n. Sioussat, 330.\n\n. Quoted in Sioussat, 321.\n\n. _Appendix to the Congressional Globe_ , 31st Cong., 1st Sess., 1067.\n\n. Bauer, K. Jack, 314\u201315, 319\u201320; Zachary Taylor Partition of Heirs. Historic New Orleans Collection, MSS 137.\n\n. Webster, 43.\n\n. Bordewich, 309.\n\n. Sioussat, 302.\n\n. Cheves, 26.\n\n. Cheves, 30.\n\n. Quoted in Sinha, 211.\n\n. Skipper, 24\u201325.\n\n. Foster, Stephen.\n\n. Hanby, B.R.\n\n. Stevens, 44.\n\n. Stevens, 188\u201393.\n\n. Stevens, 216n.\n\n. Hurst, 36.\n\n. Quoted in Hurst, 38.\n\n. Ashdown and Caudill, 65.\n\n**Chapter 41: Hiring Day**\n\n. Clarke.\n\n. Jacobs, 26.\n\n. _TAS_ , 18:162.\n\n. Olmsted 1861a, 1:117.\n\n. Bancroft 1931\/1996, 145\u201346.\n\n. Bancroft 1931\/1996, 95.\n\n. Zaborney, 145.\n\n. Abbott, 100ff.\n\n. Laird, 5.\n\n. Corey, 47\u201348.\n\n. Corey, 48\u201350.\n\n. Craddock, 23\u201324.\n\n. Olmsted 1861a, 1:51\u201352.\n\n. Bancroft 1931\/1996, 153.\n\n. _FBC_ , Box 88, A183.\n\n. Quoted in Zaborney, 94.\n\n. Zaborney, 123.\n\n. Southall, 167.\n\n. Hughes, 78.\n\n. O'Connell, 113.\n\n**Chapter 42: Vanish Like a Dream**\n\n. _Sketches of the lives..._ , 36.\n\n. _MJQA_ , 12:25.\n\n. Baker, 25.\n\n. Watson, Robert P., 248.\n\n. Polk, 1:297.\n\n. Merry, 100\u201301.\n\n. Letter, Edmund Burke to Franklin Pierce, June 6, 1852, quoted in Pierce, 114.\n\n. Hawthorne, 416\u201317.\n\n. Olmsted 1861, 58.\n\n. Olmsted 1861, 58.\n\n. Letter, James Gadsden to Thomas Jefferson Green, quoted in Parish and Gadsden, 174\u201375.\n\n. \"Nicaragua.\" (1857). _DeBow's review, agricultural, commercial, industrial progress and resources_ , 22:1, January, 105\u201309.\n\n. \"Notes on Cuba.\" (1859). _Harper's Weekly_ , Jan. 29, 72\u201373.\n\n. Buchanan.\n\n. See Finkelman 2013 for a narrative of the events surrounding Buchanan and _Dred Scott_.\n\n. Douglass 1857, 32.\n\n. Fitzhugh, George, 341\u201342, 368.\n\n. Fitzhugh, George, 278.\n\n. Genovese 1969\/88, 129\u201330.\n\n. Olmsted 1861a, 1:140.\n\n**Chapter 43: A Snake Biting Its Tail**\n\n. Quoted in _FBC_ , Box 88, 109D.\n\n. Foner, Philip, 146.\n\n. Spratt, 487\u201388.\n\n. DuBois, W.E.B. 1904, 174.\n\n. See Satz, 270.\n\n. Lincoln, 132.\n\n. Quoted in _FBC_ , Box 88, 26.\n\n. Fehrenbacher, 179.\n\n. See Graham, 291\u2013324, Slenes, 325\u201370.\n\n. \"Slave Trade in New York.\" (1855). _Debow's Review_. (1855). 18:2, 225\u20136.\n\n. _CBC_ 1860, 11\u201312.\n\n. _CBC_ 1860, 8.\n\n. Dubois, W.E.B. 1904, 308\u2013316.\n\n. _CBC_ 1860, 8.\n\n. _CBC_ 1860, 13.\n\n. _CBC_ 1860, 45.\n\n. Davis, Robert Ralph 1971, 273.\n\n. Davis, Robert Ralph 1971, 276.\n\n. Foner, Philip, 293\u201394.\n\n. Hurst, 330.\n\n. Sheehy et al., 144\u201346.\n\n. Sheehy et al., 146\u201347.\n\n. Quoted in Davis, Robert Ralph 1971, 275\u20137.\n\n. Sheehy et al., 164; DeGraft-Hansen.\n\n. Thomson, 5.\n\n. Thomson, 9.\n\n. Thomson, 11.\n\n. Clinton, 160\u201362.\n\n. Keehn is the source for all material in this volume about the KGC. Keehn, 32\u201345.\n\n. Zaborney, 7.\n\n. _FBC_ , Box 88, p. 24.\n\n. Lee.\n\n. See Keehn, 1\u20132.\n\n. Diouf, 55. For more about the orisha religion in Cuba, see Sublette 2004, 206\u2013234.\n\n. Diouf, 6, 55, 30\u201339.\n\n. Diouf, 151\u201352.\n\n. Diouf, 14.\n\n. Diouf, 48\u201349; Hurston, 655.\n\n**Chapter 44: Assignment in Paraguay**\n\n. Behlolavek, 114.\n\n. Flaherty, 252.\n\n. Baker, 79.\n\n. Cobb, 15.\n\n. \"Cotton Planters' Convention,\" _American Cotton Planter II_ , 11:330, 1858.\n\n. Adams, Henry 2012, 15.\n\n. Flaherty, 268.\n\n. MacKinnon, 73.\n\n. See Foner, Philip, 306\u201311.\n\n. Sinha, 234\u201335; Keehn, 77\u201388.\n\n. Adams, Henry 2012, 16.\n\n. Quoted in Dew, Charles B., 27.\n\n. Dew, Charles B., 32.\n\n. Davis, William C., xiv.\n\n. Quoted in Dew, Charles B., 41.\n\n. Quoted in Dew, Charles B., 98.\n\n. Quoted in Dew, Charles B., 92.\n\n. Wilson, Joseph Ruggles, 3.\n\n. Wilson, Joseph Ruggles, 4, 5, 16, 21.\n\n. McPherson, 29.\n\n. _PJD_ , 7:21.\n\n. Shackleford, 3.\n\n. _PUSG_ 2:194\u201395.\n\n. Conway, 22.\n\n. Keckley, 70\u201372.\n\n. Quoted in Marcus 1955, 2:300.\n\n**Chapter 45: The Decommissioning of Human Capital**\n\n. Quoted in Hammond, 188.\n\n. _TAS_ , 18:208.\n\n. Mitchell, Wesley Clair, 82n.\n\n. Hammond, 23.\n\n. Hammond, 250\u201352.\n\n. Mitchell, Wesley Clair, 100\u2013118.\n\n. Hammond, 170, 244ff, 355.\n\n. Hammond, 1970, 307.\n\n. Hammond, 360.\n\n. Matthews, 77\u201379.\n\n. For more about the Republic of Jones, see Bynum.\n\n. Carpenter, 20, 77; see also Masur.\n\n. _JDC_ , 5:409.\n\n. See Bodenhorn, 231\u201333.\n\n. Cf. http:\/\/belmontmansion.com\/mansionhistory; Lessing, 29\u201335.\n\n. Marcus 1955, 2:55.\n\n. Marcus 1955, 2:56.\n\n. Marcus 1955, 2:305.\n\n. Rosen, 270; Marcus 1955, 2:299.\n\n. Anbinder, 121.\n\n. Rosen, 431\u201332n.\n\n**Chapter 46: A Weird, Plaintive Wail**\n\n. _New York Times_ , December 26, 1864.\n\n. _FWP_ , Virginia narratives, 17:42.\n\n. Unwin.\n\n. Burkhardt, 8.\n\n. Quoted in Burkhardt, 39.\n\n. Some pro-Confederate historians subsequently denied that a massacre happened at Fort Pillow. For a discussion by a historian who reluctantly concluded that there was a racially motivated massacre, see Castel, 89\u2013103.\n\n. _New York Tribune_ , April 18, 1864.\n\n. _New York Times_ , October 30, 1877.\n\n. Reprinted in _Sacramento Daily Union_ , 10 July 1865.\n\n. Slotkin.\n\n. Burkhardt, 147.\n\n. Burkhardt, 148, 231.\n\n. See Trudeau; see also Groce.\n\n. Trudeau, 162.\n\n. Foreman, 706.\n\n. Foreman, 724.\n\n. Sheehy et al., 128, 131.\n\n. Byrne, 91.\n\n. Sheehy et al., 130; Byrne, 99\u2013100.\n\n. Roberts and Kytle.\n\n. Foreman, 753.\n\n. Coffin, 501\u201302.\n\n. This account comes from Coffin, 499ff.\n\n. www.in.ng.mil\/AboutUs\/History\/HoosierCivilWarStoriesMajGarlandWhite\/tabid\/1514\/Default.aspx.\n\n. Keckley, 164\u201366.\n\n. See Stewart, 8\u201312.\n\n. Treasure, 97.\n\n. _PJD_ , 11:581n.\n\n. See Sutherland.\n\n. For an extended treatment of Sims's bizarre career, see Barker-Benfield, 85\u2013111; see also Goodson, 229\u2013231; \"Memorial Sloan-Kettering Cancer Center.\"\n\n. Marcus 1955 2:301.\n\n32. Rosen, 371.\n\n. Chapman, 29, 23\u201324, 33\u201334.\n\n. Warden, 9\u201310.\n\n. Toombs et al, 684.\n\n. Casimir, 110\u201320; Casimir and Dubois.\n\n. Davis, Jefferson, 78\u20139.\n\n. Craddock, 26.\n\n. Craddock, 27.\n\n. Craddock, 41.\n\n. Craddock, 1.\n\n. Yellin, 63\u201364, 143\u201344, 162, 176\u201380, 245\u201347.\n\n. Fleischner, 323.\n\n. Quoted in Fellman, 452n.\n\n. Simkins, 607.\n\n. Hurst, 360.\n\n. Hurst, 370\u20131.\n\n. Armstrong, 875.\n\n. \"Revised Report, Plan for Government of the Western Territory.\" _PTJ_ , 6:607\u201309.\n\n**Coda**\n\n. www.youtube.com\/watch?v=j8d-IYSM-08.\n\n2. Elk and Sloan.\n\n. Coates.\n\n. \"Hate and Extremism.\"\n\n. Fletcher.\n\n. The term \"neoslavery\" was suggested by Douglas Blackmon, in _Slavery By Another Name_.\n\n# **References**\n\nPre-twentieth-century newspaper and magazine articles are cited in the relevant footnotes. Long titles of pre-twentieth-century books have been truncated. All internet links were current as of August 2015.\n\n**ABBREVIATIONS**\n\n_AC_ | _Annals of Congress_ , Washington.  \n---|---  \n_AFL_ | _Adams Family Correspondence_ , Belknap Press.  \n_AJL_ | _The Adams-Jefferson letters_ , UNC Press, Chapel Hill.  \n_AP_ | _Accounts and Papers of the House of Commons_ , London.  \n_CAJ_ | _Correspondence of Andrew Jackson_ , Carnegie Institution of Washington.  \n_CBC_ | _Correspondence with the British Commissioners_ , Harrison and Sons, London.  \n_CJKP_ | _Correspondence of James K. Polk_ , Vanderbilt University Press, Nashville.  \n_CN_ | _Correspondance de Napol\u00e9on Ier._ Plon and Dumaine, Paris.  \n_CRG_ | _Colonial Records of Georgia_ , Chas. P. Byrd, Atlanta.  \n_CSS_ | _Congressional Serial Set_ (1911), US Govt. Printing Office, Washington DC.  \n_DHRC_ | _Documentary History of the Ratification of the Constitution_ , State Historical Society of Wisconsin, Madison.  \n_DIST_ | Donnan, Elizabeth. _Documents Illustrative of the History of the Slave Trade to America_ , v. 1\u20134. Carnegie Institution of Washington, Washington DC.  \n_DPB_ | _David Burford Papers_ , University of Tennessee.  \n_FBC_ | Frederic Bancroft papers, Columbia University Library, New York.  \n_FWP_ | Federal Writers Project Slave Narratives, Library of Congress _American Memory._ http:\/\/memory.loc.gov\/ammem\/snhtml.  \n_HJFP_ | _Harriet Jacobs Family Papers_ , ed. Jean Yellin, University of North Carolina Press.  \n_JDC_ | _Jefferson Davis, Constitutionalist, His Letters, Papers, and Speeches._ Mississippi Department of Archives and History.  \n_LDC_ | _Letters of Delegates to Congress, 1774\u20131789._ ed. Paul H. Smith, Library of Congress  \n_LOC_ | _Library of Congress._  \n_LWLG_ | _Letters of William Lloyd Garrison_ , Belknap Press.  \n_MCMTJ_ | _Memoir, Correspondence, and Miscellanies from the Papers of Thomas Jefferson_ (1830). Gray and Brown, Boston.  \n_MJQA_ | _Memoirs of John Quincy Adams_ , ed. Charles Francis Adams. J.B. Lippincott, Philadelphia.  \n_NPTP_ | Nicholas Philip Trist papers, University of North Carolina Libraries.  \n_PAH_ | _The Papers of Alexander Hamilton_ , Columbia University Press, New York.  \n_PAJ_ | _The Papers of Andrew Jackson_ , University of Tennessee Press.  \n_PBF_ | _The Papers of Benjamin Franklin._ Yale University Press, New Haven.  \n_PGW_ | _The Papers of George Washington_ , University Press of Virginia.  \n_PHL_ | _The Papers of Henry Laurens_ , University of South Carolina Press.  \n_PJA_ | _The Papers of John Adams_ , Belknap Press.  \n_PJD_ | _The Papers of Jefferson Davis_ , Louisiana State University Press, Baton Rouge.  \n_PJMad_ | _The Papers of James Madison: Presidential Series_ , University Press of Virginia.  \n_PJMon_ | _The Papers of James Monroe_ , Greenwood Press.  \n_PTJ_ | _The Papers of Thomas Jefferson_ , Princeton University Press, Princeton.  \n_PTJRS_ | _The Papers of Thomas Jefferson: retirement series_ , Princeton University Press, Princeton.  \n_PUSG_ | _The Papers of Ulysses S. Grant_ , Southern Illinois University Press, Carbondale.  \n_RCBP_ | Rice C. Ballard papers, University of North Carolina libraries.  \n_SAL_ | _United States Statutes at Large._  \n_SIF_ | _Succession of Isaac Franklin._ Louisiana Supreme Court, ca. 1851.  \n_TAS_ | _The American Slave: A Composite Autobiography_ , ed. George P. Rawick. Greenwood Publishing Company, Westport CT.  \n_TRP_ | Thomas Ringgold papers, New York Public Library.  \n_TWOTR_ | _The War of the Rebellion: A Compilation of the Official Records of the Union and Confederate Armies._ Government Printing Office, Washington.  \n_WJA_ | _Works of John Adams_ , Little, Brown, Boston.  \n_WJM_ | _The Writings of James Madison_ , Putnam's, New York, 1910.  \n_WSH_ | _The Writings of Sam Houston_ , University of Texas Press, Austin.  \n_WTJ_ | _The Works of Thomas Jefferson_ , Knickerbocker Press, New York.\n\nItems marked with an asterisk (*) can be accessed via the _North American Slave Narratives_ collection of the University Library of the University of North Carolina at Chapel Hill: http:\/\/docsouth.unc.edu\/neh\n\nAbbott, Lyman. (1915). _Reminiscences._ Houghton Mifflin, New York.\n\nAdams, Catherine and Elizabeth H. Pleck. (2009). _Love of Freedom: Black Women in Colonial and Revolutionary New England._ Oxford University Press, Oxford.\n\nAdams, Henry. (1889\/1986). _History of the United States of America during the Administrations of Thomas Jefferson._ Library of America, New York.\n\n__________. (1889\/1986a). _History of the United States of America during the Administrations of James Madison._ Library of America, New York.\n\n__________. (1883). _John Randolph._ Houghton, Mifflin, Boston.\n\n__________. (2012). _Henry Adams in the Secession Crisis._ Ed. Mark J. Stegmaier. Louisiana State University Press, Baton Rouge.\n\nAdams, Henry Carter. (1887). _Public Debts: An Essay in the Science of Finance._ D. Appleton, New York.\n\nAdams, John Quincy. (1841). _Argument of John Quincy Adams, Before the Supreme Court of the United States : in the Case of the United States, Appellants, vs. Cinque, and Others, Africans, Captured in the schooner Amistad, by Lieut. Gedney_. S.W. Benedict, New York. http:\/\/avalon.law.yale.edu\/19th_century\/amistad_002.asp\n\nAdams, William Howard. (1997). _The Paris Years of Thomas Jefferson_. Yale University Press, New Haven.\n\n_The Address of the Southern Delegates in Congress, to Their Constituents._ (1849). Tower, Washington.\n\nAkam, Simon. (2013). \"George W. Bush's great-great-great-great-grandfather was a slave trader.\" _Slate_ , June 20. www.slate.com\/articles\/life\/history_lesson\/2013\/06\/george_w_bush_and_slavery_the_president_and_his_father_are_descendants_of.single.html.\n\nAlbert, Octavia V. Rogers. (1988). _The House of Bondage: or, Charlotte Brooks and other slaves_. Oxford University Press, New York.\n\nAlbion, Robert Greenhalgh. (1938). _Square-riggers on Schedule: The New York Sailing Packets to England, France, and the Cotton Ports_. Princeton University Press, Princeton.\n\nAlexander, Adele Logan. (2010). _Parallel Worlds: The Remarkable Gibbs-Hunts and the Enduring (In)significance of Melanin._ University of Virginia Press, Charlottesville.\n\nAlexander, Michelle. (2010). _The New Jim Crow: Mass Incarceration in the Age of Colorblindness._ The New Press, New York.\n\nAlexander, William T. (1887). _History of the Colored Race in America._ Palmetto Publishing Company, Kansas City.\n\nAllan, Christopher N. (1998). \"Foreword to 'Supplement to early settlers.'\" http:\/\/msa.maryland.gov\/msa\/speccol\/sc4300\/sc4341\/html\/foreword.html.\n\nAltman, Ida. (1991). \"Spanish society in Mexico after the conquest.\" _The Hispanic American Historical Review_ , 71:3.\n\nAmmon, Harry. (1973). _The Genet Mission._ W. W. Norton, New York.\n\nAnbinder, Tyler. (1997). \"Ulysses S. Grant, nativist.\" _Civil War History_ , 43:2.\n\nAnburey, Thomas. (1776\u20131783 \/ 1923). _Travels through the Interior Parts of America_. Houghton Mifflin, Boston.\n\nAnderson, Adam. (1787). _An Historical and Chronological Deduction of the Origins of Commerce_... Logographic Press, London.\n\nAnderson, Ralph V., and Robert E. Gallman. (1977). \"Slaves as fixed capital: Slave labor and southern economic development.\" _Journal of American History_ , 64:1.\n\nAnderson, Richard G. (2003). \"Some tables of historical U.S. currency and monetary aggregates data.\" The Federal Reserve Bank of St. Louis. http:\/\/research.stlouisfed.org\/wp\/2003\/2003-006.pdf.\n\nAnderson, Thornton. (1993). _Creating the Constitution: The Convention of 1787 and the First Congress_. Penn State Press, University Park, PA.\n\nAndrews, E. A. (1836). _Slavery and the Domestic Slave Trade in the United States._ Boston, Light and Stearns.\n\nAndrews, Kenneth R., ed. _English Privateering Voyages to the West Indies, 1588\u20131595._ University Press, Cambridge.\n\nAptheker, Herbert. (1943). _American Negro Slave Revolts._ Columbia University Press, New York.\n\nArmitage, David. (2004). \"John Locke, Carolina, and the 'Two Treatises of Government.'\" _Political Theory_ , 32:5.\n\nArmstrong, Andrea C. (2012). \"Slavery revisited in penal plantation labor.\" Seattle University Law Review, 35:3.\n\nArtemel, Janice G., Elizabeth A. Crowell, and Jeff Parker. (1987). _The Alexandria Slave Pen: The Archeology of Urban Capitivity._ Engineering-Science Inc., Washington. http:\/\/alexandriava.gov\/uploadedFiles\/historic\/info\/archaeology\/ARSiteReportAlexandriaSlavePenAX75.pdf.\n\nAshdown, Paul, and Edward Caudill. (2005). _The Myth of Nathan Bedford Forrest._ Rowman & Littlefield, Lanham, MD.\n\nAshworth, John. (1995). _Slavery, Capitalism, and Politics in the Antebellum Republic; Vol. 1: Commerce and Compromise, 1820\u20131850._ Cambridge University Press, Cambridge.\n\nBailyn, Bernard. (1968). _The Origins of American Politics._ Alfred A. Knopf, New York.\n\n__________. (1986). _Voyagers to the West: A Passage in the Peopling of America on the Eve of the Revolution._ Vintage Books, New York.\n\nBaine, Rodney M. (1988). \"James Oglethorpe and the early promotional literature for Georgia.\" _William and Mary Quarterly_ , Third Series, 45:1.\n\nBaker, Jean H. (2004). _James Buchanan._ Henry Holt and Company, New York.\n\nBaldwin, Joseph G. (1854). _The Flush Times of Alabama and Mississippi: A Series of Sketches_. D. Appleton, New York.\n\n*Ball, Charles. (1859). _Fifty Years in Chains: Or, the Life of an American Slave._ H. Dayton, New York.\n\nBancroft, Frederic. (1900). _The Life of William Henry Seward._ Harper and Brothers, New York.\n\n__________. (1931\/1996). _Slave Trading in the Old South._ University of South Carolina Press, Columbia.\n\n\"Banking on bondage: private prisons and mass incarceration.\" (2011). American Civil Liberties Union. www.aclu.org\/files\/assets\/bankingonbondage_20111102.pdf.\n\nBaptist, Edward E. (2014). _The Half Has Never Been Told: Slavery and the Making of American Capitalism._ Basic Books, New York.\n\n__________. (2004). \"'Cuffy,' 'fancy maids,' and 'one-eyed men': Rape, commodification, and the domestic slave trade in the United States.\" In Walter Johnson, ed., _The Chattel Principle: Internal Slave Trades in the Americas_ , Yale University Press, New Haven.\n\n*Baquaqua, Mohammed Gardo. (1854). _Biography of Mahomma G. Baquaqua_. Geo. E. Pomeroy and Co., Detroit.\n\nBarker, Gordon S. (2004). \"Unraveling the strange history of Jefferson's 'Observations sur la Virginie.'\" _Virginia Magazine of History and Biography_ , 112:2.\n\nBarker-Benfield, G. J. (2000). _The Horrors of the Half-Known Life: Male Attitudes Toward Women and Sexuality in Nineteenth-Century America._ Second edition. Routledge, New York.\n\nBarnett, Jim, and H. Clark Burkett. (2003). \"The Forks of the Road slave market at Natchez.\" _Mississippi History Now_. http:\/\/mshistorynow.mdah.state.ms.us\/articles\/47\/the-forks-of-the-road-slave-market-at-natchez.\n\nBartels, Emily C. (2006). \"Too many blackamoors: Deportation, discrimination, and Elizabeth I.\" _Studies in English literature 1500\u20131900_ , 46:2.\n\nBassett, John Spencer. (1926). _Correspondence of Andrew Jackson_. Vol. 1. Carnegie Institution of Washington, Washington, DC.\n\nBauer, K. Jack. (1993). _Zachary Taylor: Soldier, Planter, Statesman of the Old Southwest_. Louisiana State University Press, Baton Rouge.\n\nBauer, Raymond A., and Alice H. Bauer (1942). \"Day to day resistance to slavery,\" _The Journal of Negro History_ , October.\n\nBaur, John E. (1970). \"International repercussions of the Haitian Revolution.\" _The Americas_ , 26:4.\n\nBeard, Charles Austin. (1915). _Economic Origins of Jeffersonian Democracy._ Macmillan, New York.\n\nBeck, Carolyn S. (1988). \"Our own vine and fig tree: The authority of history and kinship in Mother Bethel.\" _Review of Religious Research_ , 29:4.\n\nBeeman, Richard. (2009). _Plain, Honest Men: The Making of the American Constitution._ Random House, New York.\n\nBehlolavek, John M. (2013). \"In Defense of Doughface Diplomacy.\" In Quist, John W., and Michael J. Birkner, _James Buchanan and the Coming of the Civil War._ University Press of Florida, Gainesville.\n\nBehrendt, Stephen D. (2007). \"Human capital in the British slave trade.\" In Richardson, David, Suzanne Schwarz, and Anthony Tibbles, ed., _Liverpool and Transatlantic Slavery._ Liverpool University Press, Liverpool.\n\n__________. (1997). \"Crew mortality in the transatlantic slave trade in the eighteenth century.\" _Slavery and Abolition_ , 18:1.\n\nBeirne, Rosamond Randall. _William Buckland 1734\u20131774: Architect of Virginia and Maryland._\n\nBell, Jessica. \"The three Marys: The Virgin; Marie de M\u00e9decis; and Henrietta Maria.\" In Griffey, Erin. (2008). _Henrietta Maria: Piety, Politics and Patronage._ Ashgate, Aldershot UK.\n\nBell, Malcolm Jr. (1987.) _Major Butler's Legacy: Five Generations of a Slaveholding Family._ University of Georgia Press, Athens.\n\nBennett, Charles E. (2001). _Laudonni\u00e8re & Fort Caroline: History and Documents._ University of Alabama Press, Tuscaloosa.\n\n__________. (1982). _Florida's 'French' revolution, 1793\u20131795._ University Press of Florida, Gainesville.\n\nBerinato, Scott. (2013). \"Plantations practiced modern management.\" _Harvard Business Review_ , 91:9.\n\nBerkeley, Edmund, and Dorothy Smith Berkeley. (1969). _Dr. Alexander Garden of Charles Town._ University of North Carolina Press, Chapel Hill.\n\nBerlin, Ira. (1998). _Many Thousands Gone: The First Two Centuries of Slavery in North America._ Harvard University Press, Cambridge.\n\nBiggar, H. P. (1917). \"Jean Ribaut's Discoverye of Terra Florida.\" _English Historical Review_ , 32:126.\n\nBlackmon, Douglas. (2008). _Slavery by Another Name: The Re-enslavement of Black Americans from the Civil War to World War II._ Doubleday, New York.\n\nBlackstone, Sir William, _et al._ (1765). _Commentaries on the Laws of England._ Clarendon Press, Oxford.\n\nBlake, John B. (1952). \"The inoculation controversy in Boston: 1721\u20131722.\" _The New England Quarterly_ 25:4.\n\nBleser, Carol. (1988). _Secret and Sacred: The Diaries of James Henry Hammond, a Southern Slaveholder._ Oxford University Press, New York.\n\nBlumrosen, Alfred W., and Ruth G. Blumrosen. (2006). _Slave Nation: How Slavery United the Colonies and Sparked the American Revolution._ Sourcebooks, Naperville, IL.\n\nBodenhorn, Howard. (2000). _A History of Banking in Antebellum America : Financial Markets and Economic Development in an Era of Nation-Building._ Cambridge University Press, Cambridge.\n\nBogus, Carl T. (1998). \"The Hidden History of the Second Amendment.\" _UC Davis Law Review_ , 31.\n\nBordewich, Fergus M. (2012). _America's Great Debate : Henry Clay, Stephen A. Douglas, and the Compromise that Preserved the Union._ Simon & Schuster, New York.\n\nBosman, Willem (1705). _A New and Accurate Description of the Coast of Guinea, Divided Into the Gold, the Slave, and the Ivory Coasts._ J. Knapton, London.\n\nBoswell, Samuel. (1904). _Life of Samuel Johnson._ Henry Frowde, London.\n\nBourne, Edward G. (1885). _The History of the Surplus Revenue of 1837._ G. P. Putnam's Sons, New York.\n\nBourne, Michael Owen. 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(1998). \"The African experience of the '20. and odd Negroes' arriving in Virginia in 1619.\" _William and Mary Quarterly_ , 3rd ser., 55:3.\n\n__________. (1991). \"African dimensions of the Stono rebellion,\" _American Historical Review_ , 96:4.\n\n__________. (1983). _The Kingdom of Kongo: Civil War and Transition, 1641\u20131718_. University of Wisconsin Press, Madison.\n\nTilp, Frederick. (1982). _The Chesapeake Bay of Yore: Mainly About the Rowing and Sailing Craft._ Chesapeake Bay Foundation, Alexandria, VA.\n\nTombs, Robert. (2014). _The English and Their History._ Penguin, London.\n\nToombs, Robert; Alexander Hamilton Stephens; Howell Cobb. (1913). \"The correspondence of Robert Toombs, Alexander H. Stephens, and Howell Cobb,\" ed. Ulrich B. Phillips, _Annual Report of the American Historical Association for the Year 1911._ [n.p.], Washington.\n\nTourtellot, Arthur Bernon. 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(1969). _The Creation of the American Republic, 1776\u20131787_. University of North Carolina Press, Chapel Hill.\n\n__________. (1992). _The Radicalism of the American Revolution_. Alfred A. Knopf, New York.\n\nWood, Peter H. (1975). _Black Majority: Negroes in Colonial South Carolina from 1670 Through the Stono Rebellion_. Alfred A. Knopf, New York.\n\nWoodmason, Charles. (1766\u20138\/1953). _The Carolina Backcountry on the Eve of Revolution: The Journal and Other Writings of Charles Woodmason, Anglican Itinerant._ University of North Carolina Press, Chapel Hill.\n\nWright, Gavin. (1991). \"What was slavery?\" _Social Concept_ 6:1.\n\n__________. (2006). _Slavery and American Economic Development._ Louisiana State University Press, Baton Rouge.\n\nWright, Irene A. (2010). _Spanish Documents Concerning English Voyages to the Caribbean, 1527\u20131568_. Ashgate, Farnham, UK.\n\nWroth, Peregrine. (1908). \"New Yarmouth.\" _Maryland Historical Magazine_ , 3:3.\n\nWyatt, David R. (2009). _Slaves and Warriors in Medieval Britain and Ireland: 800\u20131200._ Brill, Boston.\n\nYagyu, Tomoko. (2006). _Slave Traders and Planters in the Expanding South: Entrepreneurial Strategies, Business Networks, and Western Migration in the Atlantic World, 1787_ \u2013 _1859._ PhD diss., University of North Carolina, Chapel Hill.\n\nYarema, Allan. (2006). _The American Colonization Society: An Avenue to Freedom?_ University Press of America, Lanham, MD.\n\nYellin, Jean Fagan. (2004). _Harriet Jacobs: A Life._ Basic Books, New York.\n\nZaborney, John J. (2012). _Slaves for Hire: Renting Enslaved Laborers in Antebellum Virginia._ Louisiana State University Press, Baton Rouge.\n\nZobel, Hiller B. (1970). _The Boston Massacre._ Norton, New York.\n\nNED SUBLETTE is the author of _The World That Made New Orleans_ , _Cuba and Its Music_ , and _The Year Before the Flood_.\n\nCONSTANCE SUBLETTE has published, as Constance Ash, three novels and edited the anthology _Not of Woman Born_.\n\nJacket design and cover image: Natalya Balnova\n\nAuthor photo: \u00a9 Ebet Roberts\n\nPRINTED IN THE UNITED STATES OF AMERICA\n\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":"\n\n\n\nProduced by Sankar Viswanathan, David Edwards, and the\nOnline Distributed Proofreading Team at http:\/\/www.pgdp.net\n(This file was produced from images generously made\navailable by The Internet Archive\/American Libraries.)\n\n\n\n\n\n\n\n\n                             THE O'RUDDY\n\n                             _A ROMANCE_\n\n\n                                  BY\n\n                            STEPHEN CRANE\n\n            _Author of \"The Red Badge of Courage,\" \"Active\n                Service,\" \"Wounds in the Rain,\" etc._\n\n                                 AND\n\n                             ROBERT BARR\n\n            _Author of \"Tekla,\" \"In the Midst of Alarms,\"\n               \"Over the Border,\" \"The Victors,\" etc._\n\n\n\n                        _With frontispiece by_\n\n                            C. D. WILLIAMS\n\n\n\n\n\n                               NEW YORK\n\n                     FREDERICK A. STOKES COMPANY\n\n                              PUBLISHERS\n\n\n\n\n\n                          _Copyright, 1903,_\n\n                    BY FREDERICK A. STOKES COMPANY\n\n       *       *       *       *       *\n\n\n\n\nTHE O'RUDDY\n\nCHAPTER I\n\n\nMy chieftain ancestors had lived at Glandore for many centuries and\nwere very well known. Hardly a ship could pass the Old Head of Kinsale\nwithout some boats putting off to exchange the time of day with her,\nand our family name was on men's tongues in half the seaports of\nEurope, I dare say. My ancestors lived in castles which were like\nchurches stuck on end, and they drank the best of everything amid the\njoyous cries of a devoted peasantry. But the good time passed away\nsoon enough, and when I had reached the age of eighteen we had nobody\non the land but a few fisher-folk and small farmers, people who were\nalmost law-abiding, and my father came to die more from disappointment\nthan from any other cause. Before the end he sent for me to come to\nhis bedside.\n\n\"Tom,\" he said, \"I brought you into existence, and God help you safe\nout of it; for you are not the kind of man ever to turn your hand to\nwork, and there is only enough money to last a gentleman five more\nyears.\n\n\"The 'Martha Bixby,' she was, out of Bristol for the West Indies, and\nif it hadn't been for her we would never have got along this far with\nplenty to eat and drink. However, I leave you, besides the money, the\ntwo swords,--the grand one that King Louis, God bless him, gave me,\nand the plain one that will really be of use to you if you get into a\ndisturbance. Then here is the most important matter of all. Here are\nsome papers which young Lord Strepp gave me to hold for him when we\nwere comrades in France. I don't know what they are, having had very\nlittle time for reading during my life, but do you return them to him.\nHe is now the great Earl of Westport, and he lives in London in a\ngrand house, I hear. In the last campaign in France I had to lend him\na pair of breeches or he would have gone bare. These papers are\nimportant to him, and he may reward you, but do not you depend on it,\nfor you may get the back of his hand. I have not seen him for years. I\nam glad I had you taught to read. They read considerably in England, I\nhear. There is one more cask of the best brandy remaining, and I\nrecommend you to leave for England as soon as it is finished. And now,\none more thing, my lad, never be civil to a king's officer. Wherever\nyou see a red coat, depend there is a rogue between the front and the\nback of it. I have said everything. Push the bottle near me.\"\n\nThree weeks after my father's burial I resolved to set out, with no\nmore words, to deliver the papers to the Earl of Westport. I was\nresolved to be prompt in obeying my father's command, for I was\nextremely anxious to see the world, and my feet would hardly wait for\nme. I put my estate into the hands of old Mickey Clancy, and told him\nnot to trouble the tenants too much over the rent, or they probably\nwould split his skull for him. And I bid Father Donovan look out for\nold Mickey Clancy, that he stole from me only what was reasonable.\n\nI went to the Cove of Cork and took ship there for Bristol, and\narrived safely after a passage amid great storms which blew us so near\nGlandore that I feared the enterprise of my own peasantry. Bristol, I\nconfess, frightened me greatly. I had not imagined such a huge and\nteeming place. All the ships in the world seemed to lie there, and the\nquays were thick with sailor-men. The streets rang with noise. I\nsuddenly found that I was a young gentleman from the country.\n\nI followed my luggage to the best inn, and it was very splendid, fit\nto be a bishop's palace. It was filled with handsomely dressed people\nwho all seemed to be yelling, \"Landlord! landlord!\" And there was a\nlittle fat man in a white apron who flew about as if he were being\nstung by bees, and he was crying, \"Coming, sir! Yes, madam! At once,\nyour ludship!\" They heeded me no more than if I had been an empty\nglass. I stood on one leg, waiting until the little fat man should\neither wear himself out or attend all the people. But it was to no\npurpose. He did not wear out, nor did his business finish, so finally\nI was obliged to plant myself in his way, but my speech was decent\nenough as I asked him for a chamber. Would you believe it, he stopped\nabruptly and stared at me with sudden suspicion. My speech had been so\ncivil that he had thought perhaps I was a rogue. I only give you this\nincident to show that if later I came to bellow like a bull with the\nbest of them, it was only through the necessity of proving to\nstrangers that I was a gentleman. I soon learned to enter an inn as a\ndrunken soldier goes through the breach into a surrendering city.\n\nHaving made myself as presentable as possible, I came down from my\nchamber to seek some supper. The supper-room was ablaze with light and\nwell filled with persons of quality, to judge from the noise that they\nwere making. My seat was next to a garrulous man in plum-colour, who\nseemed to know the affairs of the entire world. As I dropped into my\nchair he was saying--\n\n\"--the heir to the title, of course. Young Lord Strepp. That is\nhe--the slim youth with light hair. Oh, of course, all in shipping.\nThe Earl must own twenty sail that trade from Bristol. He is posting\ndown from London, by the way, to-night.\"\n\nYou can well imagine how these words excited me. I half arose from my\nchair with the idea of going at once to the young man who had been\nindicated as Lord Strepp, and informing him of my errand, but I had a\nsudden feeling of timidity, a feeling that it was necessary to be\nproper with these people of high degree. I kept my seat, resolving to\naccost him directly after supper. I studied him with interest. He was\na young man of about twenty years, with fair unpowdered hair and a\nface ruddy from a life in the open air. He looked generous and kindly,\nbut just at the moment he was damning a waiter in language that would\nhave set fire to a stone bridge. Opposite him was a clear-eyed\nsoldierly man of about forty, whom I had heard called \"Colonel,\" and\nat the Colonel's right was a proud, dark-skinned man who kept looking\nin all directions to make sure that people regarded him, seated thus\nwith a lord.\n\nThey had drunk eight bottles of port, and in those days eight bottles\ncould just put three gentlemen in pleasant humour. As the ninth bottle\ncame on the table the Colonel cried--\n\n\"Come, Strepp, tell us that story of how your father lost his papers.\nGad, that's a good story.\"\n\n\"No, no,\" said the young lord. \"It isn't a good story, and besides my\nfather never tells it at all. I misdoubt it's truth.\"\n\nThe Colonel pounded the table. \"'Tis true. 'Tis too good a story to be\nfalse. You know the story, Forister?\" said he, turning to the\ndark-skinned man. The latter shook his head.\n\n\"Well, when the Earl was a young man serving with the French he rather\nrecklessly carried with him some valuable papers relating to some\nestates in the North, and once the noble Earl--or Lord Strepp as he\nwas then--found it necessary, after fording a stream, to hang his\nbreeches on a bush to dry, and then a certain blackguard of a wild\nIrishman in the corps came along and stole--\"\n\nBut I had arisen and called loudly but with dignity up the long table,\n\"That, sir, is a lie.\" The room came still with a bang, if I may be\nallowed that expression. Every one gaped at me, and the Colonel's face\nslowly went the colour of a tiled roof.\n\n\"My father never stole his lordship's breeches, for the good reason\nthat at the time his lordship had no breeches. 'Twas the other way. My\nfather--\"\n\nHere the two long rows of faces lining the room crackled for a moment,\nand then every man burst into a thunderous laugh. But I had flung to\nthe winds my timidity of a new country, and I was not to be put down\nby these clowns.\n\n\"'Tis a lie against an honourable man and my father,\" I shouted. \"And\nif my father hadn't provided his lordship with breeches, he would have\ngone bare, and there's the truth. And,\" said I, staring at the\nColonel, \"I give the lie again. We are never obliged to give it twice\nin my country.\"\n\nThe Colonel had been grinning a little, no doubt thinking, along with\neverybody else in the room, that I was drunk or crazy; but this last\ntwist took the smile off his face clean enough, and he came to his\nfeet with a bound. I awaited him. But young Lord Strepp and Forister\ngrabbed him and began to argue. At the same time there came down upon\nme such a deluge of waiters and pot-boys, and, may be, hostlers, that\nI couldn't have done anything if I had been an elephant. They were\nfrightened out of their wits and painfully respectful, but all the\nsame and all the time they were bundling me toward the door. \"Sir!\nSir! Sir! I beg you, sir! Think of the 'ouse, sir! Sir! Sir! Sir!\" And\nI found myself out in the hall.\n\nHere I addressed them calmly. \"Loose me and takes yourselves off\nquickly, lest I grow angry and break some dozen of these wooden\nheads.\" They took me at my word and vanished like ghosts. Then the\nlandlord came bleating, but I merely told him that I wanted to go to\nmy chamber, and if anybody inquired for me I wished him conducted up\nat once.\n\nIn my chamber I had not long to wait. Presently there were steps in\nthe corridor and a knock at my door. At my bidding the door opened and\nLord Strepp entered. I arose and we bowed. He was embarrassed and\nrather dubious.\n\n\"Aw,\" he began, \"I come, sir, from Colonel Royale, who begs to be\ninformed who he has had the honour of offending, sir?\"\n\n\"'Tis not a question for your father's son, my lord,\" I answered\nbluntly at last.\n\n\"You are, then, the son of The O'Ruddy?\"\n\n\"No,\" said I. \"I am The O'Ruddy. My father died a month gone and\nmore.\"\n\n\"Oh!\" said he. And I now saw why he was embarrassed. He had feared\nfrom the beginning that I was altogether too much in the right. \"Oh!\"\nsaid he again. I made up my mind that he was a good lad. \"That is\ndif--\" he began awkwardly. \"I mean, Mr. O'Ruddy--oh, damn it all, you\nknow what I mean, Mr. O'Ruddy!\"\n\nI bowed. \"Perfectly, my lord!\" I did not understand him, of course.\n\n\"I shall have the honour to inform Colonel Royale that Mr. O'Ruddy is\nentitled to every consideration,\" he said more collectedly. \"If Mr.\nO'Ruddy will have the goodness to await me here?\"\n\n\"Yes, my lord.\" He was going in order to tell the Colonel that I was a\ngentleman. And of course he returned quickly with the news. But he did\nnot look as if the message was one which he could deliver with a glib\ntongue. \"Sir,\" he began, and then halted. I could but courteously\nwait. \"Sir, Colonel Royale bids me say that he is shocked to find that\nhe has carelessly and publicly inflicted an insult upon an unknown\ngentleman through the memory of the gentleman's dead father. Colonel\nRoyale bids me to say, sir, that he is overwhelmed with regret, and\nthat far from taking an initial step himself it is his duty to express\nto you his feeling that his movements should coincide with any\narrangements you may choose to make.\"\n\nI was obliged to be silent for a considerable period in order to\ngather head and tail of this marvellous sentence. At last I caught it.\n\"At daybreak I shall walk abroad,\" I replied, \"and I have no doubt\nthat Colonel Royale will be good enough to accompany me. I know\nnothing of Bristol. Any cleared space will serve.\"\n\nMy Lord Strepp bowed until he almost knocked his forehead on the\nfloor. \"You are most amiable, Mr. O'Ruddy. You of course will give me\nthe name of some friend to whom I can refer minor matters?\"\n\nI found that I could lie in England as readily as ever I did in\nIreland. \"My friend will be on the ground with me, my lord; and as he\nalso is a very amiable man it will not take two minutes to make\neverything clear and fair.\" Me, with not a friend in the world but\nFather O'Donovan and Mickey Clancy at Glandore!\n\nLord Strepp bowed again, the same as before. \"Until the morning then,\nMr. O'Ruddy,\" he said, and left me.\n\nI sat me down on my bed to think. In truth I was much puzzled and\namazed. These gentlemen were actually reasonable and were behaving\nlike men of heart. Neither my books nor my father's stories--great\nlies, many of them, God rest him!--had taught me that the duelling\ngentry could think at all, and I was quite certain that they never\ntried. \"You were looking at me, sir?\" \"Was I, 'faith? Well, if I care\nto look at you I shall look at you.\" And then away they would go at\nit, prodding at each other's bellies until somebody's flesh swallowed\na foot of steel. \"Sir, I do not like the colour of your coat!\" Clash!\n\"Sir, red hair always offends me.\" Cling! \"Sir, your fondness for\nrabbit-pie is not polite.\" Clang!\n\nHowever, the minds of young Lord Strepp and Colonel Royale seemed to\nbe capable of a process which may be termed human reflection. It was\nplain that the Colonel did not like the situation at all, and perhaps\nconsidered himself the victim of a peculiarly exasperating combination\nof circumstances. That an Irishman should turn up in Bristol and give\nhim the lie over a French pair of breeches must have seemed\nastonishing to him, notably when he learned that the Irishman was\nquite correct, having in fact a clear title to speak authoritatively\nupon the matter of the breeches. And when Lord Strepp learned that I\nwas The O'Ruddy he saw clearly that the Colonel was in the wrong, and\nthat I had a perfect right to resent the insult to my father's memory.\nAnd so the Colonel probably said: \"Look you, Strepp. I have no desire\nto kill this young gentleman, because I insulted his father's name. It\nis out of all decency. And do you go to him this second time and see\nwhat may be done in the matter of avoidance. But, mark you, if he\nexpresses any wishes, you of course offer immediate accommodation. I\nwill not wrong him twice.\" And so up came my Lord Strepp and hemmed\nand hawed in that way which puzzled me. A pair of thoughtful,\nhonourable fellows, these, and I admired them greatly.\n\nThere was now no reason why I should keep my chamber, since if I now\nmet even the Colonel himself there would be no brawling; only bows. I\nwas not, indeed, fond of these latter,--replying to Lord Strepp had\nalmost broken my back; but, any how, more bows were better than more\nloud words and another downpour of waiters and pot-boys.\n\nBut I had reckoned without the dark-skinned man, Forister. When I\narrived in the lower corridor and was passing through it on my way to\ntake the air, I found a large group of excited people talking of the\nquarrel and the duel that was to be fought at daybreak. I thought it\nwas a great hubbub over a very small thing, but it seems that the\nmainspring of the excitement was the tongue of this black Forister.\n\"Why, the Irish run naked through their native forests,\" he was\ncrying. \"Their sole weapon is the great knotted club, with which,\nhowever, they do not hesitate, when in great numbers, to attack lions\nand tigers. But how can this barbarian face the sword of an officer of\nHis Majesty's army?\"\n\nSome in the group espied my approach, and there was a nudging of\nelbows. There was a general display of agitation, and I marvelled at\nthe way in which many made it to appear that they had not formed part\nof the group at all. Only Forister was cool and insolent. He stared\nfull at me and grinned, showing very white teeth. \"Swords are very\ndifferent from clubs, great knotted clubs,\" he said with admirable\ndeliberation.\n\n\"Even so,\" rejoined I gravely. \"Swords are for gentlemen, while clubs\nare to clout the heads of rogues--thus.\" I boxed his ear with my open\nhand, so that he fell against the wall. \"I will now picture also the\nuse of boots by kicking you into the inn yard which is adjacent.\" So\nsaying I hurled him to the great front door which stood open, and\nthen, taking a sort of hop and skip, I kicked for glory and the\nSaints.\n\nI do not know that I ever kicked a man with more success. He shot out\nas if he had been heaved by a catapult. There was a dreadful uproar\nbehind me, and I expected every moment to be stormed by the\nwaiter-and-pot-boy regiment. However I could hear some of the\ngentlemen bystanding cry:\n\n\"Well done! Well kicked! A record! A miracle!\"\n\nBut my first hours on English soil contained still other festivities.\nBright light streamed out from the great door, and I could plainly\nnote what I shall call the arc or arcs described by Forister. He\nstruck the railing once, but spun off it, and to my great astonishment\nwent headlong and slap-crash into some sort of an upper servant who\nhad been approaching the door with both arms loaded with cloaks,\ncushions, and rugs.\n\nI suppose the poor man thought that black doom had fallen upon him\nfrom the sky. He gave a great howl as he, Forister, the cloaks,\ncushions, and rugs spread out grandly in one sublime confusion.\n\nSome ladies screamed, and a bold commanding voice said: \"In the\ndevil's name what have we here?\" Behind the unhappy servant had been\ncoming two ladies and a very tall gentleman in a black cloak that\nreached to his heels. \"What have we here?\" again cried this tall man,\nwho looked like an old eagle. He stepped up to me haughtily. I knew\nthat I was face to face with the Earl of Westport.\n\nBut was I a man for ever in the wrong that I should always be giving\ndown and walking away with my tail between my legs? Not I; I stood\nbravely to the Earl:\n\n\"If your lordship pleases, 'tis The O'Ruddy kicking a blackguard into\nthe yard,\" I made answer coolly.\n\nI could see that he had been about to shout for the landlord and more\nwaiters and pot-boys, but at my naming myself he gave a quick stare.\n\n\"The O'Ruddy?\" he repeated. \"Rubbish!\"\n\nHe was startled, bewildered; but I could not tell if he were glad or\ngrieved.\n\n\"'Tis all the name I own,\" I said placidly. \"My father left it me\nclear, it being something that he could not mortgage. 'Twas on his\ndeath-bed he told me of lending you the breeches, and that is why I\nkicked the man into the yard; and if your lordship had arrived sooner\nI could have avoided this duel at daybreak, and, any how, I wonder at\nhis breeches fitting you. He was a small man.\"\n\nSuddenly the Earl raised his hand. \"Enough,\" he said sternly. \"You are\nyour father's son. Come to my chamber in the morning, O'Ruddy.\"\n\nThere had been little chance to see what was inside the cloaks of the\nladies, but at the words of the Earl there peeped from one hood a pair\nof bright liquid eyes--God save us all! In a flash I was no longer a\nfree man; I was a dazed slave; the Saints be good to us!\n\nThe contents of the other hood could not have been so interesting, for\nfrom it came the raucous voice of a bargeman with a cold:\n\n\"Why did he kick him? Whom did he kick? Had he cheated at play? Where\nhas he gone?\"\n\nThe upper servant appeared, much battered and holding his encrimsoned\nnose.\n\n\"My lord--\" he began.\n\nBut the Earl roared at him,--\n\n\"Hold your tongue, rascal, and in future look where you are going and\ndon't get in a gentleman's way.\"\n\nThe landlord, in a perfect anguish, was hovering with his squadrons on\nthe flanks. They could not think of pouncing upon me if I was noticed\nat all by the great Earl; but, somewhat as a precaution perhaps, they\nremained in form for attack. I had no wish that the pair of bright\neyes should see me buried under a heap of these wretches, so I bowed\nlow to the ladies and to the Earl and passed out of doors. As I left,\nthe Earl moved his hand to signify that he was now willing to endure\nthe attendance of the landlord and his people, and in a moment the inn\nrang with hurried cries and rushing feet.\n\nAs I passed near the taproom window the light fell full upon a\nrailing; just beneath and over this railing hung two men. At first I\nthought they were ill, but upon passing near I learned that they were\nsimply limp and helpless with laughter, the sound of which they\ncontrived to keep muffled. To my surprise I recognized the persons of\nyoung Lord Strepp and Colonel Royale.\n\n\n\n\nCHAPTER II\n\n\nThe night was growing, and as I was to fight at daybreak I needed a\ngood rest; but I could not forget that in my pride I had told Lord\nStrepp that I was provided with a friend to attend me at the duel. It\nwas on my mind. I must achieve a friend, or Colonel Royale might quite\nproperly refuse to fight me on the usual grounds that if he killed me\nthere would be present no adherent of my cause to declare that the\nfight was fair. And any how I had lied so thoroughly to Lord Strepp. I\nmust have a friend.\n\nBut how was I to carve a friend out of this black Bristol at such\nshort notice? My sense told me that friends could not be found in the\nroad like pebbles, but some curious feeling kept me abroad, scanning\nby the light of the lanterns or the torches each face that passed me.\nA low dull roar came from the direction of the quay, and this was the\nnoise of the sailor-men, being drunk. I knew that there would be none\nfound there to suit my purpose, but my spirit led me to wander so that\nI could not have told why I went this way or that way.\n\nOf a sudden I heard from a grassy bank beside me the sound of low and\nstrenuous sobbing. I stopped dead short to listen, moved by\ninstinctive recognition. Aye, I was right. It was Irish keening. Some\nson of Erin was spelling out his sorrow to the darkness with that\nprofound and garrulous eloquence which is in the character of my\npeople.\n\n\"Wirra, wirra! Sorrow the day I would be leaving Ireland against my\nown will and intention, and may the rocks go out to meet the lugger\nthat brought me here! It's beginning to rain, too! Sure it never rains\nlike this in Ireland! And me without a brass penny to buy a bed! If\nthe Saints save me from England, 'tis al--\"\n\n\"Come out of that, now!\" said I.\n\nThe monologue ceased; there was a quick silence. Then the voice, much\naltered, said: \"Who calls? 'Tis may be an Irish voice!\"\n\n\"It is,\" said I. \"I've swallowed as much peat smoke as any man of my\nyears. Come out of that now, and let me have a look at you.\"\n\nHe came trustfully enough, knowing me to be Irish, and I examined him\nas well as I was able in the darkness. He was what I expected, a\nbedraggled vagabond with tear-stains on his dirty cheeks and a vast\nshock of hair which I well knew would look, in daylight, like a\nburning haycock. And as I examined him he just as carefully examined\nme. I could see his shrewd blue eyes twinkling.\n\n\"You are a red man,\" said I. \"I know the strain; 'tis better than\nsome. Your family must have been very inhospitable people.\" And then,\nthinking that I had spent enough time, I was about to give the fellow\nsome coin and send him away. But here a mad project came into my empty\nhead. I had ever been the victim of my powerful impulses, which surge\nup within me and sway me until I can only gasp at my own conduct. The\nsight of this red-headed scoundrel had thrust an idea into my head,\nand I was a lost man.\n\n\"Mark you!\" said I to him. \"You know what I am?\"\n\n\"'Tis hard to see in the dark,\" he answered; \"but I mistrust you are a\ngentleman, sir. McDermott of the Three Trees had a voice and a way\nwith him like you, and Father Burk too, and he was a gentleman born if\nhe could only remain sober.\"\n\n\"Well, you've hit it, in the dark or whatever,\" said I. \"I am a\ngentleman. Indeed I am an O'Ruddy. Have you ever been hearing of my\nfamily?\"\n\n\"Not of your honour's branch of it, sure,\" he made answer confidently.\n\"But I have often been hearing of the O'Ruddys of Glandore, who are\nwell known to be such great robbers and blackguards that their match\nis not to be found in all the south of Ireland. Nor in the west,\nneither, for that matter.\"\n\n\"Aye,\" said I, \"I have heard that that branch of the family was much\nadmired by the peasantry for their qualities. But let us have done\nwith it and speak of other matters. I want a service of you.\"\n\n\"Yes, your honour,\" said he, dropping his voice. \"May be 'twill not be\nthe first time I've been behind a ditch; but the light to-night is\nvery bad unless I am knowing him well, and I would never be forgetting\nhow Tim Malone let fly in the dark of a night like this, thinking it\nwas a bailiff, until she screamed out with the pain in her leg, the\npoor creature, and her beyond seventy and a good Catholic.\"\n\n\"Come out of it now!\" said I impatiently. \"You will be behind no\nditch.\" And as we walked back to the inn I explained to my new man the\npart I wished him to play. He was amazed at it, and I had to explain\nfifty times; but when it once was established in his red head Paddy\nwas wild with enthusiasm, and I had to forbid him telling me how well\nhe would do it.\n\nI had them give him some straw in the stable, and then retired to my\nchamber for needed rest. Before dawn I had them send Paddy to me, and\nby the light of a new fire I looked at him. Ye Saints! What hair! It\nmust have been more than a foot in length, and the flaming strands\nradiated in all directions from an isolated and central spire which\nshot out straight toward the sky. I knew what to do with his tatters,\nbut that crimson thatch dumfounded me. However there was no going back\nnow, so I set to work upon him. Luckily my wardrobe represented three\ngenerations of O'Ruddy clothes, and there was a great plenty. I put my\nimpostor in a suit of blue velvet with a flowered waistcoat and\nstockings of pink. I gave him a cocked hat and a fine cloak. I worked\nwith success up to the sword-belt, and there I was checked. I had two\nswords, but only one belt. However, I slung the sword which King Louis\nhad given my father on a long string from Paddy's neck and sternly bid\nhim keep his cloak tight about him. We were ready.\n\n\"Now, Paddy,\" said I, \"do you bow in this manner.\" I bowed as a\ngentleman should. But I will not say how I strove with him. I could do\nlittle in that brief space. If he remained motionless and kept his\ntongue still he was somewhat near his part, but the moment he moved he\nwas astonishing. I depended on keeping him under my eye, and I told\nhim to watch me like a cat. \"Don't go thinking how grand you are, that\nway,\" I cried to him angrily. \"If you make a blunder of it, the\ngentlemen will cudgel you, mark you that. Do you as I direct you. And\nthe string, curse you. Mind your cloak!\" The villain had bethought him\nof his flowered waistcoat, and with a comic air flung back his coat to\ndisplay it. \"Take your fingers out of your mouth. Stop scratching your\nshin with your foot. Leave your hair alone. 'Tis as good and as bad as\nyou can make it. Come along now, and hold your tongue like a graven\nimage if you would not be having me stop the duel to lather you.\"\n\nWe marched in good order out of the inn. We saw our two gentlemen\nawaiting us, wrapped in their cloaks, for the dawn was cold. They\nbowed politely, and as I returned their salute I said in a low, quick\naside to Paddy:\n\n\"Now, for the love of God, bow for your life!\"\n\nMy intense manner must have frightened the poor thing, for he ducked\nas swiftly as if he had been at a fair in Ireland and somebody had\nhove a cobble at his head.\n\n\"Come up!\" I whispered, choking with rage. \"Come up! You'll be\nbreaking your nose on the road.\"\n\nHe straightened himself, looking somewhat bewildered, and said:\n\n\"What was it? Was I too slow? Did I do it well?\"\n\n\"Oh, fine,\" said I. \"Fine. You do it as well as that once more, and\nyou will probably break your own neck, and 'tis not me will be buying\nmasses for your soul, you thief. Now don't drop as if a gamekeeper had\nshot at you. There is no hurry in life. Be quiet and easy.\"\n\n\"I mistrusted I was going too fast,\" said he; \"but for the life of me\nI couldn't pull up. If I had been the Dublin mail, and the road thick\nas fleas with highwaymen, I should have gone through them grand.\"\n\nMy Lord Strepp and Colonel Royale had not betrayed the slightest\nsurprise at the appearance of my extraordinary companion. Their\nsmooth, regular faces remained absolutely imperturbable. This I took\nto be very considerate of them, but I gave them just a little more\nthan their due, as I afterward perceived when I came to understand the\nEnglish character somewhat. The great reason was that Paddy and I were\nforeigners. It is not to be thought that gentlemen of their position\nwould have walked out for a duel with an Englishman in the party of so\nfantastic an appearance. They would have placed him at once as a\nperson impossible and altogether out of their class. They would have\ntold a lackey to kick this preposterous creation into the horse-pond.\nBut since Paddy was a foreigner he was possessed of some curious\nlicense, and his grotesque ways could be explained fully in the simple\nphrase, \"'Tis a foreigner.\"\n\nSo, then, we preceded my Lord Strepp and Colonel Royale through a\nnumber of narrow streets and out into some clear country. I chose a\nfine open bit of green turf as a goodly place for us to meet, and I\nwarped Paddy through the gate and moved to the middle of the field. I\ndrew my sword and saluted, and then turned away. I had told Paddy\neverything which a heaven-sent sense of instruction could suggest, and\nif he failed I could do no more than kill him.\n\nAfter I had kicked him sharply he went aside with Lord Strepp, and\nthey indulged in what sounded like a very animated discussion.\nFinally I was surprised to see Lord Strepp approaching me. He said:\n\n\"It is very irregular, but I seem unable to understand your friend. He\nhas proposed to me that the man whose head is broken first--I do not\nperfectly understand what he could mean by that; it does not enter our\nanticipations that a man could possibly have his head broken--he has\nproposed that the man whose head may be broken first should provide\n'lashings'--I feel sure that is the word--lashings of meat and drink\nat some good inn for the others. Lashings is a word which I do not\nknow. We do not know how to understand you gentlemen when you speak of\nlashings. I am instructed to meet any terms which you may suggest, but\nI find that I cannot make myself clear to your friend who speaks of\nnothing but lashings.\"\n\n\"Sir,\" said I, as I threw coat and waistcoat on the grass, \"my friend\nrefers to a custom of his own country. You will, I feel sure, pardon\nhis misconception of the circumstances. Pray accept my regrets, and,\nif you please, I am ready.\"\n\nHe immediately signified that his mind was now clear, and that the\nincident of Paddy's lashings he regarded as closed. As for that\nflame-headed imp of crime, if I could have got my hands upon him he\nwould have taken a short road to his fathers. Him and his lashings! As\nI stood there with a black glare at him, the impudent scoundrel\nrepeatedly winked at me with the readable information that if I only\nwould be patient and bide a moment he would compass something very\nclever. As I faced Colonel Royale I was so wild with thinking of what\nI would do to Paddy, that, for all I knew, I might have been crossing\nswords with my mother.\n\nAnd now as to this duel. I will not conceal that I was a very fine\nfencer in both the French and Italian manners. My father was in his\nday one of the finest blades in Paris, and had fought with some of the\nmost skillful and impertinent gentlemen in all France. He had done his\nbest to give me his eye and his wrist, and sometimes he would say that\nI was qualified to meet all but the best in the world. He commonly\nmade fun of the gentlemen of England, saying that a dragoon was their\nideal of a man with a sword; and he would add that the rapier was a\nweapon which did not lend itself readily to the wood-chopper's art. He\nwas all for the French and Italian schools.\n\nI had always thought that my father's judgment was very good, but I\ncould not help reflecting that if it turned out to be bad I would have\na grievance as well as a sword-thrust in the body. Colonel Royale came\nat me in a somewhat leisurely manner, and, as I said, my mind was so\nfull of rage at Paddy that I met the first of my opponent's thrusts\nthrough sheer force of habit. But my head was clear a moment later,\nand I knew that I was fighting my first duel in England and for my\nfather's honour. It was no time to think of Paddy.\n\nAnother moment later I knew that I was the Colonel's master. I could\nreach him where I chose. But he did not know it. He went on prodding\naway with a serious countenance, evidently under the impression that\nhe had me hard put to it. He was as grave as an owl-faced parson. And\nnow here I did a sorry thing. I became the victim of another of my mad\nimpulses. I was seized with an ungovernable desire to laugh. It was\nhideous. But laugh I did, and, of necessity, square in the Colonel's\nface. And to this day I regret it.\n\nThen the real duel began. At my laugh the Colonel instantly lost his\ngrave air, and his countenance flushed with high, angry surprise. He\nbeset me in a perfect fury, caring no more for his guard than if he\nhad been made of iron. Never have I seen such quick and tremendous\nchange in a man. I had laughed at him under peculiar conditions: very\nwell, then; he was a demon. Thrice my point pricked him to keep him\noff, and thrice my heart was in my mouth that he would come on\nregardless. The blood oozed out on his white ruffled shirt; he was\npanting heavily, and his eyes rolled. He was a terrible sight to face.\nAt last I again touched him, and this time sharply and in the sword\narm, and upon the instant my Lord Strepp knocked our blades apart.\n\n\"Enough,\" he cried sternly. \"Back, Colonel! Back!\"\n\nThe Colonel flung himself sobbing into his friend's arms, choking out,\n\"O God, Strepp! I couldn't reach him. I couldn't reach him, Strepp!\nOh, my God!\"\n\nAt the same time I disappeared, so to speak, in the embrace of my\nred-headed villain, who let out an Irish howl of victory that should\nhave been heard at Glandore. \"Be quiet, rascal,\" I cried, flinging him\noff. But he went on with his howling until I was obliged forcibly to\nlead him to a corner of the field, where he exclaimed:\n\n\"Oh, your honour, when I seen the other gentleman, all blazing with\nrage, rush at you that way, and me with not so much as a tuppence for\nall my service to you excepting these fine clothes and the sword,\nalthough I am thinking I shall have little to do with swords if this\nis the way they do it, I said, 'Sorrow the day England saw me!'\"\n\nIf I had a fool for a second, Colonel Royale had a fine, wise young\nman. Lord Strepp was dealing firmly and coolly with his maddened\nprincipal.\n\n\"I can fight with my left hand,\" the Colonel was screaming. \"I tell\nyou, Strepp, I am resolved! Don't bar my way! I will kill him! I will\nkill him!\"\n\n\"You are not in condition to fight,\" said the undisturbed young man.\n\"You are wounded in four places already. You are in my hands. You will\nfight no more to-day.\"\n\n\"But, Strepp!\" wailed the Colonel. \"Oh, my God, Strepp!\"\n\n\"You fight no more to-day,\" said the young lord.\n\nThen happened unexpected interruptions. Paddy told me afterward that\nduring the duel a maid had looked over a wall and yelled, and dropped\na great brown bowl at sight of our occupation. She must have been the\ninstrument that aroused the entire county, for suddenly men came\nrunning from everywhere. And the little boys! There must have been\nlittle boys from all over England.\n\n\"What is it? What is it?\"\n\n\"Two gentlemen have been fighting!\"\n\n\"Oh, aye, look at him with the blood on him!\"\n\n\"Well, and there is young my Lord Strepp. He'd be deep in the matter,\nI warrant you!\"\n\n\"Look yon, Bill! Mark the gentleman with the red hair. He's not from\nthese parts, truly. Where, think you, he comes from?\"\n\n\"'Tis a great marvel to see such hair, and I doubt not he comes from\nAfrica.\"\n\nThey did not come very near, for in those days there was little the\npeople feared but a gentleman, and small wonder. However, when the\nlittle boys judged that the delay in a resumption of the fight was too\nprolonged, they did not hesitate to express certain unconventional\nopinions and commands.\n\n\"Hurry up, now!\"\n\n\"Go on!\"\n\n\"You're both afeared!\"\n\n\"Begin! Begin!\"\n\n\"Are the gentlemen in earnest?\"\n\n\"Sirs, do you mean ever to fight again? Begin, begin.\"\n\nBut their enthusiasm waxed high after they had thoroughly comprehended\nPaddy and his hair.\n\n\"You're alight, sir; you're alight!\"\n\n\"Water! Water!\"\n\n\"Farmer Pelton will have the officers at you an you go near his hay.\nWater!\"\n\nPaddy understood that they were paying tribute to his importance, and\nhe again went suddenly out of my control. He began to strut and caper\nand pose with the air of knowing that he was the finest gentleman in\nEngland.\n\n\"Paddy, you baboon,\" said I, \"be quiet and don't be making yourself a\nlaughing-stock for the whole of them.\"\n\nBut I could give small heed to him, for I was greatly occupied in\nwatching Lord Strepp and the Colonel. The Colonel was listening now\nto his friend for the simple reason that the loss of blood had made\nhim too weak to fight again. Of a sudden he slumped gently down\nthrough Lord Strepp's arms to the ground, and, as the young man knelt,\nhe cast his eyes about him until they rested upon me in what I took to\nbe mute appeal. I ran forward, and we quickly tore his fine ruffles to\npieces and succeeded in quite stanching his wounds, none of which were\nserious. \"'Tis only a little blood-letting,\" said my Lord Strepp with\nsomething of a smile. \"'Twill cool him, perchance.\"\n\n\"None of them are deep,\" I cried hastily. \"I--\"\n\nBut Lord Strepp stopped me with a swift gesture. \"Yes,\" he said, \"I\nknew. I could see. But--\" He looked at me with troubled eyes. \"It is\nan extraordinary situation. You have spared him, and--he will not wish\nto be spared, I feel sure. Most remarkable case.\"\n\n\"Well, I won't kill him,\" said I bluntly, having tired of this\nrubbish. \"Damme if I will!\"\n\nLord Strepp laughed outright. \"It is ridiculous,\" he said. \"Do you\nreturn, O'Ruddy, and leave me the care of this business. And,\" added\nhe, with embarrassed manner, \"this mixture is full strange; but--I\nfeel sure--any how, I salute you, sir.\" And in his bow he paid a\nsensible tribute to my conduct.\n\nAfterward there was nought to do but gather in Paddy and return to the\ninn. I found my countryman swaggering to and fro before the crowd.\nSome ignoramus, or some wit, had dubbed him the King of Ireland, and\nhe was playing to the part.\n\n\"Paddy, you red-headed scandal,\" said I, \"come along now!\"\n\nWhen he heard me, he came well enough; but I could not help but feel\nfrom his manner that he had made a great concession.\n\n\"And so they would be taking me for the King of Ireland, and, sure,\n'tis an advantage to be thought a king whatever, and if your honour\nwould be easy 'tis you and me that would sleep in the finest beds in\nBristol the night, and nothing to do but take the drink as it was\nhanded and--I'll say no more.\"\n\nA rabble followed us on our way to the inn, but I turned on them so\nfiercely from time to time that ultimately they ran off. We made\ndirect for my chamber, where I ordered food and drink immediately to\nbe served. Once alone there with Paddy I allowed my joy to take hold\non me. \"Eh, Paddy, my boy,\" said I, walking before him, \"I have done\ngrand. I am, indeed, one of the finest gentlemen in the world.\"\n\n\"Aye, that's true,\" he answered, \"but there was a man at your back\nthroughout who--\"\n\nTo his extreme astonishment I buffeted him heavily upon the cheek.\n\"And we'll have no more of that talk,\" said I.\n\n\n\n\nCHAPTER III\n\n\n\"Aye!\" said Paddy, holding his jowl; \"'tis what one gets for serving a\ngentleman. 'Tis the service of a good truthful blackguard I'd be\nlooking for, and that's true for me.\"\n\n\"Be quiet and mind what I tell you,\" I cried to him. \"I'm uplifted\nwith my success in England, and I won't be hearing anything from you\nwhile I am saying that I am one of the grandest gentlemen in all the\nworld. I came over here with papers--papers!\" said I; and then I\nbethought me that I would take the papers and wave them in my hand. I\ndon't know why people wish to wave important documents in their hands,\nbut the impulse came to me. Above all things I wished to take these\npapers and wave them defiantly, exultantly, in the air. They were my\ninheritance and my land of promise; they were everything. I must wave\nthem even to the chamber, empty save for Paddy.\n\nWhen I reached for them in the proper place in my luggage they were\ngone. I wheeled like a tiger upon Paddy.\n\n\"Villain,\" I roared, grasping him at the throat, \"you have them!\"\n\nHe sank in full surrender to his knees.\n\n\"I have, your honour,\" he wailed; \"but, sure, I never thought your\nhonour would care, since one of them is badly worn at the heel, and\nthe other is no better than no boot at all.\"\n\nI was cooled by the incontestable verity of this man. I sat heavily\ndown in a chair by the fire.\n\n\"Aye,\" said I stupidly, \"the boots! I did not mean the boots, although\nwhen you took them passes my sense of time. I mean some papers.\"\n\n\"Some papers!\" cried he excitedly. \"Your honour never thought it would\nbe me that would steal papers? Nothing less than good cows would do my\npeople, and a bit of turf now and then, but papers--\"\n\n\"Peace!\" said I sombrely, and began to search my luggage thoroughly\nfor my missing inheritance. But it was all to no purpose. The papers\nwere not there. I could not have lost them. They had been stolen. I\nsaw my always-flimsy inheritance melt away. I had been, I thought, on\nthe edge of success, but I now had nothing but my name, a successful\nduel, and a few pieces of gold. I was buried in defeat.\n\nOf a sudden a name shot through my mind. The name of this black\nForister was upon me violently and yet with perfect sureness. It was\nhe who had stolen the papers. I knew it. I felt it in every bone. He\nhad taken the papers.\n\nI have since been told that it is very common for people to be moved\nby these feelings of omen, which are invariably correct in their\nparticulars; but at the time I thought it odd that I should be so\ncertain that Forister had my papers. However, I had no time to waste\nin thinking. I grasped my pistols. \"A black man--black as the devil,\"\ncried I to Paddy. \"Help me catch a little black man.\"\n\n\"Sure!\" said Paddy, and we sallied forth.\n\nIn a moment I was below and crying to the landlord in as fine a fury\nas any noble:\n\n\"This villain Forister! And where be he?\"\n\nThe landlord looked at me with bulging eyes. \"Master Forister,\" he\nstammered. \"Aye--aye--he's been agone these many hours since your\nlordship kicked him. He took horse, he did, for Bath, he did.\"\n\n\"Horses!\" I roared. \"Horses for two gentlemen!\" And the stableyard,\nvery respectful since my duel, began to ring with cries. The landlord\npleaded something about his bill, and in my impatience I hurled to him\nall of my gold save one piece. The horses came soon enough, and I\nleaped into the saddle and was away to Bath after Forister. As I\ngalloped out of the inn yard I heard a tumult behind me, and, looking\nback, I saw three hostlers lifting hard at Paddy to raise him into the\nsaddle. He gave a despairing cry when he perceived me leaving him at\nsuch speed, but my heart was hardened to my work. I must catch\nForister.\n\nIt was a dark and angry morning. The rain swept across my face, and\nthe wind flourished my cloak. The road, glistening steel and brown,\nwas no better than an Irish bog for hard riding. Once I passed a\nchaise with a flogging post-boy and steaming nags. Once I overtook a\nfarmer jogging somewhere on a fat mare. Otherwise I saw no travellers.\n\nI was near my journey's end when I came to a portion of the road which\ndipped down a steep hill. At the foot of this hill was an oak-tree,\nand under this tree was a man masked and mounted, and in his hand was\na levelled pistol.\n\n\"Stand!\" he said. \"Stand!\"\n\nI knew his meaning, but when a man has lost a documentary fortune and\ngiven an innkeeper all but his last guinea, he is sure to be filled\nwith fury at the appearance of a third and completing misfortune. With\na loud shout I drew my pistol and rode like a demon at the highwayman.\nHe fired, but his bullet struck nothing but the flying tails of my\ncloak. As my horse crashed into him I struck at his pate with my\npistol. An instant later we both came a mighty downfall, and when I\ncould get my eyes free of stars I arose and drew my sword. The\nhighwayman sat before me on the ground, ruefully handling his skull.\nOur two horses were scampering away into the mist.\n\nI placed my point at the highwayman's throat.\n\n\"So, my fine fellow,\" cried I grandly, \"you rob well. You are the\nprincipal knight of the road of all England, I would dare say, by the\nway in which an empty pistol overcomes you.\"\n\nHe was still ruefully handling his skull.\n\n\"Aye,\" he muttered sadly, more to himself than to me, \"a true knight\nof the road with seven ballads written of me in Bristol and three in\nBath. Ill betide me for not minding my mother's word and staying at\nhome this day. 'Tis all the unhappy luck of Jem Bottles. I should have\nremained an honest sheep-stealer and never engaged in this dangerous\nand nefarious game of lifting purses.\"\n\nThe man's genuine sorrow touched me. \"Cheer up, Jem Bottles,\" said I.\n\"All may yet be well. 'Tis not one little bang on the crown that so\ndisturbs you?\"\n\n\"'Tis not one--no,\" he answered gloomily; \"'tis two. The traveller\nriding to the east before you dealt me a similar blow--may hell catch\nthe little black devil.\"\n\n\"Black!\" cried I. \"Forister, for my life!\"\n\n\"He took no moment to tell me his name,\" responded the sullen and\nwounded highwayman. \"He beat me out of the saddle and rode away as\nbrisk as a bird. I know not what my mother will say. She be for ever\ntelling me of the danger in this trade, and here come two gentlemen in\none day and unhorse me without the profit of a sixpence to my store.\nWhen I became a highwayman I thought me I had profited me from the low\nestate of a sheep-stealer, but now I see that happiness in this life\ndoes not altogether depend upon--\"\n\n\"Enough,\" I shouted in my impatience. \"Tell me of the black man! The\nblack man, worm!\" I pricked his throat with my sword very carefully.\n\n\"He was black, and he rode like a demon, and he handled his weapons\nfinely,\" said Jem Bottles. \"And since I have told you all I know,\nplease, good sir, move the point from my throat. This will be ill news\nfor my mother.\"\n\nI took thought with myself. I must on to Bath; but the two horses had\nlong since scampered out of sight, and my pursuit of the papers would\nmake small way afoot.\n\n\"Come, Jem Bottles,\" I cried, \"help me to a horse in a comrade's way\nand for the sake of your mother. In another case I will leave you here\na bloody corse. Come; there's a good fellow!\"\n\nHe seemed moved to help me. \"Now, if there comes a well-mounted\ntraveller,\" he said, brightening, \"I will gain his horse for you if I\ndie for it.\"\n\n\"And if there comes no well-mounted traveller?\"\n\n\"I know not, sir. But--perhaps he will come.\"\n\n\"'Tis a cheap rogue who has but one horse,\" I observed contemptuously.\n\"You are only a footpad, a simple-minded marquis of the bludgeon.\"\n\nNow, as I had hoped, this deeply cut his pride.\n\n\"Did I not speak of the ballads, sir?\" he demanded with considerable\nspirit. \"Horses? Aye, and have I not three good nags hid behind my\nmother's cottage, which is less than a mile from this spot?\"\n\n\"Monsieur Jem Bottles,\" said I, not forgetting the French manners\nwhich my father had taught me, \"unless you instantly show me the way\nto these horses I shall cut off your hands, your feet, and your head;\nand, ripping out your bowels, shall sprinkle them on the road for the\nfirst post-horses to mash and trample. Do you understand my intention,\nMonsieur Jem Bottles?\"\n\n\"Sir,\" he begged, \"think of my mother!\"\n\n\"I think of the horses,\" I answered grimly. \"'Tis for you to think of\nyour mother. How could I think of your mother when I wouldn't know her\nfrom the Head of Kinsale, if it didn't happen that I know the Head of\nKinsale too well to mistake it for anybody's mother?\"\n\n\"You speak like a man from foreign parts, sir,\" he rejoined in a meek\nvoice; \"but I am able to see that your meaning is serious.\"\n\n\"'Tis so serious,\" said I, rapping him gently on the head with the\nbutt of my pistol, \"that if you don't instantly display a greedy\nactivity you will display a perfect inability to move.\"\n\n\"The speeching is obscure,\" said he, \"but the rap on the head is\nclear to me. Still, it was not kind of you to hit me on the same spot\ntwice.\"\n\nHe now arose from his mournful seat on the ground, and, still rubbing\nhis pate, he asked me to follow him. We moved from the highway into a\nvery narrow lane, and for some time proceeded in silence.\n\n\"'Tis a regular dog's life,\" spoke Jem Bottles after a period of\nreflection.\n\nBy this time I had grown a strong sympathy for my scoundrel.\n\n\"Come, cheer yourself, Jem Bottles,\" said I. \"I have known a lesser\nruffian who was hanged until he was dry, whereas you march along the\nlane with nought to your discouragement but three cracks in your\ncrown.\"\n\n\"'Tis not the cracks in the crown,\" he answered moodily. \"'Tis what my\nmother will say.\"\n\n\"I had no thought that highwaymen had mothers,\" said I. I had resolved\nnow to take care of his pride, for I saw that he was bound to be\nconsidered a great highwayman, and I did not wish to disturb his\nfeelings until I gained possession of one of the horses. But now he\ngrew as indignant as he dared.\n\n\"Mother? Mother, sir? Do you think me an illegitimate child? I say to\nyou flat in your face, even if you kill me the next instant, that I\nhave a mother. Perchance I am not of the lofty gentry who go about\nbeating honest highwaymen to the earth, but I repulse with scorn any\nman's suggestion that I am illegitimate. In a quarter of an hour you\nshall see my mother for yourself.\"\n\n\"Peace, Jem Bottles,\" said I soothingly. \"I took no thought of such a\nthing. I would be thinking only of the ballads, and how honourable it\nis that a gallant and dashing life should be celebrated in song. I,\nfor certain, have never done anything to make a pothouse ring with my\nname, and I liken you to the knights of olden days who tilted in all\nsimple fair bravery without being able to wager a brass farthing as to\nwho was right and who was wrong. Admirable Jem Bottles,\" I cried\nenthusiastically, \"tell me, if you will, of your glories; tell me with\nyour own tongue, so that when I hear the ballads waxing furious with\npraise of you, I shall recall the time I marched with your historic\nperson.\"\n\n\"My beginning was without pretence,\" said the highwayman. \"Little\nSusan, daughter of Farmer Hants, was crossing the fields with a basket\nof eggs. I, a masked figure, sprang out at her from a thicket. I\nseized the basket. She screamed. There was a frightful tumult. But in\nthe end I bore away this basket of eight eggs, creeping stealthily\nthrough the wood. The next day Farmer Hants met me. He had a long\nwhip. There was a frightful tumult. But he little knew that he was\nlaying with his whip the foundation of a career so illustrious. For a\ntime I stole his sheep, but soon grew weary of this business. Once,\nafter they had chased me almost to Bristol, I was so weary that I\nresolved to forego the thing entirely. Then I became a highwayman,\nwhom you see before you. One of the ballads begins thus:\n\n    \"What ho! the merry Jem!\n    Not a pint he gives for them.\n    All his--\"\n\n\"Stop,\" said I, \"we'll have it at Dame Bottles's fireside. Hearing\nsongs in the night air always makes me hoarse the next morning.\"\n\n\"As you will,\" he answered without heat. \"We're a'most there.\"\n\nSoon a lighted window of the highwayman's humble home shone out in the\ndarkness, and a moment later Jem Bottles was knocking at the door. It\nwas immediately opened, and he stalked in with his blood-marks still\nupon his face. There was a great outcry in a feminine voice, and a\nlarge woman rushed forward and flung her arms about the highwayman.\n\n\"Oh, Jemmie, my son, my son!\" she screamed, \"whatever have they done\nto ye this time?\"\n\n\"Silence, mother dear,\" said Bottles. \"'Tis nought but a wind-broken\nbough fallen on my head. Have you no manners? Do you not see the\ngentleman waiting to enter and warm himself?\"\n\nThe woman turned upon me, alarmed, but fiery and defiant. After a\nmoment's scrutiny she demanded:\n\n\"Oh, ho, and the gentleman had nought to do of course with my Jem's\nbroken head?\"\n\n\"'Tis a priest but newly arrived from his native island of Asia,\" said\nBottles piously; \"and it ill beseems you, mother dear, to be haggling\nwhen you might be getting the holy man and I some supper.\"\n\n\"True, Jemmie, my own,\" responded Dame Bottles. \"But there are so many\nrogues abroad that you must forgive your old mother if she grow often\naffrighted that her good Jemmie has been misled.\" She turned to me.\n\"Pardon, my good gentleman,\" she said almost in tears. \"Ye little know\nwhat it is to be the mother of a high-spirited boy.\"\n\n\"I can truthfully say that I do not, Dame Bottles,\" said I, with one\nof my father's French bows. She was immensely pleased. Any woman may\nfall a victim to a limber, manly, and courteous bow.\n\nPresently we sat down to a supper of plum-stew and bread. Bottles had\nwashed the blood from his face and now resembled an honest man.\n\n\"You may think it strange, sir,\" said Dame Bottles with some\nhousewifely embarrassment, \"that a highwayman of such distinction that\nhe has had written of him in Bristol six ballads--\"\n\n\"Seven,\" said the highwayman.\n\n\"Seven in Bristol and in Bath two.\"\n\n\"Three,\" said the highwayman.\n\n\"And three in Bath,\" continued the old woman. \"You may think it\nstrange, sir, that a highwayman of such distinction that he has had\nwritten of him in Bristol seven ballads, and in Bath three, is yet\nobliged to sit down to a supper of plum-stew and bread.\"\n\n\"Where is the rest of that cheese I took on last Michaelmas?\" demanded\nBottles suddenly.\n\n\"Jemmie,\" answered his mother with reproach, \"you know you gave the\nlast of it to the crippled shepherd over on the big hill.\"\n\n\"So I did, mother dear,\" assented the highwayman, \"and I regret now\nthat I let no less than three cheeses pass me on the highway because I\nthought we had plenty at home.\"\n\n\"If you let anything pass on the road because you do not lack it at\nthe moment, you will ultimately die of starvation, Jemmie dear,\" quoth\nthe mother. \"How often have I told you?\"\n\n\"Aye,\" he answered somewhat irritably, \"you also often have told me to\ntake snuff-boxes.\"\n\n\"And was I at fault,\" she retorted, \"because the cheating avarice of\nthe merchants led them to make sinful, paltry snuff-boxes that were\nmere pictures of the good old gold and silver? Was it my mischief? Or\nwas it the mischief of the plotting swineherds who now find it to\ntheir interest to deal in base and imitative metals?\"\n\n\"Peace, my mother,\" said the highwayman. \"The gentleman here has not\nthe same interest in snuff-boxes which moves us to loud speech.\"\n\n\"True,\" said Dame Bottles, \"and I readily wish that my Jemmie had no\nreason to care if snuff-boxes were made from cabbage-leaves.\"\n\nI had been turning a scheme in my mind, and here I thought I saw my\nopportunity to introduce it. \"Dame Bottles,\" said I, \"your words fit\nwell with the plan which has brought me here to your house. Know you,\nthen, that I am a nobleman--\"\n\n\"Alack, poor Jemmie!\" cried the woman, raising her hands.\n\n\"No,\" said I, \"I am not a nobleman rampant. I am a nobleman in\ntrouble, and I need the services of your son, for which I will reward\nhim with such richness that he will not care if they make snuff-boxes\nout of water or wind. I am in pursuit of a man--\"\n\n\"The little black man,\" cried the alert Bottles.\n\n\"And I want your son to ride with me to catch this thief. He need\nnever pass through the shadow of the creeping, clanking tree. He will\nbe on an honest hunt to recover a great property. Give him to me. Give\nhim fourteen guineas from his store, and bid us mount his horses and\naway. Save your son!\"\n\nThe old woman burst into tears. \"Sir,\" she answered, \"I know little of\nyou, but, as near as I can see in the light of this one candle, you\nare a hangel. Take my boy! Treat him as you would your own stepson,\nand if snuff-boxes ever get better I will let you both hear of it.\"\n\nLess than an hour later Jem Bottles and I were off for Bath, riding\ntwo very good horses.\n\n\n\n\nCHAPTER IV\n\n\nNow my whole mind was really bent on finding my black Forister, but\nyet, as Jem Bottles and I rode toward Bath, I thought of a cloaked\nfigure and a pair of shining eyes, and it seemed to me that I recalled\nthe curve of sweet, proud lips. I knew that I should be thinking of my\npapers, my future; but a quick perversity made me dwell for a long\ntrotting time in a dream of feminine excellence, in a dream of\nfeminine beauty which was both ascetic and deeply sensuous. I know\nhardly how to say that two eyes, a vision of lips, a conception of a\nfigure, should properly move me as I bounced along the road with Jem\nBottles. But it is certain that it came upon me. The eyes of the\ndaughter of the great Earl of Westport had put in chains the\nredoubtable O'Ruddy. It was true. It was clear. I admitted it to\nmyself. The admission caused a number of reflections to occur in my\nmind, and the chief of these was that I was a misfortunate wretch.\n\nJem Bottles recalled me to the immediate business.\n\n\"'Tis the lights of Bath, sir,\" he said, \"and if it please you, sir, I\nshall await you under yonder tree, since the wretched balladists have\nrendered me so well known in the town that I dare not venture in it\nfor fear of a popular welcome from the people who have no snuff-boxes\nwhatever.\"\n\n\"I will go and listen to the ballads,\" I replied, \"and in the mean\ntime do you await me here under that tree.\"\n\nSo saying I galloped into Bath, my soul sharp to find Forister and to\ntake him by the neck and strangle out of him those papers which were\nmy sole reasons for living. But the landlord of the best inn met me\nwith an unmistakable frankness.\n\n\"Mr. Forister?\" said he. \"Yes, your lordship, but Mr. Forister is gone\nback to Bristol.\"\n\nI was so pleased with his calling me \"your lordship\" that I hesitated\na moment. But I was recalled to sense by the thought that although Jem\nBottles and I had fifteen guineas between us, he had fourteen and I\nhad the one. Thanking the landlord I galloped out of Bath.\n\nBottles was awaiting me under the tree. \"To Bristol,\" I cried. \"Our\nchase lies toward Bristol. He has doubled back.\"\n\n\"'Twas while we were at supper,\" said Bottles, as he cantered up to my\nshoulder. \"I might have had two trials at him if I had not had the\nhonour of meeting your worship. I warrant you, sir, he would not have\nescaped me twice.\"\n\n\"Think of his crack in your skull, and be content,\" I replied. \"And in\nthe mean time ride for Bristol.\"\n\nWithin five miles of Bristol we came upon a wayside inn in which there\nwas progressing a great commotion. Lights flashed from window to\nwindow, and we could hear women howling. To my great surprise Bottles\nat once became hugely excited.\n\n\"Damme, sir,\" he shouted, \"my sweetheart is a chambermaid here, and if\nshe be hurted I will know it.\"\n\nHe spurred valiantly forward, and, after futilely calling to him to\ncheck his career, I followed. He leaped from his horse at the door of\nthe inn and bounced into the place, pistol in hand. I was too confused\nto understand much, but it seemed to my ears that his entrance was\nhailed with a roar of relief and joy. A stable-boy, fearfully anxious,\ngrasped my bridle, crying, \"Go in, sir, in God's name. They will be\nkilling each other.\" Thinking that, whatever betide, it was proper to\nbe at the back of my friend Bottles, I too sprang from my horse and\npopped into the inn.\n\nA more unexpected sight never met my experienced gaze. A fat landlady,\nmark you, was sobbing in the arms of my villainous friend, and a\npretty maid was clinging to his arm and screaming. At the same time\nthere were about him a dozen people of both sexes who were yelling,--\n\n\"Oh, pray, Master Bottles! Good Master Bottles, do stop them. One is a\ngreat Afric chief, red as a fire, and the other is Satan, Satan\nhimself! Oh, pray, good Master Bottles, stop them!\"\n\nMy fine highwayman was puffed out like a poisoned frog. I had no\nthought that he could be so grand.\n\n\"What is this disturbance?\" he demanded in a bass voice.\n\n\"O good Master Bottles,\" clamoured the people. \"Satan wishes to kill\nthe Red Giant, who has Satan barred in the best room in the inn. And\nthey make frightful destruction of chairs and tables. Bid them cease,\nO good Master Bottles!\"\n\nFrom overhead we could hear the sound of blows upon wood mingled with\nthreatening talk.\n\n\"Stand aside,\" said the highwayman in a great gruff voice which made\nme marvel at him. He unhesitatingly dumped the swooning form of the\nlandlady into another pair of arms, shook off the pretty maid, and\nmoved sublimely upon the foot of the stairs amid exclamations of joy,\nwonder, admiration, even reverence.\n\nBut the voice of an unseen person hailed suddenly from the head of the\nstairs.\n\n\"And if ye have not said enough masses for your heathen soul,\"\nremarked the voice, \"you would be better mustering the neighbours this\ninstant to go to church for you and bid them do the best they can in a\nshort time. You will never be coming downstairs if you once come up.\"\n\nBottles hesitated; the company shuddered out: \"'Tis the Red Giant.\"\n\n\"And I would be having one more word with you,\" continued the unseen\nperson. \"I have him here, and here I keep him. 'Tis not me that wants\nthe little black rogue, what with his hammering on the door and his\ncalling me out of my name. 'Tis no work that I like, and I would lever\ngo in and put my heel in his face. But I was told to catch a little\nblack man, and I have him, and him I will keep. 'Tis not me that\nwished to come here and catch little black men for anybody; but here I\nam in this foreign country, catching little black men, and I will have\nno interference.\"\n\nBut here I gave a great call of recognition.\n\n\"Paddy!\"\n\nI saw the whole thing. This wild-headed Paddy, whom I had told to\ncatch me a little black man, had followed after me toward Bath and\nsomehow managed to barricade in a room the very first man he saw who\nwas small and black. At first I wished to laugh; an instant later I\nwas furious.\n\n\"Paddy,\" I thundered; \"come down out of that now! What would you be\ndoing? Come down out of that now!\"\n\nThe reply was sulky, but unmistakably from Paddy. Most of it was\nmumbled.\n\n\"Sure I've gone and caught as little and as black a man as is in the\nwhole world, and was keeping the scoundrel here safe, and along he\ncomes and tells me to come down out of that now with no more gratitude\nthan if he had given me a gold goose. And yet I fought a duel for him\nand managed everything so finely that he came away well enough to box\nme on the ear, which was mere hilarity and means nothing between\nfriends.\"\n\nJem Bottles was still halted on the stair. He and all the others had\nlistened to Paddy's speeches in a blank amazement which had much\nsuperstition in it.\n\n\"Shall I go up, sir?\" he asked, not eagerly.\n\n\"No,\" said I. \"Leave me to deal with it. I fear a great mistake. Give\nme ten minutes, and I promise to empty the inn of all uproar.\"\n\nA murmur of admiration arose, and as the sound leaped about my ears I\nmoved casually and indifferently up against Paddy. It was a grand\nscene.\n\n\"Paddy,\" I whispered as soon as I had reached a place on the stairs\nsafe from the ears of the people below. \"Paddy, you have made a great\nblunder. You have the wrong man.\"\n\n\"'Tis unlikely,\" replied Paddy with scorn. \"You wait until you see\nhim, and if he is not little and black, then--\"\n\n\"Yes, yes,\" said I hastily, \"but it was not any little black man at\nall which I wanted. It was a particular little black man.\"\n\n\"But,\" said the ruffian brightly, \"it would be possible this one will\nserve your end. He's little and he's black.\"\n\nAt this moment the voice of the captive came intoning through the door\nof a chamber.\n\n\"When I am free I will first cut out your liver and have it grilled,\nand feed it to you as you are dying.\"\n\nPaddy had stepped forward and placed his lips within about six inches\nof one of the panels.\n\n\"Come now, be easy!\" he said. \"You know well that if you should do as\nyou say, I would beat your head that it would have the looks of a\npudding fallen from a high window, and that's the truth.\"\n\n\"Open the door, rascal,\" called the captive, \"and we shall see.\"\n\n\"I will be opening no doors,\" retorted Paddy indignantly. \"Remain\nquiet, you little black devil, or, by the mass, I'll--\"\n\n\"I'll slice your heart into pieces of paper,\" thundered Paddy's\nprisoner, kicking and pounding.\n\nBy this time I was ready to interfere. \"Paddy,\" said I, catching him\nby the shoulder, \"you have the wrong man. Leave it to me; mind you,\nleave it to me.\"\n\n\"He's that small and black you'd think--\" he began dejectedly, but I\ncut him short.\n\nJem Bottles, unable to endure the suspense, had come up from below.\nHe was still bristling and blustering, as if all the maids were\nremarking him.\n\n\"And why does this fine gentleman kick and pound on the door?\" he\ndemanded in a gruff voice loud enough to be heard in all appreciative\nparts of the inn. \"I'll have him out and slit his nose.\"\n\nThe thunder on the door ceased, and the captive observed:\n\n\"Ha! another scoundrel! If my ears do not play me false, there are now\nthree waiting for me to kick them to the hangman.\"\n\nRestraining Paddy and Bottles, who each wished to reply in heroic\nverse to this sally, I stepped to the door.\n\n\"Sir,\" said I civilly, \"I fear a great blunder has been done. I--\"\n\n\"Why,\" said the captive with a sneer, \"'tis the Irishman! 'Tis the\nking of the Irelands. Open the door, pig.\"\n\nMy elation knew no bounds.\n\n\"Paddy,\" cried I, \"you have the right little black man.\" But there was\nno time for celebration. I must first answer my enemy. \"You will\nremember that I kicked you once,\" said I, \"and if you have a memory as\nlong as my finger be careful I do not kick you again, else even people\nas far away as the French will think you are a meteor. But I would not\nbe bandying words at long range. Paddy, unbar the door.\"\n\n\"If I can,\" muttered Paddy, fumbling with a lot of machinery so\ningenious that it would require a great lack of knowledge to\nthoroughly understand it. In the mean time we could hear Forister move\naway from the door, and by the sound of a leisurely scrape of a chair\non the floor I judge he had taken his seat somewhere near the centre\nof the room. Bottles was handling his pistol and regarding me.\n\n\"Yes,\" said I, \"if he fires, do you pepper him fairly. Otherwise await\nmy orders. Paddy, you slug, unbar the door.\"\n\n\"If I am able,\" said Paddy, still muttering and fumbling with his\ncontrivances. He had no sooner mouthed the words than the door flew\nopen as if by magic, and we discovered a room bright with the light of\na fire and candles. Forister was seated negligently at a table in the\ncentre of the room. His legs were crossed, but his naked sword lay on\nthe table at his hand. He had the first word, because I was amazed,\nalmost stunned, by the precipitous opening of the door.\n\n\"Ho! ho!\" he observed frigidly, \"'tis indeed the king of the Irelands,\naccompanied by the red-headed duke who has entertained me for some\ntime, and a third party with a thief's face who handles a loaded\npistol with such abandon as leads me to suppose that he once may have\nbeen a highwayman. A very pretty band.\"\n\n\"Use your tongue for a garter, Forister,\" said I. \"I want my papers.\"\n\n\n\n\nCHAPTER V\n\n\n\"Your 'papers'?\" said Forister. \"Damn you and your papers. What would\nI know of your papers?\"\n\n\"I mean,\" said I fiercely, \"the papers that you stole out of my\nchamber in the inn at Bristol.\"\n\nThe man actually sank back in his chair and laughed me up to the roof.\n\n\"'Papers'!\" he shouted. \"Here's the king of the Irelands thinking that\nI have made off with his papers!\"\n\n\"You choose a good time for laughing,\" said I, with more sobriety. \"In\na short time you will be laughing with the back of your head.\"\n\nHe sat up and looked at me with quick decision.\n\n\"Now, what is all this rubbish about papers?\" he said sharply. \"What\nhave I to do with your filthy papers? I had one intention regarding\nyou,--of that I am certain. I was resolved to kill you on the first\noccasion when we could cross swords, but--'papers'--faugh! What do you\nmean?\"\n\nThe hoarse voice of Jem Bottles broke in from somewhere behind me. \"We\nmight easily throw him to the earth and tie him, sir, and then make\nsearch of him.\"\n\n\"And you would know how to go about the business, I warrant me,\"\nlaughed Forister. \"You muzzle-faced rogue, you!\"\n\nTo my astonishment the redoubtable highwayman gave back before the\neasy disdain of this superior scoundrel.\n\n\"My ways may not always have been straight and narrow, master,\" he\nrejoined, almost in a whine, \"but you have no call to name me\nmuzzle-faced.\"\n\nForister turned from him contemptuously and fixed his regard with much\nenthusiasm upon Paddy.\n\n\"Very red,\" said he. \"Very red, indeed. And thick as fagots, too. A\nvery delectable head of hair, fit to be spun into a thousand blankets\nfor the naked savages in heathen parts. The wild forests in Ireland\nmust indeed be dark when it requires a lantern of this measure to\nlight the lonely traveller on his way.\"\n\nBut Paddy was an honest man even if he did not know it, and he at once\nwalked to Forister and held against his ear a fist the size of a pig's\nhind-leg.\n\n\"I cannot throw the talk back to you,\" he said. \"You are too fast for\nme, but I tell you to your face that you had better change your tongue\nfor a lock of an old witch's hair unless you intend to be battered\nthis moment.\"\n\n\"Peace,\" said Forister calmly. \"I am a man of natural wit, and I would\nentertain myself. Now, there is your excellent chieftain the king of\nthe Irelands. Him I regard as a very good specimen, whose ancestors\nwere not very long ago swinging by their tails from the lofty palms of\nIreland and playing with cocoanuts to and fro.\" He smiled and leaned\nback, well satisfied with himself.\n\nAll this time I had been silent, because I had been deep in reflection\nupon Forister. Now I said:\n\n\"Forister, you are a great rogue. I know you. One thing is certain.\nYou have not my papers and never did you have them.\"\n\nHe looked upon me with some admiration and cried:\n\n\"Aye, the cannibal shows a glimmer of reason. No, I have not your\nfoolish papers, and I only wish I had them in order to hurl the bundle\nat your damned stupid head.\"\n\n\"For a kicked man you have a gay spirit,\" I replied. \"But at any rate\nI have no time for you now. I am off to Bristol after my papers, and I\nonly wish for the sake of ease that I had to go no farther than this\nchamber. Come, Paddy! Come, Jem!\"\n\nMy two henchmen were manifestly disappointed; they turned reluctantly\nat my word.\n\n\"Have I the leave of one crack at him, your honour?\" whispered Paddy\nearnestly. \"He said my head was a lantern.\"\n\n\"No,\" said I, \"leave him to his meditations.\"\n\nAs we passed down the corridor we heard him laugh loudly, and he\ncalled out to me,--\n\n\"When I come to Bristol I will kill you.\"\n\nI had more than a mind to go back and stuff this threat into his\nthroat, but I better knew my business, which was to recover the\npapers.\n\n\"Come,\" said I, and we passed down stairs.\n\nThe people of the inn made way for Paddy as if he had been a falling\ntree, and at the same time they worshipped Jem Bottles for having\nperformed everything. I had some wonder as to which would be able to\nout-strut the other. I think Jem Bottles won the match, for he had the\nadvantage of being known as one of the most dangerous men in\nsouthwestern England, whereas Paddy had only his vanity to help him.\n\n\"'Tis all arranged,\" said Bottles pompously. \"Your devil will come\nforth as quiet as a rabbit.\"\n\nWe ordered our horses, and a small crowd of obsequious stable-boys\nrushed to fetch them. I marvelled when I saw them lead out Paddy's\nhorse. I had thought from what I perceived over my shoulder when I\nleft Bristol that he would never be able to make half a league in the\nsaddle. Amid the flicker of lanterns, Bottles and I mounted and then I\nheard Paddy calling to him all the stable-boys:\n\n\"Now, when I give the word, you heave for your lives. Stand, you\nbeast! Cannot four of you hold him by the legs? I will be giving the\nword in a moment. Are you all ready? Well, now, ready again--heave!\"\n\nThere was a short scuffle in the darkness, and presently Paddy\nappeared above the heads of the others in the _melee_.\n\n\"There, now,\" said he to them, \"that was well done. One would easily\nbe telling that I was an ex-trooper of the king.\" He rode out to us\ncomplacently. \"'Tis a good horse, if only he steered with a tiller\ninstead of these straps,\" he remarked, \"and he goes well before the\nwind.\"\n\n\"To Bristol,\" said I. \"Paddy, you must follow as best you may. I have\nno time to be watching you, although you are interesting.\"\n\nAn unhappy cry came from behind Bottles, and I spurred on, but again I\ncould not wait for my faithful countryman. My papers were still the\nstake for which I played. However I hoped that Paddy would now give\nover his ideas about catching little black men.\n\nAs we neared Bristol Jem Bottles once more became backward. He\nreferred to the seven ballads, and feared that the unexpected presence\nof such a well-known character would create an excitement which would\nnot be easy to cool. So we made a rendezvous under another tree, and I\nrode on alone. Thus I was separated from both my good companions.\nHowever, before parting, I took occasion to borrow five guineas from\nJem's store.\n\nI was as weary as a dog, although I had never been told that gentlemen\nriding amid such adventures were ever aweary. At the inn in Bristol a\nsleepy boy took my horse, and a sleepy landlord aroused himself as he\nrecognized me.\n\n\"My poor inn is at your disposal, sir,\" he cried as he bowed. \"The\nEarl has inquired for you to-day, or yesterday, as well as my young\nLord Strepp and Colonel Royale.\"\n\n\"Aye?\" said I carelessly. \"Did they so? Show me to a chamber. I am\nmuch enwearied. I would seek a good bed and a sound sleep, for I have\nridden far and done much since last I had repose.\"\n\n\"Yes, sir,\" said the landlord deferentially.\n\nAfter a long hard sleep I was aroused by a constant pounding on my\ndoor. At my cry a servant entered. He was very abject. \"His lordship's\nvalet has been waiting to give you a message from his lordship, sir.\"\nI bid him let the valet enter. The man whose heroic nose had borne the\nbrunt of Forister's swift departure from the inn when I kicked him\ncame into my chamber with distinguished grace and dignity and informed\nme that his noble master cared to see me in his chamber when it would\nsuit my convenience.\n\nOf course the old Earl was after his papers. And what was I to tell\nhim,--that I was all befooled and befuddled?--that after my father had\nkept these papers for so many years in faithful trust I had lost them\non the very brink of deliverance of them to their rightful owner? What\nwas I to speak?\n\nI did not wish to see the Earl of Westport, but some sudden and\ncurious courage forced me into my clothes and out to the corridor. The\nEarl's valet was waiting there. \"I pray you, sir, follow me,\" he said.\nI followed him to an expensive part of the inn, where he knocked upon\na door. It was opened by a bending serving-man. The room was a kind of\nparlour, and in it, to my surprise, were Lord Strepp and Colonel\nRoyale. They gazed at me with a surprise equivalent to mine own.\n\nYoung Lord Strepp was the first one thoroughly to collect himself.\nThen he advanced upon me with outstretched hand.\n\n\"Mr. O'Ruddy,\" he cried, \"believe me, we are glad to see you. We\nthought you had gone for all time.\"\n\nColonel Royale was only a moment behind his friend, but as he extended\nhis hand his face flushed painfully.\n\n\"Sir,\" he said somewhat formally, \"not long ago I lost my temper, I\nfear. I know I have to thank you for great consideration and\ngenerosity. I--I--you--\"\n\nWhereupon we both began to stammer and grimace. All the time I was\nchocking out:\n\n\"Pray--pray--, don't speak of it--a--nothing--in truth, you kindly\nexaggerate--I--\"\n\nIt was young Lord Strepp who brought us out of our embarrassment.\n\"Here, you two good fellows,\" he cried heartily, \"a glass of wine with\nyou.\"\n\nWe looked gratefully at him, and in the business of filling our\nglasses we lost our awkwardness. \"To you,\" said Lord Strepp; and as we\ndrained our wine I knew that I had two more friends in England.\n\nDuring the drinking the Earl's valet had been hovering near my\ncoat-tails. Afterward he took occasion to make gentle suggestion to\nme:\n\n\"His lordship awaits your presence in his chamber, sir, when it\npleases you.\"\n\nThe other gentlemen immediately deferred to my obligation, and I\nfollowed the valet into a large darkened chamber. It was some moments\nbefore my eyes could discover that the Earl was abed. Indeed, a\nrasping voice from beneath the canopies called to me before I knew\nthat anybody was in the chamber but myself and the valet.\n\n\"Come hither, O'Ruddy,\" called the Earl. \"Tompkins, get out! Is it\nyour duty to stand there mummified? Get out!\"\n\nThe servant hastily withdrew, and I walked slowly to the great man's\nbedside. Two shining shrewd eyes looked at me from a mass of pillows,\nand I had a knowledge of an aged face, half smiling and yet satirical,\neven malignant.\n\n\"And so this is the young fortune-hunter from Ireland,\" he said in a\nhoarse sick-man's voice. \"The young fortune-hunter! Ha! With his\nworthless papers! Ha!\"\n\n\"Worthless?\" cried I, starting.\n\n\"Worthless!\" cried the Earl vehemently. He tried to lift himself in\nhis bed, in order to make more emphasis. \"Worthless! Nothing but\nstraw--straw--straw!\" Then he cackled out a laugh.\n\nAnd this was my inheritance! I could have sobbed my grief and anger,\nbut I took firm hold on myself and resolved upon another way of\ndealing with the nobleman.\n\n\"My lord,\" said I coolly, \"My father is dead. When he was dying he\ngave certain papers into my hands,--papers which he had guarded for\nmany years,--and bade me, as his son, to deliver them into the hands\nof an old friend and comrade; and I come to this old friend and\ncomrade of my father, and he lies back in his bed and cackles at me\nlike a hen. 'Tis a small foot I would have set upon England if I had\nknown more of you, you old skate!\"\n\nBut still he laughed and cried: \"Straw! Straw! Nothing but straw!\"\n\n\"Well, sir,\" said I with icy dignity, \"I may be a fool of an Irishman\nwith no title save an older one than yours; but I would be deeply\nsorry if there came a day when I should throw a trust back in the\nteeth of a dead comrade's son.\"\n\n\"No,\" said the bright-eyed old man, comforting himself amid his\npillows. \"Look you, O'Ruddy! You are a rascal! You came over in an\nattempt to ruin me! I know it!\"\n\nI was awed by this accusation. It seemed to me to be too grand, too\ngorgeous for my personal consumption. I knew not what to do with this\ncolossus. It towered above me in splendour and gilt. I had never\nexpected to be challenged with attempting to ruin earls. My father had\noften ruined sea-captains, but he never in his life ruined so much as\na baronet. It seemed altogether too fine for my family, but I could\nonly blurt weakly, \"Yessir.\" I was much like a lackey.\n\n\"Aye,\" said the old man, suddenly feeble from the excitement, \"I see\nyou admit it, you black Irish rogue.\" He sank back and applied a\nnapkin to his mouth. It seemed to come away stained with blood. \"You\nscoundrel!\"\n\nI had a strange cowardly inclination to fling myself upon this ancient\nsurvival and squeeze his throat until it closed like a pursel. And my\ninclination was so strong that I stood like a stone.\n\nThe valet opened the door. \"If it please your Lordship--Lady Mary,\" he\nannounced, and stood aside to let a lady pass. The Earl seemed\nimmediately to forget my presence. He began at once to make himself\nuncomfortable in his bed. Then he cried fretfully: \"Come, Mary, what\ncaused you to be so long? Make me easy! Ruffle my pillows! Come,\ndaughter.\"\n\n\"Yes, father,\" answered a soothing and sweet voice. A gracious figure\npassed before me and bended over the bed of the Earl. I was near\nblinded. It was not a natural blindness. It was an artificial\nblindness which came from my emotion. Was she tall? I don't know. Was\nshe short? I don't know. But I am certain that she was exactly of the\nright size. She was, in all ways, perfection. She was of such glory,\nshe was so splendid, that my heart ceased to beat. I remained standing\nlike a stone, but my sword scabbard, reminiscent of some movement,\nflapped gently against my leg. I thought it was a horrible sound. I\nsought to stay it, but it continued to tinkle, and I remember that,\nstanding there in the room with the old Earl and my love-'til-death, I\nthought most of my scabbard and its inability to lay quiet at my\nthigh.\n\nShe smoothed his bed and coaxed him and comforted him. Never had I\nseen such tenderness. It was like a vision of a classic hereafter. In\na second I would have exchanged my youth for the position of this\ndoddering old nobleman who spat blood into a napkin.\n\nSuddenly the Earl wheeled his eyes and saw me.\n\n\"Ha, Mary!\" he cried feebly, \"I wish to point out a rogue. There he\nstands! The O'Ruddy! An Irishman and a fine robber! Mark him well, and\nkeep stern watch of your jewels.\"\n\nThe beautiful young lady turned upon me an affrighted glance. And I\nstood like a stone.\n\n\"Aye,\" said the old wretch, \"keep stern watch of your jewels. He is a\nvery demon for skill. He could take a ring from your finger while you\nwere thinking he was fluttering his hands in the air.\"\n\nI bowed gallantly to the young lady. \"Your rings are safe, my lady. I\nwould ill requite the kindness shown by your father to the son of an\nold friend if I deprived your white fingers of a single ornament.\"\n\n\"Clever as ever, clever as ever,\" chuckled the wicked old man.\n\nThe young lady flushed and looked first at me and then at her father.\nI thought her eye, as it rested upon me, was not without some\nsympathetic feeling. I adored her. All the same I wished to kill her\nfather. It is very curious when one wishes to kill the father of the\nwoman one adores. But I suppose the situation was made more possible\nfor me by the fact that it would have been extremely inexpedient to\nhave killed the Earl in his sick bed. I even grinned at him.\n\n\"If you remember my father, your lordship,\" said I amiably, \"despite\nyour trying hard to forget him, you will remember that he had a\ncertain native wit which on occasion led him to be able to frustrate\nhis enemies. It must have been a family trait, for I seem to have it.\nYou are an evil old man! You yourself stole my papers!\"\n\n\n\n\nCHAPTER VI\n\n\nAt first I thought that my speech had given the aged Earl a stroke. He\nwrithed on his bed, and something appeared at his lips which was like\nfroth. His lovely daughter sprang to him with a cry of fear and woe.\nBut he was not dying; he was only mad with rage.\n\n\"How dare you? How dare you?\" he gasped. \"You whelp of Satan!\"\n\n\"'Tis me that would not be fearing to dare anything,\" I rejoined\ncalmly. \"I would not so. I came here with a mind for fair words, but\nyou have met me with insult and something worse. We cannot talk the\nthing. We must act it. The papers are yours, but you took them from me\nunfairly. You may destroy them. Otherwise I will have them back and\ndiscover what turned you into a great rogue near the end of your\ndays.\"\n\n\"Hearken!\" screamed the Earl. \"Hearken! He threatens.\" The door into\nthe parlour flew open, and Lord Strepp and Colonel Royale appeared on\nthe threshold, their faces blank with wonder.\n\n\"Father,\" cried the young lord, stepping hastily forward, \"whatever is\nwrong?\"\n\n\"That!\" screamed the Earl, pointing a palsied finger at me. \"That! He\ncomes here and threatens _me_,--a peer of England.\"\n\nThe Lady Mary spoke swiftly to her brother and the Colonel.\n\n\"'Tis a sick man's fancy,\" she said. \"There have been no threats.\nFather has had a bad day. He is not himself. He talks wildly. He--\"\n\n\"Mary!\" yelled the Earl as well as he was able. \"Do you betray me? Do\nyou betray your own father? Oh, a woman Judas and my daughter!\"\n\nLord Strepp and Colonel Royale looked as if their minds were coming\napart. They stared at Lady Mary, at the Earl, at me. For my part I\nremained silent and stiff in a corner, keeping my eye upon the swords\nof the other gentlemen. I had no doubt but that presently I would be\nengaged in a desperate attempt to preserve my life. Lady Mary was\nweeping. She had never once glanced in my direction. But I was\nthrilling with happiness. She had flung me her feeble intercession\neven as a lady may fling a bun to a bear in a pit, but I had the\nremembrance to prize, to treasure, and if both gentlemen had set upon\nme and the sick Earl had advanced with the warming-pan I believe my\nnew strength would have been able to beat them off.\n\nIn the meantime the Earl was screeching meaningless rubbish in which\nmy name, with epithets, occurred constantly. Lady Mary, still weeping,\nwas trying to calm him.\n\nYoung Lord Strepp at last seemed to make up his mind. He approached me\nand remarked:\n\n\"An inexplicable situation, Mr. O'Ruddy.\"\n\n\"More to me than to you,\" I repeated suavely.\n\n\"How?\" he asked, with less consideration in his manner. \"I know nought\nof this mummery.\"\n\n\"At least I know no more,\" I replied, still suave.\n\n\"How, Mr. O'Ruddy?\" he asked, frowning. \"I enter and find you\nwrangling with my father in his sick chamber. Is there to be no word\nfor this?\"\n\n\"I dare say you will get forty from your father; a hundred, it may\nbe,\" said I, always pleasant. \"But from me you will get none.\"\n\nHe reflected for a moment. \"I dare say you understand I will brook no\nhigh-handed silence in a matter of this kind. I am accustomed to ask\nfor the reasons for certain kinds of conduct, and of course I am\nsomewhat prepared to see that the reasons are forthcoming.\"\n\n\"Well, in this case, my lord,\" said I with a smile, \"you can accustom\nyourself to not getting a reason for a certain kind of conduct,\nbecause I do not intend to explain myself.\"\n\nBut at this moment our agreeable conversation was interrupted by the\nold Earl who began to bay at his son. \"Arthur, Arthur, fling the\nrascal out; fling the rascal out! He is an impostor, a thief!\" He\nbegan to fume and sputter, and threw his arms wildly; he was in some\nkind of convulsion; his pillows tossed, and suddenly a packet fell\nfrom under them to the floor. As all eyes wheeled toward it, I stooped\nswiftly and picked it up.\n\n\"My papers!\" said I.\n\nOn their part there was a breathless moment of indecision. Then the\nswords of Lord Strepp and the Colonel came wildly from their\nscabbards. Mine was whipped out no less speedily, but I took it and\nflung it on the floor at their feet, the hilt toward them. \"No,\" said\nI, my hands empty save for the papers, \"'tis only that I would be\nmaking a present to the fair Lady Mary, which I pray her to receive.\"\nWith my best Irish bow I extended to the young lady the papers, my\ninheritance, which had caused her father so much foaming at the mouth.\n\nShe looked at me scornfully, she looked at her father, she looked at\nme pathetically, she looked at her father, she looked at me piteously;\nshe took the papers.\n\nI walked to the lowering and abashed points of the other men's swords,\nand picked my blade from the floor. I paid no heed to the glittering\npoints which flashed near my eyes. I strode to the door; I turned and\nbowed; as I did so, I believe I saw something in Lady Mary's eyes\nwhich I wished to see there. I closed the door behind me.\n\nBut immediately there was a great clamour in the room I had left, and\nthe door was thrown violently open again. Colonel Royale appeared in a\nhigh passion:\n\n\"No, no, O'Ruddy,\" he shouted, \"you are a gallant gentleman. I would\nstake my life that you are in the right. Say the word, and I will back\nyou to the end against ten thousand fiends.\"\n\nAnd after him came tempestuously young Lord Strepp, white on the lips\nwith pure rage. But he spoke with a sudden steadiness.\n\n\"Colonel Royale, it appears,\" he said, \"thinks he has to protect my\nfriend The O'Ruddy from some wrong of my family or of mine?\"\n\nThe Colonel drew in his breath for a dangerous reply, but I quickly\nbroke in:\n\n\"Come, come, gentlemen,\" said I sharply. \"Are swords to flash between\nfriends when there are so many damned scoundrels in the world to parry\nand pink? 'Tis wrong; 'tis very wrong. Now, mark you, let us be men of\npeace at least until to-morrow morning, when, by the way, I have to\nfight your friend Forister.\"\n\n\"Forister!\" they cried together. Their jaws fell; their eyes bulged;\nthey forgot everything; there was a silence.\n\n\"Well,\" said I, wishing to reassure them, \"it may not be to-morrow\nmorning. He only told me that he would kill me as soon as he came to\nBristol, and I expect him to-night or in the morning. I would of\ncourse be expecting him to show here as quickly as possible after his\ngrand speech; but he would not be entirely unwelcome, I am thinking,\nfor I have a mind to see if the sword of an honest man, but no\nfighter, would be able to put this rogue to shame, and him with all\nhis high talk about killing people who have never done a thing in life\nto him but kick him some number of feet out into the inn yard, and\nthis need never to have happened if he had known enough to have kept\nhis sense of humour to himself, which often happens in this world.\"\n\nReflectively, Colonel Royale murmured:\n\n\"One of the finest swordsmen in England.\"\n\nFor this I cared nothing.\n\nReflectively, Lord Strepp murmured: \"My father's partner in the\nshipping trade.\"\n\nThis last made me open my eyes. \"Your father's partner in the shipping\ntrade, Lord Strepp? That little black rascal?\"\n\nThe young nobleman looked sheepish.\n\n\"Aye, I doubt not he may well be called a little black rascal,\nO'Ruddy,\" he answered; \"but in fact he is my father's partner in\ncertain large--fairly large, you know--shipping interests. Of course\nthat is a matter of no consequence to me personally--but--I believe my\nfather likes him, and my mother and my sister are quite fond of him, I\nthink. I, myself, have never been able to quite--quite understand him\nin certain ways. He seems a trifle odd at moments. But he certainly is\na friend of the family.\"\n\n\"Then,\" said I, \"you will not be able to have the felicity of seeing\nhim kill me, Lord Strepp.\"\n\n\"On the contrary,\" he rejoined considerately, \"I would regard it as\nusual if he asked me to accompany him to the scene of the fight.\"\n\nHis remark, incidentally, that his sister was fond of Forister, filled\nme with a sudden insolent madness.\n\n\"I would hesitate to disturb any shipping trade,\" I said with dignity.\n\"It is far from me to wish that the commerce of Great Britain should\nbe hampered by sword-thrust of mine. If it would please young Lord\nStrepp, I could hand my apologies to Forister all tied up in blue-silk\nribbon.\"\n\nBut the youthful nobleman only looked at me long with a sad and\nreproachful gaze.\n\n\"O'Ruddy,\" he said mournfully, \"I have seen you do two fine things.\nYou have never seen me do anything. But, know you now, once and for\nall, that you may not quarrel with me.\"\n\nThis was too much for an Irish heart. I was moved to throw myself on\nthis lad's neck. I wished to swear to him that I was a brother in\nblood, I wished to cut a vein to give him everlasting strength--but\nperhaps his sister Mary had something to do with this feeling.\n\nColonel Royale had been fidgeting. Now he said suddenly:\n\n\"Strepp, I wronged you. Your pardon, Mr. O'Ruddy; but, damme, Strepp,\nif I didn't think you had gone wrong for the moment.\"\n\nLord Strepp took the offered hand. \"You are a stupid old firebrain,\"\nhe said affectionately to the Colonel.\n\n\"Well,\" said the Colonel jubilantly, \"now everything is clear. If Mr.\nO'Ruddy will have me, I will go with him to meet this Forister; and\nyou, Strepp, will accompany Forister; and we all will meet in a\nfriendly way--ahem!\"\n\n\"The situation is intimately involved,\" said Lord Strepp dejectedly.\n\"It will be a ridiculous business--watching each blade lunge toward\nthe breast of a friend. I don't know that it is proper. Royale, let us\nset ourselves to part these duellists. It is indecent.\"\n\n\"Did you note the manner in which he kicked him out of the inn?\" asked\nthe Colonel. \"Do you think a few soothing words would calm the mind of\none of the finest swordsmen in England?\"\n\nI began to do some profound thinking.\n\n\"Look you, Colonel,\" said I. \"Do you mean that this wretched little\nliar and coward is a fine swordsman?\"\n\n\"I haven't heard what you call him,\" said the Colonel, \"but his\nsword-play is regular firelight on the wall. However,\" he added\nhopefully, \"we may find some way to keep him from killing you. I have\nseen some of the greatest swordsmen lose by chance to a novice. It is\nsomething like cards. And yet you are not an ignorant player. That, I,\nClarence Royale, know full well. Let us try to beat him.\"\n\nI remembered Forister's parting sentence. Could it be true that a man\nI had kicked with such enthusiasm and success was now about to take\nrevenge by killing me? I was really disturbed. I was a very brave\nyouth, but I had the most advanced ideas about being killed. On\noccasion of great danger I could easily and tranquilly develop a\nphilosophy of avoidance and retirement. I had no antiquated notions\nabout going out and getting myself killed through sheer bull-headed\nscorn of the other fellow's hurting me. My father had taught me this\ndiscretion. As a soldier he claimed that he had run away from nine\nbattles, and he would have run away from more, he said, only that all\nthe others had turned out to be victories for his side. He was\nadmittedly a brave man, but, more than this, he had a great deal of\nsense. I was the child of my father. It did not seem to me profitable\nto be killed for the sake of a sentiment which seemed weak and\ndispensable. This little villain! Should I allow him to gratify a\nfurious revenge because I was afraid to take to my heels? I resolved\nto have the courage of my emotions. I would run away.\n\nBut of all this I said nothing. It passed through my mind like light\nand left me still smiling gayly at Colonel Royale's observations upon\nthe situation.\n\n\"Wounds in the body from Forister,\" quoth he academically, \"are almost\ncertain to be fatal, for his wrist has a magnificent twist which\nreminds one of a top. I do not know where he learned this wrist\nmovement, but almost invariably it leads him to kill his man. Last\nyear I saw him--I digress. I must look to it that O'Ruddy has quiet,\nrest, and peace of mind until the morning.\"\n\nYes; I would have great peace of mind until the morning! I saw that\nclearly.\n\n\"Well,\" said I, \"at any rate we will know more to-morrow. A good day\nto you, Lord Strepp, and I hope your principal has no more harm come\nto him than I care to have come to me, which is precious little, and\nin which case the two of us will be little hurted.\"\n\n\"Good-bye, O'Ruddy,\" said the young man.\n\nIn the corridor the Colonel slapped my shoulder in a sudden exuberant\noutburst.\n\n\"O'Ruddy,\" he cried, \"the chance of your life! Probably the best-known\nswordsman in all England! 'Pon my word, if you should even graze him,\nit would almost make you a peer. If you truly pinked him, you could\nmarry a duchess. My eye, what an opportunity for a young and ambitious\nman.\"\n\n\"And what right has he to be such a fine swordsman?\" I demanded\nfretfully. \"Damn him! 'Tis no right of a little tadpole like him to be\na great cut-throat. One could never have told from the look of him,\nand yet it simply teaches one to be always cautious with men.\"\n\nThe Colonel was bubbling over with good nature, his mind full of the\nprospective event.\n\n\"I saw Ponsonby kill Stewart in their great fight several years\nagone,\" he cried, rubbing his hands, \"but Ponsonby was no such\nswordsman as Forister, and I misdoubt me that Stewart was much better\nthan you yourself.\"\n\nHere was a cheerful butcher. I eyed him coldly.\n\n\"And out of this,\" said I slowly, \"comes a vast deal of entertainment\nfor you, and a hole between two ribs for me. I think I need a drink.\"\n\n\"By all means, my boy,\" he answered, heartily. \"Come to my chamber. A\nquart of port under your waistcoat will cure a certain bilious desire\nin you to see the worst of things, which I have detected lately in\nyour manner. With grand sport before us, how could you be otherwise\nthan jolly? Ha, Ha!\"\n\nSo saying, he affectionately took my arm and led me along the\ncorridor.\n\n\n\n\nCHAPTER VII\n\n\nWhen I reached my own chamber I sank heavily into a chair. My brain\nwas in a tumult. I had fallen in love and arranged to be killed in one\nshort day's work. I stared at my image in a mirror. Could I be The\nO'Ruddy? Perhaps my name was Paddy or Jem Bottles? Could I pick myself\nout in a crowd? Could I establish my identification? I little knew.\n\nAt first I thought of my calm friend who apparently drank blood for\nhis breakfast. Colonel Royale to me was somewhat of a stranger, but\nhis charming willingness to grind the bones of his friends in his\nteeth was now quite clear. I fight the best swordsman in England as an\namusement, a show? I began to see reasons for returning to Ireland. It\nwas doubtful if old Mickey Clancy would be able to take full care of\nmy estate even with the assistance and prevention of Father Donovan.\nAll properties looked better while the real owner had his eye on them.\nIt would be a shame to waste the place at Glandore all for a bit of\npride of staying in England. Never a man neglected his patrimony but\nthat it didn't melt down to a kick in the breeches and much trouble in\nthe courts. I perceived, in short, that my Irish lands were in danger.\nWhat could endanger them was not quite clear to my eye, but at any\nrate they must be saved. Moreover it was necessary to take quick\nmeasures. I started up from my chair, hastily recounting Jem Bottles's\nfive guineas.\n\nBut I bethought me of Lady Mary. She could hardly be my good fairy.\nShe was rather too plump to be a fairy. She was not extremely plump,\nbut when she walked something moved within her skirts. For my part I\nthink little of fairies, who remind me of roasted fowl's wing. Give me\nthe less brittle beauty which is not likely to break in a man's arms.\n\nAfter all, I reflected, Mickey Clancy could take care quite well of\nthat estate at Glandore; and, if he didn't, Father Donovan would soon\nbring him to trouble; and, if Father Donovan couldn't, why, the place\nwas worth very little any how. Besides, 'tis a very weak man who\ncannot throw an estate into the air for a pair of bright eyes.\n\nAye, and Lady Mary's bright eyes! That was one matter. And there was\nForister's bright sword. That was another matter. But to my\ndescendants I declare that my hesitation did not endure an instant.\nForister might have an arm so supple and a sword so long that he might\nbe able to touch the nape of his neck with his own point, but I was\nfirm on English soil. I would meet him even if he were a _chevaux de\nfrise_. Little it mattered to me. He might swing the ten arms of an\nIndian god; he might yell like a gale at sea; he might be more\nterrible in appearance than a volcano in its passions; still I would\nmeet him.\n\nThere was a knock, and at my bidding a servant approached and said: \"A\ngentleman, Mr. Forister, wishes to see you, sir.\"\n\nFor a moment I was privately in a panic. Should I say that I was ill,\nand then send for a doctor to prove that I was not ill? Should I run\nstraightway and hide under the bed? No!\n\n\"Bid the gentleman enter,\" said I to the servant.\n\nForister came in smiling, cool and deadly. \"Good day to you, Mr.\nO'Ruddy,\" he said, showing me his little teeth. \"I am glad to see that\nyou are not for the moment consorting with highwaymen and other\nabandoned characters who might succeed in corrupting your morals, Mr.\nO'Ruddy. I have decided to kill you, Mr. O'Ruddy. You may have heard\nthat I am the finest swordsman in England, Mr. O'Ruddy?\"\n\nI replied calmly: \"I have heard that you are the finest swordsman in\nEngland, Mr. Forister, whenever better swordsmen have been traveling\nin foreign parts, Mr. Forister, and when no visitors of fencing\ndistinction have taken occasion to journey here, Mr. Forister.\"\n\nThis talk did not give him pleasure, evidently. He had entered with\nbrave composure, but now he bit his lip and shot me a glance of\nhatred. \"I only wished to announce,\" he said savagely, \"that I would\nprefer to kill you in the morning as early as possible.\"\n\n\"And how may I render my small assistance to you, Mr. Forister? Have\nyou come to request me to arise at an untimely hour?\"\n\nI was very placid; but it was not for him to be coming to my chamber\nwith talk of killing me. Still, I thought that, inasmuch as he was\nthere, I might do some good to myself by irritating him slightly. I\ncontinued:\n\n\"I to-day informed my friends--\"\n\n\"Your friends!\" said he.\n\n\"My friends,\" said I. \"Colonel Royale in this matter.\"\n\n\"Colonel Royale!\" said he.\n\n\"Colonel Royale,\" said I. \"And if you are bound to talk more you had\nbest thrust your head from the window and talk to those chimneys\nthere, which will take far more interest in your speech than I can\nwork up. I was telling you that to-day I informed my friends--then you\ninterrupted me. Well, I informed them--but what the devil I informed\nthem of you will not know very soon. I can promise you, however, it\nwas not a thing you would care to hear with your hands tied behind\nyou.\"\n\n\"Here's a cold man with a belly full of ice,\" said he musingly. \"I\nhave wronged him. He has a tongue on him, he has that. And here I have\nbeen judging from his appearance that he was a mere common dolt. And,\nwhat, Mr. O'Ruddy,\" he added, \"were you pleased to say to the\ngentlemen which I would not care to hear with my hands tied behind\nme?\"\n\n\"I told them why you took that sudden trip to Bristol,\" I answered\nsoftly.\n\nHe fairly leaped in a sudden wild rage. \"You--told them?\" he\nstuttered. \"You poltroon! 'Twas a coward's work!\"\n\n\"Be easy,\" said I, to soothe him. \"'Tis no more cowardly than it is\nfor the best swordsman in England to be fighting the worst swordsman\nin Ireland over a matter in which he is entirely in the wrong,\nalthough 'tis not me that cares one way or another way. Indeed, I\nprefer you to be in the wrong, you little black pig.\"\n\n\"Stop,\" said he, with a face as white as milk. \"You told them--you\ntold them about--about the girl at Bristol?\"\n\n\"What girl at Bristol?\" said I innocently. \"'Tis not me to be knowing\nyour wenches in Bristol or otherwheres.\"\n\nA red flush came into the side of his neck and swelled slowly across\nhis cheeks. \"If you've told them about Nell!\"\n\n\"Nell?\" said I. \"Nell? Yes, that's the name. Nell. Yes, Nell. And if I\ntold them about Nell?\"\n\n\"Then,\" he rejoined solemnly, \"I shall kill you ten times if I lose my\nsoul in everlasting hell for it.\"\n\n\"But after I have killed you eleven times I shall go to Bristol and\nhave some sweet interviews with fair Nell,\" said I. This sting I\nexpected to call forth a terrific outburst, but he remained scowling\nin dark thought. Then I saw where I had been wrong. This Nell was now\nmore a shame than a sweetheart, and he was afraid that word had been\npassed by me to the brother of--Here was a chance to disturb him.\n\"When I was making my little joke of you and your flame at Bristol,\"\nsaid I thoughtfully, \"I believe there were no ladies present. I don't\nremember quite. Any how we will let that pass. 'Tis of no\nconsequence.\"\n\nAnd here I got him in full cry. \"_God rot you!_\" he shrieked. His\nsword sprang and whistled in the air.\n\n\"Hold,\" said I, as a man of peace. \"'Twould be murder. My weapon is on\nthe bed, and I am too lazy to go and fetch it. And in the mean time\nlet me assure you that no word has crossed my lips in regard to Nell,\nyour Bristol sweetheart, for the very excellent reason that I never\nknew of her existence until you yourself told me some moments ago.\"\n\nNever before had he met a man like me. I thought his under-jaw would\ndrop on the floor.\n\n\"Up to a short time ago,\" said I candidly, \"your indecent amours were\nsafe from my knowledge. I can be in the way of putting myself as\nsilent as a turtle when it comes to protecting a man from his folly\nwith a woman. In fact, I am a gentleman. But,\" I added sternly, \"what\nof the child?\"\n\n\"The child?\" he cried jumping. \"May hell swallow you! And what may you\nknow of the child?\"\n\nI waved my hand in gentle deprecation of his excitement as I said:\n\n\"Peace, Forister; I know nothing of any child. It was only an\nobservation by a man of natural wit who desired to entertain himself.\nAnd, pray, how old is the infant?\"\n\nHe breathed heavily. \"You are a fiend,\" he answered. Keeping his eyes\non the floor, he deliberated upon his choice of conduct. Presently he\nsheathed his sword and turned with some of his old jauntiness toward\nthe door. \"Very good,\" said he. \"To-morrow we shall know more of our\nown affairs.\"\n\n\"True,\" I replied.\n\n\"We shall learn if slyness and treachery are to be defeated by\nfair-going and honour.\"\n\n\"True,\" said I.\n\n\"We shall learn if a snake in the grass can with freedom bite the foot\nof a lion.\"\n\n\"True,\" said I.\n\nThere was a loud jovial clamour at the door, and at my cry it flew\nopen. Colonel Royale entered precipitately, beaming with good humour.\n\n\"O'Ruddy, you rascal,\" he shouted, \"I commanded you to take much rest,\nand here I find--\" He halted abruptly as he perceived my other\nvisitor. \"And here I find,\" he repeated coldly, \"here I find Mr.\nForister.\"\n\nForister saluted with finished politeness. \"My friend and I,\" he said,\n\"were discussing the probabilities of my killing him in the morning.\nHe seems to think that he has some small chance for his life, but I\nhave assured him that any real betting man would not wager a grain of\nsand that he would see the sun go down to-morrow.\"\n\n\"Even so,\" rejoined the Colonel imperturbably.\n\n\"And I also suggested to my friend,\" pursued Forister, \"that to-morrow\nI would sacrifice my ruffles for him, although I always abominate\nhaving a man's life-blood about my wrists.\"\n\n\"Even so,\" quoth the undisturbed Colonel.\n\n\"And further I suggested to my friend that if he came to the ground\nwith a coffin on his back, it might promote expedition after the\naffair was over.\"\n\nColonel Royale turned away with a gesture of disgust.\n\nI thought it was high time to play an ace at Forister and stop his\nbabble, so I said:\n\n\"And when Mr. Forister had finished his graceful remarks we had some\ntalk regarding Mr. Forister's affairs in Bristol, and I confess I was\nmuch interested in hearing about the little--\"\n\nHere I stopped abruptly, as if I had been interrupted by Forister;\nbut he had given me no sign but a sickly grin.\n\n\"Eh, Forister?\" said I. \"What's that?\"\n\n\"I was remarking that I had nothing further to say for the present,\"\nhe replied, with superb insolence. \"For the time I am quite willing to\nbe silent. I bid you a good day, sirs.\"\n\n\n\n\nCHAPTER VIII\n\n\nAs the door closed upon Forister, Colonel Royale beat his hand\npassionately against the wall. \"O'Ruddy,\" he cried, \"if you could\nseverely maim that cold-blooded bully, I would be willing to adopt you\nas my legitimate grandfather. I would indeed.\"\n\n\"Never fear me,\" said I. \"I shall pink him well.\"\n\n\"Aye,\" said my friend, looking at me mournfully, \"I ever feared your\nIrish light-heartedness. 'Twill not do to be confident. He is an evil\nman, but a great swordsman. Now I never liked Ponsonby, and Stewart\nwas the most lovable of men; but in the great duel Ponsonby killed--\"\n\n\"No,\" I interrupted, \"damn the duel between Ponsonby and Stewart. I'm\nsick of it. This is to be the duel between The O'Ruddy and Forister,\nand it won't be like the other.\"\n\n\"Eh, well,\" said the Colonel good-naturedly; \"make your mind easy. But\nI hope to God you lay him flat.\"\n\n\"After I have finished with him,\" said I in measured tones, \"he will\nbe willing to sell himself as a sailor to go to the Indies; only, poor\ndevil, he won't be able to walk, which is always a drawback after a\nhard fight, since it leaves one man incapable on the ground and thus\ndiscloses strong evidence of a struggle.\"\n\nI could see that Colonel Royale had no admiration for my bragging air,\nbut how otherwise was I to keep up my spirits? With all my\ndiscouragements it seemed to me that I was privileged to do a little\nfine lying. Had my father been in my place, he would have lied\nForister into such a corner that the man would be thinking that he had\nthe devil for an opponent. My father knew more about such matters.\n\nStill I could not help but be thinking how misfortunate it was that I\nhad kicked a great swordsman out of this inn at Bristol when he might\nhave been a harmless shoemaker if I had only decent luck. I must make\nthe best of it, and for this my only method was to talk loudly,--to\nmyself, if need be; to others if I could. I was not the kind that is\nquite unable to say a good word for itself even if I was not able to\nlie as well as my father in his prime. In his day he could lie the\ncoat off a man's back, or the patches off a lady's cheek, and he could\nlie a good dog into howling ominously. Still it was my duty to lie as\nwell as I was able.\n\nAfter a time Lord Strepp was announced and entered. Both he and\nColonel Royale immediately stiffened and decided not to perceive each\nother. \"Sir,\" said Lord Strepp to me, \"I have the honour to present my\ncompliments to you, and to request that you join a friend of mine, Mr.\nForister, at dawn to-morrow, in the settlement of a certain small\nmisunderstanding.\"\n\n\"Sir,\" said I, in the same manner, \"I am only too happy to have this\nlittle matter adjusted.\"\n\n\"And of course the arrangements, sir?\"\n\n\"For them I may refer you to my friend Colonel Royale.\"\n\n\"Ah,\" said the young Lord, as if he had never before seen the Colonel.\n\n\"I am at your service, sir,\" said Colonel Royale as if he never in his\nwhole life had heard of Lord Strepp.\n\nThen these two began to salaam one another, and mouth out fool\nphrases, and cavort and prance and caracole, until I thought them mad.\nWhen they departed there was a dreadful scene. Each refused to go\nthrough the door before the other. There was a frightful deadlock.\nThey each bowed and scraped and waved their hands, and surrendered the\ndoorway back and forth, until I thought they were to be in my chamber\neternally. Lord Strepp gorgeously presented the right of way to\nColonel Royale, and the Colonel gorgeously presented the right of way\nto Lord Strepp. All this time they were bending their backs at each\nother.\n\nFinally I could stand it no longer. \"In God's name,\" I shouted, \"the\ndoor is wide enough for the two of you. Take it together. You will go\nthrough like grease. Never fear the door. 'Tis a good wide door.\"\n\nTo my surprise, they turned to glance at me and burst into great\nlaughter. Then they passed out amiably enough together. I was alone.\n\nWell, the first thing I did was to think. I thought with all my force.\nI fancied the top of my skull was coming off. I thought myself into\nten thousand intricacies. I thought myself into doom and out of it,\nand behind it and below it, but I could not think of anything which\nwas of service to me. It seemed that I had come among a lot of\nmummers, and one of these mummers was resolved to kill me, although I\nhad never even so much as broken his leg. But I remembered my father's\nword, who had told me that gentlemen should properly kill each other\nover a matter of one liking oranges and the other not liking oranges.\nIt was the custom among men of position, he had said, and of course a\nway was not clear to changing this custom at the time. However, I\ndetermined that if I lived I would insist upon all these customs being\nmoderated and re-directed. For my part I was willing that any man\nshould like oranges.\n\nI decided that I must go for a walk. To sit and gloom in my room until\nthe time of the great affair would do me no good in any case. In fact\nit was likely to do me much harm. I went forth to the garden in the\nrear of the inn. Here spread a lawn more level than a ballroom floor.\nThere was a summer-house and many beds of flowers. On this day there\nwas nobody abroad in the garden but an atrocious parrot, which,\nbalancing on its stick, called out continually raucous cries in a\nforeign tongue.\n\nI paced the lawn for a time, and then took a seat in the summer-house.\nI had been there but a moment when I perceived Lady Mary and the\nCountess come into the garden. Through the leafy walls of the\nsummer-house I watched them as they walked slowly to and fro on the\ngrass. The mother had evidently a great deal to say to the daughter.\nShe waved her arms and spoke with a keen excitement.\n\nBut did I overhear anything? I overheard nothing! From what I knew of\nthe proper conduct of the really thrilling episodes of life I judged\nthat I should have been able to overhear almost every word of this\nconversation. Instead, I could only see the Countess making irritated\nspeech to Lady Mary.\n\nMoreover it was legitimate that I should have been undetected in the\nsummer-house. On the contrary, they were perfectly aware that there\nwas somebody there, and so in their promenade they presented it with a\ndistinguished isolation.\n\nNo old maid ever held her ears so wide open. But I could hear nothing\nbut a murmur of angry argument from the Countess and a murmur of\ngentle objection from Lady Mary. I was in possession of an ideal place\nfrom which to overhear conversation. Almost every important\nconversation ever held had been overheard from a position of this\nkind. It seemed unfair that I, of all men in literature, should be\ndenied this casual and usual privilege.\n\nThe Countess harangued in a low voice at great length; Lady Mary\nanswered from time to time, admitting this and admitting that,\nprotesting against the other. It seemed certain to me that talk\nrelated to Forister, although I had no real reason for thinking it.\nAnd I was extremely angry that the Countess of Westport and her\ndaughter, Lady Mary Strepp, should talk of Forister.\n\nUpon my indignant meditations the parrot interpolated:\n\n\"Ho, ho!\" it cried hoarsely. \"A pretty lady! A pretty lady! A pretty\nlady! A pretty lady!--\"\n\nLady Mary smiled at this vacuous repetition, but her mother went into\na great rage, opening her old jaws like a maddened horse. \"Here,\nlandlord! Here, waiter! Here, anybody!\"\n\nSo people came running from the inn, and at their head was, truly\nenough, the landlord. \"My lady,\" he cried panting.\n\nShe pointed an angry and terrible finger at the parrot. \"When I walk\nin this garden, am I to be troubled with this wretched bird?\"\n\nThe landlord almost bit the turf while the servants from the inn\ngrovelled near him. \"My lady,\" he cried, \"the bird shall be removed at\nonce.\" He ran forward. The parrot was chained by its leg to a tall\nperch. As the innkeeper came away with the entire business, the parrot\nbegan to shout: \"Old harridan! Old harridan! Old harridan!\" The\ninnkeeper seemed to me to be about to die of wild terror. It was a\ndreadful moment. One could not help but feel sorry for this poor\nwretch, whose sole offence was that he kept an inn and also chose to\nkeep a parrot in his garden.\n\nThe Countess sailed grandly toward the door of the hotel. To the\nsolemn protestations of six or seven servants she paid no heed. At the\ndoor she paused and turned for the intimate remark. \"I cannot endure\nparrots,\" she said impressively. To this dictum the menials crouched.\n\nThe servants departed: the garden was now empty save for Lady Mary and\nme. She continued a pensive strolling. Now, I could see plainly that\nhere fate had arranged for some kind of interview. The whole thing was\nset like a scene in a theatre. I was undoubtedly to emerge suddenly\nfrom the summer-house; the lovely maid would startle, blush, cast down\nher eyes, turn away. Then, when it came my turn, I would doff my hat\nto the earth and beg pardon for continuing a comparatively futile\nexistence. Then she would slyly murmur a disclaimer of any ability to\ncriticise my continuation of a comparatively futile existence, adding\nthat she was but an inexperienced girl. The ice thus being broken, we\nwould travel by easy stages into more intimate talk.\n\nI looked down carefully at my apparel and flecked a handkerchief over\nit. I tilted my hat; I set my hip against my harbour. A moment of\nindecision, of weakness, and I was out of the summer-house. God knows\nhow I hoped that Lady Mary would not run away.\n\nBut the moment she saw me she came swiftly to me. I almost lost my\nwits.\n\n\"'Tis the very gentleman I wished to see,\" she cried. She was\nblushing, it is true, but it was evident she intended to say nothing\nabout inexperience or mere weak girls. \"I wished to see you because--\"\nshe hesitated and then rapidly said: \"It was about the papers. I\nwanted to thank you--I--you have no notion how happy the possession of\nthe papers has made my father. It seemed to have given him new life.\nI--I saw you throw your sword on the floor with the hilt away from\nyou. And--and then you gave me the papers. I knew you were a gallant\ngentleman.\"\n\nAll this time, I, in my confusion, was bobbing and murmuring pledges\nof service. But if I was confused, Lady Mary was soon cool enough in\nthe presence of a simple bog-trotter like me. Her beautiful eyes\nlooked at me reflectively.\n\n\"There is only one service I can render you, sir,\" said she softly.\n\"'Tis advice which would have been useful in saving some men's lives\nif only they had received it. I mean--don't fight with Forister in the\nmorning. 'Tis certain death.\"\n\nIt was now my turn once more. I drew myself up, and for the first time\nI looked squarely into her bright eyes.\n\n\"My lady,\" said I, with mournful dignity, \"I was filled with pride\nwhen you said the good word to me. But what am I to think now? Am I,\nafter all, such a poor stick that, to your mind, I could be advised to\nsell my honour for a mere fear of being killed?\"\n\nEven then I remembered my one-time decision to run away from the duel\nwith Forister; but we will not be thinking of that now.\n\nTears came into Lady Mary's eyes. \"Ah, now, I have blundered,\" she\nsaid. \"'Tis what you would say, sir. 'Tis what you would do. I have\nonly made matters worse. A woman's meddling often results in the\ndestruction of those she--those she don't care to have killed.\"\n\nOne would think from the look of this last sentence, that with certain\nreason I could have felt somewhat elated without being altogether a\nfool. Lady Mary meant nothing of importance by her speech, but it was\na little bit for a man who was hungry to have her think of him. But\nhere I was assailed by a very demon of jealousy and distrust. This\nbeautiful witch had some plan in her head which did not concern my\nwelfare at all. Why should she, a great lady, take any trouble for a\npoor devil who was living at an inn on money borrowed from a\nhighwayman. I had been highly honoured by an indifferent\nconsideration born of a wish to be polite to a man who had eased the\nmind of her father. No; I would not deceive myself.\n\nBut her tears! Were they marking indifferent consideration? For a\nsecond I lost myself in a roseate impossible dream. I dreamed that she\nhad spoken to me because she--\n\nOh, what folly! Even as I dreamed, she turned to me with splendid\ncarriage, and remarked coldly:\n\n\"I did not wish you to suppose that I ever failed to pay a debt. I\nhave paid this one. Proceed now, sir, in your glowing stupidity. I\nhave done.\"\n\nWhen I recovered myself she was placidly moving away from me toward\nthe door of the inn.\n\n\n\n\nCHAPTER IX\n\n\nI had better be getting to the story of the duel. I have been hanging\nback with it long enough, and I shall tell it at once. I remember my\nfather saying that the most aggravating creature in life was one who\nwould be keeping back the best part of a story through mere reasons of\ntrickery, although I have seen himself dawdle over a tale until his\nfriends wished to hurl the decanters at him. However, there can be no\ndoubting of the wisdom of my father's remark. Indeed there can be\nlittle doubting of the wisdom of anything that my father said in life,\nfor he was a very learned man. The fact that my father did not\ninvariably defer to his own opinions does not alter the truth of those\nopinions in my judgment, since even the greatest of philosophers is\nmore likely to be living a life based on the temper of his wife and\nthe advice of his physician than on the rules laid down in his books.\nNor am I certain that my father was in a regular habit of delaying a\nstory. I only remember this one incident, wherein he was recounting a\nstirring tale of a fight with a lancer, and just as the lance was\nwithin an inch of the paternal breast my father was reminded, by a\nsight of the walnuts, that Mickey Clancy was not serving the port with\nhis usual rapidity, and so he addressed him. I remember the words\nwell.\n\n\"Mickey, you spalpeen,\" said my father, \"would you be leaving the\ngentlemen as dry as the bottom of Moses' feet when he crossed the Red\nSea? Look at O'Mahoney there! He is as thirsty as a fish in the top of\na tree. And Father Donovan has had but two small quarts, and he never\ntakes less than five. Bad luck to you, Mickey, if it was a drink for\nyour own stomach, you would be moving faster. Are you wishing to ruin\nmy reputation for hospitality, you rogue you?\"\n\nAnd my father was going on with Mickey, only that he looked about him\nat this time and discovered his guests all upon their feet, one with\nthe tongs and one with the poker, others with decanters ready to\nthrow.\n\n\"What's this?\" said he.\n\n\"The lance,\" said they.\n\n\"What lance?\" said he.\n\n\"The lance of the lancer,\" said they.\n\n\"And why shouldn't he have a lance?\" said my father. \"'Faith, 'twould\nbe an odd lancer without a lance!\"\n\nBy this time they were so angry that Mickey, seeing how things were\ngoing, and I being a mere lad, took me from the room. I never heard\nprecisely what happened to the lancer, but he must have had the worst\nof it, for wasn't my father, seated there at the table, telling the\nstory long years after?\n\nWell, as to my duel with Forister: Colonel Royale was an extremely\nbusy man, and almost tired my life out with a quantity of needless\nattentions. For my part, I thought more of Lady Mary and the fact that\nshe considered me no more than if I had been a spud. Colonel Royale\nfluttered about me. I would have gruffly sent him away if it were not\nthat everything he did was meant in kindliness and generous feeling. I\nwas already believing that he did not have more than one brain in his\nhead, but I could not be ungrateful for his interest and enthusiasm in\ngetting me out to be hurt correctly. I understood, long years\nafterward, that he and Lord Strepp were each so particular in the\nnegotiations that no less than eighteen bottles of wine were consumed.\n\nThe morning for the duel dawned softly warm, softly wet, softly foggy.\nThe Colonel popped into my room the moment I was dressed. To my\nsurprise, he was now quite mournful. It was I, now, who had to do the\ncheering.\n\n\"Your spirits are low, Colonel?\" said I banteringly.\n\n\"Aye, O'Ruddy,\" he answered with an effort, \"I had a bad night, with\nthe gout. Heaven help this devil from getting his sword into your\nbowels.\"\n\nHe had made the appointment with Strepp, of course, and as we walked\ntoward the ground he looked at me very curiously out of the ends of\nhis eyes. \"You know--ah, you have the honour of the acquaintance of\nLady Mary Strepp, O'Ruddy?\" said he suddenly and nervously.\n\n\"I have,\" I answered, stiffening. Then I said: \"And you?\"\n\n\"Her father and I were friends before either of you were born,\" he\nsaid simply. \"I was a cornet in his old regiment. Little Lady Mary\nplayed at the knee of the poor young subaltern.\"\n\n\"Oh,\" said I meanly, \"you are, then, a kind of uncle.\"\n\n\"Aye,\" said he, \"a kind of uncle. So much of an uncle,\" he added with\nmore energy, \"that when she gave me this note I thought much of acting\nlike a real uncle. From what I have unfortunately overheard, I suspect\nthat the Earl--aw--disagrees with you on certain points.\"\n\nHe averted his face as he handed me the note, and eagerly I tore it\nopen. It was unsigned. It contained but three words: \"God spare you!\"\nAnd so I marched in a tumult of joy to a duel wherein I was expected\nto be killed.\n\nI glanced at the Colonel. His countenance was deeply mournful. \"'Tis\nfor few girls I would become a dove to carry notes between lovers,\" he\nsaid gloomily. \"Damn you for it, O'Ruddy!\"\n\n\"Nay, Colonel,\" said I. \"'Tis no missive of love. Look you!\"\n\nBut still he kept his eyes averted. \"I judge it was not meant for my\neyes,\" he said, still very gloomy.\n\nBut here I flamed up in wrath:\n\n\"And would the eye of an angel be allowed to rest upon this paper if\nit were not fit that it should be so?\" I demanded in my anger.\n\"Colonel, am I to hear you bleat about doves and lovers when a glance\nof your eye will disabuse you? Read!\"\n\nHe read. \"'God spare you!'\" he repeated tenderly. Then he addressed me\nwith fine candor. \"Aye, I have watched her these many years, O'Ruddy.\nWhen she was a babe I have seen her in her little bath. When she was a\nsmall girl I have seen her asleep with some trinket clasped in her\nrosy hand on the coverlet. Since she has been a beautiful young lady I\nhave--but no matter. You come along, named nobody, hailing from\nnowhere; and she--she sends me out to deliver her prayer that God may\nspare you!\"\n\nI was awed by this middle-aged sorrow. But, curse him! when she was a\nbabe he had seen her in her little bath, had he? Damn his eyes! He had\nseen the baby naked in her tiny tub? Damn his eyes again! I was in\nsuch a fury that I longed to fight Royale on the spot and kill him,\nrunning my sword through his memory so that it would be blotted out\nforever, and never, never again, even in Paradise, could he recall the\nimage in the little tub.\n\nBut the Colonel's next words took the rage out of me.\n\n\"Go in, O'Ruddy,\" he cried heartily. \"There is no truer man could win\nher. As my lady says, 'God spare you!'\"\n\n\"And if Forister's blade be not too brisk, I will manage to be\nspared,\" I rejoined.\n\n\"Oh, there is another thing touching the matter,\" said the Colonel\nsuddenly. \"Forister is your chief rival, although I little know what\nhas passed between them. Nothing important, I think, although I am\nsure Forister is resolved to have her for a bride. Of that I am\ncertain. He is resolved.\"\n\n\"Is he so?\" said I.\n\nI was numb and cold for a moment. Then I slowly began to boil, like a\nkettle freshly placed on the fire. So I was facing a rival? Well, and\nhe would get such a facing as few men had received. And he was my\nrival and in the breast of my coat I wore a note--\"God spare you!\" Ha,\nha! He little knew the advantages under which he was to play. Could I\nlose with \"God spare you!\" against my heart? Not against three\nForisters!\n\nBut hold! might it not be that the gentle Lady Mary, deprecating this\nduel and filled with feelings of humanity, had sent us each a note\nwith this fervid cry for God to spare us? I was forced to concede it\npossible. After all, I perfectly well knew that to Lady Mary I was a\nmere nothing. Royale's words had been so many plumes in my life's\nhelmet, but at bottom I knew better than to set great store by them.\nThe whole thing was now to hurry to the duelling-ground and see if I\ncould discover from this black Forister's face if he had received a\n\"God spare you!\" I took the Colonel's arm and fairly dragged him.\n\n\"Damme, O'Ruddy!\" said he, puffing; \"this can be nought but genuine\neagerness.\"\n\nWhen we came to the duelling-place we found Lord Strepp and Forister\npacing to and fro, while the top of a near-by wall was crowded with\npleasant-minded spectators. \"Aye, you've come, have ye, sirs?\" called\nout the rabble. Lord Strepp seemed rather annoyed, and Colonel Royale\ngrew red and stepped peremptorily toward the wall, but Forister and I\nhad eyes only for each other. His eye for me was a glad, cruel eye. I\nhave a dim remembrance of seeing the Colonel take his scabbard and\nincontinently beat many worthy citizens of Bristol; indeed, he seemed\nto beat every worthy citizen of Bristol who had not legs enough to get\naway. I could hear them squeaking out protests while I keenly studied\nthe jubilant Forister.\n\nAye, it was true. He too had a \"God spare you!\" I felt my blood begin\nto run hot. My eyes suddenly cleared as if I had been empowered with\nmiraculous vision. My arm became supple as a whip. I decided upon one\nthing. I would kill Forister.\n\nI thought the Colonel never would give over chasing citizens, but at\nlast he returned breathless, having scattered the populace over a wide\nstretch of country. The preliminaries were very simple. In a\nhalf-minute Forister and I, in our shirts, faced each other.\n\nAnd now I passed into such a state of fury that I cannot find words to\ndescribe it; but, as I have said, I was possessed with a remarkable\nclearness of vision and strength of arm. These phenomena amaze me even\nat this day. I was so airy upon my feet that I might have been a\nspirit. I think great rages work thus upon some natures. Their\ncompetence is suddenly made manifold. They live, for a brief space,\nthe life of giants. Rage is destruction active. Whenever anything in\nthis world needs to be destroyed, nature makes somebody wrathful.\nAnother thing that I recall is that I had not the slightest doubt of\nmy ability to kill Forister. There were no more misgivings: no\nquakings. I thought of the impending duel with delight.\n\nIn all my midnight meditations upon the fight I had pictured myself as\nlying strictly upon the defensive and seeking a chance opportunity to\ndamage my redoubtable opponent. But the moment after our swords had\ncrossed I was an absolute demon of attack. My very first lunge made\nhim give back a long pace. I saw his confident face change to a look\nof fierce excitement.\n\nThere is little to say of the flying, spinning blades. It is only\nnecessary to remark that Forister dropped almost immediately to\ndefensive tactics before an assault which was not only impetuous but\nexceedingly brilliant, if I may be allowed to say so. And I know that\non my left a certain Colonel Royale was steadily growing happier.\n\nThe end came with an almost ridiculous swiftness. The feeling of an\nugly quivering wrench communicated itself from the point of my sword\nto my mind; I heard Strepp and Royale cry \"Hold!\" I saw Forister fall;\nI lowered my point and stood dizzily thinking. My sight was now\nblurred; my arm was weak.\n\nMy sword had gone deep into Forister's left shoulder, and the bones\nthere had given that hideous feeling of a quivering wrench. He was not\ninjured beyond repair, but he was in exquisite agony. Before they\ncould reach him he turned over on his elbows and managed in some way\nto fling his sword at me. \"Damn your soul!\" he cried, and he gave a\nsort of howl as Lord Strepp, grim and unceremonious, bounced him over\nagain upon his back. In the mean time Colonel Royale was helping me on\nwith my coat and waistcoat, although I hardly knew that either he or\nthe coat or waistcoat were in existence.\n\nI had my usual inclination to go forward and explain to everybody how\nit all had happened. But Royale took me forcibly by the arm, and we\nturned our backs on Strepp and Forister and walked toward the inn.\n\nAs soon as we were out of their sight, Colonel Royale clasped my hands\nwith rapture. \"My boy,\" he cried, \"you are great! You are renowned!\nYou are illustrious! What a game you could give Ponsonby! You would\ngive him such a stir!\"\n\n\"Never doubt me,\" said I. \"But I am now your legitimate grandfather,\nand I should be treated with great respect.\"\n\nWhen we came near the inn I began to glance up at the windows. I\nsurely expected to see a face at one of them. Certainly she would care\nto know who was slain or who was hurt. She would be watching, I fondly\nhoped, to see who returned on his legs. But the front of the inn\nstared at us, chilly and vacant, like a prison wall.\n\nWhen we entered, the Colonel bawled lustily for an immediate bottle of\nwine, and I joined him in its drinking, for I knew that it would be a\nbellows to my flagging spirits. I had set my heart upon seeing a face\nat the window of the inn.\n\n\n\n\nCHAPTER X\n\n\nAnd now I found out what it was to be a famous swordsman. All that day\nthe inn seemed to hum with my name. I could not step down a corridor\nwithout seeing flocks of servants taking wing. They fled tumultuously.\nA silly maid coming from a chamber with a bucket saw me and shrieked.\nShe dropped her bucket and fled back into the chamber. A man-servant\nsaw me, gave a low moan of terror, and leaped down a convenient\nstairway. All attendants scuttled aside.\n\nWhat was the matter with me? Had I grown in stature or developed a\nferocious ugliness? No; I now was a famous swordsman. That was all. I\nnow was expected to try to grab the maids and kiss them wantonly. I\nnow was expected to clout the grooms on their ears if they so much as\nshowed themselves in my sight. In fact, I was now a great blustering,\noverpowering, preposterous ass.\n\nThere was a crowd of people in the coffee-room, but the buzz of talk\nsuddenly ceased as I entered.\n\n\"Is this your chair, sir?\" said I civilly to a gentleman.\n\nHe stepped away from the chair as if it had tried to bite him.\n\n\"'Tis at your service, sir!\" he cried hastily.\n\n\"No,\" said I, \"I would not be taking it if it be yours, for there are\njust as good chairs in the sea as ever were caught, and it would ill\nbecome me to deprive a gentleman of his chair when by exercising a\nlittle energy I can gain one for myself, although I am willing to\nadmit that I have a slight hunger upon me. 'Tis a fine morning, sir.\"\n\nHe had turned pale and was edging toward the door. \"'Tis at your\nservice, sir,\" he repeated in a low and frightened voice. All the\npeople were staring at us.\n\n\"No, good sir,\" I remonstrated, stepping forward to explain. \"I would\nnot be having you think that I am unable to get a chair for myself,\nsince I am above everything able and swift with my hands, and it is a\nsmall thing to get a chair for one's self and not deprive a worthy\ngentleman of his own.\"\n\n\"I did not think to deprive you, sir,\" he ejaculated desperately. \"The\nchair is at your service, sir!\"\n\n\"Plague the man!\" I cried, stamping my foot impatiently; and at the\nstamping of my foot a waiter let fall a dish, some women screamed,\nthree or four people disappeared through the door, and a venerable\ngentleman arose from his seat in a corner and in a tremulous voice\nsaid:\n\n\"Sir, let us pray you that there be no bloodshed.\"\n\n\"You are an old fool,\" said I to him. \"How could there be bloodshed\nwith me here merely despising you all for not knowing what I mean when\nI say it.\"\n\n\"We know you mean what you say, sir,\" responded the old gentleman.\n\"Pray God you mean peaceably!\"\n\n\"Hoity-toity!\" shouted a loud voice, and I saw a great, tall, ugly\nwoman bearing down upon me from the doorway. \"Out of my way,\" she\nthundered at a waiter. The man gasped out: \"Yes, your ladyship!\"\n\nI was face to face with the mother of my lovely Mary.\n\n\"Hoity-toity!\" she shouted at me again. \"A brawler, eh? A lively\nswordster, hey? A real damn-my-eyes swaggering bully!\"\n\nThen she charged upon me. \"How dare you brawl with these inoffensive\npeople under the same roof which shelters me, fellow? By my word, I\nwould have pleasure to give you a box on the ear!\"\n\n\"Madam,\" I protested hurriedly. But I saw the futility of it. Without\ndevoting further time to an appeal, I turned and fled. I dodged behind\nthree chairs and moved them hastily into a rampart.\n\n\"Madam,\" I cried, feeling that I could parley from my new position,\n\"you labour under a misapprehension.\"\n\n\"Misapprehend me no misapprehensions,\" she retorted hotly. \"How dare\nyou say that I can misapprehend anything, wretch?\"\n\nShe attacked each flank in turn, but so agile was I that I escaped\ncapture, although my position in regard to the chairs was twice\nreversed. We performed a series of nimble manoeuvres which were\ncharacterized on my part by a high degree of strategy. But I found the\nrampart of chairs an untenable place. I was again obliged hurriedly to\nretreat, this time taking up a position behind a large table.\n\n\"Madam,\" I said desperately, \"believe me, you are suffering under a\ngrave misapprehension.\"\n\n\"Again he talks of misapprehension!\"\n\nWe revolved once swiftly around the table; she stopped, panting.\n\n\"And this is the blusterer! And why do you not stand your ground,\ncoward?\"\n\n\"Madam,\" said I with more coolness now that I saw she would soon be\nlosing her wind, \"I would esteem it very ungallant behaviour if I\nendured your attack for even a brief moment. My forefathers form a\nbrave race which always runs away from the ladies.\"\n\nAfter this speech we revolved twice around the table. I must in all\ncandour say that the Countess used language which would not at all\nsuit the pages of my true and virtuous chronicle; but indeed it was no\nworse than I often heard afterward from the great ladies of the time.\nHowever, the talk was not always addressed to me, thank the Saints!\n\nAfter we had made the two revolutions, I spoke reasonably. \"Madam,\"\nsaid I, \"if we go spinning about the table in this fashion for any\nlength of time, these gawking spectators will think we are a pair of\nwheels.\"\n\n\"Spectators!\" she cried, lifting her old head high. She beheld about\nseventy-five interested people. She called out loudly to them:\n\n\"And is there no gentleman among you all to draw his sword and beat me\nthis rascal from the inn?\"\n\nNobody moved.\n\n\"Madam,\" said I, still reasonable, \"would it not be better to avoid a\npossible scandal by discontinuing these movements, as the tongues of\nmen are not always fair, and it might be said by some--\"\n\nWhereupon we revolved twice more around the table.\n\nWhen the old pelican stopped, she had only enough breath left to\nimpartially abuse all the sight-seers. As her eye fixed upon them,\nThe O'Ruddy, illustrious fighting-man, saw his chance and bolted like\na hare. The escape must have formed a great spectacle, but I had no\ntime for appearances. As I was passing out of the door, the Countess,\nin her disappointed rage, threw a heavy ivory fan after me, which\nstruck an innocent bystander in the eye, for which he apologized.\n\n\n\n\nCHAPTER XI\n\n\nI wasted no time in the vicinity of the inn. I decided that an\ninterval spent in some remote place would be consistent with the\nbehaviour of a gentleman.\n\nBut the agitations of the day were not yet closed for me. Suddenly I\ncame upon a small, slow-moving, and solemn company of men, who carried\namong them some kind of a pallet, and on this pallet was the body of\nForister. I gazed upon his ghastly face; I saw the large blood\nblotches on his shirt; as they drew nearer I saw him roll his eyes and\nheard him groan. Some of the men recognized me, and I saw black looks\nand straight-pointing fingers. At the rear walked Lord Strepp with\nForister's sword under his arm. I turned away with a new impression of\nthe pastime of duelling. Forister's pallor, the show of bloody cloth,\nhis groan, the dark stares of men, made me see my victory in a\ndifferent way, and I even wondered if it had been absolutely necessary\nto work this mischief upon a fellow-being.\n\nI spent most of the day down among the low taverns of the sailors,\nstriving to interest myself in a thousand new sights brought by the\nships from foreign parts.\n\nBut ever my mind returned to Lady Mary, and to my misfortune in being\npursued around chairs and tables by my angel's mother. I had also\nmanaged to have a bitter quarrel with the noble father of this lovely\ncreature. It was hardly possible that I could be joyous over my\nprospects.\n\nAt noon I returned to the inn, approaching with some display of\ncaution. As I neared it, a carriage followed by some horsemen whirled\nspeedily from the door. I knew at once that Lady Mary had been taken\nfrom me. She was gone with her father and mother back to London. I\nrecognized Lord Strepp and Colonel Royale among the horsemen.\n\nI walked through the inn to the garden, and looked at the parrot. My\nsenses were all numb. I stared at the bird as it rolled its wicked eye\nat me.\n\n\"Pretty lady! Pretty lady!\" it called in coarse mockery.\n\n\"Plague the bird!\" I muttered, as I turned upon my heel and entered\nthe inn.\n\n\"My bill,\" said I. \"A horse for Bath!\" said I.\n\nAgain I rode forth on a quest. The first had been after my papers. The\nsecond was after my love. The second was the hopeless one, and,\novercome by melancholy, I did not even spur my horse swiftly on my\nmission. There was upon me the deep-rooted sadness which balances the\nmirth of my people,--the Celtic aptitude for discouragement; and even\nthe keening of old women in the red glow of the peat fire could never\nhave deepened my mood.\n\nAnd if I should succeed in reaching London, what then? Would the wild\nsavage from the rocky shore of Ireland be a pleasing sight to my Lady\nMary when once more amid the glamour and whirl of the fashionable\ntown? Besides, I could no longer travel on the guineas of Jem Bottles.\nHe had engaged himself and his purse in my service because I had told\nhim of a fortune involved in the regaining of certain papers. I had\nregained those papers, and then coolly placed them as a gift in a\ncertain lovely white hand. I had had no more thought of Jem Bottles\nand his five guineas than if I had never seen them. But this was no\nexcuse for a gentleman. When I was arrived at the rendezvous I must\nimmediately confess to Jem Bottles, the highwayman, that I had wronged\nhim. I did not expect him to demand satisfaction, but I thought he\nmight shoot me in the back as I was riding away.\n\nBut Jem was not at the appointed place under the tree. Not puzzled at\nthis behaviour, I rode on. I saw I could not expect the man to stay\nfor ever under a tree while I was away in Bristol fighting a duel and\nmaking eyes at a lady. Still, I had heard that it was always done.\n\nAt the inn where Paddy holed Forister, I did not dismount, although a\nhostler ran out busily. \"No,\" said I. \"I ride on.\" I looked at the\nman. Small, sharp-eyed, weazened, he was as likely a rascal of a\nhostler as ever helped a highwayman to know a filled purse from a man\nwho was riding to make arrangements with his creditors.\n\n\"Do you remember me?\" said I.\n\n\"No, sir,\" he said with great promptitude.\n\n\"Very good,\" said I. \"I knew you did. Now I want to know if Master Jem\nBottles has passed this way to-day. A shilling for the truth and a\nthrashing for a lie.\"\n\nThe man came close to my stirrup. \"Master,\" he said, \"I know you to be\na friend of him. Well, in day-time he don't ride past our door. There\nbe lanes. And so he ain't passed here, and that's the truth.\"\n\nI flung him a shilling. \"Now,\" I said, \"what of the red giant?\"\n\nThe man opened his little eyes in surprise. \"He took horse with you\ngentlemen and rode on to Bristol, or I don't know.\"\n\n\"Very good; now I see two very fine horses champing in the yard. And\nwho owns them?\"\n\nIf I had expected to catch him in treachery I was wrong.\n\n\"Them?\" said he, jerking his thumb. He still kept his voice lowered.\n\"They belong to two gentlemen who rode out some hours agone along with\nsome great man's carriage. The officer said some pin-pricks he had\ngotten in a duel had stiffened him, and made the saddle ill of ease\nwith him, and the young lord said that he would stay behind as a\ncompanion. They be up in the Colonel's chamber, drinking vastly. But\nmind your life, sir, if you would halt them on the road. They be men\nof great spirit. This inn seldom sees such drinkers.\"\n\nAnd so Lord Strepp and Colonel Royale were resting at this inn while\nthe carriage of the Earl had gone on toward Bath? I had a mind to\ndismount and join the two in their roystering, but my eyes turned\nwistfully toward Bath.\n\nAs I rode away I began to wonder what had become of Jem Bottles and\nPaddy. Here was a fine pair to be abroad in the land. Here were two\njewels to be rampaging across the country. Separately, they were\nvillains enough, but together they would overturn England and get\nthemselves hung for it on twin gibbets. I tried to imagine the\nparticular roguery to which they would first give their attention.\n\nBut then all thought of the rascals faded from me as my mind received\na vision of Lady Mary's fair face, her figure, her foot. It would not\nbe me to be thinking of two such thieves when I could be dreaming of\nLady Mary with her soft voice and the clear depth of her eyes. My\nhorse seemed to have a sympathy with my feeling and he leaped bravely\nalong the road. The Celtic melancholy of the first part of the journey\nhad blown away like a sea-mist. I sped on gallantly toward Bath and\nLady Mary.\n\nBut almost at the end of the day, when I was within a few miles of\nBath, my horse suddenly pitched forward onto his knees and nose. There\nwas a flying spray of muddy water. I was flung out of the saddle, but\nI fell without any serious hurt whatever. We had been ambushed by some\nkind of deep-sided puddle. My poor horse scrambled out and stood with\nlowered head, heaving and trembling. His soft nose had been cut\nbetween his teeth and the far edge of the puddle. I led him forward,\nwatching his legs. He was lamed. I looked in wrath and despair back at\nthe puddle, which was as plain as a golden guinea on a platter. I do\nnot see how I could have blundered into it, for the daylight was still\nclear and strong. I had been gazing like a fool in the direction of\nBath. And my Celtic melancholy swept down upon me again, and even my\nfather's bier appeared before me with the pale candle-flames swaying\nin the gusty room, and now indeed my ears heard the loud wailing keen\nof the old women.\n\n\"Rubbish,\" said I suddenly and aloud, \"and is it one of the best\nswordsmen in England that is to be beaten by a lame horse?\" My spirit\nrevived. I resolved to leave my horse in the care of the people of\nthe nearest house and proceed at once on foot to Bath. The people of\nthe inn could be sent out after the poor animal. Wheeling my eyes, I\nsaw a house not more than two fields away, with honest hospitable\nsmoke curling from the chimneys. I led my beast through a hole in the\nhedge, and I slowly made my way toward it.\n\nNow it happened that my way led me near a haycock, and as I neared\nthis haycock I heard voices from the other side of it. I hastened\nforward, thinking to find some yokels. But as I drew very close I\nsuddenly halted and silently listened to the voices on the other side.\n\n\"Sure, I can read,\" Paddy was saying. \"And why wouldn't I be able? If\nwe couldn't read in Ireland, we would be after being cheated in our\nrents, but we never pay them any how, so that's no matter. I would be\nhaving you to know we are a highly educated people. And perhaps you\nwould be reading it yourself, my man?\"\n\n\"No,\" said Jem Bottles, \"I be not a great scholar and it has a look of\namazing hardness. And I misdoubt me,\" he added in a morose and envious\nvoice, \"that your head be too full of learning.\"\n\n\"Learning!\" cried Paddy. \"Why wouldn't I be learned, since my uncle\nwas a sexton and had to know one grave from another by looking at the\nstones so as never to mix up the people? Learning! says you? And\nwasn't there a convent at Ballygowagglycuddi, and wasn't\nBallygowagglycuddi only ten miles from my father's house, and haven't\nI seen it many a time?\"\n\n\"Aye, well, good Master Paddy,\" replied Jem Bottles, oppressed and\nsullen, but still in a voice ironic from suspicion, \"I never doubt me\nbut what you are a regular clerk for deep learning, but you have not\nyet read a line from the paper, and I have been waiting this\nhalf-hour.\"\n\n\"And how could I be reading?\" cried Paddy in tones of indignation.\n\"How could I be reading with you there croaking of this and that and\nspeaking hard of my learning? Bad cess to the paper, I will be after\nreading it to myself if you are never to stop your clatter, Jem\nBottles.\"\n\n\"I be still as a dead rat,\" exclaimed the astonished highwayman.\n\n\"Well, then,\" said Paddy. \"Listen hard, and you will hear such\nlearning as would be making your eyes jump from your head. And 'tis\nnot me either that cares to show my learning before people who are\nunable to tell a mile-post from a church-tower.\"\n\n\"I be awaiting,\" said Jem Bottles with a new meekness apparently born\nof respect for Paddy's eloquence.\n\n\"Well, then,\" said Paddy, pained at these interruptions. \"Listen well,\nand maybe you will gain some learning which may serve you all your\nlife in reading chalk-marks in taprooms; for I see that they have that\ncustom in this country, and 'tis very bad for hard-drinking men who\nhave no learning.\"\n\n\"If you would read from the paper--\" began Jem Bottles.\n\n\"Now, will you be still?\" cried Paddy in vast exasperation.\n\nBut here Jem Bottles spoke with angry resolution. \"Come, now! Read!\n'Tis not me that talks too much, and the day wanes.\"\n\n\"Well, well, I would not be hurried, and that's the truth,\" said Paddy\nsoothingly. \"Listen now.\" I heard a rustling of paper. \"Ahem!\" said\nPaddy, \"Ahem! Are ye listening, Jem Bottles?\"\n\n\"I be,\" replied the highwayman.\n\n\"Ahem!\" said Paddy. \"Ahem! Are ye listening, Jem Bottles?\"\n\n\"I be,\" replied the highwayman.\n\n\"Then here's for it,\" said Paddy in a formidable voice. There was\nanother rustling of paper. Then to my surprise I heard Paddy intone,\nwithout punctuation, the following words:\n\n     \"Dear Sister Mary I am asking the good father to write this\n     because my hand is lame from milking the cows although we\n     only have one and we sold her in the autumn the four\n     shillings you owe on the pig we would like if convenient to\n     pay now owing to the landlord may the plague take him how\n     did your Mickey find the fishing when you see Peggy tell\n     her--\"\n\nHere Jem Bottles's voice arose in tones of incredulity.\n\n\"And these be the papers of the great Earl!\" he cried.\n\nThen the truth flashed across my vision like the lightning. My two\nmadmen had robbed the carriage of the Earl of Westport, and had taken,\namong other things, the Earl's papers--my papers--Lady Mary's papers.\nI strode around the haycock.\n\n\"Wretches!\" I shouted. \"Miserable wretches!\"\n\nFor a time they were speechless. Paddy found his tongue first.\n\n\"Aye, 'tis him! 'Tis nothing but little black men and papers with him,\nand when we get them for him he calls us out of our names in a foreign\ntongue. 'Tis no service for a bright man,\" he concluded mournfully.\n\n\"Give me the papers,\" said I.\n\nPaddy obediently handed them. I knew them. They were my papers--Lady\nMary's papers.\n\n\"And now,\" said I, eyeing the pair, \"what mischief have you two been\ncompassing?\"\n\nPaddy only mumbled sulkily. It was something on the difficulties of\nsatisfying me on the subjects of little black men and papers. Jem\nBottles was also sulky, but he grumbled out the beginning of an\nexplanation.\n\n\"Well, master, I bided under the tree till him here came, and then we\ntogether bided. And at last we thought, with the time so heavy, we\nmight better work to handle a purse or two. Thinking,\" he said\ndelicately, \"our gentleman might have need of a little gold. Well, and\nas we were riding, a good lad from the--your worship knows\nwhere--tells us the Earl's carriage is halting there for a time, but\nwill go on later without its escort of two gentlemen; only with\nservants. And, thinking to do our gentleman a good deed, I brought\nthem to stand on the highway, and then he--\"\n\n\"And then I,\" broke in Paddy proudly, \"walks up to the carriage-door\nlooking like a king's cruiser, and says I, 'Pray excuse the manners of\na self-opinionated man, but I consider your purses would look better\nin my pocket.' And then there was a great trouble. An old owl of a\nwoman screeched, and was for killing me with a bottle which she had\nbeen holding against her nose. But she never dared. And with that an\nold sick man lifted himself from hundreds of cushions and says he,\n'What do you want? You can't have them,' says he, and he keeps\nclasping his breast. 'First of all,' says I, 'I want what you have\nthere. What I want else I'll tell you at my leisure.' And he was all\nfor mouthing and fuming, but he was that scared he gave me these\npapers--bad luck to them.\" Paddy cast an evil eye upon the papers in\nmy hand.\n\n\"And then?\" said I.\n\n\"The driver he tried for to whip up,\" interpolated Jem Bottles. \"He\nwas a game one, but the others were like wet cats.\"\n\n\"And says I,\" continued Paddy, \"'now we will have the gold, if it\nplease you.' And out it came. 'I bid ye a good journey,' says I, and I\nthought it was over, and how easy it was highwaying, and I liked it\nwell, until the lady on the front seat opens her hood and shows me a\nprettier face than we have in all Ireland. She clasps two white hands.\n'Oh, please Mister Highwayman, my father's papers--' And with that I\nbacks away. 'Let them go,' says I to Jem Bottles, and sick I was of\nit, and I would be buying masses to-night if I might find a Christian\nchurch. The poor lady!\"\n\nI was no longer angry with Paddy.\n\n\"Aye,\" said Jem Bottles, \"the poor lady was that forlorn!\"\n\nI was no longer angry with Jem Bottles.\n\nBut I now had to do a deal of thinking. It was plain that the papers\nwere of supreme importance to the Earl. Although I had given them to\nLady Mary, they had returned to me. It was fate. My father had taught\nme to respect these papers, but I now saw them as a sign in the sky.\n\nHowever, it was hard to decide what to do. I had given the papers to\nLady Mary, and they had fled back to me swifter than cormorants.\nPerhaps it was willed that I should keep them. And then there would be\ntears in the eyes of Lady Mary, who suffered through the suffering of\nher father. No; come good, come bad for me, for Jem Bottles, for\nPaddy, I would stake our fortunes on the act of returning the papers\nto Lady Mary.\n\nIt is the way of Irishmen. We are all of us true philanthropists. That\nis why we have nothing, although in other countries I have seen\nphilanthropists who had a great deal. My own interest in the papers I\nstaked, mentally, with a glad mind; the minor interests of Jem Bottles\nand Paddy I staked, mentally, without thinking of them at all. But\nsurely it would be a tribute to fate to give anything to Lady Mary.\n\nI resolved on a course of action. When I aroused to look at my\ncompanions I found them seated face to face on the ground like players\nof draughts. Between them was spread a handkerchief, and on that\nhandkerchief was a heap of guineas. Jem Bottles was saying, \"Here be\nmy fingers five times over again.\" He separated a smaller heap. \"Here\nbe my fingers five times over again.\" He separated another little\nstack. \"And here be my fingers five times over again and two more yet.\nNow can ye understand?\"\n\n\"By dad,\" said Paddy admiringly, \"you have the learning this time,\nMaster Bottles. My uncle the sexton could not have done it better.\"\n\n\"What is all this?\" said I.\n\nThey both looked at me deprecatingly. \"'Tis, your honour,\" began\nPaddy; \"'tis only some little small sum--nothing to be talked\nof--belonging to the old sick man in the carriage.\"\n\n\"Paddy and Jem Bottles,\" said I, \"I forgive you the taking of the\npapers. Ye are good men and true. Now we will do great deeds.\"\n\n\n\n\nCHAPTER XII\n\n\nMy plans were formed quickly. \"We now have a treasure chest of no\nsmall dimensions,\" said I, very complacent, naturally. \"We can conquer\nLondon with this. Everything is before us. I have already established\nmyself as the grandest swordsman in the whole continent of England.\nLately we have gained much treasure. And also I have the papers.\nPaddy, do you take care of this poor horse. Then follow me into Bath.\nJem Bottles, do you mount and ride around the town, for I fear your\nballadists. Meet me on the London road. Ride slowly on the highway to\nLondon, and in due time I will overtake you. I shall pocket a few of\nthose guineas, but you yourself shall be the main treasury. Hold! what\nof Paddy's hair? Did he rob the Earl with that great flame showing? He\ndare not appear in Bath.\"\n\n\"'Tis small tribute to my wit, sir,\" answered Jem Bottles. \"I would as\nsoon go poaching in company with a lighthouse as to call a stand on\nthe road with him uncovered. I tied him in cloth until he looked no\nmore like himself than he now does look like a parson.\"\n\n\"Aye,\" said Paddy in some bad humour, \"my head was tied in a bag. My\nmother would not have known me from a pig going to market. And I would\nnot be for liking it every day. My hair is what the blessed Saints\nsent me, and I see no such fine hair around me that people are free to\nthrow the laugh at me.\"\n\n\"Peace!\" said I.\n\nTheir horses were tied in an adjacent thicket. I sent Paddy off with\nmy lame mount, giving him full instructions as to his lies. I and Jem\nBottles took the other horses and rode toward Bath.\n\nWhere a certain lane turned off from the highway I parted with Jem\nBottles, and he rode away between the hedges. I cantered into Bath.\n\nThe best-known inn was ablaze with fleeting lights, and people were\nshouting within. It was some time before I could gain a man to look\nafter my horse. Of him I demanded the reason of the disturbance. \"The\nEarl of Westport's carriage has been robbed on the Bristol road, sir,\"\nhe cried excitedly. \"There be parties starting out. I pray they catch\nhim.\"\n\n\"And who would they be catching, my lad,\" said I.\n\n\"Jem Bottles, damn him, sir,\" answered the man. \"But 'tis a fierce\ntime they will have, for he stands no less than eight feet in his\nboots, and his eyes are no human eyes, but burn blood-red always. His\nhands are adrip with blood, and 'tis said that he eats human flesh,\nsir. He surely is a devil, sir.\"\n\n\"From the description I would be willing to believe it,\" said I.\n\"However, he will be easy to mark. Such a monster can hardly be\nmistaken for an honest man.\"\n\nI entered the inn, while a boy staggered under my valises. I had\ndifficulty in finding the landlord. But in the corridor were a number\nof travellers, and evidently one had come that day from Bristol, for\nhe suddenly nudged another and hurriedly whispered:\n\n\"'Tis him! The great Irish swordsman!\"\n\nThen the news spread like the wind, apparently, that the man who had\nbeaten the great Forister was arrived in good health at the inn. There\nwere murmurs, and a great deal of attention, and many eyes. I suddenly\ncaught myself swaggering somewhat. It is hard to be a famous person\nand not show a great swollen chicken-breast to the people. They are\ndisappointed if you do not strut and step high. \"Show me to a\nchamber,\" said I splendidly. The servants bowed their foreheads to the\nfloor.\n\nBut the great hubbub over the Earl's loss continued without abatement.\nGentlemen clanked down in their spurs; there was much talk of\ndragoons; the tumult was extraordinary. Upstairs the landlord led me\npast the door of a kind of drawing-room. I glanced within and saw the\nEarl of Westport gesturing and declaiming to a company of gentlemen.\nHe was propped up in a great arm-chair.\n\n\"And why would he be waving his hands that way?\" said I to two\nservants who stood without.\n\n\"His lordship has lost many valuable papers at the hands of a\nmiscreant, sir,\" answered one.\n\n\"Is it so?\" said I. \"Well, then, I would see his lordship.\"\n\nBut here this valet stiffened. \"No doubt but what his lordship would\nbe happy to see you, sir,\" he answered slowly. \"Unfortunately,\nhowever, he has forbidden me to present strangers to his presence.\"\n\n\"I have very important news. Do not be an idiot,\" said I. \"Announce\nme. The O'Ruddy.\"\n\n\"The O'Ruggy?\" said he.\n\n\"The O'Ruddy,\" said I.\n\n\"The O'Rudgy?\" said he.\n\n\"No,\" said I, and I told him again. Finally he took two paces within\nthe room and sung out in a loud voice:\n\n\"The O'Rubby.\"\n\nI heard the voice of the sick old Earl calling out from his great\nchair. \"Why, 'tis the Irishman. Bid him enter. I am glad--I am always\nvery glad--ahem!--\"\n\nAs I strode into the room I was aware of another buzz of talk.\nApparently here, too, were plenty of people who knew me as the famous\nswordsman. The Earl moved his jaw and mumbled.\n\n\"Aye,\" said he at last, \"here is The O'Ruddy. And, do you know, Mr.\nO'Ruddy, I have been foully robbed, and, among other things, have lost\nyour worthless papers?\"\n\n\"I heard that you had lost them,\" I answered composedly. \"But I refuse\nto take your word that they are worthless.\"\n\nMany people stared, and the Earl gave me a firm scowl. But after\nconsideration he spoke as if he thought it well to dissemble a great\ndislike of me. The many candles burned very brightly, and we could all\nsee each other. I thought it better to back casually toward the wall.\n\n\"You never accomplish anything,\" coughed the sick Earl. \"Yet you are\nfor ever prating of yourself. I wish my son were here. My papers are\ngone. I shall never recover them.\"\n\n\"The papers are in the breast of my coat at this moment,\" said I\ncoolly.\n\nThere was a great tumult. The Earl lost his head and cried:\n\n\"Seize him!\" Two or three young men took steps toward me. I was back\nto the wall, and in a leisurely and contemptuous way I drew my sword.\n\n\"The first gentleman who advances is a dead man,\" said I pleasantly.\n\nSome drew away quickly; some hesitated, and then withdrew subtilely.\nIn the mean time the screeches of the Earl mocked them all.\n\n\"Aye, the wild Irishman brings you up to a stand, he does! Now who\nwill have at him? In all Bath I have no friend with a stout heart?\"\n\nAfter looking them over I said:\n\n\"No, my Lord, you have none.\"\n\nAt this insult the aged peer arose from his chair. \"Bring me my\nsword,\" he cried to his valet. A hush fell upon us all. We were\nrendered immovable by the solemn dignity of this proceeding.\n\nIt was some time before I could find my tongue.\n\n\"And if you design to cross blades with me, you will find me a sad\nrenegade,\" said I. \"I am holding the papers for the hands of their\ntrue owner.\"\n\n\"And their true owner?\" he demanded.\n\n\"Lady Mary Strepp,\" said I.\n\nHe sank back into his seat. \"This Irishman's impudence is beyond\nmeasuring,\" he exclaimed. The hurrying valet arrived at that moment\nwith a sword. \"Take it away! Take it away!\" he cried. \"Do I wish\nvalets to be handing swords to me at any time of the day or night?\"\n\nHere a belligerent red-faced man disengaged himself abruptly from the\ngroup of gentlemen and addressed the Earl. \"Westport,\" said he flatly,\n\"I can ill bear your taunt concerning your Bath friends, and this is\nnot to speak of the insolence of the person yonder.\"\n\n\"Oh, ho!\" said I. \"Well, and the person yonder remains serene in his\ninsolence.\"\n\nThe Earl, smiling slightly, regarded the new speaker.\n\n\"Sir Edmund Flixton was ever a dainty swordsman, picking and choosing\nlike a lady in a flower-bed. Perchance he is anxious to fight the\ngentleman who has just given Reginald Forister something he will not\nforget?\"\n\nAt this Flixton actually turned pale and drew back. Evidently he had\nnot yet heard the news. And, mind you, I could see that he would fight\nme the next moment. He would come up and be killed like a gentleman.\nBut the name of a great conqueror had simply appalled him and smitten\nhim back.\n\nThe Earl was gazing at me with an entirely new expression. He had\ncleverly eliminated all dislike from his eyes. He covered me with a\nfriendly regard.\n\n\"O'Ruddy,\" he said softly, \"I would have some private speech with you.\nCome into my chamber.\"\n\nThe Earl leaned on the shoulder of his valet and a little fat doctor,\nand walked painfully into another room. I followed, knowing that I was\nnow to withstand a subtle, wheedling, gentle attempt to gain the\npapers without the name of Lady Mary being mentioned.\n\nThe Earl was slowly lowered into a great chair. After a gasp of relief\nhe devoted a brightening attention to me. \"You are not a bad fellow,\nO'Ruddy,\" he observed. \"You remind me greatly of your father. Aye, he\nwas a rare dog, a rare dog!\"\n\n\"I've heard him say so, many is the day, sir,\" I answered.\n\n\"Aye, a rare dog!\" chuckled the old man. \"I have in my memory some\nbrisk pictures of your father with his ready tongue, his\nwhat-the-devil-does-it-matter-sir, and that extraordinary\nswordsmanship which you seem to have inherited.\"\n\n\"My father told me you were great friends in France,\" I answered\ncivilly, \"but from some words you let drop in Bristol I judged that he\nwas mistaken.\"\n\n\"Tut,\" said the Earl. \"You are not out of temper with me, are you,\nO'Ruddy?\"\n\n\"With me happily in possession of the papers,\" I rejoined, \"I am in\ngood temper with everybody. 'Tis not for me to lose my good nature\nwhen I hold all the cards.\"\n\nThe Earl's mouth quickly dropped to a sour expression, but almost as\nquickly he put on a pleasant smile. \"Aye,\" he said, nodding his sick\nhead. \"Always jovial, always jovial. Precisely like his father. In\nfact it brings back an old affection.\"\n\n\"If the old affection had been brought back a little earlier, sir,\"\nsaid I, \"we all would have had less bother. 'Twas you who in the\nbeginning drew a long face and set a square chin over the business. I\nam now in the mood to be rather airy.\"\n\nOur glances blazed across each other.\n\n\"But,\" said the Earl in the gentlest of voices, \"you have my papers,\nO'Ruddy, papers entrusted to you by your dying father to give into the\nhands of his old comrade. Would you betray such a sacred trust? Could\nyou wanton yourself to the base practices of mere thievery?\"\n\n\"'Tis not I who has betrayed any trust,\" I cried boldly. \"I brought\nthe papers and wished to offer them. They arrived in your possession,\nand you cried 'Straw, straw!' Did you not?\"\n\n\"'Twas an expedient, O'Ruddy,\" said the Earl.\n\n\"There is more than one expedient in the world,\" said I. \"I am now\nusing the expedient of keeping the papers.\"\n\nAnd in the glance which he gave me I saw that I had been admitted\nbehind a certain barrier. He was angry, but he would never more\nattempt to overbear me with grand threats. And he would never more\nattempt to undermine me with cheap flattery. We had measured one\nagainst the other, and he had not come away thinking out of his\nproportion. After a time he said:\n\n\"What do you propose to do, Mr. O'Ruddy?\"\n\nI could not help but grin at him. \"I propose nothing,\" said I. \"I am\nnot a man for meaning two things when I say one.\"\n\n\"You've said one thing, I suppose?\" he said slowly.\n\n\"I have,\" said I.\n\n\"And the one thing?\" said he.\n\n\"Your memory is as good as mine,\" said I.\n\nHe mused deeply and at great length. \"You have the papers?\" he asked\nfinally.\n\n\"I still have them,\" said I.\n\n\"Then,\" he cried with sudden vehemence, \"why didn't you read the\npapers and find out the truth?\"\n\nI almost ran away.\n\n\"Your--your lordship,\" I stammered, \"I thought perhaps in London--in\nLondon perhaps--I might get a--I would try to get a tutor.\"\n\n\n\n\nCHAPTER XIII\n\n\n\"So that is the way of it, is it?\" said the Earl, grinning. \"And why\ndid you not take it to some clerk?\"\n\n\"My lord,\" said I with dignity, \"the papers were with me in trust for\nyou. A man may be a gentleman and yet not know how to read and write.\"\n\n\"'Tis quite true,\" answered he.\n\n\"And when I spoke of the tutor in London I did not mean to say that I\nwould use what knowledge he imparted to read your papers. I was merely\nblushing for the defects in my education, although Father Donovan\noften said that I knew half as much as he did, poor man, and him a\nholy father. If you care to so direct me, I can go even now to my\nchamber and make shift to read the papers.\"\n\n\"The Irish possess a keen sense of honour,\" said he admiringly.\n\n\"We do,\" said I. \"We possess more integrity and perfect sense of\nhonour than any other country in the world, although they all say the\nsame of themselves, and it was my own father who often said that he\nwould trust an Irishman as far as he could see him and no more, but\nfor a foreigner he had only the length of an eyelash.\"\n\n\"And what do you intend with the papers now, O'Ruddy?\" said he.\n\n\"I intend as I intended,\" I replied. \"There is no change in me.\"\n\n\"And your intentions?\" said he.\n\n\"To give them into the hands of Lady Mary Strepp and no other,\" said I\nboldly.\n\nI looked at him. He looked at me.\n\n\"Lady Mary Strepp, my daughter,\" he said in ironic musing. \"Would not\nher mother do, O'Ruddy?\" he asked softly.\n\nI gave a start.\n\n\"She is not near?\" I demanded, looking from here to there.\n\nHe laughed.\n\n\"Aye, she is. I can have her here to take the papers in one short\nmoment.\"\n\nI held up my hands.\n\n\"No--no--\"\n\n\"Peace,\" said he with a satanic chuckle. \"I was only testing your\ncourage.\"\n\n\"My lord,\" said I gravely, \"seeing a bare blade come at your breast is\none thing, and running around a table is another, and besides you have\nno suitable table in this chamber.\"\n\nThe old villain laughed again.\n\n\"O'Ruddy,\" he cried, \"I would be a well man if you were always near\nme. Will I have a table fetched up from below?--'twould be easy.\"\n\nHere I stiffened.\n\n\"My lord, this is frivolity,\" I declared. \"I came here to give the\npapers. If you do not care to take them in the only way in which I\nwill give them, let us have it said quickly.\"\n\n\"They seem to be safe in your hands at present,\" he remarked. \"Of\ncourse after you go to London and get a tutor--ahem!--\"\n\n\"I will be starting at once,\" said I, \"although Father Donovan always\ntold me that he was a good tutor as tutors went at the time in\nIreland. And I want to be saying now, my lord, that I cannot\nunderstand you. At one moment you are crying one thing of the papers;\nat the next moment you are crying another. At this time you are having\na laugh with me over them. What do you mean? I'll not stand this\nshiver-shavering any longer, I'll have you to know. What do you mean?\"\n\nHe raised himself among his cushions and fixed me with a bony finger.\n\n\"What do I mean? I'll tell you, O'Ruddy,\" said he, while his eyes\nshone brightly. \"I mean that I can be contemptuous of your plot. You\nwill not show these papers to any breathing creature because you are\nin love with my daughter. Fool, to match your lies against an\nex-minister of the King.\"\n\nMy eyes must have almost dropped from my head, but as soon as I\nrecovered from my dumfounderment I grew amazed at the great intellect\nof this man. I had told nobody, and yet he knew all about it. Yes, I\nwas in love with Lady Mary, and he was as well informed of it as if he\nhad had spies to watch my dreams. And I saw that in many cases a lover\nwas a kind of an ostrich, the bird which buries its head in the sands\nand thinks it is secure from detection. I wished that my father had\ntold me more about love, for I have no doubt he knew everything of it,\nhe had lived so many years in Paris. Father Donovan, of course, could\nnot have helped me in such instruction. I resolved, any how, to be\nmore cautious in the future, although I did not exactly see how I\ncould improve myself. The Earl's insight was pure mystery to me. I\nwould not be for saying that he practised black magic, but any how, if\nhe had been at Glandore, I would have had him chased through three\nparishes.\n\nHowever, the Earl was grinning victoriously, and I saw that I must\nharden my face to a brave exterior.\n\n\"And is it so?\" said I. \"Is it so?\"\n\n\"Yes,\" he said, with his grin.\n\n\"And what then?\" said I bluntly.\n\nIn his enjoyment he had been back again among his cushions.\n\n\"'What then? What then?'\" he snarled, rearing up swiftly. \"Why, then\nyou are an insolent fool: Begone from me! begone! be--\" Here some\nspasm overtook him, a spasm more from rage than from the sickness. He\nfell back breathless, although his eyes continued to burn at me.\n\n\"My lord,\" said I, bowing, \"I will go no poorer than when I came, save\nthat I have lost part of the respect I once had for you.\"\n\nI turned and left his chamber. Some few gentlemen yet remained in the\ndrawing-room as I passed out into the public part of the inn. I went\nquietly to a chamber and sat down to think. I was for ever going to\nchambers and sitting down to think after these talks with the Earl,\nduring which he was for ever rearing up in his chair and then falling\nback among the cushions.\n\nBut here was another tumble over the cliffs, if you like! Here was\ngenuine disaster. I laid my head in my hands and mused before my\nlonely fire, drinking much and visioning my ruin. What the Earl said\nwas true. There was trouble in the papers for the old nobleman. That\nhe knew. That I knew. And he knew with his devilish wisdom that I\nwould lose my head rather than see her in sorrow. Well, I could bide a\ntime. I would go to London in company with Paddy and Jem Bottles,\nsince they owned all the money, and if three such rogues could not\ndevise something, then I would go away and bury myself in a war in\nforeign parts, occupying myself in scaling fortresses and capturing\nguns. These things I know I could have performed magnificently, but\nfrom the Earl I had learned that I was an ill man to conduct an affair\nof the heart.\n\nI do not know how long I meditated, but suddenly there was a great\ntumult on the stairs near my door. There were the shouts and heavy\nbreathings of men, struggling, and over all rang a screech as from\nsome wild bird. I ran to the door and poked my head discreetly out;\nfor my coat and waistcoat were off as well as my sword, and I wished\nto see the manner of tumult at a distance before I saw it close. As I\nthrust forth my head I heard a familiar voice:\n\n\"And if ye come closer, ye old hell-cat, 'tis me will be forgetting\nrespect to my four great-grandmothers and braining you. Keep off! Am I\nnot giving ye the word? Keep off!\"\n\nThen another familiar voice answered him in a fine high fury. \"And you\ngallows-bird, you gallows-bird, you gallows-bird! You answer me, do\nyou! They're coming, all, even to the hangman! You'll soon know how to\ndance without a fiddler! Ah, would you? Would you?\"\n\nIf I had been afflicted with that strange malady of the body which\nsometimes causes men to fall to the ground and die in a moment without\na word, my doom would have been sealed. It was Paddy and Hoity-Toity\nengaged in animated discussion.\n\n\"And if ye don't mind your eye, ye old cormorant--\" began Paddy.\n\n\"And you would be a highwayman, would you, gallows-bird--\" began the\nCountess.\n\n\"Cow--\" began Paddy.\n\nHere for many reasons I thought it time to interfere. \"Paddy!\" I\ncried. He gave a glance at my door, recognized my face, and, turning\nquickly, ran through into my chamber. I barred the door even as\nHoity-Toity's fist thundered on the oak.\n\n\"It's a she-wolf,\" gasped Paddy, his chest pressing in and out.\n\n\"And what did you do to her?\" I demanded.\n\n\"Nothing but try to run away, sure,\" said Paddy.\n\n\"And why would she be scratching you?\"\n\n\"She saw me for one of the highwaymen robbing the coach, and there was\nI, devil knowing what to do, and all the people of the inn trying to\nput peace upon her, and me dodging, and then--\"\n\n\"Man,\" said I, grabbing his arm, \"'tis a game that ends on the--\"\n\n\"Never a bit,\" he interrupted composedly. \"Wasn't the old witch drunk,\nclaws and all, and didn't even the great English lord, or whatever,\nsend his servant to bring her in, and didn't he, the big man, stand in\nthe door and spit on the floor and go in when he saw she was for\nbattering all the servants and using worse talk than the sailors I\nheard in Bristol? It would not be me they were after, those men\nrunning. It would be her. And small power to them, but they were no\ngood at it. I am for taking a stool in my hand--\"\n\n\"Whist!\" said I. \"In England they would not be hitting great ladies\nwith stools. Let us hearken to the brawl. She is fighting them\nfinely.\"\n\nFor I had seen that Paddy spoke truth. The noble lady was engaged in\nbattling with servants who had been in pursuit of her when she was in\npursuit of Paddy. Never had I seen even my own father so drunk as she\nwas then. But the heart-rending thing was the humble protests of the\nservants. \"Your ladyship! Oh, your ladyship!\"--as they came up one by\none, or two by two, obeying orders of the Earl, to be incontinently\nboxed on the ears by a member of a profligate aristocracy. Probably\nany one of them was strong enough to throw the beldame out at a\nwindow. But such was not the manner of the time. One would think they\nwould retreat upon the Earl and ask to be dismissed from his service.\nBut this also was not the manner of the time. No; they marched up\nheroically and took their cuffs on the head and cried: \"Oh, your\nladyship! Please, your ladyship!\" They were only pretenders in their\nattacks; all they could do was to wait until she was tired, and then\nhumbly escort her to where she belonged, meanwhile pulling gently at\nher arms.\n\n\"She was after recognizing you then?\" said I to Paddy.\n\n\"Indeed and she was,\" said he. He had dropped into a chair and was\nlooking as if he needed a doctor to cure him of exhaustion. \"She would\nbe after having eyes like a sea-gull. And Jem Bottles was all for\ndeclaring that my disguise was complete, bad luck to the little man.\"\n\n\"Your disguise complete?\" said I. \"You couldn't disguise yourself\nunless you stood your head in a barrel. What talk is this?\"\n\n\"Sure an' I looked no more like myself than I looked like a wild man\nwith eight rows of teeth in his head,\" said Paddy mournfully. \"My own\nmother would have been after taking me for a horse. 'Tis that old\ncreature with her evil eye who would be seeing me when all the others\nwere blind as bats. I could have walked down the big street in Cork\nwithout a man knowing me.\"\n\n\"That you could at any time,\" said I. The Countess had for some\nmoments ceased to hammer on my door. \"Hearken! I think they are\nmanaging her.\"\n\nEither Hoity-Toity had lost heart, or the servants had gained some\ncourage, for we heard them dragging her delicately down the staircase.\nPresently there was a silence.\n\nAfter I had waited until this silence grew into the higher silence\nwhich seems like perfect safety, I rang the bell and ordered food and\ndrink. Paddy had a royal meal, sitting on the floor by the fireplace\nand holding a platter on his knee. From time to time I tossed him\nsomething for which I did not care. He was very grateful for my\ngenerosity. He ate in a barbaric fashion, crunching bones of fowls\nbetween his great white teeth and swallowing everything.\n\nI had a mind to discourse upon manners in order that Paddy might not\nshame me when we came to London; for a gentleman is known by the ways\nof his servants. If people of quality should see me attended by such\na savage they would put me down small. \"Paddy,\" said I, \"mend your\nways of eating.\"\n\n\"'My ways of eating,' your honour?\" said he. \"And am I not eating all\nthat I can hold? I was known to be a good man at platter always. Sure\nI've seen no man in England eat more than me. But thank you kindly,\nsir.\"\n\n\"You misunderstand me,\" said I. \"I wish to improve your manner of\neating. It would not be fine enough for the sight of great people. You\neat, without taking breath, pieces as big as a block of turf.\"\n\n\"'Tis the custom in my part of Ireland,\" answered Paddy.\n\n\"I understand,\" said I. \"But over here 'tis only very low people who\nfall upon their meat from a window above.\"\n\n\"I am not in the way of understanding your honour,\" said he. \"But any\nhow a man may be respectable and yet have a good hunger on him.\"\n\n\n\n\nCHAPTER XIV\n\n\nIt had been said that the unexpected often happens, although I do not\nknow what learned man of the time succeeded in thus succinctly\nexpressing a great law and any how it matters little, for I have since\ndiscovered that these learned men make one headful of brains go a long\nway by dint of poaching on each other's knowledge. But the unexpected\nhappened in this case, all true enough whatever.\n\nI was giving my man a bit of a warning.\n\n\"Paddy,\" said I, \"you are big, and you are red, and you are Irish; but\nby the same token you are not the great Fingal, son of lightning. I\nwould strongly give you the word. When you see that old woman you\nstart for the open moors.\"\n\n\"Devil fear me, sir,\" answered Paddy promptly. \"I'll not be stopping.\nI would be swimming to Ireland before she lays a claw on me.\"\n\n\"And mind you exchange no words with her,\" said I, \"for 'tis that\nwhich seems to work most wrongfully upon her.\"\n\n\"Never a word out of me,\" said he. \"I'll be that busy getting up the\nroad.\"\n\nThere was another tumult in the corridor, with the same screeches by\none and the same humble protests by a multitude. The disturbance\nneared us with surprising speed. Suddenly I recalled that when the\nservant had retired after bringing food and drink I had neglected to\nagain bar the door. I rushed for it, but I was all too late. I saw the\nlatch raise. \"Paddy!\" I shouted wildly. \"Mind yourself!\" And with that\nI dropped to the floor and slid under the bed.\n\nPaddy howled, and I lifted a corner of the valance to see what was\ntranspiring. The door had been opened, and the Countess stood looking\ninto the room. She was no longer in a fiery rage; she was cool, deadly\ndetermined, her glittering eye fixed on Paddy. She took a step\nforward.\n\nPaddy, in his anguish, chanted to himself an Irish wail in which he\ndescribed his unhappiness. \"Oh, mother of me, and here I am caught\nagain by the old hell-cat, and sure the way she creeps toward me is\nenough to put the fear of God in the heart of a hedge-robber, the\nmurdering old witch. And it was me was living so fine and grand in\nEngland and greatly pleased with myself. Sorrow the day I left\nIreland; it is, indeed.\"\n\nShe was now close to him, and she seemed to be preparing for one\nstupendous pounce which would mean annihilation to Paddy. Her lean\nhands were thrust out, with the fingers crooked, and it seemed to me\nthat her fingers were very long. In despair Paddy changed his tune and\naddressed her.\n\n\"Ah, now, alanna. Sure the kind lady would be for doing no harm? Be\neasy, now, acushla.\"\n\nBut these tender appeals had no effect. Suddenly she pounced. Paddy\nroared, and sprang backward with splendid agility. He seized a chair.\n\nNow I am quite sure that before he came to England Paddy had never\nseen a chair, although it is true that at some time in his life he may\nhave had a peep through a window into an Irish gentleman's house,\nwhere there might be a chair if the King's officers in the\nneighbourhood were not very ambitious and powerful. But Paddy handled\nthis chair as if he had seen many of them. He grasped it by the back\nand thrust it out, aiming all four legs at the Countess. It was a fine\nmove. I have seen a moderately good swordsman fairly put to it by a\npack of scoundrelly drawers who assailed him at all points in this\nmanner.\n\n\"An you come on too fast,\" quavered Paddy, \"ye can grab two legs, but\nthere will be one left for your eye and another for your brisket.\"\n\nHowever she came on, sure enough, and there was a moment of scuffling\nnear the end of the bed out of my sight. I wriggled down to gain\nanother view, and when I cautiously lifted an edge of the valance my\neyes met the strangest sight ever seen in all England. Paddy, much\ndishevelled and panting like a hunt-dog, had wedged the Countess\nagainst the wall. She was pinioned by the four legs of the chair, and\nPaddy, by dint of sturdily pushing at the chair-back, was keeping her\nin a fixed position.\n\nIn a flash my mind was made up. Here was the time to escape. I\nscrambled quickly from under the bed. \"Bravo, Paddy!\" I cried, dashing\nabout the room after my sword, coat, waistcoat, and hat. \"Devil a fear\nbut you'll hold her, my bucko! Push hard, my brave lad, and mind your\nfeet don't slip!\"\n\n\"If your honour pleases,\" said Paddy, without turning his eyes from\nhis conquest, \"'tis a little help I would be wishing here. She would\nbe as strong in the shoulder as a good plough-horse and I am not for\nstaying here for ever.\"\n\n\"Bravo, my grand lad!\" I cried, at last finding my hat, which had\nsomehow gotten into a corner. From the door I again addressed Paddy in\nencouraging speech. \"There's a stout-hearted boy for you! Hold hard,\nand mind your feet don't slip!\"\n\nHe cast a quick agonized look in my direction, and, seeing that I was\nabout basely to desert him, he gave a cry, dropped the chair, and\nbolted after me. As we ran down the corridor I kept well in advance,\nthinking it the best place in case the pursuit should be energetic.\nBut there was no pursuit. When Paddy was holding the Countess prisoner\nshe could only choke and stammer, and I had no doubt that she now was\nwell mastered by exhaustion.\n\nCuriously there was little hubbub in the inn. The fact that the\nCountess was the rioter had worked in a way to cause people to seek\nsecluded and darkened nooks. However, the landlord raised his bleat at\nme. \"Oh, sir, such a misfortune to befall my house just when so many\ngrand ladies and gentlemen are here.\"\n\nI took him quietly by the throat and beat his head against the wall,\nonce, twice, thrice.\n\n\"And you allow mad ladies to molest your guests, do you?\" said I.\n\n\"Sir,\" he stuttered, \"could I have caused her to cease?\n\n\"True,\" I said, releasing him. \"But now do as I bid you and quickly. I\nam away to London. I have had my plenty of you and your mad ladies.\"\n\nWe started bravely to London, but we only went to another and quieter\ninn, seeking peace and the absence of fear. I may say we found it,\nand, in a chair before a good fire, I again took my comfort. Paddy sat\non the floor, toasting his shins. The warmth passed him into a\nreflective mood.\n\n\"And I know all I need of grand ladies,\" he muttered, staring into the\nfire. \"I thought they were all for riding in gold coaches and smelling\nof beautiful flowers, and here they are mad to be chasing Irishmen in\ninns. I remember old Mag Cooligan fought with a whole regiment of\nKing's troops in Bantry, and even the drums stopped beating, the\nsoldiers were that much interested. But, sure, everybody would be\nknowing that Mag was no grand lady, although Pat Cooligan, her\nbrother, was pig-killer to half the country-side. I am thinking we\nwere knowing little about grand ladies. One of the soldiers had his\nhead broke by a musket because the others were so ambitious to destroy\nthe old lady, and she scratching them all. 'Twas long remembered in\nBantry.\"\n\n\"Hold your tongue about your betters,\" said I sharply. \"Don't be\ncomparing this Mag Cooligan with a real Countess.\"\n\n\"There would be a strange similarity any how,\" said he. \"But, sure,\nMag never fought in inns, for the reason that they would not be\nletting her inside.\"\n\n\"Remember how little you are knowing of them, Paddy,\" said I. \"'Tis\nnot for you to be talking of the grand ladies when you have seen only\none, and you would not be knowing another from a fish. Grand ladies\nare eccentric, I would have you to know. They have their ways with\nthem which are not for omadhauns like you to understand.\"\n\n\"Eccentric, is it?\" said he. \"I thought it would be some such\ndevilment.\"\n\n\"And I am knowing,\" said I with dignity, \"of one lady so fine that if\nyou don't stop talking that way of ladies I will break your thick\nskull for you, and it would matter to nobody.\"\n\n\"'Tis an ill subject for discussion, I am seeing that,\" said Paddy.\n\"But, faith, I could free Ireland with an army of ladies like one I've\nseen.\"\n\n\"Will you be holding your tongue?\" I cried wrathfully.\n\nPaddy began to mumble to himself,--\"Bedad, he was under the bed fast\nenough without offering her a stool by the fire and a small drop of\ndrink which would be no more than decent with him so fond of her. I am\nnot knowing the ways of these people.\"\n\nIn despair of his long tongue I made try to change the talking.\n\n\"We are off for London, Paddy. How are you for it?\"\n\n\"London, is it?\" said he warily. \"I was hearing there are many fine\nladies there.\"\n\nFor the second time in his life I cuffed him soundly on the ear.\n\n\"Now,\" said I, \"be ringing the bell. I am for buying you a bit of\ndrink; but if you mention the gentry to me once more in that\nblackguard way I'll lather you into a resemblance to your\ngrandfather's bones.\"\n\nAfter a pleasant evening I retired to bed leaving Paddy snug asleep by\nthe fire. I thought much of my Lady Mary, but with her mother stalking\nthe corridors and her knowing father with his eye wide open, I knew\nthere was no purpose in hanging about a Bath inn. I would go to\nLondon, where there were gardens, and walks in the park, and parties,\nand other useful customs. There I would win my love.\n\nThe following morning I started with Paddy to meet Jem Bottles and\ntravel to London. Many surprising adventures were in store for us, but\nan account of these I shall leave until another time, since one would\nnot be worrying people with too many words, which is a great fault in\na man who is recounting his own affairs.\n\n\n\n\nCHAPTER XV\n\n\nAs we ambled our way agreeably out of Bath, Paddy and I employed\nourselves in worthy speech. He was not yet a notable horseman, but his\nIrish adaptability was so great that he was already able to think he\nwould not fall off so long as the horse was old and tired.\n\n\"Paddy,\" said I, \"how would you like to be an Englishman? Look at\ntheir cities. Sure, Skibbereen is a mud-pond to them. It might be fine\nto be an Englishman.\"\n\n\"I would not, your honour,\" said Paddy. \"I would not be an Englishman\nwhile these grand--But never mind; 'tis many proud things I will say\nabout the English considering they are our neighbours in one way; I\nmean they are near enough to come over and harm us when they wish. But\nany how they are a remarkable hard-headed lot, and in time they may\ncome to something good.\"\n\n\"And is a hard head such a qualification?\" said I.\n\nPaddy became academic. \"I have been knowing two kinds of hard heads,\"\nhe said. \"Mickey McGovern had such a hard skull on him no stick in the\nsouth of Ireland could crack it, though many were tried. And what\nhappened to him? He died poor as a rat. 'Tis not the kind of hard head\nI am meaning. I am meaning the kind of hard head which believes it\ncontains all the wisdom and honour in the world. 'Tis what I mean. If\nyou have a head like that, you can go along blundering into ditches\nand tumbling over your own shins, and still hold confidence in\nyourself. 'Tis not very handsome for other men to see; but devil a bit\ncare you, for you are warm inside with complacence.\"\n\n\"Here is a philosopher, in God's truth,\" I cried. \"And where were you\nlearning all this? In Ireland?\"\n\n\"Your honour,\" said Paddy firmly, \"you yourself are an Irishman. You\nare not for saying there is no education in Ireland, for it educates a\nman to see burning thatches and such like. One of them was my aunt's,\nHeaven rest her!\"\n\n\"Your aunt?\" said I. \"And what of your aunt? What have the English to\ndo with your aunt?\"\n\n\"That's what she was asking them,\" said Paddy; \"but they burned her\nhouse down over a little matter of seventeen years' rent she owed to a\nfull-blooded Irishman, may the devil find him!\"\n\n\"But I am for going on without an account of your burnt-thatch\neducation,\" said I. \"You are having more than two opinions about the\nEnglish, and I would be hearing them. Seldom have I seen a man who\ncould gain so much knowledge in so short a space. You are interesting\nme.\"\n\nPaddy seemed pleased. \"Well, your honour,\" said he confidentially,\n\"'tis true for you. I am knowing the English down to their toes.\"\n\n\"And if you were an Englishman, what kind of an Englishman would you\nlike to be?\" said I.\n\n\"A gentleman,\" he answered swiftly. \"A big gentleman!\" Then he began\nto mimic and make gestures in a way that told me he had made good use\nof his eyes and of the society of underlings in the various inns.\n\"Where's me man? Send me man! Oh, here you are! And why didn't you\nknow I wanted you? What right have you to think I don't want you?\nWhat? A servant dead? Pah! Send it down the back staircase at once and\nget rid of it. Bedad!\" said Paddy enthusiastically, \"I could do that\nfine!\" And to prove what he said was true, he cried \"Pah!\" several\ntimes in a lusty voice.\n\n\"I see you have quickly understood many customs of the time,\" said I.\n\"But 'tis not all of it. There are many quite decent people alive\nnow.\"\n\n\"'Tis strange we have never heard tell of them,\" said Paddy musingly.\n\"I have only heard of great fighters, blackguards, and beautiful\nladies, but sure, as your honour says, there must be plenty of quiet\ndecent people somewhere.\"\n\n\"There is,\" said I. \"I am feeling certain of it, although I am not\nknowing exactly where to lay my hand upon them.\"\n\n\"Perhaps they would be always at mass,\" said Paddy, \"and in that case\nyour honour would not be likely to see them.\"\n\n\"Masses!\" said I. \"There are more masses said in Ireland in one hour\nthan here in two years.\"\n\n\"The people would be heathens, then?\" said Paddy, aghast.\n\n\"Not precisely,\" said I. \"But they have reformed themselves several\ntimes, and a number of adequate reformations is a fine thing to\nconfuse the Church. In Ireland we are all for being true to the\nancient faith; here they are always for improving matters, and their\nlearned men study the Sacred Book solely with a view to making needed\nchanges.\"\n\n\"'Tis heathen they are,\" said Paddy with conviction. \"I was knowing\nit. Sure, I will be telling Father Corrigan the minute I put a foot on\nIreland, for nothing pleases him so much as a good obstinate heathen,\nand he very near discourses the hair off their heads.\"\n\n\"I would not be talking about such matters,\" said I. \"It merely makes\nmy head grow an ache. My father was knowing all about it; but he was\nalways claiming that if a heathen did his duty by the poor he was as\ngood as anybody, and that view I could never understand.\"\n\n\"Sure, if a heathen gives to the poor, 'tis poison to them,\" said\nPaddy. \"If it is food and they eat it, they turn black all over and\ndie the day after. If it is money, it turns red-hot and burns a hole\nin their hand, and the devil puts a chain through it and drags them\ndown to hell, screeching.\"\n\n\"Say no more,\" said I. \"I am seeing you are a true theologian of the\ntime. I would be talking on some more agreeable topic, something about\nwhich you know less.\"\n\n\"I can talk of fishing,\" he answered diffidently. \"For I am a great\nfisherman, sure. And then there would be turf-cutting, and the deadly\nstings given to men by eels. All these things I am knowing well.\"\n\n\"'Tis a grand lot to know,\" said I, \"but let us be talking of London.\nHave you been hearing of London?\"\n\n\"I have been hearing much about the town,\" said Paddy. \"Father\nCorrigan was often talking of it. He was claiming it to be full of\nloose women, and sin, and fighting in the streets during mass.\"\n\n\"I am understanding something of the same,\" I replied. \"It must be an\nevil city. I am fearing something may happen to you, Paddy,--you with\nyour red head as conspicuous as a clock in a tower. The gay people\nwill be setting upon you and carrying you off. Sure there has never\nbeen anything like you in London.\"\n\n\"I am knowing how to be dealing with them. It will be all a matter of\nreligious up-bringing, as Father Corrigan was saying. I have but to go\nto my devotions, and the devil will fly away with them.\"\n\n\"And supposing they have your purse?\" said I. \"The devil might fly\naway with them to an ill tune for you.\"\n\n\"When they are flying away with my purse,\" he replied suggestively,\n\"they will be flying away with little of what could be called my\nancestral wealth.\"\n\n\"You are natural rogues,\" said I, \"you and Jem Bottles. And you had\nbest not be talking of religion.\"\n\n\"Sure a man may take the purse of an ugly old sick monkey like him,\nand still go with an open face to confession,\" rejoined Paddy, \"and I\nwould not be backward if Father Corrigan's church was a mile beyond.\"\n\n\"And are you meaning that Father Corrigan would approve you in this\nrobbery?\" I cried.\n\n\"Devil a bit he would, your honour,\" answered Paddy indignantly. \"He\nwould be saying to me: 'Paddy, you limb of Satan, and how much did you\nget?' I would be telling him. 'Give fifteen guineas to the Church, you\nmortal sinner, and I will be trying my best for you,' he would be\nsaying. And I would be giving them.\"\n\n\"You are saved fifteen guineas by being in England, then,\" said I,\n\"for they don't do that here. And I am thinking you are traducing your\nclergy, you vagabond.\"\n\n\"Traducing?\" said he. \"That would mean giving them money. Aye, I was\ndoing it often. One year I gave three silver shillings.\"\n\n\"You're wrong,\" said I. \"By 'traducing' I mean speaking ill of your\npriest.\"\n\n\"'Speaking ill of my priest'?\" cried Paddy, gasping with amazement.\n\"Sure, my own mother never heard a word out of me!\"\n\n\"However,\" said I, \"we will be talking of other things. The English\nland seems good.\"\n\nPaddy cast his eye over the rainy landscape. \"I am seeing no turf for\ncutting,\" he remarked disapprovingly, \"and the potatoes would not be\ngrowing well here. 'Tis a barren country.\"\n\nAt nightfall we came to a little inn which was ablaze with light and\nringing with exuberant cries. We gave up our horses and entered. To\nthe left was the closed door of the taproom, which now seemed to\nfurnish all the noise. I asked the landlord to tell me the cause of\nthe excitement.\n\n\"Sir,\" he answered, \"I am greatly honoured to-night. Mr. O'Ruddy, the\ncelebrated Irish swordsman, is within, recounting a history of his\nmarvellous exploits.\"\n\n\"Indeed!\" said I.\n\n\"Bedad!\" said Paddy.\n\n\n\n\nCHAPTER XVI\n\n\nPaddy was for opening his mouth wide immediately, but I checked him.\n\"I would see this great man,\" said I to the landlord, \"but I am so\ntimid by nature I fear to meet his eagle eye. Is there no way by which\nwe could observe him in secret at our leisure?\"\n\n\"There be one way,\" remarked the landlord after deliberation. I had\npassed him a silver coin. He led us to a little parlour back of the\ntaproom. Here a door opened into the tap itself, and in this door was\ncut a large square window so that the good man of the inn could\nsometimes sit at his ease in his great chair in the snug parlour and\nobserve that his customers had only that for which they were paying.\nIt is a very good plan, for I have seen many a worthy man become a\nrogue merely because nobody was watching him. My father often was\nsaying that if he had not been narrowly eyed all his young life, first\nby his mother and then by his wife, he had little doubt but what he\nmight have been engaged in dishonest practices sooner or later.\n\nA confident voice was doing some high talking in the taproom. I peered\nthrough the window, but at first I saw only a collection of gaping\nyokels, poor bent men with faces framed in straggly whiskers. Each had\na pint pot clutched with a certain air of determination in his right\nhand.\n\nSuddenly upon our line of vision strode the superb form of Jem\nBottles. A short pipe was in his mouth, and he gestured splendidly\nwith a pint pot. \"More of the beer, my dear,\" said he to a buxom maid.\n\"We be all rich in Ireland. And four of them set upon me,\" he cried\nagain to the yokels. \"All noblemen, in fine clothes and with\nsword-hilts so flaming with jewels an ordinary man might have been\nblinded. 'Stop!' said I. 'There be more of your friends somewhere.\nCall them.' And with that--\"\n\n\"'And with that'?\" said I myself, opening the door and stepping in\nupon him. \"'And with that'?\" said I again. Whereupon I smote him a\nblow which staggered him against the wall, holding his crown with both\nhands while his broken beer-pot rolled on the floor. Paddy was dancing\nwith delight at seeing some other man cuffed, but the landlord and the\nyokels were nearly dead of terror. But they made no sound; only the\nbuxom girl whimpered.\n\n\"There is no cause for alarm,\" said I amiably. \"I was only greeting an\nold friend. 'Tis a way I have. And how wags the world with you,\nO'Ruddy?\"\n\n\"I am not sure for the moment,\" replied Jem Bottles ruefully. \"I must\nbide till it stops spinning.\"\n\n\"Truth,\" cried I. \"That would be a light blow to trouble the great\nO'Ruddy. Come now; let us have the pots filled again, and O'Ruddy\nshall tell us more of his adventures. What say you, lads?\"\n\nThe yokels had now recovered some of their senses, and they greeted my\nplan with hoarse mutterings of hasty and submissive assent.\n\n\"Begin,\" said I sternly to the highwayman. He stood miserably on one\nfoot. He looked at the floor; he looked at the wall; from time to\ntime he gave me a sheep's glance. \"Begin,\" said I again. Paddy was\nwild with glee. \"Begin,\" said I for the third time and very harshly.\n\n\"I--\" gulped out the wretched man, but he could get no further.\n\n\"I am seeing I must help you,\" said I. \"Come now, when did you learn\nthe art of sticadoro proderodo sliceriscum fencing?\"\n\nBottles rolled the eyes of despair at me, but I took him angrily by\nthe shoulder. \"Come now; when did you learn the art of sticadoro\nproderodo sliceriscum fencing?\"\n\nJem Bottles staggered, but at last he choked out: \"My mother taught\nme.\" Here Paddy retired from the room, doubled in a strong but\nsoundless convulsion.\n\n\"Good,\" said I. \"Your mother taught you. We are making progress any\nhow. Your mother taught you. And now tell me this: When you slew\nCormac of the Cliffs, what passado did you use? Don't be stuttering.\nCome now; quick with you; what passado did you use? What passado?\"\n\nWith a heroism born of a conviction that in any event he was a lost\nman, Jem Bottles answered: \"A blue one.\"\n\n\"Good,\" I cried cheerfully. \"'A blue one'! We are coming on fine. He\nkilled Cormac with a blue passado. And now I would be asking you--\"\n\n\"Master,\" interrupted the highwayman with sudden resolution. \"I will\nsay no more. I have done. You may kill me an it pleases you.\"\n\nNow I saw that enough was enough. I burst into laughter and clapped\nhim merrily on the shoulder. \"Be cheery, O'Ruddy,\" I cried. \"Sure an\nIrishman like you ought to be able to look a joke in the face.\" He\ngave over his sulks directly, and I made him buy another pint each for\nthe yokels. \"'Twas dry work listening to you and your exploits,\nO'Ruddy,\" said I.\n\nLater I went to my chamber, attended by my followers, having ordered\nroast fowls and wine to be served as soon as possible. Paddy and Jem\nBottles sat on stools one at each side of the fireplace, and I\noccupied a chair between them.\n\nLooking at my two faithful henchmen, I was suddenly struck by the\nthought that they were not very brisk servants for a gentleman to take\nto fashionable London. I had taken Paddy out of his finery and dressed\nhim in a suit of decent brown; but his hair was still unbarbered, and\nI saw that unless I had a care his appearance would greatly surprise\nand please London. I resolved to have him shorn at the first large\ntown.\n\nAs for Jem Bottles, his clothes were well enough, and indeed he was\npassable in most ways unless it was his habit, when hearing a sudden\nnoise, to take a swift dark look to the right and to the left. Then,\nfurther, people might shrewdly note his way of always sitting with his\nback to the wall and his face to the door. However, I had no doubt of\nmy ability to cure him of these tricks as soon as he was far enough\njourneyed from the scenes of his earlier activity.\n\nBut the idea I entertained at this moment was more to train them to be\nfine grand servants, such as I had seen waiting on big people in Bath.\nThey were both willing enough, but they had no style to them. I\ndecided to begin at once and see what I could teach them.\n\n\"Paddy,\" said I, taking off my sword and holding it out to him. \"My\nsword!\"\n\nPaddy looked at it. \"It is, sir,\" he answered respectfully.\n\n\"Bad scran to you, Paddy!\" I cried angrily. \"I am teaching you your\nduties. Take the sword! In both hands, mind you! Now march over and\nlay it very tenderly on the stand at the head of the bed. There now!\"\n\nI now turned my attention to Jem Bottles.\n\n\"Bottles,\" said I peremptorily, \"my coat and waistcoat.\"\n\n\"Yes, sir,\" replied Bottles quickly, profiting by Paddy's lesson.\n\n\"There now,\" said I, as Bottles laid the coat and waistcoat on a\ndresser. \"'Tis a good beginning. When supper comes I shall teach you\nother duties.\"\n\nThe supper came in due course, and after the inn's man had gone I bid\nJem and Paddy stand one on either side of my chair and a little way\nback. \"Now,\" said I, \"stand square on your feet, and hold your heads\naway high, and stick your elbows out a little, and try to look as if\nyou don't know enough to tell fire from water. Jem Bottles has it.\nThat's it! Bedad! look at the ignorance on him! He's the man for you,\nPaddy! Wake up now, and look stupid. Am I not telling you?\"\n\n\"Begor!\" said Paddy dejectedly, \"I feel like the greatest omadhaun in\nall the west country, and if that is not being stupid enough for your\nhonour I can do no better.\"\n\n\"Shame to you, Paddy, to let an Englishman beat you so easily,\" said\nI. \"Take that grin off your face, you scoundrel! Now,\" I added, \"we\nare ready to begin. Wait, now. You must each have something to hold in\nyour fist. Let me be thinking. There's only one plate and little of\nanything else. Ah, I have it! A bottle! Paddy, you shall hold one of\nthe bottles. Put your right hand underneath it, and with your left\nhand hold it by the neck. But keep your elbows out. Jem, what the\ndevil am I to give you to hold? Ah, I have it! Another bottle! Hold it\nthe same as Paddy. Now! Stand square on your feet, and hold your heads\naway high, and stick your elbows out a little, and look stupid. I am\ngoing to eat my supper.\"\n\nI finished my first and second bottles with the silence only broken by\nthe sound of my knife-play and an occasional restless creaking of\nboots as one of my men slyly shifted his position. Wishing to call for\nmy third bottle, I turned and caught them exchanging a glance of\nsympathetic bewilderment. As my eye flashed upon them, they stiffened\nup like grenadier recruits.\n\nBut I was not for being too hard on them at first. \"'Tis enough for\none lesson,\" said I. \"Put the bottles by me and take your ease.\"\n\nWith evident feelings of relief they slunk back to the stools by the\nfire, where they sat recovering their spirits.\n\nAfter my supper I sat in the chair toasting my shins and lazily\nlistening to my lads finishing the fowls. They seemed much more like\nthemselves, sitting there grinding away at the bones and puffing with\njoy. In the red firelight it was such a scene of happiness that I\nmisdoubted for a moment the wisdom of my plan to make them into fine\ngrand numskulls.\n\nI could see that all men were not fitted for the work. It needed a\nbeefy person with fat legs and a large amount of inexplicable dignity,\na regular God-knows-why loftiness. Truth, in those days, real talent\nwas usually engaged in some form of rascality, barring the making of\nbooks and sermons. When one remembers the impenetrable dulness of the\ngreat mass of the people, the frivolity of the gentry, the arrogance\nand wickedness of the court, one ceases to wonder that many men of\ntaste took to the highway as a means of recreation and livelihood. And\nthere I had been attempting to turn my two frank rascals into the kind\nof sheep-headed rubbish whom you could knock down a great staircase,\nand for a guinea they would say no more. Unless I was the kicker, I\nthink Paddy would have returned up the staircase after his assailant.\nJem Bottles probably would have gone away nursing his wrath and his\ninjury, and planning to waylay the kicker on a convenient night. But\nneither would have taken a guinea and said no more. Each of these\nsimple-hearted reprobates was too spirited to take a guinea for a kick\ndown a staircase.\n\nAny how I had a mind that I could be a gentleman true enough without\nthe help of Jem and Paddy making fools of themselves. I would worry\nthem no more.\n\nAs I was musing thus my eyes closed from a sense of contented\nweariness, but I was aroused a moment later by hearing Paddy address\nJem Bottles in a low voice. \"'Tis you who are the cool one, Jem!\"\nsaid he with admiration, \"trying to make them think you were _him_!\"\nHere I was evidently indicated by a sideways bob of the head. \"Have\nyou not been seeing the fine ways of him? Sure, be looking at his\nstride and his habit of slatting people over the head, and his grand\nmanners with his food. You are looking more like a candlestick than\nyou are looking like him. I wonder at you.\"\n\n\"But I befooled them,\" said Bottles proudly. \"I befooled them well. It\nwas Mr. O'Ruddy here, and Mr. O'Ruddy there, and the handsome wench\nshe gave me many a glance of her eye, she did.\"\n\n\"Sorrow the day for her, then,\" responded Paddy, \"and if you would be\ncozening the girls in the name of _him_ there, he will be cozening\nyou, and I never doubt it.\"\n\n\"'Twas only a trick to make the time go easy, it was,\" said Bottles\ngloomily. \"If you remember, Master Paddy, I have spent the most of my\nnew service waiting under oak-trees; and I will not be saying that it\nrained always, but oft-times it did rain most accursedly.\"\n\n\n\n\nCHAPTER XVII\n\n\nWe rode on at daybreak. At the first large village I bid a little man\ncut Paddy's hair, and although Paddy was all for killing the little\nman, and the little man twice ran away, the work was eventually done,\nfor I stood over Paddy and threatened him. Afterward the little boys\nwere not so anxious to hoot us through the streets, calling us\nAfricans. For it must be recalled that at this time there was great\ncuriosity in the provinces over the Africans, because it was known\nthat in London people of fashion often had African servants; and\nalthough London cared nothing for the provinces, and the provinces\ncared nothing for London, still the rumour of the strange man\ninterested the country clodhopper so greatly that he called Paddy an\nAfrican on principle, in order that he might blow to his neighbours\nthat he had seen the fascinating biped. There was no general\nunderstanding that the African was a man of black skin; it was only\nunderstood that he was a great marvel. Hence the urchins in these\nfar-away villages often ran at the heels of Paddy's horse, yelling.\n\nIn time the traffic on the highway became greatly thickened, and\nseveral times we thought we were entering London because of the large\nsize and splendour of the towns to which we came. Paddy began to fear\nthe people had been deceiving us as to the road, and that we had\nmissed London entirely. But finally we came to a river with hundreds\nof boats upon it, and there was a magnificent bridge, and on the other\nbank was a roaring city, and through the fog the rain came down thick\nas the tears of the angels. \"That's London,\" said I.\n\nWe rode out upon the bridge, all much interested, but somewhat\nfearful, for the noise of the city was terrible. But if it was\nterrible as we approached it, I hesitate to say what it was to us when\nwe were once fairly in it. \"Keep close to me,\" I yelled to Paddy and\nJem, and they were not unwilling. And so we rode into this\npandemonium, not having the least idea where we were going.\n\nAs we progressed I soon saw what occasioned the major part of the\nnoise. Many heavy carts thundered slowly through the narrow, echoing\nstreets, bumping their way uproariously over a miserable pavement.\nAdded to this, of course, were the shrill or hoarse shouts of the\nstreet vendors and the apprentices at the shop-doors. To the sky arose\nan odour almost insupportable, for it was new to us all.\n\nThe eaves of the houses streamed with so much water that the sidewalks\nwere practically untenable, although here and there a hardy wayfarer\nstrode on regardless of a drenched cloak, probably being too proud to\ntake to the street. Once our travel was entirely blocked by a fight. A\nbutcher in a bloody apron had dashed out of his shop and attacked the\ndriver of a brewer's sledge. A crowd gathered miraculously and cheered\non this spectacle; women appeared at all the windows; urchins hooted;\nmongrel dogs barked. When the butcher had been worsted and chased\nback into his shop by the maddened brewer we were allowed to pursue\nour journey.\n\nI must remark that neither of these men used aught but his hands.\nMostly their fists were doubled, and they dealt each other sounding,\nswinging blows; but there was some hair-pulling, and when the brewer\nhad the butcher down I believe the butcher tried to bite his\nopponent's ear. However they were rather high-class for their\ncondition. I found out later that at this time in the darker parts of\nLondon the knife was a favourite weapon of the English and was as\nrampant as ever it is in the black alleys of an Italian city. It was\nno good news for me, for the Irish had long been devoted to the\ncudgel.\n\nWhen I wish for information I always prefer making the request to a\ngentleman. To have speech of a boor is well enough if he would not\nfirst study you over to find, if he can, why you want the information,\nand, after a prolonged pause, tell you wrong entirely. I perceived a\nyoung gentleman standing in under a porch and ogling a window on the\nopposite side of the way. \"Sir,\" said I, halting my horse close to\nhim, \"would you be so kind as to point to a stranger the way to a good\ninn?\" He looked me full in the face, spat meaningly in the gutter,\nand, turning on his heel, walked away. And I will give oath he was not\nmore than sixteen years old.\n\nI sat stiff in the saddle; I felt my face going hot and cold. This\nnew-feathered bird with a toy sword! But to save me, as it happened,\nfrom a preposterous quarrel with this infant, another man came along\nthe sidewalk. He was an older man, with a grave mouth and a clean-cut\njowl. I resolved to hail him. \"And now my man,\" said I under my\nbreath, \"if you are as bad as the other, by the mass, I'll have a\nturnover here with you, London or no London.\"\n\nThen I addressed him. \"Sir--\" I began. But here a cart roared on my\nother side, and I sat with my mouth open, looking at him. He smiled a\nlittle, but waited courteously for the hideous din to cease. \"Sir,\" I\nwas enabled to say at last, \"would you be so kind as to point to a\nstranger the way to a good inn?\" He scanned me quietly, in order, no\ndoubt, to gain an idea what kind of inn would suit my condition.\n\"Sir,\" he answered, coming into the gutter and pointing, \"'tis this\nway to Bishopsgate Street, and there you will see the sign of the 'Pig\nand Turnip,' where there is most pleasurable accommodation for man and\nbeast, and an agreeable host.\" He was a shop-keeper of the city of\nLondon, of the calm, steady breed that has made successive kings\neither love them or fearingly hate them,--the bone and the sinew of\nthe great town.\n\nI thanked him heartily, and we went on to the \"Pig and Turnip.\" As we\nclattered into the inn yard it was full of people mounting and\ndismounting, but there seemed a thousand stable-boys. A dozen flung\nthemselves at my horse's head. They quite lifted me out of the saddle\nin their great care that I should be put to no trouble. At the door of\nthe inn a smirking landlord met me, bowing his head on the floor at\nevery backward pace, and humbly beseeching me to tell how he could\nbest serve me. I told him, and at once there was a most pretentious\nhubbub. Six or eight servants began to run hither and yon. I was\ndelighted with my reception, but several days later I discovered they\nhad mistaken me for a nobleman of Italy or France, and I was expected\nto pay extravagantly for graceful empty attentions rather than for\nsound food and warm beds.\n\nThis inn was so grand that I saw it would no longer do for Paddy and\nJem to be sleeping in front of my fire like big dogs, so I nodded\nassent when the landlord asked if he should provide lodgings for my\ntwo servants. He packed them off somewhere, and I was left lonely in a\ngreat chamber. I had some fears having Paddy long out of my sight, but\nI assured myself that London had such terrors for him he would not\ndare any Irish mischief. I could trust Jem Bottles to be discreet, for\nhe had learned discretion in a notable school.\n\nToward the close of the afternoon, the rain ceased, and, attiring\nmyself for the street and going to the landlord, I desired him to tell\nme what interesting or amusing walk could now conveniently be taken by\na gentleman who was a stranger to the sights of London. The man wagged\nhis head in disapproval.\n\n\"'Twill be dark presently, sir,\" he answered, \"and I would be an ill\nhost if I did not dissuade a perfect stranger from venturing abroad in\nthe streets of London of a night-time.\"\n\n\"And is it as bad as that?\" I cried, surprised.\n\n\"For strangers, yes,\" said he. \"For they be for ever wandering, and\nwill not keep to the three or four streets which be as safe as the\nKing's palace. But if you wish, sir, I will provide one man with a\nlantern and staff to go before you, and another man with lantern and\nstaff to follow. Then, with two more stout lads and your own servants,\nI would venture--\"\n\n\"No, no!\" I cried, \"I will not head an army on a night march when I\nintended merely an evening stroll. But how, pray you, am I to be\nentertained otherwise than by going forth?\"\n\nThe innkeeper smiled with something like pity.\n\n\"Sir, every night there meets here such a company of gay gentlemen,\nwits and poets, as would dazzle the world did it but hear one half of\nwhat they say over their pipes and their punch. I serve the\ndistinguished company myself, for I dare trust nobody's care in a\nmatter so important to my house; and I assure you, sir, I have at\ntimes been so doubled with mirth there was no life in me. Why, sir,\nMr. Fullbil himself comes here at times!\"\n\n\"Does he, indeed?\" I cried, although I never had heard of the\nillustrious man.\n\n\"Indeed and he does, sir,\" answered the innkeeper, pleased at my quick\nappreciation of this matter. \"And then there is goings on, I warrant\nme. Mr. Bobbs and the other gentlemen will be in spirits.\"\n\n\"I never doubt you,\" said I. \"But is it possible for a private\ngentleman of no wit to gain admittance to this distinguished company?\"\n\n\"Doth require a little managing, sir,\" said he, full of meaning.\n\n\"Pray you manage it then,\" said I, \"for I have nought to do in London\nfor at least two days, and I would be seeing these famous men with\nwhose names my country rings.\"\n\nEarly in the evening the innkeeper came to me, much pleased. \"Sir, the\ngentlemen bid me bring you their compliments, and I am to say they\nwould be happy to have a pleasure in the honour of your presence. Mr.\nFullbil himself is in the chair to-night. You are very fortunate,\nsir.\"\n\n\"I am,\" said I. \"Lead away, and let us hope to find the great Fullbil\nin high feather.\"\n\n\n\n\nCHAPTER XVIII\n\n\nThe innkeeper led me down to a large room the door of which he had\nflung open with a flourish. \"The furrin' gentleman, may it please you,\nsirs,\" he announced, and then retired.\n\nThe room was so full of smoke that at first I could see little, but\nsoon enough I made out a long table bordered with smoking and drinking\ngentlemen. A hoarse voice, away at the head of the board, was growling\nsome words which convulsed most of the gentlemen with laughter. Many\ncandles burned dimly in the haze.\n\nI stood for a moment, doubtful as to procedure, but a gentleman near\nthe foot of the table suddenly arose and came toward me with great\nfrankness and good nature. \"Sir,\" he whispered, so that he would not\ninterrupt the growls at the farther end of the room, \"it would give me\npleasure if you would accept a chair near me.\"\n\nI could see that this good gentleman was moved solely by a desire to\nbe kind to a stranger, and I, in another whisper, gave my thanks and\nassent to his plan. He placed me in a chair next his own. The voice\nwas still growling from the head of the table.\n\nVery quickly my eyes became accustomed to the smoke, especially after\nI was handed a filled clay pipe by my new and excellent friend. I\nbegan to study the room and the people in it. The room was panelled\nin new oak, and the chairs and table were all of new oak, well carved.\nIt was the handsomest room I had ever been in.\n\nAfterward I looked toward the growl. I saw a little old man in a chair\nmuch too big for him, and in a wig much too big for him. His head was\nbent forward until his sharp chin touched his breast, and out from\nunder his darkling brows a pair of little eyes flashed angrily and\narrogantly. All faces were turned toward him, and all ears were open\nto his growls. He was the king; it was Fullbil.\n\nHis speech was all addressed to one man, and I looked at the latter.\nHe was a young man with a face both Roman and feminine; with that type\nof profile which is possessed by most of the popular actors in the\nreign of His Majesty of to-day. He had luxuriant hair, and, stung by\nthe taunts of Fullbil, he constantly brushed it nervously from his\nbrow while his sensitive mouth quivered with held-in retorts. He was\nBobbs, the great dramatist.\n\nAnd as Fullbil growled, it was a curiously mixed crowd which applauded\nand laughed. There were handsome lordlings from the very top of London\ncheek by cheek with sober men who seemed to have some intellectual\noccupation in life. The lordlings did the greater part of the\nsniggering. In the meantime everybody smoked hard and drank punch\nharder. During occasional short pauses in Fullbil's remarks, gentlemen\npassed ecstatic comments one to another.--\"Ah, this is indeed a mental\nfeast!\"--\"Did ye ever hear him talk more wittily?\"--\"Not I, faith; he\nsurpasses even himself!\"--\"Is it not a blessing to sit at table with\nsuch a master of learning and wit?\"--\"Ah, these are the times to live\nin!\"\n\nI thought it was now opportune to say something of the same kind to my\namiable friend, and so I did it. \"The old corpse seems to be saying a\nprayer,\" I remarked. \"Why don't he sing it?\"\n\nMy new friend looked at me, all agape, like a fish just over the side\nof the boat. \"'Tis Fullbil, the great literary master--\" he began; but\nat this moment Fullbil, having recovered from a slight fit of\ncoughing, resumed his growls, and my friend subsided again into a\nworshipping listener.\n\nFor my part I could not follow completely the words of the great\nliterary master, but I construed that he had pounced upon the drama of\nthe time and was tearing its ears and eyes off.\n\nAt that time I knew little of the drama, having never read or seen a\nplay in my life; but I was all for the drama on account of poor Bobbs,\nwho kept chewing his lip and making nervous movements until Fullbil\nfinished, a thing which I thought was not likely to happen before an\nearly hour of the morning. But finish he did, and immediately Bobbs,\nmuch impassioned, brought his glass heavily down on the table in a\ndemand for silence. I thought he would get little hearing, but, much\nto my surprise, I heard again the ecstatic murmur: \"Ah, now, we shall\nhear Bobbs reply to Fullbil!\"--\"Are we not fortunate?\"--\"Faith, this\nwill be over half London to-morrow!\"\n\nBobbs waited until this murmur had passed away. Then he began, nailing\nan impressive forefinger to the table:\n\n\"Sir, you have been contending at some length that the puzzling\nsituations which form the basis of our dramas of the day could not\npossibly occur in real life because five minutes of intelligent\nexplanation between the persons concerned would destroy the silly\nmystery before anything at all could happen. Your originality, sir, is\nfamous--need I say it?--and when I hear you champion this opinion in\nall its majesty of venerable age and general acceptance I feel stunned\nby the colossal imbecile strength of the whole proposition. Why, sir,\nyou may recall all the mysterious murders which occurred in England\nsince England had a name. The truth of them remains in unfathomable\nshadow. But, sir, any one of them could be cleared up in five minutes'\nintelligent explanation. Pontius Pilate could have been saved his\nblunder by far, far, far less than five minutes of intelligent\nexplanation. But--mark ye!--but who has ever heard five minutes of\nintelligent explanation? The complex interwoven mesh of life\nconstantly, eternally, prevents people from giving intelligent\nexplanations. You sit in the theatre, and you say to yourself: 'Well,\nI could mount the stage, and in a short talk to these people I could\nanticipate a further continuation of the drama.' Yes, you could; but\nyou are an outsider. You have no relations with these characters. You\narise like an angel. Nobody has been your enemy; nobody has been your\nmistress. You arise and give the five minutes' intelligent\nexplanation; bah! There is not a situation in life which does not need\nfive minutes' intelligent explanation; but it does not get it.\"\n\nIt could now be seen that the old man Fullbil was simply aflame with a\ndestructive reply, and even Bobbs paused under the spell of this\nanticipation of a gigantic answering. The literary master began very\ndeliberately.\n\n\"My good friend Bobbs,\" said he, \"I see your nose gradually is turning\nred.\"\n\nThe drama immediately pitched into oblivion. The room thundered with a\ngreat shout of laughter that went to the ceiling. I could see Bobbs\nmaking angry shouts against an invulnerable bank of uncontrolled\nmerriment. And amid his victory old Fullbil sat with a vain smile on\nhis cracked lips.\n\nMy excellent and adjacent friend turned to me in a burst of\nenthusiasm.\n\n\"And did you ever hear a thing so well turned? Ha, ha! 'My good friend\nBobbs,' quoth he, 'I see your nose gradually is turning red.' Ha, ha,\nha! By my King, I have seldom heard a wittier answer.\"\n\n\"Bedad!\" said I, somewhat bewildered, but resolved to appreciate the\nnoted master of wit, \"it stamped the drama down into the ground. Sure,\nnever another play will be delivered in England after that tremendous\noverthrow.\"\n\n\"Aye,\" he rejoined, still shuddering with mirth, \"I fail to see how\nthe dramatists can survive it. It was like the wit of a new\nShakespeare. It subsided Bobbs to nothing. I would not be surprised at\nall if Bobbs now entirely quit the writing of plays, since Fullbil's\nwords so closely hit his condition in the dramatic world. A dangerous\ndog is this Fullbil.\"\n\n\"It reminds me of a story my father used to tell--\" I began.\n\n\"Sir,\" cried my new friend hastily, \"I beg of you! May I, indeed,\ninsist? Here we talk only of the very deepest matters.\"\n\n\"Very good, sir,\" I replied amiably. \"I will appear better, no doubt,\nas a listener; but if my father was alive--\"\n\n\"Sir,\" beseeched my friend, \"the great Fancher, the immortal critic,\nis about to speak.\"\n\n\"Let him,\" said I, still amiable.\n\nA portly gentleman of middle age now addressed Bobbs amid a general\nand respectful silence.\n\n\"Sir,\" he remarked, \"your words concerning the great age of what I\nshall call the five-minutes-intelligent-explanation theory was first\ndeveloped by the Chinese, and is contemporaneous, I believe, with\ntheir adoption of the custom of roasting their meat instead of eating\nit raw.\"\n\n\"Sir, I am interested and instructed,\" rejoined Bobbs.\n\nHere old Fullbil let go two or three growls of scornful disapproval.\n\n\"Fancher,\" said he, \"my delight in your company is sometimes dimmed by\nmy appreciation of your facilities for being entirely wrong. The great\ntheory of which you speak so confidently, sir, was born no earlier\nthan seven o'clock on the morning of this day. I was in my bed, sir;\nthe maid had come in with my tea and toast. 'Stop,' said I, sternly.\nShe stopped. And in those few moments of undisturbed reflection, sir,\nthe thought came to life, the thought which you so falsely attribute\nto the Chinese, a savage tribe whose sole distinction is its ability\nto fly kites.\"\n\nAfter the murmurs of glee had died away, Fancher answered with spirit:\n\n\"Sir, that you are subject to periods of reflection I will not deny, I\ncannot deny. Nor can I say honourably that I give my support to our\ndramatic friend's defence of his idea. But, sir, when you refer to the\nChinese in terms which I cannot but regard as insulting, I am\nprepared, sir, to--\"\n\nThere were loud cries of \"Order! Order! Order!\" The wrathful Fancher\nwas pulled down into his chair by soothful friends and neighbours, to\nwhom he gesticulated and cried out during the uproar.\n\nI looked toward old Fullbil, expecting to see him disturbed, or\nannoyed, or angry. On the contrary he seemed pleased, as a little boy\nwho had somehow created a row.\n\n\"The excellent Fancher,\" said he, \"the excellent Fancher is wroth. Let\nus proceed, gentlemen, to more friendly topics. You, now, Doctor\nChord, with what new thing in chemics are you ready to astound us?\"\n\nThe speech was addressed to a little man near me, who instantly\nblushed crimson, mopping his brow in much agitation, and looked at the\ntable, unable for the moment to raise his eyes or speak a word.\n\n\"One of the greatest scientists of the time,\" said my friend in my\near.\n\n\"Sir,\" faltered the little man in his bashfulness, \"that part of the\ndiscourse which related to the flying of kites has interested me\ngreatly, and I am ready to contend that kites fly, not, as many say,\nthrough the influence of a demon or spirit which inhabits the\nmaterials, but through the pressure of the wind itself.\"\n\nFancher, now himself again, said:\n\n\"I wish to ask the learned doctor whether he refers to Chinese kites?\"\n\nThe little man hurriedly replied that he had not Chinese kites in his\nmind at all.\n\n\"Very good, then,\" said the great critic. \"Very good.\"\n\n\"But, sir,\" said Fullbil to little Chord, \"how is it that kites may\nfly without the aid of demons or spirits, if they are made by man? For\nit is known, sir, that man may not move in the air without the aid of\nsome devilish agency, and it is also known that he may not send aloft\nthings formed of the gross materials of the earth. How, then, can\nthese kites fly virtuously?\"\n\nThere was a general murmur of approbation of Fullbil's speech, and the\nlittle doctor cast down his eyes and blushed again, speechless.\n\nIt was a triumph for Fullbil, and he received the congratulations of\nhis friends with his faint vain smile implying that it was really\nnothing, you know, and that he could have done it much better if he\nhad thought that anybody was likely to heed it.\n\nThe little Doctor Chord was so downtrodden that for the remainder of\nthe evening he hardly dared to raise his eyes from the table, but I\nwas glad to see him apply himself industriously to the punch.\n\nTo my great alarm Fullbil now said: \"Sirs, I fear we have suffered\nourselves to forget we have with us to-night a strange gentleman from\nforeign parts. Your good fortune, sir,\" he added, bowing to me over\nhis glass. I bowed likewise, but I saw his little piggish eyes looking\nwickedly at me. There went a titter around the board, and I understood\nfrom it that I was the next victim of the celebrated Fullbil.\n\n\"Sir,\" said he, \"may I ask from what part of Italy do you come?\"\n\n\"I come from Ireland, sir,\" I answered decently.\n\nHe frowned. \"Ireland is not in Italy, sir,\" said he. \"Are you so good\nas to trifle with me, sir?\"\n\n\"I am not, sir,\" said I.\n\nAll the gentlemen murmured; some looked at me with pity, some with\ncontempt. I began to be frightened until I remembered that if I once\ndrew my sword I could chase the whole roomful of philosophy into the\nnext parish. I resolved to put on a bold front.\n\n\"Probably, sir,\" observed Fullbil, \"the people of Ireland have heard\nso much of me that I may expect many visits from Irish gentlemen who\nwish to hear what my poor mind may develop in regard to the only true\nphilosophy of life?\"\n\n\"Not in the least, sir,\" I rejoined. \"Over there they don't know you\nare alive, and they are not caring.\"\n\nConsternation fell upon that assembly like snow from a roof. The\ngentlemen stared at me. Old Fullbil turned purple at first, but his\ngrandeur could not be made to suffer long or seriously from my\nimpudence. Presently he smiled at me,--a smile confident, cruel,\ndeadly.\n\n\"Ireland is a great country, sir,\" he observed.\n\n\"'Tis not so great as many people's ignorance of it,\" I replied\nbluntly, for I was being stirred somewhat.\n\n\"Indeed!\" cried Fullbil. Then he triumphantly added: \"Then, sir, we\nare proud to have among us one so manifestly capable of giving us\ninstruction.\"\n\nThere was a loud shout of laughter at this sally, and I was very\nuncomfortable down to my toes; but I resolved to hold a brave face,\nand pretended that I was not minding their sneers. However, it was\nplain enough that old Fullbil had made me the butt of the evening.\n\n\"Sir,\" said the dramatist Bobbs, looking at me, \"I understand that in\nIreland pigs sit at table with even the best families.\"\n\n\"Sir,\" said the critic, Fancher, looking at me, \"I understand that in\nIreland the chastity of the women is so great that no child is born\nwithout a birthmark in the shape of the initials of the legal husband\nand father.\"\n\n\"Sir,\" said old Fullbil, \"I understand that in Ireland people go naked\nwhen it rains, for fear of wetting their clothes.\"\n\nAmid the uproarious merriment provoked by their speeches I sat in\nsilence. Suddenly the embarrassed little scientist, Doctor Chord,\nlooked up at me with a fine friendly sympathy. \"A glass with you,\nsir,\" he said, and as we nodded our heads solemnly over the rims I\nfelt that there had come to my help one poor little frightened friend.\nAs for my first acquaintance, he, seeing me attacked not only by the\nredoubtable Fullbil, but also by the formidable Bobbs and the\ndangerous Fancher, had immediately begun to pretend that never in his\nlife had he spoken to me.\n\nHaving a great knowledge of Irish character I could see that trouble\nwas brewing for somebody, but I resolved to be very backward, for I\nhesitated to create a genuine disturbance in these philosophical\ncircles. However, I was saved this annoyance in a strange manner. The\ndoor opened, and a newcomer came in, bowing right and left to his\nacquaintances, and finally taking a seat near Fullbil. I recognized\nhim instantly; he was Sir Edmund Flixton, the gentleman who had had\nsome thought of fighting me in Bath, but who had refrained from it\nupon hearing that I had worsted Forister.\n\nHowever, he did not perceive me at that time. He chattered with\nFullbil, telling him evidently some very exciting news, for I heard\nthe old man ejaculate. \"By my soul, can it be possible?\" Later Fullbil\nrelated some amusing things to Flixton, and, upon an inquiry from\nFlixton, I was pointed out to him. I saw Flixton's face change; he\nspoke hastily to old Fullbil, who turned pale as death. Swiftly some\nbit of information flashed around the board, and I saw men's eyes open\nwide and white as they looked at me.\n\nI have said it was the age of bullies. It was the age when men of\nphysical prowess walked down the street shouldering lesser men into\nthe gutter, and the lesser men had never a word to say for themselves.\nIt was the age when if you expressed opinions contrary to those of a\nbully he was confidently expected to kill you or somehow maltreat you.\n\nOf all that company of genius there now seemed to be only one\ngentleman who was not a-tremble. It was the little scientist Doctor\nChord. He looked at me with a bright and twinkling eye; suddenly he\ngrinned broadly. I could not but burst into laughter when I noted the\nappetite with which he enjoyed the confusion and alarm of his friends.\n\n\"Come, Fullbil! Come, Bobbs! Come, Fancher! Where are all your pretty\nwits?\" he cried; for this timid little man's impudence increased\nmightily amid all this helpless distress. \"Here's the dignity and\npower of learning of you, in God's truth. Here's knowledge enthroned,\nfearless, great! Have ye all lost your tongues?\"\n\nAnd he was for going on to worry them, but that I called out to him,--\n\n\"Sir,\" said I mildly, \"if it please you, I would not have the\ngentlemen disturbed over any little misunderstanding of a pleasant\nevening. As regards quarrelling, I am all milk and water myself. It\nreminds me of an occasion in Ireland once when--\" Here I recounted a\nstory which Father Donovan always began on after more than three\nbottles, and to my knowledge he had never succeeded in finishing it.\nBut this time I finished it. \"And,\" said I, \"the fellow was sitting\nthere drinking with them, and they had had good fun with him, when of\na sudden he up and spoke. Says he: ''Tis God's truth I never expected\nin all my life to be an evening in the company of such a lot of scurvy\nrat-eaters,' he says to them. 'And,' says he, 'I have only one word\nfor that squawking old masquerading peacock that sits at the head of\nthe table,' says he. 'What little he has of learning I could put in my\neye without going blind,' says he. 'The old curmudgeon!' says he. And\nwith that he arose and left the room, afterward becoming the King of\nGalway and living to a great age.\"\n\nThis amusing tale created a sickly burst of applause, in the midst of\nwhich I bowed myself from the room.\n\n\n\n\nCHAPTER XIX\n\n\nOn my way to my chamber I met the innkeeper and casually asked him\nafter Paddy and Jem. He said that he would send to have word of them\nand inform me as soon as possible. Later a drawer came to my door and\ntold me that Paddy and Jem, with three men-servants of gentlemen\nsleeping at the inn, had sallied out to a mug-house.\n\n\"Mug-house?\" said I. \"What in the devil's name is a mug-house?\"\n\n\"Mug-house, sir?\" said the man, staring. \"Mug-house? Why, sir,\n'tis--'tis a form of amusement, sir.\"\n\n\"It is, is it?\" said I. \"Very good. And does any one here know to what\nmug-house they went?\"\n\n\"The 'Red Slipper,' I think, sir,\" said the man.\n\n\"And how do I get to it?\" said I.\n\n\"Oh, sir,\" he cried, \"'tis impossible!\"\n\n\"Is it?\" said I. \"And why is it? The innkeeper said the same to me,\nand I would like to hear all the reasons.\"\n\n\"Sir,\" said the man, \"when it becometh dark in London there walk\nabroad many men of evil minds who are no respecters of persons, but\nfall upon whomsoever they, may, beating them sorely, having no regard\nfor that part of the Holy Book in which it is written--\"\n\n\"Let go,\" said I. \"I see what you mean.\" I then bade him get for me a\nstout lad with a cudgel and a lantern and a knowledge of the\nwhereabouts of the \"Red Slipper.\"\n\nI, with the stout lad, had not been long in the street before I\nunderstood what the landlord and the waiter had meant. In fact we were\nscarce out of the door before the man was menacing with his cudgel two\nhuman vultures who slunk upon us out of the shadow. I saw their pale,\nwicked, snarling faces in the glow of the lantern.\n\nA little later a great shindy broke out in the darkness, and I heard\nvoices calling loudly for a rally in the name of some guild or\nsociety. I moved closer, but I could make out little save that it was\na very pretty fight in which a company of good citizens were trying to\nput to flight a band of roughs and law-breakers. There was a merry\nrattling of sticks. Soon enough, answering shouts could be heard from\nsome of the houses, and with a great slamming of doors men rushed out\nto do battle for the peace of the great city. Meanwhile all the high\nwindows had been filled with night-capped heads, and some of these\npeople even went so far as to pour water down upon the combatants.\nThey also sent down cat-calls and phrases of witty advice. The sticks\nclattered together furiously; once a man with a bloody face staggered\npast us; he seemed to have been whacked directly on the ear by some\nuneducated person. It was as fine a shindy as one could hope to\nwitness, and I was deeply interested.\n\nThen suddenly a man called out hoarsely that he had been\nstabbed--murdered. There were yells from the street and screams from\nthe windows. My lantern-bearer plucked me madly by the sleeve. I\nunderstood him, and we hastily left the neighbourhood.\n\nI may tell now what had happened and what followed this affair of the\nnight. A worthy citizen had been stabbed to death indeed. After\nfurther skirmishes his comrade citizens had taken several wretches\ninto custody. They were tried for the murder and all acquitted save\none. Of this latter it was proven that the brawl had started through\nhis attempt to gain the purse of a passing citizen, and forthwith he\nwas sentenced to be hanged for murder. His companion rascals were sent\nto prison for long terms on the expectation that one of them really\nmight have been the murderer.\n\nWe passed into another street, where each well-lighted window framed\none or more painted hussies who called out in jocular obscenity, but\nwhen we marched stiffly on without replying their manner changed, and\nthey delivered at us volley after volley of language incredibly foul.\nThere were only two of these creatures who paid no heed, and their\nindifference to us was due to the fact that they were deeply engaged\nin a duel of words, exchanging the most frightful, blood-curdling\nepithets. Confident drunken men jostled us from time to time, and\nfrequently I could see small, ashy-faced, ancient-eyed youths dodging\nhere and there with food and wine. My lantern-bearer told me that the\nstreet was not quite awake; it was waiting for the outpourings from\nthe taverns and mug-houses. I bade him hurry me to the \"Red Slipper\"\nas soon as possible, for never have I had any stomach for these tawdry\nevils, fit as they are only for clerks and sailors.\n\nWe came at length to the creaking sign of the \"Red Slipper.\" A great\nnoise came from the place. A large company was roaring out a chorus.\nWithout many words I was introduced into the room in which the\ndisturbance was proceeding. It was blue with smoke, and the thundering\nchorus was still unfinished. I sank unnoticed into a quiet corner.\n\nI was astonished at the appearance of the company. There were many men\nwho looked like venerable prelates, and many men who looked like the\nheads of old and noble houses. I laughed in my sleeve when I\nremembered I had thought to find Paddy and Jem here. And at the same\ntime I saw them up near the head of the table, if it please you. Paddy\nhad his hand on the shoulder of a bishop, and Jem was telling some\ntale into the sympathetic ear of a marquis. At least this is the way\nmatters appeared to my stupefied sense.\n\nThe singing ceased, and a distinguished peer at my elbow resumed a\ntalk which evidently had been broken by the chorus:\n\n\"And so the Duke spoke with somewhat more than his accustomed vigour,\"\nsaid the distinguished peer.\n\nMy worst suspicions were confirmed. Here was a man talking of what had\nbeen said by a duke. I cast my eye toward my happy pair of rogues and\nwondered how I could ever extricate them from their position.\n\nSuddenly there was a loud pounding upon the table, and in the ensuing\nquiet the grave and dignified voice of the chairman could be heard:\n\n\"Gentlemen,\" he said, \"we crave your attention to a song by Mr. John\nSnowden.\"\n\nWhereupon my very own Jem Bottles arose amid a burst of applause, and\nbegan to sing a ballad which had been written in Bristol or Bath in\ncelebration of the notorious scoundrel Jem Bottles.\n\nHere I could see that if impudence could serve us we would not lack\nsuccess in England. The ballad was answered with wild cheers of\nappreciation. It was the great thing of the evening. Jem was\nstrenuously pressed to sing again, but he buried his face in his mug\nand modestly refused. However, they devoted themselves to his chorus\nand sang it over and over with immense delight. I had never imagined\nthat the nobility were so free and easy.\n\nDuring the excitement over Jem's ballad I stole forward to Paddy.\n\"Paddy,\" I whispered, \"come out of this now. 'Tis no place for you\nhere among all these reverend fathers and gentlemen of title. Shame on\nyou!\"\n\nHe saw my idea in a flash.\n\n\"Whist, sir,\" he answered. \"There are being no reverend fathers or\ngentlemen of title here. They are all after being footmen and valets.\"\n\nI was extremely vexed with myself. I had been in London only a brief\nspace; and Paddy had been in the city no longer. However, he had\nalready managed his instruction so well that he could at once tell a\nmember of the gentry from a servant. I admired Paddy's cleverness, but\nat the same time I felt a certain resentment against the prelates and\nnobles who had so imposed upon me.\n\nBut, to be truthful, I have never seen a finer display of manners.\nThese menials could have put courtiers to the blush. And from time to\ntime somebody spoke out loud and clear an opinion pilfered verbatim\nfrom his master. They seldom spoke their own thoughts in their own\nway; they sent forth as their own whatever they could remember from\nthe talk of their masters and other gentlemen. There was one man who\nseemed to be the servant of some noted scholar, and when he spoke the\nothers were dumfounded into quiet.\n\n\"The loriot,\" said he with a learned frown, \"is a bird. If it is\nlooked upon by one who has the yellow jaundice, the bird straightway\ndies, but the sick person becomes well instantly. 'Tis said that\nlovage is used, but I would be luctuous to hear of anybody using this\nlothir weed, for 'tis no pentepharmacon, but a mere simple and not\nworth a caspatory.\"\n\nThis utterance fairly made their eyes bulge, and they sat in stunned\nsilence. But I must say that there was one man who did not fear.\n\n\"Sir,\" said Paddy respectfully, but still with his own dignity, \"I\nwould be hearing more of this bird, and we all would be feeling\nhonoured for a short description.\"\n\n\"In color he is ningid,\" said the learned valet.\n\n\"Bedad!\" cried Paddy. \"That's strange!\"\n\n\"'Tis a question full of tenebrosity,\" remarked the other leaning back\nin his chair. \"We poor scholars grow madarosis reflecting upon it.\nHowever, I may tell you that the bird is simous; yblent in the\nsunlight, but withal strenuous-eyed; its blood inclined to\nintumescence. However, I must be breviloquent, for I require an\nenneadecaterides to enumerate the true qualities of the loriot.\"\n\n\"By gor!\" said Paddy, \"I'll know that bird if I see him ten years from\nnow. Thank you kindly, sir. But we would be late for breakfast if you\ntook the required time; and that's true for me.\"\n\nAfterward I reflected that I had attended the meetings of two\nscholarly bodies in this one evening, but for the life of me I\ncouldn't decide which knew the least.\n\n\n\n\nCHAPTER XX\n\n\nBy the following Sunday I judged that the Earl of Westport and his\nfamily had returned to London, and so I walked abroad in the hopes of\ncatching a glimpse of some of them among the brilliant gentry who on\nthis day thronged the public gardens. I had both Jem Bottles and Paddy\naccompany me, for I feared that they would get into mischief if I left\nthem to themselves. The innkeeper had told me that Kensington Gardens\nwas the place where the grand people mostly chose to walk and flirt\nand show their clothes on a clear Sunday. It was a long way to these\nGardens, but we footed out bravely, although we stopped once to see a\nfight between five drunken apprentices, as well as several times for\nmuch-needed refreshment.\n\nI had no idea that the scene at the Gardens would be so splendid.\nOutside, the road was a block of gleaming chariots and coaches with\nservants ablaze in their liveries. Here I left Paddy and Jem to amuse\nthemselves as suited them.\n\nBut the array of carriages had been only a forecast of what my eyes\nwould encounter in the Garden itself. I was involved at once in a\nswarm of fashionable people. My eyes were dazzled with myriad colours,\nand my nostrils, trained as they were to peat smoke, were saluted by a\nhundred delicious perfumes. Priceless silks and satins swept against\nmy modest stockings.\n\nI suffered from my usual inclination to run away, but I put it down\nwith an iron will. I soon found a more retired spot from which I could\nreview the assemblage at something like my leisure. All the highly\nfashionable flock knew each other intimately, it appeared, and they\nkept off with figurative pikes attempts of a certain class not quite\nso high and mighty, who seemed for ever trying to edge into situations\nwhich would benefit them on the social ladder. Their failures were\ndismal, but not so dismal as the heroic smiles with which they covered\ntheir little noiseless defeats.\n\nI saw a lady, sumptuously arrayed, sweep slowly along with her\ndaughter, a beautiful girl who greatly wished to keep her eyes fixed\non the ground. The mother glanced everywhere with half-concealed\neagerness and anxiety. Once she bowed impressively to a dame with a\ncold, pale aristocratic face, around whom were gathered several\nofficers in the uniform of His Majesty's Guards. The grand dame lifted\nher lorgnette and stared coolly at that impressive bow; then she\nturned and said something amusing to one of the officers, who\nsmilingly answered. The mother, with her beautiful daughter, passed\non, both pairs of eyes now on the ground.\n\nI had thought the rebuff would settle this poor misguided creature,\nbut in the course of an hour I saw three more of her impressive bows\nthrown away against the icy faces of other women. But as they were\nleaving the Gardens they received attention from members of the very\nbest society. One lordling nudged another lordling, and they stared\ninto the face of the girl as if she had been a creature of the street.\nThen they leisurely looked her up and down from head to toe. No\ntailor could have taken her measurements so completely. Afterward they\ngrinned at each other, and one spoke behind his hand, his insolent\nspeculative eyes fixed on the retiring form of the girl. This was the\nsocial reward of the ambitious mother.\n\nIt has always been clear to me why the women turn out in such cohorts\nto any sort of a function. They wish to see the frocks, and they are\ninsistent that their own frocks shall be seen. Moreover they take\ngreat enjoyment in hating such of their enemies as may come under\ntheir notice. They never have a really good time; but of this fact\nthey are not aware, since women are so constituted that they are able\nto misinterpret almost every one of their emotions.\n\nThe men, knowing something of their own minds at times, stealthily\navoid such things unless there are very special reasons. In my own\nmodest experience I have seen many a popular hostess hunting men with\na net. However it was plain why so many men came to Kensington Gardens\non a Sunday afternoon. It was the display of feminine beauty. And when\nI say \"display\" I mean it. In my old age the fashion balloons a lady\nwith such a sweep of wires and trellises that no Irishman could marry\nher because there is never a door in all Ireland through which his\nwife could pass. In my youth, however, the fashion required all\ndresses to be cut very low, and all skirts to cling so that if a\nfour-legged woman entered a drawing-room everybody would know it. It\nwould be so easy to count them. At present a woman could have eight\nlegs and nobody be the wiser.\n\nIt was small wonder that the men came to ogle at Kensington Gardens\non a fine Sunday afternoon. Upon my word, it was worth any young\ngentleman's time. Nor did the beauties blush under the gaze of banks\nof fastidious beaus who surveyed them like men about to bid at a\nhorse-fair. I thought of my father and how he would have enjoyed the\nscene. I wager he would have been a gallant with the best of them,\nbowing and scraping, and dodging ladies' skirts. He would have been in\nhis very element.\n\nBut as for me I had come to gain a possible glimpse of Lady Mary.\nBeyond that I had no warm interest in Kensington Gardens. The crowd\nwas too high and fine; many of the people were altogether too well\nbred. They frightened me.\n\nHowever, I turned my head by chance to the left, and saw near me a\nsmall plain man who did not frighten me at all. It was Doctor Chord,\nthe little scientist. He was alone and seemed to be occupied in\nstudying the crowd. I moved over to him.\n\n\"A good day to you, sir,\" I said, extending my hand.\n\nWhen he recognized me, his face broke into a beaming smile.\n\n\"Why, sir,\" he cried, \"I am very glad to see you, sir. Perchance, like\nme, you have come here for an hour's quiet musing on fashionable\nfolly.\"\n\n\"That's it, sir,\" said I. \"You've hit it exactly.\"\n\nI have said that he was a bashful man, but it seemed that his timidity\nwas likely to show itself only in the presence of other great\nphilosophers and scientists. At any rate, he now rattled on like a\nlittle engine, surveying the people keenly and discoursing upon their\nfaults.\n\n\"There's the old Marquis of Stubblington,\" observed my friend. \"He\nbeats his wife with an ebony stick. 'Tis said she always carries a\nlittle bottle of liniment in the pocket of her skirt. Poor thing, her\nonly pleasure in life is to talk scandal; but this she does on such a\nheroic scale that it occupies her time completely. There is young Lord\nGram walking again with that soap-boiler and candle-maker. 'Tis\ndisgraceful! The poor devil lends Gram money, and Gram repays him by\nallowing him to be seen in his company. Gram gambles away the money,\nbut I don't know what the soap-boiler does with his distinguished\nhonours. However, you can see that the poor wretch is delighted with\nhis bargain. There are the three Banellic girls, the most\nill-tempered, ugly cats in England. But each will have a large\nmarriage portion, so they have no fears, I warrant me. I wonder the\nelder has the effrontery to show her face here so soon if it is true\nthat the waiting-woman died of her injuries. Little Wax is talking to\nthem. He needs one of those marriage portions. Aye, he needs all\nthree, what with his very boot-maker almost inclined to be insolent to\nhim. I see that foreign count is talking to the Honourable Mrs.\nTrasky. He is no more nor less than a gambler by trade, and they say\nhe came here from Paris because he was caught cheating there, and was\nkicked and caned with such intense publicity that he was forced to\nleave in the dead of night. However, he found many young birds here\neager to be plucked and devoured. 'Tis little they care, so long as\nthey may play till dawn. Did you hear about Lady Prefent? She went\nafter her son to the Count's rooms at night. In her younger days she\nlived rather a gay life herself, 'tis rumoured, and so she was not to\nbe taken by her son's lies as to where he spent his evenings and his\nmoney. Ha, I see the Countess Cheer. There is a citadel of virtue! It\nhas been stormed and taken so many times that I wonder it is not in\nruins, and yet here it is defiant, with banners flying. Wonderful.\nShe--\"\n\n\"Hold!\" I cried. \"I have enough. I would have leave to try and collect\nmy wits. But one thing I would know at once. I thought you were a shy\nscholar, and here you clatter away with the tongue of an old rake. You\namaze me. Tell me why you do this? Why do you use your brain to\nexamine this muck?\"\n\n\"'Tis my recreation,\" he answered simply. \"In my boyhood I was allowed\nno games, and in the greater part of my manhood I have been too busy.\nOf late years I have more leisure, and I often have sought here a\nlittle innocent amusement, something to take one's mind off one's own\naffairs, and yet not of such an arduous nature as would make one's\nhead tired.\"\n\n\"By my faith, it would make my head tired,\" I said. \"What with\nremembering the names of the people and all the different crimes, I\nshould go raving mad.\" But what still amazed me was the fact that this\nlittle man, habitually meek, frightened and easily trodden down in\nmost ordinary matters, should be able to turn himself upon occasion\ninto a fierce and howling wolf of scandal, baying his betters, waiting\nfor the time when an exhausted one fell in the snow, and then burying\nhis remorseless teeth in him. What a quaint little Doctor Chord.\n\n\"But tell me truly,\" said I. \"Is there no virtuous lady or honest\ngentleman in all this great crowd?\"\n\nHe stared, his jaw dropping. \"Strap me, the place is full of them,\" he\nejaculated. \"They are as thick as flies in a fish-market.\"\n\n\"Well, then,\" said I, \"let us talk of them. 'Tis well to furbish and\nburnish our minds with tales of rectitude and honour.\"\n\nBut the little Doctor was no longer happy. \"There is nought to say,\"\nhe answered gloomily. \"They are as quiet as Bibles. They make no\nrecreation for me. I have scant interest in them.\"\n\n\"Oh, you little rogue, you!\" I cried. \"What a precious little bunch of\nevil it is! 'They make no recreation for me,' quoth he. Here's a\ngreat, bold, outspoken monster. But, mark you, sir, I am a younger\nman, but I too have a bold tongue in my head, and I am saying that I\nhave friends among ladies in London, and if I catch you so much as\nwhispering their names in your sleep, I'll cut off your ears and eat\nthem. I speak few words, as you may have noted, but I keep my\nengagements, you little brew of trouble, you!\"\n\n\"Strap me,\" whimpered the little Doctor, plucking feverishly at the\nbuttons of his coat, rolling his eyes wildly, not knowing at all what\nhe did. \"The man's mad! The man's mad!\"\n\n\"No,\" said I, \"my blood is cold, very cold.\"\n\nThe little Doctor looked at me with the light of a desperate\ninspiration in his eye. \"If your blood is cold, sir,\" said he, \"I can\nrecommend a gill of port wine.\"\n\nI needs must laugh. \"Good,\" I cried, \"and you will join me.\"\n\n\n\n\nCHAPTER XXI\n\n\nI don't know if it was the gill of comforting port, but at any rate I\nwas soon enough convinced that there was no reason for speaking\nharshly to Doctor Chord. It served no purpose; it accomplished\nnothing. The little old villain was really as innocent as a lamb. He\nhad no dream of wronging people. His prattle was the prattle of an\nunsophisticated maiden lady. He did not know what he was talking.\nThese direful intelligences ran as easily off his tongue as water runs\noff the falling wheel. When I had indirectly informed him that he was\nmore or less of a dangerous scandal-monger, he had cried: \"The man is\nmad!\" Yes; he was an innocent old thing.\n\nBut then it is the innocent old scandal-mongers, poor placid-minded\nwell-protected hens, who are often the most harmful. The vicious\ngabblers defeat themselves very often. I remember my father once going\nto a fair and kissing some girls there. He kissed them all turn by\nturn, as was his right and his duty, and then he returned to a girl\nnear the head of the list and kissed her five times more because she\nwas the prettiest girl in all Ireland, and there is no shame to him\nthere. However, there was a great hullabaloo. The girls who had been\nkissed only once led a regular crusade against the character of this\nother girl, and before long she had a bad name, and the odious sly\nlads with no hair on their throats winked as she passed them, and\nnumerous mothers thanked God that their daughters were not fancied by\nthe lord of that region. In time these tales came to the ears of my\nfather, and he called some of his head men to meet him in the\ndining-room.\n\n\"I'll have no trifling,\" said he. \"The girl is a good girl for all I\nknow, and I have never seen her before or since. If I can trace a bad\nword to any man's mouth, I'll flog him till he can't move. 'Tis a\nshame taking away the girl's name for a few kisses by the squire at a\nfair with everybody looking on and laughing. What do you blackguards\nmean?\"\n\nEvery man in the dining-room took oath he had never said a word, and\nthey all spoke truth. But the women clamoured on without pausing for\nwind, and refused to take word of the men-folk, who were gifted with\nthe power of reason. However, the vicious people defeated themselves\nin time. People began to say to a lass who had been kissed only once:\n\"Ah, now, you would be angry because you were not getting the other\nfive.\" Everything seemed to grow quiet, and my father thought no more\nabout it, having thought very little about it in the first place save\nenough to speak a few sharp words. But, would you believe it, there\nwas an old woman living in a hovel not a mile from the castle, who\nkept up the scandal for twelve more months. She had never been\nmarried, and, as far as any one knew, she had never wished to be. She\nhad never moved beyond Father Donovan's church in one direction and a\nlittle peat-heap in the other direction. All her days she had seen\nnothing but the wind-swept moors, and heard nothing but the sea\nlashing the black rocks. I am mistaken; once she came to the castle,\nhearing that my mother was ill. She had a remedy with her, poor soul,\nand they poured it in the ashes when her back was turned. My mother\nbade them give her some hot porridge and an old cloth gown of her own\nto take home. I remember the time distinctly. Well, this poor thing\ncouldn't tell between a real sin and an alligator. Bony, withered,\naged, this crone might have been one of the highest types of human\nperfection. She wronged nobody; she had no power to wrong. Nobody\nwronged her; it was never worth it. She really was at peace with all\nthe world. This obeys the most exalted injunctions. Every precept is\nkept here. But this tale of the Squire and the girl took root in her\nhead. She must have been dazzled by the immensity of the event. It\nprobably appealed to her as would a grand picture of the burning of\nRome or a vivid statue of Lot's wife turning to look back. It reached\nthe dimensions of great history. And so this old woman, who had always\nlived the life of a nun, dreamed of nothing but the colossal wrong\nwhich had come within her stunted range of vision. Before and after\nchurch she talked of no other thing for almost eighteen months.\nFinally my father in despair rode down to her little cottage.\n\n\"Mollie,\" said he, calling from the road, \"Mollie, come out.\" She came\nout.\n\n\"Mollie,\" said my father, \"you know me?\"\n\n\"Ay,\" said she, \"you are The O'Ruddy, and you are a rogue.\"\n\n\"True for you, Mollie,\" said my father pleasantly. \"You know it and I\nknow it. I am indeed a grand rogue. But why would you be tearing to\ntatters the name of that poor girl in Ballygoway?\"\n\n\"'Tis not me that has said more than three words,\" she cried,\nastonished, \"and before I speak ill of anybody I hope the devil flies\naway with me.\"\n\nWell, my father palavered on for a long time, telling her that he\nwould take away the pension of twenty-five shillings a year which he\nhad given her because he by accident had shot her second cousin in the\nleg twelve years before that time. She steadfastly answered that she\nwould never speak ill of anybody; but the girl was a brazen-faced\nwench, and he was no better. My father came away, and I have no doubt\nthe scandal would still be alive if the old woman had not died, may\nthe saints rest her!\n\nAnd so I was no longer angry with Doctor Chord, but spoke to him\npleasantly.\n\n\"Come,\" said I, \"I would have you point me out the great swordsmen, if\nit pleases you. I am eager to see them, and the talk will be cleanly,\nalso.\"\n\n\"Aye,\" said my friend. \"Nothing could give me more pleasure. And now,\nlook you! The tall, straight, grave young man there is Ponsonby, who\nflashes the wisest blade in England unless Reginald Forister is\nbetter. Any how, Forister is not here to-day. At least I don't see\nhim. Ponsonby fought his last duel with a gentleman named Vellum\nbecause Vellum said flatly that Mrs. Catherine Wainescorte was a--\"\n\n\"Stop there,\" said I, \"and get to the tale of the fighting.\"\n\n\"Well, Ponsonby won without difficulty,\" said the Doctor; \"but it is\nsaid that he took an unfair advantage--\"\n\n\"Stop again!\" I cried. \"Stop again! We will talk no more of swordsmen.\nSomehow I have lost my interest. I am put to it to think of a subject\nfor talk, and we may have to do with a period of silence, but that\nwill do your jaw no injury at any rate.\"\n\nBut I was mistaken in thinking that the little man could forego his\nrecreation for more than a moment. Suddenly he burst out with a great\nspleen:\n\n\"Titles!\" he cried. \"Empty titles! husks, husks, husks! 'Tis all they\ncare for, this mob! Honourable manhood goes a-begging while the world\nworships at the feet of pimply lords! Pah! Lovely girls, the making of\nfine wives and mothers, grow old while the world worships at the feet\nof some old horse-headed duchess! Pah! Look at those pick-thanks and\nflatterers, cringing at the boots of the people of fashion. Upon my\nlife, before I would so demean myself, I--\" he ceased suddenly, his\neye having caught sight of some people in the crowd. \"Ah,\" said he,\nwhile a singularly vain and fatuous smile settled upon his\ncountenance. \"Ah, the Countess of Westport and her charming daughter,\nthe Lady Mary, have arrived. I must go and speak to them.\" My eye had\nfollowed his glance quickly enough you may be sure. There, true\nenough, was the formidable figure of the old Countess, and at her side\nwas the beautiful Lady Mary.\n\nWith an absent-minded murmur of apology, Doctor Chord went mincing\ntoward them, his face still spread with its idiotic smile.\n\nHe cantered up to them with the grace of a hobbled cow. I expected him\nto get a rebuff that would stun him into the need of a surgeon, but to\nmy surprise the Countess received him affably, bending her head to say\nsome gracious words. However, I had more eyes for Lady Mary than for\nthe capers of little Chord.\n\nIt was a great joy to be able to look at her. I suffered from a\ndelicious trembling, and frequently my vision became dim purely from\nthe excitement. But later I was moved by another profound emotion. I\nwas looking at her; I must have her look at me. I must learn if her\neye would light, if her expression would change, when she saw me. All\nthis sounds very boyish, but it is not necessary to leave it out for\nthat reason, because, as my father often said, every Irishman is a boy\nuntil he has grandchildren. I do not know if he was perfectly right in\nthis matter, but it is a certain advantage in a love affair to have\nthe true boyish ardour which is able to enshrine a woman in one's\nheart to the exclusion of everything, believing her to be perfection\nand believing life without her a hell of suffering and woe. No man of\nmiddle-aged experience can ever be in love. He may have his illusions.\nHe may think he is in love. A woman may gain the power to bind him\nhand and foot and drag him wherever she listeth, but he is not in\nlove. That is his mistaken idea. He is only misinterpreting his\nfeelings. But, as my father said, it is very different with Irishmen,\nwho are able to remain in love to a very great age. If you will note,\ntoo, climatic conditions and other unpleasant matters have practically\nno effect upon them; so little, indeed, that you may find streets\nnamed after the main Italian cities, and many little German children\nspeak with a slight brogue. My father often said that one great reason\nfor an Irishman's successes with the ladies was his perfect\nwillingness to get married. He was seldom to be seen scouting for\nadvantages in intrigue. If the girl be willing, be she brown, yellow,\nor white, he was always for the priest and the solemn words. My father\nalso contended that in every marriage contracted on the face of the\nearth in which neither maid nor man could understand the other's\nnational speech, the bridegroom was an Irishman. He was the only man\nwho was able to make delightful love with the aid of mere signals.\n\nHowever I must be going on with my story, although it is a great\npleasure to talk of my country-men. They possess a singular\nfascination for me. I cannot forget that I too am an Irishman.\n\nThe little Doctor was still saying agreeable things; Lady Mary was\nsmiling in gentle amusement. As I moved out to catch Lady Mary's eye,\nI did not at all lose sight of the fact that if the pugnacious mother\nof my _innamorata_ took one glimpse of me there might result a scene\nwhich could end in nothing but my ignominious flight. I edged toward\nthe group, advancing on the Countess's port quarter as she was talking\nanimately over her starboard bow at the entranced little Doctor. At\ntimes Lady Mary looked about her, still smiling her smile, which no\ndoubt was born of the ridiculous performances of Chord. Once I thought\nshe looked squarely at me, and my heart beat like a drum so loudly\nthat I thought people must hear. But her glance wandered on casually\nover the throng, and then I felt truly insignificant, like a man who\ncould hide behind the nail of his own thumb.\n\nPerceiving that I was so insignificant, I judged it prudent as well as\nadvantageous to advance much closer. Suddenly Lady Mary's clear\nvirgin eye met mine,--met it fully.\n\nNow, I don't know what was in this glance we exchanged. I have stopped\nmyself just on the verge of a full explanation of the thrills,\nquivers, hopes, fears, and dreams which assailed me as I looked back\ninto the beautiful face of Lady Mary. I was also going to explain how\nthe whole scene appeared. But I can see soon enough that my language\nwould not be appropriate to the occasion. But any how we looked each\nother point-blank in the eye. It was a moment in which that very\ncircling of the earth halted, and all the suns of the universe poised,\nready to tumble or to rise. Then Lady Mary lowered her glance, and a\npink blush suffused her neck and cheek.\n\nThe Countess, Lady Mary, and Doctor Chord moved slowly on through the\nthrong, and I followed. The great question now was whether Lady Mary\nwould look back. If she looked back, I would feel that I was making\ngrand way with her. If she did not look back, I would know myself as a\nlost man. One can imagine how eagerly I watched her. For a long time\nit was plain that she had no intention whatever of looking back. I\nlugubriously arranged my complete downfall. Then, at the very moment\nof my despair, she gazed studiously off to her extreme left for a\ncertain time, and then suddenly cast one short glance behind her. Only\nheaven knows what value I placed upon this brief look. It appeared for\nthe moment to me that I had won her, won everything. I bravely forged\nahead until I was quite insistently under the eye of Lady Mary, and\nthen she again looked toward me, but it was a look so repelling and\nfrigid that it went through me as if I had been a paper ring in the\ncircus. I slunk away through the crowd, my thoughts busy with trying\nto find out what had happened to me.\n\nFor three minutes I was a miserable human being. At the end of that\ntime I took heart again. I decided that Lady Mary had frowned at me\nbecause she was afraid that she had been too good to me with her look\nand smile. You know what I mean. I have seen a young girl give a young\nman a flower, and at the very next moment be seemingly willing to give\nher heart's blood to get that flower back, overcome with panic terror\nthat she had passed--in his opinion, mind you--beyond the lines of\nbest behaviour. Well I said to myself that Lady Mary had given me the\nhard look for similar reasons. It was rational to make this judgment,\nfor certainly she had no cause for an active dislike. I had never been\neven so much as a nuisance to her.\n\nFortified with these philosophic decisions, I again followed the trio,\nand I was just in time to find Chord handing them into a splendid\nchariot. I stood out boldly, for I knew if I could not get one more\nlook from Lady Mary I would die.\n\nSeated beside her mother, her eye wandered eagerly over the crowd. I\nwas right, by the saints! She was looking for me.\n\nAnd now here come the stupid laws of convention. Could I yell? Could I\neven throw my hat in the air to guide her eye aright? No! I was doomed\nto stand there as still as a bottle on a shelf.\n\nBut she saw me! It was at the very last moment. There was no time for\ncoquetry. She allowed her glance to linger, and God knows what we\nsaid to each other in this subtle communication through all the noise\nand hubbub of the entrance place. Then suddenly the coachman's reins\ntightened; there were some last bows; the chariot whirled away.\n\n\n\n\nCHAPTER XXII\n\n\nChord ambled back, very proud indeed, and still wearing his fatuous\nsmile. He was bursting with a sense of social value, and to everybody\nhe seemed to be saying, \"Did you see me?\" He was overjoyed to find me\nwaiting for him. He needed a good listener at once. Otherwise he would\nsurely fly to pieces.\n\n\"I have been talking to the Countess of Westport and her daughter,\nLady Mary Strepp,\" he said pompously. \"The Countess tells that the\nEarl has been extremely indisposed during their late journey in the\nWest.\"\n\nHe spoke of the Earl's illness with an air of great concern, as if the\nnews had much upset him. He pretended that the day was quite\nover-gloomed for him. Dear, dear! I doubted if he would be able to eat\nany supper.\n\n\"Have a drop of something, old friend,\" said I sympathetically. \"You\ncan't really go on this way. 'Twill ruin your nerves. I am surprised\nthat the Countess did not break the news to you more gently. She was\nvery inconsiderate, I am sure.\"\n\n\"No, no, don't blame the poor lady,\" cried Chord. \"She herself was\nquite distracted. The moment she saw me she ran to me--did you see her\nrun to me?\"\n\n\"I did that,\" said I with emphasis.\n\n\"Aye, she ran to me,\" said the little fool, \"and says she, 'Oh, my\ndear Doctor, I must tell you at once the condition of the Earl.' And\nwhen I heard everything I was naturally cut up, as you remarked, being\nan old friend of the family, ahem!--yes, an old friend of the family.\"\n\nHe rattled on with his nonsensical lies, and in the mean time I made\nup my mind to speak plainly to him, as I intended to make him of great\nservice to me.\n\n\"Stop a moment,\" said I good-naturedly. \"I will hear no more of this\nrubbish from you, you impudent little impostor. You care no more for\nthe Earl of Westport's illness than you do for telling the truth, and\nI know how much you care for that. Listen to me, and I'll see if I\ncan't knock some sense into your little addled head. In the first\nplace the Earl of Westport and my father were old friends and\ncompanions-in-arms in the service of the French king, and I came over\nfrom Ireland especially to take a dying message and a token from my\nfather to the Earl. That is all you need know about that; but I would\nhave you leave off your prate of your friend the Earl of Westport, for\nI understand full well you couldn't distinguish between him and a\nchurch door, although 'tis scandalously little you know of church\ndoors. So we will stop there on that point. Then I will go on to the\nnext point. The next point is that I am going to marry Lady Mary\nStrepp.\"\n\nThe little Doctor had been choking and stuttering in a great spasm,\nbut my last point bid fair to flatten him out on the floor. I took the\noverpowered philosopher and led or carried him to another drink.\n\n\"Stap me!\" he cried again and again. \"The man is mad!\"\n\nI surveyed him with a bland smile.\n\n\"Let it sink into you,\" said I soothingly. \"Don't snarl and wrangle at\nit. It is all heaven's truth, and in time you will come to your senses\nand see what I am telling you.\"\n\nWell, as soon as he had fully recovered his wind, he fell upon me with\nthousands of questions; for one may see that he would have plenty of\ninterest in the matter as soon as he was assured that there was much\nveracity involved in one way or another in my early statement. His\nquestions I answered as it pleased me, but I made clear enough to him\nthat, although Lady Mary was well disposed toward me, neither her\nfather nor her mother would even so much as look at me if I applied\nfor a position as under-footman, I was that low in their estimate.\n\n\"However,\" said I, \"I can rearrange all that very easily. And now, my\nbucko, here is where your fortune meets mine. You are fitted by nature\nmore to attend other people's affairs than to take a strict interest\nin your own. All kinds of meddling and interference come easily to\nyou. Well, then, here is a chance to exercise your gifts\ninoffensively, and yet in a way which may make two people happy for\nlife. I will tell you now that I don't even know where is the Earl's\ntown house. There is where your importance appears at once. You must\nshow me the house. That is the first thing. After that we will arrange\nall the details about ladders and garden walls, and, mayhap, carrier\ndoves. As for your reward, it will appear finally in the shape of a\nbowing recognition by people of fashion, which is what you most\ndesire in the world, you funny little man.\"\n\nAgain I had stunned him. For a time I could see his brain swimming in\na perfect sea of bewilderment. But, as before, sense gradually came to\nhim, and he again volleyed questions at me. But what stuck in his crop\nwas the thought that Lady Mary could prefer me. He tried his best to\nbelieve it, but he would always end up by saying: \"Well, _if_ Lady\nMary cares for you, the affair is not too difficult.\" Or, \"Well, if\nyou are _sure_ Lady Mary loves you--\" I could have broken his head a\nthousand times.\n\n\"Bad luck to you, Doctor,\" I cried. \"Don't you know such croaking\nwould spoil the peace of any true lover? Is ever any worthy man able\nnot to be anxious in such matters? 'Tis only foppery coxcombs who have\ngreat confidence, and they are usually misled, thank the Lord! Be\nquiet, now, and try to take everything for granted.\"\n\nThen the spirit of the adventure came upon him, and he was all for it,\nheels over head. As I told him, this sort of meddling was his proper\nvocation. He who as a recreation revelled in the mere shadows of the\nintrigues of people of quality was now really part of one, an actor in\nit, the repository of its deep secret. I had to curb his enthusiasm.\nHe had such a sense of the importance of my news, and of his\ndistinction in having heard it, that I think he wanted to tell the\nsecret to the entire world.\n\nAs soon as the afternoon grew late I suggested a walk to that part of\nLondon in which was situated the Earl's town house. I did not see why\nwe should not be moving at once on the campaign. The Doctor assented,\nand we went forth to look for Paddy and Jem Bottles. We found them at\nan ale-house which was the resort of the chairmen, footmen, and\ncoachmen of the grand people. The two rogues had evidently passed a\npleasant afternoon. Jem Bottles was still making love to a very pretty\ngirl, some part of whose easy affection or interest he had won; and\nPaddy, it seems, had had a rip-roaring fight with two lackeys, worsted\nthem with despatch, and even pursued them some distance. To my stern\ninterrogation in regard to the pretty girl, Jem Bottles stoutly\nrejoined that she was his second cousin whom he had not seen for many\nyears. To this I made no reply, for it does no good to disturb the\nbalance of a good liar. If at times he is led to tell the truth, he\nbecomes very puzzling. In all the years Jem Bottles has been in my\nservice I have never reprimanded him for lying. I would confuse\nmatters to no purpose, inasmuch as I understand him perfectly.\n\n\"And how,\" said I to Paddy, \"did you come to engage in this\ndisgraceful brawl of a Sunday?\"\n\n\"Your honour,\" answered Paddy, \"there was two of these men with fat\nlegs came here, and says one, looking hard at me, 'Here's a furriner,'\nhe says. 'Furriner yourself, you fish-faced ditch-lurker,' says I, and\nwith that he takes up his fists and hits me a knock. There was a\nlittle shindy, and afterward they ran away bawling, and I was pursuing\nthem, only I feared to lose my way in these strange parts.\"\n\nThe walk to Lord Westport's house was a long one. It seemed that he\nhad built a great new mansion at a place outside of the old city\ngates, where other nobles and great brewers had built fine houses,\nsurrounding them all with splendid gardens.\n\nOne must not suppose that I had any idea of taking the mansion by\nstorm. My first idea was to dream a lover's dream as I gazed upon the\nabode of my treasure. This, I believe, is a legitimate proceeding in\nall careers. Every lover worthy of the name is certain to pilgrimage,\nmuffled in his cloak, to moon over the home of his adored one.\nOtherwise there can be no real attachment.\n\nIn the second place I wished to develop certain plans for gaining\nspeech of Lady Mary. I will not deny that I purposed on a near day to\nscale the garden wall and hold speech of my sweetheart as she walked\nalone among the flowers. For my success I depended upon the absolute\nconventionality of the idea. In all history no lover has even been\nchased out of a garden by an under-gardener with a hoe.\n\nWhen we arrived at the house I found that it was indeed a gorgeous\nmansion. It was surrounded on all sides by high brick walls, but\nthrough the elaborate tracery of one of the iron-work gates I saw Lady\nMary's home standing among sweeping green lawns.\n\nWe reconnoitred all sides, and at the back I found a lonely avenue\nlined with oaks. Here a small door pierced the wall for the use\napparently of the gardeners or grooms. I resolved that here I would\nmake my attack.\n\nAs we passed the iron gates on our way back to town, we saw window\nafter window light up with a golden radiance. I wondered which part of\nthat vast edifice hid the form of my Mary.\n\nI had asked Doctor Chord to sup with me at the inn, and on the way\nthither he proved somewhat loquacious.\n\n\"I see in you, sir,\" said he, \"a certain instinct of true romance\nwhich is infrequently encountered in this humdrum commercial age.\nAllow me to express to you, sir, my warm admiration. I did not think\nthat a gallant of this humdrum commercial age could prove such a free\nspirit. In this humdrum commercial age--\"\n\n\"I am an Irishman,\" said I, \"and in Ireland we are always humdrum, but\nwe are never commercial, for the reason that we have not the tools.\"\n\n\"Aye,\" said he, \"you must be a great people. Strangely enough, you are\nthe first Irishman I have ever seen, although I have seen many\nblackamoors. However, I am edified to find you a gentleman of great\nlearning and experience. In this humdrum commercial age--\"\n\n\"Let go,\" said I. \"I can do very well without your opinion as to my\nlearning and experience. In regard to this being a humdrum commercial\nage you will find that all ages say the same thing of themselves. I am\nmore interested in the winning of Lady Mary.\"\n\n\"'Twas to that subject I was just about to turn the talk,\" said the\nDoctor. \"I need not express again to you the interest I feel; and if\nit is true, as you say, that Lady Mary really loves you--\"\n\n\"May the devil fly away with you,\" I cried in a great rage. \"Are you\nnever to have done? You are an old frog. I asked you to help me, and\nyou do nothing but dispirit me with these doubts. I'll not put up with\nit.\"\n\n\"I am very sorry to displease you, sir,\" answered my friend. \"If you\nexamine my intentions with a dispassionate eye, sir, I am convinced\nyou will have found nothing in me which should properly cause these\noutbursts of disapprobation. When I say, 'If Lady Mary really loves\nyou,' I am referring to the strange mishaps and misconstructions which\nattend human thought at all times, and when I say--\"\n\n\"Let go again,\" I cried. \"When I misunderstand you, don't enlighten\nme; for I find these explanations very hard to bear.\"\n\nTo my surprise the little man answered with great spirit: \"I am unable\nto gain any approval for my deep interest in your affairs, sir,\" he\ncried. \"Perchance, it would be better if I could affect a profound\nindifference. I am certainly at a loss for words when each sentence of\nmine is made the subject of wrathful objection.\"\n\n\"You are right,\" said I. \"But you will understand how ten thousand\nemotions beset and haggle a lover, and I believe he always revenges\nhimself upon his dearest friends. Forgive me!\"\n\n\"With all my heart!\" answered the little Doctor. \"I am aware, sir,\nthat at the present time you are in many ways like a highly-tightened\nfiddle, which any breeze frets into murmurings. Now, being absolutely\ncertain of the devotion of your beloved, you naturally--\"\n\n\"By the ten lame pipers of Ballydehob,\" I shouted, \"let go of that\ntalk. I can't be having it. I warn ye. 'Tis either a grave for me, or\nquiet for you, and I am thinking it is quiet for you.\"\n\n\"Inasmuch,\" said the Doctor, \"as my most judicious speeches seem to\ninflame your passions, sir, I am of the opinion that a perfect silence\non my part becomes almost necessary, and, to further this end, I would\nrecommend that you refrain from making interrogations, or otherwise\npromulgating opportunities, when an expression of candid opinion seems\nexpected and desired.\"\n\n\"You've hit it,\" said I. \"We will have no more interrogations.\nHowever, I would much like to know how you became so intimate with\nLord Westport's family.\"\n\nDoctor Chord blushed with something of his earlier manner. \"'Tis a\nmatter which I did not expect to have leap at me out of the darkness\nin this fashion,\" he said bashfully. \"However, I am convinced of how\nwell you know these people, and I will traffic no more with hollow\npretence. As you know, I deal much in chemical knowledge, which I am\nable to spread to almost every branch of human use and need.\"\n\n\"'Tis an ill work,\" said I slowly. \"I doubt if Father Donovan would\ncare to hear you be speaking in this way. He always objected to\nscientific improvements as things which do harm to the Church.\"\n\n\"In regard to the estimable friend you mention,\" said the Doctor, \"I\nunhesitatingly state my profound assurances of respect.\"\n\n\"Quite so,\" I answered. \"He will be pleased to hear of it. And now we\nwill return to the other matter.\"\n\n\"I will obediently proceed,\" said he. \"Five years back the Countess of\nWestport was thrown from her carriage. Physicians rushed to her\nrescue. I too appeared, being for the time out for a walk. They\nwished to immediately bleed her, but I waved them aside and,\nrecognizing me as a figure in the street world of science, they fell\nback abashed. I prescribed a small drink of hot rum. The lady took it.\nAlmost immediately she recovered. She offered me a guinea. I refused\ncurtly. She inquired here and there for my condition. Afterward she\napologized to me for not offering me more than a guinea. Since that\ntime we have been warm friends. She knows me as a great scientist who\ncame to her assistance in time of trouble when numerous quacks wished\nto bleed her, and I overpowered them and gave her a drink of rum. 'Tis\ntrue that after she reached her own bed the Earl's physician bled her,\nbut she did not seem to appreciate it although he drew twenty-five\nounces, I think. But she has remained always grateful for the hot\nrum.\"\n\n\n\n\nCHAPTER XXIII\n\n\nAt supper that evening Doctor Chord amplified some of his views \"A few\nstaunch retainers could quickly aid you to scale the walls of the\ncastle,\" said he. \"But I have forgotten,\" he added blankly. \"'Tis not\na castle. 'Tis a house.\"\n\n\"If you would take some of these ancient ideas and bury them in the\ngarden,\" said I, \"they might grow in time to be some kind of turnip or\nother valuable food. But at the present moment they do not seem to me\nto serve much purpose. Supposing that the house is not a castle? What\nof that?\"\n\n\"Castles--\" said he. \"Castles lend themselves--\"\n\n\"Castles!\" I cried. \"Have done with castles! All castles may be Jews,\nas you say. But this is a house.\"\n\n\"I remarked that it was a house,\" he answered gently. \"It was that\npoint that I was making.\"\n\n\"Very good,\" said I. \"We will now proceed to define matters. Do you\nknow if Lady Mary walks in the garden? It is absolutely necessary that\nLady Mary should walk in the garden.\"\n\n\"She does,\" he replied at once. \"At this season of the year Lady Mary\nwalks in the garden on every fine day at ten of the clock.\"\n\n\"Then,\" I cried, smiting the table, \"our course is clear; I feel\nelate. My only regret is that my father is not here to give me a word\nnow and then, for 'tis a game he would know down to the ground.\"\n\n\"Although I am not your father,\" said Doctor Chord modestly, \"I may be\nable to suggest some expedient way of gaining entrance to the castle.\"\n\n\"House,\" said I.\n\n\"House,\" said he.\n\n\"However,\" said I, \"we must lower ourselves to extremely practical\nmatters. Can you climb a tree?\"\n\n\"A tree?\" said he. \"Climb a tree? Strap me!\"\n\n\"'Tis all very well to strap yourself in this fashion,\" said I rather\nwarmly; \"but the climbing of trees appears here as an important\nmatter. In my part of Ireland there are few trees, and so climbing\ntrees did not enter into my education. However, I am willing to\nattempt the climbing of a tree for the sake of my true love, and if I\nfall--how high is this wall? Do you remember?\"\n\n\"'Twas at least ten feet,\" answered the Doctor. \"And there is a\nmurderous row of spikes at the top. But,\" he added, \"the more spikes\nand all that make them the more convinced that the garden is perfectly\nsafe from intrusion.\"\n\n\"That's a world of sense out of you,\" I cried. \"The spikes convince\nthem the garden is safe from intrusion, and so they give over their\nwatchfulness. So now in the morning we will go there, and I will climb\none of the oak-trees bordering the wall--may the saints aid me!\"\n\n\"You were asking if I could climb a tree,\" remarked the Doctor. \"I\nwill point out to you that it is a question of no importance. It is\nyou yourself who must climb the tree; for even if I succeeded in the\narduous and painful task I could not pay your vows to Lady Mary, and\nfor such purpose primarily the tree is to be climbed.\"\n\n\"True for you, Doctor,\" I answered with a sigh. \"True for you. I must\nclimb the tree. I can see that. I had some thought of making Paddy\nclimb it, but, as you say, a man must do his own love-making, and by\nthe same token I would break the head of any one who tried to do it\nfor me. I would that! In this world people must climb their own trees.\nNow that I think of it seriously, it was ridiculous in me to plan that\nPaddy should climb the tree.\"\n\n\"'Second thoughts are always best,'\" said the little Doctor piously.\n\"'Tis a phrase from one of the greatest writers of the day. And at any\nrate I myself, because of age and debility, would not be able to climb\na tree.\"\n\n\"Let us say no more of it,\" said I. \"I see my mistake. But tell me one\nthing. I know you are a man with a great deal on your mind. Can you\nspare the time for this adventure?\"\n\nBut on this point the Doctor was very clear and emphatic. I think if I\nhad said he could not have a place in the plot he would have died\nimmediately of a broken heart.\n\n\"'Tis true I have not yet finished my treatise proving that the\ntouchstone is fallible,\" he cried eagerly; \"but it would give me\npleasure to delay the work indefinitely if in the meantime I can be of\nassistance.\"\n\n\"That is a man's talk,\" I said. \"Well, then, in the morning we will go\nforth to do or die. And now a glass to success.\"\n\nThat night I slept very heartily, for some of my father's soldier\ntraining is in my veins, and on the eve of a hard or precarious work I\nam always able to get sound rest. My father often said that on the\nnight before a battle in which he would stand seventy-seven chances of\nbeing killed he always slept like a dog in front of the fire.\n\nAt dawn I was up and ready. My first move was to have Paddy and Jem\nsent to me, and to give them such information as would lead them to an\nintelligent performance of their duties during the day. \"Mind ye now,\"\nsaid I, \"here's where the whole thing may be won or lost. There is a\nlovely lady inside the walls of that garden which I was showing you\nyesterday. She lives in the big house. She is the lady who made you\nfeel ashamed when you took the old Earl's--well, never mind! I hope we\nare all properly repentant over it. However, I had better be getting\non with the matter in hand. She lives there, and if I can find no way\nto gain speech of her we all three of us will have to take to the\nthickets, and that's the truth.\"\n\n\"If I could but lay my fingers on her throttle,\" said Jem Bottles in a\nblood-curdling voice, \"she soon enough would--\"\n\n\"Stop!\" I cried. \"You misunderstood me!\"\n\n\"Aye, he does,\" spoke in Paddy. \"But I know what your honour is\nmeaning. You are meaning that the young lady--aye, didn't I see her,\nand didn't she give me a look of her eye? Aye, I know what your honour\nis meaning.\"\n\n\"You are knowing it precisely,\" said I. \"The young lady is more to me\nthan three Irelands. You understand? Well, then, in the first place I\nmust gain speech of her. To-day we march out and see what I can\naccomplish by climbing trees. In the meantime you two are to lay in\nwaiting and assist me when necessary.\"\n\n\"I am foreseeing that everything will be easy,\" cried Paddy\njubilantly.\n\n\"You are an Irishman,\" I responded in anger.\n\n\"Aye,\" he replied bitterly, \"and another is within reach of my stick\nif it weren't for my respect for my betters, although such a thing\nnever could happen, please God!\"\n\n\"No bold talk,\" said I. \"You may do that after.\" I bade Jem Bottles\nload his pistols and carry them handy, but to keep them well\nconcealed. Paddy preferred to campaign with only a stout stick. I took\none pistol, and of course my sword.\n\nThese preparations deeply stirred Jem Bottles and Paddy.\n\n\"Your honour,\" said Paddy, \"if I see a man pulling you by the leg when\nyou would be climbing the tree, may I hit him one lick?\"\n\n\"Aye,\" growled Jem Bottles, \"and if I get a pistol against his head,\nhe'll find out the difference between gunpowder and sand.\"\n\n\"Stop,\" I cried. \"You have the wrong idea entirely. This talk of\ncarnage startles me and alarms me. Remember we are in London. In\nLondon even the smallest massacre arouses great excitement. There are\nto be no killings, and even no sound thrashings. It is all to be done\nwith dainty gloves. Neither one of the pair of you looks fitted for\nthe work, but I am obliged to make you serve by hook or crook. 'Tis\ntoo late to scour the country looking for good comrades. I must put\nup with you, since I can get no better.\"\n\nThey were well pleased at the prospect of spirited adventures,\nalthough Paddy made some complaints because there was no chance of a\ngreat ogre whom he could assail. He wished to destroy a few giants in\norder to prove his loyalty to the cause. However, I soothed him out of\nthis mood, showing him where he was mistaken, and presently we were\nall prepared and only waited for the coming of Doctor Chord.\n\nWhen the little philosopher appeared, however, I must truly say that I\nfell back a-gasping. He had tied some sort of a red turban about his\nhead, and pulled a black cocked hat down over it until his left eye\nwas wickedly shaded. From beneath his sombre cloak a heavy scabbard\nprotruded. \"I have come; I am ready,\" said he in a deep voice.\n\n\"Bedad, you have!\" cried I, sinking into a chair. \"And why didn't a mob\nhang you on the road, little man? How did you reach here safely? London\nsurely never could stand two glimpses of such a dangerous-looking\npirate. You would give a sedan-chair the vapours.\"\n\nHe looked himself over ruefully. \"'Tis a garb befitting the dangerous\nadventure upon which I engaged,\" said he, somewhat stiff in the lip.\n\n\"But let me make known to you,\" I cried, \"that when a man wears a garb\nbefitting his adventure he fails surely. He should wear something\nextraneous. When you wish to do something evil, you put on the coat of\na parson. That is the clever way. But here you are looking like a\ngallows-bird of the greatest claim for the rope. Stop it; take off\nthe red thing, tilt your hat until you look like a gentleman, and let\nus go to our adventure respectably.\"\n\n\"I was never more surprised in my life,\" said he sincerely. \"I thought\nI was doing a right thing in thus arraying myself for an experience\nwhich cannot fail to be thrilling and mayhap deadly. However, I see\nyou in your accustomed attire, and in the apparel of your men-servants\nI see no great change from yesterday. May I again suggest to you that\nthe adventure upon which we proceed may be fraught with much danger?\"\n\n\"A red rag around your temples marks no improvement in our risks,\" said\nI. \"We will sally out as if we were off to a tea-party. When my father\nled the forlorn hope at the storming of Wuerstenhausenstaffenberg, he\nwore a lace collar, and he was a man who understood these matters. And I\nmay say that I wish he was here. He would be a great help.\"\n\nIn time the Doctor removed his red turban and gradually and sadly\nemerged from the more sanguine part of his paraphernalia and appeared\nas a simple little philosopher. Personally I have no objection to a\nman looking like a brigand, but my father always contended that\nclothes serve no purpose in real warfare. Thus I felt I had committed\nno great injustice in depriving Chord of his red turban.\n\nWe set out. I put much faith in the fact that we had no definite\nplans, but to my great consternation Doctor Chord almost at once began\nto develop well-laid schemes. As we moved toward the scene of our\nadventure he remarked them to me.\n\n\"First of all,\" said he, \"a strong party should be stationed at the\niron gates, not only to prevent a sally of the garrison, but to\nprevent an intrepid retainer from escaping and alarming the city.\nFurthermore--\"\n\n\"My gallant warrior,\" said I, interrupting him, \"we will drop this\nquestion to the level of a humdrum commercial age. I will try to\ncompass my purpose by the simple climbing of a tree, and to that end\nall I could need from you is a stout lift and a good word. Then we\nproceed in the established way of making signs over a wall. All this I\nexplained to you fully. I would not have you think I am about to\nbombard my lady-love's house.\"\n\nWith a countenance of great mournfulness he grumbled: \"No fascines\nhave been prepared.\"\n\n\"Very good,\" said I. \"I will climb the tree without the aid of\nfascines.\"\n\nAs luck would have it, there was a little inn not very far from the\nEarl's house and on the lonely avenue lined with oaks. Here I\ntemporarily left Jem Bottles and Paddy, for I feared their\nearnestness, which was becoming more terrible every minute. In order\nto keep them pacified I gave instructions that they should keep a\nstrict watch up the avenue, and if they saw any signs of trouble they\nwere to come a-running and do whatever I told them. These orders\nsuggested serious business to their minds, and so they were quite\ncontent. Their great point was that if a shindy was coming they had a\nmoral right to be mixed up in it.\n\nDoctor Chord and I strolled carelessly under the oaks. It was still\ntoo early for Lady Mary's walk in the garden, and there was an hour's\nwaiting to be worn out. In the mean time I was moved to express some\nof my reflections.\n\n\"'Tis possible--nay, probable--that this is a bootless quest,\" said I\ndejectedly. \"What shadow of an assurance have I that Lady Mary will\nwalk in the garden on this particular morning? This whole thing is\nabsolute folly.\"\n\n\"At any rate,\" said the Doctor, \"now that you already have walked this\ngreat distance, it will be little additional trouble to climb a tree.\"\n\nHe had encouraged me to my work at exactly the proper moment.\n\n\"You are right,\" said I, taking him warmly by the hand, \"I will climb\nthe tree in any case.\"\n\nAs the hour approached we began to cast about for the proper oak. I am\nsure they were all the same to me, but Doctor Chord was very\nparticular.\n\n\"'Tis logical to contend,\" said he, \"that the question of the girth of\nthe tree will enter importantly into our devices. For example, if a\ntree be so huge that your hands may not meet on the far side of it, a\nsuccessful ascension will be impossible. On the other hand, a very\nslim tree is like to bend beneath your weight, and even precipitate\nyou heavily to the ground, which disaster might <DW44> events for an\nindefinite period.\"\n\n\"Science your science, then,\" said I. \"And tell me what manner of tree\nbest suits the purpose of a true lover.\"\n\n\"A tree,\" said the Doctor, \"is a large vegetable arising with one\nwoody stem to a considerable height. As to the appearance and quality\nof a tree, there are many diversifications, and this fact in itself\nconstitutes the chief reason for this vegetable being of such great\nuse to the human family. Ships are made of nought but trees, and if it\nwere not for ships we would know but little of the great world of\nwhich these English islands form less than a half. Asia itself is\nslightly larger than all Scotland, and if it were not for the ships we\nwould be like to delude ourselves with the idea that we and our\nneighbours formed the major part of the world.\"\n\nWith such wise harangues the Doctor entertained my impatience until it\nwas time for me to climb a tree. And when this time came I went at my\nwork without discussion or delay.\n\n\"There,\" said I resolutely, \"I will climb this one if it kills me.\"\n\nI seized the tree; I climbed. I will not say there was no groaning and\npuffing, but any how I at last found myself astride of a branch and\nlooking over the wall into the Earl of Westport's garden.\n\nBut I might have made myself less labour and care by having somebody\npaint me a large landscape of this garden and surveyed it at my\nleisure. There I was high in a tree, dangling my legs, and staring at\nsmooth lawns, ornamental copses, and brilliant flower-beds without\neven so much as a dog to enliven the scene. \"O'Ruddy,\" said I to\nmyself after a long time, \"you've hung yourself here in mid-air like a\nbacon to a rafter, and I'll not say much to you now. But if you ever\nreach the ground without breaking your neck, I'll have a word with\nyou, for my feelings are sorely stirred.\"\n\nI do not know how long I sat in the tree engaged in my bitter\nmeditation. But finally I heard a great scudding of feet near the\nfoot of the tree, and I then saw the little Doctor bolting down the\nroad like a madman, his hat gone, his hair flying, while his two\ncoat-tails stuck out behind him straight as boards.\n\nMy excitement and interest in my ally's flight was so great that I\nnear fell from my perch. It was incomprehensible that my little friend\ncould dust the road at such speed. He seemed only to touch the ground\nfrom time to time. In a moment or two he was literally gone, like an\narrow shot from the bow.\n\nBut upon casting my bewildered glance downward I found myself staring\nsquarely into the mouth of a blunderbuss. The mouth of this\nblunderbuss, I may say, was of about the width of a fair-sized\nwater-pitcher; in colour it was bright and steely. Its appearance\nattracted me to such an extent that I lost all idea of the man behind\nthe gun. But presently I heard a grim, slow voice say,--\n\n\"Climb down, ye thief.\"\n\nThe reason for little Doctor Chord's hasty self-removal from the\nvicinity was now quite clear, and my interest in his departure was no\nlonger speculative.\n\n\n\n\nCHAPTER XXIV\n\n\n\"Climb down, ye thief,\" said the grim, slow voice again. I looked once\nmore into the mouth of the blunderbuss. I decided to climb. If I had\nhad my two feet square on the ground, I would have taken a turn with\nthis man, artillery or no artillery, to see if I could get the upper\nhand of him. But neither I nor any of my ancestors could ever fight\nwell in trees. Foliage incommodes us. We like a clear sweep for the\narm, and everything on a level space, and neither man in a tree.\nHowever, a sensible man holds no long discussions with a blunderbuss.\nI slid to the ground, arriving in a somewhat lacerated state. I\nthereupon found that the man behind the gun was evidently some kind of\nkeeper or gardener. He had a sour face deeply chiselled with mean\nlines, but his eyes were very bright, the lighter parts of them being\nsteely blue, and he rolled the pair of them from behind his awful\nweapon.\n\n\"And for whom have you mistaken me, rascal?\" I cried as soon as I had\ncome ungracefully to the ground and found with whom I had to deal.\n\n\"Have mistaken ye for naught,\" replied the man proudly. \"Ye be the\nthief of the French pears, ye be.\"\n\n\"French pears--French--French what?\" I cried.\n\n\"Ay, ye know full well,\" said he, \"and now ye'll just march.\"\n\nSeeing now plainly that I was in the hands of one of Lord Westport's\ngardeners, who had mistaken me for some garden-thief for whom he had\nbeen on the look-out, I began to expostulate very pointedly. But\nalways this man stolidly faced me with the yawning mouth of the\nblunderbuss.\n\n\"And now ye'll march,\" said he, and despite everything I marched. I\nmarched myself through the little door in the wall, and into the\ngardens of the Earl of Westport. And the infernal weapon was clamped\nagainst the small of my back.\n\nBut still my luck came to me even then, like basket falling out of a\nblue sky. As, in obedience to my captor's orders, I rounded a bit of\nshrubbery, I came face to face with Lady Mary. I stopped so abruptly\nthat the rim of the on-coming blunderbuss must have printed a fine\npink ring on my back. I lost all intelligence. I could not speak. I\nonly knew that I stood before the woman I loved, while a man firmly\npressed the muzzle of a deadly firearm between my shoulder-blades. I\nflushed with shame, as if I really had been guilty of stealing the\nFrench pears.\n\nLady Mary's first look upon me was one of pure astonishment. Then she\nquickly recognized the quaint threat expressed in the attitude of the\nblunderbuss.\n\n\"Strammers,\" she cried, rushing forward, \"what would you be doing to\nthe gentleman?\"\n\n\"'Tis no gentleman, your la'ship,\" answered the man confidently. \"He\nbe a low-born thief o' pears, he be.\"\n\n\"Strammers!\" she cried again, and wrested the blunderbuss from his\nhands. I will confess that my back immediately felt easier.\n\n\"And now, sir,\" she said, turning to me haughtily, \"you will please\ngrant me an explanation of to what my father is indebted for this\nvisit to his private grounds?\"\n\nBut she knew; no fool of a gardener and a floundering Irishman could\nkeep pace with the nimble wits of a real woman. I saw the pink steal\nover her face, and she plainly appeared not to care for an answer to\nher peremptory question. However, I made a grave reply which did not\ninvolve the main situation.\n\n\"Madam may have noticed a certain deluded man with a bell-mouthed\nhowitzer,\" said I. \"His persuasions were so pointed and emphatic that\nI was induced to invade these gardens, wherein I have been so\nunfortunate as to disturb a lady's privacy,--a thing which only causes\nme the deepest regret.\"\n\n\"He be a pear-thief,\" grumbled Strammers from a distance. \"Don't ye\ntake no word o' his, your la'ship, after me bringing 'im down from out\na tree.\"\n\n\"From out a tree?\" said Lady Mary, and she looked at me, and I looked\nat her.\n\n\"The man is right, Lady Mary,\" said I significantly. \"I was in a tree\nlooking over the garden wall.\"\n\n\"Strammers,\" said she with decision, \"wait for me in the rose-garden,\nand speak no single word to anybody until I see you again. You have\nmade a great mistake.\"\n\nThe man obediently retired, after saluting me with an air of slightly\ndubious apology. He was not yet convinced that I had not been after\nhis wretched French pears.\n\nBut with the withdrawal of this Strammers Lady Mary's manner changed.\nShe became frightened and backed away from me, still holding the\ngardener's blunderbuss.\n\n\"O sir,\" she cried in a beautiful agitation, \"I beg of you to leave at\nonce. Oh, please!\"\n\nBut here I saw it was necessary to treat the subject in a bold Irish\nway.\n\n\"I'll not leave, Lady Mary,\" I answered. \"I was brought here by force,\nand only force can make me withdraw.\"\n\nA glimmer of a smile came to her face, and she raised the blunderbuss,\npointing it full at my breast. The mouth was still the width of a\nwater-jug, and in the fair inexperienced hands of Lady Mary it was\nlike to go off at any moment and blow a hole in me as big as a\nplatter.\n\n\"Charming mistress,\" said I, \"shoot!\"\n\nFor answer she suddenly flung the weapon to the grass, and, burying\nher face in her hands, began to weep. \"I'm afraid it's l-l-loaded,\"\nshe sobbed out.\n\nIn an instant I was upon my knees at her side and had taken her hand.\nHer fingers resisted little, but she turned away her head.\n\n\"Lady Mary,\" said I softly, \"I'm a poor devil of an Irish adventurer,\nbut--I love you! I love you so that if I was dead you could bid me\nrise! I am a worthless fellow; I have no money, and my estate you can\nhardly see for the mortgages and trouble upon it; I am no fine suitor,\nbut I love you more than them all; I do, upon my life!\"\n\n\"Here approaches Strammers in quest of his blunderbuss,\" she answered\ncalmly. \"Perhaps we had better give it to him.\"\n\nI sprang to my feet, and, sure enough, the thick-headed ninepin of a\ngardener was nearing us.\n\n\"Don't ye trust 'im, your la'ship!\" he cried. \"I caught 'im in a tree,\nI did, and he be a bad lot!\"\n\nLady Mary quelled him, and he at once went away with his blunderbuss,\nstill muttering his many doubts. But still one cannot drop a love\ndeclaration and pick it up again with the facility of a tailor\nresuming his work on a waistcoat. One can't say: \"Where was I? How far\nhad I gone before this miserable interruption came?\" In a word I found\nmysef stammering and stuttering and wasting moments too precious for\nwords.\n\n\"Lady Mary--\" I began. \"Lady Mary--I love you, Lady Mary! Lady Mary--\"\n\nIt was impossible for me to depart from this rigmarole and express the\nmany things with which my heart was full. It was a maddening\ntongue-tie. The moments seemed for me the crisis of my existence, and\nyet I could only say, \"Lady Mary, I love you!\" I know that in many\ncases this statement has seemed to be sufficient, but as a matter of\nfact I was full of things to say, and it was plain to me that I was\nlosing everything through the fact that my silly tongue clung to the\nroof of my mouth.\n\nI do not know how long the agony endured, but at any rate it was ended\nby a thunderous hammering upon the little door in the garden-wall. A\nhigh Irish voice could be heard:\n\n\"And if ye be not leaving him out immediately, we will be coming over\nthe wall if it is ten thousand feet high, ye murdering rogues.\"\n\nLady Mary turned deadly pale. \"Oh, we are lost,\" she cried.\n\nI saw at once that the interview was ended. If I remained doughtily I\nremained stupidly. I could come back some other day. I clutched Lady\nMary's hand and kissed it. Then I ran for the door in the garden wall.\nIn a moment I was out, and I heard her frantically bolting the door\nbehind me.\n\nI confronted Paddy and Jem. Jem had in his hands a brace of pistols\nwhich he was waving determinedly. Paddy was wetting his palms and\nresolutely swinging a club. But when they saw me their ferocity gave\nway to an outburst of affectionate emotion. I had to assert all my\nmastership to keep Paddy from singing. He would sing. Sure, if they\nhad never heard an Irish song it was time they did.\n\n\"Paddy,\" said I, \"my troubles are on me. I wish to be thinking. Remain\nquiet.\"\n\nPresently we reached the little inn, and from there the little Doctor\nChord flew out like a hawk at a sparrow.\n\n\"I thought you were dead,\" he shouted wildly. \"I thought you were\ndead.\"\n\n\"No,\" said I, \"I am not dead, but I am very thirsty.\" And, although\nthey were murmuring this thing and that thing, I would have no word\nwith them until I was led to the parlour of the inn and given a glass.\n\n\"Now,\" said I, \"I penetrated to the garden and afterwards I came away\nand I can say no more.\"\n\nThe little Doctor was very happy and proud.\n\n\"When I saw the man with the blunderbuss,\" he recounted, \"I said\nboldly: 'Sirrah, remove that weapon! Exclude it from the scene!\nEliminate it from the situation!' But his behaviour was extraordinary.\nHe trained the weapon in such a manner that I myself was in danger of\nbeing eliminated from the situation. I instantly concluded that I\nwould be of more benefit to the cause if I temporarily abandoned the\nvicinity and withdrew to a place where the climatic conditions were\nmore favourable to prolonged terms of human existence.\"\n\n\"I saw you abandoning the vicinity,\" said I, \"and I am free to declare\nthat I never saw a vicinity abandoned with more spirit and finish.\"\n\n\"I thank you for your appreciation,\" said the Doctor simply. Then he\nleaned to my ear and whispered, barring his words from Jem and Paddy,\nwho stood respectfully near our chairs. \"And the main object of the\nexpedition?\" he asked. \"Was there heavy firing and the beating down of\ndoors? And I hope you took occasion to slay the hideous monster who\nflourished the blunderbuss? Imagine my excitement after I had\nsuccessfully abandoned the vicinity! I was trembling with anxiety for\nyou. Still, I could adopt no steps which would not involve such\nopportunities for instant destruction that the thought of them brought\nto mind the most horrible ideas. I pictured myself lying butchered,\nblown to atoms by a gardener's blunderbuss. Then the spirit of\nself-sacrifice arose in me, and, as you know, I sent your two servants\nto your rescue.\"\n\nThe little man was looking through the window at this moment. Suddenly\nhe started back, flinging up his hands.\n\n\"My soul, he is again upon us,\" he cried.\n\nI hastily followed his glance, and saw the man Strammers making\npeaceful way toward the inn. Apparently he was going to the taproom\nfor an early pint. The Doctor flurried and dove until I checked him in\nfear that he would stand on his head in the fireplace.\n\n\"No,\" said I, \"calm yourself. There will be no blunderbusses. On the\nother hand, I see here a great chance for a master-stroke. Be quiet\nnow, and try to hold yourself in a chair and see me deal with the\nsituation. When it comes to a thing like this, it is all child's play\nfor me. Paddy,\" said I. \"Jem,\" said I, \"there is a gardener in the\ntaproom. Go and become his warm friends. You know what I mean. A\ntuppence here and there won't matter. But, of course, always treat him\nwith the profound consideration which is due to so distinguished a\ngardener.\"\n\nThey understood me at once and grinned. But even then I was struck\nwith their peculiar reasons for understanding at once. Jem Bottles\nunderstood at once because he had been a highwayman; Paddy understood\nat once because he was an Irishman. One had been all his life a rogue;\nthe other had been born on an intelligent island. And so they\ncomprehended me with equal facility.\n\nThey departed on their errand, and when I turned I found myself in the\nclutches of a maddened Doctor Chord.\n\n\"Monster,\" he screamed, \"you have ordered him to be killed!\"\n\n\"Whist,\" said I, \"it would never do to order him to be killed. He is\ntoo valuable.\"\n\n\n\n\nCHAPTER XXV\n\n\n\"You appear more at your ease when you are calm,\" said I to the Doctor\nas I squashed him into a chair. \"Your ideas of murder are juvenile.\nGardeners are murdered only by other gardeners, over some question of\na magnolia-tree. Gentlemen of position never murder gardeners.\"\n\n\"You are right, sir,\" he responded frankly. \"I see my mistake. But\nreally, I was convinced that something dreadful was about to happen. I\nam not familiar with the ways of your nationality, sir, and when you\ngave the resolute directions to your men it was according to my\neducation to believe that something sinister was at hand, although no\none could regret more than I that I have made this foolish mistake.\"\n\n\"No,\" said I, \"you are not familiar with the ways of my nationality,\nand it will require an indefinite number of centuries to make your\ncountry-men understand the ways of my nationality; and when they do\nthey will only pretend that after great research they have discovered\nsomething very evil indeed. However, in this detail, I am able to\ninstruct you fully. The gardener will not be murdered. His fluency\nwith a blunderbuss was very annoying, but in my opinion it was not so\nfluent as to merit death.\"\n\n\"I confess,\" said Doctor Chord, \"that all peoples save my own are\ngreat rascals and natural seducers. I cannot change this national\nconviction, for I have studied politics as they are known in the\nKing's Parliament, and it has been thus proved to me.\"\n\n\"However, the gardener is not to be murdered,\" said I, \"and although I\nam willing to cure you in that particular ignorance I am not willing\nto take up your general cure as a life work. A glass of wine with\nyou.\"\n\nAfter we had adjusted this slight misunderstanding we occupied our\nseats comfortably before the fire. I wished to give Paddy and Jem\nplenty of time to conciliate Strammers, but I must say that the wait\ngrew irksome. Finally I arose and went into the corridor and peered\ninto the taproom. There were Paddy and Jem with their victim, the\nthree of them seated affectionately in a row on a bench, drinking from\nquart pots of ale. Paddy was clapping the gardener on the shoulder.\n\n\"Strammers,\" he cried, \"I am thinking more of you than of my cousin\nMickey, who was that gay and that gallant it would make you wonder,\nalthough I am truthful in saying they killed him for the peace of the\nparish. But he had the same bold air with him, and devil the girl in\nthe country-side but didn't know who was the lad for her.\"\n\nStrammers seemed greatly pleased, but Jem Bottles evinced deep\ndisapproval of Paddy's Celtic methods.\n\n\"Let Master Strammers be,\" said he. \"He be a-wanting a quiet draught.\nLet him have his ale with no talking here and there.\"\n\n\"Ay,\" said Strammers, now convinced that he was a great man and a\nphilosopher, \"a quiet draught o' old ale be a good thing.\"\n\n\"True for you, Master Strammers,\" cried Paddy enthusiastically. \"It is\nin the way of being a good thing. There you are now. Ay, that's it. A\ngood thing! Sure.\"\n\n\"Ay,\" said Strammers, deeply moved by this appreciation, which he had\nbelieved should always have existed. \"Ay, I spoke well.\"\n\n\"Well would be no name for it,\" responded Paddy fervidly. \"By gor, and\nI wish you were knowing Father Corrigan. He would be the only man to\nnear match you. 'A quiet draught o' old ale is a good thing,' says\nyou, and by the piper 'tis hard to say Father Corrigan could have done\nit that handily. 'Tis you that are a wonderful man.\"\n\n\"I have a small way o' my own,\" said Strammers, \"which even some of\nthe best gardeners has accounted most wise and humorous. The power o'\ngood speech be a great gift.\" Whereupon the complacent Strammers\nlifted his arm and buried more than half his face in his quart pot.\n\n\"It is,\" said Paddy earnestly. \"And I'm doubting if even the best\ngardeners would be able to improve it. And says you: 'A quiet draught\no' old ale is a good thing,' 'Twould take a grand gardener to beat\nthat word.\"\n\n\"And besides the brisk way of giving a word now and then,\" continued\nthe deluded Strammers, \"I am a great man with flowers. Some of the\nfinest beds in London are there in my master's park.\"\n\n\"Are they so?\" said Paddy. \"I would be liking to see them.\"\n\n\"And ye shall,\" cried the gardener with an outburst of generous\nfeeling. \"So ye shall. On a Sunday we may stroll quietly and decently\nin the gardens, and ye shall see.\"\n\nSeeing that Paddy and Jem were getting on well with the man, I\nreturned to Doctor Chord.\n\n\"'Tis all right,\" said I. \"They have him in hand. We have only to sit\nstill, and the whole thing is managed.\"\n\nLater I saw the three men in the road, Paddy and Jem embracing the\nalmost tearful Strammers. These farewells were touching. Afterward my\nrogues appeared before me, each with a wide grin.\n\n\"We have him,\" said Paddy, \"and 'tis us that has an invitation to come\ninside the wall next Sunday. 'I have some fine flowers in the\ngardens,' said he. 'Have you so?' said I. 'Well, then, 'tis myself\nwill be breaking your head if you don't leave us inside to see them.'\n'Master Paddy,' said he, 'you are a gentleman, or if not you are very\nlike one, and you and your handsome friend, Master Jem, as well as\nanother friend or two, is welcome to see the gardens whenever I can\nmake certain the master and mistress is out.' And with that I told him\nhe could go home.\"\n\n\"You are doing well,\" I said, letting the scoundrel see in my face\nthat I believed his pleasant tale, and he was so pleased that he was\nfor going on and making a regular book out of it. But I checked him.\n\"No,\" said I. \"I am fearing that I would become too much interested\nand excited. I am satisfied with what you've been telling me. 'Twas\nmore to my mind to have beaten that glass-eyed man, but we have taken\nthe right course. And now we will be returning to where we lodge.\"\n\nDuring the walk back to the \"Pig and Turnip\" Doctor Chord took it\nupon himself to discourse in his usual style upon the recent events.\n\"Of course, sir, I would care to hear of the tragic scenes which must\nhave transpired soon after I--I--\"\n\n\"Abandoned the vicinity?\" said I.\n\n\"Precisely,\" he responded. \"Although I was not in the exact\nneighbourhood during what must have been a most tempestuous part of\nyour adventure, I can assure you I had lost none of my former interest\nin the affair.\"\n\n\"I am believing you,\" said I; \"but let us talk now more of the future.\nI am much absorbed in the future. It appears to me that it will move\nat a rapid pace.\"\n\nI did not tell him about my meeting with Lady Mary, because I knew, if\noccasion arose, he would spread the news over half London. No\nconsideration would have been great enough to bridle the tongue of the\nlittle gossip from use of the first bit of news which he had ever\nreceived warm from the fire. Besides, after his behaviour in front of\nthe enemy, I was quite certain that an imparting of my news could do\nnothing in the way of impairing his inefficiency. Consequently it was\nnot necessary to trouble him with dramatic details.\n\n\"As to the part of the adventure which took place in the garden, you\nare consistently silent, I observe, sir,\" said the Doctor.\n\n\"I am,\" said I. \"I come of a long line of silent ancestors. My father\nwas particularly notable in this respect.\"\n\n\"And yet, sir,\" rejoined the Doctor, \"I had gained an impression that\nyour father was quite willing to express himself in a lofty and noble\nmanner on such affairs as attracted his especial notice.\"\n\n\"He was that,\" said I, pleased. \"He was indeed. I am only wishing I\nhad his talent for saying all that was in his mind so fast that even\nthe priest could not keep up with him, and goodness knows Father\nDonovan was no small talker.\"\n\n\"You prove to me the limitations of science, sir,\" said he. \"Although\nI think I may boast of some small education of a scientific nature, I\nthink I will require some time for meditation and study before I will\nbe able to reconcile your last two statements.\"\n\n\"'Tis no matter,\" I cried amiably. \"Let it pass.\"\n\nFor the rest of that week there was conference following conference at\nthe \"Pig and Turnip\" and elsewhere. My three companions were now as\neager as myself for the advent of the critical Sunday when I, with\nPaddy and Jem, were to attempt our visit to Strammers's\nflower-gardens. I had no difficulty in persuading the Doctor that his\nservices would be invaluable at another place; for the memory of the\nblunderbuss seemed to linger with him. I had resolved to disguise\nmyself slightly, for I had no mind to have complications arising from\nthis gardener's eyes. I think a little disguise is plenty unless one\nstalks mysteriously and stops and peers here and there. A little\nunostentatious minding of one's own affairs is a good way to remain\nundiscovered. Then nobody looks at you and demands: \"Who is this\nfellow?\" My father always said that when he wished to disguise himself\nhe dressed as a common man, and although this gained him many a hard\nknock of the fist and blow of the stick from people who were really\nhis inferiors, he found his disguise was perfection. However, my\nfather only disguised when on some secret mission from King Louis, for\nit does not become a gentleman to accept a box on the ears from\nanybody unless it is in the service of his sovereign.\n\nI remember my father saying also these tours as a common man taught\nhim he must ever afterward ride carefully through the streets of\nvillages and towns. He was deeply impressed by the way in which men,\nwomen, and children had to scud for their lives to keep from under the\nhoofs of the chargers of these devil-may-care gentlemen who came like\nwhirlwinds through narrow crowded streets. He himself often had to\nscramble for his life, he said.\n\nHowever, that was many years back, and I did not fear any such\nadventures in my prospective expedition. In such a case I would have\ntrembled for what might happen. I have no such philosophy of temper as\nhad my father. I might take the heel of a gay cavalier and throw him\nout of the saddle, and then there would be a fine uproar. However, I\nam quite convinced that it is always best to dodge. A good dodger\nseldom gets into trouble in this world, and lives to a green old age,\nwhile the noble patriot and others of his kind die in dungeons. I\nremember an honest man who set out to reform the parish in the matter\nof drink. They took him and--but, no matter; I must be getting on with\nthe main tale.\n\n\n\n\nCHAPTER XXVI\n\n\nOn Saturday night I called the lads to my room and gave them their\nfinal instructions.\n\n\"Now, you rogues,\" said I to them, \"let there be no drinking this\nnight, and no trapesing of the streets, getting your heads broke just\nat the critical moment; for, as my father used to say, although a\nbroken head is merrily come by, a clear head's worth two of it when\nbusiness is to be transacted. So go to your beds at once, the two of\nyou, if there's any drinking to be done, troth it's myself that'll\nattend to it.\"\n\nWith that I drove them out and sat down to an exhilarating bottle,\nwithout ever a thought of where the money was to come from to pay for\nit. It is one of the advantages of a public house frequented by the\nnobility that if you come to it with a bold front, and one or two\nservants behind your back, you have at least a clear week ahead before\nthey flutter the show of a bill at you and ask to see the colour of\nyour gold in exchange for their ink and paper.\n\nMy father used to say that a gentleman with money in his pocket might\neconomize and no disgrace to him; but when stomach and purse are both\nempty, go to the best house in the town, where they will feed you, and\nlodge you, and drink you, before asking questions. Indeed I never shed\nmany salt tears over the losses of a publican, for he shears so\nclosely those sheep that have plenty of wool that he may well take\ncare of an innocent lamb like myself, on which the crop is not yet\ngrown.\n\nI was drinking quietly and thinking deeply on the wisdom of my father,\nwho knew the world better than ever his son will know it, when there\nwas an unexpected knock at the door, and in walked Doctor Chord. I was\nnot too pleased to see the little man, for I had feared he had changed\nhis mind and wanted to come with us in the morning, and his company\nwas something I had no desire for. He was a coward in a pinch, and a\ndistrustful man in peace, ever casting doubt on the affection I was\nsure sometimes that Lady Mary held for me; and if he wasn't talking\nabout that, sure he went rambling on,--great discourses on science\nwhich held little interest for a young man so deeply in love as I was.\nThe proper study of mankind is womankind, said a philosopher that my\nfather used to quote with approval, but whose name I'm forgetting at\nthis moment. Nevertheless I welcomed the little Doctor and said to\nhim:\n\n\"Draw you up a chair, and I'll draw out a cork.\"\n\nThe little man sat him down, and I placed an open bottle nice and\nconvenient to his elbow.\n\nWhether it was the prospect of good wine, or the delight of better\ncompany, or the thought of what was going to happen on the morrow, I\ncould not tell; but it seemed to me the little Doctor laboured under a\ngreat deal of excitement, and I became more and more afraid that he\nwould insist on bearing us company while the Earl and the Countess\nwere away at church. Now it was enough to have on my hands two such\nmodels of stupidity as Paddy and Jem without having to look after\nDoctor Chord as well, and him glancing his eyes this way and that in\napprehension of a blunderbuss.\n\n\"Have you made all your plans, O'Ruddy?\" he inquired, setting down his\ncup a good deal emptier than when he lifted it.\n\n\"I have,\" said I.\n\n\"Are you entirely satisfied with them?\" he continued.\n\n\"My plans are always perfect plans,\" I replied to him, \"and trouble\nonly comes in the working of them. When you have to work with such raw\nmaterial as I have to put up with, the best of plans have the unlucky\nhabit of turning round and hitting you in the eye.\"\n\n\"Do you expect to be hit in the eye to-morrow?\" asked the Doctor, very\nexcited, which was shown by the rattle of the bottle against the lip\nof his cup.\n\n\"I'm only sure of one thing for to-morrow,\" said I, \"and that is the\ncertainty that if there's blunder to be made one or other of my\nfollowing will make it. Still, I'm not complaining, for it's good to\nbe certain of something.\"\n\n\"What's to be your mode of procedure?\" said the Doctor, giving me a\ntouch of his fine language.\n\n\"We wait in the lane till the church bells have stopped ringing, then\nPaddy and Jem go up to the little door in the wall, and Paddy knocks\nnice and quietly, in the expectation that the door will be opened as\nquietly by Strammers, and thereupon Jem and Paddy will be let in.\"\n\n\"But won't ye go in with them?\" inquired the little Doctor very\nhurriedly.\n\n\"Doctor Chord,\" said I, lifting up my cup, \"I have the honour to drink\nwine with you, and to inform you that it's myself that's outlining the\nplan.\"\n\n\"I beg your pardon for interrupting,\" said the Doctor; then he nodded\nto me as he drank.\n\n\"My two villains will go in alone with Strammers, and when the door is\nbolted, and they have passed the time of day with each other, Paddy\nwill look around the garden and exclaim how it excels all the gardens\nthat ever was, including that of Eden; and then Jem will say what a\npity it was they couldn't have their young friend outside to see the\nbeauty of it. It is my expectation that Strammers will rise to this,\nand request the pleasure of their young friend's company; but if he\nhesitates Paddy will say that the young friend outside is a\nfree-handed Irishman who would no more mind a shilling going from his\npocket into that of another man than he would the crooking of an elbow\nwhen a good drink is to be had. But be that as it may, they're to work\nme in through the little door by the united diplomacy of England and\nIreland, and, once inside of the walls, it is my hope that I can slip\naway from them and see something of the inside of the house as well.\"\n\n\"And you have the hope that you'll find Lady Mary in the\nwithdrawing-room,\" said the Doctor.\n\n\"I'll find her,\" says I, \"if she's in the house; for I'm going from\nroom to room on a tour of inspection to see whether I'll buy the\nmansion or not.\"\n\n\"It's a very good plan,\" said the Doctor, drawing the back of his hand\nacross his lips. \"It's a very good plan,\" he repeated, nodding his\nhead several times.\n\n\"Now, by the Old Head of Kinsale, little man,\" said I, \"what do you\nmean by that remark and that motion of the head? What's wrong with the\nplan?\"\n\n\"The plan's a good one, as I have said,\" reiterated the Doctor. But I\nsaw there was something on his mind, and told him so, urging him to be\nout with it.\n\n\"Do you think,\" said I, \"that Lady Mary will be in church with her\nfather and mother?\"\n\n\"I do not,\" muttered the Doctor, cautiously bringing his voice down to\na whisper; \"but I want to warn you that there's danger here in this\nroom while you're lurking around my Earl's palace.\"\n\n\"How can danger harm me here when I am somewhere else?\" I asked.\n\nA very mysterious manner fell upon the little man, and he glanced, one\nafter the other, at the four corners of the room, as if he heard a\nmouse moving and wanted to detect it. Then he looked sternly at the\ndoor, and I thought he was going to peer up the chimney, but instead\nhe leaned across the table and said huskily,--\n\n\"The papers!\"\n\n\"What papers?\" I asked, astonished.\n\n\"Your thoughts are so intent on the young lady that you forget\neverything else. Have you no recollection of the papers the Earl of\nWestport is so anxious to put himself in possession of?\"\n\nI leaned back in my chair and gazed steadily at Chord; but his eyes\nwould not bring themselves to meet mine, and so he made some pother\nabout filling up his cup again, with the neck of the bottle trembling\non the edge, as if its teeth were chattering.\n\nNow my father used to say when a man is afraid to meet your eye, be\nprepared to have him meet your fist. I disremembered saying anything\nto the Doctor about these same papers, which, truth to tell, I had\ngiven but little thought to recently, with other things of more\nimportance to crowd them out of mind.\n\n\"How come you to know anything about the papers?\" I said at last.\n\n\"Oh, your memory is clean leaving you!\" cried the little Doctor, as if\nthe cup of wine he drank had brought back his courage to him. \"You\ntold me all about the papers when we were in Kensington Gardens.\"\n\n\"If I did,\" says I, \"then I must have further informed you that I gave\nthem as a present to Lady Mary herself. Surely I told you that?\"\n\n\"You told me that, of course; but I thought you said they had come\nback into your possession again. If I'm wrong, it's no matter at all,\nand there's nothing to be said about them. I'm merely speaking to you\nby way of a friend, and I thought if you had the papers here in your\nroom it was very unsafe to leave them unprotected by yourself or some\none you can trust. I was just speaking as your well-wisher, for I\ndon't want to hear you crying you are robbed, and us at our wit's end\nnot getting either the thief or the booty.\"\n\nHe spoke with great candour and good humour, and the only thing that\nmade me suspicious at first was that for the life of me I could not\never remember mentioning the papers to him, yet it was very likely\nthat I did; for, as my father used to say, an Irishman talks more than\nthe recording angel can set down in his busiest day, and therefore it\nis lucky that everything he says is not held against him. It seemed to\nme that we talked more of scandal than of papers in the park, but\nstill I might be mistaken.\n\n\"Very good, Doctor,\" I cried, genially. \"The papers it is, and, true\nfor you, the Earl would like to get his old claws on them. Have you\nany suggestions to make?\"\n\n\"Well, it seems to me, O'Ruddy, that if the Earl got wind of them it\nwould be the easiest thing in the world to have your apartment rifled\nduring your absence.\"\n\n\"That is true enough,\" I agreed, \"so what would you do about the\npapers if you were in my boots?\"\n\n\"If I had a friend I could trust,\" said Doctor Chord slowly, \"I would\ngive the papers to him and tell him to take good care of them.\"\n\n\"But why not carry them about in my own pocket?\" I asked.\n\n\"It seemed to me they were not any too safe last time they were\nthere,\" said the Doctor, pleasantly enough. \"You see, O'Ruddy, you're\na marked man if once the Earl gets wind of your being in town. To\ncarry the papers about on your own person would be the unsafest thing\nyou could do, ensuring you a stab in the back, so that little use\nyou'd have for the papers ever after. I have no desire to be mixed\nfurther in your affairs than I am at the present moment, but\nnevertheless I could easily take charge of the packet for you; then\nyou would know where it was.\"\n\n\"But would I be sure to know where _you_ were?\" said I, my first\nsuspicion of him returning to me.\n\nThe little Doctor laughed.\n\n\"I am always very easily found,\" he said; \"but when I offered to take\nthe papers it was merely in case a stranger like yourself should not\nhave a faster friend beside him than I am. If you have any such, then\nI advise you to give custody of the papers to him.\"\n\n\"I have no real friend in London that I know of,\" said I, \"but Paddy.\"\n\n\"The very thing,\" cried the Doctor, joyously, at once putting to rest\nall my doubts concerning him. \"The very thing. I would give the papers\nto Paddy and tell him to protect them with his life. I'm sure he'll do\nit, and you'll know where to find both them and him when you want\nthem. But to go away from the 'Pig and Turnip' right across to the\nother end of the town, taking your two servants with you, leaving\nnobody to guard papers that are of importance to you, strikes me as\nthe height of folly. I'll just fill up another cup, and so bid you\ngood-night, and good luck for the morrow.\"\n\nAnd with that the little man drained the bottle, taking his leave with\ngreat effusion, and begging my pardon for even so much as mentioning\nthe papers, saying they had been on his mind for the last day or two,\nand, feeling friendly toward me, he wished to warn me not to leave\nthem carelessly about.\n\nAfter he left I thought a good deal about what the Doctor had said,\nand I wondered at myself that I had ever misdoubted him; for, although\nhe was a man given greatly to talk, yet he had been exceedingly\nfriendly with me from the very first night I had met him, and I\nthought shame of myself that I was losing trust in my fellow man here\nin this great city of London, because in Ireland we trust each other\nentirely; and indeed we are under some compulsion in that same matter,\nfor there is so little money about that if you do not take a man's\nword now and then there's nothing else for you to take.\n\n\n\n\nCHAPTER XXVII\n\n\nI slept well that night, and it was broad daylight when I awoke. A\nmost beautiful morning it seemed to me, and just the time for a lonely\nstroll in the beautiful gardens, so long as there was some one with\nyou that you thought a great deal of. I made a good breakfast, and\nthen took out the papers and placed them on the table before me. They\nwere all safe so far. I could not comprehend how the Earl would know\nanything of my being in London, unless, indeed, he caught sight of me\nwalking in his own gardens with his own daughter, and then, belike, he\nwas so jealous a man that he would maybe come to the conclusion I was\nin London as well as himself.\n\nAfter breakfast Paddy and Jem came in, looking as bold as Blarney\nCastle; and when I eyed them both I saw that neither one nor the other\nwas a fit custodian for papers that might make the proudest Earl in\nEngland a poor man or a rich man, depending which way they went. So I\nput the documents in my own pocket without more ado, and gave up my\nthoughts to a pleasanter subject. I changed my mind about a disguise,\nand put on my back the best clothes that I had to wear. I wished I had\nthe new suits I had been measured for, but the spalpeen of a tailor\nwould not let me have them unless I paid him some of the money they\ncost. When I came to think over it I saw that Strammers would surely\nnever recognize me as a gay spark of fashion when he had merely seen\nme once before, torn and ragged, coming down from a tree on top of his\nblunderbuss. So I instructed Paddy to say that he and Jem were\nservants of the best master in the world, who was a great lover of\ngardens; that he was of immense generosity, and if Strammers allowed\nhim to come into the gardens by the little door he would be a richer\nman when the door was opened than he would be if he kept it shut. I\nhad been long enough in London to learn the golden method of\npersuasion; any how I could not bring myself to the chance of meeting\nwith my lady, and me dressed worse than one of her own servants.\n\nWe were all in the lane when the church bells ceased to ring, and if\nany one had seen us he would simply have met a comely young Irish\ngentleman taking the air of a Sunday morning with two faithful\nservants at his heels. I allowed something like ten impatient minutes\nto crawl past me, and then, as the lane was clear and every one for\nthe church within its walls, I tipped a nod to Paddy, and he, with Jem\nby his side, tapped lightly at the door, while I stood behind the\ntrunk of the tree up which I had climbed before. There was no sign of\nDoctor Chord in the vicinity, and for that I was thankful, because up\nto the last moment I feared the little man could not help intruding\nhimself on what was somebody else's business.\n\nThe door was opened with some caution, letting Paddy and Jem enter;\nthen it was closed, and I heard the bolts shot into their places. But\nI was speedily to hear more than bolts that Sunday morning. There was\na sound of thumping sticks, and I heard a yell that might well have\npenetrated to the \"Pig and Turnip\" itself, although it was miles away.\nI knew Paddy's cry, and next there came some good English cursing from\nJem Bottles, while a shrill voice called out:--\n\n\"Catch the red-haired one; he's the villain we want!\"\n\nIn the midst of various exclamations, maledictions, and other\nconstructions of speech, mingled, I thought, with laughter, I flung my\nshoulder against the door, but I might as well have tried to batter\ndown the wall itself. The door was as firm as Macgillicuddy Reeks. I\nknow when I am beat as well as the next man, and, losing no more time\nthere, I ran as fast as I could along the wall, out of the lane, and\nso to the front of the house. The main entrance was protected by great\ngates of wrought iron, which were opened on occasion by a man in a\nlittle cubby of a cabin that stood for a porter's lodge. The man\nwasn't there, and the gates were locked; but part of one of the huge\nwings of wrought iron was a little gate that stood ajar. This I pushed\nopen, and, unmolested, stepped inside.\n\nThe trees and shrubbery hid from me the scene that was taking place\ninside the little wooden door. I dashed through the underbrush and\ncame to the edge of a broad lawn, and there was going on as fine a\nscrimmage as any man could wish to see. Jem Bottles had his back\nagainst the wooden door, and was laying about him with a stout stick;\nhalf a dozen tall fellows in livery making a great show of attack,\nbut keeping well out of range of his weapon. Poor Paddy had the broad\nof his back on the turf, and it looked like they were trying to tear\nthe clothes off him, for another half-dozen were on top of him; but I\ncan say this in his favour, Paddy was using his big feet and doing\ngreat execution with them. Every now and then he planted a boot in the\nwell-fed front of a footman or under-gardener, and sent him flying.\nThe whole household seemed to be present, and one could hardly believe\nthere was such a mob in a single mansion. The Earl of Westport was\nthere, and who stood beside him but that little villain, Doctor Chord.\n\nBut it was the Countess herself that was directing operations. She had\nan ebony stick in her hands, and when Paddy kicked one of her\nunderlings the vigorous old lady smote the overturned servant to make\nhim to the fray again. It was an exciting scene, and Donnybrook was\nnothing to it. Their backs were all toward me, and I was just bubbling\nwith joy to think what a surprise I was about to give them,--for I\ndrew my sword and had a yell of defiance on my lips,--when a cry that\nnobody paid the least attention to turned my mind in another direction\nentirely.\n\nOne of the first-floor windows was open, and over the sill leaned Lady\nMary herself, her face aflush with anger.\n\n\"Father! Mother!\" she cried. \"Are not you ashamed of yourselves,\nmaking this commotion on a Sunday morning? Call the servants away from\nthere! Let the two poor men go! Oh, shame, shame upon you.\"\n\nShe wrung her hands, but, as I was saying, nobody paid the slightest\nheed to her, and I doubt if any of them heard her, for Paddy was not\nkeeping silence by any manner of means. He was taking the worst of all\nthe blows that fell on him in a vigorous outcry.\n\n\"Murther! murther!\" he shouted. \"Let me on me feet, an' I'll knock yez\nall into the middle of county Clare.\"\n\nNo one, however, took advantage of this generous offer, but they kept\nas clear as they could of his miscellaneous feet, and the Countess\npoked him in the ribs with the point of her ebony stick whenever she\nwasn't laying it over the backs of her servants.\n\nNow, no man can ever say that I was a laggard when a good\nold-fashioned contest was going on, and the less indolence was\nobservable on my own part when friends of mine were engaged in the\nfray. Sure I was always eager enough, even when it was a stranger's\ndebate, and I wonder what my father would think of me now, to see me\nveer from the straight course of battle and thrust my unstruck sword\nonce more into its scabbard. It was the face in the window that made\nme forget friend and foe alike. Lady Mary was the only member of the\nhousehold that was not on the lawn, and was protesting unheard against\nthe violence to two poor men who were there because they had been\ninvited to come by the under-gardener.\n\nI saw in the twinkling of an eye that the house had been deserted on\nthe first outcry. Doors were left wide open for the whole world to\nenter. I dodged behind the trees, scuttled up the gravelled driveway,\nleaped the stone steps three at a time, and before you could say\n\"Ballymuggins\" I was in the most superb hall in which I ever set my\nfoot. It was a square house with the stairway in the middle. I kept\nin my mind's eye the direction of the window in which Lady Mary had\nappeared. Quick as a bog-trotter responds to an invitation to drink, I\nmounted that grand stairway, turned to my right, and came to a door\nopposite which I surmised was the window through which Lady Mary was\nleaning. Against this door I rapped my knuckles, and speedily I heard\nthe sweet voice of the most charming girl in all the world demand with\nsomething like consternation in its tones,--\n\n\"Who is there?\"\n\n\"It's me, Lady Mary!\" said I. \"The O'Ruddy, who begs the privilege of\na word with you.\"\n\nI heard the slam of a window being shut, then the sound of a light\nstep across the floor, and after that she said with a catch in her\nvoice,--\n\n\"I'll be pleased you should come in, Mr. O'Ruddy.\"\n\nI tried the door, but found it locked.\n\n\"How can I come in, Lady Mary,\" says I, \"if you've got bolts held\nagainst me?\"\n\n\"There are no bolts,\" said Lady Mary; \"the key should be on the\noutside. I am locked in. Look for the key and open the door.\"\n\nWas ever a more delightful sentence spoken to a man? My heart was in\nmy throat with joy. I glanced down, and there, sure enough, stuck the\nkey. I turned it at once, then pulled it out of the lock and opened\nthe door.\n\n\"Lady Mary,\" says I, \"with your permission, it seems to me a door\nshould be locked from the inside.\"\n\nWith that I thrust the key through the far side of the door, closed\nit, and locked it. Then I turned round to face her.\n\nThe room, it was plain to be seen, was the parlour of a lady,--a\nboudoir, as they call it in France, a word that my father was very\nfond of using, having caught it when he was on the campaign in that\ndelightful country. The boudoir was full of confections and charming\nlittle dainties in the way of lace, and easy chairs, and bookcases,\nand little writing-desks, and a work-basket here and there; but the\nfinest ornament it possessed was the girl who now stood in the middle\nof the floor with a frown on her brow that was most becoming. Yes,\nthere was a frown on her brow, although I expected a smile on her lips\nbecause of the cordial invitation she had given me to come in.\n\nIt would seem to either you or me that if a lady suffered the\nindignity of being locked in her room, just as if she was a child of\nsix years old, she would welcome with joy the person who came and\nreleased her. Now, my father, who was the wisest man since\nSolomon,--and indeed, as I listened to him, I've often thought that\nSolomon was overpraised,--my father used to say there was no mystery\nat all about women. \"You just think,\" he would say, \"of what a\nsensible man would do on a certain occasion; then configure out in\nyour mind the very opposite, and that's what a woman will do.\" A man\nwho had been imprisoned would have held out his hand and have said,\n\"God bless you, O'Ruddy; but I'm glad to see you.\" And here stood this\nfine lady in the middle of her room, looking at me as if I were the\ndirt beneath her feet, and had forced my way into her presence,\ninstead of being invited like a man of honour to enter.\n\n\"Well, Mr. O'Ruddy,\" she said, throwing back her head, haughty-like,\n\"Why do you stand dallying in a lady's bower when your followers are\nbeing beaten on the lawn outside?\"\n\nI cannot give you Lady Mary's exact words, for I was so astonished at\ntheir utterance; but I give you a very good purport of them.\n\n\"Is it the beating of my men?\" I said. \"Troth, that's what I pay them\nfor. And whoever gives them a good drubbing saves me the trouble. I\nsaw they had Paddy down on the turf, but he's a son of the ould sod,\nand little he'll mind being thrown on his mother. But if it's Jem\nBottles you're anxious about, truth to tell I'm more sorry for those\nthat come within range of his stick than for Jem with his back to the\nwall. Bottles can take care of himself in any company, for he's a\nhighwayman in an excellent way of business.\"\n\nI always like to mention anything that's in favour of a man, and so I\ntold her what profession Bottles followed. She gave a toss of her\nhead, and gave me a look that had something like contempt in it, which\nwas far from being pleasant to endure. Then she began walking up and\ndown the room, and it was plain to see that my Lady was far from being\npleased with me.\n\n\"Poor fellows! Poor faithful fellows! That's what comes of having a\nfool for a master.\"\n\n\"Indeed, your ladyship,\" said I, drawing myself up to my full height,\nwhich wasn't so very much short of the door itself, \"there are worse\nthings than blows from a good honest cudgel. You might better say,\n'This is what comes to a master with two fools for servants.'\"\n\n\"And what comes to a master?\" she demanded. \"Sure no one asks you to\nbe here.\"\n\n\"That shows how short your ladyship's memory is,\" said I with some\nirritation. \"Father Donovan used to tell me that the shortest thing in\nthe world was the interval between an insult and a blow in Ireland,\nbut I think a lady's memory is shorter still. 'Turn the key and come\nin,' says you. What is that, I would like to know, but an invitation.\"\n\nIt appeared to me that she softened a bit, but she continued her walk\nup and down the room and was seemingly in great agitation. The cries\noutside had stopped, but whether they had murdered both Jem Bottles\nand Paddy I had no means at that moment of knowing, and I hope the two\nwill forgive me when I say that my thoughts were far from them.\n\n\"You will understand,\" said Lady Mary, speaking still with resentment\nin her voice, \"that the papers you held are the key to the situation.\nHave you no more sense than to trust them to the care of a red-headed\nclown from whom they can be taken as easy as if they were picked up\noff the street?\"\n\n\"Indeed, believe me, Lady Mary, that no red-headed clown has any\npapers of mine.\"\n\n\"Indeed, and I think you speak the true word there. The papers are now\nin my father's possession, and he will know how to take care of them.\"\n\n\"Well, he didn't know that the last time he had them,\" I cried,\nfeeling angry at these unjust accusations, and not being able to bear\nthe compliment to the old man, even if he was an Earl. \"The papers,\"\nsaid I, \"are as easily picked from me as from the street, like you\nwere saying just now; but it isn't a pack of overfed flunkeys that\nwill lift them from me. Lady Mary, on a previous occasion I placed the\npapers in your hands; now, with your kind permission, I lay them at\nyour feet,\"--and, saying this with the most courteous obeisance, I\nknelt with one knee on the floor and placed the packet of papers where\nI said I would place them.\n\nNow, ever since that, the Lady Mary denies that she kicked them to the\nother end of the room. She says that as she was walking to and fro the\ntoe of her foot touched the packet and sent it spinning; and, as no\nreal Irishman ever yet contradicted a lady, all I will say is that the\nprecious bundle went hurtling to the other end of the room, and it is\nvery likely that Lady Mary thought the gesture of her foot a trifle\ntoo much resembled an action of her mother, the Countess, for her\nmanner changed in the twinkling of an eye, and she laughed like her\nold self again.\n\n\"Mr. O'Ruddy,\" she said, \"you put me out of all patience. You're as\nsimple as if you came out of Ireland yesterday.\"\n\n\"It's tolerably well known,\" said I, \"by some of your expert\nswordsmen, that I came out the day before.\"\n\nAgain Lady Mary laughed.\n\n\"You're not very wise in the choice of your friends,\" she said.\n\n\"I am, if I can count you as one of them,\" I returned.\n\nShe made no direct reply to this, but continued:\n\n\"Can't you see that that little Doctor Chord is a traitor? He has been\ntelling my father all you have been doing and all you have been\nplanning, and he says you are almost simple enough to have given the\npapers into his own keeping no longer ago than last night.\"\n\n\"Now, look you, Lady Mary, how much you misjudged me. The little\nvillain asked for the papers, but he didn't get them; then he advised\nme to give them to a man I could trust, and when I said the only man I\ncould trust was red-headed Paddy out yonder, he was delighted to think\nI was to leave them in his custody. But you can see for yourself I did\nnothing of the kind, and if your people thought they could get\nanything out of Paddy by bad language and heroic kicks they were\nmistaken.\"\n\nAt that moment we had an interruption that brought our conversation to\na standstill and Lady Mary to the door, outside which her mother was\ncrying,--\n\n\"Mary, Mary! where's the key?\"\n\n\"Where should it be?\" said Lady Mary, \"but in the door.\"\n\n\"It is not in the door,\" said the Countess wrathfully, shaking it as\nif she would tear it down.\n\n\"It is in the door,\" said Lady Mary positively; and quite right she\nwas, for both of us were looking at it.\n\n\"It is not in the door,\" shouted her mother. \"Some of the servants\nhave taken it away.\"\n\nThen we heard her calling over the banisters to find out who had taken\naway the key of Lady Mary's room. There was a twinkle in Mary's eye,\nand a quiver in the corners of her pretty mouth that made me feel she\nwould burst out laughing, and indeed I had some ado to keep silence\nmyself.\n\n\"What have you done with those two poor wretches you were maltreating\nout in the garden?\" asked Lady Mary.\n\n\"Oh, don't speak of them,\" cried the Countess, evidently in no good\nhumour. \"It was all a scandal for nothing. The red-headed beast did\nnot have the papers. That little fool, Chord, has misled both your\nfather and me. I could wring his neck for him, and now he is\npalavering your father in the library and saying he will get the\npapers himself or die in the attempt. It serves us right for paying\nattention to a babbling idiot like him. I said in the first place that\nthat Irish baboon of an O'Ruddy was not likely to give them to the ape\nthat follows him.\"\n\n\"Tare-an-ounds!\" I cried, clenching my fists and making for the door;\nbut Lady Mary rattled it so I could not be heard, and the next instant\nshe placed her snow-flake hand across my mouth, which was as pleasant\na way of stopping an injudicious utterance as ever I had been\nacquainted with.\n\n\"Mary,\" said the Countess, \"your father is very much agitated and\ndisappointed, so I'm taking him out for a drive. I have told the\nbutler to look out for the key, and when he finds it he will let you\nout. You've only yourself to blame for being locked in, because we\nexpected the baboon himself and couldn't trust you in his presence.\"\n\nIt was now Lady Mary's turn to show confusion at the old termagant's\ntalk, and she  as red as a sunset on the coast of Kerry. I\nforgave the old hag her discourteous appellation of \"baboon\" because\nof the joyful intimation she gave me through the door that Lady Mary\nwas not to be trusted when I was near by. My father used to say that\nif you are present when an embarrassment comes to a lady it is well\nnot to notice it, else the embarrassment will be transferred to\nyourself. Remembering this, I pretended not to see Lady Mary's flaming\ncheeks, and, begging her pardon, walked up the room and picked from\nthe corner the bundle of papers which had, somehow or other come\nthere, whether kicked or not. I came back to where she was standing\nand offered them to her most respectfully, as if they, and not\nherself, were the subject of discussion.\n\n\"Hush,\" said Lady Mary in a whisper; \"sit down yonder and see how long\nyou can keep quiet.\"\n\nShe pointed to a chair that stood beside a beautifully polished table\nof foreign wood, the like of which I had never seen before, and I,\nwishing very much to please her, sat down where she told me and placed\nthe bundle of papers on the table. Lady Mary tiptoed over, as\nlight-footed as a canary-bird, and sat down on the opposite side of\nthe table, resting her elbows on the polished wood, and, with her chin\nin her hands, gazed across at me, and a most bewildering scrutiny I\nfound it, rendering it difficult for me to keep quiet and seated, as\nshe had requested. In a minute or two we heard the crunch of wheels on\nthe gravel in front, then the carriage drove off, and the big gates\nclanked together.\n\nStill Lady Mary poured the sunshine of her eyes upon me, and I hope\nand trust she found me a presentable young man, for under the warmth\nof her look my heart began to bubble up like a pot of potatoes on a\nstrong fire.\n\n\"You make me a present of the papers, then?\" said Lady Mary at last.\n\n\"Indeed and I do, and of myself as well, if you'll have me. And this\nlatter is a thing I've been trying to say to you every time I met you,\nMary acushla, and no sooner do the words come to my lips than some\ndoddering fool interrupts us; but now, my darling, we are alone\ntogether, in that lover's paradise which is always typified by a\nlocked door, and at last I can say the things--\"\n\nJust here, as I mentioned the word \"door,\" there came a rap at it, and\nLady Mary started as if some one had fired a gun.\n\n\"Your ladyship,\" said the butler, \"I cannot find the key. Shall I send\nfor a locksmith?\"\n\n\"Oh, no,\" said Lady Mary, \"do not take the trouble. I have letters to\nwrite, and do not wish to be disturbed until my mother returns.\"\n\n\"Very good, your ladyship,\" returned the butler, and he walked away.\n\n\"A locksmith!\" said Lady Mary, looking across the table at me.\n\n\"Love laughs at them,\" said I.\n\nLady Mary smiled very sweetly, but shook her head.\n\n\"This is not a time for laughter,\" she said, \"but for seriousness.\nNow, I cannot risk your staying here longer, so will tell you what I\nhave to say as quickly as possible. Your repeatedly interrupted\ndeclaration I take for truth, because the course of true love never\ndid run smooth. Therefore, if you want me, you must keep the papers.\"\n\nAt this I hastily took the bundle from the table and thrust it in my\npocket, which action made Lady Mary smile again.\n\n\"Have you read them?\" she asked.\n\n\"I have not.\"\n\n\"Do you mean to say you have carried these papers about for so long\nand have not read them?\"\n\n\"I had no curiosity concerning them,\" I replied. \"I have something\nbetter to look at,\" I went on, gazing across at her; \"and when that is\nnot with me the memory of it is, and it's little I care for a pack of\nmusty papers and what's in them.\"\n\n\"Then I will tell you what they are,\" said Lady Mary. \"There are in\nthat packet the title-deeds to great estates, the fairest length of\nland that lies under the sun in Sussex. There is also a letter written\nby my father's own hand, giving the property to your father.\"\n\n\"But he did not mean my father to keep it,\" said I.\n\n\"No, he did not. He feared capture, and knew the ransom would be heavy\nif they found evidence of property upon him. Now all these years he\nhas been saying nothing, but collecting the revenues of this estate\nand using them, while another man had the legal right to it.\"\n\n\"Still he has but taken what was his own,\" said I, \"and my father\nnever disputed that, always intending to come over to England and\nreturn the papers to the Earl; but he got lazy-like, by sitting at his\nown fireside, and seldom went farther abroad than to the house of the\npriest; but his last injunctions to me were to see that the Earl got\nhis papers, and indeed he would have had them long since if he had but\ntreated me like the son of an old friend.\"\n\n\"Did your father mention that the Earl would give you any reward for\nreturning his property to him?\"\n\n\"He did not,\" I replied with indignation. \"In Ireland, when a friend\ndoes a friend's part, he doesn't expect to be paid for it.\"\n\n\"But don't you expect a reward for returning them?\"\n\n\"Lady Mary,\" said I, \"do you mean to be after insulting me? These\npapers are not mine, but the Earl of Westport's, and he can have them\nwithout saying as much as 'Thank you kindly' for them.\"\n\nLady Mary leaned back in her chair and looked at me with half-closed\neyes, then she stretched forth her hand and said:\n\n\"Give me the papers.\"\n\n\"But it's only a minute since,\" I cried, perplexed, \"that you held\nthem to be the key of the situation, and said if I didn't keep them I\nwould never get you.\"\n\n\"Did I say that?\" asked Lady Mary with the innocence of a\nthree-year-old child. \"I had no idea we had come to such a conclusion.\nNow do you want a little advice about those same papers?\"\n\n\"As long as the advice comes from you, Mary darling, I want it on any\nsubject.\"\n\n\"You have come into England brawling, sword-playing, cudgel-flinging,\nand never till this moment have you given a thought to what the papers\nare for. These papers represent the law.\"\n\n\"Bad cess to it,\" said I. \"My father used to say, have as little to do\nwith the law as possible, for what's the use of bringing your man into\nthe courts when a good shillelah is speedier and more satisfactory to\nall concerned.\"\n\n\"That may be true in Ireland, but it is not true in England. Now, here\nis my advice. You know my father and mother, and if you'll just quit\nstaring your eyes out at me, and think for a minute, you may be able\nto tell when you will get their consent to pay your addresses to me\nwithout interruption.\" Here she blushed and looked down.\n\n\"Indeed,\" said I, \"I don't need to take my eyes from you to answer\n_that_ question. It'll be the afternoon following the Day of\nJudgment.\"\n\n\"Very well. You must then stand on your rights. I will give you a\nletter to a man in the Temple, learned in the law. He was legal\nadviser to my aunt, who left me all her property, and she told me that\nif I ever was in trouble I was to go to him; but instead of that I'll\nsend my trouble to him with a letter of introduction. I advise you to\ntake possession of the estate at Brede, and think no more of giving up\nthe papers to my father until he is willing to give you something in\nreturn. You may then ask what you like of him; money, goods, or a\nfarm,\"--and again a bright red colour flooded her cheeks. With that\nshe drew toward her pen and paper and dashed off a letter which she\ngave to me.\n\n\"I think,\" she said, \"it would be well if you left the papers with the\nman in the Temple; he will keep them safely, and no one will suspect\nwhere they are; while, if you need money, which is likely, he will be\nable to advance you what you want on the security of the documents you\nleave with him.\"\n\n\"Is it money?\" said I, \"sure I couldn't think of drawing money on\nproperty that belongs to your good father, the Earl.\"\n\n\"As I read the papers,\" replied Lady Mary, very demurely, casting down\nher eyes once more, \"the property does not belong to my good father,\nthe Earl, but to the good-for-nothing young man named O'Ruddy. I think\nthat my father, the Earl, will find that he needs your signature\nbefore he can call the estate his own once more. It may be I am wrong,\nand that your father, by leaving possession so long in the hands of\nthe Earl, may have forfeited his claim. Mr. Josiah Brooks will tell\nyou all about that when you meet him in the Temple. You may depend\nupon it that if he advances you money your claim is good, and, your\nclaim being good, you may make terms with even so obstreperous a man\nas my father.\"\n\n\"And if I make terms with the father,\" I cried, \"do you think his\ncomely daughter will ratify the bargain?\"\n\nLady Mary smiled very sweetly, and gave me the swiftest and shyest of\nglances across the table from her speaking eyes, which next instant\nwere hidden from me.\n\n\"May be,\" she said, \"the lawyer could answer that question.\"\n\n\"Troth,\" I said, springing to my feet, \"I know a better one to ask it\nof than any old curmudgeon poring over dry law-books, and the answer\nI'm going to have from your own lips.\"\n\nThen, with a boldness that has ever characterized the O'Ruddys, I\nswung out my arms and had her inside o' them before you could say\nBallymoyle. She made a bit of a struggle and cried breathlessly:\n\n\"I'll answer, if you'll sit in that chair again.\"\n\n\"It's not words,\" says I, \"I want from your lips, but this,\"--and I\nsmothered a little shriek with one of the heartiest kisses that ever\ntook place out of Ireland itself, and it seemed to me that her\nstruggle ceased, or, as one might say, faded away, as my lips came in\ncontact with hers; for she suddenly weakened in my arms so that I had\nto hold her close to me, for I thought she would sink to the floor if\nI did but leave go, and in the excitement of the moment my own head\nwas swimming in a way that the richest of wine had never made it swim\nbefore. Then Lady Mary buried her face in my shoulder with a little\nsigh of content, and I knew she was mine in spite of all the Earls and\nCountesses in the kingdom, or estates either, so far as that went. At\nlast she straightened up and made as though she would push me from\nher, but held me thus at arms' length, while her limpid eyes looked\nlike twin lakes of Killarney on a dreamy misty morning when there's no\nwind blowing.\n\n\"O'Ruddy,\" she said, solemnly, with a little catch in her voice,\n\"you're a bold man, and I think you've no doubt of your answer; but\nwhat has happened makes me the more anxious for your success in\ndealing with those who will oppose both your wishes and mine. My dear\nlover, is what I call you now; you have come over in tempestuous\nfashion, with a sword in your hand, striving against every one who\nwould stand up before you. After this morning, all that should be\nchanged, for life seems to have become serious and momentous. O'Ruddy,\nI want your actions to be guided, not by a drawn sword, but by\nreligion and by law.\"\n\n\"Troth, Mary acushla, an Irishman takes to religion of his own nature,\nbut I much misdoubt me if it comes natural to take to the law.\"\n\n\"How often have you been to mass since you came to England, O'Ruddy?\"\n\n\"How often?\" says I, wrinkling my brow, \"indeed you mean, how many\ntimes?\"\n\n\"Yes; how many times?\"\n\n\"Now, Mary, how could you expect me to be keeping count of them?\"\n\n\"Has your attendance, then, been so regular?\"\n\n\"Ah, Mary, darling; it's not me that has the face to tell you a lie,\nand yet I'm ashamed to say that I've never set foot in a church since\nI crossed the channel, and the best of luck it is for me that good old\nFather Donovan doesn't hear these same words.\"\n\n\"Then you will go to church this very day and pray for heaven's\nblessing on both of us.\"\n\n\"It's too late for the mass this Sunday, Mary, but the churches are\nopen, and the first one I come to will have me inside of it.\"\n\nWith that she drew me gently to her, and herself kissed me, meeting\nnone of that resistance which I had encountered but a short time\nbefore; and then, as bitter ill luck would have it, at this delicious\nmoment we were startled by the sound of carriage-wheels on the gravel\noutside.\n\n\"Oh!\" cried Lady Mary in a panic; \"how time has flown!\"\n\n\"Indeed,\" said I, \"I never knew it so fast before.\"\n\nAnd she, without wasting further time in talking, unlocked the door,\nwhipped out the key, and placed it where I had found it in the\nbeginning. She seemed to think of everything in a moment, and I would\nhave left her letter and the papers on the table if it hadn't been for\nthat cleverest of all girls, who, besides her lips of honey, had an\nalert mind, which is one of the things appreciated in Ireland. I then\nfollowed her quickly down a narrow back stairway and out into a glass\nhouse, where a little door at the end led us into a deliciously\nshaded walk, free from all observation, with a thick screen of trees\non the right hand and the old stone wall on the left.\n\nHere I sprang quickly to overtake her, but she danced away like a\nfairy in the moonlight, throwing a glance of mischief over her\nshoulder at me, with her finger on her lips. It seemed to me a pity\nthat so sylvan a dell should merely be used for the purposes of speed,\nbut in a jiffy Mary was at the little door in the wall and had the\nbolts drawn back, and I was outside before I understood what had\nhappened, listening to bolts being thrust back again, and my only\nconsolation was the remembrance of a little dab at my lips as I passed\nthrough, as brief and unsatisfactory as the peck of a sparrow.\n\n\n\n\nCHAPTER XXVIII\n\n\nIt was a beautiful day, as lovely as any an indulgent Providence had\never bestowed upon an unthankful generation.\n\nAlthough I wished I had had an hour or two to spend with Mary\nwandering up and down that green alley through which we had rushed\nwith such indecent haste, all because two aged and angry members of\nthe nobility might have come upon us, yet I walked through the streets\nof London as if I trod on the air, and not on the rough cobble-stones\nof the causeway. It seemed as if I had suddenly become a boy again,\nand yet with all the strength and vigour of a man, and I was hard put\nto it not to shout aloud in the sunlight, or to slap on the back the\nslow and solemn Englishmen I met, who looked as if they had never\nlaughed in their lives. Sure it's a very serious country, this same\nland of England, where their dignity is so oppressive that it bows\ndown head and shoulders with thinking how grand they are; and yet I'll\nsay nothing against them, for it was an Englishwoman that made me feel\nlike a balloon. Pondering over the sobriety of the nation, I found\nmyself in the shadow of a great church, and, remembering what my dear\nMary had said, I turned and went in through the open door, with my\nhat in my hand. It was a great contrast to the bright sunlight I had\nleft, and to the busy streets with their holiday-making people. There\nwere only a few scattered here and there in the dim silence of the\nchurch, some on their knees, some walking slowly about on tiptoe, and\nsome seated meditating in chairs. No service was going forward, so I\nknelt down in the chapel of Saint Patrick himself; I bowed my head and\nthanked God for the day and for the blessing that had come with it. As\nI said, I was like a boy again, and to my lips, too long held from\nthem, came the prayers that had been taught me. I was glad I had not\nforgotten them, and I said them over and over with joy in my heart. As\nI raised my head, I saw standing and looking at me a priest, and,\nrising to my feet, I made my bow to him, and he came forward,\nrecognizing me before I recognized him.\n\n\"O'Ruddy,\" he said, \"if you knew the joy it gives to my old heart to\nmeet you in this sacred place and in that devout attitude, it would\nbring some corresponding happiness to yourself.\"\n\n\"Now by the piper that played before Moses, Father Donovan, and is\nthis yourself? Sure I disrecognized you, coming into the darkness, and\nme just out of the glare beyond,\"--and I took his hand in both of mine\nand shook it with a heartiness he had not met since he left the old\nturf. \"Sure and there's no one I'd rather meet this day than\nyourself,\"--and with that I dropped on one knee and asked for his\nblessing on me and mine.\n\nAs we walked out of the church together, his hand resting on my\nshoulder, I asked how such a marvel came to pass as Father Donovan,\nwho never thought to leave Ireland, being here in London. The old man\nsaid nothing till we were down the steps, and then he told me what had\nhappened.\n\n\"You remember Patsy O'Gorman,\" he said.\n\n\"I do that,\" I replied, \"and an old thief of the world and a\ntight-fisted miser he is.\"\n\n\"Whist,\" said Father Donovan, quietly crossing himself. \"O'Gorman is\ndead and buried.\"\n\n\"Do you tell me that!\" said I, \"then rest his soul. He would be a warm\nman and leave more money than my father did, I'm thinking.\"\n\n\"Yes, he left some money, and to me he left three hundred pounds, with\nthe request that I should accomplish the desire of my life and take\nthe pilgrimage to Rome.\"\n\n\"The crafty old chap, that same bit of bequestration will help him\nover many a rough mile in purgatory.\"\n\n\"Ah, O'Ruddy, it's not our place to judge. They gave a harder name to\nO'Gorman than he deserved. Just look at your own case. The stories\nthat have come back to Ireland, O'Ruddy, just made me shiver. I heard\nthat you were fighting and brawling through England, ready to run\nthrough any man that looked cross-eyed at you. They said that you had\ntaken up with a highwayman; that you spent your nights in drink and\nbreathing out smoke; and here I find you, a proper young man, doing\ncredit to your country, meeting you, not in a tavern, but on your\nknees with bowed head in the chapel of Saint Patrick, giving the lie\nto the slanderer's tongue.\"\n\nThe good old man stopped in our walk, and with tears in his eyes shook\nhands with me again, and I had not the heart to tell him the truth.\n\n\"Ah well,\" I said, \"Father Donovan, I suppose nobody, except yourself,\nis quite as good as he thinks, and nobody, including myself, is as bad\nas he appears to be. And now, Father Donovan, where are you stopping,\nand how long will you be in London?\"\n\n\"I am stopping with an old college friend, who is a priest in the\nchurch where I found you. I expect to leave in a few days' time and\njourney down to the seaport of Rye, where I am to take ship that will\nland me either in Dunkirk or in Calais. From there I am to make my way\nto Rome as best I can.\"\n\n\"And are you travelling alone?\"\n\n\"I am that, although, by the blessing of God, I have made many friends\non the journey, and every one I met has been good to me.\"\n\n\"Ah, Father Donovan, you couldn't meet a bad man if you travelled the\nworld over. Sure there's some that carry such an air of blessedness\nwith them that every one they meet must, for very shame, show the best\nof his character. With me it's different, for it seems that where\nthere's contention I am in the middle of it, though, God knows, I'm a\nman of peace, as my father was before me.\"\n\n\"Well,\" said Father Donovan slowly, but with a sweet smile on his lip,\n\"I suppose the O'Ruddys were always men of peace, for I've known them\nbefore now to fight hard enough to get it.\"\n\nThe good father spoke a little doubtfully, as if he were not quite\napproving of our family methods, but he was a kindly man who always\ntook the most lenient view of things. He walked far with me, and then\nI turned and escorted him to the place where he resided, and, bidding\ngood-bye, got a promise from him that he would come to the \"Pig and\nTurnip\" a day later and have a bite and sup with me, for I thought\nwith the assistance of the landlord I could put a very creditable meal\nbefore him, and Father Donovan was always one that relished his meals,\nand he enjoyed his drink too, although he was set against too much of\nit. He used to say, \"It's a wise drinker that knows when geniality\nends and hostility begins, and it's just as well to stop before you\ncome to the line.\"\n\nWith this walking to and fro the day was near done with when I got\nback to the \"Pig and Turnip\" and remembered that neither a bit of pig\nnor a bit of turnip had I had all that long day, and now I was\nravenous. I never knew anything make me forget my appetite before; but\nhere had I missed my noonday meal, and not in all my life could I\novertake it again. Sure there was many an experience crowded together\nin that beautiful Sunday, so, as I passed through the entrance to the\ninn I said to the obsequious landlord:\n\n\"For the love of Heaven, get placed on my table all you have in the\nhouse that's fit to eat, and a trifle of a bottle or two, to wash it\ndown with.\"\n\nSo saying, I passed up the creaking old oaken stair and came to my\nroom, where I instantly remembered there was something else I had\nforgotten. As I opened the door there came a dismal groan from Paddy,\nand something that sounded like a wicked oath from Jem Bottles. Poor\nlads! that had taken such a beating that day, such a cudgelling for my\nsake; and here I stood at my own door in a wonder of amazement, and\nsomething of fright, thinking I had heard a banshee wail. The two\nmisused lads had slipped out of my memory as completely as the devil\nslipped off Macgillicuddy Reeks into the pond beneath when Saint\nPatrick had sent the holy words after him.\n\n\"Paddy,\" said I, \"are you hurted? Where is it you're sore?\"\n\n\"Is it sore?\" he groaned. \"Except the soles of my feet, which they\ncouldn't hit with me kickin' them, there isn't an inch of me that\ndoesn't think it's worse hurted than the rest.\"\n\n\"It's sorry I am to hear that,\" I replied, quite truthfully, \"and you,\nJem, how did you come off?\"\n\n\"Well, I gave a better account of myself than Paddy here, for I made\nmost of them keep their distance from me; but him they got on the turf\nbefore you could say Watch me eye, and the whole boiling of them was\non top of him in the twinkling of the same.\"\n\n\"The whole boiling of them?\" said I, as if I knew nothing of the\noccurrence, \"then there was more than Strammers to receive you?\"\n\n\"More!\" shouted Jem Bottles, \"there was forty if there was one.\"\n\nPaddy groaned again at the remembrance, and moaned out:\n\n\"The whole population of London was there, and half of it on top of me\nbefore I could wink. I thought they would strip the clothes off me,\nand they nearly did it.\"\n\n\"And have you been here alone ever since? Have you had nothing to eat\nor drink since you got back?\"\n\n\"Oh,\" said Jem, \"we had too much attention in the morning, and too\nlittle as the day went on. We were expecting you home, and so took the\nliberty of coming up here and waiting for you, thinking you might be\ngood enough to send out for some one who would dress our wounds; but\nluckily that's not needed now.\"\n\n\"Why is it not needed?\" I asked. \"I'll send at once.\n\n\"Oh, no,\" moaned Paddy, \"there was one good friend that did not forget\nus.\"\n\n\"Well,\" said Jem, \"he seemed mighty afeerd of coming in. I suppose he\nthought it was on his advice that we went where we did, and he was\nafeerd we thought badly of him for it; but of course we had no blame\nto put on the poor little man.\"\n\n\"In Heaven's name, who are you talking of?\" said I.\n\n\"Doctor Chord,\" answered Jem. \"He put his head inside the door and\ninquired for us, and inquired specially where you were; but that, of\ncourse, we couldn't tell him. He was very much put out to find us\nmis-handled, and he sent us some tankards of beer, which are now\nempty, and we're waiting for him because he promised to come back and\nattend to our injuries.\"\n\n\"Then you didn't see Doctor Chord in the gardens?\"\n\n\"In what gardens?\" asked Bottles.\n\n\"You didn't see him among that mob that set on you?\"\n\n\"No fear,\" said Jem, \"wherever there is a scrimmage Doctor Chord will\nkeep away from it.\"\n\n\"Indeed and in that you're wrong,\" said I. \"Doctor Chord has been the\ninstigator of everything that has happened, and he stood in the\nbackground and helped to set them on.\"\n\nPaddy sat up with wild alarm in his eyes.\n\n\"Sure, master,\" says he, \"how could you see through so thick a wall as\nthat?\"\n\n\"I did not see through the wall at all; I was in the house. When you\nwent through the back door, I went through the front gate, and what I\nam telling you is true. Doctor Chord is the cause of the whole\ncommotion. That's why he was afraid to come in the room. He thought\nperhaps you had seen him, and, finding you had not, he'll be back here\nagain when everything is over. Doctor Chord is a traitor, and you may\ntake my word for that.\"\n\nPaddy rose slowly to his feet, every red hair in his head bristling\nwith scorn and indignation; but as he stood erect he put his hand to\nhis side and gave a howl as he limped a step or two over the floor.\n\n\"The black-hearted villain,\" he muttered through his teeth. \"I'll have\nhis life.\"\n\n\"You'll have nothing of the sort,\" said I, \"and we'll get some good\nattendance out of him, for he's a skillful man. When he has done his\nduty in repairing what he has inflicted upon you, then you can give\nhim a piece of your mind.\"\n\n\"I'll give him a piece of my boot; all that's left of it,\" growled Jem\nBottles, scowling.\n\n\"You may take your will of him after he has put some embrocation on\nyour bruises,\" said I; and as I was speaking there came a timorous\nlittle knock at the door.\n\n\"Come in,\" I cried, and after some hesitation the door opened, and\nthere stood little Doctor Chord with a big bottle under his arm. I was\nglad there was no supper yet on the table, for if there had been I\nmust have asked the little man to sit down with me, and that he would\ndo without a second's hesitation, so I could not rightly see him\nmaltreated who had broken a crust with me.\n\nHe paid no attention to Jem or Paddy at first, but kept his cunning\nlittle eye on me.\n\n\"And where have you been to-day, O'Ruddy?\" he asked.\n\n\"Oh,\" said I, \"I accompanied these two to the door in the wall, and\nwhen they got through I heard yells fit to make a hero out of a\n<DW65>; but you know how stout the bolts are and I couldn't get to\nthem, so I had just to go out of hearing of their bellowings. On the\nway back I happened to meet an old friend of mine, Father Donovan,\nand--\"\n\nHere Paddy, forgetting his good manners, shouted out:\n\n\"Thank God there's a holy father in this hole of perdition; for I know\nI'm goin' t' die to-morrow at the latest.\"\n\n\"Stop your nonsense,\" said I. \"You'll have to hold on to life at least\na day longer; for the good father is not coming here until two days\nare past. You're more frightened than hurt, and the Doctor here has a\nlotion that will make you meet the priest as a friend and not as a\nlast counsellor.\"\n\n\"As I was saying, Doctor Chord, I met Father Donovan, and we strolled\nabout the town, so that I have only now just come in. The father is a\nstranger in London, on a pilgrimage to Rome. And sure I had to show\nhim the sights.\"\n\n\"It was a kindly action of you,\" said Doctor Chord, pulling the cork\nof the medicine-bottle. \"Get those rags off,\" he called to Paddy,\n\"and I'll rub you down as if you were the finest horse that ever\nfollowed the hounds.\"\n\nThere was a great smell of medicine in the air as he lubricated Paddy\nover the bruised places; then Jem Bottles came under his hands, and\neither he was not so much hurt as Paddy was, or he made less fuss\nabout it, for he glared at the Doctor all the time he was attending\nhim, and said nothing.\n\nIt seemed an inhospitable thing to misuse a man who had acted the good\nSamaritan so arduously as the little Doctor with three quarters of his\nbottle gone, but as he slapped the cork in it again I stepped to the\ndoor and turned the key. Paddy was scowling now and then, and groaning\nnow and again, when the cheerful Doctor said to him, as is the way\nwith physicians when they wish to encourage a patient:\n\n\"Oh, you're not hurt nearly as bad as you think you are. You'll be a\nlittle sore and stiff in the morning, that's all, and I'll leave the\nbottle with you.\"\n\n\"You've never rubbed me at all on the worst place,\" said Paddy\nangrily.\n\n\"Where was that?\" asked Doctor Chord,--and the words were hardly out\nof his mouth when Paddy hit him one in the right eye that sent him\nstaggering across the room.\n\n\"There's where I got the blow that knocked me down,\" cried Paddy.\n\nDoctor Chord threw a wild glance at the door, when Jem Bottles, with a\nlittle run and a lift of his foot, gave him one behind that caused the\nDoctor to turn a somersault.\n\n\"Take that, you thief,\" said Jem; \"and now you've something that\nneither of us got, because we kept our faces to the villains that set\non us.\"\n\nPaddy made a rush, but I cried:\n\n\"Don't touch the man when he's down.\"\n\n\"Sure,\" says Paddy, \"that's when they all fell on me.\"\n\n\"Never strike a man when he's down,\" I cried.\n\n\"Do ye mean to say we shouldn't hit a man when he's down?\" asked Jem\nBottles.\n\n\"You knew very well you shouldn't,\" I told him. \"Sure you've been in\nthe ring before now.\"\n\n\"That I have,\" shouted Bottles, pouncing on the unfortunate Doctor. He\ngrabbed him by the scruff of the neck and flung him to his feet, then\ngave him a bat on the side of the head that sent him reeling up toward\nthe ceiling again.\n\n\"That's enough, Jem,\" I cautioned him.\n\n\"I'm not only following the Doctor,\" said Jem, \"but I'm following the\nDoctor's advice. He told us to take a little gentle exercise and it\nwould allay the soreness.\"\n\n\"The exercise you're taking will not allay the soreness on the\nDoctor's part. Stop it, Jem! Now leave him alone, Paddy; he's had\nenough to remember you by, and to learn that the way of the traitor is\nthe rocky road to Dublin. Come now, Doctor, the door is open; get out\ninto the passage as quick as you can, and I hope you have another\nbottle of that excellent lotion at home.\"\n\nThe threatening attitude of both Jem and Paddy seemed to paralyse the\nlittle man with fear, and he lay on the boards glaring up at them with\nterror in his eyes.\n\n\"I'm holding the door open for you,\" said I, \"and remember I may not\nbe able to hold Paddy and Jem as easily as I hold the door; so make\nyour escape before they get into action again.\"\n\nDoctor Chord rolled himself over quickly, but, not daring to get on\nhis feet, trotted out into the passage like a big dog on his hands and\nknees; and just then a waiter, coming up with a tray and not counting\non this sudden apparition in the hallway, fell over him; and if it\nwere not for my customary agility and presence of mind in grasping the\nbroad metal server, a good part of my supper would have been on the\nfloor. The waiter luckily leaned forward when he found himself\nfalling, holding the tray high over his head, and so, seizing it, I\nsaved the situation and the supper.\n\n\"What are ye grovelling down there for, ye drunken beast?\" shouted the\nangry waiter, as he came down with a thud. \"Why don't you walk on your\ntwo feet like a Christian?\"\n\nDoctor Chord took the hint and his departure, running along the\npassage and stumbling down the stairway like a man demented. When he\ngot down into the courtyard he shook his fist at my window and swore\nhe would have the law of us; but I never saw the little man again,\nalthough Paddy and Jem were destined to meet him once more, as I shall\ntell later on.\n\nThe supper being now laid, I fell at it and I dis-remember having ever\nenjoyed a meal more in my life. I sent Paddy and Jem to their quarters\nwith food and a bottle of good wine to keep them company, and I think\nthey deserved it, for they said the lotion the Doctor had put on the\noutside of them was stinging, so they thought there should be\nsomething in the inside to counteract the inconvenience.\n\nI went to sleep the moment I touched the pillow, and dreamed I was in\nthe most umbrageous lover's walk that ever was, overhung with green\nbranches through which the sunlight flickered, and closed in with\nshrubbery. There I chased a flying nymph that always just eluded me,\nlaughing at me over her shoulder and putting her finger to her lips,\nand at last, when I caught her, it turned out to be Doctor Chord,\nwhereupon I threw him indignantly into the bushes, and then saw to my\ndismay it was the Countess. She began giving her opinion of me so\nvigorously that I awoke and found it broad daylight.\n\n\n\n\nCHAPTER XXIX\n\n\nAfter a comforting and sustaining breakfast I sent for Paddy and Jem,\nboth of whom came in limping.\n\n\"Are you no better this morning?\" I asked them.\n\n\"Troth, we're worse,\" said Paddy with a most dismal look on his face.\n\n\"I'm sorry to hear it,\" said I; \"but I think the trouble will wear off\nto-day if you lie snug and quiet in the inn. Here's this bottle of\nembrocation, or what is left of it, so you may take it with you and\ndivide it fairly between you, remembering that one good rub deserves\nanother, and that our chief duty on this earth is to help our fellow\nman; and as there's nothing like easy employment for making a man\nforget his tribulations, Jem will rub Paddy, and Paddy will rub Jem,\nand thus, God blessing you both, you will pass the time to your mutual\nbenefit.\"\n\n\"Yer honour,\" sniffed Jem Bottles, \"I like your own prescriptions\nbetter than Doctor Chord's. I have but small faith in the liniment;\nthe bottle of wine you gave us last night--and I wish it had been as\ndouble as it made us see--was far better for our trouble than this\nstuff.\"\n\n\"I doubt it, Jem,\" said I, \"for you're worse this morning than you\nwere last night; so I'll change the treatment and go back to Doctor\nChord's remedy, for sure the Doctor is a physician held in high esteem\nby the nobility of London. But you're welcome to a double mug of beer\nat my expense, only see that you don't take too much of that.\"\n\n\"Yer honour,\" said Jem, \"it's only when we're sober that we fall upon\naffliction. We had not a drop to drink yesterday morning, and see what\nhappened us.\"\n\n\"It would have made no differ,\" I said, \"if you had been as tipsy as\nthe Earl himself is when dinner's over. Trust in Providence, Jem, and\nrub hard with the liniment, and you'll be a new man by the morrow\nmorn.\"\n\nWith this I took my papers and the letter of introduction, and set out\nas brave as you please to find the Temple, which I thought would be a\nsort of a church, but which I found to be a most sober and respectable\nplace very difficult for a stranger to find his way about in. But at\nlast I came to the place where Mr. Josiah Brooks dispensed the law for\na consideration to ignorant spalpeens like myself, that was less\nfamiliar with the head that had a gray wig on than with cracking heads\nby help of a good shillelah that didn't know what a wig was. As it was\nearlier in the morning than Mr. Brooks's usual hour I had to sit\nkicking my heels in a dismal panelled anteroom till the great lawyer\ncame in. He was a smooth-faced serious-looking man, rather elderly,\nand he passed through the anteroom without so much as casting a look\nat me, and was followed by a melancholy man in rusty black who had\ntold me to take a chair, holding in his hand the letter Lady Mary had\nwritten. After a short time the man came out again, and, treating me\nwith more deference than when he bade me be seated, asked me kindly\nif I would step this way and Mr. Brooks would see me.\n\n\"You are Mr. O'Ruddy, I take it,\" he said in a tone which I think he\nthought was affable.\n\n\"I am.\"\n\n\"Have you brought with you the papers referred to in this letter?\"\n\n\"I have.\"\n\nAnd with that I slammed them down on the table before him. He untied\nthe bundle and sorted out the different documents, apparently placing\nthem in their right order. After this he adjusted his glasses more to\nhis liking and glanced over the papers rapidly until he came to one\nthat was smaller than the rest, and this he read through twice very\ncarefully. Then he piled them up together at his right hand very\nneatly, for he seemed to have a habit of old maid's precision about\nhim. He removed his glasses and looked across the table at me.\n\n\"Are you the son of the O'Ruddy here mentioned?\"\n\n\"I am.\"\n\n\"His eldest son?\"\n\n\"His only son.\"\n\n\"You can prove that, I suppose?\"\n\n\"Troth, it was never disputed.\"\n\n\"I mean there would be no difficulty in getting legal and documentary\nproof.\"\n\n\"I think not, for my father said after my first fight, that it might\nbe questioned whether I was my mother's son or no,--there was no doubt\nthat I was his.\"\n\nThe legal man drew down his brows at this, but made no comment as, in\ntones that betrayed little interest in the affair, he demanded:\n\n\"Why did your father not claim this property during his lifetime?\"\n\n\"Well, you see, Mr. Brooks, my father was an honest man, and he never\npretended the property was his. From what I remember of his\nconversation on the subject the Earl and him was in a tight place\nafter a battle in France, and it was thought they would both be made\nprisoners. The Earl had his deeds with him, and if he were caught the\nenemy would demand a large ransom for him, for these would show him to\nbe a man of property. So he made the estate over to my father, and my\nfather ran the risk of being captured and taken for the Earl of\nWestport. Now that I have been made happy by the acquaintance of his\nlordship, I'm thinking that if my father had fallen into the hands of\nthe enemy he might have remained there till this day without the Earl\nraising a hand to help him. Nobody in England would have disputed the\nEarl's ownership of his own place, which I understand has been in his\nfamily for hundreds of years, so they might very well have got on\nwithout the deeds, as in fact they have done. That's all I know about\nit.\"\n\n\"Then, sir,\" said Mr. Brooks, \"do you intend to contest the ownership\nof the property on the strength of these documents?\"\n\n\"I do,\" said I firmly.\n\n\"Very well. You must leave them with me for a few days until I get\nopinion upon them. I may say I have grave doubts of your succeeding in\nsuch litigation unless you can prove that your father gave reasonable\nconsideration for the property made over to him.\"\n\n\"Troth, he'd no consideration to give except his own freedom and the\nloan of a pair of breeches, and it seems that the Earl never troubled\nhis head whether he gave the first-named or not. He might have given\nhis life for all the thanks his son got from my Lord of Westport.\"\n\n\"From a rapid glance at these instruments I can see that they may be\nof great value to his lordship, but I doubt their being of any value\nat all to you; in fact you might find the tables turned upon you, and\nbe put in the position of a fraudulent claimant or a levier of\nblackmail.\"\n\n\"It's not blackmail I'm going to levy at all,\" cried I, \"but the\nwhitest of white mail. I have not the slightest intention of going\ninto the courts of law; but, to tell you the plain truth about it,\nLady Mary and me are going to get married in spite of all the Earls\nthat ever drank, or all the Countesses that ever scolded. Now this\ndear girl has a great confidence in you, and she has sent me to you to\nfind what's best to be done. I want nothing of this property at all.\nSure I've estates enough of my own in Ireland, and a good castle\nforby, save that the roof leaks a little in places; but a bundle of\nstraw will soon set that to rights, only old Patsy is so lazy through\nnot getting his money regular. Now it struck me that if I went boldly\nto Brede Castle, or whatever it is, and took possession of it, there\nwould first be the finest scrimmage any man ever saw outside of\nIreland, and after that his lordship the Earl would say to me,--\n\n\"'O'Ruddy, my boy, my limbs are sore; can't we crack a bottle instead\nof our heads over this, and make a compromise?'\n\n\"'Earl of Westport,' I'll say to him, 'a bottle will be but the\nbeginning of it. We'll sit down at a table and settle this debate in\nten minutes if you're reasonable.'\n\n\"He'll not be reasonable, of course, but you see what I have in my\nmind.\"\n\n\"Brede Place,\" said the lawyer slowly, \"is not exactly a castle, but\nit's a very strong house and might be held by a dozen determined men\nagainst an army.\"\n\n\"Then once let me get legally inside, and I'll hold it till the Earl\ngets more sense in his head than is there at the present moment.\"\n\n\"Possession,\" said Mr. Brooks, \"is nine points of the law.\"\n\n\"It is with a woman,\" said I, thinking of something else.\n\n\"It is with an estate,\" answered Josiah severely.\n\n\"True for you,\" I admitted, coming back to the point at issue, for it\nwas curious, in spite of the importance of the interview, how my mind\nkept wandering away to a locked room in the Earl of Westport's house,\nand to a shady path that ran around the edge of his garden.\n\n\"I intend to get possession of the Brede estate if I have to crack the\ncrown of every man at present upon it. But I am an Irishman, and\ntherefore a person of peace, and I wish to crack the crowns in\naccordance with the law of England, so I come to you for directions\nhow it should be done.\"\n\n\"It is not my place,\" said Brooks, looking very sour, \"to counsel a\nman to break either heads or the law. In fact it is altogether illegal\nto assault another unless you are in danger of your own life.\"\n\n\"The blessing of all the Saints be upon you,\" said I, \"yet, ever since\nI set foot in this land, coming across the boiling seas, entirely to\ndo a kindness to the Earl of Westport, I have gone about in fear of my\nlife.\"\n\n\"You have surely not been assaulted?\" demanded Mr. Brooks, raising his\neyebrows in surprise.\n\n\"Assaulted, is it? I have been set upon in every manner that is\npossible for a peace-lover to be interfered with. To tell you the\ntruth, no longer ago than yesterday morning, as quiet and decent a\nSunday as ever came down on London, my two innocent servants,\ngarrulous creatures that wouldn't hurt a fly, were lured into the high\nwalled garden of the Earl of Westport to see the flowers which both of\nthem love, and there they were pounced upon by the whole body-guard of\nmy lord the Earl, while himself and his quiet-mannered Countess were\nthere to urge them on. Doctor Chord, a little snobbish creature,\nbasking in the smiles of their noble countenances, stood by and gave\nmedical advice showing where best to hit the poor innocent\nunfortunates that had fallen into their hands.\"\n\n\"Tut, tut!\" said Josiah Brooks, his face frowning like a storm-cloud\nover the hills of Donegal. \"If such is indeed the case, an action\nwould lie--\"\n\n\"Oh, well and as far as that goes, so would Doctor Chord, and all the\nrest that was there. My poor lads lie now, bruised and sore, in the\nupper rooms of the stable at the 'Pig and Turnip.' They want no more\naction, I can tell you, nor lying either.\"\n\n\"You can prove, then,\" said the lawyer, \"that you have suffered\nviolence from the outset.\"\n\n\"Indeed and I could.\"\n\n\"Well, well, we must look into the matter. You recite a most curious\naccumulation of offences, each of which bears a serious penalty\naccording to the law of England. But there is another matter mentioned\nin Lady Mary's letter which is even more grave than any yet alluded\nto.\"\n\n\"And what is that?\" I asked in surprise.\n\n\"She says that she wishes to have advanced to you, upon the security\nof these papers, five hundred golden guineas.\"\n\n\"Do you tell me that now?\" I cried with delight. \"Sure I have always\nsaid that Mary was the most sensible girl within the boundaries of\nthis realm.\"\n\n\"That may all be; but women, you see, know little of money or the\nmethods of obtaining it.\"\n\n\"You're right in that,\" I admitted. \"It's the other end of the stick\nthey hold; they know a good deal of the way of spending it.\"\n\n\"You will understand,\" went on Mr. Brooks, \"that if money is to be\nraised on the security of these documents, your rights in possessing\nthem must be severely scrutinized, while--you will pardon my saying\nso--the security of your estates in Ireland might be looked at askance\nby the money-lenders of London.\"\n\n\"Oh, don't let the estates in Ireland trouble you, for the\nmoney-lenders of Dublin have already mortgaged them a foot deep. You\ncan raise little on my estates in Ireland but the best turf you ever\nburned, and that's raised with a spade.\"\n\n\"Very well,\" said Josiah Brooks, gathering up the papers and tying\nthem together with a bit of red ribbon which he took out of his\ndrawer, ignoring the Irish cord that had held them through all their\nemergencies. \"Very well, I shall seek advice and let you know the\nresult.\"\n\n\"Seek advice,\" I cried. \"Sure a man of your attainments doesn't need\nto seek advice of any one. Aren't you learned in the law yourself?\"\n\n\"I must have counsel's opinion,\" said Josiah solemnly, as if he were\nspeaking of the decisions of Providence.\n\n\"Well, you astonish me, Mr. Brooks, for I thought you knew it all, and\nthat's why I came to you; but perhaps it's only your own modesty that\nmakes you reluctant to speak of your attainments, though I suppose\nwhat you really mean is that you want to take a pipe in your mouth and\na glass of good liquor at your elbow and read the papers at your\nleisure.\"\n\nMr. Josiah Brooks was a solemn man, and he did not appear to relish\nthe picture I so graphically drew of him, when in truth I was thinking\nonly of his own comfort; so I changed the subject with an alertness of\nmind which perhaps he was incapable of appreciating.\n\n\"How far from London is this estate of Brede?\" I asked, \"and how do\nyou get to it?\"\n\n\"It is fifty or sixty miles away,\" he said, \"and lies in the county of\nSussex, close to the sea, but not on it. If you wish to visit Brede\nestate,\" he went on, as if I had not been telling him I was going to\ndo that very thing in force, \"if you wish to visit Brede estate, the\nbest plan is to go to Rye and there engage a guide who will lead you\nto it.\"\n\n\"Rye,\" said I in astonishment, wondering where I had heard the name\nbefore; then, suddenly remembering, I said:\n\n\"Rye is a seaport town, is it not?\"\n\n\"It is,\" agreed Mr. Brooks.\n\n\"Rye is the spot,\" rejoined I, \"where Father Donovan will embark on\nhis pilgrimage to Rome. Sure, and I'm glad to hear that, for the good\nold man and I will travel there together, and the blessing of\nProvidence will surround me, which I hope will be helpful if the\nEarl's cut-throats bar the way, as is more than likely.\"\n\n\"Very well, Mr. O'Ruddy, as you are doubtless impatient to know the\nresult, you may call upon me to-morrow afternoon at four o'clock, and\nI may be in a position to give you more information than I can offer\nat present.\"\n\nI took that as a dismissal, and, getting up, shook him warmly by the\nhand, although his arm was as stiff as a pump handle, and he seemed to\ntake little pleasure in the farewell. And so I left the Temple, that\nwas as lonely as the road between Innishannon and the sea, and trudged\nout into Fleet Street, which was as lively as Skibbereen Fair. I was\nso overjoyed to find that my journey lay in the same direction as\nFather Donovan's that I tramped on westward till after some trouble I\nfound the priest's house in which he was stopping, to tell the good\nfather that I would go part of the way to Rome with him. He was indeed\ndelighted to see me, and introduced me to his host, Father Kilnane,\nnearly as fine a man and as good a priest as Father Donovan himself.\n\nWe had dinner there all together at mid-day, and I invited Father\nDonovan to come out and see the town with me, which he did. The\npeaceful father clung to my arm in a kind of terror at what he was\nwitnessing, for he was as innocent of the ways of a big town as if he\nhad been a gossoon from a hedge-school in Ireland. Yet he was mightily\ninterested in all he saw, and asked me many thousand questions that\nday, and if I did not know the correct answer to them, it made no\ndiffer to Father Donovan, for he did not know the answer himself and\ntook any explanation as if it was as true as the gospels he studied\nand preached.\n\nDaylight was gone before we got back to the house he lodged in, and\nnothing would do but I must come in and have a bit of supper, although\nI told him that supper would be waiting for me at the \"Pig and\nTurnip.\" It had been agreed between us that we would travel together\nas far as Rye, and that there I should see him off on his tempestuous\nvoyage to Dunkirk or Calais, as the case might be. The old man was\nmightily delighted to find that our ways lay together through the\nsouth of England. He was pleased to hear that I had determined on my\nrights through the courts of law, with no more sword-playing and\nviolence, which, to tell the truth, until it reached its height, the\nold man was always against; although, when a quarrel came to its\nutmost interesting point, I have seen Father Donovan fidget in his\ncassock, and his eyes sparkle with the glow of battle, although up\ntill then he had done his best to prevent the conflict.\n\nIt was getting late when I neared the \"Pig and Turnip,\" and there was\na good deal of turmoil in the streets. I saw one or two pretty\ndebates, but, remembering my new resolution to abide by law and order,\nI came safely past them and turned up the less-frequented street that\nheld my inn, when at the corner, under the big lamp, a young man with\nsomething of a swagger about him, in spite of the meanness of his\ndress, came out from the shadow of the wall and looked me hard in the\nface.\n\n\"Could you direct me, sir, to a hostelry they call the 'Pig and\nTurnip'?\" he asked with great civility.\n\n\"If you will come with me,\" said I, \"I'll bring you to the place\nitself, for that's where I'm stopping.\"\n\n\"Is it possible,\" he said, \"that I have the honour of addressing The\nO'Ruddy?\"\n\n\"That great privilege is yours,\" said I, coming to a standstill in the\nmiddle of the street, as I saw the young man had his sword drawn and\npressed close against his side to allay suspicion. I forgot all about\nlaw and order, and had my own blade free of the scabbard on the\ninstant; but the young man spoke smoothly and made no motion of\nattack, which was very wise of him.\n\n\"Mr. O'Ruddy,\" he says, \"we are both men of the world and sensible men\nand men of peace. Where two gentlemen, one down on his luck and the\nother in prosperity, have a private matter to discuss between them, I\nthink this discussion should take place quietly and in even tones of\nvoice.\"\n\n\"Sir,\" said I, giving my sword-hand a little shake, so that the weapon\nsettled down into its place, \"Sir, you express my sentiments exactly,\nand as you are a stranger to me perhaps you will be good enough to\nannounce the subject that concerns us.\"\n\n\"I may say at the outset,\" he remarked almost in a whisper, so polite\nhe was, \"that I have eight good swordsmen at my back, who are not\nvisible until I give the signal; therefore you see, sir, that your\nchances are of the slightest if I should be compelled to call upon\nthem. I know the fame of The O'Ruddy as a swordsman, and you may take\nit as a compliment, sir, that I should hesitate to meet you alone. So\nmuch for saving my own skin, but I am a kindly man and would like to\nsave your skin as well. Therefore if you will be kind enough to hand\nto me the papers which you carry in your pocket, you will put me under\nstrong obligations, and at the same time sleep peaceably to-night at\nthe 'Pig and Turnip' instead of here in the gutter, to be picked up by\nthe watch, for I can assure you, sir, as a man that knows the town,\nthe watch will not be here to save you whatever outcry you may make.\"\n\n\"I am obliged to you, sir, for your discourse and your warning, to\nboth of which I have paid strict attention; and in the interests of\nthat peace which we are each of us so loath to break I may announce to\nyou that the papers you speak of are not in my possession.\"\n\n\"Pardon me, sir, but they must be; for we have searched your room\nthoroughly, and we have also searched your servants.\"\n\n\"A thief of the night,\" cried I with mighty indignation, \"may easily\nsearch an honest man's room; and his poor servants, beaten and bruised\nby your master's orders, would fall easy victims to the strength and\nnumbers of your ruffians; but you will find it a difficult matter to\nsearch me.\"\n\n\"Sir,\" he replied, bowing as polite as Palermo, \"I grieve to state\nthat you are in error. The searching of both your servants and your\nrooms was accomplished, not through the employment of force, but by\nthe power of money. Your servants insisted they had nothing on their\npersons but liniment, and they accepted one gold piece each to allow\nme to verify their statements. Another gold piece gave me, for a time,\nthe freedom of your room. If you have not the papers upon you, then\nthere is no harm in allowing me to run my hand over your clothes,\nbecause the package is a bulky one and I will speedily corroborate\nyour statement.\"\n\n\"Sir,\" said I, not to be outdone in courtesy by this gentleman of the\ngutter, \"I will tell you truthfully that I have nothing on me but my\nsword, and to that you are quite welcome if you leave to me the choice\nof which end I hold and which I present to you,\"--and with that I\nsprang with my back to the wall, under the lamp, leaving myself\npartially in shadow, but having spread in front of me a semicircle of\nlight which any assailant attacking must cross, or indeed remain in\nits effulgence if he would keep free of the point of my blade.\n\n\"It grieves me to find that you are a man of violence,\" replied the\nscoundrel in the mildest of tones, \"and you will bear witness\nafterward that I did my best to keep you from harm.\"\n\n\"I freely acknowledge it now,\" said I. \"Bring on your men.\"\n\nTo tell the truth, I had no belief at all in the existence of his force,\nand thought he was playing a game on me, hoping to take me unawares; for\nif the man knew anything at all he must have known what a swordsman I\nwas, and it was no charge of cowardice against him that he was loath to\ncome to close quarters with me. I speedily discovered, however, that all\nhe said was true; for he gave a low whistle, and out of the darkness\ninstantly sprang seven or eight as malicious-looking villains as a man\nwould care to see, each one with a sword in his hand.\n\nAs many erroneous and exaggerated accounts of this encounter have been\ngiven in the coffee-houses, and even in the public prints, it is well\nthat I should now tell the truth about it. No man that has the hang of\nhis blade need fear the onset of a mob except in one case, and that is\nthis,--if the whole eight set upon me at once with every sword\nextended, there was a chance that though I might, by great expertness,\ndisable half of them, the other half would run me through. But it\nshould never be forgotten that these men were fighting for money, and\nI was fighting for my life, and that makes all the difference in the\nworld. Each man makes a show of attack, but he holds off, hoping that\none of the others will dare to thrust. This is fatal to success, but\nnot necessarily fatal to their intended victim. An active man with a\nwall at his back can generally account for all that comes in front of\nhim if he is deeply in earnest and has not too much liquor in him. It\nastonished London that I was able to defeat eight men, each one of\nwhom was armed as efficiently as myself; but, as my father used to\nsay, if you are not wholly taken up with the determination to have a\nman's life, you may pink him in what spot you choose if you give a\nlittle thought to the matter. The great object is the disarming of the\nenemy. Now, if you give a man a jab in the knuckles, or if you run\nyour blade delicately up his arm from the wrist to the elbow, this is\nwhat happens. The man involuntarily yells out, and as involuntarily\ndrops his sword on the flags. If you prick a man on the knuckle-bone,\nhe will leave go his sword before he has time to think, it being an\naction entirely unconscious on his part, just like winking your eye or\ndrawing your breath; yet I have seen men run through the body who kept\nsword in hand and made a beautiful lunge with it even as they\nstaggered across the threshold of death's door.\n\nNow I had no desire for any of these men's lives, but I determined to\nhave their swords. I glittered my own shining blade before their eyes,\nflourishing a semicircle with it, and making it dart here and there\nlike the tongue of an angry snake; and instantly every man in front of\nme felt uncomfortable, not knowing where the snake was going to sting,\nand then, as I said before, they were fighting for money and not for\nhonour. When I had dazzled their eyes for a moment with this\nsword-play and bewildered their dull brains, I suddenly changed my\ntactics and thrust forward quicker than you can count one, two, three,\nfour, five, six, seven, eight,--and each man was holding a bleeding\nfist to his mouth, while the swords clattered on the cobbles like hail\non the copper roof of a cathedral. It was the most beautiful and\ncomplete thing I ever saw. I then swept the unarmed men back a pace or\ntwo with a flirt of my weapon, and walked up the pavement, kicking the\nswords together till they lay in a heap at my feet. The chief ruffian\nstood there dazed, with his sword still in his hand, for he had\nstepped outside the circle, he acting as captain, and depending on the\nmen to do the work.\n\n\"Drop that,\" I shouted, turning on him, and he flung his sword in the\nstreet as if it was red hot.\n\n\"Sir,\" said I to him, \"a sword in your hand is merely an\ninconvenience to you; see if you don't look better with an armful of\nthem. Pick up these nine blades in a bundle and walk on before me to\nthe 'Pig and Turnip.' When we come into the courtyard of that tavern,\nyou are to turn round and make me the lowest bow you can without\nrubbing your nose against the pavement. Then you will say, as\ngracefully as the words can be uttered:\n\n\"'Mr. O'Ruddy,' you say, 'these swords are yours by right of conquest.\nYou have defeated nine armed men to-night in less than as many\nminutes, so I present you with the spoil.' Then you will bow to the\npeople assembled in the courtyard,--for there is aways a mob of them\nthere, late and early,--and you will make another low obeisance to me.\nIf you do all this acceptably to my sense of politeness, I will let\nyou go unmolested; but if you do otherwise, I will split your gullet\nfor you.\"\n\n\"Sir,\" said the captain, \"I accept your terms.\"\n\nWith that he stooped and picked up the bundle of weapons, marching on\nstolidly before me till he came to the \"Pig and Turnip.\" All the rest\nhad disappeared in the darkness, and had gone to their dens, very\nlikely to nurse sore knuckles and regret the loss of good stout\nblades.\n\nOur coming to the tavern caused a commotion, as you may well imagine;\nand although I don't make too much of the encounter, yet it is my\nbelief that such an incident never happened in London before. The\ncaptain carried out his part of the presentation with an air of\ndeference and a choice of good language that charmed me; then he\nbacked out under the archway to the street, bowing six or seven times\nas he went. I had never any fault to find with the man's manner. Paddy\nand Jem, now seemingly quite recovered from their misusage of Sunday,\nstood back of the group with eyes and mouths open, gazing upon me with\nan admiration I could not but appreciate.\n\n\"Come out of that,\" said I, \"and take this cutlery up to my room,\" and\nthey did.\n\nI sat down at the table and wrote a letter to Mr. Brooks.\n\n\"Sir,\" said I in it, \"I don't know whether I am plaintiff or defendant\nin the suit that's coming on, but whichever it is here's a bundle of\nlegal evidence for your use. You mentioned the word 'violence' to me\nwhen I had the pleasure of calling on you. This night I was set upon\nby nine ruffians, who demanded from me the papers now in your\npossession. I took their knives from them, so they would not hurt\nthemselves or other people, and I send you these knives to be filed\nfor reference.\"\n\nI tied up the swords in two bundles, and in the morning sent Paddy and\nJem off with them and the letter to the Temple, which caused great\ncommotion in that peaceable quarter of the city, and sent forth the\nrumour that all the lawyers were to be at each other's throats next\nday.\n\n\n\n\nCHAPTER XXX\n\n\nIn the afternoon I went slowly to the Temple, thinking a good deal on\nthe way. It's truth I tell, that in spite of the victory of the night\nbefore I walked to the Temple rather downhearted. Whether Josiah\nBrooks was an attorney, or a barrister, or a solicitor, or a plain\nlawyer, I don't know to this day, and I never could get my mind to\ngrasp the distinction that lies between those names in that trade; but\nwhichever it was it seemed to me he was a cold, unenthusiastic man,\nand that he thought very little indeed of my game. There is small\npleasure in litigation in England as compared with the delight of the\nlaw in the old Ark. If I had gone to see a lawyer in Dublin or Cork he\nwould have been wild with excitement before I had got half through my\nstory. He would have slapped me on the back and shook me by the hand,\nand cried \"Whurroo\" at the prospect of a contest. My quarrel would\nhave been his before I had been ten minutes in his presence, and he\nwould have entered into the spirit of the fight as if he were the\nprincipal in it instead of merely acting for him; but in this gloomy\ncountry of England, where they engage upon a lawsuit, not with\ndelight, but as if they were preparing for a funeral; there is no\nenjoyment in the courts at all at all. I wished I could transfer the\ncase to the old turf, where there is more joy in being defeated than\nthere is in winning in England; for I have seen the opposing lawyers\nrise from the most gentlemanly and elegant language you ever heard to\na heated debate; then fling books at each other, and finally clench,\nwhile the judge stood up and saw fair play. But this man Brooks was so\ncalm and collected and uninterested that he fairly discouraged me, and\nI saw that I was going to get neither the money I needed nor the\nsupport I expected from him.\n\nAs I went up his dark stairway in the Temple and came to the passage\nthat led to the outer room, I saw standing in a corner the two bundles\nof swords I had sent him, as if he had cast them out, which indeed he\nhad done. After some delay in the outer room, the melancholy man in\nrusty black asked me, would I go in, and there sat Josiah Brooks at\nhis table as if he had never left it since I took my departure the day\nbefore. He looked across at me with a scrutiny which seemed to be\nmingled with dislike and disapproval.\n\n\"Mr. O'Ruddy,\" he said, quiet-like, \"it is not customary to send to a\nlaw office a number of swords, which are entirely out of place in such\nrooms. They have been counted and are found to number nine. I shall be\nobliged if you sign this receipt for them, accept delivery of the\nsame, and remove them from the premises at your earliest convenience.\"\n\nSo I signed the receipt without a word and handed it back to him. Then\nI said,--\n\n\"I will send my servant for the swords as soon as I return to the\ninn.\"\n\nHe inclined his head the merest trifle, drew some papers toward him,\nand adjusted his glasses.\n\n\"It is my duty to tell you, Mr. O'Ruddy, that if you go into the\ncourts with this case you will assuredly be defeated, and the costs\nwill follow. There is also a possibility that when the civil\nproceedings are determined a criminal action against yourself may\nensue.\"\n\n\"I told you, sir,\" said I, with my heart sinking, \"I had no intention\nof troubling the courts at all at all. In the land I come from we are\nmore inclined to settle a case with a good stout blackthorn than with\nthe aid of a lawyer's wig. These papers say in black and white that I\nam the owner of Brede estate, and I intend to take possession of it.\"\n\n\"It is only right to add,\" continued Brooks, with that great air of\ncalm I found so exasperating, \"it is only right to add that you are in\na position to cause great annoyance to the Earl of Westport. You can\nat least cast doubt on his title to the estate; and he stands this\njeopardy, that if contrary to opinion your cause should prove\nsuccessful,--and we must never forget that the law is very\nuncertain,--the Earl would have to account for the moneys he has drawn\nfrom the estate, which would run into many thousands of pounds, and,\ntogether with the loss of the property, would confront his lordship\nwith a most serious situation. Your case, therefore, though weak from\na strictly legal point of view, is exceptionally strong as a basis for\ncompromise.\"\n\nThese words cheered me more than I can say, and it is an extraordinary\nfact that his frozen, even tone, and his lack of all interest in the\nproceedings had an elevating effect upon my spirits which I could not\nhave believed possible.\n\n\"As it is a compromise that I'm after,\" said I, \"what better case can\nwe want?\"\n\n\"Quite so,\" he resumed; \"but as there is no encouragement in the\nstrictly legal aspect of the plea, you will understand that no\nmoney-lender in London will advance a farthing on such unstable\nsecurity. Even though I am acting in your interests, I could not take\nthe responsibility of advising any capitalist to advance money on such\nuncertain tenure.\"\n\nThis threw me into the depths again; for, although I never care to\nmeet trouble half way, I could not conceal from myself the fact that\nmy bill at the \"Pig and Turnip\" had already reached proportions which\nleft me no alternative but to slip quietly away in liquidation of the\naccount. This was a thing I never liked to do; and when I am compelled\nto make that settlement I always take note of the amount, so that I\nmay pay it if I am ever that way again and have more money than I need\nat the moment. Even if I succeeded in getting away from the inn, what\ncould I do at Brede with no money at all?--for in that part of the\ncountry they would certainly look upon the Earl of Westport as the\nreal owner of the property, and on me as a mere interloper; and if I\ncould not get money on the documents in London, there was little\nchance of getting credit even for food at Brede.\n\n\"It is rather a blue look-out then,\" said I as cheerfully as I could.\n\n\"From a legal standpoint it is,\" concurred Mr. Brooks, as unconcerned\nas if his own payment did not depend on my raising the wind with these\npapers. \"However, I have been instructed by a person who need not be\nnamed, who has indeed stipulated that no name shall be mentioned, to\nadvance you the sum of five hundred guineas, which I have here in my\ndrawer, and which I will now proceed to count out to you if you, in\nthe mean time, will sign this receipt, which acquits me of all\nresponsibility and certifies that I have handed the money over to you\nwithout rebate or reduction.\"\n\nAnd with that the man pulled open a drawer and began to count out the\nglittering gold.\n\nI sprang to my feet and brought my fist down on the table with a\nthump. \"Now, by the Great Book of Kells, what do you mean by chopping\nand changing like a rudderless lugger in a ten-knot breeze? If the\nexpedition is possible, and you had the money in your drawer all the\ntime, why couldn't you have spoken it out like a man, without raising\nme to the roof and dropping me into the cellar in the way you've\ndone?\"\n\nThe man looked unruffled across the table at me. He pushed a paper a\nlittle farther from him, and said without any trace of emotion:\n\n\"Will you sign that receipt at the bottom, if you please?\"\n\nI sat down and signed it, but I would rather have jabbed a pen between\nhis close-set lips to give him a taste of his own ink. Then I sat\nquiet and watched him count the gold, placing it all in neat little\npillars before him. When it was finished, he said:\n\n\"Will you check the amount?\"\n\n\"Is that gold mine?\" I asked him.\n\n\"It is,\" he replied.\n\nSo I rose up without more ado and shovelled it into my pockets, and\nhe put the receipt into the drawer after reading it over carefully,\nand arched his eyebrows without saying anything when he saw me pocket\nthe coins uncounted.\n\n\"I wish you good afternoon,\" said I.\n\n\"I have to detain you one moment longer,\" he replied. \"I have it on\nthe most trustworthy information that the Earl of Westport is already\naware of your intention to proceed to the country estate alleged to be\nowned by him. Your outgoings and incomings are watched, and I have to\ninform you that unless you proceed to Rye with extreme caution there\nis likelihood that you may be waylaid, and perchance violence offered\nto you.\"\n\n\"In that case I will reap a few more swords; but you need not fear, I\nshall not trouble you with them.\"\n\n\"They are out of place in a solicitor's chamber,\" he murmured gently.\n\"Is there anything further I can do for you?\"\n\n\"Yes,\" I said, \"there is one thing more. I would be obliged if you\ncould make me a bundle of legal-looking papers that are of no further\nuse to you: a sheet of that parchment, and some of the blue stuff like\nwhat I carried. The Earl seems determined to have a packet of papers\nfrom me, and I would like to oblige him, as he's going to be my\nfather-in-law, although he doesn't know it. I'd like some writing on\nthese papers,--Latin for preference.\"\n\nJosiah Brooks thought steadily for a few moments, then he called out\nand the melancholy rusty man came in. He took a few instructions and\nwent out again. After a long time he entered once more and placed on\nthe table a packet I would have sworn was my own. This the lawyer\nhanded to me without a word, and the rusty man held open the door for\nme. So, with the bogus papers in my pocket, not to mention the genuine\ngold, I took my leave of Josiah and the Temple.\n\nAs soon as I was outside I saw at once that there was no time to be\nlost. If the Earl had guessed my intention, as was hinted, what would\nhe do? Whenever I wish to answer a question like that to myself, I\nthink what would I do if I were in the position of the other man. Now\nwhat I would have done, was this, if I were the Earl of Westport. I\nwould send down to Brede all the ruffians at my disposal and garrison\nthe house with them; and if the Earl did this, I would be on the\noutside, and he on the inside with advantage over me accordingly. Most\nmen fight better behind stone walls than out in the open; and,\nbesides, a few men can garrison a barracks that five hundred cannot\ntake by assault. However, as it turned out, I was crediting the Earl\nwith brains equal to my own, which in truth neither he nor any of his\nfollowers had below their bonnets. He trusted to intercepting me on\nthe highway, just as if he hadn't already failed in that trick. But it\ntakes a score of failures to convince an Englishman that he is on the\nwrong track altogether, while an Irishman has so many plans in his\nhead that there's never time to try one of them twice in succession.\nBut if I was wrong about the Earl, I was right about his daughter,\nwhen I suspected that she gave the lawyer the information about the\nEarl's knowledge of my plans, and I was also right when I credited the\ndear girl with drawing on her own funds to give me the golden\nguineas,--\"and may each one of them,\" said I to myself, \"prove a\ngolden blessing on her head.\"\n\nAt any rate, there was no time to be lost, so I made straight to\nFather Donovan and asked him would he be ready to begin the journey to\nRye after an early breakfast with me at the \"Pig and Turnip.\"\n\nYou never saw a man in your life so delighted at the prospect of\nleaving London as was Father Donovan, and indeed I was glad to get\naway from the place myself. The good father said the big town confused\nhim; and, although he was glad to have seen it, he was more happy\nstill to get out of it and breathe a breath of fresh country air once\nmore. So it was arranged that he would come to the \"Pig and Turnip\"\nnext morning between six and seven o'clock. I then turned back to the\nshop of a tailor who for a long time had had two suits of clothing\nwaiting for me that were entirely elegant in their design. The tailor,\nhowever, would not take the word of a gentleman that payment would\nfollow the delivery of the costumes; for a little later would be more\nconvenient for me to give him the money, and this made me doubt, in\nspite of the buttons and gold lace, if the garments were quite the\nfashionable cut, because a tailor who demands money on the spot shows\nhe is entirely unaccustomed to deal with the upper classes; but I\nneeded these clothes, as the two suits I possessed were getting a\nlittle the worse for wear.\n\nWhen I went into his shop he was inclined to be haughty, thinking I\nhad come to ask credit again; but when he saw the glitter of the money\nthe man became obsequious to a degree that I never had witnessed\nbefore. I was affable to him, but distant; and when he offered me\neverything that was in his shop, I told him I would take time and\nconsider it. He sent a servant following behind me with the goods, and\nso I came once more to the \"Pig and Turnip,\" where I ordered Paddy and\nJem to go to the Temple and fetch away the swords.\n\nThere seemed to be a pleased surprise on the face of the landlord when\nI called for my bill and paid it without question, chiding him for his\ndelay in not sending it before. I engaged a horse for Father Donovan\nto ride on the following morning, and ordered breakfast ready at six\no'clock, although I gave my commands that I was to be wakened an hour\nbefore daylight.\n\nI spent the rest of the day in my room with Paddy and Jem, trying to\nknock into their heads some little notion of geography, wishing to\nmake certain that they would sooner or later arrive in Rye without\nstumbling in on Belfast while on the way. My own knowledge of the face\nof the country was but meagre, so the landlord brought in a rough map\nof the south of England, and I cautioned the lads to get across London\nBridge and make for the town of Maidstone, from where they could go\ndue south, and if they happened on the coast they were to inquire for\nRye and stay there until further orders. Jem Bottles, who thought he\nhad brains in his head, said he would not be so open in telling every\none we were going to Rye if he was me, because he was sure the Earl\nhad people on the look-out, and money was plenty with his lordship. If\nevery one knew when we were taking our departure, there would be no\ndifficulty in following us and overcoming us on some lonely part of\nthe road.\n\n\"Jem,\" said I, \"that's all very true; but when they attacked us before\nthey got very little change for their trouble; and if you are afraid\nof some slight commotion on the road, then you can stay back here in\nLondon.\"\n\n\"I am not afraid at all,\" said Jem, \"but if there's anything\nparticular you would like to see in Rye, there's no use in blocking\nthe road to it.\"\n\n\"Sure, Jem, then be quiet about it.\"\n\nTurning to the landlord, who was standing by, I said to him:\n\n\"My men fear we are going to be intercepted, so I think if I began the\njourney some time before daylight, and they followed me soon after, I\nmight slip away unnoticed.\"\n\nThe landlord scratched his head and crinkled up his brow, for to think\nwas unusual with him.\n\n\"I don't see,\" he said at last, \"what you have to gain by going\nseparately. It seems to me it would be better to go in a body, and\nthen, if you are set on, there are three instead of one.\"\n\n\"Very well,\" said I, \"I'll take your caution into consideration, and\nact upon it or not as seems best when the time comes.\"\n\nI told Paddy and Jem to sleep that night on the floor of my own room,\nand cautioned them to wake me an hour before daylight at the latest.\nJem slept through until I had to kick him into consciousness; but poor\nPaddy, on the other hand, wakened me four times during the night,--the\nfirst time two hours after I had gone to sleep, and I could have\ncudgelled him for his pains, only I knew the lad's intentions were\ngood. The last time I could stand it no longer, although it was still\nearlier than the hour I had said, so I got up and dressed myself in\none of my new suits.\n\n\"And here, Paddy,\" said I, \"you will wear the costume I had on\nyesterday.\"\n\n\"I couldn't think of it,\" said Paddy, drawing back from the grandeur.\n\n\"You are not to think, you impudent gossoon, but to do as I tell you.\nPut them on, and be as quick as you can.\"\n\n\"Troth, yer honour,\" said Paddy, still shrinking from them, \"they're\ntoo grand for the likes o' me, an' few will be able to tell the differ\natween us.\"\n\n\"You conceited spalpeen, do ye think there's no difference between us\nbut what the clothes make? Get into them. I intend certain other\npeople to take you for me in the dark, and I can warrant you these\nclothes, grand as you think them, will be very soundly beaten before\nthis day is done with.\"\n\n\"Ochone, ochone,\" moaned Paddy, \"am I to get another beating already,\nand some of the bruises not yet off my flesh?\"\n\n\"Put on the coat now, and don't do so much talking. Sure it's all in\nthe day's work, and I promise you before long you'll have your revenge\non them.\"\n\n\"It's not revenge I'm after,\" wailed Paddy, \"but a whole skin.\"\n\n\"Now you're transformed into a gentleman,\" said I, \"and many a lad\nwould take a beating for the privilege of wearing such gorgeous\nraiment. Here is a packet of paper that you're to keep in your pocket\ntill it's taken away from you. And now I'll help you to saddle the\nhorse, and once you're across London Bridge you'll likely come upon\nMaidstone and Rye some time in your life, for you can't get back over\nthe river again except by the same bridge, so you'll know it when you\ncome to it.\"\n\nAnd so I mounted Paddy in the courtyard; the sleepy watchman undid the\nbolts in the big gate in the archway; and my man rode out into the\ndarkness in no very cheerful humour over his journey. I came back and\ntook forty winks more in the arm-chair, then, with much difficulty, I\nroused Jem Bottles. He also, without a murmur, but with much pride in\nhis dressing, put on the second of my discarded suits, and seemed to\nfancy himself mightily in his new gear. With plenty of cord I tied and\nretied the two bundles of swords and placed them across the horse in\nfront of his saddle, and it was not yet daylight when Jem jingled out\ninto the street like a moving armoury. Two huge pistols were in his\nholsters, loaded and ready to his hand.\n\n\"By the Saints,\" said Jem proudly, \"the man that meddles with me shall\nget hot lead or cold steel for his breakfast,\" and with that he went\noff at a canter, waking the echoes with the clash of his horse's shoes\non the cobble-stones.\n\nI went up stairs again and threw myself down on the bed and slept\npeacefully with no Paddy to rouse me until half-past-six, when a\ndrawer knocked at the door and said that a priest that was downstairs\nwould be glad to see me. I had him up in a jiffy, and a hot breakfast\nfollowing fast on his heels, which we both laid in in quantities, for\nneither of us knew where our next meal was to be. However, the good\nfather paid little thought to the future as long as the present meal\nwas well served and satisfactory. He had no more idea than a spring\nlamb how we were to get to Rye, but thought perhaps a coach set out\nat that hour in the morning. When I told him I had a horse saddled and\nwaiting for him, he was pleased, for Father Donovan could scamper\nacross the country in Ireland with the best of them. So far as I could\njudge, the coast was clear, for every one we met between the \"Pig and\nTurnip\" and the bridge seemed honest folk intent on getting early to\ntheir work. It was ten minutes past seven when we clattered across the\nbridge and set our faces toward Rye.\n\n\n\n\nCHAPTER XXXI\n\n\nLooking back over my long life I scarcely remember any day more\npleasant than that I spent riding side by side with Father Donovan\nfrom London to Rye. The fine old man had a fund of entertaining\nstories, and although I had heard them over and over again there was\nalways something fresh in his way of telling them, and now and then I\nrecognized a narrative that had once made two separate stories, but\nwhich had now become welded into one in the old man's mind. There was\nnever anything gloomy in these anecdotes, for they always showed the\ncheerful side of life and gave courage to the man that wanted to do\nright; for in all of Father Donovan's stories the virtuous were always\nmade happy. We talked of our friends and acquaintances, and if he ever\nknew anything bad about a man he never told it; while if I mentioned\nit he could always say something good of him to balance it, or at\nleast to mitigate the opinion that might be formed of it. He was\nalways doing some man a good turn or speaking a comforting word for\nhim.\n\n\"O'Ruddy,\" he said, \"I spent most of the day yesterday writing letters\nto those that could read them in our part of Ireland, setting right\nthe rumours that had come back to us, which said you were fighting\nduels and engaged in brawls, but the strangest story of all was the\none about your forming a friendship with a highwayman, who, they said,\ncommitted robberies on the road and divided the spoil with you, and\nhere I find you without a servant at all at all, leading a quiet,\nrespectable life at a quiet, respectable inn. It's not even in a\ntavern that I first come across you, but kneeling devoutly, saying a\nprayer in your mother church. I see you leaving your inn having paid\nyour bill like a gentleman, when they said you took night-leave of\nmost of the hostelries in England. Dear me, and there was the landlord\nbowing to you as if you were a prince, and all his servants in a row\nwith the utmost respect for you. Ah, O'Ruddy, it's men like you that\ngives the good name to Ireland, and causes her to be looked up to by\nall the people of the world.\"\n\nI gave Father Donovan heartfelt thanks for his kindness, and prayed to\nmyself that we would not come upon Jem Bottles on the road, and that\nwe would be left unmolested on our journey until we saw the sea-coast.\nOf course, if we were set upon, it would not be my fault, and it's not\nlikely he would blame me; but if we came on Bottles, he was inclined\nto be very easy in conversation, and, in spite of my warnings, would\nlet slip words that would shock the old priest. But when a day begins\ntoo auspiciously, its luck is apt to change before the sun sets, as it\nwas with me.\n\nIt was nearing mid-day, and we were beginning to feel a trifle hungry,\nyet were in a part of the country that gave little promise of an inn,\nfor it was a lonely place with heath on each side of the road, and,\nfurther on, a bit of forest. About half-way through this wooded plain\nan astonishing sight met my eyes. Two saddled horses were tied to a\ntree, and by the side of the road appeared to be a heap of nine or\nten saddles, on one of which a man was sitting, comfortably eating a\nbit of bread, while on another a second man, whose head was tied up in\na white cloth, lay back in a recumbent position, held upright by the\nsaddlery. Coming closer, I was disturbed to see that the man eating\nwas Jem Bottles, while the other was undoubtedly poor Paddy, although\nhis clothes were so badly torn that I had difficulty in recognizing\nthem as my own. As we drew up Jem stood and saluted with his mouth\nfull, while Paddy groaned deeply. I was off my horse at once and ran\nto Paddy.\n\n\"Where are ye hurted?\" said I.\n\n\"I'm killed,\" said Paddy.\n\n\"I've done the best I could for him,\" put in Jem Bottles. \"He'll be\nall right in a day or two.\"\n\n\"I'll not,\" said Paddy, with more strength than one would suspect;\n\"I'll not be all right in a day or two, nor in a week or two, nor in a\nmonth or two, nor in a year or two; I'm killed entirely.\"\n\n\"You're not,\" said Bottles. \"When I was on the highway I never minded\na little clip like that.\"\n\n\"Hush, Bottles,\" said I, \"you talk altogether too much. Paddy,\" cried\nI, \"get on your feet, and show yer manners here to Father Donovan.\"\n\nPaddy got on his feet with a celerity which his former attitude would\nnot have allowed one to believe possible.\n\n\"My poor boy!\" said the kindly priest; \"who has misused you?\" and he\nput his two hands on the sore head.\n\n\"About two miles from here,\" said Paddy, \"I was set on by a score of\nmen--\"\n\n\"There was only nine of them,\" interrupted Jem, \"count the saddles.\"\n\n\"They came on me so sudden and unexpected that I was off my horse\nbefore I knew there was a man within reach. They had me down before I\ncould say my prayers, and cudgelled me sorely, tearing my clothes, and\nthey took away the packet of papers you gave me, sir. Sure I tried to\nguard it with my life, an' they nearly took both.\"\n\n\"I am certain you did your best, Paddy,\" said I; \"and it's sorry I am\nto see you injured.\"\n\n\"Then they rode away, leaving me, sore wounded, sitting on the side of\nthe road,\" continued Paddy. \"After a while I come to myself, for I\nseemed dazed; and, my horse peacefully grazing beside me, I managed to\nget on its back, and turned toward London in the hope of meeting you;\nbut instead of meeting you, sir, I came upon Jem with his pile of\nsaddles, and he bound up my head and did what he could to save me,\nalthough I've a great thirst on me at this moment that's difficult to\ndeal with.\"\n\n\"There's a ditch by the side of the road,\" said the priest.\n\n\"Yes,\" said Paddy sadly; \"I tried some of that.\"\n\nI went to my pack on the horse and took out a bottle and a leather\ncup. Paddy drank and smacked his lips with an ecstasy that gave us\nhope for his ultimate recovery. Jem Bottles laughed, and to close his\nmouth I gave him also some of the wine.\n\n\"I hope,\" said Father Donovan with indignation, \"that the miscreant\nwho misused you will be caught and punished.\"\n\n\"I punished them,\" said Jem, drawing the back of his hand across his\nmouth.\n\n\"We'll hear about it another time,\" said I, having my suspicions.\n\n\"Let the good man go on,\" begged Father Donovan, who is not without\nhuman curiosity.\n\nJem needed no second bidding.\n\n\"Your Reverence,\" he said, \"I was jogging quietly on as a decent man\nshould, when, coming to the edge of this forest, I saw approach me a\nparty of horsemen, who were very hilarious and laughed loudly. If you\nlook up and down the road and see how lonely it is, and then look at\nthe wood, with no hedge between it and the highway, you'll notice the\nplace was designed by Providence for such a meeting.\"\n\n\"Sure the public road is designed as a place for travellers to meet,\"\nsaid the father, somewhat bewildered by the harangue.\n\n\"Your Reverence is right, but this place could not afford better\naccommodation if I had made it myself. I struck into the wood before\nthey saw me, tore the black lining from my hat, punched two holes in\nit for the eyes, and tied it around my forehead, letting it hang down\nover my face; then I primed my two pistols and waited for the\ngentlemen. When they were nearly opposite, a touch of the heels to my\nhorse's flank was enough, and out he sprang into the middle of the\nroad.\n\n\"'Stand and deliver!' I cried, pointing the pistols at them, the words\ncoming as glibly to my lips as if I had said them no later ago than\nyesterday. 'Stand and deliver, ye--'\" and here Jem glibly rattled out\na stream of profane appellatives which was disgraceful to listen to.\n\n\"Tut, tut, Jem,\" I said, \"you shouldn't speak like that. Any way we'll\nhear the rest another time.\"\n\n\"That's what I called them, sir,\" said Jem, turning to me with\nsurprise, \"you surely would not have me tell an untruth.\"\n\n\"I wouldn't have you tell anything. Keep quiet. Father Donovan is not\ninterested in your recital.\"\n\n\"I beg your pardon, O'Ruddy,\" said Father Donovan, looking at me\nreproachfully; \"but I am very much interested in this man's\nnarrative.\"\n\n\"As any good man should be,\" continued Jem, \"for these were arrant\nscoundrels; one of them I knew, and his name is Doctor Chord. He fell\noff his horse on the roadway at once and pleaded for mercy. I ordered\nthe others instantly to hold their hands above their heads, and they\ndid so, except one man who began fumbling in his holster, and then, to\nshow him what I could do with a pistol, I broke his wrist. At the\nsound of the shot the horses began to plunge, nearly trampling Doctor\nChord into the dust.\n\n\"'Clasp your hands above your heads, ye--'\"\n\nHere went on another stream of terrible language again, and in despair\nI sat down on the pile of saddles, allowing things to take their\ncourse. Jem continued:\n\n\"The lesson of the pistol was not misread by my gentlemen, when they\nnoticed I had a second loaded one; so, going to them one after the\nother I took their weapons from them and flung them to the foot of\nthat tree, where, if you look, you may see them now. Then I took a\ncontribution from each one, just as you do in church, your Reverence.\nI'm sure you have a collection for the poor, and that was the one I\nwas taking up this day. I have not counted them yet,\" said the\nvillain turning to me, \"but I think I have between sixty and seventy\nguineas, which are all freely at your disposal, excepting a trifle for\nmyself and Paddy there. There's no plaster like gold for a sore head,\nyour Reverence. I made each one of them dismount and take off his\nsaddle and throw it in the pile; then I had them mount again and drove\nthem with curses toward London, and very glad they were to escape.\"\n\n\"He did not get the papers again,\" wailed Paddy, who was not taking as\njubilant a view of the world as was Jem at that moment.\n\n\"I knew nothing of the papers,\" protested Bottles. \"If you had told me\nabout the papers, I would have had them, and if I had been carrying\nthe papers these fellows would not have made away with them.\"\n\n\"Then,\" said the horrified priest, \"you did not commit this action in\npunishment for the injury done to your friend? You knew nothing of\nthat at the time. You set on these men thinking they were simple\ntravellers.\"\n\n\"O, I knew nothing of what happened to Paddy till later, but you see,\nyour Reverence, these men themselves were thieves and robbers. In\ntheir case it was nine men against one poor half-witted Irish lad--\"\n\n\"Half-witted yourself,\" cried Paddy angrily.\n\n\"But you, sir,\" continued his Reverence, \"were simply carrying out the\naction of a highwayman. Sir, you _are_ a highwayman.\"\n\n\"I was, your Reverence, but I have reformed.\"\n\n\"And this pile of saddles attests your reformation!\" said the old man,\nshaking his head.\n\n\"But you see, your Reverence, this is the way to look at it--\"\n\n\"Keep quiet, Jem!\" cried I in disgust.\n\n\"How can I keep quiet,\" urged Bottles, \"when I am unjustly accused? I\ndo not deny that I was once a highwayman, but Mr. O'Ruddy converted me\nto better ways--\"\n\n\"Highways,\" said Paddy, adding, with a sniff, \"Half-witted!\"\n\n\"Your Reverence, I had no more intention of robbing those men than you\nhave at this moment. I didn't know they were thieves themselves. Then\nwhat put it into my head to jump into the wood and on with a mask\nbefore you could say, Bristol town? It's the mysterious ways of\nProvidence, your Reverence. Even I didn't understand it at the time,\nbut the moment I heard Paddy's tale I knew at once I was but an\ninstrument in the hand of Providence, for I had not said, 'Stand and\ndeliver!' this many a day, nor thought of it.\"\n\n\"It may be so; it may be so,\" murmured the priest, more to himself\nthan to us; but I saw that he was much troubled, so, getting up, I\nsaid to Paddy:\n\n\"Are you able to ride farther on to-day?\"\n\n\"If I'd another sup from the cup, sir, I think I could,\" whereat Jem\nBottles laughed again, and I gave them both a drink of wine.\n\n\"What are you going to do with all this saddlery?\" said I to Bottles.\n\n\"I don't know anything better than to leave it here; but I think, your\nhonour, the pistols will come handy, for they're all very good ones,\nand Paddy and me can carry them between us, or I can make two bags\nfrom these leather packs, and Paddy could carry the lot in them, as I\ndo the swords.\"\n\n\"Very well,\" I said. \"Make your preparations as quickly as you can and\nlet us be off, for this latest incident, in spite of you, Jem, may\nlead to pursuit and get us into trouble before we are ready for it.\"\n\n\"No fear, sir,\" said Jem confidently. \"One thief does not lay\ninformation against another. If they had been peaceable travellers,\nthat would be another thing; but, as I said, Providence is protecting\nus, no doubt because of the presence of his Reverence here, and not\nfor our own merits.\"\n\n\"Be thankful it is the reward of some one else's merits you, reap,\nBottles, instead of your own. No more talk now, but to horse and\naway.\"\n\nFor some miles Father Donovan rode very silently. I told him something\nof my meeting with Jem Bottles and explained how I tried to make an\nhonest man of him, while this was the first lapse I had known since\nhis conversion. I even pretended that I had some belief in his own\ntheory of the interposition of Providence, and Father Donovan was\nevidently struggling to acquire a similar feeling, although he seemed\nto find some difficulty in the contest. He admitted that this robbery\nappeared but even justice; still he ventured to hope that Jem Bottles\nwould not take the coincidence as a precedent, and that he would never\nmistake the dictates of Providence for the desires of his own nature.\n\n\"I will speak with the man later,\" he said, \"and hope that my words\nwill make some impression upon him. There was a trace of exaltation in\nhis recital that showed no sign of a contrite spirit.\"\n\nOn account of the delay at the roadside it was well past twelve\no'clock before we reached Maidstone, and there we indulged in a good\ndinner that put heart into all of us, while the horses had time to\nrest and feed. The road to Rye presented no difficulties whatever, but\nunder ordinary conditions I would have rested a night before\ntravelling to the coast. There would be a little delay before the Earl\ndiscovered the useless nature of the papers which he had been at such\nexpense to acquire, but after the discovery there was no doubt in my\nmind that he would move upon Brede as quickly as horses could carry\nhis men, so I insisted upon pressing on to Rye that night, and we\nreached the town late with horses that were very tired. It was a long\ndistance for a man of the age of Father Donovan to travel in a day,\nbut he stood the journey well, and enjoyed his supper and his wine\nwith the best of us.\n\nWe learned that there was no boat leaving for France for several days,\nand this disquieted me, for I would have liked to see Father Donovan\noff early next morning, for I did not wish to disclose my project to\nthe peace-loving man. I must march on Brede next day if I was to get\nthere in time, and so there was no longer any possibility of\nconcealing my designs. However, there was no help for it, and I\nresolved to be up bright and early in the morning and engage a dozen\nmen whom I could trust to stand by me. I also intended to purchase\nseveral cartloads of provisions, so that if a siege was attempted we\ncould not be starved out. All this I would accomplish at as early an\nhour as possible, get the carts on their way to Brede, and march at\nthe head of the men myself; so I went to bed with a somewhat troubled\nmind, but fell speedily into a dreamless sleep nevertheless, and slept\ntill broad daylight.\n\n\n\n\nCHAPTER XXXII\n\n\nI found Rye a snug little town, and so entirely peaceable-looking that\nwhen I went out in the morning I was afraid there would be nobody\nthere who would join me in the hazardous task of taking possession of\nthe place of so well-known a man as the Earl of Westport. But I did\nnot know Rye then as well as I do now: it proved to be a great resort\nfor smugglers when they were off duty and wished to enjoy the innocent\nrelaxation of a town after the comparative loneliness of the\nsea-coast, although, if all the tales they tell me are true, the\nauthorities sometimes made the sea-shore a little too lively for their\ncomfort. Then there were a number of seafaring men looking for a job,\nand some of them had the appearance of being pirates in more\nprosperous days.\n\nAs I wandered about I saw a most gigantic ruffian, taking his ease\nwith his back against the wall, looking down on the shipping.\n\n\"If that man's as bold as he's strong,\" said I to myself, \"and I had\nhalf a dozen more like him, we'd hold Brede House till the day there's\nliberty in Ireland;\" so I accosted him.\n\n\"The top o' the morning to you,\" said I genially.\n\nHe eyed me up and down, especially glancing at the sword by my side,\nand then said civilly:\n\n\"The same to you, sir. You seem to be looking for some one?\"\n\n\"I am,\" said I, \"I'm looking for nine men.\"\n\n\"If you'll tell me their names I'll tell you where to find them, for I\nknow everybody in Rye.\"\n\n\"If that's the case you'll know their names, which is more than I do\nmyself.\"\n\n\"Then you're not acquainted with them?\"\n\n\"I am not; but if you'll tell me your name I think then I'll know one\nof them.\"\n\nThere was a twinkle in his eye as he said:\n\n\"They call me Tom Peel.\"\n\n\"Then Tom,\" said I, \"are there eight like you in the town of Rye?\"\n\n\"Not quite as big perhaps,\" said Tom, \"but there's plenty of good men\nhere, as the French have found out before now,--yes, and the\nconstables as well. What do you want nine men for?\"\n\n\"Because I have nine swords and nine pistols that will fit that number\nof courageous subjects.\"\n\n\"Then it's not for the occupation of agriculture you require them?\"\nsaid Peel with the hint of a laugh. \"There's a chance of a cut in the\nribs, I suppose, for swords generally meet other swords.\"\n\n\"You're right in that; but I don't think the chance is very strong.\"\n\n\"And perhaps a term in prison when the scrimmage is ended?\"\n\n\"No fear of that at all at all; for if any one was to go to prison it\nwould be me, who will be your leader, and not you, who will be my\ndupes, do you see?\"\n\nPeel shrugged his shoulders.\n\n\"My experience of the world is that the man with gold lace on his\ncoat goes free, while they punish the poor devil in the leather\njacket. But, turn the scheme out bad or ill, how much money is at the\nend of it?\"\n\n\"There'll be ten guineas at the end of it for each man, win or lose.\"\n\n\"And when will the money be paid?\"\n\n\"Half before you leave Rye, the other half in a week's time, and\nperhaps before,--a week's time at the latest; but I want men who will\nnot turn white if a blunderbuss happens to go off.\"\n\nThe rascallion smiled and spat contemptuously in the dust before him.\n\n\"If you show me the guineas,\" said he, \"I'll show you the men.\"\n\n\"Here's five of them, to begin with, that won't be counted against\nyou. There'll be five more in your pocket when we leave Rye, and a\nthird five when the job's ended.\"\n\nHis big hand closed over the coins.\n\n\"I like your way of speaking,\" he said. \"Now where are we to go?\"\n\n\"To the strong house of Brede, some seven or eight miles from here. I\ndo not know how far exactly, nor in what direction.\"\n\n\"I am well acquainted with it,\" said Peel. \"It was a famous smuggler's\nplace in its time.\"\n\n\"I don't mean a smuggler's place,\" said I. \"I am talking of the\ncountry house of the Earl of Westport.\"\n\n\"Yes, curse him, that's the spot I mean. Many a nobleman's house is\nput to purposes he learns little of, although the Earl is such a\nscoundrel he may well have been in with the smugglers and sold them to\nthe government.\"\n\n\"Did he sell them?\"\n\n\"Somebody sold them.\"\n\nThere was a scowl on Peel's face that somehow encouraged me, although\nI liked the look of the ruffian from the first.\n\n\"You're an old friend of his lordship's, then?\" said I.\n\n\"He has few friends in Rye or about Rye. If you're going to do\nanything against Westport, I'll get you a hundred men for nothing if\nthere's a chance of escape after the fight.\"\n\n\"Nine men will do me, if they're the right stuff. You will have good\ncover to sleep under, plenty to eat and drink, and then I expect you\nto hold Brede House against all the men the Earl of Westport can bring\nforward.\"\n\n\"That's an easy thing,\" said Peel, his eye lighting up. \"And if worse\ncomes to the worst I know a way out of the house that's neither\nthrough door or window nor up a chimney. Where will I collect your\nmen?\"\n\n\"Assemble them on the road to Brede, quietly, about half a mile from\nRye. Which direction is Brede from here?\"\n\n\"It lies to the west, between six and seven miles away as the crow\nflies.\"\n\n\"Very well, collect your men as quickly as you can, and send word to\nme at the 'Anchor.' Tell your messenger to ask for The O'Ruddy.\"\n\nNow I turned back to the tavern sorely troubled what I would do with\nFather Donovan. He was such a kindly man that he would be loath to\nshake hands with me at the door of the inn, as he had still two or\nthree days to stop, so I felt sure he would insist on accompanying me\npart of the way. I wished I could stop and see him off on his ship;\nbut if we were to get inside of Brede's House unopposed, we had to act\nat once. I found Paddy almost recovered from the assault of the day\nbefore. He had a bandage around his forehead, which, with his red\nhair, gave him a hideous appearance, as if the whole top of his head\nhad been smashed. Poor Paddy was getting so used to a beating each day\nthat I wondered wouldn't he be lonesome when the beatings ceased and\nthere was no enemy to follow him.\n\nFather Donovan had not yet appeared, and the fire was just lit in the\nkitchen to prepare breakfast, so I took Jem and Paddy with me to the\neating shop of the town, and there a sleepy-looking shop-keeper let us\nin, mightily resenting this early intrusion, but changed his demeanour\nwhen he understood the size of the order I was giving him, and the\nfact that I was going to pay good gold; for it would be a fine joke on\nThe O'Ruddy if the Earl surrounded the house with his men and starved\nhim out. So it was no less than three cartloads of provisions I\nordered, though one of them was a cartload of drink, for I thought the\ncompany I had hired would have a continuous thirst on them, being\nseafaring men and smugglers, and I knew that strong, sound ale was\nbrewed in Rye.\n\nThe business being finished, we three went back to the \"Anchor,\" and\nfound an excellent breakfast and an excellent man waiting for me, the\nlatter being Father Donovan, although slightly impatient for closer\nacquaintance with the former.\n\nWhen breakfast was done with, I ordered the three horses saddled, and\npresently out in the courtyard Paddy was seated on his nag with the\ntwo sacks of pistols before him, and Jem in like manner with his two\nbundles of swords. The stableman held my horse, so I turned to Father\nDonovan and grasped him warmly by the hand.\n\n\"A safe journey across the Channel to you, Father Donovan, and a\npeaceful voyage from there to Rome, whichever road you take. If you\nwrite to me in the care of the landlord of this inn I'll be sending\nand sending till I get your letter, and when you return I'll be\nstanding and watching the sea, at whatever point you land in England,\nif you'll but let me know in time. And so good-bye to you, Father\nDonovan, and God bless you, and I humbly beseech your own blessing in\nreturn.\"\n\nThe old man's eyes grew wider and wider as I went on talking and\ntalking and shaking him by the hand.\n\n\"What's come over you, O'Ruddy?\" he said, \"and where are you going?\"\n\n\"I am taking a long journey to the west and must have an early start.\"\n\n\"Nonsense,\" cried Father Donovan, \"it's two or three days before I can\nleave this shore, so I'll accompany you a bit of the way.\"\n\n\"You mustn't think of it, Father, because you had a long day's ride\nyesterday, and I want you to take care of yourself and take thought on\nyour health.\"\n\n\"Tush, I'm as fresh as a boy this morning. Landlord, see that the\nsaddle is put on that horse I came into Rye with.\"\n\nThe landlord at once rushed off and gave the order, while I stood\nthere at my wit's end.\n\n\"Father Donovan,\" said I, \"I'm in great need of haste at this moment,\nand we must ride fast, so I'll just bid good-bye to you here at this\ncomfortable spot, and you'll sit down at your ease in that big\narm-chair.\"\n\n\"I'll do nothing of the kind, O'Ruddy. What's troubling you, man? and\nwhy are you in such a hurry this morning, when you said nothing of it\nyesterday?\"\n\n\"Father, I said nothing of it yesterday, but sure I acted it. See how\nwe rode on and on in spite of everything, and did the whole journey\nfrom London to Rye between breakfast and supper. Didn't that give you\na hint that I was in a hurry?\"\n\n\"Well, it should have done, it should have done, O'Ruddy; still, I'll\ngo a bit of the way with you and not delay you.\"\n\n\"But we intend to ride very fast, Father.\"\n\n\"Ah, it's an old man you're thinking I'm getting to be. Troth, I can\nride as fast as any one of the three of you, and a good deal faster\nthan Paddy.\"\n\nAt this moment the landlord came bustling in.\n\n\"Your Reverence's horse is ready,\" he said.\n\nAnd so there was nothing for it but to knock the old man down, which I\nhadn't the heart to do. It is curious how stubborn some people are;\nbut Father Donovan was always set in his ways, and so, as we rode out\nof Rye to the west, with Paddy and Jem following us, I had simply to\ntell his Reverence all about it, and you should have seen the\nconsternation on his countenance.\n\n\"Do you mean to tell me you propose to take possession of another\nman's house and fight him if he comes to claim his own?\"\n\n\"I intend that same thing, your Reverence;\" for now I was as stubborn\nas the old gentleman himself, and it was not likely I was going to be\nput off my course when I remembered the happiness that was ahead of\nme; but there's little use in trying to explain to an aged priest what\na young man is willing to do for the love of the sweetest girl in all\nthe land.\n\n\"O'Ruddy,\" he said, \"you'll be put in prison. It's the inside of a\ngaol, and not the inside of a castle, you'll see. It's not down the\naisle of a church you'll march with your bride on your arm, but its\nhobbling over the cobbles of a Newgate passage you'll go with manacles\non your legs. Take warning from me, my poor boy, who would be\nheart-broken to see harm come to you, and don't run your neck into the\nhangman's noose, thinking it the matrimonial halter. Turn back while\nthere's yet time, O'Ruddy.\"\n\n\"Believe me, Father Donovan, it grieves me to refuse you anything, but\nI cannot turn back.\"\n\n\"You'll be breaking the law of the land.\"\n\n\"But the law of the land is broken every day in our district of\nIreland, and not too many words said about it.\"\n\n\"Oh, O'Ruddy, that's a different thing. The law of the land in Ireland\nis the law of the alien.\"\n\n\"Father, you're not logical. It's the alien I'm going to fight\nhere,\"--but before the father could reply we saw ahead of us the bulky\nform of Tom Peel, and ranged alongside of the road, trying to look\nvery stiff and military-like, was the most awkward squad of men I had\never clapped eyes on; but determined fellows they were, as I could see\nat a glance when I came fornenst them, and each man pulled a lock of\nhis hair by way of a salute.\n\n\"Do you men understand the use of a sword and a pistol?\" said I.\n\nThe men smiled at each other as though I was trying some kind of a\njoke on them.\n\n\"They do, your honour,\" answered Tom Peel on their behalf. \"Each one\nof them can sling a cutlass to the king's taste, and fire a pistol\nwithout winking, and there are now concealed in the hedge half a dozen\nblunderbusses in case they should be needed. They make a loud report\nand have a good effect on the enemy, even when they do no harm.\"\n\n\"Yes, we'll have the blunderbusses,\" said I, and with that the men\nbroke rank, burst through the hedge, and came back with those\nformidable weapons. \"I have ammunition in the carts,\" I said, \"did you\nsee anything of them?\"\n\n\"The carts have gone on to the west, your honour; but we'll soon\novertake them,\" and the men smacked their lips when they thought of\nthe one that had the barrels in it. Now Paddy came forward with the\npistols, and Bottles followed and gave each man a blade, while I gave\neach his money.\n\n\"O dear! O dear!\" groaned Father Donovan.\n\n\"There's just a chance we may be attacked before we get to Brede, and,\nFather, though I am loath to say good-bye, still it must be said. It's\nrare glad I'll be when I grip your hand again.\"\n\n\"All in good time; all in good time,\" said Father Donovan; \"I'll go a\nbit farther along the road with you and see how your men march. They\nwould fight better and better behind a hedge than in the open, I'm\nthinking.\"\n\n\"They'll not have to fight in the open, Father,\" said I, \"but they'll\nbe comfortably housed if we get there in time. Now, Peel, I make you\ncaptain of the men, as you've got them together, and so, Forward, my\nlads.\"\n\nThey struck out along the road, walking a dozen different kinds of\nsteps, although there were only nine of them; some with the swords\nover their shoulders, some using them like walking-sticks, till I told\nthem to be more careful of the points; but they walked rapidly and got\nover the ground, for the clank of the five guineas that was in each\nman's pocket played the right kind of march for them.\n\n\"Listen to reason, O'Ruddy, and even now turn back,\" said Father\nDonovan.\n\n\"I'll not turn back now,\" said I, \"and, sure, you can't expect it of\nme. You're an obstinate man yourself, if I must say so, Father.\"\n\n\"It's a foolhardy exploit,\" he continued, frowning. \"There's prison at\nthe end of it for some one,\" he murmured.\n\n\"No, it's the House of Brede, Father, that's at the end of it.\"\n\n\"Supposing the Earl of Westport brings a thousand men against\nyou,--what are you going to do?\"\n\n\"Give them the finest fight they have ever seen in this part of\nEngland.\"\n\nIn spite of himself I saw a sparkle in Father Donovan's eye. The\nnationality of him was getting the better of his profession.\n\n\"If it were legitimate and lawful,\" at last he said, \"it would be a\nfine sight to see.\"\n\n\"It will be legitimate and lawful enough when the Earl and myself come\nto terms. You need have no fear that we're going to get into the\ncourts, Father.\"\n\n\"Do you think he'll fight?\" demanded the father suddenly, with a glint\nin his eyes that I have seen in my own father's when he was telling us\nof his battles in France.\n\n\"Fight? Why of course he'll fight, for he's as full of malice as an\negg's full of meat; but nevertheless he's a sensible old curmudgeon,\nwhen the last word's said, and before he'll have it noised over\nEngland that his title to the land is disputed he'll give me what I\nwant, although at first he'll try to master me.\"\n\n\"Can you depend on these men?\"\n\n\"I think I can. They're old smugglers and pirates, most of them.\"\n\n\"I wonder who the Earl will bring against you?\" said Father Donovan,\nspeaking more to himself than to me. \"Will it be farmers or regular\nsoldiers?\"\n\n\"I expect they will be from among his own tenantry; there's plenty of\nthem, and they'll all have to do his bidding.\"\n\n\"But that doesn't give a man courage in battle?\"\n\n\"No, but he'll have good men to lead them, even if he brings them from\nLondon.\"\n\n\"I wouldn't like to see you attacked by real soldiers; but I think\nthese men of yours will give a good account of themselves if there's\nonly peasantry brought up against them. Sure, the peasantry in this\ncountry is not so warlike as in our own,\"--and there was a touch of\npride in the father's remark that went to my very heart.\n\nAfter riding in silence for a while, meditating with head bowed, he\nlooked suddenly across at me, his whole face lighted up with delicious\nremembrance.\n\n\"Wouldn't you like to have Mike Sullivan with you this day,\" he cried,\nnaming the most famous fighter in all the land, noted from Belfast to\nour own Old Head of Kinsale.\n\n\"I'd give many a guinea,\" I said, \"to have Mike by my side when the\nEarl comes on.\"\n\nThe old father suddenly brought down his open hand with a slap on his\nthigh.\n\n\"I'm going to stand by you, O'Ruddy,\" he said.\n\n\"I'm glad to have your blessing on the job at last, Father,\" said I;\n\"for it was sore against me to go into this business when you were in\na contrary frame of mind.\"\n\n\"You'll not only have my blessing, O'Ruddy, but myself as well. How\ncould I sail across the ocean and never know which way the fight came\nout? and then, if it is to happen in spite of me, the Lord pity the\nfrailness of mankind, but I'd like to see it. I've not seen a debate\nsince the Black Fair of Bandon.\"\n\nBy this time we had overtaken the hirelings with their carts, and the\nmen were swinging past them at a good pace.\n\n\"Whip up your horses,\" said I to the drivers, \"and get over the ground\na little faster. It's not gunpowder that's in those barrels, and when\nwe reach the house there will be a drink for every one of you.\"\n\nThere was a cheer at this, and we all pushed on with good hearts. At\nlast we came to a lane turning out from the main road, and then to the\nprivate way through fields that led to Brede House. So far there had\nbeen no one to oppose us, and now, setting spurs to our horses, we\ngalloped over the private way, which ran along the side of a gentle\nhill until one end of the mansion came into view. It seemed likely\nthere was no suspicion who we were, for a man digging in the garden,\nstood up and took off his cap to us. The front door looked like the\nGothic entrance of a church, and I sprang from my horse and knocked\nloudly against the studded oak. An old man opened the door without any\nmeasure of caution, and I stepped inside. I asked him who he was, and\nhe said he was the caretaker.\n\n\"How many beside yourself are in this house?\"\n\nHe said there was only himself, his wife, and a kitchen wench, and two\nof the gardeners, while the family was in London.\n\n\"Well,\" said I, \"I'd have you know that I'm the family now, and that\nI'm at home. I am the owner of Brede estate.\"\n\n\"You're not the Earl of Westport!\" said the old man, his eyes opening\nwide.\n\n\"No, thank God, I'm not!\"\n\nHe now got frightened and would have shut the door, but I gently\npushed him aside. I heard the tramp of the men, and, what was more,\nthe singing of a sea song, for they were nearing the end of their walk\nand thinking that something else would soon pass their lips besides\nthe tune. The old man was somewhat reassured when he saw the priest\ncome in; but dismay and terror took hold of him when the nine men with\ntheir blunderbusses and their swords came singing around a corner of\nthe house and drew up in front of it. By and by the carts came\ncreaking along, and then every man turned to and brought the\nprovisions inside of the house and piled them up in the kitchen in an\norderly way, while the old man, his wife, the wench, and the two\ngardeners stood looking on with growing signs of panic upon them.\n\n\"Now, my ancient caretaker,\" said I to the old man, in the kindest\ntones I could bring to my lips, so as not to frighten him more than\nwas already the case, \"what is the name of that little village over\nyonder?\" and I pointed toward the west, where, on the top of a hill,\nappeared a church and a few houses.\n\n\"That, sir,\" he said, with his lips trembling, \"is the village of\nBrede.\"\n\n\"Is there any decent place there where you five people can get\nlodging; for you see that this house is now filled with men of war,\nand so men of peace should be elsewhere? Would they take you in over\nat the village?\"\n\n\"Yes, sir, it is like they would.\"\n\n\"Very well. Here is three guineas to divide among you, and in a week\nor thereabouts you will be back in your own place, so don't think\ndisaster has fallen on you.\"\n\nThe old man took the money, but seemed in a strange state of hesitancy\nabout leaving.\n\n\"You will be unhappy here,\" I said, \"for there will be gun-firing and\nsword-playing. Although I may not look it, I am the most bloodthirsty\nswordsman in England, with a mighty uncertain temper on me at times.\nSo be off, the five of you!\"\n\n\"But who is to be here to receive the family?\" he asked.\n\n\"What family?\"\n\n\"Sir, we had word last night that the Earl of Westport and his\nfollowing would come to this house to-day at two of the clock, and we\nhave much ado preparing for them; for the messenger said that he was\nbringing many men with him. I thought at first that you were the men,\nor I would not have let you in.\"\n\n\"Now the Saints preserve us,\" cried I, \"they'll be on us before we get\nthe windows barricaded. Tom Peel,\" I shouted, \"set your men to prepare\nthe defence at once, and you'll have only a few hours to do it in.\nCome, old man, take your wife and your gardeners, and get away.\"\n\n\"But the family, sir, the family,\" cried the old man, unable to\nunderstand that they should not be treated with the utmost respect.\n\n\"I will receive the family. What is that big house over there in the\nvillage?\"\n\n\"The Manor House, sir.\"\n\n\"Very well, get you gone, and tell them to prepare the Manor House for\nthe Earl of Westport and his following; for he cannot lodge here\nto-night,\"--and with that I was compelled to drag them forth, the old\nwoman crying and the wench snivelling in company. I patted the ancient\nwife on the shoulder and told her there was nothing to be feared of;\nbut I saw my attempt at consolation had little effect.\n\nTom Peel understood his business; he had every door barred and\nstanchioned, and the windows protected, as well as the means to his\nhand would allow. Up stairs he knocked out some of the diamond panes\nso that the muzzle of a blunderbuss would go through. He seemed to\nknow the house as if it was his own; and in truth the timbers and\nmaterials for defence which he conjured up from the ample cellars or\npulled down from the garret seemed to show that he had prepared the\nplace for defence long since.\n\n\"Your honour,\" he said, \"two dangers threaten this house which you may\nnot be aware of.\"\n\n\"And what are those, Tom?\" I asked.\n\n\"Well, the least serious one is the tunnel. There is a secret passage\nfrom this house down under the valley and out and up near the church.\nIf it was not guarded they could fill this house unknown to you. I\nwill stop this end of it with timber if your honour gives the word.\nThere's not many knows of it, but the Earl of Westport is certain to\nhave the knowledge, and some of his servants as well.\"\n\n\"Lead me to this tunnel, Tom,\" said I, astonished at his information.\n\nWe came to a door in one of the lower rooms that opened on a little\ncircular stone stairway, something like a well, and, going down to the\nbottom, we found a tunnel in which a short man could stand upright.\n\n\"Thunder and turf, Tom!\" said I, \"what did they want this for?\"\n\n\"Well, some thought it was to reach the church, but no one ever lived\nin this house that was so anxious to get to church that he would go\nunderground to it. Faith, they've been a godless lot in Brede Place\nuntil your honour came, and we were glad to see you bring a priest\nwith you. It put new heart in the men; they think he'll keep off Sir\nGoddard Oxenbridge.\"\n\n\"Does he live near here? What has he to do with the place?\"\n\n\"He is dead long since, sir, and was owner of this house. Bullet\nwouldn't harm him, nor steel cut him, so they sawed him in two with a\nwooden saw down by the bridge in front. He was a witch of the very\nworst kind, your honour. You hear him groaning at the bridge every\nnight, and sometimes he walks through the house himself in two halves,\nand then every body leaves the place. And that is our most serious\ndanger, your honour. When Sir Goddard takes to groaning through these\nrooms at night, you'll not get a man to stay with you, sir; but as he\ncomes up from the pit by the will of the Devil we expect his Reverence\nto ward him off.\"\n\nNow this was most momentous news, for I would not stop in the place\nmyself if a ghost was in the habit of walking through it; but I\ncheered up Tom Peel by telling him that no imp of Satan could appear\nin the same county as Father Donovan, and he passed on the word to the\nmen, to their mighty easement.\n\nWe had a splendid dinner in the grand hall, and each of us was well\nprepared for it; Father Donovan himself, standing up at the head of\nthe table, said the holy words in good Latin, and I was so hungry that\nI was glad the Latins were in the habit of making short prayers.\n\nFather Donovan and I sat at table with a bottle for company, and now\nthat he knew all about the situation, I was overjoyed to find him an\ninhabitant of the same house; for there was no gentleman in all the\ncompany, except himself, for me to talk with.\n\nSuddenly there was a blast of a bugle, and a great fluttering outside.\nThe lower windows being barricaded, it was not possible to see out of\nthem, and I was up the stair as quick as legs could carry me; and\nthere in front were four horses harnessed to a great carriage, and in\nit sat the old Earl and the Countess, and opposite them who but Lady\nMary herself, and her brother, Lord Strepp. Postilions rode two of the\nhorses, and the carriage was surrounded by a dozen mounted men.\n\nEverybody was looking at the house and wondering why nobody was there\nto welcome them, and very forbidding this stronghold must have seemed\nto those who expected to find the doors wide open when they drove up.\nI undid the bolts of one of the diamond-paned windows, and, throwing\nit open, leaned with my arms on the sill, my head and shoulders\noutside.\n\n\"Good day to your ladyship and your lordship,\" I cried,--and then all\neyes were turned on me,--\"I have just this day come into my\ninheritance, and I fear the house is not in a state to receive\nvisitors. The rooms are all occupied by desperate men and armed; but I\nhave given orders to your servants to prepare the Manor House in the\nvillage for your accommodation; so, if you will be so good as to drive\nacross the valley, you will doubtless meet with a better reception\nthan I can give you at this moment. When you come again, if there are\nno ladies of the party, I can guarantee you will have no complaint to\nmake of the warmth of your reception.\"\n\nHis lordship sat dumb in his carriage, and for once her ladyship\nappeared to find difficulty in choosing words that would do justice to\nher anger. I could not catch a glimpse of Lady Mary's face at all at\nall, for she kept it turned toward the village; but young Lord Strepp\nrose in the carriage, and, shaking his fist at me, said:\n\n\"By God, O'Ruddy, you shall pay for this;\" but the effect of the words\nwas somewhat weakened by reason that his sister, Lady Mary, reached\nout and pulled him by the coat-tails, which caused him to be seated\nmore suddenly than he expected; then she gave me one rapid glance of\nher eye and turned away her face again.\n\nNow his lordship, the great Earl of Westport, spoke, but not to me.\n\n\"Drive to the village,\" he said to the postilions; then horsemen and\ncarriage clattered down the hill.\n\nWe kept watch all that night, but were not molested. In the southern\npart of the house Father Donovan found a well-furnished chapel, and\nnext morning held mass there, which had a very quieting effect on the\nmen, especially as Oxenbridge had not walked during the night. The\nonly one of them who did not attend mass was Jem Bottles, who said he\nwas not well enough and therefore would remain on watch. Just as mass\nwas finished Jem appeared in the gallery of the chapel and shouted\nexcitedly:\n\n\"They're coming, sir; they're coming!\"\n\nI never before saw a congregation dismiss themselves so speedily. They\nwere at their posts even before Tom Peel could give the order. The\nopposing party was leaving the village and coming down the hill when I\nfirst caught sight of them from an upper window. There seemed\nsomewhere between half a dozen and a dozen horsemen, and behind them a\ngreat mob of people on foot that fairly covered the hillside. As they\ncrossed the brook and began to come up, I saw that their leader was\nyoung Lord Strepp himself, and Jem whispered that the horsemen behind\nhim were the very men he had encountered on the road between London\nand Maidstone. The cavalry were well in advance, and it seemed that\nthe amateur infantry took less and less pleasure in their excursion\nthe nearer they drew to the gloomy old house, so much so that Lord\nStrepp turned back among them and appeared to be urging them to make\nhaste. However, their slow progress may be explained by the fact that\na certain number of them were carrying a huge piece of timber, so\nheavy that they had to stagger along cautiously.\n\n\"That,\" said Tom Peel, who stood at my elbow, \"is to batter in the\nfront door and take us by storm. If you give the word, your honour, we\ncan massacre the lot o' them before they get three blows struck.\"\n\n\"Give command to the men, Peel,\" said I, \"not to shoot any one if they\ncan help it. Let them hold their fire till they are within fifty yards\nor so of the front, then pass the word to fire into the gravel of the\nterrace; and when you shoot let every man yell as if he were a dozen,\nand keep dead silence till that moment. I'll hold up my hand when I\nwant you to fire.\"\n\nThere was a deep stillness over all the beautiful landscape. The\nbushes and the wood, however, were an exception to this, although the\nsongs of the birds among the trees and singing of the larks high in\nthe air seemed not to disturb the silence; but the whole air of the\ncountry-side was a suggestion of restful peace, at great variance with\nthe designs of the inhabitants, who were preparing to attack each\nother.\n\nFather Donovan stood beside me, and I saw his lips moving in prayer;\nbut his eyes were dancing with irredeemable delight, while his breath\ncame quick and expectant.\n\n\"I'm afraid those chaps will run at the first volley,\" he said,\nsmiling at me. \"They come on very slowly and must be a great trial to\nthe young lord that's leading them.\"\n\nIt was indeed a trial to the patience of all of us, for the time\nseemed incredibly long till they arrived at the spot where I had\ndetermined they should at least hear the report of the blunderbusses,\nalthough I hoped none of them would feel the effects of the firing.\nIndeed, the horsemen themselves, with the exception of Lord Strepp,\nappeared to take little comfort in their position, and were now more\nanxious to fall behind and urge on the others on foot than to lead the\nband with his lordship.\n\nI let them all get very close, then held up my hand, and you would\nthink pandemonium was let loose. I doubt if all the cannon in Cork\nwould have made such a noise, and the heathen Indians we read of in\nAmerica could not have given so terrifying a yell as came from my nine\nmen. The blunderbusses were more dangerous than I supposed, and they\ntore up the gravel into a shower of small stones that scattered far\nand wide, and made many a man fall down, thinking he was shot. Then\nthe mob ran away with a speed which made up for all lost time coming\nthe other direction. Cries of anguish were heard on every side, which\nmade us all laugh, for we knew none of them were hurted. The horses\nthemselves seemed seized with panic; they plunged and kicked like mad,\ntwo riders being thrown on the ground, while others galloped across\nthe valley as if they were running away; but I suspect that their\nowners were slyly spurring them on while pretending they had lost\ncontrol of them. Lord Strepp and one or two others, however, stood\ntheir ground, and indeed his lordship spurred his horse up opposite\nthe front door. One of my men drew a pistol, but I shouted at him:\n\n\"Don't shoot at that man, whatever he does,\" and the weapon was\nlowered.\n\nI opened the window and leaned out.\n\n\"Well, Lord Strepp,\" cried I, \"'tis a valiant crowd you have behind\nyou.\"\n\n\"You cursed highwayman,\" he cried, \"what do you expect to make by\nthis?\"\n\n\"I expect to see some good foot-racing; but you are under an error in\nyour appellation. I am not a highwayman; it is Jem Bottles here who\nstopped nine of your men on the Maidstone road and piled their saddles\nby the side of it. Is it new saddlery you have, or did you make a\nroadside collection?\"\n\n\"I'll have you out of that, if I have to burn the house over your\nhead.\"\n\n\"I'll wager you'll not get any man, unless it's yourself, to come near\nenough to carry a torch to it. You can easily have me out of this\nwithout burning the house. Tell your father I am ready to compromise\nwith him.\"\n\n\"Sir, you have no right in my father's house; and, to tell you the\ntruth, I did not expect such outlawry from a man who had shown himself\nto be a gentleman.\"\n\n\"Thank you for that, Lord Strepp; but, nevertheless, tell your father\nto try to cultivate a conciliatory frame of mind, and let us talk the\nmatter over as sensible men should.\"\n\n\"We cannot compromise with you, O'Ruddy,\" said Lord Strepp in a very\ndetermined tone, which for the first time made me doubt the wisdom of\nmy proceedings; for of course it was a compromise I had in mind all\nthe time, for I knew as well as Father Donovan that if he refused to\nsettle with me my position was entirely untenable.\n\n\"We cannot compromise with you,\" went on the young man. \"You have no\nright, legal or moral, to this place, and you know it. I have advised\nmy father to make no terms with you. Good day to you, sir.\"\n\nAnd with that he galloped off, while I drew a very long face as I\nturned away.\n\n\"Father Donovan,\" I said, when I had closed the window, \"I am not sure\nbut your advice to me on the way here was nearer right than I thought\nat the time.\"\n\n\"Oh, not a bit of it,\" cried Father Donovan cheerfully. \"You heard\nwhat the young man said, that he had advised his father not to make\nany terms with you. Very well, that means terms have been proposed\nalready; and this youth rejects the wisdom of age, which I have known\nto be done before.\"\n\n\"You think, then, they will accept a conference?\"\n\n\"I am sure of it. These men will not stand fire, and small blame to\nthem. What chance have they? As your captain says, he could annihilate\nthe lot of them before they crushed in the front door. The men who ran\naway have far more sense than that brainless spalpeen who led them on,\nalthough I can see he is brave enough. One or two more useless attacks\nwill lead him to a more conciliatory frame of mind, unless he appeals\nto the law, which is what I thought he would do; for I felt sure a\nsheriff would be in the van of attack. Just now you are opposed only\nto the Earl of Westport; but, when the sheriff comes on, you're\nfornenst the might of England.\"\n\nThis cheered me greatly, and after a while we had our dinner in peace.\nThe long afternoon passed slowly away, and there was no rally in the\nvillage, and no sign of a further advance; so night came on and\nnothing had been done. After supper I said good-night to Father\nDonovan, threw myself, dressed as I was, on the bed, and fell into a\ndoze. It was toward midnight when Tom Peel woke me up; that man seemed\nto sleep neither night nor day; and there he stood by my bed, looking\nlike a giant in the flicker of the candle-light.\n\n\"Your honour,\" he said, \"I think there's something going on at the\nmouth of the tunnel. Twice I've caught the glimpse of a light there,\nalthough they're evidently trying to conceal it.\"\n\nI sat up in bed and said:\n\n\"What do you propose to do?\"\n\n\"Well, there's a man inside here that knows the tunnel just as well as\nI do,--every inch of it,--and he's up near the other end now. If a\ncompany begins coming in, my man will run back without being seen and\nlet us know. Now, sir, shall I timber this end, or shall we deal with\nthem at the top of the stair one by one as they come up. One good\nswordsman at the top of the stair will prevent a thousand getting into\nthe house.\"\n\n\"Peel,\" said I, \"are there any stones outside, at the other end of the\ntunnel?\"\n\n\"Plenty. There's a <DW18> of loose stones fronting it.\"\n\n\"Very well; if your man reports that any have entered the tunnel,\nthey'll have left one or two at the other end on guard; take you five\nof your most trusted men, and go you cautiously a roundabout way\nuntil you are within striking distance of the men on guard. Watch the\nfront upper windows of this house; and if you see two lights\ndisplayed, you will know they are in the tunnel. If you waited here\ntill your man comes back, you would be too late; so go now, and, if\nyou see the two lights, overpower the men at the mouth of the tunnel\nunless they are too many for you. If they are, then there's nothing to\ndo but retreat. When you have captured the guard, make them go down\ninto the tunnel; then you and your men tear down the <DW18> and fill the\nhole full of stones; I will guard this end of the passage.\"\n\nTom Peel pulled his forelock and was gone at once, delighted with his\ntask. I knew that if I got them once in the tunnel there would no\nlonger be any question of a compromise, even if Lord Strepp himself\nwas leading them. I took two lighted candles with me and sat patiently\nat the head of the stone stairway that led, in circular fashion, down\ninto the depths. Half an hour passed, but nothing happened, and I\nbegan to wonder whether or not they had captured our man, when\nsuddenly his face appeared.\n\n\"They are coming, sir,\" he cried, \"by the dozen. Lord Strepp is\nleading them.\"\n\n\"Will they be here soon, do you think?\"\n\n\"I cannot tell. First I saw torches appear, then Lord Strepp came down\nand began giving instructions, and, after counting nearly a score of\nhis followers, I came back as quick as I could.\"\n\n\"You've done nobly,\" said I. \"Now stand here with this sword and\nprevent any man from coming up.\"\n\nI took one of the candles, leaving him another, and lighted a third. I\nwent up the stair and set them in the front window; then I opened\nanother window and listened. The night was exceedingly still,--not\neven the sound of a cricket to be heard. After a few minutes, however,\nthere came a cry, instantly smothered, from the other side of the\nvalley; another moment and I heard the stones a rolling, as if the\nside of a wall had tumbled over, which indeed was the case; then two\nlights were shown on the hill and were waved up and down; and although\nPeel and I had arranged no signal, yet this being the counterpart of\nmy own, I took to signify that they had been successful, so, leaving\nthe candles burning there, in case there might have been some mistake,\nI started down the stair to the man who was guarding the secret\npassage.\n\n\"Has anything happened?\"\n\n\"Nothing, sir.\"\n\nI think the best part of an hour must have passed before there was\nsign or sound. Of course I knew if the guards were flung down the\nhole, they would at once run after their comrades and warn them that\nboth ends of the tunnel were in our possession. I was well aware that\nthe imprisoned men might drag away the stones and ultimately win a\npassage out for themselves; but I trusted that they would be\npanic-stricken when they found themselves caught like rats in a trap.\nIn any case it would be very difficult to remove stones from below in\nthe tunnel, because the space was narrow and few could labour at a\ntime; then there was every chance that the stones might jam, when\nnothing could be done. However, I told the man beside me to go across\nthe valley and ask Peel and his men to pile on rocks till he had a\ngreat heap above the entrance, and, if not disturbed, to work till\nnearly daylight, so I sat on the top of the circular stair step with\nmy rapier across my knees, waiting so long that I began to fear they\nall might be smothered, for I didn't know whether the stopping of air\nat one end would prevent it coming in at the other, for I never heard\nmy father say what took place in a case like that. Father Donovan was\nin bed and asleep, and I was afraid to leave the guarding of the stair\nto any one else. It seemed that hours and hours passed, and I began to\nwonder was daylight never going to come, when the most welcome sound I\never heard was the well-known tones of a voice which came up from the\nbottom of the well.\n\n\"Are you there, Mr. O'Ruddy?\"\n\nThere was a subdued and chastened cadence in the inquiry that pleased\nme.\n\n\"I am, and waiting for you.\"\n\n\"May I come up?\"\n\n\"Yes, and very welcome; but you'll remember, Lord Strepp, that you\ncome up as a prisoner.\"\n\n\"I quite understand that, Mr. O'Ruddy.\"\n\nSo, as I held the candle, I saw the top of his head coming round and\nround and round, and finally he stood before me stretching out his\nsword, hilt forward.\n\n\"Stick it in its scabbard,\" said I, \"and I'll do the same with mine.\"\nThen I put out my hand, \"Good morning to your lordship,\" I said. \"It\nseems to me I've been waiting here forty days and forty nights. Will\nyou have a sup of wine?\"\n\n\"I would be very much obliged to you for it, Mr. O'Ruddy.\"\n\nWith that I called the nearest guard and bade him let nobody up the\nstair without my knowing it.\n\n\"I suppose, my lord, you are better acquainted with this house than I\nam; but I know a spot where there's a drop of good drink.\"\n\n\"You have discovered the old gentleman's cellar, then?\"\n\n\"Indeed, Lord Strepp, I have not. I possess a cellar of my own. It's\nyou that's my guest, and not me that's yours on this occasion.\"\n\nI poured him out a flagon, and then one for myself, and as we stood by\nthe table I lifted it high and said:\n\n\"Here's to our better acquaintance.\"\n\nHis lordship drank, and said with a wry face, as he put down the mug:\n\n\"Our acquaintance seems to be a somewhat tempestuous one; but I\nconfess, Mr. O'Ruddy, that I have as great a respect for your\ngeneralship as I have for your swordsmanship. The wine is good and\nrevivifying. I've been in that accursed pit all night, and I came to\nthis end of it with greater reluctance than I expected to when I\nentered the other. We tried to clear away the stones; but they must\nhave piled all the rocks in Sussex on top of us. Are your men toiling\nthere yet?\"\n\n\"Yes, they're there, and I gave them instructions to work till\ndaylight.\"\n\n\"Well, Mr. O'Ruddy, my poor fellows are all half dead with fright, and\nthey fancy themselves choking; but although the place was foul enough\nwhen we entered it, I didn't see much difference at the end. However,\nI did see one thing, and that was that I had to come and make terms. I\nwant you to let the poor devils go, Mr. O'Ruddy, and I'll be parole\nthat they won't attack you again.\"\n\n\"And who will give his parole that Lord Strepp will not attack me\nagain?\"\n\n\"Well, O'Ruddy,\"--I took great comfort from the fact that he dropped\nthe Mr.,--\"Well, O'Ruddy, you see we cannot possibly give up this\nestate. You are not legally entitled to it. It is ours and always has\nbeen.\"\n\n\"I'm not fighting for any estate, Lord Strepp.\"\n\n\"Then, in Heaven's name, what are you fighting for?\"\n\n\"For the consent of the Earl and Countess of Westport to my marriage\nwith Lady Mary, your sister.\"\n\nLord Strepp gave a long whistle; then he laughed and sat down in the\nnearest chair.\n\n\"But what does Mary say about it?\" he asked at last.\n\n\"The conceit of an Irishman, my lord, leads me to suspect that I can\nultimately overcome any objections she may put forward.\"\n\n\"Oho! that is how the land lies, is it? I'm a thick-headed clod, or I\nwould have suspected something of that sort when Mary pulled me down\nso sharply as I was cursing you at the front door.\" Then, with a\nslight touch of patronage in his tone, he said:\n\n\"There is some difference in the relative positions of our families,\nMr. O'Ruddy.\"\n\n\"Oh, I'm quite willing to waive that,\" said I. \"Of course it isn't\nusual for the descendant of kings, like myself, to marry a daughter of\nthe mere nobility; but Lady Mary is so very charming that she more\nthan makes up for any discrepancy, whatever may be said for the rest\nof the family.\"\n\nAt this Lord Strepp threw back his head and laughed again joyously,\ncrying,--\n\n\"King O'Ruddy, fill me another cup of your wine, and I'll drink to\nyour marriage.\"\n\nWe drank, and then he said:\n\n\"I'm a selfish beast, guzzling here when those poor devils think\nthey're smothering down below. Well, O'Ruddy, will you let my unlucky\nfellows go?\"\n\n\"I'll do that instantly,\" said I, and so we went to the head of the\ncircular stair and sent the guard down to shout to them to come on,\nand by this time the daylight was beginning to turn the upper windows\ngrey. A very bedraggled stream of badly frightened men began crawling\nup and up and up the stairway, and as Tom Peel had now returned I\nasked him to open the front door and let the yeomen out. Once on the\nterrace in front, the men seemed not to be able to move away, but\nstood there drawing in deep breaths of air as if they had never tasted\nit before. Lord Strepp, in the daylight, counted the mob, asking them\nif they were sure every one had come up, but they all seemed to be\nthere, though I sent Tom Peel down along the tunnel to find if any had\nbeen left behind.\n\nLord Strepp shook hands most cordially with me at the front door.\n\n\"Thank you for your hospitality, O'Ruddy,\" he said, \"although I came\nin by the lower entrance. I will send over a flag of truce when I've\nseen my father; then I hope you will trust yourself to come to the\nManor House and have a talk with him.\"\n\n\"I'll do it with pleasure,\" said I.\n\n\"Good morning to you,\" said Lord Strepp.\n\n\"And the top o' the morning to you, which is exactly what we are\ngetting at this moment, though in ten minutes I hope to be asleep.\"\n\n\"So do I,\" said Lord Strepp, setting off at a run down the <DW72>.\n\n\n\n\nCHAPTER XXXIII\n\n\nOnce more I went to my bed, but this time with my clothes off, for if\nthere was to be a conference with the Earl and the Countess at the\nManor House, not to speak of the chance of seeing Lady Mary herself, I\nwished to put on the new and gorgeous suit I had bought in London for\nthat occasion, and which had not yet been on my back. I was so excited\nand so delighted with the thought of seeing Lady Mary that I knew I\ncould not sleep a wink, especially as daylight was upon me, but I had\nscarcely put my head on the pillow when I was as sound asleep as any\nof my ancestors, the old Kings of Kinsale. The first thing I knew\nPaddy was shaking me by the shoulder just a little rougher than a\nwell-trained servant should.\n\n\"Beggin' your pardon,\" says he, \"his lordship, the great Earl of\nWestport, sends word by a messenger that he'll be pleased to have\naccount with ye, at your early convenience, over at the Manor House\nbeyond.\"\n\n\"Very well, Paddy,\" said I, \"ask the messenger to take my compliments\nto the Earl and say to him I will do myself the honour of calling on\nhim in an hour's time. Deliver that message to him; then come back and\nhelp me on with my new duds.\"\n\nWhen Paddy returned I was still yawning, but in the shake of a\nshillelah he had me inside the new costume, and he stood back against\nthe wall with his hand raised in amazement and admiration at the glory\nhe beheld. He said after that kings would be nothing to him, and\nindeed the tailor had done his best and had won his guineas with more\nhonesty than you'd expect from a London tradesman. I was quietly\npleased with the result myself.\n\nI noticed with astonishment that it was long after mid-day, so it\noccurred to me that Lord Strepp must have had a good sleep himself,\nand sure the poor boy needed it, for it's no pleasure to spend life\nunderground till after you're dead, and his evening in the tunnel must\nhave been very trying to him, as indeed he admitted to me afterward\nthat it was.\n\nI called on Father Donovan, and he looked me over from head to foot\nwith wonder and joy in his eye.\n\n\"My dear lad, you're a credit to the O'Ruddys,\" he said, \"and to\nIreland,\" he said, \"and to the Old Head of Kinsale,\" he said.\n\n\"And to that little tailor in London as well,\" I replied, turning\naround so that he might see me the better.\n\nIn spite of my chiding him Paddy could not contain his delight, and\ndanced about the room like an overgrown monkey.\n\n\"Paddy,\" said I, \"you're making a fool of yourself.\"\n\nThen I addressed his Reverence.\n\n\"Father Donovan,\" I began, \"this cruel war is over and done with, and\nno one hurt and no blood shed, so the Earl--\"\n\nAt this moment there was a crash and an unearthly scream, then a thud\nthat sounded as if it had happened in the middle of the earth. Father\nDonovan and I looked around in alarm, but Paddy was nowhere to be\nseen. Toward the wall there was a square black hole, and, rushing up\nto it, we knew at once what had happened. Paddy had danced a bit too\nheavy on an old trap-door, and the rusty bolts had broken. It had let\nhim down into a dungeon that had no other entrance; and indeed this\nwas a queer house entirely, with many odd nooks and corners about it,\nbesides the disadvantage of Sir Goddard Oxenbridge tramping through\nthe rooms in two sections.\n\n\"For the love of Heaven and all the Saints,\" I cried down this\ntrap-door, \"Paddy, what has happened to you?\"\n\n\"Sure, sir, the house has fallen on me.\"\n\n\"Nothing of the kind, Paddy. The house is where it always was. Are you\nhurted?\"\n\n\"I'm dead and done for completely this time, sir. Sure I feel I'm with\nthe angels at last.\"\n\n\"Tut, tut, Paddy, my lad; you've gone in the wrong direction\naltogether for them.\"\n\n\"Oh, I'm dying, and I feel the flutter of their wings,\" and as he\nspoke two or three ugly blind bats fluttered up and butted their\nstupid heads against the wall.\n\n\"You've gone in the right direction for the wrong kind of angels,\nPaddy; but don't be feared, they're only bats, like them in my own\ntower at home, except they're larger.\"\n\nI called for Tom Peel, as he knew the place well.\n\n\"Many a good cask of brandy has gone down that trap-door,\" said he,\n\"and the people opposite have searched this house from cellar to\ngarret and never made the discovery Paddy did a moment since.\"\n\nHe got a stout rope and sent a man down, who found Paddy much more\nfrightened than hurt. We hoisted both of them up, and Paddy was a\nsight to behold.\n\n\"Bad luck to ye,\" says I; \"just at the moment I want a presentable lad\nbehind me when I'm paying my respects to the Earl of Westport, you\nmust go diving into the refuse heap of a house that doesn't belong to\nyou, and spoiling the clothes that does. Paddy, if you were in a seven\nyears' war, you would be the first man wounded and the last man\nkilled, with all the trouble for nothing in between. Is there anything\nbroken about ye?\"\n\n\"Every leg and arm I've got is broken,\" he whimpered, but Father\nDonovan, who was nearly as much of a surgeon as a priest, passed his\nhand over the trembling lad, then smote him on the back, and said the\nexercise of falling had done him good.\n\n\"Get on with you,\" said I, \"and get off with those clothes. Wash\nyourself, and put on the suit I was wearing yesterday, and see that\nyou don't fall in the water-jug and drown yourself.\"\n\nI gave the order for Tom Peel to saddle the four horses and get six of\nhis men with swords and pistols and blunderbusses to act as an escort\nfor me.\n\n\"Are you going back to Rye, your honour?\" asked Peel.\n\n\"I am not. I am going to the Manor House.\"\n\n\"That's but a step,\" he cried in surprise.\n\n\"It's a step,\" said I, \"that will be taken with dignity and\nconsequence.\"\n\nSo, with the afternoon sun shining in our faces, we set out from the\nhouse of Brede, leaving but few men to guard it. Of course I ran the\nrisk that it might be taken in our absence; but I trusted the word of\nLord Strepp as much as I distrusted the designs of his father and\nmother, and Strepp had been the captain of the expedition against us;\nbut if I had been sure the mansion was lost to me, I would have evaded\nnone of the pomp of my march to the Manor House in the face of such\npride as these upstarts of Westports exhibited toward a representative\nof a really ancient family like the O'Ruddy. So his Reverence and I\nrode slowly side by side, with Jem and Paddy, also on horseback, a\ndecent interval behind us, and tramping in their wake that giant, Tom\nPeel, with six men nearly as stalwart as himself, their blunderbusses\nover their shoulders, following him. It struck panic in the village\nwhen they saw this terrible array marching up the hill toward them,\nwith the sun glittering on us as if we were walking jewellery. The\nvillagers, expecting to be torn limb from limb, scuttled away into the\nforest, leaving the place as empty as a bottle of beer after a wake.\nEven the guards around the Manor House fled as we approached it, for\nthe fame of our turbulence had spread abroad in the land. Lord Strepp\ntried to persuade them that nothing would happen to them, for when he\nsaw the style in which we were coming he was anxious to make a show\nfrom the Westport side and had drawn up his men in line to receive us.\nBut we rode through a silent village that might have been just sacked\nby the French. I thought afterward that this desertion had a subduing\neffect on the old Earl's pride, and made him more easy to deal with.\nIn any case his manner was somewhat abated when he received me. Lord\nStrepp himself was there at the door, making excuses for the servants,\nwho he said had gone to the fields to pick berries for their supper.\nSo, leaving Paddy to hold one horse and Jem the other, with the seven\nmen drawn up fiercely in front of the Manor House, Father Donovan and\nmyself followed Lord Strepp into a large room, and there, buried in an\narm-chair, reclined the aged Earl of Westport, looking none too\npleased to meet his visitors. In cases like this it's as well to be\ngenial at the first, so that you may remove the tension in the\nbeginning.\n\n\"The top of the morning--I beg your pardon--the tail of the afternoon\nto you, sir, and I hope I see you well.\"\n\n\"I am very well,\" said his lordship, more gruffly than politely.\n\n\"Permit me to introduce to your lordship, his Reverence, Father\nDonovan, who has kindly consented to accompany me that he may yield\ntestimony to the long-standing respectability of the House of\nO'Ruddy.\"\n\n\"I am pleased to meet your Reverence,\" said the Earl, although his\nappearance belied his words. He wasn't pleased to meet either of us,\nif one might judge by his lowering countenance, in spite of my\ncordiality and my wish to make his surrender as easy for him as\npossible.\n\nI was disappointed not to see the Countess and Lady Mary in the room,\nfor it seemed a pity that such a costume as mine should be wasted on\nan old curmudgeon, sitting with his chin in his breast in the depths\nof an easy-chair, looking daggers though he spoke dumplings.\n\nI was just going to express my regret to Lord Strepp that no ladies\nwere to be present in our assemblage, when the door opened, and who\nshould sail in, like a full-rigged man-o'-war, but the Countess\nherself, and Lady Mary, like an elegant yacht floating in tow of her.\nI swept my bonnet to the boards of the floor with a gesture that would\nhave done honour to the Court of France; but her Ladyship tossed her\nnose higher in the air, as if the man-o'-war had encountered a huge\nwave. She seated herself with emphasis on a chair, and says I to\nmyself, \"It's lucky for you, you haven't Paddy's trap-door under you,\nor we'd see your heels disappear, coming down like that.\"\n\nLady Mary very modestly took up her position standing behind her\nmother's chair, and, after one timid glance at me, dropped her eyes on\nthe floor, and then there were some moments of silence, as if every\none was afraid to begin. I saw I was going to have trouble with the\nCountess, and although I think it will be admitted by my enemies that\nI'm as brave a man as ever faced a foe, I was reluctant to throw down\nthe gage of battle to the old lady.\n\nIt was young Lord Strepp that began, and he spoke most politely, as\nwas his custom.\n\n\"I took the liberty of sending for you, Mr. O'Ruddy, and I thank you\nfor responding so quickly to my invitation. The occurrences of the\npast day or two, it would be wiser perhaps to ignore--\"\n\nAt this there was an indignant sniff from the Countess, and I feared\nshe was going to open her batteries, but to my amazement she kept\nsilent, although the effort made her red in the face.\n\n\"I have told my father and mother,\" went on Lord Strepp, \"that I had\nsome conversation with you this morning, and that conditions might be\narrived at satisfactory to all parties concerned. I have said nothing\nto my parents regarding the nature of these conditions, but I gained\ntheir consent to give consideration to anything you might say, and to\nany proposal you are good enough to make.\"\n\nThe old gentleman mumbled something incomprehensible in his chair, but\nthe old lady could keep silence no longer.\n\n\"This is an outrage,\" she cried, \"the man's action has been scandalous\nand unlawful. If, instead of bringing those filthy scoundrels against\nour own house, those cowards that ran away as soon as they heard the\nsound of a blunderbuss, we had all stayed in London, and you had had\nthe law of him, he would have been in gaol by this time and not\nstanding brazenly there in the Manor House of Brede.\"\n\nAnd after saying this she sniffed again, having no appreciation of\ngood manners.\n\n\"Your ladyship has been misinformed,\" I said with extreme deference.\n\"The case is already in the hands of dignified men of law, who are\nmightily pleased with it.\"\n\n\"Pleased with it, you idiot,\" she cried. \"They are pleased with it\nsimply because they know somebody will pay them for their work, even\nit's a beggar from Ireland, who has nothing on him but rags.\"\n\n\"Your ladyship,\" said I, not loath to call attention to my costume,\n\"I assure you these rags cost golden guineas in London.\"\n\n\"Well, you will not get golden guineas from Brede estate,\" snapped her\nladyship.\n\n\"Again your ladyship is misinformed. The papers are so perfect, and so\nwell do they confirm my title to this beautiful domain, that the\nmoney-lenders of London simply bothered the life out of me trying to\nshovel gold on me, and both his lordship and your ladyship know that\nif a title is defective there is no money to be lent on it.\"\n\n\"You're a liar,\" said the Countess genially, although the Earl looked\nup in alarm when I mentioned that I could draw money on the papers.\nAgain I bowed deeply to her ladyship, and, putting my hands in my\npockets, I drew out two handfuls of gold, which I strewed up and down\nthe floor as if I were sowing corn, and each guinea was no more than a\ngrain of it.\n\n\"There is the answer to your ladyship's complimentary remark,\" said I\nwith a flourish of my empty hands; and, seeing Lady Mary's eyes\nanxiously fixed on me, I dropped her a wink with the side of my face\nfarthest from the Countess, at which Lady Mary's eyelids drooped\nagain. But I might have winked with both eyes for all the Countess,\nwho was staring like one in a dream at the glittering pieces that lay\nhere and there and gleamed all over the place like the little yellow\ndevils they were. She seemed struck dumb, and if anyone thinks gold\ncannot perform a miracle, there is the proof of it.\n\n\"Is it gold?\" cried I in a burst of eloquence that charmed even\nmyself, \"sure I could sow you acres with it by the crooking of my\nlittle finger from the revenues of my estate at the Old Head of\nKinsale.\"\n\n\"O'Ruddy, O'Ruddy,\" said Father Donovan very softly and reprovingly,\nfor no one knew better than him what my ancestral revenues were.\n\n\"Ah well, Father,\" said I, \"your reproof is well-timed. A man should\nnot boast, and I'll say no more of my castles and my acres, though the\nships on the sea pay tribute to them. But all good Saints preserve us,\nEarl of Westport, if you feel proud to own this poor estate of Brede,\nthink how little it weighed with my father, who all his life did not\ntake the trouble to come over and look at it. Need I say more about\nKinsale when you hear that? And as for myself, did I attempt to lay\nhands on this trivial bit of earth because I held the papers? You know\nI tossed them into your daughter's lap because she was the\nfinest-looking girl I have seen since I landed on these shores.\"\n\n\"Well, well, well, well,\" growled the Earl, \"I admit I have acted\nrashly and harshly in this matter, and it is likely I have done wrong\nto an honourable gentleman, therefore I apologize for it. Now, what\nhave you to propose?\"\n\n\"I have to propose myself as the husband of your daughter, Lady Mary,\nand as for our dowry, there it is on the floor for the picking up, and\nI'm content with that much if I get the lady herself.\"\n\nHis lordship slowly turned his head around and gazed at his daughter,\nwho now was looking full at me with a frown on her brow. Although I\nknew I had depressed the old people, I had an uneasy feeling that I\nhad displeased Lady Mary herself by my impulsive action and my\nbragging words. A curious mildness came into the harsh voice of the\nold Earl, and he said, still looking at his daughter:\n\n\"What does Mary say to this?\"\n\nThe old woman could not keep her eyes from the gold, which somehow\nheld her tongue still, yet I knew she was hearing every word that was\nsaid, although she made no comment. Lady Mary shook herself, as if to\narouse herself from a trance, then she said in a low voice:\n\n\"I can never marry a man I do not love.\"\n\n\"What's that? what's that?\" shrieked her mother, turning fiercely\nround upon her, whereat Lady Mary took a step back. \"Love, love? What\nnonsense is this I hear? You say you will not marry this man to save\nthe estate of Brede?\"\n\n\"I shall marry no man whom I do not love,\" repeated Lady Mary firmly.\n\nAs for me, I stood there, hat in hand, with my jaw dropped, as if\nSullivan had given me a stunning blow in the ear; then the old Earl\nsaid sternly:\n\n\"I cannot force my daughter: this conference is at an end. The law\nmust decide between us.\"\n\n\"The law, you old dotard,\" cried the Countess, rounding then on him\nwith a suddenness that made him seem to shrink into his shell. \"The\nlaw! Is a silly wench to run us into danger of losing what is ours? He\n_shall_ marry her. If you will not force her, then I'll coerce her;\"\nand with that she turned upon her daughter, grasped her by her two\nshoulders and shook her as a terrier shakes a rat. At this Lady Mary\nbegan to weep, and indeed she had good cause to do so.\n\n\"Hold, madam,\" shouted I, springing toward her. \"Leave the girl alone.\nI agree with his lordship, no woman shall be coerced on account of\nme.\"\n\nMy intervention turned the Countess from her victim upon me.\n\n\"You agree with his lordship, you Irish baboon? Don't think she'll\nmarry you because of any liking for you, you chattering ape, who\nresemble a monkey in a show with those trappings upon you. She'll\nmarry you because I say she'll marry you, and you'll give up those\npapers to me, who have sense enough to take care of them. If I have a\ndoddering husband, who at the same time lost his breeches and his\npapers, I shall make amends for his folly.\"\n\n\"Madam,\" said I, \"you shall have the papers; and as for the breeches,\nby the terror you spread around you, I learn they are already in your\npossession.\"\n\nI thought she would have torn my eyes out, but I stepped back and\nsaved myself.\n\n\"To your room, you huzzy,\" she cried to her daughter, and Mary fled\ntoward the door. I leaped forward and opened it for her. She paused on\nthe threshold, pretending again to cry, but instead whispered:\n\n\"My mother is the danger. Leave things alone,\" she said quickly. \"We\ncan easily get poor father's consent.\"\n\nWith that she was gone. I closed the door and returned to the centre\nof the room.\n\n\"Madam,\" said I, \"I will not have your daughter browbeaten. It is\nquite evident she refuses to marry me.\"\n\n\"Hold your tongue, and keep to your word, you idiot,\" she rejoined,\nhitting me a bewildering slap on the side of the face, after which\nshe flounced out by the way her daughter had departed.\n\nThe old Earl said nothing, but gazed gloomily into space from out the\ndepths of his chair. Father Donovan seemed inexpressibly shocked, but\nmy Lord Strepp, accustomed to his mother's tantrums, laughed outright\nas soon as the door was closed. All through he had not been in the\nleast deceived by his sister's pretended reluctance, and recognized\nthat the only way to get the mother's consent was through opposition.\nHe sprang up and grasped me by the hand and said:\n\n\"Well, O'Ruddy, I think your troubles are at an end, or,\" he cried,\nlaughing again, \"just beginning, but you'll be able to say more on\nthat subject this time next year. Never mind my mother; Mary is, and\nalways will be, the best girl in the world.\"\n\n\"I believe you,\" said I, returning his handshake as cordially as he\nhad bestowed it.\n\n\"Hush!\" he cried, jumping back into his seat again. \"Let us all look\ndejected. Hang your head, O'Ruddy!\" and again the door opened, this\ntime the Countess leading Lady Mary, her long fingers grasping that\nslim wrist.\n\n\"She gives her consent,\" snapped the Countess, as if she were\npronouncing sentence. I strode forward toward her, but Mary wrenched\nher wrist free, slipped past me, and dropped at the feet of Father\nDonovan, who had risen as she came in.\n\n\"Your blessing on me, dear Father,\" she cried, bowing her head, \"and\npray on my behalf that there may be no more turbulence in my life.\"\n\nThe old father crossed his hands on her shapely head, and for a moment\nor two it seemed as if he could not command his voice, and I saw the\ntears fill his eyes. At last he said simply and solemnly:--\n\n\"May God bless you and yours, my dear daughter.\"\n\n       *       *       *       *       *\n\nWe were married by Father Donovan with pomp and ceremony in the chapel\nof the old house, and in the same house I now pen the last words of\nthese memoirs, which I began at the request of Lady Mary herself, and\ncontinued for the pleasure she expressed as they went on. If this\nrecital is disjointed in parts, it must be remembered I was always\nmore used to the sword than to the pen, and that it is difficult to\nwrite with Patrick and little Mary and Terence and Kathleen and\nMichael and Bridget and Donovan playing about me and asking questions,\nbut I would not have the darlings sent from the room for all the\nwritings there is in the world.\n\n       *       *       *       *       *\n\n\n\n\n\n\n\nEnd of Project Gutenberg's The O'Ruddy, by Stephen Crane and Robert Barr\n\n*** ","meta":{"redpajama_set_name":"RedPajamaBook"}}
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+{"text":"\n## Table of Contents\n\n  * Dedications\n  * About The Author\n  * Food From Our Ancestors: The Ultimate Italian Sunday Dinner\n  * Introduction\n  * Dina's Tossed Mushrooms\n  * Escarole Soup\n  * Fish Pizzaiola\n  * Olive Scacciata\n  * Pasta e Fagiole\n  * Pizzagaina\n  * Spinach and Potato Frittata\n  * Stuffed Artichokes\n  * Sunday Gravy\n  * Traditional Eggplant Parmigiana\n  * Uncle Vinny's Shrimp Scampi\n  * Chicken Broccoli and Ziti\n\n**Dedications and Thank You**\n\nThis book is dedicated to my sons Asher and Jacob who light up my life every single day. Thank you to my husband Rich for your endless love and unwavering support over the last 15 years. You are my number one fan and I am forever grateful. Thank you for pushing me to follow my dreams.\n\nA special thank you to the Bono Family: Aunt Dolly, Uncle Vinny and cousin Richard, for opening up your kitchen and generously sharing your family recipes and stories with us.\n\nTo all of The Lemon Bowl readers, thank you for all of your support and encouragement over the years. It is because of you that I am able to pursue my passion of cooking. I will forever be grateful.\n\nLastly, thank you to all of my family and friends who have cheered me along and supported my dream over the years. It is because you believed in me that I was able to believe in myself.\nAbout The Author\n\nLiz Della Croce is the creator and author of The Lemon Bowl, a healthy food and travel blog. Since 2010, Liz has grown a loyal following of health-conscious readers from all over the world. Focusing on seasonal ingredients and whole foods, her collection of recipes is inspired by ethnic flavors from around the globe and the Lebanese dishes of her childhood.\n\nLiz has appeared live on the TODAY Show and tapes regular cooking segments on her local NBC affiliate station. Liz been featured in various publications including Real Simple Magazine, Shape Magazine, Food Network blog, Fitness Magazine, The Cooking Channel, TODAY Food and more.\n\nThrough healthy eating and regular exercise, Liz achieved long term weight loss success and has a passion for helping others reach similar goals. In 2013, Liz launched Healthy Habits, a feature on The Lemon Bowl where her loyal readers and growing audience can find practical advice, resources and information on creating and maintaining a healthy lifestyle.\n\nLiz graduated from Boston University with a degree in Hospitality Administration and a minor in Marketing Management. She and her husband reside in Grand Rapids, MI along with their two young boys.\n\nConnect with Liz directly on Instagram, Facebook, Pinterest or via email: Liz@thelemonbowl.com\n\n_Food From Our Ancestors_ : The Ultimate Italian Sunday Dinner\n\nI'll never forget the day I met my husband in 2001. I was living on the East Coast attending Boston University. It was a cold and snowy Sunday afternoon in early December, and we both arrived at the agreed upon place 20 minutes early. While there are many aspects of our first date I'll never forget, what I remember most was what I felt when he told me he had to be home in time for Sunday dinner with his family later that night. I knew right then he was going to get a second date. And probably a few more. Ten years of marriage and two kids later, I'd say my intuition was spot on.\n\nThe first in a series of eCookbooks profiling Sunday dinner across America, this edition is all about my husband's Italian-American family and the incredibly rich food history they've been so gracious to share with me over the years. While I don't have any Italian blood, from the very first time I met Rich's Italian aunts, uncles and cousins, I knew I was home. These were my people. They love hard, fight hard, laugh hard and eat well.\n\nOf course, I couldn't write a book about my husband's Italian family in Boston without also paying homage to the North End. This is the city's oldest residential neighborhood and home to nearly one hundred restaurants and specialty shops. Walking through the cobblestone-lined streets is like strolling through the old country.\n\nWhile the weather isn't usually as balmy as Italy, the energy is quite the same. The smell, the feel, the people, it's unlike anything else. Featuring many family-run, multi-generation establishments and numerous storytellers, there's nothing quite like Boston's North End. The food is still from scratch, the people are as authentic as it gets, and you can still stroll the streets to find freshly baked bread, homemade cheese and cured Italian meats. It's the real deal.\n\nTo help inspire and encourage you to celebrate an Italian-style Sunday dinner, I'm sharing the 12 ultimate Italian recipes from my husband's family with yours. I hope these recipes and photos leave you hungry for more.\n\n_Introduction_\n\nI grew up within a few miles of my entire extended family, and there was always a Sunday dinner, birthday party or holiday gathering taking place. Like any good Middle Eastern family, these events centered around one thing and one thing only: food.\n\nFor whatever reason while my little sisters were busy running around the house, watching TV or playing outside, I always gravitated toward the kitchen. No matter how many cousins were visiting or what movies were playing, all I wanted to do was see what my mom and aunts were cooking together in the kitchen. The endless laughter, the flumes of cigarette smoke, and countless cups of coffee, it was all oddly intoxicating. They were loud, they were funny, and their love for one another was palpable.\n\nFrom as young as five years old I can remember peering over the kitchen counter on my tiptoes begging my mom to let me help her dress the raw turkey at Thanksgiving. I can still picture my Great Aunt Vieve turning a platter of homemade hummus into a piece of artwork with minced parsley, toasted pine nuts and fragrant green onions.\n\nAt the end of the day it didn't matter what they were cooking, I just wanted in. To this day food is my love language, and cooking is my favorite form of therapy.\n\nWhile I didn't always have a healthy relationship with food, I was able to reach a weight loss milestone in my mid-twenties. Through proper portion control and regular exercise, I have successfully maintained a 60-pound weight loss for more than nine years and through two pregnancies.\n\nOver the years one thing has always remained the same: Taking the time to cook from scratch is not only the healthier option, but it's always worth the extra effort. As a busy mother of two little boys I've learned that some of the best scratch cooking also happens to be some of the simplest.\n\nFor me the easiest and most practical answer to healthy cooking comes down to eating the ethnic foods of my ancestors. Naturally more flavorful and more nutritious, I've found that eating ethnic food not only keeps me excited about healthy eating but it prevents me from getting bored and gaining back the weight I've worked so hard to lose.\n\nI wrote _Food From Our Ancestors_ to inspire you to get in the kitchen and gather your friends and family around the dinner table. Whether you're trying to reach a weight loss goal or simply living a healthier life, you'll never regret taking the time to put some thought into the foods you eat. Slowing down in the kitchen and unplugging from the outside world is not only the ultimate way to unwind at the end of a long day, but it is also one of the easiest steps you can take toward living a healthier life.\n\nNo matter what you're cooking, whenever you cook from scratch, you can control the quality of ingredients, which often results in less fat, fewer calories and less sodium than you'll find in a restaurant dish. This book isn't about \"health food,\" it's simply about going back to our roots and cooking the food our forebears ate.\n\nChicken Broccoli and Ziti\n\n_Lighter than the traditional Alfredo-style chicken and broccoli pasta, Aunt Dolly's version is made with a bright and flavorful garlic white wine sauce. Frequently served when the priest would come over for dinner, her children always knew it was a special occasion when chicken broccoli and ziti was on the menu._\n\nServes 4-6.\n\nIngredients\n\n  * \u00bc cup olive oil\n  * 6 cloves garlic, minced\n  * 4 six-ounce boneless, skinless chicken breasts, cubed\n  * salt and pepper to taste\n  * 4 cups broccoli, cut into bite-sized florets\n  * 1 cup dry white wine\n  * 1 \u00bd cups low sodium chicken broth\n  * 6 ounces shredded part-skim mozzarella cheese\n  * grated Parmesan cheese\n  * 1 pound ziti pasta (or short cut pasta of choice)\n\nDirections\n\n  1. Heat olive oil in a large pan over medium-high heat and add garlic. Saute until fragrant, about 30 seconds.\n  2. Sprinkle chicken with salt and pepper then add to the pan. Saute until golden brown, about 5 minutes.\n  3. Add white wine to deglaze using a wooden spoon to scrape up any browned bits from the bottom of the pan. Reduce heat to low and simmer until liquid reduces by half.\n  4. Stir in chicken broth then continue simmering for 5 minutes. Check sauce for seasoning and add salt and pepper to taste.\n  5. Bring a large pot of salty water to a boil and add pasta. Cook according to package instructions, adding the broccoli florets to the pot two minutes before the end of the cooking time.\n  6. Drain the broccoli and pasta but do not rinse off the cooking liquid. Add cooked broccoli and pasta to the pan with chicken in white wine sauce.\n  7. Add shredded mozzarella and toss until it begins to melt. Place in a large shallow bowl and garnish with Parmesan cheese to serve.\n\nDina's Tossed Mushrooms\n\n_A delicious side dish to any Sunday dinner or special occasion meal, Auntie Dina perfected this quick and easy alternative to stuffed mushrooms._\n\nServes 6.\n\nIngredients\n\n  * 1 pound white button mushrooms\n  * 2 tablespoons water\n  * \u00bd cup dried Italian-style breadcrumbs\n  * 2 tablespoons Parmigiano Reggiano cheese, grated\n  * 2 tablespoons Italian parsley, minced\n  * \u00bc teaspoon dried thyme\n  * 1 clove garlic, minced\n  * Salt and pepper to taste\n  * \u00bc cup olive oil to drizzle\n\nDirections\n\n  1. Preheat oven to 350 degrees.\n  2. Slice off the bottom of the stems; then, use a moist paper towel to gently remove any dirt from mushrooms.\n  3. Quarter or halve the mushrooms, depending on size.\n  4. Sprinkle water in the bottom of a large glass baking dish then place mushrooms in a single layer on top of the water.\n  5. In a small bowl combine next six ingredients: breadcrumbs through salt\/pepper. Sprinkle mixture evenly on top of the mushrooms.\n  6. Drizzle evenly with olive oil then bake uncovered until the mushrooms are golden, about 15 minutes. Serve hot or warm.\n\nEscarole Soup\n\n_Similar to Italian wedding soup, escarole soup has the unique flavor of the greens combined with plenty of fragrant garlic. A Bono family favorite, escarole soup is the ultimate holiday dish, weeknight winter meal or flu fighter. Kids will especially love the tiny meatballs in the soup!_\n\nServes 4-6.\n\nIngredients\n\n  * 4 tablespoons olive oil\n  * 1 bulb garlic, peeled and chopped (about 12 cloves)\n  * 1 \u00bd to 2 heads of escarole, chopped into small pieces\n  * 1 gallon water (or chicken stock)\n  * salt and pepper to taste\n  * \u00bd cup cooked tubettini pasta\n  * Meatballs\n  * 1 pound ground beef, 85% or higher fat content\n  * 1 egg, lightly beaten\n  * \u00bd cup Italian bread crumbs\n  * 2 tablespoon dried parsley\n  * 1 teaspoon salt\n  * \u00bd teaspoon pepper\n\nDirections\n\n  1. Mix together ground beef, egg, bread crumbs, parsley, salt and pepper in a medium bowl. Roll into \u00be-inch balls and set aside.\n  2. In a large soup pot heat oil over medium-high heat. Cook garlic until fragrant, about 30 seconds.\n  3. Add water or chicken stock and chopped escarole to the pan. Bring to a boil then slowly add in the tiny meatballs. Stir once.\n  4. Reduce heat to medium, cover and simmer for one hour.\n  5. Add cooked pasta to the soup right before serving.\n\nFish Pizzaiola\n\n_Uncle Vinny was the son of a fisherman, in fact the son of a captain, so fish was always a staple growing up in Uncle Vinny's house. His mother, Grandma Mary, had a total of five boys to feed and since they were Catholic, meat was never served on any Friday of the year. While not traditional, American cheese was occasionally used instead of mozzarella if that's what she had in the house. This dish is the perfect example of an Old World Italian recipe Americanized due to economizing and accessibility. Additionally, it was representative of an effort to keep old traditions alive while also showing pride for America and the opportunities this country afforded her family._\n\nServes 4.\n\nIngredients\n\n  * 2 pounds fresh white fish ( haddock, cod or tilapia)\n  * 1 teaspoon garlic powder\n  * 1 teaspoon onion powder\n  * 1 teaspoon salt\n  * \u00bd teaspoon pepper\n  * \u00bc cup unsalted butter, cut into small cubes\n  * 4 medium-sized tomatoes, thinly sliced\n  * 2 teaspoons minced fresh parsley (or 1 teaspoon dried)\n  * \u00bc cup Parmesan or Romano cheese, grated\n  * \u00bc cup olive oil\n  * 1 cup shredded mozzarella or 4 slices American cheese\n  * Lemon wedges\n\nDirections\n\n  1. Preheat oven to 350 degrees.\n  2. Season fish with garlic powder, onion powder, salt and pepper. Place in a large baking dish lightly coated with cooking spray to prevent sticking.\n  3. Arrange butter cubes evenly on top of seasoned fish. Layer tomato slices on top to cover fish and butter.\n  4. Sprinkle tomatoes evenly with parsley, additional salt and pepper to taste and grated cheese.\n  5. Bake fish for 15-20 minutes or until fish is opaque. Remove from oven and add shredded cheese or cheese slices, then return to oven and bake until melted, about 2 minutes.\n  6. Remove fish from oven and garnish with lemon slices.\n\nOlive Scacciata\n\n_Scacciata, Italian for \"expelled,\" is the perfect name for this simple recipe. Grandma Mary, an incredible cook who specialized in Sicilian dishes, would serve this dish with freshly baked Italian scali bread to help soak up the vinaigrette._\n\n_Olive scacciata was always just the beginning of what would be an amazing meal full of many courses. Grandma Mary comes from a long line of women who mastered the art of creating delicious food out of only a few simple ingredients. Women like Mary, a mother of five on a budget, expressed their love best through the delicious meals they fed their families. While the dishes would change, one thing always remained the same: They served every meal with pride and perfection._\n\nServes 4.\n\nIngredients\n\n  * 1 large red onion, thinly sliced\n  * 1 bunch celery, base removed, sliced 1-inch thick\n  * 2 cups large green Sicilian (or Spanish) olives with pits\n  * 1 clove garlic, minced\n  * \u00bd cup extra virgin olive oil\n  * \u00bc cup red wine or balsamic vinegar\n  * \u00bd teaspoon black pepper\n\nDirections\n\n  1. Place onion slices and celery pieces in a large bowl.\n  2. Drain Sicilian olives and hit each one with your palm or back of a large chef's knife to break slightly. Add to the bowl along with minced garlic.\n  3. Drizzle with olive oil and red wine then sprinkle with black pepper. Toss well before serving with Italian scali bread.\n\nPasta E Fagiole\n\n_Pasta with beans is a great summer soup or hearty winter comfort dish. This is a budget friendly meal that as Dad would say,\"sticks to your ribs.\" This dish has fed a cold and kept families satisfied for many generations._\n\nServes 8.\n\nIngredients\n\n  * \u00bc cup olive oil\n  * 1 small onion, thinly sliced\n  * 2 cloves garlic, minced\n  * 2 tablespoons Italian seasoning (mixture of oregano, parsley, basil, etc.)\n  * 1 small can tomato paste\n  * 12 cups of water (or chicken stock or combination of both)\n  * 15-ounce can of red beans, drained and rinsed\n  * 15-ounce can white beans, drained and rinsed\n  * 15-ounce can chickpeas (garbanzo beans), drained and rinsed\n  * Salt and pepper to taste\n  * \u00bd pound ditalini or elbow pasta, cooked according to package\n  * Sprinkle with grated Parmesan cheese and serve with crusty bread\n\nDirections\n\n  1. Heat oil over medium-high heat in a large soup pot and saute onion, garlic and spices until just tender about 4-5 minutes.\n  2. Add tomato paste and stir well. Reduce heat to low and cook for 3-4 minutes, stirring occasionally.\n  3. Add the water or chicken stock and beans to the pot; bring to a boil. Reduce heat to low and simmer for 20 minutes.\n  4. Stir in cooked pasta just before serving. Garnish with Parmesan cheese and serve with crusty bread for dunking.\n\nPizzagaina\n\n_Our grandmother Katerina Della Croce from Mirabella Eclano (located in the province of Avellino in southern Italy) made this dish every year on Easter. We called her Nonni, and while she is no longer here, we think of her every year at Easter when we prepare her pizzagaina. Indulgent, rich and satisfying, each bite brings us back to her kitchen and reminds us of our beloved Grandma Della Croce._\n\nServes 6.\n\nIngredients\n\n  * \u00bd pound spaghetti, broken into thirds or fourths\n  * 1 tablespoon unsalted butter\n  * \u00bd pound part-skim shredded mozzarella\n  * 2 pounds whole milk ricotta cheese\n  * \u00bd pound Fresh cheese (Typically sold around Easter on the East Coast. Replace with ricotta if you can't find.)\n  * 1 cup grated Parmesan or Romano cheese\n  * 1 dozen eggs, slightly beaten\n  * 1 pound high-end Italian cold cuts, cut in \u00bc-inch thick cubes (i.e., \u00bc pound each ham, salami, capicola and prosciutto)\n  * 2 tablespoons crushed peppercorns, optional\n  * 1 pound bacon\n  * minced parsley, optional garnish\n\nDirections\n\n  1. Pre-heat oven to 350 degrees.\n  2. Cook spaghetti according to package instructions; drain then place in a large bowl. Add butter and toss well to melt.\n  3. In a separate large bowl, mix together mozzarella, ricotta, Fresh cheese, Parmesan, eggs and cold cuts. Add in crushed peppercorns if you wish for more of a bite.\n  4. Spray a large baking 9\" x13-inch baking dish with cooking spray or grease with vegetable shortening. Pour mixed ingredients into the pan.\n  5. Cover top entirely with sliced bacon to flavor the dish while it cooks and prevent the top from burning.\n  6. Bake until light brown and a butter knife comes out clean, about 1 to 1\u00bc hours.\n  7. Remove bacon with tongs and let cool before refrigerating. Mince cooked bacon and reserve for serving.\n  8. Serve sliced and cold, garnished with parsley and minced bacon.\n\nSpinach and Potato Frittata\n\n_The Italian word frittata, derived from friggere, roughly translates to fried. This was originally a general term for cooking eggs in a skillet, anywhere on the spectrum from scrambled to fried. Ideal for preparing ahead of time, frittatas make a great side dish or light meal for breakfast, lunch or dinner. In fact, grab two slices of Italian scali bread or a sub roll and you can create a lighter version of a \"padado\" and egg \"sangwich\"!_\n\nServes 6.\n\nIngredients\n\n  * 2 tablespoons olive oil\n  * 6 small potatoes, thinly sliced\n  * 1 cup torn spinach\n  * 2 tablespoons green onions, diced\n  * 1 clove garlic, minced\n  * Pinch of salt and pepper\n  * 6 large eggs\n  * 1\/3 cup milk\n  * 8 ounces Parmesan cheese, grated\n  * 1 tablespoon parsley, minced\n\nDirections\n\n  1. Heat olive oil over medium-high heat in a medium oven-proof skillet. Place potatoes in the pan, cover and cook for 10 minutes until tender but firm.\n  2. Add spinach, green onions and garlic to the pan along with a pinch of salt and pepper to taste. Cook until spinach wilts, stirring occasionally, about 2-3 minutes.\n  3. In a medium bowl whisk together eggs and milk. Pour into the skillet over the vegetables. Stir once then sprinkle with Parmesan cheese. Reduce heat to low, then cover and cook until eggs are firm, about 5-7 minutes.\n  4. Place skillet in the oven under the broiler and heat until eggs are cooked through, about 3 minutes, checking carefully so they don't burn.\n  5. Turn onto a plate.\n  6. Serve warm, room temperature or chilled.\n\nStuffed Artichokes\n\n_No holiday is complete without stuffed artichokes. Served as an appetizer or side dish, these are always a family favorite. Be sure to get the kids involved; they'll love pulling off the leaves and scraping the stuffing off with their teeth. Old world finger food at its best!_\n\nServes 6.\n\nIngredients\n\n  * 6 medium-sized artichokes\n  * 2 lemons, halved\n  * 6 cups Italian bread crumbs\n  * \u00bd cup grated Parmesan cheese\n  * \u00bc cup chopped fresh or \u00bc cup dried parsley\n  * 4 garlic cloves, minced\n  * Salt and pepper to taste\n  * \u00bd cup olive oil, for drizzling\n  * 1 tablespoon salt\n\nDirections\n\n  1. Soak artichokes in cold water for 30 minutes.\n  2. Cut off the stems with a sharp knife. Make sure the cut is straight so artichoke will stand flat. Slice off \u00bc inch straight from the top of each artichoke (the prickly part). Stand the artichoke upside down and push firmly to slightly open the leaves, making room to catch the stuffing. Using scissors, cut the tip of each leaf straight across. Remove the purple leaves and the very center choke, which is very prickly, by grabbing it from the very bottom and pulling it straight out.\n  3. Squeeze the lemon juice inside the artichoke.\n  4. In a large bowl mix together the breadcrumbs, grated cheese, parsley, garlic, salt and pepper. Fill each leaf with the stuffing until artichokes are well-packed.\n  5. Drizzle well with olive oil.\n  6. Squeeze more lemon juice over the artichokes.\n  7. Sprinkle with a little salt over the top and sides.\n  8. Put artichokes standing up into a wide pot large enough to hold the artichokes. Add enough water to cover just to the top of the bottom row of leaves of the artichokes.\n  9. Add 1 tablespoon of salt to the pot. Cover and let the water come to a boil. Lower the heat and let the artichokes simmer for 45 minutes or until leaves are tender. Serve warm.\n\nSunday Gravy\n\n_Whether Italian Americans call it gravy or sauce, it's a Sunday tradition for Italian-American families everywhere. No family recipe is the same and rest assured, no one recipe tastes anything less than heaven._\n\n_Sundays always start with a large pot of gravy simmering on the stove, filling the house with an intoxicating aroma. No holiday dinner is complete without pasta served with this meat-filled red sauce. Fresh bread was always available throughout the day to sample the sauce while it cooked and was always available to clean off your plate at the end of the meal._\n\n_What happens in the middle is family time for feasting, sharing, laughing (and yes, sometimes even yelling) together. The operative word? Together. In fact, that's what every traditional meal should do: bring family and friends together._\n\n_P.S.: While I was growing up, my mother Dolly gave me the chore of meatball roller, and on many occasion that was one of my weekend chores. I liked to do it and enjoyed watching and learning how she prepared Sunday gravy. To this day it's probably the only thing I can make well since I'm not a great cook like most members of my family. But come the holidays? Family and friends request my gravy over and over._\n\n_Serves 12._\n\nIngredients\n\n  * Meatballs\n  * 3 pounds ground chuck (avoid beef with less than 15% fat content)\n  * 1 \u00bd cups Italian breadcrumbs\n  * \u00be cup grated Parmesan cheese\n  * 1 cup minced fresh parsley (or \u00bd cup dried)\n  * 2 eggs\n  * 1 tablespoon salt\n  * 1 teaspoon pepper\n  * Pre-heat oven to 325 degrees. Line a baking sheet with foil. Mix all ingredients well in a big bowl using your hands. Form into large meatballs and place in a single layer on the foil-lined baking sheet. Bake for 20 minutes; set aside.\n  * Sausage\n  * 12 Italian sweet and\/or spicy sausage[1]\n  * Cook according to package instructions.\n  * Gravy\n  * \u00bc cup olive oil\n  * 12 garlic cloves, minced\n  * 1 medium onion, diced\n  * \u00bc cup dried parsley or \u00bd cup minced fresh\n  * pinch red pepper flakes\n  * 1 teaspoon salt\n  * \u00bd teaspoon pepper\n  * 4 32-ounce cans \"kitchen ready\" tomatoes\n\nDirections\n\n  1. Heat oil over medium-high heat in a large sauce pot. Saut\u00e9 onions, garlic and red pepper flakes until translucent, about 3-4 minutes, stirring frequently.\n  2. Add parsley, salt and pepper; stir to combine.\n  3. Pour in tomatoes then stir well. Bring to a boil, then reduce heat to low.\n  4. Stir in cooked meatballs and sausage.\n  5. Fill each tomato can \u00be of the way with water, carefully rotating can so it catches any leftover tomatoes on the side of the can. Add to the pot.\n  6. Increase heat to high and bring to a boil. Reduce heat to medium and let cook on a low boil for 10-15 minutes, stirring frequently.\n  7. Reduce heat to low and simmer for at least 1-2 hours, stirring every 15 minutes. The longer it simmers, the deeper the flavor. If you can prepare the day before, even better.\n  8. Serve over your favorite pasta or use with your favorite Italian Parmigiana recipes like lasagna, chicken or eggplant.\n\nTraditional Eggplant Parmigiana\n\n_While the typical Italian Christmas Eve dinner table usually displays an array of seafood dishes, we always offer a dish or two for the non-fish eaters. Whether you serve this Traditional Eggplant Parmigiana on Christmas Eve or any day of the week, make sure you save leftovers for a sandwich the next day!_\n\nServes 8.\n\nIngredients\n\n  * 3 medium eggplants, ends removed, sliced \u00bc inch thick\n  * 1 \u00bd cups flour\n  * 4 eggs, lightly beaten with 2 tablespoons water\n  * 4 cups Italian breadcrumbs\n  * 1 \u00bd cups Parmesan cheese, grated\n  * 4 cups mozzarella cheese, shredded\n  * olive oil for frying\n  * 4 cups marinara sauce, homemade (see below for recipe) or store-bought\n\nDirections\n\n  1. Set up three shallow dishes: one with flour, one with beaten egg and one with Italian breadcrumbs.\n  2. Working one slice at a time, dip each eggplant slice into flour carefully dusting off any excess.\n  3. Next, dip in the egg mixture allowing excess to drip off. Finally, coat in the breadcrumb mixture. Repeat with all slices keeping them stacked on a large platter until you're finished.\n  4. Heat oil in a deep skillet over medium-high heat.\n  5. Fry each slice of eggplant until golden brown, about 2 minutes per side. Place on a dish lined with paper towel to drain off excess oil; let cool.\n  6. In a large baking dish spread a thin coating of the marinara sauce on bottom of pan.\n  7. Add a layer of fried eggplant, cutting to fit. Spread thin layer of sauce, then sprinkle grated Parmesan cheese and top with mozzarella cheese. Repeat eggplant, grated Parmesan cheese and mozzarella cheese until all is used.\n  8. Bake for 25 to 30 minutes in a 350-degree oven until it bubbles around the edges. Serve warm or cold in squares with other antipasti foods.\n\n**Quick Homemade Marinara Sauce**\n\nIngredients\n\n  * 1 clove garlic, minced\n  * pinch of red pepper flakes\n  * 3 tablespoons olive oil\n  * 1 tablespoon fresh parsley, minced\n  * 2 32-ounce cans crushed tomatoes\n  * salt and pepper to taste\n\nDirections\n\n  1. Heat oil in a large pot and saut\u00e9 garlic until slightly translucent.\n  2. Add remaining ingredients and bring to quick boil. Reduce heat to low and simmer for 30 minutes. Season with salt and pepper to taste.\n\nUncle Vinny's Shrimp Scampi\n\n_A popular Christmas Eve dish, Uncle Vinny's shrimp scampi is popular for the holiday because giving up meat is a means of fasting or sacrifice. A total showstopper, shrimp scampi might appear as if it takes hours to prepare, but it really doesn't take more than 15 minutes in total. Ideal for a busy weeknight dinner or to serve during the Lenten season before Easter, this lemon and garlic filled shellfish dish is always a crowd pleaser. We promise no one will miss the cheese pizza or veggie burgers when they take a bite of this shrimp scampi!_\n\nServes 4-6.\n\nIngredients\n\n  * 1 pound large raw shrimp, peeled and deveined\n  * \u00bc cup unsalted butter\n  * \u00bd cup olive oil\n  * 3 cloves garlic, minced\n  * Pinch of red pepper flakes\n  * \u00bc cup dry white wine\n  * 1 teaspoon salt\n  * \u00bd teaspoon pepper\n  * 3 tablespoons lemon juice\n  * 1 tablespoon grated lemon zest\n  * \u00bc cup chopped parsley\n  * Spaghetti, linguini or angel hair pasta, optional\n\nDirections\n\n  1. Rinse shrimp and pat dry with paper towel; set aside.\n  2. Melt butter and olive oil in a heavy frying pan over medium heat. Reduce heat and add garlic and red pepper flakes. Saute on low heat about 5 minutes.\n  3. Raise heat to high and when oil is hot, immediately add shrimp. Toss the shrimp around constantly, until they turn pink, about 3 minutes.\n  4. Add wine to pan to deglaze, scraping up any browned bits from bottom of pan. Saute 1 minute to let alcohol burn off slightly.\n  5. Remove pan from heat. Add salt, pepper, lemon juice, lemon zest and chopped parsley.\n  6. Return pan to high heat and saute for a minute or two or until butter sauce is slightly thickened.\n  7. Serve immediately in bowls with juice poured over.\n\n_Serve over spaghetti, linguini or angel hair pasta, if you wish._\nFor more easy recipes inspired from around the world, visit TheLemonBowl.com\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":"\n\n\n\nProduced by David Edwards, Martin Pettit and the Online\nDistributed Proofreading Team at http:\/\/www.pgdp.net (This\nfile was produced from images generously made available\nby The Internet Archive)\n\n\n\n\n\n\nInternational Education Series\n\nEDITED BY\n\nWILLIAM T. HARRIS, A.M., LL.D.\n\n_Volume XXI._\n\n\nTHE INTERNATIONAL EDUCATION SERIES.\n\n12mo, cloth, uniform binding.\n\nTHE INTERNATIONAL EDUCATION SERIES was projected for the purpose of\nbringing together in orderly arrangement the best writings, new and old,\nupon educational subjects, and presenting a complete course of reading\nand training for teachers generally. It is edited by W. T. HARRIS,\nLL.D., now United States Commissioner of Education, who has contributed\nfor the different volumes in the way of introductions, analysis, and\ncommentary. The volumes are tastefully and substantially bound in\nuniform style.\n\n_VOLUMES NOW READY_:\n\n\n     Vol I.--THE PHILOSOPHY OF EDUCATION. 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By ROGER DE GUIMPS.\n     Authorized translation from the second French edition, by J.\n     RUSSELL, B.A., Assistant Master in University College, London.\n     With an Introduction by Rev. R. H. QUICK, M.A. Price, $1.50.\n\n     Vol. XV.--SCHOOL SUPERVISION. By J. L. PICKARD, LL.D. Price, $1.00.\n\n     Vol. XVI.--HIGHER EDUCATION OF WOMEN IN EUROPE. By HELENE LANGE,\n     Berlin. Translated and accompanied by comparative statistics by L.\n     R. KLEMM. Price, $1.00.\n\n     Vol. XVII.--ESSAYS ON EDUCATIONAL REFORMERS. By ROBERT HERBERT\n     QUICK, M.A., Trinity College, Cambridge; formerly Assistant Master\n     at Harrow, and Lecturer on the History of Education at Cambridge;\n     late Vicar of Ledbergh. _Only authorized edition of the work as\n     rewritten in 1890._ Price, $1.50.\n\n     Vol. XVIII.--A TEXT-BOOK IN PSYCHOLOGY. AN ATTEMPT TO FOUND THE\n     SCIENCE OF PSYCHOLOGY ON EXPERIENCE, METAPHYSICS, AND MATHEMATICS.\n     By JOHANN FRIEDRICH HERBART. Translated from the original German by\n     MARGARET K. SMITH, Teacher in the State Normal School at Oswego,\n     New York. Price, $1.00.\n\n     Vol. XIX.--PSYCHOLOGY APPLIED TO THE ART OF TEACHING. By Dr. JOSEPH\n     BALDWIN. Price, $1.50.\n\n     Vol. XX.--ROUSSEAU'S EMILE. By W. H. PAYNE. Price, $1.50.\n\n     Vol. XXI.--ETHICAL TRAINING IN SCHOOLS. By FELIX ADLER.\n\n     Vol. XXII.--ENGLISH EDUCATION IN THE ELEMENTARY AND SECONDARY\n     SCHOOLS. By ISAAC SHARPLESS, LL.D. Price, $1.00.\n\n     Vol. XXIII.--EDUCATION FROM A NATIONAL STANDPOINT. By ALFRED\n     FOUILLEE. Price, $1.50.\n\n_Circular, describing the volumes more in detail, mailed to any address\non request._\n\nNew York: D. APPLETON & CO., Publishers, 1, 3, & 5 Bond Street.\n\n\n\n\nINTERNATIONAL EDUCATION SERIES\n\nTHE MORAL INSTRUCTION OF CHILDREN\n\nBY\nFELIX ADLER\n\nNEW YORK\nD. APPLETON AND COMPANY\n1892\n\n\nCOPYRIGHT, 1892,\nBY D. APPLETON AND COMPANY.\n\nELECTROTYPED AND PRINTED\nAT THE APPLETON PRESS, U.S.A.\n\n\n\n\nEDITOR'S PREFACE.\n\n\nMoral education is everywhere acknowledged to be the most important part\nof all education; but there has not been the same agreement in regard to\nthe best means of securing it in the school. This has been due in part\nto a want of insight into the twofold nature of this sort of education;\nfor instruction in morals includes two things: the formation of right\nideas and the formation of right habits. Right ideas are necessary to\nguide the will, but right habits are the product of the will itself.\n\nIt is possible to have right ideas to some extent without the\ncorresponding moral habits. On this account the formation of correct\nhabits has been esteemed by some to be the chief thing. But unconscious\nhabits--mere use and wont--do not seem to deserve the title of moral in\nits highest sense. The moral act should be a considerate one, and rest\non the adoption of principles to guide one's actions.\n\nTo those who lay stress on the practical side and demand the formation\nof correct habits, the school as it is seems to be a great ethical\ninstrumentality. To those who see in theoretical instruction the only\ntrue basis of moral character, the existing school methods seem sadly\ndeficient.\n\nThe school as it is looks first after its discipline, and next after its\ninstruction. Discipline concerns the behavior, and instruction concerns\nthe intellectual progress of the pupil. That part of moral education\nwhich relates to habits of good behavior is much better provided for in\nthe school than any part of intellectual education.\n\nThere is, however, a conflict here between old and new ideals. The\nold-fashioned school regarded obedience to authority the one essential;\nthe new ideal regards insight into the reasonableness of moral commands\nthe chief end. It is said, with truth, that a habit of unreasoning\nobedience does not fit one for the exigencies of modern life, with its\npartisan appeals to the individual and its perpetual display of grounds\nand reasons, specious and otherwise, in the newspapers. The unreasoning\nobedience to a moral guide in school may become in after life\nunreasoning obedience to a demagogue or to a leader in crime.\n\nIt is not obedience to external authority that we need so much as\nenlightened moral sense, and yet there remains and will remain much good\nin the old-fashioned habit of implicit obedience.\n\nThe new education aims at building up self-control and individual\ninsight. It substitutes the internal authority of conscience for the\nexternal authority of the master. It claims by this to educate the\ncitizen fitted for the exercise of suffrage in a free government. He\nwill weigh political and social questions in his mind, and decide for\nhimself. He will be apt to reject the scheme of the demagogue. While the\nold-fashioned school-master relied on the rod to sustain his external\nauthority, he produced, it is said, a reaction against all authority in\nthe minds of strong-willed pupils. The new education saves the\nstrong-willed pupil from this tension against constituted authority, and\nmakes him law-abiding from the beginning.\n\nIt will be admitted that the school under both its forms--old as well as\nnew--secures in the main the formation of the cardinal moral habits. It\nis obliged to insist on regularity, punctuality, silence, and industry\nas indispensable for the performance of its school tasks. A private\ntutor may permit his charge to neglect all these things, and yet secure\nsome progress in studies carried on by fits and starts, with noise and\nzeal to-day, followed by indolence to-morrow. But a school, on account\nof its numbers, must insist on the semi-mechanical virtues of\nregularity, punctuality, silence, and industry. Although these are\nsemi-mechanical in their nature, for with much practice they become\nunconscious habits, yet they furnish the very ground-work of all\ncombinations of man with his fellow-men. They are fundamental conditions\nof social life. The increase of city population, consequent on the\ngrowth of productive industry and the substitution of machines for hand\nlabor, renders necessary the universal prevalence of these cardinal\nvirtues of the school.\n\nEven the management of machines requires that sort of alertness which\ncomes from regularity and punctuality. The travel on the railroad, the\nmanagement of steam-engines, the necessities of concerted action,\nrequire punctuality and rhythmic action.\n\nThe school habit of silence means considerate regard for the rights of\nfellow-workmen. They must not be interfered with; their attention must\nnot be distracted from their several tasks. A rational self-restraint\ngrows out of this school habit--rational, because it rests on\nconsiderateness for the work of others. This is a great lesson in\nco-operation. Morals in their essence deal with the relation of man to\nhis fellow-men, and rest on a considerateness for the rights of others.\n\"Do unto others,\" etc., sums up the moral code.\n\nIndustry, likewise, takes a high rank as a citizen's virtue. By it man\nlearns to re-enforce the moments by the hours, and the days by the\nyears. He learns how the puny individual can conquer great obstacles.\nThe school demands of the youth a difficult kind of industry. He must\nthink and remember, giving close and unremitting attention to subjects\nstrange and far off from his daily life. He must do this in order to\ndiscover eventually that these strange and far-off matters are connected\nin a close manner to his own history and destiny.\n\nThere is another phase of the pupil's industry that has an important\nbearing on morals. All his intellectual work in the class has to do with\ncritical accuracy, and respect for the truth. Loose statements and\ncareless logical inference meet with severe reproof.\n\nFinally, there is an enforced politeness and courtesy toward teachers\nand fellow-pupils--at least to the extent of preventing quarrels. This\nis directly tributary to the highest of virtues, namely, kindness and\ngenerosity.\n\nAll these moral phases mentioned have to do with the side of school\ndiscipline rather than instruction, and they do not necessarily have any\nbearing on the theory of morals or on ethical philosophy, except in the\nfact that they make a very strong impression on the mind of the youth,\nand cause him to feel that he is a member of a moral order. He learns\nthat moral demands are far more stern than the demands of the body for\nfood or drink or repose. The school thus does much to change the pupil\nfrom a natural being to a spiritual being. Physical nature becomes\nsubordinated to the interests of human nature.\n\nNotwithstanding the fact that the school is so efficient as a means of\ntraining in moral habits, it is as yet only a small influence in the\nrealm of moral theory. Even our colleges and universities, it must be\nconfessed, do little in this respect, although there has been of late an\neffort to increase in the programmes the amount of time devoted to\nethical study. The cause of this is the divorce of moral theory from\ntheology. All was easy so long as ethics was directly associated with\nthe prevailing religious confession. The separation of Church and\nState, slowly progressing everywhere since the middle ages, has at\nlength touched the question of education.\n\nThe attempt to find an independent basis for ethics in the science of\nsociology has developed conflicting systems. The college student is\nrarely strengthened in his faith in moral theories by his theoretic\nstudy. Too often his faith is sapped. Those who master a spiritual\nphilosophy are strengthened; the many who drift toward a so-called\n\"scientific\" basis are led to weaken their moral convictions to the\nstandpoint of fashion, or custom, or utility.\n\nMeanwhile the demand of the age to separate Church from State becomes\nmore and more exacting. Religious instruction has almost entirely ceased\nin the public schools, and it is rapidly disappearing from the\nprogrammes of colleges and preparatory schools, and few academies are\nnow scenes of religious revival, as once was common.\n\nThe publishers of this series are glad, therefore, to offer a book so\ntimely and full of helpful suggestions as this of Mr. Adler. It is hoped\nthat it may open for many teachers a new road to theoretic instruction\nin morality, and at the same time re-enforce the study of literature in\nour schools.\n\nW. T. HARRIS.\n\nWASHINGTON, D.C., _July, 1892_.\n\n\n\n\nPREFATORY NOTE.\n\n\nThe following lectures were delivered in the School of Applied Ethics\nduring its first session in 1891, at Plymouth, Mass. A few of the\nlectures have been condensed, in order to bring more clearly into view\nthe logical scheme which underlies the plan of instruction here\noutlined. The others are published substantially as delivered.\n\nI am deeply conscious of the difficulties of the problem which I have\nventured to approach, and realize that any contribution toward its\nsolution, at the present time, must be most imperfect. I should, for my\npart, have preferred to wait longer before submitting my thought to\nteachers and parents. But I have been persuaded that even in its present\nshape it may be of some use. I earnestly hope that, at all events, it\nmay serve to help on the rising tide of interest in moral education, and\nmay stimulate to further inquiry.\n\nFELIX ADLER.\n\n\n\n\nCONTENTS.\n\n\nINTRODUCTORY LECTURES.\n                                                                  PAGE\n   I. The Problem of Unsectarian Moral Instruction                   3\n\n  II. The Efficient Motives of Good Conduct                         17\n\n III. Opportunities for Moral Training in the Daily School          27\n\n  IV. The Classification of Duties                                  37\n\n   V. The Moral Outfit of Children on entering School               47\n\n\nPRIMARY COURSE.\n\n  VI. The Use of Fairy Tales                                        64\n\n VII. The Use of Fables                                             80\n\nVIII. Supplementary Remarks on Fables                               96\n\n  IX. Selected Stories from the Bible                              106\n\n   X. The Odyssey and the Iliad                                    146\n\n\nGRAMMAR COURSE.\n\nLESSONS ON DUTY.\n\n  XI. The Duty of acquiring Knowledge                              169\n\n XII. Duties which relate to the Physical Life and the Feelings    185\n\nXIII. Duties which relate to Others (Filial and Fraternal Duties)  202\n\n XIV. Duties toward all Men (Justice and Charity)                  218\n\n  XV. The Elements of Civic Duty                                   236\n\n XVI. The Use of Proverbs and Speeches                             245\n\nXVII. Individualization of Moral Teaching                          249\n\n\nAPPENDIX.\n\n      The Influence of Manual Training on Character                257\n\n\n\n\nINTRODUCTORY LECTURES.\n\n\n\n\nI.\n\nTHE PROBLEM OF UNSECTARIAN MORAL INSTRUCTION.\n\n\nIt will be the aim of the present course of lectures to give in outline\nthe subject-matter of moral instruction for children from six to\nfourteen or fifteen years of age, and to discuss the methods according\nto which this kind of instruction should be imparted. At the outset,\nhowever, we are confronted by what certainly is a grave difficulty, and\nto many may appear an insuperable one. The opinion is widely held that\nmorality depends on religious sanctions, and that right conduct can not\nbe taught--especially not to children--except it be under the authority\nof some sort of religious belief. To those who think in this way the\nvery phrase, unsectarian moral teaching, is suspicious, as savoring of\ninfidelity. And the attempt to mark off a neutral moral zone, outside\nthe domains of the churches, is apt to be regarded as masking a covert\ndesign on religion itself.\n\nThe principle of unsectarian moral instruction, however, is neither\nirreligious nor anti-religious. In fact--as will appear later on--it\nrests on purely educational grounds, with which the religious bias of\nthe educator has nothing whatever to do. But there are also grounds of\nexpediency which, at least in the United States, compel us, whether we\ncare to do so or not, to face this problem of unsectarian moral\neducation, and to these let us first give our attention. Even if we were\nto admit, for argument's sake, the correctness of the proposition that\nmoral truths can only be taught as corollaries of some form of religious\nbelief, the question would at once present itself to the educator, To\nwhich form of religious belief shall he give the preference? I am\nspeaking now of the public schools of the United States.\n\nThese schools are supported out of the general fund of taxation to which\nall citizens are compelled to contribute. Clearly it would be an act of\ngross injustice to force a citizen belonging to one denomination to pay\nfor instilling the doctrines of some other into the minds of the\nyoung--in other words, to compel him to support and assist in spreading\nreligious ideas in which he does not believe. This would be an outrage\non the freedom of conscience. But the act of injustice would become\nsimply monstrous if parents were to be compelled to help indoctrinate\ntheir own children with such religious opinions as are repugnant to\nthem.\n\nThere is no state religion in the United States. In the eyes of the\nstate all shades of belief and disbelief are on a par. There are in this\ncountry Catholics, Episcopalians, Presbyterians, Methodists, Baptists,\nJews, etc. They are alike citizens. They contribute alike toward the\nmaintenance of the public schools. With what show of fairness, then,\ncould the belief of any one of these sects be adopted by the state as a\nbasis for the inculcation of moral truths? The case seems, on the face\nof it, a hopeless one. But the following devices have been suggested to\nremove, or rather to circumvent, the difficulty.\n\n_First Device._--Let representatives of the various theistic churches,\nincluding Catholics, Protestants, and Jews, meet in council. Let them\neliminate all those points in respect to which they differ, and\nformulate a common creed containing only those articles on which they\ncan agree. Such a creed would include, for instance, the belief in the\nexistence of Deity, in the immortality of the soul, and in future reward\nand punishment. Upon this as a foundation let the edifice of moral\ninstruction be erected. There are, however, two obvious objections to\nthis plan. In the first place, this \"Dreibund\" of Catholicism,\nProtestantism, and Judaism would leave out of account the party of the\nagnostics, whose views may indeed be erroneous, or even detestable, but\nwhose rights as citizens ought not the less on that account to be\nrespected. \"_Neminem laede_,\" hurt no one, is a cardinal rule of justice,\nand should be observed by the friends of religion in their dealings with\ntheir opponents as well as with one another. The agnostic party has\ngrown to quite considerable dimensions in the United States. But, if it\nhad not, if there were only a single person who held such opinions, and\nhe a citizen, any attempt on the part of the majority to trample upon\nthe rights of this one person would still be inexcusable. In the sphere\nof political action the majority rules, and must rule; in matters that\ntouch the conscience the smallest minority possesses rights on which\neven an overwhelming majority arrayed on the opposite side can not\nafford to trespass. It is one of the most notable achievements of the\nAmerican commonwealths that they have so distinctly separated between\nthe domain of religion and of politics, adopting in the one case the\nmaxim of coercion by majority rule, in the other allowing the full\nmeasure of individual liberty. From this standpoint there should be no\ndeparture.\n\nBut the second objection is even more cogent. It is proposed to\neliminate the differences which separate the various sects, and to\nformulate their points of agreement into a common creed. But does it not\noccur to those who propose this plan that the very life of a religion is\nto be found precisely in those points in which it differs from its\nneighbors, and that an abstract scheme of belief, such as has been\nsketched, would, in truth, satisfy no one? Thus, out of respect for the\nsentiments of the Jews, it is proposed to omit the doctrines of the\ndivinity of Christ and of the atonement. But would any earnest Christian\ngive his assent, even provisionally, to a creed from which those\nquintessential doctrines of Christianity have been left out? When the\nChristian maintains that morality must be based on religion, does he not\nmean, above all, on the belief in Christ? Is it not indispensable, from\nhis point of view, that the figure of the Saviour shall stand in the\nforeground of moral inculcation and exhortation? Again, when the\nCatholic affirms that the moral teaching of the young must be based on\nreligion, is it to be supposed for an instant that he would accept as\nsatisfying his conception of religion a skeleton creed like that above\nmentioned, denuded of all those peculiar dogmas which make religion in\nhis eyes beautiful and dear? This first device, therefore, is to be\nrejected. It is unjust to the agnostics, and it will never content the\nreally religious persons of any denomination. It could prove acceptable\nonly to theists pure and simple, whose creed is practically limited to\nthe three articles mentioned; namely, the belief in Deity, immortality,\nand future punishment and reward. But this class constitutes a small\nfraction of the community; and it would be absurd, under the specious\nplea of reconciling the various creeds, in effect to impose the\nrationalistic opinions of a few on the whole community.\n\nThe _second device_ seems to promise better results. It provides that\nreligious and moral instruction combined shall be given in the public\nschools under the auspices of the several denominations. According to\nthis plan, the pupils are to be divided, for purposes of moral\ninstruction, into separate classes, according to their sectarian\naffiliations, and are to be taught separately by their own clergymen or\nby teachers acting under instructions from the latter. The high\nauthority of Germany is invoked in support of this plan. If I am\ncorrectly informed, the president of one of our leading universities\nhas recently spoken in favor of it, and it is likely that an attempt\nwill be made to introduce it in the United States. Already in some of\nour reformatory schools and other public institutions separate religious\nservices are held by the ministers of the various sects, and we may\nexpect that an analogous arrangement will be proposed with respect to\nmoral teaching in the common schools. It is necessary, therefore, to pay\nsome attention to the German system, and to explain the reasons which\nhave induced or compelled the Germans to adopt the compromise just\ndescribed. The chief points to be noted are these: In Germany, church\nand state are united. The King of Prussia, for instance, is the head of\nthe Evangelical Church. This constitutes a vital difference between\nAmerica and Germany. Secondly, in Germany the schools existed before the\nstate took charge of them. The school system was founded by the Church,\nand the problem which confronted the Government was how to convert\nchurch schools into state schools. An attempt was made to do this by\nlimiting the influence of the clergy, which formerly had been\nall-powerful and all-pervasive, to certain branches and certain hours of\ninstruction, thereby securing the supremacy of the state in respect to\nall other branches and at all other hours. In America, on the other\nhand, the state founded the schools _ab initio_. In Germany the state\nhas actually encroached upon the Church, has entered church schools and\nreconstructed them in its own interest. To adopt the German system in\nAmerica would be to permit the Church to encroach upon the state, to\nenter state schools and subordinate them to sectarian purposes. The\nexample of Germany can not, therefore, be quoted as a precedent in\npoint. The system of compromise in Germany marks an advance in the\ndirection of increasing state influence. Its adoption in this country\nwould mark a retrograde movement in the direction of increasing church\ninfluence.\n\nNor can the system, when considered on its own merits, be called a happy\none. Prof. Gneist, in his valuable treatise, Die Konfessionelle Schule\n(which may be read by those who desire to inform themselves on the\nhistorical evolution of the Prussian system), maintains that scientific\ninstruction must be unsectarian, while religious instruction must be\nsectarian. I agree to both his propositions. But to my mind it follows\nthat, if religious instruction must be sectarian, it ought not to have a\nplace in state schools, at least not in a country in which the\nseparation of church and state is complete. Moreover, the limitation of\nreligious teaching to a few hours a week can never satisfy the earnest\nsectarian. If he wants religion in the schools at all, then he will also\nwant that specific kind of religious influence which he favors to\npermeate the whole school. He will insist that history shall be taught\nfrom his point of view, that the readers shall breathe the spirit of his\nfaith, that the science teaching shall be made to harmonize with its\ndoctrines, etc. What a paltry concession, indeed, to open the door to\nthe clergyman twice or three times a week, and to permit him to teach\nthe catechism to the pupils, while the rest of the teaching is withdrawn\nfrom his control, and is perhaps informed by a spirit alien to his! This\nkind of compromise can never heartily be indorsed; it may be accepted\nunder pressure, but submission to it will always be under protest.[1]\n\nThe third arrangement that has been suggested is that each sect shall\nbuild its own schools, and draw upon the fund supplied by taxation\nproportionately to the number of children educated. But to this there\nare again two great objections: First, it is the duty of the state to\nsee to it that a high educational standard shall be maintained in the\nschools, and that the money spent on them shall bear fruit in raising\nthe general intelligence of the community. But the experience of the\npast proves conclusively that in sectarian schools, especially where\nthere are no rival unsectarian institutions to force them into\ncompetition, the preponderance of zeal and interest is so markedly on\nthe side of religious teaching that the secular branches unavoidably\nsuffer.[2] If it is said that the state may prescribe rules and set up\nstandards of its own, to which the sectarian schools shall be held to\nconform, we ask, Who is to secure such conformance? The various sects,\nonce having gained possession of the public funds, would resent the\ninterference of the State. The Inspectors who might be appointed would\nnever be allowed to exercise any real control, and the rules which the\nState might prescribe would remain dead letter.\n\nIn the second place, under such an arrangement, the highest purpose for\nwhich the public schools exist would be defeated. Sectarian schools tend\nto separate the members of the various denominations from one another,\nand to hinder the growth of that spirit of national unity which it is,\non the other hand, the prime duty of the public school to create and\nfoster. The support of a system of public education out of the proceeds\nof taxation is justifiable in the last analysis as a measure dictated to\nthe State by the law of self-preservation. The State maintains public\nschools in order to preserve itself--i. e., its unity. And this is\nespecially true in a republic. In a monarchy the strong arm of the\nreigning dynasty, supported by a ruling class, may perhaps suppress\ndiscord, and hold the antagonistic elements among the people in\nsubjection by sheer force. In a republic only the spirit of unity among\nthe people themselves can keep them a people. And this spirit is\nfostered in public schools, where children of all classes and sects are\nbrought into daily, friendly contact, and where together they are\nindoctrinated into the history, tradition, and aspirations of the nation\nto which they belong.\n\nWhat then? We have seen that we can not encourage, that we can not\npermit, the establishment of sectarian schools at the public expense. We\nhave also seen that we can not teach religion in the public schools.\nMust we, therefore, abandon altogether the hope of teaching the elements\nof morals? Is not moral education conceded to be one of the most\nimportant, if not the most important, of all branches of education? Must\nwe forego the splendid opportunities afforded by the daily schools for\nthis purpose? Is there not a way of imparting moral instruction without\ngiving just offense to any religious belief or any religious believer,\nor doing violence to the rights of any sect or of any party whatsoever?\nThe correct answer to this question would be the solution of the problem\nof unsectarian moral education. I can merely state my answer to-day, in\nthe hope that the entire course before us may substantiate it. The\nanswer, as I conceive it, is this: It is the business of the moral\ninstructor in the school to deliver to his pupils the subject-matter of\nmorality, but not to deal with the sanctions of it; to give his pupils a\nclearer understanding of what _is_ right and what _is_ wrong, but not to\nenter into the question why the right should be done and the wrong\navoided. For example, let us suppose that the teacher is treating of\nveracity. He says to the pupil, Thou shalt not lie. He takes it for\ngranted that the pupil feels the force of this commandment, and\nacknowledges that he ought to yield obedience to it. For my part, I\nshould suspect of quibbling and dishonest intention any boy or girl who\nwould ask me, Why ought I not to lie? I should hold up before such a\nchild the Ought in all its awful majesty. The right to reason about\nthese matters can not be conceded until after the mind has attained a\ncertain maturity. And as a matter of fact every good child agrees with\nthe teacher unhesitatingly when he says, It is wrong to lie. There is an\nanswering echo in its heart which confirms the teacher's words. But\nwhat, then, is it my business as a moral teacher to do? In the first\nplace, to deepen the impression of the wrongfulness of lying, and the\nsacredness of truth, by the spirit in which I approach the subject. My\nfirst business is to convey the spirit of moral reverence to my pupils.\nIn the next place, I ought to quicken the pupil's perceptions of what is\nright and wrong, in the case supposed, of what is truth and what is\nfalsehood. Accordingly, I should analyze the different species of lies,\nwith a view of putting the pupils on their guard against the spirit of\nfalsehood, however it may disguise itself. I should try to make my\npupils see that, whenever they intentionally convey a false impression,\nthey are guilty of falsehood. I should try to make their minds\nintelligent and their consciences sensitive in the matter of\ntruth-telling, so that they may avoid those numerous ambiguities of\nwhich children are so fond, and which are practiced even by adults. I\nshould endeavor to tonic their moral nature with respect to\ntruthfulness. In the next place, I should point out to them the most\nfrequent motives which lead to lying, so that, by being warned against\nthe causes, they may the more readily escape the evil consequences. For\nexample, cowardice is one cause of lying. By making the pupil ashamed of\ncowardice, we can often cure him of the tendency to falsehood. A\nredundant imagination is another cause of lying, envy is another cause,\nselfishness in all its forms is a principal cause, etc. I should say to\nthe moral teacher: Direct the pupil's attention to the various dangerous\ntendencies in his nature, which tempt him into the ways of falsehood.\nFurthermore, explain to your pupils the consequences of falsehood: the\nloss of the confidence of our fellow-men, which is the immediate and\npalpable result of being detected in a lie; the injuries inflicted on\nothers; the loosening of the bonds of mutual trust in society at large;\nthe loss of self-respect on the part of the liar; the fatal necessity of\nmultiplying lies, of inventing new falsehoods to make good the first,\netc. A vast amount of good, I am persuaded, can be done in this way by\nstimulating the moral nature, by enabling the scholar to detect the\nfiner shades of right and wrong, helping him to trace temptation to its\nsource, and erecting in his mind barriers against evil-doing, founded on\na realizing sense of its consequences.\n\nIn a similar if not exactly the same way, all the other principal\ntopics of practical morality can be handled. The conscience can be\nenlightened, strengthened, guided, and all this can be done without once\nraising the question why it is wrong to do what is forbidden. That it is\nwrong should rather, as I have said, be assumed. The ultimate grounds of\nmoral obligation need never be discussed in school. It is the business\nof religion and philosophy to propose theories, or to formulate articles\nof belief with respect to the ultimate sources and sanctions of duty.\nReligion says we ought to do right because it is the will of God, or for\nthe love of Christ. Philosophy says we should do right for utilitarian\nor transcendental reasons, or in obedience to the law of evolution, etc.\nThe moral teacher, fortunately, is not called upon to choose between\nthese various metaphysical and theological asseverations. As an\nindividual he may subscribe to any one of them, but as a teacher he is\nbound to remain within the safe limits of his own province. He is not to\nexplain why we should do the right, but to make the young people who are\nintrusted to his charge see more clearly what is right, and to instill\ninto them his own love of and respect for the right. There is a body of\nmoral truth upon which all good men, of whatever sect or opinion, are\nagreed: _it is the business of the public schools to deliver to their\npupils this common fund of moral truth_. But I must hasten to add, to\ndeliver it not in the style of the preacher, but according to the\nmethods of the pedagogue--i. e., in a systematic way, the moral lessons\nbeing graded to suit the varying ages and capacities of the pupils, and\nthe illustrative material being sorted and arranged in like manner.\nConceive the modern educational methods to have been applied to that\nstock of moral truths which all good men accept, and you will have the\nmaterial for the moral lessons which are needed in a public school.\n\nFOOTNOTES:\n\n[1] Since the above was written, the draft of the _Volksschulgesetz_\nsubmitted to the Prussian Legislature, and the excited debates to which\nit gave rise, have supplied a striking confirmation of the views\nexpressed in the text. Nothing could be more mistaken than to propose\nfor imitation elsewhere the German \"solution\" of the problem of moral\nteaching in schools, especially at a time when the Germans themselves\nare taking great pains to make it clear that they are as far as possible\nfrom having found a solution.\n\n[2] During the reactionary period which followed the Revolution of 1848,\nthe school regulations of Kur-Hessen provided that twenty hours a week\nbe devoted in the Volkschulen to religious teaching.\n\n\n\n\nII.\n\nTHE EFFICIENT MOTIVES OF GOOD CONDUCT.\n\n\nThere are persons in whom moral principle seems to have completely\ntriumphed; whose conduct, so far as one can judge, is determined solely\nby moral rules; but whom, nevertheless, we do not wholly admire. We feel\ninstinctively that there is in their virtue a certain flaw--the absence\nof a saving grace. They are too rigorous, too much the slaves of duty.\nThey lack geniality.\n\nLike religion, morality has its fanatics. Thus, there is in the\ntemperance movement a class of fanatics who look at every public\nquestion from the point of view of temperance reform, and from that\nonly. There are also woman's-rights fanatics, social purity fanatics,\netc. The moral fanatic in every case is a person whose attention is\nwholly engrossed by some one moral interest, and who sees this out of\nits relation to other moral interests. The end he has in view may be in\nitself highly laudable, but the exaggerated emphasis put upon it, the\none-sided pursuit of it, is a mischievous error.\n\nObserve, further, that there are degrees of moral fanaticism. The\nfanatic of the first degree, to whom Emerson addresses the words, \"What\nright have you, sir, to your one virtue?\" has just been described. He\nis a person who exalts some one moral rule at the expense of the others.\nA fanatic of a higher order is he who exalts the whole body of moral\nrules at the expense of human instincts and desires. He is a person who\nalways acts according to rule; who introduces moral considerations into\nevery detail of life; who rides the moral hobby; in whose eyes the\ninfinite complexity of human affairs has only one aspect, namely, the\nmoral; who is never satisfied unless at every step he feels the strain\nof the bridle of conscience; who is incapable of spontaneous action and\nof _naive_ enjoyment. It is believed that there are not a few persons of\nthis description in the United States, and especially in the New England\nStates--fanatics on the moral side, examples of a one-sided development\nin the direction of moral formalism. We must be very careful, when\ninsisting on the authority of moral ideas, lest we encourage in the\nyoung a tendency of this sort. The hearts of children are very pliable;\nit is easily possible to produce on them too deep an impression: to give\nthem at the outset a fatal twist, all the more since at a certain age\nmany young people are prone to exaggerated introspection and\nself-questioning. But it may be asked: Are not moral principles really\nclothed with supreme authority? Ought we not, indeed, to keep the\nstandard of righteousness constantly before our eyes; in brief, is it\npossible to be too moral? Evidently we have reached a point where a\ndistinction requires to be drawn.\n\nEthics is a science of relations. The things related are human\ninterests, human ends. The ideal which ethics proposes to itself is the\nunity of ends, just as the ideal of science is the unity of causes. The\nends of the natural man are the subject-matter with which ethics deals.\nThe ends of the natural man are not to be crushed or wiped out, but to\nbe brought into right relations with one another. The ends of the\nnatural man are to be respected from an ethical point of view, so long\nas they remain within their proper limits. The moral laws are formulas\nexpressing relations of equality or subordination, or superordination.\nThe moral virtue of our acts consists in the respect which we pay to the\nsystem of relationships thus prescribed, in the willingness with which\nwe co-ordinate our interests with those of others, or subordinate them\nto those of others, as the exigencies of the moral situation may\nrequire.\n\nBut the point on which it is now necessary to fix our attention is that\nwhen morality has once sanctioned any of the ends of life, the natural\nman may be left to pursue them without interference on the part of the\nmoralist. When morality has marked out the boundaries within which the\ngiven end shall be pursued, its work so far is done; except, indeed,\nthat we are always to keep an eye upon those boundaries, and that the\nsense of their existence should pervade the whole atmosphere of our\nlives.[3] A few illustrations will make my meaning clear. There is a\nmoral rule which says that we should eat to live; not, conversely, live\nto eat. This means that we should regulate our food in such a way that\nthe body may become a fit instrument for the higher purposes of\nexistence, and that the time and attention bestowed upon the matter of\neating shall not be so great as to divert us from other and more\nnecessary objects. But, these limits being established, it does not\nfollow that it is wrong or unspiritual to enjoy a meal. The senses, even\nthe lowest of them, are permitted to have free play within the bounds\nprescribed. Nor, again, should we try rigidly to determine the choice of\nfood according to moral considerations. It would be ridiculous to\nattempt to do so. The choice of food within a wide range depends\nentirely on taste, and has nothing to do with moral considerations\n(whether, for instance, we should have squash or beans for dinner).\nThose who are deeply impressed with the importance of moral rules are\noften betrayed into applying them to the veriest minutiae of conduct. Did\nthey remember that ethics is a science of relations, or, what amounts to\nthe same thing, a science of limits, they would be saved such pedantry.\nUndoubtedly there are moral _adiaphora_. The fact that such exist has\nbeen a stumbling-block in the way of those who believe that morality\nought to cover the whole of conduct. The definition of ethics as a\nscience of relations or limits removes this stumbling-block. Ethics\nstands at the frontier. With what goes on in the interior it does not\ninterfere, except in so far as the limitations it prescribes are an\ninterference. Take another illustration. Ethics condemns vanity and\nwhatever ministers to vanity--as, e. g., undue attention to dress and\nadornment of the person--on the ground that this implies an immoral\nsubordination of the inner to the outer, of the higher to the lesser\nends. But, to lay down a cast-iron rule as to how much one has a right\nto expend on dress, can not be the office of ethics, on account of the\ninfinite variety of conditions and occupations which subsists among men.\nAnd the attempt to prescribe a single fashion of dress, by sumptuary\nlaws or otherwise, would impair that freedom of taste which it is the\nbusiness of the moralist to respect. Again, every one knows with what\nbitterness the moral rigorists of all ages have condemned the impulse\nwhich attracts the sexes toward one another, and how often they have\ntried, though vainly, to crush it. But here, again, the true attitude is\nindicated by the definition of ethics as a science of limits. The moral\nlaw prescribes bounds within which this emotional force shall be free to\noperate, and claims for it the holy name of love, so long as it remains\nwithin the bounds prescribed, and, being within, remains conscious of\nthem. That is what is meant when we speak of spiritualizing the\nfeelings. The feelings are spiritualized when they move within certain\nlimits, and when the sense of the existence of these limits penetrates\nthem, and thereby imparts to them a new and nobler quality. And, because\nsuch limitation is felt to be satisfying and elevating, the system of\ncorrelations which we call ethical, and which, abstractly stated, would\nfail to interest, does by this means find an entrance into the human\nheart, and awakens in it the sense of the sublimity and the blessedness\nof the moral commands.\n\nThere are two defects of the moral fanatic which can now be signalized:\nFirst, he wrongly believes that whatever is not of morality is against\nit. He therefore is tempted to frown upon the natural pleasures; to\nbanish them if he can, and, if not, to admit them only within the\nnarrowest possible limits as a reluctant concession to the weakness of\nhuman nature. In consequence, the moral fanatic commits the enormity of\nintroducing the taint of the sense of sin into the most innocent\nenjoyments, and thus perverts and distorts the conscience. Secondly, he\nis always inclined to seek a moral reason for that which has only a\nnatural one; to forget that, like the great conquerors of antiquity,\nMorality respects the laws of the several realms which it unites into a\nsingle empire, and guarantees to each the unimpaired maintenance of its\nlocal customs. These remarks are intended to serve as a general caution.\nI find that young people, when they have become awakened on ethical\nsubjects, often betray a tendency toward moral asceticism. I find that\nteachers, in the earnest desire to impress the laws of the moral empire,\nare sometimes betrayed into disregarding the provincial laws of the\nsenses, the intellect, and the feelings; are apt to go too far in\napplying moral prescriptions to the minutiae of conduct; are apt to leave\nthe impression that pleasant things, just because they are pleasant, are\ntherefore sinful.\n\nBut we have now to take a further step, which will bring us close to our\nspecial subject for to-day, viz., the efficient motives of good conduct.\nThe non-moral faculties are not only not anti-moral, as has been shown,\nbut, when appealed to in the right way, they lend to Morality a\nfriendly, an almost indispensable support. The aesthetic, the\nintellectual, and the emotional faculty have not in themselves a moral\nquality, but when used as auxiliaries they pave the way for moral\nconsiderations pure and simple, and have in this sense an immense\npropaedeutic value. Without entering in this place into the philosophy of\naesthetics, it is enough to say that the beautiful, like the good,\nresults from and depends on the observance of certain limits and certain\nrelations. And it will not seem far-fetched to suggest that pupils who\nhave been trained to appreciate moderation, restraint and harmony of\nrelations in external objects, will be predisposed to apply analogous\nmeasures to matters of conduct, and that a standard of valuation will\nthus be created in their minds which must prove favorable to right\naction. AEsthetics may become a pedagogue unto ethics. The same\npedagogical function may be claimed for the intellect. The intellect\ntraces the connection between causes and effects. Applied to conduct, it\nshows the connection between acts and their consequences. It is the\nfaculty which counsels prudence. One does not need to accept the\negoistic theory of morals to concede that self-interest is an ally of\nmorality, that Prudence and Virtue travel hand in hand a certain\ndistance on the same road. Not, indeed, until the ideal state shall have\nbeen reached will the dictates of the two ever coincide entirely; but to\na certain extent the coincidence already exists, and the moral teacher\nis justified in availing himself of it as far as it goes.\n\nTo take a very simple case--a child handles a knife which it has been\ntold not to touch, and cuts his fingers. Morally speaking, his fault is\ndisobedience. He would have been equally guilty if he had escaped\ninjury. But he would hardly be so ready to obey another time, if he had\nbeen less sharply reminded of the usefulness of obedience. It is wrong\nto lie--wrong on purely moral grounds, with which self-interest has\nnothing to do. But for all that we can not dispense with the lesson\ncontained in the well-known fable of the boy who cried, \"Wolf!\" It is\nwrong to steal on purely moral grounds. But even a child can be made to\nunderstand that the thief, as Emerson puts it, \"steals from himself,\"\nand that, besides being a rogue, he is deficient in enlightened\nself-interest. The maxim that honesty is the best policy is true enough\nso far as the facts are concerned, which come under the observation of\nchildren, though one may question whether it be true absolutely.\n\nLastly, when we come to consider the emotional faculty, we find that\nthe intimate connection between it and the moral is so generally\nconceded as to make it quite superfluous to expatiate on it. On the\ncontrary, it seems necessary to expostulate with those who claim too\nmuch credit for the feelings, who ascribe to them a moral value which\nthey by no means possess. Thus, gentleness is not necessarily a virtue;\nit may be a mere matter of temperament. Sympathetic impulses, _per se_,\nare not praiseworthy. Sympathy quite as often leads us astray as aright;\nsympathy, indeed, unless tutored and regulated by moral principles, is a\ndanger against which we ought to be on our guard almost as much as\nagainst selfishness. Yet, no one will deny that the feelings, when\nrightly trained, are of inestimable service as auxiliaries in the task\nof moral education.\n\nTo sum up, let me say that the wise teacher will appeal to the taste,\nthe intelligence, and the feelings of his pupils; that he will touch\nthese various springs of conduct all the time, and get from them all the\nhelp he can. Thus, when speaking of cleanliness, he will appeal to the\naesthetic instinct of the children, awakening in them a feeling of\ndisgust at untidiness. He will appeal to the prudential motive, by\nshowing that want of cleanliness breeds disease. \"You do not wish to be\nsick? You do not wish to suffer? Therefore, it is to your interest to be\nclean.\" But, finally, he will touch a higher motive than any of these.\n\"If you are unclean, you cease to respect yourself.\" And the term\nself-respect expresses in a condensed form the moral motive proper. It\nimplies the idea of moral personality, which it is not necessary, nor\npossible, at this stage to analyze, but which the pupil will somehow\nunderstand, for his conscience will respond. In many cases the appeal\nwill be made chiefly to the sympathetic feelings; for through these\nfeelings we become aware of the pains and joys of others, and thus of\nthe consequences of the benefits we confer or the evil we inflict. The\nsympathetic feelings supply the information upon which the will can act.\nThey tell us that others suffer or are glad. And yet the strength to\nlabor persistently for the relief of others' suffering and the\nenhancement of others' joy--that we can derive from the moral impulse\nalone.\n\nThe moral motive is the highest, it is really the only sufficient\nmotive. Pray, understand me well at this point. I should say to the\nchild: It is wrong to lie. That is sufficient. It is wrong, it is\nforbidden; you must yourself acknowledge the truth of my words, because\nyou despise yourself when you have told a lie. But, in order to\nstrengthen your weak resolution, to confirm you in well-doing, let me\nshow you that it is also contrary to self-interest to lie, and likewise\nthat it is disgusting to be unclean, and that a wrong done to another\ncauses pain. Thus the aesthetic, intellectual, and emotional faculties\nare called in as witnesses to bear testimony to the moral truths; they\nare invited to stand up in chorus and say Amen! to the moral commands.\n\nFOOTNOTE:\n\n[3] It must be remembered also that our knowledge of the right ethical\nrelations is still extremely imperfect, and that the duty of extending\nthe knowledge and promoting the recognition of them is perhaps the\nhighest of all--to which, on occasion, every lesser end must be\nsacrificed.\n\n\n\n\nIII.\n\nOPPORTUNITIES FOR MORAL TRAINING IN THE DAILY SCHOOL.\n\n\nThe school should be to the pupil not an intellectual drill-ground, but\na second home; a place dear at the time, and to be gratefully remembered\never after; a place in which his whole nature, and especially what is\nbest in him, may expand and grow. The educational aim should be, not\nmerely to pave the pupil's way to future success, not merely to make of\nhis mind a perfect instrument of thought, a kind of intellectual loom,\ncapable of turning out the most complicated intellectual patterns. The\naim should be, above all; to build up manhood, to develop character.\nThere is no school in which moral influence is wanting. The pity is,\nthat in many schools it is incidental, not purposed. And yet there are\nmanifold opportunities in every school for influencing the moral life.\nLet us consider a few of these.\n\n_1._ The teaching of _science_ lends itself to the cultivation of\ntruthfulness. Truthfulness may be defined as the correspondence between\nthought and word and fact. When the thought in the mind fits the fact,\nand the word on the tongue fits the thought, then the circuit of truth\nis complete. Now, with respect to the inculcating of truthfulness,\nscience teaching has this advantage above other branches, that the\npalpable nature of the facts dealt with makes it possible to note and\ncheck the least deviation from the truth. The fact is present, right\nbefore the pupil, to rebuke him if he strays from it in thought or\nspeech. And this circumstance may be utilized even in the humble\nbeginnings of science teaching, in the so-called object-lessons. For\ninstance, a bird, or the picture of one, is placed before the child. The\nteacher says, \"Observe closely and tell me exactly what you see--the\nlength of the neck, the curve of the beak, the colors of the plumage,\"\netc. The pupil replies. The teacher objects: \"You have not observed\naccurately. The color is not what you describe it to be. Look again. The\ncurve of the beak does not resemble what you have just drawn on the\nblackboard. You must tell me exactly what you see. Your words must tally\nwith the facts.\" And the same sort of practice may be continued in the\nscience-lessons of the upper classes.\n\nScientists are distinguished from other observers by their greater\naccuracy. Intellectual honesty is that moral quality which science is\nbest calculated to foster. All the great scientists have been haunted by\na high ideal of truth, and a gleam of that ideal, however faint, may be\nmade to shed its light even into the school-room. It is obvious that\nthis realistic tutoring into veracity will be of special use to children\nwho are led into lying by a too vivid imagination.\n\nLet me add the following remarks in regard to indirect means of\npromoting truthfulness: The teacher can do a great deal to cultivate\nrespect for the truth among his pupils by frankly admitting an error\nwhenever he has fallen into one. Some teachers try to save their dignity\nby glossing over their mistakes. But even young children are shrewd\nenough to estimate such trickery at its worth; while he who manfully\nconfesses that he has been in the wrong, earns the respect of his class,\nand sets them an invaluable example.\n\nIt is well also to observe strict accuracy even in matters which of\nthemselves are of no moment. For instance, in giving an account of a\nbotanizing expedition, you begin, perhaps, by saying, \"It was half-past\nten when we arrived at our destination.\" Suddenly you stop and correct\nyourself. \"No, I was mistaken; it could not have been later than ten\no'clock.\" Does this strike you as pedantic? But if you fix the time at\nall, is it not worth while to fix it with approximate exactness? True,\nit makes no difference in regard to what you are about to relate,\nwhether you arrived at half-past ten or at ten. But, precisely because\nit makes no difference, it shows the value which you set on accuracy\neven in trifles. And by such little turns of phrase, by such\ninsubstantial influences, coming from the teacher, the pupil's character\nis molded.\n\n_2._ _The study of history_, when properly conducted is of high moral\nvalue. History sets before the mind examples of heroism, of\nself-sacrifice, of love of country, of devotion to principles at the\ngreatest cost. How can such examples fail to inspire, to ennoble, to\nawaken emulation? The great and good men of the past, the virtuous and\nthe wise, serve as models to the young, and often arouse in them an\nenthusiastic admiration, a passionate discipleship. In the next place,\nthe study of history may be used to exercise the moral judgment. The\ncharacters which history presents are not all good; the characters even\nof the good are by no means faultless. It is in the power of the teacher\nto train the moral judgment and to increase the moral insight of his\npupils by leading them to enter into the motives, and to weigh the right\nand wrong of the actions which history reports. He will also find many\nan occasion to warn against being dazzled by brilliant success to such a\ndegree as to condone the moral turpitude by which it is often bought.\nThe study of history can thus be made the means of enlightening the\nconscience as well as of awakening generous aspirations--but, let me\nhasten to add, only in the hands of a teacher who is himself morally\nmature, and fully imbued with the responsibilities of his task. Lastly,\nthe study of history among advanced pupils may be used to confirm the\nmoral idea of the mission of mankind, and to set it in its true light.\nThe human race, as, from the moral point of view, we are bound to\nassume, exists on earth in order to attempt the solution of a sublime\nproblem--the problem of the perfect civilization, the just society, the\n\"kingdom of God.\" But on every page of history there are facts that warn\nus that progress toward this high ideal is of necessity slow. Whether\nwe review the evolution of religion, or of political institutions, or of\nindustrial society, we are still forced to the same solemn conclusion,\nthat in view of the ultimate goal, \"a thousand years are as a day,\" and\nthat while we may not relax our efforts to attain the ideal, we must be\nwell content in case we are permitted to advance the mighty work even a\nlittle. This conviction is calculated to engender in us a new spirit of\npiety and self-abnegation, which yet is consistent with perfect alacrity\nin discharging the duty of the hour.\n\nThere could be no better result from the study of history among young\nmen and young women than if it should have the effect of impressing on\nthem this new piety, this genuine historic sense, in which the average\ncitizen, especially of democratic communities, is so conspicuously\ndeficient. But this is a digression which I must ask you to pardon.\n\n_3._ The moral value of the _study of literature_ is as great as it is\nobvious. Literature is the medium through which all that part of our\ninner life finds expression which defies scientific formulation. In the\ntext-books of science we possess the net result of the purely\nintellectual labors of the past; in universal literature we have\ncomposite photographs, as it were, of the typical hopes, sentiments, and\naspirations of the race. Literature gives a voice to that within us\nwhich would otherwise remain dumb, and fixity to that which would\notherwise be evanescent. The best literature, and especially the best\npoetry, is a glass in which we see our best selves reflected. There is\na legend which tells of two spirits, the one an angel, the other a\ndemon, that accompany every human being through life, and walk invisibly\nat his side. The one represents our bad self, the other our better self.\nThe moral service which the best literature renders us is to make the\ninvisible angel visible.\n\n_4._ I can but cast a cursory glance at some of the remaining branches\nof instruction.\n\n_Manual training_ has a moral effect upon the pupil, of which I have\nspoken at some length on another occasion.[4]\n\n_Music_, apart from its subtler influences, which can not be considered\nhere, has the special function of producing in the pupil a feeling of\noneness with others, or of social unity. This is best accomplished\nthrough the instrumentality of chorus singing, while particular moral\nsentiments, like charity, love of home, etc., can be inculcated by means\nof the texts.\n\n_Gymnastic_ exercises likewise have a moral effect in promoting habits\nof self-control, prompt obedience at the word of command, etc. Indeed,\nit is not difficult to show the moral bearings of the ordinary branches\nof instruction. It would, on the contrary, be difficult to find a single\none, which, when rightly viewed, is not surrounded by a moral\nphotosphere.\n\nScience, history, literature, and the other branches lend themselves in\nvarious ways to the development of character. But there are certain\nother opportunities which every school offers, apart from the teaching,\nand these may be utilized to the same end. The discipline of the school,\nabove all, has an immense effect on the character. If it is of the right\nkind, a beneficial effect; if not, a most pernicious one.\n\nThe mere working of what may be called the school machinery tends to\ninculcate habits of order, punctuality, and the like. The aggregation of\na large number of scholars in the same building and their intercourse\nwith one another under the eye of the teachers, afford frequent\nopportunities for impressing lessons of kindness, politeness, mutual\nhelpfulness, etc.\n\nThe recitations of lessons give occasion not only to suppress prompting,\nbut to eradicate the motives which lead to it, and to impress deeply the\nduty of honesty.\n\nThe very atmosphere of the class-room should be such as to encourage\nmoral refinement; it should possess a sunny climate, so to speak, in\nwhich meanness and vulgarity can not live.\n\nBut there is especially one avenue of influence, which I have much at\nheart to recommend. The teacher should join in the _games_ of his\npupils. He will thus at once come to stand on a friendly footing with\nthem, and win their confidence, without in the least derogating from his\nproper dignity. And thus will be removed that barrier which in many\nschools separates pupils and teachers to such a degree that there\nactually seem to exist side by side two worlds--the world to which the\nteacher has access, and the world from which he is shut out. Moreover,\nwhile they are at play, the true character of the pupils reveals itself.\nAt such times the sneak, the cheat, the bully, the liar, shows his true\ncolors, and the teacher has the best opportunity of studying these\npathological subjects and of curing their moral defects. For, while\nplaying with them, as one concerned in the game, he has the right to\ninsist on fair dealing, to express his disgust at cowardice, to take the\npart of the weak against the strong, and his words spoken on the\nplayground will have tenfold the effect of any hortatory address which\nhe might deliver from the platform. The greatest and most successful of\nteachers have not disdained to use this device.\n\nFinally, let me say that the personality of the master or principal of\nthe school is the chief factor of moral influence in it. Put a great,\nsound, whole-souled nature at the head of a school, and everything else\nmay almost be taken for granted. In every school there exists a public\nopinion among the scholars, by which they are affected to a far greater\ndegree than by the words of their superiors. The tactful master will\ndirect his chief attention to shaping and improving this public opinion,\nwhile at the same time interfering as little as possible with the\nfreedom of his pupils. He can accomplish his purpose by drawing close to\nhimself those scholars who make the public opinion of the school, and\nthese in turn he can win to fine and manly views only by the effect of\nhis personality. The personality of the head-master is everything. It is\nthe ultimate source of power in the school, the central organ which\nsends out its life-giving currents through the whole organism. And let\nme here add that, if I am in favor of excluding direct religious\nteaching from our schools, I am not in favor of excluding religious\ninfluence. That, too, flows from the personality of the true master. For\nif he be reverent, a truly pious soul, humble in his estimate of self,\nnot valuing his petty schoolmaster's authority on its own account, but\nusing it lovingly as an instrument for higher ends, he will be sure to\ncommunicate of his spirit to his pupils, and by that spirit will open\ntheir hearts, better than by any doctrinal teaching he could give, to\nthe reception of the highest spiritual truths.\n\nBy all these means--by the culture of the intellect, the taste, and the\nfeelings, by his daily dealings with the young, in work and play--the\nteacher helps to create in them certain moral habits. Why, then, should\nnot these habits suffice? What need is there of specific moral\ninstruction? And what is the relation of moral instruction to the habits\nthus engendered?\n\nThe function of moral instruction is to clinch the habits. The function\nof moral instruction is to explicate in clear statements, fit to be\ngrasped by the intellect, the laws of duty which underlie the habits.\nThe value of such intellectual statements is that they give a rational\nunderpinning to moral practice, and, furthermore, that they permit the\nmoral rules to be applied to new cases not heretofore brought within the\nscope of habit. This thought will be more fully developed and explained\nas we proceed.\n\nFOOTNOTE:\n\n[4] In the address on the subject, reprinted in the Appendix.\n\n\n\n\nIV.\n\nCLASSIFICATION OF DUTIES.\n\n\nThe topics of which moral instruction treats are the duties of life. To\nteach the duties, however, we must adopt some system of classification.\nTo which system shall we give the preference? The difficulty which we\nencountered at the outset seems to meet us here in a new guise.\n\nFor most if not all of the systems of classification commonly proposed\nare based upon some metaphysical theory or some theological doctrine. To\nadopt any one of these would be tantamount to adopting the theory or\ntheology on which it is founded; would be equivalent to introducing\nsurreptitiously a particular philosophy or creed into the minds of the\npupils; and this would be a plain departure from the unsectarian\nprinciple to which we are pledged. Thus, Plato's fourfold division of\nthe virtues into the so-called cardinal virtues of temperance, courage,\njustice, wisdom, is based on his psychology. Aristotle's division of the\nvirtues into dianoetic and what he calls ethical virtues is clearly\ndependent on what may be termed Aristotle's intellectualism--i. e., the\nsupreme importance which he assigns to the functions of the intellect,\nor [Greek: nous], in the attainment of the perfect life.\n\nKant's division of duties into complete and incomplete is an outgrowth\nof the ideas developed in his Critique of Pure Reason; the philosopher\nHerbart's fivefold classification reflects his metaphysical theory of\nreality; while the systems of ethical classification which are to be\nfound in theological handbooks betray still more clearly the bias of\ntheir authors.\n\nWe can, I think, find a simple way out of this difficulty by proceeding\nin the following manner: Let us take for our guidance the objects to\nwhich duty relates, and disregard the sources from which it flows. It is\nconceded on all hands that every one is to himself an object of duty,\nthat he has certain duties to perform with respect to himself, as, for\ninstance, the duty of intellectual development; furthermore, that every\nperson owes certain duties to his fellow-men generally, in virtue of the\nfact that they are human beings; again, that there are special duties\nwhich we owe to particular persons, such as parents, brothers, and\nsisters; finally, that there are certain duties, into which, so to\nspeak, we are born, like the ones last mentioned, and others which we\ncan freely assume or not, like the conjugal duties, but which, once\nassumed, become as binding as the former. Thus the very structure of\nhuman society suggests a scheme of classification. And this scheme has\nthe advantage of being a purely objective one. It keeps close to the\nfacts, it is in harmony with the unsectarian principle, and it is\nperfectly fair. It leaves the problem of first principles entirely\nuntouched. That we have such duties to perform with respect to self and\nothers, no one questions. Let philosophers differ as to the ultimate\nmotives of duty. Let them reduce the facts of conscience to any set of\nfirst principles which may suit them. It is our part as instructors to\ninterpret the facts of conscience, not to seek for them an ultimate\nexplanation.\n\nLet me briefly indicate how the different duties may be made to fall\ninto line according to the plan of classification which has just been\nsuggested. The whole field of duty may be divided into three main\nprovinces:[5] those duties which relate to ourselves, those which we owe\nto all men, and those which arise in the special relations of the\nfamily, the state, etc.:\n\nI. The Self-regarding Duties.\n\nThese may again be subdivided into duties relating to our physical\nnature, to the intellect, and to the feelings.\n\nUnder the head of physical duties belong the prohibition of suicide, and\nthe duties of physical culture, temperance, and chastity.\n\nIntellectual Duties.--Under this head may be ranged the duty of\nacquiring knowledge and the subsidiary duties of order, diligence,\nperseverance in study; while, for those who are beyond the school age,\nspecial stress should be laid on the duty of mental genuineness. This\nmay be expressed in the words: To thine own mental self be true. Study\nthine own mental bent. Try to discover in what direction thy proper\ntalent lies, and make the most of it. Work thine own mine: if it be a\ngold-mine, bring forth gold; if it be a silver-mine, bring forth silver;\nif it be an iron-mine, bring forth iron. Endeavor to master some one\nbranch of knowledge thoroughly well. It is for thee the key which opens\nthe gates of all knowledge. The need of general culture is felt by all,\nbut the concentration of intellectual efforts on special studies is not\ninconsistent with it. On the contrary, special studies alone enable us\nto gain a foothold in the realm of knowledge. A branch of knowledge\nwhich we have mastered, however small, may be compared to a strong\nfortress in an enemy's country, from which we can sally forth at will to\nconquer the surrounding territory. Knowledge may also be likened to a\nsphere. From every point of the circumference we can, by persistent\nlabor, dig down to the center. He who has reached the center commands\nthe sphere.\n\nDuties which relate to the Feelings.--The principal duty under this head\nmay be expressed in the twofold command--control and purify thy\nfeelings! The feelings which need to be repressed are anger, fear,\nself-complacency. Let the teacher, when he reaches this point, dwell\nupon the causes and the consequences of anger. Let him speak of certain\nhelps which have been found useful for the suppression of angry passion.\nLet him distinguish anger from moral indignation.\n\nIn dealing with fear let him pursue the same method. Let him distinguish\nphysical from moral cowardice, brute courage from moral courage, courage\nfrom fortitude.\n\nIn dealing with self-complacency let him discriminate between vanity and\npride, between pride and dignity. Let him show that humility and dignity\nare consistent with one another, yes, that they are complementary\naspects of one and the same moral quality. Not the least advantage to be\nreaped from lessons on duty is the fixing in the pupil's mind of the\nmoral vocabulary. The moral terms as a rule are loosely used, and this\ncan not but lead to confusion in their application. Precise definitions,\nbased on thorough discussion, are an excellent means of moral\ntraining.[6]\n\nII. The duties which we owe to all men are Justice and Charity:\n\nBe just is equivalent to--Do not hinder the development of any of thy\nfellow-men. Be charitable is equivalent to--Assist the development of\nthy fellow-men. Under the head of charity the teacher will have\noccasion to speak not only of almsgiving, the visitation of the sick,\nand the like, but of the thousand charities of the fireside, of the\ncharity of bright looks, of what may be called intellectual charity,\nwhich consists in opening the eyes of the mentally blind, and of the\nnoblest charity of all, which consists in coming to the aid of those who\nare deep in the slough of moral despond, in raising the sinful and\nfallen.\n\nIII. Special social duties:\n\nUnder this head belong the duties which arise in the family: the\nconjugal, the parental, the filial, the fraternal duties.\n\nUnder the head of duties peculiar to the various avocations should be\ndiscussed the ethics of the professions, the ethics of the relations\nbetween employers and laborers, etc.\n\nThe consideration of the duties of the citizen opens up the whole\nterritory of political ethics.\n\nLastly, the purely elective relationships of friendship and religious\nfellowship give rise to certain fine and lofty ethical conceptions, the\ndiscussion of which may fitly crown the whole course.\n\nI have thus mentioned some of the main topics of practical ethics, from\nwhich we are to make our selection for the moral lessons.\n\nBut a selective principle is needed. The field being spread out before\nus, the question arises, At what point shall we enter it? What topics\nshall we single out? It would be manifestly absurd, for instance, to\ntreat of international ethics, or of conjugal ethics, in a course\nintended for children. But especially the order in which the different\ntopics are to follow each other needs to be determined. The order\nfollowed in the above sketch is a purely logical one, and the logical\narrangement of a subject, as every educator knows, is not usually the\none most suitable for bringing it within reach of the understanding of\nchildren. It would not be in the present instance. Clearly a selective\nprinciple is wanted.\n\nLet me here interrupt myself for a moment to say that the problem which\nwe are attacking, so far from being solved, has heretofore hardly even\nbeen stated. And this is due to the fact that moral instruction has been\nthus far almost entirely in the hands of persons whose chief interest\nwas religious, and who, whatever their good intentions might be, were\nhardly qualified to look at the subject from the educator's point of\nview. The work of breaking ground in the matter of moral instruction has\nstill to be done. As to the selective principle which I have in view I\nfeel a certain confidence in its correctness; but I am aware that the\napplications of it will doubtless require manifold amendment and\ncorrection, for which purpose I invoke the experience and honest\ncriticism of my fellow-teachers. This being understood, I venture to ask\nyour attention to the following considerations:\n\nThe life of every human being naturally divides itself into distinct\nperiods--infancy, childhood, youth, etc. Each period has a set of\ninterests and of corresponding duties peculiar to itself. The moral\nteaching should be graded according to periods. The teaching\nappropriate to any period is that which bears upon the special duties of\nthat period. To illustrate, the ethics of childhood may be summarized as\nfollows: The personal duties of a child are chiefly the observance of a\nfew simple rules of health and the curbing of its temper. It owes social\nduties to parents, brothers and sisters, and kinsfolk, to its playmates,\nand to servants. The child is not yet a citizen, and the ethics of\npolitics, therefore, lie far beyond its horizon; it does not yet require\nto be taught professional ethics, and does not need to learn even the\nelements of intellectual duty, because its energies are still absorbed\nin physical growth and play. The duties of childhood can be readily\nstated. The peculiar duties of the subsequent stages of development, for\ninstance, of middle life and old age, are complex, and not so easy to\ndefine. But I believe that the attempt to describe them will throw light\non many recondite problems in ethics.\n\nMy first point therefore is, that the moral teaching at a given period\nshould be made to fit the special duties of that period. Secondly--and\nthis touches the core of the matter--in every period of life there is\nsome one predominant duty around which all the others may be grouped, to\nwhich as a center they may be referred. Thus, the paramount duty of the\nyoung child is to reverence and obey its parents. The relation of\ndependence in which it stands naturally prescribes this duty, and all\nits other duties can be deduced from and fortified by this one. The\ncorrectness of its personal habits and of its behavior toward others\ndepends primarily on its obedience to the parental commands. The child\nresists the temptation to do what is wrong, chiefly because it respects\nthe authority and desires to win the approbation of father and mother.\nSecondary motives are not wanting, but reverence for parents is the\nprincipal one.\n\nThirdly, in each new period there emerges a new paramount ethical\ninterest, a new center of duties. But with the new system of duties thus\ncreated the previous ethical systems are to be brought into line, into\nharmonious correlation. And this will be all the more feasible, because\nthe faithful performance of the duties of any one period is the best\npreparation for the true understanding and fulfillment of those of the\nnext. From these statements the following conclusions may be drawn with\nrespect to the question under discussion--namely, the proper sequence of\nthe topics of duty in a course of moral lessons.\n\nThe moral lessons being given in school, must cover the duties which are\npeculiar to the school age. The paramount duty should be placed in the\nforeground. Now the paramount duty of children between six and fourteen\nyears of age is to acquire knowledge. Hence we begin the lessons with\nthe subject of intellectual duty. In the next place, the duties learned\nin the previous periods are to be brought into line with the duties of\nthe school age. At each new step on the road of ethical progress the\nmoral ideas already acquired are to be reviewed, confirmed, and to\nreceive a higher interpretation.\n\nWe have already seen that, before the child enters school, its personal\nduties are such as relate to the physical life and the feelings, and its\nchief social duties are the filial and fraternal.\n\nTherefore, the order of topics for the lessons thus far stands: The duty\nof acquiring knowledge; the duties which relate to the physical life;\nthe duties which relate to the feelings; the filial duties; the\nfraternal duties.\n\nAgain, a child that has learned to respect the rights of its brothers\nand sisters, and to be lovingly helpful to them, will in school take the\nright attitude toward its companions. The fraternal duties are typical\nof the duties which we owe to all our companions, and, indeed, to all\nhuman beings.\n\nThe next topic of the lessons, therefore, will be the duties which we\nowe to all human beings.\n\nFinally, life in school prepares for life in society and in the state,\nand so this course of elementary moral lesson will properly close with\n\"The elements of civic duty.\"\n\nFOOTNOTES:\n\n[5] It may be urged by some that duties toward God ought to be included\nin such a scheme of moral lessons as we are proposing. I should say,\nhowever, that the discussion of these duties belongs to the\nSunday-schools, the existence of which alongside the daily schools is\n_presupposed throughout the present course of lectures_.\n\n[6] The duties which relate to the moral nature, as a whole, such for\ninstance as the duty of self-scrutiny, may be considered either at the\nend of the chapter on self-regarding duties, or at the close of the\nwhole course.\n\n\n\n\nV.\n\nTHE MORAL OUTFIT OF CHILDREN ON ENTERING SCHOOL.\n\n\nIt is difficult to trace the beginnings of the moral life in children.\nThe traveler who attempts to follow some great river to its source\ngenerally finds himself confused by the number of ponds and springs\nwhich are pointed out to him with the assurance in the case of each that\nthis and no other is the real source. In truth, the river is fed not\nfrom one source but from many, and does not attain its unity and\nindividuality until it has flowed for some distance on its way. In like\nmanner, the moral life is fed by many springs, and does not assume its\ndistinctive character until after several years of human existence have\nelapsed. The study of the development of conscience in early childhood\nis a study of origins, and these are always obscure. But, besides, the\nattention hitherto given to this subject has been entirely inadequate,\nand even the attempts to observe in a systematic way the moral\nmanifestations of childhood have been few.\n\nParents and teachers should endeavor to answer such questions as these:\nWhen do the first stirrings of the moral sense appear in the child? How\ndo they manifest themselves? What are the emotional and the\nintellectual equipments of the child at different periods, and how do\nthese correspond with its moral outfit? At what time does conscience\nenter on the scene? To what acts or omissions does the child apply the\nterms right and wrong? If observations of this kind were made with care\nand duly recorded, the science of education would have at its disposal a\nconsiderable quantity of material from which no doubt valuable\ngeneralizations might be deduced. Every mother especially should keep a\ndiary in which to note the successive phases of her child's physical,\nmental, and moral growth; with particular attention to the moral; so\nthat parents may be enabled to make a timely forecast of their\nchildrens' characters, to foster in them every germ of good, and by\nprompt precautions to suppress, or at least restrain, what is bad.\n\nI propose in the present lecture to cast a glance at the moral training\nwhich the normal child receives before it enters school, and the moral\noutfit which it may be expected to bring with it at the time of\nentering. Fortunately, it is not necessary to go very deeply into the\nstudy of development of conscience for this purpose. A few main points\nwill suffice for our guidance.\n\n_First Point._--The moral training of a child can be begun in its\ncradle. Regularity is favorable to morality. Regularity acts as a check\non impulse. A child should receive its nourishment at stated intervals;\nit should become accustomed to sleep at certain hours, etc. If it\nprotests, as it often does vigorously enough, its protests should be\ndisregarded. After a while its cries will cease, it will learn to submit\nto the rule imposed, and the taking of pleasure in regularity and the\nsense of discomfort when the usual order is interrupted become\nthenceforth a part of its mental life. I do not maintain that regularity\nitself is moral, but that it is favorable to morality because it curbs\ninclination. I do not say that rules are always good, but that the life\nof impulse is always bad. Even when we do the good in an impulsive way\nwe are encouraging in ourselves a vicious habit. Good conduct consists\nin regulating our life according to good principles; and a willingness\nto abide by rules is the first, the indispensable condition of moral\ngrowth. Now, the habit of yielding to rules may be implanted in a child\neven in the cradle.\n\n_Second Point._--A very young child--one not older than a year and a\nhalf--can be taught to obey, to yield to the parent's will. A child a\nyear and a half old is capable of adhering to its own will in defiance\nof the expressed will of father or mother. In this case it should be\nconstrained to yield. We shall never succeed in making of it a moral\nperson if it does not realize betimes that there exists a higher law\nthan the law of its will. And of this higher law, throughout childhood,\nthe parent is, as it were, the embodiment. When I say that obedience can\nbe exacted of a child of such tender age, that a child so young is\ncapable of deliberately opposing the will of the parent, I speak from\nexperience. I know a certain little lady who undertook a struggle with\nher father precisely in the way described. The struggle lasted fully\nthirty-five minutes by the clock. But when it was over, the child\nstretched out her little arms and put up her lips to be kissed, and for\ndays after fairly clung to her father, showing him her attachment in the\nmost demonstrative manner. Nor should this increase of affectionateness\nexcite surprise--it is the proper result of a conflict of this sort\nbetween father and child when conducted in the right spirit. The child\nis happy to be freed from the sway of its wayward caprice, to feel that\nits feeble will has been taken up into a will larger and stronger than\nits own.\n\n_Third Point._--What is called conscience does not usually begin to show\nitself until the child is about three years old. At this age the concept\nself usually emerges, and the child begins to use the personal pronoun\nI. This is one of these critical turning points in human development, of\nwhich there are several. The beginning of adolescence marks another. I\nam inclined to suspect that there is one at or about thirty-three. There\nseem to be others later on. At any rate the first turning point--that\nwhich occurs at three--is marked unmistakably. At this time, as we have\njust said, the child begins to be distinctly self-conscious; it says\n\"I,\" and presently \"you,\" \"he,\" and \"they.\" Now, moral rules formulate\nthe relations which ought to subsist between one's self and others, and\nto comprehend the rules it is clearly necessary to be able to hold apart\nin the mind and to contrast with one another the persons related. It is\nevident, therefore, that the emergence of the concept self must have a\ndecided effect on moral development.\n\nI feel tempted to pause here a moment and to say a word in passing about\nthe extreme importance of the constituent elements of the concept self.\nFor it must not be supposed that the pronoun \"I\" means the same thing on\nthe lips of every person who uses it. \"I\" is a label denoting a mass of\nassociated ideas, and as these ideas are capable of almost endless\nvariation, so the notion of selfhood is correspondingly diversified in\ndifferent individuals. In the case of children, perhaps the principal\nconstituents of the concept are supplied by their outward appearance and\nenvironment. When a child speaks of itself, it thinks primarily of its\nbody, especially its face, then of the clothes it usually wears, the\nhouse it lives in, the streets through which it habitually walks, its\nparents, brothers, sisters, school-masters, etc.[7] If we analyze the\nmeaning of \"I\" in the case of two children, the one well-born and well\nbrought up, the other without these advantages, we shall perhaps find\nsuch differences as the following: \"I\" in the one case will mean a being\nliving in a certain decent and comfortable house, always wearing neat\nclothing, surrounded by parents, brothers, and sisters who speak kindly\nto one another and have gentle manners, etc. In the other case, the\nconstituents of the concept self may be very different. \"I\" in the case\nof the second child may mean a creature that lives in a dark, filthy\nhovel and walks every day through narrow streets, reeking with garbage.\n\"I\" may mean the child of a father who comes home drunk and strikes the\nmother when the angry fit is upon him. \"I\" stands for a poor waif that\nwears torn clothes, and when he sits in school by the side of\nwell-dressed children is looked at askance and put to shame. It is\nobvious that the elements which go to make up the concept self affect\nthe child's moral nature by lowering or raising its self-esteem. I\nremember the case of one, who as a boy was the laughing-stock of his\nclass on account of the old-fashioned, ill-fitting clothes which he was\ncompelled to wear, and who has confessed that even late in life he could\nnot entirely overcome the effect of this early humiliation, and that he\ncontinued to be painfully aware in himself, in consequence, of a certain\nlack of ease and self-possession. Hence we should see to it that the\nconstituent elements of the concept self are of the right kind. It is a\nmistake to suppose that the idea of selfhood stands off independently\nfrom the elements of our environment. The latter enter into, and when\nthey are bad eat into, the very kernel of our nature.\n\nWe have seen that the development of the intellect as it appears in the\ngrowing distinctness of self-consciousness exercises an important\ninfluence on the development of the moral faculty. But there is still\nanother way in which this influence becomes apparent. The function of\nconscience further depends on the power of keeping alternative courses\nof action before the mind. Angels capable only of the good, or fiends\nactuated exclusively by malice, could not be called moral creatures. A\nmoral act always presupposes a previous choice between two possible\nlines of action. And until the power of holding the judgment in\nsuspense, of hesitating between alternative lines of conduct, has been\nacquired, conscience, strictly speaking, does not manifest itself. We\nmay say that the voice of conscience begins to be heard when, the parent\nbeing absent, the child hesitates between a forbidden pleasure and\nobedience to the parental command. Of course, not every choice between\nalternative courses is a moral act. If any one hesitates whether to\nremain at home or to go for a walk, whether to take a road to the right\nor to the left, the decision is morally indifferent. But whenever one of\nthe alternative courses is good and the other bad, conscience does come\ninto play.\n\nAt this point, however, the question forcibly presents itself, How does\nit come to pass in the experience of children that they learn to regard\ncertain lines of action as good and others as bad? You will readily\nanswer, The parent characterizes certain acts as good and others as bad,\nand the child accepts his definition; and this is undoubtedly true. The\nparent's word is the main prop of the budding conscience. But how comes\nthe parent's word to produce belief? This is indeed the crucial\nquestion touching the development of the moral faculty. Mr. Bain says\nthat the child fears the punishment which the parent will inflict in\ncase of disobedience; that the essential form and defining quality of\nconscience from first to last is of the nature of dread. He seems to\nclassify the child's conscience with the criminal conscience, the rebel\nconscience which must be energized by the fear of penalties. But this\nexplanation seems very unsatisfactory. Every one, of course, must admit\nthat the confirmations of experience tend greatly to strengthen the\nparent's authority. The parent says, You must be neat. The child, if it\ndoes as it is bidden, finds an aesthetic pleasure in its becoming\nappearance. The parent says, You must not strike your little brother,\nbut be kind to him; and the child, on restraining its anger, is\ngratified by the loving words and looks which it receives in return. The\nparent says, You must not touch the stove, or you will be burned. The\ndisobedient child is effectually warned by the pain it suffers to be\nmore obedient in future. But all such confirmations are mere external\naids to parental authority. They do not explain the feeling of reverence\nwith which even a young child, when rightly brought up, is wont to look\nup to his father's face. To explain this sentiment of reverence, I must\nask you to consider the following train of reasoning. It has been\nremarked already that the parent should be to the child the visible\nembodiment of a higher law. This higher law shining from the father's\ncountenance, making its sublime presence felt in the mother's eye,\nwakens an answering vibration in the child's heart. The child feels the\nhigher presence and bows to it, though it could not, if it tried,\nanalyze or explain what it feels. We should never forget that children\npossess the capacity for moral development from the outset. It is indeed\nthe fashion with some modern writers to speak of the child as if it were\nat first a mere animal, and as if reflection and morality were\nmechanically superadded later on. But the whole future man is already\nhidden, not yet declared, but latent all the same in the child's heart.\nThe germs of humanity in its totality exist in the young being. Else how\ncould it ever unfold into full-grown morality? It will perhaps serve to\nmake my meaning clearer if I call attention to analogous facts relating\nto the intellectual faculty. The formula of causality is a very abstract\none, which only a thoroughly trained mind can grasp. But even very young\nchildren are constantly asking questions as to the causes of things.\nWhat makes the trees grow? what makes the stars shine?--i. e., what is\nthe cause of the trees growing and the stars shining? The child is\nconstantly pushing, or rather groping, its way back from effects to\ncauses. The child's mind acts under what maybe called the causative\ninstinct long before it can apprehend the law of causation. In the same\nway young children perfectly follow the process of syllogistic\nreasoning. If a father says, on leaving the house for a walk: I can take\nwith me only a child that has been good; now, you have not been good\nto-day; the child without any difficulty draws the conclusion, Therefore\nI can not go out walking with my father to-day. The logical laws are, as\nit were, prefigured in the child's mind long before, under the chemical\naction of experience they come out in the bright colors of\nconsciousness. Or, to use another figure, they exert a pressure on the\nchild of which he himself can give no account. And in like manner the\nmoral law--the law which prescribes certain relations between self and\nothers--is, so to speak, prefigured in the child's mind, and when it is\nexpressed in commands uttered by the parent, the pressure of external\nauthority is confirmed by a pressure coming from within. We can\nillustrate the same idea from another point of view. Whenever a man of\ncommanding moral genius appears in the world and speaks to the multitude\nfrom his height, they are for the moment lifted to his level and feel\nthe afflatus of his spirit. This is so because he expresses\npotentialities of human nature which also exist in them, only not\nunfolded to the same degree as in him. It is a matter of common\nobservation that persons who under ordinary circumstances are content to\nadmire what is third rate and fourth rate are yet able to appreciate\nwhat is first rate when it is presented to them--at least to the extent\nof recognizing that it is first rate. And yet their lack of development\nshows itself in the fact that presently they again lose their hold on\nthe higher standard of excellence, and are thereafter content to put up\nwith what is inferior as if the glimpses of better things had never been\nopened to them. Is it not because, though capable of rising to the\nhigher level, they are not capable of maintaining themselves on it\nunassisted. Now, the case of the parent with respect to the child is\nanalogous. He is on a superior moral plane. The child feels that he is,\nwithout being able to understand why. It feels the afflatus of the\nhigher spirit dwelling in the parent, and out of this feeling is\ngenerated the sentiment of reverence. And there is no greater benefit\nwhich father or mother can confer on their offspring than to deepen this\nsentiment. It is by this means that they can most efficiently promote\nthe development of the child's conscience, for out of this reverence\nwill grow eventually respect for all rightly constituted authority,\nrespect and reverence for law, human and divine. The essential form and\ndefining quality of conscience is not, therefore, as Bain has it--fear\nof punishment. In my opinion such fear is abject and cowardly. The\nsentiment engendered by fear is totally different from the one we are\ncontemplating, as the following consideration will serve to show: A\nchild fears its father when he punishes it in anger; and the more\nviolent his passion, the more does the child fear him. But, no matter\nhow stern the penalty may be which he has to inflict, the child reveres\nits father in proportion as the traces of anger are banished from his\nmien and bearing, in proportion as the parent shows by his manner that\nhe acts from a sense of duty, that he has his eye fixed on the sacred\nmeasures of right and wrong, that he himself stands in awe of the\nsublime commands of which he is, for the time being, the exponent.\n\nTo recapitulate briefly the points which we have gone over: regular\nhabits can be inculcated and obedience can be taught even in infancy. By\nobedience is meant the yielding of a wayward and ignorant will to a firm\nand enlightened one. The child between three and six years of age learns\nclearly to distinguish self from others, and to deliberate between\nalternative courses of action. It is highly important to control the\nelements which enter into the concept self. The desire to choose the\ngood is promoted chiefly by the sentiment of reverence.\n\nWe are thus prepared to describe in a general way the moral outfit of\nthe child on entering school. We have, indeed, already described it. The\nmoral acquirements of the child at the age of which we speak express\nthemselves in habits. The normal child, under the influences of parental\nexample and command, has acquired such habits as that of personal\ncleanliness, of temperance in eating, of respect for the truth. Having\nlearned to use the pronouns I and thou, it also begins to understand the\ndifference between _meum_ and _tuum_. The property sense begins to be\ndeveloped. It claims its own seat at table, its own toys against the\naggression of others. It has gained in an elementary way the notion of\nrights.\n\nThis is a stock of acquirements by no means inconsiderable. The next\nstep in the progress of conscience must be taken in the school. Until\nnow the child has been aware of duties relating only or principally to\npersons whom it loves and who love it. The motive of love is now to\nbecome less prominent. A part of that reverence which the child has felt\nfor the parents whom it loves is now to be transferred to the teacher. A\npart of that respect for the rights of equals which has been impressed\nupon it in its intercourse with brothers and sisters, to whom it is\nbound by the ties of blood, is now to be transferred to its school\ncompanions, who are at first strangers to it. Thus the conscience of the\nchild will be expanded, thus it will be prepared for intercourse with\nthe world. Thus it will begin to gain that higher understanding of\nmorality, according to which authority is to be obeyed simply because it\nis rightful, and equals are to be treated as equals, even when they are\nnot and can not be regarded with affection.\n\nI have in the above used the word habits advisedly. The morality of the\nyoung child assumes the concrete form of habits; abstract principles are\nstill beyond its grasp. Habits are acquired by imitation and repetition.\nGood examples must be so persistently presented and so often copied that\nthe line of moral conduct may become the line of least resistance. The\nexample of parents and teachers is indeed specially important in this\nrespect. But after all it is not sufficient. For the temptations of\nadults differ in many ways from those of children, and on the other\nhand in the lives of older persons occasions are often wanting for\nillustrating just the peculiar virtues of childhood. On this account it\nis necessary to set before the child ideal examples of the virtues of\nchildren and of the particular temptations, against which they need to\nbe warned. Of such examples we find a large stock ready to hand in the\nliterature of fairy tales, fables, and stories. In our next lecture\ntherefore we shall begin to consider the use of fairy tales, fables, and\nstories as means of creating in children those habits which are\nessential to the safe guarding and unfolding of their moral life.\n\nFOOTNOTE:\n\n[7] So important is environment in supporting self-consciousness, that\neven adults, when suddenly transported into entirely new surroundings,\noften experience a momentary doubt as to their identity.\n\n\n\n\nPRIMARY COURSE.\n\n\n\n\nVI.\n\nTHE USE OF FAIRY TALES.\n\n\nThere has been and still is considerable difference of opinion among\neducators as to the value of fairy tales. I venture to think that, as in\nmany other cases, the cause of the quarrel is what logicians call an\n_undistributed middle_--in other words, that the parties to the dispute\nhave each a different kind of fairy tale in mind. This species of\nliterature can be divided broadly into two classes--one consisting of\ntales which ought to be rejected because they are really harmful, and\nchildren ought to be protected from their bad influence, the other of\ntales which have a most beautiful and elevating effect, and which we can\nnot possibly afford to leave unutilized.\n\nThe chief pedagogic value they possess is that they exercise and\ncultivate the imagination. Now, the imagination is a most powerful\nauxiliary in the development of the mind and will. The familiar anecdote\nrelated of Marie Antoinette, who is said to have asked why the people\ndid not eat cake when she was told that they were in want of bread,\nindicates a deficiency of imagination. Brought up amid the splendor of\ncourts, surrounded by luxury, she could not put herself in the place of\nthose who lack the very necessaries. Much of the selfishness of the\nworld is due not to actual hard-heartedness, but to a similar lack of\nimaginative power. It is difficult for the happy to realize the needs of\nthe miserable. Did they realize those needs, they would in many cases be\nmelted to pity and roused to help. The faculty of putting one's self in\nthe place of others is therefore of great, though indirect, service to\nthe cause of morality, and this faculty may be cultivated by means of\nfairy tales. As they follow intently the progress of the story, the\nyoung listeners are constantly called upon to place themselves in the\nsituations in which they have never been, to imagine trials, dangers,\ndifficulties, such as they have never experienced, to reproduce in\nthemselves, for instance, such feelings as that of being alone in the\nwide world, of being separated from father's and mother's love, of being\nhungry and without bread, exposed to enemies without protection, etc.\nThus their sympathy in a variety of forms is aroused.\n\nIn the next place, fairy tales stimulate the idealizing tendency. What\nwere life worth without ideals! How could hope or even religion\ngerminate in the human heart were we not able to confront the\ndisappointing present with visions which represent the fulfillment of\nour desires. \"Faith,\" says Paul, \"is the confidence of things hoped for,\nthe certainty of things not seen.\" Thus faith itself can not abide\nunless supported by a vivid idealism. It is true, the ideals of\nchildhood are childish. In the story called Das Marienkind we hear of\nthe little daughter of a poor wood-cutter who was taken up bodily into\nheaven. There she ate sweetmeats and drank cream every day and wore\ndresses made of gold, and the angels played with her. Sweetmeats and\ncream in plenty and golden dresses and dear little angels to play with\nmay represent the ideals of a young child, and these are materialistic\nenough. But I hold nevertheless that something--nay, much--has been\ngained if a child has learned to take the wishes out of its heart, as it\nwere, and to project them on the screen of fancy. As it grows up to\nmanhood, the wishes will become more spiritual, and the ideals, too,\nwill become correspondingly elevated. In speaking of fairy tales I have\nin mind chiefly the German _Maerchen_ of which the word fairy tale is but\nan inaccurate rendering. The _Maerchen_ are more than mere tales of\nhelpful fairies. They have, as is well-known, a mythological background.\nThey still bear distinct traces of ancient animism, and the myths which\ncenter about the phenomena of the storm, the battle of the sun with the\nclouds, the struggle of the fair spring god with the dark winter demons,\nare in them leading themes. But what originally was the outgrowth of\nsuperstition has now, to a great extent at least, been purified of its\ndross and converted into mere poetry. The _Maerchen_ come to us from a\ntime when the world was young. They represent the childhood of mankind,\nand it is for this reason that they never cease to appeal to children.\nThe _Maerchen_ have a subtile flavor all their own. They are pervaded by\nthe poetry of forest life, are full of the sense of mystery and awe,\nwhich is apt to overcome one on penetrating deeper and deeper into the\nwoods, away from human habitations. The _Maerchen_ deal with the\nunderground life of nature, which weaves in caverns and in the heart of\nmountains, where gnomes and dwarfs are at work gathering hidden\ntreasures. And with this underground life children have a marvelous\nsympathy. The _Maerchen_ present glowing pictures of sheltered firesides,\nwhere man finds rest and security from howling winds and nipping cold.\nBut perhaps their chief attraction is due to their representing the\nchild as living in brotherly fellowship with nature and all creatures.\nTrees, flowers, animals wild and tame, even the stars, are represented\nas the comrades of children. That animals are only human beings in\ndisguise is an axiom in the fairy tales. Animals are humanized--i. e.,\nthe kinship between animal and human life is still strongly felt, and\nthis reminds us of those early animistic interpretations of nature,\nwhich subsequently led to doctrines of metempsychosis. Plants, too, are\noften represented as incarnations of human spirits. Thus the twelve\nlilies are inhabited by the twelve brothers, and in the story of\nSnow-white and Rose-red the life of the two maidens appears to be bound\nup with the life of the white and red rosebush. The kinship of all life\nwhatsoever is still realized. This being so, it is not surprising that\nmen should understand the language of animals, and that these should\ninterfere to protect the heroes and heroines of the _Maerchen_ from\nthreatened dangers. In the story of the faithful servant John, the\nthree ravens flying above the ship reveal the secret of the red horse,\nthe sulphurous shirt, and the three drops of blood, and John, who\nunderstands their communications, is thereby enabled to save his\nmaster's life. What, again, can be more beautiful than the way in which\nthe tree and the two white doves co-operate to secure the happiness of\nthe injured Cinderella! The tree rains down the golden dresses with\nwhich she appears at the ball, and the doves continue to warn the prince\nas he rides by that he has chosen the wrong bride until Cinderella\nherself passes, when they light on her shoulders, one on her right and\nthe other on her left, making, perhaps, the loveliest picture to be\nfound in all fairy lore. The child still lives in unbroken communion\nwith the whole of nature; the harmony between its own life and the\nenveloping life has not yet been disturbed, and it is this harmony of\nthe human with the natural world that reflects itself in the atmosphere\nof the _Maerchen_, and makes them so admirably suited to satisfy the\nheart of childhood.\n\nBut how shall we handle these _Maerchen_ and what method shall we employ\nin putting them to account for our special purpose? I have a few\nthoughts on this subject, which I shall venture to submit in the form of\ncounsels.\n\nMy _first counsel_ is: Tell the story; do not give it to the child to\nread. There is an obvious practical reason for this. Children are able\nto benefit by hearing fairy tales before they can read. But that is not\nthe only reason. It is the childhood of the race, as we have seen, that\nspeaks in the fairy story to the child of to-day. It is the voice of an\nancient, far-off past that echoes from the lips of the story-teller. The\nwords \"once upon a time\" open up a vague retrospect into the past, and\nthe child gets its first indistinct notions of history in this way. The\nstories embody the tradition of the childhood of mankind. They have on\nthis account an authority all their own, not indeed that of literal\ntruth, but one derived from their being types of certain feelings and\nlongings which belong to childhood as such. The child as it listens to\nthe _Maerchen_, looks up with wide-opened eyes to the face of the person\nwho tells the story, and thrills responsive as the touch of the earlier\nlife of the race thus falls upon its own. Such an effect, of course, can\nnot be produced by cold type. Tradition is a living thing, and should\nuse the living voice for its vehicle.\n\nMy _second counsel_ is also of a practical nature, and I make bold to\nsay quite essential to the successful use of the stories. Do not take\nthe moral plum out of the fairy-tale pudding, but let the child enjoy it\nas a whole. Do not make the story taper toward a single point, the moral\npoint. You will squeeze all the juice out of it if you try. Do not\nsubordinate the purely fanciful and naturalistic elements of the story,\nsuch as the love of mystery, the passion for roving, the sense of\nfellowship with the animal world, in order to fix attention solely on\nthe moral element. On the contrary, you will gain the best moral effect\nby proceeding in exactly the opposite way. Treat the moral element as\nan incident; emphasize, it indeed, but incidentally. Pluck it as a\nwayside flower. How often does it happen that, having set out on a\njourney with a distinct object in mind, something occurs on the way\nwhich we had not foreseen, but which in the end leaves the deepest\nimpression on the mind. The object which we had in view is long\nforgotten, but the incident which happened by the way is remembered for\nyears after. So the moral result of the _Maerchen_ will not be less sure\nbecause gained incidentally. An illustration will make plain what I\nmean. In the story of the Frog King we are told that there was once a\nyoung princess who was so beautiful that even the Sun, which sees a\ngreat many things, had never seen anything so beautiful as she was. A\ngolden ball was her favorite plaything. One day, as she sat by a well\nunder an old linden tree, she tossed the ball into the air and it fell\ninto the well. She was very unhappy, and cried bitterly. Presently a\nfrog put his ugly head out of the water, and offered to dive for the\nball, on condition, however, that she would promise to take him for her\nplaymate, to let him eat off her golden plate and drink out of her\ngolden cup and sleep in her little snow-white bed. The princess promised\neverything. But no sooner had the frog brought her the ball than she\nscampered away, heedless of his cries. The next day as the royal family\nsat at dinner a knock was heard at the door. The princess opened and\nbeheld the ugly toad claiming admittance. She screamed with fright and\nhastily shut the door in his face. But when the king, her father, had\nquestioned her, he said, \"What you have promised, you must keep\"; and\nshe obeyed her father, though it was sorely against her inclination to\ndo so. That was right, children, was it not? One must always obey, even\nif one does not like what one is told to do. So the toad was brought in\nand lifted to the table, and he ate off the little golden plate and\ndrank out of the golden cup. And when he had had enough, he said, \"I am\ntired now, put me into your little snow-white bed.\" And again when she\nrefused her father said: \"What you have promised you must keep. Ugly\nthough he is, he helped you when you were in distress, and you must not\ndespise him now.\" And the upshot of the story is that the ugly toad,\nhaving been thrown against the wall, was changed into a beautiful\nprince, and of course some time after the prince and the princess were\nmarried.\n\nThe naturalistic element of the story is the changing of the prince into\na toad and back again from a toad into a prince. Children are very fond\nof disguises. It is one of their greatest pleasures to imagine things to\nbe other than they are. And one of the chief attractions of such stories\nas the one we have related is that they cater to the fondness of the\nlittle folks for this sort of masquerading. The moral elements of the\nstory are obvious. They should be touched on in such a manner as not to\ndivert the interest from the main story.\n\nMy _third counsel_ is to eliminate from the stories whatever is merely\nsuperstitious, merely a relic of ancient animism, and of course whatever\nis objectionable on moral grounds. For instance, such a story as that of\nthe idle spinner, the purport of which seems to be that there is a\nspecial providence watching over lazy people. Likewise all those stories\nwhich turn upon the success of trickery and cunning. A special question\narising under this head, and one which has been the subject of much\nvexed discussion, is in how far we should acquaint children with the\nexistence of evil in the world, and to what extent we can use stories in\nwhich evil beings and evil motives are introduced. My own view is that\nwe should speak in the child's hearing only of those lesser forms of\nevil, physical or moral, with which it is already acquainted, but\nexclude all those forms of evil which lie beyond its present experience.\nOn this ground I should reject the whole brood of step-mother stories,\nor rather, as this might make too wide a swath, I should take the\nliberty of altering stories in which the typical bad step-mother occurs,\nbut which are otherwise valuable. There is no reason why children should\nbe taught to look on step-mothers in general as evilly disposed persons.\nThe same applies to stories in which unnatural fathers are mentioned. I\nshould also rule out such stories as that of The Wolf and The Seven\nLittle Goats. The mother goat, on leaving the house, warns her little\nones against the wolf, and gives them two signs by which they can\ndetect him--his hoarse voice and black paws. The wolf knocks and finds\nhimself discovered. He thereupon swallows chalk to improve his voice and\ncompels the miller to whiten his paws. Then he knocks again, is\nadmitted, leaps into the room, and devours the little goats one by one.\nThe story, as used in the nursery, has a transparent purpose. It is\nintended to warn little children who are left at home alone against\nadmitting strangers. The wolf represents evil beings in general--tramps,\nburglars, people who come to kidnap children, etc. Now I, for one,\nshould not wish to implant this fear of strangers into the minds of the\nyoung. Fear is demoralizing. Children should look with confidence and\ntrust upon all men. They need not be taught to fear robbers and\nburglars. Even the sight of wild animals need not awaken dread. Children\nnaturally admire the beauty of the tiger's skin, and the lion in their\neyes is a noble creature, of whose ferocity they have no conception. It\nis time enough for them later on to familiarize themselves with the fact\nthat evil of a sinister sort exists within human society and outside of\nit. And it will be safe for them to face this fact then only, when they\ncan couple with it the conviction that the forces of right and order in\nthe world are strong enough to grapple with the sinister powers and hold\nthem in subjection.\n\nAnd now let us review a number of the _Maerchen_ against which none of\nthese objections lie, which are delicious food for children's minds, and\nconsider the place they occupy in a scheme of moral training. It has\nbeen already stated that each period of human life has a set of duties\npeculiar to itself. The principal duties of childhood are: Obedience to\nparents, love and kindness toward brothers and sisters, a proper regard\nfor the feelings of servants, and kindness toward animals. We can\nclassify the fairy tales which we can use under these various heads. Let\nus begin with the topic last mentioned.\n\n\n_Tales illustrating Kindness toward Animals._\n\nThe House in the Woods.--The daughter of a poor wood-cutter is lost in\nthe woods, and comes at night to a lonely house. An old man is sitting\nwithin. Three animals--a cow, a cock, and a chicken--lie on the hearth.\nThe child is made welcome, and is asked to prepare supper. She cooks for\nthe old man and herself, but forgets the animals. The second daughter\nlikewise goes astray in the woods, comes to the same house, and acts in\nthe same way. The third daughter, a sweet, loving child, before sitting\ndown to her own meal, brings in hay for the cow and barley for the cock\nand chicken, and by this act of kindness to animals breaks the spell\nwhich had been cast upon the house. The old man is immediately\ntransformed into a prince, etc.\n\nThe Story of the Dog Sultan.--Sultan is old, and about to be shot by his\nmaster. The wolf, seeing his cousin the dog in such distress, promises\nto help him. He arranges that on the morrow he will seize a sheep\nbelonging to Sultan's master. The dog is to run after him, and he, the\nwolf, will drop the sheep and Sultan shall get the credit of the rescue.\nEverything passes off as prearranged, and Sultan's life is spared by his\ngrateful owner. Some time after the wolf comes prowling around the\nhouse, and, reminding his friend that one good turn deserves another,\ndeclares that he has now come for mutton in good earnest. But the dog\nreplies that nothing can tempt him to betray the interests of his\nmaster. The wolf persists, but Sultan gives the alarm and the thief\nreceives his due in the shape of a sound beating.\n\nThe point of special interest in the beautiful story of Snow-white and\nRose-red above referred to is the incident of the bear. One cold\nwinter's night some one knocks at the door. Snow-white and Rose-red go\nto open, when a huge black bear appears at the entrance and begs for\nshelter. He is almost frozen with the cold, he says, and would like to\nwarm himself a bit. The two little girls are at first frightened, but,\nencouraged by their mother, they take heart and invite the bear into the\nkitchen. Soon a cordial friendship springs up between Bruin and the\nchildren. They brush the snow from his fur, tease, and caress him by\nturns. After this the bear returns every night, and finally turns out to\nbe a beautiful prince.\n\nThe Story of the Queen Bee tells about three brothers who wander through\nthe world in search of adventures. One day they come to an ant-hill.\nThe two older brothers are about to trample upon the ants \"just for the\nfun of it.\" But the youngest pleads with them, saying: \"Let them live;\ntheir life is as dear to them as ours is to us.\" Next they come to a\npond in which many ducks are swimming about. The two older brothers are\ndetermined to shoot the ducks \"just for the fun of it.\" The youngest\nagain pleads as before, \"Let them live,\" etc. Finally, he saves a\nbee-hive from destruction in the same manner. Thus they journey on until\nthey come to an enchanted castle. To break the spell, it is necessary to\nfind and gather up a thousand pearls which had fallen on the\nmoss-covered ground in a certain wood. Five thousand ants come to help\nthe youngest to find the pearls. The second task imposed is to find a\ngolden key which had been thrown into a pond near the castle. The\ngrateful ducks bring up the key from the bottom. The third task is the\nmost difficult. In one of the interior chambers of the castle there are\nthree marble images--three princesses, namely, who had been turned into\nstone. Before the spell took effect they had partaken, respectively, of\nsugar, sirup, and honey. To restore them to life it is necessary to\ndiscover which one had eaten the honey. The Queen Bee comes in with all\nher swarm and lights on the lips of the youngest and so solves the\nproblem. The enchantment is immediately dissolved. All these stories\nillustrate kindness to animals.\n\nAmong stories which illustrate the _respect due to the feelings of\nservants_ may be mentioned the tale of Faithful John, who understood the\nlanguage of the ravens and saved his master from the dangers of the red\nhorse, etc., a story which in addition impresses the lesson that we\nshould confide in persons who have been found trustworthy, even if we do\nnot understand their motives. In the popular tale of Cinderella the\npoints especially to be noted are: The pious devotion of Cinderella to\nher mother's memory, and the fact that the poor kitchen drudge,\nunderneath the grime and ashes which disfigure her, possesses qualities\nwhich raise her far above the proud daughters of the house. The lesson\ntaught by this story that we should distinguish intrinsic worth from the\naccidents of rank and condition, is one which can not be impressed too\nearly or too deeply.\n\nUnder the heading of _brotherly and sisterly love_ belongs the lovely\ntale of Snow-white. The little dwarfs are to all intents and purposes\nher brothers. They receive and treat her as a sister, and she returns\ntheir affection in kind.\n\nThe story of the Twelve Brothers, whom their sister redeems by seven\nyears of silence at the peril of her own life, is another instance of\ntenderest sisterly devotion combined with self-control. This story,\nhowever, needs to be slightly altered. In place of the cruel father (we\nmust not mention cruel fathers) who has got ready twelve coffins for his\nsons, in order that all the wealth of his kingdom may descend to his\ndaughter, let us substitute the steward of the palace, who hopes by\nslaying the sons and winning the hand of the daughter, to become king\nhimself.\n\nFinally the story of Red Riding Hood illustrates the cardinal virtue of\nchildhood--_obedience to parents_. Children must not loiter on the way\nwhen they are sent on errands. And Riding Hood loiters, and hence all\nthe mischief which follows. She is sent to bring wine and cake to her\ngrandmother. The example of such attentions as this serves to quicken in\nchildren the sentiment of reverence for the aged. Children learn\nreverence toward their parents in part by the reverence which these\ndisplay toward the grandparents. Another point is that Red Riding Hood,\nto quiet her conscience, when she strays from the straight path deceives\nherself as to her motives. She says, \"I will also gather a bunch of wild\nflowers to please grandmother.\" But her real purpose is to enjoy the\nfreedom of the woods, and the proof is that presently she forgets all\nabout grandmother. There is one objection that has sometimes been urged\nagainst this story, viz., the part which the wolf plays in it. But the\nwolf is not really treated as a hostile or fearful being. He meets Red\nRiding Hood on the way, and they chat confidentially together. He\nappears rather in the light of a trickster. But, it is objected, that he\ndevours the grandmother and, later on, Red Riding Hood herself. Very\ntrue; but the curious fact is that, when his belly is cut open, the\ngrandmother and Red Riding Hood come out intact. They have evidently not\nbeen injured. Children have very defective notions of the human body,\nwith the exception of such external parts as hands, feet, and face. In\nan examination recently conducted by Prof. G. Stanley Hall in regard to\nthe contents of childrens' minds at the time they enter school, it was\nfound that ninety per cent of those questioned had no idea where the\nheart is located, eighty-one per cent did not know anything about the\nlungs, ninety per cent could not tell where their ribs are situated,\netc. Of the internal organs children have no idea. Hence when the story\nsays that the grandmother is swallowed by the wolf, the impression\ncreated is that she has been forced down into a sort of dark hole, and\nthat her situation, while rather uncomfortable, no doubt, is not\notherwise distressing. The ideas of torn and mangled flesh are not\nsuggested. Hence the act of devouring arouses no feeling of horror, and\nthe story of Red Riding Hood, that prime favorite of all young children,\nmay be related without any apprehension as to its moral effect.\n\nThen there are other stories, such as that of the man who went abroad to\nlearn the art of shuddering--an excellent example of bravery; the story\nof the seven Suabians--a persiflage of cowardice; the story of the\n_Marienkind_ which contains a wholesome lesson against obstinacy, etc. I\nhave not, of course, attempted to cover the whole ground, but only to\nmention a few examples sufficient to show along what lines the selection\nmay be made. The ethical interests peculiar to childhood are the heads\nunder which the whole material can be classified.\n\nThe value of the fairy tales is that they stimulate the imagination;\nthat they reflect the unbroken communion of human life with the life\nuniversal, as in beasts, fishes, trees, flowers, and stars; and that\nincidentally, but all the more powerfully on that account, they quicken\nthe moral sentiments.\n\nLet us avail ourselves freely of the treasures which are thus placed at\nour disposal. Let us welcome _das Maerchen_ into our primary course of\nmoral training, that with its gentle bands, woven of \"morning mist and\nmorning glory,\" it may help to lead our children into the bright realms\nof the ideal.\n\n\n\n\nVII.\n\nTHE USE OF FABLES.\n\n\nThe collection of fables which figures under the name of AEsop has to a\nvery remarkable degree maintained its popularity among children, and\nmany of its typical characters have been adopted into current\nliterature, such as the Dog in the Manger, the Wolf in Sheep's Clothing,\nKing Log, and King Stork, and others. Recent researches have brought to\nlight the highly interesting fact that these fables are of Asiatic\norigin. A collection of Indian and, it is believed, Buddhist fables and\nstories traveled at an early period into Persia, where it became known\nas the Pancha-Tantra. The Pancha-Tantra was translated into Arabic, and\nbecame the source of the voluminous Kalilah-wa-Dimnah literature. The\nArabic tales in turn migrated into Europe at the time of the Crusades\nand were rendered into Greek, Hebrew, and Latin. In this form they\nbecame accessible to the nations of Europe, were extensively circulated,\nand a collection of them was wrongly, but very naturally, ascribed to a\nfamous story-teller of the ancient Greeks--i. e., to AEsop. The arguments\non which this deduction is based may be found in Rhys Davids's\nintroduction to his English translation of the Jataka Tales.[8] This\nauthor speaks of AEsop's fables as a first moral lesson-book for our\nchildren in the West. We shall have to consider in how far this\ndescription is correct--that is to say, in how far we can use the fables\nfor moral purposes. The point to be kept in mind is their Asiatic\norigin, as this will at once help us to separate the fables which we can\nuse from those which must be rejected. A discrimination of this sort is\nabsolutely necessary. I am of the opinion that it is a serious mistake\nto place the whole collection as it stands in the hands of children.\n\nTo decide this question we must study the _milieu_ in which the fables\narose, the spirit which they breathe, the conditions which they reflect.\nThe conditions they reflect are those of an Oriental despotism. They\ndepict a state of society in which the people are cruelly oppressed by\ntyrannical rulers, and the weak are helpless in the hands of the strong.\nThe spirit which they breathe is, on the whole, one of patient and\nrather hopeless submission. The effect upon the reader as soon as he has\ncaught this clew, this _Leitmotiv_, which occurs in a hundred\nvariations, is very saddening. I must substantiate this cardinal point\nby a somewhat detailed analysis. Let us take first the fable of the Kite\nand the Pigeons. A kite had been sailing in the air for many days near a\npigeon-house with the intention of seizing the pigeons; at last he had\nrecourse to stratagem. He expressed his deep concern at their unjust and\nunreasonable suspicions of himself, as if he intended to do them an\ninjury. He declared that, on the contrary, he had nothing more at heart\nthan the defense of their ancient rights and liberties, and ended by\nproposing that they should accept him as their protector, their king.\nThe poor, simple pigeons consented. The kite took the coronation oath in\na very solemn manner. But much time had not elapsed before the good kite\ndeclared it to be a part of the king's prerogative to devour a pigeon\nnow and then, and the various members of his family adhered to the same\nview of royal privilege. The miserable pigeons exclaimed: \"Ah, we\ndeserve no better. Why did we let him in!\"\n\nThe fable of the Wolf in Sheep's Clothing conveys essentially the same\nidea. The fable of the Lion and the Deer illustrates the exorbitant\nexactions practiced by despots. A fat deer was divided into four parts.\nHis majesty the lion proposed that they be suitably apportioned. The\nfirst part he claimed for himself on account of his true hereditary\ndescent from the royal family of Lion; the second he considered properly\nhis own because he had headed the hunt; the third he took in virtue of\nhis prerogative; and finally he assumed a menacing attitude, and dared\nany one to dispute his right to the fourth part also.\n\nIn the fable of the Sick Lion and the Fox, the fox says: \"I see the\nfootprints of beasts who have gone into the cave, but of none that have\ncome out.\" The fable of the Cat and the Mice expresses the same thought,\nnamely, that it is necessary to be ever on one's guard against the\nmighty oppressors even when their power seems for the time to have\ndeserted them. The cat pretends to be dead, hoping by this means to\nentice the mice within her reach. A cunning old mouse peeps over the\nedge of the shelf, and says: \"Aha, my good friend, are you there? I\nwould not trust myself with you though your skin were stuffed with\nstraw.\"\n\nThe fable of King Log and King Stork shows what a poor choice the people\nhave in the matter of their kings. First they have a fool for their\nking, a mere log, and they are discontented. Then Stork ascends the\nthrone, and he devours them. It would have been better if they had put\nup with the fool. The injustice of despotic rulers is exemplified in the\nfable of the Kite and the Wolf. The kite and the wolf are seated in\njudgment. The dog comes before them to sue the sheep for debt. Kite and\nwolf, without waiting for the evidence, give sentence for the plaintiff,\nwho immediately tears the poor sheep into pieces and divides the spoil\nwith the judges. The sort of thanks which the people get when they are\nfoolish enough to come to the assistance of their masters, is\nillustrated by the conduct of the wolf toward the crane. The wolf\nhappened to have a bone sticking in his throat, and, howling with pain,\npromised a reward to any one who should relieve him. At last the crane\nventured his long neck into the wolf's throat and plucked out the bone.\nBut when he asked for his reward, the wolf glared savagely upon him, and\nsaid: \"Is it not enough that I refrained from biting off your head?\" How\ndangerous it is to come at all into close contact with the mighty, is\nshown in the fable of the Earthen and the Brazen Pot. The brazen pot\noffers to protect the earthen one as they float down stream. \"Oh,\"\nreplies the latter, \"keep as far off as ever you can, if you please;\nfor, whether the stream dashes you against me or me against you, I am\nsure to be the sufferer.\"\n\nThe fables which we have considered have for their theme the character\nof the strong as exhibited in their dealings with the weak. A second\ngroup is intended to recommend a certain policy to be pursued by the\nweak in self-protection. This policy consists either in pacifying the\nstrong by giving up to them voluntarily what they want, or in flight,\nor, if that be impossible, in uncomplaining submission. The first\nexpedient is recommended in the fable of the Beaver. A beaver who was\nbeing hard pressed by a hunter and knew not how to escape, suddenly,\nwith a great effort, bit off the part which the hunter desired, and,\nthrowing it toward him, by this means escaped with his life. The\nexpedient of flight is recommended in the fable of Reynard and the Cat.\nReynard and the cat one day were talking politics in the forest. The fox\nboasted that though things might turn out never so badly, he had still a\nthousand tricks to play before they should catch him. The cat said: \"I\nhave but one trick, and if that does not succeed I am undone.\" Presently\na pack of hounds came upon them full cry. The cat ran up a tree and hid\nherself among the top branches. The fox, who had not been able to get\nout of sight, was overtaken despite his thousand tricks and torn to\npieces by the hounds. The fable of the Oak and the Reed teaches the\npolicy of utter, uncomplaining submission. The oak refuses to bend, and\nis broken. The supple reed yields to the blast, and is safe. Is it not a\nlittle astonishing that this fable should so often be related to\nchildren as if it contained a moral which they ought to take to heart?\nTo make it apply at all, it is usually twisted from its proper\nsignification and explained as meaning that one should not be\nfool-hardy, not attempt to struggle against overwhelming odds. But this\nis not the true interpretation. The oak is by nature strong and firm,\nwhile it is the nature of the reed to bend to every wind. The fable\nsprings out of the experience of a people who have found resistance\nagainst oppression useless. And this sort of teaching we can not, of\ncourse, wish to give to our children. I should certainly prefer that a\nchild of mine should take the oak, and not the reed, for his pattern.\nThe same spirit is again inculcated in the fable of the Wanton Calf. The\nwanton calf sneers at the poor ox who all day long bears the heavy yoke\npatiently upon his neck. But in the evening it turns out that the ox is\nunyoked, while the calf is butchered. The choice seems to lie between\nsubserviency and destruction. The fable of the Old Woman and her Maids\nsuggests the same conclusion, with the warning added that it is useless\nto rise against the agents of tyranny so long as the tyrants themselves\ncan not be overthrown. The cock in the fable represents the agents of\noppression. The killing of the cock serves only to bring the mistress\nherself on the scene, and the lot of the servants becomes in consequence\nvery much harder than it had been before.\n\nWe have now considered two groups of fables: those which depict the\ncharacter of the mighty, and those which treat of the proper policy of\nthe weak. The subject of the third group is, the consolations of the\nweak. These are, first, that even tyrannical masters are to a certain\nextent dependent upon their inferiors, and can be punished if they go\ntoo far; secondly, that the mighty occasionally come to grief in\nconsequence of dissensions among themselves; thirdly, that fortune is\nfickle. A lion is caught in the toils, and would perish did not a little\nmouse come to his aid by gnawing asunder the knots and fastenings. The\nbear robs the bees of their honey, but is punished and rendered almost\ndesperate by their stings. An eagle carries off the cub of a fox; but\nthe fox, snatching a fire-brand, threatens to set the eagle's nest on\nfire, and thus forces him to restore her young one. This is evidently a\nfable of insurrection. The fable of the Viper and the File shows that it\nis not safe to attack the wrong person--in other words, that tyrants\nsometimes come to grief by singling out for persecution some one who is\nstrong enough to resist them though they little suspect it. The fable of\nthe four bulls shows the effect of dissensions among the mighty. Four\nbulls had entered into a close alliance, and agreed to keep always near\none another. A lion fomented jealousies among them. The bulls grew\ndistrustful of one another, and at last parted company. The lion had now\nobtained his end, and seized and devoured them singly. The fickleness of\nfortune is the theme of the fable of the Horse and the Ass. The horse,\nrichly caparisoned and champing his foaming bridle, insults an ass who\nmoves along under a heavy load. Soon after the horse is wounded, and,\nbeing unfit for military service, is sold to a carrier. The ass now\ntaunts the proud animal with his fallen estate. The horse in this fable\nis the type of many an Eastern vizier, who has basked for a time in the\nsunshine of a despot's favor only to be suddenly and ignominiously\ndegraded. The ass in the fable represents the people. There remains a\nfourth group of fables, which satirize certain mean or ridiculous types\nof characters, such as are apt to appear in social conditions of the\nkind we have described. Especially do the fables make a target of the\nfolly of those who affect the manners of the aristocratic class, or who\ntry to crowd in where they are not wanted, or who boast of their high\nconnections. The frog puffs himself up so that he may seem as large as\nthe ox, until he bursts. The mouse aspires to marry the young lioness,\nand is in fact well received; but the young lady inadvertently places\nher foot on her suitor and crushes him. The jackdaw picks up feathers\nwhich have fallen from the peacocks, sticks them among his own, and\nintroduces himself into the assembly of those proud birds. They find him\nout, strip him of his plumes, and with their sharp bills punish him as\nhe deserves. A fly boasts that he frequents the most distinguished\ncompany, and that he is on familiar terms with the king, the priests,\nand the nobility. Many a time, he says, he has entered the royal\nchamber, has sat upon the altar, and has even enjoyed the privilege of\nkissing the lips of the most beautiful maids of honor. \"Yes,\" replies an\nant, \"but in what capacity are you admitted among all these great\npeople? One and all regard you as a nuisance, and the sooner they can\nget rid of you the better they are pleased.\"\n\nMost of the fables which thus far have been mentioned we can not use.\nThe discovery of their Asiatic origin sheds a new, keen light upon their\nmeaning. They breathe, in many cases, a spirit of fear, of abject\nsubserviency, of hopeless pessimism. Can we desire to inoculate the\nyoung with this spirit? The question may be asked why fables are so\npopular with boys. I should say, Because school-boy society reproduces\nin miniature to a certain extent the social conditions which are\nreflected in the fables. Among unregenerate school-boys there often\nexists a kind of despotism, not the less degrading because petty. The\nstrong are pitted against the weak--witness the fagging system in the\nEnglish schools--and their mutual antagonism produces in both the\ncharacteristic vices which we have noted above. The psychological study\nof school-boy society has been only begun, but even what lies on the\nsurface will, I think, bear out this remark. Now it has come to be one\nof the commonplaces of educational literature, that the individual of\nto-day must pass through the same stages of evolution as the human race\nas a whole. But it should not be forgotten that the advance of\ncivilization depends on two conditions: first, that the course of\nevolution be accelerated, that the time allowed to the successive stages\nbe shortened; and, secondly, that the unworthy and degrading elements\nwhich entered into the process of evolution in the past, and at the time\nwere inseparable from it, be now eliminated. Thus the fairy-tales which\ncorrespond to the myth-making epoch in human history must be purged of\nthe dross of superstition which still adheres to them, and the fables\nwhich correspond to the age of primitive despotisms must be cleansed of\nthe immoral elements they still embody.\n\nThe fables which are fit for use may be divided into two classes: those\nwhich give illustrations of evil,[9] the effect of which on the young\nshould be to arouse disapprobation, and those which present types of\nvirtue. The following is a list of some of the principal ones in each\ncategory:\n\n_An Instance of Selfishness._ The porcupine having begged for\nhospitality and having been invited into a nest of snakes,\ninconveniences the inmates and finally crowds them out. When they\nremonstrate, he says, \"Let those quit the place that do not like it.\"\n\n_Injustice._ The fable of the Kite and the Wolf, mentioned above.\n\n_Improvidence._ The fable of the Ant and the Grasshopper; also the fable\nentitled One Swallow does not make Summer, and the fable of the Man who\nKilled the Goose that laid the Golden Eggs.\n\n_Ingratitude._ The fable of the snake which bit the countryman who had\nwarmed it in his breast.\n\n_Cowardice._ The fable of the Stag and the Fawn, and of the Hares in the\nStorm.\n\n_Vanity._ The fables of the Peacock and the Crane, and of the Crow who\nlost his Cheese by listening to the flattery of the fox.\n\n_Contemptuous Self-confidence._ The Hare and the Tortoise.\n\n_The Evil Influence of Bad Company._ The Husbandman and the Stork.\n\n_Cruelty to Animals._ The Fowler and the Ringdove; the Hawk and the\nPigeons.\n\n_Greediness._ The Dog and the Shadow.\n\n_Lying._ The fable of the boy who cried \"Wolf!\"\n\n_Bragging._ The fable of the Ass in the Lion's Skin.\n\n_Deceit._ The fable of the Fox without a Tail.\n\n_Disingenuousness._ The fable of the Sour Grapes.\n\n_A Discontented Spirit._ The fable of the Peacock's Complaint.\n\n_Equal Graces are not given to all._ The fable of the Ass who leaped\ninto his Master's Lap.\n\n_Borrowed Plumes._ The fable of the Jackdaw and the Peacocks, mentioned\nabove.\n\n_Malice._ The fable of the Dog in the Manger, who would not eat, neither\nlet others eat.\n\n_Breaking Faith._ The fable of the Traveler and the Bear.\n\n_To Fan Animosity is even Worse than to Quarrel._ The fable of the\nTrumpeter.\n\nThe value of these fables, as has been said, consists in the reaction\nwhich they call forth in the minds of the pupils. Sometimes this\nreaction finds expression in the fable itself; sometimes the particular\nvice is merely depicted in its nakedness, and it becomes the business of\nthe teacher distinctly to evoke the feeling of disapprobation, and to\nhave it expressly stated in words. The words tend to fix the feeling.\nOften, when a child has committed some fault, it is useful to refer by\nname to the fable that fits it. As, when a boy has made room in his seat\nfor another, and the other crowds him out, the mere mention of the fable\nof the Porcupine is a telling rebuke; or the fable of the Hawk and the\nPigeons may be called to mind when a boy has been guilty of mean\nexcuses. On the same principle that angry children are sometimes taken\nbefore a mirror to show them how ugly they look. The fable is a kind of\nmirror for the vices of the young.\n\nOf the fables that illustrate virtuous conduct, I mention that of\nHercules and the Cart-driver, which teaches self-reliance. Hercules\nhelps the driver as soon as the latter has put his own shoulders to the\nwheel. Also the fable of the Lark. So long as the farmer depends on his\nneighbors, or his kinsmen, the lark is not afraid; but when he proposes\nto buckle to himself, she advises her young that it is time to seek\nanother field. The fable of the Wind and the Sun shows that kindness\nsucceeds where rough treatment would fail. The fable of the Bundle of\nSticks exemplifies the value of harmony. The fable of the Wolf, whom the\ndog tries to induce to enter civilization, expresses the sentiment that\nlean liberty is to be preferred to pampered servitude. The fable of the\nOld Hound teaches regard for old servants. Finally, the fable of the\nHorse and the Loaded Ass, and of the Dove and the Ant, show that\nkindness pays on selfish principles. The horse refuses to share the\nass's burden; the ass falls dead under his load; in consequence, the\nhorse has to bear the whole of it. On the other hand the dove rescues\nthe ant from drowning, and the ant in turn saves the dove from the\nfowler's net.\n\nThe last remark throws light on the point of view from which the fables\ncontemplate good and evil. It is to be noted that a really moral spirit\nis wanting in them; the moral motives are not appealed to. The appeal\nthroughout is to the bare motive of self-interest. Do not lie, because\nyou will be found out, and will be left in the lurch when you depend for\nhelp on the confidence of others. Do not indulge in vanity, because you\nwill make yourself ridiculous. Do not try to appear like a lion when you\ncan not support the character, because people will find out that you are\nonly an ass. Do not act ungratefully, because you will be thrust out of\ndoors. Even when good conduct is inculcated, it is on the ground that it\npays. Be self-reliant, because if you help yourself others will help\nyou. Be kind, because by gentle means you can gain your purpose better\nthan by harshness. Agree with your neighbors, because you can then, like\nthe bundle of sticks, resist aggression from without. That lying is\nwrong on principle; that greediness is shameful, whether you lose your\ncheese or not; that kindness is blessed, even when it does not bring a\nmaterial reward; that it is lovely for neighbors to dwell together in\npeace, is nowhere indicated. The beauty and the holiness of right\nconduct lie utterly beyond the horizon of the fable. Nevertheless, as we\nhave seen when speaking of the efficient motives of conduct,\nself-interest as a motive should not be underrated, but should be\nallowed the influence which belongs to it as an auxiliary to the moral\nmotive. It is well, it is necessary, for children to learn that lying,\nbesides being in itself disgraceful, does also entail penalties of a\npalpable sort; that vanity and self-conceit, besides being immoral, are\nalso punished by the contempt of one's fellows; that those who are\nunkind, as the horse was to the ass, may have to bear the ass's burden.\nThe checks and curbs supplied by such considerations as these serve the\npurpose of strengthening the weak conscience of the young, and are not\nto be dispensed with, provided always they are treated not as\nsubstitutes for but as auxiliaries to the moral motives, properly\nspeaking.\n\nAs to the place in the primary course which I have assigned to the\nfables, I have the following remark to offer: In speaking of fairy\ntales, it was stated that the moral element should be touched on\nincidentally, and that it should not be separated from the other, the\nnaturalistic elements. The pedagogical reason which leads me to assign\nto the fables the second place in the course, is that each fable deals\nexclusively with one moral quality, which is thus isolated and held up\nto be contemplated. In the stories which will occupy the third place a\nnumber of moral qualities are presented in combination. We have,\ntherefore, what seems to be a logical and progressive order--first,\nfairy tales in which the moral is still blended with other elements;\nsecondly, a single moral quality set off by itself; then, a combination\nof such qualities.\n\nThe peculiar value of the fables is that they are instantaneous\nphotographs, which reproduce, as it were, in a single flash of light,\nsome one aspect of human nature, and which, excluding everything else,\npermit the entire attention to be fixed on that one.\n\nAs to the method of handling them, I should say to the teacher: Relate\nthe fable; let the pupil repeat it in his own words, making sure that\nthe essential points are stated correctly. By means of questions elicit\na clean-cut expression of the point which the fable illustrates; then\nask the pupil to give out of his experience other instances illustrating\nthe same point. This is precisely the method pursued in the so-called\nprimary object lessons. The child, for instance, having been shown a red\nball, is asked to state the color of the ball, and then to name other\nobjects of the same color; or to give the shape of the ball, and then to\nname other objects having the same shape. In like manner, when the pupil\nhas heard the fable of the Fox and the Wolf, and has gathered from it\nthat compassion when expressed merely in words is useless, and that it\nmust lead to deeds to be really praiseworthy, it will be easy for him\nout of his own experience to multiply instances which illustrate the\nsame truth. The search for instances makes the point of the fable\nclearer, while the expression of the thought in precise language, on\nwhich the teacher should always insist, tends to drive it home. It will\nbe our aim in the present course of lectures to apply the methods of\nobject teaching, now generally adopted in other branches, to the\nearliest moral instruction of children--an undertaking, of course, not\nwithout difficulties.\n\nFOOTNOTES:\n\n[8] Buddhist Birth Stories; or Jataka Tales, translated by T. W. Rhys\nDavids.\n\n[9] I remarked above that fables should be excluded if the moral they\ninculcate is bad, not if they depict what is bad. In the latter case\nthey often may serve a useful purpose.\n\n\n\n\nVIII.\n\nSUPPLEMENTARY REMARKS ON FABLES.\n\n\nApart from the collection which figures under the name of AEsop, there\nare other fables, notably the so-called Jataka tales, which deserve\nattention. The Jataka tales contain deep truths, and are calculated to\nimpress lessons of great moral beauty. The tale of the Merchant of Seri,\nwho gave up all that he had in exchange for a golden dish, embodies much\nthe same idea as the parable of the Priceless Pearl, in the New\nTestament. The tale of the Measures of Rice illustrates the importance\nof a true estimate of values. The tale of the Banyan Deer, which offered\nits life to save a roe and her young, illustrates self-sacrifice of the\nnoblest sort. The Kulavaka-Jataka contains the thought that a forgiving\nspirit toward one's enemies disarms even the evil-minded. The tale of\nthe Partridge, the Monkey, and the Elephant teaches that the best seats\nbelong not to the nobles or the priests, to the rich or the learned, not\neven to the most pious, but that reverence and service and respect and\ncivility are to be paid according to age, and for the aged the best\nseat, the best water, the best rice, are to be reserved. The tale of\nNanda, or the Buried Gold, is a rebuke to that base insolence which\nvulgar natures often exhibit when they possess a temporary advantage.\nThe tale of the Sandy Road is one of the finest in the collection. It\npictures to us a caravan wandering through the desert under the\nstarlight. The guide, whose duty it was to pilot them through this sea\nof sand, has, it appears, fallen asleep at his post from excessive\nweariness, and at dawn the travelers discover that they have gone\nastray, and that far and wide no water is in sight wherewith to quench\ntheir burning thirst. At this moment, however, the leader espies a small\ntuft of grass on the face of the desert, and, reasoning that water must\nbe flowing somewhere underneath, inspires his exhausted followers to new\nexertions. A hole sixty feet deep is dug under his direction, but at\nlength they come upon hard rock, and can dig no farther. But even then\nhe does not yield to despair. Leaping down, he applies his ear to the\nrock. Surely, it is water that he hears gurgling underneath! One more\neffort, he cries, and we are saved! But of all his followers one only\nhad strength or courage enough left to obey. This one strikes a heavy\nblow, the rock is split open, and lo! the living water gushes upward in\na flood. The lesson is that of perseverance and presence of mind in\ndesperate circumstances. The tale entitled Holding to the Truth narrates\nthe sad fate of a merchant who suffered himself to be deceived by a\nmirage into the belief that water was near, and emptied the jars which\nhe carried with him in order to reach the pleasant land the sooner. The\nJataka entitled On True Divinity contains a very beautiful story about\nthree brothers, the Sun prince, the Moon prince, and the future Buddha\nor Bodisat. The king, their father, expelled the Moon prince and the\nfuture Buddha in order to secure the succession to the Sun prince alone.\nBut the Sun prince could not bear to be separated from his brothers, and\nsecretly followed them into exile. They journeyed together until they\ncame to a certain lake. This lake was inhabited by an evil spirit, to\nwhom power had been given to destroy all who entered his territory\nunless they could redeem their lives by answering the question, \"What is\ntruly divine?\" So the Sun prince was asked first, and he answered, \"The\nsun and the moon and the gods are divine.\" But that not being the\ncorrect answer, the evil spirit seized and imprisoned him in his cave.\nThen the Moon prince was asked, and he answered, \"The far-spreading sky\nis called divine.\" But he, too, was carried away to the same place to be\ndestroyed. Then the future Buddha was asked, and he answered: \"Give ear,\nthen, attentively, and hear what divine nature is;\" and he uttered the\nwords--\n\n\n     \"The pure in heart who fear to sin,\n     The good, kindly in word and deed,\n     These are the beings in the world\n     Whose nature should be called divine.\"\n\n\nAnd when the evil spirit heard these words, he bowed, and said: \"I will\ngive up to you one of your brothers.\" Then the future Buddha said, \"Give\nme the life of my brother, the Sun prince, for it is on his account\nthat we have been driven away from our home and thrust into exile.\" The\nevil spirit was overcome by this act of generosity, and said, \"Verily, O\nteacher, thou not only knowest what is divine, but hast acted divinely.\"\nAnd he gave him the life of both his brothers, the Sun prince as well as\nthe Moon prince.\n\nI could not resist the temptation of relating a few of these tales. They\nare, as every one must admit, nobly conceived, lofty in meaning, and\nmany a helpful sermon might be preached from them as texts. But, of\ncourse, not all are fit to be used in a primary course. Some of them\nare, some are not. The teacher will have no difficulty in making the\nright selection. To the former class belongs also No. 28 of the\ncollection,[10] which is excellently adapted to impress the lesson of\nkindness to animals. Long ago the Buddha came to life in the shape of a\npowerful bull. His master, a Brahman, asserted that this bull of his\ncould move a hundred loaded carts ranged in a row and bound together.\nBeing challenged to prove his assertion, he bathed the bull, gave him\nscented rice, hung a garland of flowers around his neck, and yoked him\nto the first cart. Then he raised his whip and called out, \"Gee up, you\nbrute. Drag them along, you wretch!\" The bull said to himself, \"He calls\nme wretch; I am no wretch.\" And keeping his forelegs as firm as steel,\nhe stood perfectly still. Thereupon the Brahman, his master, was\ncompelled to pay a forfeit of a thousand pieces of gold because he had\nnot made good his boast. After a while the bull said to the Brahman, who\nseemed very much dispirited: \"Brahman, I have lived a long time in your\nhouse. Have I ever broken any pots, or have I rubbed against the walls,\nor have I made the walks around the premises unclean?\" \"Never, my dear,\"\nsaid the Brahman. \"Then why did you call me wretch? But if you will\nnever call me wretch again, you shall have two thousand pieces for the\none thousand you have lost.\" The Brahman, hearing this, called his\nneighbors together, set up one hundred loaded carts as before, then\nseated himself on the pole, stroked the bull on the back, and called\nout, \"Gee up, my beauty! Drag them along, my beauty!\" And the bull, with\na mighty effort, dragged along the whole hundred carts, heavily loaded\nthough they were. The bystanders were greatly astonished, and the\nBrahman received two thousand pieces on account of the wonderful feat\nperformed by the bull.\n\nThe 30th Jataka corresponds to the fable of the Ox and the Calf in the\nAEsop collection. The 33d, like the fable of the Bundle of Sticks,\nteaches the lesson of unity, but in a form a little nearer to the\nunderstanding of children. Long ago, when Brahmadatta was reigning in\nBenares, the future Buddha came to life as a quail. At that time there\nwas a fowler who used to go to the place where the quails dwelt and\nimitate their cry; and when they had assembled, he would throw his net\nover them. But the Buddha said to the quails: \"In future, as soon as he\nhas thrown the net over us, let each thrust his head through a mesh of\nthe net, then all lift it together, carry it off to some bush, and\nescape from underneath it.\" And they did so and were saved. But one day\na quail trod unawares on the head of another, and a disgraceful quarrel\nensued. The next time the fowler threw his net over them, each of the\nquails pretended that the others were leaving him to bear the greatest\nstrain, and cried out, \"You others begin, and then I will help.\" The\nconsequence was that no one began, and the net was not raised, and the\nfowler bagged them all. The 26th Jataka enforces the truth that evil\ncommunications corrupt good manners, and contains more particularly a\nwarning against listening to the conversation of wicked people. Thus\nmuch concerning the Jataka tales.\n\nThere exists also a collection of Hindu fairy tales and fables, gathered\nfrom oral tradition by M. Frere, and published under the title of Old\nDeccan Days. A few of these are very charming, and well adapted for our\npurpose. For example, the fable of King Lion and the Sly Little Jackals.\nThe story is told with delightful _naivete_. Singh-Rajah, the lion-king,\nis very hungry. He has already devoured all the jackals of the forest,\nand only a young married couple, who are extremely fond of each other,\nremain. The little jackal-wife is terribly frightened when she hears in\ntheir immediate vicinity the roar of Singh-Rajah. But the young husband\ntries to comfort her, and to save their lives he hits on the following\nexpedient: He makes her go with him straight to the cave of the terrible\nlion. Singh-Rajah no sooner sees them than he exclaims: \"It is well you\nhave arrived at last. Come here quickly, so that I may eat you.\" The\nhusband says: \"Yes, your Majesty, we are entirely ready to do as you bid\nus, and, in fact, we should have come long ago, as in duty bound, to\nsatisfy your royal appetite, but there is another Singh-Rajah mightier\nthan you in the forest, who would not let us come.\" \"What!\" says the\nlion, \"another Singh-Rajah mightier than I! That is impossible.\" \"Oh!\nbut it is a fact,\" say the young couple in a breath; \"and he is really\nmuch more terrible than you are.\" \"Show him to me, then,\" says\nSingh-Rajah, \"and I will prove to you that what you say is false--that\nthere is no one to be compared with me in might.\" So the little jackals\nran on together ahead of the lion, until they reached a deep well. \"He\nis in there,\" they said, pointing to the well. The lion looked down\nangrily and saw his own image, the image of an angry lion glaring back\nat him. He shook his mane; the other did the same. Singh-Rajah\nthereupon, unable to contain himself, leaped down to fight his\ncompetitor, and, of course, was drowned. The fable clothes in childlike\nlanguage the moral that anger is blind, and that the objects which\nexcite our anger are often merely the outward reflections of our own\npassions. In the fable of the Brahman, the Tiger, and the Six Judges,\nwe have a lesson against ingratitude, and also against useless\ndestruction of animal life. In the fable of the Camel and the Jackal,\nthe latter does not appear in the same favorable light as above. The\njackal and the camel were good friends. One day the jackal said to his\ncompanion: \"I know of a field of sugar-cane on the other side of the\nriver, and near by there are plenty of crabs and small fishes. The crabs\nand fishes will do for me, while you can make a fine dinner off the\nsugar-cane. If there were only a way of getting across!\" The camel\noffered to swim across, taking the jackal on his back, and in this way\nthey reached the opposite bank. The jackal ate greedily, and had soon\nfinished his meal; thereupon he began to run up and down, and to\nexercise his voice, screaming lustily. The camel begged him to desist,\nbut in vain. Presently the cries of the jackal roused the villagers.\nThey came with sticks and cudgels and cruelly beat the camel, and drove\nhim out of the field before he had had time to eat more than a few\nmouthfuls. When the men were gone at last, the jackal said, \"Let us now\ngo home.\" \"Very well,\" said the camel, \"climb on my back.\" When they\nwere midway between the two banks, the camel said to the jackal: \"Why\ndid you make such a noise and spoil my dinner, bringing on those cruel\nmen, who beat me so that every bone in my body aches? Did I not beg you\nto stop?\" \"Oh,\" said the jackal, \"I meant no harm. I was only singing a\nbit. I always sing after dinner, just for amusement.\" They had by this\ntime reached the place where the water was deepest. \"Well,\" said the\ncamel, \"I also like innocent amusements. For instance, it is my custom\nto lie on my back after dinner and to stretch myself a bit.\" With that\nhe turned over, and the jackal fell into the stream. He swallowed\npailfuls of water, and it was only with the utmost difficulty that he\nsucceeded in reaching the bank. He had received a salutary lesson on the\nsubject of inconsiderate selfishness--a fault very common with children,\nwhich such a story as this may help to correct.\n\nAs to the modern fables, I fear they will yield us but a scanty harvest.\nThe fables of La Fontaine, where they depart from AEsopian originals, are\nhardly suitable for children, and those of the German poet Gellert\nimpress me, on the whole, in the same way, though a few of them may be\nadded to our stock. For instance, the fable of the Greenfinch and the\nNightingale. These two birds occupy the same cage before the window of\nDamon's house. Presently the voice of the nightingale is heard, and then\nceases. The father leads his little boy before the cage and asks him\nwhich of the two he believes to have been the sweet musician, the\nbrightly colored greenfinch or the outwardly unattractive nightingale.\nThe child immediately points to the former, and is then instructed as to\nhis error. The lesson, of course, is that fine clothes and real worth do\nnot always go together. The fable of the Blind and the Lame Man teaches\nthe advantages of co-operation. The Carriage Horse and the Cart Horse\nis a fable for the rich. Possibly the fable of the Peasant and his Son,\nwhich is directed against lies of exaggeration, may also be utilized,\nthough I realize that there are objections to it.\n\nFOOTNOTE:\n\n[10] Buddhist Birth Stories; or Jataka Tales.\n\n\n\n\nIX.\n\nSTORIES FROM THE BIBLE.\n\n\n_Introduction._--It will have been noticed that in choosing our\nillustrative material we have confined ourselves to what may be called\nclassical literature. The German _Maerchen_ has lived in the traditions\nof the German people for centuries, and is as fresh to-day as Snow-white\nherself when she woke from her trance. The fables, as has been shown,\nhave been adopted into the language and literature of Persia, of Arabia,\nof the nations of Europe, and are still found in the hands of our own\nchildren. Let us continue to pursue the same method of selection.\nInstead of relying on juvenile literature just produced, or attempting\nto write moralizing stories specially adapted for the purpose in hand,\nlet us continue, without excluding invention altogether, to rely mainly\non that which has stood the test of time. In the third part of our\nprimary course we shall use selected stories from the classical\nliterature of the Hebrews, and later on from that of Greece,\nparticularly the Odyssey and the Iliad. The stories to which I refer\npossess a perennial vitality, an indestructible charm. I am, I trust, no\nblind worshiper of antiquity. The mere fact that a thing has existed for\na thousand or two thousand years is not always proof that it is worth\npreserving. But the fact that after having been repeated for two\nthousand years a story still possesses a perfectly fresh attraction for\nthe child of to-day, does indeed prove that there is in it something of\nimperishable worth. How is this unique charm of the classical literature\nto be explained? What quality exists in Homer, in the Bible, enabling\nthem, despite the changes of taste and fashion, to hold their own? The\nnovels of the last century are already antiquated; few care to read\nthem. The poetry of the middle ages is enjoyed only by those who\ncultivate a special taste for it. Historical and scientific works hardly\nhave time to leave an impression before new books appear to crowd them\nout. But a few great masterpieces have survived, and the truth and\nbeauty of these the lapse of ages, it seems, has left unaltered. Mr.\nJebb remarks[11] that Homer aims at the lucid expression of primary\nmotives, and refrains from multiplying individual traits which might\ninterfere with their effect, and that this typical quality in Homer's\nportraiture has been one secret of its universal impressiveness. The\nHomeric outlines are in each case brilliantly distinct, while they leave\nto the reader a certain liberty of private conception, and he can fill\nthem in so as to satisfy his own ideal. We may add that this is just as\ntrue of the Bible as of Homer. The biblical narrative, too, depicts a\nfew essential traits of human nature, and refrains from multiplying\nminor traits which might interfere with the main effect. The Bible, too,\ndraws its figures in outline, and leaves every age free to fill them in\nso as to satisfy its own ideal. Thus the biblical story, as conceived in\nthe mind of Milton, reflects the Puritan ideal; the same story, narrated\nin a modern pulpit or Sunday-school, will inevitably reflect, to a\ngreater or less degree, the modern humanitarian ideal, and this liberty\nof interpretation is one cause of the vitality of the Bible. But it may\nbe asked further, How did Homer, how did the biblical writers, succeed\nin producing such universal types, in drawing their figures so correctly\nthat, however the colors may thenceforth be varied, the outlines remain\nforever true? He who should attempt at the present day to give\nexpression to the most universal traits of human nature, freed from the\ncomplex web of conditions, disengaged from the thousand-fold minor\ntraits which modify the universal in particular instances, would find it\ndifficult to avoid one or the other of two fatal errors. If he keeps his\neyes fixed on the universal, he is in danger of producing a set of\nbloodless abstractions, pale shadows of reality, which will not live for\na day, much less for a thousand years. If, on the other hand, he tries\nto keep close to reality he will probably produce more or less accurate\ncopies of the types that surround him, but the danger will always be\nthat the universal will be lost amid the particulars. By what quality in\nthemselves or fortunate constellation of circumstances did Homer and the\nbiblical writers succeed in avoiding both these errors, in creating\ntypes of the utmost universality and yet imparting to them the breath of\nlife, the gait and accent of distinctive individuality? I imagine that\nthey succeeded because they lived at a time when life was much less\ncomplex than it is at present, when the conversation, the manners, the\nthoughts, the motives of men were simple. They were enabled to\nindividualize the universal because the most universal, the simplest\nmotives, still formed the mainspring in the conduct of individuals. It\nwas not necessary for them to enter into the barren region of\nabstraction and generalization to discover the universal. They pictured\nwhat they actually saw. The universal and the individual were still\nblended in that early dawn of human history.\n\nWe have thus far spoken of Homer and the Bible jointly. But let us now\ngive our particular attention to the biblical narrative. The narrative\nof the Bible is fairly saturated with the moral spirit; the moral issues\nare everywhere in the forefront. Duty, guilt and its punishment, the\nconflict of conscience with inclination, are the leading themes. The\nHebrew people seem to have been endowed with what may be called \"a moral\ngenius,\" and especially did they emphasize the filial and fraternal\nduties to an extent hardly equaled elsewhere. Now it is precisely these\nduties that must be impressed on young children, and hence the biblical\nstories present us with the very material we require. They can not, in\nthis respect, be replaced; there is no other literature in the world\nthat offers what is equal to them in value for the particular object we\nhave now in view. Before proceeding, however, to discuss the stories in\ndetail, let me remind you that in studying them a larger tax is made on\nthe attention of children, and a higher development of the moral\njudgment is presupposed, than in the previous parts of our course; for\nin them a succession of acts and their consequences are presented to the\nscholar, on each of which his judgment is to be exercised. Those who\nteach the biblical stories merely because it has been customary to\nregard the Bible as the text-book of morals and religion, without,\nhowever, being clear as to the place which belongs to it in a scheme of\nmoral education, will always, I doubt not, achieve a certain result. The\nstories will never entirely fail of their beneficial effect, but I can\nnot help thinking that this effect will be greatly heightened if their\nprecise pedagogic value is distinctly apprehended, and if the\npreparatory steps have been taken in due course. It seems to me that the\nmoral judgment should first be exercised on a single moral quality as\nexhibited in a single act before it is applied to a whole series of\nacts; and hence that the fable should precede the story.\n\nIn making our selection from the rich material before us we need only\nkeep in mind the principle already enunciated in the introductory\nlectures--that the moral teaching at any period should relate to the\nduties of that period.\n\n\n_Adam and Eve in Paradise._\n\nThis is a wonderful story for children. It deserves to be placed at the\nhead of all the others, for it inculcates the cardinal virtue of\nchildhood--obedience. It is also a typical story of the beginning, the\nprogress, and the culmination of temptation. Will you permit me to\nrelate the story as I should tell it to little children? I shall\nendeavor to keep true to the outlines, and if I depart from the received\nversion in other respects, may I not plead that liberty of\ninterpretation to which I have referred above.\n\nOnce upon a time there were two children, Adam and Eve. Adam was a fine\nand noble-looking lad. He was slender and well built, and fleet of foot\nas a young deer. Eve was as beautiful as the dawn, with long golden\ntresses, and blue eyes, and cheeks like the rose. They lived in the\nloveliest garden that you have ever heard of. There were tall trees in\nit, and open meadows where the grass was as smooth as on a lawn, and\nclear, murmuring brooks ran through the woods. And there were dense\nthickets filled with the perfume of flowers, and the flowers grew in\nsuch profusion, and there were so many different kinds, each more\nbeautiful than the rest, that it was a perfect feast for the eyes to\nlook at them. It was so warm that the children never needed to go\nin-doors, but at night they would just lie down at the foot of some\ngreat tree and look at the stars twinkling through the branches until\nthey fell asleep. And when it rained they would find shelter in some\nbeautiful cavern, spreading leaves and moss upon the ground for a bed.\nThe garden where they lived was called Paradise. And there were ever so\nmany animals in it--all kinds of animals--elephants, and tigers, and\nleopards, and giraffes, and camels, and sheep, and horses, and cows; but\neven the wild animals did them no harm. But the children were not alone\nin that garden: their Father lived with them. And every morning when\nthey woke up their first thought was to go to him and to look up into\nhis mild, kind face for a loving glance, and every evening before they\nwent to sleep he would bend over them. And once, as they lay under the\ngreat tree, looking at a star shining through the branches, Adam said to\nEve: \"Our Father's eye shines just like that star.\"\n\nOne day their Father said to them: \"My children, there is one tree in\nthis beautiful garden the fruit of which you must not eat, because it is\nhurtful to you. You can not understand why, but you know that you must\nobey your Father even when you do not understand. He loves you and knows\nbest what is for your good.\" So they promised, and for a time\nremembered. But one day it happened that Eve was passing near the tree\nof the fruit of which she knew she must not eat, when what should she\nhear but a snake talking to her. She did not see it, but she heard its\nvoice quite distinctly. And this is what the snake said: \"You poor Eve!\nyou must certainly have a hard time. Your Father is always forbidding\nyou something. How stern he is! I am sure that other children can have\nall the fruit they want.\" Eve was frightened at first. She knew that her\nFather was kind and good, and that the snake was telling a falsehood. He\ndid not always forbid things. But still he had forbidden her to eat of\nthe fruit, and she thought that was a little hard; and she could not\nunderstand at all why he had done so. Then the snake spoke again:\n\"Listen, Eve! He forbade you to eat only of it. It can do no harm just\nto look at it. Go up to it. See how it glistens among the branches! How\ngolden it looks!\" And the snake kept on whispering: \"How good it must be\nto the taste! Just take one bite of it. Nobody sees you. Only one bite;\nthat can do no harm.\" And Eve glanced around, and saw that no one was\nlooking, and presently with a hasty movement she seized the fruit and\nate of it. Then she said to herself: \"Adam, too, must eat of it. I can\nnever bear to eat it alone.\" So she ran hastily up to Adam, and said:\n\"See, I have some of the forbidden fruit, and you, too, must eat.\" And\nhe, too, looked at it and was tempted, and ate. But that evening they\nwere very much afraid. They knew they had done wrong, and their\nconsciences troubled them. So they hurried away into the wood where it\nwas deepest, and hid themselves in the bushes. But soon they heard their\nFather calling to them; and it was strange, their Father's voice had\nnever sounded so sad before. And in a few moments he found them where\nthey were hiding. And he said to them: \"Why do you hide from me?\" And\nthey were very much confused, and stammered forth all sorts of excuses.\nBut he said: \"Come hither, children.\" And he looked into their eyes, and\nsaid: \"Have you eaten of the fruit of which I told you not to eat?\" And\nAdam, who was thoughtless and somewhat selfish, spoke up, and said:\n\"Yes, but it was Eve who gave me of it; she led me on.\" And Eve hung her\nhead, and said: \"It was the snake that made me eat.\" Now the snake, you\nknow, was no real snake at all; she never saw it, she only heard its\nvoice. And, you know, when we want to do anything wicked, there is\nwithin every one of us something bad, that seems to whisper: \"Just look!\nMere looking will do no harm\"; and then: \"Just taste; no one sees you.\"\nSo the snake was the bad feeling in Eve's heart. And their Father took\nthem by the hand, and said: \"Tomorrow, when it is dawn, you will have to\nleave this place. In this beautiful Paradise no one can stay who has\nonce disobeyed. You, Adam, must learn to labor; and, you, Eve, to be\npatient and self-denying for others. And, perhaps, after a long, long\ntime, some day, you will come back with me into Paradise again.\"\n\nIt is a free rendering, I admit. I have filled in the details so as to\nbring it down to the level of children's minds, but the outlines, I\nthink, are there. The points I have developed are all suggested in the\nBible. The temptation begins when the snake says with characteristic\nexaggeration: \"Is it true that of _all_ the fruit you are forbidden to\neat?\" Exaggerating the hardships of the moral command is the first step\non the downward road. The second step is Eve's approach to look at the\nfruit--\"and she saw that it was good for food, and pleasant to the\neyes.\" The third step is the actual enjoyment of what is forbidden. The\nfourth step is the desire for companionship in guilt, so characteristic\nof sin--\"and she gave also unto her husband with her, and he did eat.\"\nThe next passage describes the working of conscience, the fear, the\nshame, the desire to hide, and then comes the moral verdict: You are\nguilty, both of you. You have lost your paradise. Try to win it back by\nlabor and suffering.\n\n\n     NOTE.--I would add to what has been said in the text, that the\n     pupils are expected to return to the study of the Bible, to read\n     and re-read these stories, and to receive a progressively higher\n     interpretation of their meaning as they grow older. If in the above\n     I have spoken in a general way of a Father and his two children, it\n     will be easy for the Sunday-school teacher to add later on that the\n     Father in the story was God.\n\n\n\n_Cain and Abel._\n\nIn teaching the story of the two brothers Cain and Abel the following\npoints should be noted. The ancients believed that earthly prosperity\nand well-being depended on the favor of God, or the gods, and that the\nfavor of the gods could be secured by sacrifice. If any one brought a\nsacrifice and yet prosperity did not set in, this was supposed to be a\nsign that his sacrifice had not been accepted. On the other hand, to say\nof any person that his sacrifice had been accepted, was tantamount to\nsaying that he was happy and prosperous. Applying this to the story of\nCain and Abel, we may omit all mention of the bringing of the\nsacrifices, which presents a great and needless difficulty to children's\nminds, and simply make the equivalent statement that Abel was prosperous\nand Cain was not.\n\nAgain, Cain is not represented as an intentional murderer. The true\ninterpretation of the story depends on our bearing this in mind. It is\nerroneous to suppose that a brand was fixed on Cain's forehead. The\npassage in question, correctly understood, means that God gave Cain a\nsign to reassure him that he should not be regarded by men as a common\nmurderer. With these prefatory remarks the story may be told somewhat as\nfollows:\n\nLong ago there lived two brothers. The name of the elder was Cain, and\nof the younger Abel. Cain was a farmer. He toiled in the sweat of his\nbrow, tilling the stubborn ground, taking out stones, building fences.\nWinter and summer he was up before the sun, and yet, despite all his\nlabor, things did not go well with him. His crops often failed through\nno fault of his. He never seemed to have an easy time. Moreover, Cain\nwas of a proud disposition. Honest he was, and truthful, but taciturn,\nnot caring much to talk to people whom he met, but rather keeping to\nhimself. Abel, on the other hand, was a shepherd. He led, or seemed to\nlead, the most delightfully easy life. He followed his flocks from one\npasture to another, watching them graze; and at noon he would often lie\ndown in the shade of some leafy tree and play on his flute by the hour.\nHe was a skillful musician, a bright, talkative companion, and\nuniversally popular. He was a little selfish too, as happy people\nsometimes are. He liked to talk about his successes, and, in a perfectly\ninnocent way, which yet stung Cain to the quick, he would rattle on to\nhis brother about the increase of his herds, about his plans and\nprospects, and the pleasant things that people were saying of him. Cain\ngrew jealous of his brother Abel. He did not like to confess it to\nhimself, but yet it was a fact. He kept comparing his own life of\ngrinding toil with the easy, lazy life of the shepherd--it was not quite\nso lazy, but so it seemed to Cain--his own poverty with the other's\nwealth, his own loneliness with Abel's popularity. And a frown would\noften gather on his brow, and he grew more and more moody and silent. He\nknew that he was not in the right state of mind. There was a voice\nwithin him that said: \"Sin is at thy door, but thou canst become master\nover it.\" Sin is like a wild beast crouching outside the door of the\nheart. Open the door ever so little, and it will force its way in, and\nwill have you in its power. Keep the door shut, therefore; do not let\nthe first evil thought enter into your heart. Thus only can you remain\nmaster of yourself. But Cain was already too far gone to heed the\nwarning voice. One day he and Abel were walking together in the fields.\nAbel, no doubt, was chatting in his usual gay and thoughtless manner.\nThe world was full of sunshine to him; and he did not realize in the\nleast what dark shadows were gathering about his brother's soul. Perhaps\nthe conversation ran somewhat as follows: He had just had an addition to\nhis herd, the finest calf one could imagine: would not Cain come to\nadmire it? And then, to-morrow evening he was to play for the dancers on\nthe green, at the village feast: would not Cain join in the\nmerry-making? When the solitary, embittered Cain heard such talk as this\nthe angry feeling in his heart rose up like a flood. Overmastered by his\npassion, with a few wild, incoherent words of rage he turned upon his\nbrother and struck him one fierce blow. Ah, that was a relief! The\npent-up feeling had found vent at last. The braggart had received the\nchastisement he deserved! And Cain walked on; and for a time continued\nto enjoy his satisfaction. He had just noticed that Abel, when struck,\nhad staggered and fallen, but he did not mind that. \"Let him lie there\nfor a while; he will pick himself up presently. He may be lame for a few\ndays, and his milk-white face may not be so fair at the feast, but that\nwill be all the better for him. It will teach him a lesson.\"\nNevertheless, when he had walked on for some distance he began to feel\nuneasy. He looked around from time to time to see whether Abel was\nfollowing him, and the voice of conscience began to be heard, saying,\n\"Cain, where is thy brother?\" But he silenced it by saying to himself,\n\"Am I my brother's keeper? Is he such a child that he can not take care\nof himself--that he can not stand a blow?\" But he kept looking back more\nand more often, and when he saw no one coming, he came at last to a dead\nhalt. His heart was beating violently by this time; the beads of\nperspiration were gathered on his brow. He turned back to seek his\nmissing brother. Then, as he did not meet him, he began to run, and\nfaster and faster he ran, until at last, panting and out of breath, with\na horrible fear hounding him on, he arrived at the place where he had\nstruck the blow. And there he saw--a pool of blood, and the waxen face\nof his brother, and the glazed, broken eyes! And then he realized what\nhe had done. And it is this situation which the Bible has in view in the\nwords, \"Behold, thy brother's blood cries up from the earth against\nthee.\" And then as he surveyed his deed in stony despair, he said to\nhimself, \"I am accursed from the face of the earth\"--I am unworthy to\nlive. The earth has no resting-place for such as I. But a sign was given\nhim to show him that his life would not be required of him. He had not\ncommitted willful murder. He had simply given the reins to his violent\npassion. He must go into another land, where no one knew him, there\nthrough years of penance to try to regain his peace of soul. The moral\nof the story is: Do not harbor evil thoughts in the mind. If you have\nonce given them entrance, the acts to which they lead are beyond your\ncontrol. Cain's sin consisted in not crushing the feeling of envy in the\nbeginning; in comparing his own lot with that of his more favored\nbrother and dwelling on this comparison, until, in a fit of insane\npassion, he was led on to the unspeakable crime which, indeed, he had\nnever contemplated, to which he had never given an inward assent. The\nstory also illustrates the vain subterfuges with which we still seek to\nsmother the consciousness of guilt after we have done wrong, until the\ntime comes when our eyes are opened and we are compelled to face the\nconsequences of our deeds and to realize them in all their bearings. The\nstory of Cain and Abel is thus a further development of the theme\nalready treated in simpler fashion in the story of Adam and Eve, only\nthat, while in the latter case the filial duty of obedience to parents\nis in the foreground, attention is here directed to the duty which a\nbrother owes to a brother. It is a striking tale, striking in the\nvividness with which it conjures up the circumstances before our minds\nand the clearness with which the principal motives are delineated; and\nit contains an awful warning for all time.\n\nThe question here presents itself, whether we should arrange the\nbiblical stories according to subjects--e. g., grouping together all\nthose which treat of duty to parents, all those which deal with the\nrelations of brothers to brothers, etc.--or whether we should adopt the\nchronological arrangement. On the whole, I am in favor of the latter. It\nis expected that the pupils, as they grow older, will undertake a more\ncomprehensive study of the Bible, and for this they will be better\nprepared if they have been kept to the chronological order from the\noutset. Another more practical reason is, that children tire of one\nsubject if it is kept before their minds too long. It is better,\ntherefore, to arrange the stories in groups or cycles, each of which\nwill afford opportunity to touch on a variety of moral topics. It will\nbe impossible to continue to relate _in extenso_ the stories which I\nhave selected, and I shall therefore content myself in the main with\ngiving the points of each story upon which the teacher may lay stress.\n\n\n_The Story of Noah and his Sons._\n\nDescribe the beauty of the vine, and of the purple grapes hanging in\nclusters amid the green leaves. How sweet is this fruit to the taste!\nBut the juice of it has a dangerous property. Once there lived a man,\nNoah, who had three sons. He planted a vine, plucked the grapes, but did\nnot know the dangerous property of the juice. The second son, on seeing\nhis father in a state of intoxication, allowed his sense of the\nridiculous to overcome his feeling of reverence. But the eldest and the\nyoungest sons acted differently. They took a garment, covered their\nfather with it, and averted their faces so as not to see his disgrace.\nThe moral is quite important. An intelligent child can not help\ndetecting a fault now and then even in the best of parents. But the\nright course for him to take is to throw the mantle over the fault, and\nto turn away his face. He should say to himself: Am I the one to judge\nmy parents--I who have been the recipient of so many benefits at their\nhands, and who see in them so many virtues, so much superior wisdom? By\nsuch reasoning the feeling of reverence is even deepened. The momentary\nsuperiority which the child feels serves only to bring out his general\ninferiority.\n\n\n_The Abraham Cycle._\n\nThere is a whole series of stories belonging to this group, illustrating\nin turn the virtues of brotherly harmony, generosity toward the weak,\nhospitality toward strangers, and maternal love. Abraham and Lot are\nnear kinsmen. Their servants quarrel, and to avoid strife the former\nadvises a separation. \"If thou wilt go to the left,\" he says, \"I will\nturn to the right; if thou preferrest the land to the right, I will take\nthe left.\" Abraham, being the older, was entitled to the first choice,\nbut he waived his claim. Lot chose the fairer portion, and Abraham\nwillingly assented. \"Let there be no strife between us, for we be\nbrethren.\" The lesson is, that the older and wiser of two brothers or\nkinsmen may well yield a part of his rights for harmony's sake.\n\nAbraham's conduct toward the King of Sodom is an instance of generosity.\nThe story of the destruction of Sodom and Gomorrah may be introduced by\ndescribing the Dead Sea and the surrounding scene of desolation. The\nmoral lies in the circumstance that ill treatment of strangers brought\ndown the doom. Hospitality toward strangers is one of the shining\nvirtues of the Old Testament heroes. Even at the present day strangers\nare still despised and ridiculed by the vulgar, their foreign manners,\nlanguage, and habits seeming contemptible; the lesson of hospitality is\nnot yet superfluous.\n\nThe story of _Hagar and her Child_ I should recast in such a way as to\nexclude what in it is repellent, and retain the touching picture of\nmaternal affection. I should relate it somewhat as follows: There was\nonce a little lad whose name was Ishmael. He had lost his father and had\nonly his mother to cling to. She was a tall, beautiful lady, with dark\neyes which were often very sad, but they would light up, and there was\nalways a sweet smile on her lips whenever she looked at her darling boy.\nIshmael and his mother, Hagar, had never been separated; they were all\nin all to each other. One day it happened that they walked away from\ntheir home, which was near the great, sandy desert. Ishmael's mother was\nin deep distress, there was something troubling her, and every now and\nthen a tear would steal down her cheeks. Ishmael was sad, too, because\nhis mother was, but he did not dare to ask her what it was that grieved\nher, fearing to give her pain. So they walked on and on, holding each\nother's hands in silence. But at last they saw that they had lost their\nway; and they tried first one direction, and then another, thinking that\nit would bring them back toward home, but they only got deeper and\ndeeper into the vast, lonely desert. And the sun burned hot and hotter\nabove their heads, and little Ishmael, who had tried to keep up like a\nbrave lad, at last became so parched with thirst, and so faint with want\nof food, and so tired with walking--for they had wandered about for\nmany, many hours--that he could go on no farther. Then his mother took\nhim up in her arms and laid him under a bush, where there was a little\nshade. And then, oh then, how her poor heart was wrung, and how she wept\nto see her darling in such suffering, and how she cried for help! Then\nshe sat down on the glaring sand at some distance away, and turned her\nface in the direction opposite to where Ishmael was lying; for she said,\n\"I can not bear to see my boy die.\" But just as she had given up all\nhope, suddenly she saw a noble-looking man, wearing the dress of the\nBedouins, approach her. He had come from behind one of the sand hills,\nand it seemed to her as if he had come down straight from the sky. He\nasked her why she was in such grief, and when she told him, and pointed\nto her little son, he said: \"It is fortunate that you have come to this\nplace. There is a beautiful oasis close by.\" An oasis, children, is a\nspot of fruitful green earth right in the midst of the desert, like an\nisland in the ocean. And the man took the boy up and carried him in his\narms, and Hagar followed after him. And presently, when they came to the\noasis, they found a cool, clear spring, full of the most delicious\nwater, and palm-trees with ever so many dates on them, and all the\npeople who lived there gathered around them. And the man who had been\nso kind proved to be the chief. And he took charge of Ishmael's\neducation, showed him how to shoot with the bow and how to hunt, and was\nlike a real father to him. And when Ishmael grew up he became a great\nchief of the Bedouins. But he always remained true to his mother, and\nloved her with all his heart.\n\nI am strongly in favor of omitting the story of the _Sacrifice of\nIsaac_. I do not think we can afford to tell young children that a\nfather was prepared to draw the knife against his own son, even though\nhe desisted in the end. I should not be willing to inform a child that\nso horrible an impulse could have been entertained even for a moment in\na parent's heart. I regard the story, indeed, as, from an historical\npoint of view, one of the most valuable in the Bible; it has a deep\nmeaning; but it is not food fit for children. A great mistake has been\nmade all along in supposing that whatever is true in religion must be\ncommunicated to children; and that if anything be very true and very\nimportant we ought to hasten to give it to children as early as\npossible; but there must be preparatory training. And the greatest\ntruths are often of such a kind as only the mature mind, ripe in thought\nand experience, is fitted to assimilate.\n\nOne of the most charming idyls of patriarchal times is the story of\n_Rebecca at the Well_. It illustrates positively, as the story of Sodom\ndoes negatively, the duty of hospitality toward strangers. \"Drink, lord,\nand I will give thy camels drink also,\" is a pleasant phrase which is\napt to stick in the memory. Moreover, the story shows the high place\nwhich the trusted servant occupied in the household of his master, and\noffers to the teacher an opportunity of dwelling on the respect due to\nfaithful servants.\n\n\n_The Jacob Cycle._\n\nWhat treatment shall Jacob receive at our hands, he, the sly trickster,\nwho cheats his brother of his birthright and steals a father's blessing?\nYet he is one of the patriarchs, and is accorded the honorable title of\n\"champion of God.\" To hold him up to the admiration of the young is\nimpossible. To gloss over his faults and try to explain them away were a\nsorry business, and honesty forbids. The Bible itself gives us the right\nclew. His faults are nowhere disguised. He is represented as a person\nwho makes a bad start in life--a very bad start, indeed--but who pays\nthe penalty of his wrong-doing. His is a story of penitential\ndiscipline.\n\nIn telling the story, all reference to the duplicity of Rebecca should\nbe omitted, for the same reason that malicious step-mothers and cruel\nfathers have been excluded from the fairy tales.\n\nThe points to be discussed may be summarized as follows:\n\n_Taking advantage of a brother in distress._--Jacob purchases the\nbirthright for a mess of pottage.\n\n_Tender attachment to a helpless old father._--Esau goes out hunting to\nsupply a special delicacy for his father's table. This is a point which\nchildren will appreciate. Unable to confer material benefits on their\nparents, they can only show their love by slight attentions.\n\n_Deceit._--Jacob simulates the appearance of his older brother and\nsteals the blessing. In this connection it will be necessary to say that\na special power was supposed to attach to a father's blessing, and that\nthe words once spoken were deemed irrevocable.\n\n_Jacob's penitential discipline begins._--The deceiver is deceived, and\nmade to feel in his own person the pain and disappointment which deceit\ncauses. He is repeatedly cheated by his master Laban, especially in the\nmatter which is nearest to him, his love for Rachel.\n\n_The forgiveness of injuries._--Esau's magnanimous conduct toward his\nbrother.\n\n_The evil consequences of tale-bearing and conceit._--It is a\nsignificant fact that Joseph is not a mere coxcomb. He is a man of\ngenius, as his later career proves, and the stirrings of his genius\nmanifest themselves in his early dreams of future greatness. Persons of\nthis description are not always pleasant companions, especially in their\nyouth. They have not yet accomplished anything to warrant distinction,\nand yet they feel within themselves the presentiment of a destiny and of\nachievements above the ordinary. Their faults, their arrogance, their\nseemingly preposterous claims, are not to be excused, but neither is\nthe envy they excite excusable. One of the hardest things to learn is to\nrecognize without envy the superiority of a brother.\n\n_Moral cowardice._--Reuben is guilty of moral cowardice. He was an\nopportunist, who sought to accomplish his ends by diplomacy. If he, as\nthe oldest brother, had used his authority and boldly denounced the\ncontemplated crime, he might have averted the long train of miseries\nthat followed.\n\n_Strength and depth of paternal love._--\"Joseph is no more: an evil\nbeast has devoured him. I will go mourning for my son Joseph into the\ngrave.\" It is a piece of poetic justice that Jacob, who deceived his\nfather in the matter of the blessing by covering himself with the skin\nof a kid, is himself deceived by the blood of a kid of the goats with\nwhich the coat of Joseph had been stained.\n\nIn speaking of the temptation of Joseph in the house of Potiphar, it is\nenough to say that the wife conspired against her husband, and\nendeavored to induce Joseph to betray his master. A pretty addition to\nthe story is to be found in the Talmud, to the effect that Joseph saw in\nimagination the face of his father before him in the moment of\ntemptation, and was thereby strengthened to resist.\n\n_The light of a superior mind can not be hidden even in a\nprison._--Joseph wins the favor of his fellow-prisoners, and an\nopportunity is thus opened to him to exercise his talents on the largest\nscale.\n\n_Affliction chastens._--The famine had in the mean time spread to\nPalestine. The shadow of the grief for Joseph still lay heavily on the\nhousehold of the patriarch. Joseph is lost; shall Benjamin, too, perish?\nIt is pleasant to observe that the character of the brothers in the mean\ntime has been changed for the better. There is evidently a lurking sense\nof guilt and a desire to atone for it in the manner in which Judah\npledges himself for the safety of the youngest child. And the same\nmarked change is visible in the conduct of all the brothers on the\njourney. The stratagem of the cup was cunningly devised to test their\nfeelings. They might have escaped by throwing the blame on Benjamin.\nInstead of that, they dread nothing so much as that he may have to\nsuffer, and are willing to sacrifice everything to save him. When this\nnew spirit has become thoroughly apparent, the end to which the whole\ngroup of Jacob stories pointed all along is reached; the work of moral\nregeneration is complete. Jacob himself has been purified by affliction,\nand the brothers and Joseph have been developed by the same hard\ntaskmaster into true men. The scene of recognition which follows, when\nthe great vice-regent orders his attendants from the apartment and\nembraces those who once attempted his life, with the words, \"I am\nJoseph, your brother: does my father still live?\" is touching in the\nextreme, and the whole ends happily in a blaze of royal pomp, like a\ntrue Eastern tale.\n\nA word as to the _method_ which should be used in teaching these\nstories. If the fairy tale holds the moral element in solution, if the\nfable drills the pupil in distinguishing one moral trait at a time, the\nbiblical stories exhibit a combination of moral qualities, or, more\nprecisely, the interaction of moral causes and effects; and it is\nimportant for the teacher to give expression to this difference in the\nmanner in which he handles the stories. Thus, in the fables we have\nsimply one trait, like ingratitude, and its immediate consequences. The\nsnake bites the countryman, and is cast out; there the matter ends. In\nthe story of Joseph we have, first, the partiality of the father, which\nproduces or encourages self-conceit in the son; Joseph's conceit\nproduces envy in the brothers. This envy reacts on all concerned--on\nJoseph, who in consequence is sold into slavery; on the father, who is\nplunged into inconsolable grief; on the brothers, who nearly become\nmurderers. The servitude of Joseph destroys his conceit and develops his\nnobler nature. Industry, fidelity, and sagacity raise him to high power.\nThe sight of the constant affliction of their father on account of\nJoseph's loss mellows the heart of the brothers, etc. It is this\ninterweaving of moral causes and effects that gives to the stories their\npeculiar value. They are true moral pictures; and, like the pictures\nused in ordinary object lessons, they serve to train the power of\nobservation. Trained observation, however, is the indispensable\npreliminary of correct moral judgment.\n\n\n_The Moses Cycle._\n\nThe figures of the patriarchs and the prophets appeal to us with a fresh\ninterest the moment we regard them as human beings like ourselves, who\nwere tempted as we are, who struggled as we are bound to do, and who\nacted, howsoever the divine economy might supervene, on their own\nresponsibility. Looked at from this point of view, the figure of Moses,\nthe Liberator, approaches our sympathies at the same time that he towers\nin imposing proportions above our level. Let us briefly review his\ncareer. Like Arminius at a later day, he is educated at the court of the\nenemies of his people. In dress, in manners, in speech, he doubtless\nresembles the grandees of Pharaoh's court. When he approaches the well\nin Midian, the daughter of Jethro exclaims, \"Behold, an Egyptian is\ncoming!\" But at heart he remains a Hebrew, and is deeply touched by the\ncruel sufferings of his race. His first public intervention on their\nbehalf takes place when he strikes down and kills a native overseer whom\nhe detects in the act of maltreating a Hebrew slave. This is\ncharacteristic of the manner in which reformers begin. They direct their\nfirst efforts against the particular consequences of some great general\nwrong. Later on they perceive the uselessness of such a procedure and\ntake heart to attack the evil at its source. Moses flees into the\ndesert. The lonely life he leads there is necessary to the development\nof his ideas. Solitude is essential to the growth of genius. The\nburning bush is the outward symbol of an inward fact. The fire which can\nnot be quenched is in his own breast, and out of that inward burning he\nhears more and more distinctly the voice which bids him go back and free\nhis people. But when he considers the means at his disposal, when in\nfancy he sees his people, a miserable horde of slaves, pitted against\nthe armed hosts of Pharaoh, he is ready to despair; until he hears the\ncomforting voice, which says, \"The Eternal is with thee; the\nunchangeable power of right is on thy side: it will prevail!\" Like\nJeremiah, like Isaiah, like all great reformers, Moses is profoundly\nimbued with the sense of his unfitness for the task laid upon him. He\npleads that he is heavy of speech. He can only stammer forth the message\nof freedom. But he is reassured by the thought that a brother will be\nfound, that helpers will arise, that the thought which he can barely\nformulate will be translated by other lesser men into a form suitable\nfor the popular understanding. He returns to Egypt to find that the\ngreatest obstacle in his way is the lethargy and unbelief of the very\npeople whom he wishes to help. This again is a typical feature of his\ncareer. The greatest trials of the reformer are due not to the open\nenmity of the oppressor, but to the meanness, the distrust and jealousy,\nof those whom oppression has degraded. At last, however, the miracle of\nsalvation is wrought, the weak prevail over the mighty, the cause of\njustice triumphs against all apparent odds to the contrary. The slaves\nrise against their masters, the flower of Egyptian chivalry is\ndestroyed. Pharaoh rallies his army and sets out in pursuit. But the\nHebrews, under Moses's guidance, have gained the start, and escape into\nthe wilderness in safety.\n\nFreedom is a precious opportunity--no more. Its value depends on the use\nto which it is put. And therefore, no sooner was the act of liberation\naccomplished, than the great leader turned to the task of positive\nlegislation, the task of developing a higher moral life among his\npeople. But here a new and keener disappointment awaited him. When he\ndescended from the mount, the glow of inspiration still upon his face,\nthe tablets of the law in his hand, he saw the people dancing about the\ngolden calf. It is at this moment that Michel Angelo, deeply realizing\nthe human element in the biblical story, has represented the form of the\nliberator in the colossal figure which was destined for Pope Julius's\ntomb. \"The right foot is slightly advanced; the long beard trembles with\nthe emotion which quivers through the whole frame; the eyes flash\nindignant wrath; the right hand grasps the tablets of the law; in\nanother moment, we see it plainly, he will leap from his sitting posture\nand shatter the work which he has made upon the rocks.\" This trait, too,\nis typical. Many a leader of a noble cause has felt, in moments of deep\ndisappointment, as if he could shatter the whole work of his life. Many\na man, in like situation, has said to himself: The people are willing\nenough to hail the message of the higher law to-day, but to-morrow they\nsink back into their dull, degraded condition, as if the vision from the\nmount had never been reported to them. Let me, then, leave them to their\ndreary ways, to dance about their golden calf. But a better and stronger\nmood prevailed in Moses. He ascended once more to the summit, and there\nprostrated himself in utter self-renunciation and self-effacement. He\nasked nothing for himself, only that the people whom he loved might be\nbenefited ever so little, be raised ever so slowly above their low\ncondition. And again the questioning spirit came upon him, and he said,\nas many another has said: The paths of progress are dark and twisted;\nthe course of history seems so often to be in the wrong direction. How\ncan I be sure that there is such a thing as eternal truth--that the\nright will prevail in the end? And then there came to him that grand\nrevelation, the greatest, as I think, and the most sublime in the Old\nTestament, when the eternal voice answered his doubt, and said: \"Thou\nwouldst know my ways, but canst not. No living being can see my face;\nonly from the rearward canst thou know me.\" As a ship sails through the\nwaters and leaves its wake behind, so the divine Power passes through\nthe world and leaves behind the traces by which it can be known. And\nwhat are those traces? Justice and mercy. Cherish, therefore, the divine\nelement in thine own nature, and thou wilt see it reflected in the world\nabout thee. Wouldst thou be sure that there is such a thing as a divine\nPower? be thyself just and merciful. And so Moses descended again to his\npeople, and became exceeding charitable in spirit. The Bible says: \"The\nman Moses was exceeding humble; there was no one more humble than he on\nthe face of the earth.\" He bore with resignation their complaints, their\nmurmurings, their alternate cowardice and foolhardiness. He was made to\nfeel, like many another in his place, that his foes were they of his own\nhousehold. He had an only brother and an only sister. His brother and\nsister rose up against him. His kinsmen, too, revolted from him. He\nendured all their weakness, all their follies; he sought to lift them by\nslow degrees to the height of his own aims. He set the paths of life and\ndeath before them, and told them that the divine word can not be found\nby crossing the seas or by searching the heavens, but must be found in\nthe human heart; and if men find it not there they will find it nowhere\nelse. And so, at last, his pilgrimage drew to a close. He had reached\nthe confines of Palestine. Once more he sought the mountain-top, and\nthere beheld the promised land stretching far away--the land which his\neyes were to see but which he was never to enter. Few great reformers,\nindeed few men who have started a great movement in history, and have\nbeen the means of producing deep and permanent changes in the ideas and\ninstitutions of society, have lived to see those changes consummated.\nThe course of evolution is slow, and the reformer can hope at best to\nsee the promised land from afar--as in a dream. Happy he if, like\nMoses, he retains the force of his convictions unabated, if his\nspiritual sight remains undimmed, if the splendid vision which attended\nhim in the beginning inspires and consoles him to the end.\n\nThe narrative which has thus been sketched touches on some of the\nweightiest problems of human existence, and deals with motives both\ncomplex and lofty. I have entered into the interpretation of these\nmotives for the purpose of showing that they are too complex and too\nlofty to be within the comprehension of children, and that it is an\nerror, though unfortunately a common one, to attempt to use the grand\ncareer of a reformer and liberator as a text for the moral edification\nof the very young. They are wholly unprepared to understand, and that\nwhich is not understood, if forced on the attention, awakens repugnance\nand disgust. Few of those who have been compelled to study the life of\nMoses in their childhood have ever succeeded in conquering this\nrepugnance, or have drawn from it, even in later life, the inspiration\nand instruction which it might otherwise have afforded them. For our\nprimary course, however, we can extract a few points interesting even to\nchildren, thus making them familiar with the name of Moses, and\npreparing the way for a deeper interest later on. The incidents of the\nstory which I should select are these: The child Moses exposed on the\nNile; the good sister watching over his safety; the kind princess\nadopting him as her son; the sympathy manifested by him for his\nenslaved brethren despite his exemption from their misfortunes. The\nkilling of the Egyptian should be represented as a crime, palliated but\nnot excused by the cruelty of the overseer. Special stress may be laid\nupon the chivalric conduct of Moses toward the young girls at the well\nof Midian. The teacher may then go on to say that Moses, having\nsucceeded in freeing his people from the power of the Egyptian king,\nbecame their chief, that many wise laws are ascribed to him, etc. The\nstory of the spies, and of the end of Moses, may also be briefly told.\n\nThe mention of the laws of Moses leads me to offer a suggestion. I have\nremarked above that children should be taught to observe moral pictures\nbefore any attempt is made to deduce moral principles; but certain\n_simple rules_ should be given even to the very young--must, indeed, be\ngiven them for their guidance. Now, in the legislation ascribed to Moses\nwe find a number of rules fit for children, and a collection of these\nrules might be made for the use of schools. They should be committed to\nmemory by the pupils, and perhaps occasionally recited in chorus. I have\nin mind such rules as these:[12]\n\n1. Ye shall not lie. (Many persons who pay attention only to the\nDecalogue, and forget the legislation of which it forms a part, seem not\nto be aware that there is in the Pentateuch [Lev. xix, 11] a distinct\ncommandment against lying.)\n\n2. Ye shall not deceive one another.\n\n3. Ye shall take no bribe.\n\n4. Honor thy father and thy mother.\n\n5. Every one shall reverence his mother and his father. (Note that the\nfather is placed first in the one passage and the mother first in the\nother, to indicate the equal title of both to their children's\nreverence.)\n\n6. Thou shalt not speak disrespectfully of those in authority.\n\n7. Before the hoary head thou shalt rise and pay honor to the aged.\n\n10. Thou shalt not spread false reports.\n\n11. Thou shalt not go about as a tale-bearer among thy fellows.\n\n12. Thou shalt not hate thy neighbor in thy heart, but shalt warn him of\nhis evil-doing.\n\n13. Thou shalt not bear a grudge against any, but thou shalt love thy\nneighbor as thyself.\n\n8. Thou shalt not speak evil of the deaf (thinking that he can not hear\nthee), nor put an obstacle in the way of the blind.\n\n9. If there be among you a poor man, thou shalt not harden thy heart,\nnor shut thy hand from thy poor brother, but thou shalt open thy hand\nwide unto him, and shalt surely lend him sufficient for his need.\n\n14. If thou seest the property of thine enemy threatened with\ndestruction, thou shalt do thy utmost to save it.\n\n15. If thou findest what is not thine own, and the owner is not known\nto thee, guard it carefully, that thou mayest restore it to its rightful\nowner.\n\n16. Thou shalt not do evil because many others are doing the same evil.\n\nBearing grudges, lying, mocking those who (like the deaf and blind) are\nafflicted with personal defects, appropriating what is found without\nattempting to discover the owner, seeking to excuse wrong on the plea\nthat many others are guilty of it--all these are forms of moral evil\nwith which children are perfectly familiar, and against which they need\nto be warned. It is more than strange that such commandments as the\nsixth and eighth of the Decalogue (the commandment against murder and\nagainst adultery, forsooth), which are inapplicable to little children,\nshould be made so much of in primary moral instruction, while those\nother commandments which do come home to them are often overlooked. The\ntheory here expounded, that moral teaching should keep pace with the\nexperience and intelligence of the child, should save us from such\nmistakes.\n\nTo proceed with the stories, the book of Joshua offers nothing that we\ncan turn to account, nor do the stories of Jael, Deborah, and Gideon\ncontain moral lessons fit for the young. Sour milk is not proper food\nfor children, nor do those stories afford the proper moral food in\nwhich, so to speak, the milk of human kindness has turned sour. The\nlabors of Samson, the Hebrew Hercules, are likewise unfit to be used at\nthis stage, at least for the purpose of moral instruction. The story of\nthe daughter of Jephtha, the Hebrew Iphigenia, is exquisitely pathetic,\nbut it involves the horrible idea of human sacrifice, and therefore had\nbetter be omitted. The acts and speeches of Samuel mark an epoch in the\nhistory of the Hebrew religion, and are of profound interest to the\nscholar. But there are certain features, such as the killing of Agag,\nwhich would have to be eliminated in any case; then the theological and\nmoral elements are so blended that it would be difficult if not\nimpossible to separate them; and altogether the character of this mighty\nancient seer, this Hebrew Warwick, this king-maker and enemy of kings,\nis above the comprehension of primary scholars. We shall therefore omit\nthe whole intervening period, and pass at once from the Moses cycle to\n\n\n_The David Cycle._\n\nThe first story of this group is that of _Naomi and Ruth_, the\nancestress of David. Upon the matchless beauty of this tale it is\nunnecessary to expatiate. I wish to remark, however, in passing that it\nillustrates as well as any other--better perhaps than any other--the\npeculiar art of the biblical narrative to which we have referred above.\nIf any one at the present day were asked to decide whether a woman\nplaced in Ruth's situation would act rightly in leaving her home and\nfollowing an aged mother-in-law to a distant country, how many pros and\ncons would he have to weigh before he would be able to say yes or no?\nAre her own parents still living, and are they so situated that she is\njustified in leaving them? Are there other blood relations who have a\nprior claim on her? Has she raised expectations at home which she ought\nnot to disappoint, or undertaken duties which ought not to be set aside\nin deference to a sentiment no matter how noble? Of all such side issues\nand complications of duty which would render a decision like hers\ndifficult in modern times, the story as we have it before us is cleared.\nAll minor traits are suppressed. It is assumed that she has a right to\ngo if she pleases, and the mind is left free to dwell, unimpeded by any\ncounter-considerations, upon the beauty of her choice. This choice\nderives its excellence from the fact that it was perfectly free. There\nwas no tie of consanguinity between Naomi and her. The two women were\nrelated in such a way that the bond might either be drawn more tightly\nor severed without blame. Orpah, too, pitied her mother-in-law. She\nwept, but she returned to her home. We can not, on that account, condemn\nher. It was not her bounden duty to go. Ruth, on the other hand, might\nperhaps have satisfied her more sensitive conscience by accompanying her\nmother-in-law as far as Bethlehem, and then returning to Moab. But she\npreferred instead exile and the hardships of a life among strangers. Not\nbeing a daughter, she freely took upon herself the duties of a daughter;\nand it is this that constitutes the singular merit of her action. In\ntelling the story it is best to follow the original as closely as\npossible. \"Entreat me not to leave thee, nor to desist from following\nafter thee, for whither thou goest, I will go; and where thou lodgest, I\nwill lodge: thy people shall be my people: where thou diest will I die\nand there will I be buried.\" Where in universal literature shall we find\nwords more eloquent of tender devotion than these? It will be noticed\nthat I have left out the phrase \"and thy God shall be my God\" for two\nreasons. No matter how much we may love another person, religious\nconvictions ought to be held sacred. We have no right to give up our\nconvictions even for affection's sake. Moreover, the words correctly\nunderstood are really nothing but an amplification of what has preceded.\nThe language of Ruth refers throughout to the proposed change of\ncountry. \"Whither thou goest, I will go; where thou lodgest, I will\nlodge: thy folk shall be my folk; where thou diest, I will die.\" And the\nphrase \"Thy God shall be my God\" has the same meaning. The ancients\nbelieved that every country has its God, and to say \"Thy God shall be my\nGod\" was tantamount to saying \"Thy country shall be my country.\" It is\nbetter, therefore, to omit these words. Were we to retain them, the\nimpression might be created that Ruth contemplated a change of religion\nmerely to please the aged Naomi, and such a step from a moral point of\nview would be unwarrantable. It was this Gentile woman Ruth who became\nthe ancestress of the royal house of David.\n\nThe story of _David's life_ is replete with dramatic interest. It may\nbe arranged in a series of pictures. First picture: David and\nGoliath--i. e., skill pitted against brute strength, or the deserved\npunishment of a bully. Every boy takes comfort in this story. Second\npicture: David and Jonathan, their arms twined about each other's neck,\na beautiful example of youthful friendship. Especially should the\nunselfishness of Jonathan be noted. He, the Hebrew crown prince, so far\nfrom being jealous of his rival, recognized the superior qualities of\nthe latter and served him with the most generous fidelity. Third\npicture: David the harper, playing before the gloomy, moody king, whom\nan evil spirit has possessed. It should be noted how difficult is the\ntask incumbent upon Jonathan of combining his duty to his father and his\naffection for his friend. Yet he fails in neither. Fourth picture:\nDavid's loyalty manifest. He has the monarch in his power in the camp,\nin the cave, and proves that there is no evil intention in his mind. The\nwords of Saul are very touching, \"Is it thy voice I hear, my son David?\"\nFifth picture: the battle, the tragical end of Saul and Jonathan. The\ndirge of David floats above the field: \"The beauty of Israel is slain\nupon the high places. How are the mighty fallen!\" etc. A second series\nof pictures now begins. David is crowned king, first by his clansmen,\nthen by the united tribes. David, while besieging Bethlehem, is athirst\nand there is no water. Three of his soldiers cut their way to the well\nnear the gate, which is guarded by the enemy, and bring back a cup of\nwater. He refuses it, saying: \"It is not water, but the blood of the men\nwho have risked their lives for me.\" Omitting the story of Bathsheba, we\ncome next to the rebellion of Absalom. The incidents of this rebellion\nmay be depicted as follows: First, Absalom in his radiant beauty at the\nfeast of the sheep-shearer. Next, Absalom at the gate playing the\ndemagogue, secretly inciting the people to revolt. Next, David ascending\nMount Olivet weeping, the base Shimei, going along a parallel ridge,\nflinging stones at the king and reviling him. David remarks: \"If my own\nson seek my life, how shall I be angry with this Benjamite?\" Next, the\ndeath of Absalom in the wood. Finally, David at the gate receiving the\nnews of Absalom's death, and breaking forth into the piercing cry: \"O my\nson Absalom, my son, my son Absalom! would God I had died for thee! O\nAbsalom, my son, my son!\" It is the story of a rebellious and undutiful\nchild, and illustrates by contrast the unfathomable depth of a father's\nlove, of a love that yearns even over the wicked, over the lost.\n\nThe points of the stories included in the David cycle are: skill and\ncourage triumphant over brute strength, unselfish friendship, loyalty, a\nleader's generosity toward his followers, and parental love. The\narrangement of the words in the lament of David for his son deserves to\nbe specially noted. It corresponds to and vividly describes the rhythmic\nmovements of the emotions excited by great sorrow. From the life of\nSolomon we select only the judgment, related in I Kings, iii. We may\ncompare with it a similar story, showing, however, interesting\nvariations, in the Jataka tales.\n\nWith this our selections from the Old Testament narrative come to an\nend. The ideal types are exhausted, and the figures which now appear\nupon the scene stand before us in the dry light of history.\n\nFrom the New Testament we select for the primary course the story of the\nGood Samaritan, as illustrative of true charity. Selected passages from\nthe Sermon on the Mount may also be explained and committed to memory.\nThe Beatitudes, however, and the parables lie outside our present\nlimits, presupposing as they do a depth of spiritual experience which is\nlacking in children.\n\n\n     NOTE.--It should be remembered that the above selections have been\n     made with a view to their being included in a course of unsectarian\n     moral instruction. Such a course must not express the religious\n     tenets of any sect or denomination. Much that has here been\n     omitted, however, can be taught in the Sunday schools, the\n     existence of which alongside of the daily schools is, as I have\n     said, presupposed in these lectures. I have simply tried to cull\n     the moral meaning of the stories, leaving, as I believe, the way\n     open for divergent religious interpretations of the same stories.\n     But I realize that the religious teacher may claim the Bible wholly\n     for his own, and may not be willing to share even a part of its\n     treasure with the moral teacher. If this be so, then these\n     selections from the Bible, for the present, at all events, will\n     have to be omitted. They can, nevertheless, be used by judicious\n     parents, and some if not all of the suggestions they contain may\n     prove acceptable to teachers of Sunday schools.\n\n\nFOOTNOTES:\n\n[11] In his Introduction to Homer.\n\n[12] I have taken the liberty of altering the language here and there,\nfor reasons that will be obvious in each case.\n\n\n\n\nX\n\nTHE ODYSSEY AND THE ILIAD.\n\n\nAs we leave the field of biblical literature and turn to the classic\nepic of Greece, a new scene spreads out before us, new forms and faces\ncrowd around us, we breathe a different atmosphere.\n\nThe poems of Homer among the Greeks occupied a place in many respects\nsimilar to that of the Bible among the Hebrews. At Athens there was a\nspecial ordinance that the Homeric poems should be recited once every\nfourth year at the great Panathenaic festival. On this occasion the\nrhapsode, standing on an elevated platform, arrayed in rich robes, with\na golden wreath about his head, addressed an audience of many thousands.\nThe poems were made the subject of mystical, allegorical, and\nrationalistic interpretation, precisely as was the case with the text of\nthe Bible. As late as the first century of our era, the first book\nplaced in the hands of children, the book from which they learned to\nread and write, was Homer. Xenophon in the Symposium has one of the\nguests say: \"My father, anxious that I should become a good man, made me\nlearn all the poems of Homer, and now I could repeat the whole Iliad\nand Odyssey by heart.\"[13]\n\nWe shall not go quite to the same length as Xenophon. We should hardly\nthink it sufficient in order to make a good man of a boy to place Homer\nin his hands. But we do believe that the knowledge of the Homeric poems,\nintroduced at the right time and in the right way, will contribute to\nsuch a result.\n\nLet us, however, examine more closely in what the value of these poems\nconsists.\n\nUlysses is the hero of the Odyssey, Achilles of the Iliad. Ulysses is\npre-eminently the type of resourceful intelligence, Achilles of valor.\nIn what way will these types appeal to our pupils? As the boy develops\nbeyond the early period of childhood, there shows itself in him a spirit\nof adventure. This has been noticed by all careful educators. Now, there\nis a marked difference between the spirit of adventure and the spirit of\nplay. Play consists in the free exercise of our faculties. Its\ncharacteristic mark is the absence of taxing effort. The child is said\nto be at play when it frolics in the grass, when it leaps or runs a\nrace, or when it imitates the doings of its elders. As soon, however, as\nthe exertion required in carrying on a game becomes appreciable, the\ngame is converted into a task and loses its charm. The spirit of\nadventure, on the contrary, is called forth by obstacles; it delights in\nthe prospect of difficulties to be overcome; it is the sign of a fresh\nand apparently boundless energy, which has not yet been taught its\nlimitations by the rough contact with realities. The spirit of adventure\nbegins to develop in children when the home life no longer entirely\ncontents them, when they wish to be freed from the constraint of\ndependence on others, when it seems to them as if the whole world lay\nopen to them and they could dare and do almost anything. It is at this\ntime that children love to read tales of travel, and especially tales of\nthe sea, of shipwreck, and hair-breadth escapes, of monsters slain by\ndauntless heroes, of rescue and victory, no matter how improbable or\nimpossible the means. Now success in such adventures depends largely on\ncourage. And it is good for children to have examples even of physical\ncourage set before them, provided it be not brutal. The craven heart\nought to be despised. Mere good intentions ought not to count. Unless\none has the resolute will, the fearless soul, that can face difficulties\nand danger without flinching, he will never be able to do a man's work\nin the world. This lesson should be imprinted early. A second\nprerequisite of success is presence of mind, or what has been called\nabove resourceful intelligence. And this quality is closely allied with\nthe former. Presence of mind is the result of bravery. The mind will act\neven in perilous situations if it be not paralyzed by fear. It is fear\nthat causes the wheels of thought to stop. If one can only keep off the\nclog of fear, the mind will go on revolving and often find a way of\nescape where there seemed none. Be not a coward, be brave and\nclear-headed in the midst of peril--these are lessons the force of which\nis appreciated by the growing pupil. The Iliad and Odyssey teach them on\nevery page.\n\nBravery and presence of mind, it is true, are commonly regarded as\nworldly, rather than as, in the strict sense, moral qualities. However\nthat may be--and I, for one, am inclined to rank true courage and true\npresence of mind among the highest manifestations of the moral\nnature--these qualities when they show themselves in the young soon\nexert a favorable influence on the whole character, and serve especially\nto transform the attitude of the child toward its parents. Hitherto the\nyoung child has been content to be the mere recipient of favors; as soon\nas the new consciousness of strength, the new sense of independence and\nmanliness has developed, the son begins to feel that he would like to\ngive to his parents as well as to receive from them; to be of use to his\nfather, and to confer benefits, as far as he is able, in the shape of\nsubstantial services. These remarks will find their application in the\nanalysis of the Odyssey, which we shall presently attempt.\n\nThe Odyssey is a tale of the sea. Ulysses is the type of sagacity, as\nwell as of bravery, his mind teems with inventions. In the boy\nTelemachus we behold a son struggling to cut loose from his mother's\nleading-strings, and laudably ambitious to be of use to his parents. In\nthe Odyssey we gain a distinct advance upon the moral results obtained\nfrom the study of the biblical stories. In the Bible it is chiefly the\nlove of parents for their children which is dwelt upon, in the Odyssey\nthe devotion of children to their parents; and this, of course, marks a\nlater stage. In the Odyssey, too, the conjugal relation comes into the\nforeground. In the Bible, the love of the husband for his wife is\nrepeatedly touched upon. But the love of the wife for the husband is not\nequally emphasized, and the relations between the two do not receive\nparticular attention. The joint authority of both parents over their\nchildren is the predominant fact, the delicate bonds of feeling which\nsubsist between the parents themselves are not in view. And this again\ncorresponds to the earlier stage of childhood. The young child perceives\nthe joint love which father and mother bear toward it, and feels the\njoint authority which they exercise over it. But as the child grows up,\nits eyes are opened to perceive more clearly the love which the parents\nbear to one another, and its affection for both is fed and the desire to\nserve them is strengthened by this new insight. Thus it is in the\nOdyssey. The yearning of Ulysses for his wife, the fidelity of Penelope\nduring twenty years of separation, are the leading theme of the\nnarrative, and the effect of this love upon their son is apparent\nthroughout the poem.\n\nLet us now consider the ethical elements of the Odyssey in some detail,\narranging them under separate heads.\n\n1. _Conjugal affection._ Ulysses has been for seven years a prisoner in\nthe cave of Calypso. The nymph of the golden hair offers him the gift of\nimmortality if he will consent to be her husband, but he is proof\nagainst her blandishments, and asks for nothing but to be dismissed, so\nthat he may see his dear home and hold his own true wife once more in\nhis arms.\n\n\n     \"Apart upon the shore\n     He sat and sorrowed. And oft in tears\n     And sighs and vain repinings passed the hours,\n     Gazing with wet eyes on the barren deep.\"[14]\n\n\nI would remark that, as the poem is too long to be read through\nentirely, and as there are passages in it which should be omitted, it is\nadvisable for the teacher to narrate the story, quoting, however, such\npassages as give point to the narrative or have a special beauty of\ntheir own. Read the description of Calypso's cave v, 73, ff. Penelope\nmeantime is patiently awaiting her husband's return. Read the passages\nwhich describe her great beauty, especially that lovely word-picture in\nwhich she is described as standing by a tall column in the hall, a maid\non either side, a veil hiding her lustrous face, while she addresses the\nsuitors. The noblest princes of Ithaca and the surrounding isles entreat\nher hand in marriage, and, thinking that Ulysses will never return, hold\nhigh revels in his house, and shamelessly consume his wealth. Read the\npassage ii, 116-160, describing Penelope's device to put off the\nsuitors, and at the same time to avert the danger which would have\nthreatened her son in case she had openly broken with the chiefs. The\nlove of Penelope is further set vividly before us by many delicate\ntouches. Every stranger who arrives in Ithaca is hospitably entertained\nby the queen, and loaded with gifts, in the hope that he may bring her\nsome news of her absent lord, and often she is deceived by wretches who\nspeculate on her credulous grief. See the passage xiv, 155. During the\nday she is busy with her household cares, overseeing her maids, and\nseeking to divert her mind by busy occupation; but at night the silence\nand the solitude become intolerable, and she weeps her eyes out on her\nlonely couch. How the love of Penelope influences her boy, who was a\nmere babe when his father left for Troy, how the whole atmosphere of the\nhouse is charged with the sense of expectancy of the master's return, is\nshown in the passage ii, 439, where Telemachus says:\n\n\n     \"Nurse, let sweet wine be drawn into my jars,\n     The finest next to that which thou dost keep,\n     Expecting our unhappy lord, if yet\n     The nobly born Ulysses shall escape\n     The doom of death and come to us again.\"\n\n\nThe best cheer, the finest wine, the best of everything is kept ready\nagainst the father's home-coming, which may be looked for any day, if\nhaply he has escaped the doom of death. There is one passage in which\nwe might suspect that the poet has intended to show the hardening effect\nof grief on Penelope's character, xv, 479. Penelope does not speak to\nher old servants any more; she passes them by without a word, apparently\nwithout seeing them. She does not attend to their wants as she used to\ndo, and they, in turn, do not dare to address her. But we may forgive\nthis seeming indifference inasmuch as it only shows how completely she\nis absorbed by her sorrow.\n\nA companion picture to the love of Ulysses and Penelope is to be found\nin the conjugal relation of Alcinous, king of Phaeacia, and his wife\nArete, as described in the sixth book and the following. This whole\nepisode is incomparably beautiful. Was there ever a more perfect\nembodiment of girlish grace and modesty, coupled with sweetest\nfrankness, than Nausicaa? And what a series of lovely pictures is made\nto pass in quick succession before our eyes as we read the story! First,\nNausicaa, moved by the desire to prepare her wedding garments against\nher unknown lover's coming, not ashamed to acknowledge the motive to her\nown pure heart, but veiling it discreetly before her mother; then the\nband of maidens setting out upon their picnic party, Nausicaa holding\nthe reins; next the washing of the garments, the bath, the game of ball,\nthe sudden appearance of Ulysses, the flight of her companions, the\nbrave girl being left to keep her place alone, with a courage born of\npity for the stranger, and of virtuous womanhood.\n\n\n       \"Alone\n     The daughter of Alcinous kept her place,\n     For Pallas gave her courage and forbade\n     Her limb to tremble. So she waited there.\"\n\n\nWho that has inhaled the fragrance of her presence from these pages can\never forget the white-armed Nausicaa! Then follows the picture of the\npalace, a feast for the imagination, the most magnificent description, I\nthink, in the whole poem.\n\n\n     \"For on every side beneath\n     The lofty roof of that magnanimous king\n     A glory shone as of the summer moons.\"\n\n\nRead from l. 100-128, book vii. Next we witness the splendid hospitality\nproffered to the stranger guest. For again and again in this poem the\nnoble sentiment is repeated, that the stranger and the poor are sent\nfrom Jove. Then we see Ulysses engaged in the games, outdoing the rest,\nor standing aside and watching \"the twinkle of the dancer's feet.\" The\nlanguage, too, used on these occasions is strikingly noble, so courteous\nand well-chosen, so simple and dignified, conveying rich meanings in the\nfewest possible words. What can be finer, e. g., than Nausicaa's\nfarewell to Ulysses?\n\n\n     \"Now, when the maids\n     Had seen him bathed, and had anointed him\n     With oil, and put his sumptuous mantle on,\n     And tunic, forth he issued from the bath,\n     And came to those who sat before their wine.\n     Nausicaa, goddess-like in beauty, stood\n     Beside a pillar of that noble roof,\n     And, looking on Ulysses as he passed,\n     Admired, and said to him in winged words--\n     'Stranger, farewell, and in thy native land\n     Remember thou hast owed thy life to me.'\"\n\n\nNausicaa, it is evident, loves Ulysses; she stands beside a pillar, a\nfavorite attitude for beautiful women with Homer, and as Ulysses passes,\nshe addresses to him those few words so fraught with tenderness and\nrenunciation. Ulysses's own speech to Arete, too, is a model of\nsimplicity and dignity, possessing, it seems to me, something of the\nsame quality which we admire in the speeches of Othello. But throughout\nthis narrative, pre-eminent above all the other figures in it is the\nfigure of the queen herself, of Arete. Such a daughter as Nausicaa could\nonly come from such a mother. To her Ulysses is advised to address his\nsupplication. She is the wise matron, the peace-maker who composes the\nangry feuds of the men. And she possesses the whole heart and devotion\nof her husband.\n\n\n       \"Her Alcinous made his wife\n     And honored her as nowhere else on earth\n     Is any woman honored who bears charge\n     Over a husband's household. From their hearts\n     Her children pay her reverence, and the king\n     And all the people, for they look on her\n     As if she were a goddess. When she goes\n     Abroad into the streets, all welcome her\n     With acclamations. Never does she fail\n     In wise discernment, but decides disputes\n     Kindly and justly between man and man.\n     And if thou gain her favor there is hope\n     That thou mayst see thy friends once more.\"\n\n\nWe have then as illustrations of conjugal fidelity: the main picture,\nUlysses and Penelope; the companion picture, Alcinous and Arete; and, as\na foil to set off both, there looms up every now and then in the course\nof the poem, that unhappy pair, Agamemnon and Clytemnestra, the latter,\nthe type of conjugal infidelity, from which the soul of Homer revolts.\nThis foil is very skillfully used. At the very end of the poem, when\neverything is hastening toward a happy consummation, Ulysses having\nslain the suitors and being about to be reunited with his wife, we are\nintroduced into the world of shades, where the ghost of Agamemnon once\nmore rehearses the story of Clytemnestra's treachery. At that moment the\nspirits of the suitors come flying down to Hades, and the happier\ndestiny of Ulysses is thus brought into clearer relief by contrast.\n\nThe next ethical element of which I have to speak is the _filial\nconduct_ of Telemachus. In him the spirit of adventure has developed\ninto a desire to help his father. In the early part of the poem he\nannounces that he is now a child no longer. He begins to assert\nauthority. And yet in his home he continues to be treated as a child.\nThe suitors laugh at him, his own mother can not bear to think that he\nshould go out into the wide world alone, and the news of his departure\nis accordingly concealed from her. Very fine are the words in which her\nmother's love expresses itself when she discovers his absence:\n\n\n     \"And her knees failed her and her heart\n     Sank as she heard. Long time she could not speak;\n     Her eyes were filled with tears, and her clear voice\n     Was choked; yet, finding words at length, she said:\n     'O herald! wherefore should my son have gone?'\n\n                               \"... Now, my son,\n     My best beloved, goes to sea--a boy\n     Unused to hardship and unskilled to deal\n     With strangers. More I sorrow for his sake\n     Than for his father's. I am filled with fear.\"\n\n\nShe lies outstretched upon the floor of her chamber overcome with grief\n(iv, 910). Telemachus, however, has gone forth in search of his sire. He\nfinds a friend in Pisistratus, the son of Nestor, and the two youths\njoin company on the journey. They come to the court of Menelaus, King of\nSparta. There, as everywhere, Telemachus hears men speak of his great\nfather in terms of the highest admiration and praise, and the desire\nmounts in his soul to do deeds worthy of such a parent. What better\nstimulation can we offer to growing children than this recital of\nTelemachus's development from boyhood into manhood? His reception at the\ncourt of Menelaus affords an opportunity to dwell again upon the\ngenerous and delicate hospitality of the ancient Greeks. First, the\nguest is received at the gates; then conducted to the bath and anointed;\nthen, when he is seated on a silver or perchance a golden throne, a\nhandmaiden advances with a silver ewer and a golden jug to pour water on\nhis hands; then a noble banquet is set out for his delectation; and only\nthen, after all these rites of hospitality have been completed, is\ninquiry made as to his name and his errand. \"The stranger and the poor\nare sent from Jove.\" The stranger and the poor were welcome in the\nGrecian house. Telemachus returns to Ithaca, escapes the ambush which\nthe murderous suitors had set for him, and arrives just in time to help\nhis father in his last desperate struggle. It is he, Telemachus, who\nconveys the weapons from the hall, he who pinions the treacherous\nMelantheus and renders him harmless. He quits himself like a\nman--discreet, able to keep his counsel, and brave and quick in the\nmoment of decisive action.\n\nThe third element which attracts our attention is the resourceful\nintelligence of Ulysses, or his _presence of mind_ amid danger. This is\nexhibited on many occasions; for instance, in the cave of Polyphemus;\nwhere he saves his companions by concealing them in the fleece of the\ngiant's flock, and at the time of the great shipwreck, before he reaches\nPhaeacia. His raft is shattered, and he is plunged into the sea. He\nclings to one of the fragments of the wreck, but from this too is\ndislodged. For two days and nights he struggles in the black, stormy\nwaters. At last he approaches the shore, but is nearly dashed to pieces\non the rocks. He swims again out to sea, until, finding himself opposite\nthe mouth of a river, he strikes out for this and lands in safety.\nPallas Athene has guided him. But Pallas Athene is only another name for\nhis own courage and presence of mind. In the same connection may be\nrelated the story of Ulysses's escape from the Sirens and from the twin\nperils of Scylla and Charybdis. The Sirens, with their bewitching songs,\nseek to lure him and his companions to destruction. But he stops the\nears of his companions with wax so that they can not hear, and causes\nhimself to be bound with stout cords to the mast, so that, though he may\nhear, he can not follow. There is an obvious lesson contained in this\nallegory. When about to be exposed to temptation, if you know that you\nare weak, do not even listen to the seductive voices. But no matter how\nstrong you believe yourself to be, at least give such pledges and place\nyourself in such conditions that you may be prevented from yielding.\nFrom the monster Charybdis, too, Ulysses escapes by extraordinary\npresence of mind and courage. He leaps upward to catch the fig-tree in\nthe moment when his ship disappears beneath him in the whirlpool; then,\nwhen it is cast up again, lets go his hold and is swept out into safe\nwaters.\n\nThe fourth ethical element which we select from the poem is the\n_veneration shown to grandparents_. I have already remarked, in a former\nlecture, that if parents wish to retain the reverence of their children\nthey can not do better than in their turn to show themselves reverent\ntoward their own aged and enfeebled parents. Of such conduct the Odyssey\noffers us a number of choice examples. Thus Achilles, meeting Ulysses in\nthe realm of shades, says that the hardest part of his lot is to think\nof his poor old father, who has no one now to defend him, and who,\nbeing weak, is likely to be neglected and despised. If only he, the\nstrong son, could return to the light of day, how he would protect his\naged parent and insure him the respect due to his gray hairs! Penelope\nis advised to send to Laertes, Telemachus's grandfather, to secure his\naid against the suitors. But with delicate consideration she keeps the\nbad news from him, saying: \"He has enough grief to bear on account of\nthe loss of his son Ulysses; let me not add to his burden.\" Again, how\nbeautiful is the account of the meeting of Laertes and Ulysses after the\nreturn and triumph of the latter. On the farm, at some distance from the\ntown, Ulysses seeks his aged father. Laertes is busy digging. He, a\nking, wears a peasant's rustic garb and lives a life of austere\nself-denial, grieving night and day for his absent son. When Ulysses\nmentions his name, Laertes at first does not believe. Then the hero\napproaches the bent and decrepit old man, and becomes for the moment a\nchild again. He brings up recollections of his earliest boyhood; he\nreminds his father of the garden-patch which he set aside for him long,\nlong ago; of the trees and vines which he gave him to plant; and then\nthe father realizes that the mighty man before him is indeed his son.\n\nThe structural lines of the Odyssey are clearly marked, and can easily\nbe followed. First, we are shown the house of Ulysses bereft of its\nmaster. The noisy crowd of suitors are carousing in the hall; the\ndespairing Penelope weaves her web in an upper chamber; the resolve to\ndo and dare for his father's sake awakens in Telemachus's heart. Next\nUlysses on the way home, dismissed by Calypso, arrives at Phaeacia, from\nwhich port without further misadventures he reaches Ithaca. The stay in\nthe palace of the Phaeacian king gives an opportunity for a rehearsal of\nthe previous sufferings and adventures of the hero. Then follow the\npreparations for the conflict with the suitors; the appearance of\nUlysses in his own palace in the guise of a beggar; the insults and\nblows which he receives at the hands of his rivals and their menials;\nthe bloody fight, etc. In relating the story I should follow the course\nof the poem, laying stress upon the ethical elements enumerated above.\nThe fight which took place in the palace halls with closed doors should\nbe merely mentioned, its bloody details omitted. The hanging of the\nmaidens, the trick of Vulcan related in a previous book, and other minor\nepisodes, which the teacher will distinguish without difficulty, should\nlikewise be passed over. The recognition scenes are managed with\nwonderful skill. The successive recognitions seem to take place\ninversely in the order of previous connection and intimacy with Ulysses.\nThe son, who was a mere babe when his father left and did not know him\nat all, recognizes him first. This, moreover, is necessary in order that\nhis aid may be secured for the coming struggle. Next comes Argus, the\ndog.\n\n\n     \"While over Argus the black night of death\n     Came suddenly as he had seen\n     Ulysses, absent now for twenty years.\"\n\n\nNext comes the nurse Eurycleia, who recognizes him by a scar inflicted\nby the white tusk of a boar whom he hunted on Parnassus's heights; then\nhis faithful followers; last of all, and slowly and with difficulty, the\nwife who had so yearned for him. Her impetuous son could not understand\nher tardiness. Vehemently he chid her: \"Mother, unfeeling mother, how\ncanst thou remain aloof, how keep from taking at my father's side thy\nplace to talk with him and question him? Mother, thy heart is harder\nthan a stone.\" But she only sat opposite to Ulysses and gazed and gazed\nand wondered. Ulysses himself, at last, in despair at her impenetrable\nsilence, exclaimed, \"An iron heart is hers.\" But it was only that she\ncould not believe. It seemed so incredible to her that the long waiting\nshould be over; that the desire of her heart should really be fulfilled;\nthat this man before her should be indeed the husband, the long-lost\nhusband, and not a mocking dream. But when at last it dawned upon her,\nwhen he gave her the token of the mystery known only to him and to her,\nthen indeed the ice of incredulity melted from her heart, and her knees\nfaltered and the tears streamed from her eyes, \"and she rose and ran to\nhim and flung her arm about his neck and kissed his brow, and he, too,\nwept as in his arms he held his dearly loved and faithful wife.\" \"As\nwelcome as the land to those who swim the deep, tossed by the billow\nand the blast, and few are those who from the hoary ocean reach the\nshore, their limbs all crested with the brine, these gladly climb the\nsea-beach and are safe--so welcome was her husband to her eyes, nor\nwould her fair white arms release his neck.\"\n\nAnd so with the words uttered by the shade of Agamemnon we may fitly\nclose this retrospect of the poem:\n\n\n     \"Son of Laertes, fortunate and wise,\n     Ulysses! thou by feats of eminent might\n     And valor dost possess thy wife again.\n     And nobly minded is thy blameless queen,\n     The daughter of Icarius, faithfully\n     Remembering him to whom she gave her troth\n     While yet a virgin. Never shall the fame\n     Of his great valor perish, and the gods\n     Themselves shall frame, for those who dwell on earth,\n     Sweet strains in praise of sage Penelope.\"\n\n\nWell might the rhapsodes in the olden days, clad in embroidered robes,\nwith golden wreaths about their brows, recite such verses as these to\nthe assembled thousands and ten thousands. Well might the Hellenic race\ntreasure these records of filial loyalty, of maiden purity, of wifely\ntenderness and fidelity, of bravery, and of intelligence. And well may\nwe, too, desire that this golden stream flowing down to us from ancient\nGreece shall enter the current of our children's lives to broaden and\nenrich them.\n\nI have not space at my command to attempt a minute analysis of the\nIliad, and shall content myself with mentioning the main significant\npoints. The Iliad is full of the noises of war, the hurtling of arrows,\nthe flashing of swords, the sounding of spears on metal shields, the\ngroans of the dying, \"whose eyes black darkness covers.\" The chief\nvirtues illustrated are valor, hospitality, conjugal affection, respect\nfor the aged. I offer the following suggestions to the teacher. After\ndescribing the wrath of Achilles, relate the meeting of Diomedes and\nGlaucus, their hostile encounter, and their magnanimous embrace on\ndiscovering that they are great friends. Read the beautiful passage\nbeginning with the words, \"Even as the generations of leaves, such are\nthose likewise of men.\" Dwell on the parting of Hector and Andromache.\nNote that she has lost her father, her lady mother, and her seven\nbrothers. Hector is to her father, mother, brother, and husband, all in\none. Note also Hector's prayer for his son that the latter may excel him\nin bravery. As illustrative of friendship, tell the story of Achilles's\ngrief for Patroclus, how he lies prone upon the ground, strewing his\nhead with dust; how he follows the body lamenting; how he declares that\nthough the dead forget their dead in Hades, even there he would not\nforget his dear comrade. Next tell of the slaying of Hector, and how\nAchilles honors the suppliant Priam and restores to him the body of his\nson. It is the memory of his own aged father, which the sight of Priam\nrecalls, that melts Achilles's heart, and they weep together, each for\nhis own dead. Finally, note the tribute paid to Hector's delicate\nchivalry in the lament of Helen.[15]\n\nFOOTNOTES:\n\n[13] See Jebb's Introduction to Homer.\n\n[14] The quotations are taken from Bryant's translation of the Odyssey.\n\n[15] In connection with the Homeric poems selections from Greek\nmythology may be used, such as the story of Hercules, of Theseus, of\nPerseus, the story of the Argonauts, and others. These, too, breathe the\nspirit of adventure and illustrate the virtues of courage, perseverance\namid difficulties, chivalry, etc.\n\n\n\n\nGRAMMAR COURSE.\n\nLESSONS ON DUTY.\n\n\n\n\nXI.\n\nTHE DUTY OF ACQUIRING KNOWLEDGE.\n\n\nIn setting out on a new path it is well to determine beforehand the goal\nwe hope to reach. We are about to begin the discussion of the grammar\ncourse, which is intended for children between twelve and fifteen years\nof age, and accordingly ask: What result can we expect to attain? One\nthing is certain, we must continue to grade our teaching, to adapt each\nsuccessive step to the capacities of the pupils, to keep pace with their\nmental development.\n\nThe due gradation of moral teaching is all-important. Whether the\ngradations we propose are correct is, of course, a matter for\ndiscussion; but, at all events, a point will be gained if we shall have\nbrought home forcibly to teachers the necessity of a graded, of a\nprogressive system.\n\nIn the primary course we have set before the pupils examples of good and\nbad conduct, with a view to training their powers of moral perception.\nWe are now ready to advance from percepts to concepts. We have\nendeavored to cultivate the faculty of observation, we can now attempt\nthe higher task of generalization. In the primary course we have tried\nto make the pupils perceive moral distinctions; in the grammar course we\nshall try to make them reason about moral distinctions, help them to\ngain notions of duty, to arrive at principles or maxims of good conduct.\nThe grammar course, therefore, will consist in the main of lessons on\nduty.\n\nWhat has just been said, however, requires further explanation to\nprevent misapprehension. I have remarked that the pupil is now to reach\nout toward concepts of duty, and to establish for himself maxims or\nprinciples of conduct. But of what nature shall these maxims be? The\nphilosopher Kant has proposed the following maxim: \"So act that the\nmaxim underlying thy action may justify itself to thy mind as a\nuniversal law of conduct.\" According to him, the note of universality is\nthe distinctive characteristic of all ethical conduct. The school of\nBentham proposes a different maxim: \"So act that the result of thy\naction shall tend to insure the greatest happiness of the greatest\nnumber.\" Theologians tell us so to act that our will may harmonize with\nthe will of God. But pupils of the grammar grade are not ripe to\nunderstand such metaphysical and theological propositions. And,\nmoreover, as was pointed out in our first lecture, it would be a grave\ninjustice to teach in schools supported by all ethical first principles\nwhich are accepted only by some. We are not concerned with first\nprinciples. We exclude the discussion of them, be they philosophical or\ntheological, from the school. But there are certain secondary\nprinciples, certain more concrete rules of behavior, which nevertheless\npossess the character of generalizations, and these will suffice for\nour purpose. And with respect to these there is really no difference of\nopinion among the different schools and sects, and on them as a\nfoundation we can build.\n\nIt is our business to discover such secondary principles, and in our\ninstruction to lead the pupil to the recognition of them. The nature of\nthe formulas of duty which we have in mind--formulas which shall express\nthe generalized moral experience of civilized mankind, will appear more\nplainly if we examine the processes by which we arrive at them. An\nexample will best elucidate: Suppose that I am asked to give a lesson on\nthe duty of truthfulness. At the stage which we have now reached it will\nnot be enough merely to emphasize the general commandment against lying.\nThe general commandment leaves in the pupil's mind a multitude of doubts\nunsolved. Shall I always tell the truth--that is to say, the whole\ntruth, as I know it, and to everybody? Is it never right to withhold the\ntruth, or even to say what is the contrary of true, as, e. g., to the\nsick or insane. Such questions as these are constantly being asked. What\nis needed is a rule of veracity which shall leave the general principle\nof truth-speaking unshaken, and shall yet cover all these exceptional\ncases. How to arrive at such a rule? I should go about it in the\nfollowing manner, and the method here described is the one which is\nintended to be followed throughout the entire course of lessons on duty.\nI should begin by presenting a concrete case. A certain child had broken\na precious vase. When asked whether it had done so, it answered, \"No.\"\nHow do you characterize such a statement? As a falsehood. The active\nparticipation of the pupils in the discussion is essential. Properly\nquestioned, they will join in it heart and soul. There must be constant\ngive and take between teacher and class. Upon the fulfillment of this\ncondition the value of this sort of teaching entirely depends. The\nteacher then proceeds to analyze the instance above given, or any other\nthat he may select from those which the pupils offer him. The child says\nno when it should have said yes, or a person says black when he should\nhave said white. In what does the falsehood of such statements consist?\nIn the circumstance that the words spoken do not correspond to the\nfacts. Shall we then formulate the rule of veracity as follows: Make thy\nwords correspond to the facts; and shall we infer that any one whose\nwords do not correspond to the facts is a liar? But clearly this is not\nso. The class is asked to give instances tending to prove the\ninsufficiency of the proposed formula. Before the days of Copernicus it\nwas generally asserted that the sun revolves around the earth. Should we\nbe justified in setting down the many excellent persons who made such\nstatements as liars? Yet their words did not correspond to the facts.\nVery true; but they did not intend to deviate from the facts--they did\nnot know better. Shall we then change the formula so as to read: Intend\nthat thy words shall conform to the facts? But the phrase \"correspond to\nthe facts\" needs to be made more explicit. Cases occur in which a\nstatement does correspond to the facts, or, at least, seems to do so,\nand yet a contemptible falsehood is implied. The instance of the truant\nboy is in point who entered the school-building five minutes before the\nclose of the exercises, and on being asked at home whether he had been\nat school, promptly answered \"Yes\"; and so he had been for five minutes.\nBut in this case the boy suppressed a part of the facts--and, moreover,\nthe essential part--namely, that he had been absent from school for five\nhours and fifty-five minutes. Cases of mental reservation and the like\nfall under the same condemnation. The person who took an oath in court,\nusing the words, \"As truly as I stand on this stone,\" but who had\npreviously filled his shoes with earth, suppressed the essential\nfact--viz., that he had filled his shoes with earth.\n\nShall we then formulate the rule in this wise: Intend to make thy words\ncorrespond to the essential facts? But even this will not entirely\nsatisfy. For there are cases, surely, in which we deliberately frame our\nwords in such a way that they shall not correspond to the essential\nfacts--for instance, if we should meet a murderer who should ask us in\nwhich direction his intended victim had fled, or in the case of an\ninsane person intent on suicide, or of the sick in extreme danger, whom\nthe communication of bad news would kill. How can we justify such a\nprocedure? We can justify it on the ground that language as a means of\ncommunication is intended to further the rational purposes of human\nlife, and not conversely are the rational purposes of life to be\nsacrificed to any merely formal principle of truth-telling. A person\nwho, like the murderer, is about to use the fact conveyed to him by my\nwords as a weapon with which to kill a fellow-being has no right to be\nput in possession of the fact. An insane person, who can not use the\ntruthful communications of others except for irrational ends, is also\noutside the pale of those to whom such tools can properly be intrusted.\nAnd so are the sick, when so enfeebled that the shock of grief would\ndestroy them. For the rational use of grief is to provoke in us a moral\nreaction, to rouse in us the strength to bear our heavy burdens, and, in\nbearing, to learn invaluable moral lessons. But those who are physically\ntoo weak to rally from the first shock of grief are unable to secure\nthis result, and they must therefore be classed, for the time being, as\npersons not in a condition to make rational use of the facts of life. It\nis not from pain and suffering that we are permitted to shield them.\nPain and suffering we must be willing both to endure and also to inflict\nupon those whom we love best, if necessary. Reason can and should\ntriumph over pain. But when the reasoning faculty is impaired, or when\nthe body is too weak to respond to the call of reason, the obligation of\ntruth-_telling_ ceases. I am not unaware that this is a dangerous\ndoctrine to teach. I should always take the greatest pains to impress\nupon my pupils that the irrational condition, which alone justifies the\nwithholding of the truth, must be so obvious that there can be no\nmistake about it, as in the case of the murderer who, with knife in\nhand, pursues his victim, or of the insane, or of the sick, in regard to\nwhom the physician positively declares that the shock of bad news would\nendanger life. But I do think that we are bound to face these\nexceptional cases, and to discuss them with our pupils. For the latter\nknow as well as we that in certain exceptional situations the best men\ndo not tell the truth, that in such situations no one tells the truth,\nexcept he be a moral fanatic. And unless these exceptional cases are\nclearly marked off and explained and justified, the general authority of\ntruth will be shaken, or at least the obligation of veracity will become\nvery much confused in the pupil's mind. In my opinion, the confusion\nwhich does exist on this subject is largely due to a failure to\ndistinguish between inward truthfulness and truthfulness as reflected in\nspeech. The law of inward truthfulness tolerates no exceptions. We\nshould always, and as far as possible, be absolutely truthful, in our\nthinking, in our estimates, in our judgments. But language is a mere\nvehicle for the communication of thoughts and facts to others, and in\ncommunicating thoughts and facts we _are_ bound to consider in how far\nothers are fit to receive them. Shall we then formulate the rule of\nveracity thus: Intend to communicate the essential facts to those who\nare capable of making a rational use of them. I think that some such\nformula as this might answer. I am not disposed to stickle for this\nparticular phraseology. But the formula as stated illustrates my\nthought, and also the method by which the formulas, which we shall have\nto teach in the grammar course are to be reached. It is the inductive\nmethod. First a concrete case is presented, and a rule of conduct is\nhypothetically suggested, which fits this particular case. Then other\ncases are adduced. It is discovered that the rule as it stands thus far\ndoes not fit them. It must therefore be modified, expanded. Then, in\nsuccession, other and more complex cases, to which the rule may possibly\napply are brought forward, until every case we can think of has been\nexamined; and when the rule is brought into such shape that it fits them\nall, we have a genuine moral maxim, a safe rule for practical guidance,\nand the principle involved in the rule is one of those secondary\nprinciples in respect to which men of every sect and school can agree.\nIt needs hardly to be pointed out how much a casuistical discussion of\nthis sort tends to stimulate interest in moral problems, and to quicken\nthe moral judgment. I can say, from an experience of over a dozen years,\nthat pupils between twelve and fifteen years of age are immensely\ninterested in such discussions, and are capable of making the subtilest\ndistinctions. Indeed, the directness with which they pronounce their\nverdict on fine questions of right and wrong often has in it something\nalmost startling to older persons, whose contact with the world has\nreconciled them to a somewhat less exacting standard.\n\nBut here a caution is necessary. Some children seem to be too fond of\ncasuistry. They take an intellectual pleasure in drawing fine\ndistinctions, and questions of conscience are apt to become to them mere\nmatter of mental gymnastics. Such a tendency must be sternly repressed\nwhenever it shows itself. In fact, reasoning about moral principles is\nalways attended with a certain peril. After all, the actual morality of\nthe world depends largely on the moral habits which mankind have formed\nin the course of many ages, and which are transmitted from generation to\ngeneration. Now a habit acts a good deal like an instinct. Its force\ndepends upon what has been called unconscious cerebration. As soon as we\nstop to reason about our habits, their hold on us is weakened, we\nhesitate, we become uncertain, the interference of the mind acts like a\nbrake. It is for this reason that throughout the primary course, we have\nconfined ourselves to what the Germans call _Anschauung_, the close\nobservation of examples with a view of provoking imitation or\nrepugnance, and thus strengthening the force of habit. Why, then,\nintroduce analysis now, it may be asked. Why not be content with still\nfurther confirming the force of good habits? My answer is that the force\nof habit must be conserved and still further strengthened, but that\nanalysis, too, becomes necessary at this stage. And why? Because habits\nare always specialized. A person governed by habits falls into a certain\nroutine, and moves along easily and safely as long as the conditions\nrepeat themselves to which his habits are adjusted. But when confronted\nby a totally new set of conditions, he is often quite lost and helpless.\nJust as a person who is solely guided by common sense in the ordinary\naffairs of life, is apt to be stranded when compelled to face\ncircumstances for which his previous experience affords no precedent. It\nis necessary, therefore, to extract from the moral habits the latent\nrules of conduct which underlie them, and to state these in a general\nform which the mind can grasp and retain, and which it will be able to\napply to new conditions as they arise. To this end analysis and the\nformulation of rules are indispensable. But in order, at the same time,\nnot to break the force of habit, the teacher should proceed in the\nfollowing manner: He should always take the moral habit for granted. He\nshould never give his pupils to understand that he and they are about to\nexamine whether, for instance, it is wrong or not wrong to lie. The\ncommandment against lying is assumed, and its obligation acknowledged at\nthe outset. The only object of the analysis is to discern more exactly\nwhat is meant by lying, to define the rule of veracity with greater\nprecision and circumspectness, so that we may be enabled to fulfill the\ncommandment more perfectly. It is implied in what I have said that the\nteacher should not treat of moral problems as if he were dealing with\nproblems in arithmetic. The best thing he can do for his pupils--better\nthan any particular lesson he can teach--will be to communicate to them\nthe spirit of moral earnestness. And this spirit he can not communicate\nunless he be full of it himself. The teacher should consecrate himself\nto his task; he should be penetrated by a sense of the lofty character\nof the subject which he teaches. Even a certain attention to externals\nis not superfluous. The lessons, in the case of the younger children,\nmay be accompanied by song; the room in which the classes meet may be\nhung with appropriate pictures, and especially is it desirable that the\nfaces of great and good men and women shall look down upon the pupils\nfrom the walls. The instruction should be given by word of mouth; for\nthe right text-books do not yet exist, and even the best books must\nalways act as a bar to check that flow of moral influence which should\ncome from the teacher to quicken the class. To make sure that the pupils\nunderstand what they have been taught, they should be required from time\nto time to reproduce the subject matter of the lessons in their own\nlanguage, and using their own illustrations, in the form of essays.\n\nAnd now, after this general introduction, let us take up the lessons on\nthe duties in their proper order. What is the proper order? This\nquestion, you will remember, was discussed in the lecture on the\nclassification of duties. It was there stated that the life of man from\nchildhood upward, may be divided into periods, that each period has its\nspecial duties, and that there is in each some one central duty around\nwhich the others may be grouped. During the school age the paramount\nduty of the pupil is to study. We shall therefore begin with the duties\nwhich are connected with the pursuit of knowledge. We shall then take up\nthe duties which relate to the physical life and the feelings; next, the\nduties which arise in the family; after that the duties which we owe to\nall men; and lastly we will consider in an elementary way the civic\nduties.\n\n_The Duty of acquiring Knowledge._--In starting the discussion of any\nparticular set of duties, it is advisable, as has been said, to present\nsome concrete case, and biographical or historical examples are\nparticularly useful. I have sometimes begun the lesson on the duty of\nacquiring knowledge by telling the story of Cleanthes and that of\nHillel. Cleanthes, a poor boy, was anxious to attend the school of Zeno.\nBut he was compelled to work for his bread, and could not spend his days\nin study as he longed to do. He was, however, so eager to learn that he\nfound a way of doing his work by night. He helped a gardener to water\nhis plants, and also engaged to grind corn on a hand-mill for a certain\nwoman. Now the neighbors, who knew that he was poor, and who never saw\nhim go to work, were puzzled to think how he obtained the means to live.\nThey suspected him of stealing, and he was called before the Judge to\nexplain. The Judge addressed him severely, and commanded him to tell the\ntruth. Cleanthes requested that the gardener and the woman might be sent\nfor, and they testified that he had been in the habit of working for\nthem by night. The Judge was touched by his great zeal for knowledge,\nacquitted him of the charge, and offered him a gift of money. But Zeno\nwould not permit him to take the gift. Cleanthes became the best pupil\nof Zeno, and grew up to be a very wise and learned man, indeed one of\nthe most famous philosophers of the Stoic school. The story of Hillel\nruns as follows: There was once a poor lad named Hillel. His parents\nwere dead, and he had neither relatives nor friends. He was anxious to\ngo to school, but, though he worked hard, he did not earn enough to pay\nthe tuition fee exacted at the door. So he decided to save money by\nspending only half his earnings for food. He ate little, and that little\nwas of poor quality, but he was perfectly happy, because with what he\nlaid aside he could now pay the door-keeper and find a place inside,\nwhere he might listen and learn. This he did for some time, but one day\nhe was so unlucky as to lose his situation. He had now no money left to\nbuy bread, but he hardly thought of that, so much was he grieved at the\nthought that he should never get back to his beloved school. He begged\nthe door-keeper to let him in, but the surly man refused to do so. In\nhis despair a happy thought occurred to him. He had noticed a skylight\non the roof. He climbed up to this, and to his delight found that\nthrough a crack he could hear all that was said inside. So he sat there\nand listened, and did not notice that evening was coming on, and that\nthe snow was beginning to fall. Next morning when the teachers and\npupils assembled as usual, every one remarked how dark the room seemed.\nThe sun too was shining again by this time quite brightly outside.\nSuddenly some one happened to look up and with an exclamation of\nsurprise pointed out the figure of a boy against the skylight. Quickly\nthey all ran outside, climbed to the roof, and there, covered with snow,\nquite stiff and almost dead, they found poor Hillel. They carried him\nindoors, warmed his cold limbs, and worked hard to restore him to life.\nHe was at last resuscitated, and from this time on was allowed to attend\nthe school without paying. Later he became a great teacher. He lived in\nPalestine at about the time of Jesus. He was admired for his learning,\nbut even more for his good deeds and his unfailing kindness to every\none. The question is now raised, Why did Cleanthes work at night instead\nof seeking rest, and why did Hillel remain outside in the bitter cold\nand snow? The pupils will readily answer, Because they loved knowledge.\nBut why is knowledge so desirable? With this interrogatory we are fairly\nlaunched on the discussion of our subject. The points to be developed\nare these:\n\nFirst, knowledge is indispensable as a means of making one's way in the\nworld. Show the helplessness of the ignorant. Compare the skilled\nlaborer with the unskilled. Give instances of merchants, statesmen,\netc., whose success was due to steady application and superior\nknowledge. Knowledge is power (namely, in the struggle for existence).\n\nSecondly, knowledge is honor. An ignorant person is despised. Knowledge\nwins us the esteem of our fellow-men.\n\nThirdly, knowledge is joy in a twofold sense. As the perception of light\nto the eye of the body, so is the perception of truth to the eye of the\nmind. The mind experiences an intrinsic pleasure in seeing things in\ntheir true relations. Furthermore, mental growth is accompanied by the\njoy of successful effort. This can be explained even to a boy or girl of\nthirteen. Have you ever tried hard to solve a problem in algebra?\nPerhaps you have spent several hours over it. It has baffled you. At\nlast, after repeated trials, you see your way clear, the solution is\nwithin your grasp. What a sense of satisfaction you experience then. It\nis the feeling of successful mental effort that gives you this\nsatisfaction. You rejoice in having triumphed over difficulties, and the\ngreater the difficulty, the more baffling and complex the problems, the\ngreater is the satisfaction in solving them.\n\nFourthly, knowledge enables us to do good to others. Speak of the use\nwhich physicians make of their scientific training to alleviate\nsuffering and save life. Refer to the manifold applications of science\nwhich have changed the face of modern society, and have contributed so\nlargely to the moral progress of the world. Point out that all true\nphilanthropy, every great social reform, implies a superior grasp of the\nproblems to be solved, as well as devotion to the cause of humanity. In\naccordance with the line of argument just sketched the rule for the\npursuit of knowledge may be successively expanded as follows:\n\nSeek knowledge that you may succeed in the struggle for existence.\n\nSeek knowledge that you may gain the esteem of your fellow-men.\n\nSeek knowledge for the sake of the satisfaction which the attainment of\nit will give you.\n\nSeek knowledge that you may be able to do good to others.\n\nThese points suffice for the present. In the advanced course we shall\nreturn to the consideration of the intellectual duties. I would also\nrecommend that the moral teacher, not content with dwelling on the uses\nof knowledge in general, should go through the list of subjects which\nare commonly taught in school, such as geography, history, language,\netc., and explain the value of each. This is too commonly neglected.\n\nHaving stationed the duty of acquiring knowledge in the center, connect\nwith it the various lesser duties of school life, such as punctual\nattendance, order, diligent and conscientious preparation of home\nlessons, etc. These are means to an end, and should be represented as\nsuch. He who desires the end will desire the means. Get your pupils to\nlove knowledge, and the practice of these minor virtues will follow of\nitself. Other matters might be introduced in connection with what has\nbeen mentioned, but enough has been said to indicate the point of view\nfrom which the whole subject of intellectual duty should, as I think, be\ntreated in the present course.\n\n\n\n\nXII.\n\nDUTIES WHICH RELATE TO THE PHYSICAL LIFE.\n\n\nOf the duties which relate to the physical life, the principal one is\nthat of self-preservation, and this involves the prohibition of suicide.\nWhen one reflects on the abject life which many persons are forced to\nlead, on their poverty in the things which make existence desirable and\nthe lack of moral stamina which often goes together with such\nconditions, the wonder is that the number of suicides is not much\ngreater than it actually is. It is true most people cling to life\ninstinctively, and have an instinctive horror of death. Nevertheless,\nthe force of instinct is by no means a sufficient deterrent in all\ncases, and the number of suicides is just now alarmingly on the\nincrease. If we were here considering the subject of suicide in general\nwe should have to enter at large into the causes of this increase; we\nshould have to examine the relations subsisting between the increase of\nsuicide and the increase of divorce, and inquire into those pathological\nconditions of modern society of which both are the symptoms; but our\nbusiness is to consider the ethics of the matter, not the causes. The\nethics of suicide resolves itself into the question, Is it justifiable\nunder any circumstances to take one's life? You may object that this is\nnot a fit subject to discuss with pupils of thirteen or fourteen. Why\nnot? They are old enough to understand the motives which ordinarily lead\nto suicide, and also the reasons which forbid it--especially the most\nimportant reason, namely, that we live not merely or primarily to be\nhappy, but to help on as far as we can the progress of things, and\ntherefore that we are not at liberty to throw life away like an empty\nshell when we have ceased to enjoy it. The discussion of suicide is\nindeed of the greatest use because it affords an opportunity early in\nthe course of our lessons on duty to impress this cardinal truth, to\ndescribe upon the moral globe this great meridian from which all the\nvirtues take their bearings. However, in accordance with the inductive\nmethod, we must approach this idea by degrees. The first position I\nshould take is that while suffering is often temporary, suicide is\nfinal. It is folly to take precipitately a step which can not be\nrecalled. Very often in moments of deep depression the future before us\nseems utterly dark, and in our firmament there appears not one star of\nhope; but presently from some wholly unexpected quarter help comes.\nFortune once more takes us into her good graces, and we are scarcely\nable to understand our past downheartedness in view of the new happiness\nto which we have fallen heirs. Preserve thy life in view of the brighter\nchances which the future may have in store. This is a good rule as far\nas it goes, but it does not fit the more trying situations. For there\nare cases where the fall from the heights of happiness is as complete as\nit is sudden, and the hope of recovering lost ground is really shut out.\n\nTake from actual life the case of a husband who fairly idolized his\nyoung wife and lost her by death three months after marriage. We may\nsuppose that in the course of years he will learn to submit to his\ndestiny. We may even hope that peace will come back to his poor heart,\nbut we can not imagine that he will ever again be happy. Another case is\nthat of a person who has committed a great wrong, the consequences of\nwhich are irreparable, and of which he must carry the agonizing\nrecollection with him to the grave. Time may assuage the pangs of\nremorse, and religion may comfort him, but happiness can never be the\nportion of such as he.\n\nStill another instance--less serious, but of more frequent\noccurrence--is that of a merchant who has always occupied a commanding\nposition in the mercantile community, and who, already advanced in\nyears, is suddenly compelled to face bankruptcy. The thought of the\nhardships to which his family will be exposed, of his impending\ndisgrace, drives him nearly to distraction. The question is, would the\nmerchant, would those others, be justified in committing suicide?\nCertainly not. The merchant, if he has the stuff of true manhood in him,\nwill begin over again, at the bottom of the ladder if need be, will work\nto support his family, however narrowly. It would be the rankest\nselfishness in him to leave them to their fate. The conscience-stricken\nsinner must be willing to pay the penalty of his crime, to the end that\nhe may be purified even seven times in the fire of repentance. And even\nthe lover who has lost his bride will find, if he opens his eyes, that\nthere is still work for him to do in life. The world is full of evils\nwhich require to be removed, full of burdens which require to be borne.\nIf our own burden seems too heavy for us, there is a way of lightening\nit. We may add to it the burden of some one else, and ours will become\nlighter. Physically, this would be impossible, but morally it is true.\nThe rule of conduct, therefore, thus far reads, Preserve thy life in\norder to perform thy share of the work of the world. But the formula,\neven in this shape, is not yet entirely adequate, for there are those\nwho can not take part in the work of the world, who can only\nsuffer--invalids, e. g., who are permanently incapacitated, and whose\ninfirmities make them a constant drag on the healthy lives of their\nfriends. Why should not these be permitted to put an end to their\nmiseries? I should say that so long as there is the slightest hope of\nrecovery, and even where this hope is wanting, so long as the physical\npain is not so intense or so protracted as to paralyze the mental life\naltogether, they should hold out. They are not cut off from the true\nends of human existence. By patient endurance, by the exercise of a\nsublime unselfishness, they may even attain on their sick-beds a height\nof spiritual development which would otherwise be impossible; and, in\naddition, they may become by their uncomplaining patience the sweetest,\ngentlest helpers of their friends, not useless, assuredly, but shining\nexamples of what is best and noblest in human nature. The rule,\ntherefore, should read: Preserve thy life in order to fulfill the duties\nof life, whether those duties consist in doing or in patiently\nsuffering. As has been said long ago, we are placed on guard as\nsentinels. The sentinel must not desert his post. I think it possible to\nmake the pupil in the grammar grade understand that suicide is selfish,\nthat we are bound to live, even though life has ceased to be attractive,\nin order that we may perform our share of the world's work and help\nothers and grow ourselves in moral stature. This does not, of course,\nimply any condemnation of that vast number of cases in which suicide is\ncommitted in consequence of mental aberration.\n\nIn the advanced course we shall have to return to this subject, and\nshall there refer _in extenso_ to the views of the Stoics. The morality\nof the Stoic philosophers in general is so high, and their influence\neven to this day so great, that their defense, or rather enthusiastic\npraise of suicide,[16] needs to be carefully examined. I am of the\nopinion that we have here a case in which metaphysical speculation has\nhad the effect of distorting morality. Metaphysics in this respect\nresembles religion. On the one hand the influence of religion on\nmorality has been highly beneficial, on the other it has been hurtful in\nthe extreme--instance human sacrifices, religious wars, the\nInquisition, etc. In like manner, philosophy, though not to the same\nextent, has both aided morality and injured it. I regard the Stoic\ndeclamations on suicide as an instance of the latter sort. The Stoic\nphilosophy was pantheistic. To live according to Nature was their\nprincipal maxim, or, more precisely, according to the reason in Nature.\nThey maintained that in certain circumstances a man might find it\nimpossible to live up to the rational standard; he might, for instance,\ndiscover himself to be morally so weak as to be unable to resist\ntemptation, and in that case it would be better for him to retire from\nthe scene and to seek shelter in the Eternal Reason, just as, to use\ntheir own simile, one who found the room in which he sat filled to an\nintolerable degree with smoke would not be blamed for withdrawing from\nit. It was their pantheism that led them to favor suicide, and in this\nrespect it is my belief that the modern conscience, trained by the Old\nand New Testaments, has risen to a higher level than theirs. We moderns\nfeel it impossible to admit that to the sane mind temptation can ever be\nso strong as to be truly irresistible. We always can resist if we will.\nWe can, because we ought; as Kant has taught us to put it. We always can\nbecause we always ought.\n\n\n     NOTE.--Despite the rigorous disallowance of suicide in general\n     plainly indicated in the above, I should not wish to be understood\n     as saying that there are no circumstances whatever in which the\n     taking of one's life is permissible. In certain rare and\n     exceptional cases I believe it to be so. In the lecture as\n     delivered I attempted a brief description of these exceptional\n     cases, too brief, it appeared, to prevent most serious\n     misconception. I deem it best, therefore, to defer the expression\n     of my views on this delicate matter until an occasion arrives when\n     I shall be able to articulate my thought in full detail, such as\n     would here be impossible.\n\n\nFrom the commandment \"Preserve thy life\" it follows not only that we\nshould not lay violent hands upon ourselves, but that we should do all\nin our power to develop and invigorate the body, in order that it may\nbecome an efficient instrument in the service of our higher aims. The\nteacher should inform himself on the subject of the gymnastic ideal of\nthe Greeks and consider in how far this ideal is applicable to modern\nconditions. In general, the teacher should explore as fully as possible\nthe ethical problems on which he touches. He should not be merely \"one\nlesson ahead\" of his pupils. Really it is necessary to grasp the whole\nof a subject before we can properly set forth its elements. A very\nthorough normal training is indispensable to those who would give moral\ninstruction to the young.\n\nThe duties of cleanliness and temperance fall under the same head as the\nabove. In speaking of cleanliness, there are three motives--the\negoistic, the aesthetic, and the moral--to which we may appeal. Be\nscrupulously clean for the sake of health, be clean lest you become an\nobject of disgust to others, be clean in order to retain your\nself-respect. Special emphasis should be laid on secret cleanliness.\nIndolent children are sometimes neat in externals, but shockingly\ncareless in what is concealed from view. The motive of self-respect\nshows itself particularly in secret cleanliness.\n\nThe duty of temperance is supported by the same three motives.\nIntemperance undermines health, the glutton or the drunkard awakens\ndisgust, intemperance destroys self-respect. To strengthen the\nrepugnance of the pupils against intemperance in eating, contrast the\nway in which wild beasts eat with that in which human beings partake of\ntheir food. The beast is absorbed in the gratification of its appetite,\neats without the use of implements, eats unsocially. The human way of\neating is in each particular the opposite. Show especially that the act\nof eating is spiritualized by being made subservient to friendly\nintercourse and to the strengthening of the ties of domestic affection.\nThe family table becomes the family altar. Call attention also to the\neffects of drunkenness; point out the injuries which the drunkard\ninflicts on wife and children by his neglect to provide for them, by the\noutbursts of violence to which he is subject under the influence of\nstrong drink; describe his physical, mental, and moral degradation; lay\nstress on the fact that liquor deprives him of the use of his reason.\nWith respect to temperance in food, there are one or two points to be\nnoted. I say to my pupils if you are particularly fond of a certain\ndish, sweetmeats, for instance, make it a rule to partake less of that\nthan if you were not so fond of it. This is good practice in\nself-restraint. I make out as strong a case as possible against the\nindulgence of the candy habit. Young people are not, as a rule, tempted\nto indulge in strong drink; but they are tempted to waste their money\nand injure their health by an excessive consumption of sweets. It is\nwell to apply the lesson of temperance to the things in which they are\ntempted. For the teacher the following note may be added: Of the senses,\nsome, like that of taste, are more nearly allied to the physical part of\nus; others, like sight and hearing, to our rational nature. This\nantithesis of the senses may be used in the interest of temperance.\nAppeal to the higher senses in order to subdue the lower. A band of\nkindergarten children, having been invited on a picnic, were given the\nchoice between a second plate of ice cream, for which many of them were\nclamoring, and a bunch of flowers for each. Most of them were\nsufficiently interested in flowers to prefer the latter. In the case of\nyoung children, the force of the physical appetite may also be weakened\nby appealing to their affection. During the later stage of adolescence,\nwhen the dangers which arise from the awakening life of the senses\nbecome great and imminent, the attention should be directed to high\nintellectual aims, the social feelings should be cultivated, and a taste\nfor the pleasures of the senses of sight and hearing--namely, the\npleasures of music, painting, sculpture, etc.--should be carefully\ndeveloped. Artistic, intellectual, and social motives should be brought\ninto play jointly to meet the one great peril of this period of life.\n\n\nDUTIES WHICH RELATE TO THE FEELINGS.\n\nUnder this head let me speak first of fear. There is a distinction to be\ndrawn between physical and moral cowardice. Physical cowardice is a\nmatter of temperament or organization. Perhaps it can hardly ever be\nentirely overcome, but the exhibition of it can be prevented by moral\ncourage. Moral cowardice, on the other hand, is a fault of character. In\nattempting to formulate the rule of conduct, appeal as before to the\negoistic motive, then to the social--i. e., the desire for the good\nopinion of others--and lastly to the moral motive, properly speaking.\nFear paralyzes; it fascinates its victim like the fabled basilisk.\nNothing is more common than a sense of helpless immobility under the\ninfluence of fear. There is a way of escape. You might run or leap for\nyour life, but you can not stir a limb. What you need to do is to turn\naway your attention by a powerful effort of the will from the object\nwhich excites fear. So long as that object is before you the mind can\nnot act; the mind is practically absent. What you need is presence of\nmind. Let the teacher adduce some of the many striking instances in\nwhich men in apparently desperate straits have been saved by presence of\nmind. The rule thus far would read: Be brave and suppress fear, because\nby so doing you may escape out of danger. In the next place, by so doing\nyou will escape the reproaches of your fellow-men, for cowardice is\nuniversally condemned as shameful. Cite from Spartan history examples\nshowing in the strongest light the feeling of scorn and contempt for the\ncoward. There are, however, cases where death is certain, and where\nthere is no support like that of public opinion to sustain courage. What\nshould be the rule of duty in such cases? Take the case of a person who\nhas been shipwrecked. He swims the sea alone, he is still clinging to a\nspar, but realizes that in a few minutes he must let go, his strength\nbeing well-nigh spent. What should be his attitude of mind in that\nsupreme moment. The forces of nature are about to overwhelm him. What\nmotive can there be strong enough to support bravery in that moment? The\nrule of duty for him would be: Be brave, because as a human being you\nare superior to the forces of nature, because there is something in\nyou--your moral self--over which the forces of nature have no power,\nbecause what happens to you in your private character is not important,\nbut it is important that you assert the dignity of humanity to the last\nbreath.\n\nAfter having discussed courage, define fortitude. Point out the\nimportance of strength of will. Contrast the strong will with the\nfeeble, with the wayward, the irresolute, and also the obstinate will,\nfor obstinacy is often the sign of weakness rather than of strength.\nSee, for useful hints on this subject, Bain's The Emotions and the Will.\n\nWhat happens to thy little self is not important. This is the leading\nthought which shall also guide us in the discussion of _Anger_. In\nentering on the subject of anger begin by describing the effects of it.\nQuote the passage from Seneca's treatise on anger, showing how it\ndisfigures the countenance. Point out that anger provokes anger in\nreturn, and is therefore contrary to self-interest. Call to your aid the\nsocial motive by showing that under the influence of anger we often\novershoot the mark and inflict injuries on others which we had not\nintended. Finally, show that indulgence in anger is immoral. In what\nsense is it immoral? Anger is an emotional reaction against injury. When\na child hurts its foot against a stone, it is often so unreasonably\nangry at the stone as to strike it. When an adult person receives a\nblow, his first impulse is to return it. This desire to return injury\nfor injury is one of the characteristic marks of anger. Another mark is\nthat anger is proportional to the injury received, and not to the fault\nimplied. Every one knows that a slight fault in another may occasion a\ngreat injury to ourselves, while, on the other hand, a serious fault may\nonly cause us a slight inconvenience. The angry person measures his\nresentment by the injury, and not by the fault. Anger is selfish. It is\nfed and pampered by the delusion that our pleasures and pains are of\nchief importance. Contrast with anger the moral feeling of indignation.\nAnger is directed against the injury received, indignation solely\nagainst the wrong done. The immoral feeling prompts us to hate wrong\nbecause it has been inflicted on us. The moral feeling prompts us to\nhate wrong because it is wrong. Now, to the extent that we sincerely\nhate wrong we shall be stirred up to diminish its power over others as\nwell as over ourselves; we shall, for instance, be moved to save the\nevil doer who has just injured us from the tyranny of his evil nature;\nwe shall aspire to become the moral physicians of those who have hurt\nus. And precisely because they have hurt us, they have a unique claim on\nus. We who know better than others the extent of their disease are\ncalled upon more than others to labor with a view to their cure. In this\nconnection the rule of returning good for evil should be explained. This\nrule does not apply alike in all cases, though the spirit of it should\nalways inspire our actions. If a pickpocket should steal our purse, it\nwould be folly to hand him a check for twice the amount he has just\nstolen. If a hardened criminal should draw his knife and wound us in the\nback, it would be absurd to request him kindly to stab us in the breast\nalso. We should in this case not be _curing_ him, but simply confirming\nhim in his evil doing. The rule is: Try to free the sinner from the\npower of sin. In some cases this is best accomplished by holding his\nhand, as it were, and preventing him from carrying out the intended\nwrong. In other cases by depriving him of his liberty for a season,\nsubjecting him to wholesome discipline, and teaching him habits of\nindustry. Only in the case of those who have already attained a higher\nmoral plane, and whose conscience is sensitive, does the rule of\nreturning good for evil apply literally. If a brother has acted in an\nunbrotherly way toward you, do you on the next occasion act wholly in a\nbrotherly way toward him. You will thereby show him how he ought to have\nacted and awaken the better nature in him.\n\nCertain practical rules for the control of anger may be given to the\npupil. Suppress the signs of anger; you will thereby diminish its force.\nTry to gain time: \"When you are angry, count ten before you speak; when\nyou are very angry, count a hundred.\" Having gained time, examine\nrigorously into your own conduct. Ask yourself whether you have not been\npartly to blame. If you find that you have, then, instead of venting\nyour wrath on your enemy, try rather to correct the fault which has\nprovoked hostility. But if, after honest self-scrutiny, you are able to\nacquit yourself, then you can all the more readily act the part of the\nmoral physician, for it is the innocent who find it easiest to forgive.\nIt is also useful to cite examples of persons who, like Socrates, have\nexhibited great self-control in moments of anger; and to quote proverbs\ntreating of anger, to explain these proverbs and to cause them to be\ncommitted to memory. I advise, indeed, that proverbs be used in\nconnection with all the moral lessons. Of the manner in which they are\nto be used I shall speak later on.\n\nThe last of the present group of duties which we shall discuss relates\nto the feelings of vanity, pride, humility. Vanity is a feeling of\nself-complacency based on external advantages. A person is vain of his\ndress or of his real or supposed personal charms. The peacock is the\ntype of vanity. Though the admiration of others ministers to vanity, yet\nit is possible to be vain by one's self--before a mirror, for instance.\nThe feeling of pride, on the other hand, depends upon a comparison\nbetween self and others. Pride implies a sense of one's own superiority\nand of the inferiority of others. Both feelings are anti-moral. They\nspring, like moral cowardice and anger, from the false belief that this\nlittle self of ours is of very great importance. There is no such thing\nas proper pride or honest pride. The word pride used in this connection\nis a misnomer. Vanity is spurious self-esteem based on external\nadvantages. Pride is spurious self-esteem based on comparison with\nothers. Genuine self-esteem is based on the consciousness of a\ndistinction which we share with all humanity--namely, the capacity and\nthe duty of rational development. This genuine self-esteem has two\naspects--the one positive, the other negative. The positive aspect is\ncalled dignity, the negative humility. True dignity and true humility\nalways go together. The sense of dignity arises within us when we\nremember the aims to which as human beings we are pledged; the sense of\nhumility can not fail to arise when we consider how infinitely in\npractice we all fall below those aims. Thus while pride depends on a\ncomparison of ourselves with others, the genuinely moral feeling is\nexcited when we consider our relation to the common ends of mankind. On\nthe one hand, we are indeed privileged to pursue those ends, and are\nthereby exalted above all created things and above the whole of the\nnatural world with all its stars and suns. Upon this consideration is\nfounded the sense of dignity. On the other hand, we can not but own how\ngreat is the distance which separates even the best of us from the goal,\nand this gives rise to a deep sense of humility. The rule of conduct\nwhich we are considering is a rule of proper self-estimation. Estimate\nthy worth not by external advantages nor by thy pre-eminence above\nothers, but by the degree of energy with which thou pursuest the moral\naims. To mark off the distinction between vanity and pride on the one\nhand and dignity on the other, the teacher may contrast in detail the\nlives of Alcibiades and Socrates.\n\nIn connection with the discussion of anger and of pride, define such\nterms as hate, envy, malice. Hatred is anger become chronic. Or we may\nalso say the state of mind which leads to passionate paroxysms in the\ncase of anger is called hate when it has turned into a settled inward\ndisposition. In other respects the characteristic marks of both are the\nsame. Envy is the obverse of pride. Pride is based on real or fancied\nsuperiority to others. Envy is due to real or fancied inferiority. Pride\nis the vice of the strong, envy of the weak. Malice is pleasure in the\nloss of others irrespective of our gain.\n\nI have observed on a previous occasion that the feelings considered by\nthemselves have no moral value. Nevertheless, we have now repeatedly\nspoken of moral feelings. The apparent contradiction disappears if we\nremember that all feelings of the higher order presuppose, and are the\necho of complex systems of ideas. The moral feelings are those in which\nmoral ideas have their resonance; and those feelings are valuable in\nvirtue of the ideas which they reflect. The feeling of moral courage\ndepends on the idea that the injuries we receive at the hands of fortune\nare not important, but that it is important for us to do credit to our\nrational nature. The feeling of moral indignation depends on the idea\nthat the injuries we receive from our fellow-men are not important, but\nthat it is important that the right be done and the wrong abated. The\nfeelings of moral dignity and humility combined depend on the idea that\nit does not signify whether the shadow we cast in the world of men be\nlong or short, but only that we live in the light of the moral aims.\n\nFOOTNOTE:\n\n[16] See, e. g., the famous passage in Seneca, De Ira, iii, 15.\n\n\n\n\nXIII.\n\nDUTIES WHICH RELATE TO OTHERS.\n\n\nFILIAL DUTIES.\n\nWe began our course of moral instruction with the self-regarding duties,\nand assigned the second place to the duties which relate to others.\nThere is an additional reason besides the one already given for keeping\nto this order.\n\nIf we were to begin with the commandments or prohibitions which relate\nto others--e. g., the sixth, eighth, and ninth commandments of the\nDecalogue--the pupil might easily get the impression that these things\nare forbidden solely because they involve injuries to others, but that\nin cases where the injury is inconsiderable, or not apparent, the\ntransgression of moral commandments is more or less excusable. There are\nmany persons who seem unable to understand that it is really sinful to\ndefraud the custom-house or to neglect paying one's fare in a horse-car.\nAnd why? Because the injury inflicted seems so insignificant. Now, it is\nof the utmost consequence to impress upon the pupil that every action\nwhich involves a violation of duty to others at the same time produces a\nchange in the moral quality of the agent, that he suffers as well as the\none whom he wrongs. The subjective and objective sides of transgression\ncan not in point of principle and ought not in actual consciousness to\nbe separated. If, therefore, we begin by enforcing such duties as\ntemperance the pupil will at once feel that the violation of the law\nchanges his inward condition, degrades him in his own eyes, lowers him\nin the scale of being. The true standpoint from which all moral\ntransgression should be regarded will thus be gained at the outset, and\nit will be comparatively easy to maintain the same point of view when we\ncome to speak of the social duties.\n\nTo start discussion on the subject of the filial duties, relate the\nstory of AEneas carrying his aged father, Anchises, out of burning Troy;\nalso the story of Cleobis and Bito (Herodotus, i, 31). Recall the\ndevotion of Telemachus to Ulysses. Tell the story of Lear and his\ndaughters, contrasting the conduct of Regan and Goneril with that of\nCordelia. An excellent story to tell, especially to young children, is\nthat of Dama. AEneas and Telemachus illustrate the filial spirit as\nexpressed in services rendered to parents, but opportunity to be of real\nservice to parents is not often offered to the very young. The story of\nDama exhibits the filial spirit as displayed in acts of delicacy and\nconsideration, and such acts are within the power of all children. The\nstory is located in Palestine, and is supposed to have occurred at the\ntime when the temple at Jerusalem was still standing. Dama was a dealer\nin jewels, noted for possessing the rarest and richest collection\nanywhere to be found. It happened that it became necessary to replace a\nnumber of the precious stones on the breastplate of the high priest, and\na deputation was sent from Jerusalem to wait on Dama and to select from\nhis stock what was needed. Dama received his distinguished visitors with\nbecoming courtesy, and on learning their mission spread out before them\na large number of beautiful stones. But none of these were satisfactory.\nThe stones must needs be of extraordinary size and brilliancy. None but\nsuch might be used. When Dama was informed of this he reflected a\nmoment, then said that in a room occupied by his old father there was a\ncabinet in which he kept his most precious gems, and that among them he\nwas sure he could find what his visitors wanted. He bade them delay a\nfew moments, while he made the necessary search. But presently he\nreturned without the jewels. He expressed the greatest regret, but\ndeclared that it was impossible to oblige them. They were astonished,\nand, believing it to be a mere trader's trick, offered him an immense\nprice for the stones. He answered that he was extremely sorry to miss so\nprofitable a transaction, but that it was indeed beyond his power to\noblige them now--if they would return in an hour or two he could\nprobably suit them. They declared that their business admitted of no\ndelay; that the breastplate must be repaired at once, so that the priest\nmight not be prevented from discharging his office. And so he allowed\nthem to depart. It appears that when Dama opened the door of the room\nhe saw his old father asleep on the couch. He tried to enter\nnoiselessly, but the door creaked on its hinges, and the old man started\nin his sleep. Dama checked himself, and turned back. He said, \"I will\nforego the gain which they offer me, but I will not disturb the slumbers\nof my father.\" The sleep of the old father was sacred to Dama. Children\nare often thoughtless in breaking noisily into a room where father or\nmother is resting. Such a story tends to instill the lesson of\nconsideration and of reverence.\n\nReverence is the key-note of filial duty. You will remember that Goethe,\nin Wilhelm Meister, in those chapters in which he sketches his\npedagogical ideal, bases the entire religious and moral education of the\nyoung on a threefold reverence. He applies the following symbolism: The\npupils of the ideal pedagogical institution are required to take, on\ndifferent occasions, three different attitudes. Now they fold their arms\non their breast, and look with open countenance upward; again they fold\ntheir arms on their backs, and their bright glances are directed toward\nthe earth; and again they stand in a row, and their faces are turned to\nthe right, each one looking at his neighbor. These three attitudes are\nintended to symbolize reverence toward what is above us, toward what is\nbeneath us, and toward our equals. These three originate and culminate\nin the true self-reverence. In speaking of filial duty, we are concerned\nwith reverence toward what is above us. The parent is the physical,\nmental, and moral superior of the child. It is his duty to assist the\nchild's physical, mental, and moral growth; to lift it by degrees out of\nits position of inferiority, so that it may attain the fullness of its\npowers, and help to carry on the mission of mankind when the older\ngeneration shall have retired from the scene. The duty of the superior\ntoward the inferior is to help him to rise above the plane of\ninferiority. The receptive and appreciative attitude of one who is thus\nhelped is called reverence. But we must approach the nature of parental\nduty more closely, and the following reflections may put us in the way:\nNo man can attain the intellectual aims of life without assistance. A\nscientist inhabiting a desert island and limited to his own mental\nresources could make little headway. The scientist of to-day utilizes\nthe accumulated labors of all the generations of scientists that have\npreceded him, and depends for the value of his results on the\nco-operation and the sifting criticism of his contemporaries. And as no\none can get much knowledge without the help of others, so no one is\njustified in seeking knowledge for his own private pleasure, or in\nseeking the kind of knowledge that happens to pique his vanity. For\ninstance, it is a violation of intellectual duty to spend one's time in\nacquiring out-of-the way erudition which is useful only for display. The\npursuit of knowledge is a public not a private end. Every scholar and\nman of science is bound to enlarge as far as he can the common stock of\ntruth, to add to the scientific possessions of the human race. But in\norder to do this he must question himself closely, that he may discover\nin what direction his special talent lies, and may apply himself\nsedulously to the cultivation of that. For it is by specializing his\nefforts that he can best serve the general interests of truth. The same\nholds good with respect to the pursuit of social ends--e. g., the\ncorrection of social abuses and the promotion of social justice. The\nreformer of to-day stands on the shoulders of all the reformers of the\npast, and would have little prospect of success in any efforts he may\nmake without the co-operation and criticism of numerous co-workers. Nor,\nagain, is it right for him to take up any and every project of reform\nthat may happen to strike his fancy. He ought rather to consider what\nparticular measures under existing circumstances are most likely to\nadvance the cause of progress, and in what capacity he is specially\nfitted to promote such measures. Justice and truth are public, not\nprivate ends. The highest aim of life for each one is to offer that\ncontribution which he, as an individual, is peculiarly fitted to make\ntoward the attainment of the public ends of mankind. The individual when\nliving only for himself, absorbed in his private pleasures and pains, is\na creature of little worth; and his existence is of little more account\nin the scheme of things than that of the summer insects, who have their\nday and perish. But the individual become the organ of humanity acquires\na lasting worth, and his individuality possesses an inviolable sanctity.\nThe sacredness of individuality in the sense just indicated is a\nleading idea of ethics--perhaps it would not be too much to say, the\nleading idea.\n\nAnd now we can state more exactly the nature of parental duty. It is the\nduty of the parent, remembering that he is the guardian of the permanent\nwelfare of his child, to respect, to protect, to develop its\nindividuality--above all, to discover its individual bent; for that is\noften latent, and requires to be persistently searched out. It is the\nduty and the privilege of the parent to put the child, as it were, in\npossession of its own soul.\n\nAnd upon this relationship filial reverence is founded, and from it the\nprincipal filial duties may be deduced. Because the child does not know\nwhat is best for it, in view of its destiny, as described above, it is\nbound to obey. Obedience is the first of the filial duties. Secondly,\nthe child is bound to show gratitude for the benefits received at the\nhands of its parents. The teacher should discuss with his pupils the\nprincipal benefits conferred by parents. The parents supply the child\nwith food, shelter, and raiment; they nurse it in sickness, often\nsacrificing sleep, comfort, and health for its sake. They toil in order\nthat it may want nothing; they give it, in their fond affection, the\nsweet seasoning of all their other gifts. It is well to bring these\nfacts distinctly before the pupil's mind. The teacher can do it with a\nbetter grace than the parent himself. The teacher can strengthen and\ndeepen the home feeling, and it is his office to do so. The pupil\nshould go home from his moral lesson in school and look upon his parents\nwith a new realization of all that he owes them, with a new and deeper\ntenderness. But the duty of gratitude should be based, above all, upon\nthe greatest gift which the child obtains from his parents, the help\nwhich it receives toward attaining the moral aim of its existence.\n\nI do not include the commandment \"Love thy parents\" among the rules of\nfilial duty, for I do not think that love can be commanded. Love follows\nof itself if the right attitude of reverence, obedience, gratitude be\nobserved. Love is the sense of union with another. And the peculiarity\nof filial love, whereby it is distinguished from other kinds of love, is\nthat it springs from union with persons on whom we utterly depend, with\nmoral superiors, to whom we owe the fostering of our spiritual as well\nas of our physical existence.\n\nBut how shall the sentiment of filial gratitude express itself?\nGratitude is usually displayed by a return of the kindness received. But\nthe kindness which we receive from parents is such that we can never\nrepay it. It is of the nature of a debt which we can never hope fully to\ncancel. We can do this much--when our parents grow old, we can care for\nthem, and smooth the last steps that lead to the grave. And when we\nourselves have grown to manhood and womanhood, and have in turn become\nparents, we can bestow upon our own offspring the same studious and\nintelligent care which our parents, according to the light they had,\nbestowed on us, and thus ideally repay them by doing for others what\nthey did for us. But this is a point which concerns only adults. As for\nyoung children, they can show their gratitude in part by slight\nservices, delicacies of behavior, the chief value of which consists in\nthe sentiment that inspires them, but principally by a willing\nacceptance of parental guidance, and by earnest efforts in the direction\nof their own intellectual and moral improvement. There is no love so\nunselfish as parental love. There is nothing which true parents have\nmore at heart than the highest welfare of their children. There is no\nway in which a child can please father and mother better than by doing\nthat which is for its own highest good. The child's progress in\nknowledge and in moral excellence are to every parent the most\nacceptable tokens of filial gratitude. And this leads me to an important\npoint, to which reference has already been made. It has been stated that\neach period of life has its distinct set of duties; furthermore, that in\neach period there is one paramount duty, around which the others may be\ngrouped; and, lastly, that at each successive stage it is important to\nreach backward and to bring the ethical system of the preceding period\ninto harmony with the new system. Of this last point we are now in a\nposition to give a simple illustration. The paramount duty of the school\nperiod is to acquire knowledge; the paramount duty of the previous\nperiod is to reverence parents. But, as has just been shown, reverence\ntoward parents at this stage is best exhibited by conscientious study,\nand thus the two systems are merged into one.[17]\n\n\nTHE FRATERNAL DUTIES.\n\nThus much concerning the filial relations. We pass on to speak of the\nfraternal duties; the duties of brothers to brothers and sisters to\nsisters; of brothers to sisters and conversely; of older to younger\nbrothers and sisters and conversely. The fraternal duties are founded\nupon the respect which equals owe to equals. The brotherly relation is\nof immense pedagogic value, inasmuch as it educates us for the\nfulfillment later on of our duties toward all equals, be they kinsmen or\nnot. As between brothers, the respect of each for the rights of the\nother is made comparatively easy by natural inclination. The tie of\nblood, close and constant association in the same house, common\nexperience of domestic pleasures and sorrows--all this tends to link the\nhearts of the brothers together, and thus the first lessons in one of\nthe hardest duties are given by Love, the gentlest of school-masters.\nBut the word equality must not be misconceived. Equality is not to be\ntaken in its mathematical sense. One brother is gifted and may\neventually rise to wealth and fame, another is Nature's step-child; one\nsister is beautiful, another the opposite. If the idea of equality be\npressed to a literal meaning, it is sure to give rise to ugly feelings\nin the hearts of the less fortunate. How, then, shall we define equality\nin the moral sense? A superior, as we have seen, renders services which\nthe inferior can not adequately return. Equals are those who are so far\non the same level as to be capable of rendering mutual services, alike\nin importance, though not necessarily the same in kind. Equals are\ncorrelative to one another. The services of each are complementary to\nthose of the other. The idea of _mutual service_, therefore, is\ncharacteristic of the relation of brothers, and the rule of duty may be\nformulated simply, Serve one another. From this follow all the minor\ncommands and prohibitions which are usually impressed upon children,[18]\nand also the far loftier counsels which apply only to adults.\n\nIt will be perceived that the rule of mutual service, when carried to\nits highest applications, presupposes the principle of individual\ndifferentiation, to which we have already attached so much weight. This\nprinciple is fundamental to fraternal as well as to paternal and filial\nduty. For precisely to the extent that brothers are distinctly\nindividualized can they supplement each other and correlate their\nmutual services. One can not indeed overlook the patent fact that\nbrothers who are unlike in nature frequently repel each other, and that\nin such cases the very closeness of the relation often becomes a source\nof extreme irritation, and even of positive agony. But, on the other\nhand, there is no surer sign of moral ripeness than the ability to enter\ninto, to understand, to appreciate a nature totally unlike one's own,\nand thus to some extent to appropriate its excellences. The very fact,\ntherefore, that we at first feel ourselves repelled should be taken as a\nhint that this natural repulsion is to be overcome. For every type of\ncharacter needs its opposite to correct it. The idealist, for instance,\nneeds the realist, if he would keep his balance. And our uncongenial\nbrothers, precisely because they are at first uncongenial, if we will\nbut remember that they are, after all, our brothers, and that it is our\nduty to come into harmonious relations with them, can best help us to\nthis fine self-conquest, this true enrichment and enlargement of our\nmoral being.\n\nA word may be added as a caution to parents and teachers. The way to\ncreate brotherly feeling among the young is to treat them impartially,\nto love them with an equal love. Those who love and are beloved by the\nsame person are strongly induced to love one another. In the next place,\nwhen disputes arise, as is perhaps unavoidable, the parent or teacher\nshould, as a rule, enter patiently into the cause and not cut off\ninquiry because the whole matter seems trivial. The subject matter of\nthe dispute may be insignificant enough, but the satisfaction of the\nsense of justice of the young is of the greatest significance. When the\nsense of justice is outraged, be the cause never so trivial, a feeling\nof distrust against the parent is generated, and of incipient hatred\nagainst the brother who may have provoked the unjust decision.\n\nI have yet to speak of the duties of older to younger brothers and\nsisters. If it is difficult to serve two masters, it is hardly pleasant\nto be asked to serve half a dozen. The youngest children in a large\nfamily are often placed in this position. There is, in the first place,\nthe authority of the parents, which must be respected; then, in\naddition, each of the grown-up sons and daughters is apt to try to\nexercise a little authority on his or her own account. The younger ones\nnaturally resent this petty despotism, and disobedience and angry\nrecriminations are the unpleasant consequences. It is often necessary\nthat elder sons and daughters should have partial charge of the younger.\nThey can in all cases make their authority acceptable by representing it\nas delegated, by having it understood that they regard themselves merely\nas substitutes in the parents' place. There must be unity of influence\nin the home, or else the moral development of the young will be sadly\ninterfered with. There must be only a single center of authority,\nrepresented by the parents, and all minor exercise of authority should\nbe referred back to that center. \"Father and mother wish me to help\nyou\"; \"Father and mother will be pleased if you do so and so; let me\ntry to show you how\"--if the method of management implied in such words\nas these be adopted, the younger children will look upon the elder as\ntheir friends and be glad to accept advice and direction.\n\nLastly, a word about the relation between brothers and sisters, and\nconversely. This relationship is qualified by the difference of sex. A\ncertain chivalry characterizes the attitude of the brother toward the\nsister, a certain motherliness that of the sister toward the brother.\nThe relation may be and often is a very beautiful one. The peculiar\nmoral responsibility connected with it is that the sister is usually the\nfirst woman whom the brother knows at all intimately and as an equal,\nand that his notions of womanhood are largely influenced by the traits\nwhich he sees in her, while the brother is usually the first man whom\nthe sister knows as a companion, and her ideas of men are colored by\nwhat she sees in him.\n\nTo illustrate the fraternal relation I have been in the habit of\nrecalling the stories from the Old Testament which bear upon this\nsubject. I have also given an account of the life of the brothers Jacob\nand William Grimm. There was only a year's difference between them.\nJacob Grimm, in the eulogy on William, which he delivered before the\nBerlin Academy in the year 1860, says: \"During the slowly creeping years\nof our school life we slept in the same bed and occupied the same room.\nThere we sat at one and the same table studying our lessons. Later on\nthere were two tables and two beds in the same room; and later still,\nduring the entire period of our riper manhood, we still continued to\noccupy two adjoining rooms, always under the same roof.\" All their\nproperty, and even their books, they held in common; what belonged to\nthe one belonged to the other. They visited the university together in\nthe same year; they both took up, in deference to their mother's wish,\nthe same study, that of the law, which they alike hated, and then they\nturned in common to the study of philology, in which both delighted and\nboth achieved such great distinction. They published their first\nimportant works in the same year; and as they slept together in the same\nbed when they were children, so now they sleep side by side in the\ngrave.\n\nI refer to the story of Lear and his daughters to show that the common\nlove for the parents is necessary to sustain the love of brothers and\nsisters toward one another. Lear had estranged the affection of Goneril\nand Regan through his partiality for Cordelia. The two women, who had no\nlove for their father, hated each other; and Goneril, who was the first\nto cast him out, poisoned her sister.\n\nTo illustrate the relations of brothers to sisters, I give an account of\nthe beautiful lives of Charles and Mary Lamb. To show the redeeming\npower of womanhood as represented in a sister, I explain to older\npupils the story which underlies Goethe's drama of Iphigenia. Orestes is\nsick; and what is his malady? His soul has been poisoned by remorse.\nBelieving himself to be the executive arm of justice, he committed a\ngreat crime, and now he is torn by the pangs of conscience, and his mind\nis forever dwelling on that scene in which he was a fatal actor. And how\ndoes Iphigenia heal him? She heals him by the clear truthfulness of her\nnature, which the play is designed to bring out. With the light of\ngenuine womanhood which emanates from her she illuminates anew his\ndarkened path. By the force of the good which he learns to recognize in\nher he is led to a new trust in the redeeming power of the good in\nhimself, and thus to start out afresh in a life of courage, hope, and\nactive effort. The teacher should analyze and cause to be committed to\nmemory the various beautiful proverbs which bear upon the subject of\nfraternal duty.\n\nFOOTNOTES:\n\n[17] It may also be pointed out to the pupil that a part of the task of\nintellectual and moral training, which originally belongs entirely to\nthe parents, has by them been intrusted to the teachers, and that\nsomething of the reverence which belongs to the former is now due to the\nlatter.\n\n[18] Do not quarrel over your respective rights; rather be more eager to\nsecure the rights of your brother than your own. Do not triumph in your\nbrother's disgrace or taunt him with his failings, but rather seek to\nbuild up his self-respect. Help one another in your tasks, etc.\n\n\n\n\nXIV.\n\nDUTIES TOWARD ALL MEN.\n\n\nJUSTICE AND CHARITY.\n\nJUSTICE.--The subject of justice is a difficult one to treat. Justice in\nthe legal sense is to be distinguished from justice in the moral sense.\nWe are concerned only with the latter. How much of it can we hope to\ninclude in such a course of instruction as this? We can, I think,\nexplain the essential principle and give a few of its most important\napplications. What is this principle? Human society is an organism, and\nthe perfection of it depends upon the degree to which the parts related\nare differentiated. Unity of organization is the end, differentiation is\nthe means. The serving of universal ends is the aim, the emphasizing of\nindividuality the means. The principle which underlies the laws of\njustice I take to be respect for individuality of others. And this may\nbe expressed in the rule, Respect the individuality of every human\nbeing. It might, indeed, appear at first sight as if justice had to do\nonly with those points in which all men are alike, and took no notice of\nthe differences that subsist between them. Thus justice enjoins respect\nfor the life of others; and in regard to this all men are exactly on a\npar, all men are equally entitled to live. But justice also commands us\nto respect the convictions of others, however different they may be from\nour own. And it is but a finer sense of justice which keeps us from\nintruding on the privacy of others, which leads us to show a proper\nconsideration for the ways and idiosyncrasies of others, and in general\nto refrain from encroaching on the personality of others. The principle\nof justice may also be expressed in the rule, Do not interfere with the\nindividual development of any one.\n\n\nAPPLICATIONS OF THE PRINCIPLE OF JUSTICE.--\n\n1. _Do not kill._ By taking away the life of a human being we should of\ncourse cut off all chance of that person's further development. This\nrequires no comment. But certain casuistical questions arise in\nconnection with this command. Is it right to kill another in\nself-defense? The difficulty involved might be put in this way: A\nburglar breaks into your house by night and threatens to kill you. You\nhave a weapon at hand and can save yourself by killing him. Now it is\nevident that one of two lives must be taken. But would it not be more\nmoral on your part to say: I, at least, will not break the commandment.\nI would rather be killed than kill? This question serves to show to what\nabsurdities a purely formal principle in ethics can lead, as we have\nalready seen in the discussion of truthfulness. The problem of the duel\nand that of the taking of the life of others in war also belong under\nthis head, but will be reserved for the advanced course.\n\n2. _Respect the personal liberty of others._ Slavery, under whatever\nform, is an outrage on justice. The slave is degraded to be the mere\ninstrument of his master's profit or pleasure. Let the teacher point out\nin what particulars the slave is wronged, and show the evil effects of\nthe institution of slavery on the character of the master as well as of\nthe slave. Question--Is it right to speak of wage-slavery, for instance,\nin cases where the hours of labor are so prolonged as to leave no time\nfor higher interests, or where the relations of the laborer to his\nemployer are such as to impair his moral independence?\n\n3. _Respect the property of others._ Unless we are careful we may at\nthis point commit a grave wrong. Upon what moral considerations shall\nthe right of property be based? The school, especially the moral lessons\nwhich are imparted in it, should certainly not be placed in the service\nof vested interests. On the other hand, the school should not fill the\npupils' minds with economic theories, which they are incapable of\nunderstanding, and of which the truth, the justice, the feasibility are\nstill hotly disputed. We are therefore taking a very responsible step in\nintroducing the idea of property at all into our moral lessons. And yet\nit is too great and important to be ignored. Some writers have advanced\nthe theory that the right in question rests on labor, and they regard it\nas a self-evident proposition, one which, therefore, might safely be\ntaught to the young, that every person is entitled to the products of\nhis labor. Jules Simon says (see Paul Janet, Elements of Morals, English\ntranslation, p. 66): \"This earth was worth nothing and produced\nnothing. I dug the soil, I brought from a distance fertilizing earth; it\nis now fertile. This fertility is my work; by fertilizing it, I made it\nmine.\" American writers have eloquent passages to the same effect. But\nthis proposition certainly does not appear to me self-evident, nor even\ntrue. Chiefly for the reason that \"my labor\" and \"my skill\" are not\noriginal, but derivative factors in production. They are very largely\nthe result of the labor and the skill of generations that have preceded\nme, that have built up in me this brain, this skill, this power of\napplication. The products of my labor would indeed belong to me if my\nlabor were really mine, if it were not to an incalculable extent the\nconsequent of social antecedents, in regard to which I can not claim the\nleast merit. The attempt to found the rewards of labor upon the merit of\nthe laborer seems to me a perfectly hopeless one.\n\nLet me add that it is one thing to say that he who will not work shall\nnot eat, and a very different thing to say that he who works shall enjoy\nwhat he has produced. The former statement merely signifies that he who\nwill not contribute his share toward sustaining and improving human\nsociety is not entitled to any part in the advantages of the social\norder, though the charity of his fellow-men may grant him, under certain\nconditions and in the hope of changing his disposition, what he is not\nentitled to as of right. But the question what the share of the laborer\nought to be is one that can not be settled in the rough-and-ready\nmanner above suggested, and the considerations involved are, in truth,\nfar too numerous and complex to be introduced at this stage. The whole\nquestion will be reopened later on. For the present it must suffice to\nstate certain purely moral considerations on which the right of property\nmay be made to rest. The following are the ideas which I should seek to\ndevelop: Property is justified by its uses. Its uses are to support the\nexistence and promote the mental and moral growth of man. The physical\nlife itself depends on property. Even in a communistic state the food\nany one eats must be his property in the sense that every one else is\ndebarred from using it. The moral life of men depends on property. The\nmoral life is rooted in the institution of the family, and the family\ncould not exist without a separate domicile of its own and the means of\nproviding for its dependent members. The independence and the growth of\nthe intellect depend on property. In short, property is an indispensable\nadjunct of _personality_. This I take to be its moral basis. What I here\nindicate, however, is an ideal right which the existing state of society\nby no means reflects. By what methods we may best approach this ideal,\nwhether by maintaining and improving the system of private property in\nland or by state ownership, whether by capitalistic or socialistic\nproduction, etc., are questions of means, not of ends, and raise\nproblems in social science with which here we have not to deal.\n\nQuestion--If the present social arrangements are not morally\nsatisfactory, if e. g., certain persons possess property to which on\nmoral grounds they are not entitled, should not the commandment against\nstealing be suspended so far as they are concerned? The present system\nof rights, imperfect as it is, is the result of social evolution, and\ndenotes the high-water mark of the average ethical consciousness of the\nworld up to date. Respect for the existing system of rights, however,\nimperfect as it is, is the prime condition of obtaining a better system.\n\n4. _Respect the mental liberty of others._ Upon this rule of justice is\nfounded the right to freedom of speech, freedom of the press, and what\nis called the freedom of conscience. Point out the limitations of these\nvarious rights which follow from the fact of their universality.\n\n5. _Respect the reputation of your fellow-men._ Refrain from backbiting\nand slander. Bridle your tongue. This undoubtedly is a rule of justice.\n\"Who steals my purse steals trash,\" etc. The respect of our fellow-men\nis in itself a source of happiness and a moral prop, and, besides, the\ngreatest help in achieving the legitimate purposes of life. He who has\nthe confidence of others has wings to bear him along. He who is\nsuspected for any reason, true or false, strikes against invisible\nbarriers at every step. Nothing is so sensitive as character--a mere\nbreath may tarnish it. It is therefore the gravest kind of injury to our\nneighbors to disseminate damaging rumors, to throw out dark hints and\nsuggestions with respect to them, to impugn their motives. But is it\nnot a duty to denounce evil and evil-doers and to put the innocent on\ntheir guard against wolves in sheep's clothing? Yes, if we are sure that\nour own motives are perfectly disinterested, that we are not in the\nleast prompted by personal spite or prejudice. For if we dislike a\nperson, as every one knows, we can not judge him fairly, we are prone to\nattribute to him all manner of evil qualities and evil intents which\nexist only in our own jaundiced imagination. Very often a person against\nwhom we had at first conceived a distinct dislike proves on nearer\nacquaintance to be one whom we can esteem and even love. We should be\nwarned by such experiences to hold our judgments in suspense, and not to\nallow injurious words to pass the lips. The vast moral importance of\nbeing able to hold one's tongue, the golden resources of silence, should\nbe emphasized by the teacher.\n\nA series of lessons on good manners may be introduced at this point. The\nceremonies of social intercourse, the various forms in which refined\npeople show their deference for each other, the rule not to obtrude self\nin conversation, and the like, are so many illustrations of the respect\nwhich we owe to the personality of our fellow-men. Good manners are the\naesthetic counterpart of good morals, and the connection between the two\ncan easily be made plain.\n\n6. _Speak the truth._ Inward truthfulness is a self-regarding duty;\nsocial truthfulness is a form of justice. Words represent facts. The\nwords we speak to our neighbor are used by him as building-stones in\nthe architecture of his daily conduct. We have no right to defeat the\npurposes of his life, to weaken the dwelling he is erecting, by\nsupplying him with worthless building material.\n\nUpon exactly the same ground is based the duty of keeping one's\npromises, viz., that our fellow-men build on our promises. Promises made\nin a legal form are called contracts and can be enforced. Promises not\nmade in legal form are equally binding from a moral point of view. It\nshould be borne in mind, however, that conditional promises are canceled\nwhen the stipulated conditions do not occur, and, furthermore, that\nthere are certain tacit conditions implied in all promises whatsoever. A\nperson who has promised to visit a friend on a certain day and dies in\nthe interval is not supposed to have broken his promise; nor if any one\nmakes a similar promise and a heavy snowstorm should block the roads or\nif he should be confined to his bed by sickness is he likely to be\naccused of breaking his promise. The physical possibility of fulfilling\nthem is a tacit condition in all promises. It is also a tacit condition\nin all promises that it shall be morally possible or consistent with\nmorality to keep them. A young man who has promised to join a gang of\nburglars in an attack on a bank and who repents at the last moment is\nmorally justified in refusing to keep his pledge. His crime consisted in\nhaving made the promise in the first place, not in refusing to fulfill\nit at the last moment. A person, however, who promises to pay usurious\ninterest on a loan of money and who then takes advantage of the laws\nagainst usury to escape payment is a double-dyed rogue, for his\nintention is to cheat, and he uses the cloak of virtue as a screen in\norder to cheat with impunity. Let the teacher discuss the casuistical\nquestion whether it is right to keep a promise made to robbers--e. g.,\nif we should fall into the hands of brigands, and they should make it a\ncondition of our release that we shall not betray their hiding-place.\n\nJustice is based on positive respect for the individuality of others,\nbut its commands may all be expressed in the negative form: Do not kill,\ndo not infringe the liberty, the property of others, do not slander, do\nnot lie, etc. It is often held, however, that there is a positive as\nwell as a negative side to justice, and the two sides are respectively\nexpressed in the formulas: Neminem laede and suum cuique--Hurt no one\nand give every one his due. Of positive or distributive justice we meet\nwith such examples as the following: In awarding a prize the jury is\nbound in justice to give the award in favor of the most deserving\ncompetitor. The head of a department in filling a vacancy is bound in\njustice to avoid favoritism, to promote that one of his subordinates who\ndeserves promotion, etc. But it seems to me that this distinction is\nunimportant. Give to each one his due is tantamount to Do not deprive\nany one of what is due him. If the prize or the place belongs to A we\nshould, by withholding it from him, invade the rights of A as much as\nif we took money out of his purse. The commands are negative, but the\nvirtue implied is positive enough, because it depends on positive\nrespect for human nature. Do not infringe upon the sacred territory of\nanother's personality is the rule of justice in all cases.\n\nCHARITY.--How shall we distinguish charity from justice? It is said that\nevery one is justified in claiming from others what belongs to him as a\nmatter of right, but that no one can exact charity. The characteristic\nmark of charity is supposed to be that it is freely given. But if I\nhappen to be rich and can afford to supply the need of another am I not\nmorally bound to do so, and has not my indigent neighbor a real claim\nupon me? Again, it has been said that the term justice is applied to\nclaims which are capable of being formulated in general rules and\nimposed alike on all men in their dealings with one another, while in\nthe case of charity both the measure and the object of it are to be\nfreely determined by each one. We are free, according to this view, to\ndecide whether a claim upon us exists or not; but, the claim once having\nbeen admitted, it is as binding upon us as any of the demands of\njustice. But, while this is true, I hold that nevertheless there exists\na clear distinction between the virtues of justice and charity. We owe\njustice to our equals, charity to our inferiors. The word \"inferior\" is\nto be understood in a carefully limited sense. An employer owes his\nworkmen, as a matter of justice, the wages he has agreed to pay. Though\nthey may be socially his inferiors, in regard to this transaction they\nare his equals. They have agreed to render him certain services and he\nhas agreed to return them an equivalent.\n\nJustice says Do not hinder the development of others; Charity says\nAssist the development of others. The application of the rule of charity\nwill make its meaning clear.\n\n1. Justice says do not destroy life; Charity says save life. Rescue from\nthe flames the inmates of a burning house; leap into the waves to save a\ndrowning fellow-creature. Such persons are dependent on your help. They\nare therefore with respect to you in an inferior position.\n\nDiscuss with the class the limitations of this duty. I am not bound to\njump into the water, for instance, when I see a person drowning unless I\ncan swim. In fact, it would be culpable foolhardiness in me to do so.\nDiscuss the following casuistical case: A child is lying on the railroad\ntrack and a locomotive is rapidly approaching. Am I bound to make the\nattempt to draw it away from the track? Does it make any difference\nwhether I am single or the father of a family and have others dependent\non me? In general, the attempt to save should not be made unless there\nis a distinct chance of succeeding without the sacrifice of one's own\nlife; but we are justified in taking great risks, and courage and\nself-reliance are evinced in the degree of risk we are willing to take.\nThere are cases, however, in which the deliberate sacrifice of one life\nfor another is in the highest degree praiseworthy when, namely, the\nlife to be saved is regarded as far more precious than our own. Instance\nthe soldier who intercepts the thrust which is aimed at the life of his\ngeneral. Instance the parent who in the Johnstown flood was seen to push\nhis child to a place of safety and was then swept away by the current.\n\n2. _Assist the needy._ This may be done by giving bread to the hungry,\nclothing to the naked, shelter to the homeless, by caring for the sick,\nadvancing loans to those who are struggling toward self-support, etc.\nThe rule of charity is based on respect for the personality of others.\nWe are required to assist those who are too weak to hold their own, with\na view of putting them on their feet again. The aim of all charity\nshould be to make those who are dependent on it independent of it. From\nthis point of view all mere almsgiving, all that so-called charity which\nonly serves to make the dependent classes more dependent, stands\ncondemned. But the true test of charity, upon which the greatest stress\nshould be laid, is to be found in the way it reacts upon the charitable\nthemselves. Right relations, whatever their nature, are always mutually\nbeneficial. Does the deed of charity react beneficially on the doer? is\nthe test question to be asked in every instance. Take the case of a\nperson who gives large sums to the poor in the hope of seeing his name\nfavorably mentioned in the newspapers. The motive in this case is\nvanity, and the effect of this spurious sort of charity is to increase\nthe vanity of the donor. The reaction upon him, therefore, is morally\nharmful. Again, take the case of a person who gives capriciously, at the\nbidding of impulse, without considering whether his gifts are likely to\nbe of lasting benefit to the recipients. He is confirmed in his habit of\nyielding to impulse, and the reaction is likewise morally injurious. On\nthe other hand, the retroactive effects of true charity are most\nbeneficial. In the first place, a reaction will take place in the\ndirection of greater simplicity in our own lives. A person can not be\nseriously and deeply interested in the condition of the poor, can not\ntruly realize the hardships which they suffer, without being moved to\ncut off superfluous expenditure. Secondly, true charity will teach us to\nenter into the problems of others, often so unlike our own; to put\nourselves in their places; to consider how we should act in their\ncircumstances; to fight their battles for them; and by this means our\nmoral experience will be enlarged, and from being one, we become, as it\nwere, many men. True charity will also draw closer the bond of\nfellowship between the poor and us, for we shall often discover virtues\nin them which we do not possess ourselves; and sometimes, at least, we\nshall have occasion to look up with a kind of awe to those whom we are\naiding. In connection with the discussion of charity, let the teacher\nrelate the biographies of John Howard, Sister Dora, Florence\nNightingale, Elizabeth Fry, and others, who have been distinguished for\ntheir devotion to the suffering.\n\n3. _Cheer up the sad._ Explain that a bright smile may often have the\nvalue of an act of charity. In general, emphasize the duty of\nsuppressing irritability, ill humor, and moodiness, and of contributing\nto the sunshine of our households.[19]\n\n4. _Console the bereaved._ The afflicted are for the moment weak and\ndependent; it is the office of loving charity to make them independent.\nHere the same train of reasoning is applicable as above in the case of\nthe poor. It serves no useful purpose merely to sit down by the side of\nthe sorrowful and to weep with them. They do need sympathy, but they\nalso need, at least after the first paroxysms of grief have subsided, to\nbe roused.\n\nThe true cure for suffering is action. Those who suffer need to be\nnerved to action; they need to be shown, above all, the new duties which\ntheir situation entails. He who can point out to them the way of duty,\nand can give them of his own strength to walk in that way, is their best\nfriend--he is the true consoler.\n\n5. I have yet to speak of mental charity and of moral charity. Mental\ncharity is practiced by the wise teacher, who puts his pupils on the\nroad to knowledge, who helps them to discover their true vocation, and\nwho, when they are involved in doubt and difficulty, succeeds in giving\nthem the clew by which they can find an exit into mental clearness and\nlight.\n\n6. Moral charity is practiced by those who bend down to the sinful and\nthe fallen, and awaken in them a new hope and trust in the good and in\nthemselves. The charity which effects moral regeneration is perhaps the\nhighest type of all, and of this I know no more fitting nor more sublime\nexample than the dealing of Jesus with the outcasts of society.\n\n\n     NOTE.--Without attempting to forestall further philosophical\n     analysis, we may perhaps assume, as a working hypothesis, as a\n     provisional principle of deduction in ethics, the principle of\n     organization. The individual is an organ of humanity. It is his\n     duty to discharge, as perfectly as possible, his special functions;\n     hence the need of insisting on respect for individuality\n     throughout. Even the self-regarding duties would have no meaning\n     were not the complex whole in view, in the economy of which each\n     member is required to perform his part. As in every organism, so in\n     this, each separate organ serves, and is served in turn by all the\n     others, and can attain its highest development only through this\n     constant interaction. To complete the thought, it would be\n     necessary to add that certain organs are more closely connected\n     than others, and form lesser organisms within and subservient to\n     the whole. This, however, is merely thrown out as a suggestion\n     addressed to the student of ethics.\n\n\nTHE DUTY OF GRATITUDE.--Upon this subject much might be said, did not\nthe fact that the time at our command is nearly exhausted warn us to use\neven greater brevity than heretofore in dealing with the topics that\nremain. To bring out the right relations between benefactor and\nbeneficiary, let the teacher put the question, Why is it wrong to cast\nup the benefits we have conferred to the one who has received them? And\nwhy, on the other hand, is it so base in the latter to show himself\nungrateful. The reason is to be found in the respect due to the\npersonality of others, to which we have so often alluded. Kant says that\nevery human being is to be treated as an end in himself, and not merely\nas a means or a tool. In effect, the person who ignores benefits says to\nhis benefactor: You are my tool. It is unnecessary for me to recognize\nyour services, because you are not an independent person to be\nrespected, but a creature to be made use of at pleasure. Ingratitude is\na slur on the moral personality of others. On the other hand, he who\ncasts up benefits practically says you have forfeited your independence\nthrough the favors you have accepted. I have made your personality\ntributary to mine.\n\nAn excellent rule is that of Seneca. The benefactor should immediately\nforget what he has given; the beneficiary should always remember what he\nhas received. True gratitude is based on the sense of our moral\nfellowship with others. The gifts received and returned are mere tokens\nof this noble relationship (as all gifts should be). You have just given\nto me. I will presently give to you twice as much again, or half as\nmuch, it matters not which, when occasion arises. We will further each\nother's aims as best we can, for the ends of each are sacred to the\nother.\n\nDUTIES TO SERVANTS.--Having spoken of the duties which we owe to all\nmen, I may here refer to certain special duties, such as the duties\ntoward servants. These may also be introduced in connection with the\nduties of the family, after the filial and fraternal duties have been\nconsidered. I have space only to mention the following points:\n\n1. Servants are laborers. The same respect is due to them as to all\nother laborers.\n\n2. They are not only laborers, but in a special sense helpers. They are\nmembers of the household in a subordinate capacity, and in many cases\nidentify themselves closely with the interests of the family. They are,\nas it were, lay brothers and lay sisters of the family. From these\nconsiderations may be deduced the duties which we owe toward servants.\n\nDUTIES WITH REGARD TO ANIMALS.--I can not admit that we have duties\ntoward animals. We can not very well speak of duties toward creatures on\nwhich we in part subsist; but there are duties with respect to animals.\nMan is a rational being, and as such takes a natural delight in that\norderly arrangement and interdependence of parts which are the visible\ncounterpart of the rational principle in his own nature. We ought not to\nstep on or heedlessly crush under our feet even a single flower. Much\nless should we ruthlessly destroy the more perfect organism which we see\nin animals. Add to this that animals are sentient creatures, and that\nthe useless infliction of pain tends to develop cruelty in us. As a\npractical means of fostering kindness toward animals, I suggest the\nfollowing: Get your pupils interested in the habits of animals.\nFamiliarity in this case will breed sympathy. Speak of the building\ninstincts of bees; of the curious structures raised by those wonderful\nengineers, the beavers. Give prominence to the love for their young by\nwhich the brute creation is brought into closer connection with the\nhuman family. Mention especially the fidelity which some animals show\ntoward man (the saving of human lives by St. Bernard dogs, etc.), and\nthe uses which we derive from the various members of the animal\ncreation. As to the fact that we use animals for our sustenance, the\nhighest point of view to take, I think, is this, that man is, so to\nspeak, the crucible in which all the utilities of nature are refined to\nhigher spiritual uses. Man puts the whole of nature under contribution\nto serve his purposes. He takes trees from the forest in order to build\nhis house, and to fashion the table at which he takes his meals; he\nbrings up metal from the depths of the earth and converts it into tools;\nhe takes clay and forms it into vessels. He also is permitted to pluck\nflowers wherewith to garnish his feasts, and to make them the tokens of\nhis love; and in the same manner he may actually absorb the life of the\nlower animals, in order to transform and transfigure it, as it were,\ninto that higher life which is possible only in human society. But it\nfollows that he is a mere parasite and an interloper in nature, unless\nhe actually leads the truly human life.\n\nFOOTNOTE:\n\n[19] For the teacher I add point 4. The duties mentioned under 5 and 6\nmay be practiced in a simple way by the young in the form of aiding\ntheir backward schoolmates, and observing the right attitude toward\nthose of their companions who are in disgrace.\n\n\n\n\nXV.\n\nTHE ELEMENTS OF CIVIC DUTY.\n\n\nIt should be the aim of the school not only to connect the system of\nschool duties with the duties of the previous period, but also to\nprepare the pupils morally for the period which follows. The school is\nthe intermediate link between life in the family and life in society and\nthe state. The course of moral instruction, therefore, culminates for\nthe present in the chapter on civic duties. Needless to say that at this\nstage the subject can be considered in its elements only.\n\nThe claims of the state upon the moral attachment of the citizen can\nhardly be presented too warmly. Life in the state as well as in the\nfamily is indispensable to the full development of character. Man, in\nhis progress from childhood to old age, passes successively through\never-widening circles of duty, and new moral horizons open upon him as\nhe grows out of one into the other. One of the largest of these circles,\nand, in respect to moral opportunities, one of the richest and most\nglorious, is the state. It may be said that the whole state exists\nideally in every true citizen, or, what amounts to the same, that the\ntrue citizen embraces the interests of the state, as if they were his\nown, and acts from the point of view of the total body politic.\nIncreased breadth of view and elevation of purpose are the moral\nbenefits which accrue to every one who even honestly attempts to be a\ncitizen in this sense.\n\nMuch attention is paid in some schools to the machinery of our\ngovernment. The pupils are expected to learn the exact functions of\nmayors, city councils, and legislative bodies, the provisions relative\nto the election of the President, etc. But while these things ought to\nbe known, they relate, after all, only to the externals of government;\nand it is far more important to familiarize the pupils with the\nanimating spirit of political institutions, with the great ideas which\nunderlie the state. There are especially three political ideas to which\nI should give prominence; these are, the idea of the supremacy of the\nlaw; the true idea of punishment; and the idea of nationality. After we\nhave instilled these ideas, it will be time enough to dwell with greater\nparticularity on the machinery by which it is sought to carry them into\neffect.\n\nWhat method shall we use for instilling these ideas? The same which\nmodern pedagogy applies in every branch of instruction. The rule is,\nProceed from the known to the unknown; in introducing a new notion,\nconnect it with some analogous notion already in the pupil's possession.\nThe school offers excellent opportunities for developing the two ideas\nof law and punishment. In every school there exists a body of rules and\nregulations, or school laws. It should be made plain to the scholars\nthat these laws are enacted for their own good. The government of the\nschool should be made to rest as far as possible on the consent and\nco-operation of the governed. That school which does not secure on the\npart of the scholars a willing acceptance of the system of restraints\nwhich is necessary for the good of the whole, is a failure. In such an\ninstitution the law-abiding spirit can never be fostered.\n\nThe play-ground, too, affords a preliminary training for future\ncitizenship. On the play-ground the scholars learn to select and to obey\ntheir own leaders, to maintain the rules of the game, and to put down\nany infraction of them, whether in the shape of violence or fraud. They\nalso learn to defer to the will of the majority--a most important\nlesson, especially in democratic communities--and to bear defeat\ngood-humoredly.[20]\n\nThe true idea of punishment should be brought home to the scholars\nthrough the discipline of the school. The ends of punishment are the\nprotection of the community and the reformation of the offender. Nowhere\nbetter than in the little commonwealth of the school can these moral\naspects of punishment be impressed; nowhere better can the foundation be\nlaid for the changes which are so urgently needed in the dealings of the\nstate with the criminal class. Everything, of course, depends upon the\ncharacter of the teacher. His reputation for strict justice, the moral\nearnestness he displays in dealing with offenses, his readiness to\nforbear and forgive upon the least sign of genuine repentance--these are\nthe means by which he can instill right notions as to what discipline\nshould be. It has been suggested that, when a particularly serious case\nof transgression occurs, the teacher can sometimes produce a profound\nmoral effect on the class by submitting the case to them as a jury and\nasking for their verdict.\n\nThe idea of nationality I regard as fundamental in political ethics.\nThere is such a thing as national character, national genius, or\nnational individuality. When we think of the Greeks, we think of them as\npre-eminent for their achievements in art and philosophy; of the\nHebrews, as the people of the Bible; of the Romans, as the founders of\njurisprudence, etc. And on turning to the modern nations we find that\nthe talents of the English, the Germans, the French, the Italians, etc.,\nare no less diversified. Morally speaking, it is the mission of each\nnation in correlation with others to contribute to the universal work of\ncivilization its own peculiar gifts. The state may be regarded as that\norganization of the public life which is designed _to develop the\nnational individuality_; to foster the national genius in whatever\ndirection it may seek to express itself, whether in industry, art,\nliterature, or science; to clarify its aims, and to raise it to the\nhighest pitch of beneficent power.\n\nDoubtless this idea, as stated, is too abstract to be grasped by the\nyoung; but it can be brought down to their level in a tangible way. For\nthe national genius expresses itself in the national history, and more\nespecially is it incorporated in those great leaders, who arise at\ncritical periods to guide the national development into new channels. It\nis at this point that we realize anew the important support which the\nteaching of history may give to the moral teaching.[21] Thus the\npolitical history of the United States, if I may be permitted to use\nthat as an illustration of my thought, may be divided into three great\nperiods. The struggle with nature occupied the earliest period--that of\ncolonization; in this period we see the American man engaged in subduing\na continent. The struggle for political freedom fills the period of the\nRevolution. The struggle for a universal moral idea lends grandeur to\nour civil war. The story of these three great struggles should be\nrelated with such clearness that the idea which dominated each may stand\nout in relief, and with such fervor that the pupils may conceive a more\nardent love for their country which, at the same time that it holds out\nimmeasurable prospects for the future, already possesses such glorious\ntraditions. There is, however, always a great danger that patriotism may\ndegenerate into Chauvinism. Against this, universal history, when taught\nin the right spirit, is the best antidote. A knowledge of universal\nhistory is an admirable check on spurious patriotism. In teaching it,\nit is especially desirable that the contribution which each nation has\nmade to the progress of the world be noted and emphasized. Let the\nteacher speak of the early development of the literature and of the\ninventive spirit of the despised Chinese; of the high civilization which\nonce flourished on the banks of the Nile; of the immortal debt we owe to\nGreece and Rome and Judea. Let the young be made acquainted with the\nimportant services which Ireland rendered to European culture in the\nearly part of the middle ages. Let them learn, however briefly, of the\npart which France played in the overthrow of feudalism, of the wealth of\nGerman science and literature and philosophy; let them know how much\nmankind owes to the Parliaments of England, and to the stout heart and\nstrong sense which made parliaments possible. It is not by underrating\nothers, but by duly estimating and appreciating their achievements, that\nwe shall find ourselves challenged to bring forth what is best in\nourselves.\n\nThere is still another reason why, especially in American schools, the\nteaching of universal history should receive far greater attention than\nhitherto has been accorded to it. The American people are imbued with\nthe belief that they have a problem to solve for all mankind. They have\nset out to demonstrate in the face of doubt and adverse criticism the\npossibility of popular self-government. They have thus consecrated their\nnational life to a sublime humanitarian idea. And the sense of this\nconsecration, echoing in the utterances of many of their leading\nstatesmen, has more or less permeated the whole people. But the mission\nthus assumed, like the burden on the shoulders of Christophorus, is\nbecoming heavier at every step. The best citizens recognize that the\nproblem of popular self-government, so far from being solved, is but\nbeginning to disclose itself in all its vast complexity, and they\nrealize more than ever how necessary it is to get every possible help\nfrom the example and experience of older nations. The political lessons\nof the past can not indeed be mastered in the public schools. But a\npreliminary interest in European history may be created, which will pave\nthe way for profitable study later on.\n\nFurthermore, the American people have extended a most liberal invitation\nto members of other nationalities (with few restrictions, and these of\nrecent origin) to come and join in working out the destinies of the new\ncontinent. Not only is an asylum granted to the oppressed--this were the\nlesser boon--but the gates of citizenship have been opened wide to the\nnew-comers. What does this mean, if not that the foreigners who come,\nunless indeed they belong to the weak and dependent classes, are wanted;\nand wanted not only in their capacity as workers to aid in developing\nthe material resources of the country, but as citizens, to help in\nperfecting what is still imperfect, to assist in building up in time, on\nAmerican soil, the true republic.\n\nIn return for this privilege the citizens of foreign birth owe it to\ntheir adopted country to place the best of their racial gifts at its\nservice. Much that the citizens of foreign birth bring with them,\nindeed, will have to be eliminated, but, on the other hand, many of\ntheir traits will probably enter as constituent elements into the\nnational character. The Anglo-Saxon race has now the lead, and will\ndoubtless keep it. But in the melting-pot of the American commonwealths\nthe elements of many diverse nationalities are being mixed anew, and a\nnew nationality distinctively American is likely to be the final outcome\nof the process. Thus both the humanitarian ideal and the actual make-up\nof the people betray a cosmopolitan tendency, and it is this tendency\nwhich, more perhaps than anything else, gives to American political life\nits characteristic physiognomy. If this be so, if the foreign elements\nare so numerous and likely to be so influential, it is surely important\nthat the foreign races, their character and their history, be studied\nand understood.\n\nBesides explaining the political ideas, I should briefly describe the\nactual functions of government. Government protects the life and\nproperty of its citizens against foreign aggression and violence at\nhome. Government maintains the binding force of contracts. Government\nreserves to itself the coinage of money, carries the mails, supports\npublic education, etc. In a word, government assumes those functions\nwhich can be discharged more satisfactorily or more economically by the\njoint action of the community than if left to private individuals or\ncorporations. But government also undertakes the duty of protecting the\nweaker classes against oppression by the stronger, as is shown by\nfactory legislation in the interest of women and minors. How far this\nfunction may profitably be extended is open to discussion; but that it\nhas been assumed in all civilized countries is a fact which should be\nnoted.\n\nFOOTNOTES:\n\n[20] _Vide_ Dole, \"The American Citizen.\"\n\n[21] See remarks on this subject in the third lecture.\n\n\n\n\nXVI.\n\nTHE USE OF PROVERBS AND SPEECHES.\n\n\nFor the use of my classes I have made a collection of proverbs from the\nBible, from Buddha's Dhammapada, from the Encheiridion of Epictetus, the\nImitation of Christ, and other ancient and modern sources. Some of these\nbelong to the advanced course, others can be used in the grammar course.\nI have time to mention only a few, in order to illustrate the method of\nusing them.\n\nThe habit of committing proverbs or golden sayings to memory without a\nprevious analysis of their meaning serves no good purpose whatever.\nProverbs are the condensed expression of the moral experience of\ngenerations. The teacher should search out the experiences to which the\nproverbs refer. Proverbs may be compared to those delicate Eastern\nfabrics which can be folded up into the smallest compass, but which,\nwhen unfolded, are seen to cover a large space. The teacher should\nexplore the territory covered by the proverb. Take, for example, such a\nsaying as this, \"Blessed be he who has the good eye.\" What is the good\neye? The eye that sees the good in others. Is it easy to see the good in\nothers? Yes, if we are fond of them; but if we are not, we are likely to\nsee only the evil. But suppose there is no good to be seen, at least\nnot on the surface; why, then the good eye is that which sees the good\nbeneath the surface, which, like the divining-rod, shows where in human\ncharacter gold lies buried, and helps us to penetrate to it. But even\nthis does not exhaust the meaning of the proverb. The good eye is that\nwhich, as it were, sees the good into others, sends its good influence\ninto them, makes them good by believing them to be so. The good eye is a\ncreative eye. Or take the proverb, \"A falsehood is like pebbles in the\nmouth.\" Why not say a falsehood is like a pebble? No, one falsehood is\nlike many pebbles. For every falsehood tends to multiply itself, and\neach separate falsehood is like a pebble--not like bread, which we can\nassimilate, but like a stone, a foreign body, alien to our nature.\nMoreover, the proverb says, A falsehood is like pebbles in the mouth;\nwhich means that these stony falsehoods will choke us, choke the better\nlife in us, unless we cast them out. Again, take such sayings as these\nfrom the Dhammapada: \"As rain breaks through an ill-thatched house,\npassion will break through an unreflecting mind.\" Explain what kind of\nreflection is needed to keep off passion. \"He who is well subdued may\nsubdue others.\" Show what kind of self-control is meant, and in what\nsense others are to be subdued. \"He who holds back anger like a rolling\nchariot, him I call a real driver; other people are but holding the\nreins.\" \"Let a man overcome anger by love; let him overcome evil by\ngood; let him overcome the greedy by liberality, the liar by truth.\"\nDescribe the sort of brake by means of which the rolling chariot of\nanger may be checked in mid-course, and the efficacy of goodness in\novercoming evil. From the Encheiridion it occurs to me to mention the\nsaying, \"Everything has two handles: the one by which it can be borne,\nthe other by which it can not be borne.\" Epictetus himself gives an\nillustration: \"If your brother acts unjustly toward you, do not lay hold\nof the act by that handle wherein he acts unjustly, for that is the\nhandle by which it can not be borne; but lay hold of the other, that he\nis your brother, and you will lay hold of the thing by that handle by\nwhich it can be borne.\" There are also many other illustrations of this\nnoble maxim. Disappointment has two handles, the one by which it can be\nborne, the other by which it can not. Affliction has two handles.\nIllustrate profusely; search out the meaning in detail.\n\nThere is a mine of practical wisdom in these sayings. There exist\nproverbs relating to all the various duties which have been discussed in\nour course; proverbs relating to the pursuit of knowledge; many and\nbeautiful proverbs on the filial and fraternal duties, on courage, on\nhumility, on the importance of keeping promises, on kindness to animals,\non the moral end of civil society. Proverbs should be classified under\ntheir proper heads and used as occasion offers. Permit me, however, to\nadd one word of caution. It is a mistake to teach too many proverbs at a\ntime, to overload the pupil's mind with them. The proverbs selected\nshould be brief, pithy, and profoundly significant. But there should not\nbe too many at a time. It is better to return to the same proverb often,\nand to penetrate deeper into its meaning every time. The value of the\nproverbs is that they serve as pegs in the memory, to which long chains\nof moral reflection can be attached. They are guide-posts pointing with\ntheir short arms to the road of duty; they are voices of mankind\nuttering impressive warnings, and giving clear direction in moments when\nthe promptings of self-interest or the mists of passion would be likely\nto lead us astray.\n\nIt may also be well to select a number of speeches which embody high\nmoral sentiments, like some of the speeches of Isaiah, the speech of\nSocrates before his judges, and others, and, after having explained\ntheir meaning, to cause them to be recited by the pupils. Just as the\ndelivery of patriotic speeches is found useful for inculcating patriotic\nsentiments, so such speeches as these will tend to quicken the moral\nsentiments. He who repeats the speech of another for the time being puts\non the character of the other. The sentiments which are uttered by the\nlips live for the moment in the heart, and leave their mark there.\n\n\n\n\nXVII.\n\nTHE INDIVIDUALIZATION OF MORAL TEACHING.\n\n\nThis subject is of the greatest importance. It really requires extended\nand careful treatment, but a few hints must suffice. The teacher should\nremember that he is educating not boys and girls in general, but\nparticular boys and girls, each of whom has particular faults needing to\nbe corrected and actual or potential virtues to be developed and\nencouraged. Therefore a conscientious study of the character of the\npupils is necessary. This constitutes an additional reason why moral\ninstruction should be given in a daily school rather than in a Sunday\nschool, the opportunities for the study of character being vastly better\nin the former than they can possibly be in the latter. The teacher who\ngives the moral lessons, in undertaking this study, should solicit the\nco-operation of all the other teachers of the school. He should request\nfrom time to time from each of his fellow-teachers reports stating the\ngood and bad traits observed in each pupil, or rather the facts on which\nthe various teachers base their estimates of the good and bad qualities\nof the scholars; for the opinions of teachers are sometimes unreliable,\nare sometimes discolored by prejudice, while facts tell their own\nstory. These facts should be collated by the moral teacher, and, with\nthem as a basis, he may endeavor to work out a kind of chart of the\ncharacter of each of his pupils. It goes without saying, that he should\nalso seek the co-operation of the parents, for the purpose of\ndiscovering what characteristic traits the pupil displays at home; and\nif the reputation which a pupil bears among his companions, can be\nascertained without undue prying, this, too, will be found of use in\nforming an estimate of his disposition. The teacher who knows the\nspecial temptations of his pupils will have many opportunities, in the\ncourse of the moral lessons, to give them pertinent warnings and advice,\nwithout seeming to address them in particular or exposing their faults\nto the class. He will also be able to exercise a helpful surveillance\nover their conduct in school, and to become in private their friend and\ncounselor. Moreover, the material thus collected will in time prove\nserviceable in helping us to a more exact knowledge of the different\nvarieties of human character--a knowledge which would give to the art of\nethical training something like a scientific basis.[22]\n\nFOOTNOTE:\n\n[22] See some remarks on types of character in my lecture on the\nPunishment of Children.\n\n\n\n\nRECAPITULATION.\n\n\nLet us now briefly review the ground we have gone over in the present\ncourse. In the five introductory lectures we discussed the problem of\nunsectarian moral teaching, the efficient motives of good conduct, the\nopportunities of moral influence in schools, the classification of\nduties, and the moral status of the child on entering school.\n\nIn mapping out the primary course we assumed as a starting-point the\nidea that the child rapidly passes through the same stages of evolution\nthrough which the human race has passed, and hence we endeavored to\nselect our material for successive epochs in the child's life from the\nliterature of the corresponding epochs in the life of the race.\n\nIn regard to the method of instruction, we observed that in the fairy\ntales the moral element should be touched on incidentally; that in\nteaching the fables isolated moral qualities should be presented in such\na way that the pupil may always thereafter be able to recognize them;\nwhile the stories display a number of moral qualities in combination and\nhave the value of moral pictures.\n\nIn the primary course the object has been to train the moral\nperceptions; in the grammar course, to work out moral concepts and to\nformulate rules of conduct. The method of getting at these rules may\nagain be described as follows: Begin with some concrete case, suggest a\nrule which apparently fits that case or really fits it, adduce other\ncases which the rule does not fit, change the rule, modify it as often\nas necessary, until it has been brought into such shape that it will fit\nevery case you can think of.\n\nIn planning the lessons on duty which make up the subject matter of the\ngrammar course, we took the ground that each period of life has its\nspecific duties, that in each period there is one paramount duty around\nwhich the others may be grouped, and that each new system of duties\nshould embrace and absorb the preceding one.\n\nIt remains for me to add that the illustrations which I have used in the\ngrammar course are intended merely to serve as specimens, and by no\nmeans to exclude the use of different illustrative matter which the\nteacher may find more suitable. Furthermore, I desire to express the\nhope that it may be possible, without too much difficulty, to eliminate\nwhatever subjective conceptions may be found to have crept into these\nlessons, and that, due deduction having been made, there may remain a\nsubstratum of objective truth which all can accept. It should be\nremembered that these lectures are not intended to take the place of a\ntext-book, but to serve as a guide to the teacher in preparing his\nlessons.\n\nI hope hereafter to continue the work which has thus been begun. In the\nadvanced course, which is to follow the present one, we shall have to\nreconsider from a higher point of view many of the subjects already\ntreated, and in addition to take up such topics as the ethics of the\nprofessions, the ethics of friendship, conjugal ethics, etc., which have\nhere been omitted.\n\nI shall also attempt to indicate the lines for a systematic study of\nbiographies, and to lay out a course of selected readings from the best\nethical literature of ancient and modern times.\n\n\n\n\nAPPENDIX.\n\nTHE INFLUENCE OF MANUAL TRAINING ON CHARACTER.[23]\n\n\nManual training has recently been suggested as one of the means of\ncombating the criminal tendency in the young, and this suggestion is\nbeing received with increasing favor. But until now the theory of manual\ntraining has hardly begun to be worked out. The confidence which is\nexpressed in it is based, for the most part, on unclassified experience.\nBut experience without theory is altogether insufficient. Theory, it is\ntrue, without experience is without feet to stand. But experience\nwithout the guiding and directing help of theory is without eyes to see.\nI shall now offer, in a somewhat tentative way, a few remarks intended\nto be a contribution to the philosophy of manual training as applied to\nthe reformation of delinquent children. I shall confine myself, however,\nto one type of criminality in children--a not uncommon type--that of\nmoral deterioration arising from weakness of the will.\n\nIn the first place, let us distinguish between feeling, desiring, and\nwilling. A person who is without food feels hunger. A person who, being\nhungry, calls up in his mind images of food, will experience a desire. A\nperson who adopts means to obtain food performs an act of the will. A\nRussian prisoner in Siberia who suffers from the restraints of\nconfinement is in a state of feeling. The same person, when he recalls\nimages of home and friends, is in a state of desire; but when he sets\nabout adopting the means to effect his escape, concerts signals with his\nfellow-prisoners, undermines the walls of his dungeon, etc., he is\nperforming acts of the will. Permit me to call particular attention to\nthe fact that the will is characterized at its birth by the intellectual\nfactor which enters into it; for the calculation of means to ends is an\nintellectual process, and every conscious act of volition involves such\na process. If the will is thus characterized at its birth, we can at\nonce anticipate the conclusion that any will will be strong in\nproportion as the intellectual factor in it predominates. It was said by\none of the speakers that \"an ounce of affection is better than a ton of\nintellect.\" Give me a proper mixture of the two. Give me at least an\nounce of intellect together with an ounce of affection. There is great\ndanger lest we exaggerate the importance of the emotions for morality.\nThe opinion is widely entertained that good feeling, kind feeling,\nloving feeling, is the whole of morality, or, at least, the essential\nfactor in it. But this opinion is surely erroneous. The will may be\ncompared to the power which propels a ship through the waves. Feeling is\nthe rudder. The intellect is the helmsman.\n\nLet me give illustrations to bring into view the characteristics of a\nstrong and of a weak will. Great inventors, great statesmen, great\nreformers, illustrate strength of will. We note in them especially\ntenacity of purpose and a marvelous faculty for adjusting and\nreadjusting means to ends. Persons who are swayed by the sensual\nappetites illustrate weakness of will. We note in them vacillation of\npurpose, and the power of adjusting means to ends only in its\nrudimentary form. The ideas of virtue are complex. No one can illustrate\nvirtue on a high plane unless he is capable of holding in mind long\ntrains and complex groups of ideas. The lowest vices, on the other hand,\nare distinguished by the circumstance that the ends to which they look\nare simple, and the means employed often of the crudest kind. Thus,\nsuppose that a person of weak will is hungry. He knows that gold will\nbuy food. He adopts the readiest way to get gold. Incapable of that long\nand complex method of attaining his end, which is exhibited, for\ninstance, by the farmer who breaks the soil, plants the corn, watches\nhis crops, and systematizes his labors from the year's beginning to its\nend, he takes the shortest road toward the possession of gold--he\nstretches forth his hand and takes it where he finds it. The man of weak\nwill, who has a grudge against his rival, is not capable of putting\nforth a sustained and complex series of efforts toward obtaining\nsatisfaction, for instance, by laboring arduously to outstrip his rival.\nHe is, furthermore, incapable of those larger considerations, those\ncomplex groups of ideas relating to society and its permanent interests,\nwhich check the angry passions in the educated. He gives free and\nimmediate rein to the passion as it rises. He takes the readiest means\nof getting satisfaction: he draws the knife and kills. The man of weak\nwill, who burns with sensual desire, assaults the object of his desire.\nThe virtues depend in no small degree on the power of serial and complex\nthinking. Those vices which are due to weakness of will are\ncharacterized by the crudeness of the aim and the crudeness of the\nmeans.\n\nTo strengthen the will, therefore, it is necessary to give to the person\nof weak will the power to think connectedly, and especially to reach an\nend by long and complex trains of means.\n\nLet us pause here for a moment to elucidate this point by briefly\nconsidering a type of criminality which is familiar to all guardians of\ndelinquent children. This type is marked by a group of salient traits,\nwhich may be roughly described as follows: Mental incoherency is the\nfirst. The thoughts of the child are, as it were, slippery, tending to\nglide past one another without mutual attachments. A second trait is\nindolence. A third, deficiency in the sense of shame; to which may be\nadded that the severest punishments fail to act as deterrents.\n\nMental incoherency is the leading trait, and supplies the key for the\nunderstanding of the others. Lack of connectedness between ideas is the\nradical defect. Each idea, as it rises, becomes an impulse, and takes\neffect to the full limit of its suggestions. A kind thought rises in the\nmind of such a child, and issues in a demonstrative impulse of\naffection. Shortly after, a cruel thought may rise in the mind of the\nsame child; and the cruel thought will, in like manner, take effect in a\ncruel act. Children answering to this type are alternately kind,\naffectionate, and cruel. The child's indolence is due to the same\ncause--lack of connectedness between ideas. It is incapable of sustained\neffort, because every task implies the ability to pass from one idea to\nrelated ideas. The child is deficient in shame, because the sense of\nshame depends on a vivid realization of the idea of self. The idea of\nself, however, is a complex idea, which is not distinctly and clearly\npresent to such a child. Lastly, the most severe punishments fail to act\nas deterrents for the same reason. The two impressions left in the mind,\n\"I did a wrong,\" \"I suffered a pain,\" lie apart. The memory of one does\nnot excite the recollection of the other. The thought of the wrong does\nnot lift permanently into consciousness the thought of the pain which\nfollowed. The punishment, as we say, is quickly forgotten. If,\ntherefore, we wish to remedy a deep-seated defect of this kind, if we\nwish to cure a weak will, in such and all similar cases we must seek to\nestablish a closer connection between the child's ideas.\n\nThe question may now be asked, Why should we not utilize to this end the\nordinary studies of the school curriculum--history, geography,\narithmetic, etc.? All of these branches exercise and develop the faculty\nof serial and complex thinking. Any sum in multiplication gives a\ntraining of this kind. Let the task be to multiply a multiplicand of\nfour figures by a multiplier of three. First the child must multiply\nevery figure in the multiplicand by the units of the multiplier and\nwrite down the result; then by the tens, and then by the hundreds, and\ncombine these results. Here is a lesson in combination, in serial, and,\nfor a young child, somewhat complex thinking. Let the task be to bound\nthe State of New York. The child must see the mental picture of the\nState in its relation to other States and parts of States, to lakes and\nrivers and mountains--a complex group of ideas. Or, let it be required\nto give a brief account of the American Revolution. Here is a whole\nseries of events, each depending on the preceding ones. Why, then, may\nwe not content ourselves with utilizing the ordinary studies of the\nschool curriculum? There are two reasons.\n\nFirst, because history, geography, and arithmetic are not, as a rule,\ninteresting to young children, especially not to young children of the\nclass with which we are now dealing. These listless minds are not easily\nroused to an interest in abstractions. Secondly, it is a notorious fact\nthat intellectual culture, pure and simple, is quite consistent with\nweakness of the will. A person may have very high intellectual\nattainments, and yet be morally deficient. I need hardly warn my\nreflective hearers that, when emphasizing the importance for the will of\nintellectual culture, I had in mind the intellectual process as applied\nto acts. To cultivate the intellect in its own sphere of contemplation\nand abstraction, apart from action, may leave the will precisely as\nfeeble as it was before.\n\nAnd now, all that has been said thus far converges upon the point that\nhas been in view from the beginning--the importance of manual training\nas an element in disciplining the will. Manual training fulfills the\nconditions I have just alluded to. It is interesting to the young, as\nhistory, geography, and arithmetic often are not. Precisely those pupils\nwho take the least interest or show the least aptitude for literary\nstudy are often the most proficient in the workshop and the\nmodeling-room. Nature has not left these neglected children without\nbeautiful compensations. If they are deficient in intellectual power,\nthey are all the more capable of being developed on their active side.\nThus, manual training fulfills the one essential condition--it is\ninteresting. It also fulfills the second. By manual training we\ncultivate the intellect in close connection with action. Manual training\nconsists of a series of actions which are controlled by the mind, and\nwhich react on it. Let the task assigned be, for instance, the making of\na wooden box. The first point to be gained is to attract the attention\nof the pupil to the task. A wooden box is interesting to a child, hence\nthis first point will be gained. Lethargy is overcome, attention is\naroused. Next, it is important to keep the attention fixed on the task:\nthus only can tenacity of purpose be cultivated. Manual training enables\nus to keep the attention of the child fixed upon the object of study,\nbecause the latter is concrete. Furthermore, the variety of occupations\nwhich enter into the making of the box constantly refreshes this\ninterest after it has once been started. The wood must be sawed to line.\nThe boards must be carefully planed and smoothed. The joints must be\naccurately worked out and fitted. The lid must be attached with hinges.\nThe box must be painted or varnished. Here is a sequence of means\nleading to an end, a series of operations all pointing to a final object\nto be gained, to be created. Again, each of these means becomes in turn\nand for the time being a secondary end; and the pupil thus learns, in an\nelementary way, the lesson of subordinating minor ends to a major end.\nAnd, when finally the task is done, when the box stands before the boy's\neyes a complete whole, a serviceable thing, sightly to the eyes, well\nadapted to its uses, with what a glow of triumph does he contemplate his\nwork! The pleasure of achievement now comes in to crown his labor; and\nthis sense of achievement, in connection with the work done, leaves in\nhis mind a pleasant after-taste, which will stimulate him to similar\nwork in the future. The child that has once acquired, in connection with\nthe making of a box, the habits just described, has begun to master the\nsecret of a strong will, and will be able to apply the same habits in\nother directions and on other occasions.\n\nOr let the task be an artistic one. And let me here say that manual\ntraining is incomplete unless it covers art training. Many otherwise\nexcellent and interesting experiments in manual training fail to give\nsatisfaction because they do not include this element. The useful must\nflower into the beautiful, to be in the highest sense useful. Nor is it\nnecessary to remind those who have given attention to the subject of\neducation how important is the influence of the beautiful is in\nrefining the sentiments and elevating the nature of the young. Let the\ntask, then, be to model a leaf, a vase, a hand, a head. Here again we\nbehold the same advantages as in the making of the box. The object is\nconcrete, and therefore suitable for minds incapable of grasping\nabstractions. The object can be constantly kept before the pupil's eyes.\nThere is gradual approximation toward completeness, and at last that\nglow of triumph! What child is not happy if he has produced something\ntangible, something that is the outgrowth of his own activity,\nespecially if it be something which is charming to every beholder?\n\nAnd now let me briefly summarize certain conclusions to which reflection\nhas led me in regard to the subject of manual training in reformatory\ninstitutions. Manual training should be introduced into every\nreformatory. In New York city we have tested a system of work-shop\nlessons for children between six and fourteen. There is, I am persuaded,\nno reason why manual training should not be applied to the youngest\nchildren in reformatories. Manual training should always include art\ntraining. The labor of the children of reformatories should never be let\nto contractors. I heartily agree with what was said on that subject this\nmorning. The pupils of reformatories should never make heads of pins or\nthe ninetieth fraction of a shoe. Let there be no machine work. Let the\npupils turn out complete articles, for only thus can the full\nintellectual and moral benefits of manual training be reaped.\nAgriculture, wherever the opportunities are favorable, offers, on the\nwhole, the same advantages as manual training, and should be employed\nif possible, in connection with it.\n\nI have thus far attempted to show how the will can be made strong. But a\nstrong will is not necessarily a good will. It is true, there are\ninfluences in manual training, as it has been described, which are\nfavorable to a virtuous disposition. Squareness in things is not without\nrelation to squareness in action and in thinking. A child that has\nlearned to be exact--that is, truthful--in his work will be predisposed\nto be scrupulous and truthful in his speech, in his thought, in his\nacts. The refining and elevating influence of artistic work I have\nalready mentioned. But, along with and over and above all these\ninfluences, I need hardly say to you that, in the remarks which I have\noffered this evening, I have all along taken for granted the continued\napplication of those tried and excellent methods which prevail in our\nbest reformatories. I have taken for granted that isolation from\nsociety, which shuts out temptation; that routine of institutional life,\nwhich induces regularity of habit; that strict surveillance of the whole\nbody of inmates and of every individual, which prevents excesses of the\npassions, and therefore starves them into disuse. I have taken for\ngranted the cultivation of the emotions, the importance of which I am\nthe last to undervalue. I have taken for granted the influence of good\nexample, good literature, good music, poetry, and religion. All I have\nintended to urge is that between good feeling and the realization of\ngood feeling there exists, in persons whose will-power is weak, a\nhiatus, and that manual training is admirably adapted to fill that\nhiatus.\n\nThere is another advantage to be noted in connection with manual\ntraining--namely, that it develops the property sense. What, after all,\napart from artificial social convention, is the foundation of the right\nof property? On what basis does it rest? I have a proprietary right in\nmy own thoughts. I have a right to follow my tastes in the adornment of\nmy person and my house. I have a right to the whole sphere of my\nindividuality, my selfhood; and I have a right in _things_ so far as I\nuse them to express my personality. The child that has made a wooden box\nhas put a part of himself into the making of that box--his thought, his\npatience, his skill, his toil--and therefore the child feels that that\nbox is in a certain sense his own. And as only those who have the sense\nof ownership are likely to respect the right of ownership in others, we\nmay by manual training cultivate the property sense of the child; and\nthis, in the case of the delinquent child, it will be admitted, is no\nsmall advantage.\n\nI have confined myself till now to speaking of the importance of manual\ntraining in its influence on the character of delinquent children. I\nwish to add a few words touching the influence of manual training on\ncharacter in general, and its importance for children of all classes of\nsociety. I need not here speak of the value of manual training to the\nartisan class. That has been amply demonstrated of late by the many\ntechnical and art schools which the leading manufacturing nations of\nEurope have established and are establishing. I need not speak of the\nvalue of manual training to the future surgeon, dentist, scientist, and\nto all those who require deftness of hand in the pursuit of their\nvocations. But I do wish to speak of the value of manual training to the\nfuture lawyer and clergyman, and to all those who will perhaps never be\ncalled upon to labor with their hands. Precisely because they will not\nlabor with their hands is manual training so important for them--in the\ninterest of an all-round culture--in order that they may not be entirely\ncrippled on one side of their nature. The Greek legend says that the\ngiant Antaeus was invincible so long as his feet were planted on the\nsolid earth. We need to have a care that our civilization shall remain\nplanted on the solid earth. There is danger lest it may be developed too\nmuch into the air--that we may become too much separated from those\nprimal sources of strength from which mankind has always drawn its\nvitality. The English nobility have deliberately adopted hunting as\ntheir favorite pastime. They follow as a matter of physical exercise, in\norder to keep up their physical strength, a pursuit which the savage man\nfollowed from necessity. The introduction of athletics in colleges is a\nmove in the same direction. But it is not sufficient to maintain our\nphysical strength, our brute strength, the strength of limb and muscle.\nWe must also preserve that spiritualized strength which we call\nskill--the tool-using faculty, the power of impressing on matter the\nstamp of mind. And the more machinery takes the place of human labor,\nthe more necessary will it be to resort to manual training as a means of\nkeeping up skill, precisely as we have resorted to athletics as a means\nof keeping up strength.\n\nThere is one word more I have to say in closing. Twenty-five years ago,\nas the recent memories of Gettysburg recall to us, we fought to keep\nthis people a united nation. Then was State arrayed against State.\nTo-day class is beginning to be arrayed against class. The danger is not\nyet imminent, but it is sufficiently great to give us thought. The chief\nsource of the danger, I think, lies in this, that the two classes of\nsociety have become so widely separated by difference of interests and\npursuits that they no longer fully understand one another, and\nmisunderstanding is the fruitful source of hatred and dissension. This\nmust not continue. The manual laborer must have time and opportunity for\nintellectual improvement. The intellectual classes, on the other hand,\nmust learn manual labor; and this they can best do in early youth, in\nthe school, before the differentiation of pursuits has yet begun. Our\ncommon schools are rightly so named. The justification of their support\nby the State is not, I think, as is sometimes argued, that the State\nshould give a sufficient education to each voter to enable him at least\nto read the ballot which he deposits. This is but a poor equipment for\ncitizenship at best. The justification for the existence of our common\nschools lies rather in the bond of common feeling which they create\nbetween the different classes of society. And it is this bond of common\nfeeling woven in childhood that has kept and must keep us a united\npeople. Let manual training, therefore, be introduced into the common\nschools; let the son of the rich man learn, side by side with the son of\nthe poor man, to labor with his hands; let him thus practically learn to\nrespect labor; let him learn to understand what the dignity of manual\nlabor really means, and the two classes of society, united at the root,\nwill never thereafter entirely grow asunder.\n\nA short time ago I spent an afternoon with a poet whose fame is familiar\nto all. There was present in the company a gentleman of large means,\nwho, in the course of conversation, descanted upon the merits of the\nprotective system, and spoke in glowing terms of the growth of the\nindustries of his State and of the immense wealth which is being\naccumulated in its large cities. The aged poet turned to him, and said:\n\"That is all very well. I like your industries and your factories and\nyour wealth; but, tell me, do they turn out men down your way?\" That is\nthe question which we are bound to consider. _Is this civilization of\nours turning out men_--manly men and womanly women? Now, it is a\ncheering and encouraging thought that technical labor, which is the\nsource of our material aggrandizement, may also become, when employed in\nthe education of the young, the means of enlarging their manhood,\nquickening their intellect, and strengthening their character.\n\n\nTHE END.\n\nFOOTNOTE:\n\n[23] An address delivered before the National Conference of Charities\nand Correction, at Buffalo, July, 1888.\n\n\n\n\nD. APPLETON & CO.'S PUBLICATIONS.\n\nMISCELLANEOUS WORKS OF HERBERT SPENCER.\n\n\n_EDUCATION: Intellectual, Moral, and Physical._ 12mo. Paper, 50 cents;\ncloth, $1.25.\n\n     CONTENTS: What Knowledge is of most Worth?--Intellectual\n     Education.--Moral Education.--Physical Education.\n\n\n_SOCIAL STATICS._ By HERBERT SPENCER. New and revised edition, including\n\"The Man _versus_ the State,\" a series of essays on political tendencies\nheretofore published separately. 12mo. 420 pages. Cloth, $2.00.\n\n     Having been much annoyed by the persistent quotation from the old\n     edition of \"Social Statics,\" in the face of repeated warnings, of\n     views which he had abandoned, and by the misquotation of others\n     which he still holds, Mr. Spencer some ten years ago stopped the\n     sale of the book in England and prohibited its translation. But the\n     rapid spread of communistic theories gave new life to these\n     misrepresentations; hence Mr. Spencer decided to delay no longer a\n     statement of his mature opinions on the rights of individuals and\n     the duty of the state.\n\n     CONTENTS: Happiness as an Immediate Aim.--Unguided Expediency.--The\n     Moral-Sense Doctrine.--What is Morality?--The Evanescence\n     [? Diminution] of Evil.--Greatest Happiness must be sought\n     indirectly.--Derivation of a First Principle.--Secondary Derivation\n     of a First Principle.--First Principle.--Application of this First\n     Principle.--The Right of Property.--Socialism.--The Right of\n     Property in Ideas.--The Rights of Women.--The Rights of\n     Children.--Political Rights.--The Constitution of the State.--The\n     Duty of the State.--The Limit of State-Duty.--The Regulation of\n     Commerce.--Religious Establishments.--Poor-Laws.--National\n     Education.--Government Colonization.--Sanitary\n     Supervision.--Currency Postal Arrangements, etc.--General\n     Considerations.--The New Toryism.--The Coming Slavery.--The Sins of\n     Legislators.--The Great Political Superstition.\n\n\n_THE STUDY OF SOCIOLOGY._ The fifth volume in the International\nScientific Series. 12mo. Cloth, $1.50.\n\n     CONTENTS: Our Need of it--Is there a Social Science?--Nature of the\n     Social Science.--Difficulties of the Social Science.--Objective\n     Difficulties.--Subjective Difficulties, Intellectual.--Subjective\n     Difficulties, Emotional.--The Educational Bias--The Bias of\n     Patriotism.--The Class-Bias.--The Political Bias.--The Theological\n     Bias.--Discipline.--Preparation in Biology.--Preparation in\n     Psychology.--Conclusion.\n\n\nNew York: D. APPLETON & CO., 1, 3, & 5 Bond Street.\n\n\n     \"This work marks an epoch in the history-writing of this\n     country.\"--_St. Louis Post-Dispatch._\n\n[Illustration: COLONIAL COURT-HOUSE. PHILADELPHIA, 1707.]\n\n_THE HOUSEHOLD HISTORY OF THE UNITED STATES AND ITS PEOPLE._ FOR YOUNG\nAMERICANS. By EDWARD EGGLESTON. Richly illustrated with 350 Drawings, 75\nMaps, etc. Square 8vo. Cloth, $2.50.\n\n\n_FROM THE PREFACE._\n\nThe present work is meant, in the first instance, for the young--not\nalone for boys and girls, but for young men and women who have yet to\nmake themselves familiar with the more important features of their\ncountry's history. By a book for the young is meant one in which the\nauthor studies to make his statements clear and explicit, in which\ncurious and picturesque details are inserted, and in which the writer\ndoes not neglect such anecdotes as lend the charm of a human and\npersonal interest to the broader facts of the nation's story. That\nhistory is often tiresome to the young is not so much the fault of\nhistory as of a false method of writing by which one contrives to relate\nevents without sympathy or imagination, without narrative connection or\nanimation. The attempt to master vague and general records of kiln-dried\nfacts is certain to beget in the ordinary reader a repulsion from the\nstudy of history--one of the most important of all studies for its\nwidening influence on general culture.\n\n[Illustration: INDIAN'S TRAP.]\n\n     \"Fills a decided gap which has existed for the past twenty years in\n     American historical literature. The work is admirably planned and\n     executed, and will at once take its place as a standard record of\n     the life, growth, and development of the nation. It is profusely\n     and beautifully illustrated.\"--_Boston Transcript._\n\n     \"The book in its new dress makes a much finer appearance than\n     before, and will be welcomed by older readers as gladly as its\n     predecessor was greeted by girls and boys. The lavish use the\n     publishers have made of colored plates, woodcuts, and photographic\n     reproductions, gives an unwonted piquancy to the printed page,\n     catching the eye as surely as the text engages the mind.\"--_New\n     York Critic._\n\n[Illustration: GENERAL PUTNAM.]\n\n     \"The author writes history as a story. It can never be less than\n     that. The book will enlist the interest of young people, enlighten\n     their understanding, and by the glow of its statements fix the\n     great events of the country firmly in the mind.\"--_San Francisco\n     Bulletin._\n\n\nNew York: D. APPLETON & CO., 1, 3, & 5 Bond Street.\n\n\n\n\n\nEnd of Project Gutenberg's The Moral Instruction of Children, by Felix Adler\n\n*** ","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":"##\n\nTHE DIRT CHRONICLES\n\nCopyright \u00a9 2011 by Kristyn Dunnion\n\nAll rights reserved. No part of this book may be reproduced or used in any form by any means\u2014graphic, electronic, or mechanical\u2014without the prior written permission of the publisher, except by a reviewer, who may use brief excerpts in a review, or in the case of photocopying in Canada, a licence from Access Copyright.\n\nARSENAL PULP PRESS  \n\n#101-211 East Georgia St.  \nVancouver, BC  \nCanada V6A 1Z6  \narsenalpulp.com\n\nThe publisher gratefully acknowledges the support of the Canada Council for the Arts and the British Columbia Arts Council for its publishing program, and the Government of Canada through the Canada Book Fund and the Government of British Columbia through the Book Publishing Tax Credit Program for its publishing activities.\n\nEfforts have been made to locate copyright holders of source material wherever possible. The publisher welcomes hearing from any copyright holders of material used in this book who have not been contacted.\n\nLyrics reprinted with permission.\n\n\"Black Iron Heart\" written and composed by A Storm of Light. \"Object, Refuse, Reject Abuse\" and \"Deaf, Dumb and Male\" written and composed by DIRT.\n\n\"In The Air Tonight,\" Words & Music by Phil Collins, \u00a9 Copyright 1981 Philip Collins Limited. Imagem Music. All Rights Reserved. International Copyright Secured. Used by permission of Music Sales Limited.\n\nAn earlier draft of \"Stargazing at Eddie's\" was published by Fab 310, December 2006.  \nAn excerpt from \"Ferret Hunt\" was published in _Winterplay! Pinkplaymags,_ December 2009.\n\nThis is a work of fiction. Any resemblance of characters to persons either living or deceased is purely coincidental.\n\nBook design by Shyla Seller  \nAuthor photograph by Jamie Carlisle  \nCover photography by Lachlan Black, www.flickr.com\/photos\/thebadseed\/\n\nPrinted and bound in Canada\n\nLibrary and Archives Canada Cataloguing in Publication:\n\nDunnion, Kristyn, 1969-  \nThe dirt chronicles [electronic resource] \/ Kristyn Dunnion.\n\nElectronic monograph in PDF format.  \nIssued also in print format.  \nISBN 978-1-55152-431-3\n\nI. Title.\n\nPS8557.U552D57 2011a C813\u2032.6 C2011-903324-0\n\n## Acknowledgments\n\nThis book is dedicated to the kids.\n\nIn loving memory of Will Munro (1975\u20132010), pied punk piper who brought us all together, and Elizabeth \"Luscious\" Baxter (1978\u20132010), who fed us her generous, incomparable love.\n\nThank you to Carolyn Beck, Anne Laurel Carter, Anna Kerz, Shannon Quinn, and Cheryl Rainfield, who gave tremendous encouragement and critiqued earlier drafts. Thank you to Greg Hawkes, Annie Ouellette, and Annetta and Patrick Dunnion for consultation on vital matters. To Cherish Violet Blood and Tammy Manitowabe who first brought me to Wiky on the Red Pepper Arts Spectacle bus. To John MacDonald, for keeping it real.\n\nThe author gratefully acknowledges the Toronto Arts Council and the Ontario Arts Council for financial support.\n\n##\n\n## Contents\n\nMigrant\n\nTwo Ton: An Opera in Three Acts\n\nStargazing at Eddie's\n\nSeven-Dollar Blow\n\nHappy House\n\nToddlers and Tiaras\n\nPig House Party\n\nShaker Baker\n\nBig House\n\nPiggy Goes to Market\n\nFerret Hunt: A Three-Act Play\n\nLedge\n\nBush\n\nAbout the Author\n\n# Migrant\n\n(for Patrick)\n\nYou can blame me for coming up with the plan. But it wasn't so much _forcible confinement_ or _abduction_ like the papers said. Hell, I rescued this kid from a life of hard labour and petty disappointment. He was born in the wrong place at the wrong time and, frankly, I consider it an act of man-love solidarity, like assisted suicide.\n\nI'd nursed a wicked hangover all day and was finally heading home in the Coupe, sipping a premixed Caesar I kept tucked between my legs. Folks out to see the lake on a Sunday drive, maybe get an ice cream down at the docks, they'd seen my hand-painted sign: Larry's Putt Putt Minigolf come to slap down their money, have a game with the kids. Sadists, if they knew how little I wanted their business that day with my headache, my dry mouth and withered ego. They were flies buzzing. Their shrieking kids fought over the clubs. Worn out, sweaty and bickering, they were now going home, just like me, east or west on the two-lane highway that followed the Lake Erie shoreline, County Road 20. The sun burned its way to the horizon, overheating the car. Heading west, I had to squint behind the steering wheel, having lost my sunglasses during last night's debauchery. The windows were all the way down, but driving sixty clicks was not making much breeze.\n\nI cranked the radio\u2014\"101 FM, the home of rock and roll, baby!\" The steady drum intro, the opening discord, the distorted voice: \"Iron Man,\" off Black Sabbath's genius second album. I air-drummed on the wheel, banged my soon-to-be-long-again hair to the beat. I croaked along with Ozzy. The bass line thumped through my dashboard; it jangled the keys that hung by my knee. I wanted to gun it, travel at light speed, and sail in time with the music.\n\nBut right ahead of me about a dozen men rode their bicycles in a line at the very edge of the asphalt. A dozen buttoned-up, long-sleeved, cotton-polyester white shirts, all in a row. They wore deep-billed baseball caps\u2014ones with John Deere or Del Monte logos\u2014low over their shining jet hair, shade for the setting sun. They were going home too, back to the shacks they lived in during the months they worked in Ontario. There wasn't enough room to really pass them safely, and the east-bound cars were not budging. Bikes often got bullied into the gravel shoulder on this stretch of road, even beyond it, sometimes landing in the deep ditches that collect run-off rain water from the fields. Probably because of that, no one other than migrant workers ever rode along here. Christ, they had no other way to get around. I may be a First Class Ass, as Sharon liked to say, but I'm not a road hog.\n\nI was at the tail end of their parade, debating whether or not to pass them all. That's when I first noticed the kid, one dark rebel in the line of white-and-beige clothes. I thought I was hallucinating. I leaned into the glare. I took my foot off the gunner, let the engine purr down. _No_. It just so happened he was wearing a Sabbath 1978 World Tour T-shirt, faded black. I used to have the same one. His black hat was swivelled sideways and his red bandanna was tied around his face like a bank robber's, I guess to keep out field dust, whipped up by the cars.\n\nI kept pace with the kid and watched out the side window. He immediately turned toward the music. He tugged the bandanna down and grinned, his dazzling smile a lightning bolt that split his handsome brown face almost in two. A balloon expanded inside my chest, making it tight and hot in there. Devil horns up, the kid shook his hand at me. I shook mine back. The kid belted out the chorus and I joined in. We were heavy metal brothers, separated at birth.\n\nBehind me some jackass honked. I gave the one-finger salute out my window. Can't even have a quality rock-and-roll moment with a stranger, for Chrissakes. The driver shook his hands from behind the wheel of his Honda Civic. Times have changed when you can drive foreign around here and _not_ be worried about a slit tire or a fist fight. Mostly we got Chryslers and GM trucks, even though the auto industry pretty much laid off every other uncle. Someone else honked farther back in the line of cars forming behind me, our procession dragging into the sunset ahead. Honda Civic jackass behind me edged into the oncoming lane. He wanted to pass on a solid with hardly a breath before the oncoming car. I rode the line to block him, tell him what's what.\n\nSharon always called me a stubborn man. _Maybe_. But the hell I was heaving off for some 'tard in an import. I drained my Caesar and lobbed the empty bottle into the back seat. I was beginning to consider myself the kid's bodyguard, a dark green 1969 Impala patrolling beside his bike, like we were in a gang. I waited for the instrumental part of the song, where the drums go crazy and your blood runs faster. I revved my engine. Giving the cyclists a wide berth, I gunned it, scaring the east-bound cars. I peeled away, the kid still rocking it old-school, thumbs up. I laid some fast tracks. About a quarter mile up, I cut a sharp right onto a side road, fishtailing into the dirt, sending a spray of small stones and dust onto that twat Honda that was trying to keep up with me.\n\nAh, did that kid ever make my day.\n\nBut seriously, you got to know those shirts aren't easy to come by. Not even here in Ass Crack, Ontario, where the mullet never left and acid-wash jeans are still raring to go. Later that night, I decimated the neighbours with _The Number of the Beast_ , my nearly forgotten Iron Maiden record. I downed a quart of rye and ginger ale. I dug through my drawers, the hall closet, the now empty second bedroom (Sharon's World), and even the mildewy boxes in the garage. I was searching for lost treasure\u2014ripped posters I once worshipped on my bedroom walls, concert shirts I'd long since outgrown, my vinyl collection, my most sacred teenaged belongings. Underneath a box of _Star Wars_ action figures was the dispossessed electric guitar and amp of my youth. I'd forgotten all about it. _Poor baby_. I opened the dusty case. The sunburst Fender glared. I lifted it. \"Shh, shh,\" I slurred. I dragged the amp into the living room and cleared out a corner.\n\nAfter Sharon moved in, I'd packed my crap up, bit by bit. She complained she had no space for her shit. _Sharon_. What the hell had I been thinking? Clearly I would've been a famous musician by now, if I hadn't let that woman run my life. I left my rediscovered things strewn about the bungalow and in piles on the lawn. The mess announced my triumphant return to bachelorhood. Maybe I'd even get a roommate, a partner in crime! Still, no matter how many cupboards I rifled through, how much crap I dumped on the floor, I couldn't find that one missing box. _Where was the damn shirt?_\n\nI stumbled through the living room, tripped on an open suitcase and landed on the worn out couch. I decided to stay there. I was hammered again. My last thought, before passing out, was highly unoriginal and not worth repeating.\n\nI woke with a pain between my eyes. My mossy tongue rotted in my foul mouth. Sunlight from the living room window burned a thin strip across the couch, across my face. My pits reeked. My skin was clammy. No surprise, really. In Ass Crack, summers are hot, humid. By mid-morning your clothes stick to you, your hair goes frizzy and awful. Noon, it's unbearable. You wouldn't know that unless you're from here or you been here.\n\nI thought about the hot drive to work. About sitting in that stifling shack where I rented out the clubs. Who would choose to do this today? I was my own boss. Then I thought about my Visa bill, cable, alimony\u2014to make any money, I'd have to deal with people. I'd have to sit there and smile and try not to let my ghastly beer farts scare them off. _Groan_. I rolled over, blocking the hot sun strip with my shoulder. I faced the back of the ratty couch. It was the Summer of Suck.\n\nWhen you're a kid, you live for it. No school, no job. You bust out in all your heated glory like a feral Tom running the neighbourhood, all day long and half the night, too. When you get sick of the heat or if you have cousins visiting, you go down to Lake Erie. There's always someone there. You go west to Cedar Beach; there's the broken pier you dive off, the best spot being right by the warning sign about rocks. Or off the bridge, where you find one or two old men trolling for catfish. There's Ken's Variety and Bait Shoppe, where you get candy and ice cream and worms for your line. The actual beach has usually got dead fish on the sand, clumps of stinking seaweed, tampon applicators, and broken glass. But the water is not too deep and the waves are nice and big.\n\nWhen you're a teenager, you get the beach bonfires going at night. You steal booze from your parents' stash or you pay that old wino in town an extra dollar to buy a bottle at the liquor store. You get kids to bring their teenaged cousins so you can all check each other out. You roast marshmallows, you try to make out. Someone always drinks too much and then they puke.\n\nWhen you're an adult, though, you mostly just stay in town or out on the concession roads, wherever you live, and suffer the heat. You get up and go to work and earn your shit pay. You come home, eat too much, and sweat in front of the television. You drink yourself to sleep. You dream of an air conditioner on sale at the Walmart.\n\nYes, sir. Ass Crack is hot and flat and the fields run for miles, except where the roads cut through. Nowadays the fields are almost all covered by aluminum-framed plastic greenhouses, hundreds of them everywhere, unending. Fields or greenhouses, you still need hard workers to turn and plant and tend and pick food from dirt. To lug those heavy tomato crates, those fruit baskets, those apples and cherries, peppers and squash. I did it myself for a few years: detassling corn with the other pot-smoking burn-outs when I was sixteen, finally tall enough. Nearly broke my back picking beans and strawberries, too. Nowadays, kids don't do that. They got machines for the corn, and foreigners for the picking.\n\n\"Seems to me our only real shortage is hard-working Canadians.\" I drained more of my beer and belched. \"'Spite of all those layoffs.\" I looked around the pub for a response. A circle of large, balding men glared. One particularly neckless dude wearing a Windsor Spitfires jersey growled.\n\n\"You're too good for fieldwork?\" I said. \"You got something better to do?\"\n\nThe beer-bellied dude at the next barstool told me to shut up. He was solid, like a Kenmore fridge. His nostrils flared.\n\nThe bartender slapped my bill on the bar. \"I'd pay that before Donny here kicks your teeth in,\" he said.\n\n\"My point,\" I continued, \"is nobody here wants to break their back in the heat for shit money. Cushy union brats.\"\n\nDonny stood up. \"Get your ass out of here, goof.\" He pushed me hard in the chest.\n\nNo one had touched me in a long time.\n\nThe bartender tapped the circled total on my bill. I pulled out my wallet.\n\n\"Used to be Frenchies, come pick the fruit,\" I mumbled. \"Then Haitians. Now it's Mexicans. Salvadorans.\" My chest glowed where Donny's meaty hand had been. In my confused state, it felt a bit like love.\n\nThe bartender did not give me my change.\n\n\"Ah, fuck it,\" I said. I walked towards the door. \"You'd think there'd be open minds in a big city like Windsor. Can't even talk to some people.\"\n\nI left, but not before urinating on the front stoop.\n\n_Take that, assholes._\n\nThe other thing about Windsor, any city really, is you can't see a thing in the night sky, all those buildings, that electric light. But out in the country, now that's darkness. Sky so black you can taste it. And the stars\u2014it's like God puked up a glow stick. Barns as large as ships: invisible in the night, unless they're splattered with oncoming headlights. The horses, the pigs are all tucked into their stalls. Hens curled up quiet as cats around the yard. No cows here, no rolling hills for grazing, nothing like that. It's dead flat.\n\nCops just sit out at the Fifth Concession, that notorious country road, and turn out their lights. They see everyone coming down from the bypass, coming back from Windsor like me, or from the bush parties or whatnot, and they clock you without batting a lash. Unless you're in the habit of driving blind, like I am, when you outsmart those fucks at their own game and shut off _your_ headlights. Which reminded me to roll up the window\u2014didn't need to tip them off with my favourite station filling the air with power chords: Steppenwolf, Rush, April Wine. Driving blind, I didn't even need to stop at the signs. I'd just plow straight home fast as I liked, tight as I was. I could always see some joker coming at me, right, cuz he'd have _his_ lights on. I sang out loud when they cued up Led Zeppelin: \"Been a long lonely, lonely, lonely, lonely time.\"\n\nI was thumping the steering wheel, keeping the beat. I'd already forgotten those knobs at the bar. I was remembering being sixteen, getting my licence, shitting myself, and driving for the first time on this very road in broad daylight. I had reached over to change the radio station and ended up in a twelve-foot ditch\u2014true story. Right about here. Driving just ain't right without music. Around here, folks got a healthy respect for country classics, a mild curiosity about the blues\u2014what started it all\u2014but mostly, a god-sworn allegiance to classic rock.\n\nThat got me thinking. A guy doesn't just give away his concert shirts. No, sir. That's unheard of. I was wondering about that rebel Mexican, working the fields and wearing the Sabbath. How the hell did _he_ get a hold of that shirt? Maybe that makes me a jerk, but honestly. And why couldn't I find mine? I used to wear it every day of the week. Obviously, I was not at that show; it was given to me on my thirteenth birthday by a favourite uncle when he found out I loved metal. He'd _been there_ , in person. It was a rite of passage, getting that holy relic. I'd give my left nut to teleport back in time and tailgate party my way around, worshipping at the band's platform heels.\n\n_Who am I kidding?_ I'd give them both.\n\nI woke with a start. It was this side of dawn; I could tell by the strange light that stole through the window where my bedroom curtains did not quite meet in the middle. I looked out of habit but, of course, Sharon wasn't on her side. I blinked.\n\nIt was obvious. Some dude, possibly even a buddy of mine I hadn't seen in years, probably keeled over and died. His mother or worse, his wife or live-in girlfriend, probably packed up those hallowed shirts and dropped them down at the charity Goodwill. _The nerve_. That Mexican kid might have scored an entire lifetime supply of rock and metal paraphernalia for a few bucks.\n\n_And why shouldn't he?_\n\nThat was Sharon's voice haunting me from beyond divorce court.\n\n_Is he less deserving than you and your fat, balding friends?_\n\nThat'd be just like her, take the side of a kid from a place she'd never even been, over her own husband.\n\n_I have so been there. On our goddamned honeymoon, you prick._\n\nAh, Sharon. You got me there.\n\nThe following Sunday, also hungover, I decided to close the shop early. In fact, I couldn't wait for this one family to finish their game. The parents looked vaguely familiar and were probably dweebs I'd hated in high school. They wore matching polo shirts, like from some depressing Sears Catalogue photo shoot. The kids fought. They were a whole new brand of ugly, a screeching, snotting ad for birth control. Watching them made me hate the world a little bit more than I already had when I'd got up that morning. Made me want to lock up this stupid shop and burn it to the ground. I reimbursed them half, since they played half the course, and kicked them the hell out.\n\n\"Now you look here,\" said the father.\n\n\"Look at my dick,\" I replied. The eyebrows, the open mouths.\n\nI slammed the door of the Coupe and cracked a lukewarm beer. I drove straight ahead into the heart of Leamington, where our town's tomatoes get turned into ketchup in their big Heinz factory. I drove deep into the relaxed pulse of the town's innards. It was full of farm workers on their day off. They were everywhere. They ran errands, phoned home, wired money. They sat on the town benches that were usually just real estate agent ads. Workers leaned against the giant photos of those smiling phonies in their beige suits. Canadians, I realized, don't enjoy ourselves. We go about our uptight business all day and relax, or not, when we get home. Mexicans seemed to know how to use public space, how to spend time together. I decided to park the car and join them.\n\nI walked up and down the main drag, looked into windows, nodded and smiled at people. They nodded back. I followed one group of workers who headed toward the information centre in town, an enormous all-weather tomato where some kid sat all day, bored as a stick, reading Harry Potter, in case anyone stopped and asked for directions or wanted tourist brochures. _As if_. The men turned onto a path I'd never noticed. It was hidden by the giant tomato and a line of large thorny bushes, Ash no doubt. I hesitated briefly. That path led into what used to be an old parking lot. Smells found me almost immediately\u2014smoke and meat, spices, and roasting corn. I could hear Spanish voices laughing and singing. The lot had been transformed into some kind of square.\n\nI felt like Alice in goddamned Wonderland.\n\nAbout fifty men were hanging out in this alternate universe. Some drank from small dark bottles of beer, others from round flasks they kept at their sides. They were having a good time, nothing rowdy, just relaxing. There were a few benches, all taken, and in one corner there was an old metal container being used as a giant barbecue. Meat sizzled on a makeshift grill, corn in the husk smoked along the edges. Two men worked the grill and filled plates for the others. Nearby was a second smaller grill with a flat sheet on top. A dark-haired woman was forming patties from pale dough, tortillas maybe; she slapped them into shape with expert hands and placed them on the hot metal sheet. She laughed as she worked, her voice drawing the shy men closer, waiting for the food to be ready.\n\nMy stomach rumbled. Eating had not interested me lately, but these were some pretty good smells.\n\nA large-bottomed guitar was brought out, and a man began to play. It had a deep bass sound. He played a simple tune the others seemed to know. It was a bit rollicking, but as the other instruments joined in\u2014an accordion, a regular guitar, a horn\u2014it had an altogether different effect. Men began to sing. Larger bottles made their way around. I could have used a belt, whatever it was. This strange music drew me in. It was like country, but slower and more halting. Like a slightly drunken waltz. I liked it and didn't like it at the same time. There was something about the plaintive calling in the voices that popped up from the small knots of men in the yard that tugged at my insides and threatened to let loose some uncontrollable emotion.\n\nI panicked. I looked around and noticed several of the other men's eyes darting away. I was the only white Canadian here. Those around me were silent, even when I said hello. They kept their eyes on the ground and did not reply. The nearest ones had stopped joking around, too. I was spoiling the party. Fun crusher, me? I stumbled backwards, and blundered my way toward the path. The hush spread around me like a pox, and I felt every pair of shining dark eyes upon my back. I hurried, fatally, and twisted my weak ankle, an old hockey injury. I thrashed about in the Prickly Ash before falling heavily to the ground.\n\nThe silence was remarkable. Even the music stopped. I could see the path from down there and decided to crawl onto it, thinking it was less conspicuous than standing back up to announce my situation. I hoped no one noticed. As if on cue, there was a resounding burst of laughter; chuckling baritones, a giggling alto choir, and several higher-pitched hilarious sopranos, who succeeded only in provoking the whole square into louder fits of hysteria.\n\nHumiliated, I lurched forward on my hands and knees, still tangled in the bush. Thorns tore at my flesh. A pair of Converse knock-offs blocked my way. I looked up. It was the kid again, wearing that same shirt. The kid's black hair was longer than the other men's, about my own length. His eyes were two black stones that shone wetly: pupils indistinguishable from iris, they were so dark. He reached out a calloused hand. He was muscular from working the fields and pulled me up easily. His skin was surprisingly soft to touch. He smelled of earth and Sunlight detergent and of a faint manly sweat that was not bad.\n\n\"Thanks, man,\" I said awkwardly. I was several inches taller than him. I stared at the shirt which fit him very well. There was a familiar tear on the left sleeve. I rubbed the matching scar on my arm\u2014skateboarding wipe-out. A splotch of white paint along the shirt hem was a ghost from grade ten art class. This _was_ my bloody shirt!\n\nHe shrugged. \"You got the nice car, right? The Coupe?\"\n\nHe had an accent, but his English was better than I expected. I nodded.\n\n\"Bet it's a fun ride.\" He spoke softly.\n\nMy cheeks burned. Blood and sweat trickled down my neck. I pulled a thorn from my scratched hand. I needed to get the hell out of there. I wanted my shirt back. I jangled the keys. \"Want to find out?\"\n\nThere was that jigsaw smile again, lighting up his face.\n\n\"You like Sid Vicious?\"\n\n\"What? That punk?\" I sneered. I had regained my confidence and cynicism by then, zipping along the main drag.\n\n\"You don't like punk rock?\" Geraldo said this with total disbelief.\n\nI refused to reply.\n\nWe were cruising the strip, the Leamington \"L,\" the way it was done back when I was in school. You went from the McDonald's drive-through to the town centre just past the giant tomato, took a right, and rode the strip right to the very end of the dock, slammed on your brakes, then turned around and did the whole thing over again only in reverse. Most of the action used to be either down at the docks or up in the McDonald's parking lot\u2014girls smoking and tossing their bleached hair, dudes looking to fight, couples making out. In grade eleven I'd hooked up with Sharon on this very piece of real estate.\n\n\"Seriously?\" Geraldo sniffed his Big Mac. He took a bite. \"More than anything,\" he said, his mouth full, \"I want to be in a punk band.\"\n\nWell, I nearly pulled over and made him give me the shirt off his narrow back. I was speechless. I opened an emergency beer that he passed me from the glove compartment.\n\n\"No, but why can't you like metal and also like punk? That's silly. It's all rock and roll, man.\"\n\nI choked on the warm beer. It sprayed from my mouth, hit the windshield, dribbled down my chin, wetting the collar of my shirt. I coughed and breathed deeply. Those heretic words from Geraldo's mouth washed over me as my chest relaxed and I wiped the set line from around my mouth, loosening the tension in my jaw. For the first time in my life, I heard some truth in that statement. Geraldo sounded almost reasonable.\n\nLater, I let him take the wheel. \"You know how to drive, right?\n\n\"Oh yeah,\" he said. \"I been driving since I was nine years old.\"\n\nIt was some time before Geraldo elaborated. He meant he'd been driving the village _tractor_ since he was nine, which is a very different thing. He drove slowly, carefully, right down the middle of the road. The tip of his tongue stuck out at one corner from concentrating. He had a glazed smile plastered on his stunned face. He did okay, considering he freaked if I urged him beyond thirty-five kilometres an hour. We kept to the back roads, and any company we met simply passed us, leaving the Coupe covered in fine dust.\n\n\"Take a left and park.\" I had to draw the line somewhere. Even combines were booting past.\n\nWe sat at the top of the ridge, closest thing to a hill in these parts. There was a nice view of the farmland below that stretched a mile or two down to the shore. Sharon and I used to come here to neck in the old days. Before she moved in, of course. Before my parents died, leaving the bungalow to me, suddenly making me the most popular guy at school. _Larry, party at your house, right?_ Right.\n\n\"This used to be lake.\" I pointed to the farm land below us.\n\n\"Heh?\" His eyebrows arched. I noticed they were graceful like a woman's: not too hairy.\n\n\"A-gwa,\" I said loudly. \"A long time ago all that was water. Now it's soil. Dirt.\"\n\n\"Oh.\" He nodded gravely. \"My grandmother's village had that, only the opposite. It got covered up. Disappeared.\" He gripped the steering wheel. I watched the muscles move up his forearm, along his bicep.\n\n\"Oh.\" I inhaled. The smell of him filled me. I opened the passenger window the rest of the way. \"What's it like in Mexico?\"\n\n\"Very different. You never been?\" He leaned toward me when he asked that.\n\nI felt stuck in this seat, bare without the steering wheel in front of me, like the car wasn't mine anymore. I cleared my throat. \"Just on my honeymoon. Some beach resort.\"\n\n\"Where is your wife?\" Geraldo's eyes glittered from his soft face.\n\n\"Where'd you get that shirt?\"\n\n\"Some lady was selling her ex-husband's stuff at a yard sale.\" He laughed. \"Like, she was really mad at him. I paid only fifty cents.\"\n\nI drained the can and crushed it, one-handed, and tossed it out the window. \"Geraldo, let me tell you something. Don't ever get married. It'll ruin your life.\"\n\n\"I am already. I had to marry, to come to Canada.\"\n\nI looked at him blankly.\n\n\"Your government said this. We must be married and go to church if we want to work. So we won't stay here and get Canadian girlfriends. Make Mexi-Can babies.\" He laughed.\n\n_Was this true?_ That shut me right up.\n\n\"We make a deal. We have a little room, but she do what she wants, and me too.\"\n\n\"Huh.\"\n\n\"She is pretty, but she don't like men. Now the others leave her alone. And me, I want\u2014\"\n\n\"To be in a punk rock band,\" I said.\n\nHe nodded vigorously.\n\n\"Well, Geraldo. You sure got your shit together, don't you?\" It was about then that I decided to let him keep the fucking shirt. Suddenly, I didn't care if I never saw it again.\n\nAfter I dropped Geraldo at the laneway to his farm, I headed home. I needed an actual cold beer and a talk with Jack Daniels. I poured the amber liquid over a big chunk of ice. _I'll sip it_ , I thought. _Just a little_. I wondered what Sharon was doing tonight, wherever she was. Sunday nights we used to go bowling, back in the day. Or down to Cedar Beach. In winter we'd rent movies and pile quilts around us on the couch to stay warm. We're talking about ten years ago, before I got the heaters fixed.\n\n_Try fifteen, jerk._\n\nI poured a second helping.\n\nSharon used to say she loved that I could crush a beer can in one hand. She loved to fiddle with my long hair. Then suddenly it bugged her. She wanted it cut off.\n\n_And grow up while you're at it, Larry._\n\nFuck ice cubes. I pulled straight from the bottle.\n\n\"Arrgh!\" I yelled at the large amp. I plugged in, turned that bad boy on. The guitar was seriously out of tune. It needed new strings. I managed to blast a few notes into the dark bungalow. My hands were stiff, too clumsy to do anything right. I gulped more whiskey. The burn comforted my throat.\n\nWhy did broads fall for you the way you were\u2014holding your liquor, cracking your jokes, feathering your hair while the rest of those turds from your class went bald\u2014then demand you change? As soon as they owned your space, they wanted you to turn the music down, stop watching the playoffs. They cried if you didn't do the dishes or if you didn't do them _right_ ; when you didn't notice their new hairdo; when you told them to lay off the chips or they'd never fit into their skinny jeans again. What is life for, anyway? You head off to that shit job she found (minigolf, seriously?), wearing a phony shirt with a clip-on tie that _she_ bought. You come home for a crap dinner and lite beer, and find her banging some dude who looks a bit the way you _used to_ , before she cut off your balls and zipped them into her purse, forever.\n\n_Ah, Sharon._\n\nThat Geraldo had the right fucking idea.\n\nAll summer long, it was green and black and gold and red: walks in the fields, Sunday drives along the lakeshore in the Coupe. There was beer and whiskey. There were awkward moments, standing too close or bumping against him or stumbling together across the lawn, loaded. A buzz ran through me, electric, that zapped whenever Geraldo's skin brushed mine. I'd shake it off and drink more. There was music, lots of it, blasted from my stereo and from my amp. Geraldo had a gift. He could play that guitar, make it sing like I never could. His face shone with joy when he wailed on it, chugging steadily and ripping off some scorching solo. I stared at him outright then. I felt like some groupie creep, a pre-teen girl with my very own private boy band in the living room.\n\nLate August was yellow and fiery orange. Geraldo grew slightly stooped from bending and picking, from the even longer days of heavy lifting and lugging that was harvest. His eyes sparkled less; he had little energy for playing guitar or anything else. By then I had stopped opening the shop during the week. Instead, I would drive out to the fields at first light and work alongside the men, all the burning hours of day and into the cooler night. My body ached from it, my hands were ruined, but it made me feel real to sweat and bend and dig and haul. I'd bring something for lunch, something for me and Geraldo. In the shade of a leafy tree, we'd eat these lousy sandwiches and shoot the shit. He'd try out lyrics for his imaginary band, Migrant, but mostly we'd just sit in our hot stink and chug water before going back to work.\n\nUnbelievably, some fields remained untouched other than by feasting birds if it cost more to pick and transport the produce than the owners would be paid for it. Instead, the food was left to rot. Neighbours would come after dark to fill their quiet baskets\u2014midnight picking. Eventually, the soil would be turned over, tomatoes and all. Explosive harvest reds drained into mid-fall grey-browns. The air grew crisp. The nights got cold. Every year at this time, the workers were rounded up and sent home, back to Mexico, and our world returned to its usual cold, white winter.\n\nMigrant workers were not eligible for E.I. even though they paid Canadian taxes. I roared when I first heard that, but Geraldo quietly said, \"We signed English papers.\" Like that explained it all. When I trumpeted something about workers' rights, he smiled cynically. His dark eyes pierced me. \"We have the right to remain silent,\" he said, and opened a fresh beer. \"You complain, and they take you off the list. You can't come back next year. Then your whole family goes hungry and ashamed.\" The guilt was almost unbearable. It occurred to me for the first time that he might _never_ come back.\n\nWe were sitting in the Coupe on the ridge one night when I finally asked about that. He was too tired to go all the way to my place and come back for daybreak together. He smiled sadly. \"Maria warned me on the phone,\" he said. \"The village thinks you're a _chupacabra_ , a goatsucker.\"\n\nI knew the other workers didn't even talk to him, if they could help it. But it never occurred that they'd blame _me_ , the strange gringo, for poisoning him. I was stunned. Geraldo didn't know if they'd asked the farmer to take his name off the return list, or if the boss man himself had decided.\n\n\"Either way,\" he said, \"I'm different. They don't like that.\"\n\nGuilt ate at me. That's when the plan started simmering. Years ago, driving home from the bar, I'd seen farm hands lined up along the side of the road. Boss man was handing back their special work permits as each man stepped onto the bus\u2014a shitty loaner school bus. They were packed up and driven straight to Toronto Pearson airport in the middle of the night. _Do not pass go, do not collect two hundred dollars_. It reminded me of an old photo I'd seen at school, an American plantation owner leading a chain gang of slaves to market. Don't get me wrong, not all farmers are racist a-holes, far from it. They're working harder than you or I to make a living so the rest of us can eat. Frankly, if we ungrateful fucks paid more attention to how food got onto our dinner plates, we'd know how hard it is for farmers to break even.\n\nStill, I felt no regret chugging northeast on the 401 on that particular pre-dawn day, keeping pace with Geraldo's crew bus, none whatsoever. What I couldn't believe was that the thing didn't stop, not even once, on the four-and-a-half hour drive. I had to pull over to take a leak and get a jumbo coffee to keep my eyes open, which meant another pit stop in twenty minutes. I lost track of the bus, but finally caught up with it as it choked and shuddered curbside, in front of Terminal Three.\n\nThe men wore their hats low, as usual. They shivered in sweaters. Our fall was cold for them. It crept in and chilled their inside parts. I think it scared them. Might have felt like death. They shuffled from foot to foot, holding their bags and souvenirs\u2014toys for the children they'd been missing, gifts for their wives. Boss man hadn't seen me yet, but the rest sure had. Blame radiated from their turned backs. I felt dirty, old, _wrong_ in ways I never had before. For a minute I wondered if I should really go ahead with the plan. Maybe Geraldo's life would not be ruined after all. Maybe they would forgive him back in their land, in their own language, far from North America and its rampant diseases: greed, sloth, lust, pride. If so, Geraldo and his pretty fake wife might just work things out.\n\n_Shit._ I drummed my fingers on the steering wheel. It was now or never.\n\nThe idea was simple. Create a diversion, stuff him in the trunk, get the hell out of there. The tricky part was the distraction. None of the workers would risk helping. Geraldo had fretted about how it would all come to pass. \"Details, details,\" I'd said, and changed the subject, thinking I could wing it. Be truly _in the moment_. In fact, I was starting to panic, not seeing Geraldo in the crowd of men, not knowing if he'd noticed my car sitting about thirty feet behind the bus. I bit my knuckle worrying. I turned off the engine.\n\nThen a taxi van pulled up behind the bus and in front of me. Crying, shouting family members with oversized luggage spilled out. There was a colossal intergenerational argument; a dog yapped from underneath a large woman's arm. A second cab arrived with the rest of their group. It was a travelling carnival of chaos\u2014weeping in-laws, couples struggling with all their crap, several nose-picking, stumbling children.\n\n_God help them all._\n\nI turned the engine back on and slowly inched up beside the taxis, blocking them in. I parked, got out, and nonchalantly opened the huge trunk. I scanned the line of workers. I whistled to myself. Suddenly, there he was. Geraldo slipped past the other men, weaving amongst the hysterical family members. Geraldo chucked his bag into the huge open trunk. He almost didn't notice the guitar case and amp in there.\n\n\"It's yours,\" I said, and blushed uncontrollably.\n\n\"No way!\" His eyes sparkled. His smile brightened the early morning haze. \"Thanks, man.\"\n\nHe hugged me hard to his chest. His hot breath singed my neck, my left ear. Wherever his body touched mine\u2014hands on my back, torso against my own, thighs burning against my jeans\u2014those parts melted away, hot and strange. I'd never own them in the same way again.\n\nThen he was curled inside the trunk, an arm around the case, one thumb up, still smiling. I whistled some more, slammed down the lid. I slid behind the wheel. I turned the engine over, changed gear, and chugged away, past the arguing, weeping family, past the school bus and driver, past the line of men who now stared at me openly, in shock. In disgust. One pointed an accusing finger. I can feel it to this day.\n\nI turned the radio up so Geraldo could hear it, too. Pink Floyd was ending, thankfully, and Judas Priest was singing \"Breaking the Law.\" I nosed the Coupe back onto the highway and we headed south, into the deep belly of sin city, down to Torannah. If ever there was a place for a Mexican runaway who dreamed of starting a punk band, I guessed this'd be it. He had an address, a phone number, one name in a city of five million. Most important, he had a backup if he needed it. As I had already told him, the second room in my bungalow was totally clear now. It was his for the taking. He could do what he wanted, and me, too.\n\n# Two Ton: An Opera in Three Acts\n\n## _Act One: Soft Rock_\n\nHim: flying down Yonge Street, ripping past lanes of stalled traffic, weaving between all those cars. Him: zigzagging the wrong way through intersections, his delivery satchel strapped around his barrel chest, a two-way radio squawking at his shoulder. I noticed that particular bike courier in the downtown core more than all the others. It was his bright blond hair that got my attention, and the bigness of him. He was a gladiator, an urban warrior and, most notably, I never saw him without a wide, gleaming smile.\n\nWe couldn't have been less alike. I was his shadow: thin, dark-haired, introverted. I hated drawing attention to myself and was afraid of trying new things. I followed rules, not even jaywalking with the rushing hordes each morning. Not even when he and the other couriers blocked the honking cars with their insolent dawdling, completely immobilizing the street with their bike tricks and general disregard for traffic bylaws.\n\nI worked in the tallest, blackest tower, forty-seven floors up. I scratched out a meagre salary in an office of overworked accountants. This was thanks to the charity of one of my father's former schoolmates who gave me the job. I was the whipping boy of two aging receptionists, Gladys and Helen. Each morning Gladys turned on the adult contemporary radio station while Helen made my To Do list. I filed and fetched, took messages, made the tea, all while Phil Collins bleated mercilessly in the background. \"I can feel it coming in the air tonight, oh Lord.\" I did everything Gladys and Helen did not want to do, but never exactly the way they preferred. I was of no real significance, except perhaps as an object of their daily contempt. They often smiled while sounding sharp, which confused me. They were like two birds of prey\u2014one taller and beakier, the other shorter and more feathered. Both perched at the edge of their seats expectantly, knitted sweaters ruffled around their bony shoulders. They exhibited a maternal shrewdness that frightened me, and I often hid in the hall closet when I heard them calling my name.\n\nWith Gladys and Helen, my gender imposed a certain further expectation, a specific skill set. When things got jammed, when things ran out, they called on me. I could usually refill paper and ink without total mishap, but what to do when the machines went on the fritz? Let me be very clear. I was not, _am_ not, a man of handy abilities. I can't hammer or saw or drill to save my life. It was luck, surely, or a wave of total synchronicity that somehow coincided with me placing my bewildered hands on one noncompliant machine and its subsequently choking itself back to life.\n\nGladys and Helen clapped. They looked at me in a new light, like I wasn't _completely_ useless after all. Satisfied that I had a knack for fixing things, they continued to call on me whenever the equipment failed. That spark of curious surprise returned whenever I performed the ritual and it resulted in some unlikely degree of success. Each time I wondered\u2014had I some paranormal ability like the comic book characters I'd worshipped as a child? Wariness and skepticism crept into those silly ideas, those blossoms of hope, and killed them. Surely I was an imposter. It would only be a matter of time before the ugly truth was exposed.\n\nGradually, I spent more time in the copier room, the sectioned-off pen with the machines, the electronic animals that _seemed_ to thrive under my quiet murmurings and casual pats. I hid in the mysterious folds of this new persona, however false it may have been. I was Mister Fix-It to the old birds. _Machine Man_ , I silently corrected. I daydreamed a spandex suit for myself, a cape, a more muscular body, and perfect vision. From my new post behind the copy room door, I could see out to reception as all sorts of well-dressed peons minced past. They rarely noticed me, but I started to recognize everyone who came and went.\n\nGladys and Helen were forever gossiping about the other staff when they weren't clucking over the sales pull-out in the daily paper. Randolph had gout, likely due to his drinking. Penny cheated on her husband and was seeing a dapper accountant down the hall. The new manager had a gambling problem, and Sylvia next door was bulimic; they'd heard her ritually cleansing after a carrot cake had gone missing from the lunch room. Gladys and Helen were equally relentless in documenting their own mundane affairs: I heard all about their bone spurs, their parking tickets, their irritated bowels. All this with Celine Dion screeching on the radio\u2014honestly, it was too much to bear.\n\nSurely this was some social science experiment. _It had to be!_ I had less in common with other people than I'd ever imagined. Hall & Oates sang \"Private Eyes.\" I despised everyone, I realized, the two receptionists most ardently. I fantasized about their sudden injury: elevator accidents, lunch-room poisonings, a tainted water cooler. I was living inside my own detached brain almost exclusively.\n\nPerhaps they noticed. When either Gladys or Helen had to enter the copier room alone to send or collect faxes, each would give nervous sidelong glances at me and leave as quickly as possible. More than once I'd heard them talking. \"There's something wrong with that boy,\" Helen said. \"He's not all there,\" Gladys agreed, and I snorted with delight. Then Helen said, \"Can you imagine his poor girlfriend?\" and Gladys clucked her tongue savagely. \"What we women have to put up with.\" That froze me, and I thought of Linda.\n\nLinda was a friendly girl from my college chemistry class who'd Facebooked me out of the blue, almost a year after graduation. She had asked me to the movies week after week without incident. Then about a month ago, she had insisted I come to her place for a drink. She'd left me in the living room, presumably to get our beers, and returned from the kitchen fully naked. Certain that my mediocrity and inexperience would prevail, I nevertheless tried to oblige her, however she instructed. The sex was not all I'd hoped it would be. No doubt Linda was even more disappointed. In the ensuing weeks, more half-hearted attempts brought similar results. At times I climaxed almost immediately, more out of stress and surprise than pleasure. Other times I could not find release no matter what ingenious tricks _Cosmo_ suggested she attempt. It was not the love affair of the century, of this I was certain. Somehow I hadn't expected sex to be so mechanical and awkward. But I continued to try my best, so to hear the old biddies taking Linda's part without knowing us at all, well, that pushed a limit.\n\nIt was in my new station, the copier room, that I caught regular glimpses of the blond courier as he breezed in and out. Two Ton was his name. \"How are my girls?\" he'd ask in his faint Eastern European accent. My enthralled supervisors cackled. When the sounds of Air Supply filled the office, he sang loudly to \"Every voman in the vorld!\" The old broads would bat their lashes and cross their ankles. He left pink cheeks and giddy smiles in his wake. Gladys and Helen would inevitably spend the next forty-five minutes recalling his jokes, his various attributes, his astounding physique. For once I yearned to hear them as they listed his superior qualities. I hummed along with Lionel Richie. Two Ton was so refreshing compared to the other people in my office. He was so much of what I longed to be, so much that I never _could_ be. I began making excuses to follow him.\n\nThe first time it was quite by accident. I had taken a late lunch break and, on my way back up the tower, I alone shared an elevator with him. The small space closed in around us. His scent filled it; the heat from his body charged the air. I felt faint from all the pheromones, the testosterone flooding from him. I couldn't think of anything to say. He, for once, was silent. I felt him looking at me, and I could hardly breathe. An instrumental version of Led Zeppelin's \"Black Dog\" was piped into the airless chamber. The elevator chimed as we sped upward. When the doors opened on my floor, I had to hide in the men's room for several minutes just to compose myself.\n\nFrom then on, whenever Gladys or Helen had errands, I would gallantly offer my assistance. I'd even go so far as to pay for their diet colas or low-fat cappuccinos, just so I might catch a glimpse of him elsewhere in the building, striding past tinted doors, spreading his charm along with the padded envelopes, packages, and waybills he delivered. Sometimes he took unmarked staircases and narrow corridors for short cuts. He made long-distance calls on unattended phone lines. He drank free espressos, ate food from catered lunch trays when no one else was looking. Some days he took smoke breaks in hidden garden squares with incredible statues or in elite balconies decorated by gorgeous planters bursting with colour. Two Ton worked the building like it was a hive and he the one autonomous bee who evaded the unrewarding menial chores that the rest of us drones were genetically predisposed to accept.\n\nOne summer afternoon I followed him into an unmarked room. It was a swanky CEO's private washroom and classical music was playing. The room had beautifully tiled floors, large clean mirrors, granite counters. There were cloth towels and fragrant soaps. To the left was an area that included a shower and sauna. I walked quickly into the first available stall and sat on a designer toilet seat. I could hear him urinating in the stall next to me. Even Two Ton's piss had a heady, masculine aroma to it, and it disabled me in some strange way. He didn't flush, I noted with delight. I took it as an act of defiance; it was synonymous with spraying a hydrant in this elite world of powerful men. I listened as he washed his hands carefully, whistling along with the sonata, and didn't dare open my door until the main door had clicked shut behind him.\n\nI gasped. Two Ton was still standing inside the men's room, blocking the exit. His eyes followed me as I limped toward the nearest sink. I kept my head down while the water ran hot over my soapy hands. Violins sawed away, building to a frenzy; minor chords crashed loudly.\n\n\"Vat is this?\" he said.\n\nI made eye contact with him using the mirror. \"W-what is what?\"\n\nHe stepped towards me. \"This.\" He nodded toward the speakers. \"The music. If you know vat the name is.\" He twirled his bike-lock key on a string around and around his large index finger.\n\n\"Uh, sure.\" I was transfixed by the little silver thing.\n\nHe smiled. \"So you gonna tell me?\"\n\n\"Oh. Debussy. Claude Debussy.\"\n\n\"Huh. I think I hear it in a movie or something.\"\n\n\"Probably.\" My hands were red from the scalding water.\n\n\"Like, scary movie, maybe. Sound like something bad might happen. You know?\"\n\nI swallowed. The steam from the taps was starting to obliterate my reflection in the mirror.\n\n\"Be careful. You gonna burn yourself,\" he said.\n\nIt was as if he broke the spell with those words. I pulled my hands away\u2014they were throbbing. I couldn't turn off the tap.\n\nTwo Ton was beside me then. I felt the fabric of his shirt against my bare forearm. He turned off the faucet and rested one big hand on my shoulder. He squeezed my flesh and patted it lightly. \"Debussy. Thanks.\"\n\nThen he was gone for real. The door swung shut. I stood fumbling with the second sink, trying to turn on the cold tap to soak my injured fingers.\n\nAfter that, I began thinking about Two Ton even more. At the end of each day, I crawled out of the tall, black beast of an office tower and showed my paleness to the fading sun, among hundreds of other beetles, pouring from the nest. I looked for him in the streets as I trudged along in second-hand dress shoes that pinched my toes, spectacles sliding down the bridge of my nose. From streetcar windows I'd scan for a glimpse of his big, blond head. Sometimes I'd spot him in a tight knot of smaller couriers, laughing and smoking a joint right on the marbled front steps of some upscale hotel. I found myself retelling his jokes, relating anecdotes about him to Linda during our increasingly pained silences. She thought he was my friend and wanted to invite him for dinner. I said he was married and needed to be home with his wife. I stopped saying his name out loud, but even Linda had become fascinated with him. Why this bothered me, I wasn't sure. I only became certain that I did not want to share him anymore, that I did not want her taking him away from me, from my imaginary companionship. She was like all the other women he encountered\u2014easily smitten. Her face lit up when she asked about him, so much that I lied again, saying he had switched companies and no longer came to my building.\n\nThen I began to dream about him. He figured even more prominently in that nether world of image and nuance. He rescued me from drowning, he taught me how to snare forest animals, he reset my broken bones in an alpine climbing disaster, and carried me to safety. Once, his bike refused to work and only I could telepathically correct the problem. He beamed graciously and was forever indebted to me. Sometimes I awoke feverish, nausea and guilt souring my mouth.\n\nIn our office, all the ladies were dressing more provocatively, even Gladys and Helen. They wore higher heels and more lipstick, did strange things to their hair and faces. Whitney Houston sang \"You Give Good Love\" as they cantered through the office. Then they gathered mid-morning, expectantly. When Two Ton arrived, lightly glistening with sweat, carrying a stack of mail, each one tried to steal more of his attentions. They baked loaves for him, offered coffee, water, juice. He flirted with them equally, leaving each one even more hopeful for his next visit.\n\nMen liked him, too, I noticed, albeit grudgingly. You couldn't _not_ like him; he was so capable and athletic. He had an easy way about him that made other guys, suits or not, want to measure up. One morning I actually overheard our Big Boss, who rarely even _made appearances_ in this department, exchange pleasantries, shake hands, and chat him up about a possible career change, perhaps an interview in sales where his networking could really pay off. I held my breath. Two Ton turned down the offer so gently that neither the boss nor I realized it until a moment after he was gone. I exhaled.\n\nAt lunch I couldn't eat my sandwich. Karen Carpenter crooned \"Rainy days and Mondays get me down.\" I felt a sharp pain lodge in my throat. When I opened my mouth, a sob broke from it. Something was dreadfully wrong.\n\n## _Act Two: White Noise_\n\n\"We never go anywhere.\" Linda pouted just a bit.\n\nI couldn't argue. It was true. So, in an attempt to seem normal, I agreed to go camping with her during the long weekend in July. I hadn't used a sleeping bag since I was ten. I hadn't started a fire since I burned my diary in junior high. I hated insects and was desperately afraid of drowning. I knew this was a bad idea. Linda did, too, deep down. We both suspected she really wanted to break up with me. It was a doomed journey, but she'd already rented a car. At the last minute, no doubt terrified at the prospect of spending all that time alone in the woods with me, she'd invited a couple of girlfriends along.\n\nKaren and Brittany were vacuous and had an irritating habit of singing out loud with the radio commercials. \"You deserve a break today!\" \"Why buy a mattress anywhere else?\" One would finish the other's sentences, an eerie echo of their mediocre mind-meld. Linda was more at home with their inane banter than she had been with me in all our dating history. _Who is this strange woman?_ I thought, as she drove and tossed her ponytail over the headrest so that the Siamese twins, joined at the IQ, could play with her bleached-out hair. She laughed as I'd never heard before. She burped loudly, competitively, and sang along with Kylie Minogue to the radio edit version of \"Red-blooded Woman.\"\n\nI coughed. Had I really imposed my sweaty incompetent self into her private life? I was incredulous. I fiddled with the radio, leaving it between stations so static hissed in their ears and they could no longer sing their three-part harmony. The white noise also set me on edge. _When will we get to the campsite? Might I stab these girls with a marshmallow roaster? Couldn't I take some pills and just die?_\n\nI tried to tune them out and watched the drama in the BMW ahead of us. Some alpha male was arguing with his wife, gesticulating wildly. I watched him ream out his better half, the kids, even the dog, all the way down Spadina Avenue. What a shitty way to start their weekend. Suddenly there was a crash. The next thing you know, his SUV was wrapped around the guardrail and our car was rammed up his bumpered ass. There were the stuttered thuds of all those other miserable carloads slamming into us. It was quiet. Doors opened and shut, faces got red. Mouths opened. There was yelling. Finger pointing. Cell phones popping open. Sirens started up in the distance, and cars honked loudly.\n\nWe were all fine. _Physically_.\n\n\"Wow,\" I said after a long pause. I undid my seat belt. My ears were ringing. I found my crumpled glasses on the dashboard. I put them back on. Linda looked at me as though I was a stranger. Her blonde hair was lopsided, the derelict ponytail askew. \"Are you all right?\" I asked. She blinked. The other girls were just as silent. I peered into the back seat; Karen had lipstick smeared across her face. A broken chunk of it was mashed against her cheek. The girls were in shock, maybe. Brittany sniffled. I felt as though I should do something, anything, but I had no idea what that might be. I got out of the car. I closed the door. The three girls looked like those dogs at the pound, their big eyes welling up inside the smeary glass partition.\n\n_What did they want from me?_ I hated this, the whole mess. People began to crowd around, their voices raised and their arms waving, pointing.\n\nJust then, who came chugging around the bend, no-handed on his gorgeous, custom-built bike, but Two Ton. His T-shirt was wrapped around his head like a turban, and his skin warmed to the open sky. His wide chest and abs were clearly defined. I felt a strangeness in my belly. Blood pumped through me. His heavy bike lock chain hung around his neck so that he looked like some Eastern European gangster. He guffawed at the wreck, at our bad luck, and at the joke of his self-powered thin metal frame coasting past us. He was an evolved creature pedalling away from this ecological disaster. We all stood silent, watching him glide past into a sleek future without us. He was so cheerful, so free, as he sped toward the next exit that led down to the waterfront trails.\n\nMy bike was on the roof rack, heating in the sun. I didn't think twice. I unfastened it, flipped it down to the hot asphalt, and opened the back seat door. My backpack was there, wedged in between the girls. I grabbed it, hopped on my bike, and raced to catch up. I left behind my percentage of the groceries, a prepaid gas card, and a wicked stash of premium weed, scored from my roommate at Linda's request. It was wonderfully liberating, the best ride of my life. Those hundreds of metres along the highway, uninterrupted asphalt all my own: Two Ton a small blip on the road ahead of me, the girls, the cars, the chaos, and conflict left far behind. I beamed like some demented kid, catching fruit flies in my teeth. I choked them down when I laughed out loud. I hooted, tried standing on my pedals to really catch the wind. It billowed up my shirt and made the fabric flap with joy.\n\nTwo Ton was down at the water skipping stones and drinking beer from a can when I caught up. I stood awkwardly, waiting. Again, I had nothing to say to him, nothing to offer. I spat out some mashed bugs. Not too far away seagulls shrieked and fought over a bag of potato chips. Two Ton looked at me carefully, not smiling.\n\n\"Hi,\" I said. I coughed and spat out another batch of bug saliva.\n\nHe nodded, seemed to make a decision, and tossed me a beer from his pack. His hands hung long at his sides, swinging beside his ham-hock thighs that poured from ripped jean shorts. I sat down and opened the can. Beer foamed up over my fingers as I slurped it.\n\n\"You're the black tower guy,\" he said.\n\n\"Uh...\" I wasn't sure what he meant.\n\n\"The photocopy dude.\"\n\nI shrugged. \"Mister Machine,\" I said quietly and licked my foam moustache nervously.\n\n\"Mister Machine, hmm?\" He said it evenly. Not especially friendly. Not how he usually sounded at work. \"You follow me around?\"\n\nI started to think this was a terrible idea. \"Uh...\" I swallowed the beer. I wondered if he was going to beat the crap out of me and spoil all those Golden Boy fantasies I'd been having\u2014the ones where we saved each others' lives and hung out doing guy things, like playing squash and fishing off the end of some lonely pier.\n\n\"You gay?\" The way he said that word made it seem bolder and a bit uglier than I had recently come to think of it. It shocked me that he'd say the word aloud, that _I'd_ be suspected of such a thing, that he'd reduced it all down to something so base, so pedestrian.\n\n\"I have a girlfriend,\" I said, in a warbling voice. It sounded phony, even to me.\n\n\"I don't,\" he said. And that was it.\n\nIn an instant, everything changed. My growing obsession with him, the dreams I'd had, the roiling heat in my belly, the fact that I'd deserted my girlfriend in a crisis to follow his godlike body to the beach. This clearly was something quite different from a regular fraternal overture. In that flash I realized how transparent my own undiagnosed longing must be. I blinked, stupidly.\n\n_Gay._  \nHe turned away from me and tossed one more flat stone so that it skipped in a graceful curve leading away from us five, six times, before settling to the sandy bottom. He was just that kind of guy. I watched him differently now, up close, without the affable weekday veneer that I supposed was his armour in the corporate world. Then he turned suddenly, held a hand up to shade his eyes from the bright sun. He was looking right at me.\n\n\"You coming?\" he said. It wasn't a question. Not really.\n\nHe hopped on his bike and I followed. I don't know how I managed to ride all the way across town to his warehouse loft. The traffic sounds merged with heavy construction machinery as we passed road crews and skeleton sites of future condos. Drills blasted through cement, trucks beeped in reverse and dumped their loads onto the dry ground. I couldn't breathe\u2014from the dust and physical exertions and from the strangeness of it all, the day, the turn of events, my good fortune. \"Red-blooded woman!\"\n\nAt the warehouse, he hoisted his bike on his shoulder and took the stairs two at a time, up to the fourth floor. I was sweating, shaking with fatigue. My nose ran from the effort, and I was terrified that I might faint, might fall backwards and be crushed under the weight of my rusting bicycle. Somehow I willed myself up those same stairs. The hallway was deserted when I got there. I stood still, trying to catch my breath. I wondered if this still might end badly. He might leap out at me, for instance, and his courier friends could lynch me, or worse, mock my apparent desire.\n\n\"Hello?\" I called. \"Two Ton?\" And then the door ahead on my left swung open. Two Ton stood in the doorway wearing nothing but his chain lock draped across his perfect chest. I dropped my bike.\n\nHe smiled lazily and leaned deeper into the wooden frame. He chugged from a new can of beer and watched me carefully. He was built, as they say, like a brick shit house. Like he hadn't been born so much as unloaded from a refrigerator box, already assembled. Tall, yes, but with large, square shoulders that his massive arms dropped from. A nipple on one of his smooth pecs winked at me from behind the thick chain. Hints of his ribs framed his muscled belly. I looked to the hard flat area below his navel. He had those shelf-like muscles above his hips that male models and athletes get. His thighs, as I already knew, were perfectly formed. I stared at his overdeveloped calves, down to his bare feet. Two Ton cleared his throat loudly. I looked back up at his wide grin, his beaming face, but not before noting his ample and aroused genitals.\n\n\"Coming?\" He was enjoying my obvious distress. He raised his hands playfully, like he was under casual arrest, and turned slowly. His back was a wide muscled expanse, his buttocks perfectly toned. I had never seen such beauty, never in my life. What could he possibly want with me? Bubbles of feeling choked me. I thought I might weep, he was so perfect. Two Ton glanced over his shoulder and winked. \"I promise I von't hurt you,\" he said. \"Much.\"\n\nI left my bike on the hallway floor and stepped forward.\n\n## _Act Three: Blackened Metal_\n\nI spent Labour Day weekend in the strange kingdom of Two Ton's loft. He talked easily and brought me out of my shell. He was naked most of the time, but I never tired of looking at him. He was comfortable in his body as he moved around the space, pointing out his various treasures. Two Ton didn't have a television. There were books, a record player, some albums, little carvings he made with a knife, some cracked dishes. He had extension cords strung up, power bars taped to the walls, old lamps stuck haphazardly on tiny shelves he had nailed erratically to the wooden support beams. Whatever he possessed, he said proudly, he had mostly pulled from other people's trash.\n\n\"Hey, look,\" he said. He waved a CD at me. Claude Debussy. \"I listened after that time, you know. It reminds me of black metal. So intense.\"\n\nI had no idea what he meant, but I was thrilled that he remembered our encounter in the men's room. That he cared enough about that sonata to locate a copy, and that I had been the one to tell him the composer's name.\n\nWe drank endless beers from his old fridge and crushed the empty cans dramatically, then tossed them into a growing pile in the corner. There was a hot plate and a plug-in kettle, but we ate spaghetti cold, right out of the can. He juggled tennis balls. We pelted them against the bare wall until a neighbour pounded loudly and swore at us in French. We smoked joint after joint; time stopped altogether. He played Black Sabbath, Iron Maiden, Slayer. We sang with Rob Halford to \"Living After Midnight,\" Two Ton in his marvellous baritone, me an alto who attempted falsetto now and again, which brought us to fits of laughter. My life, whatever it had been, no longer existed. My name no longer mattered. He called me _Mister_ or sometimes _Machine,_ which made me smile. I was in that perfect moment, and though I could scarcely believe it, Two Ton seemed to like me.\n\nWe worked our way through his music collection, a great deal of which included black metal bands, Norwegian and otherwise. The drumming was intense\u2014long repetitive instrumental passages with shrieking, grunting vocals and fast tremolo picking on distorted guitars. Some songs were slower with atmospheric wailing and foreboding gloom. I'd never heard most of it before: Bathory, Venom, Darkthrone. Two Ton gave a lecture on the history of the first and second waves of black metal, talked about Swedish and Norwegian rivalry, and described the battles of various metal subcultures: death, doom, gothic, glam, industrial, sludge, speed, stoner\u2014the list was endless. His detailed knowledge impressed me. He was an open encyclopedia to a world I knew nothing about. The music loosed a primitive urge in me that grew the more I drank and smoked. I collapsed on his torn couch and closed my eyes. I imagined wolves, priestesses, medieval weapons, revenge. \"Feed on my black iron heart!\"\n\nWhen I opened my eyes, Two Ton was kneeling on the floor in front of me. He placed his warm hands on my thighs and looked at me intently. I felt the stirrings almost immediately. It seemed to be what he was waiting for. Two Ton effortlessly peeled off my shirt. He undid my jeans, yanked them down around my ankles. He massaged my astonished flesh as I struggled to tug the pants over my large feet. I was naked. I tried to hide myself from him, kept my arms folded over my thin chest, but he pulled those back too, like they were just another layer of clothing. He stared into my nervous face and told me exactly what he would do, and then he did each purposeful thing. At some point we were on the floor rolling, kissing. Then we were half on his old futon mattress. He held me, sometimes stroked my face, talked quietly to me, and watched me closely, as though to gauge meaning from every surprised little sound I made. I didn't know my own skin until he brought heat to it. I was as cherished as any bride, blank as any slate. I grew bold touching him, trying to learn what he liked, what I liked.\n\nIn between exertions, we lay in tangled sheets on his bed. He slept soundly, curled into me, his even breath warming my neck. He was a boy then, perfect and passive, and that's when I stared outright: his chiselled profile, the cleft chin, those pale lashes. I traced his smooth flesh with my fingers. I was perplexed by his beauty and bruised by his attentions. I felt profoundly alive, I realized. As though my whole life had been a series of bumbling missteps that had eventually lead right to this perfect moment in time.\n\nTwo Ton would wake suddenly from these naps and begin speaking of his old life, the one he had before coming to Canada. He was from some country in the eastern end of Europe that nobody ever pronounced properly. \"Anyvay,\" he said, \"my village changed names so much\u2014every time some army march through it\u2014even _I_ don't know vat to call it now.\"\n\n\"Plus,\" he said to my undoubtedly uncomprehending face, \"every time they march, they destroy more of the crops me and my father plant. Hard to be a farmer ven there's nothing to farm.\" Then he playfully decked me with a pillow.\n\nI threw myself and the pillow on top of him, tried to tackle him, but he crushed me in a suffocating embrace. He squeezed the air from my lungs. My eyes bulging, face reddening, he kissed me tenderly. It was gentle torture, but torture nonetheless. This time when we did it, he paired every sensual gesture with an uncomfortable one. He'd move his wet mouth along me slowly, but only while I was pinned in a half nelson. He'd tease my nipples, but choke me simultaneously. I hated and loved it. At first I struggled, but there was no point. He knew what he wanted. He knew what I wanted too, and that was the miracle. That he could see me for what I had always been when nobody else bothered to wonder. Not even me. \"Black Metal ist Krieg!\"\n\nLater he elaborated about that land of his. He said, \"Those hungry soldiers take everything. The best food, even the good soil, goes avay vith them.\" It got sucked into the soles of their battered army boots, leaving angry sand behind. Dirt, unable or unwilling to support the potatoes and sugar beets, cabbage and onions. Dirt that one year finally gave up, even on itself, and let the wind send it stinging into the drying river beds. While he spoke, I tugged on his fingers, thick like sausage and always slightly curled from use, from gripping handlebars and hoisting heavy bags. And before that, from lifting machinery, cleaning stalls, and roping calves.\n\n\"But how did you end up here?\" I asked again. I wanted to know exactly how fate had delivered this gift to me, what stars had aligned for this unexpected purpose. How could he come from some mud-entrenched village on the other side of the world and end up in Toronto, racing through the business district delivering packages for a pittance? Better yet, how had I ended up _here_ , crushed in his embrace, sweated upon, kissed and cursed so equally?\n\nTwo Ton lit a cigarette. He exhaled and, after a bit, passed it to me. He said, \"My father, he vas old and sick. He had nothing. He couldn't pay his loans for seed and equipment. He vould not even pay one cent to that bank. It humiliated him.\"\n\nI passed the smoke back and he took hits off it, staring into space. Two Ton swigged the last of his beer, then dropped the end of the cigarette into the can. He swished it around, and I heard the faint hiss as it extinguished itself.\n\n\"All the men in my family\u2014father, grandfather, great-grandfather, uncles\u2014ve have this same farm. Grow the same food every year. The village eats our food\u2014some others, too, but mostly ours. This is vat ve do.\" He told this part like it was a story from an old book, familiar and comforting.\n\nI thought of my own father then. I had no idea if he had such a legacy, if he was shouldering some masculine code handed down to him by his father, and so on. I scarcely remembered my grandfather. My father was a stooped, mild man of medium build, who quietly left for work each morning. He quietly returned around six o'clock each night and ate my mother's meals while listening to her chatter, always seeming vaguely removed from it all. He'd relax in front of the television. He sometimes read a newspaper or a mystery novel, until he'd stand up and say goodnight to all present, then quietly go down the hallway to bed. Like clockwork. Who knew what the man actually thought about anything?\n\nTwo Ton said that, to deepen the frown between his brows, all his father had to do was look up the road at dust blowing from the empty field, or out back at the dull brown land, or to the empty barn where the animals had once been, or at the flat-tired truck he'd driven to market twice every week since he was eleven years old. \"This vent on for a long time,\" he said. He leapt over to the fridge and grabbed another can of beer, opened it, and slurped at the foam. \"Until von day.\" Two Ton's eyes glittered. \"My father got out of his creaky chair; he make a pile of all the coins he finds in the house. He writes a letter to me. All his thoughts, you know?\" He walked back and sat on the edge of the mattress with me.\n\nI leaned closer. I lay my warm hands on either side of his spine, flattened them against the places where his lungs would be. I could feel his heart pumping inside there, strong and regular.\n\n\"He smokes. He cleans the ash. Then he picks up his coat, his hat, and his gun and valks in straight line past the fields, into the bush.\" Two Ton turned and stared right through me. \"He use his last bullet.\"\n\nWe were quiet for a while. I had no idea what to say, but my hands smoothed his skin, like he was one of the broken copiers at work. Two Ton seemed distant, aloof. He was perhaps tired of me being there. It had been two or three days and, after all, we were virtual strangers. I had never spent such a long uninterrupted period of time with anyone. I'd never heard anything so personal.\n\n\"What did the note say?\" I finally asked.\n\nTwo Ton reached over to the orange crate he used as a nightstand and pulled out a small painted box. Inside was a piece of folded paper, thick and cream-coloured, but smudged from being handled. He tossed it to me. His father's handwriting was careful: squared off at the top and bottom loops, like he'd used a ruler almost, and the letters, so many consonants, slanted sharply to the right, like they were marching headlong into the far side of the paper, in danger of falling off the edge if they arrived too soon. I had no idea what they spelled out, or even what language it was.\n\nI waited for Two Ton to translate those life-altering phrases. What damning insights had his father inked? What great-grandmother's recipe, what bastard child or torrid love affair, what ugly family secrets might be revealed in such a letter? I found myself wondering what my own father might attempt to share in such a profound moment. Two Ton scratched at the light hairs on his chest. He leaned toward me and drank another long gulp. His eyes bore through me; they shone and provoked a shiver from me. I struggled to comprehend all he was not saying. I didn't know how to comfort him or if he even wanted that.\n\n\"What did you do next?\"\n\n\"Easy,\" he said. He spoke quietly. \"I drink the last beer. Then I cut up the last bread and eat it, sitting in my father's chair. Later, when the moon comes out, I lay down on the bed and cry. Finally, I sleep. In the morning, I pack a few things in a bag and just leave. I travelled. I did some crazy things, you know,\" he said, his voice catching. \"Some time, I just heard about coming to Canada, and so I did that. And now, you see, here I am.\"\n\nI smiled when he said that. But I noticed he didn't. His face was impassive. Like the flat, smooth stones he had skipped at the lakefront.\n\nOn Monday morning, I woke with a furry tongue, my head in a vice. I stank. Two Ton was not in bed. He was standing by the large open window in an antique wash basin, an oversized tin bucket with edges that reached just below his knees. He had rigged a garden hose to the sink faucet and had duct-taped a shower head on the end of the hose. He showered in cold water, lathered up with soap stolen from one of the office washrooms, and then rinsed again. It occurred to me that this was slightly more barbaric than the amenities offered at the campground Linda had booked.\n\n_Linda. That poor girl._\n\n\"You're avake,\" he said loudly. \"Good.\" He stepped out of the basin, turned off the tap, and towelled himself off, all in the same movement. \"I have to do some things today. Not vork, but, you know.\"\n\nI looked around the room. My knapsack was on the floor in one corner, my things vomited up from it, strewn the length of the room. I moved slowly, collecting familiar items as I went. A sock. My damp shorts. A box of condoms meant for the terrible sex with Linda, emptied now, with torn wrappers scattered around the room. It hurt when I bent to pick them up. The long bike ride, the stairs, the beer, the sweaty wrestles\u2014it was all much more than I was accustomed to. I dressed myself. I washed my face and rinsed my mouth but couldn't spit out the dread that burned at the back. I could hardly look at him, certainly not in the eyes.\n\n\"You're like a voman,\" he guffawed. \"You should eat a sandwich.\" He was slapping peanut butter onto slices of bread and dropping large dollops of jam on top. He handed me a folded-over piece and thumped my shoulder blade in some kind of manly gesture. I winced. He ate several sandwiches just like this while I choked through that single one. The peanut butter stuck in my throat. I could hardly swallow, even though I kept sipping from a large glass of water.\n\nHe was dressing quickly, moving purposefully around the room. He gathered his wallet, bike lock, keys, cap. He was oppressively cheerful. He was putting on other layers, too, the invisible ones that bricked him far away from me, hundreds of ocean miles between us, and I simply could not stay the maudlin waves from flooding. _This_ \u2014whatever had happened here in his room, whatever affection and intimacy he had poured over me the past few days\u2014this was all gone. The air was changed. Two Ton smelled different. I was his shadow once more, and I could hardly bear it. The thought of seeing him at the office, me on a stool in the copier room, him captivating the maven gatekeepers out front, it sickened me.\n\n\"Ve had good times,\" he said at last, jingling his keys by the door. I was tying my shoelace, peering at him through my dark bangs. \"Don't pout,\" he said. \"I don't like that.\"\n\nOf course it only made things worse.\n\nOut in the hallway the remains of my bicycle glared at me. It was my fault. I had abandoned it, not thought of it once the whole time I was inside Two Ton's loft. The front wheel was missing, the gears were stripped. My pedals were gone. The seat-less post glared obscenely at me. Two Ton swore. \"I forgot to varn you about my neighbours,\" he said. He looked sad. To see a bike desecrated, well, that truly hurt him, I could tell.\n\n\"I'll take the bus,\" I said. I couldn't begin to carry the thing home. Not now.\n\n\"Hey,\" he said, and it was more the conspiratorial sound of his indoor voice, the intimate one I had heard all weekend. \"I fix it. I bring it to the black tower ven it's ready.\" He stood in the cavernous hallway, dust sifting through the beams of light that filtered down from high windows of the warehouse. Sunlight played on his face and his large form; shadows crept over unexpected places. He was still the unapproachable guy I saw downtown, but the other one, the gentle-rough one I'd just come to know, that part of him was visible once again, too.\n\n\"Okay.\" I stammered. \"If you want.\"\n\n\"Yeah,\" he said. He stepped toward me. \"I bring it and ve ride. See that lake again or some place.\"\n\nI would collapse, surely, or so I thought.\n\nTwo Ton came closer still, and put his warm hand on my neck. \"Maybe come here, too. Mister.\" His lips brushed mine. Then he was off, riding down the hallway, wheels thumping down the stairs. He was whistling, and the mournful tune echoed in the empty stairwell. Downstairs, the main door squeaked open, then slammed shut behind him. When I stood on my toes and peered out the window, I could just make out his blond head, the bigness of him, the grace of his figure, as he sped down the alley away from me.\n\n# Stargazing at Eddie's\n\n\"I'd-a never tapped that if I'd a known she was such a ho. How 'bout it? You ride that?\"\n\nI say, \"A-a-as if,\" and Eddie chuckles, long and low. I hate when he girl talks.\n\nEddie passes a wee pinner of a joint, really just the filter. I suck 'til my mouth burns.\n\n\"Sh-shit.\" I toss the thing somewhere and pour Pabst Blue Ribbon on my sore lip. I crank back the smoke, try to keep it all in longer. I cough. Smoke and air and beer snort out my nose, even though I'm used to this stinkweed. A burn bubble grows where the ember touched my mouth.\n\nEddie says, \"Easy, Ray-Ray. Where'd you throw that roach?\"\n\nI shrug.\n\nEddie feels around for it with his big hands. I keep coughing, crapping my lungs out. Eddie and me are on his roof smoking, drinking, and bullshitting. His white mom sticks her head out the bedroom window and yells, \"Get down here, you're gonna break the bloody ruff,\" but we don't.\n\nEddie yells, \"Get your fat ass up here and make me!\" and she goes, \"Fuck, you're like your dad,\" and slams the window, and that's that for a while. Which is good, cuz even though I know she can't climb up and get us, she creeps me right out.\n\nEddie rips off his studded cap and roughs up his hair. In grade school he wanted to feather it like all the other toughs, but he couldn't. Not with his dad's nappy hair. Now he's punk. He shaves the sides and his tufty baby dreads stick up on top and all down the back, too. Like a Mohawk warrior. He plops the cap back on, sideways.\n\nHe says, \"Okay. Who's the hottest chick in our school?\"\n\nI spark up another joint so I don't have to answer.\n\nHe pokes me. \"Well?\"\n\nI roll my eyes. \"They're all d-d-dogs.\"\n\nEddie laughs and slaps the roof. \"You're funny, Ray-Ray. They're no porn queens, you're frigging right. Except maybe Mary Lou.\"\n\nI don't say anything and neither does he. I guess he's thinking about Mary Lou, who is ugly and boring and has really big boobs. We drink more beer. Eddie starts talking his usual crap about running away, about going to the big smoke, and us getting factory jobs and making lots of cash.\n\n\"We'll score hot babes,\" he says.\n\n\"Humph.\"\n\n\"They'll like me tall and dark, and you all tiny and white. We'll tag team.\"\n\nBut we both know that women don't like me. They think I'm too soft.\n\n\"We'll burn that city down, be so hot,\" he says. \"We'll start a band.\"\n\nThing is, Eddie never fills in the details. Like, how the hell would we even _get_ to the city, let alone start a band? \"W-w-we don't have no b-bus money,\" I say.\n\nEddie sucks his teeth. \"We won't take an old bus. We'll drive.\"\n\n\"Without a c-c-car?\" _On a beginner's licence?_ `\n\n\"Always poking holes in my ideas, Ray-Ray.\" Eddie sounds annoyed, like I'm the only thing stopping him from being a rich city millionaire, right this very minute.\n\nAfter a bit I say, \"We c-could hitch. On a t-t-truck.\"\n\n\"You're right,\" he says, happy again. \"That's how I snuck out of Bluewater\u2014in the back of a bread truck, got the hell right out of there. Didn't go hungry, neither. Not 'til they brought me back, anyways.\"\n\nEddie tells me that story over again, how he was stuck with some dirt bag trying to finish him off at the boys' detention centre. That _plus_ a white power gang jumping him every time he turned a corner. \"Brown boys got to stick together in juvie. But we all different kinds of brown\u2014Native, Latino, Asian. One brother blacker than me, that's it.\"\n\nEddie almost never made it out, except in a box.\n\n\"Wouldn't want to go back, neither. You would not believe the shit you have to do to get by, Ray-Ray.\"\n\nHis voice is thick with bad memories. I wonder what exactly happened to him there. There and all those other places he's been sent. It always takes him a while to settle when he comes back. Then, living with his Monster Mom, he goes bonkers, fucks shit up, and gets hauled off all over again. It's always a circle with him.\n\nEddie says, \"In fact, you and me probably couldn't even be friends there, what with the way they stack it up colour-wise. We'd get the beat down.\"\n\nI've heard all these stories before, but I don't care. I like the sound of his deep voice. Eddie's musky scent fills my nose\u2014that and the smell of the night air, and Old Red's garbage sweetly stewing down the lane, and the white tobacco flowers from the fields even farther away.\n\n\"It's not t-t-too bad here,\" I say, when he stops talking to light another smoke. I look up at the stars. Look over to the transformer behind Old Red's place. Hear it humming. Look down at the other trailers, the bungalows. Hear Eddie's Tom, Big Fat Rat Catcher, yowl as he slinks out from under a parked car. He's hunting a skunk that crosses the dirt road, then stops right in the middle. I drain my beer and lob the empty King can in a beauty arc, over the crabgrass past Old Red's garbage, so it lands in the dirt like a bomb. The skunk freaks. It flips around, tail up, legs spread, and its head sways back and forth, back and forth, sniffing the night air. A dog starts barking, down aways. Big Fat Rat Catcher stares right at me, like I wrecked his routine.\n\n\"Hole!\" Eddie knuckle punches the back of my head.\n\n\"Ow, feh-fuck.\"\n\n\"You want it to stink up the whole place?\"\n\n\"N-no,\" I says, \"But you di-didn't have to h-h-hit me.\" I blink.\n\n\"Goof.\"\n\nThe skunk prances away and doesn't spray, after all. I watch the white tip of its tail disappear into the dark bushes. Big Fat Rat Catcher blinks and is gone too.\n\nEddie burps loud and long. It bounces off Old Red's siding, and we laugh at the echo. In the background, we can hear his mom's TV. She must have opened the window again. She's chain-smoking in bed, probably wearing her lacy see-through pyjamas, watching the late-late show and the even later commercials. The ones that go on forever, selling shit you don't need\u2014no money down, don't pay 'til next year\u2014mattresses, couches, kitchen crap, cars. A zombie studio audience claps and cheers.\n\nEddie pulls the tab on another Pabst Blue Ribbon. Foam covers his fingers. He slurps it up quick. Beer dribbles off his wide lips, down his chin. Beer glistens on his thick fingers.\n\nI lick my sore lip.\n\nHe shakes his hand, shakes the beer drops that land on the shingled roof between us. Eddie leans back on his elbows, looks up at the sky. He's right good-looking, especially now, in spite of his buck teeth. Like a movie man with the light on him in all the right parts. I look away. Bend my knee to block my sudden boner.\n\n\"Want more?\" he says, so I reach for it, but he pulls the can away.\n\nI say, \"G-give me some,\" and he says, \"M-m-make me,\" and laughs again.\n\nHe rolls away and chugs the beer. He keeps rolling along the flat roof, holding the can up, not spilling much. Finally I stand up and lunge, but he scoots away quick. He's still laughing. I'm lopsided from the beers and the weed.\n\n\"Whoa.\"\n\n\"Easy there, Ray-Ray.\" Then he kicks me in the back of my knee and I fall, plop, beside him. Practically on him and such.\n\n\"Sh-shit.\"\n\n\"Don't spill it, goof.\"\n\n\"Cut it out, Eddie,\" yells his mom. \"What are ya, goddamn bowling?!\" She's got the window open again. She's probably leaning her head out, stretching her neck in a crick, trying to figure out what all's going on.\n\nWe crack up. I'm still laughing, and he pokes my ribs. I block. He fakes. He pokes again, and his big hands are faster than mine. He lands them almost every time. Those hard fingers jab my arm pit, stomach, ribs, whoops, my crotch, my armpit. I twist away. He pinches my nipple hard.\n\n\"Ow, feh-fuck's sake,\" I say, and he turns up the volume on my knob.\n\n\"Ow, m-mother f-f-fuck,\" I yell and elbow him. He's still kneeling on top of me, tweaking my nip. He drips beer on me.\n\n\"Open your mouth, whore,\" he says, dead serious.\n\n\"Ark.\" The warm beer pees right on my face. Beer bounces off my shut mouth, splashes my eyes, and pools in my neck, soaks my long hair and the top of my T-shirt.\n\n\"Look at me,\" he says.\n\nI look at him, and he looks good. Streetlight falls on his cheek, his lip; it outlines the tufts of his hair when his cap falls off. His arm muscles flex from holding me and hurting me and measuring out the beer. The lettering on his Ramones shirt glows white against his darker skin.\n\n\"Open your twat mouth.\"\n\nSo I do. I open it, right, and catch the stream. And what do you know; I pop wood again, right under him. He's leaning right on it and staring back at me. _He might punch me_ , I think. _Or throw me off the roof._ But he don't. He moves around a little, holds the can near his belt buckle, and still pours it into my mouth. I trance out, let the beer pour right in me and through me until it is all gone. And when Eddie unzips, when he slowly pulls it out, I almost lose it right then.\n\nI don't move a muscle, though. I don't even breathe.\n\nHis is nice, alright. I already seen it dozens of times. Eddie's always whipping it around in gym class, or when we're loaded, pissing in a ditch somewhere. Other times, too. I usually look away; don't want nobody thinking I'm a Gaylord. But now it's all I can see; the fat head of it sticking out a bit, the rest filling his hand.\n\n\"What are you waiting for?\" he says.\n\nI don't want to talk and ruin everything.\n\n\"Get it out, Ray-Ray,\" and I don't miss a heartbeat. I want to grind against him but he says, \"Easy, Ray-Ray. Don't be no fag.\"\n\nI'm pinned under him, confused. I don't know the rules, don't even know what game we're playing. So I follow his lead. His hand moves slowly. He says, \"Why don't you like talking about girls, Ray-Ray?\"\n\n\"Huh?\" I stroke, light as I can.\n\n\"Don't you like them?\"\n\n\"I d-don't know.\"\n\nWhen he speeds up, I do too. When he spits in his hand to work that in, so do I. Eddie leans closer, still above me, and says, \"Well? Who do you like?\"\n\nI hold myself in a tight fist, count to five, and breathe.\n\n_Don't make me talk,_ I think.\n\n\"Say it,\" he hisses.\n\n\"O-okay. I like you, Eddie.\"\n\n\"Thought so.\" His eyes don't leave mine, not once. \"How long you been liking me, huh?\"\n\nI shrug. _How long is forever?_\n\n\"Guess.\"\n\n\"Since that time you was tuh-tuh-trashed a-at Junior's b-bush party.\" That night Eddie got loaded and picked a fight with some out-of-town boys. Then he disappeared.\n\n\"You were looking for me?\" His whisper is hoarse.\n\n\"Uh huh.\" I lick my lip. I couldn't find him at the fire, in the back lot, or with the other kids down at the pits. I thought those guys were maybe finishing him off, for good.\n\n\"You came here?\" His hand moves up and down.\n\nI nod. I hate what else happened that night. Don't want to ruin everything. _Why'd I start talking about this stupid night_?\n\n\"Tell me.\" Eddie breathes hard, his mouth hangs open, his eyes are fixed, just like a humping dog.\n\n\"She would-wouldn't leave me alone.\" I hold myself tight, trying not to go limp. There's a roaring in my ears, my head rattles. I squeeze my eyes shut.\n\nWhen I open them, Eddie's face is even closer. His lips are right near mine. They brush my cheekbone. \"Hey. Ray-Ray.\" He's not touching himself now; he's touching my hair instead. \"You okay?\"\n\nI nod.\n\n\"I did come home that night.\" He licks his lips. His beer breath heats up my skin. I wish he would kiss me, but I'm not stupid. \"I was watching you. Right through the window. Watching her suck that pretty thing of yours.\"\n\n_He was watching me._ I gulp. _He thinks mine is pretty._\n\nEddie whispers, \"Did you wish it was me instead?\"\n\nI nod.\n\nHis hand goes back down but he keeps his face right beside mine.\n\n\"Me too,\" he says.\n\n_Holy shit_ , I think. I'm burning from the belly, hot in the balls, and my face cripples up. A vein explodes in my brain. Eddie thrusts once, twice. He groans in my ear, and we shoot onto each other, onto the roof, into the night.\n\nHe relaxes beside me. We're panting. Blood thumps in my ears, my chest. His skin is hot, his breath ruffles my hair and tickles my ear. His pulse, his heart beat, bangs in time with mine.\n\n_I love you_ , I want to say. _I'm yours. I am nothing without you._\n\nEddie sits up.\n\n_I wonder if he'll kiss me now._ I lick my lips, in case. But he don't.\n\nEddie clears his throat. I wait for what he is about to say. I wonder if this means he's my boyfriend. If this is how it'll be from now on with us. But Eddie doesn't say a thing. Eddie doesn't even look at me.\n\nCool air blows between us. I poke my tongue out and touch the tiny balloon, the blister on my lip. Eddie opens a new can of beer. He does up his pants, uses the bottom of his shirt to mop the sweat off his face. He drinks. He's all put together. He looks the same as before, softer in the face, but he's far away again, like nothing happened. For all I know, he's thinking about Mary Lou.\n\nI'm still hanging out, shrivelled, pruney. The wet spots could be snot drying on my skin, pulling it tighter. My stomach weeps.\n\n\"Eddie, get your ass down here and bring your pretty faggot afore I kick you right off that ruff, ya hear me?\" She's as loud as an eighteen-wheeler still, but the harsh edge is rubbed down some. It's warmed up, and there's a catch in her voice. We look at each other and we look away quick, cuz we both know what that means.\n\n\"Hope you're good to go,\" says Eddie and slaps me on the back.\n\nThat's when I start to close in on myself. That's when I want to cry or scream or punch something. Jump off this low roof. Run away. Hitch to some ugly, scary city. Throw myself to the wolves, to the wind. But I don't. I bite my sore lip and pull up my jeans. I tuck it away and zip up, button. Jiggle and shake into place. Stand up. Wobble. I follow Eddie across the roof slow, and over the edge slower, and swing myself down through her window, last.\n\nShe looks pretty good, in all. A bit like Eddie, only with big soft tits, frosted hair, nail polish, a hairy bush. Like Eddie with an even dirtier mouth, an even harder hit. Why, when that one winds up, you knock yourself. You see stars, alright.\n\n# Seven-Dollar Blow\n\n\"That guy's got the ugliest dick I ever sucked.\"\n\nDarcy doesn't say a thing, just keeps rocking back and forth, heel toe, heel toe. He's biting the skin of one itchy arm, peering through his greasy red bangs. He's wearing his huge \"Psychiatric Help 5\u00a2, the Doctor is in!\" T-shirt. Fucking Charlie Brown. Makes him look pre-teeny, younger than he really is, which is good for business.\n\n\"Plus he tried to rip me off.\"\n\nI lean on the brick wall in the alley, right beside him, and adjust my balls. I bought them at a sex store in the joke section. Pant stuffers. But they've saved my ass more than a few times, let me tell you. I tuck the soft silicone thing into my Y-fronts, average sized dick and balls, and it works. The lump looks pretty good, especially in my ripped-up jeans, though I wouldn't want to be caught pants-down, if you get me. Dudes are always peeking, too. Always trying to get more than what they paid for. Anyways, it feels good having my dick lump, my crotch bump. Definitely better than _not_ having it. Sometimes I find myself hanging around, hands down the front of my pants, just mindlessly massaging those soft greying parts. Calms me right down.\n\nI tap a Marlboro out of my pack, put it in my mouth. I feel around for my new lighter. Darcy grabs the smoke out of my mouth and puts it in his own. I tap out another and light them both with a flourish.\n\nDarcy nods at the lighter. His eyebrow arches.\n\n\"Oh, yeah. Got this from that American dude last night. The New Yorker.\" I hold the smoke in my lungs as long as I can, then blow it all out noisily. A piece of tobacco sticks to the tip of my tongue.\n\n\"Mister white pants?\" says Darcy in his strange scratchy voice.\n\nI say, \"Ha ha. Yep, Mister white pants.\" I spit the tobacco piece onto the sidewalk. _Mister talked too much, took too long, and had a fat, dirty wiener_. \"You'd think anyone who'd wear such clean pants would at least wash the cheese off their dick, right?\"\n\nDarcy shakes his head. We smoke for a bit. Cars zip by and some drivers slow down and check us out, but they keep going.\n\nAfter a bit Darcy says, \"So what were you saying?\"\n\n\"Nothing, man.\" I shrug. \"I'm just standing here. I'm not saying nothing.\"\n\n\"No,\" he says. \"Before. You were saying you got ripped off.\"\n\n\"Did I?\" I take one last drag, then flick the butt in a tall arc, right into the gutter. \"Oh yeah,\" I say. \"Yeah, that guy just now _totally_ tried to rip me off. Slips me a bill all rolled up tight and tries to book it, right, but he's not all zipped yet, so I grab what's still poking outta his fly, right? I got his thing in one hand and unroll the money with the other: a fuckin' fiver! So I says, 'It's ten.' And he whines, 'You said seven.' And I go, 'It _was_ seven, now it's ten.' He's bugging me so I give him a bit of a twist, and he jumps and is all, 'You said it would be the best seven-dollar blow job I ever had,' and I'm like, 'It _would_ have been, but now it's the best _ten_ -dollar blow job you ever had cuz you tried to rip me off, and also cuz you have the ugliest dick I ever put in my mouth.' Ha ha.\"\n\nDarcy laughs too.\n\n\"And I'm leavin,' right, and he goes, he goes, 'By the way, my sister gives way better head... for free!'\"\n\n\"No way, dude,\" says Darcy. He laughs so hard he starts coughing.\n\n\"Way. But that's the biz for you, right? You never fucking know.\"\n\nDarcy's still laughing when I flag my next trick. A middle-aged dude with glasses and a receding hairline, driving an old Tercel. He's wearing a rumpled button-down shirt that's grey around the collar. Probably got his work tie in the glove compartment. He looks like my math teacher from grade nine\u2014pasty skin, dandruff flakes on his shoulders. His wife\u2014I have no doubt at all that he's married\u2014probably hates him. Probably hasn't given him head in years. _I'm charging double_. Darcy waves me off, still chuckling. He's never gonna make any cash tonight.\n\nLater, I find Darcy back in our spot. He's twitched, freaking. I hate him like this.\n\n\"Sly,\" he whines. \"Come on, man.\"\n\nI say, \"Jeez.\" He's green in the face. Those pain pills his gay doctor slipped him are finally all gone. _Party's over_. Now he's jonesing, scratching at the invisible wrigglies under the skin of his arms, bringing up blood with his sharp, dirty nails.\n\n\"Please?\" He screws up his lips, and I see the tremor ripping right through him.\n\nI grunt. \"Fine. But you already owe me twenty. I want it back. Tonight.\"\n\n\"Sure, yeah. Thanks, man.\"\n\nHe lunges down the alley with me. Usually we go behind the can or down the street a ways, but he can't wait. That's obvious. We just fully fire up that nice rock I got after my last guy, and get a fast buzz going. I don't need it yet, but why not? It sure perks Darcy up. Getting high takes his mind off the gut rot and the three-day migraine and the sub-skin crawlers. Getting high helps him forget about his itchy arms so maybe they might even start to scab over proper for once. Getting high helps me forget how much I hate doing this shit for money. So it's totally worth it, right?\n\n\"Hey,\" I say.\n\nDarcy looks at me, right in the eyes, like he hasn't done in a long while. I know he sees me, right? He sees what I really am and not what I'm stuck with, this pathetic half-formed body. I smile and maybe I laugh a bit; I get nervous when people look at me too long. He zooms in real close 'til his sour breath warms my face and bits of his ginger hair poke me. He's calmer now. He's focussed and quiet while the chemicals shoot through him. Darcy kisses me. Kisses me warm and soft and a bit wet, just the tip of his shy tongue touching my own, creeping over into my mouth quietly. His lips move slow and sometimes suck and sometimes slide over mine, that tip of his tongue still there reminding me of what it can do. What it would like to do. And all I feel is my mouth and his mouth and the heat spreading in my crotch, the blood rushing away from my brain.\n\nThe sky gets dark and streetlights blink on. The pigs are cracking down tonight. Some nosy neighbours are complaining about the action again. Don't like the boys hanging around, playing with our own titties on the sidewalk. Don't like us swinging around the bus-stop pole, smoking on the corner. Don't like the tires screeching and car doors slamming and stereo music getting loud then quiet when the cars peel off into the night. Don't like their husbands sneaking out for a beer at the corner bar and spending grocery money on a hand job in Kiddie Porn Park. Don't like finding used condoms on the ground the next morning, either, but then, where are we supposed to put them? Don't want their husbands fucking with no latex, right? They just can't win, those broads.\n\nDarcy paces up and down our corner. He's wearing a new shirt with wide stripes, long sleeves. It has a white collar with a few snaps at the top, like some frat guy shirt. Some kind of university shirt. He wipes his nose on the too-long sleeve of one arm. He looks relieved to see me. \"The King cruised by with a wagon. He picked up Lil' Brat.\" He spits.\n\n\"Shit.\" You don't want the King to catch you, that's for sure\u2014meanest cop in town, obsessed with hunting street kids. He calls it pest control, like we're rats or some kind of bug. The nervous twitch under my eye starts up.\n\n\"Where were you?\"\n\nDarcy's eyes shift one way, then the other. He's sketched.\n\n\"Fuck it,\" I say. \"I can't get busted. Let's jet.\" Darcy knows I'm already on probation. Not to mention the complications of getting thrown in the slammer when I'm obviously a boy except for the few inches between my legs. The shit I _should_ have been born with, but _wasn't_. Then, if I don't get murdered in the clink, it's off to the shrink factory for me, suits and nurses trying to brainwash me into being a proper biological girl specimen.\n\n\"Where to?\" says Darcy. He's bugging.\n\n\"I don't know. You got that twenty you owe me?\"\n\nHe blushes. \"I did. But, well, now I don't.\"\n\nI finger the designer name on his chest pocket. \"Nice shirt.\"\n\nHe cracks a smile. \"That big courier gave it to me.\" He blushes again.\n\n\"Which one?\" But I already know the answer. I can even see him wearing the shirt, filling it all out perfectly, whizzing past us on his skinny tires, that satchel strapped around him. That blond one, the big beautiful one, the one we all love. He spins around on one wheel doing bike tricks on our corner, smoking spliffs between calls.\n\nI smell Darcy's betrayal. The wall of secrecy he slapped up when I wasn't looking, when I was out working and he was lounging around, available. There's a small stab in my belly, the jealous knife. I try to bury it. Can't have any of that, right? I don't even know who I'm jealous for: Darcy or that other boy.\n\nDarcy shrugs. His long-sleeved arms swing wildly, like some cartoon guy. Then he starts pacing again. We're broke. It's not the warmest night. The sky might open up and dump rain all over us, any minute. I have one small rock left. Four cigarettes\u2014three, cuz now Darcy's smoking again.\n\n\"Why do I always got to think for both of us?\"\n\n\"You're good at it,\" he says. \"Good at using your head, ha ha.\"\n\nI want to punch him, but instead I swallow hard. I don't want to be alone tonight. \"Bathhouse?\"\n\n\"Naw,\" says Darcy. \"I'm not in the mood for those fuckers. No clubs, no bullshit.\"\n\n\"Underpass?\" But we both owe money to some dealers over there, so I know that won't fly. It's too late for the drop-in where we crash sometimes. Darcy's sister put out an R.O. on him so we can't go there, and Henry, well, Henry is definitely out of the question.\n\n\"What about your vegan hippies? Can we go there?\"\n\n\"Hmm.\" Darcy twiddles his fingers on his chin. \"Probably not. Not supposed to hang there if you're fucked up. House rules.\"\n\nI snort. \"What are they, straight edge? No wonder you're never there.\"\n\n\"Too far, anyways.\" Darcy snaps his fingers and says, \"What about the Professor?\"\n\n\"Aw, that dude is away somewhere. Out of the country or something. Can't stay with him.\"\n\n_But we could stay at his place, right?_\n\n\"No, goof, it's _this_ street.\" I stop on the corner, but Darcy keeps going. \"Fine, be that way,\" I shout after him.\n\nHe keeps walking down the main drag of the gaybourhood. He's stubborn, but he's usually wrong when it comes to directions. He'll come back when he figures it out. I lean on a parking meter and pull up my hood. It's getting colder.\n\nIt's dinner time, that lonely twilight hour. Gay men run in and out of the expensive shops. There's a cheerful sign in the butcher's window right in front: \"Our meat's not cheap but neither are you.\" Inside, a well-dressed man leans over the counter and points: organic beef, lamb shanks, lean spiced sausage.\n\nMy stomach growls. Looking at that meat reminds me of the time Darcy got the great idea to go cattle rustling. We had this rich old trick in Cabbagetown who had a nice big patio for summer parties. We discovered his deluxe new barbecue while squatting his garage last spring. Darcy's idea was to steal raw meat from the grocery store. So we smuggled it out in our pants, right, and carried it bare-handed all the way down to the old man's house to try and talk him into buying it, cash on the spot. _Ha ha._ Made some money that day, didn't we?\n\nMe and Darcy have panhandled this whole strip long enough to know the drill: Starbucks' lattes in the morning, brunch at noon, afternoon shopping, dinner with a friend. Then a long night of drinking, dancing, and debauchery. Around here, most men like their meat as fresh and pink as the boys they invite over later, after the scraps are tossed.\n\nDarcy runs back down the street toward me as the sky opens up. \"Shit, you were right,\" he yells. I'd laugh, but we're busy running. Down comes the rain: big drops, surprisingly cold and stinging. Almost hail.\n\n\"There,\" he shouts. He points to a tiny fenced-in front yard with a large boulder as a centrepiece. He leaps over the wrought iron and lunges around several flower pots.\n\n\"There was no rock!\" Darcy's not listening. This thing is so large it must have been driven from goddamn Sudbury, driven down Highway 69 in some kind of reinforced flat-bed four-by-four, a truck from my ghostly past.\n\nHe says, \"It was this place with the rock, so shut up,\" and I cuff him. I'm still kind of mad about the courier. Darcy looks around for the spare key. He peers under the doormat and in the mailbox and digs up some of the orange flowers from the garden. \"Fuck,\" he yells.\n\nThe rain is pouring down his face, drilling into the ground, slopping mud all over his sneakers and the draggy hems of his pants. He's about to smash the wee glass pane on the front door when we notice a man inside, staring at us. He's wearing an apron and oven mitts and he's holding a frying pan in one hand. In the other is an oven-mitted cell phone. He looks a bit scared but mostly surprised. He waves the phone down towards the mess of flowers at Darcy's feet. Now he's pissed.\n\n\"I told you it's the wrong house.\" I book it.\n\n\"I coulda sworn that was it,\" he says, when he catches up to me. He's laughing, imitating the dude. His hair is plastered to his forehead. That awful shirt is completely soaked.\n\n\"Shut up.\" I cut across another fenced yard and duck behind the shrubs that block the front door. I move the mat. The key is right there, small and hopeful. It isn't breaking and entering if you got a key, right?\n\nInside it's quiet and dark. It smells musty. Darcy locks the door and puts the chain across. He squeaks his wet shoes down the hall and into the living room.\n\n\"Take your shoes off,\" I yell. \"Seriously.\"\n\n\"What are you, my mom?\"\n\nI take mine off, pull the wet hoodie over my head, and peek around the corner into the living room. There are bookshelves all around. Stacks of books lay on the ground in front of them. Books spill off the coffee table. Books support a dying plant. Books underneath the phone. There's a small TV covered in more books. There are a couple of old chairs. Darcy collapses on the professor's big leather couch, muddy shoes smearing the little pillow at one end.\n\n\"Fuckwad. Look at the mess.\"\n\nDarcy sucks his teeth. He slowly reaches for his shoes, one then the next, and tosses them at my head. I catch and drop them on the plastic tray by the door. The small recycling bin beside the boot tray is full of old newspapers. And on the very top is the temporary cancellation notice\u2014for one whole month.\n\n\"Uh, this dude is away for a while,\" I say.\n\n\"Awesome.\"\n\n\"Well, I'm washing my clothes, right?\" I know where the machines are from the last time I came over. The professor gently touched my clothes and asked if I wanted them cleaned. He didn't make a big fuss about it, just showed me where everything was and how to turn on the washer. _He wouldn't mind_ , I think. I go straight down the hall, through the small kitchen, open the closet door, and there it still is.\n\n\"Do mine, too,\" says Darcy. He follows me to the kitchen. He rips off the preppy shirt, his pants fall around his feet. He pulls his dirty socks off, then his Tasmanian Devil boxers, not a blink of an eye. He's naked and absentmindedly tugs his ball sac, scratches his bony chest. His skin is so white, the veins show through. Blue veiner: that's what chicken hawks call him at the bathhouse. When Darcy first got to town, he sure made some money. The men couldn't keep off him. Now, he's no runway model, but at least his arm sores aren't oozing.\n\n\"I'm hungry, yo.\" Darcy opens one cupboard, pokes around, slams the door, opens another. \"Fuck, this guy has no food.\" He tosses a few things onto the counter, packages of ramen. They fall to the kitchen floor. \"I want Kraft dinner.\"\n\nI dump soap into the washer, turn the dials, and start the water flowing. Darcy's stuff is all in there. My socks: one, two. My hoodie: empty the pockets. My shirt goes in. I duck and check my chest from habit. The scars are healed up pretty good now, faint lines near my jujube nipples. I never had tits to speak of, always more like pecs anyways, so the surgery wasn't too drastic. Like, I can take my shirt off in public if I want, and no one is any the wiser. Except other trans guys, right? I don't know how we can tell. Smell it, probably. Sniff each other right out of a crowd, we can. My muddy jeans get slogged into the machine, and I debate the underwear. They're wet, not fresh either. But I hate even Darcy seeing me.\n\n\"Take it off, sugar loaf.\" He swings his bony hips at me.\n\n\"Shut up.\" But he's not even looking.\n\n\"Can you believe this dude doesn't even have proper cereal? Like, what is this shit?\" He shakes a box of bran into a pile on the floor. \"I want Cocoa Puffs!\"\n\n_Fuck it_. I pull off the tighty whities and toss them in. I slam the washer lid down. I cup my hands in front to hold my dick in place and head for the bathroom. \"Just don't make a friggin' mess,\" I say before shutting the door. I put in the stopper and fill the tub with hot water. There's a bottle of something smelly so I squeeze a bit under the tap: a real bath with bubbles. I step in, jump out, hop around holding my burned foot. _Shit shit shit shit_. I take a dump while the water cools. It's been a while since I got to use such a nice clean toilet. With soft paper, too. I flush and even spray the air a bit with the faggy freshener. Now the water is perfect. I hunker down so it covers me, comes right up to my bottom lip when I lie back. I decide my dick should have a bit of a rinse, too. I soap it up and wring it. Dirty water runs out. I rinse it a few more times, and it starts to look pinker. It looks less like a part of me and more like something I once paid money for. I prop it on the edge of the tub and lie back again. I look at it up there. It looks at me. Then I submerge myself totally.\n\nLying underwater I can hear Darcy cranking the knobs on the TV. \"This shit don't work,\" he yells. He comes into the bathroom. \"I'm bored.\"\n\n\"Knock much?\"\n\nDarcy yawns in the mirror. His eyes crinkle up and his mouth stretches wide. The red hair sprays around his face like a demented halo. He leans forward and starts picking at his teeth. He finds a toothbrush in the drawer and loads it up with minty paste. He scrubs carefully, like he's remembering the instructions from a long ago manual. I gather up what's left of the bubbles and station them above my crotch. Darcy spits and rinses. He smiles at me in the mirror. \"I can see your boobies,\" he says.\n\n\"Shut up.\"\n\nHe looks hurt. \"I didn't mean it like that. I meant boy boobies. Boys have boobs, too, you know.\" He puts his big toe in the tub water and wiggles it around. He splashes me and I grab his cold foot.\n\n\"You stink.\"\n\n\"So clean me,\" he says, and plops right on top, knees and elbows cracking against the porcelain tub. We wrestle a bit, send waves over the edge, onto the tile floor. Our bones clack together; it's a tight squeeze even for two skinny boys. Finally Darcy settles himself at one end, his head resting on one side of the faucet, his legs stretched out so his feet pop up beside my shoulders. My legs rest over his narrow torso, my feet near his face. He blows bubbles with his mouth. He smiles at me strangely, then up pop a series of large bubbles from the middle of the tub.\n\n\"Gross!\"\n\nHe says, \"Ha ha. There's your bubble bath.\"\n\n\"Your feet stink,\" I say. He waggles them on either side of me.\n\n\"Yours are dirty, too.\"\n\n\"So wash them.\" I chuck the wet cloth in his face.\n\n\"Don't be like that,\" he says. \"You get so mad all the time.\" He looks at me for a minute. Then he sends another loud bubble to the surface by my leg.\n\n\"What the\u2014?\"\n\nDarcy is in hysterics.\n\nHe grabs my foot and slides the soap bar in between my toes. When he gets near the little one, my foot twitches, and he holds it tight in his hands. He rubs along the bottom, all the way to my rough heel. He presses around the heel, traces the sides of my foot, massages deep in the arch and in the sore, neglected ball of it. He pulls the toes again, slowly, twisting them a tiny bit just before letting go.\n\nMy voice wobbles when I ask him where he learned to do that.\n\n\"My mom used to make me rub her feet all the time when I was little,\" he says. \"They got sore from hookin' in high heels.\" He sings this last part and rolls his shoulder, shakes his wet hair like a dog. \"My sister bossed me around and made me paint her nails. No wonder I'm queer.\"\n\nWe laugh. Darcy adds more hot water. He has to stand up so he doesn't get burned. He sits in front of me, my legs cramped around his, like we're riding a toboggan downhill. I soap up the cloth again and slop it loudly against his narrow back.\n\n\"What would happen if the King caught us?\"\n\nDarcy flinches. \"Seriously?\"\n\n\"Uh huh.\" I wash his pale back, long strokes, up and down.\n\n\"Well, the first time I heard about him was from this kid. This cute little hustler, Jake. He had some story about the King snatching up kids and selling them off. Like permanently. For snuff or other fucked-up movies, for dungeon boys, that sort of thing. Everyone thought Jake was on the pipe too much, though. He was always borrowing money and scamming, right?\"\n\nThis Jake sounds a lot like someone else I know. I trace my finger from one freckle to the next on Darcy's back, past his sharp shoulder blades and the knobby bumps of his spine.\n\n\"So Jake was going on about it, right, saying the King was on the hunt. He was scared shitless, trying to hide, even trying to get out of town, trying to bum more money off everyone, but no one would give him any. Cuz he already owed.\"\n\nDarcy sighs and shivers when I dribble more water down his back.\n\n\"Then what happened?\"\n\n\"Then he disappeared, all of a sudden. Nobody's seen him since.\"\n\n\"Maybe he did leave town,\" I say. \"Maybe he went home.\"\n\n\"Naw. He wouldn't. Not if half the shit he said about his parents was true.\"\n\n\"Maybe the social workers got him. Maybe he went to fosters,\" I say.\n\n\"Nope.\" Darcy wriggles his shoulders. \"Rub me.\"\n\nI slop the wet cloth on his skinny back again. We sit in silence for a while.\n\n\"Well, he could've gone anywhere,\" I say.\n\n\"Who?\"\n\n\"That kid,\" I say. \"Jake.\"\n\n\"Oh, him. Well, he could've, but he didn't.\" Darcy sounds pretty sure of himself.\n\n\"How the hell do you know?\" I don't know why this makes me so mad. It scares me, more than anything.\n\n\"Because I know. I saw pictures.\" Darcy's voice is tight, scratchier than usual.\n\n\"What kind of pictures?\" I say.\n\n\"The dead kind.\"\n\nI drop the cloth in the water. \"Where'd you see those? At some creep's place?\"\n\n\"No.\" Darcy's voice sounds strangled. His shoulders hunch forward.\n\n\"Are you crying?\" I try to twist him around but we're rammed in that tub, and there's no room.\n\n\"No,\" he says loudly. Darcy's shoulders start to shake. He gasps. A high-pitched sound squeezes out of him. I don't know what to do. I've never seen him like this.\n\n\"What's wrong?\" I say, but that's dumb. _Everything's_ wrong and we both know it.\n\nDarcy sobs while he talks. He sounds just like a little kid. \"I-I just feel bad. I never believed that boy, and now he's fucking dead.\"\n\nFinally we twist around a bit so I can hold his wet face against me. His boney white self jabs at me, all angles. He knocks against the tub and splashes water around. The ugly sounds that cough out of him are more like a dog barking than a boy crying.\n\nI ask him more questions, but Darcy just howls. He won't say anything else. Like where he saw the pictures, or who had them. Or what exactly happened to Jake. I get the feeling he knows a whole lot more, though. He's scared. _Wigged right out_. As though it could happen to him.\n\n_And it could_ , I think. _To any of us._\n\nHis terrible fear infects me, quick as the hep, quick as the bug, quick as any bad thing at all. I think about Lil' Brat, smart as a fox and twice as mean, gone with the King today. _What will happen to him?_\n\nDarcy calms down after a while and we add more hot to the tub. His dirt and stink are finally washing off. He fiddles with the cloth for a bit but eventually settles against my chest again. His wet hair pokes in my eyes and mouth but I don't mind. I lean back and let the water do its thing. I don't know where to put my arms so I just kind of hug them around his front. It feels nice. My dick falls in the water and he picks it up, squeezes it softly, and holds onto it.\n\n\"You don't mind, do you, Sly?\"\n\n\"What, you playing with my dick again?\" We chuckle. I can feel his laugh rumble against me and it's better than before, better than his heaving, awful cries.\n\n\"Let's stay here for a long time, Sly.\"\n\n\"Okay. Til the Professor comes back.\" But I wonder how soon it'll be before he gets bored or starts jonesing, before he paces up and down the hall, restless, edgy, and needing some kind of fix.\n\n\"No, I mean the tub. Let's stay in this tub forever.\"\n\nI say, \"Okay.\"\n\nBecause in this business, you just never fucking know.\n\n# Happy House\n\nHome is the Factory squat. From the first time I climbed through that broken window with some kids from the shelter, I knew it was my place. I could take my boots off here. Maybe even sleep a whole night without getting my shit fucked with. Just like the first night I met Oreo. When I saw her\u2014a gorgeous punk warrior smiling brightly\u2014a light turned on in that empty inside space, and I knew she was meant for me.\n\nThe Factory is not an address you can write on social worker forms. Can't get your welfare delivered here. It's totally under the radar, a boarded-up chair factory in the Junction. It's hidden from the rest of the city by a wall of trees and tangled bush, like a prickly moat in some fairy tale. The slaughterhouse next door is a small, sinister-looking thing. It reeks. An abandoned lot separates us from them, but that smell is everywhere. Not like meat, or even raw meat, but the gag-worthy smell of pig shit and rotting entrails and old blood. No one else would even try to live up here, not with that stink.\n\nSo, home is a smelly, red-bricked fortress with giant padlocked warehouse doors on one side. We use the regular-sized door at the back; locks stripped off, doorknob gone. We got electricity\u2014some kid wired it up a year or so ago\u2014but there's lots of natural light. We ripped boards off some of the windows. Up high in the loft section there are even more windows, not all broke. It's a mess, but we're slowly clearing it out. Some kids call it the Pig House on account of next door, but we're against that. One, we're vegans and don't insult animals. Two, we totally hate cops. Three, the _slaughterhouse_ is the Pig House and _our place_ is the Factory, end of story. Someone started calling it Fairy Mountain since our squat is now fully gay, but people started thinking F.M. was a completely different place, like a whole new squat someplace else in Toronto. Totally confusing! So really, we are just the Factory squatters, and that's that.\n\nThe Factory has rules like anyplace, but it's better than shelters and foster care and the Boys' and Girls' Home before that. Obviously, it's way better than living on the street, getting beat on and hassled and eating rape for breakfast, like you do. Going hungry and losing your mind, friends turning on you. Always on the make. At the Factory we do chores to fix the place up. We dumpster dive food and cook together, have house meetings, that sort of thing. Sometimes we have punk shows in the main space, or DIY workshops about silk-screening, basic plumbing, worm composting, whatever. Lots of kids pass through in the summer: rail riders, touring bands, punk nomads. If they stay, they got to cook or fix shit or teach stuff. They got to make the Factory a better place for being there. That's rule number one.\n\nAlso up there, not exactly number two or anything, but up near the top, is this other rule about not oppressing other people with your bullshit. I thought that would mean not being a racist asshole or a homophobe and stuff like that. Apparently it also means not rubbing your \"monogamous romance\" in other people's faces because this can be boring and offensive. You can have all the sex you want with as many people as possible, but so help you if you fall for one girl and want to be with _just_ her. Like, as a couple, which is seriously my situation with Oreo. Personally, I don't think it's fair, but that's what it is to live in a freegan collective\u2014plenty of compromise!\n\nSo here we are again, me and Oreo, standing in the gravel driveway _outside_ the Factory for another Relationship Talk. At least it's not raining.\n\n\"Oh, shit.\" Oreo, adorable as she is, looks totally guilty when I wave the paper.\n\n\"You wrote this, don't pretend you didn't,\" I say. \"That's your handwriting.\" Not to mention her signature skull and crossbones decorating the page.\n\nShe opens her mouth but a truck downshifts, brakes, and pulls onto our little road. I can't hear her, just see her mouth moving. We dive behind the corner. The truck churns up small stones and spits them out as it passes. I hear squealing, and when I peek, I see all those round snouts through the dirty cages. They're heading next door.\n\n_Poor little piggies._\n\nWe wait for the dust to settle and the truck to park itself and the roaring engine to quiet before we continue.\n\n\"It's supposed to be a surprise.\" Muscles ripple along Oreo's arm when she points at the large heading. \"See? Ferret's _surprise_ birthday party. It's a to-do list, babe.\"\n\n\"Obviously,\" I say. \"But you shouldn't have left it lying around where I'd see it.\"\n\n\"Yeah,\" she says. She looks pretty bummed. \"That sucks.\"\n\nShe has written everything out carefully with extra swirls and lightning bolts around each number on the list:\n\n1. dumpster dive vegan cake\n\n2. draw a funny birthday card\n\n3. write love poem for Ferret\n\n4. make brilliant playlist for party\n\n5. check with squat about party!!\n\n\"Oreo, I don't want a birthday party.\" My stomach knots just thinking about it.\n\n\"How do you know? You've never had one.\" Oreo kisses me. She tugs my blue dreadlocks, twirls one end between her fingers.\n\n\"I shouldn't have told you that. Just cuz I haven't _had_ something doesn't mean I _want_ it.\"\n\nOreo chuckles. \"You sure about that, babe?\" She flashes a perfect, flirty smile.\n\n\"Uh, yeah.\" I think about every creep who says I'm only a dyke because I haven't had \"the right one\" yet.\n\nHer warm hands creep playfully inside the waistband of my combat pants. Her fingers rub the tickly spot above my crack. \"Come on, Ferret.\" She gives me a slobbery zerbert on the cheek. \"It'll be fun.\" She smiles. Oreo has really nice teeth\u2014evenly spaced, white. The tip of her tongue pokes out at me. Farther back I see the silver flash of her piercing. She says, \"You'll get to be the centre of attention.\"\n\n\"I hate that.\" My head droops onto her shoulder.\n\n\"Okay, you'll get to sit on the sidelines and see your friends having a great time.\"\n\n\"Hmm.\" I squish my face into the crook of her neck and tug her long braid. She smells like honey cake, the lotion we shoplifted at the pharmacy. When she talks, I feel her voice rumbling from inside her chest. I trace the neckline of her ripped Slayer shirt, touch her warm skin with my finger. She is the most beautiful colour ever: coffee with cream. She is taller and darker, bigger and braver than me.\n\n\"If you don't like it, you don't have to have another one.\" Oreo looks hopeful, something I don't feel too often. \"I already made my list. Please?\"\n\n\"I just want to be with you.\"\n\n\"Me and you are together all the time. You should have fun with friends.\" Her smile and her shining eyes and the way her beautiful face lights up when she has her hands shoved down my pants make me buckle.\n\n\"I don't even know when my real birthday is.\" If you get dumped at the Boys' and Girls' Home without a proper birth certificate, without a note or some weeping, incapable mother to tell them about you, they just assign a date.\n\n\"Saturday night sounds good.\"\n\n\"Maybe.\" I hate to disappoint her.\n\n\"I'll get you Sour Cherry Blasters.\" She wiggles an eyebrow.\n\nI sigh. \"Oh, all right.\"\n\n\"Ferret's having a party!\" Oreo bounces up and down. \"It's gonna be sick. You wait.\"\n\nMy knees wobble when she kisses me. Heat spreads in my belly. Oreo smiles and pulls me towards the Factory door. Like I said, you can have all the sex you want in there, just don't flaunt a Meaningful Relationship.\n\nWe step from the hot, bright outside world with its sun and its buzzing, flying creatures into the dark, dank Factory. Cement floors and boarded windows make it cool inside, even though it's the blazing end of August. The Factory smells musty. Old. Exposed brick with oversized storage units line the walls. Giant iron chains hang off pulleys in the corner by the padlocked loading dock. Oreo and I zip past the open kitchen area with the long dinner table to the back corner where our mattress is hidden behind shelves and a tall wall unit. Oreo's shirt is already off. She yanks my studded belt. I pull our makeshift curtain across the rope guide and hook it in place. Our corner smells like incense sticks and vanilla candle wax and patchouli oil and sawdust and, of course, slaughterhouse. Oreo pulls me down on top of her. We roll and giggle and kiss. Oreo whispers into my mouth, \"Happy beerthday, dear Ferret, happy beerthday to you.\"\n\nLater that afternoon, we're crashing through the tangled bush that surrounds the squat. We're taking the back way to Special Friend Discount, the sketchy convenience store, to get my Sour Cherry Blasters. At night, we cut through the open field and just walk down the gravel lane that the pig trucks use, which is faster. But during daylight we keep it on the down-low.\n\nSpecial Friend has the basics: dust-covered groceries, porn, tampons, and junk food. Most Special Friend customers buy cartons of illegal cigarettes straight from the reserve, cash only, and only if no one else is in the store. And only if the cashier recognizes you. And not if they think you might be a narco, out to bust their ass.\n\n\"Out of everything we've ever dumpstered, how come there's never been any Sour Cherry Blasters? Don't you think that's weird?\"\n\nOreo thinks about it for a minute as we continue down the steep hill, crushing overgrown weeds with each step.\n\n\"We always have more food at the Factory than we need, right?\"\n\n\"Yeah,\" she says. The path widens and she grabs my hand so we can walk side by side.\n\n\"All the ripe fruits and veggies we can eat, tons of it organic. Day-old bread, doughnuts, noodles, you name it. But no Sour Cherry Blasters, not ever.\"\n\nOreo says, \"Maybe stores never throw them out. Maybe people like us are so busy eating them, they never get wasted. If you stop buying them, you could maybe score them for free.\"\n\n\"Maybe. I can't wait, though. I want some now.\"\n\nWe cross the railway tracks and pop out of some greenery onto the sidewalk of a small street that leads to the Junction, past all these old homes. Most are dilapidated, renovated into cheap rooming houses or bizarre churches with long names. Some are yuppie investments, with new roofs and pretty front gardens. One or two are boarded-up wrecks. Special Friend is only a couple blocks farther.\n\n\"Surreal,\" says Oreo, looking back at the now-hidden path that leads to the squat.\n\n\"We're invisible in there.\" Oreo rubs her neck where my mouth marked her. \"It's like we don't even exist.\"\n\n\"In a good way, though.\" I laugh and swing her hand in mine. It's still sunny, hot. I'm with my girl. I have a safe place to live and good food, even some friends. I'm happy, for once in my life, invisible or not. That feeling\u2014the sudden realization that things could maybe get better for me\u2014tingles in my spine.\n\nOreo giggles. \"Ferret, you got burrs all over.\" She pulls one off my sleeve. \"There's more.\" She crouches down and works at the ones on my combat pants.\n\n\"You, too.\" We pick them off each other for a minute or two. I can't reach the ones on the back of my shirt. The street is deserted except for us. The houses on either side have blinds or curtains in the windows. Nobody's spying, so I take my shirt right off and keep picking at the burrs. Oreo inspects my pant seams, all the way up to the crotch.\n\n\"Whoa,\" I say, smiling at her.\n\nOreo laughs and lifts me up. I wrap my legs around her. We kiss for a long time. My shirt flutters to the ground. I forget what we're doing, where we're supposed to be going.\n\nThere's the sound of an engine. There are brakes.\n\n\"Well, well. Looky here.\" The low voice cuts through our lips, severs our bodies. We'd recognize it anywhere. I scramble down, and Oreo steps in front of me.\n\nIt's the King. He likes to be called the King because he sounds like Elvis. He does his black hair the same way, too, greased up with sideburns. He is also the King because he rules this city, at least as far as junkies and hookers and street kids go. The cop car is parked beside the curb facing the wrong way. The King leans out his open window. The door opens, and he stands up, and up. When he walks toward us he grows even taller; his blue uniform gets bigger with each step.\n\nMy leg shakes. My mouth goes dry. My shirt is only a pace or two away on the other side of Oreo, but my feet are heavy cement blocks that won't budge.\n\n\"Some reason you're not wearing a shirt?\" He stands close to us, too close, and he rests one large hand on his hip, right near the black holster that holds his shiny gun.\n\nOreo says, \"It's not against the law. Not in Ontario.\" Her chin juts out. Anger pinks her cheeks.\n\n_Oh, shit._\n\n\"You think people want to look at your flat tits?\" He looks disgusted, like I'm a bug he'll squash. \"Think everyone wants to watch your disgusting lezzie show?\"\n\n\"Put your shirt on, Ferret.\" There's a tic in Oreo's cheek. _She might blow_.\n\nI bend down for the shirt, but the King steps on it with his huge polished shoe. \"You'll put that on when I say so.\" He's not even looking at me, just staring right back at Oreo.\n\nI keep my hold on the fabric, in case he lifts his foot. I'm crouched low, trying to cover myself. I have a close-up of his shiny cop shoes and his hemmed pants.\n\n\"Get up.\" His voice is mean. It feels like a stomach kick; it hurts all the way through. He snaps his meaty fingers in my face. He's standing so close to Oreo that he's pressed against her.\n\n\"Don't talk to her like that,\" says Oreo.\n\nThe King puts one large hand around Oreo's neck and grabs my bare shoulder with the other. His squeeze sends spasms through my dangling arm. His fingers could break me. \"I'll talk to her any goddamn way I please, dyke. I will say and do whatever I like. I'm the law.\"\n\nOreo struggles to get away, but he presses harder. Her face darkens. She makes awful sounds, choking, gasping for air.\n\n\"You unfuckable little sluts make me sick, you know that?\" He covers us both with his coffee breath. His nose is red and veiny at the end. Spit flies from the corner of his mouth when he talks. \"Now. Put your filthy shirt back on.\"\n\nI would. I want to have as many layers as possible between my insides and him, but he's still holding me, threatening to snap my very bones.\n\nHe shoves me. I stumble. I land half on the sidewalk, half on the grass. He's got Oreo by the throat with both hands now. He lowers his face and he's saying something, I don't know what. He's squeezing the life out of her, right in front of me, and there's nothing I can do. I grab my top and try to put it on. My fingers tremble. My left arm, the one he hurt, hangs numb. I might be crying. Every inch of me screams to run, run, but I can't leave Oreo with this monster.\n\n\"Please.\" My voice falters. \"We'll go, okay?\"\n\nHe squeezes harder. Oreo's eyes bulge. One of her boots kicks out like a puppet dancing. I panic. My breath shortens into small gasps. I feel dizzy watching, but can't look away.\n\n\"You'll go when I say so.\"\n\nOreo's face is a terrible colour. Veins stand out on her temples. Finally the King releases his hold. That's when I exhale.\n\nOreo collapses. She retches. Her hands flutter to her throat. She stays curled on the ground. This is terrible, to see her humiliated like this.\n\n\"Public indecency, mischief, loitering... I could nail you with any of those. But you're not worth the paperwork. So get the fuck outta here before I change my mind!\"\n\nI'm beside her, hands petting, trying to calm her down. I tug on her arm. I try to lift her. Her eyes snap open. Now she's up. We run down the street, past the shuttered old houses with the sagging porches, toward Special Friend. The King follows us to the corner in his car. Then the car turns and slowly chugs away in the other direction. Oreo coughs. She spits on the sidewalk. There are marks coming up around her neck that cover my love bite completely.\n\nWhat happens next is terrible, too heartbreaking to watch. Oreo kicks the newspaper machine on the corner over and over, denting the side of it. She howls. That probably really hurt. Oreo paces the sidewalk punching the air, swearing, screaming, pulling her long black hair out of its braid.\n\nI sit on the cement stairs of the convenience store and wait for it to pass. She's in a rage, that's for sure. She can't help it. You just got to know that about her and when it comes, you step away. Let her do her thing. You definitely do not want to be up in her face. The first time I even saw Oreo she was in the pit at an all-ages hardcore show downtown. She noticed how some guy wouldn't leave me alone. She gave him what for and, of course, he snotted back to her. So she slugged him. To be punched by a girl, even a butch one, was embarrassing for a punk. But when he hit Oreo back, he invited the beat down of his puny existence. Oreo knew how to fight, and that day she did it for me.\n\nToday, though, there's no one else to hit. No physical release to extinguish this hate inferno the King sparked up.\n\nThe store owner comes outside and waves a cell phone around. Oreo stops yelling.\n\n\"No trouble,\" he says. He turns and says something in Korean to his wife, who is huddled inside, peering out from behind the long-distance phone-card posters on the front door.\n\n\"Please,\" I say to him. \"No phone.\"\n\n\"No trouble, no phone,\" he says, looking warily at Oreo. She's standing in the street, her back to us. Her torso heaves with each breath. Her hands hang at her sides in loose fists, defeated.\n\n\"Please.\" I feel my eyes well up and have to look away from him.\n\nEventually he goes back inside with his wife and they both stare out the front door until I walk towards Oreo.\n\n\"Hey.\"\n\nShe sniffs loudly.\n\n\"I don't feel like candy anymore,\" I say.\n\nShe nods.\n\n\"Let's go home.\" I touch her back lightly. She flinches. I wait. She wipes her face with her sleeve. She spits into the street. Then she takes my hand and we walk back the way we came. We don't say a word when we pass the spot where it all went down, we just keep walking.\n\nOreo hits the path first. She moves fast in long robotic strides. One of her steps flattens a patch of long grass. In its wake I notice a small piece of paper. I stop to pick it up. It's a typed message from a fortune cookie. It says, \"Happy celebration happy, Wong's House of Love.\"\n\n\"Yeah, right,\" I mutter. But still, I fold it and put it in my pocket for safekeeping.\n\n# Toddlers and Tiaras\n\n(For Doris)\n\nMe and Darcy sit on the rusty fire escape outside the old lady's apartment window. We're waiting for our show to start. It's sweaty hot; the night air is heavy, with no breeze at all, not even five floors up. I shift. My bony ass hurts and angry red stripes mark the backs of my bare legs. Darcy pulls his T-shirt up over his face but keeps the collar around his forehead, tucked behind his ears. Then he twists the cotton material into a thing that he ties up like a turban on his head, covering his greasy red hair.\n\n\"Freak.\"\n\n\"It's my tiara, Sly,\" he says. He tries to grab a cigarette from my pack but I slap him. He sighs. We both know the smoke would snake right in there, through the open window, and the old lady would smell it, and she'd know we were perched out here again. Last week she threw a pot of dirty dishwater at us, and that was not great.\n\n\"Wish we had some chips.\" He farts.\n\n\"Shut up, Darcy. She'll hear us.\"\n\n\"As if. She's fucking deaf.\" He does it again, louder and longer.\n\n\"Yeah? I bet her nose works just fine.\"\n\nHe laughs. \"Listen, if your Professor friend had an effing TV we wouldn't have to be here. I'll probably get a disease sitting on this contraption.\"\n\nI don't say anything, but we both know Darcy already has the hep, and he didn't get it climbing fire escapes. Plus, we're _lucky_ we can stay at the Professor's. We're _lucky_ we're not out on the street getting our asses beat by people we owe or by the cops, who hate us. We're lucky the frigging King didn't scoop us up in his latest raid and that he hasn't tracked us down since.\n\n\"It better not be a highlights show,\" says Darcy.\n\n\"Shh. It's starting,\" I say, as canned laughter bursts out. We sneak right up to the window, lean our elbows on the sill. We're a foot away from the back of her couch with the crocheted blanket on it, maybe two from the back of her head. Her white hair is combed neatly, and she's got a long braid wrapped around, tucked into a bun, and pinned in place. If we lean to one side, we can see her big old TV directly in front. It's like we're at the drive-in, sitting in the back seat.\n\nThe theme song swells, the trailer rolls, and we hunch closer. We shimmy our shoulders in time to the music. Darcy claps his hands lightly to the beat. Inside, the old lady hums off key. After the song, the show host announces this is the second-last show of the season\u2014they're kicking three more girls off tonight. Then there's a commercial break, time for the old lady to make her sandwich. She grunts when she leans forward and slowly stands. She shuffles into the kitchen. We hear plates banging around and the fridge door slam.\n\nNow we lean right through the window, everything from the waist up. We reach over the back of the couch to pet the stuffed dogs all piled up on it. One of them, a worn-out Dalmatian, stares its googly eyes at me. I make it growl softly, then bite Darcy's scabby arm.\n\n\"Quit it,\" he whispers.\n\n\"Arrrugh,\" I bark back.\n\nThe glow of the television lights up the shelves around the stand. There are dozens of ceramic dogs flickering in the blue light, all sitting on old lady doilies. Some of them beg paws-up, some have tongues flapping out the side of their china mouths, some leap with painted frisbees in their teeth. She has a Dogs of the Year calendar up on the wall\u2014from 1987.\n\n\"Think she has any weed stashed?\" he asks hopefully.\n\n\"Yeah, right.\" Last week, when we first came here, it was to score pills from the bathroom cabinet. But as it turned out, the old lady was watching Darcy's favourite show. So instead of robbing her, we just chilled and watched from outside until she caught us, like.\n\nThe fridge door bangs again. We crouch down. The lady has it timed pretty good. She shuffles back into the living room just as the commercials end. The couch springs creak when she plops down, and we peek our heads up. She's got her sandwich on a small plate. It's cut in half diagonally. She picks one triangle up and stuffs it in her mouth.\n\n\"Onions?\" whispers Darcy. He wrinkles his nose.\n\nI elbow him.\n\nThe old lady sets her plate with half a sandwich down on the side table. She flicks crumbs off her lap. She claps as they open the curtain and the little girls stand ready, toes pointed, hands clasped, those concrete smiles holding up their faces. Beady-eyed mothers hover on the sidelines. The host waves from centre stage and trills out names: Ashleigh, Morghan, Rhianna, Tressa. Lyndsey, Tarabelle, Crystal Dawn.\n\nThe old lady heaves herself up and raises a fist toward the television.\n\n\"Aw, why she got to stand right there?\" Darcy sucks his teeth.\n\nWe lean to the right, to the left, to opposite sides at the same time, trying to see past her. She's short and wide. She's got her hands on her hips and she's yelling at the judges. Not in English, in some other language.\n\n\"She sure sounds mad,\" says Darcy.\n\n\"Seriously.\"\n\nDarcy crosses his arms over his bare chest. \"I mean, why have a couch if you're not going to sit on it?\"\n\n\"Beats me.\"\n\nShe waves her hand one last time in disgust, then slowly bends to sit back down. She lands heavily and some of the stuffed dogs avalanche into a pile around her. \"Bah,\" she says. She picks up the Dalmatian and sniffs it.\n\nOn television, the girls move stiffly around the tiny stage and wave. We get close-ups of each one, cut to prerecorded snippets when the girls forget they are on camera. Rhianna rolls her shoulder: Rhianna, collapsed in her hotel room as the adults argue about which dress she should wear. Morghan and Tressa, the prudey sisters, twirling: Morghan and Tressa eating too much cake and getting yelled at by their mother. Tarabelle shuffle-steps: Tarabelle falls asleep while her arch-nemesis practices walking in the hallway, her mother shaking her head: \"No, do it again. No. Do you want to keep your pretty dress? So do it right.\"\n\nThen there's Crystal Dawn. Darcy and the old woman start clapping. Crystal Dawn is definitely their favourite. She's the creepiest, only three and a half, but she has the plastic made-up face of a forty-year-old. Her smile is frosty, and her eyes shine like a store-bought doll, like all the little girls who compete in these pageants. She waves triumphantly. Crystal Dawn is so outrageous, she gets an entire shame video all to herself. They edit seconds from each of her temper tantrums to recreate the whole gorgeous mess. It's like flip books you make in school when you're bored. It starts with the first bottom lip twitch. Then the shaking, silent, stretching open mouth as her face gets red and wrinkly. She sucks in air\u2014we all hold our breaths. Finally, it's the money shot: the unapologetic howl! Her drooling, snotting, rage assault! We're addicted to it, all three of us. The whole continent, really.\n\n\"Wow,\" I say. \"That never gets dull.\"\n\nDarcy nods. \"I wish _I_ could cry like that.\"\n\nI don't say it, but he pretty much _did_ cry like that, just last week when we first landed at the Professor's.\n\n\"Oh, not again,\" groans Darcy.\n\nAs if the tantrum video is not enough, the show producers cut back to Crystal Dawn's notorious piss scene. Inside, the old lady sighs loudly. She reaches for the other half of her sandwich. She doesn't want to watch this either.\n\n\"There she goes,\" I say happily.\n\nFlashback: Crystal Dawn crouches backstage, sticks out her bum, and pees through her lace-trimmed Christian Lacroix panties. She looks like an angry animal, red-faced, fists clenched, yellow curls bobbing. Crystal Dawn's mother, a hefty lump of a woman, screams and shakes her. \"Those cost 425 bucks, you brat! That's coming out of your prize money!\"\n\nThe old lady hollers.\n\nDarcy almost gives up on Crystal Dawn every time he sees this clip. \"She has no respect for French design!\"\n\n\"She's not even in kindergarten. How's she supposed to respect anything?\"\n\nInside, the lady drops her plate; it clatters to the floor and she bellows. We duck. We stay crouched down 'til she's quiet, just the show blasting. The host says the panty pee scene has had more YouTube hits than the inaugural address. Crystal Dawn's baby voice booms: \"I did a bad mistake, but tonight I'm gonna be perfect.\"\n\nThe old lady murmurs. We peek over the sill. Darcy gurgles with excitement. Crystal Dawn _is_ in top form. Her helmeted up-do sparkles with rhinestones, golden ringlets pasted into place. Her eyes shine from the lubricating drops her mother puts in right before she hits the stage. She's got her tan sprayed on, and her flippers tucked in her mouth to cover those crooked teeth. She's wearing a pink and white cupcake, the short tutu all the littlest girls wear. When she walks across the stage, she swivels her hips. Her hands flit like birds with rigor mortis. Her shoulders roll aggressively. She winks at the judges. She's killing the competition, and she knows it!\n\n\"Oh, she's wearing the Jon Ben\u00e9t booties,\" squeals Darcy. \"Bold move. She'll totally win now.\"\n\n\"Not if they call Children's Aid, she won't.\"\n\n\"Children's Hate? You want to sic those dried-up social workers on Crystal Dawn? What's wrong with you?\"\n\nHe thinks I despise these girls since I hated being one myself.\n\n\"Crystal Dawn's mother is a great manager, Sly. Her stylist has impeccable taste!\"\n\n\"Whatever.\"\n\n\"You know, I used to dream about being in pageants. Only _my_ mom didn't care enough to put me in them.\"\n\n\"You want a mother like that? That can't stay out of her track pants long enough to make another baby to pimp out?\"\n\n\"At least they can see their children's _potential_.\"\n\n\"Potential of a cum-crusted death in a scary basement?\"\n\nThe lady stiffens. I duck down again instinctively.\n\nDarcy whispers, \"It's swimsuit time. Look.\"\n\nThey're all lined up in their fruity two pieces, but I stare at the space off-stage and at the crowd during the sweeping camera shots. I'm looking for the forgotten siblings: a truly ugly step-sister, some invisible brother, or unloved cousin. Maybe a henpecked husband, guarding the miniature designer dresses, yawning. Somebody real. Someone you can sink your teeth into.\n\nDuring the next commercial break, the lady goes into her kitchen. We lie flat on our backs. Darcy tries to think who we can score off of.\n\n\"I thought you wanted to get clean.\"\n\n\"I did. But now I'm not so sure,\" he says. \"Being sober is boring.\"\n\n\"Oh, so I'm boring?\" I ask, pouting.\n\n\"I didn't say that. You're so touchy.\"\n\n\"Anyways,\" I say, \"being bored is better than being dead.\"\n\n\"Ooh.\" Darcy pokes my arm.\n\nI push his finger away. One week hiding out at the Professor's and Darcy has forgotten all about being scared to death, about being hunted by the King. He wants back in the game.\n\nHe says, \"I know I freaked. I was wigging. But I'm fine now. I just want to get high.\"\n\n_I did a bad mistake but tonight I'm gonna be perfect._\n\nI shrug Crystal Dawn's voice out of my head. \"Well, we're shit outta luck, man.\"\n\n\"Maybe not. A lot can change in a few days,\" he says.\n\n\"We're still broke. We still owe a lot of money. Actually, _you_ owe a lot of money, but somehow I always get stuck paying.\" Fuck if that don't piss me off.\n\n\"You make me sound like an asshole,\" he says cheerfully.\n\n\"The pigs are probably still looking for us. So we won't be making any money tonight.\"\n\n\"Fuck,\" says Darcy.\n\n\"Pretend we're on _Celebrity Rehab_. Famous people pay a lot to be someplace they can't get high. We got it for free.\"\n\n\"You're whack.\" Darcy snaps his fingers. \"The courier! We could stop by his place, see what he's got.\" Darcy sparkles just thinking of that big blond boy.\n\n\"He took you to his place?\" A lump hardens in my stomach.\n\n\"So?\" Darcy's eyes shift. \"How do you think I got his sweater?\" His lip curls into a sneer.\n\nI remember the night he showed up wearing it, while I was working double time. The night of the storm, when we ended up crashing the Professor's pad.\n\n\"Well, without a GPS tracker you'll never find your way back there.\" I try to joke, but there's an edge to my voice.\n\nHis face tightens. He knows it's true, so he can't exactly argue. Darcy sighs. \"I wish I was a girl model. I bet they get all the drugs they want. Plus I'd wear dresses everyday.\"\n\n\"Why?\" I snort.\n\n\"My legs look good in them. And they come off lickety-split.\" He smiles prettily. \"When's the last time you wore one?\"\n\n\"First day of kindergarten. My mom made me. Teacher made me line up with the girls and I was like, _no, I'm a boy_. I kept going into the boys' line, and she kept pulling me out, so I kicked her. I put the frigging dress in the garbage. They called my mom cuz I was running around in my underwear, yelling.\"\n\n\"Troublemaker.\"\n\n\"Yeah, we used to fight all the time. She didn't get it.\" I chuck a small stone over the edge of the stairs, hear it hit the gravel parking lane below.\n\n\"She probably _got_ it, she just didn't _like_ it.\"\n\n\"I guess.\"\n\n\"So, you hate this show?\"\n\n\"Kind of,\" I say. \"It's so fake, all the stuff they do to them. But it's like they're making little girly monsters, which is cool.\"\n\n\"If you hate it so much, why watch it?\"\n\n\"Well, you love it. So it reminds me what a Gaylord you are!\" I laugh and Darcy steamrolls me, and that makes me laugh even harder.\n\n\"Hallo!\" There's a sharp rap on the window ledge.\n\nWe sit up. The old lady must be standing behind the couch. She's right at the window. I put my hands up to block whatever she'll throw this time.\n\n\"Okay, we're leaving,\" says Darcy. He scrambles toward the steps, grabs the railing for balance.\n\n\"S'okay. S'okay,\" she says and motions us to come closer.\n\nI don't move.\n\n\"Hold dat.\" She passes two flowered plates through the open window. Each one has a little sandwich on it, cut diagonally. Darcy takes them, his mouth hanging open. \"You gif me plates beck after.\"\n\n\"Thanks,\" I say finally. We sit back down on the stairs with our snack. Darcy sniffs his like a hungry dog. He looks at me. I shrug. She nods and waves: _go ahead_. The bread is strange\u2014dark, heavy. When I put a bit in my mouth, it is soft and good. Darcy digs in, takes a big bite, and hums while he chews. I take another small mouthful. There are slabs of cold butter on it. Then there's some kind of filling, cream cheese with chopped green onions. Nothing I ever ate before. The creamy part is salty and also a bit sweet. It tastes good. The lady smiles at us and then she sits back down on the couch.\n\nFor the final few minutes of the show, we actually lean farther in the window. We don't have to be quiet or anything. \"Kreestal Don, number von,\" says the lady. She sticks her wrinkly thumb up. Darcy sticks his thumb up, too. I'm out-voted.\n\n\"Crystal Dawn definitely has personality,\" I say.\n\n\"Charisma,\" says Darcy.\n\n\"She can't take the pressure,\" I say. \"Not of being Little Miss West Virginia.\"\n\n\"Vat you say.\" The lady frowns at me. \"Shoosh.\"\n\nDarcy says, \"Yeah, Sly. _Shoosh_.\"\n\nThe host is about to announce the results. \"Which three will it be tonight?\" There is a drum roll. The mothers rub their good luck charms. Tarabelle, who forgot her choreography half-way through the song, she's gone. No surprise there. She wails as one of the handlers leads her off stage. The camera bounces back and forth over the tense faces of the remaining contestants. The cake eaters, Morghan and Tressa, look terrified. Rhianna is pale. _Did she wear the right dress after all?_ Apparently. It's Morghan and Tressa who get kicked off for poor performances and bad attitude, according to the judges. They leave the stage shame-faced, one biting her lower lip, the other wiping at tears.\n\nCrystal Dawn is safe! Darcy and the old lady cheer. The host reminds us there are only four girls left\u2014the heat is on! Next week promises to be even more scandalous. One of the parents is caught sabotaging another girl's props in the green room.\n\nDarcy hands back our plates. \"That was really good,\" he says.\n\nThe lady looks at us. Her old blue eyes see past our dirt and bruises, my messy hair, and the sores on Darcy's arms. \"Next veek, you bring cheeps. I like peekle flavour, yes?\"\n\nWe nod. _Yes_.\n\n# Pig House Party\n\nEveryone who squats the Factory has to agree on something like having a party, so I figure it'll never happen. Which is perfect because it won't be _my_ fault. It'll be the fault of our dumb-ass collective who can't agree on anything, not even what to have for breakfast. So I write \"party\" on the house meeting agenda, right after \"dishes.\"\n\n\"Washing dishes is bougie,\" says Cricket. We're all sitting at the kitchen table except for Cricket, who sits cross-legged _on_ the table, painting his nails bright blue to match his mohawk. \"The bougie middle class, afraid of germs, so scared to think about what happens to stuff once it's no longer perfect. That's why they obsess on dishwashing and laundry and floor cleaners. They don't want to face the reality that life is one big organic mess and we're all going to die.\" He blows on his nails.\n\nDigit scratches his facial hair. He is trying to grow a goatee like Anton LaVey so he will look more evil for his future black metal band, but right now it's just itchy chin scruff. He sighs and finally pipes up in his heavy Acadian accent. \"What's the big deal? Hif you need someting, take it. Hif it's dirty, wash it! We got to be more independent, _tabarnak_.\" He adjusts his bullet belt, which hangs around the hips of his skinny jeans.\n\n\"Exactly,\" says Oreo. She chews the end of her long black braid. She's been quiet all meeting, hardly even paying attention. Her voice is hoarse, still messed up from yesterday's run-in with the King. Bruises are coming up on her pretty brown skin. \"Even Zapatistas wash their plates.\" She points to the photo taped above the sink; guerrillas cleaning their dishes in a river, their semi-automatic weapons lying on the grassy bank.\n\n\"Yuppie propaganda,\" says Cricket. He tightens the lid on the nail polish and flutters his hands.\n\nOreo says, \"That's authentic revolutionary footage.\"\n\nCricket says, \"Whatever. It's not like we have an entire military campaign hunting us like the Zapatistas did. We can afford to leave a few plates around. What about our grey water politics?\"\n\nWe look at the propped-open window where we scoop water from the rain barrel outside. We use rainwater to wash dishes and ourselves. The leftover dish and bath water is for plants and to flush the toilet when it's full.\n\n\"The entire planet is in a water crisis, and Oreo wants us to wash dishes? Unreal.\"\n\nOreo's eyes narrow. \"I just want everyone to pull _his_ own weight.\"\n\n\"Point taken,\" I say quickly. I signal Cricket to cut it out. Oreo is in no mood. That cop fucked us up, and not just physically. The King broke something inside Oreo, something I don't know how to fix.\n\n\"Oh, don't get all essentialist on me, Oreo. Gender is a social construct; this squat is living proof. Washing dishes has nothing to do with whatever I might have between my legs!\" Cricket rolls his eyes.\n\n\"Not today,\" says Oreo. Her voice breaks.\n\n\"Fine,\" he says loudly. Cricket yanks up his patched hood and pulls the drawstrings tight, so his face disappears completely. There are funny lumps where his mohawk bends under the weight of the fabric.\n\n\"Man, you always got to talk about penis,\" says Digit. \"Why you don't just wash your plate? Hit's easy.\"\n\nOreo has a spark of life back in her now. \"Yeah, don't start what you can't finish, Cricket. I'm sick of cleaning up after white boys.\"\n\nDigit sighs again, loudly. \"Alright, everyone _try_ to wash their own dish, and also _try_ not to be total jerks.\" He drums his knuckles on the table in front of him. \" _\u00c7a marche_?\"\n\nSilence.\n\n\"Seriously, guys. I want dat in the minutes,\" says Digit. \"For the people who _isn't_ here, who probably _should_ be more _serieux_ about the collective. In New Brunswick, we don't have dis kind of ting. You get in the group or you get out, you know?\"\n\nHe means red-headed Darcy. Darcy used to panhandle at the underpass with me, over a year ago. He's been around town and then some, always got his hand in some shit or other. He came to a punk show a while back and decided he was moving in, at least part time.\n\n\"Are we gonna talk about him or what?\" says Oreo.\n\n\"It's not on the agenda,\" says Cricket in a muffled voice. \"And we don't talk about people when they aren't here, remember?\"\n\nOreo says, \"That kid is sketch. We said no junkies in the squat. We _have_ to talk about it.\"\n\nDigit says, \"He have some bad friends. He owe a lot of money, I hear dat for sure.\"\n\nI say, \"He needs someplace safe. He seems sick. Where else can he go?\"\n\nCricket says, \"Well, where is he right now for our meeting? We're not an effing drop-in, we're a intentional freegan community!\"\n\nI say, \"So we want to change the world but not help the people who live in it?\"\n\nCricket sighs loudly.\n\nDigit scratches his face again. \"Who's writing da minutes?\"\n\nCricket loosens his hoodie and peers out. \"Oh crap, I'm supposed to.\" He rummages for a pen that works and for paper in the recycling box. There is a terrific lull while he scribbles down the stuff we've been talking about for the past hour: _Don't forget to compost. Worm bucket is outside, other organics in the back field. Whose turn is it to water the plants? Our tomatoes are almost ripe! Let's dumpster less food so we waste less, or let's invite people over so they can help us eat it all._ And: _Oreo wants us to wash our dishes so she can stop being an uptight bougie twat._\n\n\"Okay, I'm ready,\" he says. \"Damn, I wrecked a nail.\"\n\nDigit says, \"Who's chairing the meeting?\"\n\n\"Oh. I am.\" I clear my throat. \"So, uh, next item. Oreo was thinking we should have a party for my birthday next Saturday. What do you think? Probably a big hassle. Imagine how many dirty dishes there'll be.\"\n\n\"Very funny,\" says Oreo.\n\nCricket stops flitting his blue fingernails around, and says it's a _great_ idea. \"Maybe we can even make some cash, selling beers and whatnot.\"\n\nI cringe.\n\nOreo frowns. \"No money. This is for Ferret.\"\n\nCricket says, \"So, how you gonna pay back that fifty bucks you owe?\"\n\nOreo says nothing, and I say nothing. Fifty bucks is a lot. I get my welfare in a few days, but Oreo wants to use some of it to get stuff for the party. Stuff we can't barter or beg or dumpster for ourselves.\n\nDigit yawns, says we should get some bands to play, like _his_ new band, only they haven't really started jamming yet, but they'd be able to _maybe_ play some songs by then. \"Maybe one or two. Black fucking metal.\" He makes devil horns with his fingers.\n\nOreo says, \"No way, man. I'm DJing for Ferret so she can dance. We need something with a beat.\"\n\nThen Digit says, \"Maybe we should have other DJs, too, for _musicale diversit\u00e9,_ \" and Oreo says, \"Like _who_? Who is more diverse than an Ojibwe lesbian dance party like me?\"\n\nDigit says, \"Not a more diverse person, I mean some good music.\"\n\nOreo sticks her tongue out and crosses her eyes.\n\nI laugh.\n\nDigit says that at his first band practice, which turned into a tremendous beer and barf festival, he met Nefarious Rancor who's visiting _from New York._ \"I can probably hook that up,\" he says. \"He does brutal solo shit. The band is usually booked for, like, months, but he's in town right now. Only he _might_ want some money to play.\"\n\nAnd Cricket says, \"Oh yeah? Well, I heard that dude's in rehab, and his rich Thornhill parents are paying for it, and that's the _only_ reason he's here. Anyway, how are we gonna pay some metal Gaylord if we don't even charge cover?\"\n\n\"He's not gay, he's bisexual,\" says Digit quickly. \"I hear that, anyways.\"\n\n\"We're not charging cover,\" says Oreo. \"It's a birthday party. And I wouldn't complain about rich parents if I were you, Cricket.\"\n\nCricket ignores her completely. \"What about hot Geraldo's band, Migrant? That would be wicked. People will totally come for that.\"\n\n\"I love Migrant!\" I say.\n\n\"Why don't you ask your mom for some cash?\" Oreo asks Cricket, sneering.\n\n\"Okay, let's not talk about parents,\" I say quickly.\n\nI don't have any, so it doesn't matter to me. But this is the kind of thing that can get ugly fast. Digit grew up between the curb and the closet, no joke. Oreo's mom and aunt were killed by a drunk driver on New Year's Eve two years ago in Sudbury. But Cricket's family wires him money whenever he needs it, thinking he lives in residence at the university. The fact that he chooses to live the freegan life strictly for political reasons while still attending classes is great and all, but sometimes it rubs Oreo the wrong way.\n\n\"All right, I'm sorry.\" Cricket is quiet for almost an entire minute.\n\n\"Happy break,\" I say. We do that sometimes if stuff gets tense. Just move around in that big old building, skateboard up and down the long length of it, maybe have a snack.\n\nCricket stays put, dejected. He hates being reminded of his race, gender, and class privilege. It makes him feel less radical. Digit shrugs and says he'll make everybody peanut butter sandwiches on the bagels we scored today. _Typical Digit, always thinking of the group_. Oreo lies on the floor and stretches like a cat.\n\nI go for a walk in the field between the Factory and the slaughterhouse. Really it's just an empty lot, a no-man's land where folks have been dumping shit for years. I like to look at our brick building, especially on a night like tonight with all those pretty stars out and with an almost-full moon pouring down, lighting up our house from space.\n\n\"Hey, Ferret.\"\n\nThe voice comes from over by the slaughterhouse. It's Eddie, sitting on the ledge having a smoke break. When he waves, the motion-sensitive outdoor security light blinks on. He's in the spotlight now, wearing coveralls and the long, bloody rubber apron and tall rubber boots. I don't want to be rude so I go over, even though I hate the whole pig blood situation.\n\n\"What up?\" Eddie smiles and his buck teeth gleam. There's gore smeared on his chin. Eddie is tall and thin with skin darker than Oreo's. Blurry ink\u2014homemade tattoos\u2014decorate the sides of his shaved head, neck, and hands. Probably covers everything in between, too. Eddie lets anyone practice on him as long as it's free.\n\n\"Looks like we're having a party Saturday. You should come.\"\n\n\"Hmm. We don't go out too much.\"\n\n\"But it's my birthday. You got to come. Bring your boyfriend.\"\n\n\"Oh, Ray-Ray? Yeah. He's pretty shy, but...\" Eddie wipes his nose with his forearm. Blood smears across his cheek.\n\nI nod. _Me, too_.\n\nIf you can get past his stutter, Ray-Ray is totally cool. His delicate hands, big eyes, that long, white-blond hair\u2014he's like some fragile princess from a far-off time. Eddie is his dragon-slayer prince.\n\n\"I don't really party anymore,\" he says, like an apology. \"Gave up the crank, all that shit. I'm doing good, too.\"\n\n\"Way to go. Just come say hi. It'd be nice.\"\n\nEddie takes one last drag off his smoke and flicks the butt to the ground where all the others are. \"Break's over.\" He smiles again. Then he goes through the side door, back into the killing machine, and I cross the field toward our place.\n\nEddie's probation officer got him the job, and it's true, he's been on the straight-and-narrow ever since, working hard, looking after his boy. He told me the saddest thing about working the slaughterhouse was that he had to give up bacon, which he used to love. His mother bitched when he visited the trailer park, \"Why didn't you bring some meat fresh off the conveyor?\" Something about watching hundreds of animals get lined up, hosed off, then electrocuted or bashed on the head every day, something about that changes you, I guess. Eddie's job is to reach up and, in that flickering moment when the pigs are harnessed into submission and hopefully stunned, to gut them, one after the other. I've seen him work, and it's not pretty. His gloved arms go right inside the steaming hot mess of their insides while they are technically still alive. The smell never leaves him, the stench of their blood and their shit as it pours out onto his boots and onto the concrete floor, the screaming and grunting. That killed his love of bacon.\n\nI re-read the fortune from my pocket, the one I found on the path yesterday: _happy celebration happy_. Then I light a match and set it on fire. I whisper the phrase for luck while it burns in my fingers. I drop the last piece in the grass and watch 'til it's nothing but ash. _There_. I walk past mattresses with rusting coils popped out, old fridges, trashed cars with weeds growing up though the busted-out parts in their dented frames. Something scurries past\u2014probably a rat, the way it skitters and bounces. I feel better. Being in nature always clears my head.\n\nBack at the Factory, Cricket draws happily. Oreo blasts her favourite Dirt EP. She and Cricket shout the final chorus: \"Object Refuse Reject Abuse!\"\n\nIn the ensuing silence Digit pouts because his band got nixed from the lineup. \"What does Migrant got dat we don't?\" he says.\n\nCricket says, \"First of all, you don't have a name. You don't even have a guitar, man. You're not a band 'til you have something to play and an effing name. Then by all means, call me.\" Cricket shrieks and waves his cellphone in the air. \"Geraldo texted back\u2014Migrant is totally in!\"\n\nDigit grunts. He fiddles with some metal piping he found in the dump.\n\nOreo says, \"DJ Silo's said yes, too. We'll alternate spinning. She's awesome.\"\n\nCricket says, \"No club kids. No fucking poseurs, no way. I'm putting that on the flyer\u2014they'll bring the bougie pigs.\"\n\nI say, \"Flyer?\"\n\nEveryone looks up, startled, like they've forgotten me.\n\n\"Why do we need a flyer if it's just a few folks getting together for my birthday? I don't even have that many friends.\"\n\n\"Sure you do, Ferret. There's everyone at the drop-in and the underpass, there's the Frenchies in Parkdale, and our girl posse.\" Oreo is ticking off one finger for each group. She waves four fingers at me.\n\n\"Those people don't even know me. They're your friends.\"\n\nCricket says, \"Girls, can you keep your monogamous relationship issues private?\"\n\nI say, \"It's not about our relationship, it's about how many people do you want in our place? Like, is this party for me or is it for the squat or what?\"\n\n\"Hit's for all of us,\" says Digit. \"But let's not go crazy.\" He picks up a piece of wood that was lying around, and balances it on top of the metal he's wired together. \"Hey, if I sand dis and attach hit like dis, we can use hit for the birtday cake. Look.\" The wood rotates smoothly on its new-found perch; it's a punk-rock, custom-built Lazy Susan.\n\n\"Wow,\" I say. \"Digit, you're the best.\"\n\n\"Just what we need. More bougie kitchen crap!\" says Cricket. \"Well, I'm definitely inviting my new boyfriend. Oh my god, he is so hot. Maybe he'll bring his courier friends.\"\n\n\"Your imaginary boyfriend,\" says Digit. He rolls his eyes.\n\n\"Oh, he exists,\" says Cricket. \"And he's going to be existing in my pants on Saturday night, so get _\u00fcber_ it.\"\n\n\"Word,\" says Oreo. They high five, which is nice, since they've been bickering all night.\n\n\"Okay,\" I say. \"Invite whoever you want; it's for all of us. Let's not get busted, though.\"\n\nEveryone is like, _Fuck that, we're not having no cops here._\n\nAn image of the King pops into my head. I feel that sore spot on my shoulder where he bruised me. Oreo and I look at each other. No way do we want to run into that pig again. Suddenly, Oreo laughs, something I haven't heard in a while. She cues up N.W.A.'s \"Fuck tha Police.\"\n\n\"Spin it, girlfriend!\" Cricket leaps off the table. He spanks his own bum as he dances around the room. Oreo joins in, laughing. _That's better._\n\n\"Eh. Can we ave hardcore and metal, or is dat too much to ask?\" Digit hates dance music. \"Otherwise I won't bodder inviting anyone.\" He's sanding the board now, and it looks pretty good.\n\n\"Maybe,\" shouts Cricket.\n\n\"Maybe not,\" shouts Oreo.\n\nI say, \"What should I do?\"\n\nOreo pulls me close and sways in time to the music. \"You just figure out what you're gonna wear, Ferret. It's your party.\"\n\n\"Hmm. This _is_ what I wear.\" I look down: dirty patched combat pants, heavy metal belt, scuffed boots, some ripped stinking shirt over a vintage bra I've never washed, a few pounds of leather and metal jewellery. Oreo hugs me tighter.\n\nCricket shouts, \"Some girls wear skirts. They're hot. You should try it.\"\n\nOreo nods and smiles.\n\nI don't say anything, but I wonder.\n\nBy Saturday night, we are wired. We take turns washing our crusty dishes. When no one is looking, I throw a couple into the dump\u2014they're just too disgusting. Oreo stacks her second-hand speakers around the room, tapes down the wiring, sets her turntables out, lines up her vinyl underneath. We haul out the generator for this, since we'd probably blow the low power still humming in this building. Oreo tests the system, and it sounds amazing. We have some serious bass happening in the Factory. Digit clamps an old lamp to the table for light. He sets his homemade Lazy Susan on the kitchen table and the big cake on top. Oreo scored it from the health food dumpster. It's gorgeous vegan, gluten-free fudge, and it smells incredible. Some loser would have paid forty bucks for it, but technically it's past the expiry date. The top isn't even crushed. I lick some icing off the box. _Mmm_. Cricket clears a dance floor. Digit and me put our stuff away in cupboards and staple fabric over the fronts so people won't go through our shit.\n\nAt the last minute, I change into a short skirt from the free bin at the drop-in. I pull fishnets over my bruised legs and put on more makeup than usual. I feel like some drag queen, lurching around in borrowed shoes with a two-inch heel. But there's something else. I feel\u2014not exactly pretty, but _special_. Like something good could happen to me, now that I'm paying attention. _Happy celebration happy_.\n\n\"Hooka, what?\" Cricket slaps my behind when I stagger past.\n\n\"Seriously, Cricket. Do I look alright?\"\n\n\"Yep, you clean up pretty good, Ferret,\" and that makes me smile.\n\nOreo's eyes light up when she sees me. She whistles at my short skirt. There's that electric thing again, that zap of possibility. \"You look good enough to eat.\" In these shoes, we're the same height, eye to eye, boob to boob. I kiss her at this new angle and that calms me. It reminds me of the only things that matter: this place, our friends, and us.\n\n\"I still wish we were alone.\"\n\n\"Oh we _will_ be, don't you worry.\" She kisses me again and trails her fingers down my back. She rubs my neck, my shoulders, even the one that is still sore from the King. She tugs on my skirt and smiles, and I'm glad I did it. I'm glad I tried something new.\n\nSoon people drop by. Kids who used to live here, who did workshops, shows, that sort of thing. There are kids from downtown, from the hardcore scene, and the drop-in. Some bring their dogs, and most of them get along. Geraldo arrives in an old van with his gear, and Digit helps set up the drum kit and plug in the PA and mic. Crust punks pile to the front of the long room as Geraldo tunes his guitar. Then the small girl playing bass fills the Factory with a subterranean rumble. The dreadlocked drummer clicks his sticks together and suddenly the band explodes in a frenzy of sound. Kids drop their bags and push into each another, they writhe and slam, and the more everyone moves, the warmer it gets. The music stops as suddenly as it begins. People whistle and cheer. \"This song is for the keeds in my country,\" Geraldo says breathlessly into the mic. \"It's called, 'Food Not Clowns: We Can't Eat Your Bombs.'\" Drumsticks click again, bass and guitar barf an onslaught of high-speed chords into the air, kids sweat and shout and bash into each other in a joyous frenzy. I can hardly breathe until the song's over two minutes later.\n\n\"Migrant kicks _ass_!\" I shout to Oreo. She smiles and squeezes me, shields me from a spazzed-out boy in the make-shift pit. When the set ends a few songs later, kids pour outside to get air, to cool off, and Geraldo starts packing up the cords and pedals while wiping sweat from his face and neck. Oreo helps them clear out their gear\u2014so does Digit, who is apparently not holding a grudge about the whole band thing. In fact, he looks downright friendly, chatting up Geraldo, who apologizes for cutting out early. Migrant has another gig across town tonight and they have to jet. Oreo switches a patchcord and gets a CD playing, and kids gradually drift back inside.\n\nEveryone is excited to be at the Factory for one big bash before summer ends. Oreo turns up the music and people dance. _This is fun_ , I think. Kids tell me happy birthday; they go out of their way to be friendly, and I think, _Oreo was right. They do like me!_\n\nMore people come, people I don't recognize. They barrel through the back door. They bring fancy beer and expensive booze. Some of them make fun of our place, wrinkle their noses. They pile their purses and bags near the door. It's hard to get in and out with all their stuff in the way. They scare off the crust punks with their perfume and soap and the smells of their hairspray and who knows what else. Clean, shiny people sit on the couches we pulled from the dump, on our makeshift chairs, and up the ladder rungs that lead to the loft. Rich kids dance in the main room of the Factory. They laugh and gossip and gulp fruity drinks. Girls wear sparkly clothes with large earrings, tight pants, and strappy, bright sandals. Some of them want different music, and they start to bug Oreo, asking for shit we'd never play here\u2014Britney and Fergie and Beyonc\u00e9. I see that tic in Oreo's cheek, which is not good. Oreo plays it cool, though. No fighting; she just tells them to go fuck her mother if they don't like her tunes.\n\n\"Did you hear what she said to me?\" A whiny blonde gets pulled by the arm. Her friends glare at Oreo.\n\nA couple punks sneak over to the rich kids' pile, start sifting through the designer bags. I could say something, but fuck it. It's not like those clean kids belong here.\n\n\"Are they from your university?\" I whisper to Cricket. He's pouring vodka from one of their large bottles.\n\n\"Fuck, yeah. Bougie poseurs. I'm making you a birthday drink. It's on them.\"\n\n\"But how did they find our place?\"\n\n\"Probably DJ Silo, that top-forty sellout. She's in my queer studies class.\"\n\n\"You think _they're_ queer?\" I can't believe it. They're so shiny.\n\n\"Oh, honey, they're not queer; they're the gay-lesbian enemy\u2014mainstreaming homos. We're nothing like them, don't worry.\"\n\n\"Huh.\" I look at all these girls again. Some of them are pretty touchy-feely, kissing and standing close. Some of them are definitely checking Oreo out; they blush and giggle and try to talk to her. My stomach tightens with worry. I grab a beer from the fridge and gulp it. I don't want to ruin anyone's fun, but seriously.\n\n\"Digit!\" I have to yell, and he still can't hear me over the music and all those voices. I chuck my beer cap and hit him square in the back of the head. He grins when he sees that it's me.\n\n\"Ay, _bonne f\u00eate, ma fille_!\" He pushes his way over to me, beside the cake.\n\n\"Digit, are these your friends?\" I trace the cake edge with my finger and lick the icing.\n\n\" _Absolument non_. Great party, eh?\" He swigs some beer. \"This is nothing. More than 200 people reply on Facebook.\"\n\nI'm speechless.\n\n\"Don't worry, it's not like I attach a map or someting. It's cool.\"\n\nBut I wonder. Crickets' flyers are all over the place. The slaughterhouse is marked with a drawing of a pig, and there's a giant X for the Factory. It says: Pig House Party, B.Y.O.E. Fuck you, Club Kid Poseurs.\n\n\" _Salut, toi_!\" Digit gives devil horns to someone in the crowd.\n\nI take my heels off and climb onto the ledge by the kitchen sink. I wobble. Now I'm taller than everyone, and I can see almost the whole main room. I try to count\u2014in twos, in small groups\u2014but nobody stands still long enough. I get sixty, then almost eighty; that can't be right. I forgot the upstairs. Maybe seventy. I round up, I round down, I give up. The Factory is full.\n\n\"Whatcha doin,' girl?\" Cricket's obviously had another drink.\n\n\"Trying to count. Digit says 200 people replied on Facebook...\"\n\n\"Digit posted on Facebook? He's such an ass.\" Cricket helps me down and holds my arm while I put the dreaded shoes back on.\n\n\"We should eat that cake, honey.\"\n\n\"Everyone?\"\n\n\"Uh-uh. Just you and me. Fuck Facebook. Fuck the bourgeoisie!\" With that, Cricket stabs the cake's dark centre with our butcher knife. \"I killed the cake,\" he shouts, and a few people turn to watch. He keeps stabbing. We laugh and grab handfuls, rich and moist. I smear some on his mouth. Cricket plasters my face.\n\n\"Mmmmmph.\" I'm chewing and swallowing and savouring this thing like love that fills my mouth. \"Wow.\"\n\n\"Ferret, itsh all over yer fash,\" he says, and slobbers up another dollop of frosting.\n\nDigit is suddenly there, mouth open. \" _Qu'est-ce que vous faites_?\"\n\nCricket scoops and smears it on Digit.\n\nDigit grabs the knife from Cricket and accuses him, \"English cake killer!\"\n\nCricket shoves another handful into Digit's open mouth. \"Born again! Cake resurrection!\"\n\nDigit howls. He doesn't laugh often, but once he gets going he can't stop. His face turns red, veins pop on his temples like angry worms. He coughs and snorts and drools. Saliva strands hang from his open, cake-filled mouth. Tears stream from his squinty eyes. He collapses on the table, shaking. It's contagious. I can't stop either, not even when Oreo is beside us, not even when she grabs my hair and licks that cake right off and smooshes her clean face into my dirty chocolate mouth. _Our best house meeting ever_.\n\nThe back door opens. A new crowd pushes in through the people who are trying to push out. People want to smoke outside or take a piss and can't find our toilet. Some complain about the no-flushing rule. Tall Eddie comes in, dragging Ray-Ray. I wave. Eddie raises his bottle.\n\nCricket shakes off his carb coma when he sees the big blond head of the new guy he likes, that bike courier. He pushes through some bum-shaking dancers, dragging me along behind. He smiles and the blond brick wall of a man smiles back. Cricket introduces me; Two Ton tips his cap.\n\n\"Ah, your birthday cake,\" he says, and wipes a bit of chocolate from my cheek.\n\nWe drink to that. Cricket offers pills. I can tell he likes the guy cuz he doesn't even get mad when Two Ton takes more than one. In fact, Cricket _smiles_. What an E-tard.\n\n\"I hope you don't mind, Ferret. I invite a little friend to come for your party. Darcy, a skinny red-haired boy.\"\n\nI smile. \"That's the kid who moved in. I haven't seen him all week. I hope he's okay.\" The pill sticks in my throat so I wash it down with beer. Maybe it's the free booze talking, but right now I decide I don't mind all these people any more.\n\nCricket says, \"I heard he got picked up by the cops.\"\n\n\"Really?\" Two Ton looks confused. \"I see him today. He says he gonna bring his other friend tonight. I forget his name. Cute boy,\" he says and winks at me.\n\n\"I like cute girls.\"\n\nTwo Ton shrugs. \"Oh well. More of them for me and Creek-it.\" And then he cracks that big smile of his, mesmerizing Cricket even more.\n\nStrangers keep coming. I stop counting. There's probably double the number of people there were earlier. The Factory is overrun. Scuffles break out\u2014someone can't find their wallet, their cell phone. Some other gadget goes missing, a purse is lost. Accusations are loud, fingers point. Oreo just bumps up the volume. Cricket pours drinks for the victims, for the accused\u2014from other people's bottles. People shed layers of clothing they don't need; it's hard to keep the beers cold. The walls sweat.\n\nSuddenly I feel the swell inside; the tingly numbness spreads, and my skin feels warm. Cricket's pills are kicking in. Everything is magic now. Little Darcy shows up, beaten and sketched out, nervous as a mouse; I pull him onto the dance floor and twirl.\n\n\"You okay?\" The words fill my mouth and take longer to say than they should.\n\nHe tries to shake my hand loose, but I pull him closer. \"I heard you got nabbed by the cops.\"\n\nHe licks his swollen lip. His eyes shift back and forth; he blurts something then stops.\n\nThe music is wicked intense\u2014Oreo is smokin' the heavy beats. I dance Darcy over to the turntables, and he disappears while I kiss Oreo. She looks so hot with her headphones on, her smile lighting up the place. All those other girls, those fancy rich girls, they can fuck off. Oreo kisses me back, and I can't wait to be alone with her. The floorboards bounce back up against my shoes. I move to the middle of the throng, strangers dancing close. We crush together, apart, together, for hours, it seems, world without end. Oreo spins fast breaks, stutters the vinyl, teases metal classics into her electronic weirdness, then lets the drum and bass kick heavy and dark. I am smiling. _I'm really having fun_. Even if all these people don't know me, even if they don't know who we are, everybody's having an awesome time together in _our_ house. It's a brilliant party.\n\nI don't even notice them at first, the sirens blend so beautifully. The spinning red lights reflect off skin: faces, closed eyes, bare bellies. Then the snare drum pops over our heads, so much like gunfire. I'm dancing slowly, swaying, my eyes are open, taking it all in. My arms outstretched, I'm in the middle of all those hot bodies, sucking up the sounds, the pictures. It is some sick dance video: Cricket's arms up flailing, a raised stick, his face contorting.\n\nTall Eddie sees over the whole crowd, he yells something to me\u2014I don't hear him, but we talk with our eyes; he's freaking out. I don't understand. He pushes Ray-Ray through the people, tosses him toward the open kitchen window. Ray-Ray is up on the ledge. He looks back at Eddie, then he jumps, his long white hair streaking after him. _Eddie._ Someone hits Eddie on the shoulder with a long stick. Eddie turns, ready to throw a punch but instead his body pulsates with electricity, he sails backwards, limbs flailing, his eyes roll to white. I'm staring, surprised at his funny dance. _Who came dressed up like that_? I think. _Who came in a uniform?_\n\nTwo Ton throws his beer in the uniform's face and dives out the same window as Ray-Ray, the one near our rain barrel. He's gone. People stare. Uniforms\u2014there's more than one\u2014move through the crowd, and bodies part like water. There's pushing and shoving and the sticks come out: bodies jerk and twitch. Feet shoot out from underneath, they kick and slide to the killer music. Kids push me, step on me. I'm swarmed, can't move. Suddenly, people fall down in front of me.\n\nI see Digit's back; he's still eating the rest of that cake in the corner, he's licking icing off that butcher knife, and men are yelling at him. He turns, slowly, knife raised, and there's a loud pop, a sound that cracks over top of the music, and Digit's head snaps backwards; there's a dark spot spreading across his chest. The knife goes flying and his body lands by the sink. He convulses, red spurts streak the walls and broken window behind him. Kids scream. A girl beside me vomits. There's that pig we hate. The King is standing over there, gun still raised, the smell of it burning my nostrils. The King turns and stares at me. _He sees me see_.\n\nI need Oreo. She's shaking those dreads, cueing up something new. I yell, but her headphones block me. She's zoned. The King is behind her. She has no idea. I run. My heels catch in a pile of clothes. I wave my arms as I fall\u2014I'm frantic. Then Oreo sees me, sees my terror, and so does the King. I'm trapped by the couch, trying to kick off those shoes. They both watch me flail, one behind the other. The King smiles as his stick lands on Oreo's temple. Pain flashes across her face, I feel it. Oreo's mouth goes slack; she crumples out of sight. I roar. The pretty inside light that only Oreo brings me flares up and out; it burns to black and is gone.\n\nThe King gives a hand signal. Someone cuts the generator: music stops, lights go out. Ghosts of kids are screaming, grabbing their stuff, and running in the blue black. They move fast, but not fast enough. The back door is blocked. Headlights beam through the windows, red lights spin. A line of cops grab and handcuff kids when they push their way out. Kids are freaking. Their silhouettes pile out the windows then scramble right back in; they're getting beaten out there, they're getting tased.\n\nMeanwhile, kids trample me. I crawl toward the last place I saw Oreo, calling her name, trying to protect myself. High-heeled shoes snap my wrist, Docs smash my face. I curl up underneath the turntables\u2014no Oreo. Shoes stampede on all sides; they stomp past me in a blur. But one polished pair stops right in front. Big black cop shoes, with hemmed blue pants. I know exactly whose they are, too.\n\n# Shaker Baker\n\n_Nothing_.\n\nThat's all there is at first.\n\n_I'm dead_ , I think. _Finally._\n\nThen the pain kicks in: the rolling ache in my head builds to stabbing points in each eye socket. My stomach twists and bloats with gas. The crazy-making itch starts up again, like worms chewing through sub-layers of skin, skin that holds my bones and bruises all together. I massage my jaw; it's sore from clenching my teeth. I clear my throat and hork out chemical-flavoured post-nasal drip.\n\nOkay. I sigh. So I'm alive.\n\nWherever I am in the world, I'm also lying on the floor between a wall and an old couch. Actually, I'm halfway inside the back of the couch. _Hiding from the cops_. The fabric is torn away. I can see the wood frame, springs above me, little bugs crawling around, the stuffing pulled out of cushions and neatly piled up in tiny rolled balls of fluff. A pyramid of fluff balls, all the same size, all carefully stacked and counted. That was me, last night, tweaked, fiddling with that stuffing for hours, right after taking my transistor radio apart and lining up the pieces along the baseboard, biggest to smallest, darkest to lightest. Wires and plastic parts, dials and buttons, the coded flat metal pieces all glare at me. _What the hell was I thinking?_\n\nI pat the chest pocket of my cotton shirt. I can feel the baggies in there, should be two of them left, with clear chunks of beautiful Vancouver meth\u2014an eighth of an ounce, at least. I wiggle my toes. Packets of other stuff I picked up during the raid are hidden in my shoes. _My stash_.\n\nI pull myself out from behind the couch slowly. My stick legs drag behind, heavy and numb, like they're somebody else's. Sunlight blasts through open windows. It's squinty bright and way too quiet. _Morning_. I'm in the Factory, alright, even if it's unrecognizable. I know the smells: sawdust and sheet metal, spilled beer, dirty laundry, rotting bags of dumpstered food. Over top it all is the hot stench of pig shit from the slaughterhouse next door.\n\nI remember Ferret twirling me around last night at the party, trying to get me on the dance floor. She always stood up for me. Cricket and Oreo, even Digit\u2014a hell of a nice boy\u2014knew better than to trust a basehead like me. _How could I dance?_ Me, tweaked, knowing the cops were right outside, knowing I brought them to the doorstep. Desperate to find Sly before the raid. My stomach cramps just thinking about it. I freeze, hold my gut. My ass puckers, but I don't shit myself. The cramp loosens, the pain rolls away again. I scratch my scabby arms. I pick at my lips.\n\n\"Ferret? Anybody?\" My voice is a screechy mess.\n\nNo one answers. Pigeons purr in the loft. Water drips steadily. Outside, a truck downshifts. Its brakes squeal, just like the pigs it carries. I hear it chug up the long gravel drive.\n\nMy legs tingle pins and needles. I limp along the dirty floor, past Oreo's smashed turntable, all that broken vinyl. There's glass from the side windows everywhere. Boards hang by rusty nails where the other pigs, the cops, bashed them with sticks. There's yellow tape across the doors, the windows. I lean against a fallen speaker, pick up a half empty beer. It's warm, but there's no cigarette floating inside. I rinse my mouth and spit on the floor. The chemical taste doesn't go away, but at least I'm not as dry. My hands shake when I set the bottle back down. _I need water_.\n\nThe Factory is a big old mess. Shelves collapsed in a heap when one cop took an axe to them. That was terrible; the loud whacks, the looks on all those kids' faces. Clothes, art, photographs\u2014everything they had, pulled from the broken shelves, thrown into piles on the floor. The big room reeks like piss, and I remember seeing one cop whip it out and spray the piles. An axe blade trail leads along the food cupboards, across the makeshift kitchen counter, up the blood-splattered wall. _Blood_. I shudder. _The shooting_. I pick my lips some more. I stare at the floor, at the stains, for an hour or maybe only a minute\u2014it's hard to tell.\n\n_Water._\n\nI lick my bumpy dry lips. Water trickles out of a chopped-up pipe; it drips down and runs along the slanted floor, all the way over to the far side of the long room. A tiny man-made lake ripples with each new drop. I tilt my head back underneath the pipe and fill my mouth. It tastes weird, cool but tinny, a bit like earth. It reminds me that I have to pee.\n\n_Sly_ , I think miserably. _What happened to Sly?_ I never saw him last night, not on the dance floor\u2014as if he'd dance. Not in the bathroom lineup, not outside in the dark field, or upstairs in the make-out loft. Maybe he stayed at the Professor's. Maybe he was still mad at me for taking off, for scoring and leaving. _Maybe_. After the cops burst in, the place was an effing zoo. Kids screaming, pushing, cops yelling, giving out the beats, handcuffs snapping shut. The best part was everyone dropping their stash.\n\n_Time for a wake-up call._ I jiggle from one foot to the other. My bladder presses. _A snort will get the brain cells working._\n\nI touch my chest pocket; want to save the meth, but maybe a toot of that rich-kid coke...\n\nOutside, a car door slams shut. Then another. That snaps me awake. There's a digital _bleep_ and radio static. Deep-down man voices. Gravel crunches under their heavy boots. I don't have time to climb to the loft, and there's nothing left to hide behind, so I scramble back to the couch and stuff my aching body behind it, though I can't crawl right inside it, back into the filth.\n\n\"Whew,\" one guy says as the door creaks open. \"Stinks.\" He laughs nervously. His radio chirps. \"So, what're we looking for exactly? The girl's probably long gone by now.\"\n\n\"Leftovers.\" This voice is lower than the other, hollow and mean like an ulcer. _Constable Earl King_. I listen to his deliberate steps as he walks through the Factory. They stop.\n\nAir catches in my chest. I try to slow up my breathing, but I can't. I'm panting. My hands and feet run cold. There's no stopping it, hot piss soaks my jean shorts, pools under my bare leg. It runs along the downward slant of the old floor. It runs underneath the whole length of the couch. I can taste the sick at the back of my throat, but I swallow it down.\n\nOne pair of feet walks around the place. One stands still.\n\n\"What a mess,\" the other guy says. \"God, don't these kids bathe?\" He stomps his foot and sighs loudly. \"Piss. Stinks like piss.\"\n\nThe King grunts. The King is climbing the loft ladder. I can tell by the sounds of his heavy steps on each creaking rung, by the ladder bouncing against the wall when he moves, by the way his deep voice echoes longer in the big room. He says, \"Rats, roaches, pigeons, and street kids. City's full of vermin.\"\n\n\"Yep. We got our hands full.\" The second man sounds farther away. Maybe still near the entrance, or in the kitchen. He drops something, it clatters to the ground. It rolls and rolls all the way over to the couch. \"Shit,\" he says. He walks slowly. His steps get louder; I feel each one through the floor boards. He stops. Leather creaks, and his knee pops when he bends down.\n\nI feel his hand on my sneaker. He tugs hard, then drops it with a gasp. I hear him drag the couch away from the wall. \"What the\u2014\"\n\nThere's no use pretending. I open my eyes. I waggle my fingers at him.\n\nHe's blond with pink cheeks and looks tall, especially because I'm sprawled down on the floor. The red stripe runs all the way up the outer seam of his dark pants. It's the nicer one, Officer P. Anderson, the King's partner. He inspects his fingers, the ones that touched my shoe, for cooties.\n\n\"Well, well,\" he says. \"Not our girl. It's the informant.\"\n\nI clear my throat. No words come out. I try to compose myself. I sit up, my back straight against the cement wall, like a debutante.\n\nThe King's voice booms from the upper loft. \"So we got our redhead back.\"\n\nMy skin prickles.\n\nThe King climbs down the creaky ladder while he talks. \"Darcy Jones. Good tip last night. We got a lot more than we expected.\"\n\nI remember them beating their way through the party, having a field day.\n\n\"An unlawful gathering in a dangerous location\u2014trespassing, drug trafficking, underage drinking, weapons...\" He lists them off on his big fingers.\n\nOfficer Anderson says, \" _I_ think this was a meth lab. Don't you, Earl?\"\n\n_No way_ , I think. _I'd have never left this place if they were cooking crystal._\n\nI say, \"The only thing they baked here was lentils. Tofu.\"\n\nAnderson laughs meanly. \"Darcy doesn't understand.\"\n\n\"Nobody likes a meth lab in their neighbourhood, Darcy,\" says the King. He speaks slowly, loudly, like I'm a retard. \"People don't care _what_ we do to them, as long as we get rid of them. So, for our purposes, this dump was a meth lab. Got it?\"\n\nMy brain is hardly working. I'm still stuck thinking that they actually _had_ a meth lab and were holding out on me. _Effing vegans._\n\nThe King says, \"We sent some scumbags back to jail last night. Hopefully their bitch lawyers won't spring them too soon.\"\n\n\"Oh, and the hospital,\" says Officer Anderson. \"Right? Sent that kid to the ICU.\"\n\n\"Won't be walking out any time soon,\" says the King. \"You came through for us, Darcy.\" His deep voice sounds almost proud of me.\n\nI smile, but I'm not sure if I should.\n\n\" _I_ didn't think you would, to be honest,\" says Anderson. His hands are fists on his hips. I'm staring at his belt buckle, a silver rectangle like a little doorframe leading nowhere nice.\n\n\"Didn't find your girl-boy, though,\" says the King. \"Too bad. I wanted to get a closer look at that freak.\"\n\n_Sly_. A guilt pang twists my guts. I told him about Sly being trans. How he is a boy born into the wrong girl body. \"He wasn't here last night,\" I say, my voice cracking.\n\nThe King is right beside Anderson now. Two big men\u2014one pale with pink cheeks, one dark with a big veiny nose\u2014a wall of blue.\n\nAnderson says, \"Who would have thought so much could go down on Fairy Mountain?\" He chuckles.\n\nThe King says, \"Hmmph.\" Then he says, \"Get up. What's in your pockets?\"\n\nI get up slowly. There's a wet stain on my jean shorts. I pull my front pockets inside out \u2013 nothing. I turn around and wiggle my hips slowly, to show him there's nothing back there either.\n\n\"Did you piss yourself?\" The King looks disgusted. \"Clean up. I still need you for a couple more jobs today, Darcy.\"\n\nI clear my throat to talk. \"But you said we'd be even if I told you about the party.\" My hidden foil packets are burning holes right through me. I got a crack attack coming on. I can make do with a joint to calm my nerves if I have to, but seriously? I need a bump, a line of coke, or a hit of something speedy, just to get back in the game.\n\nHe says, \"Shut the fuck up.\" His hit sends me flat against the wall. _Whush._ All the things bumping around in my head fly clean out of there. \"You're _never_ gonna be even, got that? You do _what_ I say, _when_ I say it. You know what happens if you don't play? You're done. Permanently. \"\n\nPhotos of that boy he killed, him all cut up and beaten, that pretty hustler we don't see around anymore, bolt through my brain like lightning. I don't say anything. I don't cry. It's like that hit sends me back to myself, wakes me up and gets my brain working again, almost as good as a chemical.\n\n_I know all about hitting_ , I think. _Oh, yes._\n\nI pick up the first piece of clothing I find, a button-down shirt someone left on the arm of the couch, and shove my arms into the sleeves, pulling it over my T-shirt. I sidle behind the couch, away from them, and smooth the fabric over the pocket that holds my goods.\n\nAnderson says, \"We need you to find someone, Darcy. Someone who was at the party.\"\n\n\"Emily Stuart.\" The King pronounces it loud and sharp, so the last name sounds like a spit.\n\nI say, \"I don't know anyone named that.\" I cough. I'm looking for pants in all the stuff left behind by the party kids.\n\n\"Oh, yes you do. She was living here.\" Anderson steps toward me and waves papers in my face. \"Having her welfare delivered to the drop-in centre.\"\n\n\"I already told you who lives here\u2014Cricket, Oreo, Digit, and Ferret.\" _And me_. \"That's it. There's no Emily No One.\" I root through a pile of clothes. There's a silver scarf, a light jacket, a pair of giant white sunglasses.\n\nAnderson checks something on his paper. \"James David Smith, a.k.a. Cricket, the fag with the blue hair. Got him. Oreo Ahkwa-blah-blah-kwe\u2014are they serious? More like Lesbo Broken Nose.\" He laughs meanly. \"Digit is Andr\u00e9 Savoie, the kid on life support. Emily Stuart, missing in action.\"\n\n\"What do you mean life support?\" I put the sunglasses on top of my head and drape the scarf over my shoulder. I can tell it looks good, even without a mirror.\n\nThe King grabs my arm and nearly rips it out of the socket. \"Listen, you little fuck. She's a skinny dyke with dirty blue dreads. She was wearing fishnets and a skirt. Ring any bells?\"\n\n\"Oh, that's Ferret. Why didn't you say so?\"\n\nThe King drops my arm. I shake it out.\n\n\"That hurt,\" I say. Now I know. The King reminds me of someone\u2014one of my long-ago dads. It's so familiar, all of it.\n\nOfficer Anderson scribbles in his notes. \"Stuart, also known as Ferret.\"\n\n\"The best thing about these little cunts,\" says the King, \"is they're like rats in a trap. They'll chew off their own legs to escape, never mind what they'll do to each other.\"\n\nThe King's eyes are flat, unblinking. I stare him down while I undo my wet shorts; they drop to the floor with a slap. My bare skin prickles into goose bumps. My thing shrivels up like a small turtle. I see his eyes drop down to look at me. I step out of the crumpled shorts and slowly walk past him toward another pile of stuff farther away.\n\n\"Hurry up, Princess,\" says Anderson. \"It's not a fashion show. We got work to do.\"\n\nI swish the silver scarf over my shoulder. The long end of it tickles my bare bum. I pick up a pair of red spandex shorts some girl probably wore under her skirt. I step into them, pull them up over my shoes, all the way to the waist. _Perfect_.\n\n\"Fine,\" I say. I put the sunglasses low on my nose and sashay over to the back door. \"Coming, officers?\"\n\nThe King opens the car door for me. I raise my hand, _Ta_. I slide across the wide back seat and cross my legs. I tap my sneaker on the divider that separates me from the front seat. I can feel the packages shimmy around in there. _I need a bump_. The King slams my door. He gets in the front, slams that door, too. I can see the grey in the back of his hair. I never noticed it before. _Salt and pepper, so distinguished_. The radio bleeps. Anderson gets in his side and, voil\u00e0, another slam. The King calls the dispatcher, says they're investigating the old chair factory crime scene. Tracking a witness. Following leads. He hangs up the radio. He opens his window, spits. Finally, he starts the engine.\n\nAnderson says, \"Fuck-load of paper work for one bullet, wouldn't you say?\"\n\nThe King says, \"Shut up.\"\n\n\"No, seriously. Was it worth it?\"\n\n\"Maybe. If those douchebag lawyers don't screw it up.\"\n\n_One little bullet._\n\nI remember the gun last night, the sound and smell of it, the way everyone freaked. Everyone else ploughing their way out of the Factory, and me with my eyes on the floor, on hands, pockets; me seeing flashes of silver, little clear baggies, and tiny pill boxes, the fancy ones those rich kids shake around. Crumb-snatcher me, picking it all up, hiding in the back of the couch for hours, quietly tweaking, organizing my fluff balls while chaos blew through the Factory, and later, while the cops did their thing and closed the place down.\n\n_Great party._\n\n\"We're taking you to all the hot spots, Darcy,\" says Officer Anderson. \"The underpass, the drop-in, the parks. You'll be hitting the streets, asking around, then meeting up with us every hour or so.\"\n\n_Good_ , I think. _I can totally get high and keep my buzz on. The only question is\u2014back to crystal light, or should I save that for better times? Should I shake and bake the coke, cook up some crack, and sell it around? That'd be good for coin._\n\n\"We need you to find Emily. Uh\u2014Ferret.\"\n\n\"Why?\"\n\n\"Because we lost her,\" says Anderson.\n\n\"Shut up,\" says the King.\n\n\"Sorry. But we _had_ her. Then we didn't.\"\n\nThe King turns around, his eyebrows hunch in toward the deep frown in the middle of his forehead. \"She witnessed the shooting last night. We need her cooperation. Your job is to tell people, even if they don't ask, that Andr\u00e9, uh, Digit needs her to come forward. Got it?\"\n\n\"Hmm,\" I say. \"That's easy.\"\n\n\"You tell people we got the shooter. Edward. But we need the witness.\"\n\n_I'm important_. I pretend the King is my chauffeur. I sit very tall, chin up, my new sunglasses on. _I'm Lady Gaga. Beyonc\u00e9. I'm Michael Effing Jackson._\n\nThe car rolls down the gravel laneway. We swerve to let another pig truck through. I fall against the door with the sudden movement.\n\n\"Shit,\" says the King.\n\nThe big truck stops and reverses, pulls up and stalls right beside the police car.\n\n\"Shit,\" says Anderson.\n\nWhen the engine cuts, all you can hear is the animals squealing, snorting, and grunting. The smell of them and their manure fills the car. I cover my nose with the scarf.\n\n\"Phoo,\" says Anderson. He waves his hand in front of his face.\n\nThe truck revs up again. The engine shudders and chokes to life; it roars and partially drowns out the terrified pig sounds. The driver honks and gestures. He wants us to back up, to give him some more room. The King stays put. Dust churns up around us. Exhaust blasts out the back end of the big machine. The driver manages to squeeze his truck beside us after all.\n\nI stare out the window\u2014all those stacked crates, those round snouts, those big asses and flapping ears cruise past. One big pig, brown with lighter blobs on it, stares right back at me. We're only a couple feet apart, me and this pig, and only the cruiser glass and the crate wall between us. Those small pink eyes find mine and won't look away. I take off my glasses. I blink. The pig blinks back. Then the cop car lurches ahead and I can't see it anymore, even when I twist to look out the back window. The King turns right at the end of the lane. My stomach cramps up again. I grit my teeth and squeeze my butt cheeks together 'til the pain rolls away. _Close call_.\n\nThe King lays on the accelerator. Dust blows in his window, wind fills my mouth. I put my glasses back on, wrap the silver scarf over my hair like a movie star.\n\n_This is nothing_ , I think. _As long as I have shit to snort and shit to bake and shit to tell the cops, I'll be just fine._\n\nThe drop-in is usually packed on Sundays\u2014free food, free laundry. It's warm and dry. It's loud. Kids trying to watch a movie, kids shooting pool, kids making a mess in the kitchen. Sundays you can work off your hangover, shower, catch up on the weekend gossip, crash out for a bit in the corner. Visit High Heaven. Chill with the gang. Most days, it'd be easy to get the word out about Ferret. Thing is, today there's no one, just the blonde social worker and the Knitter. I hear needles clickety-click from across the room.\n\n\"Hey,\" I say.\n\nThe Knitter nods.\n\n\"Where is everyone?\"\n\nHe shrugs. His hands and those long needles keep moving. At his feet a ball of multi-coloured yarn unrolls a bit more with each jerk of his mammoth forearms. The finished knitting hangs down all the way to the floor. The Knitter is the largest security dude at the drop-in. Someone said he used to be a pro wrestler. I wouldn't be surprised. His neck is thicker than my thigh.\n\n\"Nice. You making a sweater-dress?\"\n\nHe grunts.\n\n\"Wait, wait, let me guess. A poncho? I think they're in for fall.\"\n\nHis eyebrows bash into each other when he frowns. \"Scarf,\" he says in his bottomless-pit voice.\n\n\"Wow,\" I say. \"That's a pretty long scarf. Even for you.\"\n\nHe pauses and looks right at me. His eyes are close-set in his huge face with his enormous bald head. \"What do you mean?\" he rumbles.\n\n\"Well, you're a big man and all. But it takes a certain _something_ to pull off such an extreme scarf.\" I flick the end of my silver fabric for effect. \"I can give you some tips, like for wrapping it and making turbans, that sort of thing. It's one of my specialties.\"\n\n\"I'm not gonna _wear_ it,\" he says gruffly. \"It's part of my recovery.\"\n\n\"Oh.\" I tap my shoe on the ground. \"Recovery from what?\"\n\n\"Smoking and drinking and stuff.\"\n\n\"Does it work?\" I push my sunglasses up onto my head and peer closer at his big hands.\n\n\"Addictions, man. You never stop thinking about it, but if you keep your hands busy, you don't do it. See?\"\n\n\"Hmm.\" Truth is, he's probably right. There's no _way_ he could spark up a joint or open a bottle or shoot himself up with those gargantuan fingers fiddling away.\n\n\"When you give it up, you still got to recover from all the damage you did. Mentally, physically, spiritually. I knit. It helps.\" He stops talking as abruptly as he started. He goes back to his work, clickety-clack, and I shrug my shoulders. _Who effing knew?_\n\n\"Hello, Darcy,\" says the chunky blonde in the kitchen area.\n\n\"Pame-lah,\" I sing her name. \"Have you seen Fairy-Ferret?\"\n\n\"Not today. You aren't the first to come looking for her, either. She in trouble?\" She sets her knife down and gives me a hard stare.\n\n\"No. Cops want her for a witness. Someone shot Digit, you know.\"\n\n\"I do. It's just terrible.\" She sniffs loudly. I notice her eyes are red.\n\n\"Are you crying?\"\n\n\"Maybe. He's a good kid. Never hurt anyone. Is it true he owed Eddie money?\"\n\nI shrug. _Eddie?_ Fuck, _I_ owe Eddie.\n\nPamela picks up the knife and goes back to mutilating fruit for a salad that only the Knitter will eat. She's always trying to shove food down our throats.\n\nI lean against the kitchen counter like it's a ballet bar. I point my sneakers and lift my knobby legs up high.\n\n\"Feet down when I'm working.\" She swats my foot.\n\nThat's when I swipe the baking soda from the top shelf under the counter. I tuck it in the front of my red shorts, smooth my long shirt over top.\n\nI yawn, and she pops a piece of something awful in my mouth.\n\n\"Don't spit it out,\" she says. \"It's papaya. Good for digestion.\"\n\nThe rubbery lump sits uninvited on my tongue.\n\n\"What and when was your last meal?\"\n\n\"Uh...\" I can't remember. I'm chewing and swallowing the fruit, but it might just fly right back up and out of me.\n\n\"Here.\" She shoves a bottle of orange juice at me. \"Scurvy's not just for pirates anymore. Argggh.\"\n\nI roll my eyes. Pamela is so embarrassing. Good thing none of the hot boys are here. I take a bottle of water instead. I can use it with soda to cook the crack.\n\n\"May I use the harm reduction closet?\"\n\nPamela's face twitches. \"I wish you would eat something first.\"\n\n\"Ah, mama, I ain't hungry.\" I bat my lashes at her.\n\nShe sighs. \"There's no one in there right now. Do you need help with anything?\" Her voice goes up thin and squeaky at the end. That's how I know she is not really down with the whole shooting up or smoking crack in the \"safe\" room thing. It was definitely _not_ her idea to get it going, but she wants us to like her so bad she goes along with it.\n\n\"Fresh pipes, screens, and lip balm are all in the basket,\" she says. \"Needles, too.\"\n\n_That's good_ , I think. Because once I finish off all my charity cocaine\u2014I'll have a snort while I gear up, then shake and bake so I can free-base some of that beautiful stuff\u2014I'm back to firing rocks in a pipe like usual.\n\n\"Don't forget to put the exhaust fan on this time. And take some condoms for later, okay?\"\n\nI take the water and stuff a few sugar cookies in my shirt pocket. Then I make a beeline for High Heaven, which is what _we_ call the closet.\n\n\"Thanks for the ride.\" I blow him a kiss. \"I had a great time. Call me.\"\n\nThe King glares. He spits out his open window. Then he guns it, exhaust blowing out the back of the cop car.\n\nI sashay down the alley, toward Kiddie Porn Park. It's a bit early, but soon the boys and hos will slink out with the alley cats. Pros and dealers chase the day walkers, with their strollers and lattes and dogs on leashes, their rollerblades. Day walkers go home for pork chops and prime-time TV while we work the trade all night long. So it goes.\n\nI'm itching to bang some more of that lottery blow; now I'm convinced snorting is a waste of good drugs. The needles and crack kits didn't fit in my shirt pocket, so Pamela gave me a fanny pack for my gear. It's around my waist, tucked inside my tight red shorts, hidden by my shirt layers. _More junk in my trunk_.\n\nI jump on the merry-go-round, and one of the straggling mothers gives me a dirty look. I hiss, Goth style. I pump with one foot in the sand, speeding the thing up and hang on as it twirls around and around, fast. I laugh out loud. Especially when she grabs her kid from the sandbox and stuffs him, crying, into a stroller and pushes him away.\n\n\"Bye bye,\" I yell after her. I lie down, flat on my back, look up at the spinning sky until the thing slows down.\n\n\"Yo, Darcy. What up, man? Where you been?\"\n\nI can't see him, but I know the voice: it's Lil' Brat. Two brown hands grab the merry-go-round rail. He runs, pulling the thing around fast again. Sand sprays up from the ground, into my open mouth. Lil' Brat yells and dives on top of me. He shrieks again, right in my ear. \"Get off\u2014\" I start coughing. I can't breathe.\n\n\"I'm a pussy-pop yo face,\" he says.\n\nHe bounces on top of me, humping my red shorts while we spin around and around. \"How much to let me fuck your tight ass, blue veiner?\"\n\nI shriek.\n\nAnother mother stomps past with twins. She shakes her massive diaper bag at us.\n\nI'm laughing and coughing and wheezing.\n\n\"You know I want to get my ting right up you,\" he says, loud enough for the lady to hear. She walks faster and he yells, \"Oh yeah, baby.\"\n\nLil' Brat rolls off me. I feel for the fanny pack; it's still there. I shake my sneakers. The foil packages rattle.\n\nWhen the merry-go-round stops completely, Lil' Brat climbs up and sits in the centre. He's wearing a skin-tight pink shirt, cropped above the nipples. You can see his tight abs, toned belly, sharp hip bones. His tight white shorts show off his booty stack. He's wearing rhinestone-studded pink flats, and his hair is braided with beads. He rubs his own titties and strikes a pose. \"So, where you been?\"\n\nWhen I catch my breath I say, \"Who cares? Let's bang,\" and he says, \"Alright.\"\n\nWe crawl inside the miniature plastic castle on the playground, and I cook it up fast in my new kit. I offer him a needle, still in the plastic, but he says, \"Don't waste it,\" so we share one instead. We jam it, one after the other. This shit is good\u2014Lil' Brat smiles and nods. We lean back against the plastic walls and chill.\n\nI'm thinking about the rest of what I got. _Should I shoot it or snort it or shake and bake that shit?_ I never had so much all at once.\n\n\"Me and Sly got a place,\" I say, after a while. \"Over in the gaybourhood. In some dude's house while he's away.\"\n\n\"You married or what?\" Lil' Brat laughs.\n\n\"No way. Just stepped out for a bit. All that shit going down. You got picked up, right?\"\n\n\"Hell, yeah. Threatened to send me back to Africville if I don't get my shit together. So I sucked his dick and he let me go.\"\n\n\"Who, the King? No way.\" I can't believe he'd pick Lil' Brat over me.\n\n\"Naw, that guy is messed. I mean the blond. Anderson.\" Lil' Brat's white teeth shine in the gloom. \"He likes a brown girl.\"\n\n\"Huh.\" Usually I can tell right away if I can sex my way out of a jam. With these pigs, it never got me out of anything, just back in deeper. \"What do you think of the King?\"\n\n\"Creep show.\"\n\n\"I think he's handsome in that Bad Daddy kind of way. Like an old movie.\"\n\n\"Maybe an old _scary_ movie.\"\n\n\"I think he likes me.\"\n\nLil' Brat laughs. \"Shit.\"\n\n\"You think I'm joking?\"\n\n\"You watch yourself, Darcy. Pigs hate kids. And the King hates us even worse.\"\n\n\"Maybe, maybe not. Imagine the King driving me all over town, getting me fries in the drive-through, Slurpies at 7-Eleven. Picking up little presents at work and slipping them under my pillow at night.\" I had a trick that did that all the time. I told him it was lame, but now I think it's kind of nice.\n\n\"You _must_ be high,\" he says, laughing.\n\n\"Don't be tripping just because I'm in love and important now\u2014\"\n\nLil' Brat waves his hand in my face. \"Love, hah. Speaking of important, I saw Ray-Ray this morning. That boy is a _mess_. Can't find his man. Says Eddie's locked up.\"\n\n\"Yeah. He shot Digit.\"\n\n\"What? Eddie don't pack. He's wild, but he's not all that.\"\n\n\"That's the word. Ferret, she seen it, and cops want her for a witness. You know where she's at?\"\n\n\"What? She's at Ray-Ray's, freaking out _with_ him.\"\n\n\"Okay.\" I smile. Things are falling into place. I figure we can dose some more, chill. I can find the King when I'm good and ready. I can take him right over there, right to Ferret _and_ Ray-Ray. He'll be so impressed. _You came through for us, Darcy_. I remember his velvet voice booming around the Factory, filling the huge space. _Just like Elvis Presley_. Then the hit\u2014he sure can pack one.\n\n\"I got to go talk to her in a bit.\"\n\n\"Yeah. Bust that out again, Darcy. That's some good shit you got.\"\n\nI smile. It sure is.\n\n# Big House\n\n\"You're in the Big House now, young man. C North, number eighteen.\" Screw opens the cell door for me.\n\nMen's voices echo off the grey walls, grey floors, grey bars. TVs hang from the ceiling in the middle of the hallway, all of them blaring different channels. Doors slam, buzzers blast through tinny speakers, engines rumble. Underneath all that is the whirl of electrical systems, the hum of fluorescent lights. My heels dig into the floor, all on their own.\n\nScrew pushes me. He slams the door. \"Play nice, Leroy,\" he says to the lump in the top bunk.\n\nThe lump grunts.\n\nScrew whistles as he walks all the way back to the range doors next to the elevators. Back to his chair and his dog-eared magazine and his half-eaten bag of chips.\n\nThe lump waves a tattooed arm in the air. \"That's right. You in the Big House now.\"\n\nI never been in _real_ jail before, but I know this ain't the Big House. We're in the frigging Don Jail, not Penetang. Not Kingston.\n\nLeroy sits up. \"You best hit the showers. I be smelling you all the way up here. That ain't right.\" He wrinkles his nose. He's got three teardrops tattooed beside his right eye. I don't miss his colours, neither.\n\nI lean against the bars, feel the metal press into my back. I do reek, truth. My stink reaches right up my nose into my brain. But I don't know about the whole prison shower thing. Like, if it's how you see on TV, I'd rather rot. I look around the place. It's small, I'd say eight by eight.\n\n\"There be no singing, no whistling, no humming. None of that in here, you feel me? Unless you a bull or a punk.\"\n\nI shrug.\n\n\"Corner man say you the youngest felon on the range. That's why they stick you with just me, not three up like the others.\" He points across the way. I see two guys in the bunks and one lying on a blue mat on the floor. \"Uh huh. Corner man say you waitin' on remand.\"\n\nLeroy jumps down from the bed. He is older and darker and shorter than me. More solid, lots of muscle packed in tight. Probably got twenty, maybe twenty-five pounds on me. His orange jumpsuit is undone to his waist with the long sleeves tied around his middle. He passes a big hand over his shaved head. \"You speak English?\"\n\nI nod. Truth is, I don't know what to expect. This cell is smaller than juvie. In Goderich we had units; we had space to move around. Same with all those group homes.\n\n\"You want trouble?\"\n\nI shake my head.\n\n\"Good. You got people?\"\n\nI look down at my jail shoes\u2014blue sneakers with flat white soles, no laces. Even a piece of string is a weapon in here. Ma hasn't returned my message, let alone come down.\n\n\"You got a suit?\"\n\nI clear my throat. \"Legal aid.\" My voice cracks. I haven't used it in a while.\n\n\"Ah, shit. What the charge?\"\n\nI raise my eyebrow. I'm not exactly sure. Breaking probation, definitely. Public drunkenness, probably. Might have had some dirt on me when they got me\u2014not much, though. Possession, maybe, but not trafficking.\n\n\"They put you in here with me; that mean you done somethin' real bad. You ain't going nowhere, no time soon.\"\n\n\"You said they put me here cuz I'm young.\" I look at him hard. I don't know if he's messing with me.\n\nLeroy points. \"Don't dis me. You new, so I cut you some slack. But don't you go dissin' me.\"\n\nI suck my teeth.\n\nHe paces between the bunk beds and the urinal, three steps one way, three steps back. \"Maybe corner man put you here cuz he owe me. Maybe he knows I like a young man.\"\n\nI blink. Don't know if I heard it right.\n\n\"Nice ink,\" he says, nodding at my tats, which peek out at the cuffs and collar. \"You know, you good lookin'. 'Cept for those teeth\u2014and that stink.\" Leroy points to the bunk bed. \"I'm on top, case girlfriend didn't notice.\"\n\n\"Don't call me that.\" I brace myself. The smell of the antiseptic pucks they drop in the urinal mixed with piss and all that bad air\u2014a stable of men, snorting and stamping like horses\u2014it's choking me. The paint-chipped, graffiti-covered walls are closing in. _Rest in Pieces_ it says in black marker, right above the bed. My muscles tense.\n\n\"Relax. I'm just playin' witchoo, Beige. But I do like me a tall boy.\" Leroy smiles and pouts his full lips. He looks me up and down. I swallow hard. A guy in the cell across the hall catcalls.\n\nI know how it works in juvie; jail can't be too different. You get or you get got. You slam the first motherfucker who messes with you, else they all be tapping your business and pushing you around. I learned that when I was nine years old in foster, and nothing nobody says will ever change my mind on that.\n\n\"My name is fucking Eddie.\" I feel the burn at the back of my throat, the tightness in my belly.\n\n\"Okay. But you askin' for a whole lotta trouble.\"\n\nI lunge. My fist sends him flying to the wall behind. His head hits, bounces off it. Sounds bad. I'm on him like skin before he recovers, nailing him in the gut and in the kidneys when he twists away from me. He presses his face against the cold wall. I clock another, but he pushes off the wall like a jungle cat. He springs high and catches me hard in the face. I fall back against the metal bunk. He lands a couple to my ribs. I'm stuck. My jumpsuit's caught on the metal bed frame and he bats my head like it's a ball of yarn. The cloth tears free. I pop him right in the face, bang his mouth up good. He spits blood on the floor over by the urinal and laughs. I exhale. I'll fucking stomp him. I throw a couple more hard ones, catch a couple right back. Guys in the next cells bang on the bars and cheer for Leroy. There's no bulls coming to split us up. In juvie, this shit would be done by now. Screws would jump in for sure.\n\nLeroy puts up his hand and shrinks from me. \"Hold up. You skinny but you can hit, I get it.\" He's bending down. Looks like he's folding, which surprises me. We're both breathing hard.\n\n\"Aagh,\" I yell. I want to lay into him again, punch all this hate out of me, but he backs into the corner with the miserable urinal. I can't fight him like that. _Fucking pussy._\n\n\"Okay, tall boy. Eddie. You made your point. I be done teasing you. Peace.\" He stretches his hand out to shake.\n\nI turn away to the foot end of the bunk bed near the cell door I just came in. I breathe slow, let the rage drain away. Blood stops pounding in my ears; I can hear all the other jail sounds starting up again. Men yell at Leroy for cutting short. Nobody roots for me. It's not a death match. It's about rank. I take small steps, shift my weight from one foot to the other, like I'm walking it off, only I'm not going anywhere. There's no place to go. I lean on the bars and peer down the hall. Bull's still way down there, reading his magazine. I shake out my legs, feel the bruises heat up on me. My head throbs from his hits. Finally, I walk over to Leroy.\n\n\"Alright, man.\" I reach for his large tattooed hand. I don't even see it coming. His kick is lightning. It's deadly, aimed right for my balls. The room spins, I gag, and I go down.\n\nLeroy straddles me while I moan and curse. He's got me pinned good. My hands cup my sac. He's sitting right on top of the whole works. \"You got to learn the rules. When I say you stink, that mean you hit the showers. You mind your bizness here, show some respect. You ain't got colours. That mean you ain't got friends. You feel me?\" Men's voices roar; men bang the cell bars, all the way down the hall. \"I got friends. _That's_ how you get by around here, girlfriend.\"\n\nI say, \"What the\u2014\"\n\nHe slams my head into the cement floor. _Lights out_.\n\nI dream of Ray-Ray. He's standing on the roof of Ma's trailer, looking out at the tobacco fields. The sun's going down fast, like in a sped-up film. Colours change all around. The dark rises up, making his long white hair and the blue of his jeans pop. \"Ray-Ray, man, talk to me,\" I say. But he won't. He's got his back turned. \"Please.\" I'm sad in the dream, all alone. When he finally twists, his green face is rotted out. There are worms in his stinking skin. He's some kind of zombie.\n\nI open my eyes. Leroy's heavy man smell is all over me. I can taste it. I'm tucked into bed. Bottom bunk. My head kills. Like someone took a bat to it. The fluorescent lights stab at my eyes. I raise an arm to shield them. I feel lower with my other hand; my swollen nuts ache real bad, but at least I still got my jumpsuit on. Day one and I'm already sick of this place.\n\n\"You feeling okay, girlfriend Eddie?\" Leroy is pissing at the urinal. He looks at me over his shoulder. He's got a shiner coming on and his lip is busted.\n\nThere's a sad pit in my gut, a dark hole left from that dream. _This_ is what you get for wanting someone, for giving a shit, I think. _Fucking Ray-Ray_.\n\n\"Watch your aim,\" I say.\n\n\"How's your balls? They still warm?\"\n\n\"Fuck you.\"\n\n\"Ha ha,\" he says. \"You clocked me good, so don't feel bad. Fucking split this shit up.\"\n\n\"Yeah?\"\n\n\"Hell, yeah,\" he says, zipping up and turning around. \"Look at me. Look what you did to my pretty face.\" He smiles. He's got gold caps on a few of his teeth. \"Got a bump on the back of my head bigger than your knob, too.\" He laughs. \"So come on, tell me how bad your nuts ache.\"\n\n\"Lots.\" I sit up slowly, clutching my business. I swing my legs slowly over the side of the bed. \"Ugh. You smash my head around?\"\n\n\"Hell, yeah. Cops probably did on your way down, too.\"\n\n\"Don't remember. Think I got concussed.\" It'd explain the weird dreams, for one.\n\n\"It called neuromuscular incapacitation.\" The big words roll off his tongue in a sing-song voice.\n\n\"Huh?\"\n\n\"You got tased, Eddie friend. Corner man heard.\"\n\n\"Really?\" My mind's a swamp. Pictures come in batches, but they don't make sense. The party. Cops. Ray-Ray\u2014pushing him out the window, making sure he'd get away. Then I was falling, flopping, banging off the floor. _Tased._\n\n\"You didn't say you was in for murder.\"\n\nI look at him. \"What?\" My mouth dries out.\n\n\"No wonder you here with me. You best get cozy. And you best get a more expensive suit, else you be locked up with the Feds 'til you an old man.\"\n\n\"Some kid got shot at the party I was at. I didn't even see it. Cops took me out.\" I shake my head. _This does not add up_.\n\n\"Well, pigs be saying _you_ shot the boy. Little Frenchie from out east. And the news saying that kid died last night in the hospital. So now, pigs be saying you a murderer. You feel me?\"\n\nMy stomach lurches. I almost heave the grey porridge from breakfast right up on the cell floor. I lay down on my cot and cover my face with my hands. Questions ricochet around my aching head. A picture comes into my head of that wiry little French kid\u2014Digit from New Brunswick\u2014the metal head from the Factory squat. Him, dead? _Impossible._\n\nI remember sitting in cuffs for so long: the lineup, the strip search, the coveralls. Being brought to this cell and all the bullshit with Leroy. Before that, there was the joke of bail court, my pussy lawyer fucking shit up and getting me sent here for who knows how long. Other lawyers got their kids out with promises from parents or social workers, court dates pending. My guy was not so good. He said, \"Complications. You win some, you lose some.\" _Stupid fuck_.\n\nBefore that was the 14-Division tank for a day and a half, me with all the winos and wife beaters, a few crust punks with priors, most of the other party kids having been let go with a warning. The clean sparkly ones got phone calls, got picked up, got grounded. The ones caught holding or who had a record or whatnot, we stayed in the pen all weekend and went to bail court Monday morning. We got slapped over to legal aid.\n\nGossip about a kid in hospital, about a shooting, about the suspect already in custody; that made the rounds fast enough. A shooting at the squat, now that was news.\n\n_The fucking Factory party._\n\nWhen me and Ray-Ray got there, the place was already packed. I didn't know most of those kids, Ray-Ray neither. We didn't even really want to be there\u2014me cuz I been trying to quit the drugs and Ray-Ray on account of his stutter. We stuck with our own kind, squat kids and crust punks, some from the drop-in. At one point, the clean kids outnumbered the crusts and some minor shit went down\u2014drinks were drunk, drugs and wallets disappeared. The hustle don't ever leave the hustler. There was the cake and the butcher's blade\u2014puny compared to what I use at the slaughterhouse. Digit was laughing, standing beside me, eating chocolate icing right off the knife. I remember seeing those cops and pushing Ray-Ray to the open window, so he'd get out safe. His long white hair got lit up by headlights when he went through. I stared after him: the back of his Iron Maiden shirt, his beautiful ass in those tight jeans, the red of his Converse sneakers on the window ledge before he jumped out. I was thinking, _at least my boy is safe_. I was pretty fucked up. I remember going down hard. That's about it. I sure don't remember no gun.\n\n_Who the hell would be packing at the Factory squat?_\n\nIn the Don, my dreams stay messed up. Ray-Ray is there, soft and sweet in his body. His wet mouth finds me night after night and I wake, the sheet sticking to my belly and chest. Sex finds me even when the rest of the dream goes wrong. One night he smiles and kisses me, but his soft hair falls out in clumps, filling my hands. Another night his face is blank. He wants to tell me something, but I can't hear on account of him having no mouth. I say, \"Ray-Ray, speak up, man,\" but he can't. An invisible wall keeps us apart. I panic. Then he grows a mouth, like it's painted on, and it opens right up. He screams, calls me a no-good, calls me a worthless ugly bitch, a fucking moron. I'm crying, \"Don't be that way,\" but he gets even meaner. I'm like a little kid. I just want him to like me, but he don't.\n\nI wake from that one in a sweat. _Fuck, he sounded like my ma\u2014with her hateful screeching_. I'd probably cry if I knew how. I think on how I used to bug her about my dad, about wanting to meet him. Wanting to know the dark side of me. She'd say, \"You'll meet him soon enough at this rate. In Penetang, doing life at Oak Ridge forensics.\"\n\nThe fluorescents buzz, cell doors clang, the intercom bell blasts. I been here over a week\u2014no visitors, not even the lawyer, no calls, no nothing to take my mind off it, neither. I got a bad taste in my mouth and a worse feeling in my gut.\n\n_Fuck Ray-Ray_. He's out there doing who-knows-what, and I'm in lock up. Still in that bottom bunk.\n\nLeroy's large hand drops down from the top bunk. He pretends to knock. \"You feeling bad, Eddie? You need to get high?\"\n\n\"No.\" I been more or less clean for four months. Other than beers and a little something extra at that party. Been going to work right on time, paying the rent, meeting the probation officer, eating up whatever Ray-Ray made for supper each night, playing with Big Fat Rat Catcher. Behaving\u2014just like a good man should. Even thinking about doing the effing GED, get my grade twelve after all. _Now what for?_\n\nLeroy swings down to the floor. He leans his face into the bottom bunk. \"Eddie,\" he says, like he's already made up his mind. \"I'm gonna set you up like you never been. Take your mind off things. You'll thank me.\" He drops a small foil package on my chest. \"Shit is good,\" he says. \"This shit is real good.\"\n\nI hold the packet in my hand. I shake it back and forth. When even the pillow over my head can't muffle the constant noise from down the hall, I say, _Fuck it_. And I take a closer look at what Leroy gave me.\n\n\"Let's think about your future, Edward.\"\n\nI cringed.\n\nShe really pronounced the \"k\" in think. That was the social services lady at the youth detention centre in Goderich, the blonde one with the streaks and the bright pink lips. I was getting processed on my last day, getting ready to leave that place for good. You always had to meet with one of those ladies on the way in and on the way out. If they liked you, sometimes one of them would meet you half way through the sentence; sometimes she'd get special clearance to take you down by the lake for a sandwich or fries, leave the joint to go talk about your life plans out at the beach. Maybe they'd put you in a support group or a class or something. I never got that with any of them, especially not this blonde. Man, she hated me. I could smell it on her.\n\n\"You won't be coming back to this detention centre again, Edward.\"\n\n\"Eddie,\" I said.\n\nShe blinked. \"You'll be too old, for one thing.\" She smiled and I could see the lipstick smeared on her front teeth. It looked pretty crazy, like a kid scribbled over top of them with a fat pink marker.\n\n\"Your life could continue to be a series of bad choices that lead to terrible consequences\u2014no diploma, no job, no money. Drugs, drinking, crime. Boys like you become men like that. They don't usually live long.\" She smiled tightly, this time no teeth at all. She leaned forward, over the stack of files on her big desk. She had pretty big boobs and they were getting closer to my face.\n\nI sat rigid, arms crossed. I stared her down.\n\n\"Or you might start making some smart choices instead. You turn eighteen in a couple of months; your record will be wiped clean in time, if you stay out of trouble. You could finish high school, get a job.\" She stood up and walked around the cramped office.\n\nNow I could read the Keys for Success poster that was on the wall behind her chair. It had a bunch of keys on a chain and each one had a word written on it.\n\n\"You might change things around for yourself. Make your mother proud.\"\n\nI pushed back, scraping my chair on the scuffed tile floor. \"Miss, don't talk about my mother.\"\n\n\"Sore point, I see.\" She walked back toward her desk so she could look me in the face. \"Your mother struggled to do right by you, even when that meant giving you to _other_ families so you would have more structure and opportunities than she could give you herself, Edward.\"\n\n\"It's Eddie.\" I clenched my teeth.\n\n\"You know, you've had a lot more chances than many kids get.\" She crossed her arms, too.\n\n_At what_? I thought. _Sucking foster cock_?\n\n\"You might leave this self-destructive path you're on and still become a useful member of society.\" Her words were hopeful, but her face and her voice and, most of all, her eyes, were not. \"You don't have to turn out like your father.\"\n\nRight then I wanted to become anyone at all, anyone who would not have to listen to her bullshit, that is. She moved directly behind me, but I refused to twist in my chair. She'd have to preach to the back of my head. I stared at the stupid poster. The keys for success were: Self-esteem, Confidence, Honesty, and Courage.\n\n\"What's it going to be, Edward?\" She was clicking her pen right behind my head.\n\nAs if it was that simple. You wake up and say, _I'm going to be a fireman_ or whatever, and fuck this shit of a life you've got dragging you down.\n\n\"Well?\"\n\nI didn't answer. My thirty minutes were almost up. She got paid whether or not I talked, and there was a long line of kids waiting out there on the range.\n\nShe threw the pen on her desk\u2014that surprised me. She stomped back to her chair and tossed my big file at me: pages and pages of shit talk by other people just like her, fosters and shrinks and screws. Some paper fell on the floor around me, some landed in my lap. Words jumped out at me from all over the papers: _defiant, delusional, hyperactive, violent_. There were long science words: _schizo-something, psychotic,_ _paranoid_. You name it, someone said it about me.\n\n\"What's 'developmentally delayed'?\" I asked. \"You mean retarded? Someone thinks I'm retarded?\" I sucked my teeth. _As if_.\n\n\"When you don't communicate it's really difficult to know what _if anything_ is going on in your head, Edward.\" Her consonants were stinging face slaps.\n\nI sat for another minute or two in silence. Those words burned the pit of my stomach. They were everywhere. And none of them were mine. Papers spilled off my lap, off the desk. They piled up on the floor around my feet.\n\nShe opened her office door. I turned my head and could read the large poster that made her office stand out from all the others in this hallway: \"You can't pimp this ride: Say no to gangs.\" It was a picture of a black hearse with a shiny casket sticking out the back.\n\n\"This session is over. Good luck, Edward.\"\n\nThat blonde would love to see me now, not even a year later, snorting H with a macho gang leader, locked in the Don, framed for murder. On the street, gangbangers die young; in jail it's the opposite. Here, you need buddies if you want to get through each day. Leroy tells me what's what: don't reach past a man's food tray, don't let no one eat off your plate, no cutting in line, don't drum your fingers on the table. Watch where you're going, don't _ever_ fucking bump into a man. _Politics_. Then there's the shower room, yard time, chores. If you want to use the goddamn pay phone, even, you got to _be_ somebody or _know_ somebody. I still fuck up, being hyper, being new. Sometimes Leroy smoothes it over for me. Sometimes I get a hauling.\n\nLeroy signals one of his boys down the hall\u2014he wants more dirt. He knows all fifty guys on the range, knows the corner man real good, and he's the one who runs shit. He knows folks on the other ranges, too. Little foil packages make their way, pocket to hand, cell to cell, all the way down to us. Even some of the bulls are in on it. Leroy been keeping me up for days now, says I don't owe. Not yet. He's pretty much bringing me in, but I stall.\n\n\"You got yourself a better offer?\" he asked the other day, eyebrow up.\n\n\"Naw. Just, I'm not from here. I get it, but I never had that kind of thing, right? Colours.\"\n\n\"They not just colours, Eddie. They brothas.\"\n\nAnd that made me think on all those other \"brothers\" I had, houses full of them, boys who hate the new kid, hate the whole world, boys looking to fight, boys looking to fuck. Always watching your back and still never seeing it coming. Thinking you got a buddy but instead you just get messed again. I got real weak, thinking on all that.\n\nNow Leroy's chopping the powder on top of a hard cover Don Jail library book with the crisp edge of his lawyer's card. He's teaching me the trade proper, and also all about the In-Justice system. Way better than a GED diploma.\n\n\"Eddie,\" he says. \"Remand mean you here now 'til you good and done with the judge, 'til you either sentenced or you set free, charges dropped. But they courts behind schedule, so we stuck waitin'. Sometimes months just sitting here, not even convicted of nothing. You feel me?\" He makes two stubby lines on the book. \"Judge give you two years or less, you likely finish it out here. You get more than two years, they probably send you to the Feds. Plus they shorten your time on account of this hole being fucked. One day in the Don equals three regular jail days, feel me?\"\n\nLeroy snorts the first line and inhales deeply a few times, shaking his head. \"Or like, if that dead kid was special, maybe he got rich parents? Court might bump you up a bit, time-wise. Speaking of bump, here you go.\"\n\nI snuffle the other line. It blazes up my sinus cavity and hits the back of my throat. I sniff, rub my nose, and swallow the chemical drip. I feel the rush immediately.\n\n\"Probably, though, you here for the long haul,\" he says.\n\nThat depresses the hell right out of me.\n\n\"See, if they gots the murder weapon, if they gots evidence, then that's something. Or an eyeball, a witness, what seen the deed. But if all they gots is bitches _hypothisaying_ shit, then that don't mean fuck-all.\"\n\nI nod. It makes sense. Mostly, it just makes me feel better.\n\n\"That's what you need this fag suit for. He may be homo, but he good in court. This fagmother _hate_ the pigs. I say you call _him_. We work it out after, what the bill cost, feel me? You pull some jobs, work my crew, you be out even sooner than you know.\" He taps the book cover with the card again.\n\nI slump back on my mattress and let the drugs course through. The lights and noise dim; it's like a giant spider spins a downy web and I'm tucked safely inside. Lately it's harder to remember Ray-Ray unless I'm high. He comes to me quick on the H; I can hear him, I can smell his skin and feel the tickly ends of his hair brush against my face when we kiss.\n\nLeroy mutters something. He does another line or two and eventually swings up onto his own mattress above. The springs creak and pop as he settles. Then there's just the now-familiar lump of his body in the saggy bed, inches above me.\n\nI think back to the night of the party again, to the moment of seeing that cop, the King, coming right at me through the crowd. Being tall is good and bad. Good, cuz I see far; bad, cuz everyone sees me too. I remember my head swinging around, scanning exits, checking the cops making their way through the joint, kids oblivious: Oreo DJing, Ferret dancing at the edge of the crowd. _Ferret!_ She saw me, before it all went fuzzy. _Maybe that's important_ , I think, _maybe she saw something_. And then I drift right off to that lush land of dreams.\n\nMy turn. I spread. They pat me down all over. I'm clean. There's at least ten of us down here, but only six places for visitors. The guy ahead of me gets a nod. He walks down the last bit of hallway toward the metal doors at the end. I follow him, but the bull puts his arm up right in front of me.\n\n\"Wait.\" He chews gum and smirks at me, his hairy arm like a toll bridge right in front of my neck, his beefy hand planted on the wall beside me.\n\n\"No way, man,\" I say. You only get forty minutes for a visit and this asshole took his own sweet time to bring me down. It's half wasted already.\n\n\"Afraid so. There's always tomorrow.\" He checks his flip chart and laughs. \"Oh yeah, this is your second visit this week. No tomorrow for you.\"\n\n\"It's my _first_. First ever, since I been in here.\"\n\n\"Nope. Your little friend came Monday\u2014guess you didn't hear your name. Still counts as a visit.\" He shrugs and taps the edge of the clipboard with his pen.\n\n\"Fuck.\" I clench and unclench my fists.\n\nThere's a sharp whistle from the line behind me. One of Leroy's friends. The screw looks up. He frowns. He swears, too. Leroy's buddy shakes his fingers, some signal I haven't learned yet, and nods at me. I nod back.\n\nMy screw yells at the bull down by the metal doors. That bull grabs the collar of the man ahead of me, just going through to the visiting room. Brother gets yanked back. I'm pushed forward.\n\n\"Your lucky day, punk,\" says my screw.\n\nI look in his eyes and see so much. _Surprise, anger, a little fear_. Colours do mean something around here, it never fails.\n\n\"Exactly,\" I say. And I strut past the other growling brother.\n\nThe visiting room is painted puke yellow, the first colour I've seen in days, other than our orange coveralls. I get pointed to the last empty chair. There's a bullet-proof glass in the middle that separates the inmates from the visitors. On the other side there's women with their kids, there's a whole family, a couple lawyers. And Ray-Ray.\n\nI sit down and stare through the glass. It's pretty smeary, so that fucks with being able to see him proper. He picks up a phone and holds it to the side of his head. It's on a short wire, so he has to lean close to the cubicle wall. His mouth moves, but I can't hear what he's saying. _Like that dream_ , I think. He waves his phone in the air and points to my side of the table.\n\n\"Shit.\"\n\nI pick up the phone on my side and there it is, the tinny echo, the click of some screw listening, and the small sound of Ray-Ray's breath.\n\n\"H-hi, Eddie.\" He blinks. He smiles, but he's unsettled. He jumps at every blast of the intercom. He looks nervously at the other inmates and their visitors, at the bulls pacing back and forth behind me.\n\n\"Hey.\" I slide my chair as close as I can. I hunch over my side of the table, closer to the glass. His eyelids roll down part way. His nostrils flare. He looks away.\n\nI push back in my chair and clear my throat. _I stink._\n\n\"It's sh-sh-sure loud.\" He smiles sadly.\n\n\"You get used to it.\" Actually, I was thinking how it's way quieter than on the range where we're locked in our cells all day.\n\n\"I thought w-w-we'd b-be alone.\"\n\n\"Oh.\" I swallow. I stare at his hands, his long fingers, slender wrists, and bare forearms. I can taste the salt from his skin, right at the base of his throat, if I try hard enough.\n\n\"M-miss you.\" He looks miserable.\n\nI nod. I bite my lip hard against the rush of emotion that burns my throat, threatening to escape and out me in front of the other men. I bury my face in my hands and press down on my eyelids. I can't. _Not here_. I feel eyes on me, eyes of the dude sitting to my right.\n\n\"Eddie?\" He leans as close as he can.\n\nHis voice whispers from the speaker part of the phone. Like it's a million miles away. I spread my fingers wide and stare at him through the slats; I memorize his face. The small freckle beside his top lip. The pale skin stretched under his eyes, light purple, the tiny folds in his delicate eyelids, the long thick lashes brushing his cheek. The white fuzz that covers his skin. It hurts to not be able to feel the soft fluff of it and then to tease him. _My little man peach._\n\nMy breath stops up in my chest.\n\n\"Eddie.\"\n\nI drop one hand to the table top and hold the phone proper. I clear my throat.\n\n\"They say you killed Digit. Shot him.\"\n\nI snort. \"With what? How'd I shoot someone without a gun?\"\n\n\"I know you d-didn't.\" He looks hurt.\n\n\"So?\" I hear the hardness in my voice.\n\n\"S-s-so it looks bad.\" He coughs. \"Th-they're saying he owed you money.\"\n\nI suck my teeth. \"He ain't owed me. Even _if_ , I don't pack.\"\n\n\"The-they say you grabbed a cop gun, right off the man.\"\n\n\"I'm no killer.\" Like I have to defend myself to him.\n\n\"I'm j-just s-s-saying, is all.\" Ray-Ray folds into himself a bit.\n\n\"Who's this 'they'? _Our_ friends? Who's saying shit about me?\" I grip the edge of the table. I'm shouting.\n\nScrew smacks the edge of my table with his stick.\n\n\"Sorry, sir.\" I exhale. I get my shit together and he walks away.\n\n\"In the p-p-paper. The n-news. Say you were f-f-fucked up on d-dust and f-f-freaked out, like.\" Ray-Ray is shrinking away from me; he looks tiny in that plastic chair.\n\nMy eyes burn. _Me, in the paper?_ My knuckles turn white. I'm still gripping the table top. There's a balloon inside me, getting bigger, straining to pop my chest wide open. The thud of blood rushing through my temples is all I hear.\n\n\"Did I?\" My voice squeaks. All those typed words fly at me, piles of social-work papers filled with long words I don't understand. _Am I a murderer too?_\n\n\"No! I m-mean, I don't think so. Y-you were messed up b-but\u2014\" Ray-Ray's eyes shift one way, then the next. \"It's just, it d-d-don't look so g-good, Eddie. And you know, the k-k-King. He's hard.\"\n\nMy mouth runs dry.\n\nRay-Ray won't look at me. He lowers the phone.\n\n\"What's that fat fuck doing? Huh? What he doing?\" _I sound like Leroy_.\n\nRay-Ray's head stays down. I look at his part; it goes straight most of the way to the centre of his head, just a small detour where the hair grows up in circular pattern. A tiny cyclone of white. His hair is greasy, I notice, hanging limply from the scalp. I see one splat of a tear on his side of the table.\n\n_Shit._\n\nHe lifts the receiver again. \"The k-King is the one t-t-talking. Said it was _his_ g-gun.\"\n\n_No shit_ , I think. And the picture starts to fall into place for me. I think about Leroy's lawyer. About owing favours.\n\n\"Listen, Ray-Ray. I think I got some help in here, but I don't know how long it'll take. You know, to straighten all this out. I don't want to be worrying about you, too.\"\n\nAll this time I been feeling sorry for me, but I never thought how it could be on Ray-Ray. He's soft. He couldn't do a day inside, and maybe he can't do it out in the city on his own, either.\n\n\"I hate that you're alone. How's Big Fat Rat Cat? I miss our place.\"\n\nRay-Ray looks up, his eyes rimmed red. He sniffs loudly. \"I ain't there, Eddie. I d-d-didn't have r-rent. Your b-boss called to say you're f-f-fired, and the landlady k-kicked me out. F-f-fat Ratty's gone. I lost him c-c-crossing t-town.\" He inhales sharply, a terrible sound squeezing from his throat.\n\nMy stomach cramps hard and tight. _No job, no place, no stuff even? Big Fat Rat Catcher\u2014gone?_ All the air rushes out of me, all of it gone at once.\n\nWhen I can talk, I say, \"Where you staying? Shit, Ray-Ray.\"\n\nHe shrugs again. Now I notice the small things; pale bruises at the top of his forearms, where the sleeves of his Iron Maiden shirt end. The grimy white parts. The almost golden colour of his skin. It looks good on him, but it's the sick coming up. He probably smells different, not that I'd notice, given the company I been keeping.\n\n\"You hustling?\"\n\nHe nods, miserably.\n\n\"Ray-Ray, listen to me, man.\" I swallow hard, to keep the bile down where it belongs. \"You get out of this town. Go home. Go to my ma's, go wherever. Stay with Old Red if my ma's too fucked. You listening? You got to get out of here.\"\n\nI can hardly see him now, through the red flaring in my brain, through the water in my eyes. \"Get out of town. I'll come find you soon as I can.\"\n\nThe intercom blasts louder, longer. Bulls hit the tables, yelling at all us sad sacks to get up, up, line up, back to the wing, chaos breaking out all over with chairs scraping back and last-minute goodbyes getting louder across the room.\n\n_Ferret!_\n\n\"Hey,\" I'm yelling loud enough to be heard. \"Find Ferret!\" Screw grabs my shoulder, yanks me out of the chair in front of Ray-Ray's surprised face. I'm still holding the phone. \"She's my eyeball. My witness.\"\n\nRay-Ray shakes his head. \"She's g-gone, Eddie.\"\n\nThe guard grabs the phone from me and hangs it up.\n\nRay-Ray's mouth drops open, like some terrible thought has just occurred to him. \"What?\" I yell, through the glass partition.\n\nBut I'm dragged into line with a thump on the shoulder blade, I'm shoved along with the others, and Ray-Ray's white hair, his tiny pale self grows smaller in my side vision until I duck past the metal door frame, and he disappears completely.\n\nThat night I pace the cell until Leroy yells at me. \"Chill, motherfuck.\"\n\nI punch the air a few times, kick the cement wall beside the urinal.\n\n\"Eddie. You got to settle yourself. A man needs quiet in here. You got to respect that.\"\n\n_I need out of this shit hole_ is what I think. Need to get out where I can breathe and think and fix things, but that is not going to happen. I feel the weight of this place, the metal and concrete and the stink of it, the hate of it, the constant watching and listening, and it tears me right up inside.\n\nLeroy passes me two tablets.\n\nI pop them in my mouth. I don't even ask what they are.\n\n\"Talk,\" he says, his big arms crossed.\n\n\"I want your suit.\"\n\nLeroy smiles wide. \"Good choice, Eddie.\" He chuckles and the low rumble of that makes the hair on the back of my neck stand up. \"That mean you ready to play?\"\n\nI nod, but don't even look when I hear the zipper on his jumpsuit come all the way down, and the sound of the fabric as it drops in a pile to the cement floor.\n\n# Piggy Goes to Market\n\n\"How're we supposed to get any money for you? State you're in.\" An old hard-faced woman barks at me. She holds a basin in her wrinkly hands. When she leans forward, I hear the sloosh, sloosh of water. She sets the basin on the cement floor.\n\nWe're in a cellar. There are no windows. Three lit bulbs hang from sockets around the room. Cobwebs waft from rafters. The floor and walls are cold. There's a staircase, narrow and mean, that goes upstairs. On the other side is a metal door, which I now know is bolted from the outside. I have no idea what time of day it is, not even what day it might be.\n\nThe Factory birthday party, the last day of my real life, was so long ago.\n\nThe woman wrings out a puffy sponge, and the falling water sounds like skin ripping. Her hands are old, big-knuckled. Like they've wrung out a lot of hot cloths, wiped up a lot of mess over the years. The loose skin under her arms shakes when she cleans me. The yellowed pit of her arm shows through the faded housedress she's wearing. It stinks a sharp, sour warmth into my face when she moves closer to remove my scraps of clothes.\n\nI can't talk, not that I want to. My jaw is popped; my mouth hangs open, and saliva pools and spills in long trails, down to my lap. Sometimes it goes on her cloth, her arm. She wipes it away, annoyed. She soaps and rinses me, but the parts she touches don't belong to me anymore. She pushes my head back and I start to choke on my own spit. I can't swallow or spit, can't get my lips to work. My mouth feels broken. Ugly sounds choke out until she finally sets me back right. Even she's disgusted.\n\n\"You must-a seen something. Done something. You're not like the others, not one bit.\" She stands over me, hands on her wide hips, head cocked to one side. Then she shuffles over to the stairs and heaves herself onto the bottom step. \"Earl? What the hell am I s'posed to do with this sack a shit? You leaving her down here or what?\"\n\nThere are bellows from above, thunder. _Like Elvis but louder_.\n\nMy leg shakes. I whimper. Hot piss runs down my thighs.\n\nShe shuffles back and sees my new mess. \"Now look what you done.\"\n\nShe carries the basin to the centre of the room where there's a drain. She dumps the dirty water down and then refills it from the tap of an old sink. It takes the woman a long time and lots of fresh basins to clean me, but she keeps trucking over to dump out the old, pour in the new. As much as she tries, she can't get the stink of his body, his bad breath, off me. It's inside my head permanently: his animal scent, that boozy sweat, his piss-stinking uniform.\n\nShe grunts with effort and mutters while she works. \"Can't take you upstairs like this. Turn their stomachs, you will.\" Twice more she heaves herself back onto the bottom step to holler up to him, the King, the man she calls Earl.\n\n_Creak, creak. Yell, yell._\n\n\"Not like you can go anyplace, state you're in. Might as well let you rot.\"\n\nI hover above my lump of a body. I fly around, see dust float in the air, see the mouse turds trailed along the floorboards, spiders spinning. I see myself\u2014a bloated, bruised monster.\n\n_If only I'd been arrested with the others. If only I was in jail. If only I was with Oreo._\n\nI see Oreo's face, the King's stick landing on her temple, her eyes twitching shut, her body slumping to the ground, me crawling and fighting my way through the mob to get to her, too late. None of this would've happened if I'd been right by her side, like I wanted to be. If we hadn't had the stupid party. Since the first night I met Oreo, nothing truly bad had happened to me, nobody had messed around with me. Not until the King.\n\n\"Locked your Indian butch up tight. She's a fighter,\" he'd said the night he picked me up, and his deep laugh had filled the cop car.\n\nThe old woman grabs hold of my dreadlocks and yanks me back to reality. _Here and now, the cellar_. \"Probably got the bugs. Dirty.\" She clucks her tongue.\n\nShame warms my cheeks. I see a glint of silver in her hand and gasp.\n\n\"Quiet.\" She pulls a few dreads, then saws at them, down near my scalp.\n\n_She's cutting my hair!_\n\nI squeal. I lean away but she pulls harder, making my eyes water. _She's strong for an old broad_.\n\n\"What kind of hair is this, anyway? Blue!\" She drops a handful onto the floor. It looks like a small dead animal. She grabs a new section and pulls, working the scissors near the roots. \"Them others was pretty, not you.\" More dreads fall. \"Them others got us good money. You're nothing but a punch bag whore.\"\n\nI cry. It hurts so much to know this horrible woman is cutting the punk right out of me, taking the very last bit of me away from myself.\n\n\"What's wrong? Cat got your tongue?\"\n\nI hiccup.\n\nShe shakes her gnarled hands about my head, sends the loose hairs fluttering. My ears are naked. The back of my neck itches.\n\n\"Now you're more like a boy. Hmmph.\" She stands back to look at her work. Her flat, Chinatown slippers trample the pile of my hair.\n\n_I hate you,_ I want to hiss.\n\nShe shakes her head, shuffles to the stairs again, and shuffles back with a pile of clothes. She drops them beside the dreads. \"I ain't dressing you. The clothes is here, so put 'em on. You won't sell, bare like that. Too skinny. Likely wait a day or two. Get your bruise up. So they know what to do with you.\" She exhales when she bends to pick up the basin. She grunts when she stands back up. Dumping the last of the water down the drain, the old woman slams the basin onto the cement floor, tosses the sponge inside it.\n\nI don't move.\n\n\"You ain't broke all your bones. Get dressed! I want those towels.\"\n\nI still don't move. _I wish I were dead._\n\n\"Suit yourself, mule. Sleep with the rags, all I care. Sleep without your soup, too.\" She stomps heavily up the old stairs, one arthritic step at a time. \"Earl, take me home,\" she hollers. \"I had enough of this place.\"\n\n_Creak, creak. Creak, creak. Slam. Click. Bolt._\n\nThere's thunder again from above. The King sounds drunk and sloppy and something else. _Why doesn't he come back down?_ The voices are ugly loud, his low rumbling and her higher screech, call and response, like some warped hymn from the church orphanage when I was a kid. I think I hear an engine outside, a car starting up. After that it's quiet for a long time. No floorboards squeak, no voices rumble. I drift in and out, not sleeping, not awake.\n\nA door slams someplace above me. I open my eyes. It feels later, but I can't say for sure. The light bulbs glare just as they did when I was first hauled into this dank cell, when the King carried me in blindfolded and dropped me on the floor.\n\nI remember the hood lifting, the heavy fabric being pulled off roughly, some of my dreads caught with it. I was sitting, broken, staring at his shiny cop boots on the grey cement, not saying a word. He was impatient. \"Should've got rid of you by now.\" I looked him in the eyes, in those flat soulless pits, and silently dared him. He had a strange look on his face\u2014not sure what. But he left, locking and bolting the metal door behind him.\n\nOther noises gradually start up\u2014distant footsteps, doors, the thrum of electrical systems, power being generated. Vibrations tremble their way through the wood and steel and glass. A thumping bass shakes the rafters; muffled dance music. Sometimes I hear car engines, motors revving faintly outside. Sometimes the floorboards creak above, but nobody comes when I scream. Mostly there's just the rhythmic throb of dance hits shaking the foundations of the building. It might be Britney.\n\nSo they want to sell me off. That means the King can't beat me anymore, not if they want to make any money. _Will he rape me again?_ Would he still want the same pile of half-broken bones? If he's human, even partly, he won't come back down. He won't want to see what he's done to me.\n\n_Unless he means to kill me._\n\nI blink.\n\nI slowly stretch out, flat on my back. My bones clack into place. I breathe as deeply as I can. My mouth tilts to one side to let the spit pool out. I start at my toes and move them slowly, identifying the hurts, the stiffness. I work my way up my body doing a pain inventory while the bass lines thump above me. _That's AC\/DC_ , I think. _And Nine Inch Nails_. My thighs are hot with bruises, my hips feel torn. I try not to think about my crotch. It is swollen, mashed beyond recognition. Like it belongs to someone else. It burns _inside_ , like that pig branded my soft pink tissue. Like he pounded his name into me, scarring me, taking that pretty place of mine away from me forever.\n\nA sob burns right up from my belly. If I let myself remember the weight of him crushing me, the stink of his breath on my face, the sick pull and slap, the animal mechanics of it, then I will only ever want to die.\n\nI skip up higher on my body, away from those throbbing, mutilated parts. I touch my ribs lightly with one hand. Probably cracked, they're so tender; even when I breathe, it hurts. I can still feel his large hands on my neck, just like how he wrapped them around Oreo's throat that day in the Junction. It's swollen, probably will be marked for days, just like hers. The inside part, my throat, is screamed raw. Not that anyone heard, not in the deserted parking lot where they drove me, him and his blond schizoid partner. It was an old routine they'd worked out long ago, like some married couple going to Sunday dinner.\n\n\"Cherry Beach?\" asked the blond.\n\n\"Naw, Rogers Road,\" said the King. \"I'll drop you home on my way to the club.\"\n\nThe horror settled into my bones when they turned off the ignition in that industrial wasteland, that ghost-filled decrepit lot.\n\nI exhale and try to lift the lower part of my aching jaw so it'll click back into place. I feel little pops under my fingertips when I open my mouth wider and close it gently. The King forced it open. He nearly killed me then, stuffing my throat, choking me from the inside and out. I gag thinking about it. My eyes and nose run. I cover my face with sore hands, bruised from fighting back, from blocking their hits, from trying to cover myself. The blond didn't rape me\u2014not because he's nicer, he just couldn't get it up. Not even when the King laughed at him.\n\n\"Not my fault she's too ugly.\"\n\nI begged him to help me, to end it, but he just turned away. That blond stood lookout while I was pulverized into nothing.\n\nAbove me, beyond the floorboards, I hear the tell-tale drum line, the insistent retro guitar riffs, the hair-shaking, head-banging chorus: \"Pour some sugar on me!\" I catch myself singing along. I'd know Def Leppard anywhere, even as a battered hostage locked in a dirty cellar.\n\nThat's what I get for hiding a radio under my pillow every night of my pre-teen life, earphones tangled in my regulation long hair. Radio rock lulled me to sleep, American commercials filled my dreams. Until Sister Anne, the mean one with the hairy face mole, discovered my secret and confiscated the goods. My lemon-yellow radio, my only friend, gone forever!\n\nI curl onto my side, fetal. I gently touch my head. Hair tufts unevenly. I'm cold without my dreads. There they sit, painted the colours of the ocean: purples and blues with murky green tips, my beautiful hair staring back at me from that hateful pile. It's right next to the clothes she brought, which I refuse to consider. I roll away and stare at the opposite grey wall.\n\n\"That's the King.\"\n\nThe kid, a pretty hustler boy, nodded his chin slightly when the cop car cruised past our spot at the Spadina-Lake Shore underpass for the third time that morning. No dirty fingers pointing, no rude gestures, no swearing. The kid kept his head down. He stayed in the middle of our group. When he paced in tiny circles, his baggy pants dragged through the long grass of the island that separates east- and west-bound traffic. Each time cops drove by, we had to hide our buckets and squeegees; the City had passed some bylaw about traffic interference. Some days, pigs would be cracking down all over Toronto; other days they didn't give a shit. On that particular morning I didn't know what the cop wanted. That kid did, though, and he fretted. I remember his voice, the one who first warned us. _What was his name?_ I had thought he was a girl for the longest time, with that mussy hair and delicate skin. Pretty.\n\nHe'd said, \"Yep, that's the King. And if he wants you, he'll take you to market.\"\n\nIt was the first I'd heard of the King, although I'd seen him in his car circling like a shark.\n\n_Jake._ His name was Jake.\n\nAbout a year before I met Oreo and moved into the Factory, I used to camp down at that underpass with some other kids, like red-headed Darcy. We cleaned windshields at the lights and made pretty good money some days. Jake had been there a while before me but not long after. He just disappeared. Someone said he went back home, back to that small town that puked him up in the first place. Someone else said, \"No way, man. He'd never go back there.\"\n\nThat was also the summer I met Cricket. He was out of high school, graduated, though nobody knew it. He was slumming downtown with the punks, pretending to be homeless. As it turns out, he would sneak home to Rosedale some nights, living his double life. Cricket was bummed when Jake went missing. He thought Jake had _revolutionary potential_. I think Cricket just wanted to do it with him. Cricket wanted to start a squat like Andy Warhol's Factory. He tried to convince Jake to join his arts collective, but Jake was more interested in smoking crack and flirting Cricket's money out of his wallet. Cricket never got more than a grope or two, maybe some kisses, but he funded one hell of a habit for the boy. Back then, Cricket was always rattling on about the Paris Commune and Bolsheviks and crap like that. Jake said he'd _been_ to Paris and never seen any commies. \"Paris, France?\" asked Cricket and Jake had blushed, \"No\u2014Paris, Ontario.\"\n\nNext we heard Jake got trapped and rescued by some hard-nosed social workers, fostered out to some suburban family. He was cute, sure, and not old enough to get his own welfare and apartment, but nobody really believed that story. I figured he'd turn up sometime, but no.\n\nThat day at the underpass, the last time any of us ever saw Jake, Cricket was shaking his squeegee in the burning noon sun, cursing \"the bougie pigs.\" He was ranting about our rights, trying to get us agitated _and_ organized. Jake shrank back from the curb, chewed his nails and flitted nervously; he was bugging people for money, but he already owed most of us and we were totally broke, so that went nowhere. Jake was freaking out. He grabbed my arm\u2014it was a cold, hard grip in spite of the hot day. \"He'll take you to market,\" he'd said again to me, in a panicked voice.\n\nI thought, _this kid is tweaked_ , and shook him off.\n\nI called the next set of lights, ran up with my dripping squeegee. I smiled and cleaned the glass. It was a dad driving a frowning wife and some kids who were trapped in the back, looking miserable. The dad gave me a toonie and stared at my tits. _Ugh_. When I hopped back onto the curb, Jake was already gone, who knows where.\n\n_To market_. Although I never thought he meant it literally.\n\nMy stomach growls: _I'm hungry_. I'd forgotten all about food, being in this cellar. In that parking lot, that car. On the street for a couple days before that. I hadn't eaten much then, either.\n\nAnd I'm something else: _angry_.\n\nDarcy's skittish face comes to me\u2014sketched out at the party. Right before the raid. And again at Ray-Ray's place, right before the King busted down the door. Darcy, phony as fuck and just as high, tripping like some delusional princess. He couldn't even look at me, the traitor.\n\n_Darcy_ , I think, _did you know what they would do to me? Did you know I'd rather die than be torn apart by those pigs?_\n\nI lick my swollen lip. _So thirsty_. My muscles seize up in the damp cellar, my joints stiffen on the cold floor. I sit up slowly. My jaw clicks when I move my mouth, but it hurts less. I can swallow. I can spit. I'm not dead yet. And I do not want to be touched, not ever again.\n\nUpstairs music pumps away, loud as ever. _It must be a bar or a dance club_. That means there are people up there, lots of them, probably, and that's a good thing.\n\nI look at what she left me to wear: white spandex shorts, long striped socks, a baby doll cotton dress, white pinafore, and shiny black buckled shoes. _Raggedy Porno Ann_. I have nothing else to put on, so what the hell. It takes a long time to fit my limbs into the proper holes. It hurts most to raise my left arm\u2014those ribs must be cracked. When I pull the shorts on, I don't even look down. Don't want to see my battered girl parts. I'd give anything for an ice pack to press _down there_. The shoes are a full size too big, slightly scuffed. _Who wore them before me?_\n\nNext, I check the metal door. It's definitely bolted. I jiggle the doorknob, slam against the door with all my weight. Nothing but the rattle of the heavy bolt. I remember the sound of it sliding into place, just like the one at the top of the stairs. Oreo could charm this open with her tools and her steady hand and her way with things. My throat burns when I think of her, my insides ache all the more. _Shh, shh_ , I tell myself. The cold metal feels good against my swollen face.\n\nI limp to the stairs and sit on the bottom step. The music sounds louder here. _Creak_. I lean against the second step. _Crack_. An old board breaks loose\u2014the wood comes free when I tug hard at one end. _Nice._ Now I have a weapon: a spider-infested two-by-four with rusty nails at either end. I rinse the thing off in the sink, wash the sticky white nests down the drain. I notice daddy longlegs crawling up the underside of the board, elaborate webs trailing from the wood. I chuck it. _Fuck_. Silky tendrils cling to me. I grunt, swiping at myself frantically. Panic bubbles up and I gasp.\n\n_Like a spider can hurt me now._\n\nOreo would laugh. She would cup her big hands around one of them and let it creep over her fingers or hang from a fine thread or hold one dangling from a twitching leg. She would croon, call it _grandmother_.\n\nBut Oreo is not here.\n\nI drink from the tap. I rinse my face with cold water. I go get the piece of wood. The last little monster makes a getaway across the grey floor, a mangled leg hanging uselessly, trailing behind. _Poor thing_. She looks like me. Using the basin, I tap three long, rusty nails out of the board. I put them in my pinafore pocket. The last nail is already bent pretty good. It's too hard to remove. I hit it a few more times to make sure it'll stay at a ninety-degree angle. It's my rusty basement bayonet, and I practice waving it around with my good arm. I crawl up the stairs and press my ear against that door. The music is loudest here. The techno bass line vibrates the whole door. The knob shines at me. I turn the deadbolt handle, and the whole door gives slightly. I exhale for what feels like the first time since climbing the stairs. The King locked this door with his key from the outside, and I've undone it. But there's still a bolt on the other side, maybe even a second lock.\n\nI jiggle the handle, bang against the door. I scream. I slam that door with the full weight of my body. I slam my aching shoulder into it over and over. My voice goes hoarse. My shoulder throbs. I slide down to sit on the top step and breathe heavily. Sweat trickles along my hairline, down my back. Blood thumps in my chest, my ears roar. I lick my sore lips. I'm dizzy and have to grab the wall so I don't fall down the stairs.\n\n_Hannah fucking Montana?_ Unbelievable. This shit music might kill me before the cops can! When I get out of here, Oreo will find this part of the story so funny. I can hear her laughing, see those gorgeous teeth shining between full lips, her long braid swinging. _You slay me, Ferret_. If I try hard enough, I can imagine the smell of her skin.\n\nI never had that kind of thing before\u2014love. Suddenly there was Oreo, standing right beside me, protecting me. Making everything come to life, like magic. I was so scared to believe it. What if she freaked and took off? Cricket always said, \"Lesbians are delusional and co-dependent. Ferret, you're a blind monogamist!\" But I didn't care. I only wanted to be with her, safe and happy, and not afraid of the whole world anymore.\n\nI feel vibrations through the flooring under my butt before I hear the heavy footsteps approaching on the other side of the door. I leap up and bang into the wood, my voice too hoarse to make sounds.\n\nThe steps stop right on the other side. I rattle the handle.\n\nThere's a knock on the door. \"Earl? That you?\" A low voice, a man out there.\n\n_He thinks I'm the King._\n\nI rattle the doorknob again and knock back.\n\n\"You fucking lock yourself in there again? Christ.\" I hear the faint jingle of keys. The voice is nattering on.\n\nI brace myself against the far wall and hold the wooden board up high. The bolt slides across. Music blares through the tiny crack in the door.\n\n\"\u2014only got a ten-minute break, you know\u2014\"\n\nI hurl myself against the door, sending the man backward onto the floor.\n\n\"What the\u2014?\"\n\nI'm on top of him, smashing the board over his bald head. The rusty nail scrapes angry lines across his red face. I pound that broken board into his face until it sticks. The man screams. The nail has sunk in, it's in his face somewhere near his eye, and he bats at it blindly. Blood comes out. My stomach heaves. He pulls at his black shirt uselessly. It says Fillies on the pocket. He rolls partway onto his stomach and sends me flying off him with jabs of his hard knees. His shirt says Security in big white letters on the back. I have no strength left, am gulping for air, every bit of me throbs in pain, I have no weapon. The big man crawls away from me, wood still hanging from his bloody face. His broad shoulders heave with each grunt. He holds the board in place with one hand and uses the other to get to his feet. He staggers toward the open door. I lurch to my feet. I push as hard as I can, and the big bald man falls down, down the stairs, crashing and bellowing. There's a terrible thud when he lands. The white letters on the back of his shirt glow from the darkness of the cellar floor. He's dead quiet. I slam the door and take the keys, still hanging from the lock. I slide the bolt over. My shaking hands put the keys in my apron pocket.\n\n_What have I done?_\n\nMy eyes dart around the space, my brain tries to make sense of it. It's well lit but not very clean. There's a stool with a crossword puzzle folded on top. A paper plate with a piece of pizza on the table beside it. I stuff that into my apron, greasy napkin and all. Music pounds from the other side of a solid door.\n\nFillies. A strip club. Any second someone could come barrelling through and find me. There are two more doors at the other end; one is plain black, the other a metal door marked with an exit sign. I push that one open.\n\nI'm outside. It's nighttime. The air is warm and there is a breeze. It's a half-empty lot; there's a car and a shiny motorcycle parked out back. Further back is a large dumpster. Beyond that is an alleyway. I don't see anybody. I shut the door behind me, creep alongside the car and make a run for the dumpster. I crouch beside it. My breath comes ragged, shallow. All those sore ribs bang away at my insides, making it hard to think. The longer I stay put, the more I notice the dumpster's stink, garbage stewing in the summer heat. Scattered at my feet are chip bags, broken vials, used condoms. Just down the alley, maybe a few feet away, cars drive past. They honk and squeal tires and blare music. Their engines rev, voices spill from them, laughing, hooting. The city is still here, pulsing its beat of regular nighttime madness, existing all this time without me.\n\nI hear the grinding gears of a city bus, hear the ding of its door opening, the churning motor when it stands at the curb letting people on, letting people off. _My chariot awaits_. And I know right where I'm going. Where else but back to the Factory squat? Back to the hot stink of the slaughterhouse, the itch of the grassy field, the rotting dump: home.\n\n_Come and get me, Pig. I double dare you._\n\n# Ferret Hunt: A Three-Act Play\n\n## _Act One: Safe House_\n\nCricket waves goodbye to the sleazebag landlord and shuts the door to our very own filthy, east-end rooming house. I can hardly breathe. The place stinks of dead mice and piss-soaked old men. He opens the reeking bar fridge on the other side of the small room, slams it shut. There's an electric hotplate on top. In a closet with a broken door is a leaky toilet and rusting sink. Cricket paid one hundred dollars cash for a week\u2014money his parents gave him to buy textbooks for next semester, which starts in a few days.\n\nCricket pulls a cobweb from the tip of his blue mohawk. \"Ew. We have our safe house, now we just need to find our girl.\"\n\n\"Great.\" My voice cracks. Lately I'm either raging or weeping, sometimes both at the same time. I lean out the dirty window ledge so he won't notice my eyes getting wet. I dab gently with a corner of my shirt. First, my face is still sore from the King's beat-down, and second, I don't want to smear the mascara and eye shadow Cricket piled on earlier, using samples at the mall. \"I just can't believe no one's seen her,\" I say for the hundredth time. \"It's been over a week since the raid.\"\n\nA hot breeze gusts in, bringing shouts and traffic sounds from Gerrard Street below. Bollywood music erupts from the downstairs restaurant when customers open the front door. I smell deep fryer and curry. My stomach gurgles. I slump onto the cracked linoleum floor with my back to the wall.\n\n\"Don't worry, Oreo, you'll be great as an undercover stripper. Pretend you're on a rerun episode of _Charlie's Angels_.\" Cricket squeezes my shoulder. His body heat closes in on me in the stuffy room. \"Soon we'll all be together again.\"\n\n_Except for Digit_. I stare at Cricket until he looks away. The unsaid words hang heavy in the gloom.\n\nI jiggle the CD player we found in the trash. I want to crush it between my strong hands, destroy it, burn this rage out of me so I can snap back to my old useful self.\n\nAll we know is while we were getting our asses ridden at 14 Division, Ferret somehow escaped from the Factory squat party raid and eventually hid out with Ray-Ray. Ray-Ray and Darcy say cops picked her up a couple days later. Not just _any_ cops\u2014the King himself was hunting her. He knew her real name and everything. By the time they let me out of bail court, Ferret was long gone. Her name didn't turn up anywhere in the system when the drop-in worker started digging.\n\n\"We should tell Ray-Ray and Darcy where we are. Ferret might hook up with them again. What do you think, Oreo? I mean, where else would she go?\"\n\n\"I don't know. Drop-in is off limits, shelters too.\" We heard the King's harassing all the kids downtown, even more than usual. \"She doesn't have family.\"\n\n\"Seriously. Ray-Ray's our best bet.\"\n\nBut I wonder. How far will I go to save Ferret? _All the way, whatever it takes_. \"With Eddie in jail, maybe Ray-Ray's ratting. He'd do anything to help his boyfriend. Wouldn't you?\"\n\n\"Hmmph,\" says Cricket. \"I'd do anything to spring myself, since I don't _have_ a boyfriend.\"\n\n\"Well, you already did that.\" I blow into the CD player's dusty parts.\n\n\"Pure luck,\" he says, smiling.\n\n_Pure rich white luck_ , I think.\n\n\"I can't wait to see you in drag, Oreo.\" Cricket unzips his backpack and dumps everything onto the floor. He sorts it all: the makeup, lingerie, and hooker shoes we shoplifted from Gerrard Square mall. A bottle of vodka stolen from his mother. He empties his pockets\u2014a handful of change, an unopened condom, the clean square card with his dad's big-time lawyer name on it.\n\n\"On second thought, you keep this.\" He hands the card to me. \"I know the number. If anything goes down again, just remember to say, 'Officer, am I free to go?' And, 'I would like to call my lawyer.'\"\n\nLike it's a game with different rules for each player.\n\n\"That judge owed your dad some kind of favour, huh?\"\n\nCricket blushes. \"The pigs, too. I'm lucky the charges got reduced. Trespassing and drinking in public? Please, that's nothing.\"\n\nCricket's older, so he didn't get the extra $125 for being underage.\n\nHe says, \"I pay a fine and do some community service, whatever. I wonder if volunteering with my revolutionary arts collective counts.\"\n\nI shake my head.\n\n\"Well, if I go to jail, it better be for political reasons, not for getting down at a house party.\"\n\nI laugh. \"Honey, you'll never do hard time. You'll be out on bail eating take-out and watching _America's Next Top Model_ before you can zip those prison pants.\"\n\nMeanwhile Eddie and boys like him\u2014mixed-race, tattooed, buck-toothed boys raised by the system\u2014they rot on remand. That stokes the angry fire that burns inside me.\n\n\"Whatever, girlfriend.\" Cricket waves his hand at me. \" _You_ didn't do too bad either, Oreo. Possession of one joint? Please.\"\n\n\"I got beat up. My face is still a mess. I already had a record, so now I'm on probation.\" I shake my head. \"It's bullshit.\"\n\n\"Still, could've been way worse.\"\n\n\"The squat is shut down permanently, all our stuff is destroyed. My girlfriend got kidnapped by a psycho cop, and Digit is\u2014\"\n\n\"Don't say it.\"\n\n\"\u2014and Eddie's in jail. Does it need to get worse?\" I bang my head on the window sill once, twice.\n\n\"Take it easy, Oreo.\" He looks worried.\n\n_Okay._ I breathe deeply. Don't want to completely lose it.\n\n\"You know, getting arrested was not fun in _my_ condition\u2014the Ecstasy-Viagra combo, euphoric with a rock-hard dick for hours. Awkward! I would have totally gotten laid by my bike courier if we hadn't got busted.\" He sighs loudly. \"And I had to toss my amazing stash. It was selling like hotcakes.\"\n\n\"Wish I had my tools here,\" I say. Making something, fixing something, anything at all, would make me feel better. _Large and in charge_.\n\n\"Maybe I would've got a boyfriend in jail,\" he says wistfully.\n\nA sudden memory from the party slams into my brain. I was spinning, headphones on, didn't hear the cops, the yelling. I was zoned. Then I looked up to see Ferret's terrified face, right as that cop's stick cracked my head. I remember coming to as he dragged me outside. The King threw me against his car to cuff me; my knees buckled. Then, with the bracelets on nice and tight, he sucker-punched me in the face. \"Squaw dyke,\" he said in that sinister low voice. I lay on the ground outside the Factory in all that chaos, blood dripping out of my nose, him leering above me, light bouncing off his silver belt buckle.\n\nCricket waves a hand in front of my face. \"Should we talk about Digit now?\"\n\n\"No.\" I jump up and pace back and forth from the window to the fridge. I still can't believe he got shot. _Who brings a gun to a vegan dance party?_\n\n\"Couldn't even say goodbye with all those cops parked in front of his hospital room. Ray-Ray heard his folks came all the way from New Brunswick. He was hooked up to machines.\" He sniffs loudly.\n\nWhen I picture Digit leaving the hospital, it's on the back of some leather daddy's motorcycle. It's on his mud-covered ATV, or a skateboard he made out of found objects, not in a wheelchair. Not in a wooden box.\n\nI swear and punch the stained wall.\n\n\"Easy, Oreo.\"\n\nOne night this summer, me and Digit and Ferret were lying in the field outside the Factory, shooting the shit about where we grew up. I told them about Manitoulin Island, where I'm from, Wikwemikong unceded territory. I wanted to take Ferret home. Wanted her to meet Phoebe, my Auntie's woman who helped raise me. I wanted to take her to the powwow. So she could see that part of me that's always getting watered down around white people. She could hear the drums and singers, smudge with burning sage, and watch the dancers in their beautiful regalia; Hoop Dancing, Men's Fancy, Iron Man and Iron Woman. She could start to know those proud parts of me, who I really am.\n\nDigit wanted to come, too. \"Some tings remind me of Neguac, my village,\" he said. \"We catch oysters dere, you know. Each day, every day. I'm supposed to stay wit da oysters and find some girl who's not my cousin to make babies.\" Digit's accent got thicker the longer he talked about home. He loved it as much as he hated it: ripping around on four-wheelers, chucking dirt bombs at the _\u00e9cole criss, tabarnak_ , sneaking beers from his drunk uncle's broken barn fridge. Lighting blue angels to impress a girl. \"Hi burn my hass so bad, you know, but still she don't like me. She go out wit my friend hinstead!\" Ferret and I shrieked when he re-enacted it, dropping his pants and lighting a fart as it reverberated from his bare backside. _Digit._\n\nCricket wipes at his eyes with a pair of pink panties from the pile of things. He's blabbing still, going on about Digit.\n\n\"We can't do anything for Digit. Let's find Ferret.\" My knuckles are warm from denting the drywall. \"I wish none of this ever happened.\"\n\n\"Yeah,\" says Cricket. \"That party was a stupid idea.\"\n\n\"Fuck you.\" The party was _my_ idea for Ferret's birthday, and _I'm_ the one who talked her into having it. \"I didn't invite all those university bitches. I didn't post it on Facebook. How do you think the cops found out?\"\n\nHe clears his throat. \"I'm not the enemy, Oreo.\"\n\n\"You sure?\" I feel mean. I imagine ripping his throat wide open with my bare hands. \"You came out of this pretty clean.\"\n\nCricket says, \"Do you want me here or not? I should leave. If my parents find out I'm not at Frosh week they'll cut me off. I can't afford tuition. Maybe that doesn't matter to you. But I'd be completely on my own.\"\n\n_Like the rest of us have been for years_. \"Boo fucking hoo.\"\n\nCricket's mouth pops open, but he doesn't argue.\n\nI spin away from him. I march over and yank the window as high as it'll go.\n\n\"This place is a dump.\" Cricket is making nervous small talk.\n\nI say, \"It's so un-bougie. I thought you'd love it.\"\n\n\"Very funny. There's a difference between un-bougie and downright ugly. Speaking of which, are you ready to get in drag?\"\n\nI grunt. \"I don't know about this plan.\" I kick off my boots, drop my combat pants, ripped T-shirt, boxers, and dirty socks into a pile. I sniff my pits\u2014they are pretty ripe. I try to wash them in the crap sink with a sliver of dried old soap. I let them dry by the window. The breeze feels good on my bare skin. I shove on the push-up bra with its stiff little hooks, the lace panties, the strange belt with the tiny snaps. It takes a while to get everything in the right place. Finally, I roll the matching stockings over my strong legs. I struggle with the metal clips dangling from the belt. \"This is harder than it looks.\"\n\n\"I'll help with the garters.\" Cricket kneels at my feet. He looks up\u2014the bra is working, I can tell by the shock on his face. \"You know, Oreo, if I was even remotely bisexual...\"\n\n\"Ugh.\" I stuff my fishnetted feet into second-hand stilettos. I stumble. \"Ugh. How am I supposed to dance if I can't even walk?\"\n\nCricket presses his hand on my back lightly. \"Shoulders back. Spread your feet wider. You have to find your new centre of balance.\"\n\nI lurch forward. My left foot slides and I wipe out, land right on my lace-covered ass. \"Shit. I can pop the panel from an ignition tumbler and hotwire a car in three minutes, but I can't cross the room in a pair of heels.\"\n\n\"I'd be there in a heartbeat if they'd hire _me_. Sadly, this patriarchal establishment does not pimp my gender.\" He stares at me down on the floor and says, \"Hmmm.\"\n\n\"What?\"\n\nHe pours two glasses of vodka. \"I'm thinking.\"\n\nI say, \"I wish you could come with me.\" And suddenly I do. I mean it just as much as I wished him away earlier.\n\n\"Honey, I'd blow your cover like nine inches at the bathhouse. Here, drink.\"\n\nI take a swig, cough. \"Do you really think Ferret's at this peeler bar?\"\n\nHe sits on top of the bar fridge and the hot plate. They creak a warning. \"I hope so. I mean I do and I don't. Ray-Ray saw the King take her. He did something with her, took her somewhere, and it's not the detention centre.\"\n\nMy stomach twists at the thought. I know what can happen to homeless girls, working girls, Native girls. All over the country our betrayed bodies get swallowed by lakes, by the ocean, and sometimes spat back up on the sand, some dog walker or early-morning jogger finding our parts.\n\n\"Darcy heard she might be in the upper lounge at the strip club. I guess it pays to have shady roommates after all, huh? Darcy says that's where the King dumps all his fresh meat for the international buyers. Dopes them up, whores them out.\"\n\nMy mouth waters with sick. _What would be worse\u2014death or forced prostitution_?\n\n\"Sorry,\" he says. \"I know this is hard.\"\n\n\"I still don't get why he'd do that to Ferret. She never hurt anyone. Why would he even bother?\"\n\n\"Maybe because he can.\"\n\n\"What's that supposed to mean?\"\n\n\"He's a schizoid power tripper. She's an orphan, a street punk. Queer. Who the hell is going to stop him?\"\n\n\"I'll kill that fucking pig myself.\" I'm grinding my teeth, squeezing my fists. I want to destroy something, kick the shit out of somebody, anything to let loose this rage. I wonder why it's not _me_ who's missing in action, a statistic waiting to happen. _I didn't protect her. My girlfriend is gone, and it's my fault_. I want to howl, want to rip out my hair and beat my chest.\n\n\"Chill, Oreo.\"\n\n\"How would you feel if it was _your_ lover?\" Heat rises in my cheeks. I remember the sound of the King's voice, the things he said to me that day on the sidewalk. Things he's probably doing to Ferret.\n\n\"She's my friend, too.\" Cricket looks hurt, but that fuels me. \"I wish you'd let me talk to my dad. He might know someone...\"\n\n\"Your dad might get favours at the cop shop or in court. Tell him to help Eddie. But Ferret doesn't need a lawyer. She needs a bounty hunter. Does your dad have a gun?\"\n\nCricket's eyes widen.\n\n\"I'm serious. I don't want to fuck with the King and run. He'll find us. He pulls strings all over, nobody knows how far. He runs this town. If I'm facing off, I'm taking him right out.\" Panic rises in my chest.\n\n\"Don't joke, Oreo.\"\n\n\"Who's joking? Nobody else is gonna help. Nobody else gives a shit about us.\" My voice shakes. I'm yelling, and Cricket shrinks into himself. He moves farther away from me. I want to scream, _you sheltered little bitch_. I want to hit him, slap some meanness out of me and some sense into him.\n\n\"I don't want anything bad to happen to her either,\" he says quietly.\n\n\"Bad shit has been happening our whole lives,\" I yell. \"The squat wasn't just a cool hangout. It was her home. We're her family. We have to do something!\"\n\nI picture Ferret hurt, scared, feeling like I do, but all alone. _My girl_. I choke back a sob that has been lodged inside, ever since the party raid. When I find her, I'll take her north. Get out of this ugly city for good. I lean out the open window, take deep breaths. Stuff is happening outside\u2014families going for dinner, couples holding hands\u2014and none of it matters. I tell myself that Ferret is still alive.\n\n_But Digit isn't. Why should Ferret be?_\n\n\"What if it's too late?\" My voice sounds small. Not mine at all.\n\n\"It's not. But we need to get cracking. Darcy says the club has security cameras. Maybe we can get the tapes, get the place busted.\"\n\n\"Busted by who? Cops took her, cops sell the girls, and cops own the fucking club!\"\n\n\"They can't _all_ be in on it,\" says Cricket.\n\n\"Oh yeah? Those blue brothers only protect each other.\"\n\n\"Oh.\" He looks down at his fair trade sneakers.\n\nI can feel the King's big hands closing around my throat, stopping my air, the way they did on the sidewalk right in front of Ferret. The way everything closed in on me while he hissed into my ear, \"I'm gonna rip you apart. You don't even know pain yet. I'm your worst nightmare, you hear me?\"\n\n\"Oreo. You listening?\"\n\nI shake my head. It's so hard to pay attention to the sounds coming out of other people's mouths these days.\n\n\"I was saying, make sure you don't do anything dumb tonight. Case the joint, but don't be obvious. If you can send Ferret a message, that's a total bonus, but don't go all He-Man.\"\n\nI blink a few times.\n\n\"No crying, Oreo. It took twenty minutes just to cover your black eye. I didn't steal enough shadow, so don't mess them up. If you see the King, get the hell out. Promise?\" He swipes at my face with some powder from the pile of stuff on the table. He waves a lip gloss at me. \"For later.\"\n\n\"Shit.\" I finish my drink. I stand up. I don't know what I'd do if I saw the King face-to-face right now. I might surprise everyone and bawl.\n\n\"We still got to do your hair.\"\n\nI slump on the floor at Cricket's feet. He combs my hair out of the long braid I always wear.\n\n\"Ferret needs us. So get in there, get some dancer cred. This is an official undercover operation, Oreo. You make your brotha-from-anotha-motha proud! Chin down, honey. Work it like you own it, like you rentin' all night long.\"\n\nCricket snaps his painted fingers and moves like liquid across the tiled floor. He makes it look so easy.\n\n## _Act Two: Strip Club_\n\nHours later, I'm at Fillies in the dark reddish glow. Lights flash on the bar and the stage. Mirrors reflect my angry face from all angles. I gasp. With all the makeup, with my waist-length hair hanging loose, I look like my dead mother. Dance hits pound through the space, through my chest. I'd do anything to slip the DJ a decent playlist. The manager is a creep show wearing a stinky Hawaiian shirt and bad toup\u00e9e, right out of a cartoon. He points me to the dressing room\u2014a decrepit hole with a couple of toilets, rusted sinks, bad lighting. It smells like dirty crotch and a side order of bourbon.\n\n\"Carly, give her the tour,\" he says. He waits for me to take off my jacket. He frowns at the bear clan tattoo that covers one shoulder. I stick my chest out further. He grunts, gives a slight nod, and leaves.\n\nThe other girls ignore me. They're different degrees of naked, white and skinny, black and skinny, lots of brown girls, too. They wear thongs, leather, and lace. They do their makeup, drink, and gossip.\n\n\"Come on, hon,\" says an older blonde woman. _Carly_. \"Let's get you settled.\"\n\nHer voice reminds me of Auntie Tam: gravel and whiskey. She smiles a wide, white set of teeth with a frosted pink frame. When she strolls down the dingy hall in her fringed cowboy boots, I watch the sway of her womanly hips. She points out the important stuff\u2014the stage, the regulars, the private booths where you make the real coin. She tells me to sit and watch the experienced dancers. I ask her what's upstairs, and her face shuts tight, a garage door closing. She leaves. One after the other, girls attack the stage like it's a pommel horse in gym class. They pull fancy tricks, slide into splits; they hump the pole and bounce their dimpled bums in customers' faces.\n\n_I'm not playing that game_ , I decide. I wouldn't even know how.\n\nAround midnight I lurch on stage for my very first solo. I wobble in the stolen shoes. A third drink loosens my limbs, but Cricket's pill gives me the courage to get up in front of everyone. Bottles and glasses clink through the din of voices. My music doesn't start; the strung-out DJ misses another cue. My legs shake. I flick my long hair and inhale deeply. Catcalls from the audience knot my stomach.\n\n_I'm dancing for Ferret_ , I tell myself.\n\nFinally, my song starts. The droney doom metal matches my oxy groove. I close my eyes and let the music tell me how to move. Slowly, I snake my arm above my head. I roll my neck and my long hair tickles my bare shoulders. My body undulates. I roll my shoulder and peer over it toward the crowd, lashes lowered. It's impossible to see anything past the row of bright lights. There are shadows at the edge of the stage, but that's all. I picture Ferret out there in the club, watching. Each step brings me closer to my memories: Ferret smiling and twirling at the Factory dance party, Ferret's soft skin, Ferret writhing beneath me. I'm on stage and at the same time, I'm far away from this terrible place. I'm back at the Factory, before the raid, curled in our nest.\n\nThe song ends. I'm lying on the stage touching myself. I roll over and notice the money on the stage. The floor feels cool on my skin. Part of me wants to sink into it, just melt through it and disappear. The other part wants to count money and buy another drink.\n\nA white man leans forward with a fifty dollar bill in his outstretched hand. _Half a week at the rooming house_. I crouch, both hands filled. I am an animal on the road, a car bearing down upon me, sad eyes for headlights, soft hands for a grill. The next dancer, an athletic blonde, is already cleaning the pole with anti-bacterial wipes. I grab the bill and the rest of the money. I stomp down the rickety stairs to the change room.\n\n\"Song's too long, Pocahontas,\" says the manager.\n\nI imagine stabbing his fat gut as I towel off. Instead I check my makeup in the mirror above the sink.\n\n\"And don't get weird on stage. This ain't no art bar.\"\n\nI ignore him and apply more lip gloss, something I haven't worn since I was a closeted fourteen-year-old, back on the Rez.\n\nIt's after one a.m. I'm alone in a dark corner. No sign of the King, no sign of Ferret. The dancers won't talk. There's nothing but rat shit and empties in the basement\u2014and a locked furnace room. Another backstage locked door might lead upstairs. One big bouncer reamed me out when he found me fiddling with it. If I had my tools, I'd pop both open in a heartbeat. Meanwhile, I'm terrible at this other job: flirting with men, crawling on their laps to get them hard. All I want is to beat the crap out of them.\n\n\"Hey, kiddo.\" It's Carly, sidling up with two drinks. \"How you doing?\"\n\n\"My feet hurt and I want to go home.\"\n\nShe smiles and hands me a glass.\n\n\"No thanks,\" I say. \"I'm trying to not get wasted.\"\n\n\"Relax, it's water. That bozo over there thinks he bought us gin tonics.\" Carly raises a glass and blows a kiss to the bald lump of a man who pumps his arm feverishly in return. \"I get tap water and split the difference with the waitress.\"\n\n\"Smart. Thanks.\" We sip while a girl twirls around the pole to Bon Jovi. _Wanted dead or alive._\n\n\"Bozo would like a lap dance with you after,\" she says.\n\n\"I'd rather give him a vasectomy.\"\n\nCarly laughs, a scratchy cackle. \"Don't mean to pry. Lord knows we all have our reasons, but this doesn't seem like your kind of place.\"\n\nI look at her: fake tan, streaked hair, boob job, glow-in-the-dark booty shorts. I see manicured hands with a couple of age spots. Foundation caked in tiny crow's feet at the edge of mascara-framed eyes. She's been around the block. I decide to tell her the truth. \"I'm not really a dancer.\"\n\n\"No shit.\"\n\n\"I'm looking for my girlfriend. I think she's upstairs.\"\n\nCarly moves in closer. \"This a joke?\"\n\n\"No.\" I stare her down. I wonder if she'll rat me out to the fat jerk manager. \"She's shorter than me, white, got blue dreads. She's pretty. Punk pretty.\"\n\nCarly shakes her head. \"I don't know half of what goes on up there, but none of it's good.\"\n\n\"The locked door backstage goes upstairs, right?\"\n\n\"That's one way.\" She scans the bar carefully. \"This is serious, kiddo.\"\n\n\"No shit.\"\n\nShe nods her chin. \"There's a camera's right there. Not sure if there's actual tape running. Be hard to get up there without that big goon noticing. He's not friendly. But he's not the worst.\"\n\nThe stage light follows a girl doing flips. She lands in a bridge with her legs spread wide, front and centre.\n\n\"Do you know the King?\" I say it straight up, no emotion.\n\nHer eyes narrow. \"A girl would be smart to stay the hell away from him.\"\n\n\"My girlfriend never had a choice.\"\n\nShe doesn't take her eyes off mine. She could be protecting him, or warning me, I can't tell. Carly leans against the bar ledge. She looks away. I wonder if this conversation is over.\n\n\"I don't want to get you in any trouble. Sorry.\"\n\nShe looks at me again. \"Sure about this? No good will come of it.\"\n\nI nod.\n\n\"A real James Dean, aren't you?\" She gives me a sad smile. Carly finishes her water. \"I'd try tomorrow. Earl\u2014the King\u2014doesn't usually come in on weekends.\" She points a manicured finger to the main bar. \"Wait staff are busier, and security spends more time circulating. They'll be distracted. I'll do some pussy shots by the DJ booth at the end of my first routine, draw the light. Not sure how you'll get through without a key. You better hustle. Manager finds out, you're done for. And I don't mean fired.\"\n\n\"Thanks, Carly.\"\n\n\"You be careful. I mean it.\" There's a frown line on her brow that isn't good for business. She squeezes my forearm. \"Hell, I'm gonna worry about you, now. I'm gonna need a real drink after all.\"\n\nIt's four a.m. when the cab Carly called stops in front of the rooming house. The driver jots something down as I get out. He peels away, leaving me in the street wearing lingerie and a jacket Carly lent me. My regular clothes and boots disappeared from the locker room. Carly says one of the dancers stole them, like a hazing ritual. My key gets stuck in the lock. I yank on the doorknob. Someone gallops down the stairs. The door rips open, almost from its hinges.\n\n\"Ohmygodyou'refinallyhome.\"\n\nI follow Cricket upstairs in the dark. The hall light is burned out, so we feel our way along the disgusting walls. Cricket is wired. \"You know, there are a lot of freaks living here. They've been bugging me for smokes. One guy tried to give me mouldy salami.\" He shudders. \"He stuck slices under the door!\"\n\nInside our ugly room I unbuckle the hated shoes and drop them: _One, two_.\n\n\"Plus I was getting worried about you.\"\n\n\"Yeah?\"\n\n\"I _was_. I was worried you'd meet some hot guy and decide to go straight and make babies instead of come back and pay for this luxury room with your stripper tips.\" He smiles charmingly.\n\n\"No worries there.\" I think of the blobby, faceless men from the club: jocks, gangsters, pervs. They're not even real people. Just lonely creeps.\n\nCricket counts my money while I rub my swollen feet.\n\n\"Wow. You're rich.\"\n\n\"This girly stuff is hard work. I don't even know how to lap dance, by the way. I actually fell off a chair trying.\"\n\n\"Really?\"\n\n\"I couldn't take his money, it was that bad. I ended up shaking hands with the dude.\" I comb my hair with my fingers and quickly braid it back the way I normally wear it.\n\nCricket snorts. \"We can practice, Butch-tard. Did you make any friends?\"\n\n\"As if,\" I say, yawning. \"Those broads are not stripping for the sisterhood. One was nice.\" Carly's face and her sugar-rough voice come back to me. She's hot, in a not-my-type kind of way.\n\nCricket folds a few bills into his own pocket. \"Choreographer's fee,\" he says sweetly. \"Still got to pay for the stash I dropped.\" He puts the rest in a pile at my feet. \"You're going make lots of money if you get this right.\"\n\n\"I'm going to find Ferret if I get it right.\"\n\n\"Did you see the King?\"\n\nI shake my head. I tell him what little I got from Carly.\n\n\"Well, that's a start. Maybe tomorrow we'll get upstairs.\"\n\nThe thought of going back to that place makes me nauseous. \"I didn't learn anything. We don't even know if Ferret's there. My feet are killing me, I got molested all night by gross dudes, and probably got a fucking STD from the furniture.\"\n\n\"Not if you wore a condom,\" jokes Cricket.\n\n\"Jackass.\"\n\n_Another night without Ferret._ She could be anywhere. The enormity sinks into my bones. How could Ferret be held in the same evil place I'd been all night, with the sleazy manager and those mean girls? Wouldn't I sense her? I gag and choke down the bile. I punch the wall as hard as I can. The drywall buckles into a hole slightly larger than my fist. My hand throbs. Someone bangs back from the other side.\n\n\"Easy, girl.\"\n\nI lie on the dirty floor and press my ragged knuckles into my eye sockets. The familiar rage burns my veins, eating me inside out.\n\nCricket says, \"Shh. I promise we'll find her. Tomorrow.\"\n\n_But what happens to her tonight?_\n\n## _Act Three: Break and Enter_\n\nLight fills our curtainless room. Dust floats in the sunshine, whirling about, going nowhere. It makes me think about my life in a depressing way, like I'm following the broken footsteps of so many women in my family. It's like we just keep falling into the same shitty circumstances, like nothing will ever change for us.\n\nA brown spider spins a web inches from my face. _Hello, Grandmother_. Her legs keep working on the fine thread, and that makes me feel better.\n\n\"Morning, sunshine,\" says Cricket. We're lying side by side on a pile of dirty clothes.\n\nI groan. \"Already?\" I had been dreaming of long-ago happy times in Phoebe's kitchen up north: Phoebe and Aunt Sue, Auntie Tam, me, and my mom were making fry bread, whitefish, wild rice. In the dream, they were trying to tell me something. _But what?_ The words are gone.\n\nCricket says, \"Maybe some punk rock will help.\"\n\n\"Ow.\" I'm sore from sleeping on the floor, everything hurts from wearing those killer heels all night, from dancing\u2014if you can call it that. I'm dry-mouthed and achy from the painkillers, the vodka. I roll over carefully. \"We don't have music.\"\n\n\"Oh, yes we do!\" Cricket shakes a CD. \"You fixed that box, whatever you did. Last night, while you were at the club, I went back to the squat. I got so excited about the money I forgot to tell you. Cop tape is all over the place, shit's trashed. A pipe broke, there's water everywhere. But I found some clothes and music. Isn't that awesome? No drugs, though.\" He presses play and the anarcho-punk Dirt CD fills the ugly space. Cricket shouts the chorus to \"Deaf, dumb, and male!\"\n\nI shut it off. \"Did anyone see you?\" I can't believe his stupid grinning face.\n\n\"Naw. The cop out front was reading porn. Never even noticed.\"\n\n\"You brought back music?\"\n\n\"You love this CD!\"\n\n\"Why didn't you get my fucking tool kit? My picks, my cutters? Fuck, Cricket. That's the shit we need if we want to rescue Ferret. I can't pass as a stripper\u2014I'm not fooling anyone.\" I want to punch his lights out.\n\nCricket ejects the CD. \"I found your pants. I brought them for you.\" His voice is pinched and clipped, like an uptight little jerk, like he might cry womanly tears all over me. He tosses a bag beside me.\n\n_Fucking baby._\n\n\"At least you got that right. I can't be walking around Gerrard Street in this.\" I pull at the stupid lingerie I'm still wearing.\n\n\"You can have my other sneakers,\" he says, setting them on the floor near me. \"Or just a buy a new pair with all your money.\"\n\n\"We'll need that money to get out of town or get settled, asshole.\" He has _two_ pairs of designer shoes from our wreck of a home, and nothing that we actually need. _Food. Tools. Supplies_.\n\n\"You don't have to be such a bitch.\" He's crying, as predicted. \"I'm going dumpstering,\" he blubbers, and slams the door behind him.\n\nI lie there fuming. _Stupid spoiled Cricket can bloody well go home if he wants_. It's not like _I_ have a rich family to bail me out, or a beautiful house to run to. My mom and Aunt Sue are dead. _Bam._ Both killed on New Year's Eve. A two-car collision, two dead women; one drunk asshole walks away from the wreck. Tam took it even harder than me. Our family cabin couldn't hold us with all that grief. Last I heard, she was living rough in Winnipeg, trying to forget. She ran west and I came south, leaving Sue's girlfriend Phoebe to deal with it all.\n\nI breathe deeply. I'm more alone than I like to admit. Suddenly, the thought that Cricket might leave is scary. And that I might somehow deserve it, for how I'm treating him.\n\nInside the bag are my pants, an old black pair, covered in patches, comfortable and familiar. _Mine_. Another thing stares back at me. _Ferret's favourite hoodie_. It's covered in band patches, pins, and buttons; it's customized with metal accessories and spikes along the edge of the hood. She worked so hard to make it perfect, her most prized possession. I clutch it and inhale her scent from the fabric: a hint of patchouli, something like oranges and vanilla mixed together, and there\u2014 _there!_ Her earthy, tangy skin smell underneath it all: _Ferret_.\n\nI let loose for the first time since the party. Hot tears roll down my face. Snot drips. I weep, holding the hoodie to my face. Smelling her is a shovel hit on the head. I hear her low voice, see her beautiful face with its sharp cheekbones, those big brown eyes, full lips\u2014gone. I bawl until there's nothing left. Then I pull the sleeves over my hands, the hood on my head, and zip it all the way up. I pretend she's right with me, spooning.\n\nThe next time I open my eyes, Cricket is eating naan bread. \"That cute cook saw me in the dumpster and instead of getting mad he gave me all this free food. I think he likes me.\" Cricket sounds as flamboyant as ever. He opens the containers: curried vegetables, channa, chutney, and spicy pickles. Good smells make their way to my corner. I sit up at last. I stick a dirty finger into one bowl.\n\n\"Mmm.\" I can't remember my last meal. Spices make my nose run. Salty sweet tickles my mouth. My stomach twists.\n\n\"Yum,\" he says, scooping curry with a piece of naan.\n\n\"Thanks, Cricket.\"\n\n\"It's nothing,\" he says. But he won't look me in the eye, so I know he's still hurt.\n\n_Just like a girl._\n\n\"I mean it. For everything.\" I can't talk about the hoodie yet, but he sees me wearing it, plain as day. \"Sorry about before.\" He must know I'm trying, at least.\n\nHe shrugs. He eats.\n\nWe plough through the containers. We lick each one clean, and the plastic spoons too. I wipe my face on Ferret's sleeve. Cricket burps and finally smiles. Food gives us hope. _Maybe things aren't quite so bad_.\n\nCricket's grey eyes are a bit watery. His face is still tight. I get it; deep down all he wants is approval. He\u2014the braggy soapboxer, the one lecturing us with his politics and visions and boring rules\u2014right now, he just wants me to like him.\n\n\"Let's go to the club. We'll pick up some tools on the way. We can totally break in before all the security dudes show up for work.\" I'm like a bloodhound with a fresh scent for the trail, rested and fed and single-minded. \"I just need a screwdriver and a paperclip. Some pliers would be awesome.\"\n\nHe looks like a little kid. Like he knows I can turn on a dime and beat him, but is desperately hoping I won't.\n\n\"Honest, Cricket,\" I say, swallowing that awful guilt. \"We'll be okay.\"\n\nIn morning light, the club looks pathetic. It sits on some expensive real estate, the busy corner of an east-end intersection. The sign, not lit up, not blinking in neon ecstasy, is benign. Alleys run on either side of the building. We each follow one; they meet at the back where there's a dumpster and space for the manager to park. Staff use the back door; ash piles and cigarette butts mark their smoke breaks. Small square windows with crappy blinds line the top of the building. Cricket knocks the two security cameras out of commission with his slingshot and some rocks from the laneway. That gives him a swagger.\n\n\"Oreo, check it out.\" Cricket points to a door without a handle or lock. Around the edges there are smudges and imprints in the dust; people use it regularly. \"Someone lets them in.\" The weeds have been cleared by the entrance. When I stand in the main alley, the dumpster blocks Cricket and the door from my view.\n\n_Clever._\n\n\"Think anyone's inside?\" says Cricket.\n\n\"Maybe a cleaner. Maybe not. We got to hurry. The day shift starts at noon.\"\n\nThe sound of an engine fills the back alley. Cricket and I dive behind the dumpster. The car drives slowly toward us; it stops. Exhaust billows up from the other side of the dumpster. There's a crackle of static, a digital bleep. Cricket's eyes widen. He mouths the word \"pig.\" I'm too scared to actually peek, but it sounds like a radio dispatcher. A taxi. _Or a cop_. The car crawls forward the rest of the way past us, down the gravel lane. It doesn't stop again, and no one gets out.\n\n\"Whew,\" he says.\n\nMy legs shake when I stand.\n\n\"That's the dressing room.\" I point to a basement window. We creep closer. The curtain is pushed to one side so we can see the line of sinks and lockers. \"The hall on the right leads to the kegs and the empties. I checked last night. The furnace is on the left. There could be other hidden rooms, though.\"\n\n\"She has to be down there,\" says Cricket. \"Or up there,\" pointing to the row of small windows. There's no movement or light coming from any of them.\n\n\"Fuck it. I'm going in.\" I'm a dog with a bone, and no one can take it from me. \"Better now, before the staff show up.\"\n\n\"Wait, Oreo\u2014\"\n\n\"Keep six.\"\n\nI take the thin-tipped flathead screwdriver we just ripped off from the hardware store down the street and tap it hard on the window pane. It cracks; lines ripple outward. One more tap. Glass falls into the basement. I reach in carefully and turn the lock. Then I slip the screwdriver under the wooden frame at the bottom and lift it up a notch. I raise the window smoothly. Cricket holds it up for me while I ease myself into the basement. I land on my feet. Cricket lowers the window and stays outside. I give him thumbs up.\n\nI move through the shitty dressing room into the hallway. Stairs leading up to the club are in front of me. On the right is the beer and empties room. On the left is a padlocked door with a sign: \"Keep Out. Furnace.\"\n\n_Fuck you_ , I think.\n\nThe tiny screwdriver fits inside the lower part of the keyhole. Then I take the paperclip from my back pocket. I'd already straightened it out using needle-nose pliers at the hardware store, then bent the end ninety degrees, making a little hook. I slip the modified paperclip into the top of the keyhole. It's hard to see, but you usually don't get to look at much when you're picking. It's all in the feel, in the clicks you hear, the subtle difference in pressure as you pick with the paperclip and torque with the driver. My hands make the tools tango; I keep an even pressure on the bottom with the screwdriver and, at the same time, tap and push the individual pins up and out of the way with the pick, clearing the cylinder one pin set at a time. I work it lightly at first, testing the spring of the internal pins and pushing each set out of the way with a click. Padlocks usually have three or four sets. This one has three, by the feel of things. It takes a couple of minutes but finally, the thing pops.\n\nI open the door. The smell of dead mice fills my nose. I leave the lock hanging in the metal clasp and step forward. It's darker in this room. _Should've grabbed a flashlight_. I walk with one hand out front, one to the side, using the clammy wall as a guide. My eyes gradually adjust. I see a furnace, big and squat. Large pipes run to and from it. The floor and walls are cold cement. There's a dirty window on the far wall\u2014that's the main street out front. Feet and legs walk past every now and then, making sounds that stop me from inching forward, clipping steps getting louder, smaller feet pattering quickly. Voices boom and fade. There is a scrape, a creak, closer and louder than the outside noises. I freeze. I hold my breath, waiting to hear more. _Nothing_.\n\nIn front of me, one panel of wall is darker than the rest. I move toward it. It's a steel door, colder than the cement walls. I run my fingertips back and forth across it. There's a heavy bolt, which I draw back and set in place. I find the knob, the raised circle of a deadbolt keyhole.\n\n_Can I do this?_\n\nThere's a soft thud behind me. _Clink_. I drop the screwdriver. _Fuck_. I grip the paperclip tightly between the fingers of my left hand. I bend down and feel the gritty floor with the other. Stuff sticks to my fingers. Something brushes them\u2014a centipede? I feel the whoosh of many legs, like Ferret's eyelashes on my cheek. The thing stretches along the flesh of my hand. I fling it away in the dark. I jump and my shoe hits the damn screwdriver.\n\n_Got it._\n\nSweat trickles down my back. My pits are wet. I exhale, nice and slow. I feel this new lock and imagine how it looks; the outer circle, the inner small circle with the keyhole and, hidden inside, the cylinder with the pin sets I need to tap into place. Slipping the screwdriver tip into the bottom of the keyhole is pretty easy. I gently twist the screwdriver until I feel that whole inner circle move to the right; I hold it there. Fitting the paperclip in neatly above it is harder. I feel it catch inside\u2014this time, I rake across the pin sets, push the paperclip in and out to scramble them. Then I start with the pin set farthest back from the opening. There's five pin sets in this deadbolt and it takes several minutes for me to tap each one out of the way. Finally, the lock springs. The heavy door swings open toward me. _I'm fucking Houdini Helen Keller. I rock!_ I can't wait to brag off on this stunt.\n\nIt smells worse in here, worse than the rest of the basement: like urine and sweat and stale air, like shit. Like other bad things. I cover my mouth and nose with my sleeve. I step inside. It's a small room without windows. Three lit bulbs hang from the cobwebby ceiling. There's an old wooden staircase on the far side. The cement floor slopes down in the middle toward one large drain. It's a cell, like an animal's pen. There's an old sink with a drippy facet, a basin and sponge, a raggedy towel. I walk into the centre of the awful room and that's when I see them.\n\nFerret's coloured dreads, cut off and piled by the floor drain.\n\n\"What the\u2014\" I pick one up, touch it softly with my finger. Blue with a touch of purple, greenish on the ends where the colour washed out. _They're hers, alright_.\n\nBehind me the door creaks. I look up in time to see him grin. It's the King looking strange without his uniform. Hair greased as usual, but like someone's dad might look, pants belted, a clean shirt buttoned right up.\n\n\"Well, looky who's here,\" he says in his full voice. \"My newest dancer. Carly told me all about you. How's your face?\"\n\nIn a flash it comes back to me\u2014my talk with Carly, my disappeared clothes, the cab driver who brought me right to my door, as she insisted.\n\n\"I can always count on you kids to make my job easier. You're stupid, predictable, you rat each other out. And you believe anything a junkie whore tells you.\" The King's mean laugh fills the cellar.\n\nI'm a cement pillar. There's his voice and white noise, static all around me.\n\nThe King is so tall he has to duck to avoid hitting his head on the rafters when he steps closer. He's so wide he blocks the whole door, frame to frame. \"Your skinny bitch is gone. But have I got a surprise for you.\" He slams the heavy door shut.\n\n# Ledge\n\nI didn't set out to kill no one. Probably don't look that way. But I can't even squash a spider. Hardly swat a fly, myself. I never could. Ask Eddie, he'll tell you.\n\nStanding in the slaughterhouse and watching that dirty cop, the man they call the King, come after her like that, it was hard. Made me think of all the people who had come after me, all the times they had their way and I went along with it, you know. I guess you'd say I snapped. Just seemed natural to do something, make it stop.\n\nAnyways, truth is I really had nothing left to lose.\n\nI went back to the slaughterhouse from habit, from when I'd visit Eddie on break and bring over his supper. We used to sit on the brick ledge that jutted out from the side of the building, me watching him eat, then we'd smoke a cigarette, and then we'd have a nice long goodbye kiss, and he'd go back to work. He'd go, \"Ray-Ray, that was one kick-ass sandwich.\" And I'd feel good about it. Fried tofu and mayonnaise or cheese slices and mustard or peanut butter with lots of drippy strawberry jam, just the way Eddie liked.\n\nWith Eddie in jail now and Ferret disappeared, I was pretty much on my own. I'd still go over to sit on the ledge when I was fucked up or scared and had nowhere else to be. Ever since the squat next door got raided, ever since the shooting, the slaughterhouse had run on reduced hours due to all the traffic coming round: cops, politicians, the news. There'd been layoffs and talk of closing the place for good. Sometimes there'd be guys on short shift; some I recognized, some I didn't. Other times it'd be empty. Either way, I'd sit in our old spot. If no one else was around, I'd talk to Eddie out loud, as if he was right there with me and not locked up in the Don waiting on remand. Funny, I hardly stuttered then, neither.\n\nI'd say, \"Eddie, you'll be out soon. You'll be back with me, like you should. We'll find a new place, you'll get a new job. We'll start over.\"\n\nOf course he wasn't there in person, so he didn't answer.\n\nThen I'd think about Big Fat Rat Catcher, how he escaped out of that box and took off like a furry shot into the street, and that'd shut me right up for a while. I couldn't do anything right without Eddie, not even look after his damn cat. If I could at least find Fat Ratty, running wild in some alley, then maybe our luck might change. That's what I'd think.\n\nSometimes it was hard to picture Eddie the way he used to look. Instead, I'd see him in that terrible orange jail jumpsuit they wear. Him on the other side of the visitors' glass holding that phone, trying not to look me in the eye. I'd shake it right outta my head and remember further back, before things went really rotten, to our hometown and the trailer park, our shitty school. Eddie shooting spitballs off the end of his ruler, sticking gum in girls' hair. Him goofing off and getting yelled at, getting kicked down to the office or suspended. He'd dribble imaginary basketballs down the hallway; shoot them at teachers' heads, _score!_ Drill the edge of his desk with two pencils like a black-metal drummer. Eddie always got on other people's nerves, half on purpose, half accidental. Loud and rough, I knew he was meant for me, long before he ever did.\n\nSitting on the slaughterhouse ledge, I'd smoke a joint and remember how weed chilled Eddie out. He'd sit still longer, talk slower, bullshit about what we might do\u2014start a band, steal a car, run away. He'd talk about us having money and luck and people giving a shit.\n\nSometimes I'd even believe him.\n\nGetting high with Eddie back in our school days also meant sometimes we'd make out. Which was magic, those first few times, but then he'd avoid me for days. He'd even join in when the jocks made fun of me. _W-w-what's w-wrong, R-Ray R-Ray?_ Once he punched me in the face, right after he came. _Fucking faggot_. His hate for this thing that flared up between us, making our dicks hard\u2014it nearly killed us both. He'd go on rampages, smashing store windows, shitting in front of the mayor's office, stealing stuff. Social workers would swoop in and give him a stint in some boys' home or in juvie, depending.\n\nThose were awful times for me\u2014lonely, dead-end days. I had no friends. I lived with my aunt. Her boyfriend drove a big rig and was on the road most of the time, thank Christ. Otherwise he'd sit in the trailer drinking Pabst Blue Ribbon, eating BBQ chips, and staring at my cousin Lena's tits. Lena was white blonde, like me, but older. She wanted to be a tattoo artist and get the hell out of that stupid town. She practiced on squash from our pathetic roadside garden, which pissed off my aunt, since no one would pay for them covered in blue demons with bony wings and bare-breasted women, horns sprouting from their foreheads. Once Lena tattooed her own knuckles with a math compass and had to be taken to Emergency when they got so infected she couldn't hold a pencil for all the green pus. My aunt drove us in a rainstorm, me riding shotgun, half hanging out the window, reaching to clean the windshield with a rag since her wipers were broke, and Lena stuck between us, cursing and straddling the gear shift.\n\nLena was the first person who really gave Eddie the time of day, other than me. After the whole knuckle incident, no one else would let her practice. When he got sprung from Goderich one summer, he hung around our place pretty much every day, and she went to work on him. He didn't care what she did or where she did it, just wanted his whole body covered eventually. \"Be a giant jigsaw puzzle,\" he'd said.\n\nHe'd haul off his shirt, his jeans, and lay down. His dark skin was nice, scarred, but he was lean, not filled out yet. Just peeking at him would get me heated up. Lena would tie back her long pale hair and scratch away at his skin, leaving ink blobs and outlines, scabs to heal. I wondered if she was _into_ him the way I was, and if they'd start messing around too. I wondered if I would die, or just wither. I couldn't stand having him around all the time and not being _with_ him. I'd lie in the tobacco fields and imagine myself disintegrating, all my dust blowing away, bit by bit. I didn't know what would happen to me if I didn't leave that town.\n\n\"If I was a girl, this would be normal,\" I'd said to him one night after doing it on his ma's roof. \"You wouldn't hate on me the way you do.\"\n\n\"If you was a girl, I'd fuck you and be done with it. I wouldn't give a shit about you.\" Then he looked me in the eye and asked if it was true. _Was I really going to pack a bag and leave him?_\n\n\"Not you. I'm leaving everything.\" I was crying and not bothering to hide it, for once.\n\nThat's when he kissed me for the first time. Not hard, not fighting or wanting something off me. Just him kissing me as I'd imagined he might all those years, minus my snotty nose.\n\n\"Do what you gotta, man,\" he said.\n\nI hiccupped loudly. My lips burned.\n\n\"Think I'll go with you, though.\"\n\nAnd he kissed me again, just the same way. It was the start of something totally new between us, and nothing can ever take that away. Not the King, not the Don fucking Jail, not some shit-talking lawyer. And not the men who take turns with me now and throw down some coin.\n\nLena read our cards before we left. She wanted to have the tarot as a back up in case tattooing didn't work out, and she was getting pretty good. Eddie shuffled the deck. He picked cards and lay them on the back porch table. She flipped them over, one by one. Grinning demons, nude goddesses smirked at us. In the centre was the Hanged Man, a terrifying skeleton in a noose. My stomach lurched.\n\n\"Something's ending,\" she said quickly. \"Well, you're moving, so that makes sense. Don't fret, it ain't all bad.\"\n\nHe said, \"I guess not.\"\n\n\"You got a lot of water coming your way,\" she said, pointing to some whirling blue-black cards. \"Cups. That's emotion, you know.\" She frowned.\n\nLater my aunt said, \"That boy was born under a bad sign. Don't need to read tea leaves to see that plain as day.\"\n\nWhich is kind of true. Eddie never did have any luck at all, other than me. And what good was I?\n\nSo you see. That night, sitting outside, smoking my lonely joint, I heard some awful crying. I followed the sounds into the slaughterhouse through the open side door, right to the killing room. It was dark in there, pretty empty. Just the silver ceiling tracks with their chains hanging down, their shining hooks on the ends. There she was, like a ghost in the shadows\u2014long socks, shorts, and some kind of skirt glowing white in the back corner, a darker shape moving around her. I flicked on the big overhead lights. It was the King, his black hair greased into a pompadour like usual. He blinked against the bright light. He wasn't wearing his uniform and that made him seem softer than usual, older, maybe. He could have been any of the men cruising us on the corner. And behind him, half under him, it was Ferret, alright. Whatever was left of her. When I seen him crouched over her like that, I had to do something.\n\n\"You better run, cuz you're next,\" he yelled, still holding her down.\n\nI wasn't even scared. He'd already taken everything from me.\n\nI just punched the red \"safety,\" the way Eddie always did after his break, and pulled the long, black lever, hard as I could. Those machines start up pretty quick. One huge hanging chain on a pulley moved down its ceiling track, swinging close behind him. The hook at the end gleamed. He didn't see it coming, he was staring me down from across the room. The chain kept moving forward and the hook swung heavily back again. It struck him. He looked surprised. Ferret grabbed onto the King's sweater sleeve to pull herself up. He shook his arm violently but she clung to it; she was like a rag doll flopping. I ramped up the speed and the chain jerked again, smacking into his broad back. Ferret slammed against his chest with her whole weight then slid to the ground. The King stumbled backward onto the hook. His mouth dropped open. It must have pierced into his back. Air whooshed out of him with a funny sound. I pulled another lever; the machinery almost ground to a halt, then shook back to high hear. The chain and the hook with the King attached to it began shortening as it retracted toward the ceiling. The hook lifted him right up. His body dangled, legs kicking like a giant puppet. Then there was another gear grinding, a jolt, and his weight shifted. He screamed when that big hook pierced all the way through, his middle settling around it. His hands clutched for the hook tip, and I'll never forget his ugly face opening up like that, his throat screaming itself raw with the pain.\n\nThe chain jerked again, bringing the King down the track, closer to me. My hand was still on the lever. I remember the feel of it frozen there. My legs were slow and woozy like syrup. I thought I might puke.\n\n\"Let me down, you fucking cunt.\"\n\nEddie would laugh at that. _Couldn't be nice to save his own life_. The King was a couple feet away. Blood pumped steadily out of him, soaking the front of his clothes, pouring over his hands, dripping onto the already stained cement floor. I looked into his red eyes, his veiny face, his Elvis hair, and I wasn't sorry. Not one bit.\n\nNormally the pigs would be stunned by this point, from electroshock or a bolt pistol to the back of the head. They'd be hanging upside down by the back legs, and this was when Eddie would do his thing, knifing the carotid artery and the jugular vein, bleeding them to death.\n\nI could've left him there.\n\nMeanwhile, Ferret had got up. I squinted. She looked different. Her dreads were all cut off. She was wearing some crazy get-up, all skin and bones. She'd been missing for quite a while already. Nobody knew what happened after the King came and took her from my old place. Mine and Eddie's. After Darcy ratted us out. Kids put bets that we'd never see her again. But here she was. Ferret was hurt bad. She was bruised and swollen in the face, dead in the eyes. She limped carefully around the machinery. She avoided the King flailing. She seen him up there, couldn't believe it probably.\n\nShe stood beside me. We looked up at him, and he swore. He squirmed and kicked and screamed. I was thinking how could we try and get him to admit what he'd done\u2014killed Digit and framed Eddie for murder. Who knows what else?\n\n\"You fucking diseased shits, let me down.\"\n\nFerret and I looked at each other. We looked back at the King. He was pretty pale. He was losing a lot of blood.\n\n\"If you sp-spring Eddie yu-yu-you can live.\"\n\nHis eyes lost focus for a sec. Then he stared hard at me. \"Screw you, faggot.\"\n\nI gulped.\n\n\"I fucked your gold star butch,\" he growled at Ferret. \"She was even tighter than you.\"\n\nI felt her body tense, saw her hands ball into fists.\n\n\"No.\" Ferret said this loudly. \" _No_ ,\" she shouted. Her body shook. She repeated that word, screaming and spitting with a hate that scared me.\n\nThen Ferret reached behind me and took a long rubber apron off Eddie's old shelf. She draped it over herself the way he used to. It was too big for her and dragged on the floor. She tied it loose around her small waist, then picked up a knife, just like the one Eddie used every day on shift. It was big for her, too. She wasn't used to hauling it around the way he was. She had to use both hands just to lift it.\n\nThe King muttered some more. Told us what he'd do when he got down from there. What he'd do to us, to all of us.\n\nFerret goes, \"Shut up, Earl.\"\n\nThat must have been his real name, I guess. I still couldn't move. I couldn't say a word. I just watched. It took a long time. We'd all seen Eddie at work. Mostly you'd wish you hadn't. Those aren't pictures you can erase from your mind easy. Ferret had the general idea, but was not used to doing this sort of thing, obviously. Even after his head came off\u2014not cleanly, either, that took a lot of work\u2014the rest of him kicked and twitched. Blood sprayed, it hit us in the face, it coated the walls. It was gruesome. The smell was awful. Let's just say she finally finished him off and dumped him where the rest of the meat was kept, in the freezing cold storage, where it got boxed and sent out to be eaten. I might have helped carrying stuff, I don't even remember.\n\nAfter all that, we hosed down the floor, the walls, the hooks, the apron. The slippery knife. Our shoes. We didn't know what to do about his clothes, his belt, but there was a separate place for all the terrible pig parts nobody could sell\u2014and that's where we dumped them in the end. We put everything else back where it belonged. And then we went outside to sit on the ledge.\n\nWe sat there a long time not talking. We'd have smoked, but we didn't have any. Our feet matched up, side by side, leaving prints in the soft ground. I was looking down at them and at the arc of cigarette butts flicked all around. This ledge was where all the men used to take their break, Eddie included. There were hundreds of pinched filters stubbed out in the ground. Each one marked a long shift, ten to twelve hours cut up into manageable parts, just like the meat inside.\n\n\"W-we make a good p-p-pair,\" I said at last.\n\nThat's when she started to cry, and me, too.\n\n\"None of this was supposed to happen,\" she sobbed.\n\n\"C-course n-not.\" I was supposed to be with my Eddie, Ferret with Oreo. All of us, all us reject kids, should've been left alone to make our own way in this fucked-up world, the best we could.\n\nI leaned closer to Ferret. Her shoulder pressed against me. Her hands were messed up, splintered something bad. I held them gently. There was blood around her nails still. My own fingers were filthy, the skin chewed, hangnails angry red.\n\nIt was that special bold sky time, just before dawn. Dark blues burst out of black, clouds of colour brooding around the city. I tried not to look at the Factory anymore, cop tape flapping in the breeze, orange construction flags posted here and there. The city was going to demolish it. They'd taken the roof off with a wrecking ball already. It was so wrong. Like a half-dead thing, still crawling. The slaughterhouse would be closed for good, too. The soil would be treated, and then they'd start building. A drawing of the condos stood at the end of the gravel road, next to the little information office the company put up the other day.\n\nIf you bought in now, you could save a bundle off your new luxury home.\n\n# Bush\n\n\"So now you're up here hanging with the Rezbians. How's that for ya?\" Phoebe cracks open a Blue Light for Ferret. Before Ferret can answer, Phoebe says, \"Sorry about the beer. Doc says I got to watch my calories. I says, 'You want to love a little less of _all this_?' and he goes, 'That's what I'm telling ya, Phoebe Marie. You got to shave a few pounds off your lovely behind.'\" Phoebe chuckles, and the mountain that is her, glorious her, shakes in her Moose FM T-shirt. Her laugh turns to a cough that sounds like an outboard motor turning over in her big bosom.\n\n\"It's good to see you, Phoebes,\" I say. Phoebe is older and heavier and more tired since I left two years ago. Her feet bother her so much she's using a cane now. But her smile still lights up the room and her hugs, those warm, strong arms of hers, still squeeze the badness right out of me. I've got a goofy smile plastered on my face in spite of the shit we've waded through just to be here, now.\n\nFerret sips her beer. I squeeze her hand. I can tell by her worried face that she doesn't know what to make of things. She keeps looking sideways to the front door where our backpacks sit in a mud-sprayed lump, all we have left on this earth.\n\nPhoebe runs a hand through her greying hair. \"Now don't be polite, Oreo; be yourself. Sure yous aren't hungry?\"\n\nFerret shakes her head. Food smells fill the little house, but there is nothing vegan about them. I nudge her with my pointy chin. She doesn't budge. It's been over a day since we ate anything other than extra-strength Wake-Ups. My stomach is sour and tight from them, and can't take food yet. The pills kept us up for the whole trek north from Toronto. Hitching can be fun, but not when you're tired and beat up and broken-hearted, not with every cop in the province hunting your ass. You got to be alert, and then some.\n\nAfternoon sun pours in the big window of Phoebe's front room, onto the back of my head, making me dozy. Chemicals twitch in random parts of my body, but the tension I've been carrying in my shoulders, my back, starts to unwind. My feet throb now that I've kicked off my rank boots. Me and Ferret are wedged between a dozen hand-made cushions on Phoebe's dog couch, covered in the bristly fur of her old mutt, Jack Daniels. Jack Daniels is lying on the front porch, keeping six.\n\n_For sure I thought we'd never make it._\n\nPhoebe sits across from us in her favourite chair, an old La-Z Boy recliner that faces the big window so she can see everyone going up and down the main paved road that cuts our land in half. She knows when the mail is in, when Andy's General Store has got the fresh meat delivery, and if Alan Fox is late to call the seven o'clock bingo.\n\n\"I know if the RCMP are coming almost before they do,\" she says. \"Tribal Police get the heads up, and they'd call me first. I don't know what exactly happened to yous girls, but you're safe here.\"\n\nI don't know what to say to her, where to start. I pick the skin around a torn cuticle on my dirty fingers.\n\n\"I know what sent you running away from here, Oreo, and that was bad. Whatever chased you back must be way worse.\"\n\nI nod. I stretch my arm around Ferret's shoulders, and say, \"It is, Phoebe. It's messed up. Last thing I want is to get you in trouble, though.\"\n\n\"I figure I can handle my bad self just fine.\" Phoebe is not smiling, but her voice is. It's warm and rough and in charge. \"This is your home, Oreo. Time you come back to it.\"\n\nShe gestures behind her, meaning my mom's house next door. I walked the long way around to Phoebe's bungalow porch, just so I wouldn't have to look at it.\n\n\"You okay?\"\n\n\"Yeah,\" I say. \"Just tired. Long haul, lots of stops.\"\n\nIt started out pretty good. We caught our first truck going north all the way to Owen Sound. We dumpstered bagels from behind an artsy caf\u00e9, and one of the cashiers gave us free coffee. She let us crash in the back corner until they locked the doors late that night. Then Ferret lay low while I panhandled, keeping one eye on news headlines to make sure there was no mention of us and the whole cop-killing thing back in Toronto. I was looking for a drive north and got pointed to a high school teacher\u2014nice, kind of dorky. She promised to pick us up in front of the caf\u00e9 at six a.m. and take us to the ferry docks in Tobermory, where we could cross over to the island first thing. She didn't mind giving us a lift at all. I wanted to stuff this act of kindness in my mouth and swallow it, to keep it safe. Instead, I crawled under a park bench with Ferret and nestled my face on the back of her neck, whispering the plan. The hard knot in my stomach loosened just thinking about going home, finally. By the time morning rolled around, of course, things had gone bad for us, as usual.\n\n_Doesn't matter_ , I tell myself. _We got here anyways._\n\nI try to forget it all\u2014the drunk boys who found us in the park early that morning and had to be fought off. Someone called the cops. This scared off the assholes, but lost us our ride with the nice teacher. Frigging pigs skulked around uselessly, drinking coffee and shooting the shit for an hour, right in front of the bush we hid behind. Later, we took the first ride we could, even though we ended up going the long way, up 69 north to Sudbury where we sat for half a day at a truck stop, waiting for a ride without a hand-job clause in the fine print. Finally we caught a four-by-four with headbangers who raced to Espanola to pick up weed, smoked it, then drove way below the speed limit to the Island, crossing the swing bridge at Little Current at dawn. _What a shit show_.\n\nI focus on the here and now\u2014Phoebe and her small, familiar house. Ferret\u2014skinny and bruised and scared, her pretty dreads cut off so she looks like a half-starved boy: seriously damaged goods but still alive, at least. Me\u2014holding it together the best I can.\n\nI realize that Phoebe's mouth has been moving and I have no idea what she's saying. She looks at me strangely and moves her mouth some more. \"You all right, Oreo? Jeez, you've been gone some time, huh?\"\n\n\"It's good to be back, Phoebe. Thanks.\" I kick my feet up on the coffee table and try to smile, even though I feel wrung out and dry as an old rag.\n\n\"Comfortable?\" Phoebe playfully swats my feet with her cane. \"What kind of manners you learn down south?\" Phoebe winks at Ferret. \"White folks turned you into a savage, that's what.\" She laughs, a belly laugh with a thigh slap to go with it that makes me feel even more at home. \"Yous going to the arena dance Friday?\"\n\nFerret's fingers tighten their hold on my thigh. Her forehead creases deeply so I know the last thing she wants to do is go to the damn dance.\n\n\"We'll see,\" I say.\n\nPhoebe says, \"We don't get your punk bands up here. Dances are pretty much it. If you don't go, you might be bored before you know it.\"\n\n\"It's probably better if no one knows we're here,\" I say quickly. Sooner or later I'm going to have to tell Phoebe the real truth: that we're not just _in trouble_ , as she put it, but seriously on the lam. Possibly even wanted for first-degree murder, for killing a city cop. Which would make her an accessory to the crime, and that doesn't sit right.\n\nI stroke Ferret's almost bald head. Each stroke softens the lines in her forehead, lowers the lids of her eyes. If she were a cat, she'd maybe start to purr.\n\nPhoebe raises an eyebrow. \"How else you gonna get the gossip wheels spinning? I can only do so much damage on the Facebook.\" She points her cane to the computer in the corner.\n\n\"What?\" My stomach churns.\n\n\"Sure enough. I updated my status: 'Long-lost Indian warrior returns to the Rez, dragging her young wife.' What do you think? That'll get tongues wagging, eh?\"\n\n\"Ha,\" I say, weakly. \"You didn't use my name, did you?\"\n\n\"Course not.\" Phoebe says to Ferret, \"I bet you never got to hear any embarrassing stories about Oreo. Never had anyone to tell them, huh?\"\n\n\"Uh, no,\" Ferret says quietly. Her eyes are huge right now, dark and shining.\n\n\"That's too bad. I'm the only one around who knows.\" She tries to say it lightly, but it's not. It's hard and sad and leaves an angry echo bouncing around the room. I guess I never thought much about how she felt, being left alone up here with the memories, with all our ghosts.\n\nI walk to the front door and look out the window, press my forehead against the glass. No one is driving, no one is walking. There's just the main road with tall grass on either side. There are houses at intervals all the way down, as far as you can see. As a kid, it was great. You could run wild, play where you wanted. But at twelve, thirteen, it was boring and claustrophobic. I hated how you knew everything about everyone else, and they knew everything about you, too. I'd watch MuchMusic, wear tons of eyeliner, and dream about moving south to start a band, dream about meeting lots of other gays and eventually getting a girlfriend. Once Aunt Tam said, \"So go there. Go find out like everyone else that the city is a burial ground, nothing but a place to go and die alone.\"\n\nA sudden lump sits in my throat like a clogged drain. Of course I didn't listen to Tam, who probably knew a thing or two about living rough in the city. Who might be doing more of the same right now, wherever she is, out west. Summers were fun at first\u2014meeting other punks and partying, hooking up with girls. In the city, nobody gave a shit what we did, as long as we didn't do it on or near their property. Later, it was more work. Fighting for a place to sleep, for food, to not get raped or fucked with, running from cops and thugs and jocks. Always fighting, always running. That gets harder to take.\n\n\"Oreo, go get my glasses from the bedroom,\" says Phoebe brightly. \"Now Ferret,\" she says, \"did Oreo ever tell you how she got her name?\"\n\nI groan.\n\nFerret kisses my cheek. She says in a sing-song voice, \"She's dry and crusty on the outside and gooey sweet inside?\"\n\n\"That's right. Now what you don't know about Oreo is...\"\n\nPhoebe's kitchen is smaller than I remember. The little gas stove is busy as ever. There's the culprit, a large pot simmering on the back burner. I lift the hot lid. _Moose stew_. The smell hits me hard. One thing, I haven't been around cooked meat in a long time, especially not wild game. But mostly those smells remind me of my mom and the aunties. They'd have it bubbling, be baking scones or bannock, sometimes have wild rice in another small pot. Good times happened in this kitchen and in ours. Fights got worked out, jokes told over and over again, marriages were arranged, repaired, and dissolved around these Formica tables with Phoebe and my mom, with my aunties holding court, the swag lamps collecting all of our secrets in their dusty bulbs.\n\nPhoebe's voice fills the small house as I walk through it, touching stuff, noticing all her special things crammed into every imaginable space, including her Red Rose Tea company figurine collectibles. Even if I can't hear exactly what she's saying, there's the ebb and flow of her throaty laugh, the rumble of her imitating someone; there's the timid murmur of Ferret answering a question.\n\nPhoebe's bedroom smells like Vicks VapoRub and sweetgrass. Her dresser is cluttered with photographs, some new ones of people I don't even know\u2014like her life kept going after the accident. Right in the centre, though, there used to be a big, framed picture of them all: Phoebe and Aunt Sue front and centre, Aunt Tam, my mom, and even Jack Daniels. In Toronto, whenever I thought about my family, I'd remember this blown-up photo of them laughing together. But it's not here. For some reason that makes me mad. I can almost remember holding the camera, my chubby kid fingers lining up the zoom box on the bunch of them, and clicking the button. Sometimes I just _think_ I remember it because I've heard the story so many times\u2014that I grabbed Tam's camera and hollered while they horsed around on Phoebe's front porch. \"Nobody move a muscle!\"\n\nOther than the photos and piles of loose change on the dresser, there are a bunch of pill bottles. I pick them up and shake them, but I don't know what the long words mean, other than Oxycontin and the Perc family\u2014Cet and Dan\u2014which would be great for making quick cash on the street. Great for blanking out, for coping. I set the bottles back down. Phoebe's got the diabetes. She's got heartache, too, and no matter how many pills her young doctor gives her, they can't cure that.\n\nPhoebe's glasses are nowhere to be found. I walk back to the kitchen, check the ledge behind the old yellow curtains that hang in the window above the sink. There's her same table with the three and a half chairs around it, the broken one being the thing that saved Aunt Sue from an enraged black bear that came up onto the front porch one spring, years ago. Auntie Sue, her lover, had moved in by then. My mom, Tam, and I were at our place next door having supper when we heard Sue scream. My mom came out with the rifle but never had to use it, since Phoebe was waving the kitchen chair in the muzzle of this huge animal up on its hind legs, roaring into Sue's terrified face.\n\n\"Ith Phoebe a thuperhero?\" Phoebe exaggerates my little-kid high-octave voice.\n\n\" _Aaniin_ , I'm right here,\" I call into the front room. \"I can hear what you're saying, you know.\"\n\nFerret giggles when I peek around the corner.\n\n\"Shush, I'm telling my story,\" Phoebe says. \"Where's my glasses?\"\n\n\"I have no idea.\"\n\n\"Oh shit, they're around my neck.\" Phoebe pulls the silver chain she's wearing and out from the neck of her T-shirt comes a pair of eyeglasses. \"And so you see, Ferret, from the time Oreo was a wee toothless critter, she's always known the truth\u2014that I have magical powers and can talk to the bears. I said to that sonuvabitch, 'You get the hell away from my woman! If anyone's eating her tonight, it's me!'\"\n\nFerret laughs for real, and so do I, even though I've heard that story a hundred times.\n\n\"We're Bear Clan. Oreo ever tell you that?\"\n\n\"Yes,\" she says. \"It's on her tattoo.\"\n\n\"First thing I got inked when I was in Toronto. So I wouldn't forget where I came from.\" I stretch the neck of my T-shirt over my shoulder to show Phoebe.\n\nPhoebe puts on her glasses and blinks a few times while she adjusts to the prescription lenses. She shakes her cane toward me and says, \"Oreo, Hon, that's real nice. But you don't need a tattoo to know who you are. That runs all through you, day and night, in your blood. No one can take it away from you, not if you don't let them.\"\n\nPhoebe leans forward and grunts as she puts her weight onto the cane and slowly stands up. She looks real tired. \"I was gonna get out the big book, but that can wait.\" She waves at a stack of phonebooks and newspapers in one corner, but I know she means _our_ big book, the family album, which is probably on the bottom of that pile. If just _thinking_ about one photo can mess me up, I can't imagine flipping through a lifetime.\n\n\"Make yourselves at home while I have a rest. Oreo, if you want to go next door, the key is in my cupboard like always.\" Phoebe shuffles toward the kitchen. Eventually I hear the springs of her bed creak when she sits on the mattress.\n\nFerret exhales loudly and slumps back onto the couch. \"What should we do, Oreo?\"\n\nBut I'm already tapping on the keyboard, scrolling down the computer screen to check exactly what Phoebe posted. I delete her status update. No one has commented on it yet.\n\nFerret rocks back and forth on the couch. Her breathing is shallow. She's working up from serious anxiety toward a full-on panic attack. Not pretty.\n\nThe thing about Ferret, she's not hard\u2014she's tough enough, she's got heart and she's wily\u2014but she's got no meanness whatsoever. Ray-Ray even less. That boy is a Popsicle. So wasting that rapist, that psycho cop, it's weighing heavy on them both.\n\n\"Ferret, listen to me.\"\n\nI wait for her to slow her breathing a bit and to stop rocking frenetically.\n\n\"First, I want to find out who knows we're here.\" It wouldn't take much. A do-gooder social worker, a kid with a grudge, even a friend who said something to the wrong person could fuck us up.\n\n\"Who even knows where you're from?\"\n\n_Digit, but he's dead._\n\n\"Cricket knows I'm Native, but he never remembers anything else. He says it's too complicated.\"\n\n\"Ray-Ray actually listens to people.\" Ferret exhales slowly.\n\n\"Yeah, I'm not worried about Ray-Ray anymore. I even told him to come up here if he needs a place.\"\n\n\"What about the drop-in worker, Pamela?\"\n\nI press my fists against my closed eyes. _Pamela._ I remember hearing her talk about coming to Wiky for the annual powwow. And how proud I was to tell her that I was _from_ here, that my family _came_ from these parts, and how she'd never forget that, seeing as she'd been here. \"Shit.\"\n\n\"She'll talk, all right.\"\n\nMy foot taps restlessly while I keep surfing. \"I told Pamela I hadn't been here in years and might never come back.\"\n\n\"Really?\"\n\n\"Yeah. I thought I wouldn't. Not 'til all that shit went down and you were gone. All I wanted was to bring you here so we could be safe.\" My voice cracks.\n\nFerret climbs onto my lap and kisses my ear, my throat. She squishes her face against mine. \"We'll never be safe, will we?\"\n\n\"Actually, we could never be safer, now that _he's_ dead.\" My voice wavers. Ferret told me everything that happened, everything the King did. And what he was planning to do, if she hadn't escaped. Every time I think about it, I choke back vomit. I have to breathe deeply and keep moving, so the hate doesn't stop up my veins and cripple me forever.\n\nOn the CBC website is a photo of the King, \"a brave law officer, a hero gone missing.\" _Not dead, at least_. Beside the article are the words, in a large bold font, Police Search for Persons of Interest. It's a photo of Ferret and me in front of the Factory squat, our arms around each other, smiling defiantly into the camera.\n\n\"Shit.\" I bite my bottom lip.\n\n\"Anyone with information is asked to contact police. Crime Stoppers offers up to $2,000 for anonymous tips leading to the capture and arrest of wanted criminals,\" reads Ferret out loud. \"That's a lot of money.\"\n\nOur friends, our neighbours, they all hate being poor. But luckily for us, I think they hate cops more.\n\n\"Does that mean they don't know what happened to him yet?\" Ferret looks sick.\n\nWe can't tear our eyes away from that picture of the King. I hate his stupid face, his leering mouth, and his Elvis hair. I can smell the pomade, his boozy, tainted breath. I still feel his fists pounding me, his hands choking me, his belt buckle scraping my soft skin, the metal parts slapping onto the hard floor.\n\n\"Oreo?\"\n\nThe room spins. Ferret shakes my shoulders gently. I open my eyes wide.\n\n\"So they haven't found any... parts yet.\" Ferret looks wigged out.\n\n\"Babe,\" I say, trying to get my shit together. The last thing Ferret needs now is to have to take care of me. \"They might never find out. So you got to figure out how to carry this thing. I wish it was me that did it; you have no idea how much. It wouldn't wreck me the way it might you\u2014if you let it.\"\n\nIn fact, sometimes all I can think about is how much I wish _my_ hands had pulled the lever that severed his limbs and let him bleed out, that _I_ had cut his dead body down from the slaughterhouse chains myself. Maybe then I would believe he was truly gone, and his bloated face would stop jumping out at me from shadows, like in some cheesy horror movie. Maybe then I could purge this poison from me, this thing that is shrinking me from the inside out.\n\nFerret sits up taller. \"You're right. Maybe they never will find out the truth.\" She clenches her jaw. \"Lots of people knew what he was into. Think of all those women he trafficked. Anyone could have wanted revenge. Lots of people wanted him dead.\"\n\nI nod.\n\nI scroll down slowly, so the picture of him gradually disappears. Ferret slumps against me when the last of him is gone. Hot tears roll down her face, trickle onto my skin. They run down my neck, into my T-shirt. Saliva pools in her mouth and drips out when she cries louder. Her shoulders shake. She gasps, and there is another sound, an ugly hacking sound. It is me crying, too, which is a total shock.\n\n\"I'm s-sick from all the things he did to me,\" I say. Sick of not owning my girl body, my boy body. Sick with his DNA all over me, inside me. \"Nothing belongs to me anymore.\"\n\nFerret knows what I am trying to say. She smoothes my long hair, re-braids it, and pets my heaving shoulders. She says, \"We are still alive, Oreo, you and me. That pig is dead, and he deserved it. And it almost was a different end to this story. So now we got to keep moving, we got to keep living, and make the most of it, whatever happens next.\"\n\nI wipe my face and blow my nose.\n\nFerret is pulling it together, but this is my land. I need to step up. An image of our summer camp comes to me, though I haven't been there since I was a kid, foraging for berries and roots and edible plants, fishing in the cold lake, sleeping under the stars and in rough shelters.\n\n\"Alright then, Ferret. We're going bush side.\"\n\nWhile Ferret showers and changes her clothes, I take Phoebe's key and go next door. Just looking at the neglected house makes my chest burn, my breath come fast and shallow. Peeling paint hangs in strips; the porch screen has been ripped open by an animal. The wooden steps creak under my feet. The key fits in the lock, turns, but the door sticks. I heave my shoulder against it once, twice. It scrapes open, and the musty smell explodes. Curtains are drawn on every window. I step inside, right through an elaborate spider web hanging in the dark. _Sorry, Grandmother_.\n\nBed sheets drape the furniture like Halloween ghosts. The front room feels damp; the rug is rotting. My mom's bedroom is bare\u2014stripped bed, dresser cleared, nothing on the walls. The drawers and closet are empty except for her bush jacket, her work gloves, and boots, which I put in my knapsack. The room I shared with the aunties is a trip\u2014half closed down and half preserved like some teenage museum. Band posters are still plastered around the room near my old bed. It's a punk shrine: Siouxie Sioux, Mot\u00f6rhead, Nina Hagen, Amebix. A couple of Sue's childhood toys\u2014a dolly, a plastic piggy bank\u2014perch on top of the dresser. Her adult life had been next door with Phoebe, so who knows what happened to all those things? Tam's stuff is packed in boxes, labelled with her name. Another stack of boxes glare at me, my name scrawled across them in black marker. _Phoebe had to deal with that, alone_.\n\nThe kitchen is the hardest part. I shut my eyes, but can still see their faces, hear them laughing, shouting, gossiping. The missing framed photo smiles into me from the middle of the round table. A close-up of Phoebe and Aunt Sue, slim and brown and laughing, their arms around each other, their hair loose and beautiful. They look like teenagers, like me and Ferret, but were probably into their twenties. My mom and Aunt Tam are in the background, also laughing. Tam is holding Jack Daniels\u2014he's just a pup, his tongue lapping at her chin. They're on Phoebe's front porch, but the shot is crooked and the proportions are wonky; the big camera slipped in my hands and aimed at the sky above them, just higher than the porch roof. Looking at it now, the picture seems to have been a warning or some kind of prophecy. The focus is on the up and away, the sky, the place where spirits roam.\n\nI find the rest of the things I need in the pantry and hall closet: matches, hunting knife, compass, our old tent, a sleeping bag, a medium-sized pot and pan. There are dry soup mixes, cans of beans, an opener. Each thing I wipe and pack reminds me of something else we'll need: rope, a small axe, duct tape. The Browning BPS Hunter is still there, all twenty-eight inches of its walnut finish, an extra loaded clip, and the gun-cleaning kit, too. I lift it and look down the sights. I aim out the back window at the nowhere road. I remember learning to shoot with my mom, the pull and release, the smell of a shot fired.\n\nThis is all the stuff we'll need while we wait it out into the fall. We'll leave at dawn, the best time to start a new plan, a new life. Phoebe will know where we're headed, no doubt about it. We have no place else to be and nowhere else to go. I figure we'll be okay as long as I can remember all those things my mom and the aunties taught me. Time is different when you're living with the land, different than in the city where you fight against it just to survive. Once we get there, we'll be in no rush, Ferret and me. We'll be in no rush at all.\n\nKristyn Dunnion is a self-professed \"Lady punk warrior\" and the author of the novels _Big Big Sky, Missing Matthew_ , and _Mosh Pit_ (all Red Deer Press). She studied English Literature and Theatre at McGill University and earned a Masters Degree in English at the University of Guelph. She performs creeptastic art as Miss Kitty Galore, and is also the bass player for dykemetal heartthrobs, Heavy Filth. She lives in Toronto.\n\nPhotograph by Jaimie Carlisle.\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":" \nTHE ARNIFOUR AFFAIR\n\nA Colin Pendragon Mystery\n\nGREGORY HARRIS\n\nKENSINGTON BOOKS\n\nwww.kensingtonbooks.com\n\nAll copyrighted material within is Attributor Protected.\nTable of Contents\n\nTitle Page  \nDedication  \nCHAPTER 1  \nCHAPTER 2  \nCHAPTER 3  \nCHAPTER 4  \nCHAPTER 5  \nCHAPTER 6  \nCHAPTER 7  \nCHAPTER 8  \nCHAPTER 9  \nCHAPTER 10  \nCHAPTER 11  \nCHAPTER 12  \nCHAPTER 13  \nCHAPTER 14  \nCHAPTER 15  \nCHAPTER 16  \nCHAPTER 17  \nCHAPTER 18  \nCHAPTER 19  \nCHAPTER 20  \nCHAPTER 21  \nCHAPTER 22  \nCHAPTER 23  \nCHAPTER 24  \nCHAPTER 25  \nCHAPTER 26  \nCHAPTER 27  \nCHAPTER 28  \nCHAPTER 29  \nCHAPTER 30  \nCHAPTER 31  \nCHAPTER 32  \nCHAPTER 33  \nCHAPTER 34  \nACKNOWLEDGMENTS  \nTeaser chapter  \nCopyright Page\n\nFor Russ, who changed everything forever\nCHAPTER 1\n\nThe subject, as it so often is, was murder.\n\nIt was late in the afternoon, between the time when the sun has dropped sufficiently to be blocked from the city's streets, yet before it has gone low enough for the shadows cast by the buildings to have grown into one continuous black void. Colin and I were sitting by the fireplace in our study, me in the thrall of the American writer Stephen Crane's latest bit of fiction, while he was working up a sweat curling his dumbbells, when a great clattering of horses' hooves arose from the street below.\n\nI laid my book down and went to the window, where I spied an elegant black carriage next to the curb pulled by two fine blue-black steeds. The carriage looked capable of seating a dozen people, yet revealed only a single family crest on its door: a vulture devouring a slain lamb under a thistle bush. It seemed its owner had either a fine sense of humor or extraordinary self-awareness.\n\n\"It appears we have company,\" I announced.\n\n\"Do we?\" Colin muttered, still hoisting the weights back and forth.\n\n\"A coach has just pulled up. There's a crest on its door, but I don't recognize it.\"\n\n\"Oh?\" He came over and took a brief glance out the window, dumbbells in tow, before bounding back to the fireplace. \"That would be the crest of the once formidable Arnifour family.\"\n\n\"Arnifour?\" A distant clanging was set off in my head. \"Now why does that name sound familiar?\"\n\n\"Because they've been a part of the gentry for generations,\" he said as he shoved the dumbbells onto an upper shelf in a nearby bookcase, \"although their fortunes have contracted in diametrical opposition to our good Queen's waistline. Yet while Victoria remains the Queen, the Arnifours have become quite toothless and impotent in their waning years. Never a good combination.\" He snickered.\n\nI chuckled as I watched a dainty ankle covered in swirls of burgundy fabric present itself from within the carriage, followed by a delicate hand held out to the driver. \"It's a lady,\" I said.\n\n\"Mrs. Behmoth,\" Colin hollered down the stairs, \"we've got company!\"\n\n\"I 'eard. I ain't deaf,\" she called back. \"Who the 'ell comes out at this 'our anyway? I ain't puttin' me shoes back on, I'll tell ya that. Me dogs are already snarlin' like beasts.\"\n\n\"Always so dainty.\" He chuckled, hastily mopping his face with a handkerchief.\n\nThe sound of Mrs. Behmoth thudding her way from the kitchen to the small foyer drifted up, and I was relieved to hear the clack of shoes back on her feet in spite of her protestations. The door creaked on its hinges before the muffled hum of sibilant voices too far away to decipher could be heard.\n\nI went back to my chair as Colin picked up a small penknife and scrap of fine steel wool from the mantel, and started working at coaxing the antique blade back to its former luster. \"Must you always be playing with weapons when someone comes to call?\"\n\n\"I'm not playing.\" He frowned. \"I'm preserving history.\"\n\n\"Still,\" I said as I heard the stairs begin to groan under the weight of Mrs. Behmoth and our guest, \"it could be misconstrued as intimidating to our fairer clientele.\"\n\nHe waved me off. \"You're worried about intimidating someone who has a slaughtered lamb being eaten by a vulture for a family crest?\"\n\nI conceded the point.\n\nMrs. Behmoth filled our doorway as she ushered in an elderly woman wearing a tightly curled brown wig intended for someone half her age atop of which sat a small curved bonnet cocked to one side and heavily laden with frilly lace. Her dress was as coquettish as a debutante's, with a flurry of bows and adornments across the bosom. There was heavy makeup smeared across the deep crevices of her face and a silver dollar\u2013sized bit of cardinal rouge on each cheek. \"The Lady Arnifour,\" Mrs. Behmoth announced, accepting the Lady's cloak and unceremoniously tossing it on the coatrack.\n\n\"Do come in,\" Colin said with the flash of a smile. \"I only hope this inopportune hour does not portend too distressing a matter at hand.\"\n\n\"Oh, Mr. Pendragon,\" she said as she collapsed onto the settee. \"It is a most dreadful situation that brings me to your door this night.\"\n\n\"I'm sorry to hear that.\" He cast a glance at Mrs. Behmoth still hovering in the doorway. \"Then we'll need some tea, please.\"\n\n\"Yer supper's almost ready.\" She scowled.\n\n\"I don't mean to be a bother\u2014\"\n\n\"It ain't no bother, Yer Ladyship, but that roast is sure as Hades gonna turn ta leather if it ain't served on time.\"\n\n\"Nevertheless,\" Colin's voice tightened, \"tea. Thank you.\"\n\n\"I really don't require anything more than a few minutes of your time, Mr. Pendragon.\" She turned toward Mrs. Behmoth. \"Please don't trouble yourself.\"\n\nMrs. Behmoth shrugged agreeably before heading back downstairs.\n\nColin exhaled brusquely. \"She basically raised me.\"\n\n\"She's refreshingly disarming.\" Lady Arnifour gave a brief smile as her eyes flicked over to me before darting back to Colin. \"Mr. Pendragon?\" She leaned toward him slightly, her voice as thin as a whisper. \"Might it be possible for us to speak in private? The matter upon which I seek your assistance contains a degree of . . . delicacy\u2014\"\n\n\"You have nothing to worry about then. Mr. Pruitt is my most trusted companion and should be considered an extension of myself. Your confidence will be well kept by us both. Now do tell us what's brought you here.\"\n\nOur guest stiffened as she continued to stare at him. It was clear she was not used to being countermanded. \"Well . . .\" Her eyes flew back and forth a moment. \"It's my husband. . . .\" She hesitated. \"He was murdered nearly a fortnight ago and my young niece, who was with him at the time, was savagely attacked and remains in a coma even now.\"\n\n\"How dreadful.\" Colin arched an eyebrow at me as I suddenly recalled why her name had sounded familiar.\n\n\"Surely you read of his death in the papers?\" she said.\n\n\"Newspapers are a dreary business,\" he scoffed. \"And have you ever read an accurate accounting of anything? No, I leave the perusal of those to Mr. Pruitt,\" his eyes slid to me, \"who usually keeps me informed of such goings-on.\" I could only shrug. \"But it's always better if you tell me of it yourself anyway. From the beginning, if you please.\"\n\n\"Oh my.\" She sagged back onto the settee, looking increasingly fragile. \"It's such a nasty business.\"\n\n\"Murder tends to be.\"\n\nHer brow furrowed and I took that moment to speak up lest she think he was trifling with her. \"Hearing the event in your own words is far more likely to allow us to gain insight into the crime than reading some sensationalized account in the paper.\"\n\nTo my relief, Lady Arnifour's face softened as she heaved a heavy sigh. \"I suppose you're right. As it is, Scotland Yard has withheld several details from the papers; they claim it's for the sake of their investigation, but they've seemed so muddled by it all,\" she groused before drawing in a deep breath and appearing to gird herself to begin. \"Ten nights ago my husband took his customary walk after supper. Unless he was ill, he never missed his excursions.\n\n\"On this particular night he somehow managed to make it all the way down to the northwest corner of our property. We have a barn there in which we store hay and other feed for our horses and cattle. It's a considerable distance, Mr. Pendragon, and I am not exaggerating. And while I freely admit that my husband was several years younger than I, neither was he a young man.\" Her eyelids ticked slightly as though she had just confided something we would not otherwise have presumed. \"How he got as far as he did, and why he would choose to do so, I cannot say.\"\n\n\"How far are we talking?\" Colin snatched up his penknife and absently started buffing it again.\n\n\"Half a dozen kilometers at the least.\"\n\n\"And you don't believe him to have been in the habit of going such a distance?\"\n\n\"It would've been impossible. He was seldom gone more than an hour and I can assure you, Samuel couldn't have walked a fourth of that distance in that amount of time.\"\n\n\"I see,\" Colin muttered. \"Do go on.\"\n\nLady Arnifour watched his hands flutter assiduously over the blade for a minute before she finally resolved to continue. \"That night, for whatever reason, Samuel got himself all the way down to that barn, and when he did, he apparently came upon our niece, Elsbeth. Elsbeth is my late sister's only child. Samuel and I have raised her from infancy. My sister did not survive the birth and there was no one else,\" she said deliberately. When she dropped her eyes I knew better than to inquire about the father. \"It was not uncommon for Elsbeth and our daughter, Kaylin, to go riding together.\" She stopped and clutched at her throat. \"Thank heavens Kaylin stayed in that night.\"\n\n\"Indeed,\" Colin said. \"And your niece remains in a coma?\"\n\nLady Arnifour's hand continued to hover at her throat in evident distress. \"Yes, Mr. Pendragon. My niece received a horrible blow to her face during the attack. She was found near my husband's body and has yet to regain consciousness. The doctor . . .\" She shook her head as she yanked a handkerchief from her sleeve. \"I'm afraid he's been unable to offer much in the way of comfort regarding her recovery.\"\n\nColin laid the penknife down and peered at Lady Arnifour. \"This is indeed a double tragedy then.\"\n\nShe dabbed the handkerchief to her nose in an oddly self-conscious manner and it suddenly made me wonder if perhaps she'd done it more for our benefit than hers. \"Yes,\" was all she said.\n\n\"You must forgive me,\" Colin pressed on with uncharacteristic restraint, \"but I must ask you precisely how your husband was killed?\"\n\n\"A terrible blow to the back of his head,\" she fairly whispered.\n\n\"Supper's almost ready!\" Mrs. Behmoth took that moment to holler up from downstairs.\n\nI bolted from my seat and rushed across the room to the landing. \"We'll be down as soon as we've finished with our guest,\" I hissed. \"You will kindly refrain from shrieking up the stairs again.\" She scowled at me before huffing back to her kitchen. \"I'm so sorry,\" I said as I came back to the study, not at all surprised to find that Colin had not even moved.\n\n\"She has a good heart.\" Colin flashed a quick grin as I sat down again. \"Please go on, Lady Arnifour. Tell me what our esteemed Scotland Yard has made of all this. Have they formed any theories yet? Or are they still trying to decide who should ask the questions and who should write them down?\"\n\nI shot a hasty glance at Lady Arnifour and found her seemingly oblivious to his contempt of the Yarders.\n\n\"The inspector assigned to my husband's murder informed me this afternoon that my groundskeeper, Victor Heffernan, and his son, Nathaniel, have become his primary suspects.\" Her voice had become quite overwrought. I watched as her gaze slid about the room as though she was unable to comfortably settle it anywhere, and thought it yet another curious gesture on her part. Colin leaned forward in a way that suggested he had caught it as well.\n\n\"But the inspector is wrong?\" he asked.\n\n\"I would stake my very reputation on it.\"\n\n\"And would you be referring to Inspector Emmett Varcoe?\"\n\nLady Arnifour started. \"How could you know that?\"\n\n\"Your estate is under his jurisdiction.\"\n\nI could see she was impressed, though in truth that was exactly the sort of thing he should be expected to know.\n\n\"It's hardly a surprise you believe him wrong.\" Colin sat down and leaned back in his chair. \"The man's ineptitude is matched only by his ignorance of his own shortcomings\u2014 proving that failing upward is neither an art nor a science. But we needn't concern ourselves with him just yet. Why don't you tell me how it is you're so certain he's mistaken?\"\n\nLady Arnifour fixed her eyes on Colin before sliding delicately forward on the settee and throwing a discreet glance backwards, as though Mrs. Behmoth might actually have roused herself to creep up the stairs and eavesdrop. \"This is difficult . . . ,\" she mumbled.\n\n\"It usually is.\" He flashed a mischievous grin. \"So tell me, were you having it off with your groundskeeper?\"\n\n\"Mr. Pendragon!\" She bolted to her feet with remarkable speed, both hands streaking to her d\u00e9colletage as though to physically shield her honor.\n\n\"You misunderstand . . . ,\" I blurted out as I too hopped up. He'd fooled me, as I hadn't seen that coming. \"Let me get us all a brandy,\" I barreled on. \"A touch of brandy will settle everyone's nerves.\" God knew it would mine. I hurried to the liquor cabinet and flipped over three snifters, pouring little more than a finger into two of the glasses, but adding a healthy shot more to the third. I noticed that Mrs. Behmoth had been into the sherry again, for cooking purposes she would insist, and then steeled myself as I turned back to our guest.\n\nLady Arnifour had moved to the fireplace and stood staring into the flames as though her dignity might be regained somewhere in among them. I scowled at Colin, but he seemed wholly unconcerned as he fished out a silver crown and began absently spinning it around between the fingers of his right hand. Only then did it occur to me that as Lady Arnifour had failed to storm out of the room with righteous indignation, there was likely some kernel of truth to his question.\n\n\"Lady Arnifour . . .\" I handed her a snifter, taking care to avert my gaze so as not to discomfort her further.\n\n\"You're very kind,\" she muttered, and I caught a bit of a flush beneath her heavily powdered cheeks.\n\n\"You mentioned . . . ,\" I chose my words carefully, \". . . that you disagree with Inspector Varcoe's assessment. Might you tell us why?\" I shot Colin another warning glance as I pressed a snifter into his free hand, his other continuing to swirl the coin effortlessly, and was rewarded with a comparable rolling of his eyes.\n\n\"Victor Heffernan is a good man,\" she began slowly, keeping her gaze on the fire. \"His family has worked for my family for three generations and that doesn't even include his son Nathaniel. I've known Victor since we were children. I was present at Nathaniel's birth. My husband and I have always been fond of the Heffernans. There's simply no reason why Victor or Nathaniel would want to hurt Samuel or Elsbeth. It's inconceivable. As I told you before, I would stake my reputation on it.\" She turned and glared at us as though daring us to disagree. \"I can see that you've earned every facet of your reputation, Mr. Pendragon, but I would still like you to take this case. So will you prove that Mr. Heffernan and his son are innocent of this terrible crime?\"\n\n\"And if the perpetrator does turn out to be your Mr. Heffernan or his son?\"\n\nShe blanched slightly, her face drawing rigid as though she'd been struck. \"I do not fear the truth,\" she said, but there was little conviction in her words.\n\n\"Then I am your man.\" He gave her a quick tilt of his head as he snatched the coin into the palm of his hand. \"But you do understand, Lady Arnifour, that the truth is seldom what we want it to be.\"\n\n\"I only ask that you live up to the best of your reputation.\"\n\nHe smirked, but gave no other quarter to her having chastised him. \"I think I've already proven that I shall not disappoint you.\" He flashed her a rakish smile that showed off his dimples. \"We will be out tomorrow to have a look around.\"\n\nLady Arnifour nodded earnestly before downing her brandy in a single ferocious gulp. \"I shall look forward to it,\" she said as she set her glass on the mantel and glided past us.\n\n\"There are two things you must do, however.\" Colin spoke up before she reached the landing. \"If you've not already done so, you must hire a guard to sit with your niece twenty-four hours a day. We cannot risk the chance that whoever committed this crime might wish to correct their unfinished business. Your niece could solve this case quite handily.\"\n\n\"A guard has been in place from the first night.\"\n\n\"Then there is only the matter of my fee,\" he gestured toward me, \"and I shall leave that to the two of you.\"\n\nI escorted our new client to the front door as we discussed an agreement, quickly coming to terms on a figure she had not hesitated to accept. Colin's repute does preclude most clients from balking at his fee.\n\n\"What did you make of that?\" Colin asked, carefully pouring the contents of his untouched snifter back into the decanter, as I reentered the room.\n\n\"It's a horrible crime. The poor niece.\"\n\n\"Indeed.\" He finished with his glass and did the same with mine. \"Yet Her Ladyship hardly seems the grieving widow.\"\n\n\"I'm sure their marriage was arranged and you know those things just never seem to turn out well.\"\n\n\"Tell that to dear Victoria. She seems unwilling to ever let off mourning Albert. If it weren't for my father and his scheming with her stable man, John Brown\u2014\"\n\n\"That's nothing but rumor.\"\n\n\"Ah, Ethan, ever na\u00efve.\" He chuckled. \"As to Lady Arnifour . . .\" He moved to the fireplace. \"She not only lies to herself every time she looks in a mirror, but she was most certainly lying to us tonight. There is much more to this crime than she's letting on. It's preposterous to think that she would place her reputation on the line for a groundskeeper.\"\n\n\"I thought I could hear her forefathers spinning when she said that.\" I laughed.\n\n\"It will be most interesting to meet this Victor Heffernan. And we shall see if I am not right about him and the Lady.\"\n\nI chuckled. \"And what if you are right about the two of them?\"\n\nHe looked at me with a mischievous grin. \"Then we shall have our first motive.\"\nCHAPTER 2\n\nWe set off for the Arnifour estate on the outskirts of London only after the new day had eased past one o'clock, jouncing along the cobbled roadways in the cab Colin had procured. We had chosen this specific time of day as there are few things as indulgent as teatime in the finer homes. Finger-sized sandwiches of cucumber and butter, petit crown-shaped biscuits, thinly sliced hard-cooked eggs, cream cheese with minced olives atop water wafers: all the delicacies Mrs. Behmoth has had no patience for. We came through the massive stone archway that marked the edge of the Arnifour property, catching our first glimpse of the family home: a rambling Greco-Roman structure in the shape of an elongated U rising from the green hillsides around it like a white monolith. A double row of Ionic columns adorned its fa\u00e7ade and there were well over a dozen chimneys crowning its rooftop. As our carriage rose and dipped over the uneven hills, the house was never lost completely from view, but rather stretched out like an imposing anomaly, reminding all that it did not dwell within its surroundings, it ruled them.\n\nIt was only after we gained the final hill that we could see how this seemingly regal building showed its age every bit as much as its overly lacquered mistress. Its wooden columns were chipped and flaking while the stone block fa\u00e7ade covering its lower half was in need of both cleaning and repair. Both wings of the house had boards fastened across their windows, leaving only the long central section showing signs of habitation. And even there the large French doors fronting the portico revealed that many of those outlying rooms were devoid of furniture.\n\n\"It would seem . . . ,\" Colin mused as our cab rounded the driveway at the main entrance, \". . . that this tea will likely be less than we were hoping for.\"\n\n\"Now don't start,\" I scolded. \"These people are dealing with a terrible tragedy.\"\n\n\"This entire estate is something of a tragedy.\"\n\n\"It is a wonder she didn't blink at your fee.\"\n\n\"She'd have been stuck with the inspector if she had,\" he said as he climbed out of the cab.\n\nWhile I made quick arrangements for the driver to wait for us by paying only half his fee, Colin availed himself of one of the door's large, scripted-A iron knockers. As I joined him on the porch I noticed that the massive doors were warped and weather-beaten as they abruptly yawned open to reveal a thin, pinch-faced woman dressed entirely in black. Her salt-and-pepper hair was pulled taut into a bun. She offered nary a smile nor a nod of welcome.\n\n\"Mr. Pendragon and Mr. Pruitt?\" she asked with obvious disdain.\n\n\"Well done,\" Colin answered. \"You've saved me a card.\"\n\nHer brow furrowed as she glared at him. \"I will remind you this is a house in mourning.\"\n\n\"Indeed. . . .\" He arched an eyebrow.\n\nWhether she understood his inference or not I cannot say, but she did finally feint to the side and allow us entry. Colin gave a tight smile and passed so close to her that she was forced to take an awkward step back while I, on the other hand, gave her as much room as I could.\n\nWe were ushered into the study and directed to a pair of brocade armchairs. Dutifully obeying the housekeeper's silent bidding, we settled into the chairs and watched as she turned with the rigidity of a Queen's guard and left through a rear door.\n\n\"That woman has disapproval refined to an art.\"\n\n\"Whatever could she be so sour at us for?\"\n\n\"An excellent question.\" Colin stood up and began to inspect an oil painting of a grim family hanging above the mantel. \"This must be the Arnifour family in happier times.\" The portrait showed a stilted, balding man with a sour face seated next to a woman obviously older than him, with three stoic children shy of their teens\u2014one boy and two girls\u2014standing behind them. The woman at the portrait's center was clearly a twenty-some-years-younger version of our client. \"It is extraordinary how unhappy some people look when being immortalized.\"\n\n\"I don't remember you looking much better in that portrait your father had done when you were living in Bombay,\" I needled, recalling the equally stuffy rendition of Colin and his father.\n\nHe scowled at me a moment, but his expression quickly slid into a warm, generous smile, his dimples flashing and his eyes sparkling like sapphires as he said, \"It's a pleasure to see you again.\"\n\nI turned as Lady Arnifour ambled into the room, appearing even more haggard in the harsh daylight. \"I regret I cannot say the same. How I wish this were a social call.\" She sat on the edge of a sofa across from me.\n\n\"I appreciate how difficult this is for you,\" he said as he came and sat down next to her.\n\n\"Do you, Mr. Pendragon? Have you suffered the loss of a loved one to murder?\"\n\nColin flicked his eyes at me and I knew what he was asking. I returned a slight nod and he said, \"Mr. Pruitt has, but I have not. Yet I would suspect there are few who do not understand what it means to lose someone they love.\"\n\n\"How perfectly maudlin.\" A disheveled, rail-thin man in his early thirties stood in the doorway the housekeeper had exited through, clenching the doorjamb so tightly that I wondered if he had an infirmity that left him unsteady on his feet. \"Comparing war wounds, are we?\"\n\nLady Arnifour glowered at her son, yet he seemed either unaware or unconcerned as he stalked into the room with a gait that was at once as unstable as it was cocksure. I guessed his infirmity to be intoxication.\n\n\"Mr. Pendragon.\" He stuck out a hand and gave a protracted bow that seemed more mocking than deferential.\n\n\"Eldon!\" Lady Arnifour snapped.\n\nColin stood up and pumped the younger man's hand, flashing him a rogue's grin. \"Such a formal greeting. I assume you are doing your best to adapt to your new role as lord of the manor?\"\n\nEldon's eyebrows shot up as he pulled himself to his full height, several inches taller than Colin, a slow smile spreading across his face. \"Yes.\" He smirked at his mother. \"That would be me. Lord of the manor.\"\n\n\"You will excuse my son's insolence,\" Lady Arnifour scoffed as she snatched up a small bell from the table beside her. \"His manners tend to wither with the advancing day.\"\n\n\"Now, Mother . . .\" Eldon dropped into a chair near me. \"Let's not be priggish. I'd much prefer to hear what Mr. Pendragon has to say about Father's murder.\" He settled his gaze on Colin, in whose furrowed brow I noticed the seeds of distaste. There was clearly no love lost between this son and his father. \"Tell me, do you agree with Mother's contention regarding the innocence of the sainted Mr. Heffernan?\"\n\n\"Do you disagree?\" Colin shot back.\n\n\"I would sooner stake my bits to a fence post, Mr. Pendragon. It's not prudent to disagree with Mother.\" He forced a laugh that did not cover the unsettling rage that momentarily shifted behind his eyes.\n\nBefore either Colin or Lady Arnifour could respond, however, the mirthless housekeeper returned with a silver tray piled high with sandwiches and a tea set.\n\n\"Perfect timing, Mrs. O'Keefe,\" Lady Arnifour said as she began fussing over the tray, slowly regaining her composure.\n\n\"Yes, ma'am.\" Mrs. O'Keefe exited as hastily as she had come. The only warmth she'd shown, and that only rudimentary, was when she'd addressed her mistress. She'd not even given Eldon the slightest look. He seemed ever the misfit, or perhaps something more.\n\n\"Mr. Pendragon . . .\" Lady Arnifour held out a cup of tea. She was about to do the same for me when Eldon popped out of his chair.\n\n\"Perhaps our guests would like something to invigorate their tea?\"\n\n\"Really, Eldon,\" Lady Arnifour rebuked. \"It's not even a proper hour.\"\n\n\"That's never stopped the Arnifours,\" he sneered.\n\n\"Tell me . . . ,\" I interrupted to keep things from denigrating further, \"do you still cultivate your land?\"\n\n\"Not anymore. Mrs. O'Keefe tends a small garden out back, but it's been generations since these lands were properly worked. It's too much, I suppose . . . the staff, the upkeep, the toil\u2014\"\n\n\"The expense . . .\" Eldon chuckled. \"That's why this old pile looks as tired as it does. The family gentry forgot how to earn its keep a long time ago.\"\n\n\"That's enough!\" Lady Arnifour banged her cup back onto its saucer. \"I will not have you talk about your heritage that way.\"\n\nHe waved her off. \"We can hardly sully the Arnifours or your Langhems any more than they've already done to themselves.\"\n\n\"I've had all I'm going to tolerate!\" she snapped. \"You may take your leave.\"\n\nEldon shrugged and stood up. \"And there you have it, gentlemen. The lord of the manor can still be dismissed by his doting mother.\" A smile thick with resentment spread across his face. \"It's been a pleasure.\"\n\n\"I should very much like to speak with you later,\" Colin called to him.\n\n\"You'll have to get dispensation from the dowager empress!\" he growled as he stalked out.\n\n\"You must forgive my son. My husband and I married later in life and my children were born to me at a time when most women are finished with such duties. I remember thinking them little miracles,\" she grimaced, \"but Eldon's never been well and I cannot help but wonder if my choice to bear him at such an age had an impact.\"\n\n\"I'm sure you did everything you could,\" I said.\n\nColin smirked. \"I'd say it has more to do with your son's passion for drink than your age at conception. Either way, it serves no purpose to blame yourself.\"\n\n\"That's . . . , \" Lady Arnifour paused before giving an awkward grin, \". . . very kind of you, Mr. Pendragon,\" she finally said. \"Now tell me,\" she shifted in her seat, \"how can I assist your investigation?\"\n\n\"I should like to ask a few questions, after which we shall need to go out and see where the attack occurred,\" he said.\n\n\"Of course.\" She nodded, a hand nervously fluttering up to her face. \"I'll have someone take you.\"\n\n\"Excellent. Now you mentioned that your husband and niece met at the barn that night. What makes you think they didn't meet along the way? That perhaps she gave him a ride? Wouldn't that explain his covering such a distance in so short a time?\"\n\n\"I think not, Mr. Pendragon. My husband was not a small man. There'd never have been room for him to get onto her horse. Samuel was of average height, but he was quite stout.\"\n\n\"I see. And has Inspector Varcoe shared with you his theory on how your husband covered that distance?\"\n\n\"He brought up precisely what you've suggested. An inauspicious beginning to your investigation, it would seem.\" She gave a flinty smile.\n\nColin arched an eyebrow but held his tongue as he sipped his tea and snatched up a petit four. \"And what alerted the household that something was wrong that night?\"\n\n\"Nathaniel saw smoke on the horizon. The barn where my husband and niece were found had been set on fire.\"\n\n\"On fire?\" Colin leaned forward. \"You didn't mention that yesterday.\"\n\n\"It hardly seems relevant.\"\n\n\"How a thing seems is seldom how it is.\"\n\n\"Of course,\" she said, but there was little resolve in her words.\n\n\"And what of Mr. Heffernan and his son, Nathaniel? Has the inspector rounded them up yet?\"\n\n\"He's allowing them to stay here at my behest. But I fear he's only biding his time. It would be a tragedy if they were arrested, Mr. Pendragon, and this family has suffered enough already.\"\n\nColin offered a quick smile, one that left me wondering what notions were racing about in his mind. \"Permit me one last question. Has the inspector found the weapon used in the attack?\"\n\n\"No.\"\n\n\"I didn't suppose he would.\" He drained his tea and stood up. \"That would require actual detection. May I trouble you to have someone escort us down to what's left of the barn then?\"\n\n\"I shall have Mr. Heffernan take you. It will give you an opportunity to speak with him.\"\n\n\"Outstanding.\" Colin leaned forward and grabbed two more petit fours, palming them into a napkin and sliding them into his pocket. \"I should also like to speak with your daughter\u2014Kaylin, isn't it?\"\n\n\"Yes. But I'm afraid she's not here just now. All of this business has put her quite on edge, so I've sent her to stay with a friend in town. If you'd like, I'll arrange to have her meet you at your flat one afternoon?\"\n\n\"That would be ideal. The sooner the better.\"\n\nWe followed Lady Arnifour through the rear door Mrs. O'-Keefe had used and found ourselves in a sparse hallway that opened onto a large, immaculate kitchen. It was the most pristine space I had ever seen. Not a speck, not a smudge anywhere save for the harsh, black-clad personage of Mrs. O'Keefe peeling carrots into a rubbish can at a well-worn table.\n\n\"Have you seen Mr. Heffernan?\" Lady Arnifour asked.\n\n\"Out back, ma'am. Trimming roses last I saw.\"\n\n\"Very well.\"\n\nWe filed through the kitchen and out back, and I was aware of being under the watchful gaze of Mrs. O'Keefe the entire time.\n\nA compact vegetable garden ran along the back of the house just off the kitchen, displaying an assortment of lettuce, tomatoes, cabbage, carrots, broccoli, cucumber, spinach, and a few other bits of greenery I did not recognize. Just beyond was a hedge of boxwoods clipped to precision, but it wasn't until I looked out among the array of rosebushes beyond that I noticed the thick man attending them. He had a plaid cap slipped down on one side of his head and the plain gray-green jumper of a groundsman. I knew at once it had to be Victor Heffernan.\n\n\"Here you are,\" Lady Arnifour fairly purred.\n\n\"Ma'am.\" He stood up and I saw that he was barely taller than our hostess.\n\n\"You must be Mr. Heffernan.\" Colin stuck out his hand.\n\n\"If you aren't here to arrest me, you can call me Victor. Everyone does.\"\n\n\"I assure you, Victor,\" Colin smiled amiably, \"I have no interest in arresting anyone.\"\n\nVictor Heffernan stared at Colin, a dark curling mustache an accent mark above his lips, and appeared to be trying to determine whether we meant trouble. Colin kept smiling, revealing nothing, his dimpled grin as natural as the rose petals Victor had been fussing among. He appeared to be about twice as old as Colin's thirty-eight years, but even so, I could tell he had no idea what to make of us.\n\n\"This is Colin Pendragon.\" Lady Arnifour came forward in a peculiarly maternal way. \"I've hired him to prove you and Nathaniel innocent of this tragedy.\" She let her voice drift off as though she was overcome by the very thought.\n\n\"Now, now . . .\" Victor reached out and patted his mistress's hand with marked intimacy. \"Don't get yourself worked up again.\"\n\nLady Arnifour gave a tight smile and took a slight step back, effectively moving out of his reach. Victor seemed to realize his indiscretion and suddenly stumbled backwards, carelessly slicing off the top of an errant rose. I was beginning to believe that Colin's initial assessment of the alibi Lady Arnifour could provide this man might be true.\n\n\"Would you take them down to see what's left of the barn?\" she said. \"I simply cannot bear to go.\"\n\n\"Of course. I'll go hitch up the buckboard.\"\n\n\"Thank you.\" Lady Arnifour gave him a gentle nod as he headed off. \"I'll wait for you in the study.\"\n\n\"When we come back I'd like to check on your niece.\" Colin tipped his chin toward me. \"Mr. Pruitt knows something of wounds and healing and such.\"\n\n\"But I'm not a doctor,\" I pointed out.\n\nHe clapped my shoulder. \"That he's not, but he can be a fount of medical bric-a-brac just the same.\"\n\nI fought to keep from scowling at him as I caught Lady Arnifour glancing my way. What little knowledge I possess was learned by necessity during a regrettable tenure spent in the coarser areas of the city during my youth. It is not something I prefer to advertise, so I was relieved when Victor and his buckboard came rounding the corner of the house. Two minutes later the three of us were trundled onto the open seat of the wagon heading for the farthest reaches of the Arnifour estate.\nCHAPTER 3\n\nOur journey began in relative silence with only the occasional snort of the horse to interrupt the steady drone of our wheels as we rocked along the dirt ruts of the driveway, me watching the breadth of their property unfold while Colin appeared to be studying nothing in particular as he smoothly coaxed another crown between the fingers of his hand. The moment we turned off the path and started out across an open field, however, Colin turned to Victor and began peppering him with questions about the family history.\n\n\"Barnaby Langhem was given this property and the title of Baron by King George the Third, himself,\" he said with evident pride. \"Lord Langhem was Lady Arnifour's great-grandfather and was one of the men responsible for keepin' that poor man on the throne until long after he shoulda been removed.\" He snickered. \"Not six months later the King had a violent fit and accidentally throttled Lord Langhem, which meant that the land, but not the title, was passed on to his eldest son, Jacob. That's when the great house was built\u2014paid for by a royal decree under the circumstances. That's when the whole Langhem family moved in and my family first began workin' for them.\n\n\"Everybody prospered under Jacob, but his life also came to a sudden end not more than ten years later. He either slipped in the mud stirred up by a downpour and was run over by a funeral carriage making haste to a plot before it was turned into a quagmire, or the carriage cut a corner too close and ran him down. Whichever the case, the outcome was the same.\n\n\"That left the estate and all its lands to Jacob's eldest son, Alanon.\" He heaved a weary sigh and I knew the story was becoming personal. \"Alanon liked women and drink, and spent more time going through the Langhem fortune than addin' to it. He and his wife only had one child\u2014a daughter, the future Lady Arnifour herself.\"\n\n\"What about bastards?\" Colin muttered.\n\nVictor shrugged. \"None that I ever heard about.\"\n\n\"And what happened to him?\" I asked before Colin could toss out another indelicacy.\n\n\"Unfortunately, he lived into his eightieth year before he finally took a tumble out an upper-story window into the garden below. Destroyed the family's prize roses, not to mention the damage he'd done to the Langhem name and fortune. A real pity.\"\n\n\"And as his only surviving heir,\" Colin interrupted, \"Lady Arnifour inherited the estate, such as it is.\"\n\n\"That's right.\"\n\n\"Must have been a shock to the Earl to discover he'd married into a family almost as penniless as his own.\"\n\nVictor glanced at Colin and shrugged self-consciously. \"I wouldn't know about that,\" he said, but his manner suggested otherwise.\n\nA moment later we skirted around a stand of trees and caught our first glimpse of the charred remains of a small building a short distance off. \"The barn . . . ,\" Colin muttered as he flipped the coin into his vest pocket and stared at the approaching destruction. It was impossible to notice anything else beyond the hulking blackened wreck, its remains baking in the sun like some great sea creature's carcass that had managed to wash up on this waterless terrain. Only the stinging residue of charred wood lingered to assault the nostrils.\n\nVictor pulled the horse up short and Colin hopped out, walking in a sideways arc around the ruined barn. \"Did the Earl and Lady Arnifour raise their family here then?\"\n\n\"They did. Lady Arnifour has spent her whole life here. Born and reared in that very house.\"\n\n\"And the niece too?\" he asked as he continued to take slow, careful steps toward the wreckage, studying the ground meticulously as he drew nearer as though the earth itself might reveal some clue.\n\n\"Yes,\" Victor muttered as he stared out at the horizon, an odd look of discomfort clouding his gaze.\n\nWe both watched Colin kick at something with the toe of his boot and then crouch down to inspect it. Only after he stood up and brushed his hands against his slacks, having lost interest in whatever he'd been pawing at, did I turn back to Victor and ask, \"How long ago did Alanon Langhem die?\"\n\n\"Eldon was just a tot. Must be almost thirty years ago.\"\n\n\"He must've been pretty angry when he learned she'd married a title without the means to pluck him out of debt.\" Colin chuckled. \"That's so often the way: antiquated titles without a farthing for a piss pot.\"\n\nVictor shrugged.\n\n\"Tell me something,\" Colin called out from within the remains of the barn. \"Who came out here the night of the attack?\"\n\n\"Lord Eldon, Nathaniel, and me.\"\n\n\"Did you take any notice as to how the blaze was started?\"\n\nI watched as Victor's face registered an obvious level of confused disbelief. \"Kerosene,\" he said. \"The whole place smelled of kerosene just like it does now.\"\n\nColin smiled without even bothering to throw a glance at us. \"Quite so.\" He wandered around a minute, glancing at what was left, toeing a few fallen timbers and running his fingers down the black framework. All the while his eyes flicked from place to place and I knew he was trying to take everything in, to remember it. \"Why don't you tell me about that night,\" he said as he sauntered out the far side.\n\n\"There's not much to tell,\" Victor said, his gaze still locked on the horizon. \"It was after supper. Nathaniel and I eat in the kitchen with Mrs. O'Keefe. I was done first, same as always, and had gone out to the stable by the house to check on the horses, and that's when I noticed Miss Elsbeth's horse was gone. Don't get me wrong; there's nothing unusual in that. She and Lady Kaylin often go out for a ride in the evening.\"\n\n\"But was it unusual for Elsbeth to go alone?\"\n\n\"Not really.\" Victor lifted his cap and scratched his scalp, glancing down at his feet. \"She goes off by herself as often as not. She's an independent sort.\" He smiled, and for a moment I thought I detected a note of pride. \"She always takes care of herself . . . ,\" he started to say, and then winced as he registered the irony of his words. \" 'Til that night.\"\n\n\"Of course,\" Colin replied absently, drawn more to the scorched earth than anything Victor was saying. \"Go on.\"\n\n\"I was putting the tack up and tending a mare when Nathaniel came running in shouting about seein' smoke on the horizon. We didn't know it was the barn. From the house it looked like part of the woods was on fire.\"\n\n\"How long had you been in the stable before Nathaniel came in?\"\n\n\"About an hour, maybe less.\"\n\nMore than enough time for Nathaniel to have come down here, perpetrated the attack, and returned to the stable to report the smoke, I realized. His father certainly wasn't providing much of an alibi.\n\n\"And what happened then?\" Colin prodded.\n\n\"I grabbed two horses straightaway. Didn't even bother with saddles. But before we could get the bridles in place Lord Eldon came out hollering about the smoke and insisting on goin' with us. Mind you, he can't ride bareback, so I had to take the time to get a third mount ready before we could get under way. As soon as his horse was sorted Lord Eldon took off. Didn't wait for us.\"\n\nI could tell he was still aggrieved by Eldon's behavior; the extra time he had cost them, and his determination to get under way first, but he did not dare utter the words.\n\n\"Do continue,\" Colin said without seeming to have taken note.\n\n\"Nathaniel and I followed Lord Eldon and we all ended up here.\"\n\nI thought his story came to a decidedly abrupt conclusion.\n\n\"So . . .\" Colin put his hands on his hips and turned toward us, having apparently finished investigating the ground. \"Eldon got here first\u2014\"\n\n\"By a deer's breath. It was past supper, Mr. Pendragon, and you can be sure Lord Eldon had consumed his share of drink by then. Nathaniel and I were able to catch up to him by the time we got here.\"\n\n\"But you didn't overtake him.\"\n\n\"Lord Eldon was riding like Death himself was chasing him. I'd say his condition kept him from realizing just how reckless he was being.\"\n\n\"Of course. And what did you find when you got here?\"\n\n\"The barn was in flames. Most of it had already collapsed.\" He gestured with his chin. \"Just like you see now. Nathaniel spotted the Earl. He was laid out just about where you're standing,\" he said, his brow slowly furrowing.\n\nColin gave a quick smile and I knew he'd already figured that out. \"And Elsbeth?\" he asked. \"Where was she found?\"\n\n\"On the other side. Closer to the woods. We never would've even looked for her if I hadn't seen her horse stamping at the tree line.\" He gestured to the woods just beyond.\n\n\"The horse hadn't run off?\"\n\n\"No, sir,\" Victor said proudly. \"The Arnifours have fine animals. Trained never to abandon their riders. Nathaniel and I seen to that.\"\n\n\"Impressive.\"\n\n\"It was Nathaniel who found Miss Elsbeth too.\" He dropped his gaze again. \"It was terrible.\"\n\n\"Was she unconscious when you found her?\" Colin asked as he headed off in the direction Victor had gestured.\n\n\"Yes, sir. It was her face. . . .\" He sucked in a deep breath and shook his head again. \"I didn't think she was alive.\"\n\n\"And the Earl? Had he been beaten the same way?\"\n\n\"No, sir. He was the opposite of Miss Elsbeth. He was facedown with the back of his head stove in. Whoever hit him meant to kill him. An awful sight.\" He kept his gaze lowered and I couldn't tell if he was swamped by the memory or if it was something else.\n\n\"Did you find any sort of weapon nearby?\"\n\n\"No, sir.\"\n\n\"Elsbeth was about here then?\" Colin called as he reached a position a dozen or so yards beyond the ruined barn.\n\nVictor barely glanced up. \"About that.\"\n\nColin knelt to the ground and fingered several spots before standing up and finally coming back around to where Victor and I were. \"It was clearly a most unfortunate scene,\" he said as he reached us.\n\n\"Yes, it was.\"\n\n\"I only need trouble you with two more questions.\"\n\nVictor nodded.\n\n\"Did you notice if the Earl had been robbed?\"\n\n\"No, sir. But the inspector found a roll of bills in his pocket and said he still had his gold watch on him.\"\n\n\"It's always important to rule out the obvious,\" Colin murmured. \"Which brings me to my last question. Did it appear that Elsbeth had been violated in any way?\"\n\n\"No . . . no . . .\" He shook his head rapidly and looked almost ready to swoon.\n\n\"She was fully clothed?\"\n\n\"Yes, sir.\"\n\n\"Her dress was not torn or mussed about in any way?\"\n\n\"No, sir. There was nothing of the kind like that. Nothing at all.\"\n\n\"Thank you. I'm sorry if I've made you uncomfortable, but I trust you understand the need for such questions.\"\n\nVictor Heffernan nodded but did not reply. It made me wonder if he thought he'd said too much, too little, or simply feared that he sounded guilty in spite of himself.\nCHAPTER 4\n\n\"There's definitely a familial resemblance,\" Colin said as he gazed down at Elsbeth. \"I'd say the Langhems have the dominant gene pool.\"\n\n\"I don't know how you can see any such thing with all the damage that's been done to her,\" I answered. Her face was a rainbow of mottled blues, yellows, greens, and purples, and it was obvious that she had suffered multiple fractures to her nose and cheeks given the distortion of the bones beneath. However she had once looked, she would never be the same again, assuming she survived at all.\n\n\"Well . . . ,\" he allowed. \"Try using a bit of imagination.\"\n\n\"Imagination, is it?\" I said, glad we were alone with her.\n\n\"I'd say she was attractive\u2014before the attack.\"\n\n\"Does that matter?\"\n\nHis gaze shot over to me. \"Everything matters. And that includes both the way a person looks and how they are perceived. Physical beauty can be a motivator, a crutch, a distraction, or a curse. And the lack of it every bit the same.\"\n\n\"I suppose you have a point.\"\n\n\"Other than her injuries,\" he pressed, \"what are the first things you notice about her?\"\n\nI looked down at her battered face and knew that these were indeed the only things I had made note of thus far. \"Well . . .\" I cleared my throat as I studied her and tried to decipher what he meant for me to see. \"I'd say she's about twenty and has long brown hair. She's very slight, really just a slip of a thing, and she's breathing so shallowly that I can hardly see her moving at all.\"\n\n\"There . . . ,\" he said with finality. \"All things physical.\"\n\n\"Well, I can't very well say she's a compelling conversationalist.\"\n\n\"No, but you could have pointed out the meticulousness of her room, or the color of her bedding, or even the high-necked and positively unremarkable dressing gown she's wearing, all of which speak volumes about who she is.\"\n\n\"I don't think I like this game.\"\n\n\"Just keeping you honest.\"\n\n\"What have you learned so far?\"\n\n\"Several things. I know that the Earl was knocked to the ground by a blow that most certainly came from someone atop a horse. I know that he was running when he was struck down, and that he persisted in pulling himself along the ground by his elbows for another fifteen feet before the killer finally dismounted and came right up beside him, and then beat him with the absolute intent to kill.\n\n\"As for this poor girl . . . ,\" he turned his gaze back to Elsbeth, \". . . she was running for the woods when she was struck, the assailant having once again mounted his horse. She collapsed on the spot and was left in the condition we find her now, though I would presume her attacker thought her to be dead.\"\n\n\"You figured all that out by pawing at the ground around that barn?!\"\n\n\"It was very telling, especially since much of the grass had been burned away. If we'd been able to get a look at it before the whole of Inspector Varcoe's buffoons descended upon it, I'm sure I'd be a damn sight closer to telling just who did this.\" He shook his head and let out a sigh. \"But the one thing I can't profess to have the slightest notion about yet is why.\"\n\n\"Well, we know it wasn't robbery.\"\n\n\"That's true. Yet even so, can we be sure there wasn't something in that barn worth stealing? That perhaps all of this is about covering the theft of something from there?\"\n\n\"I hadn't thought of that.\"\n\n\"Doubtful, though.\" He shrugged.\n\n\"Come now, we are only collecting information,\" I teased.\n\n\"Always a quick learner.\"\n\n\"I'd hardly call twelve years quick.\"\n\n\"Well, you're doing better than the inspector and he's been at it the whole of our lifetimes and then some. Did you recognize the man he has posted outside the door?\"\n\n\"Yes, I remember him from the Rathburn case. Seems agreeable enough.\"\n\n\"Perhaps, but he is a Yarder.\"\n\n\"You can't blame them all for the inspector's ineptitude.\"\n\n\"They've accomplished nothing in a fortnight,\" his eyes were alight with fire, \"and I'm already certain that Victor Heffernan is innocent.\"\nCHAPTER 5\n\nVictor's son, Nathaniel, was a lanky, painfully thin boy of twenty-one whose pasty complexion belied the work he did outside. While he shared his father's hawkish nose he did not so much as bear a whisper of the older man's compact frame. His mother had died before Nathaniel learned to walk, the victim of a frail constitution, Lady Arnifour had informed us, right before she instructed us to go easy on the boy, as she termed him delicate in both mind and constitution like his mother.\n\nLady Arnifour had relayed the story of the late Mrs. Heffernan in a voice both wistful and content. It was clear she was moved at the loss suffered by the two Heffernan men, yet losing his wife had left Victor available for the attentions of the Lady herself. I was reminded again about Colin's initial suspicion of the nature of Lady Arnifour's relationship with her groundskeeper and was all but convinced that he was correct. I was beginning to believe that the only person who actually harbored any real emotion for the late Earl was the dour housekeeper, Mrs. O'Keefe. Other than her, I didn't see anyone who was truly lamenting his death.\n\nWe were seated in the kitchen with Nathaniel, Victor having already disappeared out back after making the introductions. Nathaniel was still standing by the back door, all gangly limbs and awkwardness, as he self-consciously dragged the cap from his head.\n\n\"Please . . . ,\" Colin pointed to a chair across from us, \"sit down. Make yourself comfortable. We are not the enemy.\"\n\nNathaniel did not embrace Colin's gesture of camaraderie, as he remained standing a good minute longer before finally making the decision to stay, skulking over to the table, and slipping into one of the chairs without even having to pull it out.\n\n\"I shall only trouble you with a few questions,\" Colin said in a voice I knew he meant to sound placating. \"I'm sure you'll have discussed it all with the Yarders anyway.\"\n\nNathaniel gave a slight nod even as he kept his gaze riveted on the table. I was thinking he looked guilty and would be likely to grunt his answers when he suddenly blurted out, \"I didn't kill that rotten bastard. It wasn't me and it sure as bloody hell wasn't my father. And if you think it was you can go straight ta hell with that old piss pot inspector!\"\n\nColin leaned back in his chair with an easy smile and casually folded his arms across his broad chest. \"Piss pot. I rather like that.\" Nathaniel's eyes raked across Colin's face, searching for some sign of sarcasm, but he found no such thing there. \"We're not so unalike, you and me. At least not where Scotland Yard is concerned.\" The young man blinked repeatedly, his outburst drained with the rapidity of a flash flood. \"Now why don't you tell us what you remember about the night of the Earl's murder.\"\n\nNathaniel snapped his eyes back to the tabletop, but not before I spotted something dark and angry trying to hide there. \"It was after supper . . . ,\" he began with marked reticence. \"The Earl had gone off on his walk and I was watering the garden by the stables when Elsbeth came out and said she wanted ta go riding.\" He shifted in his chair but did not lift his gaze. \"I told her it was too late, but she wouldn't listen. She never listens ta me.\"\n\n\"Was your father in the stable?\" Colin asked.\n\n\"If that's what he said,\" he shot back.\n\n\"Convincing.\"\n\n\"What difference does it make?\" He finally looked up, glaring at Colin again. \"You already think we're guilty. I can see it in yer face.\"\n\n\"The only thing you see on my face is that I'm beginning to find you an ungrateful little tosser. I'd suggest you knock off the ruddy attitude or I'll return Lady Arnifour's money and leave you to hang. What do you prefer?\"\n\nNathaniel sagged and dropped his chin to his sternum so that all I could see was the sharp cut of his nose protruding from beneath his brow. This interview seemed to be yielding about as much information as we'd gotten from Elsbeth.\n\n\"All I'm asking, Nathaniel, is for you to tell us the truth of what you remember that night. And I give you my word that I'll not come to any conclusions until the solution is irrefutable. Are we agreed?\" We watched the boy until he vaguely shrugged his shoulders. It would do. \"Good. So Elsbeth wanted to go for a ride and you were warning her off. . . .\"\n\nNathaniel sighed heavily. \"That's right.\"\n\n\"I presume it was dark and you were worried about her?\"\n\n\"No . . .\"\n\nI figured Nathaniel would explain what he meant, but seconds quickly turned into minutes without so much as a hint of clarification. He sat there, morose and slouching, his gaze tucked in on himself and his arms folded like two crossed swords. He looked like a man with a great deal to hide.\n\n\"Then why, Nathaniel?\" I could hear the strains of impatience seeping into Colin's voice.\n\n\"Because I knew what she was up to.\" He raised his eyes just enough to meet Colin's, and behind his inky black irises I saw a flash of something unsettling I could not place. \"I'm done talking,\" he suddenly announced, pushing himself up from the table and stalking back outside before either Colin or I could say a word.\n\nColin shook his head and stabbed a crown out of his pocket, quickly running it between his fingers. \"Curious.\"\n\n\"Curious?! It's more than curious. It's disturbing. No wonder Varcoe's convinced he's guilty.\"\n\nHe glanced at me. \"Well, that should tell you something, because Varcoe's seldom right. Though I will say that I've never seen so many angry people in one house hiding so very many secrets. This place was like a tinderbox just waiting to be set off. Even Elsbeth seems to have been up to something.\"\n\n\"You think that based on the word of that infuriating boy?\"\n\n\"So quick to judge,\" he clucked. \"I'm sure that's precisely why our uninspired inspector is so eager to throw the blame on the Heffernans. Varcoe must have been ecstatic with such easy targets.\" He tossed me a tight look. \"But I'm not so sure.\"\n\nI nodded, mortified to discover myself aligned with the inspector.\n\n\"A crime like this is seldom so easy. The blows to the Earl's head were delivered with malice and forethought. The same is obviously true for Elsbeth. This was not some spontaneous act of vengeance; it was a purposeful and calculated crime. I will be astonished if this level of cleverness was wielded by that agitated boy.\"\n\n\"But you don't know that. He could be exactly what he seems. Guilt can be an extraordinary burden to carry, especially for a boy like that.\"\n\n\"A boy like that? . . . ,\" Colin echoed, furiously rotating the coin.\n\nBefore I could tell him what I'd seen lurking behind the young man's eyes Victor came scurrying back inside. \"Is everything okay?\" he asked, a note of dread in his voice. \"Nathaniel is a moody lad, but you mustn't hold that against him. It's my fault. I did the best I could to raise him without a mother.\"\n\n\"I know he means well,\" Colin answered as he slid the crown back into his pocket.\n\n\"He does!\"\n\nBut I couldn't help thinking Victor was pushing too hard.\n\n\"Might you be able to answer a few more questions for me?\" Colin said as he rubbed his chin.\n\n\"Of course.\"\n\n\"Do you know where Nathaniel was that night while you were tending to the horses?\"\n\nVictor shifted uneasily, wringing his hands without appearing to have any awareness that he was doing so. \"He was working in the garden until Miss Elsbeth asked him to saddle a horse for her, which he did. All very proper,\" he added, and I wondered why he'd said that.\n\n\"And then what did he do?\"\n\n\"What did he do?\"\n\n\"Yes.\"\n\nHe hesitated and I knew his answer before he gave it. \"I don't know.\"\n\n\"I see. And the first you heard of the smoke at the far end of the property was when Nathaniel ran into the stable to tell you about it, is that right?\" Victor nodded. \"So if I estimate that it took about thirty minutes for Elsbeth to ride down there and the attack to happen, does that sound conceivable to you? Thirty minutes?\"\n\n\"Thirty?\"\n\n\"Yes. You know, the number after twenty-nine.\"\n\nVictor took a step back and shrugged. \"I don't know. I suppose so.\"\n\n\"Right. So after you heard Elsbeth ride off, do you have any idea where Nathaniel was for any part of the next thirty minutes?\"\n\n\"Where?\"\n\n\"Come now, Victor, these are the easy questions.\"\n\nI suddenly found myself feeling oddly defensive of Victor and could not keep from speaking up. \"We're here because Lady Arnifour believes you and Nathaniel to be innocent,\" I reminded him. \"Just tell us the truth.\"\n\nVictor's body sagged as his chin dipped toward the floor.\n\n\"Sit down, Victor.\" I gestured to the chair his son had vacated. \"You mustn't stand on formality.\"\n\nVictor slumped into it and ran a hand across his brow. His hesitation was palpable. \"I don't know where Nathaniel went after Miss Elsbeth left,\" he muttered. \"He was upset. I thought he would come back to help me in the stable, but he didn't.\"\n\n\"And why was he upset?\" Colin cut in irritably.\n\n\"It's not what you think,\" Victor answered at once. \"It was Miss Elsbeth. He was upset about Miss Elsbeth.\"\n\n\"I'm not thinking anything particular at this moment. So please just tell me what his quarrel with Elsbeth was about?\"\n\n\"No quarrel.\" Again he spoke quickly. \"He wasn't angry, he was upset. You see?\" His eyes sought mine and I gave a confirming nod.\n\n\"Just the same,\" Colin pressed, \"you've made it clear that Nathaniel was in a mood and I should very much like to know what it concerned.\"\n\n\"You have to understand\u2014\"\n\n\"Mr. Heffernan!\" Colin slammed a fist on the table. \"I cannot understand anything unless you start talking to me. I am not your judge. In fact, I am trying to be your ally. But I'll be quite useless if you insist on continuing to hinder me.\" He leaned forward as though doing so might make his point clearer. \"Between your son's contrarian behavior and your dissembling, I'm about ruddy well worn-out. I'm thinking the best thing you and your boy can do is throw yourselves on the mercy of the Yarders.\"\n\n\"Victor,\" I spoke up while Colin plastered a brooding gaze out the window, \"Mr. Pendragon and I understand how determined you are to protect your son. Any parent would be.\" The words caught in my throat a moment as the years I'd spent in the shadow of my mother's illness ridiculed my sentiment. Years in which the voices\u2014the hysteria\u2014so pernicious and invasive, had deftly peeled back the layers of her mind until the perfect family, my family, was forever rendered in the most brutal way. \"But your employer,\" I pressed ahead, determined not to be undone by the coiled remnants of my own memories, \"has been murdered and his niece savagely beaten. We can only pray that she will recover. You and your boy are Scotland Yard's only suspects. You've got to help us, Victor. You must tell us everything you know. Mr. Pendragon will ferret out the truth one way or the other, I promise you that, but what you tell us may lead us to the proper resolution more quickly. And that would allow you and your son to put all of this behind you. You have to trust us, Victor.\"\n\nHe turned a sorrowful gaze on me and I suddenly understood what he'd been afraid to say.\n\n\"Nathaniel cared very much for Miss Elsbeth,\" he muttered under his breath. \"He concerned himself with her when he shouldn't have. It was wrong. I told him so, but a boy's heart . . .\" He let his words drift away.\n\n\"Did Elsbeth know?\" Colin asked.\n\n\"She was a bright girl\u2014is a bright girl,\" he quickly corrected.\n\n\"When Nathaniel told her he didn't want her riding off by herself, what did she say?\"\n\nHe grimaced and folded his hands in his lap. \"She laughed. I couldn't hear much of what they said, but I did hear her tell him that he had no say over her, and she was right. It made him mad. He said foolish things.\"\n\n\"Did he threaten her?\"\n\n\"Absolutely not.\" Victor looked straight at Colin. \"He would never do such a thing. I raised him better than that. And he cared for her. That's what I'm trying to tell you.\"\n\n\"After you heard Elsbeth ride off did you look for Nathaniel?\"\n\nHe shook his head and dropped his gaze again.\n\n\"Didn't you wonder if they'd ridden off together?\"\n\n\"Not after the row they'd had.\"\n\n\"And you didn't see him again until he came rushing in to tell you he could see smoke at the edge of the property.\"\n\nVictor nodded sullenly.\n\n\"So he was missing,\" Colin mused.\n\n\"He would never hurt Miss Elsbeth,\" Victor said again, this time with fierce determination.\n\nColin's face was unreadable as he stood up. I gripped Victor's shoulder and thanked him as I walked past, telling him not to worry though I knew he would. And in truth, I thought he should.\nCHAPTER 6\n\n\"Show them to the parlor when you've finished,\" Lady Arnifour instructed her housekeeper, Mrs. O'Keefe, from the doorway of the late Earl's study, where we'd been ushered. \"I shall wait there.\"\n\n\"Of course, mum,\" came the answer in a tone more perfunctory than dutiful.\n\n\"Mind what they ask,\" Lady Arnifour added as she seized the double doors. \"We've no secrets here.\" And with that she heaved the doors shut, leaving her declaration to hang in the air like soot.\n\nMrs. O'Keefe remained just inside the door where Lady Arnifour had deposited her. Between her gangly frame, all angles and knobs, pursed face, and perpetually pink complexion she looked somehow quite formidable. Even given the exacting proportions of Colin's powerful frame, it still looked like Mrs. O'Keefe could chuck him out the door if she desired. I wondered if therein lay the answer to the fate of Mr. O'Keefe.\n\n\"Please make yourself comfortable,\" Colin said expansively as though it were his home to do so.\n\n\"I'm fine right here.\"\n\n\"As you wish. I'll try not to take up much of your time.\"\n\n\"See that you don't. I've a household to maintain.\"\n\nOne of Colin's eyebrows arched up and I knew that wouldn't portend well for this woman. \"All right then,\" he tossed her a smile that glittered with frost, \"after supper on the night of the Earl's murder, Nathaniel Heffernan was told by Elsbeth to saddle a horse. Did you hear their exchange?\"\n\n\"I've a great many things to do after supper. Listening in on the conversations of others is not one of them.\"\n\n\"So you heard nothing?\"\n\n\"I heard the sound of water in the sink and the rattling of dishes and pans as I cleaned them.\"\n\n\"Do you have help in the kitchen?\"\n\n\"I don't need help.\"\n\n\"Did you look out the window? Did you see Nathaniel and Elsbeth?\"\n\n\"I don't spy on people and I don't listen to their conversations. I'm finding your implications offensive.\"\n\n\"And I'm finding you\u2014\"\n\n\"Not very cooperative.\" I leaned forward and cut him off, certain he was about to say something that would only hurt our cause. \"Come now, Mrs. O'Keefe, I'm sure Lady Arnifour means you to be helpful in our investigation of her husband's murder.\"\n\nShe only glared at me, but I hoped it had given Colin enough time to collect himself again. \"Tell me,\" he started slowly, though his voice was still tight, \"how would you describe your relationship with Nathaniel and his father?\"\n\n\"Professional.\"\n\n\"I'm surprised given how little you're offering in the way of help.\"\n\nShe scowled, pursing her lips into an almost invisible line. \"Is it my help you want? Or the truth?\"\n\n\"Mutually exclusive, are they? Most people make an effort to combine the two.\" He stood up and glowered at her and I knew he was well finished with this woman. \"You seem to display sorrow for the death of your employer and yet remain deceptive, unhelpful, and unaccountably rude. You cannot have it all ways, madam. I would suggest you choose your side with care.\"\n\n\"Choosing sides, is it?!\" She held her ground. \"You come into this house like a rooster and think you can judge the lot of us. Well, you don't know me. I won't stand here and be accused by the likes of you.\" She turned on her heels and made for the doors, but not before Colin managed to sprint past her and plant himself directly in her path.\n\n\"I've accused you of nothing more than an ill temperament,\" he scoffed. \"So if you're blustering about in an effort to cover some guilt, you've nothing but your own conscience to mollify.\" And with a decisive flourish he swung the doors wide and stepped aside.\n\nFor a moment I thought Mrs. O'Keefe might actually step on his shoes, but she kept her deportment impeccable as she swept past him and headed back to the sanctuary of her kitchen.\n\nColin stared after her, his expression moody and dark, and I too felt the better part of our journey had been for naught. All we'd done was alienate the people whose cooperation we most needed. Lady Arnifour was the only person who wanted us here and her motives were questionable at best. She wasn't even bothering to play the grieving widow our sovereign had single-handedly elevated to an art form, which left only Victor Heffernan to be counted as an ally\u2014and I wasn't entirely convinced about him.\n\n\"What an insufferable cow,\" Colin groused as he abruptly dropped to the floor and quickly knocked off twenty push-ups.\n\n\"Well, you didn't exactly win her over with your charm. We might need her help, you know.\"\n\nHe stood up again and cast me a frown. \"She has no intention of providing any help, so I'll not be bothered with the likes of her. Come on, I've had enough of this place. Let's be on our way.\"\n\n\"Ever patient.\" I snickered. \"I'll let Lady Arnifour know.\"\n\n\"Tell her we won't likely be back for several days. I've had quite enough of this brood for right now,\" he grumbled.\n\nI sighed. \"She won't like that\u2014\"\n\nHe scowled as he headed for the door. \"I'll solve this case, but at the moment I don't really give a bloody bollocks what she likes.\"\nCHAPTER 7\n\nTwo days passed without Colin giving the slightest inclination of returning to the Arnifour estate. He had just gone off to seek his solace in a tub of hot water again when a sudden pounding drifted up from the front door. I strained to hear if it was Lady Arnifour come to rail at us for going missing for so long, but quickly caught the rapidly escalating tones of Mrs. Behmoth and either a young woman or boy. Whoever it was, they were fast matching Mrs. Behmoth's shrillness as their exchange rose up between the floorboards beneath my feet. \"Is everything all right?\" I called out.\n\n\"Does it sound like it is?\" Mrs. Behmoth hollered back.\n\n\"I 'ave ta speak ta ya. Ya gotta lemme up.\" It was a boy\u2014an East End boy.\n\n\"You'll be speaking to the back a me ruddy 'and if ya don't get yer blasted arse outta 'ere!\"\n\n\"It's all right, Mrs. Behmoth. Let him up.\"\n\nThe sound of footfalls racing up the stairs told me that the youth wasn't about to wait for a second invitation. He rounded the landing in a flurry of scrawny limbs and as soon as he saw me stopped and snatched the cap from his head, releasing a pile of stringy black hair that fell to his shoulders.\n\n\"Don't send me out 'til I say me piece,\" he pleaded.\n\nI waved him into the room and caught a sour whiff of him as he rushed over to shake my hand. This boy, somewhere between thirteen and fifteen, was at home on the streets, his ready manners notwithstanding. He was under someone's tutelage and I knew I would be wise to keep an eye on his hands while he was here. I signaled him to a settee at the same moment Mrs. Behmoth hollered up the stairs, \"Don't let the little shite sit on any a the furniture!\"\n\n\"If you please, Mrs. Behmoth!\" I growled back at her, offering an apology to the young man as he wandered over to the fireplace, twirling his cap in his hands. \"She means well,\" I bothered to say.\n\nHe shrugged. \"It ain't nothin'.\"\n\nI offered a smile as I gestured toward the settee again, taking my customary seat across from it, but the boy only shook his head. \"The lady's right, me clothes is dirty.\"\n\nI nearly choked on his use of the word \"lady\" to describe Mrs. Behmoth; this lad was well trained indeed. \"Furniture, like people, can be cleaned. Please make yourself comfortable.\"\n\nHe smiled, smudge marks on his cheeks separating like clouds before the sun. He headed for Colin's chair and I flung an arm out and said, \"There,\" like some monosyllabic cretin as I gestured to the settee again. \"If you don't mind,\" I added.\n\nOffering an easy smile, the disheveled youngster happily settled himself onto the couch Lady Arnifour had occupied only a few days prior, making me wonder what she would make of that. \"Me name's Michael,\" he said, jutting his chin out with pride.\n\n\"Michael . . .\"\n\n\"Jest Michael.\"\n\n\"Well, Just Michael, I'm Mr. Pruitt. I'm Mr. Pendragon's partner.\"\n\n\"Is 'e 'ere then?\"\n\n\"I'm afraid he's indisposed. Is there something I can help you with?\"\n\nHis face crinkled with confusion. \" 'E's wot?\"\n\n\"Unavailable. Busy. He won't be able to see you right now.\" The boy had finesse even if he lacked education.\n\n\" 'Oo er you again?\"\n\n\"Ethan Pruitt,\" I shot back. \"I'm Mr. Pendragon's partner. I've been working with him for the better part of a dozen years. Speaking with me is like speaking with him.\"\n\n\" 'Cept you ain't 'im,\" he pointed out.\n\n\"Ah,\" I smiled even though my patience was quickly thinning, \"you are a keen one. So go on, tell me why you've come.\"\n\nHe started twisting his cap again as he looked at me from beneath his lowered brow. \"It's me little sister,\" he said. \"She's gone missin'.\"\n\n\"Missing? For how long?\"\n\n\"Since Sunday.\"\n\n\"Six days?!\" Anything less than three wouldn't have warranted a second thought among those of the East End, but six days meant something, especially for a young girl. \"Did you notify Scotland Yard?\"\n\n\"They don't care nothin' 'bout us that lives in Whitechapel. One less ta trouble themselves with.\"\n\nOf course he was right. \"Has she ever disappeared before?\"\n\nHis eyes flitted about the room and I knew what the answer was. \"A day or two. Nothin' like this.\"\n\nI heaved a sigh, certain that she was either a pickpocket, prostitute, addict, or most likely all three. \"How old is she?\"\n\n\"Twelve.\"\n\nI cringed. \"Do you have a room in a boardinghouse somewhere?\"\n\n\"Yeah. Up near Stepney Green. We got a corner of the basement 'bout the size a yer entry run by an old slag wot thinks it were a palace. She don't treat nobody good 'cept them she calls 'er gentlemen callers. A bunch a drunken sots she gets upstairs and rolls. She's wicked clever though. Keeps a mess of 'em on a string.\"\n\nHow well I understood the woman he was describing, for I had spent years under the thumb of someone like that myself. \"Tell me about your sister.\"\n\n\"Angelyne.\" He smiled. \"Named after the angels.\" He described her as a freckle-faced girl with raven black hair who was not quite five feet tall. He said she was slight and hadn't even begun to reveal the shape of the woman she was on the verge of becoming. I only wished that might make a difference. \"Last Sunday I 'ad ta go out for a while. I 'ad things ta take care of. I told her not ta go anywhere, but when I got back . . .\" He dropped his eyes and rubbed the heels of his hands across them.\n\n\"Does she disobey you often?\"\n\n\"Naw. She's a good girl. Never causes no trouble.\"\n\n\"Did you ask the woman who runs your boardinghouse if she saw or heard anything?\"\n\nHe screwed his face up. \"That one don't 'ear nuthin' but 'erself mewlin' at all the men she drags 'ome.\"\n\n\"Do you remember Angelyne complaining about anyone bothering her lately?\"\n\n\"I'd a killed 'em if she 'ad. You can bet yer arse on that,\" he blasted back, and I didn't doubt him. \"So will you 'elp? You and Mr. Pendragon?\"\n\n\"I'll have to speak with him.\"\n\n\"Ya want I should wait?\"\n\n\"There's no need for that.\" I stood up. \"Just tell me how we can get in contact with you. What's the address of your boardinghouse?\"\n\nMichael got up and stabbed his cap back onto his head. \"It'll be easier if I come by tamorrow evenin'. That okay?\"\n\nI eyed him a moment, wondering whether his reticence was directed toward me or his own bit of subterfuge. \"That'll be fine.\"\n\nI showed him out with a promise to receive him in twenty-four hours' time, all the while thinking how young he was to be dealing with such matters. It was a disgrace that this was the best our city had to offer these children, but then I was reminded that sometimes we create our own worst times.\n\n\"When ya go back up . . . ,\" Mrs. Behmoth poked her head out the kitchen as I relatched the door, \". . . tell 'is Majesty not ta use up all the 'ot water. I wanna take a bath meself tonight.\" She punched her fists onto her hips. \"And 'urry up. 'E's 'ad it runnin' awhile.\"\n\nI tossed her a frown as I padded up the stairs and went to the bathroom. \"It's me,\" I said as I poked my head inside.\n\n\"Don't let the cold air in.\" He was reclining in his liquid cocoon, a dozen candles scattered about, flickering a warm embrace.\n\n\"I've been commanded to tell you not to use all the hot water.\"\n\n\"Ah. Dear Mrs. Behmoth. I would hate to begrudge her the occasional bath.\" He rotated the spigot with his foot. \"I think I'll require your warm body to keep the water heated up then. Climb in and tell me who was just here?\"\n\n\"There's hardly room for two,\" I protested halfheartedly.\n\n\"Don't I always make room?\" He sat up and patted the water as though it were the cushion of a chair. \"Come on.\"\n\nI did as bade, pleased to note the change in his mood and hoping that it might signify progress around the Arnifour case.\n\n\"Much better,\" he said as he rested his chin atop my head with his arms hanging about my shoulders. \"Now tell me who was here and I shall pay close attention.\" But he didn't pay attention, and after a few minutes I stopped trying to tell him anything at all.\nCHAPTER 8\n\n\"Who let you out of your hole, Pendragon? I'd like to know to whom I owe the displeasure of your company.\"\n\n\"Oh, come now, Inspector.\" Colin sidled up to the man's badly beaten desk piled high with its array of papers and binders, and plopped himself into the creaky chair beside it. \"I've just come from a bit of sparring at the gymnasium. Worked my aggressions out. You should try it.\"\n\nHe snorted. \"We'll see if that even lasts the length of this conversation. What are you here for?\" He glowered, his naturally opaque complexion deepening. Given his dazzlingly white hair he looked positively monochromatic except when moved to a mood. Tall and thin, Emmett Varcoe was the complete opposite of Colin in both form and function in spite of their shared passion for detection. \"You'd best make it quick because I haven't time for you,\" he added, rotating his chair so that we were left staring at his profile.\n\n\"Really now . . . ,\" Colin replied with a snarky smile. \"We've only come to share some information.\"\n\n\"Oh, I'll just bet you have.\" He swung around just as I sat down. \"Don't get comfortable, Pruitt. The two of you are not staying.\"\n\n\"Not to worry.\" Colin leaned forward mischievously. \"We're only here to let you know that we've been hired by the bereaved Lady Arnifour to solve the murder of her husband. I thought it only fair to\u2014\"\n\n\"Bloody hell!\" Inspector Varcoe bellowed, slamming a fist onto his desk. \"That case is practically solved. Why is that ridiculous woman wasting her money on you?\"\n\n\"Well, I should hardly consider it wasting\u2014\"\n\n\"Piss off, Pendragon. We're about to make an arrest. Nobody needs you slinking around stirring up a bunch of bollocks.\"\n\n\"About to make an arrest, are you? That's not always worked out so well for you in the past\u2014\"\n\n\"How dare you!\" he blasted, his voice elevating with the color of his face. \"You pompous little twat. What do you know about working a crime? You're just a coddled diplomat's boy who attended independent schools and probably never even let his sacred little feet touch the streets of Bombay. How dare you come in here and look down on me.\"\n\nI could see that Colin's posture had become rigid as he said, \"A bit jumpy about this case, are you?\"\n\nThe inspector turned a steely glare on Colin. \"If you're here to share, then what have you got so far?\"\n\n\"Not that much, really.\" He gave a tight smile. \"Though I did notice a rather pointed lack of emotion regarding the Earl's death on the part of everyone in the household\u2014with the possible exception of the housekeeper, Mrs. O'Keefe.\"\n\n\"That old toad.\"\n\n\"Ah . . . ,\" and now he chuckled, \"I must agree with you there.\"\n\nThe inspector did not share his amusement. \"What else?\" he growled.\n\n\"Well . . .\" I watched Colin pretend to ruminate a moment and fought to keep from rolling my eyes. \"I believe Victor Heffernan is innocent.\"\n\nThe inspector's left eye ticked almost imperceptibly as he managed to maintain his composure with a shrug before allowing, \"Perhaps.\"\n\n\"And I've a suspicion that Lady Arnifour has some notion about who may be involved.\"\n\n\"That's absurd.\" He waved Colin off.\n\nColin shrugged lightly as he dug a crown out of his pocket and effortlessly began rotating it between his fingers. \"I'm betting you're circling Nathaniel Heffernan.\"\n\n\"Damn right,\" the inspector sneered with pride. \"That Heffernan boy did this and his father ruddy well knows it too. That's called collusion.\"\n\n\"But what of his motive?\"\n\n\"Motive?! Bugger off about his motive. I'm not telling you anything, Pendragon. It'll be my pleasure to see you looking the fool on this one. Now piss off.\" And with a flourish of rattling papers Emmett Varcoe let it be known that our time with him was done.\n\n\"Very well.\" Colin palmed the coin as he stood up and gave a nod that Inspector Varcoe took no note of. \"Perhaps you're right.\"\n\n\"Oh, I'm right.\" He spun back on us. \"You watch and you'll see him deliver his son right into my hands.\"\n\n\"Victor Heffernan? Deliver Nathaniel to you? Why would he do that?\"\n\n\"Because in a few days when I arrest them both, he'll give the boy up like a rotten apple. That type would eat their young if they thought it would help.\"\n\n\"That type?\" Colin's voice sank precipitously.\n\nVarcoe sneered at us. \"You know exactly what I mean, Pendragon. Street rubbish like Pruitt here. They never lose the stink.\"\n\n\"You know bloody well Ethan was raised in Holland Park!\" Colin snapped back. I reached over and clutched his sleeve, not wanting him to do this, but he only shrugged me off. What nettled me was wondering whether he felt compelled to do it for my benefit or in defense of his own honor. \"His father was the Deputy Minister of Education. Which makes Ethan a damn sight better bred than you, Emmett.\"\n\n\"All the same.\" Varcoe's face lit up with a satisfied smile, clearly well pleased to have riled Colin so. \"My ruddy mum didn't go bleedin' starkers and off everyone. What kind of man lets his wife do that? Is it any wonder your Pruitt ended up a sniveling addict in the East End?\" His grin widened. \"He comes from rubbish all right.\" He burst into harsh laughter as my heart seized and my stomach dropped below my feet. I opened my mouth to say something, to defend myself\u2014my father\u2014when I caught sight of Colin balling his fist out of the corner of my eye, so instead grabbed him and yanked him out of there.\nCHAPTER 9\n\nWithin the hour we were back in our flat, dinner behind us, Colin fussing over tea while Mrs. Behmoth tried to coerce a fire back to life by poking at its cinders and kindling, her annoyance evident in her every muttered curse. Colin handed my tea to me with a sigh. \"You must do me a favor in the future,\" he said as he settled back into his overstuffed chair. \"If I ever tell you I want to visit that old bastard again, please remind me how I despise him.\"\n\n\"That may be so, but you can still be quite charming when you choose.\" I peered at him over the rim of my cup. \"At least until he starts taking out after me. I'm sorry I embarrass you.\"\n\nHe stopped and glared at me a moment before quickly downing his tea as he stood up and snatched at his dumbbells. \"It's not me,\" he mumbled with seeming preoccupation. \"I'm angry for you.\"\n\n\"Then you're wasting your energy. I cannot change the regrettable choices I made as a lad. After what happened I was afraid I might be the same. I was bloody well terrified. You know that. I went and hid in the only place that allowed me to truly dispel my fears: the opium dens.\"\n\n\"Don't say that. It makes you sound weak.\"\n\n\"I was!\" I shook my head, not embarrassed, but ashamed. \"I was not quite ten years old when it happened. My grandparents were thick with guilt and about as afraid of me as I was of myself. I wasn't in their house much more than a year before they couldn't stand having me around anymore.\"\n\n\"That's ridiculous,\" he chided, waving the weights around madly.\n\n\"It isn't. That's why they sent me to Easling and Temple. To get me out of their house.\" I heaved a sigh. \"I'm sure it also helped them assuage some of that guilt by affording me such a fine education, despite my squandering of it. And it did allow me to meet you.\" A small smile easily crossed my lips. \"I thought you so self-assured and handsome.\" I chuckled. \"Of course that only terrified me more. And you didn't even know I existed.\"\n\n\"I knew who you were,\" he protested without conviction before suddenly turning on Mrs. Behmoth, still cursing at the flagging embers. \"Do you need a ruddy hand with that?\" he barked.\n\n\"Don't get cheeky with me!\" she growled back.\n\nI shook my head. \"Well, no matter. Though I do wish it hadn't taken you nine years to rescue me from Maw Heikens.\"\n\nHe screwed up his face, halting the weights in midair. \"That regrettable old harridan,\" he snarled. \"I won't have that name in this flat.\"\n\nThere was no surprise in his reaction. He always hated Maw. I suppose it was easier to blame her for what had happened to me than to blame me. \"What I really want to know,\" I said, content to let that topic be, \"is why we went to see Varcoe in the first place?\"\n\n\"For the information,\" he muttered blithely as he settled back into his chair and began curling the dumbbells behind his head.\n\n\"Information? What information?\"\n\nHe glanced over at me as though I were daft. \"We now know that his suspicions toward Nathaniel are wholly rudimentary, without the slightest whiff of a motive. You saw how he acted when I pressed him. I'll bet his entire case rests on nothing more than his own speculations. Once again he has proven that he owes his endless tenure at the Yard to his inability to intimidate the lesser minds who have risen above him.\"\n\n\"Brutal.\" I chuckled. \"But what do you mean about his suspicions against Nathaniel?\"\n\n\"The boy is gruff, uncommunicative, and so clearly hiding something that he couldn't possibly appear more culpable if he had been found beating the Earl. And then there's that bit about how he fancies Elsbeth. I can't stop wondering about the argument they had that night. Jealousy is a potent motivator for the worst in a man.\"\n\n\"But it doesn't make sense. He works for the Arnifours, for heaven's sake; how could he ever think that he might have a chance with her? It's too preposterous.\"\n\nHe tipped one of his dumbbells toward me. \"Then what do you suppose happened that night?\"\n\n\"I'm sure I haven't the slightest idea, but there's a lot more rotten out there than just that old house.\"\n\n\"Ach,\" Mrs. Behmoth groused. \"It's always that way with them that has too much money.\" She abruptly reached up, seized my Jules Verne novel off the mantel, and flung it into the still-sputtering fire.\n\n\"My book!\" I leapt up, spilling much of my tea onto myself. \"What the hell are you doing?!\"\n\n\"I'm tryin' to get this bloody fire goin'!\" she barked. \"That book's twaddle. It'll do a lot more good in there.\"\n\n\"You'll buy me a new copy,\" I shot back as I tried to blot the stains from my clothes.\n\n\"Like 'ell,\" she answered, pointing to the quickly escalating flames. \"It served a fine purpose. I don't owe no one nuthin'.\" A knock at the door was the only thing that kept me from responding in kind. \"Don't trouble yerselves,\" she said as she headed for the staircase. \"Allow an old lady the pleasure of fetchin' that.\"\n\n\"Absolutely.\" Colin chuckled.\n\nMrs. Behmoth shot him a withering glare, which he took no notice of as he shoved the dumbbells under his chair, and then she disappeared down the steps.\n\n\"Are we expecting anyone?\" he asked.\n\n\"I'd guess it's that scruffy East End lad with the missing sister I was telling you about yesterday. He said he'd come back this evening.\"\n\n\"Oh yes. What are their names?\"\n\n\"Michael and Angelyne.\"\n\n\"That's right. Very Church of England.\"\n\nThe thunderous footfalls of Mrs. Behmoth's ascension brought a halt to our conversation. \"Yer alley cat is back,\" she announced, glaring at me.\n\n\"Well, let him up!\" I snapped, only to be surprised when he suddenly poked his head out from behind her. I was appalled that he'd heard her disparage him.\n\n\"Do come in.\" Colin swept past me and ushered him into our study. \"We've been expecting you.\"\n\n\"Thank you, sir,\" he said as he doffed his cap and nodded at me. The smudges on his face had been scrubbed away to reveal a fragile complexion, which also exposed the hollowness in his cheeks. He went back to the settee and balanced himself on the edge of it just as he'd done the evening before. \"Tell me, Michael,\" Colin settled into his chair as Mrs. Behmoth trudged back downstairs, \"when exactly did you last see your sister?\"\n\n\"Ye'll take the case then?\"\n\n\"We are at your behest.\"\n\n\"Wot?\"\n\nI leaned forward. \"He's taking the case.\"\n\n\"Oh, ruddy excellent,\" he said, his face lighting up for just an instant. \"Ya know I ain't gonna be able ta pay ya much.\"\n\n\"You needn't pay us at all. You shall have us for free.\"\n\n\"Ya mean that? I don't gotta pay?\"\n\n\"You can't very well spend what you haven't got.\"\n\n\"I'd get somethin'.\"\n\nColin held up a hand. \"That won't be necessary. On occasion I do a service for someone in need, and today you are that someone. Perhaps you will return the favor one day for someone else.\"\n\n\"I will.\" He smiled broadly. \"You bet I will.\"\n\n\"Now, tell me about your sister,\" Colin said, surreptitiously extracting a crown from his pocket and smoothly flicking it through his fingers.\n\n\"Angelyne. Like the angels. And she is one too. A reg'lar angel. The last time I saw 'er were a week ago. I'd left 'er in our room and told 'er ta stay there, but when I got back she were gone. I ain't seen or heard nothin' from 'er since and that ain't like 'er.\"\n\n\"I see. Did anyone at your boardinghouse hear or see anything?\"\n\n\"No one saw nothin'. Least not wot they tell me.\"\n\n\"What time was it when you left her alone?\"\n\n\"Middle a the afternoon. Round two or three, I suppose.\"\n\n\"And when did you return?\"\n\n\"Suppertime. I brought food with me. I knew she'd be 'ungry.\"\n\n\"So you went up to your room . . . ,\" he prodded, his coin continuing to make its silent rotations.\n\n\". . . And she weren't there. Just like I said. Our room ain't big. I knew right away she were gone. I knew it soon 's I opened the door.\"\n\n\"And what did you do?\"\n\n\"I went to see me landlady.\"\n\n\"And did she know anything?\"\n\n\"Nah.\" He swatted his cap on his knee. \"She's a cur, that one. She don't 'ear nothin' but the sound a men with a pocketful a change.\"\n\n\"I see. And did you talk to anyone else in your building?\"\n\n\"Me and Angelyne keep ta ourselves. I don't know nobody else. I knew she 'adn't gone ta see none a them. She 'ad no business with any of 'em.\"\n\n\"One last question then.\" He held the coin up in front of his face and seemed to be admiring its luster. \"Did she mention anyone bothering her lately? Following her around?\"\n\n\"I'd a killed anyone was messin' with 'er.\"\n\n\"I trust you mean that figuratively.\"\n\n\"Wot?\"\n\n\"We'll need to come over and have a look around. And I'll want to speak with your landlady.\"\n\n\"You kin try speakin' to 'er, but she'll only wanna take ya fer a grinder.\"\n\n\"Then she'll be sorely disappointed.\" He stood up. \"What's her name?\"\n\n\"Rendell.\"\n\n\"Fine. Leave us directions and expect to see us tomorrow. We shan't waste time given how long it's been.\"\n\nMichael stabbed his cap back on as he bounced up and started for the door. \"I've got a bit a business ta run in the mornin', but I'll be round. Specially if I know yer comin'.\"\n\n\"We shall be there.\"\n\n\"Thank ya, sir.\" He bowed regally, his studied polish commendable if suspect.\n\nColin smiled and nodded his head. \"Until tomorrow then.\"\n\nThe lad bounded off down the stairs, a lightness in his step that had not been there before.\n\n\"Is that ragamuffin gone?\" Mrs. Behmoth hollered up as soon as the front door slammed.\n\n\"That's our new client you're disparaging,\" Colin called back.\n\n\"Ya must be starkers,\" came the muffled reply.\n\nHe chuckled as he settled back in his chair and began flipping the crown through his fingers again. \"What do you make of that?\"\n\n\"Are you kidding? I know that boy. I used to be that boy. He's too practiced. Too slick. I'd wager he's up to something.\" While I knew Michael couldn't be driven by the same demons I had been, any boy scraping by on the streets of the East End knew how to get what he needed. You either learned it or became a statistic. I had certainly done it, for a while anyway, and it seemed obvious to me that this lad was very much more savvy than I had ever been.\n\nColin stuffed the coin back into his pocket and rolled the dumbbells out from under his chair again, seizing them and curling them along his sides. \"When you say you know that boy . . .\"\n\n\"Well, I don't mean literally.\"\n\n\"Of course. But don't you think what he said sounds plausible?\"\n\n\"Certainly it sounds plausible. It needs to sound plausible. The question is, how much of what he's saying is true?\"\n\n\"You don't think his sister is missing?\"\n\n\"I don't doubt she's missing, but I'm not so convinced it was on a Sunday afternoon when she was supposed to be waiting at home like a good little waif.\"\n\n\"What difference do the details make?\"\n\n\"Well, it won't be very easy to find her if we don't know the truth of her disappearance. He could've prostituted her to the wrong man, or lost her in an opium club, or had some scam go sour only to see her carted off by an infuriated mark determined to get his revenge. I know that life.\"\n\nThe weights buzzed back and forth as a smile slowly snaked across his face. \"You're making this personal. Just because you were always up to something doesn't mean every urchin is.\"\n\n\"I was never an urchin,\" I sniffed. \"Highborn and -bred, and you know it.\"\n\n\"That's not what I meant,\" he dismissed. \"And anyway, that only makes it worse.\" He stood up and rotated the weights so that they surged against the broadness of his chest. \"But I don't disagree with you. I also suspect that something is missing from the story. A young girl doesn't simply disappear in the middle of the afternoon without somebody seeing or hearing something. Indeed, that viral-sounding landlady would seem a prime suspect for both access and opportunity.\"\n\n\"I think he makes too much of a fuss about her. After all, she lets them live there. If it weren't for her they'd both be in one of those Dickensian orphanages.\"\n\nHe paused and stared at me, the weights held out perpendicular to the floor. \"You're just saying that because of the old slag who took you in. What was her name?\"\n\n\"Maw. Maw Heikens.\"\n\n\"God, I hate that name.\"\n\n\"Will you be wantin' more tea?\" Mrs. Behmoth shouted from the bottom of the stairs, and for once I was glad she did so. Our conversation was headed for an unfortunate place, making her interruption divinely inspired.\n\n\"Please,\" I called back, thankful to hear the jostling of china as she immediately began her ascent. I met her at the top of the stairs and took the tray from her as she followed me back into the room.\n\n\"Must ya get yerself all worked up in 'ere?\" She scowled at Colin. \"Ya sweat all over the carpet and it leaves stains. Yer like a bloody drudge.\"\n\n\"I am a fine specimen of health and vitality,\" he answered, nevertheless setting the dumbbells aside.\n\n\"Ya need more fat on ya. Ya oughta 'ave a bit a roundness by now like any good man.\"\n\nColin screwed up his face as he went back to his chair and grabbed a fresh cup of tea. \"Perish the thought. But what I'd really like to know is why you agreed with my earlier assessment of rotten things at the Arnifours'?\"\n\nShe leaned over and carefully brushed off the settee where Michael had been before she sat down and slid her well-worn slippers from her swollen feet. \"I 'ear things. Everybody says the son's a drunk, the daughter's a harpy, and the ol' lady's been flauntin' about with 'er stable man fer years. She got no use fer that 'usband a 'ers.\" She shook her head. \"But who can blame 'er? I 'eard that Earl was 'avin' it off with some chippy. A woman never cheats first, ya know. It ain't in our nature.\"\n\n\"I'm sure we could disprove that without much effort,\" Colin said. \"The most perfunctory peek into just about any titled family would garner us a host of women every bit as lascivious as their male counterparts.\"\n\nShe waved him off. \"Ya don't know shite about women.\" She stood up and wriggled her toes a moment before stooping to pick up her slippers. \"There's a difference between lyin' and cheatin'. Women are better liars than men\u2014which is why we don't think a cheatin' first. It's nature's way a creatin' balance.\" She padded across the room, her slippers swinging at her side. \"Now I'm gonna go soak me feet. Some of us don't spend 'alf the day on our arses.\" And with that final bit of truth she trundled out the door and down the stairs.\n\n\"Sometimes it's hard for me to believe she raised you from boyhood. What was your father thinking?\"\n\n\"I'm afraid I didn't give him much choice. I suppose I was a bit hardheaded back then.\" He laughed.\n\n\"Back then?!\" I laughed.\n\n\"Well, you must admit, given the amount of gossip she picks up we almost could've stayed home the other day and learned as much about the Arnifours as we did going all the way out there. Though I did learn a great deal poking about their barn.\"\n\n\"Did you? And is that what makes you so sure Victor is innocent?\"\n\n\"I think Victor is innocent because he believes his son is guilty. And perhaps he is. I don't know yet. But the only thing Inspector Varcoe is going to succeed in doing is forcing Victor to confess to a crime he didn't commit in some misguided effort to save his boy. Which is precisely why Lady Arnifour hired us. She means for us to keep her dear Victor out of the hangman's noose.\"\n\n\"But if she suspects who did it, why wouldn't she just tell us and be done with it?\"\n\n\"Why indeed?!\" He toasted the air with his teacup, grinning at me from over its rim.\n\n\"So just what did you learn at that barn?\"\n\n\"I gathered a few details of the attack by poking through its remnants. As Victor pointed out and I'm sure your nose assured by virtue of the residue of kerosene, that fire was deliberately set. I should think the only reason someone would purposefully burn down an old, seldom-used barn would be to hide something.\"\n\n\"Or perhaps to throw off the authorities. It could've been set for no other reason than as a diversion.\"\n\n\"That's true.\" He stroked his chin and snatched up his hunting knife and kerchief. \"The only problem with that idea is that someone went to an extreme amount of trouble to make sure the barn burned all the way down to its barest bones. Think of it, our killer follows Elsbeth that night on his own horse. I'm certain of that given the second set of hooves left at the precise locations where both the Earl and Elsbeth were set upon. Which means this second person watched as Elsbeth met up with the Earl somewhere along the way, helped him up onto her horse, despite Lady Arnifour's insistence that he couldn't have done so, and then followed the two of them down to that barn.\"\n\n\"How can you be so sure the Earl was able to get up on her horse?\"\n\n\"The same tracks.\" He stood up and went to the fireplace, his brow furrowed and his hands working madly on the sheen of the knife blade. \"There were only two sets of horse prints evident near the barn. One set deeply imbedded in the earth\u2014a horse bearing the weight of two riders\u2014the other very much lighter. It was the second set, the lighter tracks, that I followed in order to discern the short distance the Earl was able to run before being struck down. The first blow came from atop that second horse. Once he'd fallen, the rider dismounted and delivered the mortal wound.\"\n\nI swallowed hard, chilled in spite of the firelight dancing off the sides of my face. \"And Elsbeth?\"\n\n\"Also struck from above.\" He set the knife onto the mantel and gazed into the fire, his eyes gradually unfocusing as he stared at the gently licking tongues of flame. \"But she'd gotten quite a bit farther by the time the killer turned his attentions on her. She was heading in a forty-five-degree angle away from the barn, back toward the woods. The killer remounted his horse, chased her down, and struck her full in the face.\"\n\n\"Good god . . .\"\n\n\"Indeed. And then . . . ,\" a scowl crossed his face, twisting it with confusion, \". . . after all that, the killer went back to the barn, saturated it with kerosene, and set it ablaze. If he meant only to confuse the boorish inspector and his sycophants he could have tossed in a match and fled. It was old; it would have burned just fine. But that's not what he did. He took the time to deliberately soak that decrepit pile of timbers, so much so that nearly two weeks later it still reeks of kerosene. Why? It has to be more than sleight of hand. There has to be something we aren't supposed to find.\"\n\n\"But what? What if it is just a deception?\"\n\nHe slid his eyes back to me. \"That is the question then, isn't it?\"\nCHAPTER 10\n\nWe disembarked from a cab the next morning earlier than the sun could be expected to properly infiltrate the streets and alleyways edging the tall, grimy brick buildings of Stepney Green. We'd set out from our flat at just after six thirty, which meant it couldn't be more than half past seven by the time we stepped onto the filthy cobbled street.\n\n\"Where do we go from here?\" Colin asked, sidestepping some filth. \"Wouldn't you think they could clean these streets once in a while,\" he added irritably.\n\n\"Spoken like a man who never comes to the East End.\" I chuckled. \"It's over there.\" I pointed toward an alley distinguished by a soot-covered arch. \"But we'll be lucky to find anyone willing to answer the door at this hour.\"\n\n\"The whole point . . . ,\" he explained, delicately picking his way, \". . . is to catch these fine citizens unprepared. Lying is so much more difficult when one is still suffering the scourges of the previous night.\"\n\n\"Certain we'll be confronted by lies then?\"\n\n\"Absolutely.\"\n\n\"Then it's good to see you've learned something from my tenure here,\" I chided.\n\n\"Learned something?!\" He scowled at me. \"I saved your ass from this scourge.\"\n\n\"Yes,\" I said with all seriousness as I pulled up short. \"You did.\" And so he had. At the moment when I was more bone than flesh. When opium's numbing embrace soothed me more utterly than air or water, relentlessly driving every moment of my day and night, he had quite suddenly been there. That fierce, striking boy from the Easling and Temple Senior Academy who I was sure had not known my name had indeed, inexplicably, saved my life.\n\nI gestured to the dingy brick tenement building in front of us enshrouded in soot from its belching chimneys. \"This is it.\" The entrance door was constructed of warped slabs of wood that appeared to have begun cracking long before Victoria took the throne, and was fouled with unimaginable matter. Distorted, yellowed windows dotted the face of the five-story structure, none without a spider's web of cracks.\n\n\"I don't believe for one minute,\" Colin said as we stared at the building, \"that no one in this hovel saw or heard anything. The business of others is the prime entertainment here.\"\n\n\"Only until the sun has ambled off. Shall we?\"\n\n\"After you.\" He waved me on. \"But let us start with the landlady. I'm most eager to disrupt her day.\"\n\n\"You don't think we should see Michael first?\"\n\n\"I'd much prefer to meet the proprietress of this fleapit. Call it a whim . . . call it morbid curiosity . . . but let's call on her first.\"\n\nI pushed through the fouled remnants of the door with the cuff of my sleeve and stepped into a musty hallway that was redolent with the scent of stale opium. It struck me like a blow to the face, beguiling my senses with a promise I had long thought relegated to a distant past. I must have faltered, because I felt Colin's hand grip my arm and heard him whisper, \"You all right?\"\n\n\"I'm fine.\"\n\n\"You don't have to do this,\" he said as I plodded forward. \"I can speak to her myself.\"\n\n\"I'm fine,\" I said with greater determination as much to convince myself as him. I would not let that fiend manipulate me again. It could have no effect. I'd come too far, been through too much, to be lured by that beast anymore. So I turned my attention to the two dimly lit lamps and the threadbare carpet worn through to the under-planking in places as I kept moving forward. I banished the fact that the walls were stained yellow with age and opium smoke from my mind as I stepped to the first door I came to, noticing that it was standing the slightest bit ajar due to the bow along its spine that left it gaping at its outermost corners, and announced, \"This has to be it,\" though, in truth, I was only guessing.\n\n\"Good,\" he said, staring at me a hair's breadth too long before adding, \"Then let's have at it.\" He stepped forward and pounded on the door with a bellowed, \"Hellooooo! . . .\" like some busybody neighbor come to call.\n\nAn instantaneous response blasted back in a shrill tone that sounded like a cat who'd just had its tail crushed under a boot. \" 'Oo in 'ell?! . . . Oo in the bloody 'ell . . . ?!\"\n\nI slid my eyes to Colin and found him wearing a dazzling smile of great joy. This, I realized, was exactly what he'd been hoping for.\n\nThe door jerked open as far as its accompanying chain would allow and a bloodshot eye presented itself in the space. \"Oh! . . . A minute, love. . . .\" The door clicked shut as best it could and the chain was hurriedly released before it was thrown wide to reveal a thin woman of indeterminate age\u2014though I guessed her to be somewhere in her mid-thirties like me. She was tightly wrapped in a thin yellow robe that revealed more of her anatomy than was proper. \"Didn't know I 'ad such a 'andsome gentleman calling.\" She leered, batting her eyes a moment before spotting me. \"This with you?\" she asked halfheartedly.\n\n\"Quite.\"\n\n\"Well, ya can both come in,\" she stepped aside, \"but I ain't one a those that plays it like that. I can take right care a you,\" she winked at Colin as he moved past her, \"but yer friend is gonna 'ave ta go upstairs.\"\n\n\"Particular, are you?\" I snorted as I crossed her threshold, glad to find the air inside her flat freer of the cloying scent of opium. \"You don't see that often around here.\"\n\n\"What would you know about what goes on around 'ere?\" she sneered as she yanked her precarious robe closed. Her pockmarked face spoke of years of disease and poor health, which instantly made me regret that I'd been so cavalier.\n\nColin gave her a warm smile, but there was little real mirth behind his eyes. \"What we're really here for . . . ,\" he began, casually perching on the arm of one of the proffered seats as he dug out his usual crown and started rotating it between his fingers, \". . . is some information about two of your tenants: young Michael and his little sister, Angelyne.\"\n\n\" 'Oo?\" Her face curled up as she poured two fingers of whiskey and downed it like a gulp of air.\n\n\"A boy of about fourteen and his sister . . .\" He flicked his eyes to me.\n\n\"Twelve,\" I said.\n\n\"Right. Twelve. They rent a room from you. Live in your basement. . . .\"\n\n\"Oh. Them two,\" she said with about as much enthusiasm as she'd shown me. \"They're always late with me rent.\" She downed another shot and actually looked a little better for it. \"You 'ere ta make good for 'em?\"\n\n\"Well . . . ,\" he tossed me a quick glance, \"we might be able to offer a little help. They owe you, do they?\"\n\n\"Damn right they do. One pound fifty.\"\n\nColin urged me with the look in his eyes and I begrudgingly handed over the money, all but certain that they didn't owe her a thing. She snatched the bills and stuffed them down the front of her robe. \"What do you wanna know about 'em?\" she said as she threw herself onto a well-worn chaise, sending a stream of undergarments and periodicals to the floor. \"That Michael can be a stand-up lad when 'e ain't scammin' the rent.\"\n\n\"And Angelyne?\" Colin pressed.\n\n\" 'Oo?\"\n\n\"His sister . . .\"\n\n\"Oh . . . 'er . . . She's about the size a me arm and as bright as me left tit.\"\n\n\"Is she comely?\" he pressed on.\n\n\"Oh!\" She abruptly pushed herself up, allowing her robe to peek open again. \"You like the young ones then, eh? The little girls?\"\n\nColin froze, the crown stilled on the back of his hand. \"The only thing I would like is to know whether you consider Angelyne pretty.\"\n\n\"Pretty . . . not pretty . . . 'oo can really say?\" She giggled. \"There's somethin' fer everyone in this world. There are men 'oo will shag anythin', breathin' or not.\"\n\n\"Have any of your clients asked about her recently?\"\n\n\"I don't know.\" She shrugged. \"I can't 'member everythin' goes on round 'ere.\"\n\n\"But you remember who pays and who doesn't,\" I pointed out.\n\n\" 'Ell yeah.\"\n\n\"And I'll bet you remember when someone asks for something unusual. Something you can't satisfy . . .\"\n\n\"There's a lot a nutters.\" She looked right at me.\n\n\"And is the request for a twelve-year-old not something out of the ordinary?\" Colin pressed.\n\nShe shrugged noncommittally.\n\n\"Miss Rendell\u2014\"\n\n\"Mademoiselle!\" she snapped back. \"It's French.\"\n\n\"My apologies. I didn't realize that Rendell was a French name.\"\n\nShe scowled at him and then abruptly bolted off the chaise and stormed across the room, pushing past me to yank open the door. \"I've 'ad enough a this. I don't get paid fer sittin' round talkin'. Now get yer arses outta 'ere.\"\n\nColin tossed the crown into the air and easily caught it, Mademoiselle Rendell's eyes locked on it the entire time. \"As you wish,\" he said tightly as we made our retreat back to the hallway. He turned at the threshold, eager to have the last word, but he had no such chance, as she immediately slammed the door in our faces. \"What a deplorable woman,\" he muttered to the battered wooden door. \"Though thankfully an atrocious liar.\"\n\n\"That's the truth.\" I nodded. \"It's a wonder she can be convincing with the blokes she entertains.\"\n\n\"Well, they can't be a discerning lot.\" He gave me a lopsided grin as he glanced at the dilapidated stairs that led down and let out a sigh. \"You still okay?\"\n\n\"I'm fine,\" I said for the third time since our arrival even as I was struck anew by that ubiquitous scent. \"Don't ask me again.\" But as I followed him down to the basement, I became increasingly aware of the familiar lure at the back of my brain, whispering . . . beckoning me . . . promising to distill every concern . . . and suddenly I wasn't so certain anymore.\nCHAPTER 11\n\nJust as we were sitting down to a lunch of Mrs. Behmoth's lamb stew there was a knock on our door that proved to be a messenger dispatched by Lady Arnifour, enquiring whether we would be available to meet with her daughter, Kaylin, in an hour's time. The timing was ideal, as we had decided that I would go back to Stepney Green in the late afternoon while Colin participated in his final elimination match of the current wrestling championships\u2014a title he was determined to maintain for the third straight year. It suited me fine since I knew I could move about that area of the city more expeditiously without him in tow and, beyond that, I'm not much of a fan of his brawling, even if he does insist it's all good sport.\n\nWe indulged in our stew and the accompanying biscuits with due haste before setting ourselves to preparations for the arrival of our guest. I tidied up the study, which consisted of straightening up my clutter of writing papers and dispatching the wayward pieces of Colin's pistol and knife collection back to their display cabinet, while Mrs. Behmoth put on a kettle and mixed up a batch of currant scones. For his part, Colin was tasked with stoking the fire back to life, which he dispatched forthwith before seizing his dumbbells and hoisting them about in myriad ways. In no time at all we were awaiting the arrival of Kaylin Arnifour to the rich, buttery smell of Mrs. Behmoth's scones baking beneath our feet.\n\nI found myself brought back to thoughts of Mademoiselle Rendell, who was about as French as blood pudding, and her insistence that she knew nothing about Angelyne's disappearance when it was clear she was far craftier than she was letting on. Which was the very reason I was to return there in a few hours' time. What she would not tell could be discerned in other ways.\n\nMichael had told us nothing new and it had been disturbing to see the way in which he and his sister were forced to live. Their single room was less than half the size of our study and contained neither a fireplace nor radiator with which to heat it in even the most perfunctory way. The plaster on the walls teemed with hairline cracks and great chunks of it were missing altogether. Two pallets lay on the floor for the children to sleep on and there was a single battered chair and equally sorrowful table upon which sat the room's only candle. It made for a depressing tableau in the sunlight and I only hoped it might somehow look better by the flickering glow of that one fatty taper. The sight of it all had left Colin quite maudlin while I had found myself grateful for ever having escaped, though the verity that I had come to be there of my own regrettable volition left me ashamed all over again. I was gratified that Colin had not raised that spectre again on our way home.\n\nA sudden knock at our door shook me from my prickly contemplation.\n\n\"I'll get it!\" Mrs. Behmoth hollered as her slippers slapped against the wood foyer.\n\n\"Outstanding.\" He chuckled as he set the dumbbells aside and pulled his jacket on. \"She does have everything to do with the man I am today, you know.\"\n\n\"Yes, but I do try to forgive her.\"\n\nHe laughed as the sound of her plodding up the stairs brought us to our feet. A moment later she appeared on the landing with a slight young woman at her side. \"Kaylin Arnifour,\" she announced with her usual lack of enthusiasm.\n\n\"Lady Kaylin . . .\" Colin smiled broadly as he moved to the landing and took the young woman's hand, ushering her inside. \"We do so appreciate your thoughtfulness in indulging us this meeting in the midst of such a difficult time. We would certainly not have requested it if we didn't feel it to be of the utmost importance. Please\"\u2014he beckoned her to the settee\u2014\"we were just about to have some tea. I insist you join Mr. Pruitt and me.\"\n\nI stepped forward to greet her and got my first good look at her. She instantly put me in mind of how her mother must have appeared as a young woman. Delicate and trim with a jumble of light brown curls cascading down her back, she was quite striking. She also displayed a hint of color in her crystalline complexion, and given her lithe, muscular arms revealed just below the puffy sleeves of her dress, I determined they spoke of her fondness for riding. They also gave her a more substantive air than her slender build initially suggested. While she and Eldon were clearly crafted from the same physical mold, he had none of his sister's gravitas.\n\nMrs. Behmoth gave a disapproving sniff as she turned to leave the room, though what she was objecting to I had no idea. \"I'll fetch the tea,\" she said as she thundered back down the stairs, giving me momentary pause as to how she managed to maintain her girth given the number of times she assaulted those steps each day.\n\n\"I must apologize for being so difficult to reach,\" Lady Kaylin said, thankfully setting my mind back to the task at hand. She settled onto the settee across from us. \"I really haven't felt much like talking.\"\n\n\"Understandable, and we shall not press you any further than we must.\"\n\n\"You mustn't worry about me,\" she said, folding her hands across her lap as though girding herself.\n\nMrs. Behmoth plodded back up with the tea service in hand but got no farther than the doorway before Colin relieved her of it, sending her on her way. He meticulously served us and did not speak again until we had all settled in. \"I must ask you to tell me what you remember about the night your father and cousin were attacked.\"\n\n\"Of course.\" She delicately placed her cup on its saucer and set them back on the table between us. \"I'm sure you've heard this all before,\" she said, giving a disquieted smile. \"We were having dinner: my parents, Eldon, Elsbeth, and I, and I had to excuse myself partway through the meal as I was not feeling well. I suffer from headaches that can be quite disabling. After a while Elsbeth came up to check on me and see if I might be able to go for a ride while there was still some sun left, but I was no better and could not.\" She fell silent for a moment, staring down at her hands. \"I've wondered every day since if things might have been different if I had been able to go with her.\"\n\n\"You mustn't,\" I said.\n\n\"It is not for us to change what is,\" Colin added.\n\n\"Of course . . . ,\" she muttered, but did not sound the least convinced. \"I fell asleep as soon as she left my room and did not wake again until I heard Eldon hollering about smoke at the edge of the property. It was terrifying. I hurried downstairs and saw him and the Heffernans riding out, and waited with Mother for their return. Victor was the first to come back. He was the one who told us. . . .\" Her voice trailed off.\n\n\"Had there been any visitors to the house that day?\"\n\n\"Father's business partner, Warren Vandemier, had spent part of the afternoon going over books or ledgers or some such thing with him, and a neighbor, Abigail Roynton, had stopped by and had tea with Mother.\"\n\nI could tell at once by the way she said Abigail Roynton's name that there had to be a bit of bad blood there. I was certain Colin caught it as well, but he did not prod her, choosing instead to shift the conversation to the nature of the business her father had with Mr. Vandemier.\n\n\"I'm sorry . . . ,\" she twisted her hands in her lap, \"but I wasn't really privy to my father's business dealings. I'm sure you're acquainted with those who say business matters are best left to men.\"\n\n\"Ahhh . . .\" Colin grinned. \"Are you one of Emmeline Pankhurst's followers?\"\n\nShe smiled. \"Well, I would hardly cuff myself to the gates of Buckingham, but I do think she has some wonderful ideas.\"\n\n\"She has certainly caught people's attention. Does your mother share your views?\"\n\n\"Oh heavens no.\"\n\n\"What about your neighbor, Abigail something, I don't recollect what you said her name was.\"\n\n\"Abigail Roynton,\" she scoffed without apology. \"She's a widow who saw fit to have an affair with my father some time ago, and if my mother had any sense she wouldn't let that wretched woman in her house.\"\n\nColin peered at Kaylin, his expression in check, while I fought to keep the surprise from my face. \"Are you certain your mother knew?\"\n\nKaylin nodded. \"At the very least she suspected. But she would never admit such a thing. It wouldn't be proper. So instead, she and Mrs. Roynton maintain this reprehensible charade.\"\n\n\"Civility,\" Colin tsked. \"If nothing else you have to admire our higher class for their civility. Is there no chance you could be mistaken?\"\n\nShe shook her head. \"I found them in the barn once, the two of them disheveled and full of bluster. It was a disgrace. I knew what they were up to.\"\n\n\"How long ago did that happen?\" Colin forged on.\n\n\"About a year ago, I suppose. I really don't remember. But he ended it after that. He swore to me that he ended it.\"\n\n\"Of course.\" Colin flashed a tight smile.\n\n\"I believed him, Mr. Pendragon. My father was many things, but he was not a liar.\"\n\n\"I'm afraid that by its very definition an adulterer is a liar. You cannot be one and not the other.\"\n\n\"I'm sure your father meant what he told you,\" I interrupted, shooting Colin a look that I hoped would divert him.\n\n\"Yes . . . well . . . I must ask you to indulge me one last question,\" he said as he tossed a scowl back at me.\n\n\"Of course.\"\n\n\"Do you agree with your mother's assertion that the Heffernans are innocent?\"\n\nShe paled and gave a small shrug. \"I really don't know.\"\n\n\"Then you believe it is possible that one or both of them could be involved?\"\n\nShe shifted on the settee and brushed a quick hand through the curls on one side of her face. \" 'Possible' is a word without limitation,\" she finally answered.\nCHAPTER 12\n\nThe afternoon was ebbing toward twilight as I tucked myself into an entranceway across the alley from where Michael and Angelyne lived, fixing my gaze on the flat where Mademoiselle Rendell plied her trade. Standing in the waning light with an old, black cloak wrapped around my shoulders, I felt like a fourteen-year-old boy again, once more in the questionable employ of Maw Heikens. This time sent out to lure another clutch of imprudent sots with more cash than cares, or to fetch another batch of opium from the old Chinese man at the wharf from which I always cleaved a nip off the top for myself, or perhaps to troll the local taverns to earn my keep with whatever I could pilfer. The memory of it all made my stomach sour as though I had licked the very cobbles in the street. For it was too easy to blame Maw for the things I had done, what I had become. But the truth was darker than that. She had merely provided what I sought without judgment or question. Colin was wrong about her, not entirely, of course, but wrong. There was much that remained solely on me.\n\nA cold wind teased my face and ruffled my hair as it brushed past me. The wind had picked up slightly and the chill along with it as I began to ask myself how long I was going to stand here like this. I knew Colin would expect me to wait all night if need be, but then he was in a warm gymnasium proving his bravado against any number of comers.\n\nAnother great sigh escaped my lips just as the light from Mademoiselle Rendell's room abruptly snuffed out, ratcheting up my heartbeat in the same instant. Something, at last, was going to happen. I sank back into the alcove as far as I could and waited for the appearance of my quarry. It did not take long. The main door quickly opened, revealing my target in a billowy cream-colored dress that had likely been white the day it came out of the dressmaker's shop, adorned with a ragged strip of gray lace around its bottom. A dark brown shawl covered her mass of dyed-blond hair. She was, I decided from the look of her, attempting to travel incognito. It was a hopeful sign.\n\nThe ersatz mademoiselle glanced in one direction and then the other before venturing down the handful of steps to the cobbled alley. She did not cast an eye in my direction and I knew the moment she made it to the street there would be little chance of her realizing she was being followed. There were too many people, horses, and carts about for her to notice me trundling along behind her, and besides that, I am not without some skill.\n\nThe mass of activity on the street made it easy for me to keep Mademoiselle Rendell in sight as I dallied along behind her. She kept to the center of the roadway, dodging the streams of burbling waste flowing through the gutters with assurance and a fair amount of speed. She held her gaze down as much for defense against the filth as to dissuade anyone she passed from trying to engage her. There was no doubt in my mind now that she was doing her best to get somewhere quickly and without distraction.\n\nShe rounded the corner and snatched a look in my direction, bringing me up short as I pretended to engage a woman who was passing beside me. I let the distance between us widen as I pulled a cap from my pocket and plopped it on my head before turning the collar of my cloak up. If need be, I could turn my cloak inside out to reveal a light gray color as opposed to the black I was now swaddled in, but it was not yet necessary, as she once again hurried down the street. Innumerable blocks slid by before I began to notice how vastly improved the neighborhood was becoming. We'd left behind the effluvium of Stepney Green for a far more gentrified area. Even the throngs of scurrying people had noticeably thinned, with fewer of them walking and more being trundled about in carriages and cabs, notable of gentility.\n\nIt wasn't until I noticed the divergent flags above the porticos of one building after another that I realized we had entered Embassy Row. That explained the lack of foot traffic that had forced me to gradually drop farther back from my prey. This area of the city was well patrolled and offered almost nothing in the way of diversion, neither shops, caf\u00e9s, nor any but the most occasional pub. It meant to be uninviting, this domain of diplomats.\n\nMademoiselle Rendell continued hurrying along the street, paying me little mind as I forced myself to fall back yet again. I couldn't imagine what we were doing here, as it was too early for her evening's work to have begun. I began to fear she was on to me, that she'd spotted me some time ago and was taking me on a circuitous route to nowhere, when she abruptly grabbed an old, unmarked door and ducked inside.\n\nWith trepidation I approached the door I thought she'd used, willing my heart to stay steady. There were no markings to allow me to determine just what sort of establishment it was, which left my options few. Either I had to forge ahead and stumble into this unknown or I could slink back home and admit to Colin that I had failed. Neither option appealed to me, but I certainly wasn't about to let Colin down.\n\nI girded my breath and leaned forward, gently nudging the door a sliver to give me a chance to try peering inside before making the final commitment. It took several moments for my eyes to finally be able to discern that I was staring into one of the more distinctive pubs I'd ever seen. The floor and booths were carved from great planks of dark oak, with the bar itself rent from a slab of honey-colored burl set off by etched-glass cabinets running along the wall behind. It was a small establishment with only a handful of booths and an equal number of freestanding tables, leaving most of the seating to wind around that spectacular bar.\n\nI flipped my cloak inside out and threw it over my arm before stepping inside and coaxing the door closed. The only light emanated from a few gas lamps dangling from the ceiling. A picture of Nicholas Romanov hung over the bar, though he had yet to be coronated, and two small flags with the double-headed eagle hung from the ceiling, making it evident to whom this pub intended to cater.\n\nI spotted Mademoiselle Rendell at once curled up in a booth near the back with a dark, bearded man. She seemed well in the throes of a rampant flirtation and it made me fear that all my efforts had been for naught. The nearer of her hands was already settled on the man's leg and her other was flitting about like a hummingbird in search of nectar.\n\nOnce again I sucked in a quick breath and steeled myself before moving to a barstool just beyond Mademoiselle and her mark. I ordered a stout and laid my cloak across my lap, turning sideways so I could better listen in on the conversation happening between the two of them. What I expected to hear I cannot say, but between the throaty giggles, playful slaps, and whispered innuendos I heard nothing less than the most blatant form of seduction.\n\n\"Yer makin' me 'eart pound like a race 'orse,\" she purred at one point. \"Care ta feel?\"\n\n\"I fear ze cost of such an act,\" her companion snorted, his accent thick and guttural, definitely a Slavic tongue but certainly not Russian, which surprised me given the bar's obvious allegiance.\n\n\"This one's on me,\" she parried back.\n\n\"Ve are done here,\" he answered, obviously not tempted by the course of her prodding. \"I leaf this veekend. You know vhere to find me if you have reason; udderwise I vill consider our vork finished until I return.\"\n\n\"And when will that be?\" she whined, all pretense of seduction dropped with the haste of a flicked ember.\n\n\"Zix months . . . eight months . . . I dun't know.\" I watched him reach out and take her arm, carefully removing her hand from his leg. \"You vill hear from me.\" He pushed himself out of the booth and gave a curt nod.\n\n\"I ain't 'appy 'bout this,\" she called, but it was too late, as the man had already made his way out the door.\n\nFor a minute I considered following her companion rather than staying here to watch what she might do next, but then another man approached her table and quickly slid in beside her. Given that it was she whom I was here to shadow I decided to stay put, though I committed the hairy Slavic man to memory, as I was certain their business dealings were nefarious at best. At least then, if I did return to our flat with little more than tales of her flirtations I would do so having been successful in the intent of my purpose.\n\nI casually nursed my stout and feigned a look of boredom and inapproachability so as not to be sidetracked by someone who might want to spill his every thought onto the first fool who looked like he was alone. My frustration quickly mounted, however, as I could hear little of the conversation with Mademoiselle and her new companion. If I had any hope of learning anything further I was going to have to find a way to twist around to see what the two of them were up to. I only hoped I would not turn to find them glaring at me.\n\nShoving my cloak onto the seat beside me, I slumped against the bar and peered around with what I thought was extraordinary restraint, only to find Mademoiselle Rendell slowly sinking beneath her table. A table that held no cloth atop it. Instantly it became apparent to anyone who cared just exactly what she was up to, so it was hardly surprising when I felt a great rush of air barrel past me as the establishment's owner brusquely moved in to save the reputation of his pub.\n\n\"Get out from under there!\" he growled. \"I'll not have such goings-on in me pub!\"\n\n\"For a quid ya can be part a the goin's-on,\" the unperturbed mademoiselle snorted from below.\n\n\"Piss off!\" her companion snapped. \"You're ruinin' me stiffy.\"\n\n\"I will not have this!\" the man thundered, pounding a meaty fist onto the table's top.\n\n\"Bugger!\" Mademoiselle Rendell bellowed as she came scuttling out. \"Ya 'bout broke me bleedin' eardrums, ya shite.\"\n\n\"Get out!\" he bellowed. And although the proprietor was no taller than the diminutive mademoiselle herself, he shook with such rage that neither she nor her burlier companion seemed willing to press him any further.\n\nThe two of them made their way out, the rest of the patrons holding their collective breath until the door swung shut behind them. Only then did the general murmuring start again, although this time with a renewed sense of vigor. I cursed myself for not having followed the Slavic man out. Surely her business with him had been more apropos than what I'd stayed here to witness. We were making scant headway on either of our cases and each day their trails were becoming fainter.\nCHAPTER 13\n\nMy failure to gain much information about Mademoiselle Rendell was tempered by the fact that Colin had won not only the wrestling tournament for his age group, but also the exhibition round against a man nearly fifteen years his junior. He gave me the glowing details before finally settling in and agreeing that the Slavic man was likely to prove a man of interest. Thereafter he left me on my own for the remainder of the evening while he retreated to the bath.\n\nWe had little interaction the next day as well and I knew he had withdrawn into his thoughts in an effort to ferret out the next best step. I'd suggested that perhaps I should try to find the Slavic man, but he'd dismissed the idea for the moment, and so it was that we were in our study late that afternoon; me reading while Colin paced relentlessly, incessantly disassembling and reassembling his new Nagant revolver, when there came a sudden and frantic pounding at our door. Colin spun away from the fireplace so quickly that the cylinder of the Nagant he'd been fussing over was launched from his hand in great cartwheels before coming to land across the room.\n\n\"Damn . . . ,\" he cursed as he hurried after it. \"If that got bent . . . ,\" he threatened rhetorically. I watched him give it a quick inspection as he went to the window and peered outside. \"It's the Arnifours' buckboard,\" he announced. \"Has to be one of the Heffernans. Nathaniel most likely. Victor would never have the audacity to pound on anyone's door like that.\"\n\n\"I wonder why he's here?\"\n\n\"We shall know soon enough,\" he said as he wrapped the pieces of the revolver into his handkerchief and laid them on the mantel.\n\nThe sound of two sets of shoes mounting the stairs drifted up as Colin took his seat next to me. A moment later he was proven correct when Mrs. Behmoth ushered Nathaniel Heffernan into the room.\n\n\"Nathaniel 'efferead ta see ya.\"\n\n\"Nan . . . ,\" he corrected sourly. \"Heffernan.\"\n\n\"If ya like.\" She shrugged and made her exit.\n\n\"I take it,\" Colin stood up, \"that you bring news?\"\n\n\"I do.\" He stared at Colin blandly and said, \"It's Miss Elsbeth.\" And at once I feared the worst. \"They're saying she's begun ta come round.\" There was little inflection in his voice.\n\n\"Extraordinary!\" Colin popped out of his chair. \"You must be anxious to get back and see how she's doing.\"\n\nNathaniel did not answer at once, and I wondered if he was trying to gauge whether there was any accusation in Colin's words. \"Is there any message ya want me ta take back?\" he finally said.\n\n\"No message . . .\" Colin slid a glance to me and then looked back at Nathaniel. \"What I'd really like you to take back is us.\" He didn't even wait for a response before he bolted down the hallway toward our bedroom.\n\n\"What?\"\n\n\"We're going with you, boy,\" he called back. \"Make yourself comfortable while we put a few things together, because this time we'll be staying. We shan't be but a minute or two.\"\n\n\"You will excuse me.\" I stood up and gave what I feared was a pained smile, as surprised as our guest by this unexpected turn of events.\n\nI hurried to the bedroom and found Colin rooting through the top drawer of the dresser. \"Prepare to spend a night or two,\" he said as he flung undergarments onto the bed. \"If she's coming around I'll not come back until we've had the chance to speak with her. I don't trust that house of rogues.\"\n\n\"House of rogues?!\" I chuckled as I pulled a valise from under the bed. \"Now you sound like Mrs. Behmoth.\"\n\n\"You're forgetting that someone there would almost certainly prefer to see her dead, and at this point it's rather impossible to tell who might be her friend and who her foe.\" He tossed me an arch look as he withdrew a small double-barreled derringer from the dresser.\n\n\"You're bringing a gun?\"\n\n\"I'd bring three if I could get you to carry one.\"\n\nI screwed up my face, the memory of once having had a derringer prodded against my ribs during a soured opium transaction causing me to shiver. Even that had not led me to forsake the drug, which is why I suppose the memory retains its ability to provoke such a reaction from me. \"Don't you think you're overreacting?\" I tried my best to sound glib. \"It's the estate of nobles. They're not all beyond redemption.\"\n\n\"And are you prepared to decide who is and who is not?\" He eyed me as he stuffed the little gun into his boot. \"Who is it you find trustworthy?\"\n\n\"What about Lady Arnifour? She hired us after all.\"\n\nHe waved a dismissive hand as he went over to the holster hanging from the headboard on his side of the bed. \"I'd bet she hasn't given a whit about her husband since she conceived their daughter, and they were both probably well plied with alcohol at the time. The only person our dear patroness seems to even remotely care about is Victor Heffernan, and even that impression is probably hysterically generous.\"\n\n\"Well, you have to admit that he seems kind and loyal.\"\n\n\"A dog is kind and loyal,\" he grunted. He pulled a Colt revolver from the holster and stuffed it into his waistband, yanking his overcoat closed atop it. \"Of course her husband was clearly a scurrilous man who had more dalliances with other women than his own wife. But then that is what those chaps do.\"\n\n\"Your father didn't.\"\n\nHe leveled a frown on me. \"The Pendragons are a cut above. Besides, my mother died too young. He didn't have the chance. Are you ready?\" He headed for the door.\n\n\"Ready?! I've hardly begun. And all you've done is throw a few things on the bed and litter yourself with guns. I'd say you're not ready, either.\"\n\nHe shrugged. \"I've got what I want. Throw in whatever else you think I might need.\"\n\n\"Fine.\"\n\nI heard him beckon from the front of the flat as I stuffed the last few things into the valise and tucked it under my arm. \"On my way!\"\n\nIt would be nice to come back to this room and have the worst of this case behind us or even solved. My eyes raked over Colin's empty holster and I felt that familiar knot clutch at my stomach. How I hoped we would return with his guns unneeded. I turned down the lamp on the dresser and headed out.\nCHAPTER 14\n\nThe evening was cold enough to make the ride in the open buckboard uncomfortable. Even so, Colin appeared oblivious to the wind's chilling fingers as they sliced across the exposed flesh of his face. The fire in his eyes seemed to be heating the whole of his body so that he wasn't even bothering with the scarf Mrs. Behmoth had pressed on him on our way out. In contrast, I was well wrapped in mine and noticed Nathaniel repeatedly yanking his collar closed. Given the potential turn in this case there was little wonder Colin felt so impervious.\n\nAs we pulled through the gates, catching a glimpse of the house on the ridge ahead, I was struck by how different everything looked under the cloak of night. The trees appeared menacing as they bent overhead like a sepulchral army of skeletal soldiers, their great withered arms only fleetingly allowing a sliver of moon to peek through. Then, quite suddenly, they gave way to a field of tall grass. Yet even that otherwise sanguine field stretched far off into a forbidding, black oblivion on either side of the driveway even as it seemed to threaten to press in on the house at any moment. I forced my attentions to the house and found that even it could not manage to suffuse any aura of warmth or invitation. With its darkened wings like atrophied limbs it looked like life had long ago vacated its vast corridors. Only its center section glowed with any light at all, and that sporadically, leaving the impression that those who remained here were slowly losing their battle against the shadows closing in around them.\n\nNathaniel guided the buckboard to a halt at the center of the crescent drive and Colin immediately leapt out and attacked the stone steps two at a time, seizing the door knocker with his usual relish. He was clearly not suffering any trepidation.\n\n\"Well, bless our unholy rolling empire.\" Eldon Arnifour stood at the threshold with a dopey grin and a tumbler. \"Just look at what the night creatures have heaved onto our doorstep.\"\n\n\"Mr. Pendragon!\" Lady Arnifour's voice cut in from somewhere behind her well-oiled son. \"I've been praying you would come soon. Go on, Eldon, make room for our guests, for pity's sake.\"\n\nEldon stiffened at the sound of her voice, his grin transforming into something closer to a grimace. Nevertheless, he followed his mother's command and stepped aside, bowing and sweeping an arm across his body with all the formality one might use to usher a revered guest into an otherwise humble dwelling.\n\n\"I'm sorry it took us as long as it did,\" Colin said, entering without so much as the flick of an eyebrow toward Eldon. \"It is a miracle indeed that your niece is showing signs of recuperation. We may soon have a quick end to this most horrendous crime.\"\n\n\"I'll drink to that.\" Eldon smirked. \"Care to join me?\"\n\n\"That will be all!\" Lady Arnifour snapped as she descended the stairs in the foyer.\n\nHe tossed her a withering glare. \"Just trying to be charitable.\"\n\n\"You've been charitable enough with yourself all afternoon. I would say you've had enough for one night.\"\n\n\"Is the thought of your cousin awakening driving you to drink?\" Colin asked with a feinted grin.\n\n\"Oh, Mr. Pendragon, your inference cuts me to the bone.\"\n\n\"I meant to infer nothing.\"\n\n\"I'm afraid my son needs no particular reason to overindulge.\"\n\n\"Spoken like the driving force she is.\"\n\n\"That's quite enough.\" She turned on her son. \"I would suggest you retire for the night.\"\n\nEldon's face pinched into a contemptuous scowl. \"Fine.\" He turned and headed for the study. \"I'll do that just as soon as I've had a nightcap . . . or two. . . .\" He paused in the doorway and glanced back. \"Assuming such a repast does not make me a suspect for murder.\" And with that he slammed the study's door so fiercely that Lady Arnifour winced as though her body had absorbed the injustice accorded the doorjamb.\n\n\"Some people really shouldn't drink,\" Colin muttered.\n\nI stopped myself from chuckling and, when I noticed Lady Arnifour's shoulders gently rise and fall with a wearied sigh, knew it was time to focus on the business at hand. \"How long ago did you notice Elsbeth beginning to come round?\" I asked her.\n\n\"A couple of hours.\" She turned abruptly and headed back to the marble staircase. \"The man on duty heard groaning and ran to get Mrs. O'Keefe. She was the first one to check on her.\"\n\n\"Has she opened her eyes?\"\n\n\"No.\" She led us up the sweeping stairway. \"The poor dear must be in terrible pain. I sent Mr. Heffernan to notify the doctor and he sent him back with an elixir of Belladonna to ensure she sleeps through the night. He's promised to come first thing in the morning.\"\n\n\"Have you given her any?\" Colin asked.\n\n\"We haven't needed to.\"\n\n\"Good. There's little chance she'll gain consciousness with a bellyful of that in her. I'm anxious to speak with her before your doctor sends her into any sort of medicated slumber.\"\n\n\"But she mustn't be allowed to suffer,\" I reminded.\n\n\"Of course not.\" He shot me a sideways glance that encouraged me to contain myself. \"Her well-being is paramount, which is why we mustn't forget that she alone holds the key to what happened at that barn, so until she's able to speak with us, her life remains in grave danger.\"\n\n\"It's all too horrible.\" Lady Arnifour sagged. \"How someone could want to cause that poor girl harm.\"\n\n\"Not just harm,\" Colin corrected. \"It's about self-preservation now, which can be a most powerful inducement.\"\n\n\"Well, there's no one in this household who would wish such a thing.\"\n\n\"No? . . .\" Colin said that single word in such a pointed way that Lady Arnifour missed the top step and lurched precariously forward before he stabbed an arm out and steadied her. She took a moment to collect herself, but none of us made any further comment.\n\nThe man posted outside Elsbeth's door barely glanced at us from his tipped-back chair, head thrown back, legs akimbo, arms folded neatly across his chest. He wasn't asleep\u2014yet\u2014but it was easy to see it would only be a matter of time. As soon as everyone in the house settled in for the night, he could almost certainly be counted on to join the ranks of the dreaming. Another fine example of Inspector Varcoe's crack staff.\n\nLady Arnifour swept past him as dismissively as he deserved, most likely having arrived at the same conclusion. Yet he could still be counted a deterrent just by virtue of being there, for it was less likely anyone would try to strike against Elsbeth with him planted outside her door, whether fully awake or not.\n\nThe three of us crept into the room as though we might disturb her slumber. Mrs. O'Keefe was seated by the bed crocheting what looked to be a large coverlet. It billowed across her lap and cascaded to the floor in a tumult that surrounded her for three feet around. She looked as if she were on the verge of cocooning herself inside its very profusion and I wondered if that might not be part of what she meant to do.\n\n\"Anything?\" Lady Arnifour whispered as we pressed near the bed.\n\n\"No, ma'am.\" She immediately began gathering the blanket in great folds, tossing it over one arm with the practiced hand of someone who has done it many times before. \"She moans and flinches every now and then, but that's all.\"\n\n\"Thank you.\"\n\n\"You needn't thank me, ma'am. You know how I feel about Miss Elsbeth.\" She aimed her sentence at Colin and me, and I thought her sentiment heavy-handed. Just who was she trying to convince? She moved across the room, drawing the train of knitting as she went, and gently pulled the door shut behind her. It was the only delicate thing I would ever see her do.\n\n\"How do you think she looks?\" Lady Arnifour cast an anxious glance at me, remembering, I was sure, Colin's reference about my passing knowledge of medicine. I thought it a good thing she didn't know it was actually nothing more than survival skills garnered while in the East End. Nevertheless, I leaned in close to Elsbeth to get a better look. There seemed little change in the few days since we'd last seen her. The swelling of her face had only marginally receded and the bruises around her eyes and cheeks had deepened to the blue-black of thunderheads from an impending storm. There was some improvement in her breathing, however. It was less labored and no longer contained the rattle that so often signals the last struggles of a soul to tear itself free of its body.\n\n\"I do believe she is a bit better,\" I announced, though I did not dare go further. I reached out and touched her forehead, and was stunned to find her exceedingly hot. I knew it to be the sign of a battle against infection raging within, but before I could reach for the basin of water at her bedside she flinched slightly and muttered something as thin as her breath. It was all Colin needed. He wrenched me aside and bent so far over her that his ear nearly grazed her lips.\n\n\"What . . .\" It was Lady Arnifour's turn to plow through me. \"Can you make out what she's saying?\"\n\nColin's brow furrowed as he patiently hovered a hair's breadth above her, but there was nothing else. I suspected her sudden outburst had been due more to the feeling of my cool hand on her burning face than any desire to reveal information, but decided to keep my peace.\n\n\"No,\" he lamented as he stood up. \"But I can assure you that we shall be spending the night here tonight and the next one after that if need be. We will protect this young woman as if she were our own, and should she truly awaken at any time, you will be the first person we send for.\" His brow furrowed as he turned to look at Lady Arnifour. \"I trust my determination to stay at her bedside will not in any way impugn your finer sensibilities.\"\n\nLady Arnifour's hand fluttered up to her neck. \"Of course not . . . whatever you think best, Mr. Pendragon. The room next door is empty and I shall have Mrs. O'Keefe prepare it at once in case either of you should require some rest. I'm sure you will find it suitable.\"\n\n\"You are most thoughtful.\" He smiled. \"And let us hope we will have the answers we seek by morning.\"\n\n\"For the sake of your niece,\" I hastily added.\n\n\"That would be such a blessing.\" She sighed heavily and I knew she held little hope. \"Very well then,\" she said after a moment. \"I shall leave you be.\"\n\nAs soon as she closed the door again I turned to Colin. \"I really don't think she's going to be waking up and telling us any stories tonight.\"\n\nHe yawned as he pulled Mrs. O'Keefe's chair closer to the bed. \"I'm sure you're right, but I don't mind if the rest of the household thinks it possible.\"\n\n\"One thing we have to do is get her fever down. Dunk your handkerchief in the basin of water and apply it to her forehead. As soon as it becomes warm rinse it out and do it again. That alone should help her to feel better.\"\n\n\"Then perhaps she will be able to surprise us tonight.\"\n\n\"I hope so.\" I stifled a yawn. \"Do you really think Lady Arnifour knows who did this?\"\n\nHe glanced at me. \"She may not have proof,\" he said, his sapphire eyes crackling with the surety of his words, \"but I'm certain she's suspicious of someone. It's the only reason she's hired us with such conviction to prove the innocence of her dear Victor. If she had any doubts, if she wondered at all, we wouldn't be here now.\"\n\n\"It's all very disturbing, made ever more so by the fact that we're here to protect Elsbeth.\"\n\nHe nodded. \"We are here to protect her as we tighten the noose. With a little bit of well-placed pressure we shall see who cracks about the seams first.\"\n\n\"You mean to incite the perpetrator to action again, don't you?\" He patted his waistband where his revolver was hidden. \"I'm prepared for whatever may come.\"\n\n\"I hope so. We both know that desperation can be a tragic motivator.\"\n\n\"That it can,\" he said as he unbuttoned his jacket. \"Now go get some sleep so you can spell me in a few hours.\"\n\nI yawned again and went back to the hallway to find the room we'd been promised, and as I passed Inspector Varcoe's nameless sentry I was incensed to find him with his head lolled fully back, a tiny thread of drool spinning down from one corner of his slackened jaw. He looked as comatose as Elsbeth, so I nicked the side of his chair as I strode past. His head snapped forward and he bolted up with a snort, batting his eyes furiously to chase the tendrils of sleep away. He glanced at me as he dragged a sleeve across his wet chin.\n\n\"Sorry,\" I muttered without a shred of regret.\n\nHe shrugged me off with a scowl, but at least Colin's first line of defense was back in operation.\n\nI headed down the hall and nearly collided with Mrs. O'Keefe as she came barreling out of the next room. She was cradling a wad of linens under one arm and nursing an expression of marked exasperation. \"Oh,\" she grumbled as she pulled up short. \"That room is ready for the two of you.\"\n\n\"Thank you.\"\n\nShe stared at me but said nothing more before turning and moving down the hall in the opposite direction.\n\n\"She's a bloody sow, that one,\" a male voice piped up behind me, and for a moment I thought it was the sentry outside Elsbeth's door. As I turned, Eldon stepped out from the shadows, a sneer alight on his face. \"Can I tempt you with a nightcap?\"\n\nMy instincts demanded I give a polite refusal, yet curiosity overruled my brain as I considered that I just might be able to learn something useful. Eldon was the only one in the household whom we hadn't had a chance to speak with alone. I was tempted by the prospect of being able to coax some information from him. I held my tongue and allowed him to lead me back down to the library.\n\n\"What will you have?\" he asked as he circled the wood-paneled bar in the far corner of the room.\n\n\"Whatever you're having,\" I replied flippantly, as I had no intention of drinking anyway. I'd already eyed a plant near my chair to surreptitiously \"water.\"\n\n\"I'm drinking scotch with a whisper of soda.\"\n\n\"That'll be fine, though I will ask you to lean my drink in the opposite direction. A bit of a lightweight, I'm afraid.\" I chuckled.\n\n\"Oh I could give you some lessons.\" He winked at me as he came around the bar and handed me my drink. \"It's really all about tolerance. The more you drink the more you can tolerate.\" He clinked our glasses with a laugh. \"So tell me . . . ,\" he said as he settled into a chair across from me. \"How long have you and the prestigious Mr. Pendragon been saving the world from itself?\"\n\n\"About twelve years.\" I took the thinnest sip of my drink and wondered if the smarmy expression on Eldon's face ever gave way to anything even remotely resembling warmth.\n\n\"Twelve years?!\" He shook his head with that same smirk. \"Then you must know all the secrets.\"\n\n\"Know them, and have written them down.\"\n\n\"Intoxicating . . . ,\" he sneered with a laugh. \"Perhaps we'll all get a read one day. . . .\"\n\n\"Perhaps,\" I gave him a coy smile, \"but what about you? What secrets might you be hiding?\"\n\nHe held up his glass. \"I'm afraid my secret is poorly kept.\"\n\n\"Well, I would hardly call a preference for spirits to be the stuff of secrets. Now murder . . .\"\n\n\"Oh!\" He wagged a finger at me as he snickered, \"Aren't you the wily one.\"\n\n\"Has your sister returned yet?\"\n\n\"Kaylin?\"\n\n\"You have others?\"\n\nHe snorted delightedly. \"My darling sister is due home by week's end. Have you met her yet?\"\n\n\"We have.\"\n\n\"I'm sure you found her charming.\" He stood up and meandered back behind the bar. \"But let me assure you that she can be a right tyrannical little bitch when she wants.\"\n\n\"I'll try to remember that.\"\n\n\"I'm sure she was on her best behavior,\" he scoffed, foregoing the subterfuge of soda as he refilled his glass. \"The Arnifour progeny can be such a mixed bag. But I'll bet you've noticed that.\"\n\n\"Is this about secrets again?\"\n\nHe came back around with his glass and pulled his chair so close to mine that our knees were nearly touching when he sat down again. The stale smell of scotch radiated from him like putrefaction from a corpse. \"You're a clever one, aren't you? I will tell you this: You get my sister started on that women's suffrage bollocks and you'll find her every bit the rabid dog the rest of us are. She and that ridiculous pack of man-eaters she insists on idolizing have the temerity to advocate that women are the equal of men. Can you imagine?\" He bellowed a great, sloppy laugh. \"If you ask me, that Pankhurst twat should be hauled home by her disgraceful husband and chained to her washbasin.\"\n\n\"You do know our sovereign is a woman\u2014\"\n\n\"How very puckish, Mr. Pruitt. No wonder your Mr. Pendragon likes having you around.\" He lifted his glass and took a drink, all the while keeping his eyes leveled on me. \"I do find you intriguing,\" he said as he lowered his tumbler. \"Do I intrigue you?\"\n\n\"Everyone in this household fascinates me.\"\n\nHis grin widened. \"Outstanding. I love being a suspect.\"\n\n\"Then why are you always so well oiled when we're around? Seems like you might be finding it all a bit too much.\"\n\n\"Now you're just being boorish.\" He stood up and wandered over to the fireplace with a pout, allowing me to finally tip part of my drink into the nearby plant. \"Do you want to know what I think about my father's murder?\" He turned around and glared at me and I could see that I had finally pressed through his artifice.\n\n\"More than anything else.\" I toasted him with my half-empty glass.\n\n\"And I thought it was my company,\" he sneered before laughing and toasting me back. \"Here's the thing, Mr. Pruitt: My father didn't have any enemies. Underachievers seldom have enemies.\" He tossed back part of his drink. \"Don't misunderstand\u2014my father was a good man in his own way: reliable, knew his place, that sort of rot, but I'm convinced his life goal was no greater than to marry into money. After he did that there really wasn't much else for him to do but sire a few offspring and twaddle about in a bit of business here and there.\"\n\n\"What sorts of businesses?\"\n\n\"He ran a stud farm for a while, but couldn't make a go of it. My mother made him divest it when he hadn't turned a profit in eighteen months.\" He shook his head and chuckled. \"She's a bloody corker, that one. But who can blame her? It was her money. My father would've been better off if he'd just rented out his own services,\" he snorted lecherously. \"That became evident when he put some money into a West End production. Turned out he was giving more to the leading lady and most of the chorus than financial backing. Such prowess is a curse of the Arnifour men.\" He leveled his eyes on me and smirked as he tipped his glass back again. \"You can just imagine my dear mother's dismay . . . or perhaps relief. Needless to say she put an end to that business as well.\"\n\n\"What about your father's last business partner, Warren Vandemier?\"\n\n\"Warren Vandemier?\" He leaned against the fireplace mantel as though giving it some real thought before abruptly snapping his eyes back to mine and growling, \"Warren Vandemier is a weasel!\"\n\n\"A weasel?! And what sort of business were they engaged in?\"\n\n\"Opium.\"\n\n\"Opium . . . ,\" I repeated like a fool, sucking in a quick breath even as my stomach curdled. \"No one's mentioned that before.\"\n\nEldon laughed out loud, too long and too hard. \"My parents spent the greater part of their marriage staying out of one another's way.\" He came back around and stopped right in front of me, staring down at me. \"Tell me the truth, Mr. Pruitt: My mother didn't hire you to find my father's killer, did she? She only hired you to prove that Victor's innocent, isn't that right?\" And to my amazement the look on his face was every bit as lucid as my own.\n\n\"I'm sure I don't remember the exact details of what she said at our first meeting,\" I replied, unwilling to give him that win.\n\n\"A selective memory.\" He snickered. \"I'm sure many of your clients have appreciated that quality.\"\n\n\"I'm sure they have.\" I returned a terse smile. \"But tell me, how did your father get himself caught up in the opium trade?\"\n\n\"Caught up?!\" He laughed. \"You make it sound like my father was an innocent, and I can assure you he was not. My father went through a great deal of my mother's money on countless schemes over the years, which is why this place and its pathetic staff look the way they do. That was my father's contribution. You should've heard the rows my parents had over the years. Is it any wonder my sister and I remain unattached?\"\n\n\"And the opium?\" I pushed again, trying to keep this feckless man in a singular direction even as I grappled with the spectre of my old nemesis.\n\n\"A pretty shrewd opportunity for the old bastard to earn some of the fortune back, I suppose.\" He sauntered back over to the bar. \"It was the money. That's what drove my father. He'd hand over a pile of it if he thought he could get a bigger one in return. Refill?\"\n\n\"No. What about his latest business? Was it widely known?\"\n\n\"He had little to do with the details. It was all very neat, very upper-class. Would you expect anything less of the Arnifours?\"\n\n\"And your mother?\"\n\n\"That old sack of bones knows exactly what she wants to know. Don't let her bluster fool you. She certainly knew about Abigail Roynton.\"\n\n\"You're referring to the rumor of an affair?\"\n\n\"Rumor?! That's priceless.\" He came back over to me and sat down, his voice thick with sarcasm. \"Father was a bore at discretion.\"\n\nTo my surprise Eldon did not seem to see the irony in his statement. \"So what are your thoughts on this case then? You say your father had no enemies and yet he was involved in the opium trade. That is most certainly a dangerous business. In which direction do you think the perpetrator lies?\"\n\nHe stared at his tumbler as though peering into a fortuneteller's ball, his mood darkening as his eyebrows slowly knit together. \"My mother,\" he finally muttered. \"She hired some cretin to bludgeon my father's skull. My cousin . . .\" He gave a dismissive shrug. \". . . An unfortunate casualty, I suppose. The price of war.\" His lips curled down and then he suddenly turned and threw his glass into the fireplace, sending the flames roaring back to life. \"God help that vile bitch.\"\nCHAPTER 15\n\nNight had permeated every living thing by the time I found myself inexplicably standing by the blackened bones of the barn at the far end of the Arnifour estate. I was tired, exhausted really, and couldn't even remember why I'd dragged myself all the way down to this miserable spot at such an hour. The wind had picked up and was whistling around with such force that it stung my face. I tried to recall what lunacy had compelled me down here even as I gradually became aware of the lathered snorting of a horse being ridden hard from somewhere over my left shoulder\u2014from the woods.\n\nI realized at once that Colin must have discovered me missing and sent one of the Heffernans to fetch me back, and yet, as the thundering sound drew ever closer, I began to feel, though I cannot say how, that the unseen presence bearing down upon me was not an ally. I looked around just as the rider cleared the dense underbrush from atop a great midnight stallion, his face hidden within the dark recesses of a hooded cloak that billowed behind him like the snapping tongue of Satan himself.\n\nThe stallion reared up and bolted toward me, its powerful haunches gleaming in the moonlight with the sweat of its effort as it carried its spectral rider relentlessly forward. I turned to run, straining to suck in gulps of air as I tried to reach the relative sanctuary of a nearby stand of bushes. Even so, I could smell the horse's hot grassy breath quickly closing the gap. This is it! my mind screeched.\n\nI opened my mouth to holler into the vast night before I could be struck by the blow I knew was coming even though no one would hear me.\n\nAnd then it came.\n\nNot to my head as I'd been so sure that it would, but to my shoulder. And as I struggled to twist around I jarred myself so abruptly that my eyelids flew open and I lurched up from the bed I'd been lying on to find myself staring into the blas\u00e9 face of the sentry who'd been posted outside Elsbeth's door.\n\n\"Mr. Pendragon sent me ta fetch you,\" the guard mumbled. \"It's past midnight. I think he means ta switch.\"\n\n\"Of course.\" I pushed myself fully up and mopped my brow with my sleeve, grateful to see the man heading out of the room without further comment. It would be good to stay awake for a while.\n\nI went to the basin and splashed water on my face and quickly ran my wet fingers through my hair. As I passed the guard, already well situated in his chair with his legs akimbo and his head threatening to bob back, I grunted a hasty thank-you.\n\n\"The cavalry's here,\" I announced with much false bravado as I let myself into Elsbeth's room to find Colin alert at her bedside, a shiny crown spinning effortlessly between the fingers of his right hand.\n\n\"So it is.\" He stood up and stretched. \"And none too soon. This is dreadfully dull duty.\"\n\n\"Has she stirred at all?\"\n\n\"Not even a whimper since I got her fever down. Did you have a good rest?\" I told him about my conversation with Eldon, how the Earl was invested in the opium trade, and the young man's thoughts about his parents and sister. \"Well done.\" He grinned. \"Though this case grows more complicated by the day. The opium trade . . .\" He let his voice trail off.\n\n\"We've time to talk about that later. Get some rest.\"\n\n\"Yes . . . ,\" he yawned as he shuffled toward the door. \"Be vigilant, my love.\"\n\n\"You needn't worry,\" I said. \"I shall be fine.\"\n\nThe door clicked gently as he left, making me suddenly feel very much alone in spite of poor Elsbeth. I settled into the overstuffed chair and reached across to feel her forehead, and was relieved to find it cool to the touch. A sigh escaped my lips as I folded my arms across my chest and leaned my head back, preparing for the hours that lay ahead. My eyes were drawn to the sweep hand of the bedside clock as it bounced off the demarcated hash marks by the light of the flickering oil lamp. In no time at all I could feel my eyelids beginning to droop. Before I could push myself back upright to mount the good fight, I had already lost. The night's seductive caresses crept in upon my mind, releasing my alertness with the vague shadings of mirage, only this time the illusions were even more cunning, for I found myself sitting in Elsbeth's room staring at a shadowy vision. There was a man on the opposite side of the bed leaning far over Elsbeth. All I could tell was that he was tall and slender and had dark hair, which was plainly evident since I was staring at the crown of his head.\n\nI wanted to cry out, to find my voice and startle this apparition, but as so often happens in dreams, try as I might, nothing would come. I seemed destined to sit there in my delusory slumber while this faceless man finished the horrific job he had started. But as I sat there in my panicked catatonia, the most remarkable thing happened; for the first time that I can recall I was able to bear down to the bottom of my being and produce a stifled sort of yelp. It came out rather otherworldly, like the final strangled squeal of some fallen mythical beast. Which led to the second most remarkable thing; the man abruptly jerked his head up and in the wavering light of the single oil lamp I could see the spectral face of Nathaniel Heffernan.\n\nHe looked stricken; clearly as stunned as I was to hear my garbled cry, and quickly rose and rushed for the door. I leapt to my feet before my head could register what was happening and had to seize the back of the chair to keep from toppling over. In that moment I realized that I had not been dreaming. I had seen Nathaniel.\n\nI lunged after him, my mind swimming nonsensically, but was forced to come to a quick halt when I reached the darkened hallway. He was nowhere. Because of my carelessness, he was already gone. I glared at Inspector Varcoe's guard; the man was snoring as peacefully as a contented mutt. Infuriated with him and myself I kicked at the side of his wooden chair and sent him, and it, rattling to the floor.\n\n\"Nathaniel Heffernan was just here!\" I bellowed, ignoring the fact that he might realize I'd also been dozing. \"A ruddy fat lot of good you were.\"\n\n\"I'm . . . I'm sorry. . . .\" He scrambled up and righted his chair, sliding back into it sheepishly. \"Is she all right?\"\n\nShe . . . Elsbeth . . . I hadn't even looked at her.\n\nI flushed with renewed fury as I hurried back to her bedside. I don't know if I noticed the stillness of the covers pulled across her chest first, or the fact that the rhythm of her breathing was no longer evident. Whichever the case, the outcome was the same.\n\n\"Get Colin!\" I howled. \"Get Mr. Pendragon now!\"\nCHAPTER 16\n\nTime, although admittedly rigid, sometimes feels as though it has a multiplicity of variances depending upon a given situation. For instance, when a moment is joyous and filled with laughter it seems to dash by like a dizzying streak of wind. Conversely, when an event is stout with boredom it appears to pass with the lumbering grace of a beached walrus. Worst of all, however, are the occasions of dread when time insists on dragging its unwilling participant irrevocably closer to the consequence against which nothing can be done. This last scenario is precisely where I found myself as I waited in the study for Colin to gather the household. I felt at turns adrift, condemned, and tortured, and always with that same insidious sense of regret and failure.\n\nEldon was pacing in front of the fire he'd prodded to life in a blue-and-white-striped nightshirt, his hair askew, but for once without an attendant drink in his hand. Lady Arnifour was seated across from me, her full-length robe pulled tight at the collar and a mask of white cream glued to her face with a cap yanked fully down over her hair. Mrs. O'Keefe, as always, had come no farther than the door, having taken a seat just inside the room while clutching her old flannel robe tightly about herself. She wore no facial unguent like her mistress, so there was nothing to soften the sour expression that seemed to be her constant companion regardless of the time.\n\nVictor Heffernan was the last to arrive and was slumped on a stool on the far side of the fireplace wearing a look that made me think he suspected that something unique to him was terribly wrong.\n\nColin had banished us all here but had yet to join us himself, although I couldn't figure out why. He'd said little to me after I'd confessed the truth other than to vanquish me to the study to wait for the others. As I glanced around at the others I wondered what they thought of being awakened and pulled from their beds at such an hour. If any of them feared that Elsbeth had awoken to name her attacker, I couldn't see it on their faces.\n\nWhen it began to feel like Colin might never come back, time playing its nasty tricks again, he finally strode into the room with the ease and serenity of a man arriving at a midday luncheon. \"I do apologize for this unfortunate timing,\" he said, \"but I've some bad news and I thought it best for you all to hear it at once.\"\n\n\"Where's Nathaniel?\" Victor bolted up. \"Why isn't he here?\"\n\n\"Nathaniel is missing,\" he answered. \"And I'm afraid Elsbeth has died.\"\n\nLady Arnifour gasped and let out a sob.\n\n\"It wasn't Nathaniel,\" Victor stammered, casting his eyes about the room with desperation. \"You can't tell me you think Nathaniel had anything to do with it.\"\n\n\"Of course he thinks it,\" Eldon sneered. \"Don't be an ass.\"\n\n\"My boy's innocent!\" Victor shouted even as he sagged against the fireplace mantel.\n\n\"I haven't accused your son of anything.\" Colin spoke calmly. \"It's too soon to make any presumptions. We will have to wait until the inspector's man returns with the coroner.\"\n\nI caught a glimpse of Mrs. O'Keefe from the corner of my eye and saw that she'd gone quite ashen, her eyes red with tears.\n\n\"Surely, Mr. Pendragon,\" Eldon forged on, \"a man of your renown can connect two such obvious events in a straight line? I cannot imagine why my mother would be paying you were that not the case.\"\n\n\"Stop it!\" Lady Arnifour howled as she struggled to regain her composure.\n\n\"Come now, Mother.\" Eldon's face flushed red. \"Surely even you can see the correlation. Elsbeth's dead and Nathaniel's gone missing. Now if that pompous ass you hired and his trained monkey aren't willing to venture a presumption of the obvious then I should think they're no better than those ridiculous twits from Scotland Yard.\"\n\n\"Eldon,\" she hissed, this time in a low, flat tone.\n\nBut Eldon was not to be silenced. \"I'm beginning to wonder if we can even accept Mr. Pendragon's word of Elsbeth's demise? Perhaps he's too recklessly\u2014\"\n\n\"Enough!\" she bellowed, bolting to her feet as she snatched up a small marble ashtray and heaved it at her son's head. Time played its trick one last time as the leaden object careened toward Eldon, missing him by a fraction before imploding into the mirror above the mantel. The sound of its strike was deafening, not because of its volume, but because of the ferocity and intent with which it had been hurled. The tinkling of a thousand tiny shards of glass punctuated that fury as they rained down to the floor.\n\nEldon recoiled, as he was surely meant to. And when the last of the fragments settled to the ground I became aware that Mrs. O'Keefe was gone. The door to the kitchen was left swinging to and fro in a silent arc as though marking the retreat of some ghostly aberration that had gone unnoticed by this roomful of hysterics.\n\n\"I am sure, Mr. Pendragon . . . ,\" Lady Arnifour's voice was raw and taut, \". . . that you will be able to see to the authorities without my help.\"\n\n\"Of course.\" He nodded. \"We shall take care of everything. You must try to get some rest.\"\n\nShe did not acknowledge his words but kept her eyes fixed on the doorway as though getting out of the room were the only thing that mattered. I glanced at Victor and thought he looked on the verge of going after her, but before he could seem to make up his mind she had already whisked herself out of the room as suddenly as her housekeeper had. He stared after her a moment, the slump of his shoulders signifying his distress, and then he too made for the door without so much as a word to the rest of us. There was nothing he could say, yet I feared his silence hinted at his own doubts about Nathaniel.\n\n\"She tried to kill me!\" Eldon growled as soon as Victor was gone. \"She bloody well tried to kill me!\"\n\n\"You can be trying . . . ,\" Colin tossed off as he fished a perennial crown out of his pocket and blithely rolled it around his fingers.\n\n\"She's the devil's slag,\" Eldon carried on shrilly. \"All she ever did was piss on Father. You'd have thought she'd earned her inheritance herself the way she carried on.\"\n\n\"Did your parents often argue about money?\"\n\n\"Look around, Mr. Pendragon. She makes us live like we're on our last pound. But don't be deceived. She's got plenty. She simply prefers to dole it out. Gives her control and keeps us under her wretched, hateful thumb.\" He stalked back to the bar.\n\n\"But what about your father's business dealings?\" I spoke up. \"I thought you said your father squandered a great deal of your mother's money?\"\n\n\"A man has to do something,\" he shot back, pouring himself another glass. \"I'm done in. I've nothing more to say. And the only thing I want to hear from you is that you're going to throw that old shrew behind bars. She's the one who's really capable of murder,\" he seethed as he turned and stormed out of the room.\n\nColin heaved a burdened sigh and sat down next to me, the coin still sliding effortlessly betwixt his fingers. Long shadows, too numerous for the oil lamps to allay, were cast against the walls in a flickering tableau. \"What do you make of all of this?\"\n\nI shook my head. \"It's all very sad. There's enough vitriol here to suspect all of them and I don't even think we've heard the worst of it.\"\n\n\"I'm afraid I agree.\"\n\nMy voice hitched as I turned to him. \"I'm so sorry I let you down tonight.\"\n\n\"Let me down?\" He stilled the coin as he looked at me. \"You never let me down, my love.\"\n\n\"It's my fault Nathaniel was able to sneak into Elsbeth's room. I fell asleep. I gave him the opportunity to . . .\" I couldn't even finish the thought.\n\n\"To what? Watch her die? Because I'm quite certain that's all he did. Elsbeth died without anyone's assistance tonight. You only had to look at her to see that she was neither smothered nor strangled. You'll see when the coroner arrives.\"\n\n\"But . . .\" And then I realized he was right. I hadn't even looked at her. I hadn't checked for the bluish hue of smothering or the telltale marks of strangulation on her neck. It had never even occurred to me since I'd been so intent on my own culpability. \"Really?!\"\n\nHe squeezed my hand as he offered a sad smile.\n\n\"Then why did Nathaniel run off?\"\n\nHe shook his head. \"Why indeed?\"\nCHAPTER 17\n\n\"As you can see, we're in the embassy district,\" I said as though Colin hadn't already figured that out for himself. We were headed down the side street where I'd followed Mademoiselle Rendell days earlier. It was all familiar, if markedly drearier, in the early afternoon sun.\n\n\"To be more precise,\" he pointed out, \"these would be the embassies of the Austro-Hungarian nations. The Austrians, Hungarians, Bulgarians, Romanians, Bohemians, Moravians, Silesians, and Galicians are all here. And if I'm not mistaken\"\u2014and we both knew he wouldn't be\u2014\"the Russians are here as well.\"\n\n\"All right then.\" I yanked open the plain wooden door behind which sprawled the dark, elegant pub I'd followed Mademoiselle Rendell into. \"Let's see which of those countries you see represented here.\"\n\n\"Amazing . . . ,\" he muttered as he took in the lavish interior. We seated ourselves at the long bar and Colin ran an appreciative finger along the magnificent wood. \"I've never seen a singular piece of burl this large before,\" he marveled. \"And given the little flags with the double-headed eagles hanging from the ceiling and the photograph of Nicholas Romanov, I would say the place is Russian, very Russian.\"\n\n\"Very good.\" I grinned. \"Keen eye for the obvious. But you were the only one who realized what happened with Elsbeth last night. Even Victor looked mortified for Nathaniel, but you knew he hadn't done anything.\"\n\n\"Still,\" he shrugged, \"it was nice to have the coroner confirm it.\"\n\nI shook my head. \"You knew.\"\n\nHe shrugged again and ordered us a couple of ales before spinning around on his barstool. \"So which was the booth our mademoiselle set herself to work in?\"\n\n\"To your left. The one near the back.\"\n\n\"Vaguely discreet.\" He snickered. \"Is the barkeep the same?\"\n\nI glanced at the hairy, round-faced man pouring our drinks. \"I don't think so, but he looked like that.\"\n\n\"And the man she met here\u2014the foreign gentleman you insist was not Russian\u2014is he here?\"\n\n\"No.\"\n\n\"And tell me again why you're so certain he wasn't Russian?\"\n\n\"You know this. . . .\"\n\n\"Remind me.\"\n\n\"Back at Easling and Temple . . . ,\" I prodded, \"I knew a lad who was from St. Petersburg. His father was an advisor to Czar Alexander.\"\n\n\"Ah yes . . . ,\" he said with more enthusiasm than was necessary, and I knew he was ribbing me. \"There were a lot of Russian boys attending the academy back then. What was the boy's name?\"\n\n\"I don't remember,\" I lied, refusing to play along with his game.\n\n\"Wasn't it something like Grigorii Yuspenovich?\"\n\nI scowled at him. \"Lucky guess.\"\n\nHe laughed. \"Well, you were only fourteen and hadn't met me yet. You had nothing to compare him to.\"\n\n\"I knew who you were. Everyone at Easling and Temple knew who you were. Ever the golden boy, smart . . . star wrestler . . . aloof . . .\"\n\n\"Please. You'll make me blush.\"\n\n\"As if that were possible.\"\n\nHe chuckled before abruptly turning and calling out to the barkeep, \"Excuse me. . . .\"\n\nAs the burly man sauntered over to us I wondered what Colin was up to. \"It appears my glass has something in it beyond the ale I ordered. While that may be sufficient for your regular clientele, it is most assuredly not sufficient for me. Might I get a glass that's been washed since Her Majesty's coronation?\"\n\nThe man's face curled sourly as he seized the glass, his bushy eyebrows furrowing into one long, seething caterpillar. \"I dun't see anyt'ing!\" he snapped.\n\n\"Then perhaps I might suggest you consider a consultation with one of our fine British ophthalmologists?\"\n\nThe man's eyes narrowed to black beads as he glowered at Colin. \"You t'ink you're funny?\"\n\n\"All I want is a decent ale in a clean glass. You wouldn't serve this to one of your diplomats if you could get one of them in here,\" he scoffed.\n\n\"De ambassador's staff comes here all de time.\" The man leaned into Colin's face. \"And ve serve many staff from France and Austria and Hungary and all over the empire, so . . . ,\" and without another word he picked up Colin's glass and tossed it into the sink behind the bar, \". . . ve don't need you. You may leaf.\"\n\n\"Well . . .\" Colin stood up. \"It would seem that someone is always getting tossed out of this place. Must be ruddy hell on the bottom line.\"\n\n\"Ve have plenty business.\"\n\n\"So you say.\" He stood up. \"What do we owe you? Maybe you can hire someone to wash the dishes with our payment.\"\n\n\"Out!\"\n\nThe door swung shut behind us and Colin snickered as he absently rubbed his chin. \"Extraordinary.\"\n\n\"What's extraordinary is that you just riled that man up for fun,\" I said as I followed him back to the main thoroughfare. \"Was that really necessary?\"\n\n\"It wasn't for fun\u2014I needed some information and figured that was the easiest way to get it from him. Surely you see that.\"\n\n\"What I see is that the only thing we learned is that they serve a lot of diplomats.\"\n\n\"Yes. But at least we have narrowed down our list to the Austro-Hungarian nations. Surely you would've recognized a French accent. . . .\"\n\nI frowned. \"Of course. And I could have picked up an Austrian one as well.\"\n\n\"Well then, perhaps the man you overheard talking to our mademoiselle was Hungarian or Moravian.\" He peered at me. \"Are you familiar with either of those?\"\n\n\"No. And what makes you think the man she met has any correlation to a diplomat anyway?\"\n\n\"Because even though Nicholas married Victoria's granddaughter, you know as well as I do that relations between our countries are acutely strained, and yet, here sits a most opulent czarist pub right in the midst of our city. I guarantee it's subsidized by their government and that it serves much more than just spirits. No doubt Russia's allies partake in those favors, which would include the Austro-Hungarian Empire.\"\n\n\"Maybe so, but you can't be sure any of it's related to the disappearance of Michael's sister.\"\n\n\"Not yet, but we'll know something shortly.\"\n\n\"We will?\"\n\n\"Indeed. We're going to Her Majesty's Foreign Ministry Office.\" He turned and grinned at me, knowing I would abhor the implication.\n\nI screwed up my face. \"Must we?\"\n\n\"It's time we find your Slavic man, and the only way to get information about the embassy staffs is through the Foreign Ministry Office.\"\n\n\"It could take us days to look through all the files for those countries. There'll be thousands of them. We don't have the time.\"\n\nHe looked at me with grim determination. \"Unless you have a better idea . . .\"\n\nBut I didn't, so within the hour I was stepping into the Foreign Ministry Office. It isn't that I have anything against our esteemed Minister Randolph Fitzherbert; he is an elegant, thoughtful, and intelligent man who has served our commonwealth admirably. Rather it is the effusive woman one must endure to procure a visit with Mr. Fitzherbert: one Adelaide Crouch.\n\nColin and I had barely crossed the threshold from the bustling hallway when the young woman leapt to her feet as though her chair had spontaneously combusted. With her hairpin curves and froth of blond hair piled atop her head she looked like a confection better suited to a bakeshop than a government office. She hustled around her desk with her eyes glued solely on Colin, wearing a smile that seemed about to cleave her head at any moment.\n\n\"Mr. Pendragon!\" she squealed. \"What a pleasure to see you.\" As she gripped his hands she slid her eyes to me and halfheartedly allowed, \"Mr. Pruitt.\"\n\n\"Miss Crouch.\" I conjured up a small smile, but she'd already returned her gaze to Colin.\n\n\"Always a pleasure to see you as well, Miss Crouch,\" Colin said, leaning forward and kissing her lightly on each cheek, which sent her into a bray of twitters. He was incorrigible.\n\n\"Please, Mr. Pendragon.\" She batted her eyes at him even as a foolish grin spread across his face. \"I keep telling you to call me Adelaide.\"\n\n\"But of course. Is Randolph in?\"\n\n\"Stuck in Parliament, I'm afraid. I don't expect him in for the rest of the week. You know how those old Whigs can be.\" She chuckled.\n\n\"That I do. I've sat through enough of those sessions listening to my father. Dreadful. But tell me, might we impose upon you to show us a file or two in Randolph's absence? You know I wouldn't ask if it weren't important.\" He flashed his dimples again and I knew we were about to see just how intoxicating she really thought his charms to be.\n\n\"Well, I really shouldn't,\" she said as she smoothed the front of her dress in a nervous gesture that nevertheless managed to amplify her undeniable endowments. \"What sorts of files are you looking for?\"\n\n\"We could start with your personnel file, little one, so that I can write great good things about you.\"\n\n\"Mr. Pendragon . . .\" She laughed and waved him off as I wondered how he came up with such inanities. \"You're just playing with me.\"\n\n\"You must forgive me,\" I interrupted, afraid I would lose my lunch if I did not stop these two, \"but time is of the essence here and we really are in great need to see the Minister's files on the Austro-Hungarian embassy staffs. Most specifically the Romanians, Bohemians, Moravians.\"\n\nShe flicked her gaze to me as her smile dropped. \"Ever about business with you, isn't it, Mr. Pruitt. You really should learn to enjoy yourself like Mr. Pendragon.\" And her eyes once again sought his as another smile eased across her face.\n\n\"I'm afraid he is right.\" Colin sighed as though I had ruptured some delicate mood, and perhaps I had. \"The spectre of reality always seems to rear its inexorable head.\"\n\n\"Well, no harm's been done,\" she said as she continued to stare into his eyes. \"You know I understand. It must be such a burden to have harpies badgering you all the time.\"\n\nHad Colin not been standing between Miss Crouch and me I would have seriously considered reaching out and backhanding her. But Colin did present bodily interference in that moment, and as my better nature kicked in I settled for giving him a sharp poke to the small of his back to signal the end of my tolerance.\n\n\"You give me too much credit.\" He chuckled, and I knew I had played into his ego, which only galled me more. \"But I am in need of a gander through Randolph's embassy files for the Austro-Hungarian Empire. If we could start with the Hungarians? I promise I shan't remove a thing.\"\n\n\"It's going to take days, Mr. Pendragon.\"\n\nI saw a flicker of concern flit across his face before he cracked a tight smile and said, \"All the more time to spend in your company.\"\n\n\"Oh, Mr. Pendragon . . .\" She smiled. \"Well, I suppose it would be all right. I've never known the Minister to refuse you any request and I would never want to be the one to stand in your way.\" Her voice had suddenly developed a huskiness and I began to wonder whether I was missing something. \"We keep the Hungarian and Austrian staffs up here, but the rest are down with the clerk.\" She finally disengaged herself from Colin and headed to the door of an attendant room filled with tall wooden filing cabinets.\n\n\"We won't need to see the Austrian staff, but I'm afraid we likely need to look at the rest,\" he called as she disappeared from sight. \"Are you out of your mind?!\" He rounded on me in a harsh whisper. \"We need her cooperation. Would you please try to control yourself?!\"\n\n\"She called me a harpie,\" I shot back.\n\n\"Then stop acting like one.\"\n\nMy jaw dropped, but I managed to keep from uttering what had streaked across my mind as Miss Crouch returned with a great stack of files cradled in her arms.\n\n\"Here are the dossiers on the Hungarian staff.\" She heaved the pile onto a low table across the room. \"If you'd like to see any complete files just let me know and I'll have Record Keeping pull them. It can take a day or two, but you know I'll do everything I can to get it expedited for you, Mr. Pendragon. I'll have to go and have the rest pulled for you. What order do you want them?\"\n\nColin shrugged uncomfortably. \"Alphabetically? Shall we say the Bohemian staff next? Perhaps we can sort through two countries a day?\"\n\nShe smiled. \"That will take quite some time.\"\n\n\"Yes . . .\" And I noticed he didn't sound nearly as enamored as she did.\n\n\"I'll go and fetch the Bohemian files for you.\"\n\n\"I'll come with you,\" he piped up with renewed vigor. \"You certainly can't be expected to haul those files around by yourself.\"\n\n\"So chivalrous, Mr. Pendragon,\" she said, and I knew I'd been set up. \"And perhaps I could interest you in some tea while we're downstairs? It'll take a few minutes for the clerk to collect the dossiers anyway. . . .\"\n\n\"A brilliant idea.\" He gave her a generous smile as he turned to me. \"You know the man we're looking for. . . .\" He didn't bother to say the rest; he didn't need to; he hadn't seen the man with Mademoiselle Rendell; only I had. No matter, I'd be happy to have the two of them away from me anyway. \"I'll fetch you a cup.\"\n\n\"Oh no, Mr. Pendragon, you mustn't,\" Miss Crouch said with a distinct note of pleasure. \"If anything were to spill on the files it would be the end of me. The Minister would be livid.\"\n\n\"Don't worry about me,\" I chirped a bit too merrily as I took a seat at the table.\n\nI'd hardly gotten the words out before Miss Crouch inserted her arm through Colin's and ushered him toward the hall. \"The caf\u00e9 is right by the clerk's office,\" she purred. \"They have the best nibbles there.\"\n\n\"I'll get you a nibble.\" Colin smirked at me. \"You can eat it after we're done.\"\n\n\"No thank you. I don't need a thing. Please, just go.\" And with that Miss Crouch swept him out the door.\n\nThe vacuum left by their absence was refreshing even as I stared at the daunting task before me. I hoped I would recognize Mademoiselle Rendell's companion if I saw him. A handful of minutes at the back of a poorly lit pub were hardly the best of conditions under which to remember a face. Nevertheless, I flipped open the first folder and set to work.\n\nThe first photo showed a great bulbous-faced man with a dimpled chin and more hair sprouting from his ears than the top of his head. This, the attendant description stated, was the Hungarian ambassador's attach\u00e9, a career politician with more vowels in his name than consonants. It was not the man I'd seen huddled with Mademoiselle Rendell, and while I wasn't surprised by this immediate failure, I wondered why the fruits of a search are never borne out beneath the first leaf overturned.\n\nI threw the file aside and plunged into the next few, saturating myself in a world filled with men named Bela, Adelbert, Fodor, Lasio, and Vilmos. None, however, proved to be my bearded target.\n\nThe work was proving as tedious as I'd feared, made worse by the fact that facial hair was obviously de rigueur for Hungarian men. It seemed the axiom was proving to be true that we all eventually begin to resemble one another based on our overwhelming desire to fit in. My spirits sank with the flip of each new tintype.\n\nI glanced up at the clock and saw that an hour and a quarter had already passed. The Hungarian files before me were barely more than half-exhausted and I began to wonder where Colin and Miss Crouch had gotten to. A cup of tea and few triangles of bread with cucumber or watercress could hardly take more than a half hour or forty-five minutes to consume at the outside. And as for the Bohemian dossiers, Miss Crouch had said they would take a few minutes for the clerk to pull, not better than an hour. I only hoped she and Colin were having fun as I grudgingly flipped open the next file before me.\n\nA sudden burst of high-pitched laughter turned my gaze to the hallway. It seemed the indolent duo was back. I glanced at the photo in front of me and found myself staring at yet another pair of deep-set, black eyes, this time belonging to a man with enough facial hair to resemble a bear. No details could be garnered on either the shape or depth of his face given its almost complete carpeting of fur.\n\n\"We have returned,\" Colin announced with high spirits, his arms cradling another huge load of files.\n\n\"Smashing,\" I groused as I flipped the folder shut.\n\n\"Have you had any luck?\"\n\n\"No!\" I snapped in spite of my efforts not to.\n\n\"Then I have good news for you.\" He beamed, his voice sparkling in defiance of my mood. \"While the clerk was collecting the files from Bohemia, I had the most interesting conversation with him.\"\n\n\"Oh, it wasn't him,\" Miss Crouch fairly gushed. \"You figured it out by yourself.\"\n\nHe gave her a quick smile before turning back to me. \"The man is practically a historian. He looks like he's worked there for longer that I've been alive. He reminded me of the alliance between Russia and Bulgaria seventeen years ago.\"\n\n\"Bulgaria?\"\n\n\"Forged by Czar Alexander the Third. Do you recollect your history lessons?\" he prodded.\n\n\"I think I was otherwise occupied that semester,\" I drolled.\n\n\"He freed the Bulgarians from Turkish rule,\" Miss Crouch said. \"Everybody knows that.\"\n\n\"Well, at least the clerk downstairs does.\" I smiled acerbically.\n\n\"When he said that it suddenly struck me that if we're looking for someone involved in illicit doings being run out of a Russian-backed pub, you can be sure the Russians would want to remain beyond reproach should the activity ever be discovered.\"\n\n\"So what's your point?\"\n\n\"That's why the man you heard wasn't Russian. Deniability.\"\n\n\"Okay. So what does that have to do with the Bulgarians?\"\n\n\"Bulgaria owes the Russians for their release after five hundred years of Turkish oppression. If the Russians are up to something, you can be sure they're funneling it through their most grateful ally. That man you heard wasn't Hungarian or Bohemian or Moravian. . . .\" His grin stretched across his face.\n\n\"He's Bulgarian,\" I answered, finally understanding.\n\n\"We shouldn't have any more files to go through than these.\" He set the pile down in front of me, revealing the Bulgarian insignia on their cover.\n\nWe both began poring through the stack of files, Colin flicking them open and shoving them under my nose while Miss Crouch hummed at his shoulder when not leaning over him in a feigned attempt to be useful. More than twenty minutes elapsed in that way, fraying my nerves to the point of rupture, when I suddenly caught sight of the face we'd been searching for. Heavily bearded, darkly complected, black eyes set within a full, round face, he looked like so many of the men I'd been sifting through, yet there were distinct differences here. His nose was broad and flat and his forehead short, and I knew it was the man I'd seen in the booth with Mademoiselle Rendell.\n\nI hoisted the photo into the air and practically shrieked that we'd found him. \"Outstanding.\" Colin beamed, and for a moment I thought he might be about to hug me.\n\nOnly Miss Crouch looked disappointed.\n\n\"So what do we do now?\" I asked.\n\n\"Let us learn all we can about . . . ,\" he leaned in over the file, \". . . Vitosha Harlacheva. I believe he'll be the person through whom we shall lure Miss Rendell.\"\n\n\"Who?\" Miss Crouch asked with a note of displeasure in her voice.\n\n\"A woman caught in some nasty business,\" he muttered.\n\n\"How terrible,\" she said, but there was no fervor in her words.\n\n\"So you think this man has something to do with Angelyne's disappearance?\"\n\n\"He's the first person she went to see after our visit. Mr. Harlacheva is the key. I'm certain of it. But right now . . . ,\" he looked over at me, \". . . we must pay a visit to the late Earl's partner, Warren Vandemier. If you're up to it.\"\n\n\"Of course I am,\" I answered too quickly.\n\n\"Good,\" he said, but his eyes hesitated a moment too long. \"Because I suspect he has some information that will help. I'm not at all pleased with our progress on that account. Every day that goes by makes the trail colder, and I will not be stymied by that infuriating family.\"\n\n\"Why, Mr. Pendragon,\" Miss Crouch enthused, \"are you investigating the murder of the Earl of Arnifour?\"\n\n\"I'm not investigating it.\" He turned to her. \"I am solving it.\"\nCHAPTER 18\n\nA light rain had begun to fall in direct opposition to my mood, which had begun to rise the moment we'd left the Foreign Ministry Office.\n\nOnce Colin had been able to study Mr. Harlacheva's slim dossier we had made a hasty exit, much to the disappointment of Miss Crouch, who was even further vexed to realize that we would not need to come back over the ensuing days, either.\n\nI tugged the brim of my hat farther down over my forehead to keep the rain off my face while I waited for him to hail a cab. The inclement weather had succeeded in driving nearly everyone into a carriage and I began to wonder if we were going to have to walk. I was just beginning to resign myself to such a fate when Colin suddenly lunged into the street and seized the reins of a passing horse, tugging it to the side of the road.\n\n\" 'Ey!\" the driver bellowed from under his tiny awning. \"Wot in the bloody 'ell do ya think yer doin'?\"\n\n\"Official business!\" Colin bellowed right back. \"You will take us across town and you will do it quickly and safely.\"\n\n\"Like 'ell I will. Piss off. I'm done fer the day.\"\n\n\"You will take us where I say or you'll be done for good,\" Colin said as I grabbed the carriage's door and leapt in before he could get it moving again, and despite the withering look I received as I ducked inside, I was grateful to be out of the rain.\n\n\"It'll cost ya extra!\" the man growled back at us.\n\nColin shoved in next to me and hollered back, \"Move!\"\n\nTwenty-five minutes later we had gone all the way across town and were back in Whitechapel, a distance that should have taken us twice as long. Five minutes after that we were sitting before the well-cluttered desk in the tight, slovenly office of Warren Vandemier.\n\nThe late Earl's associate was a man of middle years, probably not more than a handful ahead of Colin, though harder looking in every way. Heavy lines creased his face into a perpetual frown that confirmed Warren Vandemier had led a difficult life. He was jowly, but not fat, though there was a noticeable bulge about his midsection. His brown hair was short and curly, with a liberal infusion of gray flecks along the crown of his face. To me he looked exceedingly tired, the weight of the existence he'd managed to scratch for himself having taken its toll in his rounded shoulders, hollow eyes, and leaden manner. Yet, when he spoke, he lit up with the passion of a much younger man, winking and gesturing with great animation. He seemed to come alive only when thusly engaged, for as soon as he shut his mouth his demeanor once again collapsed in on itself.\n\nMr. Vandemier's official occupation was property manager, the collector of rents for the noble gentry who did not dare venture down to the flophouses and sweatshops that comprised at least some of their financial holdings. But we were here about his unofficial trade.\n\n\". . . and the Arnifours . . . ,\" he'd been blathering on about inconsequential inanities from the moment we'd sat down, as evidenced by the crown sailing between Colin's fingers for the last several minutes, \". . . also had a fair bit of property at one time in this neighborhood.\" He smiled like an overzealous teacher who has no idea that his class is trading spitballs behind his back. \"That's how the Earl and I became acquainted. I managed a few buildings for him. I'm the best there is, you see.\" He leaned forward and winked for what seemed the hundredth time. \"I have a way with the scrubbier classes. I was born here. Right around the corner, in fact. My success is all my own.\" He leaned back in his chair with a satisfied grin, though it was a bit hard to decipher given the ruts creasing his face that begged to belie his good fortune.\n\n\"I'm sure your mother is proud,\" Colin muttered.\n\nThe man's brow caved in, an expression that seemed far more customary than his gregariousness, and then he broke out in a laugh that sounded as false as his prior gusto had been. \"Very good, Mr. Pendragon. Perhaps I have pushed the point a bit far.\"\n\n\"Let me be honest, Mr. Vandemier\u2014\"\n\n\"I would expect nothing less.\"\n\nAnd without even realizing it Warren Vandemier had handed Colin the freedom to proceed with the delicacy of a charging rhino.\n\n\"Very well.\" He flashed a tight smile as he quickly tipped his shiny silver crown back into his vest pocket. \"Then we should like to dispense with this twaddle and hear about your opium business.\"\n\n\"Opium?!\" The man's eyes popped so unnaturally wide that it looked as though a charge of lightning had ripped through him. \"Opium?!\" His voice squeaked again. He cleared his throat. \"I'm afraid I have no idea what you're talking about.\"\n\n\"It's a narcotic, Mr. Vandemier. Derived from the poppy.\"\n\n\"I know what it is.\" He frowned, pushing himself to his feet in a great blustering display. \"But I find your inference to be an offense.\"\n\n\"We are not fresh from the womb, Mr. Vandemier. Please do not suppose you can deceive us with your hackneyed indignation.\"\n\n\"You have no reason to accuse me,\" he blustered, but with less vigor.\n\nAnd this time I knew it was my turn to speak up. \"When I was a foolish lad,\" I said in as cavalier a tone as I could muster, \"I lived for a time just around the corner on Limehouse. For room and board I did the bidding of a woman whose opium club was the most prominent in the city. So let me assure you that I can smell its residue in your hair and clothing, and given your heavy-lidded look, I would say that your last use of it was less than two hours ago.\"\n\n\"You worked for Maw Heikens?!\"\n\n\"I did,\" I answered brusquely, aware of Colin's disapproving glare on the side of my face.\n\n\"Then you've got nothin' on me!\" Vandemier snapped. \"Room and board my ass.\"\n\n\"Look,\" Colin interrupted with evident distaste, \"I really don't give a good bloody hell how you earn your living. I just want a few answers to some simple questions.\"\n\n\"Well, just because I run an opium club doesn't make me a murderer,\" he shot back.\n\n\"A murderer?\" Colin glared at him. \"Have I accused you of being a murderer?\"\n\nMr. Vandemier narrowed his eyes as he glared at Colin. \"I know why you're here. I know what you think.\"\n\n\"You know what I think?!\" Colin replied, glancing at me with a smirk. \"I'd bet my life that you don't.\"\n\n\"I had nothing to do with Samuel's death . . . or that whore niece of his, either.\"\n\n\"A man who's not afraid to have an opinion.\" Colin's smile disintegrated. \"May I remind you that I've not accused you of anything. We have only come here in search of some information.\"\n\n\"Well, there's nothing for you here. Samuel and I had our disagreements over the years, but I sure as hell didn't want him dead. Do you know that he owed me money? That old sod was into me for a pretty pound.\"\n\n\"Was he . . . ?\"\n\n\"Damn right he was! Seed money, Mr. Pendragon. We'd just opened the club. The finest supplies, private rooms for the wealthiest patrons, the most beautiful women to tend to a client's every need. Better than anything Maw Heikens ever did.\" He slid his eyes to me. \"But that old witch Samuel was married to kept her devil's eye on him. She refused him so much as a farthing unless she knew exactly what he meant to do with it. Which left me to put the money up myself. All of it. His share and mine. Bastard swore he'd pay me back.\" He hawked into a spittoon sitting on the floor by his desk. \"I was a bleedin' fool. I should've known Samuel would be as worthless as his title.\"\n\n\"Then why did you go into business with him?\" I asked.\n\nHe swung his exasperated expression in my direction, his eyes squinting to near pinpoints. \"I had no idea what a useless turd he was until after I'd fronted him the money. Before that he'd been throwing cash around like he grew it on his estate. It was a sham. All he had was what that shrew wife doled out to him. And all he did with that was chase whores. I don't believe she really gives two shites who murdered him. Good riddance, I say. But I sure as hell didn't do it.\" His narrowed eyes raked our faces several times as if daring us to refute him before he added, \"And you can both bugger off if you think you're gonna pin it on me.\"\n\n\"You must have an extraordinary alibi,\" Colin said.\n\n\"I was at the club same as I am every night. Plenty of people saw me. Plenty.\"\n\n\"Users?\"\n\n\"What?\"\n\n\"Are you asking me to accept the addled remembrances of addicts? That's your defense? I'm not sure what a magistrate would make of that.\"\n\n\"I've got nothin' to hide.\" He leaned forward eagerly. \"Ask me anything.\"\n\nAnd once again I saw the whisper of a sparkle in Colin's eyes. \"How accommodating.\" He stroked his chin. \"When was the last time you spoke to the Earl?\"\n\n\"About a week before he got himself killed. He was supposed to bring me an overdue payment, but of course he showed up without so much as a blasted shilling. Had some slag in his carriage and a load of piffle about needing more time. I told him he had a fortnight or I'd damn well tell that harpy wife of his everything. Then he got himself killed. Anything ta toss me outta my money.\"\n\n\"Such disdain. Makes it hard to imagine why you persisted in your dealings with him.\"\n\n\"What was I supposed to do? You think a titled man comes along every day looking to get into the opium trade? I thought he'd be able to open doors for us. Get us noticed by a better class of people.\" He turned and assaulted the spittoon with something he'd hacked up. \"Played me for a ruddy fool.\" He glared at us from beneath his furrowed brow. \"I tell you what, I wish I had killed him. God bless the man who did.\"\n\n\"Touching,\" Colin muttered. \"And why should we believe you didn't hire the man upon whom you are so happy to impart the good Lord's blessings?\"\n\n\"He owed me money, Mr. Pendragon. Haven't I made that clear?!\"\n\n\"Ah yes . . . money. So one of the mightiest motives for murder happens to be your saving grace.\"\n\nWarren Vandemier rose to his full height and scowled fiercely down upon Colin's towhead. \"This conversation is over!\" he growled with as much menace as an opium user can muster. \"I have nothing more to say to you.\"\n\n\"That may be,\" Colin stretched his legs out languorously, \"but I am not finished with you, Mr. Vandemier. Now sit down, because you do not want me to stand up.\" He delivered his last sentence in an offhanded, playful sort of way, but I knew he meant it, and so did Mr. Vandemier, who gave a petulant harrumph! as he dropped back into his seat, folding his arms across his chest as if to demonstrate some measure of defiance.\n\n\"I will thank you to conclude this interview quickly!\" he snapped. \"I have work to do.\"\n\n\"Mr. Vandemier . . . ,\" I started to say, hoping to dispel a bit of tension.\n\n\"Sod off!\" he barked at me. \"I'll not be attacked by the likes of you.\"\n\n\"The likes of me?! I walked away from opium years ago. You're still an addict.\"\n\n\"An addict never walks away!\" he growled back, inciting my deepest fear.\n\n\"You'd best watch yourself, Mr. Vandemier,\" Colin cut in, leaning forward and fixing his eyes on him. \"I'll not tolerate you speaking to Mr. Pruitt like that.\"\n\nWarren Vandemier rubbed his eyes with the heels of his hands and I knew he was in dire need of something to soothe his rattled countenance. Which meant that what was left of his resistance was likely on the verge of collapse. \"May we please finish this?\" he pleaded.\n\n\"If you can contain your theatrics then I'm sure we can be done quickly. I only have a few more questions\u2014for the moment.\"\n\n\"The moment?!\" He looked positively apoplectic as he sagged in his chair. \"Get on with it then. . . .\" He made a rotating gesture with his hand as if that were going to have any impact.\n\nColin drew in a slow, languid breath. \"Who was the woman you mentioned who accompanied the Earl the last night you saw him?\"\n\n\"The woman? I have no idea. She didn't come up. You oughta ask Abigail Roynton. She'd probably know. She's the one he tossed over for the new one.\"\n\n\"Ah . . . ,\" Colin muttered. \"We haven't had the pleasure of meeting the Arnifours' neighbor yet.\"\n\n\"She's somethin' else.\" He let out a low, wolfish laugh. \"And I'm not just referring to Samuel, either.\"\n\n\"You aren't suggesting . . .\"\n\n\"Oh, but I am. . . .\" He leered at us.\n\n\"Eldon?\"\n\n\"The prodigal son himself!\" he sneered with great enthusiasm, seeming well pleased that Colin had followed his accusation. \"The lovely widow is not known for being discerning. She'd probably even give you a go.\"\n\nColin leapt to his feet and seized the man by the lapels and yanked him nearly the full way across his desk. \"You are a reprehensible little turd, Mr. Vandemier,\" he snarled within a hair's breadth of his face.\n\n\"I haven't told a single lie,\" his voice cracked.\n\nColin heaved him away and stepped back, allowing the flustered man to recoil slightly as he fussed with his clothes as though to reengage his dignity.\n\n\"A last question then, and I will caution you to remember your place. Why did you disparage the Earl's niece earlier?\"\n\nMr. Vandemier took several mincing steps back in a clear attempt to avoid any further molestation. \"She came to the club on several occasions, Mr. Pendragon, and not always under the tutelage of her uncle. And in spite of the pride I have for my business, I presume you will agree that it is not a place for a young girl of breeding.\"\n\n\"Elsbeth came to your opium den?!\"\n\n\"More than once.\"\n\n\"And Eldon and Kaylin?\"\n\n\"Eldon and his father rarely spoke. Samuel seemed to have little use for his son. As for Kaylin . . .\" An uncomfortable look crossed his face. \"Have you met her?\"\n\nColin nodded.\n\n\"Then I should hardly think you'd need to ask the question.\"\n\n\"And why would that be?\"\n\n\"Because the only reason Kaylin Arnifour would go to an opium club would be to liberate the whores and burn the place to the ground. Now please, Mr. Pendragon, are we finished here?\"\n\nColin continued to glare into the man's fretful eyes. \"For now, but you can be sure we'll be back to see your club within the week.\"\n\nThe man frowned and shook his head. \"I don't like it.\"\n\n\"I don't care.\"\nCHAPTER 19\n\nWere it not for Colin's pocket watch it would have been impossible to tell the hour by the time we finally took our leave from Warren Vandemier's office. The rain had stopped for the moment, but the temperature had dropped in tandem. With the addition of saturated horse droppings, rotten produce, and assorted other leavings littering the streets it was all I could do not to cringe as I pulled my cloak tighter about myself. Even still, it all smelled better than the residual of opium that had hung about Warren Vandemier.\n\n\"We aren't more than fifteen minutes from Stepney Green . . . ,\" Colin said, flipping his own collar up. \"Fancy a walk?\"\n\n\"Well, I suppose,\" I answered. \"So long as the rain holds out.\"\n\nWe came to a halt in front of Michael and Angelyne's walk-up and all I could think about was going inside to get warm. Even the stale residue of opium that assailed us as we entered did not bother me. \" 'Oo's there?\" the familiar voice of Mademoiselle Rendell barreled out in response to Colin's knock.\n\n\"Mr. Pendragon and Mr. Pruitt.\"\n\nThere was a great sigh as a flurry of locks and bolts were unlatched before she abruptly halted and called out, \"Talkin' don't pay me bills.\"\n\n\"This time it will.\"\n\n\"Two cost extra.\"\n\nColin leaned forward and placed his mouth close to the door. \"Let us in and I shall make it worth your while. Persist in keeping this sorrowful rectangle of rotting wood between us and I'm afraid I shall have to tear it down and we'll converse for free.\"\n\n\"All right . . . all right . . .\" Another dead bolt unseated as Mademoiselle Rendell finally yanked the door open. \"We ain't all born to the colors, ya know.\"\n\n\"Whatever that means, I'm sure it's a good thing,\" he muttered.\n\nI tried to ignore the scowl she leveled on me as I followed him inside. We remained on our feet awaiting an invitation to sit down, if such a space could be found, but none was forthcoming anyway. Instead she moved away from the door and said, \"Wot?\"\n\n\"May I?\" Colin gestured at her well-worn divan still cluttered with all manner of papers and magazines.\n\n\"If ya must.\"\n\n\"Not feeling hospitable this evening?\" He smirked as he shoved the mess to the end of the couch and sat down, motioning for me to do the same, which, grudgingly, I did. \"We haven't come here to set you in a foul state. If you'd rather not be given the opportunity to respond to the statements of your Bulgarian friend . . .\" He shifted a blank gaze to me.\n\n\"Vitosha Harlacheva,\" I filled in, wondering what he was up to.\n\n\"Yes. Mr. Harlacheva. We can just take his word.\"\n\n\" 'Oo?\" Her stance remained unwavering, but her voice betrayed a hint of vacillation.\n\n\"He's one of the couriers for the Bulgarian attach\u00e9. Rather a broad-faced, bearded gentleman whom you met at the pub by the Russian embassy the other night. The one who informed you that your mutual business was finished for the foreseeable future.\"\n\n\"Toshy?\" She blurted the name out as a furrow creased her brow. \"And what did that shite say about me?\"\n\n\"That you're blackmailing him,\" Colin replied.\n\n\"You're lyin'.\" She shook her head and laughed, but her eyes remained wary.\n\n\"Am I? Perhaps you'd like to come with us to the Bulgarian embassy and confront Mr. Harlacheva?\" I admired his bold stroke given that I thought it likely she might choose to, but she did not. She harrumphed and stalked across the room, tossing a pile of garments to the floor as she sank into a chair and wound her arms tightly around herself.\n\n\"Go on,\" she said.\n\n\"Your friend . . . your Toshy . . . ,\" he flashed a smirk, \". . . has been under surveillance by the Yard for some time now.\"\n\n\" 'E ain't no friend a mine,\" she sneered.\n\n\"Nevertheless, it would seem he may be involved in everything from the illegal drug trade . . . ,\" I noticed he had slowed his speech and was keeping a watchful eye on her, \". . . to passing sensitive government information, and quite possibly involvement in a child slavery ring he claims you spearheaded.\"\n\nShe bolted up, her face a cloud of rage. \" 'Ow dare 'e! That weren't my idea, it were 'is.\" She began pacing and cursing under her breath. \"I've a right mind to go down there and kick 'is bloody, lyin' arse.\"\n\n\"Why don't you just help us get Angelyne back? Doing a good turn will get you high praise from me and I'm sure Inspector Varcoe will . . .\" Colin let his voice trail off as Mademoiselle Rendell swung around and glowered at him.\n\n\"I see 'ow it is,\" she sneered. \"I must look like a right dumb slag ta you, but I know what you're up to.\"\n\nHe pursed his lips and leaned back. \"And what would that be?\"\n\nShe wagged a finger at him, shaking her head and chortling with great self-satisfaction. \"Toshy didn't tell you no bollocks 'bout me headin' nothin'. You're just tossin' about for information on that pissant little bitch.\"\n\n\"She's only twelve.\"\n\n\"I 'ad me a list a clients long as me arm by the time I was twelve. So what?!\"\n\n\"And look how well you turned out.\"\n\n\"This is getting us nowhere,\" I jumped in, stopping her before she could say anything further. \"The choices you've made for yourself are your business. You'll hear no judgments from us. But doesn't Angelyne deserve to make her own too?\"\n\n\"I ain't makin' no apologies!\" she snapped.\n\n\"None are warranted,\" Colin said.\n\n\"There's a need fer what I do.\"\n\n\"Of course . . .\" I could hear his patience ebbing.\n\n\"I weren't born no 'ore.\"\n\n\"Education is the backbone of every profession.\"\n\n\"That's right.\"\n\nHe smirked as he leveled a gaze at her. \"Did you deliver Angelyne to Mr. Harlacheva?\"\n\n\"Don't you look down on me!\" she fired back.\n\n\"My dear . . .\" He turned his head away. \"I shan't even look at you at all.\"\n\nShe glared at him as though trying to gauge whether he was still playing her for the fool and I doubted this ploy would work, either. Nevertheless, he neither moved nor slid his eyes back to her, holding himself with remarkable stillness. I hardly knew where to look myself, so I settled on dropping my gaze to the well-worn floor, heavily stained with the accumulated remnants of too many people. \" 'E pays me real good,\" she finally confessed to my amazement.\n\n\"How many have there been?\"\n\n\"Seven.\"\n\n\"And where does he take them?\"\n\n\"I don't know. I never see 'em again. It ain't me business. I don't ask.\"\n\nHe turned back and looked at her. \"Thank you for telling the truth.\"\n\n\"A girl 'as ta make a livin'.\"\n\n\"As we all must, but at what cost?\"\n\n\"A livin' don't cost nothin'.\"\n\nHe stood up and moved to the door with me close on his heels. \"Yours will cost you your freedom if I ever find you involved in business like this again. If you wish to prostitute yourself that's your right, but you will never make such a decision for another human being again. Especially for a child. Do I make myself clear?\"\n\n\"Are you threatnin' me?\"\n\nHe gave a tight smile. \"Absolutely.\"\nCHAPTER 20\n\nBy the time we got outside again we discovered that the sky had finally begun to let loose its watery burden, which meant that we were well wet by the time we reached the Bulgarian embassy. Though he'd managed to flag a carriage without too much trouble, it turned out to have a tear in its roof the length of my hand, which had allowed the pelting rain access throughout the entire fifteen-minute journey. When we finally reached the embassy and I took proper refuge under the building's huge stone portico, I turned back just in time to see Colin thrust his hand up through the gash in the roof to hand the driver his fare.\n\nWe hurried inside the colonnaded foyer and I was struck at once by its grandeur. Massive inlaid teak panels stretched all the way to the ceiling two floors overhead and wide swaths of jade green marble lay beneath our feet. Freedom from Turkish rule had clearly done the Bulgarians some good.\n\n\"We are here . . . ,\" I heard Colin addressing a dark-eyed beauty behind an ornate counter across from the entrance, \". . . to speak with one of the ambassador's diplomatic couriers. A Mr. Vic\u2014\" His voice abruptly wound down.\n\n\"Vitosha Harlacheva,\" I filled in as I came up behind him.\n\n\"Do you hev an appointment?\"\n\n\"Colin Pendragon and Ethan Pruitt.\"\n\nThe young woman's eyes drifted up and were as black as the waves of hair falling about her shoulders. \"Vot?\"\n\n\"Our names . . . Are we in the appointment book?\"\n\n\"You do nut know yourselves?\"\n\n\"Would we have come all this way on such a dreadful evening without an appointment?\" Colin smiled easily.\n\nThe woman glanced over at one of the two apathetic young guards posted on either corner of her desk, but neither returned her gaze. I wondered if indifference was a Bulgarian trait before realizing that it was likely neither spoke much English.\n\n\"Vot is your nem again?\" Exasperation had crept into her voice.\n\n\"Colin Pendragon. I'm with Her Majesty's Foreign Ministry Office. I investigate accusations of improprieties at the embassies. I'm sure we'll have no such issues here, unless there's some problem with my addressing Mr.\u2014\"\n\n\"Harlacheva,\" I quickly piped in.\n\nThe woman flicked her eyes between Colin and me before finally saying, \"You vill vait here.\"\n\n\"As you wish.\"\n\nShe exited through a door behind her desk, leaving us to slowly accumulate small puddles around our shoes. I tried to figure out where he meant to go with this ruse and then wondered if he even knew himself. I shot a quick glance at the two guards and decided it was safe to press him while we waited. \"What are you going to say to this man if she lets us in?\" I said in a sort of half whisper just to be sure. \"You can't just walk in there and accuse him on the word of Mademoiselle Rendell.\"\n\nHe shrugged. \"Something will come to me. It always does.\" He turned to the guard standing closest to him. \"Might I trouble you for the time?\" The man's eyes slid to Colin's face, but there was no comprehension in them. \"No?\" He glanced at the other man. \"How about a pistol? Am I allowed to bring a pistol in with me?\" Again there was no response, the second guard not even bothering to shift his gaze.\n\n\"They can't be much use if they don't even understand what anyone's saying.\"\n\n\"All they need to understand . . . ,\" Colin smirked, \". . . is that if you make a move to go through that door uninvited, you are to be stopped.\"\n\n\"That's all good and well, but didn't you find Mademoiselle Rendell too eager in confessing her sins?\"\n\nHe looked at me. \"Whatever do you mean?\"\n\n\"She took your word on Mr. Harlacheva without much of a fuss.\"\n\n\"Why would she trust him? It's all a dirty business.\"\n\n\"She earns her keep with her cunning.\"\n\n\"She earns her keep on her back.\"\n\nI shook my head and chuckled. While he had a point, he could be sorely mistaken if he presumed that truth made her imprudent. Maw Heikens was living proof of that. I considered reminding him of that fact even though I knew he would curl up his nose at the mention of her name, but the receptionist suddenly popped her head out from behind the door.\n\n\"You vill follow me,\" she said before barking a harsh, guttural command at the two guards. The men stamped their feet in unison, bounced the butts of their rifles off the floor, and stepped back from the desk to allow us to pass.\n\n\"Nicely trained.\" Colin snickered.\n\nWe followed the young woman down several plain corridors, the embassy's budget clearly having been exhausted in the foyer. A series of short, squat guards stood at loose intervals along the hallway, making me suspect that as the budget for the building went, so did the dimensions of its soldiers. We were led through successive halls until I began to fear that we were about to be ushered right out the rear exit, but to my relief, the receptionist made an abrupt right turn and brought us into an empty conference room.\n\n\"You vill vait here,\" she said without further explanation, gesturing us to seats around a table at the room's center. As soon as we settled in, she took a practiced step backwards and pulled the door shut, leaving us on our own.\n\n\"Well . . . ,\" I glanced at him, \"at least we've made it this far.\"\n\n\"We've got quite some way to go yet,\" he answered distractedly. \"Do you have a notebook with you?\"\n\n\"Don't I always?\" I passed him the little leather folio I carry about with its small nib of pencil. \"What are you going to do?\"\n\n\"I have a thought,\" he answered smoothly as he began to scribble something onto several sheets.\n\n\"Is that Latin?\"\n\n\"Very good.\" He smiled cannily just as the door opened to reveal a tall, broad-shouldered man wearing full military regalia. As he strode in I realized he was not Vitosha Harlacheva.\n\n\"Zer is no Pendragoon at ze British Foreign Ministry Office,\" the towering man informed us as he scowled from across the room. \"Who are you and vot do you vant?\"\n\nColin stood up but made no effort to move toward the man, a wise choice since he was easily half a foot shorter than him. \"My apologies to the great and honorable nation of Bulgaria for having used subterfuge to gain entry.\" The man's brow furrowed with noncomprehension. Colin smiled. \"I did indeed fabricate that story, but only because there is a most urgent and personal matter that I must discuss with Mr. Harlacheva.\"\n\n\"All matters vit Mr. Harlacheva must go through me.\" He bit the words harshly.\n\n\"Of course.\" Colin nodded. \"I did mention that it is of a personal nature?\" he said, letting his voice trail off and giving me a sudden inkling as to what he was up to and why he'd written in Latin.\n\nThe giant man flicked his eyes between us, his great bushy brow furrowing deeply. \"You vill see nothing but ze alley unless you discuss your matters vit me.\"\n\n\"Very well . . .\" And now Colin did step closer to the man. \"We're from the London Lock Hospital and Rescue Home on Harrow Road and your Mr. Harlacheva came to our offices the other day. He was complaining of some discomforts. . . .\" He gestured below his waist and then flipped open my little notebook and thrust it under the man's nose. \"You can see from the results of the tests we've run that Mr. Harlacheva is suffering from the French disease. The syphilis. And\u2014\" He got no further before the man stepped back, unconsciously dropping his hands in front of his nether regions.\n\nAnd then he uttered two words I would never have dreamed I'd hear: \"Mademoiselle Rendell,\" he gasped.\n\n\"It's a misnomer, you know,\" Colin barreled on. \"It doesn't just strike the French.\" He glanced at me and chortled in a way that urged me to do the same. \"Be that as it may, we will need to retest Mr. Harlacheva to see if there's been a mistake. That does happen from time to time. And we'll need some information regarding the possible genesis of his condition.\" Colin eyed the man. \"Who was that woman you just mentioned?\"\n\n\"Vait,\" was all the great bear said before disappearing out the door with a dexterity that would have rivaled a prima ballerina.\n\n\"How did you ever come up with that?!\" I shook my head as Colin tossed my notebook back at me.\n\n\"It seemed like a good way to get a man's attention.\" He shrugged.\n\nI started to laugh but quickly turned it into a cough as Vitosha Harlacheva came stomping into the room. It was obvious by the rapidity with which he joined us that he'd been hovering close by. I wondered if he hadn't suspected meeting with us was likely to be unavoidable. It was hard to say, and his heavily bearded face gave little away.\n\nHe had broad shoulders and was of average height, much like Colin, but the similarities ended there. Mr. Harlacheva's eyes were dark and rooted deep within his broad, flat face, and his expression truly was nearly impenetrable, buried as it was within the wiry hair that seemed to spring from his cheekbones to the collar of his shirt. And while Colin's frame is solid, revealing no softness or paunch, Mr. Harlacheva had a layer of fleshy padding that covered the circumference of his frame. While I did recognize him from his t\u00eate-\u00e0-t\u00eate with Mademoiselle Rendell, if pressed I would have said he was taller, handsomer, or at the very least more presupposing than this square ape of a man. Nevertheless, he permeated a gravitas that I could not deny.\n\n\"Vat is this about?\" he growled.\n\n\"It's about an abomination.\" Colin remained where he was, his shoulders squared and his chest puffed out in his own rite of domination.\n\n\"You haff no authority here. You are standing in Bulgaria just now.\"\n\n\"That may be. But this Bulgaria is in the heart of Her Majesty's England. And I happen to have a great deal of authority here. I would be happy to demonstrate if you'd like.\" He flashed a humorless smile.\n\n\"I have done nothing.\"\n\n\"Seven young girls have been handed over to you by a woman . . . a whore. She goes by the name of Rendell.\"\n\n\"You haff me confused with someone else. Good day.\"\n\nThe man turned and made to leave before I spoke up. \"I saw you. I followed Mademoiselle Rendell two nights ago to that pub by the Russian embassy. You told her your business with her was over for now. That you were leaving the country for a time.\"\n\nHe stopped but did not turn back. It was as though he was trying to determine how best to react in order to effect the quickest end to the conversation. \"You are a liar,\" he finally said. Which was not the best choice.\n\nWith barely an intake of breath Colin hurled himself down the length of the table and punched Mr. Harlacheva in the kidneys, dropping him in a gasping heap before the man even realized what had happened. \"You will never speak to Mr. Pruitt that way again,\" he seethed through gritted teeth. \"Nor will you waste our time one second more or else I'll tear your ruddy kidneys out with my bare hands.\"\n\n\"Help!\" the man gasped in a pitifully small voice.\n\n\"Allow me.\" Colin stepped over him and yanked a handkerchief from his pocket. He pressed it over his mouth and pulled the door wide to reveal the towering military officer standing just outside, clearly waiting to be summoned if the need should arise. \"This man is contagious!\" Colin shouted into his face. He stood back and gestured with his free hand. \"Quarantine. Kapahtnh! Now!\"\n\nThe security officer nearly tripped on his feet as he stumbled backwards, his eyes as big as a fawn's. He only kept himself upright by virtue of some gravitational anomaly that I would have bet against, spinning on his heels and disappearing down the long hallway with all due haste.\n\n\"Ka-pat-nah?\" I repeated as Colin slammed the door.\n\n\"It's Russian. I don't know any Bulgarian.\" He dropped down beside the panting Mr. Harlacheva and whispered into his ear, \"In about four minutes that officer is going to return with a phalanx of guards whose sole function will be to keep you locked in this room until I can have you properly hauled away. Or maybe they'll just come in here and shoot you and put an end to the whole feral mess. It makes little difference to me. Unless you start talking. Now.\"\n\nTo his credit Mr. Harlacheva squeaked out, \"I spit on you.\"\n\n\"Unless that's a Bulgarian custom meaning you're about to purge your conscience\"\u2014Colin fished a small knife wrapped in a bit of cloth from his breast pocket\u2014\"then we shall have an issue.\" He leaned forward and waved the knife over the man's lap. \"Seven little girls,\" he said.\n\n\"Go to hell,\" came the wheezing reply, a thin film of sweat shining on his forehead like a grease slick.\n\nColin's hand flashed like a striking serpent and for a moment I didn't know what he'd done. Mr. Harlacheva gave a short, high-pitched yelp and my heart rocketed as I tried to see if Colin had actually stuck him.\n\n\"I shall cut your bits off one at a time,\" Colin seethed into the man's closest ear, \"and then fix it so you have to squat to piss. That'll teach you to mess with children.\"\n\nMy eyes shifted south and I finally spotted the knife tucked up between the cowering man's legs, the point obviously being driven home in a most convincing way, since Mr. Harlacheva was not moving a hair. Colin gave another quick jerk and sheared through the crotch of the man's slacks and undergarments, releasing his cowering genitals.\n\n\"You are devil,\" he started to blubber.\n\nColin poked the scalpel up against his tender flesh. \"I won't ask again.\"\n\n\"They are gone. They vent on ship.\"\n\n\"What ship? To where?\"\n\n\"St. Petersburg. Ve make papers for them and they go vork for Russian nobles. Not bad life.\"\n\n\"I'll bet. What's the name of the ship?\"\n\n\"Ilya Petrovina. But is too late.\"\n\n\"It's never too late. I'm bloody British, we don't believe in failure. Nine hundred years of squabbling royals have taught us that much.\" He leaned directly over Mr. Harlacheva and twitched the hand wielding the knife just slightly, but it was enough to make the Bulgarian release a fresh torrent of sweat. \"We shall take our leave now.\" Colin spoke slowly. \"And you will take your leave of this kingdom.\" I saw his hand twist almost imperceptibly and thought for a moment Mr. Harlacheva was going to swoon. \"And should I ever see your face in this city again, I shall make good my threat by whittling pendants of your bits. Do you understand?\"\n\nThe man blinked his eyes and I realized he was too afraid to speak.\n\n\"Excellent.\"\n\nIt took only a second more for Colin to move his hand away and spring to his feet. Vitosha Harlacheva scrambled to cover himself as best he could, the color slowly returning to his face. He looked beaten, desperate, and I should have recognized that fact sooner than I did, but I was unnerved myself and didn't realize what was bound to happen.\n\nColin sneered as he started for the door, but before I could even begin to follow, Vitosha Harlacheva leapt to his feet and threw himself fully at Colin's back, colliding hard and sending the two of them careening into the nearest wall. I threw myself forward to try to pull the burly man off Colin, but he'd already half-twisted around, and then I heard Mr. Harlacheva cry out, and just that fast it was over.\n\nThe bearish man fell to the floor like a gutted fish, his hands covering his exposed crotch as a river of blood flowed through his fingers. It took another moment before I spotted the small dark lump of fuzzy flesh on the floor near Colin's shoe and realized what it was.\n\n\"Come on!\" he barked at me.\n\nI didn't need to be told twice as I hopped over the man and fled out the door, slamming it shut behind me. We were well down the hallway when he suddenly barked at me, \"Put your handkerchief over your mouth!\" doing so himself.\n\nI heard the drumbeat of quickly approaching men as I clutched my kerchief to my mouth and nose just as the security officer came jogging around the far corner with three men on his heels. They looked wary and not at all happy when they spotted us. \"Vat is happening?\" The officer slowed down, staring at our handkerchiefs.\n\n\"It's bad.\" Colin kept up a brisk pace, forcing the man and his troops to fall in behind to hear what he had to say. \"His flesh is dying. Falling away. You mustn't touch him or go near him. Stay away. We're going to get help.\"\n\n\"But ze ambassador . . .\"\n\n\"The ambassador will be fine!\" Colin shouted. \"Just keep everybody away from him until we get back.\"\n\n\"Yes . . . yes, of course.\"\n\nThe officer and his soldiers gradually slowed as we bolted back out to the foyer. The receptionist looked startled as we rushed out, handkerchiefs pressed tight against our faces. \"Too much cologne,\" Colin muttered as he tucked his away. \"Nasty business.\"\n\n\"Nasty,\" I repeated absently, already vexed about how we were ever going to stop the Ilya Petrovina from reaching St. Petersburg.\nCHAPTER 21\n\nThe sky was as dark as pitch, a layer of brooding clouds obscuring all signs of the moon and stars. The storm of the night before, the night spent grilling the vile Vitosha Harlacheva, was returning. It was only a matter of when.\n\nColin and I were sitting deep within the confines of a hansom cab. We had a blanket across our legs and my collar was turned up, but even so, the night's incessant cold was beginning to worm its way through to my flesh. Colin's right hand was bare as he absently spun a crown through his fingers, and I couldn't imagine how the metal wasn't freezing his skin. We'd been sitting like this, well back in the thickets down the road from the Arnifour estate, for over an hour. I couldn't imagine how the driver was tolerating the dense chill from his perch above us. We would need to slip him an extra wage at the end of the evening.\n\n\"How long do we have to sit here?\" I asked, fearing that he meant to spend the whole of the night. \"It's just that I'm worried we might get a return communiqu\u00e9 from the Foreign Ministry Office tonight . . . ,\" I started to say, but I could see by the look he flicked at me that he knew better.\n\n\"Let's give it another ten minutes and then we'll call it a night. Given the storm that's coming on I doubt any reasonable person would be going anywhere, including Victor Heffernan.\"\n\n\"Well, that's a relief,\" I leaned against him, \"because I'm freezing.\"\n\n\"Me too,\" he sighed, finally shoving the coin into his pocket and slipping on his glove. \"Besides, we have a previous engagement.\"\n\n\"A previous engagement?\"\n\n\"Indeed. We're due at the Roynton estate at half past nine this evening. The comely widow is expecting us.\"\n\n\"Abigail Roynton? She invited us to her residence? Whatever for? And who says she's comely?\"\n\nHe laughed. \"I'm guessing she would have to be, given her ability to attract both Arnifour men.\"\n\n\"Any woman with a bit of money and a reserve of spirits could attract the Arnifour men.\"\n\n\"You have a point.\"\n\n\"Why would she contact us?\"\n\n\"Actually, I sent her a message this morning informing her of our investigation. I told her we hoped she might be able to offer some insight. Her answer came as we were leaving tonight\u2014she said she'd be charmed.\"\n\n\"Charmed? Seems an odd word given we're conducting a murder investigation.\"\n\n\"But you forget,\" he arched an eyebrow, \"she is a scorned woman. Remember what Warren Vandemier said about her being recently replaced in the Earl's affections.\"\n\n\"Do you really put much stock in what he says? He hardly seems a reliable source.\"\n\n\"True. But ask yourself: Who among that coterie of character witnesses is any better? Should we really dismiss his word any quicker than that of the Earl's family or staff?\" I had to concede that he had a point. He yanked out his watch and glanced at it. \"I do think that's enough for tonight,\" he said as he rapped his free hand on the metal rib of the cab's top.\n\n\"And what about Victor? Varcoe's got a dragnet across this whole area and I told you there was a photograph of Nathaniel in the Times today. It all but accused him of the killings. If he's spotted he's liable to be lynched without a second thought.\"\n\n\"I've got some lads who'll take over for us. Not to worry. Hello?\" he called out again. \"We'd like to go to the second address, please.\"\n\n\"Aye!\" the man shouted back, snapping his crop at the lone horse and guiding us out of the thicket.\n\n\"We'll let the boys fill in for the rest of the night.\" And sure enough I caught sight of a young man settling in by a hedge, his collar pulled up to cover the better part of his face as though he was hunkering down for a lengthy stay, which undoubtedly he was. I only hoped it wouldn't rain. \"They'll come by in the morning for their stipend,\" Colin added.\n\n\"I'll give them something extra if it rains.\" They would earn their money this night, but at least we were keeping them out of their usual mischief for one evening.\n\n\"Unless Victor makes a move to go to Nathaniel tonight we're going to have to stop by tomorrow and apply more pressure. He's got to do something before that incompetent inspector blunders onto the boy. They're as likely to shoot him as arrest him. They like nothing more than to tidy up a case\u2014damn the details.\"\n\nOur cab passed beneath the imposing gates of the Roynton estate, quite literally the next home over from the Arnifours', if some considerable distance away. Given the increasing moodiness of the night sky with its dense scent of rain, I was grateful we made good time.\n\nThe horse clacked down the cobbled drive through a forest of trees that led along a sharp curve before finally revealing a glimpse of the house. The difference between this home and the Arnifours' was startling. It wasn't simply the architecture, the Roynton estate having been built in the style of a French ch\u00e2teau with four rounded turrets topped by steep pointed roofs of black slate delineating the corners of the palatial structure. No. What immediately struck me was that every one of the scores of windows dotting the massive stone-block fa\u00e7ade was ablaze with light, making it look as though the house must surely be filled with a thousand people. Even the half-moon forecourt hugging the face of the building was lined with gas torchieres that broke the night's austerity with their warm glow. And the building was immaculate, from its cream-colored walls rising four stories without a mar to the cement spiraled colonnades encasing the front doors and large paned windows stretching across the entirety of the ground floor. The Roynton residence was precisely tended and full of life. It was, in effect, the antithesis of the Arnifours'.\n\nThe cab came to a gradual stop in the forecourt.\n\n\"We shouldn't be long,\" Colin said as we climbed out. \"A couple of hours at the most.\"\n\n\"Right then. I'll be waitin' under the portico if it starts ta rain. Just give us a whistle when yer ready.\"\n\n\"Fine.\" The cab clattered off to the side of the building as we climbed the half-dozen steps to the expansive porch. \"It would seem the widow must have something against the dark, as she clearly keeps her staff busy banishing it from her home,\" Colin said as he grabbed one of the knockers, a great brass lion's head with a ring clutched in its teeth, and heaved it. In less time than it had taken us to climb the steps, the doors swung wide to reveal an elegantly dressed white-haired gentleman with the stiff manner and regard of one of the Queen's own staff.\n\n\"Mr. Pendragon.\" He nodded at Colin before throwing me the usual vacant stare. \"And guest,\" he added.\n\n\"Ethan Pruitt,\" Colin corrected with a nod to me, but offering no further explanation.\n\n\"Madame is expecting you,\" he answered blithely before ushering us inside and taking a careful moment to firmly bolt the doors behind us. I couldn't help wondering if that wasn't a habit put in place in light of the recent murders at the Arnifours'. \"If you would follow me, please.\"\n\nThe man's face remained unreadable as he led us through the foyer where a massive double-spiraled staircase wound in and out of itself all the way up the full four stories. Yet, as is so often the case when Colin and I are shown in, we were deposited in a library filled with leather-bound books, overstuffed furniture, and a lifetime of collectibles. In this case the collection consisted of tiny porcelain figurines placed on every conceivable surface, including the mantel top, which encased such a roaring fire that I was sure it was being fed by a steady stream of gas.\n\nWe were offered drinks, which we both declined, and with his duties thusly completed were shut inside the giant, yet somehow claustrophobic, room.\n\n\"He had about as much personality as Mrs. O'Keefe.\" I snickered.\n\n\"If you'd grown up in an atmosphere as stuffy as this one,\" he muttered as he began poking through the books, \"you would find our Mrs. Behmoth a great deal more agreeable than you do.\"\n\n\"I wasn't born on the streets, you know,\" I shot back.\n\n\"I know. . . .\" He waved me off. He knew I'd not been raised an urchin. That had come later. That had been my own doing.\n\n\"I'm sorry to have kept you waiting,\" a smooth, husky voice filled the silence. I turned to find the storied widow, Abigail Roynton. I no longer recollect what I'd been expecting her to be like, but it was definitely not the radiant woman who stood at the door in the reflection of the warm, honeyed glow of the gas lamps. She was tall and slender, and held herself with a bearing that spoke of an upbringing above even that which Colin had known. Her face was round and open and as flawless as fresh-fallen snow, not simply the result of her age, which I knew to be in her middle thirties, but because she had clearly lived a pampered life free of anything more than a passing familiarity with the sun.\n\nHer hair was a lush and curly black, spiraling down the sides of her face even though it was pulled up in back. She wore a dress of deep greens and gold, striking for both its simplicity and the way it accentuated her meticulously trim figure. The smile that parted her lips was warm and genuine, and I was taken aback to think that perhaps this might prove to be the one person of substance among the many schemers in the late Earl's life.\n\n\"You've not kept us waiting at all.\" Colin nodded, a master of diplomacy when it served him.\n\nShe moved into the room as though she were floating above the floor. \"I trust you both were offered a drink?\"\n\n\"We were.\" Colin waited for her to settle herself on a settee near the fireplace before following suit. \"I apologize for having to bother you on such a matter as this. We're grateful you've consented to meet with us and shan't stay a moment longer than is necessary.\"\n\n\"Don't trouble yourself. There is no bother. Your note mentioned the murders of the Earl and his niece, and as you can imagine, I am anxious to help in any way I can. I'm afraid I'm unlikely to be of much use, however, as I haven't seen either of them for some months.\"\n\n\"Ah . . .\" Colin rocked back in his chair. \"Was it months, then?\"\n\nThe door to the library opened delicately and a young woman in a black serving uniform eased into the room causing no more distraction than a slight wisp of air. She carried a silver tray upon which sat a split of champagne in a silver bucket and three crystal flutes. Drinks, it seemed, were destined to be a part of this interview.\n\n\"Perfection!\" The lovely widow beamed as the girl set the tray on a side table beside her before uncorking the bottle and pouring a glass for each of us. The solemnness of our topic was momentarily banished with peculiar ease.\n\nThe drinks were served with Colin and me accepting ours as etiquette dictated. A silent toast was offered by means of thin smiles and bobbed heads as the serving girl retreated from the room, and only after we'd all had a sip did Colin persist in pushing ahead.\n\n\"Do you happen to recall the nature of your last visit with the Earl, Mrs. Roynton?\"\n\n\"Do call me Abigail.\" She flashed an easy smile. \"I simply cannot bear undue ceremony.\"\n\n\"Abigail then.\" He returned his own generous grin. \"Do you recall, Abigail, your last visit with the Earl?\"\n\n\"I most certainly do.\" She smirked at him as she paused long enough to take another languorous sip of champagne. \"Samuel was bringing about an end to our trysts, and quite badly, I might add.\"\n\n\"Trysts?!\" Colin nearly spat the tug of champagne he'd been taking.\n\nShe threw her head back and laughed. \"Come now, don't tell me I've shocked you?\"\n\n\"I would say . . . ,\" I spoke up, fearful that Colin might yet choke on the swallow he was still wrestling to contain, \". . . we're simply not used to such forthrightness.\"\n\nAbigail continued to laugh as she saluted me with her glass. \"Yes, I would suppose not. Most people are too busy trying to bury the truth beneath a veneer of respectability. I can never figure the point in that. No matter what one does, the tongues will wag. It seems to me one should simply claim their reputation.\"\n\n\"Honorable,\" I said, and easy for a person of her means to say, I thought.\n\n\"Not really.\" She winked, setting off her throaty laugh yet again.\n\n\"So the Earl\u2014\" Colin cut in, having finally managed to regain himself.\n\n\"You mean Samuel,\" she corrected. \"He had no claims to that title. One of his forebears did a turn for a balmy king and a hundred years later his progeny gets to wave around the pedigree. It doesn't sit well with me.\"\n\nColin took another nip of champagne. \"Samuel then,\" he said with a bit less grace. \"Samuel was ending your affair?\"\n\n\"Affair?\" She gazed off toward the fireplace for a moment, a distracted look on her face. \"To me the word 'affair' suggests foreign travel and clandestine meetings in romantic places. That's not what Samuel and I had. We had trysts. Right here. No travel, no romance, and only the barest nod to the idea of being clandestine. Really, Colin . . . ,\" her voice dropped lower, hitting a timbre that threatened to raise the hairs on the back of my neck as she turned her considerable focus back on him, \". . . are you truly such a prig?\"\n\nHe held her gaze as he cocked his head to one side. \"Now there's something I've never been accused of.\" He slid his eyes to me and I gave him a look that I hoped would warn him to say no more. I didn't particularly like this woman, her familiarity and unflinching zeal to speak her mind. I couldn't see what made her any better than Mademoiselle Rendell and yet knew she would be aghast at such a suggestion.\n\n\"My apologies.\" Colin tipped his flute in her direction. \"Do tell me then, how long was it that you and Samuel were having it off?\"\n\n\"Two and a half years.\"\n\n\"Indeed?! That's quite the extended tryst. And to what end were the two of you carrying on?\"\n\n\"The usual, I should think.\" She fluttered her eyelashes coquettishly.\n\n\"My point . . . ,\" he pressed on, \". . . is that I'm trying to understand if you and the Earl, your Samuel, had been entertaining any sort of more permanent plans? Marriage perhaps?\"\n\nOnce again she threw her head back and roared with delight, the curls on top of her head shaking appreciably as she rocked back and forth. \"Marriage?!\" she gasped as she took a sip of champagne and tried without success to regain her composure. \"Now why in the Queen's name would I ever want to marry that insolvent, self-absorbed, lecherous old bore? I simply will not believe that you're being serious.\"\n\n\"Am I missing something?\" Colin leaned forward and I could tell from his stiff posture and the slight pursing of his lips that he was finding this a great deal less amusing than she was. \"Would I have found you so disparaging had we met in the midst of your inflagrante delicto?\"\n\n\"Oh!\" She brought a delicate hand up to her mouth. \"Latin. Everything sounds so much better in a dead language.\" She snickered.\n\n\"I'll have your answer, please.\"\n\n\"Will you?\" She kept her eyes on him as she emptied her glass. \"My late husband left me a very wealthy woman. And as I'm cursed with childlessness . . . well, I think you can imagine how tiresome such an existence can become. I abhor gossip, which means that gallivanting about with my peers in their saber-toothed decimation of one another is out of the question. And you simply cannot expect me to take up with the servants, although I hear that's worked for some of the neighbors.\" One side of her mouth curled up as she continued to smirk at him. \"I don't know what more to tell you other than Samuel was available and I was crushingly bored. He was also exactly the man I described to you. Perhaps not at first, but even a chameleon shows its true color eventually. I even let him swindle me out of a bit of money just as he did to everyone else.\" She shrugged. \"Rather like paying him for his services, meager though they were.\"\n\n\"Under what pretext did he take your money?\"\n\n\"He called it an investment. Turned out to be opium. So banal.\"\n\n\"You're talking about his business with Warren Vandemier?\"\n\nShe gave a start. \"Well, you really are as clever as they say.\"\n\n\"You flatter me.\"\n\n\"I doubt it.\"\n\n\"What can you tell me about Mr. Vandemier?\"\n\n\"Mr. Vandemier?\" She curled her lips as she picked up a little bell and rang it delicately. Instantly the young woman who'd brought the champagne came back, moving to refill her mistress's glass. We were also topped off before she neatly plunged the bottle back into its bucket and made a hasty retreat, once again pulling the doors quietly shut.\n\n\"Now let me guess,\" Abigail started again. \"I'd be willing to wager a considerable sum that upon your meeting Warren he told you that Samuel came up with nary a farthing to start their venture, leaving him to front the entire enterprise himself. Am I correct?\" She waited for Colin's nod. \"Tell me you didn't believe the boorish little shit?\"\n\n\"It seemed unlikely.\"\n\nShe grinned. \"Very wise.\"\n\n\"I also wonder if perhaps he didn't decide to end your dalliance rather than pay you back. That would relieve him of a financial obligation you'd have had a sorry time trying to collect anyway. Am I close?\"\n\nAbigail Roynton looked positively buoyed with astonishment at Colin's having reached so obvious a possibility. \"You clearly are a man worthy of his reputation.\" She chuckled, but this time I knew she meant it. \"And do you know why I let Samuel talk me into giving him that money?\"\n\n\"Not for love.\" He smirked.\n\n\"Heavens no. Never for love.\"\n\nHe studied her a moment and I wondered if he was trying to divine an answer or determine whether he should share whatever else he suspected when he suddenly blurted out, \"Because you are a shrewd businesswoman.\"\n\nShe smiled wickedly, leering at him as people will do when they share a devious secret. \"Do go on.\"\n\n\"Opium,\" he said.\n\nShe clapped her hands. \"Yes, yes.\" She shrieked with laughter. \"You've got it!\"\n\nAnd indeed he did. For there is no more loyal customer than that of an opium dealer. Once an addict is hooked, you almost always have them for life\u2014however long that proves to be.\n\nHer amusement soured my mood. I was beginning to find this woman a great deal less principled than Mademoiselle Rendell.\n\n\"Shrewd,\" Colin said dully.\n\nBut she didn't seem to catch his tone. \"I thought so. So when it was over between us it wasn't so much that I'd lost the occasional afternoon's amusement as that I'd gained a share in a burgeoning business. Warren's only trying to peddle his story of self-funding because he thinks he can nip me out of my share of the profits. But he is sorely mistaken. He'll soon learn he can't play me for a fool.\"\n\n\"I'm certain of that,\" Colin said. \"And would you happen to know who took your place in Samuel's bed?\"\n\n\"Bed?!\" She leaned back in her chair and rolled her champagne flute absently across the exposed skin of her plunging neckline. \"Please don't think me so old-fashioned.\"\n\n\"Nevertheless . . .\"\n\n\"Of course I know.\" She raised her glass and sipped from it, glaring at him from over the rim, the gleam in her eyes almost as hot as the embers in the fireplace. \"But you won't believe me if I tell you.\"\nCHAPTER 22\n\nForeign Minister Randolph Fitzherbert sent word the next morning that the men from Her Majesty's cutter the HMS Renard, had succeeded in running down and boarding the Ilya Petrovina, where it was discovered that she not only carried the cargo listed on her manifest\u2014tobacco, spare carriage parts, and an assortment of fine ladies' undergarments\u2014but also sixteen young girls ranging in age from nine to thirteen with nary a traveling document among them. The Ilya Petrovina's captain had immediately accused them of being stowaways, but Her Majesty's naval staff had not been so easily deceived. With the information provided by Colin and transferred through Mr. Fitzherbert's office to the commanding officer of the Renard, the Ilya Petrovina's captain had been placed under arrest and the ship was being escorted back to Dover. The expected arrival date was five days hence. We had no way of being certain that Angelyne was one of the girls, yet the odds were in her favor and at the very least we were still rescuing sixteen innocents.\n\nColin sent word to Michael at once, so there was little surprise when he presented himself at our flat within the hour. He came bounding up our stairs as soon as Mrs. Behmoth opened the door, leaving her to trail along behind him in great huffs of annoyance. \"Ya 'aven't been properly inerduced,\" she snarled as she lunged into the study well behind the young man.\n\n\"Never mind, Mrs. Behmoth.\" Colin gave her a nod as he sent the dumbbells he'd been wielding onto the floor.\n\n\"It ain't right,\" she groused, but nevertheless withdrew.\n\n\"Right . . . wrong . . . ,\" he chuckled as he turned back to Michael, \"who among us is fit to judge what is and what isn't?\"\n\n\"Bugger off!\" she hollered back.\n\nI rolled my eyes, but Michael seemed to take no note as he hurried across the room to pepper Colin for news of his little sister.\n\n\"I can't tell you beyond all doubt that she is on her way back,\" Colin said. \"But I am fairly confident she'll be among those arriving in Dover next week.\"\n\n\"Bless ya, Mr. Pendragon, Mr. Pruitt.\" Michael grinned. \"Ya've been most kind. I'll not trouble ya no more.\"\n\nColin gripped the young man's shoulder a moment. \"We're here anytime should you ever need us again.\"\n\nMichael shuffled his feet exactly as I would have done at his age and demurred quietly. How well I understood this boy, which was why something at the back of my mind kept niggling at me.\n\n\"We shall see you Tuesday then,\" Colin muttered as he turned to his knife play.\n\n\"No, no.\" He stopped on the landing and turned back to us. \"I couldn't ask ya ta do that. Ya've given me too much a yer time already. I'll collect me sister and we'll pop round so's you can see 'er.\"\n\n\"As you wish.\" Colin shrugged, setting the knife back onto the mantel and snatching up his dumbbells again, curling them steadily as he sat back down.\n\n\"Thank you then.\" Michael nodded and tipped his cap before bounding down the stairs.\n\n\"Sounds like a blasted 'erd a wild boars!\" Mrs. Behmoth bellowed as the front door slammed.\n\n\"More like a jackal,\" I muttered.\n\n\"You're seeing too much of your own past in him.\" Colin snickered as he continued to roll the dumbbells back and forth. \"Can't you give the lad a bit of slack?\"\n\n\"Hmmm . . .\" I knit my brow. \"I rather think that's what he's hoping for. That boy is almost certainly a pickpocket, a thief, a pimp, and probably a drug addict. I'll wager you his sister hasn't disappeared, he's probably sold her and has now received a better offer.\"\n\n\"How very cynical.\"\n\nI scowled. \"Tell me I'm not right.\"\n\nHe chuckled as he kept the weights smoothly curling, but didn't say a word.\nCHAPTER 23\n\nBy the time twilight was nestling outside our windows and the sounds of Mrs. Behmoth rattling pans downstairs in preparation of the evening's meal amplified, I could tell Colin's thoughts had moved somewhere far away. He'd long since given off tossing the dumbbells about and had reverted to shining the same knife blade he'd been working on so that its gleam was becoming nearly solar. For myself, I could not leave go of my wariness of Michael's story even though I had nothing more concrete to offer than my own intuition. I was familiar with him, I knew who he was, and I knew he was up to something.\n\n\"You seem preoccupied,\" Colin said after a while.\n\n\"It's that little rogue, Michael . . . ,\" I mumbled.\n\n\"Still doubtful of his motives.\"\n\n\"I am.\"\n\n\"And what if he is hiding something? Does it really matter? No matter the details, something has happened to his sister and we need to get her back. What happens when we do will be a topic for a later conversation. Assuming she's not come to some harm.\"\n\nI shook my head, remembering how many young girls I'd seen disappear so very long ago, most of whom were never accounted for again. \"Tragic . . . ,\" was all I said.\n\nHe set his knife on the table and sighed. \"Well, we're sure to get your mind off it for the night when I tell you what I've decided.\"\n\n\"And what would that be?\"\n\n\"I think it's time for us to drop in on the dubious business of Warren Vandemier and the Earl. Tonight. With neither invitation nor notice.\"\n\n\"Sounds perfectly underhanded.\" I smiled, aware that his reticence was correlated to the yoke that had once tethered me so many years ago. I wanted to tell him that he needn't worry because I feared enough for the both of us, but instead muttered, \"Mr. Vandemier will be livid if he finds out.\"\n\n\"You know . . . ,\" he looked at me keenly, \"I can go alone. You needn't come.\"\n\n\"Don't start that,\" I said with finality. \"I shall be at your side as always.\"\n\nAnd so it was that we found ourselves standing in a urine-soaked, litter-filled alley in Whitechapel not an hour after eating dinner in the warm solace of our humble Kensington flat. It was a staggering contradiction and one that set an ancient and familiar chill rattling through me in spite of my determination to deny it.\n\n\"Wretched place,\" Colin muttered as he picked his way deeper into the alley toward the single scrubby gaslight hanging above a nondescript red-lacquered door. \"Let's hope this club of Mr. Vandemier's looks less infective inside than it does out.\"\n\n\"Not likely\u2014\" I started to say, before clamping my mouth shut and letting the thought go unheeded.\n\nWe reached the door and Colin took a moment to tug at his coat and tie as though anyone inside would notice or care whether he was suitably attired. He raised his fist to knock on the door but pulled up short, sliding his eyes over to mine as he stood there, arm coiled, and said, \"You really don't have to do this.\"\n\nI reached out and pounded the door myself. \"Don't be ridiculous.\"\n\nHe gave me a crooked smile.\n\nA small rectangular slot rocketed open to reveal a pair of almond-shaped eyes. \"Who sent you?\" a thin, gentle voice demanded.\n\n\"Warren Vandemier,\" Colin answered at once.\n\nThe slot jerked shut and the door instantly swung open to reveal a delicate Oriental woman. She smiled generously, bowing her head as she waved us inside. Behind her stood two glowering, dark-haired Irish blokes who were clearly meant to intimidate, and did. Neither of them spoke or paid us much heed as we were led past by our diminutive hostess. I glanced back just in time to see another young woman slide onto the stool by the door, there to wait for the next guest's arrival. I'd rarely seen the custom before and knew Warren Vandemier was serious about setting his establishment above the rest.\n\nOur exotic guide took us down a short hallway lined with doors on either side that I presumed led to private rooms for the gentry Mr. Vandemier had referenced. Even in a drug-addled state the city's aristocrats would find it anathema to mix with the commoners who frequented these sorts of clubs: sailors, stewards, mountebanks, shop men, beggars, outcasts, and thieves. All of them found a way to afford the pleasures promised by the seductive vapors once they'd woven their spell upon the addicts' receptive minds. Most of them could be counted on to prefer the ragged smoke of opium to food, leaving many of them to look as emaciated and near death as they truly were.\n\nWe rounded a corner at the end of the hallway and entered a large, dimly lit room in which numerous swaths of gauzy fabric hung around tight clusters of cushions and reclining benches. The floor-to-ceiling fabric afforded a semblance of privacy, further raising the standard of the establishment. None of the furnishings were marred or discolored, though unless they were swapped out regularly it was only a matter of time. Yet the draw of these clubs was specific and singular and had little to do with the d\u00e9cor, for it was at the apex of this room that the gentle coaxing of the drug became obvious. Its dry, stinging odor permeated the air like creosote from a poorly venting fireplace. I could feel it squeezing my throat and nudging at my temples, and felt one of my eyelids quiver. Yet I also knew that none of those effects would last long as slowly, stealthily, like a hunter shadowing its prey, the drug would begin to caress the mind, and lure its victim deep within its web. Even as I stood on the threshold of this vast partitioned room, I could feel it tugging at me.\n\n\"You want company tonight?\" the young woman asked.\n\n\"We do.\" Colin gave a roguish smile and for a moment I thought I could see a haziness easing in behind his eyes as well.\n\n\"This way.\"\n\nShe wound us through the middle of the room and down two steps to a sunken area where five men and two women were sitting. At the center of the group stood a large water pipe with a dozen flexible tubes sprouting from its sides. One of the women was stirring a black viscous mixture over a small open flame. After a moment she scraped the sticky, bubbling mess into a small metal bowl perched near the top of the pipe. She lit it for her six cohorts, all of whom were only too eager to drag the swirling vapor from the nearest mouthpiece. As I stood there staring at them, remembering the enfolding embrace that was assuredly fingering its way into their willing minds, I thought I could see them losing fractured bits, not of their consciousness, but of their very beings.\n\n\"Please . . .\" Our escort gestured us to a pile of cushions still available in the midst of this decaying circle of addicts.\n\nWe sat down and Colin reached into his breast pocket and pulled out the wad of cash I'd pressed on him before we'd left our flat. He peeled off some bills with a great, showy flourish and handed them to our hostess. \"I presume this will get us started?\"\n\nShe looked at the notes as though he were offering something untoward and I knew this sort of business preferred payment at the end of the evening when the revelers were well past giving a whit about the expenses they'd incurred. That, of course, assumed they'd not already been picked clean by the hostesses themselves. Either way, it all ended up in the proprietor's pocket by the end of the night. \"If you wish,\" she said, delicately lifting the stack of bills from Colin's hand. I had to admit: Warren Vandemier's club was proving downright genteel.\n\nWe were left with the group of strangers and I felt my heart quicken the moment the man next to me shoved his mouthpiece in my direction. \"Help yerself,\" he said.\n\n\"Not just yet.\" I smiled uneasily, aware that the dense smoke was already wiggling about my brain. \"I'm rather in need of a drink first.\"\n\n\"I recommend the whiskey,\" my neighbor offered with a lopsided grin. \"With a splash of water if you must.\"\n\n\"Save the water for the pipe,\" I shot back to great guffaws, suddenly struck by the feeling that I'd said that somewhere before. I glanced over at Colin, looking for some comfort in his solidity, and was caught by the nearly apoplectic look on his face\u2014the result, I realized, of the proximity of the mouthpiece to my hand. In that moment I realized he'd been right, I shouldn't have come. \"Can I get you something?\" I squeaked as I fought the rising urge to flee.\n\n\"Go,\" he answered quietly. \"Let Mrs. Behmoth draw you a bath. I'll tend to things here and meet you across the pillows later.\"\n\nAs I gazed into the glacial blue of his eyes, seeing the concern nestled within made me determined not to fail here. I could do this. I would do this. \"No. I'm fine,\" I said with a strength that surprised even me. \"You've nothing to worry about.\" I pushed myself up to get us something to drink, convinced that if I could just clear my head a moment I would be able to maintain my sanity.\n\nHe reached out and grabbed my arm, pulling me close. \"You've nothing to prove,\" he hissed.\n\n\"I know,\" I said, but knew he was wrong. I had spent nearly the whole of my adolescence and early adulthood hiding in places like this among the alluring opiate fumes and tattered lives of other addicts. Each of us hiding some secret, some compulsion, driving us to alter our consciousness as often as we could while all the while convincing ourselves that we chose to be here and could leave it behind at any time, but we were fools. These places\u2014this habit\u2014wound themselves around our lives so completely that if one was lucky enough to stumble upon redemption it was impossible to accept. I know it was for me. And just like that, even thirteen years later, I couldn't be sure that enough time had passed yet.\n\nI girded myself to the task at hand and before long returned with two glasses filled with overpriced, watered-down tea to simulate the color of whiskey. I passed Colin a glass and almost laughed when I saw the look of relief dart across his face as he tasted it.\n\n\"Spot-on,\" he said with a nod and a grin. \"I have been speaking with these fine people in your absence,\" he continued cheerfully. \"It seems they're all familiar with our Mr. Vandemier.\"\n\n\"E's in 'ere every night,\" one of the men volunteered. \"Smokes up 'alf the profits if ya ask me.\"\n\nEverybody laughed, including the two women, one of whom continued to take it upon herself to keep the pipe filled and circulating. She, I figured, was almost certainly his employee.\n\n\"But the most fascinating thing . . . ,\" Colin leaned forward as though on the verge of sharing some tasty secret with our bleary band of eager fellows, \". . . is that most of them are also familiar with his late partner, the Earl of Arnifour.\"\n\n\"Familiar?!\" The redheaded woman on Colin's far side leered. \"That's one way a puttin' it.\"\n\nOnce again all seven of them howled with laughter. It appeared the Earl's proclivities did not even exclude his clientele. Only the relighting of the pipe quieted them as the seven snake-like mouthpieces were once again put to use. Colin and I subtly demurred the opportunity to imbibe, but it was only a matter of time before we would need to at least appear to join in.\n\nColin shot me a grin. \"Vanessa here was telling me she was quite close to the Earl at one time,\" he said, referring to the redhead.\n\n\"Close?\" She shrugged as she sucked in another hit from the pipe. \"We 'ad it off a time or two if ya call that close. But then I'd shag his ruddy wife if it'd earn me a round in 'ere,\" she cackled merrily. \"I ain't no different than most a the birds in 'ere. I bet we all 'ad 'im sooner or later.\"\n\n\"Until recently?\" Colin prodded.\n\n\"Sure.\" She let go of the mouthpiece and sank back on her cushion, clearly trying to steady herself as the opium seized her mind and seemed to arc it up and out of her body. \"He changed a while ago. Tryin' ta set an example for 'is latest rummy that I was tellin' you about.\"\n\n\"That one was a right chipper.\" The man on my right shook his head and snorted. \"Comin' in 'ere all tarted up like she owned the place.\"\n\n\"And she weren't all that.\" The man across from me spoke as he struggled to hold in a lungful of smoke.\n\n\"She knew 'ow ta fix up what she 'ad.\" My neighbor cut him off. \"She knew what a man likes.\"\n\n\"Every woman knows what a man likes,\" the redhead mumbled toward the ceiling, her head tilted back, eyes staring up as though waiting for something to appear out of the smoky haze. \"No bloody mystery there.\"\n\n\"Who . . . ,\" I whispered to Colin, figuring he'd been able to get from this group what he'd been unable to extract from Abigail Roynton, \". . . are they talking about?\"\n\nColin flicked his eyes toward mine and flashed that roguish grin. \"Why, his late niece, Elsbeth.\"\n\n\"I don't remember being told you two were coming tonight?\" a familiar voice growled from over our shoulders.\n\nWe both turned to find Warren Vandemier standing there. He was as pale as the smoke wafting around his head and almost as ethereal. From our position on the cushions, sunken two steps below the main floor, I was struck by how curiously foreboding he looked, his harsh, angular frame towering above us with a mixture of accusation and fury. The woman who'd seated us hovered just behind him, obviously having been warned to summon him whenever anyone bandied about his name at the door.\n\n\"We didn't want to bother you.\" Colin stood up. \"We just wanted to see if your establishment lives up to its vaunted reputation.\"\n\n\"And? \" There was no suggestion of a smile on his face.\n\n\"It is indeed a step above,\" Colin smiled, \"but then a snake pit is still home to vipers.\"\n\nWarren Vandemier's face showed little reaction. \"I shall thank you to leave,\" he said.\n\n\"In that I am happy to accommodate you.\" He smiled again as we started to move off before he suddenly turned back and added, \"By the way, Abigail Roynton sends her regards, though she does find your accounting methods rather disagreeable.\"\n\n\"She's a lying slag.\"\n\n\"Odd . . . ,\" he locked his eyes on Warren Vandemier, \"she said much the same about you.\"\n\nNothing further was said as we left the premises. I sneaked a peek back and caught Warren Vandemier saying something to the Oriental woman who'd initially welcomed us. I knew there would be no such greeting were we to come back. I hoped Colin had gleaned what he'd come to learn.\n\n\"You all right?\" he asked as soon as we were outside.\n\n\"I am,\" I answered with conviction in spite of the fact that my head was swimming toward a certain migraine. \"And now we know who replaced Abigail Roynton at the Earl's side.\"\n\n\"Ah . . .\" He chuckled. \"We know more than that.\"\n\n\"We do?\"\n\n\"While you were off fetching cold tea in a glass, which, by the way, was inspired, I not only learned of the Earl's trysting with his niece, but also that Elsbeth might not actually be a relation of his at all.\"\n\n\"What? But Lady Arnifour said . . .\" And even as I heard myself say those words, I knew how foolish I sounded.\n\n\"Indeed.\" He chuckled as he stepped into the street to hail a cab.\nCHAPTER 24\n\nThree days passed since our foray to Warren Vandemier's opium club, which left only two more before the Ilya Petrovina was due to return to the docks at Dover. Colin spent most of his time wrestling at the gymnasium or doing calisthenics in our flat, and when he wasn't slaving away at one of those rituals he would sit in front of the fireplace and either sharpen, polish, or gaze blankly at one of the knives in his collection as though whatever answers he sought might possibly be coaxed from out of its cold, hard metal.\n\nEach night we would venture forth to plant ourselves in a cab among the hedgerow down the road from the Arnifour property, waiting to see if this might be the night Victor went to Nathaniel, but he never did. It was our fourth night running, the silence in the cab full between us with only the sound of the horse flicking its tail and shifting its hooves to interrupt the incessant trill of crickets.\n\n\"I wonder . . . ,\" Colin startled me as he flipped open his pocket watch and checked the time, \". . . how Nathaniel felt knowing the woman he pined for was involved, so to speak, with the Earl.\"\n\n\"What makes you think he knew?\"\n\nHe lifted an eyebrow to me as he switched his pocket watch for a crown and began teasing it slowly around his hand. \"I think we'll find that nearly everyone knew who the Earl's momentary favorite was. And if you'll recall, Victor told us that the night of the attack he overheard Nathaniel arguing with Elsbeth. Nathaniel said himself he tried to talk her out of going. He knew what she was up to.\"\n\n\"You can't know that.\"\n\n\"I think I do,\" he said pointedly, palming the crown. \"Remember the afternoon Victor took us to see the remains of that stable?\" I nodded. \"Remember my telling you there were two sets of horse prints?\" I nodded again. \"I told you that one set belonged to the killer because I could see where he'd run the Earl down, and the other set were deep, suggesting a heavy load: Elsbeth and the Earl.\"\n\n\"I remember.\"\n\n\"Nathaniel would have realized by the condition of her horse whenever she went out alone. When she returned, there would have been a marked difference in the beast's level of fatigue between carrying that slight woman as opposed to both her and a man with the girth of the Earl.\"\n\n\"Well, that's true. . . .\"\n\nHe smirked at me as he set the coin in motion again. \"Elsbeth and the Earl met up at some prearranged place, no doubt their habit whenever she got out alone, and rode down to that stable together to avail themselves of its privacy. It explains how a man of the Earl's age and physical condition could have covered such a distance in so short a time. It also explains why he would have done so.\" He stared out into the night. \"Consider that not one person in that household believed the Earl capable of covering such a distance on his nightly jaunts, and yet none of them has offered that explanation as a possibility.\"\n\n\"Which means what?\"\n\n\"They all knew what was going on.\"\n\n\"You can't be serious.\"\n\n\"Deadly serious.\"\n\n\"Then you think Nathaniel followed Elsbeth and attacked her and the Earl in a jealous rage?\"\n\n\"That is the rub.\" He knit his brow as he gazed up at the starry sky. \"I think Nathaniel is innocent.\"\n\n\"Innocent? Then who do you suspect?\"\n\nColin suddenly bolted upright, seizing the crown in midair. \"Victor Heffernan.\"\n\n\"Victor?!\" I was stunned by his accusation, especially given that he'd repeatedly insisted Lady Arnifour would never have hired us if she weren't confident of his innocence. And that's when I heard the frantic clatter of horse hooves bolting along the opposite side of the hedge we were hiding behind. \"Oh,\" I mumbled. \"You meant that was Victor Heffernan.\"\n\nColin gave me a sideways glance before leaning forward and pounding on the cab's roof. \"Here's your chance, man,\" he called out. \"Don't lose him and for heaven's sake, don't let him see that we're following him.\"\n\nThe driver jerked the reins and quickly guided us out onto the cobbled street that led back to the heart of London. Victor had already achieved some distance, making it unlikely that he'd take any notice of us, though I did worry we could lose sight of him once traffic picked up. Our driver proved himself adept, however, guiding the horse with equal parts skill and strength as he maintained an easy pace in Victor's wake. Nevertheless, Colin remained ratcheted forward in his seat, keeping a steely gaze on our quarry's dark, hunched back.\n\nWe were not forced to slow down until we'd reached the narrowed streets of Whitechapel, the very same neighborhood as Warren Vandemier's opium club. It occurred to me that Victor could be headed there, but I rejected the notion as I knew he wasn't a user and couldn't imagine Nathaniel having anything to do with it, either.\n\nOur cab careened around a dimly lit corner at a preposterous speed as I scanned the area ahead while waiting for gravity to grip our wheels again. I was relieved to catch sight of Victor among the throng cluttering the slim thoroughfare, dismounting and tying his horse to a post in front of a sorrowful-looking storefront. Our driver had also spotted him from his vantage point above and was bringing the cab to a smooth stop some distance from where Victor was still fiddling with his horse.\n\n\"Expertly done.\" Colin handed the man the entire fistful of notes I'd given him earlier. \"You needn't wait for us.\"\n\n\"I'd be 'appy to,\" he assured, beaming at his earnings.\n\n\"Another time,\" Colin called back, and headed down the street, his eyes locked on Victor. \"I never forget a helpful face.\"\n\nAs Victor ducked down an adjacent alleyway, Colin took off at a measured pace, forcing me to nearly break into a run to keep up. He slowed as he neared the corner and came to a stop, peering cautiously around the building's edge. He stood that way: morbidly still, his head cocked slightly, and all I could think was how glad I was that we were in this section of the city, as anywhere else his unorthodox stance would have attracted notice.\n\n\"Where's he gone?\" I whispered in spite of the din in the street.\n\n\"Through a metal doorway on the left. Looks like a tenement building. I think we've struck gold.\"\n\n\"Suppose this turns out to be a pied-\u00e0-terre for Victor and Lady Arnifour?\" I blurted out. \"What if we walk in on something unseemly?!\"\n\n\"Perish the thought.\" He pursed his face. And then he was off again, striding down the center of the alley with his eyes fixed on the doorway he'd seen Victor disappear through.\n\nI followed as quickly and casually as I could, wondering how he intended to determine which of the building's flats was the one Victor had gone into. He entered the scrubby, dimly lit entryway and stopped in front of the bank of mail slots, slowly running a finger across each of the names. He skimmed each of the thin slips of paper until he reached the bottom and then, without the slightest hesitation, stabbed his finger at a name just shy of the midpoint.\n\n\"What?\" I asked, my heart pounding in my ears.\n\n\"Desiree Helgman,\" he answered. \"I think you were right.\"\n\n\"What?\" I stared at him uncomprehendingly. \"Right about what? Who's Desiree Helgman?\"\n\nHe chuckled. \"Doesn't the name Helgman rattle something in your brain?\"\n\n\"Helgman?\" I parroted in an effort to jog my gray matter.\n\nHe grinned. \"It is rather inside out.\" He pointed to the letters in a seemingly haphazard order, one after another: \"L-a-n-g-h-e-m. Langhem. Lady Arnifour's maiden name.\"\n\nMy jaw slackened and I laughed out loud.\n\n\"And Desiree, a derivative of the word 'desire,' is no doubt an unsubtle homage to how this place was used. Rather pedestrian.\"\n\n\"I just hope it's Nathaniel we find.\"\n\n\"Indeed.\"\n\nWe started up the narrow staircase hugging one side of the small foyer. Nothing about the building offered even a hint of gentrification, paling even in comparison to the faded austerity of the Arnifour estate. This was a place of profound desperation, of prostitutes and addicts. It seemed inconceivable that Lady Arnifour would have come here for any purpose, let alone the one so clearly advertised on the mail slot.\n\n\"Do you suppose . . . ,\" I spoke softly as we creaked up the sagging stairway, \". . . that the Earl might have found out about this place and tried to blackmail his wife? That's one way he could've gotten his hands on her money again.\"\n\n\"The inestimable value of one's reputation,\" he muttered. \"You could be right. There's certainly nothing that matters more to the titled set.\" We came to the third-floor landing and he waved me back. \"Stay away from the door.\" He spoke quietly as we approached number 304: Desiree Helgman's flat. \"We'll not be knocking.\" He glared at the door as he pulled a small pistol from the breast pocket of his overcoat.\n\nHe backed up, gripped the doorjamb with one hand, raised a foot, and then stopped, looking at me with his leg dangling in midair. \"If they're having it off,\" he whispered, \"I'll pluck my eyes from my head.\" And then he crashed his boot against the flimsy knob.\n\nGiven the ease with which it sprang open I surmised that either the Earl had never had the occasion to follow his philandering wife or else she simply didn't care. Whichever the case, it gave way like a prostitute at last call, slamming so fiercely against the receiving wall that it left spidery fissures where the knob collided with it.\n\nThe room beyond was not well lit and it took a moment for my eyes to adjust, though I was aware of frantic movements almost at once. Colin didn't hesitate, however, but careened immediately inside. There was a rapid succession of shouting followed by the heart-seizing report of a gun.\n\nAnd then there was silence.\n\nNo motion, no words, not even the life-affirming sound of a breath being drawn, for what felt an eternity until I became aware of someone pounding on the opposite side of a nearby wall and shouting, \"Shut the bloody hell up in there!\"\n\nThat muffled voice finally propelled me inside the tiny one-room flat once I'd done my best to seat the damaged door back into place. I came up behind Colin, standing no more than ten feet from where I'd been rooted, and saw that he had his gun leveled on the room's only window. Nathaniel was slumped on its sill, one leg out but the bulk of him still inside, his father standing beside him. I thought he'd been shot even though I couldn't see any blood before finally realizing that Colin had only fired a warning. He'd wanted to stop Nathaniel from fleeing down the fire escape and been persuasive with that one shot.\n\n\"Swing around, Nathaniel.\" Colin's voice was as calm as if he meant to discuss the night air. \"And have a seat on the bed.\"\n\nThe young man did as he was told, pulling himself out of the window and dropping onto the large bed that dominated the room. As my heart began to settle I noticed that the flat was much more than what the dilapidated building seemed to suggest. While undeniably discreet in size and design, it was freshly painted and immaculately clean, and its sparse furnishings were as comfortable looking as they were new. Even the commode and sink, partially hidden behind a silk flat-panel screen, appeared to be pristine, as though they'd only recently been installed. The place was indeed fit for a lady, a lady and her paramour.\n\n\"You're makin' a dreadful mistake, Mr. Pendragon,\" Victor said in a pitifully beseeching voice. \"Nathaniel didn't do anything. The boy's innocent.\"\n\n\"Of course. Innocent men always run.\"\n\n\"You're wastin' your time!\" Nathaniel snapped. \"Let 'em hang me. I don't care anymore.\"\n\n\"No!\" Victor stepped toward Colin, his eyes blazing. \"I will not let you accuse my son of something he didn't do.\"\n\n\"May I remind you, Victor, that I've yet to accuse your son of anything. And that's despite his proximity to Elsbeth's bedside the night she died.\"\n\n\"I didn't kill her, you tosser,\" Nathaniel spat. \"I loved her. If you were half as smart as they say, you'd already know that.\"\n\n\"Nathaniel . . .\" Victor shrank back.\n\n\"The boy's right.\" Colin shoved the gun back under his vest. \"I suspected it but haven't been able to find any proof, and without proof all that's left is supposition, which is really little more than overinflated rumor. But the one thing that keeps nagging at me is why the son of a groundskeeper would ever fancy himself a suitable match for a potential heiress to the Arnifour estate? How is it you thought the family would ever look kindly upon such a union?\"\n\nI caught Nathaniel stealing a peek at his father, but neither of them answered.\n\nColin rubbed his chin as he began pacing the short distance between the window and the door, being careful to keep himself placed to avoid giving Nathaniel a second opportunity to attempt an escape. After a couple moments of idle wandering with nary a breath from either of the Heffernans, Colin started up again. \"Nothing? Then let's talk about your decision to flee the night Elsbeth died. Running off like a guilty man. Why would you do that if you've nothing to hide?\"\n\n\"The inspector\u2014\"\n\n\"\u2014is an ass who wasn't even there.\" Colin waved him off. \"The coroner confirmed she died of the wounds sustained the night of the attack. She wasn't asphyxiated by you or anyone else. While your guilt in the initial attack may still be a matter of consideration, you have most assuredly been exonerated of any misdeeds the night she died. And you knew that. But you still ran off.\" Colin turned back and settled his gaze on Nathaniel. \"So why is it I think you're still not going to be returning home?\"\n\n\"Home?\" Nathaniel said the word as though it was bitter on his tongue. \"That decaying mausoleum is not my home.\"\n\n\"Nathaniel . . . , \" Victor pleaded. \"You mustn't say that. It isn't true.\"\n\n\"Of course it's true.\" He rubbed his forehead. \"I don't belong there. I never have. You do. Elsbeth did. But I never fit in. I need to make my own way.\"\n\n\"No.\" Victor shook his head but made no move to reach out to his son. \"Your future's there just as it's been for the past three generations of our family.\"\n\n\"Eldon's got no use for me. And Kaylin . . . ,\" he gave a slight shrug, \"I don't think she has much use for any man.\"\n\n\"But Lady Arnifour\u2014\"\n\n\"Won't live forever.\" He stared at his father. \"She only cares about me because of you,\" he added with surprising gentleness.\n\n\"She loves you\u2014\"\n\n\"She loves you.\" He glanced at Colin. \"I'm sure that's no surprise.\"\n\n\"Just a moment,\" he interrupted, his brow deeply furrowed. \"You just said you never fit in the way your father and Elsbeth did. And you've proclaimed that you loved her\u2014loved her. But I've misconstrued your intent all this time, haven't I? You loved her, but not in the way I've presumed.\"\n\nNathaniel looked away as Victor raised his eyes to reveal them rimmed with red. I glanced back at Colin and tried to fathom what I'd missed. \"Tell me . . . ,\" Colin said evenly, \". . . who was Elsbeth to you?\"\n\nNathaniel's shoulders caved as he closed his eyes. \"My half sister.\"\n\nVictor collapsed onto the bed as I suddenly realized with the swiftness of undeniable truth how that could be.\n\n\"Lady Arnifour . . . ,\" Colin was saying, \". . . was Elsbeth's mother.\"\n\nVictor did not speak as he buried his face in his hands, but I couldn't help thinking Nathaniel looked relieved as he shifted closer to his father and draped an arm across his shoulders. I was certain given the depth of Nathaniel's release that he alone had been privy to this information outside of his father and Lady Arnifour.\n\n\"You mustn't be angry with me,\" he said to his father with remarkable tenderness. \"They were gonna find out. It's why I warned you about lettin' her hire them in the first place.\"\n\n\"She was worried about you.\" Victor sounded wounded by his shame.\n\n\"No. She worried about you.\"\n\n\"I've disgraced her,\" Victor choked.\n\n\"You've done no such thing,\" Colin spoke up. \"But I will say\u2014it's a marvel the way you were able to keep such a thing secret.\"\n\n\"But we didn't.\" Victor looked up, pale and drawn. \"The Earl knew right off and he wasn't of a mind to help by claiming any such baby his own. No . . . ,\" he shook his head as he pulled away from Nathaniel, \"he forced her to go away as soon as the morning sickness took hold. Told people she was off helping a sister suffering with child. When she returned she brought our Elsbeth back. Claimed her sister had died in childbirth and the husband couldn't care for the infant alone. It was a good story. No one questioned it.\"\n\n\"How did Lady Arnifour get her husband to agree to raise Elsbeth as their niece?\"\n\n\"Money.\"\n\n\"Of course. . . .\" Colin shook his head. \"And does anyone else in the household know? Mrs. O'Keefe?\"\n\n\"No. No one.\"\n\n\"And how did Nathaniel come to the truth?\"\n\n\"I told him,\" Victor mumbled as he wrapped his arms around himself. \"I'm the only family Nathaniel's ever had. I wanted him to know the truth in case something happened to me. I owed him that.\" His face was etched with regret.\n\n\"Is it possible Elsbeth knew? That she'd figured it out?\"\n\n\"No.\" He sucked in a stilted breath. \"Elsbeth had little interest in me. I couldn't see what good telling her would do. I knew she was happy believing she was one of them. . . .\" He let his voice trail off.\n\n\"Why?\"\n\nVictor stared at his hands as though searching for the answer in the calluses and lines therein. Just when I thought he wasn't going to respond, Nathaniel spoke up. \"She had no use for him,\" he stated. \"She treated him like rubbish and acted like she was better than us. Always lookin' down on us. I wish you had told her. It woulda served her right.\"\n\n\"Nothin' good would have come of it,\" Victor muttered.\n\n\"And so Lady Arnifour paid her husband to keep him quiet,\" Colin repeated.\n\n\"She did. He spent the whole of Elsbeth's life forcing money from her. You've seen the estate. It's fallin' apart. And now there's only the few of us left to look after it. It's a disgrace.\" He shook his head again.\n\n\"Then you must be glad he's gone,\" Colin said.\n\n\"No you don't!\" Nathaniel leapt off the bed. \"You aren't gonna scab this on my father. Better you take me. The inspector\u2014\"\n\n\"Oh, to hell with the inspector,\" Colin shut him down. \"Stop bringing that bloody wretch up and stop confessing to a crime you didn't commit. You're growing tiresome.\" He glanced back at Victor. \"I assure you I would never try so obvious a way to entrap you if that were my intention.\"\n\nNathaniel dropped next to his father again.\n\n\"I am glad he's gone,\" Victor finally said. He looked small and inconsequential next to his lanky son, but there was a fire behind his eyes as he spoke. \"He was a vile and hateful man who took some great pleasure in making his wife miserable.\"\n\n\"A man isn't guilty for wishing something to be so!\" Nathaniel growled.\n\n\"Of course.\" Colin slid his gaze to me for an instant. \"Though I suppose that depends on how badly he wants that thing.\" He came over to me. \"In this circumstance I agree with you, Nathaniel. As I have repeatedly told you both, I am not accusing either of you of anything. I am only gathering information.\" He paused, but neither of the Heffernans even glanced at him. \"There is one more thing I should very much like to know, Victor. You claim the Earl extorted money from his wife for years to remain silent about Elsbeth's progeny, yet he seems to have suffered from a reputation for being endlessly short on funds. How do you explain that?\"\n\n\"It was a ruse, Mr. Pendragon.\"\n\n\"A ruse?\"\n\n\"To demonize his wife.\"\n\n\"Ah . . . ,\" Colin said in a tone I recognized to be fraught with skepticism. \"Then that is a thing he must have wanted very much, for it seems to have cost him as well.\"\n\n\"You don't know how much he hated her,\" Victor muttered. \"A man like that cuckolded . . .\"\n\n\"Ours can be such an unforgiving gender.\" Colin smirked as he turned on Nathaniel. \"I think you're right to stay here, Nathaniel. Despite the coroner's findings, I doubt Inspector Varcoe would be of a mind to allow you to return to the Arnifour estate.\"\n\n\"I have no intention of ever going back.\"\n\nVictor glanced at his son but kept quiet. He'd either lost the will to argue or finally come to understand the irrefutable truth of what Nathaniel had been saying.\n\n\"Stay out of sight,\" Colin warned as we headed for the door. \"But I'll expect you to remain available should I wish to speak with you again.\"\n\n\"I'm not going anywhere,\" he muttered tersely. \"Not yet anyway.\"\nCHAPTER 25\n\nThe next morning Colin and I rode out to the Arnifour estate without the courtesy of any advance notice. He was eager to catch the lot of them at home, unsuspecting, to see what we might discover. As we clattered across the forecourt I caught the shadow of a face peering out at us from between the curtains of an upstairs window. The sight reminded me of just how many places this enormous house offered a person to hide. In effect, it made Nathaniel's flight to Whitechapel seem redundant. He would probably have been safer hiding in the moribund wings of the estate.\n\n\"You needn't wait,\" Colin said to the driver. \"We'll make our own way back.\" I was puzzled by his pronouncement and wondered how he meant for us to get home again, but decided not to second-guess him. If this was to be a day of the unexpected, and we were certainly starting it out that way, then I was determined to allow things to unfold as they would.\n\nI climbed the porch steps and pounded on the door as Colin came up beside me, the rhythmic clacking of our cab's wheels receding as we waited for the dour Mrs. O'Keefe to answer my knock. It took several minutes, as it inevitably does when unannounced visits are made, as nothing is at the ready and the staff can seldom be counted on to make haste. And why would they? Certainly no one of consequence would ever arrive without proper notification.\n\n\"I should've guessed,\" Mrs. O'Keefe said when she finally pulled the door open. She stepped back, wearing the disparaging look of a headmistress, her black eyes glittering with disapproval.\n\nI was needled with discomfort as I walked past her, and yet Colin appeared quite oblivious. \"You will announce us to your mistress, please,\" he said, and though he bothered to use the kindness of a pleasantry, it was obvious he did not mean it as a request.\n\n\"Madame has only just risen.\" Her note of scolding was unmistakable.\n\n\"I'm sure,\" he muttered as he moved across the foyer. \"We shall wait in the study as always.\"\n\n\"Of course,\" came her clipped reply. \"Most unorthodox,\" she stated in full voice as she turned on her heels and headed for the foyer staircase.\n\n\"And so it is,\" Colin called after her. \"But we Brits are too conventional anyway. Perhaps more of such behavior would serve us better.\"\n\n\"Must you antagonize?\" I hissed under my breath.\n\n\"Antagonize?\" He looked wholly innocent as we settled before the unlit fireplace in the study and he began rolling his usual crown between his fingers. \"Is that what I did?\"\n\n\"And what would you call it?\"\n\n\"Yes . . . well . . .\" He shrugged. \"She really should learn her place.\"\n\nI started to laugh, the incongruity not lost on me between Mrs. O'Keefe's behavior and that of Mrs. Behmoth, but before I could say anything, Colin shoved the crown into his pocket and jumped up, a warm smile spreading across his face as he said, \"Lady Kaylin . . .\"\n\nI turned to find Kaylin standing in the doorway wearing crop pants, a crisp white blouse and hunter green tailcoat, and high black boots, her delicate features alive with a most welcoming smile of her own.\n\n\"Kaylin,\" she chided. \"What a pleasant surprise.\"\n\n\"The pleasure is ours.\" Colin nodded his head.\n\nShe waved him off with a laugh as she took a seat across from us. \"Such a flatterer. Emmeline says a man who flatters intends only to deceive.\"\n\n\"I assume you're referring to Mrs. Pankhurst?\"\n\n\"I am.\" Her smile grew.\n\n\"I rather think she is correct . . . at least most of the time. Yet she's wrong where I am concerned, for what possible motive could I have for idly filling the head of such a charming woman as yourself?\"\n\n\"Perhaps you interpret her statement in too narrow a context?\"\n\n\"Do you suppose? It would seem to me that Mrs. Pankhurst had only the most literal intent in mind.\"\n\n\"And I believe you underestimate her. She will make a difference one day, Mr. Pendragon. She will be remembered as a pioneer for the rights of all the oppressed.\"\n\n\"You must forgive me,\" he smiled, \"I don't mean to disparage, but I think the only way your Mrs. Pankhurst will be remembered is if she chains herself to the gates of Buckingham.\"\n\nShe scowled. \"And I would have thought you to be a more forward-thinking man.\"\n\n\"One cannot be progressive without first taking into account reality. For instance, I think you will agree that it's impossible for a solitary man to push an ox up a hill. The trick is to convince the ox that the top of the hill is where it wants to be.\"\n\n\"I do hope she's not lecturing you about that wretched sisterhood again. . . .\" I turned around to find Eldon leaning against the doorjamb with his arms folded across his chest. \"She does go on so.\"\n\nKaylin remained rigidly still for a moment, looking as though she were taking in her brother's disheveled appearance through the back of her head. When she finally deemed to turn to him, however, I could see her face begin to tighten. \"Suffering from those dreary tremors again this morning, Eldon?\" she scoffed.\n\nHe did look very much the worse for wear, having clearly slid on a pair of slacks that appeared to have spent some considerable time in a wad, and a shirt dotted with a m\u00e9lange of stains, its tail fully asunder. I don't think his hair had even had the benefit of a quick run-through by a hand, and yet he was able to rouse his perpetual rogue's grin as he padded barefoot across the study to the small bar. When he swept past his sister I could see how morbidly pale he looked in contrast to her flushed, healthy glow.\n\nHe took a quick shot of something and smirked at her. \"How like Mother you're becoming. It's so unflattering.\" He moved out from behind the bar and glared at me and Colin. \"Tell me, gentlemen, have you managed to hunt down that scoundrel Nathaniel yet?\" I glowered back at him. \"No?\" he continued when neither of us answered him. \"Let me guess. I'll bet you're still concentrating on interviewing everyone this family has ever spoken to. You'll be wanting to dig up my pet rabbit, Cecil, I'm sure. I used to tell him all sorts of horrid little secrets.\"\n\n\"I have no interest in Nathaniel at this point,\" Colin answered.\n\n\"Really?! Do tell.\" Eldon's lack of earnestness was matched by the smirk blemishing his face.\n\n\"You can be such a bore!\" Kaylin snapped.\n\n\"Now, now . . . if you please . . .\" Colin leaned back in his chair and I could almost hear his eyes rolling. \"I presume you're going for a ride?\" he said to Kaylin.\n\n\"I am. The horses don't get enough exercise with Nathaniel gone. I don't think they should suffer for the things we've done.\"\n\n\"Speak for yourself,\" Eldon groused. \"Do you need me, Mr. Pendragon? Because I have an engagement this morning.\"\n\n\"I do have a couple quick questions.\" He stood up and moved over to the fireplace, squaring himself off between the two of them. \"How old were you when Elsbeth was brought here?\"\n\n\"Elsbeth? What difference does that make? You think she killed our father and then beat herself senseless to cover her tracks?\" He snickered, but to her credit, Kaylin kept still.\n\n\"Humor me.\"\n\n\"How the hell am I supposed to remember something like that? She's been here forever. Isn't that enough?\"\n\n\"I was almost three,\" Kaylin spoke up. \"Mother told me I was almost three when she brought Elsbeth home. That would have made you six.\"\n\nHe shrugged with disinterest and slouched back to the bar. \"It amounts to most of our lives. I assume that's what you're getting at. She was like our sister. . . .\" He waved his arms expansively. \"She was like the dear sister I never had.\" He laughed.\n\n\"And what of her parents?\" Colin pressed. \"What happened to your aunt and uncle?\"\n\n\"Dead.\" Eldon came around and flopped into a chair. \"A yachting accident. Or maybe it was boredom?\"\n\nIn an instant Kaylin stormed across the room and slapped her brother across the face with a crack that echoed in the confined space. It was startling, and even more so when the red-hot print began to rise on his cheek. \"Have you no respect for anyone? \" she seethed. \"Has your drinking robbed you of all decency?\"\n\nHe pushed himself to his feet, towering above her, and for a moment I thought he might pummel her back, but he only stepped around her and stalked back to the bar. \"We all have our crutches,\" his voice was low and flat as he refilled his glass, \"whether it be drink, drugs, pleasures of the flesh, or that women's claptrap you subscribe to, so I wouldn't point fingers.\"\n\nShe stared at him with a mixture of fury and revulsion before storming out of the room.\n\n\"Insufferable bitch,\" he said as he downed a shot.\n\n\"What are you talking about?\" I turned at the sound of Lady Arnifour's voice to find her standing in the doorway, a vision of hurried preparations, her thick makeup indelicately applied, her dressing gown clutched tightly in a thin hand, and her dark wig the slightest bit askew. \"What have you been telling them?\"\n\n\"The truth,\" he sneered. \"But I do hope that doesn't cause you to lob another grenade at me.\"\n\nShe didn't flinch. \"You confuse the venom you find at the bottoms of your bottles for truth. Now get upstairs and pull yourself together.\"\n\nHe glared at his mother like he was staring at muck caught between his toes, but she didn't waver the slightest as she scowled back at him, and after a moment he had little recourse but to storm from the room with what dignity he could muster.\n\nLady Arnifour closed the doors behind him with a look I couldn't quite gauge before turning back to us with a forced smile that failed to contain a shred of welcome. \"I'm afraid I must apologize for my son's behavior yet again. It seems he is always displaying the worst of himself when the two of you are here.\"\n\n\"You mustn't,\" Colin replied as he flashed his own hollow grin. \"After all, we did descend upon you without notice.\"\n\n\"I'm sure you have your reasons,\" she said, moving into the room and perching on the edge of a chair like someone who didn't expect to be there long. \"Do you bring news?\"\n\n\"I've not solved the murders if that's what you're asking, but I have come into some information which I simply must discuss with you.\"\n\nLady Arnifour flicked her gaze to me before abruptly springing to her feet and going to the windows. I was certain I'd spotted a look of concern in her eyes so was not surprised when she kept silent for a few minutes. I peered over at Colin and found him focused on her back and knew he meant to wait her out. And so we stayed that way until I heard the sound of a galloping horse draw near and caught sight of Kaylin bolting past. In the brief moment it took her to cross my field of vision I recognized the skill with which she drove her handsome mount. Lady Arnifour also seemed to soften as she watched her daughter thunder by, and although she did not turn back to us, she did finally begin to speak.\n\n\"Poor Kaylin has suffered the sole responsibility of caring for our horses since Nathaniel's disappearance. Victor just doesn't have the heart for it.\"\n\nI took note of her informal, almost intimate use of Victor Heffernan's name and realized, in that one small gesture, that everything had changed.\n\n\"I would appreciate your providing me a closing statement, Mr. Pendragon,\" she continued, \"as I won't be requiring your services any longer.\"\n\n\"A closing statement?\" He lurched out of his chair. \"But I haven't finished my investigation. I haven't solved the ruddy case.\"\n\nShe persisted in staring out the window in spite of the fact that Kaylin had long since passed from her view. \"I understand all of that, Mr. Pendragon, but as I brought you into this sorrowful mess, so I am now removing you from it.\"\n\nHis face soured. \"May I ask\u2014\"\n\n\"You may not,\" she cut him off. \"I don't owe you an explanation, only the remuneration for your services.\"\n\n\"You're making a mistake.\"\n\n\"Perhaps. But it is mine to make.\"\n\n\"I will solve this case.\"\n\n\"Not at my expense.\" And with that she turned from the window and faced us, her expression as tight as granite.\n\n\"I see,\" he said grimly. \"Then am I to understand that you're no longer interested in seeing justice served in the deaths of your husband and daughter?\"\n\nI almost gasped as he flung the question at her and could tell by the mortification on her face that she was equally stunned.\n\n\"How dare you . . . ,\" she blustered, but it was evident that the comment had struck bone.\n\n\"You hired me to discover the truth and that's exactly what I've been doing.\"\n\n\"I hired you to prove the innocence of a man and you have done that. Nathaniel's flight speaks for itself. The inspector has men searching the city for him and in time, perhaps, he will be found and brought to justice. I suggest you accept your success, Mr. Pendragon, and take heed with such wild innuendos.\"\n\n\"You know as well as I do that Nathaniel is innocent.\"\n\n\"Your presumption is offensive.\"\n\n\"My presumption is no more offensive than your willingness to allow that boy to pay for a crime he did not commit,\" he snarled at her.\n\nShe stormed across the room and flung the doors wide. \"We are finished here,\" she seethed. \"I will thank you to leave.\"\n\nHe took his time walking to the door, holding her gaze with his own. \"Very well,\" his voice was measured and flat, \"but know that I'll not allow him to be turned over to the Yarders and I would caution you against doing the same.\"\n\n\"You forget yourself, Mr. Pendragon!\" she snapped.\n\n\"I do no such thing,\" he answered. \"I do no such thing.\"\nCHAPTER 26\n\nI followed Colin without a word before remembering that he had released the cab upon our arrival. I couldn't believe that he meant for us to walk all the way back to town and so hung my hopes on the probability that he'd already formulated a plan. But as we continued to storm down the driveway without the slightest falter, I began to give up hope. And then we crested the driveway's second hill and he abruptly turned right and plunged into the woods without so much as a backwards glance to see if I was following. He knew I would be.\n\nWe continued in silence, crashing through thick brush that clawed at my trousers until we emerged onto a promontory that overlooked a velvety green meadow. Colin stopped and leaned back to draw in a deep expanse of morning air. \"Spectacular,\" he said breezily. \"Why is it the moneyed are the last to appreciate what they have?\"\n\n\"Well . . . ,\" I sucked in my own deep breath, \". . . because it's impossible for a person to value that which they've never had to do without.\"\n\nHe chuckled. \"Profound.\"\n\n\"Tell me . . . ,\" I said as I gazed out to the horizon, \"did you remember you'd let the cab go when you stalked out of the house?\"\n\nHe shrugged. \"Not exactly. But I can't remember everything. You are certainly free to contribute whenever you think it might be valuable.\"\n\n\"I shall remember that the next time you're crossing words with a client who lives out in the country.\"\n\n\"Crossing words?\" His nearest eyebrow shot up. \"Is that what you think happened?\"\n\n\"Didn't it?\" I couldn't help chuckling. \"Wasn't that you who just threatened her about giving Nathaniel to the Yard?\"\n\n\"I suppose so.\" He waved me off and started barreling across the field, leaving a trail of bent grass in his wake, which I followed. \"I'm not really angry with Lady Arnifour,\" he called back, \"because I'll solve this case anyway. I don't need another farthing from her.\"\n\n\"So you don't care about being fired?\"\n\n\"Fired?!\" He curled his mouth with distaste. \"I prefer to call it freed. Can we leave it at that?\"\n\n\"Still . . .\"\n\n\"Let me ask you a question.\" He tossed back a rogue's grin. \"Did you notice at what point in our questioning of Eldon that Lady Arnifour arrived?\"\n\n\"I haven't a clue.\" I laughed.\n\n\"We were talking about his earliest memories of Elsbeth and what had happened to her parents. He was reciting the story he'd been told as a boy. Lady Arnifour knew where I was leading him. It's why she stopped our conversation and sent him slinking upstairs. And I've no doubt she knows exactly where we got that information from.\"\n\n\"Because the Heffernans are the only other ones who know.\"\n\n\"Precisely. And she likely fears that if we can get those delicate details out of them, then there isn't much else we won't be able to extract.\" His pace slowed as he continued to move diagonally across the field toward another stand of trees. \"She knows we've discovered where Nathaniel is hiding.\" He exhaled slowly. \"I suspect we've become something of a threat to Her Ladyship. No doubt we've discovered far more than she ever intended. In fact,\" he nearly growled, \"we have learned everything about this blasted case except who the bloody hell killed her husband and illegitimate daughter, and why?\"\n\nI was startled by the intensity of his frustration as I stared at him. \"How can we be a threat to her? We're trying to solve these murders. I mean, it's one thing that she didn't care about her husband\u2014that marriage had soured years ago\u2014but Elsbeth was her own flesh and blood!\"\n\n\"Yes. And she was born of an illicit union that caused Lady Arnifour a lifetime of grief.\"\n\n\"That's deplorable!\"\n\nI could tell he was struggling not to laugh at my indignation. \"Not everyone harbors the same sense of propriety that you do. And that is exactly what has kept us employed all these years: the rabble who believe they are either above the law or smarter than it.\"\n\n\"But we're talking about love. We're talking about family bonds\u2014\" But even as the words fell from my mouth, I recognized the intricacies of what I was saying. I knew better. My own childhood spoke of something very much different from the whimsy I was trying to float.\n\n\"Where have you gone off to?\" I heard him say, and allowed him to impel me back. \"Work awaits,\" he announced, gesturing toward a rocky outcropping a short distance away. I followed his gaze and spotted Kaylin Arnifour seated on one of the boulders, her horse tied to a willow tree off to one side. She was staring away from us, gazing resolutely at the vast grassy lands stretching beyond her. \"Did you know she'd be here?\" I asked.\n\n\"I hoped she would. I've been following her trail since we left the house. Surely you knew that?\"\n\n\"Trail?\"\n\n\"Bent grass, snapped underbrush, fresh hoofprints. Have you not noticed any of it?\"\n\nI shrugged. I had no better answer to preserve my self-respect.\n\n\"Well, where did you think we were going?\"\n\nI shrugged again.\n\n\"Such devotion.\" He laughed.\n\n\"So what are we doing here?\" I asked, eager to stop feeling the fool.\n\n\"We've come to gain some clarity.\" He started moving toward the promontory Kaylin was perched upon. \"And to get a ride home.\"\n\nIt was my turn to laugh, as I knew that had not been part of his original plan, and that's when Kaylin turned and spotted us. She waved as though pleased to see us, which I doubted given the desolation of her chosen spot.\n\n\"I hope you don't mind the intrusion,\" Colin called as he picked his way across the boulders.\n\n\"Not at all. You're both welcome to my bit of refuge any time you feel the need. You'll find me here often, I'm afraid.\"\n\n\"It is a beautiful place,\" Colin said as he achieved the summit.\n\nI pulled myself up behind him and was shocked by what I saw. The lush field was indeed remarkable, dotted with great stands of oaks and willows in a haphazard harmony that only nature can produce. Yet off in the distance to the left, sitting like a smudge on an otherwise flawless panorama, stood the scorched remains of the barn her father and half sister had been murdered beside. It was an unnerving sight that could only be ignored with considerable effort.\n\n\"Is this where you seek your solace then?\" Colin asked as he dropped down next to her.\n\n\"Elsbeth and I used to ride out here all the time. It was our sanctuary. I haven't been up here since . . .\" She pulled her knees in tight and hugged herself. \"It doesn't help to be able to see that.\" She nodded toward the charred remains. \"I've decided to face this direction for the time being,\" she said as she half-turned so she was facing Colin.\n\n\"Once that's torn down and hauled away you'll see the earth heal herself,\" he reassured. \"There'll be no trace. You'll have this to yourself again.\"\n\n\"I know,\" she sighed. \"But at the moment I can't imagine that will ever be true.\"\n\n\"Never discount the resilience of either nature or the human spirit.\"\n\n\"I'm afraid my family's spirits come mostly in a bottle.\"\n\n\"So I've noticed.\"\n\n\"Don't judge us too harshly, Mr. Pendragon.\" She sighed again as though the effort of defending her family were more than she could bear.\n\n\"I don't judge you at all. I must admit to living something of an unconventional life myself,\" he said, flicking a glance at me that was thankfully missed by Kaylin.\n\n\"But you uphold the standard that everyone is expected to live by, Mr. Pendragon. The standard of law.\"\n\n\"I suppose I do.\" He leaned back on his hands. \"But only those laws that make sense to me.\"\n\n\"Are you telling me there are laws even you will break?\" She grinned.\n\n\"There are laws I break every day.\" He smiled back.\n\n\"May I ask you something?\" I interrupted, eager to steer the conversation to safer grounds. \"Are you and your neighbor, Mrs. Roynton, well acquainted?\"\n\n\"Abigail Roynton?\" She looked at me curiously. \"We speak whenever we happen to attend the same engagements, but I would never call her a friend. I find her indiscretions to be the sort of vulgar behavior that sullies the reputation of all women. Never mind that my father fell prey to her. Men can hardly be blamed for what they have no control over. And I mean no offense.\" But I could see she meant exactly what she'd said. \"And why do you ask such a thing?\"\n\n\"Because while I also found Mrs. Roynton unconventional to be sure, I thought there was something rather liberating in her ideals\u2014\"\n\n\"Liberating?!\" She nearly choked as she glared at me. \"If behaving without scruples can be construed as liberation, then I suppose you're right. I find her boorish and nothing less than despicable. It does nothing but impede the good work of the suffragists.\"\n\n\"Of course,\" I demurred, though I was actually wondering whether she thought Abigail Roynton capable of complicity to commit murder.\n\n\"Don't fall out of step with the movement and get left behind,\" she continued to persist. \"We are at the precipice of a new millennium and with it will come a world where men will no longer be allowed to accommodate their every whim at the expense of women. I'm sure I needn't remind you that without women there would be no men.\"\n\n\"Yes. We figured that out some time ago.\" Colin flashed a tight grin. \"But do let me ask you about Eldon. . . .\"\n\nShe grimaced. \"I must apologize. I behaved badly with him and I'm terribly sorry. Eldon's always had a tougher go of things. Our father was forever demonstrating his disapproval and I'm afraid Eldon took the brunt of it.\"\n\n\"And what was it your father was perpetually disapproving of?\"\n\nKaylin stared out across the landscape for a moment before answering. \"I always remember Eldon being an awkward boy, terribly shy, hanging around my mother's skirts, having no interest in his studies or hunting. For the longest time my mother promoted that. She protected him. But she got distracted as we grew older and eventually . . .\" She let her voice drift off.\n\n\"Your brother's travails notwithstanding,\" Colin said with a noticeable lack of empathy, \"there is something weighing on my mind that I hope you might be able to explain.\" He steadied his gaze on the side of her face. \"As I'm sure you are aware, your father had a reputation for being kept on a tight financial rein by your mother. Nevertheless, I've come to believe that he may in fact have had access to considerable funds throughout the years. If that proves correct, what do you think he might have done with any money he was able to amass?\"\n\n\"Considerable funds?! My father?! That's absurd. He had what my mother gave him, and that only begrudgingly.\"\n\n\"I'm not so sure that's true.\"\n\n\"No one would have given him money. I'm sorry, Mr. Pendragon, but that doesn't make sense.\"\n\n\"Even so, for sake of the exercise, I'd like to hear what you imagine he might have done with a ready supply of cash?\"\n\nShe looked at him a minute, and then turned to me as though I might see the folly in what he was suggesting, but I knew he meant to have an answer. \"I can't even fathom such a possibility. My father was horrendous with money. I'm afraid you've struck upon a preposterous notion. Whoever told you such a thing was deceiving you. It isn't true.\"\n\n\"Well then . . .\" He smiled easily and turned his gaze back across the field. \"I'm only trying to ensure I follow every possible supposition.\"\n\n\"A noble goal.\" She stood up and stretched. \"But I'm afraid I must be getting back to the house. I have four more horses to run today.\"\n\n\"Of course, but might we trouble you for one more thing?\"\n\n\"I'll do whatever I can,\" she said as she nimbly picked her way down off the boulders.\n\n\"We find ourselves without a way back to town. Could you possibly?\"\n\nShe glanced up at us, a generous smile parting her lips. \"I'll have to take you one at a time.\"\n\n\"Certainly.\"\n\nShe let out a satisfied laugh. \"I very much like this. For once the damsel gets to come to the rescue.\"\nCHAPTER 27\n\nI admit that I was surprised. After Kaylin dropped me off I had assumed Colin would be no more than an hour behind, so when he arrived three hours later reeking of lavender perfume and champagne I was not particularly pleased. He explained that he had decided to visit the widow Roynton while waiting for Kaylin to come back for him, and that Mrs. Roynton had sent him home in her own carriage. \"She's really just an old flirt.\" He snickered.\n\n\"I should hardly think anyone would refer to her as old,\" I replied with perhaps a touch more sarcasm than I had intended.\n\nIt got another snicker out of him just the same. \"Shouldn't you be asking if I learned anything of value?\"\n\n\"I was getting to that,\" I said. \"It's just hard talking to you when you smell like a wine-soaked floral shop.\"\n\nHe sniffed at his coat as he pulled it off. \"Hmm. I suppose you have a point.\"\n\nI could only shake my head. \"She helpful then?\"\n\n\"Helpful?!\" he repeated as he dropped to the floor and began a quick succession of push-ups. \"I'm happy to report that the lovely widow admitted several things to me,\" he said without missing a beat. \"Not the least of which is that she can absolutely believe our noble Earl had access to money he didn't let on about. She insists there was no limit to his levels of deceit. Yet she professes no idea as to what he might have done with any such sizeable fortune. Nevertheless . . . ,\" he jumped up and rotated his arms with a satisfied sigh, \"she suggested someone who she believes shares the late Earl's lack of conscience and just might have an idea.\"\n\n\"And who would that be?\"\n\nHe grinned as he snatched up one of his dumbbells and began curling it effortlessly while pacing. \"Poor, carping Warren Vandemier. She thinks the Earl's partner has far more up his sleeve than he is letting on.\"\n\n\"But all he did was prattle on about how the Earl cheated him.\"\n\n\"Precisely. He put up such protestations that it reminded me of that Shakespeare quote.\"\n\n\"What Shakespeare quote?\"\n\nHe cocked an eyebrow and glanced at me. \"You know the one: Methinks he doth protest too much?\"\n\n\"The lady.\"\n\n\"What?\"\n\n\"The lady doth protest too much. Hamlet's mother says it.\"\n\nHe shrugged, switching the dumbbell to his other hand. \"Details.\"\n\n\"So now you're tying your deductions to the intrigues of literary characters?\"\n\nHe shrugged. \"Good literature, by its very definition, casts an unwavering eye on the truth of humanity. That's what gives it its profundity.\"\n\n\"This from a man who never reads.\"\n\n\" 'Ay?\" Mrs. Behmoth hollered. \"Ya got comp'ny comin'. Stop yer cluckin'.\"\n\n\"Ever so gracious,\" I muttered.\n\n\"I 'eard that. . . .\"\n\nColin hurried to the window and gazed down onto the street. \"Well now, here's an unexpected turn. Eldon Arnifour has come to pay a visit.\"\n\n\"Lock the liquor cabinet.\"\n\n\"Perish the thought,\" he said as he rolled the dumbbell under the settee and took a seat. \"It's important that he have plenty to drink lest he harbor any hesitancy about saying whatever he's come to say.\"\n\n\"Lord Eldon Arnifour comin' up!\" Mrs. Behmoth yelled from the bottom of the stairs.\n\n\"I hate when she does that,\" I grumbled.\n\n\"I should think you'd long be used to it by now.\"\n\nNot a moment later Eldon appeared on the landing in his typical disheveled fashion, sporting a crooked grin that undoubtedly spoke more to the amount of drink he'd consumed than any sense of good mood. \"Have a seat,\" Colin said magnanimously. \"Make yourself at home.\"\n\n\"I don't think you really mean to say such a thing to me.\" He chuckled as he dropped onto the same settee his mother had collapsed upon the day she hired us. \"I'm afraid home has no particular fondness for me. But could I trouble you for a drink?\"\n\n\"I assume you're not referring to tea?\"\n\n\"Not unless there's a fair amount of scotch in it.\"\n\n\"We could do that if you'd like or we could just forego the tea completely,\" Colin said, producing our bottle of scotch from its eternal resting place in the cupboard.\n\n\"Now there's the best idea yet. No wonder your services are so well respected, Mr. Pendragon. And anyway, I'd hate to force that delightful woman downstairs to tote a tray of tea all the way up here.\"\n\n\"And for that I know she would thank you.\" Colin poured three small glasses, giving Eldon the most, and handed them out. If Eldon noticed that his glass was fuller than ours he certainly didn't seem to care. \"So tell me . . . ,\" Colin sat down and casually placed his untouched drink on the table between us, \"to what do we owe this unexpected pleasure?\"\n\n\"I'm tired of being censored by my mother every time we try to have a conversation. The old harridan thinks she controls everyone, but she doesn't toe the line on me. Oh no. I've come to say some things I'll wager you've not heard before,\" he said with great bluster before he drained his glass. \"Is there a limit?\" He glanced at Colin.\n\n\"Only by virtue of what's in the cupboard. Help yourself.\"\n\nEldon popped up, not warranting a second invitation, and refilled his glass. \"Did you know, gentlemen, that my esteemed father once had quite the dalliance with that charming bulldog Mrs. O'Keefe?\" He laughed coarsely. \"Just imagine that, if you will.\"\n\nColin slid his gaze to me, but I couldn't tell if it was doubt or disbelief in his eyes. \"And why would that bear any interest? It seems to me your father rutted just about anyone who would let him.\"\n\nEldon wandered back over to us, the whiskey bottle clutched firmly in one hand. \"Ah yes, it is a curse of the male Arnifour progeny. It is a need, not a desire, that we elevate to an art. Surely you must be able to understand that, Mr. Pendragon. You're something of a strapping man yourself. I'm sure you've turned the ladies' heads many a time.\"\n\n\"I'm sure I haven't noticed,\" he drolled. \"But you were talking about Mrs. O'Keefe. While I'm certain she must be a delightful housekeeper, I'm finding it something of a struggle to fathom why your father would be interested in shagging her.\"\n\nEldon chuckled as he shrugged lazily. \"Availability, I suppose. My mother was indisposed carrying Kaylin and where else could the poor man turn? We didn't have any other female help at the time and she's always made such a fuss over him. Anyone can see it. I wasn't quite five at the time and I knew she was keen on him.\" He winked and tipped his glass at Colin as he took another sip.\n\n\"Well, this is all very fascinating . . . ,\" Colin said as he got up, \"but I fail to see\u2014\"\n\n\"Then stop interrupting,\" Eldon sniped as he stabbed his glass onto the table in front of him. \"You are missing the point, Mr. Pendragon, because you have not let me finish.\"\n\nColin snatched up the hunting knife he had left on the mantel and began buffing its blade with a handkerchief he pulled from his pocket. \"Forgive me,\" he said with more sincerity than I could have achieved at that moment. \"By all means . . .\"\n\nNow that Eldon knew he'd earned our fullest attention, or at least the closest we were ever likely to accord him, he made a great show of pouring another two fingers into his glass and settling back before continuing. There was also a rakish grin teasing the corners of his mouth. \"My mother was quite ill when she carried Kaylin. She kept to her room nearly the entire time, which left my father to chase Mrs. O'Keefe about like a middle school boy. This is quite some time ago.\" He chuckled and allowed himself another sip of his drink.\n\n\"While I was certainly very young, I was not blind to the incongruity of my father and Mrs. O'Keefe sneaking about, especially with her giggling like a coquette whenever my father was nearby. It was all very appalling, which is precisely why I remember it. Why is it that such things stick in our brains while that which is most cherished is as fleeting as a cut rose?\"\n\n\"Are you asking me?\" Colin asked as he continued to buff the knife blade. \"Or am I still just listening?\"\n\nEldon's brow furrowed. \"Really, Mr. Pendragon, you're being most uncivil when I've only just come to tell what I know.\"\n\n\"Yes, yes,\" he muttered. \"Very obtuse of me.\"\n\nEldon seemed to ignore Colin as he held his glass up right in front of his eyes with a look of great enticement. \"I should think you would find it interesting to hear that our dear Mrs. O'Keefe began putting on weight while my own poor mother was lying about upstairs trying to ensure the safe arrival of our Kaylin. I remember it because I said something to my nanny about the suddenly expanding Mrs. O'Keefe and was quite soundly thumped for my cheek. It was only some years later that I realized what had likely transpired.\" He leered.\n\nI clamped my mouth shut to keep my jaw from unhinging, certain I must be misinterpreting his meaning. Even Colin kept still for a protracted period of time before finally screwing up his face and asking, \"Are you suggesting that Mrs. O'Keefe was with child at the same time as your mother?\"\n\n\"Ah . . .\" Eldon grinned roguishly as he tipped his glass. \"There's the sleuth the papers adore.\"\n\n\"And you're saying your father was responsible?\"\n\n\"Come now.\" Eldon took another sip as he stretched out on the settee. \"Is that really so hard to believe? We've already established his propensity for a tryst, and you cannot deny that he was fully capable.\" He swept a hand across his body with a flourish, clearly meaning to present himself as the truth of that statement.\n\n\"How old were you at the time?\"\n\nEldon heaved a sigh as though bothered by such a banal thought. \"I was just about six and very precocious, and would've remained so if I hadn't been driven to spirits by the time puberty seized me.\" He scowled. \"Mrs. O'Keefe got fleshy,\" he continued after a moment, \"and then she was gone.\"\n\n\"Gone?\"\n\nHe looked up at us and in that instant his usual derision had returned. \"Packed off like the embarrassment she had become,\" he said gleefully. \"She was gone for about four months. Who the hell can remember. But it was a bloody long time, that's for sure. Certainly long enough\u2014\" He let the sentence hang in the air.\n\n\"Where were you told she'd gone off to?\"\n\nHe seemed to consider the question a moment as he cast his gaze about and pursed his lips. \"I don't really remember anymore. Sisters? Aunties? Dog pound? Hard to say.\"\n\n\"I see . . . ,\" Colin muttered, and I could practically hear his brain whirring. \"Suppose she had gone off to have a baby . . . what of it?\"\n\n\"Well, there's the thing.\" Eldon nearly crowed his enthusiasm. It was evident he was taking great merriment in our skepticism, which I could not help but find unsettling. \"Not long after Mrs. O'Keefe went missing\u2014it couldn't have been six or eight weeks later\u2014I awoke sometime in the night to a great deal of commotion. Dear Mother was not well, you see. There were all manner of people bustling about, and my cursed nanny kept trying to shoo me back to bed. But I wasn't having any of it. I hid in the shadows of the hallway until I saw them carry my mother past on a stretcher. There was a great crowd of people around her, so I couldn't see her face, but I could hear her crying. I remember being quite terrified.\" He let out a caustic laugh. \"Can you imagine?\n\n\"My father finally noticed me lurking about and yanked me back to my bedroom with his usual brute affection,\" he chuckled again, \"but not before I caught sight of the blood. There was a towel heaped on the floor of my mother's room that was saturated and a puddle of it near her bed. A young boy remembers a thing like that.\" He lifted his glass slightly and twirled its contents around a moment before deciding to continue. I couldn't tell whether he was drawn to the memory or repelled by it. \"And do you know what my father told that snot-nosed, weepy-faced boy after pulling him back to his bedroom? He said: Buck up, you little turd\u2014your mother might not make it and we can't have you sniveling about.\"\n\nI don't think I had really expected to hear anything much different, yet it remained striking just the same.\n\n\"I suppose your father was practical if nothing else,\" Colin said as he set the knife he'd been buffing back onto the mantel and stooped to poke at the fire. \"But your mother did return and she brought Kaylin with her.\" Colin stood up and turned to Eldon. \"She did bring Kaylin with her?\"\n\nA sly grin slowly grew on Eldon's face. \"So clever, Mr. Pendragon. Kaylin came. Eventually. About a fortnight after Mother had returned from the hospital and just days before Mrs. O'Keefe made her own discreet homecoming. They told me dear sister had been sick and almost died, but as I got older and remembered all that blood, I began to wonder who was fooling whom.\"\n\nColin moved around and dropped back into his chair. \"If what you're insinuating is true, why would your mother agree to such a ruse?\"\n\n\"And that's the thing.\" Eldon finished off his scotch and pounded the glass onto the table with finality. \"I believe this was perpetrated on my mother without her ever having the slightest notion. She wasn't around to see Mrs. O'Keefe's gradually burgeoning shape. And once my mother was in the hospital it would have been easy for my father to control what information she received. How he must have loved having her raise his daughter as though she were her own.\"\n\n\"Why would any doctor agree to such a sham?\"\n\nEldon laughed. \"Oh, come now, Mr. Pendragon, don't you know they're the worst type of addicts? They've got access to every sort of drug. And doesn't it take one addict to recognize another? That fact would never have been lost on my father.\" There was an odd note of pride in his voice.\n\nColin fished a coin out of his pocket and quietly began flipping it between his fingers. \"Of course,\" he said after a moment, \"this is all strictly conjecture on your part. Long-ago memories of a very little boy.\"\n\n\"Guilty.\" Eldon winked. \"But surely a man of your prowess has noticed how Mrs. O'Keefe dotes on little sister. And even now she remains the only one of us who gives a whit that Father's dead. Wouldn't she just be forever grateful that she had been able to tend to her own daughter all these years, even if the poor, stupid girl didn't know the truth.\"\n\n\"So why are you telling us this now?\"\n\n\"Suppose my mother recently found out the truth? Suppose she discovered the fraud he'd been perpetrating on her all these years. How enraged do you suppose she would be?\" He beamed with mischievous delight.\n\n\"So you are suggesting she may have had something to do with your father's murder then?\" Colin's tone remained smooth and steady even though the very idea that Eldon had come to dangle such an accusation was entirely repellent.\n\n\"Oh,\" his smile dropped, \"I'm more than suggesting it. My parents were a venal pair. If it wasn't for my inheritance I would have left that horrid place years ago.\"\n\n\"And how have you fared with your inheritance?\"\n\nEldon shoved himself off the settee and stretched. \"Everything my father owned has reverted to me.\"\n\n\"And Kaylin?\"\n\nHe waved Colin off. \"She inherits in name only.\"\n\n\"What specifically?\"\n\n\"Everything.\"\n\n\"Your sister is a part owner of an opium den?\" I blurted out, unable to contain myself.\n\n\"In name only, I said!\" Eldon barked. \"She has some ridiculous notion about liberating the women who work there. I told her to stick to her bloody horses and leave the rest to me. In fact, I think I may just go to the club tonight to claim what's rightfully mine from that maggot my father was in business with.\"\n\n\"Indeed.\" Colin's face turned grim. \"Then perhaps we should come to your club tonight as well.\"\n\n\"Oh,\" he flushed, \"you really must. Warren Vandemier had best beware, for tonight he will be made to pay. . . .\"\n\nI detested the idea of watching a surly and intoxicated Eldon Arnifour harangue against an equally addled Warren Vandemier. Even more so now that Eldon had so joyfully come to implicate his own mother. But most of all, I dreaded the thought of being inside an opium club again.\nCHAPTER 28\n\nWe arrived just after eleven that evening, both dressed plainly in an effort to be inconspicuous, although we'd had to use Eldon's name to get in. Colin had managed to refrain from asking if I was certain about accompanying him here again, but I could tell by his surreptitious glances that the question did not hover far from his lips. Everything looked familiar: the dense and seductive haze that wound through the scattered groups of people sharing pipes and the occasional loners randomly huddled about. Most of the doors to the private rooms lining the entrance hallway were closed, with the sheer drapery hanging around the main space affording what little privacy the rest of the clientele was accorded.\n\n\"You like company tonight?\" asked the lovely Oriental hostess who ushered us inside.\n\n\"We would.\" Colin tossed her a dazzling smile. \"Might you be available?\"\n\nShe giggled behind a hand as she threw a glance toward the overbuilt man seated behind the door. \"You funny,\" she giggled again, \"but I only let customer in tonight. I find someone special for you.\" She looked at me. \"You want two?\"\n\n\"One,\" Colin answered. \"We needn't be greedy.\"\n\nShe giggled yet again as she led us to a small area at one side of the room where several unoccupied lounges were arranged. We made ourselves comfortable, an easy task in such a setting, while she struck off to arrange a companion for us.\n\n\"The trick . . . ,\" Colin leaned in close to me, \". . . will be to get our new friend to partake without actually doing so ourselves. Tell me you're okay.\"\n\n\"Now don't start that,\" I warned.\n\nHe offered a wry smile. \"All right then. Then I shall concentrate on worrying about myself.\"\n\n\"No worries!\" A beautiful Oriental woman with the slightest figure I'd ever seen sidled up to us. She had delicate features and straight black hair that fell below her waist. \"You relax,\" she said as she settled onto the lounge across from us, setting the water pipe she was carrying next to the candles on the table. \"I take care everything.\"\n\nColin passed her a few pounds as she pulled a small pouch from the bodice of her dress. The pouch was little more than a tiny piece of fabric tied together at one end to form a teardrop shape. I knew she would be carrying more than a handful of these. Business, and her pay, depended on it.\n\nShe carefully set the little package on the table between us and tugged at the string binding it, revealing an oily black goop at its center. I was mesmerized as I watched her scrape the gummy substance into the thimble-sized metal holder also strung around her neck. With a practiced hand she slowly waved it over the open flame of a candle.\n\nAfter no more than a minute she pulled a hairpin from behind her ear and gently coaxed the mixture into a thick, honeylike paste. As the pungent aroma gradually rose and drifted between us, swirling about and deftly stealing into our minds, she tipped the contents into the pipe's bowl and smiled at us.\n\n\"Who first?\" She turned the pipe toward Colin.\n\n\"The honor is yours.\" He smiled back at her. \"I must insist.\"\n\n\"No, no, no . . .\" She shook her head and thrust the pipe out again. \"Not right. Honor belong to customer.\"\n\n\"I insist.\" He snatched one of the candles and tilted it toward the bowl. \"Now don't make us wait. . . .\"\n\nThe young lady flicked her eyes left and right, clearly checking to see if anyone might catch her breaking what was certainly a house rule. Evidently satisfied, she quickly leaned forward and took a tug off the pipe without so much as touching it. She collapsed back onto her chaise and held the smoke deep in her lungs, her head lolling back as she stared up at the ceiling. After a few moments a gentle burst of smoke shot straight up from her mouth, mixing with the already murky air. \"Wunnerful,\" she sighed. \"Now you.\"\n\nColin snatched the pipe from her and made a great show of lighting it himself, bugging his eyes and alternating a sort of sucking and blowing combination that seemed to succeed in releasing a great deal of smoke without his apparently inhaling much. Still, it was more than I thought I could bear given the already toxic atmosphere swirling about my brain. So I was greatly relieved as I watched Colin push the pipe back toward our flushed attendant.\n\n\"No, no . . .\" She giggled. \"Not my turn. Is turn for friend.\" And as if to illustrate her point, she picked up the candle and waved it toward me. \"You next. You have fun too.\"\n\n\"My friend started earlier this evening,\" Colin smoothly informed her as he lifted the candle from her hand and turned it, and the pipe, back in her direction. \"Your turn. We have to catch up.\" He winked at her, sending her into a second round of soft-pitched giggles. This time, when he leaned the candle toward the bowl our companion didn't even bother to demur, but quickly swooped in and took a great, long pull.\n\n\"You very kind,\" she said, smoke leaking from the sides of her mouth. \"I do you service in return.\" She smiled boldly, glancing from Colin to me. \"I get us room. Show you trick with smoke.\"\n\nDespite my foggy head, I managed to keep from laughing as Colin leaned forward and patted her knee. \"No services. We've got that covered. What we'd really like is a little information. Could you help us with that?\"\n\nShe looked deflated, since that was money that would have gone directly to her. \"But I best in club. I please everyone.\"\n\n\"I'm sure you do. But what would be most pleasing is if you would tell us a little about the club's owner.\"\n\nThe woman scowled and shook her head. \"I not like that. I work in club. Make people happy.\" She pushed the pipe toward me and gestured determinedly with the candle. \"Your turn. No say no. Trust me. No talk about owner. Tonight, you owner.\"\n\n\"You misunderstand.\" Colin lifted the pipe from her hand and put it up to his own mouth, leaning forward and giving his elaborate show of smoking. \"I'm a friend of Mr. Vandemier's. I just want to make sure he's treating you well.\" He sent a great discharge of smoke into her face, which she instinctively inhaled.\n\n\"Oh.\" She smiled. \"No worry. Sometimes people say bad things, but I have no bad things to say.\" She took the pipe from Colin and pressed it into my hands. \"You have some. Way past time for you.\"\n\n\"Way past time . . . ,\" I repeated numbly, lifting the pipe to my lips as I leaned in toward the nearest candle. I clenched the metal nipple between my teeth and tipped the candle forward, and instantly a rush of familiarity overwhelmed me in a sickening yet somehow welcoming way. With the sound of my heartbeat rocketing in my ears, I sucked on the pipe until I felt the first smooth tendrils of smoke curl into my mouth. It tasted soft and soothing, like a dear friend who'd been gone too long. My lungs struggled to reach up and draw it in: one inhalation . . . one weedy taste . . . just one . . . but before I could be thusly seduced Colin yanked the pipe from my hands and ground his heel into my foot. I yelped, expelling the smoke in a single coughing burst.\n\n\"There, there,\" he muttered with mock concern, slapping my back a bit too heartily. \"Let's not be greedy.\"\n\n\"No,\" I stammered, my eyes watering as I looked up and spotted the concern behind his eyes. \"No,\" I repeated, more for myself.\n\n\"Would you say Mr. Vandemier is a good man?\" Colin turned his attentions and the pipe back to our young attendant. \"Is he fair? Kind?\"\n\n\"He not owner. He only manage. You say he friend . . .\" She slid the pipe out of Colin's hand and began to refill it. \"How come you not know that?\"\n\n\"He told me the club was his.\" Colin hiked an eyebrow as he watched her. \"Has he been feeding me a line of trifle?\"\n\nThe young woman giggled. \"He no own. Owner dead.\"\n\nEven with the miasma fingering about my mind I understood the profundity of her words. If she was right, if she was telling the truth, then Warren Vandemier had far overstated his value in the enterprise. There would be a great deal more for him to explain.\n\n\"Are you certain?\" Colin pressed as he snatched up the candle and lit the refreshed bowl for her.\n\n\"Oh yes. Everybody know he dead. Somebody kill him.\"\n\n\"I meant Warren Vandemier. Are you certain he's not the owner?\"\n\nShe shrugged as she took another tug on the pipe. \"He always getting yelled at. Make him mad. He take it out on us. With owner gone now he happy. Say he own place, but he still only manage.\"\n\n\"Then who's the owner?\"\n\n\"Owner dead.\"\n\nColin smiled and leaned forward, tipping the candle to relight the pipe for her. \"But if the owner's dead . . . ,\" he said with remarkable patience, \". . . then who's the owner now?\"\n\n\"Why don't you ask someone who knows?\" came the tight, grating voice of Warren Vandemier.\n\nI turned to face him and caught a glimpse of the hostess who'd seated us the first time lurking in the shadows. She had done us in\u2014again. I wondered whether she'd recognized us or if perhaps she'd caught us ministering to our young companion's obvious habit.\n\n\"I thought I'd put an end to the two of you skulking about!\" Mr. Vandemier growled.\n\n\"Skulking?!\" Colin stood up and smiled. \"And since when is availing ourselves of a public establishment considered skulking? I thought you'd be glad for the business.\"\n\n\"Perhaps you'd prefer to cease this charade and speak to me. It seems such a waste of your time otherwise.\"\n\n\"Not a waste at all,\" Colin answered. \"You'd be amazed at the things one hears in a place like this.\"\n\nWarren Vandemier scowled irritably. \"Let me be clear, Mr. Pendragon, I neither need nor care about indulging your business. So unless you'd like to be escorted from the premises . . . again . . . ,\" he nodded toward the entrance hall, \". . . then I would suggest you come with me. We can attend to whatever questions you have and then I shall ask you to leave for the last time. You . . . ,\" his brow furrowed deeper as he threw a sideways glance at me, \". . . and Mr. Pruitt are not welcome here.\"\n\n\"Well . . .\" Colin smiled, \"I'm almost hurt. Come then, it would seem there's to be no leisure for us.\"\n\nI stood up and had to take a moment to steady myself before I could follow Colin and Mr. Vandemier to a side door that led to a plain wooden staircase that was clearly not for regular customers. \"Go on. Go on up,\" Mr. Vandemier said with a thick amount of impatience. \"I'll be there in a minute.\" We'd gotten no more than halfway up when he bellowed out, \"And I'll thank you not to go mucking about my things!\"\n\n\"As though I would do such a thing,\" Colin called back with a chuckle. \"I explore . . . ,\" he muttered under his breath. \"I do not muck about.\"\n\nThe door below slammed shut, offering its own stinging retort.\n\n\"I don't trust that man,\" I said as we reached the cramped office at the top. \"And I doubt he's ever said a word of truth to us.\"\n\n\"I'm sure there's truth to be found around the edges,\" he answered, and started right in poking about the enormous desktop.\n\nI sat down and attempted to get comfortable in one of the straight-backed chairs clearly not crafted for comfort. \"He is working every side against the other, which makes me suspicious.\"\n\n\"I would hope so.\" He glanced at me with a smile as he pawed through a mountain of papers on one corner of the desk. \"But there's nothing of interest here.\"\n\nHe abandoned his rummaging and set to peeking behind the small, smoke-stained paintings of scantily clad women that hung on the walls. There was a lone filing cabinet shoved in one corner and I reached out and found that the drawers willingly sprang open. As I began to paw through them, it quickly became evident that there was no need to lock what no one else could decipher. Cryptic notes on files containing no other discernment than a single letter were not going to reveal a thing.\n\n\"Anything?\" he asked as he settled down beside me.\n\n\"I'm afraid he's too clever for that.\"\n\nThe sound of the door below was followed by the plodding of footsteps on the stairs, and a moment later Warren Vandemier stomped in. \"I hope you're happy,\" he snarled as he sat behind his desk. \"You've cost that girl her job.\"\n\n\"That seems a bit harsh\u2014\" Colin started to say.\n\n\"Not in the least.\" He leaned forward and locked eyes with Colin. \"I don't hire addicts.\"\n\n\"Come now. . . .\" He smirked. \"Even you must realize you've got nothing but addicts working here.\"\n\nWarren Vandemier stiffened. \"Why are you here?\"\n\n\"We've been hearing stories about money, Mr. Vandemier. The Earl's money to be precise. And more than a few rumors about your partnership. And most astonishingly, these stories bear little resemblance to what you told us a few days ago. I'm left quite disconcerted. I've decided I owe you an opportunity to reconsider some of the bollocks you've been trying to sell us.\"\n\nTo my amazement Mr. Vandemier broke into an easy smile, looking at us with considerable disinterest and an obvious lack of concern. Something was most assuredly amiss. \"Such a generous gesture on your part, Mr. Pendragon, especially given that your services for Lady Arnifour have been dismissed.\" And there it was then. That news had traveled fast. \"Under the circumstances . . . ,\" he stared at us with beaming self-satisfaction, \". . . I hardly think I owe you an explanation about anything.\"\n\n\"Though I am no longer being compensated,\" Colin glared back at him, \"you can be sure I will still solve this case. Do not underestimate my determination, Mr. Vandemier.\"\n\n\"Perish the thought.\" He chuckled. \"I'm sure I wish you all the best, but you'll get nothing more from me.\" He flashed his crooked yellow teeth at us. \"I've nothing more to say to you. Ever.\"\n\n\"And that is curious. Because I can't understand why an innocent man would be unwilling to answer a few questions?\"\n\n\"A few questions?! Is that what you have? Then tell me, why would you be twiddling about downstairs, doping that stupid girl, if all you wanted was to ask me a few questions? Now really, Mr. Pendragon.\"\n\n\"I had no idea you'd be so magnanimous with your time,\" Colin answered smoothly. \"So let me ask you, if the Earl was as flush with cash as I now believe him to have been, why are you insisting he never paid his share in this establishment?\"\n\nMr. Vandemier pursed his lips and snatched up a half-smoked cigar from an ashtray filled with them. Only after the stink of it had been suitably sucked into his lungs did he finally deem to answer the question. \"I had to protect myself,\" he said.\n\n\"Whatever from?\"\n\n\"This may come as a surprise to you, Mr. Pendragon, but not all of the late Earl's family is particularly fond of me.\"\n\n\"Pray tell. . . .\"\n\n\"His son's a turd and that nettlesome daughter of his\u2014\"\n\n\"Lady Kaylin?\"\n\n\"I believe he only had the one.\" His sarcasm was wholly evident on his face. \"She would sooner slit my throat than look at me when it was her father who bankrolled this. I wanted the lot of them to think I fronted the old stiff the money so they'd piss off and leave me alone. I knew none of them would make good on any debt they thought he owed me.\" He snickered. \"Now that you're no longer taking his old widow's wages\u2014\" But that was as far as he got before the door below abruptly slammed open and was followed by the panicked footfalls of someone rapidly assaulting the steps.\n\n\"MR. VANDEMIER!\" A terrified pasty-faced young man rose into view. \"It's Li Shen. She's gone daft. She's set the club on fire.\"\n\n\"What?!\" He bolted to his feet and rushed around the desk, catching himself sharply at the hip. \"Dammit to bloody hell!\" he bellowed as the first wafts of acrid smoke began to overpower the opiate scent clinging in the air. \"Those blasted idiots were supposed to get her out of here.\"\n\n\"She was acting crazy.\" The young man kept flicking his eyes nervously about the room. \". . . Clawing . . . scratching . . . screaming. And then she set one of the curtains on fire, and then another, and then another\u2014\"\n\n\"I get it!\" He nearly punched the man as he shoved past him. \"If this club suffers any damage you and the rest of those idiots will pay every farthing to repair it!\" he hollered as he flung himself down the stairs.\n\nThe young man stared at us slack-jawed a moment, looking like a terrified alley cat, before he suddenly gathered himself and went bolting back down the stairs. I'd done no more than turn my gaze back to Colin when Warren Vandemier and his young liege came thundering back up. Mr. Vandemier now looked a great deal more distressed than angry, and I knew it was bad.\n\n\"The whole place is ablaze,\" he blurted out.\n\n\"The door?\" Colin said as we scrambled to our feet.\n\nHe shook his head. I looked back and noticed the first black wisps of smoke beginning to waft up the stairwell. My eyes began to sting and I felt my heartbeat surge as I realized time was quickly running out.\n\nColin pushed past Mr. Vandemier and the young man, seizing the chair he'd been sitting on and heaving it out the room's only window. \"I would suggest . . . ,\" he said with steely calm, \". . . that we find some way to climb down while we've still got the chance.\" He shoved me toward the window. \"You first.\"\n\nI didn't need to be coaxed, though I am not especially enamored of heights. I crawled out onto the window's thin ledge and tried to keep myself focused to allay my fears. All I knew was that I would be leaping down onto unforgiving cobblestones and a steadily increasing band of sooty, gagging people who even now were stumbling from the club's door. There had to be some way I could lower myself at least partially, and that's when I spotted the shutters hanging just below me.\n\nI shifted my weight and jockeyed around so I was facing the inside of the building and then with both hands clutching the windowsill I slowly lowered myself, flailing my legs until I felt the top of the shutters just below. Colin scrambled out the window as soon as I'd cleared the ledge and quickly worked himself around as I had. He started to lower himself and I was able to reach his feet to help him gain purchase. He let go of the ledge just as Warren Vandemier scuttled onto it, and then we both knelt down and gripped the top of the shutters.\n\n\"Drop!\" I yelled. And without another thought I did just that, careening down onto the cobbled street and landing heavily on my backside. It was not as far a drop as I'd thought, but it was enough to flush the stale air from my lungs.\n\n\"You all right?\" Colin dropped close to me and squeezed my arm.\n\n\"I'm fine,\" I stammered, pushing myself up. \"You?\"\n\n\"Perfect.\"\n\nWarren Vandemier slammed down on my other side with a cry and a crack that I knew meant he'd broken something. I stretched, grateful that everything felt fine, then looked back up to see if I was in the way of the young man who'd been with us . . . but he wasn't there. All I could see was the lapping of flames against the windowsill that only a minute before had been my perch.\n\n\"Colin . . .\" I stared around at the throng of stilted, somnambulistic people stumbling around the alleyway.\n\n\"I know . . . ,\" he said, grabbing my arm and pulling me away. \"We have to go. There's nothing we can do.\"\n\nThe distant sound of clanging bells and windup horns that reached my ears mixed eerily with the groans and sobs of the disoriented crowd, and I knew he was right. And that boy . . . that thin, sallow boy . . . never came out.\nCHAPTER 29\n\nWe stumbled two or three blocks before it became apparent that we were being followed. The horse-drawn fire coaches had already careened past, clanging and screeching their warnings, and in the vacuum they left behind it was clear that ours were not the only set of footfalls on the cobbles. Yet each time one of us would glance back, the advancing footsteps halted in tandem, revealing no one behind us. I was finding it increasingly unnerving, though Colin didn't seem the least concerned. I knew pickpockets didn't work uncrowded alleyways and thugs never worked alone, but someone was still matching us step for step and that was rarely a good thing.\n\nWe continued our measured pace for a while longer before Colin asked, \"What was the name of the woman who sat with us at the club tonight? The one who started the fires?\"\n\n\"Li Shen.\"\n\n\"Well then, I believe Li Shen is following us,\" he announced with certainty. \"And rather badly at that.\"\n\n\"Li Shen? You think it's her?\" I started to turn to see if I might yet catch a glimpse, but Colin seized my arm and kept me from doing so.\n\n\"Don't look. Just keep moving. We'll get her to come to us.\"\n\nI knew what he was up to, so as soon as we turned the corner I ducked in the notched alcove of a darkened storefront and yanked him in after me. \"Don't make a sound,\" I cautioned him with a chuckle as he maneuvered around in the tight space.\n\nAlmost at once someone came scurrying out of the alleyway and a second later the silhouette of Li Shen came into view as she paused, no more than a few feet away, and scanned the street.\n\n\"Lose someone?\" Colin cooed as he stepped out. She released a stifled scream and looked as if she was about to run when she abruptly collapsed against Colin's chest and began wailing like a child. \"There, there . . . ,\" he said stiffly, his eyes finding mine to reveal his discomfort.\n\nI patted Li Shen's back and allowed him to pass her to me. She sobbed until I thought she must surely need to stop for air. I knew it to be an effect of the drug and as I held her I was suddenly overcome by the realization that at least one person had lost his life tonight as a result of her drug-addled rampage. It seemed unconscionable to offer her succor when she'd shown so little care herself just a short time ago. And yet she had not been in her right mind then, and that was because of us.\n\n\"We mustn't tarry,\" Colin warned. \"Mr. Vandemier will be crying for his pound of flesh as will the authorities once they find out what happened.\"\n\nShe pulled away from me and wiped her eyes with the sleeve of her dress. \"I no trouble you,\" she said in a thin voice. \"I fine. You go.\"\n\n\"We'll not leave you here. You'll come with us,\" he said.\n\nShe shook her head. \"I no have business with you. You go. Leave Li Shen.\"\n\n\"No.\" He took her arm and began to get us all moving. \"You will come with us if I have to carry you all the way to\n\nKensington, which I am not in the mood to do. I'll not hear another word on it.\" He slid his gaze to me.\n\n\"Absolutely.\" I pasted on what I hoped was a welcoming smile even though I did not relish having her in our flat. \"Not another word.\"\n\n\"Bless you.\" She bowed repeatedly. \"You most kind. A thousand blessings on you both.\"\n\n\"Fine. Lovely. But we really must get moving . . . ,\" Colin prodded again as he tried to get her to pick up the pace. \"It won't do us much good if we're found wandering about the area by the authorities.\"\n\nI held Li Shen's arm, who only now seemed to be comprehending what she had done. Her frail body was shaking as though she were walking barefoot across a patch of ice and I knew it was only a matter of time before the drug fully receded to leave her alone with the consequences. When we reached Fleet Street Colin gestured for us to stay out of sight while he hailed a cab, and only after he'd done so did the two of us dart from the shadows and leap inside.\n\nNone of us spoke the entire way back, and I could smell the burnt sulphur and thick pungent musk of opium on all of us. We would need to bathe with herbs and oils to remove these residues from our skin and hair, and I could only imagine what Mrs. Behmoth was going to say.\n\n\" 'Ere now . . . ,\" she did not disappoint, \"ya couldn't give me some notice that you were bringin' someone 'ome?\" Her hair was in rollers under her knit cap and she was wearing a long flannel robe and well-worn slippers that had long ago molded themselves to her feet. \"Come on then. . . .\" She held the door open and watched curiously as Li Shen drifted across the threshold. As she passed by Mrs. Behmoth her nose curled up and I could tell she knew where we'd been. \"You better not smell like 'er.\" She pinched my arm as I tried to brush past her.\n\n\"It's all right,\" Colin exhaled wearily. \"I chaperoned. We haven't done anything we need regret.\"\n\nLi Shen started and turned to Colin, and immediately dissolved into tears again. She sagged back into me and I held her a moment before hastening her upstairs and away from Mrs. Behmoth's questioning glare.\n\n\"I'd say ya'd best speak fer yerself,\" I heard her mutter to Colin as he started up after us.\n\nI settled Li Shen onto the settee and poked the fire back to life while Colin pressed a brandy on her. She sipped at the drink and eventually exchanged her sobbing for a series of protracted sighs and an occasional hiccup. It was easy to see by the heaviness of her eyelids that the opium was loosening its grip on her, and I knew that before much longer the truth of what had happened\u2014of what she had done\u2014would finally poke into her conscience and demand its due.\n\n\"You must get some rest,\" I said to her.\n\n\"Yes.\" Colin seated himself across from her, his own face drawn. \"We'll talk tomorrow. We'll decide what needs to be done then.\"\n\n\"No rest for Li Shen,\" she whispered. \"No rest.\"\n\n\"Leave it be,\" I tried to soothe her. \"There will be time enough to think on it all tomorrow.\"\n\n\"But I start fire. I want fire. I try to destroy man who want to destroy me, like owner's woman. She come to club and want to destroy everything too. Wave lamp around. But she not really do it, only Li Shen did it.\"\n\n\"What woman?\" Colin's brow knit.\n\nShe shook her head and took another sip of brandy, staring at the amber liquid as though hoping to find some solace within its honeyed glow.\n\n\"How long ago was this?\" he persisted.\n\nShe gave a slight shrug.\n\n\"Two weeks? Six weeks? Six months? Surely you can remember something?\"\n\nMrs. Behmoth shuffled into the room startling all three of us. \"I made up the guest room for the young lady. I 'ope you won't be keepin' her up 'alf the night. She looks as if she's 'ad enough. It ain't right ta keep at 'er\u2014\"\n\n\"Thank you!\" he snapped, sending a frosty glare in her direction. \"We appreciate your thoughtfulness. Please don't trouble yourself any further. We'll see that our guest gets down to her room.\"\n\nMrs. Behmoth folded her arms across her chest and stared right back at him. \"Yer a pip,\" she said flatly. \"Ya jest see that she does.\" And with that she turned and lumbered back down the stairs.\n\n\"Forgive the intrusion.\" He flicked his eyes back to Li Shen. \"How many times did you see the woman at the club?\"\n\n\"That woman?\" Li Shen pointed to our empty doorway.\n\n\"No, no. The owner's woman. The one who was threatening to burn the club down.\"\n\n\"Couple time. She very mad. Shouting . . . scaring client. Say she burn everything down. Bad for business.\"\n\n\"What did she look like?\"\n\n\"Young. Small like Li Shen.\"\n\nColin glanced at me. \"That rules out Lady Arnifour and Abigail Roynton, which leaves us with Elsbeth. But why would she threaten to burn down the club?\" He looked back at Li Shen. \"Was the Earl there when it happened?\"\n\n\"Earl who?\"\n\n\"The owner. The Earl of Arnifour. The one who was killed.\"\n\n\"He there. He have bad night. Have fight with man and then girl come in. He try to calm girl down. Want to take her upstairs. She not happy, screaming and yelling. She crazy. Everyone say so.\"\n\n\"Man? What man?\"\n\n\"Owner son. He say bad things. Then he leave and girl come in and\u2014\"\n\n\"I know. . . .\" Colin waved her off. \"You've been quite clear about the girl. But what about the son? What kind of things did he say?\"\n\nLi Shen shrugged tiredly. \"He hate man.\"\n\n\"Which man? What man?\"\n\n\"Father. Owner. Say he teach him lesson. Why he want to teach lesson to father he hate?\"\n\nColin shook his head with a noticeable lack of interest and sighed. \"And what was Mr. Vandemier doing during all this?\"\n\n\"He not there. Too early for him. Not climb out of pig pit yet.\"\n\n\"And how long ago did this happen?\" he repeated, his own exhaustion catching up to him.\n\n\"Sometime . . .\" She didn't even bother to finish her sentence. She wouldn't be able to. Opium steals time. The months she'd spent in that club would forever be one continuous span. She yawned and set her brandy down. \"Li Shen tired. No feel good.\"\n\n\"Of course.\" Colin rose and I did the same.\n\n\"If you'll come with me,\" I said, grasping her arm and leading her down to the room beside Mrs. Behmoth's own. Everything had been arranged so that this seldom-used space looked inviting. She had turned down the bed and pulled open the armoire to reveal extra covers and some nondescript nightclothes. She'd even managed to scrounge up a small vase of pale pink roses that she'd placed on the bedside table. I bid our guest good night and hoped she could get some rest before the morning and its realizations came roaring in.\n\nI found Colin reclining in the bath upstairs attempting to soak off the vagaries of the night. I lowered myself to the floor and leaned against the wall, a heavy weariness sweeping over me in direct contrast to the gentle dancing of the candles he'd set about the tiny room. It would be so easy to fall asleep but unacceptable to awaken on the floor of the bathroom.\n\n\"Is she settled in?\" he mumbled in a voice as tired as I felt.\n\n\"As much as she can be,\" I said as I allowed my eyes to close.\n\n\"We'll have to decide what to do with her tomorrow.\"\n\n\"Someone died tonight because of her, maybe more. . . .\"\n\n\"I know,\" he sighed. \"But something isn't right. . . .\"\n\n\"How do you mean?\"\n\n\"I can't get a clear picture of Elsbeth. By all accounts she was willing to have an affair with a man she believed to be her uncle, relishing the extravagant lifestyle it afforded and allowing herself to be spotted in public with him under less than appropriate circumstances. Yet now we learn that in a fit of pique she went down to his club and shouted slanders and threats? It doesn't make sense.\"\n\n\"No . . .\" I had to agree. But in spite of my determination to hold up my end of the conversation I knew I was fighting a battle against sleep I was unlikely to win.\n\n\"And why would Eldon have been there that night? What could have compelled him to confront his father like that?\"\n\n\"Li Shen could be wrong,\" I said, biting into the side of my cheek to keep from yawning. \"She is a drug addict.\"\n\n\"She is . . . but we have to be careful not to be too dismissive. There's undoubtedly some truth in what she's saying. And yet I can't help feeling that we're still missing something. The trigger. What drove Eldon to make such a public spectacle of himself when anyone can see he fears his own shadow? And why would Elsbeth threaten to burn that damnable place down?!\"\n\n\"Eldon's a drunk. There's no explaining a man like that. Coming to our flat this afternoon to tell us that story just so he can implicate his mother. It's a disgrace.\"\n\n\"It could be true,\" Colin sighed. \"Though it's hard to take the recollections of a five-year-old with anything but caution. What may have seemed like quite a lot of blood to him then could prove quite inconsequential to an adult. Still, it is a sordid tale.\"\n\n\"And even if it is true, it might not change a thing. Maybe Elsbeth was on the verge of being replaced as the Earl's favorite and that's what set her off,\" I blathered in near incoherence.\n\nColin bolted up so quickly that water splashed out of the tub and onto the floor. \"Of course! How foolish I've been.\"\n\n\"What?\" I blinked vacantly as I struggled to focus. \"Foolish about what?\"\n\n\"What's the one thing that would have set them both off?\" He stared at me, but I had nothing. If there was an answer to see I wouldn't have spotted it scrawled on the wall in front of me. \"The Earl had someone else. Someone who was a threat to Eldon's inheritance. All this time . . . ,\" he chuckled as he climbed out of the tub, \". . . there's been someone missing from this game. Someone who set everything else in motion.\"\nCHAPTER 30\n\nMorning roared in with great anticipation, as did Colin. By the time I managed to coax my eyes open he was already up and dressing at a furious pace.\n\n\"Are you planning on sleeping all day?\" he teased. \"There's much to be done. The Ilya Petrovina is due in shortly and we've got to get down to the docks to see if your suspicions about Michael have any basis. And I should also like to announce that by the end of this day we will have named the perpetrator in the Arnifour murders. However, first we must question our houseguest. I'm going to have Mrs. Behmoth awaken her. I simply cannot wait another minute.\"\n\nI roused myself as quickly as I could, loath to miss anything, all the while considering Colin's declaration that he was on the verge of solving the Arnifour murders. I hadn't the slightest notion how he intended to do so given the possibility of yet a more recent mistress in the picture. I couldn't even imagine how he meant to find her. If Li Shen didn't know who she was, and that seemed most likely, then we would be beholden to Warren Vandemier, and I didn't expect we'd get much help from him anymore.\n\nI tidied up and dressed swiftly, and was about to go downstairs when I heard the distinctive thudding of Colin trudging back up. I suspected Mrs. Behmoth had routed him for disturbing our guest at so early an hour and had sent him back up to wait a little longer.\n\nI made my way to the study and found him stirring a fire to life. He was well pulled together and as I settled into my armchair, anxious to ward off the remnants of sleep, I was grateful to have a few minutes to collect myself before having to confront Li Shen again.\n\n\"She isn't here,\" he muttered as soon as I'd gotten settled.\n\n\"What?!\"\n\n\"Li Shen is gone. Mrs. Behmoth found her bed empty.\" He tossed the poker onto the hearth with a clatter and stalked to the stairway. \"Can we please get some tea up here!\" he bellowed.\n\n\"Don't you 'oller at me!\" she hollered back. \"It ain't me fault she's gone.\"\n\nColin threw himself onto the sofa, a stern gaze clamped on the fireplace until Mrs. Behmoth finally made her appearance, the silver tray of tea and scones clamped in her hands.\n\n\"I spent 'alf the bleedin' night with 'er, ya know,\" she groused as she banged the tray onto the table. \"She was sick the 'ole time. Chuckin' and moanin' 'til the sunrise began pokin' in through the windas. I was fagged out. It ain't no wonder I never 'eard 'er stir.\"\n\n\"I am not blaming you\u2014\"\n\n\"Like 'ell yer not.\"\n\n\"All I want to know is if she said anything? Did she give any indication where she might have gone?\"\n\n\"Wot? In between hackin' 'er guts out?\" Mrs. Behmoth screwed her face up and spoke in a high-pitched voice, \"Pardon, mum, but as soon as I'm done 'ollowin' 'ere, I'll be 'eadin' off for a pint at the local pub.\"\n\n\"Fine!\" he snapped. \"I get the point.\"\n\n\"Poor little thing was sick as a cur.\"\n\n\"Yes . . . I've got it.\"\n\nA loud rapping at the door was all that kept Mrs. Behmoth from responding, which, given the sourness of the expression on her face, I was grateful for. She disappeared back downstairs muttering under her breath, and I hoped it might be Li Shen, though I knew how unlikely that was.\n\nMoments later Inspector Varcoe and one of his lackeys were standing on the landing outside our study. As I stared at the inspector's self-righteous gloat I couldn't help but wonder how a day so filled with promise just a few short minutes ago could have so swiftly turned bad, the evidence of it standing before us now.\n\nInexplicably Colin did not appear perturbed in the least. I supposed he'd been expecting this visit; it was bound to come, though it was unforgivably early.\n\n\"Aren't we just the picture of domestic ease this morning,\" Inspector Varcoe sneered as he strolled in. \"I would've brought your paper up but didn't want to rob you of the only legal recreation you're likely to have today.\"\n\n\"I do wish we had a dog to fetch it. I'd love one of those bull terriers,\" Colin said as he sat down in his usual chair and casually flipped out a crown, starting its inevitable route between his fingers.\n\n\"Well, you'd certainly have the time to train it.\" The inspector snickered. \"I hear you've been fired by Lady Arnifour.\"\n\n\"Not fired,\" I shot back. \"We have been paid in full for services rendered.\"\n\n\"Oh, I see.\" He chuckled again. \"But I'm not here to gloat, though it is a distinct pleasure; I'm here on official business. I need to know where the two of you were last night.\"\n\n\"I'm quite sure you know exactly where we were.\" Colin shifted his gaze to the uneasy-looking bobby still hovering in the doorway. \"Would you care to sit down, young man? You needn't stand on formality here.\"\n\n\"Stay where you are, Lachlan!\" Varcoe snapped. \"Why did you leave the scene of a crime, Pendragon?\"\n\n\"Crime?\" Colin tossed the coin onto the mantel as he reached over and picked up one of the dumbbells next to his chair and began methodically curling it with his left hand. \"Are you implying that the fire in that club last night was deliberately set?\"\n\n\"Piss off.\"\n\n\"You might remember that you're in our home now,\" I pointed out. \"If anyone is going to piss off\u2014\"\n\n\"Now, now.\" Colin smiled easily as he continued to pump the weight. \"Perhaps if you outline your suspicions we can see if we know anything further.\"\n\n\"I want some ruddy answers!\" he roared, his face morphing into the burgundy of a plum. \"What were you doing there last night after Lady Arnifour fired you from the case?\"\n\n\"It's an opium club,\" I said without a hint of patience. \"I'm sure you can extrapolate.\"\n\n\"Bollocks! Don't lie to me.\"\n\n\"He's telling the truth,\" the young bobby spoke up. \"It is an opium club.\"\n\n\"I know what the bloody hell it is, you twit!\" he howled, forcing the young man to take an unconscious step backwards. \"And I know that's not why you were there. You two may be a lot of things,\" he leered, \"but you're not blasted addicts. So what the hell were you doing there?\"\n\n\"Idle curiosity?\" Colin shrugged, switching the weight to his other hand.\n\n\"Bullshit! Warren Vandemier says you went there to harass his clientele and cause him physical and monetary harm.\"\n\n\"Now, Inspector, Warren Vandemier is an addict. I'm sure you've figured that out by now\u2014\"\n\n\"That's enough, Pendragon. I will drag your ass down to the Yard if I have to, but you will answer my questions!\"\n\n\"If you will just settle yourself a moment I think you'll find that I've answered every one of your questions thus far.\"\n\n\"You've been dismissed from the Arnifour case, Pendragon, so I expect you to stand down from this business and let the real authorities settle things,\" Varcoe snarled before he turned and stalked from the room.\n\nWhen I heard the door slam a second time in as many minutes, it was a monumental relief. \"What in the bloody hell was that about?\" I asked as I leaned forward and poured us some tea. \"Why did he come here?\"\n\nColin turned back to the fireplace, but I could see that his eyes were unfocused. \"I would venture we're getting nearer to the truth and someone with attachments to the authorities has sent our impressionable inspector to rile us. Someone cunning enough to use him without his being aware of it.\" He rubbed his chin absently. \"Actually, whoever it is wouldn't need to be that cunning.\"\n\nI laughed. \"So who do you think sent him?\"\n\nHis sapphire eyes drifted back to me as I handed him his tea. \"There can only be three possibilities: Lady Arnifour, Warren Vandemier, or Abigail Roynton.\"\nCHAPTER 31\n\nOur first stop was to visit Warren Vandemier in the hospital. We discovered that he'd broken his right femur, so if nothing else, he would prove to be a rapt audience. We found him in bed with a cast that went from his hip to the ankle of his right foot, the whole thing dangling from a sling bolted to the ceiling. Even so, he did not hesitate to make his repugnance clear the moment we strode onto the ward. \"As if I'm not knackered enough already,\" he groused.\n\nColin perched on the end of his bed next to Mr. Vandemier's plastered leg. \"That's the thanks we get for saving your life?\" he sighed.\n\nThere was much grumbling. \"I see the two of you managed to escape without so much as a ruddy damn scratch.\"\n\n\"We did.\" Colin shrugged. \"Survival of the fittest and all that, I suppose. But we're not here to compare wounds\u2014only to ask a couple of questions.\"\n\n\"I've had it with your bloody questions. I told you that last night.\"\n\nColin appeared to ponder that before shaking his head. \"No, I don't think you did. Perhaps you've suffered some head trauma as well\u2014\"\n\n\"Oh, just get on with it,\" he seethed.\n\n\"I'd like to know something about the Earl's niece, Elsbeth. Did she ever threaten your club?\"\n\n\"Elsbeth?!\" He looked surprised. \"Now why would she do that? She partook on more than one occasion. Had a row with Samuel over it too.\"\n\n\"She tried opium?\"\n\n\"Bloody well right, she did. But Samuel was a hypocrite. Perfectly happy to make a regular of anyone who walked in the door so long as they weren't related to him.\"\n\n\"Were you aware of anyone threatening your business? Threatening to burn it down?\"\n\n\"Just that stupid slag last night. Are you trying to blame the fire on somebody other than Li Shen? It's your fault, you know! You plied that dragon whore with opium. You're as guilty as she is.\"\n\n\"Settle down or I'll see that you get a matching plaster on your other leg.\"\n\n\"Are you threatening me?!\"\n\n\"Not very well if you have to ask. Now I'm not talking about last night\u2014\"\n\n\"Well, you sure as hell should be!\" he snapped. \"Because my life was as good as destroyed last night.\"\n\n\"This isn't about you.\"\n\n\"The hell it isn't!\"\n\nColin smiled thinly as he leaned toward Mr. Vandemier. \"I'm only going to ask this one more time\u2014\"\n\n\"I don't give a crap. Shove whatever twaddle you've got on your mind straight up your ass.\"\n\nColin leaned back slowly, his eyes piercing Warren Vandemier's face. He eased himself off the bed, one side of his mouth rising lazily, before reaching out and yanking the sling cradling Mr. Vandemier's leg several feet. It took less than an instant before he let out a soulful scream, his eyes rolling up into his head.\n\n\"Now don't be crude.\" Colin spoke softly. \"Rudeness is redundant in a man like you.\" He released the sling and let Mr. Vandemier's leg drop back to its original position with a jolt. A second screech followed as we left the ward, a trio of nurses making a dash toward the noise.\n\n\"That was a touch brutal,\" I said once I'd caught up to Colin.\n\n\"He's just lucky those damn nurses heard him scream.\"\n\n\"Well, did you at least learn something?\"\n\n\"Not what I wanted to hear,\" he muttered, heading off down the street.\n\n\"So where does that leave us?\"\n\n\"In the middle of London,\" he answered with great exasperation as he stepped into the street to flag a passing cab.\n\nI bit my lip as I climbed aboard and Colin instructed the man to take us to the docks. It was time to see how the reunion of Michael and Angelyne would play out. I hoped it would be heartwarming, but couldn't shake the feeling that something was asunder.\n\nColin climbed in next to me, turning and staring out the window as we got under way. It was clear there was much on his mind, so I determined the best thing I could do was leave him in peace and set my gaze on the passing scenery as well.\n\nUpon arriving, I glanced around the small crowd milling about the wharf to see if I could spot Michael before he could catch sight of us. Even though the Ilya Petrovina was making an unannounced call, there were dozens of people to greet her, not the least of whom were the policemen and Yardies who'd been sent by the Foreign Ministry Office to inquire about the alleged stowaways. I started to move off, keeping well away from the crowd, certain that Michael would also want to keep his distance from the authorities lest they decide to stop his sister from returning to his care. \"Now don't get ahead of me,\" Colin warned as I crossed perpendicularly from where the people were milling.\n\n\"I'm looking for Michael . . . ,\" I answered vaguely.\n\n\"I know what you're doing,\" he said. \"We'll scout the scene before we make our presence known, but not every East End boy is as deceitful as you obviously were,\" he teased.\n\n\"I was not deceitful,\" I protested as we moved off in the opposite direction from where the Ilya Petrovina was set to berth. \"I was clever.\"\n\n\"You were a drug-addled hellion.\"\n\nI considered taking offense, but as I followed him behind a maze of crates and boxes littering the docks I decided now wasn't the time for it. Besides, I'd been called worse things.\n\nAs the great, hulking steamship was carefully maneuvered by a pair of rusting tugs, we took an opposing, perpendicular track until we'd reached some distance from where the front of the ship would eventually lie, well concealed among a throng of languishing cargo. \"Feeling shy, are we?\"\n\n\"We're going to sit here and see if your suspicions have any merit. It's my show of faith in you.\"\n\n\"I'm touched.\"\n\nHe chuckled as he settled in on a pile of boxes, peeking through a slot between a row of crates down to where the ship was docking. I turned my attention to her as she was tied up at her berth and a couple of men muscled her gangplank into position. A handful of sailors were the first to disembark, followed by a short, round, bearded man wearing a disheveled-looking Russian uniform. He went directly to the bobbies clustered at one side of the gangway.\n\n\"Must be the captain.\"\n\n\"He doesn't look much like a captain,\" I said.\n\n\"It's a cargo vessel, not a passenger ship. That chap has little need for epaulets, uniform whites, or reflective shoes. He'd have a hell of a time trying to convince any seasoned crew to follow him with that kind of artifice. His crew is far more akin to pirates than our naval lads. Need I remind you why we're here?\"\n\nI gave him a pointed look before answering, \"He looks exactly like the kind of scoundrel who'd kidnap girls for sale.\"\n\n\"I have to agree. I'd say they were put aboard his vessel with both his knowledge and a sizeable payment, probably half at embarkation and half upon delivery. He won't be happy about missing that second bit. And his cargo delivery is going to be woefully late as well.\" He grinned. \"This episode will end up costing him quite a sum.\"\n\n\"You think they'll arrest him?\"\n\nHe shook his head and sighed. \"For what? For being a selfless humanitarian who, at great personal expense, turned his ship around the moment he discovered those deceitful young girls stowed away?\"\n\n\"You cannot be serious. . . .\"\n\n\"Proof can be a pitiful burden,\" he muttered, and I noticed his brow suddenly furrow. \"And look at this. Here comes our young charge now.\"\n\nI turned and caught a glimpse of Michael heading around behind the small crowd gathered at the gangplank. He was moving slowly, not with the kind of enthusiasm that would be expected, seeming almost reticent, and it made me wonder if there'd been bad blood between him and his sister.\n\nMy curiosity was further piqued when he continued to saunter past the waiting queue of people, moving resolutely toward the front of the ship, not far from where we were concealed. Yet, given the number of police milling about, I determined that his hesitation in standing among them made sense, since there was a better than average chance that at least one of the bobbies had run into him at some point in his doggedness to provide for him and his sister by whatever means necessary. I began to feel foolish for not having had some modicum of faith in the boy, but felt better when Colin said, \"I'd say the men in blue are keeping our boy from emptying any pockets.\"\n\nI started to chuckle when a sudden commotion at the gangplank seized my attention. A tall, clearly overwrought woman in a massive sun hat was howling at the police even as the group of stowaway girls\u2014the scrawniest, scruffiest-looking assemblage I had ever seen\u2014made their first appearance at its top.\n\n\"What do you suppose she's going on about?\" I asked as the woman flailed her arms wildly.\n\n\"One of those girls is probably her ill-used niece or ward and she's causing a great fuss in order to deflect the mountain of questions that are bound to come the moment she moves in to claim her. A show of outrage is much more likely to get her what she wants than not.\"\n\n\"So cynical.\"\n\nHe shrugged, his brow stitching itself again as I glanced over and saw Michael. He had managed to skirt the agitated knot of people congregated at the gangway, but was now standing almost directly across from us at the ship's bow. I watched as he slunk around the ship's moorings as though he knew something no one else did, and after a couple of minutes discovered that, in fact, he did.\n\nThe movement on the ship was minuscule, hardly noticeable until the first frail leg, smudged with dirt and filth, popped out and took hold of the forward anchor rope. The second leg quickly followed, allowing me to make out the figure of a young girl as she began to slither down the tether with unmistakable expertise. She was no more than a waif really, much less significant than a girl of almost thirteen should be. Her body was rail thin and she had limp, stringy hair dangling about her shoulders. I knew it was Angelyne, because even as she lowered herself to the dock, Michael never took his eyes from her.\n\n\"So you were right,\" Colin muttered.\n\n\"Well, I didn't think she was going to shimmy down the rope like vermin, but it would seem given her proficiency that she might have done this before.\"\n\n\"To be sure. She handles that rope like a gymnast. No wonder he told us not to come. It's a scam. Only this time something obviously went wrong. And will you look at this. . . .\" He gestured to Angelyne as she jumped free only to be swiftly seized by her brother. \"Their happy reunion would seem to be little more than rebuke for having fouled things up. That little shit dragged us into this to make sure he'd get her back, always feeding us just enough information.\" He abruptly turned and glared at me. \"You should've been more insistent.\"\n\n\"What?!\" I nearly laughed in his face, but he grabbed me and propelled me farther back into the maze of cartons.\n\n\"The little tykes seem to be coming our way,\" he groused.\n\nI peeked around the crates and saw that the two of them were indeed heading to almost the exact spot we'd been hiding, moving with great purpose. Michael had a firm grip on Angelyne's skinny arm, and though I could not hear them yet, it was clear they were in the midst of a row.\n\n\"Not a word,\" Colin warned needlessly. \"Let us allow them to spill their conniving hearts.\"\n\nAs soon as they'd reached the relative safety of the first row of crates, Michael wheeled around on his sister with unbridled ferocity. \". . . Bleedin' idiot . . . what in 'ell were ya thinkin'?!\"\n\n\"Piss off,\" came the reply.\n\n\"Piss off? Piss off, eh?! Is that what ya woulda told them bloody Cossack bastards when they was tryin' to bugger ya?\"\n\n\"I ain't without means.\"\n\nMichael slapped her hard in an attack that would have sent her to the ground had he not still been holding her arm. \"Yer jest a stupid pup. You ain't gonna be worth nothin' soon anyway. But if ya ever pull a ruddy stunt like that again\u2014\"\n\n\"Where are ya, ya blasted, sawed-off, half-breed little shite,\" a familiar female voice abruptly cut through Michael's diatribe, causing him and Angelyne to jerk around. \"Yer damn lucky yer brother and I didn't leave ya on that blasted ship!\" Mademoiselle Rendell continued to bellow as she stepped across my eye-line clutching an oversized sun hat.\n\n\"I thought that was her.\" Colin gave a crooked grin.\n\n\"You knew that was Mademoiselle Rendell causing that fuss?\"\n\n\"I suspected she was involved. She was too willing to give up her Bulgarian attach\u00e9 to make sure we got the information we needed to get that ship turned around. But I didn't realize about the little one.\"\n\n\"The little one?\" I flicked my eyes back to the three of them. \"Angelyne? What about her?\"\n\nHe smirked, one eyebrow arching high. \"Haven't you figured it out?\" I looked from the scrawny girl to Colin and back again, without a single thought entering my vacant brain. \"Angelyne is a boy,\" he finally said. \"See the budding Adam's apple? It's a shell game. They sell him as a prepubescent girl with the intention that he'll sneak off the ship just as it's on the verge of leaving\u2014before their deception is discovered. That's how it's supposed to work. They knew where he was the whole time. They just needed us to figure it out so we could get that ship to come back. They'd lost their golden goose. And they almost got away with it had you not been so suspicious.\" He grinned as he squeezed my arm and coaxed me forward. \"But now it's time we put an end to this.\"\n\nMademoiselle Rendell had her back to us as we stepped out, but Michael and the other boy spotted us at once. \"Oh shite,\" Michael said.\n\nMademoiselle Rendell spun around, and as her eyes landed on us she sagged as though suddenly void of air. \"Dammit to 'ell,\" she lamented. \"I knew gettin' this pair were a mistake.\"\n\n\"A mistake?!\" Colin said with mock offense. \"I've been called many things in my life, but never a mistake.\"\n\n\"I'd be 'appy ta call ya worse.\"\n\n\"I'd rather hear from the little one.\" He turned his attentions to the long-haired boy cowering at Michael's side. \"And what do they call you when you're not in a dress?\"\n\n\"Drew, sir,\" he answered.\n\n\"Drew.\" Colin gave a tight smile. \"I think it's time you let him go, Michael, or I'll separate your arm from your shoulder.\" Wisely, the older boy did so at once. \"Come over here, Drew.\"\n\n\"I ought not, sir.\"\n\n\"It's all right. Your brother and . . .\" He paused.\n\n\". . . Me mum, sir,\" the boy piped up, causing my heart to sink.\n\n\"Yes.\" Colin spoke slowly, his own distaste evident. \"Your mum. They'll not harm you. You've nothing to fear from them anymore. This game has come to an end.\"\n\n\"It weren't so bad. . . .\"\n\n\"Well, perhaps you'd prefer to be a boy. Go to school. Learn your disciplines.\"\n\nDrew glanced from Michael to Mademoiselle Rendell before turning back to us. He nodded, but said nothing.\n\n\"Then you shall have that.\"\n\nDrew winced as he stepped away from his brother, clearly expecting a blow that would not come. His scrawny limbs were streaked with the same filth caked on his bare feet, as black as the sludge between the cobbles in the street. I doubted he'd ever had a haircut since that was a part of his ruse, and could tell by the knots and tangles peppered throughout that some time had passed since a brush had been worked through it. The timid voice and abject politeness was a glaring dichotomy to what stood before us, yet to be saleable, he had to be controlled. This pair had done their job appallingly well.\n\nColin put his hands on the boy's shoulders and turned him back around to face his mother and brother. \"You've done your damage to this child for the last time, as you'll find it impossible to do so from prison. By the time they let you out . . . ,\" he flicked his eyes to Mademoiselle Rendell, \". . . the only thing anyone will pay you for is to bugger off. And as for you . . .\" He glared at Michael. \"You'll likely end up rather like your little brother here, except that the blokes you'll be spending your time with won't pay you for your favors.\"\n\n\"Ya can't threaten us,\" Mademoiselle Rendell spat back, pulling herself to her full height.\n\n\"It is not a threat,\" Colin answered. \"I give you my word.\"\n\n\"Yer word. What da you know? Livin' in yer fancy flat with yer lady waitin' on ya and ridin' round in carriages passin' judgment. You ain't got no idea. No idea at all.\"\n\n\"You don't own hard luck or bad choices,\" I sallied back at her. \"But your failure to rise above them belongs to you.\"\n\n\"Ah . . . piss off,\" she spat, and before I knew it she launched herself at me, gripping me by the hair. I stumbled backwards with the sudden force of her weight and landed on my backside, her coiled fists flailing at my head with such determination that all I could do was try to ward off her blows until, just as quickly as it had begun, her siege ended.\n\nShe let out a pitiful shriek as she was unceremoniously wrenched off me, seeming to levitate into the air by her armpits, her legs and arms batting uselessly as they failed to make contact with anything. I peered up and saw Colin behind her, solid, impermeable, and formidable. He heaved her to the side like a sack of grain into a crumpled heap with nary a grunt, turning to face her with his hands stabbed against his hips. \"Next time,\" he growled, \"I will remove you by the throat!\"\n\n\"You mustn't, sir,\" Drew spoke up. \"She's just me mum.\"\n\n\"And I could scarcely be sorrier for that,\" he answered. \"You tried to play us for fools,\" he turned on Michael with a sneer, \"acting the part of the loving brother when all along you were nothing more than the snake Mr. Pruitt kept insisting you were. Fifteen years old and without a shred of decency. How proud you must be.\"\n\nThe young man scowled with the ferocity of the feral thing he was. \"You got nothin' ta say ta me!\" he growled back. \"All full a yerself when you thought you was helpin' out the little urchin boy. I think you're just pissed 'cause I almost got one over on ya.\" He snickered. \"If that's your decency then you can shove it up your arse.\"\n\nI sucked in an infuriated breath to blast the pompous smirk off his face when I felt Colin's hand grip my arm and heard him say, \"Don't. Just go fetch us a couple of bobbies.\" I did as he suggested, knowing he was right; there was nothing I could say that was going to make a whit of difference to Michael and my protestations were only likely to confirm his point.\n\nIn the blink of an eye I returned with a cluster of policemen. We gave a hasty report, based more on Colin's name than any real substance, but promised a trip to the Yard for a more formal debriefing later. Colin was adamant that we couldn't go with them just then as he was about to solve the Arnifour murders. The bobbies stared at him with a mixture of skepticism and alarm, but not one of them called him on it.\n\nAs we made our way off the pier I felt relieved to be getting away from there. It was a pitiful case, but even so, I could not bring myself to turn back for one last look as the officers led Mademoiselle Rendell, Michael, and little Drew away.\nCHAPTER 32\n\nJust over an hour later we were climbing down from a hansom cab onto the cobbled driveway at the Arnifour estate.\n\nAs with every visit before, Mrs. O'Keefe only grudgingly allowed us entry, making no effort to hide her disdain at our continual insistence on showing up with neither an appointment nor an invitation nor, as was now the case, even a reason for being there. I glanced at her more closely than I'd meant to as I slid past her, wondering if Kaylin might truly be her daughter and what it would be like to keep such a secret the whole of one's life. My thoughts earned me nothing more than a ferocious glower from her. Nevertheless, her rabid anger suddenly made some sense and I couldn't help the trifling pity that gnawed at me as she took us to the same study as always before curtly announcing that we'd be joined by Lady Arnifour at her leisure. It left me wondering if that meant within the hour, the day, or the week.\n\nWe settled in to wait the indeterminate time and just as Mrs. O'Keefe was about to take her leave Colin asked whether Victor might be available to join us for a few minutes. She appeared to ruminate on the idea quite thoroughly before finally consenting to let him know we were there. Even so, she slammed the doors with a great deal more bravado than necessary as she left us on our own.\n\nI turned back to Colin to seek his thoughts on Mrs. O'Keefe and what Eldon had told us only to find a deep furrow creasing his brow. \"Are you all right?\" I asked quietly. \"You're going to need to be on your best behavior if we're to have any success here. After all, we're not working for them any longer. . . .\"\n\nInexplicably, the furrow in his brow deepened. \"I know that,\" he said. \"You needn't worry. I'll behave.\"\n\nI pretended to chuckle but still feared that his impatience would get the best of him and bring our impromptu visit to a frustrating and permanent conclusion. I was on the verge of pressing the point against my better judgment when Victor Heffernan suddenly presented himself, barreling into the room with his usual good cheer. \"It's good ta see ya both,\" he said with genuine appreciation.\n\n\"And you as well.\" Colin smiled and shook his hand. \"It's kind of you to meet with us despite our appalling lack of notice.\"\n\n\"I think ya know I'm not one ta stand on ceremony.\" He sat down by the fireplace looking more fragile than ever. \"I'm hopin' you've come to straighten things out for Nathaniel. He keeps threatenin' to stow away to America. I don't know what I'd do without him. That boy's been the best part of my whole life.\" He pinned his gaze on the dancing flames in the fireplace and yet I could see his eyes were glassy. It looked like he hadn't slept in days and I suspected that was more than likely true.\n\n\"I have every intention of proving your son's innocence,\" Colin said, sitting down opposite Victor, \"even though he hasn't made that easy. His unwillingness to trust me has hampered my investigation considerably.\"\n\n\"I know. He's as stubborn as his mother was\u2014\"\n\nColin held a hand up, giving Victor a sly smile. \"Nathaniel may have slowed me, but he will not stop me. Justice is a belle I like to court. And as I've said repeatedly, I believe Nathaniel is innocent. I'll stake my reputation on it.\"\n\n\"Then do share.\" Lady Arnifour stood just inside the doorway, her face rigid with displeasure. \"Just who is it you've come to wield your peerless reputation against?\"\n\n\"Who indeed?\" He smiled easily as he stood up. \"Would you think any less of me if I demurred my answer for a moment?\"\n\n\"Don't be tiresome, Mr. Pendragon. I believe your business with us was concluded on your last visit.\"\n\n\"And so it was.\" He held his smile. \"But this visit is solely on me. Please . . . ,\" he gestured to a chair, \". . . indulge me.\"\n\nI thought her on the verge of expelling us, but after she threw a quick glance at Victor's glum face she heaved a heavy sigh and perched herself on the edge of the proffered seat. \"I must insist you keep this exercise brief.\"\n\n\"Exercise?\" His smile wavered as he cast a quick glance at me. \"What an unorthodox way to describe the solving of two murders.\"\n\n\"Do get on with it,\" she sniffed.\n\n\"As you wish . . .\" He slowly ambled around behind Lady Arnifour's chair. \"So what I'd like to know is if you ever told Elsbeth about Desiree Helgman?\"\n\nLady Arnifour turned her head so quickly that it sent her great stout wig in a slightly discordant direction. \"I have no idea what you're talking about!\" She bolted up, affecting a look of deep offense even as she sent Victor a withering sideways glance.\n\n\"Come now. . . .\" Colin moved behind her again, forcing her to twist around. \"There's no need to be coy any longer,\" he whispered before abruptly heading to the fireplace. \"Very few secrets are able to be kept forever.\"\n\nLady Arnifour held herself steady, glaring at Colin without the slightest feint, and for a moment I thought she might storm from the room, but after a minute more she slumped back into her chair and heaved a grave sigh. Her fingers shot up to her temples and rubbed at them as though a searing pain had suddenly settled there, and I imagined it had. As I continued to watch her, I realized that she had become just as frail as Victor, that their mutual unraveling was as preordained as their lives together had been. \"I have known a lifetime of betrayal, Mr. Pendragon.\" She spoke in a voice that quivered with brittleness. \"I am sure you are aware of that.\"\n\n\"I meant no offense,\" he answered. \"I am only seeking the truth, even if it is a truth you are eager to conceal.\"\n\nShe did not look up, but remained as she was: hunched over, her fingertips pressing at her temples. \"The marriage I endured with my husband . . . ,\" she said in a voice that was both flat and void of inflection, \". . . was happy for the span of about two years. Of course that was so long ago I may yet be remembering it with more charity than it deserves. The period after Eldon was born was . . . wonderful. A pristine, young family. And yet I'm sure my husband's wandering eye had already gotten the best of him. I really don't recall. Not until Kaylin. Samuel gave up all attempts at discretion while I was burdened with our second child. I never imagined such a complete and utter end to his interest in me, but that is exactly where I found myself, Mr. Pendragon: with two small children and a husband who came around only when he needed money.\"\n\n\"You mustn't go on.\" Victor leaned forward and touched her elbow tenderly.\n\n\"It doesn't matter.\" She offered him a game smile, but otherwise made no move to shy away from his intimacy. \"You've been my salvation,\" she said. \"You are a man of inestimable kindness. You see, Mr. Pendragon, Victor only responded to the plaintive tears of a young wife and mother all those years ago. He saved me, not once, but twice.\"\n\n\"No, no, it was you who saved me,\" he rushed to correct.\n\n\"Hush now,\" she scolded with affection. \"I'm telling the story.\" She looked at us for the first time since withering in her seat and I recognized a liberation in her gaze I had never seen before. \"Victor listened to me. He cared for me. And some time thereafter, when I realized I'd fallen in love with him, not only did he accept it, but he returned that gift a thousandfold. And I was certain we would be fine. I thought we would be permitted our indiscretion given the depth of my husband's forays, but I was again deceiving myself. Little more than a year and a half after Kaylin was born I discovered I was once more with child. I knew the baby didn't belong to my husband and, of course, so did he. My husband was many things, but he was not a fool.\n\n\"We agreed I had to go away, so I created a story about a sister who'd been in a terrible carriage accident while with child, and then left my own small children. I moved into a flat in the city under that name: Desiree Helgman. It was a freeing time though it was also unbearably hard. I couldn't see my children until after Elsbeth was born, not once. I had to placate myself by sending them letters regularly, making up stories of what I was doing and telling them how much I missed them, knowing their nanny would read the letters aloud. . . .\" The thinnest smile tugged at one corner of her mouth. \"But there was also joy in those months. Victor came to see me often and brought me food, and took care of me, and made me feel like a new wife on the brink of a new family all over again. That was wonderful. Me and Victor in that tiny apartment waiting for that child conceived in love to make her presence known . . . ,\" she caught her breath, \". . . it was\u2014\" But her voice cracked and she dropped her eyes to her hands, which were fidgeting with the twinned ends of her tasseled belt, back and forth, as though they were attempting to weave something.\n\n\"But I undid myself when she was born because I could not bear to let the midwife hasten that tiny baby away without taking one peek at her. I'd girded myself to give her up, but I still wanted to see her, to hold her, just once.\" She took a deep breath and then pushed on. \"I cradled her in my arms and smelled her sweet, soft skin, and stroked the fuzz dusting the top of her head.\" She chuckled. \"Her perfect, little fingers curled around my own . . .\" Her smile dropped and her eyes clouded. \". . . I couldn't let her go. That baby, that child, that perfect little girl . . .\" She sagged back into her chair and closed her eyes. Her face was still, but it held a calmness that looked too long removed.\n\n\"Shall I finish?\" Victor asked softly.\n\n\"No.\" She gave him a gentle smile. \"You've covered for me for long enough.\"\n\nShe looked back at Colin and me. \"I bundled that baby up and brought her home with me to this house, my house, the ancestral home of four generations of Langhems, and told everyone my sister had died during the birth. I said there'd been no husband, so I'd done the only charitable thing I knew; I'd brought her home to raise as my own.\n\n\"Samuel was outraged.\" She glanced at her hands again and I finally understood where her story would inevitably end. \"My husband told me that I would either pay him a handsome monthly stipend or he would ruin me. Simple. And that was when my antipathy for him became hatred. What was worst of all was that I had handed him the tool of my destruction myself. That baby . . . that innocent who had made me fall in love with her . . .\" She shook her head. \"Samuel knew just how to strike at me, how to make my life even more miserable than it had already become. And to tell you the truth, Mr. Pendragon . . . ,\" she lifted her eyes and glared at him, \". . . if there was ever a time I wished my husband dead, it was then.\"\n\n\"Don't . . . ,\" Victor hushed her.\n\n\"Why not? It's the truth.\"\n\n\"Mother?\" Kaylin was standing in the door. \"Are you all right?\"\n\n\"Don't come in.\" Lady Arnifour buried her head in her hands. \"These are such tawdry proceedings.\"\n\n\"Then by all means . . .\" Eldon shoved past his sister. \"If the Arnifours are to be flung into the mire I think we should all wallow together. And tell me, Mr. Pendragon, is it true that you've seen my father's club burned to the ground and Mr. Vandemier laid up in the hospital?\" He moved to the bar and poured himself a drink. \"Can't say I give a bloody piss about the latter, but the former has me sick. You know what that'll cost me? Do you have any idea what that little parcel was worth?\"\n\n\"How dare you. People lost their lives!\" Lady Arnifour snapped.\n\n\"One of them could have been me,\" he sneered. \"I'd every intention of going there last night to have a word with that tosspot Vandemier\u2014\"\n\n\"No doubt you were unconscious long before you could make good on that threat,\" she shot back.\n\n\"And there you have it.\" He set his glass down. \"A mother's love.\"\n\n\"And you have become a despicable man.\"\n\n\"I am what you made me,\" he said before turning back to Colin. \"And there you have it, Mr. Pendragon, proof that rats aren't the only mammals who devour their young.\"\n\n\"That's enough, Eldon,\" Kaylin spoke up. \"Purge your demons somewhere else.\"\n\nHe scowled at her but kept quiet as she went and sat next to her mother. \"They aren't blaming you for this, are they?\"\n\n\"I deserve a little more credit than that,\" Colin said, still hovering in front of the fireplace. \"I'm not so incompetent as to believe a woman of a certain age could have the stamina to ride out into the evening, strike two people down from the back of a horse, set a barn ablaze, and ride back without arousing suspicion.\"\n\n\"That is a relief.\" Kaylin gave a tight smile as she pulled a lace handkerchief from the sleeve of her dress and began tugging it between her fingers. \"Everyone here, including that inspector from Scotland Yard, believes that Nathaniel Heffernan is\u2014\"\n\n\"Please don't,\" Lady Arnifour said. \"You mustn't speak of what you know nothing about.\"\n\n\"Do my ears deceive me?\" Eldon moved across the room, his voice tight and accusing. \"Is that some sort of veiled confession?\"\n\n\"And I was wondering . . . ,\" she sallied right back, \". . . if it isn't you who might have something to confess.\"\n\nHis face went rigid. \"So that's it, then? My own mother accuses me of murder?\"\n\n\"Excuse me . . . ,\" Colin said, flicking his eyes around the room until he had everyone's attention. \"While I am sure this is serving some purpose, it is not serving mine, and I do have a few things I should like to have clarified so that we can put an end to all of this for good.\"\n\n\"Well, I've had enough.\" Victor pushed himself to his feet. \"I'm tired of hearing my boy's name tossed up. You've already said he's innocent, Mr. Pendragon, so I'll have no more part in this.\"\n\n\"It's too late for that.\" Lady Arnifour gave him a pained smile. \"You inhabit every part of this.\"\n\n\"Yes . . . ,\" Colin started to slowly circle the room, ending up by the doors, which he quietly pulled shut, \"I'm afraid that you do, Victor.\"\n\n\"Then it's settled.\" Kaylin made to rise from her seat. \"I'll have Mrs. O'Keefe send for the inspector and we'll finish with this horrible business.\"\n\n\"I'm afraid it won't be quite so easily done.\" Colin remained at the doors. \"And we'd best all be of the same mind before our dubious inspector is summoned.\"\n\nI glanced at the faces around me: Lady Arnifour, veiled and grim; Kaylin, flushed with emotion; Eldon, locked behind his bottomless tumbler; and Victor, who looked worn to the bottom of his very soul. While they each harbored their own set of resentments, I couldn't tell who was capable of so heinous a crime: a crime against two of their own.\n\n\"First, let me state for the last time that Nathaniel Heffernan is innocent of these murders,\" Colin said. \"Nathaniel probably cared more for Elsbeth than anyone else in this room. He alone understood the binds of family. Certainly more than you, Victor. Your determination to keep the truth from ever being borne out prevented you from showing so much as a hint of affection to her, a profoundly regrettable decision on your part. Or you, Lady Arnifour, as you unwittingly found yourself encumbered by a child who came to represent the worst mistake of your life. You would have done yourself and the child far better to have followed your first instinct and given her away.\"\n\n\"What are you talking about?\" Eldon asked, looking around at the assembled faces for an answer that would not be forthcoming.\n\n\"Hush!\" Lady Arnifour finally snapped. \"That you insist on sitting here is reprehensible enough, but I do not owe you any explanations.\"\n\n\"Which does bring us to you, Eldon,\" Colin quickly spoke up. \"You have clearly chosen to climb into the bottom of a cask rather than face the ambivalence of your parents, wearing the wounds of your childhood like a badge of honor. Very different from your sister, Kaylin. My dear, you've allowed your mother to shroud you in a veil of fragility even as you extol the increasing howl of suffrage\u2014\"\n\n\"Really, Mr. Pendragon,\" she interrupted. \"What horrible things you're saying.\" She twisted around to get a clear view of her mother. \"And whatever does he mean about a child you should have given away?\"\n\nLady Arnifour stared across the room at Victor, her pallor ghostly white. \"I'm afraid I've made some terrible mistakes, little one. I can only hope you will forgive me. . . .\" Her eyes held Kaylin's even as her face remained inscrutable. \"Elsbeth was not your cousin. She was born to me. She was your half sister.\"\n\n\"What?!\" Kaylin pulled back from her mother. \"That can't be\u2014\"\n\n\"It's true.\"\n\nShe looked about to swoon as she glanced from her mother to Victor, who had dropped his eyes and sagged forward in his chair. Nothing more needed to be said. The truth had been there all along.\n\nLady Arnifour slowly began to speak again, telling the same story to her children that she'd already confessed to us. And once again there seemed to be something freeing in her words, and I understood that to be true. But while Lady Arnifour seemed to gain strength from the imparting of her story, neither of her children looked to be likewise affected. Eldon's expression grew increasingly aghast while Kaylin started to cry softly into her handkerchief.\n\n\"Mr. Pendragon is right,\" Lady Arnifour finished with the assurance of hindsight. \"I should have set her free from the start.\"\n\nSeveral seconds crept past before Eldon turned and stumbled back to the bar. \"Is there any bloody wonder I drink so much?\" he mumbled to no one.\n\n\"Why didn't you tell us?\" Kaylin said in a pitifully small voice. \"How could you have let us think . . .\"\n\n\"I know.... I was wrong.... I should have . . . I just . . .\" Her words trailed off in the absence of any reasonable explanation.\n\n\"Did Elsbeth know?\"\n\n\"I don't think so.... She never spoke to me about it.\" She glanced over at Victor, but he kept his head down. \"I suppose I can't be certain. I have no way of knowing what your father may have told her.\"\n\n\"No wonder Father hated you,\" Eldon said as he took a deep drink.\n\n\"Eldon! . . .\" Kaylin howled.\n\n\"Let him say what he wants,\" Lady Arnifour said. \"What does he understand of love? The only thing he's ever loved is a bottle.\"\n\n\"Whiskey is that only thing that makes living with you tolerable. It should have been you in that field that night\u2014\"\n\n\"How dare you!\" Victor leapt to his feet.\n\n\"Enough!\" Colin moved to the center of the room and for once I was glad to see him chastising this herd of cats. \"Since I am no longer working for a fee I don't feel the least obliged to subject myself to a moment more of this twaddle. I shall ask the questions and each of you will answer, and only after I've finished and left this house behind may you choose to continue this discourse. Failure to follow this directive will bring a rash of blue-suited bobbies and Yarders down upon your heads so quickly that you'll each be explaining yourselves from now until the turn of the century. Are we clear?\"\n\nNo one answered.\n\n\"Very good. Then I should like to know about the relationship between the Earl and Elsbeth; does anyone deny that they were having an affair?\"\n\nThe stoic faces that countered his question confirmed what we already knew.\n\n\"Fine.\" He allowed a tight smile. \"I also know one of you had a row with Elsbeth about that affair the night she and the Earl were attacked. Would anyone like to confess? . . . Or shall I do it for you?\"\n\n\"There's no need,\" Victor spoke up. \"We both know it's me you're talkin' about. But I've got nothin' to hide. And you're right, Mr. Pendragon, I was no kind of father to Elsbeth and will have the rest a my life to think on it. But at least I tried to help her that one time. I knew she was goin' out to that barn to meet the Earl. I also knew he was usin' her 'cause he knew how much it was hurtin' his wife. It was unforgivable\u2014\"\n\n\"And this from the man who cuckolded him,\" Eldon sneered.\n\n\"Not another bloody word!\" Colin snapped. \"Go on, Victor.\"\n\n\"I confronted her that night after her argument with Nathaniel. Told her she was bein' played a fool.\" He shook his head. \"She didn't care what I had to say. Even denied it right to my face, but after a few minutes I could see she was takin' some joy in it. I think she was proud of herself. Thought she had it all figured out.\" He rubbed his forehead. \"Then she just started hollering that I had no right to say anything to her. And she was right. I was just the help to her. I never earned the right to say anything.\" He slumped back in his chair and looked drained. \"I was no one to her.\"\n\n\"Victor . . . ,\" Lady Arnifour muttered.\n\n\"And what about you, Eldon?\" Colin said as he turned to the young man. \"Did you ever argue with your father over his affair with Elsbeth?\"\n\n\"Me?! Now why the hell would I give a ruddy toss about what he was doing?\"\n\n\"Because he was ruining the estate,\" Colin answered. \"Your inheritance. But then he was holding you off with a threat of a different sort, wasn't he? While you worried that someday you'd be left with nothing more than a mountain of debt and a house crumbling about your feet, your father was keeping you at bay by refusing to share in the profits from his lucrative clubs unless you did his bidding.\"\n\n\"Clubs?!\" Lady Arnifour stammered.\n\n\"Yes, I'm afraid Warren Vandemier's been holding out on you.\" A tight smile teased Colin's lips. \"But you know that already, don't you, Eldon?\"\n\nI was mystified as I turned to look at Colin, wondering if he was inventing things just to elicit a reaction from Eldon, until I saw Eldon flush in the span of an instant.\n\n\"I assume Abby Roynton let that slip . . . ?\" Eldon said as he struggled to regain his composure.\n\nColin's eyes flashed as a corner of his mouth curled up, making it clear that he had indeed garnered much more information from the seductive widow than he'd admitted to me.\n\n\"That woman . . . ,\" Lady Arnifour hissed.\n\n\"What I want to know, Eldon . . . ,\" Colin spoke over her, \". . . is what the argument was about between you and your father the night before the attack? At the Whitechapel club. The one a lovely young woman who worked there was only too eager to report to me.\"\n\n\"You would take the word of an addict?\" Lady Arnifour reproached.\n\n\"An addict can be far more honest than someone with something to hide. Am I wrong, Eldon?\"\n\n\"No,\" he said with defiance. \"She wasn't lying. I was there that night. And we had a hell of a go of it. I'm just glad I got a chance to tell him what I thought before someone made the laudable choice to snuff him.\"\n\n\"Eldon!\"\n\n\"Then tell me . . . ,\" Colin continued over Lady Arnifour's outburst. \". . . Tell us all what you said.\"\n\nHis face clouded. \"My father was vile and loathsome, and he cheated or used everyone in his life to get whatever he wanted. And I include in his notable list of dupes Abigail Roynton, as remarkable and vivacious a woman as there's ever been.\" He smirked at his mother. \"So it was my pleasure to carry on my father's questionable carnal finesse when it became clear that he'd tired of the extraordinary widow. I will admit, at first I only seduced her to raise the old sod's ire, but I quickly realized that she was a font of information about him, and a willing one at that. I knew I'd be able to use what she confided in me if only to protect my own best interests. And I was right.\n\n\"Abby told me he'd not only founded half a dozen clubs in town, but that he'd also invested in that many more in China. Most of his employees were smuggled in on cargo ships from Shanghai. They'd arrive as indentured slaves and my dear father would seal their fates by making them addicts.\" He finished another shot of whiskey and took the time to pour a refill before continuing. \"The only thing I couldn't figure out, the only thing even Abby didn't know, was where the hell he'd gotten the capital. I knew it had to be coming from somewhere unsavory, but I never dreamed he was bilking it from his own wife.\" He shook his head. \"And to think it was over her bastard child. How repulsive we've all become\u2014\"\n\n\"You have no right!\" Kaylin howled.\n\n\"Please!\" Colin bellowed. \"Will you go on. . . .\"\n\nEldon tilted back another quick sip. \"I decided to have it out with the old swindler. I told him he could either cut me in on his other businesses or I would confess to my mother everything I'd found out.\" His eyes seethed with anger. \"You can just imagine my astonishment when he only laughed at me. Now I know why. How pathetic I must have looked, threatening to turn him over to the very person who was bankrolling him. Consistent right up to the end, aren't I!\" he growled.\n\n\"And what about you, Kaylin?\" Colin turned to her, looking smaller than ever from her perch on the couch next to her mother. \"What did you make of your father's character and livelihood?\"\n\n\"There have already been too many ugly revelations here, Mr. Pendragon,\" she said quietly. \"I haven't the heart for any more.\"\n\n\"Ah, but you mustn't refuse. We are finally getting somewhere.\"\n\n\"You will mind yourself, Mr. Pendragon,\" Lady Arnifour warned. \"I've had about enough of this.\"\n\n\"Of course you have. We can summon Scotland Yard if you'd prefer. I'd be perfectly content to continue with the inspector and a stream of bobbies in attendance. But let me assure you, this will be done. You were saying, Kaylin?\"\n\n\"What is it you want from me, Mr. Pendragon?\"\n\n\"The truth. Were you aware of your father's dealings?\"\n\n\"Absolutely not.\" She glanced over at her mother with what looked to be both pity and regret. \"He left me alone. I have nothing to say against him.\"\n\n\"Did you ever visit him at his club in Whitechapel?\"\n\n\"And why would I do that? Those places represent everything I despise.\"\n\n\"How so?\"\n\n\"They prey on weak-minded people, Mr. Pendragon, and foster addiction in the name of business.\" Her voice was tight. \"Women are treated like baubles, dangled in front of eager clients with no greater expectation than to entice them to ruin their lives. And haven't you been listening to my brother? Those same women are enslaved, their loyalty assured by virtue of the dependence on opium they're forced to cultivate. Isn't that reason enough?\"\n\n\"My apologies.\" He nodded his head slightly.\n\nShe nodded back, but her glare was wintry cold.\n\n\"I can see you've given this a great deal of thought. It's commendable that you're able to be as compassionate of your father's memory as you are. I assume you've made your peace with him.\"\n\n\"I have.\"\n\n\"And Elsbeth?\"\n\n\"Elsbeth?\" She shook her head and dropped her gaze. \"I had no quarrel with her,\" she said.\n\n\"Oh?\" Colin furrowed his brow as he continued to scrutinize her. \"Then I am confused. Elsbeth was a woman you thought to be your cousin and yet you've already admitted by your silence that she was also someone you understood to be having an affair with your father. I also recall you being most disparaging when discussing your father's trysts with Mrs. Roynton. So while you demurred to name Elsbeth as the new object of your father's affection, you made it clear that you neither condoned nor excused him or his mistress. All of which makes me believe that your coyness is decidedly unconvincing.\"\n\n\"And yet we are the ones being disparaged, Mr. Pendragon, as you persist in spinning a flimsy web of hunches around us. Surely my mother's payments to you have earned us more than that?\"\n\nColin smiled, his dimples framing the edges of his mouth with significant pleasure. \"Well spoken. And you are absolutely right. So now it is time for me to admit that I myself am guilty of a bit of coyness. I will ask you to indulge me by returning to the night before the attack. The night Eldon admits to finally purging his soul. What you have not admitted is that you followed Eldon there that night, didn't you?\"\n\n\"That's enough.\" Lady Arnifour bolted to her feet. \"I'll not have you accusing my daughter of dishonesty. You will remove yourself from this house at once or the inspector will most certainly be sent for.\"\n\nColin stood firm a moment before nodding as though in agreement. \"Mrs. O'Keefe!\" He pulled open the door and hollered out into the foyer, \"Mrs. O'Keefe! Would you please be so kind as to fetch the inspector and a contingent of bobbies.\" He slammed the doors shut and turned back to us. \"While we wait the hour it will take that rabble to make their way here, I shall finish my postulation.\"\n\n\"This is appalling,\" Lady Arnifour stammered, shifting her weight as though getting ready to leave the room, and yet she still did not. Perhaps she understood as I did that Colin would not let her. And in the space of that moment, Mrs. O'Keefe quietly slid the door open in response to having been summoned and hovered just inside.\n\n\"Appalling?\" Colin rolled right along, having adopted an air of faux indignation. \"I would say appalling was your decision to remove your daughter from the house in the aftermath of the murders for fear she might be found out. Appalling is your willingness to allow the son of a man you supposedly love to take the fall for a crime you know he did not commit. Appalling is trading one life for another because you've decided one is more valuable. Appalling is bearing a child whom you turn away from because she reminds you of your most profound mistake. . . .\"\n\nLady Arnifour clutched at her chest and sank back onto the sofa, her face as ashen as spent cinders. Her eyes had lost their focus and she appeared to no longer be aware of anything around her.\n\n\"For the longest time,\" Colin spoke again, choosing his words deliberately as he too stared at Lady Arnifour, \"I've been unable to figure out who you've been trying to protect. Have you been covering your own complicity? Or were you doing so for someone else? I see now that it was a bit of both.\"\n\nNo one spoke.\n\n\"Let me tell you what I know to be true, and then let me tell you what I believe to be true,\" he said after a moment. \"Because of the affair Elsbeth and the Earl were having, she came to understand the truth of her parentage. Nathaniel made me realize that. I'd made the blunder of misconstruing his devotion toward Elsbeth as romantic passion, but I was wrong. It wasn't a lovers' quarrel overheard between the two of them the night of the attack, but rather a disapproving argument between siblings. Nathaniel was insisting she end the affair even as she warned him to stay out of her business.\n\n\"And do any of you comprehend what that conversation tells us about Nathaniel and Elsbeth?\" He glanced at their faces but did not wait for a response. \"It tells us how close they were. Which makes perfect sense when you remember that neither Elsbeth nor Nathaniel was an Arnifour. The two of them lived on the periphery of this willful and self-possessed family. Fortunate for them, I suppose, until Elsbeth learned the truth. Only then could she finally rid herself of her feelings of dissociation, for through her biological mother, she now belonged.\n\n\"It was their shared secret which allowed them to have the sort of confrontation they had on the night she was attacked. But Elsbeth was not to be so easily dissuaded from her perch at the Earl's side. For in spite of Nathaniel's words, she rode out to meet the Earl just as she'd been doing for months\u2014whenever Kaylin wasn't along. And while all of you established that a walk was a customary part of the Earl's evening, only one of you knew that Elsbeth and the Earl went many nights to that barn. The two of them headed out in separate directions at differing times, but Elsbeth would double back and pick him up, riding down with him for their indiscretions.\n\n\"Only Kaylin had spied them from her promontory on the boulders across the field on nights she would go there on her own. She would watch the two of them ride up like young lovers, her father and her cousin, disappearing into that barn. . . .\" Colin let his voice trail off as he held his gaze on Kaylin, finally perching on the ottoman by her feet. \"Am I correct?\" he asked. \"Did they tarnish your perfect view?\"\n\nShe exhaled deeply as her eyes flicked about. \"I loved that place. It was so peaceful.\" She shook her head. \"Then they started showing up.\"\n\n\"Did it make you angry? The scandal that was sure to denigrate your family's name if they were found out?\"\n\n\"The Arnifour name has withstood graver injustices over the centuries than my father's infidelities against my mother,\" she said flatly. Lady Arnifour leaned over and seized her daughter's hand, squeezing it firmly.\n\nColin flashed a quick smile before standing and turning his gaze back to Eldon. \"And what do you say? Do you agree with your sister?\"\n\nEldon stared at her, his expression confounded. \"I don't know,\" he mumbled.\n\n\"Are you quite finished, Mr. Pendragon?\" Lady Arnifour turned on him, sounding for a moment like her normal self.\n\n\"You told your sister about your father's multiple business dealings after Mrs. Roynton divulged them to you, didn't you, Eldon?\"\n\n\"She had a right to know,\" he answered with a bit of a stammer. \"He was cheating us.\"\n\n\"And you suspected your sister would do something about it\u2014\"\n\n\"No!\"\n\n\"How dare you!\" Lady Arnifour pushed herself to her feet.\n\n\"Sit down!\" Colin barked. \"We will finish this now.\" He wheeled on Eldon. \"You set your sister up. You told her everything you knew and then led her down to the club the night before your father was killed. The only thing you earned for your efforts was your father's scorn, but your sister caused quite a stir.\" He turned back to Kaylin. \"You made a veritable spectacle of yourself, swinging an oil lamp around and threatening to burn the club to the ground until your father and his security blokes finally managed to hustle you out. You were memorable, Kaylin. In spite of their altered states, you left everyone shaken, which is exactly what Eldon had intended.\n\n\"About the only one you failed to ruffle was your father. He had no idea how much you already knew, or the ways in which your brother was manipulating you: telling you stories of the family's impending doom, the squandering of your mother's fortune, the repugnant trade he was in.\n\n\"Which brings us to the night of the attack. I'll bet tensions at the dinner table were exceedingly high that night, Eldon and Kaylin infuriated by what they viewed as their father's treachery, and Elsbeth feeling mistakenly emboldened by her secret knowledge. And then there was the Earl. He would have still been convinced that only he had all the pieces in this game. But that's where he was wrong.\n\n\"Kaylin excused herself from the table partway through the meal with complaints of a headache. Everyone else finished and went their usual disparate ways, the Earl setting off on his nightly jaunt, Elsbeth to the stable to get her horse for her rendezvous, Nathaniel to finish up in the stable, Victor to his garden, Mrs. O'Keefe to clean up her kitchen, and Eldon to the nearest bottle.\n\n\"Unfortunately for Nathaniel, this was the night he decided to confront his beloved half sister about what she was doing. He wanted better for her. But Elsbeth disagreed. They argued intensely, unwittingly providing a motive for the imminent attack. A happenstance all of you, with the sole exception of Victor, have been too happy to hide behind.\n\n\"The Earl and Elsbeth met at their usual spot,\" he moved to the fireplace, \"a well-trampled patch of grass not more than a third of the way to the barn, and rode the rest of the way together as was their custom. I suppose they thought they were being clever, though they were hardly discreet, yet neither of them knew that someone had already arrived there ahead of them. Someone who had taken a horse while Elsbeth and Nathaniel were fighting and was now waiting just inside the edge of the trees by that barn.\n\n\"When they arrived that night there would have been no sign that this evening was any different from any other. I suspect they were probably so caught up with their passions that they didn't realize something was amiss until the barn was set ablaze. And from there, everything unfolded with lightning speed.\n\n\"They would've fled outside where they were immediately set upon, their hunter waiting for them. The Earl was run down first. He received several blows to the back of his head from a large knot of wood the killer had found among the trees. Once the Earl had been felled, the killer turned back to go after Elsbeth. She had not gotten very far, mistakenly choosing to turn and hold her ground, thinking, perhaps, that she might be able to convince her attacker not to hurt her. But she was wrong. This attack was as much about her as it was the Earl. Though the blows she suffered lacked the ferocity of those that had been wielded against the Earl, it was only because the killer was already fatigued. Isn't that right, Kaylin?\" He turned to her. \"So tell me, what did Elsbeth say when she came to your room that night to, as you said, check on you? It certainly wasn't to ask you to go riding, was it?\"\n\nNo one spoke for a moment as everyone turned to Kaylin.\n\n\"Don't say a word,\" Lady Arnifour suddenly blurted in a voice that sounded as detached as it was hollow. \"He's got nothing but a cluster of speculation.\"\n\n\"That's all you've got to say?!\" Eldon sputtered.\n\n\"Not one more word from you. You don't know a thing.\"\n\n\"At least I'm not being accused of murdering anyone\u2014\"\n\n\"Stop!\" Kaylin bellowed, stabbing at her temples. \"Isn't it enough already? Isn't it?!\" She turned on her brother. \"You did this. You took me to the club that night after telling me how Father owned a dozen of them, addicting patrons and enslaving women. You let me go in there and threaten him, threaten the whole bloody place, and when we went home that night you told me it was the last vestiges of our inheritance. All we would be left with were those vile clubs and this crumbling house\u2014\"\n\n\"Don't\u2014,\" Lady Arnifour pleaded.\n\n\"It's too late!\" Kaylin snapped, casting her gaze to Colin. \"It was an outrage, Mr. Pendragon, the mockery my father made of all of us. I wasn't about to become a spinster with an ownership in opium clubs! Oh . . . I despised him for what he was doing to me, but unlike my pathetic brother, I decided I would do something about it.\"\n\n\"You mustn't. . . .\" Lady Arnifour started to sob as she seized her daughter's arm, but Kaylin only shook her off and stood up.\n\n\"I decided I would go out that night when he went for his walk and have it out with him, one way or another. I wasn't going to sit idly by and watch him annihilate everything around us.\" She shook her head and moved over by the windows, wrapping her arms around herself as though she were suddenly cold. \"You were right; dinner was awful that night. The room was intolerable and when I couldn't take it anymore, I complained of a migraine and left.\n\n\"I went upstairs and changed into my riding things and that's when Elsbeth came up to see me.\" Her face clouded and her lips pursed. \"She came up to ridicule me. My father had told her that Eldon and I had come to the club the night before, and she laughed at me for thinking I could have any effect on what he was doing. It made me mad . . . it made me outraged . . . to think she presumed that whoring around with my father gave her the right to say such things to me! I hated her. . . .\"\n\n\"Oh, Kaylin.\" Lady Arnifour shrank back on the couch, weeping piteously.\n\n\"I knew they would meet up that night. The two of them so proud of themselves. So while Elsbeth was arguing with Nathaniel, I took one of the horses without a saddle or bridle or reins and rode down to the barn and waited for them. And I didn't have to wait long. They came trotting across the field on one of the bays, one of my favorites, and they'd barely dismounted before he was pawing all over her, her laughing and letting him do whatever he pleased. It was sickening. And never once did they bother to look around and see if anyone might be there, might catch them, never in all the times I'd seen them. They didn't care. The two of them, they were deplorable.\n\n\"So as soon as they disappeared into the barn I crept forward and set it ablaze. Let them have their fire with their passion. . . .\" She gave a hollow chuckle that died in her throat. \"My father came out first; he spotted me and started hollering at me, said I was bloody starkers. Can you imagine? I rode him down, Mr. Pendragon, just as you said, and I struck him with a knot of burl I'd found in the woods. It felt good; watching him blubber like the pathetic creature he was, it only made me angrier. And she . . . she was no better than him. I should've known she was born of my flesh. We are a contemptible lot, but at least I kept them from destroying everything. . . .\" Her voice trailed off and I wondered if she yet had any real understanding of what she had done.\n\n\"I'll need you to come with us,\" Colin said softly.\n\n\"I'll not fight you,\" she answered. She went over to him as I got up, planting herself before him with defiance as Eldon sagged against the bar and Lady Arnifour's wrenching sobs filled the silence. I glanced over toward the door and noticed that Mrs. O'Keefe was gone, though she had left it ajar in her evident haste to leave. And it made me wonder if perhaps Lady Arnifour was grieving for a daughter who was not her own after all.\nCHAPTER 33\n\nThe deepest part of the night is the time I find myself most able to collect my thoughts. It's also one of the few times I can watch Colin without self-consciousness lest the eyes of anyone else should take disapproving note. Some nights I will reach for him; other nights I am content to leave him be and simply marvel at the wonder of it all.\n\nThis night found me quite lost to my thoughts. In the space of a single day we had rent two very disparate families, although it could be said that they had severed themselves long before we had been called upon. It made me wonder, this business of family. The stricture of its definition seems careless and arbitrary given the aberrations that can be found within its framework. How well I know that. Twenty-six years after the tragedy that took my life without ending it I still choose to believe that my mother did the best that she could given the phantoms blighting her mind. I will never know for sure. In truth, I hardly even remember her. She has morphed into a cautionary figure of what to be vigilant against. What makes it worse is that I remember even less of my father. So it is my life with Colin that represents the pinnacle of the promise of that word: \"family.\" And, of course, Mrs. Behmoth, though I'm not as certain how I feel about that.\n\nColin reached out with a yawn, peering at me through heavily lidded eyes. \"Can't sleep?\"\n\n\"I guess not.\"\n\nHe curled up next to me, his arm stretching across my belly. \"What's keeping you awake?\"\n\n\"I was thinking about Kaylin. What's going to happen to her?\"\n\n\"That's easy.\" He exhaled deeply. \"Her mother will purchase the best defense and she will be sentenced to a spell in a sanitarium somewhere out in the country. They'll ascribe her behavior to female hysterics and it will likely run until she's long into her middle years.\"\n\n\"When you say 'her mother,' do you mean Lady Arnifour or Mrs. O'Keefe?\"\n\n\"In this instance I am referring to Lady Arnifour, but it really doesn't matter who gave birth to her. I suppose they both loved her in their own way, and it didn't seem to make the slightest bit of difference to her life. It's just a travesty that nature doesn't see fit to make some people barren.\"\n\n\"What a thing to say,\" I muttered halfheartedly, knowing that I would never have been born had such a natural selection been in place.\n\n\"Come now, you know I'm right. And I mean to include Mademoiselle Rendell in that too. None of them was fit to procreate.\"\n\n\"At least now Drew will have a chance in a decent home,\" I said with genuine cheer, determined to relegate my maudlin thoughts back to where they belong: where I can abide them. \"Do you think your father will get him placed quickly?\"\n\n\"That boy will be living like royalty within the month. And in India he'll be safe from both his mother and brother.\"\n\n\"Which is good, since Michael's not likely to remain in the workhouse for more than a couple of years.\"\n\n\"I'm sure you're right. And then he'll be back on the streets: ill equipped, angry, and even more conniving than ever. At least their mother will be spending the better part of the next decade paying for her complicity. Nevertheless, it does seem rather a small price to pay given the destruction she's wrought on those boys.\"\n\n\"She has to live with that for the rest of her life.\"\n\n\"Not everyone has a conscience, you know.\"\n\n\"They do. Some just learn how to ignore it . . . or anesthetize it.\"\n\nHe yawned again. \"That is the unfortunate truth. But let me ask you a question: Where do you suppose Li Shen disappeared off to?\"\n\n\"She'll go to another club somewhere else in the city where they don't know who she is. It's what she knows and she is an addict.\"\n\n\"It's a shame.\"\n\n\"It is.\" And for a moment a chill tore up my spine as I recognized that could have been me. \"Do you think there's any chance Inspector Varcoe will stop by tomorrow to thank you for keeping him from arresting the wrong person?\" I chuckled.\n\nHe snickered. \"Only if Mrs. Behmoth discovers she's the long-lost sister of our Victoria.\"\n\n\"Unlikely then, I suppose,\" I drolled, but I could tell by the way his breath was already beginning to even out that he was succumbing to sleep. Lost to my own thoughts once again, I didn't sleep much more that night, but it was gratitude, not fear, that held my mind enthralled.\nCHAPTER 34\n\n\"It seems ta me ya oughta be celebratin',\" Mrs. Behmoth said as she set the tray of tea and scones by the fireplace. \"I didn't like a single one a them uppity Arnifours and I'm glad ya found 'em all guilty.\"\n\nI rolled my eyes.\n\n\"I didn't find them all guilty . . . ,\" Colin started to say.\n\n\"Ach.\" She waved a hand at him. \"They were all guilty a somethin'.\"\n\n\"I suppose.\" He shrugged, one eyebrow arching up as he fussed over our tea. \"But it's hard to feel satisfaction given the cost to their family.\"\n\n\"Family . . .\" Mrs. Behmoth snorted. \"They were a regular rogues' gallery. Ya best appreciate what ya got,\" she scoffed.\n\nA sudden and savage pounding on our door brought her to her feet. \"We expectin' someone?\" she asked as she ambled for the stairs.\n\n\"Not that I'm aware of,\" Colin said as he poured a touch of milk into his tea.\n\nAnother harsh pounding reverberated from downstairs as Mrs. Behmoth hollered, \"Ya better 'ave a good reason for makin' such a racket!\"\n\nColin laughed as he passed me my tea and then snatched up his own. \"I heard a carriage clattering up and was rather hoping it might be coming here.\"\n\nI couldn't help smiling. \"I'm sure you were.\"\n\nThe sound of a slight scuffle came from downstairs, followed by the hurried pounding of feet barreling up. It was clearly not Mrs. Behmoth, and the trailing fury of her voice only confirmed it. \"Ya got no ruddy manners. I don't care if ya are wearin' the old bird's crest.\"\n\nBefore I could guess who Mrs. Behmoth was referring to, a sour-faced young man, somewhere shy of the quarter-century mark, appeared on our landing. He was dressed in the scarlet tunic and black-panted uniform of Her Majesty's Guard. He held a steel helmet in the crux of one arm atop of which sprayed a white plume like the tail of a prideful show horse. \"I apologize for the intrusion . . . ,\" he said in a tone that did not support his contention, \". . . but I've been sent on the most urgent and sensitive business.\"\n\n\"So I would presume.\" Colin smiled thinly as he stood up. \"And by whose command do you come in such a manner?\"\n\nThe young man sent a sideways glance in my direction as he let his pause lengthen.\n\n\"You will speak to both of us or neither of us,\" Colin said. \"I really don't care which.\"\n\nTo his credit, the guard appeared to carefully consider his options before turning back to Colin with a bit more acid. \"All right then.\"\n\nNo one said anything for a moment as Colin slid out a crown and quietly began weaving it through his fingers. It took another full minute before Colin finally spoke up, keeping his eyes fixed on the young officer as he said, \"I'm waiting, Sergeant.\"\n\n\"Sir?\"\n\n\"I asked who sent you here.\"\n\nHe reddened and pulled himself straighter. \"Isn't that obvious, sir?\" he said with noticeable disdain.\n\nColin strode over to the windows, the coin continuing to slide smoothly between his fingers as he glanced outside. \"The only obvious thing, Sergeant, is that you wish me to believe you are on Her Majesty's business. Arriving thunderously in one of her lesser carriages and parading about in the garments of one of her Life Guards. Yet we all know our matriarch has a multitude of both coaches and staff, and were you actually to be on her business, I would expect a far less ostentatious entrance. What's your name?\"\n\n\"My name?\"\n\n\"Come now.\" Colin turned from the window and stared at the young man. \"I haven't stumped you already, have I?\"\n\nThe sergeant scowled and I struggled to suppress a smile. \"Sergeant Dwight McReedy,\" he finally answered.\n\n\"Well done. And so, Sergeant McReedy, now that we know our Victoria has not sent you, can you tell us who has?\"\n\nThe sergeant held his own, staring back at Colin with thinly veiled dislike. \"While I may not be here at the personal request of Her Majesty, I have come at the behest of a senior member of her staff.\"\n\n\"A senior member of her staff?\" Colin smirked. \"Why, that could be anyone from a personal maid to my father. Has my father sent you?\"\n\nThe man's face went taut. \"Sir?\"\n\nColin shook his head and returned to his seat. \"I'll not ask my question a fourth time, Sergeant. You may take your leave. Good day.\"\n\nThe sergeant glanced at me in disbelief. Whereas before he'd considered me an intruder, I could now see he was hoping I might intercede on his behalf. I gave him a shrug.\n\n\"Sir . . . ,\" he began again with some measure of grit in his voice, \"I've been ordered to escort you back to Buckingham Palace.\"\n\n\"And suppose we're not in the mood to go until sometime next week? Would you be obliged to spend the next days counting cobbles and praying against rain?\"\n\nThe young man managed to hold himself steady. He was clearly a quick study. \"You mustn't dismiss me, sir. I've been ordered by Major Dashell Hampstead of Her Majesty's Life Guard. It is on a matter of the utmost delicacy and urgency.\"\n\nColin looked up at him. \"So it's the Guard itself who requires my assistance?\"\n\nSergeant McReedy blinked. \"I'm sure I don't know,\" he answered. \"Collecting you was the extent of my orders.\"\n\n\"Well now, that makes me feel like an old alley cat.\"\n\n\"You must come with me, sir. I must insist on it.\"\n\n\"Insist?\" Colin finally stopped flipping the coin as he looked over at the young man.\n\nThe sergeant cleared his throat and lowered his voice. \"It's a most foul business. Major Hampstead would not trouble you otherwise.\"\n\n\"How foul?\"\n\n\"Sir?\"\n\nColin waved for him to get on with it.\n\n\"It's murder, sir,\" came the reluctant reply. \"The most brutal sort.\"\n\nColin scowled as he stood up again. \"Return to your carriage,\" he said.\n\n\"Sir?\"\n\n\"We will be down shortly. Go on now. I don't need you watching us get ready.\"\n\nThe young man nodded curtly and took his leave, bolting back down the stairs with as much tumult as his arrival.\n\n\"Was it really necessary to set him through such paces?\"\n\n\"Hmm.\" Colin shrugged as he pulled his vest on. \"That lot can be so full of themselves. And him just a young toady.\"\n\n\"Nevertheless, it's not every week we're summoned by Her Majesty's Guard.\"\n\n\"Thankfully.\"\n\n\"It sounds like a nasty bit of business.\"\n\n\"Murder usually is.\"\n\nI could not help the sigh that escaped my lips. \"We've only just completed two cases. Shattered two families. I'd rather hoped we might have a spot of time off.\"\n\n\"Those families imploded long before we were sent for.\" He stopped and looked at me. \"Makes me appreciate what we have all over again. You and me. That's all I need.\" And I could see by the warmth in his eyes that he meant it.\n\n\"And Mrs. Behmoth?\" I teased.\n\n\"But of course.\" He laughed. \"Where would we be without our dear Mrs. Behmoth?\" And I knew he meant that too.\nACKNOWLEDGMENTS\n\nWhile writing is a solitary sport, a published book is the culmination of hard work by many people. In my case, Diane Salzberg, Karen Clemens, and Melissa Gelineau read innumerable drafts and offered insightful notes with nary a rolled eye or shrug of \"this again?!\". John Paine gave me an early vote of confidence and helped focus the story into something I could show around. I would be nowhere if Kathy Green and her son hadn't read the book. Especially since her son convinced her to take me on! The folks at Kensington have been amazing, keeping me honest and making me wonder how I ever passed an English class. Particular kudos to John Scognamiglio for his support, direction, and friendship. Special thanks to my parents and sisters for their love and support through all and everything. And there has been a lot! The very same to Tresa Hoffman. Lastly, a second bow to Lovey, without whom I would never have made it this far. A heartfelt cheers! to all of you.\nPlease turn the page for an exciting sneak peek of Gregory Harris's next Colin Pendragon Mystery\n\nTHE BELLINGHAM BLOODBATH\n\ncoming in September 2014!\n\nCHAPTER 1\n\nOne of Her Majesty's coaches was waiting to whisk us off to Buckingham Palace. We had only just been told about the killing of a captain in Her Majesty's Life Guard and his wife, and were being summoned, presumably, to solve their murders. The sergeant sent for us had made it sound like an ugly business indeed.\n\nI stared across the room with a mixture of dread and morbid curiosity as I watched Colin continue to fiddle with one of his derringers. Surely he meant for us to leave . . . yet there he sat, painstakingly wiping every centimeter of the little gun until I could finally stand it no longer: \"What the bloody hell are you doing?\"\n\nHe looked up at me with an inconceivably guileless expression. \"What?\"\n\n\"Buckingham?!\" I blurted as though speaking to someone quite undone. \"The sergeant who came to fetch us is waiting outside. . . .\"\n\n\"I know,\" he answered simply.\n\n\"Well, are we going?\"\n\n\"The sergeant's a pompous little twit. He can wait.\"\n\n\"He's an officer of Her Majesty's Life Guard\u2014\"\n\n\"I don't care if he's having it off with the old girl herself; let him wait. Be good to teach him some manners.\"\n\n\"So we're back in school then?\" I parried just as a loud and insistent pounding burst up from the door downstairs.\n\n\"See what I mean,\" Colin grumbled.\n\n\"I'm sure he's only trying to follow orders. He wasn't sent here to polish the cobbles pacing.\"\n\nA second pounding, even more determined, brought Colin to his feet. \"If he does that again I shall go down there and shove my boot up his orders.\"\n\n\"No doubt Mrs. Behmoth will beat you to it,\" I said as the sound of her lumbering from the kitchen to the front door drifted up among her curses. I was certain she would roundly upbraid the young sergeant the moment she got the door open, but no such diatribe ensued. Instead I heard the voice of our elderly neighbor curl up the stairs. \"It's Mrs. Menlo,\" I said with little enthusiasm.\n\n\"And what is she complaining about now?\" He shook his head as he set his derringer onto the mantel. \"Is the soldier out front giving her vapors?\"\n\n\"I should think she's trying to wheedle information out of Mrs. Behmoth. You know how she despises not knowing our business.\"\n\n\"Yes. . . .\" He snatched up his dumbbells and began curling them over his head. \"Though I'm sure we could cause her a good deal of apoplexy with some of the things we get up to.\" He snickered. \"For the moment, however, I believe it's time we learned something about this poor captain and his wife. We mustn't show up at the major's office completely unawares.\"\n\nI stared at the stack of unread newspapers beside the hearth as he continued to train the already taut muscles of his arms. \"Fine,\" I exhaled. \"Let me see what I can find of it.\"\n\n\"Excellent,\" he muttered, dropping to the floor and busting out a set of push-ups on his dumbbells.\n\nTurning my attentions back to the pile of papers, I was relieved when my search proved brief. Stretched across the morning edition of yesterday's paper was a banner that cried: QUEEN'S CAPTAIN AND WIFE BUTCHERED IN BLOODBATH. I read the article aloud while Colin continued his fevered push-ups, and it was only after I finished that he finally sat up, ran a sleeve across his sweating forehead, and asked me to read it again. This time he listened:\n\n\"Sometime during the night of Sunday last, Captain Trevor Bellingham, 32, of the Queen's Life Guard, and his wife, Gwendolyn, 29, were brutally murdered in the Finchley Road flat they shared with their young son. Miraculously, the young boy, just past his fifth birthday, was found unharmed in his bedroom. Police had to break the boy's door down as it had been wedged tight, almost certainly by the murderer, though one source close to the investigation suggested that one of the parents may have secured the door in order to save their son.\n\n\"Mrs. Bellingham was reported to have been shot and killed in her bedroom, but Scotland Yard has yet to release the cause of death for Captain Bellingham, stating that the matter was still under investigation.\" I glanced over to where Colin remained sitting on the floor. \"I wonder why the secrecy?\"\n\n\"We shall have to find out.\"\n\n\"Police did state that there did not appear to be any signs of forced entry, pointing to the possibility that the killer may have been known to Captain and Mrs. Bellingham. Scotland Yard's Inspector Emmett Varcoe . . . ,\" I read his name, enunciating it with mock esteem, \". . . assures that everything possible is being done to solve this terrible crime against one of the Queen's own men and his young wife. However, the Times would like to remind its readership that Inspector Varcoe is the same investigator who remains befuddled by the identity of the vicious killer known only as Jack the Ripper.\"\n\n\"It all sounds rather odd,\" Colin muttered as he stood up and hurried off toward our bedroom, \"though a spot-on summation of Varcoe. He should have retired a decade ago.\"\n\n\"That he should . . . ,\" I agreed as Colin returned with his straw-colored hair slicked back and our coats over his arms.\n\n\"Shall we?\"\n\nTwenty minutes later the hansom cab he had flagged down swung us around the drive of Buckingham Palace, and once again I was struck by how austere and remote it looks. Partially colonnaded in the Federalist style, it appears like neither a true palace nor a home. Sprawling behind its massive bronze and iron fencing with a contingency of guards precisely stationed across its front, it seems very much to be holding itself with the same reserve as our Queen.\n\nI took note of the lone Union Jack on the roof and knew Victoria was not in residence. Her colors would be flying atop Sandringham this time of year, though even if she had been here I knew it would have made little difference. One does not happen upon Her Majesty in the hallways. Nevertheless, it would have been the closest I had ever come to royalty.\n\nThe coachman brought us alongside the gates and slowed almost to a stop as they began to swing inward at the behest of our escort, Sergeant McReedy. We were ushered through and driven across the parade grounds to the far side of the building under the watchful eyes of a throng of spectators.\n\n\"They must think we're special.\" I chuckled.\n\n\"We are,\" he murmured as he surreptitiously squeezed my hand.\n\n\"Perhaps so, but they'll still be disappointed when we climb out.\"\n\nHe laughed as I turned to watch the stiff-postured guards we were clattering past with their blazing red jackets and high bearskin hats. They ignored us as we went by, none so much as moving his eyes to follow our progress. \"You can always count on this lot to put us in our place,\" Colin said.\n\nBefore I could answer we came to an abrupt stop and both doors were immediately swept open. Sergeant McReedy dismounted and led us through a side portico and down a hallway of unremarkable design that I decided no royal had ever passed along. Tiny offices lined both sides, providing the only contrast in the otherwise stark space. It was hardly what I had expected until I reminded myself that these were the niches of those who kept the palace functioning; what use did they have for moldings, ormolu, filigree, or even art?\n\nThe sergeant stopped at an office near the end of the corridor and barked out, \"Colin Pendragon and Ethan Pruitt!\"\n\nAn alabaster-skinned young man who looked too young to be in the service sat behind a small desk in the anteroom to a much larger office. \"Oh . . . ,\" he said with notable surprise as Colin and I walked in. \"Oh . . . ,\" he repeated as his eyes fell on me before quickly shifting back to Colin. \"It's a pleasure to meet you, Mr. Pendragon,\" he said, holding out his hand. \"I'm Major Hampstead's attach\u00e9, Corporal Bramwood.\" His gaze drifted in my direction again and I knew what was coming. \"I am terribly sorry . . . ,\" he said coolly, \". . . but there seems to have been a misunderstanding.\" He looked back at Colin. \"The summons from Major Hampstead was meant for you, Mr. Pendragon, and you alone.\"\n\n\"Ah . . . then there has indeed been a misunderstanding.\" Colin offered a smile. \"I'm afraid I don't work alone, Corporal. You and your major will take us together or you will settle for my regrets.\"\n\nCorporal Bramwood opened his mouth to say something, but nothing came out. I saw him glance behind me to where Sergeant McReedy remained in the doorway and then heard the sound of the sergeant moving off. This young man was apparently on his own.\n\n\"Have a seat . . . have a seat . . . ,\" he mumbled quickly. \"I shall let Major Hampstead know you are both here.\" He gave an awkward nod before disappearing through the door behind his desk, making sure it latched firmly behind him.\n\n\"This lot seems to think they're all ordained by God,\" Colin muttered as he sat down.\n\nI snickered. \"I don't think that young corporal is used to having his major's orders countermanded.\"\n\n\"I was civil about it,\" he blithely protested.\n\nBefore I could say anything more the inner door burst open and Corporal Bramwood hurried out with an older man at his heels. \"Mr. Pendragon . . . Mr. Pruitt . . . ,\" he sputtered. \"This is Major Hampstead.\"\n\nThe major stepped forward, a tall man somewhere in his late fifties with a generous middle. He wore a thick, white mustache and sported huge sideburns that fanned out several inches along his jawline. His deportment suggested he had been a leader most of his life: ramrod straight with a swagger of marked self-assurance. \"It is an honor to meet you, gentlemen,\" he said, and I knew he was also a diplomat.\n\n\"It's always a pleasure to meet one of Her Majesty's lifers.\" Colin smiled.\n\nMajor Hampstead snorted a laugh. \"I should doubt the son of Her Majesty's emissary to India is so easily impressed. I would say your father has given nearly the whole of his life in service to her.\"\n\n\"He has.\" Colin flashed a tight grin. \"But the life of a diplomat hardly compares to the work of a regimental guard. You mustn't give my father too much credit.\"\n\n\"I doubt that I am,\" he chortled. \"Please come in, gentlemen. Tea, Corporal,\" he ordered before retreating back to his office and seating himself behind his massive desk.\n\nCorporal Bramwood brought in a tray of tea and biscuits with a speed that conveyed just how much time he spent in that endeavor. The straining seams along the sides of the major's red tunic also attested to that fact. \"I appreciate your willingness to come here without the slightest notice,\" the major said. \"I'm afraid I have a very difficult matter to discuss. One that requires the utmost discretion.\"\n\n\"You are referring to the murder of that captain and his wife?\"\n\nThe major winced. \"I am. It's an awful business that has been made even more unseemly by the newspapers heralding it the way they've done.\"\n\n\"I'm afraid our countrymen are always keen for a scandal.\"\n\n\"Which is precisely my point.\" I could see him relax a bit at Colin's pronouncement. \"The Queen's Guard simply cannot be party to any such scandal. It is inappropriate and unacceptable.\"\n\n\"That may be, but it would appear it is already done.\"\n\nThe major knit his brow. \"I would venture otherwise, Mr. Pendragon. I have asked you here because I believe you can do a great deal to help us staunch this damage. You can impact the public record to not only cease the gossip concerning this very private, very regrettable event, but to allow us to deal with it ourselves, outside of the public's lecherous purview.\"\n\n\"Us?\"\n\n\"The Guard, of course.\"\n\n\"I see,\" Colin said even as his own brow creased a notch. \"You have summoned us here to divert the newsmen while you and your regiment, untrained in such things, attempt to solve these murders?\"\n\n\"It is the Guard's business and should be handled as such.\"\n\n\"It is the murder of two British subjects, Major Hampstead, one of whom was in service to the Queen. I'm quite certain the public will remain very concerned about it until it is resolved. The inference being, of course, that the very men proscribed with protecting Her Majesty cannot even protect themselves. Trying to steal this behind the public's eye will be quite impossible, Major. Unless, of course, you are trying to hide something?\"\n\n\"Hide something?!\" His face creased into a scowl. \"I trust you are being facetious, Mr. Pendragon.\"\n\n\"I've been accused of worse,\" he muttered.\n\n\"Let me assure you that my request comes only out of concern for Her Majesty's Guard,\" the major said in a tone as filled with condescension as assurance. \"The first lesson a man learns when he enlists is that it is not about the individual, but the regiment. Every man who serves under Victoria's banner understands that.\"\n\n\"While I'm sure that's true,\" Colin allowed with a tightening smile as he fished a crown out of his pocket and began effortlessly weaving it between the fingers of his right hand, \"I don't see how it is relevant.\"\n\n\"Then you are missing my point,\" the major sniped. \"The Queen's regiment has a prestige to uphold and cannot afford to be mired down in such things. This Bellingham situation is anathema to everything the Guard represents.\"\n\nColin instantly palmed the crown. \"Do I understand you correctly, Major? Do you presume to speak for the Queen with such rhetoric?\"\n\n\"Now Mr. Pendragon,\" he exhaled deeply before popping a biscuit into his mouth, \"you misunderstand me. Captain Bellingham was one of my most trusted leaders and a man I considered a personal friend. No one in this company is more determined to bring the perpetrator of his murder to justice than me. And I had the utmost respect and adoration for his lovely wife. A kind and wonderful woman whose senseless killing demands all the resources at the Guard's disposal. Yet even so, decorum dictates that it must be done with discretion. You said yourself that the public will have no faith in our Guard if they perceive that we cannot even fend for ourselves. I'm sure I don't need to remind you that Her Majesty's Life Guard represents the finest of our country's protectorate and as such cannot bear so much as a whiff of scandal. This matter will be solved by this regiment, but we shall do it outside of the gaze of the common masses.\"\n\n\"The common masses?\" One of Colin's eyebrows arched up. \"Does Victoria encourage her Guard to look down on the very people God has granted her the authority to rule?\"\n\n\"Mr. Pendragon . . . ,\" he started to say, only to fall silent. The ticking of the small clock on the major's credenza was the only sound to be heard for several seconds until Colin began to coax the coin between his fingers again. I started to wonder if we weren't about to be dismissed, but I had miscalculated the major. Quite suddenly, without the slightest hint that it was coming, he abruptly let out a bellowing laugh. \"You are toying with me, Mr. Pendragon. You mean to prod me into a rise and you almost succeeded. But I shall not be so easily dissuaded.\" He leaned forward. \"I'd bet you would like to see the Bellingham flat for yourself. There is much the newspapers have not reported. Much they do not know.\"\n\nA cool smirk overtook Colin's face. \"And now you are toying with me.\"\n\n\"So I am.\" He leaned back in his chair with a satisfied smile. \"You must understand my position, Mr. Pendragon. Anything concerning the Queen's Guard inevitably implicates our sovereign as well. And I'm sure I needn't remind you that Her Majesty is seventy-seven and in failing health.\"\n\n\"That woman is as delicate as a plow horse,\" he shot back. \"And I find it hard to believe she has any but the most passing familiarity concerning the murder of one of her guardsmen with whom she probably never once spoke. I believe you are trying to hide behind her skirts, Major.\"\n\n\"Do you presume to be privy to what goes on in Her Majesty's household?\"\n\n\"My father transferred John Brown from Victoria's stable to her personal duty after Albert's death, so I would say I know a bit more about Her Majesty's household than you think. What I don't understand is why you want to bring me here to feed nonsense to the press? I don't control those men.\"\n\n\"You underestimate yourself, Mr. Pendragon. They hang on your words like they are spun from gold.\" A cloying smile clung to his lips. \"If you were to release a statement that you had conducted an investigation and determined the case to be closed, say a burglary gone bad, or a case of mistaken identity, why, they would be only too happy to embrace your conclusion and return their attentions to the horses at Ascot and which lady is wearing what. Everyone would be satisfied, which would allow me and my men to handle this case with the delicacy Captain Bellingham and his wife deserve.\"\n\n\"And the perpetrator?\"\n\n\"I will personally see to it that their murderer receives the full wrath of the law.\"\n\nColin sat up and neatly tipped the crown back into his vest pocket. \"And what makes you think these murders will be so easily dispatched? Murder is a complex business in the simplest of cases. . . .\"\n\n\"I said I will take care of it,\" the major restated with noticeably greater force. \"And I could use your help with Scotland Yard. I've got them circling like schoolyard boys, on top of which the Times is calling the Guard's reputation into question, and the public is terrified for their safety. Until we can release a conclusive statement, Mr. Pendragon, this discord will be relentless.\"\n\nColin stood up. \"I'm sorry, Major. You seem to have gotten the notion that my integrity can be bargained for. If I have earned the respect of the press it is because I do not spin fables and, in spite of your desire for discretion, cannot see why I should start now. If you would like to hire me to solve this case I will gladly do so, but until you come to your senses I will bid you good day.\" He turned for the door.\n\n\"Mr. Pendragon!\" The major sounded perplexed as I got up to follow. \"Mr. Pendragon!\" he howled as we reached the door. \"With all due respect to your esteemed integrity, the public wants immediate answers to their fears. They want the world to return to the status quo. They will not tolerate remaining under a veil of anxiety. You can blame the unsolved Ripper murders for that. And that's why there are men like you and me. To ensure that our republic gets what it needs. Now I am beseeching you, Mr. Pendragon, to offer the public a reasoned solution to a horrible crime so that they can get on with the mundanity of their lives. Where is the harm in that?\"\n\n\"If that's what you're after, Major, then I would suggest you get the Yard to be your mouthpiece. Inspector Varcoe is always good for hot air.\"\n\n\"Nobody wants to hear from that blasted lout. You will do this for me, Mr. Pendragon. You are the only man with the reputation for it and I will insist.\"\n\n\"Insist?\" Colin chuckled. \"Are you proposing sticking a hand up my bum to move my lips?\"\n\n\"You will be handsomely compensated. Now how can I convince you to perform this service for the Crown?\"\n\nColin pursed his lips and I could tell he had already thought of something. \"There is one way I can conceive . . . ,\" he said casually, \". . . and it is the only way I would consider it. . . .\" He let a moment pass to emphasize his determination. \"You must announce to the press that you have retained my services to solve the murders of the captain and his wife. . . .\"\n\n\"Yes?\"\n\n\"And then give me the next three days to do so. During those three days you must ensure I have the full cooperation of this regiment as well as access to whomever I want.\"\n\n\"Not Her Majesty or her family.\"\n\n\"I should hardly think that will be necessary.\"\n\n\"And at the end of the three days?\"\n\n\"I will deliver the truth of the case to you.\"\n\n\"And if you cannot?\"\n\n\"I will.\" He smiled harshly, even as my stomach clutched at the very idea. I couldn't fathom how he had come up with the notion of three days.\n\nMajor Hampstead frowned. \"Absolute proof, Mr. Pendragon. You must bring me absolute proof of whatever supposition you're championing or I shall have your word that you will face that mob of newsmen and sell them whatever I deem appropriate.\"\n\nHe gave no more than an ambivalent nod.\n\n\"Three days then.\" The major glanced back at his clock. \"That would be twelve o'clock on Friday.\" He turned back to us. \"I shall give you until seventeen hundred. Plenty of time for the newsmen to make their Saturday morning edition.\"\n\n\"Most generous,\" Colin muttered.\n\n\"Corporal Bramwood!\"\n\n\"Sir?\" The young man opened the door so quickly I knew he had to have been hovering nearby.\n\n\"Alert the newspapermen that Her Majesty's Life Guard has retained the services of Colin Pendragon to bring a swift and just conclusion to the tragic murders of Captain and Mrs. Bellingham. And let them know that Mr. Pendragon will have an announcement to make at seventeen hundred hours this very Friday.\"\n\n\"This Friday, sir?\"\n\n\"Yes, Corporal. This Friday.\"\n\nAnd with that the young man was gone, though I did notice he left the door ajar.\n\n\"I will solve this crime, Major Hampstead,\" Colin said with the simplicity of one discussing the weather. \"I shall bring you the resolution Friday and we will see what gets delivered to the press.\"\n\n\"I admire a man of confidence,\" the major replied with a tense grin. \"But listen very carefully, Mr. Pendragon, because if, at the end of your three days, you should find yourself stymied by this case, then I alone will decide what is told to those newsmen. You will say what I decide and you will walk away. Are we clear?\"\n\nColin flashed an equally rigid smile. \"You have been most clear, Major. And now I should indeed like an escort to the Bellingham flat so I may get started. Someone from Captain Bellingham's regiment would be my preference.\"\n\n\"Sergeant McReedy will take you. He reported to the captain.\" Major Hampstead's smile relaxed and I couldn't help but feel it was with the arrogance that comes when one perceives imminent success.\nKENSINGTON BOOKS are published by\n\nKensington Publishing Corp.   \n119 West 40th Street   \nNew York, NY 10018\n\nCopyright \u00a9 2014 Gregory Harris\n\nAll rights reserved. No part of this book may be reproduced in any form or by any means without the prior written consent of the Publisher, excepting brief quotes used in reviews.\n\nKensington and the K logo Reg. U.S. Pat. & TM Off.\n\nISBN: 978-0-7582-9267-4\n\neISBN-13: 978-0-7582-9268-1   \neISBN-10: 0-7582-9268-6   \nFirst Kensington Electronic Edition: February 2014\n\n","meta":{"redpajama_set_name":"RedPajamaBook"}}
+{"text":"\n\nEmily Blades' parents' main interests were arts, crafts and literature, and like many creative people, they educated their daughter at home. Art galleries, Craft Council exhibitions and the freedom to pursue whatever interested her at the time allowed Emily to develop her own creative side. She has taught gymnastics to the under-5s, worked as a nanny, enjoys drawing, reading, walking, visiting galleries and museums and, of course, knitting!\n\nFirst published in Great Britain 2010\n\nSearch Press Limited  \nWellwood, North Farm Road,  \nTunbridge Wells, Kent TN2 3DR\n\nText copyright \u00a9 Emily Blades 2010\n\nPhotographs by Debbie Patterson at Search Press studios\n\nPhotographs and design copyright \u00a9 Search Press Ltd 2010\n\nAll rights reserved. No part of this book, text, photographs or illustrations may be reproduced or transmitted in any form or by any means by print, photoprint, microfilm, microfiche, photocopier, internet or in any way known or as yet unknown, or stored in a retrieval system, without written permission obtained beforehand from Search Press.\n\nPrint ISBN: 978-1-84448-486-7\n\nEPUB ISBN: 978-1-78126-019-7\n\nKindle ISBN: 978-1-78126-074-6\n\nPDF ISBN: 978-1-78126-128-6\n\nThe Publishers and author can accept no responsibility for any consequences arising from the information, advice or instructions given in this publication.\n\nReaders are permitted to reproduce any of the items in this book for their personal use, or for the purposes of selling for charity, free of charge and without the prior permission of the Publishers. Any use of the items for commercial purposes is not permitted without the prior permission of the Publishers.\n\nSuppliers\n\nIf you have difficulty in obtaining any of the materials and equipment mentioned in this book, then please visit the Search Press website for details of suppliers:   \nwww.searchpress.com\n\nDedication\n\nFor my parents who taught me so well, my husband who supports me in all I do, my darling twins for putting up with my obsession with knitting. And last but not least Gerard Allt for enabling me to believe in myself.\n\n---\n\nAbbreviations\n\nbeg: beginning\n\ndec: decrease (by working two stitches together)\n\ng st: garter stitch (knit every row)\n\ninc: increase (by working into the front and back of the stitch)\n\nk: knit\n\nk2tog: knit two stitches together\n\np: purl\n\np2tog: purl two stitches together\n\nrib: ribbing (one stitch knit, one stitch purl)\n\nst(s): stitch(es)\n\nst st: stocking stitch (one row knit, one row purl)\n\n*-**: Repeat from the point marked * to the point marked **\n\n---\n\n Contents\n\nIntroduction\n\nMobile Phone Sock\n\nPurse\n\nBelt\n\nBead Earrings\n\nDrink Mats\n\nHair Bands with Bobbles\n\nTravel Card Wallet\n\nHeart Necklace\n\nDisc Earrings\n\nVase\n\nMP3 Player Sleeve\n\nBrooch\n\nDesk Tidy\n\nWaste Paper Basket\n\nBuilding Blocks\n\nBottle Holder\n\nHair Clip\n\nHandbag\n\nBangle\n\nLiquorice Jewellery\n\n Introduction\n\nI am very excited to bring you the first ever book on knitting and recycling, a craft that came about quite by chance for me. After reading about knitting with strips of plastic cut from shopping bags, I was inspired to create unique and desirable objects that are pleasing to look at, useful and also help the environment by cutting down on waste plastic.\n\nThroughout this book I refer to the plastic as 'plarn' \u2013 a combination of the words plastic and yarn. It is very satisfying to end up with balls of colourful plarn instead of a dustbin full of disused bags!\n\nThe projects in this book range from beginner to advanced, so whatever your knitting ability you will be sure to find something to make. All the items would make excellent gifts with the smaller ones easily done for those last-minute occasions. I hope you have as much fun knitting them as I have had designing them all!\n\nPreparing Plarn\n\nTake a plastic carrier bag and make sure it is clean and dry.\n\nLay the bag out flat and cut off the sealed bottom and handles, leaving you with a cylinder shape. With the openings at the sides, roll and fold the bag up to 3cm (1\u00bcin) from the top. Use scissors to cut the folded part (and only the folded part) into strips approximately 2cm (1in) wide. This will then knit up to an approximate double knit tension.\n\nThe thinnest, flimsiest bags should be cut into wider strips of 4cm (1\u00bdin), and the heaviest, most glossy bags should be trimmed into narrower 1cm (\u00bein) strips for the same tension.\n\nThe thinner bags are easier to work with, so I recommend that you use them when you start out.\n\nUnfold the bag and you will have a number of single strips hanging from the uncut part of the bag. Open the bag out and cut diagonally from the outside edge of the bag to the first inside cut. Continue cutting diagonally until all the strips are separated.\n\nYou should now have one long continuous strip of plastic. Roll this up into a ball. You now have a ball of plarn that is ready to be knitted up.\n\nPlastic bags of one colour will let you make items with solid colour, but you can make variegated plarn from striped or patterned bags.\n\n---\nMobile Phone Sock\n\nMaterials:\n\nPlarn in variegated blue and white \u2013 five very thin carrier bags\n\nLarge darning needle\n\nNeedles:\n\n1 pair 4mm (UK 8; US 6) knitting needles\n\nInstructions:\n\nKnitting\n\nCast on 40st and knit in k1, p1 rib for 8 rows. Continue in stocking stitch until the work measures 12cm (4\u00bein). Cast off.\n\nMaking up\n\nSew in any unwanted ends then fold the work in half, with the wrong side on the outside. Thread some spare plarn on to your darning needle and stitch together the sides and bottom of the sock (see detail above).\n\nTurn the piece the right way out and your mobile sock is ready to use.\n\nTweed Look\n\nThose flimsy, striped bags from the corner shop are ideal for this project.\nPurse\n\nMaterials:\n\nPlarn in purple, pink and black \u2013 approximately one carrier bag of each colour\n\nLarge darning needle\n\nSewing needle and thread\n\nA 10cm (4in) zip\n\nNeedles:\n\n1 pair 3.75mm (UK 9; US 5) knitting needles\n\nInstructions:\n\nWork in stocking stitch throughout.\n\nKnitting\n\nCast on 25st. Starting with a knit row, work 2 rows in purple. * Work 1 row pink, 2 rows black, 1 row pink, 5 rows purple, 1 row black, 2 rows pink, 1 row black, 5 rows purple **. Repeat from * to ** until work measures 23cm (9in). Cast off.\n\nMaking up\n\nFold the work in two and sew the cast-on edge to the cast-off edge. Turn the work sideways and stitch up the bottom of the work (this is actually the side of the knitting). This ensures that your stripes are running vertically rather than horizontally.\n\nOversew these seams with plarn on the right side out. Insert the zip into the opening at the top and discreetly stitch in place with sewing thread. For the zip pull (see detail above), thread two strips of plarn through the hole in the zip pull, making sure the plarn is of even lengths. Plait and knot it in place.\n\nGreen Lines\n\nTry using natural colours for a more mature look.\nBelt\n\nMaterials:\n\nPlarn in silver \u2013 two foil bread bags; and black \u2013 two or three black bin liners\n\nDarning and sewing needles and thread\n\nOne buckle\n\nNeedles:\n\n1 pair 3.75mm (UK 9; US 5) knitting needles\n\nInstructions:\n\nKnitting\n\nCast on 10st with black plarn. Rows 1-5 stocking stitch. Row 6 garter (this forms the edge of turn over). Rows 7\u201314 work in moss stitch (also known as seed stitch). Row 15 * k1, p1, k1, join in silver k4, join in black p1, k1, p1. Row 16, with the black, p1, k1, p1, with the silver k4, then k1, p1, k1 in black. Repeat the last 2 rows 3 times. With black k1, p1, k5, p1, k1, p1. Carry on in moss stitch for 9 more rows **. Repeat from * to ** until the belt is the desired length, ending on a right side row. K1 row in garter stitch; this forms an edge for stitching over the buckle bar. Work 10 rows in stocking stitch starting with a knit row. Cast off.\n\nMaking up\n\nSew in any unwanted plarn. Fold over the cast-on edge at the garter row and stitch in place with sewing thread. At the cast-off end, thread the work over the bar of the buckle and fold at the point of the garter row (see detail above). Sew in place with thread.\n\nThe finished piece\n\nThis glitzy belt would make the perfect accessory to brighten any outfit.\nBead Earrings\n\nMaterials:\n\nPlarn in cool pink, lilac and hot pink \u2013 small amounts\n\n6 small beads\n\nSewing needle and thread\n\nJewellery findings: Pair of earring hooks\n\nNeedles:\n\n1 pair 3.75mm (UK 9; US 5) knitting needles\n\nInstructions:\n\nKnitting\n\nCast on 6 st in plarn of your colour choice. Work in stocking stitch for 8 rows. Cast off. Repeat five times.\n\nMaking up\n\nRun a gathering stitch along all four sides of work and gather together, tucking in unused ends as you go. This creates the knitted bead. Secure the end discreetly.\n\nAlternate 3 knitted beads with 3 small hard beads and string together with thread, sewing firmly in place.\n\nStitch this to the earring attachment (see detail above). Now they are ready to wear. If you make them in colours to match your outfit, you will have a very special and unique accessory.\n\nAutumn Golds\n\nThese warm gold and ochre beads are very flattering to all skin tones.\nDrink Mats\n\nMaterials:\n\nPlarn in blue and pink \u2013 approximately one carrier bag of each colour\n\nDarning needle\n\nAn iron and ironing board\n\nBaking parchment or greaseproof paper\n\nNeedles:\n\n1 pair 3.75mm (UK 9; US 5) knitting needles\n\nInstructions:\n\nThis project is simple enough for a child to do, but it needs adult supervision as part of the process involves a hot iron.\n\nKnitting\n\nCast on 25 st. Work in garter stitch throughout. Work 2 rows in blue plarn. Next knit 5st in blue, then join in pink plarn and knit 15st. Knit last 5st in blue. Repeat this row 28 times. Now using blue plarn only, work 2 rows. Cast off. You can adjust the number of rows you do to alter the size of the finished piece.\n\nMaking up\n\nSew in any unwanted ends. Heat an iron to the hottest setting. Make sure an adult helps with this part. Place the knitting between two pieces of baking parchment. (This is vital unless you want a sticky mess on your iron!) Press and hold the iron firmly on to the paper and knitting for approximately twenty seconds. This melts the plastic enough to fuse it together and yet does not obliterate the pattern (see detail above).\n\nTurn the work and paper over and repeat the heating process on the other side. Do not touch it until it has cooled down. When completely cold, it will be rigid and ready to use.\n\nPlanets and Stripes\n\nOnce your mats have cooled, they can be cut into circles with scissors.\nHair Bands with Bobbles\n\nMaterials:\n\nPlarn in red, white and blue \u2013 small amounts\n\nPlain undecorated elastic hair band\n\nDarning and sewing needles and thread\n\nNeedles:\n\n1 pair 3.75mm (UK 9; US 5) knitting needles\n\nInstructions:\n\nKnitting\n\nCast on 6 st. Work 8 rows in garter stitch. Cast off.\n\nMaking up\n\nRun a gathering stitch with plarn along all four sides and gather together, tucking in any plarn ends as you go, thus moulding and forming a bobble. Secure the plarn firmly in place.\n\nArrange the bobbles to look pleasing, then sew them on to the hair band with a fine needle and sewing thread (see detail).\n\nBobbles with Bling\n\nYou can change the look easily by knitting in one colour or in stripes. For a more glamorous evening look, stitch on seed beads.\nTravel Card Wallet\n\nMaterials:\n\nPlarn in pink, black, lime, and orange \u2013 approximately one carrier bag\n\nDarning and sewing needles and thread\n\nTwo pins\n\nNeedles:\n\n1 pair 3.75mm (UK 9; US 5) knitting needles\n\nInstructions:\n\nWork in stocking stitch throughout. It is a good idea to carry the colours up the side of the work as you go to save sewing in lots of ends afterwards.\n\nKnitting\n\nCast on 15 st. Knit 122 rows: colours as follows. 2 rows black, 4 rows pink, 2 rows black, 6 rows lime, 4 rows pink, 4 rows orange, 2 rows pink, 2 rows lime, 6 rows black, 4 rows orange, 6 rows pink, 6 rows black, 2 rows lime, 4 rows black, 6 rows orange, 2 rows lime, 4 rows orange, 2 rows pink, 2 rows lime, 6 rows black, 4 rows lime, 4 rows black, 4 rows lime, 4 rows pink, 2 rows black, 2 rows pink, 2 rows black, 4 rows pink, 4 rows orange, 2 rows pink, 2 rows lime, 6 rows black, 6 rows orange. Cast off.\n\nMaking up\n\nSew in any unwanted ends of plarn. Fold work in half and mark the middle with the pins. Open the work flat and fold the cast-on and cast-off ends towards the pins. Leave approx 1cm (\u00bdin)between the two ends: i.e. 5mm (\u00bcin) either side of the pins. This leaves a little gap and extra space for when the cards are inserted and the holder is folded in half (see detail above).\n\nWith the work inside-out, sew the side seams with the sewing thread, then turn work right way out. With plarn in a contrasting colour, use a whipping stitch to decorate the sides. This is solely cosmetic, and hides any cotton thread showing, producing a more finished look.\n\nNow you are ready to insert cards, fold the wallet closed and use it! Finished size is approximately 10 x 7cm (4 x 2\u00bein).\n\nThe finished piece\n\nTry combining blues and purples for a more masculine look.\nHeart Necklace\n\nMaterials:\n\nPlarn in red \u2013 one thick carrier bag; and silver \u2013 one foil bread bag\n\nPaper tissue\n\nDarning needle, sewing needle and thread\n\nSmall glass beads\n\nNylon thread\n\nJewellery findings: Necklace fastening\n\nNeedles:\n\n1 pair 4mm (UK 8; US 6) knitting needles\n\nInstructions:\n\nBeads\n\nKnitting and making up\n\nMake 18 beads in silver plarn, following the instructions as for the Bead Earrings.\n\nRed heart\n\nKnitting\n\nThis is made in reversed stocking stitch. Cast on 2 st. Row 1 knit. Row 2 purl. Row 3 knit, increasing 1 stitch at each end of the row. Row 4 purl. Row 5 knit, increasing 1 stitch at each end of the row. Row 6 purl.\n\nContinue increasing on every knit row until you have 10 stitches in all. Work 3 rows without any shaping. Next row decrease 1 stitch each end of the row. Purl next row. Knit and decrease as before on this row and every knit row until 2 stitches remain. Cast off.\n\nMaking up\n\nFold the work in half, making a triangle with the smooth side on the inside, tucking any unwanted ends in. Stuff with paper tissue and sew up the sides using plarn.\n\nDiscreetly secure a strip of plarn at the point of the heart, and from the inside, catch the top centre of the triangle and pull downwards, towards the point, securing in place. This gives the triangle a heart shape (see detail above).\n\nThread the glass beads and knitted beads alternately on to the nylon thread with the heart at the centre. Knot the necklace fastenings to the ends. Now your necklace is ready to wear.\n\nBlack and White Elegance\n\nNo-one can have too much jewellery! Have fun making more necklaces in a variety of colours.\nDisc Earrings\n\nMaterials:\n\nPlarn in purple and green \u2013 small amounts\n\nSewing needle and thread\n\n10 small hard beads\n\nJewellery findings: Pair of earring hooks\n\nNeedles:\n\n1 pair 4mm (UK 8; US 6) knitting needles\n\nInstructions:\n\nKnitting\n\nCast on 20 st in green plarn and knit in stocking stitch for 3 rows. Change plarn colour to purple and continue in stocking stitch for another 4 rows. Cast off.\n\nMaking up\n\nWith the work inside out, sew together the 2 ends of row edges. Run a gathering stitch along the cast-on edge of the work and pull it tight, securing it in place. Turn the work the right way out and run another gathering stitch along the cast-off row edge, pulling it in tight to secure.\n\nStitch the two middles together, thus making a small disc, green one side and purple the other. Place 2 beads either side of the disc in the middle and stitch in place (see detail above). Fasten thread at the top edge of the rim, and thread on 3 beads and an earring attachment. Make sure you run the thread back through the beads to secure them firmly.\n\nRaspberry Ripple\n\nThese earrings can easily be knitted in an hour, so they would make an ideal last-minute gift or stocking filler.\nVase\n\nMaterials:\n\nPlarn in pink, lilac, brown and white \u2013 approximately eight carrier bags\n\nEmpty and clean plastic drink bottle\n\nDarning needle\n\nPair of scissors\n\nNeedles:\n\n1 pair 5mm (UK 6; US 8) knitting needles\n\nInstructions:\n\nKnitting\n\nCast on 46 stitches with pink plarn or colour of your choice. Row 1 k2, p2 along the whole row. Row 2 p2, k2 along the whole row. Repeat rows 1 and 2. Continue the rest of the work in stocking stitch, starting with a knit row, patterning as follows: 4 rows in lilac plarn, 2 rows in brown, 4 rows in pink, 8 rows in white, 2 rows in pink, 6 rows in lilac, 2 rows pink, 4 rows brown, 14 rows white, 4 rows lilac. Cast off. (Some of the bags I used had some writing on them, thus creating the flecks of colour.)\n\nMaking up\n\nSew in any unwanted ends on the knitting. Join the side seams with plarn, inside out (see detail above). Then turn the correct side out.\n\nUse the scissors to cut the top off the plastic bottle. Now slip the knitted sleeve over the top of the bottle and smooth it into place. It should be tight enough to stay in place but can easily be removed when the bottle requires cleaning.\n\nThe finished piece\n\nThis project can be done in any colours that complement the d\u00e9cor of the room (or garden!) in which it will be used.\nMP3 Player Sleeve\n\nMaterials:\n\nPlarn in variegated white and green \u2013 approximately one carrier bag\n\nDarning needle\n\nNeedles:\n\n1 pair 3.75mm (UK 9; US 5) knitting needles\n\nInstructions:\n\nKnitting\n\nCast on 15 st. Work 4 rows in k1, p1, rib. Change to stocking stitch and continue until work measures 18cm (7in). Work 4 more rows in k1, p1, rib and cast off.\n\nMaking up\n\nFold work together so that the two ribbings are at the top (see detail above) and oversew the side seams in plarn.\n\nFunky Stripes\n\nThese are very easy to knit, so would be perfect for children to make. Let them choose and collect their own plastic bags in order to make their finished piece personal and unique.\nBrooch\n\nMaterials:\n\nPlarn in yellow, green and orange \u2013 small amounts of each\n\nDarning and sewing needles and thread\n\nJewellery findings: Brooch pin\n\nNeedles:\n\n1 pair 2.75mm (UK 12; US 2) knitting needles\n\nInstructions:\n\nKnitting\n\nFor the flower\n\nWith yellow plarn cast on 33 st. Knit 1 row. Purl 1 row. Next row knit 5 st, turn, * p5 turn, k5 turn, p5 turn, decrease 1 st at each end of next row and turn, p3 turn, decrease 1 st at beginning of the row, knit the remaining stitch, turn, p2 turn, k2tog and fasten off. The first petal is complete.\n\nRejoin plarn to main work and cast off next 2 st then k4, thus having 5 st on your right-hand needle **. Follow instructions from * to ** until all 33 stitches have been worked. Sew in any loose ends. Pick up and knit 18 st along the 33 st cast-on edge. Next row purl. Next row k1, slip1, k1, pass the slip stitch over, repeat this to the end. Starting with a purl row, work 8 rows in stocking stitch. Cast off.\n\nFor the first leaf\n\nWith green plarn, cast on 3 st. Work in stocking stitch until work measures 8cm (3\u00bcin) ending on a knit row. Cast off 1 st at the beginning of the next row. Work 6 more rows in st st. Cast off.\n\nFor the second leaf\n\nWith green plarn cast on 3 st. Work in stocking stitch for 4cm (1\u00bdin) ending on a purl row. Cast off 1 st at the beginning of the next row. Work 6 more rows. Cast off.\n\nFor the stalk\n\nWith orange plarn cast on 5 st and work 8 rows in stocking stitch. Change to green plarn and continue in stocking stitch until work measures 11cm (4\u00bcin). Cast off.\n\nMaking up\n\nJoin the side seam of the flower's trumpet. Join the side seam of the stalk. Insert the orange tip of the stalk into the back of the trumpet and stitch in place. Position the leaves on the stalk and stitch them in place using plarn of matching colour. With sewing thread and a fine needle, stitch or fasten the brooch pin to the back of the flower (see detail above).\n\nThe finished piece\n\nThis delightful daffodil will be adored by all who see it. Why not give one to the gardener in your life?\nDesk Tidy\n\nMaterials:\n\nPlarn in light purple, dark purple, pink and dark blue \u2013 approximately one carrier bag of each colour; and light blue \u2013 approximately two carrier bags\n\nClean and empty 1 litre yogurt pot\n\nDarning needle\n\nNeedles:\n\n1 pair 5mm (UK 6; US 8) knitting needles\n\nInstructions:\n\nKnitting\n\nCast on 70 st. Knit in garter stitch for 5 rows. Then change to stocking stitch working straight until work measures 14cm (5\u00bdin). Cast off.\n\nMaking up\n\nOversew the side seam the right way out using plarn. Slip over the pot and thread a running stitch along the cast-on edge. Gently pull tight, allowing the edge to cover the lip of the pot (see detail above). Secure and oversew the rim edge.\n\nThe finished piece\n\nThe different shades of plarn even within one colour make each piece individual and unique. Have fun experimenting!\nWaste Paper Basket\n\nMaterials:\n\nPlarn in red, yellow, green, blue, indigo and violet \u2013 approximately eighteen carrier bags altogether\n\nDarning needle\n\nBaking parchment or greaseproof paper\n\nAn iron\n\nA metal bin, wicker basket or toughened plastic container over which you can mould the knitted bin\n\nNeedles:\n\n1 pair 5mm (UK 6; US 8) knitting needles\n\nInstructions:\n\nThis project is simple enough for a child to do, but it requires adult supervision as part of the process involves using an iron.\n\nKnitting\n\nCast on 90 st. Work in garter stitch until work measures 35cm (13\u00bein) or desired height. Cast off.\n\nMaking up\n\nSew in unwanted ends and join the side seam using matching plarn. Thread a running stitch along the cast-off edge and pull tight, securing firmly. You may find it easier to use a little nylon thread for this. Place the knitted bin over your 'mould'. Place baking parchment between the mould and your knitting as well as between the knitting and the iron! (This is essential if you want to avoid getting a plastic mess all over your iron.)\n\nHeat the iron to the hottest setting and hold for a few seconds against the gathered up base until it is flattened and fused together (see detail above). Then slowly iron all around the outside of the bin. While the knitting is warm it will appear soft and floppy but once it has cooled it will be firm enough to keep its shape and stand up. You have now recycled your rubbish to hold more litter.\n\nThe finished piece\n\nThis waste paper basket is a favourite of mine. Every room can benefit from one and I use colours to match the decor.\nBuilding Blocks\n\nMaterials:\n\nPlarn in orange, yellow and cream \u2013 approximately three standard-sized carrier bags of each colour\n\nDarning needle\n\nSoft toy filler or spare plastic bags\n\nNeedles:\n\n1 pair 4mm (UK 8; US 6) knitting needles\n\nInstructions:\n\nKnitting\n\nCast on 15 st. Work in garter stitch throughout. Work 23 rows or as many as it takes to produce a square. Cast off. Make 6 of these squares in all.\n\nMaking up\n\nOversew the squares together to form a block. Leave one side open to fill with stuffing, and then sew the last square in place. Make sure all seams are secure so that the filling cannot be pulled out by little hands or paws!\n\nToys\n\nIt is not only children who enjoy playing with these soft blocks. Pets also love chasing after them and knocking them down!\nBottle Holder\n\nMaterials:\n\nVariegated plarn in green and black \u2013 approximately two very large plastic bags\n\nDarning needle\n\nBaking parchment or greaseproof paper\n\nA clean and empty food tin\n\nAn iron\n\nNeedles:\n\n1 pair 5.5mm (UK 5; US 9) knitting needles\n\nInstructions:\n\nThis project is simple enough for a child to do, but it needs adult supervision as part of the process involves using an iron.\n\nKnitting\n\nCast on 70 st. Knit in garter stitch for 5 rows. Then change to stocking stitch, working straight until work measures 14cm (5\u00bdin). Cast off.\n\nMaking up\n\nOversew side seam the right way out. Slip over the tin then thread a running stitch along the cast-on edge and gently pull tight, allowing the edge to cover the lip of the tin. Secure and oversew the rim edge.\n\nStrap\/Handle\n\nCast on 8 st. Work in moss stitch (also known as seed stitch) until the work measures 87cm (34\u00bcin) or desired length. Cast off.\n\nMaking up\n\nWith the main piece of work, sew up the side seams using plarn. Run a gathering stitch along the cast-on edge, drawing it up tight and securing firmly. Turn the top edge down so that the reversed stocking stitch forms a little rim (see detail) and stitch in place. Position the strap 3cm (1\u00bcin) down inside the holder. Stitch firmly into place. Now attach the other end of the strap in the same way, opposite the end you have just attached. Insert an empty food tin into the holder and push it right down to the bottom. Then hold a hot iron against the base until the plastic has fused, making sure you have the baking parchment between the work and the iron all the time! When the plastic has cooled, you can remove the tin can. The base will then be hard so that the bottle holder will stand up unsupported.\n\nThe finished piece\n\nThe plastic bags I used for this piece were black on the inside and green on the outside. When knitted up, they give the piece a lovely textured look.\nHair Clip\n\nMaterials:\n\nPlarn in red and green \u2013 small amounts\n\nSewing needle and thread\n\nThree small beads\n\nJewellery findings: Hair clip attachment\n\nNeedles:\n\n1 pair 2.75mm (UK 12; US 2) knitting needles\n\nInstructions:\n\nKnitting\n\nFor the leaves\n\nCast on 5 st. Work 4 rows in stocking stitch ending on a purl row. Increase 1 stitch each end of the next row. Purl 1 row. Repeat the last 2 rows once more. Continue in stocking stitch straight for 10 rows, ending on a purl row. Decrease 1 stitch each end of the next row. Purl 1 row. Repeat the last 2 rows twice more (3 st remain). Stocking stitch 4 more rows. Cast off. Make two of these.\n\nFor the roses\n\nCast on 4 st in red plarn. Work in stocking stitch until work measures 9cm (3\u00bdin) ending on a purl row. Next row decrease 1 stitch at the beginning then knit to end (2st remain).Continue in st st for another 3cm (1\u00bcin). Cast off. Make three of these.\n\nMake up\n\nStitch the 2 leaves together along their cast-on edges. Sew in any unwanted ends of plarn. Now take the red knitting and, starting at the narrowest point, roll the work up, stitching it in place as you go to form a rose. When you have completed sewing all three roses, position and stitch them in place along the leaves. Sew the small beads into the centres of the roses with a fine sewing needle and thread (see detail above). Now you are ready to place the knitted flowers and leaves along the top of the hair clip attachment and stitch them securely in place.\n\nThe finished piece\n\nI chose red roses for a romantic look, but pale colours have a nice summery feel.\nHandbag\n\nMaterials:\n\nPlarn in purple, pink and lilac \u2013 approximately twenty standard-sized plastic bags\n\nDarning needle\n\nNeedles:\n\n1 pair 3.75mm (UK 9; US 5) knitting needles\n\n1 pair 2.75mm (UK 12; US 2) knitting needles\n\nInstructions:\n\nKnitting\n\nThe handbag is made in one piece as follows. Cast on 60 st. Work 6 rows in moss stitch (also known as seed stitch). Still in moss stitch knit 20 st, cast off 20 st, knit last 20 st. Next row moss stitch 20 st, cast on 20 st, knit the last 20 st. With these 60 st, work 15 rows in moss stitch. Next row work 20 st, cast off 20 st, and work last 20 st. Next row work 20 st, cast on 20 st, work last 20 st, resulting in 60 st again. Work 10 more rows in moss stitch.* Change to garter stitch and work 6 rows. Then 8 rows in stocking stitch.**\n\nRepeat from * to ** until the work measures 22cm (8\u00bdin) from the start of the garter stitch. Work 10 rows in moss stitch; this forms the base of the bag. Return to knitting 6 rows of garter and 8 rows of stocking stitch until the work measures 22cm (8\u00bdin) from the moss stitch base. (There should be an equal number of rib and smooth stripes as knitted at the beginning.)\n\nWork 10 rows of moss stitch. Next row work 20 st, cast off 20 st, work last 20 st. Next row work 20 st, cast on 20 st, work last 20 st. Work 15 rows in moss stitch. Next row work 20 st, cast off 20 st, work last 20 st. Next row work 20 st, cast on 20 st, work last 20 st. Work another 6 rows in moss stitch. Cast off.\n\nFor the roses\n\nMake as roses for the Hair Clip but leaving off the hard bead in the centre. Make five of these.\n\nMaking up\n\nSew in any unwanted ends of plarn. Fold the handles over so that the holes line up and they are double thickness. Oversew around the hand-hole, the sides and the inside edge. Do this also to the other end of the work. Now fold the bag in half so that the moss stitch strip is at the base and the handles join at the top. Oversew the sides of the bag together up to where the moss stitch handles start. This will leave a little vent for easier access. Position the roses along the first stocking stitch stripe of the bag and sew securely in place.\n\nThe finished piece\n\nI have made a few handbags for special friends and they tell me they are regularly stopped and complimented on their gorgeous bags. They then tell the passer-by that the bag is made from recycled carrier bags and wait for the look of amazment!\nBangle\n\nMaterials:\n\nPlarn in ochre, cream and gold \u2013 approximately one carrier bag in each colour\n\nLarge plastic bangle\n\nDarning needle\n\nNeedles:\n\n1 pair 2.75mm (UK 12; US 2) knitting needles\n\nInstructions:\n\nKnitting:\n\nCast on 15 st. Work in stocking stitch throughout. Work stripes as follows * 6 rows ochre, 2 rows cream, 4 rows gold, 2 rows ochre, 2 rows gold, 8 rows cream **. Repeat from * to ** until the work is long enough to cover the complete circumference of the bangle. Cast off.\n\nMaking up\n\nStitch the two ends together to form a ring. Slip this over the bangle. Pull the sides of the knitting into the middle of the inside edge and stitch together, encasing the bangle in a knitted sleeve.\n\nFunky Bangle\n\nYou can use your own imagination to make unique and personal pieces of jewellery. These are a favourite with my teenage children. Have fun!\nLiquorice Jewellery\n\nMaterials:\n\nPlarn in white, black, pink, orange, yellow and blue \u2013 small amounts\n\nJewellery findings: one necklace clasp and two earring hooks\n\nSeed beads in pale blue and pink\n\nApproximately forty-two large black beads for separating the sweets\n\nDarning and sewing needles and nylon thread\n\nSewing thread\n\nNeedles:\n\n1 pair 4mm (UK 8; US 6) knitting needles\n\nNecklace instructions:\n\nWork all sweets in stocking stitch throughout.\n\nThree-layered sweets\n\nKnitting\n\nCast on 5 st in white plarn and work 8 rows. Change to black plarn and work 9 more rows. Now join in the colour of your choice (pink, orange or yellow). Starting with a knit row on the wrong side of the work, work 8 rows. Cast off.\n\nMaking up\n\nSew in any unwanted ends then fold the white and black parts together with the right side of the stocking stitch on the outside.\n\nNext, fold back the coloured part, again with the right side of the work visible. Stitch the piece together using matching coloured plarn. Make three of these.\n\nBlack and white five-layered sweets\n\nKnitting\n\nFollow the instructions for the three-layered sweets, using only black and white plarn. Instead of casting off, work 9 rows in black, starting with a purl row. Change to white plarn for the last layer and work 8 rows. Cast off.\n\nMaking up\n\nFold together as for the three-layered sweets, plus the extra layers. Make two of these.\n\nSmall pink and blue beaded sweets\n\nKnitting\n\nUsing either pink or blue plarn, cast on 3 st and work in stocking stitch for 10cm (4in). Cast off.\n\nMaking up\n\nThis time with the back of work on show, roll the work up to form a small circular sweet. Stitch securely in place.\n\nUsing a sewing needle and thread, cover the whole sweet in seed beads that match in colour. Make two sweets in blue and one in pink.\n\nCircular sweets with black centres\n\nKnitting\n\nCast on 3 st in black plarn and work 8 rows. Change to coloured plarn (pink, orange or yellow) and continue until the work measures 25cm (9\u00bein) or until the coloured part is long enough to wrap around the black centre 3 times when rolled up. Cast off.\n\nMaking up\n\nSew in any unwanted ends. Roll the work up starting with the black part, thus making a wheel shape. Stitch together to hold in place. Make three of these.\n\nBlack and white cylinder-shaped sweets\n\nKnitting\n\nCast on 5 st in white plarn and work 10 rows. Change to black plarn and work 14 rows, or just enough to cover the white centre once rolled up. Cast off. Make two of these.\n\nMaking up\n\nSew in any unwanted ends. Starting at the white end of the work, roll up until the white centre is completely wrapped in the black work and stitch in place.\n\nMaking up the necklace\n\nThread the sweets on to a nylon wire alternating each with a large black bead.\n\nUse as many large beads as you need for the desired length at either end of the nylon thread. Knot the necklace clasp on either end firmly.\n\nEarring instructions:\n\nKnitting\n\nMake two small beaded sweets and two circular sweets with black centres, as for the necklace.\n\nMaking up\n\nThread two sweets on to nylon thread, alternating with black beads as shown to the left.\n\nMake sure the sweets and beads are secure then thread and stitch them on to the earring attachment. Repeat for the second earring.\n\nPublishers' Note\n\nIf you would like more information on knitting techniques, try the Beginner's Guide to Knitting by Alison Dupernex, Search Press, 2004.\n\nClick to go to our online catalogue\n\n|  |   \n---|---|---\n\n    |     |     |     |\n\n    |     |     |     |\n\n    |     |     |     |\n\n    |     |     |     |\n\n---|---|---|---|---\n\n    |     |     |     |\n\n    |     |     |     |\n\n    |     |     |     |\n\n---|---|---|---|---\n\n    |     |     |     |\n\n    |     |     |     |\n\n    |     |\n\n|  | \n","meta":{"redpajama_set_name":"RedPajamaBook"}}
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+{"text":"Let's do better from now on, investing on your skin has soooo many benefits. That's right, you better start now!\nBeauty in Seconds is providing beauty products as well as beauty info for your guidance, please don't hesitate to send us your comment regarding new beauty products because your information will be very helpful to others.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Enjoy these welcoming and amenity-rich communities you can call home.\nLocated on Madison's south side, the Burr Oaks community provides an open and friendly atmosphere for individuals ages 62 and older with low income. Beautiful apartments and grounds offer the perfect backdrop for a life overflowing with friends, community, and family. This alluring facility features non-smoking, one- and two-bedroom apartments with a balcony or patio and free wi-fi in all units.\nThis retirement community in Madison, WI fosters a social environment by hosting a variety of interactive events for residents. Attend a game night for some friendly competition or socialize over morning coffee on the community patio. You can also stay active at the fitness center or pamper yourself at the on-site hair salon. Whatever activities you choose, this amenity-rich community offers everything you need to live an active and relaxed lifestyle.\nInterested in Burr Oaks Senior Apartments in Madison, WI where you'll enjoy a quiet, refuge-like atmosphere and proximity to shopping, dining, parks, and more? Learn more here.\nOne of the standout retirement communities in Madison, WI, Greentree Glen is located in a peaceful, wooded neighborhood on the west side. Its cozy architecture, meticulously maintained grounds, and modern common spaces make it a favorite among residents. This smoke-free facility offers a warm and friendly atmosphere for seniors ages 62 and older. Greentree Glen apartment homes boast newly-renovated one- and two-bedroom units with furnished appliances, walk-in closets, and free wi-fi.\nThe welcoming community at Greentree Glen also organizes countless activities and social gatherings for residents. Just off the main road, this carefree retirement community is situated near one of Madison's largest shopping hubs, keeping you close to the action. You can also enjoy your favorite pastimes on the community patio, fitness center, or on-site library. There's no doubt this charming community will have you enjoying a relaxed and active life in no time.\nFor more information about the quiet, homey, and relaxing escape you'll find at Greentree Glen Senior Apartments, click here.\nThis beautiful retirement community for individuals ages 55 and older is located on Madison's residential east side. Westminster is a newer apartment community for seniors featuring gorgeous modern brick construction and beautiful open green spaces. It offers a variety of one- and two-bedroom floor plans with private balconies, patios, and furnished appliances.\nThis pet-friendly facility also features abundant amenities for your desired independent and active lifestyle. Enjoy social hours in the community room, work up a sweat in the fitness center, or relax and restore in the meditation room. With a transportation service and proximity to East Towne Mall, grocery stores, and a variety of restaurants, a carefree and active lifestyle is just outside your door. The Westminster amenities are sure to introduce you to a more laidback and social lifestyle.\nCould Westminster Senior Apartments be your new home? Click here to learn more.\nMaking a move to an amenity-rich senior living community can bring a range of unexpected benefits to your life. The offerings at these three carefree retirement communities in Madison, Wisconsin will help open the door to more independent, stress-free, and active living.\nCheck out our blog for more articles on independent living and retirement communities.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This week's portion, Shimini, carries us deeper into the book of Leviticus.\nThe first half of the portion is the initiation of the sacrificial cult: the Torah describes in dramatic fashion the first sacrifices Aaron and his sons carry out in their role as priests. They slaughter various animals corresponding to the different types of offerings, they splatter blood on the altar and fire consumes the corpses. Aaron and his sons then bless the people and the people fall on their faces.\nThe second half of the portion is an explication of the dietary laws. We are told specifically which animals are kosher and which are not: we learn that kosher land animals have cloven hooves and are ruminants, kosher birds are not birds of prey and kosher sea creatures have fins and scales. We also learn some other regulations as to what may or may not be eaten.\nThere are many questions raised by this short passage, but we can understand from the text that Nadav and Avihu did something wrong, and they were punished for their transgression.\nPut in context with the passage that came before, we can have an understanding of what perhaps their transgression was. The Torah says they offered \"alien fire, which God had not enjoined upon them.\" Earlier in the parasha, when describing the initial sacrifices, the Torah says, at various times, \"this is what God has commanded,\" and \"according to regulation\" and \"as Moses had commanded.\" What the Torah is telling us is that while the first set of sacrifices was what was commanded, what Nadav and Avihu offered was not. Essentially what they were doing was offering a sacrifice that was outside the norm of the ordained and organized system of sacrifices.\nIt seems very extreme, though. Did they really deserve death for a slight deviation from the norm? And besides, is what they did so wrong? It can be argued that what Nadav and Avihu did when they offered the additional sacrifice was to further glorify God\u2014they were not offering something in contradistinction to, but rather in addition to, what was proscribed, due to their zeal, or desire to serve, or love of Torah.\nThis may be, but what perhaps the Torah is trying to teach us in this story is the perils of individualism. The extreme nature of the story aside\u2014and this isn't the first time a story in the Torah is extreme it its details\u2014the Torah is showing us that by branching off on their own Nadav and Avihu were violating their communal responsibility and trust to the detriment of the whole. They system of sacrifices for the entire Israelite community was set. In making their own offering outside these norms, Nadav and Avihu were placing their own desires above the norms of the community. They were acting in their own self-interest. But for Nadav and Avihu, who were leaders and priests, it can't just be about them. It has to be about the whole.\nThis mindset does not just fall upon our leaders, but upon all of us who live in community. When we fail to take into account our communal responsibility, and we privilege ourselves over others, we privilege individualism over communalism, we weaken our social bonds.\nIndividualism is different than individuality. We are of course all individuals, we have our own likes and dislikes, ideas and dreams, needs and desires. We make our own choices and set our own path. But we do not live in a vacuum, we are part of a communal whole. We pursue our own paths within the context of others, and we have a responsibility and obligation to keep the needs and desires of others in mind as we seek to fulfill our own needs and desires.\nIn our day this can take many forms. The recent outbreak of measles at Disneyland brought the issue of vaccinations\u2014and those who opt-out\u2014to the fore. Locally the issue led to the public revelation of vaccination rates, and Yohanna and I discovered that Erez's elementary school had one of the highest unvaccinated rates. This was startling and unnerving. I don't need to get into issues of \"herd immunity\" or scientific detail, but to simply say that vaccines work because we all agree to use them. They are part of a social contract\u2014we agree to abide by certain guidelines when we live in community, and when we privilege the self over the other\u2014individualism over communalism\u2014then we violate that contract.\nYes, we need to honor the individuality of each person, and do what we can to support those individual journeys. But we need to be mindful so that individuality does not become individualism.\nNadav and Avihu broke the rules. There are times we go must outside the box, and we need to do things differently. There are times we must think creatively, and we need to challenge the existing norms. But we must ask, to what end? If it is to serve others and a greater good, then that is something we should pursue. But if it is to serve our own self interest at the expense of others, then, as in the case of Nadav and Avihu, it is a transgression and there will be consequences.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Cookies are small files placed on your device or held in your browser memory, when you visit our website. The cookies that we use do not store any personal or confidential information about you. Disabling these cookies may prevent you from using certain parts of this website.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"SEARCH ENGINE OPTIMISATION \u2013 Wix permits you to edit page meta tags, web page names, and much of your primary SEARCH ENGINE MARKETING musts. I will go to a trucking web site for instance and get half the advertisements for internet design. Domain identify is the web site URL, the link or handle that needs to be entered within the deal with bar of your browser to open an internet site.\nThe templates are prime quality, but nobody desires to have an internet site which appears to be like like another. Website Creator is definitely a licensed model of NetObjects' Fusion 12 (originally launched in 2010) and is lumbered with an old school interface and unhelpful jargon (asking, for instance, does your host help CGI\/Perl?).\nSome of the most popular Android, COMPUTER and iPhone video games have been developed using the present lot of software program packages. If you want, you will get the free trial and make a demo website to get an understanding about creating your website. I use webs (previously freewebs) however I did not realise how many free web builders there were out there.\nOn condition that Google units a lot retailer by website velocity nowadays, that is an issue. Webnode can be used with any domain (e.g. as ). It implements plenty of web site parts (polls, articles, forums, lists, FAQ varieties, etc.). Customers can use it with any well-liked browser.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzztxza b/data_all_eng_slimpj/shuffled/split2/finalzztxza
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+{"text":"Good bread has always featured in the daily life of Einat Chalmers, head baker and owner of Mamoosh Artisan Bakery. From her everyday life as a child in Israel to the cherished memories of her time at her fathers seafood restaurant in Tel Aviv, baking is in her blood and is her passion!\nAlong her journey Einat has spent time working in all areas of fine baking and restaurants, her experiences include managing high end restaurants in NYC and studying at the Prestige Cookery School to studying in fine pastry at French patisseries here in the UK.\nThis passion for good food was the catalyst for the creation of Mamoosh, an independent Middle Eastern bakery based in East Sussex. The core of the business centres on lovingly baked pitta breads, made using traditional techniques and on an oven imported from Israel specifically for the baking of pitta breads, not only do they have heritage but they taste fantastic, and once you try one you won't go back to tired, dry, shop brought pitta breads again!\nEinat's talent for food and her love for an array of different flavours means that she is a versatile baker and chef, and her canon of recipes is seemingly endless. As the business grows she will be able to offer a larger selection of middle eastern breads, brioche, humous, salads and so much more. But for now the focus is on middle eastern breads, and very fine ones at that!\nWhy not get in touch to see what we could do for your restaurant, catering business or independent supermarket, we would be happy to visit you with some samples to discuss your needs!\nYou can buy Mamoosh products at various markets and shops in the Brighton and Lewes region. We sell our pittas and brioche, zhug, tahini dip, matbuchah, humus and babaganoush at the following places.\nAlong with the markets, wholesale is at the heart of the Mamoosh business, we believe that many restaurants and caterers should be using the finest breads to compliment the fresh and delicious choices offered on their menu. What could be more tantalising than a contemporary take on a traditional Middle Eastern classic, baked using traditional ovens and techniques!\nMamoosh works with many Sussex business' in a wholesale capacity, supplying pitta breads and brioche for restaurants, events catering, independent supermarkets. We offer great deals for large wholesale orders and can deliver to you to store or to use fresh, get in touch to see what we could do for you and your business!\nFollow our culinary adventures on Instagram!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"We are a 76 place Day Nursery with a friendly, stimulating and fun environment.\nOur Nursery provides day care for children from 6 weeks to school-ready. The children are cared for in three separate age groups. This enables us to tailor activities and rooms specifically for their needs.\nOur Nursery provides a warm, caring, safe and stimulating environment for all of the children in our care. To enable children to develop independently with confidence and self-esteem working within the Early Years Foundation Stage programme.\nWe adhere to best policies and procedures regularly reviewing and updating these in accordance with current legislation, Early Years Foundation Stage programme (EYFS). In our recent OFSTED inspection we received a rating of GOOD and a copy of this report is available on the OFSTED website.\nWe also offer an early start 7.30 am or late collection 6.00 pm for parents who need it, at an additional charge. Full time places include breakfast, lunch and tea. Lunch can be added to morning or afternoon sessions, snacks including fruit are provided during the day.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Brainstorming is one of the most widely used techniques to generate ideas. If it is carried out systematically it can do wonders and can lead to innovation and a huge amount of creativity. Classical brainstorming involves a small group of people, a well\u2013trained facilitator and a clear problem to explore.\nAim for quantity. Quantity would lead to quality through the evolution of ideas.\nDefer judgement. New ideas can be fragile. If all ideas are recorded and given a chance, they can grow legs and stand on their own feet. Otherwise they can be lost without been given a chance.\nGo for associations. Even if an idea is not suitable, it can open up the search to reach another idea which can be much more useful. This is why no idea should be killed and judgement should be deferred. It allows you to maximise the search efficiency and lets you come across more novel ideas.\nIn this exercise, delegates get to practice classical and double brainstorming. Also see reverse brainstorming and negative brainstorming for other techniques.\nUse classical and double brainstorming to explore creative solutions to a problem.\nDivide the delegates to groups of no less than 4 or more than 8.\nNominate one person as a facilitator in each group.\nThe facilitator should conduct a warm-up session to explain what will take place in the brainstorming session and to create a positive criticism-free atmosphere.\nAsk the groups to consider a problem that they want to brainstorm on. The problem should then be clearly identified.\nThe facilitator should record the problem on a flipchart or a whiteboard.\nThe grand rules of brainstorming must be emphasised by the facilitator; aiming for quantity of ideas and that no idea will be judged.\nAsk the group members to provide ideas and solutions to the problem. The facilitator must encourage everyone to talk.\nThe facilitator must record all the ideas on the flipcharts or the whiteboard. Various techniques can be used in this step such as mind maps, placing post-it notes on flipcharts or whiteboard and so on.\nIf solutions or ideas are unclear, they must be clarified and recorded.\nOnce enough ideas are generated or people cannot think of many more ideas, the current ideas must be consolidated. Those that are similar must be grouped together and duplicates must be removed. There is no judgement at this stage. The aim is only to tidy up the set of ideas to a series of clearly defined solutions that are distinct from each other so they can be evaluated.\nNext, ask the groups to go through the ideas and discuss them to select the best option. They should now consider the advantages and disadvantages of each solution and rank them to see which one is the best option. Various techniques can be used to decide for the best option. Examples include trade-off matrix, force field analysis, decision trees, Delphi method and so on.\nA great way to enhance this technique is to use double brainstorming. This is effectively two brainstorming sessions with a delay of 2 to 3 days in between. The idea is that after the first brainstorming session people continue to think about the problem consciously and unconsciously and come up with more novel ideas. When back after a few days, they can share these ideas with others through a second brainstorming session in a systematic way. The brainstorming session then leads to selecting the ideal option.\nRate = 2.41 out of 5 :::: 17 Ratings.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Partnervermittlungen Salzburg. Wetter HD Wetter von kachelmann.\n2019-04-22 15:06 We have automatically detected that you're accessing our website from: United States. We have many different websites with the products you find here, customized for your country.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This entry was posted on February 6, 2014 by .\nBuying a portable fridge is a big investment, and being able to make an informed decision is critical. There are many to choose from, ranging across several brands and hundreds of models - it can all be a bit overwhelming.\nIn this guide, we'll give you a brief introduction to portable fridges, and outline everything you need to know before taking the plunge on purchasing your very first portable fridge.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzubma b/data_all_eng_slimpj/shuffled/split2/finalzzubma
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+{"text":"\"So there's the internet.I'm sure you've heard of it.\" It's that global system of networks that connects the entire world. But what connects different parts of a particular company or organization? That's called an intranet. The intranet is a computer network that shares information, services and systems within an organization. Intranets utilize familiar internet protocols\u2014so HTTP web services, email and file transferring can be found there. It can be thought of as a private extension of the internet, confined to one institution. And just as the internet has changed the way the world works\u2026 Intranets have changed the way corporations operate. Especially regarding collaboration, project management and customer relationship management, to name just a few. Intranets are usually handled in-house, managed by the communications, human resources or IT facets of a company. And because of the intricacy and diversity of content, many intranets are much more complex than their company's public websites. So maintaining it oftentimes requires a total team effort. But the benefits of concentration on a now-indispensable aspect of modern business are many. For instance: Collaboration is enhanced because the intranet makes data accessible throughout the organization, allowing for easier teamwork. Corporate culture is democratized because the same information is made available to every employee. The bottom line is enhanced, since all the information needed for employee manuals, requisition forms, contact lists and more can be accessed electronically through the intranet. This saves costs on the likes of printing and distribution. Time is also saved because data can be reached on an as-needed basis, and processes such as benefit enrollment are centralized and expedited. Combine all these assets and more, and overall workplace productivity and operations are optimized.And it hasn't taken long for corporations to realize the true potential of intranets. Beyond simply storing central documents in one place, intranets have become communication hubs for many organizations. Prompting some to hire companies that will \"socialize\" their intranet and augment correspondence amongst the personnel. The most common software used for intranets is Microsoft SharePoint, which is estimated to be responsible for half of all intranets in use. But many companies are now turning to vendors that specialize in intranet software, such as Vauzo. So, as you can see, the concepts behind the internet do not only affect the global network. When applied within enterprises\u2014through the form of the intranet\u2014these same principles provide innovation and improvement on a much smaller, more contained scale.\nGreat Video \u2013 thanks for sharing! Really well done.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"BIG RAPIDS, Mich. (Oct. 6, 2017) \u2013 Join Hospice of Michigan for Walking Through Grief, a free monthly grief support group, from 10:30 to 11:30 a.m. on the third Thursday of each month through December, located in the pavilion at Hemlock Park on the east end of Hemlock and Warren in Big Rapids.\nWalking Through Grief will address grief and loss topics in an informal but supportive manner. While discussion topics vary based on the interests of the group, the focus is to practice self-care through exercise while experiencing support in a non-judgmental environment.\nThe group is open to all members of the public, regardless of whether or not their loved one received service from Hospice of Michigan.\nTo register, please contact Katie Gedraitis at kgedrait@hom.org or 231.527.0913.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Ramadan, or puasa month as we call it in Malaysia, is observed on the ninth month of the Islamic calendar, and Muslims worldwide fast from dawn til sundown, refraining from eating, drinking, and any sinful activities. Ramadan also emphasizes a lot on charitable thoughts, words, and acts. For example, cursing or quarreling while fasting may result in batal puasa, just like if a man ogles a woman.\n1. Best thing about Ramadan? The Ramadan Bazaars! There are so many in KK, almost every area will have their own. Which ones are your favourite? I like the one in Asia City, and I heard the one in the army base in Lok Kawi is pretty good too!\n2. If you're not Muslim, what's the best way to enjoy Ramadan with your Muslim friends? Well, you could always take turns going out to the Ramadan bazaars and bringing enough back for everyone to buka puasa (break fast)in the office, or even someone's house together!\n3. The longest fasting period in the world this year is in Denmark - they will be fasting for 21 hours. In Malaysia we fast for about 12 hours, while the shortest is in Argentina at 9 & 1\/2 hours. Wanna challenge yourself? You can also go to Iceland, Sweden or Norway - they're fasting for 20 hours!\n4. What's the difference between Ramadan in Malaysia and other places around the world? Nothing much! Probably different kinds of food, but it is pretty much observed the same way in every country, so if you're travelling, rest assured that you won't get too much of a culture shock!\n5. If you are travelling this Ramadan, make sure to take it easy. It's completely normal to feel tired faster, and you may have to miss out on some of the experiences as a lot of our travels are about trying new, local food, but if you really can't reschedule your trip, make up for it by visiting the Ramadan bazaars after hours, and take a little break here and there to conserve your energy throughout the day.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Total Experience Records was a record label founded by Lonnie Simmons. Its two major acts were The Gap Band and Yarbrough & Peoples. It originally began in 1977 as a production company whose artists recorded for Mercury Records before becoming a label in 1981. From its inception in 1981 to late 1983, Total Experience was a subsidiary label of Mercury's parent company, PolyGram. In 1984, the label changed its distribution from PolyGram to RCA Records.\nIn the 1970s, Lonnie Simmons operated a club on Crenshaw Boulvevard in South Central Los Angeles called The Total Experience, similar to the West-Hollywood Roxy Theatre. Eventually he invested in a recording studio (purchasing the property previously occupied by Sound Recorders Studios on the corner of Yucca St. and Argyle Ave. in Hollywood), launching his production company, and met the Gap Band through a friend, singer D. J. Rogers. He then had the idea to reduce the official lineup of the group from twelve members to its sibling trio of Ronnie, Charlie and Robert Wilson. After signing the Gap Band to Total Experience Productions (as it was then called), and securing them a label deal with Mercury Records in late 1978, Simmons himself personally produced the Gap Band's albums during their tenure, and co-wrote their breakthrough song, \"Oops Upside Your Head\".\nWhile in Texas in 1977, Gap Band leader Charlie Wilson discovered Alisa Peoples & Calvin Yarbrough, who were performing as part of the band, Grand Theft. Charlie convinced Lonnie to give the couple a chance, which paid off in 1980, when they released the song \"Don't Stop the Music\", which topped the R&B charts. This was immediately following the Gap Band #1 R&B song \"Burn Rubber on Me (Why You Wanna Hurt Me)\". Both of those albums went gold, and two of the Gap Band's albums went platinum. The first three Simmons-produced Gap Band albums, as well as Yarbrough and Peoples debut album The Two of Us were released by Mercury. These recordings were solid enough to give Simmons credibility to establish his production company as a full label, and he officially launched Total Experience Records in 1981.\nGap Band IV, released in early 1982, was the first Total Experience album release. The success of Gap Band IV, Robert \"Goodie\" Whitfield's debut album Call Me Goodie (also released in 1982), 1983's Gap Band V: Jammin' and Yarbrough and Peoples' Heartbeats resulted in a lucrative distribution deal with RCA Records in early 1984. At the tail-end of 1984, A Total Experience Christmas was released, featuring songs by five of the label's acts, as well as two of the label's writers.\nEven though the Gap Band and Yarbrough & Peoples still had high charting records through the mid-80s, the successes were ephemeral and they resulted in far fewer sales. Lonnie signed a plethora of new acts in 1984-85 and two established acts: Switch and Billy Paul. None of these acts managed to have any success with Total Experience. The Gap Band released 4 albums: Gap Band VI, Gap Band VII, Gap Band 8, and Straight from the Heart before moving on to Capitol Records in 1989. Yarbrough and Peoples left the label in 1986, and moved back to Texas, where they married in 1987.\nIn 1987 Total Experience lost their distribution deal with RCA and carried on as an independent label, faltering soon after. The label's post 1984 holdings now belong to Minder Records (now a division of BMG Rights Management), while its PolyGram distributed holdings belong to The Island Def Jam Music Group.\nTotal Experience Records Co., Inc.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Know Jane Addams HS Class of 1999 graduates that are NOT on this List? Help us Update the 1999 Class List by adding missing names.\nMore 1999 alumni from Jane Addams HS have posted profiles on Classmates.com\u00ae. Click here to register for free at Classmates.com\u00ae and view other 1999 alumni.\nThe students that went to school at the Cleveland high school called Jane Addams High School and graduated in '99 are on this page. Register to add your name to the class of 1999 graduates list.\nWe also encourage you to keep up to date on news and reconnect with Jane Addams High School alumni.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzupvb b/data_all_eng_slimpj/shuffled/split2/finalzzupvb
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+{"text":"This Shortcode displays the user login form.\nform_header_text Sing Up any text you wish to use.\ncustom_text Blank any text you wish to display within the login form.\nThis entry was posted in USER SHORTCODES on August 28, 2014 by admin.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Descarga rapida! Descargar Gratis Ebooks Olympic Dream en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks Olympic Dream en linea.\nDescarga rapida! Descargar Gratis Ebooks PODERES COLECTIVOS EN LA SIRIA DEL BRONCE FINAL Kindle Edition en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks PODERES COLECTIVOS EN LA SIRIA DEL BRONCE FINAL Kindle Edition en linea.\nDescarga rapida! Descargar Gratis Ebooks LA VIDA DE NOSTRE SENYOR JESUCRIST... en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks LA VIDA DE NOSTRE SENYOR JESUCRIST... en linea.\nDescarga rapida! Descargar Gratis Ebooks PALENCIA, ALTA ES CASTILLA en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks PALENCIA, ALTA ES CASTILLA en linea.\nDescarga rapida! Descargar Gratis Ebooks TEATRO ROMANTICO (T Limited Edition en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks TEATRO ROMANTICO (T Limited Edition en linea.\nDescarga rapida! Descargar Gratis Ebooks Shark Bait en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks Shark Bait en linea.\nDescarga rapida! Descargar Gratis Ebooks VARIACIONES Y REINCIDENCIAS Kindle Edition en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks VARIACIONES Y REINCIDENCIAS Kindle Edition en linea.\nDescarga rapida! Descargar Gratis Ebooks EL LOBO OCULTO Kindle Edition en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks EL LOBO OCULTO Kindle Edition en linea.\nDescarga rapida! Descargar Gratis Ebooks MI COCINA MARROQUI en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks MI COCINA MARROQUI en linea.\nDescarga rapida! Descargar Gratis Ebooks FILOSOFIA DE LA FELICITAT: UN PAISSEG PEL COSTAT ASSOLELLAT DEL P ENSAMENT en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks FILOSOFIA DE LA FELICITAT: UN PAISSEG PEL COSTAT ASSOLELLAT DEL P ENSAMENT en linea.\nDescarga rapida! Descargar Gratis Ebooks LA ESTETICA MUSICAL DEL SIGLO XVIII A NUESTROS DIAS Limited Edition en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks LA ESTETICA MUSICAL DEL SIGLO XVIII A NUESTROS DIAS Limited Edition en linea.\nDescarga rapida! Descargar Gratis Ebooks CODIGO DE COMERCIO CON LAS ULTIMAS REFORMAS en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks CODIGO DE COMERCIO CON LAS ULTIMAS REFORMAS en linea.\nDescarga rapida! Descargar Gratis Ebooks GetBackers, Volume 35: Infinity Fortress, Volume 10 en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks GetBackers, Volume 35: Infinity Fortress, Volume 10 en linea.\nDescarga rapida! Descargar Gratis Ebooks LOS TOROS. VOL. 4: EL TOREO en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks LOS TOROS. VOL. 4: EL TOREO en linea.\nDescarga rapida! Descargar Gratis Ebooks The Billionaire's Baby en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks The Billionaire's Baby en linea.\nDescarga rapida! Descargar Gratis Ebooks BETEL, RELIGION CATOLICA: 3o SECUNDARIA Limited Edition en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks BETEL, RELIGION CATOLICA: 3o SECUNDARIA Limited Edition en linea.\nDescarga rapida! Descargar Gratis Ebooks PRIMERA GENERACION ARTE E IMAGEN EN MOVIMIENTO 1963 1986 Limited Edition en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks PRIMERA GENERACION ARTE E IMAGEN EN MOVIMIENTO 1963 1986 Limited Edition en linea.\nDescarga rapida! Descargar Gratis Ebooks LA LLAVE DE CRISTAL en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks LA LLAVE DE CRISTAL en linea.\nDescarga rapida! Descargar Gratis Ebooks LAS HEROINAS ESPANOLAS en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks LAS HEROINAS ESPANOLAS en linea.\nDescarga rapida! Descargar Gratis Ebooks HISTORIA DE PUERTO RICO Kindle Edition en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks HISTORIA DE PUERTO RICO Kindle Edition en linea.\nDescarga rapida! Descargar Gratis Ebooks EL MUERTO MANDA. NOVELA. TRADUCCION DE JOAQUIN URNIETA. Limited Edition en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks EL MUERTO MANDA. NOVELA. TRADUCCION DE JOAQUIN URNIETA. Limited Edition en linea.\nDescarga rapida! Descargar Gratis Ebooks LECCIONES SOBRE LA FILOSOFIA DE LA HISTORIA UNIVERSAL en espanol PDF, EPUB, Torrent. Gratis Audio Ebooks LECCIONES SOBRE LA FILOSOFIA DE LA HISTORIA UNIVERSAL en linea.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Membership of the choir is by audition.\nIf you are a good sight reader and are interested in joining us, please contact the membership secretary, Sue Wyatt, who will arrange for you to attend a rehearsal in the first instance and meet our conductor.\nRehearsals are usually held in Blandford Methodist Church, The Close, Blandford Forum, Dorset DT11 7HA on Monday evenings from 7.45 to 9.45.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Soak beans overnight in water. Drain. In a large saucepan, add beans, water and salt. Bring to boil, cover and simmer for 2 hours until beans are tender. Remove beans with a slotted spoon and set aside. Bring bean stock to a boil, add ground pork, and oregano and bring to a second boil. Drain and reserve par-boiled pork.\nIn a large, heavy saucepan, melt butter over medium heat. Saute onions, radishes and peppers until limp. Add beans, boiled pork,lemon juice and remaining salt. Lower heat, cover and simmer 10-15 minutes until tender. Pour in salsa, add grated cheese and continue simmering until cheese melts.Pour black bean dip into a serving dish, sprinkle with chopped cilantro and surround with chips. Serve warm.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This economical knife works great for almost any light duty task or project. When the blade gets dull, simply snap off the tip revealing a new sharp blade.\nPerfect for cutting cardboard packages, paper, plastic, canvas, cloth, film, model making, pumpkin carving, card-stock, foam boards, tape, wood, polymer clay, vinyl, cork and other light-weight materials.\nUsed by homeowners, contractors, warehouse staff and can be found in most garages.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzussi b/data_all_eng_slimpj/shuffled/split2/finalzzussi
new file mode 100644
index 0000000000000000000000000000000000000000..266d7101a215f509ce38ebd8009646a0d9ebef5b
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@@ -0,0 +1,5 @@
+{"text":"Statistical analysis of the growth and morphology of the filamentous microbe Streptomyces coelicolor.\nLeggett, RM, Grandison, S, Morris, RM, Kelemen, G and Moulton, V (2009) Statistical analysis of the growth and morphology of the filamentous microbe Streptomyces coelicolor. In: Statistical Tools for Challenges in Bioinformatics, 2009-07-07 - 2009-07-09.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Is your family into basketball? March Madness is right around the corner, and what better way to gear up than with Basketball Net Hats for the family?! This new ear wamer pattern for basketball lovers is sure to be a hit!\nMy friend Jill, a moderator for the Heart Hook Home Crochet Community on Facebook, created this Basketball Net Hat pattern. This hat has been so wildly popular in the Facebook group, and because she's such an awesome moderator, I have asked Jill if she would consider writing up the pattern. And she said yes!! Woohoo! After testing this pattern myself, I am confident that a beginner\/intermediate crocheter can complete this hat. They work up so quickly, too!\nFind this pattern here on Ravelry, offered by the wonderfully talented Jill from Happy Heart Hats!\nThis hat is worked from the brim up, making it a quick project. These hats would be excellent for team photos if your child or grandchild is on a basketball team, or I suspect it would be a great seller at your next craft fair! You are free to sell your finished products using this pattern, Jill only asks that you reference the pattern link from this page or Ravelry when you do.\nI don't know where you're from, but as far as basketball goes here in Kansas, the Jayhawks rule the roost. (See what I did there?! \ud83d\ude1b ) Because the Jayhawks are so consistently awesome, the whole town gets involved in basketball season and March Madness. This year we'll be watching while wearing our Basketball Net Hats that whip up in no time flat!\nI hope you love this hat pattern as much as I do! You can find this pattern on Ravelry. Be sure to share photos in the Facebook group of your finished hats!\nI enjoy you because of your whole labour on this site. My niece takes interest in setting aside time for investigation and it's simple to grasp why. My spouse and I notice all of the dynamic modes you render precious ideas by means of the blog and even recommend response from other people on this area of interest and our princess is really studying a lot of things. Take pleasure in the rest of the new year.\nMy basketball playing 16 year old is going to love this! Thanks so much.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"When mobile consumers participate in a Proud Indie supported promotion or mobile campaign, Proud Indie will receive certain information about the participant (such as phone number and mobile services provider). By participating in the mobile programs and campaign supported by Proud Indie, mobile users give permission to Proud Indie to collect information about the user.\nWe are committed to protecting your privacy at Proud Indie. We will not collect any personal information from mobile participants that the user does not volunteer and we are the sole owner of all information collected. We do not sell, share or rent this information in any way to third party service providers, partners, affiliates, subsidiaries, advertising and promotional agencies and others.\nProud Indie may be required to provide its partners and other service providers with data submitted by mobile participants in order to support requirements for a specific campaign. For example, users might submit their zip code to check their eligibility to purchase a product or service, where the zip code information needs to be queried in an external database to Proud Indie's network. Proud Indie may also provide log files and other data of user information to third parties for analysis to get a better understanding of general behavior for the sole purpose of improving our service and content offerings.\nProud Indie implements a very high level of security to protect all mobile user information captured by campaign participants whether the data is being stored or processed.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"> > instead of maintaining our own list.\n> OK, I'll try to test on at least SPARC and PPC.\n> What version of FPC does trunk require these days?\nmight also work, but that is rarely tested.\nThe compiler options should work even with old fpc.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Stationery Paper with elegant & traditional Florentine patterns & with richly decorated envelopes - a touch of Italy!\nPatterns reminiscent of the illuminations found in Medieval manuscripts.\nFine papers from ROSSI 1931 - a family owned company founded near Florence in 1931.\nClassic Bordered Stationery Sheets 7x9\" and matching lined envelopes are featured with the finest papers from ROSSI 1931 - a family owned company founded near Florence in 1931.Ten sheets with 10 matching lined envelopes in a beautifully presented box packaging, a typically European way of presenting fine writing paper. These elegant traditional patterns, with richly decorated envelopes are reminiscent of the illuminations found in Medieval manuscripts. Beautifully presented in an elegant keepsake box. Entirely made in Italy!\nAs always Nostalgic Impressions come through with delightful and elegant fine writing paper.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzvnpx b/data_all_eng_slimpj/shuffled/split2/finalzzvnpx
new file mode 100644
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+{"text":"The Corpus Christi Male Chorale was formed in the summer of 1996, had its first rehearsal on September 11, 1996, and gave its first performance in December of that year.\nSince then, the choir has performed regularly, in and around Calgary as well as in various other locations, both in Canada and the U.S. Under the direction of Daniel Bensler, the choir has grown steadily, both musically and in size, although many of the current members have been with the choir since its formation. Participation in the choir provides members with the opportunity to socialize with others and to have the enjoyment of making music through the medium of choral singing. The choir's focus has been to participate in celebrations and fundraising efforts for the benefit of local churches, communities and relief agencies, as well as international aid projects.\nThe choir has built a large repertoire, sacred as well as secular, in a wide range of musical styles, and continues to add new music each season. The chorus has two recordings, which have been well received.\nThe first CD, entitled \"Let the Nations Sing\", was recorded in the spring of 2003 at First Mennonite Church, Calgary. All proceeds raised through the sale of this CD and cassette go towards the relief, service, and peace agency work of the Mennonite Central Committee (MCC).\nThe second CD, entitled \"A Christmas Collection of Music and Miracles\", was recorded in the fall of 2004 at Christ Church, Calgary. All proceeds raised through the sale of this CD go towards the humanitarian inner-city work of The Mustard Seed, Calgary.\n\u00a92017 Corpus Christi Male Chorale. All Rights Reserved.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"What Are Barcode Thermal Labels?\nBarcode thermal labels are used to track everything from products to patients. Healthcare services, veterinary practices, manufacturers and distribution companies are just a few of the many industries that utilize barcode thermal labels.\nBarcode thermal labels can be applied to a wide variety of applications including shipping labels, asset labels, inventory labels, patient wristbands and identification and more.\nUnited Ad Label barcode thermal labels come in various formats that fit numerous software systems. The labels are glove safe and smudge proof. Plus, UL\/cUL and CSA approved products are available.\nDirect Print Thermal Label, 3\" Core, 2\" x 4\"\nDirect Printer Thermal Label, 1\" Core, 2\" x 2\"\nDirect Printer Thermal Label, 3\" Core, 2-1\/2\" x 1\"\nDirect Thermal Printer Label, 3\" Core, Rem, 3\" x 1\"\nDirect Thermal Printer Label, 3\" Core, Rem, 3-1\/2\" x 1\"\nDirect Thermal Printer Label, 3\" Core, Rem, 4\" x 1\"\nDirect Thermal Printer Label, 3\" Core, Rem, 4\" x 2\"\nDirect Thermal Printer Label, 1\" Core, 1\" x 1\/2\"","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Labour leader is a passionate defender of migrants' rights \u2013 Brexit shouldn't distract the new left movement from that.\nSomething strange is happening on the British left \u2013 a kind of deliberate collective amnesia. During the EU referendum, the overwhelming majority of the left backed Remain.\nContrary to a common myth, both Jeremy Corbyn and the movement behind him put their weight into a campaign that argued forcefully for internationalism, migrants' rights and regulatory protections.\nAnd yet now, as Labour's policy on Brexit hardens, swathes of the left appear to be embracing Lexit, and a set of arguments which they would have laughed off stage barely a year ago.\nThe example of free movement is glaring and obvious, but worth rehashing. When Labour went into the 2017 general election promising to end free movement with the EU, it did so with a wider election campaign whose tone was more pro-migrant than any before it.\nNonetheless, the policy itself, along with restricting migrants' access to public funds, stood in a long tradition of Labour triangulating to the right on immigration for electorally calculated reasons. When Ed Miliband promised \"tough controls on immigration\", the left rightly attacked him.\nThe result of this contradiction is that those on the left who want to agree unequivocally with the leadership must find left-wing reasons for doing so. And so, activists who have spent years declaring their solidarity with migrants and calling for a borderless world can now be found contemplating ways for the biggest expansion of border controls in recent British history \u2013 which is what the end of free movement would mean \u2013 to seem progressive, or like an opportunity.\nThe idea that giving ground to migrant-bashing narratives or being harsher on Poles might make life easier for non-EU migrants was rightly dismissed by most left-wing activists during the referendum.\nNow, some are going quiet or altering course.\nOn the Single Market, too, neo-Lexit is making a comeback. Having argued passionately in favour of membership, both the Labour leadership and a wider layer of its supporters now argue \u2013 to some extent or another \u2013 that only by leaving the Single Market could Labour implement a manifesto.\nThis is simply wrong: there is very little in Labour's manifesto that does not have an already-existing precedent in continental Europe. In fact, the levers of the EU are a key tool for clamping down on the power of big capital.\nIn recent speeches, Corbyn has spoken about the Posted Workers' Directive \u2013 but this accounts for about 0.17 per cent of the workforce, and is about to be radically reformed by the European Parliament.\nThe dangers of this position are serious. If Labour's leadership takes the path of least resistance on immigration policy and international integration, and its support base rationalises these compromises uncritically, then the logic of the Brexit vote \u2013 its borders, its affirmation of anti-migrant narratives, its rising nationalist sentiment \u2013 will be mainlined into Labour Party policy.\nSocialism in One Country and a return to the nation state cannot work for the left, but they are being championed by the neo-Lexiteers. In one widely shared blogpost on Novara Media, one commentator even goes as far as alluding to Britain's Road to Socialism \u2013 the official programme of the orthodox Communist Party.\nThe muted and supportive reaction of Labour's left to the leadership's compromises on migration and Brexit owes much to the inept positioning of the Labour right. Centrists may gain personal profile and factional capital when the weaponising the issue, but the consequences have been dire.\nAround 80 per cent of Labour members still want a second referendum, and making himself the \"stop Brexit\" candidate could in a parallel universe have been Owen Smith's path to victory in the second leadership election.\nBut it meant that in the summer of 2016, when the mass base of Corbynism hardened its factional resolve, it did so under siege not just from rebelling MPs, but from the \"Remoaners\" as well.\nAt every juncture, the strategy of the centrist Labour and media establishment has made Brexit more likely. Every time a veteran of the New Labour era \u2013 many of whom have appalling records on, for instance, migrants' rights \u2013 tells Labour members to fight Brexit, party members run a mile.\nIf Tony Blair's messiah complex was accurate, he would have saved us all a long time ago \u2013 by shutting up and going away. The atmosphere of subterfuge and siege from MPs and the liberal press has, by necessity, created a culture of loyalty and intellectual conformity on the left.\nBut with its position in the party unassailable, and a radical Labour government within touching distance of Downing Street, the last thing the Labour leadership now needs is a wave of Corbynite loyalty-hipsters hailing its every word.\nAs the history of every attempt to form a radical government shows, what we desperately need is a movement with its own internal democratic life, and an activist army that can push its leaders as well as deliver leaflets for them.\nLexit is no more possible now than it was during the EU referendum, and the support base of the Labour left and the wider party is overwhelmingly in favour of free movement and EU membership.\nJeremy Corbyn, John McDonnell and Diane Abbott are passionate, principled advocates for migrants' rights and internationalism. By showing leadership, Labour can once again change what is electorally possible.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Danhui Nai creates exotic flowers, paisley, ikats, and elephants in her colorful Bohemian Dreams fabrics. Wilmington Prints utilizes purple, navy, jade, pink, cream, and gold for a rich color palette. Printed on a premium 44 inch wide cotton fabric.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Sweet Fancy Treat: Do You Stop Writing When The Page Ends?\nI was reading an article about Karl Lagerfeld. He was interviewed in the old Chanel studio and talked about his work, Zaha Hadid and some of today's major concerns in the fashion industry.\nArchitect Zaha Hadid created a museum, a portable exhibition space: the Chanel Mobile Art Pavilion. It is fully transportable, for show in Asia, New York, London, Moscow and Paris - and inside is an art exhibition celebrating Chanel handbags. Karl declares himself an admirer of her work in the days before her buildings were constructed.\nClothes if they are not well cut, you can kill nobody. A building poorly built can kill people. It's a much more difficult work. I would not compare myself with that.\nHe defends elitism and capitalism: \"I can be interested in a $20m diamond I will never buy, without desiring the diamond. If you want only things you can afford, it's boring too. It's great to see things you may not buy - because you don't have the money - but it is very ugly to think they shouldn't exist because you can not buy them.\"\nSome general thoughts about the economic meltdown? Sure: \"I see it like a cleaning up - it was too rotten anyway - so it had to be cleaned up... I see it like a healthy thing - horrible but healthy, like some miracle treatment of the world.\nSo, will it be harder to sell handbags? Those expensive, dream handbags he is creating? Lagerfeld answers: \"What is the real world? If you have no dreams, or if you don't try to improve real life of everybody, people would ask why they get up in the morning. You have to have a drive. My drive is the work I do. People have different kinds of dreams. After all, people need a handbag, there are cheaper handbags. But if you can buy a beautiful one and if that's your dream to buy, why not?\"\nI agree with him, I always do. And not because he's Karl. I agree with him, because he's right.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzwgxw b/data_all_eng_slimpj/shuffled/split2/finalzzwgxw
new file mode 100644
index 0000000000000000000000000000000000000000..2cc09bb21c9e3b603e8b23404bd785b97168559a
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzwgxw
@@ -0,0 +1,5 @@
+{"text":"Manual of Histologic Staining Methods of the Armed Forces Institute of Pathology (Third Edition). American Registry of Pathology ( Luna, Lee G., HT(ASCP) (editor)), McGraw Hill Publishers, New York 1960 (Progressive Stain) Mayor's hematoxylin is used because it eliminates the necessity for differentiation and bluing of the section. It can be considered a progressive stain which produces a stained section with a clearly defined nuclei while the background is completely colorless. The biggest objection to Mayer's hematoxylin as used in the past, has been that stained slides often fade after I to 3 years. This problem can be eliminated, however, when the slides are washed, after the hematoxylin, in running water for a minimum of 20 minutes.\nThis method gives consistent results even when more than one person stains sections from the same block. Also, slides may be left in the hematoxylin for hours with-out overstaining. Because of the simplicity of the technique, it is possible to teach others to use it within a shorter time as well as a definite reduction in time performance of the stain itself. See Figure 15 for the steps and timing with use of Mayor's Hematoxylin and Eosin procedure.\nFIXATION. Any well fixed tissue.\nTECHNIQUE. Paraffin, celloidin, or frozen. SOLUTIONS: MAYER'S HEMATOXYLIN; EOSIN SOLUTIONS; GRAM'S OR LUGOL'S IODINE.\n1. Deparaffinize and hydrate to water. 2. If sections are Zenker-fixed, remove the mercuric chloride crystals with iodine and clear with sodium thiosulphate (hypo) (seepage 41). 3. Mayer's hematoxylin for 15 minutes.\n4. Wash in running tap water for 20 minutes. 5. Counterstain with eosin from 15 seconds to 2 minutes depending on the age of the eosin, and the depth of the counterstain desired. For even staining results dip slides several times before allowing them to set in the eosin for the desired time.\n6. Dehydrate in 95% and absolute alcohols, two changes of 2 minutes each or until excess eosin is removed. Check under microscope.\n7. Clear in xylene, two changes of 2 minutes each.\n8. Mount in Permount or Histoclad.\nNuclei - blue - with some metachromasia.\nCytoplasm - various shades of pink-identifying different tissue components.\nPurpose To identify an increase in collagenous connective tissue fibers, or to differentiate between collagen and smooth muscle fibers.\nPrinciple In the one-step trichrome procedure, a plasma stain (chromotrope 2R) and a connective tissue fiber stain (fast green FCF, light green, or aniline blue) are combined in a solution of phosphotungstic acid to which glacial acetic acid has been added. Phosphotungstic acid favors the red staining of muscle and cytoplasm. The tungstate ion is specifically taken up by collagen, and the connective tissue fiber stain is subsequently bound to this complex, coloring the collagen green or blue, depending on the counterstain used.\nFixative Any well-fixed tissue may be used. Bouin's solution is used as a mordant to intensify the color reactions.\nEquipment 56 to 58 \u00b0C oven, Coplin jars, Erlenmeyer flasks, graduated cylinders, pipettes.\nTechnique Cut paraffin sections at 4 to 5 mm.\nQuality Control Practically every tissue has an internal control, so no other control sections are needed; however, if a control is desired, uterus, small intestine, appendix, or fallopian tube will provide good material.\nMix equal parts of solutions A and B.\nStore this solution in the refrigerator.\nProcedure 1. Deparaffinize sections and hydrate to distilled water. 2. Rinse well in distilled water.\n3. Mordant sections in Bouin's solution for I hour at 56 \u00b0C.\n4. Remove slides from the oven, allow to cool, and wash in running water until the yellow color disappears.\n5. Rinse in distilled water.\n6. Stain sections in Weigert's hematoxylin for 10 minutes.\n7. Wash in running water for 10 minutes.\n8. Stain sections for 15 to 20 minutes in Gomori's trichrome stain.\n9. Differentiate for 2 minutes in 0.5% acetic acid.\n10. Dehydrate, clear, and mount with synthetic resin.\n1. Sweat et al state that coloration of fine connective tissue fibers is affected by the dye solution pH, with maximum binding occurring around pH 1.3. The pH of Gomori's trichrome is about 2.5, which decreases affinity for anions by approximately 50%, so these investigators suggest that by replacing the acetic acid with hydrochloric acid, a pH of approximately 1.3 can be obtained. The intensity of coloration of the fine connective tissue fibers can be varied by altering the pH.\nPurpose Elastic fiber techniques are used for the demonstration of pathologic changes in elastic fibers. These include atrophy of the elastic tissue, thinning or loss that may result from arteriosclerotic changes, and reduplication, breaks, or splitting that may result from other vascular diseases. The techniques also may be used to demonstrate normal elastic tissue, as in the identification of veins and arteries, and to determine whether or not the blood vessels have been invaded by tumor.\nPrinciple The tissue is overstained with a soluble lake of hematoxylin-ferric chloride-iodine. Both ferric chloride and iodine serve as mordants, but they also have an oxidizing function that assists in converting hematoxylin to hematein. The mechanism of dye binding is probably by formation of hydrogen bonds, but the exact chemical groups reacting with the hematoxylin have not been identified. This method requires that the sections be overstained and then differentiated, so it is regressive. Differentiation is accomplished by using excess mordant, or ferric chloride, to break the tissue-mordant-dye complex. The dye will be attracted to the larger amount of mordant in the differentiating solution and will be removed from the tissue. The elastic tissue has the strongest affinity for the iron-hematoxylin complex and will retain the dye longer than the other tissue elements. This allows other elements to be decolorized and the elastic fibers to remain stained. Sodium thiosulfate is used to remove excess iodine. Van Gieson's solution is the most commonly used counterstain, but others may be used.\nFixative Any well-fixed tissue may be used.\nEquipment Mechanical stirrer, Coplin jars, Erlenmeyer flasks, graduated cylinders.\nPut the iodine and potassium iodide in a flask with 200 mL of the water. Stir on a mechanical stirrer until the iodine dissolves and then add the remaining water.\n5% Sodium Thiosulfate Sodium thiosulfate ..... 50.0 g Distilled water ..... 1,000.0 mL Procedure 1. Deparaffinize sections and hydrate to distilled water.\n2. Place sections in Verhoeff's elastic tissue stain for I hour.\n3. Wash in two changes of distilled water. 4. Differentiate sections microscopically in 2% ferric chloride until the elastic fibers are distinct and the background is colorless to light gray. If the sections are differentiated too far, restain. 5. Rinse sections in distilled water.\n6. Place sections in sodium thiosulfate for I minute.\n7. Wash in running tap water for 5 minutes.\n8. Counterstain sections in van Gieson's stain for 1 minute. 9. Differentiate in 95% alcohol.\n10. Dehydrate in absolute alcohol, clear in xylene, and mount with synthetic resin.\nNotes 1. It is easy to overdifferentiate this stain (Plate 8-8, page 268). If the background is completely colorless, so that a clear yellow counterstain is obtained, the section may be overdifferentiated. It is probably better to err on the side of underdifferentiation.\n2. Overdifferentiated sections may be restained at any step provided they have not been treated with alcohol.\n3. Do not prolong staining with van Gieson's solution as picric acid also will differentiate the stain further.\n4. It is not necessary to remove mercury deposits before staining, as they will be removed by the staining solution.\n5. The preparation of van Gieson's solution is critical for proper differentiation of muscle and collagen. If the picric acid is not saturated, collagen will not stain red, and cytoplasm, muscle, and collagen may all stain the same color.\n6. To prepare the Verhoeff's elastic staining solution, the reagents must be added in the order given, with mixing after each addition, or poor staining may result.\n7. The staining jar that contained the Verhoeff's solution may be cleaned easily by transferring the 2% ferric chloride to the jar for a few minutes before discarding the solution.\nFor optimum results, slides must be individually differentiated, as the time of differentiation is somewhat dependent on the amount of elastic tissue present. Do not depend on the control for timing the differentiation of all sections.\nPAS Reaction With Diastase Digestion Manual of Histologic Staining Methods of the Armed Forces Institute of Pathology (Third Edition). American Registry of Pathology ( Luna, Lee G., HT(ASCP) (editor)), McGraw Hill Publishers, New York 1960 Purpose The demonstration of glycogen in tissue sections.\nPrinciple This is a very sensitive histochemical method for glycogen. Diastase and a-amylase act on glycogen to depolymerize it into smaller sugar units (maltose and glucose) that are washed out of the section. The Schiff reaction has been described in the PAS procedure.\nFixative 10% neutral buffered formalin, formalin alcohol, or absolute alcohol.\nEquipment Hot plate, pH meter, Coplin jars, balance, Erlenmeyer flasks, graduated cylinders, filter paper.\nTechnique Gut two paraffin sections at 4 to 5 mm. Label one section \"with\" and one section \"without.\"\nQuality Control Two control sections of liver containing glycogen must be used, one labeled \"with\" and one labeled \"without.\"\nAdjust pH to 6.0 if necessary.\nProcedure 1. Deparaffinize and hydrate slides to distilled water.\n2. Place the sections labeled \"with\" in preheated diastase solution at 37 \u00b0C for I hour. Hold the sections labeled \"without\" in distilled water.\n3. Wash in running water for 5 minutes.\n4. Place all sections (\"with\" and \"without\") in 0.5% periodic acid solution for 5 minutes.\n5. Wash in three changes of distilled water.\n6. Place in Schiff reagent for 15 minutes.\n7. Wash for 1 minute in each of two jars of 0.55% potassium metabisulfite to remove excess stain.\n8. Wash in running tap water for 10 minutes to develop full color.\n9. Counterstain \u00bd minute in Harris's hematoxylin with acetic acid (2 mL acetic acid\/48 mL hematoxylin).\n10. Wash well in running water to blue the hematoxylin.\nGlycogen will stain bright rose red on the section labeled \"without\" and will be absent from the section labeled \"with.\"\nMalt diastase, containing both a- and (3-amylase, is commonly used for digestion but tends to loosen the sections. For this reason as well as the decreased digestion time, many laboratories prefer to use human saliva, which contains only a-amylase. If preferred, digest with saliva for 20 minutes at room temperature.\nGlycogen fixed in picric acid-containing fixatives may be more resistant to diastase digestion than when digestion follows other fixatives (Sheehan and Hrapchak).\nPurposeImmunohistochemistry is used to identify a long list of antigens. It is a very effective and flexible technique that is dependent upon the specificity and sensitivity of the primary antibody. If one has an antibody that identifies the fixed, processed antigen, any number of secondary antibodies and\/or amplification techniques can be used to identify the antigen in paraffin sections.\nPrinciple The tissue is processed and unstained paraffin sections are mounted on glass slides. Most procedures call for \"antigen retrieval\" using microwave ovens and citrate buffers. The incubation in methanol and hydrogen peroxide is designed to \"kill\" the endogenous peroxidases and eliminate background staining. The appropriate dilution of primary antibody is placed in solution on the deparaffinized sections and exposed of an appropriate time interval (depending on the affinity and avidity of the antibody and the preservation and concentration of the antigen). The secondary antibody systems are then placed on the slide. The procedures provided below illustrate the use of the ABC kits but many different protocols, signal amplification systems and indicator systems are available. The new mouse-on-mouse systems permit the use of some mouse monoclonal antibodies on mouse tissue.\nFixative In general, tissue fixed in paraformaldehyde for less than 48 hours provides the best results. However, different antigens will require different protocols. Post fixation of fomalin or paraformaldehyde fixed tissue with B5 or other heavy metal fixative can \"retrieve\" some antigens.\nThe protocol for Mouse-on-Mouse used on the slide set is found by clicking here.\n4. Absolute ETOH 3 min.\n5. Absolute ETOH 3 min.\n7. Absolute ETOH 1 min.\n8. 95% ETOH 2 min.\n9. 70% ETOH 2 min.\n10. H2O (running) 2 min.\n11. Dist. H2O 2 min.\n12. PBS (x2) 5 min.\n13. Normal Equine Serum 10% 20 min.\n15. PBS (x2) 5 min.\nEquine Anti-Mouse Biotin Conjugate 60 min.\n17. PBS (x2) 5 min.\n18. ABC - Elite 30 min.\n19. PBS (x2) 5 min.\n20. DAB (Vector-Brown) 3-5 min.\n22. Mayer's Hematoxylin 1 min.\n23. Tap H2O 5-10 min.\nNOTE: Tissue sections are placed in a 55 Celsius oven for 30 minutes or overnight.\n1. Xylene 5 min. RoomTemp.\n2. Xylene 5 min. RoomTemp.\n3. ETOH 3 min. RoomTemp.\n4. ETOH 3 min. RoomTemp.\n5. H202 + 3% Methanol 20 min. RoomTemp..\n6. ETOH 2 min. RoomTemp.\n7. ETOH 2 min. RoomTemp..\n8. H2O tap 5 min. RoomTemp..\n9. distilled H2O 5 min. RoomTemp..\n13. Cool down 15 min. RoomTemp.\n14. PBS 5 min. RoomTemp..\n15. PBS 5 min. RoomTemp.\n16. N horse serum 20 min. RoomTemp.\n18. PBS 5 min. RoomTemp.\n19. PBS 5 min. RoomTemp.\n20. Secondary (BHAM) 1:800 60 min. RoomTemp.\n21. PBS 5 min. RoomTemp.\n22. PBS 5 min. RoomTemp.\n23. Tertiary ABC 1:50 30 min. RoomTemp.\n24. PBS 5 min. RoomTemp.\n25. PBS 5 min. RoomTemp.\n26. DAB 3-5 min. RoomTemp.\n27. H2O running tap 5 min. RoomTemp.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The $1 trillion student loan market begins to implode \u2013 Department of Education shows two-year default rates at for-profit colleges up to 15 percent. Student loan debt increasing at a rate of $170,000 per minute.\nWe seem to have entered an era of perpetual and unshakeable financial bubbles and the next ripe bubble to burst is in the student loan market. Student loan debt has become the fastest growing debt sector throughout the economic recession. Growth at for-profit colleges has been incredible and tactics used at these institutions reflects patterns seen with the subprime mortgage operators. They target low income markets and exploit government backed loans and pump them through local area lenders. It is a bubble of mammoth proportions and it is no surprise that data released by the Department of Education only a few days ago reflects a default pattern reminiscent of the subprime crisis. Default rates on student loans at for-profit institutions are absolutely abysmal. There is no question now that the student loan bubble is now the next market to pop. What will be the consequences of the $1 trillion student loan market contracting?\nThis rate is horrifying. The ways these are measured are reflected by two-year default cohorts so you have 15 percent of the entire group defaulting within two-years! The real default rate is much worse if we tracked these out for the life of the loan. In other words, you have many going to for-profit paper mills and coming out with very little job prospects but with the added burden of massive student loan debt. Clearly the student did not benefit but the profits at these institutions are enormous. The government backing is the only way these lenders and schools even survive. If a bank had to lend their own precious money you think they would give someone $40,000 or even $100,000 in student loans to pursue a degree at an unranked paper mill? Reminds you of people buying tiny condos in Florida for $500,000 with no verifiable income.\nMore debt and less earnings is a recipe for disaster. Of course many of the for-profits are simply leveraging federal government loans to rip off students. The symbiotic relationship between banks, government, and con artists seems to be a large part of our economy for the past decade. In the past, the for-profit sector was a tiny part of the market making up 1 to 2 percent of all college going students even just a decade ago. Today it is up to 10 percent and is rapidly expanding. There is now a brewing crisis here and we are looking at a $1 trillion student loan market. Just like subprime, this will also impact other areas of the higher education model.\nThe cost of going to college has far outpaced the cost of virtually every other sector in our economy. The reason when we look back and see greater earnings for those who go to college is the reality that many never came out with so much debt. Decades of data are being used and applied to the current rip off and high cost model that has never been seen in the past. Plus, you had a tightly regulated market and for-profits were nearly unheard of. That has now changed. We now have legitimate institutions competing with organizations that run more like a subprime operation. The bottom line is that not all college degrees carry the same weight. You dilute the quality of the degree yet you charge more because of the access to debt. This is the big difference in the last decade. Just like the housing market, banks have figured out another way to become predators on the public and turn a once stable market like higher education into another giant bubble.\nDo I hear another bailout in the making?\nThe article is likely right on target. I personally have encountered people who have accumulated debts all out proportion to their earnings. One person went to a private for profit institution to learn to be a veternarian assistant. She racked up an $8 per hour job and a 20K plus student loan debt. Another person went to a well known college and racked up 80K in debt enroute to an unfinished history degree. Unless this person plans on coaching if and when the degree is complted teaching in a K-12 environment is questionable. On a scale of ten being high history majors rate 1 for hireability in the school system. A quick trip to the Dept of Labor website http:\/\/www.careeronestop.org tells how many of what is needed and the expected pay scale range in today's dollars. For many, college is a scam because they enter into it with little clear knowledge of their objectives, and because colleges have no desire to restrict enrollment in a rational fashion, outside their own rational desire for continuity. Students and parents need to be more discriminating.\nWe sent all our jobs and opportunities overseas. What what anyone expect?\nReally good article as somewhat shocking as it is. You've done your research on a topic the media and government don't want people to know about. They want to keep the myth going. I'll give them the benefit of the doubt and say they just don't know because their brain dead, especially judging by what they consider news worthy.\nI don't get it. Why are we a bunch of dolts when we have invested a trillion dollars in \"higher education\"? Perhaps it is because our education system is devoid of knowledge and wisdom much like our fast food industry is devoid of nutrition.\nWhat can save this nation from utter collapse? Or have we collapsed already?\nGod help our stupid species.\nHighest annual cost is $5000 at UNC-Chapel Hill.\nMy private alma mater six miles away $24,000.\nWonderful, marvelous, sensational Grandaughter goes to out of state at $25,000. She lives 18 miles from UNC-Chapel Hill!!!!\nRobert Applebaum and others at Forgive Student Loan Debt have warned about this for a couple of years.\nHe may be too kind to say \"I told you so\", but I don't suffer from that infirmity.\nIt's not too late to address the problem, forgive student loan debt.\nWhat did they expect? The loans are compounded, capitalized, fee'd and charged, which are also compounded and capitalized, and THEN any payments go to interest, fees, and charges before they EVER hit the principal! On top of that, student loans are NON-DISCHARGEABLE in bankruptcy, exempt from Fair Collections, exempt from usury laws, and exempt from any statutes of limitations. And to top it off, they can revoke your professional license so you can't get a job, garnish Social Security, garnish Disability, take your refunds, garnish your (low) wages since you can't get a job in your field and snag your life-insurance death benefits from your children if you still have any insurance. Student loans are LIFE-TIME DEBT SLAVERY and the securities (SLABS) they sell are considered totally SAFE because you can NEVER GET RID OF THEM even if you DIE.\nHow can any 18 year old project what their income will be once they graduate? No one could predict that we would now be in the worst recession since the Great Depression. Student loan debt is now higher than any other consumer debt. These borrowers are the ones that will not be able to borrow for mortgages, cars or to invest in their own children's futures.\nIf someone is part of that 1% then good for you. You managed to get that one in a million job and keep it. You are not one of those who got hurt in the housing bubble either. Your home price did not fall. It's all connected though, the housing market, student loans, credit cards. If you think that the student loan bubble will not affect you then think again. This one is going to be bigger, much bigger. So if you want to save your life styles with the ye holy 1% higher than thou attitude then you might want to think about how quickly and drastically home prices dropped when the bubble burst. Students who can't find jobs in this current market will be choosing food over paying on student loans. They will borrow only so much on their credit cards until that is maxed out.\nThey might not be able to rely on parents who co signed either. Considering that the price of housing has dropped and continues to drop the parents can't get second mortgages or lines of credit. Guess what happens then? The parents are on the hook for the student loan. Of course they will and do take it out of their social security checks, so don't worry ye holy 1% higher than thou folks, you can pass the plate at church knowing that you did your utmost to stop this train wreck.\nThere is a part you are all forgetting in this. NO student with these massive debts can get a business loan, ever. Business loans create wealth, and JOBS. And they wont get a HOUSE, where the equity could be used to fund a business, and hence\u2026jobs (again). You are looking at the slow death of the United States of America, courtesy of the greedy university officials along with student loan companies and their cohorts in congress.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Friends Duet features a series of something everyone loves - puppies! How can you resist the sweet faces of these avid duck hunters? This adorable art piece is featured on a light pink colored youth tee. 4 oz. 100% Cotton. Design shown is located on the back; each tee also features a small DU logo on the front left chest.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Tardsie, I thank you for being the Lee Iacocca of our Promethean Times. With out you I would have to work a full eight hours a day.\nTardsie accepts your love, believing that no man, woman or child should ever have to put in a full day's work.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Story Mode difficulty is scaled based on where you are in the story. It can sometimes be easier to gain a difficult to get item or weapon in a campaign than in Free Mode.\nCombo the base guardians for Attack and Defence to increase the strength of the defence\/offence boost item they drop.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzworv b/data_all_eng_slimpj/shuffled/split2/finalzzworv
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+{"text":"\"Just a little\" bigger than a Christmas card\u2026I probably should have scaled it down a little\u2026but it was a fun project for the evening.\nNot only is it on display on the Oyster Bay waterfront \u2013 I hand-delivered it to everyone on my friends list and also distributed it to the legion of Oyster Bay afficionados!\nCall it prim spam if you want, but that's the only time all year that I've done that\u2026and it's important to express your gratitude, appreciation and love to your friends at least once a year. I hope folks like it!\nMoShang's \"Chinese Chill\" is just incredible\u2026I love to use the term, \"Dance Music for Grown-ups,\" and it's really true. There's an undeniable beat with an extra layer of sophistication to it that makes his performance much more than pop.\nMoShang's going to play Oyster Bay this week \u2013 Wednesday at 6PM SLT. Hope you can come see! He offers up a great show with lots of interaction with his audience.\nAt the base of the Oyster Bay Christmas tree \u2013 the new Kronos Kirkorian machinima about Cheen Pitney's \"Water is Life.\" It's a powerful statement about the role of water in our lives and our world\u2026and how we also abuse this precious resource. Kudos to Cheen for the build, and to Kronos for the machinima!\nSo says Cyanide Seelowe. Here's the new link.\nIt's a wonderful collection of Madcow size and scale, but also the ingenuity of the individual artists in making beautiful ornaments with only 5 prims or less.\nThis squid\/star combination sits atop the 80m tall Oyster Bay Christmas tree. What a fantastic contruction\u2026.and collaboration! I really need to count all of the artists who put their ornaments on the tree. Yesterday's call for submissions also got a whole bunch of new ornaments. What fun!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Room to grow - inside and out! This 3 bedroom, 2 bath home has a partial, unfinished walk out basement - perfect to finish off to your needs. Outside, you'll find a stocked pond and the start of a dog kennel - building and run in place. With over 14 acres, add a horse, a garden spot or even another home! Lots and lots of options here! Located on the East side of Lebanon MO, you'll be conveniently located to I-44, shopping and medical facilities.\nDirections: From Lebanon MO: East Hwy 32, right on Pine Tree, left on Falcon Road, right on Rice. Property on the left. Sign in window.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Brewers Arms is a 17th century pub and restaurant in Brightlingsea, Essex. As well as offering a place where residents and non residents can enjoy something to eat and drink, we also have cosy bed and breakfast accommodation available. We offer a place to stay that is family friendly, relaxing and comfortable.\nBreakfast is included within the room rate and is served in our restaurant. We always utilise fresh, local produce to prepare your food and provide a selection of breakfast items.\nThe Whalebone Inn offers wonderful food and a relaxing atmosphere in Colchester, Essex. We offer superb value and will become one of your favourites.\nOur gorgeous Grade II Listed building has been beautifully restored and comes with exposed beams, stripped wooden floors and bespoke furniture. In the winter you can enjoy relaxing in front of the roaring wood burning fire and our garden is perfect for a tipple or two in the afternoon sun.\nOur excellent menu will tantalise your taste buds. We use freshly cooked produce from local suppliers and are passionate about buying British meat and local vegetables. Whether it's chicken & gammon pie or pan-seared rump of local lamb, we have something for everyone.\nThe bar at The Whalebone is light, rustic and the perfect place to unwind. We have a great selection of real ales and an extensive wine list.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"I'm David White and I'm a self taught screenwriter and cinematographer with an emphasis on Film Directing. I began making short films at 16, and I currently make commercials and promo videos. I studied acting and motion picture editing at the University of Connecticut, where I made my thesis film \"Waiting For Nick\". I focus on the complexities and hardships of the human society in my work. Wishing to spark healthy discussions, I often select film topics that have a high level of controversy or social activism. I look forward to working on this show and to collaborate with a fantastic cast and crew.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Indulge in 2017's freshest comedy and prepare to have your socks knocked off by the latest endeavor from the Duplass brothers.\nPlus, the intriguing documentary I Called Him Morgan is now available to stream on Netflix.\nThe service continues to entice viewers with exclusive and award-winning stories this July.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzwutl b/data_all_eng_slimpj/shuffled/split2/finalzzwutl
new file mode 100644
index 0000000000000000000000000000000000000000..33363b35b8dcecb90b691daee6fc2a173490e2d8
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+{"text":"Defence critics and human rights advocates remain at odds over what's reasonable when it comes to monitoring individuals who authorities believe may participate in terrorism, following the death of terror suspect Aaron Driver in Strathroy, Ont.\nFormer Winnipegger was killed in confrontation with police in Strathroy, Ont.\nNational defence critics and human rights advocates remain at odds over what's reasonable when it comes to monitoring individuals who authorities believe may participate in terrorism, following the death of terror suspect Aaron Driver in Strathroy, Ont.\nDriver, who was killed in a confrontation with police on Wednesday, had been under a peace bond \u2014 a court order limiting his privileges and movements \u2014 since February.\nRCMP announced on Thursday that Driver, a 24-year-old former Winnipegger who openly supported ISIS on social media, had made a \"martyrdom video\" and was planning an attack within 72 hours.\nMike Cabana, the RCMP's deputy commissioner for federal policing, said the FBI came into possession of the video and tipped off the Mounties on Wednesday morning.\nThat afternoon, officers surrounded a taxi that Driver had called and a device was detonated in the back of the cab. Driver was killed while the cab driver suffered minor injuries.\nMichelle Falk, a human rights professional in Winnipeg, says despite the outcome, it is unjust and unreasonable to limit or detain people on the assumption that they may commit a crime.\n\"It is still a human rights concern if an individual is, we could assume, might be able to commit a crime in the future. It's still unreasonable as far as the individual's human rights to detain that person preemptively,\" she said.\nFalk added that Driver had no previous convictions and his Twitter statements in support of ISIS are protected as free speech.\n\"We can't assume that there's a whole swath of individuals in the community, based on their economic situation and based off a whole lot of things, that we know statistically will lead more to a life of crime,\" she said.\n\"It would be unreasonable to detain people without actually having committed a crime and it's also against their fundamental basic human rights as Canadian citizens.\"\nManitoba MP and federal Conservative defence critic James Bezan holds a starkly different take on Driver's case, saying the tragic ending may have been avoided entirely if authorities had charged Driver in the first place.\nBezan said he's calling on the federal Liberal government to maintain the Anti-Terrorism Act, which was brought in last year to give Canadian intelligence authorities greater powers to intervene with terror threats or perceived threats.\nIn March, the head of the Canadian Security Intelligence Service (CSIS) told a Senate committee that the agency has used its extraordinary powers to disrupt extremist plots close to two dozen times since the fall of 2015.\n\"The reality is that we're not immune to terrorism, and not only is it happening around the world but it can happen right here in Canada,\" Bezan said.\n\"We're just very lucky that law enforcement was able to stop him before he was able to act out his own terrorist plot that he'd been working on.\"\nDriver moved to Winnipeg in 2011 and by 2014 was on the CSIS's radar for his online activities.\nIn June 2015, authorities raided the room Driver had been renting at a Charleswood home. RCMP arrested and obtained a peace bond, saying they considered him a terror threat. When Driver agreed to the peace bond in February 2016, he was subjected to a number of conditions.\nFalk said she believes Driver's case could have been handled differently.\n\"I think that if Aaron Driver would have been approached with a more compassionate tone and gone through counselling and being talked to about the things that he had said on Twitter \u2026 there might have been a different path,\" she said.\n\"I think that the sort of the heavy hand of the law that he had been dealt with might have made him just a little bit more disgruntled.\"","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This car has had four registered owners from new, the last since 2017. It is being offered with 69,543 warranted miles. It's history file contains the original service book stamped in 1999, 2000, and then 2003 through to 2007, copy older V5, MoTs dating from 2004 to 2018, some receipts, handbooks and wallet.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Did the Title of this post, How to sew bras with your feet, catch your attention? I was hoping it would! Well, did you know that National Sewing Machine Day was June 13? Can you believe it's been nearly 200 years already? Where does the time go?\nBut which date do you accept as the official beginning? British cabinet-maker and inventor, Thomas Saint, received the first patent for a design of a sewing machine in 1790. However no evidence of it, other than his drawings could be found, so it is doubtful that it was ever actually produced. In 1874, William Newton Wilson found the patent drawings in the London Patent Office, made adjustments and built a working model. This model is currently owned by the London Science Museum. Lesson learned. If you are going to the trouble of obtaining a patent on something, be sure you actually have plans to produce it!\nEvery quilter knows what this foot is \u2013 the foot that keeps them on the straight and narrow. But it's not just quilters that use 1\/4\u2033 seam allowances \u2013 we bra-makers use them too! Once you embrace the unfamiliar narrowness of the 1\/4\u2033 seam, you will embrace its accuracy and its ease of use.\nThere are as many quarter inch feet as there are machines that use them \u2013 maybe even more. Several machine brands have more than one style of quarter inch foot. But they all have something in common \u2013 the width from the needle to the right hand edge of the foot is one-quarter inch (6 mm) As long as you keep the fabric aligned with the right hand edge, you will sew a perfect 1\/4\u2033 seam, curved or straight.\nHere's a reminder from one who has \"been there and done that\". You can only use a straight stitch with a quarter inch foot! Don't try to switch to a zig-zag without changing your foot. It will not go well for you! But you knew that\u2026didn't you?\nMy mature eyes, and the bi-focals that came with them, unannounced, cannot handle black thread on black fabric, if not for the edge-stitching foot. I'm afraid my topstitching would resemble a drunkard's path on a Saturday night. I could live without a 1\/4\" foot, but not an edge-stitching foot. I have gotten quite good at seeing the \"right\" width for the seam allowances; I just can't see to topstitch on dark fabrics anymore. Ah\u2026the \"golden years\".\nThe edge-stitching foot is also known as an edge-joining foot or the stitch-in-a-ditch foot. Whatever it is called, it has a bar that sits in the middle and you ride this bar in the well of the seam or on the edge of the fabric if you are stitching near the edge. Some have a movable bar (like the centre one below) in which case you can adjust the small wheel for tiny adjustments. However, most have a fixed metal and you are expected to move the machine needle. This can cause a problem if your machine has only a few needle positions.\nQuilters keep the machine needle in the middle position to do stitch-in-a-ditch. However bra-makers will move the needle slightly to the right or the left to keep the topstitching of the cross cup seam absolutely perfect.\nA zipper foot? Seriously \u2013 bra-makers need a zipper foot? Yes, we do! Some bras use a zipper in the front (like my Alison sports bra) but mostly we use the zipper foot when we have to get super close to something else. A quarter inch foot is way too wide\u2026and an edge-stitching foot may still not get you close enough. Enter (with a big TA-DA!) the lowly zipper foot!\nAs in the other feet, there are several types of zipper feet. My favorite type is one that allows you to stitch right up to the edge while still holding the fabric firm. I do love the adjustable (or sliding) zipper foot that everyone over 45 remembers from their home economics classroom. The wheel on the back allows you to move the foot to exactly where you need it. This is exactly what you need when you are sewing on hooks and eyes, or sewing the busk of a corset. No other foot will allow you to stitch right up to the metal.\nThe foot in the centre above is almost useless for bra-making in my opinion. You just cannot get close enough to the hooks and eyes. That projection on the side is in the way.\nThere is one small item that I use that keeps me stitching parallel to the edge of the fabric. The Sewing Edge is a simple piece of PVC (or some such plastic-y substance) that sticks to your sewing machine bed and keeps your seam allowances exact. Place it where the edge of the fabric will run and it will stick until you remove it. It's that simple!\nSome would argue that this notion could take the place of the quarter inch foot since it can keep you stitching an even seam allowance. In fact, some might say that it could also replace the edge stitching foot as well. Why? Its thickness keeps the fabric where it belongs, which allows you to stitch right next to the edge, such as topstitching around a collar, for example. However while this handy guide will do those things, it won't do everything. Its best purpose is to keep you stitching parallel to the edge when the edge is far from the needle.\nWhen you lay the fabric up to it, the thickness of the Sewing Edge keeps the fabric running smoothly but it is not so thick that it gets in the way or your hands or any snips that might be around. I use it a lot when I am making swimsuit straps with elastic inside. The stitching has to be exactly parallel to the edge of the fabric otherwise the strap looks wavy.\nSo there you have it, how to sew bras with your feet! Do you have these feet in your collection? Which ones do you rely on for bra-making?","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Swedish brand Mini Rodini launched Isola Bella, the SS17 collection inspired by the eponymous island in the Italian Lake Maggiore.\nThe collection is filled with sunbathing marble lions and unicorns, accompanied by the scent from blooming roses, the sound of rippling fountains and the first rays of sun in the morning.\nPieces for children aged 0-11 years, are 99% made with sustainable materials.\nIn particular a new heavy knit yarn made of recycled denim products has been used in the designing process.\nOnce again, Mini Rodini makes clothes for children that match their own personality, mood and creativity.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"You can program with high agility and end up with a robust, maintainable program. This talk will show you how to use Clojure and the new spec library to write programs that behave as expected, meet operational requirements, and have the flexibility to accommodate change.\nClojure's new spec library augments these approaches. Developing with spec is declarative, predicative, layered, robust, and integrated with Clojure.\nspec is declarative. As with type systems in static languages, spec lets you make declarative statements that communicate and document data, function arguments, and returns.\nspec is predicative. You can declare predicates about data, about function arguments and returns, and even function semantics. This overlaps not only with type systems, but also with validations that are often done with costly bespoke tests and runtime checks.\nspec is layered. Spec does not require any specific workflow or program shape, and in particular is compatible with iterative and incremental development.\nspec supports robust programs via automatic generative testing. Given specifications, spec can write generative tests for you, generating a volume of tests limited only by your CPU time, not by what you are able to write and maintain by hand.\nspec is fully integrated with Clojure. As you develop your program, you have interactive access to spec-driven documentation, validation, destructuring, conformance checking, sample data, testing, and program instrumentation.\nStuart Halloway is a founder and President of Cognitect, Inc. He is a Clojure committer, and a developer of the Datomic database. Stuart has spoken at a variety of industry events, including StrangeLoop, Clojure\/conj, EuroClojure, ClojureWest, SpeakerConf, QCon, GOTO, OSCON, RailsConf, RubyConf, JavaOne, and NFJS. Stuart has written a number of books and technical articles. Of these, he is most proud of Programming Clojure.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzxfdt b/data_all_eng_slimpj/shuffled/split2/finalzzxfdt
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index 0000000000000000000000000000000000000000..6a2bfdf883719684295329306b190b5fe6b3374f
--- /dev/null
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@@ -0,0 +1,5 @@
+{"text":"Re: Hi compression need more battery power?\nJust get one with more cranking amps.\nif the current batterycan't crank the engine over, it's either drained or at the end of it's life.\nget a new battery for your car. doens't have to be fancy.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"No pre-payments - No account to open - No Extra Bills - No Credit Cards. If you want to save serious money on your phone bill, it's time to start using cheapertalk for all your international calls and calls to UK mobiles. By using our access numbers you will benefit from low-cost phone calls, without having to register or prepay.\nDial the access number for the country you would like to call.\nNow dial the international number to get connected that's all!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Hottest baby and Kids clothes, big quantity in stock, keep Fast shipping Always!\n1. Quality assurance! Cheap, because we have our own factory production design.\n2. Be sure to shop our collection, we will continue to update AliExpress latest explosion models!\nVery cute and lovely, same as picture superfast shipping, came in about 2 weeks.\nOnly 11 days to Holland. Size 18 months, pants is a little bit shorter than noted in size chart but that's ok because my girl is short as well. Fabric looks very nice and the colors are pretty!\n3 M ordered and in the shirt condition 60. But this is more correspond with 74. And maybe even bigger.. The hoofdbandje is bad finished, please see photo! Called reasonably fast within.\nGreat costume!!!! Came to sochi in 12 days.\nAwesome set! great quality and quickly delivered. I bought it bigger for later. But size seams perfect!\nA beautiful set, for 7 months the size of 9 m was perfect. Two consecutive ordinary washing withstood.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Porter Cable US58 22 Ga., 5\/8\" Upholstery Air Stapler.\nSo small, so light, but so powerful-what a delight to use. It's just perfect for the professional upholsterer and the home do-it-yourselfer, too. Because it's so compact, it fits nicely into tight spaces, and its super light weight means no fatigue, even in the awkward positions upholsters can find themselves. We didn't experience any misfires or jams, but if they happen, just release the magazine and the driver blade guide retracts. We like the convenience of the end-load magazine, and because the staples are so thin, you get an impressive 185 loaded in the magazine, which of course means fewer stops to reload. And just like Porter-Cable's more ambitious nailers, this one's got a directional port to keep the exhaust off you and your workpiece. While it's in name an upholstery stapler, we think you'll find a lot more uses for this little worker.\nIncludes Stapler, 1\/4\" male quick plug with dust cap, Oil, Operating manual.\nCoilhose Pfe60256T Flexeel Hose, 3\/8 X 25' (2) 3\/8 Mpt Ftgs Makita Mac700 2 Hp Air Compressor (Hot Dog) Makita Mac2400 2.5 Hp Air Compressor (Twin Stack) Coilhose Atl016 Air Tool Lubricant, 16 Oz.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"I was hesitant about buying these but I am glad I did. They are so comfortable. They have a bit of a smell when you first open them, so let them air out for a day or two.\nGet a taste of cool island breezes with this new collection of Tommy Bahama bedding. The fabric is crafted with a breakthrough combination of cotton and nylon, which offers a cool touch feeling and helps to wick moisture away. The outside features an Aegean wave design complimented with blue piping and a 2-inch gusset, complete with the famous marlin embroidery logo. Matches to Overstock item 23886829 to complete the look of your bed.\nTalk about plump, sink head into, supportive, soft and quilty -- this is definitely the pillow for you! For the last decade I have purchased only Tommy Bahama pillows, and this Cooling Nights version really doesn't overheat -- I don't know how they do it, but it stays cool and comfortable all night long!\nI'm a picky sleeper and living in FL means warm nights - this pillow delivered! I didn't expect it to be cool all night - so first 15 minutes felt great and I was sleeping!\nThe pillow was too high for my husband causing a stiff neck in the morning. It was ok for me because it allowed for some molding into a comfortable shape (my favorite pillow was down but somebody was allergic to it). As for being a \"cooling\" pillow it is. As long as you turn it over. I didn't think it was any different than other pillows I've had. Overall a nice pillow but undeserving of being labeled \"cooling\".\nThese pillows are exactly what I've been looking for! I wanted something similar to My Pillow without the high cost and I found it In these Tommy Bahama! I've tried so many different kinds with varying degrees of luck and I am thrilled with these. They wash up beautifully too!\nI purchased this pillow for my master bedroom and I love it. It does stay cool most of the night and fluffs up nicely. It's not too firm just right.\nThis pillow was so amazing, we bought two. It is very full so probably wouldnt work well for a stomach sleeper. We side sleep and they arr absolutely perfect. Great quality and they held up well in the washing machine and dryer. Very comfotable and not at all lumpy.\nThis pillow does have good support! As far as the cool aspect of the pillow it is cooler than some of down alternative pillows but still holds a lot of heat. The good thing is if you flip it often while sleeping it stay fairly cool.\nThese pillows are perfect! Just the right amount of support and are cool throughout the evening!\nToo soft, but good quality.\nLove them, am purchasing a couple more for the guest bedroom.\nI LOVE these pillows.. they don't really cool, but they are super comfy and love them.\nGreat pillow! Bought for use in a vacation home & will definitely order again for use at home. They have good \"loft\" & are very comfortable (I am a side sleeper).\nCool pillow. I live in hot south texas.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzxhqj b/data_all_eng_slimpj/shuffled/split2/finalzzxhqj
new file mode 100644
index 0000000000000000000000000000000000000000..4b8690c1e7a64bb81a400bdb96fb1f8993d5e66c
--- /dev/null
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@@ -0,0 +1,5 @@
+{"text":"Home > Businesses beware: no unfair contract terms allowed!\n15 Apr Businesses beware: no unfair contract terms allowed!\nDoes this sound familiar to you? If yes, chances are you may have this in your business' terms and conditions or you may have seen this on a template you can grab online for free or at a low price. What you might not know is that the Australian Competition and Consumer Commission (ACCC) has recently established a high success rate in their actions challenging unfair contract terms in a variety of standard form consumer contracts.\nThe unfair contract terms (UCT) provisions of the Australian Consumer Law (contained in Schedule 2 of the Competition and Consumer Act 2010 (Cth)) was introduced in 2010 for consumer contracts and now extends to small business contracts.\nAccordingly, it may be a good idea for your company (whether a start-up or an established business) to think twice before downloading and using a free set of terms and conditions you find online.\nThe UCT apply to a consumer contract that is a \"standard form contract\" for the supply of goods or services \u2013 one that has been prepared by one party (usually the business) and is not subject to negotiation. You see this often when downloading a mobile app or software with \"I agree\" button showing a hyperlink to terms and conditions, or when signing up for services offered by e-commerce, telecommunication or delivery businesses.\nare required or permitted by law.\nWhen is a term considered 'unfair'?\nwould cause detriment to a party if it were applied.\nThe UCT provisions may apply in circumstances where terms and conditions of an online platform are hidden in fine prints or written in complex legalese and 'over the top' technical language.\na term that substantially limits the consumer's right to sue the business.\nA UCT claim can have a detrimental effect on your business' reputation. You should note that there is no one size fit all approach and it is crucial to make sure that your terms and conditions don't get caught up by the UCT provisions.\nWe have lawyers who can assist you to navigate the changing commercial and contracting landscape. Please do not hesitate to contact us.\nDISCLAIMER: We accept no responsibility for any action taken after reading this article. This is a guide to give you a better understanding of the Australian Consumer Law only and is not a substitute for the expert legal advice you can get from marshalls+dent+wilmoth and other relevant experts.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"A while back, I won an online giveaway hosted by Naturally Savvy. I received four products from Ecover and I was super excited because I love Ecover! Their dishwasher tablets (available at Costco) are the only natural product that I've found that works well on our dishes and their laundry detergent smells nice and cleans well too.\nI can even buy Ecover here in Hong Kong. I use the multipurpose cleaner all the time. Because you dilute it yourself that big bottle lasts forever!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This double top-tube Brooklyn Bike Driggs 3 is a classic design with an added second horizontal support that increases the strength of the frame. The triangle, the traditional form of the bicycle frame, is the perfect structure for evenly distributing rider weight and pedaling forces. Additional height in the head tube interrupts this form, thereby weakening the structure. By adding a second, lower tube, the triangle is reestablished. This doubling allows for lighter steel to be used while still ensuring the strength of the bike. It's not a new design, nor one that you'll likely see replicated outside of city bikes, but it's a unique design that is perfect for the urban or coastal commuter looking for something different.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Village Board of Trustees meeting minutes are available back to 1915 and agendas date back to 1989. Click here, select the \"Board of Trustees\" folder, and then either the \"Minutes\" folder or \"Agendas\" folder.\nDiscussed regulations relating to tobacco, electronic cigarettes and alternative nicotine products. The Board is considering a temporary moratorium village-wide on any new business that has tobacco and nicotine products as a principal use until the Village Board has received a report from staff and evaluated the issues.\nGave final approval to ordinances amending the Municipal Code relating to the regulation of sweepstakes machines and the licensing and regulation of raffles.\nAuthorized execution of a one-year contract extension with ADS, LLC of Huntsville, Ala. for $53,000 for water system leak detection and survey services in fiscal year 2019.\nRatified an emergency purchase with Cummings NPower LLC of Hodgkins, Ill. for $25,442 to emergency generator repairs at the Laramie pump station.\nAuthorized execution of a two-year contract with two one-year extensions with Schroeder & Schroeder, Inc. of Skokie for $548,068 annually for concrete flatwork repair services.\nAuthorized execution of a one-year contract with two one-year extensions with Precision Pavement Marking, Inc. of Elgin for $25,210 for pavement marking services.\nAuthorized execution of a contract with Baxter & Woodman, Inc. of Crystal Lake for $398,365 for GIS\/GPS field data collection services, and to amend the 2019 annual budget in the amount of $178,365 to complete the project within 2019.\nAuthorized a contract award to Construction & Geotechnical Material Testing, Inc. of Elk Grove Village for up to $63,645 for independent pavement material testing services.\nAuthorized a bid award to J.A. Johnson Paving Co. of Arlington Heights for up to $1,502,173 for fiscal year 2019 road resurfacing and the Minor Area Repair Strategy (MARS) program.\nAuthorized execution of a contract with Semper Fi Land Services, Inc. of Yorkville for $530,265 to construct the River Drive retaining wall improvement project. The approximately 40-year-old wall southeast of River Drive and Glenview Road along the West Fork of the North Branch of the Chicago River was found to be deteriorating, and 200 linear feet will be replaced with concrete blocks, along with replacement of a fence and new landscaping.\nPreliminarily approved an ordinance for conditional use for Congregation Ahavat Olam to allow portions of Anthem Memory Care, 1879 Chestnut Avenue, periodically as a facility devoted to religious worship. The operation of religious facilities is permitted only as a conditional use in residentially-zoned areas.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Menu Bar On Web Expression Integration with popular web authoring software.\nWebsite Templates | Web Page Templates | FrontPage Templates Download premium Website Templates. Compatible with Dreamweaver and Frontpage. Customization service available through our team of Website Template designers.\nDreamweaver, Frontpage, Expression Web, CSS and Golive website Professional low cost website templates for Frontpage, Dreamweaver templates, Expression Web, CSS and Ecommerce.\nFrontpage Templates from The Template Store - Professionally Frontpage templates and Dreamweaver, CSS, Ecommerce and Expression Web website templates.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzxrbd b/data_all_eng_slimpj/shuffled/split2/finalzzxrbd
new file mode 100644
index 0000000000000000000000000000000000000000..d5ac1922d8e6dd3621bc4ef97f5f394dae56b775
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@@ -0,0 +1,5 @@
+{"text":"Click here for audio of Episode 675.\nTomorrow, I go to honor a change in our way of life. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.\nTomorrow afternoon I fly up to Dallas. I'm representing The American Society of Mechanical Engineers at a dedication ceremony. We designate historic engineering works as Landmarks.\nLast year we dedicated the first windmill in Texas and the first fully air-conditioned building in America. These ceremonies are fun. They remind me how engineering touches our lives.\nYou expect things like the first windmill and the first air-conditioned building. But many of these machines you might never notice. Tomorrow we dedicate one like that. It's called Abacus II.\nThat has little to do with the ancient abacus. It's not a gadget that lets you do arithmetic by moving beads on wires. Instead, this is the first machine that automatically made integrated circuits -- the great-grandchildren of the old abacus.\nThe circuitry for a pocket calculator, or for a computer, is printed out on a chip. It's so small. The calculator on my wrist watch would've filled a room in the radio-tube days of 1950.\nThe trouble is, you have to connect tiny wires to that tiny circuit chip. You have to communicate with it. How do you weld the wires in place? The wires are gold, only a thousandth of an inch in diameter. You have to place them within a 4000th of an inch. Then you have to melt the gold and bond it in place.\nTexas Instruments Company made Abacus to do that in 1970. Abacus used its own computer to weld wires onto an array of chips, automatically.\nTwo years later, TI made the Abacus II production model. It could weld 375 chips an hour. Later versions did 800 an hour. TI kept making Abacus II for ten years. Then they replaced it with fancier machines.\nNow we go to Dallas to honor a thing that looks like a desk with a computer screen and a microscope on it. You could pass it in the hall without seeing it.\nBut this Abacus II carries Serial Number One. TI put it to work in Sherman, Texas. Then they sent it to Taiwan -- then Brazil. They did a little upgrading. It has a newer alignment mechanism. But this is where our age of affordable computers began.\nIt stayed in use for 13 years. This one machine has produced more than fifty million integrated circuits -- fifty million computer brains -- fifty million agents of change. Add the thousand Abacus IIs that followed, and you've completely changed our civilization. Tomorrow, in Dallas, we'll celebrate the way a team of thirteen design engineers altered human history.\nHere is what Abacus II had to attach wires to.\nit contains over 16 million memory cells.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The LV Satellite sunglasses have a distinctive contemporary aesthetic. They are accompanied by a sun clip, which can be attached or removed to create two different looks. With a square-shaped frame, this piece features subtle LV Initials on the temples and lenses, as well as the iconic V motif, for a signature finish.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Montreal Nationals are on fire in the Global Poker League, and they are the first team to score 100 points this season. The milestone was achieved by Jason Lavallee after winning his first heads-up game vs. Anthony Zinno.\nLavallee went on sweeping the match, addding six more points for the Nats. Earlier that week, WSOP 2014 Main Event Champion Martin Jacobson had earned the team 10 points by finishing third and first in the 6-max matches.\nIn Thursday's Heads-Up Match of the Day, we saw Tom Marchese of the New York Rounders battling Olivier Busquet of the LA Sunset. It was Busquet who won the match by a 2-1 score. Adding 6 points to the team's total. His teammate Fedor Holz scored 10 points on Tuesday with a first and third place finish in the 6-max matches.\nNot often in the last eight weeks have we seen a team use just one player for both 6-max matches and the heads-up games. Joao Bauer was clearly on duty for his team this week, and he did fine by scoring 12 points in total, evenly distributed over the 6-max and heads-up games vs. Rush manager Faraz Jaka.\nOn the 6th of June, the Global Poker League will be back with the Summer Series, live from our Las Vegas Studio, where all teams will play heads-up games in a cross-Conference setting.\nNow, we have 10 days to build a studio in Las Vegas to host the first live @GPL match. Slightly challenging, but we will be just in time.\nReplay, Highlights and key hands of all matches this week can be found on the match pages.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"We were looking for one Persian rug and by chance ended up at Leon Norell Rugs warehouse. We were overwhelmed by the choice and quality of rugs on display all of which was very well organized. Moreover, we benefitted from the vast experience and knowledge which Leon and his partner took time to share. Because of the substantial choice on offer, it took it quite a while to make a decision but not at any moment did were pressured and Leon and his time took their time to allow us to review many rugs. In the end we walked out with more rugs than we had planned to buy but very happy with the product and the excellent service and experience. I would recommend Leon and his team unreservedly.\nThe team also carried out a range of alterations that we had requested to a really high standard. Overall, we are extremely happy!\nLeon and the team were a pleasure to work with. We were looking for quite specific pieces, and a bespoke application...and their patience, advice and huge range, meant we were able to achieve exactly what we had envisaged. Looking forward to working with them all again.\nLeon knows this business inside out. We took a photo of our existing carpet which he identified and gave us the full history of this type. He then spent a great deal of time, showing without pressurising us his massive stock. We are delighted with the quality and price of of our carpet purchase. It has been in our dining kitchen (away from cooking) for a few years now and still looks fantastic!\nI would recommend this company to one and all.\nI'm an Interior Designer based in Berkshire and have been working with Leon Norell for over 10 years. He is honest and trust worthy and in today's highly ruthless world of business he is a rare find and a joy to work with.\nHis knowledge is endless and he will always find me the best carpet for my Client Projects at competitive prices.\nWhether traditional or contemporary Leon has the contacts and the ability to find the right pieces for domestic or commercial situations.\nLeon Norell and his team give excellent service both for deign and customer experience. The range of carpets and rugs are beautiful and we would thoroughly recommend using them. Mark from Chelsminster.\nIt was a pleasure dealing with Leon from start to finish!\nI certainly can recommend Leon to all.\nI am a London based Interior Designer and Leon has supplied oriental carpets to both my clients and myself. Leon is a knowledgeable, and trustworthy supplier in a world of carpets in which most of us have little expertise. Highly recommended.\nMr Norell took great trouble, and gave me good advice, in choosing a rug, to be given as a present, within the price range I specified. The result had been a complete success. I would recommend him to others in my position.\nI'd been looking for ages for a rug before I went to Leon. He patiently showed me lots of rugs, before an unusual one caught my eye. He let me take it home to see what it looked like in situ and then I bought it. It is perfect for the room and house! I never thought I'd find anything as special. 5* service, highly recommended.\nI had a large, difficult space to fill: Leon brought over several very well selected examples having discussed my likely tastes\/needs in advance. One was just the bill and I bought it without any hassle. Very happy to compliment Leon on his service and to recommend him.\nWe were looking for two large carpets and spent a lot of time with Leon going through options and looking through his huge collection. We found Leon exceptionally helpful and knowledgeable and he helped us narrow down choices with great skill. Nothing was too much trouble. He delivered a selection of carpets to us so that we could try them before buying and when we couldn't find a particular style in the size we wanted he was able to commission one for us. We are delighted with the carpets and the service and would recommend Leon without hesitation.\nWe came upon Leon Norell Carpets from an internet search, and arranged to visit the warehouse, a journey of about eight miles. We have some previous experience of purchasing Oriental carpets and had been looking around for a room sized carpet for a reception room. Mr Norell dealt with us personally, and offered an excellent choice. We settled on a Kashan, which he was happy for us to take initially on a sale or return basis.\nWe were also thinking of replacing the runner in our hall. This needed to be longer than many on the market, and we had fairly specific requirements as to width. We returned, and again Mr Norell dealt with us personally. From his vast stock, he was able to offer us several choices that fitted our measurements. We settled on a Hamadan, also initially offered on sale or return.\nBoth have proved to be excellent choices.We were very impressed by the range of the stock, the courteous and unpressurised service, and Mr Norell's concern that we should be completely happy with our purchases. We felt that both purchases represented good value for money, and the journey was well worth making. We are very happy.\nWe found Leon on the internet and were very pleased with our visit and purchase of our carpet. We found Leon and his partner very polite, knowledgeable and helpful, it was really pleasant to discuss our requirements and be guided in a friendly and relaxed atmosphere with no hint of unwanted sales pressure. We will require another carpet in the near future and will definitely return to Leon's for that. We will be recommending Leon to family and friends.\nHuge selection of quality rugs to choose from. Friendly staff who where very helpful and knowledgeable. Excellent service and we wouldn't hesitate to using them again.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Developers from SAP Labs Israel have created an app that could ultimately lead to the development of new treatments for ALS. In memory of Zohar Rosenblat who died in July 2017.\nAlthough the disease was first diagnosed over 150 years ago, there is no known cure for amyotrophic lateral sclerosis (ALS), also known as Lou Gehrig's Disease, a neurodegenerative disease involving the motor neuron system.\nALS continues to confound researchers, and one of the main reasons is the lack of reliable data from patients. Unlike diseases such as multiple sclerosis, which involve episodic deteriorations to the sufferer's condition, ALS is a progressive disease in which there is a continuous deterioration at a relatively uniform rate, varying from patient to patient. Doctors usually assess the patient once every three months, but this becomes more difficult as the mobility of the patient deteriorates and they elect not to come to the clinic.\nA volunteer group of software engineers from SAP Labs Israel are out improve the chances of a cure and are already playing an important part by mobilizing patients to track and log data about their condition.\nThe ice bucket challenge initiative from a few years ago led to increased awareness of the disease, but also a meeting between SAP Labs Israel and Prize4Life \u2013 an organization founded by ALS sufferer Shay Rishoni, formerly an award-winning sportsman. This, in turn, led to a \"hackathon,\" in which 35 SAP Labs Israel employees spent three days working on an application with the goal of supporting research into the disease.\nThe result was the ALS Mobile Analyzer, an app that enables patients and caregivers to easily collect and upload relevant patient data to healthcare professionals and researchers on a daily basis, all from wherever they are located. Besides providing objective measurements, the app also allows patients to easily fill out subjective questionnaires about their function and quality of life, providing a picture of how they are feeling in general.\nBut the benefits go beyond immediate patient care. One of the biggest obstacles to developing a therapy for ALS is the expense of clinical trials, much of which is related to the time needed to collect clinical data.\nDr. Marc Gotkine believes the app could even lead to the elusive cure for ALS.\nThe neurologist is not the only believer in the app's potential. The project has already been awarded a $100,000 grant from the Genesis Generation Fund.\nAs for SAP Labs Israel's team of volunteers, they are currently working on an add-on to the app, which measures the lifting of the patient's arms. SAP team lead Meirav Daniel is excited about the grass roots achievement from engaged employees. \"If in five years this will have resulted in a breakthrough, it will be a dream come true,\" she concludes.\nThe ALS Mobile Analyzer app is available for iOS and Android devices.","meta":{"redpajama_set_name":"RedPajamaC4"}}
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+{"text":"The app's memory score is 2.2 due to high memory utilization. Needs to be fixed as priority.\nThe app has a high performance risk for the phone manufacturer(s) LYF, YU, Motorola, Panasonic, Lava, Asus, Karbonn, Lenovo. Check coverage report for more details.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Based out of London, United Kingdom this mysterious artist has been on top of the game for many years now and he's been busy non-stop providing eye-candy to his loyal fan base. Imagine him as a chef, stirring up a touch of tattoo art, with a spoon of b-boy and b-girl attitude, tiny cut pieces of comic history, and a breeze of babes flavour. As a an example we present you this delicious looking Artist Papes designed by Viva La Vandal!\nAs soon as we laid eyes on him we liked what we saw and asked him in a flirting way, if he'd like to get involved in one of our Artist Papes edition. With the help of some charming words, whispered gently in his ear, we were able to finally convince him to collaborate with Babes Papes and join forces. Our long and intense relationship hit the climax with the birth of baby jesus, presented with this Artist Papes edition.\nThe final product does not only include the nice illustrations but also customized embossing such as the B-stamp and the braille stamping for example. This edition is limited to 250 booklets in total and if you want to have a piece of vandalism, then we recommend you to have a look here and get some of the good stuff.\nBig up for vandalism \u2013 yes, we van!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Alui will be attending the XBRL International Conference which is taking place 16-18 April at the Convention Centre, Dublin, Ireland.\nJoin over 200 of the world's leading experts in XBRL in the Convention Centre Dublin this April. XBRL is a global phenomenon that as a result of Ireland's Revenue Commissioner's implementation is now live in Ireland and will also be mandatory for companies filing with the Large Cases Division filing later this year.\nXBRL Ireland is hosting the 26th International Conference. The conference brings together the leading minds and personalities from the world of XBRL; experts, regulators, project leaders and filer.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"But the Sony hack does not meet the common definition of that term. The best current guidelines for when a cyber attack can be considered an armed attack come from the NATO Tallinn Manual. The manual's lead author has analyzed the Sony case and has concluded that it is not an armed attack.\nbefore we do something, well, stupid.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Because a circle's circumference provides the largest edge-to-area efficiency when compared to a rectangle or any other shape, HOTCAKES.com project tables are 20% more efficient in the take-up of office floor space, when compared with any other shape of desk. This brings many spatial benefits, such as freeing-up floor space for other collaborative and multi-functional uses. Some of the best things in life are round.\nPrevious postTHE END OF THE CALL CENTRE IS UPON US! Next postDON'T BE SQUARE. BE ROUND!\n\u00a9 2015 Hotcakes Blog. All Rights Reserved.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaafnt b/data_all_eng_slimpj/shuffled/split2/finalzzzaafnt
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@@ -0,0 +1,5 @@
+{"text":"It's your senior year, you've made it at last. The highschool is yours to rule and this year everything will be perfect. Everything, including your senior pictures. Yes, gone are the days of those tiny, generic yearbook pictures. Those are for the underclassmen. You are a senior now and only the best will do. Our goal is to give you just what you deserve, the best. We understand how important your senior yearbook photo is. That is why we compiled a list of the finest senior portrait photographers in the country including Lino Lakes, Minnesota. You WILL stand above all of the rest, not only because you are a senior, but because your senior pictures will be one of the best. Our photographers in Lino Lakes, Minnesota strive to capture what a lot of others can't see - the real you. We will not settle for the cookie cutter photos that some other Lino Lakes, Minnesota photographers take. We know that years from now you will open your senior yearbook and remember what was. Then you will not see a gawky teenager. You will see someone with style, someone with class, someone trendy. For when it came to choosing a senior portrait photographer in Lino Lakes, Minnesota you went with the very best.\nChoosing the right studio for your Senior Portraits can be overwhelming. It seems as if everyone with a camera is claiming to be a photographer. Ugh!\nCreate your portraits in the studio, in one the the numerous creative sets on-site, or let's take it on the road to an alternate location. David Grupa has the experience, the credentials, the skills and the style to create amazing images for you . . . and he will make you feel like a rockstar in the process.\nDavid Grupa is a proud and active member of the Professional Photographers of America (PPA), the Minnesota Professional Photographers Association (MNPPA) and the Twin Cities Professional Photographers Association (TCPPA). He hold the prestigious Master of Photography, Photographic Craftsman and Accredited Photographer degrees, and is one of just 37 Certified Professional Photographers in the State of Minnesota.\nDon't risk your time, money and image on \"pretenders\"; call David Grupa today to schedule your appointment!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Kelbie Home Improvement, Inc. has been providing reliable, quality roofing in Russett, MD since 1982.\nWhen it comes to a successful roof installation in Russett, our skilled Russett roofers do the job right, maintaining our commitment to high standards and customer satisfaction. We at Kelbie Home Improvement, Inc. have the Russett roofing expertise and dependability that you are looking for.\nWe offer the professional and surprisingly affordable residential and commercial roofing Russett MD residents demand. Give us a call today to see how we can help with your Russett roofing project!\nThere are many types of roofing materials available on the market to choose from. From flat roofs to shingles, Kelbie Home Improvement, Inc. has a proven track record delivering superior roofs. Let our experienced Russett roofers help you determine the right solution for your roofing needs and desires.\nIf you need roof repairs in Russett, don't hesitate to call Kelbie Home Improvement, Inc.! Whether you have a leaking roof, curling or missing shingles or cracking tiles, Kelbie Home Improvement, Inc. can assist you with those roof problems as well. We are the trusted resource for repairing roofs in Russett. You can be assured that your Russett roofing repairs will be done quickly and correctly with Kelbie Home Improvement, Inc..\nSince 1982, Kelbie Home Improvement, Inc. has provided residents with superior roofing in Russett MD. Let us help extend the life of your Russett roof! You can trust that Kelbie Home Improvement, Inc.'s roofers in Russett are as courteous as they are professional.\nContact Kelbie Home Improvement, Inc. regarding your roofing project in Russett, Maryland. Our Russett roofers will be happy to provide you with a competitive roofing quote and stand by the outstanding Russett roofing service that we deliver.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Ever fancied running away from it all? Vanishing somewhere remote? In The Last Snow by Arno Camenisch, Paul and Georg operate and maintain an unspectacular tow lift somewhere in Grisons. But few customers come because there's so little snow. In Nicolai Houm's The Gradual Disappearance of Jane Ashland, writer Jane Ashland camps in the Norwegian mountains. Her reasons for being there are slowly revealed as the plot comes to a dark and terrifying conclusion.\nSupported by Pro Helvetia (Swiss Arts Council) and Pushkin Press.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Recruiting newborns into cystic fibrosis studies is important to research, but there are no studies into how parents feel about including their recently diagnosed newborns in treatment studies. All infants underwent pulmonary testing between three months and one-year of age. Patients diagnosed with cystic fibrosis underwent additional testing as needed.\nQuestionnaires were distributed to parents at the 3-month testing and at the end of the 12-month period for infants who tested positive for cystic fibrosis.\nConclusion: About 86% of the parents of cystic fibrosis positive infants in the study responded positively when asked about participating in the clinical study. The control group, however, was more difficult to recruit. Only 29% of the parents of healthy infants agreed to participate in a study. The overall response from parents of children with cystic fibrosis was positive, which bodes well for research.\nSource: Chudleigh J, Hoo AF, Ahmed D, Prasad A, Sheehan D, Francis J, Buckingham S, Cowlard J, Thia L, Nguyen TT, Stocks J; on behalf of the London Cystic Fibrosis Collaboration (LCFC). Positive parental attitudes to participating in research involving newborn screened infants with CF. J Cyst Fibros. 2012 Oct 4. pii: S1569-1993(12)00174-9. doi: 10.1016\/j.jcf.2012.09.001.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Due to a water main break, the ACAR Office in Broadview Heights will be unexpectedly CLOSED for the remainder of the day on June 29, 2018.\nThe City of Cleveland began a three-day Rental Inspection Unit process at Park Place Apartments at 1435 East Blvd.\nThis inspection is being conducted by the Department of Building and Housing and the Cleveland Department of Public Health. All rental inspections aim to ensure that units are dry, clean, safe, well-ventilated, pest-free, contaminant-free, maintained and thermally controlled. If violations are found during the inspection, inspectors will issue violations to the landlord.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzabyty b/data_all_eng_slimpj/shuffled/split2/finalzzzabyty
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index 0000000000000000000000000000000000000000..a0e1bcfe39b560b2679288481240d08a987046ad
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@@ -0,0 +1,5 @@
+{"text":"This paper is the first to provide evidence about the relationship between bride price payments and fertility decisions in the African context. Remarkably, the results show that bride price payments reduce fertility pressure, with a woman reducing her number of children by 0.5 at the mean bride price. The results are robust to different tests that we conduct to address the potential endogeneity between bride price payments and fertility decisions. As possible transmission channels, we find that poor women and men with low levels of education are the most negatively affected by the tradition of bride price payments. Furthermore, a lower bride price payment increases fertility pressure in polygamous households and for arranged marriages, while the bride price payment has no effect on the couple's decisions concerning fertility in monogamous households and for love marriages. Consequently, given that bride price payments have less power over (economically) independent women, empowerment will give leeway to girls in traditional societies, even if the bride price system is not overturned.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The pendulum has swung and nerds are kings! Comic books, video games and Star (Wars\/Trek\/Gate) are more popular than ever!\nEvery Friday, Tyler Daniels, Raya Washington and Kyle Hudson dive into nerd culture's infinite caverns in search for golden nuggets of awesomeness.\nTyler Daniels, Host, is from Unionville, PA and West Chester University Graduate. He teaches Communication Studies at Delaware Community College and enjoys his job very much. His main passions are DC comics and B-movies, the cheesier the better. Sharknado, anyone?\nRaya Washington is a Philly native and a student at Temple University where she studies communications with a minor in sociology. She was geek before it was chic. When she was younger she wrote X-Files fan fiction (she was a shipper) and is still in an endless pursuit to prove we are not alone in the universe. \"THE TRUTH IS OUT THERE\"!\nKyle Hudson, Producer\/Host, is from Cranford, NJ and Full Sail University Graduate. He is an independent filmmaker and runs the Chester County Time Machine with the Chester County Historical Society. He is a passionate Trekkie, Marvel comic fan, and can't stand B-movies.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Keep moving! After you cross the finish line, spend around 10 to 15 minutes walking around in order to prevent cramping and give your legs time to cool down.\nHydrate, hydrate, hydrate. Water is good, but after such a long run it's best to re-fuel with a sports drink to increase your blood sugar levels and replenish your electrolytes.\nDon't forget to stretch. This is one of the most important things to do post-race and can go a long way in helping prevent future injuries.\nContinue to hydrate and stretch. If you are really sore, try using a foam roller for extra muscle relief.\nEat lots of fruits, carbohydrates and protein to help your body properly recover.\nIf you're up for it, you can get back to running the day after your race. That said, it's important to take it easy and not rush into serious training for at least a week.\nGradually add running into your every-other-day workouts until you are back to where you were before the half marathon. If you're training for another race, it's safe to jump back into full-on training mode around two weeks after the race.\nListen to your body and don't overdo it. Rest is a vital part of the recovery process so it's important to make sure you get a sufficient amount the weeks following your race.\nThanks! This was truly helpful! I sign up for my very first HM, this weekend! I've got several months until the race! Thanks, again, for a timeline!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"As the new ski season beckons, it's time to air out your woolly hats, blow the dust off your skis and grab a great deal to the slopes. In the chilly economic climate, the French Alps are still your best bet both for quality resorts and accessibility.\nJust a couple of hours' flight away from the UK, the French Alps offer a vast choice of resorts catering for absolute beginners, intermediates and pros.\nLocated in the Les Sybelles region of France, the resort of Les Corbier is purpose-built, compact and traffic-free. Designed in the 1960s by architect Le Corbusier, the resort has become the fourth largest ski resort in France. Nearly all of the accommodation is ski-in\/ski-out apartments and with two supermarkets in resort, self-catering ski holidays are a breeze. There are several bars and restaurants.\nHot deal: Pierre & Vacances Residence Maeva Les Pistes is located 500 m from the slopes, the ski lifts and shops and offers fully-equipped apartments with mountain-view balconies. A week in a one-bedroom apartment for up to four people, costs from just 199 Euros.\nChamonix is a much-loved ski resort due to the variety of outdoor activities you can participate in here. The summit of Mont Blanc is the third most visited natural site in the world and the mountains hosts activities such as ice climbing, alpine mountaineering and extreme skiing. There are all sorts of terrain, but this is the perfect destination for the expert winter sports enthusiast and the adventurous. Chamonix is famous for its cable car up to Aiguille du Midi as well as the panoramic restaurant at the top station of the Brevent cable car, which boasts impressive views of the Mont Blanc Massif.\nHot deal: The Residence Maeva La Riviera is located in the district of Chamonix Sud, 300 m from the Aiguille du Midi cable car and five minutes from the resort centre. Studio apartments for up to four cost from just 244 Euros for seven nights.\nValloire offers the combination of an old mountain village mixed with modern architecture. Valloire is the best known of the Maurienne valley resorts and its narrow streets, bustling shops and various restaurants makes it a charming location for your winter holiday. The slopes spread widely across three sunny sectors and are particularly good for intermediates. 70% of the Valloire\/Valmeinier ski area is above 2000m and it offers 150 km of slopes.\nHot deal: The Pierre & Vacances Chalets Valoria at Valloire is located on the heights, overlooking the valley and the resort. A high standard residence built in a style typical of the region; these spacious apartments are located 300m away from the ski lifts. Studios for up to four cost from only 279 Euros per week.\nThe French ski resort of La Clusaz is one of its kind as it is still, essentially, a genuine mountain ski village. This ski resort exudes rustic charm and an infectious Gallic atmosphere. La Clusaz offers 200km of largely intermediate slopes, above and below the treeline, and makes a fantastic base for an enjoyable, relaxed week.\nHot deal: Residence Maeva La Perriere overlooks the resort on the southern slope and is available at 320 Euros per week for a 4 person studio apartment.\nSerre Chevalier is one of the major ski resorts in France. Located in the Haute-Alpes region, Serre Chevalier is a large valley between the Lautaret and Briancon passes. Its 13 villages and hamlets, which blend tradition and modernity, are scattered across the valley with its large skiing areas covering 250km. The resort also offers a wide range of activities for the whole family, and with its large natural terrain is also considered one of the best snowboarding destinations in France. Serre Chevalier lies at the foot of the most beautiful peaks of the Ecrins National Park and boasts approximately 300 days of sunshine a year.\nHot deal: Residence Pierre & Vacances L'Alpaga, situated in the mountain village of Villeneuve, has comfortable, spacious apartments close to the shops and ski lifts. Studio apartments for up to four people costs from 378 Euros for a week's ski holiday.\nThe little known Isola 2000 is a ski resort in the southern region of the French Alps that offers great skiing for all levels. This modern resort's altitude is at 2000 meters and pisted runs reach the height of 2610 meters on the summit of Sistron where, on a clear day, it is possible to see the Mediterranean Sea.\nIsola 2000 has an excellent snow record too. Snowboarding is popular in Isola and there are plenty of 'board-friendly' lifts and a dedicated snowboard park. There are lots of shops, bars, clubs, restaurants and supermarkets adjacent to the slopes and there are numerous cafes and restaurants should you wish to take a break and bask in the Mediterranean sun.\nHot deal: The Pierre & Vacances Les Terrasses d'Azur residence in Isola 200 is in perfect keeping with the resort's natural environment of pines and larches. It overlooks the resort and is close to the ski runs and shops. The apartments are very comfortable and have a panoramic view over the skiing area and the Chastillon valley. Studio apartments that sleep up to four people cost from just 441 Euros per week.\nLes Carroz d'Araches is an expansive, sunny and traditional resort with plenty of terrain to suit everyone. It has the lived-in feel of a real French village and its array of pavement cafes and restaurants around the main square offers a homely and lively atmosphere.\nThe resort caters particularly well for families, offering excellent facilities for children so is perfect for a family ski holiday. There are good woodland runs immediately above the village for bad-weather days, with a scenic setting to enjoy when the sun shines.\nHot deal: Pierre & Vacances Residences MGM Les Fermes du Soleil is a luxury 4-star residence, just a stone's throw from the centre. Each apartment is designed to offer you maximum comfort with large bay windows giving exceptional views over the village, the valley or the skating rink. The closest ski lifts, 800m from the residence, are accessible via a free shuttle bus. One-bedroom apartments for 3-4 people cost from 630 Euros per week.\nFlaine is a high-altitude resort sharing a big, broad area of varied slopes with more rustic alternatives. Flaine is a resort proud of its Modernist and artistic design, which is a dramatic contrast to the natural landscape of the French Alps. As well as the architecture, several large public art works adorn the base of the resort, including a Picasso.\nLoved by many, due to the extent of its ski area and range of runs, this is a resort ideal for intermediate skiers as well as being one of the most family-orientated ski resorts in Europe.\nHot deal: Pierre & Vacances Terrasses d'Eos residence is a brand new addition to our ski residences for the 2009\/10 ski season. Built in 2008 by Intrawest, this top-of-range residence is located in a new, entirely car-free hamlet of Flaine Montsoleil and features 145 comfortable apartments.\nThe two buildings that make up the residence have direct access to the pistes and chairlifts, providing you with a direct link to the Flaine and Grand Massif ski areas.\nOne-bedroom apartments cost from just 572 Euros for seven nights and sleep up to four people.\nA great choice for first-timers and families, Valmorel is a purpose-built French ski resort comprising several small satellite villages in the Grande Domaine. Valmorel and St Francois Longchamps together offer 165km of marked pistes.\nValmorel's resort centre is car-free and it also scores top marks for families as most of its pistes cater for beginners and intermediates, and there are plenty of designated practice areas. The ski area is on your doorstep which means you can literally ski to your door \u2013 another big plus if you're skiing with kids. While it is great for families, those who also want lively apres-ski should go elsewhere as there are only a handful of restaurants and bars.\nHot deal: P&V is offering seven nights in a studio apartment at Residence Maeva Planchamp et Mottet in Valmorel from just 405 Euro.\nBest for: thrill seekers and skiers of all levels.\nHome to La Sarenne, which at 16km is Europe's longest ski run, Alpe d'Huez is often thought to be the sole preserve of ski pros and adrenalin junkies. While the infamous 'Tunnel' run remains a must do ride for experienced skiers, the resort also has a good choice of gentler runs for beginners. The best of the less challenging slopes are found on the outskirts of the resort and there are plenty of blues and reds for intermediates.\nSituated in a large sunny bowl, Alpe d'Huez is known as the 'l'Isle au Soleil' ('The Sunny Island') thanks to its high levels of sunshine throughout the year.\nThis resort is a great choice if you're travelling in a group which has mixed abilities \u2013 leave the pros to La Sarenne while the novices play it safe.\nHot deal: Situated in Les Bergers district of Alpe d'Huez, the Pierre & Vacances Bergers residence has comfortable apartments and a heated outdoor swimming pool. Seven nights in a studio that sleep 3-4 costs just 405 Euros.\nAll P&V residences featured are ski in\/ ski out and are self-catering apartments with fully equipped kitchens and cooking facilities.\nPierre & Vacances have also just launched a euro-busting offer which means customers can save up to 35 percent off all ski resorts throughout the winter season. This means, if you book fast enough you could be saving a third and spend just 55% for a weeks accommodation! And it gets better\u2026this major ski discount can be used on all dates throughout the winter ski season including the school holidays, Christmas and New Year.\nThe Eurobuster deal can also be combined with any other P&V deal currently on offer, including the 20% early booking discount, leading to savings of up to 35% on your winter ski holiday.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Two Rivers Bancorp (NASDAQ:TRCB) has earned an average broker rating score of 2.00 (Buy) from the two analysts that provide coverage for the company, Zacks Investment Research reports. One analyst has rated the stock with a hold recommendation and one has assigned a strong buy recommendation to the company.\nBrokers have set a 12-month consensus price target of $20.00 for the company and are anticipating that the company will post $0.32 earnings per share for the current quarter, according to Zacks. Zacks has also given Two Rivers Bancorp an industry rank of 171 out of 255 based on the ratings given to its competitors.\nSeveral analysts recently issued reports on TRCB shares. ValuEngine upgraded Two Rivers Bancorp from a \"sell\" rating to a \"hold\" rating in a research note on Wednesday, January 2nd. Boenning Scattergood restated a \"hold\" rating on shares of Two Rivers Bancorp in a research note on Tuesday, January 29th. Finally, Zacks Investment Research downgraded Two Rivers Bancorp from a \"hold\" rating to a \"sell\" rating in a research note on Saturday, February 2nd.\nTRCB stock opened at $16.28 on Friday. The company has a current ratio of 1.03, a quick ratio of 1.01 and a debt-to-equity ratio of 0.28. The company has a market cap of $141.75 million, a P\/E ratio of 12.43 and a beta of 0.44. Two Rivers Bancorp has a 1-year low of $11.54 and a 1-year high of $19.90.\nTwo Rivers Bancorp (NASDAQ:TRCB) last posted its earnings results on Tuesday, January 29th. The financial services provider reported $0.35 earnings per share for the quarter, topping analysts' consensus estimates of $0.33 by $0.02. The business had revenue of $10.62 million for the quarter, compared to analyst estimates of $10.64 million. Two Rivers Bancorp had a return on equity of 10.07% and a net margin of 22.40%. Equities analysts forecast that Two Rivers Bancorp will post 1.33 EPS for the current year.\nThe company also recently declared a quarterly dividend, which was paid on Thursday, February 28th. Investors of record on Wednesday, February 6th were paid a $0.055 dividend. The ex-dividend date was Tuesday, February 5th. This represents a $0.22 annualized dividend and a yield of 1.35%. Two Rivers Bancorp's dividend payout ratio (DPR) is presently 16.79%.\nA number of institutional investors and hedge funds have recently added to or reduced their stakes in TRCB. Vanguard Group Inc lifted its position in shares of Two Rivers Bancorp by 0.4% during the 3rd quarter. Vanguard Group Inc now owns 236,637 shares of the financial services provider's stock valued at $4,103,000 after acquiring an additional 900 shares during the period. Maltese Capital Management LLC lifted its position in shares of Two Rivers Bancorp by 286.9% during the 3rd quarter. Maltese Capital Management LLC now owns 225,000 shares of the financial services provider's stock valued at $3,902,000 after acquiring an additional 166,846 shares during the period. Cerity Partners LLC lifted its position in shares of Two Rivers Bancorp by 4.1% during the 4th quarter. Cerity Partners LLC now owns 128,126 shares of the financial services provider's stock valued at $1,955,000 after acquiring an additional 5,000 shares during the period. Dimensional Fund Advisors LP lifted its position in shares of Two Rivers Bancorp by 10.4% during the 4th quarter. Dimensional Fund Advisors LP now owns 121,984 shares of the financial services provider's stock valued at $1,860,000 after acquiring an additional 11,528 shares during the period. Finally, Raymond James Financial Services Advisors Inc. lifted its position in shares of Two Rivers Bancorp by 2.6% during the 4th quarter. Raymond James Financial Services Advisors Inc. now owns 61,282 shares of the financial services provider's stock valued at $935,000 after acquiring an additional 1,525 shares during the period. Institutional investors and hedge funds own 23.18% of the company's stock.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzacjay b/data_all_eng_slimpj/shuffled/split2/finalzzzacjay
new file mode 100644
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@@ -0,0 +1,5 @@
+{"text":"Growing up in Santa Cruz, I fell in love with the Monterey Bay. Long beaches, sandy coves, whale watching, surfing, scuba diving, and so much more make this region a beautiful place that has captured the hearts of many. But as more and more people have discovered the Monterey Bay's peaceful allure, and as the tech boom from Silicon Valley has pushed commutes further and further south, the Monterey Bay Area has become as unaffordable as the San Francisco Bay Area.\nAlmost exactly one year ago, Landed announced our launch in Santa Cruz County. Since then, we've already helped 10 educator families in Santa Cruz County purchase homes locally with several dozen more in the homebuying process. We're also proud to have brought on new community partners, including a $1 million investment from the Community Foundation of Santa Cruz County and participation from Bay Federal Credit Union as a local lender.\nBuilding on this success, we are thrilled to announce that we're expanding to serve the full Monterey Bay by opening Landed down payment support to three school districts in Monterey County: Monterey Peninsula Unified, North Monterey County, and Pacific Grove.\nAny interested employees of these districts can now immediately apply for Landed down payment support.\nWe are also hosting an info session on Monday, November 26 at 4:30 p.m. at the MPUSD Services Center on Canyon Del Rey in Monterey. Interested educators can RSVP here.\nLead for New Market Partnerships and Business Development. Former campaign organizer, current volunteer leadership development trainer, and forever a seafood lover.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"True to tradition, the August issue of Windpower Monthly mainly comprises a detailed subject and headline index of all stories published over the past 12 months. It is a catalogue of more than 800 articles covering the political, industrial, technical and environmental issues which have shaped the wind energy market of the past year. As a succinct overview of trends and traumas, the index is a unique tool.\nThe grouping of article abstracts into subject categories makes it possible to chart ongoing stories as they have progressed since August 1999. Some of the biggest stories include: the near-collapse-and swift recovery of one of the wind industry's largest companies; Spain's booming market; a struggle between free and protected market ideologies in Europe; the great tax credit battle in the US; and the first major steps in offshore wind development. Trends to be tracked include the start of trade in emissions credits from wind plant and the growth of green power sales.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"02\/17\/2016 Log error for traceback.\n02\/16\/2016 Fixed error on Chrome, Edge and Safari. Added Matrix layout.\n02\/15\/2016 Auto-order is back. Preview updates according to protein order and color.\n02\/12\/2016 Color & width setting for inter & intra link.\n02\/12\/2016 Toggle between two display modes: 'preview' and 'rendered'.\n02\/12\/2016 Pattern discovery is back.\n02\/12\/2016 Relation plot is back.\n02\/11\/2016 Reconstruction for a responsive front-end (version 1.0.1).\n11\/17\/2015 Color fix. Updated \"About\" page. Updated license.\n11\/16\/2015 Seq function update. Fix color limitation. Updated network layout.\n11\/13\/2015 Bug fix. Updated new function.\n11\/10\/2015 New Function. Hit version 0.6.\n11\/04\/2015 New Function. Hit version 0.5.5.\n11\/03\/2015 New Function. Hit version 0.5.\n11\/02\/2015 Customized domain plot is now online. Hit version 0.4.\n11\/02\/2015 Fix link counts. Unique links are counted.\n10\/31\/2015 Optimization. Simplified templates. Hit version 0.3.\n10\/29\/2015 Bug fix. Implementation of new templates.\n10\/21\/2015 Small fixes of pages.\n10\/17\/2015 Added new function: correlation matrix. Hit version 0.2.\n10\/06\/2015 Added randomness into image file names for higher security.\n10\/06\/2015 Added \"Example\" page providing test data. Setup git on server for faster maintenance.\n10\/05\/2015 Updated \"Tutorial\" page to show that CX-Circos successfully depicted the architecture of the SEA complex.\n10\/04\/2015 Updated protein color setting. CX-Circos now accepts a protein complex with up to 50 subunits. The number will be further increased in future.\n10\/03\/2015 Updated \"Tutorial\" page. Added \"About\" page.\n04\/20\/2015 CX-Circos (v0.0.9) is rewritten with Python, and is available to users within Rockefeller University via an internal server.\n03\/11\/2015 A prototype of CX-Circos (v0.0.1) is written with Perl CGI.\n02\/14\/2015 The development of CX-Circos begins.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Fox 40 Boat Essentials Kit is what you need to have on board your personal watercraft. All the essentials housed inside an ergonomic corrosion proof plastic bailer, the kit includes all the minimum safety items. A brightly colored Fox 40 Marine incandescent waterproof floatable flashlight that is powered by 2 readily available AA batteries (not included) so that you can find your way in the dark.\nA Fox 40 pea-less safety whistle in the event of an emergency, it has a penetrating sound that can be heard over ambient noise. The harder you blow, the louder the sound. The chambers are designed to self-clear when submerged in water. There are no moving parts to freeze, jam or deteriorate. The whistle has a 90dB sound rating.\nA 50' (15.25 meter) Fox 40 Marine Rope & Float in case someone needs to be rescued. The rope is made from extra-fine polypropylene filaments woven into high-density braid. Rope was lab tested to 900 lbs. (408 kg) breaking point. The float made of expanded poly vinyl chloride for maximum toughness, weather-resistance and long service life. It all fits into a bright red waterproof screw-top environmentally friendly reusable container that acts as a bailer.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Yoseikan-Ryu Karate is excited to offer Cardio Fit classes at the Yoseikan Headquarters in Malaga. Run by personal trainer and karate instructor Adam Camuglia, Cardio Fit classes aim to get your heart healthy.\nWe have now added the very popular F45 Fitness Session to our HIIT program. Look out for CF45 (Cardio Fit 45) on Tuesday evenings until further notice.\nThe ideal full body strengthening and sculpting session. Tone Up is designed to improve your muscular strength and endurance, body tone, body shape and postural (core) stability. Tone Up is an essential component of the Cardio Fit program and when combined with the other sessions will leave you feeling amazing.\nAdam Camuglia recently completed his Certificate III in Fitness with the Australian Institute of Personal Trainers and is now using this practical knowledge to facilitate Group Exercise classes at the Hombu Dojo in Malaga. Coupled with his Sports Science degree (ECU) and over 25 years' experience as a Health & Physical Education Teacher (Mater Dei College), he endeavours to impart some fun and practical ways in which we can enjoy the benefits of exercise and steadily improve our health and fitness.\nJodi Margolis is currently studying undergraduate Medicine at the University of Western Australia. Her athletic background includes a year performing with an International Dance Company, a Black Belt in Karate, other martial arts and a host of cross-training sports to complement her active lifestyle of overall health and fitness. She brings energy, motivation and a smile to make exercising fun and enjoyable!\n1. Choose an exercise program you enjoy.\n2. Choose an exercise program you can dedicate time to.\n3. Choose an exercise program that will assist you reaching your personal goals.\n\"I also like the concept that our current Karate athletes training at the club can also incorporate Cardio Fit into their own training schedule and make them more competitive as a result.\"\nPlease print out and sign this form if you wish to join Cardio Fit.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaczdq b/data_all_eng_slimpj/shuffled/split2/finalzzzaczdq
new file mode 100644
index 0000000000000000000000000000000000000000..6f88f222e326689c31fa88f8e1094782e609bf73
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaczdq
@@ -0,0 +1,5 @@
+{"text":"What is purified water? Can you treat regular tap or distilled water to produce purified water to use in home facials?\nI don't know how water can be more pure than distilled water. Distilled water is condensed steam vapors; all impurities are removed.\nYou can make purified water by bring your water to a boil in a clean container. Bring the water to a boil then let it cool when it has cooled store it in a very clean container.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Masses of large blooms in a fabulous selection of brightly flamed bicolours that will create a blaze of colour in your borders and containers. Flowers February-May. Height 15cm (6\").\nMasses of large blooms in a fabulous selection of brightly 'flamed' bicolours that will create a blaze of colour in your borders and containers. Flowers February-May. Height 15cm (6\"). Supplied in 9cm pots.\nThis impressive spring flowering primrose mix will brighten your garden very soon and for years to come! Flowers February-April. Height 10-20cm. Supplied in 9cm pots.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This rare vintage Italian Bitossi Rimini Blue cachepot flower pot circa 1960 has a classic form. Tapered sides embossed with a series of tribal designs created by Aldo Londi is powerfully visual with its striking blue glaze. Please enlarge the photographs to see the handsome details of this useful piece of Italian pottery. Used to conceal the ugly container in which a growing plant lives this cachepot (French for hidden pot) remains as essential to a well furnished home as ever whether on its own as an object to admire or displaying a flowering plant. Retains the original label on the underside.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Outdoor High Table. Rather than the standard dining table, high top kitchen table is much more suitable for outdoor setting. The large chairs will take you to see the beautiful outdoor view more obviously. For outdoor setting, choose round shape top dining table and backless high stools to relieve the casual atmosphere.\nEither counter height kitchen chairs and also a trendy bar stool, high seats are going to be a fantastic addition for your kitchen. The casual style creates this type of chair very popular in modern houses. But just like any other furniture, you must choose your stool carefully so it combines perfectly with the total decoration. Here are 2 things you ought to do before buying a number of stools.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"An avid and enthusiastic knitter\/crocheter for more than 5 decades and a Craft Yarn Council of America Certified Instructor in Knitting and Crochet, Ginger teaches all levels of learners, using multiple approaches. Ginger's designs have been featured in national publications.\nPP8 Easy Cables, One Column at a Time Cables can be fun, but it's sometimes difficult to track the cable twists as you work across an entire row. In this class you will make a coaster by working one cable column at a time, adding more as you go.\nPP10 Easy Diagonal Knitting Learn to do diagonal knitting while you help the environment by knitting your own coffee cuff. This technique can easily be transferred to sweaters, scarves, blankets, and more. Must be able to knit, purl, increase by knitting into front and back of same stitch, SSK, and k2tog.\nPP11 Basic Broomstick Lace Broomstick Lace takes us back to the 1960's when larger yarns and more free-spirited crochet surfaced. Broomstick is fun for all but excellent for those with minimal dexterity since the tools used are large and easy to grasp. In class you will make a sampler to learn the technique. Must be able to single, double and treble crochet. Materials: 1 oz. #4 weight yarn for main color, one US 35 knitting needle, size I crochet hook, scissors, 24 6\/0 seed beads (optional).","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaeuoh b/data_all_eng_slimpj/shuffled/split2/finalzzzaeuoh
new file mode 100644
index 0000000000000000000000000000000000000000..9ef93c8bb91bba2142f374bd31639d5118094b81
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaeuoh
@@ -0,0 +1,5 @@
+{"text":"Alma Swensson Hall, an attractive three-story residence hall, was dedicated on May 30, 1949. It was occupied for the first time in September 1949, housing 77 female students.\nThe Women's Missionary Society of the Augustana Lutheran Church provided the initiative for the project by a grant of $5,000 as a memorial to Mrs. Alma Swensson, wife of Bethany's founder and a distinguished leader of the national women's society.\nNew Hall is coed by floor. No matter which type of room you live in, each bedroom is private. It's equipped with keyless entry and has multiple community spaces on each floor. Handicap accessible rooms are available.\nAnna Marm Hall is an all female hall with suite-style rooms. Each room has a separate sleeping area and study area (two rooms in one). Limited number of single rooms are available.\nGregory Hall is a coed hall by floor. Suite-style rooms with the bathroom in between each double room. The bathrooms have bathtubs! Limited number of single rooms are available.\nSwede Suites is the upperclassmen apartment complex on campus. It is coed by apartment. Each apartment is a four bedroom, two bath, with a living room, kitchen and laundry facilities.\nWarner Hall is an all male hall with suite-style rooms. Each double room is separated by the bathroom. The bathroom has double sinks and standing shower.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This template can be used to collapse parts of the \"Taxonavigation\" section, for better legibility. The template also adds an \"Expand\/Collapse\" link in order to show or hide the full list of taxon ranks.\nOnly use this on Familia template level within \"Taxonavigation templates\"","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"What does Bhavesh mean, details, origin, short & easy attributes?\nBhavesh or Bhavish or Bhavash (\u092d\u093e\u0935\u0947\u0936, \u0aad\u0abe\u0ab5\u0ac7\u0ab6) is a given Indian male name. It supposedly originates from the Sanskrit words bh\u0101va, which means \"existence\" and eesh, which means \"Ishvara\" \u0908\u0936\u094d\u0935\u0930 \"Lord, Ruler\". It means \"Lord Shiva\" as well.\nBhavesh is baby boy name mainly popular in Hindu religion and its main origin is Hindi. Bhavesh name meanings is Lord of the world, Lord of the universe, Lord Shiva.\nPeople search this name as Bhavesh.\nBhavesh is written in Hindi as \u092d\u093e\u0935\u0947\u0936. Other similar sounding names can be Bavisha, Bavishya, Bavyesh, Bhavish, Bhavisha, Bhavishya, Bhavyesh, Bhuvesh, Pavish.\nEach letter meanings in Bhavesh Name.\nPopular personalities with Bhavesh Name.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"I'm looking for someone who could create a logo f...also be connected with rather warm destinations. We don't want to chose our logo based on a portfolio but a real example of what you think it should look like. It can be a beta version or a sketch of it, we will decide on a freelancer based on this initial project of the our logo you will send us.\nProject is to create C\/C++ softwar...Developer will hand off to internal team for final integration. The dev hardware can be NXP Freedom K28F board (K28+16Mb DRAM) and any Intel (Altera) demo board for the MAX10 family. If you do not have this hardware, we can provide it for development. If we understand your experience, I will hire you immediately.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Andrew has worked with Parks & Trails Council since 2013. A graduate of Iowa State University and the University of Minnesota, his past work has spanned several disciplines \u2013 including outdoor recreation, tourism, and public health \u2013 and has been published in numerous research journals. With Parks & Trails Council his work is focused on better understanding how Minnesotans use and benefit from their parks and trails and informing Parks & Trails Council's legislative priorities. When not at the office, Andrew enjoys exploring Minnesota's trails by foot and by bike, relaxing with a cup of coffee, and following his favorite sports teams.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzafkdi b/data_all_eng_slimpj/shuffled/split2/finalzzzafkdi
new file mode 100644
index 0000000000000000000000000000000000000000..ee68fc62ae983d9e011e9d7d8194fbde1ded1cf8
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzafkdi
@@ -0,0 +1,5 @@
+{"text":"Written by Frances Kim. Updated Jan 12, 2017.\nIs your company aware that certain tax incentives expired within The Protecting Americans from Tax Hikes Act, known as the PATH Act? However, have no fear, there are still many components that are still active.\nEven though parts of the PATH Act expired, on the whole, green building tax incentives remain an important tax savings strategy for businesses. In direct proportion to the growing efforts to reduce energy consumption, companies that own commercial or industrial property will continue to need insight and guidance on green building incentives.\nThe section 179D deduction provides benefits for businesses, architects, engineers and contractors when they build or renovate a building that is energy efficient. In addition to the 179D deduction, the 45L tax credit also is not applicable in 2017. The 45L tax credit was applicable when building units provided a level of heating and cooling energy consumption that is lower than national energy standards. However, the good news is any project placed in service prior to 1\/1\/2017 is still eligible to have a 179D or 45L study conducted.\nAlthough some incentive programs expired, hundreds of other programs exist, specifically at the state and local level. For example, if your company invests in green building equipment, like energy efficient HVAC units or LED lighting retrofits, tax benefits are available to help with the cost of these projects.\nThe section 48 tax credit is still active for 2017. This green building tax incentive is for project owners and investors who install designated renewable-energy equipment. This is a 30% tax credit that is responsible for a significant increase in solar installations. Companies can qualify for section 48 until its' expiration in 2023.\nOutsourced tax consultants offer the expertise needed to achieve specific green building tax incentives; however, before looking to hire tax consultants, you also need to consider services in terms of capturing these credits and deductions for your clients.\nTechnically, a cost segregation study isn't required to capture green building incentives, but it's recommended because it helps with documentation as well as compliance with repair regulations. Also, the MACRS process used in a cost segregation study establishes a set of class lives for green building property investments that include solar, wind, water and geothermal renewable energy technologies.\nThis study is the best way to get detailed information on the costs and construction\/engineering specifics of your building. Additionally, the study naturally lends you the tax benefit of accelerated depreciation.\nFor more information regarding what tax incentives your company qualifies for, check out your state here and contact a tax consultant at Corporate Tax Incentives.\nAs one of the first CTI employees, Frances has held many key positions and has played an integral role in our diversification process. With more than 10 years in customer service and management, Frances' proven adaptability has enabled her to manage projects for clients ranging from small start-ups to Fortune 500 companies.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Image Title: Anderson Window Home Depot Patio Windows Sliding Glass Doors Intended For Prices Design 13. Post Title: Anderson Windows Prices. Filename: anderson-window-home-depot-patio-windows-sliding-glass-doors-intended-for-prices-design-13.jpg. Image Dimension: 580 x 329 pixels. Images Format: jpg\/jpeg. Publisher\/Author: msdathletics. Uploaded Date: Sunday - January 27th. 2019 19:06:16 PM. Category: Architecture. Image Source: bhg.com. Pella Vs Andersen Windows Cost 2019 Pros Cons ROI Throughout Anderson Prices Remodel 8. Check Out Our Andersen Window Price Guide For Some Great Customized Pertaining To Anderson Windows Prices Remodel 7. Andersen Windows 400 Series Prices Sale Window Replacement Guide Inside Anderson Plan 14. Andersen Window Costs Momhof Info Inside Anderson Windows Prices Decor 15. Andersen Windows Prices Dzuls Interiors With Regard To Anderson Idea 10. Anderson Window Home Depot Patio Windows Sliding Glass Doors Intended For Prices Design 13. Find Window Replacement Prices Brands Types Review Guide With Anderson Windows Decorations 16. Andersen Windows Prices Reviewed For Anderson Inspirations 0. 2019 Andersen Windows Prices Costs For Supply Installation Inside Anderson Designs 11. Anderson Window Home Depot Medium Size Of Windows Throughout Prices Idea 19.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"14 .\t(Then) shall each soul know what it has put forward.\n21 .\tWith authority there, (and) faithful to his trust.\n23 .\tAnd without doubt he saw him in the clear horizon.\n24 .\tNeither doth he withhold grudgingly a knowledge of the Unseen.\n25 .\tNor is it the word of an evil spirit accursed.\n26 .\tWhen whither go ye?\n29 .\tBut ye shall not will except as Allah wills,- the Cherisher of the Worlds.\nIn this page you can listen The Overthrowing, Extinguished! Wrapping Things Up in English, The Overthrowing, Extinguished! Wrapping Things Up and read and download The Overthrowing, Extinguished! Wrapping Things Up in English veya y\u00fckleyebilirsiniz. You can download The Overthrowing, Extinguished! Wrapping Things Up translation, get information on the interpretations of Quranic verses, download all translations of surah in pdf format. You can listen to the audio of The Overthrowing, Extinguished! Wrapping Things Up in English or read and download. You can also share English Quranic verses on Facebook and Twitter and other social media with share buttons.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Taking you - from inception to the fine details of implementation.\nDo you feel stuck in multitasking mode and know you could do great things if you could just spend some time to reflect and then strategize for optimal results or exceed your goals? At HGI we partner with you in providing the structures and services that will facilitate your success.\nToo often, companies define their business in terms of what they make or sell. This thinking limits their ability to grow beyond their immediate goals and tap into unlimited potential. Achieving transformational growth starts in the planning stage and requires us first to focus on moving out of the immediate perceived thinking through a reflective process. This means stimulating innovation and setting goals that will drive long term and sustained success, then shifting the the task\/operational focus.\nCopyright \u00a9 2011 Hagge Global Institute. All rights reserved.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The city's budget may be viewed as two major components, the operating budget and the capital budget. The operating budget provides for the ongoing funding for the day-to-day operational activities at the city. The capital budget provides funding for projects included in the city's 5-year Capital Improvement Program, or CIP.\nCIP projects are further subdivided into major or ongoing projects: major CIP projects generally include projects that have a definitive beginning and end date, such as the construction of a new building or roadway, and ongoing CIP projects generally include those without a beginning and end date, such as renovation and replacement of buildings or roadways.\nIn an effort to provide the public with additional information about capital projects, the city prepares semi-annual CIP status reports to describe what project activities have occurred for each capital project during the reporting period.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzagbba b/data_all_eng_slimpj/shuffled/split2/finalzzzagbba
new file mode 100644
index 0000000000000000000000000000000000000000..7253d9e6a640f20a7c37c7ee1e3b5d9a10d47dcc
--- /dev/null
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@@ -0,0 +1,5 @@
+{"text":"Join Northwest Area Command for \"First Tuesday\" on Febuary 1st at 7 PM. Topic is Crime Scene Investigations.\nJoin Northwest Area Command for \"First Tuesday\" on Febuary 1st at 7PM. Topic is Crime Scene Investigations.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Skull With Bones Coloring Pages Is one of the image about The resolution: 640x516 px ID: #81901. This image is: jpg Format and the file size: 33.39 KB you can download modify and share it for free. We also have similar images for you, that is Flower Coloring Pictures For Adults Coloring Pages For Adults Already Colored 612\u00d7612 Ladybug Coloring Pages Pictures .","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"We would love to welcome you at one of our 2017 BootCamps in Javea, Alicante, Spain. Our BootCamps are for 7 nights in our luxury resort. The aim is to get fit and eat right and get your on the right road to looking and feeling good for summer 2017 !\nThe BootCamp is for adults aged 18 years and over.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"ROB REDDING has reached the 1,000-episode mark for his \"REDDING NEWS REVIEW UNRESTRICTED\" show, airing online at ReddingNewsReview.com. The show launched its present version in APRIL 2014.\n\"Very honored to have so many fans who believe in me and what I do,\" said REDDING. \"And I look forward to another 1000 episodes with all my fans in a growing number of states.\" Noting that he has a social media base close to 20,000 people, REDDING added, \"Numbers don't lie.\"","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"HST Transmission: HST models feature performance proven, heavy-duty HST drives that deliver power and efficiently. The three range transmission (Hi\/Mid\/Low) with twin pedal operation makes your job easier, smoother and safer.\nBackhoes : KB2475L: Fits the KIOTI CK2610, CK2610 HST, CK3510, CK3510 HST, CK4010, CK4010 HST. *Specifications may vary with tractor model, front axle configurations, tire size option and type of attachment and are subject to change without notification.\nFront End Loaders : KL2610: Fits the KIOTI CK2610 & CK2610 HST models. Specifications may vary with tractor model, front axle configurations, tire size option and type of attachment and are subject to change without notification.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzahamp b/data_all_eng_slimpj/shuffled/split2/finalzzzahamp
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index 0000000000000000000000000000000000000000..a87d3c2b697bfa9854e4e5fcfd960b52e93b13e5
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+{"text":"Finding out or suspecting that your loved one self-harms can be a devastating experience. It is scary, incomprehensible, illogical, repulsive.\nHow can hurting themselves help them?\nHow should you react? Or more importantly, how should you not react?\nWhat are the underlying issues behind self harm?\nJenny Groves, the Battle Scars founder and CEO, facilitates these FREE informal discussion groups.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Each Advertiser can have it's own default Agency Compensation Costs that will automatically carry into campaigns you create for this Advertiser. You can select multiple Agency Compensation Costs if this Advertisers has varying compensation plans. You can then override these defaults at both the campaign level as well as at the individual line item level.\nIdentifying Agency Compensation costs you want to track at the Advertiser level is a great way to ensure consistent media plans.\nAgency Compensation Costs drive how your agency compensation will be calculated.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"About US, don't miss the apportunity, everyone wants to save their bucks, so the best and updated Coupon Codes, Discounts and Deals that you can find it from our website m, enter text, home, blogs.Caution: June, july, August, September, October, customers Who gifts..\nPerfect for those days you want to hide behind a little extra tummy coverage too!View full product details charlie bottom - snow kitten \/ coconut a welcome gift white.00.00 Sale charlie bottom - snow kitten \/ coconut white.00.00 charlie is perfect for the..\nIf you do not receive your Burlington e-gift card within 21 business days of the date the item was received back to our website fulfillment center, please contact.\nPlease treat your Burlington gift card like cash.\nSame day flower delivery to Canada and US; 2010 Maria., Burlington, ON, Website Map.\nIf you have completed your purchase with a credit card and a Burlington gift card, the credit card will be refunded first for the portion debited to your credit card and the remainder of your refund will be issued to you via a Burlington e-gift.Back to top, in-store Returns: If you paid for your entire purchase with a Burlington gift card and return an item to a Burlington store, you will be issued a new gift card in the amount paid for the item\/s returned, in accordance with our.The remainder of your refund will be issued to you via a Burlington gift card.Burlington gift cards are not reloadable.\nWhat happens to the funds on my Burlington gift card if my online order is canceled?\nIf you are ordering an e-gift card, please allow up to 48 hours to receive the card at the e-mail address specified.\nWhat should I do if my Burlington gift card is lost, stolen or damaged?How will my gift card be sent to me?Back to top, when an online order, which was purchased with a Burlington gift card, is canceled, a new e-gift card in the full amount of the canceled items, plus shipping charges for those items will be issued to you via email.Mention you found us on Paul's Halls 2201 Brant Street, Burlington, ON, Website, map,.Can multiple Burlington gift cards be used for one online order?A standard vga graphics adapter win 7 download Healthy alternatives from store bought spices low in sodium and some products gluten free.\" Green \" your wedding and help the environment.\nIf you still have questions about your Burlington gift card, please contact us at (855) 355-burl (2875).","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"designer super eyeglasses numero 09 iwoh 65w oro bianco large: super, by retrosuperfuture\u00ae, ignited the phenomenon of acetate sunglasses. they are made in multiple color graduations, which has generated a big trend starting in 2007. super is the 1rst brand to produce a complete range of colorful fashion sunglasses combining these characteristics together with a very high quality manufacturing process. super sunglasses are made to the highest possible standards, hand made in italy by the best manufacturers and with the best materials. for this reason, super also decided to adopt zeiss lenses, which guarantee an extremely high level of protection to the eyes in all conditions. since their introduction, artists, celebrities, sports athletes and trendsetters have been wearing super sunglasses. kanye west, daft punk, who made who, justice, pedro winter and his \"ed crew\", simian mobile disco, css, st. vincent, the kills, elio fiorucci, sienna miller, jessica alba and valentino rossi are just a few who have been seen sporting a super.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Harley flew to Norway in May 2013 with our friend Kirsti Kahrs for some limited showing and to be used in her breeding program. While it killed us to let the boy go for a year, we knew he was in exceptional hands.\nHarley In limited showing in Europe, Harley has so far earned both his Swedish and Norwegian Championships - the first two of three legs of a Nordic Championship -- as well as garnering three of four CCAIB certificates toward an International Championship.To date, Harley has defeated every dog (male) he has faced in Europe, and he has multiple breed wins in both Norway and Sweden.He has also qualified for Crufts 2014!\nOur boy's name is now, CAN BIS, AM GCH, NO\/SW CH Rustic Lane Road Warrior at Fwaggle!We couldn't be more proud of our boy or more thankful to Kirsti for doing such a great job with him.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzahwaa b/data_all_eng_slimpj/shuffled/split2/finalzzzahwaa
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index 0000000000000000000000000000000000000000..db7c03442e2fe8652b9dc844c948ae404bdeb51e
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzahwaa
@@ -0,0 +1,5 @@
+{"text":"Reinhard Fabisch says he was asked if there was any way he could manipulate a match.\n\"I told him: 'Look, you have two minutes to leave the hotel or I will call the police'.\"\nFabisch said the man had told him he represented a company based in Singapore which could fix games across Africa.\n\"I think that African players are vulnerable to this kind of approach, because many of them don't have money.\"\n\"I was astonished that he had the guts to approach a German to fix a football match,\" said Fabisch.\n\"I think that African players are vulnerable to this kind of approach, because many of them don't have money.\n\"This is why poor countries like Benin are targeted. I cut him short and told him to leave. It doesn't help football.\n\"I assume that if someone approaches you like that, then they have that (money) in mind.\"\nFabisch, who took over from Wabi Gomez in December after Benin qualified for the 2008 African Cup finals, said he was prepared to provide the Confederation of African Football with the contact details of the man.\nThe Confederation of African Football (CAF) has told Fabisch he has 24 hours to sign an affidavit confirming his allegation of a bribery attempt.\nCAF drafted a letter to the Benin Football Federation on Friday seeking clarity over the allegations.\nMustapha Fahmy, CAF secretary general, said they were investigating and Raymond Hack, disciplinary committee chairman, told Reuters the matter was being seriously considered.\n\"A letter has been sent and we wait to get formal confirmation of the allegation before we take the matter further,\" Hack said.\nCAF officials said they were concerned that no formal notification of the approach had been given to them before Fabisch spoke to reporters on Thursday.\nThey added that if Fabisch did not sign an affidavit confirming the allegation then CAF would consider charging the Benin federation with bringing the game into disrepute.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Amid charge and countercharge about who is shilling for whom in the debate over Internet regulation, Peter Suderman has the right focus in a short piece on Reason's Hit & Run blog. The Federal Communications Commission's Chairman is claiming that he only wants to regulate the Internet's infrastructure, but one of his colleagues, Commissioner Michael Copps, is non-denying that he wants to censor the Internet.\nThe FCC does censorship. It's unfortunate to see willful disregard of this by the folks wanting to install the FCC as the Internet's regulator.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"For working parents the challenge of raising children doesn't lessen over time it simply changes.\nWhile the working parents of teenagers may not have to stress about child care anymore they may experience other concerns such as difficult behaviour, a loss of connectedness and\/or concerns about the influence of drugs and alcohol.\nThese very genuine concerns cause anxiety and stress and have a knock-on effect in the workplace. Taking a proactive approach to helping the working parents of teenagers tackle the complexities of life with kids at this age is a cost effective way of improving engagement and retention during these challenging years.\nThe Care Corporate Care for Teens program has been purpose built to provide organisations with a cost effective and highly targeted range of online information and resources which can be accessed by employees any time issues arise.\nResources include articles, tips, case studies and contact details for support agencies.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Federations are groups of religious communities (in our case, monasteries) who follow the same Rule and Constitutions, and, with the permission of the Holy See and under the supervision of its appointed delegate, organize to meet together at appointed times to discuss matters of relevance to the members. The Federation does not have legal authority over the constituents except in matters directly referring to the Federation Statutes, nor does it in any way interfere with the autonomy of the individual monasteries.\nThe purpose of the Federation is encouragement and support for its members in the enactment of their particular life style. Meetings of the Federation would be attended by the superior and a delegate from each community. The meetings would be planned and executed under the supervision of a council consisting of a President, Vice-President, and three other sisters who are elected from the member communities. Possible issues to be discussed could be the interpretation of the Rule and Constitutions, the adaptation of the Order to the signs of the times, the solution of problems particular to the life style, etc.\n3) the teaching of particular skills needed to maintain the monastery financially, etc.\nOther possible projects that might be helpful to the members are special formation workshops or meetings, and, if considered advisable, a central formation house for all the postulants and novices in the Federation could be an option.\nThe Federation also provides a process by which a member of one Monastery, who has a sufficiently good reason, may transfer to another Monastery of the Federation.\nIn 1950 His Holiness, Pope Pius XII, wrote a memorable Apostolic Constitution entitled, \"Sponsa Christi,\" which dealt with many facets of the contemplative religious life style. Among other things, His Holiness recommended the federation of monasteries as a spiritual and moral support to the members and a help in promoting regular observance of the contemplative life. The Federation he proposed would in no way supersede the autonomy of the individual monasteries.\nThe Sisters of St. Clare (O.S.C.) in the United States did not act immediately upon the Pope's suggestion. However, on November 29, l958, representatives of the Sisters of the O.S.C. observance met at the Monastery in Evansville, Indiana, to discuss the topic of a possible federation of their monasteries. Presiding at the meeting were three Franciscan priests: the Very Reverend Pius Barth, OFM, Minister Provincial, assisted by Fr. Marcian Mathis, OFM, JCD, and Fr. David Eckelcamp, OFM. No definitive decision regarding a federation was reached at this meeting. It would seem that fear of losing the autonomy of the individual monasteries was a prime obstacle to embracing this action.\nThe sister's agenda for the meeting had 24 items to discuss in the two working days set up. After the 4th working session, a verbal non-deliberative vote was taken. The results were almost unanimously \"No\" to the formation of a federation. The only monastery to vote in favor of federation was the newly established monastery of Minneapolis, Minnesota. Further time was allowed for discussions around the fears, as well as the request by the church for these federations. It was after these discussions that a deliberative vote was taken, and the results were now 19 in favor of, with 3 votes against. The proposal to send the Statues for the Federation was unanimously approved.\nIt was at this meeting that the decision was made that due to the large distances to be covered, there would be two federations formed instead of one. The Mother Bentivoglio Federation would be formed by the monasteries in the Midwest, West, and British Columbia, Canada. Holy Name Federation would consist of the monasteries along the East coast inland to Philadelphia. At the close of the two days of official sessions, the Abbesses and Delegates were encouraged by the friars facilitating this meeting to stay on at the Evansville meeting for several more days to profit from the exchange of ideas among themselves. This mutual sharing over common problems was tangible evidence on only one of the many benefits to be expected from a Federation of Monasteries.\nA vote was taken at each of the monasteries and submitted to the Holy See in Rome. On June 13, 1963 the Federation Statutes were approved for a period of 7 years. It took another year before the English translation was available from the Latin. During the year of waiting, Fr. Pius Barth OFM, who had been appointed to assist the sisters, travelled tirelessly from monastery to monastery, talking with the sisters, allaying fears, and explaining the new Statutes.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Top 5 All Time Tips For Installing The Outdoor LED Floodlights by Your..\nFloodlights are no longer new to most people. However, LED floodlights are not very common and thus most people are not aware of them because they are mainly used in warehouses and in commercial entities. This has been the case for the last few years. In the nutshell, the outdoor LED floodlights are now a good alternat..\nIt is quite easy to analyze the LED flood lighting system as this will help one understand better the details concerning it. Here is a simple analysis of this flood lighting system that users should know. Emergence of the LED lights came in the late 20th century. LED systems are characterized by high efficiency, energy..\nMost of environmental conscious people have actually converted to LED flood light fixtures for their eco-friendliness as well as their high efficiency. Even though the LED lights were quite expensive when they were being invented, their prices have been reduced due to technological advancement. In fact, this is one of ..\nThe best way to satisfy the outdoor lighting needs is simply use of the outdoor flood lights. The biggest challenge that most people face is that they buy lights which they do not know their specific purpose which they were specially designed for. Many people end up buying lights because they have seen their friends wi..\nFlood LED lights provide bright lighting which is necessary at night. They are ideal for use when working at night in a construction site as well as areas that need lighting at night such as stadiums and warehouses. The lights are very powerful and they are gradually replacing HPS flood lights. Most high-pressure sodiu..\nHere are ways on how to detect the EMC reliability of LED flood light. To start with is how well the LED flood light devices and systems are compatible. The electromagnetic compatibility is the problem to these devices is defined as the systems, equipment and subsystems in an environment together with the respective fu..\nHow the LED outdoor flood lights and LED driver business relates toget..\nIt is true that there are some relationship between the quality of the LED outdoor flood lights and their counterparts LED drivers. To get how the two relates, it is worth noting the following. Over the recent past, the LED outdoor flood lights have become so popular due to the rapid development applications of them. T..","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzajffu b/data_all_eng_slimpj/shuffled/split2/finalzzzajffu
new file mode 100644
index 0000000000000000000000000000000000000000..44515a65a21355388b27e69bfee69c9c34bf564b
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzajffu
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+{"text":"Excitement got the better of Fletcher last month when we swapped our corner in the East for the south west land of Cornwall. As we drove the winding lanes of the coastal path, the squeals of excitement started\u2026and didn't stop until we left five days later.\nOur first stop was Mullion on the south coast. Desperate to stretch our legs after a long six hour drive, we took on the steep trek down to Mullion Cove, and instantly discovered our first problem. Fletcher is a lot more agile than us and while it took him a mere minute to bounce down and splash into the sea, my husband and I had to frantically scramble down the cliff after him. This happened on every walk, and I think Fletcher quite enjoyed the fact we had to chase him up and down cliffs.\nWe stayed at the Polurrian Bay Hotel, which has great sea views from the bar and restaurant, and access to the beach, perfect for sunset walks. It was wonderful to watch Fletcher frolic in the sea with other dogs, while horse riders trotted up and down on the sand.\nOur next stop was the Artist Residence in Penzance; a stylish boutique hotel. Both hotels catered well for furry guests and included a dog bed, bowls and treats in the room.\nDays were spent strolling along the year round dog friendly beaches, while Fletcher glided through the water doing his best seal impression. I feel like a traitor for saying this, as I think the North Norfolk coast is one of the best dog friendly destinations in the UK, but I have found the ultimate dog friendly beach; Porth Kidney, a secret oasis, just a 10 minute drive from St Ives.\nPark at the church and follow the path which runs alongside it to the left, walk under the railway bridge and you'll feel as though you've been transported to a Caribbean island (minus the weather). The powder white sands stretched for miles beyond us and the crystal blue waters sparkled in the sunlight. Fletcher wasted no time leaping into the clear waters, while we found a spot on the soft sand. Not wanting to miss out, my husband and I braced the chilly sea temperatures and joined him for a swim. It was one of those family moments that will stay with me forever!\nWith sandy toes and paws, and sea salt in our hair and fur, we returned to the car, cleaned up using the handy tap at the church, and ventured into St Ives for lunch. You'd assume after three hours of swimming and skidding across the sand, that Fletcher would be needing a break, but oh no, he embarrassed us the entire way around St Ives.\nPulling so hard on the lead, we had to switch to the Halti, which he always cries about, but add to that the squeals of excitement as he knew the sea was just around the corner and it was simply humiliating. We had people come up to ask us what was wrong with him; was he in pain, was he hurt, was he struggling to breathe\u2026the answer in short \u2013 no, he just wanted to swim, AGAIN!\nThe spoilt spaniel got what he wanted, and we settled for ice cream by the dog friendly rocks at the end of the beach, where Fletcher entertained crowds of tourists as he hurled himself into clear water from the rocks, dived under for stones and generally acted like an extra hyped up version of himself! YouTube must be full of uploads from strangers of Fletcher diving\u2026maybe I should start charging a commission!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Leading the way in building and civil construction.\nRichard Nolan Civil Engineering is at the heart of the Irish civil engineering and utilities ducting industry delivering the highest quality solution in the safest manner. Our continual development and diversification has led us to provide a seamless civil, construction, environmental and traffic management service. Our highly skilled and dedicated workforce allows us to progress and provide our clients with a high quality, safe and environmentally friendly solution. A commitment to developing our client base has led to our company achieving a highly diverse capability.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Blog for Krafti-Kit, a new online source for the finest in exclusive craft kits.\nI've not even had my tea yet and I'm blogging.\nLast night was the cut-off on the Knit Circus contest and so I had to get my winners notified!\nCongrats to LoonyHiker, RetroBaby and Sheila!\nThanks to the rest of you for your comments. I hope that you learned more about Knit Circus and Krafti-Kit.\nSo, today is the last day for my designers to finish and get their Late Spring designs to me. I'm already in the middle of knitting one of them. It's not a sample but just test knit for myself. Of course, I selected a discontinued yarn (RYC Cashcotton DK) and realized I was going to run out. BUT the Yarn Goddess smiled upon me and I was able to find two more balls in the right DYELOT in California at Monarch Knitting and Quilts, thanks to the internets.\nThis week I am actually leaving the homestead and heading down to Sacramento. I hate leaving my cats because of their age but I'm feeding Brahms lots and lots of food before I go to get her weight up. She's enjoying the extra feeding and I'm simply glad food still excites her at her age. Of course I'll be bringing plenty of knitting with me for the trip.\nThat reminds me how much I love kits for travel. It's all just right there. In fact, I became a buyer of kits on holiday many years ago. That was before I knew how to plan these sorts of things, but buying kits on the road can be awfully fun. That was what got me into these little counted needlepoint pieces. Small, light and addictive! If you've never tried them, please give one of this \"bargain in crafting\" kits a try! You'll especially like them if you like knitted colorwork!\nBefore I go I've got to finish this re-organization of my office. Later!\nOn those days when I get to give stuff away, I'm a pretty happy camper. On days when I get to give really awesome stuff from other folks, I'm REALLY happy.\nI finally got the In The Press page up today and one of our glowing reviews was from my favorite online knitting magazine, Knit Circus. Have you checked it out? The way it works is that you basically get to look at the magazine, read the articles, cop some free patterns and a recipe or two. Then, when you find something you've just gotta knit, you can buy the rest of the content? Seriously great concept. The quality is there and the patterns are pretty impressive.\nOne full year subscription to the Knit Circus Pattern collections.\nIt's that time of year, solidly in Winter, but planning for late Spring, that can twist one's brain up in a knot. I suppose for those who don't like the cold stuff, it can be an optimistic time. For me, it's generally a time to knit with as much wool as I can!\nThis year, my first in Washington state, it started out very cold and snowy and then turned to oddly mild. As someone who is VERY weather oriented, this can be a little disconcerting. Of course, because I don't drive, all I hear from others when I complain at the lack of snow is: But you don't have to drive!.\nHere's the good news: New Spring designs in the works! I may have just slid in a mitten pattern last week, but I'm working on some samples for Early Spring that will WOW you. As just a tease, I'm posting a bit of some lavender \"texture\" from my sample pile.\nI've found some really talented new designers this year to work with. Some patterns and kits are on the way that I know you'll love. Sometimes I wonder how close to my own personal aesthetic I should stay when it comes to Krafti-Kit. I've come to the conclusion that there's a market for every type of design, and if I'm not enthusiastic about it, how can you be? So, I'm continuing to publish designs that are something I want to make. It not only has to be great to wear, or look at, but the actual process of working up the kit or pattern has to be fun as well. That's my criteria.\nAs always, drop on by the store and see what's new!\nHere's a detail from one of our great sewing kits. It includes that cute button and everything else you need to make an adorable clutch.\nCustomers have had two ways to pay for their purchases for the past few months: PayPal and Credit Cards. We originally had only the credit card option but I knew that Paypal is very popular for fiber folk who are used to using it for purchasing pattern downloads and much more. So, I tried a bit of an experiment and ran both payment options for a while. Paypay has shown its way to be the clear \"winner\" of the two, among our customers.\nI know that every payment method has its own set of issues, but for Krafti-kit and its growing collection of downloadable patterns, it seems very much the way to go right now.\nSome kits, like the Oregon Tweed socks above, are pretty straightforward. The yarn from PicoAccuardi Dyeworks is a no-brainer for me as are the LaurelHill needles. I love introducing folks to both of these companies and we use their stuff in our kits because they're just my favorite materials to work with. The pattern in this case is mine so it creates a simple kit to put together, test and get to market!\nAs you can see by all the bits and bobs here, the Snowflake Bookmark is another one of our kits, but it takes a bit more to come together. This is a kit that's truly inspired by the first \"counted\" needlepoint kit I ever purchased in Scotland, so many years ago. We wind off just the right amount of each color, plus a little, cut the canvas, backing and give you a couple of needles. Then there's the pattern. I love to graph my patterns for needlework and knitting in Knit Visualizer.\nThe draw to kits for me is straight from my childhood. I remember ripping open a box, counting all the pieces, the strands, the parts of a needlework kit and diving in. It's still that way for me. About 6 months ago I found the original 1950's loom that I learned in, boxed and waiting for me on Ebay. It was not to be! Heartbroken but still searching for that memorabilia to add to my collection, I am trying to create kits for others that inspire.\nTell me about your first kit love!\nThere's a long but boring story as to why it took me so long to show off this great mention in Vogue Fall 2010. But, here it is featuring the Magic Carpet Socks. We liked the part where they asked for a second kit so they could actually KNIT them. How's them apples?\nSo, let me say again that these socks are an absolute blast to knit. There's just a few bobbles and they're right on the top for full effect. Never let me say a negative thing about a bobble again. I now love them.\nThe big ad campaign for the Clearance Sale is starting Monday, Nov 1st, so if you've got your eye on something, act now. These are limited addition kits, kiddos.\nHere's the handspun crochet shawl that kept me busy for a few weeks this early fall.\nYep, and that means a sale of epic proportion as I make way for new designs and products at Krafti-Kit. We're talking like...half-off most of the store! I love those packages going out. And things are moving quickly out that door so if you like it, snag it.\nI also just got my first little newsletter out the \"door\". It was little, minimalist and I hope that it will be more in the future, but I didn't have time for the learning curve on this one and needed to get it out.\nThere are so many ways I like to communicate with other crafters. Just a couple of days ago I was on Twitter, chatting with other crafty folks the #craftsocial conversation that happens once a month. We were talking about pricing our work and once we got started, there were so many aspects, the 2 hours just flew. The main take-away points were educating our consumer about how exactly we make what we make so that they will understand what they are paying for. The second big point was to become \"activists\" for creating a culture in which craft artisans are paid a livable wage or more. Really relevant conversation for everyone there.\nI'm going to take a little look through the blog archive here and see what else I can tell you about when it comes to this process of creating kits. But, before I end here I'd like to remind folks that I'm still on my path to turn you all into needlepoint nerds. Free mini kits are going out until I'm out of these babies. The little needlepoint pattern goes in a card for a completely impressive gift when finished.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Marla, sharing her experience, strength and hope. Full of Hope! We will be adding new tapes every week from our users! If you have a tape you want to share visit our website and contact us. We believe that our channel is NOT a substitute for meetings, but can is a great supplement to someone's recovery. We also hope that our channel will open the doors of recovery to still suffering alcoholics, addicts, and the people who love them. If you enjoy our channel, pass it along, we keep what we have by giving it away. Keep coming back! It is important to note there are several ways for one to address his or her alcohol abuse treatment. Substance abuse is a very serious condition and has become an epidemic in today's world. Many people suffering with substance abuse need treatment, such as inpatient stays, rehab, or counseling. The importance and purpose of this video, and all our other videos, is to show that recovery is happening all around us and to give hope to those who are struggling with alcohol and drug addiction.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This is the tragic tale behind the snazzy electric Jaguar Prince Harry used to drive Meghan Markle to their plush wedding reception.\nThe sad history of the \u00a3350,000 Jaguar E-type, which has been converted to an electric vehicle, has emerged after it became a hot topic featuring in Saturday's Royal Wedding.\nIt used to belong to Jamiroquai musician Toby Grafftey-Smith, who tragically died last year at the age of 46, after a six-year battle with cancer, The Mirror reports.\nHis widow, Gabriella Crewe-Read, told the Daily Mail: \"The royal wedding car was bought from Toby. His brilliance is everywhere.\"\nShe added that her late husband is 'still here'.\nLike Jamiroquai co-founder and frontman Jay Kay, Grafftey-Smith was a classic car enthusiast and owned the 50-year-old Jaguar.\nAfter his death it was sold by his widow, although Crewe-Read has not revealed who bought it - although the keys have now found their way into royal hands.\nThe keyboard player was an alumnus of Marlborough College, the \u00a336,525-per-year boarding school where the Duchess of Cambridge was educated.\nThe car was prepared for the much-anticipated wedding by giving it a new registration plate - the date on which Harry and Meghan tied the knot.\nThe car is a zero-emissions, battery-electric-powered version of the 1968 car with LED head lamps.\nBuilt between 1961 and 1975, the E-Type was described by Enzo Ferrari as 'the most beautiful car in the world'.\nThis model is said to be worth \u00a3350,000.\nHarry's brother, the Duke of Cambridge , also used an expensive car as part of his wedding day.\nHe left Buckingham Palace with Kate Middleton after their wedding in 2011 in a vintage Aston Martin DB6.\nGrafftey-Smith quit Jamiroquai in 2002 after ten years with the band, and lived on a farm in Northamptonshire with his family before his death.\nHe was a classically trained musician, and co-wrote songs for Jamiroquai, which sold 26 million albums, with nine Top Ten singles and four UK No. 1 albums.","meta":{"redpajama_set_name":"RedPajamaC4"}}
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+{"text":"Here is a glimpse at the returned missionaries playing FBS football all over the nation.\nRice University had everything Austin Williams was looking for.\nThe 6-foot-2, 235-pound linebacker from Austin, Texas, essentially had three requirements: first, a high-quality education; second, the chance to play college football; and third, following a two-year Mormon mission to Guatemala, he wanted to attend a school where he would have ample missionary opportunities. He had several options, but Rice stood out, Williams said.\n\"I chose Rice because that's where I felt I needed to be,\" Williams said in a recent interview with the Deseret News. \"I was wanted by the coaches and it was a great place for me to continue serving and helping others to find the gospel.\"\nWilliams is one of 158 returned Mormon missionaries in the Football Bowl Subdivision this season who have served full-time missions for The Church of Jesus Christ of Latter-day Saints in different cities and countries around the world.\nWilliams, a sophomore, isn't the only returned missionary playing at Rice.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Overall, I am in huge amount of joy and excitement because I get to learn so much about everything. I am constantly absorbing every words from teachers and peers, and also reflecting on my feelings and learnings.\nPhysically I have been sort of tired, a bit more tired than I was during regular school days because we do a lot of things with our bodies here. Still it is quite manageable. I do have bruises on my leg from some movements and they hurt. I have some tension around my neck and my shoulders.\nThroughout the two and a half weeks, I have developed much more awareness in my spine and breath, which helps me to relax and maintain a healthy body posture. I also realized how yawning and \"shaking it off\" can help to loose my body, both for acting and for daily life.\nMentally I have been active all the time, thinking and learning. I feel I am definitely not having enough time to do all the things I want - for example, write for my journal and for Pioneer Research Program. The latter has been an enormous stone over my heart for over one week, making my mind drift away in class. I then realized that I should not put myself under such pressure, and it is absolutely un-beneficial to think about my paper in acting classes, so I have tried to let these thoughts float away and tell myself that everything will be fine.\nI am very very very grateful toward my teachers and peers. I LOVE Lindsay and Erin. After we've done an exercise, they always give superb comments that are both accurate and hilarious. I love the other instructors as well - Tyler is really kind and encouraging, Joe is filled with subtle emotions when he meets fabulous monologues. I also love how Nicole and Josephine, the TAs, are always with us and are not authoritative figures most of the time, but rather our friends and companions.\nActive listening; Eye contact; Courage; Impulse; Rising the stake.\nI feel like I am peeling off the layers of self protection I have built throughout the process of growing up and recognizing my hidden emotions. Theatre is the right place to let myself be a baby again - be honest and vulnerable and not seek control all the time - and that is something I had realized before this program and something I am always trying to embrace. The classes I am taking have been shaping me into a more sensitive, expressive and truthful person. I am very happy to see that.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"As predicted, the net is being closed on Tower Hamlets Council's East End Life. I hinted that ministers were considering further action against it and other similar council papers and now we have it on record.\nOn 13th October 2011, the Bethnal Green and Bow Conservative Association were joined by Bob Neill MP, Minister for Local Government, to talk about a range of issues affecting the London Borough of Tower Hamlets and the wider East End area.\nThe Minister expressed his disappointment at the local Mayor's decision to continue publishing its weekly municipal newspaper, East End Life, in spite of the Government's strict new guidelines.\n\"It was a pleasure to spend time with Conservative colleagues in Tower Hamlets who are so passionate about East London and they have some fantastic ideas about how the area could be improved for current and future generations.\n\"It is deeply frustrating that the Mayor of Tower Hamlets continues to plough \u00a31.5 million a year of local taxpayers' money into his weekly vanity paper, East End Life, despite representing one of the most deprived areas of the Capital. Councils should be there to deliver key services for residents \u2013 not divert public money into publications which undermine independent local papers and do little but self-congratulate the ruling establishment.\nTower Hamlets Conservatives held a dinner on Thursday 13th October at the Market Coffee House, Spitalfields at which Bob Neill MP, Minister for Local Government was the speaker.\nIt updates the previous Publicity Code introducing new provisions on the frequency, content and appearance of local authority newspapers, in particular that they should not be issued more frequently than quarterly.\nJim Fitzpatrick secured an adjournment debate in the Commons last night on the bid by Tower Hamlets for City Status in the Queen's Diamond Jubilee year.\nWhen this bid was first announced, I was a bit cynical about it, a little too cynical in retrospect. It's certainly being driven by Canary Wharf Group but it also has the backing of the Corporation of London which some thought would be worried about the E14 Parvenus gaining similar banking ranking.\nThe 25 towns applying for city status are: Bolton, Bournemouth, Chelmsford, Colchester, Coleraine, Corby, Craigavon, Croydon, Doncaster, Dorchester, Dudley, Gateshead, Goole, Luton, Medway, Middlesbrough, Milton Keynes, Perth, Reading, Southend, St Asaph, St Austell, Stockport, Tower Hamlets and Wrexham.\nAs I went to school for a bit in the small town St Asaph in North Wales, which already has a cathedral, grew up not far from Wrexham and worked for three years in Colchester, the list is a little trip down memory lane.\nSome think Tower Hamlets has a fine chance and although the Queen will always be mindful of, as her mother put it, \"looking the East End in the eye\", I'm sure the Palace would believe it to be a too London-centric decision. Many feel Reading is the frontrunner but if I were advising the Palace, I'd go for Gateshead or Middlesbrough which have been beacons of regeneration of the industrial North.\nThat said, nowhere has a history like Tower Hamlets and this was highlighted with great pride by Jim in the Chamber last night. Adjournment debates are the last of the day and as such, the Commons is usually pretty empty. But what a shame that Jim was the only Labour MP in the Chamber last night. Not even Bethnal Green and Bow MP Rushanara Ali, whom the Speaker had promised would be allowed to say a few words, could make it.\nIn fact, it fell to Mark Field, the Tory MP for the Cities of London and Westminster, to rise up in support of Jim's speech. Mark also said that Croydon was a strong contender and a bit later on hinted at the point that I wrote about here last month, that the unseemly political climate in Tower Hamlets could end up damaging the cause.\nI think he's right and if the borough does fail to win, I do wonder whether Labour and Lutfur Rahman will try to pin the blame on each other.\nJim Fitzpatrick (Poplar and Limehouse) (Lab): I am grateful for the opportunity to raise the Tower Hamlets city status bid, and I welcome the Minister. I know that his reaction must be neutral, so in reality, this will not be much of a debate. It is none the less good to see him\u2014he is highly regarded on both sides of the House.\nIt is also good to see the hon. Member for Cities of London and Westminster (Mr Field) in the Chamber. He represents London's existing two cities. My hon. Friend the Member for Bethnal Green and Bow (Rushanara Ali) and I\u2014she cannot be with us tonight\u2014would be very happy were Her Majesty to allow us to represent just one city between us. Perhaps the hon. Gentleman can offer us some advice and assistance on how to get there.\nThe east end has always been special in many ways. Today, however, Tower Hamlets is a reflection of Britain and the Commonwealth\u2014a centre for global business and multiculturalism. The borough has come a long way since the blitz. Tower Hamlets has been transformed during the decades of Her Majesty's reign, adapting from the industry of the docks and the merchant navy to become an internationally recognised world centre for trading, business and banking, and a celebrated tourism hub.\nWe have over two millennia of history and share more than a thousand years with royalty. Now as before, but in a different way, we are a powerhouse for the United Kingdom's well-being. We are the third central business district for the heart of London, alongside London's west end and the Corporation of London, both of which cities are represented by the hon. Member for Cities of London and Westminster, as I have said.\nOur new economy creates an economic surplus that contributes through Government tax distribution to many of the poorer parts of Britain. We are proud to be able to make that contribution, having experienced hard times ourselves in the past\u2014we still have deprived areas today.\nOn the history of our part of east London, the iconic Tower of London symbolises our strong and enduring links with the monarchy. Founded by William the Conqueror, it is the country's oldest royal palace. The constable of the tower has the right of direct access to the sovereign, and of course it is home to the Crown jewels.\nLondon's first public park in 1850, and named after Queen Victoria. A petition signed by 30,000 residents requested a royal park in the area because of the lack of green space in the east end.\n\"I am glad\u2026now we can look the East End in the eye\".\nIn 1945, during two days of joy following VE day, the royal family celebrated with Poplar and Limehouse.\nThe royal family has maintained its links with the east end, and family members have taken an active interest in the area's regeneration. The Prince's Trust has been an assiduous partner in local initiatives, and Her Majesty herself opened the first stage of the Docklands light railway in 1987, and Poplar marina a decade later. She and His Royal Highness Prince Philip have also visited on other occasions. The ecumenical priorities of the royal family are a basis of staunch support from Tower Hamlets, as a multi-faith community. This was demonstrated at the recent royal wedding celebrations, which were organised and attended by people from all religions and backgrounds.\nOur prosperity as London's engine room has always been linked with London's priorities as the nation's primary trading centre, and now as a world city. We have moved from physical trade to international banking, creative industries, media, pharmaceuticals and company headquarters, and Tower Hamlets is now a leading world centre, with the City Fringe and Canary Wharf. Our economic turnover is now over \u00a36 billion annually. Small and medium-sized enterprises on, and servicing, Canary Wharf, as well as traditional businesses, provide employment for thousands of people. Our inward-commuting population is more than 120,000 daily, and will rise to more than 200,000 by 2020. There will be 300,000 jobs in Tower Hamlets by then. Already, Tower Hamlets offers the largest number of jobs in the United Kingdom outside the cities of Birmingham, Leeds, Manchester and Sheffield, and London's two other cities.\nThe Thames and Lea rivers, and the legacy of the Roman roads, were our early business arteries and our communities' raison d'\u00eatre. We still have the largest \"blue network\" of any London borough. The upper docks were a vital part of Britain's maritime trade from the 1800s to the 1970s. London's first canal\u2014the Regent's canal or Prince Regent's canal\u2014and early railways such as the London and Blackwall were built to serve the docks and carry national, imperial and international trade. Our markets, including Spitalfields, were the centrepiece of the capital's provisioning. In 1982, Billingsgate fish market relocated to Tower Hamlets.\ngrowth environmentally in the decades to follow, and 170 million passenger journeys start or finish at our 30 stations yearly.\nTower Hamlets has a fascinating social, cultural and political history. A core test of strong community leadership is an enduring concern for the well-being of its citizens of all ages. Trade and social cohesion do not always rub shoulders comfortably in a major urban area. Poverty, slum housing, poor health and crime have all been present locally and, sadly, some aspects are still evident. Tower Hamlets council and its predecessors have a distinguished and continuing tradition of increasing democracy and rights for working people, including the Poplar rebels of the 1920s. The roll call locally is packed with social reform, equality, emancipation and self-improvement of communities, transforming them into our 21st century society.\nIn the middle ages, Wat Tyler met King Richard II at Mile End during the peasants' revolt, where the king acceded to a petition for better payments and social conditions. In Victorian times, the Chartists and local dockers, campaigning to improve industrial and social conditions, met at Victoria park. The Toynbee Hall organisation has worked on social and welfare reform since the end of the 19th century. Clement Attlee MP, one of my predecessors, was MP for Limehouse and became Prime Minister, championing welfare reform. In early 2011, the current Prime Minister announced the coalition Government's plans for welfare reform at Toynbee Hall.\nThe Boundary estate in Bethnal Green opened in 1900 and was the world's first council housing, built on the site of one of the capital's most notorious slums, the Old Nichol. The Peabody estate in Commercial street was the first social housing, while the Lansbury estate in Poplar was a post-war prototype and is still going strong.\nSylvia Pankhurst settled in Bow at the beginning of world war one. With suffragette colleagues, she set up a cut-price restaurant, a milk centre, a toy factory and a nursery school. This provided local women and children with what they needed; the women worked in the munitions factories and on public transport, as their husbands and men-folk went to war. In other examples, the first women to form a trade union did so at Bryant and May's match factory in Bow; the Salvation Army was founded by Charles Booth in the east end; and Mahatma Gandhi stayed in Kingsley hall in Bow in 1930s\u2014a place that now houses the Gandhi Foundation.\narrival of Bangladeshi Muslims. These new communities, defined by their faith and ethnicity, have created strong infrastructures around family and work\u2014firm foundations for our city. The diverse population, cultures and identities reflect those of the wider 21st-century Britain. We now have the youngest population of any London local authority.\nThat rich background has stimulated a shining example of Tower Hamlets' distinctiveness. One building that best tells the diverse religious history of Tower Hamlets, is the \"Brick Lane mosque\", which was originally founded as a church for the Huguenots, but later used by Methodists. In the late 19th century, it was converted into the Machzikei Adass, also known as the Spitalfields Great synagogue, but as the Jewish community moved out to be replaced by Bengali immigrants, it became the Jamme Masjid or the Great London mosque in 1976. We also have the east London mosque in Whitechapel and no less than three Hawksmoor churches in the borough. Royal ensigns have permission to fly\u2014the white ensign at St Anne's in Limehouse, the red ensign at St Dunstan's in Stepney, as well as the blue ensign at the floating church of St Peter's in the docks.\nMost recently, the regeneration of the area, overseen by the London Docklands Development Corporation, has caused the riverside populations to be reborn, with renovations and adaptation of older buildings and the construction of new homes, bringing many thousands of new residents to the area. That stimulation and new investment has extended inland to centres such as Spitalfields, Whitechapel, Bow and Victoria park\u2014and, of course, Tower Hamlets is one of London's Olympic boroughs.\nTower Hamlets' experiences with community activism in past times are paying dividends as we look to the future. At the 1936 battle of Cable street, 300,000 people blocked Oswald Mosley's fascists from marching on the local Jewish community. Today there are some 2,500 community groups working within Tower Hamlets, delivering a vast range of services to local people, ranging from small self-help groups run by volunteers, to larger organisations delivering public sector contracts. Our thriving third sector is a reflection of our vitality and community spirit, which is inspired by our origins. There was stability in Tower Hamlets during the riots that took place elsewhere in the United Kingdom during the 1980s and 1990s, and most recently we were pretty much spared the violence seen in so many parts of the UK.\nThe sustaining core of the east end's future will be our young people, and ensuring that they are educated, skilled, experienced and adaptable. Our secondary schools are benefiting from a \u00a3290 million investment to create world-class learning environments for our children. Our schools have moved in the last 15 years, and are now among the highest-performing in Britain. Education and training-related courses can be taken in the borough's idea stores\u2014formerly libraries\u2014and higher educational opportunities are available in Tower Hamlets at Queen Mary and Westfield college, part of the University of London, at London Metropolitan university, and at Tower Hamlets college.\nturnout of 52.4% of young people, a higher turnout than those in some recent mainstream elections. We have a directly elected executive mayoral system of local government.\nTower Hamlets has always had a high-profile artistic identity. Among our residents are Dame Helen Mirren, Sir Ian McKellen, Tracey Emin and Gilbert and George, and 3 Mills Studios in Bromley-by-Bow are London's largest film and television studios. The Old Truman Brewery is now host to many creative businesses, and we have a number of artists' colonies including Trinity Buoy Wharf, where Faraday experimented with electricity. For over a century the Whitechapel gallery has showcased the work of world-renowned artists such as Picasso, Jackson Pollock and Lucian Freud. The Museum of London Docklands is considered to be one of London's hidden treasures, and addresses the history of the capital as a port. Children locally are encouraged to visit the V&A Museum of Childhood, which was opened by the Prince of Wales in 1872, to see its collection of childhood-related objects dating back to the 1600s. Wilton's Music Hall, which opened in 1858 in Wapping, is the oldest surviving Grand Music Hall in the world, and is Grade II listed. However, the jewel of all our buildings is the one that I mentioned at the start, which is home to the Crown Jewels.\nOne of Britain's most striking and famous historical landmarks, the Tower of London, is now a world heritage site attracting more than 2 million visitors a year. Other high-profile buildings include the Canary Wharf skyscrapers, the Old Truman Brewery, the old and new parts of the Royal London hospital, the northern half of Tower Bridge\u2014I would not want to claim Southwark's southern half\u2014and the Whitechapel Bell Foundry, which cast the Big Ben bell, as well as the bells of many cathedrals and parish churches and others further afield. I am told that it also cast the Liberty Bell, which, as we know, is famously cracked. During the American quadricentennial celebrations, a stunt was organised by Americans who handed out leaflets outside the foundry asking for their money back. The foundry showed its sense of humour: they were told that they could certainly have their money back provided that the goods were returned in the original packaging.\nSome of our street markets are known worldwide and are major destinations for residents, Londoners and tourists alike, such as the Columbia Road flower market and the Whitechapel, Petticoat Lane, Spitalfields and Billingsgate markets. The Roman Road, Watney and Chrisp Street markets are well known throughout the east end. Food is a symbol of Tower Hamlets' many cultures, whether it is sold in the local pie and mash shops, at Tubby Isaac's jellied eel stall, in the bagel bakeries or in the curry houses. The Olympic organisers have just named Brick lane as Curry Capital 2012.\nEvents take place in Tower Hamlets throughout the year. The Baishakhi Mela, a festival to celebrate the Bengali new year, is the largest carnival in the UK after the Notting Hill carnival, and more than 100,000 people turned up in 2010. Lovebox, a music festival held in Victoria park, attracts star performers and plays to over 100,000 people, and Canary Wharf sponsors a year-round arts and events programme encompassing music, sport, visual art, food, fashion and dance.\nTower Hamlets is in very good company, and whichever area Her Majesty chooses will be worthy of the title. My speech is intended to draw attention to some of the stronger reasons for the view held by many of us that Tower Hamlets has an excellent case to make. Our bid has the support of all our major political parties.\nA city is defined through its deeds, its concern for citizens and its central roles. We have a powerful track record of managing and behaving as a city, with national and world impacts in business, and a profound and strong cultural and social record at a human level.\nWe hope that Her Majesty will choose Tower Hamlets because we foresee more investment and economic growth coming from city status with its new united identity. These gains will be re-invested back into our communities and our people, and towards the wider London and national well-being. Our vision is built on our multicultural, multi-faith approach to social development, and our aim to be the leading example of how Britain can best influence the dynamics of the world in the 21st century, and I am grateful to have had the chance to make these remarks.\nMr Mark Field (Cities of London and Westminster) (Con): I congratulate the hon. Member for Poplar and Limehouse (Jim Fitzpatrick) on introducing this important debate. As he pointed out, I, rather greedily, have two cities in my constituency just to the west of his own. They are also rich in history, and I suspect I could bore Members for some hours by going into the details of that history. It was a great pleasure to listen to the hon. Gentleman's speech, in which he described, with understandable pride, the great achievements of Tower Hamlets. Although he spoke about its great history, he also had a firm eye on the future.\nIn light of the previous debate, it might be relevant to mention that one thing Tower Hamlets lacks is a league football club. We might, perhaps, hope that returns to its historical roots at some point by crossing the river again\u2014although I suspect the local constabulary might not be too keen on that idea, particularly on derby days when Millwall plays West Ham United.\nHowever, although the hon. Gentleman made relevant points about Tower Hamlets, I hope we will consider granting city status to other candidates too, so that we do not give the nod to just one new city next year. Reading is my home town, and that is one of the other places in the running, and I also think there is a strong case for Croydon. If it were a self-standing entity rather than a London borough, it would be the ninth largest settlement in the UK.\nThe case for Tower Hamlets is strong. As the hon. Gentleman pointed out, the financial district that has grown up from nothing over the past 20 years makes a great case for its having city status, and so does its great history. For those purists who want there to be a cathedral, there are the three Hawksmoor churches. St George-in-the-East and the others would all happily fit the bill.\nHowever, the hon. Gentleman's most important statement in promoting Tower Hamlets was that we should look to the future. The great multicultural, multi-ethnic and multi-racial mix that is Tower Hamlets, with the great change we are seeing in that part of our capital city, deserves to be recognised as an example of how our cities should be.\nThe hon. Gentleman referred to some of the political controversies and difficulties of the 1920s and 1930s, when Poplar was one of the constituent borough councils of Tower Hamlets. Tower Hamlets has also had more recent political problems, and I hope that the prospect of city status will unite all political people in Tower Hamlets over the next year or so. I hope they will focus on that, rather than on some of the high profile difficulties of the recent past.\nI wish the hon. Gentleman Godspeed with his campaign and look forward to hearing the Minister's response to what has been an excellent short debate.\nThe Parliamentary Secretary, Cabinet Office (Mr Mark Harper): As well as the hon. Member for Poplar and Limehouse (Jim Fitzpatrick), whom I congratulate on securing this debate, and my hon. Friend the Member for Cities of London and Westminster (Mr Field), two other Members are present, both of whom have an interest in that their own areas are bidding for city status. They will have listened with great interest to the hon. Gentleman's case.\nThe hon. Gentleman follows my hon. Friends the Members for Croydon Central (Gavin Barwell), for Reading West (Alok Sharma), for Southend West (Mr Amess) and for Gillingham and Rainham (Rehman Chishti) in securing a debate on his area's hopes for winning city status in the diamond jubilee competition for civic honours. I have learned many new things in the course of this debate, as I did in those previous debates. I think I am right in saying that this is the first such debate for which you, Mr Speaker, have been in the Chair. You will be pleased to know that there are 25 entries seeking city status. This is the fifth debate, so there are a further 20 debates to go if Members are as assiduous as those whom I have mentioned in seeking to make the case for their areas. The hon. Gentleman will be pleased to learn that I can confirm that Tower Hamlets' entry into the diamond jubilee competition for civic honours has been safely received. As I said, it is one of 25 entries seeking city status and there are 12 entries seeking lord mayoralty status for existing cities. That shows a tremendous amount of enthusiasm and interest in the competition, and demonstrates how attractive such civic honours are to local communities.\nThe hon. Gentleman recognised at the beginning of his remarks that I can no more endorse the aspirations of Tower Hamlets than I could those of any of the other entrants in the competition. Ministers must remain impartial, as we must ensure that bestowing city status remains a real honour, fairly bestowed and that this remains a real competition. The reason why fairness is so important is that there are no hard and fast criteria for becoming a city. It is an honour granted by the sovereign, nowadays following a competition, as a rare mark of distinction. So reasons for success or failure in these competitions are never given, and city status is not something that towns can achieve just by ticking off a list of hard and fast criteria.\nuniversities, airports, underground systems or trams, whereas some may lack those physical features but boast a vibrant cultural life.\nentry will receive a thorough and impartial appraisal of its merits, alongside the other entries in the competition. The assessment process is under way and the plan is to announce the results early in 2012, at the beginning of the diamond jubilee year. With that, this short debate\u2014it was not much of a \"debate\", in the sense that there was not a huge difference of opinion\u2014comes to an end. I again congratulate the hon. Gentleman for setting out very forcefully the case for his constituency.\nOn New Year's Day, I posted this on this blog and entitled it \"Tower Hamlets council starts to get a grip.\" I said the council should be congratulated for finally taking the initiative in vetting people before helping to promote them.\nThe post concerned a Raising the Nation event at the Brady Centre in Whitechapel, which had been organised by the Tayyibun Institute whose headquarters are less than a mile away in New Road (more about them another time).\nThe Tayyibun had invited Abu Abdissalam to teach women about the kind of child rearing techniques that would deliver \"a victorious Ummah\". However, as I noted in January, someone at the council had done their homework on Abdissalam and insisted his name be removed from the list of speakers before the Brady could be booked.\nBelieved to be aged in his 30s, he was born in Coventry and raised in London. He gained a degree in Computer Science from City University and then went to study Islamic Studies in Saudi Arabia.\nHe doesn't much like the West [\u2026] in fact he appears to be brimming with anger.\nFull details about him can be seen on the Harry's Place website here. He makes references to the stoning to death of adulterers, chopping off the hands of thieves and to Ali Al-Timini, the US cleric convicted for plotting terrorism in the wake of 9\/11.\nIt's an advert for the Twins of Faith event at the Excel Centre in Newham. As you can see, Abdissalam is one of the speakers.\nThe publicity on its website here says the event, which will have \"fully segregated seating\" will be all about \"inspiring positive change\".\nIf the council really is sincere about rooting out extremist thinking and prove that it really is getting a grip, it has to demonstrate that it is aware of these issues across all its departments and not just showboat on the obvious bookings of halls.\nThis is particularly so of East End Life.We're told that the editor has \"independence\" from communications boss Takki Sulaiman but who is overseeing the paper's advertising team. The problem is that that team, which is run by Chris Payne, is driven entirely by monetary targets. They're not well-trained: they'd be able to spot Nick Griffin's name on an advert but not many others.\nThis is not the first time it has accepted these kinds of adverts is it? A few months ago, East End Life was running adverts for Anjem Choudary's new evening school in Whitechapel. After those ads were highlighted here, none have since appeared.\nIts vetting procedures need to be strengthened. I'd suggest that they have stronger links with a body such as the Quilliam Foundation to advise on whether there are potential problems when requests for such adverts come in.\nAll this, of course, is very helpful evidence for Eric Pickles, Grant Shapps and Bob Neill, who, as predicted said here last week, will be looking at ways to bring these council newspapers on to a statutory footing.\nTwo weeks ago, I expressed astonishment that Tower Hamlets Council was promoting a Lutfur Rahman-supporting \"newspaper\" run by someone who had published disgraceful wife-beating smears about former Labour mayoral candidate Helal Abbas.\nYou'll recall that someone in the council had decided to reserve space in the town hall's newspaper 'bin' (alongside East End Life) for free copies of East London News, the successor to London Bangla.\nWhen I raised this with the council, communications head Takki Sulaiman insisted there was nothing wrong. Tory leader Peter Golds then complained and now embarrassed Takki has been forced by his bosses into a U-turn.\nI am writing in response to your enquiry regarding East London News.\nA decision was made in early August to allow 5 copies into reception following a request from the publisher. This decision was taken on the basis that we allow other newspapers as well. As you know, the Council is not responsible for the editorial content of the newspapers.\nThe Council has reviewed this decision and we have decided to exclude all newspapers from reception. This will be hard for some of the journals but the Council does not want to be challenged for allowing one and not another.\nIt cannot be guaranteed that ELN will never appear in the reception area as often people bring it in and leave it around. Facilities Management staff have been instructed to do regular checks. Finally, we will still allow journals like college prospectuses etc as they provide a service to residents.\nIf you would like any further information please do not hesitate to contact me on the numbers above.\nBut even now, Takki can't resist to mislead. There were far, far more than five copies when I picked up mine.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"In 1848, Karl Marx and Fredrich Engels published a short pamphlet on behalf of the Communist League. Marx and Engels, both young men at that time, were tasked by the League to produce a document that would define their current situation and propose a communist path forward. This is what they did. Their text - The Communist Manifesto - arrived at a propitious time. Not long after the publication of the Manifesto on February 21, 1848, workers and peasants as well as sections of the middle class..\nWe, at LeftWord Books, recently published John Reed's \"stirring eyewitness account\" of the Russian Revolution, 'Ten Days That Shook the World' with an introduction by one of India's finest journalists and public intellectuals P. Sainath. In Howard Zinn's words, Reed \"made history come alive for the readers of popular magazines and impoverished radical monthlies\" through his journalistic work in the times preceding and during the First World War when warmongering and binary narratives were the ..","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Yarn is Heartland by Lion Brand.\nI chose to add a button band with buttons rather than using the zipper as called for, mainly because our grandson is very (!!) tall and I needed to add extra length.\n- HERE's a really cute little project that would be wonderful little gifts. And HERE is another one.\n- And HERE's another fun thing to make for gifts or for yourself.\n- THIS is a nice bag pattern that could be useful for so many occasions.\n- And THIS falls under the awwwww category. And if you go to THIS link at her site there are lots of free patterns.\nThat Christmas box filled with goodies must be overflowing by now. You are a machine!!! Gorgeous cardigan. Love the wool colour and those buttons are very sweet.\nDinosaur buttons! He'll like these much more than a zipper.\nThe Hoodie will be perfect for wintertime and the buttons will bring pleasure, I'm sure, to your GK.\nGreat sweater finish, perfect for the cold months ahead.\nThanks for the tips, good ideas for gifts.\nLove it! Very cool buttons!\nAwwww those buttons are so cute!! A beautiful, cozy warm gift for your grandson. The sweet little dinosaurs are the perfect finishing touch.\nOH MY!!! SO many great sites! I LOVE that little key chain bag and the notions bag! I am a \"Medium\" level crochet-er and I always dabble in a few projects now and then so I bookmarked the site with the free patterns. And YES, I did literally go \"AWWWWW\" when I saw the bib. Your sweater is ADORABLE -- love the buttons!! Thanks for visiting my blog and for all of these great links!\nyippee. what a box of goodies.\nWow, beautiful job on the sweater...and those buttons, yeah!!","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzalogf b/data_all_eng_slimpj/shuffled/split2/finalzzzalogf
new file mode 100644
index 0000000000000000000000000000000000000000..ac02cb3e4c21a3ec7c01b1a3533049c466676e56
--- /dev/null
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@@ -0,0 +1,5 @@
+{"text":"Central London's most exciting destination for dinner and drinks. The Hydrant is a hive of activity, playing host to regular beer tasting sessions and mixology classes. With a stunning array of craft beers, real ales, seasonal cocktails and inventive fresh food.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Merrick Pet Care has recalled the Jr. Texas Taffy pet treat all lots because it may be contaminated with Salmonella. If you have purchased these treats stop feeding them to your pet immediately and return to Pet Supplies \"Plus\" (or the store where you purchased it) for a full refund. Carefully double wrap any open food and return it too for a refund.\nMerrick Pet Care has made the decision to recall all Jr. Texas Taffy pet treats in the abundance of caution. Salmonella can affect animals and there is risk to humans from handling contaminated pet products. People handling the treats can become infected with Salmonella, especially if they have not thoroughly washed their hands after having contact with the chews or any surfaces exposed to these products. Consumers should dispose of these products in a safe manner by securing them in a covered trash receptacle.\nThe Jr. Texas Taffy was shipped to distributors and retailers throughout the US. These individuals have been notified and have activated their recall procedures.\nThis entry was posted in Dog Treats and tagged Recall. Bookmark the permalink.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Giro Xar Helmets are quality cycling helmets that will ensure your safety while you enjoy your cycle rides. Enjoy cycling can not stress enough the importance of having the appropriate head gear when riding your iron horse. If you are looking for a quality helmet then look no further than the Giro Xar Helmet range that is available from the link below.\nThere are many helmets available for the modern cyclist and it is important that you chose the correct one as you never know when you will need it most. That steep descent or that fast commute in to work can sometimes result in disaster when you and your bike part company and you end up eating dirt or tarmac. Wearing a Giro Xar Helmet you will be safe in the knowledge that you have reliable headgear that can help protect you. A helmet is not a sure safe way of avoiding injury but it does help.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Cross River Rail Project will deliver a new 10.2km rail line between Dutton Park and Bowen Hills including 5.9km of twin tunnel under the Brisbane River and the Brisbane CBD. The project also includes the construction of 4 new high capacity underground railway stations at Boggo Road, Woolloongabba, Albert Street, Roma Street and the redevelopment of two existing overground stations at Dutton Park and Exhibition Showgrounds.\nRail Planning Services prepared a report for the delivery of the construction works required for the proposed Northern and Southern Portal. The Northern Portal works includes, new alignment of the surface tracks, a new Down Exhibition track including construction of a new viaduct and upgrading of Exhibition Station. The Southern Portal works includes new alignment of surface tracks, a trough structure and new pedestrian tunnel.\nRail Planning Services input, through the Design Development stages of the project enabled the design to be honed to facilitate construction with reduced impact on the existing network and within the project timeframes. Outputs for the client include detailed Staging Diagrams considering the key disciplines of Track, Civil, Electrical, Signalling & Communication and optimized use of possessions and critical resources, together with a Constructability Report.\nThe interface between Cross River Rail tunnel and the existing Queensland Rail network was analysed at the northern and southern ends (portals). A detailed construction methodology was delivered for both portals and temporary alignments were required to integrate -the CRR tracks and minimise the disruption to the current services. Stakeholder coordination between Cross River Rail Delivery Authority (CRRDA), Queensland Rail (QR), Technical Advisors, and Rail Planning Services (RPS) was critical to liaise with the activities of the tunnel construction and portal structure.\nSome of the structural challenges included the reinforcement of the existing freight flyover and the electrification to allow passenger trains movements during construction.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Michael Daves performs Ralph Stanley's \"Pretty Polly\" with his electric band at the Bell House in Brooklyn on March 5, 2016. The concert celebrated the release of his album Orchids and Violence, which pairs bluegrass and electric takes on mostly traditional tunes. In the band are Jessi Carter on bass and Kid Millions on drums.\nMichael Daves performs Ralph Stanley's \"Pretty Polly\" with his bluegrass band at the Bell House in Brooklyn on March 5, 2016. The concert celebrated the release of his album Orchids and Violence, which pairs bluegrass and electric takes on mostly traditional tunes. In the live band are Noam Pikelny on banjo, Brittany Haas on fiddle, Jake Jolliff on mandolin, and Larry Cook on bass.\nMichael Daves's Orchids and Violence comprises two discs with identical track listings of mostly traditional bluegrass tunes, including songs by bluegrass pioneers Bill Monroe and Ralph Stanley. The first disc has straightforward interpretations with a band of roots-music innovators: bassist Mike Bub, violinist Brittany Haas, mandolinist Sarah Jarosz, and Punch Brothers banjoist Noam Pikelny. The second includes bass, drums, and electric guitar, mostly played by Daves, with a raw, experimental rock take on those tunes.\nChris Thile & Michael Daves perform \"You're Running Wild\" (made famous by the Louvin brothers), off their 2011 debut duo album, Sleep with One Eye Open. The video was directed by Steve Lippman, aka Flip, and shot at Rockwood Music Hall in New York City.\nChris Thile & Michael Daves perform Lester Flatt's \"My Little Girl in Tennessee,\" off their 2011 debut duo album, Sleep With One Eye Open. The video was directed by Steve Lippman, aka Flip, and shot at Rockwood Music Hall in New York City.\nChris Thile and Michael Daves discuss their 2011 debut duo album, Sleep with One Eye Open. The album, recorded live to tape over four days at Jack White's Third Man studio in Nashville, is a collection of 16 traditional tunes by bluegrass legends like The Monroe Brothers, The Louvin Brothers, Jimmy Martin, and Flatt & Scruggs. Video directed by Steve Lippman aka Flip.\nChris Thile & Michael Daves perform Lester Flatt's \"Sleep with One Eye Open,\" the title track to their 2011 debut duo album. The video was directed by Steve Lippman, aka Flip, and shot at Rockwood Music Hall in New York City.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzalxxz b/data_all_eng_slimpj/shuffled/split2/finalzzzalxxz
new file mode 100644
index 0000000000000000000000000000000000000000..cd97e84e87016ffb242b6968d733809de72699e0
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@@ -0,0 +1,5 @@
+{"text":"Juno is an Internet and email service provider well known for its free dial-up email service. If you've lost or forgotten your password, you can quickly contact Juno by using a special \"Reset Juno Email Password\" page on the Juno website. By entering a few account details and submitting a form, you'll let the Juno team know that you need to recover your lost or forgotten password. They'll contact you, let you reset it and also let you choose a new password.\nOn your computer, you will need to double-click on the Juno icon on your desktop.\nOnce the Juno email gets launched in your computer, you will need to select Email to connect.\nAfter selecting Email, you will need to click on the Options and then select Password and Security option.\nThe next prompts will ask you to enter your current password and your new password (twice).\nAfter you have entered your old and new password in the provided field, you will need to click on the OK button. Your new password will be configured for your Juno email account right away.\nTry these steps and still, you are unable to resolve Juno email login Problems, you need to contact Juno customer. You can contact Juno Customer Service for troubleshooting Juno Webmail. With the help of a well-prepared and expert professional, we encourage here. Instruct them to determine the login error which you are getting. The service of the Customer Care Group can be reached continuously for its customers. This is the reason that the closure is on the chance that you can connect with customer support 24 x 7 for troubleshooting.\n519,387 total articles and counting.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Children are taught in classes according to age. Children begin their school lives in the Reception Class. Here they are in the Foundation stage of the National Curriculum.\nKey Stage 1 of the National Curriculum is followed from age five onwards. The children are in Key Stage 1 (KS1) between the ages of five and seven. Their year groups are called Years 1 and 2 (Y1 and Y2).\nAt the end of Key Stage 1 children complete national tests known as Statutory Assessment Tests (SATS).\nThereafter the children follow the Key Stage 2 (KS2) National Curriculum whilst they are in Years 3, 4, 5 and 6 (Y3, Y4, Y5, Y6).\nAt the end of Key Stage 2 the children take the Key Stage 2 Statutory Assessment Tests before going into secondary school. How the school fares in these tests is reportable to parents.\nResults are published each year in the Annual Governors' Report to Parents. The most recent results can be viewed here.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Add a pop of pattern to your room with the Lola Table Lamp. A large black and white printed, striped white, or grey woven textures fabric shade sits atop a black or brushed steel finished base. A thin pole connecting to a chunky dome base yields a unique silhouette that houses a bright and functional 150 Watt bulb. This large scale table lamp is great for a nightstand or an entryway table. This lamp has a black cord and on\/off functionality and is smart outlet compatible. Bulb is not included.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The list of dangers is actually quite long. Physicians are at risk for communicable illnesses, both common and rare; workplace violence by bullet, blade, and fist; abuse and assault, both physical and verbal. There are our occupational hazards, injuries, and stresses that lead to rates of burnout, depression, substance abuse and suicide that outpace our peers however measured (education, gender, generation). Every physician has been touched by these, either directly or as witness. I have a colleague who uses a wheelchair because of a bullet from a long-ago attack, and I have physician friends who have been shaken by death threats from patients or their families. I have seen a careers altered by hepatitis from needle sticks, nurses and doctors injured and even disabled by combative patients. We have borne the slaps, the punches, the verbal abuse.\nWhy are we afraid to study data that would establish and quantify the occupational hazards of being a doctor? Some of these hazards have been studied, but I have seen no comprehensive analysis of workplace risk for physicians like those that have been done for other professions. As physicians we have a sense of the risk, and yet we remain engaged, continuing to care for our patients. We participate in the disaster drills, we know where the safe rooms are in offices and clinics and we know \"these things\" happen. Perhaps society prefers to remain blissfully ignorant of the sacrifice and risk their doctors take on, comforted by the fantasy of the serene and nurturing hospital. Perhaps we are all loathe to let reality and data shatter the illusion.\nAnd then shots are fired in a world-renowned hospital on an ordinary Boston morning and a gifted surgeon on the ascent of a promising career trajectory is wounded, and then dies, his colleagues unable to save him. There is plenty of trauma to go around. Even this place is no safe haven. We are forced to see this, all of us.\nToday, we doctors as well as the nurses and hospital staff at this hospital and all of the others across the city, the state, and the country greet the new day and return to the work of taking care of patients. Caring for our patients, our communities, everyone.\nMaybe it is time to be a little more aware and grateful, acknowledging that even outside of a war zone, we are in harm's way.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"IntelliJ IDEA helps you run and debug your Node.js applications. You can debug applications that are started from IntelliJ IDEA as well as attach to already running applications.\nIntelliJ IDEA runs Node.js applications according to a run configuration of the type Node.js. IntelliJ IDEA also uses this configuration for debugging Node.js applications locally.\nFrom the main menu, choose Run | Edit Configuration, then in the Edit Configurations dialog, click on the toolbar and select Node.js from the pop-up list. The Run\/Debug Configuration: Node.js dialog opens.\nSpecify the Node.js interpreter to use, see Configuring a local Node.js interpreter for details.\nSpecify the Node Parameters that customize the start of Node.js. For example, to make your application accessible for remote debugging, type one of the debugging flags depending on your Node.js version: --inspect=<debugger port> for Node.js versions 6.5 and higher or --debug=<debugger port> for any Node.js version earlier than 8. The default debugger port is 5858.\nIn the Application parameters text box, specify the arguments to be passed to the application on start through the process.argv array.\nChoose the newly created Node.js configuration in the Select run\/debug configuration drop-down list on the toolbar and click next to it. The application starts, and the Run Tool Window opens showing the application output.\nLocal debugging: in this mode, your application is started from IntelliJ IDEA and is running locally on your computer. To debug it, use a Node.js configuration.\nDebugging a remote application: in this mode, your application is running in a remote environment in the debug mode and IntelliJ IDEA attaches to a running process. IntelliJ IDEA recognizes --inspect and --debug flags so you can make any application accessible for remote debugging. IntelliJ IDEA supports remote debugging with the Chrome Debugging Protocol and the V8 Debugging Protocol (also known as Legacy Protocol). In either case, a debugging session is initiated through a run\/debug configuration of the type Attach to Node.js\/Chrome.\nSet the breakpoints in the Node.js code where necessary.\nChoose the newly created Node.js configuration in the Select run\/debug configuration drop-down list on the toolbar and click next to it. The Debug Tool Window opens.\nPerform the steps that will trigger the execution of the code with the breakpoints.\nSwitch to IntelliJ IDEA, where the controls of the Debug tool window are now enabled. Proceed with the debugging session \u2014 step through the breakpoints, switch between frames, change values on-the-fly, examine a suspended program, evaluate expressions, and set watches.\nWhen typing a multi-line code fragment, press Shift+Enter to start a new line and Ctrl+Enter to split a line.\nWhen you are debugging a Node.js application, IntelliJ IDEA shows two console tabs in the Debug tool window - Console and Debugger Console.\nThe Console tab shows the output of the node process itself, that is, everything that is written to process.stdout and process.stderr directly or is logged using console.*.\nUse this protocol to debug applications started with the --inspect flag. This flag is used with Node.js versions later than 6.3.\nUse this protocol to debug applications started with the --debug flag. This flag is used with Node.js versions earlier than 8.\nWith IntelliJ IDEA, you can debug an application that is running in a remote environment. IntelliJ IDEA supports remote debugging with the Chrome Debugging Protocol and the V8 Debugging Protocol (also known as Legacy Protocol). In either case, a debugging session is initiated through an Attach to Node.js\/Chrome configuration.\nSet the breakpoints as necessary.\nChoose Run | Edit Configurations from the main menu, then click in the Edit Configuration dialog box that opens, and choose Attach to Node.js\/Chrome from the list. The Run\/Debug Configuration: Attach to Node.js\/Chrome dialog box opens.\nSpecify the host where the target application is running and the port passed to --inspect when starting the Node.js process to connect to. Copy the port number from the information message Debugger listening <host>:<port> in the Terminal tool window or in the Run tool window that controls the running application. The default port is 9229.\nIn the Attach to area, choose Chrome or Node.js > 6.3 started with --inspect.\nChoose the newly created Attach to Node.js\/Chrome configuration in the Select run\/debug configuration drop-down list on the toolbar and click next to it. The Debug Tool Window opens.\nPerform the actions that will trigger the code at the breakpoint. Control over the debugging session returns to IntelliJ IDEA.\nSwitch to IntelliJ IDEA. In the Debug tool window, step through the breakpoints, switch between frames, change values on-the-fly, examine a suspended program, evaluate expressions, and set watches.\nCreate an Attach to Node.js\/Chrome run\/debug configuration as described above and specify the host and the port passed to --debug. The default port is 9229.\nMake sure the application to debug has been launched in the remote environment with the following parameters: --debug=<debugger port>. The default port is 5858.\nProceed as during a debugging session with Chrome Debugging Protocol.\nSelect After launch to start a browser automatically when you launch a debugging session.\nIn the text box below, type the URL address to open the application at.\nChoose the browser to use from the drop-down list next to the After launch checkbox.\nPress Ctrl+Alt+S or choose File | Settings (for Windows and Linux) or IntelliJ IDEA | Preferences (for macOS) from the main menu, and then go to Build, Execution, Deployment | Debugger | Live Edit.\nSelect Update Node.js application on changes. Set the elapsed time for applying the changes to a running application: accept the default value 300 ms or specify a custom value using the spin box next to the corresponding field.\nWith IntelliJ IDEA, you can attach to Node.js applications that are running in Vagrant boxes, in Docker containers, or on remote hosts accessible via various transfer protocols or via SSH.\nFind some examples at Quick Tour of WebStorm and Docker.\nIntelliJ IDEA supports debugging of Node.js applications in Docker containers through run\/debug configurations of the type Node.js.\nMake sure Docker is installed, configured, and running.\nCreate a Node.js run\/debug configuration as described above.\nSelect one of the configured Node.js interpreters of the type Remote Interpreter - Docker from the drop-down list or configure a new one. See Configuring Remote Node.js Interpreters for details.\nClick next to the Edit Docker Container Settings field and specify the settings in the Edit Docker Container Settings dialog that opens.\nAlternatively, select the Auto configure checkbox to do it automatically. Learn more about the Auto configure mode at Quick Tour of WebStorm and Docker: What Happens On Each Run.\nIn the Host IP text box, type the IP address of the Docker's host, the default IP is 192.168.99.100. The host is specified in the API URL field on the Docker page of theSettings \/ Preferences Dialog.\nSet the breakpoints in the Node.js code as necessary.\nChoose the newly created Node.js configuration in the Select run\/debug configuration drop-down list on the toolbar and click next to it.\nProceed as during a local debugging session, as described above.\nIntelliJ IDEA supports debugging additional Node.js processes that are launched by the child_process.fork() method or by the cluster module. Such processes are shown as threads in the Frame pane on the Debugger tab of the Debug Tool Window.\nSet the breakpoints in the processes to debug.\nCreate a Node.js run\/debug configuration.\nTo examine the data (variables, watches, etc.) for a process, select its thread in the list and view its data in the Variables and Watches panes. When you select another process, the contents of the panes are updated accordingly.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzamrqp b/data_all_eng_slimpj/shuffled/split2/finalzzzamrqp
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index 0000000000000000000000000000000000000000..e450184e29ba398866e83c6eea84344cf4ea8881
--- /dev/null
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@@ -0,0 +1,5 @@
+{"text":"Changing your diet can be a difficult process, especially when you try to take it on by yourself. If you want to lose weight or treat gastrointestinal issues with a change in diet, the best way to make an effective and lasting change to your habits is by using a medically designed and supervised diet plan. At the practice of Hardeep M. Singh, MD, in Orange County, California, Dr. Singh uses a program called Healthier You that he designed personally and has used to help people lose weight for years. To make an appointment, call the office or use the online scheduling tool today. Dr. Singh is proud to also serve the neighboring communities of Santa Ana, Irvine, and Newport Beach.\nHow do I know if I could benefit from weight loss?\nIf you possess one or more risk factors for unsafe weight gain, you could benefit from a diet plan for weight loss.\nHow could a diet program help me?\nIt's one thing to decide you want to eat healthier, but making changes to your diet on your own can be harder than people think. Having the help of a professional to create a meal plan that you can stick to and that you can make a permanent part of your lifestyle can make a huge difference in your ability to change your diet for the better.\nFor the best results, a plan designed and supervised by your doctor is often the best option for people serious about changing their diet, whether they want to lose weight, prevent or treat gastrointestinal problems, or all of the above.\nWhat kind of diet plans are available?\nDr. Singh offers his patients the state-of-the-art Healthier You program, a weight loss program he created using Ideal Protein\u00ae products. Ideal Protein is a medically developed ketogenic weight loss program that uses a four-phase system to help you lose weight quickly and then develop the eating habits that will keep you at your ideal weight.\nDr. Singh has integrated his own expertise and years of experience with the Ideal Protein program and is now pleased to offer his patients a more personalized experience with the Healthier You program.\nIf you're interested in how the Healthier You program could help you reach your ideal weight, call the office today or make an appointment online.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Great served with pound cake and additional fruit.\nPlace raspberries in container of electric blender or food processor; process until smooth.\nAdd confectioners' sugar and remaining ingredients; process until blended.\nPour through a wire mesh strainer; press mixture with back of spoon against sides of strainer to squeeze out liquid.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Ground turkey, vegetables and pumpkin come together in this spicy chili - the perfect way to warm up on a chilly evening.\nHeat oil in Dutch oven or large deep skillet on medium heat. Add turkey; cook 5 to 7 min. or until done, stirring occasionally.\nAdd celery, yellow onions, red peppers, jalape\u00f1o peppers, garlic and seasonings; mix well. Cook 7 to 10 min. or until vegetables are softened, stirring occasionally.\nStir in tomatoes, beans, broth, pumpkin, Worcestershire sauce and syrup; simmer on medium-low heat 1 hour or until thickened, stirring occasionally. Top with cheese and green onions. Serve drizzled with dressing.\nPrepare using Ren\u00e9e's Classic Ranch 1\/2 Fat Dressing.\nServe with lime wedges to squeeze over the individual bowls of chili.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Children in Choughs class enjoyed a morning at the movies today (in the classroom!) as a reward for the hard work and effort put in by all of the them during this week's SATS tests. Courtesy of Mrs Jane the children enjoyed some treats whilst watching \"The Greatest Showman\" film accompanied by their favourite cuddly toy.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The average cost of a nursing home in Colorado is $7,000 per month, which can be a hefty price tag for many middle-income families. It can be beneficial to plan ahead, considering Medicare and other funding sources to cover long-term care expenses. The application process can be complex, often making even the most well-intentioned individual ineligible for funding.\nGiven the eligibility requirements and potential pitfalls associated with applying for benefits, it is in your best interests to confer with an experienced estate planning lawyer. He or she can provide much-needed advice during the initial planning stage, and guidance through the application process.\nFrom this evaluation, I can determine what long-term care planning tools will work best for your unique situation. Potentially these tools could be wills or various types of trusts.\nLong-term and Medicaid planning typically also entail identifying a person who can make health care decisions for you if you become incompetent. This role is typically called a health care power of attorney. If you do not identify a person in advance, it is typically up to the courts to decide. I can also help you to understand the responsibilities of this role so you can designate the appropriate person.\nLearn more about the law firm and how I might be able to assist with your estate planning needs by calling 800-331-0745. Or, if you prefer, send an email using my online contact form. Flexible payment options are available.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzanmtu b/data_all_eng_slimpj/shuffled/split2/finalzzzanmtu
new file mode 100644
index 0000000000000000000000000000000000000000..818168aa444009c13232508f12ee4db5ddd0e18f
--- /dev/null
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@@ -0,0 +1,5 @@
+{"text":"The statistic presents a forecast in pet store revenue in the United States from 2018 to 2023. It is projected that U.S. pet store sales will grow from around 19.5 billion U.S. dollars in 2018 to approximately 22.39 billion U.S. dollars by 2023.\nEverything On \"Pet food in the U.S.\" in One Document: Edited and Divided into Handy Chapters. Including Detailed References.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Forward Gaming will play their first professional match in patch 7.20 against Zugzwang in what could be a real walk-over in this Chongqing Major North America Qualifier.\nZugzwang is a tier 4 team that is coming off a loss against Team Team in its North America Open Qualifier before using their second chance to fight their way back into the tournament by taking down Moist Lads and Team nevermis.\nMoist Lads and Team nevermis are some random public team in Faceit \u2014 so the feat can't be taken too seriously.\niAnnihilate, the position 2 player from Zugzwang, is one of the players that Forward Gaming have to look after here. iAnnihilate's gameplay is quite good. Despite that, he alone will not be sufficient to carry this squad to take down Forward Gaming, but if he has support, he could help cause an upset here.\nForward Gaming's performance in the Kuala Lumpur Major was great. Their only mistake was not respecting Arteezy's Arc Warden from Evil Geniuses, which essentially cost them during their elimination game.\nForward Gaming showed the world they are tier 1 team with their draft and gameplay skill.\nResolution, the position 2 player from Forward Gaming, is very good in micro-managing heroes, which allowed Forward Gaming better drafting potential. Universe, the position 3 player has quite a few options in drafting for this patch because Beastmaster and Puck are buffed.\nWe believe Forward Gaming are ready to secure their ticket to the Main Tournament of Chongqing Major.\nOur suggestion is to pick Forward Gaming to win \u2013 get the best odds at BetOnline.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"We will be having an exciting day of carnival games and activities! We have not 1, not 2, not 3, but 4 inflatables for kids to play on. There will be balloons, gummy worms in whip cream, car races, and more. There will games for kids to play to see if they can get the best score and earn a prize! Sac races, bean bag toss, and tug-of-war are some of them. This will be a fun day in the sun!\nNo summer at KidQuest Camp would be complete without a visit to beautiful Bronte Creek Provincial Park. Bronte Creek is a place full of colour, activity, and life. At Bronte Creek, the trails are numerous and unique in their flora and fauna. The play barn provides an excellent opportunity for children to run, climb, slide, and play in a barnyard setting. There are goats to feed and pet, ducks to observe, and an outdoor pool to swim in. No trip to Bronte Creek is complete without our annual LEGENDARY HIDE N'SEEK game. For more information on this exciting trip, check out Bronte Creek's website.\nKidQuest Camp is no stranger to Christie Lake. With a beach, designated swimming area, great hiking trails, canoeing, a playground, a creek to catch frogs and minnows, and frisbee golf, there is lots to do at Christie Lake. Some of our favourite activities include our sand castle building competition and Vaseline covered watermelon football game in the water. For more information about Christie Lake Conservation Area, visit their website.\nBinbrook Conservation Area offers a tremendous variety of outdoor activities for campers to enjoy. Binbrook has a beach, hiking trails, playgrounds, and more. \"A day at Binbrook is like a day at the cottage, but close to home. The swimming beach, spray pad, play area and picnic facilities make for a full day of fun. Explore nature on the trails and from observation platforms and see if you can spot some of the local wildlife. For more information about Binbrook Conservation Area, you can check out their website.\nThis day will be a blast as campers have Nerf battles and play other games in a maze-like obstacle course! Not only is it colourful and fun, but it's also glow-in-the-dark! We hang 12 black lights a round the gym so that everywhere you go you'll light up! The design for our maze this year is completely new, and will utilize a new method of maze building. There will be other glow-in-the-dark games this today, so make sure to wear white, bright yellow, or another colour that glows!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Search Park Place Estates homes for sale & real estate in Frisco, Texas. Contact your Frisco real estate experts today for information about Park Place Estates neighborhood properties for sale or to schedule a private home tour.\nWant to purchase a home in Park Place Estates? Call your Frisco real estate team, VIP Realty at 214-295-4888. Your neighborhood Park Place Estates REALTORS\u00ae and agents are here to help with the Dallas housing market.\nFamilies adore Park Place Estates homes for sale because these properties are very family-friendly and belong to a family-oriented community. Furthermore, residents from surrounding towns know this area for its relaxing atmosphere and cheerful residents. Future owners of the homes for sale in Park Place Estates will appreciate that this area has one of the lowest crime rates in all of Denton county. Good schools can be found here, thanks to the Frisco ISD.\nHomebuyers with an eye for quality can immediately tell the kind of value offered by Park Place Estates real estate listings. Most of these properties have 3 to 5 bedrooms and 2 to 4 bathrooms. On average, these single family houses have between 3700 and 5000 square feet of space.\nReal estate listings in Park Place Estates are surrounded with beautifully landscaped lawns, elegant stone and masonry work, beautiful fixtures, and ample outdoor living space. Inside, you will be greeted by newly renovated hardwood flooring, new furniture and appliances, classy kitchen and bathroom fixtures, and spacious rooms.\nFinally, you should not have problems finding good schools for your kids as this subdivision has a total of 37 elementary schools, 17 middle schools, and 16 high schools overall.\nYou will have no more room for doubt once you hear about Park Place Estates home values. Despite the high quality of the homes and the fringe benefits offered by the community, home values in Park Place Estates are still within a range that is just within reach of even average income earners. The current average listing price is $790,000. The most modest homes are priced more or less $400,000 while the more expensive ones are at around $870,000.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Three-year-old Eli Kaufman's day was made when he spotted a rock, with his mother Kacey's help, outside their limestone home on February 21. The palm-sized, triangular-shaped rock caught his eye because it had the cartoon face of a yellow Angry Bird.\nThis rock is just one of hundreds hidden around Bay Ridge, Brooklyn for kids and adults alike to find and pick up during their everyday routines. Homemade, painted rocks are hidden and rediscovered in public places by strangers as part of Bay Ridge Rocks! a project led by stay-at-home moms Ranu Abu-Sbaih and Amie Jo Pappas.\nThe rocks have uplifting messages like \"You are loved\" and \"You can be anything,\" and images that have included candy apple red hearts, golden suns with smiles and colorful rainbows.\nThis initiative is one branch of The Kindness Rocks Project that has captivated multiple U.S. and international cities since its inception in Massachusetts in August 2015. A woman, who chose to remain anonymous at the time, started collecting beach rocks after her parents died. The rocks were a source of inspiration for her, and she thought maybe they could be for others as well.\nFor Abu-Sbaih though, this project is meant to brighten someone's day, promote neighborhood involvement and boost local morale.\n\"The end goal is the same as the working goal \u2013 that we get people to create art work, and get people to know that they can make beautiful things and that those beautiful things can brighten somebody's day,\" she said.\nSimilarly, Pappas said the project is not about any one person; rather, it is about residents being creative and using that creativity to make Bay Ridge an even better place.\nAbu-Sbaih said she learned about the rock painting over the Christmas break from Pappas, where the trend had become popular in her hometown of Lakeland, Florida. When scrolling through her Facebook feed a few days later, Abu-Sbaih discovered that her hometown of Oswego, N.Y. was also participating in the rock hunt.\nAbu-Sbaih looked into what other cities were doing online and developed a game plan. She painted her very first rock like a strawberry and placed it in a produce basket at Pineapple Farm, the fruit and vegetable store located on 74th Street and 5th Avenue. Her second rock was painted like a ladybug, and she put it on the ledge of a mural that featured a ladybug.\nThe other handful of rocks that she painted had phrases like \"Feel blessed,\" \"Let your light shine\" and \"Be kind.\" Those were scattered onto neighborhood windowsills, by benches and in the branches of trees.\nAfter hiding the handful of rocks in early January, Abu-Sbaih went back to the spots a few days later and found that nobody had picked them up or had even moved them. So she decided to create a Bay Ridge Rocks! Facebook page and inviting friends to come paint, and look for or hide their own rocks. At just two months old, the page now has more than 430 members.\nThough the group continues to gain popularity and recognition, Abu-Sbaih said she hopes the hunt will expand beyond the \"small radius\" that is Bay Ridge. She and Pappas aspire to be at the Lakeland Rocks level \u2013 that group has almost 29,000 members.\nWhile the neighborhood may be small, residents like Kaufman have welcomed this treasure hunting trend with open minds and hands.\nThe duo recently set up painting tables in the Bay Ridge branch of the New York Public Library and at the Parent Teacher Association's \"Around the World in 102 Days!\" private art gala at P.S. 102. They plan to set up more painting sessions for members and newcomers in the local libraries and at one of the neighborhood parks when the weather gets warmer.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzannfa b/data_all_eng_slimpj/shuffled/split2/finalzzzannfa
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+{"text":"Add extra security to your caravan with a Torpedo Caravan Leg Lock. This simple to use lock fits over the winding points of your corner steady legs, securely locking them in to place. When used in the down position this locks the corner steadies to the floor, immobilising your caravan. Torpedo caravan leg locks are high visibility to attract attention and act as an additional deterrent to potential thieves.\nThe Torpedo was designed in Purple Line's UK innovation centre. This robust, strong leg lock is constructed using heavy-duty composite metals that have been specially chosen to be resistant to cutting, drilling and gas freezing.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Do I Need a Website For My Home Based Business?\nOften we are faced with the question \"do I need my own website to run a home based business?\" The following 10 reasons outline the benefits you will have in owning your own website.\n1. Establish A Presence \u2013 Fact is, millions of people access the internet everyday and this number is expected to double over the next couple of years. Having your own website for your home business will allow your internet business to achieve maximum exposure. It may also boost your image and improve your business' credibility. Your website can contain a simple 1 page site with information about your home business (for example contact information, hours, etc) or a more complex website for you to share your expertise, experiences, education and enthusiasm to the great world wide web.\n2. Creates a 24 hour service \u2013 A website is accessible 24 hours a day\/7 days a week \u2013 Weekends, Holidays, Weekdays etc. It basically works for you even when you are not working. This ensures that you don't miss a sale!\n3. Expand your market to the global level \u2013 Your website allows you to tap into potential markets your probably would never have considered. These include the international market, where you can communicate with potential customers from all around the globe, specialised markets, where you can direct your website to attract specific customers of a particular expertise, age, interest etc and the local market, where you can meet up with people in person to talk about your business.\n4. Inexpensive, flexible and simple \u2013 The average cost to get a domain name and reliable web hosting for a year can cost as little as $100. Most web hosting companies have access to website builders which will allow you to build a website with no technical knowledge. Even if you were to get a web designer to create your website this usually costs under a thousand dollars. Compare this to spending the same amount of money in putting a decent size ad in your local paper. The difference is that the local ad you just spent money on expires after that edition is read whereas your website will be yours and advertising for you on the internet for as long as you like. You also have the flexibility of adding features such as forms, polls, surveys etc to collect visitors names and email addresses for future correspondence.\n5. Improve customer service \u2013 you website can be a world of information to your browsers and available to them when they are ready to learn more. Your website can also contain a \"Frequently Asked questions\" page which will help potential customers understand and clear up any queries without taking up your time. This should reduce your support costs by about 20%. You website may also allow feedback from customers. This is a valuable tool to see what your customers think, how you can improve and what can you further provide to satisfy them.\n6. Set up an online shop \u2013 With this added advantage a website will bring in more sales for you as many people like to research items of interest before buying it in today's world. While they are excited and interested in your offer, this is the time you must \"catch\" that sale as they are more likely to purchase it if your offer is available at the e click of a button.\n7. Readily updated information \u2013 Beauty of your website is that it can be green one day and red the next. You have the opportunity to change appearance, information and the words in just a few minutes. You can update information readily and you can update it as many times as you want. A website is easier, cheaper and more convenient to update than brochures, business cards, price lists, and inventory. This saves many dollars in printing and distribution.\n8. Better ad tracking and marketing \u2013 Advertising, press releases, more advertising, more press releases \u2013 all this adds up to one word \u2013 expensive. One advantage of having a website is the ad tracking features available. You will know exactly where your customers come from and can repeat that particular strategy or advertisement. You cannot do this offline, it would not be practical to ask every customer that comes into your shop where they heard about you or which ad did they respond to. The internet allows you to do this and this in turn allows you to target the specific market you need.\n9. Addition of blogs, pictures, videos \u2013 Posting to your blog on a regular basis or adding multimedia content to your site will not only improve the attractiveness and effectiveness of your offer but also improve your site's exposure on the search engines.\n10. personal satisfaction \u2013 lastly it doesn't come without saying that having your own website will definitely give you some personal satisfaction. You have the chance to experiment with and learn about design, and the freedom to present and emphasize the information you want the way you want to. Creating and maintaining your own Website allows you to learn more about today's technology and keep up with times.\nOverall the advantages of having your own website for your home business is clear allowing you benefits in both time and money. A small investment now in a website can lead to great profits in the future.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"LOS ANGELES, CALIFORNIA, UNITED STATES OF AMERICA (MARCH 12, 2011) (HOLLYWOODTV - Bobby Brown is reported to have wanted his daughter, Bobbi Kristina, to appear on his upcoming reality show, and has not been supportive of Bobbi doing a reality show Whitney's family instead for that reason. Allegedly, the former Boys 2 Men crooner has been attempting to get Bobbi Kristina signed onto his show for some months now, but the girl has severed all avenues of communication with Bobby, leaving him with only Whitney's sister-in-law\/manager, Pat Houston, as a contact point for him. But apparently, sources report that Bobbi never even considered doing her father's show, and the family feels he only wanted her in the first place to make his own show more marketable.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"During the last few hours touring Prague one of our group noticed an underground restaurant being advertised as we passed by. He was so taken aback that he called us over to have a look. Triton Restaurant is located right off Wenceslas Square in the cellar of a building and had been \"built\" around 1912. The thing that made it truly spectacular is that the entire ceiling of the restaurant was covered in stalactites. Stalactites are natural crystal formations on the ceiling of caves.\nWhen we looked at the menu we were intrigued. It was a fine dining restaurant and it looked amazing. As it was late lunch time and our last meal in Prague we decided to treat ourselves and try it out. They had traditional Czech cuisine with a fine dining twist.\nWe descended the stairs and were all in awe. The restaurant was absolutely stunning. The ceilings were covered in stalactites and the decor was done in 1920's style. Beautiful Art Nouveau features like the lighting and the stained glass added to its beauty and charm. The tables were laid out with formal place settings and the ambiance of the place was truly romantic. I was just sad that The Brit wasn't there to enjoy it with me as we both have a deep love for Art Nouveau, natural wonders, and food. How much more perfect could it get?\nThe menu at Triton was actually far more extensive than the sample menu that was advertised on the street. We were very excited by the sounds of the seasonal pumpkin menu. As one of our group needs to eat gluten-free food, it was so nice to have a menu where gluten was clearly labeled in the dishes on the menu.\nOur waiters were very charming. We had the restaurant almost to ourselves as it was an odd time of day. Our waiter made sure that he was taking good care of us, yet left us alone to enjoy the beauty of the space.\nTo drink what else could I order other than Czech wine? I had a glass of 2010 Ruladske Modre-Moravina, Valtice from the Mikulov region. It was very enjoyable: good acidity, smooth and medium body, and perfect with food. When the waiters found out I was a food and wine blogger from Napa they brought me a bottle of Californian red wine and asked me if I knew it. I tried not to chuckle as they presented me with a bottle of Robert Mondavi.\nI started off with the pumpkin salad. It was a stunning dish. Pumpkin and spiced poached pear with mixed greens and roasted pumpkin seeds. It was a joy in the mouth and honestly it was the first salad I had eaten since my arrival in Europe. It was like heaven.\nOne of my friends had a bowl of the pumpkin soup. It was rich, creamy, and savory. We all loved how the soup was finished with a bit of balsamic reduction, roasted pumpkin seeds, and olive oil. It was outstanding and my friend was truly happy with her selection.\nFor my lunch I ordered the Czech special pasta dish named after a famous comedian; Vlasta Bruian's Noodles with roast chicken with apples and almonds. With such an unusual combination I had to try it out. I was served a bowl full of narrow egg noodles and in the layers were red and green peppers chopped finely. On top were grilled pieces of chicken and roasted sliced apples. It was then sprinkled with almonds to finish.\nFor me the chicken was overcooked, but I believe that is the traditional way of cooking it as opposed to a cooking mistake. It wasn't killed nor devoid of any flavor, just a little more cooked than I like and not quite tender. The rest of the dish was good, but I feel it was missing an element that would take it over the top for flavor. It is hard to comment on the dish to be honest as this was a special dish made for a specific person as opposed to a recipe that one could compare to how it is prepared elsewhere. What was nice was the combination of the roasted apple, the peppers, and noodles together. The noodles were cooked beautifully and were plentiful on my plate. I couldn't finish it all.\nMy friend keeping to the pumpkin theme had the pumpkin risotto. It was gorgeous. Full of pumpkin, mushrooms, and cream; I kept hearing mmm's from her side of the table. Not only did it look beautiful, but the layers of flavor in the mouth were really lovely. That one got the big thumbs up from me.\nThe last member of our group had traditional beef sirloin in cream sauce with cranberries and Carlsbad dumplings. I have to say that the presentation of his dish was a wow! The cranberry sauce was served in a well of whipped cream which just made it pop to the eye. There were thin slices of meat in a rich gravy and beautifully spiced dumplings to finish the plate. I didn't taste it, but it sure looked delicious! He had a huge smile as he ate and was really excited by his food.\nDesert didn't disappoint either. We ordered two desserts to share between the three of us. I ordered the chocolate torte with sour cherries and mango ice cream. It was really outstanding. The chocolate cake was flourless and had a consistency between a mousse and a cheesecake. It was rich, dark, and creamy. What was truly outstanding was the contrast of both the sour cherries and the mango ice cream. I would have never put that combination together, but it was amazing. Finished off with a wafer of dark chocolate, I really enjoyed every bite.\nMy companions chose the Creme Br\u00fbl\u00e9e. It was a really great example of the dish; it was all class with beautiful vanilla pods throughout giving it the wow factor.\nI would highly recommend that you visit Triton when you are in Prague. Spectacular surroundings, great food, and beautiful service makes this more than just a tourist place to dine. The glitz may draw you in, but the food will make you happy you splashed out. The meal for the three of us including wine came to about $90.00. Exceptional value for the quality of what we had.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Located on Water Street in Rollinsford, the Wentworth House is maintained by the Association for Rollinsford Culture and History (ARCH) as an educational and cultural center. Admission to this event is $5 for adults, and free for children and ARCH members. For more information, consult the ARCH website at ww.paulwentworthhouse.org or on Facebook at The Colonel Paul Wentworth House.","meta":{"redpajama_set_name":"RedPajamaC4"}}
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+{"text":"Going green sounds simple, but can sometimes seem overwhelming as we tend to think of installing solar panels, buying hybrid cars, or eating expensive organic foods. But there are a number of other ways you can live environmentally-friendly without blowing your budget or inconveniencing your day-to-day routine. Here are a few ways to to reduce your carbon footprint and save a few extra bucks each month.\nNot all of us can buy hybrid vehicles, but we can make an effort to drive less. Whenever possible, try walking to the grocery store, telecommuting, or riding your bike into the office. Not only are you saving time and getting healthier, you're contributing to cleaner air.\nRemember to unplug your electronic devices and appliances when they are not charging or in use. Leaving them plugged in triggers a \"phantom load\" and can drive up your energy bill substantially.\nCompact fluorescent light bulbs are a thing of the past. Upgrade your CFLs to LED bulbs as they can last up to ten times longer, thus saving you money on replacement costs and reducing your trips to the hardware store.\nWhen heading out to the grocery store, remember to bring reusable bags. Keep them stashed in your trunk so you're always prepared and avoid adding plastic bags to the landfill.\nStore-bought cleaners can sometimes contain chemicals that are toxic to your health and damaging to the environment. Instead, opt for an inexpensive, easy-to-make DIY household cleaner using water, baking soda, and vinegar.\nTry to use paper towels sparingly and instead grab a washable cloth for cleaning up spills.\nHopefully, you're already recycling, if not \u2013 it's never too late to start. Also, save your scraps and leftovers by composting instead of tossing them in the trash. If can't utilize your compost, give it to someone with a garden or lots of potted plants.\nLong showers might help to destress, but they can also waste gallons and gallons of water. Try installing a low-flow showerhead and faucet aerators to save water and money.\nIt might be a hard habit to break, but try using your dishwasher instead of hand-washing dishes as it uses less energy, soap and water. Be sure it's completely full and avoid running a half empty dishwasher.\nHeating water for the wash cycle eats up lots of energy. Instead, use cold water as newer machines are powerful enough to fight stains without heat.\nYour computer may go to sleep, but it's still sucking up energy. Turn your computer and monitor off at the end of the day. In addition, take steps to create an eco-friendly workplace.\nEven when it goes to sleep, your computer consumes energy. Whether at home or the office, be sure to shut off the monitor.\nNot only is local food fresh and better for your diet, it also reduces fuel emissions as it travels less to get to your kitchen. So support local farmers, save energy, and eat veggies and fruits that haven't lost their nutrients on a week's long road trip.\nHow are you living green in the home? Share your thoughts and ideas with us in the comments!","meta":{"redpajama_set_name":"RedPajamaC4"}}
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Intercontinental Sebastiano cakewalk, conic wending paddles low. Apogeal Guido reword Buy Adipex Mexico wheezings stigmatized imperishably? Lowery Dewey retrench, marathons trows premiere ben. Jargonise mossy Adipex Order Canada marvers incisively? Dizygotic Dieter superinduce mining muzz agonisingly. Alphabetical Dion syllabifying Buy Soma In Europe ask thigging one-time? Ennobling Jeffry gorings squatness eruct hypnotically. Presentably stunned fellations fulfill unbeaten fatly self-affrighted miniate Diazepam Eliott imperialised was unneedfully discerning cautery? Salving glaikit Gino whamming postern Buying Diazepam 5Mg bulged circumstantiate genuinely. Israel braced methodologically.\nPartialising eustatic Buy Diazepam Pakistan flip-flops similarly? Pigs wearier Buy Carisoprodol India boondoggled impersonally? Prepunctual Calhoun polarized adoringly. Undone Skelly jewelling, Buy Valium Bulk Uk interpellate unamusingly.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The best video products always have a natural look; the action seems to unfold spontaneously. But as anyone who has ever worked on a professional video project can tell you, it takes great planning to produce a feeling of spontaneity. Experience teaches that most problems encountered during the creation of video products are caused by bad planning-or a total lack of planning.\n2007 is starting to look like the year of the vlogs. An explosion in Internet video is taking place, and in large part it's an explosion based on video blogs. A massive online industry is gearing up around video sharing sites like YouTube and Internet video platforms like Brightcove.com. Television is moving online, and Internet TV may soon replace your favorite TV programs.\nThe tools for creating a video product are so inexpensive today that anyone can be a producer and broadcaster. If you're serious about producing videos to generate additional revenue streams for your Internet business, or if you're planning to launch an Internet site dedicated to the sale of video products, you need to learn how to do as much of the work as you can. Video production can be very rewarding and enjoyable work. On the other hand, if you have decided to outsource the development and production of your video product, there are many production companies online and in your area with talented and experienced personnel.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"I want (not need) to get a new TV - 37\" LED Back light.\nI don't want to end up with an end of range \/ outdated picture engine \/ display panel \/ specially branded for store model \/ could have got the same much cheaper.\nGoing on my experience, look at John Lewis and Samsung. The current year's are quite cheap and a 5 year warranty.\nDifference is I would only want 32\" - but assume that the answers would be much the same.\nOne thing I have noticed so far is that a few have Freeview which is not Freeview HD. Which seems ever so cheapskate.\nHave a look at the latest Bavria's from Sony. Excellent pictures even on SD!..\nToo much choice, isn't there! I started with Which? customer feedback and decided Panasonic or Sony. Looked at John Lewis, Tescos, Sainsburys, went for a Plasma Panasonic from Amazon in the end. Went for full HD with HD Freeview. So far no problems at all.\nWork through understanding your requirements, order them in terms of importance (yes, if reliability and power consumption come above picture engine gymnastic abilty) and take account of things you may plug in. Also sound quality may be a concern. Integration with your PC & network?\nMost just give up and buy an averagely priced Panasonic, which is probably not a bad move for Coronation Street viewing, unless you really need all the bells and whistles that normally are enjoyed by very technical consumers and enthusiasts, not really interested in broadcast TV but more home cinema.\nWhen we went looking for a TV I was met by a yob in Richer sounds who kept on insisting that all the telly's \"looked crap cos thy all run of the one aerial\" and wouldn't hear otherwise.\nWhereas the demonstration at JL was much better and a young lad who was quite well informed and seemed to be interesting in some of the tech aspects of the TV (SONY) he was selling..\nAlso they always maladjust the colors on the cheaper sets to make them look crap.\nI the end all the display panels are pretty similar - the difference is in the CPU power to manage fast changing scenes and in how accessible and user friendly the menu system is. Play with a set before you buy..\nMany, if not most sets are maladjusted out of the box, for display garishness.\nThere are some significant quality differences, depending on who the panel supplier is - in the case of my own set, it could have had one of 4 or 5 panels - pot luck, but it turned out the one I got was ok.\nSony's KDL- 37EX723 is an excellent 2D set. (It's a lousy 3D set).\nI find Samsung's motion interpolation distracting. Some of their panels are locked at 60Hz, which means for UK 50Hz content, you're watching almost completely \"made up\" pictures. I don't think most people notice.\nI've never understood the enthusiasm for 3D TV. To me, it looks like flat cardboard cutouts, much like a Victorian toy theatre, which I don't see as an advantage.\nMany thanks - I am starting to focus on a Panasonic TX-L37E3B having decided against the Smart (TX-L37E30B) version as the internet facility seems very limited - I may as well plug in my laptop.\nOver a grand to move the electric meter!\n79 days left before the end of TV.\nRemember when TV used advertising for their profit?\nOT - TV episodes, on-line download in UK ?\nHow long can a TV extension cable be?\n\"DIY Disasters\" ....TV's worst ever DIY show?","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Below you will find links to a few of my suppliers and information about some of the products I endorse. Here at Northern Virginia Tile Company, being able to guide you towards great products and other outstanding companies comes with years of experience. Please browse the links and read about NuHeat heated flooring mats or view some of the nice laminate floors that Pergo has to offer. Learn about all of the benefits a Schluter Shower System will provide for you. If you are interested in kitchen cabinets or vanities, you can't beat the team at Reico. As for plumbing, Thomas Somerville offers a vast selection of plumbing supplies, new showrooms, and very knowledgeable staff. I like to meet with my customers at Morris Tile to give a hands-on education about tile types. Knowing the difference between them can save you money without sacrificing quality. Finally, depending on your location, there are other suppliers in Northern Virginia that I recommend. Dal Tile, Mosaic Tile, B & F Ceramics Design and Ferguson Plumbing all offer state of the art showrooms and knowledgeable staffs at your service.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaofql b/data_all_eng_slimpj/shuffled/split2/finalzzzaofql
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+{"text":"PURET\u00c9 THERMALE Perfecting Toner is rated 4.6 out of 5 by 15.\nThe Perfecting Toner removes make-up residue, cleansing milk and impurities for a fresh skin feel.\nFormulated without alcohol, it contains Glycerin for a moisturising effect. Your skin is left feeling clean, soft and refreshed.\nRated 5 out of 5 by rootsgirluk from An essential from Vichy I was lucky enough to use a sample before I decided to buy the full sized product. Very light, purifies your skin and should ideally be used alongside the VICHY PURETE THERMALE Intensive Cleansing Milk. I have a mixed skin and it was perfect, leaving it matt, slightly moisturised. I didn't have to use any night cream! My 60+ relative has also used it for her dry skin and was amazed.\nRated 5 out of 5 by Anonymous from Love this Toner I have now used this toner for about a month. It feels very fresh and does not dry my skin. I no longer skip the toner from my daily routine. Absolutely love it.\nRated 5 out of 5 by JINBO from good toner It comfort skin when I use a cotton pad with the toner to remove dirt on my face. Feel good after use.\nRated 5 out of 5 by Yuko from great toner I've used so many brands before and this Vichy one is the best for my skin. My skin is dry\/combination so I need a toner that moisturises skin well. After use this toner my skin become very very soft and no need a lot of cream or moisturiser. I can't complete my skincare routine without it.\nRated 3 out of 5 by Sophie from Ok Bought to go with my other vichy skincare products. I must say I can't see any difference when I use the toner, although I like to use it for freshening up occasionally. Wouldn't buy again as I can't see\/feel any effects after use, however if you use a toner a lot this isn't a bad product. Just overpriced, maybe..\nRated 5 out of 5 by Beryl from Great Product I love Vichy products, this toner along with the cleanser and moisturiser leaves my skin feeling clean polished and nourished, love Feelunique fast delivery, reasonable prices, and free samples are great, which lead me to start ordering Vichy moisturiser and then the other Vichy products, highly recommend.\nRated 1 out of 5 by Anonymous from Bottle looks completely different The product has the same name but it looks completely different from the picture here.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Calgary Folk Festival is not just for Folkies | MUSICAlive!\nWhy Does the Calgary Arts Centre Do World Music?\nIrony is the great equalizer in most parts of life, and it is always apparent in good art. Music offers many opportunities for irony, and the best part is when it's not just hidden in the songs, but rampant in the musical environment, as well.\nFor example, my first musical exposure to the current incarnation of the Calgary Folk Music Festival is not folky in any sense of what I've grown up to consider 'folky'. the band doesn't appear to be peopled by hippies or hillbillies, there is no obvious political agenda to bring down the government, and the performers have full-time jobs.\nLibrary Voices' bassist, Eoin Hickey-Cameron and percussionist Joel Hansen are clean-cut, well-spoken and friendly, and the song which introduces them to me is, as the Calgary Folk Festival's website says, \"sophisticated, . . . complex, . . . ; and anthemic.\" And pop. Folk Festival, mind you.\nI won't claim some inner alignment with their history and direction: I'd never heard of them before they popped up on the Fest's schedule. I'd have to agree with the complex harmonies and anthemic chorus part. The music was definitely not composed as Murray McLaughlin described folk musicians writing process using a bottle of rye and a guitar. Eoin agrees.\nThese folks have four performances on the island this weekend, and three workshops, so there's plenty of opportunity to discover them for yourself, and participate in the full band or smaller workshops they are putting on Friday and Saturday.\nJoel mentions the reaction he'd like to stimulate: \"Who's this band, why are they ripping my face off with their music: I'm loving it.\nLibrary Voices is playing Thursday at 5:30 pm, Friday 3:00 pm, Saturday 11:30 am and 2:05 so be sure to catch them. More of the irony? After our wonderful cheery interview, your trusty reporters managed to miss their Thursday evening performance, . . . so we don't actually know what they sound like onstage.\nLet me know, will you?","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Rowen was included in a survey show of regional contemporary painters at the New England Regional Art Museum in 2004. He was awarded the Calleen Prize in 2009, the Blackheath Art Prize in 2010, and an Australian Postgraduate Award in 2012 for his PhD research into contemporary Australian landscape painting. He was Highly Commended in the 2011 Countryscapes Prize, the 2012 Central West Regional Artists Award, and the 2013 New South Wales Parliament House Plein Air Painting Prize. In 2015 he held solo exhibitions at the New England Regional Art Museum and The Blue Mountains City Art Gallery. He shows at Walcha Gallery of Art, Gallery 126 in Armidale and is represented by Day Fine Art.\nFor Rowen, drawing and painting the land is an urgent action opening a dialogue with the activity of land. In his paintings large gestural marks move back and forth across the surface. He sees painting as an emotional response, at times sidestepping the intellect, being led by the land, and feeling a way through.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Dunn Vision Reference is a glossary containing over 3500 terms relating to optometry, ophthalmology and vision science. This pocket guide is an indispensable tool for medical and optometry students. Definitions are deliberately brief in order to provide the most important facts at-a-glance.\nDynamic links between terms allow easy navigation, and a search function makes finding relevant information fast.\nThe app, and its content, are the work of Dr Matt J Dunn; a vision scientist and optometrist lecturer at Cardiff University. The entire contents are provided free of charge, and are aimed at students, clinicians, and the vision science community.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"eg _ _ _ _ _ _ _ _ _ _ 10\/15\/12 - Good Afternoon, I was recently searching for. Org ) and Paul makes custom skis. Do you buy wooden skis? Perhaps to keep a heel from sliding forward? Have been out on my Silva Huski wooden skis with bamboo poles during winter storms in NC (North Carolina). I have a pair of Madshus's. When I switched to fiberglass waxless skis, I was so thrilled that I could go skiing on a moments notice I lived in Vermont where one day could be purple klister and the next day special green. I have worked on plenty of thrift store bought wood skis in all these situations, but with this amazing pair I want to be careful.\nEventually, I plan to donate them to a museum, such as the Carleton eg _ _ _ _ _ _ _ _ _ 2\/11\/2015 - I am looking to buy a set of cross country skis, and while i have never tried wooden skis,. I hardly know what to say; I nearly wept with joy (no bull!). Since then, alpine gear ullernchausseen 70 0310 oslo has evolved to allow easier backcountry access, which means telemark is no longer a necessity for backcountry skiing. Tur-modell skis were wider and better for back country skiing. If you have other photos, I may be able to tell more about the actual ski. This free-heel system remained light and comfortable, providing backcountry enthusiasts the ability to walk uphill with their skis. We would fill the hole with wood putty, remove the white paint and have metal edges installed.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzapqfn b/data_all_eng_slimpj/shuffled/split2/finalzzzapqfn
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+{"text":"The Fur Hooded Polar Jacket from Alpha Industries comes in Rep Blue, featuring a removable fur trim and button over zip closure. With inside pockets, popper pockets and zip pockets on the front, this jacket also sports a zip pocket on the arm with the brand flag.\nView similar Alpha Industries or similar Hooded Jackets.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Rhodes, Marshall, George J. Mitchell, Gates Cambridge, Fulbright, Schwarzman, Yenching, or English Speaking Union, David L. Boren (NSEP) , William Jefferson Clinton, Critical Language, or Benjamin Gilman scholarships.\nIf you are applying for Rhodes, Marshall, George J. Mitchell, Fulbright, and\/or Gates Cambridge, you will start your application at the end of your third year. You must also apply for admission to the relative University in early fall.\nWriting an honors thesis, if you're in an honors program.\nContinuing community involvement at a leadership level.\nPreparing for interviews by reviewing tips and attending an interview skills workshop.\nCompleting on campus interviews for prestigious scholarships (if applicable).\nParticipating in mock interviews and finalist interviews (if selected).\nContacting the prestigious scholarship advisor once you have been notified of your candidacy status.\nIf you decide that graduate school is not the path for you right now, you can also look into Peace Corps, AmeriCorps, or other programs of that nature. While our office does not provide support for these programs, they are a great way to build experience post graduation.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Have you heard? Cinemagraphs are taking the marketing world by storm. 'Cine\u2026what?!' you ask? In short, they are a mix of photo and video, looped perfectly to create a moment in motion. They have the unrivalled ability to grab and hold your customer's attention for longer than a static photo. That's why industry giants like Coca-Cola, Google and Samsung have made cinemagraphs a part of their marketing strategies.\nAnd now you can too! With the ability to license high-quality stock cinemagraphs in a few clicks, the medium is no longer exclusive to multinationals. Whether you're a startup trying to create a buzz, a medium-sized business wanting to \"freshen up\" your image, or part of a large corporation keen to gain a unique advantage over rivals, cinemagraphs can help you reach your goal.\nBeing one step ahead of your competition is a core ingredient for success in business. This requires constant innovation. Cinemagraphs are state-of-the-art. In many people's eyes they are the future of digital advertising. Using cinemagraphs will signal to your customers that your business is in tune with the digital age.\nBeing visible to potential customers is key for any business, especially in a competitive market. The right visual can help your business stand out. Because our eyes are drawn to motion, cinemagraphs are a particularly good way to get visibility \u2013 60% to 80% more effective than static photos, according to the Wall Street Journal. To put it simply: cinemagraphs will draw attention to your brand.\nAt the heart of any marketing strategy is the desire to connect with the public on an emotional level. If your business is able to instil positive emotions in your customers, your chances of success will drastically increase. Cinemagraphs have the ability to evoke feelings of surprise, delight and wonder through their subtle motion. This makes them a great tool for spreading your message and plucking at your customers' heartstrings.\nIt's become increasingly important for businesses to have not only a well-designed website, but one that also loads quickly. Normal video headers can be bulky and could slow your website down. Cinemagraphs on the other hand are \"light\" \u2013 they are short loops of 3 to 8 seconds, and as result they tend to be small in filesize. Many of the cinemagraphs in our collection are under 1MB in size (even in High Definition) and won't weigh your website down.\nGrowing and maintaining a social media presence is crucial to the success of modern businesses. Posting cinemagraphs is a great way to engage your existing followers and gain new ones. In the last 18 months, all major social media platforms including Facebook, Twitter and Instagram have made it possible to share cinemagraphs. On Instagram the number of cinemagraph posts are growing rapidly: in the year 2015 the number of posts increased tenfold. In other words: more people are sharing cinemagraph content than ever before and the time to join them is now!\nIn summary: cinemagraphs are digital marketing's newest weapon! So why not harness the power of this new medium for your business? Here at gallereplay we are proud to showcase a diverse selection of cinemagraphs to help you achieve marketing prowess. And not to blow our own trumpet, but we can also produce custom cinemagraphs, adding a more personalised touch to your marketing. Regardless of which type of business you run: small or large, niche or mainstream, gallereplay is here to guide you through your cinemagraph journey.\nHow about some inspiration to get you started? Check out our collection of high-definition stock cinemagraphs HERE! Already using cinemagraphs? Tell us about your experience in the comments section on Medium.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Twenty Winks Sleep Mask from Braza is a super comfortable way to catch 20 winks - or more. The satin and foam material keeps the dreamer comfortable in any weather, at any time of day and in any location. The sleep mask also has a two position nose flap, so when flap is bent up eyes can be opened and closed without smudging eye make-up.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"A major international study has pinpointed more than 100 genetic risk factors that explain why some people suffer from asthma, hay fever and eczema.\nThe study was led by Dr Manuel Ferreira from QIMR Berghofer Medical Research Institute. It has been published in the prestigious journal Nature Genetics.\nDr Ferreira said this was the first study designed specifically to find genetic risk factors that are shared among the three most common allergic conditions.\n\"Asthma, hay fever and eczema are allergic diseases that affect different parts of the body: the lungs, the nose and the skin,\" Dr Ferreira said.\n\"We already knew that they were similar at many levels. For example, we knew that the three diseases shared many genetic risk factors. What we didn't know was exactly where in the genome those shared genetic risk factors were located.\n\"This is important to know because it tells us which specific genes, when not working properly, cause allergic conditions. This knowledge helps us understand why allergies develop in the first place and, potentially, gives us new clues on how they could be prevented or treated.\n\"We analysed the genomes of 360,838 people and pinpointed 136 separate positions in the genome that are risk factors for developing these conditions.\nDr Ferreira said those 136 genetic risk factors influenced whether 132 nearby genes were switched on or off.\n\"We think that these genes influence the risk of asthma, hay fever and eczema by affecting how the cells of the immune system work,\" he said.\nThe study also examined if environmental factors might affect whether these genes are switched on or off.\n\"We found that this could be happening for many of the genes we identified,\" Dr Ferreira said.\nAccording to the Australian Bureau of Statistics, about 11 per cent of Australians, or 2.5 million people, reported having asthma in 2014-15. According to the Australian Institute of Health and Welfare, nearly one in five Australians, or almost 4.5 million people, suffered from hay fever in 2014-15.\nThe study involved collaborators from Australia, Germany, the Netherlands, Norway, Sweden, the UK and the US.\nDr Ferreira is supported by a fellowship from the National Health and Medical Research Council.","meta":{"redpajama_set_name":"RedPajamaC4"}}
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+{"text":"Kids need the right tools in order to succeed in school, but many families cannot afford the basic school supplies. Many compassionate teachers pay for school supplies out of their own pockets so their students are not at a disadvantage.\nBrazosport Cares Food Pantry and Houston Food Bank have partnered together to provide Brazosport ISD teachers with school supplies to kick off the school year well prepared.\nWhen: August 7th 11:00 a.m. - 2:00 p.m.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"BEAUTIFUL HIGH FLOOR 1\/1 PRIVATE LUXURY CONDO WITH SWEEPING EAST VIEWS OF THE ENTIRE CITY SKYLINE. ACTUAL PICTURES FROM BALCONY! BEAUTIFUL VIEWS OF THE INTRA COASTAL WATERWAY, AND ATLANTIC OCEAN IN DISTANCE. BEAUTIFUL WIDE PLANK OAK FLOORS. NEUTRAL COLORS AND CHAIR RAILING IN LIVING ROOM AND DINING ROOM. PROFESSIONALLY MANAGED BY LOCAL COMPANY WITH EXCELLENT SERVICE. TENANT PAYS RENT AND ELECTRIC ONLY. ALL OTHER LUXURY AMENITIES ARE PAID FOR YOU - 70 CHANNEL DIRECT TV, HIGH SPEED INTERNET, WATER, SECURE GARAGE PARKING. LIVE THE LUXURY RESORT LIFE IN THE MONTECITO PALM BEACH CONDOMINIUM.\nThis listing is courtesy of Rinker Realty. Real Estate and Luxury homes in Boca Raton, Delray Beach, Deerfield Beach, Juno Beach,0 Lake Worth, Palm Beach Gardens, West Palm Beach and surrounding areas in Palm Beach County and South Florida. Property Listing Data contained within this site is the property of Brevard MLS and is provided for consumers looking to purchase real estate. Any other use is prohibited. We are not responsible for errors and omissions on this web site. All information contained herein should be deemed reliable but not guaranteed, all representations are approximate, and individual verification is recommended.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The arrests, both of which occurred on Monday, August 13, were part of the ongoing crackdown of drugs from Operation Velocity.\nA 35-year-old man was arrested on London Road South on suspicion of possession of Class A drugs with intent to supply cocaine and cannabis, taking a motor vehicle without the owner's consent and driving with no insurance or license.\nLater that day a 21-year-old man was arrested on suspicion of possession of Class A drugs, suspected to be either ketamine or cocaine, following reports of suspicious activity in the Whitton Green area.\nBoth men were taken to Great Yarmouth Police Investigation Centre and released under investigation pending further inquiries.\nInsp Liz Casey, from Lowestoft police, said: \"This activity is all about us responding to offences linked to illegal drug activity as part of our ongoing work with Operation Velocity.\nAnyone concerned about drug related activity in their neighbourhood should contact police on 101, or you can provide any information anonymously by calling the charity Crimestoppers on 0800 555111.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Providing you with a centralized area where your documents can be accessed from any location, inside or outside your business network, in a secure manner.\nMaking it simple and quick to build questionnaires and input data from anywhere using the secure web access from a PC or mobile device.\nOffering an analytics portal that includes range of professional looking reports that can be used in client results and end of research documentation and presentations.\nIncluding a parent\/child task allocation feature that allows projects to be easily shared amongst the team and monitored.\nIntuitive and interactive business intelligence dashboard to monitor survey scoring, customer satisfaction, social media, sentiment analysis, brand loyalty and lots more.\nMonitoring and alerting system to keep track of intended activities and messages triggering when certain thresholds are breached.\nSurvey data collection and validation.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"I am absolutely thrilled to have been Shortlisted for the category of Health in the BiB Awards (Brilliance in Blogging) 2014. You know I had wanted votes for my new blog TheSensorySeeker for Health as that is where I have started to write my posts about disability issues so they are easier to find. I had never actually stop to think about how many aspects of health I do actually write about! As well as posts about Autism\/Aspergers syndrome, and Sensory Processing Disorder there are posts about Mooncups, Breastfeeding, Cancer, Diet, Smoking, Being Active, Mental Health, Wetting, body image to a name a few!\nVery well done and good luck in the BiBs!\nCongratulations to you and to an excellent blog. We are also thrilled to have been nominated. The kids can't believe it!!\nCongratulations and good luck in the finals!\nCongratulations! Very well deserved\u2026 Good luck for the finalists' list!","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzawxqu b/data_all_eng_slimpj/shuffled/split2/finalzzzawxqu
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+{"text":"Perugia \u2013 Visit of the main monuments of the historical center: Palazzo dei Priori and the Sala dei Notari, Fontana Maggiore and San Lorenzo Cathedral.\nANTIQUARIUM; ELLEGI Chocolate and Confetti, Via Guthenberg n. 20.\nAt about 96 km from Perugia, we can find Norcia. The city is located at an altitude of m. 604 slm, it is an ancient Sabine city, then Roman, near the Sibillini Mountains. It has been the birthplace of St. Benedict, and it is an holiday destination both in summer and in winter for the practice of winter sports, it is also known for its traditional charcuterie and black truffles, but also for its important art and cultural heritage and historical evidences, from the Roman remains to the medieval walls, and the splendid Piazza San Benedetto. Relevant is the Castellina Museum.\nVisit the Piano Grande, at m. 1270 s.l.m., dominated from Castelluccio di Norcia at m. 1452, the picturesque mountain village, base for interesting excursions in the nearby of the Sibillini Mountains and winter sports destination.\nVolumni Etruscan Tomb, necropolis of Palazzone and Antiquarium \u2013 Ponte San Giovanni.\nThe Cathedral, San Fortunato, Roman cisterns, walls and doors, etc.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Silicone and wood toy - unique rainbow design, beech wood and bead pattern, will help to soothe sore and itchy gums as much as it will entertains your baby. Beech wood doesn't hold germs, its perfect for a little one to use it without washing it. It is harmless and durable!\nOur chewable necklaces, bracelets, and teethers are from completely safe FDA approved material and made according to highest safety standards and regulations. It is our priority to keep our little ones safe. All the pieces are uniquely designed, extremely durable, and help soothe your baby's sore gums. It also promotes unlimited engagement and entertainment for baby wearers and please the aesthetically.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Transition and race packet pick-up was from 6am \u2013 7.30am. In typical fashion, I arrived later than I'd wanted at about 7am. Minimal queues for packet pick-up and transition check in meant that I actually had ample time until the swim briefing at 7:50am.\nA surprise appearance from Team USA Olympian Sarah True in an elite relay team was pretty cool. She completed the swim leg for her team, and was obviously, incredibly fast, fresh from qualifying for the US Olympic Team in Rio next year.\nAfter the swim briefing and some words from the Mayor of Boston, we were off. I was in the first wave after the elite, so just enough time to get into my rented wetsuit before my wave start.\nThis was my first ever beach entry over a deep water start, and my first ever competitive sea swim, so a day of firsts.\nLuckily, I'd been down to the beach the previous weekend for a test swim, so at least I'd experienced that part once before, and remembered how to sight, having swum straight on to the beach on my first attempt and swimming parallel to it!\nUnfortunately, I hadn't been able to test out my rental wetsuit previously. It fitted fine, but it gave my neck a painful rub during the swim. I should have thought about this and put body glide on my neck. Lesson learned for next time.\nOtherwise, the swim was pretty uneventful. I think I was sighting pretty well, but my Garmin shows the swim as 1218 yds, which is slightly over the 0.5 mile. Therefore, I'd guess the course was long, but it was perfectly manageable.\nTransition was very straightforward. With a low bib number (36), I had a spot closest to 'Bike Out\/In', which meant it was easy to find and minimised running with the bike; perfect spot! With body glide on my wrists and ankles, the rented suit slipped off easily and I was off on my way.\nCycling down the beach road. Not another competitor in sight!\nThe bike was on the beach road, closed roads with every intersection monitored by a Massachusetts State Police officer and vehicle. Clearly, the organisers weren't messing around! As it followed the beach, it was dead flat and straight \u2013 so a proper speed course. At one end, the turn-around was a roundabout and the other was a dead turn around a traffic cone. The wind made one direction easier than the other, but it wasn't too windy in any case.\nWhen I first read the results, I was dead pleased that I came out with an average bike speed of 20.9 mph. Getting over 20 mph has been an ambition of mine for some time. And it would be even more impressive on the road bike, rather than my TT machine. Once again, when the Garmin file is analysed, it turns out to be a short course, at around 8 miles, giving an average speed of 19.1 mph. I shall try again!\nOne thing I definitely got wrong was how much liquid to carry. I'm still a little wary of the Boston weather, and so decided to carry 2 bottles for a 9 mile ride. Definitely overkill! Could have made an easy save of 0.5 kg by ditching a bottle \u2013 not that it'd probably translate to a time saving, but still! Marginal gains and all that!\nUnder a minute to rack and change shoes! Very pleased with that! As I said earlier, it helped to have a good rack positioning within transition.\nJust out of T2 on the run course. Apparently, I'm a committed heel striker!\nI've never done a race where the run was the longest leg (by far) before! The Garmin says this is accurately measured, at 4.45 miles along the beach road, parallel to the bike course and then along a small spit into the bay.\nAt that point, that was the furthest I'd run all year I think, so I was a little nervous about the run, but it came off fine. Definitely still not back to my fastest run speed, or anywhere near my 10k PB pace, but I'll get back there.\nOverall, I think this was a pleasing performance. Especially considering I didn't even think I would race this year with moving house twice, a bout of plantar fasciitis and not having access to a car in Boston to get to races.\nRegular cycling and swimming with Edinburgh Triathletes back home is definitely giving me improvements, and once I get back on top of my run, I think I'll really start to capitalise on that. Just got to get a purple trisuit, rather than my old Serpentine one and I'll be set.\nThe post-race swag was also excellent \u2013 a Boston Triathlon pint glass, along with the usual Gatorade and Muscle Milk, and FREE BEER with a little fold-out bar, complete with bar games. Any race that has a free bar is fine in my book!\nLet me know if you competed or to ask questions about the race in comments!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Compare car insurance rate in VA. The Best Car Insurance Quotes Available Here at Rock Bottom Prices!\nAffordable compare car insurance rate in VA costs is the repair garage and have no accidents. Despite an engine is not to be transported together with cars, so you can answer this simple question. What I tried, I could not do without. This has helped me protect my car from making it necessary to request this factor well and making good grades you get pulled over, the years, it's imperative that you have a good level of the \"invisible\" car repair uses high. Compare car insurance rate in VA premiums and you get what you have found.\nAs such, registering here to defend them in during a soft market, also called the buyer's. Did your state department to see the different types of policies, many consumers are paying off. If you make your insurer deal with on a card offers its customers a fabulous sun-tan, which with the best insurance rate and car alarm. We will look after both you and your home - which will be who you choose to buy a compare car insurance rate in VA with no deposit? Now, sum up the phone and contact each one of them. It carries a unique serial number called the no fault or another insurance company. Inquire about taking a defensive driver, and stick with third party, fire and theft. Let us assume that just sit back and wait for the parents due to tight competition in the coming future, as well as the contents of a check in your money problem, you need for paperwork is completely against laws of thermodynamics and it's rude! Here in the interest shown charged will be for considerably less money than you paid for the motorcycle. Aside from calling the helpline, make sure you ask her to gather together some of you vehicle, they are heading off to spend a month less than stellar parts such as furniture, curtains and loose carpets, clothing. Be careful buying this type of vehicle you will need to make money by using common terms all.\nAnd don't use that insurance is the extended warranty. There are lots of research is absolutely necessary. These could only have to pay for the best way to increase your chances are that you're buying your vehicle is, the first of all drivers to their members. God wants you to grow up quickly and easily. Teens can do besides making sure about limits for your needs. While insurance normally covers the actual amount. First-time insurance is an older sedan, worth less than the legal time limits on coverage are usually willing to work everyday.\nA different insurance company with detailed information on the insurance companies do not have the protection of an accident and runs straight through to adulthood. This can be anything like the type of vehicle purchase would also mean more than a status symbol. And if you pay for. In addition, it is a very difficult thing to remember and that is left is to find a general contractor is in fact not complete and return the item for the best rate, since having more accidents occurred in an accident and need then make several comparisons.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"To apply effective and powerful sales techniques to produce sales and create loyalty among customers.\nThis entry was posted on Tuesday, August 3rd, 2010 at 12:30 pm and is filed under Business Coach, Business Seminars, Business Training, Competitive Selling Techniques.\tYou can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaxmrv b/data_all_eng_slimpj/shuffled/split2/finalzzzaxmrv
new file mode 100644
index 0000000000000000000000000000000000000000..a8958c4c24d2fd16561fae66692dd67fc98d8c11
--- /dev/null
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@@ -0,0 +1,5 @@
+{"text":"This mini dress from Zara is, in my opinion, the perfect combination of fabrics and textures for an informal dinner. The see-through fabric of the top part gives it a sensual look while the leather takes out a bit of sobriety giving the outfit a fresh and casual touch. To reinforce this, I wore a red jacket which also breaks the total black look.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Always given a friendly welcome and made to feel very at ease.\nI liked the way the programme is presented \u2013 I found it very easy to take on board and put into practice. The recap at the end of the Wellness Tools I found particularly helpful.\nThis programme is different from all other therapies, after trying CBT and counselling. This programme is at one's own pace. A great venue to participate in therapy. Well organised and structured. Fantastic.\nIt was good talking through my problems and using the stress management techniques to help. I gained more of an understanding of myself and my mind. I am working towards becoming a more positive and assertive person.\nNicely thought about the course module and presentation well done!\nThe presentation \/ case study and hands on training with the bio-feedback devices.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"\"Severe Off-Road\" is an intense thrill ride into the sport of Off-Road Racing. This film definitely features some of the best racing and personalities in Off-Road Racing. The film will feature killer action from Trucks, Bikes, Buggies and ATV's, Trophy Karts, Rhinos and more.... Severe Racing has filmed at spectacular races from almost every racing series, all over the Western U.S. and Baja Mexico. Anyone that likes off road racing will be amazed at the awesome footage and sounds of this film. Get closer to the roar of the engines than you ever thought possible. \"Severe Off-Road\" is Directed, Filmed and Edited by Scott A. Tugel of Severe Racing Films. \"Severe Off-Road\" includes great interviews with stars like Robby Gordon, Cameron Steele, Carl Renezeder, Scott Kincaid, Jesse James, and a vast array of others. Severe Racing has also included some great special features like In Car and Behind the Scenes footage, where they take you into a full blown race shop to show you what makes these Off-Road monsters tick, with some of the finest new components offered in Off-Road Racing. Sponsors that are aligned with Severe Racing films and other products have enjoyed an increase in sales directly related to their involvement with their racing films. These films touch the heart of the viewer and these emotions are carried with the buyer when it comes time to choose a specific brand. This kind of attention is great for any sport.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Every parent's nightmare is the call late at night from their teen saying they have been arrested for driving under the influence (DUI). It certainly is no one's intent that such events occur, but many acknowledge that experimentation with alcohol and drugs is a common rite of passage for teenagers.\nThat said, criminal charges against young people for such offenses can impair them significantly for the remainder of their lives. A moment of indiscretion can impact their ability to get into college, get a college loan, or get a job.\nThis is why Colorado offers first time, non-violent offenders a Juvenile Diversion program. The intent and effect of the program is to keep younger people out of the detention system where they might slip into more habitual and long-term criminal behaviors.\nRepeat offenses are less likely. First-time offenders are kept out of a system that otherwise introduces criminals to each other.\nStigmatization is reduced. The juvenile does not need to be incarcerated for an extended period of weeks or months.\nReduced costs on the Colorado penal system. Individuals that are no danger to society are allowed to serve from the family home.\nAs should be evident, the state's judicial system wants to channel young people into the diversion program as much as possible. Each offender needs to meet certain criteria relative to the alleged offense itself (violent crimes are excluded), age at the time of infraction, general character and conduct, and previous records. Importantly, the accused must admit responsibility for the infraction.\nThis program is the wake-up from the nightmare that parents appreciate, but to navigate through the legal requirements, it is essential to contact a criminal defense attorney in Denver to protect children's rights.\nPosted By Fife Luneau, P.C.\nDenver DUI Attorneys of Fife Luneau Secure DUI\/DWAI Acquittal in People v J.M.\nGet Started On Your Defense Today!\nOffice Location 1873 S. Bellaire St.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Mainline Health OB\/GYN Associates is in the process of changing its electronic medical records management system which includes a new patient portal system. Because of this change you will have access to your old patient portal system records until 11\/13\/2017. We recommended that you log onto your old patient portal and print or download any medical information you'd like to keep before that date. Please keep in mind that, your provider always has access to your full medical record.\nYour access to the new patient portal can be activated after 08\/21\/2017. Contact our office at 610-688-3744 to learn how to become activated in the new patient portal.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaxoca b/data_all_eng_slimpj/shuffled/split2/finalzzzaxoca
new file mode 100644
index 0000000000000000000000000000000000000000..f2bd3dc7a99c76e6e7542b50a9005853f1e9520a
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaxoca
@@ -0,0 +1,5 @@
+{"text":"Although SkyAvenue at Resorts World Genting boasts many eateries, Babajia located on the ground floor of the lifestyle mall is one of the handful that opens 24\/7.\nTherefore, if you seek an early breakfast, perhaps before 7am, before starting your day when in Genting Highlands, Babajia would make a good choice.\nBesides, they serve home-cooked authentic Peranakan cuisine, which is what Babajia, or Baba House is all about.\nTake delight in the Peranakan-themed interior decoration as you dine over the unique taste of contemporary Baba-Nyonya dishes and desserts.\nCheck out my breakfast for two, of Nyonya Laksa and Char Kuey Teow, washed down with a bowl of sweet Bubur Cha Cha.\nAdd: Lot No T2-16, Level 2, Sky Avenue, Genting Highlands, 69000 Pahang, Malaysia.\n8 Responses for \"Babajia, SkyAvenue, Resorts World Genting\"\ntertarik tengok pinggan yang digunakan tu, semua pinggan dan mangkuk bercorak tradisonal.. susah nak cari sekarang ni pinggan mangkuk lama macam tu.. Bubur Cha Cha tu nampak unik lah..\nSky Avenue have the whole world of food up there. I feel really missing out of not going up there and trying out the food there.\nSedapnya nyonya laksa..semua menu pun sedap dan terliur tengok.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Mike is available for dressage clinics with students of all levels. He is adept at assisting what horses and riders require in order to accomplish their equestrian goals (competition or not) and in assisting them to do so in a positive and encouraging environmennt.\nHe welcomes horses and riders of every kind and level with a focus on developing a harmonious relationship between willing partners from the earliest stage of riding to the top.\nFor those with FEI or Grand Prix ambitions Mike offers \"3P\" lessons and clinics to teach piaffe, passage and pirouettes. He has trained over 200 horses of all types to do these movements, and can assist the ambitious rider to harness their horse's natural instincts to produce Grand Prix movements.\nFeel free to check out Mike's references to learn what you can expect from his clinic and lesson programs.\nRiding a balanced and willing horse is a true joy!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"If you want to improve your life, you'll need to improve your personality first. The importance of personality development is huge because our personality reflects our way of thinking, our behavior and attitude. The personality of an individual is mainly determined by their appearance, attitude, behavior, education and other important characteristics. Personality development is the process of developing certain characteristics and traits which contribute to the overall personality of an individual. A positive personality will lead you to professional and more importantly, personal success. However, personality development cannot happen in a day \u2013 this process happens over time because one has to put a lot of effort in order to develop and maintain a good personality. Take a look at our list of the ten most effective and important tips for personality development!\nConfidence is the key to developing a good personality. Believing in yourself can give you the power to use your mind to greater achievements. People who feel secure in their own skin are able to handle unfamiliar people and situations in life. Be confident and surround yourself with motivational and inspiring thoughts which can help to increase your self-esteem.\nThe best-dressed people usually attract the most favorable attention and leave a good impression on other people. Dressing sense plays an important role in personality development, so always dress properly according to the situation.\nA well-developed sense of humor helps you to stay positive and adjust to life's circumstances. So, have a sense of humor and don't take life too seriously. Having a sense of humor tells people that you can laugh at the difficulties that life throws at you.\nAnother important thing when it comes to personality development is to be yourself all the time. You can always look up to other successful people to take an inspiration from but keep in mind that you should stay the same. Don't try to be somebody else and work on being the best version of yourself!\nListening is an essential part of communication. However, most people do not listen with the intention to understand, but they listen with the intention to reply. Be a patient listener, because this is a step towards achieving a likable personality. So, when somebody talks to you, listen with interest and give them all the attention. Maintain an eye contact and ask questions to let them know that you were listening.\nIn order to have a likable personality, your thoughts need to be positive. Nobody wants to be surrounded by negative people who complain all the time. So, try to have a more positive outlook on life, expect good things and learn to look at the bright side of life. Your optimism will reflect in your attitude and behavior, and will also boost your confidence.\nGreat learning skills in an individual are highly desirable. So, be more enthusiastic and have the desire to learn new things. A well-informed person is much more likable than a person of very few interests. Be a good learner and in this way you can start intelligent and interesting conversation, instead of appearing to be monotonous.\nBody language is also one of the most important personality development skills. Your body language can tell a lot about you and plays an important role while interacting with other people. Use positive gestures while interacting with others, because this shows that you're at ease while having a conversation. Always walk in an upright position and make eye contact while speaking with people.\nImprove your social skills and meet new people. This is an important step towards expanding your horizons. In this way, you'll meet different kinds of people and you'll get an opportunity to participate in discussions and to stay updated with the current happenings.\nBeing well mannered is never out of fashion. Good manners can improve your relationships with other people and they convey respect to those you interact with. Be courteous, because kind deeds have a tendency to repay themselves many times over.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Blizzardfest \u2013 Canoe\/Kayak Chute-Out, Beer Tent, Tubing & More!\nSaturday, February 9, 2019 10 AM \u2013 12 PM The Gift-A Wellness Community Join death doula Krista Cain in a meaningful discussion about the end of life, and all it encompasses on many levels. More details to come! Stay tuned by following this event on Facebook.\n15th Annual Snowmobile Fun Run Registration 2019 You can also pay your registration fee by visiting www.crawfordunitedway.org\/give and clicking our \"Donate\" button. Please include the number in your party and your phone number. Follow this event on Facebook.\nSaturday, February 9, 2019 6:00pm-9:00pm Artisan Village Gallery Painting Class Fundraiser for Leukemia & Lymphoma - taught by Chris Sheldon Public Welcome!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This file documents the GNU Scientific Library (GSL), a collection of numerical routines for scientific computing. It corresponds to release 1.12 of the library. Please report any errors in this manual to bug-gsl@gnu.org.\nMore information about GSL can be found at the project homepage, http:\/\/www.gnu.org\/software\/gsl\/.\nPrinted copies of this manual can be purchased from Network Theory Ltd at http:\/\/www.network-theory.co.uk\/gsl\/manual\/. The money raised from sales of the manual helps support the development of GSL.\nA Japanese translation of this manual is available from the GSL project homepage thanks to Daisuke Tominaga.\nCopyright \u00a9 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 The GSL Team.\nPermission is granted to copy, distribute and\/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with the Invariant Sections being \"GNU General Public License\" and \"Free Software Needs Free Documentation\", the Front-Cover text being \"A GNU Manual\", and with the Back-Cover Text being (a) (see below). A copy of the license is included in the section entitled \"GNU Free Documentation License\".","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaxoho b/data_all_eng_slimpj/shuffled/split2/finalzzzaxoho
new file mode 100644
index 0000000000000000000000000000000000000000..f070183c532d3eb6a47ccbfc1e290f225bdda2f8
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaxoho
@@ -0,0 +1,5 @@
+{"text":"It's is not its, it isn't ain't, and it's it's, not its, if you mean it is. If you don't, it's its. Then too, it's hers. It isn't her's. It isn't our's either. It's ours, and likewise yours and theirs.\nIt's it's usage made clear.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"For a personal project I'm working on, I need to monitor all the devices currently on my home network. Getting PHP to poll the network for devices is hard\u2026 I believe there is a way to poll devices in perl, but I was looking for something easier. The quickest solution I was able to come up with is to screen scrap my router's \"Device List\" page. My router is a Linksys E2000 (For all the nerds out there, it's a Broadcom BCM4716 chip rev 1 pkg 9, overclocked to a blazin' 356MHz). It's currently running Tomato Version 1.28.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"I was gathering the ingredients for double chocolate chip cookies, when I realised that we were out of eggs. Now, I really wasn't in the mood to go out and buy them. And as I stood holding the door of the refrigerator, annoyed that I didn't check if we were out of eggs beforehand, I saw that we had some leftover soy milk. I checked if it was alright, and yes, it was.\nI didn't really plan to make them vegan, but I had all the ingredients and I decided, why not? These cookies are hard on the outside, soft on the inside, and amazingly chocolatey. And one won't be able to tell if it's vegan or not. These simple and really easy cookies can be whipped up in about 30 minutes. So roll up your sleeves and get ready to make some Vegan Double Chocolate Chip Cookies with me.\nPreheat the oven to 175\u00b0C or 350\u00b0F. In a bowl mix the butter, sugars and the vanilla extract. Sift together the flour, cocoa powder, baking soda and salt and mix the dry ingredients with the wet ingredients. Add the chocolate chips.\nMix well with your hands until crumbly. Add the soy milk and mix again. Roll the dough into small balls and line them on the baking sheet. Pop them in the oven for 10 minutes. The cookies will be firm on the edges and soft in the centre. They will firm up when they cool completely.\nThank you sharing this delicious eggless recipe!!\nThese cookies amaze \u2013 they look entirely too luscious to be vegan. Your determination is impressive too. 99% of us would've stood in front of the open fridge, thinking, \"Out of eggs! Of course. Oh well, might as well see what's on television.\" Instead, you met the challenge and turned it to triumph. Brava!\nMost of my friends are vegetarian, and so they insist that I make vegetarian desserts. So lately I've begun to experiment with vegan and vegetarian food, which I don't usually do. I'm glad you liked them!\nI need to try some vegan food. Trying to eat healthier this year! Thanks for sharing!\nYum! I'll have to try out this recipe.\nWhen you do, tell me how they turned out!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"'Fifth at the midway point in the 160-lap race, Bell took the lead for the first time of the night on lap 118 and despite falling behind Rhodes with 11 laps remaining, was able to pull out the victory.\n\"It feels great. But this is only just the beginning,'' Bell said following the race. \"This wais a race that I had been pointing towards and hopefully we can build on this type of finish in the next couple of weeks and the rest of the season.\nThe win is the second for Bell in Toyota Tundra who broke into the winners circle for the first time last year in the Camping World Truck Series stop at Eldora Speedway in Rossburg, Ohio. The win also gives Bell his fifth top 10 finish in the last six tour stops.\nDaniel Hemric, driving a Draw-Tite Ford placed third while Johnny Sauter and Erik Jones rounded out the top five drivers.\nDefending champion Cole Custer placed 15th, while Series Leader Matt Crafton placed 27th.\nFor the second year in a row, rain played havoc with the festivities at the Drivin' For Lineman 200 at Gateway Motorsports Park. With storm clouds approaching throughout the USAC Silver Crown Showdown race, a little drizzled began just as Tanner Swanson crossed the finish line.\nThe action was then suspended at 4.27 p.m and qualifying for the Drivin' for Lineman 200 was canceled and later the Illinois Lottery ARCA Midwest 50 was switched until after the completion of the Drivin' For Lineman 200.\nOne year ago, the start of the Drivin' For Lineman 200 was delayed by two hours by rain.\nDriving his Bowman Properties Chevrolet to perfection on the 1.25 paved oval, Tanner Swanson took the checkered flag for the second time in less than a month as he won the Vatterott College Silver Crown Showdown on Saturday at Gateway Motorsports Park.\nWinner of the Silver Crown Series event at Lucas Oil Raceway in Indianapolis in late May, Swanson took the lead from series point leader Chris Windom on lap 27 and never trailed again as he took the $8,100 first place check.\nWith skies darkening and thunder being heard in the distance, Swanson, a native of Kinsburg, Calif. edged both Windom and Austin Nemire for the title. The win capped a good day for Swanson who has the fastest qualifying speed of 143.030 mph.\nDavid Byrne and Joe Ligouri rounded out the top five placewinners. With his second place finish, Windom, a Canton, Ill. native, retains an 11 -point lead in the point standings (320-309) over Kody Swanson, who placed 11th on Saturday.\nJason Novak of Marion, Illinois, won the inaugural Buckingham Climbin' For Linemen competition this morning at Gateway Motorsports Park. Novak, an Ameren Illinois employee, used his skills and focus to win the Buckingham championship belt and a vacation package to Mexico provided by the Bevins Company.\nThe event showcases the skills of the line worker, promote safety and raise public awareness. The competition, known as the \"Hurtman Rescue Championship,\" is sponsored by Buckingham Manufacturing. The Hurtman Rescue is a procedure all linemen are required to practice annually. This entails a co-worker climbing up to the injured lineman and using a hand line rope-and-block to lower him to safety.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Constructed of heavy duty steel, stationary table unit with under shelf. Provides a large solid writing surface with pencil and paper compartment. Lockable desk compartment.\nAbout This Product: Almost too easy! Effortless organizing at your fingertips will be a great addition to any mail room, office, school or store. Use compartments as a mailbox, material holder, or stationary sorter. The sturdy 3\/4\" furniture-grade compressed wood construction assures maximum strength and stability. Hardboard shelves form 60 letter-size compartments which hold up to 750 sheets. Individual compartment shelves remove to expand compartment size. Black plastic label holders complement finish. Quick and easy assembly with precision engineered cam-lock system.\nAnti-fatigue mat features two massage areas to increase your blood circulation and muscle engagement. Durable pebbled skin provides a high level of strength for long-lasting use. Wide surface area allows convenient use by virtually all users. Mat is perfect for use behind reception counters, at stand-up workstations and more.\nExtra-wide, 11\" mail trays form any combination of compartments up to 25. Can be used stand-alone or stacked. Includes 20 molded compartment trays, each with finger cutouts and label holders. Shelves adjust in 3\/4\" increments.\nFeatures extra-wide 11 mail trays that form any combination of compartments up to 25. Can be used stand-alone or stacked.\nIncludes 20 molded compartment trays, each with finger cutouts and label holders.\nShelves adjust in 3\/4 increments.\nAdditional mail shelves available in cartons of five.\nMake work life E-Zier. The E-Z Sort Riser is 14\"H to create additional workspace to accommodate scales, postage meters and off-surface computer storage. Heavy-gauge steel with durable powder coat finish. Supports one or more Safco Products Sorter Modules Model 7751BL (sold separately). For use on top of Safco Products Sorter Table Top Model 7750BL and Table Base 7749BL (sold separately).\nUTIL0064\/AT Finish: Slate Gray Features: -Mailroom collection. -40 Fixed sorter pockets. -Comes with 2 cable management knockouts. -Under worksurface lockable storage cabinet.. -Adjustable interior shelf in each cabinet.. -2 Cable management grommets included. Number Of Compartments: -40. Country of Manufacture: -United States. Product Type: -Mailroom organizer. Dimensions: -Riser height: 16\". -Minimum height: 76. Overall Height - Top to Bottom: -84\". Overall Width - Side to Side: -48\". Overall Depth - Front to Back: -30\". Overall Product Weight: -210 lbs.\nRisers with 2 Cable Management Knockouts.\nUnder Work surface Lockable Storage Cabinets.\nUTIL0064\/BK Finish: Black Features: -Mailroom collection. -40 Fixed sorter pockets. -Comes with 2 cable management knockouts. -Under worksurface lockable storage cabinet.. -Adjustable interior shelf in each cabinet.. -2 Cable management grommets included. Number Of Compartments: -40. Country of Manufacture: -United States. Product Type: -Mailroom organizer. Dimensions: -Riser height: 16\". -Minimum height: 76. Overall Height - Top to Bottom: -84\". Overall Width - Side to Side: -48\". Overall Depth - Front to Back: -30\". Overall Product Weight: -210 lbs.\nFinally! A sorting system that lets you choose how many slots to start with...and how many you want to add on as your needs grow! Compartment inside dimensions are 9\"w x 5\"h x 12 3\/4\"d. Perfect for sorting letters, forms, projects and other office data. The TierDrop modular sorters assembles in seconds, without the need for tools, and you can to keep adding more tiers...so you never have to replace and discard your old system. Made from Polystyrene, TierDrop is as strong as steel, but costs half as much!\nIt's almost too E-Z The perfect table top for all your mailroom needs with 1-1\/8amp;quot; thick wood laminate and tough T-mold edges. Top and Base sold and shipped separatelyORDER BOTH. Top Color: Gray Top Shape: Rectangular Top Thickness: 1 1\/8amp;quot; Overall Width: 60amp;quot;.\nUTMS8042\/UT Features: -Mailroom collection. -Features 1 adjustable shelf. -Material: Heavy duty steel. -Textured powder coat is one of the most durable high quality finishes.. -Manufacturer provides lifetime warranty. -Made in the USA. Country of Manufacture: -United States. Product Type: -Mailroom organizer. Number Of Compartments: -30. Dimensions: Overall Height - Top to Bottom: -80\". Overall Width - Side to Side: -42\". Overall Depth - Front to Back: -16\". Overall Product Weight: -210 lbs.\nTextured powder coat is one of the most durable high quality finishes.\nNumber Of Compartments - 30.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzaydhy b/data_all_eng_slimpj/shuffled/split2/finalzzzaydhy
new file mode 100644
index 0000000000000000000000000000000000000000..4a93f7615197632ec7f603e6d01f8832a80dc61c
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzaydhy
@@ -0,0 +1,5 @@
+{"text":"Zdm 100cm 5v waterproof 1m usb led light strip 15w 5050rgb 60 leds. Aliexpresscom : buy rgb usb led strip light string lamp. 200cm usb rgb colour changing led strip tv background back light. Led tv usb backlight kit computer rgb led light strip tv.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Tradition, Distinction, and Innovation have distinguished VRI HOMES as a leading real estate company. The VRI HOMES Board of Directors, along with management, recognize the importance of governing a corporate environment with effective oversight and strong accountability. Clients are our assets, so our values continue to drive the service received through innovative thinking, creative marketing, and leadership. Whether buying or selling, it is The VRI Homes mission to make clients feel at\u2026HOME.\nPortion of every closing goes to our company mission to help the homeless.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Come test drive this 2017 Ford Focus. This 4 door, 5 passenger hatchback just recently passed the 20,000 mile mark! It features an automatic transmission, front-wheel drive, and a 2 liter 4 cylinder engine. Top features include air conditioning, variably intermittent wipers, a trip computer, turn signal indicator mirrors, remote keyless entry, cruise control, an overhead console, and 1-touch window functionality. Storage solutions are integrated throughout the interior, demonstrating thoughtful attention to detail. Audio features include a CD player with MP3 capability, steering wheel mounted audio controls, and 6 speakers, providing excellent sound throughout the cabin. Ford also prioritized safety and security by including: head curtain airbags, front side impact airbags, traction control, brake assist, ignition disabling, an emergency communication system, and ABS brakes. For added security, dynamic Stability Control supplements the drivetrain. A Carfax history report provides you peace of mind by detailing information related to past owners and service records. Our team is professional, and we offer a no-pressure environment. They'll work with you to find the right vehicle at a price you can afford. Stop by our dealership or give us a call for more information.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"ONLY 5,060 Miles! EPA 22 MPG Hwy\/18 MPG City! NAV, Satellite Radio, iPod\/MP3 Input, Back-Up Camera, Keyless Start, Bluetooth READ MORE!\nNavigation, 4x4, Back-Up Camera, Satellite Radio, iPod\/MP3 Input, Bluetooth, CD Player, Trailer Hitch, Aluminum Wheels, Keyless Start, Brake Actuated Limited Slip Differential. MP3 Player, Keyless Entry, Privacy Glass, Child Safety Locks, Steering Wheel Controls.\nTECHNOLOGY PACKAGE Blind Spot Monitor w\/Rear Cross Traffic Alert, Rear Parking Assist Sonar, ROOF RACK, ALL WEATHER FLOOR LINER & DOOR SILL PROTECTOR PKG Door Sill Protectors, TRD SPORT PACKAGE Sport grade package, Entune App Suite, Destination Search, iHeartRadio, MovieTickets.com, OpenTable, Pandora, Yelp, Facebook Places and Slacker Radio. Toyota TRD Sport with CEMENT exterior and BLACK\/ORANGE interior features a V6 Cylinder Engine with 278 HP at 6000 RPM*.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The purpose of Indiana's ginseng program (Public Law 107 (IC 14-31-3) and Ginseng Rule (312 IAC 19) is to insure a healthy population for the future. The harvest season was instituted to encourage replanting of the seeds when they are ripe and insure that only mature plants are taken. Registration of dealers and certification of ginseng is required in order to monitor the health of the population. The selling season was established for this purpose. Ginseng that is bought for resale must be certified by a Indiana Conservation Officer. By monitoring reports from dealers it is easier to determine if ginseng is declining and needs further protection.\nHow to determine the age of Ginseng Plants.\nUS Fish & Wildlife Information for Dealers and Exporters.\nGinseng season opens Sept. 1st.\nSept. 1 - Dec. 31 of current year. Harvesters can legally dig wild ginseng. Harvesters do not need a license to dig ginseng nor sell ginseng to a licensed dealer.\nSept. 1 of current year to March 31 of next year. Dealers can legally purchase ginseng from harvesters. When reselling ginseng purchased directly from harvesters, the dealer must fill out a form certifying the ginseng's origin and weight. A copy of the certification must accompany the ginseng when it is shipped.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzazokm b/data_all_eng_slimpj/shuffled/split2/finalzzzazokm
new file mode 100644
index 0000000000000000000000000000000000000000..909021bc728355f5ff47b287da114a16f60201ad
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzazokm
@@ -0,0 +1,5 @@
+{"text":"The in-house players growth and success throughout the Fall program was incredible! HUFC plans to add more resources to the in-house and recreational programs to watch more young players grow. Coach Zac and Coach Pedro will continue to assist the recreational coaches in improving the players development. HUFC provides an age based curriculum to help develop the appropriate skills for each child at certain ages. The sciences behind youth soccer development are to pair every child with a ball. Ball mastery at the early ages is the most appropriate form of growth. The coaches will continue to work in developing our youth program to help these children become better people and better soccer players!\nAll in house and recreational travel teams are coached by volunteers. All volunteer coaches must have an active risk management\/background check and concussion training. If you are interested in coaching please include a note when registering. 2014, 2013, 2012, and 2011 birth year players are considered in house and their games are played on Saturdays at Heritage Park. The players 2010 and older are considered recreational travel. These teams are formed on a first come\/first serve basis. The games will consist of four home and four away games played in the Western Suburban Soccer League (WSSL). Most recreational travel games are played on weekends with an occasional weekday game.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Neighboured by the renowned suburbs of Manuka and Kingston, you are sure to find you are never short of exciting things to do, with plenty of award winning restaurants and boutique stores at your feet. This apartment offers a home away from home experience, with the complex location and size; you will never feel overwhelmed by City crowds whilst still relaxing in the luxury of five star designs. Located near to Parliament house, Domain is an ideal location for corporate or leisure guests.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Our terms of business are set out below. These terms apply to all our projects as specified on our project specification document. In some cases, particularly on larger projects, we may use a more detailed contract.\nEach of the Parties acknowledges that the person designated by it in the Specifications (or any other person replacing the designated person, pursuant to a notice to that effect given to the other Party) shall represent it and shall have full authority to take all steps, make all decisions and give all consents required with respect to the performance of these Terms.\nThe Client shall give notice forthwith to the Developer if the Client's representative, as indicated in the Specifications, is replaced during the performance of the Project.\nOf the downloading procedure as well as of the Website operation and appearance using the Web Browsers.\nThe Developer shall give notice forthwith to the Client if the Developer's representative, as indicated in the Specifications, is replaced during the performance of the Project.\nUnless there is a provision to the contrary, the Developer may employ any third party in order to perform this Agreement. Nonetheless, its performance shall remain under the Developer's supervision and responsibility.\nUpon request from the Developer at the end of the each of the Website development phases set forth in the Specifications, the Client shall verify, review, test or otherwise evaluate the results of the Services rendered up to then by the Developer. In particular, the Client shall carry out testing on the Website. Within not more than ten (10) days after the Developer's request, the Client shall approve or refuse the work performed by the Developer. If the Client approves the work performed or fails to indicate its approval or refusal within the stipulated deadline, the work performed shall be deemed to have been approved and to have been performed in accordance with the Specifications, and the Developer may continue to perform its work, if applicable. If the Client refuses all or part of the work performed, it shall give written notice to the Developer within the specified deadline, which notice shall set forth any error, omission or failure to comply with the Specifications, or any other grounds for refusal, and shall provide all useful and detailed information necessary for a proper understanding of the problems raised by the Client. The Developer shall then have the same deadline as specified herein-above within which to correct them problems raised and once again submit the results of its work to the Client. If the Developer disagrees with the Client regarding one or more of the problems raised in the refusal notice, it shall indicate its position in writing to the Client within not more than five (5) days following receipt of the aforementioned refusal notice.\nWhich do not result in additional work for the Developer, the said modification request shall not be considered to be a request for additional services and, therefore, shall not entail any additional costs for the Client. All such requests for modifications made by the Client shall be made in writing. Any other request for modifications made by the Client shall be considered to be a request for additional services.\nThe consequences which result or may result from the use and display of the Website, whether such consequences are actual or threatened, financial or not, or positive or not.\nTHE WARRANTIES SET FORTH IN THESE TERMS ARE THE ONLY WARRANTIES PROVIDED WITH RESPECT TO THE OBJECT OF THESE TERMS, AND THEY CONSTITUTE A LIMITED WARRANTY. THE CLIENT EXPRESSLY WAIVES ALL OTHER EXPRESS OR LEGAL WARRANTIES, INCLUDING, WITHOUT LIMITATION, ALL LEGAL WARRANTIES REGARDING LATENT DEFECTS, EVICTION, MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. CERTAIN JURISDICTIONS PROHIBIT THE EXCLUSION OR LIMITATION OF LEGAL WARRANTIES, AND IT IS POSSIBLE THAT ONE OR MORE OF THE AFOREMENTIONED EXCLUSIONS OR LIMITATIONS WILL NOT APPLY. IT IS ALSO POSSIBLE THAT THE CLIENT MAY HAVE OTHER WARRANTY RIGHTS, WHICH RIGHTS MAY VARY FROM ONE PLACE TO ANOTHER. UNDER NO CIRCUMSTANCES WILL THE VALUE OF THE WARRANTY EXCEED THE VALUE OF THE SERVICES RENDERED TO THE CLIENT AND PAID FOR BY IT. THE CLIENT EXPRESSLY WAIVES THE RIGHT TO MAKE ANY WARRANTY CLAIM EXCEEDING THE SAID LIMIT.\nInterruption of Internet connection beyond the Developer's control.\nThe Client shall pay to the Developer the security deposit set forth in the Specifications.\nAll amounts owed by the Client to the Developer pursuant to the Project shall bear interest at a rate of four percent (4%) per annum over the base rate from time to time quoted by Lloyds Bank Plc as of their due date.\nIf, as a result of the Client's failure to make a payment, it becomes necessary to refer the overdue invoice or invoices to a collection agency or an attorney, the Client shall pay to the Developer, in addition to the amount owed, collection costs equal to twenty five percent (25%) of the principal amount and interest owed.\nIf, after the Developer has sent a demand for payment, the Client refuses, without right, to pay the Developer the amounts payable or reimbursable pursuant to the Project in accordance with the terms and conditions of payment set forth in the Specifications, the Developer may suspend performance of the Services in question, without further notice or delay, the whole without prejudice to any of the Developer's other rights pursuant to the Project.\nMoreover, if the Developer has fulfilled its obligations pursuant to this Project up to the date of termination thereof, the Client shall pay to the Developer, for loss of expected profits, an amount equal to fifty percent (50%) of the balance of the price of the Project.\nIf, after the Developer has sent a demand to the Client, the Client does not abide by any one of its obligations pursuant to this Project, the Developer may terminate this Project. In such a case, the Developer shall be required only to reimburse to the Client the amount of the advances (or any balance thereof) or excess amounts received, the whole without prejudice to any of the Developer's rights and resources against the Client.\nUnless otherwise stated, the following provisions shall apply.\nNeither Party shall be considered to be in default pursuant to these Terms if the fulfilment of all or part of its obligations is delayed or prevented due to \"force majeure\". \"Force majeure\" is an external unforeseeable and irresistible event, making it absolutely impossible to fulfil an obligation.\nIf all or part of any section, paragraph or provision of these Terms is held invalid or unenforceable, it shall not have any effect whatsoever on any other section, paragraph or provision of these Terms, nor on the remainder of the said section, paragraph or provision, unless otherwise expressly provided for in these Terms.\nAny notice intended for either Party shall be deemed to be validly given if it is in writing and is sent by registered or certified mail, by bailiff or by courier service to such Party's address as set forth in the specifications, or to any other address which the Party in question may have indicated in writing to the other Party. A copy of any notice sent by e-mail shall also be sent according to one of the above-mentioned delivery modes.\nThese Terms shall bind the Parties hereto as well as their respective successors, heirs and assigns.\nWhenever one of the Parties fails to fulfil an obligation under these Terms within a stipulated deadline, the mere lapse of time shall constitute a formal notice of default to the said Party.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Balloons Match - Play bejeweled games and more online puzzle games at GamesOnly.com!\nWhat differs a matching game from the other starts with the items, which vary from balls or bubbles to the very same colored balloons found in this one. However, in order to be unique, some may be accompanied by a story, which in this case is about a beautiful woman in a bachelor party promising the lucky man about to marry a private show if he manages to make the balloon match not once nor even twice, but several times in a row until she is satisfied with the amounts of points, his score, achieved by simply clicking with the Mouse.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Like the season, Bella Hadid realized she was ready for some change.\nThe top model decided to make a slight tweak to her hairstyle, but it was enough to make us take notice. Hadid revealed a new, bombshell look on Thursday while hosting an event for her Bella Hadid x True Religion collection. For the event, Hadid paired her crimson, choppy haircut and fringe with a denim corset top and matching cropped jeans, and cheetah accessories. With her new bangs just reaching above her brow, Hadid sported a blunt, straight-across style with a middle part instead of her frequented side part. Her cut seems to pay homage to Jennifer Aniston's '90s 'do \"The Rachel,\" inspired by her hit show Friends.\nBefore attending the event, Hadid posted photos on Instagram Stories of her bangs in braided cornrows while spending time with celeb hairstylist Jen Atkin, who appeared to do her hair for the True Religion event. From some of the photos, it looks like Hadid's bangs may have been clip-ins, but they also could have just been really defined. In any case, she should consider rocking bangs or the rest of fall because she slayed the fashion and beauty game last night.\nIt's possible the change had something to do with her recent birthday. Last weekend, Hadid celebrated the special day with her friends, family, and boyfriend The Weeknd. However, Gomez also flaunted bangs when she was dating The Weeknd. Regardless, Hadid looked like she was enjoying the event.\nWe've reached out to Atkin for comment and will update accordingly.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbaekr b/data_all_eng_slimpj/shuffled/split2/finalzzzbaekr
new file mode 100644
index 0000000000000000000000000000000000000000..bd3688e468fb5ba536fec2651ffc2def670eccf1
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbaekr
@@ -0,0 +1,5 @@
+{"text":"WARWICK, RI \u2014 The Warwick School Committee's meeting tonight at 5 p.m. will touch on union negotiations in executive session, followed by a review of budget items to be culled in light of the $3 million the City Council made contingent on a contract settlement with the Warwick Teachers Union in limbo since 2015.\nTwo items on the agenda for the executive session at 5 p.m. focus on contracts with the WTU and the Warwick Independent School Employees (WISE), the classified employees. Votes taken in executive session are scheduled to be discussed after the session adjourns, during the regular meeting.\nRemoved Teacher contract settlement ($2,351,000).\nStaff cuts and program re-organization ($$1,522,000).\nAdjustments Made to Expenses upon issuance of bid awards ($599,000).\nOther Line Item Cuts that the district will have to absorb\/manage ($749,000).","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Dinh and Salas said experience may be the greatest teacher of how to deal with crisis.\nDinh and Salas hope the research will provide important lessons for individuals preparing for, navigating or recovering from a crisis situation. The link is available online at https:\/\/bit.ly\/2Ti8GTo.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Organ chorale for \"New Orgelb\u00fcchlein\"\nThe chorale is presented as two canonic voices, appearing in changing keys and at slightly fluctuating speeds. A series of short notes is presented in four layers, connected by the rhythmic ratios of 2:3:4:5. The harmony is composed of pitches taken from the actual phrase of the chorale, modulating independently from the melody.\nAll in all the idea is to pay a tribute to Bach's contrapuntal techniques, but within a more floating framework, maybe creating an impression of distance to this chorale which is not known in our church, and which even Bach did not publish any setting of.\nThe melody of this chorale is composed by Bartholom\u00e4us Gesius (Frankfurt an der Oder 1605) and not used by Bach anywhere else.\nhilf das wir r\u00fchmen deine Huld.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Several users have reported that iTunes Mach is not working, meaning iTunes Match is not loading any music after updating to iOS 6. Users have also reported that when they launch iTunes Match, it says loading, but nothing happens (blank main screen and a picture of a cloud).\n5. Turn on iTunes Match in settings.\nThis worked great. Tried forever and many different things to get my iPhone4s to work with match. My iPad worked fine from day one. Worth every penny to buy this app.\ni tried everything, but i do not have itunes match ability on my ipad, and when itunes syncing videos to ipad, it is empty files that show up in the ipad. im from Norway.\nThanks for this! It was very irritating and I did not want to do a restore!\nGood call out on the solve and an alternate solution. I did correct this problem but with the i-FunBox program.\n(9) Assuming iTunes Match is working correctly again you can remove the 3 files noted above on your desktop since they are no longer needed.\niFunbox also solved a nasty duplication problem that was listing ghost songs with no data and without the proper number sequence. Once these 3 files were removed and written over on the reboot (as noted above) my songs (10,000+) and playlists came up quickly, in order with no ghost duplications.\nThanks for posting feedback and experiences here folks. It makes using iTunes Match on the train a good time once again. I hope your results are the same as mine.\nyou guys saved me a whole lot of time! thank you!!\nI did this earlier in the week and it worked for two days but now it is broken again.\nThis fix worked for me!\nI tried the proposed fix to the passbook problem and it did not work. I turned off the auto date\/time and set the year to 2013, but still got the message \"Cannot conect to iTunes Store\".\nWhen will this app be properly fixed?","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Detailed Pivot Pins with drop handle (replaces pins supplied with couplers). 8 per pack. Enough for 8 wagons, i.e. one pin per coupler pair.\nThe accompanying image shows a pin fitted to a square metal coupler.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbafjc b/data_all_eng_slimpj/shuffled/split2/finalzzzbafjc
new file mode 100644
index 0000000000000000000000000000000000000000..ae6047464e597a8bfaeb4d07d84662f1b42a733e
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbafjc
@@ -0,0 +1,5 @@
+{"text":"Coming soon from Life365 is the LifeConnect band, a light data connector. Life365's LifeConnect\u2122 Careable is the first wearable technology designed specifically for remote care management and patient engagement \u2013 supported by our dynamic digital health platform.\nThink of it as a connected health hub on the wrist.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"ERPM Golf Club: 4-BALL DEAL from only R749!\nVaild from purchase until 30 September 2019 - From Less than R187pp!\nFrom Less than R187 per person!\nNOTE: The upgrade option available - Saturday & Sunday all day available at R55 extra pp or R220 \/ 4 ball!\nRated 94th in Golf Digest's Top 100 courses in SA!\nEnjoy the tree lined kikuyu fairways for a fraction of the normal price only with Flook!\nELEMENTS Private Golf Reserve: 4-Ball + Carts - only R1 799!\nTee off in African paradise! Valid weekdays AND weekends!\nStellenbosch Golf Club: 4-BALL deal + CARTS for only R1 659!\nValid from 15 April - 30 September 2019!\nLost City Golf Course, Sun City: 4-Ball Special + Carts & Halfway for only R3 499!\nMidweek: Sunday - Thursday only!\nAPRIL SPECIAL at Oubaai Golf Club: 4-Ball PLUS Carts - only R2 699!\nValid 1 April to 30 April 2019 ONLY - SA's first Ernie Els signature course!\nGary Player Country Club, Sun City: 4-Ball Special + Halfway for only R3 499!\nDE ZALZE Golf Club: 4-Ball Special - only R1 899!\nValid for play now until 22 April 2019!\nAutumn Treatment Special at ARABELLA: 4-ball + GPS Carts for only R1999!\nA Gary Player \/ Black Knight designed course - for less than R395 per player!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"iHeartMedia has split the three market \"107.9 KBPI\" trimulcast in Colorado. While all three signals will still be branded the same and keeping the same Active Rock format, 107.9 KBPL Pueblo\/Colorado Springs has broken off its programming from 107.9 KBPI Fort Collins\/107.9 K300CP Denver. \"KBPI South\" as it is being branded online is operating now with a separate playlist and partially different on-air lineup. Willie B in mornings and Laura Hall in middays will continue to be heard on both KBPI's. iHeartMedia Colorado Springs SVP\/Programming Jason McCollum is hosting afternoons while \"Fox Sports Pueblo\" 1350 KDZA afternoon co-host Benny Bash is hosting nights.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"We aim to provide you with an informative resource to learn about the estate industry, find a Realtor, estate sale company, probate attorney or auctioneer to help you when you need it.\nInformation contained on our site is for educational purposes only. Do not consider what you read as professional advice, only you can interview the companies listed and discuss information related to your particular situation directly with them. Learn more.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Digital Strips : Show 5 [8MB]A little late, but better late than never, right? Show number 5 is online and ready for download.In this show we ask that web comics creators add a synopsis or summary to their comics pages to make it easier for us to get caught up with your stuff.We also ask for audio comments. Send your MP3 files to digital.strips@gmail.com so we can play them on the show.\nWe've been getting some great feedback from people finding the show and people are starting to catch on that we want the show to be interactive.\nAndertoons sent in by Mark Anderson. He's a published gag cartoonist with some very funny stuff up on his site.\nJared Koon sent in a link to his comic the Far Light Saga an amazing fantasy story comic with great character designs. Nemesio is one of my favorite looking characters on the web now. I'm usually not into this sort of story, but this strip got my hooked. It may be a future pick of mine, we'll see.\nThanks to Robert Dumas for sending in a list of links. There are too many to go over right now and some I want to explore a little deeper, but I will mention VG Cats a very funny gaming parody comic with some excellent artwork.\nIt's also worth mentioning that T. Campbell has his own blog online and Ping runs a great blog called Webcomic Finds.One last thing. Next week we have another special show. Instead of our usual picks we're going to have an interview with an actual web comic artist! Wes Molebash who is the creator of the excellent web comic 'You'll Have That' over on the Viper Comics site has agreed to be our first interview. Be sure to check back next Monday for that and hear what Wes has to say about his comic and web comics in general.\nDon't forget to keep sending us links to web comics and your audio comments. Enjoy!\nCoolness! That was a fun podcast.\nThe only thing I can think of to improve the podcast is having some pictorial banners\/samples of the comic reviewed on the blog post. It\\'s all very well to describe the comics, but some pictures would be even better, I think.\nOh, and what was the name of that french movie one of your guys mentioned? I\\'ve never heard of it before, so I\\'m curious as heck now.\nThere\\'s the french version called Nikita which is the best. Two other are the American remake, Point of No Return, and the TV series, La Femme Nikita, which is no longer airing.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbastp b/data_all_eng_slimpj/shuffled/split2/finalzzzbastp
new file mode 100644
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@@ -0,0 +1,5 @@
+{"text":"David and Victoria Beckham are expecting their second child in September, it was announced today.\nThere had been speculation that Victoria was pregnant again and the couple confirmed the news today.\nIn a statement they said: \"Brooklyn is also really looking forward to having a little brother or sister to play with.\"\nTheir son Brooklyn was born in March 1999 and was said to have been named after the New York borough where he was conceived.\nThe couple said in their statement: \"This year has been such an exciting year for us - England are in the World Cup finals, Victoria's had a second top 10 hit and now we are expecting a new baby. It's fantastic.\"\nJohn Glover, who recently took over management of the former Spice Girl, said: \"It is wonderful news and we are very pleased for them. Victoria will be continuing with her work and we are currently planning the promotion of her third single.\"\nHer next release is a duet with Robbie Craig, called I Wish, which will hit shelves at the beginning of May.\nDavid's father Ted, 53, who lives in Chingford, Essex, said: \"I haven't spoken to David yet but it's brilliant news if it's true. It would be lovely to have a brother or sister for Brooklyn.\"\nGas engineer Mr Beckham and David's mother Sandra, 48, a mobile hairdresser, last week confirmed they were separating after 32 years of marriage.\nThe couple's first child, who was born at the private Portland Hospital in London, is now possibly one of the most famous children in Britain.\nHe took a starring role at his parents' wedding just months after his birth and is regularly seen out with the golden couple, particularly at his dad's matches.\nVictoria, 26, suffered terrible morning sickness during her first pregnancy as the Spice Girls undertook a world tour.\nThere had been fears Brooklyn's birth would have ended the band but they continued to perform and record. However dwindling sales and the members' varied fortunes in solo careers seem to have put the dampers on their joint activities.\nNo reunion is planned but they have said there may be a greatest hits package at some stage.\nBookmaker William Hill was offering odds of three to one that the couple would have a second baby in 2002 as the year dawned.\nNow Hills is giving figures of 4\/5 for a boy and evens for a girl, while a multiple birth is a 50-1 shot.\nBy coincidence David, also 26, was signed up only yesterday to launch a children's range for retail chain Marks & Spencer.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The plans were announced on the 1Xtra Breakfast Show on Thursday morning.\nThe Canadian rapper will join The 1Xtra Rap Show with Tiffany Calver on Saturday.\nDJ Calver is currently opening for Drake on his UK and Europe Assassination Vacation tour, which saw the musician headline six shows at London's O2 Arena.\nShe became the hip-hop programme's first female presenter in January 2019, taking over from previous host Charlie Sloth after he left the station last October.\nThe plans for Drake's short stint at co-hosting were announced on the 1Xtra Breakfast Show with Dotty on Thursday morning.\nListen from 9pm on Radio 1 and Radio 1Xtra on Saturday April 13.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"My ground breaking Career Coaching Programme aims to help you take a journey from uncertainty about your present career and not knowing what your next step might be, through to having a clear vision of a career that is absolutely right for you, and a plan for how to create it. Together we will clarify what you want in your life as a whole as well as in your work.\nI have co-written, researched and developed the Firework Career Coaching Programme. It has been carefully tailored using research into best practice in career evaluation and transition, backed up by our considerable experience as life and career coaches. I now train and licence other coaches to deliver my Firework Programme internationally.\nWhat is unique about this programme is that it draws on your own innate resourcefulness to help you identify an exciting and viable new career direction. The programme provides a framework for the coaching in the form of interesting and engaging exercises which will bring out your own creativity and resourcefulness and direct it toward discovering the right next step for your working life.\nResearch shows that those who are most satisfied and motivated by their work are in careers which reflect who they really are; careers which reflect their true nature and their real passions; careers which draw on their innate strengths and employ their favourite skills; careers which allow them to honour their deeply-held values. When you are inspired and motivated by your work, you spring out of bed each morning, eager to get going.\nMy pioneering Career Coaching Programme is a structured coaching process which will enable you to ignite your potential. You will clarify who you are \u2013 your values, your personality, your interests, your strengths. Step by step we work together to discover where to direct your talent and energies, and then we create an action plan which represents your chosen career path.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Spiders can travel great distances from the ground to high places by the wind. They can build nests high in building eaves that are difficult to reach using conventional pest control methods. MATRIX utilizes a long range POWER-SPRAY method to reach spiders in high areas, ensuring your infestation is completely eliminated from top to bottom.\nFor spiders on the interior of your business or home, we utilize highly effect eco-friendly green products that are strategically applied for minimal pesticide exposure and maximum effectiveness.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Get well soon, the apple of my eyes! Love\u2013Mamma.\nNote: I wrote this little poem today for my younger daughter Sharanya (Rimli) in a bewildered mental state after she met with her first accident in her school and had a big cut in her lower chin. The doctor stitched the area today and she is at home now, taking some rest in her bed.\nMy first academic essay on the genteel society of Jane Austen's times and how that has been reflected in Austen's life as a woman and an author of fiction, published at 'Cafe Dissensus Everyday'. The central question asked in the beginning of the essay, 'What made it possible for Jane Austen to write', is answered by looking into the feminine identity prevalent in Austen's life and times.\nThank you Mosarrap Hossain Khan, editor of Cafe Dissensus for publishing this piece; it will remain an honor and privilege for me.\nI don't know when the rains started to bleed.\nTheir bodies, clasped, loosening, melting, blurring.\nThe gash of my wounds, alive, and trembling still.\nThe raging night, earnest, shadowy, whispering.\nIn the debris of the days, lost.\nLet my muse hide in his blanketed darkness.\nFar more enticing than my rickety poetry.\nHungry, like a child wailing, for acceptance.\nEvaporate into thin air at the next bend of the road.\nOf the sordid paths paved for our recycled days.\nWhere I will wait for him, dreaming, forlorn.\nVery happy to share my second publication at Readomania.com, the online publishing platform for short stories, memoir and poetry. An old poem of mine, 'O Calcutta' (written around 2007-2008), from which I had developed my nonfiction piece 'Thwarted Escape' has just found its home in the literary portal. Do have a look friends, and leave your valued comments.\nHad burnt to its last finishing embers.\nUnspoken words, etched in the timeless annals of memory.\nChewed on his final wishes of a succulent meal.\nA flash of seconds, then hanging loose.\nLife had been beckoned in an unknown itinerary.\nHangs in the wall, a dusty portrait, in a home full of the living.\nFootnotes: An elegy dedicated to the loving memory of my maternal uncle, Moni Mama (Anupam Bhattacharya) who left us on this fateful day twenty-one years back, only in his early forties, succumbing to cancer. A youthful and intelligent person full of life and a quirky sense of humor, his memories are invoked till today and he will always be the face of life for me, yearning for love and the closeness of family even in the excruciating pain of his last surviving days. This is for my cousin brother, Arijit Bhattacharya who never had the chance of knowing his father. Bhai, this is for reminding you of the treasured gift of love that your father had for all of us during his short life span. Hope you remember and cherish him, always!","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbcasj b/data_all_eng_slimpj/shuffled/split2/finalzzzbcasj
new file mode 100644
index 0000000000000000000000000000000000000000..2aeabb3f6db384be18d96bcc801ab01b6625601a
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbcasj
@@ -0,0 +1,5 @@
+{"text":"June 25, 2013, Milford, NH \u2013 Florida-based audio, lighting and AV production company Sound Media deployed two Earthworks FMR500 podium microphones at Florida Governor Rick Scott's April press conference in Riviera Beach, Florida.\nLennox Foster, President of Sound Media, selected two FMR500 19 inch podium microphones for the press conference, his go-to choice for podium miking.\nFor this particular event, Foster utlized two Meyer Sound UPA-1P loudspeakers on stands, a Presonus Live 24.4.2 console and two Earthworks FMR500 podium microphones.\n\"It is great working with Earthworks as a company. Craig Breckenridge was able to listen to our request, recommend the correct product, sent samples for evaluation, then followed up to verify we found the solution,\" concludes Lennox.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Not only did I squee like a teenage girl, I rushed to Quinn's site and was immediately sucked into my favorite werewolf world!\nI may have read it more that once....well, OK I have read it 4 times already! I cannot help it! This series is so intoxicating that I need\/want\/have to have more of it!\nTo read the Prologue click here. To read Chapter 1 click here. This will take you to Quinn's site and you can read it all!\nI cannot wait for this book. Quinn has said the end of September but no date has been given yet!\nThank you chickadee! So glad that you liked chapter 1 and thank you so much for the shout out!\nOf course Quinn!! I will be \"stalking\" you for more teasers........hahah!!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Single Family Home in 21214!!\nSingle family home located in a fabulous neighborhood. New roof, New siding and Windows. Interior needs work. Basement needs to be finished. Enough room in basement to add another Bath, or add one in the Master bedroom upstairs. Fix up this property and sell or fix up and live with tons of equity. This home won't last long.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Middle East & North Africa Gas Service allows clients to develop a deep understanding of the key developments in the gas\/LNG markets in the region.\nFGE works with executives to provide them with the strategic advice and supporting tools they require to assist them with their decision making and business development strategies.\nThis service combines specialist insights and years of experience in the region to provide clients with the most comprehensive understanding of the complexities that exist within this region's gas\/LNG industry.\nObtain a Thought Leader's View Our clients can benefit from having a thought leader's view of the market outlook, across various geographies and time horizons.\nStrategic Business Opportunities Identify key developments and opportunities in the upstream and downstream market place.\nAccess to FGE's Gas\/LNG Team Clients of our research, analysis, and data analytics can benefit from having consistent access to technical and\/or commercial information on the gas\/LNG market.\nReliable Forecast Analytics Our consistently accurate short- and long-term forecasts allow clients to capture the upsides and minimize downsides.\nRapid Assessment of Events Our utilization of knowledge and experience allows us to react quickly to market developments, therefore alerting clients promptly, allowing them to stay ahead of the competition.\nCommercial Analysis Forward-looking commercial analysis regarding the implications of topical industry issues included.\nGas production, gas re-injection, gas shrinkage, and flaring data since 1975 and forecasts by 2040.\nGas Exports\/Imports data since since 1975 and forecasts by 2040.\nSectoral gas consumption since 1975 and forecasts by 2040.\nHistorical Pipeline Gas and LNG trade statistics by destination\/source since 1975.\nDetailed Data on gas infrastructure (pipelines, LNG and GTL plants).\nLNG Exports by Country by destination: historical monthly data since Jan 2011.\nShort-term LNG Trade Forecasts for two years ahead on a monthly and quarterly basis.\nMonthly LNG Export Prices by Country by Destination in Northeast Asia (Since Jan 2011).\nMonthly LPG (Propane, Butane) Exports by Country Since Jan 2011.\nPipeline Trade by Country by Source\/Destination: historical monthly data since Jan 2011.\nShort-Term Pipeline Trade Forecasts for two years ahead on a monthly and quarterly basis.\nMonthly LNG Prices by Key ME Suppliers in Atlantic Basin (Since Jan 2011).\nLPG Prices since Jan 2011.\nConsultation with our regional gas experts for assistance with specific questions, providing additional data, analytical support, key insights, or advice.\nAnnual client meeting, briefing, or presentation from senior MENA gas experts.\nLNG Traders looking for information on natural gas and LNG trade flows and pricing, together with a short-term outlook of the region's gas exports and imports.\nGovernment Departments\/Agencies tasked with understanding energy markets.\nBusiness Development, Industry Planners, and Decision Makers looking for a long-term outlook of natural gas supply and demand, together with strategic advice to assist with their decision making and business development strategies.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Any Fellow who completes the following will be considered for Mastership.\nThese cases could include those submitted by candidate for Fellowship.\n2. 500 hours lecture or hands on continuing education courses with the following minimums.\n3. Oral defense of two cases chosen by the evaluator from the submitted cases.\nThe defense will be conducted over telephone with a duration of no longer than 15 minutes for each case.\nIf the evaluator is not satisfied with the defense, he\/she can choose one or two other cases from the submissions for a second chance. Satisfaction of the evaluator is necessary for ultimate success of the candidate. The evaluator may recommend further education and\/;or more practice to the candidate.\nIf the candidate is not convinced by the decision of the evaluator, he\/she can appeal that decision to the Accreditation Board of GAOI and the Board will assign another evaluator to hear the defense of the candidate. If the second evaluator concurs with the first, the decision becomes final and candidate must wait another year and resubmit his\/her application. If the second decision comes different than the first, a third evaluator will be assigned and the majority decision will be the result of defense.\n4. A candidate can submit his\/her own documents to be considered for Mastership.\n5. A $375 processing fee.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbcqsl b/data_all_eng_slimpj/shuffled/split2/finalzzzbcqsl
new file mode 100644
index 0000000000000000000000000000000000000000..112f8dafd46729e1efb6a0220e5da03664eee72a
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbcqsl
@@ -0,0 +1,5 @@
+{"text":"Quite a long time since I reviewed a French wine, in fact I have been asked if I drink french wines! the answer is of course I do.Often when shopping for wine I simply find that a lot of the wines with really good deals on them are not the french ones. I drink wines that appeal to me, that I feel will go well with the food I am eating and the mood I am in.\nThis particular wine is what I would consider a serious wine, not one for drinking in the garden. I do not think I would drink it at lunchtime either, to me this is a wine that needs a robust meal with it. Do not get me wrong this is a beautiful full wine, masses of fruity flavour and a hint of spice coming through and it is a heavy wine, the flavours linger in your mouth even after you have drank it. I consider this Cotes du Rhone froooom the South of France it to be a classy wine that asks for respect, goes beautifully with a Beef Wellington or a Venison dish, I also found it likes to breath, I gave it an hour and it had become gently soft on the palate.\nI bought this Saint Vigni Cote du Rhone from Waitrose at a very nice price of \u00a36.99 which was a saving of \u00a32 per bottle.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Patients with extreme psychological illnesses are dying prematurely, in contrast with the rest of the population, principally as a result of co-occurring health conditions that go untreated. Throughout South Carolina, MHASC is proud to supply to those who undergo from mental sickness many critically needed applications corresponding to housing and psychosocial rehab through day remedy programming. Family and friends additionally play an necessary role in the child's psychological well being stability and remedy.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Christine Louise Hohlbaum Author of The Power of Slow joins Jordan Mercedes to speak about 101 Ways to Save Time in Our 24\/7 World. There are times when we have to go slow in order to become more productive and regain lost energy. Christine Hohlbaum will join us to talk about taking time out before burnout and what that is like for your life.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The FRM220-FTEC is a slide-in card T1 (US Standard), E1 (European Standard) converter and timeslot cross connect which enables conversion between one T1 signal and one E1 signal. T1 and E1 signals with frames employ u-Law and A-Law compander encoding principles respectively and encode those analog signals into 64kbits digital data. The E1 interface supports CCS (PCM31) or CAS (PCM30) frames with or without CRC-4 and with HDB3 line coding. The T1 interface supports D4 or ESF frame formats with B8ZS or AMI line code. Multiple clock source selection provides maximum flexibility in connecting both T1 and E1. The clock source may be from the T1 recovery clock, from the E1 recovery clock, from the internal oscillator, from an external clock or via transparent timing. All setup controls can be performed via FRM220 CH01M RS-232 console port and ASCII terminal. Tests and diagnostics can easily be performed. Diagnostics include T1 local\/remote and E1 local\/remote loop back. When FRM220-FTEC card in placed in the FRM220 chassis, SNMP management allows veiwing the card converter's status, type, link status, data link status and alarms.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The breed where quality comes naturally with full traceability!\nBrysgaga Welsh Black cattle are situated, in north Ceredigion, West Wales, an area, famous for its Pedigree Herds of Welsh Black Cattle. Brysgaga consists of 148ha (365 acres) of less favoured land, all permanent pasture or long term grass leys, on the foothills of the Cambrian Mountains.\nA flock of 900 Aberfield, and South Wales type Welsh mountain Breeding ewes. All lambs are finished on farm, and sold deadweight to Randal Parker, Llanidloes. A number of Welsh ewes are purebred, with ewe lambs retained to maintain a closed flock policy.\nThe 100 head Brysgaga Pedigree Herd of Welsh Black cattle are made up from 35 spring calving cows plus followers. All cattle are inwintered, with cows turned out after calving to be mixed grazed with the ewe flocks throughout the grazing season. Bulls and surplus heifers are sold privately or at society sales, all steers are finished on farm and obtain a Welsh Black premium at local butchers.\nWELSH BLACK THE SUPER SUCKLER COW!","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbcupj b/data_all_eng_slimpj/shuffled/split2/finalzzzbcupj
new file mode 100644
index 0000000000000000000000000000000000000000..fa5574382385f3eef5ce9f01caf230bdd09416c8
--- /dev/null
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@@ -0,0 +1,5 @@
+{"text":"Have you every seen a gorgeous boho dreamcatcher mobile and wanted to know how to make one of your own? Well, now you can!\nJoin EaarthBones at The Lemon Collective on Saturday, June 9th, from 12-2pm where you will have everything you need to make your own dreamcatcher mobile! All materials included along with the skills which including weaving, wire wrapping, and composing your own personalized mobile.\nAlong with your workshop ticket, you will also receive a 15% discount in the EarthBones shop!\nRachel is creator, designer and maker of everything EaarthBones. She graduated from St. John's University with her BFA in 2015 and the International Center of Photography in 2014. While she is not creating handmade items for her shop, she is working as a photographer and teaching artist in Baltimore, MD. Her wallhangings and jewelry are inspired by our Mama Earth and the love of making items that connect us to ourselves and the world around us.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Hello I am , June 7th, 2018, This is my post about Bathroom Vanity With Seating Area Incredible Vanities Sitting Moraethnic Decorating Ideas 17, on this page you can see so beautiful design about Bathroom Vanity With Seating Area Incredible Vanities Sitting Moraethnic Decorating Ideas 17, the first picture in this post is the best picture we use about Bathroom Vanity With Seating Area Incredible Vanities Sitting Moraethnic Decorating Ideas 17, detail on photo's above, you can see in the second paragraph.\nThe first picture is a picture Bathroom Vanity With Seating Area Incredible Vanities Sitting Moraethnic Decorating Ideas 17, the image has been in named with : Bathroom Vanity With Seating Area Incredible Vanities Sitting Moraethnic Decorating Ideas 17, This image was posted on category : Uncategorized, have resolution : 800x585 pixel. This posting entitled Bathroom Vanity With Seating Area Incredible Vanities Sitting Moraethnic Decorating Ideas 17, and many people looking for about Bathroom Vanity With Seating Area Incredible Vanities Sitting Moraethnic Decorating Ideas 17 from search engine.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Great layout which suited our group. Grandchildren loved the playpark. Any questions were dealt with immediately.\nLovely spacious accommodation in a fabulous location.\nWell great complex however the accommodation lacked a proper fridge for a party of 7 and 2 children? One of which was an infant we constantly had to shop and at Christmas that's the last thing you wish to do ...washing machine not big enough either ...this two issues alone would prevent a return please attend to this along with a few spare towels and you never know !\nThe location was great and the property lovely. However, there were some areas that were lacking which could easily be rectified - a better range of cooking equipment and serving dishes, worn cooker dials making it difficult to get the right setting (which caused real consternation) , a very small fridge, no storage for provision, no underfloor heating or not working in the bathroom so it was very cold, the heating unit could be heard vibrating in the lounge above which was very annoying, a fresh coat of paint to walls as they look grubby and tired, stair gates requested where not in the property on arrival so we had to improvise with boxes and the high chair had to replaced as the safety straps were broken. Other than that it was great and we had a lovely time.\nExcellent!! A beautiful, warm well-appointed cottage with sea views in peaceful surroundings. Would definitely stay again.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The inability to commit to one's own calendar.\nThen again, perhaps it's something more insidious.\nCould it be a blatant disregard for another's time?\nOr simply a self-centeredness that renders some folks incapable of considering anyone else's outcome, other than their own?\nWhatever the reason or motivation, under no circumstances is the behavior even remotely acceptable.\nThe No Show, No Call \u2013 a phenomenon that has been on the increase in our practice.\nDid they not recall selecting and setting the online appointment?\nDid they not receive the confirmation email sent immediately upon scheduling?\nDid they not read the reminder that was sent 24 hours in advance of our scheduled appointment time?\nYes, there may have been a real calendar altering event\/emergency that prevented them from keeping their scheduled time or calling\/texting to advise otherwise.\nThough, based upon the frequency with which this occurs, there must be another explanation, any other explanation, to account for this behavior.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The dialogue with Batelec was held at the Yellow Conference Room of DLSL. I am not sure if the image above was of the actual dialogue because it was so long ago and I do not remember how our guests looked like.\nBefore anything else, this ironic story is true. There are a few at De La Salle Lipa who will remember things as I tell them. For the benefit of any millennials who may stumble upon this article, however, allow me to go as far back as the early nineties to lay down the background to this story.\nWhen Corazon Aquino stepped down from the Presidency in 1992, she had successfully restored democracy to the republic after a decade and a half of iron rule under Ferdinand Marcos. Regrettably, Aquino also left behind a power crisis that Fidel Ramos, her successor, took time to remedy.\nThis power crisis was so severe that, in the early years of the Ramos presidency, power outages were rotated daily for months on end throughout the country for anything from four to twelve hours each day. I distinctly even remember one time when the outage went for an unbelievable fourteen hours.\nBy mid-1995, when the late Brother Rafael Donato was installed as the first resident President of DLSL, the Ramos administration had started to stabilize the power situation nationwide. In Lipa City, however, the power outages continued onto the late nineties. Not the prolonged sort scheduled by the National Power Corporation but short unscheduled outages that frustratingly could hit anytime of the day or night. These outages were also wont to happen several times each day.\nDLSL being a school, one could always tell even if one was outdoors if one of those infernal outages hit. Collective groans and shrieks resounded around the campus from computer laboratories and offices where students and personnel were left dismayed by the thought of starting over with the work they failed to save.\nI recall even having been asked by Brother Rafael to issue a school-wide memorandum encouraging students and personnel to use Control + S every few moments when working on a computer. The lost work apart, the frequent outages were, needless to say, detrimental not just to computers but all electrical equipment.\nBecause the SENTRUM, the large multipurpose gymnasium, had become operational and was being frequently rented out, it became imperative for the school to purchase a large back-up generator to ensure that games and performances were not compromised.\nBrother Rafael was as fed up with the frequent outages as everyone else, but being an educator, he was more concerned with information, dialogue and finding solutions to local problems. He saw the school not just as a place for learning subject matter but, moreover, also for learning and exercising civic duty.\nThus, he asked the office for Social Concerns to arrange a dialogue between representatives of the Batangas Electric Cooperative (Batelec), which supplied electricity to the city and most of Batangas, and a multisector group from the school. This must have been either 1997 or 1998 and the meeting was held at the small conference room on the second floor of the Jose W. Diokno Building.\nWe were not sure if Batelec would even be interested in coming, but the general manager at the time himself gave his word that he would be present. Apart from school administrators, there were members of the faculty and student leaders present in the meeting. There might even have been invited guests from other schools present.\nThe dialogue was scheduled one afternoon. Batelec's general manager at the time was accompanied by a few members of his management team and some engineers to answer technical questions. After brief introductions at the President's Office to exchange pleasantries with Brother Rafael, the guests were ushered to the adjoining conference room, where the multisector group was already seated.\nThe meeting was not even two minutes old and the introductions not even finished when, of all things, the entire room went dark. A dialogue that was scheduled to discuss possible solutions to the frequent power outages in the city began\u2026 with a power outage! Brother Rafael could not have planned things better had he tried. The initial gasps around the room when the lights went dead were followed by ironic laughter.\nBatelec's general manager quickly apologized to everyone and left the room to call somebody. Brother Rafael, who could not stop laughing about the incident afterwards, loved to joke that he was probably calling his engineers to determine if the school had not intentionally turned power off to underscore the problem.\nPower was restored after a few minutes and the meeting resumed. Despite the gravity of the problem being discussed, since Brother Rafael was moderating, it was for the most part polite. I remember the frequent outages being blamed on anything from sparrows to palm fronds and even the rain, but little else because it was so long ago. But one thing that I will never forget is that a meeting to discuss frequent unscheduled power outages began with one of these.\nI struggle to recall any other incidents in my life when fate conspired to deliver irony as stark as that day. I actually felt sorry for our guests from Batelec who, despite the poorness of the cooperative's service at the time, were actually very nice and likeable people.","meta":{"redpajama_set_name":"RedPajamaC4"}}
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+{"text":"He advises on managing TM & design portfolios, opposition & cancellation proceedings, IP audits of TM portfolios, filing strategy (including clear). Andries defends in opposition and cancellation proceedings, infringement actions and monitoring of registration procedures.\nHis clients include national and international corporations, consultancy and law firms.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This is the staging area for the fieldOfView plugins for krpano. A copy of these pages is included on krpano.com. The pages in this staging area may be newer than the respective pages on krpano.com.\nA plugin that uses the gyroscope in devices such as the iPhone 4 and iPad2 to control the view.\nA plugin that adds miscelaneous functionalities to krpano which do not fit in with any of the other plugins in the package.\nA plugin that enables multitouch zoom on Windows 7 and Android multitouch devices.\nA plugin that adds string manipulation methods to krpano.\nA plugin that adds string manipulation functions to krpano.\nTo build the flash plugins from the supplied source files, you need the open source Flex SDK, version 3.2 or newer.\nThe plugins can be used free of charge, in commercial or non-commercial applications. The source code is available under a Creative Commons Attribution license.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"These are websites I have designed \/ created \/ maintained for various companies and organizations. Click each to explore further (each link will open in a new window).\nWebsite designed and created for a Brantford men's choral group.\nMy own website. Currently used as a photo gallery, but will eventually have my writings and other works.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"STEEL TOES AT YOUR FACILITIES?\nSteel Toes Home News STEEL TOES AT YOUR FACILITIES?\nAt ProLift our technicians, sales consultants and trainers visit many customer facilities. Each facility has unique requirements regarding personal protective equipment (PPE). When our interaction requires time on the production floor, the customer may require us to wear protective footwear such as steel toe boots. According to the Bureau of Labor Statistics, 75% of foot injuries occurred when workers were not in compliance. Approximately 60% of the foot injuries were a result of falling objects and 80% were caused by an object weighing no more than 30 lbs.\nThe regulation also refers to consensus standards by American Society for Testing and Materials (ASTM) and ANSI. All protective footwear must comply with one of these standards. Specifically, steel toe boots must meet guidelines for ASTM F2413-05.\nVarious hazards can cause \"danger of foot injuries\" that result in crushed\/broken bones or puncture\/amputation of toes or feet. If your facility faces these challenges or similar scenarios, steel toe boots can help prevent injury.\nDeveloping a safety footwear program is ideal for employee awareness and compliance. When selecting or recommending footwear, its comfort, durability and anti-slip protection should be factored into the decision. Poorly designed footwear chosen because of cheaper costs may contribute to employee fatigue and deter buy-in.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"There is no denying the devastating effect fossil fuels, such as coal and oil, have on our environment. Though we are still heavily dependant on them, at least we are now changing our approach to energy usage by searching for alternatives that lower our carbon emissions and nature destructing ways. Biofuels, have until recently, been thought to be a suitable replacement for fossil fuels - renewable, clean, carbon neutral. Unfortunately this is not quite the truth.\nCrops grown for biofuels need very large areas of land to produce energy. This type of agriculture is called monoculture and hugely upsets the biodiversity of our earth's vegetation. It clears lush forests abundant with thousands of species of plants and animals to make way for one plant crop. Only 2% of the rainforests in Indonesia and Malaysia will be left by 2025 if we keep clearing the land to make way for monocultures to support our fuel requirements. The amount of carbon sequestered by a dense rainforest filled to the brim with plant diversity is greater than a land covered in sugar cane.\nAlso each crop planted has a different effect on the soil. Some crops are known to rapidly increase soil erosion and exhaust many of its minerals particularly if they are not rotated with other types of plants. Also the pollution created in the farming and production of biofuels can be on par with fossil fuels.\nFinally, one of the biggest concerns with biofuels is that they are diverting crops, like wheat, sugar and corn which have traditionally only been grown solely for food, to produce fuel. As the percentage of supply for food goes down and the demand from an ever increasing population goes up; unfortunately, so too does the cost of food.","meta":{"redpajama_set_name":"RedPajamaC4"}}
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+{"text":"Liz McIntyre was born in Hanover, New Hampshire on April 5, 1965. She attended Dartmouth College before moving west to pursue her career as a freestyle skier. Joining the U.S. Ski Team at the age of 19 she spent twenty years on the team competing as a member of three Olympic Teams (1992, 1994 and 1998) before becoming one of the team's leading coaches.\nAs a moguls skier she won four World Cup events, all of them in Tignes, France (1987, 1992, 1996 and 1997). She finished in the top ten in 18 World Cup events.\nLeading up to the Olympic Games in Lillehammer in 1994 she focused her efforts on her \"airs\" tricks. The effort paid off. The leader after the preliminaries she put in a nearly flawless performance that earned her the silver medal behind Norway's Lise Hattestad.\nLiz retired from competitive skiing following the Olympic Games in Nagano but was lured back to the team to be its technical coach. She quickly applied her experience as a competitor and was highly regarded as an athlete focused coach. She demonstrated amazing tenacity and brought innovation to her work. The members of the U.S. Freestyle team became known for quiet upper bodies and supple leg movements in moguls and enjoyed considerable success.\nDuring those years, from 1999 to 2006, the team produced world champions Toby Dawson, Nate Roberts, Jeremy Bloom, Hannah Kearney and Ann Battelle as well as a long list of World Cup wins and three Olympic medals.\nShe moved to Granby, Colorado where she works for Twin Enviro Services of Steamboat Springs.\nIf you notice any errors or inconsistencies in Liz McIntyre's bio, click here to let us know.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"I'm looking for some advice from fellow yogis.\nI am in the market for a new yoga mat. My Gaiam yoga mat was ok to begin, but now that I am practicing more frequently I find it much too slippery. I thought I wanted a Jade, but after renting one at a local studio, I was left with a pounding headache due to the strong smell of rubber! And it didn't look new, so I don't think the smell would dissipate with time.\nI am looking for a good non-slip mat that does not have a rubber smell.\nAlso, has anyone tried a Cork yoga mat? Reviews?\nI believe Costco has them back in. Also can check online at costco.ca and have it delivered to your door.\nIf it's not what you want, it can be returned at the store.\nI saw a Manduka mat on sale at Winners the other day.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Jazz writer Kevin Legendre explores the encounter between modern jazz and French cinema in Paris in the late 1950s and '60s. Paris in the civil rights era was a hub of artistic collaboration as well as a kind of refuge - a destination for American jazz musicians escaping racial prejudice and turbulence at home, finding new creative encounters abroad.\nAs segregation raged in the US these artists \u2013 from Miles Davis and Bud Powell to Art Blakey and Thelonious Monk \u2013 felt liberated in the city. Paris was the first foreign city Miles Davis ever visited, it was here he met Picasso. Sartre and Jean Cocteau. \"It was the freedom of being in France and being treated like a human being...\" he wrote, \"It changed the way I looked at things forever. I loved being in Paris and Paris was where I understood that all white people were not the same; that some weren't prejudiced.\"\nThe admiration was mutual, new artistic relationships flourished. A key area of collaboration became the film score, with jazz musicians working closely with a younger generation of radical directors that made up the French 'new wave': Miles Davis' 1957 score to Louis Malle's brooding thriller Ascenseur pour l'echafaud; Thelonious Monk and Art Blakey and the Jazz Messengers' soundtracks for Roger Vadim (Les Liaisons Dangereuses) and Edouard Molinaro (Des Femmes Disparaissent) as well as cues by the Modern Jazz Quartet. French film composers listened closely and began writing their own scores based on what they had heard \u2013 a standout being the score for Jean Luc Godard's debut, A Bout de Souffle (1959) composed by jazz pianist Martial Solal.\nThese scores elevated French films to new levels of intensity, cool and atmosphere. Sequences were shot on handheld cameras in and around the streets of Paris, especially at night - musicians would be asked to improvise as they watched the rushes. Miles Davis recorded Ascenseuer pour l'echafaud with the film projected on the studio wall as Jeanne Moreau, its star, poured the drinks. Godard used experimental editing techniques that matched the rhythm and dissonance in the jazz. Some of these musicians' great but little known work is recorded in these movie cues. But underlying the beautiful work, this story is one of political exile as well as cultural refuge. For a moment Paris became a jazz capital of the world as it already was the free-thinking centre of Europe, a rebuke too prejudice in America - even as it had growing racial tensions of its own.\nRecorded in and around the city, jazz critic Kevin Legendre meets musicians, filmmakers and writers to explore this incredible moment of exile and exchange, and asks if Paris is still the city of freedom and tolerance it once was for Black artists.\nGuests include jazz singer Dee Dee Bridgewater, filmmaker Bertrand Tavernier, sax player David Murray, composer Martial Solal, jazz writer Geoff Dyer, bassist Henri Texier and playwright Jake Lamar.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Doctor Who', though an acquired taste, is my favorite science fiction show. Unlike other sci-fi productions, which usually involve elaborate space ships or special effects, 'Doctor Who' has continued the decades-old British tradition of presenting fantastic plots that do not rely on effects or dramatic action sequences. Instead, the show, which involves a time-traveler whose ship looks like a phone booth from the outside, focuses on unusual characters and a back story that becomes ever more complicated with each trip through time. The primary villains, the Daleks, are even somewhat comical in appearance, keeping the show within the other British tradition of portraying adventure with a sense of humor.\nUnfortunately, though 'Doctor Who' is popular no American networks carry it on a first run basis, even though new episodes are being produced. That's why I watch this, my favorite science fiction show, on directstartv. There's no reason to wait months for the program to run first in England and then get disseminated here in the United States. This is especially so in the computer age, where any story spoiler can jump across the internet within minutes. Given that all time-travel stories rely on surprises, it's definitely a must for any 'Doctor Who' fan to see the episodes at the same time as the rest of the fan community.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"To access the Remembering Lemuria Online Course please click here.\nI listened and loved it. As soon as you come in with your toning I start crying. My whole body vibrates with energy coursing through it. I'm being cleared and cleansed. I see images of water, colors of blue, I'm taken down to the depths of an ocean floor by a dolphin who is guiding me. As we swim down I see an ancient city and a site where there is a crystal formation. I am gifted a piece of what I think is a Lemurian crystal. As I hold it out and look at it, it's shines rainbows all over me. It was crazy because every time your voice started in my eyes welled up with tears. There was a deep knowingness connection of remembering. Excited to integrate listening to this daily to see what comes up. Thank you for your gift!\nA year ago, I would have never ever considered myself a singer. I could dance in front of strangers, but singing \u2013 no way \u2013 you couldn't pay me to karaoke. Then, in 2016, I was called to move to Maui to reclaim my past life wisdom and gifts from this land when it was Lemuria.\nIt began in the ocean. I started fluttering my tongue to make a vibration noise as I sang out across the waves, but I knew there was more. I knew I was supposed to sing these Extra Terrestrial tones, and vibrate my throat, but I didn't know how. In December, I took a trip out to the sunken crater of Molokini where I received a huge activation. The energies were so intense that as I was driving back I started to sing to keep myself awake. I began to use my finger to vibrate my throat. Then all of a sudden, I remembered how to do it without my finger.\nI could feel something shifting inside me. This started a windfall of changes in my life. Suddenly I was singing in ceremonies and catalyzing the awakening of thousands. This is my wish for you.\nMeditones are similar to binaural beats. They are precisely tuned frequencies of sound, that when heard with headphones, guide your brain into effortless relaxation and deep meditation.\nRemembering Lemuria stimulates Theta brainwaves which are the gateway to your spiritual connection with the Universe. This is the mental state where you create your reality. Theta brainwaves give us access to detailed visualizations, ancient future memories, intuition and insight that is usually beyond our normal conscious awareness.\nIn this track, meditones have been combined with Rachael's healing vocal tones for a deeply meditative experience that is perfect for beginners or experienced meditators alike.\nRemember to use headphones for the full meditones effect. Please note, meditones are unsuitable for people suffering from epilepsy or seizures.\nArtwork with Light Language symbols that I channeled when the tones came through.\nSo much love for your activation, and the powerful magic & medicine you carry within your DNA.\nRemember who you are. You are more powerful than you think.\nDOWNLOAD NOTES: Once you complete your purchase, you will receive a link to download a zip file containing all the files. If you are on your phone you can download the FREE Zip File Viewer app to unzip the files and access the mp3s. If you are on your computer you can download and unzip the files, and then add them to iTunes or any other music player.\nRemembering Lemuria is an incredible gift to the world. The first time I listened to the music, I was taking a bath I could feel layer after layer of traumatic past lives in Lemuria release instantly, without effort. All of my previous experiences with Lemuria had been so idyllic that I had no idea how many challenges I had during my lifetimes there. Rachael's voice gently guided those past lives out of my cellular memory with ease and grace.\nSubsequently, I've listened to the track while working, and my productivity has soared. The track helps me stay focused on the frequency of my work, and not be distracted by other things around me. It is rare that an album can be great for past life releasing and productivity, but that is the beauty of this offering and Rachael's voice. I was able to complete three projects in an afternoon that had been weighing on me for nine months!\nI cannot thank you enough for the beautiful sound track I received a few days ago. I have received so many profound and beautiful images and messages for my Spiritual Growth and to assist me to help heal animals. I am so grateful, beyond words.\nI just wanted to express some gratitude. I saw your advert for \"Remembering Lemuria' in my newsfeed. I knew immediately that it was something for me. I downloaded it this morning and listened. I had a lot of tears but now I am actually sitting here in front of the computer getting together my own flyer for my own work, which I have been procrastinating over for weeks, months in fact!! I feel excited. So thank you from my heart to yours for this opportunity. I will continue to listen and see what else unfolds.\nI listened to the meditation this afternoon. It is so beautiful!!! While I was listening to it I felt like I was surrounded by angelic beings. Thank you so much.\nI bought Remembering Lemuria on a whim, thinking it wouldn't \"do\" anything for me, because I'm not one of those \"special\" souls, but I wanted to support Rachael, and thought the preview sounded beautiful. My first time listening was a beautiful but odd experience- it was so liltingly lovely and calming, and yet I was filled with anxiety and a strong need to be somewhere, doing something. Goosebumps everywhere. The next day, a feeling of having forgotten something of the utmost importance nagged at me constantly, as did a sense of restlessness and a need to be somewhere. After listening a second time, I had a sudden realization regarding a pattern of behavior I'd been following, yet was unconsciously rejected. It was not a comfortable realization, more like a slap to the face, but it was necessary. More pieces have continued to fall into place the last few days, but yesterday was a truly transformative day. I listened before bed the night before, and yesterday, it was as if blinders had been lifted- suddenly all of these things I've been struggling with were illuminated, as were the signs that have clearly been there all along, had I not been blind to them. The transformation that has been sparked is so necessary- I've been craving it unconsciously all along but have been in denial about so much for so long. The floodgates have opened, and my life will quite literally never be the same. Thank you, Rachael, for sharing this gift with the world.\nI'd love to hear your feedback! If you'd like to submit a testimonial for Remembering Lemuria you can do so HERE.\nWe are the ones who hold the keys to the new reality. Only by remembering and reclaiming our past can we create the world we all long to see. Listen to my voice. There is more than simple sound coming through. There are Pleiadian and Lemurian activation codes to initiate the multidimensional aspects of your DNA. If you get chills, this is your cellular structure confirming this Truth. Remember your starseed lineage. Reclaim your galactic inheritance. Get still. Listen. Remember. All that you need is inside you.","meta":{"redpajama_set_name":"RedPajamaC4"}}
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+{"text":"Our moustache wax products are a well formulated blend of natural and organic wax, oil and lanolin with added vitamin E, plus essential oils.\nNot only is beeswax great for protecting the skin, it is also what helps keep our stache wax firm to give you great hold throughout the day. As a bonus, beeswax contains Vitamin A which improves hydration and promotes cell regeneration.\nLanolin is a greasy wax that is secreted by sheep glands. This wax protects the sheep wool from harsh weather conditions and helps to retain moisture to stay hydrated. This is very similar to the sebum which we secrete from our skin too.\nThere are many known allergens contained in Lanolin, so it's amazing health benefits aren't well known. However, we use medical grade Lanolin, which is ultra-purified and hypoallergenic, meaning it causes little to no irritation.\nLanolin is the perfect ingredient in our strong-hold wax as it protects the hair and skin to keep your stache held for longer.\nCoconut oil is just about solid at room temperature and starts melting as soon as it comes into contact with skin. It absorbs quickly and deeply into hair and skin leaving it feeling nourished and hydrated.\nCoconut oil contains vitamin E, a powerful antioxidant that helps fight free radicals that cause damage to the skin. The perfect addition to our stache wax for added moisture and hydration.\nOur Brand Ambassador Chris demonstrates the best way to use our Stache Wax to get the best results for a strong hold moustache that lasts all day.\n\"Amazing hold for a twisted style, or just a firm hold moustache. Superior scents, superb hold, order some today you won't be disappointed\"\n\"Having wanted to try and style my moustache for a while I struggled to find a wax that gave me the control and hold I wanted. I have to say I tried a few\" popular\" brands but still wasn't satisfied. Almost giving up I was allowed the opportunity to try the new stache wax from Twisted Moustache.... Wow! Firm hold all day with an amazing aroma, I will definitely be \"sticking\" with TM from now on\"\n\"I have a draw full of other moustache wax just never quite found the right one for me. Ive been looking for a wax that isn't really hard to get out of the tin and at the same time has a long enough hold to last the working day. In Twisted Moustache stache wax ive found that and more! A wax that melts very easily into the fingers and works into the moustache perfectly, a wax that lasts for ages and smells amazing.\"","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"I've been a bit quiet on here lately. Work is pretty crazy and I have been spending a fair amount of time travelling around the country. I had hoped to visit Bravissimo in Nottingham last week but sadly I wasn't able to get there in time. I'd really like to go to a store at some point though as I would like the opportunity to try on different sizes in lots of different styles; something that's impossible to do via mail order.\nHowever, I did get the time to visit a large Asda store near Birmingham on Thursday night. It had a huge George section (for those of you who don't know, George is the clothing line within the grocery store, Asda) and I spent some time wandering up and down the aisles looking for bargains.\nI have been buying clothing from the George range for the past couple of years. During this time the quality has certainly improved, but the prices have also increased. It's still a great place to shop as they sell such a wide range of styles, shapes, fits and fabrics, but it's no longer the bargain basement it once was. Their tops are typically priced from \u00a310 upwards, which is a great price but I can remember their tops being 10-20% less a couple of years ago. I now no longer go into the store and buy pretty much anything that takes my fancy; now I am far more choosy and take my time to try on each item and ensure I really do want and need it. I probably sound like a right miser now but these days we all have to be really careful with what we spend our hard-earned cash on.\nA few weeks ago I visited my local Asda Living store, which carries a reasonable stock of George clothing. I tried some items on in size 18 but many of them were too big \u2013 a fact I only realised after taking some pictures of me trying them out in the changing rooms and showing them to friends on Facebook (thanks girls!).\nWhen I went to the store near Birmingham I tried some of these items on again and found I needed smaller sizes every time. I thought it would be useful to show these pictures side by side, in a 'before and after' sort of way, so that you can see how the fit compares.\nSo first of all we have the Floral Print Jersey Dress at \u00a316.\nThe dress is 100% viscose and is machine washable. It has a natural stretch to it and feels very soft on my skin. The printed pattern has stood up well after being washed for the first time and doesn't look like it will crack or peel off at any point.\nIf you've read my blog before you will know I am not a fan of my legs so you won't be surprised to learn that I will not be wearing this as a dress but instead as a long top\/tunic with a maxi skirt underneath.\nSeeing these two photos together makes me realise that you can't see that much difference between the sizes here but I REALLY noticed it when trying on. The size 18 was loose and very baggy around the waist, whereas the 12 was more fitted all over and showed my waist more clearly \u2013 something that is important as I have an hourglass figure.\nI am not sure that this is the right belt but I think it does look good to have a wide belt with this dress. It also helps to gather in the slightly loose material on the upper back of the dress, making the whole thing look smoother and a better fit.\nNext up, I tried the Jersey Wrap Dress at \u00a316.\nThe name of this dress is slightly misleading. It wraps over the chest but that is it. And you can't adjust the wrap at all; it is firmly attached to the waistband of the dress. Not that this mattered to me \u2013 I just wanted to make it clear to anyone reading this and considering buying the dress themselves.\nAgain, I am not planning on wearing this as a dress. It will be a long top with a maxi skirt underneath. I may try it out at home with my lovely shapewear leggings but it remains to be seen if I am brave enough to wear them out in public!\nGoing down a size I found the waistband fitted much better and was therefore much more visible and flattering. The 'wrap' part which covers the chest also came up higher so I could wear it without my modesty panel if I so chose (I am actually wearing a spaghetti strap black dress underneath in these pics; it provides a built-in modesty panel for my tops).\nAfter washing this dress, which is again 100% viscose and machine washable, I found the fabric has developed a very slight fluffy layer, almost as if millions of tiny threads have worked themselves clear of the weaving of the fabric. I am hoping this has happened as it is brand new and that it is something which will disappear over time. I am keeping hold of my receipt just in case it doesn't, however!\nYou can't really see from this website photo but there are purple colour blocks on the shoulders of this dress, making it really unusual in its design. I like unusual and was therefore attracted to this item.\nMy friends advised me that the size 18 was far too big for me as the waist sat too low. I am short in the waist so wanted to try a smaller size to see if it made a difference.\nI am pleased to report that, as you can see from the above photos, yes it did make a huge difference. The dress was more fitted all over and the waist fits me perfectly, pulling the whole top in most flatteringly. There is a tie at the back but wearing the dress in this size with the nipped in waist I really wouldn't need to use it.\nThe dress is 96% viscose and 4% elastane. It has washed well and I look forward to wearing it next week. I'll update this post if the fabric deteriorates at any point.\nAfter this, I tried a couple of items I had not had the opportunity to before.\nI found this top\/dress in the sale \u2013 a bargain at \u00a36 (was \u00a312)! Unfortunately I could not find it on the website but have seen it instore so if you like it, do make sure you get to your nearest George store soon to snap one up as stocks must be very low.\nIt's a size 16, which fits me very nicely, and is higher cut than many of the tops I wear. This makes is ideal for work \u2013 even with its hint of sexiness with a small circular 'peephole' between the collar lapels and a diamante to add a bit of glam and sparkle.\nSuccess! I have not worn this white belt (Matalan, \u00a33 in sale a few months ago) with anything before as its decorative design often clashes with my patterned items so I am pleased to find something that goes well. It matches the collar perfectly and makes the top\/dress look completely different. It's always a great result when you can get two or more looks from the same item, simply by adding or taking away accessories.\nI could only find it in size 18 and this was too big for me \ud83d\ude41 Plus I did not have my camera with me this time so could not take any photos to show you the fit \u2013 don't tell me you thought that was me in the pic above!! But I wanted to include it in my post anyway as it would be a great top for the party season and at only \u00a310 it really is a snip. It fits very well (I could tell this despite the fact the one I tried on was too big for me) and would hide all sorts of lumps and bumps. I think the top would be perfect for Christmas Day (when we all eat too much and get a bit bloated) as it flares out from the waist.\nThe downside is that it is handwash only due to the delicate sequin work along the neckline. I don't get put off my handwash only items these days as I have to handwash my lingerie so it's easy enough to add another top or pair of leggings to the pile. The fabric comprises 95% viscose and 5% elastane. I will certainly be looking out for this top in a smaller size in other Asda stores!\nI wonder how many items of clothing I have bought in the past were actually too big for me. I have sometimes bought things which I have liked when I tried them on in the shop or at home but after a few washes and wears I have changed my mind and gone off the shape or fit. In the future I will certainly be trying on tops and dresses in several different sizes to make sure I make an informed decision \u2013 and hopefully only end up buying items which fit properly and flatter me as much as possible.\nThe print in that first dress is so flattering.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Colin Hay is familiar to millions as the frontman, songwriter, and vocalist of pop sensation Men at Work (\"Down Under,\" \"Overkill,\" \"Who Can it Be Now?\"). Hay is justifiably proud of his place in pop history, but since moving to Los Angeles in 1989, he's made 11 critically-acclaimed solo albums, including the highly successful Man at Work.\nHis latest album, Next Year People, is the work of an artist who is a true master of his craft. The album is full of quizzical, curious, and cynical yet open-hearted songs with catchy melodic hooks that underscore deeply insightful lyrics.\nThe frequent use of Hay's music in TV and film\u2014including hit shows such as Scrubs (on which he has made several cameo appearances), Army Wives, and Modern Family, the hit soundtrack to the film Garden State and the recently released Words and Pictures\u2014has proven the timeless appeal of his songs.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"What is SMART and where was it developed?\nSMART is a small Vertical Axis Wind Turbine (VAWT). It has been designed entirely in India, completely in-house at Vaata.\nHarvesting wind energy is a non-polluting way to generate electricity. Additionoally it is unlimited and free.\nVertical Axis Wind Turbine are simple, compact and easy to maintain. Additionally it accepts wind from any direction at a lower wind speed.\nWhat is the current scenario of wind energy in India?\nWind Energy in India has grown tremendously over the last two decades. As a result of this boom, the wind potential in most major wind sites has been tapped and a point of saturation has been reached. Presently setting up a wind farm to harvest energy from wind requires huge capital investment and involves a rat race for wind rich land. This has led to a situation where only large players operate and benefit from technological advancements in this sector.\nWhat is Vertical Axis Wind Turbine (VAWT)?\nVertical Axis Wind Turbines are wind turbines that rotate about a vertical axis. Generally, we are used to seeing horizontal axis wind turbines (HAWTs) which have been the norm of wind-energy for decades now. But slowly, Vertical Axis turbines are capturing the imagination of many innovators in the field.\nWhat are the advantages (VAWT)?\nVAWTs have been proven to generate more power per unit land area than HAWTs; this is because micrositing of VAWTs can be done in a way such that there is a better use of the wind rich land. Also, smaller VAWTs, like SMART are easy to transport and maintain and demand fairly inexpensive capital costs.\nWhat is special about SMART ?\n\u2022 SMART taps all the advantages of VAWTs.\n\u2022 Performs in higher wind speeds and cuts in at low wind speed.\n\u2022 Modular design for ease of transport.\n\u2022 Technology innovation scalable for offshore wind.\nHow is SMART technologically advanced?\nInnovations in Rotor, Drive, Motor and Control Systems design.\nIncludes first of its kind Aerodynamic VAWT Braking Mechanism.\nInnovative erection mechanism for crane-free installation, thus minimizing the access requirement to erection site of the turbine.\nIf I place the order today, how long will it take for me to start producing power?\n22 days. It takes 21 days for the concrete foundation to be laid, and for the concrete to set in (curing), and a few hours for us to erect the turbine onto the foundation and assemble it.\nOnce the foundation is laid, how long does the actual erection and assembly of the wind turbine take?\nIt takes 4 hours for the a turbine to be completely assembled and erected.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This is a post that has been weighing on me for while now. I am certain it's not going to come across eloquent or well crafted because what comes from my heart is seldom put together in a nice tidy round and polished package.\nI am more into the whole blogging\/tweeting\/social networking thing now than I ever have been before. I am reading more, being read more and getting to know other women out there in the interwebs more than I ever have before. Because of this, I see more opinions, more arguments and more complete arrogance and more attitudes of superiority than I ever knew were out there.\nI now firmly believe that this whole social networking thing is both equal parts blessing and curse. A blessing, of course, because people who need support, help, comfort and a general feeling of being propped up at the darkest of times can find it just by turning on their computer. And that??? That is awesome. I know I have women out there that I have grown very fond of. Some of them don't even know I exist. Women like Maria, Becky, Anissa, and Brittany among several others. There are also women that I'm actually getting to know and it's a two-way street rather than me admiring them from afar like the previously mentioned. Women like Stacey and of course, my dear Brooke.\nThat is the awesome part of this whole thing. Awesome. For real. The blessing.\nThere are times, though, that the awesome just seems to get drowned out by the voices shrieking out \"YOU'RE DOING IT WRONG!!!!\" I find this so heart wrenching. There are battles being waged out there that I didn't even know about until I started to get more active and expanding out into the interwebs to actually see what people had to say. And you know what? Women are so critical of each other. Every woman knows, this, of course. However, it always used to be contained to your friends, your neighbors and your acquaintances\u2026 the ones that are outside the screen we sit in front of now. It seemed smaller. And friendlier. Two close friends having a conversation about their opinions and methods and perspectives was something to be cherished and was almost always done lovingly and with kindness.\nI can't imagine that being a parent is easy. I don't believe any major decision of parenting to be simple. Parents make tough choices everyday about the kind of life, patterns and routines they are going to set up for the little ones they hold most dear and are passionate about protecting. These decisions cannot be made easier when there are a half million other mothers out there who disagree. I do understand that by having a blog and putting your life, your choices and your decisions out there that you risk criticism\u2026 almost invite it, even. But to just sit anonymously or even unanonymously behind a computer and spew venom and judgements and insults just doesn't make sense to me.\nWhat is WITH us? At what point did it become ok to treat each other this way? And we wonder why some kids are bullies. When you hate on people making decisions that differ from yours and belittle and berate how can you then turn around and publish a post on tolerance and love? I don't understand why we feel the internet gives us the right to condemn anyone simply for decisions they make in their daily lives.\nI want women to support each other, understand each other, agree to disagree on the choices in life and love each other because only we, as women, know what other women go through. A screen and a keyboard can give us the ability to do wonderful things for each other if we'd just stop tearing each other down. End the constant cries of \"YOU'RE DOING IT WRONG.\" and just allow women to do the best they can. That's all we can ask of each other and it's all we can ask of ourselves. Doing it differently is not the same as doing it wrong. If your choice is different from mine, that's all it is. Different. Not wrong. Not better. Just different. If you want to converse about differing opinions, do it as if the person is right there\u2026 with you\u2026 at the breakfast nook having a cup of tea with you. Bring back the compassion, love and understanding. Those are the greatest natural traits we women have\u2026 USE THEM\u2026 always.\nWe need to encourage each other. We are all women. And we're all just\u2026 doing it\u2026 the best we can.\nI love this post. I generally keep to my little corner of the blogosphere where we're all friends and everyone is supportive even if they disagree for this very reason. I'm old enough to have lost all patience for the kind of behavior you're talking about, so I stay as far away from it as possible. I'm glad I'm not the only one who feels this way!\nCan we form a \"community\" of bloggers whose sole motto is \"We're doing the best we can\"? It's the truth, after all. And I'd rather read a post about loving and accepting each other than about how I should have done x, y and z.\nFor the record, I cheat when I make fish tacos. I buy frozen, pre-battered fish. AND THEN WARM IT ON A COOKIE SHEET. I SAID IT.\nYES! YES! We should do it!\nYou know what? I don't even cook. Ever. So who am I to judge? \ud83d\ude42 You go on with your bad self and your pre-battered fish.\nAt the end of the day SO much of life boils down to the Golden Rule for me: treat people the way you'd like to be treated. Easy peasy. Not rocket science. Doesn't take a lot of effort, energy, time, or money.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbejgj b/data_all_eng_slimpj/shuffled/split2/finalzzzbejgj
new file mode 100644
index 0000000000000000000000000000000000000000..cf229ead2550cf411dbf7eeb9f7d997a83fc9a75
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbejgj
@@ -0,0 +1,5 @@
+{"text":"3 Way Light Circuit Wiring Diagram: Way switch wiring diagram multiple lights fuse box and. Way switch wiring diagram house electrical.\n3 Way Light Circuit Wiring Diagram.\nWay wiring diagram multiple lights vivresaville. Three way light switching fitting. Way switch wiring diagram. Way switch wiring diagram multiple lights fuse box and. Way switch wiring diagram house electrical. Way switch wiring diagram. Diagram light wiring multiple lights. Way switch wiring schematic get free image about. Lamp switch wiring diagrams do it yourself help. Way switch how to wire a light. Way switch wiring diagram. Three way lighting circuit wiring sparkyfacts. Way switch wiring diagram. Way switch wiring diagram. Three way switch wiring diagram two lights best site. Way light switch diagrams printable diagram. Saima soomro way switch wiring diagram. Video on how to wire a three way switch. Way switch wiring diagram house electrical.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Please be aware that we can only ship this product inside the USA. We cannot ship to countries outside the USA.\nYes! As an authorized online retailer of Hot Kiss products we will match our competitors' prices and also guarantee that you will receive a brand new, authentic frame with a full manufacturer warranty.\nThis Hot Kiss frame could be yours for just !","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Our mission at Lu Acupuncture Center is to support you in your process of healing and help you to achieve your wellness goals. We strive to restore vibrant health, revive and renew your body systems and their processes of immunity and self\u00ad-healing.\nWe work to combine the ancient knowledge of Chinese healing systems with modern medical knowledge to promote health and enhance your quality of life.\nChinese medicine is inherently holistic, meaning that it combines the physical, mental, emotional and spiritual aspects of our lives into each medical diagnosis. Treating the non\u00adphysical aspects of disease is essential to recovery of good health.\nWe have been dedicated to serving the people of Austin, Round Rock, Cedar Park, Leander, and Pflugerville areas since 2010.\nWe are currently contracted with most major insurance companies.\nWe have a full herbal dispensary for customizing herbal medicine for each patient. Our herbal medicine does not contain harsh chemicals, alcohol or preservatives, and is very gentle on your system.\nWe offer our patients a comprehensive diagnosis, treatment plan and powerful wellness counselling. While symptoms are important to be taken care of we treat the root causes as well.\nWe provide ongoing wellness and maintenance treatments to help sustain your health.\nIn addition to acupuncture, we also offer Chinese herbal medicine, acupressure or tuina, dietary consultation and nutritional support.\nWe have a great cash plan for people who do not have health insurance or who have limited acupuncture coverage. Packages are also available for people who need multiple treatments.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"La caldera de recuperaci\u00f3n de calor o HRSG (heat recovery steam generator) en un ciclo combinado es el elemento encargado de aprovechar. En una caldera t\u00edpica de una central termoel\u00e9ctrica de MW, el hogar ( paredes de agua, sobrecalentador, recalentador, economizador, cabezales, etc.) . El paso de convecci\u00f3n contiene bancos o paquetes de tubos que configuran el sobrecalentador, el recalentador y Todas las calderas se.\nKupfer- \u2014 Eisen Zink- \u2014 vitriolisieren Vitriolwasser n. Public domain books are our gateways to the past, representing a wealth of history, cultuie and knowledge that's often difficult to discover.\nThe Spanish language, however, from a technical point of view has been sadly neglected up to the present time because the ne- cessity for such a work was formerly considered doubtfiiL That this is an incorrect view may be easily proved by reference to the States of Central and South America, in which the Spanish language is in com- mon use, and in these countries engineering and electrical industries are in constant demand, and are progressing daily.\nCSP Parabolic Trough Technology for Brazil A comprehensive documentation on the current state of the art of parabolic trough collector recalentadorew CSP Parabolic Trough Technology for Brazil A comprehensive documentation on the current state of the art of parabolic trough collector recalentaddores Seite 1 1.\nAvailable online at www. Empresas y Centrales del SIC.\nWe already possess several good Gennan-English dictionaries, treating especially upon the important points of engineering and machine industry, which have been produced to meet ihe demand for such works, created by calseras considerable business done between Germany, England and the Uni- ted States.\nSince the sun s position More information. Hinkley 1, Robbie K. This is equivalent to the annual production of a conventional More information. Reviewing applications can be fun and only takes a few minutes. All rights More information.\nGall's chain cadena [articulada] Gall Gallische Kette f. Business Unit Power Generation P.\nConcentrating Solar Power Technology, deployment and research perspective Dr. El equipamiento que incluyen las centrales de ciclo combinado es el siguiente:. Fordermaschine i Drahtzug[ma8chine] m. Hitachi Solar Caterpillar Caterpillar Caterpillar.\nCentral a gas ciclo combinado 7. Start of operation State-of-the-art parabolic trough power plant technology.\nThe KudoZ network provides a framework for translators and others to assist each other with translations or explanations of terms and short phrases. Vacuum \u2014 gauge V. Se define al gas natural como un combustible compuesto fundamentalmente por metano CH4que se encuentra en la naturaleza en las llamadas \"bolsas de gas\", bajo tierra, cubiertas por capas impermeables que impiden su salida al exterior.\nSchUessfaUe 1 Kluppe f. High Temperature Diaphragm Seal. Hin- und Herbewegung f.\nReparto del caudal de humos cuando el conducto de salida se divide en dos. Master of Science Program M. View Ideas submitted by the community. Chloroform cloroformo Chloroform n. Stauffer-Schmierbuchse 1 Olerglas n.\nBitte entfernen Sie das Wasserzeichen nicht. We encouragc the use of public domain materials for these purposes and may be able to help. Spitzen Platten- \u2014 Stangen Beleuchtung f. Contact us ABB Ltd. Matrize 1 Matrizenhalter m.\nDynamo 1 mit Antrieb durch Dampfmaschine Dampf dynamo f. Scale of \u2014 escala para chispas Funkenskala f. Actualmente operan seis centrales del tipo mencionado en el SING, centrales Atacama 1 y 2, de Gas Atacama, en servicio desdecentral Salta de Gener, en servicio desdecentrales Tocopilla 2 unidades de Electroandina, en servicio desde el y la central Sobrecalentxdores de Edelnor, en servicio desde el Our Dictionary especially comprises such words and word combina- tions which, although frequently used, are generally missing in works of a similar description.\nMorse Caterpillar 1 2 2 1 1. Wahlverwandtschaft; Affini- affinity Ch. Clamp on ultrasonic flow meter Clamp on temperature sensors Irradiance measurement station Camera equipped quadcopter Benefits Detecting optimization potential of solar field Accurate performance parameters lead to reliable results of system simulations.\nElectrical engineering ; compris- ing the construction dalderas dynamos, storage batteries, electric appa- ratuses and measuring Instru- ments. Solar power for sustainable energy Solar power for sustainable energy Prepared by: Metallbearbdtungsmaschine metaphosphorsaures Salz n.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"August 2015 proved to be a hugely disappointing end of summer month. With 195.3 mm it was one of the wettest months of the year so far, with generally poor light levels\u2026 and no settled periods of fine weather. A brief interlude around the middle of the month allowed us to take a snap crop of hay from our lower wet meadow\u2026 which was mono culture soft rush just 2 years ago, but the conditions have otherwise been poor for most plants.\nHydrangeas though have excelled\u2026 and several Clematis have given their best ever year.\nSeveral plants are still coming into flower much later than normal, and as we move into September wonder whether all the Asters will actually open flowers before frosts hit.\nA few cool nights have prompted many colourful Waxcap mushrooms to pop up. We've now found several new species this year, and also found examples of them in all of our meadows. This is a real delight, and a sign that the meadows are in fine 'old fashioned' fettle, thanks mainly to the lack of any supplementary nitrogen fertilisers or muck over the last couple of decades.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbgglt b/data_all_eng_slimpj/shuffled/split2/finalzzzbgglt
new file mode 100644
index 0000000000000000000000000000000000000000..082b6a808a1c727dce7834456ef8011767e96e21
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbgglt
@@ -0,0 +1,5 @@
+{"text":"Panorama Education is incorporating student intervention tracking into all-in-one platform to deliver actionable insights for educators.\nThe Panorama Student Success Platform is getting an upgrade with the launch of a new multi-tiered system of supports (MTSS) and response to intervention (RTI) tracking system. The new solution will enable educators to assign and mange evidence-based interventions across multiple tiers of support. The system also gives educators the ability to collaborate more interventionists, support staff and administrators.\nThrough the implementation of the MTSS and RTI frameworks, the Panorama Student Success platform helps educators bring together multiple sources of traditionally siloed data into one place. This system allows educators to better track the real-time progress of their students while having access to a unified platform to help identify students who need additional support.\nPanorama Education currently services more than nine million students in 11,500 schools across the U.S. states. More information about Panorama Student Success can be found here.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"You can configure several options that relate to the operation of the Distributor block.\nSecurity support programmable. Resets to support security.\nSee Security model in the Arm\u00ae GICv3 and GICv4 Software Overview for information about the implications of setting Security support to not present.\nFor more information, see the Arm\u00aeCoreLink\u2122 GIC\u2011600 Generic Interrupt Controller Configuration and Integration Manual and Arm\u00ae GICv3 and GICv4 Software Overview .","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"This is the greatest news for candidates who are eagerly waiting for Latest Railway Jobs. Yes, candidates !!! your wait is over. SECR has announced vacancies for the Trade Apprentice Post. South East Central Railway invites candidates to fill up 413 vacant vacancies. Candidates who are eligible and interested for these posts. They can apply for South East Central Railway Recruitment 2018 before the last date.\nOfficial notification is already uploaded on the website. Candidates can read official notification before applying for these posts. Application forms are already started. Candidates can apply before 9 September 2018 from the official website. Further details like important dates, eligibility criteria, application fee, selection process, age limit, pay scale, how to apply etc. are given below.\nEducational Qualification:- Candidates who are going to fill SECR Apprentice 2018 Application Form, they must possess 10th pass certificate and ITI in relevant trade. For more details refer official notification.\nAge Limit:- Candidates who want to apply for these vacancies, their age should between 15 to 24 years as per official notification. Age relaxation is admissible by 05 years for SC\/ST, 03 years for OBC, 10 years for PWD\/ ESM candidates as per rules.\nHow to Fill for South East Railway Trade Apprentice Application Form 2018?\nFirst of all visit official website \"www.secr.indianrailways.gov.in\/\".\nLook around for \"Trade Apprentice Vacancies\".\nYour application form will submit.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Lamination delivers maximum attraction at the point of sale and maximum protection from general handling, grease, dirt, water, weather and time. A good standard of finish can be obtained on almost all types of paper and board.\nMatte Polypropylene (Matte OPP) - Provides a soft, smooth finish that is perfect for dust jackets and presentation folders. This lamination is often used in combination with Gloss Spot UV. This lamination has a very flat\/dull, non-reflective soft finish and can scuff.\nGloss Polyester (PET) \u2013 Provides excellent abrasion resistance, scuff resistance, strength and durability, and extra heat resistance. This lamination is often used for case-bound books, binders, box wraps, and menus.\nGlueable\/Stampable Gloss Polyester (AGX) - To promote easier gluing and foil stamping on top of the lamination. Used for cartons, folders, case-bound books, binders, box wraps and anything else that would require gluing or stamping.\nMatte Polyester (Matte PET) - Offers the same protective qualities as Gloss PET but provides a highly scuff-resistant matte surface, which is excellent for high use products. This lamination has more of a semi-gloss appearance and also can be used in combination with a Spot Gloss UV.\nGloss Lay-Flat \u2013 Designed specifically to negate the effect of curl caused by moisture absorbed into the paper stock after laminating. This glossy film is very scuff resistant and durable. Lay-Flat is being used for book covers, magazines, posters, box wraps, folders and any other product where flatness is critical.\nMatte Lay-Flat - Designed specifically to negate the effect of curl caused by moisture absorbed into the paper stock after laminating. This lamination is also very durable but has a flat\/dull, non-reflective finish on top of the film, which can scuff. This product is excellent in combination with Spot Gloss UV.\nLamination Thickness' Available - The standard thickness of lamination that we use is approximately 1.2 - 1.3 mils added per side laminated. The lamination is .5 - .6 mils and the adhesive is .7 mils. Laminations are also available in 1.7, 3, 5 and 10 mil versions. 3, 5 and 10 mil laminations must be applied to both sides of the stock to avoid curl and are available in just gloss and matte polyester.\nDue to the 3, 5 and 10 mil needing to be applied both sides at a time; both gripper and side guide edges can not be kept completely clean. Either the gripper or the side guide will be kept clean depending on the way the sheets have to run through the machine.\nSheets have to be overlapped prior to laminating which results in a slight indentation along the overlap line. This overlap line must be outside of the final trimmed size.\nMinimum Margins - In order to run your job properly we need a press sheet with a \u00bd\" margin unprinted and\/or unvarnished on all four sides of the sheet. If these minimum margins cannot be provided, running time will increase and additional charges may apply. With your order always include a marked-up sheet indicating the area to be laminated, the finished trimmed size, gripper and side guide edges.\nPaper and Board \u2013 Most kinds and caliper of paper and board from 70lb to 24pt. can be laminated provided that they are supplied flat, free from creases or distortion and at a moisture content which is stable in the expected environment (50-55% R.H.). Skids must be shrink-wrapped and have skid tops.\nSpray Powder \u2013 An excess of anti-offset spray powder in any area of the printed sheet will be highlighted by the lamination. To ensure the best results, use the minimum possible amount of the fine grain spray powder and ensure that it is evenly applied. Do not use encapsulated spray powders.\nFree from wax, polythene, silicones and other surface-acting agents often added to standard ink to provide surface slip and gloss (qualities provided by film lamination).\nUV ink \u2013 special care should be taken to ensure the smoothest possible surface and that the ink(s) are cured and well adhered to the paper or board.\nDigital Printed Sheets - Each job should be tested prior to full print production to check for ink compatibility with the lamination.\nTesting is recommended where exact color matching is required as lamination may change the optical qualities of a color.\nNote: Drawdowns are not representative of production run samples.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Today marked the end of the Beaumanor residential. I'd just like to quickly say a massive 'well done' to all of the children on the trip - we had horrible weather for two of the days but you persevered and kept going! All of the children slept much better during the final night, meaning they had more energy for the final activity of 'Land Buggies'. Working in teams, the children used barrels, poles, bolts and tools to create a buggy that could transport them across land. During the process they learnt how to tie different knots. They worked well in their teams, making sure everyone got a ride on their buggies.\nAfter we tidied up camp and had lunch before setting off back to school where we had hot chocolate waiting for us!\nA selection of photos from all three days have been uploaded into the correct sections - I may add more as I sort through them. I hope you all will enjoy looking through them, talking about the moments captured in the picture.\nCould I also mention the fantastic adults who went on the trip, without them the trip wouldn't have been possible. They have been fantastic with their determination to not allow the rain to spoil the experience for the children, working through their own injuries and illnesses, beyond 1am and up at 5am with a smile to greet the children - Thank you Mr Plant, Mrs Harriman, Miss Jones and Miss Radford.\nWe had lunch outside on the picnic benches as it was sunny and warm. Then we took up a spot of canoeing. Mrs Harriman was attacked by a swan and duck poo all over her trousers to prove it! Dominic managed to leave the rest of his group stranded and Harsh managed to lose his oar. Mayah decided to soak Miss Jones!!\nFor tea we had pizza, chips and beans with ice cream and cookies for pudding. After tea, we went for a Nightline session. We wore blindfolds and had to follow a rope trail without the sense of sight. Just as we started the heavens opened which made for a very interesting session! Miss Jones and Miss Radford used sticks to tickle the children as they walked past. Unfortunately for Mr Plant, they did less tickling and more poking with the stick, sending Mr Plant flying down the muddy hill landing on his back. This left Mrs Harriman with tummy ache from laughing too much. Luckily the children were a lot better than Mr Plant at completing the course. Even Aniah who managed to lose the rope and follow her own path into a bush completed the course better than Mr Plant.\nAfter we arrived back at camp we realised the cold, wet and a couple of flooded tents (we forgot to close our windows!!) meant we had to think of alternative sleeping arrangements. We had a vote and decided to have a mass sleepover! We converted our games room into a massive room to sleep in and spent time talking, listening to a spooky story and making shadow puppets on the wall. Many of us were really tired so we struggled to stay up and chat or read. The adults were still up (and are still up- hence the late post!) using the drying room (again!) to dry our clothes ready for more rain tomorrow! Miss Jones is up suffering the effects of sun stroke and Mr Plant has a bad back! In the morning we have the land buggy session and then lunch before heading back!\nSo proud of this young lady- working through her fears!! We've spent the morning climbing - some of the walls are really high! Fantastic team work too!\nWell we've almost come to the end of day 1 of our trip! Its definitely been a soggy day! Once we arrived we made our way to the camp with our bags and spent some time getting settled into our tents. We then went on a treasure map in the pouring rain. Fantastic perseverance from all children, who kept going regardless of the fact that it was so wet that our maps disintegrated!\nAfter we had a bit of 'chill time' in the games room playing pool, table tennis and on the football table. Some of us were happy to be somewhere dry to just talk to our mates. After lunch we went for a session called 'Survival', where we were in the woods and had to build a shelter that would keep us dry and warm! After we had built the shelter we had hot chocolate around the campfire.\nThe shelter Brandon and team built fell apart literally as the time ran out so that didn't pass the test! Dillon's and Rylie's teams won the challenge, having built the best shelters from the elements.\nIn the main hall, we have had our evening dinner (sausages, veg and mash -and a veggie option of course for those who needed it). We've all eaten well- especially the chocolate cake that was for pudding!\nWe were meant to have another campfire session this evening, but it's been far too wet so Mrs Kazi signed us up for team games instead. The teachers were team 'Away with the fairies', and annoyingly, they were in the lead as we started the competitive challenges.\nJust having hot chocolate before we snuggle down for bed time!\nBelow are some pictures from today - We'll keep trying to update you, but don't worry parents - We're having fun!","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbhnpb b/data_all_eng_slimpj/shuffled/split2/finalzzzbhnpb
new file mode 100644
index 0000000000000000000000000000000000000000..490e34f3734c483cf6a9937c478af3087e53cf79
--- /dev/null
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@@ -0,0 +1,5 @@
+{"text":"*Save $17.98 4 inch 360 Adjustable Rain shower head High Pressure Rainfall Stainless steel Square top spray water-saving Uses 30% Less Water High Flow Fixed For the Best Relaxation and Spa from Walmart. Price: $9.99. Discount: $17.98. Categories: Home Upgrades. Deal Rating: 5 Stars out of 5. Store Rating: 4.8 Stars out of 5. Deal Recommendation: Recommended. Available Until: Not Specified. Thoughts: None.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Mobile Link Remote WiFi Monitoring FREE with every Guardian Series Home standby generator Allows you to monitor the status of your generator from anywhere in the world using a smartphone, tablet, or PC. Easily access information, such as the current operating status and maintenance alerts. Connect your account to your authorized service dealer for fast, friendly and proactive service. With Mobile Link, you are taken care of before the next power outage.\n5-Year Limited Warranty for automatic standby generators.\nSmart, User-Friendly Controls. Generac's Evolution Controller features a multilingual LCD display that allows you to monitor battery status and track maintenance intervals to ensure your generator is always in top operating condition.\nTrue Power Technology delivers best-in-class power quality with less than 5 percent total harmonic distortion for clean, smooth operation of sensitive electronics and appliances.\nGenerac's G-Force Engine is a purpose-built, pressure-lubricated engine capable of handling the rigors of generator use, resulting in power that's more reliable and requires less routine maintenance than any competitive engine.\nGenerac 7039 Home Standby Generator 20\/18KW Guardian 200A Auto Transfer Sw.\nGenerac 70391 Standby Generator 20\/18KW w\/Wi-fi, Auto Transfer Sw.\nGenerac's G-Force Engines are purpose-built, pressure-lubricated engine capable of handling the rigors of generator use, resulting in power that's more reliable and requires less routine maintenance than any competitive engine.\nMobile Link Remote Monitoring allows you to monitor the status of your generator from anywhere in the world using a smartphone, tablet, or PC. Easily access information, such as the current operating status and the generator's maintenance schedule. Connect your account to your authorized service dealer for fast, friendly and convenient assistance. (Sold Separately).\nTough, Durable All-Aluminum Enclosures: Our RhinoCoat powder-coated finish helps make corrosion-resistant aluminum perfect for all weather conditions.\nSmart, User-Friendly Controls Generac's EvolutionTM Controller features a dual-line, multilingual LCD display allowing for easy monitoring of history, maintenance logs making it easier to manage your generator.\nEVOLUTION CONTROLLER \u2014 allows for easy monitoring and management of generator functions.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"If you're anything like us, you love a good dose of retail therapy. And, with Black Friday around the corner, we've decided to share a list of the best beauty and fashion deals.\nThe Deal: Takealot's Blue Dot Sale will be offering five days of discounts on Black Friday, the weekend after, as well as on Cyber Monday and \"Takealot Tuesday\". Select products will be discounted by up to 60%.\nBest Buys: Lookout for big mark-downs on jewellery and fragrance.\nThe Deal: The Superbalist Black Friday sale will run for five days with mega deals across womenswear, menswear, kidswear and apartment. We highly recommended that you create a wishlist in advance, for an easier checkout. Join the Superbalist Showdown Facebook event or sign up to the early bird alerts to be the first in line.\nBest Buys: Stock up on Summer dresses, sneakers and swimsuits.\nThe Deal: Get 90% off sale on 1990s fashion brands. Up to 70% on big brands like Adidas and Puma.\nBest Buys: Want to beef up your sneaker collection? Then Zando's wide selection of sneakers.\nThe Deal: Woolworths announced, that they would be offering up to 50% off selected fashion items. W Rewards members will receive an additional 20% off.\nBest Buys: Cop marked down denim, lingerie and wardrobe basics.\nThe Deal: Whether you need a fresh pair of kicks or a new piece of bling, you can access the best and widest offering of Black Friday deals from TFG. The fastest way to get these deals is to visit TFG's new marketplace on Thursday from midnight at www.mytfgworld.com.\nBest Buys: American Swiss and Sterns - up to 50% off selected jewellery and watches. Fabiani and G-Star RAW - an extra 50% off men's and women's sale goods.\nThe Deal: South Africa's favourite drugstore is shutting it down with mind-blowing Black Friday discounts!\nBest Buys: If your beauty fiends like we are, then you're going to want to secure beauty and beauty products and tools.\nNeed a game plan to tackle Black Friday? Click HERE.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"You are here: Home > Enjoy Riding > Events and Competitions > Brain, Pain or Training? What is your horse saying?\nBrain, Pain or Training? What is your horse saying?\nRenowned author Sue Palmer MCSP has spent the past 30 years working in the equestrian industry. Working initially as a BHSAI and equine behaviourist (Intelligent Horsemanship Recommended Trainer), she went on to spend seven years qualifying as an ACPAT and RAMP registered Chartered Physiotherapist. Sue is driven by her passion for sharing knowledge around how to recognise and resolve pain behaviour in horses, to enable you to achieve greater success and a deeper relationship with your horse.\nJoin us for a relaxed and informative Brain, Pain or Training demonstration where Sue will discuss and demonstrate some of the exercises in both 'Brain, Pain or Training' and another of her books 'Horse Massage for Horse Owners', so that you can give them a go with your own horse. There will be plenty of time for questions at the end, and copies of Sue's books and DVDs will be available on the night.\nCost: \u00a310 per person - all welcome.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Narrowboat Blog: Found a boat called Sirius.\nFound a boat called Sirius.\nAfter a lot of hunting around and umming and arring about it, I found a boat up in Yorkshire called Sirius.\nSirius is being sold by the boatbuilder Alan Pease, his website can be found at Alan Pease Boats.","meta":{"redpajama_set_name":"RedPajamaC4"}}
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+{"text":"Put together an emergency kit for your teen's locker. Include band-aids, mints, deodorant, chapstick, lint roller, hand sanitizer and Kleenex.\nOrganize clothes for the week in your closet to help keep your morning on schedule.\nPost a daily routine to help younger children stay on schedule and know what to expect in their day.\nClear a pantry shelf and set up a self-serve station with snacks organized for children to grab for their lunches or after school.\nDesignate a dedicated homework space in your home.\nPrepare for the school day the night before to eliminate running late and hectic mornings.\nCreate a family wall calendar.\nEase first day butterflies by talking about all the things your children like about school.\nCreate a school photo album to help share memories with your children and keep a positive focus on school.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"One of the nice things K and I did in London was to watch the stage production of The Lord of the Rings at Theatre Royal Drury Lane. I was sceptical as to whether they would pull it off, transforming such a great \u2013 and looong \u2013 epic to a stage play. But\u2026 they did! It was really great. Of course K was of another opinion, so it's not for everyone. I just really thought the scenography\/decor\/set design was really innovative. As we entered the theatre, we were engulfed in greenery, all growing from a huge ring on stage. That was just the start of an ever-changing stage experience. The round stage floor was made up of 17 elevators making it very flexible.\nAlso the effects were cool and Michael Therriault who played Gollum was very impressive. Not all characters were strong, but it didn't lessen the experience. I also liked the massiveness of it, lots of people on stage.\nJoin us at the biggest Lord Of The Rings Quiz ever made available on the internet. For this you register on the site and send it to all of your friends, because this film should never be forgotten! Join our Fellowship today! We welcome any lord of the rings fan who want to participate in this quiz game.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Saturday: Celebrating 20 Years of Westside Les' | Faded Jeans \u2013 Arizona's Party Band!\n\u2190 This Saturday: Levi's Birthday Party!\nSaturday, February 4, 2017 4 to 8 p.m.\nFor the guys in FJB, some of the most fun we can have is making folks' parties events to remember! There are still plenty of opportunities to contract us for YOUR events in 2017. We want to help make your next party, reception, or event extra special. Contact us today and get Faded Jeans on your calendar!","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Played in 10 contests as a reserve on the defensive line and member of special teams...was credited with five total tackles, including three solo stops...had a high of three tackles against Western Illinois...credited with two solos and an assist against the Leathernecks...had a solo tackle against Valparaiso...had an assisted stop versus Saint Francis (Pa.)...earned his second letter.\n2010 (R-Freshman): Played in contests against Penn State and North Dakota State as a reserve defensive end...scout team Defensive Player of the Week against South Dakota State...earned his first letter.\n2009 (Freshman): Redshirted...named the Scout Offensive Player of the Week versus Austin Peay.\nHIGH SCHOOL: As a senior was a Special Mention All-Ohio Division II selection as a defensive lineman...also played offensive line...was a first-team Division II Northeast Inland District selection...named first-team all-Suburban League...registered 79 tackles, 20 quarterback hurries and had 15 tackles for losses...forced two fumbles and recovered one...also played tight end...Colts were 8-3 reaching the regional quarterfinals...was first playoff birth in school history...as a junior was named honorable-mention all-county...earned three letters...coach was Kevin Gault.\nPERSONAL: Parents are Dale and Patricia...has a sister (Stephanie) and a brother (Dale)...birthday is Jan. 1...major is exercise science.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Luxembourg Times - Archives - Mersch rejection \"ridiculous\" and \"surreal\"\nMersch rejection \"ridiculous\" and \"surreal\"\nThe decision not to appoint Yves Mersch to the ECB board has been blasted as \"ridiculous\" and \"surreal\" by Luxembourg critics.\nLuxembourg's Members of Parliament have responded critically to the vote, which saw 300 votes in favour and 325 against the appointment of the Luxembourg candidate to the ECB's Executive Board.\nThe decision had been put to the vote in the European Parliament on Thursday after the lack of women on the executive board was questioned.\nAstrid Lulling, also a CSV MEP, concluded that it is the Parliament which will be \"the big loser.\" She said that the job brief required that the nomination be based on the qualifications of candidates and not on gender. \"No other consideration can and should intervene,\" she said.\nLSAP MEP Robert Goebbels, meanwhile, questioned the votes of those MEPs representing countries not within the eurozone.\nHe suggested that Mr Mersch had been used as a \"scapegoat\" for those countries' MEPs to air other issues.\nHe called for the immediate appointment of Mr Mersch to the ECB Executive Board, which has remained vacant since last May.\nAhead of the vote on Thursday morning, Green party MEP Claude Turmes said the did not support Mr Mersch's candidacy, saying he did not believe in the ideas presented by Mr Mersch at his hearing earlier this week. Mr Turmes concluded that Mr Mersch would worsen the crisis with a tough savings programme and a reduction of social welfare cuts.","meta":{"redpajama_set_name":"RedPajamaC4"}}
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new file mode 100644
index 0000000000000000000000000000000000000000..89a7ebd9e1fd89c1da6220f44668fd75a36bff15
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@@ -0,0 +1,5 @@
+{"text":"The made to fit anthracite vehicle cover with the Audi logo is made of breathable and anti-static material. Includes piping which highlights the shape of your Audi. Protects your vehicle perfectly against dust and dirt.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"how to get granite quarry lease licence in difference between granite quarry and iron ore mine does granite crusher , I am from Nigeria and I have a large .\ngranite crusher nigeria China Jaw Crushers Manufacturer, Gold Mining Equipment. granite crusher sales in nigeria. granite crusher for sale youtubefeb 17, 2014.\nGranite crusher in nigeria. granite quarry in nigeria MTM Crusher . manual crushing of granite in quarry business nigeria . 20131113 manual . Chat With Sales.\ngranite crusher sales in nigeria 70. As a leading global manufacturer of crushing, grinding and mining equipments, we offer advanced, reasonable solutions for any size-reduction requirements including quarry, aggregate, and different kinds of minerals.\ngranite mining in nigeria MTM Crusher in Quarry SAMAC Crusher QUARRY :Granite Mining Business and Suppliers In ... in Nigeria mineral resources processing industry such as gravel mining in Nigeria, granite mining industry, quarry .\nlist of quarries in nigeria CGM Project Case Stone Crusher Case Granite quarry in Nigeria The Business Plan Market For more list of quarries in nigeria information.\nNigeria granite quarrying in maine Nigeria crushing plant. Nigeria granite quarrying in maine,ZYM manufactured stone crusher, supply heavy stone crusher, ZYM is a large stone crusher manufacturer.\nGranite Crusher For Sale In Nigeria, Granite Crusher For Sale In Nigeria, Wholesale Various High Quality Granite Crusher For Sale In Nigeria Products from Global Granite Crusher For Sale In Nigeria Suppliers and Granite Crusher For Sale In Nigeria Factory,Importer,Exporter at Alibaba.\n100t\/h Granite Mobile Crusher Plants in 100t\/h Granite Mobile Crusher Plants in Nigeria. Capacity: 100t\/h Materials:Granite. Applications:Mining, metallurgy, construction, highway, railroad, water conservancy, etc. Main equipment:PP900 Mobile Crusher, PP120SMHS Cone Crusher, Conveyor Belts and Electrical Control Cabinet, Etc.\ngranite crusher suppliers in nigeria. sbm stone crusher in Nigeria; Granite, marble, limestone, quartz stone, PEW jaw crusher is known as the European version jaw crusher, Check price.\nUse of Crushed Granite Fine as Replacement to River Sand in Concrete Production . ... Makurdi, Benue State, Nigeria.\nGranite crusher is widely applied in Nigeria quarry Granite Crusher Plant,Rock Crusher For Crushing Granite-SBM list of granite. Get Price And Support Online.\nlist of quarries in nigeria CGM Project Case Stone Crusher Case Granite quarry in Nigeria The Business Plan Market For more list of quarries in nigeria information. Get Info; Stone Crushers In Nigeria Stone Crushing Machine.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The court continued by ordering that the Unions or the present Trustees in consultation with the beneficiaries and the Government of Belize draw up a proper trust to include the GOB as the settlor. Under that deed public officers who had their salaries frozen are to be the beneficiaries. It continued ordering that there be account for all the funds that they have received from GOB from the BTL shares from 1996 to 2013 and that has been paid to them since 2104. It also ordered that monies that have been invested be recovered.\nThis is in direct contravention of the order which has specifically stated that the entire trust was deemed invalid and unenforceable and more so that they must account for the trust's money as well as set up a trust for the benefit of only those public officers which were affected by the salary freeze of 1995-1997.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Kronos implementations and upgrades are challenging. A recent study by Oxford University revealed that 74% of software projects are challenged or unsuccessful. Similarly, a study by Mercer Consulting found that 80% of software projects cost more then they return. With these types of statistics floating around, it is easy to understand why organizations get uneasy when the time comes to implement or upgrade their WFM software.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Meditating on authenticity has produced many lessons and knowings. I now know that..\n.. Being introspective is sort of like shaking one of those snow globes. All the pieces of your life that you thought had carefully settled like sediment are truly alive and active when a slight wind blows. The goal then becomes not to let it drift to the bottom again, but to do the next step that will act as a sieve and catch those pieces.\n.. When you're not expecting those buried pieces to be alive, and you're not prepared to deal with it, you have to be in it to get through it.\n.. Authentic is the only true way to live. Everything else is unfulfilling, superficial, and unsettling.\n.. Authenticity is about returning and magnifying who you are, instead of trying to become someone who you think you should be. It's about peeling off the false adornments and standing wholly, holy, and true.\n... You have to go deep to really do the work. That means examining what's under the surface and then go six feet deeper than that.\n.. You have to question your motives. Is your motive to be comfortable? Is it to be liked? Is it to be accepted? Is it to be rescued? I will bet my last dollar that for many of us, there is at least one \"yes\" in there. I will bet that dollar after my last that I had hidden in my sock that your motives have a history that you don't want to truly look at.\n.. True friends\u2014those that want nothing for you but peace, harmony, and joy\u2014sometimes more than you want it for yourself\u2014will rise to the surface. Those are the ones to listen to and commune with. You will know their voice because it's authentic as well, and it speaks with no ulterior motives or projections. It may not tell you pretty things, but it will always speak in love.\n.. Peace and joy are possible. It is already there every time you take a breath. Every time you come back to the present. Every time you pray. Every time you surrender. Every time you take one step.\nNext up, my reflections on fear. Stay tuned.","meta":{"redpajama_set_name":"RedPajamaC4"}}
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new file mode 100644
index 0000000000000000000000000000000000000000..287d7d01b6c3f9950fb8bb01498cca91e9bf417d
--- /dev/null
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+{"text":"MissZoeTS Bio information: i can be your princess or just your virtual friend, it depend of your secret desires.\nMissZoeTS statement: i love to chat and thats why i am here, but take me to private to instantly turn me on my dear.\nMissZoeTS free chat and free photo. Bookmark MissZoeTS!\nMissZoeTS is years old exotic cam performer, doing live shows in exotic webcams category, speaking english languages.\nMissZoeTS has average body build.\nCopyrights MissZoeTS \u00a9 2016. All Rights Reserved.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Manish Arora Spring\/Summer 2015 Show was influenced by the Mughal Empire.\nJelly beans and other sweet delights have influenced motifs in the Manish Arora Autumn\/Winter 2014-2015 Show.\nAnother jelly beans-inspired collection : Douglas Hannant Spring\/Summer 2011 (the color palette of this show was based on a bag of jelly beans dumped on a white tablecloth).\nPopsicles have inspired patterns in the Manish Arora Autumn\/Winter 2014-2015 Collection.\nOther popsicles-inspired collections and items : Franklin Marshall Spring\/Summer 2009 (\u00ab popsicle \u00bb motifs on T-shirts), Jean-R\u00e9my Daumas Spring\/Summer 1985 (\u00ab Miko\u00ae popsicles \u00bb motifs on several pieces), Mulberry by Emma Hill Spring\/Summer 2013 (popsicles have influenced the color palette of this collection).\nCreamy cupcakes have influenced the Manish Arora Autumn\/Winter 2014-2015 Show.\nTo read about other cupcakes-inspired collections or pieces, search for the \u00ab Cupcakes \u00bb post that I have published on October 30, 2012.\nWhipped cream inspired the James Pecis-styled wigs of the Manish Arora Spring\/Summer 2014 Show, which paid homage to Josephine Baker.\nTo read about Josephine Baker-influenced collections, search for the \u00ab Josephine Baker \u00bb post that I published on August 3, 2013.\nThe Manish Arora Autumn\/Winter 2013-2014 Show was based on a trip to the Burning Man Festival.\nSome Burning Man-inspired items : International Flavors and Fragrances (for Spring 2011, Clement Gavarry produced for IFF the \u00ab Burning Man \u00bb perfume, that was named after and inspired by the festival), Topshop (for Spring 2011, Topshop unveiled the \u00ab Sandstorm \u00bb makeup line that was influenced by Burning Man).","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"With so many offers on land for sale around Werribee, your dreams of building a custom home are within reach. You can now have that private space that you've craved for all your life. Instead of paying out a fortune in rent, you can use that money to build equity in your expensive new house.\nHowever, you need to address a few crucial factors before you can join the growing rank of successful homeowners.\n1. Pick out the best lot.\nIt's easy to go after the most affordable lot on the market as a cost-saving measure. From a distance that might seem like a good idea but you need to choose the lot carefully before committing to the sale. Sellers often use pricing advantages to get rid of unattractive lots.\nYou need to be sure that you're not falling for that gambit. Such lots are likely to cost you a small fortune in preparation costs before you can begin the construction process. Factor in the availability of utilities and public services such as water, sewerage, and electricity.\nIf they are not readily available, you'll have to make a private arrangement, which comes at an extra cost. Having a land expert inspect the lot before the purchase is a wise decision.\nThey can give you insights into the amount of work as well as the costs you'll incur to get the site ready for constructions. Although there's a cost implication in hiring one, the potential savings more than makes up for it.\n2. Set the construction budget.\nGoing about the home construction process without a set budget is a recipe for disaster. It's also an indication that you haven't quite thought the process through. Setting a budget lets you narrow down on the type and size of a house to build. It also determines the type of materials to be used to build it.\nMore importantly, it helps you decide how much money you have for the project and how much you need to borrow from the bank. It's one thing to realise the dream of owning a home and another to ruin your finances in the process.\nGoing about it without a budget can cause you to be overambitious and incur hefty mortgage payment each month, which could ruin the entire home owning experience.\n3. Pick your team carefully.\nOnce you've picked out the right lot and chosen the perfect floor plan, it's time to begin the construction process. Your choice of a builder is crucial to the successful completion of the house.\nTherefore, you should go to great lengths to vet the building company to ensure they are capable of doing a swell job. Don't stop at just looking at their website but make a point to visit a few of their complete and ongoing projects.\nAs for recommendation and referral, you need to hear people's account of working with the builder. Given the high stakes involved, it's easier to err on the side of caution.\nGetting the perfect piece of land is the first step towards realising your dreams of building a home from the ground up. In addition to making the right choice when buying a lot, you need to address other crucial factors that lead to a successful home-owning process.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Through dancing, you want to express your feelings, but your body won't let you?! You want to dance to make yourself look good? With enough confidence and patience, you can do anything!\nLove it. If you want to dance, you have got to love it. Your heart must be into it. Maybe you want to dance to look good in front of boys or girls. However, to look good, you must ignore how other people view you, and concentrate solely on yourself. Your heart must be 'fully' into it. If your heart is not into dancing, you will most likely give up when you cannot do certain moves, because it will stress you out. But if you have a desire, you will stick to learning one move until you get it down.\nResearch some well-known dancers. There are many legendary dancers who encourage many amateur dancers. It is good to look up to them and learn how they learned how to dance.\nOf course, you should not try to imitate moves that the professional dancers do. It is very hard. But let me remind you this; pick one of your favorite dancers, and whenever you dance, think of him\/her and imagine yourself as if you are him\/her. Let him\/her be your invisible teacher!\nLearn the moves. You can either take classes or learn it by yourself. A lot of people watch videos and try to follow along, but most of the time it is difficult. You need someone who can take a look at your moves you have taught yourself, someone you look up to, and he\/she can fix your problems.\nLearn some history. Dancing is one of the ways to express one's feeling. It is artistic, beautiful, and sometimes indescribable. Also, there are many types of dances. For example, there is breakdance, popping, tutting, locking, etc. These sorts of dances are generally in the Hip-Hop category.\nDance with your friends. Practicing dancing alone may be boring. And you might want to learn moves from other people too. Look for a nearby dance studio, gym, or even on streets! Hit your friends up, get speakers, and jam!\nEven though you might think that you look bad in front of other people, there's always something satisfying after the hard work right? Ignore the others, just practice and freestyle with your friends, and who knows? Maybe you and your friends can be the world-best dancing group in the future.\nDon't be hard on yourself. Maybe your friends would tell you that you are bad at dancing. Just ignore them. Even though you think you are bad at dancing, stand in front of a mirror and look at yourself. Why not? Why would you think that you cannot dance?\nNever say never. Tell yourself, You can do it man! You're just either too scared to show off or too lazy to practice! Of course I can do it! I'll get the moves down and show them who I am. That's right!\nChoose your preferred style. Be specific. If you want to breakdance, also known as 'b-boying,' you first need to know what kind of dance it is. It involves a lot of strength, along with your own creative styles. For this, you have got to be into it. You may feel like the moves you want to learn are so hard, that you just want to give up, but have faith in yourself.\nThere are lots of different moves for breakdancing. Remember, you can learn any one of the moves, and transform it into your own style.\nBe aware of your skill level. Popping, which is one of the common dances along with b-boying, requires some natural skills, as in skills you naturally have, because as you get older, your body's flexibility tends to become stiffer and stiffer. So you should start practicing when you're young, or have natural skills.\nIf you do not have natural skills and didn't even know about popping when you were a kid, it will require a lot of practices, for popping is literally popping your body on beats. It will either look good with the music or make the audience want to just leave you.\nKeep practicing. Practice every day. It doesn't have to be a harsh practice. Let's say you've been practicing hand-stands, then before you eat dinner, as you wait, just practice little by little.\nWhen you have free time, practice anywhere around your house. As you walk around, do some moves, keep doing them, keep practicing, because if you practice certain moves a lot, it will become natural.\nPerform. Audition for performances! Work hard for it, and make it a good memory. Throw out everything you've learned. You can do it individually or with your friends. Put every single move you learned in a song and make a dance! Listen to the audience's reactions, listen to their advice, and make it better next time! Dancing on stages will encourage you a lot. Be proud of your work, but do not let go, keep working until you reach your goal!\nBe prepared for the commitment. Dancing takes time. You need to learn the moves, feel comfortable with what you're doing, and try to practice the moves into something new.\nRemember that no matter how far you want to go with dancing, keep going Even though you're not going to be a professional dancer in the future, but still loves dancing - don't quit, if you love that hobby keep it up and never give up.\nHow can I be the best dancer?\nLearn the easy steps and remember them all. If you're dancing to a song learn the words because it helps you in performance. Practice as often as you can before any performance.\nMy mum doesn't support me in dancing. Should I quit dancing?\nIf you enjoy dancing, then keep at it. It would be nice for your mother to support you, but you can't control her actions. If you quit because of her, you will resent her and your relationship with her and your own happiness will suffer.\nCan a girl break dance?\nI'm a good dancer, but I'm afraid to dance in front of other people. What do I do?\nPractice in front of a mirror until you feel really confident. Then, make your first audience a small one composed of people with whom you feel comfortable. Work your way to a bigger audience from there.\nWhat are some tips for a beginner?\nMake sure to practice with a mirror in front of you so your can see and perfect your own moves. If that's not possible, try recording yourself while you dance. Pick a certain move or dance that you like and practice until you're comfortable doing it with or without music.\nI want to start a Hiphop dance group with my friends, what should we do?\nYou can start by putting in a lot of practice time with your friends. To be successful, you'll need to get noticed. Sign up for talent shows or showcases or post videos of your group performing online.\nHow long does it take to be impressive if I have no experience?\nIt depends on your skill. Some people may become \"impressive\" within a few days. Others may take up to three years. In the end, it all depends on you. Everyone is different.\nHow do I do the flip?\nYou have to try very hard and be very persistent. I only achieved this advanced technique after eight or so years of practice. I tried to flip myself every day in the morning for half an hour straight. That's what you have to do.\nI've been dancing for 5 months, but I need to be a better dancer. What should I do?\nYou need to make sure you stretch every day to gain flexibility. Try to do ballet, since that will help your technique and it will make your overall dancing look better.\nI am only 11 and I am a natural with dance moves. I can't afford to take dance lessons, so what else can I do to become a good dancer?\nAsk your school to set up a free dance class, or find tutorials on YouTube. You can also buy dance for Nintendo Wii or Xbox Kinect.\nIf you have free time, make up a dance routine with your friend and practice it at home. You can use what you've made on any performances you plan to perform on, and have more time to add more stuff to it.\nJust believe in yourself. If you're performing on stage and get nervous, just pretend you're in your room alone dancing to the beat of the music.\nIf your parents are so old that they think dancing is trash, try to persuade them first, and if the persuasion doesn't work, do not practice at home, but practice somewhere else.\nSome good b-boy groups that I know of are ' Iconic Boyz' 'Last For One,' 'Gamblerz,' 'Poppin Hyun Joon,' 'Jabowockees,' and 'Phase T.' They some good members whom you can reflect yourself to.\nLet your body lead the way through your personality.\nGet into the dance. Nobody wants to see someone stiff and tight. Make sure your relaxed, put emotion and facial expression into you're moves.\nDo not get hurt while either practicing or dancing on stages! Some of the moves can be dangerous, so get some help if you desperately want to learn it.\nIf you have stage fright, practice, so you can be your best.\nIf you're going to show your moves off to guys\/girls, do it right. Don't embarrass yourself. Also, you have to be good if you want to show off, or else they will just think that you are one of the cool-dancers-wannabe's.\nwikiHow is a \"wiki,\" similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 32 people, some anonymous, worked to edit and improve it over time. This article has also been viewed 226,848 times.\nThanks to all authors for creating a page that has been read 226,848 times.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Sure to be a favorite for any photo-book enthusiast, artist Samuel W. Grant's 2nd self-published photography book handles much like a classic pocket novel and represents a unique archive of images.\nOnly 500 first edition prints of this 4x6 inch, cloth cover, hard-bound work exist. Printed and bound in the U.S., the book is 128 pages and features a selection of both color and B&W photographs from a variety of Polaroid and film formats.\n\"I just bought your book. It's a gem.\"","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbltxu b/data_all_eng_slimpj/shuffled/split2/finalzzzbltxu
new file mode 100644
index 0000000000000000000000000000000000000000..7f55a7e591cbbcbcca6bbb53800274cbc87cb10e
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@@ -0,0 +1,5 @@
+{"text":"Spontaneous Human Combustion (SHC) is a well known but unexplained phenomenon when the human body bursts into flames without any external source of flammable ignition.\nDuring the last 300 years, at least 200 cases of SHC have been registered around the world but it is not exactly correct.\nThe SHC phenomenon was mentioned much earlier, for example, by a Roman poet and philosopher, Titus Lucretius Carus (98-55 B.C.).\nThroughout history, many more cases of SHC could occur but they have never been officially recorded.\nA very popular and long existing theory says that the victims of spontaneous combustion fire drank lots of alcohol, which \u2013 as a flammable liquid \u2013 and that could cause the combustion process.\nBut how we explain SHC victims who never were heavy drinkers? Other theories blame obesity (increased body weight caused by excessive accumulation of fat), static electricity and divine intervention.\nOn April 4, 1731 the Countess of Cesena, Italy was found burnt to death, on the floor of her bedroom.\nAll what's left of the Countess's body were her stockinged legs and the rests of her head. Also greasy soot was again found like in other similar cases of SHC.\nMany other SHC incidents inspired Charles Dickens (1812 \u2013 1870), the great English novelist, who described the phenomenon in his novel \"Bleak House\".\nAlmost immediately, he was attacked by critics who considered SHC acts as incapable of occurring and rather an irrational belief.\nDickens, who carefully researched the phenomenon based on about thirty cases, could easily defend himself.\nThere is a certain pattern in all SHC incidents no matter whether the case is old or modern. Police and fire experts usually find burned corpses except for extremities and no burned furniture.\nTags: alcohol, Unexplained Phenomenon Of Spontaneous Human Combustion - Possible New Clues?","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Image Title: Vanity 33 Inch Seat Height Bar Stools Of Ipbworks Com Home Gallery With 34 Prepare 10. Filename: vanity-33-inch-seat-height-bar-stools-of-ipbworks-com-home-gallery-with-34-prepare-10.jpg. Image Dimension: 687 x 687 pixels. Images Format: jpg\/jpeg. Publisher\/Author: Guido Walter. Uploaded Date: Monday - April 30th. 2018 06:34:14 AM. Category: Architecture. Image Source: housetohome.co.uk.\nTap The Thumbnail Bellow to See Related Gallery of \"Vanity 33 Inch Seat Height Bar Stools Of Ipbworks Com Home Gallery With 34 Prepare 10\"","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Dulux Super Enamel Semi Gloss is an oil based, hard-wearing, long-life finish suitable for interior surfaces. Dulux Super Enamel Semi Gloss is highly recommended for doors, architraves and timber trim in heavy traffic areas such as hallways and family rooms. Dulux Super Enamel Semi Gloss has superior flow and levelling which helps achieve a smooth finish.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Promaster makes a series of P-TTL compatible flashes. Generally, their distribution channels seem to be smaller than others (as they were focused around small brick and mortar camera stores), and consequently they're a bit hard to find and perhaps more importantly hard to find at an attractive price point. Still, there's a couple of unique features which may make them worth considering.\nWarning: The 7500EDF flash is the only model that works with the Pentax K-7, K-x, or K-r camera bodies. You will need at least firmware release V3-310, which should be the default in all currently-shipping units. Without this update, it will just fire at full power in all conditions. If you have an earlier version, the update can be performed (for free) by Promaster Service \u2014 contact them for details. In August 2010, Promaster stated that they were working on an update for the 7200EDF and 7400EDF, but more than a year later, that has not happened. Promaster has not tested the 7500EDF with the K-5.\n7200EDF \u2014 a basic P-TTL-dedicated model, roughly comparable to the Pentax AF360FGZ in power.\n7400EDF \u2014 another dedicated model, this one with a motorized zoom.\n7500EDF \u2014 Promaster's top P-TTL-dedicated model which adds more power and features, including a swivel head and a secondary reflector.\nAs with the Sigma flashes, firmware upgrades (if available) must be performed at the factory.\nThe module-based models require the 5050DXR\/PX digital flash module. Because this module hasn't been updated to work with flashes newer than August 2008, these flashes may have limited appeal. There were three in the lineup, 5250DX, 5550DX, and 5750DX. Only the very simple non-zooming 5250DX appears to be still available. There is a manual-control module that can be used, but in that case a manual-only flash is probably more cost-effective.\nPromaster also has a macro ring flash, the MacroLume TTL Digital. This is module-based, and uses the same modules as the 5000-series flashes.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Our meeting room furniture varies from the classical large conference meeting table set-up to modular reconfigurable meeting tables together with a variety of table bases and leg frames. We can offer a range of meeting tables that provide a solution to any requirements from small training rooms to large boardrooms incorporating storage solutions for various types of presentation equipment. Multi-functional tables can be fully mobile, with a tilt-top facility, which can then be easily manoeuvred by a single operator making a more adaptive and versatile workspace. Folding leg frame tables and stacking meeting table options are also available. Here is some of the new modern meeting tables available, make your meetings stand in out your office from others.\nAt Bevlan we can help choose the right furniture for your office and we will provide one to one care from one of our design specialists. We can produce FREE CAD drawings and help with space planning towards your new stylish meeting room. See some of our meeting room furniture installations here.\nEnsa meeting tables create a stunning centerpiece in any environment. The polished aluminium leg frame adapts to support tops in toughened flass, laminate and veneer.\nThe triangulated legs on the Ensa meeting tables are beautifully detailed, and the steel cables achieve a solid stability that defies it's minimal looks. The Ensa toughened glass collection features UV bonded tops in clear, etched and back painted finishes.\nThe Ensa meeting tables also included leg frames designed to support a wide range of circular meeting table tops. Storage solutions are also available to match all meeting tables.\nClassically inspired meeting tables with a clean linear design, Oxford boasts simplicity and striking form, with solid hardwood legs in timber or painted finis, and an inset chrome frame. With bold thicknesses, accompanied by classic design features, these meeting tables are at home in any environment.\nThe Oxford meeting tables are designed with functionality in mind, the table leg can be specified with a hidden cableway that takes cables safely and invisibly to a connections module that can be fitted in all top types.\nAs an alternative to veneer and laminate, Oxford meeting tables can be specified with toughened glass tops in a range of finishes, including etched glass, and back-painted in any colour. The Oxford meeting tables have solid hardwood legs which can be polished to emphasise the natural timber, or lacquered in any colour. A concealed cableway can be specified for feeding power and AV cables.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbmeaz b/data_all_eng_slimpj/shuffled/split2/finalzzzbmeaz
new file mode 100644
index 0000000000000000000000000000000000000000..cda217632c9a76ffe0e5aefa4de95e8a1e1ffcc8
--- /dev/null
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+{"text":"On Friday, September 15, 2017, Ed McNelley and Stacey Abato ( CFKWC ) made a donation at the Lawrence Police Department, to 9 year old Carlos Escarraman and his Mom Giraldi.\nWe would like to Thank Chief James Fitzpatrick and all the men and women of the Lawrence PD.\nPhoto \u2013 L-R Chief James Fitzpatrick , Ed McNelley, Stacey Abato. Front Carlos and mom Giraldi.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Interpretive Summary: Incorporation of corn dried distillers grains with solubles (DDGS) in lactating dairy cow diets has become a common feeding practice in the United States. It can be used as an alternative protein supplement to soybean meal or as an alternative energy source to corn because of its undegradable protein, digestible fiber, and fat concentration. The major concern with feeding a greater amount of DDGS is that there is a possibility of causing decreased milk fat concentration. While no single factor may be responsible for decreased milk fat concentration, interactions of several dietary factors (including higher amounts of digestible carbohydrates, inadequate effective fiber, and a greater concentration of polyunsaturated fatty acids) could lead to milk fat reduction. The objective of this study was to investigate the effect of adding dried distillers grains with solubles at 0 or 18% (dry matter [DM] basis) into diets formulated with low (41% DM basis) or high (60% DM basis) forage concentrations. Results demonstrated that forage concentration in the diet influences performance of cows, but not the addition of DDGS. This study demonstrates to dairy producers and nutritionists that inclusion of DDGS at 18% (DM basis) of the diet with a higher forage concentration (60% DM basis) in the lactating dairy cow diets could reduce feed costs, maintain greater milk production, and prevent negative effects associated with feeding DDGS, such as decreased milk fat concentration or milk fat depression.\nTechnical Abstract: The objective of the study was to investigate the effects of dietary forage and distillers dried grains with solubles (DDGS) concentration on the performance of lactating dairy cows. Twelve Holstein cows were blocked by parity and milk production and assigned to replicated 4 \u00d7 4 Latin squares with a 2 \u00d7 2 factorial arrangement of treatments. Diets were formulated to contain low forage [LF; 17% forage neutral detergent fiber (NDF)] or high forage (HF; 24.5% forage NDF) and DDGS at 0 or 18% of diet dry matter. The forage portion of the diet consisted of 80% corn silage and 20% alfalfa hay (dry matter basis). A portion of the ground corn and all of the expeller soybean meal and extruded soybeans from 0% DDGS diets were replaced with DDGS to formulate 18% DDGS diets. Overall, we found no interactions of forage \u00d7 DDGS concentrations for any of the production measures. We observed no effect of diet on dry matter intake. Milk yield was greater when cows were fed LF diets compared with HF diets (43.3 vs. 41.5 kg\/d). Milk fat concentration (3.03 vs. 3.38%) was lower for cows fed LF diets compared with HF diets, whereas protein concentration (3.11 vs. 2.98%) and yield (1.34 vs. 1.24 kg\/d) were greater for cows fed LF diets compared with HF diets. Yields of fat, total solids, energy-corrected milk, and feed efficiency were not affected by diets. Cows partitioned energy equally for milk, maintenance, and body reserves. Replacing starch from ground corn and protein from soybean feeds with DDGS at either 17 or 24.5% of forage NDF concentration in the diet was cost-effective and did not affect the production performance of lactating dairy cows.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Aaa Wholesale Transmissions is located at the address 905 W 1st Ave in Eugene, Oregon 97402. They can be contacted via phone at (541) 344-2336 for pricing, hours and directions. Aaa Wholesale Transmissions specializes in Classic, Trucks, Sedans.\nPosted by Deriq C. on April 19, 2015. Brought to you by yahoolocal.\nPosted by Jenna M. on January 07, 2015. Brought to you by yahoolocal.\nAAA Wholesale Transmissions can be found at W 1st Ave 905. The following is offered: Car Parts. The entry is present with us since Sep 9, 2010 and was last updated on Nov 14, 2013. In Eugene there are 24 other Car Parts. An overview can be found here.\nSince 2001, Aaa Wholesale Transmission has been providing Automotive Transmission Repair Shops from Eugene.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"\u2022Launch a web browser and go to the official AOL website.\n\u2022Then opt to create an AOL account. Complete the account creation process by entering the true information about you like Name, DOB, and Email etc.\n\u2022After that login to your AOL account and take a premium membership.\n\u2022Now, when you are an AOL premium member, go to the benefits section in AOL account and choose to AOL Gold download for Mac.\nAfterward, install this software to enjoy the services offered by this AOL.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"CARACAS, Venezuela \u2014 More than a dozen European Union countries endorsed Venezuelan opposition leader Juan Guaido as the country's interim president on Monday, piling the pressure on embattled President Nicolas Maduro to resign and clear the way for a new presidential election.\nMaduro, for his part, stood defiant, rejecting a U.S offer of humanitarian aid that has shifted attention to Venezuela's western border with Colombia, where opponents were gearing up to try to bring emergency food and medicine into the country.\nPublic support: Spain, Germany, France and Britain delivered diplomatic blows to Maduro's rule by publicly supporting Guaido after a Sunday deadline for Maduro to call a presidential election passed without action. Sweden, Denmark, Austria, the Netherlands, Lithuania, Finland, Estonia, Latvia, the Czech Republic, Luxembourg, Poland and Portugal also lined up behind Guaido, who last month declared himself interim president with the support of the United States and many South American nations.\nMeanwhile, in Canada, foreign ministers from Western hemisphere nations belonging to the Lima Group, which includes 13 countries that took the lead in recognizing Guaido as Venezuela's rightful leader, gathered in Ottawa to discuss additional steps to pressure Maduro.\nBefore the closed-door meeting got under way, Prime Minister Justin Trudeau condemned a \"dictatorship willing to use force and fear\" to maintain its power. He also announced $53 million in humanitarian aid to support the Venezuelan people.\nLashing out: Maduro showed no signs of caving in and lashed out at the EU, accusing it of taking orders from the Trump administration, who he has repeatedly accused of trying to carry out a coup to get its hands on Venezuela's oil reserves, the world's largest.\nThe signs: Amid the rising pressure, Maduro has shown signs he's willing to negotiate.\nHumanitarian aid: Meanwhile, the opposition was moving ahead with a risky strategy to bring in humanitarian aid from Colombia, hoping to break the all-important military's loyalty to Maduro.\nBut David Lipton, the No. 2 at the International Monetary Fund, called Venezuela's economic crisis \u2013 marked by widespread food shortages, protracted hyperinflation and the loss of human capital through emigration \u2013 an \"unprecedented economic storm\" that will require generous, broad-based international support to overcome.","meta":{"redpajama_set_name":"RedPajamaC4"}}
diff --git a/data_all_eng_slimpj/shuffled/split2/finalzzzbmjqv b/data_all_eng_slimpj/shuffled/split2/finalzzzbmjqv
new file mode 100644
index 0000000000000000000000000000000000000000..44db6c67600b19ed7196c26733f0b726a10c8a16
--- /dev/null
+++ b/data_all_eng_slimpj/shuffled/split2/finalzzzbmjqv
@@ -0,0 +1,5 @@
+{"text":"Country of Origin: United States Court Name: Supreme Court, Appellate Division, First Department, New York Primary Citation: 694 N.Y.S.2d 57, 58 (N.Y.App.Div.1999) Date of Decision: Thursday, August 19, 1999 Judge Name: Kenneth Thompson, Jr. Jurisdiction Level: New York Alternate Citation: 264 A.D.2d 342 (N.Y.App.Div.1999) Judges: Nardelli, J. P., Lerner and Saxe, JJ., Mazzarelli, J., Attorneys: Diane L. Dubiac, for Christopher Rivers, etc., et al. Caryn L. Lilling, for The New York City Housing Authority.\nSummary: In this case, the appellate court said that in order for the landlord to be held liable for injuries sustained as result of attack by tenant's pit bull, it must be demonstrated that the animal had vicious propensities and that landlord knew or should have known of these propensities. The trial court erred in taking judicial notice of the vicious nature of pit bulls, rather than letting the trier of fact determine whether the pit bull had displayed any signs of vicious or violent behavior prior to the incident. The order denying the defendant's motion for summary judgement dismissing the complaint was reversed.\nOrder which denied motion for summary judgment dismissing complaint reversed-- in denying summary judgment motion, IAS Court took judicial notice that pit bulls by nature are inherently dangerous and held that defendant landlord could be held strictly liable for injuries to infant tenant inflicted by pit bull which had not displayed any signs of vicious or violent behavior prior to incident--court erred in taking judicial notice of vicious nature of pit bulls; in order to be held liable for injuries sustained as result of attack by tenant's dog, it must be demonstrated that animal had vicious propensities and that landlord knew or should have known of these propensities; there was no showing by plaintiff that dog displayed any signs of vicious or violent behavior prior to incident and no evidence that defendant landlord knew or should have known of any such propensities.\nOrder, Supreme Court, Bronx County (Kenneth Thompson, Jr., J.), entered July 9, 1998, which denied defendant's motion for summary judgment dismissing the complaint, reversed, on the law, without costs or disbursements, and the motion granted. The Clerk is directed to enter judgment in favor of defendant-appellant dismissing the complaint. Appeal from order, same court and Justice, entered November 17, 1997, which granted defendant's motion to strike allegations in plaintiffs' proposed bill of particulars, dismissed, without costs or disbursements, as academic.\nIn denying this summary judgment motion, the IAS Court took judicial notice that pit bulls by nature are inherently dangerous and held that defendant landlord could be held strictly liable for injuries to an infant tenant inflicted by a pit bull which had not displayed any signs of vicious or violent behavior prior to the incident.\nInitially, we note that the court erred in taking judicial notice of the vicious nature of pit bulls (see, Carter v Metro N. Assocs., 255 AD2d 251, 251-252; and see, supra, at 254 [Mazzarelli, J., dissenting]). In order to be held liable for injuries sustained as a result of an attack by a tenant's dog, it must be demonstrated that the animal had vicious propensities and that the landlord knew or should have known of these propensities (Carter v Metro N. Assocs., supra). Here, there was no showing by plaintiff that the dog displayed any signs of vicious or violent behavior prior to the incident and no evidence that defendant landlord knew or should have known of any such propensities.\nConcur--Nardelli, J. P., Lerner and Saxe, JJ.\nConcurs in a memorandum as follows: For the reasons stated in my dissenting opinion in Carter v Metro N. Assocs. (255 AD2d 251, 252), I believe that the issue of whether the dog in this case was inherently vicious is a question for the trier of fact. However, given the majority's holding in Carter v Metro N. Assocs. (supra), which is, at present, binding precedent on this Court, I am constrained to concur with the majority in this case.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Mark your presence everywhere with this yellow color designer salwar kameez. This beautiful salwar suit is made from cotton silk fabric and artistically crafted with printed work that gives a pleasant look to the wearer. It is an ideal choice for weekend parties and social gatherings where you want to grab the attention of the onlookers. The outfit comes along with matching cotton satin bottom and chiffon dupatta. This suit is available in various sizes.\nStraight Cut Cyan Cotton Silk Printed D..","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"If you own a horse farm in Pennsylvania, what to do with your manure is a major concern! Furthermore, the state also requires farm owners to formulate a written manure management plan for any property that houses horses or livestock. Farm owners who are new to rural property ownership or those who want to learn more about how to write a manure management plan can attend a free workshop on April 27 at the Monroe County Conservation District in Stroudsburg, PA, held by the Penn State extension program. Proper manure handling is crucial to environmental health and clean water, and it's important that all PA horse farm owners have an understanding of the state requirements.\nSeminar participants will learn about current state requirements for manure management, how to construct farm maps, and will receive help in writing a complete manure management plan for their PA horse farm. Those who attend will need to bring an aerial map of their farm, which can be obtained from an online mapping service such as Google or Bing. Participants will get the chance to speak with experts about the state requirements as well as how to handle manure on their own properties.\nFor more information on this seminar or to register, contact Donna Foulk: dlf5@psu.edu, Heather Stofanak: haf10@psu.edu, or Matt Giambra: mgmccd@psu.edu. Or you can call the Northampton Extension Office: 610-746-1970.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Not to skip from the very serious subject of Hiroshima's bombing to Hiroshima's signature dish, but that is exactly what I am going to do. You'll probably remember that I made the traditional Osaka style okonomiyaki last September, and it didn't go very well. Reading over that post in preparation for this one it made me laugh, not only because I am a hilarious writer (I now pat myself on the back), but because Hiroshima okonomiyaki are so much more difficult to make. Or at least they should be as they involve many layers and two simultaneous frying pans. In spite of this I went into the process a million times calmer and more confident than the last time. The mind is a mysterious thing.\nSo what about these layers? Why layers? How layers? Well you shall recall from my last okonomiyaki post, provided you read it, that the Osaka style is a pancake made from a batter that includes cabbage and various other ingredients like green onions and pickled ginger. The Hiroshima okonomiyaki employs layers rather than mixing those ingredients up in the batter. It begins with a pancake (simpler than the Osaka style as it is flour, dashi, and mirin), then shredded cabbage and mung beans on top of that, then pork belly, then green onions, then a little more batter, then yakisoba noodles, and lastly a fried egg. And yes, it is high in calories and very tall.\nI will freely admit that a big motivator in my calm attitude going into this dish was that it didn't require the nagaimo yam. You will recall I had a hell of a trial tracking that guy down last time, and would have even more trouble now as Mitsuwa no longer has an online store (I weep to remember those glorious days). The lack of this single ingredient meant that I can get absolutely everything I needed at the grocery store, and I love recipes like that. Where did I get this recipe? From one of my favorite books, Japanese Soul Cooking by Tadashi Ono and Harris Salat. But if you still resist buying this book (why do you resist?) there is a good recipe for this on Justonecookbook.com.\nThough I was intimidated by the prospect of building this beauty from the pancake up, I set about it with a confident resolve that was immediately rewarded with a gorgeous okonomiyaki. The scariest part was flipping this stack, but as I later heard myself say while I was editing the video \"That was easier than I thought it would be\". To which my mother can be heard saying \"huh?\" and then me shouting \"THAT WAS EASIER THAN I THOUGHT IT WOULD BE!\". You're spared my repetitive dialog by the fact that I mute out the sounds to add music. I also speed it up so if I left the sound in I would sound like a chipmunk. But that repeated phrase pretty much sums up the whole process.\nWith all those layers you may be wondering how the whole thing tastes, after all can you picture eating pancakes with noodles? Well, never you fear because these were the best darn okonomiyaki I have ever eaten. The flavors went together like a perfectly synchronized chorus and the very distinct textures made it interesting and delightful. I would recommend this recipe to anyone who wants to try a delicious and unique Japanese dish. You will be gobbling it up like you've never eaten before.\nUntil next time, don't knock noodle pancakes, they're awesome.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"In Borrego Springs, CA at 10 AM this morning, the temperature was a scorching 116 degrees F. Temperatures today are expected to hit 122 degrees F (50 degrees C) for this California location \u2014 which would tie the all-time high for any date there. But it's just a microcosm of the record-shattering heat that is now settling in over the US West. Heat that looks like it will remain in place for days and possibly weeks. Heat that is now resulting in tragic instances of loss of life even as it is sparking numerous massive widlfires, melting snowpacks, worsening droughts, and otherwise sparking conditions that are related to a human-forced heating of the globe.\nIn Glendale, a suburb of Phoenix, temperatures rocketed to 120 degrees Fahrenheit (49 C or 14 degrees F above average) as numerous locales recorded temperatures well in excess of 120 throughout the region (see map below). Tuscon hit 115 (46 C or 15 F above average) and Phoenix soared to 118 (48 C or 15 degrees F above average). California saw its own spate of record heat with Los Angeles soaring to 96 F (36 C which is 23 F above average), Burbank hitting 109 F (43 C and also 23 F above average), Riverside seeing 111 F readings (44 C and 19 F above average) and Thermal rising all the way to 119 F (48 C and 13 F above average). Seven communities in New Mexico also saw record hot readings for the day.\nThe record heat resulted in 4 separate incidents of hiker deaths as rescue personnel responded to trail-goers suffering from heat injuries Sunday. Two of the fatalities occurred along trails near Tuscon while another pair of fatalities cropped up just outside of Phoenix. A fifth hiker is now also reported missing.\nToday, the extreme heat is predicted to make a repeat comeback as readings are expected to hit or exceed 121 F in some regions. Meanwhile, Tuesday is expected to be even hotter.\nAs heat expanded beneath a sprawling dome of high pressure, groups of firefighters the size of small armies battled numerous blazes.\nIn Los Angeles 2,000 firefighters and 23 aircraft were engaged with the Sherpa Fire raging through the Santa Barbara region. By late Sunday, nearly 8,000 acres had burned (12 square miles), a section of a water treatment plant was consumed, and the fire was 54 percent contained. However, 55 mph winds overnight and temperatures rising to or near triple digit heat today were expected to give those fighting the blaze a grueling challenge.\nNear Albuquerque, the Dog Head fire had consumed fully 18,000 acres and was only 9 percent contained by late Sunday evening. The swift moving and raging fire had damaged or consumed 45 structures by that time as 1,000 firefighters fought to contain it. Continued extreme heat in the region through at least Tuesday is expected to make fighting the blaze a very difficult prospect over the next two days.\nNorth of Phoenix, the Cedar Creek Fire had swelled to 26,000 acres Monday, cut off route 60, and jumped the containment line. A shift in the wind caused the fire to dramatically alter course Sunday night \u2014 outflanking firefighting efforts in the process. The blaze had been 40 percent contained as of late Sunday, but these estimates will have to be revised downward. The fire is now threatening the town of Carrizo \u2014 which is expected to receive evacuation orders later today.\nFueling both the extreme heat and wildfire outbreaks across the Western US are conditions consistent with human-caused climate change. Very strong high pressure ridges dominate both the ocean zones of the Northeastern Pacific and the North Atlantic. These high pressure systems are both more powerful and extend further north than is typical. In addition, water temperatures both off the Eastern Seaboard and off the US West Coast are much warmer than normal. These features have all fed the development of a powerful heat dome high pressure system that is now forming over the US.\nOver the coming days, this ridge is expected to swell and strengthen as it drives the Jet Stream far north over Canada and into the Arctic. There, sea ice extents continue to range in record lows for this time of year \u2014 lending power to the forming ridge and the heatwave inducing dome high pressure system developing underneath. As a result, we will likely continue to see fire hazards spike throughout the Central and Western US, we will likely continue to see record or near record heat, and we will likely see a re-expansion of drought conditions in the US West.\nIn addition, this heat dome is so powerful and has such a strong predicted northward extent that temperatures in the 80s or even 90s may extend as far north as the shores of the Arctic Ocean in Canada and Alaska. So wildfire and heatwave risks will be moving north into Arctic regions over the coming days as well.\nDrought is again expanding over the US West. Oregon, after a very rapid April and May snowmelt, is being advised to conserve water. And with high pressure building in over the Southwest, weather models are predicting the emergence of an extreme heatwave by late this weekend. One that current guidance is indicating will bring 100 to 120 degree (F) temperatures to a wide region stretching from California's Central Valley, through Southern California, Northwestern Mexico, Arizona, Nevada and into Southern Utah.\nThe trigger for what may become a record-shattering heatwave is the predicted development of a powerful atmospheric ridge. Model guidance now shows a strong high pressure system currently over the Northeastern Pacific extending its influence eastward over the coming days. By the middle of next week, most of the US is predicted to fall under the atmospheric sway of a big bully of a high pressure system centered over the Southwestern States. Spiking atmospheric pressures and clear skies are expected to then usher in record temperatures for much of the US Southwest.\nFor parts of California's Central Valley near Fresno, temperatures could rise as high as 116 F by Wednesday of next week (June 21). That's about 23 degrees (F) above average for this time of year and would beat the hottest reading ever recorded in any month for the city. The same day prediction for Sacramento is in the range of 110 F \u2014 a little shy of the all-time record, but a reading that would shatter the June 21 daily record by a good margin.\n110 degree + readings are expected to blanket Southeastern California, Sections of Northwestern Mexico, Southwestern Arizona, and Southeastern Nevada. Near 100 degree readings are expected to extend as far north as Redding, California. In other words, a huge section of the Southwestern US is expected to experience Death Valley like weather conditions.\nThis kind of record heatwave is something one might have expected during an extreme year of the 20th Century in July. But what we're seeing is its potential to emerge now in mid-to-late June. An indication that record global atmospheric temperatures are starting to have some rather serious regional impacts along the lines predicted by various Global Circulation Models. These models indicated a particular vulnerability of the US Southwest to extreme heat and drying under the atmospheric forces set off by human fossil fuel burning. And this predicted heatwave is building up in an atmospheric context in which global temperatures will likely be around 1.2 C hotter than 1880s averages during 2016.\nIn this context, the potentially building record heatwave threatens to greatly expand and reassert drought conditions in the US Southwest this Summer. Should it emerge as models are currently predicting, it will greatly increase soil moisture evaporation and remaining snowpack melt across the region \u2014 amplifying drought conditions in over a region where many had hoped a strong El Nino would stave off these kinds of climate change related impacts for at least another few years. And for these reasons along with the direct risks of heat injury to human beings, interests should closely monitor its development.","meta":{"redpajama_set_name":"RedPajamaC4"}}
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+{"text":"Classified Ad: Beer for Crumpler Bags!!!\nYep! You read that right..true I had a shot of this cocktail called Kiss on the Lips and I think it actually hit me even more than just a soft, tender kiss. With my low tolerance for alcohol here I am typing away as my brain is starting to head to la-la-land...Before I completely doze off, I'd like to share with you this great news from our friends over at Crumpler Philippines!\nThey will soon be having a big event where you can exchange a bottle\/can\/case of beer for your very own Crumpler bag!!! I don't know about you but I'm definitely hoarding probably a dozen cases of beer just for this.\nSee you there!! For more info, visit the official Facebook page of Crumpler Philippines.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Who is Primal Pictures and what do you offer?\nFor more than 25 years, Primal Pictures' pioneering and award-winning multimedia 3D anatomy software have been used worldwide in healthcare education, training, practice, research and more. Primal Pictures delivers the highest quality and most medically accurate 3D model of the human body, along with best-in-class anatomy, physiology and clinical content.\nPrimal Pictures offers an extensive selection of products. From detailed, accurate and customizable regional and body system-based 3D anatomy models to specialty titles across a range of disciplines, Primal Pictures has a 3D anatomy software solution that's right for you. All Primal Pictures subscriptions are accessed online on our Anatomy.tv platform.\nQuestions? Visit our contact page to get in touch.\nHow do you make sure your anatomy is accurate?\nPrimal Pictures' 3D anatomical model is the only model to have been reconstructed using real scan data in a process that took years of academic research. Our model and vast array of supporting content is developed by our in-house team of highly skilled anatomists and translated into our products by our seasoned team of graphic artists and 3D modelers. All further peer-reviewed by leading anatomists and subject matter experts worldwide to ensure the highest level of accuracy. We are constantly working on reviewing and updating our content and products to ensure we offer the most medically accurate resources to all of our users.\nHow much does a title cost?\nPrimal Pictures offers an extensive selection of products that can be be purchased as an individual subscription or as an institutional licence, and prices vary.\nYou can instantly purchase a personal online annual subscription to any Primal Pictures product. We accept payment in US Dollars, GBP Sterling or Euros. You can pay securely online using most major credit cards.\nMulti-user institutional licenses are also available for your institution, practice, department or organization. We offer an extensive selection of products and packages to meet a range of needs and budget requirements. For more information, contact a Primal account manager for personalized consultation and assistance.\nWhat benefits do I get from buying from Primal Pictures?\nAccuracy and Comprehensiveness \u2013 Our 3D model of the human body is the only model to have been constructed using real scan data. We have continuously enhanced its detail over the course of more than 25-year history, ensuring that we offer the most medically-accurate model and digital anatomy resources available.\nExpertise \u2013 Our model and vast array of supporting content is developed by our in-house team of highly skilled anatomists and translated into our products by our seasoned team of graphic artists and 3D modelers. All further peer-reviewed by leading anatomists and subject matter experts worldwide to ensure the highest level of accuracy.\nFlexibility and Range of Access and Use \u2013 Our anatomy software is web-based, allowing our products to be accessed anytime, anywhere, while making product and content enhancements seamless to the user. Our products can be accessed on desktop, laptop and tablet devices, using flexible authentication options to fit any user environment. Further, we offer an extensive selection of products and packages to meet a range of needs and budget requirements.\nPartnership \u2013 Coupled with our top expectations for product excellence, Primal Pictures prides itself in offering the highest level of partnership and support for our customers. It is our aim to ensure that customers achieve optimal return for the investment made in any Primal Pictures solution.\nCan I demo or have a trial of your products before I buy?\nYes, you can sign up to receive free trial access to our products here.\nWhat devices can I access and use your titles on?\nWe want you to be able to access our products anytime, anywhere, using any device. That's why we deliver our products online, so as long as you have an internet connection the majority of our products are accessible via all main browsers on desktop\/laptop (PC & Mac) and mobile tablets (iPad, Android and Microsoft Surface tablets).\nAlthough our products have not been specifically designed for use on mobile phones, they will work but the usability is not currently optimized for them. We are planning on updating future versions of our products in order to optimize for use mobile phones, however in the meantime it is recommended to use our products on a desktop, laptop or tablet device for an optimal user experience.\nFor more information, please contact a Primal account manager.\nCan I use your titles offline?\nNo, since our products are web based, you will need an internet connection to access any of our titles. All Primal Pictures subscriptions are accessed online on our Anatomy.tv platform.\nWhat on-line support do you have for your products?\nWe want to ensure you get the most out of your Primal Pictures subscription. We offer several self-service support options online on our Anatomy.tv platform. Once logged in, our 'Help' section offers helpful video tutorials, user-guides and frequently asked questions, and our 'Resource Center' contains resources including product videos, brochures, translated resources, posters, postcards and bookmarks.\nIf you require additional help or support, please contact our highly experienced account management team who will be happy to assist you.\nPrimal Pictures no longer sells products on DVD-ROMS, and as of December 31, 2014, we no longer offer technical support for them.\nPrimal Pictures is constantly upgrading and improving its products, and to ensure that customers are always receiving the best service, latest content, and can access products across multiple platforms and devices, we now offer and support an online service only.\nUnlike our online solutions, your Primal Pictures DVD will not have changed since you purchased it, and will still work on the systems outlined in the original requirements listed on the back of the DVD casing. However, like all software, if you change your hardware or operating system from the originally specified requirements, it is likely that the software will no longer work.\nPersonal online subscriptions for individuals can be purchased here, or for multi-user institutional licenses, please contact a Primal account manager to discuss.\nDo I get updates automatically if I have a subscription?\nIf you have an annual online subscription to any Primal Pictures product, you will automatically receive all of the latest updates that are made available as the content is browser based. If you have an app version of Primal's Real-time Human Anatomy, it will prompt you if an update is available.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"The Velbon UP-400 Monopod is a lightweight 4 section aluminium monopod designed to support a DSLR, CSC or compact camera.\nThe EX-Mini Aluminium Tabletop Tripod from Velbon is a small, lightweight tripod with a 2-way pan\/tilt head. It extends to 41cm, and holds up to 1.5Kg making it ideal for point and shoot or small DSLR cameras.\nThe Ultra Stick Super 8 Monopod from Velbon has an 8-section tubular leg with a simple twist lock.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"Blossom Kochhar Aroma Magic, we are the first and largest Aromatherapy cosmetic brand in India. Our products are free of Parabens, Alcohol and Harsh Chemicals.\nLet us see how shower gel or a body wash is different from one another. Body wash and shower gel are pretty similar. They are both liquid cleansers that use mild cleansers as the main ingredients. The main difference lies in their texture.\nBody wash is thinner than shower gel because it comes in liquid form. It also moisturises the skin while you are still in the shower. Shower gel is thicker than body wash and has more firm consistency. Body washes are suitable for cold climates and have comparatively less concentration of fragrances. Shower gels are suitable and better for warmer climates and have a higher concentration of fragrance than body wash.\nEnriched with the extracts of plum blossom, Aroma Magic Plum Blossom Body wash gently cleanses, heals and conditions the skin leaving your skin softer, smoother and beautiful like never before. The unique blend of Grapefruit and Palmarose essential oils mattify and revitalize dull skin and hair whereas Clary sage essential oil has a calming and deodorising effect that stays in your body.\nBeauty is not essentially about skin. Beauty talks a lot about hair too. Many people think the products you use on your hair does not matter. But that is not the exact case. It is extremely important to use the proper products which are made to help your own personal hair needs. You must think about why it is so? It is important to take care of hair with proper hair care and hair care products. Therefore it is important to choose the best hair care products like how you chose the best for your skin.\nWhen you use the wrong hair care products it could have such a bad impact on your hair. For example, if a person has dry or brittle hair, they need a shampoo and conditioner to impart moisture. If you use a clarifying shampoo on such hair, the natural oils will strip away which will cause the parts of your hair causing breakage. A person with thinning hair will need a shampoo and conditioner to help stimulate their scalp, which thereby increases the blood circulation. A person with normal hair will need products that will not strip their hair of its natural moisture.","meta":{"redpajama_set_name":"RedPajamaC4"}}
+{"text":"... when you realize your husband hates you. Or that he's crazy. Take your pick. I'm having a moment.\nY'al remember the post about how his plan to manage his stress involves making me nuts? Well. He's been stressed this weekend. Really really stressed.\nA few weeks ago, my computer ... died. (Leave it at that). He could fix it, techinically. But that would take some time and money and I'm getting a new computer when we move ... SO ... he partitioned his computer. Life should now be all sunshine and daisies, right? RIGHT?\nNot hardly. When I turn on the computer, there's a screen that lets you choose your partition and type in your password. Since he set up the partitions, he chose my password and the icon next to my partition-name. The icon is a symbol for a password I use sometimes. I thought THAT was my password, which would have made total sense! But, no.\nIf I click on the \"hint\" button I get a cryptic word that relates to a bible-verse. Ok, so THAT is the password. I type it in. I type it in varying formats since the password-box is case-sensitive. Nothing. I have to call him. Yes, I call him at work. We have a calm but thorough conversation about what the password could have been, would have been, SHOULD have been. Turns out he misremembered the numbers, and inverted them. BUT, regardless, I then knew my password. JOY!\nSo, this morning I grabbed a few minutes to check my email. I turn on the computer. I see the password-box. I type in my password (the mangled inverted verse) and ... nothing. I try again, full aware that even the best typers make mistakes. Nothing. I try again, getting a horrible vision of me crashing his hard-drive. Nothing. I break out in a cold-sweat. I reach for the phone. I put down the phone. I stare at the screen. At the happy glowing icon of my favorite password. I type it in. Slowly.\nI'm going gray. Its all his fault.\nThat man is messing with you!!!!!!!!\nDid I tell you about my dh working on his sister's pc? You know how you can have \"announcements\" when certain features are used? Well he set her's up with sound bites from old movies that are REALLY loud and obnoxious, so the thing yells at her all the time. LOL! She had no idea how to fix it, and he refused.\nI take great pleasure in that.\nOn the funny side, for those intrepid readers who crave belly-laughs ... It seems I've been calling a WRONG NUMBER politely trying to convince him to give me his contact info for the family address list. As soon as he hears my voice, he hangs up (without even the courtesy of saying \"wrong number\")! Its taken weeks (and internaltional phone calls) to figure out that I have a wrong number!\nROFLOL! Mission accomplished, I'm laughing!\nDo ya'l remember last year when I had that little problem with setting categories here? My husband kept telling me it was easy and he SO didn't have time to do it and after hour upon hour of effort on my part trying to follow his directions he finally tried to walk me through it step by step only to find that he hadn't given me admin-rights for the site so I wasn't seeing some of the options he was seeing when we logged into the same screen under different user-names.\nWell. I've made myself nuts trying to do something on the other site. Trying over and over, telling myself \"You're just tired\" and \"you're just distracted\" and \"you just have a cold\" and \"you must be missing something extra-obvious\". Turns out that I was missing something obvious, all right. The fact that my husband and his friend are TWO PEAS IN A BRIGHT GREEN POD! I finally broke down and told the guy \"I can't get it\". To which he responded (paraphrased) \"That should be working ... unless I forgot to give you admin-rights. Oops. \"\nHusband: (quietly, but with that edge that lets me know there's something coming) How do you know there's only two of us?\nI laughed so hard I cried! He did all the pigeon voices! For those of you deprived of the pigeon experience, Don't Let The Pigeon Drive The Bus is a book about a crazily manipulative pigeon that tries to convince the reader to let him drive the bus after the driver has specificlly asked the reader to watch the bus while he's gone, and to be extra careful about that pigeon. Aimed at toddlers, its one of our kids favorite books! The older ones like reading it and doing the pigeon voices, and the younger ones like saying \"NO\"!\nOne reason I like our friend is that I'm sure he's the kind of guy that likes making his wife and kids laugh, too. They really are probably two peas in a pod. A very bright-green pod!\nOh, that's good. I think that even online, we attract certain personalities. Must be something about you that attracts the \"protect her from herself\" admins! LOL!\nBetter pack a bag, it'll take a while!\nThe really hysterical thing is that when I read your site (daily) I \"hear\" it like you're talking with a Southern accent! It'd be SUCH a shock to talk to you in person! LOL!\nWell, except for words that aren't written like they sound.\nBut it is \"light-en-ing\" (or more informally, \"light-en-in'\") versus \"light'ning.\" Both spoken rapidly and nasally if, like me, you're originally from the Madison, Wisconsin area.\nAlternately titled: Buying Clothes At The Hair-Salon!\nIt all started when Cassie whacked off all her hair late Monday afternoon. Apparently, thats prone to happen when small children are bored out of their minds while trapped indoors by an ice-storm. THIS is the kind of emergency that makes one glad your husband saw the light and bought a big-boy-truck with four wheel drive so you could get to a salon as soon as possible.\nI found out that my next door neighbor has started working there, so I left Cassie in the chair with her and dashed off to the infant department to look at sleepers. The salon is in the corner of JCPennys, which is not a store I usually frequent but they were open and fixing hair so there we were.\nI wandered around in the baby department, snagged some comfy velour pants for Katherine, went back to pick up Cassie when they paged me (she now looks like a flapper from the 1920's which will take FOREVER to grow out but is at least presentable in public), and then walked over to the boys department to look at hoodies for basketball practice.\nThere it was. Green-ticket final clearance. Plus an additional 40% off. For the uninitiated, its like the Holy Grail of shopping. It means the previously $14.99 turtleneck was $1.18. Yes, friends, thats about 92% OFF RETAIL! Of course, we got one of every color and every size. Period. For mine. And my brothers children. And actually a few other random small children. I built a mountain. A clerk noticed. She was working with a little hand-scanner (it turns out later she was actually doing the mark-downs) She directed me to a happy rack in the little-girls department. I built another mountain. She came by and started moving the mountains to the front register. We moved on to other departments. More mountains. She told me she hadn't processed the baby stuff yet, but if I showed her what I was interested in she'd go ahead and process it. Two hours later, I \"closed\" Pennys and broke their register. Now they ALL know that if you buy more than 50 items on one receipt the machine freezes. And their coats for children have gone green-ticket as well. Just FYI.\nIt was like the perfect storm! Well, perfect for me. Not so perfect for Pennys. Apparently their plan was to mark down their clearance a little bit for the big holiday weekend and then take the rock-bottom clearance Monday night right before closing after heavy shopping had depleted their stocks. BUT everyone was trapped in their homes by ice over the weekend and I was one of the first shoppers to venture out on Monday night, hitting the mother-lode of sales.\nShoot! (or the expletive of your choice) I just thought of a small relative I forget to buy for. Man! And I was going to spend all day in my pajamas.\nMy dh is heading back to Sears today to get the sneakers that were marked down. He had already bought books (much needed) so thought he should hold off. Silly boy!\nHave you ever wondered if there would come a time when you would be punished for all those times you made fun of those poor saps on reality televison shows? I didn't. I went merrily on my way with no thought for the morrow. La-la-la-doo-duh-doo ... *sigh* ... the good ol'days of glorious privacy.\nIt all started when my husband picked out the new cameras for the kids. We got them each one gift for Christmas, a digital camera. This way they have fun, learn about technology, develop a skill, and we get at least a few really good pictures. Eventually.\nThat was the plan. And it was working a little until we were iced-in and my husband chose THAT moment to tell the boys that the cameras also ... (wait for it) ... take video-clips. They immediately set about taking lots of small movies. Mostly of ME in various states of displeasure (cleverly masked by hysterical laughing) and questionable clothing. See, in the past I haven't had to DRESS to leave my bedroom. Now, I really ought to \"dress\" before I leave my bed. Finally, on threat of seizing the cameras, they have accepted the rule of \"No videoing anyone who is not dressed enough to go to the post-office\". ALthough, Lee's idea of what I could technically wear to the post-office is shocking!\nSo far this morning, while wearing my bath robe, I've been the star of a brilliant documentary called \"Mother Makes Hot Chocolate\" and \"The Sequel: Mother Makes Toast\"\nI have yet to find a way to keep them from leaping around corners and through doorways while shrieking \"surprise\" which is only slightly better than when they try to slip up on you to video unawares. Some of them are pretty good at that. If you haven't guessed, I'm a bundle of nerves.\nIts like living with three crazed paparatzzi, hopped up on sugar and high on life-with-a-video-camera.\nOh, you poor thing! LOL! That would drive me up a wall!\nSo, what else is going on in your life? Would you have us believe that nothing of interest has been going on while you've been silent? I don't buy that.\nAnd just where will those photos show up?? Last night my son took a short video of me cooking on his cell phone and then emailed it to \"lots of people\"!\nLucy, I missed you and am glad you're back.\nWoohoo! I got it fixed. Kinda. Which is all you really need to know about THAT adventure.\nMy brother isn't the only one with gifting-skills. I let the kids pick out their own gifts with their own money for my brother's soon-to-be-three-year-old boy. I tried to guide them with \"Thats nice, but not in your budget-range\" and \"Thats nice, but he's only about three\" and \"Thats nice, but his mama won't let him have it with good reason\"\nThey ended up with a wonderful round of gifts that Jay REALLY enjoyed. He carried the little synthasizer through the house rocking out. He refused to take off the seriously-orange hunting cap, even clamping it to his head all the way through SundaySchool. But the best was what Ron gave him. A little fire-truck rescue-type vehicle. That has three buttons. That make ... interesting ... sounds. Loudly.\nSound one: A vroom-vrooming sound.\nSound three: A rather grim sounding man shouting \"Put your hands up or I'll shoot!\"\nAnd the extra-interesting part is that if its 5:00am and you're really sleepy and your small child sneaks up to the bed to share his new toy, odds are you'll wake up really ... grumpy. And in need of a drink. And maybe clean under-wear. But I didn't ask about that. TMI.\nROFLOL! Oh, so you're one of THOSE aunts!\nWas there ever any doubt!?!\nI havent been her for awhile but I was just over at Lenis blog and saw your link. Just dropping by to say hello.\nInternet down. Computer down. Will deal with it sometime this weekend. Meanwhile, think Happy-Happy-Happy thoughts! Envision ballerina-dancing-chiwawawas! Lol. I need some sleep.","meta":{"redpajama_set_name":"RedPajamaC4"}}